LMFDB - Embedded newform 864.2.y.b.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(97,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("864.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.y (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.1
Character	$\chi$	$=$	864.193
Dual form			864.2.y.b.385.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72098 - 0.195544i) q^{3} +(0.359864 - 2.04089i) q^{5} +(2.05212 - 1.72193i) q^{7} +(2.92353 + 0.673052i) q^{9} +O(q^{10})$	\(q+(-1.72098 - 0.195544i) q^{3} +(0.359864 - 2.04089i) q^{5} +(2.05212 - 1.72193i) q^{7} +(2.92353 + 0.673052i) q^{9} +(0.982213 + 5.57041i) q^{11} +(-0.917880 + 0.334081i) q^{13} +(-1.01840 + 3.44195i) q^{15} +(3.69395 - 6.39811i) q^{17} +(2.54122 + 4.40152i) q^{19} +(-3.86836 + 2.56213i) q^{21} +(-5.43554 - 4.56096i) q^{23} +(0.662742 + 0.241218i) q^{25} +(-4.89971 - 1.72998i) q^{27} +(4.14277 + 1.50785i) q^{29} +(0.954848 + 0.801212i) q^{31} +(-0.601108 - 9.77861i) q^{33} +(-2.77579 - 4.80780i) q^{35} +(3.29080 - 5.69983i) q^{37} +(1.64498 - 0.395460i) q^{39} +(-1.43279 + 0.521492i) q^{41} +(-0.751695 - 4.26308i) q^{43} +(2.42569 - 5.72438i) q^{45} +(6.06095 - 5.08574i) q^{47} +(0.0306027 - 0.173557i) q^{49} +(-7.60832 + 10.2887i) q^{51} -11.8675 q^{53} +11.7220 q^{55} +(-3.51269 - 8.07184i) q^{57} +(1.02912 - 5.83641i) q^{59} +(11.5213 - 9.66749i) q^{61} +(7.15837 - 3.65293i) q^{63} +(0.351510 + 1.99351i) q^{65} +(9.83396 - 3.57927i) q^{67} +(8.46258 + 8.91220i) q^{69} +(0.838061 - 1.45156i) q^{71} +(3.01127 + 5.21567i) q^{73} +(-1.09340 - 0.544726i) q^{75} +(11.6075 + 9.73983i) q^{77} +(4.31076 + 1.56899i) q^{79} +(8.09400 + 3.93537i) q^{81} +(-10.6938 - 3.89222i) q^{83} +(-11.7285 - 9.84139i) q^{85} +(-6.83477 - 3.40506i) q^{87} +(-2.61064 - 4.52176i) q^{89} +(-1.30833 + 2.26610i) q^{91} +(-1.48660 - 1.56558i) q^{93} +(9.89750 - 3.60240i) q^{95} +(1.66446 + 9.43964i) q^{97} +(-0.877652 + 16.9463i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q+O(q^{10}) $ 54 * q	$ 54 q - 9 q^{11} + 12 q^{17} + 18 q^{19} + 12 q^{21} - 21 q^{27} + 6 q^{29} + 36 q^{31} - 9 q^{33} + 24 q^{39} + 3 q^{41} - 21 q^{43} + 42 q^{45} - 18 q^{49} + 24 q^{51} + 36 q^{53} - 72 q^{55} + 39 q^{57} + 18 q^{59} - 18 q^{61} - 30 q^{63} + 48 q^{65} - 27 q^{67} + 24 q^{69} - 84 q^{75} + 36 q^{77} + 72 q^{79} + 36 q^{81} + 6 q^{87} + 33 q^{89} + 36 q^{91} + 72 q^{93} + 36 q^{95} + 9 q^{97} + 120 q^{99}+O(q^{100}) $ 54 * q - 9 * q^11 + 12 * q^17 + 18 * q^19 + 12 * q^21 - 21 * q^27 + 6 * q^29 + 36 * q^31 - 9 * q^33 + 24 * q^39 + 3 * q^41 - 21 * q^43 + 42 * q^45 - 18 * q^49 + 24 * q^51 + 36 * q^53 - 72 * q^55 + 39 * q^57 + 18 * q^59 - 18 * q^61 - 30 * q^63 + 48 * q^65 - 27 * q^67 + 24 * q^69 - 84 * q^75 + 36 * q^77 + 72 * q^79 + 36 * q^81 + 6 * q^87 + 33 * q^89 + 36 * q^91 + 72 * q^93 + 36 * q^95 + 9 * q^97 + 120 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{9}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.72098	−	0.195544i	−0.993607	−	0.112897i
$3$	−1.72098	−	0.195544i	−0.993607	−	0.112897i
$4$		0			0
$5$	0.359864	−	2.04089i	0.160936	−	0.912713i	−0.792221	−	0.610235i	$-0.791075\pi$
$5$	0.359864	−	2.04089i	0.160936	−	0.912713i	0.953156	−	0.302478i	$-0.0978138\pi$
$6$		0			0
$7$	2.05212	−	1.72193i	0.775628	−	0.650829i	−0.166516	−	0.986039i	$-0.553252\pi$
$7$	2.05212	−	1.72193i	0.775628	−	0.650829i	0.942143	+	0.335210i	$0.108807\pi$
$8$		0			0
$9$	2.92353	+	0.673052i	0.974508	+	0.224351i
$10$		0			0
$11$	0.982213	+	5.57041i	0.296148	+	1.67954i	0.662498	+	0.749064i	$0.269496\pi$
$11$	0.982213	+	5.57041i	0.296148	+	1.67954i	−0.366350	+	0.930477i	$0.619393\pi$
$12$		0			0
$13$	−0.917880	+	0.334081i	−0.254574	+	0.0926574i	−0.466155	−	0.884703i	$-0.654361\pi$
$13$	−0.917880	+	0.334081i	−0.254574	+	0.0926574i	0.211581	+	0.977360i	$0.432139\pi$
$14$		0			0
$15$	−1.01840	+	3.44195i	−0.262950	+	0.888708i
$16$		0			0
$17$	3.69395	−	6.39811i	0.895915	−	1.55177i	0.0632464	−	0.997998i	$-0.479855\pi$
$17$	3.69395	−	6.39811i	0.895915	−	1.55177i	0.832668	−	0.553772i	$-0.186812\pi$
$18$		0			0
$19$	2.54122	+	4.40152i	0.582996	+	1.00978i	0.995122	+	0.0986515i	$0.0314529\pi$
$19$	2.54122	+	4.40152i	0.582996	+	1.00978i	−0.412126	+	0.911127i	$0.635214\pi$
$20$		0			0
$21$	−3.86836	+	2.56213i	−0.844145	+	0.559102i
$22$		0			0
$23$	−5.43554	−	4.56096i	−1.13339	−	0.951026i	−0.134186	−	0.990956i	$-0.542842\pi$
$23$	−5.43554	−	4.56096i	−1.13339	−	0.951026i	−0.999202	+	0.0399300i	$0.987287\pi$
$24$		0			0
$25$	0.662742	+	0.241218i	0.132548	+	0.0482437i
$26$		0			0
$27$	−4.89971	−	1.72998i	−0.942950	−	0.332936i
$28$		0			0
$29$	4.14277	+	1.50785i	0.769294	+	0.280000i	0.696701	−	0.717362i	$-0.254650\pi$
$29$	4.14277	+	1.50785i	0.769294	+	0.280000i	0.0725929	+	0.997362i	$0.476873\pi$
$30$		0			0
$31$	0.954848	+	0.801212i	0.171496	+	0.143902i	0.724496	−	0.689279i	$-0.242073\pi$
$31$	0.954848	+	0.801212i	0.171496	+	0.143902i	−0.553000	+	0.833181i	$0.686517\pi$
$32$		0			0
$33$	−0.601108	−	9.77861i	−0.104640	−	1.70224i
$34$		0			0
$35$	−2.77579	−	4.80780i	−0.469193	−	0.812667i
$36$		0			0
$37$	3.29080	−	5.69983i	0.541004	−	0.937046i	−0.457843	−	0.889033i	$-0.651378\pi$
$37$	3.29080	−	5.69983i	0.541004	−	0.937046i	0.998847	−	0.0480131i	$-0.0152889\pi$
$38$		0			0
$39$	1.64498	−	0.395460i	0.263407	−	0.0633243i
$40$		0			0
$41$	−1.43279	+	0.521492i	−0.223764	+	0.0814434i	−0.451469	−	0.892287i	$-0.649100\pi$
$41$	−1.43279	+	0.521492i	−0.223764	+	0.0814434i	0.227705	+	0.973730i	$0.426878\pi$
$42$		0			0
$43$	−0.751695	−	4.26308i	−0.114632	−	0.650113i	−0.986932	−	0.161140i	$-0.948483\pi$
$43$	−0.751695	−	4.26308i	−0.114632	−	0.650113i	0.872299	−	0.488973i	$-0.162628\pi$
$44$		0			0
$45$	2.42569	−	5.72438i	0.361601	−	0.853340i
$46$		0			0
$47$	6.06095	−	5.08574i	0.884081	−	0.741832i	−0.0829332	−	0.996555i	$-0.526429\pi$
$47$	6.06095	−	5.08574i	0.884081	−	0.741832i	0.967014	+	0.254723i	$0.0819844\pi$
$48$		0			0
$49$	0.0306027	−	0.173557i	0.00437182	−	0.0247938i
$50$		0			0
$51$	−7.60832	+	10.2887i	−1.06538	+	1.44070i
$52$		0			0
$53$	−11.8675			−1.63013			−0.815063	−	0.579372i	$-0.803298\pi$
$53$	−11.8675			−1.63013			−0.815063	+	0.579372i	$0.803298\pi$
$54$		0			0
$55$	11.7220			1.58060
$56$		0			0
$57$	−3.51269	−	8.07184i	−0.465267	−	1.06914i
$58$		0			0
$59$	1.02912	−	5.83641i	0.133980	−	0.759836i	−0.841585	−	0.540124i	$-0.818377\pi$
$59$	1.02912	−	5.83641i	0.133980	−	0.759836i	0.975565	−	0.219712i	$-0.0705117\pi$
$60$		0			0
$61$	11.5213	−	9.66749i	1.47515	−	1.23780i	0.563961	−	0.825802i	$-0.309277\pi$
$61$	11.5213	−	9.66749i	1.47515	−	1.23780i	0.911187	−	0.411994i	$-0.135168\pi$
$62$		0			0
$63$	7.15837	−	3.65293i	0.901870	−	0.460225i
$64$		0			0
$65$	0.351510	+	1.99351i	0.0435995	+	0.247265i
$66$		0			0
$67$	9.83396	−	3.57927i	1.20141	−	0.437277i	0.337694	−	0.941256i	$-0.390353\pi$
$67$	9.83396	−	3.57927i	1.20141	−	0.437277i	0.863716	+	0.503979i	$0.168131\pi$
