LMFDB - Embedded newform 108.2.i.a.61.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,2,Mod(13,108)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("108.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	108.i (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.862384341830$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 24 x^{16} - 66 x^{15} + 153 x^{14} - 315 x^{13} + 651 x^{12} - 1350 x^{11} + \cdots + 19683 $ x^18 - 6x^17 + 24x^16 - 66x^15 + 153x^14 - 315x^13 + 651x^12 - 1350x^11 + 2700x^10 - 4941x^9 + 8100x^8 - 12150x^7 + 17577x^6 - 25515x^5 + 37179x^4 - 48114x^3 + 52488x^2 - 39366*x + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			61.2
Root			$0.960398 + 1.44140i$ of defining polynomial
Character	$\chi$	$=$	108.61
Dual form			108.2.i.a.85.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.409491 + 1.68295i) q^{3} +(-0.103132 - 0.584890i) q^{5} +(2.18780 + 1.83578i) q^{7} +(-2.66463 + 1.37830i) q^{9} +O(q^{10})$	\(q+(0.409491 + 1.68295i) q^{3} +(-0.103132 - 0.584890i) q^{5} +(2.18780 + 1.83578i) q^{7} +(-2.66463 + 1.37830i) q^{9} +(0.0708902 - 0.402038i) q^{11} +(-0.182629 - 0.0664716i) q^{13} +(0.942109 - 0.413073i) q^{15} +(-3.66536 - 6.34858i) q^{17} +(2.06586 - 3.57817i) q^{19} +(-2.19364 + 4.43369i) q^{21} +(3.12150 - 2.61925i) q^{23} +(4.36700 - 1.58946i) q^{25} +(-3.41076 - 3.92004i) q^{27} +(-9.66797 + 3.51885i) q^{29} +(-4.78061 + 4.01141i) q^{31} +(0.705639 - 0.0453265i) q^{33} +(0.848099 - 1.46895i) q^{35} +(-2.88349 - 4.99435i) q^{37} +(0.0370833 - 0.334575i) q^{39} +(7.92488 + 2.88442i) q^{41} +(-1.03999 + 5.89808i) q^{43} +(1.08097 + 1.41637i) q^{45} +(8.62443 + 7.23675i) q^{47} +(0.200835 + 1.13899i) q^{49} +(9.18341 - 8.76830i) q^{51} -3.42431 q^{53} -0.242459 q^{55} +(6.86783 + 2.01150i) q^{57} +(0.813604 + 4.61418i) q^{59} +(3.34605 + 2.80767i) q^{61} +(-8.35995 - 1.87623i) q^{63} +(-0.0200437 + 0.113673i) q^{65} +(-11.4215 - 4.15710i) q^{67} +(5.68628 + 4.18076i) q^{69} +(4.09409 + 7.09117i) q^{71} +(1.96938 - 3.41106i) q^{73} +(4.46323 + 6.69857i) q^{75} +(0.893148 - 0.749440i) q^{77} +(-8.47868 + 3.08599i) q^{79} +(5.20055 - 7.34536i) q^{81} +(-7.91972 + 2.88254i) q^{83} +(-3.33521 + 2.79857i) q^{85} +(-9.88100 - 14.8298i) q^{87} +(2.38468 - 4.13038i) q^{89} +(-0.277529 - 0.480694i) q^{91} +(-8.70861 - 6.40288i) q^{93} +(-2.30589 - 0.839276i) q^{95} +(1.34377 - 7.62091i) q^{97} +(0.365235 + 1.16899i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{5} + 6 q^{9}+O(q^{10}) $ 18 * q + 3 * q^5 + 6 * q^9	$ 18 q + 3 q^{5} + 6 q^{9} + 3 q^{11} - 9 q^{15} - 12 q^{17} - 30 q^{21} - 30 q^{23} + 9 q^{25} - 27 q^{27} - 24 q^{29} + 9 q^{31} - 18 q^{33} - 21 q^{35} + 3 q^{39} + 21 q^{41} - 9 q^{43} + 45 q^{45} + 45 q^{47} - 18 q^{49} + 63 q^{51} + 66 q^{53} + 54 q^{57} + 60 q^{59} - 18 q^{61} + 57 q^{63} + 33 q^{65} - 27 q^{67} - 9 q^{69} - 12 q^{71} + 9 q^{73} - 33 q^{75} - 75 q^{77} - 36 q^{79} - 54 q^{81} - 45 q^{83} - 36 q^{85} - 63 q^{87} - 48 q^{89} + 9 q^{91} - 33 q^{93} + 6 q^{95} - 27 q^{97} + 27 q^{99}+O(q^{100}) $ 18 * q + 3 * q^5 + 6 * q^9 + 3 * q^11 - 9 * q^15 - 12 * q^17 - 30 * q^21 - 30 * q^23 + 9 * q^25 - 27 * q^27 - 24 * q^29 + 9 * q^31 - 18 * q^33 - 21 * q^35 + 3 * q^39 + 21 * q^41 - 9 * q^43 + 45 * q^45 + 45 * q^47 - 18 * q^49 + 63 * q^51 + 66 * q^53 + 54 * q^57 + 60 * q^59 - 18 * q^61 + 57 * q^63 + 33 * q^65 - 27 * q^67 - 9 * q^69 - 12 * q^71 + 9 * q^73 - 33 * q^75 - 75 * q^77 - 36 * q^79 - 54 * q^81 - 45 * q^83 - 36 * q^85 - 63 * q^87 - 48 * q^89 + 9 * q^91 - 33 * q^93 + 6 * q^95 - 27 * q^97 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$1$

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
$3$	0.409491	+	1.68295i	0.236420	+	0.971651i
$3$	0.409491	+	1.68295i	0.236420	+	0.971651i
$4$		0			0
$5$	−0.103132	−	0.584890i	−0.0461220	−	0.261571i	0.953024	−	0.302896i	$-0.0979533\pi$
$5$	−0.103132	−	0.584890i	−0.0461220	−	0.261571i	−0.999146	+	0.0413246i	$0.986842\pi$
$6$		0			0
$7$	2.18780	+	1.83578i	0.826911	+	0.693860i	0.954579	−	0.297956i	$-0.0963050\pi$
$7$	2.18780	+	1.83578i	0.826911	+	0.693860i	−0.127669	+	0.991817i	$0.540749\pi$
$8$		0			0
$9$	−2.66463	+	1.37830i	−0.888211	+	0.459435i
$10$		0			0
$11$	0.0708902	−	0.402038i	0.0213742	−	0.121219i	−0.972254	−	0.233929i	$-0.924842\pi$
$11$	0.0708902	−	0.402038i	0.0213742	−	0.121219i	0.993628	+	0.112709i	$0.0359529\pi$
$12$		0			0
$13$	−0.182629	−	0.0664716i	−0.0506523	−	0.0184359i	0.316570	−	0.948569i	$-0.397469\pi$
$13$	−0.182629	−	0.0664716i	−0.0506523	−	0.0184359i	−0.367222	+	0.930133i	$0.619691\pi$
$14$		0			0
$15$	0.942109	−	0.413073i	0.243251	−	0.106655i
$16$		0			0
$17$	−3.66536	−	6.34858i	−0.888980	−	1.53976i	−0.841083	−	0.540905i	$-0.818082\pi$
$17$	−3.66536	−	6.34858i	−0.888980	−	1.53976i	−0.0478962	−	0.998852i	$-0.515252\pi$
$18$		0			0
$19$	2.06586	−	3.57817i	0.473940	−	0.820889i	−0.525615	−	0.850723i	$-0.676165\pi$
$19$	2.06586	−	3.57817i	0.473940	−	0.820889i	0.999555	+	0.0298342i	$0.00949794\pi$
$20$		0			0
$21$	−2.19364	+	4.43369i	−0.478692	+	0.967511i
$22$		0			0
$23$	3.12150	−	2.61925i	0.650877	−	0.546151i	−0.256460	−	0.966555i	$-0.582556\pi$
$23$	3.12150	−	2.61925i	0.650877	−	0.546151i	0.907337	+	0.420404i	$0.138112\pi$
$24$		0			0
$25$	4.36700	−	1.58946i	0.873401	−	0.317892i
$26$		0			0
$27$	−3.41076	−	3.92004i	−0.656401	−	0.754412i
$28$		0			0
$29$	−9.66797	+	3.51885i	−1.79530	+	0.653435i	−0.796488	+	0.604655i	$0.793311\pi$
$29$	−9.66797	+	3.51885i	−1.79530	+	0.653435i	−0.998810	+	0.0487800i	$0.984467\pi$
$30$		0			0
$31$	−4.78061	+	4.01141i	−0.858623	+	0.720470i	−0.961671	−	0.274206i	$-0.911585\pi$
$31$	−4.78061	+	4.01141i	−0.858623	+	0.720470i	0.103048	+	0.994676i	$0.467140\pi$
$32$		0			0
$33$	0.705639	−	0.0453265i	0.122836	−	0.00789033i
$34$		0			0
$35$	0.848099	−	1.46895i	0.143355	−	0.248298i
$36$		0			0
$37$	−2.88349	−	4.99435i	−0.474043	−	0.821066i	0.525516	−	0.850784i	$-0.323872\pi$
$37$	−2.88349	−	4.99435i	−0.474043	−	0.821066i	−0.999558	+	0.0297179i	$0.990539\pi$
$38$		0			0
$39$	0.0370833	−	0.334575i	0.00593808	−	0.0535749i
$40$		0			0
$41$	7.92488	+	2.88442i	1.23766	+	0.450471i	0.876214	−	0.481923i	$-0.160061\pi$
$41$	7.92488	+	2.88442i	1.23766	+	0.450471i	0.361445	+	0.932394i	$0.382284\pi$
$42$		0			0
$43$	−1.03999	+	5.89808i	−0.158597	+	0.899449i	0.796826	+	0.604209i	$0.206511\pi$
$43$	−1.03999	+	5.89808i	−0.158597	+	0.899449i	−0.955423	+	0.295240i	$0.904600\pi$
$44$		0			0
$45$	1.08097	+	1.41637i	0.161141	+	0.211140i
$46$		0			0
$47$	8.62443	+	7.23675i	1.25800	+	1.05559i	0.995892	+	0.0905508i	$0.0288628\pi$
$47$	8.62443	+	7.23675i	1.25800	+	1.05559i	0.262110	+	0.965038i	$0.415582\pi$
$48$		0			0
$49$	0.200835	+	1.13899i	0.0286908	+	0.162713i
$50$		0			0
$51$	9.18341	−	8.76830i	1.28593	−	1.22781i
$52$		0			0
$53$	−3.42431			−0.470365			−0.235183	−	0.971951i	$-0.575569\pi$
$53$	−3.42431			−0.470365			−0.235183	+	0.971951i	$0.575569\pi$
$54$		0			0
$55$	−0.242459			−0.0326932
$56$		0			0
$57$	6.86783	+	2.01150i	0.909666	+	0.266430i
$58$		0			0
$59$	0.813604	+	4.61418i	0.105922	+	0.600715i	0.990848	+	0.134982i	$0.0430978\pi$
$59$	0.813604	+	4.61418i	0.105922	+	0.600715i	−0.884926	+	0.465732i	$0.845791\pi$
$60$		0			0
