LMFDB - Embedded newform 1458.2.c.g.973.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1458,2,Mod(487,1458)] 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("1458.487"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1458, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1458 = 2 \cdot 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1458.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,6,0,-6,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$11.6421886147$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			973.6
Root			$0.500000 + 0.677980i$ of defining polynomial
Character	$\chi$	$=$	1458.973
Dual form			1458.2.c.g.487.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.77684 - 3.07758i) q^{5} +(0.159750 + 0.276696i) q^{7} -1.00000 q^{8} +3.55368 q^{10} +(2.22603 + 3.85559i) q^{11} +(2.33937 - 4.05190i) q^{13} +(-0.159750 + 0.276696i) q^{14} +(-0.500000 - 0.866025i) q^{16} -1.13471 q^{17} +1.85779 q^{19} +(1.77684 + 3.07758i) q^{20} +(-2.22603 + 3.85559i) q^{22} +(0.0721058 - 0.124891i) q^{23} +(-3.81433 - 6.60661i) q^{25} +4.67874 q^{26} -0.319501 q^{28} +(-2.17962 - 3.77521i) q^{29} +(-0.335846 + 0.581702i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.567354 - 0.982686i) q^{34} +1.13540 q^{35} +7.58877 q^{37} +(0.928896 + 1.60890i) q^{38} +(-1.77684 + 3.07758i) q^{40} +(1.08865 - 1.88559i) q^{41} +(3.54885 + 6.14680i) q^{43} -4.45206 q^{44} +0.144212 q^{46} +(-5.16327 - 8.94305i) q^{47} +(3.44896 - 5.97377i) q^{49} +(3.81433 - 6.60661i) q^{50} +(2.33937 + 4.05190i) q^{52} -0.805554 q^{53} +15.8212 q^{55} +(-0.159750 - 0.276696i) q^{56} +(2.17962 - 3.77521i) q^{58} +(1.49142 - 2.58322i) q^{59} +(1.74732 + 3.02645i) q^{61} -0.671692 q^{62} +1.00000 q^{64} +(-8.31337 - 14.3992i) q^{65} +(-3.72162 + 6.44604i) q^{67} +(0.567354 - 0.982686i) q^{68} +(0.567702 + 0.983289i) q^{70} +8.09856 q^{71} +14.6013 q^{73} +(3.79438 + 6.57207i) q^{74} +(-0.928896 + 1.60890i) q^{76} +(-0.711218 + 1.23187i) q^{77} +(6.29350 + 10.9007i) q^{79} -3.55368 q^{80} +2.17729 q^{82} +(-2.70681 - 4.68834i) q^{83} +(-2.01620 + 3.49215i) q^{85} +(-3.54885 + 6.14680i) q^{86} +(-2.22603 - 3.85559i) q^{88} -5.05248 q^{89} +1.49486 q^{91} +(0.0721058 + 0.124891i) q^{92} +(5.16327 - 8.94305i) q^{94} +(3.30100 - 5.71750i) q^{95} +(-9.33706 - 16.1723i) q^{97} +6.89792 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 12 q^{8} + 6 q^{10} + 3 q^{11} - 9 q^{13} + 6 q^{14} - 6 q^{16} - 12 q^{17} + 18 q^{19} + 3 q^{20} - 3 q^{22} - 3 q^{23} - 15 q^{25} - 18 q^{26} + 12 q^{28}+ \cdots - 24 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 - 6 * q^4 + 3 * q^5 - 6 * q^7 - 12 * q^8 + 6 * q^10 + 3 * q^11 - 9 * q^13 + 6 * q^14 - 6 * q^16 - 12 * q^17 + 18 * q^19 + 3 * q^20 - 3 * q^22 - 3 * q^23 - 15 * q^25 - 18 * q^26 + 12 * q^28 + 3 * q^29 - 12 * q^31 + 6 * q^32 - 6 * q^34 + 6 * q^35 + 30 * q^37 + 9 * q^38 - 3 * q^40 + 3 * q^41 - 12 * q^43 - 6 * q^44 - 6 * q^46 - 9 * q^47 - 12 * q^49 + 15 * q^50 - 9 * q^52 + 12 * q^53 + 18 * q^55 + 6 * q^56 - 3 * q^58 - 3 * q^59 - 12 * q^61 - 24 * q^62 + 12 * q^64 - 3 * q^65 - 21 * q^67 + 6 * q^68 + 3 * q^70 + 24 * q^71 + 42 * q^73 + 15 * q^74 - 9 * q^76 - 3 * q^77 - 6 * q^80 + 6 * q^82 - 27 * q^83 + 12 * q^86 - 3 * q^88 + 24 * q^89 + 12 * q^91 - 3 * q^92 + 9 * q^94 - 30 * q^95 - 18 * q^97 - 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1458\mathbb{Z}\right)^\times$.

$n$	$731$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.77684	−	3.07758i	0.794627	−	1.37633i	−0.128448	−	0.991716i	$-0.541000\pi$
$5$	1.77684	−	3.07758i	0.794627	−	1.37633i	0.923076	−	0.384619i	$-0.125667\pi$
$6$		0			0
$7$	0.159750	+	0.276696i	0.0603800	+	0.104581i	0.894635	−	0.446797i	$-0.147435\pi$
$7$	0.159750	+	0.276696i	0.0603800	+	0.104581i	−0.834255	+	0.551378i	$0.814102\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	3.55368			1.12377
$11$	2.22603	+	3.85559i	0.671173	+	1.16250i	0.977572	+	0.210602i	$0.0675424\pi$
$11$	2.22603	+	3.85559i	0.671173	+	1.16250i	−0.306399	+	0.951903i	$0.599124\pi$
$12$		0			0
$13$	2.33937	−	4.05190i	0.648824	−	1.12380i	−0.334580	−	0.942367i	$-0.608594\pi$
$13$	2.33937	−	4.05190i	0.648824	−	1.12380i	0.983404	−	0.181429i	$-0.0580722\pi$
$14$	−0.159750	+	0.276696i	−0.0426951	+	0.0739501i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.13471			−0.275207			−0.137604	−	0.990487i	$-0.543940\pi$
$17$	−1.13471			−0.275207			−0.137604	+	0.990487i	$0.543940\pi$
$18$		0			0
$19$	1.85779			0.426207			0.213103	−	0.977030i	$-0.431643\pi$
$19$	1.85779			0.426207			0.213103	+	0.977030i	$0.431643\pi$
$20$	1.77684	+	3.07758i	0.397314	+	0.688167i
$21$		0			0
$22$	−2.22603	+	3.85559i	−0.474591	+	0.822015i
$23$	0.0721058	−	0.124891i	0.0150351	−	0.0260416i	−0.858410	−	0.512964i	$-0.828547\pi$
$23$	0.0721058	−	0.124891i	0.0150351	−	0.0260416i	0.873445	+	0.486923i	$0.161881\pi$
$24$		0			0
$25$	−3.81433	−	6.60661i	−0.762865	−	1.32132i
$26$	4.67874			0.917576
$27$		0			0
$28$	−0.319501			−0.0603800
$29$	−2.17962	−	3.77521i	−0.404745	−	0.701039i	0.589547	−	0.807734i	$-0.299306\pi$
$29$	−2.17962	−	3.77521i	−0.404745	−	0.701039i	−0.994292	+	0.106695i	$0.965973\pi$
$30$		0			0
$31$	−0.335846	+	0.581702i	−0.0603197	+	0.104477i	−0.894608	−	0.446851i	$-0.852545\pi$
$31$	−0.335846	+	0.581702i	−0.0603197	+	0.104477i	0.834289	+	0.551328i	$0.185879\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−0.567354	−	0.982686i	−0.0973004	−	0.168529i
$35$	1.13540			0.191918
$36$		0			0
$37$	7.58877			1.24759			0.623793	−	0.781590i	$-0.285591\pi$
$37$	7.58877			1.24759			0.623793	+	0.781590i	$0.285591\pi$
$38$	0.928896	+	1.60890i	0.150687	+	0.260997i
$39$		0			0
$40$	−1.77684	+	3.07758i	−0.280943	+	0.486608i
$41$	1.08865	−	1.88559i	0.170018	−	0.294480i	−0.768408	−	0.639960i	$-0.778951\pi$
$41$	1.08865	−	1.88559i	0.170018	−	0.294480i	0.938426	+	0.345481i	$0.112284\pi$
$42$		0			0
$43$	3.54885	+	6.14680i	0.541195	+	0.937378i	0.998836	+	0.0482404i	$0.0153614\pi$
$43$	3.54885	+	6.14680i	0.541195	+	0.937378i	−0.457640	+	0.889137i	$0.651305\pi$
$44$	−4.45206			−0.671173
$45$		0			0
$46$	0.144212			0.0212628
$47$	−5.16327	−	8.94305i	−0.753141	−	1.30448i	−0.946293	−	0.323309i	$-0.895205\pi$
$47$	−5.16327	−	8.94305i	−0.753141	−	1.30448i	0.193153	−	0.981169i	$-0.438129\pi$
$48$		0			0
$49$	3.44896	−	5.97377i	0.492709	−	0.853396i
$50$	3.81433	−	6.60661i	0.539427	−	0.934315i
$51$		0			0
$52$	2.33937	+	4.05190i	0.324412	+	0.561898i
$53$	−0.805554			−0.110651			−0.0553257	−	0.998468i	$-0.517620\pi$
$53$	−0.805554			−0.110651			−0.0553257	+	0.998468i	$0.517620\pi$
$54$		0			0
$55$	15.8212			2.13333
$56$	−0.159750	−	0.276696i	−0.0213476	−	0.0369750i
$57$		0			0
$58$	2.17962	−	3.77521i	0.286198	−	0.495709i
$59$	1.49142	−	2.58322i	0.194167	−	0.336307i	−0.752460	−	0.658638i	$-0.771133\pi$
$59$	1.49142	−	2.58322i	0.194167	−	0.336307i	0.946627	+	0.322331i	$0.104466\pi$
$60$		0			0
$61$	1.74732	+	3.02645i	0.223721	+	0.387497i	0.955935	−	0.293578i	$-0.0948461\pi$
$61$	1.74732	+	3.02645i	0.223721	+	0.387497i	−0.732214	+	0.681075i	$0.761513\pi$
$62$	−0.671692			−0.0853050
$63$		0			0
$64$	1.00000			0.125000
$65$	−8.31337	−	14.3992i	−1.03115	−	1.78600i
$66$		0			0
$67$	−3.72162	+	6.44604i	−0.454669	+	0.787509i	−0.998669	−	0.0515756i	$-0.983576\pi$
