LMFDB - Embedded newform 432.2.u.c.193.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(49,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("432.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (of order $9$, degree $6$, not 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.2
Root			$0.500000 - 1.27297i$ of defining polynomial
Character	$\chi$	$=$	432.193
Dual form			432.2.u.c.385.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.68842 + 0.386327i) q^{3} +(-0.477505 + 2.70806i) q^{5} +(-1.82076 + 1.52780i) q^{7} +(2.70150 + 1.30456i) q^{9} +(0.0434396 + 0.246358i) q^{11} +(-2.45446 + 0.893351i) q^{13} +(-1.85243 + 4.38787i) q^{15} +(0.146688 - 0.254072i) q^{17} +(-1.39237 - 2.41166i) q^{19} +(-3.66443 + 1.87615i) q^{21} +(5.12472 + 4.30015i) q^{23} +(-2.40714 - 0.876128i) q^{25} +(4.05728 + 3.24631i) q^{27} +(0.333645 + 0.121437i) q^{29} +(-2.11847 - 1.77761i) q^{31} +(-0.0218307 + 0.432738i) q^{33} +(-3.26796 - 5.66027i) q^{35} +(3.49619 - 6.05558i) q^{37} +(-4.48928 + 0.560124i) q^{39} +(9.13156 - 3.32362i) q^{41} +(-0.0452712 - 0.256746i) q^{43} +(-4.82282 + 6.69291i) q^{45} +(8.75249 - 7.34421i) q^{47} +(-0.234540 + 1.33014i) q^{49} +(0.345826 - 0.372309i) q^{51} +5.43137 q^{53} -0.687897 q^{55} +(-1.41922 - 4.60980i) q^{57} +(-1.03788 + 5.88612i) q^{59} +(-9.07515 + 7.61495i) q^{61} +(-6.91190 + 1.75206i) q^{63} +(-1.24723 - 7.07342i) q^{65} +(1.70113 - 0.619160i) q^{67} +(6.99139 + 9.24026i) q^{69} +(-0.185255 + 0.320871i) q^{71} +(-2.51339 - 4.35333i) q^{73} +(-3.72579 - 2.40921i) q^{75} +(-0.455479 - 0.382193i) q^{77} +(0.754406 + 0.274581i) q^{79} +(5.59624 + 7.04855i) q^{81} +(-2.58947 - 0.942488i) q^{83} +(0.617998 + 0.518562i) q^{85} +(0.516417 + 0.333932i) q^{87} +(-5.22533 - 9.05054i) q^{89} +(3.10412 - 5.37650i) q^{91} +(-2.89012 - 3.81976i) q^{93} +(7.19580 - 2.61906i) q^{95} +(-2.57600 - 14.6092i) q^{97} +(-0.204037 + 0.722208i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} - 3 q^{5} + 6 q^{7} - 3 q^{11} - 6 q^{13} - 9 q^{15} + 9 q^{17} + 3 q^{19} - 12 q^{21} + 12 q^{23} + 3 q^{25} + 9 q^{27} - 6 q^{29} - 3 q^{31} - 12 q^{35} - 3 q^{37} - 33 q^{39} + 15 q^{41}+ \cdots + 27 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 - 3 * q^5 + 6 * q^7 - 3 * q^11 - 6 * q^13 - 9 * q^15 + 9 * q^17 + 3 * q^19 - 12 * q^21 + 12 * q^23 + 3 * q^25 + 9 * q^27 - 6 * q^29 - 3 * q^31 - 12 * q^35 - 3 * q^37 - 33 * q^39 + 15 * q^41 - 3 * q^43 - 9 * q^45 + 15 * q^47 + 12 * q^49 + 18 * q^51 - 18 * q^53 + 12 * q^55 - 3 * q^57 + 12 * q^59 + 12 * q^61 - 9 * q^63 + 3 * q^65 + 15 * q^67 + 9 * q^69 - 27 * q^71 + 6 * q^73 - 39 * q^75 + 15 * q^77 + 42 * q^79 + 36 * q^81 - 39 * q^83 - 27 * q^85 - 9 * q^87 + 9 * q^89 - 6 * q^91 - 39 * q^93 + 33 * q^95 + 3 * q^97 + 27 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{9}\right)$

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			0
$2$		0			0
$3$	1.68842	+	0.386327i	0.974808	+	0.223046i
$3$	1.68842	+	0.386327i	0.974808	+	0.223046i
$4$		0			0
$5$	−0.477505	+	2.70806i	−0.213547	+	1.21108i	0.669864	+	0.742484i	$0.266352\pi$
$5$	−0.477505	+	2.70806i	−0.213547	+	1.21108i	−0.883411	+	0.468600i	$0.844759\pi$
$6$		0			0
$7$	−1.82076	+	1.52780i	−0.688183	+	0.577454i	−0.918385	−	0.395689i	$-0.870506\pi$
$7$	−1.82076	+	1.52780i	−0.688183	+	0.577454i	0.230202	+	0.973143i	$0.426061\pi$
$8$		0			0
$9$	2.70150	+	1.30456i	0.900501	+	0.434854i
$10$		0			0
$11$	0.0434396	+	0.246358i	0.0130975	+	0.0742798i	0.990656	−	0.136385i	$-0.0435483\pi$
$11$	0.0434396	+	0.246358i	0.0130975	+	0.0742798i	−0.977558	+	0.210665i	$0.932437\pi$
$12$		0			0
$13$	−2.45446	+	0.893351i	−0.680745	+	0.247771i	−0.659167	−	0.751996i	$-0.729091\pi$
$13$	−2.45446	+	0.893351i	−0.680745	+	0.247771i	−0.0215777	+	0.999767i	$0.506869\pi$
$14$		0			0
$15$	−1.85243	+	4.38787i	−0.478294	+	1.13294i
$16$		0			0
$17$	0.146688	−	0.254072i	0.0355772	−	0.0616215i	−0.847689	−	0.530494i	$-0.822006\pi$
$17$	0.146688	−	0.254072i	0.0355772	−	0.0616215i	0.883266	+	0.468873i	$0.155340\pi$
$18$		0			0
$19$	−1.39237	−	2.41166i	−0.319432	−	0.553273i	0.660937	−	0.750441i	$-0.270159\pi$
$19$	−1.39237	−	2.41166i	−0.319432	−	0.553273i	−0.980370	+	0.197168i	$0.936825\pi$
$20$		0			0
$21$	−3.66443	+	1.87615i	−0.799645	+	0.409410i
$22$		0			0
$23$	5.12472	+	4.30015i	1.06858	+	0.896643i	0.994923	−	0.100641i	$-0.0320894\pi$
$23$	5.12472	+	4.30015i	1.06858	+	0.896643i	0.0736543	+	0.997284i	$0.476534\pi$
$24$		0			0
$25$	−2.40714	−	0.876128i	−0.481428	−	0.175226i
$26$		0			0
$27$	4.05728	+	3.24631i	0.780823	+	0.624752i
$28$		0			0
$29$	0.333645	+	0.121437i	0.0619562	+	0.0225502i	0.372812	−	0.927907i	$-0.378394\pi$
$29$	0.333645	+	0.121437i	0.0619562	+	0.0225502i	−0.310856	+	0.950457i	$0.600616\pi$
$30$		0			0
$31$	−2.11847	−	1.77761i	−0.380488	−	0.319268i	0.432406	−	0.901679i	$-0.357665\pi$
$31$	−2.11847	−	1.77761i	−0.380488	−	0.319268i	−0.812894	+	0.582411i	$0.802109\pi$
$32$		0			0
$33$	−0.0218307	+	0.432738i	−0.00380023	+	0.0753299i
$34$		0			0
$35$	−3.26796	−	5.66027i	−0.552386	−	0.956760i
$36$		0			0
$37$	3.49619	−	6.05558i	0.574770	−	0.995531i	−0.421297	−	0.906923i	$-0.638425\pi$
$37$	3.49619	−	6.05558i	0.574770	−	0.995531i	0.996067	−	0.0886080i	$-0.0282418\pi$
$38$		0			0
$39$	−4.48928	+	0.560124i	−0.718860	+	0.0896917i
$40$		0			0
$41$	9.13156	−	3.32362i	1.42611	−	0.519062i	0.490296	−	0.871556i	$-0.336888\pi$
$41$	9.13156	−	3.32362i	1.42611	−	0.519062i	0.935814	+	0.352494i	$0.114666\pi$
$42$		0			0
$43$	−0.0452712	−	0.256746i	−0.00690379	−	0.0391534i	0.981161	−	0.193191i	$-0.0618836\pi$
$43$	−0.0452712	−	0.256746i	−0.00690379	−	0.0391534i	−0.988065	+	0.154037i	$0.950772\pi$
$44$		0			0
$45$	−4.82282	+	6.69291i	−0.718943	+	0.997720i
$46$		0			0
$47$	8.75249	−	7.34421i	1.27668	−	1.07126i	0.282989	−	0.959123i	$-0.408674\pi$
$47$	8.75249	−	7.34421i	1.27668	−	1.07126i	0.993692	−	0.112140i	$-0.0357704\pi$
$48$		0			0
$49$	−0.234540	+	1.33014i	−0.0335057	+	0.190020i
$50$		0			0
$51$	0.345826	−	0.372309i	0.0484253	−	0.0521337i
$52$		0			0
$53$	5.43137			0.746056			0.373028	−	0.927820i	$-0.378320\pi$
$53$	5.43137			0.746056			0.373028	+	0.927820i	$0.378320\pi$
$54$		0			0
$55$	−0.687897			−0.0927560
$56$		0			0
$57$	−1.41922	−	4.60980i	−0.187980	−	0.610583i
$58$		0			0
$59$	−1.03788	+	5.88612i	−0.135121	+	0.766308i	0.839655	+	0.543121i	$0.182757\pi$
$59$	−1.03788	+	5.88612i	−0.135121	+	0.766308i	−0.974776	+	0.223188i	$0.928354\pi$
$60$		0			0
$61$	−9.07515	+	7.61495i	−1.16195	+	0.974995i	−0.999930	−	0.0117924i	$-0.996246\pi$
$61$	−9.07515	+	7.61495i	−1.16195	+	0.974995i	−0.162023	+	0.986787i	$0.551802\pi$
$62$		0			0
$63$	−6.91190	+	1.75206i	−0.870817	+	0.220739i
$64$		0			0
$65$	−1.24723	−	7.07342i	−0.154700	−	0.877350i
$66$		0			0
$67$	1.70113	−	0.619160i	0.207826	−	0.0756424i	−0.236010	−	0.971751i	$-0.575840\pi$
$67$	1.70113	−	0.619160i	0.207826	−	0.0756424i	0.443835	+	0.896108i	$0.353617\pi$
$68$		0			0
$69$	6.99139	+	9.24026i	0.841665	+	1.11240i
$70$		0			0
$71$	−0.185255	+	0.320871i	−0.0219857	+	0.0380804i	−0.876809	−	0.480839i	$-0.840332\pi$
$71$	−0.185255	+	0.320871i	−0.0219857	+	0.0380804i	0.854823	+	0.518919i	$0.173666\pi$
