LMFDB - Embedded newform 475.2.p.g.407.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(107,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("475.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.p (of order $12$, degree $4$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	16.0.11007531417600000000.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} + 48x^{8} - 7x^{4} + 1 $ x^16 - 7x^12 + 48x^8 - 7*x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			407.2
Root			$0.159959 - 0.596975i$ of defining polynomial
Character	$\chi$	$=$	475.407
Dual form			475.2.p.g.468.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.578737 - 2.15988i) q^{2} +(0.368951 - 0.0988601i) q^{3} +(-2.59808 + 1.50000i) q^{4} +(-0.427051 - 0.739674i) q^{6} +(-1.22474 - 1.22474i) q^{7} +(1.58114 + 1.58114i) q^{8} +(-2.47172 + 1.42705i) q^{9} +O(q^{10})$	\(q+(-0.578737 - 2.15988i) q^{2} +(0.368951 - 0.0988601i) q^{3} +(-2.59808 + 1.50000i) q^{4} +(-0.427051 - 0.739674i) q^{6} +(-1.22474 - 1.22474i) q^{7} +(1.58114 + 1.58114i) q^{8} +(-2.47172 + 1.42705i) q^{9} -1.85410 q^{11} +(-0.810272 + 0.810272i) q^{12} +(0.479877 - 1.79092i) q^{13} +(-1.93649 + 3.35410i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.639042 - 0.171231i) q^{17} +(4.51273 + 4.51273i) q^{18} +(-4.33013 + 0.500000i) q^{19} +(-0.572949 - 0.330792i) q^{21} +(1.07304 + 4.00463i) q^{22} +(-5.01910 - 1.34486i) q^{23} +(0.739674 + 0.427051i) q^{24} -4.14590 q^{26} +(-1.58114 + 1.58114i) q^{27} +(5.01910 + 1.34486i) q^{28} +(-0.330792 - 0.572949i) q^{29} +1.47935i q^{31} +(6.47963 + 1.73621i) q^{32} +(-0.684072 + 0.183297i) q^{33} +(-0.739674 - 1.28115i) q^{34} +(4.28115 - 7.41517i) q^{36} +(-6.86474 + 6.86474i) q^{37} +(3.58594 + 9.06317i) q^{38} -0.708204i q^{39} +(3.92705 + 2.26728i) q^{41} +(-0.382883 + 1.42894i) q^{42} +(-0.831171 - 3.10197i) q^{43} +(4.81710 - 2.78115i) q^{44} +11.6190i q^{46} +(1.00240 - 3.74101i) q^{47} +(-0.0988601 + 0.368951i) q^{48} -4.00000i q^{49} +(0.218847 - 0.126351i) q^{51} +(1.43963 + 5.37277i) q^{52} +(3.48685 - 13.0131i) q^{53} +(4.33013 + 2.50000i) q^{54} -3.87298i q^{56} +(-1.54817 + 0.612552i) q^{57} +(-1.04606 + 1.04606i) q^{58} +(7.13264 - 12.3541i) q^{59} +(4.78115 + 8.28120i) q^{61} +(3.19521 - 0.856153i) q^{62} +(4.77501 + 1.27946i) q^{63} -13.0000i q^{64} +(0.791796 + 1.37143i) q^{66} +(-5.79555 - 1.55291i) q^{67} +(-1.40343 + 1.40343i) q^{68} -1.98475 q^{69} +(3.35410 + 1.93649i) q^{71} +(-6.16451 - 1.65177i) q^{72} +(-3.07261 - 11.4671i) q^{73} +(18.7999 + 10.8541i) q^{74} +(10.5000 - 7.79423i) q^{76} +(2.27080 + 2.27080i) q^{77} +(-1.52963 + 0.409864i) q^{78} +(-6.80185 + 11.7812i) q^{79} +(3.85410 - 6.67550i) q^{81} +(2.62432 - 9.79410i) q^{82} +(-10.5549 + 10.5549i) q^{83} +1.98475 q^{84} +(-6.21885 + 3.59045i) q^{86} +(-0.178688 - 0.178688i) q^{87} +(-2.93159 - 2.93159i) q^{88} +(-1.27491 - 2.20820i) q^{89} +(-2.78115 + 1.60570i) q^{91} +(15.0573 - 4.03459i) q^{92} +(0.146248 + 0.545807i) q^{93} -8.66025 q^{94} +2.56231 q^{96} +(-2.21609 - 8.27055i) q^{97} +(-8.63950 + 2.31495i) q^{98} +(4.58283 - 2.64590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 20 q^{6}+O(q^{10}) $ 16 * q + 20 * q^6	$ 16 q + 20 q^{6} + 24 q^{11} - 8 q^{16} - 36 q^{21} - 120 q^{26} - 12 q^{36} + 36 q^{41} + 84 q^{51} - 4 q^{61} + 120 q^{66} + 168 q^{76} + 8 q^{81} - 180 q^{86} + 36 q^{91} - 120 q^{96}+O(q^{100}) $ 16 * q + 20 * q^6 + 24 * q^11 - 8 * q^16 - 36 * q^21 - 120 * q^26 - 12 * q^36 + 36 * q^41 + 84 * q^51 - 4 * q^61 + 120 * q^66 + 168 * q^76 + 8 * q^81 - 180 * q^86 + 36 * q^91 - 120 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.578737	−	2.15988i	−0.409229	−	1.52726i	−0.796121	−	0.605138i	$-0.793118\pi$
$2$	−0.578737	−	2.15988i	−0.409229	−	1.52726i	0.386892	−	0.922125i	$-0.373549\pi$
$3$	0.368951	−	0.0988601i	0.213014	−	0.0570769i	−0.150734	−	0.988574i	$-0.548164\pi$
$3$	0.368951	−	0.0988601i	0.213014	−	0.0570769i	0.363748	+	0.931497i	$0.381497\pi$
$4$	−2.59808	+	1.50000i	−1.29904	+	0.750000i
$5$		0			0
$5$		0			0
$6$	−0.427051	−	0.739674i	−0.174343	−	0.301971i
$7$	−1.22474	−	1.22474i	−0.462910	−	0.462910i	0.436698	−	0.899608i	$-0.356148\pi$
$7$	−1.22474	−	1.22474i	−0.462910	−	0.462910i	−0.899608	+	0.436698i	$0.856148\pi$
$8$	1.58114	+	1.58114i	0.559017	+	0.559017i
$9$	−2.47172	+	1.42705i	−0.823908	+	0.475684i
$10$		0			0
$11$	−1.85410			−0.559033			−0.279516	−	0.960141i	$-0.590174\pi$
$11$	−1.85410			−0.559033			−0.279516	+	0.960141i	$0.590174\pi$
$12$	−0.810272	+	0.810272i	−0.233905	+	0.233905i
$13$	0.479877	−	1.79092i	0.133094	−	0.496713i	−0.866905	−	0.498474i	$-0.833894\pi$
$13$	0.479877	−	1.79092i	0.133094	−	0.496713i	0.999998	+	0.00176097i	$0.000560533\pi$
$14$	−1.93649	+	3.35410i	−0.517549	+	0.896421i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.639042	−	0.171231i	0.154990	−	0.0415295i	−0.180490	−	0.983577i	$-0.557768\pi$
$17$	0.639042	−	0.171231i	0.154990	−	0.0415295i	0.335480	+	0.942047i	$0.391102\pi$
$18$	4.51273	+	4.51273i	1.06366	+	1.06366i