$68$		0			0
$69$	8.46258	+	8.91220i	1.01877	+	1.07290i
$70$		0			0
$71$	0.838061	−	1.45156i	0.0994595	−	0.172269i	−0.812002	−	0.583655i	$-0.801622\pi$
$71$	0.838061	−	1.45156i	0.0994595	−	0.172269i	0.911461	+	0.411386i	$0.134955\pi$
$72$		0			0
$73$	3.01127	+	5.21567i	0.352442	+	0.610448i	0.986677	−	0.162693i	$-0.0520180\pi$
$73$	3.01127	+	5.21567i	0.352442	+	0.610448i	−0.634235	+	0.773141i	$0.718685\pi$
$74$		0			0
$75$	−1.09340	−	0.544726i	−0.126254	−	0.0628996i
$76$		0			0
$77$	11.6075	+	9.73983i	1.32279	+	1.10996i
$78$		0			0
$79$	4.31076	+	1.56899i	0.484999	+	0.176525i	0.572935	−	0.819601i	$-0.305805\pi$
$79$	4.31076	+	1.56899i	0.484999	+	0.176525i	−0.0879359	+	0.996126i	$0.528027\pi$
$80$		0			0
$81$	8.09400	+	3.93537i	0.899333	+	0.437264i
$82$		0			0
$83$	−10.6938	−	3.89222i	−1.17380	−	0.427227i	−0.319789	−	0.947489i	$-0.603612\pi$
$83$	−10.6938	−	3.89222i	−1.17380	−	0.427227i	−0.854007	+	0.520262i	$0.825834\pi$
$84$		0			0
$85$	−11.7285	−	9.84139i	−1.27214	−	1.06745i
$86$		0			0
$87$	−6.83477	−	3.40506i	−0.732764	−	0.365061i
$88$		0			0
$89$	−2.61064	−	4.52176i	−0.276727	−	0.479305i	0.693842	−	0.720127i	$-0.255916\pi$
$89$	−2.61064	−	4.52176i	−0.276727	−	0.479305i	−0.970569	+	0.240822i	$0.922583\pi$
$90$		0			0
$91$	−1.30833	+	2.26610i	−0.137151	+	0.237552i
$92$		0			0
$93$	−1.48660	−	1.56558i	−0.154153	−	0.162343i
$94$		0			0
$95$	9.89750	−	3.60240i	1.01546	−	0.369598i
$96$		0			0
$97$	1.66446	+	9.43964i	0.169001	+	0.958450i	0.944843	+	0.327523i	$0.106214\pi$
$97$	1.66446	+	9.43964i	0.169001	+	0.958450i	−0.775843	+	0.630927i	$0.782675\pi$
$98$		0			0
$99$	−0.877652	+	16.9463i	−0.0882073	+	1.70317i
$100$		0			0
$101$	0.135437	−	0.113645i	0.0134765	−	0.0113081i	−0.636025	−	0.771669i	$-0.719422\pi$
$101$	0.135437	−	0.113645i	0.0134765	−	0.0113081i	0.649501	+	0.760361i	$0.274978\pi$
$102$		0			0
$103$	0.146984	−	0.833588i	0.0144828	−	0.0821359i	−0.976710	−	0.214565i	$-0.931167\pi$
$103$	0.146984	−	0.833588i	0.0144828	−	0.0821359i	0.991192	+	0.132429i	$0.0422777\pi$
$104$		0			0
$105$	3.83693	+	8.81691i	0.374446	+	0.860442i
$106$		0			0
$107$	−6.25552			−0.604744			−0.302372	−	0.953190i	$-0.597778\pi$
$107$	−6.25552			−0.604744			−0.302372	+	0.953190i	$0.597778\pi$
$108$		0			0
$109$	−13.8229			−1.32400			−0.661998	−	0.749506i	$-0.730291\pi$
$109$	−13.8229			−1.32400			−0.661998	+	0.749506i	$0.730291\pi$
$110$		0			0
$111$	−6.77795	+	9.16578i	−0.643335	+	0.869978i
$112$		0			0
$113$	−0.746884	+	4.23579i	−0.0702610	+	0.398470i	0.929313	+	0.369292i	$0.120400\pi$
$113$	−0.746884	+	4.23579i	−0.0702610	+	0.398470i	−0.999574	+	0.0291774i	$0.990711\pi$
$114$		0			0
$115$	−11.2645	+	9.45201i	−1.05042	+	0.881404i
$116$		0			0
$117$	−2.90830	+	0.358913i	−0.268872	+	0.0331815i
$118$		0			0
$119$	−3.43668	−	19.4904i	−0.315040	−	1.78668i
$120$		0			0
$121$	−19.7281	+	7.18043i	−1.79346	+	0.652767i
$122$		0			0
$123$	2.56777	−	0.617304i	0.231528	−	0.0556604i
$124$		0			0
$125$	5.91173	−	10.2394i	0.528761	−	0.915841i
$126$		0			0
$127$	1.13220	+	1.96103i	0.100466	+	0.174013i	0.911877	−	0.410464i	$-0.134633\pi$
$127$	1.13220	+	1.96103i	0.100466	+	0.174013i	−0.811411	+	0.584477i	$0.801300\pi$
$128$		0			0
$129$	0.460033	+	7.48364i	0.0405036	+	0.658898i
$130$		0			0
$131$	−11.0297	−	9.25498i	−0.963665	−	0.808611i	0.0178801	−	0.999840i	$-0.494308\pi$
$131$	−11.0297	−	9.25498i	−0.963665	−	0.808611i	−0.981545	+	0.191229i	$0.938753\pi$
$132$		0			0
$133$	12.7940	+	4.65663i	1.10938	+	0.403781i
$134$		0			0
$135$	−5.29393	+	9.37720i	−0.455629	+	0.807061i
$136$		0			0
$137$	−7.06490	−	2.57141i	−0.603595	−	0.219691i	0.0221035	−	0.999756i	$-0.492964\pi$
$137$	−7.06490	−	2.57141i	−0.603595	−	0.219691i	−0.625698	+	0.780065i	$0.715186\pi$
$138$		0			0
$139$	8.82890	+	7.40833i	0.748857	+	0.628366i	0.935200	−	0.354119i	$-0.115219\pi$
$139$	8.82890	+	7.40833i	0.748857	+	0.628366i	−0.186343	+	0.982485i	$0.559664\pi$
$140$		0			0
$141$	−11.4252	+	7.56727i	−0.962179	+	0.637279i
$142$		0			0
$143$	−2.76252	−	4.78483i	−0.231014	−	0.400127i
$144$		0			0
$145$	4.56818	−	7.91232i	0.379367	−	0.657082i
$146$		0			0
$147$	−0.0866045	+	0.292703i	−0.00714302	+	0.0241417i
$148$		0			0
$149$	13.0049	−	4.73338i	1.06540	−	0.387774i	0.250945	−	0.968001i	$-0.419259\pi$
$149$	13.0049	−	4.73338i	1.06540	−	0.387774i	0.814454	+	0.580228i	$0.197036\pi$
$150$		0			0
$151$	1.05788	+	5.99956i	0.0860894	+	0.488237i	0.997116	+	0.0758902i	$0.0241798\pi$
$151$	1.05788	+	5.99956i	0.0860894	+	0.488237i	−0.911027	+	0.412347i	$0.864709\pi$
$152$		0			0
$153$	15.1056	−	16.2188i	1.22122	−	1.31121i
$154$		0			0
$155$	1.97880	−	1.66041i	0.158941	−	0.133367i
$156$		0			0
$157$	−1.63950	+	9.29808i	−0.130847	+	0.742068i	0.846816	+	0.531886i	$0.178517\pi$
$157$	−1.63950	+	9.29808i	−0.130847	+	0.742068i	−0.977662	+	0.210181i	$0.932595\pi$
$158$		0			0
$159$	20.4237	+	2.32061i	1.61970	+	0.184037i
$160$		0			0
$161$	−19.0080			−1.49804
$162$		0			0
$163$	−15.8882			−1.24446			−0.622231	−	0.782834i	$-0.713773\pi$
$163$	−15.8882			−1.24446			−0.622231	+	0.782834i	$0.713773\pi$
$164$		0			0
$165$	−20.1734	−	2.29217i	−1.57049	−	0.178445i
$166$		0			0
$167$	−2.78221	+	15.7787i	−0.215294	+	1.22099i	0.665102	+	0.746753i	$0.268388\pi$
$167$	−2.78221	+	15.7787i	−0.215294	+	1.22099i	−0.880396	+	0.474240i	$0.842723\pi$
$168$		0			0
$169$	−9.22768	+	7.74295i	−0.709822	+	0.595611i
$170$		0			0
$171$	4.46686	+	14.5783i	0.341590	+	1.11483i
$172$		0			0
$173$	3.54316	+	20.0943i	0.269381	+	1.52774i	0.756262	+	0.654269i	$0.227024\pi$
$173$	3.54316	+	20.0943i	0.269381	+	1.52774i	−0.486880	+	0.873469i	$0.661865\pi$
$174$		0			0
$175$	1.77539	−	0.646188i	0.134207	−	0.0488472i
$176$		0			0
$177$	−2.91236	+	9.84309i	−0.218906	+	0.739852i
$178$		0			0
$179$	4.63944	−	8.03574i	0.346768	−	0.600619i	−0.638905	−	0.769285i	$-0.720613\pi$
$179$	4.63944	−	8.03574i	0.346768	−	0.600619i	0.985673	+	0.168666i	$0.0539459\pi$
$180$		0			0
$181$	0.873953	+	1.51373i	0.0649604	+	0.112515i	0.896676	−	0.442687i	$-0.145975\pi$
$181$	0.873953	+	1.51373i	0.0649604	+	0.112515i	−0.831716	+	0.555201i	$0.812641\pi$
$182$		0			0
$183$	−21.7183	+	14.3846i	−1.60546	+	1.06334i
$184$		0			0
$185$	−10.4485	−	8.76731i	−0.768187	−	0.644585i
$186$		0			0
$187$	39.2683	+	14.2925i	2.87158	+	1.04517i
$188$		0			0
$189$	−13.0337	+	4.88683i	−0.948062	+	0.355465i
$190$		0			0
$191$	−0.418346	−	0.152266i	−0.0302705	−	0.0110176i	0.326841	−	0.945080i	$-0.394016\pi$
$191$	−0.418346	−	0.152266i	−0.0302705	−	0.0110176i	−0.357111	+	0.934062i	$0.616238\pi$
$192$		0			0
$193$	13.8417	+	11.6145i	0.996345	+	0.836033i	0.986474	−	0.163918i	$-0.0524134\pi$
$193$	13.8417	+	11.6145i	0.996345	+	0.836033i	0.00987134	+	0.999951i	$0.496858\pi$
$194$		0			0
$195$	−0.215122	−	3.49953i	−0.0154052	−	0.250606i
$196$		0			0
$197$	1.05477	+	1.82691i	0.0751491	+	0.130162i	0.901151	−	0.433505i	$-0.142723\pi$
$197$	1.05477	+	1.82691i	0.0751491	+	0.130162i	−0.826002	+	0.563667i	$0.809390\pi$
