LMFDB - Embedded newform 882.2.l.c.227.18

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			227.18
Character	$\chi$	$=$	882.227
Dual form			882.2.l.c.509.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-0.765075 - 1.55392i) q^{3} -1.00000 q^{4} +(-0.474556 + 0.821956i) q^{5} +(1.55392 - 0.765075i) q^{6} -1.00000i q^{8} +(-1.82932 + 2.37773i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-0.765075 - 1.55392i) q^{3} -1.00000 q^{4} +(-0.474556 + 0.821956i) q^{5} +(1.55392 - 0.765075i) q^{6} -1.00000i q^{8} +(-1.82932 + 2.37773i) q^{9} +(-0.821956 - 0.474556i) q^{10} +(-1.51873 + 0.876838i) q^{11} +(0.765075 + 1.55392i) q^{12} +(0.720756 - 0.416129i) q^{13} +(1.64032 + 0.108564i) q^{15} +1.00000 q^{16} +(2.73638 - 4.73955i) q^{17} +(-2.37773 - 1.82932i) q^{18} +(3.21232 - 1.85463i) q^{19} +(0.474556 - 0.821956i) q^{20} +(-0.876838 - 1.51873i) q^{22} +(0.888998 + 0.513263i) q^{23} +(-1.55392 + 0.765075i) q^{24} +(2.04959 + 3.55000i) q^{25} +(0.416129 + 0.720756i) q^{26} +(5.09436 + 1.02347i) q^{27} +(-6.58867 - 3.80397i) q^{29} +(-0.108564 + 1.64032i) q^{30} -11.0016i q^{31} +1.00000i q^{32} +(2.52447 + 1.68913i) q^{33} +(4.73955 + 2.73638i) q^{34} +(1.82932 - 2.37773i) q^{36} +(-2.19830 - 3.80756i) q^{37} +(1.85463 + 3.21232i) q^{38} +(-1.19806 - 0.801626i) q^{39} +(0.821956 + 0.474556i) q^{40} +(-4.05647 - 7.02601i) q^{41} +(3.08463 - 5.34273i) q^{43} +(1.51873 - 0.876838i) q^{44} +(-1.08627 - 2.63199i) q^{45} +(-0.513263 + 0.888998i) q^{46} -6.80125 q^{47} +(-0.765075 - 1.55392i) q^{48} +(-3.55000 + 2.04959i) q^{50} +(-9.45841 - 0.625999i) q^{51} +(-0.720756 + 0.416129i) q^{52} +(1.88177 + 1.08644i) q^{53} +(-1.02347 + 5.09436i) q^{54} -1.66444i q^{55} +(-5.33961 - 3.57275i) q^{57} +(3.80397 - 6.58867i) q^{58} +10.8659 q^{59} +(-1.64032 - 0.108564i) q^{60} -1.09663i q^{61} +11.0016 q^{62} -1.00000 q^{64} +0.789907i q^{65} +(-1.68913 + 2.52447i) q^{66} +14.4481 q^{67} +(-2.73638 + 4.73955i) q^{68} +(0.117419 - 1.77412i) q^{69} -11.0131i q^{71} +(2.37773 + 1.82932i) q^{72} +(-3.16204 - 1.82561i) q^{73} +(3.80756 - 2.19830i) q^{74} +(3.94831 - 5.90091i) q^{75} +(-3.21232 + 1.85463i) q^{76} +(0.801626 - 1.19806i) q^{78} +9.84819 q^{79} +(-0.474556 + 0.821956i) q^{80} +(-2.30717 - 8.69925i) q^{81} +(7.02601 - 4.05647i) q^{82} +(-2.41103 + 4.17603i) q^{83} +(2.59713 + 4.49837i) q^{85} +(5.34273 + 3.08463i) q^{86} +(-0.870230 + 13.1486i) q^{87} +(0.876838 + 1.51873i) q^{88} +(2.15943 + 3.74024i) q^{89} +(2.63199 - 1.08627i) q^{90} +(-0.888998 - 0.513263i) q^{92} +(-17.0957 + 8.41708i) q^{93} -6.80125i q^{94} +3.52051i q^{95} +(1.55392 - 0.765075i) q^{96} +(-3.90396 - 2.25395i) q^{97} +(0.693358 - 5.21514i) 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
$3$	−0.765075	−	1.55392i	−0.441716	−	0.897155i
$3$	−0.765075	−	1.55392i	−0.441716	−	0.897155i
$4$	−1.00000			−0.500000
$5$	−0.474556	+	0.821956i	−0.212228	+	0.367590i	−0.952412	−	0.304815i	$-0.901405\pi$
$5$	−0.474556	+	0.821956i	−0.212228	+	0.367590i	0.740183	+	0.672405i	$0.234739\pi$
$6$	1.55392	−	0.765075i	0.634384	−	0.312341i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−1.82932	+	2.37773i	−0.609773	+	0.792576i
$10$	−0.821956	−	0.474556i	−0.259925	−	0.150068i
$11$	−1.51873	+	0.876838i	−0.457914	+	0.264377i	−0.711167	−	0.703024i	$-0.751833\pi$
$11$	−1.51873	+	0.876838i	−0.457914	+	0.264377i	0.253253	+	0.967400i	$0.418500\pi$
$12$	0.765075	+	1.55392i	0.220858	+	0.448577i
$13$	0.720756	−	0.416129i	0.199902	−	0.115413i	−0.396708	−	0.917945i	$-0.629847\pi$
$13$	0.720756	−	0.416129i	0.199902	−	0.115413i	0.596610	+	0.802532i	$0.296514\pi$
$14$		0			0
$15$	1.64032	+	0.108564i	0.423530	+	0.0280310i
$16$	1.00000			0.250000
$17$	2.73638	−	4.73955i	0.663670	−	1.14951i	−0.315975	−	0.948768i	$-0.602331\pi$
$17$	2.73638	−	4.73955i	0.663670	−	1.14951i	0.979644	−	0.200742i	$-0.0643352\pi$
$18$	−2.37773	−	1.82932i	−0.560436	−	0.431175i
$19$	3.21232	−	1.85463i	0.736957	−	0.425482i	−0.0840051	−	0.996465i	$-0.526771\pi$
$19$	3.21232	−	1.85463i	0.736957	−	0.425482i	0.820962	+	0.570983i	$0.193438\pi$
$20$	0.474556	−	0.821956i	0.106114	−	0.183795i
$21$		0			0
$22$	−0.876838	−	1.51873i	−0.186942	−	0.323794i
$23$	0.888998	+	0.513263i	0.185369	+	0.107023i	0.589813	−	0.807540i	$-0.299202\pi$
$23$	0.888998	+	0.513263i	0.185369	+	0.107023i	−0.404444	+	0.914563i	$0.632535\pi$
$24$	−1.55392	+	0.765075i	−0.317192	+	0.156170i
$25$	2.04959	+	3.55000i	0.409918	+	0.710000i
$26$	0.416129	+	0.720756i	0.0816096	+	0.141352i
$27$	5.09436	+	1.02347i	0.980410	+	0.196968i
$28$		0			0
$29$	−6.58867	−	3.80397i	−1.22348	−	0.706379i	−0.257826	−	0.966191i	$-0.583006\pi$
$29$	−6.58867	−	3.80397i	−1.22348	−	0.706379i	−0.965659	+	0.259812i	$0.916339\pi$
$30$	−0.108564	+	1.64032i	−0.0198209	+	0.299481i
$31$		−	11.0016i		−	1.97595i	−0.154602	−	0.987977i	$-0.549409\pi$
$31$		−	11.0016i		−	1.97595i	0.154602	−	0.987977i	$-0.450591\pi$
$32$			1.00000i			0.176777i
$33$	2.52447	+	1.68913i	0.439455	+	0.294040i
$34$	4.73955	+	2.73638i	0.812826	+	0.469285i
$35$		0			0
$36$	1.82932	−	2.37773i	0.304887	−	0.396288i
$37$	−2.19830	−	3.80756i	−0.361398	−	0.625959i	0.626794	−	0.779185i	$-0.284367\pi$
$37$	−2.19830	−	3.80756i	−0.361398	−	0.625959i	−0.988191	+	0.153226i	$0.951034\pi$
$38$	1.85463	+	3.21232i	0.300861	+	0.521107i
$39$	−1.19806	−	0.801626i	−0.191844	−	0.128363i
$40$	0.821956	+	0.474556i	0.129963	+	0.0750340i
$41$	−4.05647	−	7.02601i	−0.633514	−	1.09728i	−0.986828	−	0.161774i	$-0.948278\pi$
$41$	−4.05647	−	7.02601i	−0.633514	−	1.09728i	0.353314	−	0.935505i	$-0.385055\pi$
$42$		0			0
$43$	3.08463	−	5.34273i	0.470401	−	0.814759i	−0.529026	−	0.848606i	$-0.677443\pi$
$43$	3.08463	−	5.34273i	0.470401	−	0.814759i	0.999427	+	0.0338470i	$0.0107759\pi$
$44$	1.51873	−	0.876838i	0.228957	−	0.132188i
$45$	−1.08627	−	2.63199i	−0.161932	−	0.392353i
$46$	−0.513263	+	0.888998i	−0.0756766	+	0.131076i
$47$	−6.80125			−0.992064			−0.496032	−	0.868304i	$-0.665210\pi$
$47$	−6.80125			−0.992064			−0.496032	+	0.868304i	$0.665210\pi$
$48$	−0.765075	−	1.55392i	−0.110429	−	0.224289i
$49$		0			0
$50$	−3.55000	+	2.04959i	−0.502046	+	0.289856i
$51$	−9.45841	−	0.625999i	−1.32444	−	0.0876573i
$52$	−0.720756	+	0.416129i	−0.0999509	+	0.0577067i
$53$	1.88177	+	1.08644i	0.258480	+	0.149234i	0.623641	−	0.781711i	$-0.285653\pi$
$53$	1.88177	+	1.08644i	0.258480	+	0.149234i	−0.365161	+	0.930944i	$0.618986\pi$
$54$	−1.02347	+	5.09436i	−0.139277	+	0.693255i
$55$		−	1.66444i		−	0.224433i
$56$		0			0
$57$	−5.33961	−	3.57275i	−0.707249	−	0.473222i
$58$	3.80397	−	6.58867i	0.499486	−	0.865134i
$59$	10.8659			1.41462			0.707311	−	0.706902i	$-0.249908\pi$
$59$	10.8659			1.41462			0.707311	+	0.706902i	$0.249908\pi$
$60$	−1.64032	−	0.108564i	−0.211765	−	0.0140155i
$61$		−	1.09663i		−	0.140409i	−0.997533	−	0.0702043i	$-0.977635\pi$
$61$		−	1.09663i		−	0.140409i	0.997533	−	0.0702043i	$-0.0223651\pi$
$62$	11.0016			1.39721
$63$		0			0
$64$	−1.00000			−0.125000
$65$			0.789907i			0.0979759i
$66$	−1.68913	+	2.52447i	−0.207918	+	0.310741i
$67$	14.4481			1.76512			0.882559	−	0.470202i	$-0.155819\pi$
$67$	14.4481			1.76512			0.882559	+	0.470202i	$0.155819\pi$
$68$	−2.73638	+	4.73955i	−0.331835	+	0.574755i
$69$	0.117419	−	1.77412i	0.0141355	−	0.213578i
$70$		0			0
$71$		−	11.0131i		−	1.30701i	−0.756922	−	0.653505i	$-0.773298\pi$
$71$		−	11.0131i		−	1.30701i	0.756922	−	0.653505i	$-0.226702\pi$
$72$	2.37773	+	1.82932i	0.280218	+	0.215587i
$73$	−3.16204	−	1.82561i	−0.370089	−	0.213671i	0.303408	−	0.952861i	$-0.401875\pi$
$73$	−3.16204	−	1.82561i	−0.370089	−	0.213671i	−0.673497	+	0.739190i	$0.735209\pi$
$74$	3.80756	−	2.19830i	0.442620	−	0.255547i
$75$	3.94831	−	5.90091i	0.455912	−	0.681379i
$76$	−3.21232	+	1.85463i	−0.368478	+	0.212741i
$77$		0			0
$78$	0.801626	−	1.19806i	0.0907663	−	0.135654i
$79$	9.84819			1.10801			0.554004	−	0.832514i	$-0.313099\pi$
$79$	9.84819			1.10801			0.554004	+	0.832514i	$0.313099\pi$
$80$	−0.474556	+	0.821956i	−0.0530570	+	0.0918975i
$81$	−2.30717	−	8.69925i	−0.256353	−	0.966583i
$82$	7.02601	−	4.05647i	0.775893	−	0.447962i
$83$	−2.41103	+	4.17603i	−0.264645	+	0.458379i	−0.967471	−	0.252983i	$-0.918588\pi$
$83$	−2.41103	+	4.17603i	−0.264645	+	0.458379i	0.702825	+	0.711363i	$0.251922\pi$
