LMFDB - Embedded newform 1232.2.q.a.529.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1232,2,Mod(177,1232)] 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("1232.177"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1232, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1232 = 2^{4} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1232.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,-3,0,4,0,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$9.83756952902$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1232.529
Dual form			1232.2.q.a.177.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 + 2.59808i) q^{3} +(2.00000 + 3.46410i) q^{5} +(2.50000 + 0.866025i) q^{7} +(-3.00000 - 5.19615i) q^{9} +(-0.500000 + 0.866025i) q^{11} -1.00000 q^{13} -12.0000 q^{15} +(-1.00000 + 1.73205i) q^{17} +(3.00000 + 5.19615i) q^{19} +(-6.00000 + 5.19615i) q^{21} +(-1.00000 - 1.73205i) q^{23} +(-5.50000 + 9.52628i) q^{25} +9.00000 q^{27} +1.00000 q^{29} +(2.00000 - 3.46410i) q^{31} +(-1.50000 - 2.59808i) q^{33} +(2.00000 + 10.3923i) q^{35} +(1.00000 + 1.73205i) q^{37} +(1.50000 - 2.59808i) q^{39} -2.00000 q^{41} -4.00000 q^{43} +(12.0000 - 20.7846i) q^{45} +(1.00000 + 1.73205i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-3.00000 - 5.19615i) q^{51} +(6.00000 - 10.3923i) q^{53} -4.00000 q^{55} -18.0000 q^{57} +(4.50000 - 7.79423i) q^{59} +(2.50000 + 4.33013i) q^{61} +(-3.00000 - 15.5885i) q^{63} +(-2.00000 - 3.46410i) q^{65} +(-4.50000 + 7.79423i) q^{67} +6.00000 q^{69} -4.00000 q^{71} +(1.00000 - 1.73205i) q^{73} +(-16.5000 - 28.5788i) q^{75} +(-2.00000 + 1.73205i) q^{77} +(-7.50000 - 12.9904i) q^{79} +(-4.50000 + 7.79423i) q^{81} +6.00000 q^{83} -8.00000 q^{85} +(-1.50000 + 2.59808i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(-2.50000 - 0.866025i) q^{91} +(6.00000 + 10.3923i) q^{93} +(-12.0000 + 20.7846i) q^{95} -5.00000 q^{97} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{3} + 4 q^{5} + 5 q^{7} - 6 q^{9} - q^{11} - 2 q^{13} - 24 q^{15} - 2 q^{17} + 6 q^{19} - 12 q^{21} - 2 q^{23} - 11 q^{25} + 18 q^{27} + 2 q^{29} + 4 q^{31} - 3 q^{33} + 4 q^{35} + 2 q^{37} + 3 q^{39}+ \cdots + 12 q^{99}+O(q^{100}) $ 2 * q - 3 * q^3 + 4 * q^5 + 5 * q^7 - 6 * q^9 - q^11 - 2 * q^13 - 24 * q^15 - 2 * q^17 + 6 * q^19 - 12 * q^21 - 2 * q^23 - 11 * q^25 + 18 * q^27 + 2 * q^29 + 4 * q^31 - 3 * q^33 + 4 * q^35 + 2 * q^37 + 3 * q^39 - 4 * q^41 - 8 * q^43 + 24 * q^45 + 2 * q^47 + 11 * q^49 - 6 * q^51 + 12 * q^53 - 8 * q^55 - 36 * q^57 + 9 * q^59 + 5 * q^61 - 6 * q^63 - 4 * q^65 - 9 * q^67 + 12 * q^69 - 8 * q^71 + 2 * q^73 - 33 * q^75 - 4 * q^77 - 15 * q^79 - 9 * q^81 + 12 * q^83 - 16 * q^85 - 3 * q^87 - 6 * q^89 - 5 * q^91 + 12 * q^93 - 24 * q^95 - 10 * q^97 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1232\mathbb{Z}\right)^\times$.

$n$	$309$	$353$	$463$	$673$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	+	2.59808i	−0.866025	+	1.50000i			1.00000i	$0.5\pi$
$3$	−1.50000	+	2.59808i	−0.866025	+	1.50000i	−0.866025	+	0.500000i	$0.833333\pi$
$4$		0			0
$5$	2.00000	+	3.46410i	0.894427	+	1.54919i	0.834512	+	0.550990i	$0.185750\pi$
$5$	2.00000	+	3.46410i	0.894427	+	1.54919i	0.0599153	+	0.998203i	$0.480917\pi$
$6$		0			0
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$		0			0
$9$	−3.00000	−	5.19615i	−1.00000	−	1.73205i
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$		0			0
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$		0			0
$15$	−12.0000			−3.09839
$16$		0			0
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$		0			0
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	0.972404	+	0.233301i	$0.0749529\pi$
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	−0.284157	+	0.958778i	$0.591714\pi$
$20$		0			0
$21$	−6.00000	+	5.19615i	−1.30931	+	1.13389i
$22$		0			0
$23$	−1.00000	−	1.73205i	−0.208514	−	0.361158i	0.742732	−	0.669588i	$-0.233529\pi$
$23$	−1.00000	−	1.73205i	−0.208514	−	0.361158i	−0.951247	+	0.308431i	$0.900196\pi$
$24$		0			0
$25$	−5.50000	+	9.52628i	−1.10000	+	1.90526i
$26$		0			0
$27$	9.00000			1.73205
$28$		0			0
$29$	1.00000			0.185695			0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000			0.185695			0.0928477	+	0.995680i	$0.470403\pi$
$30$		0			0
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$		0			0
$33$	−1.50000	−	2.59808i	−0.261116	−	0.452267i
$34$		0			0
$35$	2.00000	+	10.3923i	0.338062	+	1.75662i
$36$		0			0
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$		0			0
$39$	1.50000	−	2.59808i	0.240192	−	0.416025i
$40$		0			0
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$		0			0
$45$	12.0000	−	20.7846i	1.78885	−	3.09839i
$46$		0			0
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	0.929695	−	0.368329i	$-0.120070\pi$
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	−0.783830	+	0.620975i	$0.786737\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$		0			0
$51$	−3.00000	−	5.19615i	−0.420084	−	0.727607i
$52$		0			0
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	−0.0783936	−	0.996922i	$-0.524979\pi$
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	0.902557	−	0.430570i	$-0.141688\pi$
$54$		0			0
$55$	−4.00000			−0.539360
$56$		0			0
$57$	−18.0000			−2.38416
$58$		0			0
$59$	4.50000	−	7.79423i	0.585850	−	1.01472i	−0.408919	−	0.912571i	$-0.634094\pi$
$59$	4.50000	−	7.79423i	0.585850	−	1.01472i	0.994769	−	0.102151i	$-0.0325726\pi$
$60$		0			0
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	0.980507	−	0.196485i	$-0.0629528\pi$
$61$	2.50000	+	4.33013i	0.320092	+	0.554416i	−0.660415	+	0.750901i	$0.729619\pi$
$62$		0			0
$63$	−3.00000	−	15.5885i	−0.377964	−	1.96396i
$64$		0			0
$65$	−2.00000	−	3.46410i	−0.248069	−	0.429669i
$66$		0			0
$67$	−4.50000	+	7.79423i	−0.549762	+	0.952217i	0.448528	+	0.893769i	$0.351948\pi$
$67$	−4.50000	+	7.79423i	−0.549762	+	0.952217i	−0.998290	+	0.0584478i	$0.981385\pi$
$68$		0			0
$69$	6.00000			0.722315
$70$		0			0
$71$	−4.00000			−0.474713			−0.237356	−	0.971423i	$-0.576281\pi$
$71$	−4.00000			−0.474713			−0.237356	+	0.971423i	$0.576281\pi$
$72$		0			0
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	−0.801553	−	0.597924i	$-0.795992\pi$
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	0.918594	+	0.395203i	$0.129326\pi$
$74$		0			0
$75$	−16.5000	−	28.5788i	−1.90526	−	3.30000i
$76$		0			0
$77$	−2.00000	+	1.73205i	−0.227921	+	0.197386i