$198$		0			0
$199$	7.46578	−	12.9311i	0.529235	−	0.916663i	−0.470183	−	0.882569i	$-0.655812\pi$
$199$	7.46578	−	12.9311i	0.529235	−	0.916663i	0.999419	−	0.0340939i	$-0.0108545\pi$
$200$		0			0
$201$	−17.6239	+	4.23687i	−1.24310	+	0.298846i
$202$		0			0
$203$	11.0979	−	4.03929i	0.778918	−	0.283503i
$204$		0			0
$205$	0.548699	+	3.11183i	0.0383228	+	0.217339i
$206$		0			0
$207$	−12.8212	−	16.9925i	−0.891133	−	1.18106i
$208$		0			0
$209$	−22.0222	+	18.4789i	−1.52331	+	1.27821i
$210$		0			0
$211$	0.219941	−	1.24734i	0.0151413	−	0.0858707i	−0.976301	−	0.216418i	$-0.930562\pi$
$211$	0.219941	−	1.24734i	0.0151413	−	0.0858707i	0.991442	+	0.130548i	$0.0416736\pi$
$212$		0			0
$213$	−1.72613	+	2.33423i	−0.118272	+	0.159939i
$214$		0			0
$215$	−8.97097			−0.611815
$216$		0			0
$217$	3.33909			0.226672
$218$		0			0
$219$	−4.16243	−	9.56488i	−0.281271	−	0.646335i
$220$		0			0
$221$	−1.25312	+	7.10678i	−0.0842937	+	0.478053i
$222$		0			0
$223$	7.84358	−	6.58155i	0.525245	−	0.440733i	−0.341211	−	0.939987i	$-0.610837\pi$
$223$	7.84358	−	6.58155i	0.525245	−	0.440733i	0.866456	+	0.499254i	$0.166392\pi$
$224$		0			0
$225$	1.77519	+	1.15127i	0.118346	+	0.0767512i
$226$		0			0
$227$	0.399676	+	2.26667i	0.0265274	+	0.150444i	0.995194	−	0.0979187i	$-0.0312185\pi$
$227$	0.399676	+	2.26667i	0.0265274	+	0.150444i	−0.968667	+	0.248363i	$0.920107\pi$
$228$		0			0
$229$	−4.30042	+	1.56522i	−0.284180	+	0.103433i	−0.480177	−	0.877171i	$-0.659428\pi$
$229$	−4.30042	+	1.56522i	−0.284180	+	0.103433i	0.195998	+	0.980604i	$0.437205\pi$
$230$		0			0
$231$	−18.0716	−	19.0318i	−1.18903	−	1.25220i
$232$		0			0
$233$	0.376054	−	0.651345i	0.0246361	−	0.0426710i	−0.853444	−	0.521184i	$-0.825491\pi$
$233$	0.376054	−	0.651345i	0.0246361	−	0.0426710i	0.878081	+	0.478513i	$0.158824\pi$
$234$		0			0
$235$	−8.19831	−	14.1999i	−0.534799	−	0.926299i
$236$		0			0
$237$	−7.11192	−	3.54314i	−0.461969	−	0.230152i
$238$		0			0
$239$	3.67746	+	3.08576i	0.237875	+	0.199601i	0.753930	−	0.656954i	$-0.228156\pi$
$239$	3.67746	+	3.08576i	0.237875	+	0.199601i	−0.516055	+	0.856555i	$0.672600\pi$
$240$		0			0
$241$	19.9150	+	7.24845i	1.28284	+	0.466914i	0.891369	−	0.453278i	$-0.149746\pi$
$241$	19.9150	+	7.24845i	1.28284	+	0.466914i	0.391467	+	0.920192i	$0.371968\pi$
$242$		0			0
$243$	−13.1601	−	8.35542i	−0.844218	−	0.536000i
$244$		0			0
$245$	−0.343197	−	0.124913i	−0.0219260	−	0.00798042i
$246$		0			0
$247$	−3.80300	−	3.19109i	−0.241979	−	0.203044i
$248$		0			0
$249$	17.6427	+	8.78953i	1.11806	+	0.557014i
$250$		0			0
$251$	3.91693	+	6.78433i	0.247235	+	0.428223i	0.962758	−	0.270366i	$-0.0871448\pi$
$251$	3.91693	+	6.78433i	0.247235	+	0.428223i	−0.715523	+	0.698589i	$0.753811\pi$
$252$		0			0
$253$	20.0675	−	34.7580i	1.26164	−	2.18522i
$254$		0			0
$255$	18.2601	+	19.2302i	1.14349	+	1.20424i
$256$		0			0
$257$	25.4314	−	9.25629i	1.58637	−	0.577391i	0.609793	−	0.792561i	$-0.291253\pi$
$257$	25.4314	−	9.25629i	1.58637	−	0.577391i	0.976577	+	0.215170i	$0.0690304\pi$
$258$		0			0
$259$	−3.06161	−	17.3632i	−0.190239	−	1.07890i
$260$		0			0
$261$	11.0966	+	7.19653i	0.686865	+	0.445454i
$262$		0			0
$263$	−10.5941	+	8.88949i	−0.653259	+	0.548150i	−0.908058	−	0.418845i	$-0.862435\pi$
$263$	−10.5941	+	8.88949i	−0.653259	+	0.548150i	0.254799	+	0.966994i	$0.417991\pi$
$264$		0			0
$265$	−4.27068	+	24.2202i	−0.262346	+	1.48784i
$266$		0			0
$267$	3.60865	+	8.29233i	0.220846	+	0.507483i
$268$		0			0
$269$	17.6670			1.07717			0.538587	−	0.842570i	$-0.318958\pi$
$269$	17.6670			1.07717			0.538587	+	0.842570i	$0.318958\pi$
$270$		0			0
$271$	15.6064			0.948022			0.474011	−	0.880519i	$-0.342806\pi$
$271$	15.6064			0.948022			0.474011	+	0.880519i	$0.342806\pi$
$272$		0			0
$273$	2.69473	−	3.64407i	0.163093	−	0.220549i
$274$		0			0
$275$	−0.692731	+	3.92867i	−0.0417732	+	0.236908i
$276$		0			0
$277$	−23.8550	+	20.0167i	−1.43331	+	1.20269i	−0.489585	+	0.871956i	$0.662852\pi$
$277$	−23.8550	+	20.0167i	−1.43331	+	1.20269i	−0.943724	+	0.330734i	$0.892704\pi$
$278$		0			0
$279$	2.25226	+	2.98503i	0.134839	+	0.178709i
$280$		0			0
$281$	2.44891	+	13.8884i	0.146089	+	0.828514i	0.966486	+	0.256719i	$0.0826416\pi$
$281$	2.44891	+	13.8884i	0.146089	+	0.828514i	−0.820397	+	0.571795i	$0.806247\pi$
$282$		0			0
$283$	0.543578	−	0.197846i	0.0323124	−	0.0117607i	−0.325813	−	0.945434i	$-0.605638\pi$
$283$	0.543578	−	0.197846i	0.0323124	−	0.0117607i	0.358126	+	0.933673i	$0.383416\pi$
$284$		0			0
$285$	−17.7378	+	4.26425i	−1.05070	+	0.252592i
$286$		0			0
$287$	−2.04228	+	3.53733i	−0.120552	+	0.208802i
$288$		0			0
$289$	−18.7906	−	32.5462i	−1.10533	−	1.91448i
$290$		0			0
$291$	−1.01864	−	16.5709i	−0.0597138	−	0.971402i
$292$		0			0
$293$	10.4645	+	8.78073i	0.611341	+	0.512976i	0.895068	−	0.445929i	$-0.147127\pi$
$293$	10.4645	+	8.78073i	0.611341	+	0.512976i	−0.283728	+	0.958905i	$0.591571\pi$
$294$		0			0
$295$	−11.5411	−	4.20062i	−0.671950	−	0.244570i
$296$		0			0
$297$	4.82416	−	28.9926i	0.279926	−	1.68232i
$298$		0			0
$299$	6.51290	+	2.37050i	0.376651	+	0.137090i
$300$		0			0
$301$	−8.88329	−	7.45396i	−0.512024	−	0.429639i
$302$		0			0
$303$	−0.255306	+	0.169097i	−0.0146670	+	0.00971435i
$304$		0			0
$305$	−15.5842	−	26.9926i	−0.892348	−	1.54559i
$306$		0			0
$307$	2.31710	−	4.01334i	0.132244	−	0.229053i	−0.792297	−	0.610135i	$-0.791115\pi$
$307$	2.31710	−	4.01334i	0.132244	−	0.229053i	0.924541	+	0.381082i	$0.124448\pi$
$308$		0			0
$309$	−0.415959	+	1.40584i	−0.0236631	+	0.0799757i
$310$		0			0
$311$	−7.79469	+	2.83704i	−0.441996	+	0.160874i	−0.553425	−	0.832899i	$-0.686680\pi$
$311$	−7.79469	+	2.83704i	−0.441996	+	0.160874i	0.111429	+	0.993772i	$0.464457\pi$
$312$		0			0
$313$	2.55347	+	14.4815i	0.144331	+	0.818540i	0.967902	+	0.251328i	$0.0808672\pi$
$313$	2.55347	+	14.4815i	0.144331	+	0.818540i	−0.823571	+	0.567213i	$0.808022\pi$
$314$		0			0
$315$	−4.87918	−	15.9240i	−0.274910	−	0.897215i
$316$		0			0
$317$	−20.4637	+	17.1711i	−1.14935	+	0.964422i	−0.999704	−	0.0243167i	$-0.992259\pi$
$317$	−20.4637	+	17.1711i	−1.14935	+	0.964422i	−0.149650	+	0.988739i	$0.547815\pi$
$318$		0			0
$319$	−4.33023	+	24.5580i	−0.242446	+	1.37498i
$320$		0			0
$321$	10.7656	+	1.22323i	0.600877	+	0.0682739i
$322$		0			0
$323$	37.5486			2.08926
$324$		0			0
$325$	−0.688904			−0.0382135
$326$		0			0
$327$	23.7889	+	2.70298i	1.31553	+	0.149475i
$328$		0			0
$329$	3.68049	−	20.8731i	0.202912	−	1.15077i
$330$		0			0
$331$	−10.6199	+	8.91116i	−0.583723	+	0.489802i	−0.886167	−	0.463365i	$-0.846642\pi$
$331$	−10.6199	+	8.91116i	−0.583723	+	0.489802i	0.302445	+	0.953167i	$0.402197\pi$
$332$		0			0
$333$	13.4570	−	14.4487i	0.737440	−	0.791785i
$334$		0			0
$335$	−3.76600	−	21.3581i	−0.205759	−	1.16692i
$336$		0			0
$337$	−5.94733	+	2.16465i	−0.323972	+	0.117916i	−0.498886	−	0.866668i	$-0.666257\pi$
$337$	−5.94733	+	2.16465i	−0.323972	+	0.117916i	0.174914	+	0.984584i	$0.444035\pi$
