LMFDB - Embedded newform 847.2.f.v.148.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
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} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			148.3
Root			$0.183009 - 0.132964i$ of defining polynomial
Character	$\chi$	$=$	847.148
Dual form			847.2.f.v.372.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0699031 - 0.215140i) q^{2} +(0.177280 + 0.128801i) q^{3} +(1.57664 - 1.14549i) q^{4} +(-0.771159 + 2.37338i) q^{5} +(0.0153178 - 0.0471435i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-0.722670 - 0.525051i) q^{8} +(-0.912213 - 2.80750i) q^{9} +0.564516 q^{10} +0.427046 q^{12} +(-1.58680 - 4.88366i) q^{13} +(-0.183009 - 0.132964i) q^{14} +(-0.442405 + 0.321426i) q^{15} +(1.14200 - 3.51471i) q^{16} +(0.444220 - 1.36717i) q^{17} +(-0.540239 + 0.392506i) q^{18} +(-4.90950 - 3.56696i) q^{19} +(1.50286 + 4.62532i) q^{20} +0.219130 q^{21} +7.08292 q^{23} +(-0.0604875 - 0.186161i) q^{24} +(-0.993180 - 0.721588i) q^{25} +(-0.939748 + 0.682767i) q^{26} +(0.403037 - 1.24042i) q^{27} +(0.602221 - 1.85345i) q^{28} +(5.27292 - 3.83100i) q^{29} +(0.100077 + 0.0727103i) q^{30} +(2.37602 + 7.31263i) q^{31} -2.62252 q^{32} -0.325184 q^{34} +(0.771159 + 2.37338i) q^{35} +(-4.65420 - 3.38147i) q^{36} +(3.22339 - 2.34193i) q^{37} +(-0.424206 + 1.30557i) q^{38} +(0.347714 - 1.07015i) q^{39} +(1.80344 - 1.31028i) q^{40} +(5.46006 + 3.96696i) q^{41} +(-0.0153178 - 0.0471435i) q^{42} +0.802299 q^{43} +7.36674 q^{45} +(-0.495119 - 1.52382i) q^{46} +(-5.46266 - 3.96885i) q^{47} +(0.655152 - 0.475996i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-0.0858158 + 0.264114i) q^{50} +(0.254844 - 0.185155i) q^{51} +(-8.09600 - 5.88209i) q^{52} +(2.03385 + 6.25954i) q^{53} -0.295037 q^{54} -0.893270 q^{56} +(-0.410925 - 1.26470i) q^{57} +(-1.19279 - 0.866616i) q^{58} +(-2.32694 + 1.69062i) q^{59} +(-0.329320 + 1.01354i) q^{60} +(0.264315 - 0.813478i) q^{61} +(1.40715 - 1.02235i) q^{62} +(-2.38820 - 1.73513i) q^{63} +(-2.10068 - 6.46522i) q^{64} +12.8145 q^{65} -1.64668 q^{67} +(-0.865708 - 2.66437i) q^{68} +(1.25566 + 0.912288i) q^{69} +(0.456703 - 0.331814i) q^{70} +(1.39700 - 4.29951i) q^{71} +(-0.814852 + 2.50786i) q^{72} +(-12.0122 + 8.72740i) q^{73} +(-0.729166 - 0.529770i) q^{74} +(-0.0831292 - 0.255845i) q^{75} -11.8264 q^{76} -0.254539 q^{78} +(-0.757990 - 2.33285i) q^{79} +(7.46110 + 5.42081i) q^{80} +(-6.93339 + 5.03741i) q^{81} +(0.471776 - 1.45198i) q^{82} +(-0.694608 + 2.13778i) q^{83} +(0.345487 - 0.251011i) q^{84} +(2.90225 + 2.10861i) q^{85} +(-0.0560832 - 0.172606i) q^{86} +1.42822 q^{87} +1.73566 q^{89} +(-0.514958 - 1.58488i) q^{90} +(-4.15429 - 3.01827i) q^{91} +(11.1672 - 8.11343i) q^{92} +(-0.520655 + 1.60241i) q^{93} +(-0.472001 + 1.45267i) q^{94} +(12.2518 - 8.90144i) q^{95} +(-0.464920 - 0.337784i) q^{96} +(-3.73217 - 11.4864i) q^{97} -0.226211 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} + 4 q^{7} - 5 q^{8} - 2 q^{9} - 12 q^{10} + 18 q^{12} - 13 q^{13} - 3 q^{14} + 7 q^{15} - 18 q^{16} - 10 q^{17} + 19 q^{18} + 6 q^{19} - 24 q^{20}+ \cdots - 2 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 + 2 * q^6 + 4 * q^7 - 5 * q^8 - 2 * q^9 - 12 * q^10 + 18 * q^12 - 13 * q^13 - 3 * q^14 + 7 * q^15 - 18 * q^16 - 10 * q^17 + 19 * q^18 + 6 * q^19 - 24 * q^20 - 8 * q^21 + 32 * q^23 - 45 * q^24 - 23 * q^25 + 33 * q^26 - 20 * q^27 + 11 * q^28 + 12 * q^29 - 38 * q^30 - 2 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 - 38 * q^36 - 11 * q^37 + 15 * q^38 + 24 * q^39 - 5 * q^40 - 20 * q^41 - 2 * q^42 + 8 * q^43 + 70 * q^45 - 38 * q^46 + 7 * q^47 + 39 * q^48 - 4 * q^49 + 58 * q^50 - 16 * q^51 - 8 * q^52 - 41 * q^53 - 60 * q^54 - 9 * q^57 - 5 * q^58 - 18 * q^59 + 25 * q^60 + 12 * q^61 + 61 * q^62 + 12 * q^63 - 3 * q^64 + 8 * q^65 - 38 * q^67 + 7 * q^68 - 30 * q^69 + 12 * q^70 + q^71 - 35 * q^72 - 60 * q^73 + 4 * q^74 + 4 * q^75 - 52 * q^76 - 58 * q^78 + 15 * q^79 + 83 * q^80 + 6 * q^81 - 6 * q^82 - 20 * q^83 + 17 * q^84 + 9 * q^85 + 48 * q^86 + 72 * q^87 + 74 * q^89 - 16 * q^90 - 7 * q^91 + 20 * q^92 - 53 * q^93 - 66 * q^94 + 53 * q^95 - 48 * q^96 - 35 * q^97 - 2 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.0699031	−	0.215140i	−0.0494290	−	0.152127i	0.923295	−	0.384090i	$-0.125485\pi$
$2$	−0.0699031	−	0.215140i	−0.0494290	−	0.152127i	−0.972724	+	0.231964i	$0.925485\pi$
$3$	0.177280	+	0.128801i	0.102352	+	0.0743634i	0.637784	−	0.770215i	$-0.279851\pi$
$3$	0.177280	+	0.128801i	0.102352	+	0.0743634i	−0.535432	+	0.844578i	$0.679851\pi$
$4$	1.57664	−	1.14549i	0.788318	−	0.572746i
$5$	−0.771159	+	2.37338i	−0.344873	+	1.06141i	0.616779	+	0.787136i	$0.288437\pi$
$5$	−0.771159	+	2.37338i	−0.344873	+	1.06141i	−0.961652	+	0.274273i	$0.911563\pi$
$6$	0.0153178	−	0.0471435i	0.00625348	−	0.0192462i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$	−0.722670	−	0.525051i	−0.255503	−	0.185633i
$9$	−0.912213	−	2.80750i	−0.304071	−	0.935834i
$10$	0.564516			0.178516
$11$		0			0
$11$		0			0
$12$	0.427046			0.123278
$13$	−1.58680	−	4.88366i	−0.440099	−	1.35448i	−0.887771	−	0.460286i	$-0.847747\pi$
$13$	−1.58680	−	4.88366i	−0.440099	−	1.35448i	0.447672	−	0.894198i	$-0.352253\pi$
$14$	−0.183009	−	0.132964i	−0.0489112	−	0.0355360i
$15$	−0.442405	+	0.321426i	−0.114229	+	0.0829919i
$16$	1.14200	−	3.51471i	0.285500	−	0.878679i
$17$	0.444220	−	1.36717i	0.107739	−	0.331587i	−0.882624	−	0.470079i	$-0.844226\pi$
$17$	0.444220	−	1.36717i	0.107739	−	0.331587i	0.990364	+	0.138492i	$0.0442255\pi$
$18$	−0.540239	+	0.392506i	−0.127336	+	0.0925147i
$19$	−4.90950	−	3.56696i	−1.12632	−	0.818317i	−0.141162	−	0.989986i	$-0.545084\pi$
$19$	−4.90950	−	3.56696i	−1.12632	−	0.818317i	−0.985155	+	0.171669i	$0.945084\pi$
$20$	1.50286	+	4.62532i	0.336049	+	1.03425i
$21$	0.219130			0.0478180
$22$		0			0
$23$	7.08292			1.47689			0.738446	−	0.674313i	$-0.235560\pi$
$23$	7.08292			1.47689			0.738446	+	0.674313i	$0.235560\pi$
$24$	−0.0604875	−	0.186161i	−0.0123470	−	0.0380001i
$25$	−0.993180	−	0.721588i	−0.198636	−	0.144318i
$26$	−0.939748	+	0.682767i	−0.184300	+	0.133902i
$27$	0.403037	−	1.24042i	0.0775645	−	0.238719i
$28$	0.602221	−	1.85345i	0.113809	−	0.350268i
$29$	5.27292	−	3.83100i	0.979156	−	0.711399i	0.0216365	−	0.999766i	$-0.493112\pi$
$29$	5.27292	−	3.83100i	0.979156	−	0.711399i	0.957520	+	0.288367i	$0.0931123\pi$
$30$	0.100077	+	0.0727103i	0.0182715	+	0.0132750i
$31$	2.37602	+	7.31263i	0.426745	+	1.31339i	0.901313	+	0.433168i	$0.142604\pi$
$31$	2.37602	+	7.31263i	0.426745	+	1.31339i	−0.474568	+	0.880219i	$0.657396\pi$
$32$	−2.62252			−0.463601
$33$		0			0
$34$	−0.325184			−0.0557687
$35$	0.771159	+	2.37338i	0.130350	+	0.401175i
$36$	−4.65420	−	3.38147i	−0.775700	−	0.563579i
$37$	3.22339	−	2.34193i	0.529921	−	0.385010i	−0.290407	−	0.956903i	$-0.593791\pi$
$37$	3.22339	−	2.34193i	0.529921	−	0.385010i	0.820328	+	0.571893i	$0.193791\pi$
$38$	−0.424206	+	1.30557i	−0.0688153	+	0.211792i
$39$	0.347714	−	1.07015i	0.0556788	−	0.171362i
$40$	1.80344	−	1.31028i	0.285149	−	0.207173i
$41$	5.46006	+	3.96696i	0.852718	+	0.619536i	0.925894	−	0.377783i	$-0.123314\pi$
$41$	5.46006	+	3.96696i	0.852718	+	0.619536i	−0.0731765	+	0.997319i	$0.523314\pi$
$42$	−0.0153178	−	0.0471435i	−0.00236359	−	0.00727440i
$43$	0.802299			0.122349			0.0611747	−	0.998127i	$-0.480515\pi$
$43$	0.802299			0.122349			0.0611747	+	0.998127i	$0.480515\pi$
$44$		0			0
$45$	7.36674			1.09817
$46$	−0.495119	−	1.52382i	−0.0730012	−	0.224675i
$47$	−5.46266	−	3.96885i	−0.796811	−	0.578917i	0.113166	−	0.993576i	$-0.463901\pi$
$47$	−5.46266	−	3.96885i	−0.796811	−	0.578917i	−0.909977	+	0.414659i	$0.863901\pi$
$48$	0.655152	−	0.475996i	0.0945631	−	0.0687041i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	−0.0858158	+	0.264114i	−0.0121362	+	0.0373513i
$51$	0.254844	−	0.185155i	0.0356853	−	0.0259269i
$52$	−8.09600	−	5.88209i	−1.12271	−	0.815699i
$53$	2.03385	+	6.25954i	0.279371	+	0.859814i	0.988030	+	0.154263i	$0.0493004\pi$
$53$	2.03385	+	6.25954i	0.279371	+	0.859814i	−0.708659	+	0.705551i	$0.750700\pi$
$54$	−0.295037			−0.0401495
$55$		0			0
$56$	−0.893270			−0.119368
$57$	−0.410925	−	1.26470i	−0.0544284	−	0.167513i
$58$	−1.19279	−	0.866616i	−0.156622	−	0.113792i
$59$	−2.32694	+	1.69062i	−0.302941	+	0.220100i	−0.728862	−	0.684661i	$-0.759950\pi$
$59$	−2.32694	+	1.69062i	−0.302941	+	0.220100i	0.425921	+	0.904761i	$0.359950\pi$
$60$	−0.329320	+	1.01354i	−0.0425151	+	0.130848i
$61$	0.264315	−	0.813478i	0.0338421	−	0.104155i	−0.932709	−	0.360631i	$-0.882561\pi$
$61$	0.264315	−	0.813478i	0.0338421	−	0.104155i	0.966551	+	0.256476i	$0.0825614\pi$
$62$	1.40715	−	1.02235i	0.178708	−	0.129839i
$63$	−2.38820	−	1.73513i	−0.300885	−	0.218606i
$64$	−2.10068	−	6.46522i	−0.262585	−	0.808152i
$65$	12.8145			1.58944
$66$		0			0
$67$	−1.64668			−0.201174			−0.100587	−	0.994928i	$-0.532072\pi$
$67$	−1.64668			−0.201174			−0.100587	+	0.994928i	$0.532072\pi$
