LMFDB - Embedded newform 950.2.u.h.199.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(99,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("950.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.u (of order $18$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			199.4
Character	$\chi$	$=$	950.199
Dual form			950.2.u.h.549.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 + 0.173648i) q^{2} +(1.43596 + 1.71131i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.71131 - 1.43596i) q^{6} +(-2.43877 - 1.40802i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.345659 + 1.96033i) q^{9} +O(q^{10})$	\(q+(-0.984808 + 0.173648i) q^{2} +(1.43596 + 1.71131i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.71131 - 1.43596i) q^{6} +(-2.43877 - 1.40802i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.345659 + 1.96033i) q^{9} +(3.20088 + 5.54408i) q^{11} +(1.93466 + 1.11698i) q^{12} +(3.07096 - 3.65983i) q^{13} +(2.64622 + 0.963145i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-6.82171 + 1.20285i) q^{17} -1.99057i q^{18} +(2.52636 + 3.55211i) q^{19} +(-1.09241 - 6.19536i) q^{21} +(-4.11497 - 4.90403i) q^{22} +(1.86031 + 5.11116i) q^{23} +(-2.09923 - 0.764059i) q^{24} +(-2.38879 + 4.13750i) q^{26} +(1.95291 - 1.12751i) q^{27} +(-2.77327 - 0.489002i) q^{28} +(-1.30757 + 7.41560i) q^{29} +(0.656622 - 1.13730i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(-4.89131 + 13.4388i) q^{33} +(6.50920 - 2.36916i) q^{34} +(0.345659 + 1.96033i) q^{36} +6.63035i q^{37} +(-3.10479 - 3.05945i) q^{38} +10.6729 q^{39} +(-1.76595 + 1.48181i) q^{41} +(2.15163 + 5.91154i) q^{42} +(-2.83936 + 7.80108i) q^{43} +(4.90403 + 4.11497i) q^{44} +(-2.71959 - 4.71047i) q^{46} +(7.59414 + 1.33905i) q^{47} +(2.20002 + 0.387923i) q^{48} +(0.465064 + 0.805515i) q^{49} +(-11.8542 - 9.94683i) q^{51} +(1.63403 - 4.48945i) q^{52} +(-1.19395 - 3.28035i) q^{53} +(-1.72745 + 1.44950i) q^{54} +2.81605 q^{56} +(-2.45102 + 9.42408i) q^{57} -7.53000i q^{58} +(-1.48065 - 8.39721i) q^{59} +(2.80676 - 1.02158i) q^{61} +(-0.449156 + 1.23405i) q^{62} +(3.60317 - 4.29409i) q^{63} +(0.500000 - 0.866025i) q^{64} +(2.48338 - 14.0840i) q^{66} +(-8.84725 - 1.56001i) q^{67} +(-5.99891 + 3.46347i) q^{68} +(-6.07546 + 10.5230i) q^{69} +(2.34030 + 0.851798i) q^{71} +(-0.680815 - 1.87052i) q^{72} +(-4.50807 - 5.37250i) q^{73} +(-1.15135 - 6.52962i) q^{74} +(3.58889 + 2.47383i) q^{76} -18.0276i q^{77} +(-10.5107 + 1.85333i) q^{78} +(2.36089 - 1.98102i) q^{79} +(10.3454 + 3.76542i) q^{81} +(1.48181 - 1.76595i) q^{82} +(0.320496 + 0.185039i) q^{83} +(-3.14547 - 5.44811i) q^{84} +(1.44158 - 8.17562i) q^{86} +(-14.5680 + 8.41085i) q^{87} +(-5.54408 - 3.20088i) q^{88} +(0.130434 + 0.109447i) q^{89} +(-12.6425 + 4.60150i) q^{91} +(3.49624 + 4.16666i) q^{92} +(2.88916 - 0.509437i) q^{93} -7.71129 q^{94} -2.23396 q^{96} +(14.4896 - 2.55490i) q^{97} +(-0.597875 - 0.712520i) q^{98} +(-11.9746 + 4.35841i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 12 q^{11} + 30 q^{14} + 30 q^{19} - 36 q^{21} - 18 q^{26} + 24 q^{29} + 18 q^{31} + 18 q^{34} - 132 q^{39} + 36 q^{41} - 6 q^{46} + 54 q^{49} - 6 q^{51} - 54 q^{54} - 12 q^{56} - 72 q^{59} + 24 q^{61} + 24 q^{64} + 96 q^{66} - 42 q^{69} - 78 q^{71} - 36 q^{74} + 12 q^{76} + 84 q^{79} - 72 q^{81} - 18 q^{84} - 78 q^{86} + 72 q^{89} + 24 q^{91} - 24 q^{94} + 12 q^{96} - 102 q^{99}+O(q^{100}) $ 48 * q - 12 * q^11 + 30 * q^14 + 30 * q^19 - 36 * q^21 - 18 * q^26 + 24 * q^29 + 18 * q^31 + 18 * q^34 - 132 * q^39 + 36 * q^41 - 6 * q^46 + 54 * q^49 - 6 * q^51 - 54 * q^54 - 12 * q^56 - 72 * q^59 + 24 * q^61 + 24 * q^64 + 96 * q^66 - 42 * q^69 - 78 * q^71 - 36 * q^74 + 12 * q^76 + 84 * q^79 - 72 * q^81 - 18 * q^84 - 78 * q^86 + 72 * q^89 + 24 * q^91 - 24 * q^94 + 12 * q^96 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$3$	1.43596	+	1.71131i	0.829052	+	0.988026i	0.999996	+	0.00274525i	$0.000873842\pi$
$3$	1.43596	+	1.71131i	0.829052	+	0.988026i	−0.170944	+	0.985281i	$0.554682\pi$
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$		0			0
$5$		0			0
$6$	−1.71131	−	1.43596i	−0.698640	−	0.586228i
$7$	−2.43877	−	1.40802i	−0.921768	−	0.532183i	−0.0375695	−	0.999294i	$-0.511962\pi$
$7$	−2.43877	−	1.40802i	−0.921768	−	0.532183i	−0.884199	+	0.467111i	$0.845295\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−0.345659	+	1.96033i	−0.115220	+	0.653443i
$10$		0			0
$11$	3.20088	+	5.54408i	0.965100	+	1.67160i	0.709346	+	0.704861i	$0.248991\pi$
$11$	3.20088	+	5.54408i	0.965100	+	1.67160i	0.255755	+	0.966742i	$0.417676\pi$
$12$	1.93466	+	1.11698i	0.558490	+	0.322444i
$13$	3.07096	−	3.65983i	0.851732	−	1.01505i	−0.147928	−	0.988998i	$-0.547261\pi$
$13$	3.07096	−	3.65983i	0.851732	−	1.01505i	0.999660	−	0.0260567i	$-0.00829505\pi$
$14$	2.64622	+	0.963145i	0.707232	+	0.257411i
$15$		0			0
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−6.82171	+	1.20285i	−1.65451	+	0.291734i	−0.921469	−	0.388452i	$-0.873010\pi$
$17$	−6.82171	+	1.20285i	−1.65451	+	0.291734i	−0.733039	+	0.680186i	$0.761899\pi$
$18$		−	1.99057i		−	0.469182i
$19$	2.52636	+	3.55211i	0.579586	+	0.814911i
$19$	2.52636	+	3.55211i	0.579586	+	0.814911i
$20$		0			0
$21$	−1.09241	−	6.19536i	−0.238383	−	1.35194i
$22$	−4.11497	−	4.90403i	−0.877314	−	1.04554i
$23$	1.86031	+	5.11116i	0.387902	+	1.06575i	0.967944	+	0.251165i	$0.0808137\pi$
$23$	1.86031	+	5.11116i	0.387902	+	1.06575i	−0.580043	+	0.814586i	$0.696964\pi$
$24$	−2.09923	−	0.764059i	−0.428504	−	0.155963i
$25$		0			0
$26$	−2.38879	+	4.13750i	−0.468479	+	0.811430i
$27$	1.95291	−	1.12751i	0.375838	−	0.216990i
$28$	−2.77327	−	0.489002i	−0.524098	−	0.0924126i
$29$	−1.30757	+	7.41560i	−0.242810	+	1.37704i	0.582715	+	0.812677i	$0.301991\pi$
$29$	−1.30757	+	7.41560i	−0.242810	+	1.37704i	−0.825525	+	0.564366i	$0.809121\pi$
$30$		0			0
$31$	0.656622	−	1.13730i	0.117933	−	0.204266i	−0.801016	−	0.598644i	$-0.795707\pi$
$31$	0.656622	−	1.13730i	0.117933	−	0.204266i	0.918948	+	0.394378i	$0.129040\pi$
$32$	−0.642788	+	0.766044i	−0.113630	+	0.135419i
$33$	−4.89131	+	13.4388i	−0.851468	+	2.33939i
$34$	6.50920	−	2.36916i	1.11632	−	0.406307i
$35$		0			0
$36$	0.345659	+	1.96033i	0.0576098	+	0.326721i
$37$			6.63035i			1.09002i	0.838429	+	0.545011i	$0.183475\pi$
$37$			6.63035i			1.09002i	−0.838429	+	0.545011i	$0.816525\pi$
$38$	−3.10479	−	3.05945i	−0.503664	−	0.496309i
$39$	10.6729			1.70903
$40$		0			0
$41$	−1.76595	+	1.48181i	−0.275796	+	0.231420i	−0.770185	−	0.637821i	$-0.779836\pi$
$41$	−1.76595	+	1.48181i	−0.275796	+	0.231420i	0.494389	+	0.869241i	$0.335392\pi$
$42$	2.15163	+	5.91154i	0.332003	+	0.912171i
$43$	−2.83936	+	7.80108i	−0.432999	+	1.18965i	0.510964	+	0.859602i	$0.329289\pi$
$43$	−2.83936	+	7.80108i	−0.432999	+	1.18965i	−0.943963	+	0.330052i	$0.892934\pi$
$44$	4.90403	+	4.11497i	0.739310	+	0.620354i
$45$		0			0
$46$	−2.71959	−	4.71047i	−0.400982	−	0.694521i
$47$	7.59414	+	1.33905i	1.10772	+	0.195321i	0.697443	−	0.716640i	$-0.254321\pi$
$47$	7.59414	+	1.33905i	1.10772	+	0.195321i	0.410276	+	0.911961i	$0.365432\pi$
$48$	2.20002	+	0.387923i	0.317545	+	0.0559918i
$49$	0.465064	+	0.805515i	0.0664378	+	0.115074i
$50$		0			0
$51$	−11.8542	−	9.94683i	−1.65992	−	1.39283i
$52$	1.63403	−	4.48945i	0.226599	−	0.622575i
$53$	−1.19395	−	3.28035i	−0.164002	−	0.450591i	0.830284	−	0.557340i	$-0.188178\pi$
$53$	−1.19395	−	3.28035i	−0.164002	−	0.450591i	−0.994286	+	0.106749i	$0.965956\pi$
$54$	−1.72745	+	1.44950i	−0.235076	+	0.197252i
$55$		0			0
$56$	2.81605			0.376310
$57$	−2.45102	+	9.42408i	−0.324646	+	1.24825i
$58$		−	7.53000i		−	0.988738i
$59$	−1.48065	−	8.39721i	−0.192765	−	1.09322i	−0.915566	−	0.402167i	$-0.868257\pi$
$59$	−1.48065	−	8.39721i	−0.192765	−	1.09322i	0.722801	−	0.691056i	$-0.242854\pi$
$60$		0			0
$61$	2.80676	−	1.02158i	0.359369	−	0.130800i	−0.156025	−	0.987753i	$-0.549868\pi$
$61$	2.80676	−	1.02158i	0.359369	−	0.130800i	0.515394	+	0.856954i	$0.327646\pi$
$62$	−0.449156	+	1.23405i	−0.0570429	+	0.156724i
$63$	3.60317	−	4.29409i	0.453957	−	0.541005i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$		0			0
$66$	2.48338	−	14.0840i	0.305684	−	1.73362i
$67$	−8.84725	−	1.56001i	−1.08086	−	0.190585i	−0.395266	−	0.918567i	$-0.629348\pi$
$67$	−8.84725	−	1.56001i	−1.08086	−	0.190585i	−0.685597	+	0.727981i	$0.740459\pi$
$68$	−5.99891	+	3.46347i	−0.727475	+	0.420008i
