LMFDB - Embedded newform 686.2.e.f.393.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [686,2,Mod(99,686)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(686, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([10]))

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

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

chi := DirichletCharacter("686.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 686 = 2 \cdot 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	686.e (of order $7$, degree $6$, 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:	$5.47773757866$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{7})$
Twist minimal:	no (minimal twist has level 98)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			393.1
Character	$\chi$	$=$	686.393
Dual form			686.2.e.f.295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.623490 - 0.781831i) q^{2} +(-0.625881 + 0.301408i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(-1.65798 + 0.798443i) q^{5} +(0.625881 + 0.301408i) q^{6} +(0.900969 - 0.433884i) q^{8} +(-1.56959 + 1.96820i) q^{9} +O(q^{10})$	\(q+(-0.623490 - 0.781831i) q^{2} +(-0.625881 + 0.301408i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(-1.65798 + 0.798443i) q^{5} +(0.625881 + 0.301408i) q^{6} +(0.900969 - 0.433884i) q^{8} +(-1.56959 + 1.96820i) q^{9} +(1.65798 + 0.798443i) q^{10} +(2.49315 + 3.12631i) q^{11} +(-0.154580 - 0.677258i) q^{12} +(-3.60921 - 4.52581i) q^{13} +(0.797043 - 0.999460i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(-0.769280 - 3.37044i) q^{17} +2.51743 q^{18} +3.03954 q^{19} +(-0.409488 - 1.79409i) q^{20} +(0.889796 - 3.89845i) q^{22} +(1.79281 - 7.85483i) q^{23} +(-0.433123 + 0.543119i) q^{24} +(-1.00605 + 1.26155i) q^{25} +(-1.28811 + 5.64359i) q^{26} +(0.852883 - 3.73672i) q^{27} +(0.392906 + 1.72143i) q^{29} -1.27836 q^{30} -5.40203 q^{31} +(0.222521 + 0.974928i) q^{32} +(-2.50271 - 1.20524i) q^{33} +(-2.15547 + 2.70288i) q^{34} +(-1.56959 - 1.96820i) q^{36} +(-1.36978 - 6.00138i) q^{37} +(-1.89512 - 2.37641i) q^{38} +(3.62305 + 1.74477i) q^{39} +(-1.14736 + 1.43874i) q^{40} +(2.82949 - 1.36261i) q^{41} +(-3.50635 - 1.68857i) q^{43} +(-3.60271 + 1.73497i) q^{44} +(1.03086 - 4.51648i) q^{45} +(-7.25896 + 3.49573i) q^{46} +(-4.54132 - 5.69464i) q^{47} +0.694675 q^{48} +1.61358 q^{50} +(1.49735 + 1.87762i) q^{51} +(5.21546 - 2.51163i) q^{52} +(1.99150 - 8.72533i) q^{53} +(-3.45325 + 1.66300i) q^{54} +(-6.62979 - 3.19274i) q^{55} +(-1.90239 + 0.916142i) q^{57} +(1.10090 - 1.38048i) q^{58} +(-6.47526 - 3.11832i) q^{59} +(0.797043 + 0.999460i) q^{60} +(0.861266 + 3.77345i) q^{61} +(3.36811 + 4.22347i) q^{62} +(0.623490 - 0.781831i) q^{64} +(9.59761 + 4.62197i) q^{65} +(0.618119 + 2.70816i) q^{66} +1.85465 q^{67} +3.45711 q^{68} +(1.24542 + 5.45656i) q^{69} +(1.61191 - 7.06223i) q^{71} +(-0.560180 + 2.45431i) q^{72} +(-7.31001 + 9.16646i) q^{73} +(-3.83803 + 4.81273i) q^{74} +(0.249426 - 1.09281i) q^{75} +(-0.676361 + 2.96333i) q^{76} +(-0.894819 - 3.92046i) q^{78} -4.46206 q^{79} +1.84022 q^{80} +(-1.08806 - 4.76712i) q^{81} +(-2.82949 - 1.36261i) q^{82} +(-3.42482 + 4.29459i) q^{83} +(3.96656 + 4.97390i) q^{85} +(0.865998 + 3.79419i) q^{86} +(-0.764766 - 0.958986i) q^{87} +(3.60271 + 1.73497i) q^{88} +(7.12809 - 8.93834i) q^{89} +(-4.17385 + 2.01002i) q^{90} +(7.25896 + 3.49573i) q^{92} +(3.38102 - 1.62822i) q^{93} +(-1.62078 + 7.10110i) q^{94} +(-5.03951 + 2.42690i) q^{95} +(-0.433123 - 0.543119i) q^{96} +9.72695 q^{97} -10.0664 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 7 q^{3} - 4 q^{4} - 7 q^{6} + 4 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 + 7 * q^3 - 4 * q^4 - 7 * q^6 + 4 * q^8 + 3 * q^9	$ 24 q + 4 q^{2} + 7 q^{3} - 4 q^{4} - 7 q^{6} + 4 q^{8} + 3 q^{9} - 7 q^{11} + 14 q^{13} - 7 q^{15} - 4 q^{16} + 14 q^{17} - 10 q^{18} - 7 q^{20} - 7 q^{22} - 21 q^{23} - 8 q^{25} - 7 q^{26} - 35 q^{27} - 11 q^{29} - 56 q^{31} + 4 q^{32} - 28 q^{33} + 7 q^{34} + 3 q^{36} + 48 q^{37} - 7 q^{38} + 38 q^{39} - 7 q^{40} + 28 q^{41} + 10 q^{43} + 7 q^{45} - 21 q^{46} + 35 q^{47} - 14 q^{48} + 8 q^{50} - 36 q^{51} - 7 q^{52} - 10 q^{53} - 63 q^{54} + 56 q^{55} - 33 q^{57} - 24 q^{58} + 14 q^{59} - 7 q^{60} - 28 q^{61} + 28 q^{62} - 4 q^{64} + 21 q^{66} + 72 q^{67} + 28 q^{68} - 35 q^{69} + 4 q^{72} - 49 q^{73} + q^{74} + 56 q^{75} - 24 q^{78} + 52 q^{79} - 5 q^{81} - 28 q^{82} - 7 q^{83} + 49 q^{85} + 32 q^{86} - 28 q^{87} + 7 q^{89} - 21 q^{90} + 21 q^{92} - 60 q^{93} - 35 q^{94} + 7 q^{95} - 126 q^{97} - 14 q^{99}+O(q^{100}) $ 24 * q + 4 * q^2 + 7 * q^3 - 4 * q^4 - 7 * q^6 + 4 * q^8 + 3 * q^9 - 7 * q^11 + 14 * q^13 - 7 * q^15 - 4 * q^16 + 14 * q^17 - 10 * q^18 - 7 * q^20 - 7 * q^22 - 21 * q^23 - 8 * q^25 - 7 * q^26 - 35 * q^27 - 11 * q^29 - 56 * q^31 + 4 * q^32 - 28 * q^33 + 7 * q^34 + 3 * q^36 + 48 * q^37 - 7 * q^38 + 38 * q^39 - 7 * q^40 + 28 * q^41 + 10 * q^43 + 7 * q^45 - 21 * q^46 + 35 * q^47 - 14 * q^48 + 8 * q^50 - 36 * q^51 - 7 * q^52 - 10 * q^53 - 63 * q^54 + 56 * q^55 - 33 * q^57 - 24 * q^58 + 14 * q^59 - 7 * q^60 - 28 * q^61 + 28 * q^62 - 4 * q^64 + 21 * q^66 + 72 * q^67 + 28 * q^68 - 35 * q^69 + 4 * q^72 - 49 * q^73 + q^74 + 56 * q^75 - 24 * q^78 + 52 * q^79 - 5 * q^81 - 28 * q^82 - 7 * q^83 + 49 * q^85 + 32 * q^86 - 28 * q^87 + 7 * q^89 - 21 * q^90 + 21 * q^92 - 60 * q^93 - 35 * q^94 + 7 * q^95 - 126 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/686\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{6}{7}\right)$

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 $

$2$	−0.623490	−	0.781831i	−0.440874	−	0.552838i
$2$	−0.623490	−	0.781831i	−0.440874	−	0.552838i
$3$	−0.625881	+	0.301408i	−0.361352	+	0.174018i	−0.605746	−	0.795658i	$-0.707125\pi$
$3$	−0.625881	+	0.301408i	−0.361352	+	0.174018i	0.244394	+	0.969676i	$0.421411\pi$
$4$	−0.222521	+	0.974928i	−0.111260	+	0.487464i
$5$	−1.65798	+	0.798443i	−0.741473	+	0.357075i	−0.766185	−	0.642620i	$-0.777847\pi$
$5$	−1.65798	+	0.798443i	−0.741473	+	0.357075i	0.0247120	+	0.999695i	$0.492133\pi$
$6$	0.625881	+	0.301408i	0.255515	+	0.123049i
$7$		0			0
$7$		0			0
$8$	0.900969	−	0.433884i	0.318541	−	0.153401i
$9$	−1.56959	+	1.96820i	−0.523197	+	0.656068i
$10$	1.65798	+	0.798443i	0.524301	+	0.252490i
$11$	2.49315	+	3.12631i	0.751714	+	0.942619i	0.999658	−	0.0261552i	$-0.00832641\pi$
$11$	2.49315	+	3.12631i	0.751714	+	0.942619i	−0.247944	+	0.968774i	$0.579755\pi$
$12$	−0.154580	−	0.677258i	−0.0446233	−	0.195508i
$13$	−3.60921	−	4.52581i	−1.00101	−	1.25523i	−0.966724	−	0.255821i	$-0.917654\pi$
$13$	−3.60921	−	4.52581i	−1.00101	−	1.25523i	−0.0342904	−	0.999412i	$-0.510917\pi$
$14$		0			0
$15$	0.797043	−	0.999460i	0.205796	−	0.258060i
$16$	−0.900969	−	0.433884i	−0.225242	−	0.108471i
$17$	−0.769280	−	3.37044i	−0.186578	−	0.817451i	−0.978404	−	0.206704i	$-0.933726\pi$
$17$	−0.769280	−	3.37044i	−0.186578	−	0.817451i	0.791826	−	0.610747i	$-0.209131\pi$
$18$	2.51743			0.593363
$19$	3.03954			0.697318			0.348659	−	0.937250i	$-0.386637\pi$
$19$	3.03954			0.697318			0.348659	+	0.937250i	$0.386637\pi$
$20$	−0.409488	−	1.79409i	−0.0915644	−	0.401170i
$21$		0			0
$22$	0.889796	−	3.89845i	0.189705	−	0.831152i
$23$	1.79281	−	7.85483i	0.373828	−	1.63785i	−0.342094	−	0.939666i	$-0.611136\pi$
$23$	1.79281	−	7.85483i	0.373828	−	1.63785i	0.715922	−	0.698180i	$-0.246007\pi$
$24$	−0.433123	+	0.543119i	−0.0884108	+	0.110864i
$25$	−1.00605	+	1.26155i	−0.201210	+	0.252309i
$26$	−1.28811	+	5.64359i	−0.252620	+	1.10680i
$27$	0.852883	−	3.73672i	0.164137	−	0.719133i
$28$		0			0
$29$	0.392906	+	1.72143i	0.0729607	+	0.319662i	0.998218	−	0.0596793i	$-0.0190078\pi$
$29$	0.392906	+	1.72143i	0.0729607	+	0.319662i	−0.925257	+	0.379341i	$0.876151\pi$
$30$	−1.27836			−0.233395
$31$	−5.40203			−0.970233			−0.485116	−	0.874450i	$-0.661223\pi$
$31$	−5.40203			−0.970233			−0.485116	+	0.874450i	$0.661223\pi$
$32$	0.222521	+	0.974928i	0.0393365	+	0.172345i
$33$	−2.50271	−	1.20524i	−0.435666	−	0.209806i
$34$	−2.15547	+	2.70288i	−0.369661	+	0.463540i
$35$		0			0
$36$	−1.56959	−	1.96820i	−0.261598	−	0.328034i
$37$	−1.36978	−	6.00138i	−0.225190	−	0.986621i	−0.953505	−	0.301378i	$-0.902553\pi$
$37$	−1.36978	−	6.00138i	−0.225190	−	0.986621i	0.728315	−	0.685243i	$-0.240304\pi$
$38$	−1.89512	−	2.37641i	−0.307429	−	0.385504i
$39$	3.62305	+	1.74477i	0.580152	+	0.279387i
$40$	−1.14736	+	1.43874i	−0.181414	+	0.227486i
$41$	2.82949	−	1.36261i	0.441893	−	0.212804i	−0.199689	−	0.979859i	$-0.563993\pi$
$41$	2.82949	−	1.36261i	0.441893	−	0.212804i	0.641581	+	0.767055i	$0.278279\pi$
$42$		0			0
$43$	−3.50635	−	1.68857i	−0.534714	−	0.257505i	0.146983	−	0.989139i	$-0.453044\pi$
$43$	−3.50635	−	1.68857i	−0.534714	−	0.257505i	−0.681697	+	0.731634i	$0.738758\pi$
$44$	−3.60271	+	1.73497i	−0.543129	+	0.261557i
$45$	1.03086	−	4.51648i	0.153671	−	0.673277i
$46$	−7.25896	+	3.49573i	−1.07028	+	0.515417i
$47$	−4.54132	−	5.69464i	−0.662420	−	0.830648i	0.331184	−	0.943566i	$-0.392552\pi$