$67$	−3.72162	+	6.44604i	−0.454669	+	0.787509i	0.544000	+	0.839085i	$0.316909\pi$
$68$	0.567354	−	0.982686i	0.0688018	−	0.119168i
$69$		0			0
$70$	0.567702	+	0.983289i	0.0678534	+	0.117526i
$71$	8.09856			0.961122			0.480561	−	0.876961i	$-0.340433\pi$
$71$	8.09856			0.961122			0.480561	+	0.876961i	$0.340433\pi$
$72$		0			0
$73$	14.6013			1.70895			0.854477	−	0.519489i	$-0.173878\pi$
$73$	14.6013			1.70895			0.854477	+	0.519489i	$0.173878\pi$
$74$	3.79438	+	6.57207i	0.441088	+	0.763987i
$75$		0			0
$76$	−0.928896	+	1.60890i	−0.106552	+	0.184553i
$77$	−0.711218	+	1.23187i	−0.0810508	+	0.140384i
$78$		0			0
$79$	6.29350	+	10.9007i	0.708074	+	1.22642i	0.965571	+	0.260141i	$0.0837692\pi$
$79$	6.29350	+	10.9007i	0.708074	+	1.22642i	−0.257496	+	0.966279i	$0.582897\pi$
$80$	−3.55368			−0.397314
$81$		0			0
$82$	2.17729			0.240442
$83$	−2.70681	−	4.68834i	−0.297111	−	0.514612i	0.678362	−	0.734727i	$-0.262690\pi$
$83$	−2.70681	−	4.68834i	−0.297111	−	0.514612i	−0.975474	+	0.220115i	$0.929357\pi$
$84$		0			0
$85$	−2.01620	+	3.49215i	−0.218687	+	0.378777i
$86$	−3.54885	+	6.14680i	−0.382683	+	0.662826i
$87$		0			0
$88$	−2.22603	−	3.85559i	−0.237295	−	0.411008i
$89$	−5.05248			−0.535562			−0.267781	−	0.963480i	$-0.586290\pi$
$89$	−5.05248			−0.535562			−0.267781	+	0.963480i	$0.586290\pi$
$90$		0			0
$91$	1.49486			0.156704
$92$	0.0721058	+	0.124891i	0.00751755	+	0.0130208i
$93$		0			0
$94$	5.16327	−	8.94305i	0.532551	−	0.922405i
$95$	3.30100	−	5.71750i	0.338676	−	0.586603i
$96$		0			0
$97$	−9.33706	−	16.1723i	−0.948035	−	1.64204i	−0.749557	−	0.661939i	$-0.769734\pi$
$97$	−9.33706	−	16.1723i	−0.948035	−	1.64204i	−0.198478	−	0.980105i	$-0.563600\pi$
$98$	6.89792			0.696795
$99$		0			0
$100$	7.62865			0.762865
$101$	−1.20983	−	2.09550i	−0.120383	−	0.208510i	0.799536	−	0.600619i	$-0.205079\pi$
$101$	−1.20983	−	2.09550i	−0.120383	−	0.208510i	−0.919919	+	0.392109i	$0.871746\pi$
$102$		0			0
$103$	−0.997676	+	1.72802i	−0.0983039	+	0.170267i	−0.910983	−	0.412445i	$-0.864675\pi$
$103$	−0.997676	+	1.72802i	−0.0983039	+	0.170267i	0.812679	+	0.582712i	$0.198008\pi$
$104$	−2.33937	+	4.05190i	−0.229394	+	0.397322i
$105$		0			0
$106$	−0.402777	−	0.697630i	−0.0391212	−	0.0677599i
$107$	−8.87072			−0.857565			−0.428783	−	0.903408i	$-0.641057\pi$
$107$	−8.87072			−0.857565			−0.428783	+	0.903408i	$0.641057\pi$
$108$		0			0
$109$	−1.97204			−0.188887			−0.0944434	−	0.995530i	$-0.530107\pi$
$109$	−1.97204			−0.188887			−0.0944434	+	0.995530i	$0.530107\pi$
$110$	7.91059	+	13.7015i	0.754245	+	1.30639i
$111$		0			0
$112$	0.159750	−	0.276696i	0.0150950	−	0.0261453i
$113$	−4.81433	+	8.33866i	−0.452894	+	0.784435i	−0.998564	−	0.0535648i	$-0.982942\pi$
$113$	−4.81433	+	8.33866i	−0.452894	+	0.784435i	0.545671	+	0.838000i	$0.316275\pi$
$114$		0			0
$115$	−0.256241	−	0.443823i	−0.0238946	−	0.0413867i
$116$	4.35924			0.404745
$117$		0			0
$118$	2.98285			0.274593
$119$	−0.181270	−	0.313969i	−0.0166170	−	0.0287815i
$120$		0			0
$121$	−4.41040	+	7.63903i	−0.400945	+	0.694457i
$122$	−1.74732	+	3.02645i	−0.158195	+	0.274002i
$123$		0			0
$124$	−0.335846	−	0.581702i	−0.0301599	−	0.0522384i
$125$	−9.34139			−0.835520
$126$		0			0
$127$	0.159210			0.0141276			0.00706379	−	0.999975i	$-0.497752\pi$
$127$	0.159210			0.0141276			0.00706379	+	0.999975i	$0.497752\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	8.31337	−	14.3992i	0.729131	−	1.26289i
$131$	−4.74292	+	8.21497i	−0.414391	+	0.717745i	−0.995364	−	0.0961768i	$-0.969339\pi$
$131$	−4.74292	+	8.21497i	−0.414391	+	0.717745i	0.580974	+	0.813922i	$0.302672\pi$
$132$		0			0
$133$	0.296783	+	0.514044i	0.0257344	+	0.0445732i
$134$	−7.44325			−0.642999
$135$		0			0
$136$	1.13471			0.0973004
$137$	5.85468	+	10.1406i	0.500199	+	0.866370i	1.00000		0.000229878i	$7.31726e-5\pi$
$137$	5.85468	+	10.1406i	0.500199	+	0.866370i	−0.499801	+	0.866140i	$0.666593\pi$
$138$		0			0
$139$	2.62513	−	4.54686i	0.222661	−	0.385660i	−0.732954	−	0.680278i	$-0.761859\pi$
$139$	2.62513	−	4.54686i	0.222661	−	0.385660i	0.955615	+	0.294618i	$0.0951924\pi$
$140$	−0.567702	+	0.983289i	−0.0479796	+	0.0831031i
$141$		0			0
$142$	4.04928	+	7.01356i	0.339808	+	0.588564i
$143$	20.8300			1.74189
$144$		0			0
$145$	−15.4913			−1.28649
$146$	7.30065	+	12.6451i	0.604206	+	1.04652i
$147$		0			0
$148$	−3.79438	+	6.57207i	−0.311896	+	0.540220i
$149$	−8.14612	+	14.1095i	−0.667356	+	1.15589i	0.311285	+	0.950317i	$0.399241\pi$
$149$	−8.14612	+	14.1095i	−0.667356	+	1.15589i	−0.978641	+	0.205578i	$0.934093\pi$
$150$		0			0
$151$	7.80897	+	13.5255i	0.635485	+	1.10069i	0.986412	+	0.164289i	$0.0525330\pi$
$151$	7.80897	+	13.5255i	0.635485	+	1.10069i	−0.350928	+	0.936403i	$0.614134\pi$
$152$	−1.85779			−0.150687
$153$		0			0
$154$	−1.42244			−0.114623
$155$	1.19349	+	2.06718i	0.0958634	+	0.166040i
$156$		0			0
$157$	−8.81577	+	15.2694i	−0.703575	+	1.21863i	0.263628	+	0.964624i	$0.415081\pi$
$157$	−8.81577	+	15.2694i	−0.703575	+	1.21863i	−0.967203	+	0.254003i	$0.918253\pi$
$158$	−6.29350	+	10.9007i	−0.500684	+	0.867210i
$159$		0			0
$160$	−1.77684	−	3.07758i	−0.140472	−	0.243304i
$161$	0.0460757			0.00363128
$162$		0			0
$163$	−15.8801			−1.24382			−0.621912	−	0.783087i	$-0.713644\pi$
$163$	−15.8801			−1.24382			−0.621912	+	0.783087i	$0.713644\pi$
$164$	1.08865	+	1.88559i	0.0850090	+	0.147240i
$165$		0			0
$166$	2.70681	−	4.68834i	0.210090	−	0.363886i
$167$	−6.78921	+	11.7593i	−0.525365	+	0.909958i	0.474199	+	0.880418i	$0.342738\pi$
$167$	−6.78921	+	11.7593i	−0.525365	+	0.909958i	−0.999564	+	0.0295407i	$0.990596\pi$
$168$		0			0
$169$	−4.44529	−	7.69947i	−0.341945	−	0.592267i
$170$	−4.03239			−0.309270
$171$		0			0
$172$	−7.09771			−0.541195
$173$	3.22220	+	5.58102i	0.244980	+	0.424317i	0.962126	−	0.272606i	$-0.0878854\pi$
$173$	3.22220	+	5.58102i	0.244980	+	0.424317i	−0.717146	+	0.696923i	$0.754552\pi$
$174$		0			0
$175$	1.21868	−	2.11082i	0.0921236	−	0.159563i
$176$	2.22603	−	3.85559i	0.167793	−	0.290626i
$177$		0			0
$178$	−2.52624	−	4.37558i	−0.189350	−	0.327963i
$179$	12.5123			0.935210			0.467605	−	0.883938i	$-0.345117\pi$
$179$	12.5123			0.935210			0.467605	+	0.883938i	$0.345117\pi$
$180$		0			0
$181$	0.304503			0.0226335			0.0113168	−	0.999936i	$-0.496398\pi$
$181$	0.304503			0.0226335			0.0113168	+	0.999936i	$0.496398\pi$
$182$	0.747430	+	1.29459i	0.0554032	+	0.0959612i
$183$		0			0
$184$	−0.0721058	+	0.124891i	−0.00531571	+	0.00920708i
$185$	13.4840	−	23.3550i	0.991366	−	1.71710i
$186$		0			0
$187$	−2.52589	−	4.37497i	−0.184712	−	0.319930i
$188$	10.3265			0.753141
$189$		0			0
$190$	6.60200			0.478960
$191$	−7.19635	−	12.4645i	−0.520710	−	0.901896i	−0.999710	−	0.0240812i	$-0.992334\pi$
$191$	−7.19635	−	12.4645i	−0.520710	−	0.901896i	0.479000	−	0.877815i	$-0.340999\pi$
$192$		0			0
$193$	−1.52531	+	2.64192i	−0.109794	+	0.190170i	−0.915687	−	0.401892i	$-0.868353\pi$
$193$	−1.52531	+	2.64192i	−0.109794	+	0.190170i	0.805892	+	0.592062i	$0.201686\pi$
$194$	9.33706	−	16.1723i	0.670362	−	1.16110i
$195$		0			0
$196$	3.44896	+	5.97377i	0.246354	+	0.426698i
$197$	−22.2642			−1.58626			−0.793129	−	0.609053i	$-0.791550\pi$
$197$	−22.2642			−1.58626			−0.793129	+	0.609053i	$0.791550\pi$
$198$		0			0
$199$	24.5634			1.74125			0.870626	−	0.491945i	$-0.163714\pi$
$199$	24.5634			1.74125			0.870626	+	0.491945i	$0.163714\pi$
