LMFDB - Embedded newform 882.2.t.a.803.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(803,882)]

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, 5]))

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

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

chi := DirichletCharacter("882.803");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.t (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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			803.2
Root			$1.58110 - 0.707199i$ of defining polynomial
Character	$\chi$	$=$	882.803
Dual form			882.2.t.a.815.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.361565 + 1.69389i) q^{3} +(0.500000 - 0.866025i) q^{4} +0.900258 q^{5} +(-0.533822 - 1.64774i) q^{6} +1.00000i q^{8} +(-2.73854 - 1.22490i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.361565 + 1.69389i) q^{3} +(0.500000 - 0.866025i) q^{4} +0.900258 q^{5} +(-0.533822 - 1.64774i) q^{6} +1.00000i q^{8} +(-2.73854 - 1.22490i) q^{9} +(-0.779646 + 0.450129i) q^{10} -3.12809i q^{11} +(1.28617 + 1.16007i) q^{12} +(-1.99033 + 1.14912i) q^{13} +(-0.325502 + 1.52494i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.57638 - 4.46242i) q^{17} +(2.98410 - 0.308473i) q^{18} +(-2.38111 - 1.37474i) q^{19} +(0.450129 - 0.779646i) q^{20} +(1.56404 + 2.70900i) q^{22} +1.71570i q^{23} +(-1.69389 - 0.361565i) q^{24} -4.18954 q^{25} +(1.14912 - 1.99033i) q^{26} +(3.06502 - 4.19591i) q^{27} +(-1.85590 - 1.07151i) q^{29} +(-0.480577 - 1.48339i) q^{30} +(-8.66298 - 5.00158i) q^{31} +(0.866025 + 0.500000i) q^{32} +(5.29864 + 1.13101i) q^{33} +(4.46242 + 2.57638i) q^{34} +(-2.43007 + 1.75919i) q^{36} +(-4.73701 + 8.20475i) q^{37} +2.74947 q^{38} +(-1.22685 - 3.78689i) q^{39} +0.900258i q^{40} +(1.22134 + 2.11542i) q^{41} +(-0.273155 + 0.473119i) q^{43} +(-2.70900 - 1.56404i) q^{44} +(-2.46539 - 1.10273i) q^{45} +(-0.857850 - 1.48584i) q^{46} +(-3.93034 - 6.80755i) q^{47} +(1.64774 - 0.533822i) q^{48} +(3.62824 - 2.09477i) q^{50} +(8.49038 - 2.75065i) q^{51} +2.29824i q^{52} +(12.0733 - 6.97054i) q^{53} +(-0.556425 + 5.16627i) q^{54} -2.81608i q^{55} +(3.18958 - 3.53629i) q^{57} +2.14301 q^{58} +(-3.99222 + 6.91472i) q^{59} +(1.15789 + 1.04436i) q^{60} +(-6.28224 + 3.62705i) q^{61} +10.0032 q^{62} -1.00000 q^{64} +(-1.79181 + 1.03450i) q^{65} +(-5.15426 + 1.66984i) q^{66} +(-1.83525 + 3.17875i) q^{67} -5.15276 q^{68} +(-2.90621 - 0.620337i) q^{69} -14.1484i q^{71} +(1.22490 - 2.73854i) q^{72} +(10.9190 - 6.30409i) q^{73} -9.47403i q^{74} +(1.51479 - 7.09662i) q^{75} +(-2.38111 + 1.37474i) q^{76} +(2.95593 + 2.66612i) q^{78} +(3.27402 + 5.67077i) q^{79} +(-0.450129 - 0.779646i) q^{80} +(5.99922 + 6.70890i) q^{81} +(-2.11542 - 1.22134i) q^{82} +(0.184437 - 0.319454i) q^{83} +(-2.31940 - 4.01733i) q^{85} -0.546311i q^{86} +(2.48605 - 2.75628i) q^{87} +3.12809 q^{88} +(6.00244 - 10.3965i) q^{89} +(2.68646 - 0.277705i) q^{90} +(1.48584 + 0.857850i) q^{92} +(11.6044 - 12.8658i) q^{93} +(6.80755 + 3.93034i) q^{94} +(-2.14361 - 1.23762i) q^{95} +(-1.16007 + 1.28617i) q^{96} +(8.86815 + 5.12003i) q^{97} +(-3.83161 + 8.56640i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 6 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 - 6 * q^9	$ 16 q + 8 q^{4} - 6 q^{9} + 6 q^{13} - 18 q^{15} - 8 q^{16} - 18 q^{17} + 12 q^{18} + 6 q^{24} + 16 q^{25} + 12 q^{26} + 36 q^{27} + 6 q^{29} - 18 q^{30} - 6 q^{31} - 18 q^{33} - 2 q^{37} - 30 q^{39} - 6 q^{41} - 2 q^{43} + 12 q^{44} - 12 q^{45} + 6 q^{46} + 18 q^{47} - 12 q^{50} + 36 q^{53} - 18 q^{54} + 6 q^{57} - 12 q^{58} - 30 q^{59} - 6 q^{60} + 60 q^{61} + 36 q^{62} - 16 q^{64} + 42 q^{65} - 48 q^{66} + 14 q^{67} - 36 q^{68} - 42 q^{69} - 30 q^{75} - 16 q^{79} + 54 q^{81} - 12 q^{85} + 48 q^{87} - 24 q^{89} + 18 q^{90} + 6 q^{92} + 30 q^{93} - 66 q^{95} + 6 q^{96} + 6 q^{97} + 18 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 - 6 * q^9 + 6 * q^13 - 18 * q^15 - 8 * q^16 - 18 * q^17 + 12 * q^18 + 6 * q^24 + 16 * q^25 + 12 * q^26 + 36 * q^27 + 6 * q^29 - 18 * q^30 - 6 * q^31 - 18 * q^33 - 2 * q^37 - 30 * q^39 - 6 * q^41 - 2 * q^43 + 12 * q^44 - 12 * q^45 + 6 * q^46 + 18 * q^47 - 12 * q^50 + 36 * q^53 - 18 * q^54 + 6 * q^57 - 12 * q^58 - 30 * q^59 - 6 * q^60 + 60 * q^61 + 36 * q^62 - 16 * q^64 + 42 * q^65 - 48 * q^66 + 14 * q^67 - 36 * q^68 - 42 * q^69 - 30 * q^75 - 16 * q^79 + 54 * q^81 - 12 * q^85 + 48 * q^87 - 24 * q^89 + 18 * q^90 + 6 * q^92 + 30 * q^93 - 66 * q^95 + 6 * q^96 + 6 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.361565	+	1.69389i	−0.208750	+	0.977969i
$3$	−0.361565	+	1.69389i	−0.208750	+	0.977969i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	0.900258			0.402608			0.201304	−	0.979529i	$-0.435482\pi$
$5$	0.900258			0.402608			0.201304	+	0.979529i	$0.435482\pi$
$6$	−0.533822	−	1.64774i	−0.217932	−	0.672685i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−2.73854	−	1.22490i	−0.912847	−	0.408301i
$10$	−0.779646	+	0.450129i	−0.246546	+	0.142343i
$11$		−	3.12809i		−	0.943154i	−0.881825	−	0.471577i	$-0.843685\pi$
$11$		−	3.12809i		−	0.943154i	0.881825	−	0.471577i	$-0.156315\pi$
$12$	1.28617	+	1.16007i	0.371286	+	0.334883i
$13$	−1.99033	+	1.14912i	−0.552019	+	0.318708i	−0.749936	−	0.661511i	$-0.769916\pi$
$13$	−1.99033	+	1.14912i	−0.552019	+	0.318708i	0.197917	+	0.980219i	$0.436582\pi$
$14$		0			0
$15$	−0.325502	+	1.52494i	−0.0840442	+	0.393738i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.57638	−	4.46242i	−0.624863	−	1.08230i	−0.988567	−	0.150780i	$-0.951821\pi$
$17$	−2.57638	−	4.46242i	−0.624863	−	1.08230i	0.363704	−	0.931515i	$-0.381512\pi$
$18$	2.98410	−	0.308473i	0.703359	−	0.0727078i
$19$	−2.38111	−	1.37474i	−0.546264	−	0.315386i	0.201350	−	0.979519i	$-0.435467\pi$
$19$	−2.38111	−	1.37474i	−0.546264	−	0.315386i	−0.747614	+	0.664134i	$0.768801\pi$
$20$	0.450129	−	0.779646i	0.100652	−	0.174334i
$21$		0			0
$22$	1.56404	+	2.70900i	0.333455	+	0.577561i
$23$			1.71570i			0.357748i	0.983872	+	0.178874i	$0.0572455\pi$
$23$			1.71570i			0.357748i	−0.983872	+	0.178874i	$0.942755\pi$
$24$	−1.69389	−	0.361565i	−0.345764	−	0.0738041i
$25$	−4.18954			−0.837907
$26$	1.14912	−	1.99033i	0.225361	−	0.390336i
$27$	3.06502	−	4.19591i	0.589863	−	0.807504i
$28$		0			0
$29$	−1.85590	−	1.07151i	−0.344633	−	0.198974i	0.317686	−	0.948196i	$-0.397094\pi$
$29$	−1.85590	−	1.07151i	−0.344633	−	0.198974i	−0.662319	+	0.749222i	$0.730428\pi$
$30$	−0.480577	−	1.48339i	−0.0877410	−	0.270828i
$31$	−8.66298	−	5.00158i	−1.55592	−	0.898309i	−0.997640	−	0.0686548i	$-0.978129\pi$
$31$	−8.66298	−	5.00158i	−1.55592	−	0.898309i	−0.558277	−	0.829655i	$-0.688537\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	5.29864	+	1.13101i	0.922375	+	0.196883i
$34$	4.46242	+	2.57638i	0.765298	+	0.441845i
$35$		0			0
$36$	−2.43007	+	1.75919i	−0.405011	+	0.293199i
$37$	−4.73701	+	8.20475i	−0.778760	+	1.34885i	0.153896	+	0.988087i	$0.450818\pi$
$37$	−4.73701	+	8.20475i	−0.778760	+	1.34885i	−0.932657	+	0.360766i	$0.882515\pi$
$38$	2.74947			0.446023
$39$	−1.22685	−	3.78689i	−0.196453	−	0.606388i
$40$			0.900258i			0.142343i
$41$	1.22134	+	2.11542i	0.190741	+	0.330373i	0.945496	−	0.325634i	$-0.105578\pi$
$41$	1.22134	+	2.11542i	0.190741	+	0.330373i	−0.754755	+	0.656007i	$0.772244\pi$
$42$		0			0
$43$	−0.273155	+	0.473119i	−0.0416558	+	0.0721499i	−0.886102	−	0.463491i	$-0.846597\pi$
$43$	−0.273155	+	0.473119i	−0.0416558	+	0.0721499i	0.844446	+	0.535641i	$0.179930\pi$
$44$	−2.70900	−	1.56404i	−0.408397	−	0.235788i
$45$	−2.46539	−	1.10273i	−0.367519	−	0.164385i
$46$	−0.857850	−	1.48584i	−0.126483	−	0.219075i
$47$	−3.93034	−	6.80755i	−0.573299	−	0.992983i	−0.996224	−	0.0868184i	$-0.972330\pi$
$47$	−3.93034	−	6.80755i	−0.573299	−	0.992983i	0.422925	−	0.906165i	$-0.361003\pi$
$48$	1.64774	−	0.533822i	0.237830	−	0.0770505i
$49$		0			0
$50$	3.62824	−	2.09477i	0.513111	−	0.296245i
$51$	8.49038	−	2.75065i	1.18889	−	0.385168i
$52$			2.29824i			0.318708i
$53$	12.0733	−	6.97054i	1.65840	−	0.957478i	0.684947	−	0.728593i	$-0.259825\pi$
$53$	12.0733	−	6.97054i	1.65840	−	0.957478i	0.973454	−	0.228885i	$-0.0735079\pi$
$54$	−0.556425	+	5.16627i	−0.0757199	+	0.703041i
$55$		−	2.81608i		−	0.379721i
$56$		0			0
$57$	3.18958	−	3.53629i	0.422470	−	0.468393i
$58$	2.14301			0.281391
$59$	−3.99222	+	6.91472i	−0.519742	+	0.900220i	0.479994	+	0.877272i	$0.340639\pi$
$59$	−3.99222	+	6.91472i	−0.519742	+	0.900220i	−0.999737	+	0.0229484i	$0.992695\pi$
$60$	1.15789	+	1.04436i	0.149482	+	0.134827i
$61$	−6.28224	+	3.62705i	−0.804359	+	0.464397i	−0.844993	−	0.534777i	$-0.820395\pi$
$61$	−6.28224	+	3.62705i	−0.804359	+	0.464397i	0.0406343	+	0.999174i	$0.487062\pi$
$62$	10.0032			1.27040