$68$	−0.865708	−	2.66437i	−0.104982	−	0.323103i
$69$	1.25566	+	0.912288i	0.151163	+	0.109827i
$70$	0.456703	−	0.331814i	0.0545864	−	0.0396594i
$71$	1.39700	−	4.29951i	0.165793	−	0.510258i	−0.833301	−	0.552819i	$-0.813552\pi$
$71$	1.39700	−	4.29951i	0.165793	−	0.510258i	0.999094	+	0.0425617i	$0.0135519\pi$
$72$	−0.814852	+	2.50786i	−0.0960312	+	0.295554i
$73$	−12.0122	+	8.72740i	−1.40593	+	1.02147i	−0.412027	+	0.911171i	$0.635179\pi$
$73$	−12.0122	+	8.72740i	−1.40593	+	1.02147i	−0.993899	+	0.110294i	$0.964821\pi$
$74$	−0.729166	−	0.529770i	−0.0847639	−	0.0615846i
$75$	−0.0831292	−	0.255845i	−0.00959894	−	0.0295425i
$76$	−11.8264			−1.35658
$77$		0			0
$78$	−0.254539			−0.0288209
$79$	−0.757990	−	2.33285i	−0.0852805	−	0.262466i	0.899319	−	0.437294i	$-0.144063\pi$
$79$	−0.757990	−	2.33285i	−0.0852805	−	0.262466i	−0.984599	+	0.174828i	$0.944063\pi$
$80$	7.46110	+	5.42081i	0.834177	+	0.606065i
$81$	−6.93339	+	5.03741i	−0.770377	+	0.559712i
$82$	0.471776	−	1.45198i	0.0520990	−	0.160344i
$83$	−0.694608	+	2.13778i	−0.0762431	+	0.234652i	−0.981913	−	0.189330i	$-0.939368\pi$
$83$	−0.694608	+	2.13778i	−0.0762431	+	0.234652i	0.905670	+	0.423983i	$0.139368\pi$
$84$	0.345487	−	0.251011i	0.0376958	−	0.0273876i
$85$	2.90225	+	2.10861i	0.314793	+	0.228711i
$86$	−0.0560832	−	0.172606i	−0.00604761	−	0.0186126i
$87$	1.42822			0.153121
$88$		0			0
$89$	1.73566			0.183980			0.0919898	−	0.995760i	$-0.470677\pi$
$89$	1.73566			0.183980			0.0919898	+	0.995760i	$0.470677\pi$
$90$	−0.514958	−	1.58488i	−0.0542814	−	0.167061i
$91$	−4.15429	−	3.01827i	−0.435488	−	0.316401i
$92$	11.1672	−	8.11343i	1.16426	−	0.845884i
$93$	−0.520655	+	1.60241i	−0.0539895	+	0.166162i
$94$	−0.472001	+	1.45267i	−0.0486832	+	0.149832i
$95$	12.2518	−	8.90144i	1.25701	−	0.913268i
$96$	−0.464920	−	0.337784i	−0.0474507	−	0.0344749i
$97$	−3.73217	−	11.4864i	−0.378944	−	1.16627i	−0.940779	−	0.339021i	$-0.889904\pi$
$97$	−3.73217	−	11.4864i	−0.378944	−	1.16627i	0.561834	−	0.827250i	$-0.310096\pi$
$98$	−0.226211			−0.0228508
$99$		0			0
$100$	−2.39246			−0.239246
$101$	1.14132	+	3.51261i	0.113565	+	0.349518i	0.991645	−	0.128996i	$-0.0411755\pi$
$101$	1.14132	+	3.51261i	0.113565	+	0.349518i	−0.878080	+	0.478514i	$0.841175\pi$
$102$	−0.0576485	−	0.0418841i	−0.00570805	−	0.00414714i
$103$	0.931634	−	0.676872i	0.0917966	−	0.0666942i	−0.540940	−	0.841061i	$-0.681931\pi$
$103$	0.931634	−	0.676872i	0.0917966	−	0.0666942i	0.632737	+	0.774367i	$0.281931\pi$
$104$	−1.41744	+	4.36243i	−0.138991	+	0.427771i
$105$	−0.168984	+	0.520079i	−0.0164911	+	0.0507545i
$106$	1.20450	−	0.875124i	0.116992	−	0.0849995i
$107$	0.944233	+	0.686025i	0.0912825	+	0.0663206i	0.632490	−	0.774568i	$-0.282033\pi$
$107$	0.944233	+	0.686025i	0.0912825	+	0.0663206i	−0.541208	+	0.840889i	$0.682033\pi$
$108$	−0.785450	−	2.41737i	−0.0755800	−	0.232611i
$109$	−9.30234			−0.891003			−0.445501	−	0.895281i	$-0.646975\pi$
$109$	−9.30234			−0.891003			−0.445501	+	0.895281i	$0.646975\pi$
$110$		0			0
$111$	0.873083			0.0828694
$112$	−1.14200	−	3.51471i	−0.107909	−	0.332109i
$113$	−2.66760	−	1.93812i	−0.250946	−	0.182323i	0.455200	−	0.890389i	$-0.349568\pi$
$113$	−2.66760	−	1.93812i	−0.250946	−	0.182323i	−0.706146	+	0.708066i	$0.749568\pi$
$114$	−0.243362	+	0.176813i	−0.0227929	+	0.0165600i
$115$	−5.46206	+	16.8105i	−0.509340	+	1.56759i
$116$	3.92509	−	12.0802i	0.364435	−	1.12162i
$117$	−12.2634	+	8.90988i	−1.13375	+	0.823718i
$118$	0.526379	+	0.382437i	0.0484571	+	0.0352062i
$119$	−0.444220	−	1.36717i	−0.0407215	−	0.125328i
$120$	0.488478			0.0445918
$121$		0			0
$122$	−0.193488			−0.0175176
$123$	0.457007	+	1.40652i	0.0412069	+	0.126822i
$124$	12.1227	+	8.80764i	1.08865	+	0.790949i
$125$	−7.61610	+	5.53342i	−0.681205	+	0.494924i
$126$	−0.206353	+	0.635089i	−0.0183834	+	0.0565782i
$127$	0.0893693	−	0.275050i	0.00793024	−	0.0244068i	−0.947013	−	0.321195i	$-0.895916\pi$
$127$	0.0893693	−	0.275050i	0.00793024	−	0.0244068i	0.954943	+	0.296788i	$0.0959155\pi$
$128$	−5.48741	+	3.98684i	−0.485023	+	0.352390i
$129$	0.142231	+	0.103337i	0.0125228	+	0.00909831i
$130$	−0.895772	−	2.75690i	−0.0785644	−	0.241796i
$131$	16.5059			1.44212			0.721062	−	0.692871i	$-0.243654\pi$
$131$	16.5059			1.44212			0.721062	+	0.692871i	$0.243654\pi$
$132$		0			0
$133$	−6.06848			−0.526204
$134$	0.115108	+	0.354266i	0.00994383	+	0.0306040i
$135$	2.63319	+	1.91312i	0.226629	+	0.164655i
$136$	−1.03886	+	0.754773i	−0.0890812	+	0.0647213i
$137$	2.88185	−	8.86944i	0.246213	−	0.757767i	−0.749221	−	0.662320i	$-0.769572\pi$
$137$	2.88185	−	8.86944i	0.246213	−	0.757767i	0.995435	−	0.0954470i	$-0.0304281\pi$
$138$	0.108495	−	0.333914i	0.00923572	−	0.0284246i
$139$	3.90471	−	2.83694i	0.331193	−	0.240626i	−0.409744	−	0.912201i	$-0.634382\pi$
$139$	3.90471	−	2.83694i	0.331193	−	0.240626i	0.740937	+	0.671575i	$0.234382\pi$
$140$	3.93453	+	2.85860i	0.332529	+	0.241596i
$141$	−0.457225	−	1.40719i	−0.0385053	−	0.118507i
$142$	−1.02265			−0.0858189
$143$		0			0
$144$	−10.9093			−0.909109
$145$	5.02617	+	15.4690i	0.417401	+	1.28463i
$146$	2.71731	+	1.97424i	0.224886	+	0.163389i
$147$	0.177280	−	0.128801i	0.0146218	−	0.0106233i
$148$	2.39944	−	7.38473i	0.197233	−	0.607021i
$149$	−0.284887	+	0.876793i	−0.0233389	+	0.0718297i	−0.962048	−	0.272882i	$-0.912023\pi$
$149$	−0.284887	+	0.876793i	−0.0233389	+	0.0718297i	0.938709	+	0.344711i	$0.112023\pi$
$150$	−0.0492315	+	0.0357688i	−0.00401974	+	0.00292051i
$151$	14.6403	+	10.6368i	1.19141	+	0.865611i	0.993413	−	0.114591i	$-0.0365559\pi$
$151$	14.6403	+	10.6368i	1.19141	+	0.865611i	0.197999	+	0.980202i	$0.436556\pi$
$152$	1.67512	+	5.15548i	0.135870	+	0.418164i
$153$	−4.24355			−0.343070
$154$		0			0
$155$	−19.1880			−1.54121
$156$	−0.677635	−	2.08555i	−0.0542543	−	0.166977i
$157$	9.92933	+	7.21408i	0.792447	+	0.575746i	0.908689	−	0.417475i	$-0.137085\pi$
$157$	9.92933	+	7.21408i	0.792447	+	0.575746i	−0.116242	+	0.993221i	$0.537085\pi$
$158$	−0.448903	+	0.326147i	−0.0357128	+	0.0259469i
$159$	−0.445676	+	1.37165i	−0.0353444	+	0.108779i
$160$	2.02238	−	6.22426i	0.159883	−	0.492071i
$161$	5.73020	−	4.16324i	0.451603	−	0.328109i
$162$	1.56841	+	1.13952i	0.123226	+	0.0895290i
$163$	2.50277	+	7.70273i	0.196032	+	0.603324i	0.999963	+	0.00860182i	$0.00273808\pi$
$163$	2.50277	+	7.70273i	0.196032	+	0.603324i	−0.803931	+	0.594723i	$0.797262\pi$
$164$	13.1526			1.02705
$165$		0			0
$166$	0.508478			0.0394655
$167$	4.03317	+	12.4128i	0.312096	+	0.960532i	0.976933	+	0.213544i	$0.0685007\pi$
$167$	4.03317	+	12.4128i	0.312096	+	0.960532i	−0.664838	+	0.746988i	$0.731499\pi$
$168$	−0.158358	−	0.115054i	−0.0122176	−	0.00887662i
$169$	−10.8150	+	7.85756i	−0.831923	+	0.604428i
$170$	0.250769	−	0.771787i	0.0192331	−	0.0591934i
$171$	−5.53574	+	17.0373i	−0.423329	+	1.30287i
$172$	1.26493	−	0.919027i	0.0964502	−	0.0700752i
$173$	4.78306	+	3.47510i	0.363649	+	0.264207i	0.754573	−	0.656217i	$-0.227844\pi$
$173$	4.78306	+	3.47510i	0.363649	+	0.264207i	−0.390923	+	0.920423i	$0.627844\pi$
$174$	−0.0998369	−	0.307266i	−0.00756862	−	0.0232938i
$175$	−1.22764			−0.0928007
$176$		0			0
$177$	−0.630271			−0.0473741
$178$	−0.121328	−	0.373410i	−0.00909393	−	0.0279882i
$179$	−3.50715	−	2.54810i	−0.262137	−	0.190454i	0.448952	−	0.893556i	$-0.351798\pi$
$179$	−3.50715	−	2.54810i	−0.262137	−	0.190454i	−0.711089	+	0.703102i	$0.751798\pi$
$180$	11.6147	−	8.43855i	0.865706	−	0.628972i
$181$	3.34687	−	10.3006i	0.248771	−	0.765639i	−0.746222	−	0.665697i	$-0.768134\pi$
$181$	3.34687	−	10.3006i	0.248771	−	0.765639i	0.994993	−	0.0999417i	$-0.0318656\pi$
$182$	−0.358952	+	1.10474i	−0.0266073	+	0.0818888i
$183$	0.151635	−	0.110169i	0.0112091	−	0.00814392i
$184$	−5.11862	−	3.71889i	−0.377350	−	0.274160i
$185$	3.07255	+	9.45633i	0.225898	+	0.695243i
$186$	0.381138			0.0279464
$187$		0			0
$188$	−13.1589			−0.959713
$189$	−0.403037	−	1.24042i	−0.0293166	−	0.0902273i
$190$	−2.77149	−	2.01361i	−0.201065	−	0.146082i
$191$	−9.42959	+	6.85100i	−0.682301	+	0.495721i	−0.874120	−	0.485710i	$-0.838561\pi$
$191$	−9.42959	+	6.85100i	−0.682301	+	0.495721i	0.191819	+	0.981430i	$0.438561\pi$
$192$	0.460320	−	1.41672i	0.0332208	−	0.102243i
$193$	−6.93602	+	21.3469i	−0.499265	+	1.53658i	0.310937	+	0.950431i	$0.399357\pi$
$193$	−6.93602	+	21.3469i	−0.499265	+	1.53658i	−0.810202	+	0.586151i	$0.800643\pi$
$194$	−2.21030	+	1.60588i	−0.158690	+	0.115295i
$195$	2.27174	+	1.65052i	0.162683	+	0.118196i
$196$	−0.602221	−	1.85345i	−0.0430158	−	0.132389i
$197$	−24.1022			−1.71721			−0.858604	−	0.512639i	$-0.828668\pi$
$197$	−24.1022			−1.71721			−0.858604	+	0.512639i	$0.828668\pi$
$198$		0			0
$199$	18.7205			1.32706			0.663531	−	0.748148i	$-0.269057\pi$
$199$	18.7205			1.32706			0.663531	+	0.748148i	$0.269057\pi$
$200$	0.338872	+	1.04294i	0.0239619	+	0.0737470i
$201$	−0.291923	−	0.212094i	−0.0205906	−	0.0149600i
$202$	0.675921	−	0.491085i	0.0475576	−	0.0345527i
$203$	2.01408	−	6.19869i	0.141360	−	0.435063i