$338$		0			0
$339$	2.11365	−	7.14365i	0.114798	−	0.387990i
$340$		0			0
$341$	−3.52521	+	6.10585i	−0.190901	+	0.330650i
$342$		0			0
$343$	9.13992	+	15.8308i	0.493509	+	0.854783i
$344$		0			0
$345$	21.2342	−	14.0640i	1.14321	−	0.757180i
$346$		0			0
$347$	−10.7910	−	9.05469i	−0.579289	−	0.486081i	0.305424	−	0.952216i	$-0.401202\pi$
$347$	−10.7910	−	9.05469i	−0.579289	−	0.486081i	−0.884714	+	0.466135i	$0.845646\pi$
$348$		0			0
$349$	−2.38621	−	0.868508i	−0.127731	−	0.0464902i	0.277364	−	0.960765i	$-0.410539\pi$
$349$	−2.38621	−	0.868508i	−0.127731	−	0.0464902i	−0.405095	+	0.914275i	$0.632761\pi$
$350$		0			0
$351$	5.07530	−	0.0489812i	0.270899	−	0.00261442i
$352$		0			0
$353$	−9.55203	−	3.47665i	−0.508403	−	0.185044i	0.0750666	−	0.997179i	$-0.476083\pi$
$353$	−9.55203	−	3.47665i	−0.508403	−	0.185044i	−0.583470	+	0.812135i	$0.698305\pi$
$354$		0			0
$355$	−2.66089	−	2.23275i	−0.141225	−	0.118502i
$356$		0			0
$357$	2.10323	+	34.2146i	0.111315	+	1.81083i
$358$		0			0
$359$	−0.171055	−	0.296276i	−0.00902793	−	0.0156368i	0.861476	−	0.507798i	$-0.169540\pi$
$359$	−0.171055	−	0.296276i	−0.00902793	−	0.0156368i	−0.870504	+	0.492161i	$0.836207\pi$
$360$		0			0
$361$	−3.41559	+	5.91598i	−0.179768	+	0.311367i
$362$		0			0
$363$	35.3557	−	8.49966i	1.85569	−	0.446116i
$364$		0			0
$365$	11.7282	−	4.26873i	0.613884	−	0.223435i
$366$		0			0
$367$	−5.97632	−	33.8934i	−0.311962	−	1.76922i	−0.588774	−	0.808298i	$-0.700389\pi$
$367$	−5.97632	−	33.8934i	−0.311962	−	1.76922i	0.276812	−	0.960924i	$-0.410722\pi$
$368$		0			0
$369$	−4.53978	+	0.560254i	−0.236332	+	0.0291657i
$370$		0			0
$371$	−24.3535	+	20.4350i	−1.26437	+	1.06093i
$372$		0			0
$373$	3.40368	−	19.3032i	0.176236	−	0.999482i	−0.760472	−	0.649370i	$-0.775032\pi$
$373$	3.40368	−	19.3032i	0.176236	−	0.999482i	0.936708	−	0.350112i	$-0.113856\pi$
$374$		0			0
$375$	−12.1762	+	16.4658i	−0.628776	+	0.850290i
$376$		0			0
$377$	−4.30631			−0.221786
$378$		0			0
$379$	15.7651			0.809798			0.404899	−	0.914361i	$-0.367307\pi$
$379$	15.7651			0.809798			0.404899	+	0.914361i	$0.367307\pi$
$380$		0			0
$381$	−1.56502	−	3.59628i	−0.0801785	−	0.184243i
$382$		0			0
$383$	−4.71505	+	26.7404i	−0.240928	+	1.36637i	0.588836	+	0.808253i	$0.299586\pi$
$383$	−4.71505	+	26.7404i	−0.240928	+	1.36637i	−0.829763	+	0.558115i	$0.811525\pi$
$384$		0			0
$385$	24.0550	−	20.1845i	1.22596	−	1.02870i
$386$		0			0
$387$	0.671673	−	12.9691i	0.0341431	−	0.659258i
$388$		0			0
$389$	−2.08450	−	11.8218i	−0.105688	−	0.599389i	−0.990943	−	0.134282i	$-0.957127\pi$
$389$	−2.08450	−	11.8218i	−0.105688	−	0.599389i	0.885255	−	0.465106i	$-0.153984\pi$
$390$		0			0
$391$	−49.2602	+	17.9292i	−2.49119	+	0.906720i
$392$		0			0
$393$	17.1720	+	18.0844i	0.866214	+	0.912237i
$394$		0			0
$395$	4.75342	−	8.23316i	0.239170	−	0.414255i
$396$		0			0
$397$	−6.40851	−	11.0999i	−0.321634	−	0.557086i	0.659192	−	0.751975i	$-0.270899\pi$
$397$	−6.40851	−	11.0999i	−0.321634	−	0.557086i	−0.980825	+	0.194889i	$0.937565\pi$
$398$		0			0
$399$	−21.1076	−	10.5157i	−1.05670	−	0.526446i
$400$		0			0
$401$	16.7646	+	14.0672i	0.837187	+	0.702483i	0.956929	−	0.290322i	$-0.0937624\pi$
$401$	16.7646	+	14.0672i	0.837187	+	0.702483i	−0.119742	+	0.992805i	$0.538207\pi$
$402$		0			0
$403$	−1.14410	−	0.416420i	−0.0569919	−	0.0207434i
$404$		0			0
$405$	10.9444	−	15.1027i	0.543831	−	0.750462i
$406$		0			0
$407$	34.9826	+	12.7326i	1.73402	+	0.631133i
$408$		0			0
$409$	−24.9289	−	20.9179i	−1.23266	−	1.03432i	−0.998062	−	0.0622284i	$-0.980179\pi$
$409$	−24.9289	−	20.9179i	−1.23266	−	1.03432i	−0.234595	−	0.972093i	$-0.575376\pi$
$410$		0			0
$411$	11.6557	+	5.80684i	0.574933	+	0.286430i
$412$		0			0
$413$	−7.93803	−	13.7491i	−0.390605	−	0.676548i
$414$		0			0
$415$	−11.7919	+	20.4242i	−0.578841	+	1.00258i
$416$		0			0
$417$	−13.7457	−	14.4760i	−0.673129	−	0.708893i
$418$		0			0
$419$	−3.60955	+	1.31377i	−0.176338	+	0.0641817i	−0.428680	−	0.903456i	$-0.641021\pi$
$419$	−3.60955	+	1.31377i	−0.176338	+	0.0641817i	0.252342	+	0.967638i	$0.418799\pi$
$420$		0			0
$421$	0.432258	+	2.45146i	0.0210670	+	0.119477i	0.993528	−	0.113590i	$-0.0362351\pi$
$421$	0.432258	+	2.45146i	0.0210670	+	0.119477i	−0.972461	+	0.233067i	$0.925124\pi$
$422$		0			0
$423$	21.1423	−	10.7890i	1.02797	−	0.524577i
$424$		0			0
$425$	3.99148	−	3.34925i	0.193615	−	0.162462i
$426$		0			0
$427$	6.99624	−	39.6777i	0.338572	−	1.92014i
$428$		0			0
$429$	3.81859	+	8.77477i	0.184363	+	0.423650i
$430$		0			0
$431$	−7.82650			−0.376989			−0.188495	−	0.982074i	$-0.560361\pi$
$431$	−7.82650			−0.376989			−0.188495	+	0.982074i	$0.560361\pi$
$432$		0			0
$433$	0.715996			0.0344086			0.0172043	−	0.999852i	$-0.494523\pi$
$433$	0.715996			0.0344086			0.0172043	+	0.999852i	$0.494523\pi$
$434$		0			0
$435$	−9.40894	+	12.7236i	−0.451124	+	0.610052i
$436$		0			0
$437$	6.26226	−	35.5151i	0.299565	−	1.69892i
$438$		0			0
$439$	−27.0678	+	22.7126i	−1.29188	+	1.08401i	−0.300388	+	0.953817i	$0.597116\pi$
$439$	−27.0678	+	22.7126i	−1.29188	+	1.08401i	−0.991488	+	0.130196i	$0.958439\pi$
$440$		0			0
$441$	0.206280	−	0.486800i	0.00982288	−	0.0231809i
$442$		0			0
$443$	5.65518	+	32.0721i	0.268686	+	1.52379i	0.758331	+	0.651870i	$0.226015\pi$
$443$	5.65518	+	32.0721i	0.268686	+	1.52379i	−0.489645	+	0.871922i	$0.662874\pi$
$444$		0			0
$445$	−10.1679	+	3.70080i	−0.482003	+	0.175435i
$446$		0			0
$447$	−23.3067	+	5.60302i	−1.10237	+	0.265014i
$448$		0			0
$449$	−11.5847	+	20.0653i	−0.546717	+	0.946942i	0.451779	+	0.892130i	$0.350789\pi$
$449$	−11.5847	+	20.0653i	−0.546717	+	0.946942i	−0.998497	+	0.0548124i	$0.982544\pi$
$450$		0			0
$451$	−4.31223	−	7.46900i	−0.203055	−	0.351701i
$452$		0			0
$453$	−0.647419	−	10.5320i	−0.0304184	−	0.494835i
$454$		0			0
$455$	4.15403	+	3.48565i	0.194744	+	0.163410i
$456$		0			0
$457$	26.6611	+	9.70386i	1.24715	+	0.453927i	0.879439	−	0.476011i	$-0.157918\pi$
$457$	26.6611	+	9.70386i	1.24715	+	0.453927i	0.367716	+	0.929938i	$0.380140\pi$
$458$		0			0
$459$	−29.1679	+	24.9584i	−1.36144	+	1.16496i
$460$		0			0
$461$	0.0555796	+	0.0202293i	0.00258860	+	0.000942173i	0.343314	−	0.939221i	$-0.388450\pi$
$461$	0.0555796	+	0.0202293i	0.00258860	+	0.000942173i	−0.340726	+	0.940163i	$0.610673\pi$
$462$		0			0
$463$	−8.86124	−	7.43546i	−0.411817	−	0.345555i	0.413223	−	0.910630i	$-0.364403\pi$
$463$	−8.86124	−	7.43546i	−0.411817	−	0.345555i	−0.825040	+	0.565075i	$0.808847\pi$
$464$		0			0
$465$	−3.73015	+	2.47059i	−0.172982	+	0.114571i
$466$		0			0
$467$	3.03520	+	5.25712i	0.140452	+	0.243271i	0.927667	−	0.373408i	$-0.121811\pi$
$467$	3.03520	+	5.25712i	0.140452	+	0.243271i	−0.787215	+	0.616679i	$0.788478\pi$
$468$		0			0
$469$	14.0172	−	24.2785i	0.647254	−	1.12108i
$470$		0			0
$471$	4.63973	−	15.6812i	0.213787	−	0.722551i
$472$		0			0
$473$	23.0087	−	8.37450i	1.05794	−	0.385060i
$474$		0			0
$475$	0.622445	+	3.53006i	0.0285597	+	0.161970i
$476$		0			0
$477$	−34.6949	−	7.98745i	−1.58857	−	0.365720i
