LMFDB - Embedded newform 432.2.be.a.335.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(47,432)]

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([9, 0, 7]))

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

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

chi := DirichletCharacter("432.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.be (of order $18$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			335.5
Character	$\chi$	$=$	432.335
Dual form			432.2.be.a.383.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.873396 + 1.49572i) q^{3} +(-0.268878 + 0.738735i) q^{5} +(-3.49766 - 0.616732i) q^{7} +(-1.47436 + 2.61271i) q^{9} +O(q^{10})$	\(q+(0.873396 + 1.49572i) q^{3} +(-0.268878 + 0.738735i) q^{5} +(-3.49766 - 0.616732i) q^{7} +(-1.47436 + 2.61271i) q^{9} +(-4.77372 + 1.73749i) q^{11} +(-4.34250 + 3.64379i) q^{13} +(-1.33978 + 0.243043i) q^{15} +(6.45925 - 3.72925i) q^{17} +(2.31140 + 1.33449i) q^{19} +(-2.13239 - 5.77017i) q^{21} +(0.749727 + 4.25191i) q^{23} +(3.35679 + 2.81668i) q^{25} +(-5.19559 + 0.0767079i) q^{27} +(3.09583 - 3.68947i) q^{29} +(-2.76226 + 0.487060i) q^{31} +(-6.76815 - 5.62263i) q^{33} +(1.39604 - 2.41802i) q^{35} +(0.526507 + 0.911937i) q^{37} +(-9.24281 - 3.31269i) q^{39} +(-1.18342 - 1.41034i) q^{41} +(3.64664 + 10.0191i) q^{43} +(-1.53368 - 1.79166i) q^{45} +(1.36451 - 7.73852i) q^{47} +(5.27542 + 1.92010i) q^{49} +(11.2194 + 6.40412i) q^{51} +3.08817i q^{53} -3.99368i q^{55} +(0.0227487 + 4.62274i) q^{57} +(5.15076 + 1.87472i) q^{59} +(-1.62926 + 9.24000i) q^{61} +(6.76815 - 8.22910i) q^{63} +(-1.52419 - 4.18769i) q^{65} +(-6.27089 - 7.47336i) q^{67} +(-5.70486 + 4.83499i) q^{69} +(-1.72857 - 2.99398i) q^{71} +(-4.99284 + 8.64785i) q^{73} +(-1.28116 + 7.48089i) q^{75} +(17.7684 - 3.13305i) q^{77} +(-0.929972 + 1.10830i) q^{79} +(-4.65254 - 7.70415i) q^{81} +(1.12835 + 0.946797i) q^{83} +(1.01818 + 5.77438i) q^{85} +(8.22230 + 1.40813i) q^{87} +(-3.10319 - 1.79163i) q^{89} +(17.4358 - 10.0666i) q^{91} +(-3.14105 - 3.70617i) q^{93} +(-1.60732 + 1.34870i) q^{95} +(-2.87618 + 1.04684i) q^{97} +(2.49860 - 15.0340i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{5} - 12 q^{9}+O(q^{10}) $ 36 * q - 6 * q^5 - 12 * q^9	$ 36 q - 6 q^{5} - 12 q^{9} - 36 q^{21} + 18 q^{25} - 24 q^{29} - 36 q^{33} - 18 q^{41} - 18 q^{45} + 42 q^{65} + 54 q^{69} - 18 q^{73} + 90 q^{77} + 36 q^{81} + 72 q^{85} + 72 q^{89} + 54 q^{93} + 54 q^{97}+O(q^{100}) $ 36 * q - 6 * q^5 - 12 * q^9 - 36 * q^21 + 18 * q^25 - 24 * q^29 - 36 * q^33 - 18 * q^41 - 18 * q^45 + 42 * q^65 + 54 * q^69 - 18 * q^73 + 90 * q^77 + 36 * q^81 + 72 * q^85 + 72 * q^89 + 54 * q^93 + 54 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{18}\right)$

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
$3$	0.873396	+	1.49572i	0.504256	+	0.863554i
$3$	0.873396	+	1.49572i	0.504256	+	0.863554i
$4$		0			0
$5$	−0.268878	+	0.738735i	−0.120246	+	0.330372i	−0.985183	−	0.171508i	$-0.945136\pi$
$5$	−0.268878	+	0.738735i	−0.120246	+	0.330372i	0.864937	+	0.501880i	$0.167358\pi$
$6$		0			0
$7$	−3.49766	−	0.616732i	−1.32199	−	0.233103i	−0.532273	−	0.846573i	$-0.678662\pi$
$7$	−3.49766	−	0.616732i	−1.32199	−	0.233103i	−0.789718	+	0.613470i	$0.789773\pi$
$8$		0			0
$9$	−1.47436	+	2.61271i	−0.491453	+	0.870904i
$10$		0			0
$11$	−4.77372	+	1.73749i	−1.43933	+	0.523873i	−0.939590	−	0.342302i	$-0.888793\pi$
$11$	−4.77372	+	1.73749i	−1.43933	+	0.523873i	−0.499740	+	0.866176i	$0.666571\pi$
$12$		0			0
$13$	−4.34250	+	3.64379i	−1.20439	+	1.01061i	−0.204899	+	0.978783i	$0.565686\pi$
$13$	−4.34250	+	3.64379i	−1.20439	+	1.01061i	−0.999494	+	0.0318218i	$0.989869\pi$
$14$		0			0
$15$	−1.33978	+	0.243043i	−0.345929	+	0.0627534i
$16$		0			0
$17$	6.45925	−	3.72925i	1.56660	−	0.904476i	0.570036	−	0.821620i	$-0.306929\pi$
$17$	6.45925	−	3.72925i	1.56660	−	0.904476i	0.996562	−	0.0828560i	$-0.0264042\pi$
$18$		0			0
$19$	2.31140	+	1.33449i	0.530271	+	0.306152i	0.741127	−	0.671365i	$-0.234292\pi$
$19$	2.31140	+	1.33449i	0.530271	+	0.306152i	−0.210856	+	0.977517i	$0.567625\pi$
$20$		0			0
$21$	−2.13239	−	5.77017i	−0.465325	−	1.25915i
$22$		0			0
$23$	0.749727	+	4.25191i	0.156329	+	0.886585i	0.957561	+	0.288231i	$0.0930672\pi$
$23$	0.749727	+	4.25191i	0.156329	+	0.886585i	−0.801232	+	0.598354i	$0.795822\pi$
$24$		0			0
$25$	3.35679	+	2.81668i	0.671358	+	0.563336i
$26$		0			0
$27$	−5.19559	+	0.0767079i	−0.999891	+	0.0147624i
$28$		0			0
$29$	3.09583	−	3.68947i	0.574882	−	0.685117i	−0.397744	−	0.917497i	$-0.630207\pi$
$29$	3.09583	−	3.68947i	0.574882	−	0.685117i	0.972625	+	0.232379i	$0.0746511\pi$
$30$		0			0
$31$	−2.76226	+	0.487060i	−0.496116	+	0.0874786i	−0.416107	−	0.909316i	$-0.636606\pi$
$31$	−2.76226	+	0.487060i	−0.496116	+	0.0874786i	−0.0800087	+	0.996794i	$0.525495\pi$
$32$		0			0
$33$	−6.76815	−	5.62263i	−1.17818	−	0.978774i
$34$		0			0
$35$	1.39604	−	2.41802i	0.235974	−	0.408720i
$36$		0			0
$37$	0.526507	+	0.911937i	0.0865573	+	0.149922i	0.906054	−	0.423163i	$-0.139080\pi$
$37$	0.526507	+	0.911937i	0.0865573	+	0.149922i	−0.819496	+	0.573084i	$0.805747\pi$
$38$		0			0
$39$	−9.24281	−	3.31269i	−1.48003	−	0.530455i
$40$		0			0
$41$	−1.18342	−	1.41034i	−0.184818	−	0.220258i	0.665678	−	0.746239i	$-0.268143\pi$
$41$	−1.18342	−	1.41034i	−0.184818	−	0.220258i	−0.850496	+	0.525981i	$0.823698\pi$
$42$		0			0
$43$	3.64664	+	10.0191i	0.556107	+	1.52789i	0.825237	+	0.564787i	$0.191042\pi$
$43$	3.64664	+	10.0191i	0.556107	+	1.52789i	−0.269130	+	0.963104i	$0.586736\pi$
$44$		0			0
$45$	−1.53368	−	1.79166i	−0.228628	−	0.267085i
$46$		0			0
$47$	1.36451	−	7.73852i	0.199034	−	1.12878i	−0.707521	−	0.706692i	$-0.750187\pi$
$47$	1.36451	−	7.73852i	0.199034	−	1.12878i	0.906555	−	0.422087i	$-0.138702\pi$
$48$		0			0
$49$	5.27542	+	1.92010i	0.753632	+	0.274300i
$50$		0			0
$51$	11.2194	+	6.40412i	1.57103	+	0.896755i
$52$		0			0
$53$			3.08817i			0.424192i	0.977249	+	0.212096i	$0.0680290\pi$
$53$			3.08817i			0.424192i	−0.977249	+	0.212096i	$0.931971\pi$
$54$		0			0
$55$		−	3.99368i		−	0.538508i
$56$		0			0
$57$	0.0227487	+	4.62274i	0.00301313	+	0.612297i
$58$		0			0
$59$	5.15076	+	1.87472i	0.670572	+	0.244068i	0.654794	−	0.755807i	$-0.272755\pi$
$59$	5.15076	+	1.87472i	0.670572	+	0.244068i	0.0157780	+	0.999876i	$0.494977\pi$
$60$		0			0
$61$	−1.62926	+	9.24000i	−0.208606	+	1.18306i	0.683058	+	0.730364i	$0.260649\pi$
$61$	−1.62926	+	9.24000i	−0.208606	+	1.18306i	−0.891664	+	0.452698i	$0.850462\pi$
$62$		0			0
$63$	6.76815	−	8.22910i	0.852706	−	1.03677i
$64$		0			0
$65$	−1.52419	−	4.18769i	−0.189053	−	0.519419i
$66$		0			0
$67$	−6.27089	−	7.47336i	−0.766111	−	0.913016i	0.232107	−	0.972690i	$-0.425438\pi$
$67$	−6.27089	−	7.47336i	−0.766111	−	0.913016i	−0.998218	+	0.0596746i	$0.980994\pi$
$68$		0			0
$69$	−5.70486	+	4.83499i	−0.686785	+	0.582064i
$70$		0			0