$19$	−4.33013	+	0.500000i	−0.993399	+	0.114708i
$19$	−4.33013	+	0.500000i	−0.993399	+	0.114708i
$20$		0			0
$21$	−0.572949	−	0.330792i	−0.125028	−	0.0721848i
$22$	1.07304	+	4.00463i	0.228772	+	0.853790i
$23$	−5.01910	−	1.34486i	−1.04655	−	0.280423i	−0.305727	−	0.952119i	$-0.598900\pi$
$23$	−5.01910	−	1.34486i	−1.04655	−	0.280423i	−0.740827	+	0.671696i	$0.765566\pi$
$24$	0.739674	+	0.427051i	0.150985	+	0.0871714i
$25$		0			0
$26$	−4.14590			−0.813077
$27$	−1.58114	+	1.58114i	−0.304290	+	0.304290i
$28$	5.01910	+	1.34486i	0.948520	+	0.254155i
$29$	−0.330792	−	0.572949i	−0.0614266	−	0.106394i	0.833677	−	0.552253i	$-0.186232\pi$
$29$	−0.330792	−	0.572949i	−0.0614266	−	0.106394i	−0.895103	+	0.445859i	$0.852898\pi$
$30$		0			0
$31$			1.47935i			0.265699i	0.991136	+	0.132849i	$0.0424127\pi$
$31$			1.47935i			0.265699i	−0.991136	+	0.132849i	$0.957587\pi$
$32$	6.47963	+	1.73621i	1.14545	+	0.306922i
$33$	−0.684072	+	0.183297i	−0.119082	+	0.0319079i
$34$	−0.739674	−	1.28115i	−0.126853	−	0.219716i
$35$		0			0
$36$	4.28115	−	7.41517i	0.713525	−	1.23586i
$37$	−6.86474	+	6.86474i	−1.12856	+	1.12856i	−0.138144	+	0.990412i	$0.544114\pi$
$37$	−6.86474	+	6.86474i	−1.12856	+	1.12856i	−0.990412	+	0.138144i	$0.955886\pi$
$38$	3.58594	+	9.06317i	0.581717	+	1.47024i
$39$		−	0.708204i		−	0.113403i
$40$		0			0
$41$	3.92705	+	2.26728i	0.613302	+	0.354090i	0.774257	−	0.632872i	$-0.218124\pi$
$41$	3.92705	+	2.26728i	0.613302	+	0.354090i	−0.160954	+	0.986962i	$0.551457\pi$
$42$	−0.382883	+	1.42894i	−0.0590802	+	0.220490i
$43$	−0.831171	−	3.10197i	−0.126752	−	0.473046i	0.873144	−	0.487463i	$-0.162078\pi$
$43$	−0.831171	−	3.10197i	−0.126752	−	0.473046i	−0.999896	+	0.0144165i	$0.995411\pi$
$44$	4.81710	−	2.78115i	0.726205	−	0.419275i
$45$		0			0
$46$			11.6190i			1.71312i
$47$	1.00240	−	3.74101i	0.146215	−	0.545683i	−0.853483	−	0.521121i	$-0.825514\pi$
$47$	1.00240	−	3.74101i	0.146215	−	0.545683i	0.999698	−	0.0245623i	$-0.00781922\pi$
$48$	−0.0988601	+	0.368951i	−0.0142692	+	0.0532535i
$49$		−	4.00000i		−	0.571429i
$50$		0			0
$51$	0.218847	−	0.126351i	0.0306447	−	0.0176927i
$52$	1.43963	+	5.37277i	0.199641	+	0.745070i
$53$	3.48685	−	13.0131i	0.478955	−	1.78748i	−0.126907	−	0.991915i	$-0.540505\pi$
$53$	3.48685	−	13.0131i	0.478955	−	1.78748i	0.605862	−	0.795570i	$-0.292828\pi$
$54$	4.33013	+	2.50000i	0.589256	+	0.340207i
$55$		0			0
$56$		−	3.87298i		−	0.517549i
$57$	−1.54817	+	0.612552i	−0.205061	+	0.0811345i
$58$	−1.04606	+	1.04606i	−0.137354	+	0.137354i
$59$	7.13264	−	12.3541i	0.928591	−	1.60837i	0.142910	−	0.989736i	$-0.454354\pi$
$59$	7.13264	−	12.3541i	0.928591	−	1.60837i	0.785681	−	0.618631i	$-0.212313\pi$
$60$		0			0
$61$	4.78115	+	8.28120i	0.612164	+	1.06030i	0.990875	+	0.134784i	$0.0430341\pi$
$61$	4.78115	+	8.28120i	0.612164	+	1.06030i	−0.378711	+	0.925515i	$0.623633\pi$
$62$	3.19521	−	0.856153i	0.405792	−	0.108732i
$63$	4.77501	+	1.27946i	0.601594	+	0.161197i
$64$		−	13.0000i		−	1.62500i
$65$		0			0
$66$	0.791796	+	1.37143i	0.0974634	+	0.168811i
$67$	−5.79555	−	1.55291i	−0.708040	−	0.189719i	−0.113211	−	0.993571i	$-0.536114\pi$
$67$	−5.79555	−	1.55291i	−0.708040	−	0.189719i	−0.594829	+	0.803852i	$0.702780\pi$
$68$	−1.40343	+	1.40343i	−0.170191	+	0.170191i
$69$	−1.98475			−0.238936
$70$		0			0
$71$	3.35410	+	1.93649i	0.398059	+	0.229819i	0.685646	−	0.727935i	$-0.259520\pi$
$71$	3.35410	+	1.93649i	0.398059	+	0.229819i	−0.287587	+	0.957754i	$0.592853\pi$
$72$	−6.16451	−	1.65177i	−0.726494	−	0.194663i
$73$	−3.07261	−	11.4671i	−0.359622	−	1.34213i	−0.874567	−	0.484904i	$-0.838855\pi$
$73$	−3.07261	−	11.4671i	−0.359622	−	1.34213i	0.514946	−	0.857223i	$-0.327812\pi$
$74$	18.7999	+	10.8541i	2.18544	+	1.26176i
$75$		0			0
$76$	10.5000	−	7.79423i	1.20443	−	0.894059i
$77$	2.27080	+	2.27080i	0.258782	+	0.258782i
$78$	−1.52963	+	0.409864i	−0.173197	+	0.0464079i
$79$	−6.80185	+	11.7812i	−0.765268	+	1.32548i	0.174837	+	0.984597i	$0.444060\pi$
$79$	−6.80185	+	11.7812i	−0.765268	+	1.32548i	−0.940105	+	0.340886i	$0.889273\pi$
$80$		0			0
$81$	3.85410	−	6.67550i	0.428234	−	0.741722i
$82$	2.62432	−	9.79410i	0.289808	−	1.08158i
$83$	−10.5549	+	10.5549i	−1.15855	+	1.15855i	−0.173762	+	0.984788i	$0.555592\pi$
$83$	−10.5549	+	10.5549i	−1.15855	+	1.15855i	−0.984788	+	0.173762i	$0.944408\pi$
$84$	1.98475			0.216554
$85$		0			0
$86$	−6.21885	+	3.59045i	−0.670596	+	0.387169i
$87$	−0.178688	−	0.178688i	−0.0191574	−	0.0191574i
$88$	−2.93159	−	2.93159i	−0.312509	−	0.312509i
$89$	−1.27491	−	2.20820i	−0.135140	−	0.234069i	0.790511	−	0.612448i	$-0.209815\pi$
$89$	−1.27491	−	2.20820i	−0.135140	−	0.234069i	−0.925651	+	0.378379i	$0.876482\pi$
$90$		0			0
$91$	−2.78115	+	1.60570i	−0.291544	+	0.168323i
$92$	15.0573	−	4.03459i	1.56983	−	0.420635i
$93$	0.146248	+	0.545807i	0.0151653	+	0.0565975i
$94$	−8.66025			−0.893237
$95$		0			0
$96$	2.56231			0.261514
$97$	−2.21609	−	8.27055i	−0.225010	−	0.839747i	−0.982401	−	0.186786i	$-0.940193\pi$
$97$	−2.21609	−	8.27055i	−0.225010	−	0.839747i	0.757391	−	0.652962i	$-0.226474\pi$
