LMFDB - Embedded newform 441.2.i.b.68.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(68,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 5]))

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

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

chi := DirichletCharacter("441.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.4
Root			$0.187540 - 0.324828i$ of defining polynomial
Character	$\chi$	$=$	441.68
Dual form			441.2.i.b.227.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.718167i q^{2} +(0.271473 + 1.71064i) q^{3} +1.48424 q^{4} +(0.723774 + 1.25361i) q^{5} +(-1.22853 + 0.194963i) q^{6} +2.50226i q^{8} +(-2.85261 + 0.928786i) q^{9} +O(q^{10})$	\(q+0.718167i q^{2} +(0.271473 + 1.71064i) q^{3} +1.48424 q^{4} +(0.723774 + 1.25361i) q^{5} +(-1.22853 + 0.194963i) q^{6} +2.50226i q^{8} +(-2.85261 + 0.928786i) q^{9} +(-0.900304 + 0.519791i) q^{10} +(-1.55933 - 0.900281i) q^{11} +(0.402930 + 2.53900i) q^{12} +(1.88867 + 1.09042i) q^{13} +(-1.94800 + 1.57844i) q^{15} +1.17143 q^{16} +(-1.95230 - 3.38149i) q^{17} +(-0.667023 - 2.04865i) q^{18} +(3.47456 + 2.00604i) q^{19} +(1.07425 + 1.86066i) q^{20} +(0.646552 - 1.11986i) q^{22} +(-4.91522 + 2.83781i) q^{23} +(-4.28048 + 0.679296i) q^{24} +(1.45230 - 2.51546i) q^{25} +(-0.783106 + 1.35638i) q^{26} +(-2.36323 - 4.62765i) q^{27} +(8.49418 - 4.90412i) q^{29} +(-1.13358 - 1.39899i) q^{30} -2.83050i q^{31} +5.84581i q^{32} +(1.11674 - 2.91186i) q^{33} +(2.42847 - 1.40208i) q^{34} +(-4.23394 + 1.37854i) q^{36} +(-0.411767 + 0.713202i) q^{37} +(-1.44067 + 2.49531i) q^{38} +(-1.35261 + 3.52686i) q^{39} +(-3.13687 + 1.81107i) q^{40} +(-5.90617 + 10.2298i) q^{41} +(-3.76766 - 6.52578i) q^{43} +(-2.31442 - 1.33623i) q^{44} +(-3.22898 - 2.90383i) q^{45} +(-2.03802 - 3.52995i) q^{46} -2.33839 q^{47} +(0.318012 + 2.00390i) q^{48} +(1.80652 + 1.04299i) q^{50} +(5.25452 - 4.25767i) q^{51} +(2.80323 + 1.61845i) q^{52} +(0.996713 - 0.575453i) q^{53} +(3.32343 - 1.69719i) q^{54} -2.60640i q^{55} +(-2.48837 + 6.48831i) q^{57} +(3.52198 + 6.10024i) q^{58} +9.79110 q^{59} +(-2.89130 + 2.34278i) q^{60} -2.35536i q^{61} +2.03277 q^{62} -1.85540 q^{64} +3.15688i q^{65} +(2.09120 + 0.802008i) q^{66} -0.312805 q^{67} +(-2.89768 - 5.01893i) q^{68} +(-6.18882 - 7.63781i) q^{69} +1.94933i q^{71} +(-2.32407 - 7.13797i) q^{72} +(-2.42847 + 1.40208i) q^{73} +(-0.512198 - 0.295717i) q^{74} +(4.69732 + 1.80149i) q^{75} +(5.15706 + 2.97743i) q^{76} +(-2.53287 - 0.971396i) q^{78} +12.4317 q^{79} +(0.847852 + 1.46852i) q^{80} +(7.27471 - 5.29892i) q^{81} +(-7.34669 - 4.24162i) q^{82} +(-3.60916 - 6.25124i) q^{83} +(2.82605 - 4.89486i) q^{85} +(4.68660 - 2.70581i) q^{86} +(10.6951 + 13.1992i) q^{87} +(2.25274 - 3.90186i) q^{88} +(5.28999 - 9.16253i) q^{89} +(2.08544 - 2.31895i) q^{90} +(-7.29536 + 4.21198i) q^{92} +(4.84198 - 0.768404i) q^{93} -1.67935i q^{94} +5.80767i q^{95} +(-10.0001 + 1.58698i) q^{96} +(13.4322 - 7.75510i) q^{97} +(5.28433 + 1.11986i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{3} - 8 q^{4} - 12 q^{6} + 3 q^{9}+O(q^{10}) $ 10 * q + 3 * q^3 - 8 * q^4 - 12 * q^6 + 3 * q^9	$ 10 q + 3 q^{3} - 8 q^{4} - 12 q^{6} + 3 q^{9} + 15 q^{10} - 12 q^{11} + 12 q^{12} + 6 q^{13} - 3 q^{15} + 12 q^{16} - 12 q^{17} + 24 q^{18} - 3 q^{19} - 3 q^{20} + 5 q^{22} - 15 q^{23} + 7 q^{25} + 3 q^{26} + 27 q^{27} - 15 q^{29} + 6 q^{30} + 3 q^{34} - 18 q^{36} + 6 q^{37} - 18 q^{38} + 18 q^{39} - 15 q^{40} - 9 q^{41} + 3 q^{43} - 24 q^{44} - 30 q^{45} - 13 q^{46} - 30 q^{47} - 15 q^{48} + 3 q^{50} + 21 q^{51} + 12 q^{52} + 9 q^{53} - 9 q^{54} - 36 q^{57} + 8 q^{58} + 36 q^{59} - 48 q^{60} + 12 q^{62} + 6 q^{64} + 39 q^{66} + 20 q^{67} + 27 q^{68} - 3 q^{69} - 30 q^{72} - 3 q^{73} - 30 q^{74} - 6 q^{75} + 9 q^{76} + 24 q^{78} - 40 q^{79} - 30 q^{80} + 15 q^{81} - 9 q^{82} - 15 q^{83} + 18 q^{85} + 54 q^{86} - 6 q^{87} - 8 q^{88} + 24 q^{89} + 24 q^{90} + 39 q^{92} + 36 q^{93} - 33 q^{96} + 6 q^{97} + 21 q^{99}+O(q^{100}) $ 10 * q + 3 * q^3 - 8 * q^4 - 12 * q^6 + 3 * q^9 + 15 * q^10 - 12 * q^11 + 12 * q^12 + 6 * q^13 - 3 * q^15 + 12 * q^16 - 12 * q^17 + 24 * q^18 - 3 * q^19 - 3 * q^20 + 5 * q^22 - 15 * q^23 + 7 * q^25 + 3 * q^26 + 27 * q^27 - 15 * q^29 + 6 * q^30 + 3 * q^34 - 18 * q^36 + 6 * q^37 - 18 * q^38 + 18 * q^39 - 15 * q^40 - 9 * q^41 + 3 * q^43 - 24 * q^44 - 30 * q^45 - 13 * q^46 - 30 * q^47 - 15 * q^48 + 3 * q^50 + 21 * q^51 + 12 * q^52 + 9 * q^53 - 9 * q^54 - 36 * q^57 + 8 * q^58 + 36 * q^59 - 48 * q^60 + 12 * q^62 + 6 * q^64 + 39 * q^66 + 20 * q^67 + 27 * q^68 - 3 * q^69 - 30 * q^72 - 3 * q^73 - 30 * q^74 - 6 * q^75 + 9 * q^76 + 24 * q^78 - 40 * q^79 - 30 * q^80 + 15 * q^81 - 9 * q^82 - 15 * q^83 + 18 * q^85 + 54 * q^86 - 6 * q^87 - 8 * q^88 + 24 * q^89 + 24 * q^90 + 39 * q^92 + 36 * q^93 - 33 * q^96 + 6 * q^97 + 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			0.718167i			0.507821i	0.967228	+	0.253910i	$0.0817168\pi$
$2$			0.718167i			0.507821i	−0.967228	+	0.253910i	$0.918283\pi$
$3$	0.271473	+	1.71064i	0.156735	+	0.987641i
$3$	0.271473	+	1.71064i	0.156735	+	0.987641i
$4$	1.48424			0.742118
$5$	0.723774	+	1.25361i	0.323682	+	0.560633i	0.981245	−	0.192766i	$-0.0617460\pi$
$5$	0.723774	+	1.25361i	0.323682	+	0.560633i	−0.657563	+	0.753400i	$0.728413\pi$
$6$	−1.22853	+	0.194963i	−0.501544	+	0.0795931i
$7$		0			0
$7$		0			0
$8$			2.50226i			0.884683i
$9$	−2.85261	+	0.928786i	−0.950868	+	0.309595i
$10$	−0.900304	+	0.519791i	−0.284701	+	0.164372i
$11$	−1.55933	−	0.900281i	−0.470156	−	0.271445i	0.246149	−	0.969232i	$-0.420835\pi$
$11$	−1.55933	−	0.900281i	−0.470156	−	0.271445i	−0.716305	+	0.697787i	$0.754168\pi$
$12$	0.402930	+	2.53900i	0.116316	+	0.732946i
$13$	1.88867	+	1.09042i	0.523823	+	0.302429i	0.738497	−	0.674256i	$-0.235536\pi$
$13$	1.88867	+	1.09042i	0.523823	+	0.302429i	−0.214675	+	0.976686i	$0.568869\pi$
$14$		0			0
$15$	−1.94800	+	1.57844i	−0.502972	+	0.407552i
$16$	1.17143			0.292858
$17$	−1.95230	−	3.38149i	−0.473503	−	0.820131i	0.526037	−	0.850462i	$-0.323677\pi$
$17$	−1.95230	−	3.38149i	−0.473503	−	0.820131i	−0.999540	+	0.0303308i	$0.990344\pi$
$18$	−0.667023	−	2.04865i	−0.157219	−	0.482870i
$19$	3.47456	+	2.00604i	0.797118	+	0.460216i	0.842462	−	0.538755i	$-0.181105\pi$
$19$	3.47456	+	2.00604i	0.797118	+	0.460216i	−0.0453446	+	0.998971i	$0.514439\pi$
$20$	1.07425	+	1.86066i	0.240210	+	0.416056i
$21$		0			0
$22$	0.646552	−	1.11986i	0.137845	−	0.238755i
$23$	−4.91522	+	2.83781i	−1.02490	+	0.591723i	−0.915518	−	0.402277i	$-0.868219\pi$
$23$	−4.91522	+	2.83781i	−1.02490	+	0.591723i	−0.109377	+	0.994000i	$0.534886\pi$
$24$	−4.28048	+	0.679296i	−0.873749	+	0.138661i
$25$	1.45230	−	2.51546i	0.290460	−	0.503092i
$26$	−0.783106	+	1.35638i	−0.153580	+	0.266008i
$27$	−2.36323	−	4.62765i	−0.454803	−	0.890592i
$28$		0			0
$29$	8.49418	−	4.90412i	1.57733	−	0.910672i	0.582100	−	0.813117i	$-0.302231\pi$
$29$	8.49418	−	4.90412i	1.57733	−	0.910672i	0.995230	−	0.0975551i	$-0.0311022\pi$
$30$	−1.13358	−	1.39899i	−0.206963	−	0.255419i
$31$		−	2.83050i		−	0.508374i	−0.967155	−	0.254187i	$-0.918192\pi$
$31$		−	2.83050i		−	0.508374i	0.967155	−	0.254187i	$-0.0818078\pi$
$32$			5.84581i			1.03340i
$33$	1.11674	−	2.91186i	0.194400	−	0.506890i
$34$	2.42847	−	1.40208i	0.416479	−	0.240454i
$35$		0			0
$36$	−4.23394	+	1.37854i	−0.705657	+	0.229756i
$37$	−0.411767	+	0.713202i	−0.0676941	+	0.117250i	−0.897886	−	0.440228i	$-0.854898\pi$
$37$	−0.411767	+	0.713202i	−0.0676941	+	0.117250i	0.830192	+	0.557478i	$0.188231\pi$
$38$	−1.44067	+	2.49531i	−0.233707	+	0.404793i
$39$	−1.35261	+	3.52686i	−0.216590	+	0.564750i
$40$	−3.13687	+	1.81107i	−0.495983	+	0.286356i
$41$	−5.90617	+	10.2298i	−0.922389	+	1.59762i	−0.126681	+	0.991943i	$0.540433\pi$
$41$	−5.90617	+	10.2298i	−0.922389	+	1.59762i	−0.795708	+	0.605681i	$0.792901\pi$
$42$		0			0
$43$	−3.76766	−	6.52578i	−0.574563	−	0.995172i	−0.996089	−	0.0883555i	$-0.971839\pi$
$43$	−3.76766	−	6.52578i	−0.574563	−	0.995172i	0.421526	−	0.906816i	$-0.361494\pi$
$44$	−2.31442	−	1.33623i	−0.348912	−	0.201444i
$45$	−3.22898	−	2.90383i	−0.481348	−	0.432878i
$46$	−2.03802	−	3.52995i	−0.300489	−	0.520463i
$47$	−2.33839			−0.341089			−0.170545	−	0.985350i	$-0.554553\pi$
$47$	−2.33839			−0.341089			−0.170545	+	0.985350i	$0.554553\pi$
$48$	0.318012	+	2.00390i	0.0459010	+	0.289238i
$49$		0			0
$50$	1.80652	+	1.04299i	0.255480	+	0.147502i
$51$	5.25452	−	4.25767i	0.735780	−	0.596194i
$52$	2.80323	+	1.61845i	0.388738	+	0.224438i
$53$	0.996713	−	0.575453i	0.136909	−	0.0790445i	−0.429981	−	0.902838i	$-0.641480\pi$
$53$	0.996713	−	0.575453i	0.136909	−	0.0790445i	0.566890	+	0.823793i	$0.308146\pi$
$54$	3.32343	−	1.69719i	0.452261	−	0.230958i
$55$		−	2.60640i		−	0.351447i
$56$		0			0
$57$	−2.48837	+	6.48831i	−0.329592	+	0.859398i