$61$	3.34605	+	2.80767i	0.428417	+	0.359485i	0.831354	−	0.555743i	$-0.187566\pi$
$61$	3.34605	+	2.80767i	0.428417	+	0.359485i	−0.402937	+	0.915228i	$0.632011\pi$
$62$		0			0
$63$	−8.35995	−	1.87623i	−1.05326	−	0.236383i
$64$		0			0
$65$	−0.0200437	+	0.113673i	−0.00248612	+	0.0140995i
$66$		0			0
$67$	−11.4215	−	4.15710i	−1.39536	−	0.507870i	−0.468564	−	0.883430i	$-0.655228\pi$
$67$	−11.4215	−	4.15710i	−1.39536	−	0.507870i	−0.926798	+	0.375559i	$0.877451\pi$
$68$		0			0
$69$	5.68628	+	4.18076i	0.684548	+	0.503305i
$70$		0			0
$71$	4.09409	+	7.09117i	0.485879	+	0.841567i	0.999868	−	0.0162298i	$-0.00516635\pi$
$71$	4.09409	+	7.09117i	0.485879	+	0.841567i	−0.513990	+	0.857796i	$0.671833\pi$
$72$		0			0
$73$	1.96938	−	3.41106i	0.230498	−	0.399234i	−0.727457	−	0.686153i	$-0.759298\pi$
$73$	1.96938	−	3.41106i	0.230498	−	0.399234i	0.957955	+	0.286919i	$0.0926312\pi$
$74$		0			0
$75$	4.46323	+	6.69857i	0.515369	+	0.773485i
$76$		0			0
$77$	0.893148	−	0.749440i	0.101784	−	0.0854067i
$78$		0			0
$79$	−8.47868	+	3.08599i	−0.953926	+	0.347201i	−0.771651	−	0.636047i	$-0.780569\pi$
$79$	−8.47868	+	3.08599i	−0.953926	+	0.347201i	−0.182276	+	0.983247i	$0.558346\pi$
$80$		0			0
$81$	5.20055	−	7.34536i	0.577839	−	0.816151i
$82$		0			0
$83$	−7.91972	+	2.88254i	−0.869302	+	0.316400i	−0.737885	−	0.674927i	$-0.764175\pi$
$83$	−7.91972	+	2.88254i	−0.869302	+	0.316400i	−0.131418	+	0.991327i	$0.541953\pi$
$84$		0			0
$85$	−3.33521	+	2.79857i	−0.361754	+	0.303548i
$86$		0			0
$87$	−9.88100	−	14.8298i	−1.05935	−	1.58992i
$88$		0			0
$89$	2.38468	−	4.13038i	0.252775	−	0.437819i	−0.711514	−	0.702672i	$-0.751990\pi$
$89$	2.38468	−	4.13038i	0.252775	−	0.437819i	0.964289	+	0.264853i	$0.0853234\pi$
$90$		0			0
$91$	−0.277529	−	0.480694i	−0.0290929	−	0.0503905i
$92$		0			0
$93$	−8.70861	−	6.40288i	−0.903041	−	0.663948i
$94$		0			0
$95$	−2.30589	−	0.839276i	−0.236580	−	0.0861079i
$96$		0			0
$97$	1.34377	−	7.62091i	0.136439	−	0.773787i	−0.837407	−	0.546580i	$-0.815930\pi$
$97$	1.34377	−	7.62091i	0.136439	−	0.773787i	0.973847	−	0.227207i	$-0.0729593\pi$
$98$		0			0
$99$	0.365235	+	1.16899i	0.0367075	+	0.117488i
$100$		0			0
$101$	9.10369	+	7.63890i	0.905851	+	0.760099i	0.971325	−	0.237755i	$-0.0764115\pi$
$101$	9.10369	+	7.63890i	0.905851	+	0.760099i	−0.0654741	+	0.997854i	$0.520856\pi$
$102$		0			0
$103$	−0.637037	−	3.61282i	−0.0627691	−	0.355981i	−0.999974	−	0.00720217i	$-0.997707\pi$
$103$	−0.637037	−	3.61282i	−0.0627691	−	0.355981i	0.937205	−	0.348779i	$-0.113404\pi$
$104$		0			0
$105$	2.81946	+	0.825785i	0.275151	+	0.0805884i
$106$		0			0
$107$	−5.24784			−0.507328			−0.253664	−	0.967292i	$-0.581636\pi$
$107$	−5.24784			−0.507328			−0.253664	+	0.967292i	$0.581636\pi$
$108$		0			0
$109$	−7.04007			−0.674316			−0.337158	−	0.941448i	$-0.609466\pi$
$109$	−7.04007			−0.674316			−0.337158	+	0.941448i	$0.609466\pi$
$110$		0			0
$111$	7.22447	−	6.89791i	0.685717	−	0.654720i
$112$		0			0
$113$	−0.168513	−	0.955687i	−0.0158524	−	0.0899035i	0.975855	−	0.218419i	$-0.0700899\pi$
$113$	−0.168513	−	0.955687i	−0.0158524	−	0.0899035i	−0.991708	+	0.128515i	$0.958979\pi$
$114$		0			0
$115$	−1.85390	−	1.55561i	−0.172877	−	0.145061i
$116$		0			0
$117$	0.578259	−	0.0745963i	0.0534600	−	0.00689643i
$118$		0			0
$119$	3.63555	−	20.6182i	0.333270	−	1.89007i
$120$		0			0
$121$	10.1800	+	3.70522i	0.925455	+	0.336838i
$122$		0			0
$123$	−1.60916	+	14.5183i	−0.145094	+	1.30907i
$124$		0			0
$125$	−2.86482	−	4.96201i	−0.256237	−	0.443816i
$126$		0			0
$127$	−4.40538	+	7.63034i	−0.390914	+	0.677084i	−0.992570	−	0.121672i	$-0.961174\pi$
$127$	−4.40538	+	7.63034i	−0.390914	+	0.677084i	0.601656	+	0.798755i	$0.294508\pi$
$128$		0			0
$129$	−10.3520	+	0.664960i	−0.911446	+	0.0585465i
$130$		0			0
$131$	−3.66300	+	3.07362i	−0.320038	+	0.268544i	−0.788626	−	0.614873i	$-0.789207\pi$
$131$	−3.66300	+	3.07362i	−0.320038	+	0.268544i	0.468588	+	0.883417i	$0.344763\pi$
$132$		0			0
$133$	11.0884	−	4.03586i	0.961488	−	0.349953i
$134$		0			0
$135$	−1.94103	+	2.39920i	−0.167058	+	0.206490i
$136$		0			0
$137$	−13.6526	+	4.96912i	−1.16642	+	0.424541i	−0.851386	−	0.524540i	$-0.824237\pi$
$137$	−13.6526	+	4.96912i	−1.16642	+	0.424541i	−0.315031	+	0.949081i	$0.602015\pi$
$138$		0			0
$139$	11.4949	−	9.64533i	0.974981	−	0.818107i	−0.00834324	−	0.999965i	$-0.502656\pi$
$139$	11.4949	−	9.64533i	0.974981	−	0.818107i	0.983325	+	0.181859i	$0.0582113\pi$
$140$		0			0
$141$	−8.64746	+	17.4779i	−0.728248	+	1.47190i
$142$		0			0
$143$	−0.0396708	+	0.0687118i	−0.00331744	+	0.00574597i
$144$		0			0
$145$	3.05522	+	5.29180i	0.253722	+	0.439460i
$146$		0			0
$147$	−1.83463	+	0.804403i	−0.151318	+	0.0663461i
$148$		0			0
$149$	−3.89834	−	1.41888i	−0.319365	−	0.116239i	0.177364	−	0.984145i	$-0.443243\pi$
$149$	−3.89834	−	1.41888i	−0.319365	−	0.116239i	−0.496728	+	0.867906i	$0.665465\pi$
$150$		0			0
$151$	−0.787624	+	4.46684i	−0.0640959	+	0.363506i	0.935843	+	0.352418i	$0.114641\pi$
$151$	−0.787624	+	4.46684i	−0.0640959	+	0.363506i	−0.999939	+	0.0110879i	$0.996471\pi$
$152$		0			0
$153$	18.5171	+	11.8647i	1.49702	+	0.959202i
$154$		0			0
$155$	2.83927	+	2.38243i	0.228055	+	0.191361i
$156$		0			0
$157$	2.35733	+	13.3691i	0.188135	+	1.06697i	0.921860	+	0.387522i	$0.126669\pi$
$157$	2.35733	+	13.3691i	0.188135	+	1.06697i	−0.733725	+	0.679446i	$0.762220\pi$
$158$		0			0
$159$	−1.40222	−	5.76294i	−0.111204	−	0.457031i
$160$		0			0
$161$	11.6376			0.917170
$162$		0			0
$163$	19.9421			1.56199			0.780994	−	0.624539i	$-0.214713\pi$
$163$	19.9421			1.56199			0.780994	+	0.624539i	$0.214713\pi$
$164$		0			0
$165$	−0.0992849	−	0.408047i	−0.00772932	−	0.0317664i
$166$		0			0
$167$	−1.93890	−	10.9961i	−0.150037	−	0.850901i	−0.963184	−	0.268843i	$-0.913359\pi$
$167$	−1.93890	−	10.9961i	−0.150037	−	0.850901i	0.813147	−	0.582058i	$-0.197752\pi$
$168$		0			0
$169$	−9.92964	−	8.33196i	−0.763819	−	0.640920i
$170$		0			0
$171$	−0.572945	+	12.3819i	−0.0438142	+	0.946867i
$172$		0			0
$173$	3.74703	−	21.2504i	0.284881	−	1.61564i	−0.420829	−	0.907140i	$-0.638261\pi$
$173$	3.74703	−	21.2504i	0.284881	−	1.61564i	0.705710	−	0.708501i	$-0.250628\pi$
$174$		0			0
$175$	12.4720	+	4.53945i	0.942797	+	0.343150i
$176$		0			0
$177$	−7.43226	+	3.25872i	−0.558643	+	0.244940i
$178$		0			0
$179$	7.67057	+	13.2858i	0.573325	+	0.993029i	0.996221	+	0.0868504i	$0.0276802\pi$
$179$	7.67057	+	13.2858i	0.573325	+	0.993029i	−0.422896	+	0.906178i	$0.638986\pi$
$180$		0			0
$181$	−3.69921	+	6.40721i	−0.274960	+	0.476245i	−0.970125	−	0.242606i	$-0.921998\pi$
$181$	−3.69921	+	6.40721i	−0.274960	+	0.476245i	0.695165	+	0.718850i	$0.255331\pi$
$182$		0			0
$183$	−3.35498	+	6.78094i	−0.248008	+	0.501262i
$184$		0			0
$185$	−2.62377	+	2.20160i	−0.192903	+	0.161865i
$186$		0			0
$187$	−2.81221	+	1.02356i	−0.205649	+	0.0748502i
$188$		0			0
$189$	−0.265723	−	14.8377i	−0.0193285	−	1.07928i
$190$		0			0
$191$	11.6275	−	4.23208i	0.841339	−	0.306223i	0.114835	−	0.993385i	$-0.463366\pi$
$191$	11.6275	−	4.23208i	0.841339	−	0.306223i	0.726504	+	0.687162i	$0.241144\pi$
$192$		0			0
$193$	11.9443	−	10.0224i	0.859767	−	0.721430i	−0.102151	−	0.994769i	$-0.532573\pi$
$193$	11.9443	−	10.0224i	0.859767	−	0.721430i	0.961918	+	0.273339i	$0.0881281\pi$