$72$		0			0
$73$	−2.51339	−	4.35333i	−0.294171	−	0.509518i	0.680621	−	0.732636i	$-0.261710\pi$
$73$	−2.51339	−	4.35333i	−0.294171	−	0.509518i	−0.974792	+	0.223117i	$0.928377\pi$
$74$		0			0
$75$	−3.72579	−	2.40921i	−0.430217	−	0.278192i
$76$		0			0
$77$	−0.455479	−	0.382193i	−0.0519067	−	0.0435549i
$78$		0			0
$79$	0.754406	+	0.274581i	0.0848773	+	0.0308928i	0.384110	−	0.923287i	$-0.374508\pi$
$79$	0.754406	+	0.274581i	0.0848773	+	0.0308928i	−0.299233	+	0.954180i	$0.596731\pi$
$80$		0			0
$81$	5.59624	+	7.04855i	0.621804	+	0.783173i
$82$		0			0
$83$	−2.58947	−	0.942488i	−0.284231	−	0.103452i	0.195971	−	0.980610i	$-0.437214\pi$
$83$	−2.58947	−	0.942488i	−0.284231	−	0.103452i	−0.480201	+	0.877158i	$0.659436\pi$
$84$		0			0
$85$	0.617998	+	0.518562i	0.0670313	+	0.0562460i
$86$		0			0
$87$	0.516417	+	0.333932i	0.0553657	+	0.0358012i
$88$		0			0
$89$	−5.22533	−	9.05054i	−0.553884	−	0.959356i	−0.997989	−	0.0633809i	$-0.979812\pi$
$89$	−5.22533	−	9.05054i	−0.553884	−	0.959356i	0.444105	−	0.895975i	$-0.353522\pi$
$90$		0			0
$91$	3.10412	−	5.37650i	0.325401	−	0.563611i
$92$		0			0
$93$	−2.89012	−	3.81976i	−0.299692	−	0.396091i
$94$		0			0
$95$	7.19580	−	2.61906i	0.738273	−	0.268709i
$96$		0			0
$97$	−2.57600	−	14.6092i	−0.261553	−	1.48334i	−0.778673	−	0.627430i	$-0.784107\pi$
$97$	−2.57600	−	14.6092i	−0.261553	−	1.48334i	0.517120	−	0.855913i	$-0.327004\pi$
$98$		0			0
$99$	−0.204037	+	0.722208i	−0.0205065	+	0.0725846i
$100$		0			0
$101$	3.06826	−	2.57457i	0.305303	−	0.256180i	−0.477244	−	0.878771i	$-0.658364\pi$
$101$	3.06826	−	2.57457i	0.305303	−	0.256180i	0.782548	+	0.622591i	$0.213920\pi$
$102$		0			0
$103$	1.02789	−	5.82943i	0.101281	−	0.574391i	−0.891360	−	0.453296i	$-0.850248\pi$
$103$	1.02789	−	5.82943i	0.101281	−	0.574391i	0.992641	−	0.121095i	$-0.0386407\pi$
$104$		0			0
$105$	−3.33096	−	10.8194i	−0.325069	−	1.05586i
$106$		0			0
$107$	0.258978			0.0250364			0.0125182	−	0.999922i	$-0.496015\pi$
$107$	0.258978			0.0250364			0.0125182	+	0.999922i	$0.496015\pi$
$108$		0			0
$109$	−8.55787			−0.819695			−0.409848	−	0.912154i	$-0.634418\pi$
$109$	−8.55787			−0.819695			−0.409848	+	0.912154i	$0.634418\pi$
$110$		0			0
$111$	8.24246	−	8.87367i	0.782340	−	0.842251i
$112$		0			0
$113$	−0.541640	+	3.07179i	−0.0509532	+	0.288970i	−0.999628	−	0.0272843i	$-0.991314\pi$
$113$	−0.541640	+	3.07179i	−0.0509532	+	0.288970i	0.948675	+	0.316254i	$0.102425\pi$
$114$		0			0
$115$	−14.0922	+	11.8247i	−1.31410	+	1.10266i
$116$		0			0
$117$	−7.79617	−	0.788606i	−0.720756	−	0.0729066i
$118$		0			0
$119$	0.121086	+	0.686714i	0.0111000	+	0.0629510i
$120$		0			0
$121$	10.2778	−	3.74082i	0.934347	−	0.340074i
$122$		0			0
$123$	16.7019	−	2.08388i	1.50596	−	0.187897i
$124$		0			0
$125$	−3.35257	+	5.80682i	−0.299863	+	0.519378i
$126$		0			0
$127$	−9.22726	−	15.9821i	−0.818787	−	1.41818i	−0.906576	−	0.422042i	$-0.861314\pi$
$127$	−9.22726	−	15.9821i	−0.818787	−	1.41818i	0.0877893	−	0.996139i	$-0.472020\pi$
$128$		0			0
$129$	0.0227511	−	0.450983i	0.00200312	−	0.0397069i
$130$		0			0
$131$	−10.8973	−	9.14396i	−0.952105	−	0.798911i	0.0275454	−	0.999621i	$-0.491231\pi$
$131$	−10.8973	−	9.14396i	−0.952105	−	0.798911i	−0.979651	+	0.200709i	$0.935675\pi$
$132$		0			0
$133$	6.21971	+	2.26379i	0.539317	+	0.196295i
$134$		0			0
$135$	−10.7286	+	9.43724i	−0.923369	+	0.812228i
$136$		0			0
$137$	18.4984	+	6.73287i	1.58042	+	0.575228i	0.975296	−	0.220900i	$-0.0708995\pi$
$137$	18.4984	+	6.73287i	1.58042	+	0.575228i	0.605128	+	0.796128i	$0.293122\pi$
$138$		0			0
$139$	13.7206	+	11.5129i	1.16377	+	0.976515i	0.999950	−	0.00997617i	$-0.00317556\pi$
$139$	13.7206	+	11.5129i	1.16377	+	0.976515i	0.163815	+	0.986491i	$0.447620\pi$
$140$		0			0
$141$	17.6151	−	9.01876i	1.48346	−	0.759517i
$142$		0			0
$143$	−0.326705	−	0.565870i	−0.0273205	−	0.0473205i
$144$		0			0
$145$	−0.488175	+	0.845544i	−0.0405408	+	0.0702186i
$146$		0			0
$147$	−0.909870	+	2.15522i	−0.0750449	+	0.177760i
$148$		0			0
$149$	−15.3071	+	5.57132i	−1.25401	+	0.456421i	−0.881753	−	0.471711i	$-0.843637\pi$
$149$	−15.3071	+	5.57132i	−1.25401	+	0.456421i	−0.372252	+	0.928132i	$0.621414\pi$
$150$		0			0
$151$	−2.47880	−	14.0580i	−0.201722	−	1.14402i	−0.902515	−	0.430659i	$-0.858281\pi$
$151$	−2.47880	−	14.0580i	−0.201722	−	1.14402i	0.700793	−	0.713365i	$-0.252830\pi$
$152$		0			0
$153$	0.727731	−	0.495012i	0.0588336	−	0.0400193i
$154$		0			0
$155$	5.82546	−	4.88814i	0.467912	−	0.392625i
$156$		0			0
$157$	0.132555	−	0.751757i	0.0105790	−	0.0599968i	−0.979061	−	0.203566i	$-0.934747\pi$
$157$	0.132555	−	0.751757i	0.0105790	−	0.0599968i	0.989640	+	0.143569i	$0.0458580\pi$
$158$		0			0
$159$	9.17041	+	2.09828i	0.727261	+	0.166405i
$160$		0			0
$161$	−15.9006			−1.25315
$162$		0			0
$163$	−5.12834			−0.401682			−0.200841	−	0.979624i	$-0.564368\pi$
$163$	−5.12834			−0.401682			−0.200841	+	0.979624i	$0.564368\pi$
$164$		0			0
$165$	−1.16146	−	0.265753i	−0.0904193	−	0.0206889i
$166$		0			0
$167$	−1.54566	+	8.76590i	−0.119607	+	0.678325i	0.864759	+	0.502188i	$0.167471\pi$
$167$	−1.54566	+	8.76590i	−0.119607	+	0.678325i	−0.984366	+	0.176137i	$0.943640\pi$
$168$		0			0
$169$	−4.73227	+	3.97085i	−0.364021	+	0.305450i
$170$		0			0
$171$	−0.615340	−	8.33154i	−0.0470562	−	0.637129i
$172$		0			0
$173$	−1.18276	−	6.70776i	−0.0899235	−	0.509982i	−0.996185	−	0.0872644i	$-0.972188\pi$
$173$	−1.18276	−	6.70776i	−0.0899235	−	0.509982i	0.906262	−	0.422717i	$-0.138924\pi$
$174$		0			0
$175$	5.72137	−	2.08241i	0.432495	−	0.157415i
$176$		0			0
$177$	−4.02635	+	9.53727i	−0.302639	+	0.716865i
$178$		0			0
$179$	−9.17382	+	15.8895i	−0.685684	+	1.18764i	0.287538	+	0.957769i	$0.407163\pi$
$179$	−9.17382	+	15.8895i	−0.685684	+	1.18764i	−0.973221	+	0.229870i	$0.926170\pi$
$180$		0			0
$181$	−5.66282	−	9.80830i	−0.420914	−	0.729045i	0.575115	−	0.818073i	$-0.304957\pi$
$181$	−5.66282	−	9.80830i	−0.420914	−	0.729045i	−0.996029	+	0.0890276i	$0.971624\pi$
$182$		0			0
$183$	−18.2645	+	9.35124i	−1.35015	+	0.691264i
$184$		0			0
$185$	14.7295	+	12.3595i	1.08293	+	0.908687i
$186$		0			0
$187$	0.0689648	+	0.0251011i	0.00504321	+	0.00183558i
$188$		0			0
$189$	−12.3470	+	0.287957i	−0.898115	+	0.0209458i
$190$		0			0
$191$	6.44480	+	2.34571i	0.466329	+	0.169730i	0.564489	−	0.825441i	$-0.309073\pi$
$191$	6.44480	+	2.34571i	0.466329	+	0.169730i	−0.0981596	+	0.995171i	$0.531296\pi$
$192$		0			0
$193$	15.6371	+	13.1211i	1.12558	+	0.944477i	0.998873	−	0.0474627i	$-0.0151135\pi$
$193$	15.6371	+	13.1211i	1.12558	+	0.944477i	0.126711	+	0.991940i	$0.459558\pi$
$194$		0			0
$195$	0.626800	−	12.4247i	0.0448861	−	0.889753i
$196$		0			0
$197$	−1.51786	−	2.62902i	−0.108143	−	0.187310i	0.806875	−	0.590723i	$-0.201157\pi$
$197$	−1.51786	−	2.62902i	−0.108143	−	0.187310i	−0.915018	+	0.403413i	$0.867824\pi$
$198$		0			0
$199$	−1.13124	+	1.95936i	−0.0801912	+	0.138895i	−0.903332	−	0.428942i	$-0.858886\pi$
$199$	−1.13124	+	1.95936i	−0.0801912	+	0.138895i	0.823141	+	0.567837i	$0.192220\pi$
$200$		0			0
$201$	3.11141	−	0.388209i	0.219462	−	0.0273821i
$202$		0			0
$203$	−0.793018	+	0.288635i	−0.0556589	+	0.0202582i