$58$	3.52198	+	6.10024i	0.462458	+	0.801001i
$59$	9.79110			1.27469			0.637346	−	0.770577i	$-0.280032\pi$
$59$	9.79110			1.27469			0.637346	+	0.770577i	$0.280032\pi$
$60$	−2.89130	+	2.34278i	−0.373265	+	0.302452i
$61$		−	2.35536i		−	0.301573i	−0.988566	−	0.150786i	$-0.951819\pi$
$61$		−	2.35536i		−	0.301573i	0.988566	−	0.150786i	$-0.0481806\pi$
$62$	2.03277			0.258163
$63$		0			0
$64$	−1.85540			−0.231925
$65$			3.15688i			0.391563i
$66$	2.09120	+	0.802008i	0.257409	+	0.0987204i
$67$	−0.312805			−0.0382152			−0.0191076	−	0.999817i	$-0.506083\pi$
$67$	−0.312805			−0.0382152			−0.0191076	+	0.999817i	$0.506083\pi$
$68$	−2.89768	−	5.01893i	−0.351395	−	0.608634i
$69$	−6.18882	−	7.63781i	−0.745047	−	0.919484i
$70$		0			0
$71$			1.94933i			0.231343i	0.993288	+	0.115671i	$0.0369019\pi$
$71$			1.94933i			0.231343i	−0.993288	+	0.115671i	$0.963098\pi$
$72$	−2.32407	−	7.13797i	−0.273894	−	0.841218i
$73$	−2.42847	+	1.40208i	−0.284231	+	0.164101i	−0.635337	−	0.772235i	$-0.719139\pi$
$73$	−2.42847	+	1.40208i	−0.284231	+	0.164101i	0.351106	+	0.936336i	$0.385806\pi$
$74$	−0.512198	−	0.295717i	−0.0595418	−	0.0343765i
$75$	4.69732	+	1.80149i	0.542399	+	0.208018i
$76$	5.15706	+	2.97743i	0.591556	+	0.341535i
$77$		0			0
$78$	−2.53287	−	0.971396i	−0.286792	−	0.109989i
$79$	12.4317			1.39867			0.699336	−	0.714793i	$-0.253479\pi$
$79$	12.4317			1.39867			0.699336	+	0.714793i	$0.253479\pi$
$80$	0.847852	+	1.46852i	0.0947927	+	0.164186i
$81$	7.27471	−	5.29892i	0.808302	−	0.588769i
$82$	−7.34669	−	4.24162i	−0.811306	−	0.468408i
$83$	−3.60916	−	6.25124i	−0.396157	−	0.686163i	0.597092	−	0.802173i	$-0.296323\pi$
$83$	−3.60916	−	6.25124i	−0.396157	−	0.686163i	−0.993248	+	0.116010i	$0.962990\pi$
$84$		0			0
$85$	2.82605	−	4.89486i	0.306528	−	0.530923i
$86$	4.68660	−	2.70581i	0.505369	−	0.291775i
$87$	10.6951	+	13.1992i	1.14664	+	1.41510i
$88$	2.25274	−	3.90186i	0.240143	−	0.415939i
$89$	5.28999	−	9.16253i	0.560737	−	0.971226i	−0.436695	−	0.899610i	$-0.643851\pi$
$89$	5.28999	−	9.16253i	0.560737	−	0.971226i	0.997432	−	0.0716161i	$-0.0228156\pi$
$90$	2.08544	−	2.31895i	0.219824	−	0.244438i
$91$		0			0
$92$	−7.29536	+	4.21198i	−0.760593	+	0.439129i
$93$	4.84198	−	0.768404i	0.502090	−	0.0796798i
$94$		−	1.67935i		−	0.173212i
$95$			5.80767i			0.595854i
$96$	−10.0001	+	1.58698i	−1.02063	+	0.161970i
$97$	13.4322	−	7.75510i	1.36384	−	0.787411i	0.373704	−	0.927548i	$-0.378088\pi$
$97$	13.4322	−	7.75510i	1.36384	−	0.787411i	0.990132	+	0.140137i	$0.0447543\pi$
$98$		0			0
$99$	5.28433	+	1.11986i	0.531095	+	0.112550i
$100$	2.15556	−	3.73354i	0.215556	−	0.373354i
$101$	1.97309	−	3.41749i	0.196330	−	0.340053i	−0.751006	−	0.660295i	$-0.770431\pi$
$101$	1.97309	−	3.41749i	0.196330	−	0.340053i	0.947336	+	0.320242i	$0.103764\pi$
$102$	3.05772	+	3.77362i	0.302759	+	0.373644i
$103$	−3.59853	+	2.07761i	−0.354573	+	0.204713i	−0.666698	−	0.745328i	$-0.732293\pi$
$103$	−3.59853	+	2.07761i	−0.354573	+	0.204713i	0.312124	+	0.950041i	$0.398959\pi$
$104$	−2.72853	+	4.72595i	−0.267554	+	0.463417i
$105$		0			0
$106$	0.413271	+	0.715806i	0.0401404	+	0.0695253i
$107$	−4.91092	−	2.83532i	−0.474757	−	0.274101i	0.243472	−	0.969908i	$-0.421714\pi$
$107$	−4.91092	−	2.83532i	−0.474757	−	0.274101i	−0.718229	+	0.695807i	$0.755047\pi$
$108$	−3.50759	−	6.86853i	−0.337518	−	0.660925i
$109$	5.99916	+	10.3908i	0.574615	+	0.995262i	0.996083	+	0.0884193i	$0.0281815\pi$
$109$	5.99916	+	10.3908i	0.574615	+	0.995262i	−0.421468	+	0.906843i	$0.638485\pi$
$110$	1.87183			0.178472
$111$	−1.33182	−	0.510772i	−0.126411	−	0.0484804i
$112$		0			0
$113$	6.27800	+	3.62461i	0.590585	+	0.340974i	0.765329	−	0.643640i	$-0.222576\pi$
$113$	6.27800	+	3.62461i	0.590585	+	0.340974i	−0.174744	+	0.984614i	$0.555910\pi$
$114$	−4.65969	−	1.78706i	−0.436420	−	0.167374i
$115$	−7.11502	−	4.10786i	−0.663479	−	0.383060i
$116$	12.6074	−	7.27887i	1.17057	−	0.675826i
$117$	−6.40040	−	1.35638i	−0.591717	−	0.125397i
$118$			7.03164i			0.647315i
$119$		0			0
$120$	−3.94968	−	4.87441i	−0.360554	−	0.444971i
$121$	−3.87899	−	6.71861i	−0.352635	−	0.610782i
$122$	1.69154			0.153145
$123$	−19.1029	−	7.32625i	−1.72245	−	0.660586i
$124$		−	4.20114i		−	0.377273i
$125$	11.4423			1.02343
$126$		0			0
$127$	−0.881336			−0.0782059			−0.0391030	−	0.999235i	$-0.512450\pi$
$127$	−0.881336			−0.0782059			−0.0391030	+	0.999235i	$0.512450\pi$
$128$			10.3591i			0.915626i
$129$	10.1405	−	8.21669i	0.892818	−	0.723439i
$130$	−2.26717			−0.198844
$131$	1.48721	+	2.57592i	0.129938	+	0.225059i	0.923652	−	0.383232i	$-0.125189\pi$
$131$	1.48721	+	2.57592i	0.129938	+	0.225059i	−0.793714	+	0.608291i	$0.791856\pi$
$132$	1.65751	−	4.32189i	0.144268	−	0.376173i
$133$		0			0
$134$		−	0.224646i		−	0.0194065i
$135$	4.09085	−	6.31195i	0.352084	−	0.543246i
$136$	8.46137	−	4.88517i	0.725556	−	0.418900i
$137$	−10.3045	−	5.94930i	−0.880372	−	0.508283i	−0.00959114	−	0.999954i	$-0.503053\pi$
$137$	−10.3045	−	5.94930i	−0.880372	−	0.508283i	−0.870781	+	0.491671i	$0.836386\pi$
$138$	5.48522	−	4.44461i	0.466933	−	0.378350i
$139$	−10.4143	−	6.01268i	−0.883327	−	0.509989i	−0.0115731	−	0.999933i	$-0.503684\pi$
$139$	−10.4143	−	6.01268i	−0.883327	−	0.509989i	−0.871754	+	0.489944i	$0.837017\pi$
$140$		0			0
$141$	−0.634809	−	4.00015i	−0.0534606	−	0.336874i
$142$	−1.39994			−0.117481
$143$	−1.96338	−	3.40067i	−0.164186	−	0.284378i
$144$	−3.34163	+	1.08801i	−0.278469	+	0.0906674i
$145$	12.2957	+	7.09895i	1.02111	+	0.589536i
$146$	−1.00693	−	1.74405i	−0.0833338	−	0.144338i
$147$		0			0
$148$	−0.611160	+	1.05856i	−0.0502370	+	0.0870131i
$149$	6.13061	−	3.53951i	0.502239	−	0.289968i	−0.227399	−	0.973802i	$-0.573022\pi$
$149$	6.13061	−	3.53951i	0.502239	−	0.289968i	0.729638	+	0.683834i	$0.239689\pi$
$150$	−1.29377	+	3.37346i	−0.105636	+	0.275442i
$151$	−7.79093	+	13.4943i	−0.634017	+	1.09815i	0.352706	+	0.935734i	$0.385262\pi$
$151$	−7.79093	+	13.4943i	−0.634017	+	1.09815i	−0.986723	+	0.162415i	$0.948072\pi$
$152$	−5.01963	+	8.69425i	−0.407146	+	0.705197i
$153$	8.70982	+	7.83277i	0.704147	+	0.633242i
$154$		0			0
$155$	3.54836	−	2.04865i	0.285011	−	0.164551i
$156$	−2.00759	+	5.23470i	−0.160736	+	0.419111i
$157$			2.08628i			0.166503i	0.996529	+	0.0832517i	$0.0265305\pi$
$157$			2.08628i			0.166503i	−0.996529	+	0.0832517i	$0.973469\pi$
$158$			8.92801i			0.710274i
$159$	1.25498	+	1.54880i	0.0995260	+	0.122828i
$160$	−7.32839	+	4.23105i	−0.579360	+	0.334494i
$161$		0			0
$162$	3.80551	+	5.22446i	0.298989	+	0.410472i
$163$	−5.58983	+	9.68188i	−0.437830	+	0.758343i	−0.997522	−	0.0703575i	$-0.977586\pi$
$163$	−5.58983	+	9.68188i	−0.437830	+	0.758343i	0.559692	+	0.828700i	$0.310919\pi$
$164$	−8.76616	+	15.1834i	−0.684522	+	1.18563i
$165$	4.45862	−	0.707566i	0.347103	−	0.0550839i
$166$	4.48944	−	2.59198i	0.348448	−	0.201176i
$167$	0.960750	−	1.66407i	0.0743450	−	0.128769i	−0.826456	−	0.563001i	$-0.809647\pi$
$167$	0.960750	−	1.66407i	0.0743450	−	0.128769i	0.900801	+	0.434232i	$0.142980\pi$
$168$		0			0
$169$	−4.12195	−	7.13943i	−0.317073	−	0.549187i
$170$	3.51533	+	2.02958i	0.269613	+	0.155661i
$171$	−11.7747	−	2.49531i	−0.900435	−	0.190821i
$172$	−5.59210	−	9.68580i	−0.426393	−	0.738535i
$173$	−15.2258			−1.15760			−0.578798	−	0.815471i	$-0.696478\pi$
$173$	−15.2258			−1.15760			−0.578798	+	0.815471i	$0.696478\pi$
$174$	−9.47922	+	7.68089i	−0.718618	+	0.582287i
$175$		0			0
$176$	−1.82665	−	1.05462i	−0.137689	−	0.0794948i
$177$	2.65802	+	16.7491i	0.199789	+	1.25894i
$178$	6.58022	+	3.79909i	0.493208	+	0.284754i
$179$	0.299401	−	0.172859i	0.0223783	−	0.0129201i	−0.488769	−	0.872413i	$-0.662554\pi$
$179$	0.299401	−	0.172859i	0.0223783	−	0.0129201i	0.511147	+	0.859493i	$0.329221\pi$
$180$	−4.79257	−	4.30998i	−0.357217	−	0.321247i
$181$		−	3.27661i		−	0.243548i	−0.992558	−	0.121774i	$-0.961142\pi$
$181$		−	3.27661i		−	0.243548i	0.992558	−	0.121774i	$-0.0388583\pi$
$182$		0			0
$183$	4.02918	−	0.639415i	0.297846	−	0.0472669i
$184$	−7.10094	−	12.2992i	−0.523488	−	0.906708i
$185$	−1.19211			−0.0876454
$186$	0.551842	+	3.47735i	0.0404630	+	0.254972i
$187$			7.03048i			0.514120i
$188$	−3.47073			−0.253129
$189$		0			0
$190$	−4.17087			−0.302587
$191$		−	7.39120i		−	0.534808i	−0.963584	−	0.267404i	$-0.913834\pi$
$191$		−	7.39120i		−	0.534808i	0.963584	−	0.267404i	$-0.0861659\pi$
$192$	−0.503691	−	3.17393i	−0.0363507	−	0.229059i
$193$	13.0285			0.937812			0.468906	−	0.883248i	$-0.344648\pi$
$193$	13.0285			0.937812			0.468906	+	0.883248i	$0.344648\pi$
$194$	5.56945	+	9.64658i	0.399863	+	0.692584i
$195$	−5.40030	+	0.857007i	−0.386724	+	0.0613716i
$196$		0			0
$197$		−	4.03035i		−	0.287151i	−0.989639	−	0.143575i	$-0.954140\pi$
$197$		−	4.03035i		−	0.287151i	0.989639	−	0.143575i	$-0.0458599\pi$
$198$	−0.804246	+	3.79503i	−0.0571553	+	0.269701i
$199$	−14.2096	+	8.20390i	−1.00729	+	0.581559i	−0.910397	−	0.413736i	$-0.864224\pi$