$71$	−1.72857	−	2.99398i	−0.205144	−	0.355320i	0.745035	−	0.667026i	$-0.232433\pi$
$71$	−1.72857	−	2.99398i	−0.205144	−	0.355320i	−0.950179	+	0.311706i	$0.899100\pi$
$72$		0			0
$73$	−4.99284	+	8.64785i	−0.584367	+	1.01215i	0.410587	+	0.911822i	$0.365324\pi$
$73$	−4.99284	+	8.64785i	−0.584367	+	1.01215i	−0.994954	+	0.100332i	$0.968009\pi$
$74$		0			0
$75$	−1.28116	+	7.48089i	−0.147935	+	0.863819i
$76$		0			0
$77$	17.7684	−	3.13305i	2.02490	−	0.357044i
$78$		0			0
$79$	−0.929972	+	1.10830i	−0.104630	+	0.124693i	−0.815818	−	0.578309i	$-0.803713\pi$
$79$	−0.929972	+	1.10830i	−0.104630	+	0.124693i	0.711188	+	0.703002i	$0.248157\pi$
$80$		0			0
$81$	−4.65254	−	7.70415i	−0.516949	−	0.856016i
$82$		0			0
$83$	1.12835	+	0.946797i	0.123852	+	0.103925i	0.702610	−	0.711575i	$-0.252018\pi$
$83$	1.12835	+	0.946797i	0.123852	+	0.103925i	−0.578758	+	0.815500i	$0.696462\pi$
$84$		0			0
$85$	1.01818	+	5.77438i	0.110437	+	0.626320i
$86$		0			0
$87$	8.22230	+	1.40813i	0.881523	+	0.150967i
$88$		0			0
$89$	−3.10319	−	1.79163i	−0.328938	−	0.189912i	0.326432	−	0.945221i	$-0.394154\pi$
$89$	−3.10319	−	1.79163i	−0.328938	−	0.189912i	−0.655369	+	0.755308i	$0.727487\pi$
$90$		0			0
$91$	17.4358	−	10.0666i	1.82777	−	1.05526i
$92$		0			0
$93$	−3.14105	−	3.70617i	−0.325712	−	0.384312i
$94$		0			0
$95$	−1.60732	+	1.34870i	−0.164907	+	0.138374i
$96$		0			0
$97$	−2.87618	+	1.04684i	−0.292031	+	0.106291i	−0.483882	−	0.875133i	$-0.660773\pi$
$97$	−2.87618	+	1.04684i	−0.292031	+	0.106291i	0.191850	+	0.981424i	$0.438551\pi$
$98$		0			0
$99$	2.49860	−	15.0340i	0.251119	−	1.51098i
$100$		0			0
$101$	9.66552	+	1.70429i	0.961755	+	0.169583i	0.632417	−	0.774628i	$-0.282063\pi$
$101$	9.66552	+	1.70429i	0.961755	+	0.169583i	0.329339	+	0.944212i	$0.393174\pi$
$102$		0			0
$103$	2.73206	−	7.50626i	0.269197	−	0.739614i	−0.729268	−	0.684229i	$-0.760139\pi$
$103$	2.73206	−	7.50626i	0.269197	−	0.739614i	0.998465	−	0.0553854i	$-0.0176387\pi$
$104$		0			0
$105$	4.83598	−	0.0237980i	0.471943	−	0.00232245i
$106$		0			0
$107$	15.2633			1.47555			0.737777	−	0.675044i	$-0.235875\pi$
$107$	15.2633			1.47555			0.737777	+	0.675044i	$0.235875\pi$
$108$		0			0
$109$	1.31092			0.125563			0.0627817	−	0.998027i	$-0.480003\pi$
$109$	1.31092			0.125563			0.0627817	+	0.998027i	$0.480003\pi$
$110$		0			0
$111$	−0.904154	+	1.58399i	−0.0858185	+	0.150346i
$112$		0			0
$113$	−0.0329085	+	0.0904152i	−0.00309577	+	0.00850555i	−0.941231	−	0.337764i	$-0.890329\pi$
$113$	−0.0329085	+	0.0904152i	−0.00309577	+	0.00850555i	0.938135	+	0.346269i	$0.112552\pi$
$114$		0			0
$115$	−3.34262	−	0.589395i	−0.311701	−	0.0549613i
$116$		0			0
$117$	−3.11778	−	16.7179i	−0.288239	−	1.54557i
$118$		0			0
$119$	−24.8922	+	9.06002i	−2.28186	+	0.830531i
$120$		0			0
$121$	11.3430	−	9.51791i	1.03118	−	0.865265i
$122$		0			0
$123$	1.07588	−	3.00184i	0.0970091	−	0.270667i
$124$		0			0
$125$	−6.38745	+	3.68780i	−0.571311	+	0.329847i
$126$		0			0
$127$	9.78038	+	5.64670i	0.867868	+	0.501064i	0.866639	−	0.498935i	$-0.166276\pi$
$127$	9.78038	+	5.64670i	0.867868	+	0.501064i	0.00122880	+	0.999999i	$0.499609\pi$
$128$		0			0
$129$	−11.8007	+	14.2049i	−1.03900	+	1.25068i
$130$		0			0
$131$	2.07281	+	11.7555i	0.181102	+	1.02708i	0.930862	+	0.365372i	$0.119058\pi$
$131$	2.07281	+	11.7555i	0.181102	+	1.02708i	−0.749759	+	0.661711i	$0.769831\pi$
$132$		0			0
$133$	−7.26147	−	6.09310i	−0.629649	−	0.528339i
$134$		0			0
$135$	1.34031	−	3.85879i	0.115355	−	0.332111i
$136$		0			0
$137$	−3.22440	+	3.84269i	−0.275479	+	0.328303i	−0.885990	−	0.463705i	$-0.846520\pi$
$137$	−3.22440	+	3.84269i	−0.275479	+	0.328303i	0.610511	+	0.792008i	$0.290964\pi$
$138$		0			0
$139$	−5.82044	+	1.02630i	−0.493684	+	0.0870497i	−0.414947	−	0.909846i	$-0.636200\pi$
$139$	−5.82044	+	1.02630i	−0.493684	+	0.0870497i	−0.0787369	+	0.996895i	$0.525089\pi$
$140$		0			0
$141$	12.7664	−	4.71787i	1.07513	−	0.397316i
$142$		0			0
$143$	14.3988	−	24.9395i	1.20409	−	2.08554i
$144$		0			0
$145$	1.89314	+	3.27901i	0.157217	+	0.272307i
$146$		0			0
$147$	1.73561	+	9.56756i	0.143150	+	0.789119i
$148$		0			0
$149$	−13.2535	−	15.7949i	−1.08577	−	1.29397i	−0.953048	−	0.302819i	$-0.902072\pi$
$149$	−13.2535	−	15.7949i	−1.08577	−	1.29397i	−0.132723	−	0.991153i	$-0.542372\pi$
$150$		0			0
$151$	1.71324	+	4.70708i	0.139421	+	0.383057i	0.989678	−	0.143312i	$-0.0457753\pi$
$151$	1.71324	+	4.70708i	0.139421	+	0.383057i	−0.850256	+	0.526369i	$0.823553\pi$
$152$		0			0
$153$	0.220216	+	22.3744i	0.0178034	+	1.80886i
$154$		0			0
$155$	0.382900	−	2.17154i	0.0307553	−	0.174422i
$156$		0			0
$157$	−12.7218	−	4.63034i	−1.01531	−	0.369542i	−0.219838	−	0.975536i	$-0.570553\pi$
$157$	−12.7218	−	4.63034i	−1.01531	−	0.369542i	−0.795469	+	0.605995i	$0.792775\pi$
$158$		0			0
$159$	−4.61903	+	2.69719i	−0.366313	+	0.213901i
$160$		0			0
$161$		−	15.3341i		−	1.20850i
$162$		0			0
$163$			7.88546i			0.617637i	0.951121	+	0.308819i	$0.0999336\pi$
$163$			7.88546i			0.617637i	−0.951121	+	0.308819i	$0.900066\pi$
$164$		0			0
$165$	5.97343	−	3.48807i	0.465031	−	0.271546i
$166$		0			0
$167$	17.4302	+	6.34409i	1.34879	+	0.490920i	0.912571	−	0.408919i	$-0.134094\pi$
$167$	17.4302	+	6.34409i	1.34879	+	0.490920i	0.436221	+	0.899839i	$0.356316\pi$
$168$		0			0
$169$	3.32267	−	18.8438i	0.255590	−	1.44952i
$170$		0			0
$171$	−6.89446	+	4.07151i	−0.527233	+	0.311356i
$172$		0			0
$173$	6.11376	+	16.7974i	0.464820	+	1.27708i	0.921821	+	0.387617i	$0.126702\pi$
$173$	6.11376	+	16.7974i	0.464820	+	1.27708i	−0.457000	+	0.889467i	$0.651076\pi$
$174$		0			0
$175$	−10.0038	−	11.9220i	−0.756214	−	0.901221i
$176$		0			0
$177$	1.69459	+	9.34148i	0.127374	+	0.702149i
$178$		0			0
$179$	−5.34490	−	9.25764i	−0.399497	−	0.691949i	0.594167	−	0.804342i	$-0.297482\pi$
$179$	−5.34490	−	9.25764i	−0.399497	−	0.691949i	−0.993664	+	0.112393i	$0.964148\pi$
$180$		0			0
$181$	−0.113154	+	0.195989i	−0.00841069	+	0.0145678i	−0.870200	−	0.492698i	$-0.836011\pi$
$181$	−0.113154	+	0.195989i	−0.00841069	+	0.0145678i	0.861789	+	0.507266i	$0.169344\pi$
$182$		0			0
$183$	−15.2435	+	5.63327i	−1.12683	+	0.416423i
$184$		0			0
$185$	−0.815246	+	0.143750i	−0.0599381	+	0.0105687i
$186$		0			0
$187$	−24.3551	+	29.0253i	−1.78102	+	2.12254i
$188$		0			0
$189$	18.2197	+	2.93599i	1.32529	+	0.213562i
$190$		0			0
$191$	−13.7279	−	11.5191i	−0.993319	−	0.833493i	−0.00727404	−	0.999974i	$-0.502315\pi$
$191$	−13.7279	−	11.5191i	−0.993319	−	0.833493i	−0.986045	+	0.166480i	$0.946760\pi$
$192$		0			0
$193$	0.973127	+	5.51888i	0.0700472	+	0.397258i	0.999592	+	0.0285493i	$0.00908874\pi$
$193$	0.973127	+	5.51888i	0.0700472	+	0.397258i	−0.929545	+	0.368708i	$0.879800\pi$
$194$		0			0
$195$	4.93238	−	5.93728i	0.353215	−	0.425177i
$196$		0			0
$197$	14.2915	+	8.25120i	1.01823	+	0.587873i	0.913590	−	0.406637i	$-0.133299\pi$
$197$	14.2915	+	8.25120i	1.01823	+	0.587873i	0.104637	+	0.994510i	$0.466632\pi$
$198$		0			0