$47$	−4.54132	−	5.69464i	−0.662420	−	0.830648i	−0.993604	+	0.112918i	$0.963980\pi$
$48$	0.694675			0.100268
$49$		0			0
$50$	1.61358			0.228194
$51$	1.49735	+	1.87762i	0.209672	+	0.262920i
$52$	5.21546	−	2.51163i	0.723254	−	0.348301i
$53$	1.99150	−	8.72533i	0.273553	−	1.19852i	−0.632232	−	0.774779i	$-0.717861\pi$
$53$	1.99150	−	8.72533i	0.273553	−	1.19852i	0.905785	−	0.423737i	$-0.139282\pi$
$54$	−3.45325	+	1.66300i	−0.469928	+	0.226305i
$55$	−6.62979	−	3.19274i	−0.893961	−	0.430509i
$56$		0			0
$57$	−1.90239	+	0.916142i	−0.251978	+	0.121346i
$58$	1.10090	−	1.38048i	0.144555	−	0.181266i
$59$	−6.47526	−	3.11832i	−0.843007	−	0.405971i	−0.0380299	−	0.999277i	$-0.512108\pi$
$59$	−6.47526	−	3.11832i	−0.843007	−	0.405971i	−0.804977	+	0.593306i	$0.797822\pi$
$60$	0.797043	+	0.999460i	0.102898	+	0.129030i
$61$	0.861266	+	3.77345i	0.110274	+	0.483141i	0.999662	+	0.0259888i	$0.00827344\pi$
$61$	0.861266	+	3.77345i	0.110274	+	0.483141i	−0.889388	+	0.457152i	$0.848869\pi$
$62$	3.36811	+	4.22347i	0.427750	+	0.536382i
$63$		0			0
$64$	0.623490	−	0.781831i	0.0779362	−	0.0977289i
$65$	9.59761	+	4.62197i	1.19044	+	0.573284i
$66$	0.618119	+	2.70816i	0.0760852	+	0.333351i
$67$	1.85465			0.226581			0.113291	−	0.993562i	$-0.463861\pi$
$67$	1.85465			0.226581			0.113291	+	0.993562i	$0.463861\pi$
$68$	3.45711			0.419237
$69$	1.24542	+	5.45656i	0.149931	+	0.656892i
$70$		0			0
$71$	1.61191	−	7.06223i	0.191298	−	0.838133i	−0.784616	−	0.619981i	$-0.787140\pi$
$71$	1.61191	−	7.06223i	0.191298	−	0.838133i	0.975915	−	0.218152i	$-0.0700027\pi$
$72$	−0.560180	+	2.45431i	−0.0660179	+	0.289243i
$73$	−7.31001	+	9.16646i	−0.855572	+	1.07285i	0.140991	+	0.990011i	$0.454971\pi$
$73$	−7.31001	+	9.16646i	−0.855572	+	1.07285i	−0.996563	+	0.0828423i	$0.973600\pi$
$74$	−3.83803	+	4.81273i	−0.446162	+	0.559469i
$75$	0.249426	−	1.09281i	0.0288013	−	0.126187i
$76$	−0.676361	+	2.96333i	−0.0775840	+	0.339917i
$77$		0			0
$78$	−0.894819	−	3.92046i	−0.101318	−	0.443905i
$79$	−4.46206			−0.502021			−0.251011	−	0.967984i	$-0.580763\pi$
$79$	−4.46206			−0.502021			−0.251011	+	0.967984i	$0.580763\pi$
$80$	1.84022			0.205743
$81$	−1.08806	−	4.76712i	−0.120896	−	0.529680i
$82$	−2.82949	−	1.36261i	−0.312465	−	0.150475i
$83$	−3.42482	+	4.29459i	−0.375923	+	0.471393i	−0.933420	−	0.358787i	$-0.883191\pi$
$83$	−3.42482	+	4.29459i	−0.375923	+	0.471393i	0.557497	+	0.830179i	$0.311762\pi$
$84$		0			0
$85$	3.96656	+	4.97390i	0.430233	+	0.539496i
$86$	0.865998	+	3.79419i	0.0933830	+	0.409138i
$87$	−0.764766	−	0.958986i	−0.0819915	−	0.102814i
$88$	3.60271	+	1.73497i	0.384050	+	0.184949i
$89$	7.12809	−	8.93834i	0.755576	−	0.947462i	−0.244177	−	0.969731i	$-0.578518\pi$
$89$	7.12809	−	8.93834i	0.755576	−	0.947462i	0.999752	+	0.0222691i	$0.00708906\pi$
$90$	−4.17385	+	2.01002i	−0.439963	+	0.211875i
$91$		0			0
$92$	7.25896	+	3.49573i	0.756799	+	0.364455i
$93$	3.38102	−	1.62822i	0.350596	−	0.168838i
$94$	−1.62078	+	7.10110i	−0.167171	+	0.732422i
$95$	−5.03951	+	2.42690i	−0.517043	+	0.248995i
$96$	−0.433123	−	0.543119i	−0.0442054	−	0.0554318i
$97$	9.72695			0.987622			0.493811	−	0.869569i	$-0.335603\pi$
$97$	9.72695			0.987622			0.493811	+	0.869569i	$0.335603\pi$
$98$		0			0
$99$	−10.0664			−1.01172
$100$	−1.00605	−	1.26155i	−0.100605	−	0.126155i
$101$	7.17775	−	3.45662i	0.714213	−	0.343947i	−0.0412404	−	0.999149i	$-0.513131\pi$
$101$	7.17775	−	3.45662i	0.714213	−	0.343947i	0.755453	+	0.655202i	$0.227417\pi$
$102$	0.534400	−	2.34136i	0.0529135	−	0.231829i
$103$	−15.9852	+	7.69804i	−1.57506	+	0.758511i	−0.998294	−	0.0583953i	$-0.981402\pi$
$103$	−15.9852	+	7.69804i	−1.57506	+	0.758511i	−0.576771	+	0.816906i	$0.695687\pi$
$104$	−5.21546	−	2.51163i	−0.511418	−	0.246286i
$105$		0			0
$106$	−8.06342	+	3.88314i	−0.783188	+	0.377164i
$107$	1.91199	−	2.39756i	0.184839	−	0.231781i	−0.680775	−	0.732492i	$-0.738357\pi$
$107$	1.91199	−	2.39756i	0.184839	−	0.231781i	0.865614	+	0.500712i	$0.166928\pi$
$108$	3.45325	+	1.66300i	0.332289	+	0.160022i
$109$	−8.24828	−	10.3430i	−0.790042	−	0.990682i	−0.999916	−	0.0129532i	$-0.995877\pi$
$109$	−8.24828	−	10.3430i	−0.790042	−	0.990682i	0.209874	−	0.977728i	$-0.432695\pi$
$110$	1.63742	+	7.17402i	0.156122	+	0.684016i
$111$	2.66618	+	3.34329i	0.253063	+	0.317331i
$112$		0			0
$113$	−6.47458	+	8.11886i	−0.609077	+	0.763758i	−0.986762	−	0.162176i	$-0.948149\pi$
$113$	−6.47458	+	8.11886i	−0.609077	+	0.763758i	0.377685	+	0.925934i	$0.376720\pi$
$114$	1.90239	+	0.916142i	0.178175	+	0.0858046i
$115$	3.29918	+	14.4547i	0.307650	+	1.34790i
$116$	−1.76570			−0.163941
$117$	14.5727			1.34725
$118$	1.59926	+	7.00680i	0.147224	+	0.645028i
$119$		0			0
$120$	0.284461	−	1.24631i	0.0259677	−	0.113772i
$121$	−1.11030	+	4.86455i	−0.100936	+	0.442231i
$122$	2.41321	−	3.02607i	0.218482	−	0.273968i
$123$	−1.36022	+	1.70567i	−0.122647	+	0.153795i
$124$	1.20206	−	5.26659i	0.107949	−	0.472953i
$125$	2.70818	−	11.8653i	0.242227	−	1.06127i
$126$		0			0
$127$	2.76490	+	12.1138i	0.245346	+	1.07493i	0.936071	+	0.351812i	$0.114434\pi$
$127$	2.76490	+	12.1138i	0.245346	+	1.07493i	−0.690725	+	0.723117i	$0.742709\pi$
$128$	−1.00000			−0.0883883
$129$	2.70351			0.238031
$130$	−2.37041	−	10.3855i	−0.207899	−	0.910865i
$131$	6.65430	+	3.20454i	0.581389	+	0.279982i	0.701374	−	0.712794i	$-0.252570\pi$
$131$	6.65430	+	3.20454i	0.581389	+	0.279982i	−0.119985	+	0.992776i	$0.538285\pi$
$132$	1.73193	−	2.17177i	0.150745	−	0.189029i
$133$		0			0
$134$	−1.15635	−	1.45002i	−0.0998938	−	0.125263i
$135$	1.56949	+	6.87640i	0.135081	+	0.591827i
$136$	−2.15547	−	2.70288i	−0.184830	−	0.231770i
$137$	11.0692	+	5.33065i	0.945707	+	0.455429i	0.842179	−	0.539198i	$-0.181273\pi$
$137$	11.0692	+	5.33065i	0.945707	+	0.455429i	0.103528	+	0.994627i	$0.466987\pi$
$138$	3.48960	−	4.37582i	0.297055	−	0.372495i
$139$	1.06666	−	0.513677i	0.0904730	−	0.0435695i	−0.388100	−	0.921617i	$-0.626868\pi$
$139$	1.06666	−	0.513677i	0.0904730	−	0.0435695i	0.478573	+	0.878048i	$0.341154\pi$
$140$		0			0
$141$	4.55874	+	2.19537i	0.383915	+	0.184884i
$142$	−6.52649	+	3.14299i	−0.547691	+	0.263754i
$143$	5.15078	−	22.5670i	0.430730	−	1.88715i
$144$	2.26812	−	1.09227i	0.189010	−	0.0910225i
$145$	−2.02590	−	2.54039i	−0.168242	−	0.210968i
$146$	11.7243			0.970314
$147$		0			0
$148$	6.15572			0.505997
$149$	9.94048	+	12.4650i	0.814356	+	1.02117i	0.999262	+	0.0384137i	$0.0122305\pi$
$149$	9.94048	+	12.4650i	0.814356	+	1.02117i	−0.184906	+	0.982756i	$0.559198\pi$
$150$	−1.00991	+	0.486346i	−0.0824586	+	0.0397099i
$151$	2.73823	−	11.9970i	0.222834	−	0.976299i	−0.732499	−	0.680768i	$-0.761646\pi$
$151$	2.73823	−	11.9970i	0.222834	−	0.976299i	0.955333	−	0.295531i	$-0.0954966\pi$
$152$	2.73853	−	1.31881i	0.222124	−	0.106969i
$153$	7.84116	+	3.77610i	0.633920	+	0.305280i
$154$		0			0
$155$	8.95647	−	4.31321i	0.719401	−	0.346445i
$156$	−2.50723	+	3.14397i	−0.200739	+	0.251719i
$157$	19.6324	+	9.45448i	1.56684	+	0.754550i	0.997706	−	0.0676959i	$-0.0215648\pi$
$157$	19.6324	+	9.45448i	1.56684	+	0.754550i	0.569133	+	0.822246i	$0.307279\pi$
$158$	2.78205	+	3.48858i	0.221328	+	0.277537i
$159$	1.38345	+	6.06127i	0.109714	+	0.480690i
$160$	−1.14736	−	1.43874i	−0.0907068	−	0.113743i
$161$		0			0
$162$	−3.04869	+	3.82293i	−0.239527	+	0.300358i
$163$	−7.73961	−	3.72720i	−0.606213	−	0.291937i	0.105487	−	0.994421i	$-0.466360\pi$
$163$	−7.73961	−	3.72720i	−0.606213	−	0.291937i	−0.711700	+	0.702484i	$0.752074\pi$
$164$	0.698827	+	3.06176i	0.0545692	+	0.239083i
$165$	5.11178			0.397951
$166$	5.49299			0.426338
$167$	−0.890473	−	3.90142i	−0.0689069	−	0.301901i	0.928718	−	0.370788i	$-0.120912\pi$
$167$	−0.890473	−	3.90142i	−0.0689069	−	0.301901i	−0.997624	+	0.0688871i	$0.978055\pi$
$168$		0			0
$169$	−4.56375	+	19.9951i	−0.351058	+	1.53808i
$170$	1.41565	−	6.20236i	0.108575	−	0.475699i
$171$	−4.77083	+	5.98243i	−0.364834	+	0.457488i
$172$	2.42647	−	3.04270i	0.185017	−	0.232004i
$173$	4.10898	−	18.0026i	0.312400	−	1.36871i	−0.538164	−	0.842840i	$-0.680882\pi$
$173$	4.10898	−	18.0026i	0.312400	−	1.36871i	0.850563	−	0.525873i	$-0.176261\pi$
$174$	−0.272942	+	1.19584i	−0.0206917	+	0.0906561i
$175$		0			0
$176$	−0.889796	−	3.89845i	−0.0670709	−	0.293857i
$177$	4.99263			0.375269
$178$	−11.4326			−0.856907
$179$	−3.17117	−	13.8938i	−0.237024	−	1.03847i	−0.943666	−	0.330899i	$-0.892648\pi$
$179$	−3.17117	−	13.8938i	−0.237024	−	1.03847i	0.706642	−	0.707571i	$-0.250209\pi$
$180$	4.17385	+	2.01002i	0.311101	+	0.149818i
$181$	−11.7758	+	14.7664i	−0.875291	+	1.09758i	0.119211	+	0.992869i	$0.461963\pi$
$181$	−11.7758	+	14.7664i	−0.875291	+	1.09758i	−0.994503	+	0.104712i	$0.966608\pi$
$182$		0			0
$183$	−1.67640	−	2.10214i	−0.123923	−	0.155395i
$184$	−1.79281	−	7.85483i	−0.132168	−	0.579066i
$185$	7.06283	+	8.85651i	0.519269	+	0.651143i
$186$	−3.38102	−	1.62822i	−0.247909	−	0.119387i
$187$	8.61911	−	10.8080i	0.630292	−	0.790361i
$188$	6.56240	−	3.16029i	0.478612	−	0.230488i
$189$		0			0
$190$	5.03951	+	2.42690i	0.365604	+	0.176066i