$98$	−8.63950	+	2.31495i	−0.872722	+	0.233845i
$99$	4.58283	−	2.64590i	0.460592	−	0.265923i
$100$		0			0
$101$	−7.85410	−	13.6037i	−0.781512	−	1.35362i	−0.931061	−	0.364865i	$-0.881115\pi$
$101$	−7.85410	−	13.6037i	−0.781512	−	1.35362i	0.149548	−	0.988754i	$-0.452218\pi$
$102$	−0.399558	−	0.399558i	−0.0395622	−	0.0395622i
$103$	−6.86474	−	6.86474i	−0.676403	−	0.676403i	0.282782	−	0.959184i	$-0.408743\pi$
$103$	−6.86474	−	6.86474i	−0.676403	−	0.676403i	−0.959184	+	0.282782i	$0.908743\pi$
$104$	3.59045	−	2.07295i	0.352073	−	0.203269i
$105$		0			0
$106$	−30.1246			−2.92596
$107$	0.770867	−	0.770867i	0.0745225	−	0.0745225i	−0.668863	−	0.743386i	$-0.733219\pi$
$107$	0.770867	−	0.770867i	0.0745225	−	0.0745225i	0.743386	+	0.668863i	$0.233219\pi$
$108$	1.73621	−	6.47963i	0.167067	−	0.623502i
$109$	−7.54153	+	13.0623i	−0.722347	+	1.25114i	0.237709	+	0.971336i	$0.423603\pi$
$109$	−7.54153	+	13.0623i	−0.722347	+	1.25114i	−0.960057	+	0.279806i	$0.909730\pi$
$110$		0			0
$111$	−1.85410	+	3.21140i	−0.175984	+	0.304812i
$112$	1.67303	−	0.448288i	0.158087	−	0.0423592i
$113$	8.71597	+	8.71597i	0.819929	+	0.819929i	0.986097	−	0.166168i	$-0.0531395\pi$
$113$	8.71597	+	8.71597i	0.819929	+	0.819929i	−0.166168	+	0.986097i	$0.553139\pi$
$114$	2.21902	+	2.98936i	0.207830	+	0.279979i
$115$		0			0
$116$	1.71885	+	0.992377i	0.159591	+	0.0921399i
$117$	1.36962	+	5.11148i	0.126621	+	0.472557i
$118$	−30.8113	−	8.25585i	−2.83641	−	0.760013i
$119$	−0.992377	−	0.572949i	−0.0909710	−	0.0525222i
$120$		0			0
$121$	−7.56231			−0.687482
$122$	15.1193	−	15.1193i	1.36884	−	1.36884i
$123$	1.67303	+	0.448288i	0.150852	+	0.0404207i
$124$	−2.21902	−	3.84346i	−0.199274	−	0.345153i
$125$		0			0
$126$		−	11.0539i		−	0.984759i
$127$	−11.1683	−	2.99254i	−0.991029	−	0.265545i	−0.273346	−	0.961916i	$-0.588130\pi$
$127$	−11.1683	−	2.99254i	−0.991029	−	0.265545i	−0.717683	+	0.696370i	$0.754797\pi$
$128$	−15.1191	+	4.05116i	−1.33635	+	0.358075i
$129$	−0.613323	−	1.06231i	−0.0540000	−	0.0935308i
$130$		0			0
$131$	9.13525	−	15.8227i	0.798151	−	1.38244i	−0.122668	−	0.992448i	$-0.539145\pi$
$131$	9.13525	−	15.8227i	0.798151	−	1.38244i	0.920819	−	0.389990i	$-0.127522\pi$
$132$	1.50233	−	1.50233i	0.130761	−	0.130761i
$133$	5.91567	+	4.69093i	0.512954	+	0.406755i
$134$			13.4164i			1.15900i
$135$		0			0
$136$	1.28115	+	0.739674i	0.109858	+	0.0634265i
$137$	−1.00240	+	3.74101i	−0.0856410	+	0.319616i	−0.995435	−	0.0954440i	$-0.969573\pi$
$137$	−1.00240	+	3.74101i	−0.0856410	+	0.319616i	0.909794	+	0.415060i	$0.136240\pi$
$138$	1.14865	+	4.28682i	0.0977796	+	0.364918i
$139$	2.11111	−	1.21885i	0.179062	−	0.103381i	−0.407790	−	0.913076i	$-0.633700\pi$
$139$	2.11111	−	1.21885i	0.179062	−	0.103381i	0.586852	+	0.809694i	$0.300367\pi$
$140$		0			0
$141$		−	1.47935i		−	0.124584i
$142$	2.24144	−	8.36516i	0.188097	−	0.701989i
$143$	−0.889741	+	3.32056i	−0.0744039	+	0.277679i
$144$		−	2.85410i		−	0.237842i
$145$		0			0
$146$	−22.9894	+	13.2729i	−1.90261	+	1.09847i
$147$	−0.395440	−	1.47580i	−0.0326154	−	0.121722i
$148$	7.53800	−	28.1322i	0.619620	−	2.31245i
$149$	8.40755	+	4.85410i	0.688773	+	0.397664i	0.803152	−	0.595774i	$-0.203154\pi$
$149$	8.40755	+	4.85410i	0.688773	+	0.397664i	−0.114379	+	0.993437i	$0.536488\pi$
$150$		0			0
$151$		−	4.69075i		−	0.381728i	−0.981617	−	0.190864i	$-0.938871\pi$
$151$		−	4.69075i		−	0.381728i	0.981617	−	0.190864i	$-0.0611289\pi$
$152$	−7.63710	−	6.05596i	−0.619451	−	0.491203i
$153$	−1.33518	+	1.33518i	−0.107943	+	0.107943i
$154$	3.59045	−	6.21885i	0.289327	−	0.501129i
$155$		0			0
$156$	1.06231	+	1.83997i	0.0850525	+	0.147315i
$157$	1.42894	−	0.382883i	0.114042	−	0.0305574i	−0.201347	−	0.979520i	$-0.564532\pi$
$157$	1.42894	−	0.382883i	0.114042	−	0.0305574i	0.315389	+	0.948963i	$0.397865\pi$
$158$	29.3823	+	7.87297i	2.33753	+	0.626340i
$159$		−	5.14590i		−	0.408096i
$160$		0			0
$161$	4.50000	+	7.79423i	0.354650	+	0.614271i
$162$	−16.6488	−	4.46102i	−1.30805	−	0.350491i
$163$	1.22474	−	1.22474i	0.0959294	−	0.0959294i	−0.657513	−	0.753443i	$-0.728392\pi$
$163$	1.22474	−	1.22474i	0.0959294	−	0.0959294i	0.753443	+	0.657513i	$0.228392\pi$
$164$	−13.6037			−1.06227
$165$		0			0
$166$	28.9058	+	16.6888i	2.24352	+	1.29530i
$167$	−5.42660	−	1.45405i	−0.419923	−	0.112518i	0.0426690	−	0.999089i	$-0.486414\pi$
$167$	−5.42660	−	1.45405i	−0.419923	−	0.112518i	−0.462592	+	0.886571i	$0.653081\pi$
$168$	−0.382883	−	1.42894i	−0.0295401	−	0.110245i
$169$	8.28120	+	4.78115i	0.637015	+	0.367781i
$170$		0			0
$171$	9.98936	−	7.41517i	0.763905	−	0.567053i
$172$	6.81241	+	6.81241i	0.519441	+	0.519441i
$173$	4.37358	−	1.17190i	0.332517	−	0.0890977i	−0.0886977	−	0.996059i	$-0.528270\pi$
$173$	4.37358	−	1.17190i	0.332517	−	0.0890977i	0.421215	+	0.906961i	$0.361604\pi$
$174$	−0.282530	+	0.489357i	−0.0214186	+	0.0370980i
$175$		0			0
$176$	0.927051	−	1.60570i	0.0698791	−	0.121034i
$177$	1.41027	−	5.26319i	0.106002	−	0.395606i
$178$	−4.03161	+	4.03161i	−0.302182	+	0.302182i