$199$	−7.43752	+	4.29405i	−0.527231	+	0.304397i	−0.739888	−	0.672730i	$-0.765122\pi$
$199$	−7.43752	+	4.29405i	−0.527231	+	0.304397i	0.212657	+	0.977127i	$0.431788\pi$
$200$		0			0
$201$	5.70108	−	15.9067i	0.402123	−	1.12197i
$202$		0			0
$203$	−13.1036	+	10.9952i	−0.919691	+	0.771713i
$204$		0			0
$205$	1.36006	−	0.495022i	0.0949908	−	0.0345738i
$206$		0			0
$207$	−12.2144	−	4.31002i	−0.848959	−	0.299567i
$208$		0			0
$209$	−13.3526	−	2.35443i	−0.923620	−	0.162859i
$210$		0			0
$211$	4.01203	−	11.0230i	0.276200	−	0.758852i	−0.721585	−	0.692326i	$-0.756586\pi$
$211$	4.01203	−	11.0230i	0.276200	−	0.758852i	0.997785	−	0.0665263i	$-0.0211916\pi$
$212$		0			0
$213$	2.96842	−	5.20039i	0.203393	−	0.356325i
$214$		0			0
$215$	−8.38192			−0.571642
$216$		0			0
$217$	9.96182			0.676253
$218$		0			0
$219$	−17.2955	+	0.0851116i	−1.16872	+	0.00575131i
$220$		0			0
$221$	−14.4607	+	39.7304i	−0.972730	+	2.67255i
$222$		0			0
$223$	23.3625	+	4.11943i	1.56447	+	0.275858i	0.887729	−	0.460367i	$-0.152282\pi$
$223$	23.3625	+	4.11943i	1.56447	+	0.275858i	0.676737	+	0.736225i	$0.263393\pi$
$224$		0			0
$225$	−12.3083	+	4.61753i	−0.820552	+	0.307835i
$226$		0			0
$227$	9.14518	−	3.32857i	0.606987	−	0.220925i	−0.0201973	−	0.999796i	$-0.506429\pi$
$227$	9.14518	−	3.32857i	0.606987	−	0.220925i	0.627184	+	0.778871i	$0.284207\pi$
$228$		0			0
$229$	−5.04383	+	4.23227i	−0.333306	+	0.279677i	−0.794045	−	0.607859i	$-0.792029\pi$
$229$	−5.04383	+	4.23227i	−0.333306	+	0.279677i	0.460740	+	0.887535i	$0.347584\pi$
$230$		0			0
$231$	20.2050	+	23.8402i	1.32939	+	1.56857i
$232$		0			0
$233$	−18.4755	+	10.6669i	−1.21037	+	0.698809i	−0.962841	−	0.270070i	$-0.912953\pi$
$233$	−18.4755	+	10.6669i	−1.21037	+	0.698809i	−0.247532	+	0.968880i	$0.579620\pi$
$234$		0			0
$235$	5.34983	+	3.08873i	0.348984	+	0.201486i
$236$		0			0
$237$	−2.46994	−	0.422995i	−0.160440	−	0.0274765i
$238$		0			0
$239$	3.46984	+	19.6784i	0.224445	+	1.27289i	0.863743	+	0.503933i	$0.168114\pi$
$239$	3.46984	+	19.6784i	0.224445	+	1.27289i	−0.639298	+	0.768959i	$0.720775\pi$
$240$		0			0
$241$	4.53930	+	3.80892i	0.292402	+	0.245354i	0.777173	−	0.629287i	$-0.216653\pi$
$241$	4.53930	+	3.80892i	0.292402	+	0.245354i	−0.484771	+	0.874641i	$0.661097\pi$
$242$		0			0
$243$	7.45974	−	13.6877i	0.478542	−	0.878065i
$244$		0			0
$245$	−2.83689	+	3.38087i	−0.181242	+	0.215996i
$246$		0			0
$247$	−14.8998	+	2.62724i	−0.948054	+	0.167167i
$248$		0			0
$249$	−0.430648	+	2.51462i	−0.0272912	+	0.159358i
$250$		0			0
$251$	−7.81361	+	13.5336i	−0.493191	+	0.854232i	−0.999969	−	0.00784478i	$-0.997503\pi$
$251$	−7.81361	+	13.5336i	−0.493191	+	0.854232i	0.506778	+	0.862076i	$0.330836\pi$
$252$		0			0
$253$	−10.9666	−	18.9948i	−0.689467	−	1.19419i
$254$		0			0
$255$	−7.74759	+	6.56624i	−0.485173	+	0.411194i
$256$		0			0
$257$	−10.0813	−	12.0145i	−0.628856	−	0.749441i	0.353710	−	0.935355i	$-0.384920\pi$
$257$	−10.0813	−	12.0145i	−0.628856	−	0.749441i	−0.982566	+	0.185914i	$0.940476\pi$
$258$		0			0
$259$	−1.27912	−	3.51436i	−0.0794808	−	0.218372i
$260$		0			0
$261$	5.07516	+	13.5281i	0.314145	+	0.837369i
$262$		0			0
$263$	−5.24105	+	29.7235i	−0.323177	+	1.83283i	0.199012	+	0.979997i	$0.436227\pi$
$263$	−5.24105	+	29.7235i	−0.323177	+	1.83283i	−0.522189	+	0.852830i	$0.674884\pi$
$264$		0			0
$265$	−2.28134	−	0.830339i	−0.140141	−	0.0510073i
$266$		0			0
$267$	−0.0305415	−	6.20631i	−0.00186911	−	0.379820i
$268$		0			0
$269$			6.99110i			0.426255i	0.977024	+	0.213127i	$0.0683649\pi$
$269$			6.99110i			0.426255i	−0.977024	+	0.213127i	$0.931635\pi$
$270$		0			0
$271$		−	21.8898i		−	1.32971i	−0.746973	−	0.664855i	$-0.768493\pi$
$271$		−	21.8898i		−	1.32971i	0.746973	−	0.664855i	$-0.231507\pi$
$272$		0			0
$273$	30.2852	+	17.2870i	1.83294	+	1.04626i
$274$		0			0
$275$	−20.9183	−	7.61364i	−1.26142	−	0.459120i
$276$		0			0
$277$	−0.365886	+	2.07504i	−0.0219840	+	0.124677i	−0.993825	−	0.110961i	$-0.964607\pi$
$277$	−0.365886	+	2.07504i	−0.0219840	+	0.124677i	0.971841	+	0.235639i	$0.0757182\pi$
$278$		0			0
$279$	2.80001	−	7.93509i	0.167632	−	0.475061i
$280$		0			0
$281$	−8.95821	−	24.6125i	−0.534402	−	1.46826i	−0.853782	−	0.520631i	$-0.825697\pi$
$281$	−8.95821	−	24.6125i	−0.534402	−	1.46826i	0.319380	−	0.947627i	$-0.396525\pi$
$282$		0			0
$283$	−10.7458	−	12.8063i	−0.638769	−	0.761255i	0.345406	−	0.938453i	$-0.387741\pi$
$283$	−10.7458	−	12.8063i	−0.638769	−	0.761255i	−0.984175	+	0.177198i	$0.943297\pi$
$284$		0			0
$285$	−3.42110	−	1.22615i	−0.202648	−	0.0726307i
$286$		0			0
$287$	3.26938	+	5.66274i	0.192986	+	0.334261i
$288$		0			0
$289$	19.3146	−	33.4538i	1.13615	−	1.96787i
$290$		0			0
$291$	−4.07783	−	3.38765i	−0.239046	−	0.198587i
$292$		0			0
$293$	13.7176	−	2.41877i	0.801388	−	0.141306i	0.242069	−	0.970259i	$-0.422174\pi$
$293$	13.7176	−	2.41877i	0.801388	−	0.141306i	0.559319	+	0.828953i	$0.311063\pi$
$294$		0			0
$295$	−2.76985	+	3.30098i	−0.161267	+	0.192190i
$296$		0			0
$297$	24.6690	−	9.39346i	1.43144	−	0.545064i
$298$		0			0
$299$	−18.7488	−	15.7321i	−1.08427	−	0.909810i
$300$		0			0
$301$	−6.57563	−	37.2922i	−0.379013	−	2.14949i
$302$		0			0
$303$	5.89269	+	15.9454i	0.338526	+	0.916042i
$304$		0			0
$305$	−6.38784	−	3.68802i	−0.365767	−	0.211176i
$306$		0			0
$307$	21.4253	−	12.3699i	1.22281	−	0.705988i	0.257292	−	0.966334i	$-0.417170\pi$
$307$	21.4253	−	12.3699i	1.22281	−	0.705988i	0.965516	+	0.260346i	$0.0838365\pi$
$308$		0			0
$309$	13.6134	−	2.46955i	0.774441	−	0.140488i
$310$		0			0
$311$	11.6982	−	9.81598i	0.663346	−	0.556613i	−0.247742	−	0.968826i	$-0.579688\pi$
$311$	11.6982	−	9.81598i	0.663346	−	0.556613i	0.911088	+	0.412213i	$0.135244\pi$
$312$		0			0
$313$	14.3850	−	5.23571i	0.813088	−	0.295940i	0.0981890	−	0.995168i	$-0.468695\pi$
$313$	14.3850	−	5.23571i	0.813088	−	0.295940i	0.714899	+	0.699228i	$0.246473\pi$
$314$		0			0
$315$	4.25932	+	7.21249i	0.239986	+	0.406378i
$316$		0			0
$317$	−26.1063	−	4.60325i	−1.46628	−	0.258544i	−0.617197	−	0.786809i	$-0.711732\pi$
$317$	−26.1063	−	4.60325i	−1.46628	−	0.258544i	−0.849080	+	0.528265i	$0.822843\pi$
$318$		0			0
$319$	−8.36821	+	22.9915i	−0.468530	+	1.28727i
$320$		0			0
$321$	13.3309	+	22.8296i	0.744057	+	1.27422i
$322$		0			0
$323$	19.9065			1.10763
$324$		0			0
$325$	−24.8402			−1.37789
$326$		0			0
$327$	1.14495	+	1.96077i	0.0633161	+	0.108431i
$328$		0			0
$329$	−9.54519	+	26.2252i	−0.526243	+	1.44584i
$330$		0			0
$331$	−10.9290	−	1.92707i	−0.600710	−	0.105921i	−0.134980	−	0.990848i	$-0.543097\pi$
$331$	−10.9290	−	1.92707i	−0.600710	−	0.105921i	−0.465730	+	0.884927i	$0.654208\pi$
$332$		0			0
$333$	−3.15889	+	0.0310908i	−0.173106	+	0.00170376i
$334$		0			0
$335$	7.20693	−	2.62311i	0.393757	−	0.143316i
$336$		0			0
$337$	−6.52591	+	5.47589i	−0.355489	+	0.298291i	−0.802990	−	0.595993i	$-0.796759\pi$
$337$	−6.52591	+	5.47589i	−0.355489	+	0.298291i	0.447501	+	0.894284i	$0.352314\pi$