$69$	−6.07546	+	10.5230i	−0.731399	+	1.26682i
$70$		0			0
$71$	2.34030	+	0.851798i	0.277742	+	0.101090i	0.477136	−	0.878830i	$-0.341675\pi$
$71$	2.34030	+	0.851798i	0.277742	+	0.101090i	−0.199394	+	0.979919i	$0.563897\pi$
$72$	−0.680815	−	1.87052i	−0.0802348	−	0.220443i
$73$	−4.50807	−	5.37250i	−0.527629	−	0.628804i	0.434738	−	0.900557i	$-0.356841\pi$
$73$	−4.50807	−	5.37250i	−0.527629	−	0.628804i	−0.962367	+	0.271753i	$0.912397\pi$
$74$	−1.15135	−	6.52962i	−0.133841	−	0.759052i
$75$		0			0
$76$	3.58889	+	2.47383i	0.411674	+	0.283768i
$77$		−	18.0276i		−	2.05444i
$78$	−10.5107	+	1.85333i	−1.19011	+	0.209848i
$79$	2.36089	−	1.98102i	0.265621	−	0.222883i	−0.500243	−	0.865885i	$-0.666756\pi$
$79$	2.36089	−	1.98102i	0.265621	−	0.222883i	0.765864	+	0.643002i	$0.222312\pi$
$80$		0			0
$81$	10.3454	+	3.76542i	1.14949	+	0.418380i
$82$	1.48181	−	1.76595i	0.163639	−	0.195017i
$83$	0.320496	+	0.185039i	0.0351790	+	0.0203106i	0.517486	−	0.855691i	$-0.326868\pi$
$83$	0.320496	+	0.185039i	0.0351790	+	0.0203106i	−0.482307	+	0.876002i	$0.660201\pi$
$84$	−3.14547	−	5.44811i	−0.343199	−	0.594437i
$85$		0			0
$86$	1.44158	−	8.17562i	0.155450	−	0.881600i
$87$	−14.5680	+	8.41085i	−1.56186	+	0.901738i
$88$	−5.54408	−	3.20088i	−0.591001	−	0.341214i
$89$	0.130434	+	0.109447i	0.0138260	+	0.0116014i	0.649674	−	0.760213i	$-0.274905\pi$
$89$	0.130434	+	0.109447i	0.0138260	+	0.0116014i	−0.635848	+	0.771814i	$0.719350\pi$
$90$		0			0
$91$	−12.6425	+	4.60150i	−1.32529	+	0.482368i
$92$	3.49624	+	4.16666i	0.364508	+	0.434404i
$93$	2.88916	−	0.509437i	0.299592	−	0.0528262i
$94$	−7.71129			−0.795359
$95$		0			0
$96$	−2.23396			−0.228002
$97$	14.4896	−	2.55490i	1.47119	−	0.259411i	0.620141	−	0.784490i	$-0.287075\pi$
$97$	14.4896	−	2.55490i	1.47119	−	0.259411i	0.851053	+	0.525079i	$0.175964\pi$
$98$	−0.597875	−	0.712520i	−0.0603945	−	0.0719754i
$99$	−11.9746	+	4.35841i	−1.20349	+	0.438036i
$100$		0			0
$101$	0.227034	+	0.190505i	0.0225908	+	0.0189559i	0.654013	−	0.756483i	$-0.273084\pi$
$101$	0.227034	+	0.190505i	0.0225908	+	0.0189559i	−0.631422	+	0.775439i	$0.717529\pi$
$102$	13.4013	+	7.73726i	1.32693	+	0.766103i
$103$	0.294103	−	0.169800i	0.0289788	−	0.0167309i	−0.485441	−	0.874270i	$-0.661341\pi$
$103$	0.294103	−	0.169800i	0.0289788	−	0.0167309i	0.514419	+	0.857539i	$0.328007\pi$
$104$	−0.829617	+	4.70499i	−0.0813506	+	0.461362i
$105$		0			0
$106$	1.74544	+	3.02319i	0.169532	+	0.293638i
$107$	−1.30319	−	0.752397i	−0.125984	−	0.0727370i	0.435683	−	0.900100i	$-0.356507\pi$
$107$	−1.30319	−	0.752397i	−0.125984	−	0.0727370i	−0.561668	+	0.827363i	$0.689840\pi$
$108$	1.44950	−	1.72745i	0.139478	−	0.166224i
$109$	−1.74455	−	0.634964i	−0.167098	−	0.0608185i	0.257117	−	0.966380i	$-0.417227\pi$
$109$	−1.74455	−	0.634964i	−0.167098	−	0.0608185i	−0.424214	+	0.905562i	$0.639450\pi$
$110$		0			0
$111$	−11.3466	+	9.52092i	−1.07697	+	0.903685i
$112$	−2.77327	+	0.489002i	−0.262049	+	0.0462063i
$113$			12.1717i			1.14502i	0.819898	+	0.572509i	$0.194030\pi$
$113$			12.1717i			1.14502i	−0.819898	+	0.572509i	$0.805970\pi$
$114$	0.777312	−	9.70652i	0.0728019	−	0.909099i
$115$		0			0
$116$	1.30757	+	7.41560i	0.121405	+	0.688521i
$117$	6.11297	+	7.28515i	0.565144	+	0.673512i
$118$	2.91632	+	8.01252i	0.268469	+	0.737613i
$119$	18.3302	+	6.67166i	1.68033	+	0.611590i
$120$		0			0
$121$	−14.9912	+	25.9655i	−1.36284	+	2.36050i
$122$	−2.58673	+	1.49345i	−0.234191	+	0.135210i
$123$	−5.07168	−	0.894274i	−0.457298	−	0.0806339i
$124$	0.228042	−	1.29329i	0.0204788	−	0.116141i
$125$		0			0
$126$	−2.80277	+	4.85454i	−0.249691	+	0.432477i
$127$	3.15223	−	3.75668i	0.279715	−	0.333351i	−0.607835	−	0.794064i	$-0.707962\pi$
$127$	3.15223	−	3.75668i	0.279715	−	0.333351i	0.887549	+	0.460713i	$0.152406\pi$
$128$	−0.342020	+	0.939693i	−0.0302306	+	0.0830579i
$129$	−17.4273	+	6.34302i	−1.53439	+	0.558471i
$130$		0			0
$131$	−3.06811	−	17.4001i	−0.268062	−	1.52026i	−0.760172	−	0.649722i	$-0.774885\pi$
$131$	−3.06811	−	17.4001i	−0.268062	−	1.52026i	0.492109	−	0.870533i	$-0.336226\pi$
$132$			14.3012i			1.24476i
$133$	−1.15974	−	12.2200i	−0.100562	−	1.05961i
$134$	8.98373			0.776076
$135$		0			0
$136$	5.30635	−	4.45256i	0.455016	−	0.381804i
$137$	1.57120	+	4.31683i	0.134237	+	0.368812i	0.988539	−	0.150964i	$-0.0482377\pi$
$137$	1.57120	+	4.31683i	0.134237	+	0.368812i	−0.854303	+	0.519776i	$0.826015\pi$
$138$	4.15586	−	11.4181i	0.353770	−	0.971975i
$139$	−3.91995	−	3.28923i	−0.332486	−	0.278989i	0.461226	−	0.887283i	$-0.347410\pi$
$139$	−3.91995	−	3.28923i	−0.332486	−	0.278989i	−0.793712	+	0.608294i	$0.791854\pi$
$140$		0			0
$141$	8.61335	+	14.9188i	0.725375	+	1.25639i
$142$	−2.45265	−	0.432469i	−0.205822	−	0.0362920i
$143$	30.1202	+	5.31100i	2.51878	+	0.444128i
$144$	0.995285	+	1.72388i	0.0829404	+	0.143657i
$145$		0			0
$146$	5.37250	+	4.50807i	0.444632	+	0.373090i
$147$	−0.710673	+	1.95256i	−0.0586153	+	0.161044i
$148$	2.26771	+	6.23049i	0.186405	+	0.512143i
$149$	−1.80044	+	1.51075i	−0.147498	+	0.123766i	−0.713551	−	0.700603i	$-0.752914\pi$
$149$	−1.80044	+	1.51075i	−0.147498	+	0.123766i	0.566053	+	0.824369i	$0.308470\pi$
$150$		0			0
$151$	7.58643			0.617375			0.308687	−	0.951164i	$-0.400110\pi$
$151$	7.58643			0.617375			0.308687	+	0.951164i	$0.400110\pi$
$152$	−3.96395	−	1.81304i	−0.321519	−	0.147057i
$153$		−	13.7886i		−	1.11474i
$154$	3.13047	+	17.7538i	0.252260	+	1.43064i
$155$		0			0
$156$	10.0292	−	3.65035i	0.802982	−	0.292262i
$157$	8.17926	−	22.4723i	0.652776	−	1.79349i	0.0455435	−	0.998962i	$-0.485498\pi$
$157$	8.17926	−	22.4723i	0.652776	−	1.79349i	0.607232	−	0.794524i	$-0.292280\pi$
$158$	−1.98102	+	2.36089i	−0.157602	+	0.187823i
$159$	3.89924	−	6.75368i	0.309230	−	0.535602i
$160$		0			0
$161$	2.65977	−	15.0843i	0.209619	−	1.18881i
$162$	−10.8421	−	1.91175i	−0.851835	−	0.150201i
$163$	−5.07680	+	2.93109i	−0.397646	+	0.229581i	−0.685468	−	0.728103i	$-0.740402\pi$
$163$	−5.07680	+	2.93109i	−0.397646	+	0.229581i	0.287822	+	0.957684i	$0.407069\pi$
$164$	−1.15264	+	1.99644i	−0.0900064	+	0.155896i
$165$		0			0
$166$	−0.347759	−	0.126574i	−0.0269913	−	0.00982404i
$167$	8.03455	+	22.0747i	0.621732	+	1.70819i	0.702708	+	0.711478i	$0.251974\pi$
$167$	8.03455	+	22.0747i	0.621732	+	1.70819i	−0.0809763	+	0.996716i	$0.525804\pi$
$168$	4.04373	+	4.81914i	0.311981	+	0.371804i
$169$	−1.70613	−	9.67592i	−0.131240	−	0.744302i
$170$		0			0
$171$	−7.83657	+	3.72467i	−0.599277	+	0.284833i
$172$			8.30174i			0.633002i
$173$	18.1598	−	3.20206i	1.38066	−	0.243448i	0.566490	−	0.824069i	$-0.308301\pi$
$173$	18.1598	−	3.20206i	1.38066	−	0.243448i	0.814174	+	0.580620i	$0.197190\pi$
$174$	12.8862	−	10.8128i	0.976898	−	0.819715i
$175$		0			0
$176$	6.01568	+	2.18953i	0.453449	+	0.165042i
$177$	12.2441	−	14.5919i	0.920321	−	1.09680i
$178$	−0.147458	−	0.0851350i	−0.0110525	−	0.00638114i
$179$	−8.61253	−	14.9173i	−0.643731	−	1.11497i	−0.984593	−	0.174862i	$-0.944052\pi$
$179$	−8.61253	−	14.9173i	−0.643731	−	1.11497i	0.340862	−	0.940113i	$-0.389281\pi$
$180$		0			0
$181$	−1.25559	+	7.12080i	−0.0933272	+	0.529285i	0.901920	+	0.431903i	$0.142158\pi$
$181$	−1.25559	+	7.12080i	−0.0933272	+	0.529285i	−0.995247	+	0.0973815i	$0.968953\pi$
$182$	11.6514	−	6.72694i	0.863659	−	0.498634i
$183$	5.77864	+	3.33630i	0.427169	+	0.246626i
$184$	−4.16666	−	3.49624i	−0.307170	−	0.257746i
$185$		0			0
$186$	−2.75681	+	1.00340i	−0.202139	+	0.0735725i
$187$	−28.5042	−	33.9699i	−2.08443	−	2.48413i
$188$	7.59414	−	1.33905i	0.553860	−	0.0976604i
$189$	−6.35026			−0.461914
$190$		0			0
$191$	22.6036			1.63554			0.817769	−	0.575547i	$-0.195211\pi$
$191$	22.6036			1.63554			0.817769	+	0.575547i	$0.195211\pi$
$192$	2.20002	−	0.387923i	0.158773	−	0.0279959i
$193$	−10.0362	−	11.9607i	−0.722425	−	0.860952i	0.272439	−	0.962173i	$-0.412170\pi$
$193$	−10.0362	−	11.9607i	−0.722425	−	0.860952i	−0.994864	+	0.101221i	$0.967725\pi$
$194$	−13.8258	+	5.03218i	−0.992635	+	0.361289i
$195$		0			0
$196$	0.712520	+	0.597875i	0.0508943	+	0.0427054i
$197$	−13.5426	−	7.81884i	−0.964872	−	0.557069i	−0.0672029	−	0.997739i	$-0.521407\pi$
$197$	−13.5426	−	7.81884i	−0.964872	−	0.557069i	−0.897669	+	0.440670i	$0.854741\pi$
$198$	11.0359	−	6.37156i	0.784285	−	0.452807i
$199$	1.98627	−	11.2647i	0.140803	−	0.798534i	−0.829838	−	0.558004i	$-0.811568\pi$
$199$	1.98627	−	11.2647i	0.140803	−	0.798534i	0.970642	−	0.240530i	$-0.0773214\pi$
$200$		0			0