$199$	−14.2096	+	8.20390i	−1.00729	+	0.581559i	−0.0968925	+	0.995295i	$0.530890\pi$
$200$	6.29434	+	3.63404i	0.445077	+	0.256965i
$201$	−0.0849180	−	0.535098i	−0.00598965	−	0.0377429i
$202$	2.45433	+	1.41701i	0.172686	+	0.0997003i
$203$		0			0
$204$	7.79895	−	6.31940i	0.546036	−	0.442446i
$205$	−17.0989			−1.19424
$206$	−1.49207	−	2.58434i	−0.103957	−	0.180060i
$207$	11.3855	−	12.6603i	0.791346	−	0.879954i
$208$	2.21245	+	1.27736i	0.153406	+	0.0885688i
$209$	−3.61199	−	6.25615i	−0.249847	−	0.432747i
$210$		0			0
$211$	−6.00827	+	10.4066i	−0.413627	+	0.716422i	−0.995283	−	0.0970121i	$-0.969071\pi$
$211$	−6.00827	+	10.4066i	−0.413627	+	0.716422i	0.581657	+	0.813434i	$0.302405\pi$
$212$	1.47936	−	0.854108i	0.101603	−	0.0586604i
$213$	−3.33461	+	0.529189i	−0.228483	+	0.0362594i
$214$	2.03623	−	3.52686i	0.139194	−	0.241091i
$215$	5.45387	−	9.44638i	0.371951	−	0.644238i
$216$	11.5796	−	5.91341i	0.787892	−	0.402357i
$217$		0			0
$218$	−7.46236	+	4.30839i	−0.505415	+	0.291801i
$219$	−3.05772	−	3.77362i	−0.206622	−	0.254998i
$220$		−	3.86851i		−	0.260815i
$221$		−	8.51535i		−	0.572804i
$222$	0.366820	−	0.956467i	0.0246193	−	0.0641939i
$223$	−22.7932	+	13.1597i	−1.52635	+	0.881237i	−0.526836	+	0.849967i	$0.676622\pi$
$223$	−22.7932	+	13.1597i	−1.52635	+	0.881237i	−0.999511	+	0.0312693i	$0.990045\pi$
$224$		0			0
$225$	−1.80652	+	8.52449i	−0.120435	+	0.568300i
$226$	−2.60307	+	4.50865i	−0.173154	+	0.299911i
$227$	−5.40410	+	9.36018i	−0.358683	+	0.621257i	−0.987741	−	0.156101i	$-0.950107\pi$
$227$	−5.40410	+	9.36018i	−0.358683	+	0.621257i	0.629058	+	0.777358i	$0.283441\pi$
$228$	−3.69332	+	9.63019i	−0.244596	+	0.637775i
$229$	8.39777	−	4.84846i	0.554941	−	0.320395i	−0.196172	−	0.980570i	$-0.562851\pi$
$229$	8.39777	−	4.84846i	0.554941	−	0.320395i	0.751112	+	0.660174i	$0.229518\pi$
$230$	2.95013	−	5.10977i	0.194526	−	0.336928i
$231$		0			0
$232$	12.2714	+	21.2547i	0.805657	+	1.39544i
$233$	1.92897	+	1.11369i	0.126371	+	0.0729605i	0.561853	−	0.827237i	$-0.310089\pi$
$233$	1.92897	+	1.11369i	0.126371	+	0.0729605i	−0.435482	+	0.900198i	$0.643422\pi$
$234$	0.974107	−	4.59655i	0.0636793	−	0.300486i
$235$	−1.69247	−	2.93144i	−0.110404	−	0.191226i
$236$	14.5323			0.945973
$237$	3.37486	+	21.2661i	0.219220	+	1.38138i
$238$		0			0
$239$	−15.9697	−	9.22008i	−1.03299	−	0.596398i	−0.115151	−	0.993348i	$-0.536735\pi$
$239$	−15.9697	−	9.22008i	−1.03299	−	0.596398i	−0.917840	+	0.396950i	$0.870068\pi$
$240$	−2.28195	+	1.84904i	−0.147299	+	0.119355i
$241$	−5.60475	−	3.23591i	−0.361034	−	0.208443i	0.308500	−	0.951224i	$-0.400173\pi$
$241$	−5.60475	−	3.23591i	−0.361034	−	0.208443i	−0.669534	+	0.742781i	$0.733506\pi$
$242$	4.82508	−	2.78576i	0.310168	−	0.179075i
$243$	11.0394	+	11.0059i	0.708181	+	0.706031i
$244$		−	3.49591i		−	0.223803i
$245$		0			0
$246$	5.26147	−	13.7191i	0.335459	−	0.874695i
$247$	4.37486	+	7.57748i	0.278366	+	0.482143i
$248$	7.08266			0.449750
$249$	9.71387	−	7.87102i	0.615591	−	0.498806i
$250$			8.21748i			0.519719i
$251$	0.416679			0.0263005			0.0131503	−	0.999914i	$-0.495814\pi$
$251$	0.416679			0.0263005			0.0131503	+	0.999914i	$0.495814\pi$
$252$		0			0
$253$	10.2193			0.642481
$254$		−	0.632946i		−	0.0397146i
$255$	9.14057	+	3.50555i	0.572404	+	0.219526i
$256$	−11.1504			−0.696899
$257$	10.5642	+	18.2977i	0.658976	+	1.14138i	0.980881	+	0.194607i	$0.0623433\pi$
$257$	10.5642	+	18.2977i	0.658976	+	1.14138i	−0.321906	+	0.946772i	$0.604323\pi$
$258$	5.90095	+	7.28254i	0.367377	+	0.453391i
$259$		0			0
$260$			4.68556i			0.290586i
$261$	−19.6757	+	21.8788i	−1.21789	+	1.35426i
$262$	−1.84994	+	1.06806i	−0.114290	+	0.0659851i
$263$	−19.2653	−	11.1228i	−1.18795	−	0.685862i	−0.230108	−	0.973165i	$-0.573908\pi$
$263$	−19.2653	−	11.1228i	−1.18795	−	0.685862i	−0.957840	+	0.287304i	$0.907241\pi$
$264$	7.28625	+	2.79439i	0.448437	+	0.171983i
$265$	1.44279	+	0.832996i	0.0886299	+	0.0511705i
$266$		0			0
$267$	17.1099	+	6.56191i	1.04711	+	0.401582i
$268$	−0.464277			−0.0283602
$269$	−14.5164	−	25.1432i	−0.885083	−	1.53301i	−0.845619	−	0.533788i	$-0.820768\pi$
$269$	−14.5164	−	25.1432i	−0.885083	−	1.53301i	−0.0394642	−	0.999221i	$-0.512565\pi$
$270$	4.53303	+	2.93791i	0.275871	+	0.178795i
$271$	−20.8174	−	12.0189i	−1.26456	−	0.730097i	−0.290610	−	0.956842i	$-0.593858\pi$
$271$	−20.8174	−	12.0189i	−1.26456	−	0.730097i	−0.973954	+	0.226745i	$0.927192\pi$
$272$	−2.28699	−	3.96118i	−0.138669	−	0.240182i
$273$		0			0
$274$	4.27259	−	7.40034i	0.258117	−	0.447071i
$275$	−4.52924	+	2.61496i	−0.273124	+	0.157688i
$276$	−9.18568	−	11.3363i	−0.552913	−	0.682366i
$277$	−4.03243	+	6.98437i	−0.242285	+	0.419650i	−0.961365	−	0.275278i	$-0.911230\pi$
$277$	−4.03243	+	6.98437i	−0.242285	+	0.419650i	0.719080	+	0.694928i	$0.244564\pi$
$278$	4.31811	−	7.47918i	0.258983	−	0.448572i
$279$	2.62893	+	8.07431i	0.157390	+	0.483396i
$280$		0			0
$281$	−12.0876	+	6.97879i	−0.721087	+	0.416320i	−0.815153	−	0.579246i	$-0.803347\pi$
$281$	−12.0876	+	6.97879i	−0.721087	+	0.416320i	0.0940658	+	0.995566i	$0.470014\pi$
$282$	2.87278	−	0.455899i	0.171071	−	0.0271484i
$283$			15.5375i			0.923609i	0.886982	+	0.461805i	$0.152798\pi$
$283$			15.5375i			0.923609i	−0.886982	+	0.461805i	$0.847202\pi$
$284$			2.89326i			0.171684i
$285$	−9.93485	+	1.57662i	−0.588490	+	0.0933911i
$286$	2.44225	−	1.41003i	0.144413	−	0.0833769i
$287$		0			0
$288$	−5.42950	−	16.6758i	−0.319937	−	0.982630i
$289$	0.877036	−	1.51907i	0.0515904	−	0.0893571i
$290$	−5.09823	+	8.83039i	−0.299378	+	0.518539i
$291$	16.9127	+	20.8725i	0.991440	+	1.22357i
$292$	−3.60442	+	2.08102i	−0.210933	+	0.121782i
$293$	6.73712	−	11.6690i	0.393587	−	0.681712i	−0.599333	−	0.800500i	$-0.704567\pi$
$293$	6.73712	−	11.6690i	0.393587	−	0.681712i	0.992920	+	0.118788i	$0.0379008\pi$
$294$		0			0
$295$	7.08655	+	12.2743i	0.412595	+	0.714635i
$296$	−1.78462	−	1.03035i	−0.103729	−	0.0598879i
$297$	−0.481132	+	9.34361i	−0.0279181	+	0.542171i
$298$	2.54196	+	4.40280i	0.147252	+	0.255047i
$299$	−12.3776			−0.715818
$300$	6.97193	+	2.67384i	0.402525	+	0.154374i
$301$		0			0
$302$	−9.69114	−	5.59518i	−0.557663	−	0.321967i
$303$	6.38175	+	2.44750i	0.366622	+	0.140605i
$304$	4.07020	+	2.34993i	0.233442	+	0.134778i
$305$	2.95271	−	1.70475i	0.169072	−	0.0976136i
$306$	−5.62524	+	6.25510i	−0.321573	+	0.357580i
$307$			8.62791i			0.492421i	0.969216	+	0.246210i	$0.0791854\pi$
$307$			8.62791i			0.492421i	−0.969216	+	0.246210i	$0.920815\pi$
$308$		0			0
$309$	−4.53095	−	5.59178i	−0.257757	−	0.318106i
$310$	1.47127	+	2.54831i	0.0835625	+	0.144734i
$311$	16.2440			0.921113			0.460556	−	0.887630i	$-0.347650\pi$
$311$	16.2440			0.921113			0.460556	+	0.887630i	$0.347650\pi$
$312$	−8.82513	−	3.38457i	−0.499625	−	0.191614i
$313$		−	6.77692i		−	0.383054i	−0.981487	−	0.191527i	$-0.938656\pi$
$313$		−	6.77692i		−	0.383054i	0.981487	−	0.191527i	$-0.0613440\pi$
$314$	−1.49830			−0.0845538
$315$		0			0
$316$	18.4515			1.03798
$317$		−	21.9676i		−	1.23382i	−0.787033	−	0.616911i	$-0.788384\pi$
$317$		−	21.9676i		−	1.23382i	0.787033	−	0.616911i	$-0.211616\pi$
$318$	−1.11230	+	0.901281i	−0.0623746	+	0.0505413i
$319$	−17.6603			−0.988789
$320$	−1.34289	−	2.32596i	−0.0750699	−	0.130025i
$321$	3.51705	−	9.17056i	0.196302	−	0.511850i
$322$		0			0
$323$		−	15.6655i		−	0.871654i
$324$	10.7974	−	7.86485i	0.599855	−	0.436936i
$325$	5.48584	−	3.16725i	0.304299	−	0.175687i
$326$	−6.95320	−	4.01443i	−0.385102	−	0.222339i
$327$	−16.1464	+	13.0833i	−0.892900	+	0.723505i
$328$	−25.5976	−	14.7788i	−1.41339	−	0.816022i
$329$		0			0
$330$	0.508150	+	3.20203i	0.0279728	+	0.176266i
$331$	−14.6036			−0.802685			−0.401342	−	0.915928i	$-0.631456\pi$
$331$	−14.6036			−0.802685			−0.401342	+	0.915928i	$0.631456\pi$
$332$	−5.35684	−	9.27833i	−0.293995	−	0.509214i
$333$	0.512198	−	2.41693i	0.0280683	−	0.132447i
$334$	1.19508	+	0.689978i	0.0653917	+	0.0377539i
$335$	−0.226400	−	0.392137i	−0.0123696	−	0.0214247i
$336$		0			0
$337$	−16.2629	+	28.1681i	−0.885894	+	1.53441i	−0.0412090	+	0.999151i	$0.513121\pi$
$337$	−16.2629	+	28.1681i	−0.885894	+	1.53441i	−0.844685	+	0.535263i	$0.820212\pi$
$338$	5.12730	−	2.96025i	0.278888	−	0.161016i
$339$	−4.49610	+	11.7234i	−0.244195	+	0.636728i
$340$	4.19453	−	7.26514i	0.227480	−	0.394007i
$341$	−2.54825	+	4.41370i	−0.137995	+	0.239015i
$342$	1.79205	−	8.45621i	0.0969029	−	0.457259i
$343$		0			0
$344$	16.3292	−	9.42767i	0.880412	−	0.508306i
$345$	5.09555	−	13.2864i	0.274335	−	0.715318i
$346$		−	10.9347i		−	0.587851i
$347$			3.18703i			0.171089i	0.996334	+	0.0855444i	$0.0272630\pi$
$347$			3.18703i			0.171089i	−0.996334	+	0.0855444i	$0.972737\pi$
$348$	15.8741	+	19.5907i	0.850942	+	1.05017i
$349$	−6.48224	+	3.74252i	−0.346986	+	0.200333i	−0.663357	−	0.748303i	$-0.730869\pi$