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.79181	+	1.03450i	−0.222247	+	0.128314i
$66$	−5.15426	+	1.66984i	−0.634446	+	0.205543i
$67$	−1.83525	+	3.17875i	−0.224212	+	0.388346i	−0.956083	−	0.293097i	$-0.905314\pi$
$67$	−1.83525	+	3.17875i	−0.224212	+	0.388346i	0.731871	+	0.681443i	$0.238647\pi$
$68$	−5.15276			−0.624863
$69$	−2.90621	−	0.620337i	−0.349867	−	0.0746798i
$70$		0			0
$71$		−	14.1484i		−	1.67911i	−0.543275	−	0.839555i	$-0.682816\pi$
$71$		−	14.1484i		−	1.67911i	0.543275	−	0.839555i	$-0.317184\pi$
$72$	1.22490	−	2.73854i	0.144356	−	0.322740i
$73$	10.9190	−	6.30409i	1.27797	−	0.737838i	0.301498	−	0.953467i	$-0.402513\pi$
$73$	10.9190	−	6.30409i	1.27797	−	0.737838i	0.976475	+	0.215629i	$0.0691801\pi$
$74$		−	9.47403i		−	1.10133i
$75$	1.51479	−	7.09662i	0.174913	−	0.819447i
$76$	−2.38111	+	1.37474i	−0.273132	+	0.157693i
$77$		0			0
$78$	2.95593	+	2.66612i	0.334693	+	0.301878i
$79$	3.27402	+	5.67077i	0.368356	+	0.638011i	0.989309	−	0.145837i	$-0.0465875\pi$
$79$	3.27402	+	5.67077i	0.368356	+	0.638011i	−0.620953	+	0.783848i	$0.713254\pi$
$80$	−0.450129	−	0.779646i	−0.0503259	−	0.0871671i
$81$	5.99922	+	6.70890i	0.666580	+	0.745433i
$82$	−2.11542	−	1.22134i	−0.233609	−	0.134874i
$83$	0.184437	−	0.319454i	0.0202446	−	0.0350646i	−0.855726	−	0.517430i	$-0.826889\pi$
$83$	0.184437	−	0.319454i	0.0202446	−	0.0350646i	0.875970	+	0.482365i	$0.160222\pi$
$84$		0			0
$85$	−2.31940	−	4.01733i	−0.251575	−	0.435740i
$86$		−	0.546311i		−	0.0589102i
$87$	2.48605	−	2.75628i	0.266532	−	0.295504i
$88$	3.12809			0.333455
$89$	6.00244	−	10.3965i	0.636258	−	1.10203i	−0.349990	−	0.936754i	$-0.613815\pi$
$89$	6.00244	−	10.3965i	0.636258	−	1.10203i	0.986247	−	0.165277i	$-0.0528518\pi$
$90$	2.68646	−	0.277705i	0.283178	−	0.0292727i
$91$		0			0
$92$	1.48584	+	0.857850i	0.154909	+	0.0894370i
$93$	11.6044	−	12.8658i	1.20332	−	1.33412i
$94$	6.80755	+	3.93034i	0.702145	+	0.405384i
$95$	−2.14361	−	1.23762i	−0.219930	−	0.126977i
$96$	−1.16007	+	1.28617i	−0.118399	+	0.131269i
$97$	8.86815	+	5.12003i	0.900424	+	0.519860i	0.877338	−	0.479873i	$-0.159317\pi$
$97$	8.86815	+	5.12003i	0.900424	+	0.519860i	0.0230864	+	0.999733i	$0.492651\pi$
$98$		0			0
$99$	−3.83161	+	8.56640i	−0.385091	+	0.860955i
$100$	−2.09477	+	3.62824i	−0.209477	+	0.362824i
$101$	2.71939			0.270589			0.135294	−	0.990805i	$-0.456802\pi$
$101$	2.71939			0.270589			0.135294	+	0.990805i	$0.456802\pi$
$102$	−5.97756	+	6.62733i	−0.591867	+	0.656203i
$103$		−	1.37248i		−	0.135235i	−0.997711	−	0.0676174i	$-0.978460\pi$
$103$		−	1.37248i		−	0.135235i	0.997711	−	0.0676174i	$-0.0215397\pi$
$104$	−1.14912	−	1.99033i	−0.112680	−	0.195168i
$105$		0			0
$106$	−6.97054	+	12.0733i	−0.677039	+	1.17267i
$107$	−12.3585	−	7.13519i	−1.19474	−	0.689785i	−0.235364	−	0.971907i	$-0.575628\pi$
$107$	−12.3585	−	7.13519i	−1.19474	−	0.689785i	−0.959378	+	0.282122i	$0.908962\pi$
$108$	−2.10126	−	4.75234i	−0.202194	−	0.457294i
$109$	−2.64583	−	4.58271i	−0.253425	−	0.438944i	0.711042	−	0.703150i	$-0.248224\pi$
$109$	−2.64583	−	4.58271i	−0.253425	−	0.438944i	−0.964466	+	0.264206i	$0.914890\pi$
$110$	1.40804	+	2.43880i	0.134252	+	0.232531i
$111$	−12.1852	−	10.9905i	−1.15657	−	1.04318i
$112$		0			0
$113$	−2.30371	+	1.33005i	−0.216715	+	0.125121i	−0.604428	−	0.796659i	$-0.706598\pi$
$113$	−2.30371	+	1.33005i	−0.216715	+	0.125121i	0.387713	+	0.921780i	$0.373265\pi$
$114$	−0.994112	+	4.65731i	−0.0931071	+	0.436197i
$115$			1.54457i			0.144032i
$116$	−1.85590	+	1.07151i	−0.172316	+	0.0994869i
$117$	6.85817	−	0.708944i	0.634038	−	0.0655419i
$118$		−	7.98443i		−	0.735026i
$119$		0			0
$120$	−1.52494	−	0.325502i	−0.139207	−	0.0297141i
$121$	1.21507			0.110461
$122$	3.62705	−	6.28224i	0.328378	−	0.568767i
$123$	−4.02489	+	1.30395i	−0.362912	+	0.117574i
$124$	−8.66298	+	5.00158i	−0.777959	+	0.449155i
$125$	−8.27295			−0.739955
$126$		0			0
$127$	6.10587			0.541808			0.270904	−	0.962606i	$-0.412677\pi$
$127$	6.10587			0.541808			0.270904	+	0.962606i	$0.412677\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−0.702649	−	0.633759i	−0.0618648	−	0.0557993i
$130$	1.03450	−	1.79181i	0.0907320	−	0.157152i
$131$	7.95758			0.695257			0.347629	−	0.937632i	$-0.386987\pi$
$131$	7.95758			0.695257			0.347629	+	0.937632i	$0.386987\pi$
$132$	3.62880	−	4.02326i	0.315847	−	0.350179i
$133$		0			0
$134$		−	3.67050i		−	0.317083i
$135$	2.75930	−	3.77740i	0.237483	−	0.325107i
$136$	4.46242	−	2.57638i	0.382649	−	0.220923i
$137$			21.8400i			1.86591i	0.359988	+	0.932957i	$0.382781\pi$
$137$			21.8400i			1.86591i	−0.359988	+	0.932957i	$0.617219\pi$
$138$	2.82702	−	0.915878i	0.240652	−	0.0779647i
$139$	−11.7109	+	6.76127i	−0.993302	+	0.573483i	−0.906260	−	0.422721i	$-0.861075\pi$
$139$	−11.7109	+	6.76127i	−0.993302	+	0.573483i	−0.0870425	+	0.996205i	$0.527742\pi$
$140$		0			0
$141$	12.9523	−	4.19620i	1.09078	−	0.353384i
$142$	7.07421	+	12.2529i	0.593655	+	1.02824i
$143$	3.59454	+	6.22593i	0.300591	+	0.520639i
$144$	0.308473	+	2.98410i	0.0257061	+	0.248675i
$145$	−1.67079	−	0.964632i	−0.138752	−	0.0801083i
$146$	−6.30409	+	10.9190i	−0.521730	+	0.903663i
$147$		0			0
$148$	4.73701	+	8.20475i	0.389380	+	0.674426i
$149$			5.09444i			0.417353i	0.977985	+	0.208676i	$0.0669156\pi$
$149$			5.09444i			0.417353i	−0.977985	+	0.208676i	$0.933084\pi$
$150$	2.23647	+	6.90325i	0.182607	+	0.563648i
$151$	−21.1755			−1.72324			−0.861618	−	0.507557i	$-0.830549\pi$
$151$	−21.1755			−1.72324			−0.861618	+	0.507557i	$0.830549\pi$
$152$	1.37474	−	2.38111i	0.111506	−	0.193134i
$153$	1.58949	+	15.3763i	0.128502	+	1.24310i
$154$		0			0
$155$	−7.79892	−	4.50271i	−0.626424	−	0.361666i
$156$	−3.89297	−	0.830962i	−0.311687	−	0.0665302i
$157$	0.311703	+	0.179962i	0.0248766	+	0.0143625i	0.512387	−	0.858755i	$-0.328761\pi$
$157$	0.311703	+	0.179962i	0.0248766	+	0.0143625i	−0.487510	+	0.873117i	$0.662095\pi$
$158$	−5.67077	−	3.27402i	−0.451142	−	0.260467i
$159$	7.44206	+	22.9712i	0.590193	+	1.82174i
$160$	0.779646	+	0.450129i	0.0616364	+	0.0355858i
$161$		0			0
$162$	−8.54993	−	2.81047i	−0.671746	−	0.220811i
$163$	6.18640	−	10.7152i	0.484557	−	0.839277i	−0.515286	−	0.857018i	$-0.672314\pi$
$163$	6.18640	−	10.7152i	0.484557	−	0.839277i	0.999843	+	0.0177416i	$0.00564762\pi$
$164$	2.44268			0.190741
$165$	4.77014	+	1.01820i	0.371355	+	0.0792665i
$166$			0.368874i			0.0286301i
$167$	−7.40866	−	12.8322i	−0.573299	−	0.992984i	−0.996224	−	0.0868188i	$-0.972330\pi$
$167$	−7.40866	−	12.8322i	−0.573299	−	0.992984i	0.422925	−	0.906165i	$-0.361003\pi$
$168$		0			0
$169$	−3.85905	+	6.68407i	−0.296850	+	0.514159i
$170$	4.01733	+	2.31940i	0.308115	+	0.177890i
$171$	4.83685	+	6.68140i	0.369883	+	0.510940i
$172$	0.273155	+	0.473119i	0.0208279	+	0.0360750i
$173$	−2.31772	−	4.01441i	−0.176213	−	0.305210i	0.764367	−	0.644781i	$-0.223051\pi$
$173$	−2.31772	−	4.01441i	−0.176213	−	0.305210i	−0.940580	+	0.339571i	$0.889718\pi$
$174$	−0.774838	+	3.63003i	−0.0587403	+	0.275192i
$175$		0			0
$176$	−2.70900	+	1.56404i	−0.204199	+	0.117894i
$177$	−10.2693	−	9.26250i	−0.771891	−	0.696212i
$178$			12.0049i			0.899804i
$179$	5.25855	−	3.03602i	0.393042	−	0.226923i	−0.290435	−	0.956895i	$-0.593800\pi$
$179$	5.25855	−	3.03602i	0.393042	−	0.226923i	0.683477	+	0.729972i	$0.260467\pi$
$180$	−2.18769	+	1.58373i	−0.163061	+	0.118044i
$181$			7.12701i			0.529746i	0.964283	+	0.264873i	$0.0853301\pi$
$181$			7.12701i			0.529746i	−0.964283	+	0.264873i	$0.914670\pi$
$182$		0			0
$183$	−3.87240	−	11.9529i	−0.286256	−	0.883581i
$184$	−1.71570			−0.126483
$185$	−4.26453	+	7.38639i	−0.313535	+	0.543058i
$186$	−3.61679	+	16.9443i	−0.265196	+	1.24241i
$187$	−13.9588	+	8.05913i	−1.02077	+	0.589342i
$188$	−7.86068			−0.573299
$189$		0			0
$190$	2.47523			0.179572
$191$	−12.4713	+	7.20032i	−0.902394	+	0.520997i	−0.877976	−	0.478705i	$-0.841106\pi$
$191$	−12.4713	+	7.20032i	−0.902394	+	0.520997i	−0.0244176	+	0.999702i	$0.507773\pi$
$192$	0.361565	−	1.69389i	0.0260937	−	0.122246i
$193$	−8.90573	+	15.4252i	−0.641048	+	1.11033i	0.344151	+	0.938914i	$0.388167\pi$
$193$	−8.90573	+	15.4252i	−0.641048	+	1.11033i	−0.985199	+	0.171414i	$0.945166\pi$
$194$	−10.2401			−0.735193
$195$	−1.10448	−	3.40918i	−0.0790935	−	0.244136i
$196$		0			0
$197$			19.1025i			1.36100i	0.732750	+	0.680498i	$0.238236\pi$
$197$			19.1025i			1.36100i	−0.732750	+	0.680498i	$0.761764\pi$
$198$	−0.964930	−	9.33452i	−0.0685746	−	0.663375i
$199$	−11.6008	+	6.69771i	−0.822357	+	0.474788i	−0.851229	−	0.524795i	$-0.824142\pi$
$199$	−11.6008	+	6.69771i	−0.822357	+	0.474788i	0.0288716	+	0.999583i	$0.490809\pi$
$200$		−	4.18954i		−	0.296245i
$201$	−4.72090	−	4.25804i	−0.332986	−	0.300339i
$202$	−2.35506	+	1.35969i	−0.165701	+	0.0956677i
