LMFDB - Embedded newform 882.2.l.c.227.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(227,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("882.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			227.1
Character	$\chi$	$=$	882.227
Dual form			882.2.l.c.509.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.70306 + 0.315583i) q^{3} -1.00000 q^{4} +(0.220087 - 0.381202i) q^{5} +(0.315583 + 1.70306i) q^{6} +1.00000i q^{8} +(2.80082 - 1.07491i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.70306 + 0.315583i) q^{3} -1.00000 q^{4} +(0.220087 - 0.381202i) q^{5} +(0.315583 + 1.70306i) q^{6} +1.00000i q^{8} +(2.80082 - 1.07491i) q^{9} +(-0.381202 - 0.220087i) q^{10} +(0.450580 - 0.260142i) q^{11} +(1.70306 - 0.315583i) q^{12} +(-5.55020 + 3.20441i) q^{13} +(-0.254520 + 0.718665i) q^{15} +1.00000 q^{16} +(-0.163672 + 0.283489i) q^{17} +(-1.07491 - 2.80082i) q^{18} +(3.67178 - 2.11990i) q^{19} +(-0.220087 + 0.381202i) q^{20} +(-0.260142 - 0.450580i) q^{22} +(-1.25636 - 0.725359i) q^{23} +(-0.315583 - 1.70306i) q^{24} +(2.40312 + 4.16233i) q^{25} +(3.20441 + 5.55020i) q^{26} +(-4.43073 + 2.71453i) q^{27} +(5.74668 + 3.31785i) q^{29} +(0.718665 + 0.254520i) q^{30} +7.01085i q^{31} -1.00000i q^{32} +(-0.685267 + 0.585233i) q^{33} +(0.283489 + 0.163672i) q^{34} +(-2.80082 + 1.07491i) q^{36} +(-1.84115 - 3.18897i) q^{37} +(-2.11990 - 3.67178i) q^{38} +(8.44106 - 7.20884i) q^{39} +(0.381202 + 0.220087i) q^{40} +(2.96701 + 5.13902i) q^{41} +(5.21400 - 9.03091i) q^{43} +(-0.450580 + 0.260142i) q^{44} +(0.206665 - 1.30425i) q^{45} +(-0.725359 + 1.25636i) q^{46} +8.05267 q^{47} +(-1.70306 + 0.315583i) q^{48} +(4.16233 - 2.40312i) q^{50} +(0.189279 - 0.534450i) q^{51} +(5.55020 - 3.20441i) q^{52} +(6.89072 + 3.97836i) q^{53} +(2.71453 + 4.43073i) q^{54} -0.229016i q^{55} +(-5.58425 + 4.76907i) q^{57} +(3.31785 - 5.74668i) q^{58} +4.90410 q^{59} +(0.254520 - 0.718665i) q^{60} -1.54358i q^{61} +7.01085 q^{62} -1.00000 q^{64} +2.82100i q^{65} +(0.585233 + 0.685267i) q^{66} +6.52412 q^{67} +(0.163672 - 0.283489i) q^{68} +(2.36856 + 0.838844i) q^{69} +16.2646i q^{71} +(1.07491 + 2.80082i) q^{72} +(3.57364 + 2.06324i) q^{73} +(-3.18897 + 1.84115i) q^{74} +(-5.40622 - 6.33031i) q^{75} +(-3.67178 + 2.11990i) q^{76} +(-7.20884 - 8.44106i) q^{78} -1.32465 q^{79} +(0.220087 - 0.381202i) q^{80} +(6.68913 - 6.02126i) q^{81} +(5.13902 - 2.96701i) q^{82} +(8.55240 - 14.8132i) q^{83} +(0.0720443 + 0.124784i) q^{85} +(-9.03091 - 5.21400i) q^{86} +(-10.8340 - 3.83693i) q^{87} +(0.260142 + 0.450580i) q^{88} +(5.86239 + 10.1540i) q^{89} +(-1.30425 - 0.206665i) q^{90} +(1.25636 + 0.725359i) q^{92} +(-2.21250 - 11.9399i) q^{93} -8.05267i q^{94} -1.86625i q^{95} +(0.315583 + 1.70306i) q^{96} +(-10.6061 - 6.12344i) q^{97} +(0.982361 - 1.21294i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} + 16 q^{9}+O(q^{10}) $ 48 * q - 48 * q^4 + 16 * q^9	$ 48 q - 48 q^{4} + 16 q^{9} - 48 q^{11} + 48 q^{15} + 48 q^{16} + 16 q^{18} - 48 q^{23} - 24 q^{25} - 16 q^{30} - 16 q^{36} + 32 q^{39} + 48 q^{44} - 48 q^{50} - 48 q^{51} + 96 q^{53} - 80 q^{57} - 48 q^{60} - 48 q^{64} - 16 q^{72} + 32 q^{78} - 96 q^{79} + 96 q^{81} + 48 q^{85} - 96 q^{86} + 48 q^{92} + 104 q^{99}+O(q^{100}) $ 48 * q - 48 * q^4 + 16 * q^9 - 48 * q^11 + 48 * q^15 + 48 * q^16 + 16 * q^18 - 48 * q^23 - 24 * q^25 - 16 * q^30 - 16 * q^36 + 32 * q^39 + 48 * q^44 - 48 * q^50 - 48 * q^51 + 96 * q^53 - 80 * q^57 - 48 * q^60 - 48 * q^64 - 16 * q^72 + 32 * q^78 - 96 * q^79 + 96 * q^81 + 48 * q^85 - 96 * q^86 + 48 * q^92 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.70306	+	0.315583i	−0.983261	+	0.182202i
$3$	−1.70306	+	0.315583i	−0.983261	+	0.182202i
$4$	−1.00000			−0.500000
$5$	0.220087	−	0.381202i	0.0984259	−	0.170479i	−0.812607	−	0.582812i	$-0.801953\pi$
$5$	0.220087	−	0.381202i	0.0984259	−	0.170479i	0.911033	+	0.412333i	$0.135286\pi$
$6$	0.315583	+	1.70306i	0.128836	+	0.695271i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	2.80082	−	1.07491i	0.933605	−	0.358304i
$10$	−0.381202	−	0.220087i	−0.120547	−	0.0695976i
$11$	0.450580	−	0.260142i	0.135855	−	0.0784359i	−0.430532	−	0.902575i	$-0.641674\pi$
$11$	0.450580	−	0.260142i	0.135855	−	0.0784359i	0.566387	+	0.824139i	$0.308341\pi$
$12$	1.70306	−	0.315583i	0.491631	−	0.0911009i
$13$	−5.55020	+	3.20441i	−1.53935	+	0.888743i	−0.540471	+	0.841362i	$0.681754\pi$
$13$	−5.55020	+	3.20441i	−1.53935	+	0.888743i	−0.998877	+	0.0473809i	$0.984913\pi$
$14$		0			0
$15$	−0.254520	+	0.718665i	−0.0657169	+	0.185558i
$16$	1.00000			0.250000
$17$	−0.163672	+	0.283489i	−0.0396964	+	0.0687561i	−0.885191	−	0.465228i	$-0.845972\pi$
$17$	−0.163672	+	0.283489i	−0.0396964	+	0.0687561i	0.845495	+	0.533984i	$0.179306\pi$
$18$	−1.07491	−	2.80082i	−0.253359	−	0.660158i
$19$	3.67178	−	2.11990i	0.842365	−	0.486339i	−0.0157027	−	0.999877i	$-0.504999\pi$
$19$	3.67178	−	2.11990i	0.842365	−	0.486339i	0.858067	+	0.513537i	$0.171665\pi$
$20$	−0.220087	+	0.381202i	−0.0492130	+	0.0852394i
$21$		0			0
$22$	−0.260142	−	0.450580i	−0.0554625	−	0.0960639i
$23$	−1.25636	−	0.725359i	−0.261969	−	0.151248i	0.363263	−	0.931686i	$-0.381662\pi$
$23$	−1.25636	−	0.725359i	−0.261969	−	0.151248i	−0.625232	+	0.780439i	$0.714996\pi$
$24$	−0.315583	−	1.70306i	−0.0644180	−	0.347635i
$25$	2.40312	+	4.16233i	0.480625	+	0.832466i
$26$	3.20441	+	5.55020i	0.628436	+	1.08848i
$27$	−4.43073	+	2.71453i	−0.852694	+	0.522411i
$28$		0			0
$29$	5.74668	+	3.31785i	1.06713	+	0.616109i	0.927396	−	0.374080i	$-0.122042\pi$
$29$	5.74668	+	3.31785i	1.06713	+	0.616109i	0.139735	+	0.990189i	$0.455375\pi$
$30$	0.718665	+	0.254520i	0.131210	+	0.0464689i
$31$			7.01085i			1.25919i	0.776925	+	0.629593i	$0.216778\pi$
$31$			7.01085i			1.25919i	−0.776925	+	0.629593i	$0.783222\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.685267	+	0.585233i	−0.119290	+	0.101876i
$34$	0.283489	+	0.163672i	0.0486179	+	0.0280696i
$35$		0			0
$36$	−2.80082	+	1.07491i	−0.466803	+	0.179152i
$37$	−1.84115	−	3.18897i	−0.302684	−	0.524263i	0.674059	−	0.738677i	$-0.264549\pi$
$37$	−1.84115	−	3.18897i	−0.302684	−	0.524263i	−0.976743	+	0.214414i	$0.931216\pi$
$38$	−2.11990	−	3.67178i	−0.343894	−	0.595642i
$39$	8.44106	−	7.20884i	1.35165	−	1.15434i
$40$	0.381202	+	0.220087i	0.0602733	+	0.0347988i
$41$	2.96701	+	5.13902i	0.463370	+	0.802580i	0.999126	−	0.0417927i	$-0.0133069\pi$
$41$	2.96701	+	5.13902i	0.463370	+	0.802580i	−0.535757	+	0.844372i	$0.679974\pi$
$42$		0			0
$43$	5.21400	−	9.03091i	0.795127	−	1.37720i	−0.127631	−	0.991822i	$-0.540737\pi$
$43$	5.21400	−	9.03091i	0.795127	−	1.37720i	0.922758	−	0.385379i	$-0.125929\pi$
$44$	−0.450580	+	0.260142i	−0.0679275	+	0.0392179i
$45$	0.206665	−	1.30425i	0.0308078	−	0.194426i
$46$	−0.725359	+	1.25636i	−0.106948	+	0.185240i
$47$	8.05267			1.17460			0.587301	−	0.809368i	$-0.300190\pi$
$47$	8.05267			1.17460			0.587301	+	0.809368i	$0.300190\pi$
$48$	−1.70306	+	0.315583i	−0.245815	+	0.0455504i
$49$		0			0
$50$	4.16233	−	2.40312i	0.588643	−	0.339853i
$51$	0.189279	−	0.534450i	0.0265044	−	0.0748380i
$52$	5.55020	−	3.20441i	0.769674	−	0.444372i
$53$	6.89072	+	3.97836i	0.946513	+	0.546470i	0.891996	−	0.452043i	$-0.149305\pi$
$53$	6.89072	+	3.97836i	0.946513	+	0.546470i	0.0545172	+	0.998513i	$0.482638\pi$
$54$	2.71453	+	4.43073i	0.369400	+	0.602946i
$55$		−	0.229016i		−	0.0308805i
$56$		0			0
$57$	−5.58425	+	4.76907i	−0.739652	+	0.631679i
$58$	3.31785	−	5.74668i	0.435655	−	0.754576i
$59$	4.90410			0.638460			0.319230	−	0.947677i	$-0.396576\pi$
$59$	4.90410			0.638460			0.319230	+	0.947677i	$0.396576\pi$
$60$	0.254520	−	0.718665i	0.0328584	−	0.0927792i
$61$		−	1.54358i		−	0.197635i	−0.995106	−	0.0988177i	$-0.968494\pi$
$61$		−	1.54358i		−	0.197635i	0.995106	−	0.0988177i	$-0.0315061\pi$
$62$	7.01085			0.890379
$63$		0			0
$64$	−1.00000			−0.125000
$65$			2.82100i			0.349902i
$66$	0.585233	+	0.685267i	0.0720372	+	0.0843506i
$67$	6.52412			0.797048			0.398524	−	0.917158i	$-0.369523\pi$
$67$	6.52412			0.797048			0.398524	+	0.917158i	$0.369523\pi$
$68$	0.163672	−	0.283489i	0.0198482	−	0.0343781i
$69$	2.36856	+	0.838844i	0.285141	+	0.100985i
$70$		0			0
$71$			16.2646i			1.93026i	0.261774	+	0.965129i	$0.415693\pi$
$71$			16.2646i			1.93026i	−0.261774	+	0.965129i	$0.584307\pi$
$72$	1.07491	+	2.80082i	0.126680	+	0.330079i
$73$	3.57364	+	2.06324i	0.418263	+	0.241484i	0.694334	−	0.719653i	$-0.255699\pi$