$349$	−6.48224	+	3.74252i	−0.346986	+	0.200333i	0.316371	+	0.948636i	$0.397536\pi$
$350$		0			0
$351$	0.582750	−	11.3170i	0.0311049	−	0.604058i
$352$	5.26287	−	9.11556i	0.280512	−	0.485861i
$353$	5.69040	−	9.85606i	0.302869	−	0.524585i	−0.673915	−	0.738809i	$-0.735389\pi$
$353$	5.69040	−	9.85606i	0.302869	−	0.524585i	0.976785	+	0.214223i	$0.0687220\pi$
$354$	−12.0286	+	1.90890i	−0.639315	+	0.101457i
$355$	−2.44370	+	1.41087i	−0.129698	+	0.0748814i
$356$	7.85159	−	13.5994i	0.416134	−	0.720764i
$357$		0			0
$358$	0.124142	+	0.215020i	0.00656109	+	0.0113641i
$359$	4.77569	+	2.75725i	0.252051	+	0.145522i	0.620703	−	0.784046i	$-0.286847\pi$
$359$	4.77569	+	2.75725i	0.252051	+	0.145522i	−0.368652	+	0.929568i	$0.620181\pi$
$360$	7.26616	−	8.07976i	0.382960	−	0.425841i
$361$	−1.45164	−	2.51432i	−0.0764022	−	0.132332i
$362$	2.35315			0.123679
$363$	10.4401	−	8.45949i	0.547963	−	0.444008i
$364$		0			0
$365$	−3.51533	−	2.02958i	−0.184001	−	0.106233i
$366$	0.459207	+	2.89362i	0.0240031	+	0.151252i
$367$	18.2753	+	10.5512i	0.953962	+	0.550770i	0.894309	−	0.447449i	$-0.147667\pi$
$367$	18.2753	+	10.5512i	0.953962	+	0.550770i	0.0596526	+	0.998219i	$0.481001\pi$
$368$	−5.75785	+	3.32430i	−0.300149	+	0.173291i
$369$	7.34669	−	34.6671i	0.382454	−	1.80470i
$370$		−	0.856131i		−	0.0445081i
$371$		0			0
$372$	7.18665	−	1.14049i	0.372611	−	0.0591318i
$373$	−7.68498	−	13.3108i	−0.397913	−	0.689206i	0.595555	−	0.803314i	$-0.296932\pi$
$373$	−7.68498	−	13.3108i	−0.397913	−	0.689206i	−0.993468	+	0.114109i	$0.963599\pi$
$374$	−5.04906			−0.261080
$375$	3.10627	+	19.5737i	0.160407	+	1.01078i
$376$		−	5.85127i		−	0.301756i
$377$	21.3903			1.10166
$378$		0			0
$379$	−32.3630			−1.66238			−0.831188	−	0.555991i	$-0.812339\pi$
$379$	−32.3630			−1.66238			−0.831188	+	0.555991i	$0.812339\pi$
$380$			8.61995i			0.442194i
$381$	−0.239259	−	1.50765i	−0.0122576	−	0.0772394i
$382$	5.30811			0.271587
$383$	−9.91730	−	17.1773i	−0.506750	−	0.877718i	−0.999969	−	0.00781236i	$-0.997513\pi$
$383$	−9.91730	−	17.1773i	−0.506750	−	0.877718i	0.493219	−	0.869905i	$-0.335820\pi$
$384$	−17.7208	+	2.81222i	−0.904310	+	0.143510i
$385$		0			0
$386$			9.35663i			0.476240i
$387$	16.8087	+	15.1161i	0.854434	+	0.768395i
$388$	19.9366	−	11.5104i	1.01213	−	0.584352i
$389$	4.41918	+	2.55141i	0.224061	+	0.129362i	0.607829	−	0.794068i	$-0.292040\pi$
$389$	4.41918	+	2.55141i	0.224061	+	0.129362i	−0.383768	+	0.923429i	$0.625374\pi$
$390$	−0.615474	−	3.87832i	−0.0311657	−	0.196386i
$391$	19.1920	+	11.0805i	0.970581	+	0.560365i
$392$		0			0
$393$	−4.00274	+	3.24337i	−0.201912	+	0.163607i
$394$	2.89446			0.145821
$395$	8.99772	+	15.5845i	0.452724	+	0.784141i
$396$	7.84319	+	1.66214i	0.394135	+	0.0835256i
$397$	11.5288	+	6.65615i	0.578613	+	0.334062i	0.760582	−	0.649242i	$-0.224914\pi$
$397$	11.5288	+	6.65615i	0.578613	+	0.334062i	−0.181969	+	0.983304i	$0.558247\pi$
$398$	−5.89177	−	10.2048i	−0.295328	−	0.511522i
$399$		0			0
$400$	1.70127	−	2.94669i	0.0850636	−	0.147334i
$401$	14.1750	−	8.18392i	0.707864	−	0.408685i	−0.102406	−	0.994743i	$-0.532654\pi$
$401$	14.1750	−	8.18392i	0.707864	−	0.408685i	0.810270	+	0.586057i	$0.199321\pi$
$402$	0.384289	−	0.0609852i	0.0191666	−	0.00304167i
$403$	3.08645	−	5.34589i	0.153747	−	0.266298i
$404$	2.92853	−	5.07237i	0.145700	−	0.252360i
$405$	11.9080	+	5.28446i	0.591716	+	0.262587i
$406$		0			0
$407$	1.28416	−	0.741412i	0.0636536	−	0.0367504i
$408$	10.6538	+	13.1482i	0.527443	+	0.650933i
$409$			4.33710i			0.214456i	0.994234	+	0.107228i	$0.0341975\pi$
$409$			4.33710i			0.214456i	−0.994234	+	0.107228i	$0.965803\pi$
$410$		−	12.2799i		−	0.606460i
$411$	7.37975	−	19.2424i	0.364016	−	0.949157i
$412$	−5.34107	+	3.08367i	−0.263135	+	0.151921i
$413$		0			0
$414$	9.09223	+	8.17667i	0.446859	+	0.401862i
$415$	5.22443	−	9.04898i	0.256457	−	0.444197i
$416$	−6.37441	+	11.0408i	−0.312531	+	0.541320i
$417$	7.45837	−	19.4474i	0.365238	−	0.952343i
$418$	4.49296	−	2.59401i	0.219758	−	0.126877i
$419$	−9.41294	+	16.3037i	−0.459852	+	0.796487i	−0.998953	−	0.0457540i	$-0.985431\pi$
$419$	−9.41294	+	16.3037i	−0.459852	+	0.796487i	0.539100	+	0.842241i	$0.318764\pi$
$420$		0			0
$421$	0.913453	+	1.58215i	0.0445190	+	0.0771092i	0.887426	−	0.460950i	$-0.152491\pi$
$421$	0.913453	+	1.58215i	0.0445190	+	0.0771092i	−0.842907	+	0.538059i	$0.819158\pi$
$422$	−7.47370	−	4.31494i	−0.363814	−	0.210048i
$423$	6.67051	−	2.17186i	0.324331	−	0.105600i
$424$	1.43993	+	2.49404i	0.0699294	+	0.121121i
$425$	−11.3413			−0.550135
$426$	−0.380046	−	2.39480i	−0.0184133	−	0.116029i
$427$		0			0
$428$	−7.28897	−	4.20829i	−0.352326	−	0.203415i
$429$	5.28433	−	4.28182i	0.255130	−	0.206728i
$430$	6.78407	+	3.91679i	0.327157	+	0.188884i
$431$	12.4526	−	7.18954i	0.599823	−	0.346308i	−0.169149	−	0.985590i	$-0.554102\pi$
$431$	12.4526	−	7.18954i	0.599823	−	0.346308i	0.768972	+	0.639283i	$0.220769\pi$
$432$	−2.76836	−	5.42098i	−0.133193	−	0.260817i
$433$		−	2.22130i		−	0.106749i	−0.998575	−	0.0533745i	$-0.983002\pi$
$433$		−	2.22130i		−	0.106749i	0.998575	−	0.0533745i	$-0.0169977\pi$
$434$		0			0
$435$	−8.80582	+	22.9608i	−0.422207	+	1.10089i
$436$	8.90417	+	15.4225i	0.426432	+	0.738602i
$437$	−22.7710			−1.08928
$438$	2.71009	−	2.19595i	0.129493	−	0.104927i
$439$		−	10.0448i		−	0.479413i	−0.970845	−	0.239706i	$-0.922949\pi$
$439$		−	10.0448i		−	0.479413i	0.970845	−	0.239706i	$-0.0770512\pi$
$440$	6.52190			0.310919
$441$		0			0
$442$	6.11544			0.290882
$443$		−	13.8934i		−	0.660097i	−0.943964	−	0.330049i	$-0.892935\pi$
$443$		−	13.8934i		−	0.660097i	0.943964	−	0.330049i	$-0.107065\pi$
$444$	−1.97673	−	0.758107i	−0.0938116	−	0.0359782i
$445$	15.3150			0.726002
$446$	−9.45084	−	16.3693i	−0.447510	−	0.775110i
$447$	7.71913	+	9.52640i	0.365102	+	0.450583i
$448$		0			0
$449$		−	10.5630i		−	0.498498i	−0.968439	−	0.249249i	$-0.919816\pi$
$449$		−	10.5630i		−	0.498498i	0.968439	−	0.249249i	$-0.0801837\pi$
$450$	−6.12201	−	1.29738i	−0.288594	−	0.0611592i
$451$	18.4194	−	10.6344i	0.867334	−	0.500755i
$452$	9.31804	+	5.37977i	0.438284	+	0.253043i
$453$	−25.1989	−	9.66417i	−1.18395	−	0.454063i
$454$	−6.72217	−	3.88105i	−0.315487	−	0.182147i
$455$		0			0
$456$	−16.2355	−	6.22655i	−0.760295	−	0.291585i
$457$	5.11307			0.239179			0.119590	−	0.992823i	$-0.461842\pi$
$457$	5.11307			0.239179			0.119590	+	0.992823i	$0.461842\pi$
$458$	3.48200	+	6.03100i	0.162703	+	0.281810i
$459$	−11.0346	+	17.0258i	−0.515051	+	0.794696i
$460$	−10.5604	−	6.09704i	−0.492380	−	0.284276i
$461$	−4.16691	−	7.21730i	−0.194072	−	0.336143i	0.752524	−	0.658565i	$-0.228836\pi$
$461$	−4.16691	−	7.21730i	−0.194072	−	0.336143i	−0.946596	+	0.322422i	$0.895503\pi$
$462$		0			0
$463$	10.0143	−	17.3452i	0.465403	−	0.806102i	−0.533817	−	0.845600i	$-0.679243\pi$
$463$	10.0143	−	17.3452i	0.465403	−	0.806102i	0.999220	+	0.0394986i	$0.0125761\pi$
$464$	9.95036	−	5.74484i	0.461934	−	0.266698i
$465$	4.46779	+	5.51383i	0.207189	+	0.255698i
$466$	−0.799817	+	1.38532i	−0.0370508	+	0.0641739i
$467$	−10.3896	+	17.9953i	−0.480773	+	0.832723i	−0.999757	−	0.0220611i	$-0.992977\pi$
$467$	−10.3896	+	17.9953i	−0.480773	+	0.832723i	0.518984	+	0.854784i	$0.326310\pi$
$468$	−9.49971	−	2.01319i	−0.439124	−	0.0930597i
$469$		0			0
$470$	2.10526	−	1.21547i	0.0971085	−	0.0560656i
$471$	−3.56888	+	0.566368i	−0.164445	+	0.0260969i
$472$			24.4999i			1.12770i
$473$			13.5678i			0.623848i
$474$	−15.2726	+	2.42371i	−0.701496	+	0.111325i
$475$	10.0922	−	5.82674i	0.463062	−	0.267349i
$476$		0			0
$477$	−2.30876	+	2.56727i	−0.105711	+	0.117547i
$478$	6.62156	−	11.4689i	0.302863	−	0.524574i
$479$	16.0308	−	27.7662i	0.732468	−	1.26867i	−0.223357	−	0.974737i	$-0.571702\pi$
$479$	16.0308	−	27.7662i	0.732468	−	1.26867i	0.955825	−	0.293935i	$-0.0949650\pi$
$480$	−9.22727	−	11.3876i	−0.421165	−	0.519773i
$481$	−1.55538	+	0.898002i	−0.0709194	+	0.0409454i
$482$	2.32392	−	4.02515i	0.105852	−	0.183340i
$483$		0			0
$484$	−5.75734	−	9.97200i	−0.261697	−	0.453273i
$485$	19.4438	+	11.2259i	0.882897	+	0.509741i
$486$	−7.90410	+	7.92816i	−0.358537	+	0.359629i
$487$	11.8375	+	20.5032i	0.536408	+	0.929087i	0.999094	+	0.0425641i	$0.0135527\pi$
$487$	11.8375	+	20.5032i	0.536408	+	0.929087i	−0.462685	+	0.886523i	$0.653114\pi$
$488$	5.89373			0.266796
$489$	−18.0797	−	6.93385i	−0.817594	−	0.313560i
$490$		0			0
$491$	15.4664	+	8.92951i	0.697987	+	0.402983i	0.806597	−	0.591101i	$-0.201307\pi$
$491$	15.4664	+	8.92951i	0.697987	+	0.402983i	−0.108610	+	0.994084i	$0.534640\pi$
$492$	−28.3532	−	10.8739i	−1.27826	−	0.490233i
$493$	−33.1664	−	19.1486i	−1.49374	−	0.862411i
$494$	−5.44189	+	3.14188i	−0.244842	+	0.141360i
$495$	2.42079	+	7.43503i	0.108806	+	0.334180i
$496$		−	3.31574i		−	0.148881i
$497$		0			0
$498$	5.65271	+	6.97617i	0.253304	+	0.312610i
$499$	11.5602	+	20.0229i	0.517506	+	0.896346i	0.999793	+	0.0203330i	$0.00647265\pi$