$191$	−14.9686	+	7.20849i	−1.08309	+	0.521588i	−0.888303	−	0.459258i	$-0.848115\pi$
$191$	−14.9686	+	7.20849i	−1.08309	+	0.521588i	−0.194785	+	0.980846i	$0.562401\pi$
$192$	−0.154580	+	0.677258i	−0.0111558	+	0.0488769i
$193$	−24.1057	+	11.6087i	−1.73516	+	0.835611i	−0.750562	+	0.660800i	$0.770217\pi$
$193$	−24.1057	+	11.6087i	−1.73516	+	0.835611i	−0.984602	+	0.174811i	$0.944069\pi$
$194$	−6.06465	−	7.60484i	−0.435417	−	0.545995i
$195$	−7.40006			−0.529929
$196$		0			0
$197$	−7.32209			−0.521677			−0.260839	−	0.965382i	$-0.583999\pi$
$197$	−7.32209			−0.521677			−0.260839	+	0.965382i	$0.583999\pi$
$198$	6.27633	+	7.87026i	0.446039	+	0.559315i
$199$	3.42759	−	1.65064i	0.242976	−	0.117011i	−0.308433	−	0.951246i	$-0.599805\pi$
$199$	3.42759	−	1.65064i	0.242976	−	0.117011i	0.551409	+	0.834235i	$0.314090\pi$
$200$	−0.359055	+	1.57312i	−0.0253890	+	0.111236i
$201$	−1.16079	+	0.559006i	−0.0818757	+	0.0394293i
$202$	−7.17775	−	3.45662i	−0.505025	−	0.243207i
$203$		0			0
$204$	−2.16374	+	1.04200i	−0.151492	+	0.0729548i
$205$	−3.60329	+	4.51838i	−0.251664	+	0.315577i
$206$	15.9852	+	7.69804i	1.11374	+	0.536348i
$207$	12.6459	+	15.8575i	0.878953	+	1.10217i
$208$	1.28811	+	5.64359i	0.0893145	+	0.391312i
$209$	7.57803	+	9.50255i	0.524184	+	0.657305i
$210$		0			0
$211$	13.3917	−	16.7927i	0.921923	−	1.15605i	−0.0654839	−	0.997854i	$-0.520859\pi$
$211$	13.3917	−	16.7927i	0.921923	−	1.15605i	0.987407	−	0.158201i	$-0.0505695\pi$
$212$	8.06342	+	3.88314i	0.553798	+	0.266695i
$213$	1.11975	+	4.90596i	0.0767242	+	0.336151i
$214$	−3.06659			−0.209628
$215$	7.16171			0.488424
$216$	−0.852883	−	3.73672i	−0.0580313	−	0.254252i
$217$		0			0
$218$	−2.94378	+	12.8975i	−0.199378	+	0.873531i
$219$	1.81235	−	7.94041i	0.122467	−	0.536563i
$220$	4.58796	−	5.75312i	0.309320	−	0.387875i
$221$	−12.4774	+	15.6462i	−0.839324	+	1.05248i
$222$	0.951550	−	4.16901i	0.0638638	−	0.279806i
$223$	−1.33464	+	5.84744i	−0.0893741	+	0.391573i	−0.999754	−	0.0222010i	$-0.992933\pi$
$223$	−1.33464	+	5.84744i	−0.0893741	+	0.391573i	0.910379	+	0.413774i	$0.135790\pi$
$224$		0			0
$225$	−0.903894	−	3.96022i	−0.0602596	−	0.264014i
$226$	10.3844			0.690761
$227$	−10.5567			−0.700670			−0.350335	−	0.936624i	$-0.613932\pi$
$227$	−10.5567			−0.700670			−0.350335	+	0.936624i	$0.613932\pi$
$228$	−0.469851	−	2.05855i	−0.0311167	−	0.136331i
$229$	−8.03094	−	3.86750i	−0.530700	−	0.255571i	0.149290	−	0.988794i	$-0.452301\pi$
$229$	−8.03094	−	3.86750i	−0.530700	−	0.255571i	−0.679989	+	0.733222i	$0.738016\pi$
$230$	9.24410	−	11.5917i	0.609538	−	0.764336i
$231$		0			0
$232$	1.10090	+	1.38048i	0.0722774	+	0.0906330i
$233$	0.349296	+	1.53037i	0.0228832	+	0.100258i	0.985080	−	0.172098i	$-0.0550545\pi$
$233$	0.349296	+	1.53037i	0.0228832	+	0.100258i	−0.962197	+	0.272355i	$0.912197\pi$
$234$	−9.08592	−	11.3934i	−0.593965	−	0.744809i
$235$	12.0763	+	5.81563i	0.787770	+	0.379370i
$236$	4.48102	−	5.61902i	0.291689	−	0.365767i
$237$	2.79272	−	1.34490i	0.181407	−	0.0873608i
$238$		0			0
$239$	−20.8411	−	10.0366i	−1.34810	−	0.649211i	−0.386150	−	0.922436i	$-0.626195\pi$
$239$	−20.8411	−	10.0366i	−1.34810	−	0.649211i	−0.961950	+	0.273225i	$0.911910\pi$
$240$	−1.15176	+	0.554659i	−0.0743458	+	0.0358031i
$241$	−1.14248	+	5.00555i	−0.0735939	+	0.322436i	−0.998303	−	0.0582395i	$-0.981451\pi$
$241$	−1.14248	+	5.00555i	−0.0735939	+	0.322436i	0.924709	+	0.380675i	$0.124308\pi$
$242$	4.49552	−	2.16493i	0.288983	−	0.139167i
$243$	9.28702	+	11.6456i	0.595763	+	0.747063i
$244$	−3.87049			−0.247783
$245$		0			0
$246$	2.18163			0.139096
$247$	−10.9703	−	13.7564i	−0.698026	−	0.875297i
$248$	−4.86706	+	2.34385i	−0.309058	+	0.148835i
$249$	0.849105	−	3.72017i	0.0538098	−	0.235756i
$250$	−10.9652	+	5.28056i	−0.693501	+	0.333972i
$251$	4.60431	+	2.21732i	0.290622	+	0.139956i	0.573514	−	0.819196i	$-0.305580\pi$
$251$	4.60431	+	2.21732i	0.290622	+	0.139956i	−0.282893	+	0.959152i	$0.591294\pi$
$252$		0			0
$253$	29.0264	−	13.9784i	1.82488	−	0.878814i
$254$	7.74709	−	9.71454i	0.486096	−	0.609545i
$255$	−3.98177	−	1.91752i	−0.249348	−	0.120080i
$256$	0.623490	+	0.781831i	0.0389681	+	0.0488645i
$257$	3.50598	+	15.3607i	0.218697	+	0.958174i	0.958442	+	0.285287i	$0.0920889\pi$
$257$	3.50598	+	15.3607i	0.218697	+	0.958174i	−0.739745	+	0.672887i	$0.765054\pi$
$258$	−1.68561	−	2.11369i	−0.104942	−	0.131593i
$259$		0			0
$260$	−6.64175	+	8.32849i	−0.411904	+	0.516511i
$261$	−4.00483	−	1.92862i	−0.247893	−	0.119379i
$262$	−1.64348	−	7.20054i	−0.101534	−	0.444851i
$263$	−1.85362			−0.114299			−0.0571494	−	0.998366i	$-0.518201\pi$
$263$	−1.85362			−0.114299			−0.0571494	+	0.998366i	$0.518201\pi$
$264$	−2.77780			−0.170962
$265$	3.66480	+	16.0566i	0.225127	+	0.986346i
$266$		0			0
$267$	−1.76724	+	7.74280i	−0.108153	+	0.473851i
$268$	−0.412698	+	1.80815i	−0.0252095	+	0.110450i
$269$	0.936100	−	1.17383i	0.0570750	−	0.0715698i	−0.752475	−	0.658621i	$-0.771140\pi$
$269$	0.936100	−	1.17383i	0.0570750	−	0.0715698i	0.809550	+	0.587051i	$0.199711\pi$
$270$	4.39763	−	5.51445i	0.267631	−	0.335599i
$271$	−3.67055	+	16.0817i	−0.222970	+	0.976896i	0.732258	+	0.681027i	$0.238466\pi$
$271$	−3.67055	+	16.0817i	−0.222970	+	0.976896i	−0.955228	+	0.295869i	$0.904391\pi$
$272$	−0.769280	+	3.37044i	−0.0466444	+	0.204363i
$273$		0			0
$274$	−2.73387	−	11.9779i	−0.165159	−	0.723610i
$275$	−6.45222			−0.389084
$276$	−5.59688			−0.336893
$277$	−3.46842	−	15.1961i	−0.208397	−	0.913048i	−0.965634	−	0.259907i	$-0.916308\pi$
$277$	−3.46842	−	15.1961i	−0.208397	−	0.913048i	0.757236	−	0.653141i	$-0.226549\pi$
$278$	−1.06666	−	0.513677i	−0.0639741	−	0.0308083i
$279$	8.47897	−	10.6323i	0.507622	−	0.636538i
$280$		0			0
$281$	−0.198061	−	0.248361i	−0.0118153	−	0.0148160i	0.775889	−	0.630870i	$-0.217302\pi$
$281$	−0.198061	−	0.248361i	−0.0118153	−	0.0148160i	−0.787704	+	0.616054i	$0.788730\pi$
$282$	−1.12592	−	4.93296i	−0.0670473	−	0.293753i
$283$	−13.3427	−	16.7312i	−0.793138	−	0.994564i	−0.999869	−	0.0161663i	$-0.994854\pi$
$283$	−13.3427	−	16.7312i	−0.793138	−	0.994564i	0.206731	−	0.978398i	$-0.433718\pi$
$284$	6.52649	+	3.14299i	0.387276	+	0.186502i
$285$	2.42264	−	3.03790i	0.143505	−	0.179950i
$286$	−20.8551	+	10.0433i	−1.23319	+	0.593872i
$287$		0			0
$288$	−2.26812	−	1.09227i	−0.133650	−	0.0643626i
$289$	4.54843	−	2.19041i	0.267554	−	0.128847i
$290$	−0.723034	+	3.16782i	−0.0424580	+	0.186021i
$291$	−6.08791	+	2.93178i	−0.356880	+	0.171864i
$292$	−7.31001	−	9.16646i	−0.427786	−	0.536427i
$293$	−9.40795			−0.549618			−0.274809	−	0.961499i	$-0.588615\pi$
$293$	−9.40795			−0.549618			−0.274809	+	0.961499i	$0.588615\pi$
$294$		0			0
$295$	13.2257			0.770029
$296$	−3.83803	−	4.81273i	−0.223081	−	0.279734i
$297$	13.8085	−	6.64984i	0.801252	−	0.385863i
$298$	3.54772	−	15.5436i	0.205514	−	0.900414i
$299$	−42.0201	+	20.2358i	−2.43009	+	1.17027i
$300$	1.00991	+	0.486346i	0.0583070	+	0.0280792i
$301$		0			0
$302$	−11.0869	+	5.33915i	−0.637977	+	0.307234i
$303$	−3.45056	+	4.32687i	−0.198230	+	0.248572i
$304$	−2.73853	−	1.31881i	−0.157066	−	0.0756388i
$305$	−4.44085	−	5.56865i	−0.254283	−	0.318860i
$306$	−1.93661	−	8.48482i	−0.110708	−	0.485045i
$307$	−16.7984	−	21.0645i	−0.958736	−	1.20222i	−0.979297	−	0.202429i	$-0.935117\pi$
$307$	−16.7984	−	21.0645i	−0.958736	−	1.20222i	0.0205607	−	0.999789i	$-0.493455\pi$
$308$		0			0
$309$	7.68455	−	9.63612i	0.437159	−	0.548179i
$310$	−8.95647	−	4.31321i	−0.508694	−	0.244974i
$311$	2.60597	+	11.4175i	0.147771	+	0.647427i	0.993502	+	0.113817i	$0.0363079\pi$
$311$	2.60597	+	11.4175i	0.147771	+	0.647427i	−0.845731	+	0.533610i	$0.820835\pi$
$312$	4.02128			0.227660
$313$	−18.7188			−1.05805			−0.529025	−	0.848606i	$-0.677442\pi$
$313$	−18.7188			−1.05805			−0.529025	+	0.848606i	$0.677442\pi$
$314$	−4.84881	−	21.2440i	−0.273634	−	1.19887i
$315$		0			0
$316$	0.992902	−	4.35019i	0.0558551	−	0.244717i
$317$	−4.56788	+	20.0132i	−0.256558	+	1.12405i	0.668345	+	0.743851i	$0.267003\pi$
$317$	−4.56788	+	20.0132i	−0.256558	+	1.12405i	−0.924903	+	0.380202i	$0.875854\pi$
$318$	3.87633	−	4.86076i	0.217374	−	0.272578i
$319$	−4.40216	+	5.52014i	−0.246474	+	0.309068i
$320$	−0.409488	+	1.79409i	−0.0228911	+	0.100292i
$321$	−0.474033	+	2.07687i	−0.0264579	+	0.115920i
$322$		0			0
$323$	−2.33826	−	10.2446i	−0.130104	−	0.570023i
$324$	4.88971			0.271651
$325$	9.34055			0.518121
$326$	1.91153	+	8.37494i	0.105870	+	0.463845i
$327$	8.27991	+	3.98740i	0.457880	+	0.220504i
$328$	1.95807	−	2.45534i	0.108116	−	0.135574i
$329$		0			0
$330$	−3.18714	−	3.99655i	−0.175446	−	0.220003i
$331$	−3.86297	−	16.9248i	−0.212328	−	0.930270i	−0.962980	−	0.269572i	$-0.913118\pi$
$331$	−3.86297	−	16.9248i	−0.212328	−	0.930270i	0.750652	−	0.660698i	$-0.229739\pi$
$332$	−3.42482	−	4.29459i	−0.187962	−	0.235696i
$333$	13.9619	+	6.72371i	0.765109	+	0.368457i
$334$	−2.49505	+	3.12869i	−0.136523	+	0.171195i
$335$	−3.07498	+	1.48083i	−0.168004	+	0.0809065i
$336$		0			0
$337$	−9.11274	−	4.38846i	−0.496403	−	0.239055i	0.168894	−	0.985634i	$-0.445981\pi$