$73$	3.57364	+	2.06324i	0.418263	+	0.241484i	−0.276071	+	0.961137i	$0.589033\pi$
$74$	−3.18897	+	1.84115i	−0.370710	+	0.214030i
$75$	−5.40622	−	6.33031i	−0.624256	−	0.730961i
$76$	−3.67178	+	2.11990i	−0.421182	+	0.243170i
$77$		0			0
$78$	−7.20884	−	8.44106i	−0.816241	−	0.955762i
$79$	−1.32465			−0.149035			−0.0745173	−	0.997220i	$-0.523742\pi$
$79$	−1.32465			−0.149035			−0.0745173	+	0.997220i	$0.523742\pi$
$80$	0.220087	−	0.381202i	0.0246065	−	0.0426197i
$81$	6.68913	−	6.02126i	0.743237	−	0.669028i
$82$	5.13902	−	2.96701i	0.567510	−	0.327652i
$83$	8.55240	−	14.8132i	0.938748	−	1.62596i	0.170938	−	0.985282i	$-0.445320\pi$
$83$	8.55240	−	14.8132i	0.938748	−	1.62596i	0.767810	−	0.640677i	$-0.221346\pi$
$84$		0			0
$85$	0.0720443	+	0.124784i	0.00781430	+	0.0135348i
$86$	−9.03091	−	5.21400i	−0.973828	−	0.562240i
$87$	−10.8340	−	3.83693i	−1.16152	−	0.411363i
$88$	0.260142	+	0.450580i	0.0277313	+	0.0480320i
$89$	5.86239	+	10.1540i	0.621413	+	1.07632i	0.989223	+	0.146417i	$0.0467742\pi$
$89$	5.86239	+	10.1540i	0.621413	+	1.07632i	−0.367810	+	0.929901i	$0.619892\pi$
$90$	−1.30425	−	0.206665i	−0.137480	−	0.0217844i
$91$		0			0
$92$	1.25636	+	0.725359i	0.130984	+	0.0756239i
$93$	−2.21250	−	11.9399i	−0.229426	−	1.23811i
$94$		−	8.05267i		−	0.830569i
$95$		−	1.86625i		−	0.191474i
$96$	0.315583	+	1.70306i	0.0322090	+	0.173818i
$97$	−10.6061	−	6.12344i	−1.07689	−	0.621741i	−0.146832	−	0.989161i	$-0.546908\pi$
$97$	−10.6061	−	6.12344i	−1.07689	−	0.621741i	−0.930055	+	0.367421i	$0.880241\pi$
$98$		0			0
$99$	0.982361	−	1.21294i	0.0987310	−	0.121905i
$100$	−2.40312	−	4.16233i	−0.240312	−	0.416233i
$101$	5.40492	+	9.36159i	0.537809	+	0.931513i	0.999022	+	0.0442233i	$0.0140813\pi$
$101$	5.40492	+	9.36159i	0.537809	+	0.931513i	−0.461212	+	0.887290i	$0.652585\pi$
$102$	−0.534450	−	0.189279i	−0.0529184	−	0.0187414i
$103$	−9.69122	−	5.59523i	−0.954904	−	0.551314i	−0.0603031	−	0.998180i	$-0.519207\pi$
$103$	−9.69122	−	5.59523i	−0.954904	−	0.551314i	−0.894601	+	0.446866i	$0.852540\pi$
$104$	−3.20441	−	5.55020i	−0.314218	−	0.544242i
$105$		0			0
$106$	3.97836	−	6.89072i	0.386412	−	0.669286i
$107$	−0.587790	+	0.339361i	−0.0568238	+	0.0328072i	−0.528143	−	0.849156i	$-0.677111\pi$
$107$	−0.587790	+	0.339361i	−0.0568238	+	0.0328072i	0.471319	+	0.881963i	$0.343778\pi$
$108$	4.43073	−	2.71453i	0.426347	−	0.261205i
$109$	−9.11016	+	15.7793i	−0.872595	+	1.51138i	−0.0132920	+	0.999912i	$0.504231\pi$
$109$	−9.11016	+	15.7793i	−0.872595	+	1.51138i	−0.859303	+	0.511467i	$0.829102\pi$
$110$	−0.229016			−0.0218358
$111$	4.14197	+	4.84996i	0.393139	+	0.460338i
$112$		0			0
$113$	−9.18833	+	5.30488i	−0.864365	+	0.499041i	−0.865472	−	0.500958i	$-0.832981\pi$
$113$	−9.18833	+	5.30488i	−0.864365	+	0.499041i	0.00110649	+	0.999999i	$0.499648\pi$
$114$	4.76907	+	5.58425i	0.446664	+	0.523013i
$115$	−0.553017	+	0.319284i	−0.0515691	+	0.0297734i
$116$	−5.74668	−	3.31785i	−0.533566	−	0.308054i
$117$	−12.1006	+	14.9409i	−1.11870	+	1.38129i
$118$		−	4.90410i		−	0.451459i
$119$		0			0
$120$	−0.718665	−	0.254520i	−0.0656048	−	0.0232344i
$121$	−5.36465	+	9.29185i	−0.487696	+	0.844714i
$122$	−1.54358			−0.139749
$123$	−6.67478	−	7.81571i	−0.601845	−	0.704719i
$124$		−	7.01085i		−	0.629593i
$125$	4.31646			0.386076
$126$		0			0
$127$	−2.88189			−0.255726			−0.127863	−	0.991792i	$-0.540812\pi$
$127$	−2.88189			−0.255726			−0.127863	+	0.991792i	$0.540812\pi$
$128$			1.00000i			0.0883883i
$129$	−6.02974	+	17.0256i	−0.530889	+	1.49902i
$130$	2.82100			0.247418
$131$	8.34798	−	14.4591i	0.729367	−	1.26330i	−0.227784	−	0.973712i	$-0.573148\pi$
$131$	8.34798	−	14.4591i	0.729367	−	1.26330i	0.957151	−	0.289589i	$-0.0935185\pi$
$132$	0.685267	−	0.585233i	0.0596449	−	0.0509380i
$133$		0			0
$134$		−	6.52412i		−	0.563598i
$135$	0.0596363	+	2.28643i	0.00513268	+	0.196785i
$136$	−0.283489	−	0.163672i	−0.0243090	−	0.0140348i
$137$	−14.2714	+	8.23961i	−1.21929	+	0.703957i	−0.964766	−	0.263109i	$-0.915252\pi$
$137$	−14.2714	+	8.23961i	−1.21929	+	0.703957i	−0.254524	+	0.967066i	$0.581919\pi$
$138$	0.838844	−	2.36856i	0.0714071	−	0.201625i
$139$	−1.71999	+	0.993034i	−0.145887	+	0.0842281i	−0.571167	−	0.820834i	$-0.693509\pi$
$139$	−1.71999	+	0.993034i	−0.145887	+	0.0842281i	0.425280	+	0.905062i	$0.360176\pi$
$140$		0			0
$141$	−13.7142	+	2.54128i	−1.15494	+	0.214015i
$142$	16.2646			1.36490
$143$	−1.66720	+	2.88768i	−0.139419	+	0.241480i
$144$	2.80082	−	1.07491i	0.233401	−	0.0895759i
$145$	2.52954	−	1.46043i	0.210067	−	0.121282i
$146$	2.06324	−	3.57364i	0.170755	−	0.295756i
$147$		0			0
$148$	1.84115	+	3.18897i	0.151342	+	0.262132i
$149$	14.6722	+	8.47103i	1.20200	+	0.693973i	0.960999	−	0.276552i	$-0.0891918\pi$
$149$	14.6722	+	8.47103i	1.20200	+	0.693973i	0.240998	+	0.970526i	$0.422525\pi$
$150$	−6.33031	+	5.40622i	−0.516868	+	0.441416i
$151$	−4.54082	−	7.86493i	−0.369527	−	0.640039i	0.619965	−	0.784630i	$-0.287147\pi$
$151$	−4.54082	−	7.86493i	−0.369527	−	0.640039i	−0.989492	+	0.144591i	$0.953813\pi$
$152$	2.11990	+	3.67178i	0.171947	+	0.297821i
$153$	−0.153691	+	0.969933i	−0.0124252	+	0.0784144i
$154$		0			0
$155$	2.67255	+	1.54300i	0.214664	+	0.123937i
$156$	−8.44106	+	7.20884i	−0.675825	+	0.577169i
$157$			9.87924i			0.788449i	0.919014	+	0.394224i	$0.128987\pi$
$157$			9.87924i			0.788449i	−0.919014	+	0.394224i	$0.871013\pi$
$158$			1.32465i			0.105383i
$159$	−12.9908	−	4.60079i	−1.03024	−	0.364866i
$160$	−0.381202	−	0.220087i	−0.0301367	−	0.0173994i
$161$		0			0
$162$	−6.02126	−	6.68913i	−0.473074	−	0.525548i
$163$	−2.63485	−	4.56369i	−0.206377	−	0.357456i	0.744194	−	0.667964i	$-0.232834\pi$
$163$	−2.63485	−	4.56369i	−0.206377	−	0.357456i	−0.950571	+	0.310508i	$0.899501\pi$
$164$	−2.96701	−	5.13902i	−0.231685	−	0.401290i
$165$	0.0722734	+	0.390027i	0.00562648	+	0.0303636i
$166$	−14.8132	−	8.55240i	−1.14973	−	0.663795i
$167$	6.69964	+	11.6041i	0.518433	+	0.897953i	0.999771	+	0.0214174i	$0.00681789\pi$
$167$	6.69964	+	11.6041i	0.518433	+	0.897953i	−0.481337	+	0.876535i	$0.659849\pi$
$168$		0			0
$169$	14.0365	−	24.3119i	1.07973	−	1.87015i
$170$	0.124784	−	0.0720443i	0.00957053	−	0.00552555i
$171$	8.00527	−	9.88430i	0.612179	−	0.755871i
$172$	−5.21400	+	9.03091i	−0.397564	+	0.688600i
$173$	−15.1541			−1.15215			−0.576074	−	0.817397i	$-0.695416\pi$
$173$	−15.1541			−1.15215			−0.576074	+	0.817397i	$0.695416\pi$
$174$	−3.83693	+	10.8340i	−0.290877	+	0.821322i
$175$		0			0
$176$	0.450580	−	0.260142i	0.0339637	−	0.0196090i
$177$	−8.35197	+	1.54765i	−0.627773	+	0.116328i
$178$	10.1540	−	5.86239i	0.761072	−	0.439405i
$179$	−18.1158	−	10.4592i	−1.35404	−	0.781756i	−0.365228	−	0.930918i	$-0.619009\pi$
$179$	−18.1158	−	10.4592i	−1.35404	−	0.781756i	−0.988813	+	0.149163i	$0.952342\pi$
$180$	−0.206665	+	1.30425i	−0.0154039	+	0.0972131i
$181$		−	14.5567i		−	1.08199i	−0.841026	−	0.540995i	$-0.818048\pi$
$181$		−	14.5567i		−	1.08199i	0.841026	−	0.540995i	$-0.181952\pi$
$182$		0			0
$183$	0.487127	+	2.62881i	0.0360095	+	0.194327i
$184$	0.725359	−	1.25636i	0.0534742	−	0.0926200i
$185$	−1.62086			−0.119168
$186$	−11.9399	+	2.21250i	−0.875475	+	0.162229i
$187$			0.170312i			0.0124545i
$188$	−8.05267			−0.587301
$189$		0			0
$190$	−1.86625			−0.135392
$191$			19.6487i			1.42173i	0.703329	+	0.710865i	$0.251696\pi$
$191$			19.6487i			1.42173i	−0.703329	+	0.710865i	$0.748304\pi$
$192$	1.70306	−	0.315583i	0.122908	−	0.0227752i
$193$	11.7572			0.846303			0.423151	−	0.906059i	$-0.360924\pi$
$193$	11.7572			0.846303			0.423151	+	0.906059i	$0.360924\pi$
$194$	−6.12344	+	10.6061i	−0.439637	+	0.761474i
$195$	−0.890257	−	4.80432i	−0.0637527	−	0.344045i
$196$		0			0
$197$			12.6642i			0.902290i	0.892451	+	0.451145i	$0.148984\pi$
$197$			12.6642i			0.902290i	−0.892451	+	0.451145i	$0.851016\pi$
$198$	−1.21294	−	0.982361i	−0.0862002	−	0.0698133i
$199$	−15.4338	−	8.91071i	−1.09407	−	0.631663i	−0.159415	−	0.987212i	$-0.550961\pi$
$199$	−15.4338	−	8.91071i	−1.09407	−	0.631663i	−0.934658	+	0.355548i	$0.884294\pi$
$200$	−4.16233	+	2.40312i	−0.294321	+	0.169926i
$201$	−11.1110	+	2.05890i	−0.783706	+	0.145224i
$202$	9.36159	−	5.40492i	0.658679	−	0.380289i
$203$		0			0
$204$	−0.189279	+	0.534450i	−0.0132522	+	0.0374190i
$205$	2.61201			0.182430
$206$	−5.59523	+	9.69122i	−0.389838	+	0.675219i
$207$	−4.29852	−	0.681123i	−0.298768	−	0.0473413i
$208$	−5.55020	+	3.20441i	−0.384837	+	0.222186i
$209$	1.10295	−	1.91037i	0.0762929	−	0.132143i
$210$		0			0
$211$	−0.975723	−	1.69000i	−0.0671715	−	0.116344i	0.830484	−	0.557043i	$-0.188064\pi$