$200$	3.81433	+	6.60661i	0.269714	+	0.467158i
$201$		0			0
$202$	1.20983	−	2.09550i	0.0851237	−	0.147439i
$203$	0.696390	−	1.20618i	0.0488770	−	0.0846574i
$204$		0			0
$205$	−3.86870	−	6.70079i	−0.270202	−	0.468004i
$206$	−1.99535			−0.139023
$207$		0			0
$208$	−4.67874			−0.324412
$209$	4.13550	+	7.16289i	0.286058	+	0.495468i
$210$		0			0
$211$	1.50965	−	2.61480i	0.103929	−	0.180010i	−0.809371	−	0.587297i	$-0.800192\pi$
$211$	1.50965	−	2.61480i	0.103929	−	0.180010i	0.913300	+	0.407287i	$0.133525\pi$
$212$	0.402777	−	0.697630i	0.0276628	−	0.0479135i
$213$		0			0
$214$	−4.43536	−	7.68227i	−0.303195	−	0.525149i
$215$	25.2230			1.72019
$216$		0			0
$217$	−0.214606			−0.0145684
$218$	−0.986018	−	1.70783i	−0.0667816	−	0.115669i
$219$		0			0
$220$	−7.91059	+	13.7015i	−0.533332	+	0.923758i
$221$	−2.65450	+	4.59773i	−0.178561	+	0.309277i
$222$		0			0
$223$	−4.99020	−	8.64328i	−0.334168	−	0.578797i	0.649156	−	0.760655i	$-0.275122\pi$
$223$	−4.99020	−	8.64328i	−0.334168	−	0.578797i	−0.983325	+	0.181858i	$0.941789\pi$
$224$	0.319501			0.0213476
$225$		0			0
$226$	−9.62865			−0.640488
$227$	−10.5612	−	18.2925i	−0.700970	−	1.21412i	−0.968126	−	0.250463i	$-0.919417\pi$
$227$	−10.5612	−	18.2925i	−0.700970	−	1.21412i	0.267156	−	0.963653i	$-0.413916\pi$
$228$		0			0
$229$	11.6404	−	20.1617i	0.769217	−	1.33232i	−0.168771	−	0.985655i	$-0.553980\pi$
$229$	11.6404	−	20.1617i	0.769217	−	1.33232i	0.937988	−	0.346668i	$-0.112687\pi$
$230$	0.256241	−	0.443823i	0.0168960	−	0.0292648i
$231$		0			0
$232$	2.17962	+	3.77521i	0.143099	+	0.247855i
$233$	−26.7243			−1.75077			−0.875383	−	0.483429i	$-0.839391\pi$
$233$	−26.7243			−1.75077			−0.875383	+	0.483429i	$0.839391\pi$
$234$		0			0
$235$	−36.6973			−2.39386
$236$	1.49142	+	2.58322i	0.0970834	+	0.168153i
$237$		0			0
$238$	0.181270	−	0.313969i	0.0117500	−	0.0203516i
$239$	−12.0299	+	20.8365i	−0.778152	+	1.34780i	0.154854	+	0.987937i	$0.450509\pi$
$239$	−12.0299	+	20.8365i	−0.778152	+	1.34780i	−0.933006	+	0.359861i	$0.882824\pi$
$240$		0			0
$241$	0.745760	+	1.29169i	0.0480386	+	0.0832053i	0.889045	−	0.457820i	$-0.151370\pi$
$241$	0.745760	+	1.29169i	0.0480386	+	0.0832053i	−0.841006	+	0.541025i	$0.818036\pi$
$242$	−8.82079			−0.567022
$243$		0			0
$244$	−3.49464			−0.223721
$245$	−12.2565	−	21.2289i	−0.783039	−	1.35626i
$246$		0			0
$247$	4.34606	−	7.52760i	0.276533	−	0.478970i
$248$	0.335846	−	0.581702i	0.0213262	−	0.0369381i
$249$		0			0
$250$	−4.67070	−	8.08988i	−0.295401	−	0.511649i
$251$	−14.5750			−0.919963			−0.459982	−	0.887928i	$-0.652144\pi$
$251$	−14.5750			−0.919963			−0.459982	+	0.887928i	$0.652144\pi$
$252$		0			0
$253$	0.642038			0.0403646
$254$	0.0796049	+	0.137880i	0.00499485	+	0.00865134i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−5.51231	+	9.54761i	−0.343849	+	0.595563i	−0.985144	−	0.171731i	$-0.945064\pi$
$257$	−5.51231	+	9.54761i	−0.343849	+	0.595563i	0.641295	+	0.767294i	$0.278397\pi$
$258$		0			0
$259$	1.21231	+	2.09978i	0.0753292	+	0.130474i
$260$	16.6267			1.03115
$261$		0			0
$262$	−9.48583			−0.586037
$263$	−6.57003	−	11.3796i	−0.405125	−	0.701697i	0.589211	−	0.807979i	$-0.299439\pi$
$263$	−6.57003	−	11.3796i	−0.405125	−	0.701697i	−0.994336	+	0.106282i	$0.966105\pi$
$264$		0			0
$265$	−1.43134	+	2.47916i	−0.0879266	+	0.152293i
$266$	−0.296783	+	0.514044i	−0.0181969	+	0.0315180i
$267$		0			0
$268$	−3.72162	−	6.44604i	−0.227334	−	0.393755i
$269$	10.3086			0.628528			0.314264	−	0.949336i	$-0.398242\pi$
$269$	10.3086			0.628528			0.314264	+	0.949336i	$0.398242\pi$
$270$		0			0
$271$	1.01454			0.0616288			0.0308144	−	0.999525i	$-0.490190\pi$
$271$	1.01454			0.0616288			0.0308144	+	0.999525i	$0.490190\pi$
$272$	0.567354	+	0.982686i	0.0344009	+	0.0595841i
$273$		0			0
$274$	−5.85468	+	10.1406i	−0.353694	+	0.612616i
$275$	16.9816	−	29.4130i	1.02403	−	1.77367i
$276$		0			0
$277$	5.41584	+	9.38051i	0.325406	+	0.563620i	0.981595	−	0.190977i	$-0.0611656\pi$
$277$	5.41584	+	9.38051i	0.325406	+	0.563620i	−0.656188	+	0.754597i	$0.727832\pi$
$278$	5.25027			0.314890
$279$		0			0
$280$	−1.13540			−0.0678534
$281$	−4.23836	−	7.34106i	−0.252840	−	0.437931i	0.711467	−	0.702720i	$-0.248031\pi$
$281$	−4.23836	−	7.34106i	−0.252840	−	0.437931i	−0.964306	+	0.264789i	$0.914698\pi$
$282$		0			0
$283$	−3.15214	+	5.45966i	−0.187375	+	0.324543i	−0.944374	−	0.328873i	$-0.893331\pi$
$283$	−3.15214	+	5.45966i	−0.187375	+	0.324543i	0.756999	+	0.653416i	$0.226665\pi$
$284$	−4.04928	+	7.01356i	−0.240280	+	0.416178i
$285$		0			0
$286$	10.4150	+	18.0393i	0.615852	+	1.06669i
$287$	0.695647			0.0410628
$288$		0			0
$289$	−15.7124			−0.924261
$290$	−7.74567	−	13.4159i	−0.454841	−	0.787808i
$291$		0			0
$292$	−7.30065	+	12.6451i	−0.427238	+	0.739999i
$293$	−1.21653	+	2.10709i	−0.0710703	+	0.123097i	−0.899371	−	0.437187i	$-0.855975\pi$
$293$	−1.21653	+	2.10709i	−0.0710703	+	0.123097i	0.828300	+	0.560284i	$0.189308\pi$
$294$		0			0
$295$	−5.30005	−	9.17995i	−0.308581	−	0.534477i
$296$	−7.58877			−0.441088
$297$		0			0
$298$	−16.2922			−0.943784
$299$	−0.337364	−	0.584332i	−0.0195103	−	0.0337928i
$300$		0			0
$301$	−1.13386	+	1.96391i	−0.0653547	+	0.113198i
$302$	−7.80897	+	13.5255i	−0.449356	+	0.778307i
$303$		0			0
$304$	−0.928896	−	1.60890i	−0.0532759	−	0.0922765i
$305$	12.4188			0.711101
$306$		0			0
$307$	−23.7258			−1.35410			−0.677050	−	0.735937i	$-0.736742\pi$
$307$	−23.7258			−1.35410			−0.677050	+	0.735937i	$0.736742\pi$
$308$	−0.711218	−	1.23187i	−0.0405254	−	0.0701920i
$309$		0			0
$310$	−1.19349	+	2.06718i	−0.0677857	+	0.117408i
$311$	−5.40030	+	9.35360i	−0.306223	+	0.530394i	−0.977533	−	0.210783i	$-0.932399\pi$
$311$	−5.40030	+	9.35360i	−0.306223	+	0.530394i	0.671310	+	0.741177i	$0.265732\pi$
$312$		0			0
$313$	7.94559	+	13.7622i	0.449112	+	0.777884i	0.998328	−	0.0577958i	$-0.0184072\pi$
$313$	7.94559	+	13.7622i	0.449112	+	0.777884i	−0.549217	+	0.835680i	$0.685074\pi$
$314$	−17.6315			−0.995005
$315$		0			0
$316$	−12.5870			−0.708074
$317$	−1.61752	−	2.80163i	−0.0908490	−	0.157355i	0.817020	−	0.576610i	$-0.195625\pi$
$317$	−1.61752	−	2.80163i	−0.0908490	−	0.157355i	−0.907869	+	0.419255i	$0.862291\pi$
$318$		0			0
$319$	9.70378	−	16.8074i	0.543307	−	0.941036i
$320$	1.77684	−	3.07758i	0.0993284	−	0.172042i
$321$		0			0
$322$	0.0230379	+	0.0399028i	0.00128385	+	0.00222369i
$323$	−2.10805			−0.117295
$324$		0			0
$325$	−35.6925			−1.97986
$326$	−7.94004	−	13.7526i	−0.439758	−	0.761683i
$327$		0			0
$328$	−1.08865	+	1.88559i	−0.0601105	+	0.104114i
$329$	1.64967	−	2.85731i	0.0909493	−	0.157529i
$330$		0			0
$331$	8.83183	+	15.2972i	0.485441	+	0.840809i	0.999860	−	0.0167301i	$-0.00532561\pi$
$331$	8.83183	+	15.2972i	0.485441	+	0.840809i	−0.514419	+	0.857539i	$0.671992\pi$
$332$	5.41363			0.297111
$333$		0			0
$334$	−13.5784			−0.742978
$335$	13.2255	+	22.9072i	0.722584	+	1.25155i
$336$		0			0
$337$	5.27144	−	9.13040i	0.287154	−	0.497365i	−0.685976	−	0.727625i	$-0.740624\pi$
$337$	5.27144	−	9.13040i	0.287154	−	0.497365i	0.973129	+	0.230260i	$0.0739577\pi$
$338$	4.44529	−	7.69947i	0.241792	−	0.418796i
$339$		0			0
$340$	−2.01620	−	3.49215i	−0.109344	−	0.189389i
$341$	−2.99041			−0.161940
$342$		0			0
$343$	4.44040			0.239759
$344$	−3.54885	−	6.14680i	−0.191341	−	0.331413i
$345$		0			0
$346$	−3.22220	+	5.58102i	−0.173227	+	0.300037i