$337$	−9.11274	−	4.38846i	−0.496403	−	0.239055i	−0.665296	+	0.746579i	$0.731695\pi$
$338$	18.4783	−	8.89866i	1.00508	−	0.484023i
$339$	1.60522	−	7.03293i	0.0871836	−	0.381976i
$340$	−5.73184	+	2.76031i	−0.310853	+	0.149699i
$341$	−13.4681	−	16.8884i	−0.729337	−	0.914560i
$342$	7.65182			0.413763
$343$		0			0
$344$	−3.89176			−0.209830
$345$	−6.42164	−	8.05249i	−0.345730	−	0.433531i
$346$	−16.6369	+	8.01191i	−0.894406	+	0.430723i
$347$	−3.24206	+	14.2044i	−0.174043	+	0.762531i	0.810264	+	0.586065i	$0.199324\pi$
$347$	−3.24206	+	14.2044i	−0.174043	+	0.762531i	−0.984307	+	0.176466i	$0.943533\pi$
$348$	1.10512	−	0.532197i	0.0592406	−	0.0285288i
$349$	5.70747	+	2.74857i	0.305514	+	0.147128i	0.580359	−	0.814361i	$-0.302912\pi$
$349$	5.70747	+	2.74857i	0.305514	+	0.147128i	−0.274845	+	0.961489i	$0.588627\pi$
$350$		0			0
$351$	−19.9899	+	9.62663i	−1.06698	+	0.513832i
$352$	−2.49315	+	3.12631i	−0.132885	+	0.166633i
$353$	−31.3904	−	15.1168i	−1.67074	−	0.804588i	−0.997898	−	0.0648069i	$-0.979357\pi$
$353$	−31.3904	−	15.1168i	−1.67074	−	0.804588i	−0.672847	−	0.739782i	$-0.734929\pi$
$354$	−3.11285	−	3.90339i	−0.165446	−	0.207463i
$355$	2.96627	+	12.9961i	0.157433	+	0.689761i
$356$	7.12809	+	8.93834i	0.377788	+	0.473731i
$357$		0			0
$358$	−8.88541	+	11.1420i	−0.469609	+	0.588871i
$359$	15.4408	+	7.43587i	0.814932	+	0.392450i	0.794442	−	0.607340i	$-0.207763\pi$
$359$	15.4408	+	7.43587i	0.814932	+	0.392450i	0.0204895	+	0.999790i	$0.493478\pi$
$360$	−1.03086	−	4.51648i	−0.0543309	−	0.238039i
$361$	−9.76120			−0.513747
$362$	18.8870			0.992678
$363$	−0.771298	−	3.37928i	−0.0404827	−	0.177366i
$364$		0			0
$365$	4.80098	−	21.0345i	0.251295	−	1.10099i
$366$	−0.598300	+	2.62132i	−0.0312737	+	0.137019i
$367$	−20.6678	+	25.9166i	−1.07885	+	1.35284i	−0.147357	+	0.989083i	$0.547077\pi$
$367$	−20.6678	+	25.9166i	−1.07885	+	1.35284i	−0.931495	+	0.363754i	$0.881495\pi$
$368$	−5.02336	+	6.29909i	−0.261860	+	0.328363i
$369$	−1.75925	+	7.70776i	−0.0915827	+	0.401250i
$370$	2.52069	−	11.0439i	0.131045	−	0.574144i
$371$		0			0
$372$	0.835044	+	3.65857i	0.0432950	+	0.189688i
$373$	2.37539			0.122993			0.0614966	−	0.998107i	$-0.480413\pi$
$373$	2.37539			0.122993			0.0614966	+	0.998107i	$0.480413\pi$
$374$	−13.8240			−0.714821
$375$	1.88131	+	8.24255i	0.0971503	+	0.425643i
$376$	−6.56240	−	3.16029i	−0.338430	−	0.162979i
$377$	6.37279	−	7.99122i	0.328215	−	0.411569i
$378$		0			0
$379$	−9.78749	−	12.2731i	−0.502749	−	0.630428i	0.464098	−	0.885784i	$-0.346379\pi$
$379$	−9.78749	−	12.2731i	−0.502749	−	0.630428i	−0.966847	+	0.255356i	$0.917807\pi$
$380$	−1.24466	−	5.45319i	−0.0638495	−	0.279743i
$381$	−5.38171	−	6.74845i	−0.275713	−	0.345734i
$382$	14.9686	+	7.20849i	0.765859	+	0.368818i
$383$	−10.3991	+	13.0401i	−0.531370	+	0.666317i	−0.972980	−	0.230890i	$-0.925836\pi$
$383$	−10.3991	+	13.0401i	−0.531370	+	0.666317i	0.441610	+	0.897207i	$0.354408\pi$
$384$	0.625881	−	0.301408i	0.0319393	−	0.0153812i
$385$		0			0
$386$	24.1057	+	11.6087i	1.22695	+	0.590866i
$387$	8.82699	−	4.25085i	0.448701	−	0.216083i
$388$	−2.16445	+	9.48307i	−0.109883	+	0.481430i
$389$	13.9020	−	6.69486i	0.704860	−	0.339443i	−0.0468814	−	0.998900i	$-0.514928\pi$
$389$	13.9020	−	6.69486i	0.704860	−	0.339443i	0.751742	+	0.659458i	$0.229214\pi$
$390$	4.61386	+	5.78560i	0.233632	+	0.292965i
$391$	−27.8534			−1.40861
$392$		0			0
$393$	−5.13067			−0.258808
$394$	4.56525	+	5.72464i	0.229994	+	0.288403i
$395$	7.39803	−	3.56270i	0.372235	−	0.179259i
$396$	2.24000	−	9.81406i	0.112564	−	0.493175i
$397$	23.4203	−	11.2786i	1.17543	−	0.566059i	0.258856	−	0.965916i	$-0.416654\pi$
$397$	23.4203	−	11.2786i	1.17543	−	0.566059i	0.916578	+	0.399857i	$0.130940\pi$
$398$	−3.42759	−	1.65064i	−0.171810	−	0.0827392i
$399$		0			0
$400$	1.45378	−	0.700105i	0.0726891	−	0.0350052i
$401$	13.1769	−	16.5234i	0.658025	−	0.825137i	−0.335102	−	0.942182i	$-0.608771\pi$
$401$	13.1769	−	16.5234i	0.658025	−	0.825137i	0.993127	+	0.117045i	$0.0373421\pi$
$402$	1.16079	+	0.559006i	0.0578949	+	0.0278807i
$403$	19.4970	+	24.4485i	0.971217	+	1.21787i
$404$	1.77276	+	7.76696i	0.0881980	+	0.386421i
$405$	5.61027	+	7.03505i	0.278776	+	0.349574i
$406$		0			0
$407$	15.3471	−	19.2447i	0.760730	−	0.953925i
$408$	2.16374	+	1.04200i	0.107121	+	0.0515868i
$409$	0.654372	+	2.86699i	0.0323566	+	0.141764i	0.988526	−	0.151050i	$-0.0482655\pi$
$409$	0.654372	+	2.86699i	0.0323566	+	0.141764i	−0.956169	+	0.292814i	$0.905408\pi$
$410$	5.77922			0.285415
$411$	−8.53471			−0.420986
$412$	−3.94801	−	17.2973i	−0.194504	−	0.852179i
$413$		0			0
$414$	4.51328	−	19.7740i	0.221816	−	0.971837i
$415$	2.24931	−	9.85489i	0.110414	−	0.483757i
$416$	3.60921	−	4.52581i	0.176956	−	0.221896i
$417$	−0.512776	+	0.643001i	−0.0251108	+	0.0314879i
$418$	2.70457	−	11.8495i	0.132285	−	0.579578i
$419$	−2.46363	+	10.7939i	−0.120356	+	0.527315i	0.878422	+	0.477887i	$0.158597\pi$
$419$	−2.46363	+	10.7939i	−0.120356	+	0.527315i	−0.998778	+	0.0494281i	$0.984260\pi$
$420$		0			0
$421$	4.29276	+	18.8078i	0.209216	+	0.916637i	0.965090	+	0.261919i	$0.0843554\pi$
$421$	4.29276	+	18.8078i	0.209216	+	0.916637i	−0.755873	+	0.654718i	$0.772787\pi$
$422$	−21.4786			−1.04556
$423$	18.3362			0.891537
$424$	−1.99150	−	8.72533i	−0.0967157	−	0.423739i
$425$	5.02589	+	2.42034i	0.243792	+	0.117404i
$426$	3.13748	−	3.93427i	0.152011	−	0.190616i
$427$		0			0
$428$	1.91199	+	2.39756i	0.0924194	+	0.115890i
$429$	3.57812	+	15.6768i	0.172753	+	0.756881i
$430$	−4.46525	−	5.59925i	−0.215334	−	0.270020i
$431$	9.28694	+	4.47235i	0.447336	+	0.215426i	0.643969	−	0.765051i	$-0.277286\pi$
$431$	9.28694	+	4.47235i	0.447336	+	0.215426i	−0.196633	+	0.980477i	$0.563001\pi$
$432$	−2.38972	+	2.99662i	−0.114976	+	0.144175i
$433$	2.91822	−	1.40534i	0.140241	−	0.0675364i	−0.362447	−	0.932004i	$-0.618059\pi$
$433$	2.91822	−	1.40534i	0.140241	−	0.0675364i	0.502688	+	0.864468i	$0.332344\pi$
$434$		0			0
$435$	2.03367	+	0.979361i	0.0975068	+	0.0469568i
$436$	11.9191	−	5.73994i	0.570822	−	0.274893i
$437$	5.44933	−	23.8751i	0.260677	−	1.14210i
$438$	−7.33804	+	3.53381i	−0.350625	+	0.168852i
$439$	−22.5466	−	28.2725i	−1.07609	−	1.34937i	−0.933087	−	0.359650i	$-0.882896\pi$
$439$	−22.5466	−	28.2725i	−1.07609	−	1.34937i	−0.143002	−	0.989722i	$-0.545675\pi$
$440$	−7.35851			−0.350803
$441$		0			0
$442$	20.0123			0.951886
$443$	−6.11243	−	7.66475i	−0.290410	−	0.364163i	0.615128	−	0.788427i	$-0.289104\pi$
$443$	−6.11243	−	7.66475i	−0.290410	−	0.364163i	−0.905539	+	0.424264i	$0.860533\pi$
$444$	−3.85275	+	1.85538i	−0.182843	+	0.0880526i
$445$	−4.68150	+	20.5110i	−0.221924	+	0.972314i
$446$	5.40384	−	2.60235i	0.255879	−	0.123225i
$447$	−9.97860	−	4.80544i	−0.471972	−	0.227290i
$448$		0			0
$449$	−6.60499	+	3.18080i	−0.311709	+	0.150111i	−0.583197	−	0.812331i	$-0.698198\pi$
$449$	−6.60499	+	3.18080i	−0.311709	+	0.150111i	0.271488	+	0.962442i	$0.412484\pi$
$450$	−2.53265	+	3.17585i	−0.119390	+	0.149711i
$451$	11.3143	+	5.44868i	0.532770	+	0.256569i
$452$	−6.47458	−	8.11886i	−0.304538	−	0.381879i
$453$	1.90218	+	8.33399i	0.0893722	+	0.391565i
$454$	6.58197	+	8.25353i	0.308907	+	0.387357i
$455$		0			0
$456$	−1.31649	+	1.65083i	−0.0616505	+	0.0773073i
$457$	−26.4449	−	12.7352i	−1.23704	−	0.595727i	−0.303033	−	0.952980i	$-0.597999\pi$
$457$	−26.4449	−	12.7352i	−1.23704	−	0.595727i	−0.934008	+	0.357253i	$0.883713\pi$
$458$	1.98348	+	8.69019i	0.0926819	+	0.406066i
$459$	−13.2505			−0.618480
$460$	−14.8264			−0.691284
$461$	0.0546636	+	0.239497i	0.00254594	+	0.0111545i	0.976185	−	0.216940i	$-0.0696076\pi$
$461$	0.0546636	+	0.239497i	0.00254594	+	0.0111545i	−0.973639	+	0.228095i	$0.926750\pi$
$462$		0			0
$463$	2.07391	−	9.08638i	0.0963826	−	0.422280i	−0.903599	−	0.428380i	$-0.859085\pi$
$463$	2.07391	−	9.08638i	0.0963826	−	0.422280i	0.999981	+	0.00610002i	$0.00194171\pi$
$464$	0.392906	−	1.72143i	0.0182402	−	0.0799155i
$465$	−4.30565	+	5.39911i	−0.199670	+	0.250378i
$466$	0.978707	−	1.22726i	0.0453377	−	0.0568517i
$467$	2.37370	−	10.3998i	0.109842	−	0.481248i	−0.889846	−	0.456261i	$-0.849188\pi$
$467$	2.37370	−	10.3998i	0.109842	−	0.481248i	0.999688	−	0.0249869i	$-0.00795440\pi$
$468$	−3.24273	+	14.2073i	−0.149895	+	0.656733i
$469$		0			0
$470$	−2.98260	−	13.0676i	−0.137577	−	0.602764i
$471$	−15.1372			−0.697486
$472$	−7.18700			−0.330808
$473$	−3.46287	−	15.1718i	−0.159223	−	0.697602i
$474$	−2.79272	−	1.34490i	−0.128274	−	0.0617734i
$475$	−3.05793	+	3.83452i	−0.140307	+	0.175940i
$476$		0			0
$477$	14.0474	+	17.6149i	0.643185	+	0.806529i
$478$	5.14733	+	22.5519i	0.235434	+	1.03150i
$479$	8.14985	+	10.2196i	0.372376	+	0.466945i	0.932346	−	0.361568i	$-0.117759\pi$
$479$	8.14985	+	10.2196i	0.372376	+	0.466945i	−0.559970	+	0.828513i	$0.689187\pi$
$480$	1.15176	+	0.554659i	0.0525704	+	0.0253166i
$481$	−22.2173	+	27.8596i	−1.01302	+	1.27029i
$482$	4.62582	−	2.22768i	0.210700	−	0.101468i
$483$		0			0
$484$	−4.49552	−	2.16493i	−0.204342	−	0.0984057i
$485$	−16.1271	+	7.76642i	−0.732295	+	0.352655i