$78$		0			0
$79$	−7.50000	−	12.9904i	−0.843816	−	1.46153i	−0.886646	−	0.462450i	$-0.846971\pi$
$79$	−7.50000	−	12.9904i	−0.843816	−	1.46153i	0.0428296	−	0.999082i	$-0.486363\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$		0			0
$85$	−8.00000			−0.867722
$86$		0			0
$87$	−1.50000	+	2.59808i	−0.160817	+	0.278543i
$88$		0			0
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		0			0
$91$	−2.50000	−	0.866025i	−0.262071	−	0.0907841i
$92$		0			0
$93$	6.00000	+	10.3923i	0.622171	+	1.07763i
$94$		0			0
$95$	−12.0000	+	20.7846i	−1.23117	+	2.13246i
$96$		0			0
$97$	−5.00000			−0.507673			−0.253837	−	0.967247i	$-0.581693\pi$
$97$	−5.00000			−0.507673			−0.253837	+	0.967247i	$0.581693\pi$
$98$		0			0
$99$	6.00000			0.603023
$100$		0			0
$101$	7.50000	−	12.9904i	0.746278	−	1.29259i	−0.203317	−	0.979113i	$-0.565172\pi$
$101$	7.50000	−	12.9904i	0.746278	−	1.29259i	0.949595	−	0.313478i	$-0.101494\pi$
$102$		0			0
$103$	6.00000	+	10.3923i	0.591198	+	1.02398i	0.994071	+	0.108729i	$0.0346780\pi$
$103$	6.00000	+	10.3923i	0.591198	+	1.02398i	−0.402874	+	0.915255i	$0.631989\pi$
$104$		0			0
$105$	−30.0000	−	10.3923i	−2.92770	−	1.01419i
$106$		0			0
$107$	4.00000	+	6.92820i	0.386695	+	0.669775i	0.992003	−	0.126217i	$-0.0402834\pi$
$107$	4.00000	+	6.92820i	0.386695	+	0.669775i	−0.605308	+	0.795991i	$0.706950\pi$
$108$		0			0
$109$	−5.00000	+	8.66025i	−0.478913	+	0.829502i	−0.999708	−	0.0241802i	$-0.992302\pi$
$109$	−5.00000	+	8.66025i	−0.478913	+	0.829502i	0.520794	+	0.853682i	$0.325636\pi$
$110$		0			0
$111$	−6.00000			−0.569495
$112$		0			0
$113$	17.0000			1.59923			0.799613	−	0.600516i	$-0.205038\pi$
$113$	17.0000			1.59923			0.799613	+	0.600516i	$0.205038\pi$
$114$		0			0
$115$	4.00000	−	6.92820i	0.373002	−	0.646058i
$116$		0			0
$117$	3.00000	+	5.19615i	0.277350	+	0.480384i
$118$		0			0
$119$	−4.00000	+	3.46410i	−0.366679	+	0.317554i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$	3.00000	−	5.19615i	0.270501	−	0.468521i
$124$		0			0
$125$	−24.0000			−2.14663
$126$		0			0
$127$	−5.00000			−0.443678			−0.221839	−	0.975083i	$-0.571206\pi$
$127$	−5.00000			−0.443678			−0.221839	+	0.975083i	$0.571206\pi$
$128$		0			0
$129$	6.00000	−	10.3923i	0.528271	−	0.914991i
$130$		0			0
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	−0.928199	−	0.372084i	$-0.878643\pi$
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	0.141865	−	0.989886i	$-0.454690\pi$
$132$		0			0
$133$	3.00000	+	15.5885i	0.260133	+	1.35169i
$134$		0			0
$135$	18.0000	+	31.1769i	1.54919	+	2.68328i
$136$		0			0
$137$	4.50000	−	7.79423i	0.384461	−	0.665906i	−0.607233	−	0.794524i	$-0.707721\pi$
$137$	4.50000	−	7.79423i	0.384461	−	0.665906i	0.991694	+	0.128618i	$0.0410540\pi$
$138$		0			0
$139$	−8.00000			−0.678551			−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000			−0.678551			−0.339276	+	0.940687i	$0.610182\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$		0			0
$143$	0.500000	−	0.866025i	0.0418121	−	0.0724207i
$144$		0			0
$145$	2.00000	+	3.46410i	0.166091	+	0.287678i
$146$		0			0
$147$	−19.5000	+	7.79423i	−1.60833	+	0.642857i
$148$		0			0
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	0.994847	−	0.101391i	$-0.0323294\pi$
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	−0.585231	+	0.810867i	$0.698996\pi$
$150$		0			0
$151$	4.50000	−	7.79423i	0.366205	−	0.634285i	−0.622764	−	0.782410i	$-0.713990\pi$
$151$	4.50000	−	7.79423i	0.366205	−	0.634285i	0.988969	+	0.148124i	$0.0473236\pi$
$152$		0			0
$153$	12.0000			0.970143
$154$		0			0
$155$	16.0000			1.28515
$156$		0			0
$157$	−2.00000	+	3.46410i	−0.159617	+	0.276465i	−0.934731	−	0.355357i	$-0.884359\pi$
$157$	−2.00000	+	3.46410i	−0.159617	+	0.276465i	0.775113	+	0.631822i	$0.217693\pi$
$158$		0			0
$159$	18.0000	+	31.1769i	1.42749	+	2.47249i
$160$		0			0
$161$	−1.00000	−	5.19615i	−0.0788110	−	0.409514i
$162$		0			0
$163$	6.50000	+	11.2583i	0.509119	+	0.881820i	0.999944	+	0.0105623i	$0.00336213\pi$
$163$	6.50000	+	11.2583i	0.509119	+	0.881820i	−0.490825	+	0.871258i	$0.663305\pi$
$164$		0			0
$165$	6.00000	−	10.3923i	0.467099	−	0.809040i
$166$		0			0
$167$	17.0000			1.31550			0.657750	−	0.753237i	$-0.271508\pi$
$167$	17.0000			1.31550			0.657750	+	0.753237i	$0.271508\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$		0			0
$171$	18.0000	−	31.1769i	1.37649	−	2.38416i
$172$		0			0
$173$	2.50000	+	4.33013i	0.190071	+	0.329213i	0.945274	−	0.326278i	$-0.105795\pi$
$173$	2.50000	+	4.33013i	0.190071	+	0.329213i	−0.755202	+	0.655492i	$0.772461\pi$
$174$		0			0
$175$	−22.0000	+	19.0526i	−1.66304	+	1.44024i
$176$		0			0
$177$	13.5000	+	23.3827i	1.01472	+	1.75755i
$178$		0			0
$179$	6.50000	−	11.2583i	0.485833	−	0.841487i	−0.514035	−	0.857769i	$-0.671850\pi$
$179$	6.50000	−	11.2583i	0.485833	−	0.841487i	0.999867	+	0.0162823i	$0.00518305\pi$
$180$		0			0
$181$	−22.0000			−1.63525			−0.817624	−	0.575753i	$-0.804709\pi$
$181$	−22.0000			−1.63525			−0.817624	+	0.575753i	$0.804709\pi$
$182$		0			0
$183$	−15.0000			−1.10883
$184$		0			0
$185$	−4.00000	+	6.92820i	−0.294086	+	0.509372i
$186$		0			0
$187$	−1.00000	−	1.73205i	−0.0731272	−	0.126660i
$188$		0			0
$189$	22.5000	+	7.79423i	1.63663	+	0.566947i
$190$		0			0
$191$	7.00000	+	12.1244i	0.506502	+	0.877288i	0.999972	+	0.00752447i	$0.00239513\pi$
$191$	7.00000	+	12.1244i	0.506502	+	0.877288i	−0.493469	+	0.869763i	$0.664272\pi$
$192$		0			0
$193$	11.0000	−	19.0526i	0.791797	−	1.37143i	−0.133056	−	0.991109i	$-0.542479\pi$
$193$	11.0000	−	19.0526i	0.791797	−	1.37143i	0.924853	−	0.380325i	$-0.124188\pi$
$194$		0			0
$195$	12.0000			0.859338
$196$		0			0
$197$	−3.00000			−0.213741			−0.106871	−	0.994273i	$-0.534083\pi$
$197$	−3.00000			−0.213741			−0.106871	+	0.994273i	$0.534083\pi$
$198$		0			0
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	−0.632581	−	0.774494i	$-0.718005\pi$
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	0.987022	+	0.160585i	$0.0513380\pi$
$200$		0			0
$201$	−13.5000	−	23.3827i	−0.952217	−	1.64929i
$202$		0			0
$203$	2.50000	+	0.866025i	0.175466	+	0.0607831i
$204$		0			0
$205$	−4.00000	−	6.92820i	−0.279372	−	0.483887i
$206$		0			0
$207$	−6.00000	+	10.3923i	−0.417029	+	0.722315i
$208$		0			0
$209$	−6.00000			−0.415029
$210$		0			0
$211$	14.0000			0.963800			0.481900	−	0.876226i	$-0.339947\pi$
$211$	14.0000			0.963800			0.481900	+	0.876226i	$0.339947\pi$