$347$	16.2523	−	28.1499i	0.872471	−	1.51116i	0.0130381	−	0.999915i	$-0.495850\pi$
$347$	16.2523	−	28.1499i	0.872471	−	1.51116i	0.859433	−	0.511249i	$-0.170817\pi$
$348$		0			0
$349$	10.0351	+	17.3814i	0.537169	+	0.930404i	0.999055	+	0.0434648i	$0.0138396\pi$
$349$	10.0351	+	17.3814i	0.537169	+	0.930404i	−0.461886	+	0.886939i	$0.652827\pi$
$350$	2.43736			0.130282
$351$		0			0
$352$	4.45206			0.237295
$353$	5.51803	+	9.55750i	0.293695	+	0.508694i	0.974680	−	0.223602i	$-0.0717817\pi$
$353$	5.51803	+	9.55750i	0.293695	+	0.508694i	−0.680986	+	0.732297i	$0.738448\pi$
$354$		0			0
$355$	14.3898	−	24.9239i	0.763734	−	1.32283i
$356$	2.52624	−	4.37558i	0.133890	−	0.231905i
$357$		0			0
$358$	6.25613	+	10.8359i	0.330647	+	0.572697i
$359$	3.92087			0.206936			0.103468	−	0.994633i	$-0.467006\pi$
$359$	3.92087			0.206936			0.103468	+	0.994633i	$0.467006\pi$
$360$		0			0
$361$	−15.5486			−0.818348
$362$	0.152251	+	0.263707i	0.00800216	+	0.0138601i
$363$		0			0
$364$	−0.747430	+	1.29459i	−0.0391760	+	0.0678548i
$365$	25.9442	−	44.9367i	1.35798	−	2.35209i
$366$		0			0
$367$	−14.5756	−	25.2457i	−0.760841	−	1.31782i	−0.942418	−	0.334438i	$-0.891453\pi$
$367$	−14.5756	−	25.2457i	−0.760841	−	1.31782i	0.181577	−	0.983377i	$-0.441880\pi$
$368$	−0.144212			−0.00751755
$369$		0			0
$370$	26.9681			1.40200
$371$	−0.128688	−	0.222894i	−0.00668113	−	0.0115721i
$372$		0			0
$373$	−3.13591	+	5.43155i	−0.162371	+	0.281235i	−0.935719	−	0.352747i	$-0.885247\pi$
$373$	−3.13591	+	5.43155i	−0.162371	+	0.281235i	0.773348	+	0.633982i	$0.218581\pi$
$374$	2.52589	−	4.37497i	0.130611	−	0.226224i
$375$		0			0
$376$	5.16327	+	8.94305i	0.266275	+	0.461203i
$377$	−20.3957			−1.05043
$378$		0			0
$379$	−26.9562			−1.38465			−0.692324	−	0.721587i	$-0.743413\pi$
$379$	−26.9562			−1.38465			−0.692324	+	0.721587i	$0.743413\pi$
$380$	3.30100	+	5.71750i	0.169338	+	0.293302i
$381$		0			0
$382$	7.19635	−	12.4645i	0.368198	−	0.637737i
$383$	−1.62814	+	2.82001i	−0.0831938	+	0.144096i	−0.904620	−	0.426219i	$-0.859845\pi$
$383$	−1.62814	+	2.82001i	−0.0831938	+	0.144096i	0.821426	+	0.570315i	$0.193179\pi$
$384$		0			0
$385$	2.52744	+	4.37766i	0.128810	+	0.223106i
$386$	−3.05063			−0.155273
$387$		0			0
$388$	18.6741			0.948035
$389$	0.694840	+	1.20350i	0.0352298	+	0.0610198i	0.883103	−	0.469180i	$-0.155450\pi$
$389$	0.694840	+	1.20350i	0.0352298	+	0.0610198i	−0.847873	+	0.530200i	$0.822117\pi$
$390$		0			0
$391$	−0.0818191	+	0.141715i	−0.00413777	+	0.00716682i
$392$	−3.44896	+	5.97377i	−0.174199	+	0.301721i
$393$		0			0
$394$	−11.1321	−	19.2814i	−0.560827	−	0.971381i
$395$	44.7302			2.25062
$396$		0			0
$397$	2.14020			0.107414			0.0537069	−	0.998557i	$-0.482896\pi$
$397$	2.14020			0.107414			0.0537069	+	0.998557i	$0.482896\pi$
$398$	12.2817	+	21.2725i	0.615626	+	1.06630i
$399$		0			0
$400$	−3.81433	+	6.60661i	−0.190716	+	0.330330i
$401$	−4.27666	+	7.40739i	−0.213566	+	0.369907i	−0.952828	−	0.303511i	$-0.901841\pi$
$401$	−4.27666	+	7.40739i	−0.213566	+	0.369907i	0.739262	+	0.673418i	$0.235175\pi$
$402$		0			0
$403$	1.57133	+	2.72163i	0.0782738	+	0.135574i
$404$	2.41967			0.120383
$405$		0			0
$406$	1.39278			0.0691225
$407$	16.8928	+	29.2592i	0.837345	+	1.45032i
$408$		0			0
$409$	−13.6359	+	23.6181i	−0.674254	+	1.16784i	0.302433	+	0.953171i	$0.402201\pi$
$409$	−13.6359	+	23.6181i	−0.674254	+	1.16784i	−0.976686	+	0.214671i	$0.931132\pi$
$410$	3.86870	−	6.70079i	0.191062	−	0.330929i
$411$		0			0
$412$	−0.997676	−	1.72802i	−0.0491519	−	0.0851337i
$413$	0.953022			0.0468952
$414$		0			0
$415$	−19.2383			−0.944372
$416$	−2.33937	−	4.05190i	−0.114697	−	0.198661i
$417$		0			0
$418$	−4.13550	+	7.16289i	−0.202274	+	0.350348i
$419$	8.00767	−	13.8697i	0.391200	−	0.677578i	−0.601408	−	0.798942i	$-0.705393\pi$
$419$	8.00767	−	13.8697i	0.391200	−	0.677578i	0.992608	+	0.121364i	$0.0387267\pi$
$420$		0			0
$421$	9.07351	+	15.7158i	0.442216	+	0.765941i	0.997854	−	0.0654841i	$-0.0208591\pi$
$421$	9.07351	+	15.7158i	0.442216	+	0.765941i	−0.555638	+	0.831425i	$0.687526\pi$
$422$	3.01931			0.146978
$423$		0			0
$424$	0.805554			0.0391212
$425$	4.32815	+	7.49657i	0.209946	+	0.363637i
$426$		0			0
$427$	−0.558270	+	0.966953i	−0.0270166	+	0.0467941i
$428$	4.43536	−	7.68227i	0.214391	−	0.371337i
$429$		0			0
$430$	12.6115	+	21.8438i	0.608181	+	1.05340i
$431$	−2.13698			−0.102935			−0.0514673	−	0.998675i	$-0.516390\pi$
$431$	−2.13698			−0.102935			−0.0514673	+	0.998675i	$0.516390\pi$
$432$		0			0
$433$	25.1733			1.20975			0.604876	−	0.796320i	$-0.293223\pi$
$433$	25.1733			1.20975			0.604876	+	0.796320i	$0.293223\pi$
$434$	−0.107303	−	0.185854i	−0.00515071	−	0.00892130i
$435$		0			0
$436$	0.986018	−	1.70783i	0.0472217	−	0.0817904i
$437$	0.133958	−	0.232021i	0.00640806	−	0.0110991i
$438$		0			0
$439$	−12.9259	−	22.3884i	−0.616922	−	1.06854i	−0.990044	−	0.140758i	$-0.955046\pi$
$439$	−12.9259	−	22.3884i	−0.616922	−	1.06854i	0.373122	−	0.927782i	$-0.378287\pi$
$440$	−15.8212			−0.754245
$441$		0			0
$442$	−5.30900			−0.252523
$443$	6.96929	+	12.0712i	0.331121	+	0.573518i	0.982732	−	0.185035i	$-0.0592399\pi$
$443$	6.96929	+	12.0712i	0.331121	+	0.573518i	−0.651611	+	0.758553i	$0.725907\pi$
$444$		0			0
$445$	−8.97745	+	15.5494i	−0.425572	+	0.737112i
$446$	4.99020	−	8.64328i	0.236293	−	0.409271i
$447$		0			0
$448$	0.159750	+	0.276696i	0.00754750	+	0.0130727i
$449$	−29.1538			−1.37585			−0.687927	−	0.725780i	$-0.741479\pi$
$449$	−29.1538			−1.37585			−0.687927	+	0.725780i	$0.741479\pi$
$450$		0			0
$451$	9.69343			0.456446
$452$	−4.81433	−	8.33866i	−0.226447	−	0.392217i
$453$		0			0
$454$	10.5612	−	18.2925i	0.495661	−	0.858510i
$455$	2.65613	−	4.60055i	0.124521	−	0.215677i
$456$		0			0
$457$	−11.8991	−	20.6098i	−0.556615	−	0.964086i	−0.997776	−	0.0666579i	$-0.978766\pi$
$457$	−11.8991	−	20.6098i	−0.556615	−	0.964086i	0.441161	−	0.897428i	$-0.354567\pi$
$458$	23.2807			1.08784
$459$		0			0
$460$	0.512482			0.0238946
$461$	15.4067	+	26.6851i	0.717559	+	1.24285i	0.961964	+	0.273176i	$0.0880741\pi$
$461$	15.4067	+	26.6851i	0.717559	+	1.24285i	−0.244405	+	0.969673i	$0.578593\pi$
$462$		0			0
$463$	−18.0701	+	31.2983i	−0.839787	+	1.45455i	0.0502857	+	0.998735i	$0.483987\pi$
$463$	−18.0701	+	31.2983i	−0.839787	+	1.45455i	−0.890073	+	0.455819i	$0.849347\pi$
$464$	−2.17962	+	3.77521i	−0.101186	+	0.175260i
$465$		0			0
$466$	−13.3621	−	23.1439i	−0.618990	−	1.07212i
$467$	36.9754			1.71102			0.855509	−	0.517788i	$-0.173244\pi$
$467$	36.9754			1.71102			0.855509	+	0.517788i	$0.173244\pi$
$468$		0			0
$469$	−2.37812			−0.109812
$470$	−18.3486	−	31.7808i	−0.846359	−	1.46594i
$471$		0			0
$472$	−1.49142	+	2.58322i	−0.0686483	+	0.118902i
$473$	−15.7997	+	27.3659i	−0.726471	+	1.25828i
$474$		0			0
$475$	−7.08623	−	12.2737i	−0.325138	−	0.563156i
$476$	0.362540			0.0166170
$477$		0			0
$478$	−24.0599			−1.10047
$479$	19.1905	+	33.2389i	0.876835	+	1.51872i	0.854795	+	0.518965i	$0.173683\pi$
$479$	19.1905	+	33.2389i	0.876835	+	1.51872i	0.0220394	+	0.999757i	$0.492984\pi$
$480$		0			0
$481$	17.7529	−	30.7490i	0.809464	−	1.40203i
$482$	−0.745760	+	1.29169i	−0.0339684	+	0.0588351i
$483$		0			0
$484$	−4.41040	−	7.63903i	−0.200473	−	0.347229i
$485$	−66.3619			−3.01334
$486$		0			0
$487$	34.3088			1.55468			0.777339	−	0.629082i	$-0.216569\pi$
$487$	34.3088			1.55468			0.777339	+	0.629082i	$0.216569\pi$