$204$	0.189702	−	0.583843i	0.0132818	−	0.0408772i
$205$	−13.6257	+	9.89965i	−0.951660	+	0.691422i
$206$	−0.210746	−	0.153116i	−0.0146834	−	0.0106681i
$207$	−6.46113	−	19.8853i	−0.449080	−	1.38213i
$208$	−18.9768			−1.31580
$209$		0			0
$210$	0.123702			0.00853625
$211$	2.33813	+	7.19603i	0.160964	+	0.495395i	0.998716	−	0.0506548i	$-0.0161308\pi$
$211$	2.33813	+	7.19603i	0.160964	+	0.495395i	−0.837753	+	0.546050i	$0.816131\pi$
$212$	10.3769	+	7.53926i	0.712688	+	0.517798i
$213$	0.801440	−	0.582280i	0.0549138	−	0.0398972i
$214$	0.0815865	−	0.251097i	0.00557714	−	0.0171647i
$215$	−0.618700	+	1.90416i	−0.0421950	+	0.129863i
$216$	−0.942547	+	0.684800i	−0.0641322	+	0.0465947i
$217$	6.22049	+	4.51945i	0.422275	+	0.306800i
$218$	0.650263	+	2.00130i	0.0440414	+	0.135545i
$219$	−3.25362			−0.219859
$220$		0			0
$221$	−7.38167			−0.496545
$222$	−0.0610313	−	0.187835i	−0.00409615	−	0.0126067i
$223$	−14.1775	−	10.3006i	−0.949397	−	0.689777i	0.00126729	−	0.999999i	$-0.499597\pi$
$223$	−14.1775	−	10.3006i	−0.949397	−	0.689777i	−0.950664	+	0.310222i	$0.899597\pi$
$224$	−2.12167	+	1.54148i	−0.141760	+	0.102995i
$225$	−1.11987	+	3.44660i	−0.0746578	+	0.229773i
$226$	−0.230494	+	0.709387i	−0.0153322	+	0.0471877i
$227$	−20.7733	+	15.0927i	−1.37877	+	1.00174i	−0.381782	+	0.924253i	$0.624689\pi$
$227$	−20.7733	+	15.0927i	−1.37877	+	1.00174i	−0.996993	+	0.0774861i	$0.975311\pi$
$228$	−2.09658	−	1.52326i	−0.138850	−	0.100880i
$229$	−6.12993	−	18.8660i	−0.405077	−	1.24670i	−0.920831	−	0.389963i	$-0.872488\pi$
$229$	−6.12993	−	18.8660i	−0.405077	−	1.24670i	0.515753	−	0.856737i	$-0.327512\pi$
$230$	3.99842			0.263648
$231$		0			0
$232$	−5.82205			−0.382236
$233$	6.24665	+	19.2252i	0.409232	+	1.25949i	0.917310	+	0.398174i	$0.130356\pi$
$233$	6.24665	+	19.2252i	0.409232	+	1.25949i	−0.508078	+	0.861311i	$0.669644\pi$
$234$	2.77412	+	2.01552i	0.181350	+	0.131758i
$235$	13.6322	−	9.90437i	0.889267	−	0.646090i
$236$	−1.73214	+	5.33097i	−0.112753	+	0.347017i
$237$	0.166098	−	0.511197i	0.0107892	−	0.0332058i
$238$	−0.263080	+	0.191139i	−0.0170529	+	0.0123897i
$239$	13.8345	+	10.0514i	0.894880	+	0.650168i	0.937146	−	0.348938i	$-0.113458\pi$
$239$	13.8345	+	10.0514i	0.894880	+	0.650168i	−0.0422657	+	0.999106i	$0.513458\pi$
$240$	0.624495	+	1.92200i	0.0403109	+	0.124064i
$241$	24.1529			1.55582			0.777912	−	0.628373i	$-0.216279\pi$
$241$	24.1529			1.55582			0.777912	+	0.628373i	$0.216279\pi$
$242$		0			0
$243$	−5.79074			−0.371476
$244$	−0.515105	−	1.58533i	−0.0329762	−	0.101490i
$245$	2.01892	+	1.46683i	0.128984	+	0.0937125i
$246$	0.270653	−	0.196641i	0.0172562	−	0.0125374i
$247$	−9.62945	+	29.6364i	−0.612707	+	1.88572i
$248$	2.12242	−	6.53215i	0.134774	−	0.414792i
$249$	−0.398489	+	0.289519i	−0.0252532	+	0.0183475i
$250$	1.72285	+	1.25172i	0.108962	+	0.0791659i
$251$	3.67568	+	11.3126i	0.232007	+	0.714044i	0.997504	+	0.0706047i	$0.0224929\pi$
$251$	3.67568	+	11.3126i	0.232007	+	0.714044i	−0.765498	+	0.643439i	$0.777507\pi$
$252$	−5.75291			−0.362399
$253$		0			0
$254$	−0.0654215			−0.00410491
$255$	0.242918	+	0.747626i	0.0152121	+	0.0468181i
$256$	−9.75797	−	7.08958i	−0.609873	−	0.443099i
$257$	−18.5758	+	13.4961i	−1.15872	+	0.841862i	−0.989616	−	0.143735i	$-0.954089\pi$
$257$	−18.5758	+	13.4961i	−1.15872	+	0.841862i	−0.169108	+	0.985598i	$0.554089\pi$
$258$	0.0122895	−	0.0378231i	0.000765110	−	0.00235477i
$259$	1.23122	−	3.78932i	0.0765045	−	0.235457i
$260$	20.2038	−	14.6789i	1.25298	−	0.910346i
$261$	−15.5656	−	11.3090i	−0.963484	−	0.700012i
$262$	−1.15381	−	3.55107i	−0.0712827	−	0.219386i
$263$	−1.93774			−0.119486			−0.0597432	−	0.998214i	$-0.519028\pi$
$263$	−1.93774			−0.119486			−0.0597432	+	0.998214i	$0.519028\pi$
$264$		0			0
$265$	−16.4247			−1.00896
$266$	0.424206	+	1.30557i	0.0260097	+	0.0800497i
$267$	0.307697	+	0.223555i	0.0188308	+	0.0136813i
$268$	−2.59621	+	1.88626i	−0.158589	+	0.115222i
$269$	2.22083	−	6.83501i	0.135406	−	0.416738i	−0.860247	−	0.509878i	$-0.829690\pi$
$269$	2.22083	−	6.83501i	0.135406	−	0.416738i	0.995653	+	0.0931402i	$0.0296905\pi$
$270$	0.227521	−	0.700237i	0.0138465	−	0.0426151i
$271$	0.963622	−	0.700112i	0.0585359	−	0.0425288i	−0.558133	−	0.829752i	$-0.688482\pi$
$271$	0.963622	−	0.700112i	0.0585359	−	0.0425288i	0.616668	+	0.787223i	$0.288482\pi$
$272$	−4.29790	−	3.12261i	−0.260599	−	0.189336i
$273$	−0.347714	−	1.07015i	−0.0210446	−	0.0647687i
$274$	−2.10962			−0.127447
$275$		0			0
$276$	3.02473			0.182067
$277$	−3.19531	−	9.83415i	−0.191988	−	0.590877i	−0.999999	−	0.00170957i	$-0.999456\pi$
$277$	−3.19531	−	9.83415i	−0.191988	−	0.590877i	0.808011	−	0.589167i	$-0.200544\pi$
$278$	−0.883290	−	0.641748i	−0.0529762	−	0.0384895i
$279$	18.3628	−	13.3413i	1.09935	−	0.798725i
$280$	0.688853	−	2.12007i	0.0411669	−	0.126699i
$281$	4.06398	−	12.5076i	0.242437	−	0.746143i	−0.753611	−	0.657321i	$-0.771690\pi$
$281$	4.06398	−	12.5076i	0.242437	−	0.746143i	0.996047	−	0.0888223i	$-0.0283103\pi$
$282$	−0.270782	+	0.196734i	−0.0161248	+	0.0117154i
$283$	0.242730	+	0.176354i	0.0144288	+	0.0104831i	0.594976	−	0.803743i	$-0.297161\pi$
$283$	0.242730	+	0.176354i	0.0144288	+	0.0104831i	−0.580547	+	0.814226i	$0.697161\pi$
$284$	−2.72250	−	8.37900i	−0.161551	−	0.497202i
$285$	3.31850			0.196571
$286$		0			0
$287$	6.74900			0.398381
$288$	2.39230	+	7.36274i	0.140968	+	0.433854i
$289$	12.0815	+	8.77770i	0.710675	+	0.516336i
$290$	2.97665	−	2.16266i	0.174795	−	0.126996i
$291$	0.817829	−	2.51702i	0.0479420	−	0.147550i
$292$	−8.94175	+	27.5199i	−0.523276	+	1.61048i
$293$	13.0608	−	9.48926i	0.763023	−	0.554369i	−0.136813	−	0.990597i	$-0.543686\pi$
$293$	13.0608	−	9.48926i	0.763023	−	0.554369i	0.899836	+	0.436228i	$0.143686\pi$
$294$	−0.0401026	−	0.0291363i	−0.00233883	−	0.00169926i
$295$	−2.21805	−	6.82645i	−0.129140	−	0.397451i
$296$	−3.55908			−0.206867
$297$		0			0
$298$	0.208548			0.0120808
$299$	−11.2392	−	34.5906i	−0.649978	−	2.00043i
$300$	−0.424134	−	0.308151i	−0.0244874	−	0.0177911i
$301$	0.649073	−	0.471579i	0.0374120	−	0.0271814i
$302$	1.26500	−	3.89326i	0.0727924	−	0.224032i
$303$	−0.250096	+	0.769717i	−0.0143677	+	0.0442191i
$304$	−18.1435	+	13.1820i	−1.04060	+	0.756041i
$305$	1.72687	+	1.25464i	0.0988801	+	0.0718406i
$306$	0.296637	+	0.912956i	0.0169576	+	0.0521902i
$307$	28.6376			1.63443			0.817217	−	0.576330i	$-0.195516\pi$
$307$	28.6376			1.63443			0.817217	+	0.576330i	$0.195516\pi$
$308$		0			0
$309$	0.252341			0.0143552
$310$	1.34130	+	4.12809i	0.0761807	+	0.234460i
$311$	25.7452	+	18.7049i	1.45987	+	1.06066i	0.983396	+	0.181474i	$0.0580867\pi$
$311$	25.7452	+	18.7049i	1.45987	+	1.06066i	0.476478	+	0.879186i	$0.341913\pi$
$312$	−0.813168	+	0.590801i	−0.0460366	+	0.0334475i
$313$	0.0105756	−	0.0325482i	0.000597766	−	0.00183974i	−0.950757	−	0.309937i	$-0.899692\pi$
$313$	0.0105756	−	0.0325482i	0.000597766	−	0.00183974i	0.951355	+	0.308097i	$0.0996921\pi$
$314$	0.857944	−	2.64048i	0.0484166	−	0.149011i
$315$	5.95982	−	4.33006i	0.335798	−	0.243971i
$316$	−3.86734	−	2.80979i	−0.217555	−	0.158063i
$317$	6.91871	+	21.2936i	0.388594	+	1.19597i	0.933840	+	0.357692i	$0.116436\pi$
$317$	6.91871	+	21.2936i	0.388594	+	1.19597i	−0.545246	+	0.838276i	$0.683564\pi$
$318$	0.326251			0.0182952
$319$		0			0
$320$	16.9644			0.948339
$321$	0.0790323	+	0.243237i	0.00441115	+	0.0135761i
$322$	−1.29624	−	0.941771i	−0.0722365	−	0.0524829i
$323$	−7.05753	+	5.12760i	−0.392691	+	0.285307i
$324$	−5.16112	+	15.8843i	−0.286729	+	0.882461i
$325$	−1.94801	+	5.99537i	−0.108056	+	0.332563i
$326$	1.48221	−	1.07689i	0.0820921	−	0.0596434i
$327$	−1.64911	−	1.19815i	−0.0911963	−	0.0662580i
$328$	−1.86296	−	5.73361i	−0.102865	−	0.316586i
$329$	−6.75222			−0.372262
$330$		0			0
$331$	10.7577			0.591297			0.295648	−	0.955297i	$-0.404464\pi$
$331$	10.7577			0.591297			0.295648	+	0.955297i	$0.404464\pi$
$332$	1.35367	+	4.16617i	0.0742924	+	0.228648i
$333$	−9.51538	−	6.91333i	−0.521439	−	0.378848i
$334$	2.38856	−	1.73539i	0.130696	−	0.0949563i
$335$	1.26985	−	3.90821i	0.0693795	−	0.213528i
$336$	0.250246	−	0.770178i	0.0136520	−	0.0420166i
$337$	6.07161	−	4.41128i	0.330742	−	0.240298i	−0.410004	−	0.912084i	$-0.634473\pi$
$337$	6.07161	−	4.41128i	0.330742	−	0.240298i	0.740745	+	0.671786i	$0.234473\pi$
$338$	2.44648	+	1.77747i	0.133071	+	0.0966816i
$339$	−0.223278	−	0.687178i	−0.0121268	−	0.0373224i
$340$	6.99118			0.379150
$341$		0			0
$342$	4.05236			0.219126
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$	−0.579798	−	0.421248i	−0.0312606	−	0.0227121i
$345$	−3.13352	+	2.27664i	−0.168703	+	0.122570i
$346$	0.413281	−	1.27195i	0.0222181	−	0.0683803i
$347$	8.55415	−	26.3270i	0.459211	−	1.41331i	−0.406909	−	0.913469i	$-0.633393\pi$
$347$	8.55415	−	26.3270i	0.459211	−	1.41331i	0.866120	−	0.499837i	$-0.166607\pi$
$348$	2.25178	−	1.63601i	0.120708	−	0.0876995i
$349$	−8.94813	−	6.50120i	−0.478983	−	0.348001i	0.321949	−	0.946757i	$-0.395662\pi$