$204$		0			0
$205$	4.64020	+	26.3159i	0.324086	+	1.83798i
$206$		0			0
$207$	8.23463	+	18.3024i	0.572346	+	1.27210i
$208$		0			0
$209$	0.533649	−	0.447784i	0.0369132	−	0.0309739i
$210$		0			0
$211$	−4.41601	+	25.0445i	−0.304011	+	1.72413i	0.324113	+	0.946018i	$0.394934\pi$
$211$	−4.41601	+	25.0445i	−0.304011	+	1.72413i	−0.628124	+	0.778113i	$0.716177\pi$
$212$		0			0
$213$	−0.436749	+	0.470195i	−0.0299255	+	0.0322172i
$214$		0			0
$215$	0.716901			0.0488923
$216$		0			0
$217$	6.57305			0.446208
$218$		0			0
$219$	−2.56185	−	8.32122i	−0.173114	−	0.562296i
$220$		0			0
$221$	−0.133066	+	0.754654i	−0.00895097	+	0.0507635i
$222$		0			0
$223$	2.93497	−	2.46274i	0.196540	−	0.164917i	−0.539206	−	0.842174i	$-0.681276\pi$
$223$	2.93497	−	2.46274i	0.196540	−	0.164917i	0.735747	+	0.677257i	$0.236831\pi$
$224$		0			0
$225$	−5.35994	−	5.50713i	−0.357329	−	0.367142i
$226$		0			0
$227$	−0.436897	−	2.47777i	−0.0289979	−	0.164455i	0.966870	−	0.255269i	$-0.0821642\pi$
$227$	−0.436897	−	2.47777i	−0.0289979	−	0.164455i	−0.995868	+	0.0908142i	$0.971053\pi$
$228$		0			0
$229$	14.9783	−	5.45167i	0.989797	−	0.360257i	0.204155	−	0.978939i	$-0.434555\pi$
$229$	14.9783	−	5.45167i	0.989797	−	0.360257i	0.785642	+	0.618682i	$0.212333\pi$
$230$		0			0
$231$	−0.621388	−	0.821264i	−0.0408843	−	0.0540352i
$232$		0			0
$233$	−14.0641	+	24.3598i	−0.921372	+	1.59586i	−0.124077	+	0.992273i	$0.539597\pi$
$233$	−14.0641	+	24.3598i	−0.921372	+	1.59586i	−0.797295	+	0.603590i	$0.793736\pi$
$234$		0			0
$235$	15.7092	+	27.2092i	1.02476	+	1.77493i
$236$		0			0
$237$	1.16767	+	0.755055i	0.0758485	+	0.0490461i
$238$		0			0
$239$	11.2653	+	9.45270i	0.728691	+	0.611444i	0.929774	−	0.368130i	$-0.120002\pi$
$239$	11.2653	+	9.45270i	0.728691	+	0.611444i	−0.201083	+	0.979574i	$0.564446\pi$
$240$		0			0
$241$	−7.93378	−	2.88766i	−0.511059	−	0.186010i	0.0736022	−	0.997288i	$-0.476550\pi$
$241$	−7.93378	−	2.88766i	−0.511059	−	0.186010i	−0.584662	+	0.811277i	$0.698773\pi$
$242$		0			0
$243$	6.72574	+	14.0629i	0.431456	+	0.902134i
$244$		0			0
$245$	−3.49012	−	1.27030i	−0.222975	−	0.0811564i
$246$		0			0
$247$	5.57198	+	4.67545i	0.354537	+	0.297492i
$248$		0			0
$249$	−4.00799	−	2.59169i	−0.253996	−	0.164242i
$250$		0			0
$251$	−11.6102	−	20.1095i	−0.732832	−	1.26930i	−0.955668	−	0.294447i	$-0.904865\pi$
$251$	−11.6102	−	20.1095i	−0.732832	−	1.26930i	0.222835	−	0.974856i	$-0.428469\pi$
$252$		0			0
$253$	−0.836762	+	1.44931i	−0.0526067	+	0.0911176i
$254$		0			0
$255$	0.843104	+	1.11430i	0.0527972	+	0.0697801i
$256$		0			0
$257$	−6.45118	+	2.34804i	−0.402413	+	0.146466i	−0.535294	−	0.844666i	$-0.679799\pi$
$257$	−6.45118	+	2.34804i	−0.402413	+	0.146466i	0.132881	+	0.991132i	$0.457577\pi$
$258$		0			0
$259$	2.88598	+	16.3672i	0.179326	+	1.01701i
$260$		0			0
$261$	0.742920	+	0.763321i	0.0459856	+	0.0472484i
$262$		0			0
$263$	−2.56850	+	2.15523i	−0.158381	+	0.132897i	−0.718534	−	0.695492i	$-0.755187\pi$
$263$	−2.56850	+	2.15523i	−0.158381	+	0.132897i	0.560154	+	0.828389i	$0.310742\pi$
$264$		0			0
$265$	−2.59351	+	14.7085i	−0.159318	+	0.903536i
$266$		0			0
$267$	−5.32607	−	17.2998i	−0.325950	−	1.05873i
$268$		0			0
$269$	12.7416			0.776869			0.388434	−	0.921476i	$-0.373016\pi$
$269$	12.7416			0.776869			0.388434	+	0.921476i	$0.373016\pi$
$270$		0			0
$271$	23.5566			1.43096			0.715481	−	0.698632i	$-0.246208\pi$
$271$	23.5566			1.43096			0.715481	+	0.698632i	$0.246208\pi$
$272$		0			0
$273$	7.31814	−	7.87857i	0.442914	−	0.476833i
$274$		0			0
$275$	0.111276	−	0.631078i	0.00671020	−	0.0380554i
$276$		0			0
$277$	3.20300	−	2.68763i	0.192450	−	0.161484i	−0.541472	−	0.840719i	$-0.682133\pi$
$277$	3.20300	−	2.68763i	0.192450	−	0.161484i	0.733921	+	0.679235i	$0.237688\pi$
$278$		0			0
$279$	−3.40406	−	7.56589i	−0.203795	−	0.452958i
$280$		0			0
$281$	−3.75705	−	21.3073i	−0.224127	−	1.27109i	−0.864347	−	0.502896i	$-0.832268\pi$
$281$	−3.75705	−	21.3073i	−0.224127	−	1.27109i	0.640220	−	0.768192i	$-0.278843\pi$
$282$		0			0
$283$	4.91209	−	1.78785i	0.291993	−	0.106277i	−0.191870	−	0.981420i	$-0.561455\pi$
$283$	4.91209	−	1.78785i	0.291993	−	0.106277i	0.483864	+	0.875143i	$0.339233\pi$
$284$		0			0
$285$	13.1613	−	1.64213i	0.779609	−	0.0972713i
$286$		0			0
$287$	−11.5486	+	20.0027i	−0.681690	+	1.18072i
$288$		0			0
$289$	8.45697	+	14.6479i	0.497469	+	0.861641i
$290$		0			0
$291$	1.29457	−	25.6617i	0.0758893	−	1.50431i
$292$		0			0
$293$	−4.70517	−	3.94811i	−0.274879	−	0.230651i	0.494918	−	0.868940i	$-0.335198\pi$
$293$	−4.70517	−	3.94811i	−0.274879	−	0.230651i	−0.769797	+	0.638289i	$0.779643\pi$
$294$		0			0
$295$	−15.4444	−	5.62131i	−0.899208	−	0.327285i
$296$		0			0
$297$	−0.623508	+	1.14056i	−0.0361796	+	0.0661821i
$298$		0			0
$299$	−16.4200	−	5.97638i	−0.949591	−	0.345623i
$300$		0			0
$301$	0.474684	+	0.398307i	0.0273603	+	0.0229580i
$302$		0			0
$303$	6.17513	−	3.16160i	0.354752	−	0.181629i
$304$		0			0
$305$	−16.2884	−	28.2123i	−0.932669	−	1.61543i
$306$		0			0
$307$	9.50194	−	16.4578i	0.542304	−	0.939298i	−0.456467	−	0.889740i	$-0.650885\pi$
$307$	9.50194	−	16.4578i	0.542304	−	0.939298i	0.998771	−	0.0495580i	$-0.0157813\pi$
$308$		0			0
$309$	3.98757	−	9.44541i	0.226845	−	0.537331i
$310$		0			0
$311$	−20.2475	+	7.36948i	−1.14813	+	0.417885i	−0.844843	−	0.535015i	$-0.820306\pi$
$311$	−20.2475	+	7.36948i	−1.14813	+	0.417885i	−0.303286	+	0.952900i	$0.598084\pi$
$312$		0			0
$313$	−0.662228	−	3.75568i	−0.0374313	−	0.212284i	0.960355	−	0.278778i	$-0.0899295\pi$
$313$	−0.662228	−	3.75568i	−0.0374313	−	0.212284i	−0.997787	+	0.0664949i	$0.978818\pi$
$314$		0			0
$315$	−1.44423	−	19.5545i	−0.0813731	−	1.10177i
$316$		0			0
$317$	3.25913	−	2.73473i	0.183051	−	0.153598i	−0.546658	−	0.837356i	$-0.684100\pi$
$317$	3.25913	−	2.73473i	0.183051	−	0.153598i	0.729709	+	0.683758i	$0.239656\pi$
$318$		0			0
$319$	−0.0154235	+	0.0874713i	−0.000863553	+	0.00489745i
$320$		0			0
$321$	0.437264	+	0.100050i	0.0244057	+	0.00558426i
$322$		0			0
$323$	−0.816980			−0.0454580
$324$		0			0
$325$	6.69092			0.371146
$326$		0			0
$327$	−14.4493	−	3.30614i	−0.799046	−	0.182830i
$328$		0			0
$329$	−4.71570	+	26.7441i	−0.259985	+	1.47445i
$330$		0			0
$331$	10.9497	−	9.18787i	0.601849	−	0.505011i	−0.290191	−	0.956969i	$-0.593719\pi$
$331$	10.9497	−	9.18787i	0.601849	−	0.505011i	0.892039	+	0.451958i	$0.149274\pi$
$332$		0			0
$333$	17.3448	−	11.7982i	0.950491	−	0.646536i
$334$		0			0
$335$	0.864428	+	4.90242i	0.0472288	+	0.267848i
$336$		0			0
$337$	−33.5644	+	12.2164i	−1.82837	+	0.665472i	−0.835037	+	0.550194i	$0.814554\pi$
$337$	−33.5644	+	12.2164i	−1.82837	+	0.665472i	−0.993333	+	0.115278i	$0.963224\pi$
$338$		0			0
$339$	−2.10123	+	4.97721i	−0.114123	+	0.270325i
$340$		0			0
$341$	0.345903	−	0.599121i	0.0187317	−	0.0324442i
$342$		0			0
$343$	−9.92407	−	17.1890i	−0.535849	−	0.928118i
$344$		0			0
$345$	−28.3616	+	14.5209i	−1.52694	+	0.781778i
$346$		0			0
$347$	14.8931	+	12.4968i	0.799502	+	0.670862i	0.948078	−	0.318039i	$-0.103024\pi$
$347$	14.8931	+	12.4968i	0.799502	+	0.670862i	−0.148575	+	0.988901i	$0.547469\pi$
$348$		0			0
$349$	7.53700	+	2.74324i	0.403446	+	0.146842i	0.535770	−	0.844364i	$-0.320022\pi$