$201$	−10.0346	−	17.3805i	−0.707789	−	1.22593i
$202$	−0.256666	−	0.148186i	−0.0180590	−	0.0104263i
$203$	13.6302	−	16.2439i	0.956653	−	1.14010i
$204$	−14.5413	−	5.29260i	−1.01809	−	0.370556i
$205$		0			0
$206$	−0.260149	+	0.218291i	−0.0181255	+	0.0152091i
$207$	−10.6626	+	1.88010i	−0.741101	+	0.130676i
$208$		−	4.77757i		−	0.331265i
$209$	−11.6066	+	25.3762i	−0.802848	+	1.75531i
$210$		0			0
$211$	3.58376	+	20.3245i	0.246716	+	1.39920i	0.816472	+	0.577385i	$0.195927\pi$
$211$	3.58376	+	20.3245i	0.246716	+	1.39920i	−0.569756	+	0.821814i	$0.692962\pi$
$212$	−2.24389	−	2.67417i	−0.154111	−	0.183663i
$213$	1.90288	+	5.22812i	0.130383	+	0.358225i
$214$	1.41404	+	0.514670i	0.0966621	+	0.0351821i
$215$		0			0
$216$	−1.12751	+	1.95291i	−0.0767176	+	0.132879i
$217$	−3.20270	+	1.84908i	−0.217413	+	0.125524i
$218$	1.82831	+	0.322380i	0.123829	+	0.0218343i
$219$	2.72062	−	15.4294i	0.183843	−	1.04262i
$220$		0			0
$221$	−16.5470	+	28.6602i	−1.11307	+	1.92790i
$222$	9.52092	−	11.3466i	0.639002	−	0.761533i
$223$	3.87615	−	10.6496i	0.259566	−	0.713152i	−0.739628	−	0.673016i	$-0.764999\pi$
$223$	3.87615	−	10.6496i	0.259566	−	0.713152i	0.999194	−	0.0401361i	$-0.0127792\pi$
$224$	2.64622	−	0.963145i	0.176808	−	0.0643529i
$225$		0			0
$226$	−2.11360	−	11.9868i	−0.140594	−	0.797350i
$227$			13.4384i			0.891940i	0.895048	+	0.445970i	$0.147141\pi$
$227$			13.4384i			0.891940i	−0.895048	+	0.445970i	$0.852859\pi$
$228$	0.920017	+	9.69404i	0.0609296	+	0.642003i
$229$	−1.18399			−0.0782400			−0.0391200	−	0.999235i	$-0.512455\pi$
$229$	−1.18399			−0.0782400			−0.0391200	+	0.999235i	$0.512455\pi$
$230$		0			0
$231$	30.8509	−	25.8870i	2.02984	−	1.70324i
$232$	−2.57541	−	7.07589i	−0.169084	−	0.464555i
$233$	1.38074	−	3.79354i	0.0904551	−	0.248523i	−0.886213	−	0.463278i	$-0.846673\pi$
$233$	1.38074	−	3.79354i	0.0904551	−	0.248523i	0.976668	+	0.214755i	$0.0688953\pi$
$234$	−7.28515	−	6.11297i	−0.476245	−	0.399617i
$235$		0			0
$236$	−4.26337	−	7.38438i	−0.277522	−	0.480682i
$237$	6.78030	+	1.19555i	0.440428	+	0.0776593i
$238$	−19.2103	−	3.38729i	−1.24522	−	0.219565i
$239$	−8.34259	−	14.4498i	−0.539638	−	0.934680i	−0.998923	−	0.0463911i	$-0.985228\pi$
$239$	−8.34259	−	14.4498i	−0.539638	−	0.934680i	0.459286	−	0.888289i	$-0.348105\pi$
$240$		0			0
$241$	−9.67592	−	8.11906i	−0.623281	−	0.522995i	0.275552	−	0.961286i	$-0.411139\pi$
$241$	−9.67592	−	8.11906i	−0.623281	−	0.522995i	−0.898833	+	0.438292i	$0.855584\pi$
$242$	10.2546	−	28.1743i	0.659190	−	1.81111i
$243$	6.09799	+	16.7541i	0.391186	+	1.07478i
$244$	2.28809	−	1.91994i	0.146480	−	0.122911i
$245$		0			0
$246$	5.14992			0.328347
$247$	20.7585	+	1.66237i	1.32083	+	0.105774i
$248$			1.31324i			0.0833911i
$249$	0.143561	+	0.814177i	0.00909783	+	0.0515964i
$250$		0			0
$251$	16.3691	−	5.95787i	1.03321	−	0.376058i	0.230907	−	0.972976i	$-0.425831\pi$
$251$	16.3691	−	5.95787i	1.03321	−	0.376058i	0.802302	+	0.596918i	$0.203608\pi$
$252$	1.91721	−	5.26748i	0.120773	−	0.331820i
$253$	−22.3821	+	26.6739i	−1.40715	+	1.67697i
$254$	−2.45200	+	4.24698i	−0.153852	+	0.266479i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	7.38300	+	1.30182i	0.460539	+	0.0812054i	0.399104	−	0.916906i	$-0.369321\pi$
$257$	7.38300	+	1.30182i	0.460539	+	0.0812054i	0.0614349	+	0.998111i	$0.480432\pi$
$258$	16.0611	−	9.27287i	0.999919	−	0.577304i
$259$	9.33569	−	16.1699i	0.580091	−	1.00475i
$260$		0			0
$261$	−14.0850	−	5.12654i	−0.871842	−	0.317325i
$262$	6.04300	+	16.6030i	0.373338	+	1.02574i
$263$	5.61507	+	6.69179i	0.346240	+	0.412633i	0.910858	−	0.412719i	$-0.135421\pi$
$263$	5.61507	+	6.69179i	0.346240	+	0.412633i	−0.564618	+	0.825352i	$0.690976\pi$
$264$	−2.48338	−	14.0840i	−0.152842	−	0.866809i
$265$		0			0
$266$	3.26410	+	11.8329i	0.200135	+	0.725523i
$267$			0.380376i			0.0232786i
$268$	−8.84725	+	1.56001i	−0.540432	+	0.0952927i
$269$	8.10594	−	6.80169i	0.494228	−	0.414706i	−0.361311	−	0.932445i	$-0.617671\pi$
$269$	8.10594	−	6.80169i	0.494228	−	0.414706i	0.855539	+	0.517739i	$0.173226\pi$
$270$		0			0
$271$	−21.7285	−	7.90854i	−1.31991	−	0.480410i	−0.416484	−	0.909143i	$-0.636738\pi$
$271$	−21.7285	−	7.90854i	−1.31991	−	0.480410i	−0.903431	+	0.428734i	$0.858960\pi$
$272$	−4.45256	+	5.30635i	−0.269976	+	0.321745i
$273$	−26.0287	−	15.0277i	−1.57533	−	0.909517i
$274$	−2.29694	−	3.97841i	−0.138763	−	0.240345i
$275$		0			0
$276$	−2.10998	+	11.9663i	−0.127006	+	0.720288i
$277$	16.6749	−	9.62727i	1.00190	−	0.578446i	0.0930891	−	0.995658i	$-0.470326\pi$
$277$	16.6749	−	9.62727i	1.00190	−	0.578446i	0.908809	+	0.417211i	$0.136993\pi$
$278$	4.43156	+	2.55856i	0.265788	+	0.153452i
$279$	2.00252	+	1.68031i	0.119888	+	0.100598i
$280$		0			0
$281$	18.3170	−	6.66682i	1.09270	−	0.397709i	0.268078	−	0.963397i	$-0.413611\pi$
$281$	18.3170	−	6.66682i	1.09270	−	0.397709i	0.824620	+	0.565688i	$0.191389\pi$
$282$	−11.0731	−	13.1964i	−0.659394	−	0.785836i
$283$	1.77089	−	0.312256i	0.105269	−	0.0185617i	−0.120766	−	0.992681i	$-0.538535\pi$
$283$	1.77089	−	0.312256i	0.105269	−	0.0185617i	0.226034	+	0.974119i	$0.427424\pi$
$284$	2.49049			0.147783
$285$		0			0
$286$	−30.5848			−1.80852
$287$	6.39318	−	1.12729i	0.377377	−	0.0665418i
$288$	−1.27951	−	1.52486i	−0.0753960	−	0.0898535i
$289$	29.1141	−	10.5967i	1.71260	−	0.623334i
$290$		0			0
$291$	25.1787	+	21.1274i	1.47600	+	1.23851i
$292$	−6.07370	−	3.50665i	−0.355436	−	0.205211i
$293$	12.5225	−	7.22986i	0.731571	−	0.422373i	−0.0874253	−	0.996171i	$-0.527864\pi$
$293$	12.5225	−	7.22986i	0.731571	−	0.422373i	0.818997	+	0.573798i	$0.194531\pi$
$294$	0.360818	−	2.04630i	0.0210433	−	0.119343i
$295$		0			0
$296$	−3.31517	−	5.74205i	−0.192691	−	0.333750i
$297$	12.5020	+	7.21806i	0.725442	+	0.418834i
$298$	1.51075	−	1.80044i	0.0875155	−	0.104297i
$299$	24.4189	+	8.88777i	1.41218	+	0.513993i
$300$		0			0
$301$	17.9087	−	15.0272i	1.03224	−	0.866151i
$302$	−7.47118	+	1.31737i	−0.429918	+	0.0758061i
$303$			0.662084i			0.0380357i
$304$	4.21856	+	1.09717i	0.241951	+	0.0629268i
$305$		0			0
$306$	2.39436	+	13.5791i	0.136876	+	0.776265i
$307$	−9.72009	−	11.5840i	−0.554755	−	0.661131i	0.413673	−	0.910426i	$-0.364246\pi$
$307$	−9.72009	−	11.5840i	−0.554755	−	0.661131i	−0.968428	+	0.249294i	$0.919801\pi$
$308$	−6.16582	−	16.9404i	−0.351330	−	0.965271i
$309$	0.712902	+	0.259475i	0.0405556	+	0.0147610i
$310$		0			0
$311$	11.3930	−	19.7332i	0.646035	−	1.11897i	−0.338026	−	0.941137i	$-0.609759\pi$
$311$	11.3930	−	19.7332i	0.646035	−	1.11897i	0.984061	−	0.177829i	$-0.0569074\pi$
$312$	−9.24300	+	5.33645i	−0.523282	+	0.302117i
$313$	5.39852	+	0.951904i	0.305142	+	0.0538048i	0.324123	−	0.946015i	$-0.394931\pi$
$313$	5.39852	+	0.951904i	0.305142	+	0.0538048i	−0.0189805	+	0.999820i	$0.506042\pi$
$314$	−4.15272	+	23.5512i	−0.234351	+	1.32907i
$315$		0			0
$316$	1.54096	−	2.66903i	0.0866860	−	0.150144i
$317$	−9.35347	+	11.1470i	−0.525343	+	0.626080i	−0.961836	−	0.273628i	$-0.911776\pi$
$317$	−9.35347	+	11.1470i	−0.525343	+	0.626080i	0.436492	+	0.899708i	$0.356221\pi$
$318$	−2.66724	+	7.32817i	−0.149571	+	0.410943i
$319$	−45.2981	+	16.4871i	−2.53620	+	0.923103i
$320$		0			0
$321$	−0.583744	−	3.31058i	−0.0325814	−	0.184778i
$322$			15.3170i			0.853584i
$323$	−21.5068	−	21.1927i	−1.19667	−	1.17919i
$324$	11.0093			0.611630
$325$		0			0
$326$	4.49070	−	3.76814i	0.248717	−	0.208698i
$327$	−1.41848	−	3.89725i	−0.0784423	−	0.215518i
$328$	0.788455	−	2.16626i	0.0435351	−	0.119612i
$329$	−16.6349	−	13.9584i	−0.917114	−	0.769550i
$330$		0			0
$331$	−4.40390	−	7.62778i	−0.242060	−	0.419261i	0.719241	−	0.694761i	$-0.244490\pi$
$331$	−4.40390	−	7.62778i	−0.242060	−	0.419261i	−0.961301	+	0.275500i	$0.911157\pi$
$332$	0.364455	+	0.0642632i	0.0200021	+	0.00352690i
$333$	−12.9977	−	2.29184i	−0.712267	−	0.125592i
$334$	−11.7457	−	20.3442i	−0.642697	−	1.11318i
$335$		0			0
$336$	−4.81914	−	4.04373i	−0.262905	−	0.220604i
$337$	−1.30049	+	3.57308i	−0.0708425	+	0.194638i	−0.970061	−	0.242862i	$-0.921914\pi$
$337$	−1.30049	+	3.57308i	−0.0708425	+	0.194638i	0.899218	+	0.437500i	$0.144136\pi$
$338$	3.36041	+	9.23266i	0.182782	+	0.502190i
$339$	−20.8296	+	17.4781i	−1.13131	+	0.949280i
$340$		0			0
$341$	8.40706			0.455268
$342$	7.07073	−	5.02889i	0.382341	−	0.271931i
$343$			17.0931i			0.922938i
$344$	−1.44158	−	8.17562i	−0.0777249	−	0.440800i
$345$		0			0
$346$	−17.3279	+	6.30683i	−0.931553	+	0.339057i