$211$	−0.975723	−	1.69000i	−0.0671715	−	0.116344i	−0.897655	+	0.440698i	$0.854731\pi$
$212$	−6.89072	−	3.97836i	−0.473257	−	0.273235i
$213$	−5.13284	−	27.6996i	−0.351696	−	1.89795i
$214$	0.339361	+	0.587790i	0.0231982	+	0.0401805i
$215$	−2.29507	−	3.97517i	−0.156522	−	0.271105i
$216$	−2.71453	−	4.43073i	−0.184700	−	0.301473i
$217$		0			0
$218$	15.7793	+	9.11016i	1.06871	+	0.617018i
$219$	−6.73724	−	2.38604i	−0.455260	−	0.161234i
$220$			0.229016i			0.0154402i
$221$		−	2.09789i		−	0.141119i
$222$	4.84996	−	4.14197i	0.325508	−	0.277991i
$223$	3.44154	+	1.98697i	0.230463	+	0.133058i	0.610785	−	0.791796i	$-0.290854\pi$
$223$	3.44154	+	1.98697i	0.230463	+	0.133058i	−0.380323	+	0.924854i	$0.624187\pi$
$224$		0			0
$225$	11.2048	+	9.07478i	0.746989	+	0.604985i
$226$	5.30488	+	9.18833i	0.352876	+	0.611198i
$227$	3.63558	+	6.29701i	0.241302	+	0.417947i	0.961085	−	0.276251i	$-0.0890922\pi$
$227$	3.63558	+	6.29701i	0.241302	+	0.417947i	−0.719783	+	0.694199i	$0.755759\pi$
$228$	5.58425	−	4.76907i	0.369826	−	0.315839i
$229$	−1.51483	−	0.874590i	−0.100103	−	0.0577945i	0.449113	−	0.893475i	$-0.351740\pi$
$229$	−1.51483	−	0.874590i	−0.100103	−	0.0577945i	−0.549216	+	0.835681i	$0.685073\pi$
$230$	0.319284	+	0.553017i	0.0210530	+	0.0364648i
$231$		0			0
$232$	−3.31785	+	5.74668i	−0.217827	+	0.377288i
$233$	5.96755	−	3.44537i	0.390947	−	0.225713i	−0.291623	−	0.956533i	$-0.594195\pi$
$233$	5.96755	−	3.44537i	0.390947	−	0.225713i	0.682570	+	0.730820i	$0.260862\pi$
$234$	14.9409	+	12.1006i	0.976719	+	0.791043i
$235$	1.77229	−	3.06969i	0.115611	−	0.200245i
$236$	−4.90410			−0.319230
$237$	2.25595	−	0.418036i	0.146540	−	0.0271543i
$238$		0			0
$239$	16.3611	−	9.44606i	1.05831	−	0.611015i	0.133345	−	0.991070i	$-0.457428\pi$
$239$	16.3611	−	9.44606i	1.05831	−	0.611015i	0.924964	+	0.380055i	$0.124095\pi$
$240$	−0.254520	+	0.718665i	−0.0164292	+	0.0463896i
$241$	14.1951	−	8.19555i	0.914387	−	0.527922i	0.0325469	−	0.999470i	$-0.489638\pi$
$241$	14.1951	−	8.19555i	0.914387	−	0.527922i	0.881840	+	0.471549i	$0.156305\pi$
$242$	9.29185	+	5.36465i	0.597303	+	0.344853i
$243$	−9.49178	+	12.3655i	−0.608898	+	0.793249i
$244$			1.54358i			0.0988177i
$245$		0			0
$246$	−7.81571	+	6.67478i	−0.498311	+	0.425569i
$247$	−13.5861	+	23.5318i	−0.864462	+	1.49729i
$248$	−7.01085			−0.445189
$249$	−9.89045	+	27.9267i	−0.626782	+	1.76978i
$250$		−	4.31646i		−	0.272997i
$251$	0.663086			0.0418536			0.0209268	−	0.999781i	$-0.493338\pi$
$251$	0.663086			0.0418536			0.0209268	+	0.999781i	$0.493338\pi$
$252$		0			0
$253$	−0.754786			−0.0474530
$254$			2.88189i			0.180826i
$255$	−0.162075	−	0.189779i	−0.0101496	−	0.0118844i
$256$	1.00000			0.0625000
$257$	2.83784	−	4.91529i	0.177020	−	0.306607i	−0.763839	−	0.645407i	$-0.776688\pi$
$257$	2.83784	−	4.91529i	0.177020	−	0.306607i	0.940858	+	0.338800i	$0.110021\pi$
$258$	17.0256	+	6.02974i	1.05997	+	0.375395i
$259$		0			0
$260$		−	2.82100i		−	0.174951i
$261$	19.6618	+	3.11551i	1.21703	+	0.192845i
$262$	−14.4591	−	8.34798i	−0.893288	−	0.515740i
$263$	−8.73855	+	5.04520i	−0.538842	+	0.311101i	−0.744610	−	0.667500i	$-0.767364\pi$
$263$	−8.73855	+	5.04520i	−0.538842	+	0.311101i	0.205767	+	0.978601i	$0.434031\pi$
$264$	−0.585233	−	0.685267i	−0.0360186	−	0.0421753i
$265$	3.03312	−	1.75117i	0.186323	−	0.107574i
$266$		0			0
$267$	−13.1884	−	15.4427i	−0.807118	−	0.945079i
$268$	−6.52412			−0.398524
$269$	9.66698	−	16.7437i	0.589406	−	1.02088i	−0.404904	−	0.914359i	$-0.632695\pi$
$269$	9.66698	−	16.7437i	0.589406	−	1.02088i	0.994310	−	0.106522i	$-0.0339715\pi$
$270$	2.28643	−	0.0596363i	0.139148	−	0.00362935i
$271$	10.6461	−	6.14652i	0.646703	−	0.373374i	−0.140489	−	0.990082i	$-0.544867\pi$
$271$	10.6461	−	6.14652i	0.646703	−	0.373374i	0.787192	+	0.616708i	$0.211534\pi$
$272$	−0.163672	+	0.283489i	−0.00992409	+	0.0171890i
$273$		0			0
$274$	8.23961	+	14.2714i	0.497773	+	0.862168i
$275$	2.16560	+	1.25031i	0.130590	+	0.0753964i
$276$	−2.36856	−	0.838844i	−0.142571	−	0.0504925i
$277$	4.08322	+	7.07235i	0.245337	+	0.424936i	0.962226	−	0.272251i	$-0.0877680\pi$
$277$	4.08322	+	7.07235i	0.245337	+	0.424936i	−0.716889	+	0.697187i	$0.754435\pi$
$278$	0.993034	+	1.71999i	0.0595582	+	0.103158i
$279$	7.53604	+	19.6361i	0.451171	+	1.17558i
$280$		0			0
$281$	−27.6901	−	15.9869i	−1.65185	−	0.953697i	−0.976310	−	0.216375i	$-0.930577\pi$
$281$	−27.6901	−	15.9869i	−1.65185	−	0.953697i	−0.675541	−	0.737322i	$-0.736090\pi$
$282$	2.54128	+	13.7142i	0.151331	+	0.816667i
$283$			10.0668i			0.598408i	0.954189	+	0.299204i	$0.0967212\pi$
$283$			10.0668i			0.598408i	−0.954189	+	0.299204i	$0.903279\pi$
$284$		−	16.2646i		−	0.965129i
$285$	0.588957	+	3.17834i	0.0348868	+	0.188269i
$286$	2.88768	+	1.66720i	0.170752	+	0.0985839i
$287$		0			0
$288$	−1.07491	−	2.80082i	−0.0633398	−	0.165040i
$289$	8.44642	+	14.6296i	0.496848	+	0.860567i
$290$	−1.46043	−	2.52954i	−0.0857594	−	0.148540i
$291$	19.9953	+	7.08147i	1.17214	+	0.415123i
$292$	−3.57364	−	2.06324i	−0.209131	−	0.120742i
$293$	−6.64697	−	11.5129i	−0.388320	−	0.672590i	0.603904	−	0.797057i	$-0.293611\pi$
$293$	−6.64697	−	11.5129i	−0.388320	−	0.672590i	−0.992224	+	0.124467i	$0.960278\pi$
$294$		0			0
$295$	1.07933	−	1.86945i	0.0628410	−	0.108844i
$296$	3.18897	−	1.84115i	0.185355	−	0.107015i
$297$	−1.29023	+	2.37573i	−0.0748669	+	0.137854i
$298$	8.47103	−	14.6722i	0.490713	−	0.849940i
$299$	9.29739			0.537682
$300$	5.40622	+	6.33031i	0.312128	+	0.365481i
$301$		0			0
$302$	−7.86493	+	4.54082i	−0.452576	+	0.261295i
$303$	−12.1592	−	14.2376i	−0.698530	−	0.817931i
$304$	3.67178	−	2.11990i	0.210591	−	0.121585i
$305$	−0.588416	−	0.339722i	−0.0336926	−	0.0194524i
$306$	0.969933	+	0.153691i	0.0554474	+	0.00878591i
$307$			5.44565i			0.310799i	0.987852	+	0.155400i	$0.0496665\pi$
$307$			5.44565i			0.310799i	−0.987852	+	0.155400i	$0.950333\pi$
$308$		0			0
$309$	18.2705	+	6.47062i	1.03937	+	0.368101i
$310$	1.54300	−	2.67255i	0.0876364	−	0.151791i
$311$	0.259547			0.0147176			0.00735878	−	0.999973i	$-0.497658\pi$
$311$	0.259547			0.0147176			0.00735878	+	0.999973i	$0.497658\pi$
$312$	7.20884	+	8.44106i	0.408120	+	0.477881i
$313$			30.8024i			1.74106i	0.492119	+	0.870528i	$0.336222\pi$
$313$			30.8024i			1.74106i	−0.492119	+	0.870528i	$0.663778\pi$
$314$	9.87924			0.557518
$315$		0			0
$316$	1.32465			0.0745173
$317$		−	16.0476i		−	0.901325i	−0.892694	−	0.450662i	$-0.851188\pi$
$317$		−	16.0476i		−	0.901325i	0.892694	−	0.450662i	$-0.148812\pi$
$318$	−4.60079	+	12.9908i	−0.257999	+	0.728488i
$319$	3.45245			0.193300
$320$	−0.220087	+	0.381202i	−0.0123032	+	0.0213098i
$321$	0.893944	−	0.763447i	0.0498951	−	0.0426115i
$322$		0			0
$323$			1.38788i			0.0772236i
$324$	−6.68913	+	6.02126i	−0.371618	+	0.334514i
$325$	−26.6756	−	15.4012i	−1.47970	−	0.854304i
$326$	−4.56369	+	2.63485i	−0.252759	+	0.145931i
$327$	10.5355	−	29.7480i	0.582613	−	1.64507i
$328$	−5.13902	+	2.96701i	−0.283755	+	0.163826i
$329$		0			0
$330$	0.390027	−	0.0722734i	0.0214703	−	0.00397852i
$331$	−27.2137			−1.49580			−0.747901	−	0.663810i	$-0.768938\pi$
$331$	−27.2137			−1.49580			−0.747901	+	0.663810i	$0.768938\pi$
$332$	−8.55240	+	14.8132i	−0.469374	+	0.812980i
$333$	−8.58459	−	6.95264i	−0.470432	−	0.381002i
$334$	11.6041	−	6.69964i	0.634949	−	0.366588i
$335$	1.43587	−	2.48701i	0.0784502	−	0.135880i
$336$		0			0
$337$	−2.35738	−	4.08310i	−0.128415	−	0.222421i	0.794648	−	0.607071i	$-0.207656\pi$
$337$	−2.35738	−	4.08310i	−0.128415	−	0.222421i	−0.923063	+	0.384650i	$0.874322\pi$
$338$	−24.3119	−	14.0365i	−1.32239	−	0.763484i
$339$	13.9741	−	11.9342i	0.758970	−	0.648177i
$340$	−0.0720443	−	0.124784i	−0.00390715	−	0.00676738i
$341$	1.82382	+	3.15895i	0.0987653	+	0.171067i
$342$	−9.88430	−	8.00527i	−0.534482	−	0.432876i
$343$		0			0
$344$	9.03091	+	5.21400i	0.486914	+	0.281120i
$345$	0.841059	−	0.718282i	0.0452811	−	0.0386710i
$346$			15.1541i			0.814692i
$347$			5.59102i			0.300142i	0.988675	+	0.150071i	$0.0479502\pi$
$347$			5.59102i			0.300142i	−0.988675	+	0.150071i	$0.952050\pi$
$348$	10.8340	+	3.83693i	0.580762	+	0.205681i
$349$	−3.38689	−	1.95542i	−0.181296	−	0.104671i	0.406605	−	0.913604i	$-0.366712\pi$
$349$	−3.38689	−	1.95542i	−0.181296	−	0.104671i	−0.587902	+	0.808932i	$0.700046\pi$
$350$		0			0
$351$	15.8930	−	29.2640i	0.848304	−	1.56200i
$352$	−0.260142	−	0.450580i	−0.0138656	−	0.0240160i
$353$	0.359707	+	0.623031i	0.0191453	+	0.0331606i	0.875439	−	0.483328i	$-0.160572\pi$