$488$	−1.74732	−	3.02645i	−0.0790975	−	0.137001i
$489$		0			0
$490$	12.2565	−	21.2289i	0.553692	−	0.959023i
$491$	−8.70382	+	15.0755i	−0.392798	+	0.680346i	−0.992817	−	0.119639i	$-0.961826\pi$
$491$	−8.70382	+	15.0755i	−0.392798	+	0.680346i	0.600019	+	0.799985i	$0.295160\pi$
$492$		0			0
$493$	2.47323	+	4.28376i	0.111389	+	0.192931i
$494$	8.69212			0.391077
$495$		0			0
$496$	0.671692			0.0301599
$497$	1.29375	+	2.24084i	0.0580325	+	0.100515i
$498$		0			0
$499$	−13.1416	+	22.7619i	−0.588299	+	1.01896i	0.406156	+	0.913804i	$0.366869\pi$
$499$	−13.1416	+	22.7619i	−0.588299	+	1.01896i	−0.994455	+	0.105161i	$0.966464\pi$
$500$	4.67070	−	8.08988i	0.208880	−	0.361791i
$501$		0			0
$502$	−7.28748	−	12.6223i	−0.325256	−	0.563360i
$503$	18.1786			0.810544			0.405272	−	0.914196i	$-0.367177\pi$
$503$	18.1786			0.810544			0.405272	+	0.914196i	$0.367177\pi$
$504$		0			0
$505$	−8.59873			−0.382639
$506$	0.321019	+	0.556021i	0.0142710	+	0.0247182i
$507$		0			0
$508$	−0.0796049	+	0.137880i	−0.00353189	+	0.00611742i
$509$	−12.3195	+	21.3380i	−0.546052	+	0.945790i	0.452488	+	0.891771i	$0.350537\pi$
$509$	−12.3195	+	21.3380i	−0.546052	+	0.945790i	−0.998540	+	0.0540195i	$0.982797\pi$
$510$		0			0
$511$	2.33257	+	4.04012i	0.103187	+	0.178724i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−11.0246			−0.486275
$515$	3.54542	+	6.14085i	0.156230	+	0.270598i
$516$		0			0
$517$	22.9872	−	39.8150i	1.01097	−	1.75106i
$518$	−1.21231	+	2.09978i	−0.0532658	+	0.0922591i
$519$		0			0
$520$	8.31337	+	14.3992i	0.364565	+	0.631446i
$521$	−30.0131			−1.31490			−0.657449	−	0.753499i	$-0.728364\pi$
$521$	−30.0131			−1.31490			−0.657449	+	0.753499i	$0.728364\pi$
$522$		0			0
$523$	−27.3437			−1.19566			−0.597829	−	0.801623i	$-0.703970\pi$
$523$	−27.3437			−1.19566			−0.597829	+	0.801623i	$0.703970\pi$
$524$	−4.74292	−	8.21497i	−0.207195	−	0.358873i
$525$		0			0
$526$	6.57003	−	11.3796i	0.286467	−	0.496175i
$527$	0.381087	−	0.660062i	0.0166004	−	0.0287528i
$528$		0			0
$529$	11.4896	+	19.9006i	0.499548	+	0.865242i
$530$	−2.86268			−0.124347
$531$		0			0
$532$	−0.593566			−0.0257344
$533$	−5.09349	−	8.82219i	−0.220624	−	0.382131i
$534$		0			0
$535$	−15.7619	+	27.3003i	−0.681445	+	1.18030i
$536$	3.72162	−	6.44604i	0.160750	−	0.278427i
$537$		0			0
$538$	5.15432	+	8.92754i	0.222218	+	0.384894i
$539$	30.7099			1.32277
$540$		0			0
$541$	8.65632			0.372164			0.186082	−	0.982534i	$-0.440421\pi$
$541$	8.65632			0.372164			0.186082	+	0.982534i	$0.440421\pi$
$542$	0.507269	+	0.878615i	0.0217891	+	0.0377398i
$543$		0			0
$544$	−0.567354	+	0.982686i	−0.0243251	+	0.0421323i
$545$	−3.50399	+	6.06910i	−0.150095	+	0.259972i
$546$		0			0
$547$	−13.7724	−	23.8545i	−0.588866	−	1.01994i	−0.994381	−	0.105857i	$-0.966241\pi$
$547$	−13.7724	−	23.8545i	−0.588866	−	1.01994i	0.405516	−	0.914088i	$-0.367092\pi$
$548$	−11.7094			−0.500199
$549$		0			0
$550$	33.9632			1.44819
$551$	−4.04928	−	7.01356i	−0.172505	−	0.298787i
$552$		0			0
$553$	−2.01078	+	3.48277i	−0.0855070	+	0.148103i
$554$	−5.41584	+	9.38051i	−0.230097	+	0.398540i
$555$		0			0
$556$	2.62513	+	4.54686i	0.111330	+	0.192830i
$557$	26.1805			1.10931			0.554653	−	0.832082i	$-0.312851\pi$
$557$	26.1805			1.10931			0.554653	+	0.832082i	$0.312851\pi$
$558$		0			0
$559$	33.2083			1.40456
$560$	−0.567702	−	0.983289i	−0.0239898	−	0.0415515i
$561$		0			0
$562$	4.23836	−	7.34106i	0.178785	−	0.309664i
$563$	−1.98613	+	3.44008i	−0.0837055	+	0.144982i	−0.904839	−	0.425754i	$-0.860009\pi$
$563$	−1.98613	+	3.44008i	−0.0837055	+	0.144982i	0.821133	+	0.570736i	$0.193342\pi$
$564$		0			0
$565$	17.1086	+	29.6329i	0.719763	+	1.24667i
$566$	−6.30428			−0.264988
$567$		0			0
$568$	−8.09856			−0.339808
$569$	−20.2456	−	35.0664i	−0.848738	−	1.47006i	−0.882335	−	0.470623i	$-0.844029\pi$
$569$	−20.2456	−	35.0664i	−0.848738	−	1.47006i	0.0335963	−	0.999435i	$-0.489304\pi$
$570$		0			0
$571$	−19.1507	+	33.1701i	−0.801434	+	1.38812i	0.117239	+	0.993104i	$0.462596\pi$
$571$	−19.1507	+	33.1701i	−0.801434	+	1.38812i	−0.918672	+	0.395020i	$0.870738\pi$
$572$	−10.4150	+	18.0393i	−0.435473	+	0.754261i
$573$		0			0
$574$	0.347824	+	0.602448i	0.0145179	+	0.0251457i
$575$	−1.10014			−0.0458790
$576$		0			0
$577$	8.27856			0.344641			0.172320	−	0.985041i	$-0.444874\pi$
$577$	8.27856			0.344641			0.172320	+	0.985041i	$0.444874\pi$
$578$	−7.85622	−	13.6074i	−0.326776	−	0.565992i
$579$		0			0
$580$	7.74567	−	13.4159i	0.321621	−	0.557065i
$581$	0.864830	−	1.49793i	0.0358792	−	0.0621446i
$582$		0			0
$583$	−1.79319	−	3.10589i	−0.0742662	−	0.128633i
$584$	−14.6013			−0.604206
$585$		0			0
$586$	−2.43305			−0.100509
$587$	−6.97141	−	12.0748i	−0.287741	−	0.498382i	0.685529	−	0.728045i	$-0.259571\pi$
$587$	−6.97141	−	12.0748i	−0.287741	−	0.498382i	−0.973270	+	0.229663i	$0.926238\pi$
$588$		0			0
$589$	−0.623932	+	1.08068i	−0.0257087	+	0.0445287i
$590$	5.30005	−	9.17995i	0.218199	−	0.377932i
$591$		0			0
$592$	−3.79438	−	6.57207i	−0.155948	−	0.270110i
$593$	41.2342			1.69329			0.846644	−	0.532160i	$-0.178620\pi$
$593$	41.2342			1.69329			0.846644	+	0.532160i	$0.178620\pi$
$594$		0			0
$595$	−1.28835			−0.0528173
$596$	−8.14612	−	14.1095i	−0.333678	−	0.577947i
$597$		0			0
$598$	0.337364	−	0.584332i	0.0137958	−	0.0238951i
$599$	−1.56812	+	2.71606i	−0.0640716	+	0.110975i	−0.896282	−	0.443485i	$-0.853742\pi$
$599$	−1.56812	+	2.71606i	−0.0640716	+	0.110975i	0.832210	+	0.554460i	$0.187075\pi$
$600$		0			0
$601$	17.4178	+	30.1684i	0.710485	+	1.23060i	0.964675	+	0.263442i	$0.0848577\pi$
$601$	17.4178	+	30.1684i	0.710485	+	1.23060i	−0.254190	+	0.967154i	$0.581809\pi$
$602$	−2.26772			−0.0924256
$603$		0			0
$604$	−15.6179			−0.635485
$605$	15.6731	+	27.1467i	0.637204	+	1.10367i
$606$		0			0
$607$	0.386602	−	0.669615i	0.0156917	−	0.0271788i	−0.858073	−	0.513528i	$-0.828338\pi$
$607$	0.386602	−	0.669615i	0.0156917	−	0.0271788i	0.873765	+	0.486349i	$0.161672\pi$
$608$	0.928896	−	1.60890i	0.0376717	−	0.0652493i
$609$		0			0
$610$	6.20942	+	10.7550i	0.251412	+	0.435458i
$611$	−48.3152			−1.95462
$612$		0			0
$613$	13.9984			0.565389			0.282695	−	0.959210i	$-0.408772\pi$
$613$	13.9984			0.565389			0.282695	+	0.959210i	$0.408772\pi$
$614$	−11.8629	−	20.5471i	−0.478747	−	0.829214i
$615$		0			0
$616$	0.711218	−	1.23187i	0.0286558	−	0.0496333i
$617$	5.85672	−	10.1441i	0.235783	−	0.408388i	−0.723717	−	0.690097i	$-0.757568\pi$
$617$	5.85672	−	10.1441i	0.235783	−	0.408388i	0.959500	+	0.281709i	$0.0909013\pi$
$618$		0			0
$619$	−24.0198	−	41.6035i	−0.965438	−	1.67219i	−0.708434	−	0.705777i	$-0.750598\pi$
$619$	−24.0198	−	41.6035i	−0.965438	−	1.67219i	−0.257004	−	0.966410i	$-0.582735\pi$
$620$	−2.38698			−0.0958634
$621$		0			0
$622$	−10.8006			−0.433065
$623$	−0.807136	−	1.39800i	−0.0323372	−	0.0560097i
$624$		0			0
$625$	2.47346	−	4.28416i	0.0989385	−	0.171366i
$626$	−7.94559	+	13.7622i	−0.317570	+	0.550047i
$627$		0			0
$628$	−8.81577	−	15.2694i	−0.351787	−	0.609314i
$629$	−8.61104			−0.343345
$630$		0			0
$631$	39.5449			1.57426			0.787130	−	0.616788i	$-0.211566\pi$
$631$	39.5449			1.57426			0.787130	+	0.616788i	$0.211566\pi$
$632$	−6.29350	−	10.9007i	−0.250342	−	0.433605i
$633$		0			0
$634$	1.61752	−	2.80163i	0.0642400	−	0.111267i
$635$	0.282890	−	0.489980i	0.0112262	−	0.0194443i
$636$		0			0