$338$		0			0
$339$	−0.163978	+	0.0297465i	−0.00890606	+	0.00161561i
$340$		0			0
$341$	12.3400	−	7.12448i	0.668247	−	0.385812i
$342$		0			0
$343$	4.26308	+	2.46129i	0.230185	+	0.132897i
$344$		0			0
$345$	−2.03787	−	5.51440i	−0.109715	−	0.296885i
$346$		0			0
$347$	−2.54186	−	14.4156i	−0.136454	−	0.773871i	−0.973836	−	0.227252i	$-0.927026\pi$
$347$	−2.54186	−	14.4156i	−0.136454	−	0.773871i	0.837382	−	0.546619i	$-0.184085\pi$
$348$		0			0
$349$	2.11745	+	1.77675i	0.113345	+	0.0951075i	0.697699	−	0.716392i	$-0.254208\pi$
$349$	2.11745	+	1.77675i	0.113345	+	0.0951075i	−0.584354	+	0.811499i	$0.698652\pi$
$350$		0			0
$351$	22.2823	−	19.2647i	1.18934	−	1.02827i
$352$		0			0
$353$	−4.00818	+	4.77676i	−0.213334	+	0.254242i	−0.862090	−	0.506755i	$-0.830845\pi$
$353$	−4.00818	+	4.77676i	−0.213334	+	0.254242i	0.648756	+	0.760996i	$0.275289\pi$
$354$		0			0
$355$	2.67653	−	0.471945i	0.142056	−	0.0250482i
$356$		0			0
$357$	−35.2920	−	29.3188i	−1.86785	−	1.55171i
$358$		0			0
$359$	12.3686	−	21.4231i	0.652791	−	1.13067i	−0.329652	−	0.944103i	$-0.606931\pi$
$359$	12.3686	−	21.4231i	0.652791	−	1.13067i	0.982443	−	0.186564i	$-0.0597353\pi$
$360$		0			0
$361$	−5.93829	−	10.2854i	−0.312541	−	0.541338i
$362$		0			0
$363$	24.1431	+	8.65305i	1.26718	+	0.454168i
$364$		0			0
$365$	−5.04600	−	6.01359i	−0.264120	−	0.314766i
$366$		0			0
$367$	0.425247	+	1.16836i	0.0221977	+	0.0609877i	0.950297	−	0.311346i	$-0.100780\pi$
$367$	0.425247	+	1.16836i	0.0221977	+	0.0609877i	−0.928099	+	0.372334i	$0.878558\pi$
$368$		0			0
$369$	5.42959	−	1.01258i	0.282653	−	0.0527128i
$370$		0			0
$371$	1.90457	−	10.8014i	0.0988804	−	0.560779i
$372$		0			0
$373$	22.0894	+	8.03989i	1.14375	+	0.416290i	0.843265	−	0.537498i	$-0.180631\pi$
$373$	22.0894	+	8.03989i	1.14375	+	0.416290i	0.300481	+	0.953788i	$0.402853\pi$
$374$		0			0
$375$	−11.0947	−	6.33293i	−0.572928	−	0.327031i
$376$		0			0
$377$			27.3021i			1.40613i
$378$		0			0
$379$			4.98764i			0.256198i	0.991761	+	0.128099i	$0.0408875\pi$
$379$			4.98764i			0.256198i	−0.991761	+	0.128099i	$0.959112\pi$
$380$		0			0
$381$	0.0962579	+	19.5605i	0.00493144	+	1.00212i
$382$		0			0
$383$	28.2451	+	10.2804i	1.44326	+	0.525302i	0.940699	−	0.339243i	$-0.110171\pi$
$383$	28.2451	+	10.2804i	1.44326	+	0.525302i	0.502556	+	0.864544i	$0.332393\pi$
$384$		0			0
$385$	−2.46303	+	13.9686i	−0.125528	+	0.711903i
$386$		0			0
$387$	−31.5533	−	5.24405i	−1.60395	−	0.266570i
$388$		0			0
$389$	3.00042	+	8.24360i	0.152128	+	0.417967i	0.992223	−	0.124471i	$-0.0397235\pi$
$389$	3.00042	+	8.24360i	0.152128	+	0.417967i	−0.840096	+	0.542438i	$0.817501\pi$
$390$		0			0
$391$	20.6991	+	24.6682i	1.04680	+	1.24753i
$392$		0			0
$393$	−15.7726	+	13.3676i	−0.795620	+	0.674304i
$394$		0			0
$395$	−0.568690	−	0.985000i	−0.0286139	−	0.0495607i
$396$		0			0
$397$	−9.80757	+	16.9872i	−0.492228	+	0.852563i	−0.999960	−	0.00895158i	$-0.997151\pi$
$397$	−9.80757	+	16.9872i	−0.492228	+	0.852563i	0.507732	+	0.861515i	$0.330484\pi$
$398$		0			0
$399$	2.77143	−	16.1828i	0.138745	−	0.810154i
$400$		0			0
$401$	26.5005	−	4.67276i	1.32337	−	0.233346i	0.533075	−	0.846068i	$-0.321036\pi$
$401$	26.5005	−	4.67276i	1.32337	−	0.233346i	0.790299	+	0.612722i	$0.209925\pi$
$402$		0			0
$403$	10.2203	−	12.1801i	0.509112	−	0.606736i
$404$		0			0
$405$	6.94229	−	1.36552i	0.344965	−	0.0678533i
$406$		0			0
$407$	−4.09788	−	3.43853i	−0.203124	−	0.170442i
$408$		0			0
$409$	−1.36327	−	7.73147i	−0.0674092	−	0.382297i	−0.999784	−	0.0208025i	$-0.993378\pi$
$409$	−1.36327	−	7.73147i	−0.0674092	−	0.382297i	0.932374	−	0.361494i	$-0.117733\pi$
$410$		0			0
$411$	−8.56377	−	1.46661i	−0.422419	−	0.0723424i
$412$		0			0
$413$	−16.8594	−	9.73379i	−0.829598	−	0.478969i
$414$		0			0
$415$	−1.00282	+	0.578978i	−0.0492265	+	0.0284209i
$416$		0			0
$417$	−6.61861	−	7.80939i	−0.324115	−	0.382427i
$418$		0			0
$419$	11.5624	−	9.70203i	0.564861	−	0.473975i	−0.315075	−	0.949067i	$-0.602030\pi$
$419$	11.5624	−	9.70203i	0.564861	−	0.473975i	0.879936	+	0.475092i	$0.157585\pi$
$420$		0			0
$421$	−12.2598	+	4.46218i	−0.597504	+	0.217474i	−0.623027	−	0.782201i	$-0.714097\pi$
$421$	−12.2598	+	4.46218i	−0.597504	+	0.217474i	0.0255229	+	0.999674i	$0.491875\pi$
$422$		0			0
$423$	18.2068	+	14.9744i	0.885243	+	0.728081i
$424$		0			0
$425$	32.1864	+	5.67533i	1.56127	+	0.275294i
$426$		0			0
$427$	11.3972	−	31.3136i	0.551550	−	1.51537i
$428$		0			0
$429$	49.8783	−	0.245453i	2.40815	−	0.0118506i
$430$		0			0
$431$	−3.23665			−0.155904			−0.0779519	−	0.996957i	$-0.524838\pi$
$431$	−3.23665			−0.155904			−0.0779519	+	0.996957i	$0.524838\pi$
$432$		0			0
$433$	9.26788			0.445386			0.222693	−	0.974889i	$-0.428515\pi$
$433$	9.26788			0.445386			0.222693	+	0.974889i	$0.428515\pi$
$434$		0			0
$435$	−3.25103	+	5.69549i	−0.155875	+	0.273078i
$436$		0			0
$437$	−3.94121	+	10.8284i	−0.188533	+	0.517991i
$438$		0			0
$439$	−18.8470	−	3.32323i	−0.899516	−	0.158609i	−0.295277	−	0.955412i	$-0.595412\pi$
$439$	−18.8470	−	3.32323i	−0.899516	−	0.158609i	−0.604240	+	0.796803i	$0.706523\pi$
$440$		0			0
$441$	−12.7945	+	10.9523i	−0.609263	+	0.521536i
$442$		0			0
$443$	16.5782	−	6.03398i	0.787655	−	0.286683i	0.0832943	−	0.996525i	$-0.473456\pi$
$443$	16.5782	−	6.03398i	0.787655	−	0.286683i	0.704361	+	0.709842i	$0.251234\pi$
$444$		0			0
$445$	2.15792	−	1.81071i	0.102295	−	0.0858358i
$446$		0			0
$447$	12.0492	−	33.6188i	0.569909	−	1.59012i
$448$		0			0
$449$	1.70349	−	0.983512i	0.0803928	−	0.0464148i	−0.459265	−	0.888299i	$-0.651887\pi$
$449$	1.70349	−	0.983512i	0.0803928	−	0.0464148i	0.539658	+	0.841885i	$0.318554\pi$
$450$		0			0
$451$	8.09974	+	4.67639i	0.381402	+	0.220203i
$452$		0			0
$453$	−5.54414	+	6.67367i	−0.260487	+	0.313557i
$454$		0			0
$455$	2.74843	+	15.5871i	0.128848	+	0.730736i
$456$		0			0
$457$	−18.4817	−	15.5080i	−0.864539	−	0.725434i	0.0984023	−	0.995147i	$-0.468627\pi$
$457$	−18.4817	−	15.5080i	−0.864539	−	0.725434i	−0.962941	+	0.269713i	$0.913071\pi$
$458$		0			0
$459$	−33.2735	+	19.8711i	−1.55307	+	0.927504i
$460$		0			0
$461$	0.876842	−	1.04498i	0.0408386	−	0.0486695i	−0.745239	−	0.666798i	$-0.767664\pi$
$461$	0.876842	−	1.04498i	0.0408386	−	0.0486695i	0.786077	+	0.618128i	$0.212109\pi$
$462$		0			0
$463$	37.2025	−	6.55980i	1.72895	−	0.304860i	0.781293	−	0.624164i	$-0.214560\pi$
$463$	37.2025	−	6.55980i	1.72895	−	0.304860i	0.947652	+	0.319305i	$0.103449\pi$
$464$		0			0
$465$	3.58243	−	1.32390i	0.166131	−	0.0613944i
$466$		0			0
$467$	−9.08669	+	15.7386i	−0.420482	+	0.728296i	−0.995987	−	0.0895025i	$-0.971472\pi$
$467$	−9.08669	+	15.7386i	−0.420482	+	0.728296i	0.575505	+	0.817798i	$0.304806\pi$
$468$		0			0
$469$	17.3244	+	30.0067i	0.799966	+	1.38558i
$470$		0			0
$471$	−4.18544	−	23.0723i	−0.192855	−	1.06312i
$472$		0			0
$473$	−34.8160	−	41.4921i	−1.60084	−	1.90781i
$474$		0			0
$475$	4.00006	+	10.9901i	0.183535	+	0.504259i