$353$	0.359707	+	0.623031i	0.0191453	+	0.0331606i	−0.856294	+	0.516489i	$0.827239\pi$
$354$	1.54765	+	8.35197i	0.0822567	+	0.443902i
$355$	6.20012	+	3.57964i	0.329068	+	0.189988i
$356$	−5.86239	−	10.1540i	−0.310706	−	0.538159i
$357$		0			0
$358$	−10.4592	+	18.1158i	−0.552785	+	0.957451i
$359$	16.9780	−	9.80225i	0.896064	−	0.517343i	0.0201431	−	0.999797i	$-0.493588\pi$
$359$	16.9780	−	9.80225i	0.896064	−	0.517343i	0.875921	+	0.482454i	$0.160254\pi$
$360$	1.30425	+	0.206665i	0.0687400	+	0.0108922i
$361$	−0.512011	+	0.886830i	−0.0269480	+	0.0466752i
$362$	−14.5567			−0.765082
$363$	6.20397	−	17.5176i	0.325624	−	0.919433i
$364$		0			0
$365$	1.57302	−	0.908185i	0.0823358	−	0.0475366i
$366$	2.62881	−	0.487127i	0.137410	−	0.0254626i
$367$	12.1913	−	7.03862i	0.636378	−	0.367413i	−0.146840	−	0.989160i	$-0.546910\pi$
$367$	12.1913	−	7.03862i	0.636378	−	0.367413i	0.783218	+	0.621747i	$0.213577\pi$
$368$	−1.25636	−	0.725359i	−0.0654922	−	0.0378120i
$369$	13.8340	+	11.2042i	0.720172	+	0.583265i
$370$			1.62086i			0.0842643i
$371$		0			0
$372$	2.21250	+	11.9399i	0.114713	+	0.619054i
$373$	6.40178	−	11.0882i	0.331471	−	0.574125i	−0.651329	−	0.758795i	$-0.725788\pi$
$373$	6.40178	−	11.0882i	0.331471	−	0.574125i	0.982801	+	0.184670i	$0.0591216\pi$
$374$	0.170312			0.00880664
$375$	−7.35118	+	1.36220i	−0.379613	+	0.0703436i
$376$			8.05267i			0.415285i
$377$	−42.5269			−2.19025
$378$		0			0
$379$	−33.3624			−1.71371			−0.856856	−	0.515556i	$-0.827585\pi$
$379$	−33.3624			−1.71371			−0.856856	+	0.515556i	$0.827585\pi$
$380$			1.86625i			0.0957368i
$381$	4.90802	−	0.909474i	0.251446	−	0.0465938i
$382$	19.6487			1.00531
$383$	4.03360	−	6.98639i	0.206107	−	0.356988i	−0.744378	−	0.667759i	$-0.767254\pi$
$383$	4.03360	−	6.98639i	0.206107	−	0.356988i	0.950485	+	0.310771i	$0.100587\pi$
$384$	−0.315583	−	1.70306i	−0.0161045	−	0.0869088i
$385$		0			0
$386$		−	11.7572i		−	0.598427i
$387$	4.89602	−	30.8985i	0.248879	−	1.57066i
$388$	10.6061	+	6.12344i	0.538443	+	0.310870i
$389$	29.8901	−	17.2571i	1.51549	−	0.874968i	0.515655	−	0.856796i	$-0.327549\pi$
$389$	29.8901	−	17.2571i	1.51549	−	0.874968i	0.999835	−	0.0181720i	$-0.00578465\pi$
$390$	−4.80432	+	0.890257i	−0.243276	+	0.0450799i
$391$	0.411262	−	0.237442i	0.0207984	−	0.0120080i
$392$		0			0
$393$	−9.65405	+	27.2592i	−0.486983	+	1.37505i
$394$	12.6642			0.638016
$395$	−0.291538	+	0.504958i	−0.0146689	+	0.0254072i
$396$	−0.982361	+	1.21294i	−0.0493655	+	0.0609527i
$397$	16.6436	−	9.60920i	0.835320	−	0.482272i	−0.0203509	−	0.999793i	$-0.506478\pi$
$397$	16.6436	−	9.60920i	0.835320	−	0.482272i	0.855671	+	0.517521i	$0.173145\pi$
$398$	−8.91071	+	15.4338i	−0.446653	+	0.773626i
$399$		0			0
$400$	2.40312	+	4.16233i	0.120156	+	0.208117i
$401$	13.8907	+	8.01983i	0.693671	+	0.400491i	0.804986	−	0.593294i	$-0.202173\pi$
$401$	13.8907	+	8.01983i	0.693671	+	0.400491i	−0.111315	+	0.993785i	$0.535506\pi$
$402$	2.05890	+	11.1110i	0.102689	+	0.554164i
$403$	−22.4656	−	38.9116i	−1.11909	−	1.93833i
$404$	−5.40492	−	9.36159i	−0.268905	−	0.465757i
$405$	−0.823123	−	3.87511i	−0.0409013	−	0.192556i
$406$		0			0
$407$	−1.65917	−	0.957923i	−0.0822421	−	0.0474825i
$408$	0.534450	+	0.189279i	0.0264592	+	0.00937072i
$409$			23.9751i			1.18549i	0.805390	+	0.592745i	$0.201956\pi$
$409$			23.9751i			1.18549i	−0.805390	+	0.592745i	$0.798044\pi$
$410$		−	2.61201i		−	0.128998i
$411$	21.7048	−	18.5363i	1.07062	−	0.914331i
$412$	9.69122	+	5.59523i	0.477452	+	0.275657i
$413$		0			0
$414$	−0.681123	+	4.29852i	−0.0334753	+	0.211261i
$415$	−3.76455	−	6.52038i	−0.184794	−	0.320073i
$416$	3.20441	+	5.55020i	0.157109	+	0.272121i
$417$	2.61585	−	2.23399i	0.128099	−	0.109399i
$418$	−1.91037	−	1.10295i	−0.0934393	−	0.0539472i
$419$	13.9896	+	24.2307i	0.683436	+	1.18375i	0.973926	+	0.226868i	$0.0728485\pi$
$419$	13.9896	+	24.2307i	0.683436	+	1.18375i	−0.290490	+	0.956878i	$0.593818\pi$
$420$		0			0
$421$	4.45075	−	7.70893i	0.216916	−	0.375710i	−0.736947	−	0.675950i	$-0.763733\pi$
$421$	4.45075	−	7.70893i	0.216916	−	0.375710i	0.953864	+	0.300240i	$0.0970668\pi$
$422$	−1.69000	+	0.975723i	−0.0822680	+	0.0474974i
$423$	22.5540	−	8.65590i	1.09661	−	0.420864i
$424$	−3.97836	+	6.89072i	−0.193206	+	0.334643i
$425$	−1.57330			−0.0763162
$426$	−27.6996	+	5.13284i	−1.34205	+	0.248687i
$427$		0			0
$428$	0.587790	−	0.339361i	0.0284119	−	0.0164036i
$429$	1.92804	−	5.44403i	0.0930869	−	0.262840i
$430$	−3.97517	+	2.29507i	−0.191700	+	0.110678i
$431$	1.95536	+	1.12893i	0.0941863	+	0.0543785i	0.546353	−	0.837555i	$-0.316016\pi$
$431$	1.95536	+	1.12893i	0.0941863	+	0.0543785i	−0.452167	+	0.891933i	$0.649349\pi$
$432$	−4.43073	+	2.71453i	−0.213174	+	0.130603i
$433$		−	12.6020i		−	0.605612i	−0.953052	−	0.302806i	$-0.902077\pi$
$433$		−	12.6020i		−	0.605612i	0.953052	−	0.302806i	$-0.0979234\pi$
$434$		0			0
$435$	−3.84707	+	3.28548i	−0.184453	+	0.157527i
$436$	9.11016	−	15.7793i	0.436297	−	0.755689i
$437$	−6.15077			−0.294231
$438$	−2.38604	+	6.73724i	−0.114009	+	0.321918i
$439$			28.1972i			1.34578i	0.739744	+	0.672888i	$0.234947\pi$
$439$			28.1972i			1.34578i	−0.739744	+	0.672888i	$0.765053\pi$
$440$	0.229016			0.0109179
$441$		0			0
$442$	−2.09789			−0.0997865
$443$		−	31.4952i		−	1.49638i	−0.663485	−	0.748190i	$-0.730923\pi$
$443$		−	31.4952i		−	1.49638i	0.663485	−	0.748190i	$-0.269077\pi$
$444$	−4.14197	−	4.84996i	−0.196569	−	0.230169i
$445$	5.16095			0.244652
$446$	1.98697	−	3.44154i	0.0940860	−	0.162962i
$447$	−27.6610	−	9.79634i	−1.30832	−	0.463351i
$448$		0			0
$449$		−	24.8151i		−	1.17110i	−0.810638	−	0.585548i	$-0.800880\pi$
$449$		−	24.8151i		−	1.17110i	0.810638	−	0.585548i	$-0.199120\pi$
$450$	9.07478	−	11.2048i	0.427789	−	0.528201i
$451$	2.67375	+	1.54369i	0.125902	+	0.0726896i
$452$	9.18833	−	5.30488i	0.432183	−	0.249521i
$453$	10.2153	+	11.9614i	0.479957	+	0.561997i
$454$	6.29701	−	3.63558i	0.295533	−	0.170626i
$455$		0			0
$456$	−4.76907	−	5.58425i	−0.223332	−	0.261507i
$457$	16.0818			0.752277			0.376138	−	0.926563i	$-0.377252\pi$
$457$	16.0818			0.752277			0.376138	+	0.926563i	$0.377252\pi$
$458$	−0.874590	+	1.51483i	−0.0408669	+	0.0707836i
$459$	−0.0443498	−	1.70035i	−0.00207007	−	0.0793657i
$460$	0.553017	−	0.319284i	0.0257845	−	0.0148867i
$461$	−11.7250	+	20.3083i	−0.546089	+	0.945853i	0.452449	+	0.891790i	$0.350550\pi$
$461$	−11.7250	+	20.3083i	−0.546089	+	0.945853i	−0.998538	+	0.0540628i	$0.982783\pi$
$462$		0			0
$463$	8.40381	+	14.5558i	0.390558	+	0.676467i	0.992523	−	0.122056i	$-0.0389486\pi$
$463$	8.40381	+	14.5558i	0.390558	+	0.676467i	−0.601965	+	0.798523i	$0.705615\pi$
$464$	5.74668	+	3.31785i	0.266783	+	0.154027i
$465$	−5.03845	−	1.78440i	−0.233653	−	0.0827498i
$466$	−3.44537	−	5.96755i	−0.159603	−	0.276441i
$467$	−3.20836	−	5.55704i	−0.148465	−	0.257149i	0.782195	−	0.623033i	$-0.214100\pi$
$467$	−3.20836	−	5.55704i	−0.148465	−	0.257149i	−0.930660	+	0.365884i	$0.880767\pi$
$468$	12.1006	−	14.9409i	0.559352	−	0.690645i
$469$		0			0
$470$	−3.06969	−	1.77229i	−0.141594	−	0.0817496i
$471$	−3.11772	−	16.8249i	−0.143657	−	0.775251i
$472$			4.90410i			0.225730i
$473$		−	5.42553i		−	0.249466i
$474$	−0.418036	−	2.25595i	−0.0192010	−	0.103619i
$475$	17.6475	+	10.1888i	0.809722	+	0.467493i
$476$		0			0
$477$	23.5760	+	3.73574i	1.07947	+	0.171048i
$478$	−9.44606	−	16.3611i	−0.432053	−	0.748337i
$479$	−6.35492	−	11.0070i	−0.290364	−	0.502925i	0.683532	−	0.729921i	$-0.260443\pi$
$479$	−6.35492	−	11.0070i	−0.290364	−	0.502925i	−0.973896	+	0.226996i	$0.927110\pi$
$480$	0.718665	+	0.254520i	0.0328024	+	0.0116172i
$481$	20.4375	+	11.7996i	0.931871	+	0.538016i
$482$	−8.19555	−	14.1951i	−0.373297	−	0.646569i
$483$		0			0
$484$	5.36465	−	9.29185i	0.243848	−	0.422357i
$485$	−4.66853	+	2.69538i	−0.211987	+	0.122391i
$486$	12.3655	+	9.49178i	0.560912	+	0.430556i
$487$	1.31296	−	2.27412i	0.0594960	−	0.103050i	−0.834743	−	0.550639i	$-0.814384\pi$
$487$	1.31296	−	2.27412i	0.0594960	−	0.103050i	0.894239	+	0.447589i	$0.147717\pi$
$488$	1.54358			0.0698746
$489$	5.92752	+	6.94071i	0.268052	+	0.313870i
$490$		0			0
$491$	−4.13045	+	2.38472i	−0.186405	+	0.107621i	−0.590298	−	0.807185i	$-0.700990\pi$
$491$	−4.13045	+	2.38472i	−0.186405	+	0.107621i	0.403894	+	0.914806i	$0.367657\pi$
$492$	6.67478	+	7.81571i	0.300922	+	0.352359i
$493$	−1.88114	+	1.08608i	−0.0847225	+	0.0489145i
$494$	23.5318	+	13.5861i	1.05875	+	0.611267i
$495$	−0.246172	−	0.641431i	−0.0110646	−	0.0288302i