$347$	2.37542	−	6.52641i	0.127519	−	0.350356i	−0.859460	−	0.511203i	$-0.829200\pi$
$347$	2.37542	−	6.52641i	0.127519	−	0.350356i	0.986979	+	0.160846i	$0.0514224\pi$
$348$	−10.8128	+	12.8862i	−0.579626	+	0.690772i
$349$	7.35609	−	12.7411i	0.393762	−	0.682017i	−0.599180	−	0.800614i	$-0.704507\pi$
$349$	7.35609	−	12.7411i	0.393762	−	0.682017i	0.992942	+	0.118598i	$0.0378399\pi$
$350$		0			0
$351$	1.87081	−	10.6099i	0.0998563	−	0.566313i
$352$	−6.30449	−	1.11165i	−0.336031	−	0.0592513i
$353$	−12.4310	+	7.17704i	−0.661635	+	0.381995i	−0.792900	−	0.609352i	$-0.791430\pi$
$353$	−12.4310	+	7.17704i	−0.661635	+	0.381995i	0.131265	+	0.991347i	$0.458096\pi$
$354$	−9.52420	+	16.4964i	−0.506206	+	0.876774i
$355$		0			0
$356$	0.160002	+	0.0582358i	0.00848006	+	0.00308649i
$357$	14.9042	+	40.9490i	0.788814	+	2.16725i
$358$	11.0721	+	13.1952i	0.585177	+	0.697386i
$359$	−2.99298	−	16.9740i	−0.157963	−	0.895854i	−0.956026	−	0.293280i	$-0.905253\pi$
$359$	−2.99298	−	16.9740i	−0.157963	−	0.895854i	0.798063	−	0.602574i	$-0.205858\pi$
$360$		0			0
$361$	−6.23503	+	17.9478i	−0.328160	+	0.944622i
$362$		−	7.23065i		−	0.380034i
$363$	−65.9619	+	11.6309i	−3.46210	+	0.610462i
$364$	−10.3063	+	8.64798i	−0.540195	+	0.453277i
$365$		0			0
$366$	−6.27019	−	2.28216i	−0.327748	−	0.119291i
$367$	13.9006	−	16.5661i	0.725607	−	0.864745i	−0.269555	−	0.962985i	$-0.586877\pi$
$367$	13.9006	−	16.5661i	0.725607	−	0.864745i	0.995163	+	0.0982396i	$0.0313212\pi$
$368$	4.71047	+	2.71959i	0.245550	+	0.141769i
$369$	−2.29442	−	3.97405i	−0.119443	−	0.206881i
$370$		0			0
$371$	−1.70705	+	9.68114i	−0.0886254	+	0.502620i
$372$	2.54069	−	1.46687i	0.131728	−	0.0760535i
$373$	10.4203	+	6.01614i	0.539541	+	0.311504i	0.744893	−	0.667184i	$-0.232501\pi$
$373$	10.4203	+	6.01614i	0.539541	+	0.311504i	−0.205352	+	0.978688i	$0.565834\pi$
$374$	33.9699	+	28.5042i	1.75654	+	1.47391i
$375$		0			0
$376$	−7.24625	+	2.63742i	−0.373697	+	0.136014i
$377$	23.1244	+	27.5585i	1.19097	+	1.41934i
$378$	6.25379	−	1.10271i	0.321660	−	0.0567174i
$379$	29.1137			1.49547			0.747736	−	0.663996i	$-0.231141\pi$
$379$	29.1137			1.49547			0.747736	+	0.663996i	$0.231141\pi$
$380$		0			0
$381$	10.9553			0.561258
$382$	−22.2602	+	3.92507i	−1.13893	+	0.200824i
$383$	4.31574	+	5.14330i	0.220524	+	0.262810i	0.864952	−	0.501855i	$-0.167349\pi$
$383$	4.31574	+	5.14330i	0.220524	+	0.262810i	−0.644428	+	0.764665i	$0.722904\pi$
$384$	−2.09923	+	0.764059i	−0.107126	+	0.0389907i
$385$		0			0
$386$	11.9607	+	10.0362i	0.608785	+	0.510831i
$387$	−14.3112	−	8.26259i	−0.727481	−	0.420011i
$388$	12.7419	−	7.35655i	0.646873	−	0.373472i
$389$	−1.78415	+	10.1184i	−0.0904600	+	0.513024i	0.905584	+	0.424166i	$0.139433\pi$
$389$	−1.78415	+	10.1184i	−0.0904600	+	0.513024i	−0.996044	+	0.0888579i	$0.971678\pi$
$390$		0			0
$391$	−18.8385	−	32.6292i	−0.952703	−	1.65013i
$392$	−0.805515	−	0.465064i	−0.0406847	−	0.0234893i
$393$	25.3713	−	30.2364i	1.27981	−	1.52522i
$394$	14.6946	+	5.34840i	0.740304	+	0.269448i
$395$		0			0
$396$	−9.76180	+	8.19112i	−0.490549	+	0.411619i
$397$	−20.6710	+	3.64486i	−1.03745	+	0.182930i	−0.666331	−	0.745656i	$-0.732136\pi$
$397$	−20.6710	+	3.64486i	−1.03745	+	0.182930i	−0.371117	+	0.928586i	$0.621025\pi$
$398$			11.4385i			0.573359i
$399$	19.2468	−	19.5321i	0.963546	−	0.977826i
$400$		0			0
$401$	4.02973	+	22.8537i	0.201235	+	1.14126i	0.903255	+	0.429104i	$0.141171\pi$
$401$	4.02973	+	22.8537i	0.201235	+	1.14126i	−0.702020	+	0.712157i	$0.747718\pi$
$402$	12.9003	+	15.3740i	0.643408	+	0.766783i
$403$	−2.14587	−	5.89574i	−0.106894	−	0.293688i
$404$	0.278499	+	0.101365i	0.0138558	+	0.00504312i
$405$		0			0
$406$	−10.6024	+	18.3639i	−0.526189	+	0.911387i
$407$	−36.7592	+	21.2229i	−1.82208	+	1.05198i
$408$	15.2394	+	2.68712i	0.754464	+	0.133032i
$409$	3.03460	−	17.2100i	0.150051	−	0.850982i	−0.813121	−	0.582095i	$-0.802233\pi$
$409$	3.03460	−	17.2100i	0.150051	−	0.850982i	0.963172	−	0.268887i	$-0.0866558\pi$
$410$		0			0
$411$	−5.13127	+	8.88761i	−0.253107	+	0.438394i
$412$	0.218291	−	0.260149i	0.0107544	−	0.0128166i
$413$	−8.21250	+	22.5637i	−0.404111	+	1.11028i
$414$	10.1741	−	3.70308i	0.500031	−	0.181996i
$415$		0			0
$416$	0.829617	+	4.70499i	0.0406753	+	0.230681i
$417$		−	11.4315i		−	0.559801i
$418$	7.02378	−	27.0062i	0.343544	−	1.32091i
$419$	−6.91207			−0.337677			−0.168838	−	0.985644i	$-0.554002\pi$
$419$	−6.91207			−0.337677			−0.168838	+	0.985644i	$0.554002\pi$
$420$		0			0
$421$	8.92365	−	7.48783i	0.434912	−	0.364934i	−0.398889	−	0.916999i	$-0.630604\pi$
$421$	8.92365	−	7.48783i	0.434912	−	0.364934i	0.833801	+	0.552065i	$0.186160\pi$
$422$	−7.05864	−	19.3934i	−0.343609	−	0.944058i
$423$	−5.24996	+	14.4242i	−0.255262	+	0.701326i
$424$	2.67417	+	2.24389i	0.129869	+	0.108973i
$425$		0			0
$426$	−2.78183	−	4.81826i	−0.134780	−	0.233446i
$427$	−8.28345	−	1.46060i	−0.400864	−	0.0706832i
$428$	−1.48193	−	0.261305i	−0.0716320	−	0.0126306i
$429$	34.1626	+	59.1714i	1.64939	+	2.85682i
$430$		0			0
$431$	−20.4624	−	17.1700i	−0.985640	−	0.827050i	−0.000709419	−	1.00000i	$-0.500226\pi$
$431$	−20.4624	−	17.1700i	−0.985640	−	0.827050i	−0.984931	+	0.172949i	$0.944670\pi$
$432$	0.771264	−	2.11903i	0.0371075	−	0.101952i
$433$	−1.17551	−	3.22969i	−0.0564914	−	0.155209i	0.908237	−	0.418456i	$-0.137429\pi$
$433$	−1.17551	−	3.22969i	−0.0564914	−	0.155209i	−0.964728	+	0.263247i	$0.915206\pi$
$434$	2.83295	−	2.37713i	0.135986	−	0.114106i
$435$		0			0
$436$	−1.85651			−0.0889108
$437$	−13.4556	+	19.5207i	−0.643670	+	0.933800i
$438$			15.6674i			0.748619i
$439$	1.85479	+	10.5190i	0.0885241	+	0.502045i	0.996540	+	0.0831103i	$0.0264854\pi$
$439$	1.85479	+	10.5190i	0.0885241	+	0.502045i	−0.908016	+	0.418935i	$0.862404\pi$
$440$		0			0
$441$	−1.73983	+	0.633245i	−0.0828489	+	0.0301545i
$442$	11.3188	−	31.0982i	0.538381	−	1.47919i
$443$	25.6112	−	30.5222i	1.21682	−	1.45015i	0.361252	−	0.932468i	$-0.382349\pi$
$443$	25.6112	−	30.5222i	1.21682	−	1.45015i	0.855571	−	0.517686i	$-0.173206\pi$
$444$	−7.40596	+	12.8275i	−0.351471	+	0.608766i
$445$		0			0
$446$	−1.96797	+	11.1609i	−0.0931862	+	0.528485i
$447$	−5.17073	−	0.911740i	−0.244567	−	0.0431238i
$448$	−2.43877	+	1.40802i	−0.115221	+	0.0665229i
$449$	−1.13752	+	1.97023i	−0.0536827	+	0.0929811i	−0.891618	−	0.452788i	$-0.850429\pi$
$449$	−1.13752	+	1.97023i	−0.0536827	+	0.0929811i	0.837935	+	0.545770i	$0.183763\pi$
$450$		0			0
$451$	−13.8679	−	5.04749i	−0.653012	−	0.237677i
$452$	4.16297	+	11.4377i	0.195810	+	0.537983i
$453$	10.8938	+	12.9827i	0.511836	+	0.609983i
$454$	−2.33356	−	13.2343i	−0.109519	−	0.621115i
$455$		0			0
$456$	−2.58939	−	9.38700i	−0.121259	−	0.439587i
$457$			15.7375i			0.736171i	0.929792	+	0.368086i	$0.119987\pi$
$457$			15.7375i			0.736171i	−0.929792	+	0.368086i	$0.880013\pi$
$458$	1.16600	−	0.205597i	0.0544836	−	0.00960692i
$459$	−11.9660	+	10.0406i	−0.558523	+	0.468657i
$460$		0			0
$461$	−30.4211	−	11.0724i	−1.41685	−	0.515692i	−0.483719	−	0.875223i	$-0.660714\pi$
$461$	−30.4211	−	11.0724i	−1.41685	−	0.515692i	−0.933133	+	0.359532i	$0.882936\pi$
$462$	−25.8870	+	30.8509i	−1.20437	+	1.43531i
$463$	−2.19285	−	1.26604i	−0.101910	−	0.0588379i	0.448179	−	0.893944i	$-0.352073\pi$
$463$	−2.19285	−	1.26604i	−0.101910	−	0.0588379i	−0.550089	+	0.835106i	$0.685406\pi$
$464$	3.76500	+	6.52117i	0.174786	+	0.302738i
$465$		0			0
$466$	−0.701018	+	3.97567i	−0.0324741	+	0.184170i
$467$	2.24679	−	1.29719i	0.103969	−	0.0600266i	−0.447114	−	0.894477i	$-0.647548\pi$
$467$	2.24679	−	1.29719i	0.103969	−	0.0600266i	0.551083	+	0.834450i	$0.314215\pi$
$468$	8.23598	+	4.75504i	0.380708	+	0.219802i
$469$	19.3799	+	16.2616i	0.894879	+	0.750893i
$470$		0			0
$471$	50.2022	−	18.2721i	2.31320	−	0.841935i
$472$	5.48089	+	6.53187i	0.252278	+	0.300654i
$473$	−52.3383	+	9.22865i	−2.40652	+	0.424334i
$474$	−6.88489			−0.316234
$475$		0			0
$476$	19.5066			0.894085
$477$	6.84327	−	1.20665i	0.313332	−	0.0552488i
$478$	10.7250	+	12.7816i	0.490552	+	0.584617i
$479$	−26.4897	+	9.64146i	−1.21034	+	0.440529i	−0.866823	−	0.498616i	$-0.833842\pi$
$479$	−26.4897	+	9.64146i	−1.21034	+	0.440529i	−0.343521	+	0.939145i	$0.611620\pi$
$480$		0			0
$481$	24.2660	+	20.3616i	1.10643	+	0.928407i
$482$	10.9388	+	6.31551i	0.498248	+	0.287663i
$483$	29.6333	−	17.1088i	1.34836	−	0.778477i
$484$	−5.20639	+	29.5269i	−0.236654	+	1.34213i
$485$		0			0
$486$	−8.91467	−	15.4407i	−0.404377	−	0.700402i