$476$		0			0
$477$	−8.06849	−	4.55306i	−0.369431	−	0.208470i
$478$		0			0
$479$	−2.04750	+	11.6119i	−0.0935526	+	0.530563i	0.901629	+	0.432511i	$0.142372\pi$
$479$	−2.04750	+	11.6119i	−0.0935526	+	0.530563i	−0.995181	+	0.0980521i	$0.968739\pi$
$480$		0			0
$481$	−5.60926	−	2.04161i	−0.255760	−	0.0930892i
$482$		0			0
$483$	22.9356	−	13.3928i	1.04360	−	0.609392i
$484$		0			0
$485$		−	2.40620i		−	0.109260i
$486$		0			0
$487$			27.5642i			1.24905i	0.781003	+	0.624527i	$0.214708\pi$
$487$			27.5642i			1.24905i	−0.781003	+	0.624527i	$0.785292\pi$
$488$		0			0
$489$	−11.7944	+	6.88713i	−0.533363	+	0.311447i
$490$		0			0
$491$	−3.63911	−	1.32453i	−0.164231	−	0.0597752i	0.258596	−	0.965985i	$-0.416740\pi$
$491$	−3.63911	−	1.32453i	−0.164231	−	0.0597752i	−0.422827	+	0.906210i	$0.638962\pi$
$492$		0			0
$493$	6.23780	−	35.3763i	0.280936	−	1.59327i
$494$		0			0
$495$	10.4344	+	5.88812i	0.468989	+	0.264651i
$496$		0			0
$497$	4.19949	+	11.5380i	0.188373	+	0.517550i
$498$		0			0
$499$	−12.5019	−	14.8992i	−0.559664	−	0.666981i	0.409812	−	0.912170i	$-0.365594\pi$
$499$	−12.5019	−	14.8992i	−0.559664	−	0.666981i	−0.969475	+	0.245189i	$0.921150\pi$
$500$		0			0
$501$	5.73453	+	31.6117i	0.256200	+	1.41230i
$502$		0			0
$503$	−7.58734	−	13.1417i	−0.338303	−	0.585958i	0.645811	−	0.763497i	$-0.276519\pi$
$503$	−7.58734	−	13.1417i	−0.338303	−	0.585958i	−0.984114	+	0.177540i	$0.943186\pi$
$504$		0			0
$505$	−3.85786	+	6.68201i	−0.171673	+	0.297346i
$506$		0			0
$507$	31.0870	−	11.4883i	1.38062	−	0.510214i
$508$		0			0
$509$	24.1974	−	4.26666i	1.07253	−	0.189116i	0.390621	−	0.920552i	$-0.372260\pi$
$509$	24.1974	−	4.26666i	1.07253	−	0.189116i	0.681911	+	0.731436i	$0.261149\pi$
$510$		0			0
$511$	22.7966	−	27.1680i	1.00846	−	1.20184i
$512$		0			0
$513$	−12.1114	−	6.75614i	−0.534733	−	0.298291i
$514$		0			0
$515$	4.81055	+	4.03653i	0.211978	+	0.177871i
$516$		0			0
$517$	6.93183	+	39.3123i	0.304861	+	1.72895i
$518$		0			0
$519$	−19.7845	+	23.8153i	−0.868443	+	1.04537i
$520$		0			0
$521$	−15.3333	−	8.85266i	−0.671762	−	0.387842i	0.124982	−	0.992159i	$-0.460113\pi$
$521$	−15.3333	−	8.85266i	−0.671762	−	0.387842i	−0.796744	+	0.604317i	$0.793446\pi$
$522$		0			0
$523$	−15.4545	+	8.92267i	−0.675779	+	0.390161i	−0.798263	−	0.602309i	$-0.794247\pi$
$523$	−15.4545	+	8.92267i	−0.675779	+	0.390161i	0.122484	+	0.992471i	$0.460914\pi$
$524$		0			0
$525$	9.09476	−	25.3755i	0.396928	−	1.10748i
$526$		0			0
$527$	−16.0257	+	13.4472i	−0.698092	+	0.585769i
$528$		0			0
$529$	4.09625	−	1.49091i	0.178098	−	0.0648223i
$530$		0			0
$531$	−12.4922	+	10.6935i	−0.542115	+	0.464056i
$532$		0			0
$533$	10.2780	+	1.81228i	0.445188	+	0.0784986i
$534$		0			0
$535$	−4.10395	+	11.2755i	−0.177429	+	0.487482i
$536$		0			0
$537$	9.17862	−	16.0801i	0.396087	−	0.693906i
$538$		0			0
$539$	−28.5195			−1.22842
$540$		0			0
$541$	8.91858			0.383440			0.191720	−	0.981450i	$-0.438593\pi$
$541$	8.91858			0.383440			0.191720	+	0.981450i	$0.438593\pi$
$542$		0			0
$543$	−0.391973	+	0.00192891i	−0.0168212	+	8.27776e-5i
$544$		0			0
$545$	−0.352477	+	0.968423i	−0.0150985	+	0.0414827i
$546$		0			0
$547$	−1.30961	−	0.230919i	−0.0559947	−	0.00987337i	0.145581	−	0.989346i	$-0.453495\pi$
$547$	−1.30961	−	0.230919i	−0.0559947	−	0.00987337i	−0.201575	+	0.979473i	$0.564606\pi$
$548$		0			0
$549$	−21.7394	−	17.8799i	−0.927814	−	0.763094i
$550$		0			0
$551$	12.0793	−	4.39649i	0.514594	−	0.187297i
$552$		0			0
$553$	3.93625	−	3.30291i	0.167386	−	0.140454i
$554$		0			0
$555$	−0.927043	−	1.09383i	−0.0393508	−	0.0464305i
$556$		0			0
$557$	24.3179	−	14.0399i	1.03038	−	0.594891i	0.113288	−	0.993562i	$-0.463862\pi$
$557$	24.3179	−	14.0399i	1.03038	−	0.594891i	0.917094	+	0.398671i	$0.130528\pi$
$558$		0			0
$559$	−52.3428	−	30.2201i	−2.21386	−	1.27818i
$560$		0			0
$561$	−64.6853	−	11.0778i	−2.73102	−	0.467707i
$562$		0			0
$563$	−5.14982	−	29.2061i	−0.217039	−	1.23089i	−0.877333	−	0.479882i	$-0.840679\pi$
$563$	−5.14982	−	29.2061i	−0.217039	−	1.23089i	0.660294	−	0.751007i	$-0.270432\pi$
$564$		0			0
$565$	−0.0579446	−	0.0486213i	−0.00243775	−	0.00204551i
$566$		0			0
$567$	11.5216	+	29.8159i	0.483862	+	1.25215i
$568$		0			0
$569$	−7.18324	+	8.56066i	−0.301137	+	0.358881i	−0.895300	−	0.445463i	$-0.853039\pi$
$569$	−7.18324	+	8.56066i	−0.301137	+	0.358881i	0.594163	+	0.804345i	$0.297483\pi$
$570$		0			0
$571$	−37.3754	+	6.59029i	−1.56411	+	0.275795i	−0.887592	−	0.460630i	$-0.847624\pi$
$571$	−37.3754	+	6.59029i	−1.56411	+	0.275795i	−0.676519	+	0.736425i	$0.736512\pi$
$572$		0			0
$573$	5.23943	−	30.5939i	0.218880	−	1.27808i
$574$		0			0
$575$	−9.45960	+	16.3845i	−0.394493	+	0.683282i
$576$		0			0
$577$	19.7897	+	34.2768i	0.823856	+	1.42696i	0.902790	+	0.430081i	$0.141515\pi$
$577$	19.7897	+	34.2768i	0.823856	+	1.42696i	−0.0789341	+	0.996880i	$0.525152\pi$
$578$		0			0
$579$	−7.40477	+	6.27569i	−0.307732	+	0.260809i
$580$		0			0
$581$	−3.36266	−	4.00746i	−0.139507	−	0.166258i
$582$		0			0
$583$	−5.36566	−	14.7420i	−0.222223	−	0.610553i
$584$		0			0
$585$	13.1884	+	2.19187i	0.545275	+	0.0906226i
$586$		0			0
$587$	−0.480765	+	2.72655i	−0.0198433	+	0.112537i	−0.993121	−	0.117096i	$-0.962641\pi$
$587$	−0.480765	+	2.72655i	−0.0198433	+	0.112537i	0.973277	+	0.229633i	$0.0737526\pi$
$588$		0			0
$589$	−7.03466	−	2.56041i	−0.289858	−	0.105500i
$590$		0			0
$591$	0.140656	+	28.5826i	0.00578582	+	1.17573i
$592$		0			0
$593$		−	20.8421i		−	0.855881i	−0.903807	−	0.427941i	$-0.859239\pi$
$593$		−	20.8421i		−	0.855881i	0.903807	−	0.427941i	$-0.140761\pi$
$594$		0			0
$595$		−	20.8248i		−	0.853733i
$596$		0			0
$597$	−12.9186	−	7.37403i	−0.528723	−	0.301799i
$598$		0			0
$599$	−26.8393	−	9.76870i	−1.09662	−	0.399138i	−0.270553	−	0.962705i	$-0.587206\pi$
$599$	−26.8393	−	9.76870i	−1.09662	−	0.399138i	−0.826070	+	0.563567i	$0.809429\pi$
$600$		0			0
$601$	−5.28624	+	29.9798i	−0.215630	+	1.22290i	0.664179	+	0.747574i	$0.268781\pi$
$601$	−5.28624	+	29.9798i	−0.215630	+	1.22290i	−0.879809	+	0.475327i	$0.842330\pi$
$602$		0			0
$603$	28.7713	−	5.36564i	1.17166	−	0.218506i
$604$		0			0
$605$	3.98134	+	10.9386i	0.161864	+	0.444719i
$606$		0			0
$607$	23.6515	+	28.1868i	0.959985	+	1.14407i	0.989505	+	0.144502i	$0.0461579\pi$
$607$	23.6515	+	28.1868i	0.959985	+	1.14407i	−0.0295193	+	0.999564i	$0.509398\pi$
$608$		0			0
$609$	−27.8904	−	9.99611i	−1.13018	−	0.405063i
$610$		0			0
$611$	22.2722	+	38.5765i	0.901035	+	1.56064i
$612$		0			0
$613$	−0.0873020	+	0.151211i	−0.00352609	+	0.00610737i	−0.867783	−	0.496943i	$-0.834456\pi$
$613$	−0.0873020	+	0.151211i	−0.00352609	+	0.00610737i	0.864257	+	0.503051i	$0.167789\pi$
$614$		0			0
$615$	1.92829	+	1.60192i	0.0777560	+	0.0645957i
$616$		0			0
$617$	41.1918	−	7.26323i	1.65832	−	0.292407i	0.735468	−	0.677559i	$-0.236962\pi$
$617$	41.1918	−	7.26323i	1.65832	−	0.292407i	0.922853	+	0.385152i	$0.125851\pi$