$496$			7.01085i			0.314796i
$497$		0			0
$498$	27.9267	+	9.89045i	1.25143	+	0.443202i
$499$	9.73459	−	16.8608i	0.435780	−	0.754793i	−0.561579	−	0.827423i	$-0.689806\pi$
$499$	9.73459	−	16.8608i	0.435780	−	0.754793i	0.997359	+	0.0726299i	$0.0231392\pi$
$500$	−4.31646			−0.193038
$501$	−15.0719	−	17.6482i	−0.673364	−	0.788463i
$502$		−	0.663086i		−	0.0295950i
$503$	−9.40949			−0.419549			−0.209774	−	0.977750i	$-0.567273\pi$
$503$	−9.40949			−0.419549			−0.209774	+	0.977750i	$0.567273\pi$
$504$		0			0
$505$	4.75821			0.211738
$506$			0.754786i			0.0335543i
$507$	−16.2325	+	45.8342i	−0.720912	+	2.03557i
$508$	2.88189			0.127863
$509$	−9.40879	+	16.2965i	−0.417037	+	0.722330i	−0.995640	−	0.0932799i	$-0.970265\pi$
$509$	−9.40879	+	16.2965i	−0.417037	+	0.722330i	0.578603	+	0.815610i	$0.303598\pi$
$510$	−0.189779	+	0.162075i	−0.00840356	+	0.00717682i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−10.5141	+	19.3599i	−0.464210	+	0.854759i
$514$	−4.91529	−	2.83784i	−0.216804	−	0.125172i
$515$	−4.26582	+	2.46287i	−0.187975	+	0.108527i
$516$	6.02974	−	17.0256i	0.265445	−	0.749511i
$517$	3.62837	−	2.09484i	0.159576	−	0.0921310i
$518$		0			0
$519$	25.8084	−	4.78239i	1.13286	−	0.209923i
$520$	−2.82100			−0.123709
$521$	8.35221	−	14.4665i	0.365917	−	0.633787i	−0.623006	−	0.782217i	$-0.714089\pi$
$521$	8.35221	−	14.4665i	0.365917	−	0.633787i	0.988923	+	0.148430i	$0.0474220\pi$
$522$	3.11551	−	19.6618i	0.136362	−	0.860573i
$523$	−13.4109	+	7.74277i	−0.586416	+	0.338568i	−0.763679	−	0.645596i	$-0.776609\pi$
$523$	−13.4109	+	7.74277i	−0.586416	+	0.338568i	0.177263	+	0.984164i	$0.443276\pi$
$524$	−8.34798	+	14.4591i	−0.364683	+	0.631650i
$525$		0			0
$526$	5.04520	+	8.73855i	0.219981	+	0.381019i
$527$	−1.98750	−	1.14748i	−0.0865767	−	0.0499851i
$528$	−0.685267	+	0.585233i	−0.0298224	+	0.0254690i
$529$	−10.4477	−	18.0960i	−0.454248	−	0.786781i
$530$	−1.75117	−	3.03312i	−0.0760660	−	0.131750i
$531$	13.7355	−	5.27148i	0.596069	−	0.228763i
$532$		0			0
$533$	−32.9350	−	19.0150i	−1.42657	−	0.823633i
$534$	−15.4427	+	13.1884i	−0.668272	+	0.570718i
$535$			0.298756i			0.0129163i
$536$			6.52412i			0.281799i
$537$	34.1530	+	12.0955i	1.47381	+	0.521961i
$538$	−16.7437	−	9.66698i	−0.721872	−	0.416773i
$539$		0			0
$540$	−0.0596363	−	2.28643i	−0.00256634	−	0.0983925i
$541$	−11.3525	−	19.6632i	−0.488084	−	0.845386i	0.511822	−	0.859091i	$-0.328971\pi$
$541$	−11.3525	−	19.6632i	−0.488084	−	0.845386i	−0.999906	+	0.0137053i	$0.995637\pi$
$542$	−6.14652	−	10.6461i	−0.264016	−	0.457288i
$543$	4.59384	+	24.7909i	0.197140	+	1.06388i
$544$	0.283489	+	0.163672i	0.0121545	+	0.00701739i
$545$	4.01006	+	6.94562i	0.171772	+	0.297518i
$546$		0			0
$547$	−22.2991	+	38.6232i	−0.953441	+	1.65141i	−0.215546	+	0.976494i	$0.569153\pi$
$547$	−22.2991	+	38.6232i	−0.953441	+	1.65141i	−0.737895	+	0.674915i	$0.764180\pi$
$548$	14.2714	−	8.23961i	0.609645	−	0.351979i
$549$	−1.65921	−	4.32329i	−0.0708135	−	0.184513i
$550$	1.25031	−	2.16560i	0.0533133	−	0.0923414i
$551$	28.1341			1.19855
$552$	−0.838844	+	2.36856i	−0.0357036	+	0.100813i
$553$		0			0
$554$	7.07235	−	4.08322i	0.300475	−	0.173480i
$555$	2.76041	−	0.511514i	0.117173	−	0.0217126i
$556$	1.71999	−	0.993034i	0.0729436	−	0.0421140i
$557$	21.8862	+	12.6360i	0.927348	+	0.535405i	0.885972	−	0.463739i	$-0.153492\pi$
$557$	21.8862	+	12.6360i	0.927348	+	0.535405i	0.0413761	+	0.999144i	$0.486826\pi$
$558$	19.6361	−	7.53604i	0.831262	−	0.319026i
$559$			66.8311i			2.82666i
$560$		0			0
$561$	−0.0537476	−	0.290052i	−0.00226923	−	0.0122460i
$562$	−15.9869	+	27.6901i	−0.674366	+	1.16804i
$563$	27.1453			1.14404			0.572020	−	0.820240i	$-0.306160\pi$
$563$	27.1453			1.14404			0.572020	+	0.820240i	$0.306160\pi$
$564$	13.7142	−	2.54128i	0.577470	−	0.107007i
$565$			4.67015i			0.196474i
$566$	10.0668			0.423139
$567$		0			0
$568$	−16.2646			−0.682449
$569$			15.4940i			0.649541i	0.945793	+	0.324770i	$0.105287\pi$
$569$			15.4940i			0.649541i	−0.945793	+	0.324770i	$0.894713\pi$
$570$	3.17834	−	0.588957i	0.133126	−	0.0246687i
$571$	−1.56966			−0.0656881			−0.0328441	−	0.999460i	$-0.510456\pi$
$571$	−1.56966			−0.0656881			−0.0328441	+	0.999460i	$0.510456\pi$
$572$	1.66720	−	2.88768i	0.0697093	−	0.120740i
$573$	−6.20079	−	33.4629i	−0.259042	−	1.39793i
$574$		0			0
$575$		−	6.97251i		−	0.290774i
$576$	−2.80082	+	1.07491i	−0.116701	+	0.0447880i
$577$	−10.6325	−	6.13867i	−0.442637	−	0.255556i	0.262079	−	0.965046i	$-0.415592\pi$
$577$	−10.6325	−	6.13867i	−0.442637	−	0.255556i	−0.704715	+	0.709490i	$0.748925\pi$
$578$	14.6296	−	8.44642i	0.608513	−	0.351325i
$579$	−20.0232	+	3.71037i	−0.832137	+	0.154198i
$580$	−2.52954	+	1.46043i	−0.105033	+	0.0606411i
$581$		0			0
$582$	7.08147	−	19.9953i	0.293536	−	0.828830i
$583$	4.13976			0.171451
$584$	−2.06324	+	3.57364i	−0.0853775	+	0.147878i
$585$	3.03232	+	7.90109i	0.125371	+	0.326670i
$586$	−11.5129	+	6.64697i	−0.475593	+	0.274584i
$587$	7.79739	−	13.5055i	0.321833	−	0.557431i	−0.659033	−	0.752114i	$-0.729034\pi$
$587$	7.79739	−	13.5055i	0.321833	−	0.557431i	0.980866	+	0.194683i	$0.0623677\pi$
$588$		0			0
$589$	14.8623	+	25.7423i	0.612392	+	1.06069i
$590$	−1.86945	−	1.07933i	−0.0769642	−	0.0444353i
$591$	−3.99662	−	21.5680i	−0.164399	−	0.887187i
$592$	−1.84115	−	3.18897i	−0.0756709	−	0.131066i
$593$	−11.8449	−	20.5160i	−0.486412	−	0.842491i	0.513466	−	0.858110i	$-0.328361\pi$
$593$	−11.8449	−	20.5160i	−0.486412	−	0.842491i	−0.999878	+	0.0156193i	$0.995028\pi$
$594$	2.37573	+	1.29023i	0.0974774	+	0.0529389i
$595$		0			0
$596$	−14.6722	−	8.47103i	−0.600999	−	0.346987i
$597$	29.0967	+	10.3048i	1.19085	+	0.421748i
$598$		−	9.29739i		−	0.380198i
$599$		−	2.19371i		−	0.0896327i	−0.998995	−	0.0448164i	$-0.985730\pi$
$599$		−	2.19371i		−	0.0896327i	0.998995	−	0.0448164i	$-0.0142703\pi$
$600$	6.33031	−	5.40622i	0.258434	−	0.220708i
$601$	−4.26683	−	2.46345i	−0.174047	−	0.100486i	0.410445	−	0.911885i	$-0.365373\pi$
$601$	−4.26683	−	2.46345i	−0.174047	−	0.100486i	−0.584493	+	0.811399i	$0.698707\pi$
$602$		0			0
$603$	18.2729	−	7.01285i	0.744128	−	0.285585i
$604$	4.54082	+	7.86493i	0.184763	+	0.320019i
$605$	2.36138	+	4.09003i	0.0960038	+	0.166283i
$606$	−14.2376	+	12.1592i	−0.578364	+	0.493936i
$607$	5.09255	+	2.94018i	0.206700	+	0.119338i	0.599777	−	0.800167i	$-0.295256\pi$
$607$	5.09255	+	2.94018i	0.206700	+	0.119338i	−0.393077	+	0.919506i	$0.628589\pi$
$608$	−2.11990	−	3.67178i	−0.0859735	−	0.148910i
$609$		0			0
$610$	−0.339722	+	0.588416i	−0.0137550	+	0.0238243i
$611$	−44.6939	+	25.8040i	−1.80812	+	1.04392i
$612$	0.153691	−	0.969933i	0.00621258	−	0.0392072i
$613$	−13.2436	+	22.9387i	−0.534906	+	0.926484i	0.464262	+	0.885698i	$0.346320\pi$
$613$	−13.2436	+	22.9387i	−0.534906	+	0.926484i	−0.999168	+	0.0407862i	$0.987014\pi$
$614$	5.44565			0.219768
$615$	−4.44840	+	0.824303i	−0.179377	+	0.0332391i
$616$		0			0
$617$	−17.9549	+	10.3663i	−0.722839	+	0.417331i	−0.815797	−	0.578339i	$-0.803701\pi$
$617$	−17.9549	+	10.3663i	−0.722839	+	0.417331i	0.0929578	+	0.995670i	$0.470368\pi$
$618$	6.47062	−	18.2705i	0.260286	−	0.734946i
$619$	5.47577	−	3.16144i	0.220090	−	0.127069i	−0.385902	−	0.922540i	$-0.626110\pi$
$619$	5.47577	−	3.16144i	0.220090	−	0.127069i	0.605992	+	0.795471i	$0.292776\pi$
$620$	−2.67255	−	1.54300i	−0.107332	−	0.0619683i
$621$	7.53559	−	0.196548i	0.302393	−	0.00788721i
$622$		−	0.259547i		−	0.0104069i
$623$		0			0
$624$	8.44106	−	7.20884i	0.337913	−	0.288585i
$625$	−11.0656	+	19.1662i	−0.442625	+	0.766649i
$626$	30.8024			1.23111
$627$	−1.27551	+	3.60155i	−0.0509391	+	0.143832i
$628$		−	9.87924i		−	0.394224i
$629$	1.20538			0.0480617
$630$		0			0
$631$	−9.24859			−0.368180			−0.184090	−	0.982909i	$-0.558934\pi$
$631$	−9.24859			−0.368180			−0.184090	+	0.982909i	$0.558934\pi$
$632$		−	1.32465i		−	0.0526917i
$633$	2.19505	+	2.57025i	0.0872453	+	0.102158i
$634$	−16.0476			−0.637333
$635$	−0.634266	+	1.09858i	−0.0251701	+	0.0435959i
$636$	12.9908	+	4.60079i	0.515119	+	0.182433i
$637$		0			0
$638$		−	3.45245i		−	0.136684i
$639$	17.4831	+	45.5543i	0.691619	+	1.80210i
$640$	0.381202	+	0.220087i	0.0150683	+	0.00869971i
$641$	39.0779	−	22.5616i	1.54349	−	0.891132i	0.544870	−	0.838520i	$-0.316579\pi$
$641$	39.0779	−	22.5616i	1.54349	−	0.891132i	0.998615	−	0.0526111i	$-0.0167544\pi$
$642$	−0.763447	−	0.893944i	−0.0301309	−	0.0352812i
$643$	10.5183	−	6.07274i	0.414801	−	0.239486i	−0.278049	−	0.960567i	$-0.589688\pi$