$349$	7.53700	+	2.74324i	0.403446	+	0.146842i	−0.132323	+	0.991207i	$0.542244\pi$
$350$		0			0
$351$	−12.8585	−	4.34336i	−0.686337	−	0.231832i
$352$		0			0
$353$	−8.22589	−	2.99398i	−0.437820	−	0.159354i	0.113700	−	0.993515i	$-0.463730\pi$
$353$	−8.22589	−	2.99398i	−0.437820	−	0.159354i	−0.551520	+	0.834162i	$0.685952\pi$
$354$		0			0
$355$	−0.780479	−	0.654900i	−0.0414235	−	0.0347585i
$356$		0			0
$357$	−0.0608521	+	1.20624i	−0.00322063	+	0.0638409i
$358$		0			0
$359$	−4.13896	−	7.16888i	−0.218446	−	0.378359i	0.735887	−	0.677104i	$-0.236765\pi$
$359$	−4.13896	−	7.16888i	−0.218446	−	0.378359i	−0.954333	+	0.298745i	$0.903432\pi$
$360$		0			0
$361$	5.62260	−	9.73862i	0.295926	−	0.512559i
$362$		0			0
$363$	18.7984	−	2.34547i	0.986661	−	0.123105i
$364$		0			0
$365$	12.9892	−	4.72770i	0.679888	−	0.247459i
$366$		0			0
$367$	2.56997	+	14.5750i	0.134151	+	0.760809i	0.975447	+	0.220234i	$0.0706822\pi$
$367$	2.56997	+	14.5750i	0.134151	+	0.760809i	−0.841296	+	0.540575i	$0.818207\pi$
$368$		0			0
$369$	29.0048	+	2.93392i	1.50993	+	0.152734i
$370$		0			0
$371$	−9.88922	+	8.29804i	−0.513423	+	0.430813i
$372$		0			0
$373$	4.43383	−	25.1455i	0.229575	−	1.30198i	−0.624168	−	0.781290i	$-0.714562\pi$
$373$	4.43383	−	25.1455i	0.229575	−	1.30198i	0.853743	−	0.520694i	$-0.174327\pi$
$374$		0			0
$375$	−7.90387	+	8.50915i	−0.408154	+	0.439411i
$376$		0			0
$377$	−0.927403			−0.0477637
$378$		0			0
$379$	−20.1244			−1.03372			−0.516861	−	0.856070i	$-0.672899\pi$
$379$	−20.1244			−1.03372			−0.516861	+	0.856070i	$0.672899\pi$
$380$		0			0
$381$	−9.40516	−	30.5492i	−0.481841	−	1.56508i
$382$		0			0
$383$	4.14346	−	23.4987i	0.211721	−	1.20073i	−0.674785	−	0.738014i	$-0.735764\pi$
$383$	4.14346	−	23.4987i	0.211721	−	1.20073i	0.886507	−	0.462716i	$-0.153125\pi$
$384$		0			0
$385$	1.25250	−	1.05097i	0.0638331	−	0.0535623i
$386$		0			0
$387$	0.212640	−	0.752659i	0.0108091	−	0.0382598i
$388$		0			0
$389$	6.59400	+	37.3964i	0.334329	+	1.89607i	0.433760	+	0.901029i	$0.357187\pi$
$389$	6.59400	+	37.3964i	0.334329	+	1.89607i	−0.0994307	+	0.995044i	$0.531702\pi$
$390$		0			0
$391$	1.84428	−	0.671264i	0.0932694	−	0.0339473i
$392$		0			0
$393$	−14.8667	−	19.6487i	−0.749926	−	0.991148i
$394$		0			0
$395$	−1.10382	+	1.91187i	−0.0555390	+	0.0961964i
$396$		0			0
$397$	−10.1747	−	17.6230i	−0.510651	−	0.884474i	−0.999924	−	0.0123433i	$-0.996071\pi$
$397$	−10.1747	−	17.6230i	−0.510651	−	0.884474i	0.489272	−	0.872131i	$-0.337262\pi$
$398$		0			0
$399$	9.62690	+	6.22506i	0.481948	+	0.311643i
$400$		0			0
$401$	5.32015	+	4.46414i	0.265676	+	0.222928i	0.765887	−	0.642975i	$-0.222300\pi$
$401$	5.32015	+	4.46414i	0.265676	+	0.222928i	−0.500212	+	0.865903i	$0.666744\pi$
$402$		0			0
$403$	6.78773	+	2.47053i	0.338121	+	0.123066i
$404$		0			0
$405$	−21.7602	+	11.7893i	−1.08127	+	0.585813i
$406$		0			0
$407$	1.64372	+	0.598264i	0.0814760	+	0.0296548i
$408$		0			0
$409$	−8.35444	−	7.01021i	−0.413101	−	0.346633i	0.412431	−	0.910989i	$-0.364680\pi$
$409$	−8.35444	−	7.01021i	−0.413101	−	0.346633i	−0.825531	+	0.564356i	$0.809124\pi$
$410$		0			0
$411$	28.6319	+	18.5143i	1.41231	+	0.913244i
$412$		0			0
$413$	−7.10308	−	12.3029i	−0.349520	−	0.605386i
$414$		0			0
$415$	3.78880	−	6.56240i	0.185985	−	0.322135i
$416$		0			0
$417$	18.7183	+	24.7393i	0.916640	+	1.21149i
$418$		0			0
$419$	−9.46194	+	3.44386i	−0.462246	+	0.168244i	−0.562637	−	0.826704i	$-0.690213\pi$
$419$	−9.46194	+	3.44386i	−0.462246	+	0.168244i	0.100391	+	0.994948i	$0.467991\pi$
$420$		0			0
$421$	−0.539623	−	3.06035i	−0.0262996	−	0.149152i	0.968830	−	0.247726i	$-0.0796832\pi$
$421$	−0.539623	−	3.06035i	−0.0262996	−	0.149152i	−0.995130	+	0.0985733i	$0.968572\pi$
$422$		0			0
$423$	33.2258	−	8.42224i	1.61550	−	0.409504i
$424$		0			0
$425$	−0.575699	+	0.483069i	−0.0279255	+	0.0234323i
$426$		0			0
$427$	4.88955	−	27.7300i	0.236622	−	1.34195i
$428$		0			0
$429$	−0.333004	−	1.08164i	−0.0160776	−	0.0522221i
$430$		0			0
$431$	28.0701			1.35209			0.676044	−	0.736862i	$-0.263693\pi$
$431$	28.0701			1.35209			0.676044	+	0.736862i	$0.263693\pi$
$432$		0			0
$433$	19.5251			0.938317			0.469158	−	0.883114i	$-0.344557\pi$
$433$	19.5251			0.938317			0.469158	+	0.883114i	$0.344557\pi$
$434$		0			0
$435$	−1.15090	+	1.23904i	−0.0551814	+	0.0594072i
$436$		0			0
$437$	3.23498	−	18.3465i	0.154750	−	0.877631i
$438$		0			0
$439$	−11.2069	+	9.40371i	−0.534876	+	0.448815i	−0.869781	−	0.493437i	$-0.835740\pi$
$439$	−11.2069	+	9.40371i	−0.534876	+	0.448815i	0.334905	+	0.942252i	$0.391296\pi$
$440$		0			0
$441$	−2.36886	+	3.28741i	−0.112803	+	0.156543i
$442$		0			0
$443$	−3.18748	−	18.0771i	−0.151442	−	0.858868i	−0.961967	−	0.273165i	$-0.911930\pi$
$443$	−3.18748	−	18.0771i	−0.151442	−	0.858868i	0.810526	−	0.585703i	$-0.199182\pi$
$444$		0			0
$445$	27.0046	−	9.82886i	1.28014	−	0.465933i
$446$		0			0
$447$	−27.9971	+	3.49318i	−1.32422	+	0.165222i
$448$		0			0
$449$	−6.92969	+	12.0026i	−0.327032	+	0.566437i	−0.981922	−	0.189288i	$-0.939382\pi$
$449$	−6.92969	+	12.0026i	−0.327032	+	0.566437i	0.654889	+	0.755725i	$0.272715\pi$
$450$		0			0
$451$	1.21547	+	2.10526i	0.0572344	+	0.0991328i
$452$		0			0
$453$	1.24573	−	24.6934i	0.0585294	−	1.16020i
$454$		0			0
$455$	13.0777	+	10.9735i	0.613091	+	0.514445i
$456$		0			0
$457$	−16.5838	−	6.03602i	−0.775758	−	0.282353i	−0.0763555	−	0.997081i	$-0.524328\pi$
$457$	−16.5838	−	6.03602i	−0.775758	−	0.282353i	−0.699403	+	0.714728i	$0.746551\pi$
$458$		0			0
$459$	1.41995	−	0.554644i	0.0662776	−	0.0258886i
$460$		0			0
$461$	−24.0919	−	8.76872i	−1.12207	−	0.408400i	−0.286663	−	0.958032i	$-0.592546\pi$
$461$	−24.0919	−	8.76872i	−1.12207	−	0.408400i	−0.835407	+	0.549631i	$0.814768\pi$
$462$		0			0
$463$	−14.0549	−	11.7935i	−0.653189	−	0.548090i	0.254848	−	0.966981i	$-0.417975\pi$
$463$	−14.0549	−	11.7935i	−0.653189	−	0.548090i	−0.908037	+	0.418891i	$0.862419\pi$
$464$		0			0
$465$	11.7242	−	6.00268i	0.543698	−	0.278368i
$466$		0			0
$467$	−8.13092	−	14.0832i	−0.376254	−	0.651692i	0.614260	−	0.789104i	$-0.289455\pi$
$467$	−8.13092	−	14.0832i	−0.376254	−	0.651692i	−0.990514	+	0.137412i	$0.956121\pi$
$468$		0			0
$469$	−2.15139	+	3.72632i	−0.0993421	+	0.172066i
$470$		0			0
$471$	0.514232	−	1.21807i	0.0236946	−	0.0561257i
$472$		0			0
$473$	0.0612849	−	0.0223059i	0.00281788	−	0.00102563i
$474$		0			0
$475$	1.23872	+	7.02510i	0.0568362	+	0.322334i
$476$		0			0
$477$	14.6729	+	7.08555i	0.671824	+	0.324425i
$478$		0			0
$479$	7.25575	−	6.08830i	0.331524	−	0.278181i	−0.461797	−	0.886986i	$-0.652795\pi$
$479$	7.25575	−	6.08830i	0.331524	−	0.278181i	0.793320	+	0.608804i	$0.208351\pi$
$480$		0			0
$481$	−3.17151	+	17.9865i	−0.144608	+	0.820114i
$482$		0			0
$483$	−26.8469	−	6.14284i	−1.22158	−	0.279509i
$484$		0			0
$485$	40.7928			1.85231
$486$		0			0
$487$	0.467564			0.0211874			0.0105937	−	0.999944i	$-0.496628\pi$
$487$	0.467564			0.0211874			0.0105937	+	0.999944i	$0.496628\pi$
$488$		0			0
$489$	−8.65877	−	1.98121i	−0.391563	−	0.0895936i
$490$		0			0
$491$	−4.34936	+	24.6665i	−0.196284	+	1.11318i	0.714294	+	0.699846i	$0.246748\pi$