$618$		0			0
$619$	2.93870	−	3.50220i	0.118116	−	0.140765i	−0.703746	−	0.710451i	$-0.748491\pi$
$619$	2.93870	−	3.50220i	0.118116	−	0.140765i	0.821862	+	0.569686i	$0.192935\pi$
$620$		0			0
$621$	−4.22143	−	22.0337i	−0.169400	−	0.884181i
$622$		0			0
$623$	9.74896	+	8.18035i	0.390584	+	0.327739i
$624$		0			0
$625$	2.79775	+	15.8668i	0.111910	+	0.634673i
$626$		0			0
$627$	−8.14057	−	22.0281i	−0.325103	−	0.879719i
$628$		0			0
$629$	6.80168	+	3.92695i	0.271201	+	0.156578i
$630$		0			0
$631$	−17.5521	+	10.1337i	−0.698740	+	0.403418i	−0.806878	−	0.590718i	$-0.798844\pi$
$631$	−17.5521	+	10.1337i	−0.698740	+	0.403418i	0.108138	+	0.994136i	$0.465511\pi$
$632$		0			0
$633$	19.9914	−	3.62654i	0.794585	−	0.144142i
$634$		0			0
$635$	−6.80114	+	5.70683i	−0.269895	+	0.226469i
$636$		0			0
$637$	−29.9049	+	10.8845i	−1.18488	+	0.431260i
$638$		0			0
$639$	10.3709	−	0.102074i	0.410268	−	0.00403798i
$640$		0			0
$641$	19.8935	+	3.50776i	0.785747	+	0.138548i	0.552105	−	0.833775i	$-0.313825\pi$
$641$	19.8935	+	3.50776i	0.785747	+	0.138548i	0.233641	+	0.972323i	$0.424936\pi$
$642$		0			0
$643$	−14.5397	+	39.9476i	−0.573392	+	1.57538i	0.225717	+	0.974193i	$0.427528\pi$
$643$	−14.5397	+	39.9476i	−0.573392	+	1.57538i	−0.799108	+	0.601187i	$0.794695\pi$
$644$		0			0
$645$	−7.32074	−	12.5370i	−0.288254	−	0.493644i
$646$		0			0
$647$	−8.10818			−0.318765			−0.159383	−	0.987217i	$-0.550950\pi$
$647$	−8.10818			−0.318765			−0.159383	+	0.987217i	$0.550950\pi$
$648$		0			0
$649$	−27.8456			−1.09304
$650$		0			0
$651$	8.70062	+	14.9001i	0.341004	+	0.583981i
$652$		0			0
$653$	0.613037	−	1.68431i	0.0239900	−	0.0659120i	−0.927120	−	0.374766i	$-0.877723\pi$
$653$	0.613037	−	1.68431i	0.0239900	−	0.0659120i	0.951110	+	0.308854i	$0.0999454\pi$
$654$		0			0
$655$	−9.24154	−	1.62953i	−0.361097	−	0.0636711i
$656$		0			0
$657$	−15.2331	−	25.7949i	−0.594300	−	1.00635i
$658$		0			0
$659$	10.8091	−	3.93418i	0.421062	−	0.153254i	−0.122795	−	0.992432i	$-0.539186\pi$
$659$	10.8091	−	3.93418i	0.421062	−	0.153254i	0.543857	+	0.839178i	$0.316964\pi$
$660$		0			0
$661$	12.1899	−	10.2285i	0.474131	−	0.397843i	−0.374168	−	0.927361i	$-0.622072\pi$
$661$	12.1899	−	10.2285i	0.474131	−	0.397843i	0.848299	+	0.529518i	$0.177627\pi$
$662$		0			0
$663$	−72.0554	+	13.0712i	−2.79840	+	0.507645i
$664$		0			0
$665$	6.45363	−	3.72601i	0.250261	−	0.144488i
$666$		0			0
$667$	18.0083	+	10.3971i	0.697285	+	0.402578i
$668$		0			0
$669$	14.2432	+	38.5416i	0.550673	+	1.49010i
$670$		0			0
$671$	−8.27679	−	46.9400i	−0.319522	−	1.81210i
$672$		0			0
$673$	35.1997	+	29.5361i	1.35685	+	1.13853i	0.976941	+	0.213509i	$0.0684893\pi$
$673$	35.1997	+	29.5361i	1.35685	+	1.13853i	0.379909	+	0.925024i	$0.375955\pi$
$674$		0			0
$675$	−17.6565	−	14.3768i	−0.679601	−	0.553364i
$676$		0			0
$677$	33.3997	−	39.8042i	1.28366	−	1.52980i	0.599984	−	0.800012i	$-0.295173\pi$
$677$	33.3997	−	39.8042i	1.28366	−	1.52980i	0.683672	−	0.729790i	$-0.260382\pi$
$678$		0			0
$679$	10.7055	−	1.88767i	0.410840	−	0.0724421i
$680$		0			0
$681$	12.9660	+	10.7715i	0.496858	+	0.412764i
$682$		0			0
$683$	−18.8480	+	32.6457i	−0.721199	+	1.24915i	0.239321	+	0.970941i	$0.423075\pi$
$683$	−18.8480	+	32.6457i	−0.721199	+	1.24915i	−0.960520	+	0.278212i	$0.910258\pi$
$684$		0			0
$685$	−1.97176	−	3.41519i	−0.0753371	−	0.130488i
$686$		0			0
$687$	−10.7356	−	3.84770i	−0.409587	−	0.146799i
$688$		0			0
$689$	−11.2526	−	13.4104i	−0.428691	−	0.510894i
$690$		0			0
$691$	10.5475	+	28.9791i	0.401247	+	1.10242i	0.961670	+	0.274210i	$0.0884164\pi$
$691$	10.5475	+	28.9791i	0.401247	+	1.10242i	−0.560423	+	0.828207i	$0.689361\pi$
$692$		0			0
$693$	−18.0112	+	51.0430i	−0.684190	+	1.93896i
$694$		0			0
$695$	0.806822	−	4.57572i	0.0306045	−	0.173567i
$696$		0			0
$697$	−12.9035	−	4.69648i	−0.488754	−	0.177892i
$698$		0			0
$699$	−32.0911	−	18.3178i	−1.21380	−	0.692845i
$700$		0			0
$701$		−	3.12015i		−	0.117846i	−0.998263	−	0.0589232i	$-0.981233\pi$
$701$		−	3.12015i		−	0.117846i	0.998263	−	0.0589232i	$-0.0187667\pi$
$702$		0			0
$703$			2.81047i			0.105999i
$704$		0			0
$705$	0.0526527	+	10.6995i	0.00198302	+	0.402968i
$706$		0			0
$707$	−32.7556	−	11.9221i	−1.23190	−	0.448376i
$708$		0			0
$709$	−3.06472	+	17.3809i	−0.115098	+	0.652753i	0.871604	+	0.490211i	$0.163080\pi$
$709$	−3.06472	+	17.3809i	−0.115098	+	0.652753i	−0.986702	+	0.162542i	$0.948031\pi$
$710$		0			0
$711$	−1.52455	−	4.06378i	−0.0571752	−	0.152404i
$712$		0			0
$713$	−4.14188	−	11.3797i	−0.155115	−	0.426174i
$714$		0			0
$715$	14.5521	+	17.3426i	0.544219	+	0.648575i
$716$		0			0
$717$	−26.4029	+	22.3770i	−0.986034	+	0.835684i
$718$		0			0
$719$	0.448200	+	0.776305i	0.0167150	+	0.0289513i	0.874262	−	0.485454i	$-0.161346\pi$
$719$	0.448200	+	0.776305i	0.0167150	+	0.0289513i	−0.857547	+	0.514406i	$0.828013\pi$
$720$		0			0
$721$	−14.1852	+	24.5694i	−0.528283	+	0.915013i
$722$		0			0
$723$	−1.73248	+	10.1162i	−0.0644315	+	0.376226i
$724$		0			0
$725$	20.7841	−	3.66480i	0.771902	−	0.136107i
$726$		0			0
$727$	29.2965	−	34.9142i	1.08655	−	1.29490i	0.133842	−	0.991003i	$-0.457268\pi$
$727$	29.2965	−	34.9142i	1.08655	−	1.29490i	0.952706	−	0.303895i	$-0.0982871\pi$
$728$		0			0
$729$	26.9882	−	0.797085i	0.999564	−	0.0295217i
$730$		0			0
$731$	60.9181	+	51.1163i	2.25314	+	1.89061i
$732$		0			0
$733$	4.21540	+	23.9067i	0.155699	+	0.883014i	0.958144	+	0.286287i	$0.0924212\pi$
$733$	4.21540	+	23.9067i	0.155699	+	0.883014i	−0.802445	+	0.596727i	$0.796468\pi$
$734$		0			0
$735$	−7.53456	−	1.29035i	−0.277916	−	0.0475952i
$736$		0			0
$737$	42.9203	+	24.7801i	1.58099	+	0.912786i
$738$		0			0
$739$	−27.2841	+	15.7525i	−1.00366	+	0.579464i	−0.909330	−	0.416077i	$-0.863405\pi$
$739$	−27.2841	+	15.7525i	−1.00366	+	0.579464i	−0.0943320	+	0.995541i	$0.530072\pi$
$740$		0			0
$741$	−16.9431	−	19.9914i	−0.622420	−	0.734401i
$742$		0			0
$743$	22.7123	−	19.0578i	0.833232	−	0.699165i	−0.122799	−	0.992432i	$-0.539187\pi$
$743$	22.7123	−	19.0578i	0.833232	−	0.699165i	0.956031	+	0.293267i	$0.0947425\pi$
$744$		0			0
$745$	15.2319	−	5.54394i	0.558052	−	0.203114i
$746$		0			0
$747$	−4.13730	+	1.55213i	−0.151376	+	0.0567896i
$748$		0			0
$749$	−53.3857	−	9.41334i	−1.95067	−	0.343956i
$750$		0			0
$751$	−5.19638	+	14.2769i	−0.189618	+	0.520972i	−0.997676	−	0.0681305i	$-0.978297\pi$
$751$	−5.19638	+	14.2769i	−0.189618	+	0.520972i	0.808058	+	0.589103i	$0.200519\pi$
$752$		0			0
$753$	−27.0668	+	0.133197i	−0.986370	+	0.00485396i
$754$		0			0
$755$	−3.93794			−0.143316
$756$		0			0
$757$	15.3617			0.558330			0.279165	−	0.960243i	$-0.409942\pi$
$757$	15.3617			0.558330			0.279165	+	0.960243i	$0.409942\pi$
$758$		0			0
$759$	18.8327	−	32.9930i	0.683582	−	1.19757i
$760$		0			0
$761$	−16.5195	+	45.3870i	−0.598832	+	1.64528i	0.154774	+	0.987950i	$0.450535\pi$
$761$	−16.5195	+	45.3870i	−0.598832	+	1.64528i	−0.753606	+	0.657326i	$0.771687\pi$