$478$		0			0
$479$	5.21611	−	4.37684i	0.238330	−	0.199983i	−0.515798	−	0.856710i	$-0.672504\pi$
$479$	5.21611	−	4.37684i	0.238330	−	0.199983i	0.754128	+	0.656728i	$0.228060\pi$
$480$		0			0
$481$	−1.11635	+	6.33115i	−0.0509013	+	0.288676i
$482$		0			0
$483$	32.7124	+	3.71690i	1.48847	+	0.169125i
$484$		0			0
$485$	19.8642			0.901988
$486$		0			0
$487$	−41.4345			−1.87758			−0.938788	−	0.344496i	$-0.888050\pi$
$487$	−41.4345			−1.87758			−0.938788	+	0.344496i	$0.888050\pi$
$488$		0			0
$489$	27.3433	+	3.10684i	1.23651	+	0.140496i
$490$		0			0
$491$	1.04493	−	5.92607i	0.0471568	−	0.267440i	−0.952109	−	0.305760i	$-0.901090\pi$
$491$	1.04493	−	5.92607i	0.0471568	−	0.267440i	0.999266	+	0.0383201i	$0.0122006\pi$
$492$		0			0
$493$	24.9506	−	20.9360i	1.12372	−	0.942911i
$494$		0			0
$495$	34.2697	+	7.88955i	1.54031	+	0.354609i
$496$		0			0
$497$	−0.779694	−	4.42186i	−0.0349741	−	0.198348i
$498$		0			0
$499$	21.1472	−	7.69695i	0.946679	−	0.344563i	0.177879	−	0.984052i	$-0.443076\pi$
$499$	21.1472	−	7.69695i	0.946679	−	0.344563i	0.768800	+	0.639489i	$0.220854\pi$
$500$		0			0
$501$	7.87354	−	26.6107i	0.351764	−	1.18888i
$502$		0			0
$503$	−14.6026	+	25.2924i	−0.651097	+	1.12773i	0.331759	+	0.943364i	$0.392358\pi$
$503$	−14.6026	+	25.2924i	−0.651097	+	1.12773i	−0.982857	+	0.184370i	$0.940976\pi$
$504$		0			0
$505$	−0.183198	−	0.317308i	−0.00815220	−	0.0141200i
$506$		0			0
$507$	17.3947	−	11.5210i	0.772527	−	0.511666i
$508$		0			0
$509$	23.4530	+	19.6794i	1.03953	+	0.872273i	0.991955	−	0.126594i	$-0.0404046\pi$
$509$	23.4530	+	19.6794i	1.03953	+	0.872273i	0.0475801	+	0.998867i	$0.484849\pi$
$510$		0			0
$511$	15.1605	+	5.51797i	0.670661	+	0.244101i
$512$		0			0
$513$	−4.83667	−	25.9624i	−0.213544	−	1.14627i
$514$		0			0
$515$	−1.64837	−	0.599956i	−0.0726356	−	0.0264372i
$516$		0			0
$517$	34.2828	+	28.7667i	1.50776	+	1.26516i
$518$		0			0
$519$	−2.16839	−	35.2746i	−0.0951819	−	1.54838i
$520$		0			0
$521$	−16.8996	−	29.2709i	−0.740384	−	1.28238i	−0.952321	−	0.305099i	$-0.901311\pi$
$521$	−16.8996	−	29.2709i	−0.740384	−	1.28238i	0.211937	−	0.977283i	$-0.432023\pi$
$522$		0			0
$523$	−15.0731	+	26.1073i	−0.659098	+	1.14159i	0.321751	+	0.946824i	$0.395729\pi$
$523$	−15.0731	+	26.1073i	−0.659098	+	1.14159i	−0.980849	+	0.194768i	$0.937605\pi$
$524$		0			0
$525$	−3.18176	+	0.764909i	−0.138863	+	0.0333834i
$526$		0			0
$527$	8.65341	−	3.14958i	0.376948	−	0.137198i
$528$		0			0
$529$	4.74884	+	26.9320i	0.206471	+	1.17096i
$530$		0			0
$531$	6.93686	−	16.3702i	0.301034	−	0.710408i
$532$		0			0
$533$	1.14091	−	0.957334i	0.0494181	−	0.0414667i
$534$		0			0
$535$	−2.25113	+	12.7668i	−0.0973249	+	0.551957i
$536$		0			0
$537$	−9.55570	+	12.9221i	−0.412359	+	0.557630i
$538$		0			0
$539$	0.996839			0.0429369
$540$		0			0
$541$	21.8374			0.938863			0.469432	−	0.882969i	$-0.344459\pi$
$541$	21.8374			0.938863			0.469432	+	0.882969i	$0.344459\pi$
$542$		0			0
$543$	−1.20805	−	2.77599i	−0.0518425	−	0.119129i
$544$		0			0
$545$	−4.97436	+	28.2110i	−0.213078	+	1.20843i
$546$		0			0
$547$	−33.8575	+	28.4098i	−1.44764	+	1.21472i	−0.513362	+	0.858172i	$0.671600\pi$
$547$	−33.8575	+	28.4098i	−1.44764	+	1.21472i	−0.934279	+	0.356543i	$0.883955\pi$
$548$		0			0
$549$	40.1895	−	20.5087i	1.71524	−	0.875292i
$550$		0			0
$551$	3.89088	+	22.0663i	0.165757	+	0.940055i
$552$		0			0
$553$	11.5479	−	4.20309i	0.491066	−	0.178733i
$554$		0			0
$555$	16.2672	+	17.1315i	0.690504	+	0.727191i
$556$		0			0
$557$	−0.672159	+	1.16421i	−0.0284803	+	0.0493293i	−0.879914	−	0.475133i	$-0.842400\pi$
$557$	−0.672159	+	1.16421i	−0.0284803	+	0.0493293i	0.851434	+	0.524462i	$0.175733\pi$
$558$		0			0
$559$	2.11418	+	3.66186i	0.0894202	+	0.154880i
$560$		0			0
$561$	−64.7851	−	32.2757i	−2.73523	−	1.36268i
$562$		0			0
$563$	−4.04346	−	3.39287i	−0.170411	−	0.142992i	0.553593	−	0.832787i	$-0.313256\pi$
$563$	−4.04346	−	3.39287i	−0.170411	−	0.142992i	−0.724005	+	0.689795i	$0.757701\pi$
$564$		0			0
$565$	8.37600	+	3.04861i	0.352381	+	0.128256i
$566$		0			0
$567$	23.3863	−	5.86147i	0.982132	−	0.246158i
$568$		0			0
$569$	3.05637	+	1.11243i	0.128129	+	0.0466353i	0.405289	−	0.914189i	$-0.367171\pi$
$569$	3.05637	+	1.11243i	0.128129	+	0.0466353i	−0.277160	+	0.960824i	$0.589393\pi$
$570$		0			0
$571$	−19.9173	−	16.7126i	−0.833515	−	0.699402i	0.122580	−	0.992459i	$-0.460883\pi$
$571$	−19.9173	−	16.7126i	−0.833515	−	0.699402i	−0.956095	+	0.293056i	$0.905328\pi$
$572$		0			0
$573$	0.690190	+	0.343851i	0.0288331	+	0.0143646i
$574$		0			0
$575$	−2.50217	−	4.33389i	−0.104348	−	0.180736i
$576$		0			0
$577$	−8.57097	+	14.8453i	−0.356814	+	0.618020i	−0.987427	−	0.158078i	$-0.949470\pi$
$577$	−8.57097	+	14.8453i	−0.356814	+	0.618020i	0.630613	+	0.776098i	$0.282804\pi$
$578$		0			0
$579$	−21.5500	−	22.6950i	−0.895590	−	0.943172i
$580$		0			0
$581$	−28.6471	+	10.4267i	−1.18848	+	0.432571i
$582$		0			0
$583$	−11.6564	−	66.1068i	−0.482759	−	2.73786i
$584$		0			0
$585$	−0.314090	+	6.06467i	−0.0129860	+	0.250743i
$586$		0			0
$587$	33.9905	−	28.5214i	1.40294	−	1.17721i	0.443161	−	0.896442i	$-0.353857\pi$
$587$	33.9905	−	28.5214i	1.40294	−	1.17721i	0.959777	−	0.280763i	$-0.0905876\pi$
$588$		0			0
$589$	−1.10008	+	6.23884i	−0.0453278	+	0.257067i
$590$		0			0
$591$	−1.45799	−	3.35032i	−0.0599737	−	0.137814i
$592$		0			0
$593$	26.6236			1.09330			0.546650	−	0.837361i	$-0.315903\pi$
$593$	26.6236			1.09330			0.546650	+	0.837361i	$0.315903\pi$
$594$		0			0
$595$	−41.0145			−1.68143
$596$		0			0
$597$	−15.3770	+	20.7943i	−0.629341	+	0.851053i
$598$		0			0
$599$	6.47258	−	36.7078i	0.264462	−	1.49984i	−0.506099	−	0.862475i	$-0.668913\pi$
$599$	6.47258	−	36.7078i	0.264462	−	1.49984i	0.770561	−	0.637366i	$-0.219976\pi$
$600$		0			0
$601$	−21.4634	+	18.0099i	−0.875509	+	0.734640i	−0.965251	−	0.261325i	$-0.915840\pi$
$601$	−21.4634	+	18.0099i	−0.875509	+	0.734640i	0.0897413	+	0.995965i	$0.471396\pi$
$602$		0			0
$603$	31.1589	−	3.84531i	1.26889	−	0.156593i
$604$		0			0
$605$	7.55504	+	42.8468i	0.307156	+	1.74197i
$606$		0			0
$607$	19.3766	−	7.05251i	0.786472	−	0.286252i	0.0826034	−	0.996583i	$-0.473677\pi$
$607$	19.3766	−	7.05251i	0.786472	−	0.286252i	0.703869	+	0.710330i	$0.251454\pi$
$608$		0			0
$609$	−19.8890	+	4.78141i	−0.805945	+	0.193753i
$610$		0			0
$611$	−3.86418	+	6.69295i	−0.156328	+	0.270768i
$612$		0			0
$613$	−17.6262	−	30.5294i	−0.711915	−	1.23307i	−0.964138	−	0.265403i	$-0.914495\pi$
$613$	−17.6262	−	30.5294i	−0.711915	−	1.23307i	0.252223	−	0.967669i	$-0.418838\pi$
$614$		0			0
$615$	−0.335800	−	5.46268i	−0.0135408	−	0.220276i
$616$		0			0
$617$	−17.5772	−	14.7490i	−0.707630	−	0.593772i	0.216303	−	0.976326i	$-0.430600\pi$
$617$	−17.5772	−	14.7490i	−0.707630	−	0.593772i	−0.923933	+	0.382554i	$0.875045\pi$
$618$		0			0
$619$	5.49929	+	2.00158i	0.221035	+	0.0804502i	0.450164	−	0.892946i	$-0.351366\pi$
$619$	5.49929	+	2.00158i	0.221035	+	0.0804502i	−0.229129	+	0.973396i	$0.573588\pi$