$637$	−16.1368	−	27.9497i	−0.639362	−	1.10741i
$638$	19.4076			0.768353
$639$		0			0
$640$	3.55368			0.140472
$641$	0.330657	+	0.572715i	0.0130602	+	0.0226209i	0.872482	−	0.488647i	$-0.162509\pi$
$641$	0.330657	+	0.572715i	0.0130602	+	0.0226209i	−0.859421	+	0.511268i	$0.829176\pi$
$642$		0			0
$643$	−0.906722	+	1.57049i	−0.0357576	+	0.0619340i	−0.883350	−	0.468713i	$-0.844718\pi$
$643$	−0.906722	+	1.57049i	−0.0357576	+	0.0619340i	0.847593	+	0.530647i	$0.178051\pi$
$644$	−0.0230379	+	0.0399028i	−0.000907819	+	0.00157239i
$645$		0			0
$646$	−1.05403	−	1.82563i	−0.0414701	−	0.0718283i
$647$	−4.13765			−0.162668			−0.0813339	−	0.996687i	$-0.525918\pi$
$647$	−4.13765			−0.162668			−0.0813339	+	0.996687i	$0.525918\pi$
$648$		0			0
$649$	13.2798			0.521278
$650$	−17.8462	−	30.9106i	−0.699987	−	1.21241i
$651$		0			0
$652$	7.94004	−	13.7526i	0.310956	−	0.538591i
$653$	13.4370	−	23.2736i	0.525831	−	0.910766i	−0.473717	−	0.880677i	$-0.657088\pi$
$653$	13.4370	−	23.2736i	0.525831	−	0.910766i	0.999547	−	0.0300882i	$-0.00957881\pi$
$654$		0			0
$655$	16.8548	+	29.1934i	0.658572	+	1.14068i
$656$	−2.17729			−0.0850090
$657$		0			0
$658$	3.29934			0.128622
$659$	7.22882	+	12.5207i	0.281595	+	0.487737i	0.971778	−	0.235898i	$-0.0758033\pi$
$659$	7.22882	+	12.5207i	0.281595	+	0.487737i	−0.690183	+	0.723635i	$0.742470\pi$
$660$		0			0
$661$	−11.1408	+	19.2964i	−0.433326	+	0.750543i	−0.997157	−	0.0753471i	$-0.975994\pi$
$661$	−11.1408	+	19.2964i	−0.433326	+	0.750543i	0.563831	+	0.825890i	$0.309327\pi$
$662$	−8.83183	+	15.2972i	−0.343259	+	0.594542i
$663$		0			0
$664$	2.70681	+	4.68834i	0.105045	+	0.181943i
$665$	2.10935			0.0817969
$666$		0			0
$667$	−0.628652			−0.0243415
$668$	−6.78921	−	11.7593i	−0.262682	−	0.454979i
$669$		0			0
$670$	−13.2255	+	22.9072i	−0.510944	+	0.884982i
$671$	−7.77917	+	13.4739i	−0.300311	+	0.520154i
$672$		0			0
$673$	−12.4510	−	21.5658i	−0.479951	−	0.831299i	0.519785	−	0.854297i	$-0.326012\pi$
$673$	−12.4510	−	21.5658i	−0.479951	−	0.831299i	−0.999736	+	0.0229981i	$0.992679\pi$
$674$	10.5429			0.406096
$675$		0			0
$676$	8.89058			0.341945
$677$	3.99194	+	6.91424i	0.153423	+	0.265736i	0.932484	−	0.361212i	$-0.117637\pi$
$677$	3.99194	+	6.91424i	0.153423	+	0.265736i	−0.779061	+	0.626948i	$0.784304\pi$
$678$		0			0
$679$	2.98320	−	5.16705i	0.114485	−	0.198293i
$680$	2.01620	−	3.49215i	0.0773176	−	0.133918i
$681$		0			0
$682$	−1.49520	−	2.58977i	−0.0572543	−	0.0991674i
$683$	35.0612			1.34158			0.670789	−	0.741648i	$-0.265955\pi$
$683$	35.0612			1.34158			0.670789	+	0.741648i	$0.265955\pi$
$684$		0			0
$685$	41.6113			1.58989
$686$	2.22020	+	3.84550i	0.0847676	+	0.146822i
$687$		0			0
$688$	3.54885	−	6.14680i	0.135299	−	0.234344i
$689$	−1.88449	+	3.26403i	−0.0717933	+	0.124350i
$690$		0			0
$691$	0.991019	+	1.71650i	0.0377001	+	0.0652986i	0.884260	−	0.466995i	$-0.154663\pi$
$691$	0.991019	+	1.71650i	0.0377001	+	0.0652986i	−0.846560	+	0.532294i	$0.821330\pi$
$692$	−6.44441			−0.244980
$693$		0			0
$694$	32.5047			1.23386
$695$	−9.32889	−	16.1581i	−0.353865	−	0.612912i
$696$		0			0
$697$	−1.23530	+	2.13960i	−0.0467902	+	0.0810430i
$698$	−10.0351	+	17.3814i	−0.379836	+	0.657895i
$699$		0			0
$700$	1.21868	+	2.11082i	0.0460618	+	0.0797814i
$701$	−42.8694			−1.61916			−0.809578	−	0.587013i	$-0.800304\pi$
$701$	−42.8694			−1.61916			−0.809578	+	0.587013i	$0.800304\pi$
$702$		0			0
$703$	14.0984			0.531730
$704$	2.22603	+	3.85559i	0.0838966	+	0.145313i
$705$		0			0
$706$	−5.51803	+	9.55750i	−0.207674	+	0.359701i
$707$	0.386543	−	0.669513i	0.0145375	−	0.0251796i
$708$		0			0
$709$	−17.5588	−	30.4127i	−0.659434	−	1.14217i	−0.980762	−	0.195205i	$-0.937463\pi$
$709$	−17.5588	−	30.4127i	−0.659434	−	1.14217i	0.321329	−	0.946968i	$-0.395871\pi$
$710$	28.7797			1.08008
$711$		0			0
$712$	5.05248			0.189350
$713$	0.0484329	+	0.0838882i	0.00181383	+	0.00314164i
$714$		0			0
$715$	37.0116	−	64.1059i	1.38415	−	2.39743i
$716$	−6.25613	+	10.8359i	−0.233802	+	0.404958i
$717$		0			0
$718$	1.96044	+	3.39557i	0.0731628	+	0.126722i
$719$	−15.0484			−0.561212			−0.280606	−	0.959823i	$-0.590535\pi$
$719$	−15.0484			−0.561212			−0.280606	+	0.959823i	$0.590535\pi$
$720$		0			0
$721$	−0.637516			−0.0237424
$722$	−7.77430	−	13.4655i	−0.289330	−	0.501134i
$723$		0			0
$724$	−0.152251	+	0.263707i	−0.00565838	+	0.00980060i
$725$	−16.6275	+	28.7998i	−0.617532	+	1.06960i
$726$		0			0
$727$	−7.31281	−	12.6662i	−0.271217	−	0.469762i	0.697957	−	0.716140i	$-0.254093\pi$
$727$	−7.31281	−	12.6662i	−0.271217	−	0.469762i	−0.969174	+	0.246378i	$0.920759\pi$
$728$	−1.49486			−0.0554032
$729$		0			0
$730$	51.8884			1.92048
$731$	−4.02692	−	6.97482i	−0.148941	−	0.257973i
$732$		0			0
$733$	−7.53748	+	13.0553i	−0.278403	+	0.482209i	−0.970988	−	0.239128i	$-0.923139\pi$
$733$	−7.53748	+	13.0553i	−0.278403	+	0.482209i	0.692585	+	0.721336i	$0.256472\pi$
$734$	14.5756	−	25.2457i	0.537996	−	0.931836i
$735$		0			0
$736$	−0.0721058	−	0.124891i	−0.00265786	−	0.00460354i
$737$	−33.1377			−1.22064
$738$		0			0
$739$	47.8062			1.75858			0.879290	−	0.476288i	$-0.158018\pi$
$739$	47.8062			1.75858			0.879290	+	0.476288i	$0.158018\pi$
$740$	13.4840	+	23.3550i	0.495683	+	0.858548i
$741$		0			0
$742$	0.128688	−	0.222894i	0.00472427	−	0.00818268i
$743$	−23.2589	+	40.2857i	−0.853288	+	1.47794i	0.0249367	+	0.999689i	$0.492062\pi$
$743$	−23.2589	+	40.2857i	−0.853288	+	1.47794i	−0.878224	+	0.478249i	$0.841272\pi$
$744$		0			0
$745$	28.9487	+	50.1407i	1.06060	+	1.83701i
$746$	−6.27181			−0.229627
$747$		0			0
$748$	5.05178			0.184712
$749$	−1.41710	−	2.45449i	−0.0517798	−	0.0896852i
$750$		0			0
$751$	−0.882896	+	1.52922i	−0.0322173	+	0.0558020i	−0.881684	−	0.471839i	$-0.843590\pi$
$751$	−0.882896	+	1.52922i	−0.0322173	+	0.0558020i	0.849467	+	0.527641i	$0.176924\pi$
$752$	−5.16327	+	8.94305i	−0.188285	+	0.326120i
$753$		0			0
$754$	−10.1979	−	17.6632i	−0.371384	−	0.643256i
$755$	55.5012			2.01989
$756$		0			0
$757$	3.34143			0.121446			0.0607232	−	0.998155i	$-0.480659\pi$
$757$	3.34143			0.121446			0.0607232	+	0.998155i	$0.480659\pi$
$758$	−13.4781	−	23.3448i	−0.489547	−	0.847921i
$759$		0			0
$760$	−3.30100	+	5.71750i	−0.119740	+	0.207396i
$761$	23.8761	−	41.3546i	0.865507	−	1.49910i	−0.00103625	−	0.999999i	$-0.500330\pi$
$761$	23.8761	−	41.3546i	0.865507	−	1.49910i	0.866543	−	0.499102i	$-0.166337\pi$
$762$		0			0
$763$	−0.315034	−	0.545654i	−0.0114050	−	0.0197540i
$764$	14.3927			0.520710
$765$		0			0
$766$	−3.25627			−0.117654
$767$	−6.97798	−	12.0862i	−0.251960	−	0.436408i
$768$		0			0
$769$	3.39257	−	5.87611i	0.122339	−	0.211898i	−0.798350	−	0.602193i	$-0.794294\pi$
$769$	3.39257	−	5.87611i	0.122339	−	0.211898i	0.920690	+	0.390295i	$0.127627\pi$
$770$	−2.52744	+	4.37766i	−0.0910827	+	0.157760i
$771$		0			0
$772$	−1.52531	−	2.64192i	−0.0548972	−	0.0950848i
$773$	30.1367			1.08394			0.541970	−	0.840398i	$-0.317678\pi$
$773$	30.1367			1.08394			0.541970	+	0.840398i	$0.317678\pi$
$774$		0			0
$775$	5.12410			0.184063
$776$	9.33706	+	16.1723i	0.335181	+	0.580551i
$777$		0			0
$778$	−0.694840	+	1.20350i	−0.0249112	+	0.0431475i
$779$	2.02248	−	3.50304i	0.0724629	−	0.125509i
$780$		0			0
$781$	18.0276	+	31.2247i	0.645079	+	1.11731i
$782$	−0.163638			−0.00585169
$783$		0			0
$784$	−6.89792			−0.246354
$785$	31.3284	+	54.2624i	1.11816	+	1.93671i