$84$		0			0
$85$	2.59713	+	4.49837i	0.281699	+	0.487916i
$86$	5.34273	+	3.08463i	0.576121	+	0.332624i
$87$	−0.870230	+	13.1486i	−0.0932984	+	1.40967i
$88$	0.876838	+	1.51873i	0.0934712	+	0.161897i
$89$	2.15943	+	3.74024i	0.228899	+	0.396465i	0.957482	−	0.288493i	$-0.0931541\pi$
$89$	2.15943	+	3.74024i	0.228899	+	0.396465i	−0.728583	+	0.684957i	$0.759821\pi$
$90$	2.63199	−	1.08627i	0.277436	−	0.114503i
$91$		0			0
$92$	−0.888998	−	0.513263i	−0.0926845	−	0.0535114i
$93$	−17.0957	+	8.41708i	−1.77274	+	0.872811i
$94$		−	6.80125i		−	0.701495i
$95$			3.52051i			0.361197i
$96$	1.55392	−	0.765075i	0.158596	−	0.0780851i
$97$	−3.90396	−	2.25395i	−0.396387	−	0.228854i	0.288537	−	0.957469i	$-0.406831\pi$
$97$	−3.90396	−	2.25395i	−0.396387	−	0.228854i	−0.684924	+	0.728615i	$0.740164\pi$
$98$		0			0
$99$	0.693358	−	5.21514i	0.0696851	−	0.524141i
$100$	−2.04959	−	3.55000i	−0.204959	−	0.355000i
$101$	6.33624	+	10.9747i	0.630480	+	1.09202i	0.987454	+	0.157909i	$0.0504751\pi$
$101$	6.33624	+	10.9747i	0.630480	+	1.09202i	−0.356974	+	0.934114i	$0.616192\pi$
$102$	0.625999	−	9.45841i	0.0619831	−	0.936522i
$103$	−7.33341	−	4.23394i	−0.722582	−	0.417183i	0.0931202	−	0.995655i	$-0.470316\pi$
$103$	−7.33341	−	4.23394i	−0.722582	−	0.417183i	−0.815702	+	0.578472i	$0.803649\pi$
$104$	−0.416129	−	0.720756i	−0.0408048	−	0.0706760i
$105$		0			0
$106$	−1.08644	+	1.88177i	−0.105524	+	0.182773i
$107$	−1.28657	+	0.742804i	−0.124378	+	0.0718096i	−0.560898	−	0.827885i	$-0.689544\pi$
$107$	−1.28657	+	0.742804i	−0.124378	+	0.0718096i	0.436520	+	0.899694i	$0.356211\pi$
$108$	−5.09436	−	1.02347i	−0.490205	−	0.0984838i
$109$	7.60276	−	13.1684i	0.728213	−	1.26130i	−0.229425	−	0.973326i	$-0.573685\pi$
$109$	7.60276	−	13.1684i	0.728213	−	1.26130i	0.957638	−	0.287975i	$-0.0929820\pi$
$110$	1.66444			0.158698
$111$	−4.23477	+	6.32904i	−0.401947	+	0.600726i
$112$		0			0
$113$	−17.0031	+	9.81676i	−1.59952	+	0.923483i	−0.607941	+	0.793982i	$0.708004\pi$
$113$	−17.0031	+	9.81676i	−1.59952	+	0.923483i	−0.991579	+	0.129501i	$0.958662\pi$
$114$	3.57275	−	5.33961i	0.334618	−	0.500101i
$115$	−0.843760	+	0.487145i	−0.0786810	+	0.0454265i
$116$	6.58867	+	3.80397i	0.611742	+	0.353190i
$117$	−0.329053	+	2.47500i	−0.0304210	+	0.228813i
$118$			10.8659i			1.00029i
$119$		0			0
$120$	0.108564	−	1.64032i	0.00991047	−	0.149740i
$121$	−3.96231	+	6.86292i	−0.360210	+	0.623902i
$122$	1.09663			0.0992838
$123$	−7.81434	+	11.6788i	−0.704595	+	1.05305i
$124$			11.0016i			0.987977i
$125$	−8.63615			−0.772441
$126$		0			0
$127$	18.7051			1.65981			0.829903	−	0.557907i	$-0.188395\pi$
$127$	18.7051			1.65981			0.829903	+	0.557907i	$0.188395\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−10.6621	−	0.705666i	−0.938748	−	0.0621305i
$130$	−0.789907			−0.0692794
$131$	3.32193	−	5.75375i	0.290238	−	0.502707i	−0.683628	−	0.729831i	$-0.739599\pi$
$131$	3.32193	−	5.75375i	0.290238	−	0.502707i	0.973866	+	0.227124i	$0.0729321\pi$
$132$	−2.52447	−	1.68913i	−0.219727	−	0.147020i
$133$		0			0
$134$			14.4481i			1.24813i
$135$	−3.25881	+	3.70164i	−0.280474	+	0.318587i
$136$	−4.73955	−	2.73638i	−0.406413	−	0.234643i
$137$	−17.6798	+	10.2074i	−1.51049	+	0.872080i	−0.510562	+	0.859841i	$0.670563\pi$
$137$	−17.6798	+	10.2074i	−1.51049	+	0.872080i	−0.999925	+	0.0122395i	$0.996104\pi$
$138$	1.77412	+	0.117419i	0.151023	+	0.00999534i
$139$	−10.9829	+	6.34099i	−0.931559	+	0.537836i	−0.887304	−	0.461184i	$-0.847425\pi$
$139$	−10.9829	+	6.34099i	−0.931559	+	0.537836i	−0.0442550	+	0.999020i	$0.514091\pi$
$140$		0			0
$141$	5.20346	+	10.5686i	0.438211	+	0.890035i
$142$	11.0131			0.924196
$143$	−0.729755	+	1.26397i	−0.0610252	+	0.105699i
$144$	−1.82932	+	2.37773i	−0.152443	+	0.198144i
$145$	6.25339	−	3.61040i	0.519316	−	0.299827i
$146$	1.82561	−	3.16204i	0.151088	−	0.261693i
$147$		0			0
$148$	2.19830	+	3.80756i	0.180699	+	0.312979i
$149$	17.1827	+	9.92046i	1.40767	+	0.812716i	0.995163	−	0.0982404i	$-0.0313214\pi$
$149$	17.1827	+	9.92046i	1.40767	+	0.812716i	0.412503	+	0.910956i	$0.364655\pi$
$150$	5.90091	+	3.94831i	0.481807	+	0.322378i
$151$	−0.872422	−	1.51108i	−0.0709967	−	0.122970i	0.828342	−	0.560223i	$-0.189285\pi$
$151$	−0.872422	−	1.51108i	−0.0709967	−	0.122970i	−0.899338	+	0.437253i	$0.855951\pi$
$152$	−1.85463	−	3.21232i	−0.150431	−	0.260553i
$153$	6.26364	+	15.1765i	0.506385	+	1.22695i
$154$		0			0
$155$	9.04287	+	5.22090i	0.726341	+	0.419353i
$156$	1.19806	+	0.801626i	0.0959218	+	0.0641815i
$157$		−	9.49564i		−	0.757835i	−0.925431	−	0.378917i	$-0.876296\pi$
$157$		−	9.49564i		−	0.757835i	0.925431	−	0.378917i	$-0.123704\pi$
$158$			9.84819i			0.783480i
$159$	0.248543	−	3.75532i	0.0197108	−	0.297816i
$160$	−0.821956	−	0.474556i	−0.0649813	−	0.0375170i
$161$		0			0
$162$	8.69925	−	2.30717i	0.683478	−	0.181269i
$163$	−5.92061	−	10.2548i	−0.463738	−	0.803217i	0.535406	−	0.844595i	$-0.320159\pi$
$163$	−5.92061	−	10.2548i	−0.463738	−	0.803217i	−0.999144	+	0.0413777i	$0.986825\pi$
$164$	4.05647	+	7.02601i	0.316757	+	0.548639i
$165$	−2.58640	+	1.27342i	−0.201351	+	0.0991355i
$166$	−4.17603	−	2.41103i	−0.324123	−	0.187133i
$167$	−1.73229	−	3.00041i	−0.134048	−	0.232179i	0.791185	−	0.611577i	$-0.209464\pi$
$167$	−1.73229	−	3.00041i	−0.134048	−	0.232179i	−0.925234	+	0.379398i	$0.876131\pi$
$168$		0			0
$169$	−6.15367	+	10.6585i	−0.473359	+	0.819883i
$170$	−4.49837	+	2.59713i	−0.345009	+	0.199191i
$171$	−1.46655	+	11.0307i	−0.112150	+	0.843542i
$172$	−3.08463	+	5.34273i	−0.235201	+	0.407379i
$173$	−3.09982			−0.235675			−0.117838	−	0.993033i	$-0.537596\pi$
$173$	−3.09982			−0.235675			−0.117838	+	0.993033i	$0.537596\pi$
$174$	−13.1486	−	0.870230i	−0.996790	−	0.0659719i
$175$		0			0
$176$	−1.51873	+	0.876838i	−0.114478	+	0.0660941i
$177$	−8.31325	−	16.8848i	−0.624862	−	1.26914i
$178$	−3.74024	+	2.15943i	−0.280343	+	0.161856i
$179$	0.500470	+	0.288947i	0.0374069	+	0.0215969i	0.518587	−	0.855025i	$-0.326458\pi$
$179$	0.500470	+	0.288947i	0.0374069	+	0.0215969i	−0.481180	+	0.876622i	$0.659792\pi$
$180$	1.08627	+	2.63199i	0.0809659	+	0.196177i
$181$		−	26.0581i		−	1.93688i	−0.249238	−	0.968442i	$-0.580180\pi$
$181$		−	26.0581i		−	1.93688i	0.249238	−	0.968442i	$-0.419820\pi$
$182$		0			0
$183$	−1.70407	+	0.839001i	−0.125968	+	0.0620207i
$184$	0.513263	−	0.888998i	0.0378383	−	0.0655378i
$185$	4.17286			0.306795
$186$	−8.41708	−	17.0957i	−0.617171	−	1.25351i
$187$			9.59745i			0.701835i
$188$	6.80125			0.496032
$189$		0			0
$190$	−3.52051			−0.255405
$191$			1.77964i			0.128770i	0.997925	+	0.0643852i	$0.0205086\pi$
$191$			1.77964i			0.128770i	−0.997925	+	0.0643852i	$0.979491\pi$
$192$	0.765075	+	1.55392i	0.0552145	+	0.112144i
$193$	−1.48335			−0.106774			−0.0533871	−	0.998574i	$-0.517002\pi$
$193$	−1.48335			−0.106774			−0.0533871	+	0.998574i	$0.517002\pi$
$194$	2.25395	−	3.90396i	0.161824	−	0.280288i
$195$	1.22745	−	0.604338i	0.0878995	−	0.0432775i
$196$		0			0
$197$			2.44809i			0.174419i	0.996190	+	0.0872096i	$0.0277950\pi$
$197$			2.44809i			0.174419i	−0.996190	+	0.0872096i	$0.972205\pi$
$198$	5.21514	+	0.693358i	0.370624	+	0.0492748i
$199$	9.47403	+	5.46984i	0.671596	+	0.387746i	0.796681	−	0.604400i	$-0.206587\pi$
$199$	9.47403	+	5.46984i	0.671596	+	0.387746i	−0.125085	+	0.992146i	$0.539920\pi$
$200$	3.55000	−	2.04959i	0.251023	−	0.144928i
$201$	−11.0539	−	22.4512i	−0.779681	−	1.58358i
$202$	−10.9747	+	6.33624i	−0.772177	+	0.445816i
$203$		0			0
$204$	9.45841	+	0.625999i	0.662221	+	0.0438287i
$205$	7.70010			0.537798
$206$	4.23394	−	7.33341i	0.294993	−	0.510943i
$207$	−2.84666	+	1.17487i	−0.197857	+	0.0816593i
$208$	0.720756	−	0.416129i	0.0499755	−	0.0288534i
$209$	−3.25243	+	5.63337i	−0.224975	+	0.389668i
$210$		0			0
$211$	12.7481	+	22.0804i	0.877617	+	1.52008i	0.853949	+	0.520357i	$0.174201\pi$
$211$	12.7481	+	22.0804i	0.877617	+	1.52008i	0.0236678	+	0.999720i	$0.492466\pi$
$212$	−1.88177	−	1.08644i	−0.129240	−	0.0746169i
$213$	−17.1134	+	8.42582i	−1.17259	+	0.577328i
$214$	−0.742804	−	1.28657i	−0.0507770	−	0.0879484i
$215$	2.92766	+	5.07085i	0.199665	+	0.345829i
$216$	1.02347	−	5.09436i	0.0696386	−	0.346627i
$217$		0			0
$218$	13.1684	+	7.60276i	0.891875	+	0.514924i
$219$	−0.417642	+	6.31028i	−0.0282216	+	0.426409i