$349$	−8.94813	−	6.50120i	−0.478983	−	0.348001i	−0.800932	+	0.598756i	$0.795662\pi$
$350$	0.0858158	+	0.264114i	0.00458705	+	0.0141175i
$351$	−6.69733			−0.357477
$352$		0			0
$353$	31.9202			1.69894			0.849469	−	0.527638i	$-0.176922\pi$
$353$	31.9202			1.69894			0.849469	+	0.527638i	$0.176922\pi$
$354$	0.0440580	+	0.135596i	0.00234165	+	0.00720687i
$355$	9.12708	+	6.63121i	0.484415	+	0.351948i
$356$	2.73650	−	1.98819i	0.145034	−	0.105374i
$357$	0.0973416	−	0.299587i	0.00515186	−	0.0158558i
$358$	−0.303036	+	0.932648i	−0.0160159	+	0.0492920i
$359$	2.89488	−	2.10325i	0.152786	−	0.111005i	−0.508766	−	0.860905i	$-0.669898\pi$
$359$	2.89488	−	2.10325i	0.152786	−	0.111005i	0.661552	+	0.749899i	$0.269898\pi$
$360$	−5.32373	−	3.86791i	−0.280585	−	0.203857i
$361$	5.50867	+	16.9539i	0.289930	+	0.892312i
$362$	−2.45003			−0.128771
$363$		0			0
$364$	−10.0072			−0.524520
$365$	−11.4501	−	35.2399i	−0.599327	−	1.84454i
$366$	−0.0343015	−	0.0249215i	−0.00179297	−	0.00130267i
$367$	−1.85586	+	1.34836i	−0.0968750	+	0.0703838i	−0.635168	−	0.772374i	$-0.719069\pi$
$367$	−1.85586	+	1.34836i	−0.0968750	+	0.0703838i	0.538293	+	0.842758i	$0.319069\pi$
$368$	8.08870	−	24.8944i	0.421652	−	1.29771i
$369$	6.15652	−	18.9478i	0.320496	−	0.986385i
$370$	1.81965	−	1.32205i	0.0945992	−	0.0687303i
$371$	5.32469	+	3.86861i	0.276444	+	0.200848i
$372$	1.01467	+	3.12283i	0.0526081	+	0.161911i
$373$	−7.96856			−0.412596			−0.206298	−	0.978489i	$-0.566142\pi$
$373$	−7.96856			−0.412596			−0.206298	+	0.978489i	$0.566142\pi$
$374$		0			0
$375$	−2.06289			−0.106527
$376$	1.86385	+	5.73635i	0.0961209	+	0.295830i
$377$	−27.0764	−	19.6721i	−1.39450	−	1.01317i
$378$	−0.238690	+	0.173419i	−0.0122769	+	0.00891969i
$379$	−3.59115	+	11.0524i	−0.184465	+	0.567724i	−0.999939	−	0.0110695i	$-0.996476\pi$
$379$	−3.59115	+	11.0524i	−0.184465	+	0.567724i	0.815474	+	0.578794i	$0.196476\pi$
$380$	9.12005	−	28.0686i	0.467849	−	1.43989i
$381$	0.0512701	−	0.0372499i	0.00262665	−	0.00190837i
$382$	2.13308	+	1.54977i	0.109138	+	0.0792933i
$383$	3.88696	+	11.9628i	0.198614	+	0.611271i	0.999915	+	0.0130104i	$0.00414144\pi$
$383$	3.88696	+	11.9628i	0.198614	+	0.611271i	−0.801301	+	0.598261i	$0.795859\pi$
$384$	−1.48632			−0.0758482
$385$		0			0
$386$	5.07741			0.258433
$387$	−0.731867	−	2.25246i	−0.0372029	−	0.114499i
$388$	−19.0419	−	13.8347i	−0.966706	−	0.702353i
$389$	0.354587	−	0.257623i	0.0179783	−	0.0130620i	−0.578760	−	0.815498i	$-0.696463\pi$
$389$	0.354587	−	0.257623i	0.0179783	−	0.0130620i	0.596738	+	0.802436i	$0.296463\pi$
$390$	0.196290	−	0.604119i	0.00993954	−	0.0305908i
$391$	3.14637	−	9.68354i	0.159119	−	0.489718i
$392$	−0.722670	+	0.525051i	−0.0365004	+	0.0265191i
$393$	2.92615	+	2.12597i	0.147605	+	0.107241i
$394$	1.68482	+	5.18534i	0.0848799	+	0.261233i
$395$	6.12128			0.307995
$396$		0			0
$397$	16.8147			0.843905			0.421952	−	0.906618i	$-0.361345\pi$
$397$	16.8147			0.843905			0.421952	+	0.906618i	$0.361345\pi$
$398$	−1.30862	−	4.02753i	−0.0655954	−	0.201882i
$399$	−1.07582	−	0.781627i	−0.0538582	−	0.0391303i
$400$	−3.67039	+	2.66669i	−0.183519	+	0.133335i
$401$	11.3906	−	35.0568i	0.568821	−	1.75065i	−0.0874935	−	0.996165i	$-0.527886\pi$
$401$	11.3906	−	35.0568i	0.568821	−	1.75065i	0.656315	−	0.754487i	$-0.272114\pi$
$402$	−0.0252236	+	0.0776302i	−0.00125804	+	0.00387184i
$403$	31.9421	−	23.2073i	1.59115	−	1.15604i
$404$	5.82311	+	4.23074i	0.289711	+	0.210487i
$405$	−6.60895	−	20.3402i	−0.328401	−	1.01072i
$406$	−1.47437			−0.0731720
$407$		0			0
$408$	−0.281384			−0.0139306
$409$	−5.02891	−	15.4774i	−0.248664	−	0.765308i	−0.995012	−	0.0997528i	$-0.968195\pi$
$409$	−5.02891	−	15.4774i	−0.248664	−	0.765308i	0.746349	−	0.665555i	$-0.231805\pi$
$410$	3.08229	+	2.23941i	0.152223	+	0.110597i
$411$	1.65329	−	1.20118i	0.0815506	−	0.0592500i
$412$	0.693496	−	2.13436i	0.0341661	−	0.105152i
$413$	−0.888810	+	2.73548i	−0.0437355	+	0.134604i
$414$	−3.82647	+	2.78009i	−0.188061	+	0.136634i
$415$	−4.53813	−	3.29714i	−0.222768	−	0.161850i
$416$	4.16142	+	12.8075i	0.204030	+	0.627940i
$417$	1.05763			0.0517922
$418$		0			0
$419$	5.56352			0.271796			0.135898	−	0.990723i	$-0.456608\pi$
$419$	5.56352			0.271796			0.135898	+	0.990723i	$0.456608\pi$
$420$	0.329320	+	1.01354i	0.0160692	+	0.0494559i
$421$	−17.3869	−	12.6323i	−0.847386	−	0.615662i	0.0770384	−	0.997028i	$-0.475454\pi$
$421$	−17.3869	−	12.6323i	−0.847386	−	0.615662i	−0.924424	+	0.381366i	$0.875454\pi$
$422$	1.38471	−	1.00605i	0.0674066	−	0.0489738i
$423$	−6.15946	+	18.9569i	−0.299483	+	0.921714i
$424$	1.81678	−	5.59146i	0.0882304	−	0.271545i
$425$	−1.42772	+	1.03730i	−0.0692547	+	0.0503165i
$426$	−0.181295	−	0.131718i	−0.00878376	−	0.00638178i
$427$	−0.264315	−	0.813478i	−0.0127911	−	0.0393670i
$428$	2.27455			0.109944
$429$		0			0
$430$	0.452910			0.0218413
$431$	8.56557	+	26.3621i	0.412589	+	1.26982i	0.914390	+	0.404835i	$0.132671\pi$
$431$	8.56557	+	26.3621i	0.412589	+	1.26982i	−0.501801	+	0.864983i	$0.667329\pi$
$432$	−3.89945	−	2.83312i	−0.187613	−	0.136309i
$433$	−7.51424	+	5.45942i	−0.361112	+	0.262363i	−0.753516	−	0.657430i	$-0.771644\pi$
$433$	−7.51424	+	5.45942i	−0.361112	+	0.262363i	0.392404	+	0.919793i	$0.371644\pi$
$434$	0.537482	−	1.65420i	0.0258000	−	0.0794041i
$435$	−1.10138	+	3.38971i	−0.0528073	+	0.162524i
$436$	−14.6664	+	10.6558i	−0.702393	+	0.510319i
$437$	−34.7736	−	25.2645i	−1.66345	−	1.20857i
$438$	0.227439	+	0.699984i	0.0108674	+	0.0334465i
$439$	14.7118			0.702156			0.351078	−	0.936346i	$-0.385815\pi$
$439$	14.7118			0.702156			0.351078	+	0.936346i	$0.385815\pi$
$440$		0			0
$441$	−2.95198			−0.140571
$442$	0.516002	+	1.58809i	0.0245437	+	0.0755378i
$443$	−1.97679	−	1.43622i	−0.0939202	−	0.0682370i	0.539834	−	0.841771i	$-0.318487\pi$
$443$	−1.97679	−	1.43622i	−0.0939202	−	0.0682370i	−0.633754	+	0.773534i	$0.718487\pi$
$444$	1.37653	−	1.00011i	0.0653274	−	0.0474631i
$445$	−1.33847	+	4.11939i	−0.0634496	+	0.195278i
$446$	−1.22501	+	3.77019i	−0.0580059	+	0.178524i
$447$	−0.163437	+	0.118744i	−0.00773029	+	0.00561638i
$448$	−5.49964	−	3.99573i	−0.259834	−	0.188780i
$449$	1.47381	+	4.53592i	0.0695534	+	0.214063i	0.979791	−	0.200022i	$-0.0641014\pi$
$449$	1.47381	+	4.53592i	0.0695534	+	0.214063i	−0.910238	+	0.414086i	$0.864101\pi$
$450$	0.819782			0.0386449
$451$		0			0
$452$	−6.42593			−0.302250
$453$	1.22539	+	3.77138i	0.0575740	+	0.177195i
$454$	4.69917	+	3.41414i	0.220543	+	0.160234i
$455$	10.3671	−	7.53216i	0.486019	−	0.353113i
$456$	−0.367067	+	1.12972i	−0.0171895	+	0.0529038i
$457$	−9.60657	+	29.5660i	−0.449376	+	1.38304i	0.428236	+	0.903667i	$0.359135\pi$
$457$	−9.60657	+	29.5660i	−0.449376	+	1.38304i	−0.877612	+	0.479371i	$0.840865\pi$
$458$	−3.63033	+	2.63759i	−0.169634	+	0.123246i
$459$	−1.51682	−	1.10204i	−0.0707993	−	0.0514387i
$460$	10.6446	+	32.7608i	0.496308	+	1.52748i
$461$	−29.7215			−1.38427			−0.692134	−	0.721769i	$-0.743329\pi$
$461$	−29.7215			−1.38427			−0.692134	+	0.721769i	$0.743329\pi$
$462$		0			0
$463$	−25.4553			−1.18301			−0.591505	−	0.806302i	$-0.701466\pi$
$463$	−25.4553			−1.18301			−0.591505	+	0.806302i	$0.701466\pi$
$464$	−7.44320	−	22.9078i	−0.345542	−	1.06347i
$465$	−3.40163	−	2.47143i	−0.157747	−	0.114610i
$466$	3.69945	−	2.68780i	0.171374	−	0.124510i
$467$	−0.984192	+	3.02903i	−0.0455430	+	0.140167i	−0.971242	−	0.238093i	$-0.923478\pi$
$467$	−0.984192	+	3.02903i	−0.0455430	+	0.140167i	0.925699	+	0.378260i	$0.123478\pi$
$468$	−9.12870	+	28.0953i	−0.421974	+	1.29870i
$469$	−1.33219	+	0.967895i	−0.0615149	+	0.0446932i
$470$	−3.08376	−	2.24048i	−0.142243	−	0.103346i
$471$	0.831085	+	2.55782i	0.0382944	+	0.117858i
$472$	2.56927			0.118260
$473$		0			0
$474$	−0.121590			−0.00558479
$475$	2.30214	+	7.08527i	0.105630	+	0.325095i
$476$	−2.26645	−	1.64667i	−0.103883	−	0.0754752i
$477$	15.7184	−	11.4201i	0.719695	−	0.522889i
$478$	1.19537	−	3.67898i	0.0546750	−	0.168272i
$479$	−0.999218	+	3.07528i	−0.0456554	+	0.140513i	−0.971286	−	0.237916i	$-0.923536\pi$
$479$	−0.999218	+	3.07528i	−0.0456554	+	0.140513i	0.925630	+	0.378429i	$0.123536\pi$
$480$	1.16022	−	0.842948i	0.0529565	−	0.0384751i
$481$	−16.5520	−	12.0258i	−0.754708	−	0.548328i
$482$	−1.68836	−	5.19625i	−0.0769028	−	0.236683i
$483$	1.55208			0.0706220
$484$		0			0
$485$	30.1398			1.36858
$486$	0.404791	+	1.24582i	0.0183617	+	0.0565114i
$487$	−7.98577	−	5.80200i	−0.361870	−	0.262914i	0.391962	−	0.919982i	$-0.371797\pi$
$487$	−7.98577	−	5.80200i	−0.361870	−	0.262914i	−0.753832	+	0.657068i	$0.771797\pi$
$488$	−0.618130	+	0.449098i	−0.0279814	+	0.0203297i
$489$	−0.548430	+	1.68790i	−0.0248009	+	0.0763293i
$490$	0.174445	−	0.536886i	0.00788062	−	0.0242541i
$491$	3.41891	−	2.48398i	0.154293	−	0.112101i	−0.507960	−	0.861381i	$-0.669600\pi$
$491$	3.41891	−	2.48398i	0.154293	−	0.112101i	0.662253	+	0.749280i	$0.269600\pi$
$492$	2.33169	+	1.69408i	0.105121	+	0.0763748i
$493$	−2.89528	−	8.91077i	−0.130397	−	0.401321i
$494$	7.04910			0.317154