$486$	3.31450	−	14.5218i	0.150349	−	0.658721i
$487$	−2.69990	+	1.30020i	−0.122344	+	0.0589177i	−0.494054	−	0.869431i	$-0.664486\pi$
$487$	−2.69990	+	1.30020i	−0.122344	+	0.0589177i	0.371711	+	0.928349i	$0.378771\pi$
$488$	2.41321	+	3.02607i	0.109241	+	0.136984i
$489$	5.96748			0.269859
$490$		0			0
$491$	5.19765			0.234567			0.117283	−	0.993098i	$-0.462581\pi$
$491$	5.19765			0.234567			0.117283	+	0.993098i	$0.462581\pi$
$492$	−1.36022	−	1.70567i	−0.0613236	−	0.0768973i
$493$	5.49972	−	2.64853i	0.247695	−	0.119284i
$494$	−3.91527	+	17.1539i	−0.176156	+	0.771791i
$495$	16.6900	−	8.03748i	0.750160	−	0.361258i
$496$	4.86706	+	2.34385i	0.218537	+	0.105242i
$497$		0			0
$498$	−3.43796	+	1.65563i	−0.154058	+	0.0741906i
$499$	−4.61612	+	5.78844i	−0.206646	+	0.259126i	−0.874344	−	0.485306i	$-0.838708\pi$
$499$	−4.61612	+	5.78844i	−0.206646	+	0.259126i	0.667698	+	0.744432i	$0.267280\pi$
$500$	10.9652	+	5.28056i	0.490379	+	0.236154i
$501$	1.73325	+	2.17343i	0.0774359	+	0.0971015i
$502$	−1.13717	−	4.98228i	−0.0507545	−	0.222370i
$503$	−6.13267	−	7.69012i	−0.273442	−	0.342886i	0.626081	−	0.779758i	$-0.284658\pi$
$503$	−6.13267	−	7.69012i	−0.273442	−	0.342886i	−0.899524	+	0.436872i	$0.856086\pi$
$504$		0			0
$505$	−9.14068	+	11.4621i	−0.406755	+	0.510055i
$506$	−29.0264	−	13.9784i	−1.29038	−	0.621415i
$507$	−3.17032	−	13.8901i	−0.140799	−	0.616881i
$508$	−12.4254			−0.551286
$509$	31.6672			1.40362			0.701812	−	0.712362i	$-0.252375\pi$
$509$	31.6672			1.40362			0.701812	+	0.712362i	$0.252375\pi$
$510$	0.983415	+	4.30862i	0.0435463	+	0.190789i
$511$		0			0
$512$	0.222521	−	0.974928i	0.00983413	−	0.0430861i
$513$	2.59237	−	11.3579i	0.114456	−	0.501464i
$514$	9.82354	−	12.3183i	0.433298	−	0.543338i
$515$	20.3567	−	25.5265i	0.897023	−	1.12483i
$516$	−0.601587	+	2.63573i	−0.0264834	+	0.116031i
$517$	6.48102	−	28.3952i	0.285035	−	1.24882i
$518$		0			0
$519$	2.85441	+	12.5060i	0.125294	+	0.548951i
$520$	10.6525			0.467145
$521$	14.6688			0.642652			0.321326	−	0.946969i	$-0.395871\pi$
$521$	14.6688			0.642652			0.321326	+	0.946969i	$0.395871\pi$
$522$	0.989111	+	4.33358i	0.0432922	+	0.189676i
$523$	14.7847	+	7.11994i	0.646490	+	0.311333i	0.728243	−	0.685319i	$-0.240337\pi$
$523$	14.7847	+	7.11994i	0.646490	+	0.311333i	−0.0817525	+	0.996653i	$0.526052\pi$
$524$	−4.60492	+	5.77438i	−0.201167	+	0.252255i
$525$		0			0
$526$	1.15571	+	1.44922i	0.0503914	+	0.0631888i
$527$	4.15567	+	18.2072i	0.181024	+	0.793117i
$528$	1.73193	+	2.17177i	0.0753726	+	0.0945143i
$529$	−37.7620	−	18.1852i	−1.64182	−	0.790661i
$530$	10.2686	−	12.8764i	0.446037	−	0.559313i
$531$	16.3010	−	7.85014i	0.707403	−	0.340667i
$532$		0			0
$533$	−16.3792	−	7.88778i	−0.709460	−	0.341658i
$534$	7.15542	−	3.44587i	0.309645	−	0.149117i
$535$	−1.25573	+	5.50173i	−0.0542901	+	0.237860i
$536$	1.67098	−	0.804702i	0.0721754	−	0.0347578i
$537$	6.17248	+	7.74004i	0.266362	+	0.334007i
$538$	−1.50139			−0.0647294
$539$		0			0
$540$	−7.05324			−0.303523
$541$	−6.04969	−	7.58607i	−0.260097	−	0.326151i	0.634587	−	0.772852i	$-0.281170\pi$
$541$	−6.04969	−	7.58607i	−0.260097	−	0.326151i	−0.894683	+	0.446701i	$0.852599\pi$
$542$	14.8618	−	7.15705i	0.638367	−	0.307422i
$543$	2.91955	−	12.7914i	0.125290	−	0.548930i
$544$	3.11475	−	1.49999i	0.133544	−	0.0643113i
$545$	21.9338	+	10.5628i	0.939542	+	0.452460i
$546$		0			0
$547$	20.1772	−	9.71681i	0.862713	−	0.415461i	0.0504324	−	0.998727i	$-0.483940\pi$
$547$	20.1772	−	9.71681i	0.862713	−	0.415461i	0.812281	+	0.583267i	$0.198226\pi$
$548$	−7.66014	+	9.60551i	−0.327225	+	0.410327i
$549$	−8.77876	−	4.22763i	−0.374668	−	0.180431i
$550$	4.02289	+	5.04455i	0.171537	+	0.215100i
$551$	1.19425	+	5.23236i	0.0508768	+	0.222906i
$552$	3.48960	+	4.37582i	0.148527	+	0.186247i
$553$		0			0
$554$	−9.71830	+	12.1864i	−0.412891	+	0.517749i
$555$	−7.08991	−	3.41432i	−0.300950	−	0.144930i
$556$	0.263444	+	1.15422i	0.0111725	+	0.0489499i
$557$	42.8265			1.81462			0.907309	−	0.420464i	$-0.138133\pi$
$557$	42.8265			1.81462			0.907309	+	0.420464i	$0.138133\pi$
$558$	−13.5992			−0.575700
$559$	5.01302	+	21.9635i	0.212028	+	0.928957i
$560$		0			0
$561$	−2.13691	+	9.36240i	−0.0902203	+	0.395281i
$562$	−0.0706871	+	0.309701i	−0.00298176	+	0.0130639i
$563$	−7.01892	+	8.80145i	−0.295812	+	0.370937i	−0.907420	−	0.420224i	$-0.861951\pi$
$563$	−7.01892	+	8.80145i	−0.295812	+	0.370937i	0.611608	+	0.791161i	$0.290523\pi$
$564$	−3.15474	+	3.95592i	−0.132839	+	0.166574i
$565$	4.25230	−	18.6305i	0.178895	−	0.783792i
$566$	−4.76194	+	20.8634i	−0.200159	+	0.876955i
$567$		0			0
$568$	−1.61191	−	7.06223i	−0.0676342	−	0.296325i
$569$	34.0346			1.42680			0.713402	−	0.700755i	$-0.247154\pi$
$569$	34.0346			1.42680			0.713402	+	0.700755i	$0.247154\pi$
$570$	−3.88562			−0.162751
$571$	2.30916	+	10.1171i	0.0966355	+	0.423388i	0.999985	−	0.00551792i	$-0.00175642\pi$
$571$	2.30916	+	10.1171i	0.0966355	+	0.423388i	−0.903349	+	0.428906i	$0.858899\pi$
$572$	20.8551	+	10.0433i	0.871995	+	0.419931i
$573$	7.19585	−	9.02330i	0.300611	−	0.376954i
$574$		0			0
$575$	8.10557	+	10.1641i	0.338026	+	0.423871i
$576$	0.560180	+	2.45431i	0.0233408	+	0.102263i
$577$	25.9429	+	32.5314i	1.08002	+	1.35430i	0.930815	+	0.365491i	$0.119099\pi$
$577$	25.9429	+	32.5314i	1.08002	+	1.35430i	0.149202	+	0.988807i	$0.452330\pi$
$578$	−4.54843	−	2.19041i	−0.189190	−	0.0911089i
$579$	11.5883	−	14.5313i	0.481594	−	0.603900i
$580$	2.92750	−	1.40981i	0.121558	−	0.0585393i
$581$		0			0
$582$	6.08791	+	2.93178i	0.252352	+	0.121526i
$583$	32.2432	−	15.5275i	1.33538	−	0.643084i
$584$	−2.60891	+	11.4304i	−0.107958	+	0.472993i
$585$	−24.1613	+	11.6355i	−0.998946	+	0.481067i
$586$	5.86576	+	7.35543i	0.242312	+	0.303850i
$587$	1.39293			0.0574923			0.0287461	−	0.999587i	$-0.490849\pi$
$587$	1.39293			0.0574923			0.0287461	+	0.999587i	$0.490849\pi$
$588$		0			0
$589$	−16.4197			−0.676561
$590$	−8.24608	−	10.3403i	−0.339486	−	0.425701i
$591$	4.58276	−	2.20694i	0.188509	−	0.0907813i
$592$	−1.36978	+	6.00138i	−0.0562975	+	0.246655i
$593$	23.3572	−	11.2483i	0.959167	−	0.461910i	0.112276	−	0.993677i	$-0.464186\pi$
$593$	23.3572	−	11.2483i	0.959167	−	0.461910i	0.846891	+	0.531767i	$0.178472\pi$
$594$	−13.8085	−	6.64984i	−0.566571	−	0.272846i
$595$		0			0
$596$	−14.3644	+	6.91753i	−0.588389	+	0.283353i
$597$	−1.64775	+	2.06621i	−0.0674378	+	0.0845643i
$598$	42.0201	+	20.2358i	1.71833	+	0.827504i
$599$	−23.5087	−	29.4789i	−0.960538	−	1.20448i	−0.978837	−	0.204643i	$-0.934397\pi$
$599$	−23.5087	−	29.4789i	−0.960538	−	1.20448i	0.0182990	−	0.999833i	$-0.494175\pi$
$600$	−0.249426	−	1.09281i	−0.0101828	−	0.0446137i
$601$	−5.44595	−	6.82900i	−0.222145	−	0.278561i	0.658253	−	0.752797i	$-0.271296\pi$
$601$	−5.44595	−	6.82900i	−0.222145	−	0.278561i	−0.880398	+	0.474236i	$0.842724\pi$
$602$		0			0
$603$	−2.91104	+	3.65032i	−0.118547	+	0.148653i
$604$	11.0869	+	5.33915i	0.451118	+	0.217247i
$605$	−2.04320	−	8.95185i	−0.0830680	−	0.363944i
$606$	5.53427			0.224814
$607$	17.5488			0.712284			0.356142	−	0.934432i	$-0.384092\pi$
$607$	17.5488			0.712284			0.356142	+	0.934432i	$0.384092\pi$
$608$	0.676361	+	2.96333i	0.0274301	+	0.120179i
$609$		0			0
$610$	−1.58492	+	6.94400i	−0.0641716	+	0.281154i
$611$	−9.38224	+	41.1063i	−0.379565	+	1.66298i
$612$	−5.42625	+	6.80430i	−0.219343	+	0.275048i
$613$	1.64085	−	2.05756i	0.0662732	−	0.0831040i	−0.747590	−	0.664161i	$-0.768789\pi$
$613$	1.64085	−	2.05756i	0.0662732	−	0.0831040i	0.813863	+	0.581057i	$0.197361\pi$
$614$	−5.99529	+	26.2671i	−0.241950	+	1.06005i
$615$	0.893351	−	3.91403i	0.0360234	−	0.157829i
$616$		0			0
$617$	6.31918	+	27.6861i	0.254401	+	1.11460i	0.927138	+	0.374720i	$0.122261\pi$
$617$	6.31918	+	27.6861i	0.254401	+	1.11460i	−0.672737	+	0.739881i	$0.734882\pi$
$618$	−12.3251			−0.495786
$619$	−25.4591			−1.02329			−0.511644	−	0.859197i	$-0.670963\pi$
$619$	−25.4591			−1.02329			−0.511644	+	0.859197i	$0.670963\pi$
$620$	2.21207	+	9.69170i	0.0888387	+	0.389228i
$621$	−27.8223	−	13.3985i	−1.11647	−	0.537663i
$622$	7.30177	−	9.15613i	0.292774	−	0.367127i
$623$		0			0
$624$	−2.50723	−	3.14397i	−0.100369	−	0.125859i
$625$	3.18839	+	13.9692i	0.127535	+	0.558770i
$626$	11.6710	+	14.6349i	0.466466	+	0.584930i
$627$	−7.60709	−	3.66338i	−0.303798	−	0.146301i
$628$	−13.5861	+	17.0364i	−0.542143	+	0.679826i
$629$	−19.1735	+	9.23348i	−0.764499	+	0.368163i
$630$		0			0
$631$	−6.67445	−	3.21424i	−0.265706	−	0.127957i	0.296288	−	0.955099i	$-0.404251\pi$
$631$	−6.67445	−	3.21424i	−0.265706	−	0.127957i	−0.561994	+	0.827142i	$0.689965\pi$
$632$	−4.02018	+	1.93602i	−0.159914	+	0.0770106i
$633$	−3.32016	+	14.5466i	−0.131965	+	0.578175i
$634$	18.4950	−	8.90671i	0.734530	−	0.353731i
$635$	−14.2564	−	17.8769i	−0.565747	−	0.709424i
$636$	−6.21715			−0.246526
$637$		0			0
$638$	7.06052			0.279529
$639$	11.3699	+	14.2574i	0.449785	+	0.564013i
$640$	1.65798	−	0.798443i	0.0655376	−	0.0315612i
$641$	3.10543	−	13.6058i	0.122657	−	0.537396i	−0.875840	−	0.482601i	$-0.839692\pi$