$786$		0			0
$787$	−8.07732	+	13.9903i	−0.287925	+	0.498701i	−0.973314	−	0.229476i	$-0.926299\pi$
$787$	−8.07732	+	13.9903i	−0.287925	+	0.498701i	0.685389	+	0.728177i	$0.259632\pi$
$788$	11.1321	−	19.2814i	0.396565	−	0.686870i
$789$		0			0
$790$	22.3651	+	38.7375i	0.795715	+	1.37822i
$791$	−3.07636			−0.109383
$792$		0			0
$793$	16.3505			0.580623
$794$	1.07010	+	1.85347i	0.0379765	+	0.0657772i
$795$		0			0
$796$	−12.2817	+	21.2725i	−0.435313	+	0.753985i
$797$	−0.275639	+	0.477421i	−0.00976365	+	0.0169111i	−0.870866	−	0.491521i	$-0.836441\pi$
$797$	−0.275639	+	0.477421i	−0.00976365	+	0.0169111i	0.861102	+	0.508432i	$0.169775\pi$
$798$		0			0
$799$	5.85881	+	10.1478i	0.207270	+	0.359002i
$800$	−7.62865			−0.269714
$801$		0			0
$802$	−8.55331			−0.302028
$803$	32.5029	+	56.2967i	1.14700	+	1.98667i
$804$		0			0
$805$	0.0818693	−	0.141802i	0.00288551	−	0.00499785i
$806$	−1.57133	+	2.72163i	−0.0553479	+	0.0958654i
$807$		0			0
$808$	1.20983	+	2.09550i	0.0425618	+	0.0737193i
$809$	3.04561			0.107078			0.0535389	−	0.998566i	$-0.482950\pi$
$809$	3.04561			0.107078			0.0535389	+	0.998566i	$0.482950\pi$
$810$		0			0
$811$	−7.71732			−0.270992			−0.135496	−	0.990778i	$-0.543263\pi$
$811$	−7.71732			−0.270992			−0.135496	+	0.990778i	$0.543263\pi$
$812$	0.696390	+	1.20618i	0.0244385	+	0.0423287i
$813$		0			0
$814$	−16.8928	+	29.2592i	−0.592093	+	1.02553i
$815$	−28.2164	+	48.8722i	−0.988376	+	1.71192i
$816$		0			0
$817$	6.59304	+	11.4195i	0.230661	+	0.399517i
$818$	−27.2719			−0.953539
$819$		0			0
$820$	7.73741			0.270202
$821$	11.7272	+	20.3121i	0.409282	+	0.708898i	0.994809	−	0.101755i	$-0.0324458\pi$
$821$	11.7272	+	20.3121i	0.409282	+	0.708898i	−0.585527	+	0.810653i	$0.699112\pi$
$822$		0			0
$823$	14.9392	−	25.8754i	0.520746	−	0.901959i	−0.478963	−	0.877835i	$-0.658987\pi$
$823$	14.9392	−	25.8754i	0.520746	−	0.901959i	0.999709	−	0.0241238i	$-0.00767959\pi$
$824$	0.997676	−	1.72802i	0.0347557	−	0.0601986i
$825$		0			0
$826$	0.476511	+	0.825342i	0.0165799	+	0.0287173i
$827$	19.4419			0.676060			0.338030	−	0.941135i	$-0.390240\pi$
$827$	19.4419			0.676060			0.338030	+	0.941135i	$0.390240\pi$
$828$		0			0
$829$	−10.2719			−0.356757			−0.178379	−	0.983962i	$-0.557085\pi$
$829$	−10.2719			−0.356757			−0.178379	+	0.983962i	$0.557085\pi$
$830$	−9.61916	−	16.6609i	−0.333886	−	0.578307i
$831$		0			0
$832$	2.33937	−	4.05190i	0.0811030	−	0.140475i
$833$	−3.91356	+	6.77849i	−0.135597	+	0.234861i
$834$		0			0
$835$	24.1267	+	41.7886i	0.834938	+	1.44616i
$836$	−8.27099			−0.286058
$837$		0			0
$838$	16.0153			0.553241
$839$	−6.73782	−	11.6702i	−0.232615	−	0.402901i	0.725962	−	0.687735i	$-0.241395\pi$
$839$	−6.73782	−	11.6702i	−0.232615	−	0.402901i	−0.958577	+	0.284834i	$0.908062\pi$
$840$		0			0
$841$	4.99853	−	8.65771i	0.172363	−	0.298542i
$842$	−9.07351	+	15.7158i	−0.312694	+	0.541602i
$843$		0			0
$844$	1.50965	+	2.61480i	0.0519644	+	0.0900050i
$845$	−31.5943			−1.08688
$846$		0			0
$847$	−2.81825			−0.0968363
$848$	0.402777	+	0.697630i	0.0138314	+	0.0239567i
$849$		0			0
$850$	−4.32815	+	7.49657i	−0.148454	+	0.257130i
$851$	0.547194	−	0.947768i	0.0187576	−	0.0324891i
$852$		0			0
$853$	−23.7562	−	41.1470i	−0.813398	−	1.40885i	−0.910473	−	0.413570i	$-0.864282\pi$
$853$	−23.7562	−	41.1470i	−0.813398	−	1.40885i	0.0970745	−	0.995277i	$-0.469051\pi$
$854$	−1.11654			−0.0382072
$855$		0			0
$856$	8.87072			0.303195
$857$	11.6082	+	20.1059i	0.396528	+	0.686806i	0.993295	−	0.115608i	$-0.0368818\pi$
$857$	11.6082	+	20.1059i	0.396528	+	0.686806i	−0.596767	+	0.802414i	$0.703548\pi$
$858$		0			0
$859$	−9.23523	+	15.9959i	−0.315102	+	0.545772i	−0.979459	−	0.201643i	$-0.935372\pi$
$859$	−9.23523	+	15.9959i	−0.315102	+	0.545772i	0.664357	+	0.747415i	$0.268705\pi$
$860$	−12.6115	+	21.8438i	−0.430049	+	0.744866i
$861$		0			0
$862$	−1.06849	−	1.85068i	−0.0363928	−	0.0630343i
$863$	21.1288			0.719233			0.359616	−	0.933100i	$-0.382908\pi$
$863$	21.1288			0.719233			0.359616	+	0.933100i	$0.382908\pi$
$864$		0			0
$865$	22.9014			0.778670
$866$	12.5867	+	21.8007i	0.427712	+	0.740819i
$867$		0			0
$868$	0.107303	−	0.185854i	0.00364210	−	0.00630831i
$869$	−28.0190	+	48.5304i	−0.950480	+	1.64628i
$870$		0			0
$871$	17.4125	+	30.1593i	0.590000	+	1.02191i
$872$	1.97204			0.0667816
$873$		0			0
$874$	0.267915			0.00906237
$875$	−1.49229	−	2.58473i	−0.0504487	−	0.0873797i
$876$		0			0
$877$	−8.10671	+	14.0412i	−0.273744	+	0.474139i	−0.969817	−	0.243832i	$-0.921595\pi$
$877$	−8.10671	+	14.0412i	−0.273744	+	0.474139i	0.696073	+	0.717971i	$0.254929\pi$
$878$	12.9259	−	22.3884i	0.436229	−	0.755572i
$879$		0			0
$880$	−7.91059	−	13.7015i	−0.266666	−	0.461879i
$881$	−44.5020			−1.49931			−0.749655	−	0.661829i	$-0.769780\pi$
$881$	−44.5020			−1.49931			−0.749655	+	0.661829i	$0.769780\pi$
$882$		0			0
$883$	16.2665			0.547412			0.273706	−	0.961813i	$-0.411751\pi$
$883$	16.2665			0.547412			0.273706	+	0.961813i	$0.411751\pi$
$884$	−2.65450	−	4.59773i	−0.0892805	−	0.154638i
$885$		0			0
$886$	−6.96929	+	12.0712i	−0.234138	+	0.405539i
$887$	10.2843	−	17.8130i	0.345314	−	0.598102i	−0.640096	−	0.768295i	$-0.721106\pi$
$887$	10.2843	−	17.8130i	0.345314	−	0.598102i	0.985411	+	0.170193i	$0.0544390\pi$
$888$		0			0
$889$	0.0254338	+	0.0440527i	0.000853023	+	0.00147748i
$890$	−17.9549			−0.601850
$891$		0			0
$892$	9.98040			0.334168
$893$	−9.59229	−	16.6143i	−0.320994	−	0.555977i
$894$		0			0
$895$	22.2323	−	38.5074i	0.743143	−	1.28716i
$896$	−0.159750	+	0.276696i	−0.00533689	+	0.00924376i
$897$		0			0
$898$	−14.5769	−	25.2479i	−0.486438	−	0.842535i
$899$	2.92806			0.0976564
$900$		0			0
$901$	0.914069			0.0304521
$902$	4.84672	+	8.39476i	0.161378	+	0.279515i
$903$		0			0
$904$	4.81433	−	8.33866i	0.160122	−	0.277340i
$905$	0.541053	−	0.937131i	0.0179852	−	0.0311513i
$906$		0			0
$907$	−8.27376	−	14.3306i	−0.274726	−	0.475839i	0.695340	−	0.718681i	$-0.255254\pi$
$907$	−8.27376	−	14.3306i	−0.274726	−	0.475839i	−0.970066	+	0.242842i	$0.921920\pi$
$908$	21.1224			0.700970
$909$		0			0
$910$	5.31226			0.176100
$911$	13.4166	+	23.2383i	0.444513	+	0.769918i	0.998018	−	0.0629271i	$-0.0200436\pi$
$911$	13.4166	+	23.2383i	0.444513	+	0.769918i	−0.553506	+	0.832846i	$0.686710\pi$
$912$		0			0
$913$	12.0509	−	20.8727i	0.398826	−	0.690787i
$914$	11.8991	−	20.6098i	0.393587	−	0.681712i
$915$		0			0
$916$	11.6404	+	20.1617i	0.384609	+	0.666162i
$917$	−3.03073			−0.100084
$918$		0			0
$919$	−26.3725			−0.869947			−0.434974	−	0.900443i	$-0.643242\pi$
$919$	−26.3725			−0.869947			−0.434974	+	0.900443i	$0.643242\pi$
$920$	0.256241	+	0.443823i	0.00844802	+	0.0146324i
$921$		0			0
$922$	−15.4067	+	26.6851i	−0.507391	+	0.878827i
$923$	18.9455	−	32.8146i	0.623599	−	1.08010i
$924$		0			0
$925$	−28.9460	−	50.1360i	−0.951740	−	1.64846i
$926$	−36.1401			−1.18764
$927$		0			0
$928$	−4.35924			−0.143099
$929$	21.4057	+	37.0757i	0.702297	+	1.21641i	0.967658	+	0.252266i	$0.0811757\pi$
$929$	21.4057	+	37.0757i	0.702297	+	1.21641i	−0.265361	+	0.964149i	$0.585491\pi$
$930$		0			0
$931$	6.40745	−	11.0980i	0.209996	−	0.363723i
$932$	13.3621	−	23.1439i	0.437692	−	0.758104i
$933$		0			0
$934$	18.4877	+	32.0217i	0.604936	+	1.04778i
$935$	−17.9524			−0.587107
$936$		0			0
$937$	−14.1482			−0.462201			−0.231100	−	0.972930i	$-0.574233\pi$