$212$		0			0
$213$	6.00000	−	10.3923i	0.411113	−	0.712069i
$214$		0			0
$215$	−8.00000	−	13.8564i	−0.545595	−	0.944999i
$216$		0			0
$217$	8.00000	−	6.92820i	0.543075	−	0.470317i
$218$		0			0
$219$	3.00000	+	5.19615i	0.202721	+	0.351123i
$220$		0			0
$221$	1.00000	−	1.73205i	0.0672673	−	0.116510i
$222$		0			0
$223$	26.0000			1.74109			0.870544	−	0.492090i	$-0.163767\pi$
$223$	26.0000			1.74109			0.870544	+	0.492090i	$0.163767\pi$
$224$		0			0
$225$	66.0000			4.40000
$226$		0			0
$227$	5.00000	−	8.66025i	0.331862	−	0.574801i	−0.651015	−	0.759065i	$-0.725657\pi$
$227$	5.00000	−	8.66025i	0.331862	−	0.574801i	0.982877	+	0.184263i	$0.0589899\pi$
$228$		0			0
$229$	8.00000	+	13.8564i	0.528655	+	0.915657i	0.999442	+	0.0334101i	$0.0106368\pi$
$229$	8.00000	+	13.8564i	0.528655	+	0.915657i	−0.470787	+	0.882247i	$0.656030\pi$
$230$		0			0
$231$	−1.50000	−	7.79423i	−0.0986928	−	0.512823i
$232$		0			0
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	0.750867	−	0.660454i	$-0.229636\pi$
$233$	−3.00000	−	5.19615i	−0.196537	−	0.340411i	−0.947403	+	0.320043i	$0.896303\pi$
$234$		0			0
$235$	−4.00000	+	6.92820i	−0.260931	+	0.451946i
$236$		0			0
$237$	45.0000			2.92306
$238$		0			0
$239$	−19.0000			−1.22901			−0.614504	−	0.788914i	$-0.710644\pi$
$239$	−19.0000			−1.22901			−0.614504	+	0.788914i	$0.710644\pi$
$240$		0			0
$241$	−15.0000	+	25.9808i	−0.966235	+	1.67357i	−0.259975	+	0.965615i	$0.583714\pi$
$241$	−15.0000	+	25.9808i	−0.966235	+	1.67357i	−0.706260	+	0.707953i	$0.749619\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−4.00000	+	27.7128i	−0.255551	+	1.77051i
$246$		0			0
$247$	−3.00000	−	5.19615i	−0.190885	−	0.330623i
$248$		0			0
$249$	−9.00000	+	15.5885i	−0.570352	+	0.987878i
$250$		0			0
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	2.00000			0.125739
$254$		0			0
$255$	12.0000	−	20.7846i	0.751469	−	1.30158i
$256$		0			0
$257$	10.5000	+	18.1865i	0.654972	+	1.13444i	0.981901	+	0.189396i	$0.0606529\pi$
$257$	10.5000	+	18.1865i	0.654972	+	1.13444i	−0.326929	+	0.945049i	$0.606014\pi$
$258$		0			0
$259$	1.00000	+	5.19615i	0.0621370	+	0.322873i
$260$		0			0
$261$	−3.00000	−	5.19615i	−0.185695	−	0.321634i
$262$		0			0
$263$	1.50000	−	2.59808i	0.0924940	−	0.160204i	−0.816066	−	0.577959i	$-0.803849\pi$
$263$	1.50000	−	2.59808i	0.0924940	−	0.160204i	0.908560	+	0.417755i	$0.137183\pi$
$264$		0			0
$265$	48.0000			2.94862
$266$		0			0
$267$	18.0000			1.10158
$268$		0			0
$269$	−6.00000	+	10.3923i	−0.365826	+	0.633630i	−0.988908	−	0.148527i	$-0.952547\pi$
$269$	−6.00000	+	10.3923i	−0.365826	+	0.633630i	0.623082	+	0.782157i	$0.285880\pi$
$270$		0			0
$271$	12.5000	+	21.6506i	0.759321	+	1.31518i	0.943197	+	0.332233i	$0.107802\pi$
$271$	12.5000	+	21.6506i	0.759321	+	1.31518i	−0.183876	+	0.982949i	$0.558865\pi$
$272$		0			0
$273$	6.00000	−	5.19615i	0.363137	−	0.314485i
$274$		0			0
$275$	−5.50000	−	9.52628i	−0.331662	−	0.574456i
$276$		0			0
$277$	1.50000	−	2.59808i	0.0901263	−	0.156103i	−0.817438	−	0.576017i	$-0.804606\pi$
$277$	1.50000	−	2.59808i	0.0901263	−	0.156103i	0.907564	+	0.419914i	$0.137940\pi$
$278$		0			0
$279$	−24.0000			−1.43684
$280$		0			0
$281$	−10.0000			−0.596550			−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000			−0.596550			−0.298275	+	0.954480i	$0.596411\pi$
$282$		0			0
$283$	−3.00000	+	5.19615i	−0.178331	+	0.308879i	−0.941309	−	0.337546i	$-0.890403\pi$
$283$	−3.00000	+	5.19615i	−0.178331	+	0.308879i	0.762978	+	0.646425i	$0.223737\pi$
$284$		0			0
$285$	−36.0000	−	62.3538i	−2.13246	−	3.69352i
$286$		0			0
$287$	−5.00000	−	1.73205i	−0.295141	−	0.102240i
$288$		0			0
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$		0			0
$291$	7.50000	−	12.9904i	0.439658	−	0.761510i
$292$		0			0
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$		0			0
$295$	36.0000			2.09600
$296$		0			0
$297$	−4.50000	+	7.79423i	−0.261116	+	0.452267i
$298$		0			0
$299$	1.00000	+	1.73205i	0.0578315	+	0.100167i
$300$		0			0
$301$	−10.0000	−	3.46410i	−0.576390	−	0.199667i
$302$		0			0
$303$	22.5000	+	38.9711i	1.29259	+	2.23883i
$304$		0			0
$305$	−10.0000	+	17.3205i	−0.572598	+	0.991769i
$306$		0			0
$307$	−32.0000			−1.82634			−0.913168	−	0.407583i	$-0.866372\pi$
$307$	−32.0000			−1.82634			−0.913168	+	0.407583i	$0.866372\pi$
$308$		0			0
$309$	−36.0000			−2.04797
$310$		0			0
$311$	−14.0000	+	24.2487i	−0.793867	+	1.37502i	0.129689	+	0.991555i	$0.458602\pi$
$311$	−14.0000	+	24.2487i	−0.793867	+	1.37502i	−0.923556	+	0.383464i	$0.874731\pi$
$312$		0			0
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	0.851549	−	0.524276i	$-0.175664\pi$
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	−0.879810	+	0.475325i	$0.842331\pi$
$314$		0			0
$315$	48.0000	−	41.5692i	2.70449	−	2.34216i
$316$		0			0
$317$	6.00000	+	10.3923i	0.336994	+	0.583690i	0.983866	−	0.178908i	$-0.0572566\pi$
$317$	6.00000	+	10.3923i	0.336994	+	0.583690i	−0.646872	+	0.762598i	$0.723923\pi$
$318$		0			0
$319$	−0.500000	+	0.866025i	−0.0279946	+	0.0484881i
$320$		0			0
$321$	−24.0000			−1.33955
$322$		0			0
$323$	−12.0000			−0.667698
$324$		0			0
$325$	5.50000	−	9.52628i	0.305085	−	0.528423i
$326$		0			0
$327$	−15.0000	−	25.9808i	−0.829502	−	1.43674i
$328$		0			0
$329$	1.00000	+	5.19615i	0.0551318	+	0.286473i
$330$		0			0
$331$	3.50000	+	6.06218i	0.192377	+	0.333207i	0.946038	−	0.324057i	$-0.105047\pi$
$331$	3.50000	+	6.06218i	0.192377	+	0.333207i	−0.753660	+	0.657264i	$0.771714\pi$
$332$		0			0
$333$	6.00000	−	10.3923i	0.328798	−	0.569495i
$334$		0			0
$335$	−36.0000			−1.96689
$336$		0			0
$337$	−30.0000			−1.63420			−0.817102	−	0.576493i	$-0.804421\pi$
$337$	−30.0000			−1.63420			−0.817102	+	0.576493i	$0.804421\pi$
$338$		0			0
$339$	−25.5000	+	44.1673i	−1.38497	+	2.39884i
$340$		0			0
$341$	2.00000	+	3.46410i	0.108306	+	0.187592i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$	12.0000	+	20.7846i	0.646058	+	1.11901i
$346$		0			0
$347$	−14.0000	+	24.2487i	−0.751559	+	1.30174i	0.195507	+	0.980702i	$0.437365\pi$
$347$	−14.0000	+	24.2487i	−0.751559	+	1.30174i	−0.947067	+	0.321037i	$0.895969\pi$
$348$		0			0
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$		0			0
$351$	−9.00000			−0.480384
$352$		0			0
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	−0.520689	−	0.853746i	$-0.674325\pi$
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	0.999711	+	0.0240566i	$0.00765819\pi$