$203$		0			0
$204$	1.86306	−	8.72821i	0.130440	−	0.611097i
$205$	1.09952	+	1.90442i	0.0767937	+	0.133011i
$206$	0.686242	+	1.18861i	0.0478127	+	0.0828141i
$207$	2.10157	−	4.69852i	0.146069	−	0.326569i
$208$	1.99033	+	1.14912i	0.138005	+	0.0796771i
$209$	−4.30029	+	7.44832i	−0.297457	+	0.515211i
$210$		0			0
$211$	−9.37193	−	16.2327i	−0.645190	−	1.11750i	−0.984258	−	0.176740i	$-0.943445\pi$
$211$	−9.37193	−	16.2327i	−0.645190	−	1.11750i	0.339067	−	0.940762i	$-0.389889\pi$
$212$		−	13.9411i		−	0.957478i
$213$	23.9659	+	5.11557i	1.64212	+	0.350513i
$214$	14.2704			0.975503
$215$	−0.245910	+	0.425929i	−0.0167709	+	0.0290481i
$216$	4.19591	+	3.06502i	0.285496	+	0.208548i
$217$		0			0
$218$	4.58271	+	2.64583i	0.310380	+	0.179198i
$219$	6.73052	+	20.7750i	0.454807	+	1.40384i
$220$	−2.43880	−	1.40804i	−0.164424	−	0.0949302i
$221$	10.2557	+	5.92113i	0.689873	+	0.398298i
$222$	16.0480	+	3.42548i	1.07707	+	0.229903i
$223$	2.21609	+	1.27946i	0.148400	+	0.0856789i	0.572362	−	0.820001i	$-0.306027\pi$
$223$	2.21609	+	1.27946i	0.148400	+	0.0856789i	−0.423961	+	0.905680i	$0.639361\pi$
$224$		0			0
$225$	11.4732	+	5.13178i	0.764881	+	0.342119i
$226$	1.33005	−	2.30371i	0.0884736	−	0.153241i
$227$	8.72909			0.579370			0.289685	−	0.957122i	$-0.406449\pi$
$227$	8.72909			0.579370			0.289685	+	0.957122i	$0.406449\pi$
$228$	−1.46773	−	4.53040i	−0.0972026	−	0.300033i
$229$			3.93729i			0.260183i	0.991502	+	0.130092i	$0.0415272\pi$
$229$			3.93729i			0.260183i	−0.991502	+	0.130092i	$0.958473\pi$
$230$	−0.772286	−	1.33764i	−0.0509230	−	0.0882013i
$231$		0			0
$232$	1.07151	−	1.85590i	0.0703478	−	0.121846i
$233$	3.92147	+	2.26406i	0.256904	+	0.148324i	0.622921	−	0.782284i	$-0.285946\pi$
$233$	3.92147	+	2.26406i	0.256904	+	0.148324i	−0.366018	+	0.930608i	$0.619279\pi$
$234$	−5.58488	+	4.04305i	−0.365095	+	0.264302i
$235$	−3.53832	−	6.12855i	−0.230815	−	0.399782i
$236$	3.99222	+	6.91472i	0.259871	+	0.450110i
$237$	−10.7894	+	3.49548i	−0.700849	+	0.227056i
$238$		0			0
$239$	−7.55315	+	4.36081i	−0.488573	+	0.282078i	−0.723982	−	0.689819i	$-0.757690\pi$
$239$	−7.55315	+	4.36081i	−0.488573	+	0.282078i	0.235409	+	0.971896i	$0.424357\pi$
$240$	1.48339	−	0.480577i	0.0957522	−	0.0310211i
$241$		−	19.7816i		−	1.27424i	−0.770763	−	0.637122i	$-0.780125\pi$
$241$		−	19.7816i		−	1.27424i	0.770763	−	0.637122i	$-0.219875\pi$
$242$	−1.05229	+	0.607537i	−0.0676435	+	0.0390540i
$243$	−13.5333	+	7.73633i	−0.868159	+	0.496286i
$244$			7.25411i			0.464397i
$245$		0			0
$246$	2.83368	−	3.14170i	0.180669	−	0.200307i
$247$	6.31894			0.402064
$248$	5.00158	−	8.66298i	0.317600	−	0.550100i
$249$	0.474435	+	0.427919i	0.0300661	+	0.0271183i
$250$	7.16459	−	4.13648i	0.453128	−	0.261614i
$251$	3.80791			0.240353			0.120176	−	0.992753i	$-0.461654\pi$
$251$	3.80791			0.240353			0.120176	+	0.992753i	$0.461654\pi$
$252$		0			0
$253$	5.36686			0.337411
$254$	−5.28784	+	3.05293i	−0.331788	+	0.191558i
$255$	7.64353	−	2.47630i	0.478657	−	0.155072i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	15.0754			0.940379			0.470189	−	0.882566i	$-0.344186\pi$
$257$	15.0754			0.940379			0.470189	+	0.882566i	$0.344186\pi$
$258$	0.925391	+	0.197527i	0.0576123	+	0.0122975i
$259$		0			0
$260$			2.06901i			0.128314i
$261$	3.76998	+	5.20767i	0.233356	+	0.322347i
$262$	−6.89147	+	3.97879i	−0.425756	+	0.245811i
$263$		−	7.61931i		−	0.469827i	−0.972016	−	0.234913i	$-0.924519\pi$
$263$		−	7.61931i		−	0.469827i	0.972016	−	0.234913i	$-0.0754806\pi$
$264$	−1.13101	+	5.29864i	−0.0696086	+	0.326109i
$265$	10.8691	−	6.27529i	0.667684	−	0.385488i
$266$		0			0
$267$	15.4403	+	13.9265i	0.944933	+	0.852289i
$268$	1.83525	+	3.17875i	0.112106	+	0.194173i
$269$	−4.32720	−	7.49493i	−0.263834	−	0.456974i	0.703424	−	0.710771i	$-0.251654\pi$
$269$	−4.32720	−	7.49493i	−0.263834	−	0.456974i	−0.967257	+	0.253797i	$0.918320\pi$
$270$	−0.500926	+	4.65098i	−0.0304854	+	0.283050i
$271$	15.6611	+	9.04193i	0.951343	+	0.549258i	0.893498	−	0.449068i	$-0.148244\pi$
$271$	15.6611	+	9.04193i	0.951343	+	0.549258i	0.0578449	+	0.998326i	$0.481577\pi$
$272$	−2.57638	+	4.46242i	−0.156216	+	0.270574i
$273$		0			0
$274$	−10.9200	−	18.9140i	−0.659700	−	1.14263i
$275$			13.1052i			0.790275i
$276$	−1.99033	+	2.20668i	−0.119804	+	0.132827i
$277$	9.98145			0.599727			0.299864	−	0.953982i	$-0.403059\pi$
$277$	9.98145			0.599727			0.299864	+	0.953982i	$0.403059\pi$
$278$	6.76127	−	11.7109i	0.405514	−	0.702371i
$279$	17.5975	+	24.3083i	1.05353	+	1.45530i
$280$		0			0
$281$	−13.0297	−	7.52272i	−0.777289	−	0.448768i	0.0581797	−	0.998306i	$-0.481470\pi$
$281$	−13.0297	−	7.52272i	−0.777289	−	0.448768i	−0.835469	+	0.549538i	$0.814804\pi$
$282$	−9.11894	+	10.1102i	−0.543025	+	0.602053i
$283$	3.48950	+	2.01467i	0.207429	+	0.119759i	0.600116	−	0.799913i	$-0.295121\pi$
$283$	3.48950	+	2.01467i	0.207429	+	0.119759i	−0.392687	+	0.919672i	$0.628454\pi$
$284$	−12.2529	−	7.07421i	−0.727076	−	0.419777i
$285$	2.87144	−	3.18357i	0.170090	−	0.188579i
$286$	−6.22593	−	3.59454i	−0.368147	−	0.212550i
$287$		0			0
$288$	−1.75919	−	2.43007i	−0.103662	−	0.143193i
$289$	−4.77544	+	8.27131i	−0.280908	+	0.486548i
$290$	1.92926			0.113290
$291$	−11.8792	+	13.1705i	−0.696370	+	0.772066i
$292$		−	12.6082i		−	0.737838i
$293$	6.59608	+	11.4248i	0.385347	+	0.667441i	0.991817	−	0.127665i	$-0.0407483\pi$
$293$	6.59608	+	11.4248i	0.385347	+	0.667441i	−0.606470	+	0.795106i	$0.707415\pi$
$294$		0			0
$295$	−3.59402	+	6.22503i	−0.209252	+	0.362435i
$296$	−8.20475	−	4.73701i	−0.476891	−	0.275333i
$297$	−13.1252	−	9.58763i	−0.761600	−	0.556331i
$298$	−2.54722	−	4.41192i	−0.147557	−	0.255575i
$299$	−1.97154	−	3.41481i	−0.114017	−	0.197484i
$300$	−5.38846	−	4.86016i	−0.311103	−	0.280601i
$301$		0			0
$302$	18.3385	−	10.5877i	1.05526	−	0.609256i
$303$	−0.983234	+	4.60635i	−0.0564853	+	0.264628i
$304$			2.74947i			0.157693i
$305$	−5.65564	+	3.26528i	−0.323841	+	0.186970i
$306$	−9.06470	−	12.5215i	−0.518194	−	0.715809i
$307$		−	28.7690i		−	1.64194i	−0.570974	−	0.820968i	$-0.693434\pi$
$307$		−	28.7690i		−	1.64194i	0.570974	−	0.820968i	$-0.306566\pi$
$308$		0			0
$309$	2.32484	+	0.496242i	0.132255	+	0.0282302i
$310$	9.00541			0.511473
$311$	−15.4228	+	26.7132i	−0.874550	+	1.51476i	−0.0173077	+	0.999850i	$0.505509\pi$
$311$	−15.4228	+	26.7132i	−0.874550	+	1.51476i	−0.857242	+	0.514914i	$0.827824\pi$
$312$	3.78689	−	1.22685i	0.214390	−	0.0694567i
$313$	−15.9055	+	9.18304i	−0.899032	+	0.519056i	−0.876886	−	0.480698i	$-0.840383\pi$
$313$	−15.9055	+	9.18304i	−0.899032	+	0.519056i	−0.0221460	+	0.999755i	$0.507050\pi$
$314$	−0.359924			−0.0203117
$315$		0			0
$316$	6.54804			0.368356
$317$	15.1173	−	8.72800i	0.849074	−	0.490213i	−0.0112642	−	0.999937i	$-0.503586\pi$
$317$	15.1173	−	8.72800i	0.849074	−	0.490213i	0.860338	+	0.509723i	$0.170252\pi$
$318$	−17.9306	−	16.1726i	−1.00550	−	0.906917i
$319$	−3.35176	+	5.80543i	−0.187663	+	0.325042i
$320$	−0.900258			−0.0503259
$321$	16.5546	−	18.3542i	0.923990	−	1.02443i
$322$		0			0
$323$			14.1673i			0.788292i
$324$	8.80969	−	1.84103i	0.489427	−	0.102279i
$325$	8.33857	−	4.81428i	0.462541	−	0.267048i
$326$			12.3728i			0.685267i
$327$	8.71926	−	2.82480i	0.482176	−	0.156212i
$328$	−2.11542	+	1.22134i	−0.116804	+	0.0674371i
$329$		0			0
$330$	−4.64016	+	1.50329i	−0.255433	+	0.0827532i
$331$	−5.21472	−	9.03216i	−0.286627	−	0.496452i	0.686375	−	0.727247i	$-0.259201\pi$
$331$	−5.21472	−	9.03216i	−0.286627	−	0.496452i	−0.973002	+	0.230795i	$0.925867\pi$
$332$	−0.184437	−	0.319454i	−0.0101223	−	0.0175323i
$333$	23.0225	−	16.6667i	1.26163	−	0.913328i
$334$	12.8322	+	7.40866i	0.702145	+	0.405384i
$335$	−1.65220	+	2.86169i	−0.0902693	+	0.156351i
$336$		0			0
$337$	−15.8312	−	27.4204i	−0.862380	−	1.49369i	−0.869626	−	0.493712i	$-0.835640\pi$
$337$	−15.8312	−	27.4204i	−0.862380	−	1.49369i	0.00724616	−	0.999974i	$-0.497693\pi$
$338$		−	7.71810i		−	0.419809i
$339$	−1.42002	−	4.38314i	−0.0771248	−	0.238060i
$340$	−4.63881			−0.251575
$341$	−15.6454	+	27.0986i	−0.847244	+	1.46747i
$342$	−7.52954	−	3.36784i	−0.407151	−	0.182112i
$343$		0			0
$344$	−0.473119	−	0.273155i	−0.0255089	−	0.0147275i
$345$	−2.61634	−	0.558463i	−0.140859	−	0.0300666i
$346$	4.01441	+	2.31772i	0.215816	+	0.124601i
$347$	−10.8472	−	6.26261i	−0.582306	−	0.336195i	0.179743	−	0.983714i	$-0.442473\pi$
$347$	−10.8472	−	6.26261i	−0.582306	−	0.336195i	−0.762049	+	0.647519i	$0.775807\pi$
$348$	−1.14399	−	3.53112i	−0.0613241	−	0.189288i
$349$	12.2560	+	7.07599i	0.656047	+	0.378769i	0.790769	−	0.612115i	$-0.209681\pi$
$349$	12.2560	+	7.07599i	0.656047	+	0.378769i	−0.134722	+	0.990883i	$0.543014\pi$
$350$		0			0
$351$	−1.27880	+	11.8733i	−0.0682572	+	0.633751i