$762$		0			0
$763$	−4.58516	−	0.808487i	−0.165994	−	0.0292692i
$764$		0			0
$765$	−16.5880	−	5.85329i	−0.599739	−	0.211626i
$766$		0			0
$767$	−29.1983	+	10.6273i	−1.05429	+	0.383730i
$768$		0			0
$769$	−1.83911	+	1.54319i	−0.0663199	+	0.0556490i	−0.675345	−	0.737502i	$-0.736005\pi$
$769$	−1.83911	+	1.54319i	−0.0663199	+	0.0556490i	0.609025	+	0.793151i	$0.291561\pi$
$770$		0			0
$771$	9.16527	−	25.5722i	0.330079	−	0.920961i
$772$		0			0
$773$	−25.9787	+	14.9988i	−0.934389	+	0.539470i	−0.888197	−	0.459463i	$-0.848042\pi$
$773$	−25.9787	+	14.9988i	−0.934389	+	0.539470i	−0.0461920	+	0.998933i	$0.514709\pi$
$774$		0			0
$775$	−10.6442	−	6.14543i	−0.382351	−	0.220750i
$776$		0			0
$777$	4.13932	−	4.98264i	0.148497	−	0.178751i
$778$		0			0
$779$	−0.853266	−	4.83911i	−0.0305714	−	0.173379i
$780$		0			0
$781$	13.4537	+	11.2890i	0.481413	+	0.403953i
$782$		0			0
$783$	−15.8017	+	19.4064i	−0.564705	+	0.693529i
$784$		0			0
$785$	6.84119	−	8.15301i	0.244173	−	0.290994i
$786$		0			0
$787$	38.5152	−	6.79128i	1.37292	−	0.242083i	0.561950	−	0.827171i	$-0.310051\pi$
$787$	38.5152	−	6.79128i	1.37292	−	0.242083i	0.810970	+	0.585088i	$0.198940\pi$
$788$		0			0
$789$	−49.0355	+	18.1212i	−1.74571	+	0.645132i
$790$		0			0
$791$	0.170865	−	0.295946i	0.00607524	−	0.0105226i
$792$		0			0
$793$	−26.5936	−	46.0614i	−0.944365	−	1.63569i
$794$		0			0
$795$	−0.750557	−	4.13746i	−0.0266195	−	0.146740i
$796$		0			0
$797$	3.66765	+	4.37094i	0.129915	+	0.154827i	0.827080	−	0.562084i	$-0.190000\pi$
$797$	3.66765	+	4.37094i	0.129915	+	0.154827i	−0.697165	+	0.716910i	$0.745556\pi$
$798$		0			0
$799$	−20.0452	−	55.0736i	−0.709147	−	1.94836i
$800$		0			0
$801$	9.25623	−	5.46625i	0.327053	−	0.193140i
$802$		0			0
$803$	8.80883	−	49.9574i	0.310857	−	1.76296i
$804$		0			0
$805$	11.3279	+	4.12300i	0.399255	+	0.145317i
$806$		0			0
$807$	−10.4567	+	6.10600i	−0.368094	+	0.214941i
$808$		0			0
$809$		−	2.69898i		−	0.0948912i	−0.998874	−	0.0474456i	$-0.984892\pi$
$809$		−	2.69898i		−	0.0948912i	0.998874	−	0.0474456i	$-0.0151081\pi$
$810$		0			0
$811$			16.7724i			0.588958i	0.955658	+	0.294479i	$0.0951461\pi$
$811$			16.7724i			0.588958i	−0.955658	+	0.294479i	$0.904854\pi$
$812$		0			0
$813$	32.7410	−	19.1185i	1.14828	−	0.670514i
$814$		0			0
$815$	−5.82527	−	2.12022i	−0.204050	−	0.0742682i
$816$		0			0
$817$	−4.94146	+	28.0244i	−0.172880	+	0.980450i
$818$		0			0
$819$	0.594441	+	60.3965i	0.0207714	+	2.11043i
$820$		0			0
$821$	−13.8978	−	38.1840i	−0.485038	−	1.33263i	−0.905125	−	0.425146i	$-0.860223\pi$
$821$	−13.8978	−	38.1840i	−0.485038	−	1.33263i	0.420087	−	0.907484i	$-0.361999\pi$
$822$		0			0
$823$	−0.497261	−	0.592613i	−0.0173334	−	0.0206572i	0.757308	−	0.653058i	$-0.226514\pi$
$823$	−0.497261	−	0.592613i	−0.0173334	−	0.0206572i	−0.774642	+	0.632401i	$0.782070\pi$
$824$		0			0
$825$	−6.88210	−	37.9377i	−0.239604	−	1.32082i
$826$		0			0
$827$	−7.01112	−	12.1436i	−0.243800	−	0.422275i	0.717993	−	0.696050i	$-0.245061\pi$
$827$	−7.01112	−	12.1436i	−0.243800	−	0.422275i	−0.961794	+	0.273775i	$0.911728\pi$
$828$		0			0
$829$	18.0048	−	31.1853i	0.625334	−	1.08311i	−0.363142	−	0.931734i	$-0.618296\pi$
$829$	18.0048	−	31.1853i	0.625334	−	1.08311i	0.988476	−	0.151377i	$-0.0483707\pi$
$830$		0			0
$831$	−3.42325	+	1.26507i	−0.118751	+	0.0438849i
$832$		0			0
$833$	41.2358	−	7.27098i	1.42874	−	0.251925i
$834$		0			0
$835$	−9.37320	+	11.1705i	−0.324373	+	0.386573i
$836$		0			0
$837$	14.3142	−	2.74245i	0.494771	−	0.0947930i
$838$		0			0
$839$	23.7095	+	19.8946i	0.818543	+	0.686839i	0.952630	−	0.304131i	$-0.0983659\pi$
$839$	23.7095	+	19.8946i	0.818543	+	0.686839i	−0.134088	+	0.990969i	$0.542810\pi$
$840$		0			0
$841$	1.00779	+	5.71547i	0.0347515	+	0.197085i
$842$		0			0
$843$	28.9893	−	34.8954i	0.998445	−	1.20186i
$844$		0			0
$845$	13.0272	+	7.52124i	0.448148	+	0.258739i
$846$		0			0
$847$	−45.5440	+	26.2948i	−1.56491	+	0.903501i
$848$		0			0
$849$	9.76933	−	27.2576i	0.335282	−	0.935479i
$850$		0			0
$851$	−3.48274	+	2.92237i	−0.119387	+	0.100177i
$852$		0			0
$853$	25.5167	−	9.28732i	0.873675	−	0.317992i	0.134021	−	0.990979i	$-0.457211\pi$
$853$	25.5167	−	9.28732i	0.873675	−	0.317992i	0.739655	+	0.672987i	$0.234989\pi$
$854$		0			0
$855$	−1.15400	−	6.18792i	−0.0394661	−	0.211622i
$856$		0			0
$857$	30.9412	+	5.45576i	1.05693	+	0.186365i	0.674994	−	0.737823i	$-0.264146\pi$
$857$	30.9412	+	5.45576i	1.05693	+	0.186365i	0.381936	+	0.924189i	$0.375257\pi$
$858$		0			0
$859$	14.7909	−	40.6376i	0.504658	−	1.38654i	−0.382021	−	0.924154i	$-0.624772\pi$
$859$	14.7909	−	40.6376i	0.504658	−	1.38654i	0.886680	−	0.462384i	$-0.153006\pi$
$860$		0			0
$861$	−5.61441	+	9.83590i	−0.191338	+	0.335207i
$862$		0			0
$863$	−4.89374			−0.166585			−0.0832924	−	0.996525i	$-0.526544\pi$
$863$	−4.89374			−0.166585			−0.0832924	+	0.996525i	$0.526544\pi$
$864$		0			0
$865$	−14.0527			−0.477806
$866$		0			0
$867$	66.9069	−	0.329251i	2.27228	−	0.0111819i
$868$		0			0
$869$	2.51377	−	6.90652i	0.0852737	−	0.234288i
$870$		0			0
$871$	54.4627	+	9.60324i	1.84540	+	0.325393i
$872$		0			0
$873$	1.50541	−	9.05804i	0.0509505	−	0.306568i
$874$		0			0
$875$	24.6155	−	8.95932i	0.832157	−	0.302880i
$876$		0			0
$877$	−31.8866	+	26.7561i	−1.07674	+	0.903488i	−0.995646	−	0.0932187i	$-0.970284\pi$
$877$	−31.8866	+	26.7561i	−1.07674	+	0.903488i	−0.0810895	+	0.996707i	$0.525840\pi$
$878$		0			0
$879$	15.5987	+	18.4051i	0.526130	+	0.620788i
$880$		0			0
$881$	17.9282	−	10.3508i	0.604016	−	0.348729i	−0.166604	−	0.986024i	$-0.553280\pi$
$881$	17.9282	−	10.3508i	0.604016	−	0.348729i	0.770620	+	0.637295i	$0.219947\pi$
$882$		0			0
$883$	−3.10427	−	1.79225i	−0.104467	−	0.0603141i	0.446856	−	0.894606i	$-0.352544\pi$
$883$	−3.10427	−	1.79225i	−0.104467	−	0.0603141i	−0.551323	+	0.834292i	$0.685877\pi$
$884$		0			0
$885$	−7.35652	−	1.25986i	−0.247287	−	0.0423496i
$886$		0			0
$887$	1.96954	+	11.1698i	0.0661308	+	0.375047i	0.999855	+	0.0170523i	$0.00542817\pi$
$887$	1.96954	+	11.1698i	0.0661308	+	0.375047i	−0.933724	+	0.357994i	$0.883461\pi$
$888$		0			0
$889$	−30.7259	−	25.7821i	−1.03051	−	0.864704i
$890$		0			0
$891$	35.5958	+	28.6937i	1.19250	+	0.961274i
$892$		0			0
$893$	13.4809	−	16.0659i	0.451121	−	0.537625i
$894$		0			0
$895$	8.27607	−	1.45929i	0.276638	−	0.0487788i
$896$		0			0
$897$	7.15569	−	41.7832i	0.238921	−	1.39510i
$898$		0			0
$899$	−6.75449	+	11.6991i	−0.225275	+	0.390187i
$900$		0			0
$901$	11.5165	+	19.9472i	0.383672	+	0.664539i
$902$		0			0
$903$	50.0356	−	42.4062i	1.66508	−	1.41119i
$904$		0			0
$905$	−0.114359	−	0.136288i	−0.00380143	−	0.00453037i
$906$		0			0
$907$	−19.7858	−	54.3610i	−0.656977	−	1.80503i	−0.590195	−	0.807261i	$-0.700949\pi$
$907$	−19.7858	−	54.3610i	−0.656977	−	1.80503i	−0.0667822	−	0.997768i	$-0.521273\pi$
$908$		0			0
$909$	−18.7033	+	22.7405i	−0.620348	+	0.754255i
$910$		0			0