$354$		0			0
$355$	−8.00000	−	13.8564i	−0.424596	−	0.735422i
$356$		0			0
$357$	−3.00000	−	15.5885i	−0.158777	−	0.825029i
$358$		0			0
$359$	−15.5000	−	26.8468i	−0.818059	−	1.41692i	−0.907111	−	0.420892i	$-0.861717\pi$
$359$	−15.5000	−	26.8468i	−0.818059	−	1.41692i	0.0890519	−	0.996027i	$-0.471616\pi$
$360$		0			0
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$		0			0
$363$	3.00000			0.157459
$364$		0			0
$365$	8.00000			0.418739
$366$		0			0
$367$	−7.00000	+	12.1244i	−0.365397	+	0.632886i	−0.988840	−	0.148983i	$-0.952400\pi$
$367$	−7.00000	+	12.1244i	−0.365397	+	0.632886i	0.623443	+	0.781869i	$0.285733\pi$
$368$		0			0
$369$	6.00000	+	10.3923i	0.312348	+	0.541002i
$370$		0			0
$371$	24.0000	−	20.7846i	1.24602	−	1.07908i
$372$		0			0
$373$	3.50000	+	6.06218i	0.181223	+	0.313888i	0.942297	−	0.334777i	$-0.108661\pi$
$373$	3.50000	+	6.06218i	0.181223	+	0.313888i	−0.761074	+	0.648665i	$0.775328\pi$
$374$		0			0
$375$	36.0000	−	62.3538i	1.85903	−	3.21994i
$376$		0			0
$377$	−1.00000			−0.0515026
$378$		0			0
$379$	29.0000			1.48963			0.744815	−	0.667271i	$-0.232538\pi$
$379$	29.0000			1.48963			0.744815	+	0.667271i	$0.232538\pi$
$380$		0			0
$381$	7.50000	−	12.9904i	0.384237	−	0.665517i
$382$		0			0
$383$	4.00000	+	6.92820i	0.204390	+	0.354015i	0.949938	−	0.312437i	$-0.101145\pi$
$383$	4.00000	+	6.92820i	0.204390	+	0.354015i	−0.745548	+	0.666452i	$0.767812\pi$
$384$		0			0
$385$	−10.0000	−	3.46410i	−0.509647	−	0.176547i
$386$		0			0
$387$	12.0000	+	20.7846i	0.609994	+	1.05654i
$388$		0			0
$389$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$389$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$390$		0			0
$391$	4.00000			0.202289
$392$		0			0
$393$	54.0000			2.72394
$394$		0			0
$395$	30.0000	−	51.9615i	1.50946	−	2.61447i
$396$		0			0
$397$	15.0000	+	25.9808i	0.752828	+	1.30394i	0.946447	+	0.322860i	$0.104644\pi$
$397$	15.0000	+	25.9808i	0.752828	+	1.30394i	−0.193618	+	0.981077i	$0.562022\pi$
$398$		0			0
$399$	−45.0000	−	15.5885i	−2.25282	−	0.780399i
$400$		0			0
$401$	−7.50000	−	12.9904i	−0.374532	−	0.648709i	0.615725	−	0.787961i	$-0.288863\pi$
$401$	−7.50000	−	12.9904i	−0.374532	−	0.648709i	−0.990257	+	0.139253i	$0.955530\pi$
$402$		0			0
$403$	−2.00000	+	3.46410i	−0.0996271	+	0.172559i
$404$		0			0
$405$	−36.0000			−1.78885
$406$		0			0
$407$	−2.00000			−0.0991363
$408$		0			0
$409$	16.0000	−	27.7128i	0.791149	−	1.37031i	−0.134107	−	0.990967i	$-0.542817\pi$
$409$	16.0000	−	27.7128i	0.791149	−	1.37031i	0.925256	−	0.379344i	$-0.123850\pi$
$410$		0			0
$411$	13.5000	+	23.3827i	0.665906	+	1.15338i
$412$		0			0
$413$	18.0000	−	15.5885i	0.885722	−	0.767058i
$414$		0			0
$415$	12.0000	+	20.7846i	0.589057	+	1.02028i
$416$		0			0
$417$	12.0000	−	20.7846i	0.587643	−	1.01783i
$418$		0			0
$419$	20.0000			0.977064			0.488532	−	0.872546i	$-0.337533\pi$
$419$	20.0000			0.977064			0.488532	+	0.872546i	$0.337533\pi$
$420$		0			0
$421$	−20.0000			−0.974740			−0.487370	−	0.873195i	$-0.662044\pi$
$421$	−20.0000			−0.974740			−0.487370	+	0.873195i	$0.662044\pi$
$422$		0			0
$423$	6.00000	−	10.3923i	0.291730	−	0.505291i
$424$		0			0
$425$	−11.0000	−	19.0526i	−0.533578	−	0.924185i
$426$		0			0
$427$	2.50000	+	12.9904i	0.120983	+	0.628649i
$428$		0			0
$429$	1.50000	+	2.59808i	0.0724207	+	0.125436i
$430$		0			0
$431$	0.500000	−	0.866025i	0.0240842	−	0.0417150i	−0.853732	−	0.520712i	$-0.825666\pi$
$431$	0.500000	−	0.866025i	0.0240842	−	0.0417150i	0.877816	+	0.478997i	$0.159000\pi$
$432$		0			0
$433$	−10.0000			−0.480569			−0.240285	−	0.970702i	$-0.577241\pi$
$433$	−10.0000			−0.480569			−0.240285	+	0.970702i	$0.577241\pi$
$434$		0			0
$435$	−12.0000			−0.575356
$436$		0			0
$437$	6.00000	−	10.3923i	0.287019	−	0.497131i
$438$		0			0
$439$	−2.50000	−	4.33013i	−0.119318	−	0.206666i	0.800179	−	0.599761i	$-0.204738\pi$
$439$	−2.50000	−	4.33013i	−0.119318	−	0.206666i	−0.919498	+	0.393095i	$0.871404\pi$
$440$		0			0
$441$	6.00000	−	41.5692i	0.285714	−	1.97949i
$442$		0			0
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	0.687557	−	0.726130i	$-0.258683\pi$
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	−0.972626	+	0.232377i	$0.925350\pi$
$444$		0			0
$445$	12.0000	−	20.7846i	0.568855	−	0.985285i
$446$		0			0
$447$	−30.0000			−1.41895
$448$		0			0
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$		0			0
$451$	1.00000	−	1.73205i	0.0470882	−	0.0815591i
$452$		0			0
$453$	13.5000	+	23.3827i	0.634285	+	1.09861i
$454$		0			0
$455$	−2.00000	−	10.3923i	−0.0937614	−	0.487199i
$456$		0			0
$457$	−1.00000	−	1.73205i	−0.0467780	−	0.0810219i	0.841688	−	0.539964i	$-0.181562\pi$
$457$	−1.00000	−	1.73205i	−0.0467780	−	0.0810219i	−0.888466	+	0.458942i	$0.848229\pi$
$458$		0			0
$459$	−9.00000	+	15.5885i	−0.420084	+	0.727607i
$460$		0			0
$461$	−3.00000			−0.139724			−0.0698620	−	0.997557i	$-0.522256\pi$
$461$	−3.00000			−0.139724			−0.0698620	+	0.997557i	$0.522256\pi$
$462$		0			0
$463$	14.0000			0.650635			0.325318	−	0.945605i	$-0.394529\pi$
$463$	14.0000			0.650635			0.325318	+	0.945605i	$0.394529\pi$
$464$		0			0
$465$	−24.0000	+	41.5692i	−1.11297	+	1.92773i
$466$		0			0
$467$	−6.00000	−	10.3923i	−0.277647	−	0.480899i	0.693153	−	0.720791i	$-0.256221\pi$
$467$	−6.00000	−	10.3923i	−0.277647	−	0.480899i	−0.970799	+	0.239892i	$0.922888\pi$
$468$		0			0
$469$	−18.0000	+	15.5885i	−0.831163	+	0.719808i
$470$		0			0
$471$	−6.00000	−	10.3923i	−0.276465	−	0.478852i
$472$		0			0
$473$	2.00000	−	3.46410i	0.0919601	−	0.159280i
$474$		0			0
$475$	−66.0000			−3.02829
$476$		0			0
$477$	−72.0000			−3.29665
$478$		0			0
$479$	−18.5000	+	32.0429i	−0.845287	+	1.46408i	0.0400855	+	0.999196i	$0.487237\pi$
$479$	−18.5000	+	32.0429i	−0.845287	+	1.46408i	−0.885372	+	0.464883i	$0.846096\pi$
$480$		0			0
$481$	−1.00000	−	1.73205i	−0.0455961	−	0.0789747i
$482$		0			0
$483$	15.0000	+	5.19615i	0.682524	+	0.236433i
$484$		0			0
$485$	−10.0000	−	17.3205i	−0.454077	−	0.786484i
$486$		0			0
$487$	−2.00000	+	3.46410i	−0.0906287	+	0.156973i	−0.907776	−	0.419456i	$-0.862221\pi$
$487$	−2.00000	+	3.46410i	−0.0906287	+	0.156973i	0.817147	+	0.576429i	$0.195554\pi$
$488$		0			0
$489$	−39.0000			−1.76364
$490$		0			0
$491$	−18.0000			−0.812329			−0.406164	−	0.913800i	$-0.633134\pi$
$491$	−18.0000			−0.812329			−0.406164	+	0.913800i	$0.633134\pi$
$492$		0			0
$493$	−1.00000	+	1.73205i	−0.0450377	+	0.0780076i