$491$	−4.34936	+	24.6665i	−0.196284	+	1.11318i	−0.910578	+	0.413337i	$0.864363\pi$
$492$		0			0
$493$	0.0797954	−	0.0669563i	0.00359380	−	0.00301556i
$494$		0			0
$495$	−1.85836	−	0.897404i	−0.0835269	−	0.0403353i
$496$		0			0
$497$	−0.152922	−	0.867261i	−0.00685947	−	0.0389020i
$498$		0			0
$499$	−13.1878	+	4.79996i	−0.590367	+	0.214876i	−0.619891	−	0.784688i	$-0.712823\pi$
$499$	−13.1878	+	4.79996i	−0.590367	+	0.214876i	0.0295240	+	0.999564i	$0.490601\pi$
$500$		0			0
$501$	−5.99623	+	14.2034i	−0.267892	+	0.634559i
$502$		0			0
$503$	14.1558	−	24.5186i	0.631176	−	1.09323i	−0.356136	−	0.934434i	$-0.615906\pi$
$503$	14.1558	−	24.5186i	0.631176	−	1.09323i	0.987312	−	0.158794i	$-0.0507607\pi$
$504$		0			0
$505$	5.50701	+	9.53842i	0.245059	+	0.424454i
$506$		0			0
$507$	−9.52410	+	4.87624i	−0.422980	+	0.216562i
$508$		0			0
$509$	−21.9759	−	18.4399i	−0.974063	−	0.817336i	0.00912008	−	0.999958i	$-0.497097\pi$
$509$	−21.9759	−	18.4399i	−0.974063	−	0.817336i	−0.983183	+	0.182622i	$0.941541\pi$
$510$		0			0
$511$	11.2273	+	4.08640i	0.496666	+	0.180772i
$512$		0			0
$513$	2.17975	−	14.3048i	0.0962382	−	0.631574i
$514$		0			0
$515$	15.2957	+	5.56716i	0.674007	+	0.245319i
$516$		0			0
$517$	2.18951	+	1.83722i	0.0962946	+	0.0808008i
$518$		0			0
$519$	0.594397	−	11.7824i	0.0260911	−	0.517191i
$520$		0			0
$521$	12.4548	+	21.5724i	0.545655	+	0.945102i	0.998565	+	0.0535462i	$0.0170525\pi$
$521$	12.4548	+	21.5724i	0.545655	+	0.945102i	−0.452910	+	0.891556i	$0.649614\pi$
$522$		0			0
$523$	−12.9324	+	22.3995i	−0.565494	+	0.979464i	0.431510	+	0.902108i	$0.357981\pi$
$523$	−12.9324	+	22.3995i	−0.565494	+	0.979464i	−0.997004	+	0.0773554i	$0.975352\pi$
$524$		0			0
$525$	10.4646	−	1.30566i	0.456711	−	0.0569835i
$526$		0			0
$527$	−0.762395	+	0.277489i	−0.0332104	+	0.0120876i
$528$		0			0
$529$	3.77754	+	21.4235i	0.164241	+	0.931456i
$530$		0			0
$531$	−10.4827	+	14.5474i	−0.454908	+	0.631303i
$532$		0			0
$533$	−19.4439	+	16.3154i	−0.842209	+	0.706698i
$534$		0			0
$535$	−0.123663	+	0.701330i	−0.00534644	+	0.0303212i
$536$		0			0
$537$	−21.6278	+	23.2841i	−0.933308	+	1.00478i
$538$		0			0
$539$	−0.337880			−0.0145535
$540$		0			0
$541$	−21.9158			−0.942232			−0.471116	−	0.882071i	$-0.656149\pi$
$541$	−21.9158			−0.942232			−0.471116	+	0.882071i	$0.656149\pi$
$542$		0			0
$543$	−5.77200	−	18.7482i	−0.247700	−	0.804562i
$544$		0			0
$545$	4.08643	−	23.1753i	0.175043	−	0.992720i
$546$		0			0
$547$	7.64210	−	6.41248i	0.326752	−	0.274178i	−0.464623	−	0.885509i	$-0.653810\pi$
$547$	7.64210	−	6.41248i	0.326752	−	0.274178i	0.791375	+	0.611331i	$0.209366\pi$
$548$		0			0
$549$	−34.4507	+	8.73273i	−1.47032	+	0.372704i
$550$		0			0
$551$	−0.171694	−	0.973722i	−0.00731439	−	0.0414820i
$552$		0			0
$553$	−1.79310	+	0.652634i	−0.0762502	+	0.0277528i
$554$		0			0
$555$	20.0947	+	26.5583i	0.852971	+	1.12734i
$556$		0			0
$557$	9.26650	−	16.0500i	0.392634	−	0.680062i	−0.600162	−	0.799879i	$-0.704897\pi$
$557$	9.26650	−	16.0500i	0.392634	−	0.680062i	0.992796	+	0.119816i	$0.0382305\pi$
$558$		0			0
$559$	0.340480	+	0.589729i	0.0144008	+	0.0249429i
$560$		0			0
$561$	0.106744	+	0.0690241i	0.00450674	+	0.00291420i
$562$		0			0
$563$	−33.4632	−	28.0789i	−1.41031	−	1.18339i	−0.956300	−	0.292388i	$-0.905550\pi$
$563$	−33.4632	−	28.0789i	−1.41031	−	1.18339i	−0.454005	−	0.890999i	$-0.650005\pi$
$564$		0			0
$565$	−8.05997	−	2.93359i	−0.339086	−	0.123417i
$566$		0			0
$567$	−20.9582	−	4.28380i	−0.880161	−	0.179903i
$568$		0			0
$569$	−12.7485	−	4.64008i	−0.534446	−	0.194522i	0.0606766	−	0.998157i	$-0.480674\pi$
$569$	−12.7485	−	4.64008i	−0.534446	−	0.194522i	−0.595122	+	0.803635i	$0.702896\pi$
$570$		0			0
$571$	−18.1926	−	15.2654i	−0.761335	−	0.638836i	0.177139	−	0.984186i	$-0.443316\pi$
$571$	−18.1926	−	15.2654i	−0.761335	−	0.638836i	−0.938474	+	0.345350i	$0.887760\pi$
$572$		0			0
$573$	9.97529	+	6.45034i	0.416724	+	0.269467i
$574$		0			0
$575$	−8.56844	−	14.8410i	−0.357329	−	0.618911i
$576$		0			0
$577$	4.05951	−	7.03128i	0.169000	−	0.292716i	−0.769069	−	0.639166i	$-0.779280\pi$
$577$	4.05951	−	7.03128i	0.169000	−	0.292716i	0.938068	+	0.346450i	$0.112613\pi$
$578$		0			0
$579$	21.3329	+	28.1949i	0.886566	+	1.17174i
$580$		0			0
$581$	6.15473	−	2.24014i	0.255341	−	0.0929366i
$582$		0			0
$583$	0.235937	+	1.33806i	0.00977150	+	0.0554169i
$584$		0			0
$585$	5.85830	−	20.7360i	0.242211	−	0.857326i
$586$		0			0
$587$	2.82823	−	2.37317i	0.116734	−	0.0979511i	−0.582552	−	0.812793i	$-0.697946\pi$
$587$	2.82823	−	2.37317i	0.116734	−	0.0979511i	0.699286	+	0.714842i	$0.253501\pi$
$588$		0			0
$589$	−1.33729	+	7.58412i	−0.0551019	+	0.312498i
$590$		0			0
$591$	−1.54713	−	5.02527i	−0.0636403	−	0.206712i
$592$		0			0
$593$	29.4590			1.20974			0.604869	−	0.796325i	$-0.293226\pi$
$593$	29.4590			1.20974			0.604869	+	0.796325i	$0.293226\pi$
$594$		0			0
$595$	−1.91749			−0.0786093
$596$		0			0
$597$	−2.66695	+	2.87119i	−0.109151	+	0.117510i
$598$		0			0
$599$	3.79862	−	21.5431i	0.155207	−	0.880225i	−0.803388	−	0.595455i	$-0.796972\pi$
$599$	3.79862	−	21.5431i	0.155207	−	0.880225i	0.958596	−	0.284770i	$-0.0919172\pi$
$600$		0			0
$601$	27.9764	−	23.4750i	1.14118	−	0.957566i	0.141706	−	0.989909i	$-0.454741\pi$
$601$	27.9764	−	23.4750i	1.14118	−	0.957566i	0.999477	+	0.0323424i	$0.0102967\pi$
$602$		0			0
$603$	5.40333	+	0.546563i	0.220041	+	0.0222578i
$604$		0			0
$605$	5.22267	+	29.6192i	0.212332	+	1.20419i
$606$		0			0
$607$	−6.18395	+	2.25077i	−0.250999	+	0.0913561i	−0.464456	−	0.885596i	$-0.653750\pi$
$607$	−6.18395	+	2.25077i	−0.250999	+	0.0913561i	0.213457	+	0.976953i	$0.431528\pi$
$608$		0			0
$609$	−1.45045	+	0.180972i	−0.0587753	+	0.00733335i
$610$		0			0
$611$	−14.9217	+	25.8451i	−0.603667	+	1.04558i
$612$		0			0
$613$	3.57434	+	6.19093i	0.144366	+	0.250049i	0.929136	−	0.369737i	$-0.120552\pi$
$613$	3.57434	+	6.19093i	0.144366	+	0.250049i	−0.784770	+	0.619787i	$0.787219\pi$
$614$		0			0
$615$	−2.33194	+	46.2249i	−0.0940330	+	1.86397i
$616$		0			0
$617$	12.6684	+	10.6301i	0.510012	+	0.427951i	0.861133	−	0.508379i	$-0.169755\pi$
$617$	12.6684	+	10.6301i	0.510012	+	0.427951i	−0.351121	+	0.936330i	$0.614200\pi$
$618$		0			0
$619$	−1.40893	−	0.512808i	−0.0566296	−	0.0206115i	0.313550	−	0.949572i	$-0.398482\pi$
$619$	−1.40893	−	0.512808i	−0.0566296	−	0.0206115i	−0.370180	+	0.928960i	$0.620704\pi$
$620$		0			0
$621$	6.83279	+	34.0833i	0.274190	+	1.36772i
$622$		0			0
$623$	23.3415	+	8.49561i	0.935157	+	0.340369i
$624$		0			0
$625$	−23.9360	−	20.0847i	−0.957439	−	0.803387i
$626$		0			0
$627$	1.07401	−	0.549884i	0.0428919	−	0.0219602i
$628$		0			0
$629$	−1.02570	−	1.77657i	−0.0408974	−	0.0708363i
$630$		0			0
$631$	−17.9456	+	31.0827i	−0.714404	+	1.23738i	0.248785	+	0.968559i	$0.419969\pi$
$631$	−17.9456	+	31.0827i	−0.714404	+	1.23738i	−0.963189	+	0.268826i	$0.913364\pi$
$632$		0			0
$633$	−17.1314	+	40.5795i	−0.680913	+	1.61289i
$634$		0			0
$635$	47.6866	−	17.3565i	1.89238	−	0.688772i
$636$		0			0
$637$	−0.612614	−	3.47431i	−0.0242727	−	0.137657i
$638$		0			0
$639$	−0.919063	+	0.625157i	−0.0363576	+	0.0247308i
$640$		0			0
$641$	30.0504	−	25.2152i	1.18692	−	0.995942i	0.187010	−	0.982358i	$-0.440120\pi$