$499$	11.5602	+	20.0229i	0.517506	+	0.896346i	−0.482288	+	0.876013i	$0.660194\pi$
$500$	16.9831			0.759506
$501$	3.10744	+	1.19175i	0.138830	+	0.0532436i
$502$			0.299245i			0.0133560i
$503$	−13.9995			−0.624206			−0.312103	−	0.950048i	$-0.601033\pi$
$503$	−13.9995			−0.624206			−0.312103	+	0.950048i	$0.601033\pi$
$504$		0			0
$505$	5.71228			0.254193
$506$			7.33915i			0.326265i
$507$	11.0940	−	8.98935i	0.492703	−	0.399231i
$508$	−1.30811			−0.0580381
$509$	6.79171	+	11.7636i	0.301037	+	0.521411i	0.976371	−	0.216100i	$-0.0693339\pi$
$509$	6.79171	+	11.7636i	0.301037	+	0.521411i	−0.675334	+	0.737512i	$0.736001\pi$
$510$	−2.51757	+	6.56445i	−0.111480	+	0.290679i
$511$		0			0
$512$			12.7104i			0.561727i
$513$	1.07208	−	20.8198i	0.0473333	−	0.919214i
$514$	−13.1408	+	7.58684i	−0.579616	+	0.334641i
$515$	−5.20904	−	3.00744i	−0.229538	−	0.132524i
$516$	15.0508	−	12.1955i	0.662577	−	0.536878i
$517$	3.64633	+	2.10521i	0.160365	+	0.0925870i
$518$		0			0
$519$	−4.13339	−	26.0459i	−0.181435	−	1.14329i
$520$	−7.89935			−0.346409
$521$	15.9477	+	27.6222i	0.698682	+	1.21015i	0.968924	+	0.247360i	$0.0795630\pi$
$521$	15.9477	+	27.6222i	0.698682	+	1.21015i	−0.270242	+	0.962792i	$0.587104\pi$
$522$	−15.7126	−	14.1304i	−0.687723	−	0.618472i
$523$	1.20531	+	0.695886i	0.0527046	+	0.0304290i	0.526121	−	0.850410i	$-0.323646\pi$
$523$	1.20531	+	0.695886i	0.0527046	+	0.0304290i	−0.473416	+	0.880839i	$0.656979\pi$
$524$	2.20737	+	3.82327i	0.0964293	+	0.167020i
$525$		0			0
$526$	7.98803	−	13.8357i	0.348295	−	0.603264i
$527$	−9.57131	+	5.52600i	−0.416933	+	0.240716i
$528$	1.30819	−	3.41105i	0.0569316	−	0.148447i
$529$	4.60628	−	7.97832i	0.200273	−	0.346883i
$530$	−0.598230	+	1.03616i	−0.0259854	+	0.0450081i
$531$	−27.9301	+	9.09384i	−1.21207	+	0.394639i
$532$		0			0
$533$	−22.3096	+	12.8805i	−0.966337	+	0.557915i
$534$	−4.71254	+	12.2878i	−0.203932	+	0.531744i
$535$		−	8.20854i		−	0.354886i
$536$		−	0.782720i		−	0.0338084i
$537$	0.376979	+	0.465242i	0.0162679	+	0.0200767i
$538$	18.0570	−	10.4252i	0.778493	−	0.449463i
$539$		0			0
$540$	6.07178	−	9.36842i	0.261288	−	0.403153i
$541$	12.9736	−	22.4709i	0.557779	−	0.966101i	−0.439903	−	0.898045i	$-0.644987\pi$
$541$	12.9736	−	22.4709i	0.557779	−	0.966101i	0.997682	−	0.0680555i	$-0.0216795\pi$
$542$	8.63158	−	14.9503i	0.370758	−	0.642172i
$543$	5.60511	−	0.889509i	0.240538	−	0.0381725i
$544$	19.7675	−	11.4128i	0.847525	−	0.489319i
$545$	−8.68407	+	15.0413i	−0.371985	+	0.644296i
$546$		0			0
$547$	−9.32438	−	16.1503i	−0.398682	−	0.690537i	0.594882	−	0.803813i	$-0.297199\pi$
$547$	−9.32438	−	16.1503i	−0.398682	−	0.690537i	−0.993564	+	0.113276i	$0.963865\pi$
$548$	−15.2943	−	8.83017i	−0.653340	−	0.377206i
$549$	2.18762	+	6.71891i	0.0933655	+	0.286756i
$550$	−1.87798	−	3.25275i	−0.0800772	−	0.138698i
$551$	39.3514			1.67642
$552$	19.1118	−	15.4861i	0.813453	−	0.659131i
$553$		0			0
$554$	−5.01594	−	2.89595i	−0.213107	−	0.123037i
$555$	−0.323624	−	2.03927i	−0.0137371	−	0.0865621i
$556$	−15.4572	−	8.92424i	−0.655533	−	0.378472i
$557$	−36.3567	+	20.9905i	−1.54048	+	0.889398i	−0.541674	+	0.840589i	$0.682209\pi$
$557$	−36.3567	+	20.9905i	−1.54048	+	0.889398i	−0.998808	+	0.0488092i	$0.984457\pi$
$558$	−5.79870	+	1.88801i	−0.245479	+	0.0799259i
$559$		−	16.4334i		−	0.695058i
$560$		0			0
$561$	−12.0266	+	1.90858i	−0.507765	+	0.0805804i
$562$	−5.01193	−	8.68092i	−0.211416	−	0.366183i
$563$	−38.6011			−1.62684			−0.813422	−	0.581675i	$-0.802398\pi$
$563$	−38.6011			−1.62684			−0.813422	+	0.581675i	$0.802398\pi$
$564$	−0.942207	−	5.93718i	−0.0396741	−	0.250000i
$565$			10.4936i			0.441468i
$566$	−11.1585			−0.469028
$567$		0			0
$568$	−4.87773			−0.204665
$569$			35.1560i			1.47382i	0.675993	+	0.736908i	$0.263715\pi$
$569$			35.1560i			1.47382i	−0.675993	+	0.736908i	$0.736285\pi$
$570$	−1.13228	−	7.13488i	−0.0474259	−	0.298847i
$571$	−35.3532			−1.47948			−0.739742	−	0.672891i	$-0.765052\pi$
$571$	−35.3532			−1.47948			−0.739742	+	0.672891i	$0.765052\pi$
$572$	−2.91411	−	5.04739i	−0.121845	−	0.211042i
$573$	12.6437	−	2.00651i	0.528198	−	0.0838230i
$574$		0			0
$575$			16.4854i			0.687489i
$576$	5.29273	−	1.72327i	0.220530	−	0.0718029i
$577$	−23.2557	+	13.4267i	−0.968147	+	0.558960i	−0.898671	−	0.438624i	$-0.855466\pi$
$577$	−23.2557	+	13.4267i	−0.968147	+	0.558960i	−0.0694761	+	0.997584i	$0.522133\pi$
$578$	1.09095	+	0.629858i	0.0453774	+	0.0261986i
$579$	3.53688	+	22.2871i	0.146988	+	0.926221i
$580$	18.2498	+	10.5365i	0.757781	+	0.437505i
$581$		0			0
$582$	−14.9899	+	12.1461i	−0.621352	+	0.503473i
$583$	−2.07228			−0.0858249
$584$	−3.50837	−	6.07667i	−0.145177	−	0.251454i
$585$	−2.93207	−	9.00534i	−0.121226	−	0.372325i
$586$	8.38031	+	4.83837i	0.346187	+	0.199871i
$587$	15.6788	+	27.1565i	0.647134	+	1.12087i	0.983804	+	0.179246i	$0.0573657\pi$
$587$	15.6788	+	27.1565i	0.647134	+	1.12087i	−0.336671	+	0.941622i	$0.609301\pi$
$588$		0			0
$589$	5.67809	−	9.83474i	0.233962	−	0.405234i
$590$	−8.81496	+	5.08932i	−0.362906	+	0.209524i
$591$	6.89450	−	1.09413i	0.283602	−	0.0450065i
$592$	−0.482357	+	0.835467i	−0.0198248	+	0.0343375i
$593$	−4.56131	+	7.90043i	−0.187311	+	0.324432i	−0.944353	−	0.328935i	$-0.893310\pi$
$593$	−4.56131	+	7.90043i	−0.187311	+	0.324432i	0.757042	+	0.653366i	$0.226644\pi$
$594$	−6.71027	−	0.345533i	−0.275326	−	0.0141774i
$595$		0			0
$596$	9.09927	−	5.25347i	0.372721	−	0.215190i
$597$	−17.8915	−	22.0804i	−0.732248	−	0.903690i
$598$		−	8.88921i		−	0.363507i
$599$			1.28537i			0.0525186i	0.999655	+	0.0262593i	$0.00835956\pi$
$599$			1.28537i			0.0525186i	−0.999655	+	0.0262593i	$0.991640\pi$
$600$	−4.50781	+	11.7539i	−0.184030	+	0.479852i
$601$	−16.7126	+	9.64903i	−0.681721	+	0.393592i	−0.800503	−	0.599328i	$-0.795434\pi$
$601$	−16.7126	+	9.64903i	−0.681721	+	0.393592i	0.118782	+	0.992920i	$0.462101\pi$
$602$		0			0
$603$	0.892309	−	0.290529i	0.0363376	−	0.0118312i
$604$	−11.5636	+	20.0287i	−0.470515	+	0.814956i
$605$	5.61502	−	9.72551i	0.228283	−	0.395398i
$606$	−1.75771	+	4.58316i	−0.0714022	+	0.186178i
$607$	−33.7319	+	19.4751i	−1.36913	+	0.790470i	−0.990817	−	0.135206i	$-0.956830\pi$
$607$	−33.7319	+	19.4751i	−1.36913	+	0.790470i	−0.378317	+	0.925676i	$0.623497\pi$
$608$	−11.7269	+	20.3116i	−0.475589	+	0.823744i
$609$		0			0
$610$	1.22429	+	2.12054i	0.0495702	+	0.0858581i
$611$	−4.41645	−	2.54984i	−0.178670	−	0.103155i
$612$	12.9274	+	11.6257i	0.522561	+	0.469941i
$613$	−3.65018	−	6.32229i	−0.147429	−	0.255355i	0.782847	−	0.622214i	$-0.213767\pi$
$613$	−3.65018	−	6.32229i	−0.147429	−	0.255355i	−0.930277	+	0.366859i	$0.880433\pi$
$614$	−6.19628			−0.250061
$615$	−4.64189	−	29.2502i	−0.187179	−	1.17948i
$616$		0			0
$617$	38.3641	+	22.1495i	1.54448	+	0.891706i	0.998548	+	0.0538763i	$0.0171577\pi$
$617$	38.3641	+	22.1495i	1.54448	+	0.891706i	0.545932	+	0.837829i	$0.316176\pi$
$618$	4.01583	−	3.25398i	0.161541	−	0.130894i
$619$	0.408449	+	0.235818i	0.0164169	+	0.00947832i	0.508186	−	0.861247i	$-0.330316\pi$
$619$	0.408449	+	0.235818i	0.0164169	+	0.00947832i	−0.491769	+	0.870726i	$0.663650\pi$
$620$	5.26660	−	3.04068i	0.211512	−	0.122116i
$621$	24.7482	+	16.0396i	0.993110	+	0.643646i
$622$			11.6659i			0.467760i
$623$		0			0
$624$	−1.58448	+	4.13148i	−0.0634302	+	0.165391i
$625$	1.02013	+	1.76692i	0.0408052	+	0.0706768i
$626$	4.86696			0.194523
$627$	9.72149	−	7.87720i	0.388239	−	0.314585i
$628$			3.09653i			0.123565i
$629$	3.21558			0.128213
$630$		0			0
$631$	10.2247			0.407038			0.203519	−	0.979071i	$-0.434762\pi$
$631$	10.2247			0.407038			0.203519	+	0.979071i	$0.434762\pi$
$632$			31.1073i			1.23738i
$633$	−19.4331	−	7.45290i	−0.772398	−	0.296226i
$634$	15.7764			0.626560
$635$	−0.637888	−	1.10485i	−0.0253138	−	0.0438448i
$636$	1.86268	+	2.29879i	0.0738601	+	0.0911529i
$637$		0			0
$638$		−	12.6831i		−	0.502127i
$639$	−1.81051	−	5.56066i	−0.0716226	−	0.219976i
$640$	−12.9863	+	7.49767i	−0.513330	+	0.296371i
$641$	43.4584	+	25.0907i	1.71651	+	0.991025i	0.925091	+	0.379745i	$0.123988\pi$
$641$	43.4584	+	25.0907i	1.71651	+	0.991025i	0.791414	+	0.611280i	$0.209345\pi$
$642$	6.58599	+	2.52583i	0.259928	+	0.0996864i
$643$	9.18633	+	5.30373i	0.362274	+	0.209159i	0.670078	−	0.742291i	$-0.266261\pi$
$643$	9.18633	+	5.30373i	0.362274	+	0.209159i	−0.307804	+	0.951450i	$0.599594\pi$
$644$		0			0
$645$	17.6400	+	6.76520i	0.694573	+	0.266379i
$646$	11.2505			0.442644
$647$	14.9203	+	25.8427i	0.586577	+	1.01598i	0.994677	+	0.103044i	$0.0328582\pi$
$647$	14.9203	+	25.8427i	0.586577	+	1.01598i	−0.408100	+	0.912937i	$0.633809\pi$
$648$	13.2593	+	18.2032i	0.520874	+	0.715091i
$649$	−15.2676	−	8.81474i	−0.599305	−	0.346009i
$650$	2.27461	+	3.93975i	0.0892177	+	0.154530i
$651$		0			0
$652$	−8.29664	+	14.3702i	−0.324921	+	0.562780i
$653$	−30.5327	+	17.6281i	−1.19484	+	0.689839i	−0.959400	−	0.282050i	$-0.908986\pi$