$220$			1.66444i			0.112216i
$221$		−	4.55475i		−	0.306385i
$222$	−6.32904	−	4.23477i	−0.424777	−	0.284219i
$223$	13.3108	+	7.68501i	0.891359	+	0.514626i	0.874387	−	0.485230i	$-0.161264\pi$
$223$	13.3108	+	7.68501i	0.891359	+	0.514626i	0.0169720	+	0.999856i	$0.494597\pi$
$224$		0			0
$225$	−12.1903	−	1.62071i	−0.812686	−	0.108047i
$226$	−9.81676	−	17.0031i	−0.653001	−	1.13103i
$227$	4.17388	+	7.22937i	0.277030	+	0.479830i	0.970645	−	0.240515i	$-0.0773165\pi$
$227$	4.17388	+	7.22937i	0.277030	+	0.479830i	−0.693615	+	0.720346i	$0.743983\pi$
$228$	5.33961	+	3.57275i	0.353625	+	0.236611i
$229$	−11.3671	−	6.56281i	−0.751161	−	0.433683i	0.0749523	−	0.997187i	$-0.476120\pi$
$229$	−11.3671	−	6.56281i	−0.751161	−	0.433683i	−0.826113	+	0.563504i	$0.809453\pi$
$230$	−0.487145	−	0.843760i	−0.0321214	−	0.0556359i
$231$		0			0
$232$	−3.80397	+	6.58867i	−0.249743	+	0.432567i
$233$	9.84350	−	5.68315i	0.644869	−	0.372315i	−0.141619	−	0.989921i	$-0.545231\pi$
$233$	9.84350	−	5.68315i	0.644869	−	0.372315i	0.786488	+	0.617606i	$0.211897\pi$
$234$	−2.47500	−	0.329053i	−0.161796	−	0.0215109i
$235$	3.22758	−	5.59033i	0.210544	−	0.364673i
$236$	−10.8659			−0.707311
$237$	−7.53460	−	15.3033i	−0.489425	−	0.994054i
$238$		0			0
$239$	4.67039	−	2.69645i	0.302102	−	0.174419i	−0.341285	−	0.939960i	$-0.610862\pi$
$239$	4.67039	−	2.69645i	0.302102	−	0.174419i	0.643387	+	0.765541i	$0.277529\pi$
$240$	1.64032	+	0.108564i	0.105882	+	0.00700776i
$241$	−12.1233	+	6.99936i	−0.780928	+	0.450869i	−0.836759	−	0.547572i	$-0.815552\pi$
$241$	−12.1233	+	6.99936i	−0.780928	+	0.450869i	0.0558314	+	0.998440i	$0.482219\pi$
$242$	−6.86292	−	3.96231i	−0.441165	−	0.254707i
$243$	−11.7528	+	10.2407i	−0.753940	+	0.656944i
$244$			1.09663i			0.0702043i
$245$		0			0
$246$	−11.6788	−	7.81434i	−0.744616	−	0.498224i
$247$	1.54353	−	2.67348i	0.0982127	−	0.170109i
$248$	−11.0016			−0.698605
$249$	8.33384	+	0.551570i	0.528135	+	0.0349543i
$250$		−	8.63615i		−	0.546198i
$251$	−16.5094			−1.04207			−0.521033	−	0.853536i	$-0.674453\pi$
$251$	−16.5094			−1.04207			−0.521033	+	0.853536i	$0.674453\pi$
$252$		0			0
$253$	−1.80019			−0.113177
$254$			18.7051i			1.17366i
$255$	5.00309	−	7.47732i	0.313306	−	0.468248i
$256$	1.00000			0.0625000
$257$	3.06000	−	5.30007i	0.190878	−	0.330610i	−0.754664	−	0.656112i	$-0.772200\pi$
$257$	3.06000	−	5.30007i	0.190878	−	0.330610i	0.945541	+	0.325502i	$0.105533\pi$
$258$	0.705666	−	10.6621i	0.0439329	−	0.663795i
$259$		0			0
$260$		−	0.789907i		−	0.0489879i
$261$	21.0976	−	8.70738i	1.30591	−	0.538973i
$262$	5.75375	+	3.32193i	0.355468	+	0.205229i
$263$	−14.1668	+	8.17923i	−0.873565	+	0.504353i	−0.868531	−	0.495634i	$-0.834936\pi$
$263$	−14.1668	+	8.17923i	−0.873565	+	0.504353i	−0.00503369	+	0.999987i	$0.501602\pi$
$264$	1.68913	−	2.52447i	0.103959	−	0.155371i
$265$	−1.78601	+	1.03115i	−0.109714	+	0.0633432i
$266$		0			0
$267$	4.15990	−	6.21714i	0.254582	−	0.380483i
$268$	−14.4481			−0.882559
$269$	2.65845	−	4.60457i	0.162088	−	0.280745i	−0.773529	−	0.633761i	$-0.781510\pi$
$269$	2.65845	−	4.60457i	0.162088	−	0.280745i	0.935617	+	0.353015i	$0.114844\pi$
$270$	−3.70164	−	3.25881i	−0.225275	−	0.198325i
$271$	−14.2825	+	8.24602i	−0.867601	+	0.500910i	−0.866550	−	0.499090i	$-0.833668\pi$
$271$	−14.2825	+	8.24602i	−0.867601	+	0.500910i	−0.00105086	+	0.999999i	$0.500334\pi$
$272$	2.73638	−	4.73955i	0.165917	−	0.287377i
$273$		0			0
$274$	−10.2074	−	17.6798i	−0.616654	−	1.06808i
$275$	−6.22554	−	3.59432i	−0.375414	−	0.216746i
$276$	−0.117419	+	1.77412i	−0.00706777	+	0.106789i
$277$	−7.31402	−	12.6682i	−0.439457	−	0.761161i	0.558191	−	0.829713i	$-0.311496\pi$
$277$	−7.31402	−	12.6682i	−0.439457	−	0.761161i	−0.997648	+	0.0685513i	$0.978162\pi$
$278$	−6.34099	−	10.9829i	−0.380308	−	0.658712i
$279$	26.1589	+	20.1255i	1.56609	+	1.20488i
$280$		0			0
$281$	3.62307	+	2.09178i	0.216134	+	0.124785i	0.604159	−	0.796864i	$-0.293509\pi$
$281$	3.62307	+	2.09178i	0.216134	+	0.124785i	−0.388025	+	0.921649i	$0.626842\pi$
$282$	−10.5686	+	5.20346i	−0.629350	+	0.309862i
$283$		−	9.70591i		−	0.576957i	−0.957486	−	0.288478i	$-0.906851\pi$
$283$		−	9.70591i		−	0.576957i	0.957486	−	0.288478i	$-0.0931493\pi$
$284$			11.0131i			0.653505i
$285$	5.47059	−	2.69346i	0.324050	−	0.159547i
$286$	−1.26397	−	0.729755i	−0.0747403	−	0.0431513i
$287$		0			0
$288$	−2.37773	−	1.82932i	−0.140109	−	0.107794i
$289$	−6.47555	−	11.2160i	−0.380915	−	0.659764i
$290$	3.61040	+	6.25339i	0.212010	+	0.367212i
$291$	−0.515633	+	7.79087i	−0.0302270	+	0.456709i
$292$	3.16204	+	1.82561i	0.185045	+	0.106836i
$293$	−1.01377	−	1.75591i	−0.0592253	−	0.102581i	0.834893	−	0.550413i	$-0.185530\pi$
$293$	−1.01377	−	1.75591i	−0.0592253	−	0.102581i	−0.894118	+	0.447832i	$0.852196\pi$
$294$		0			0
$295$	−5.15650	+	8.93131i	−0.300223	+	0.520001i
$296$	−3.80756	+	2.19830i	−0.221310	+	0.127773i
$297$	−8.63437	+	2.91255i	−0.501017	+	0.169003i
$298$	−9.92046	+	17.1827i	−0.574677	+	0.995370i
$299$	0.854335			0.0494075
$300$	−3.94831	+	5.90091i	−0.227956	+	0.340689i
$301$		0			0
$302$	1.51108	−	0.872422i	0.0869528	−	0.0502022i
$303$	12.2061	−	18.2425i	0.701220	−	1.04800i
$304$	3.21232	−	1.85463i	0.184239	−	0.106371i
$305$	0.901378	+	0.520411i	0.0516128	+	0.0297986i
$306$	−15.1765	+	6.26364i	−0.867584	+	0.358068i
$307$		−	9.79004i		−	0.558747i	−0.960183	−	0.279374i	$-0.909873\pi$
$307$		−	9.79004i		−	0.558747i	0.960183	−	0.279374i	$-0.0901268\pi$
$308$		0			0
$309$	−0.968595	+	14.6348i	−0.0551014	+	0.832545i
$310$	−5.22090	+	9.04287i	−0.296527	+	0.513600i
$311$	−13.7039			−0.777076			−0.388538	−	0.921433i	$-0.627020\pi$
$311$	−13.7039			−0.777076			−0.388538	+	0.921433i	$0.627020\pi$
$312$	−0.801626	+	1.19806i	−0.0453832	+	0.0678270i
$313$			18.8585i			1.06595i	0.846132	+	0.532974i	$0.178926\pi$
$313$			18.8585i			1.06595i	−0.846132	+	0.532974i	$0.821074\pi$
$314$	9.49564			0.535870
$315$		0			0
$316$	−9.84819			−0.554004
$317$		−	7.86426i		−	0.441701i	−0.975308	−	0.220850i	$-0.929117\pi$
$317$		−	7.86426i		−	0.441701i	0.975308	−	0.220850i	$-0.0708832\pi$
$318$	3.75532	+	0.248543i	0.210588	+	0.0139376i
$319$	13.3419			0.747000
$320$	0.474556	−	0.821956i	0.0265285	−	0.0459487i
$321$	2.13858	+	1.43093i	0.119364	+	0.0798667i
$322$		0			0
$323$		−	20.2999i		−	1.12952i
$324$	2.30717	+	8.69925i	0.128176	+	0.483292i
$325$	2.95451	+	1.70579i	0.163887	+	0.0946202i
$326$	10.2548	−	5.92061i	0.567960	−	0.327912i
$327$	−26.2792	−	1.73928i	−1.45325	−	0.0961821i
$328$	−7.02601	+	4.05647i	−0.387947	+	0.223981i
$329$		0			0
$330$	−1.27342	−	2.58640i	−0.0700994	−	0.142376i
$331$	22.7350			1.24963			0.624813	−	0.780774i	$-0.285175\pi$
$331$	22.7350			1.24963			0.624813	+	0.780774i	$0.285175\pi$
$332$	2.41103	−	4.17603i	0.132323	−	0.229190i
$333$	13.0747	+	1.73830i	0.716490	+	0.0952582i
$334$	3.00041	−	1.73229i	0.164175	−	0.0947866i
$335$	−6.85644	+	11.8757i	−0.374608	+	0.648839i
$336$		0			0
$337$	−10.0639	−	17.4312i	−0.548217	−	0.949539i	−0.998397	−	0.0566014i	$-0.981974\pi$
$337$	−10.0639	−	17.4312i	−0.548217	−	0.949539i	0.450180	−	0.892938i	$-0.351360\pi$
$338$	−10.6585	−	6.15367i	−0.579745	−	0.334716i
$339$	28.2631	+	18.9109i	1.53504	+	1.02710i
$340$	−2.59713	−	4.49837i	−0.140849	−	0.243958i
$341$	9.64666	+	16.7085i	0.522396	+	0.904816i
$342$	−11.0307	−	1.46655i	−0.596474	−	0.0793019i
$343$		0			0
$344$	−5.34273	−	3.08463i	−0.288061	−	0.166312i
$345$	1.40252	+	0.938431i	0.0755093	+	0.0505234i
$346$		−	3.09982i		−	0.166647i
$347$		−	22.6395i		−	1.21535i	−0.794185	−	0.607677i	$-0.792102\pi$
$347$		−	22.6395i		−	1.21535i	0.794185	−	0.607677i	$-0.207898\pi$
$348$	0.870230	−	13.1486i	0.0466492	−	0.704837i
$349$	13.3378	+	7.70058i	0.713955	+	0.412202i	0.812524	−	0.582928i	$-0.198093\pi$
$349$	13.3378	+	7.70058i	0.713955	+	0.412202i	−0.0985684	+	0.995130i	$0.531426\pi$
$350$		0			0
$351$	4.09769	−	1.38224i	0.218719	−	0.0737783i
$352$	−0.876838	−	1.51873i	−0.0467356	−	0.0809485i
$353$	−15.6132	−	27.0429i	−0.831009	−	1.43935i	−0.897239	−	0.441545i	$-0.854430\pi$
$353$	−15.6132	−	27.0429i	−0.831009	−	1.43935i	0.0662300	−	0.997804i	$-0.478903\pi$
$354$	16.8848	−	8.31325i	0.897414	−	0.441844i
$355$	9.05225	+	5.22632i	0.480444	+	0.277384i