$194$		0			0
$195$	−0.199514	+	0.0128157i	−0.0142875	+	0.000917754i
$196$		0			0
$197$	−8.59949	+	14.8948i	−0.612688	+	1.06121i	0.378097	+	0.925766i	$0.376579\pi$
$197$	−8.59949	+	14.8948i	−0.612688	+	1.06121i	−0.990785	+	0.135441i	$0.956755\pi$
$198$		0			0
$199$	8.88885	+	15.3959i	0.630114	+	1.09139i	0.987528	+	0.157443i	$0.0503251\pi$
$199$	8.88885	+	15.3959i	0.630114	+	1.09139i	−0.357414	+	0.933946i	$0.616342\pi$
$200$		0			0
$201$	2.31917	−	20.9242i	0.163582	−	1.47588i
$202$		0			0
$203$	−27.6114	−	10.0497i	−1.93794	−	0.705354i
$204$		0			0
$205$	0.869761	−	4.93266i	0.0607468	−	0.344512i
$206$		0			0
$207$	−4.70753	+	11.2817i	−0.327196	+	0.784133i
$208$		0			0
$209$	−1.29211	−	1.08421i	−0.0893773	−	0.0749964i
$210$		0			0
$211$	−3.27862	−	18.5940i	−0.225710	−	1.28006i	−0.861324	−	0.508056i	$-0.830364\pi$
$211$	−3.27862	−	18.5940i	−0.225710	−	1.28006i	0.635614	−	0.772007i	$-0.280747\pi$
$212$		0			0
$213$	−10.2576	+	9.79391i	−0.702838	+	0.671067i
$214$		0			0
$215$	3.55699			0.242585
$216$		0			0
$217$	−17.8231			−1.20991
$218$		0			0
$219$	6.54708	+	1.91756i	0.442410	+	0.129577i
$220$		0			0
$221$	0.247401	+	1.40308i	0.0166420	+	0.0943814i
$222$		0			0
$223$	−1.14380	−	0.959759i	−0.0765942	−	0.0642702i	0.603687	−	0.797222i	$-0.293698\pi$
$223$	−1.14380	−	0.959759i	−0.0765942	−	0.0642702i	−0.680281	+	0.732951i	$0.738142\pi$
$224$		0			0
$225$	−9.44571	+	10.2544i	−0.629714	+	0.683626i
$226$		0			0
$227$	3.38640	−	19.2052i	0.224763	−	1.27470i	−0.638374	−	0.769727i	$-0.720393\pi$
$227$	3.38640	−	19.2052i	0.224763	−	1.27470i	0.863137	−	0.504970i	$-0.168496\pi$
$228$		0			0
$229$	0.0297781	+	0.0108384i	0.00196779	+	0.000716219i	0.343004	−	0.939334i	$-0.388556\pi$
$229$	0.0297781	+	0.0108384i	0.00196779	+	0.000716219i	−0.341036	+	0.940050i	$0.610778\pi$
$230$		0			0
$231$	1.62701	+	1.19623i	0.107049	+	0.0787064i
$232$		0			0
$233$	−6.71592	−	11.6323i	−0.439975	−	0.762058i	0.557712	−	0.830034i	$-0.311679\pi$
$233$	−6.71592	−	11.6323i	−0.439975	−	0.762058i	−0.997687	+	0.0679760i	$0.978346\pi$
$234$		0			0
$235$	3.34325	−	5.79068i	0.218090	−	0.377743i
$236$		0			0
$237$	−8.66551	−	13.0055i	−0.562885	−	0.844798i
$238$		0			0
$239$	−11.8722	+	9.96198i	−0.767951	+	0.644387i	−0.940183	−	0.340669i	$-0.889346\pi$
$239$	−11.8722	+	9.96198i	−0.767951	+	0.644387i	0.172232	+	0.985056i	$0.444902\pi$
$240$		0			0
$241$	−22.0779	+	8.03570i	−1.42216	+	0.517625i	−0.934675	−	0.355504i	$-0.884309\pi$
$241$	−22.0779	+	8.03570i	−1.42216	+	0.517625i	−0.487489	+	0.873129i	$0.662087\pi$
$242$		0			0
$243$	14.4914	+	5.74440i	0.929626	+	0.368504i
$244$		0			0
$245$	0.645474	−	0.234933i	0.0412378	−	0.0150093i
$246$		0			0
$247$	−0.615133	+	0.516158i	−0.0391400	+	0.0328423i
$248$		0			0
$249$	−8.09423	−	12.1481i	−0.512951	−	0.769855i
$250$		0			0
$251$	−5.28209	+	9.14885i	−0.333403	+	0.577470i	−0.983177	−	0.182657i	$-0.941530\pi$
$251$	−5.28209	+	9.14885i	−0.333403	+	0.577470i	0.649774	+	0.760127i	$0.274863\pi$
$252$		0			0
$253$	−0.831754	−	1.44064i	−0.0522919	−	0.0905723i
$254$		0			0
$255$	−6.07559	−	4.46700i	−0.380468	−	0.279734i
$256$		0			0
$257$	11.3120	+	4.11723i	0.705623	+	0.256826i	0.669810	−	0.742533i	$-0.266376\pi$
$257$	11.3120	+	4.11723i	0.705623	+	0.256826i	0.0358132	+	0.999359i	$0.488598\pi$
$258$		0			0
$259$	2.86004	−	16.2201i	0.177714	−	1.00787i
$260$		0			0
$261$	20.9116	−	22.7019i	1.29439	−	1.40521i
$262$		0			0
$263$	2.72267	+	2.28459i	0.167887	+	0.140874i	0.722860	−	0.690994i	$-0.242827\pi$
$263$	2.72267	+	2.28459i	0.167887	+	0.140874i	−0.554973	+	0.831868i	$0.687272\pi$
$264$		0			0
$265$	0.353156	+	2.00285i	0.0216942	+	0.123034i
$266$		0			0
$267$	7.92772	+	2.32193i	0.485169	+	0.142100i
$268$		0			0
$269$	25.8590			1.57665			0.788327	−	0.615257i	$-0.210948\pi$
$269$	25.8590			1.57665			0.788327	+	0.615257i	$0.210948\pi$
$270$		0			0
$271$	−2.86426			−0.173991			−0.0869957	−	0.996209i	$-0.527727\pi$
$271$	−2.86426			−0.173991			−0.0869957	+	0.996209i	$0.527727\pi$
$272$		0			0
$273$	0.695338	−	0.663907i	0.0420838	−	0.0401815i
$274$		0			0
$275$	−0.329446	−	1.86838i	−0.0198663	−	0.112668i
$276$		0			0
$277$	−8.67298	−	7.27749i	−0.521109	−	0.437262i	0.343909	−	0.939003i	$-0.388249\pi$
$277$	−8.67298	−	7.27749i	−0.521109	−	0.437262i	−0.865018	+	0.501741i	$0.832693\pi$
$278$		0			0
$279$	7.20963	−	17.2781i	0.431629	−	1.03441i
$280$		0			0
$281$	−3.59173	+	20.3697i	−0.214265	+	1.21516i	0.667913	+	0.744239i	$0.267188\pi$
$281$	−3.59173	+	20.3697i	−0.214265	+	1.21516i	−0.882178	+	0.470916i	$0.843923\pi$
$282$		0			0
$283$	1.44755	+	0.526866i	0.0860480	+	0.0313189i	0.384685	−	0.923048i	$-0.374310\pi$
$283$	1.44755	+	0.526866i	0.0860480	+	0.0313189i	−0.298637	+	0.954367i	$0.596532\pi$
$284$		0			0
$285$	0.468217	−	4.22438i	0.0277348	−	0.250230i
$286$		0			0
$287$	12.0429	+	20.8589i	0.710869	+	1.23126i
$288$		0			0
$289$	−18.3697	+	31.8172i	−1.08057	+	1.87160i
$290$		0			0
$291$	13.3759	−	0.859195i	0.784107	−	0.0503669i
$292$		0			0
$293$	4.14678	−	3.47956i	0.242258	−	0.203278i	−0.513572	−	0.858046i	$-0.671678\pi$
$293$	4.14678	−	3.47956i	0.242258	−	0.203278i	0.755830	+	0.654768i	$0.227234\pi$
$294$		0			0
$295$	2.61488	−	0.951738i	0.152244	−	0.0554123i
$296$		0			0
$297$	−1.81780	+	1.09336i	−0.105479	+	0.0634434i
$298$		0			0
$299$	−0.744183	+	0.270860i	−0.0430372	+	0.0156643i
$300$		0			0
$301$	−13.1029	+	10.9946i	−0.755238	+	0.633720i
$302$		0			0
$303$	−9.12801	+	18.4491i	−0.524390	+	1.05987i
$304$		0			0
$305$	1.29709	−	2.24663i	0.0742713	−	0.128642i
$306$		0			0
$307$	−6.07028	−	10.5140i	−0.346449	−	0.600068i	0.639167	−	0.769068i	$-0.279279\pi$
$307$	−6.07028	−	10.5140i	−0.346449	−	0.600068i	−0.985616	+	0.169000i	$0.945946\pi$
$308$		0			0
$309$	5.81932	−	2.55152i	0.331050	−	0.145151i
$310$		0			0
$311$	11.4065	+	4.15161i	0.646801	+	0.235416i	0.644528	−	0.764581i	$-0.277054\pi$
$311$	11.4065	+	4.15161i	0.646801	+	0.235416i	0.00227362	+	0.999997i	$0.499276\pi$
$312$		0			0
$313$	0.180419	−	1.02320i	0.0101979	−	0.0578350i	−0.979284	−	0.202491i	$-0.935096\pi$
$313$	0.180419	−	1.02320i	0.0101979	−	0.0578350i	0.989482	+	0.144656i	$0.0462075\pi$
$314$		0			0
$315$	−0.235212	+	5.08316i	−0.0132527	+	0.286403i
$316$		0			0
$317$	13.3002	+	11.1602i	0.747016	+	0.626821i	0.934712	−	0.355406i	$-0.115657\pi$
$317$	13.3002	+	11.1602i	0.747016	+	0.626821i	−0.187696	+	0.982227i	$0.560102\pi$
$318$		0			0
$319$	0.729349	+	4.13635i	0.0408357	+	0.231591i
$320$		0			0
$321$	−2.14894	−	8.83184i	−0.119942	−	0.492945i
$322$		0			0
$323$	−30.2884			−1.68529
$324$		0			0
$325$	−0.903197			−0.0501003
$326$		0			0
$327$	−2.88285	−	11.8481i	−0.159422	−	0.655200i
$328$		0			0
$329$	5.58342	+	31.6651i	0.307824	+	1.74576i
$330$		0			0
$331$	1.78810	+	1.50039i	0.0982829	+	0.0824691i	0.690605	−	0.723232i	$-0.257344\pi$
$331$	1.78810	+	1.50039i	0.0982829	+	0.0824691i	−0.592322	+	0.805701i	$0.701789\pi$
$332$		0			0
$333$	14.5672	+	9.33379i	0.798277	+	0.511488i
$334$		0			0
$335$	−1.25352	+	7.10907i	−0.0684872	+	0.388410i
$336$		0			0
$337$	4.78041	+	1.73993i	0.260405	+	0.0947798i	0.468924	−	0.883239i	$-0.344642\pi$
$337$	4.78041	+	1.73993i	0.260405	+	0.0947798i	−0.208518	+	0.978018i	$0.566864\pi$