$179$	−9.06914			−0.677859			−0.338930	−	0.940812i	$-0.610065\pi$
$179$	−9.06914			−0.677859			−0.338930	+	0.940812i	$0.610065\pi$
$180$		0			0
$181$	13.2812	−	7.66788i	0.987180	−	0.569949i	0.0827501	−	0.996570i	$-0.473630\pi$
$181$	13.2812	−	7.66788i	0.987180	−	0.569949i	0.904430	+	0.426622i	$0.140296\pi$
$182$	5.07767	+	5.07767i	0.376382	+	0.376382i
$183$	2.58269	+	2.58269i	0.190918	+	0.190918i
$184$	−5.80948	−	10.0623i	−0.428280	−	0.741803i
$185$		0			0
$186$	1.09424	−	0.631757i	0.0802332	−	0.0463227i
$187$	−1.18485	+	0.317479i	−0.0866447	+	0.0232164i
$188$	3.00721	+	11.2230i	0.219323	+	0.818525i
$189$	3.87298			0.281718
$190$		0			0
$191$	7.14590			0.517059			0.258530	−	0.966003i	$-0.416762\pi$
$191$	7.14590			0.517059			0.258530	+	0.966003i	$0.416762\pi$
$192$	−1.28518	−	4.79636i	−0.0927500	−	0.346148i
$193$	8.00926	−	2.14607i	0.576519	−	0.154478i	0.0412344	−	0.999150i	$-0.486871\pi$
$193$	8.00926	−	2.14607i	0.576519	−	0.154478i	0.535285	+	0.844672i	$0.320204\pi$
$194$	−16.5808	+	9.57295i	−1.19043	+	0.687298i
$195$		0			0
$196$	6.00000	+	10.3923i	0.428571	+	0.742307i
$197$	1.33518	+	1.33518i	0.0951276	+	0.0951276i	0.753069	−	0.657941i	$-0.228573\pi$
$197$	1.33518	+	1.33518i	0.0951276	+	0.0951276i	−0.657941	+	0.753069i	$0.728573\pi$
$198$	−8.36706	−	8.36706i	−0.594621	−	0.594621i
$199$	18.2945	−	10.5623i	1.29686	−	0.748742i	0.316999	−	0.948426i	$-0.397325\pi$
$199$	18.2945	−	10.5623i	1.29686	−	0.748742i	0.979860	+	0.199684i	$0.0639915\pi$
$200$		0			0
$201$	−2.29180			−0.161651
$202$	−24.8369	+	24.8369i	−1.74751	+	1.74751i
$203$	−0.296580	+	1.10685i	−0.0208159	+	0.0776858i
$204$	−0.379054	+	0.656541i	−0.0265391	+	0.0459671i
$205$		0			0
$206$	−10.8541	+	18.7999i	−0.756241	+	1.30985i
$207$	14.3250	−	3.83838i	0.995658	−	0.266786i
$208$	1.31105	+	1.31105i	0.0909048	+	0.0909048i
$209$	8.02850	−	0.927051i	0.555343	−	0.0641255i
$210$		0			0
$211$	−15.8435	−	9.14723i	−1.09071	−	0.629721i	−0.156944	−	0.987608i	$-0.550164\pi$
$211$	−15.8435	−	9.14723i	−1.09071	−	0.629721i	−0.933765	+	0.357887i	$0.883497\pi$
$212$	10.4605	+	39.0393i	0.718433	+	2.68123i
$213$	1.42894	+	0.382883i	0.0979094	+	0.0262347i
$214$	−2.11111	−	1.21885i	−0.144312	−	0.0833187i
$215$		0			0
$216$	−5.00000			−0.340207
$217$	1.81182	−	1.81182i	0.122995	−	0.122995i
$218$	32.5775	+	8.72912i	2.20643	+	0.591211i
$219$	−2.26728	−	3.92705i	−0.153209	−	0.265366i
$220$		0			0
$221$		−	1.22665i		−	0.0825131i
$222$	8.00926	+	2.14607i	0.537546	+	0.144035i
$223$	−16.2798	+	4.36216i	−1.09018	+	0.292112i	−0.758759	−	0.651372i	$-0.774194\pi$
$223$	−16.2798	+	4.36216i	−1.09018	+	0.292112i	−0.331418	+	0.943484i	$0.607527\pi$
$224$	−5.80948	−	10.0623i	−0.388162	−	0.672316i
$225$		0			0
$226$	13.7812	−	23.8697i	0.916709	−	1.58779i
$227$	−9.52624	+	9.52624i	−0.632279	+	0.632279i	−0.948639	−	0.316360i	$-0.897539\pi$
$227$	−9.52624	+	9.52624i	−0.632279	+	0.632279i	0.316360	+	0.948639i	$0.397539\pi$
$228$	3.10345	−	3.91372i	0.205531	−	0.259192i
$229$			11.0000i			0.726900i	0.931614	+	0.363450i	$0.118401\pi$
$229$			11.0000i			0.726900i	−0.931614	+	0.363450i	$0.881599\pi$
$230$		0			0
$231$	1.06231	+	0.613323i	0.0698946	+	0.0403537i
$232$	0.382883	−	1.42894i	0.0251375	−	0.0938145i
$233$	2.34727	+	8.76011i	0.153774	+	0.573894i	0.999207	+	0.0398121i	$0.0126759\pi$
$233$	2.34727	+	8.76011i	0.153774	+	0.573894i	−0.845433	+	0.534082i	$0.820657\pi$
$234$	10.2475	−	5.91641i	0.669901	−	0.386768i
$235$		0			0
$236$			42.7959i			2.78577i
$237$	−1.34486	+	5.01910i	−0.0873583	+	0.326025i
$238$	−0.663174	+	2.47500i	−0.0429872	+	0.160430i
$239$		−	23.8328i		−	1.54162i	−0.637067	−	0.770808i	$-0.719853\pi$
$239$		−	23.8328i		−	1.54162i	0.637067	−	0.770808i	$-0.280147\pi$
$240$		0			0
$241$	−13.2812	+	7.66788i	−0.855514	+	0.493931i	−0.862508	−	0.506044i	$-0.831107\pi$
$241$	−13.2812	+	7.66788i	−0.855514	+	0.493931i	0.00699331	+	0.999976i	$0.497774\pi$
$242$	4.37659	+	16.3336i	0.281338	+	1.04997i
$243$	2.49824	−	9.32358i	0.160262	−	0.598108i
$244$	−24.8436	−	14.3435i	−1.59045	−	0.918246i
$245$		0			0
$246$		−	3.87298i		−	0.246932i
$247$	−1.18247	+	7.99487i	−0.0752385	+	0.508701i
$248$	−2.33905	+	2.33905i	−0.148530	+	0.148530i
$249$	−2.85078	+	4.93769i	−0.180661	+	0.312914i
$250$		0			0
$251$	3.13525	+	5.43042i	0.197896	+	0.342765i	0.947846	−	0.318729i	$-0.103256\pi$
$251$	3.13525	+	5.43042i	0.197896	+	0.342765i	−0.749950	+	0.661494i	$0.769923\pi$
$252$	−14.3250	+	3.83838i	−0.902391	+	0.241795i
$253$	9.30592	+	2.49351i	0.585058	+	0.156766i
$254$			25.8541i			1.62223i
$255$		0			0
$256$	4.50000	+	7.79423i	0.281250	+	0.487139i
$257$	24.9193	+	6.67711i	1.55442	+	0.416507i	0.930893	−	0.365292i	$-0.119031\pi$
$257$	24.9193	+	6.67711i	1.55442	+	0.416507i	0.623531	+	0.781799i	$0.285697\pi$
$258$	−1.93950	+	1.93950i	−0.120748	+	0.120748i
$259$	16.8151			1.04484
$260$		0			0
$261$	1.63525	+	0.944115i	0.101220	+	0.0584392i
$262$	−39.4620	−	10.5738i	−2.43797	−	0.653253i
$263$	3.34967	+	12.5011i	0.206549	+	0.770853i	0.988972	+	0.148104i	$0.0473172\pi$