$620$		0			0
$621$	18.7422	+	31.7508i	0.752098	+	1.27412i
$622$		0			0
$623$	−13.1435	−	4.78384i	−0.526583	−	0.191660i
$624$		0			0
$625$	−16.0687	−	13.4832i	−0.642748	−	0.539330i
$626$		0			0
$627$	41.5132	−	27.4954i	1.65788	−	1.09806i
$628$		0			0
$629$	−24.3121	−	42.1098i	−0.969387	−	1.67903i
$630$		0			0
$631$	16.3134	−	28.2557i	0.649427	−	1.12484i	−0.333832	−	0.942632i	$-0.608342\pi$
$631$	16.3134	−	28.2557i	0.649427	−	1.12484i	0.983260	−	0.182209i	$-0.0583247\pi$
$632$		0			0
$633$	−0.622423	+	2.10364i	−0.0247391	+	0.0836123i
$634$		0			0
$635$	4.40967	−	1.60499i	0.174992	−	0.0636920i
$636$		0			0
$637$	0.0298923	+	0.169528i	0.00118438	+	0.00671694i
$638$		0			0
$639$	3.42707	−	3.67963i	0.135573	−	0.145564i
$640$		0			0
$641$	5.45686	−	4.57885i	0.215533	−	0.180854i	−0.528629	−	0.848853i	$-0.677294\pi$
$641$	5.45686	−	4.57885i	0.215533	−	0.180854i	0.744162	+	0.668000i	$0.232849\pi$
$642$		0			0
$643$	−1.68965	+	9.58246i	−0.0666331	+	0.377895i	0.933195	+	0.359370i	$0.117008\pi$
$643$	−1.68965	+	9.58246i	−0.0666331	+	0.377895i	−0.999828	+	0.0185255i	$0.994103\pi$
$644$		0			0
$645$	15.4388	+	1.75422i	0.607903	+	0.0690722i
$646$		0			0
$647$	−49.7867			−1.95732			−0.978658	−	0.205494i	$-0.934120\pi$
$647$	−49.7867			−1.95732			−0.978658	+	0.205494i	$0.934120\pi$
$648$		0			0
$649$	33.5220			1.31585
$650$		0			0
$651$	−5.74650	−	0.652938i	−0.225223	−	0.0255907i
$652$		0			0
$653$	5.99181	−	33.9813i	0.234478	−	1.32979i	−0.609233	−	0.792991i	$-0.708523\pi$
$653$	5.99181	−	33.9813i	0.234478	−	1.32979i	0.843711	−	0.536798i	$-0.180366\pi$
$654$		0			0
$655$	−22.8575	+	19.1798i	−0.893118	+	0.749415i
$656$		0			0
$657$	5.29310	+	17.2749i	0.206503	+	0.673957i
$658$		0			0
$659$	6.19566	+	35.1373i	0.241349	+	1.36876i	0.828822	+	0.559512i	$0.189012\pi$
$659$	6.19566	+	35.1373i	0.241349	+	1.36876i	−0.587473	+	0.809244i	$0.699877\pi$
$660$		0			0
$661$	−41.6551	+	15.1612i	−1.62020	+	0.589703i	−0.983420	−	0.181345i	$-0.941955\pi$
$661$	−41.6551	+	15.1612i	−1.62020	+	0.589703i	−0.636777	+	0.771048i	$0.719733\pi$
$662$		0			0
$663$	3.54627	−	11.9856i	0.137726	−	0.465481i
$664$		0			0
$665$	14.1078	−	24.4354i	0.547076	−	0.947563i
$666$		0			0
$667$	−15.6410	−	27.0910i	−0.605622	−	1.04897i
$668$		0			0
$669$	−14.7856	+	9.79293i	−0.571645	+	0.378617i
$670$		0			0
$671$	65.1682	+	54.6826i	2.51579	+	2.11100i
$672$		0			0
$673$	−37.7104	−	13.7255i	−1.45363	−	0.529078i	−0.510027	−	0.860158i	$-0.670365\pi$
$673$	−37.7104	−	13.7255i	−1.45363	−	0.529078i	−0.943603	+	0.331080i	$0.892587\pi$
$674$		0			0
$675$	−2.82994	−	2.32843i	−0.108924	−	0.0896215i
$676$		0			0
$677$	−12.1076	−	4.40679i	−0.465332	−	0.169367i	0.0987049	−	0.995117i	$-0.468530\pi$
$677$	−12.1076	−	4.40679i	−0.465332	−	0.169367i	−0.564036	+	0.825750i	$0.690752\pi$
$678$		0			0
$679$	19.6701	+	16.5052i	0.754868	+	0.633410i
$680$		0			0
$681$	−0.244599	−	3.97905i	−0.00937306	−	0.152477i
$682$		0			0
$683$	21.7166	+	37.6142i	0.830961	+	1.43927i	0.897277	+	0.441469i	$0.145542\pi$
$683$	21.7166	+	37.6142i	0.830961	+	1.43927i	−0.0663153	+	0.997799i	$0.521124\pi$
$684$		0			0
$685$	−7.79036	+	13.4933i	−0.297654	+	0.515553i
$686$		0			0
$687$	7.70699	−	1.85279i	0.294040	−	0.0706885i
$688$		0			0
$689$	10.8929	−	3.96471i	0.414988	−	0.151043i
$690$		0			0
$691$	3.10611	+	17.6156i	0.118162	+	0.670130i	0.985136	+	0.171777i	$0.0549507\pi$
$691$	3.10611	+	17.6156i	0.118162	+	0.670130i	−0.866974	+	0.498354i	$0.833938\pi$
$692$		0			0
$693$	27.3793	+	36.2871i	1.04005	+	1.37843i
$694$		0			0
$695$	18.2968	−	15.3528i	0.694036	−	0.582365i
$696$		0			0
$697$	−1.95608	+	11.0935i	−0.0740920	+	0.420196i
$698$		0			0
$699$	−0.774547	+	1.04741i	−0.0292960	+	0.0396168i
$700$		0			0
$701$	−35.3400			−1.33477			−0.667386	−	0.744712i	$-0.732587\pi$
$701$	−35.3400			−1.33477			−0.667386	+	0.744712i	$0.732587\pi$
$702$		0			0
$703$	33.4506			1.26161
$704$		0			0
$705$	11.3324	+	26.0408i	0.426803	+	0.980754i
$706$		0			0
$707$	0.0822434	−	0.466426i	0.00309308	−	0.0175417i
$708$		0			0
$709$	5.44977	−	4.57290i	0.204670	−	0.171739i	−0.534691	−	0.845048i	$-0.679572\pi$
$709$	5.44977	−	4.57290i	0.204670	−	0.171739i	0.739361	+	0.673309i	$0.235128\pi$
$710$		0			0
$711$	11.5466	+	7.48835i	0.433032	+	0.280835i
$712$		0			0
$713$	−1.53582	−	8.71005i	−0.0575168	−	0.326194i
$714$		0			0
$715$	−10.7594	+	3.91611i	−0.402380	+	0.146454i
$716$		0			0
$717$	−5.72543	−	6.02962i	−0.213820	−	0.225180i
$718$		0			0
$719$	−17.9082	+	31.0179i	−0.667864	+	1.15677i	0.310637	+	0.950529i	$0.399458\pi$
$719$	−17.9082	+	31.0179i	−0.667864	+	1.15677i	−0.978500	+	0.206245i	$0.933876\pi$
$720$		0			0
$721$	−1.13375	−	1.96372i	−0.0422231	−	0.0731326i
$722$		0			0
$723$	−32.8558	−	16.3687i	−1.22192	−	0.608757i
$724$		0			0
$725$	2.38187	+	1.99863i	0.0884605	+	0.0742271i
$726$		0			0
$727$	17.1870	+	6.25554i	0.637429	+	0.232005i	0.640462	−	0.767990i	$-0.278743\pi$
$727$	17.1870	+	6.25554i	0.637429	+	0.232005i	−0.00303240	+	0.999995i	$0.500965\pi$
$728$		0			0
$729$	21.0143	+	16.9528i	0.778308	+	0.627883i
$730$		0			0
$731$	−30.0524	−	10.9382i	−1.11153	−	0.404563i
$732$		0			0
$733$	−14.1799	−	11.8983i	−0.523746	−	0.439475i	0.342189	−	0.939631i	$-0.388832\pi$
$733$	−14.1799	−	11.8983i	−0.523746	−	0.439475i	−0.865936	+	0.500156i	$0.833276\pi$
$734$		0			0
$735$	0.566208	+	0.282083i	0.0208849	+	0.0104048i
$736$		0			0
$737$	29.5970	+	51.2636i	1.09022	+	1.88832i
$738$		0			0
$739$	12.1992	−	21.1297i	0.448755	−	0.777267i	−0.549550	−	0.835461i	$-0.685201\pi$
$739$	12.1992	−	21.1297i	0.448755	−	0.777267i	0.998305	+	0.0581936i	$0.0185341\pi$
$740$		0			0
$741$	5.92087	+	6.23545i	0.217509	+	0.229065i
$742$		0			0
$743$	9.07984	−	3.30479i	0.333107	−	0.121241i	−0.170051	−	0.985435i	$-0.554393\pi$
$743$	9.07984	−	3.30479i	0.333107	−	0.121241i	0.503159	+	0.864194i	$0.332171\pi$
$744$		0			0
$745$	−4.98033	−	28.2448i	−0.182465	−	1.03481i
$746$		0			0
$747$	−28.6439	−	18.5765i	−1.04803	−	0.679678i
$748$		0			0
$749$	−12.8371	+	10.7716i	−0.469056	+	0.393585i
$750$		0			0
$751$	7.04205	−	39.9375i	0.256968	−	1.45734i	−0.534002	−	0.845483i	$-0.679312\pi$
$751$	7.04205	−	39.9375i	0.256968	−	1.45734i	0.790970	−	0.611855i	$-0.209576\pi$
$752$		0			0
$753$	−5.41432	−	12.4416i	−0.197309	−	0.453397i
$754$		0			0
$755$	12.6251			0.459475
$756$		0			0
$757$	−38.7960			−1.41007			−0.705033	−	0.709175i	$-0.749068\pi$
$757$	−38.7960			−1.41007			−0.705033	+	0.709175i	$0.749068\pi$
$758$		0			0
$759$	−41.3325	+	55.8937i	−1.50027	+	2.02881i
$760$		0			0
$761$	−8.49474	+	48.1761i	−0.307934	+	1.74638i	0.301429	+	0.953489i	$0.402537\pi$
$761$	−8.49474	+	48.1761i	−0.307934	+	1.74638i	−0.609363	+	0.792892i	$0.708575\pi$
$762$		0			0
$763$	−28.3662	+	23.8021i	−1.02693	+	0.861694i
$764$		0			0
$765$	−27.6648	−	36.6654i	−1.00022	−	1.32564i
$766$		0			0
$767$	1.00523	+	5.70093i	0.0362967	+	0.205849i
$768$		0			0