$641$	30.0504	−	25.2152i	1.18692	−	0.995942i	0.999908	−	0.0135840i	$-0.00432406\pi$
$642$		0			0
$643$	1.80915	−	10.2602i	0.0713461	−	0.404624i	−0.928130	−	0.372256i	$-0.878584\pi$
$643$	1.80915	−	10.2602i	0.0713461	−	0.404624i	0.999476	−	0.0323674i	$-0.0103047\pi$
$644$		0			0
$645$	1.21043	+	0.276958i	0.0476606	+	0.0109052i
$646$		0			0
$647$	39.1517			1.53921			0.769606	−	0.638519i	$-0.220453\pi$
$647$	39.1517			1.53921			0.769606	+	0.638519i	$0.220453\pi$
$648$		0			0
$649$	−1.49518			−0.0586910
$650$		0			0
$651$	11.0981	+	2.53935i	0.434967	+	0.0995248i
$652$		0			0
$653$	5.71474	−	32.4099i	0.223635	−	1.26830i	−0.641642	−	0.767004i	$-0.721747\pi$
$653$	5.71474	−	32.4099i	0.223635	−	1.26830i	0.865277	−	0.501294i	$-0.167142\pi$
$654$		0			0
$655$	29.9660	−	25.1444i	1.17087	−	0.982474i
$656$		0			0
$657$	−1.11076	−	15.0394i	−0.0433349	−	0.586743i
$658$		0			0
$659$	3.74532	+	21.2407i	0.145897	+	0.827422i	0.966643	+	0.256128i	$0.0824470\pi$
$659$	3.74532	+	21.2407i	0.145897	+	0.827422i	−0.820746	+	0.571293i	$0.806442\pi$
$660$		0			0
$661$	−24.7105	+	8.99389i	−0.961127	+	0.349822i	−0.774475	−	0.632604i	$-0.781986\pi$
$661$	−24.7105	+	8.99389i	−0.961127	+	0.349822i	−0.186652	+	0.982426i	$0.559764\pi$
$662$		0			0
$663$	−0.516213	+	1.22276i	−0.0200481	+	0.0474882i
$664$		0			0
$665$	−9.10043	+	15.7624i	−0.352900	+	0.611240i
$666$		0			0
$667$	1.18764	+	2.05705i	0.0459855	+	0.0796493i
$668$		0			0
$669$	5.90688	−	3.02427i	0.228373	−	0.116925i
$670$		0			0
$671$	−2.27023	−	1.90495i	−0.0876412	−	0.0735397i
$672$		0			0
$673$	−10.8272	−	3.94080i	−0.417360	−	0.151907i	0.124800	−	0.992182i	$-0.460171\pi$
$673$	−10.8272	−	3.94080i	−0.417360	−	0.151907i	−0.542160	+	0.840275i	$0.682393\pi$
$674$		0			0
$675$	−6.92226	−	11.3690i	−0.266438	−	0.437593i
$676$		0			0
$677$	31.8791	+	11.6030i	1.22521	+	0.445941i	0.871955	−	0.489585i	$-0.162852\pi$
$677$	31.8791	+	11.6030i	1.22521	+	0.445941i	0.353257	+	0.935526i	$0.385074\pi$
$678$		0			0
$679$	27.0103	+	22.6643i	1.03656	+	0.869776i
$680$		0			0
$681$	0.219563	−	4.35229i	0.00841369	−	0.166780i
$682$		0			0
$683$	18.3777	+	31.8310i	0.703201	+	1.21798i	0.967337	+	0.253495i	$0.0815801\pi$
$683$	18.3777	+	31.8310i	0.703201	+	1.21798i	−0.264135	+	0.964486i	$0.585087\pi$
$684$		0			0
$685$	−27.0661	+	46.8799i	−1.03414	+	1.79119i
$686$		0			0
$687$	27.3958	−	3.41816i	1.04522	−	0.130411i
$688$		0			0
$689$	−13.3311	+	4.85212i	−0.507874	+	0.184851i
$690$		0			0
$691$	−2.32309	−	13.1749i	−0.0883744	−	0.501196i	−0.996577	−	0.0826660i	$-0.973657\pi$
$691$	−2.32309	−	13.1749i	−0.0883744	−	0.501196i	0.908203	−	0.418530i	$-0.137455\pi$
$692$		0			0
$693$	−0.731885	−	1.62670i	−0.0278020	−	0.0617930i
$694$		0			0
$695$	−37.7294	+	31.6588i	−1.43116	+	1.20089i
$696$		0			0
$697$	0.495057	−	2.80761i	0.0187516	−	0.106346i
$698$		0			0
$699$	−33.1570	+	35.6961i	−1.25411	+	1.35015i
$700$		0			0
$701$	5.00452			0.189018			0.0945091	−	0.995524i	$-0.469872\pi$
$701$	5.00452			0.189018			0.0945091	+	0.995524i	$0.469872\pi$
$702$		0			0
$703$	−19.4720			−0.734400
$704$		0			0
$705$	16.0121	+	52.0094i	0.603050	+	1.95879i
$706$		0			0
$707$	−1.65313	+	9.37537i	−0.0621724	+	0.352597i
$708$		0			0
$709$	13.1330	−	11.0199i	0.493218	−	0.413859i	−0.361960	−	0.932194i	$-0.617892\pi$
$709$	13.1330	−	11.0199i	0.493218	−	0.413859i	0.855178	+	0.518334i	$0.173448\pi$
$710$		0			0
$711$	1.67982	+	1.72595i	0.0629982	+	0.0647282i
$712$		0			0
$713$	−3.21258	−	18.2195i	−0.120312	−	0.682324i
$714$		0			0
$715$	1.68842	−	0.614533i	0.0631432	−	0.0229822i
$716$		0			0
$717$	15.3687	+	20.3122i	0.573954	+	0.758572i
$718$		0			0
$719$	−21.6760	+	37.5439i	−0.808377	+	1.40015i	0.105610	+	0.994408i	$0.466320\pi$
$719$	−21.6760	+	37.5439i	−0.808377	+	1.40015i	−0.913987	+	0.405742i	$0.867013\pi$
$720$		0			0
$721$	7.03467	+	12.1844i	0.261985	+	0.453771i
$722$		0			0
$723$	−12.2799	−	7.94060i	−0.456696	−	0.295314i
$724$		0			0
$725$	−0.696735	−	0.584630i	−0.0258761	−	0.0217126i
$726$		0			0
$727$	−34.1521	−	12.4303i	−1.26663	−	0.461016i	−0.380642	−	0.924722i	$-0.624297\pi$
$727$	−34.1521	−	12.4303i	−1.26663	−	0.461016i	−0.885989	+	0.463706i	$0.846519\pi$
$728$		0			0
$729$	5.92298	+	26.3423i	0.219370	+	0.975642i
$730$		0			0
$731$	−0.0718726	−	0.0261595i	−0.00265830	−	0.000967544i
$732$		0			0
$733$	2.96889	+	2.49119i	0.109658	+	0.0920143i	0.695968	−	0.718073i	$-0.254975\pi$
$733$	2.96889	+	2.49119i	0.109658	+	0.0920143i	−0.586310	+	0.810087i	$0.699420\pi$
$734$		0			0
$735$	−5.40202	−	3.49312i	−0.199257	−	0.128846i
$736$		0			0
$737$	0.226432	+	0.392191i	0.00834071	+	0.0144465i
$738$		0			0
$739$	13.2241	−	22.9048i	0.486456	−	0.842567i	−0.513422	−	0.858136i	$-0.671623\pi$
$739$	13.2241	−	22.9048i	0.486456	−	0.842567i	0.999879	+	0.0155689i	$0.00495594\pi$
$740$		0			0
$741$	7.60158	+	10.0467i	0.279251	+	0.369075i
$742$		0			0
$743$	−12.6514	+	4.60474i	−0.464136	+	0.168932i	−0.563494	−	0.826120i	$-0.690543\pi$
$743$	−12.6514	+	4.60474i	−0.464136	+	0.168932i	0.0993584	+	0.995052i	$0.468321\pi$
$744$		0			0
$745$	−7.77830	−	44.1129i	−0.284975	−	1.61617i
$746$		0			0
$747$	−5.76591	−	5.92425i	−0.210964	−	0.216757i
$748$		0			0
$749$	−0.471538	+	0.395667i	−0.0172296	+	0.0144574i
$750$		0			0
$751$	−0.654359	+	3.71106i	−0.0238779	+	0.135418i	−0.994416	−	0.105528i	$-0.966347\pi$
$751$	−0.654359	+	3.71106i	−0.0238779	+	0.135418i	0.970538	+	0.240946i	$0.0774578\pi$
$752$		0			0
$753$	−11.8341	−	38.4386i	−0.431258	−	1.40078i
$754$		0			0
$755$	39.2536			1.42859
$756$		0			0
$757$	−33.7073			−1.22511			−0.612556	−	0.790427i	$-0.709859\pi$
$757$	−33.7073			−1.22511			−0.612556	+	0.790427i	$0.709859\pi$
$758$		0			0
$759$	−1.97271	+	2.12378i	−0.0716049	+	0.0770884i
$760$		0			0
$761$	−1.67665	+	9.50874i	−0.0607784	+	0.344692i	0.939221	+	0.343314i	$0.111550\pi$
$761$	−1.67665	+	9.50874i	−0.0607784	+	0.344692i	−0.999999	+	0.00137744i	$0.999562\pi$
$762$		0			0
$763$	15.5818	−	13.0747i	0.564100	−	0.473336i
$764$		0			0
$765$	0.993028	+	2.20711i	0.0359030	+	0.0797984i
$766$		0			0
$767$	−2.71093	−	15.3745i	−0.0978861	−	0.555139i
$768$		0			0
$769$	−36.3764	+	13.2399i	−1.31177	+	0.477445i	−0.900812	−	0.434210i	$-0.857027\pi$
$769$	−36.3764	+	13.2399i	−1.31177	+	0.477445i	−0.410957	+	0.911655i	$0.634805\pi$
$770$		0			0
$771$	−11.7994	+	1.47220i	−0.424944	+	0.0530200i
$772$		0			0
$773$	−12.1519	+	21.0478i	−0.437075	+	0.757036i	−0.997462	−	0.0711944i	$-0.977319\pi$
$773$	−12.1519	+	21.0478i	−0.437075	+	0.757036i	0.560387	+	0.828231i	$0.310652\pi$
$774$		0			0
$775$	3.54205	+	6.13500i	0.127234	+	0.220376i
$776$		0			0
$777$	−1.45036	+	28.7496i	−0.0520312	+	1.03139i
$778$		0			0
$779$	−20.7300	−	17.3945i	−0.742728	−	0.623223i
$780$		0			0
$781$	−0.0870967	−	0.0317006i	−0.00311656	−	0.00113434i
$782$		0			0
$783$	0.959467	+	1.57581i	0.0342886	+	0.0563150i
$784$		0			0
$785$	1.97251	+	0.717936i	0.0704020	+	0.0256242i
$786$		0			0
$787$	−16.0414	−	13.4604i	−0.571816	−	0.479810i	0.310432	−	0.950596i	$-0.399526\pi$
$787$	−16.0414	−	13.4604i	−0.571816	−	0.479810i	−0.882248	+	0.470785i	$0.843971\pi$
$788$		0			0