$263$	3.34967	+	12.5011i	0.206549	+	0.770853i	−0.782422	+	0.622748i	$0.786016\pi$
$264$	−1.37143	−	0.791796i	−0.0844057	−	0.0487317i
$265$		0			0
$266$	6.70820	−	15.4919i	0.411306	−	0.949871i
$267$	−0.688681	−	0.688681i	−0.0421466	−	0.0421466i
$268$	17.3867	−	4.65874i	1.06206	−	0.284578i
$269$	−7.41517	+	12.8435i	−0.452111	+	0.783080i	−0.998517	−	0.0544410i	$-0.982662\pi$
$269$	−7.41517	+	12.8435i	−0.452111	+	0.783080i	0.546406	+	0.837521i	$0.315996\pi$
$270$		0			0
$271$	−0.281153	+	0.486971i	−0.0170788	+	0.0295814i	−0.874439	−	0.485136i	$-0.838770\pi$
$271$	−0.281153	+	0.486971i	−0.0170788	+	0.0295814i	0.857360	+	0.514718i	$0.172103\pi$
$272$	−0.171231	+	0.639042i	−0.0103824	+	0.0387476i
$273$	−0.867369	+	0.867369i	−0.0524956	+	0.0524956i
$274$	8.66025			0.523185
$275$		0			0
$276$	5.15654	−	2.97713i	0.310387	−	0.179202i
$277$	19.5959	+	19.5959i	1.17740	+	1.17740i	0.980403	+	0.197001i	$0.0631203\pi$
$277$	19.5959	+	19.5959i	1.17740	+	1.17740i	0.197001	+	0.980403i	$0.436880\pi$
$278$	−3.85433	−	3.85433i	−0.231168	−	0.231168i
$279$	−2.11111	−	3.65654i	−0.126389	−	0.218911i
$280$		0			0
$281$	−4.50000	+	2.59808i	−0.268447	+	0.154988i	−0.628182	−	0.778067i	$-0.716201\pi$
$281$	−4.50000	+	2.59808i	−0.268447	+	0.154988i	0.359734	+	0.933055i	$0.382867\pi$
$282$	−3.19521	+	0.856153i	−0.190272	+	0.0509832i
$283$	8.19045	+	30.5672i	0.486871	+	1.81703i	0.571482	+	0.820615i	$0.306369\pi$
$283$	8.19045	+	30.5672i	0.486871	+	1.81703i	−0.0846102	+	0.996414i	$0.526964\pi$
$284$	−11.6190			−0.689458
$285$		0			0
$286$	7.68692			0.454537
$287$	−2.03279	−	7.58648i	−0.119992	−	0.447816i
$288$	−18.4935	+	4.95532i	−1.08974	+	0.291995i
$289$	−14.3434	+	8.28115i	−0.843728	+	0.487127i
$290$		0			0
$291$	−1.63525	−	2.83234i	−0.0958603	−	0.166035i
$292$	25.1836	+	25.1836i	1.47376	+	1.47376i
$293$	4.01196	+	4.01196i	0.234381	+	0.234381i	0.814519	−	0.580138i	$-0.197001\pi$
$293$	4.01196	+	4.01196i	0.234381	+	0.234381i	−0.580138	+	0.814519i	$0.697001\pi$
$294$	−2.95870	+	1.70820i	−0.172555	+	0.0996245i
$295$		0			0
$296$	−21.7082			−1.26176
$297$	2.93159	−	2.93159i	0.170108	−	0.170108i
$298$	5.61850	−	20.9685i	0.325471	−	1.21467i
$299$	−4.81710	+	8.34346i	−0.278580	+	0.482515i
$300$		0			0
$301$	−2.78115	+	4.81710i	−0.160303	+	0.277653i
$302$	−10.1314	+	2.71471i	−0.582998	+	0.156214i
$303$	−4.24264	−	4.24264i	−0.243733	−	0.243733i
$304$	1.73205	−	4.00000i	0.0993399	−	0.229416i
$305$		0			0
$306$	3.65654	+	2.11111i	0.209031	+	0.120684i
$307$	−4.84204	−	18.0707i	−0.276350	−	1.03135i	−0.954931	−	0.296826i	$-0.904072\pi$
$307$	−4.84204	−	18.0707i	−0.276350	−	1.03135i	0.678582	−	0.734525i	$-0.262595\pi$
$308$	−9.30592	−	2.49351i	−0.530254	−	0.142081i
$309$	−3.21140	−	1.85410i	−0.182690	−	0.105476i
$310$		0			0
$311$	−9.00000			−0.510343			−0.255172	−	0.966896i	$-0.582132\pi$
$311$	−9.00000			−0.510343			−0.255172	+	0.966896i	$0.582132\pi$
$312$	1.11977	−	1.11977i	0.0633944	−	0.0633944i
$313$	11.2230	+	3.00721i	0.634364	+	0.169977i	0.561649	−	0.827375i	$-0.310167\pi$
$313$	11.2230	+	3.00721i	0.634364	+	0.169977i	0.0727147	+	0.997353i	$0.476834\pi$
$314$	−1.65396	−	2.86475i	−0.0933384	−	0.161667i
$315$		0			0
$316$		−	40.8111i		−	2.29580i
$317$	−17.2790	−	4.62990i	−0.970486	−	0.260041i	−0.261453	−	0.965216i	$-0.584202\pi$
$317$	−17.2790	−	4.62990i	−0.970486	−	0.260041i	−0.709033	+	0.705175i	$0.750868\pi$
$318$	−11.1145	+	2.97812i	−0.623270	+	0.167005i
$319$	0.613323	+	1.06231i	0.0343395	+	0.0594777i
$320$		0			0
$321$	0.208204	−	0.360620i	0.0116208	−	0.0201278i
$322$	14.2302	−	14.2302i	0.793021	−	0.793021i
$323$	−2.68152	+	1.06097i	−0.149204	+	0.0590340i
$324$			23.1246i			1.28470i
$325$		0			0
$326$	−3.35410	−	1.93649i	−0.185767	−	0.107252i
$327$	−1.49111	+	5.56490i	−0.0824587	+	0.307740i
$328$	2.62432	+	9.79410i	0.144904	+	0.540789i
$329$	−5.80948	+	3.35410i	−0.320287	+	0.184918i
$330$		0			0
$331$			10.3923i			0.571213i	0.958347	+	0.285606i	$0.0921950\pi$
$331$			10.3923i			0.571213i	−0.958347	+	0.285606i	$0.907805\pi$
$332$	11.5901	−	43.2548i	0.636088	−	2.37391i
$333$	7.17141	−	26.7641i	0.392991	−	1.46666i
$334$			12.5623i			0.687379i
$335$		0			0
$336$	0.572949	−	0.330792i	0.0312569	−	0.0180462i
$337$	−5.20863	−	19.4389i	−0.283732	−	1.05890i	−0.949761	−	0.312977i	$-0.898674\pi$
$337$	−5.20863	−	19.4389i	−0.283732	−	1.05890i	0.666028	−	0.745926i	$-0.267993\pi$
$338$	5.53406	−	20.6534i	0.301013	−	1.12340i
$339$	4.07742	+	2.35410i	0.221455	+	0.127857i
$340$		0			0
$341$		−	2.74286i		−	0.148534i
$342$	−21.7971	−	17.2843i	−1.17865	−	0.934630i
$343$	−13.4722	+	13.4722i	−0.727430	+	0.727430i
$344$	3.59045	−	6.21885i	0.193584	−	0.335298i
$345$		0			0
$346$	−5.06231	−	8.76817i	−0.272151	−	0.471380i
$347$	21.8070	−	5.84318i	1.17066	−	0.313678i	0.379446	−	0.925214i	$-0.376114\pi$
$347$	21.8070	−	5.84318i	1.17066	−	0.313678i	0.791217	+	0.611535i	$0.209448\pi$
$348$	0.732277	+	0.196213i	0.0392541	+	0.0105181i
$349$			11.0000i			0.588817i	0.955680	+	0.294408i	$0.0951225\pi$
$349$			11.0000i			0.588817i	−0.955680	+	0.294408i	$0.904877\pi$