$495$		0			0
$496$	28.4152			1.27588
$497$	−1.39700	−	4.29951i	−0.0626638	−	0.192859i
$498$	0.0901427	+	0.0654925i	0.00403939	+	0.00293479i
$499$	16.5001	−	11.9880i	0.738647	−	0.536658i	−0.153640	−	0.988127i	$-0.549100\pi$
$499$	16.5001	−	11.9880i	0.738647	−	0.536658i	0.892287	+	0.451468i	$0.149100\pi$
$500$	−5.66932	+	17.4484i	−0.253540	+	0.780315i
$501$	−0.883786	+	2.72001i	−0.0394846	+	0.121521i
$502$	2.17684	−	1.58157i	0.0971573	−	0.0705889i
$503$	−19.3834	−	14.0829i	−0.864265	−	0.627925i	0.0647768	−	0.997900i	$-0.479366\pi$
$503$	−19.3834	−	14.0829i	−0.864265	−	0.627925i	−0.929042	+	0.369974i	$0.879366\pi$
$504$	0.814852	+	2.50786i	0.0362964	+	0.111709i
$505$	−9.21692			−0.410147
$506$		0			0
$507$	−2.92934			−0.130097
$508$	−0.174165	−	0.536026i	−0.00772734	−	0.0237823i
$509$	−2.98803	−	2.17093i	−0.132442	−	0.0962249i	0.519592	−	0.854415i	$-0.326084\pi$
$509$	−2.98803	−	2.17093i	−0.132442	−	0.0962249i	−0.652034	+	0.758190i	$0.726084\pi$
$510$	0.143863	−	0.104523i	0.00637037	−	0.00462835i
$511$	−4.58827	+	14.1212i	−0.202973	+	0.624687i
$512$	−5.03515	+	15.4966i	−0.222524	+	0.684859i
$513$	−6.40324	+	4.65223i	−0.282710	+	0.205401i
$514$	4.20205	+	3.05297i	0.185344	+	0.134661i
$515$	0.888038	+	2.73310i	0.0391316	+	0.120435i
$516$	0.342618			0.0150829
$517$		0			0
$518$	−0.901299			−0.0396008
$519$	0.400342	+	1.23213i	0.0175731	+	0.0540844i
$520$	−9.26065	−	6.72825i	−0.406106	−	0.295053i
$521$	0.192764	−	0.140051i	0.00844515	−	0.00613576i	−0.583555	−	0.812074i	$-0.698339\pi$
$521$	0.192764	−	0.140051i	0.00844515	−	0.00613576i	0.592000	+	0.805938i	$0.298339\pi$
$522$	−1.34494	+	4.13931i	−0.0588666	+	0.181173i
$523$	6.79573	−	20.9151i	0.297156	−	0.914553i	−0.685332	−	0.728231i	$-0.740343\pi$
$523$	6.79573	−	20.9151i	0.297156	−	0.914553i	0.982489	−	0.186323i	$-0.0596570\pi$
$524$	26.0237	−	18.9073i	1.13685	−	0.825971i
$525$	−0.217635	−	0.158121i	−0.00949838	−	0.00690097i
$526$	0.135454	+	0.416885i	0.00590609	+	0.0181771i
$527$	11.0531			0.481479
$528$		0			0
$529$	27.1678			1.18121
$530$	1.14814	+	3.53361i	0.0498720	+	0.153490i
$531$	6.86907	+	4.99067i	0.298092	+	0.216577i
$532$	−9.56778	+	6.95140i	−0.414816	+	0.301381i
$533$	10.7093	−	32.9598i	0.463871	−	1.42765i
$534$	0.0265866	−	0.0818251i	0.00115051	−	0.00354092i
$535$	−2.35636	+	1.71199i	−0.101874	+	0.0740159i
$536$	1.19001	+	0.864591i	0.0514005	+	0.0373446i
$537$	−0.293549	−	0.903450i	−0.0126676	−	0.0389868i
$538$	−1.62573			−0.0700900
$539$		0			0
$540$	6.34305			0.272961
$541$	−8.84744	−	27.2296i	−0.380381	−	1.17069i	−0.939776	−	0.341791i	$-0.888966\pi$
$541$	−8.84744	−	27.2296i	−0.380381	−	1.17069i	0.559395	−	0.828901i	$-0.311034\pi$
$542$	−0.217982	−	0.158373i	−0.00936314	−	0.00680272i
$543$	1.92006	−	1.39501i	0.0823978	−	0.0598655i
$544$	−1.16498	+	3.58543i	−0.0499479	+	0.153724i
$545$	7.17359	−	22.0780i	0.307283	−	0.945719i
$546$	−0.205926	+	0.149614i	−0.00881284	+	0.00640290i
$547$	5.18456	+	3.76681i	0.221676	+	0.161057i	0.693081	−	0.720860i	$-0.256253\pi$
$547$	5.18456	+	3.76681i	0.221676	+	0.161057i	−0.471405	+	0.881917i	$0.656253\pi$
$548$	−5.61624	−	17.2850i	−0.239914	−	0.738379i
$549$	−2.52495			−0.107762
$550$		0			0
$551$	−39.5524			−1.68499
$552$	−0.428429	−	1.31857i	−0.0182351	−	0.0561220i
$553$	−1.98444	−	1.44178i	−0.0843871	−	0.0613108i
$554$	−1.89236	+	1.37488i	−0.0803985	+	0.0584129i
$555$	−0.673286	+	2.07216i	−0.0285794	+	0.0879583i
$556$	2.90661	−	8.94563i	0.123268	−	0.379379i
$557$	−18.2185	+	13.2365i	−0.771941	+	0.560848i	−0.902550	−	0.430586i	$-0.858307\pi$
$557$	−18.2185	+	13.2365i	−0.771941	+	0.560848i	0.130608	+	0.991434i	$0.458307\pi$
$558$	−4.15387	−	3.01796i	−0.175847	−	0.127761i
$559$	−1.27309	−	3.91816i	−0.0538458	−	0.165720i
$560$	9.22243			0.389719
$561$		0			0
$562$	−2.97498			−0.125492
$563$	9.21696	+	28.3669i	0.388449	+	1.19552i	0.933948	+	0.357410i	$0.116340\pi$
$563$	9.21696	+	28.3669i	0.388449	+	1.19552i	−0.545499	+	0.838111i	$0.683660\pi$
$564$	−2.33281	−	1.69488i	−0.0982289	−	0.0713674i
$565$	6.65705	−	4.83663i	0.280064	−	0.203478i
$566$	0.0209731	−	0.0645485i	0.000881564	−	0.00271318i
$567$	−2.64832	+	8.15069i	−0.111219	+	0.342297i
$568$	−3.26703	+	2.37363i	−0.137081	+	0.0995955i
$569$	23.6851	+	17.2082i	0.992930	+	0.721406i	0.960561	−	0.278070i	$-0.0896947\pi$
$569$	23.6851	+	17.2082i	0.992930	+	0.721406i	0.0323695	+	0.999476i	$0.489695\pi$
$570$	−0.231974	−	0.713942i	−0.00971632	−	0.0299037i
$571$	−37.9252			−1.58712			−0.793559	−	0.608493i	$-0.791774\pi$
$571$	−37.9252			−1.58712			−0.793559	+	0.608493i	$0.791774\pi$
$572$		0			0
$573$	−2.55409			−0.106699
$574$	−0.471776	−	1.45198i	−0.0196916	−	0.0606044i
$575$	−7.03462	−	5.11095i	−0.293364	−	0.213141i
$576$	−16.2349	+	11.7953i	−0.676452	+	0.491471i
$577$	2.71089	−	8.34327i	0.112856	−	0.347335i	−0.878638	−	0.477489i	$-0.841547\pi$
$577$	2.71089	−	8.34327i	0.112856	−	0.347335i	0.991494	+	0.130154i	$0.0415471\pi$
$578$	1.04390	−	3.21279i	0.0434205	−	0.133635i
$579$	−3.97911	+	2.89100i	−0.165366	+	0.120146i
$580$	25.6440	+	18.6315i	1.06481	+	0.773630i
$581$	0.694608	+	2.13778i	0.0288172	+	0.0886902i
$582$	−0.598679			−0.0248161
$583$		0			0
$584$	13.2632			0.548836
$585$	−11.6895	−	35.9767i	−0.483303	−	1.48745i
$586$	−2.95451	−	2.14658i	−0.122050	−	0.0886743i
$587$	−7.41878	+	5.39006i	−0.306206	+	0.222472i	−0.730267	−	0.683162i	$-0.760604\pi$
$587$	−7.41878	+	5.39006i	−0.306206	+	0.222472i	0.424061	+	0.905634i	$0.360604\pi$
$588$	0.131964	−	0.406145i	0.00544212	−	0.0167491i
$589$	14.4188	−	44.3765i	0.594117	−	1.82850i
$590$	−1.31359	+	0.954380i	−0.0540797	+	0.0392912i
$591$	−4.27282	−	3.10439i	−0.175760	−	0.127697i
$592$	−4.55010	−	14.0038i	−0.187008	−	0.575551i
$593$	−7.25596			−0.297967			−0.148983	−	0.988840i	$-0.547600\pi$
$593$	−7.25596			−0.297967			−0.148983	+	0.988840i	$0.547600\pi$
$594$		0			0
$595$	3.58738			0.147068
$596$	0.555196	+	1.70872i	0.0227417	+	0.0699919i
$597$	3.31877	+	2.41122i	0.135828	+	0.0986848i
$598$	−6.65616	+	4.83598i	−0.272191	+	0.197758i
$599$	−6.18592	+	19.0383i	−0.252750	+	0.777884i	0.741515	+	0.670936i	$0.234108\pi$
$599$	−6.18592	+	19.0383i	−0.252750	+	0.777884i	−0.994265	+	0.106947i	$0.965892\pi$
$600$	−0.0742568	+	0.228539i	−0.00303152	+	0.00933007i
$601$	−9.11808	+	6.62467i	−0.371934	+	0.270226i	−0.758013	−	0.652240i	$-0.773829\pi$
$601$	−9.11808	+	6.62467i	−0.371934	+	0.270226i	0.386078	+	0.922466i	$0.373829\pi$
$602$	−0.146828	−	0.106677i	−0.00598425	−	0.00434781i
$603$	1.50212	+	4.62306i	0.0611712	+	0.188266i
$604$	35.2668			1.43499
$605$		0			0
$606$	0.183079			0.00743709
$607$	4.17977	+	12.8640i	0.169652	+	0.522135i	0.999349	−	0.0360793i	$-0.0114869\pi$
$607$	4.17977	+	12.8640i	0.169652	+	0.522135i	−0.829697	+	0.558214i	$0.811487\pi$
$608$	12.8753	+	9.35444i	0.522162	+	0.379373i
$609$	1.15545	−	0.839485i	0.0468213	−	0.0340177i
$610$	0.149210	−	0.459221i	0.00604134	−	0.0185933i
$611$	−10.7144	+	32.9756i	−0.433459	+	1.33405i
$612$	−6.69053	+	4.86095i	−0.270449	+	0.196492i
$613$	−24.9151	−	18.1019i	−1.00631	−	0.731129i	−0.0428801	−	0.999080i	$-0.513653\pi$
$613$	−24.9151	−	18.1019i	−1.00631	−	0.731129i	−0.963432	+	0.267951i	$0.913653\pi$
$614$	−2.00186	−	6.16109i	−0.0807884	−	0.248641i
$615$	−3.69064			−0.148821
$616$		0			0
$617$	23.6896			0.953707			0.476853	−	0.878983i	$-0.341777\pi$
$617$	23.6896			0.953707			0.476853	+	0.878983i	$0.341777\pi$
$618$	−0.0176395	−	0.0542887i	−0.000709563	−	0.00218381i
$619$	26.2832	+	19.0958i	1.05641	+	0.767527i	0.973421	−	0.229024i	$-0.0735533\pi$
$619$	26.2832	+	19.0958i	1.05641	+	0.767527i	0.0829892	+	0.996550i	$0.473553\pi$
$620$	−30.2524	+	21.9797i	−1.21497	+	0.882725i
$621$	2.85468	−	8.78580i	0.114554	−	0.352562i
$622$	2.22451	−	6.84634i	0.0891948	−	0.274513i
$623$	1.40418	−	1.02020i	0.0562573	−	0.0408733i
$624$	−3.36420	−	2.44423i	−0.134676	−	0.0978476i
$625$	−9.15651	−	28.1808i	−0.366260	−	1.12723i
$626$	−0.00774169			−0.000309420
$627$		0			0
$628$	23.9186			0.954456
$629$	−1.76991	−	5.44724i	−0.0705711	−	0.217196i
$630$	−1.34818	−	0.979509i	−0.0537127	−	0.0390246i
$631$	12.2431	−	8.89515i	0.487391	−	0.354110i	−0.316789	−	0.948496i	$-0.602605\pi$
$631$	12.2431	−	8.89515i	0.487391	−	0.354110i	0.804180	+	0.594386i	$0.202605\pi$
$632$	−0.677089	+	2.08387i	−0.0269332	+	0.0828917i
$633$	−0.512354	+	1.57686i	−0.0203642	+	0.0626747i
$634$	4.09746	−	2.97698i	0.162731	−	0.118231i
$635$	0.583882	+	0.424215i	0.0231707	+	0.0168345i
$636$	0.868547	+	2.67311i	0.0344401	+	0.105996i
$637$	−5.13499			−0.203456
$638$		0			0
$639$	−13.3452			−0.527929
$640$	−5.23063	−	16.0982i	−0.206759	−	0.636338i
$641$	13.3894	+	9.72799i	0.528850	+	0.384232i	0.819928	−	0.572467i	$-0.194014\pi$
$641$	13.3894	+	9.72799i	0.528850	+	0.384232i	−0.291077	+	0.956700i	$0.594014\pi$
$642$	0.0468052	−	0.0340060i	0.00184726	−	0.00134211i
$643$	0.616506	−	1.89741i	0.0243126	−	0.0748266i	−0.938164	−	0.346191i	$-0.887475\pi$