$769$	−8.53774	+	3.10748i	−0.307879	+	0.112059i	−0.491339	−	0.870968i	$-0.663492\pi$
$769$	−8.53774	+	3.10748i	−0.307879	+	0.112059i	0.183460	+	0.983027i	$0.441270\pi$
$770$		0			0
$771$	−45.5769	+	10.9569i	−1.64141	+	0.394603i
$772$		0			0
$773$	6.67996	−	11.5700i	0.240261	−	0.416145i	−0.720527	−	0.693427i	$-0.756100\pi$
$773$	6.67996	−	11.5700i	0.240261	−	0.416145i	0.960789	+	0.277282i	$0.0894335\pi$
$774$		0			0
$775$	0.439551	+	0.761324i	0.0157891	+	0.0273476i
$776$		0			0
$777$	1.87369	+	30.4804i	0.0672181	+	1.09348i
$778$		0			0
$779$	−5.93639	−	4.98122i	−0.212693	−	0.178471i
$780$		0			0
$781$	8.90896	+	3.24260i	0.318788	+	0.116029i
$782$		0			0
$783$	−17.6898	−	14.5549i	−0.632183	−	0.520151i
$784$		0			0
$785$	18.3863	+	6.69208i	0.656237	+	0.238851i
$786$		0			0
$787$	10.0637	+	8.44446i	0.358733	+	0.301012i	0.804285	−	0.594243i	$-0.202548\pi$
$787$	10.0637	+	8.44446i	0.358733	+	0.301012i	−0.445553	+	0.895256i	$0.646993\pi$
$788$		0			0
$789$	19.9705	−	13.2270i	0.710967	−	0.470894i
$790$		0			0
$791$	5.76105	+	9.97843i	0.204839	+	0.354792i
$792$		0			0
$793$	−7.34541	+	12.7226i	−0.260843	+	0.451794i
$794$		0			0
$795$	12.0859	−	40.8474i	0.428641	−	1.44871i
$796$		0			0
$797$	−39.2577	+	14.2886i	−1.39058	+	0.506129i	−0.925368	−	0.379071i	$-0.876244\pi$
$797$	−39.2577	+	14.2886i	−1.39058	+	0.506129i	−0.465211	+	0.885200i	$0.654022\pi$
$798$		0			0
$799$	−10.1503	−	57.5651i	−0.359091	−	2.03651i
$800$		0			0
$801$	−4.58889	−	14.9766i	−0.162140	−	0.529171i
$802$		0			0
$803$	−26.0957	+	21.8969i	−0.920897	+	0.772724i
$804$		0			0
$805$	−6.84030	+	38.7933i	−0.241089	+	1.36728i
$806$		0			0
$807$	−30.4044	−	3.45466i	−1.07029	−	0.121610i
$808$		0			0
$809$	−28.2120			−0.991881			−0.495941	−	0.868356i	$-0.665177\pi$
$809$	−28.2120			−0.991881			−0.495941	+	0.868356i	$0.665177\pi$
$810$		0			0
$811$	−16.5624			−0.581584			−0.290792	−	0.956786i	$-0.593919\pi$
$811$	−16.5624			−0.581584			−0.290792	+	0.956786i	$0.593919\pi$
$812$		0			0
$813$	−26.8583	−	3.05174i	−0.941961	−	0.107029i
$814$		0			0
$815$	−5.71759	+	32.4261i	−0.200279	+	1.13584i
$816$		0			0
$817$	16.8538	−	14.1420i	0.589640	−	0.494766i
$818$		0			0
$819$	−5.35015	+	5.74442i	−0.186949	+	0.200726i
$820$		0			0
$821$	3.57185	+	20.2569i	0.124658	+	0.706972i	0.981510	+	0.191410i	$0.0613059\pi$
$821$	3.57185	+	20.2569i	0.124658	+	0.706972i	−0.856852	+	0.515563i	$0.827583\pi$
$822$		0			0
$823$	11.8031	−	4.29596i	0.411429	−	0.149748i	−0.128009	−	0.991773i	$-0.540859\pi$
$823$	11.8031	−	4.29596i	0.411429	−	0.149748i	0.539438	+	0.842025i	$0.318637\pi$
$824$		0			0
$825$	1.96040	−	6.62569i	0.0682524	−	0.230677i
$826$		0			0
$827$	−6.60938	+	11.4478i	−0.229831	+	0.398078i	−0.957758	−	0.287576i	$-0.907151\pi$
$827$	−6.60938	+	11.4478i	−0.229831	+	0.398078i	0.727927	+	0.685654i	$0.240484\pi$
$828$		0			0
$829$	16.5508	+	28.6668i	0.574833	+	0.995640i	0.996060	+	0.0886844i	$0.0282663\pi$
$829$	16.5508	+	28.6668i	0.574833	+	0.995640i	−0.421227	+	0.906955i	$0.638400\pi$
$830$		0			0
$831$	44.9681	−	29.7837i	1.55993	−	1.03318i
$832$		0			0
$833$	−0.997389	−	0.836909i	−0.0345575	−	0.0289972i
$834$		0			0
$835$	31.2013	+	11.3564i	1.07977	+	0.393003i
$836$		0			0
$837$	−3.29239	−	5.57758i	−0.113802	−	0.192789i
$838$		0			0
$839$	−13.7035	−	4.98765i	−0.473096	−	0.172193i	0.0944583	−	0.995529i	$-0.469888\pi$
$839$	−13.7035	−	4.98765i	−0.473096	−	0.172193i	−0.567554	+	0.823336i	$0.692110\pi$
$840$		0			0
$841$	−7.32631	−	6.14750i	−0.252631	−	0.211983i
$842$		0			0
$843$	−1.49871	−	24.3805i	−0.0516185	−	0.839710i
$844$		0			0
$845$	12.4818	+	21.6191i	0.429386	+	0.743719i
$846$		0			0
$847$	−28.1201	+	48.7055i	−0.966219	+	1.67354i
$848$		0			0
$849$	−0.974173	+	0.234196i	−0.0334335	+	0.00803758i
$850$		0			0
$851$	−43.8840	+	15.9725i	−1.50432	+	0.547529i
$852$		0			0
$853$	7.55426	+	42.8423i	0.258653	+	1.46689i	0.786519	+	0.617566i	$0.211881\pi$
$853$	7.55426	+	42.8423i	0.258653	+	1.46689i	−0.527866	+	0.849328i	$0.677008\pi$
$854$		0			0
$855$	31.3602	−	3.87016i	1.07250	−	0.132357i
$856$		0			0
$857$	−11.8624	+	9.95375i	−0.405213	+	0.340014i	−0.822504	−	0.568759i	$-0.807424\pi$
$857$	−11.8624	+	9.95375i	−0.405213	+	0.340014i	0.417292	+	0.908773i	$0.362979\pi$
$858$		0			0
$859$	−1.41739	+	8.03841i	−0.0483607	+	0.274267i	−0.999393	−	0.0348229i	$-0.988913\pi$
$859$	−1.41739	+	8.03841i	−0.0483607	+	0.274267i	0.951033	+	0.309090i	$0.100024\pi$
$860$		0			0
$861$	4.20641	−	5.68830i	0.143354	−	0.193857i
$862$		0			0
$863$	15.4206			0.524924			0.262462	−	0.964942i	$-0.415466\pi$
$863$	15.4206			0.524924			0.262462	+	0.964942i	$0.415466\pi$
$864$		0			0
$865$	42.2852			1.43774
$866$		0			0
$867$	25.9739	+	59.6856i	0.882120	+	2.02703i
$868$		0			0
$869$	−4.50582	+	25.5538i	−0.152850	+	0.866853i
$870$		0			0
$871$	−7.83063	+	6.57068i	−0.265331	+	0.222639i
$872$		0			0
$873$	−1.48727	+	28.7173i	−0.0503365	+	0.971933i
$874$		0			0
$875$	−5.50000	−	31.1921i	−0.185934	−	1.05448i
$876$		0			0
$877$	13.7748	−	5.01362i	0.465142	−	0.169298i	−0.0988084	−	0.995106i	$-0.531503\pi$
$877$	13.7748	−	5.01362i	0.465142	−	0.169298i	0.563950	+	0.825809i	$0.309281\pi$
$878$		0			0
$879$	−16.2921	−	17.1577i	−0.549519	−	0.578715i
$880$		0			0
$881$	−4.06970	+	7.04892i	−0.137112	+	0.237484i	−0.926402	−	0.376536i	$-0.877115\pi$
$881$	−4.06970	+	7.04892i	−0.137112	+	0.237484i	0.789291	+	0.614020i	$0.210449\pi$
$882$		0			0
$883$	−3.63523	−	6.29640i	−0.122335	−	0.211891i	0.798353	−	0.602190i	$-0.205705\pi$
$883$	−3.63523	−	6.29640i	−0.122335	−	0.211891i	−0.920688	+	0.390299i	$0.872372\pi$
$884$		0			0
$885$	19.0406	+	9.48597i	0.640043	+	0.318867i
$886$		0			0
$887$	8.00584	+	6.71770i	0.268810	+	0.225558i	0.767221	−	0.641382i	$-0.221639\pi$
$887$	8.00584	+	6.71770i	0.268810	+	0.225558i	−0.498412	+	0.866941i	$0.666083\pi$
$888$		0			0
$889$	5.70016	+	2.07469i	0.191177	+	0.0695828i
$890$		0			0
$891$	−13.9716	+	48.9523i	−0.468066	+	1.63996i
$892$		0			0
$893$	37.7872	+	13.7534i	1.26450	+	0.460241i
$894$		0			0
$895$	−14.7305	−	12.3603i	−0.492386	−	0.413161i
$896$		0			0
$897$	−10.7450	−	5.35314i	−0.358766	−	0.178736i
$898$		0			0
$899$	2.74761	+	4.75901i	0.0916380	+	0.158722i
$900$		0			0
$901$	−43.8380	+	75.9296i	−1.46045	+	2.52958i
$902$		0			0
$903$	13.8304	+	14.5652i	0.460246	+	0.484699i
$904$		0			0
$905$	3.40386	−	1.23890i	0.113148	−	0.0411826i
$906$		0			0
$907$	5.41097	+	30.6871i	0.179668	+	1.01895i	0.932616	+	0.360869i	$0.117520\pi$
$907$	5.41097	+	30.6871i	0.179668	+	1.01895i	−0.752948	+	0.658080i	$0.771369\pi$
$908$		0			0
$909$	0.472442	−	0.241088i	0.0156699	−	0.00799638i
$910$		0			0
$911$	21.0692	−	17.6791i	0.698053	−	0.585736i	−0.223166	−	0.974780i	$-0.571639\pi$
$911$	21.0692	−	17.6791i	0.698053	−	0.585736i	0.921219	+	0.389045i	$0.127195\pi$
$912$		0			0
$913$	11.1777	−	63.3918i	0.369927	−	2.09796i
$914$		0			0
$915$	21.5418	+	49.5010i	0.712150	+	1.63645i
$916$		0			0
$917$	−38.5706			−1.27371
$918$		0			0