$356$	−2.15943	−	3.74024i	−0.114449	−	0.198232i
$357$		0			0
$358$	−0.288947	+	0.500470i	−0.0152713	+	0.0264507i
$359$	1.39179	−	0.803552i	0.0734560	−	0.0424098i	−0.462822	−	0.886451i	$-0.653163\pi$
$359$	1.39179	−	0.803552i	0.0734560	−	0.0424098i	0.536278	+	0.844041i	$0.319830\pi$
$360$	−2.63199	+	1.08627i	−0.138718	+	0.0572515i
$361$	−2.62067	+	4.53913i	−0.137930	+	0.238902i
$362$	26.0581			1.36958
$363$	13.6959	+	0.906453i	0.718847	+	0.0475765i
$364$		0			0
$365$	3.00114	−	1.73271i	0.157087	−	0.0906941i
$366$	−0.839001	−	1.70407i	−0.0438553	−	0.0890730i
$367$	16.1877	−	9.34599i	0.844992	−	0.487856i	−0.0139659	−	0.999902i	$-0.504446\pi$
$367$	16.1877	−	9.34599i	0.844992	−	0.487856i	0.858958	+	0.512046i	$0.171112\pi$
$368$	0.888998	+	0.513263i	0.0463422	+	0.0267557i
$369$	24.1265	+	3.20765i	1.25598	+	0.166984i
$370$			4.17286i			0.216937i
$371$		0			0
$372$	17.0957	−	8.41708i	0.886368	−	0.436405i
$373$	−18.7682	+	32.5075i	−0.971781	+	1.68317i	−0.281609	+	0.959529i	$0.590868\pi$
$373$	−18.7682	+	32.5075i	−0.971781	+	1.68317i	−0.690173	+	0.723645i	$0.742465\pi$
$374$	−9.59745			−0.496272
$375$	6.60731	+	13.4199i	0.341200	+	0.692999i
$376$			6.80125i			0.350748i
$377$	−6.33177			−0.326103
$378$		0			0
$379$	−8.63192			−0.443392			−0.221696	−	0.975116i	$-0.571159\pi$
$379$	−8.63192			−0.443392			−0.221696	+	0.975116i	$0.571159\pi$
$380$		−	3.52051i		−	0.180599i
$381$	−14.3108	−	29.0661i	−0.733164	−	1.48910i
$382$	−1.77964			−0.0910545
$383$	4.19997	−	7.27456i	0.214608	−	0.371713i	−0.738543	−	0.674206i	$-0.764486\pi$
$383$	4.19997	−	7.27456i	0.214608	−	0.371713i	0.953151	+	0.302494i	$0.0978191\pi$
$384$	−1.55392	+	0.765075i	−0.0792980	+	0.0390426i
$385$		0			0
$386$		−	1.48335i		−	0.0755007i
$387$	7.06078	+	17.1080i	0.358920	+	0.869647i
$388$	3.90396	+	2.25395i	0.198193	+	0.114427i
$389$	12.3475	−	7.12883i	0.626043	−	0.361446i	−0.153175	−	0.988199i	$-0.548950\pi$
$389$	12.3475	−	7.12883i	0.626043	−	0.361446i	0.779218	+	0.626753i	$0.215617\pi$
$390$	0.604338	+	1.22745i	0.0306018	+	0.0621544i
$391$	4.86527	−	2.80897i	0.246047	−	0.142056i
$392$		0			0
$393$	−11.4824	−	0.759954i	−0.579209	−	0.0383346i
$394$	−2.44809			−0.123333
$395$	−4.67352	+	8.09477i	−0.235150	+	0.407292i
$396$	−0.693358	+	5.21514i	−0.0348426	+	0.262071i
$397$	22.2162	−	12.8265i	1.11500	−	0.643744i	0.174879	−	0.984590i	$-0.444047\pi$
$397$	22.2162	−	12.8265i	1.11500	−	0.643744i	0.940119	+	0.340846i	$0.110713\pi$
$398$	−5.46984	+	9.47403i	−0.274178	+	0.474890i
$399$		0			0
$400$	2.04959	+	3.55000i	0.102480	+	0.177500i
$401$	22.5981	+	13.0470i	1.12849	+	0.651536i	0.943556	−	0.331214i	$-0.107458\pi$
$401$	22.5981	+	13.0470i	1.12849	+	0.651536i	0.184938	+	0.982750i	$0.440791\pi$
$402$	22.4512	−	11.0539i	1.11976	−	0.551318i
$403$	−4.57810	−	7.92951i	−0.228052	−	0.394997i
$404$	−6.33624	−	10.9747i	−0.315240	−	0.546011i
$405$	8.24528	+	2.23189i	0.409711	+	0.110904i
$406$		0			0
$407$	6.67722	+	3.85510i	0.330978	+	0.191090i
$408$	−0.625999	+	9.45841i	−0.0309915	+	0.468261i
$409$			30.8308i			1.52448i	0.647292	+	0.762242i	$0.275901\pi$
$409$			30.8308i			1.52448i	−0.647292	+	0.762242i	$0.724099\pi$
$410$			7.70010i			0.380281i
$411$	29.3879	+	19.6635i	1.44960	+	0.969929i
$412$	7.33341	+	4.23394i	0.361291	+	0.208591i
$413$		0			0
$414$	−1.17487	−	2.84666i	−0.0577418	−	0.139906i
$415$	−2.28834	−	3.96353i	−0.112330	−	0.194562i
$416$	0.416129	+	0.720756i	0.0204024	+	0.0353380i
$417$	18.2561	+	12.2152i	0.894007	+	0.598182i
$418$	−5.63337	−	3.25243i	−0.275537	−	0.159081i
$419$	13.9168	+	24.1047i	0.679883	+	1.17759i	0.975016	+	0.222135i	$0.0713026\pi$
$419$	13.9168	+	24.1047i	0.679883	+	1.17759i	−0.295133	+	0.955456i	$0.595364\pi$
$420$		0			0
$421$	7.39960	−	12.8165i	0.360634	−	0.624637i	−0.627431	−	0.778672i	$-0.715894\pi$
$421$	7.39960	−	12.8165i	0.360634	−	0.624637i	0.988065	+	0.154035i	$0.0492269\pi$
$422$	−22.0804	+	12.7481i	−1.07486	+	0.620569i
$423$	12.4417	−	16.1715i	0.604934	−	0.786286i
$424$	1.08644	−	1.88177i	0.0527621	−	0.0913866i
$425$	22.4339			1.08820
$426$	−8.42582	−	17.1134i	−0.408232	−	0.829147i
$427$		0			0
$428$	1.28657	−	0.742804i	0.0621889	−	0.0359048i
$429$	2.52243	+	0.166945i	0.121784	+	0.00806019i
$430$	−5.07085	+	2.92766i	−0.244538	+	0.141184i
$431$	−24.7338	−	14.2801i	−1.19139	−	0.687847i	−0.232765	−	0.972533i	$-0.574777\pi$
$431$	−24.7338	−	14.2801i	−1.19139	−	0.687847i	−0.958621	+	0.284686i	$0.908111\pi$
$432$	5.09436	+	1.02347i	0.245103	+	0.0492419i
$433$		−	18.0220i		−	0.866080i	−0.901375	−	0.433040i	$-0.857441\pi$
$433$		−	18.0220i		−	0.866080i	0.901375	−	0.433040i	$-0.142559\pi$
$434$		0			0
$435$	−10.3946	−	6.95503i	−0.498382	−	0.333468i
$436$	−7.60276	+	13.1684i	−0.364106	+	0.630651i
$437$	3.80766			0.182145
$438$	−6.31028	−	0.417642i	−0.301517	−	0.0199557i
$439$			24.5104i			1.16982i	0.811099	+	0.584909i	$0.198870\pi$
$439$			24.5104i			1.16982i	−0.811099	+	0.584909i	$0.801130\pi$
$440$	−1.66444			−0.0793489
$441$		0			0
$442$	4.55475			0.216647
$443$		−	10.5547i		−	0.501469i	−0.968056	−	0.250734i	$-0.919328\pi$
$443$		−	10.5547i		−	0.501469i	0.968056	−	0.250734i	$-0.0806720\pi$
$444$	4.23477	−	6.32904i	0.200973	−	0.300363i
$445$	−4.09908			−0.194315
$446$	−7.68501	+	13.3108i	−0.363896	+	0.630286i
$447$	2.26949	−	34.2905i	0.107343	−	1.62188i
$448$		0			0
$449$		−	17.2540i		−	0.814267i	−0.913369	−	0.407133i	$-0.866528\pi$
$449$		−	17.2540i		−	0.814267i	0.913369	−	0.407133i	$-0.133472\pi$
$450$	1.62071	−	12.1903i	0.0764011	−	0.574656i
$451$	12.3213	+	7.11373i	0.580190	+	0.334973i
$452$	17.0031	−	9.81676i	0.799760	−	0.461742i
$453$	−1.68062	+	2.51176i	−0.0789626	+	0.118013i
$454$	−7.22937	+	4.17388i	−0.339291	+	0.195890i
$455$		0			0
$456$	−3.57275	+	5.33961i	−0.167309	+	0.250050i
$457$	1.37536			0.0643368			0.0321684	−	0.999482i	$-0.489759\pi$
$457$	1.37536			0.0643368			0.0321684	+	0.999482i	$0.489759\pi$
$458$	6.56281	−	11.3671i	0.306660	−	0.531151i
$459$	18.7909	−	21.3444i	0.877084	−	0.996269i
$460$	0.843760	−	0.487145i	0.0393405	−	0.0227132i
$461$	18.7031	−	32.3947i	0.871088	−	1.50877i	0.0102165	−	0.999948i	$-0.496748\pi$
$461$	18.7031	−	32.3947i	0.871088	−	1.50877i	0.860872	−	0.508822i	$-0.169919\pi$
$462$		0			0
$463$	−5.18312	−	8.97742i	−0.240880	−	0.417216i	0.720085	−	0.693886i	$-0.244103\pi$
$463$	−5.18312	−	8.97742i	−0.240880	−	0.417216i	−0.960965	+	0.276669i	$0.910769\pi$
$464$	−6.58867	−	3.80397i	−0.305871	−	0.176595i
$465$	1.19438	−	18.0463i	0.0553880	−	0.836875i
$466$	5.68315	+	9.84350i	0.263267	+	0.455991i
$467$	18.1423	+	31.4234i	0.839527	+	1.45410i	0.890291	+	0.455393i	$0.150501\pi$
$467$	18.1423	+	31.4234i	0.839527	+	1.45410i	−0.0507637	+	0.998711i	$0.516166\pi$
$468$	0.329053	−	2.47500i	0.0152105	−	0.114407i
$469$		0			0
$470$	5.59033	+	3.22758i	0.257862	+	0.148877i
$471$	−14.7554	+	7.26488i	−0.679895	+	0.334748i
$472$		−	10.8659i		−	0.500145i
$473$			10.8189i			0.497452i
$474$	15.3033	−	7.53460i	0.702902	−	0.346076i
$475$	13.1679	+	7.60248i	0.604184	+	0.348826i
$476$		0			0
$477$	−6.02561	+	2.48688i	−0.275894	+	0.113867i
$478$	2.69645	+	4.67039i	0.123333	+	0.213619i
$479$	−11.5975	−	20.0875i	−0.529905	−	0.917822i	−0.999391	−	0.0348822i	$-0.988894\pi$
$479$	−11.5975	−	20.0875i	−0.529905	−	0.917822i	0.469487	−	0.882939i	$-0.344439\pi$
$480$	−0.108564	+	1.64032i	−0.00495523	+	0.0748702i
$481$	−3.16887	−	1.82955i	−0.144488	−	0.0834202i
$482$	−6.99936	−	12.1233i	−0.318812	−	0.552199i
$483$		0			0
$484$	3.96231	−	6.86292i	0.180105	−	0.311951i
$485$	3.70529	−	2.13925i	0.168249	−	0.0971385i
$486$	−10.2407	−	11.7528i	−0.464529	−	0.533116i
$487$	−14.3695	+	24.8887i	−0.651144	+	1.12781i	0.331701	+	0.943384i	$0.392377\pi$
$487$	−14.3695	+	24.8887i	−0.651144	+	1.12781i	−0.982846	+	0.184430i	$0.940956\pi$
$488$	−1.09663			−0.0496419
$489$	−11.4054	+	17.0458i	−0.515770	+	0.770839i
$490$		0			0
$491$	21.0143	−	12.1326i	0.948364	−	0.547538i	0.0557919	−	0.998442i	$-0.482232\pi$
$491$	21.0143	−	12.1326i	0.948364	−	0.547538i	0.892572	+	0.450904i	$0.148898\pi$
$492$	7.81434	−	11.6788i	0.352298	−	0.526523i
$493$	−36.0582	+	20.8182i	−1.62398	+	0.937605i
$494$	2.67348	+	1.54353i	0.120285	+	0.0694468i
$495$	3.95758	+	3.04479i	0.177880	+	0.136853i
$496$		−	11.0016i		−	0.493988i
$497$		0			0