$487$	6.99226	+	4.03698i	0.316850	+	0.182933i	0.649987	−	0.759945i	$-0.274774\pi$
$487$	6.99226	+	4.03698i	0.316850	+	0.182933i	−0.333138	+	0.942878i	$0.608107\pi$
$488$	−1.91994	+	2.28809i	−0.0869115	+	0.103577i
$489$	−12.3061	−	4.47906i	−0.556501	−	0.202550i
$490$		0			0
$491$	−25.4647	+	21.3674i	−1.14921	+	0.964298i	−0.999701	−	0.0244628i	$-0.992212\pi$
$491$	−25.4647	+	21.3674i	−1.14921	+	0.964298i	−0.149505	+	0.988761i	$0.547768\pi$
$492$	−5.07168	+	0.894274i	−0.228649	+	0.0403170i
$493$		−	52.1599i		−	2.34917i
$494$	−20.7318	+	1.96756i	−0.932768	+	0.0885247i
$495$		0			0
$496$	−0.228042	−	1.29329i	−0.0102394	−	0.0580706i
$497$	−4.50809	−	5.37253i	−0.202215	−	0.240991i
$498$	−0.282761	−	0.776879i	−0.0126708	−	0.0348128i
$499$	12.2072	+	4.44307i	0.546471	+	0.198899i	0.600478	−	0.799641i	$-0.294977\pi$
$499$	12.2072	+	4.44307i	0.546471	+	0.198899i	−0.0540066	+	0.998541i	$0.517199\pi$
$500$		0			0
$501$	−26.2394	+	45.4481i	−1.17229	+	2.03047i
$502$	−15.0859	+	8.70983i	−0.673315	+	0.388739i
$503$	0.828779	+	0.146136i	0.0369534	+	0.00651588i	0.192094	−	0.981376i	$-0.438472\pi$
$503$	0.828779	+	0.146136i	0.0369534	+	0.00651588i	−0.155141	+	0.987892i	$0.549583\pi$
$504$	−0.973392	+	5.52038i	−0.0433583	+	0.245897i
$505$		0			0
$506$	17.4102	−	30.1553i	0.773976	−	1.34057i
$507$	14.1086	−	16.8140i	0.626584	−	0.746734i
$508$	1.67726	−	4.60825i	0.0744166	−	0.204458i
$509$	−24.0450	+	8.75166i	−1.06578	+	0.387911i	−0.814595	−	0.580030i	$-0.803041\pi$
$509$	−24.0450	+	8.75166i	−1.06578	+	0.387911i	−0.251180	+	0.967940i	$0.580819\pi$
$510$		0			0
$511$	3.42952	+	19.4498i	0.151713	+	0.860407i
$512$			1.00000i			0.0441942i
$513$	8.93881	+	4.08846i	0.394658	+	0.180510i
$514$	−7.49690			−0.330674
$515$		0			0
$516$	−14.2069	+	11.9210i	−0.625422	+	0.524792i
$517$	16.8841	+	46.3887i	0.742561	+	2.04017i
$518$	−6.38599	+	17.5454i	−0.280584	+	0.770899i
$519$	31.5565	+	26.4790i	1.38518	+	1.16230i
$520$		0			0
$521$	−8.51397	−	14.7466i	−0.373004	−	0.646062i	0.617022	−	0.786946i	$-0.288339\pi$
$521$	−8.51397	−	14.7466i	−0.373004	−	0.646062i	−0.990026	+	0.140884i	$0.955006\pi$
$522$	14.7613	+	2.60281i	0.646083	+	0.113922i
$523$	1.23763	+	0.218228i	0.0541178	+	0.00954243i	0.200642	−	0.979665i	$-0.435697\pi$
$523$	1.23763	+	0.218228i	0.0541178	+	0.00954243i	−0.146524	+	0.989207i	$0.546808\pi$
$524$	−8.83427	−	15.3014i	−0.385927	−	0.668445i
$525$		0			0
$526$	−6.69179	−	5.61507i	−0.291776	−	0.244829i
$527$	−3.11128	+	8.54817i	−0.135529	+	0.372364i
$528$	4.89131	+	13.4388i	0.212867	+	0.584848i
$529$	−5.04421	+	4.23259i	−0.219313	+	0.184026i
$530$		0			0
$531$	16.9731			0.736569
$532$	−5.26927	−	11.0864i	−0.228452	−	0.480654i
$533$			11.0137i			0.477055i
$534$	−0.0660516	−	0.374597i	−0.00285833	−	0.0162104i
$535$		0			0
$536$	8.44195	−	3.07262i	0.364637	−	0.132717i
$537$	13.1610	−	36.1595i	0.567938	−	1.56040i
$538$	−6.80169	+	8.10594i	−0.293242	+	0.349472i
$539$	−2.97723	+	5.15671i	−0.128238	+	0.222115i
$540$		0			0
$541$	−4.43718	+	25.1645i	−0.190769	+	1.08191i	0.727547	+	0.686058i	$0.240660\pi$
$541$	−4.43718	+	25.1645i	−0.190769	+	1.08191i	−0.918316	+	0.395848i	$0.870451\pi$
$542$	22.7717	+	4.01527i	0.978130	+	0.172471i
$543$	−13.9889	+	8.07648i	−0.600320	+	0.346595i
$544$	3.46347	−	5.99891i	0.148495	−	0.257201i
$545$		0			0
$546$	28.2428	+	10.2795i	1.20868	+	0.439924i
$547$	−0.0777074	−	0.213499i	−0.00332253	−	0.00912857i	0.938020	−	0.346580i	$-0.112657\pi$
$547$	−0.0777074	−	0.213499i	−0.00332253	−	0.00912857i	−0.941343	+	0.337452i	$0.890435\pi$
$548$	2.95289	+	3.51911i	0.126141	+	0.150329i
$549$	1.03245	+	5.85529i	0.0440637	+	0.249898i
$550$		0			0
$551$	−29.6445	+	14.0898i	−1.26290	+	0.600247i
$552$		−	12.1509i		−	0.517177i
$553$	−8.54700	+	1.50707i	−0.363456	+	0.0640870i
$554$	−14.7498	+	12.3766i	−0.626660	+	0.525830i
$555$		0			0
$556$	−4.80853	−	1.75016i	−0.203927	−	0.0742234i
$557$	−14.8253	+	17.6681i	−0.628167	+	0.748620i	−0.982452	−	0.186518i	$-0.940280\pi$
$557$	−14.8253	+	17.6681i	−0.628167	+	0.748620i	0.354285	+	0.935137i	$0.384724\pi$
$558$	−2.26388	−	1.30705i	−0.0958377	−	0.0553319i
$559$	19.8311	+	34.3484i	0.838765	+	1.45278i
$560$		0			0
$561$	17.2023	−	97.5590i	0.726281	−	4.11894i
$562$	−16.8810	+	9.74625i	−0.712082	+	0.411121i
$563$	−15.2110	−	8.78208i	−0.641067	−	0.370120i	0.143958	−	0.989584i	$-0.454017\pi$
$563$	−15.2110	−	8.78208i	−0.641067	−	0.370120i	−0.785026	+	0.619463i	$0.787350\pi$
$564$	13.1964	+	11.0731i	0.555670	+	0.466262i
$565$		0			0
$566$	−1.68977	+	0.615025i	−0.0710262	+	0.0258514i
$567$	−19.9282	−	23.7496i	−0.836907	−	0.997388i
$568$	−2.45265	+	0.432469i	−0.102911	+	0.0181460i
$569$	18.5739			0.778659			0.389330	−	0.921098i	$-0.372707\pi$
$569$	18.5739			0.778659			0.389330	+	0.921098i	$0.372707\pi$
$570$		0			0
$571$	−31.3550			−1.31216			−0.656082	−	0.754689i	$-0.727788\pi$
$571$	−31.3550			−1.31216			−0.656082	+	0.754689i	$0.727788\pi$
$572$	30.1202	−	5.31100i	1.25939	−	0.222064i
$573$	32.4579	+	38.6818i	1.35595	+	1.61595i
$574$	−6.10030	+	2.22033i	−0.254622	+	0.0926747i
$575$		0			0
$576$	1.52486	+	1.27951i	0.0635360	+	0.0533130i
$577$	8.92077	+	5.15041i	0.371377	+	0.214414i	0.674060	−	0.738677i	$-0.264549\pi$
$577$	8.92077	+	5.15041i	0.371377	+	0.214414i	−0.302683	+	0.953091i	$0.597882\pi$
$578$	−26.8317	+	15.4913i	−1.11605	+	0.644353i
$579$	6.05688	−	34.3503i	0.251715	−	1.42755i
$580$		0			0
$581$	−0.521078	−	0.902533i	−0.0216179	−	0.0374434i
$582$	−28.4649	−	16.4342i	−1.17991	−	0.681221i
$583$	14.3648	−	17.1194i	0.594931	−	0.709011i
$584$	6.59035	+	2.39869i	0.272711	+	0.0992586i
$585$		0			0
$586$	−11.0768	+	9.29453i	−0.457578	+	0.383953i
$587$	−13.2143	+	2.33003i	−0.545411	+	0.0961707i	−0.439563	−	0.898212i	$-0.644867\pi$
$587$	−13.2143	+	2.33003i	−0.545411	+	0.0961707i	−0.105848	+	0.994382i	$0.533756\pi$
$588$			2.07787i			0.0856899i
$589$	5.69869	−	0.540837i	0.234810	−	0.0222848i
$590$		0			0
$591$	−6.06621	−	34.4032i	−0.249531	−	1.41516i
$592$	4.26190	+	5.07914i	0.175163	+	0.208751i
$593$	4.34064	+	11.9258i	0.178249	+	0.489734i	0.996352	−	0.0853367i	$-0.0271966\pi$
$593$	4.34064	+	11.9258i	0.178249	+	0.489734i	−0.818103	+	0.575071i	$0.804974\pi$
$594$	−13.5655	−	4.93744i	−0.556600	−	0.202586i
$595$		0			0
$596$	−1.17516	+	2.03543i	−0.0481363	+	0.0833745i
$597$	22.1296	−	12.7765i	0.905706	−	0.522909i
$598$	−25.5913	−	4.51244i	−1.04651	−	0.184527i
$599$	4.76038	−	26.9974i	0.194504	−	1.10309i	−0.718620	−	0.695403i	$-0.755226\pi$
$599$	4.76038	−	26.9974i	0.194504	−	1.10309i	0.913124	−	0.407683i	$-0.133663\pi$
$600$		0			0
$601$	−8.74300	+	15.1433i	−0.356634	+	0.617709i	−0.987396	−	0.158268i	$-0.949409\pi$
$601$	−8.74300	+	15.1433i	−0.356634	+	0.617709i	0.630762	+	0.775976i	$0.282742\pi$
$602$	−15.0272	+	17.9087i	−0.612461	+	0.729903i
$603$	6.11626	−	16.8043i	0.249073	−	0.684323i
$604$	7.12891	−	2.59471i	0.290071	−	0.105577i
$605$		0			0
$606$	−0.114970	−	0.652025i	−0.00467032	−	0.0264867i
$607$			1.57783i			0.0640422i	0.999487	+	0.0320211i	$0.0101944\pi$
$607$			1.57783i			0.0640422i	−0.999487	+	0.0320211i	$0.989806\pi$
$608$	−4.34499	−	0.347953i	−0.176213	−	0.0141114i
$609$	47.3707			1.91956
$610$		0			0
$611$	28.2220	−	23.6811i	1.14174	−	0.958035i
$612$	−4.71597	−	12.9570i	−0.190632	−	0.523756i
$613$	5.88952	−	16.1813i	0.237876	−	0.653558i	−0.762106	−	0.647453i	$-0.775834\pi$
$613$	5.88952	−	16.1813i	0.237876	−	0.653558i	0.999981	−	0.00610534i	$-0.00194340\pi$
$614$	11.5840	+	9.72009i	0.467490	+	0.392271i
$615$		0			0
$616$	9.01382	+	15.6124i	0.363177	+	0.629041i
$617$	22.4275	+	3.95458i	0.902898	+	0.159205i	0.605777	−	0.795635i	$-0.292862\pi$
$617$	22.4275	+	3.95458i	0.902898	+	0.159205i	0.297121	+	0.954840i	$0.403974\pi$
$618$	−0.747128	−	0.131739i	−0.0300539	−	0.00529932i
$619$	22.4806	+	38.9375i	0.903570	+	1.56503i	0.822825	+	0.568294i	$0.192397\pi$
$619$	22.4806	+	38.9375i	0.903570	+	1.56503i	0.0807447	+	0.996735i	$0.474270\pi$
$620$		0			0
$621$	9.39593	+	7.88412i	0.377045	+	0.316379i
$622$	−7.79324	+	21.4117i	−0.312480	+	0.858533i
$623$	−0.163995	−	0.450572i	−0.00657031	−	0.0180518i
$624$	8.17591	−	6.86040i	0.327298	−	0.274636i
$625$		0			0
$626$	−5.48180			−0.219097
$627$	−60.0933	+	16.5766i	−2.39989	+	0.662007i
$628$		−	23.9145i		−	0.954294i
$629$	−7.97532	−	45.2303i	−0.317997	−	1.80345i
$630$		0			0
$631$	−13.5548	+	4.93355i	−0.539608	+	0.196401i	−0.597423	−	0.801926i	$-0.703809\pi$