$789$	−5.16932	+	2.64664i	−0.184033	+	0.0942229i
$790$		0			0
$791$	−3.70688	−	6.42051i	−0.131802	−	0.228287i
$792$		0			0
$793$	15.4718	−	26.7979i	0.549419	−	0.951621i
$794$		0			0
$795$	−10.0612	+	23.8321i	−0.356834	+	0.845239i
$796$		0			0
$797$	−11.2169	+	4.08261i	−0.397322	+	0.144614i	−0.532951	−	0.846146i	$-0.678917\pi$
$797$	−11.2169	+	4.08261i	−0.397322	+	0.144614i	0.135628	+	0.990760i	$0.456695\pi$
$798$		0			0
$799$	−0.582068	−	3.30107i	−0.0205921	−	0.116783i
$800$		0			0
$801$	−2.30926	−	31.2668i	−0.0815939	−	1.10476i
$802$		0			0
$803$	0.963297	−	0.808303i	0.0339940	−	0.0285244i
$804$		0			0
$805$	7.59263	−	43.0600i	0.267605	−	1.51766i
$806$		0			0
$807$	21.5131	+	4.92242i	0.757298	+	0.173277i
$808$		0			0
$809$	8.60808			0.302644			0.151322	−	0.988485i	$-0.451647\pi$
$809$	8.60808			0.302644			0.151322	+	0.988485i	$0.451647\pi$
$810$		0			0
$811$	−1.53770			−0.0539958			−0.0269979	−	0.999635i	$-0.508595\pi$
$811$	−1.53770			−0.0539958			−0.0269979	+	0.999635i	$0.508595\pi$
$812$		0			0
$813$	39.7734	+	9.10055i	1.39491	+	0.319170i
$814$		0			0
$815$	2.44881	−	13.8879i	0.0857779	−	0.486471i
$816$		0			0
$817$	−0.556149	+	0.466665i	−0.0194572	+	0.0163265i
$818$		0			0
$819$	15.3998	−	10.4751i	0.538112	−	0.366030i
$820$		0			0
$821$	5.03168	+	28.5361i	0.175607	+	0.995915i	0.937441	+	0.348144i	$0.113188\pi$
$821$	5.03168	+	28.5361i	0.175607	+	0.995915i	−0.761835	+	0.647772i	$0.775701\pi$
$822$		0			0
$823$	−10.5779	+	3.85004i	−0.368722	+	0.134204i	−0.519734	−	0.854328i	$-0.673969\pi$
$823$	−10.5779	+	3.85004i	−0.368722	+	0.134204i	0.151012	+	0.988532i	$0.451747\pi$
$824$		0			0
$825$	0.431683	−	1.02253i	0.0150293	−	0.0356001i
$826$		0			0
$827$	15.4640	−	26.7844i	0.537734	−	0.931383i	−0.461291	−	0.887249i	$-0.652614\pi$
$827$	15.4640	−	26.7844i	0.537734	−	0.931383i	0.999026	−	0.0441346i	$-0.0140530\pi$
$828$		0			0
$829$	4.91762	+	8.51757i	0.170796	+	0.295827i	0.938698	−	0.344739i	$-0.112033\pi$
$829$	4.91762	+	8.51757i	0.170796	+	0.295827i	−0.767902	+	0.640567i	$0.778699\pi$
$830$		0			0
$831$	6.44630	−	3.30044i	0.223620	−	0.114491i
$832$		0			0
$833$	0.303547	+	0.254706i	0.0105173	+	0.00882505i
$834$		0			0
$835$	−23.0006	−	8.37152i	−0.795967	−	0.289708i
$836$		0			0
$837$	−2.82456	−	14.0894i	−0.0976310	−	0.487003i
$838$		0			0
$839$	−12.3506	−	4.49524i	−0.426389	−	0.155193i	0.119907	−	0.992785i	$-0.461740\pi$
$839$	−12.3506	−	4.49524i	−0.426389	−	0.155193i	−0.546296	+	0.837592i	$0.683963\pi$
$840$		0			0
$841$	−22.1187	−	18.5598i	−0.762714	−	0.639993i
$842$		0			0
$843$	1.88811	−	37.4271i	0.0650301	−	1.28906i
$844$		0			0
$845$	−8.49363	−	14.7114i	−0.292190	−	0.506088i
$846$		0			0
$847$	−12.9982	+	22.5136i	−0.446624	+	0.773575i
$848$		0			0
$849$	8.98435	−	1.12097i	0.308342	−	0.0384717i
$850$		0			0
$851$	43.9569	−	15.9990i	1.50682	−	0.548438i
$852$		0			0
$853$	2.68153	+	15.2077i	0.0918139	+	0.520703i	0.995677	+	0.0928812i	$0.0296077\pi$
$853$	2.68153	+	15.2077i	0.0918139	+	0.520703i	−0.903863	+	0.427821i	$0.859281\pi$
$854$		0			0
$855$	22.8562	+	2.31197i	0.781665	+	0.0790678i
$856$		0			0
$857$	16.8398	−	14.1302i	0.575235	−	0.482680i	−0.308143	−	0.951340i	$-0.599708\pi$
$857$	16.8398	−	14.1302i	0.575235	−	0.482680i	0.883378	+	0.468660i	$0.155263\pi$
$858$		0			0
$859$	−3.39772	+	19.2694i	−0.115929	+	0.657464i	0.870358	+	0.492420i	$0.163888\pi$
$859$	−3.39772	+	19.2694i	−0.115929	+	0.657464i	−0.986286	+	0.165044i	$0.947223\pi$
$860$		0			0
$861$	−27.2264	+	29.3114i	−0.927873	+	0.998929i
$862$		0			0
$863$	−21.8676			−0.744383			−0.372191	−	0.928156i	$-0.621393\pi$
$863$	−21.8676			−0.744383			−0.372191	+	0.928156i	$0.621393\pi$
$864$		0			0
$865$	18.7298			0.636833
$866$		0			0
$867$	8.62001	+	27.9989i	0.292751	+	0.950893i
$868$		0			0
$869$	−0.0348743	+	0.197782i	−0.00118303	+	0.00670929i
$870$		0			0
$871$	−3.62223	+	3.03941i	−0.122734	+	0.102986i
$872$		0			0
$873$	12.0996	−	42.8275i	0.409508	−	1.44949i
$874$		0			0
$875$	−2.76743	−	15.6949i	−0.0935563	−	0.530584i
$876$		0			0
$877$	36.7419	−	13.3729i	1.24068	−	0.451572i	0.363441	−	0.931617i	$-0.381602\pi$
$877$	36.7419	−	13.3729i	1.24068	−	0.451572i	0.877244	+	0.480045i	$0.159380\pi$
$878$		0			0
$879$	−6.41903	−	8.48379i	−0.216509	−	0.286151i
$880$		0			0
$881$	3.65254	−	6.32639i	0.123057	−	0.213141i	−0.797915	−	0.602771i	$-0.794063\pi$
$881$	3.65254	−	6.32639i	0.123057	−	0.213141i	0.920972	+	0.389629i	$0.127397\pi$
$882$		0			0
$883$	−1.74646	−	3.02496i	−0.0587732	−	0.101798i	0.835142	−	0.550035i	$-0.185386\pi$
$883$	−1.74646	−	3.02496i	−0.0587732	−	0.101798i	−0.893915	+	0.448237i	$0.852052\pi$
$884$		0			0
$885$	−23.9049	−	15.4577i	−0.803556	−	0.519605i
$886$		0			0
$887$	−21.7720	−	18.2688i	−0.731031	−	0.613408i	0.199381	−	0.979922i	$-0.436107\pi$
$887$	−21.7720	−	18.2688i	−0.731031	−	0.613408i	−0.930413	+	0.366514i	$0.880551\pi$
$888$		0			0
$889$	41.2181	+	15.0021i	1.38241	+	0.503156i
$890$		0			0
$891$	−1.49337	+	1.68487i	−0.0500298	+	0.0564452i
$892$		0			0
$893$	−29.8985	−	10.8821i	−1.00051	−	0.364157i
$894$		0			0
$895$	−38.6493	−	32.4306i	−1.29190	−	1.08404i
$896$		0			0
$897$	−25.4149	−	16.4341i	−0.848579	−	0.548718i
$898$		0			0
$899$	−0.490949	−	0.850349i	−0.0163741	−	0.0283607i
$900$		0			0
$901$	0.796719	−	1.37996i	0.0265426	−	0.0459731i
$902$		0			0
$903$	0.647588	+	0.855892i	0.0215504	+	0.0284823i
$904$		0			0
$905$	29.2655	−	10.6518i	0.972819	−	0.354077i
$906$		0			0
$907$	−9.22362	−	52.3097i	−0.306265	−	1.73692i	−0.617489	−	0.786579i	$-0.711850\pi$
$907$	−9.22362	−	52.3097i	−0.306265	−	1.73692i	0.311224	−	0.950337i	$-0.399261\pi$
$908$		0			0
$909$	11.6476	−	2.95249i	0.386327	−	0.0979279i
$910$		0			0
$911$	6.18649	−	5.19108i	0.204968	−	0.171988i	−0.534526	−	0.845152i	$-0.679510\pi$
$911$	6.18649	−	5.19108i	0.204968	−	0.171988i	0.739493	+	0.673164i	$0.235065\pi$
$912$		0			0
$913$	0.119704	−	0.678878i	0.00396164	−	0.0224676i
$914$		0			0
$915$	−16.6024	−	53.9267i	−0.548858	−	1.78276i
$916$		0			0
$917$	33.8116			1.11656
$918$		0			0
$919$	47.9961			1.58325			0.791623	−	0.611009i	$-0.209236\pi$
$919$	47.9961			1.58325			0.791623	+	0.611009i	$0.209236\pi$
$920$		0			0
$921$	22.4013	−	24.1168i	0.738149	−	0.794677i
$922$		0			0
$923$	0.168051	−	0.953063i	0.00553146	−	0.0313705i
$924$		0			0
$925$	−13.7213	+	11.5135i	−0.451153	+	0.378562i
$926$		0			0
$927$	10.3817	−	14.4073i	0.340979	−	0.473197i
$928$		0			0
$929$	−5.03474	−	28.5534i	−0.165185	−	0.936808i	−0.948874	−	0.315655i	$-0.897776\pi$
$929$	−5.03474	−	28.5534i	−0.165185	−	0.936808i	0.783689	−	0.621153i	$-0.213335\pi$
$930$		0			0
$931$	3.53442	−	1.28642i	0.115836	−	0.0421608i
$932$		0			0
$933$	−37.0332	+	4.62061i	−1.21241	+	0.151272i
$934$		0			0
$935$	−0.100907	+	0.174775i	−0.00330000	+	0.00571576i
$936$		0			0
$937$	−2.51425	−	4.35481i	−0.0821369	−	0.142265i	0.822031	−	0.569443i	$-0.192841\pi$
$937$	−2.51425	−	4.35481i	−0.0821369	−	0.142265i	−0.904168	+	0.427178i	$0.859508\pi$
$938$		0			0
$939$	0.332803	−	6.59699i	0.0108606	−	0.215285i
$940$		0			0
$941$	−42.7767	−	35.8939i	−1.39448	−	1.17011i	−0.963487	−	0.267755i	$-0.913718\pi$