$643$	0.616506	−	1.89741i	0.0243126	−	0.0748266i	0.962477	+	0.271365i	$0.0874749\pi$
$644$	4.26549	−	13.1278i	0.168084	−	0.517308i
$645$	−0.354941	+	0.257880i	−0.0139758	+	0.0101540i
$646$	1.59649	+	1.15992i	0.0628132	+	0.0456365i
$647$	12.5003	+	38.4719i	0.491436	+	1.51248i	0.822438	+	0.568855i	$0.192613\pi$
$647$	12.5003	+	38.4719i	0.491436	+	1.51248i	−0.331002	+	0.943630i	$0.607387\pi$
$648$	7.65545			0.300735
$649$		0			0
$650$	1.42602			0.0559329
$651$	0.520655	+	1.60241i	0.0204061	+	0.0628035i
$652$	12.7694	+	9.27749i	0.500087	+	0.363335i
$653$	33.5626	−	24.3846i	1.31341	−	0.954245i	0.313416	−	0.949616i	$-0.398527\pi$
$653$	33.5626	−	24.3846i	1.31341	−	0.954245i	0.999989	−	0.00462886i	$-0.00147342\pi$
$654$	−0.142492	+	0.438545i	−0.00557187	+	0.0171485i
$655$	−12.7286	+	39.1747i	−0.497349	+	1.53068i
$656$	20.1781	−	14.6603i	0.787823	−	0.572387i
$657$	35.4599	+	25.7631i	1.38342	+	1.00512i
$658$	0.472001	+	1.45267i	0.0184005	+	0.0566310i
$659$	51.1359			1.99197			0.995985	−	0.0895158i	$-0.0285320\pi$
$659$	51.1359			1.99197			0.995985	+	0.0895158i	$0.0285320\pi$
$660$		0			0
$661$	−42.8840			−1.66800			−0.833998	−	0.551768i	$-0.813954\pi$
$661$	−42.8840			−1.66800			−0.833998	+	0.551768i	$0.813954\pi$
$662$	−0.751997	−	2.31441i	−0.0292272	−	0.0899521i
$663$	−1.30862	−	0.950767i	−0.0508225	−	0.0369247i
$664$	1.62442	−	1.18021i	0.0630396	−	0.0458010i
$665$	4.67976	−	14.4028i	0.181473	−	0.558518i
$666$	−0.822177	+	2.53040i	−0.0318587	+	0.0980510i
$667$	37.3477	−	27.1347i	1.44611	−	1.05066i
$668$	20.5776	+	14.9505i	0.796172	+	0.578453i
$669$	−1.18666	−	3.65216i	−0.0458789	−	0.141201i
$670$	−0.929577			−0.0359127
$671$		0			0
$672$	−0.574672			−0.0221685
$673$	7.72766	+	23.7833i	0.297879	+	0.916778i	0.982239	+	0.187634i	$0.0600818\pi$
$673$	7.72766	+	23.7833i	0.297879	+	0.916778i	−0.684360	+	0.729145i	$0.739918\pi$
$674$	−1.37347	−	0.997882i	−0.0529040	−	0.0384370i
$675$	−1.29536	+	0.941135i	−0.0498585	+	0.0362243i
$676$	−8.05054	+	24.7770i	−0.309636	+	0.952962i
$677$	3.06511	−	9.43343i	0.117802	−	0.362556i	−0.874719	−	0.484630i	$-0.838954\pi$
$677$	3.06511	−	9.43343i	0.117802	−	0.362556i	0.992521	+	0.122073i	$0.0389543\pi$
$678$	−0.132232	+	0.0960719i	−0.00507832	+	0.00368962i
$679$	−9.77095	−	7.09901i	−0.374975	−	0.272435i
$680$	−0.990244	−	3.04766i	−0.0379741	−	0.116872i
$681$	−5.62665			−0.215614
$682$		0			0
$683$	−39.8980			−1.52666			−0.763328	−	0.646011i	$-0.776436\pi$
$683$	−39.8980			−1.52666			−0.763328	+	0.646011i	$0.776436\pi$
$684$	10.7882	+	33.2027i	0.412498	+	1.26954i
$685$	18.8282	+	13.6795i	0.719389	+	0.522667i
$686$	−0.183009	+	0.132964i	−0.00698731	+	0.00507658i
$687$	1.34325	−	4.13410i	0.0512482	−	0.157726i
$688$	0.916225	−	2.81985i	0.0349307	−	0.107506i
$689$	27.3422	−	19.8653i	1.04165	−	0.756806i
$690$	0.708838	+	0.515001i	0.0269850	+	0.0196058i
$691$	−2.04384	−	6.29029i	−0.0777513	−	0.239294i	0.904625	−	0.426209i	$-0.140151\pi$
$691$	−2.04384	−	6.29029i	−0.0777513	−	0.239294i	−0.982376	+	0.186915i	$0.940151\pi$
$692$	11.5218			0.437995
$693$		0			0
$694$	−6.26194			−0.237700
$695$	3.72199	+	11.4551i	0.141183	+	0.434517i
$696$	−1.03213	−	0.749887i	−0.0391228	−	0.0284244i
$697$	7.84897	−	5.70261i	0.297301	−	0.216002i
$698$	−0.773164	+	2.37955i	−0.0292647	+	0.0900674i
$699$	−1.36883	+	4.21281i	−0.0517737	+	0.159343i
$700$	−1.93554	+	1.40625i	−0.0731565	+	0.0531513i
$701$	11.8130	+	8.58261i	0.446169	+	0.324161i	0.788081	−	0.615571i	$-0.211075\pi$
$701$	11.8130	+	8.58261i	0.446169	+	0.324161i	−0.341912	+	0.939732i	$0.611075\pi$
$702$	0.468165	+	1.44086i	0.0176697	+	0.0543818i
$703$	−24.1788			−0.911920
$704$		0			0
$705$	3.69240			0.139064
$706$	−2.23132	−	6.86730i	−0.0839768	−	0.258454i
$707$	2.98801	+	2.17091i	0.112376	+	0.0816456i
$708$	−0.993708	+	0.721971i	−0.0373458	+	0.0271333i
$709$	−1.28058	+	3.94123i	−0.0480934	+	0.148016i	−0.972219	−	0.234072i	$-0.924795\pi$
$709$	−1.28058	+	3.94123i	−0.0480934	+	0.148016i	0.924126	+	0.382088i	$0.124795\pi$
$710$	0.788626	−	2.42714i	0.0295966	−	0.0910890i
$711$	−5.85804	+	4.25611i	−0.219694	+	0.159617i
$712$	−1.25431	−	0.911310i	−0.0470073	−	0.0341528i
$713$	16.8291	+	51.7948i	0.630256	+	1.93973i
$714$	−0.0712575			−0.00266674
$715$		0			0
$716$	−8.44832			−0.315729
$717$	1.15795	+	3.56380i	0.0432444	+	0.133093i
$718$	−0.654854	−	0.475779i	−0.0244389	−	0.0177559i
$719$	−13.7713	+	10.0054i	−0.513583	+	0.373140i	−0.814181	−	0.580611i	$-0.802814\pi$
$719$	−13.7713	+	10.0054i	−0.513583	+	0.373140i	0.300598	+	0.953751i	$0.402814\pi$
$720$	8.41282	−	25.8920i	0.313527	−	0.964938i
$721$	0.355853	−	1.09520i	0.0132526	−	0.0407874i
$722$	3.26239	−	2.37027i	0.121414	−	0.0882122i
$723$	4.28181	+	3.11092i	0.159242	+	0.115696i
$724$	−6.52248	−	20.0741i	−0.242406	−	0.746049i
$725$	−8.00136			−0.297163
$726$		0			0
$727$	−21.6199			−0.801837			−0.400918	−	0.916114i	$-0.631309\pi$
$727$	−21.6199			−0.801837			−0.400918	+	0.916114i	$0.631309\pi$
$728$	1.41744	+	4.36243i	0.0525338	+	0.161682i
$729$	19.7736	+	14.3664i	0.732356	+	0.532088i
$730$	−6.78110	+	4.92676i	−0.250980	+	0.182347i
$731$	0.356397	−	1.09688i	0.0131818	−	0.0405694i
$732$	0.112875	−	0.347392i	0.00417197	−	0.0128400i
$733$	−39.0210	+	28.3504i	−1.44127	+	1.04715i	−0.453497	+	0.891258i	$0.649824\pi$
$733$	−39.0210	+	28.3504i	−1.44127	+	1.04715i	−0.987775	+	0.155887i	$0.950176\pi$
$734$	0.419816	+	0.305014i	0.0154957	+	0.0112583i
$735$	0.168984	+	0.520079i	0.00623306	+	0.0191834i
$736$	−18.5751			−0.684688
$737$		0			0
$738$	−4.50679			−0.165897
$739$	2.52265	+	7.76392i	0.0927973	+	0.285601i	0.986673	−	0.162713i	$-0.0520246\pi$
$739$	2.52265	+	7.76392i	0.0927973	+	0.285601i	−0.893876	+	0.448314i	$0.852025\pi$
$740$	15.6764	+	11.3896i	0.576278	+	0.418690i
$741$	−5.52430	+	4.01364i	−0.202940	+	0.147445i
$742$	0.460080	−	1.41598i	0.0168901	−	0.0519822i
$743$	−6.04476	+	18.6039i	−0.221761	+	0.682509i	0.776844	+	0.629694i	$0.216820\pi$
$743$	−6.04476	+	18.6039i	−0.221761	+	0.682509i	−0.998604	+	0.0528156i	$0.983180\pi$
$744$	1.21761	−	0.884646i	0.0446398	−	0.0324327i
$745$	−1.86127	−	1.35229i	−0.0681918	−	0.0495442i
$746$	0.557027	+	1.71435i	0.0203942	+	0.0627669i
$747$	6.63546			0.242779
$748$		0			0
$749$	1.16714			0.0426462
$750$	0.144202	+	0.443810i	0.00526553	+	0.0162056i
$751$	−0.903104	−	0.656143i	−0.0329547	−	0.0239430i	0.571186	−	0.820821i	$-0.306484\pi$
$751$	−0.903104	−	0.656143i	−0.0329547	−	0.0239430i	−0.604141	+	0.796878i	$0.706484\pi$
$752$	−20.1877	+	14.6673i	−0.736171	+	0.534860i
$753$	−0.805450	+	2.47892i	−0.0293522	+	0.0903369i
$754$	−2.33953	+	7.20035i	−0.0852008	+	0.262221i
$755$	−36.5352	+	26.5444i	−1.32965	+	0.966050i
$756$	−2.05633	−	1.49401i	−0.0747882	−	0.0543368i
$757$	−8.21284	−	25.2765i	−0.298501	−	0.918691i	−0.982023	−	0.188761i	$-0.939553\pi$
$757$	−8.21284	−	25.2765i	−0.298501	−	0.918691i	0.683522	−	0.729930i	$-0.260447\pi$
$758$	2.62885			0.0954840
$759$		0			0
$760$	−13.5277			−0.490701
$761$	−1.94682	−	5.99168i	−0.0705720	−	0.217198i	0.909550	−	0.415595i	$-0.136427\pi$
$761$	−1.94682	−	5.99168i	−0.0705720	−	0.217198i	−0.980122	+	0.198397i	$0.936427\pi$
$762$	−0.0115979	−	0.00842636i	−0.000420147	−	0.000305255i
$763$	−7.52575	+	5.46778i	−0.272451	+	0.197947i
$764$	−7.01926	+	21.6030i	−0.253948	+	0.781571i
$765$	3.27245	−	10.0716i	0.118316	−	0.364138i
$766$	2.30197	−	1.67248i	0.0831735	−	0.0604291i
$767$	11.9488	+	8.68130i	0.431445	+	0.313463i
$768$	−0.816743	−	2.51368i	−0.0294717	−	0.0907044i
$769$	−13.1916			−0.475700			−0.237850	−	0.971302i	$-0.576443\pi$
$769$	−13.1916			−0.475700			−0.237850	+	0.971302i	$0.576443\pi$
$770$		0			0
$771$	−5.03141			−0.181202
$772$	13.5171	+	41.6014i	0.486491	+	1.49727i
$773$	−37.0674	−	26.9310i	−1.33322	−	0.968641i	−0.999664	−	0.0259112i	$-0.991751\pi$
$773$	−37.0674	−	26.9310i	−1.33322	−	0.968641i	−0.333556	−	0.942730i	$-0.608249\pi$
$774$	−0.433433	+	0.314907i	−0.0155794	+	0.0113191i
$775$	2.91689	−	8.97726i	0.104778	−	0.322473i
$776$	−3.33383	+	10.2605i	−0.119678	+	0.368330i
$777$	0.706339	−	0.513185i	0.0253398	−	0.0184104i
$778$	−0.0802116	−	0.0582772i	−0.00287573	−	0.00208934i
$779$	−12.6561	−	38.9516i	−0.453454	−	1.39559i
$780$	5.47237			0.195942
$781$		0			0
$782$	−2.30326			−0.0823643
$783$	−2.62687	−	8.08467i	−0.0938766	−	0.288923i
$784$	−2.98979	−	2.17221i	−0.106778	−	0.0775790i
$785$	−24.7789	+	18.0029i	−0.884396	+	0.642551i
$786$	0.252834	−	0.778144i	0.00901830	−	0.0277555i
$787$	5.82433	−	17.9255i	0.207615	−	0.638973i	−0.791981	−	0.610546i	$-0.790950\pi$
$787$	5.82433	−	17.9255i	0.207615	−	0.638973i	0.999596	−	0.0284274i	$-0.00904994\pi$
$788$	−38.0003	+	27.6089i	−1.35371	+	0.983525i
$789$	−0.343522	−	0.249583i	−0.0122297	−	0.00888540i
$790$	−0.427897	−	1.31693i	−0.0152239	−	0.0468543i
$791$	−3.29733			−0.117240
$792$		0			0
$793$	−4.39217			−0.155970
$794$	−1.17540	−	3.61751i	−0.0417134	−	0.128381i
$795$	−2.91177	−	2.11552i	−0.103270	−	0.0750298i