$350$		0			0
$351$	2.07295	+	3.59045i	0.110646	+	0.191644i
$352$	−12.0139	−	3.21911i	−0.640342	−	0.171579i
$353$	15.5643	−	15.5643i	0.828405	−	0.828405i	−0.158892	−	0.987296i	$-0.550792\pi$
$353$	15.5643	−	15.5643i	0.828405	−	0.828405i	0.987296	+	0.158892i	$0.0507920\pi$
$354$	−12.1840			−0.647573
$355$		0			0
$356$	6.62461	+	3.82472i	0.351104	+	0.202710i
$357$	−0.422780	−	0.113284i	−0.0223759	−	0.00599560i
$358$	5.24864	+	19.5882i	0.277399	+	1.03527i
$359$	−26.8284	−	15.4894i	−1.41595	−	0.817497i	−0.420007	−	0.907521i	$-0.637972\pi$
$359$	−26.8284	−	15.4894i	−1.41595	−	0.817497i	−0.995940	+	0.0900240i	$0.971306\pi$
$360$		0			0
$361$	18.5000	−	4.33013i	0.973684	−	0.227901i
$362$	−24.2480	−	24.2480i	−1.27444	−	1.27444i
$363$	−2.79012	+	0.747610i	−0.146443	+	0.0392394i
$364$	4.81710	−	8.34346i	0.252485	−	0.437316i
$365$		0			0
$366$	4.08359	−	7.07299i	0.213453	−	0.369711i
$367$	4.86576	−	18.1593i	0.253991	−	0.947906i	−0.714659	−	0.699473i	$-0.753418\pi$
$367$	4.86576	−	18.1593i	0.253991	−	0.947906i	0.968649	−	0.248433i	$-0.0799154\pi$
$368$	3.67423	−	3.67423i	0.191533	−	0.191533i
$369$	−12.9421			−0.673740
$370$		0			0
$371$	−20.2082	+	11.6672i	−1.04916	+	0.605731i
$372$	−1.19867	−	1.19867i	−0.0621484	−	0.0621484i
$373$	−10.7979	−	10.7979i	−0.559093	−	0.559093i	0.369956	−	0.929049i	$-0.379373\pi$
$373$	−10.7979	−	10.7979i	−0.559093	−	0.559093i	−0.929049	+	0.369956i	$0.879373\pi$
$374$	1.37143	+	2.37539i	0.0709150	+	0.122828i
$375$		0			0
$376$	7.50000	−	4.33013i	0.386783	−	0.223309i
$377$	−1.18485	+	0.317479i	−0.0610228	+	0.0163510i
$378$	−2.24144	−	8.36516i	−0.115287	−	0.430258i
$379$	27.2074			1.39755			0.698775	−	0.715341i	$-0.253729\pi$
$379$	27.2074			1.39755			0.698775	+	0.715341i	$0.253729\pi$
$380$		0			0
$381$	−4.41641			−0.226259
$382$	−4.13560	−	15.4343i	−0.211595	−	0.789685i
$383$	−17.3328	+	4.64432i	−0.885667	+	0.237314i	−0.672850	−	0.739779i	$-0.734930\pi$
$383$	−17.3328	+	4.64432i	−0.885667	+	0.237314i	−0.212816	+	0.977092i	$0.568264\pi$
$384$	−5.17772	+	2.98936i	−0.264224	+	0.152550i
$385$		0			0
$386$	−9.27051	−	16.0570i	−0.471857	−	0.817279i
$387$	6.48110	+	6.48110i	0.329453	+	0.329453i
$388$	18.1634	+	18.1634i	0.922107	+	0.922107i
$389$	−1.60570	+	0.927051i	−0.0814122	+	0.0470034i	−0.540153	−	0.841567i	$-0.681634\pi$
$389$	−1.60570	+	0.927051i	−0.0814122	+	0.0470034i	0.458741	+	0.888570i	$0.348300\pi$
$390$		0			0
$391$	−3.43769			−0.173852
$392$	6.32456	−	6.32456i	0.319438	−	0.319438i
$393$	1.80622	−	6.74092i	0.0911119	−	0.340034i
$394$	2.11111	−	3.65654i	0.106356	−	0.184214i
$395$		0			0
$396$	−7.93769	+	13.7485i	−0.398884	+	0.690888i
$397$	−21.2612	+	5.69693i	−1.06707	+	0.285921i	−0.749289	−	0.662243i	$-0.769605\pi$
$397$	−21.2612	+	5.69693i	−1.06707	+	0.285921i	−0.317782	+	0.948164i	$0.602938\pi$
$398$	−33.4009	−	33.4009i	−1.67424	−	1.67424i
$399$	2.64634	+	1.14590i	0.132483	+	0.0573667i
$400$		0			0
$401$	23.5623	+	13.6037i	1.17665	+	0.679337i	0.955236	−	0.295844i	$-0.0956010\pi$
$401$	23.5623	+	13.6037i	1.17665	+	0.679337i	0.221409	+	0.975181i	$0.428934\pi$
$402$	1.32635	+	4.94999i	0.0661522	+	0.246883i
$403$	2.64940	+	0.709905i	0.131976	+	0.0353629i
$404$	40.8111	+	23.5623i	2.03043	+	1.17227i
$405$		0			0
$406$	2.56231			0.127165
$407$	12.7279	−	12.7279i	0.630900	−	0.630900i
$408$	0.545807	+	0.146248i	0.0270215	+	0.00724038i
$409$	11.6190	+	20.1246i	0.574520	+	0.995098i	0.996094	+	0.0883038i	$0.0281446\pi$
$409$	11.6190	+	20.1246i	0.574520	+	0.995098i	−0.421573	+	0.906794i	$0.638522\pi$
$410$		0			0
$411$			1.47935i			0.0729709i
$412$	28.1322	+	7.53800i	1.38597	+	0.371371i
$413$	−23.8663	+	6.39495i	−1.17438	+	0.314675i
$414$	−16.5808	−	28.7188i	−0.814904	−	1.41145i
$415$		0			0
$416$	6.21885	−	10.7714i	0.304904	−	0.528109i
$417$	0.658399	−	0.658399i	0.0322419	−	0.0322419i
$418$	−6.64870	−	16.8040i	−0.325199	−	0.821912i
$419$		−	31.4164i		−	1.53479i	−0.641173	−	0.767396i	$-0.721552\pi$
$419$		−	31.4164i		−	1.53479i	0.641173	−	0.767396i	$-0.278448\pi$
$420$		0			0
$421$	−29.1246	−	16.8151i	−1.41945	−	0.819518i	−0.423197	−	0.906038i	$-0.639092\pi$
$421$	−29.1246	−	16.8151i	−1.41945	−	0.819518i	−0.996250	+	0.0865199i	$0.972425\pi$
$422$	−10.5877	+	39.5137i	−0.515400	+	1.92350i
$423$	2.86096	+	10.6772i	0.139104	+	0.519145i
$424$	26.0887	−	15.0623i	1.26698	−	0.731490i
$425$		0			0
$426$		−	3.30792i		−	0.160269i
$427$	4.28666	−	15.9980i	0.207446	−	0.774200i
$428$	−0.846470	+	3.15907i	−0.0409157	+	0.152699i
$429$			1.31308i			0.0633962i
$430$		0			0
$431$	−21.9271	+	12.6596i	−1.05619	+	0.609791i	−0.924376	−	0.381484i	$-0.875413\pi$
$431$	−21.9271	+	12.6596i	−1.05619	+	0.609791i	−0.131813	+	0.991275i	$0.542080\pi$
$432$	−0.578737	−	2.15988i	−0.0278445	−	0.103917i
$433$	−3.65572	+	13.6433i	−0.175683	+	0.655656i	0.820752	+	0.571285i	$0.193555\pi$
$433$	−3.65572	+	13.6433i	−0.175683	+	0.655656i	−0.996434	+	0.0843715i	$0.973112\pi$
$434$	−4.96188	−	2.86475i	−0.238178	−	0.137512i
$435$		0			0
$436$		−	45.2492i		−	2.16704i