$338$		0			0
$339$	1.53937	−	0.674945i	0.0836070	−	0.0366580i
$340$		0			0
$341$	1.27384	+	2.20636i	0.0689823	+	0.119481i
$342$		0			0
$343$	8.34434	−	14.4528i	0.450552	−	0.780379i
$344$		0			0
$345$	1.85885	−	3.75702i	0.100077	−	0.202271i
$346$		0			0
$347$	−4.31592	+	3.62149i	−0.231691	+	0.194412i	−0.751240	−	0.660029i	$-0.770544\pi$
$347$	−4.31592	+	3.62149i	−0.231691	+	0.194412i	0.519550	+	0.854440i	$0.326100\pi$
$348$		0			0
$349$	11.1539	−	4.05967i	0.597052	−	0.217309i	−0.0257760	−	0.999668i	$-0.508206\pi$
$349$	11.1539	−	4.05967i	0.597052	−	0.217309i	0.622828	+	0.782358i	$0.285983\pi$
$350$		0			0
$351$	0.362333	+	0.942633i	0.0193399	+	0.0503140i
$352$		0			0
$353$	3.92715	−	1.42936i	0.209021	−	0.0760774i	−0.235388	−	0.971902i	$-0.575636\pi$
$353$	3.92715	−	1.42936i	0.209021	−	0.0760774i	0.444409	+	0.895824i	$0.353414\pi$
$354$		0			0
$355$	3.72532	−	3.12592i	0.197720	−	0.165906i
$356$		0			0
$357$	36.1881	−	2.32453i	1.91528	−	0.123027i
$358$		0			0
$359$	13.7474	−	23.8112i	0.725559	−	1.25670i	−0.233185	−	0.972432i	$-0.574915\pi$
$359$	13.7474	−	23.8112i	0.725559	−	1.25670i	0.958744	−	0.284272i	$-0.0917519\pi$
$360$		0			0
$361$	0.964465	+	1.67050i	0.0507613	+	0.0879212i
$362$		0			0
$363$	−2.06707	+	18.6497i	−0.108493	+	0.978855i
$364$		0			0
$365$	−2.19820	−	0.800079i	−0.115059	−	0.0418781i
$366$		0			0
$367$	−5.21415	+	29.5709i	−0.272177	+	1.54359i	0.475613	+	0.879655i	$0.342226\pi$
$367$	−5.21415	+	29.5709i	−0.272177	+	1.54359i	−0.747790	+	0.663936i	$0.768885\pi$
$368$		0			0
$369$	−25.0925	+	3.23698i	−1.30626	+	0.168510i
$370$		0			0
$371$	−7.49171	−	6.28629i	−0.388950	−	0.326368i
$372$		0			0
$373$	−1.77672	−	10.0763i	−0.0919952	−	0.521730i	−0.995627	−	0.0934200i	$-0.970220\pi$
$373$	−1.77672	−	10.0763i	−0.0919952	−	0.521730i	0.903632	−	0.428310i	$-0.140891\pi$
$374$		0			0
$375$	7.17770	−	6.85324i	0.370655	−	0.353900i
$376$		0			0
$377$	1.99956			0.102983
$378$		0			0
$379$	−12.4688			−0.640478			−0.320239	−	0.947337i	$-0.603763\pi$
$379$	−12.4688			−0.640478			−0.320239	+	0.947337i	$0.603763\pi$
$380$		0			0
$381$	−14.6454	−	4.28947i	−0.750309	−	0.219756i
$382$		0			0
$383$	−3.68308	−	20.8878i	−0.188197	−	1.06732i	−0.921779	−	0.387715i	$-0.873264\pi$
$383$	−3.68308	−	20.8878i	−0.188197	−	1.06732i	0.733583	−	0.679600i	$-0.237847\pi$
$384$		0			0
$385$	−0.530452	−	0.445102i	−0.0270344	−	0.0226845i
$386$		0			0
$387$	−5.35816	−	17.1497i	−0.272371	−	0.871766i
$388$		0			0
$389$	−0.904899	+	5.13194i	−0.0458802	+	0.260200i	−0.999117	−	0.0420264i	$-0.986619\pi$
$389$	−0.904899	+	5.13194i	−0.0458802	+	0.260200i	0.953236	+	0.302226i	$0.0977298\pi$
$390$		0			0
$391$	−28.0699	−	10.2166i	−1.41956	−	0.516676i
$392$		0			0
$393$	−6.67272	−	4.90602i	−0.336594	−	0.247476i
$394$		0			0
$395$	2.67939	+	4.64084i	0.134815	+	0.233506i
$396$		0			0
$397$	15.7685	−	27.3119i	0.791399	−	1.37074i	−0.133701	−	0.991022i	$-0.542686\pi$
$397$	15.7685	−	27.3119i	0.791399	−	1.37074i	0.925101	−	0.379722i	$-0.123980\pi$
$398$		0			0
$399$	11.3327	+	17.0086i	0.567347	+	0.851495i
$400$		0			0
$401$	19.3407	−	16.2288i	0.965829	−	0.810427i	−0.0160623	−	0.999871i	$-0.505113\pi$
$401$	19.3407	−	16.2288i	0.965829	−	0.810427i	0.981892	+	0.189444i	$0.0606686\pi$
$402$		0			0
$403$	1.13972	−	0.414826i	0.0567737	−	0.0206639i
$404$		0			0
$405$	−4.83257	−	2.28421i	−0.240132	−	0.113503i
$406$		0			0
$407$	−2.21233	+	0.805222i	−0.109661	+	0.0399134i
$408$		0			0
$409$	−8.56969	+	7.19082i	−0.423744	+	0.355563i	−0.829585	−	0.558380i	$-0.811423\pi$
$409$	−8.56969	+	7.19082i	−0.423744	+	0.355563i	0.405841	+	0.913944i	$0.366979\pi$
$410$		0			0
$411$	−13.9534	−	20.9417i	−0.688270	−	1.03298i
$412$		0			0
$413$	−6.69062	+	11.5885i	−0.329224	+	0.570232i
$414$		0			0
$415$	2.50275	+	4.33489i	0.122855	+	0.212791i
$416$		0			0
$417$	20.9396	+	15.3956i	1.02542	+	0.753925i
$418$		0			0
$419$	1.42956	+	0.520317i	0.0698385	+	0.0254191i	0.376703	−	0.926334i	$-0.377058\pi$
$419$	1.42956	+	0.520317i	0.0698385	+	0.0254191i	−0.306865	+	0.951753i	$0.599280\pi$
$420$		0			0
$421$	−1.09652	+	6.21866i	−0.0534410	+	0.303079i	−0.999799	−	0.0200407i	$-0.993620\pi$
$421$	−1.09652	+	6.21866i	−0.0534410	+	0.303079i	0.946358	+	0.323119i	$0.104732\pi$
$422$		0			0
$423$	−32.9554	−	7.39621i	−1.60235	−	0.359616i
$424$		0			0
$425$	−26.0974	−	21.8983i	−1.26591	−	1.06223i
$426$		0			0
$427$	2.16622	+	12.2852i	0.104831	+	0.594524i
$428$		0			0
$429$	−0.131883	−	0.0386270i	−0.00636738	−	0.00186493i
$430$		0			0
$431$	−22.8116			−1.09880			−0.549398	−	0.835561i	$-0.685143\pi$
$431$	−22.8116			−1.09880			−0.549398	+	0.835561i	$0.685143\pi$
$432$		0			0
$433$	30.2232			1.45243			0.726216	−	0.687466i	$-0.241277\pi$
$433$	30.2232			1.45243			0.726216	+	0.687466i	$0.241277\pi$
$434$		0			0
$435$	−7.65474	+	7.30872i	−0.367017	+	0.350426i
$436$		0			0
$437$	−2.92354	−	16.5802i	−0.139852	−	0.793140i
$438$		0			0
$439$	2.02132	+	1.69609i	0.0964725	+	0.0809500i	0.689748	−	0.724049i	$-0.257721\pi$
$439$	2.02132	+	1.69609i	0.0964725	+	0.0809500i	−0.593276	+	0.804999i	$0.702166\pi$
$440$		0			0
$441$	−2.10503	−	2.75819i	−0.100240	−	0.131342i
$442$		0			0
$443$	−5.12622	+	29.0722i	−0.243554	+	1.38126i	0.580273	+	0.814422i	$0.302946\pi$
$443$	−5.12622	+	29.0722i	−0.243554	+	1.38126i	−0.823827	+	0.566841i	$0.808165\pi$
$444$		0			0
$445$	−2.66176	−	0.968800i	−0.126179	−	0.0459255i
$446$		0			0
$447$	0.791567	−	7.14173i	0.0374398	−	0.337792i
$448$		0			0
$449$	−15.8871	−	27.5173i	−0.749759	−	1.29862i	−0.947938	−	0.318455i	$-0.896836\pi$
$449$	−15.8871	−	27.5173i	−0.749759	−	1.29862i	0.198178	−	0.980166i	$-0.436497\pi$
$450$		0			0
$451$	1.72144	−	2.98163i	0.0810596	−	0.140399i
$452$		0			0
$453$	−7.83999	+	0.503599i	−0.368355	+	0.0236611i
$454$		0			0
$455$	−0.252531	+	0.211899i	−0.0118389	+	0.00993398i
$456$		0			0
$457$	9.54928	−	3.47565i	0.446696	−	0.162584i	−0.108871	−	0.994056i	$-0.534723\pi$
$457$	9.54928	−	3.47565i	0.446696	−	0.162584i	0.555567	+	0.831472i	$0.312501\pi$
$458$		0			0
$459$	−12.3850	+	36.0218i	−0.578085	+	1.68136i
$460$		0			0
$461$	19.9197	−	7.25019i	0.927754	−	0.337675i	0.166435	−	0.986052i	$-0.446774\pi$
$461$	19.9197	−	7.25019i	0.927754	−	0.337675i	0.761319	+	0.648377i	$0.224552\pi$
$462$		0			0
$463$	−3.72195	+	3.12308i	−0.172973	+	0.145142i	−0.725165	−	0.688576i	$-0.758236\pi$
$463$	−3.72195	+	3.12308i	−0.172973	+	0.145142i	0.552191	+	0.833718i	$0.313792\pi$
$464$		0			0
$465$	−2.84685	+	5.75392i	−0.132019	+	0.266832i
$466$		0			0
$467$	14.8078	−	25.6479i	0.685225	−	1.18684i	−0.288141	−	0.957588i	$-0.593037\pi$
$467$	14.8078	−	25.6479i	0.685225	−	1.18684i	0.973366	−	0.229256i	$-0.0736294\pi$
$468$		0			0
$469$	−17.3565	−	30.0623i	−0.801449	−	1.38815i
$470$		0			0
$471$	−21.5342	+	9.44178i	−0.992242	+	0.435054i
$472$		0			0
$473$	2.29753	+	0.836232i	0.105641	+	0.0384500i
$474$		0			0
$475$	3.33425	−	18.9095i	0.152986	−	0.867626i
$476$		0			0
$477$	9.12453	−	4.71974i	0.417784	−	0.216102i
$478$		0			0
$479$	−21.1912	−	17.7816i	−0.968253	−	0.812461i	0.0140230	−	0.999902i	$-0.495536\pi$
$479$	−21.1912	−	17.7816i	−0.968253	−	0.812461i	−0.982276	+	0.187441i	$0.939981\pi$
$480$		0			0
$481$	0.194627	+	1.10378i	0.00887423	+	0.0503283i