$653$	−30.5327	+	17.6281i	−1.19484	+	0.689839i	−0.235437	+	0.971890i	$0.575652\pi$
$654$	−9.39595	−	11.5958i	−0.367411	−	0.453433i
$655$	−2.15280	+	3.72877i	−0.0841170	+	0.145695i
$656$	−6.91868	+	11.9835i	−0.270129	+	0.467877i
$657$	5.62524	−	6.25510i	0.219461	−	0.244035i
$658$		0			0
$659$	29.3751	−	16.9597i	1.14429	−	0.660656i	0.196801	−	0.980443i	$-0.436945\pi$
$659$	29.3751	−	16.9597i	1.14429	−	0.660656i	0.947489	+	0.319787i	$0.103611\pi$
$660$	6.61765	−	1.05020i	0.257592	−	0.0408788i
$661$		−	15.7674i		−	0.613281i	−0.951825	−	0.306641i	$-0.900795\pi$
$661$		−	15.7674i		−	0.613281i	0.951825	−	0.306641i	$-0.0992050\pi$
$662$		−	10.4878i		−	0.407620i
$663$	14.5667	−	2.31168i	0.565725	−	0.0897783i
$664$	15.6423	−	9.03106i	0.607037	−	0.350473i
$665$		0			0
$666$	1.73576	+	0.367843i	0.0672592	+	0.0142536i
$667$	−27.8339	+	48.2097i	−1.07773	+	1.86669i
$668$	1.42598	−	2.46987i	0.0551728	−	0.0955621i
$669$	−28.6992	−	35.4186i	−1.10958	−	1.36936i
$670$	0.281619	−	0.162593i	0.0108799	−	0.00628152i
$671$	−2.12048	+	3.67279i	−0.0818604	+	0.141786i
$672$		0			0
$673$	−7.35627	−	12.7414i	−0.283563	−	0.491146i	0.688696	−	0.725050i	$-0.258183\pi$
$673$	−7.35627	−	12.7414i	−0.283563	−	0.491146i	−0.972260	+	0.233904i	$0.924850\pi$
$674$	−20.2294	−	11.6794i	−0.779207	−	0.449875i
$675$	−15.0728	−	0.776146i	−0.580152	−	0.0298739i
$676$	−6.11795	−	10.5966i	−0.235306	−	0.407562i
$677$	−3.98434			−0.153131			−0.0765654	−	0.997065i	$-0.524395\pi$
$677$	−3.98434			−0.153131			−0.0765654	+	0.997065i	$0.524395\pi$
$678$	−8.41936	−	3.22895i	−0.323344	−	0.124007i
$679$		0			0
$680$	12.2482	+	7.07152i	0.469698	+	0.271181i
$681$	−17.4790	−	6.70347i	−0.669797	−	0.256877i
$682$	−3.16977	−	1.83007i	−0.121377	−	0.0700769i
$683$	19.2812	−	11.1320i	0.737774	−	0.425954i	−0.0834856	−	0.996509i	$-0.526605\pi$
$683$	19.2812	−	11.1320i	0.737774	−	0.425954i	0.821259	+	0.570555i	$0.193272\pi$
$684$	−17.4765	−	3.70363i	−0.668229	−	0.141612i
$685$		−	17.2238i		−	0.658088i
$686$		0			0
$687$	10.5737	+	13.0494i	0.403414	+	0.497865i
$688$	−4.41356	−	7.64450i	−0.168265	−	0.291444i
$689$	2.50995			0.0956215
$690$	9.54188	+	3.65946i	0.363253	+	0.139313i
$691$			48.3823i			1.84055i	0.391271	+	0.920275i	$0.372035\pi$
$691$			48.3823i			1.84055i	−0.391271	+	0.920275i	$0.627965\pi$
$692$	−22.5987			−0.859073
$693$		0			0
$694$	−2.28882			−0.0868824
$695$		−	17.4073i		−	0.660297i
$696$	−33.0278	+	26.7620i	−1.25192	+	1.01441i
$697$	46.1225			1.74701
$698$	−2.68775	−	4.65533i	−0.101733	−	0.176207i
$699$	−1.38147	+	3.60212i	−0.0522520	+	0.136245i
$700$		0			0
$701$			23.3129i			0.880514i	0.897872	+	0.440257i	$0.145113\pi$
$701$			23.3129i			0.880514i	−0.897872	+	0.440257i	$0.854887\pi$
$702$	8.12751	+	0.418511i	0.306753	+	0.0157957i
$703$	−2.86142	+	1.65204i	−0.107920	+	0.0623079i
$704$	2.89319	+	1.67038i	0.109041	+	0.0629549i
$705$	4.55519	−	3.69101i	0.171558	−	0.139012i
$706$	7.07830	+	4.08666i	0.266395	+	0.153803i
$707$		0			0
$708$	3.94512	+	24.8596i	0.148267	+	0.934281i
$709$	17.6777			0.663899			0.331949	−	0.943297i	$-0.392294\pi$
$709$	17.6777			0.663899			0.331949	+	0.943297i	$0.392294\pi$
$710$	−1.01324	−	1.75499i	−0.0380263	−	0.0658635i
$711$	−35.4626	+	11.5464i	−1.32995	+	0.433022i
$712$	22.9270	+	13.2369i	0.859227	+	0.496075i
$713$	8.03242	+	13.9126i	0.300817	+	0.521030i
$714$		0			0
$715$	2.84208	−	4.92263i	0.106288	−	0.184096i
$716$	0.444382	−	0.256564i	0.0166073	−	0.00958824i
$717$	11.4370	−	29.8214i	0.427121	−	1.11370i
$718$	−1.98016	+	3.42974i	−0.0738990	+	0.127997i
$719$	15.2102	−	26.3449i	0.567246	−	0.982498i	−0.429591	−	0.903024i	$-0.641342\pi$
$719$	15.2102	−	26.3449i	0.567246	−	0.982498i	0.996837	−	0.0794749i	$-0.0253244\pi$
$720$	−3.78253	−	3.40164i	−0.140967	−	0.126772i
$721$		0			0
$722$	1.80570	−	1.04252i	0.0672011	−	0.0387986i
$723$	4.01395	−	10.4662i	0.149280	−	0.389242i
$724$		−	4.86326i		−	0.180742i
$725$		−	28.4890i		−	1.05806i
$726$	6.07532	+	7.49773i	0.225476	+	0.278267i
$727$	38.5219	−	22.2406i	1.42870	−	0.824859i	0.431680	−	0.902027i	$-0.357921\pi$
$727$	38.5219	−	22.2406i	1.42870	−	0.824859i	0.997018	+	0.0771674i	$0.0245876\pi$
$728$		0			0
$729$	−15.8303	+	21.8724i	−0.586308	+	0.810088i
$730$	1.45757	−	2.52459i	0.0539472	−	0.0934393i
$731$	−14.7112	+	25.4806i	−0.544114	+	0.942433i
$732$	5.98026	−	0.949044i	0.221037	−	0.0350777i
$733$	39.2270	−	22.6477i	1.44888	−	0.836512i	0.450466	−	0.892794i	$-0.351258\pi$
$733$	39.2270	−	22.6477i	1.44888	−	0.836512i	0.998415	+	0.0562818i	$0.0179245\pi$
$734$	−7.57755	+	13.1247i	−0.279692	+	0.484442i
$735$		0			0
$736$	−16.5893	−	28.7335i	−0.611489	−	1.05913i
$737$	0.487767	+	0.281612i	0.0179671	+	0.0103733i
$738$	24.8968	+	5.27615i	0.916463	+	0.194218i
$739$	−10.3086	−	17.8550i	−0.379208	−	0.656808i	0.611739	−	0.791060i	$-0.290470\pi$
$739$	−10.3086	−	17.8550i	−0.379208	−	0.656808i	−0.990947	+	0.134252i	$0.957137\pi$
$740$	−1.76937			−0.0650432
$741$	−11.7747	+	9.54090i	−0.432555	+	0.350494i
$742$		0			0
$743$	7.69885	+	4.44493i	0.282443	+	0.163069i	0.634529	−	0.772899i	$-0.281194\pi$
$743$	7.69885	+	4.44493i	0.282443	+	0.163069i	−0.352086	+	0.935968i	$0.614527\pi$
$744$	1.92275	+	12.1159i	0.0704914	+	0.444191i
$745$	8.87435	+	5.12361i	0.325131	+	0.187714i
$746$	9.55935	−	5.51909i	0.349993	−	0.202068i
$747$	16.1016	+	14.4802i	0.589126	+	0.529803i
$748$			10.4349i			0.381538i
$749$		0			0
$750$	−14.0572	+	2.23082i	−0.513295	+	0.0814580i
$751$	12.5008	+	21.6521i	0.456162	+	0.790095i	0.998754	−	0.0499007i	$-0.0158905\pi$
$751$	12.5008	+	21.6521i	0.456162	+	0.790095i	−0.542592	+	0.839996i	$0.682557\pi$
$752$	−2.73927			−0.0998907
$753$	0.113117	+	0.712789i	0.00412221	+	0.0259755i
$754$			15.3618i			0.559443i
$755$	−22.5555			−0.820878
$756$		0			0
$757$	−27.1262			−0.985919			−0.492959	−	0.870052i	$-0.664085\pi$
$757$	−27.1262			−0.985919			−0.492959	+	0.870052i	$0.664085\pi$
$758$		−	23.2420i		−	0.844189i
$759$	2.77426	+	17.4816i	0.100699	+	0.634541i
$760$	−14.5323			−0.527142
$761$	1.58366	+	2.74298i	0.0574075	+	0.0994328i	0.893301	−	0.449459i	$-0.148383\pi$
$761$	1.58366	+	2.74298i	0.0574075	+	0.0994328i	−0.835893	+	0.548892i	$0.815050\pi$
$762$	1.08275	−	0.171828i	0.0392237	−	0.00622465i
$763$		0			0
$764$		−	10.9703i		−	0.396891i
$765$	−3.51533	+	16.5879i	−0.127097	+	0.599737i
$766$	12.3361	−	7.12228i	0.445723	−	0.257338i
$767$	18.4922	+	10.6765i	0.667713	+	0.385504i
$768$	−3.02702	−	19.0743i	−0.109228	−	0.688286i
$769$	2.48873	+	1.43687i	0.0897460	+	0.0518149i	0.544201	−	0.838955i	$-0.316833\pi$
$769$	2.48873	+	1.43687i	0.0897460	+	0.0518149i	−0.454455	+	0.890770i	$0.650166\pi$
$770$		0			0
$771$	−28.4330	+	23.0389i	−1.02399	+	0.829725i
$772$	19.3374			0.695967
$773$	6.15679	+	10.6639i	0.221444	+	0.383553i	0.955247	−	0.295810i	$-0.0955895\pi$
$773$	6.15679	+	10.6639i	0.221444	+	0.383553i	−0.733802	+	0.679363i	$0.762256\pi$
$774$	−10.8559	+	12.0714i	−0.390207	+	0.433899i
$775$	−7.12002	−	4.11075i	−0.255759	−	0.147662i
$776$	19.4053	+	33.6110i	0.696610	+	1.20656i
$777$		0			0
$778$	−1.83234	+	3.17371i	−0.0656926	+	0.113783i
$779$	−41.0426	+	23.6960i	−1.47051	+	0.848997i
$780$	−8.01533	+	1.27200i	−0.286995	+	0.0455450i
$781$	1.75494	−	3.03965i	0.0627968	−	0.108767i
$782$	−7.95765	+	13.7831i	−0.284565	+	0.492881i
$783$	−42.7682	−	27.7186i	−1.52841	−	0.990581i
$784$		0			0
$785$	−2.61539	+	1.51000i	−0.0933473	+	0.0538941i
$786$	−2.32928	−	2.87464i	−0.0830827	−	0.102535i
$787$		−	3.81570i		−	0.136015i	−0.997685	−	0.0680076i	$-0.978336\pi$
$787$		−	3.81570i		−	0.136015i	0.997685	−	0.0680076i	$-0.0216642\pi$
$788$		−	5.98200i		−	0.213100i
$789$	13.7972	−	35.9755i	0.491192	−	1.28076i
$790$	−11.1923	+	6.46186i	−0.398203	+	0.229903i
$791$		0			0
$792$	−2.80218	+	13.2228i	−0.0995713	+	0.469851i
$793$	2.56834	−	4.44849i	0.0912044	−	0.157971i
$794$	−4.78022	+	8.27959i	−0.169644	+	0.293832i
$795$	−1.03328	+	2.69424i	−0.0366467	+	0.0955547i
$796$	−21.0904	+	12.1765i	−0.747528	+	0.431585i
$797$	24.5682	−	42.5535i	0.870252	−	1.50732i	0.00851609	−	0.999964i	$-0.497289\pi$
$797$	24.5682	−	42.5535i	0.870252	−	1.50732i	0.861736	−	0.507357i	$-0.169377\pi$
$798$		0			0
$799$	4.56524	+	7.90724i	0.161507	+	0.279738i
$800$	14.7049	+	8.48988i	0.519897	+	0.300162i
$801$	−6.58022	+	31.0503i	−0.232501	+	1.09711i
$802$	5.87742	+	10.1800i	0.207539	+	0.359468i
$803$	5.04906			0.178177
$804$	−0.126038	−	0.794212i	−0.00444503	−	0.0280097i
$805$		0			0
$806$	3.83924	+	2.21659i	0.135231	+	0.0780759i
$807$	39.0703	−	31.6581i	1.37534	−	1.11442i
$808$	8.55146	+	4.93719i	0.300839	+	0.173690i
$809$	−39.4929	+	22.8012i	−1.38850	+	0.801648i	−0.993146	−	0.116882i	$-0.962710\pi$
$809$	−39.4929	+	22.8012i	−1.38850	+	0.801648i	−0.395350	+	0.918531i	$0.629377\pi$
$810$	−3.79512	+	8.55196i	−0.133347	+	0.300485i