$796$	29.5154	−	21.4442i	1.04615	−	0.760070i
$797$	−8.70234	+	26.7830i	−0.308253	+	0.948704i	0.670191	+	0.742189i	$0.266212\pi$
$797$	−8.70234	+	26.7830i	−0.308253	+	0.948704i	−0.978443	+	0.206515i	$0.933788\pi$
$798$	−0.0929560	+	0.286089i	−0.00329061	+	0.0101274i
$799$	−7.85271	+	5.70533i	−0.277809	+	0.201840i
$800$	2.60464	+	1.89238i	0.0920879	+	0.0669058i
$801$	−1.58329	−	4.87287i	−0.0559429	−	0.172174i
$802$	−8.33835			−0.294437
$803$		0			0
$804$	−0.703208			−0.0248002
$805$	5.46206	+	16.8105i	0.192512	+	0.592492i
$806$	−7.22568	−	5.24976i	−0.254514	−	0.184915i
$807$	1.27406	−	0.925662i	0.0448492	−	0.0325849i
$808$	1.01950	−	3.13771i	0.0358660	−	0.110384i
$809$	2.02268	−	6.22516i	0.0711135	−	0.218865i	−0.909183	−	0.416397i	$-0.863293\pi$
$809$	2.02268	−	6.22516i	0.0711135	−	0.218865i	0.980296	+	0.197532i	$0.0632927\pi$
$810$	−3.91401	+	2.84369i	−0.137524	+	0.0999172i
$811$	15.2133	+	11.0531i	0.534210	+	0.388127i	0.821930	−	0.569588i	$-0.192897\pi$
$811$	15.2133	+	11.0531i	0.534210	+	0.388127i	−0.287720	+	0.957715i	$0.592897\pi$
$812$	−3.92509	−	12.0802i	−0.137744	−	0.423931i
$813$	0.261006			0.00915387
$814$		0			0
$815$	−20.2116			−0.707980
$816$	−0.359735	−	1.10715i	−0.0125932	−	0.0387580i
$817$	−3.93889	−	2.86177i	−0.137804	−	0.100121i
$818$	−2.97827	+	2.16384i	−0.104133	+	0.0756568i
$819$	−4.68420	+	14.4165i	−0.163679	+	0.503753i
$820$	−10.1428	+	31.2163i	−0.354201	+	1.09012i
$821$	−9.37489	+	6.81125i	−0.327186	+	0.237714i	−0.739236	−	0.673447i	$-0.764813\pi$
$821$	−9.37489	+	6.81125i	−0.327186	+	0.237714i	0.412050	+	0.911161i	$0.364813\pi$
$822$	−0.373992	−	0.271721i	−0.0130445	−	0.00947737i
$823$	3.81524	+	11.7421i	0.132991	+	0.409304i	0.995272	−	0.0971256i	$-0.0309649\pi$
$823$	3.81524	+	11.7421i	0.132991	+	0.409304i	−0.862281	+	0.506430i	$0.830965\pi$
$824$	−1.02866			−0.0358349
$825$		0			0
$826$	0.650640			0.0226387
$827$	1.38927	+	4.27575i	0.0483098	+	0.148682i	0.972301	−	0.233730i	$-0.0750933\pi$
$827$	1.38927	+	4.27575i	0.0483098	+	0.148682i	−0.923992	+	0.382413i	$0.875093\pi$
$828$	−32.9653	−	23.9507i	−1.14562	−	0.832345i
$829$	16.0694	−	11.6751i	0.558113	−	0.405493i	−0.272655	−	0.962112i	$-0.587902\pi$
$829$	16.0694	−	11.6751i	0.558113	−	0.405493i	0.830768	+	0.556619i	$0.187902\pi$
$830$	−0.392117	+	1.20681i	−0.0136106	+	0.0418891i
$831$	0.700187	−	2.15495i	0.0242892	−	0.0747545i
$832$	−28.2406	+	20.5180i	−0.979066	+	0.711333i
$833$	−1.16298	−	0.844956i	−0.0402949	−	0.0292760i
$834$	−0.0739314	−	0.227537i	−0.00256003	−	0.00787898i
$835$	−32.5706			−1.12715
$836$		0			0
$837$	10.0284			0.346631
$838$	−0.388908	−	1.19694i	−0.0134346	−	0.0413474i
$839$	35.4777	+	25.7760i	1.22483	+	0.889888i	0.996491	−	0.0836954i	$-0.0266723\pi$
$839$	35.4777	+	25.7760i	1.22483	+	0.889888i	0.228334	+	0.973583i	$0.426672\pi$
$840$	0.395187	−	0.287120i	0.0136353	−	0.00990659i
$841$	4.16562	−	12.8205i	0.143642	−	0.442085i
$842$	−1.50232	+	4.62365i	−0.0517732	+	0.159342i
$843$	2.33146	−	1.69390i	0.0802997	−	0.0583411i
$844$	11.9294	+	8.66721i	0.410626	+	0.298338i
$845$	−10.3089	−	31.7276i	−0.354638	−	1.09146i
$846$	4.50894			0.155021
$847$		0			0
$848$	24.3232			0.835261
$849$	0.0203165	+	0.0625277i	0.000697260	+	0.00214595i
$850$	0.322967	+	0.234649i	0.0110777	+	0.00804840i
$851$	22.8310	−	16.5877i	0.782636	−	0.568619i
$852$	0.596581	−	1.83609i	0.0204385	−	0.0629033i
$853$	−12.0951	+	37.2250i	−0.414130	+	1.27456i	0.498897	+	0.866661i	$0.333738\pi$
$853$	−12.0951	+	37.2250i	−0.414130	+	1.27456i	−0.913027	+	0.407899i	$0.866262\pi$
$854$	−0.156535	+	0.113729i	−0.00535652	+	0.00389174i
$855$	−36.1670	−	26.2769i	−1.23689	−	0.898651i
$856$	−0.322171	−	0.991541i	−0.0110116	−	0.0338902i
$857$	−35.0524			−1.19737			−0.598684	−	0.800986i	$-0.704309\pi$
$857$	−35.0524			−1.19737			−0.598684	+	0.800986i	$0.704309\pi$
$858$		0			0
$859$	−32.5206			−1.10959			−0.554794	−	0.831988i	$-0.687203\pi$
$859$	−32.5206			−1.10959			−0.554794	+	0.831988i	$0.687203\pi$
$860$	1.20574	+	3.71089i	0.0411154	+	0.126540i
$861$	1.19646	+	0.869279i	0.0407752	+	0.0296249i
$862$	5.07278	−	3.68559i	0.172779	−	0.125532i
$863$	3.92265	−	12.0727i	0.133529	−	0.410959i	−0.861830	−	0.507198i	$-0.830681\pi$
$863$	3.92265	−	12.0727i	0.133529	−	0.410959i	0.995358	+	0.0962391i	$0.0306814\pi$
$864$	−1.05697	+	3.25303i	−0.0359590	+	0.110670i
$865$	−11.9362	+	8.67219i	−0.405844	+	0.294863i
$866$	1.69981	+	1.23498i	0.0577618	+	0.0419664i
$867$	1.01122	+	3.11221i	0.0343428	+	0.105696i
$868$	14.9844			0.508605
$869$		0			0
$870$	0.806251			0.0273345
$871$	2.61295	+	8.04183i	0.0885364	+	0.272487i
$872$	6.72253	+	4.88420i	0.227654	+	0.165400i
$873$	−28.8437	+	20.9561i	−0.976210	+	0.709258i
$874$	−3.00462	+	9.24726i	−0.101633	+	0.312793i
$875$	−2.90909	+	8.95326i	−0.0983452	+	0.302676i
$876$	−5.12978	+	3.72700i	−0.173319	+	0.125924i
$877$	−22.7609	−	16.5367i	−0.768580	−	0.558406i	0.132950	−	0.991123i	$-0.457555\pi$
$877$	−22.7609	−	16.5367i	−0.768580	−	0.558406i	−0.901530	+	0.432717i	$0.857555\pi$
$878$	−1.02840	−	3.16509i	−0.0347069	−	0.106817i
$879$	3.53765			0.119322
$880$		0			0
$881$	−36.7964			−1.23970			−0.619850	−	0.784720i	$-0.712807\pi$
$881$	−36.7964			−1.23970			−0.619850	+	0.784720i	$0.712807\pi$
$882$	0.206353	+	0.635089i	0.00694826	+	0.0213846i
$883$	1.84795	+	1.34262i	0.0621885	+	0.0451826i	0.618445	−	0.785828i	$-0.287763\pi$
$883$	1.84795	+	1.34262i	0.0621885	+	0.0451826i	−0.556257	+	0.831011i	$0.687763\pi$
$884$	−11.6382	+	8.45565i	−0.391435	+	0.284394i
$885$	0.486040	−	1.49588i	0.0163380	−	0.0502833i
$886$	−0.170805	+	0.525683i	−0.00573830	+	0.0176607i
$887$	34.1952	−	24.8443i	1.14816	−	0.834190i	0.159928	−	0.987129i	$-0.448874\pi$
$887$	34.1952	−	24.8443i	1.14816	−	0.834190i	0.988236	+	0.152939i	$0.0488738\pi$
$888$	−0.630951	−	0.458413i	−0.0211733	−	0.0153833i
$889$	−0.0893693	−	0.275050i	−0.00299735	−	0.00922489i
$890$	0.979808			0.0328432
$891$		0			0
$892$	−34.1520			−1.14349
$893$	12.6622	+	38.9702i	0.423724	+	1.30409i
$894$	0.0369712	+	0.0268612i	0.00123650	+	0.000898371i
$895$	8.75218	−	6.35883i	0.292553	−	0.212552i
$896$	−2.09601	+	6.45084i	−0.0700226	+	0.215508i
$897$	2.46283	−	7.57982i	0.0822316	−	0.253083i
$898$	0.872833	−	0.634151i	0.0291268	−	0.0211619i
$899$	40.5432	+	29.4564i	1.35219	+	0.982425i
$900$	2.18243	+	6.71683i	0.0727476	+	0.223894i
$901$	9.46132			0.315202
$902$		0			0
$903$	0.175807			0.00585050
$904$	0.910180	+	2.80125i	0.0302721	+	0.0931681i
$905$	21.8663	+	15.8868i	0.726862	+	0.528096i
$906$	0.725714	−	0.527262i	0.0241102	−	0.0175171i
$907$	12.2150	−	37.5939i	0.405592	−	1.24828i	−0.514807	−	0.857306i	$-0.672136\pi$
$907$	12.2150	−	37.5939i	0.405592	−	1.24828i	0.920400	−	0.390979i	$-0.127864\pi$
$908$	−15.4634	+	47.5914i	−0.513171	+	1.57938i
$909$	8.82055	−	6.40850i	0.292559	−	0.212557i
$910$	−2.34516	−	1.70386i	−0.0777414	−	0.0564824i
$911$	−10.8865	−	33.5053i	−0.360687	−	1.11008i	−0.952638	−	0.304106i	$-0.901642\pi$
$911$	−10.8865	−	33.5053i	−0.360687	−	1.11008i	0.591951	−	0.805974i	$-0.298358\pi$
$912$	−4.91433			−0.162730
$913$		0			0
$914$	7.03234			0.232609
$915$	0.144539	+	0.444845i	0.00477831	+	0.0147061i
$916$	−31.2755	−	22.7230i	−1.03337	−	0.750789i
$917$	13.3535	−	9.70190i	0.440972	−	0.320385i
$918$	−0.131061	+	0.403365i	−0.00432567	+	0.0133130i
$919$	12.2403	−	37.6718i	0.403770	−	1.24268i	−0.518147	−	0.855292i	$-0.673378\pi$
$919$	12.2403	−	37.6718i	0.403770	−	1.24268i	0.921918	−	0.387386i	$-0.126622\pi$
$920$	12.7736	−	9.28059i	0.421134	−	0.305972i
$921$	5.07686	+	3.68856i	0.167288	+	0.121542i
$922$	2.07763	+	6.39428i	0.0684230	+	0.210584i
$923$	−23.2141			−0.764101
$924$		0			0
$925$	−4.89131			−0.160825
$926$	1.77941	+	5.47645i	0.0584750	+	0.179967i
$927$	−2.75017	−	1.99811i	−0.0903273	−	0.0656267i
$928$	−13.8284	+	10.0469i	−0.453938	+	0.329805i
$929$	0.808565	−	2.48851i	0.0265281	−	0.0816452i	−0.936916	−	0.349555i	$-0.886333\pi$
$929$	0.808565	−	2.48851i	0.0265281	−	0.0816452i	0.963444	+	0.267910i	$0.0863328\pi$
$930$	−0.293918	+	0.904587i	−0.00963796	+	0.0296626i
$931$	−4.90950	+	3.56696i	−0.160902	+	0.116902i
$932$	31.8710	+	23.1556i	1.04397	+	0.758489i
$933$	2.15487	+	6.63201i	0.0705473	+	0.217122i
$934$	0.720463			0.0235743
$935$		0			0
$936$	13.5405			0.442586
$937$	−16.6375	−	51.2050i	−0.543523	−	1.67279i	−0.724475	−	0.689301i	$-0.757918\pi$
$937$	−16.6375	−	51.2050i	−0.543523	−	1.67279i	0.180952	−	0.983492i	$-0.442082\pi$
$938$	0.301357	+	0.218949i	0.00983966	+	0.00714893i
$939$	0.00606708	−	0.00440799i	0.000197992	−	0.000143849i
$940$	10.1476	−	31.2312i	0.330979	−	1.01865i
$941$	−9.16161	+	28.1965i	−0.298660	+	0.919181i	0.683307	+	0.730131i	$0.260541\pi$
$941$	−9.16161	+	28.1965i	−0.298660	+	0.919181i	−0.981967	+	0.189050i	$0.939459\pi$
$942$	0.492193	−	0.357599i	0.0160365	−	0.0116512i
$943$	38.6732	+	28.0977i	1.25937	+	0.914987i
$944$	3.28468	+	10.1092i	0.106907	+	0.329026i