$437$	22.4058	+	3.31388i	1.07181	+	0.158524i
$438$	−7.16978	+	7.16978i	−0.342585	+	0.342585i
$439$	−12.7377	+	22.0623i	−0.607936	+	1.05298i	0.383644	+	0.923481i	$0.374669\pi$
$439$	−12.7377	+	22.0623i	−0.607936	+	1.05298i	−0.991580	+	0.129495i	$0.958664\pi$
$440$		0			0
$441$	5.70820	+	9.88690i	0.271819	+	0.470805i
$442$	−2.64940	+	0.709905i	−0.126019	+	0.0337667i
$443$	−31.3927	−	8.41164i	−1.49151	−	0.399649i	−0.581264	−	0.813715i	$-0.697442\pi$
$443$	−31.3927	−	8.41164i	−1.49151	−	0.399649i	−0.910247	+	0.414066i	$0.864108\pi$
$444$		−	11.1246i		−	0.527951i
$445$		0			0
$446$	18.8435	+	32.6378i	0.892264	+	1.54545i
$447$	3.58185	+	0.959754i	0.169416	+	0.0453948i
$448$	−15.9217	+	15.9217i	−0.752229	+	0.752229i
$449$	14.2653			0.673221			0.336610	−	0.941644i	$-0.390720\pi$
$449$	14.2653			0.673221			0.336610	+	0.941644i	$0.390720\pi$
$450$		0			0
$451$	−7.28115	−	4.20378i	−0.342856	−	0.197948i
$452$	−35.7187	−	9.57080i	−1.68007	−	0.450172i
$453$	−0.463728	−	1.73065i	−0.0217878	−	0.0813133i
$454$	26.0887	+	15.0623i	1.22440	+	0.706909i
$455$		0			0
$456$	−3.41641	−	1.47935i	−0.159988	−	0.0692768i
$457$	24.1375	+	24.1375i	1.12911	+	1.12911i	0.990323	+	0.138783i	$0.0443190\pi$
$457$	24.1375	+	24.1375i	1.12911	+	1.12911i	0.138783	+	0.990323i	$0.455681\pi$
$458$	23.7586	−	6.36611i	1.11017	−	0.297469i
$459$	−0.739674	+	1.28115i	−0.0345250	+	0.0597991i
$460$		0			0
$461$	−1.71885	+	2.97713i	−0.0800547	+	0.138659i	−0.903273	−	0.429066i	$-0.858843\pi$
$461$	−1.71885	+	2.97713i	−0.0800547	+	0.138659i	0.823219	+	0.567725i	$0.192176\pi$
$462$	0.709905	−	2.64940i	0.0330278	−	0.123261i
$463$	17.8351	−	17.8351i	0.828868	−	0.828868i	−0.158492	−	0.987360i	$-0.550663\pi$
$463$	17.8351	−	17.8351i	0.828868	−	0.828868i	0.987360	+	0.158492i	$0.0506633\pi$
$464$	0.661585			0.0307133
$465$		0			0
$466$	17.5623	−	10.1396i	0.813558	−	0.469708i
$467$	3.60598	+	3.60598i	0.166865	+	0.166865i	0.785600	−	0.618735i	$-0.212354\pi$
$467$	3.60598	+	3.60598i	0.166865	+	0.166865i	−0.618735	+	0.785600i	$0.712354\pi$
$468$	−11.2256	−	11.2256i	−0.518903	−	0.518903i
$469$	5.19615	+	9.00000i	0.239936	+	0.415581i
$470$		0			0
$471$	0.489357	−	0.282530i	0.0225484	−	0.0130183i
$472$	30.8113	−	8.25585i	1.41820	−	0.380006i
$473$	1.54108	+	5.75137i	0.0708588	+	0.264448i
$474$	11.6190			0.533676
$475$		0			0
$476$	3.43769			0.157566
$477$	9.95181	+	37.1407i	0.455662	+	1.70055i
$478$	−51.4759	+	13.7929i	−2.35445	+	0.630874i
$479$	22.6246	−	13.0623i	1.03374	−	0.596832i	0.115689	−	0.993286i	$-0.463093\pi$
$479$	22.6246	−	13.0623i	1.03374	−	0.596832i	0.918055	+	0.396454i	$0.129759\pi$
$480$		0			0
$481$	9.00000	+	15.5885i	0.410365	+	0.710772i
$482$	24.2480	+	24.2480i	1.10446	+	1.10446i
$483$	2.43082	+	2.43082i	0.110606	+	0.110606i
$484$	19.6474	−	11.3435i	0.893066	−	0.515612i
$485$		0			0
$486$	−21.5836			−0.979052
$487$	−18.4729	+	18.4729i	−0.837087	+	0.837087i	−0.988474	−	0.151388i	$-0.951626\pi$
$487$	−18.4729	+	18.4729i	−0.837087	+	0.837087i	0.151388	+	0.988474i	$0.451626\pi$
$488$	−5.53406	+	20.6534i	−0.250515	+	0.934935i
$489$	0.330792	−	0.572949i	0.0149589	−	0.0259097i
$490$		0			0
$491$	−4.06231	+	7.03612i	−0.183329	+	0.317536i	−0.943012	−	0.332758i	$-0.892021\pi$
$491$	−4.06231	+	7.03612i	−0.183329	+	0.317536i	0.759683	+	0.650294i	$0.225354\pi$
$492$	−5.01910	+	1.34486i	−0.226278	+	0.0606311i
$493$	−0.309496	−	0.309496i	−0.0139390	−	0.0139390i
$494$	17.9523	−	2.07295i	0.807711	−	0.0932664i
$495$		0			0
$496$	−1.28115	−	0.739674i	−0.0575255	−	0.0332123i
$497$	−1.73621	−	6.47963i	−0.0778797	−	0.290651i
$498$	12.3147	+	3.29970i	0.551833	+	0.147863i
$499$	−26.0887	−	15.0623i	−1.16789	−	0.674281i	−0.214708	−	0.976678i	$-0.568880\pi$
$499$	−26.0887	−	15.0623i	−1.16789	−	0.674281i	−0.953182	+	0.302397i	$0.902213\pi$
$500$		0			0
$501$	−2.14590			−0.0958717
$502$	9.91455	−	9.91455i	0.442508	−	0.442508i
$503$	−28.7433	−	7.70174i	−1.28160	−	0.343403i	−0.447135	−	0.894466i	$-0.647556\pi$
$503$	−28.7433	−	7.70174i	−1.28160	−	0.343403i	−0.834464	+	0.551063i	$0.814222\pi$
$504$	5.52694	+	9.57295i	0.246190	+	0.426413i
$505$		0			0
$506$		−	21.5427i		−	0.957691i
$507$	3.52802	+	0.945330i	0.156685	+	0.0419836i
$508$	33.5050	−	8.97763i	1.48654	−	0.398318i
$509$	−16.1535	−	27.9787i	−0.715992	−	1.24013i	−0.962576	−	0.271013i	$-0.912641\pi$
$509$	−16.1535	−	27.9787i	−0.715992	−	1.24013i	0.246584	−	0.969122i	$-0.420692\pi$
$510$		0			0
$511$	−10.2812	+	17.8075i	−0.454811	+	0.787757i
$512$	−7.90569	+	7.90569i	−0.349386	+	0.349386i
$513$	6.05596	−	7.63710i	0.267377	−	0.337186i
$514$		−	57.6869i		−	2.54446i
$515$		0			0
$516$	3.18692	+	1.83997i	0.140296	+	0.0810001i
$517$	−1.85856	+	6.93622i	−0.0817392	+	0.305055i
$518$	−9.73152	−	36.3185i	−0.427579	−	1.59574i
$519$	1.49778	−	0.864745i	0.0657454	−	0.0379581i
$520$		0			0
$521$			28.5306i			1.24995i	0.780646	+	0.624974i	$0.214890\pi$
$521$			28.5306i			1.24995i	−0.780646	+	0.624974i	$0.785110\pi$
$522$	1.09279	−	4.07834i	0.0478300	−	0.178504i