$494$		0			0
$495$	12.0000	+	20.7846i	0.539360	+	0.934199i
$496$		0			0
$497$	−10.0000	−	3.46410i	−0.448561	−	0.155386i
$498$		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
$501$	−25.5000	+	44.1673i	−1.13926	+	1.97325i
$502$		0			0
$503$	21.0000			0.936344			0.468172	−	0.883637i	$-0.344913\pi$
$503$	21.0000			0.936344			0.468172	+	0.883637i	$0.344913\pi$
$504$		0			0
$505$	60.0000			2.66996
$506$		0			0
$507$	18.0000	−	31.1769i	0.799408	−	1.38462i
$508$		0			0
$509$	−1.00000	−	1.73205i	−0.0443242	−	0.0767718i	0.843012	−	0.537895i	$-0.180780\pi$
$509$	−1.00000	−	1.73205i	−0.0443242	−	0.0767718i	−0.887336	+	0.461123i	$0.847447\pi$
$510$		0			0
$511$	4.00000	−	3.46410i	0.176950	−	0.153243i
$512$		0			0
$513$	27.0000	+	46.7654i	1.19208	+	2.06474i
$514$		0			0
$515$	−24.0000	+	41.5692i	−1.05757	+	1.83176i
$516$		0			0
$517$	−2.00000			−0.0879599
$518$		0			0
$519$	−15.0000			−0.658427
$520$		0			0
$521$	13.0000	−	22.5167i	0.569540	−	0.986473i	−0.427071	−	0.904218i	$-0.640455\pi$
$521$	13.0000	−	22.5167i	0.569540	−	0.986473i	0.996611	−	0.0822547i	$-0.0262121\pi$
$522$		0			0
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	0.997478	−	0.0709788i	$-0.0226123\pi$
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	−0.560208	+	0.828352i	$0.689279\pi$
$524$		0			0
$525$	−16.5000	−	85.7365i	−0.720119	−	3.74185i
$526$		0			0
$527$	4.00000	+	6.92820i	0.174243	+	0.301797i
$528$		0			0
$529$	9.50000	−	16.4545i	0.413043	−	0.715412i
$530$		0			0
$531$	−54.0000			−2.34340
$532$		0			0
$533$	2.00000			0.0866296
$534$		0			0
$535$	−16.0000	+	27.7128i	−0.691740	+	1.19813i
$536$		0			0
$537$	19.5000	+	33.7750i	0.841487	+	1.45750i
$538$		0			0
$539$	−6.50000	+	2.59808i	−0.279975	+	0.111907i
$540$		0			0
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	0.999042	+	0.0437584i	$0.0139332\pi$
$541$	12.5000	+	21.6506i	0.537417	+	0.930834i	−0.461625	+	0.887075i	$0.652733\pi$
$542$		0			0
$543$	33.0000	−	57.1577i	1.41617	−	2.45287i
$544$		0			0
$545$	−40.0000			−1.71341
$546$		0			0
$547$		0			0			−	1.00000i	$-0.5\pi$
$547$		0			0				1.00000i	$0.5\pi$
$548$		0			0
$549$	15.0000	−	25.9808i	0.640184	−	1.10883i
$550$		0			0
$551$	3.00000	+	5.19615i	0.127804	+	0.221364i
$552$		0			0
$553$	−7.50000	−	38.9711i	−0.318932	−	1.65722i
$554$		0			0
$555$	−12.0000	−	20.7846i	−0.509372	−	0.882258i
$556$		0			0
$557$	−19.0000	+	32.9090i	−0.805056	+	1.39440i	0.111198	+	0.993798i	$0.464531\pi$
$557$	−19.0000	+	32.9090i	−0.805056	+	1.39440i	−0.916253	+	0.400599i	$0.868802\pi$
$558$		0			0
$559$	4.00000			0.169182
$560$		0			0
$561$	6.00000			0.253320
$562$		0			0
$563$	13.0000	−	22.5167i	0.547885	−	0.948964i	−0.450535	−	0.892759i	$-0.648767\pi$
$563$	13.0000	−	22.5167i	0.547885	−	0.948964i	0.998419	−	0.0562051i	$-0.0179001\pi$
$564$		0			0
$565$	34.0000	+	58.8897i	1.43039	+	2.47751i
$566$		0			0
$567$	−18.0000	+	15.5885i	−0.755929	+	0.654654i
$568$		0			0
$569$	−18.0000	−	31.1769i	−0.754599	−	1.30700i	−0.945573	−	0.325409i	$-0.894498\pi$
$569$	−18.0000	−	31.1769i	−0.754599	−	1.30700i	0.190974	−	0.981595i	$-0.438835\pi$
$570$		0			0
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	−0.995788	−	0.0916910i	$-0.970773\pi$
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	0.577301	+	0.816532i	$0.304106\pi$
$572$		0			0
$573$	−42.0000			−1.75458
$574$		0			0
$575$	22.0000			0.917463
$576$		0			0
$577$	3.50000	−	6.06218i	0.145707	−	0.252372i	−0.783930	−	0.620850i	$-0.786788\pi$
$577$	3.50000	−	6.06218i	0.145707	−	0.252372i	0.929636	+	0.368478i	$0.120121\pi$
$578$		0			0
$579$	33.0000	+	57.1577i	1.37143	+	2.37539i
$580$		0			0
$581$	15.0000	+	5.19615i	0.622305	+	0.215573i
$582$		0			0
$583$	6.00000	+	10.3923i	0.248495	+	0.430405i
$584$		0			0
$585$	−12.0000	+	20.7846i	−0.496139	+	0.859338i
$586$		0			0
$587$	3.00000			0.123823			0.0619116	−	0.998082i	$-0.480280\pi$
$587$	3.00000			0.123823			0.0619116	+	0.998082i	$0.480280\pi$
$588$		0			0
$589$	24.0000			0.988903
$590$		0			0
$591$	4.50000	−	7.79423i	0.185105	−	0.320612i
$592$		0			0
$593$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$593$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$594$		0			0
$595$	−20.0000	−	6.92820i	−0.819920	−	0.284029i
$596$		0			0
$597$	15.0000	+	25.9808i	0.613909	+	1.06332i
$598$		0			0
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	−0.999938	−	0.0111569i	$-0.996449\pi$
$599$	−12.0000	+	20.7846i	−0.490307	+	0.849236i	0.509631	+	0.860393i	$0.329782\pi$
$600$		0			0
$601$	26.0000			1.06056			0.530281	−	0.847822i	$-0.322086\pi$
$601$	26.0000			1.06056			0.530281	+	0.847822i	$0.322086\pi$
$602$		0			0
$603$	54.0000			2.19905
$604$		0			0
$605$	2.00000	−	3.46410i	0.0813116	−	0.140836i
$606$		0			0
$607$	−8.00000	−	13.8564i	−0.324710	−	0.562414i	0.656744	−	0.754114i	$-0.271933\pi$
$607$	−8.00000	−	13.8564i	−0.324710	−	0.562414i	−0.981454	+	0.191700i	$0.938600\pi$
$608$		0			0
$609$	−6.00000	+	5.19615i	−0.243132	+	0.210559i
$610$		0			0
$611$	−1.00000	−	1.73205i	−0.0404557	−	0.0700713i
$612$		0			0
$613$	−11.0000	+	19.0526i	−0.444286	+	0.769526i	−0.998002	−	0.0631797i	$-0.979876\pi$
$613$	−11.0000	+	19.0526i	−0.444286	+	0.769526i	0.553716	+	0.832705i	$0.313209\pi$
$614$		0			0
$615$	24.0000			0.967773
$616$		0			0
$617$	−27.0000			−1.08698			−0.543490	−	0.839416i	$-0.682897\pi$
$617$	−27.0000			−1.08698			−0.543490	+	0.839416i	$0.682897\pi$
$618$		0			0
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	−0.592025	−	0.805919i	$-0.701671\pi$
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	0.993959	+	0.109749i	$0.0350048\pi$
$620$		0			0
$621$	−9.00000	−	15.5885i	−0.361158	−	0.625543i
$622$		0			0
$623$	−3.00000	−	15.5885i	−0.120192	−	0.624538i
$624$		0			0
$625$	−20.5000	−	35.5070i	−0.820000	−	1.42028i
$626$		0			0
$627$	9.00000	−	15.5885i	0.359425	−	0.622543i
$628$		0			0
$629$	−4.00000			−0.159490
$630$		0			0
$631$		0			0			−	1.00000i	$-0.5\pi$
$631$		0			0				1.00000i	$0.5\pi$
$632$		0			0
$633$	−21.0000	+	36.3731i	−0.834675	+	1.44570i
$634$		0			0
$635$	−10.0000	−	17.3205i	−0.396838	−	0.687343i
$636$		0			0
$637$	−5.50000	−	4.33013i	−0.217918	−	0.171566i
$638$		0			0
$639$	12.0000	+	20.7846i	0.474713	+	0.822226i
$640$		0			0
$641$	−4.50000	+	7.79423i	−0.177739	+	0.307854i	−0.941106	−	0.338112i	$-0.890212\pi$
$641$	−4.50000	+	7.79423i	−0.177739	+	0.307854i	0.763367	+	0.645966i	$0.223545\pi$