$641$	3.10543	−	13.6058i	0.122657	−	0.537396i	0.998498	−	0.0547955i	$-0.0174507\pi$
$642$	1.91932	−	0.924296i	0.0757495	−	0.0364791i
$643$	39.4273	+	18.9872i	1.55486	+	0.748782i	0.996717	−	0.0809624i	$-0.0257994\pi$
$643$	39.4273	+	18.9872i	1.55486	+	0.748782i	0.558144	+	0.829744i	$0.311514\pi$
$644$		0			0
$645$	−4.48238	+	2.15860i	−0.176493	+	0.0849947i
$646$	−6.55165	+	8.21551i	−0.257771	+	0.323235i
$647$	−13.6966	−	6.59594i	−0.538469	−	0.259313i	0.144824	−	0.989457i	$-0.453738\pi$
$647$	−13.6966	−	6.59594i	−0.538469	−	0.259313i	−0.683293	+	0.730144i	$0.739453\pi$
$648$	−3.04869	−	3.82293i	−0.119764	−	0.150179i
$649$	−6.39496	−	28.0181i	−0.251024	−	1.09981i
$650$	−5.82374	−	7.30274i	−0.228426	−	0.286437i
$651$		0			0
$652$	5.35598	−	6.71618i	0.209756	−	0.263026i
$653$	10.3443	+	4.98154i	0.404803	+	0.194943i	0.625195	−	0.780468i	$-0.285019\pi$
$653$	10.3443	+	4.98154i	0.404803	+	0.194943i	−0.220392	+	0.975411i	$0.570734\pi$
$654$	−2.04497	−	8.95960i	−0.0799647	−	0.350348i
$655$	−13.5914			−0.531058
$656$	−3.14050			−0.122616
$657$	−6.56774	−	28.7752i	−0.256232	−	1.12263i
$658$		0			0
$659$	−5.36325	+	23.4979i	−0.208923	+	0.915350i	0.756363	+	0.654152i	$0.226975\pi$
$659$	−5.36325	+	23.4979i	−0.208923	+	0.915350i	−0.965285	+	0.261197i	$0.915883\pi$
$660$	−1.13748	+	4.98361i	−0.0442762	+	0.193987i
$661$	19.1085	−	23.9613i	0.743233	−	0.931985i	−0.256166	−	0.966633i	$-0.582459\pi$
$661$	19.1085	−	23.9613i	0.743233	−	0.931985i	0.999400	+	0.0346477i	$0.0110309\pi$
$662$	−10.8238	+	13.5726i	−0.420679	+	0.527515i
$663$	3.09349	−	13.5535i	0.120141	−	0.526373i
$664$	−1.22230	+	5.35527i	−0.0474346	+	0.207825i
$665$		0			0
$666$	−3.44831	−	15.1080i	−0.133619	−	0.585424i
$667$	14.2260			0.550832
$668$	4.00175			0.154832
$669$	−0.927141	−	4.06207i	−0.0358453	−	0.157049i
$670$	3.07498	+	1.48083i	0.118797	+	0.0572095i
$671$	−9.64973	+	12.1004i	−0.372524	+	0.467130i
$672$		0			0
$673$	−3.94480	−	4.94662i	−0.152061	−	0.190678i	0.699966	−	0.714176i	$-0.253198\pi$
$673$	−3.94480	−	4.94662i	−0.152061	−	0.190678i	−0.852027	+	0.523498i	$0.824627\pi$
$674$	2.25066	+	9.86079i	0.0866922	+	0.379823i
$675$	3.85600	+	4.83528i	0.148418	+	0.186110i
$676$	−18.4783	−	8.89866i	−0.710702	−	0.342256i
$677$	6.70801	−	8.41157i	0.257810	−	0.323283i	−0.636035	−	0.771660i	$-0.719426\pi$
$677$	6.70801	−	8.41157i	0.257810	−	0.323283i	0.893844	+	0.448377i	$0.147998\pi$
$678$	−6.49941	+	3.12995i	−0.249608	+	0.120205i
$679$		0			0
$680$	5.73184	+	2.76031i	0.219806	+	0.105853i
$681$	6.60721	−	3.18187i	0.253189	−	0.121929i
$682$	−4.80670	+	21.0595i	−0.184058	+	0.806411i
$683$	38.3641	−	18.4752i	1.46796	−	0.706932i	0.482352	−	0.875978i	$-0.339783\pi$
$683$	38.3641	−	18.4752i	1.46796	−	0.706932i	0.985608	+	0.169046i	$0.0540685\pi$
$684$	−4.77083	−	5.98243i	−0.182417	−	0.228744i
$685$	−22.6088			−0.863838
$686$		0			0
$687$	6.19211			0.236244
$688$	2.42647	+	3.04270i	0.0925084	+	0.116002i
$689$	−46.6769	+	22.4784i	−1.77825	+	0.856359i
$690$	−2.29186	+	10.0413i	−0.0872496	+	0.382265i
$691$	16.6319	−	8.00948i	0.632706	−	0.304695i	−0.0899047	−	0.995950i	$-0.528656\pi$
$691$	16.6319	−	8.00948i	0.632706	−	0.304695i	0.722611	+	0.691255i	$0.242942\pi$
$692$	16.6369	+	8.01191i	0.632440	+	0.304567i
$693$		0			0
$694$	13.1268	−	6.32154i	0.498287	−	0.239963i
$695$	−1.35837	+	1.70334i	−0.0515258	+	0.0646113i
$696$	−1.10512	−	0.532197i	−0.0418894	−	0.0201729i
$697$	−6.76927	−	8.48839i	−0.256404	−	0.321521i
$698$	−1.40963	−	6.17598i	−0.0533552	−	0.233764i
$699$	−0.679883	−	0.852547i	−0.0257155	−	0.0322463i
$700$		0			0
$701$	5.44005	−	6.82161i	0.205468	−	0.257649i	−0.668411	−	0.743792i	$-0.733025\pi$
$701$	5.44005	−	6.82161i	0.205468	−	0.257649i	0.873879	+	0.486143i	$0.161597\pi$
$702$	19.9899	+	9.62663i	0.754471	+	0.363334i
$703$	−4.16349	−	18.2414i	−0.157029	−	0.687989i
$704$	3.99871			0.150707
$705$	−9.31119			−0.350680
$706$	7.75280	+	33.9672i	0.291780	+	1.27837i
$707$		0			0
$708$	−1.11096	+	4.86745i	−0.0417526	+	0.182930i
$709$	−1.36340	+	5.97343i	−0.0512034	+	0.224337i	−0.994055	−	0.108875i	$-0.965275\pi$
$709$	−1.36340	+	5.97343i	−0.0512034	+	0.224337i	0.942852	+	0.333212i	$0.108132\pi$
$710$	8.31131	−	10.4221i	0.311918	−	0.391133i
$711$	7.00361	−	8.78224i	0.262656	−	0.329360i
$712$	2.54398	−	11.1459i	0.0953398	−	0.417711i
$713$	−9.68483	+	42.4320i	−0.362700	+	1.58909i
$714$		0			0
$715$	9.47859	+	41.5284i	0.354479	+	1.55307i
$716$	14.2511			0.532589
$717$	16.0692			0.600114
$718$	−3.81355	−	16.7083i	−0.142320	−	0.623547i
$719$	12.4948	+	6.01718i	0.465977	+	0.224403i	0.652114	−	0.758121i	$-0.273882\pi$
$719$	12.4948	+	6.01718i	0.465977	+	0.224403i	−0.186137	+	0.982524i	$0.559597\pi$
$720$	−2.88840	+	3.62193i	−0.107644	+	0.134982i
$721$		0			0
$722$	6.08601	+	7.63161i	0.226498	+	0.284019i
$723$	−0.793655	−	3.47723i	−0.0295164	−	0.129320i
$724$	−11.7758	−	14.7664i	−0.437646	−	0.548790i
$725$	−2.56695	−	1.23618i	−0.0953340	−	0.0459104i
$726$	−2.16113	+	2.70997i	−0.0802071	+	0.100576i
$727$	43.4455	−	20.9222i	1.61130	−	0.775963i	0.611421	−	0.791306i	$-0.290598\pi$
$727$	43.4455	−	20.9222i	1.61130	−	0.775963i	0.999882	+	0.0153432i	$0.00488408\pi$
$728$		0			0
$729$	3.89381	+	1.87516i	0.144215	+	0.0694504i
$730$	−19.4388	+	9.36122i	−0.719461	+	0.346474i
$731$	−2.99385	+	13.1169i	−0.110732	+	0.485147i
$732$	2.42247	−	1.16660i	0.0895370	−	0.0431187i
$733$	27.2001	+	34.1079i	1.00466	+	1.25980i	0.965455	+	0.260571i	$0.0839109\pi$
$733$	27.2001	+	34.1079i	1.00466	+	1.25980i	0.0392043	+	0.999231i	$0.487518\pi$
$734$	33.1486			1.22354
$735$		0			0
$736$	8.05684			0.296979
$737$	4.62392	+	5.79821i	0.170324	+	0.213580i
$738$	7.12304	−	3.43028i	0.262203	−	0.126270i
$739$	7.12309	−	31.2083i	0.262027	−	1.14802i	−0.657021	−	0.753872i	$-0.728184\pi$
$739$	7.12309	−	31.2083i	0.262027	−	1.14802i	0.919049	−	0.394144i	$-0.128959\pi$
$740$	−10.2061	+	4.91499i	−0.375183	+	0.180679i
$741$	11.0124	+	5.30329i	0.404551	+	0.194821i
$742$		0			0
$743$	−35.8504	+	17.2646i	−1.31522	+	0.633378i	−0.954197	−	0.299179i	$-0.903287\pi$
$743$	−35.8504	+	17.2646i	−1.31522	+	0.633378i	−0.361025	+	0.932556i	$0.617573\pi$
$744$	2.33974	−	2.93394i	0.0857791	−	0.107564i
$745$	−26.4337	−	12.7298i	−0.968457	−	0.466384i
$746$	−1.48103	−	1.85716i	−0.0542245	−	0.0679954i
$747$	−3.07706	−	13.4815i	−0.112584	−	0.493262i
$748$	8.61911	+	10.8080i	0.315146	+	0.395180i
$749$		0			0
$750$	5.27131	−	6.61001i	0.192481	−	0.241363i
$751$	17.0083	+	8.19078i	0.620643	+	0.298886i	0.717657	−	0.696397i	$-0.245215\pi$
$751$	17.0083	+	8.19078i	0.620643	+	0.298886i	−0.0970136	+	0.995283i	$0.530929\pi$
$752$	1.62078	+	7.10110i	0.0591037	+	0.258950i
$753$	−3.55007			−0.129372
$754$	−10.2212			−0.372233
$755$	5.03895	+	22.0771i	0.183386	+	0.803468i
$756$		0			0
$757$	−2.55517	+	11.1949i	−0.0928691	+	0.406886i	−0.999899	−	0.0141791i	$-0.995487\pi$
$757$	−2.55517	+	11.1949i	−0.0928691	+	0.406886i	0.907030	+	0.421065i	$0.138344\pi$
$758$	−3.49311	+	15.3043i	−0.126876	+	0.555878i
$759$	−13.9539	+	17.4976i	−0.506494	+	0.635123i
$760$	−3.48745	+	4.37312i	−0.126503	+	0.158630i
$761$	−6.05672	+	26.5362i	−0.219556	+	0.961937i	0.738251	+	0.674526i	$0.235652\pi$
$761$	−6.05672	+	26.5362i	−0.219556	+	0.961937i	−0.957807	+	0.287411i	$0.907205\pi$
$762$	−1.92071	+	8.41518i	−0.0695800	+	0.304850i
$763$		0			0
$764$	−3.69693	−	16.1973i	−0.133750	−	0.585998i
$765$	−16.0155			−0.579042
$766$	16.6789			0.602633
$767$	9.25766	+	40.5604i	0.334275	+	1.46455i
$768$	−0.625881	−	0.301408i	−0.0225845	−	0.0108761i
$769$	−21.5252	+	26.9918i	−0.776220	+	0.973348i	−0.999999	−	0.00129128i	$-0.999589\pi$
$769$	−21.5252	+	26.9918i	−0.776220	+	0.973348i	0.223780	+	0.974640i	$0.428160\pi$
$770$		0			0
$771$	−6.82417	−	8.55724i	−0.245766	−	0.308181i
$772$	−5.95361	−	26.0845i	−0.214275	−	0.938800i
$773$	2.13383	+	2.67574i	0.0767485	+	0.0962395i	0.818723	−	0.574188i	$-0.194682\pi$
$773$	2.13383	+	2.67574i	0.0767485	+	0.0962395i	−0.741975	+	0.670428i	$0.766111\pi$
$774$	−8.82699	−	4.25085i	−0.317280	−	0.152794i
$775$	5.43470	−	6.81490i	0.195220	−	0.244799i
$776$	8.76368	−	4.22037i	0.314598	−	0.151502i
$777$		0			0
$778$	−13.9020	−	6.69486i	−0.498412	−	0.240022i
$779$	8.60036	−	4.14171i	0.308140	−	0.148392i
$780$	1.64667	−	7.21452i	0.0589602	−	0.258321i
$781$	26.0975	−	12.5679i	0.933842	−	0.449715i
$782$	17.3663	+	21.7767i	0.621018	+	0.778732i
$783$	6.76761			0.241855
$784$		0			0
$785$	−40.0991			−1.43120
$786$	3.19892	+	4.01132i	0.114102	+	0.143079i
$787$	36.7222	−	17.6845i	1.30900	−	0.630383i	0.356325	−	0.934362i	$-0.384030\pi$
$787$	36.7222	−	17.6845i	1.30900	−	0.630383i	0.952679	+	0.303979i	$0.0983154\pi$
$788$	1.62932	−	7.13851i	0.0580421	−	0.254299i
$789$	1.16014	−	0.558695i	0.0413022	−	0.0198901i
$790$	−7.39803	−	3.56270i	−0.263210	−	0.126755i
$791$		0			0
$792$	−9.06955	+	4.36767i	−0.322273	+	0.155198i
$793$	13.9694	−	17.5171i	0.496069	−	0.622051i
$794$	−23.4203	−	11.2786i	−0.831157	−	0.400264i
$795$	−7.13331	−	8.94489i	−0.252992	−	0.317242i