$498$	−0.551570	+	8.33384i	−0.0247164	+	0.373448i
$499$	−13.2911	+	23.0209i	−0.594992	+	1.03056i	0.398556	+	0.917144i	$0.369511\pi$
$499$	−13.2911	+	23.0209i	−0.594992	+	1.03056i	−0.993548	+	0.113412i	$0.963822\pi$
$500$	8.63615			0.386221
$501$	−3.33706	+	4.98737i	−0.149089	+	0.222819i
$502$		−	16.5094i		−	0.736852i
$503$	33.9478			1.51366			0.756829	−	0.653613i	$-0.226748\pi$
$503$	33.9478			1.51366			0.756829	+	0.653613i	$0.226748\pi$
$504$		0			0
$505$	−12.0276			−0.535222
$506$		−	1.80019i		−	0.0800284i
$507$	21.2704	+	1.40777i	0.944652	+	0.0625212i
$508$	−18.7051			−0.829903
$509$	5.70574	−	9.88263i	0.252902	−	0.438040i	−0.711421	−	0.702766i	$-0.751948\pi$
$509$	5.70574	−	9.88263i	0.252902	−	0.438040i	0.964324	+	0.264726i	$0.0852815\pi$
$510$	7.47732	+	5.00309i	0.331101	+	0.221541i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	18.2629	−	6.16045i	0.806326	−	0.271990i
$514$	5.30007	+	3.06000i	0.233776	+	0.134971i
$515$	6.96023	−	4.01849i	0.306704	−	0.177076i
$516$	10.6621	+	0.705666i	0.469374	+	0.0310652i
$517$	10.3292	−	5.96359i	0.454280	−	0.262278i
$518$		0			0
$519$	2.37160	+	4.81687i	0.104101	+	0.211437i
$520$	0.789907			0.0346397
$521$	−9.24387	+	16.0108i	−0.404981	+	0.701448i	−0.994319	−	0.106439i	$-0.966055\pi$
$521$	−9.24387	+	16.0108i	−0.404981	+	0.701448i	0.589338	+	0.807887i	$0.299389\pi$
$522$	8.70738	+	21.0976i	0.381112	+	0.923416i
$523$	0.133147	−	0.0768726i	0.00582212	−	0.00336140i	−0.497086	−	0.867701i	$-0.665597\pi$
$523$	0.133147	−	0.0768726i	0.00582212	−	0.00336140i	0.502908	+	0.864340i	$0.332263\pi$
$524$	−3.32193	+	5.75375i	−0.145119	+	0.251354i
$525$		0			0
$526$	−8.17923	−	14.1668i	−0.356631	−	0.617704i
$527$	−52.1428	−	30.1047i	−2.27138	−	1.31138i
$528$	2.52447	+	1.68913i	0.109864	+	0.0735100i
$529$	−10.9731	−	19.0060i	−0.477092	−	0.826348i
$530$	−1.03115	−	1.78601i	−0.0447904	−	0.0775792i
$531$	−19.8773	+	25.8362i	−0.862600	+	1.12120i
$532$		0			0
$533$	−5.84746	−	3.37603i	−0.253281	−	0.146232i
$534$	6.21714	+	4.15990i	0.269042	+	0.180016i
$535$		−	1.41001i		−	0.0609600i
$536$		−	14.4481i		−	0.624063i
$537$	0.0661020	−	0.998756i	0.00285251	−	0.0430995i
$538$	4.60457	+	2.65845i	0.198517	+	0.114614i
$539$		0			0
$540$	3.25881	−	3.70164i	0.140237	−	0.159293i
$541$	17.9635	+	31.1136i	0.772309	+	1.33768i	0.936294	+	0.351216i	$0.114232\pi$
$541$	17.9635	+	31.1136i	0.772309	+	1.33768i	−0.163985	+	0.986463i	$0.552435\pi$
$542$	−8.24602	−	14.2825i	−0.354197	−	0.613487i
$543$	−40.4922	+	19.9364i	−1.73769	+	0.855553i
$544$	4.73955	+	2.73638i	0.203206	+	0.117321i
$545$	7.21588	+	12.4983i	0.309094	+	0.535367i
$546$		0			0
$547$	10.2216	−	17.7043i	0.437044	−	0.756983i	−0.560416	−	0.828211i	$-0.689359\pi$
$547$	10.2216	−	17.7043i	0.437044	−	0.756983i	0.997460	+	0.0712286i	$0.0226920\pi$
$548$	17.6798	−	10.2074i	0.755244	−	0.436040i
$549$	2.60748	+	2.00608i	0.111284	+	0.0856174i
$550$	3.59432	−	6.22554i	0.153262	−	0.265458i
$551$	−28.2199			−1.20221
$552$	−1.77412	−	0.117419i	−0.0755114	−	0.00499767i
$553$		0			0
$554$	12.6682	−	7.31402i	0.538222	−	0.310743i
$555$	−3.19255	−	6.48428i	−0.135516	−	0.275242i
$556$	10.9829	−	6.34099i	0.465780	−	0.268918i
$557$	18.8181	+	10.8646i	0.797348	+	0.460349i	0.842543	−	0.538629i	$-0.181058\pi$
$557$	18.8181	+	10.8646i	0.797348	+	0.460349i	−0.0451952	+	0.998978i	$0.514391\pi$
$558$	−20.1255	+	26.1589i	−0.851982	+	1.10739i
$559$		−	5.13441i		−	0.217162i
$560$		0			0
$561$	14.9136	−	7.34277i	0.629654	−	0.310012i
$562$	−2.09178	+	3.62307i	−0.0882365	+	0.152830i
$563$	−20.8519			−0.878805			−0.439402	−	0.898290i	$-0.644810\pi$
$563$	−20.8519			−0.878805			−0.439402	+	0.898290i	$0.644810\pi$
$564$	−5.20346	−	10.5686i	−0.219105	−	0.445017i
$565$		−	18.6344i		−	0.783957i
$566$	9.70591			0.407970
$567$		0			0
$568$	−11.0131			−0.462098
$569$		−	11.6914i		−	0.490128i	−0.969507	−	0.245064i	$-0.921191\pi$
$569$		−	11.6914i		−	0.490128i	0.969507	−	0.245064i	$-0.0788090\pi$
$570$	2.69346	+	5.47059i	0.112816	+	0.229138i
$571$	13.5544			0.567235			0.283617	−	0.958938i	$-0.408465\pi$
$571$	13.5544			0.567235			0.283617	+	0.958938i	$0.408465\pi$
$572$	0.729755	−	1.26397i	0.0305126	−	0.0528494i
$573$	2.76542	−	1.36156i	0.115527	−	0.0568800i
$574$		0			0
$575$			4.20792i			0.175483i
$576$	1.82932	−	2.37773i	0.0762217	−	0.0990720i
$577$	20.0748	+	11.5902i	0.835727	+	0.482507i	0.855809	−	0.517291i	$-0.173060\pi$
$577$	20.0748	+	11.5902i	0.835727	+	0.482507i	−0.0200828	+	0.999798i	$0.506393\pi$
$578$	11.2160	−	6.47555i	0.466523	−	0.269347i
$579$	1.13488	+	2.30501i	0.0471639	+	0.0957929i
$580$	−6.25339	+	3.61040i	−0.259658	+	0.149914i
$581$		0			0
$582$	−7.79087	−	0.515633i	−0.322942	−	0.0213737i
$583$	−3.81052			−0.157816
$584$	−1.82561	+	3.16204i	−0.0755442	+	0.130846i
$585$	−1.87818	−	1.44499i	−0.0776533	−	0.0597431i
$586$	1.75591	−	1.01377i	0.0725358	−	0.0418786i
$587$	−4.22194	+	7.31262i	−0.174258	+	0.301824i	−0.939904	−	0.341438i	$-0.889086\pi$
$587$	−4.22194	+	7.31262i	−0.174258	+	0.301824i	0.765646	+	0.643262i	$0.222419\pi$
$588$		0			0
$589$	−20.4040	−	35.3408i	−0.840733	−	1.45619i
$590$	−8.93131	−	5.15650i	−0.367696	−	0.212290i
$591$	3.80413	−	1.87297i	0.156481	−	0.0770438i
$592$	−2.19830	−	3.80756i	−0.0903494	−	0.156490i
$593$	−16.3255	−	28.2765i	−0.670407	−	1.16118i	−0.977789	−	0.209592i	$-0.932786\pi$
$593$	−16.3255	−	28.2765i	−0.670407	−	1.16118i	0.307382	−	0.951586i	$-0.400547\pi$
$594$	−2.91255	−	8.63437i	−0.119503	−	0.354272i
$595$		0			0
$596$	−17.1827	−	9.92046i	−0.703833	−	0.406358i
$597$	1.25133	−	18.9067i	0.0512134	−	0.773800i
$598$			0.854335i			0.0349364i
$599$		−	47.9900i		−	1.96082i	−0.196974	−	0.980409i	$-0.563112\pi$
$599$		−	47.9900i		−	1.96082i	0.196974	−	0.980409i	$-0.436888\pi$
$600$	−5.90091	−	3.94831i	−0.240904	−	0.161189i
$601$	20.1783	+	11.6499i	0.823090	+	0.475211i	0.851481	−	0.524386i	$-0.175705\pi$
$601$	20.1783	+	11.6499i	0.823090	+	0.475211i	−0.0283909	+	0.999597i	$0.509038\pi$
$602$		0			0
$603$	−26.4302	+	34.3537i	−1.07632	+	1.39899i
$604$	0.872422	+	1.51108i	0.0354983	+	0.0614849i
$605$	−3.76068	−	6.51369i	−0.152893	−	0.264819i
$606$	18.2425	+	12.2061i	0.741049	+	0.495838i
$607$	−21.3385	−	12.3198i	−0.866101	−	0.500044i	−5.03773e−5	−	1.00000i	$-0.500016\pi$
$607$	−21.3385	−	12.3198i	−0.866101	−	0.500044i	−0.866051	+	0.499956i	$0.833349\pi$
$608$	1.85463	+	3.21232i	0.0752153	+	0.130277i
$609$		0			0
$610$	−0.520411	+	0.901378i	−0.0210708	+	0.0364957i
$611$	−4.90204	+	2.83020i	−0.198315	+	0.114497i
$612$	−6.26364	−	15.1765i	−0.253193	−	0.613474i
$613$	−17.2009	+	29.7928i	−0.694736	+	1.20332i	0.275533	+	0.961291i	$0.411146\pi$
$613$	−17.2009	+	29.7928i	−0.694736	+	1.20332i	−0.970270	+	0.242027i	$0.922188\pi$
$614$	9.79004			0.395094
$615$	−5.89115	−	11.9653i	−0.237554	−	0.482488i
$616$		0			0
$617$	−22.4321	+	12.9512i	−0.903083	+	0.521395i	−0.878199	−	0.478295i	$-0.841255\pi$
$617$	−22.4321	+	12.9512i	−0.903083	+	0.521395i	−0.0248838	+	0.999690i	$0.507922\pi$
$618$	−14.6348	−	0.968595i	−0.588698	−	0.0389626i
$619$	10.1907	−	5.88361i	0.409599	−	0.236482i	−0.281018	−	0.959702i	$-0.590672\pi$
$619$	10.1907	−	5.88361i	0.409599	−	0.236482i	0.690618	+	0.723220i	$0.257339\pi$
$620$	−9.04287	−	5.22090i	−0.363170	−	0.209676i
$621$	4.00357	+	3.52461i	0.160658	+	0.141438i
$622$		−	13.7039i		−	0.549476i
$623$		0			0
$624$	−1.19806	−	0.801626i	−0.0479609	−	0.0320907i
$625$	−6.14962	+	10.6515i	−0.245985	+	0.426058i
$626$	−18.8585			−0.753739
$627$	11.2421	+	0.744054i	0.448968	+	0.0297146i
$628$			9.49564i			0.378917i
$629$	−24.0615			−0.959394
$630$		0			0
$631$	16.4353			0.654277			0.327139	−	0.944976i	$-0.393916\pi$
$631$	16.4353			0.654277			0.327139	+	0.944976i	$0.393916\pi$
$632$		−	9.84819i		−	0.391740i
$633$	24.5578	−	36.7027i	0.976087	−	1.45880i
$634$	7.86426			0.312329
$635$	−8.87661	+	15.3747i	−0.352258	+	0.610128i
$636$	−0.248543	+	3.75532i	−0.00985538	+	0.148908i
$637$		0			0
$638$			13.3419i			0.528209i
$639$	26.1861	+	20.1464i	1.03590	+	0.796980i
$640$	0.821956	+	0.474556i	0.0324907	+	0.0187585i
$641$	−13.4048	+	7.73929i	−0.529460	+	0.305684i	−0.740796	−	0.671730i	$-0.765552\pi$
$641$	−13.4048	+	7.73929i	−0.529460	+	0.305684i	0.211337	+	0.977413i	$0.432218\pi$