$642$		0			0
$643$	−1.00000			−0.0394362			−0.0197181	−	0.999806i	$-0.506277\pi$
$643$	−1.00000			−0.0394362			−0.0197181	+	0.999806i	$0.506277\pi$
$644$		0			0
$645$	48.0000			1.89000
$646$		0			0
$647$	12.0000	−	20.7846i	0.471769	−	0.817127i	−0.527710	−	0.849425i	$-0.676949\pi$
$647$	12.0000	−	20.7846i	0.471769	−	0.817127i	0.999478	+	0.0322975i	$0.0102824\pi$
$648$		0			0
$649$	4.50000	+	7.79423i	0.176640	+	0.305950i
$650$		0			0
$651$	6.00000	+	31.1769i	0.235159	+	1.22192i
$652$		0			0
$653$	−11.0000	−	19.0526i	−0.430463	−	0.745584i	0.566450	−	0.824096i	$-0.308316\pi$
$653$	−11.0000	−	19.0526i	−0.430463	−	0.745584i	−0.996913	+	0.0785119i	$0.974983\pi$
$654$		0			0
$655$	36.0000	−	62.3538i	1.40664	−	2.43637i
$656$		0			0
$657$	−12.0000			−0.468165
$658$		0			0
$659$	32.0000			1.24654			0.623272	−	0.782006i	$-0.285803\pi$
$659$	32.0000			1.24654			0.623272	+	0.782006i	$0.285803\pi$
$660$		0			0
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	−0.752252	−	0.658876i	$-0.771032\pi$
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	0.946729	+	0.322031i	$0.104366\pi$
$662$		0			0
$663$	3.00000	+	5.19615i	0.116510	+	0.201802i
$664$		0			0
$665$	−48.0000	+	41.5692i	−1.86136	+	1.61199i
$666$		0			0
$667$	−1.00000	−	1.73205i	−0.0387202	−	0.0670653i
$668$		0			0
$669$	−39.0000	+	67.5500i	−1.50783	+	2.61163i
$670$		0			0
$671$	−5.00000			−0.193023
$672$		0			0
$673$	16.0000			0.616755			0.308377	−	0.951264i	$-0.400214\pi$
$673$	16.0000			0.616755			0.308377	+	0.951264i	$0.400214\pi$
$674$		0			0
$675$	−49.5000	+	85.7365i	−1.90526	+	3.30000i
$676$		0			0
$677$	−19.0000	−	32.9090i	−0.730229	−	1.26479i	−0.956785	−	0.290796i	$-0.906080\pi$
$677$	−19.0000	−	32.9090i	−0.730229	−	1.26479i	0.226556	−	0.973998i	$-0.427253\pi$
$678$		0			0
$679$	−12.5000	−	4.33013i	−0.479706	−	0.166175i
$680$		0			0
$681$	15.0000	+	25.9808i	0.574801	+	0.995585i
$682$		0			0
$683$	−16.5000	+	28.5788i	−0.631355	+	1.09354i	0.355920	+	0.934516i	$0.384168\pi$
$683$	−16.5000	+	28.5788i	−0.631355	+	1.09354i	−0.987275	+	0.159022i	$0.949166\pi$
$684$		0			0
$685$	36.0000			1.37549
$686$		0			0
$687$	−48.0000			−1.83131
$688$		0			0
$689$	−6.00000	+	10.3923i	−0.228582	+	0.395915i
$690$		0			0
$691$	7.50000	+	12.9904i	0.285313	+	0.494177i	0.972685	−	0.232128i	$-0.0745690\pi$
$691$	7.50000	+	12.9904i	0.285313	+	0.494177i	−0.687372	+	0.726306i	$0.741236\pi$
$692$		0			0
$693$	15.0000	+	5.19615i	0.569803	+	0.197386i
$694$		0			0
$695$	−16.0000	−	27.7128i	−0.606915	−	1.05121i
$696$		0			0
$697$	2.00000	−	3.46410i	0.0757554	−	0.131212i
$698$		0			0
$699$	18.0000			0.680823
$700$		0			0
$701$	39.0000			1.47301			0.736505	−	0.676432i	$-0.236475\pi$
$701$	39.0000			1.47301			0.736505	+	0.676432i	$0.236475\pi$
$702$		0			0
$703$	−6.00000	+	10.3923i	−0.226294	+	0.391953i
$704$		0			0
$705$	−12.0000	−	20.7846i	−0.451946	−	0.782794i
$706$		0			0
$707$	30.0000	−	25.9808i	1.12827	−	0.977107i
$708$		0			0
$709$	−3.00000	−	5.19615i	−0.112667	−	0.195146i	0.804178	−	0.594389i	$-0.202606\pi$
$709$	−3.00000	−	5.19615i	−0.112667	−	0.195146i	−0.916845	+	0.399244i	$0.869273\pi$
$710$		0			0
$711$	−45.0000	+	77.9423i	−1.68763	+	2.92306i
$712$		0			0
$713$	−8.00000			−0.299602
$714$		0			0
$715$	4.00000			0.149592
$716$		0			0
$717$	28.5000	−	49.3634i	1.06435	−	1.84351i
$718$		0			0
$719$	−13.0000	−	22.5167i	−0.484818	−	0.839730i	0.515030	−	0.857172i	$-0.327781\pi$
$719$	−13.0000	−	22.5167i	−0.484818	−	0.839730i	−0.999848	+	0.0174426i	$0.994448\pi$
$720$		0			0
$721$	6.00000	+	31.1769i	0.223452	+	1.16109i
$722$		0			0
$723$	−45.0000	−	77.9423i	−1.67357	−	2.89870i
$724$		0			0
$725$	−5.50000	+	9.52628i	−0.204265	+	0.353797i
$726$		0			0
$727$	34.0000			1.26099			0.630495	−	0.776193i	$-0.282852\pi$
$727$	34.0000			1.26099			0.630495	+	0.776193i	$0.282852\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	4.00000	−	6.92820i	0.147945	−	0.256249i
$732$		0			0
$733$	0.500000	+	0.866025i	0.0184679	+	0.0319874i	0.875112	−	0.483921i	$-0.160788\pi$
$733$	0.500000	+	0.866025i	0.0184679	+	0.0319874i	−0.856644	+	0.515908i	$0.827454\pi$
$734$		0			0
$735$	−66.0000	−	51.9615i	−2.43445	−	1.91663i
$736$		0			0
$737$	−4.50000	−	7.79423i	−0.165760	−	0.287104i
$738$		0			0
$739$	9.00000	−	15.5885i	0.331070	−	0.573431i	−0.651652	−	0.758518i	$-0.725924\pi$
$739$	9.00000	−	15.5885i	0.331070	−	0.573431i	0.982722	+	0.185088i	$0.0592569\pi$
$740$		0			0
$741$	18.0000			0.661247
$742$		0			0
$743$	−36.0000			−1.32071			−0.660356	−	0.750953i	$-0.729595\pi$
$743$	−36.0000			−1.32071			−0.660356	+	0.750953i	$0.729595\pi$
$744$		0			0
$745$	−20.0000	+	34.6410i	−0.732743	+	1.26915i
$746$		0			0
$747$	−18.0000	−	31.1769i	−0.658586	−	1.14070i
$748$		0			0
$749$	4.00000	+	20.7846i	0.146157	+	0.759453i
$750$		0			0
$751$	−22.0000	−	38.1051i	−0.802791	−	1.39048i	−0.917772	−	0.397108i	$-0.870014\pi$
$751$	−22.0000	−	38.1051i	−0.802791	−	1.39048i	0.114981	−	0.993368i	$-0.463319\pi$
$752$		0			0
$753$	18.0000	−	31.1769i	0.655956	−	1.13615i
$754$		0			0
$755$	36.0000			1.31017
$756$		0			0
$757$	26.0000			0.944986			0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000			0.944986			0.472493	+	0.881334i	$0.343354\pi$
$758$		0			0
$759$	−3.00000	+	5.19615i	−0.108893	+	0.188608i
$760$		0			0
$761$	−27.0000	−	46.7654i	−0.978749	−	1.69524i	−0.666962	−	0.745091i	$-0.732406\pi$
$761$	−27.0000	−	46.7654i	−0.978749	−	1.69524i	−0.311787	−	0.950152i	$-0.600927\pi$
$762$		0			0
$763$	−20.0000	+	17.3205i	−0.724049	+	0.627044i
$764$		0			0
$765$	24.0000	+	41.5692i	0.867722	+	1.50294i
$766$		0			0
$767$	−4.50000	+	7.79423i	−0.162486	+	0.281433i
$768$		0			0
$769$	−38.0000			−1.37032			−0.685158	−	0.728395i	$-0.740267\pi$
$769$	−38.0000			−1.37032			−0.685158	+	0.728395i	$0.740267\pi$
$770$		0			0
$771$	−63.0000			−2.26889
$772$		0			0
$773$	12.0000	−	20.7846i	0.431610	−	0.747570i	−0.565402	−	0.824815i	$-0.691279\pi$
$773$	12.0000	−	20.7846i	0.431610	−	0.747570i	0.997012	+	0.0772449i	$0.0246123\pi$
$774$		0			0
$775$	22.0000	+	38.1051i	0.790263	+	1.36878i
$776$		0			0
$777$	−15.0000	−	5.19615i	−0.538122	−	0.186411i
$778$		0			0
$779$	−6.00000	−	10.3923i	−0.214972	−	0.372343i
$780$		0			0
$781$	2.00000	−	3.46410i	0.0715656	−	0.123955i
$782$		0			0
$783$	9.00000			0.321634
$784$		0			0
$785$	−16.0000			−0.571064
$786$		0			0