$482$		0			0
$483$	4.76548	+	19.5855i	0.216837	+	0.891169i
$484$		0			0
$485$	−4.59598			−0.208693
$486$		0			0
$487$	16.7022			0.756847			0.378423	−	0.925633i	$-0.376466\pi$
$487$	16.7022			0.756847			0.378423	+	0.925633i	$0.376466\pi$
$488$		0			0
$489$	8.16612	+	33.5616i	0.369285	+	1.51771i
$490$		0			0
$491$	1.17188	+	6.64605i	0.0528861	+	0.299932i	0.999765	−	0.0216569i	$-0.00689414\pi$
$491$	1.17188	+	6.64605i	0.0528861	+	0.299932i	−0.946879	+	0.321589i	$0.895783\pi$
$492$		0			0
$493$	57.7763	+	48.4801i	2.60211	+	2.18343i
$494$		0			0
$495$	0.646065	−	0.334183i	0.0290385	−	0.0150204i
$496$		0			0
$497$	−4.06079	+	23.0299i	−0.182151	+	1.03303i
$498$		0			0
$499$	26.5655	+	9.66907i	1.18924	+	0.432847i	0.859456	−	0.511210i	$-0.170803\pi$
$499$	26.5655	+	9.66907i	1.18924	+	0.432847i	0.329781	+	0.944057i	$0.393025\pi$
$500$		0			0
$501$	17.7119	−	7.76587i	0.791308	−	0.346953i
$502$		0			0
$503$	−14.6111	−	25.3071i	−0.651476	−	1.12839i	−0.982765	−	0.184860i	$-0.940817\pi$
$503$	−14.6111	−	25.3071i	−0.651476	−	1.12839i	0.331289	−	0.943529i	$-0.392517\pi$
$504$		0			0
$505$	3.52904	−	6.11248i	0.157040	−	0.272002i
$506$		0			0
$507$	9.95616	−	20.1229i	0.442169	−	0.893691i
$508$		0			0
$509$	3.85753	−	3.23685i	0.170982	−	0.143471i	−0.553281	−	0.832995i	$-0.686625\pi$
$509$	3.85753	−	3.23685i	0.170982	−	0.143471i	0.724263	+	0.689524i	$0.242180\pi$
$510$		0			0
$511$	10.5706	−	3.84737i	0.467614	−	0.170198i
$512$		0			0
$513$	−21.0727	+	4.10604i	−0.930383	+	0.181286i
$514$		0			0
$515$	−2.04740	+	0.745193i	−0.0902193	+	0.0328371i
$516$		0			0
$517$	3.52084	−	2.95433i	0.154846	−	0.129931i
$518$		0			0
$519$	37.2978	−	2.39581i	1.63719	−	0.105164i
$520$		0			0
$521$	−1.16671	+	2.02079i	−0.0511143	+	0.0885325i	−0.890450	−	0.455080i	$-0.849611\pi$
$521$	−1.16671	+	2.02079i	−0.0511143	+	0.0885325i	0.839336	+	0.543613i	$0.182944\pi$
$522$		0			0
$523$	0.325630	+	0.564007i	0.0142388	+	0.0246623i	0.873057	−	0.487618i	$-0.162134\pi$
$523$	0.325630	+	0.564007i	0.0142388	+	0.0246623i	−0.858818	+	0.512280i	$0.828801\pi$
$524$		0			0
$525$	−2.53247	+	22.8486i	−0.110526	+	0.997197i
$526$		0			0
$527$	42.9894	+	15.6469i	1.87265	+	0.681588i
$528$		0			0
$529$	−1.11062	+	6.29863i	−0.0482878	+	0.273854i
$530$		0			0
$531$	−8.52770	−	11.1737i	−0.370071	−	0.484897i
$532$		0			0
$533$	−1.25558	−	1.05356i	−0.0543854	−	0.0456347i
$534$		0			0
$535$	0.541220	+	3.06941i	0.0233990	+	0.132702i
$536$		0			0
$537$	−19.2183	+	18.3496i	−0.829332	+	0.791844i
$538$		0			0
$539$	0.472156			0.0203372
$540$		0			0
$541$	−12.1207			−0.521111			−0.260555	−	0.965459i	$-0.583906\pi$
$541$	−12.1207			−0.521111			−0.260555	+	0.965459i	$0.583906\pi$
$542$		0			0
$543$	−12.2978	−	3.60188i	−0.527749	−	0.154571i
$544$		0			0
$545$	0.726056	+	4.11767i	0.0311008	+	0.176382i
$546$		0			0
$547$	2.23516	+	1.87552i	0.0955684	+	0.0801914i	0.689320	−	0.724457i	$-0.257909\pi$
$547$	2.23516	+	1.87552i	0.0955684	+	0.0801914i	−0.593752	+	0.804648i	$0.702354\pi$
$548$		0			0
$549$	−12.7858	−	2.86953i	−0.545685	−	0.122469i
$550$		0			0
$551$	−7.38159	+	41.8631i	−0.314466	+	1.78343i
$552$		0			0
$553$	−24.2149	−	8.81349i	−1.02972	−	0.374788i
$554$		0			0
$555$	−4.77959	−	3.51413i	−0.202882	−	0.149166i
$556$		0			0
$557$	−7.24377	−	12.5466i	−0.306928	−	0.531615i	0.670761	−	0.741674i	$-0.265968\pi$
$557$	−7.24377	−	12.5466i	−0.306928	−	0.531615i	−0.977689	+	0.210059i	$0.932635\pi$
$558$		0			0
$559$	0.581988	−	1.00803i	0.0246155	−	0.0426353i
$560$		0			0
$561$	−2.87418	−	4.31367i	−0.121348	−	0.182123i
$562$		0			0
$563$	26.0712	−	21.8763i	1.09877	−	0.921977i	0.101428	−	0.994843i	$-0.467659\pi$
$563$	26.0712	−	21.8763i	1.09877	−	0.921977i	0.997342	+	0.0728661i	$0.0232146\pi$
$564$		0			0
$565$	−0.541593	+	0.197124i	−0.0227850	+	0.00829306i
$566$		0			0
$567$	24.8622	−	6.52309i	1.04412	−	0.273944i
$568$		0			0
$569$	−4.14004	+	1.50685i	−0.173559	+	0.0631705i	−0.427338	−	0.904092i	$-0.640549\pi$
$569$	−4.14004	+	1.50685i	−0.173559	+	0.0631705i	0.253779	+	0.967262i	$0.418326\pi$
$570$		0			0
$571$	−27.9533	+	23.4556i	−1.16981	+	0.981586i	−0.999992	−	0.00388952i	$-0.998762\pi$
$571$	−27.9533	+	23.4556i	−1.16981	+	0.981586i	−0.169816	+	0.985476i	$0.554317\pi$
$572$		0			0
$573$	11.8837	+	17.8356i	0.496451	+	0.745091i
$574$		0			0
$575$	9.46840	−	16.3998i	0.394860	−	0.683917i
$576$		0			0
$577$	15.2458	+	26.4066i	0.634693	+	1.09932i	0.986580	+	0.163278i	$0.0522066\pi$
$577$	15.2458	+	26.4066i	0.634693	+	1.09932i	−0.351887	+	0.936042i	$0.614460\pi$
$578$		0			0
$579$	21.7583	+	15.9975i	0.904244	+	0.664833i
$580$		0			0
$581$	−22.6185	−	8.23246i	−0.938373	−	0.341540i
$582$		0			0
$583$	−0.242750	+	1.37670i	−0.0100537	+	0.0570172i
$584$		0			0
$585$	−0.103268	−	0.330525i	−0.00426959	−	0.0136655i
$586$		0			0
$587$	1.83541	+	1.54009i	0.0757554	+	0.0635663i	0.679879	−	0.733324i	$-0.262032\pi$
$587$	1.83541	+	1.54009i	0.0757554	+	0.0635663i	−0.604124	+	0.796891i	$0.706477\pi$
$588$		0			0
$589$	4.47744	+	25.3928i	0.184490	+	1.04629i
$590$		0			0
$591$	−28.5885	−	8.37324i	−1.17597	−	0.344429i
$592$		0			0
$593$	6.03623			0.247878			0.123939	−	0.992290i	$-0.460447\pi$
$593$	6.03623			0.247878			0.123939	+	0.992290i	$0.460447\pi$
$594$		0			0
$595$	−12.4343			−0.509758
$596$		0			0
$597$	−22.2707	+	21.2640i	−0.911478	+	0.870277i
$598$		0			0
$599$	4.67557	+	26.5164i	0.191038	+	1.08343i	0.917948	+	0.396700i	$0.129845\pi$
$599$	4.67557	+	26.5164i	0.191038	+	1.08343i	−0.726910	+	0.686733i	$0.759044\pi$
$600$		0			0
$601$	−26.2747	−	22.0471i	−1.07177	−	0.899321i	−0.0765573	−	0.997065i	$-0.524393\pi$
$601$	−26.2747	−	22.0471i	−1.07177	−	0.899321i	−0.995212	+	0.0977443i	$0.968837\pi$
$602$		0			0
$603$	36.1640	−	4.66521i	1.47271	−	0.189982i
$604$		0			0
$605$	1.11726	−	6.33632i	0.0454232	−	0.257608i
$606$		0			0
$607$	−10.9170	−	3.97345i	−0.443106	−	0.161277i	0.110825	−	0.993840i	$-0.464651\pi$
$607$	−10.9170	−	3.97345i	−0.443106	−	0.161277i	−0.553931	+	0.832563i	$0.686873\pi$
$608$		0			0
$609$	5.60657	−	50.5839i	0.227190	−	2.04976i
$610$		0			0
$611$	−1.09403	−	1.89492i	−0.0442599	−	0.0766604i
$612$		0			0
$613$	18.3050	−	31.7051i	0.739330	−	1.28056i	−0.213467	−	0.976950i	$-0.568475\pi$
$613$	18.3050	−	31.7051i	0.739330	−	1.28056i	0.952797	−	0.303608i	$-0.0981912\pi$
$614$		0			0
$615$	8.65758	−	0.556117i	0.349107	−	0.0224248i
$616$		0			0
$617$	−15.3365	+	12.8689i	−0.617425	+	0.518081i	−0.896993	−	0.442045i	$-0.854253\pi$
$617$	−15.3365	+	12.8689i	−0.617425	+	0.518081i	0.279568	+	0.960126i	$0.409809\pi$
$618$		0			0
$619$	19.1186	−	6.95860i	0.768442	−	0.279690i	0.0720971	−	0.997398i	$-0.477031\pi$
$619$	19.1186	−	6.95860i	0.768442	−	0.279690i	0.696344	+	0.717708i	$0.254809\pi$
$620$		0			0
$621$	−20.9142	−	3.30277i	−0.839259	−	0.132536i
$622$		0			0
$623$	12.7997	−	4.65870i	0.512808	−	0.186647i
$624$		0			0
$625$	15.1933	−	12.7487i	0.607731	−	0.509947i
$626$		0			0
$627$	1.29556	−	2.61853i	0.0517398	−	0.104574i
$628$		0			0
$629$	−21.1380	+	36.6121i	−0.842828	+	1.45982i
$630$		0			0
$631$	−20.9873	−	36.3512i	−0.835493	−	1.44712i	−0.893628	−	0.448808i	$-0.851849\pi$
$631$	−20.9873	−	36.3512i	−0.835493	−	1.44712i	0.0581353	−	0.998309i	$-0.481485\pi$
$632$		0			0