$352$	1.56404	−	2.70900i	0.0833638	−	0.144390i
$353$	4.96535			0.264279			0.132139	−	0.991231i	$-0.457815\pi$
$353$	4.96535			0.264279			0.132139	+	0.991231i	$0.457815\pi$
$354$	13.5248	+	2.88689i	0.718833	+	0.153436i
$355$		−	12.7372i		−	0.676022i
$356$	−6.00244	−	10.3965i	−0.318129	−	0.551015i
$357$		0			0
$358$	−3.03602	+	5.25855i	−0.160459	+	0.277923i
$359$	−15.0013	−	8.66098i	−0.791736	−	0.457109i	0.0488375	−	0.998807i	$-0.484448\pi$
$359$	−15.0013	−	8.66098i	−0.791736	−	0.457109i	−0.840573	+	0.541698i	$0.817782\pi$
$360$	1.10273	−	2.46539i	0.0581189	−	0.129938i
$361$	−5.72021	−	9.90769i	−0.301063	−	0.521457i
$362$	−3.56350	−	6.17217i	−0.187294	−	0.324402i
$363$	−0.439328	+	2.05821i	−0.0230588	+	0.108028i
$364$		0			0
$365$	9.82992	−	5.67531i	0.514522	−	0.297059i
$366$	9.33003	+	8.41528i	0.487688	+	0.439874i
$367$			1.37177i			0.0716057i	0.999359	+	0.0358029i	$0.0113988\pi$
$367$			1.37177i			0.0716057i	−0.999359	+	0.0358029i	$0.988601\pi$
$368$	1.48584	−	0.857850i	0.0774547	−	0.0447185i
$369$	−0.753500	−	7.28919i	−0.0392256	−	0.379460i
$370$		−	8.52907i		−	0.443405i
$371$		0			0
$372$	−5.33990	−	16.4826i	−0.276861	−	0.854581i
$373$	−4.80975			−0.249040			−0.124520	−	0.992217i	$-0.539739\pi$
$373$	−4.80975			−0.249040			−0.124520	+	0.992217i	$0.539739\pi$
$374$	8.05913	−	13.9588i	0.416728	−	0.721794i
$375$	2.99121	−	14.0135i	0.154465	−	0.723653i
$376$	6.80755	−	3.93034i	0.351073	−	0.202692i
$377$	4.92515			0.253658
$378$		0			0
$379$	19.5669			1.00508			0.502542	−	0.864553i	$-0.332398\pi$
$379$	19.5669			1.00508			0.502542	+	0.864553i	$0.332398\pi$
$380$	−2.14361	+	1.23762i	−0.109965	+	0.0634884i
$381$	−2.20767	+	10.3427i	−0.113102	+	0.529872i
$382$	7.20032	−	12.4713i	0.368401	−	0.638089i
$383$	−31.4697			−1.60803			−0.804014	−	0.594610i	$-0.797306\pi$
$383$	−31.4697			−1.60803			−0.804014	+	0.594610i	$0.797306\pi$
$384$	0.533822	+	1.64774i	0.0272415	+	0.0840857i
$385$		0			0
$386$		−	17.8115i		−	0.906579i
$387$	1.32757	−	0.961067i	0.0674843	−	0.0488538i
$388$	8.86815	−	5.12003i	0.450212	−	0.259930i
$389$			4.06605i			0.206157i	0.994673	+	0.103078i	$0.0328693\pi$
$389$			4.06605i			0.206157i	−0.994673	+	0.103078i	$0.967131\pi$
$390$	2.66110	+	2.40019i	0.134750	+	0.121539i
$391$	7.65617	−	4.42029i	0.387189	−	0.223544i
$392$		0			0
$393$	−2.87718	+	13.4793i	−0.145135	+	0.679940i
$394$	−9.55124	−	16.5432i	−0.481185	−	0.833436i
$395$	2.94746	+	5.10515i	0.148303	+	0.256868i
$396$	5.50291	+	7.60147i	0.276532	+	0.381988i
$397$	3.81692	+	2.20370i	0.191566	+	0.110601i	0.592715	−	0.805412i	$-0.298056\pi$
$397$	3.81692	+	2.20370i	0.191566	+	0.110601i	−0.401150	+	0.916013i	$0.631389\pi$
$398$	6.69771	−	11.6008i	0.335726	−	0.581494i
$399$		0			0
$400$	2.09477	+	3.62824i	0.104738	+	0.181412i
$401$		−	18.5428i		−	0.925985i	−0.886362	−	0.462992i	$-0.846776\pi$
$401$		−	18.5428i		−	0.925985i	0.886362	−	0.462992i	$-0.153224\pi$
$402$	6.21744	+	1.32713i	0.310098	+	0.0661910i
$403$	22.9896			1.14519
$404$	1.35969	−	2.35506i	0.0676472	−	0.117168i
$405$	5.40085	+	6.03974i	0.268370	+	0.300117i
$406$		0			0
$407$	25.6652	+	14.8178i	1.27218	+	0.734491i
$408$	2.75065	+	8.49038i	0.136178	+	0.420336i
$409$	−21.5555	−	12.4451i	−1.06585	−	0.615370i	−0.138807	−	0.990319i	$-0.544327\pi$
$409$	−21.5555	−	12.4451i	−1.06585	−	0.615370i	−0.927045	+	0.374949i	$0.877660\pi$
$410$	−1.90442	−	1.09952i	−0.0940527	−	0.0543014i
$411$	−36.9945	−	7.89656i	−1.82481	−	0.389509i
$412$	−1.18861	−	0.686242i	−0.0585584	−	0.0338087i
$413$		0			0
$414$	0.529247	+	5.11982i	0.0260111	+	0.251625i
$415$	0.166041	−	0.287591i	0.00815062	−	0.0141173i
$416$	−2.29824			−0.112680
$417$	−7.21862	−	22.2816i	−0.353498	−	1.09113i
$418$		−	8.60058i		−	0.420668i
$419$	−2.57422	−	4.45869i	−0.125759	−	0.217821i	0.796270	−	0.604941i	$-0.206803\pi$
$419$	−2.57422	−	4.45869i	−0.125759	−	0.217821i	−0.922029	+	0.387120i	$0.873470\pi$
$420$		0			0
$421$	−13.5022	+	23.3864i	−0.658055	+	1.13978i	0.323063	+	0.946377i	$0.395287\pi$
$421$	−13.5022	+	23.3864i	−0.658055	+	1.13978i	−0.981119	+	0.193408i	$0.938046\pi$
$422$	16.2327	+	9.37193i	0.790193	+	0.456218i
$423$	2.42481	+	23.4570i	0.117898	+	1.14052i
$424$	6.97054	+	12.0733i	0.338520	+	0.586333i
$425$	10.7938	+	18.6955i	0.523577	+	0.906863i
$426$	−23.3129	+	7.55274i	−1.12951	+	0.365931i
$427$		0			0
$428$	−12.3585	+	7.13519i	−0.597371	+	0.344892i
$429$	−11.8457	+	3.83769i	−0.571917	+	0.185285i
$430$		−	0.491820i		−	0.0237177i
$431$	8.10874	−	4.68159i	0.390584	−	0.225504i	−0.291829	−	0.956471i	$-0.594264\pi$
$431$	8.10874	−	4.68159i	0.390584	−	0.225504i	0.682413	+	0.730966i	$0.260930\pi$
$432$	−5.16627	−	0.556425i	−0.248562	−	0.0267710i
$433$		−	21.0373i		−	1.01099i	−0.862830	−	0.505494i	$-0.831310\pi$
$433$		−	21.0373i		−	1.01099i	0.862830	−	0.505494i	$-0.168690\pi$
$434$		0			0
$435$	2.23808	−	2.48136i	0.107308	−	0.118972i
$436$	−5.29166			−0.253425
$437$	2.35863	−	4.08527i	0.112829	−	0.195425i
$438$	−16.2163	−	14.6264i	−0.774844	−	0.698876i
$439$	17.6867	−	10.2114i	0.844141	−	0.487365i	−0.0145289	−	0.999894i	$-0.504625\pi$
$439$	17.6867	−	10.2114i	0.844141	−	0.487365i	0.858670	+	0.512530i	$0.171292\pi$
$440$	2.81608			0.134252
$441$		0			0
$442$	−11.8423			−0.563279
$443$	28.0288	−	16.1825i	1.33169	−	0.768852i	0.346131	−	0.938186i	$-0.387495\pi$
$443$	28.0288	−	16.1825i	1.33169	−	0.768852i	0.985559	+	0.169334i	$0.0541618\pi$
$444$	−15.6107	+	5.05744i	−0.740851	+	0.240016i
$445$	5.40375	−	9.35956i	0.256162	−	0.443686i
$446$	−2.55892			−0.121168
$447$	−8.62944	−	1.84197i	−0.408158	−	0.0871223i
$448$		0			0
$449$			21.5693i			1.01792i	0.860791	+	0.508958i	$0.169969\pi$
$449$			21.5693i			1.01792i	−0.860791	+	0.508958i	$0.830031\pi$
$450$	−12.5020	+	1.29236i	−0.589349	+	0.0609224i
$451$	6.61721	−	3.82045i	0.311592	−	0.179898i
$452$			2.66010i			0.125121i
$453$	7.65631	−	35.8690i	0.359725	−	1.68527i
$454$	−7.55962	+	4.36455i	−0.354790	+	0.204838i
$455$		0			0
$456$	3.53629	+	3.18958i	0.165602	+	0.149366i
$457$	−10.5350	−	18.2471i	−0.492806	−	0.853564i	0.507160	−	0.861852i	$-0.330695\pi$
$457$	−10.5350	−	18.2471i	−0.492806	−	0.853564i	−0.999966	+	0.00828760i	$0.997362\pi$
$458$	−1.96865	−	3.40979i	−0.0919887	−	0.159329i
$459$	−26.6205	−	2.86712i	−1.24254	−	0.133826i
$460$	1.33764	+	0.772286i	0.0623677	+	0.0360080i
$461$	15.8412	−	27.4378i	0.737800	−	1.27791i	−0.215684	−	0.976463i	$-0.569198\pi$
$461$	15.8412	−	27.4378i	0.737800	−	1.27791i	0.953484	−	0.301444i	$-0.0974687\pi$
$462$		0			0
$463$	4.40058	+	7.62202i	0.204512	+	0.354225i	0.949977	−	0.312319i	$-0.101106\pi$
$463$	4.40058	+	7.62202i	0.204512	+	0.354225i	−0.745465	+	0.666545i	$0.767773\pi$
$464$			2.14301i			0.0994869i
$465$	10.4469	−	11.5825i	0.484464	−	0.537126i
$466$	−4.52812			−0.209761
$467$	9.49444	−	16.4449i	0.439350	−	0.760977i	−0.558289	−	0.829646i	$-0.688542\pi$
$467$	9.49444	−	16.4449i	0.439350	−	0.760977i	0.997639	+	0.0686693i	$0.0218753\pi$
$468$	2.81512	−	6.29382i	0.130129	−	0.290932i
$469$		0			0
$470$	6.12855	+	3.53832i	0.282689	+	0.163211i
$471$	−0.417537	+	0.462923i	−0.0192391	+	0.0213304i
$472$	−6.91472	−	3.99222i	−0.318276	−	0.183757i
$473$	1.47996	+	0.854453i	0.0680485	+	0.0392878i
$474$	7.59618	−	8.42190i	0.348904	−	0.386830i
$475$	9.97575	+	5.75950i	0.457719	+	0.264264i
$476$		0			0
$477$	−41.6016	+	4.30045i	−1.90481	+	0.196904i
$478$	4.36081	−	7.55315i	0.199459	−	0.345473i
$479$	−24.1401			−1.10299			−0.551495	−	0.834178i	$-0.685942\pi$
$479$	−24.1401			−1.10299			−0.551495	+	0.834178i	$0.685942\pi$
$480$	−1.04436	+	1.15789i	−0.0476684	+	0.0528500i
$481$		−	21.7736i		−	0.992790i
$482$	9.89079	+	17.1314i	0.450513	+	0.780312i
$483$		0			0
$484$	0.607537	−	1.05229i	0.0276153	−	0.0478312i
$485$	7.98362	+	4.60935i	0.362518	+	0.209300i
$486$	7.85198	−	13.4665i	0.356173	−	0.610852i
$487$	7.05542	+	12.2204i	0.319712	+	0.553757i	0.980428	−	0.196879i	$-0.0630806\pi$
$487$	7.05542	+	12.2204i	0.319712	+	0.553757i	−0.660716	+	0.750636i	$0.729747\pi$
$488$	−3.62705	−	6.28224i	−0.164189	−	0.284384i
$489$	15.9136	+	14.3533i	0.719636	+	0.649080i
$490$		0			0
$491$	−18.8344	+	10.8740i	−0.849982	+	0.490738i	−0.860645	−	0.509206i	$-0.829939\pi$
$491$	−18.8344	+	10.8740i	−0.849982	+	0.490738i	0.0106626	+	0.999943i	$0.496606\pi$
$492$	−0.883186	+	4.13763i	−0.0398171	+	0.186539i
$493$			11.0424i			0.497326i
$494$	−5.47236	+	3.15947i	−0.246213	+	0.142151i
$495$	−3.44943	+	7.71196i	−0.155040	+	0.346627i
$496$			10.0032i			0.449155i
$497$		0			0
$498$	−0.624832	−	0.133372i	−0.0279994	−	0.00597653i
$499$	−8.42465			−0.377139			−0.188570	−	0.982060i	$-0.560385\pi$
$499$	−8.42465			−0.377139			−0.188570	+	0.982060i	$0.560385\pi$
$500$	−4.13648	+	7.16459i	−0.184989	+	0.320410i