$787$	−11.0000	+	19.0526i	−0.392108	+	0.679150i	−0.992727	−	0.120384i	$-0.961587\pi$
$787$	−11.0000	+	19.0526i	−0.392108	+	0.679150i	0.600620	+	0.799535i	$0.294921\pi$
$788$		0			0
$789$	4.50000	+	7.79423i	0.160204	+	0.277482i
$790$		0			0
$791$	42.5000	+	14.7224i	1.51113	+	0.523469i
$792$		0			0
$793$	−2.50000	−	4.33013i	−0.0887776	−	0.153767i
$794$		0			0
$795$	−72.0000	+	124.708i	−2.55358	+	4.42292i
$796$		0			0
$797$	38.0000			1.34603			0.673015	−	0.739629i	$-0.264999\pi$
$797$	38.0000			1.34603			0.673015	+	0.739629i	$0.264999\pi$
$798$		0			0
$799$	−4.00000			−0.141510
$800$		0			0
$801$	−18.0000	+	31.1769i	−0.635999	+	1.10158i
$802$		0			0
$803$	1.00000	+	1.73205i	0.0352892	+	0.0611227i
$804$		0			0
$805$	16.0000	−	13.8564i	0.563926	−	0.488374i
$806$		0			0
$807$	−18.0000	−	31.1769i	−0.633630	−	1.09748i
$808$		0			0
$809$	24.0000	−	41.5692i	0.843795	−	1.46150i	−0.0428684	−	0.999081i	$-0.513650\pi$
$809$	24.0000	−	41.5692i	0.843795	−	1.46150i	0.886664	−	0.462415i	$-0.153017\pi$
$810$		0			0
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$		0			0
$813$	−75.0000			−2.63036
$814$		0			0
$815$	−26.0000	+	45.0333i	−0.910740	+	1.57745i
$816$		0			0
$817$	−12.0000	−	20.7846i	−0.419827	−	0.727161i
$818$		0			0
$819$	3.00000	+	15.5885i	0.104828	+	0.544705i
$820$		0			0
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	0.966708	−	0.255884i	$-0.0823665\pi$
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	−0.704956	+	0.709251i	$0.749033\pi$
$822$		0			0
$823$	19.0000	−	32.9090i	0.662298	−	1.14713i	−0.317712	−	0.948187i	$-0.602914\pi$
$823$	19.0000	−	32.9090i	0.662298	−	1.14713i	0.980010	−	0.198947i	$-0.0637522\pi$
$824$		0			0
$825$	33.0000			1.14891
$826$		0			0
$827$	22.0000			0.765015			0.382507	−	0.923952i	$-0.375061\pi$
$827$	22.0000			0.765015			0.382507	+	0.923952i	$0.375061\pi$
$828$		0			0
$829$	−8.00000	+	13.8564i	−0.277851	+	0.481253i	−0.970851	−	0.239686i	$-0.922956\pi$
$829$	−8.00000	+	13.8564i	−0.277851	+	0.481253i	0.692999	+	0.720938i	$0.256289\pi$
$830$		0			0
$831$	4.50000	+	7.79423i	0.156103	+	0.270379i
$832$		0			0
$833$	−13.0000	+	5.19615i	−0.450423	+	0.180036i
$834$		0			0
$835$	34.0000	+	58.8897i	1.17662	+	2.03796i
$836$		0			0
$837$	18.0000	−	31.1769i	0.622171	−	1.07763i
$838$		0			0
$839$	−54.0000			−1.86429			−0.932144	−	0.362089i	$-0.882064\pi$
$839$	−54.0000			−1.86429			−0.932144	+	0.362089i	$0.882064\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$		0			0
$843$	15.0000	−	25.9808i	0.516627	−	0.894825i
$844$		0			0
$845$	−24.0000	−	41.5692i	−0.825625	−	1.43002i
$846$		0			0
$847$	−0.500000	−	2.59808i	−0.0171802	−	0.0892710i
$848$		0			0
$849$	−9.00000	−	15.5885i	−0.308879	−	0.534994i
$850$		0			0
$851$	2.00000	−	3.46410i	0.0685591	−	0.118748i
$852$		0			0
$853$	50.0000			1.71197			0.855984	−	0.517003i	$-0.172952\pi$
$853$	50.0000			1.71197			0.855984	+	0.517003i	$0.172952\pi$
$854$		0			0
$855$	144.000			4.92470
$856$		0			0
$857$	2.00000	−	3.46410i	0.0683187	−	0.118331i	−0.829843	−	0.557998i	$-0.811570\pi$
$857$	2.00000	−	3.46410i	0.0683187	−	0.118331i	0.898161	+	0.439666i	$0.144903\pi$
$858$		0			0
$859$	−8.50000	−	14.7224i	−0.290016	−	0.502323i	0.683797	−	0.729672i	$-0.260327\pi$
$859$	−8.50000	−	14.7224i	−0.290016	−	0.502323i	−0.973813	+	0.227349i	$0.926994\pi$
$860$		0			0
$861$	12.0000	−	10.3923i	0.408959	−	0.354169i
$862$		0			0
$863$	5.00000	+	8.66025i	0.170202	+	0.294798i	0.938490	−	0.345305i	$-0.112225\pi$
$863$	5.00000	+	8.66025i	0.170202	+	0.294798i	−0.768288	+	0.640104i	$0.778891\pi$
$864$		0			0
$865$	−10.0000	+	17.3205i	−0.340010	+	0.588915i
$866$		0			0
$867$	−39.0000			−1.32451
$868$		0			0
$869$	15.0000			0.508840
$870$		0			0
$871$	4.50000	−	7.79423i	0.152477	−	0.264097i
$872$		0			0
$873$	15.0000	+	25.9808i	0.507673	+	0.879316i
$874$		0			0
$875$	−60.0000	−	20.7846i	−2.02837	−	0.702648i
$876$		0			0
$877$	−12.5000	−	21.6506i	−0.422095	−	0.731090i	0.574049	−	0.818821i	$-0.305372\pi$
$877$	−12.5000	−	21.6506i	−0.422095	−	0.731090i	−0.996144	+	0.0877308i	$0.972038\pi$
$878$		0			0
$879$	9.00000	−	15.5885i	0.303562	−	0.525786i
$880$		0			0
$881$	9.00000			0.303218			0.151609	−	0.988441i	$-0.451555\pi$
$881$	9.00000			0.303218			0.151609	+	0.988441i	$0.451555\pi$
$882$		0			0
$883$	−1.00000			−0.0336527			−0.0168263	−	0.999858i	$-0.505356\pi$
$883$	−1.00000			−0.0336527			−0.0168263	+	0.999858i	$0.505356\pi$
$884$		0			0
$885$	−54.0000	+	93.5307i	−1.81519	+	3.14400i
$886$		0			0
$887$	−8.50000	−	14.7224i	−0.285402	−	0.494331i	0.687305	−	0.726369i	$-0.258794\pi$
$887$	−8.50000	−	14.7224i	−0.285402	−	0.494331i	−0.972707	+	0.232038i	$0.925460\pi$
$888$		0			0
$889$	−12.5000	−	4.33013i	−0.419237	−	0.145228i
$890$		0			0
$891$	−4.50000	−	7.79423i	−0.150756	−	0.261116i
$892$		0			0
$893$	−6.00000	+	10.3923i	−0.200782	+	0.347765i
$894$		0			0
$895$	52.0000			1.73817
$896$		0			0
$897$	−6.00000			−0.200334
$898$		0			0
$899$	2.00000	−	3.46410i	0.0667037	−	0.115534i
$900$		0			0
$901$	12.0000	+	20.7846i	0.399778	+	0.692436i
$902$		0			0
$903$	24.0000	−	20.7846i	0.798670	−	0.691669i
$904$		0			0
$905$	−44.0000	−	76.2102i	−1.46261	−	2.53331i
$906$		0			0
$907$	22.0000	−	38.1051i	0.730498	−	1.26526i	−0.226173	−	0.974087i	$-0.572621\pi$
$907$	22.0000	−	38.1051i	0.730498	−	1.26526i	0.956671	−	0.291172i	$-0.0940453\pi$
$908$		0			0
$909$	−90.0000			−2.98511
$910$		0			0
$911$	54.0000			1.78910			0.894550	−	0.446968i	$-0.147496\pi$
$911$	54.0000			1.78910			0.894550	+	0.446968i	$0.147496\pi$
$912$		0			0
$913$	−3.00000	+	5.19615i	−0.0992855	+	0.171968i
$914$		0			0
$915$	−30.0000	−	51.9615i	−0.991769	−	1.71780i
$916$		0			0
$917$	−9.00000	−	46.7654i	−0.297206	−	1.54433i
$918$		0			0
$919$	−12.0000	−	20.7846i	−0.395843	−	0.685621i	0.597365	−	0.801970i	$-0.296214\pi$
$919$	−12.0000	−	20.7846i	−0.395843	−	0.685621i	−0.993208	+	0.116348i	$0.962881\pi$
$920$		0			0
$921$	48.0000	−	83.1384i	1.58165	−	2.73950i
$922$		0			0
$923$	4.00000			0.131662
$924$		0			0
$925$	−22.0000			−0.723356
$926$		0			0
$927$	36.0000	−	62.3538i	1.18240	−	2.04797i
$928$		0			0
$929$	16.5000	+	28.5788i	0.541347	+	0.937641i	0.998827	+	0.0484211i	$0.0154190\pi$
$929$	16.5000	+	28.5788i	0.541347	+	0.937641i	−0.457480	+	0.889220i	$0.651248\pi$
$930$		0			0
$931$	−6.00000	+	41.5692i	−0.196642	+	1.36238i
$932$		0			0
$933$	−42.0000	−	72.7461i	−1.37502	−	2.38160i
$934$		0			0