$937$	−14.1482			−0.462201			−0.231100	+	0.972930i	$0.574233\pi$
$938$	−1.18906	−	2.05952i	−0.0388243	−	0.0672456i
$939$		0			0
$940$	18.3486	−	31.7808i	0.598466	−	1.03657i
$941$	12.9593	−	22.4462i	0.422462	−	0.731725i	−0.573718	−	0.819053i	$-0.694499\pi$
$941$	12.9593	−	22.4462i	0.422462	−	0.731725i	0.996180	+	0.0873276i	$0.0278327\pi$
$942$		0			0
$943$	−0.156996	−	0.271924i	−0.00511248	−	0.00885507i
$944$	−2.98285			−0.0970834
$945$		0			0
$946$	−31.5994			−1.02738
$947$	8.21202	+	14.2236i	0.266855	+	0.462206i	0.968048	−	0.250765i	$-0.0806822\pi$
$947$	8.21202	+	14.2236i	0.266855	+	0.462206i	−0.701193	+	0.712971i	$0.747349\pi$
$948$		0			0
$949$	34.1578	−	59.1631i	1.10881	−	1.92052i
$950$	7.08623	−	12.2737i	0.229908	−	0.398212i
$951$		0			0
$952$	0.181270	+	0.313969i	0.00587500	+	0.0101758i
$953$	37.2534			1.20676			0.603379	−	0.797455i	$-0.293821\pi$
$953$	37.2534			1.20676			0.603379	+	0.797455i	$0.293821\pi$
$954$		0			0
$955$	−51.1471			−1.65508
$956$	−12.0299	−	20.8365i	−0.389076	−	0.673899i
$957$		0			0
$958$	−19.1905	+	33.2389i	−0.620016	+	1.07390i
$959$	−1.87058	+	3.23993i	−0.0604040	+	0.104623i
$960$		0			0
$961$	15.2744	+	26.4561i	0.492723	+	0.853421i
$962$	35.5058			1.14475
$963$		0			0
$964$	−1.49152			−0.0480386
$965$	5.42048	+	9.38854i	0.174491	+	0.302228i
$966$		0			0
$967$	4.97857	−	8.62314i	0.160100	−	0.277302i	−0.774804	−	0.632201i	$-0.782152\pi$
$967$	4.97857	−	8.62314i	0.160100	−	0.277302i	0.934904	+	0.354900i	$0.115485\pi$
$968$	4.41040	−	7.63903i	0.141756	−	0.245528i
$969$		0			0
$970$	−33.1809	−	57.4711i	−1.06538	−	1.84529i
$971$	−2.62332			−0.0841864			−0.0420932	−	0.999114i	$-0.513403\pi$
$971$	−2.62332			−0.0841864			−0.0420932	+	0.999114i	$0.513403\pi$
$972$		0			0
$973$	1.67746			0.0537771
$974$	17.1544	+	29.7123i	0.549662	+	0.952042i
$975$		0			0
$976$	1.74732	−	3.02645i	0.0559304	−	0.0968742i
$977$	−3.31902	+	5.74871i	−0.106185	+	0.183918i	−0.914222	−	0.405214i	$-0.867197\pi$
$977$	−3.31902	+	5.74871i	−0.106185	+	0.183918i	0.808037	+	0.589132i	$0.200530\pi$
$978$		0			0
$979$	−11.2470	−	19.4803i	−0.359454	−	0.622593i
$980$	24.5130			0.783039
$981$		0			0
$982$	−17.4076			−0.555500
$983$	−23.6981	−	41.0463i	−0.755851	−	1.30917i	−0.944950	−	0.327215i	$-0.893890\pi$
$983$	−23.6981	−	41.0463i	−0.755851	−	1.30917i	0.189099	−	0.981958i	$-0.439443\pi$
$984$		0			0
$985$	−39.5599	+	68.5198i	−1.26048	+	2.18322i
$986$	−2.47323	+	4.28376i	−0.0787637	+	0.136423i
$987$		0			0
$988$	4.34606	+	7.52760i	0.138267	+	0.239485i
$989$	1.02357			0.0325477
$990$		0			0
$991$	44.1149			1.40136			0.700678	−	0.713478i	$-0.252881\pi$
$991$	44.1149			1.40136			0.700678	+	0.713478i	$0.252881\pi$
$992$	0.335846	+	0.581702i	0.0106631	+	0.0184691i
$993$		0			0
$994$	−1.29375	+	2.24084i	−0.0410352	+	0.0710750i
$995$	43.6452	−	75.5958i	1.38365	−	2.39655i
$996$		0			0
$997$	−24.9073	−	43.1408i	−0.788823	−	1.36628i	−0.926688	−	0.375831i	$-0.877357\pi$
$997$	−24.9073	−	43.1408i	−0.788823	−	1.36628i	0.137865	−	0.990451i	$-0.455976\pi$
$998$	−26.2832			−0.831981
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1458.2.c.g.973.6		12
3.2	odd	2		1458.2.c.f.973.1		12
9.2	odd	6		1458.2.c.f.487.1		12
9.4	even	3		1458.2.a.f.1.1		6
9.5	odd	6		1458.2.a.g.1.6		6
9.7	even	3	inner	1458.2.c.g.487.6		12
27.2	odd	18		486.2.e.h.271.2		12
27.4	even	9		486.2.e.e.217.1		12
27.5	odd	18		54.2.e.b.7.1	✓	12
27.7	even	9		162.2.e.b.145.1		12
27.11	odd	18		486.2.e.f.109.1		12
27.13	even	9		486.2.e.g.379.2		12
27.14	odd	18		486.2.e.f.379.1		12
27.16	even	9		486.2.e.g.109.2		12
27.20	odd	18		54.2.e.b.31.1	yes	12
27.22	even	9		162.2.e.b.19.1		12
27.23	odd	18		486.2.e.h.217.2		12
27.25	even	9		486.2.e.e.271.1		12
108.47	even	18		432.2.u.b.193.2		12
108.59	even	18		432.2.u.b.385.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.b.7.1	✓	12	27.5	odd	18
54.2.e.b.31.1	yes	12	27.20	odd	18
162.2.e.b.19.1		12	27.22	even	9
162.2.e.b.145.1		12	27.7	even	9
432.2.u.b.193.2		12	108.47	even	18
432.2.u.b.385.2		12	108.59	even	18
486.2.e.e.217.1		12	27.4	even	9
486.2.e.e.271.1		12	27.25	even	9
486.2.e.f.109.1		12	27.11	odd	18
486.2.e.f.379.1		12	27.14	odd	18
486.2.e.g.109.2		12	27.16	even	9
486.2.e.g.379.2		12	27.13	even	9
486.2.e.h.217.2		12	27.23	odd	18
486.2.e.h.271.2		12	27.2	odd	18
1458.2.a.f.1.1		6	9.4	even	3
1458.2.a.g.1.6		6	9.5	odd	6
1458.2.c.f.487.1		12	9.2	odd	6
1458.2.c.f.973.1		12	3.2	odd	2
1458.2.c.g.487.6		12	9.7	even	3	inner
1458.2.c.g.973.6		12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1458 = 2 \cdot 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1458.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.77684 - 3.07758i) q^{5} +(0.159750 + 0.276696i) q^{7} -1.00000 q^{8} +3.55368 q^{10} +(2.22603 + 3.85559i) q^{11} +(2.33937 - 4.05190i) q^{13} +(-0.159750 + 0.276696i) q^{14} +(-0.500000 - 0.866025i) q^{16} -1.13471 q^{17} +1.85779 q^{19} +(1.77684 + 3.07758i) q^{20} +(-2.22603 + 3.85559i) q^{22} +(0.0721058 - 0.124891i) q^{23} +(-3.81433 - 6.60661i) q^{25} +4.67874 q^{26} -0.319501 q^{28} +(-2.17962 - 3.77521i) q^{29} +(-0.335846 + 0.581702i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.567354 - 0.982686i) q^{34} +1.13540 q^{35} +7.58877 q^{37} +(0.928896 + 1.60890i) q^{38} +(-1.77684 + 3.07758i) q^{40} +(1.08865 - 1.88559i) q^{41} +(3.54885 + 6.14680i) q^{43} -4.45206 q^{44} +0.144212 q^{46} +(-5.16327 - 8.94305i) q^{47} +(3.44896 - 5.97377i) q^{49} +(3.81433 - 6.60661i) q^{50} +(2.33937 + 4.05190i) q^{52} -0.805554 q^{53} +15.8212 q^{55} +(-0.159750 - 0.276696i) q^{56} +(2.17962 - 3.77521i) q^{58} +(1.49142 - 2.58322i) q^{59} +(1.74732 + 3.02645i) q^{61} -0.671692 q^{62} +1.00000 q^{64} +(-8.31337 - 14.3992i) q^{65} +(-3.72162 + 6.44604i) q^{67} +(0.567354 - 0.982686i) q^{68} +(0.567702 + 0.983289i) q^{70} +8.09856 q^{71} +14.6013 q^{73} +(3.79438 + 6.57207i) q^{74} +(-0.928896 + 1.60890i) q^{76} +(-0.711218 + 1.23187i) q^{77} +(6.29350 + 10.9007i) q^{79} -3.55368 q^{80} +2.17729 q^{82} +(-2.70681 - 4.68834i) q^{83} +(-2.01620 + 3.49215i) q^{85} +(-3.54885 + 6.14680i) q^{86} +(-2.22603 - 3.85559i) q^{88} -5.05248 q^{89} +1.49486 q^{91} +(0.0721058 + 0.124891i) q^{92} +(5.16327 - 8.94305i) q^{94} +(3.30100 - 5.71750i) q^{95} +(-9.33706 - 16.1723i) q^{97} +6.89792 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} + 3 q^{5} - 6 q^{7} - 12 q^{8} + 6 q^{10} + 3 q^{11} - 9 q^{13} + 6 q^{14} - 6 q^{16} - 12 q^{17} + 18 q^{19} + 3 q^{20} - 3 q^{22} - 3 q^{23} - 15 q^{25} - 18 q^{26} + 12 q^{28}+ \cdots - 24 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 + 3 * q^5 - 6 * q^7 - 12 * q^8 + 6 * q^10 + 3 * q^11 - 9 * q^13 + 6 * q^14 - 6 * q^16 - 12 * q^17 + 18 * q^19 + 3 * q^20 - 3 * q^22 - 3 * q^23 - 15 * q^25 - 18 * q^26 + 12 * q^28 + 3 * q^29 - 12 * q^31 + 6 * q^32 - 6 * q^34 + 6 * q^35 + 30 * q^37 + 9 * q^38 - 3 * q^40 + 3 * q^41 - 12 * q^43 - 6 * q^44 - 6 * q^46 - 9 * q^47 - 12 * q^49 + 15 * q^50 - 9 * q^52 + 12 * q^53 + 18 * q^55 + 6 * q^56 - 3 * q^58 - 3 * q^59 - 12 * q^61 - 24 * q^62 + 12 * q^64 - 3 * q^65 - 21 * q^67 + 6 * q^68 + 3 * q^70 + 24 * q^71 + 42 * q^73 + 15 * q^74 - 9 * q^76 - 3 * q^77 - 6 * q^80 + 6 * q^82 - 27 * q^83 + 12 * q^86 - 3 * q^88 + 24 * q^89 + 12 * q^91 - 3 * q^92 + 9 * q^94 - 30 * q^95 - 18 * q^97 - 24 * q^98

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