$501$	24.4150	−	7.90981i	1.09078	−	0.353384i
$502$	−3.29774	+	1.90395i	−0.147186	+	0.0849776i
$503$	−8.71316			−0.388501			−0.194250	−	0.980952i	$-0.562227\pi$
$503$	−8.71316			−0.388501			−0.194250	+	0.980952i	$0.562227\pi$
$504$		0			0
$505$	2.44815			0.108941
$506$	−4.64783	+	2.68343i	−0.206621	+	0.119293i
$507$	−9.92680	−	8.95354i	−0.440865	−	0.397641i
$508$	3.05293	−	5.28784i	0.135452	−	0.234610i
$509$	29.8354			1.32243			0.661214	−	0.750197i	$-0.270041\pi$
$509$	29.8354			1.32243			0.661214	+	0.750197i	$0.270041\pi$
$510$	−5.38134	+	5.96630i	−0.238290	+	0.264192i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−13.0664	+	5.77735i	−0.576896	+	0.255076i
$514$	−13.0557	+	7.53771i	−0.575862	+	0.332474i
$515$		−	1.23559i		−	0.0544465i
$516$	−0.900176	+	0.291632i	−0.0396280	+	0.0128384i
$517$	−21.2946	+	12.2944i	−0.936536	+	0.540709i
$518$		0			0
$519$	7.63798	−	2.47450i	0.335270	−	0.108618i
$520$	−1.03450	−	1.79181i	−0.0453660	−	0.0785762i
$521$	−9.89004	−	17.1301i	−0.433291	−	0.750482i	0.563864	−	0.825868i	$-0.309314\pi$
$521$	−9.89004	−	17.1301i	−0.433291	−	0.750482i	−0.997154	+	0.0753863i	$0.975981\pi$
$522$	−5.86873	−	2.62498i	−0.256867	−	0.114892i
$523$	10.5932	+	6.11597i	0.463207	+	0.267433i	0.713392	−	0.700766i	$-0.247158\pi$
$523$	10.5932	+	6.11597i	0.463207	+	0.267433i	−0.250185	+	0.968198i	$0.580491\pi$
$524$	3.97879	−	6.89147i	0.173814	−	0.301055i
$525$		0			0
$526$	3.80965	+	6.59852i	0.166109	+	0.287709i
$527$			51.5438i			2.24528i
$528$	−1.66984	−	5.15426i	−0.0726705	−	0.224310i
$529$	20.0564			0.872016
$530$	−6.27529	+	10.8691i	−0.272581	+	0.472124i
$531$	19.4027	−	14.0462i	0.842006	−	0.609552i
$532$		0			0
$533$	−4.86174	−	2.80693i	−0.210585	−	0.121581i
$534$	−20.3350	−	4.34054i	−0.879981	−	0.187834i
$535$	−11.1258	−	6.42351i	−0.481012	−	0.277713i
$536$	−3.17875	−	1.83525i	−0.137301	−	0.0792708i
$537$	3.24139	+	10.0051i	0.139876	+	0.431753i
$538$	7.49493	+	4.32720i	0.323129	+	0.186559i
$539$		0			0
$540$	−1.89167	−	4.27833i	−0.0814047	−	0.184110i
$541$	−0.348944	+	0.604389i	−0.0150023	+	0.0259847i	−0.873429	−	0.486951i	$-0.838109\pi$
$541$	−0.348944	+	0.604389i	−0.0150023	+	0.0259847i	0.858427	+	0.512936i	$0.171442\pi$
$542$	−18.0839			−0.776768
$543$	−12.0724	−	2.57688i	−0.518076	−	0.110584i
$544$		−	5.15276i		−	0.220923i
$545$	−2.38193	−	4.12562i	−0.102031	−	0.176722i
$546$		0			0
$547$	21.0049	−	36.3815i	0.898103	−	1.55556i	0.0681854	−	0.997673i	$-0.478279\pi$
$547$	21.0049	−	36.3815i	0.898103	−	1.55556i	0.829917	−	0.557887i	$-0.188388\pi$
$548$	18.9140	+	10.9200i	0.807964	+	0.466478i
$549$	21.6470	−	2.23770i	0.923870	−	0.0955026i
$550$	−6.55262	−	11.3495i	−0.279404	−	0.483943i
$551$	2.94608	+	5.10275i	0.125507	+	0.217385i
$552$	0.620337	−	2.90621i	0.0264033	−	0.123697i
$553$		0			0
$554$	−8.64419	+	4.99073i	−0.367257	+	0.212036i
$555$	−10.9698	−	9.89432i	−0.465644	−	0.419991i
$556$			13.5225i			0.573483i
$557$	−4.85612	+	2.80368i	−0.205760	+	0.118796i	−0.599340	−	0.800495i	$-0.704570\pi$
$557$	−4.85612	+	2.80368i	−0.205760	+	0.118796i	0.393579	+	0.919291i	$0.371237\pi$
$558$	−27.3940	−	12.2529i	−1.15968	−	0.518707i
$559$		−	1.25555i		−	0.0531042i
$560$		0			0
$561$	−8.60428	−	26.5586i	−0.363273	−	1.12131i
$562$	15.0454			0.634654
$563$	17.5948	−	30.4751i	0.741532	−	1.28437i	−0.210266	−	0.977644i	$-0.567433\pi$
$563$	17.5948	−	30.4751i	0.741532	−	1.28437i	0.951798	−	0.306727i	$-0.0992338\pi$
$564$	2.84215	−	13.3151i	0.119676	−	0.560669i
$565$	−2.07394	+	1.19739i	−0.0872512	+	0.0503745i
$566$	−4.02933			−0.169365
$567$		0			0
$568$	14.1484			0.593655
$569$	7.63608	−	4.40869i	0.320121	−	0.184822i	−0.331325	−	0.943517i	$-0.607496\pi$
$569$	7.63608	−	4.40869i	0.320121	−	0.184822i	0.651447	+	0.758695i	$0.274162\pi$
$570$	−0.894957	+	4.19278i	−0.0374856	+	0.175616i
$571$	5.94140	−	10.2908i	0.248640	−	0.430657i	−0.714509	−	0.699626i	$-0.753350\pi$
$571$	5.94140	−	10.2908i	0.248640	−	0.430657i	0.963149	+	0.268970i	$0.0866831\pi$
$572$	7.18909			0.300591
$573$	−7.68738	−	23.7285i	−0.321145	−	0.991271i
$574$		0			0
$575$		−	7.18799i		−	0.299760i
$576$	2.73854	+	1.22490i	0.114106	+	0.0510377i
$577$	−15.8314	+	9.14028i	−0.659071	+	0.380515i	−0.791923	−	0.610621i	$-0.790920\pi$
$577$	−15.8314	+	9.14028i	−0.659071	+	0.380515i	0.132852	+	0.991136i	$0.457587\pi$
$578$		−	9.55089i		−	0.397265i
$579$	−22.9086	−	20.6625i	−0.952048	−	0.858706i
$580$	−1.67079	+	0.964632i	−0.0693758	+	0.0400542i
$581$		0			0
$582$	3.70245	−	17.3456i	0.153471	−	0.718996i
$583$	−21.8045	−	37.7664i	−0.903049	−	1.56413i
$584$	6.30409	+	10.9190i	0.260865	+	0.451832i
$585$	6.17412	−	0.638233i	0.255268	−	0.0263877i
$586$	−11.4248	−	6.59608i	−0.471952	−	0.272482i
$587$	−1.75389	+	3.03782i	−0.0723907	+	0.125384i	−0.899949	−	0.435996i	$-0.856396\pi$
$587$	−1.75389	+	3.03782i	−0.0723907	+	0.125384i	0.827558	+	0.561380i	$0.189730\pi$
$588$		0			0
$589$	13.7517	+	23.8186i	0.566628	+	0.981429i
$590$		−	7.18805i		−	0.295927i
$591$	−32.3576	−	6.90679i	−1.33101	−	0.284107i
$592$	9.47403			0.389380
$593$	−24.2336	+	41.9738i	−0.995155	+	1.72366i	−0.412428	+	0.910990i	$0.635319\pi$
$593$	−24.2336	+	41.9738i	−0.995155	+	1.72366i	−0.582727	+	0.812668i	$0.698014\pi$
$594$	16.1606	+	1.74055i	0.663076	+	0.0714155i
$595$		0			0
$596$	4.41192	+	2.54722i	0.180719	+	0.104338i
$597$	−7.15077	−	22.0721i	−0.292661	−	0.903352i
$598$	3.41481	+	1.97154i	0.139642	+	0.0806224i
$599$	21.7773	+	12.5731i	0.889796	+	0.513724i	0.873876	−	0.486149i	$-0.161599\pi$
$599$	21.7773	+	12.5731i	0.889796	+	0.513724i	0.0159203	+	0.999873i	$0.494932\pi$
$600$	7.09662	+	1.51479i	0.289718	+	0.0618410i
$601$	11.2731	+	6.50854i	0.459840	+	0.265489i	0.711977	−	0.702203i	$-0.247800\pi$
$601$	11.2731	+	6.50854i	0.459840	+	0.265489i	−0.252137	+	0.967692i	$0.581133\pi$
$602$		0			0
$603$	8.91958	−	6.45713i	0.363233	−	0.262955i
$604$	−10.5877	+	18.3385i	−0.430809	+	0.746183i
$605$	1.09388			0.0444726
$606$	−1.45167	−	4.48083i	−0.0589699	−	0.182021i
$607$			8.20468i			0.333018i	0.986040	+	0.166509i	$0.0532494\pi$
$607$			8.20468i			0.333018i	−0.986040	+	0.166509i	$0.946751\pi$
$608$	−1.37474	−	2.38111i	−0.0557529	−	0.0965668i
$609$		0			0
$610$	3.26528	−	5.65564i	0.132207	−	0.228990i
$611$	15.6454	+	9.03286i	0.632944	+	0.365430i
$612$	14.1110	+	6.31163i	0.570405	+	0.255133i
$613$	2.35051	+	4.07120i	0.0949361	+	0.164434i	0.909582	−	0.415525i	$-0.136402\pi$
$613$	2.35051	+	4.07120i	0.0949361	+	0.164434i	−0.814646	+	0.579959i	$0.803069\pi$
$614$	14.3845	+	24.9147i	0.580512	+	1.00548i
$615$	−3.62343	+	1.17389i	−0.146111	+	0.0473360i
$616$		0			0
$617$	17.0178	−	9.82521i	0.685109	−	0.395548i	−0.116668	−	0.993171i	$-0.537221\pi$
$617$	17.0178	−	9.82521i	0.685109	−	0.395548i	0.801777	+	0.597623i	$0.203888\pi$
$618$	−2.26149	+	0.732661i	−0.0909705	+	0.0294720i
$619$			34.7087i			1.39506i	0.716555	+	0.697531i	$0.245718\pi$
$619$			34.7087i			1.39506i	−0.716555	+	0.697531i	$0.754282\pi$
$620$	−7.79892	+	4.50271i	−0.313212	+	0.180833i
$621$	7.19893	+	5.25865i	0.288883	+	0.211022i
$622$		−	30.8457i		−	1.23680i
$623$		0			0
$624$	−2.66612	+	2.95593i	−0.106730	+	0.118332i
$625$	13.4999			0.539996
$626$	9.18304	−	15.9055i	0.367028	−	0.635712i
$627$	−11.0618	−	9.97728i	−0.441767	−	0.398454i
$628$	0.311703	−	0.179962i	0.0124383	−	0.00718126i
$629$	48.8174			1.94648
$630$		0			0
$631$	22.9139			0.912188			0.456094	−	0.889932i	$-0.349248\pi$
$631$	22.9139			0.912188			0.456094	+	0.889932i	$0.349248\pi$
$632$	−5.67077	+	3.27402i	−0.225571	+	0.130233i
$633$	30.8849	−	10.0059i	1.22757	−	0.397698i
$634$	−8.72800	+	15.1173i	−0.346633	+	0.600386i
$635$	5.49685			0.218136
$636$	23.6147	+	5.04061i	0.936384	+	0.199873i
$637$		0			0
$638$		−	6.70353i		−	0.265395i
$639$	−17.3305	+	38.7461i	−0.685583	+	1.53277i
$640$	0.779646	−	0.450129i	0.0308182	−	0.0177929i
$641$			13.8527i			0.547148i	0.961851	+	0.273574i	$0.0882059\pi$
$641$			13.8527i			0.547148i	−0.961851	+	0.273574i	$0.911794\pi$
$642$	−5.15967	+	24.1725i	−0.203636	+	0.954012i
$643$	−27.9684	+	16.1476i	−1.10297	+	0.636797i	−0.936998	−	0.349334i	$-0.886408\pi$
$643$	−27.9684	+	16.1476i	−1.10297	+	0.636797i	−0.165967	+	0.986131i	$0.553075\pi$
$644$		0			0
$645$	−0.632565	−	0.570546i	−0.0249072	−	0.0224652i
$646$	−7.08367	−	12.2693i	−0.278703	−	0.482729i
$647$	−8.96715	−	15.5316i	−0.352535	−	0.610609i	0.634158	−	0.773204i	$-0.281347\pi$
$647$	−8.96715	−	15.5316i	−0.352535	−	0.610609i	−0.986693	+	0.162595i	$0.948014\pi$
$648$	−6.70890	+	5.99922i	−0.263551	+	0.235672i
$649$	21.6298	+	12.4880i	0.849046	+	0.490197i
$650$	−4.81428	+	8.33857i	−0.188831	+	0.327066i
$651$		0			0
$652$	−6.18640	−	10.7152i	−0.242278	−	0.419638i