$643$	10.5183	−	6.07274i	0.414801	−	0.239486i	0.692851	+	0.721081i	$0.256355\pi$
$644$		0			0
$645$	5.16313	+	6.04567i	0.203298	+	0.238048i
$646$	1.38788			0.0546053
$647$	8.01417	−	13.8810i	0.315070	−	0.545717i	−0.664383	−	0.747393i	$-0.731305\pi$
$647$	8.01417	−	13.8810i	0.315070	−	0.545717i	0.979452	+	0.201676i	$0.0646388\pi$
$648$	6.02126	+	6.68913i	0.236537	+	0.262774i
$649$	2.20969	−	1.27576i	0.0867379	−	0.0500782i
$650$	−15.4012	+	26.6756i	−0.604084	+	1.04630i
$651$		0			0
$652$	2.63485	+	4.56369i	0.103189	+	0.178728i
$653$	−1.92426	−	1.11097i	−0.0753020	−	0.0434756i	0.461876	−	0.886944i	$-0.347176\pi$
$653$	−1.92426	−	1.11097i	−0.0753020	−	0.0434756i	−0.537178	+	0.843469i	$0.680510\pi$
$654$	−29.7480	−	10.5355i	−1.16324	−	0.411970i
$655$	−3.67457	−	6.36454i	−0.143577	−	0.248683i
$656$	2.96701	+	5.13902i	0.115842	+	0.200645i
$657$	12.2269	+	1.93741i	0.477017	+	0.0755857i
$658$		0			0
$659$	2.93978	+	1.69728i	0.114518	+	0.0661168i	0.556165	−	0.831072i	$-0.312272\pi$
$659$	2.93978	+	1.69728i	0.114518	+	0.0661168i	−0.441647	+	0.897189i	$0.645606\pi$
$660$	−0.0722734	−	0.390027i	−0.00281324	−	0.0151818i
$661$		−	2.63062i		−	0.102319i	−0.998690	−	0.0511596i	$-0.983708\pi$
$661$		−	2.63062i		−	0.102319i	0.998690	−	0.0511596i	$-0.0162917\pi$
$662$			27.2137i			1.05769i
$663$	0.662058	+	3.57283i	0.0257122	+	0.138757i
$664$	14.8132	+	8.55240i	0.574863	+	0.331898i
$665$		0			0
$666$	−6.95264	+	8.58459i	−0.269409	+	0.332646i
$667$	−4.81326	−	8.33681i	−0.186370	−	0.322803i
$668$	−6.69964	−	11.6041i	−0.259217	−	0.448976i
$669$	−6.48820	−	2.29784i	−0.250848	−	0.0888397i
$670$	−2.48701	−	1.43587i	−0.0960815	−	0.0554727i
$671$	−0.401551	−	0.695507i	−0.0155017	−	0.0268497i
$672$		0			0
$673$	−9.02538	+	15.6324i	−0.347903	+	0.602585i	−0.985877	−	0.167473i	$-0.946439\pi$
$673$	−9.02538	+	15.6324i	−0.347903	+	0.602585i	0.637974	+	0.770058i	$0.279773\pi$
$674$	−4.08310	+	2.35738i	−0.157275	+	0.0908029i
$675$	−21.9463	−	11.9188i	−0.844715	−	0.458756i
$676$	−14.0365	+	24.3119i	−0.539864	+	0.935073i
$677$	−39.6834			−1.52516			−0.762578	−	0.646897i	$-0.776066\pi$
$677$	−39.6834			−1.52516			−0.762578	+	0.646897i	$0.776066\pi$
$678$	−11.9342	−	13.9741i	−0.458330	−	0.536673i
$679$		0			0
$680$	−0.124784	+	0.0720443i	−0.00478526	+	0.00276277i
$681$	−8.17883	−	9.57685i	−0.313414	−	0.366986i
$682$	3.15895	−	1.82382i	0.120962	−	0.0698376i
$683$	25.9383	+	14.9755i	0.992500	+	0.573020i	0.906021	−	0.423234i	$-0.139105\pi$
$683$	25.9383	+	14.9755i	0.992500	+	0.573020i	0.0864793	+	0.996254i	$0.472438\pi$
$684$	−8.00527	+	9.88430i	−0.306089	+	0.377936i
$685$			7.25373i			0.277151i
$686$		0			0
$687$	2.85586	+	1.01142i	0.108958	+	0.0385882i
$688$	5.21400	−	9.03091i	0.198782	−	0.344300i
$689$	−50.9932			−1.94268
$690$	−0.718282	−	0.841059i	−0.0273445	−	0.0320186i
$691$			22.5070i			0.856206i	0.903730	+	0.428103i	$0.140818\pi$
$691$			22.5070i			0.856206i	−0.903730	+	0.428103i	$0.859182\pi$
$692$	15.1541			0.576074
$693$		0			0
$694$	5.59102			0.212232
$695$			0.874216i			0.0331609i
$696$	3.83693	−	10.8340i	0.145439	−	0.410661i
$697$	−1.94247			−0.0735764
$698$	−1.95542	+	3.38689i	−0.0740139	+	0.128196i
$699$	−9.07579	+	7.75091i	−0.343278	+	0.293166i
$700$		0			0
$701$		−	6.00423i		−	0.226777i	−0.993551	−	0.113388i	$-0.963830\pi$
$701$		−	6.00423i		−	0.226777i	0.993551	−	0.113388i	$-0.0361704\pi$
$702$	−29.2640	−	15.8930i	−1.10450	−	0.599842i
$703$	−13.5206	−	7.80613i	−0.509940	−	0.294414i
$704$	−0.450580	+	0.260142i	−0.0169819	+	0.00980448i
$705$	−2.04957	+	5.78717i	−0.0771912	+	0.217957i
$706$	0.623031	−	0.359707i	0.0234481	−	0.0135378i
$707$		0			0
$708$	8.35197	−	1.54765i	0.313886	−	0.0581642i
$709$	11.9958			0.450512			0.225256	−	0.974300i	$-0.427678\pi$
$709$	11.9958			0.450512			0.225256	+	0.974300i	$0.427678\pi$
$710$	3.57964	−	6.20012i	0.134341	−	0.232686i
$711$	−3.71009	+	1.42388i	−0.139139	+	0.0533996i
$712$	−10.1540	+	5.86239i	−0.380536	+	0.219703i
$713$	5.08538	−	8.80814i	0.190449	−	0.329867i
$714$		0			0
$715$	0.733861	+	1.27108i	0.0274448	+	0.0475358i
$716$	18.1158	+	10.4592i	0.677020	+	0.390878i
$717$	−24.8828	+	21.2505i	−0.929266	+	0.793613i
$718$	−9.80225	−	16.9780i	−0.365817	−	0.633613i
$719$	−17.4869	−	30.2882i	−0.652151	−	1.12956i	−0.982600	−	0.185735i	$-0.940533\pi$
$719$	−17.4869	−	30.2882i	−0.652151	−	1.12956i	0.330448	−	0.943824i	$-0.392800\pi$
$720$	0.206665	−	1.30425i	0.00770195	−	0.0486065i
$721$		0			0
$722$	0.886830	+	0.512011i	0.0330044	+	0.0190551i
$723$	−21.5887	+	18.4372i	−0.802893	+	0.685688i
$724$			14.5567i			0.540995i
$725$			31.8928i			1.18447i
$726$	−17.5176	−	6.20397i	−0.650137	−	0.230251i
$727$	37.2435	+	21.5026i	1.38129	+	0.797486i	0.992312	−	0.123763i	$-0.0394963\pi$
$727$	37.2435	+	21.5026i	1.38129	+	0.797486i	0.388974	+	0.921249i	$0.372830\pi$
$728$		0			0
$729$	12.2627	−	24.0546i	0.454174	−	0.890913i
$730$	−0.908185	−	1.57302i	−0.0336134	−	0.0582202i
$731$	1.70677	+	2.95622i	0.0631273	+	0.109340i
$732$	−0.487127	−	2.62881i	−0.0180047	−	0.0971636i
$733$	−41.5096	−	23.9656i	−1.53319	−	0.885188i	−0.999212	−	0.0396905i	$-0.987363\pi$
$733$	−41.5096	−	23.9656i	−1.53319	−	0.885188i	−0.533979	−	0.845498i	$-0.679304\pi$
$734$	−7.03862	−	12.1913i	−0.259800	−	0.449987i
$735$		0			0
$736$	−0.725359	+	1.25636i	−0.0267371	+	0.0463100i
$737$	2.93964	−	1.69720i	0.108283	−	0.0625171i
$738$	11.2042	−	13.8340i	0.412431	−	0.509238i
$739$	4.62010	−	8.00224i	0.169953	−	0.294367i	−0.768450	−	0.639910i	$-0.778972\pi$
$739$	4.62010	−	8.00224i	0.169953	−	0.294367i	0.938403	+	0.345543i	$0.112305\pi$
$740$	1.62086			0.0595838
$741$	15.7117	−	44.3635i	0.577183	−	1.62974i
$742$		0			0
$743$	39.7222	−	22.9336i	1.45726	−	0.841352i	0.458389	−	0.888752i	$-0.348427\pi$
$743$	39.7222	−	22.9336i	1.45726	−	0.841352i	0.998876	+	0.0473999i	$0.0150935\pi$
$744$	11.9399	−	2.21250i	0.437737	−	0.0811143i
$745$	6.45834	−	3.72873i	0.236615	−	0.136610i
$746$	−11.0882	−	6.40178i	−0.405968	−	0.234386i
$747$	8.03083	−	50.6821i	0.293833	−	1.85436i
$748$		−	0.170312i		−	0.00622724i
$749$		0			0
$750$	1.36220	+	7.35118i	0.0497405	+	0.268427i
$751$	11.0946	−	19.2165i	0.404849	−	0.701219i	−0.589455	−	0.807801i	$-0.700657\pi$
$751$	11.0946	−	19.2165i	0.404849	−	0.701219i	0.994304	+	0.106582i	$0.0339908\pi$
$752$	8.05267			0.293651
$753$	−1.12927	+	0.209258i	−0.0411530	+	0.00762580i
$754$			42.5269i			1.54874i
$755$	−3.99750			−0.145484
$756$		0			0
$757$	−0.971966			−0.0353267			−0.0176633	−	0.999844i	$-0.505623\pi$
$757$	−0.971966			−0.0353267			−0.0176633	+	0.999844i	$0.505623\pi$
$758$			33.3624i			1.21178i
$759$	1.28545	−	0.238197i	0.0466587	−	0.00864602i
$760$	1.86625			0.0676962
$761$	−11.9307	+	20.6646i	−0.432488	+	0.749091i	−0.997087	−	0.0762743i	$-0.975698\pi$
$761$	−11.9307	+	20.6646i	−0.432488	+	0.749091i	0.564599	+	0.825365i	$0.309031\pi$
$762$	−0.909474	−	4.90802i	−0.0329468	−	0.177799i
$763$		0			0
$764$		−	19.6487i		−	0.710865i
$765$	0.335915	+	0.272057i	0.0121450	+	0.00983624i
$766$	−6.98639	−	4.03360i	−0.252429	−	0.145740i
$767$	−27.2188	+	15.7148i	−0.982812	+	0.567427i
$768$	−1.70306	+	0.315583i	−0.0614538	+	0.0113876i
$769$	−2.29392	+	1.32440i	−0.0827209	+	0.0477589i	−0.540790	−	0.841158i	$-0.681875\pi$
$769$	−2.29392	+	1.32440i	−0.0827209	+	0.0477589i	0.458069	+	0.888917i	$0.348541\pi$
$770$		0			0
$771$	−3.28183	+	9.26660i	−0.118192	+	0.333729i
$772$	−11.7572			−0.423151
$773$	17.7849	−	30.8043i	0.639678	−	1.10795i	−0.345825	−	0.938299i	$-0.612401\pi$
$773$	17.7849	−	30.8043i	0.639678	−	1.10795i	0.985503	−	0.169656i	$-0.0542656\pi$
$774$	−30.8985	−	4.89602i	−1.11062	−	0.175984i
$775$	−29.1815	+	16.8479i	−1.04823	+	0.605196i
$776$	6.12344	−	10.6061i	0.219819	−	0.380737i
$777$		0			0
$778$	−17.2571	−	29.8901i	−0.618696	−	1.07161i
$779$	21.7885	+	12.5796i	0.780652	+	0.450710i
$780$	0.890257	+	4.80432i	0.0318763	+	0.172022i
$781$	4.23112	+	7.32852i	0.151402	+	0.262235i
$782$	−0.237442	−	0.411262i	−0.00849092	−	0.0147067i
$783$	−34.4683	+	0.899027i	−1.23180	+	0.0321286i
$784$		0			0
$785$	3.76598	+	2.17429i	0.134414	+	0.0776038i
$786$	27.2592	+	9.65405i	0.972304	+	0.344349i
$787$			28.4614i			1.01454i	0.861788	+	0.507269i	$0.169345\pi$
$787$			28.4614i			1.01454i	−0.861788	+	0.507269i	$0.830655\pi$
$788$		−	12.6642i		−	0.451145i
$789$	13.2901	−	11.3500i	0.473139	−	0.404071i
$790$	0.504958	+	0.291538i	0.0179656	+	0.0103725i
$791$		0			0
$792$	1.21294	+	0.982361i	0.0431001	+	0.0349067i