$919$	40.8149			1.34636			0.673180	−	0.739479i	$-0.264928\pi$
$919$	40.8149			1.34636			0.673180	+	0.739479i	$0.264928\pi$
$920$		0			0
$921$	−4.77247	+	6.45377i	−0.157258	+	0.212659i
$922$		0			0
$923$	−0.284299	+	1.61234i	−0.00935783	+	0.0530709i
$924$		0			0
$925$	3.55585	−	2.98372i	0.116916	−	0.0981040i
$926$		0			0
$927$	0.990760	−	2.33809i	0.0325408	−	0.0767929i
$928$		0			0
$929$	2.51042	+	14.2373i	0.0823643	+	0.467111i	0.997894	+	0.0648613i	$0.0206605\pi$
$929$	2.51042	+	14.2373i	0.0823643	+	0.467111i	−0.915530	+	0.402250i	$0.868228\pi$
$930$		0			0
$931$	0.841681	−	0.306347i	0.0275850	−	0.0100401i
$932$		0			0
$933$	13.9693	−	3.35827i	0.457333	−	0.109945i
$934$		0			0
$935$	43.3006	−	74.9989i	1.41608	−	2.45273i
$936$		0			0
$937$	−17.5105	−	30.3290i	−0.572042	−	0.990807i	−0.996356	−	0.0852912i	$-0.972818\pi$
$937$	−17.5105	−	30.3290i	−0.572042	−	0.990807i	0.424314	−	0.905515i	$-0.360515\pi$
$938$		0			0
$939$	−1.56271	−	25.4216i	−0.0509971	−	0.829602i
$940$		0			0
$941$	−8.40186	−	7.05000i	−0.273893	−	0.229823i	0.495486	−	0.868616i	$-0.334990\pi$
$941$	−8.40186	−	7.05000i	−0.273893	−	0.229823i	−0.769379	+	0.638792i	$0.779434\pi$
$942$		0			0
$943$	10.1665	+	3.70030i	0.331066	+	0.120498i
$944$		0			0
$945$	5.28312	+	28.3589i	0.171860	+	0.922515i
$946$		0			0
$947$	30.5935	+	11.1351i	0.994155	+	0.361843i	0.787328	−	0.616534i	$-0.211464\pi$
$947$	30.5935	+	11.1351i	0.994155	+	0.361843i	0.206828	+	0.978377i	$0.433686\pi$
$948$		0			0
$949$	−4.50643	−	3.78135i	−0.146285	−	0.122748i
$950$		0			0
$951$	38.5752	−	25.5495i	1.25089	−	0.828498i
$952$		0			0
$953$	−3.54773	−	6.14484i	−0.114922	−	0.199051i	0.802826	−	0.596213i	$-0.203329\pi$
$953$	−3.54773	−	6.14484i	−0.114922	−	0.199051i	−0.917749	+	0.397162i	$0.869995\pi$
$954$		0			0
$955$	−0.461305	+	0.799003i	−0.0149275	+	0.0258551i
$956$		0			0
$957$	12.2544	−	41.4170i	0.396128	−	1.33882i
$958$		0			0
$959$	−18.9258	+	6.88843i	−0.611146	+	0.222439i
$960$		0			0
$961$	−5.11330	−	28.9990i	−0.164945	−	0.935451i
$962$		0			0
$963$	−18.2882	−	4.21029i	−0.589328	−	0.135675i
$964$		0			0
$965$	28.6851	−	24.0696i	0.923406	−	0.774829i
$966$		0			0
$967$	−9.05399	+	51.3477i	−0.291157	+	1.65123i	0.391268	+	0.920277i	$0.372036\pi$
$967$	−9.05399	+	51.3477i	−0.291157	+	1.65123i	−0.682425	+	0.730955i	$0.739075\pi$
$968$		0			0
$969$	−64.6202	−	7.34238i	−2.07590	−	0.235871i
$970$		0			0
$971$	25.0048			0.802444			0.401222	−	0.915981i	$-0.368586\pi$
$971$	25.0048			0.802444			0.401222	+	0.915981i	$0.368586\pi$
$972$		0			0
$973$	30.8746			0.989793
$974$		0			0
$975$	1.18559	+	0.134711i	0.0379692	+	0.00431420i
$976$		0			0
$977$	−6.94588	+	39.3920i	−0.222218	+	1.26026i	0.645714	+	0.763580i	$0.276560\pi$
$977$	−6.94588	+	39.3920i	−0.222218	+	1.26026i	−0.867932	+	0.496683i	$0.834551\pi$
$978$		0			0
$979$	22.6238	−	18.9836i	0.723061	−	0.606720i
$980$		0			0
$981$	−40.4116	−	9.30355i	−1.29024	−	0.297039i
$982$		0			0
$983$	1.79966	+	10.2064i	0.0574004	+	0.325534i	0.999964	−	0.00849311i	$-0.00270347\pi$
$983$	1.79966	+	10.2064i	0.0574004	+	0.325534i	−0.942564	+	0.334027i	$0.891592\pi$
$984$		0			0
$985$	4.10809	−	1.49522i	0.130895	−	0.0476418i
$986$		0			0
$987$	−10.4156	+	35.2024i	−0.331533	+	1.12051i
$988$		0			0
$989$	−15.3578	+	26.6006i	−0.488351	+	0.845849i
$990$		0			0
$991$	14.1132	+	24.4447i	0.448319	+	0.776512i	0.998277	−	0.0586807i	$-0.0186894\pi$
$991$	14.1132	+	24.4447i	0.448319	+	0.776512i	−0.549957	+	0.835193i	$0.685356\pi$
$992$		0			0
$993$	20.0191	−	13.2592i	0.635288	−	0.420769i
$994$		0			0
$995$	−23.7043	−	19.8903i	−0.751477	−	0.630564i
$996$		0			0
$997$	−4.48641	−	1.63292i	−0.142086	−	0.0517151i	0.269998	−	0.962861i	$-0.412977\pi$
$997$	−4.48641	−	1.63292i	−0.142086	−	0.0517151i	−0.412084	+	0.911146i	$0.635199\pi$
$998$		0			0
$999$	−25.9846	+	22.2345i	−0.822116	+	0.703468i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.y.b.193.1	✓	54
4.3	odd	2		864.2.y.c.193.9	yes	54
27.7	even	9	inner	864.2.y.b.385.1	yes	54
108.7	odd	18		864.2.y.c.385.9	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.y.b.193.1	✓	54	1.1	even	1	trivial
864.2.y.b.385.1	yes	54	27.7	even	9	inner
864.2.y.c.193.9	yes	54	4.3	odd	2
864.2.y.c.385.9	yes	54	108.7	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.y (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72098 - 0.195544i) q^{3} +(0.359864 - 2.04089i) q^{5} +(2.05212 - 1.72193i) q^{7} +(2.92353 + 0.673052i) q^{9} +O(q^{10})\)	\(q+(-1.72098 - 0.195544i) q^{3} +(0.359864 - 2.04089i) q^{5} +(2.05212 - 1.72193i) q^{7} +(2.92353 + 0.673052i) q^{9} +(0.982213 + 5.57041i) q^{11} +(-0.917880 + 0.334081i) q^{13} +(-1.01840 + 3.44195i) q^{15} +(3.69395 - 6.39811i) q^{17} +(2.54122 + 4.40152i) q^{19} +(-3.86836 + 2.56213i) q^{21} +(-5.43554 - 4.56096i) q^{23} +(0.662742 + 0.241218i) q^{25} +(-4.89971 - 1.72998i) q^{27} +(4.14277 + 1.50785i) q^{29} +(0.954848 + 0.801212i) q^{31} +(-0.601108 - 9.77861i) q^{33} +(-2.77579 - 4.80780i) q^{35} +(3.29080 - 5.69983i) q^{37} +(1.64498 - 0.395460i) q^{39} +(-1.43279 + 0.521492i) q^{41} +(-0.751695 - 4.26308i) q^{43} +(2.42569 - 5.72438i) q^{45} +(6.06095 - 5.08574i) q^{47} +(0.0306027 - 0.173557i) q^{49} +(-7.60832 + 10.2887i) q^{51} -11.8675 q^{53} +11.7220 q^{55} +(-3.51269 - 8.07184i) q^{57} +(1.02912 - 5.83641i) q^{59} +(11.5213 - 9.66749i) q^{61} +(7.15837 - 3.65293i) q^{63} +(0.351510 + 1.99351i) q^{65} +(9.83396 - 3.57927i) q^{67} +(8.46258 + 8.91220i) q^{69} +(0.838061 - 1.45156i) q^{71} +(3.01127 + 5.21567i) q^{73} +(-1.09340 - 0.544726i) q^{75} +(11.6075 + 9.73983i) q^{77} +(4.31076 + 1.56899i) q^{79} +(8.09400 + 3.93537i) q^{81} +(-10.6938 - 3.89222i) q^{83} +(-11.7285 - 9.84139i) q^{85} +(-6.83477 - 3.40506i) q^{87} +(-2.61064 - 4.52176i) q^{89} +(-1.30833 + 2.26610i) q^{91} +(-1.48660 - 1.56558i) q^{93} +(9.89750 - 3.60240i) q^{95} +(1.66446 + 9.43964i) q^{97} +(-0.877652 + 16.9463i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q+O(q^{10}) \) 54 * q	\( 54 q - 9 q^{11} + 12 q^{17} + 18 q^{19} + 12 q^{21} - 21 q^{27} + 6 q^{29} + 36 q^{31} - 9 q^{33} + 24 q^{39} + 3 q^{41} - 21 q^{43} + 42 q^{45} - 18 q^{49} + 24 q^{51} + 36 q^{53} - 72 q^{55} + 39 q^{57} + 18 q^{59} - 18 q^{61} - 30 q^{63} + 48 q^{65} - 27 q^{67} + 24 q^{69} - 84 q^{75} + 36 q^{77} + 72 q^{79} + 36 q^{81} + 6 q^{87} + 33 q^{89} + 36 q^{91} + 72 q^{93} + 36 q^{95} + 9 q^{97} + 120 q^{99}+O(q^{100}) \) 54 * q - 9 * q^11 + 12 * q^17 + 18 * q^19 + 12 * q^21 - 21 * q^27 + 6 * q^29 + 36 * q^31 - 9 * q^33 + 24 * q^39 + 3 * q^41 - 21 * q^43 + 42 * q^45 - 18 * q^49 + 24 * q^51 + 36 * q^53 - 72 * q^55 + 39 * q^57 + 18 * q^59 - 18 * q^61 - 30 * q^63 + 48 * q^65 - 27 * q^67 + 24 * q^69 - 84 * q^75 + 36 * q^77 + 72 * q^79 + 36 * q^81 + 6 * q^87 + 33 * q^89 + 36 * q^91 + 72 * q^93 + 36 * q^95 + 9 * q^97 + 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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