$653$		−	7.49493i		−	0.293299i	−0.989188	−	0.146650i	$-0.953151\pi$
$653$		−	7.49493i		−	0.293299i	0.989188	−	0.146650i	$-0.0468490\pi$
$654$	−6.13870	+	6.80598i	−0.240042	+	0.266135i
$655$	7.16388			0.279916
$656$	1.22134	−	2.11542i	0.0476852	−	0.0825932i
$657$	−37.6241	+	3.88928i	−1.46785	+	0.151735i
$658$		0			0
$659$	−9.32497	−	5.38377i	−0.363249	−	0.209722i	0.307256	−	0.951627i	$-0.400589\pi$
$659$	−9.32497	−	5.38377i	−0.363249	−	0.209722i	−0.670505	+	0.741905i	$0.733923\pi$
$660$	3.26686	−	3.62197i	0.127162	−	0.140985i
$661$	10.0813	+	5.82044i	0.392117	+	0.226389i	0.683077	−	0.730346i	$-0.260641\pi$
$661$	10.0813	+	5.82044i	0.392117	+	0.226389i	−0.290960	+	0.956735i	$0.593975\pi$
$662$	9.03216	+	5.21472i	0.351045	+	0.202676i
$663$	−13.7379	+	15.2312i	−0.533534	+	0.591530i
$664$	0.319454	+	0.184437i	0.0123972	+	0.00715754i
$665$		0			0
$666$	−11.6048	+	25.9450i	−0.449676	+	1.00535i
$667$	1.83838	−	3.18417i	0.0711825	−	0.123292i
$668$	−14.8173			−0.573299
$669$	−2.96853	+	3.29121i	−0.114770	+	0.127245i
$670$		−	3.30440i		−	0.127660i
$671$	11.3457	+	19.6514i	0.437997	+	0.758634i
$672$		0			0
$673$	−0.550931	+	0.954241i	−0.0212368	+	0.0367833i	−0.876449	−	0.481496i	$-0.840094\pi$
$673$	−0.550931	+	0.954241i	−0.0212368	+	0.0367833i	0.855212	+	0.518279i	$0.173427\pi$
$674$	27.4204	+	15.8312i	1.05619	+	0.609794i
$675$	−12.8410	+	17.5789i	−0.494250	+	0.676613i
$676$	3.85905	+	6.68407i	0.148425	+	0.257080i
$677$	5.61618	+	9.72751i	0.215847	+	0.373859i	0.953534	−	0.301284i	$-0.0974153\pi$
$677$	5.61618	+	9.72751i	0.215847	+	0.373859i	−0.737687	+	0.675143i	$0.764082\pi$
$678$	3.42134	+	3.08590i	0.131396	+	0.118513i
$679$		0			0
$680$	4.01733	−	2.31940i	0.154057	−	0.0889451i
$681$	−3.15613	+	14.7861i	−0.120943	+	0.566606i
$682$		−	31.2907i		−	1.19818i
$683$	−37.6792	+	21.7541i	−1.44175	+	0.832396i	−0.997967	−	0.0637365i	$-0.979698\pi$
$683$	−37.6792	+	21.7541i	−1.44175	+	0.832396i	−0.443786	+	0.896133i	$0.646365\pi$
$684$	8.20469	−	0.848137i	0.313714	−	0.0324293i
$685$			19.6616i			0.751231i
$686$		0			0
$687$	−6.66935	−	1.42359i	−0.254451	−	0.0543132i
$688$	0.546311			0.0208279
$689$	−16.0200	+	27.7474i	−0.610312	+	1.05709i
$690$	2.54505	−	0.824526i	0.0968883	−	0.0313892i
$691$	27.9085	−	16.1130i	1.06169	−	0.612967i	0.135791	−	0.990738i	$-0.456642\pi$
$691$	27.9085	−	16.1130i	1.06169	−	0.612967i	0.925899	+	0.377770i	$0.123309\pi$
$692$	−4.63544			−0.176213
$693$		0			0
$694$	12.5252			0.475451
$695$	−10.5428	+	6.08689i	−0.399911	+	0.230889i
$696$	2.75628	+	2.48605i	0.104477	+	0.0942333i
$697$	6.29326	−	10.9002i	0.238374	−	0.412876i
$698$	−14.1520			−0.535660
$699$	−5.25294	+	5.82394i	−0.198684	+	0.220282i
$700$		0			0
$701$		−	21.8995i		−	0.827133i	−0.910474	−	0.413566i	$-0.864283\pi$
$701$		−	21.8995i		−	0.827133i	0.910474	−	0.413566i	$-0.135717\pi$
$702$	−4.82919	−	10.9220i	−0.182266	−	0.412224i
$703$	22.5587	−	13.0243i	0.850818	−	0.491220i
$704$			3.12809i			0.117894i
$705$	11.6604	−	3.77766i	0.439157	−	0.142275i
$706$	−4.30012	+	2.48267i	−0.161837	+	0.0934366i
$707$		0			0
$708$	−13.1562	+	4.26226i	−0.494442	+	0.160186i
$709$	9.02351	+	15.6292i	0.338885	+	0.586966i	0.984223	−	0.176931i	$-0.0566168\pi$
$709$	9.02351	+	15.6292i	0.338885	+	0.586966i	−0.645338	+	0.763897i	$0.723284\pi$
$710$	6.36862	+	11.0308i	0.239010	+	0.413977i
$711$	−2.01989	−	19.5400i	−0.0757519	−	0.732807i
$712$	10.3965	+	6.00244i	0.389627	+	0.224951i
$713$	8.58120	−	14.8631i	0.321369	−	0.556627i
$714$		0			0
$715$	3.23602	+	5.60494i	0.121020	+	0.209613i
$716$		−	6.07205i		−	0.226923i
$717$	−4.65579	−	14.3709i	−0.173874	−	0.536693i
$718$	17.3220			0.646450
$719$	−4.65944	+	8.07039i	−0.173768	+	0.300975i	−0.939734	−	0.341906i	$-0.888928\pi$
$719$	−4.65944	+	8.07039i	−0.173768	+	0.300975i	0.765966	+	0.642881i	$0.222261\pi$
$720$	0.277705	+	2.68646i	0.0103495	+	0.100118i
$721$		0			0
$722$	9.90769	+	5.72021i	0.368726	+	0.212884i
$723$	33.5079	+	7.15233i	1.24617	+	0.265998i
$724$	6.17217	+	3.56350i	0.229387	+	0.132437i
$725$	7.77537	+	4.48911i	0.288770	+	0.166722i
$726$	−0.648633	−	2.00212i	−0.0240730	−	0.0743057i
$727$	−6.73516	−	3.88855i	−0.249793	−	0.144218i	0.369876	−	0.929081i	$-0.379400\pi$
$727$	−6.73516	−	3.88855i	−0.249793	−	0.144218i	−0.619670	+	0.784863i	$0.712733\pi$
$728$		0			0
$729$	−8.21136	−	25.7211i	−0.304124	−	0.952632i
$730$	−5.67531	+	9.82992i	−0.210053	+	0.363822i
$731$	2.81500			0.104117
$732$	−12.2877	−	2.62283i	−0.454166	−	0.0969426i
$733$		−	36.1238i		−	1.33426i	−0.744941	−	0.667131i	$-0.767522\pi$
$733$		−	36.1238i		−	1.33426i	0.744941	−	0.667131i	$-0.232478\pi$
$734$	−0.685884	−	1.18799i	−0.0253164	−	0.0438494i
$735$		0			0
$736$	−0.857850	+	1.48584i	−0.0316208	+	0.0547688i
$737$	9.94341	+	5.74083i	0.366270	+	0.211466i
$738$	4.29714	+	5.93587i	0.158180	+	0.218502i
$739$	12.0693	+	20.9046i	0.443975	+	0.768987i	0.997980	−	0.0635263i	$-0.0202347\pi$
$739$	12.0693	+	20.9046i	0.443975	+	0.768987i	−0.554005	+	0.832513i	$0.686901\pi$
$740$	4.26453	+	7.38639i	0.156767	+	0.271529i
$741$	−2.28471	+	10.7036i	−0.0839308	+	0.393207i
$742$		0			0
$743$	10.5762	−	6.10618i	0.388003	−	0.224014i	−0.293291	−	0.956023i	$-0.594751\pi$
$743$	10.5762	−	6.10618i	0.388003	−	0.224014i	0.681295	+	0.732009i	$0.261417\pi$
$744$	12.8658	+	11.6044i	0.471682	+	0.425436i
$745$			4.58631i			0.168029i
$746$	4.16537	−	2.40488i	0.152505	−	0.0880488i
$747$	−0.896388	+	0.648921i	−0.0327971	+	0.0237428i
$748$			16.1183i			0.589342i
$749$		0			0
$750$	4.41628	+	13.6316i	0.161260	+	0.497757i
$751$	−23.4381			−0.855268			−0.427634	−	0.903952i	$-0.640653\pi$
$751$	−23.4381			−0.855268			−0.427634	+	0.903952i	$0.640653\pi$
$752$	−3.93034	+	6.80755i	−0.143325	+	0.248246i
$753$	−1.37681	+	6.45019i	−0.0501736	+	0.235058i
$754$	−4.26531	+	2.46258i	−0.155333	+	0.0896818i
$755$	−19.0634			−0.693788
$756$		0			0
$757$	3.52341			0.128060			0.0640302	−	0.997948i	$-0.479605\pi$
$757$	3.52341			0.128060			0.0640302	+	0.997948i	$0.479605\pi$
$758$	−16.9454	+	9.78346i	−0.615486	+	0.355351i
$759$	−1.94047	+	9.09088i	−0.0704345	+	0.329978i
$760$	1.23762	−	2.14361i	0.0448931	−	0.0777571i
$761$	−21.4042			−0.775900			−0.387950	−	0.921680i	$-0.626817\pi$
$761$	−21.4042			−0.775900			−0.387950	+	0.921680i	$0.626817\pi$
$762$	−3.25944	−	10.0609i	−0.118077	−	0.364466i
$763$		0			0
$764$			14.4006i			0.520997i
$765$	1.43095	+	13.8427i	0.0517360	+	0.500482i
$766$	27.2536	−	15.7349i	0.984712	−	0.568524i
$767$		−	18.3501i		−	0.662585i
$768$	−1.28617	−	1.16007i	−0.0464107	−	0.0418604i
$769$	−23.4043	+	13.5125i	−0.843982	+	0.487273i	−0.858616	−	0.512620i	$-0.828675\pi$
$769$	−23.4043	+	13.5125i	−0.843982	+	0.487273i	0.0146339	+	0.999893i	$0.495342\pi$
$770$		0			0
$771$	−5.45074	+	25.5361i	−0.196304	+	0.919661i
$772$	8.90573	+	15.4252i	0.320524	+	0.555164i
$773$	8.10280	+	14.0345i	0.291437	+	0.504784i	0.974150	−	0.225903i	$-0.0725332\pi$
$773$	8.10280	+	14.0345i	0.291437	+	0.504784i	−0.682712	+	0.730687i	$0.739200\pi$
$774$	−0.669178	+	1.49609i	−0.0240531	+	0.0537760i
$775$	36.2939	+	20.9543i	1.30371	+	0.752700i
$776$	−5.12003	+	8.86815i	−0.183798	+	0.318348i
$777$		0			0
$778$	−2.03303	−	3.52130i	−0.0728875	−	0.126245i
$779$		−	6.71607i		−	0.240628i
$780$	−3.50467	−	0.748080i	−0.125487	−	0.0267856i
$781$	−44.2575			−1.58366
$782$	−4.42029	+	7.65617i	−0.158069	+	0.273784i
$783$	−10.1843	+	4.50302i	−0.363958	+	0.160925i
$784$		0			0
$785$	0.280613	+	0.162012i	0.0100155	+	0.00578246i
$786$	−4.24793	−	13.1120i	−0.151519	−	0.467690i
$787$	33.1317	+	19.1286i	1.18102	+	0.681860i	0.956249	−	0.292553i	$-0.0945047\pi$
$787$	33.1317	+	19.1286i	1.18102	+	0.681860i	0.224767	+	0.974413i	$0.427838\pi$
$788$	16.5432	+	9.55124i	0.589328	+	0.340249i
$789$	12.9063	+	2.75487i	0.459476	+	0.0980761i
$790$	−5.10515	−	2.94746i	−0.181633	−	0.104866i
$791$		0			0
$792$	−8.56640	−	3.83161i	−0.304394	−	0.136150i
$793$	8.33583	−	14.4381i	0.296014	−	0.512712i
$794$	−4.40740			−0.156413
$795$	6.69977	+	20.6800i	0.237616	+	0.733445i
$796$			13.3954i			0.474788i
$797$	4.38709	+	7.59866i	0.155399	+	0.269158i	0.933204	−	0.359347i	$-0.117000\pi$
$797$	4.38709	+	7.59866i	0.155399	+	0.269158i	−0.777805	+	0.628505i	$0.783667\pi$
$798$		0			0
$799$	−20.2521	+	35.0776i	−0.716467	+	1.24096i
$800$	−3.62824	−	2.09477i	−0.128278	−	0.0740612i
$801$	−29.1727	+	21.1189i	−1.03077	+	0.746201i
$802$	9.27141	+	16.0586i	0.327385	+	0.567047i
$803$	−19.7197	−	34.1556i	−0.695895	−	1.20532i
$804$	−6.04802	+	1.95940i	−0.213297	+	0.0691025i
$805$		0			0
$806$	−19.9096	+	11.4948i	−0.701286	+	0.404887i
$807$	14.2602	−	4.61991i	0.501981	−	0.162628i
$808$			2.71939i			0.0956677i
$809$	−26.6053	+	15.3606i	−0.935394	+	0.540050i	−0.888513	−	0.458851i	$-0.848261\pi$