$793$	4.94627	+	8.56718i	0.175647	+	0.304230i
$794$	−9.60920	−	16.6436i	−0.341018	−	0.590660i
$795$	−4.61294	+	3.93955i	−0.163604	+	0.139721i
$796$	15.4338	+	8.91071i	0.547036	+	0.315832i
$797$	25.5890	+	44.3214i	0.906408	+	1.56995i	0.819015	+	0.573772i	$0.194520\pi$
$797$	25.5890	+	44.3214i	0.906408	+	1.56995i	0.0873931	+	0.996174i	$0.472146\pi$
$798$		0			0
$799$	−1.31800	+	2.28284i	−0.0466274	+	0.0807611i
$800$	4.16233	−	2.40312i	0.147161	−	0.0849632i
$801$	27.3341	+	22.1378i	0.965803	+	0.782202i
$802$	8.01983	−	13.8907i	0.283190	−	0.490499i
$803$	2.14694			0.0757640
$804$	11.1110	−	2.05890i	0.391853	−	0.0726118i
$805$		0			0
$806$	−38.9116	+	22.4656i	−1.37060	+	0.791318i
$807$	−11.1794	+	31.5662i	−0.393534	+	1.11118i
$808$	−9.36159	+	5.40492i	−0.329340	+	0.190144i
$809$	−27.5306	−	15.8948i	−0.967925	−	0.558832i	−0.0693222	−	0.997594i	$-0.522084\pi$
$809$	−27.5306	−	15.8948i	−0.967925	−	0.558832i	−0.898603	+	0.438762i	$0.855417\pi$
$810$	−3.87511	+	0.823123i	−0.136158	+	0.0289216i
$811$		−	42.1668i		−	1.48068i	−0.672235	−	0.740338i	$-0.734666\pi$
$811$		−	42.1668i		−	1.48068i	0.672235	−	0.740338i	$-0.265334\pi$
$812$		0			0
$813$	−16.1912	+	13.8276i	−0.567849	+	0.484955i
$814$	−0.957923	+	1.65917i	−0.0335752	+	0.0581539i
$815$	−2.31958			−0.0812514
$816$	0.189279	−	0.534450i	0.00662610	−	0.0187095i
$817$		−	44.2127i		−	1.54681i
$818$	23.9751			0.838268
$819$		0			0
$820$	−2.61201			−0.0912152
$821$		−	9.86506i		−	0.344293i	−0.985071	−	0.172146i	$-0.944930\pi$
$821$		−	9.86506i		−	0.344293i	0.985071	−	0.172146i	$-0.0550702\pi$
$822$	−18.5363	−	21.7048i	−0.646529	−	0.757041i
$823$	−40.5668			−1.41407			−0.707035	−	0.707178i	$-0.749968\pi$
$823$	−40.5668			−1.41407			−0.707035	+	0.707178i	$0.749968\pi$
$824$	5.59523	−	9.69122i	0.194919	−	0.337610i
$825$	−4.08271	−	1.44592i	−0.142142	−	0.0503406i
$826$		0			0
$827$			3.24077i			0.112693i	0.998411	+	0.0563463i	$0.0179451\pi$
$827$			3.24077i			0.112693i	−0.998411	+	0.0563463i	$0.982055\pi$
$828$	4.29852	+	0.681123i	0.149384	+	0.0236706i
$829$	41.2692	+	23.8268i	1.43334	+	0.827539i	0.997374	−	0.0724251i	$-0.0230738\pi$
$829$	41.2692	+	23.8268i	1.43334	+	0.827539i	0.435965	+	0.899964i	$0.356407\pi$
$830$	−6.52038	+	3.76455i	−0.226326	+	0.130669i
$831$	−9.18588	−	10.7560i	−0.318655	−	0.373123i
$832$	5.55020	−	3.20441i	0.192419	−	0.111093i
$833$		0			0
$834$	−2.23399	−	2.61585i	−0.0773568	−	0.0905795i
$835$	5.89801			0.204109
$836$	−1.10295	+	1.91037i	−0.0381465	+	0.0660716i
$837$	−19.0311	−	31.0632i	−0.657812	−	1.07370i
$838$	24.2307	−	13.9896i	0.837035	−	0.483262i
$839$	−3.12066	+	5.40514i	−0.107737	+	0.186606i	−0.914853	−	0.403787i	$-0.867694\pi$
$839$	−3.12066	+	5.40514i	−0.107737	+	0.186606i	0.807116	+	0.590393i	$0.201027\pi$
$840$		0			0
$841$	7.51621	+	13.0185i	0.259180	+	0.448912i
$842$	−7.70893	−	4.45075i	−0.265667	−	0.153383i
$843$	52.2030	+	18.4881i	1.79797	+	0.636763i
$844$	0.975723	+	1.69000i	0.0335858	+	0.0581722i
$845$	−6.17849	−	10.7015i	−0.212547	−	0.368142i
$846$	−8.65590	−	22.5540i	−0.297596	−	0.775424i
$847$		0			0
$848$	6.89072	+	3.97836i	0.236628	+	0.136617i
$849$	−3.17690	−	17.1443i	−0.109031	−	0.588392i
$850$			1.57330i			0.0539637i
$851$			5.34199i			0.183121i
$852$	5.13284	+	27.6996i	0.175848	+	0.948974i
$853$	−14.6158	−	8.43842i	−0.500435	−	0.288926i	0.228458	−	0.973554i	$-0.426632\pi$
$853$	−14.6158	−	8.43842i	−0.500435	−	0.288926i	−0.728893	+	0.684628i	$0.759965\pi$
$854$		0			0
$855$	−2.00606	−	5.22703i	−0.0686057	−	0.178761i
$856$	−0.339361	−	0.587790i	−0.0115991	−	0.0200902i
$857$	12.3709	+	21.4270i	0.422581	+	0.731932i	0.996191	−	0.0871967i	$-0.0277909\pi$
$857$	12.3709	+	21.4270i	0.422581	+	0.731932i	−0.573610	+	0.819128i	$0.694458\pi$
$858$	−5.44403	−	1.92804i	−0.185856	−	0.0658224i
$859$	−36.8928	−	21.3001i	−1.25877	−	0.726749i	−0.285932	−	0.958250i	$-0.592303\pi$
$859$	−36.8928	−	21.3001i	−1.25877	−	0.726749i	−0.972835	+	0.231500i	$0.925637\pi$
$860$	2.29507	+	3.97517i	0.0782611	+	0.135552i
$861$		0			0
$862$	1.12893	−	1.95536i	0.0384514	−	0.0665998i
$863$	−39.7891	+	22.9723i	−1.35444	+	0.781985i	−0.988868	−	0.148799i	$-0.952459\pi$
$863$	−39.7891	+	22.9723i	−1.35444	+	0.781985i	−0.365570	+	0.930784i	$0.619126\pi$
$864$	2.71453	+	4.43073i	0.0923500	+	0.150736i
$865$	−3.33523	+	5.77679i	−0.113401	+	0.196417i
$866$	−12.6020			−0.428232
$867$	−19.0016	−	22.2496i	−0.645328	−	0.755635i
$868$		0			0
$869$	−0.596859	+	0.344597i	−0.0202471	+	0.0116897i
$870$	3.28548	+	3.84707i	0.111388	+	0.130428i
$871$	−36.2102	+	20.9059i	−1.22693	+	0.708371i
$872$	−15.7793	−	9.11016i	−0.534353	−	0.308509i
$873$	−36.2879	−	5.75000i	−1.22816	−	0.194608i
$874$			6.15077i			0.208053i
$875$		0			0
$876$	6.73724	+	2.38604i	0.227630	+	0.0806169i
$877$	−2.28391	+	3.95585i	−0.0771222	+	0.133580i	−0.902007	−	0.431721i	$-0.857907\pi$
$877$	−2.28391	+	3.95585i	−0.0771222	+	0.133580i	0.824885	+	0.565301i	$0.191240\pi$
$878$	28.1972			0.951608
$879$	14.9534	+	17.5095i	0.504367	+	0.590579i
$880$		−	0.229016i		−	0.00772012i
$881$	−13.8959			−0.468165			−0.234082	−	0.972217i	$-0.575209\pi$
$881$	−13.8959			−0.468165			−0.234082	+	0.972217i	$0.575209\pi$
$882$		0			0
$883$	−37.2914			−1.25495			−0.627477	−	0.778635i	$-0.715912\pi$
$883$	−37.2914			−1.25495			−0.627477	+	0.778635i	$0.715912\pi$
$884$			2.09789i			0.0705597i
$885$	−1.24819	+	3.52441i	−0.0419576	+	0.118472i
$886$	−31.4952			−1.05810
$887$	−21.1209	+	36.5825i	−0.709171	+	1.22832i	0.255993	+	0.966679i	$0.417597\pi$
$887$	−21.1209	+	36.5825i	−0.709171	+	1.22832i	−0.965165	+	0.261642i	$0.915736\pi$
$888$	−4.84996	+	4.14197i	−0.162754	+	0.138996i
$889$		0			0
$890$		−	5.16095i		−	0.172995i
$891$	1.44760	−	4.45318i	0.0484966	−	0.149187i
$892$	−3.44154	−	1.98697i	−0.115231	−	0.0665288i
$893$	29.5676	−	17.0709i	0.989443	−	0.571255i
$894$	−9.79634	+	27.6610i	−0.327639	+	0.925122i
$895$	−7.97412	+	4.60386i	−0.266545	+	0.153890i
$896$		0			0
$897$	−15.8340	+	2.93409i	−0.528682	+	0.0979666i
$898$	−24.8151			−0.828089
$899$	−23.2609	+	40.2891i	−0.775795	+	1.34372i
$900$	−11.2048	−	9.07478i	−0.373495	−	0.302493i
$901$	−2.25564	+	1.30229i	−0.0751463	+	0.0433857i
$902$	1.54369	−	2.67375i	0.0513993	−	0.0890262i
$903$		0			0
$904$	−5.30488	−	9.18833i	−0.176438	−	0.305599i
$905$	−5.54904	−	3.20374i	−0.184456	−	0.106496i
$906$	11.9614	−	10.2153i	0.397392	−	0.339381i
$907$	12.9784	+	22.4792i	0.430939	+	0.746409i	0.996954	−	0.0779859i	$-0.0248489\pi$
$907$	12.9784	+	22.4792i	0.430939	+	0.746409i	−0.566015	+	0.824395i	$0.691516\pi$
$908$	−3.63558	−	6.29701i	−0.120651	−	0.208974i
$909$	25.2011	+	20.4103i	0.835866	+	0.676966i
$910$		0			0
$911$	11.2478	+	6.49395i	0.372658	+	0.215154i	0.674619	−	0.738166i	$-0.264308\pi$
$911$	11.2478	+	6.49395i	0.372658	+	0.215154i	−0.301961	+	0.953320i	$0.597641\pi$
$912$	−5.58425	+	4.76907i	−0.184913	+	0.157920i
$913$		−	8.89937i		−	0.294526i
$914$		−	16.0818i		−	0.531940i
$915$	1.10932	+	0.392873i	0.0366729	+	0.0129880i
$916$	1.51483	+	0.874590i	0.0500515	+	0.0288973i
$917$		0			0
$918$	−1.70035	+	0.0443498i	−0.0561200	+	0.00146376i
$919$	16.9859	+	29.4204i	0.560313	+	0.970490i	0.997469	+	0.0711043i	$0.0226523\pi$
$919$	16.9859	+	29.4204i	0.560313	+	0.970490i	−0.437156	+	0.899386i	$0.644014\pi$
$920$	−0.319284	−	0.553017i	−0.0105265	−	0.0182324i
$921$	−1.71855	−	9.27425i	−0.0566282	−	0.305597i
$922$	20.3083	+	11.7250i	0.668819	+	0.386143i
$923$	−52.1186	−	90.2720i	−1.71550	−	2.97134i
$924$		0			0
$925$	8.84903	−	15.3270i	0.290954	−	0.503948i
$926$	14.5558	−	8.40381i	0.478334	−	0.276166i
$927$	−33.1577	−	5.25400i	−1.08904	−	0.172564i
$928$	3.31785	−	5.74668i	0.108914	−	0.188644i
$929$	−20.1608			−0.661454			−0.330727	−	0.943726i	$-0.607294\pi$
$929$	−20.1608			−0.661454			−0.330727	+	0.943726i	$0.607294\pi$
$930$	−1.78440	+	5.03845i	−0.0585129	+	0.165217i
$931$		0			0
$932$	−5.96755	+	3.44537i	−0.195474	+	0.112857i
$933$	−0.442024	+	0.0819085i	−0.0144712	+	0.00268156i
$934$	−5.55704	+	3.20836i	−0.181832	+	0.104981i
$935$	0.0649234	+	0.0374836i	0.00212322	+	0.00122584i
$936$	−14.9409	−	12.1006i	−0.488360	−	0.395521i
$937$		−	44.7538i		−	1.46204i	−0.682354	−	0.731022i	$-0.739044\pi$
$937$		−	44.7538i		−	1.46204i	0.682354	−	0.731022i	$-0.260956\pi$
$938$		0			0
$939$	−9.72071	−	52.4583i	−0.317223	−	1.71191i
$940$	−1.77229	+	3.06969i	−0.0578057	+	0.100122i
$941$	−23.2270			−0.757180			−0.378590	−	0.925564i	$-0.623591\pi$
$941$	−23.2270			−0.757180			−0.378590	+	0.925564i	$0.623591\pi$