$911$	3.67979	−	20.8691i	0.121917	−	0.691426i	−0.861174	−	0.508310i	$-0.830270\pi$
$911$	3.67979	−	20.8691i	0.121917	−	0.691426i	0.983091	−	0.183116i	$-0.0586184\pi$
$912$		0			0
$913$	−7.03147	−	2.55925i	−0.232708	−	0.0846987i
$914$		0			0
$915$	−0.0628688	−	12.7755i	−0.00207838	−	0.422346i
$916$		0			0
$917$		−	42.3951i		−	1.40001i
$918$		0			0
$919$			7.68271i			0.253429i	0.991939	+	0.126715i	$0.0404432\pi$
$919$			7.68271i			0.253429i	−0.991939	+	0.126715i	$0.959557\pi$
$920$		0			0
$921$	37.2147	+	21.2424i	1.22627	+	0.699962i
$922$		0			0
$923$	18.4158	+	6.70279i	0.606162	+	0.220625i
$924$		0			0
$925$	−0.801262	+	4.54418i	−0.0263453	+	0.149412i
$926$		0			0
$927$	15.5837	+	18.2050i	0.511835	+	0.597930i
$928$		0			0
$929$	−6.39595	−	17.5727i	−0.209844	−	0.576542i	0.789461	−	0.613800i	$-0.210360\pi$
$929$	−6.39595	−	17.5727i	−0.209844	−	0.576542i	−0.999306	+	0.0372578i	$0.988138\pi$
$930$		0			0
$931$	9.63127	+	11.4781i	0.315652	+	0.376179i
$932$		0			0
$933$	24.8992	+	8.92404i	0.815162	+	0.292160i
$934$		0			0
$935$	−14.8934	−	25.7962i	−0.487068	−	0.843626i
$936$		0			0
$937$	−1.60988	+	2.78839i	−0.0525924	+	0.0910926i	−0.891123	−	0.453762i	$-0.850082\pi$
$937$	−1.60988	+	2.78839i	−0.0525924	+	0.0910926i	0.838531	+	0.544854i	$0.183415\pi$
$938$		0			0
$939$	20.3950	+	16.9431i	0.665564	+	0.552916i
$940$		0			0
$941$	−44.8305	+	7.90482i	−1.46143	+	0.257690i	−0.847132	−	0.531383i	$-0.821673\pi$
$941$	−44.8305	+	7.90482i	−1.46143	+	0.257690i	−0.614300	+	0.789073i	$0.710562\pi$
$942$		0			0
$943$	5.10940	−	6.08915i	0.166385	−	0.198290i
$944$		0			0
$945$	−7.06779	+	12.6701i	−0.229915	+	0.412159i
$946$		0			0
$947$	7.22304	+	6.06085i	0.234717	+	0.196951i	0.752558	−	0.658526i	$-0.228820\pi$
$947$	7.22304	+	6.06085i	0.234717	+	0.196951i	−0.517841	+	0.855477i	$0.673264\pi$
$948$		0			0
$949$	−9.82954	−	55.7461i	−0.319080	−	1.80959i
$950$		0			0
$951$	−15.9160	−	43.0682i	−0.516111	−	1.39658i
$952$		0			0
$953$	20.9106	+	12.0727i	0.677361	+	0.391074i	0.798860	−	0.601517i	$-0.205437\pi$
$953$	20.9106	+	12.0727i	0.677361	+	0.391074i	−0.121499	+	0.992592i	$0.538770\pi$
$954$		0			0
$955$	12.2007	−	7.04408i	0.394806	−	0.227941i
$956$		0			0
$957$	−41.6975	+	7.56416i	−1.34789	+	0.244515i
$958$		0			0
$959$	13.6478	−	11.4518i	0.440709	−	0.369799i
$960$		0			0
$961$	−21.7376	+	7.91185i	−0.701214	+	0.255221i
$962$		0			0
$963$	−22.5035	+	39.8785i	−0.725165	+	1.28507i
$964$		0			0
$965$	−4.33864	−	0.765019i	−0.139666	−	0.0246268i
$966$		0			0
$967$	5.43085	−	14.9211i	0.174644	−	0.479832i	−0.821228	−	0.570601i	$-0.806710\pi$
$967$	5.43085	−	14.9211i	0.174644	−	0.479832i	0.995872	+	0.0907693i	$0.0289326\pi$
$968$		0			0
$969$	17.3863	+	29.7746i	0.558528	+	0.956498i
$970$		0			0
$971$	−13.9015			−0.446119			−0.223059	−	0.974805i	$-0.571604\pi$
$971$	−13.9015			−0.446119			−0.223059	+	0.974805i	$0.571604\pi$
$972$		0			0
$973$	20.9909			0.672937
$974$		0			0
$975$	−21.6954	−	37.1540i	−0.694808	−	1.18988i
$976$		0			0
$977$	−10.0299	+	27.5570i	−0.320886	+	0.881627i	0.669440	+	0.742866i	$0.266534\pi$
$977$	−10.0299	+	27.5570i	−0.320886	+	0.881627i	−0.990326	+	0.138761i	$0.955688\pi$
$978$		0			0
$979$	17.9267	+	3.16096i	0.572940	+	0.101025i
$980$		0			0
$981$	−1.93277	+	3.42506i	−0.0617085	+	0.109354i
$982$		0			0
$983$	−17.8368	+	6.49207i	−0.568906	+	0.207065i	−0.610427	−	0.792073i	$-0.709002\pi$
$983$	−17.8368	+	6.49207i	−0.568906	+	0.207065i	0.0415207	+	0.999138i	$0.486780\pi$
$984$		0			0
$985$	−9.93811	+	8.33906i	−0.316655	+	0.265705i
$986$		0			0
$987$	−47.5623	+	8.62805i	−1.51392	+	0.274634i
$988$		0			0
$989$	−39.8662	+	23.0167i	−1.26767	+	0.731890i
$990$		0			0
$991$	−53.7186	−	31.0144i	−1.70643	−	0.985206i	−0.938902	−	0.344186i	$-0.888155\pi$
$991$	−53.7186	−	31.0144i	−1.70643	−	0.985206i	−0.767524	−	0.641020i	$-0.778512\pi$
$992$		0			0
$993$	−6.66295	−	18.0297i	−0.211442	−	0.572157i
$994$		0			0
$995$	−1.17239	−	6.64893i	−0.0371671	−	0.210785i
$996$		0			0
$997$	21.9558	+	18.4231i	0.695348	+	0.583466i	0.920446	−	0.390870i	$-0.127826\pi$
$997$	21.9558	+	18.4231i	0.695348	+	0.583466i	−0.225098	+	0.974336i	$0.572270\pi$
$998$		0			0
$999$	−2.80547	−	4.69766i	−0.0887610	−	0.148627i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.be.a.335.5	yes	36
4.3	odd	2	inner	432.2.be.a.335.2	✓	36
27.5	odd	18	inner	432.2.be.a.383.2	yes	36
108.59	even	18	inner	432.2.be.a.383.5	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.be.a.335.2	✓	36	4.3	odd	2	inner
432.2.be.a.335.5	yes	36	1.1	even	1	trivial
432.2.be.a.383.2	yes	36	27.5	odd	18	inner
432.2.be.a.383.5	yes	36	108.59	even	18	inner

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.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.873396 + 1.49572i) q^{3} +(-0.268878 + 0.738735i) q^{5} +(-3.49766 - 0.616732i) q^{7} +(-1.47436 + 2.61271i) q^{9} +O(q^{10})\)	\(q+(0.873396 + 1.49572i) q^{3} +(-0.268878 + 0.738735i) q^{5} +(-3.49766 - 0.616732i) q^{7} +(-1.47436 + 2.61271i) q^{9} +(-4.77372 + 1.73749i) q^{11} +(-4.34250 + 3.64379i) q^{13} +(-1.33978 + 0.243043i) q^{15} +(6.45925 - 3.72925i) q^{17} +(2.31140 + 1.33449i) q^{19} +(-2.13239 - 5.77017i) q^{21} +(0.749727 + 4.25191i) q^{23} +(3.35679 + 2.81668i) q^{25} +(-5.19559 + 0.0767079i) q^{27} +(3.09583 - 3.68947i) q^{29} +(-2.76226 + 0.487060i) q^{31} +(-6.76815 - 5.62263i) q^{33} +(1.39604 - 2.41802i) q^{35} +(0.526507 + 0.911937i) q^{37} +(-9.24281 - 3.31269i) q^{39} +(-1.18342 - 1.41034i) q^{41} +(3.64664 + 10.0191i) q^{43} +(-1.53368 - 1.79166i) q^{45} +(1.36451 - 7.73852i) q^{47} +(5.27542 + 1.92010i) q^{49} +(11.2194 + 6.40412i) q^{51} +3.08817i q^{53} -3.99368i q^{55} +(0.0227487 + 4.62274i) q^{57} +(5.15076 + 1.87472i) q^{59} +(-1.62926 + 9.24000i) q^{61} +(6.76815 - 8.22910i) q^{63} +(-1.52419 - 4.18769i) q^{65} +(-6.27089 - 7.47336i) q^{67} +(-5.70486 + 4.83499i) q^{69} +(-1.72857 - 2.99398i) q^{71} +(-4.99284 + 8.64785i) q^{73} +(-1.28116 + 7.48089i) q^{75} +(17.7684 - 3.13305i) q^{77} +(-0.929972 + 1.10830i) q^{79} +(-4.65254 - 7.70415i) q^{81} +(1.12835 + 0.946797i) q^{83} +(1.01818 + 5.77438i) q^{85} +(8.22230 + 1.40813i) q^{87} +(-3.10319 - 1.79163i) q^{89} +(17.4358 - 10.0666i) q^{91} +(-3.14105 - 3.70617i) q^{93} +(-1.60732 + 1.34870i) q^{95} +(-2.87618 + 1.04684i) q^{97} +(2.49860 - 15.0340i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{5} - 12 q^{9}+O(q^{10}) \) 36 * q - 6 * q^5 - 12 * q^9	\( 36 q - 6 q^{5} - 12 q^{9} - 36 q^{21} + 18 q^{25} - 24 q^{29} - 36 q^{33} - 18 q^{41} - 18 q^{45} + 42 q^{65} + 54 q^{69} - 18 q^{73} + 90 q^{77} + 36 q^{81} + 72 q^{85} + 72 q^{89} + 54 q^{93} + 54 q^{97}+O(q^{100}) \) 36 * q - 6 * q^5 - 12 * q^9 - 36 * q^21 + 18 * q^25 - 24 * q^29 - 36 * q^33 - 18 * q^41 - 18 * q^45 + 42 * q^65 + 54 * q^69 - 18 * q^73 + 90 * q^77 + 36 * q^81 + 72 * q^85 + 72 * q^89 + 54 * q^93 + 54 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more