$796$	0.846545	+	3.70896i	0.0300050	+	0.131460i
$797$	−24.6176	−	30.8695i	−0.872000	−	1.09345i	−0.994883	−	0.101033i	$-0.967785\pi$
$797$	−24.6176	−	30.8695i	−0.872000	−	1.09345i	0.122883	−	0.992421i	$-0.460786\pi$
$798$		0			0
$799$	−15.6999	+	19.6870i	−0.555421	+	0.696476i
$800$	−1.45378	−	0.700105i	−0.0513990	−	0.0247524i
$801$	6.40429	+	28.0590i	0.226285	+	0.991417i
$802$	−21.1342			−0.746273
$803$	−46.8822			−1.65444
$804$	−0.286691	−	1.25608i	−0.0101108	−	0.0442984i
$805$		0			0
$806$	6.95842	−	30.4868i	0.245100	−	1.07385i
$807$	−0.232084	+	1.01683i	−0.00816975	+	0.0357940i
$808$	4.96716	−	6.22862i	0.174744	−	0.219122i
$809$	1.04307	−	1.30797i	0.0366725	−	0.0459859i	−0.763157	−	0.646213i	$-0.776352\pi$
$809$	1.04307	−	1.30797i	0.0366725	−	0.0459859i	0.799830	+	0.600227i	$0.204923\pi$
$810$	2.00228	−	8.77256i	0.0703530	−	0.308237i
$811$	5.23122	−	22.9195i	0.183693	−	0.804812i	−0.796159	−	0.605087i	$-0.793138\pi$
$811$	5.23122	−	22.9195i	0.183693	−	0.804812i	0.979852	−	0.199724i	$-0.0640046\pi$
$812$		0			0
$813$	−2.54984	−	11.1716i	−0.0894269	−	0.391805i
$814$	−24.6149			−0.862752
$815$	15.8081			0.553734
$816$	−0.534400	−	2.34136i	−0.0187077	−	0.0819639i
$817$	−10.6577	−	5.13248i	−0.372866	−	0.179563i
$818$	1.83351	−	2.29915i	0.0641072	−	0.0803878i
$819$		0			0
$820$	−3.60329	−	4.51838i	−0.125832	−	0.157789i
$821$	−5.24930	−	22.9987i	−0.183202	−	0.802659i	−0.980093	−	0.198537i	$-0.936381\pi$
$821$	−5.24930	−	22.9987i	−0.183202	−	0.802659i	0.796892	−	0.604122i	$-0.206476\pi$
$822$	5.32131	+	6.67271i	0.185602	+	0.232737i
$823$	−31.3718	−	15.1078i	−1.09355	−	0.526626i	−0.201926	−	0.979401i	$-0.564720\pi$
$823$	−31.3718	−	15.1078i	−1.09355	−	0.526626i	−0.891625	+	0.452774i	$0.850434\pi$
$824$	−11.0621	+	13.8714i	−0.385365	+	0.483233i
$825$	4.03832	−	1.94475i	0.140596	−	0.0677076i
$826$		0			0
$827$	29.7539	+	14.3287i	1.03464	+	0.498258i	0.872554	−	0.488518i	$-0.162462\pi$
$827$	29.7539	+	14.3287i	1.03464	+	0.498258i	0.162089	+	0.986776i	$0.448177\pi$
$828$	−18.2739	+	8.80024i	−0.635062	+	0.305830i
$829$	−1.69234	+	7.41461i	−0.0587773	+	0.257520i	−0.995776	−	0.0918117i	$-0.970734\pi$
$829$	−1.69234	+	7.41461i	−0.0587773	+	0.257520i	0.936999	+	0.349332i	$0.113591\pi$
$830$	−9.10729	+	4.38584i	−0.316119	+	0.152235i
$831$	6.75106	+	8.46557i	0.234192	+	0.293667i
$832$	−5.78872			−0.200688
$833$		0			0
$834$	0.822429			0.0284784
$835$	4.59145	+	5.75750i	0.158894	+	0.199246i
$836$	−10.9506	+	5.27352i	−0.378734	+	0.182389i
$837$	−4.60729	+	20.1859i	−0.159251	+	0.697726i
$838$	9.97503	−	4.80372i	0.344582	−	0.165942i
$839$	−27.2423	−	13.1192i	−0.940510	−	0.452926i	−0.100161	−	0.994971i	$-0.531936\pi$
$839$	−27.2423	−	13.1192i	−0.940510	−	0.452926i	−0.840349	+	0.542046i	$0.817650\pi$
$840$		0			0
$841$	23.3191	−	11.2299i	0.804108	−	0.387238i
$842$	12.0281	−	15.0827i	0.414514	−	0.519784i
$843$	0.198820	+	0.0957469i	0.00684774	+	0.00329770i
$844$	13.3917	+	16.7927i	0.460961	+	0.578027i
$845$	−8.39832	−	36.7955i	−0.288911	−	1.26580i
$846$	−11.4324	−	14.3358i	−0.393056	−	0.492876i
$847$		0			0
$848$	−5.58006	+	6.99717i	−0.191620	+	0.240284i
$849$	13.3938	+	6.45012i	0.459675	+	0.221368i
$850$	−1.24129	−	5.43846i	−0.0425760	−	0.186538i
$851$	−49.5956			−1.70012
$852$	−5.03213			−0.172398
$853$	−11.4752	−	50.2759i	−0.392902	−	1.72142i	−0.654345	−	0.756197i	$-0.727055\pi$
$853$	−11.4752	−	50.2759i	−0.392902	−	1.72142i	0.261443	−	0.965219i	$-0.415802\pi$
$854$		0			0
$855$	3.13333	−	13.7280i	0.107158	−	0.469488i
$856$	0.682381	−	2.98971i	0.0233233	−	0.102186i
$857$	11.5144	−	14.4386i	0.393325	−	0.493214i	−0.545258	−	0.838269i	$-0.683568\pi$
$857$	11.5144	−	14.4386i	0.393325	−	0.493214i	0.938583	+	0.345055i	$0.112140\pi$
$858$	10.0257	−	12.5718i	0.342271	−	0.429194i
$859$	−3.31554	+	14.5263i	−0.113125	+	0.495633i	0.886343	+	0.463028i	$0.153237\pi$
$859$	−3.31554	+	14.5263i	−0.113125	+	0.495633i	−0.999468	+	0.0326042i	$0.989620\pi$
$860$	−1.59363	+	6.98215i	−0.0543423	+	0.238089i
$861$		0			0
$862$	−2.29368	−	10.0493i	−0.0781232	−	0.342280i
$863$	4.21019			0.143317			0.0716583	−	0.997429i	$-0.477171\pi$
$863$	4.21019			0.143317			0.0716583	+	0.997429i	$0.477171\pi$
$864$	3.83282			0.130395
$865$	7.56144	+	33.1288i	0.257097	+	1.12641i
$866$	−2.91822	−	1.40534i	−0.0991651	−	0.0477554i
$867$	−2.18657	+	2.74187i	−0.0742597	+	0.0931187i
$868$		0			0
$869$	−11.1246	−	13.9498i	−0.377376	−	0.473215i
$870$	−0.502274	−	2.20061i	−0.0170287	−	0.0746075i
$871$	−6.69381	−	8.39378i	−0.226811	−	0.284412i
$872$	−11.9191	−	5.73994i	−0.403632	−	0.194379i
$873$	−15.2673	+	19.1446i	−0.516720	+	0.647947i
$874$	−22.0639	+	10.6254i	−0.746322	+	0.359410i
$875$		0			0
$876$	7.33804	+	3.53381i	0.247929	+	0.119397i
$877$	−22.3036	+	10.7408i	−0.753139	+	0.362693i	−0.770738	−	0.637153i	$-0.780112\pi$
$877$	−22.3036	+	10.7408i	−0.753139	+	0.362693i	0.0175989	+	0.999845i	$0.494398\pi$
$878$	−8.04678	+	35.2552i	−0.271566	+	1.18981i
$879$	5.88826	−	2.83563i	0.198606	−	0.0956436i
$880$	4.58796	+	5.75312i	0.154660	+	0.193938i
$881$	−7.51988			−0.253351			−0.126676	−	0.991944i	$-0.540431\pi$
$881$	−7.51988			−0.253351			−0.126676	+	0.991944i	$0.540431\pi$
$882$		0			0
$883$	−27.5069			−0.925681			−0.462840	−	0.886442i	$-0.653170\pi$
$883$	−27.5069			−0.925681			−0.462840	+	0.886442i	$0.653170\pi$
$884$	−12.4774	−	15.6462i	−0.419662	−	0.526239i
$885$	−8.27770	+	3.98633i	−0.278252	+	0.133999i
$886$	−2.18150	+	9.55778i	−0.0732890	+	0.321100i
$887$	13.5184	−	6.51012i	0.453904	−	0.218588i	−0.192941	−	0.981210i	$-0.561803\pi$
$887$	13.5184	−	6.51012i	0.453904	−	0.218588i	0.646844	+	0.762622i	$0.276088\pi$
$888$	3.85275	+	1.85538i	0.129290	+	0.0622626i
$889$		0			0
$890$	18.9550	−	9.12825i	0.635373	−	0.305980i
$891$	12.1908	−	15.2868i	0.408407	−	0.512126i
$892$	−5.40384	−	2.60235i	−0.180934	−	0.0871333i
$893$	−13.8035	−	17.3091i	−0.461918	−	0.579226i
$894$	2.46451	+	10.7977i	0.0824256	+	0.361130i
$895$	16.3511	+	20.5037i	0.546559	+	0.685363i
$896$		0			0
$897$	20.2003	−	25.3304i	0.674469	−	0.845758i
$898$	6.60499	+	3.18080i	0.220412	+	0.106145i
$899$	−2.12249	−	9.29922i	−0.0707889	−	0.310146i
$900$	4.06206			0.135402
$901$	−30.9402			−1.03077
$902$	−2.79440	−	12.2431i	−0.0930435	−	0.407650i
$903$		0			0
$904$	−2.31075	+	10.1241i	−0.0768544	+	0.336721i
$905$	7.73400	−	33.8849i	0.257087	−	1.12637i
$906$	5.32979	−	6.68334i	0.177070	−	0.222039i
$907$	−3.28061	+	4.11375i	−0.108931	+	0.136595i	−0.833308	−	0.552809i	$-0.813556\pi$
$907$	−3.28061	+	4.11375i	−0.108931	+	0.136595i	0.724377	+	0.689404i	$0.242127\pi$
$908$	2.34908	−	10.2920i	0.0779569	−	0.341552i
$909$	−4.46279	+	19.5528i	−0.148021	+	0.648524i
$910$		0			0
$911$	−11.1707	−	48.9420i	−0.370102	−	1.62152i	−0.726486	−	0.687182i	$-0.758848\pi$
$911$	−11.1707	−	48.9420i	−0.370102	−	1.62152i	0.356384	−	0.934340i	$-0.384009\pi$
$912$	2.11149			0.0699185
$913$	−21.9648			−0.726930
$914$	6.53135	+	28.6157i	0.216038	+	0.946524i
$915$	4.45788	+	2.14680i	0.147373	+	0.0709711i
$916$	5.55758	−	6.96899i	0.183628	−	0.230262i
$917$		0			0
$918$	8.26154	+	10.3596i	0.272672	+	0.341919i
$919$	−3.77944	−	16.5588i	−0.124672	−	0.546224i	−0.998228	−	0.0595008i	$-0.981049\pi$
$919$	−3.77944	−	16.5588i	−0.124672	−	0.546224i	0.873556	−	0.486723i	$-0.161808\pi$
$920$	9.24410	+	11.5917i	0.304769	+	0.382168i
$921$	16.8628	+	8.12071i	0.555649	+	0.267587i
$922$	0.153164	−	0.192062i	0.00504419	−	0.00632522i
$923$	−37.7800	+	18.1939i	−1.24354	+	0.598859i
$924$		0			0
$925$	8.94908	+	4.30965i	0.294244	+	0.141700i
$926$	−8.39707	+	4.04382i	−0.275945	+	0.132888i
$927$	9.93882	−	43.5448i	0.326434	−	1.43020i
$928$	−1.59084	+	0.766109i	−0.0522219	+	0.0251488i
$929$	35.1893	+	44.1260i	1.15452	+	1.44773i	0.872698	+	0.488261i	$0.162369\pi$
$929$	35.1893	+	44.1260i	1.15452	+	1.44773i	0.281826	+	0.959466i	$0.409060\pi$
$930$	6.90572			0.226448
$931$		0			0
$932$	−1.56972			−0.0514180
$933$	−5.07236	−	6.36054i	−0.166062	−	0.208235i
$934$	−9.61090	+	4.62837i	−0.314478	+	0.151445i
$935$	−5.66076	+	24.8014i	−0.185127	+	0.811092i
$936$	13.1295	−	6.32285i	0.429152	−	0.206669i
$937$	−5.59766	−	2.69569i	−0.182868	−	0.0880644i	0.340210	−	0.940350i	$-0.389502\pi$
$937$	−5.59766	−	2.69569i	−0.182868	−	0.0880644i	−0.523077	+	0.852285i	$0.675216\pi$
$938$		0			0
$939$	11.7157	−	5.64200i	0.382329	−	0.184120i
$940$	−8.35705	+	10.4794i	−0.272577	+	0.341801i
$941$	−46.9734	−	22.6212i	−1.53129	−	0.737430i	−0.536943	−	0.843618i	$-0.680421\pi$
$941$	−46.9734	−	22.6212i	−1.53129	−	0.737430i	−0.994346	+	0.106188i	$0.966135\pi$
$942$	9.43790	+	11.8348i	0.307503	+	0.385597i
$943$	−5.63034	−	24.6681i	−0.183349	−	0.803304i
$944$	4.48102	+	5.61902i	0.145845	+	0.182884i
$945$		0			0
$946$	−9.70275	+	12.1669i	−0.315464	+	0.395579i
$947$	−41.4083	−	19.9412i	−1.34559	−	0.648001i	−0.384214	−	0.923244i	$-0.625527\pi$
$947$	−41.4083	−	19.9412i	−1.34559	−	0.648001i	−0.961375	+	0.275243i	$0.911242\pi$
$948$	0.689745	+	3.02197i	0.0224019	+	0.0981490i