$633$	29.9502	−	13.1318i	1.19041	−	0.521943i
$634$		0			0
$635$	4.91725	+	1.78973i	0.195135	+	0.0710234i
$636$		0			0
$637$	0.0390324	−	0.221364i	0.00154652	−	0.00877074i
$638$		0			0
$639$	−20.6830	−	13.2525i	−0.818208	−	0.524259i
$640$		0			0
$641$	−17.2085	−	14.4396i	−0.679693	−	0.570330i	0.236224	−	0.971699i	$-0.424090\pi$
$641$	−17.2085	−	14.4396i	−0.679693	−	0.570330i	−0.915917	+	0.401369i	$0.868535\pi$
$642$		0			0
$643$	−0.660834	−	3.74778i	−0.0260608	−	0.147798i	0.969001	−	0.247058i	$-0.0794637\pi$
$643$	−0.660834	−	3.74778i	−0.0260608	−	0.147798i	−0.995062	+	0.0992596i	$0.968353\pi$
$644$		0			0
$645$	1.45655	+	5.98623i	0.0573518	+	0.235708i
$646$		0			0
$647$	19.6269			0.771613			0.385807	−	0.922580i	$-0.373923\pi$
$647$	19.6269			0.771613			0.385807	+	0.922580i	$0.373923\pi$
$648$		0			0
$649$	1.91275			0.0750821
$650$		0			0
$651$	−7.29839	−	29.9953i	−0.286047	−	1.17561i
$652$		0			0
$653$	−6.83089	−	38.7399i	−0.267314	−	1.51601i	−0.762365	−	0.647147i	$-0.775962\pi$
$653$	−6.83089	−	38.7399i	−0.267314	−	1.51601i	0.495052	−	0.868864i	$-0.335149\pi$
$654$		0			0
$655$	2.17550	+	1.82547i	0.0850040	+	0.0713268i
$656$		0			0
$657$	−0.546187	+	11.8036i	−0.0213088	+	0.460503i
$658$		0			0
$659$	−3.88186	+	22.0151i	−0.151216	+	0.857586i	0.810949	+	0.585117i	$0.198951\pi$
$659$	−3.88186	+	22.0151i	−0.151216	+	0.857586i	−0.962164	+	0.272469i	$0.912160\pi$
$660$		0			0
$661$	−30.5051	−	11.1030i	−1.18651	−	0.431855i	−0.328014	−	0.944673i	$-0.606379\pi$
$661$	−30.5051	−	11.1030i	−1.18651	−	0.431855i	−0.858497	+	0.512818i	$0.828602\pi$
$662$		0			0
$663$	−2.26000	+	0.990912i	−0.0877713	+	0.0384838i
$664$		0			0
$665$	−3.50410	−	6.06929i	−0.135883	−	0.235357i
$666$		0			0
$667$	−20.9618	+	36.3069i	−0.811644	+	1.40581i
$668$		0			0
$669$	1.14685	−	2.31796i	0.0443398	−	0.0896176i
$670$		0			0
$671$	1.36599	−	1.14620i	0.0527335	−	0.0442487i
$672$		0			0
$673$	−20.7211	+	7.54186i	−0.798739	+	0.290717i	−0.708964	−	0.705245i	$-0.750837\pi$
$673$	−20.7211	+	7.54186i	−0.798739	+	0.290717i	−0.0897752	+	0.995962i	$0.528615\pi$
$674$		0			0
$675$	−21.1255	−	11.6976i	−0.813123	−	0.450239i
$676$		0			0
$677$	31.1471	−	11.3366i	1.19708	−	0.435701i	0.334875	−	0.942263i	$-0.391306\pi$
$677$	31.1471	−	11.3366i	1.19708	−	0.435701i	0.862204	+	0.506562i	$0.169084\pi$
$678$		0			0
$679$	16.9302	−	14.2062i	0.649723	−	0.545182i
$680$		0			0
$681$	33.7081	−	2.16523i	1.29170	−	0.0829718i
$682$		0			0
$683$	−7.88787	+	13.6622i	−0.301821	+	0.522769i	−0.976548	−	0.215298i	$-0.930928\pi$
$683$	−7.88787	+	13.6622i	−0.301821	+	0.522769i	0.674727	+	0.738067i	$0.264261\pi$
$684$		0			0
$685$	4.31441	+	7.47277i	0.164845	+	0.285520i
$686$		0			0
$687$	−0.00604652	+	0.0545533i	−0.000230689	+	0.00208134i
$688$		0			0
$689$	0.625380	+	0.227620i	0.0238251	+	0.00867161i
$690$		0			0
$691$	−7.38751	+	41.8967i	−0.281034	+	1.59382i	0.438082	+	0.898935i	$0.355658\pi$
$691$	−7.38751	+	41.8967i	−0.281034	+	1.59382i	−0.719116	+	0.694890i	$0.755453\pi$
$692$		0			0
$693$	−1.34696	+	3.22801i	−0.0511666	+	0.122622i
$694$		0			0
$695$	−6.82695	−	5.72849i	−0.258961	−	0.217294i
$696$		0			0
$697$	−10.7355	−	60.8842i	−0.406637	−	2.30615i
$698$		0			0
$699$	16.8265	−	16.0659i	0.636436	−	0.607667i
$700$		0			0
$701$	3.93434			0.148598			0.0742990	−	0.997236i	$-0.476328\pi$
$701$	3.93434			0.148598			0.0742990	+	0.997236i	$0.476328\pi$
$702$		0			0
$703$	−23.8275			−0.898672
$704$		0			0
$705$	11.1145	+	3.25529i	0.418595	+	0.122601i
$706$		0			0
$707$	5.89369	+	33.4248i	0.221655	+	1.25707i
$708$		0			0
$709$	−25.5308	−	21.4229i	−0.958829	−	0.804553i	0.0219334	−	0.999759i	$-0.493018\pi$
$709$	−25.5308	−	21.4229i	−0.958829	−	0.804553i	−0.980762	+	0.195207i	$0.937462\pi$
$710$		0			0
$711$	18.3392	−	19.9092i	0.687772	−	0.746655i
$712$		0			0
$713$	−4.41579	+	25.0432i	−0.165373	+	0.937875i
$714$		0			0
$715$	0.0442802	+	0.0161167i	0.00165599	+	0.000602729i
$716$		0			0
$717$	−21.6271	−	15.9010i	−0.807678	−	0.593834i
$718$		0			0
$719$	16.3373	+	28.2970i	0.609277	+	1.05530i	0.991360	+	0.131171i	$0.0418736\pi$
$719$	16.3373	+	28.2970i	0.609277	+	1.05530i	−0.382083	+	0.924128i	$0.624793\pi$
$720$		0			0
$721$	5.23863	−	9.07358i	0.195097	−	0.337918i
$722$		0			0
$723$	−22.5644	−	33.8654i	−0.839178	−	1.25947i
$724$		0			0
$725$	−36.6270	+	30.7337i	−1.36029	+	1.14142i
$726$		0			0
$727$	−25.3122	+	9.21290i	−0.938778	+	0.341687i	−0.765683	−	0.643218i	$-0.777599\pi$
$727$	−25.3122	+	9.21290i	−0.938778	+	0.341687i	−0.173095	+	0.984905i	$0.555377\pi$
$728$		0			0
$729$	−3.73342	+	26.7406i	−0.138275	+	0.990394i
$730$		0			0
$731$	41.2564	−	15.0161i	1.52592	−	0.555391i
$732$		0			0
$733$	−28.9337	+	24.2783i	−1.06869	+	0.896738i	−0.994933	−	0.100538i	$-0.967944\pi$
$733$	−28.9337	+	24.2783i	−1.06869	+	0.896738i	−0.0737575	+	0.997276i	$0.523499\pi$
$734$		0			0
$735$	0.659696	+	0.990096i	0.0243333	+	0.0365203i
$736$		0			0
$737$	−2.48099	+	4.29720i	−0.0913883	+	0.158289i
$738$		0			0
$739$	1.45061	+	2.51253i	0.0533615	+	0.0924248i	0.891472	−	0.453075i	$-0.149673\pi$
$739$	1.45061	+	2.51253i	0.0533615	+	0.0924248i	−0.838111	+	0.545500i	$0.816340\pi$
$740$		0			0
$741$	−1.12056	−	0.823875i	−0.0411648	−	0.0302658i
$742$		0			0
$743$	7.34852	+	2.67464i	0.269591	+	0.0981231i	0.473279	−	0.880913i	$-0.343070\pi$
$743$	7.34852	+	2.67464i	0.269591	+	0.0981231i	−0.203687	+	0.979036i	$0.565293\pi$
$744$		0			0
$745$	−0.427846	+	2.42643i	−0.0156751	+	0.0888977i
$746$		0			0
$747$	17.1301	−	18.5967i	0.626759	−	0.680418i
$748$		0			0
$749$	−11.4812	−	9.63389i	−0.419515	−	0.352015i
$750$		0			0
$751$	6.94180	+	39.3689i	0.253310	+	1.43659i	0.800374	+	0.599501i	$0.204634\pi$
$751$	6.94180	+	39.3689i	0.253310	+	1.43659i	−0.547064	+	0.837091i	$0.684254\pi$
$752$		0			0
$753$	−17.5600	−	5.14312i	−0.639922	−	0.187426i
$754$		0			0
$755$	2.69384			0.0980389
$756$		0			0
$757$	29.6529			1.07775			0.538877	−	0.842384i	$-0.318849\pi$
$757$	29.6529			1.07775			0.538877	+	0.842384i	$0.318849\pi$
$758$		0			0
$759$	2.08393	−	1.98973i	0.0756418	−	0.0722226i
$760$		0			0
$761$	0.306862	+	1.74030i	0.0111237	+	0.0630859i	0.989864	−	0.142016i	$-0.0453585\pi$
$761$	0.306862	+	1.74030i	0.0111237	+	0.0630859i	−0.978741	+	0.205102i	$0.934247\pi$
$762$		0			0
$763$	−15.4023	−	12.9240i	−0.557599	−	0.467882i
$764$		0			0
$765$	5.02983	−	12.0541i	0.181854	−	0.435817i
$766$		0			0
$767$	0.158124	−	0.896765i	0.00570952	−	0.0323803i
$768$		0			0
$769$	44.8432	+	16.3216i	1.61709	+	0.588571i	0.982824	−	0.184546i	$-0.0590816\pi$
$769$	44.8432	+	16.3216i	1.61709	+	0.588571i	0.634263	+	0.773118i	$0.281304\pi$
$770$		0			0
$771$	−2.29693	+	20.7235i	−0.0827218	+	0.746338i
$772$		0			0
$773$	14.7370	+	25.5253i	0.530054	+	0.918081i	0.999385	+	0.0350584i	$0.0111617\pi$
$773$	14.7370	+	25.5253i	0.530054	+	0.918081i	−0.469331	+	0.883022i	$0.655505\pi$
$774$		0			0
$775$	−14.5010	+	25.1164i	−0.520890	+	0.902208i
$776$		0			0
$777$	28.4688	−	1.82868i	1.02131	−	0.0656036i
$778$		0			0
$779$	26.6926	−	22.3978i	0.956362	−	0.802483i
$780$		0			0
$781$	3.14115	−	1.14329i	0.112399	−	0.0409100i
$782$		0			0
$783$	46.7692	+	25.8969i	1.67139	+	0.925478i
$784$		0			0
$785$	7.57633	−	2.75756i	0.270411	−	0.0984214i