$809$	−26.6053	+	15.3606i	−0.935394	+	0.540050i	−0.0468805	+	0.998901i	$0.514928\pi$
$810$	−7.69714	−	2.53015i	−0.270450	−	0.0889002i
$811$		−	8.70634i		−	0.305721i	−0.988248	−	0.152861i	$-0.951151\pi$
$811$		−	8.70634i		−	0.305721i	0.988248	−	0.152861i	$-0.0488485\pi$
$812$		0			0
$813$	−20.9785	+	23.2589i	−0.735750	+	0.815726i
$814$	−29.6356			−1.03873
$815$	5.56936	−	9.64641i	0.195086	−	0.337899i
$816$	−6.62733	−	5.97756i	−0.232003	−	0.209256i
$817$	1.30083	−	0.751032i	0.0455101	−	0.0262753i
$818$	24.8902			0.870265
$819$		0			0
$820$	2.19904			0.0767937
$821$	45.4098	−	26.2173i	1.58481	−	0.914992i	0.590670	−	0.806914i	$-0.298864\pi$
$821$	45.4098	−	26.2173i	1.58481	−	0.914992i	0.994142	−	0.108078i	$-0.0344697\pi$
$822$	35.9865	−	11.6586i	1.25517	−	0.406642i
$823$	−4.18199	+	7.24342i	−0.145775	+	0.252490i	−0.929662	−	0.368414i	$-0.879901\pi$
$823$	−4.18199	+	7.24342i	−0.145775	+	0.252490i	0.783887	+	0.620904i	$0.213234\pi$
$824$	1.37248			0.0478127
$825$	−22.1988	−	4.73839i	−0.772865	−	0.164970i
$826$		0			0
$827$		−	26.4934i		−	0.921267i	−0.887590	−	0.460634i	$-0.847622\pi$
$827$		−	26.4934i		−	0.921267i	0.887590	−	0.460634i	$-0.152378\pi$
$828$	−3.01825	−	4.16927i	−0.104891	−	0.144892i
$829$	5.14134	−	2.96835i	0.178566	−	0.103095i	−0.408053	−	0.912958i	$-0.633792\pi$
$829$	5.14134	−	2.96835i	0.178566	−	0.103095i	0.586619	+	0.809863i	$0.300459\pi$
$830$			0.332081i			0.0115267i
$831$	−3.60894	+	16.9075i	−0.125193	+	0.586515i
$832$	1.99033	−	1.14912i	0.0690024	−	0.0398385i
$833$		0			0
$834$	17.3923	+	15.6871i	0.602246	+	0.543200i
$835$	−6.66970	−	11.5523i	−0.230815	−	0.399783i
$836$	4.30029	+	7.44832i	0.148729	+	0.257606i
$837$	−47.5383	+	21.0192i	−1.64317	+	0.726530i
$838$	4.45869	+	2.57422i	0.154023	+	0.0889251i
$839$	−3.80537	+	6.59110i	−0.131376	+	0.227550i	−0.924207	−	0.381891i	$-0.875273\pi$
$839$	−3.80537	+	6.59110i	−0.131376	+	0.227550i	0.792831	+	0.609441i	$0.208606\pi$
$840$		0			0
$841$	−12.2037	−	21.1375i	−0.420819	−	0.728880i
$842$		−	27.0043i		−	0.930630i
$843$	17.4538	−	19.3510i	0.601140	−	0.666484i
$844$	−18.7439			−0.645190
$845$	−3.47414	+	6.01739i	−0.119514	+	0.207004i
$846$	−13.8285	−	19.1020i	−0.475433	−	0.656740i
$847$		0			0
$848$	−12.0733	−	6.97054i	−0.414600	−	0.239369i
$849$	−4.67431	+	5.18241i	−0.160422	+	0.177860i
$850$	−18.6955	−	10.7938i	−0.641249	−	0.370225i
$851$	−14.0769	−	8.12730i	−0.482550	−	0.278600i
$852$	16.4132	−	18.1973i	0.562306	−	0.623429i
$853$	−24.8764	−	14.3624i	−0.851751	−	0.491759i	0.00949029	−	0.999955i	$-0.496979\pi$
$853$	−24.8764	−	14.3624i	−0.851751	−	0.491759i	−0.861241	+	0.508196i	$0.830312\pi$
$854$		0			0
$855$	4.35442	+	6.01498i	0.148918	+	0.205708i
$856$	7.13519	−	12.3585i	0.243876	−	0.422405i
$857$	40.2396			1.37456			0.687280	−	0.726393i	$-0.258805\pi$
$857$	40.2396			1.37456			0.687280	+	0.726393i	$0.258805\pi$
$858$	8.33985	−	9.24640i	0.284718	−	0.315667i
$859$			15.3871i			0.525001i	0.964932	+	0.262501i	$0.0845472\pi$
$859$			15.3871i			0.525001i	−0.964932	+	0.262501i	$0.915453\pi$
$860$	0.245910	+	0.425929i	0.00838547	+	0.0145241i
$861$		0			0
$862$	−4.68159	+	8.10874i	−0.159455	+	0.276185i
$863$	−16.6494	−	9.61252i	−0.566751	−	0.327214i	0.189099	−	0.981958i	$-0.439443\pi$
$863$	−16.6494	−	9.61252i	−0.566751	−	0.327214i	−0.755851	+	0.654744i	$0.772776\pi$
$864$	4.75234	−	2.10126i	0.161678	−	0.0714863i
$865$	−2.08655	−	3.61400i	−0.0709447	−	0.122880i
$866$	10.5186	+	18.2188i	0.357438	+	0.619101i
$867$	−12.2841	−	11.0797i	−0.417189	−	0.376286i
$868$		0			0
$869$	17.7386	−	10.2414i	0.601742	−	0.347416i
$870$	−0.697554	+	3.26797i	−0.0236493	+	0.110794i
$871$		−	8.43569i		−	0.285833i
$872$	4.58271	−	2.64583i	0.155190	−	0.0895991i
$873$	−18.0143	−	24.8840i	−0.609690	−	0.842197i
$874$			4.71727i			0.159564i
$875$		0			0
$876$	21.3569	+	4.55868i	0.721583	+	0.154023i
$877$	−10.7807			−0.364038			−0.182019	−	0.983295i	$-0.558263\pi$
$877$	−10.7807			−0.364038			−0.182019	+	0.983295i	$0.558263\pi$
$878$	−10.2114	+	17.6867i	−0.344619	+	0.596898i
$879$	−21.7372	+	7.04227i	−0.733178	+	0.237530i
$880$	−2.43880	+	1.40804i	−0.0822120	+	0.0474651i
$881$	−44.2875			−1.49208			−0.746041	−	0.665900i	$-0.768048\pi$
$881$	−44.2875			−1.49208			−0.746041	+	0.665900i	$0.768048\pi$
$882$		0			0
$883$	−47.6098			−1.60220			−0.801098	−	0.598533i	$-0.795751\pi$
$883$	−47.6098			−1.60220			−0.801098	+	0.598533i	$0.795751\pi$
$884$	10.2557	−	5.92113i	0.344936	−	0.199149i
$885$	−9.24506	−	8.33864i	−0.310769	−	0.280300i
$886$	−16.1825	+	28.0288i	−0.543660	+	0.941647i
$887$	−1.97993			−0.0664795			−0.0332398	−	0.999447i	$-0.510582\pi$
$887$	−1.97993			−0.0664795			−0.0332398	+	0.999447i	$0.510582\pi$
$888$	10.9905	−	12.1852i	0.368818	−	0.408909i
$889$		0			0
$890$			10.8075i			0.362268i
$891$	20.9860	−	18.7661i	0.703058	−	0.628687i
$892$	2.21609	−	1.27946i	0.0742001	−	0.0428395i
$893$			21.6127i			0.723242i
$894$	8.39430	−	2.71952i	0.280747	−	0.0909545i
$895$	4.73405	−	2.73320i	0.158242	−	0.0913609i
$896$		0			0
$897$	6.49717	−	2.10491i	0.216934	−	0.0702807i
$898$	−10.7846	−	18.6795i	−0.359888	−	0.623344i
$899$	10.7184	+	18.5649i	0.357480	+	0.619173i
$900$	10.1809	−	7.37021i	0.339362	−	0.245674i
$901$	−62.2109	−	35.9175i	−2.07255	−	1.19659i
$902$	−3.82045	+	6.61721i	−0.127207	+	0.220329i
$903$		0			0
$904$	−1.33005	−	2.30371i	−0.0442368	−	0.0766204i
$905$			6.41615i			0.213280i
$906$	11.3039	+	34.8916i	0.375548	+	1.15920i
$907$	34.0505			1.13063			0.565314	−	0.824876i	$-0.308755\pi$
$907$	34.0505			1.13063			0.565314	+	0.824876i	$0.308755\pi$
$908$	4.36455	−	7.55962i	0.144843	−	0.250875i
$909$	−7.44715	−	3.33099i	−0.247006	−	0.110482i
$910$		0			0
$911$	−6.58371	−	3.80111i	−0.218128	−	0.125936i	0.386955	−	0.922099i	$-0.373527\pi$
$911$	−6.58371	−	3.80111i	−0.218128	−	0.125936i	−0.605083	+	0.796162i	$0.706860\pi$
$912$	−4.65731	−	0.994112i	−0.154219	−	0.0329183i
$913$	−0.999280	−	0.576934i	−0.0330713	−	0.0190937i
$914$	18.2471	+	10.5350i	0.603561	+	0.348466i
$915$	−3.48616	−	10.7607i	−0.115249	−	0.355736i
$916$	3.40979	+	1.96865i	0.112663	+	0.0650459i
$917$		0			0
$918$	24.4876	−	10.8273i	0.808212	−	0.357353i
$919$	−4.11136	+	7.12109i	−0.135621	+	0.234903i	−0.925835	−	0.377929i	$-0.876636\pi$
$919$	−4.11136	+	7.12109i	−0.135621	+	0.234903i	0.790213	+	0.612832i	$0.209970\pi$
$920$	−1.54457			−0.0509230
$921$	48.7316	+	10.4019i	1.60576	+	0.342753i
$922$			31.6825i			1.04341i
$923$	16.2582	+	28.1601i	0.535146	+	0.926900i
$924$		0			0
$925$	19.8459	−	34.3741i	0.652529	−	1.13021i
$926$	−7.62202	−	4.40058i	−0.250475	−	0.144612i
$927$	−1.68116	+	3.75860i	−0.0552165	+	0.123449i
$928$	−1.07151	−	1.85590i	−0.0351739	−	0.0609230i
$929$	−2.53982	−	4.39909i	−0.0833287	−	0.144329i	0.821349	−	0.570426i	$-0.193222\pi$
$929$	−2.53982	−	4.39909i	−0.0833287	−	0.144329i	−0.904678	+	0.426096i	$0.859888\pi$
$930$	−3.25604	+	15.2542i	−0.106770	+	0.500205i
$931$		0			0
$932$	3.92147	−	2.26406i	0.128452	−	0.0741618i
$933$	−39.6728	−	35.7832i	−1.29883	−	1.17149i
$934$			18.9889i			0.621335i
$935$	−12.5665	+	7.25530i	−0.410970	+	0.237274i
$936$	0.708944	+	6.85817i	0.0231726	+	0.224166i
$937$			10.8127i			0.353236i	0.984280	+	0.176618i	$0.0565157\pi$
$937$			10.8127i			0.353236i	−0.984280	+	0.176618i	$0.943484\pi$
$938$		0			0
$939$	−9.80422	−	30.2625i	−0.319949	−	0.987578i
$940$	−7.07664			−0.230815
$941$	9.58193	−	16.5964i	0.312362	−	0.541027i	−0.666511	−	0.745495i	$-0.732213\pi$
$941$	9.58193	−	16.5964i	0.312362	−	0.541027i	0.978873	+	0.204468i	$0.0655464\pi$
$942$	0.130136	−	0.609672i	0.00424005	−	0.0198642i
$943$	−3.62942	+	2.09545i	−0.118190	+	0.0682372i
$944$	7.98443			0.259871
$945$		0			0
$946$	−1.70891			−0.0555613
$947$	−21.9930	+	12.6977i	−0.714676	+	0.412618i	−0.812790	−	0.582557i	$-0.802052\pi$
$947$	−21.9930	+	12.6977i	−0.714676	+	0.412618i	0.0981139	+	0.995175i	$0.468719\pi$
$948$	−2.36754	+	11.0917i	−0.0768941	+	0.360241i
$949$	−14.4883	+	25.0945i	−0.470310	+	0.814601i
$950$	−11.5190			−0.373726
$951$	9.31839	+	28.7629i	0.302170	+	0.932700i
$952$		0			0
$953$			18.4818i			0.598686i	0.954146	+	0.299343i	$0.0967674\pi$
$953$			18.4818i			0.598686i	−0.954146	+	0.299343i	$0.903233\pi$
$954$	33.8778	−	24.5251i	1.09683	−	0.794029i
$955$	−11.2274	+	6.48215i	−0.363310	+	0.209757i
$956$			8.72163i			0.282078i
$957$	−8.62189	−	7.77657i	−0.278706	−	0.251381i
$958$	20.9060	−	12.0701i	0.675441	−	0.389966i
$959$		0			0
$960$	0.325502	−	1.52494i	0.0105055	−	0.0492172i
$961$	34.5315	+	59.8103i	1.11392	+	1.92937i
$962$	10.8868	+	18.8565i	0.351004	+	0.607957i
$963$	25.1044	+	34.6780i	0.808977	+	1.11748i
$964$	−17.1314	−	9.89079i	−0.551764	−	0.318561i