$941$	−42.7767	−	35.8939i	−1.39448	−	1.17011i	−0.430995	−	0.902354i	$-0.641837\pi$
$942$		0			0
$943$	61.0887	+	22.2345i	1.98932	+	0.724054i
$944$		0			0
$945$	5.11596	−	33.5741i	0.166422	−	1.09216i
$946$		0			0
$947$	39.9645	+	14.5459i	1.29867	+	0.472678i	0.896564	−	0.442914i	$-0.146055\pi$
$947$	39.9645	+	14.5459i	1.29867	+	0.472678i	0.402109	+	0.915592i	$0.368277\pi$
$948$		0			0
$949$	10.0581	+	8.43973i	0.326499	+	0.273965i
$950$		0			0
$951$	6.55926	−	3.35828i	0.212699	−	0.108900i
$952$		0			0
$953$	−10.9074	−	18.8922i	−0.353325	−	0.611977i	0.633505	−	0.773739i	$-0.281616\pi$
$953$	−10.9074	−	18.8922i	−0.353325	−	0.611977i	−0.986830	+	0.161762i	$0.948282\pi$
$954$		0			0
$955$	−9.42977	+	16.3328i	−0.305140	+	0.528518i
$956$		0			0
$957$	−0.0598339	+	0.141729i	−0.00193415	+	0.00458146i
$958$		0			0
$959$	−43.9676	+	16.0029i	−1.41979	+	0.516761i
$960$		0			0
$961$	−4.05507	−	22.9974i	−0.130809	−	0.741852i
$962$		0			0
$963$	0.699631	+	0.337853i	0.0225453	+	0.0108872i
$964$		0			0
$965$	−42.9996	+	36.0809i	−1.38421	+	1.16149i
$966$		0			0
$967$	−0.803746	+	4.55827i	−0.0258467	+	0.146584i	−0.995000	−	0.0998746i	$-0.968156\pi$
$967$	−0.803746	+	4.55827i	−0.0258467	+	0.146584i	0.969153	+	0.246459i	$0.0792669\pi$
$968$		0			0
$969$	−1.37940	−	0.315621i	−0.0443128	−	0.0101392i
$970$		0			0
$971$	21.6509			0.694809			0.347405	−	0.937715i	$-0.387063\pi$
$971$	21.6509			0.694809			0.347405	+	0.937715i	$0.387063\pi$
$972$		0			0
$973$	−42.5714			−1.36478
$974$		0			0
$975$	11.2971	+	2.58488i	0.361796	+	0.0827825i
$976$		0			0
$977$	−3.83499	+	21.7493i	−0.122692	+	0.695822i	0.859960	+	0.510362i	$0.170489\pi$
$977$	−3.83499	+	21.7493i	−0.122692	+	0.695822i	−0.982652	+	0.185460i	$0.940623\pi$
$978$		0			0
$979$	2.00269	−	1.68046i	0.0640063	−	0.0537076i
$980$		0			0
$981$	−23.1191	−	11.1643i	−0.738137	−	0.356448i
$982$		0			0
$983$	2.40729	+	13.6524i	0.0767807	+	0.435445i	0.998829	+	0.0483713i	$0.0154031\pi$
$983$	2.40729	+	13.6524i	0.0767807	+	0.435445i	−0.922049	+	0.387074i	$0.873486\pi$
$984$		0			0
$985$	7.84434	−	2.85511i	0.249941	−	0.0909712i
$986$		0			0
$987$	−18.2940	+	43.3334i	−0.582305	+	1.37932i
$988$		0			0
$989$	0.872042	−	1.51042i	0.0277293	−	0.0480286i
$990$		0			0
$991$	17.4112	+	30.1570i	0.553084	+	0.957970i	0.998050	+	0.0624224i	$0.0198826\pi$
$991$	17.4112	+	30.1570i	0.553084	+	0.957970i	−0.444966	+	0.895548i	$0.646784\pi$
$992$		0			0
$993$	22.0371	−	11.2828i	0.699328	−	0.358049i
$994$		0			0
$995$	−4.76590	−	3.99906i	−0.151089	−	0.126779i
$996$		0			0
$997$	23.2572	+	8.46492i	0.736562	+	0.268087i	0.682940	−	0.730475i	$-0.260701\pi$
$997$	23.2572	+	8.46492i	0.736562	+	0.268087i	0.0536221	+	0.998561i	$0.482923\pi$
$998$		0			0
$999$	33.8433	−	13.2195i	1.07075	−	0.418245i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.u.c.193.2		12
4.3	odd	2		27.2.e.a.4.2	✓	12
12.11	even	2		81.2.e.a.64.1		12
20.3	even	4		675.2.u.b.274.3		24
20.7	even	4		675.2.u.b.274.2		24
20.19	odd	2		675.2.l.c.301.1		12
27.7	even	9	inner	432.2.u.c.385.2		12
36.7	odd	6		243.2.e.c.28.1		12
36.11	even	6		243.2.e.b.28.2		12
36.23	even	6		243.2.e.a.109.2		12
36.31	odd	6		243.2.e.d.109.1		12
108.7	odd	18		27.2.e.a.7.2	yes	12
108.11	even	18		243.2.e.b.217.2		12
108.23	even	18		729.2.c.b.244.3		12
108.31	odd	18		729.2.c.e.244.4		12
108.43	odd	18		243.2.e.c.217.1		12
108.47	even	18		81.2.e.a.19.1		12
108.59	even	18		729.2.c.b.487.3		12
108.67	odd	18		729.2.a.a.1.3		6
108.79	odd	18		243.2.e.d.136.1		12
108.83	even	18		243.2.e.a.136.2		12
108.95	even	18		729.2.a.d.1.4		6
108.103	odd	18		729.2.c.e.487.4		12
540.7	even	36		675.2.u.b.574.3		24
540.223	even	36		675.2.u.b.574.2		24
540.439	odd	18		675.2.l.c.601.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.4.2	✓	12	4.3	odd	2
27.2.e.a.7.2	yes	12	108.7	odd	18
81.2.e.a.19.1		12	108.47	even	18
81.2.e.a.64.1		12	12.11	even	2
243.2.e.a.109.2		12	36.23	even	6
243.2.e.a.136.2		12	108.83	even	18
243.2.e.b.28.2		12	36.11	even	6
243.2.e.b.217.2		12	108.11	even	18
243.2.e.c.28.1		12	36.7	odd	6
243.2.e.c.217.1		12	108.43	odd	18
243.2.e.d.109.1		12	36.31	odd	6
243.2.e.d.136.1		12	108.79	odd	18
432.2.u.c.193.2		12	1.1	even	1	trivial
432.2.u.c.385.2		12	27.7	even	9	inner
675.2.l.c.301.1		12	20.19	odd	2
675.2.l.c.601.1		12	540.439	odd	18
675.2.u.b.274.2		24	20.7	even	4
675.2.u.b.274.3		24	20.3	even	4
675.2.u.b.574.2		24	540.223	even	36
675.2.u.b.574.3		24	540.7	even	36
729.2.a.a.1.3		6	108.67	odd	18
729.2.a.d.1.4		6	108.95	even	18
729.2.c.b.244.3		12	108.23	even	18
729.2.c.b.487.3		12	108.59	even	18
729.2.c.e.244.4		12	108.31	odd	18
729.2.c.e.487.4		12	108.103	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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.68842 + 0.386327i) q^{3} +(-0.477505 + 2.70806i) q^{5} +(-1.82076 + 1.52780i) q^{7} +(2.70150 + 1.30456i) q^{9} +(0.0434396 + 0.246358i) q^{11} +(-2.45446 + 0.893351i) q^{13} +(-1.85243 + 4.38787i) q^{15} +(0.146688 - 0.254072i) q^{17} +(-1.39237 - 2.41166i) q^{19} +(-3.66443 + 1.87615i) q^{21} +(5.12472 + 4.30015i) q^{23} +(-2.40714 - 0.876128i) q^{25} +(4.05728 + 3.24631i) q^{27} +(0.333645 + 0.121437i) q^{29} +(-2.11847 - 1.77761i) q^{31} +(-0.0218307 + 0.432738i) q^{33} +(-3.26796 - 5.66027i) q^{35} +(3.49619 - 6.05558i) q^{37} +(-4.48928 + 0.560124i) q^{39} +(9.13156 - 3.32362i) q^{41} +(-0.0452712 - 0.256746i) q^{43} +(-4.82282 + 6.69291i) q^{45} +(8.75249 - 7.34421i) q^{47} +(-0.234540 + 1.33014i) q^{49} +(0.345826 - 0.372309i) q^{51} +5.43137 q^{53} -0.687897 q^{55} +(-1.41922 - 4.60980i) q^{57} +(-1.03788 + 5.88612i) q^{59} +(-9.07515 + 7.61495i) q^{61} +(-6.91190 + 1.75206i) q^{63} +(-1.24723 - 7.07342i) q^{65} +(1.70113 - 0.619160i) q^{67} +(6.99139 + 9.24026i) q^{69} +(-0.185255 + 0.320871i) q^{71} +(-2.51339 - 4.35333i) q^{73} +(-3.72579 - 2.40921i) q^{75} +(-0.455479 - 0.382193i) q^{77} +(0.754406 + 0.274581i) q^{79} +(5.59624 + 7.04855i) q^{81} +(-2.58947 - 0.942488i) q^{83} +(0.617998 + 0.518562i) q^{85} +(0.516417 + 0.333932i) q^{87} +(-5.22533 - 9.05054i) q^{89} +(3.10412 - 5.37650i) q^{91} +(-2.89012 - 3.81976i) q^{93} +(7.19580 - 2.61906i) q^{95} +(-2.57600 - 14.6092i) q^{97} +(-0.204037 + 0.722208i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} - 3 q^{5} + 6 q^{7} - 3 q^{11} - 6 q^{13} - 9 q^{15} + 9 q^{17} + 3 q^{19} - 12 q^{21} + 12 q^{23} + 3 q^{25} + 9 q^{27} - 6 q^{29} - 3 q^{31} - 12 q^{35} - 3 q^{37} - 33 q^{39} + 15 q^{41}+ \cdots + 27 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 - 3 * q^5 + 6 * q^7 - 3 * q^11 - 6 * q^13 - 9 * q^15 + 9 * q^17 + 3 * q^19 - 12 * q^21 + 12 * q^23 + 3 * q^25 + 9 * q^27 - 6 * q^29 - 3 * q^31 - 12 * q^35 - 3 * q^37 - 33 * q^39 + 15 * q^41 - 3 * q^43 - 9 * q^45 + 15 * q^47 + 12 * q^49 + 18 * q^51 - 18 * q^53 + 12 * q^55 - 3 * q^57 + 12 * q^59 + 12 * q^61 - 9 * q^63 + 3 * q^65 + 15 * q^67 + 9 * q^69 - 27 * q^71 + 6 * q^73 - 39 * q^75 + 15 * q^77 + 42 * q^79 + 36 * q^81 - 39 * q^83 - 27 * q^85 - 9 * q^87 + 9 * q^89 - 6 * q^91 - 39 * q^93 + 33 * q^95 + 3 * q^97 + 27 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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