$935$	4.00000	−	6.92820i	0.130814	−	0.226576i
$936$		0			0
$937$	−12.0000			−0.392023			−0.196011	−	0.980602i	$-0.562799\pi$
$937$	−12.0000			−0.392023			−0.196011	+	0.980602i	$0.562799\pi$
$938$		0			0
$939$	3.00000			0.0979013
$940$		0			0
$941$	−27.5000	+	47.6314i	−0.896474	+	1.55274i	−0.0645052	+	0.997917i	$0.520547\pi$
$941$	−27.5000	+	47.6314i	−0.896474	+	1.55274i	−0.831969	+	0.554822i	$0.812786\pi$
$942$		0			0
$943$	2.00000	+	3.46410i	0.0651290	+	0.112807i
$944$		0			0
$945$	18.0000	+	93.5307i	0.585540	+	3.04256i
$946$		0			0
$947$	−8.00000	−	13.8564i	−0.259965	−	0.450273i	0.706267	−	0.707945i	$-0.250378\pi$
$947$	−8.00000	−	13.8564i	−0.259965	−	0.450273i	−0.966232	+	0.257673i	$0.917044\pi$
$948$		0			0
$949$	−1.00000	+	1.73205i	−0.0324614	+	0.0562247i
$950$		0			0
$951$	−36.0000			−1.16738
$952$		0			0
$953$	56.0000			1.81402			0.907009	−	0.421111i	$-0.138360\pi$
$953$	56.0000			1.81402			0.907009	+	0.421111i	$0.138360\pi$
$954$		0			0
$955$	−28.0000	+	48.4974i	−0.906059	+	1.56934i
$956$		0			0
$957$	−1.50000	−	2.59808i	−0.0484881	−	0.0839839i
$958$		0			0
$959$	18.0000	−	15.5885i	0.581250	−	0.503378i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$	24.0000	−	41.5692i	0.773389	−	1.33955i
$964$		0			0
$965$	88.0000			2.83282
$966$		0			0
$967$	−56.0000			−1.80084			−0.900419	−	0.435023i	$-0.856740\pi$
$967$	−56.0000			−1.80084			−0.900419	+	0.435023i	$0.856740\pi$
$968$		0			0
$969$	18.0000	−	31.1769i	0.578243	−	1.00155i
$970$		0			0
$971$	−6.50000	−	11.2583i	−0.208595	−	0.361297i	0.742677	−	0.669650i	$-0.233556\pi$
$971$	−6.50000	−	11.2583i	−0.208595	−	0.361297i	−0.951272	+	0.308353i	$0.900222\pi$
$972$		0			0
$973$	−20.0000	−	6.92820i	−0.641171	−	0.222108i
$974$		0			0
$975$	16.5000	+	28.5788i	0.528423	+	0.915255i
$976$		0			0
$977$	−7.00000	+	12.1244i	−0.223950	+	0.387893i	−0.956004	−	0.293354i	$-0.905229\pi$
$977$	−7.00000	+	12.1244i	−0.223950	+	0.387893i	0.732054	+	0.681247i	$0.238562\pi$
$978$		0			0
$979$	6.00000			0.191761
$980$		0			0
$981$	60.0000			1.91565
$982$		0			0
$983$	9.00000	−	15.5885i	0.287055	−	0.497195i	−0.686050	−	0.727554i	$-0.740657\pi$
$983$	9.00000	−	15.5885i	0.287055	−	0.497195i	0.973106	+	0.230360i	$0.0739903\pi$
$984$		0			0
$985$	−6.00000	−	10.3923i	−0.191176	−	0.331126i
$986$		0			0
$987$	−15.0000	−	5.19615i	−0.477455	−	0.165395i
$988$		0			0
$989$	4.00000	+	6.92820i	0.127193	+	0.220304i
$990$		0			0
$991$	−10.0000	+	17.3205i	−0.317660	+	0.550204i	−0.979999	−	0.199000i	$-0.936231\pi$
$991$	−10.0000	+	17.3205i	−0.317660	+	0.550204i	0.662339	+	0.749204i	$0.269564\pi$
$992$		0			0
$993$	−21.0000			−0.666415
$994$		0			0
$995$	40.0000			1.26809
$996$		0			0
$997$	21.0000	−	36.3731i	0.665077	−	1.15195i	−0.314188	−	0.949361i	$-0.601732\pi$
$997$	21.0000	−	36.3731i	0.665077	−	1.15195i	0.979265	−	0.202586i	$-0.0649345\pi$
$998$		0			0
$999$	9.00000	+	15.5885i	0.284747	+	0.493197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1232.2.q.a.529.1		2
4.3	odd	2		154.2.e.d.67.1	yes	2
7.2	even	3	inner	1232.2.q.a.177.1		2
7.3	odd	6		8624.2.a.d.1.1		1
7.4	even	3		8624.2.a.bd.1.1		1
12.11	even	2		1386.2.k.a.991.1		2
28.3	even	6		1078.2.a.f.1.1		1
28.11	odd	6		1078.2.a.a.1.1		1
28.19	even	6		1078.2.e.g.177.1		2
28.23	odd	6		154.2.e.d.23.1	✓	2
28.27	even	2		1078.2.e.g.67.1		2
84.11	even	6		9702.2.a.cg.1.1		1
84.23	even	6		1386.2.k.a.793.1		2
84.59	odd	6		9702.2.a.bb.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.e.d.23.1	✓	2	28.23	odd	6
154.2.e.d.67.1	yes	2	4.3	odd	2
1078.2.a.a.1.1		1	28.11	odd	6
1078.2.a.f.1.1		1	28.3	even	6
1078.2.e.g.67.1		2	28.27	even	2
1078.2.e.g.177.1		2	28.19	even	6
1232.2.q.a.177.1		2	7.2	even	3	inner
1232.2.q.a.529.1		2	1.1	even	1	trivial
1386.2.k.a.793.1		2	84.23	even	6
1386.2.k.a.991.1		2	12.11	even	2
8624.2.a.d.1.1		1	7.3	odd	6
8624.2.a.bd.1.1		1	7.4	even	3
9702.2.a.bb.1.1		1	84.59	odd	6
9702.2.a.cg.1.1		1	84.11	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:	\( N \)	\(=\)	\( 1232 = 2^{4} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1232.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 2.59808i) q^{3} +(2.00000 + 3.46410i) q^{5} +(2.50000 + 0.866025i) q^{7} +(-3.00000 - 5.19615i) q^{9} +(-0.500000 + 0.866025i) q^{11} -1.00000 q^{13} -12.0000 q^{15} +(-1.00000 + 1.73205i) q^{17} +(3.00000 + 5.19615i) q^{19} +(-6.00000 + 5.19615i) q^{21} +(-1.00000 - 1.73205i) q^{23} +(-5.50000 + 9.52628i) q^{25} +9.00000 q^{27} +1.00000 q^{29} +(2.00000 - 3.46410i) q^{31} +(-1.50000 - 2.59808i) q^{33} +(2.00000 + 10.3923i) q^{35} +(1.00000 + 1.73205i) q^{37} +(1.50000 - 2.59808i) q^{39} -2.00000 q^{41} -4.00000 q^{43} +(12.0000 - 20.7846i) q^{45} +(1.00000 + 1.73205i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-3.00000 - 5.19615i) q^{51} +(6.00000 - 10.3923i) q^{53} -4.00000 q^{55} -18.0000 q^{57} +(4.50000 - 7.79423i) q^{59} +(2.50000 + 4.33013i) q^{61} +(-3.00000 - 15.5885i) q^{63} +(-2.00000 - 3.46410i) q^{65} +(-4.50000 + 7.79423i) q^{67} +6.00000 q^{69} -4.00000 q^{71} +(1.00000 - 1.73205i) q^{73} +(-16.5000 - 28.5788i) q^{75} +(-2.00000 + 1.73205i) q^{77} +(-7.50000 - 12.9904i) q^{79} +(-4.50000 + 7.79423i) q^{81} +6.00000 q^{83} -8.00000 q^{85} +(-1.50000 + 2.59808i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(-2.50000 - 0.866025i) q^{91} +(6.00000 + 10.3923i) q^{93} +(-12.0000 + 20.7846i) q^{95} -5.00000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{3} + 4 q^{5} + 5 q^{7} - 6 q^{9} - q^{11} - 2 q^{13} - 24 q^{15} - 2 q^{17} + 6 q^{19} - 12 q^{21} - 2 q^{23} - 11 q^{25} + 18 q^{27} + 2 q^{29} + 4 q^{31} - 3 q^{33} + 4 q^{35} + 2 q^{37} + 3 q^{39}+ \cdots + 12 q^{99}+O(q^{100}) \) 2 * q - 3 * q^3 + 4 * q^5 + 5 * q^7 - 6 * q^9 - q^11 - 2 * q^13 - 24 * q^15 - 2 * q^17 + 6 * q^19 - 12 * q^21 - 2 * q^23 - 11 * q^25 + 18 * q^27 + 2 * q^29 + 4 * q^31 - 3 * q^33 + 4 * q^35 + 2 * q^37 + 3 * q^39 - 4 * q^41 - 8 * q^43 + 24 * q^45 + 2 * q^47 + 11 * q^49 - 6 * q^51 + 12 * q^53 - 8 * q^55 - 36 * q^57 + 9 * q^59 + 5 * q^61 - 6 * q^63 - 4 * q^65 - 9 * q^67 + 12 * q^69 - 8 * q^71 + 2 * q^73 - 33 * q^75 - 4 * q^77 - 15 * q^79 - 9 * q^81 + 12 * q^83 - 16 * q^85 - 3 * q^87 - 6 * q^89 - 5 * q^91 + 12 * q^93 - 24 * q^95 - 10 * q^97 + 12 * q^99

Introduction

L-functions

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Database

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