$786$		0			0
$787$	−14.2270	+	11.9379i	−0.507137	+	0.425539i	−0.860121	−	0.510091i	$-0.829612\pi$
$787$	−14.2270	+	11.9379i	−0.507137	+	0.425539i	0.352983	+	0.935630i	$0.385167\pi$
$788$		0			0
$789$	−2.72994	+	5.51763i	−0.0971884	+	0.196433i
$790$		0			0
$791$	1.38576	−	2.40021i	0.0492720	−	0.0853415i
$792$		0			0
$793$	−0.424456	−	0.735180i	−0.0150729	−	0.0261070i
$794$		0			0
$795$	−3.22607	+	1.41449i	−0.114417	+	0.0501668i
$796$		0			0
$797$	−18.8975	−	6.87813i	−0.669384	−	0.243636i	−0.0151012	−	0.999886i	$-0.504807\pi$
$797$	−18.8975	−	6.87813i	−0.669384	−	0.243636i	−0.654282	+	0.756250i	$0.727029\pi$
$798$		0			0
$799$	14.3315	−	81.2782i	0.507013	−	2.87541i
$800$		0			0
$801$	−0.661366	+	14.2928i	−0.0233682	+	0.505010i
$802$		0			0
$803$	−1.23177	−	1.03357i	−0.0434681	−	0.0364741i
$804$		0			0
$805$	−1.20021	−	6.80671i	−0.0423017	−	0.239905i
$806$		0			0
$807$	10.5890	+	43.5194i	0.372752	+	1.53196i
$808$		0			0
$809$	36.1888			1.27233			0.636165	−	0.771553i	$-0.280520\pi$
$809$	36.1888			1.27233			0.636165	+	0.771553i	$0.280520\pi$
$810$		0			0
$811$	−10.3479			−0.363364			−0.181682	−	0.983357i	$-0.558154\pi$
$811$	−10.3479			−0.363364			−0.181682	+	0.983357i	$0.558154\pi$
$812$		0			0
$813$	−1.17289	−	4.82041i	−0.0411350	−	0.169059i
$814$		0			0
$815$	−2.05667	−	11.6640i	−0.0720420	−	0.408571i
$816$		0			0
$817$	18.9559	+	15.9059i	0.663182	+	0.556476i
$818$		0			0
$819$	1.40206	+	0.898355i	0.0489918	+	0.0313911i
$820$		0			0
$821$	−0.324743	+	1.84171i	−0.0113336	+	0.0642760i	−0.989950	−	0.141418i	$-0.954834\pi$
$821$	−0.324743	+	1.84171i	−0.0113336	+	0.0642760i	0.978616	+	0.205694i	$0.0659451\pi$
$822$		0			0
$823$	21.1741	+	7.70673i	0.738081	+	0.268640i	0.683582	−	0.729874i	$-0.260421\pi$
$823$	21.1741	+	7.70673i	0.738081	+	0.268640i	0.0544998	+	0.998514i	$0.482644\pi$
$824$		0			0
$825$	3.00948	−	1.31952i	0.104777	−	0.0459400i
$826$		0			0
$827$	12.1614	+	21.0641i	0.422892	+	0.732470i	0.996221	−	0.0868548i	$-0.0276816\pi$
$827$	12.1614	+	21.0641i	0.422892	+	0.732470i	−0.573329	+	0.819325i	$0.694348\pi$
$828$		0			0
$829$	−14.9600	+	25.9116i	−0.519584	+	0.899946i	0.480157	+	0.877183i	$0.340580\pi$
$829$	−14.9600	+	25.9116i	−0.519584	+	0.899946i	−0.999741	+	0.0227630i	$0.992754\pi$
$830$		0			0
$831$	8.69614	−	17.5762i	0.301666	−	0.609713i
$832$		0			0
$833$	6.49486	−	5.44984i	0.225034	−	0.188826i
$834$		0			0
$835$	−6.23153	+	2.26809i	−0.215651	+	0.0784906i
$836$		0			0
$837$	32.0304	+	5.05823i	1.10713	+	0.174838i
$838$		0			0
$839$	−22.7505	+	8.28051i	−0.785435	+	0.285875i	−0.703437	−	0.710757i	$-0.748352\pi$
$839$	−22.7505	+	8.28051i	−0.785435	+	0.285875i	−0.0819981	+	0.996632i	$0.526130\pi$
$840$		0			0
$841$	58.8721	−	49.3995i	2.03007	−	1.70343i
$842$		0			0
$843$	−35.7520	+	2.29652i	−1.23136	+	0.0790963i
$844$		0			0
$845$	−3.84922	+	6.66704i	−0.132417	+	0.229353i
$846$		0			0
$847$	15.4698	+	26.7946i	0.531550	+	0.920672i
$848$		0			0
$849$	−0.293929	+	2.65190i	−0.0100876	+	0.0910131i
$850$		0			0
$851$	−22.0822	−	8.03728i	−0.756969	−	0.275514i
$852$		0			0
$853$	−3.43429	+	19.4768i	−0.117588	+	0.666875i	0.867848	+	0.496829i	$0.165502\pi$
$853$	−3.43429	+	19.4768i	−0.117588	+	0.666875i	−0.985436	+	0.170045i	$0.945609\pi$
$854$		0			0
$855$	7.30114	−	0.941859i	0.249694	−	0.0322109i
$856$		0			0
$857$	−12.7880	−	10.7304i	−0.436828	−	0.366543i	0.397693	−	0.917519i	$-0.369811\pi$
$857$	−12.7880	−	10.7304i	−0.436828	−	0.366543i	−0.834521	+	0.550976i	$0.814256\pi$
$858$		0			0
$859$	1.00085	+	5.67610i	0.0341485	+	0.193666i	0.997110	−	0.0759737i	$-0.0242065\pi$
$859$	1.00085	+	5.67610i	0.0341485	+	0.193666i	−0.962961	+	0.269640i	$0.913095\pi$
$860$		0			0
$861$	−30.1730	+	28.8091i	−1.02829	+	0.981811i
$862$		0			0
$863$	−56.2504			−1.91478			−0.957392	−	0.288791i	$-0.906747\pi$
$863$	−56.2504			−1.91478			−0.957392	+	0.288791i	$0.906747\pi$
$864$		0			0
$865$	−12.8156			−0.435744
$866$		0			0
$867$	−61.0690	−	17.8864i	−2.07401	−	0.607453i
$868$		0			0
$869$	0.639630	+	3.62752i	0.0216980	+	0.123055i
$870$		0			0
$871$	1.80958	+	1.51842i	0.0613152	+	0.0514496i
$872$		0			0
$873$	6.92328	+	22.1591i	0.234318	+	0.749971i
$874$		0			0
$875$	2.84152	−	16.1151i	0.0960610	−	0.544789i
$876$		0			0
$877$	13.7638	+	5.00963i	0.464772	+	0.169163i	0.563783	−	0.825923i	$-0.309346\pi$
$877$	13.7638	+	5.00963i	0.464772	+	0.169163i	−0.0990107	+	0.995086i	$0.531568\pi$
$878$		0			0
$879$	7.55400	+	5.55397i	0.254790	+	0.187331i
$880$		0			0
$881$	0.282288	+	0.488938i	0.00951053	+	0.0164727i	0.870742	−	0.491741i	$-0.163639\pi$
$881$	0.282288	+	0.488938i	0.00951053	+	0.0164727i	−0.861231	+	0.508214i	$0.830306\pi$
$882$		0			0
$883$	10.7764	−	18.6653i	0.362656	−	0.628138i	−0.625741	−	0.780031i	$-0.715203\pi$
$883$	10.7764	−	18.6653i	0.362656	−	0.628138i	0.988397	+	0.151892i	$0.0485367\pi$
$884$		0			0
$885$	2.67250	+	4.01098i	0.0898349	+	0.134828i
$886$		0			0
$887$	−37.9854	+	31.8735i	−1.27542	+	1.07021i	−0.281566	+	0.959542i	$0.590854\pi$
$887$	−37.9854	+	31.8735i	−1.27542	+	1.07021i	−0.993858	+	0.110665i	$0.964702\pi$
$888$		0			0
$889$	−23.6457	+	8.60635i	−0.793053	+	0.288648i
$890$		0			0
$891$	−2.58445	−	2.61153i	−0.0865822	−	0.0874897i
$892$		0			0
$893$	43.7112	−	15.9096i	1.46274	−	0.532393i
$894$		0			0
$895$	6.97967	−	5.85663i	0.233304	−	0.195766i
$896$		0			0
$897$	−0.760580	−	1.14151i	−0.0253950	−	0.0381138i
$898$		0			0
$899$	32.1032	−	55.6044i	1.07070	−	1.85451i
$900$		0			0
$901$	12.5513	+	21.7395i	0.418145	+	0.724249i
$902$		0			0
$903$	−23.8689	−	17.5493i	−0.794308	−	0.584004i
$904$		0			0
$905$	4.12902	+	1.50284i	0.137253	+	0.0499562i
$906$		0			0
$907$	3.72207	−	21.1089i	0.123589	−	0.700910i	−0.858546	−	0.512736i	$-0.828632\pi$
$907$	3.72207	−	21.1089i	0.123589	−	0.700910i	0.982136	−	0.188174i	$-0.0602569\pi$
$908$		0			0
$909$	−34.7867	−	7.80722i	−1.15380	−	0.258949i
$910$		0			0
$911$	−2.62795	−	2.20511i	−0.0870679	−	0.0730586i	0.598215	−	0.801336i	$-0.295877\pi$
$911$	−2.62795	−	2.20511i	−0.0870679	−	0.0730586i	−0.685283	+	0.728277i	$0.740321\pi$
$912$		0			0
$913$	0.597462	+	3.38837i	0.0197731	+	0.112139i
$914$		0			0
$915$	4.31211	+	1.26297i	0.142554	+	0.0417524i
$916$		0			0
$917$	−13.6564			−0.450975
$918$		0			0
$919$	−23.1771			−0.764542			−0.382271	−	0.924050i	$-0.624858\pi$
$919$	−23.1771			−0.764542			−0.382271	+	0.924050i	$0.624858\pi$
$920$		0			0
$921$	15.2089	−	14.5214i	0.501149	−	0.478496i
$922$		0			0
$923$	−0.276339	−	1.56720i	−0.00909580	−	0.0515849i
$924$		0			0
$925$	−20.5305	−	17.2271i	−0.675039	−	0.566425i
$926$		0			0
$927$	6.67703	+	8.74880i	0.219302	+	0.287348i
$928$		0			0
$929$	10.0619	−	57.0639i	0.330121	−	1.87221i	−0.140809	−	0.990037i	$-0.544970\pi$
$929$	10.0619	−	57.0639i	0.330121	−	1.87221i	0.470930	−	0.882171i	$-0.343918\pi$
$930$		0			0
$931$	4.49041	+	1.63438i	0.147167	+	0.0535645i
$932$		0			0
$933$	−2.31611	+	20.8965i	−0.0758260	+	0.684122i
$934$		0			0
$935$	0.888700	+	1.53927i	0.0290636	+	0.0503396i
$936$		0			0
$937$	−13.3543	+	23.1304i	−0.436267	+	0.755636i	−0.997398	−	0.0720904i	$-0.977033\pi$
$937$	−13.3543	+	23.1304i	−0.436267	+	0.755636i	0.561131	+	0.827727i	$0.310366\pi$
$938$		0			0
$939$	1.79588	−	0.115358i	0.0586064	−	0.00376456i