$642$	−1.43093	+	2.13858i	−0.0564743	+	0.0844031i
$643$	−3.28185	+	1.89478i	−0.129423	+	0.0747226i	−0.563314	−	0.826243i	$-0.690474\pi$
$643$	−3.28185	+	1.89478i	−0.129423	+	0.0747226i	0.433890	+	0.900966i	$0.357140\pi$
$644$		0			0
$645$	5.63981	−	8.42893i	0.222067	−	0.331889i
$646$	20.2999			0.798690
$647$	−11.0730	+	19.1789i	−0.435323	+	0.754002i	−0.997322	−	0.0731360i	$-0.976699\pi$
$647$	−11.0730	+	19.1789i	−0.435323	+	0.754002i	0.561999	+	0.827138i	$0.310033\pi$
$648$	−8.69925	+	2.30717i	−0.341739	+	0.0906343i
$649$	−16.5024	+	9.52765i	−0.647775	+	0.373993i
$650$	−1.70579	+	2.95451i	−0.0669066	+	0.115886i
$651$		0			0
$652$	5.92061	+	10.2548i	0.231869	+	0.401609i
$653$	−6.54842	−	3.78073i	−0.256259	−	0.147951i	0.366368	−	0.930470i	$-0.380601\pi$
$653$	−6.54842	−	3.78073i	−0.256259	−	0.147951i	−0.622627	+	0.782519i	$0.713935\pi$
$654$	1.73928	−	26.2792i	0.0680110	−	1.02760i
$655$	3.15289	+	5.46096i	0.123193	+	0.213377i
$656$	−4.05647	−	7.02601i	−0.158379	−	0.274320i
$657$	10.1252	−	4.17886i	0.395021	−	0.163033i
$658$		0			0
$659$	−12.2514	−	7.07334i	−0.477246	−	0.275538i	0.242022	−	0.970271i	$-0.422189\pi$
$659$	−12.2514	−	7.07334i	−0.477246	−	0.275538i	−0.719268	+	0.694733i	$0.755523\pi$
$660$	2.58640	−	1.27342i	0.100675	−	0.0495678i
$661$			22.9586i			0.892985i	0.894787	+	0.446492i	$0.147327\pi$
$661$			22.9586i			0.892985i	−0.894787	+	0.446492i	$0.852673\pi$
$662$			22.7350i			0.883620i
$663$	−7.07770	+	3.48472i	−0.274875	+	0.135335i
$664$	4.17603	+	2.41103i	0.162062	+	0.0935663i
$665$		0			0
$666$	−1.73830	+	13.0747i	−0.0673577	+	0.506635i
$667$	−3.90488	−	6.76344i	−0.151197	−	0.261882i
$668$	1.73229	+	3.00041i	0.0670242	+	0.116089i
$669$	1.75809	−	26.5635i	0.0679717	−	1.02701i
$670$	−11.8757	−	6.85644i	−0.458799	−	0.264888i
$671$	0.961563	+	1.66548i	0.0371207	+	0.0642950i
$672$		0			0
$673$	−1.86542	+	3.23100i	−0.0719066	+	0.124546i	−0.899737	−	0.436433i	$-0.856242\pi$
$673$	−1.86542	+	3.23100i	−0.0719066	+	0.124546i	0.827830	+	0.560979i	$0.189575\pi$
$674$	17.4312	−	10.0639i	0.671426	−	0.387648i
$675$	6.80803	+	20.1827i	0.262041	+	0.776831i
$676$	6.15367	−	10.6585i	0.236680	−	0.409941i
$677$	−47.5314			−1.82678			−0.913390	−	0.407087i	$-0.866545\pi$
$677$	−47.5314			−1.82678			−0.913390	+	0.407087i	$0.866545\pi$
$678$	−18.9109	+	28.2631i	−0.726269	+	1.08544i
$679$		0			0
$680$	4.49837	−	2.59713i	0.172505	−	0.0995955i
$681$	8.04052	−	12.0169i	0.308113	−	0.460488i
$682$	−16.7085	+	9.64666i	−0.639802	+	0.369390i
$683$	28.5275	+	16.4704i	1.09158	+	0.630222i	0.933996	−	0.357284i	$-0.116297\pi$
$683$	28.5275	+	16.4704i	1.09158	+	0.630222i	0.157580	+	0.987506i	$0.449631\pi$
$684$	1.46655	−	11.0307i	0.0560749	−	0.421771i
$685$		−	19.3760i		−	0.740320i
$686$		0			0
$687$	−1.50137	+	22.6846i	−0.0572807	+	0.865472i
$688$	3.08463	−	5.34273i	0.117600	−	0.203690i
$689$	1.80839			0.0688943
$690$	−0.938431	+	1.40252i	−0.0357254	+	0.0533931i
$691$		−	7.93611i		−	0.301904i	−0.988541	−	0.150952i	$-0.951766\pi$
$691$		−	7.93611i		−	0.301904i	0.988541	−	0.150952i	$-0.0482339\pi$
$692$	3.09982			0.117838
$693$		0			0
$694$	22.6395			0.859385
$695$		−	12.0366i		−	0.456576i
$696$	13.1486	+	0.870230i	0.498395	+	0.0329860i
$697$	−44.4002			−1.68178
$698$	−7.70058	+	13.3378i	−0.291471	+	0.504843i
$699$	−16.3622	−	10.9480i	−0.618874	−	0.414090i
$700$		0			0
$701$			25.1838i			0.951180i	0.879667	+	0.475590i	$0.157765\pi$
$701$			25.1838i			0.951180i	−0.879667	+	0.475590i	$0.842235\pi$
$702$	1.38224	+	4.09769i	0.0521691	+	0.154657i
$703$	−14.1233	−	8.15406i	−0.532669	−	0.307536i
$704$	1.51873	−	0.876838i	0.0572392	−	0.0330471i
$705$	−11.1562	−	0.738369i	−0.420168	−	0.0278086i
$706$	27.0429	−	15.6132i	1.01777	−	0.587612i
$707$		0			0
$708$	8.31325	+	16.8848i	0.312431	+	0.634568i
$709$	21.5021			0.807530			0.403765	−	0.914863i	$-0.367701\pi$
$709$	21.5021			0.807530			0.403765	+	0.914863i	$0.367701\pi$
$710$	−5.22632	+	9.05225i	−0.196140	+	0.339725i
$711$	−18.0155	+	23.4163i	−0.675634	+	0.878180i
$712$	3.74024	−	2.15943i	0.140171	−	0.0809280i
$713$	5.64674	−	9.78044i	0.211472	−	0.366280i
$714$		0			0
$715$	−0.692620	−	1.19965i	−0.0259025	−	0.0448645i
$716$	−0.500470	−	0.288947i	−0.0187035	−	0.0107984i
$717$	−7.76326	−	5.19441i	−0.289924	−	0.193989i
$718$	0.803552	+	1.39179i	0.0299883	+	0.0519412i
$719$	−8.30671	−	14.3876i	−0.309788	−	0.536569i	0.668528	−	0.743687i	$-0.266925\pi$
$719$	−8.30671	−	14.3876i	−0.309788	−	0.536569i	−0.978316	+	0.207119i	$0.933591\pi$
$720$	−1.08627	−	2.63199i	−0.0404829	−	0.0980884i
$721$		0			0
$722$	−4.53913	−	2.62067i	−0.168929	−	0.0975312i
$723$	20.1516	+	13.4835i	0.749447	+	0.501457i
$724$			26.0581i			0.968442i
$725$		−	31.1863i		−	1.15823i
$726$	−0.906453	+	13.6959i	−0.0336416	+	0.508302i
$727$	−39.4866	−	22.7976i	−1.46448	−	0.845517i	−0.465265	−	0.885171i	$-0.654041\pi$
$727$	−39.4866	−	22.7976i	−1.46448	−	0.845517i	−0.999213	+	0.0396542i	$0.987374\pi$
$728$		0			0
$729$	24.9050	+	10.4279i	0.922408	+	0.386218i
$730$	1.73271	+	3.00114i	0.0641304	+	0.111077i
$731$	−16.8814	−	29.2395i	−0.624382	−	1.08146i
$732$	1.70407	−	0.839001i	0.0629841	−	0.0310104i
$733$	−14.3262	−	8.27123i	−0.529150	−	0.305505i	0.211520	−	0.977374i	$-0.432159\pi$
$733$	−14.3262	−	8.27123i	−0.529150	−	0.305505i	−0.740670	+	0.671869i	$0.765492\pi$
$734$	9.34599	+	16.1877i	0.344967	+	0.597500i
$735$		0			0
$736$	−0.513263	+	0.888998i	−0.0189191	+	0.0327689i
$737$	−21.9427	+	12.6686i	−0.808271	+	0.466656i
$738$	−3.20765	+	24.1265i	−0.118075	+	0.888110i
$739$	7.75506	−	13.4322i	0.285274	−	0.494110i	−0.687401	−	0.726278i	$-0.741249\pi$
$739$	7.75506	−	13.4322i	0.285274	−	0.494110i	0.972676	+	0.232168i	$0.0745819\pi$
$740$	−4.17286			−0.153397
$741$	−5.33528	−	0.353112i	−0.195997	−	0.0129719i
$742$		0			0
$743$	36.0654	−	20.8224i	1.32311	−	0.763899i	0.338888	−	0.940827i	$-0.389949\pi$
$743$	36.0654	−	20.8224i	1.32311	−	0.763899i	0.984224	+	0.176928i	$0.0566160\pi$
$744$	8.41708	+	17.0957i	0.308585	+	0.626757i
$745$	−16.3084	+	9.41564i	−0.597492	+	0.344962i
$746$	−32.5075	−	18.7682i	−1.19018	−	0.687153i
$747$	−5.51892	−	13.3721i	−0.201927	−	0.489259i
$748$		−	9.59745i		−	0.350917i
$749$		0			0
$750$	−13.4199	+	6.60731i	−0.490024	+	0.241265i
$751$	6.21569	−	10.7659i	0.226814	−	0.392853i	−0.730048	−	0.683395i	$-0.760503\pi$
$751$	6.21569	−	10.7659i	0.226814	−	0.392853i	0.956862	+	0.290543i	$0.0938359\pi$
$752$	−6.80125			−0.248016
$753$	12.6310	+	25.6543i	0.460298	+	0.934895i
$754$		−	6.33177i		−	0.230589i
$755$	1.65605			0.0602699
$756$		0			0
$757$	24.8661			0.903775			0.451887	−	0.892075i	$-0.350751\pi$
$757$	24.8661			0.903775			0.451887	+	0.892075i	$0.350751\pi$
$758$		−	8.63192i		−	0.313526i
$759$	1.37728	+	2.79735i	0.0499922	+	0.101538i
$760$	3.52051			0.127702
$761$	5.68277	−	9.84285i	0.206000	−	0.356803i	−0.744451	−	0.667678i	$-0.767289\pi$
$761$	5.68277	−	9.84285i	0.206000	−	0.356803i	0.950451	+	0.310874i	$0.100622\pi$
$762$	29.0661	−	14.3108i	1.05296	−	0.518425i
$763$		0			0
$764$		−	1.77964i		−	0.0643852i
$765$	−15.4469	−	2.05368i	−0.558483	−	0.0742509i
$766$	7.27456	+	4.19997i	0.262841	+	0.151751i
$767$	7.83169	−	4.52163i	0.282786	−	0.163266i
$768$	−0.765075	−	1.55392i	−0.0276073	−	0.0560722i
$769$	−29.8857	+	17.2545i	−1.07771	+	0.622214i	−0.930277	−	0.366859i	$-0.880433\pi$
$769$	−29.8857	+	17.2545i	−1.07771	+	0.622214i	−0.147429	+	0.989073i	$0.547100\pi$
$770$		0			0
$771$	−10.5770	−	0.700033i	−0.380922	−	0.0252111i
$772$	1.48335			0.0533871
$773$	10.6262	−	18.4051i	0.382197	−	0.661984i	−0.609179	−	0.793033i	$-0.708501\pi$
$773$	10.6262	−	18.4051i	0.382197	−	0.661984i	0.991376	+	0.131048i	$0.0418344\pi$
$774$	−17.1080	+	7.06078i	−0.614933	+	0.253795i
$775$	39.0558	−	22.5489i	1.40293	−	0.809980i
$776$	−2.25395	+	3.90396i	−0.0809121	+	0.140144i
$777$		0			0
$778$	7.12883	+	12.3475i	0.255581	+	0.442679i
$779$	−26.0614	−	15.0465i	−0.933745	−	0.539098i
$780$	−1.22745	+	0.604338i	−0.0439498	+	0.0216388i
$781$	9.65667	+	16.7258i	0.345543	+	0.598498i
$782$	2.80897	+	4.86527i	0.100448	+	0.173982i
$783$	−29.6718	−	26.1221i	−1.06038	−	0.933528i
$784$		0			0
$785$	7.80500	+	4.50622i	0.278572	+	0.160834i
$786$	0.759954	−	11.4824i	0.0271067	−	0.409563i