$631$	−13.5548	+	4.93355i	−0.539608	+	0.196401i	0.0578152	+	0.998327i	$0.481587\pi$
$632$	−1.05408	+	2.89606i	−0.0419291	+	0.115199i
$633$	−29.6355	+	35.3182i	−1.17790	+	1.40377i
$634$	7.27571	−	12.6019i	0.288955	−	0.500485i
$635$		0			0
$636$	1.35419	−	7.68000i	0.0536972	−	0.304532i
$637$	4.37625	+	0.771650i	0.173393	+	0.0305739i
$638$	41.7469	−	24.1026i	1.65278	−	0.954231i
$639$	−2.47875	+	4.29332i	−0.0980577	+	0.169841i
$640$		0			0
$641$	−21.7784	−	7.92668i	−0.860194	−	0.313085i	−0.126004	−	0.992030i	$-0.540215\pi$
$641$	−21.7784	−	7.92668i	−0.860194	−	0.313085i	−0.734189	+	0.678945i	$0.762438\pi$
$642$	1.14975	+	3.15892i	0.0453771	+	0.124672i
$643$	−16.6932	−	19.8942i	−0.658316	−	0.784551i	0.328827	−	0.944390i	$-0.393347\pi$
$643$	−16.6932	−	19.8942i	−0.658316	−	0.784551i	−0.987143	+	0.159839i	$0.948902\pi$
$644$	−2.65977	−	15.0843i	−0.104810	−	0.594405i
$645$		0			0
$646$	24.8601	+	17.1361i	0.978107	+	0.674211i
$647$		−	24.0125i		−	0.944030i	−0.881590	−	0.472015i	$-0.843527\pi$
$647$		−	24.0125i		−	0.944030i	0.881590	−	0.472015i	$-0.156473\pi$
$648$	−10.8421	+	1.91175i	−0.425917	+	0.0751007i
$649$	41.8154	−	35.0873i	1.64140	−	1.37730i
$650$		0			0
$651$	−7.76330	−	2.82561i	−0.304268	−	0.110744i
$652$	−3.76814	+	4.49070i	−0.147572	+	0.175869i
$653$	−20.2843	−	11.7112i	−0.793787	−	0.458293i	0.0475068	−	0.998871i	$-0.484872\pi$
$653$	−20.2843	−	11.7112i	−0.793787	−	0.458293i	−0.841294	+	0.540578i	$0.818206\pi$
$654$	2.07368	+	3.59173i	0.0810875	+	0.140448i
$655$		0			0
$656$	−0.400309	+	2.27027i	−0.0156294	+	0.0886390i
$657$	12.0901	−	6.98023i	0.471681	−	0.272325i
$658$	18.8061	+	10.8577i	0.733137	+	0.423277i
$659$	−3.31918	−	2.78513i	−0.129297	−	0.108493i	0.575846	−	0.817558i	$-0.304673\pi$
$659$	−3.31918	−	2.78513i	−0.129297	−	0.108493i	−0.705143	+	0.709065i	$0.749117\pi$
$660$		0			0
$661$	5.56220	−	2.02448i	0.216345	−	0.0787430i	−0.231574	−	0.972817i	$-0.574388\pi$
$661$	5.56220	−	2.02448i	0.216345	−	0.0787430i	0.447919	+	0.894074i	$0.352165\pi$
$662$	5.66155	+	6.74717i	0.220042	+	0.262236i
$663$	−72.8074	+	12.8379i	−2.82761	+	0.498583i
$664$	−0.370077			−0.0143618
$665$		0			0
$666$	13.1982			0.511418
$667$	−40.3348	+	7.11212i	−1.56177	+	0.275382i
$668$	15.1000	+	17.9955i	0.584237	+	0.696266i
$669$	23.7908	−	8.65915i	0.919806	−	0.334782i
$670$		0			0
$671$	14.6478	+	12.2910i	0.565472	+	0.474487i
$672$	5.44811	+	3.14547i	0.210165	+	0.121339i
$673$	−38.5096	+	22.2335i	−1.48444	+	0.857039i	−0.999843	−	0.0177013i	$-0.994365\pi$
$673$	−38.5096	+	22.2335i	−1.48444	+	0.857039i	−0.484592	+	0.874740i	$0.661032\pi$
$674$	0.660278	−	3.74463i	0.0254330	−	0.144238i
$675$		0			0
$676$	−4.91260	−	8.50886i	−0.188946	−	0.327264i
$677$	24.8736	+	14.3608i	0.955970	+	0.551930i	0.894931	−	0.446206i	$-0.147225\pi$
$677$	24.8736	+	14.3608i	0.955970	+	0.551930i	0.0610399	+	0.998135i	$0.480558\pi$
$678$	17.4781	−	20.8296i	0.671242	−	0.799955i
$679$	−38.9341	−	14.1709i	−1.49415	−	0.543828i
$680$		0			0
$681$	−22.9973	+	19.2971i	−0.881260	+	0.739465i
$682$	−8.27934	+	1.45987i	−0.317032	+	0.0559013i
$683$			34.0249i			1.30193i	0.759108	+	0.650964i	$0.225635\pi$
$683$			34.0249i			1.30193i	−0.759108	+	0.650964i	$0.774365\pi$
$684$	−6.09005	+	6.18031i	−0.232859	+	0.236310i
$685$		0			0
$686$	−2.96818	−	16.8334i	−0.113326	−	0.642701i
$687$	−1.70016	−	2.02617i	−0.0648651	−	0.0773032i
$688$	2.83936	+	7.80108i	0.108250	+	0.297414i
$689$	−15.6721	−	5.70418i	−0.597060	−	0.217312i
$690$		0			0
$691$	0.602498	−	1.04356i	0.0229201	−	0.0396988i	−0.854338	−	0.519718i	$-0.826037\pi$
$691$	0.602498	−	1.04356i	0.0229201	−	0.0396988i	0.877258	+	0.480019i	$0.159370\pi$
$692$	15.9695	−	9.21997i	0.607068	−	0.350491i
$693$	35.3401	+	6.23141i	1.34246	+	0.236712i
$694$	−1.20603	+	6.83975i	−0.0457804	+	0.259633i
$695$		0			0
$696$	8.41085	−	14.5680i	0.318813	−	0.552200i
$697$	10.2644	−	12.2327i	0.388793	−	0.463345i
$698$	−5.03186	+	13.8249i	−0.190459	+	0.523281i
$699$	8.47462	−	3.08451i	0.320539	−	0.116667i
$700$		0			0
$701$	0.888317	+	5.03789i	0.0335513	+	0.190279i	0.996977	−	0.0776966i	$-0.0247566\pi$
$701$	0.888317	+	5.03789i	0.0335513	+	0.190279i	−0.963426	+	0.267975i	$0.913645\pi$
$702$			10.7736i			0.406621i
$703$	−23.5517	+	16.7506i	−0.888271	+	0.631762i
$704$	6.40175			0.241275
$705$		0			0
$706$	10.9959	−	9.22662i	0.413835	−	0.347249i
$707$	−0.285450	−	0.784267i	−0.0107354	−	0.0294954i
$708$	6.51494	−	17.8996i	0.244846	−	0.672710i
$709$	−27.8006	−	23.3275i	−1.04407	−	0.876082i	−0.0516160	−	0.998667i	$-0.516437\pi$
$709$	−27.8006	−	23.3275i	−1.04407	−	0.876082i	−0.992458	+	0.122585i	$0.960882\pi$
$710$		0			0
$711$	3.06739	+	5.31288i	0.115036	+	0.199249i
$712$	−0.167683	−	0.0295671i	−0.00628420	−	0.00110807i
$713$	7.03446	+	1.24037i	0.263443	+	0.0464520i
$714$	−21.7885	−	37.7388i	−0.815414	−	1.41234i
$715$		0			0
$716$	−13.1952	−	11.0721i	−0.493127	−	0.413782i
$717$	12.7485	−	35.0261i	0.476100	−	1.30807i
$718$	5.89501	+	16.1964i	0.220000	+	0.604445i
$719$	12.6534	−	10.6175i	0.471894	−	0.395966i	−0.375591	−	0.926785i	$-0.622560\pi$
$719$	12.6534	−	10.6175i	0.471894	−	0.395966i	0.847485	+	0.530820i	$0.178116\pi$
$720$		0			0
$721$	−0.956332			−0.0356157
$722$	3.02370	−	18.7579i	0.112531	−	0.698095i
$723$		−	28.2172i		−	1.04941i
$724$	1.25559	+	7.12080i	0.0466636	+	0.264642i
$725$		0			0
$726$	62.9401	−	22.9083i	2.33593	−	0.850208i
$727$	−7.32588	+	20.1277i	−0.271702	+	0.746495i	0.726535	+	0.687130i	$0.241130\pi$
$727$	−7.32588	+	20.1277i	−0.271702	+	0.746495i	−0.998236	+	0.0593646i	$0.981093\pi$
$728$	8.64798	−	10.3063i	0.320516	−	0.381976i
$729$	−3.40098	+	5.89066i	−0.125962	+	0.218173i
$730$		0			0
$731$	9.98576	−	56.6321i	0.369337	−	2.09461i
$732$	6.57122	+	1.15868i	0.242879	+	0.0428262i
$733$	−15.6826	+	9.05434i	−0.579249	+	0.334430i	−0.760835	−	0.648946i	$-0.775210\pi$
$733$	−15.6826	+	9.05434i	−0.579249	+	0.334430i	0.181586	+	0.983375i	$0.441877\pi$
$734$	−10.8128	+	18.7283i	−0.399107	+	0.691273i
$735$		0			0
$736$	−5.11116	−	1.86031i	−0.188400	−	0.0685720i
$737$	−19.6701	−	54.0432i	−0.724558	−	1.99071i
$738$	2.94965	+	3.51525i	0.108578	+	0.129398i
$739$	−7.90252	−	44.8174i	−0.290699	−	1.64863i	−0.684188	−	0.729306i	$-0.739843\pi$
$739$	−7.90252	−	44.8174i	−0.290699	−	1.64863i	0.393489	−	0.919329i	$-0.371268\pi$
$740$		0			0
$741$	26.9636	+	37.9113i	0.990531	+	1.39271i
$742$		−	9.83048i		−	0.360888i
$743$	34.8297	−	6.14141i	1.27778	−	0.225306i	0.506741	−	0.862099i	$-0.330850\pi$
$743$	34.8297	−	6.14141i	1.27778	−	0.225306i	0.771035	+	0.636792i	$0.219739\pi$
$744$	−2.24737	+	1.88577i	−0.0823926	+	0.0691356i
$745$		0			0
$746$	−11.3067	−	4.11528i	−0.413966	−	0.150671i
$747$	−0.473519	+	0.564318i	−0.0173251	+	0.0206473i
$748$	−38.4035	−	22.1723i	−1.40417	−	0.810700i
$749$	2.11879	+	3.66985i	0.0774188	+	0.134093i
$750$		0			0
$751$	−0.722804	+	4.09923i	−0.0263755	+	0.149583i	−0.995151	−	0.0983553i	$-0.968642\pi$
$751$	−0.722804	+	4.09923i	−0.0263755	+	0.149583i	0.968776	+	0.247938i	$0.0797530\pi$
$752$	6.67818	−	3.85565i	0.243528	−	0.140601i
$753$	33.7012	+	19.4574i	1.22814	+	0.709067i
$754$	−27.5585	−	23.1244i	−1.00362	−	0.842140i
$755$		0			0
$756$	−5.96730	+	2.17192i	−0.217028	+	0.0789919i
$757$	−34.4064	−	41.0040i	−1.25052	−	1.49031i	−0.802925	−	0.596080i	$-0.796724\pi$
$757$	−34.4064	−	41.0040i	−1.25052	−	1.49031i	−0.447597	−	0.894235i	$-0.647720\pi$
$758$	−28.6714	+	5.05555i	−1.04139	+	0.183626i
$759$	−77.7871			−2.82349
$760$		0			0
$761$	9.00004			0.326251			0.163126	−	0.986605i	$-0.447842\pi$
$761$	9.00004			0.326251			0.163126	+	0.986605i	$0.447842\pi$
$762$	−10.7889	+	1.90237i	−0.390840	+	0.0689156i
$763$	3.36051	+	4.00490i	0.121659	+	0.144987i
$764$	21.2404	−	7.73088i	0.768451	−	0.279693i
$765$		0			0
$766$	−5.14330	−	4.31574i	−0.185835	−	0.155934i
$767$	−35.2794	−	20.3686i	−1.27387	−	0.735467i
$768$	1.93466	−	1.11698i	0.0698112	−	0.0403055i
$769$	−6.21540	+	35.2493i	−0.224133	+	1.27112i	0.640202	+	0.768206i	$0.278851\pi$
$769$	−6.21540	+	35.2493i	−0.224133	+	1.27112i	−0.864335	+	0.502916i	$0.832261\pi$
$770$		0			0
$771$	8.37388	+	14.5040i	0.301578	+	0.522348i
$772$	−13.5218	−	7.80681i	−0.486660	−	0.280973i
$773$	24.6571	−	29.3852i	0.886856	−	1.05691i	−0.111151	−	0.993804i	$-0.535454\pi$
$773$	24.6571	−	29.3852i	0.886856	−	1.05691i	0.998007	−	0.0631098i	$-0.0201018\pi$
$774$	15.5286	+	5.65195i	0.558164	+	0.203155i