$811$			39.1391i			1.37436i	0.726488	+	0.687180i	$0.241151\pi$
$811$			39.1391i			1.37436i	−0.726488	+	0.687180i	$0.758849\pi$
$812$		0			0
$813$	14.9087	−	38.8739i	0.522872	−	1.36337i
$814$	0.532458	+	0.922243i	0.0186626	+	0.0323246i
$815$	−16.1831			−0.566870
$816$	6.15531	−	4.98757i	0.215479	−	0.174600i
$817$		−	30.2322i		−	1.05769i
$818$	−3.11476			−0.108905
$819$		0			0
$820$	−25.3789			−0.886269
$821$		−	11.8906i		−	0.414985i	−0.978237	−	0.207492i	$-0.933470\pi$
$821$		−	11.8906i		−	0.414985i	0.978237	−	0.207492i	$-0.0665302\pi$
$822$	13.8192	+	5.29989i	0.482001	+	0.184855i
$823$	3.02389			0.105406			0.0527031	−	0.998610i	$-0.483216\pi$
$823$	3.02389			0.105406			0.0527031	+	0.998610i	$0.483216\pi$
$824$	−5.19873	−	9.00446i	−0.181106	−	0.313685i
$825$	−5.70283	−	7.03803i	−0.198547	−	0.245033i
$826$		0			0
$827$		−	15.2436i		−	0.530071i	−0.964239	−	0.265035i	$-0.914616\pi$
$827$		−	15.2436i		−	0.530071i	0.964239	−	0.265035i	$-0.0853836\pi$
$828$	16.8987	−	18.7909i	0.587272	−	0.653030i
$829$	29.7306	−	17.1649i	1.03259	−	0.596163i	0.114861	−	0.993382i	$-0.463358\pi$
$829$	29.7306	−	17.1649i	1.03259	−	0.596163i	0.917724	+	0.397218i	$0.130024\pi$
$830$	6.49868	+	3.75201i	0.225572	+	0.130234i
$831$	−13.0425	−	5.00198i	−0.452438	−	0.173517i
$832$	−3.50424	−	2.02317i	−0.121488	−	0.0701409i
$833$		0			0
$834$	13.9665	+	5.35635i	0.483619	+	0.185475i
$835$	2.78146			0.0962565
$836$	−5.36105	−	9.28561i	−0.185416	−	0.321150i
$837$	−13.0986	+	6.68912i	−0.452753	+	0.231210i
$838$	−11.7088	−	6.76006i	−0.404473	−	0.233522i
$839$	−6.16024	−	10.6698i	−0.212675	−	0.368364i	0.739876	−	0.672744i	$-0.234884\pi$
$839$	−6.16024	−	10.6698i	−0.212675	−	0.368364i	−0.952551	+	0.304379i	$0.901551\pi$
$840$		0			0
$841$	33.6008	−	58.1983i	1.15865	−	2.00684i
$842$	−1.13625	+	0.656012i	−0.0391576	+	0.0226077i
$843$	−15.2197	−	18.7831i	−0.524194	−	0.646923i
$844$	−8.91770	+	15.4459i	−0.306960	+	0.531670i
$845$	5.96672	−	10.3347i	0.205262	−	0.355523i
$846$	1.55976	+	4.79054i	0.0536257	+	0.164702i
$847$		0			0
$848$	1.16758	−	0.674104i	0.0400949	−	0.0231488i
$849$	−26.5792	+	4.21801i	−0.912194	+	0.144762i
$850$		−	8.14496i		−	0.279370i
$851$		−	4.67406i		−	0.160225i
$852$	−4.94934	+	0.785442i	−0.169562	+	0.0269088i
$853$	−3.92537	+	2.26631i	−0.134402	+	0.0775971i	−0.565693	−	0.824616i	$-0.691391\pi$
$853$	−3.92537	+	2.26631i	−0.134402	+	0.0775971i	0.431291	+	0.902213i	$0.358058\pi$
$854$		0			0
$855$	−5.39408	−	16.5670i	−0.184474	−	0.566579i
$856$	7.09472	−	12.2884i	0.242493	−	0.420010i
$857$	16.1307	−	27.9392i	0.551014	−	0.954384i	−0.447188	−	0.894440i	$-0.647574\pi$
$857$	16.1307	−	27.9392i	0.551014	−	0.954384i	0.998202	−	0.0599442i	$-0.0190923\pi$
$858$	3.07506	+	3.79503i	0.104981	+	0.129560i
$859$	−15.2711	+	8.81675i	−0.521042	+	0.300824i	−0.737361	−	0.675499i	$-0.763928\pi$
$859$	−15.2711	+	8.81675i	−0.521042	+	0.300824i	0.216319	+	0.976323i	$0.430595\pi$
$860$	8.09483	−	14.0207i	0.276032	−	0.478101i
$861$		0			0
$862$	5.16329	+	8.94307i	0.175862	+	0.304602i
$863$	26.4091	+	15.2473i	0.898975	+	0.519023i	0.876867	−	0.480732i	$-0.159629\pi$
$863$	26.4091	+	15.2473i	0.898975	+	0.519023i	0.0221074	+	0.999756i	$0.492962\pi$
$864$	27.0524	−	13.8150i	0.920340	−	0.469995i
$865$	−11.0200	−	19.0873i	−0.374693	−	0.648987i
$866$	1.59526			0.0542093
$867$	2.83668	+	1.08791i	0.0963388	+	0.0369474i
$868$		0			0
$869$	−19.3851	−	11.1920i	−0.657594	−	0.379662i
$870$	−16.4897	−	6.32405i	−0.559053	−	0.214405i
$871$	−0.590785	−	0.341090i	−0.0200180	−	0.0115574i
$872$	−26.0006	+	15.0115i	−0.880492	+	0.508352i
$873$	−31.1140	+	34.5979i	−1.05305	+	1.17096i
$874$		−	16.3533i		−	0.553160i
$875$		0			0
$876$	−4.53838	−	5.60095i	−0.153338	−	0.189239i
$877$	−4.40363	−	7.62730i	−0.148700	−	0.257556i	0.782047	−	0.623219i	$-0.214176\pi$
$877$	−4.40363	−	7.62730i	−0.148700	−	0.257556i	−0.930747	+	0.365663i	$0.880842\pi$
$878$	7.21385			0.243456
$879$	21.7905	+	8.35699i	0.734975	+	0.281874i
$880$		−	3.05322i		−	0.102924i
$881$	−38.6776			−1.30308			−0.651540	−	0.758614i	$-0.725877\pi$
$881$	−38.6776			−1.30308			−0.651540	+	0.758614i	$0.725877\pi$
$882$		0			0
$883$	37.4489			1.26026			0.630128	−	0.776491i	$-0.283002\pi$
$883$	37.4489			1.26026			0.630128	+	0.776491i	$0.283002\pi$
$884$		−	12.6388i		−	0.425089i
$885$	−19.0731	+	15.4547i	−0.641135	+	0.519503i
$886$	9.97781			0.335211
$887$	−13.7025	−	23.7335i	−0.460086	−	0.796892i	0.538879	−	0.842383i	$-0.318848\pi$
$887$	−13.7025	−	23.7335i	−0.460086	−	0.796892i	−0.998965	+	0.0454915i	$0.985515\pi$
$888$	1.27809	−	3.33256i	0.0428898	−	0.111833i
$889$		0			0
$890$			10.9987i			0.368679i
$891$	−16.1142	+	1.71349i	−0.539846	+	0.0574040i
$892$	−33.8305	+	19.5321i	−1.13273	+	0.653982i
$893$	−8.12487	−	4.69090i	−0.271888	−	0.156975i
$894$	−6.84155	+	5.54362i	−0.228816	+	0.185406i
$895$	0.433397	+	0.250222i	0.0144869	+	0.00836400i
$896$		0			0
$897$	−3.36019	−	21.1737i	−0.112194	−	0.706971i
$898$	7.58598			0.253147
$899$	−13.8811	−	24.0428i	−0.462962	−	0.801873i
$900$	−2.68130	+	12.6524i	−0.0893768	+	0.421745i
$901$	−3.89177	−	2.24691i	−0.129654	−	0.0748556i
$902$	7.63729	+	13.2282i	0.254294	+	0.440450i
$903$		0			0
$904$	−9.06971	+	15.7092i	−0.301654	+	0.522480i
$905$	4.10760	−	2.37152i	0.136541	−	0.0788321i
$906$	6.94049	−	18.0970i	0.230582	−	0.601234i
$907$	11.8216	−	20.4757i	0.392531	−	0.679883i	−0.600252	−	0.799811i	$-0.704933\pi$
$907$	11.8216	−	20.4757i	0.392531	−	0.679883i	0.992783	+	0.119928i	$0.0382663\pi$
$908$	−8.02097	+	13.8927i	−0.266185	+	0.461046i
$909$	−2.45433	+	11.5813i	−0.0814049	+	0.384128i
$910$		0			0
$911$	−3.92249	+	2.26465i	−0.129958	+	0.0750313i	−0.563570	−	0.826069i	$-0.690572\pi$
$911$	−3.92249	+	2.26465i	−0.129958	+	0.0750313i	0.433612	+	0.901100i	$0.357239\pi$
$912$	−2.91495	+	7.60061i	−0.0965237	+	0.251681i
$913$			12.9970i			0.430139i
$914$			3.67204i			0.121460i
$915$	3.71780	+	4.58824i	0.122907	+	0.151683i
$916$	12.4643	−	7.19626i	0.411832	−	0.237771i
$917$		0			0
$918$	−12.2274	−	7.92469i	−0.403563	−	0.261554i
$919$	16.9149	−	29.2975i	0.557971	−	0.966434i	−0.439695	−	0.898147i	$-0.644913\pi$
$919$	16.9149	−	29.2975i	0.557971	−	0.966434i	0.997666	−	0.0682866i	$-0.0217532\pi$
$920$	10.2789	−	17.8037i	0.338887	−	0.586969i
$921$	−14.7593	+	2.34224i	−0.486335	+	0.0771795i
$922$	5.18323	−	2.99254i	0.170700	−	0.0985540i
$923$	−2.12559	+	3.68164i	−0.0699648	+	0.121183i
$924$		0			0
$925$	1.19602	+	2.07157i	0.0393249	+	0.0681127i
$926$	12.4568	+	7.19192i	0.409355	+	0.236341i
$927$	8.33552	−	9.26886i	0.273774	−	0.304429i
$928$	28.6685	+	49.6554i	0.941091	+	1.63002i
$929$	−32.9164			−1.07995			−0.539976	−	0.841680i	$-0.681567\pi$
$929$	−32.9164			−1.07995			−0.539976	+	0.841680i	$0.681567\pi$
$930$	−3.95985	+	3.20861i	−0.129849	+	0.105215i
$931$		0			0
$932$	2.86305	+	1.65298i	0.0937824	+	0.0541453i
$933$	4.40980	+	27.7877i	0.144370	+	0.909729i
$934$	−12.9236	−	7.46146i	−0.422874	−	0.244146i
$935$	−8.81350	+	5.08848i	−0.288232	+	0.166411i
$936$	3.39402	−	16.0155i	0.110937	−	0.523482i
$937$		−	38.1057i		−	1.24486i	−0.782676	−	0.622430i	$-0.786146\pi$
$937$		−	38.1057i		−	1.24486i	0.782676	−	0.622430i	$-0.213854\pi$
$938$		0			0
$939$	11.5929	−	1.83975i	0.378320	−	0.0600379i
$940$	−2.51202	−	4.35095i	−0.0819331	−	0.141912i
$941$	19.8771			0.647975			0.323987	−	0.946061i	$-0.394976\pi$
$941$	19.8771			0.647975			0.323987	+	0.946061i	$0.394976\pi$
$942$	−0.406747	−	2.56305i	−0.0132525	−	0.0835088i
$943$		−	67.0423i		−	2.18320i
$944$	11.4696			0.373304
$945$		0			0
$946$	−9.74394			−0.316803
$947$		−	20.7495i		−	0.674267i	−0.941457	−	0.337134i	$-0.890543\pi$
$947$		−	20.7495i		−	0.674267i	0.941457	−	0.337134i	$-0.109457\pi$
$948$	5.00908	+	31.5640i	0.162687	+	1.02515i
$949$	−6.11544			−0.198516
$950$	4.18457	+	7.24789i	0.135765	+	0.235152i
$951$	37.5787	−	5.96359i	1.21857	−	0.193383i
$952$		0			0
$953$		−	12.8345i		−	0.415751i	−0.978155	−	0.207876i	$-0.933345\pi$
$953$		−	12.8345i		−	0.415751i	0.978155	−	0.207876i	$-0.0666549\pi$
$954$	−1.84373	−	1.65807i	−0.0596930	−	0.0536821i
$955$	9.26571	−	5.34956i	0.299831	−	0.173108i
$956$	−23.7027	−	13.6848i	−0.766602	−	0.442598i
$957$	−4.79430	−	30.2105i	−0.154978	−	0.976568i
$958$	19.9408	+	11.5128i	0.644258	+	0.371962i
$959$		0			0
$960$	3.61433	−	2.92864i	0.116652	−	0.0945215i
$961$	22.9882			0.741556
$962$	−0.644915	−	1.11703i	−0.0207929	−	0.0360143i
$963$	16.6423	+	3.52686i	0.536292	+	0.113652i
$964$	−8.31878	−	4.80285i	−0.267930	−	0.154689i
$965$	9.42969	+	16.3327i	0.303552	+	0.525768i
$966$		0			0
$967$	−17.8941	+	30.9936i	−0.575437	+	0.996685i	0.420557	+	0.907266i	$0.361835\pi$
$967$	−17.8941	+	30.9936i	−0.575437	+	0.996685i	−0.995994	+	0.0894195i	$0.971499\pi$
$968$	16.8117	−	9.70625i	0.540349	−	0.311971i