$787$			11.9663i			0.426551i	0.976992	+	0.213276i	$0.0684132\pi$
$787$			11.9663i			0.426551i	−0.976992	+	0.213276i	$0.931587\pi$
$788$		−	2.44809i		−	0.0872096i
$789$	23.5485	+	15.7564i	0.838351	+	0.560942i
$790$	−8.09477	−	4.67352i	−0.287999	−	0.166276i
$791$		0			0
$792$	−5.21514	−	0.693358i	−0.185312	−	0.0246374i
$793$	−0.456338	−	0.790400i	−0.0162050	−	0.0280679i
$794$	12.8265	+	22.2162i	0.455196	+	0.788422i
$795$	2.96876	+	1.98640i	0.105291	+	0.0704504i
$796$	−9.47403	−	5.46984i	−0.335798	−	0.193873i
$797$	2.86820	+	4.96786i	0.101597	+	0.175971i	0.912343	−	0.409427i	$-0.134272\pi$
$797$	2.86820	+	4.96786i	0.101597	+	0.175971i	−0.810746	+	0.585398i	$0.800938\pi$
$798$		0			0
$799$	−18.6108	+	32.2348i	−0.658403	+	1.14039i
$800$	−3.55000	+	2.04959i	−0.125511	+	0.0724640i
$801$	−12.8436	−	1.70756i	−0.453805	−	0.0603338i
$802$	−13.0470	+	22.5981i	−0.460706	+	0.797966i
$803$	6.40305			0.225959
$804$	11.0539	+	22.4512i	0.389841	+	0.791792i
$805$		0			0
$806$	7.92951	−	4.57810i	0.279305	−	0.161257i
$807$	−9.18903	−	0.608170i	−0.323469	−	0.0214086i
$808$	10.9747	−	6.33624i	0.386088	−	0.222908i
$809$	27.5185	+	15.8878i	0.967500	+	0.558586i	0.898473	−	0.439028i	$-0.144677\pi$
$809$	27.5185	+	15.8878i	0.967500	+	0.558586i	0.0690269	+	0.997615i	$0.478011\pi$
$810$	−2.23189	+	8.24528i	−0.0784206	+	0.289710i
$811$			41.2541i			1.44863i	0.689471	+	0.724314i	$0.257843\pi$
$811$			41.2541i			1.44863i	−0.689471	+	0.724314i	$0.742157\pi$
$812$		0			0
$813$	23.7408	+	15.8850i	0.832627	+	0.557113i
$814$	−3.85510	+	6.67722i	−0.135121	+	0.234037i
$815$	11.2386			0.393673
$816$	−9.45841	−	0.625999i	−0.331110	−	0.0219143i
$817$		−	22.8834i		−	0.800589i
$818$	−30.8308			−1.07797
$819$		0			0
$820$	−7.70010			−0.268899
$821$		−	13.5045i		−	0.471309i	−0.971837	−	0.235655i	$-0.924277\pi$
$821$		−	13.5045i		−	0.471309i	0.971837	−	0.235655i	$-0.0757234\pi$
$822$	−19.6635	+	29.3879i	−0.685843	+	1.02502i
$823$	−18.9133			−0.659277			−0.329638	−	0.944107i	$-0.606927\pi$
$823$	−18.9133			−0.659277			−0.329638	+	0.944107i	$0.606927\pi$
$824$	−4.23394	+	7.33341i	−0.147496	+	0.255471i
$825$	−0.822268	+	12.4239i	−0.0286277	+	0.432545i
$826$		0			0
$827$			33.8495i			1.17706i	0.808475	+	0.588531i	$0.200293\pi$
$827$			33.8495i			1.17706i	−0.808475	+	0.588531i	$0.799707\pi$
$828$	2.84666	−	1.17487i	0.0989284	−	0.0408296i
$829$	21.8963	+	12.6418i	0.760489	+	0.439068i	0.829471	−	0.558550i	$-0.188642\pi$
$829$	21.8963	+	12.6418i	0.760489	+	0.439068i	−0.0689825	+	0.997618i	$0.521975\pi$
$830$	3.96353	−	2.28834i	0.137576	−	0.0794296i
$831$	−14.0896	+	21.0575i	−0.488764	+	0.730478i
$832$	−0.720756	+	0.416129i	−0.0249877	+	0.0144267i
$833$		0			0
$834$	−12.2152	+	18.2561i	−0.422979	+	0.632159i
$835$	3.28827			0.113795
$836$	3.25243	−	5.63337i	0.112487	−	0.194834i
$837$	11.2599	−	56.0463i	0.389199	−	1.93724i
$838$	−24.1047	+	13.9168i	−0.832683	+	0.480750i
$839$	1.28248	−	2.22133i	0.0442763	−	0.0766888i	−0.843038	−	0.537854i	$-0.819235\pi$
$839$	1.28248	−	2.22133i	0.0442763	−	0.0766888i	0.887314	+	0.461165i	$0.152568\pi$
$840$		0			0
$841$	14.4404	+	25.0114i	0.497943	+	0.862463i
$842$	12.8165	+	7.39960i	0.441685	+	0.255007i
$843$	0.478535	−	7.23033i	0.0164816	−	0.249026i
$844$	−12.7481	−	22.0804i	−0.438808	−	0.760038i
$845$	−5.84053	−	10.1161i	−0.200920	−	0.348004i
$846$	16.1715	+	12.4417i	0.555988	+	0.427753i
$847$		0			0
$848$	1.88177	+	1.08644i	0.0646201	+	0.0373084i
$849$	−15.0822	+	7.42575i	−0.517619	+	0.254851i
$850$			22.4339i			0.769475i
$851$		−	4.51322i		−	0.154711i
$852$	17.1134	−	8.42582i	0.586295	−	0.288664i
$853$	−1.98108	−	1.14378i	−0.0678310	−	0.0391622i	0.465701	−	0.884942i	$-0.345802\pi$
$853$	−1.98108	−	1.14378i	−0.0678310	−	0.0391622i	−0.533532	+	0.845780i	$0.679136\pi$
$854$		0			0
$855$	−8.37082	−	6.44015i	−0.286276	−	0.220248i
$856$	0.742804	+	1.28657i	0.0253885	+	0.0439742i
$857$	10.3313	+	17.8943i	0.352911	+	0.611259i	0.986758	−	0.162199i	$-0.0518586\pi$
$857$	10.3313	+	17.8943i	0.352911	+	0.611259i	−0.633847	+	0.773458i	$0.718525\pi$
$858$	−0.166945	+	2.52243i	−0.00569942	+	0.0861143i
$859$	14.3879	+	8.30688i	0.490910	+	0.283427i	0.724952	−	0.688800i	$-0.241862\pi$
$859$	14.3879	+	8.30688i	0.490910	+	0.283427i	−0.234042	+	0.972226i	$0.575195\pi$
$860$	−2.92766	−	5.07085i	−0.0998323	−	0.172915i
$861$		0			0
$862$	14.2801	−	24.7338i	0.486381	−	0.842437i
$863$	−5.54125	+	3.19924i	−0.188626	+	0.108904i	−0.591339	−	0.806423i	$-0.701401\pi$
$863$	−5.54125	+	3.19924i	−0.188626	+	0.108904i	0.402713	+	0.915326i	$0.368067\pi$
$864$	−1.02347	+	5.09436i	−0.0348193	+	0.173314i
$865$	1.47104	−	2.54792i	0.0500169	−	0.0866318i
$866$	18.0220			0.612411
$867$	−12.4744	+	18.6435i	−0.423654	+	0.633168i
$868$		0			0
$869$	−14.9567	+	8.63526i	−0.507372	+	0.292931i
$870$	6.95503	−	10.3946i	0.235798	−	0.352409i
$871$	10.4136	−	6.01228i	0.352850	−	0.203718i
$872$	−13.1684	−	7.60276i	−0.445937	−	0.257462i
$873$	12.5009	−	5.15934i	0.423090	−	0.174617i
$874$			3.80766i			0.128796i
$875$		0			0
$876$	0.417642	−	6.31028i	0.0141108	−	0.213205i
$877$	−5.08369	+	8.80522i	−0.171664	+	0.297331i	−0.939002	−	0.343912i	$-0.888248\pi$
$877$	−5.08369	+	8.80522i	−0.171664	+	0.297331i	0.767338	+	0.641243i	$0.221581\pi$
$878$	−24.5104			−0.827187
$879$	−1.95292	+	2.91872i	−0.0658704	+	0.0984460i
$880$		−	1.66444i		−	0.0561081i
$881$	−47.2933			−1.59335			−0.796675	−	0.604407i	$-0.793410\pi$
$881$	−47.2933			−1.59335			−0.796675	+	0.604407i	$0.793410\pi$
$882$		0			0
$883$	−16.5706			−0.557645			−0.278822	−	0.960343i	$-0.589944\pi$
$883$	−16.5706			−0.557645			−0.278822	+	0.960343i	$0.589944\pi$
$884$			4.55475i			0.153193i
$885$	17.8236	+	1.17965i	0.599135	+	0.0396533i
$886$	10.5547			0.354592
$887$	11.3965	−	19.7393i	0.382656	−	0.662780i	−0.608785	−	0.793335i	$-0.708343\pi$
$887$	11.3965	−	19.7393i	0.382656	−	0.662780i	0.991441	+	0.130556i	$0.0416761\pi$
$888$	6.32904	+	4.23477i	0.212389	+	0.142110i
$889$		0			0
$890$		−	4.09908i		−	0.137402i
$891$	11.1318	+	11.1888i	0.372929	+	0.374838i
$892$	−13.3108	−	7.68501i	−0.445679	−	0.257313i
$893$	−21.8478	+	12.6138i	−0.731108	+	0.422105i
$894$	34.2905	+	2.26949i	1.14684	+	0.0759032i
$895$	−0.475003	+	0.274243i	−0.0158776	+	0.00916694i
$896$		0			0
$897$	−0.653630	−	1.32757i	−0.0218241	−	0.0443261i
$898$	17.2540			0.575774
$899$	−41.8499	+	72.4862i	−1.39577	+	2.41755i
$900$	12.1903	+	1.62071i	0.406343	+	0.0540237i
$901$	10.2985	−	5.94581i	0.343091	−	0.198084i
$902$	−7.11373	+	12.3213i	−0.236861	+	0.410256i
$903$		0			0
$904$	9.81676	+	17.0031i	0.326501	+	0.565516i
$905$	21.4186	+	12.3660i	0.711979	+	0.411061i
$906$	−2.51176	−	1.68062i	−0.0834476	−	0.0558350i
$907$	24.0653	+	41.6824i	0.799077	+	1.38404i	0.920218	+	0.391406i	$0.128011\pi$
$907$	24.0653	+	41.6824i	0.799077	+	1.38404i	−0.121142	+	0.992635i	$0.538656\pi$
$908$	−4.17388	−	7.22937i	−0.138515	−	0.239915i
$909$	−37.6858	−	5.01037i	−1.24996	−	0.166184i
$910$		0			0
$911$	20.5958	+	11.8910i	0.682368	+	0.393966i	0.800747	−	0.599003i	$-0.204436\pi$
$911$	20.5958	+	11.8910i	0.682368	+	0.393966i	−0.118378	+	0.992969i	$0.537770\pi$
$912$	−5.33961	−	3.57275i	−0.176812	−	0.118305i
$913$		−	8.45635i		−	0.279864i
$914$			1.37536i			0.0454930i
$915$	0.119054	−	1.79882i	0.00393580	−	0.0594672i
$916$	11.3671	+	6.56281i	0.375580	+	0.216841i
$917$		0			0
$918$	21.3444	+	18.7909i	0.704469	+	0.620192i
$919$	−10.9692	−	18.9992i	−0.361841	−	0.626727i	0.626423	−	0.779483i	$-0.284518\pi$
$919$	−10.9692	−	18.9992i	−0.361841	−	0.626727i	−0.988264	+	0.152757i	$0.951185\pi$
$920$	0.487145	+	0.843760i	0.0160607	+	0.0278179i
$921$	−15.2129	+	7.49011i	−0.501283	+	0.246808i
$922$	32.3947	+	18.7031i	1.06686	+	0.615953i
$923$	−4.58286	−	7.93774i	−0.150847	−	0.261274i
$924$		0			0
$925$	9.01122	−	15.6079i	0.296287	−	0.513184i
$926$	8.97742	−	5.18312i	0.295016	−	0.170328i
$927$	23.4823	−	9.69160i	0.771261	−	0.318314i
$928$	3.80397	−	6.58867i	0.124871	−	0.216284i
$929$	50.4538			1.65534			0.827668	−	0.561217i	$-0.189667\pi$
$929$	50.4538			1.65534			0.827668	+	0.561217i	$0.189667\pi$
$930$	18.0463	+	1.19438i	0.591760	+	0.0391653i
$931$		0			0
$932$	−9.84350	+	5.68315i	−0.322435	+	0.186158i
$933$	10.4845	+	21.2947i	0.343247	+	0.697158i