$775$		0			0
$776$	−11.2709	+	9.45740i	−0.404602	+	0.339501i
$777$	41.0774	−	7.24305i	1.47364	−	0.259843i
$778$		−	10.2745i		−	0.368359i
$779$	−9.72499	−	2.52928i	−0.348434	−	0.0906210i
$780$		0			0
$781$	2.76856	+	15.7013i	0.0990669	+	0.561836i
$782$	24.2183	+	28.8622i	0.866044	+	1.03211i
$783$	5.80762	+	15.9563i	0.207547	+	0.570232i
$784$	0.874035	+	0.318123i	0.0312155	+	0.0113615i
$785$		0			0
$786$	−19.7354	+	34.1827i	−0.703938	+	1.21926i
$787$	23.9044	−	13.8012i	0.852101	−	0.491961i	−0.00925846	−	0.999957i	$-0.502947\pi$
$787$	23.9044	−	13.8012i	0.852101	−	0.491961i	0.861359	+	0.507997i	$0.169614\pi$
$788$	−15.4001	−	2.71545i	−0.548606	−	0.0967340i
$789$	−3.38870	+	19.2183i	−0.120641	+	0.684189i
$790$		0			0
$791$	17.1381	−	29.6840i	0.609359	−	1.05544i
$792$	8.19112	−	9.76180i	0.291059	−	0.346871i
$793$	4.88066	−	13.4095i	0.173317	−	0.476185i
$794$	19.7241	−	7.17897i	0.699981	−	0.254772i
$795$		0			0
$796$	−1.98627	−	11.2647i	−0.0704016	−	0.399267i
$797$			24.9241i			0.882855i	0.897297	+	0.441428i	$0.145528\pi$
$797$			24.9241i			0.882855i	−0.897297	+	0.441428i	$0.854472\pi$
$798$	−15.5627	+	22.5775i	−0.550914	+	0.799235i
$799$	−53.4157			−1.88971
$800$		0			0
$801$	−0.259639	+	0.217863i	−0.00917389	+	0.00769780i
$802$	−7.93702	−	21.8068i	−0.280266	−	0.770024i
$803$	15.3558	−	42.1898i	0.541895	−	1.48885i
$804$	−15.3740	−	12.9003i	−0.542198	−	0.454958i
$805$		0			0
$806$	3.13706	+	5.43354i	0.110498	+	0.191388i
$807$	23.2796	+	4.10483i	0.819481	+	0.144497i
$808$	−0.291870	−	0.0514645i	−0.0102679	−	0.00181052i
$809$	−21.4372	−	37.1303i	−0.753692	−	1.30543i	−0.946022	−	0.324103i	$-0.894938\pi$
$809$	−21.4372	−	37.1303i	−0.753692	−	1.30543i	0.192329	−	0.981330i	$-0.438396\pi$
$810$		0			0
$811$	17.4105	+	14.6091i	0.611365	+	0.512996i	0.895076	−	0.445914i	$-0.147121\pi$
$811$	17.4105	+	14.6091i	0.611365	+	0.512996i	−0.283711	+	0.958910i	$0.591566\pi$
$812$	7.25249	−	19.9260i	0.254512	−	0.699267i
$813$	−17.6673	−	48.5406i	−0.619621	−	1.70239i
$814$	32.5154	−	27.2836i	1.13966	−	0.956291i
$815$		0			0
$816$	−15.4745			−0.541716
$817$	−34.8836	+	9.62259i	−1.22042	+	0.336652i
$818$			17.4755i			0.611018i
$819$	−4.65045	−	26.3740i	−0.162500	−	0.921582i
$820$		0			0
$821$	14.7373	−	5.36393i	0.514335	−	0.187202i	−0.0717956	−	0.997419i	$-0.522873\pi$
$821$	14.7373	−	5.36393i	0.514335	−	0.187202i	0.586130	+	0.810217i	$0.300651\pi$
$822$	3.50999	−	9.64362i	0.122425	−	0.336360i
$823$	28.6726	−	34.1706i	0.999463	−	1.19111i	0.0179263	−	0.999839i	$-0.494294\pi$
$823$	28.6726	−	34.1706i	0.999463	−	1.19111i	0.981537	−	0.191274i	$-0.0612620\pi$
$824$	−0.169800	+	0.294103i	−0.00591528	+	0.0102456i
$825$		0			0
$826$	4.16959	−	23.6469i	0.145079	−	0.822782i
$827$	21.2172	+	3.74117i	0.737795	+	0.130093i	0.529902	−	0.848059i	$-0.322229\pi$
$827$	21.2172	+	3.74117i	0.737795	+	0.130093i	0.207892	+	0.978152i	$0.433340\pi$
$828$	−9.37652	+	5.41354i	−0.325857	+	0.188133i
$829$	−24.5999	+	42.6083i	−0.854390	+	1.47985i	0.0228201	+	0.999740i	$0.492735\pi$
$829$	−24.5999	+	42.6083i	−0.854390	+	1.47985i	−0.877210	+	0.480107i	$0.840598\pi$
$830$		0			0
$831$	40.4198	+	14.7116i	1.40215	+	0.510340i
$832$	−1.63403	−	4.48945i	−0.0566496	−	0.155644i
$833$	−4.14145	−	4.93559i	−0.143493	−	0.171008i
$834$	1.98505	+	11.2578i	0.0687367	+	0.389825i
$835$		0			0
$836$	−2.22751	+	27.8155i	−0.0770399	+	0.962020i
$837$		−	2.96140i		−	0.102361i
$838$	6.80706	−	1.20027i	0.235146	−	0.0414626i
$839$	−42.5976	+	35.7436i	−1.47063	+	1.23401i	−0.555088	+	0.831791i	$0.687316\pi$
$839$	−42.5976	+	35.7436i	−1.47063	+	1.23401i	−0.915545	+	0.402216i	$0.868240\pi$
$840$		0			0
$841$	−26.0303	−	9.47427i	−0.897598	−	0.326699i
$842$	−7.48783	+	8.92365i	−0.258048	+	0.307529i
$843$	37.7114	+	21.7727i	1.29885	+	0.749892i
$844$	10.3190	+	17.8731i	0.355196	+	0.615217i
$845$		0			0
$846$	2.66548	−	15.1167i	0.0916409	−	0.519722i
$847$	73.1202	−	42.2160i	2.51244	−	1.45056i
$848$	−3.02319	−	1.74544i	−0.103817	−	0.0599386i
$849$	3.07730	+	2.58216i	0.105613	+	0.0886195i
$850$		0			0
$851$	−33.8888	+	12.3345i	−1.16169	+	0.422821i
$852$	3.57625	+	4.26201i	0.122520	+	0.146014i
$853$	44.0420	−	7.76580i	1.50797	−	0.265896i	0.642278	−	0.766472i	$-0.277990\pi$
$853$	44.0420	−	7.76580i	1.50797	−	0.265896i	0.865693	+	0.500576i	$0.166878\pi$
$854$	8.41124			0.287827
$855$		0			0
$856$	1.50479			0.0514328
$857$	−16.3532	+	2.88351i	−0.558615	+	0.0984988i	−0.445825	−	0.895120i	$-0.647090\pi$
$857$	−16.3532	+	2.88351i	−0.558615	+	0.0984988i	−0.112789	+	0.993619i	$0.535979\pi$
$858$	−43.9186	−	52.3402i	−1.49936	−	1.78686i
$859$	23.1547	−	8.42763i	0.790029	−	0.287547i	0.0846806	−	0.996408i	$-0.473013\pi$
$859$	23.1547	−	8.42763i	0.790029	−	0.287547i	0.705348	+	0.708861i	$0.250791\pi$
$860$		0			0
$861$	11.1095	+	9.32197i	0.378611	+	0.317692i
$862$	23.1331	+	13.3559i	0.787916	+	0.454904i
$863$	−10.5018	+	6.06323i	−0.357486	+	0.206395i	−0.667978	−	0.744181i	$-0.732840\pi$
$863$	−10.5018	+	6.06323i	−0.357486	+	0.206395i	0.310491	+	0.950576i	$0.399506\pi$
$864$	−0.391581	+	2.22077i	−0.0133219	+	0.0755520i
$865$		0			0
$866$	1.71848	+	2.97649i	0.0583963	+	0.101145i
$867$	59.9410	+	34.6069i	2.03570	+	1.17531i
$868$	−2.37713	+	2.83295i	−0.0806851	+	0.0961567i
$869$	18.5399	+	6.74796i	0.628922	+	0.228909i
$870$		0			0
$871$	−32.8789	+	27.5887i	−1.11406	+	0.934808i
$872$	1.82831	−	0.322380i	0.0619143	−	0.0109172i
$873$			29.2875i			0.991230i
$874$	9.86148	−	21.5606i	0.333569	−	0.729300i
$875$		0			0
$876$	−2.72062	−	15.4294i	−0.0919213	−	0.521311i
$877$	−8.33008	−	9.92741i	−0.281287	−	0.335225i	0.606839	−	0.794825i	$-0.292437\pi$
$877$	−8.33008	−	9.92741i	−0.281287	−	0.335225i	−0.888126	+	0.459600i	$0.847993\pi$
$878$	−3.65322	−	10.0371i	−0.123290	−	0.338737i
$879$	30.3543	+	11.0481i	1.02383	+	0.372642i
$880$		0			0
$881$	5.81201	−	10.0667i	0.195812	−	0.339156i	−0.751355	−	0.659899i	$-0.770599\pi$
$881$	5.81201	−	10.0667i	0.195812	−	0.339156i	0.947166	+	0.320743i	$0.103933\pi$
$882$	1.60343	−	0.925743i	0.0539904	−	0.0311714i
$883$	46.8763	+	8.26555i	1.57751	+	0.278158i	0.892731	−	0.450591i	$-0.148787\pi$
$883$	46.8763	+	8.26555i	1.57751	+	0.278158i	0.684781	+	0.728749i	$0.259898\pi$
$884$	−5.74671	+	32.5912i	−0.193283	+	1.09616i
$885$		0			0
$886$	−19.9220	+	34.5058i	−0.669291	+	1.15925i
$887$	2.26555	−	2.69998i	0.0760697	−	0.0906563i	−0.726667	−	0.686989i	$-0.758932\pi$
$887$	2.26555	−	2.69998i	0.0760697	−	0.0906563i	0.802737	+	0.596333i	$0.203376\pi$
$888$	5.06597	−	13.9186i	0.170003	−	0.467079i
$889$	−12.9770	+	4.72326i	−0.435236	+	0.158413i
$890$		0			0
$891$	12.2386	+	69.4083i	0.410007	+	2.32527i
$892$		−	11.3331i		−	0.379460i
$893$	14.4291	+	30.3582i	0.482850	+	1.01590i
$894$	5.25050			0.175603
$895$		0			0
$896$	2.15722	−	1.81012i	0.0720676	−	0.0604719i
$897$	19.8549	+	54.5509i	0.662936	+	1.82140i
$898$	0.778107	−	2.13783i	0.0259658	−	0.0713403i
$899$	7.57521	+	6.35635i	0.252647	+	0.211996i
$900$		0			0
$901$	12.0906	+	20.9415i	0.402795	+	0.697662i
$902$	14.5337	+	2.56268i	0.483918	+	0.0853279i
$903$	51.4323	+	9.06890i	1.71156	+	0.301794i
$904$	−6.08585	−	10.5410i	−0.202413	−	0.350589i
$905$		0			0
$906$	−12.9827	−	10.8938i	−0.431323	−	0.361923i
$907$	−17.7021	+	48.6361i	−0.587788	+	1.61494i	0.186749	+	0.982408i	$0.440205\pi$
$907$	−17.7021	+	48.6361i	−0.587788	+	1.61494i	−0.774538	+	0.632528i	$0.782017\pi$
$908$	4.59621	+	12.6280i	0.152531	+	0.419075i
$909$	−0.451928	+	0.379212i	−0.0149895	+	0.0125777i
$910$		0			0
$911$	14.4334			0.478199			0.239100	−	0.970995i	$-0.423148\pi$
$911$	14.4334			0.478199			0.239100	+	0.970995i	$0.423148\pi$
$912$	4.18009	+	8.79475i	0.138417	+	0.291223i
$913$			2.36914i			0.0784072i
$914$	−2.73280	−	15.4985i	−0.0903928	−	0.512643i
$915$		0			0
$916$	−1.11258	+	0.404947i	−0.0367608	+	0.0133798i
$917$	−17.0174	+	46.7549i	−0.561963	+	1.54398i
$918$	10.0406	−	11.9660i	0.331390	−	0.394936i
$919$	22.2554	−	38.5474i	0.734137	−	1.27156i	−0.220964	−	0.975282i	$-0.570920\pi$
$919$	22.2554	−	38.5474i	0.734137	−	1.27156i	0.955101	−	0.296281i	$-0.0957464\pi$
$920$		0			0
$921$	5.86608	−	33.2682i	0.193294	−	1.09622i
$922$	31.8816	+	5.62159i	1.04997	+	0.185137i
$923$	10.3044	−	5.94925i	0.339174	−	0.195822i
$924$	20.1365	−	34.8774i	0.662442	−	1.14738i
$925$		0			0
$926$	2.37938	+	0.866023i	0.0781912	+	0.0284593i
$927$	0.231205	+	0.635231i	0.00759378	+	0.0208637i