$965$	−8.01745	+	13.8866i	−0.258091	+	0.447026i
$966$		0			0
$967$	−9.64551	−	16.7065i	−0.310179	−	0.537245i	0.668222	−	0.743962i	$-0.267056\pi$
$967$	−9.64551	−	16.7065i	−0.310179	−	0.537245i	−0.978401	+	0.206717i	$0.933722\pi$
$968$			1.21507i			0.0390540i
$969$	−23.9980	−	5.12242i	−0.770926	−	0.164556i
$970$	−9.21869			−0.295994
$971$	−0.975444	+	1.68952i	−0.0313035	+	0.0542192i	−0.881253	−	0.472645i	$-0.843299\pi$
$971$	−0.975444	+	1.68952i	−0.0313035	+	0.0542192i	0.849949	+	0.526865i	$0.176633\pi$
$972$	−0.0667715	+	15.5883i	−0.00214170	+	0.499995i
$973$		0			0
$974$	−12.2204	−	7.05542i	−0.391565	−	0.226070i
$975$	5.13993	+	15.8653i	0.164609	+	0.508097i
$976$	6.28224	+	3.62705i	0.201090	+	0.116099i
$977$	−14.4856	−	8.36326i	−0.463435	−	0.267564i	0.250052	−	0.968232i	$-0.419552\pi$
$977$	−14.4856	−	8.36326i	−0.463435	−	0.267564i	−0.713488	+	0.700668i	$0.752885\pi$
$978$	−20.9582	−	4.47357i	−0.670170	−	0.143049i
$979$	−32.5213	−	18.7762i	−1.03938	−	0.600089i
$980$		0			0
$981$	1.63233	+	15.7908i	0.0521164	+	0.504162i
$982$	10.8740	−	18.8344i	0.347004	−	0.601028i
$983$	32.2916			1.02994			0.514970	−	0.857208i	$-0.327803\pi$
$983$	32.2916			1.02994			0.514970	+	0.857208i	$0.327803\pi$
$984$	−1.30395	−	4.02489i	−0.0415685	−	0.128309i
$985$			17.1972i			0.547947i
$986$	−5.52121	−	9.56302i	−0.175831	−	0.304549i
$987$		0			0
$988$	3.15947	−	5.47236i	0.100516	−	0.174099i
$989$	−0.811730	−	0.468652i	−0.0258115	−	0.0149023i
$990$	−0.868686	−	8.40347i	−0.0276087	−	0.267080i
$991$	4.25134	+	7.36353i	0.135048	+	0.233910i	0.925616	−	0.378464i	$-0.123548\pi$
$991$	4.25134	+	7.36353i	0.135048	+	0.233910i	−0.790568	+	0.612375i	$0.790214\pi$
$992$	−5.00158	−	8.66298i	−0.158800	−	0.275050i
$993$	17.1850	−	5.56746i	0.545348	−	0.176678i
$994$		0			0
$995$	−10.4437	+	6.02967i	−0.331087	+	0.191153i
$996$	0.607806	−	0.196913i	0.0192591	−	0.00623942i
$997$			11.2975i			0.357797i	0.983868	+	0.178898i	$0.0572533\pi$
$997$			11.2975i			0.357797i	−0.983868	+	0.178898i	$0.942747\pi$
$998$	7.29596	−	4.21233i	0.230950	−	0.133339i
$999$	19.9074	+	45.0238i	0.629842	+	1.42449i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.t.a.803.2		16
3.2	odd	2		2646.2.t.b.1979.6		16
7.2	even	3		882.2.m.b.587.5		16
7.3	odd	6		882.2.l.b.227.1		16
7.4	even	3		126.2.l.a.101.4	yes	16
7.5	odd	6		882.2.m.a.587.8		16
7.6	odd	2		126.2.t.a.47.3	yes	16
9.4	even	3		2646.2.l.a.1097.2		16
9.5	odd	6		882.2.l.b.509.5		16
21.2	odd	6		2646.2.m.b.1763.3		16
21.5	even	6		2646.2.m.a.1763.2		16
21.11	odd	6		378.2.l.a.143.7		16
21.17	even	6		2646.2.l.a.521.6		16
21.20	even	2		378.2.t.a.89.7		16
28.11	odd	6		1008.2.ca.c.353.1		16
28.27	even	2		1008.2.df.c.929.4		16
63.4	even	3		378.2.t.a.17.7		16
63.5	even	6		882.2.m.b.293.5		16
63.11	odd	6		1134.2.k.b.647.7		16
63.13	odd	6		378.2.l.a.341.3		16
63.20	even	6		1134.2.k.a.971.2		16
63.23	odd	6		882.2.m.a.293.8		16
63.25	even	3		1134.2.k.a.647.2		16
63.31	odd	6		2646.2.t.b.2285.6		16
63.32	odd	6		126.2.t.a.59.3	yes	16
63.34	odd	6		1134.2.k.b.971.7		16
63.40	odd	6		2646.2.m.b.881.3		16
63.41	even	6		126.2.l.a.5.8	✓	16
63.58	even	3		2646.2.m.a.881.2		16
63.59	even	6	inner	882.2.t.a.815.2		16
84.11	even	6		3024.2.ca.c.2033.6		16
84.83	odd	2		3024.2.df.c.1601.6		16
252.67	odd	6		3024.2.df.c.17.6		16
252.95	even	6		1008.2.df.c.689.4		16
252.139	even	6		3024.2.ca.c.2609.6		16
252.167	odd	6		1008.2.ca.c.257.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.8	✓	16	63.41	even	6
126.2.l.a.101.4	yes	16	7.4	even	3
126.2.t.a.47.3	yes	16	7.6	odd	2
126.2.t.a.59.3	yes	16	63.32	odd	6
378.2.l.a.143.7		16	21.11	odd	6
378.2.l.a.341.3		16	63.13	odd	6
378.2.t.a.17.7		16	63.4	even	3
378.2.t.a.89.7		16	21.20	even	2
882.2.l.b.227.1		16	7.3	odd	6
882.2.l.b.509.5		16	9.5	odd	6
882.2.m.a.293.8		16	63.23	odd	6
882.2.m.a.587.8		16	7.5	odd	6
882.2.m.b.293.5		16	63.5	even	6
882.2.m.b.587.5		16	7.2	even	3
882.2.t.a.803.2		16	1.1	even	1	trivial
882.2.t.a.815.2		16	63.59	even	6	inner
1008.2.ca.c.257.1		16	252.167	odd	6
1008.2.ca.c.353.1		16	28.11	odd	6
1008.2.df.c.689.4		16	252.95	even	6
1008.2.df.c.929.4		16	28.27	even	2
1134.2.k.a.647.2		16	63.25	even	3
1134.2.k.a.971.2		16	63.20	even	6
1134.2.k.b.647.7		16	63.11	odd	6
1134.2.k.b.971.7		16	63.34	odd	6
2646.2.l.a.521.6		16	21.17	even	6
2646.2.l.a.1097.2		16	9.4	even	3
2646.2.m.a.881.2		16	63.58	even	3
2646.2.m.a.1763.2		16	21.5	even	6
2646.2.m.b.881.3		16	63.40	odd	6
2646.2.m.b.1763.3		16	21.2	odd	6
2646.2.t.b.1979.6		16	3.2	odd	2
2646.2.t.b.2285.6		16	63.31	odd	6
3024.2.ca.c.2033.6		16	84.11	even	6
3024.2.ca.c.2609.6		16	252.139	even	6
3024.2.df.c.17.6		16	252.67	odd	6
3024.2.df.c.1601.6		16	84.83	odd	2

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.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.361565 + 1.69389i) q^{3} +(0.500000 - 0.866025i) q^{4} +0.900258 q^{5} +(-0.533822 - 1.64774i) q^{6} +1.00000i q^{8} +(-2.73854 - 1.22490i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.361565 + 1.69389i) q^{3} +(0.500000 - 0.866025i) q^{4} +0.900258 q^{5} +(-0.533822 - 1.64774i) q^{6} +1.00000i q^{8} +(-2.73854 - 1.22490i) q^{9} +(-0.779646 + 0.450129i) q^{10} -3.12809i q^{11} +(1.28617 + 1.16007i) q^{12} +(-1.99033 + 1.14912i) q^{13} +(-0.325502 + 1.52494i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.57638 - 4.46242i) q^{17} +(2.98410 - 0.308473i) q^{18} +(-2.38111 - 1.37474i) q^{19} +(0.450129 - 0.779646i) q^{20} +(1.56404 + 2.70900i) q^{22} +1.71570i q^{23} +(-1.69389 - 0.361565i) q^{24} -4.18954 q^{25} +(1.14912 - 1.99033i) q^{26} +(3.06502 - 4.19591i) q^{27} +(-1.85590 - 1.07151i) q^{29} +(-0.480577 - 1.48339i) q^{30} +(-8.66298 - 5.00158i) q^{31} +(0.866025 + 0.500000i) q^{32} +(5.29864 + 1.13101i) q^{33} +(4.46242 + 2.57638i) q^{34} +(-2.43007 + 1.75919i) q^{36} +(-4.73701 + 8.20475i) q^{37} +2.74947 q^{38} +(-1.22685 - 3.78689i) q^{39} +0.900258i q^{40} +(1.22134 + 2.11542i) q^{41} +(-0.273155 + 0.473119i) q^{43} +(-2.70900 - 1.56404i) q^{44} +(-2.46539 - 1.10273i) q^{45} +(-0.857850 - 1.48584i) q^{46} +(-3.93034 - 6.80755i) q^{47} +(1.64774 - 0.533822i) q^{48} +(3.62824 - 2.09477i) q^{50} +(8.49038 - 2.75065i) q^{51} +2.29824i q^{52} +(12.0733 - 6.97054i) q^{53} +(-0.556425 + 5.16627i) q^{54} -2.81608i q^{55} +(3.18958 - 3.53629i) q^{57} +2.14301 q^{58} +(-3.99222 + 6.91472i) q^{59} +(1.15789 + 1.04436i) q^{60} +(-6.28224 + 3.62705i) q^{61} +10.0032 q^{62} -1.00000 q^{64} +(-1.79181 + 1.03450i) q^{65} +(-5.15426 + 1.66984i) q^{66} +(-1.83525 + 3.17875i) q^{67} -5.15276 q^{68} +(-2.90621 - 0.620337i) q^{69} -14.1484i q^{71} +(1.22490 - 2.73854i) q^{72} +(10.9190 - 6.30409i) q^{73} -9.47403i q^{74} +(1.51479 - 7.09662i) q^{75} +(-2.38111 + 1.37474i) q^{76} +(2.95593 + 2.66612i) q^{78} +(3.27402 + 5.67077i) q^{79} +(-0.450129 - 0.779646i) q^{80} +(5.99922 + 6.70890i) q^{81} +(-2.11542 - 1.22134i) q^{82} +(0.184437 - 0.319454i) q^{83} +(-2.31940 - 4.01733i) q^{85} -0.546311i q^{86} +(2.48605 - 2.75628i) q^{87} +3.12809 q^{88} +(6.00244 - 10.3965i) q^{89} +(2.68646 - 0.277705i) q^{90} +(1.48584 + 0.857850i) q^{92} +(11.6044 - 12.8658i) q^{93} +(6.80755 + 3.93034i) q^{94} +(-2.14361 - 1.23762i) q^{95} +(-1.16007 + 1.28617i) q^{96} +(8.86815 + 5.12003i) q^{97} +(-3.83161 + 8.56640i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 6 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 - 6 * q^9	\( 16 q + 8 q^{4} - 6 q^{9} + 6 q^{13} - 18 q^{15} - 8 q^{16} - 18 q^{17} + 12 q^{18} + 6 q^{24} + 16 q^{25} + 12 q^{26} + 36 q^{27} + 6 q^{29} - 18 q^{30} - 6 q^{31} - 18 q^{33} - 2 q^{37} - 30 q^{39} - 6 q^{41} - 2 q^{43} + 12 q^{44} - 12 q^{45} + 6 q^{46} + 18 q^{47} - 12 q^{50} + 36 q^{53} - 18 q^{54} + 6 q^{57} - 12 q^{58} - 30 q^{59} - 6 q^{60} + 60 q^{61} + 36 q^{62} - 16 q^{64} + 42 q^{65} - 48 q^{66} + 14 q^{67} - 36 q^{68} - 42 q^{69} - 30 q^{75} - 16 q^{79} + 54 q^{81} - 12 q^{85} + 48 q^{87} - 24 q^{89} + 18 q^{90} + 6 q^{92} + 30 q^{93} - 66 q^{95} + 6 q^{96} + 6 q^{97} + 18 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 - 6 * q^9 + 6 * q^13 - 18 * q^15 - 8 * q^16 - 18 * q^17 + 12 * q^18 + 6 * q^24 + 16 * q^25 + 12 * q^26 + 36 * q^27 + 6 * q^29 - 18 * q^30 - 6 * q^31 - 18 * q^33 - 2 * q^37 - 30 * q^39 - 6 * q^41 - 2 * q^43 + 12 * q^44 - 12 * q^45 + 6 * q^46 + 18 * q^47 - 12 * q^50 + 36 * q^53 - 18 * q^54 + 6 * q^57 - 12 * q^58 - 30 * q^59 - 6 * q^60 + 60 * q^61 + 36 * q^62 - 16 * q^64 + 42 * q^65 - 48 * q^66 + 14 * q^67 - 36 * q^68 - 42 * q^69 - 30 * q^75 - 16 * q^79 + 54 * q^81 - 12 * q^85 + 48 * q^87 - 24 * q^89 + 18 * q^90 + 6 * q^92 + 30 * q^93 - 66 * q^95 + 6 * q^96 + 6 * q^97 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more