$949$	67.8690			2.20312
$950$	4.90453			0.159124
$951$	−3.17320	−	13.9027i	−0.102898	−	0.450825i
$952$		0			0
$953$	5.15402	−	22.5812i	0.166955	−	0.731478i	−0.820248	−	0.572008i	$-0.806164\pi$
$953$	5.15402	−	22.5812i	0.166955	−	0.731478i	0.987203	−	0.159470i	$-0.0509784\pi$
$954$	5.01345	−	21.9654i	0.162317	−	0.711155i
$955$	19.0621	−	23.9031i	0.616835	−	0.773486i
$956$	14.4225	−	18.0853i	0.466457	−	0.584919i
$957$	1.09141	−	4.78180i	0.0352804	−	0.154573i
$958$	2.90865	−	12.7436i	0.0939741	−	0.411728i
$959$		0			0
$960$	−0.284461	−	1.24631i	−0.00918095	−	0.0402244i
$961$	−1.81811			−0.0586486
$962$	35.6337			1.14888
$963$	1.71784	+	7.52636i	0.0553567	+	0.242534i
$964$	−4.62582	−	2.22768i	−0.148988	−	0.0717487i
$965$	30.6979	−	38.4940i	0.988202	−	1.23917i
$966$		0			0
$967$	6.29969	+	7.89956i	0.202584	+	0.254033i	0.872737	−	0.488190i	$-0.162343\pi$
$967$	6.29969	+	7.89956i	0.202584	+	0.254033i	−0.670153	+	0.742223i	$0.733771\pi$
$968$	1.11030	+	4.86455i	0.0356864	+	0.156352i
$969$	4.55127	+	5.70711i	0.146208	+	0.183339i
$970$	16.1271	+	7.76642i	0.517811	+	0.249365i
$971$	18.1442	−	22.7521i	0.582276	−	0.730151i	−0.400223	−	0.916418i	$-0.631067\pi$
$971$	18.1442	−	22.7521i	0.582276	−	0.730151i	0.982499	+	0.186267i	$0.0596388\pi$
$972$	−13.4201	+	6.46279i	−0.430451	+	0.207294i
$973$		0			0
$974$	2.69990	+	1.30020i	0.0865102	+	0.0416611i
$975$	−5.84607	+	2.81532i	−0.187224	+	0.0901624i
$976$	0.861266	−	3.77345i	0.0275685	−	0.120785i
$977$	28.1566	−	13.5595i	0.900811	−	0.433808i	0.0746290	−	0.997211i	$-0.476223\pi$
$977$	28.1566	−	13.5595i	0.900811	−	0.433808i	0.826182	+	0.563404i	$0.190508\pi$
$978$	−3.72066	−	4.66556i	−0.118974	−	0.149188i
$979$	45.7154			1.46107
$980$		0			0
$981$	33.3036			1.06330
$982$	−3.24068	−	4.06369i	−0.103414	−	0.129678i
$983$	−26.6727	+	12.8449i	−0.850728	+	0.409689i	−0.807848	−	0.589391i	$-0.799368\pi$
$983$	−26.6727	+	12.8449i	−0.850728	+	0.409689i	−0.0428801	+	0.999080i	$0.513653\pi$
$984$	−0.485458	+	2.12693i	−0.0154758	+	0.0678040i
$985$	12.1399	−	5.84627i	0.386810	−	0.186278i
$986$	−5.49972	−	2.64853i	−0.175147	−	0.0843462i
$987$		0			0
$988$	15.8526	−	7.63421i	0.504338	−	0.242876i
$989$	−19.5497	+	24.5145i	−0.621644	+	0.779517i
$990$	−16.6900	−	8.03748i	−0.530443	−	0.255448i
$991$	24.6549	+	30.9162i	0.783187	+	0.982086i	0.999983	+	0.00586893i	$0.00186815\pi$
$991$	24.6549	+	30.9162i	0.783187	+	0.982086i	−0.216795	+	0.976217i	$0.569560\pi$
$992$	−1.20206	−	5.26659i	−0.0381656	−	0.167214i
$993$	7.51903	+	9.42856i	0.238609	+	0.299206i
$994$		0			0
$995$	−4.36495	+	5.47347i	−0.138378	+	0.173521i
$996$	3.43796	+	1.65563i	0.108936	+	0.0524607i
$997$	−11.0852	−	48.5674i	−0.351071	−	1.53814i	−0.774712	−	0.632314i	$-0.782105\pi$
$997$	−11.0852	−	48.5674i	−0.351071	−	1.53814i	0.423641	−	0.905830i	$-0.360752\pi$
$998$	7.40369			0.234360
$999$	−23.5938			−0.746473

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	686.2.e.f.393.1		24
7.2	even	3		98.2.g.a.95.2	yes	24
7.3	odd	6		686.2.g.c.79.1		24
7.4	even	3		686.2.g.a.79.2		24
7.5	odd	6		686.2.g.b.557.1		24
7.6	odd	2		686.2.e.e.393.4		24
21.2	odd	6		882.2.z.d.487.1		24
28.23	odd	6		784.2.bg.a.193.1		24
49.6	odd	14		686.2.e.e.295.4		24
49.10	odd	42		686.2.g.b.569.1		24
49.16	even	21		686.2.g.a.165.2		24
49.22	even	7		4802.2.a.i.1.10		12
49.27	odd	14		4802.2.a.k.1.3		12
49.33	odd	42		686.2.g.c.165.1		24
49.39	even	21		98.2.g.a.65.2	✓	24
49.43	even	7	inner	686.2.e.f.295.1		24
147.137	odd	42		882.2.z.d.163.1		24
196.39	odd	42		784.2.bg.a.65.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.g.a.65.2	✓	24	49.39	even	21
98.2.g.a.95.2	yes	24	7.2	even	3
686.2.e.e.295.4		24	49.6	odd	14
686.2.e.e.393.4		24	7.6	odd	2
686.2.e.f.295.1		24	49.43	even	7	inner
686.2.e.f.393.1		24	1.1	even	1	trivial
686.2.g.a.79.2		24	7.4	even	3
686.2.g.a.165.2		24	49.16	even	21
686.2.g.b.557.1		24	7.5	odd	6
686.2.g.b.569.1		24	49.10	odd	42
686.2.g.c.79.1		24	7.3	odd	6
686.2.g.c.165.1		24	49.33	odd	42
784.2.bg.a.65.1		24	196.39	odd	42
784.2.bg.a.193.1		24	28.23	odd	6
882.2.z.d.163.1		24	147.137	odd	42
882.2.z.d.487.1		24	21.2	odd	6
4802.2.a.i.1.10		12	49.22	even	7
4802.2.a.k.1.3		12	49.27	odd	14

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:	\( N \)	\(=\)	\( 686 = 2 \cdot 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	686.e (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.623490 - 0.781831i) q^{2} +(-0.625881 + 0.301408i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(-1.65798 + 0.798443i) q^{5} +(0.625881 + 0.301408i) q^{6} +(0.900969 - 0.433884i) q^{8} +(-1.56959 + 1.96820i) q^{9} +O(q^{10})\)	\(q+(-0.623490 - 0.781831i) q^{2} +(-0.625881 + 0.301408i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(-1.65798 + 0.798443i) q^{5} +(0.625881 + 0.301408i) q^{6} +(0.900969 - 0.433884i) q^{8} +(-1.56959 + 1.96820i) q^{9} +(1.65798 + 0.798443i) q^{10} +(2.49315 + 3.12631i) q^{11} +(-0.154580 - 0.677258i) q^{12} +(-3.60921 - 4.52581i) q^{13} +(0.797043 - 0.999460i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(-0.769280 - 3.37044i) q^{17} +2.51743 q^{18} +3.03954 q^{19} +(-0.409488 - 1.79409i) q^{20} +(0.889796 - 3.89845i) q^{22} +(1.79281 - 7.85483i) q^{23} +(-0.433123 + 0.543119i) q^{24} +(-1.00605 + 1.26155i) q^{25} +(-1.28811 + 5.64359i) q^{26} +(0.852883 - 3.73672i) q^{27} +(0.392906 + 1.72143i) q^{29} -1.27836 q^{30} -5.40203 q^{31} +(0.222521 + 0.974928i) q^{32} +(-2.50271 - 1.20524i) q^{33} +(-2.15547 + 2.70288i) q^{34} +(-1.56959 - 1.96820i) q^{36} +(-1.36978 - 6.00138i) q^{37} +(-1.89512 - 2.37641i) q^{38} +(3.62305 + 1.74477i) q^{39} +(-1.14736 + 1.43874i) q^{40} +(2.82949 - 1.36261i) q^{41} +(-3.50635 - 1.68857i) q^{43} +(-3.60271 + 1.73497i) q^{44} +(1.03086 - 4.51648i) q^{45} +(-7.25896 + 3.49573i) q^{46} +(-4.54132 - 5.69464i) q^{47} +0.694675 q^{48} +1.61358 q^{50} +(1.49735 + 1.87762i) q^{51} +(5.21546 - 2.51163i) q^{52} +(1.99150 - 8.72533i) q^{53} +(-3.45325 + 1.66300i) q^{54} +(-6.62979 - 3.19274i) q^{55} +(-1.90239 + 0.916142i) q^{57} +(1.10090 - 1.38048i) q^{58} +(-6.47526 - 3.11832i) q^{59} +(0.797043 + 0.999460i) q^{60} +(0.861266 + 3.77345i) q^{61} +(3.36811 + 4.22347i) q^{62} +(0.623490 - 0.781831i) q^{64} +(9.59761 + 4.62197i) q^{65} +(0.618119 + 2.70816i) q^{66} +1.85465 q^{67} +3.45711 q^{68} +(1.24542 + 5.45656i) q^{69} +(1.61191 - 7.06223i) q^{71} +(-0.560180 + 2.45431i) q^{72} +(-7.31001 + 9.16646i) q^{73} +(-3.83803 + 4.81273i) q^{74} +(0.249426 - 1.09281i) q^{75} +(-0.676361 + 2.96333i) q^{76} +(-0.894819 - 3.92046i) q^{78} -4.46206 q^{79} +1.84022 q^{80} +(-1.08806 - 4.76712i) q^{81} +(-2.82949 - 1.36261i) q^{82} +(-3.42482 + 4.29459i) q^{83} +(3.96656 + 4.97390i) q^{85} +(0.865998 + 3.79419i) q^{86} +(-0.764766 - 0.958986i) q^{87} +(3.60271 + 1.73497i) q^{88} +(7.12809 - 8.93834i) q^{89} +(-4.17385 + 2.01002i) q^{90} +(7.25896 + 3.49573i) q^{92} +(3.38102 - 1.62822i) q^{93} +(-1.62078 + 7.10110i) q^{94} +(-5.03951 + 2.42690i) q^{95} +(-0.433123 - 0.543119i) q^{96} +9.72695 q^{97} -10.0664 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 7 q^{3} - 4 q^{4} - 7 q^{6} + 4 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 + 7 * q^3 - 4 * q^4 - 7 * q^6 + 4 * q^8 + 3 * q^9	\( 24 q + 4 q^{2} + 7 q^{3} - 4 q^{4} - 7 q^{6} + 4 q^{8} + 3 q^{9} - 7 q^{11} + 14 q^{13} - 7 q^{15} - 4 q^{16} + 14 q^{17} - 10 q^{18} - 7 q^{20} - 7 q^{22} - 21 q^{23} - 8 q^{25} - 7 q^{26} - 35 q^{27} - 11 q^{29} - 56 q^{31} + 4 q^{32} - 28 q^{33} + 7 q^{34} + 3 q^{36} + 48 q^{37} - 7 q^{38} + 38 q^{39} - 7 q^{40} + 28 q^{41} + 10 q^{43} + 7 q^{45} - 21 q^{46} + 35 q^{47} - 14 q^{48} + 8 q^{50} - 36 q^{51} - 7 q^{52} - 10 q^{53} - 63 q^{54} + 56 q^{55} - 33 q^{57} - 24 q^{58} + 14 q^{59} - 7 q^{60} - 28 q^{61} + 28 q^{62} - 4 q^{64} + 21 q^{66} + 72 q^{67} + 28 q^{68} - 35 q^{69} + 4 q^{72} - 49 q^{73} + q^{74} + 56 q^{75} - 24 q^{78} + 52 q^{79} - 5 q^{81} - 28 q^{82} - 7 q^{83} + 49 q^{85} + 32 q^{86} - 28 q^{87} + 7 q^{89} - 21 q^{90} + 21 q^{92} - 60 q^{93} - 35 q^{94} + 7 q^{95} - 126 q^{97} - 14 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 7 * q^3 - 4 * q^4 - 7 * q^6 + 4 * q^8 + 3 * q^9 - 7 * q^11 + 14 * q^13 - 7 * q^15 - 4 * q^16 + 14 * q^17 - 10 * q^18 - 7 * q^20 - 7 * q^22 - 21 * q^23 - 8 * q^25 - 7 * q^26 - 35 * q^27 - 11 * q^29 - 56 * q^31 + 4 * q^32 - 28 * q^33 + 7 * q^34 + 3 * q^36 + 48 * q^37 - 7 * q^38 + 38 * q^39 - 7 * q^40 + 28 * q^41 + 10 * q^43 + 7 * q^45 - 21 * q^46 + 35 * q^47 - 14 * q^48 + 8 * q^50 - 36 * q^51 - 7 * q^52 - 10 * q^53 - 63 * q^54 + 56 * q^55 - 33 * q^57 - 24 * q^58 + 14 * q^59 - 7 * q^60 - 28 * q^61 + 28 * q^62 - 4 * q^64 + 21 * q^66 + 72 * q^67 + 28 * q^68 - 35 * q^69 + 4 * q^72 - 49 * q^73 + q^74 + 56 * q^75 - 24 * q^78 + 52 * q^79 - 5 * q^81 - 28 * q^82 - 7 * q^83 + 49 * q^85 + 32 * q^86 - 28 * q^87 + 7 * q^89 - 21 * q^90 + 21 * q^92 - 60 * q^93 - 35 * q^94 + 7 * q^95 - 126 * q^97 - 14 * q^99

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