$942$	−16.8249	+	3.11772i	−0.548185	+	0.101581i
$943$		−	8.60860i		−	0.280335i
$944$	4.90410			0.159615
$945$		0			0
$946$	−5.42553			−0.176399
$947$		−	54.4558i		−	1.76958i	−0.465994	−	0.884788i	$-0.654303\pi$
$947$		−	54.4558i		−	1.76958i	0.465994	−	0.884788i	$-0.345697\pi$
$948$	−2.25595	+	0.418036i	−0.0732699	+	0.0135772i
$949$	−26.4459			−0.858469
$950$	10.1888	−	17.6475i	0.330568	−	0.572560i
$951$	5.06435	+	27.3301i	0.164223	+	0.886238i
$952$		0			0
$953$		−	47.2143i		−	1.52942i	−0.644373	−	0.764711i	$-0.722882\pi$
$953$		−	47.2143i		−	1.52942i	0.644373	−	0.764711i	$-0.277118\pi$
$954$	3.73574	−	23.5760i	0.120949	−	0.763302i
$955$	7.49012	+	4.32442i	0.242375	+	0.139935i
$956$	−16.3611	+	9.44606i	−0.529154	+	0.305507i
$957$	−5.87972	+	1.08953i	−0.190064	+	0.0352196i
$958$	−11.0070	+	6.35492i	−0.355621	+	0.205318i
$959$		0			0
$960$	0.254520	−	0.718665i	0.00821461	−	0.0231948i
$961$	−18.1520			−0.585549
$962$	11.7996	−	20.4375i	0.380435	−	0.658932i
$963$	−1.28151	+	1.58231i	−0.0412960	+	0.0509892i
$964$	−14.1951	+	8.19555i	−0.457193	+	0.263961i
$965$	2.58761	−	4.48187i	0.0832982	−	0.144277i
$966$		0			0
$967$	4.23256	+	7.33101i	0.136110	+	0.235749i	0.926021	−	0.377472i	$-0.123207\pi$
$967$	4.23256	+	7.33101i	0.136110	+	0.235749i	−0.789911	+	0.613222i	$0.789873\pi$
$968$	−9.29185	−	5.36465i	−0.298651	−	0.172426i
$969$	−0.437990	−	2.36364i	−0.0140703	−	0.0759310i
$970$	2.69538	+	4.66853i	0.0865434	+	0.149898i
$971$	15.2217	+	26.3648i	0.488489	+	0.846088i	0.999912	−	0.0132412i	$-0.00421492\pi$
$971$	15.2217	+	26.3648i	0.488489	+	0.846088i	−0.511423	+	0.859329i	$0.670882\pi$
$972$	9.49178	−	12.3655i	0.304449	−	0.396624i
$973$		0			0
$974$	−2.27412	−	1.31296i	−0.0728674	−	0.0420700i
$975$	50.2905	+	17.8107i	1.61058	+	0.570400i
$976$		−	1.54358i		−	0.0494088i
$977$			21.8679i			0.699617i	0.936821	+	0.349808i	$0.113753\pi$
$977$			21.8679i			0.699617i	−0.936821	+	0.349808i	$0.886247\pi$
$978$	6.94071	−	5.92752i	0.221940	−	0.189541i
$979$	5.28295	+	3.05011i	0.168844	+	0.0974821i
$980$		0			0
$981$	−8.55457	+	53.9874i	−0.273126	+	1.72368i
$982$	2.38472	+	4.13045i	0.0760994	+	0.131808i
$983$	8.24949	+	14.2885i	0.263118	+	0.455734i	0.967069	−	0.254515i	$-0.0819158\pi$
$983$	8.24949	+	14.2885i	0.263118	+	0.455734i	−0.703951	+	0.710249i	$0.748582\pi$
$984$	7.81571	−	6.67478i	0.249156	−	0.212784i
$985$	4.82764	+	2.78724i	0.153821	+	0.0888088i
$986$	1.08608	+	1.88114i	0.0345878	+	0.0599078i
$987$		0			0
$988$	13.5861	−	23.5318i	0.432231	−	0.748646i
$989$	−13.1013	+	7.56404i	−0.416597	+	0.240522i
$990$	−0.641431	+	0.246172i	−0.0203860	+	0.00782385i
$991$	15.1320	−	26.2094i	0.480685	−	0.832571i	−0.519070	−	0.854732i	$-0.673721\pi$
$991$	15.1320	−	26.2094i	0.480685	−	0.832571i	0.999754	+	0.0221614i	$0.00705477\pi$
$992$	7.01085			0.222595
$993$	46.3466	−	8.58818i	1.47076	−	0.272538i
$994$		0			0
$995$	−6.79356	+	3.92226i	−0.215370	+	0.124344i
$996$	9.89045	−	27.9267i	0.313391	−	0.884892i
$997$	35.1065	−	20.2688i	1.11184	−	0.641919i	0.172531	−	0.985004i	$-0.444805\pi$
$997$	35.1065	−	20.2688i	1.11184	−	0.641919i	0.939304	+	0.343086i	$0.111472\pi$
$998$	−16.8608	−	9.73459i	−0.533719	−	0.308143i
$999$	16.8142	+	9.13160i	0.531977	+	0.288911i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.l.c.227.1		48
3.2	odd	2		2646.2.l.c.521.3		48
7.2	even	3		882.2.t.c.803.7		48
7.3	odd	6		882.2.m.c.587.16	yes	48
7.4	even	3		882.2.m.c.587.21	yes	48
7.5	odd	6		882.2.t.c.803.6		48
7.6	odd	2	inner	882.2.l.c.227.12		48
9.4	even	3		2646.2.t.c.2285.15		48
9.5	odd	6		882.2.t.c.815.6		48
21.2	odd	6		2646.2.t.c.1979.16		48
21.5	even	6		2646.2.t.c.1979.15		48
21.11	odd	6		2646.2.m.c.1763.11		48
21.17	even	6		2646.2.m.c.1763.12		48
21.20	even	2		2646.2.l.c.521.4		48
63.4	even	3		2646.2.m.c.881.12		48
63.5	even	6	inner	882.2.l.c.509.13		48
63.13	odd	6		2646.2.t.c.2285.16		48
63.23	odd	6	inner	882.2.l.c.509.24		48
63.31	odd	6		2646.2.m.c.881.11		48
63.32	odd	6		882.2.m.c.293.16	✓	48
63.40	odd	6		2646.2.l.c.1097.3		48
63.41	even	6		882.2.t.c.815.7		48
63.58	even	3		2646.2.l.c.1097.4		48
63.59	even	6		882.2.m.c.293.21	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.l.c.227.1		48	1.1	even	1	trivial
882.2.l.c.227.12		48	7.6	odd	2	inner
882.2.l.c.509.13		48	63.5	even	6	inner
882.2.l.c.509.24		48	63.23	odd	6	inner
882.2.m.c.293.16	✓	48	63.32	odd	6
882.2.m.c.293.21	yes	48	63.59	even	6
882.2.m.c.587.16	yes	48	7.3	odd	6
882.2.m.c.587.21	yes	48	7.4	even	3
882.2.t.c.803.6		48	7.5	odd	6
882.2.t.c.803.7		48	7.2	even	3
882.2.t.c.815.6		48	9.5	odd	6
882.2.t.c.815.7		48	63.41	even	6
2646.2.l.c.521.3		48	3.2	odd	2
2646.2.l.c.521.4		48	21.20	even	2
2646.2.l.c.1097.3		48	63.40	odd	6
2646.2.l.c.1097.4		48	63.58	even	3
2646.2.m.c.881.11		48	63.31	odd	6
2646.2.m.c.881.12		48	63.4	even	3
2646.2.m.c.1763.11		48	21.11	odd	6
2646.2.m.c.1763.12		48	21.17	even	6
2646.2.t.c.1979.15		48	21.5	even	6
2646.2.t.c.1979.16		48	21.2	odd	6
2646.2.t.c.2285.15		48	9.4	even	3
2646.2.t.c.2285.16		48	63.13	odd	6

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.70306 + 0.315583i) q^{3} -1.00000 q^{4} +(0.220087 - 0.381202i) q^{5} +(0.315583 + 1.70306i) q^{6} +1.00000i q^{8} +(2.80082 - 1.07491i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.70306 + 0.315583i) q^{3} -1.00000 q^{4} +(0.220087 - 0.381202i) q^{5} +(0.315583 + 1.70306i) q^{6} +1.00000i q^{8} +(2.80082 - 1.07491i) q^{9} +(-0.381202 - 0.220087i) q^{10} +(0.450580 - 0.260142i) q^{11} +(1.70306 - 0.315583i) q^{12} +(-5.55020 + 3.20441i) q^{13} +(-0.254520 + 0.718665i) q^{15} +1.00000 q^{16} +(-0.163672 + 0.283489i) q^{17} +(-1.07491 - 2.80082i) q^{18} +(3.67178 - 2.11990i) q^{19} +(-0.220087 + 0.381202i) q^{20} +(-0.260142 - 0.450580i) q^{22} +(-1.25636 - 0.725359i) q^{23} +(-0.315583 - 1.70306i) q^{24} +(2.40312 + 4.16233i) q^{25} +(3.20441 + 5.55020i) q^{26} +(-4.43073 + 2.71453i) q^{27} +(5.74668 + 3.31785i) q^{29} +(0.718665 + 0.254520i) q^{30} +7.01085i q^{31} -1.00000i q^{32} +(-0.685267 + 0.585233i) q^{33} +(0.283489 + 0.163672i) q^{34} +(-2.80082 + 1.07491i) q^{36} +(-1.84115 - 3.18897i) q^{37} +(-2.11990 - 3.67178i) q^{38} +(8.44106 - 7.20884i) q^{39} +(0.381202 + 0.220087i) q^{40} +(2.96701 + 5.13902i) q^{41} +(5.21400 - 9.03091i) q^{43} +(-0.450580 + 0.260142i) q^{44} +(0.206665 - 1.30425i) q^{45} +(-0.725359 + 1.25636i) q^{46} +8.05267 q^{47} +(-1.70306 + 0.315583i) q^{48} +(4.16233 - 2.40312i) q^{50} +(0.189279 - 0.534450i) q^{51} +(5.55020 - 3.20441i) q^{52} +(6.89072 + 3.97836i) q^{53} +(2.71453 + 4.43073i) q^{54} -0.229016i q^{55} +(-5.58425 + 4.76907i) q^{57} +(3.31785 - 5.74668i) q^{58} +4.90410 q^{59} +(0.254520 - 0.718665i) q^{60} -1.54358i q^{61} +7.01085 q^{62} -1.00000 q^{64} +2.82100i q^{65} +(0.585233 + 0.685267i) q^{66} +6.52412 q^{67} +(0.163672 - 0.283489i) q^{68} +(2.36856 + 0.838844i) q^{69} +16.2646i q^{71} +(1.07491 + 2.80082i) q^{72} +(3.57364 + 2.06324i) q^{73} +(-3.18897 + 1.84115i) q^{74} +(-5.40622 - 6.33031i) q^{75} +(-3.67178 + 2.11990i) q^{76} +(-7.20884 - 8.44106i) q^{78} -1.32465 q^{79} +(0.220087 - 0.381202i) q^{80} +(6.68913 - 6.02126i) q^{81} +(5.13902 - 2.96701i) q^{82} +(8.55240 - 14.8132i) q^{83} +(0.0720443 + 0.124784i) q^{85} +(-9.03091 - 5.21400i) q^{86} +(-10.8340 - 3.83693i) q^{87} +(0.260142 + 0.450580i) q^{88} +(5.86239 + 10.1540i) q^{89} +(-1.30425 - 0.206665i) q^{90} +(1.25636 + 0.725359i) q^{92} +(-2.21250 - 11.9399i) q^{93} -8.05267i q^{94} -1.86625i q^{95} +(0.315583 + 1.70306i) q^{96} +(-10.6061 - 6.12344i) q^{97} +(0.982361 - 1.21294i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} + 16 q^{9}+O(q^{10}) \) 48 * q - 48 * q^4 + 16 * q^9	\( 48 q - 48 q^{4} + 16 q^{9} - 48 q^{11} + 48 q^{15} + 48 q^{16} + 16 q^{18} - 48 q^{23} - 24 q^{25} - 16 q^{30} - 16 q^{36} + 32 q^{39} + 48 q^{44} - 48 q^{50} - 48 q^{51} + 96 q^{53} - 80 q^{57} - 48 q^{60} - 48 q^{64} - 16 q^{72} + 32 q^{78} - 96 q^{79} + 96 q^{81} + 48 q^{85} - 96 q^{86} + 48 q^{92} + 104 q^{99}+O(q^{100}) \) 48 * q - 48 * q^4 + 16 * q^9 - 48 * q^11 + 48 * q^15 + 48 * q^16 + 16 * q^18 - 48 * q^23 - 24 * q^25 - 16 * q^30 - 16 * q^36 + 32 * q^39 + 48 * q^44 - 48 * q^50 - 48 * q^51 + 96 * q^53 - 80 * q^57 - 48 * q^60 - 48 * q^64 - 16 * q^72 + 32 * q^78 - 96 * q^79 + 96 * q^81 + 48 * q^85 - 96 * q^86 + 48 * q^92 + 104 * q^99

Introduction

L-functions

Modular forms

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