$969$	26.7982	−	4.25277i	0.860881	−	0.136619i
$970$	−8.06205	+	13.9639i	−0.258857	+	0.448353i
$971$	14.5129	−	25.1370i	0.465740	−	0.806686i	−0.533494	−	0.845804i	$-0.679121\pi$
$971$	14.5129	−	25.1370i	0.465740	−	0.806686i	0.999235	+	0.0391177i	$0.0124547\pi$
$972$	16.3852	+	16.3354i	0.525554	+	0.523959i
$973$		0			0
$974$	−14.7247	+	8.50130i	−0.471809	+	0.272399i
$975$	6.90729	+	8.52449i	0.221210	+	0.273002i
$976$		−	2.75914i		−	0.0883180i
$977$			8.93090i			0.285725i	0.989743	+	0.142862i	$0.0456306\pi$
$977$			8.93090i			0.285725i	−0.989743	+	0.142862i	$0.954369\pi$
$978$	4.97966	−	12.9843i	0.159232	−	0.415191i
$979$	−16.4977	+	9.52495i	−0.527268	+	0.304419i
$980$		0			0
$981$	−26.7641	−	24.0690i	−0.854512	−	0.768466i
$982$	−6.41288	+	11.1074i	−0.204643	+	0.354452i
$983$	26.1346	−	45.2665i	0.833566	−	1.44378i	−0.0616269	−	0.998099i	$-0.519629\pi$
$983$	26.1346	−	45.2665i	0.833566	−	1.44378i	0.895193	−	0.445679i	$-0.147038\pi$
$984$	18.3322	−	47.8004i	0.584409	−	1.52382i
$985$	5.05250	−	2.91707i	0.160986	−	0.0929454i
$986$	13.7519	−	23.8190i	0.437950	−	0.758552i
$987$		0			0
$988$	6.49333	+	11.2468i	0.206580	+	0.357807i
$989$	37.0378	+	21.3838i	1.17773	+	0.679964i
$990$	−5.33959	+	1.73853i	−0.169703	+	0.0552541i
$991$	−21.9151	−	37.9581i	−0.696158	−	1.20578i	−0.969789	−	0.243946i	$-0.921558\pi$
$991$	−21.9151	−	37.9581i	−0.696158	−	1.20578i	0.273631	−	0.961835i	$-0.411775\pi$
$992$	16.5466			0.525355
$993$	−3.96447	−	24.9815i	−0.125809	−	0.792764i
$994$		0			0
$995$	−20.5690	−	11.8755i	−0.652082	−	0.376480i
$996$	14.4177	−	11.6825i	0.456842	−	0.370173i
$997$	38.9689	+	22.4987i	1.23416	+	0.712542i	0.967894	−	0.251358i	$-0.0808772\pi$
$997$	38.9689	+	22.4987i	1.23416	+	0.712542i	0.266264	+	0.963900i	$0.414211\pi$
$998$	−14.3797	+	8.30215i	−0.455183	+	0.262800i
$999$	4.27355	+	0.220059i	0.135209	+	0.00696235i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.i.b.68.4		10
3.2	odd	2		1323.2.i.b.1097.2		10
7.2	even	3		441.2.o.c.293.4		10
7.3	odd	6		441.2.s.b.374.2		10
7.4	even	3		63.2.s.b.59.2	yes	10
7.5	odd	6		441.2.o.d.293.4		10
7.6	odd	2		63.2.i.b.5.4	✓	10
9.2	odd	6		441.2.s.b.362.2		10
9.7	even	3		1323.2.s.b.656.4		10
21.2	odd	6		1323.2.o.d.881.2		10
21.5	even	6		1323.2.o.c.881.2		10
21.11	odd	6		189.2.s.b.17.4		10
21.17	even	6		1323.2.s.b.962.4		10
21.20	even	2		189.2.i.b.152.2		10
28.11	odd	6		1008.2.df.b.689.2		10
28.27	even	2		1008.2.ca.b.257.3		10
63.2	odd	6		441.2.o.d.146.4		10
63.4	even	3		567.2.p.c.80.4		10
63.11	odd	6		63.2.i.b.38.2	yes	10
63.13	odd	6		567.2.p.d.404.2		10
63.16	even	3		1323.2.o.c.440.2		10
63.20	even	6		63.2.s.b.47.2	yes	10
63.25	even	3		189.2.i.b.143.4		10
63.32	odd	6		567.2.p.d.80.2		10
63.34	odd	6		189.2.s.b.89.4		10
63.38	even	6	inner	441.2.i.b.227.2		10
63.41	even	6		567.2.p.c.404.4		10
63.47	even	6		441.2.o.c.146.4		10
63.52	odd	6		1323.2.i.b.521.4		10
63.61	odd	6		1323.2.o.d.440.2		10
84.11	even	6		3024.2.df.b.17.4		10
84.83	odd	2		3024.2.ca.b.2609.4		10
252.11	even	6		1008.2.ca.b.353.3		10
252.83	odd	6		1008.2.df.b.929.2		10
252.151	odd	6		3024.2.ca.b.2033.4		10
252.223	even	6		3024.2.df.b.1601.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.4	✓	10	7.6	odd	2
63.2.i.b.38.2	yes	10	63.11	odd	6
63.2.s.b.47.2	yes	10	63.20	even	6
63.2.s.b.59.2	yes	10	7.4	even	3
189.2.i.b.143.4		10	63.25	even	3
189.2.i.b.152.2		10	21.20	even	2
189.2.s.b.17.4		10	21.11	odd	6
189.2.s.b.89.4		10	63.34	odd	6
441.2.i.b.68.4		10	1.1	even	1	trivial
441.2.i.b.227.2		10	63.38	even	6	inner
441.2.o.c.146.4		10	63.47	even	6
441.2.o.c.293.4		10	7.2	even	3
441.2.o.d.146.4		10	63.2	odd	6
441.2.o.d.293.4		10	7.5	odd	6
441.2.s.b.362.2		10	9.2	odd	6
441.2.s.b.374.2		10	7.3	odd	6
567.2.p.c.80.4		10	63.4	even	3
567.2.p.c.404.4		10	63.41	even	6
567.2.p.d.80.2		10	63.32	odd	6
567.2.p.d.404.2		10	63.13	odd	6
1008.2.ca.b.257.3		10	28.27	even	2
1008.2.ca.b.353.3		10	252.11	even	6
1008.2.df.b.689.2		10	28.11	odd	6
1008.2.df.b.929.2		10	252.83	odd	6
1323.2.i.b.521.4		10	63.52	odd	6
1323.2.i.b.1097.2		10	3.2	odd	2
1323.2.o.c.440.2		10	63.16	even	3
1323.2.o.c.881.2		10	21.5	even	6
1323.2.o.d.440.2		10	63.61	odd	6
1323.2.o.d.881.2		10	21.2	odd	6
1323.2.s.b.656.4		10	9.7	even	3
1323.2.s.b.962.4		10	21.17	even	6
3024.2.ca.b.2033.4		10	252.151	odd	6
3024.2.ca.b.2609.4		10	84.83	odd	2
3024.2.df.b.17.4		10	84.11	even	6
3024.2.df.b.1601.4		10	252.223	even	6

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+0.718167i q^{2} +(0.271473 + 1.71064i) q^{3} +1.48424 q^{4} +(0.723774 + 1.25361i) q^{5} +(-1.22853 + 0.194963i) q^{6} +2.50226i q^{8} +(-2.85261 + 0.928786i) q^{9} +O(q^{10})\)	\(q+0.718167i q^{2} +(0.271473 + 1.71064i) q^{3} +1.48424 q^{4} +(0.723774 + 1.25361i) q^{5} +(-1.22853 + 0.194963i) q^{6} +2.50226i q^{8} +(-2.85261 + 0.928786i) q^{9} +(-0.900304 + 0.519791i) q^{10} +(-1.55933 - 0.900281i) q^{11} +(0.402930 + 2.53900i) q^{12} +(1.88867 + 1.09042i) q^{13} +(-1.94800 + 1.57844i) q^{15} +1.17143 q^{16} +(-1.95230 - 3.38149i) q^{17} +(-0.667023 - 2.04865i) q^{18} +(3.47456 + 2.00604i) q^{19} +(1.07425 + 1.86066i) q^{20} +(0.646552 - 1.11986i) q^{22} +(-4.91522 + 2.83781i) q^{23} +(-4.28048 + 0.679296i) q^{24} +(1.45230 - 2.51546i) q^{25} +(-0.783106 + 1.35638i) q^{26} +(-2.36323 - 4.62765i) q^{27} +(8.49418 - 4.90412i) q^{29} +(-1.13358 - 1.39899i) q^{30} -2.83050i q^{31} +5.84581i q^{32} +(1.11674 - 2.91186i) q^{33} +(2.42847 - 1.40208i) q^{34} +(-4.23394 + 1.37854i) q^{36} +(-0.411767 + 0.713202i) q^{37} +(-1.44067 + 2.49531i) q^{38} +(-1.35261 + 3.52686i) q^{39} +(-3.13687 + 1.81107i) q^{40} +(-5.90617 + 10.2298i) q^{41} +(-3.76766 - 6.52578i) q^{43} +(-2.31442 - 1.33623i) q^{44} +(-3.22898 - 2.90383i) q^{45} +(-2.03802 - 3.52995i) q^{46} -2.33839 q^{47} +(0.318012 + 2.00390i) q^{48} +(1.80652 + 1.04299i) q^{50} +(5.25452 - 4.25767i) q^{51} +(2.80323 + 1.61845i) q^{52} +(0.996713 - 0.575453i) q^{53} +(3.32343 - 1.69719i) q^{54} -2.60640i q^{55} +(-2.48837 + 6.48831i) q^{57} +(3.52198 + 6.10024i) q^{58} +9.79110 q^{59} +(-2.89130 + 2.34278i) q^{60} -2.35536i q^{61} +2.03277 q^{62} -1.85540 q^{64} +3.15688i q^{65} +(2.09120 + 0.802008i) q^{66} -0.312805 q^{67} +(-2.89768 - 5.01893i) q^{68} +(-6.18882 - 7.63781i) q^{69} +1.94933i q^{71} +(-2.32407 - 7.13797i) q^{72} +(-2.42847 + 1.40208i) q^{73} +(-0.512198 - 0.295717i) q^{74} +(4.69732 + 1.80149i) q^{75} +(5.15706 + 2.97743i) q^{76} +(-2.53287 - 0.971396i) q^{78} +12.4317 q^{79} +(0.847852 + 1.46852i) q^{80} +(7.27471 - 5.29892i) q^{81} +(-7.34669 - 4.24162i) q^{82} +(-3.60916 - 6.25124i) q^{83} +(2.82605 - 4.89486i) q^{85} +(4.68660 - 2.70581i) q^{86} +(10.6951 + 13.1992i) q^{87} +(2.25274 - 3.90186i) q^{88} +(5.28999 - 9.16253i) q^{89} +(2.08544 - 2.31895i) q^{90} +(-7.29536 + 4.21198i) q^{92} +(4.84198 - 0.768404i) q^{93} -1.67935i q^{94} +5.80767i q^{95} +(-10.0001 + 1.58698i) q^{96} +(13.4322 - 7.75510i) q^{97} +(5.28433 + 1.11986i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{3} - 8 q^{4} - 12 q^{6} + 3 q^{9}+O(q^{10}) \) 10 * q + 3 * q^3 - 8 * q^4 - 12 * q^6 + 3 * q^9	\( 10 q + 3 q^{3} - 8 q^{4} - 12 q^{6} + 3 q^{9} + 15 q^{10} - 12 q^{11} + 12 q^{12} + 6 q^{13} - 3 q^{15} + 12 q^{16} - 12 q^{17} + 24 q^{18} - 3 q^{19} - 3 q^{20} + 5 q^{22} - 15 q^{23} + 7 q^{25} + 3 q^{26} + 27 q^{27} - 15 q^{29} + 6 q^{30} + 3 q^{34} - 18 q^{36} + 6 q^{37} - 18 q^{38} + 18 q^{39} - 15 q^{40} - 9 q^{41} + 3 q^{43} - 24 q^{44} - 30 q^{45} - 13 q^{46} - 30 q^{47} - 15 q^{48} + 3 q^{50} + 21 q^{51} + 12 q^{52} + 9 q^{53} - 9 q^{54} - 36 q^{57} + 8 q^{58} + 36 q^{59} - 48 q^{60} + 12 q^{62} + 6 q^{64} + 39 q^{66} + 20 q^{67} + 27 q^{68} - 3 q^{69} - 30 q^{72} - 3 q^{73} - 30 q^{74} - 6 q^{75} + 9 q^{76} + 24 q^{78} - 40 q^{79} - 30 q^{80} + 15 q^{81} - 9 q^{82} - 15 q^{83} + 18 q^{85} + 54 q^{86} - 6 q^{87} - 8 q^{88} + 24 q^{89} + 24 q^{90} + 39 q^{92} + 36 q^{93} - 33 q^{96} + 6 q^{97} + 21 q^{99}+O(q^{100}) \) 10 * q + 3 * q^3 - 8 * q^4 - 12 * q^6 + 3 * q^9 + 15 * q^10 - 12 * q^11 + 12 * q^12 + 6 * q^13 - 3 * q^15 + 12 * q^16 - 12 * q^17 + 24 * q^18 - 3 * q^19 - 3 * q^20 + 5 * q^22 - 15 * q^23 + 7 * q^25 + 3 * q^26 + 27 * q^27 - 15 * q^29 + 6 * q^30 + 3 * q^34 - 18 * q^36 + 6 * q^37 - 18 * q^38 + 18 * q^39 - 15 * q^40 - 9 * q^41 + 3 * q^43 - 24 * q^44 - 30 * q^45 - 13 * q^46 - 30 * q^47 - 15 * q^48 + 3 * q^50 + 21 * q^51 + 12 * q^52 + 9 * q^53 - 9 * q^54 - 36 * q^57 + 8 * q^58 + 36 * q^59 - 48 * q^60 + 12 * q^62 + 6 * q^64 + 39 * q^66 + 20 * q^67 + 27 * q^68 - 3 * q^69 - 30 * q^72 - 3 * q^73 - 30 * q^74 - 6 * q^75 + 9 * q^76 + 24 * q^78 - 40 * q^79 - 30 * q^80 + 15 * q^81 - 9 * q^82 - 15 * q^83 + 18 * q^85 + 54 * q^86 - 6 * q^87 - 8 * q^88 + 24 * q^89 + 24 * q^90 + 39 * q^92 + 36 * q^93 - 33 * q^96 + 6 * q^97 + 21 * q^99

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