$928$	−4.84019	−	5.76832i	−0.158887	−	0.189354i
$929$	7.42512	+	42.1099i	0.243610	+	1.38158i	0.823698	+	0.567028i	$0.191907\pi$
$929$	7.42512	+	42.1099i	0.243610	+	1.38158i	−0.580088	+	0.814554i	$0.696982\pi$
$930$		0			0
$931$	−1.68636	+	3.68698i	−0.0552683	+	0.120836i
$932$		−	4.03700i		−	0.132236i
$933$	50.1294	−	8.83917i	1.64116	−	0.289381i
$934$	−1.98740	+	1.66763i	−0.0650299	+	0.0545665i
$935$		0			0
$936$	−8.93656	−	3.25264i	−0.292101	−	0.106316i
$937$	−16.8705	+	20.1055i	−0.551136	+	0.656819i	−0.967646	−	0.252313i	$-0.918809\pi$
$937$	−16.8705	+	20.1055i	−0.551136	+	0.656819i	0.416509	+	0.909131i	$0.363253\pi$
$938$	−21.9092	−	12.6493i	−0.715362	−	0.413015i
$939$	6.12305	+	10.6054i	0.199818	+	0.346095i
$940$		0			0
$941$	−0.771897	+	4.37765i	−0.0251631	+	0.142707i	−0.994801	−	0.101838i	$-0.967528\pi$
$941$	−0.771897	+	4.37765i	−0.0251631	+	0.142707i	0.969638	+	0.244545i	$0.0786387\pi$
$942$	−46.2666	+	26.7120i	−1.50745	+	0.870326i
$943$	−10.8590	−	6.26945i	−0.353618	−	0.204161i
$944$	−6.53187	−	5.48089i	−0.212594	−	0.178388i
$945$		0			0
$946$	49.9406	−	18.1769i	1.62371	−	0.590982i
$947$	−18.8369	−	22.4490i	−0.612117	−	0.729493i	0.367576	−	0.929993i	$-0.380188\pi$
$947$	−18.8369	−	22.4490i	−0.612117	−	0.729493i	−0.979694	+	0.200500i	$0.935743\pi$
$948$	6.78030	−	1.19555i	0.220214	−	0.0388296i
$949$	−33.5066			−1.08767
$950$		0			0
$951$	−32.5073			−1.05412
$952$	−19.2103	+	3.38729i	−0.622609	+	0.109783i
$953$	−13.3772	−	15.9423i	−0.433330	−	0.516423i	0.504550	−	0.863383i	$-0.331659\pi$
$953$	−13.3772	−	15.9423i	−0.433330	−	0.516423i	−0.937880	+	0.346960i	$0.887214\pi$
$954$	−6.52977	+	2.37664i	−0.211409	+	0.0769466i
$955$		0			0
$956$	−12.7816	−	10.7250i	−0.413386	−	0.346872i
$957$	−93.2609	−	53.8442i	−3.01470	−	1.74054i
$958$	24.4130	−	14.0949i	0.788749	−	0.455384i
$959$	2.24641	−	12.7400i	0.0725405	−	0.411398i
$960$		0			0
$961$	14.6377	+	25.3532i	0.472184	+	0.817846i
$962$	−27.4330	−	15.8385i	−0.884477	−	0.510653i
$963$	1.92540	−	2.29461i	0.0620453	−	0.0739427i
$964$	−11.8693	−	4.32006i	−0.382283	−	0.139140i
$965$		0			0
$966$	−26.2122	+	21.9946i	−0.843363	+	0.707666i
$967$	13.7604	−	2.42634i	0.442506	−	0.0780257i	0.0520439	−	0.998645i	$-0.483426\pi$
$967$	13.7604	−	2.42634i	0.442506	−	0.0780257i	0.390462	+	0.920619i	$0.372315\pi$
$968$		−	29.9824i		−	0.963671i
$969$	5.38440	−	67.2366i	0.172972	−	2.15995i
$970$		0			0
$971$	4.51454	+	25.6033i	0.144879	+	0.821647i	0.967465	+	0.253007i	$0.0814195\pi$
$971$	4.51454	+	25.6033i	0.144879	+	0.821647i	−0.822586	+	0.568641i	$0.807469\pi$
$972$	11.4605	+	13.6581i	0.367595	+	0.438082i
$973$	4.92854	+	13.5410i	0.158002	+	0.434106i
$974$	−7.58705	−	2.76146i	−0.243105	−	0.0884829i
$975$		0			0
$976$	1.49345	−	2.58673i	0.0478041	−	0.0827991i
$977$	20.3244	−	11.7343i	0.650235	−	0.375413i	−0.138311	−	0.990389i	$-0.544167\pi$
$977$	20.3244	−	11.7343i	0.650235	−	0.375413i	0.788546	+	0.614976i	$0.210834\pi$
$978$	12.8969	+	2.27408i	0.412398	+	0.0727169i
$979$	−0.189281	+	1.07347i	−0.00604945	+	0.0343081i
$980$		0			0
$981$	1.84776	−	3.20041i	0.0589943	−	0.102181i
$982$	21.3674	−	25.4647i	0.681862	−	0.812611i
$983$	−12.9972	+	35.7096i	−0.414547	+	1.13896i	0.540200	+	0.841537i	$0.318349\pi$
$983$	−12.9972	+	35.7096i	−0.414547	+	1.13896i	−0.954746	+	0.297421i	$0.903874\pi$
$984$	4.83934	−	1.76138i	0.154272	−	0.0561506i
$985$		0			0
$986$	9.05748	+	51.3675i	0.288449	+	1.63587i
$987$		−	48.5112i		−	1.54413i
$988$	20.0752	−	5.53771i	0.638676	−	0.176178i
$989$	−45.1547			−1.43584
$990$		0			0
$991$	41.2567	−	34.6185i	1.31056	−	1.09969i	0.322346	−	0.946622i	$-0.395528\pi$
$991$	41.2567	−	34.6185i	1.31056	−	1.09969i	0.988215	−	0.153070i	$-0.0489160\pi$
$992$	0.449156	+	1.23405i	0.0142607	+	0.0391810i
$993$	6.72968	−	18.4896i	0.213560	−	0.586751i
$994$	5.37253	+	4.50809i	0.170406	+	0.142988i
$995$		0			0
$996$	0.413369	+	0.715975i	0.0130981	+	0.0226865i
$997$	25.3749	+	4.47428i	0.803631	+	0.141702i	0.560352	−	0.828254i	$-0.310666\pi$
$997$	25.3749	+	4.47428i	0.803631	+	0.141702i	0.243279	+	0.969956i	$0.421777\pi$
$998$	−12.7933	−	2.25581i	−0.404966	−	0.0714064i
$999$	7.47580	+	12.9485i	0.236524	+	0.409671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.u.h.199.4		48
5.2	odd	4		950.2.l.j.351.4	✓	24
5.3	odd	4		950.2.l.k.351.1	yes	24
5.4	even	2	inner	950.2.u.h.199.5		48
19.17	even	9	inner	950.2.u.h.549.5		48
95.17	odd	36		950.2.l.j.701.4	yes	24
95.74	even	18	inner	950.2.u.h.549.4		48
95.93	odd	36		950.2.l.k.701.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.l.j.351.4	✓	24	5.2	odd	4
950.2.l.j.701.4	yes	24	95.17	odd	36
950.2.l.k.351.1	yes	24	5.3	odd	4
950.2.l.k.701.1	yes	24	95.93	odd	36
950.2.u.h.199.4		48	1.1	even	1	trivial
950.2.u.h.199.5		48	5.4	even	2	inner
950.2.u.h.549.4		48	95.74	even	18	inner
950.2.u.h.549.5		48	19.17	even	9	inner

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.173648i) q^{2} +(1.43596 + 1.71131i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.71131 - 1.43596i) q^{6} +(-2.43877 - 1.40802i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.345659 + 1.96033i) q^{9} +O(q^{10})\)	\(q+(-0.984808 + 0.173648i) q^{2} +(1.43596 + 1.71131i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-1.71131 - 1.43596i) q^{6} +(-2.43877 - 1.40802i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.345659 + 1.96033i) q^{9} +(3.20088 + 5.54408i) q^{11} +(1.93466 + 1.11698i) q^{12} +(3.07096 - 3.65983i) q^{13} +(2.64622 + 0.963145i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-6.82171 + 1.20285i) q^{17} -1.99057i q^{18} +(2.52636 + 3.55211i) q^{19} +(-1.09241 - 6.19536i) q^{21} +(-4.11497 - 4.90403i) q^{22} +(1.86031 + 5.11116i) q^{23} +(-2.09923 - 0.764059i) q^{24} +(-2.38879 + 4.13750i) q^{26} +(1.95291 - 1.12751i) q^{27} +(-2.77327 - 0.489002i) q^{28} +(-1.30757 + 7.41560i) q^{29} +(0.656622 - 1.13730i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(-4.89131 + 13.4388i) q^{33} +(6.50920 - 2.36916i) q^{34} +(0.345659 + 1.96033i) q^{36} +6.63035i q^{37} +(-3.10479 - 3.05945i) q^{38} +10.6729 q^{39} +(-1.76595 + 1.48181i) q^{41} +(2.15163 + 5.91154i) q^{42} +(-2.83936 + 7.80108i) q^{43} +(4.90403 + 4.11497i) q^{44} +(-2.71959 - 4.71047i) q^{46} +(7.59414 + 1.33905i) q^{47} +(2.20002 + 0.387923i) q^{48} +(0.465064 + 0.805515i) q^{49} +(-11.8542 - 9.94683i) q^{51} +(1.63403 - 4.48945i) q^{52} +(-1.19395 - 3.28035i) q^{53} +(-1.72745 + 1.44950i) q^{54} +2.81605 q^{56} +(-2.45102 + 9.42408i) q^{57} -7.53000i q^{58} +(-1.48065 - 8.39721i) q^{59} +(2.80676 - 1.02158i) q^{61} +(-0.449156 + 1.23405i) q^{62} +(3.60317 - 4.29409i) q^{63} +(0.500000 - 0.866025i) q^{64} +(2.48338 - 14.0840i) q^{66} +(-8.84725 - 1.56001i) q^{67} +(-5.99891 + 3.46347i) q^{68} +(-6.07546 + 10.5230i) q^{69} +(2.34030 + 0.851798i) q^{71} +(-0.680815 - 1.87052i) q^{72} +(-4.50807 - 5.37250i) q^{73} +(-1.15135 - 6.52962i) q^{74} +(3.58889 + 2.47383i) q^{76} -18.0276i q^{77} +(-10.5107 + 1.85333i) q^{78} +(2.36089 - 1.98102i) q^{79} +(10.3454 + 3.76542i) q^{81} +(1.48181 - 1.76595i) q^{82} +(0.320496 + 0.185039i) q^{83} +(-3.14547 - 5.44811i) q^{84} +(1.44158 - 8.17562i) q^{86} +(-14.5680 + 8.41085i) q^{87} +(-5.54408 - 3.20088i) q^{88} +(0.130434 + 0.109447i) q^{89} +(-12.6425 + 4.60150i) q^{91} +(3.49624 + 4.16666i) q^{92} +(2.88916 - 0.509437i) q^{93} -7.71129 q^{94} -2.23396 q^{96} +(14.4896 - 2.55490i) q^{97} +(-0.597875 - 0.712520i) q^{98} +(-11.9746 + 4.35841i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 12 q^{11} + 30 q^{14} + 30 q^{19} - 36 q^{21} - 18 q^{26} + 24 q^{29} + 18 q^{31} + 18 q^{34} - 132 q^{39} + 36 q^{41} - 6 q^{46} + 54 q^{49} - 6 q^{51} - 54 q^{54} - 12 q^{56} - 72 q^{59} + 24 q^{61} + 24 q^{64} + 96 q^{66} - 42 q^{69} - 78 q^{71} - 36 q^{74} + 12 q^{76} + 84 q^{79} - 72 q^{81} - 18 q^{84} - 78 q^{86} + 72 q^{89} + 24 q^{91} - 24 q^{94} + 12 q^{96} - 102 q^{99}+O(q^{100}) \) 48 * q - 12 * q^11 + 30 * q^14 + 30 * q^19 - 36 * q^21 - 18 * q^26 + 24 * q^29 + 18 * q^31 + 18 * q^34 - 132 * q^39 + 36 * q^41 - 6 * q^46 + 54 * q^49 - 6 * q^51 - 54 * q^54 - 12 * q^56 - 72 * q^59 + 24 * q^61 + 24 * q^64 + 96 * q^66 - 42 * q^69 - 78 * q^71 - 36 * q^74 + 12 * q^76 + 84 * q^79 - 72 * q^81 - 18 * q^84 - 78 * q^86 + 72 * q^89 + 24 * q^91 - 24 * q^94 + 12 * q^96 - 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more