$934$	−31.4234	+	18.1423i	−1.02821	+	0.593635i
$935$	−7.88868	−	4.55453i	−0.257987	−	0.148949i
$936$	2.47500	+	0.329053i	0.0808978	+	0.0107554i
$937$			42.6251i			1.39250i	0.717799	+	0.696250i	$0.245150\pi$
$937$			42.6251i			1.39250i	−0.717799	+	0.696250i	$0.754850\pi$
$938$		0			0
$939$	29.3046	−	14.4282i	0.956320	−	0.470847i
$940$	−3.22758	+	5.59033i	−0.105272	+	0.182336i
$941$	55.0404			1.79427			0.897133	−	0.441761i	$-0.145646\pi$
$941$	55.0404			1.79427			0.897133	+	0.441761i	$0.145646\pi$
$942$	−7.26488	−	14.7554i	−0.236703	−	0.480758i
$943$		−	8.32815i		−	0.271202i
$944$	10.8659			0.353656
$945$		0			0
$946$	−10.8189			−0.351752
$947$			25.6884i			0.834760i	0.908732	+	0.417380i	$0.137052\pi$
$947$			25.6884i			0.834760i	−0.908732	+	0.417380i	$0.862948\pi$
$948$	7.53460	+	15.3033i	0.244712	+	0.497027i
$949$	−3.03875			−0.0986421
$950$	−7.60248	+	13.1679i	−0.246657	+	0.427223i
$951$	−12.2204	+	6.01675i	−0.396274	+	0.195106i
$952$		0			0
$953$			17.3463i			0.561903i	0.959722	+	0.280952i	$0.0906500\pi$
$953$			17.3463i			0.561903i	−0.959722	+	0.280952i	$0.909350\pi$
$954$	−2.48688	−	6.02561i	−0.0805158	−	0.195086i
$955$	−1.46279	−	0.844541i	−0.0473347	−	0.0273287i
$956$	−4.67039	+	2.69645i	−0.151051	+	0.0872094i
$957$	−10.2075	−	20.7321i	−0.329962	−	0.670175i
$958$	20.0875	−	11.5975i	0.648998	−	0.374699i
$959$		0			0
$960$	−1.64032	−	0.108564i	−0.0529412	−	0.00350388i
$961$	−90.0362			−2.90439
$962$	1.82955	−	3.16887i	0.0589870	−	0.102169i
$963$	0.587371	−	4.41795i	0.0189278	−	0.142366i
$964$	12.1233	−	6.99936i	0.390464	−	0.225434i
$965$	0.703935	−	1.21925i	0.0226605	−	0.0392491i
$966$		0			0
$967$	2.61334	+	4.52644i	0.0840393	+	0.145560i	0.904981	−	0.425451i	$-0.139885\pi$
$967$	2.61334	+	4.52644i	0.0840393	+	0.145560i	−0.820942	+	0.571011i	$0.806551\pi$
$968$	6.86292	+	3.96231i	0.220583	+	0.127353i
$969$	−31.5444	+	15.5310i	−1.01335	+	0.498927i
$970$	2.13925	+	3.70529i	0.0686873	+	0.118970i
$971$	−14.2195	−	24.6289i	−0.456326	−	0.790379i	0.542438	−	0.840096i	$-0.317501\pi$
$971$	−14.2195	−	24.6289i	−0.456326	−	0.790379i	−0.998763	+	0.0497167i	$0.984168\pi$
$972$	11.7528	−	10.2407i	0.376970	−	0.328472i
$973$		0			0
$974$	−24.8887	−	14.3695i	−0.797485	−	0.460428i
$975$	0.390231	−	5.89613i	0.0124974	−	0.188827i
$976$		−	1.09663i		−	0.0351021i
$977$			24.3217i			0.778119i	0.921213	+	0.389059i	$0.127200\pi$
$977$			24.3217i			0.778119i	−0.921213	+	0.389059i	$0.872800\pi$
$978$	−17.0458	−	11.4054i	−0.545065	−	0.364704i
$979$	−6.55917	−	3.78694i	−0.209632	−	0.121031i
$980$		0			0
$981$	17.4029	+	42.1665i	0.555632	+	1.34627i
$982$	12.1326	+	21.0143i	0.387168	+	0.670595i
$983$	−13.4186	−	23.2417i	−0.427987	−	0.741295i	0.568707	−	0.822540i	$-0.307444\pi$
$983$	−13.4186	−	23.2417i	−0.427987	−	0.741295i	−0.996694	+	0.0812449i	$0.974110\pi$
$984$	11.6788	+	7.81434i	0.372308	+	0.249112i
$985$	−2.01222	−	1.16176i	−0.0641147	−	0.0370166i
$986$	−20.8182	−	36.0582i	−0.662987	−	1.14833i
$987$		0			0
$988$	−1.54353	+	2.67348i	−0.0491063	+	0.0850547i
$989$	5.48446	−	3.16645i	0.174396	−	0.100687i
$990$	−3.04479	+	3.95758i	−0.0967697	+	0.125780i
$991$	−3.51093	+	6.08111i	−0.111528	+	0.193173i	−0.916387	−	0.400294i	$-0.868908\pi$
$991$	−3.51093	+	6.08111i	−0.111528	+	0.193173i	0.804858	+	0.593467i	$0.202241\pi$
$992$	11.0016			0.349303
$993$	−17.3940	−	35.3283i	−0.551980	−	1.12111i
$994$		0			0
$995$	−8.99193	+	5.19149i	−0.285063	+	0.164581i
$996$	−8.33384	−	0.551570i	−0.264068	−	0.0174772i
$997$	−9.60463	+	5.54524i	−0.304182	+	0.175619i	−0.644320	−	0.764756i	$-0.722859\pi$
$997$	−9.60463	+	5.54524i	−0.304182	+	0.175619i	0.340138	+	0.940375i	$0.389526\pi$
$998$	−23.0209	−	13.2911i	−0.728713	−	0.420723i
$999$	−7.30197	−	21.6470i	−0.231024	−	0.684880i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.l.c.227.18		48
3.2	odd	2		2646.2.l.c.521.6		48
7.2	even	3		882.2.t.c.803.24		48
7.3	odd	6		882.2.m.c.587.10	yes	48
7.4	even	3		882.2.m.c.587.3	yes	48
7.5	odd	6		882.2.t.c.803.13		48
7.6	odd	2	inner	882.2.l.c.227.19		48
9.4	even	3		2646.2.t.c.2285.8		48
9.5	odd	6		882.2.t.c.815.13		48
21.2	odd	6		2646.2.t.c.1979.7		48
21.5	even	6		2646.2.t.c.1979.8		48
21.11	odd	6		2646.2.m.c.1763.16		48
21.17	even	6		2646.2.m.c.1763.15		48
21.20	even	2		2646.2.l.c.521.5		48
63.4	even	3		2646.2.m.c.881.15		48
63.5	even	6	inner	882.2.l.c.509.6		48
63.13	odd	6		2646.2.t.c.2285.7		48
63.23	odd	6	inner	882.2.l.c.509.7		48
63.31	odd	6		2646.2.m.c.881.16		48
63.32	odd	6		882.2.m.c.293.10	yes	48
63.40	odd	6		2646.2.l.c.1097.6		48
63.41	even	6		882.2.t.c.815.24		48
63.58	even	3		2646.2.l.c.1097.5		48
63.59	even	6		882.2.m.c.293.3	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.l.c.227.18		48	1.1	even	1	trivial
882.2.l.c.227.19		48	7.6	odd	2	inner
882.2.l.c.509.6		48	63.5	even	6	inner
882.2.l.c.509.7		48	63.23	odd	6	inner
882.2.m.c.293.3	✓	48	63.59	even	6
882.2.m.c.293.10	yes	48	63.32	odd	6
882.2.m.c.587.3	yes	48	7.4	even	3
882.2.m.c.587.10	yes	48	7.3	odd	6
882.2.t.c.803.13		48	7.5	odd	6
882.2.t.c.803.24		48	7.2	even	3
882.2.t.c.815.13		48	9.5	odd	6
882.2.t.c.815.24		48	63.41	even	6
2646.2.l.c.521.5		48	21.20	even	2
2646.2.l.c.521.6		48	3.2	odd	2
2646.2.l.c.1097.5		48	63.58	even	3
2646.2.l.c.1097.6		48	63.40	odd	6
2646.2.m.c.881.15		48	63.4	even	3
2646.2.m.c.881.16		48	63.31	odd	6
2646.2.m.c.1763.15		48	21.17	even	6
2646.2.m.c.1763.16		48	21.11	odd	6
2646.2.t.c.1979.7		48	21.2	odd	6
2646.2.t.c.1979.8		48	21.5	even	6
2646.2.t.c.2285.7		48	63.13	odd	6
2646.2.t.c.2285.8		48	9.4	even	3

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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-0.765075 - 1.55392i) q^{3} -1.00000 q^{4} +(-0.474556 + 0.821956i) q^{5} +(1.55392 - 0.765075i) q^{6} -1.00000i q^{8} +(-1.82932 + 2.37773i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-0.765075 - 1.55392i) q^{3} -1.00000 q^{4} +(-0.474556 + 0.821956i) q^{5} +(1.55392 - 0.765075i) q^{6} -1.00000i q^{8} +(-1.82932 + 2.37773i) q^{9} +(-0.821956 - 0.474556i) q^{10} +(-1.51873 + 0.876838i) q^{11} +(0.765075 + 1.55392i) q^{12} +(0.720756 - 0.416129i) q^{13} +(1.64032 + 0.108564i) q^{15} +1.00000 q^{16} +(2.73638 - 4.73955i) q^{17} +(-2.37773 - 1.82932i) q^{18} +(3.21232 - 1.85463i) q^{19} +(0.474556 - 0.821956i) q^{20} +(-0.876838 - 1.51873i) q^{22} +(0.888998 + 0.513263i) q^{23} +(-1.55392 + 0.765075i) q^{24} +(2.04959 + 3.55000i) q^{25} +(0.416129 + 0.720756i) q^{26} +(5.09436 + 1.02347i) q^{27} +(-6.58867 - 3.80397i) q^{29} +(-0.108564 + 1.64032i) q^{30} -11.0016i q^{31} +1.00000i q^{32} +(2.52447 + 1.68913i) q^{33} +(4.73955 + 2.73638i) q^{34} +(1.82932 - 2.37773i) q^{36} +(-2.19830 - 3.80756i) q^{37} +(1.85463 + 3.21232i) q^{38} +(-1.19806 - 0.801626i) q^{39} +(0.821956 + 0.474556i) q^{40} +(-4.05647 - 7.02601i) q^{41} +(3.08463 - 5.34273i) q^{43} +(1.51873 - 0.876838i) q^{44} +(-1.08627 - 2.63199i) q^{45} +(-0.513263 + 0.888998i) q^{46} -6.80125 q^{47} +(-0.765075 - 1.55392i) q^{48} +(-3.55000 + 2.04959i) q^{50} +(-9.45841 - 0.625999i) q^{51} +(-0.720756 + 0.416129i) q^{52} +(1.88177 + 1.08644i) q^{53} +(-1.02347 + 5.09436i) q^{54} -1.66444i q^{55} +(-5.33961 - 3.57275i) q^{57} +(3.80397 - 6.58867i) q^{58} +10.8659 q^{59} +(-1.64032 - 0.108564i) q^{60} -1.09663i q^{61} +11.0016 q^{62} -1.00000 q^{64} +0.789907i q^{65} +(-1.68913 + 2.52447i) q^{66} +14.4481 q^{67} +(-2.73638 + 4.73955i) q^{68} +(0.117419 - 1.77412i) q^{69} -11.0131i q^{71} +(2.37773 + 1.82932i) q^{72} +(-3.16204 - 1.82561i) q^{73} +(3.80756 - 2.19830i) q^{74} +(3.94831 - 5.90091i) q^{75} +(-3.21232 + 1.85463i) q^{76} +(0.801626 - 1.19806i) q^{78} +9.84819 q^{79} +(-0.474556 + 0.821956i) q^{80} +(-2.30717 - 8.69925i) q^{81} +(7.02601 - 4.05647i) q^{82} +(-2.41103 + 4.17603i) q^{83} +(2.59713 + 4.49837i) q^{85} +(5.34273 + 3.08463i) q^{86} +(-0.870230 + 13.1486i) q^{87} +(0.876838 + 1.51873i) q^{88} +(2.15943 + 3.74024i) q^{89} +(2.63199 - 1.08627i) q^{90} +(-0.888998 - 0.513263i) q^{92} +(-17.0957 + 8.41708i) q^{93} -6.80125i q^{94} +3.52051i q^{95} +(1.55392 - 0.765075i) q^{96} +(-3.90396 - 2.25395i) q^{97} +(0.693358 - 5.21514i) 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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