$940$		0			0
$941$	−10.3206	+	8.66005i	−0.336444	+	0.282310i	−0.795319	−	0.606191i	$-0.792697\pi$
$941$	−10.3206	+	8.66005i	−0.336444	+	0.282310i	0.458876	+	0.888500i	$0.348252\pi$
$942$		0			0
$943$	32.2925	−	11.7535i	1.05159	−	0.382747i
$944$		0			0
$945$	−8.65101	+	1.68566i	−0.281417	+	0.0548344i
$946$		0			0
$947$	−3.71945	+	1.35377i	−0.120866	+	0.0439916i	−0.401745	−	0.915752i	$-0.631596\pi$
$947$	−3.71945	+	1.35377i	−0.120866	+	0.0439916i	0.280879	+	0.959743i	$0.409374\pi$
$948$		0			0
$949$	−0.586404	+	0.492052i	−0.0190355	+	0.0159727i
$950$		0			0
$951$	−13.3358	+	26.9536i	−0.432442	+	0.874032i
$952$		0			0
$953$	−5.52400	+	9.56785i	−0.178940	+	0.309933i	−0.941518	−	0.336963i	$-0.890600\pi$
$953$	−5.52400	+	9.56785i	−0.178940	+	0.309933i	0.762578	+	0.646897i	$0.223933\pi$
$954$		0			0
$955$	−3.67447	−	6.36437i	−0.118903	−	0.205946i
$956$		0			0
$957$	−6.66260	+	2.92125i	−0.215371	+	0.0944308i
$958$		0			0
$959$	−38.9913	−	14.1917i	−1.25909	−	0.458273i
$960$		0			0
$961$	1.37974	−	7.82489i	0.0445077	−	0.252416i
$962$		0			0
$963$	13.9836	−	7.23312i	0.450614	−	0.233084i
$964$		0			0
$965$	−7.09385	−	5.95245i	−0.228359	−	0.191616i
$966$		0			0
$967$	−3.75988	−	21.3233i	−0.120910	−	0.685712i	−0.983654	−	0.180071i	$-0.942367\pi$
$967$	−3.75988	−	21.3233i	−0.120910	−	0.685712i	0.862744	−	0.505641i	$-0.168744\pi$
$968$		0			0
$969$	−12.4028	−	50.9739i	−0.398436	−	1.63752i
$970$		0			0
$971$	−2.69387			−0.0864503			−0.0432252	−	0.999065i	$-0.513763\pi$
$971$	−2.69387			−0.0864503			−0.0432252	+	0.999065i	$0.513763\pi$
$972$		0			0
$973$	42.8552			1.37387
$974$		0			0
$975$	−0.369851	−	1.52003i	−0.0118447	−	0.0486800i
$976$		0			0
$977$	−7.14808	−	40.5388i	−0.228687	−	1.29695i	−0.855509	−	0.517788i	$-0.826756\pi$
$977$	−7.14808	−	40.5388i	−0.228687	−	1.29695i	0.626822	−	0.779163i	$-0.284355\pi$
$978$		0			0
$979$	−1.49152	−	1.25153i	−0.0476692	−	0.0399992i
$980$		0			0
$981$	18.7592	−	9.70336i	0.598936	−	0.309805i
$982$		0			0
$983$	2.66866	−	15.1347i	0.0851170	−	0.482722i	−0.912214	−	0.409713i	$-0.865629\pi$
$983$	2.66866	−	15.1347i	0.0851170	−	0.482722i	0.997331	−	0.0730090i	$-0.0232602\pi$
$984$		0			0
$985$	9.59868	+	3.49363i	0.305839	+	0.111316i
$986$		0			0
$987$	−51.0044	+	22.3632i	−1.62349	+	0.711828i
$988$		0			0
$989$	12.2022	+	21.1348i	0.388008	+	0.672049i
$990$		0			0
$991$	5.77326	−	9.99957i	0.183394	−	0.317647i	−0.759640	−	0.650343i	$-0.774625\pi$
$991$	5.77326	−	9.99957i	0.183394	−	0.317647i	0.943034	+	0.332696i	$0.107958\pi$
$992$		0			0
$993$	−1.79288	+	3.62368i	−0.0568952	+	0.114994i
$994$		0			0
$995$	8.08821	−	6.78681i	0.256413	−	0.215156i
$996$		0			0
$997$	4.11238	−	1.49678i	0.130240	−	0.0474036i	−0.276078	−	0.961135i	$-0.589035\pi$
$997$	4.11238	−	1.49678i	0.130240	−	0.0474036i	0.406318	+	0.913732i	$0.366813\pi$
$998$		0			0
$999$	−9.74316	+	28.3379i	−0.308260	+	0.896572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.2.i.a.61.2	✓	18
3.2	odd	2		324.2.i.a.181.2		18
4.3	odd	2		432.2.u.d.385.2		18
9.2	odd	6		972.2.i.b.865.2		18
9.4	even	3		972.2.i.a.217.2		18
9.5	odd	6		972.2.i.d.217.2		18
9.7	even	3		972.2.i.c.865.2		18
27.2	odd	18		2916.2.a.c.1.6		9
27.4	even	9	inner	108.2.i.a.85.2	yes	18
27.5	odd	18		972.2.i.d.757.2		18
27.7	even	9		2916.2.e.c.1945.6		18
27.11	odd	18		2916.2.e.d.973.4		18
27.13	even	9		972.2.i.c.109.2		18
27.14	odd	18		972.2.i.b.109.2		18
27.16	even	9		2916.2.e.c.973.6		18
27.20	odd	18		2916.2.e.d.1945.4		18
27.22	even	9		972.2.i.a.757.2		18
27.23	odd	18		324.2.i.a.145.2		18
27.25	even	9		2916.2.a.d.1.4		9
108.31	odd	18		432.2.u.d.193.2		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.i.a.61.2	✓	18	1.1	even	1	trivial
108.2.i.a.85.2	yes	18	27.4	even	9	inner
324.2.i.a.145.2		18	27.23	odd	18
324.2.i.a.181.2		18	3.2	odd	2
432.2.u.d.193.2		18	108.31	odd	18
432.2.u.d.385.2		18	4.3	odd	2
972.2.i.a.217.2		18	9.4	even	3
972.2.i.a.757.2		18	27.22	even	9
972.2.i.b.109.2		18	27.14	odd	18
972.2.i.b.865.2		18	9.2	odd	6
972.2.i.c.109.2		18	27.13	even	9
972.2.i.c.865.2		18	9.7	even	3
972.2.i.d.217.2		18	9.5	odd	6
972.2.i.d.757.2		18	27.5	odd	18
2916.2.a.c.1.6		9	27.2	odd	18
2916.2.a.d.1.4		9	27.25	even	9
2916.2.e.c.973.6		18	27.16	even	9
2916.2.e.c.1945.6		18	27.7	even	9
2916.2.e.d.973.4		18	27.11	odd	18
2916.2.e.d.1945.4		18	27.20	odd	18

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	108.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.409491 + 1.68295i) q^{3} +(-0.103132 - 0.584890i) q^{5} +(2.18780 + 1.83578i) q^{7} +(-2.66463 + 1.37830i) q^{9} +O(q^{10})\)	\(q+(0.409491 + 1.68295i) q^{3} +(-0.103132 - 0.584890i) q^{5} +(2.18780 + 1.83578i) q^{7} +(-2.66463 + 1.37830i) q^{9} +(0.0708902 - 0.402038i) q^{11} +(-0.182629 - 0.0664716i) q^{13} +(0.942109 - 0.413073i) q^{15} +(-3.66536 - 6.34858i) q^{17} +(2.06586 - 3.57817i) q^{19} +(-2.19364 + 4.43369i) q^{21} +(3.12150 - 2.61925i) q^{23} +(4.36700 - 1.58946i) q^{25} +(-3.41076 - 3.92004i) q^{27} +(-9.66797 + 3.51885i) q^{29} +(-4.78061 + 4.01141i) q^{31} +(0.705639 - 0.0453265i) q^{33} +(0.848099 - 1.46895i) q^{35} +(-2.88349 - 4.99435i) q^{37} +(0.0370833 - 0.334575i) q^{39} +(7.92488 + 2.88442i) q^{41} +(-1.03999 + 5.89808i) q^{43} +(1.08097 + 1.41637i) q^{45} +(8.62443 + 7.23675i) q^{47} +(0.200835 + 1.13899i) q^{49} +(9.18341 - 8.76830i) q^{51} -3.42431 q^{53} -0.242459 q^{55} +(6.86783 + 2.01150i) q^{57} +(0.813604 + 4.61418i) q^{59} +(3.34605 + 2.80767i) q^{61} +(-8.35995 - 1.87623i) q^{63} +(-0.0200437 + 0.113673i) q^{65} +(-11.4215 - 4.15710i) q^{67} +(5.68628 + 4.18076i) q^{69} +(4.09409 + 7.09117i) q^{71} +(1.96938 - 3.41106i) q^{73} +(4.46323 + 6.69857i) q^{75} +(0.893148 - 0.749440i) q^{77} +(-8.47868 + 3.08599i) q^{79} +(5.20055 - 7.34536i) q^{81} +(-7.91972 + 2.88254i) q^{83} +(-3.33521 + 2.79857i) q^{85} +(-9.88100 - 14.8298i) q^{87} +(2.38468 - 4.13038i) q^{89} +(-0.277529 - 0.480694i) q^{91} +(-8.70861 - 6.40288i) q^{93} +(-2.30589 - 0.839276i) q^{95} +(1.34377 - 7.62091i) q^{97} +(0.365235 + 1.16899i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 18 * q + 3 * q^5 + 6 * q^9	\( 18 q + 3 q^{5} + 6 q^{9} + 3 q^{11} - 9 q^{15} - 12 q^{17} - 30 q^{21} - 30 q^{23} + 9 q^{25} - 27 q^{27} - 24 q^{29} + 9 q^{31} - 18 q^{33} - 21 q^{35} + 3 q^{39} + 21 q^{41} - 9 q^{43} + 45 q^{45} + 45 q^{47} - 18 q^{49} + 63 q^{51} + 66 q^{53} + 54 q^{57} + 60 q^{59} - 18 q^{61} + 57 q^{63} + 33 q^{65} - 27 q^{67} - 9 q^{69} - 12 q^{71} + 9 q^{73} - 33 q^{75} - 75 q^{77} - 36 q^{79} - 54 q^{81} - 45 q^{83} - 36 q^{85} - 63 q^{87} - 48 q^{89} + 9 q^{91} - 33 q^{93} + 6 q^{95} - 27 q^{97} + 27 q^{99}+O(q^{100}) \) 18 * q + 3 * q^5 + 6 * q^9 + 3 * q^11 - 9 * q^15 - 12 * q^17 - 30 * q^21 - 30 * q^23 + 9 * q^25 - 27 * q^27 - 24 * q^29 + 9 * q^31 - 18 * q^33 - 21 * q^35 + 3 * q^39 + 21 * q^41 - 9 * q^43 + 45 * q^45 + 45 * q^47 - 18 * q^49 + 63 * q^51 + 66 * q^53 + 54 * q^57 + 60 * q^59 - 18 * q^61 + 57 * q^63 + 33 * q^65 - 27 * q^67 - 9 * q^69 - 12 * q^71 + 9 * q^73 - 33 * q^75 - 75 * q^77 - 36 * q^79 - 54 * q^81 - 45 * q^83 - 36 * q^85 - 63 * q^87 - 48 * q^89 + 9 * q^91 - 33 * q^93 + 6 * q^95 - 27 * q^97 + 27 * q^99

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