$945$	3.25480			0.105879
$946$		0			0
$947$	−15.7861			−0.512980			−0.256490	−	0.966547i	$-0.582566\pi$
$947$	−15.7861			−0.512980			−0.256490	+	0.966547i	$0.582566\pi$
$948$	−0.323696	−	0.996235i	−0.0105132	−	0.0323562i
$949$	61.6827	+	44.8151i	2.00230	+	1.45476i
$950$	1.36340	−	0.990566i	0.0442344	−	0.0321382i
$951$	−1.51609	+	4.66606i	−0.0491627	+	0.151307i
$952$	−0.396808	+	1.22125i	−0.0128606	+	0.0395809i
$953$	−28.4061	+	20.6383i	−0.920165	+	0.668539i	−0.943565	−	0.331187i	$-0.892551\pi$
$953$	−28.4061	+	20.6383i	−0.920165	+	0.668539i	0.0233999	+	0.999726i	$0.492551\pi$
$954$	−3.55568	−	2.58335i	−0.115119	−	0.0836390i
$955$	−8.98833	−	27.6632i	−0.290856	−	0.895162i
$956$	33.3257			1.07783
$957$		0			0
$958$	0.731463			0.0236325
$959$	−2.88185	−	8.86944i	−0.0930599	−	0.286409i
$960$	3.00744	+	2.18503i	0.0970648	+	0.0705217i
$961$	−22.7495	+	16.5285i	−0.733856	+	0.533178i
$962$	−1.43018	+	4.40164i	−0.0461108	+	0.141915i
$963$	1.06468	−	3.27674i	0.0343087	−	0.105591i
$964$	38.0803	−	27.6670i	1.22648	−	0.891093i
$965$	−45.3155	−	32.9237i	−1.45876	−	1.05985i
$966$	−0.108495	−	0.333914i	−0.00349077	−	0.0107435i
$967$	49.2820			1.58480			0.792401	−	0.610001i	$-0.208831\pi$
$967$	49.2820			1.58480			0.792401	+	0.610001i	$0.208831\pi$
$968$		0			0
$969$	−1.91160			−0.0614093
$970$	−2.10687	−	6.48427i	−0.0676475	−	0.208198i
$971$	−30.2107	−	21.9493i	−0.969506	−	0.704388i	−0.0141673	−	0.999900i	$-0.504510\pi$
$971$	−30.2107	−	21.9493i	−0.969506	−	0.704388i	−0.955339	+	0.295512i	$0.904510\pi$
$972$	−9.12988	+	6.63325i	−0.292841	+	0.212761i
$973$	1.49147	−	4.59026i	0.0478142	−	0.147157i
$974$	−0.690011	+	2.12364i	−0.0221094	+	0.0680457i
$975$	−1.11755	+	0.811950i	−0.0357904	+	0.0260032i
$976$	−2.55730	−	1.85798i	−0.0818570	−	0.0594726i
$977$	12.3757	+	38.0884i	0.395932	+	1.21855i	0.928233	+	0.371999i	$0.121328\pi$
$977$	12.3757	+	38.0884i	0.395932	+	1.21855i	−0.532301	+	0.846555i	$0.678672\pi$
$978$	0.401470			0.0128376
$979$		0			0
$980$	4.86335			0.155354
$981$	8.48571	+	26.1163i	0.270928	+	0.833831i
$982$	−0.773396	−	0.561905i	−0.0246801	−	0.0179311i
$983$	42.1024	−	30.5892i	1.34286	−	0.975644i	0.343525	−	0.939144i	$-0.388379\pi$
$983$	42.1024	−	30.5892i	1.34286	−	0.975644i	0.999334	−	0.0365000i	$-0.0116209\pi$
$984$	0.408230	−	1.25640i	0.0130139	−	0.0400527i
$985$	18.5866	−	57.2037i	0.592219	−	1.82266i
$986$	−1.71467	+	1.24578i	−0.0546062	+	0.0396738i
$987$	−1.19703	−	0.869693i	−0.0381019	−	0.0276826i
$988$	18.7661	+	57.7562i	0.597031	+	1.83747i
$989$	5.68262			0.180697
$990$		0			0
$991$	45.4828			1.44481			0.722404	−	0.691471i	$-0.243037\pi$
$991$	45.4828			1.44481			0.722404	+	0.691471i	$0.243037\pi$
$992$	−6.23116	−	19.1775i	−0.197840	−	0.608888i
$993$	1.90712	+	1.38560i	0.0605206	+	0.0439708i
$994$	−0.827341	+	0.601098i	−0.0262417	+	0.0190657i
$995$	−14.4365	+	44.4310i	−0.457668	+	1.40856i
$996$	−0.296629	+	0.912932i	−0.00939907	+	0.0289273i
$997$	22.6196	−	16.4341i	0.716370	−	0.520473i	−0.168852	−	0.985641i	$-0.554006\pi$
$997$	22.6196	−	16.4341i	0.716370	−	0.520473i	0.885222	+	0.465168i	$0.154006\pi$
$998$	−3.73252	−	2.71183i	−0.118151	−	0.0858415i
$999$	−1.60583	−	4.94224i	−0.0508062	−	0.156365i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.v.148.3		16
11.2	odd	10		847.2.f.w.372.2		16
11.3	even	5		847.2.a.o.1.5		8
11.4	even	5		847.2.f.x.729.2		16
11.5	even	5		847.2.f.x.323.2		16
11.6	odd	10		77.2.f.b.15.3	✓	16
11.7	odd	10		77.2.f.b.36.3	yes	16
11.8	odd	10		847.2.a.p.1.4		8
11.9	even	5	inner	847.2.f.v.372.3		16
11.10	odd	2		847.2.f.w.148.2		16
33.8	even	10		7623.2.a.ct.1.5		8
33.14	odd	10		7623.2.a.cw.1.4		8
33.17	even	10		693.2.m.i.631.2		16
33.29	even	10		693.2.m.i.190.2		16
77.6	even	10		539.2.f.e.246.3		16
77.17	even	30		539.2.q.f.422.2		32
77.18	odd	30		539.2.q.g.520.3		32
77.39	odd	30		539.2.q.g.422.2		32
77.40	even	30		539.2.q.f.410.2		32
77.41	even	10		5929.2.a.bt.1.4		8
77.51	odd	30		539.2.q.g.410.2		32
77.61	even	30		539.2.q.f.312.3		32
77.62	even	10		539.2.f.e.344.3		16
77.69	odd	10		5929.2.a.bs.1.5		8
77.72	odd	30		539.2.q.g.312.3		32
77.73	even	30		539.2.q.f.520.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.15.3	✓	16	11.6	odd	10
77.2.f.b.36.3	yes	16	11.7	odd	10
539.2.f.e.246.3		16	77.6	even	10
539.2.f.e.344.3		16	77.62	even	10
539.2.q.f.312.3		32	77.61	even	30
539.2.q.f.410.2		32	77.40	even	30
539.2.q.f.422.2		32	77.17	even	30
539.2.q.f.520.3		32	77.73	even	30
539.2.q.g.312.3		32	77.72	odd	30
539.2.q.g.410.2		32	77.51	odd	30
539.2.q.g.422.2		32	77.39	odd	30
539.2.q.g.520.3		32	77.18	odd	30
693.2.m.i.190.2		16	33.29	even	10
693.2.m.i.631.2		16	33.17	even	10
847.2.a.o.1.5		8	11.3	even	5
847.2.a.p.1.4		8	11.8	odd	10
847.2.f.v.148.3		16	1.1	even	1	trivial
847.2.f.v.372.3		16	11.9	even	5	inner
847.2.f.w.148.2		16	11.10	odd	2
847.2.f.w.372.2		16	11.2	odd	10
847.2.f.x.323.2		16	11.5	even	5
847.2.f.x.729.2		16	11.4	even	5
5929.2.a.bs.1.5		8	77.69	odd	10
5929.2.a.bt.1.4		8	77.41	even	10
7623.2.a.ct.1.5		8	33.8	even	10
7623.2.a.cw.1.4		8	33.14	odd	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0699031 - 0.215140i) q^{2} +(0.177280 + 0.128801i) q^{3} +(1.57664 - 1.14549i) q^{4} +(-0.771159 + 2.37338i) q^{5} +(0.0153178 - 0.0471435i) q^{6} +(0.809017 - 0.587785i) q^{7} +(-0.722670 - 0.525051i) q^{8} +(-0.912213 - 2.80750i) q^{9} +0.564516 q^{10} +0.427046 q^{12} +(-1.58680 - 4.88366i) q^{13} +(-0.183009 - 0.132964i) q^{14} +(-0.442405 + 0.321426i) q^{15} +(1.14200 - 3.51471i) q^{16} +(0.444220 - 1.36717i) q^{17} +(-0.540239 + 0.392506i) q^{18} +(-4.90950 - 3.56696i) q^{19} +(1.50286 + 4.62532i) q^{20} +0.219130 q^{21} +7.08292 q^{23} +(-0.0604875 - 0.186161i) q^{24} +(-0.993180 - 0.721588i) q^{25} +(-0.939748 + 0.682767i) q^{26} +(0.403037 - 1.24042i) q^{27} +(0.602221 - 1.85345i) q^{28} +(5.27292 - 3.83100i) q^{29} +(0.100077 + 0.0727103i) q^{30} +(2.37602 + 7.31263i) q^{31} -2.62252 q^{32} -0.325184 q^{34} +(0.771159 + 2.37338i) q^{35} +(-4.65420 - 3.38147i) q^{36} +(3.22339 - 2.34193i) q^{37} +(-0.424206 + 1.30557i) q^{38} +(0.347714 - 1.07015i) q^{39} +(1.80344 - 1.31028i) q^{40} +(5.46006 + 3.96696i) q^{41} +(-0.0153178 - 0.0471435i) q^{42} +0.802299 q^{43} +7.36674 q^{45} +(-0.495119 - 1.52382i) q^{46} +(-5.46266 - 3.96885i) q^{47} +(0.655152 - 0.475996i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-0.0858158 + 0.264114i) q^{50} +(0.254844 - 0.185155i) q^{51} +(-8.09600 - 5.88209i) q^{52} +(2.03385 + 6.25954i) q^{53} -0.295037 q^{54} -0.893270 q^{56} +(-0.410925 - 1.26470i) q^{57} +(-1.19279 - 0.866616i) q^{58} +(-2.32694 + 1.69062i) q^{59} +(-0.329320 + 1.01354i) q^{60} +(0.264315 - 0.813478i) q^{61} +(1.40715 - 1.02235i) q^{62} +(-2.38820 - 1.73513i) q^{63} +(-2.10068 - 6.46522i) q^{64} +12.8145 q^{65} -1.64668 q^{67} +(-0.865708 - 2.66437i) q^{68} +(1.25566 + 0.912288i) q^{69} +(0.456703 - 0.331814i) q^{70} +(1.39700 - 4.29951i) q^{71} +(-0.814852 + 2.50786i) q^{72} +(-12.0122 + 8.72740i) q^{73} +(-0.729166 - 0.529770i) q^{74} +(-0.0831292 - 0.255845i) q^{75} -11.8264 q^{76} -0.254539 q^{78} +(-0.757990 - 2.33285i) q^{79} +(7.46110 + 5.42081i) q^{80} +(-6.93339 + 5.03741i) q^{81} +(0.471776 - 1.45198i) q^{82} +(-0.694608 + 2.13778i) q^{83} +(0.345487 - 0.251011i) q^{84} +(2.90225 + 2.10861i) q^{85} +(-0.0560832 - 0.172606i) q^{86} +1.42822 q^{87} +1.73566 q^{89} +(-0.514958 - 1.58488i) q^{90} +(-4.15429 - 3.01827i) q^{91} +(11.1672 - 8.11343i) q^{92} +(-0.520655 + 1.60241i) q^{93} +(-0.472001 + 1.45267i) q^{94} +(12.2518 - 8.90144i) q^{95} +(-0.464920 - 0.337784i) q^{96} +(-3.73217 - 11.4864i) q^{97} -0.226211 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} + 4 q^{7} - 5 q^{8} - 2 q^{9} - 12 q^{10} + 18 q^{12} - 13 q^{13} - 3 q^{14} + 7 q^{15} - 18 q^{16} - 10 q^{17} + 19 q^{18} + 6 q^{19} - 24 q^{20}+ \cdots - 2 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 + 2 * q^6 + 4 * q^7 - 5 * q^8 - 2 * q^9 - 12 * q^10 + 18 * q^12 - 13 * q^13 - 3 * q^14 + 7 * q^15 - 18 * q^16 - 10 * q^17 + 19 * q^18 + 6 * q^19 - 24 * q^20 - 8 * q^21 + 32 * q^23 - 45 * q^24 - 23 * q^25 + 33 * q^26 - 20 * q^27 + 11 * q^28 + 12 * q^29 - 38 * q^30 - 2 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 - 38 * q^36 - 11 * q^37 + 15 * q^38 + 24 * q^39 - 5 * q^40 - 20 * q^41 - 2 * q^42 + 8 * q^43 + 70 * q^45 - 38 * q^46 + 7 * q^47 + 39 * q^48 - 4 * q^49 + 58 * q^50 - 16 * q^51 - 8 * q^52 - 41 * q^53 - 60 * q^54 - 9 * q^57 - 5 * q^58 - 18 * q^59 + 25 * q^60 + 12 * q^61 + 61 * q^62 + 12 * q^63 - 3 * q^64 + 8 * q^65 - 38 * q^67 + 7 * q^68 - 30 * q^69 + 12 * q^70 + q^71 - 35 * q^72 - 60 * q^73 + 4 * q^74 + 4 * q^75 - 52 * q^76 - 58 * q^78 + 15 * q^79 + 83 * q^80 + 6 * q^81 - 6 * q^82 - 20 * q^83 + 17 * q^84 + 9 * q^85 + 48 * q^86 + 72 * q^87 + 74 * q^89 - 16 * q^90 - 7 * q^91 + 20 * q^92 - 53 * q^93 - 66 * q^94 + 53 * q^95 - 48 * q^96 - 35 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more