$523$	0.409864	−	1.52963i	0.0179221	−	0.0668862i	−0.956386	−	0.292107i	$-0.905644\pi$
$523$	0.409864	−	1.52963i	0.0179221	−	0.0668862i	0.974308	+	0.225221i	$0.0723103\pi$
$524$			54.8115i			2.39445i
$525$		0			0
$526$	25.0623	−	14.4697i	1.09277	−	0.630910i
$527$	0.253310	+	0.945365i	0.0110343	+	0.0411807i
$528$	0.183297	−	0.684072i	0.00797696	−	0.0297704i
$529$	3.46410	+	2.00000i	0.150613	+	0.0869565i
$530$		0			0
$531$			40.7146i			1.76686i
$532$	−22.4058	−	3.31388i	−0.971413	−	0.143675i
$533$	5.94504	−	5.94504i	0.257508	−	0.257508i
$534$	−1.08890	+	1.88603i	−0.0471213	+	0.0816166i
$535$		0			0
$536$	−6.70820	−	11.6190i	−0.289750	−	0.501862i
$537$	−3.34607	+	0.896575i	−0.144393	+	0.0386901i
$538$	32.0317	+	8.58287i	1.38099	+	0.370034i
$539$			7.41641i			0.319447i
$540$		0			0
$541$	−12.2812	−	21.2716i	−0.528008	−	0.914537i	−0.999467	−	0.0326487i	$-0.989606\pi$
$541$	−12.2812	−	21.2716i	−0.528008	−	0.914537i	0.471459	−	0.881888i	$-0.343728\pi$
$542$	1.21451	+	0.325427i	0.0521677	+	0.0139783i
$543$	4.14205	−	4.14205i	0.177752	−	0.177752i
$544$	4.43804			0.190280
$545$		0			0
$546$	2.37539	+	1.37143i	0.101657	+	0.0586918i
$547$	−1.36814	−	0.366593i	−0.0584977	−	0.0156744i	0.229452	−	0.973320i	$-0.426307\pi$
$547$	−1.36814	−	0.366593i	−0.0584977	−	0.0156744i	−0.287949	+	0.957646i	$0.592973\pi$
$548$	−3.00721	−	11.2230i	−0.128461	−	0.479425i
$549$	−23.6354	−	13.6459i	−1.00873	−	0.582393i
$550$		0			0
$551$	1.71885	+	2.31555i	0.0732253	+	0.0986456i
$552$	−3.13817	−	3.13817i	−0.133569	−	0.133569i
$553$	22.7594	−	6.09837i	0.967830	−	0.259329i
$554$	30.9839	−	53.6656i	1.31638	−	2.28003i
$555$		0			0
$556$	−3.65654	+	6.33332i	−0.155072	+	0.268592i
$557$	1.14865	−	4.28682i	0.0486699	−	0.181638i	−0.937312	−	0.348492i	$-0.886694\pi$
$557$	1.14865	−	4.28682i	0.0486699	−	0.181638i	0.985982	+	0.166853i	$0.0533606\pi$
$558$	−6.67590	+	6.67590i	−0.282613	+	0.282613i
$559$	−5.95426			−0.251838
$560$		0			0
$561$	−0.405765	+	0.234268i	−0.0171314	+	0.00989082i
$562$	8.21584	+	8.21584i	0.346564	+	0.346564i
$563$	−16.7005	−	16.7005i	−0.703841	−	0.703841i	0.261392	−	0.965233i	$-0.415819\pi$
$563$	−16.7005	−	16.7005i	−0.703841	−	0.703841i	−0.965233	+	0.261392i	$0.915819\pi$
$564$	2.21902	+	3.84346i	0.0934377	+	0.161839i
$565$		0			0
$566$	61.2812	−	35.3807i	2.57584	−	1.48716i
$567$	−12.8961	+	3.45549i	−0.541584	+	0.145117i
$568$	2.24144	+	8.36516i	0.0940487	+	0.350994i
$569$	40.2461			1.68720			0.843601	−	0.536970i	$-0.180431\pi$
$569$	40.2461			1.68720			0.843601	+	0.536970i	$0.180431\pi$
$570$		0			0
$571$	21.1246			0.884037			0.442019	−	0.897006i	$-0.354262\pi$
$571$	21.1246			0.884037			0.442019	+	0.897006i	$0.354262\pi$
$572$	−2.66922	−	9.96167i	−0.111606	−	0.416518i
$573$	2.63649	−	0.706444i	0.110141	−	0.0295121i
$574$	−15.2094	+	8.78115i	−0.634828	+	0.366518i
$575$		0			0
$576$	18.5517	+	32.1324i	0.772986	+	1.33885i
$577$	−16.4317	−	16.4317i	−0.684060	−	0.684060i	0.276853	−	0.960912i	$-0.410709\pi$
$577$	−16.4317	−	16.4317i	−0.684060	−	0.684060i	−0.960912	+	0.276853i	$0.910709\pi$
$578$	26.1873	+	26.1873i	1.08925	+	1.08925i
$579$	2.74286	−	1.58359i	0.113989	−	0.0658118i
$580$		0			0
$581$	25.8541			1.07261
$582$	−5.17113	+	5.17113i	−0.214350	+	0.214350i
$583$	−6.46497	+	24.1276i	−0.267752	+	0.999262i
$584$	13.2729	−	22.9894i	0.549237	−	0.951306i
$585$		0			0
$586$	6.34346	−	10.9872i	0.262046	−	0.453877i
$587$	−18.7983	+	5.03699i	−0.775889	+	0.207899i	−0.624972	−	0.780647i	$-0.714889\pi$
$587$	−18.7983	+	5.03699i	−0.775889	+	0.207899i	−0.150918	+	0.988546i	$0.548223\pi$
$588$	3.24109	+	3.24109i	0.133660	+	0.133660i
$589$	−0.739674	−	6.40576i	−0.0304777	−	0.263945i
$590$		0			0
$591$	0.624612	+	0.360620i	0.0256931	+	0.0148339i
$592$	−2.51267	−	9.37740i	−0.103270	−	0.385409i
$593$	12.5011	+	3.34967i	0.513360	+	0.137554i	0.506193	−	0.862420i	$-0.331052\pi$
$593$	12.5011	+	3.34967i	0.513360	+	0.137554i	0.00716635	+	0.999974i	$0.497719\pi$
$594$	−8.02850	−	4.63525i	−0.329413	−	0.190187i
$595$		0			0
$596$	−29.1246			−1.19299
$597$	5.70556	−	5.70556i	0.233513	−	0.233513i
$598$	20.8087	+	5.57567i	0.850930	+	0.228006i
$599$	2.97713	+	5.15654i	0.121642	+	0.210691i	0.920415	−	0.390942i	$-0.127851\pi$
$599$	2.97713	+	5.15654i	0.121642	+	0.210691i	−0.798773	+	0.601632i	$0.794517\pi$
$600$		0			0
$601$			31.1769i			1.27173i	0.771799	+	0.635866i	$0.219357\pi$
$601$			31.1769i			1.27173i	−0.771799	+	0.635866i	$0.780643\pi$
$602$	12.0139	+	3.21911i	0.489650	+	0.131201i
$603$	16.5411	−	4.43218i	0.673606	−	0.180492i
$604$	7.03612	+	12.1869i	0.286296	+	0.495879i
$605$		0			0
$606$	−6.70820	+	11.6190i	−0.272502	+	0.471988i
$607$	1.93004	−	1.93004i	0.0783379	−	0.0783379i	−0.666852	−	0.745190i	$-0.732359\pi$
$607$	1.93004	−	1.93004i	0.0783379	−	0.0783379i	0.745190	+	0.666852i	$0.232359\pi$
$608$	−28.9257	−	4.27820i	−1.17309	−	0.173504i
$609$			0.437694i			0.0177363i
$610$		0			0
$611$	−6.21885	−	3.59045i	−0.251588	−	0.145254i
$612$	1.46613	−	5.47167i	0.0592648	−	0.221179i
$613$	−4.80036	−	17.9152i	−0.193885	−	0.723587i	−0.992553	−	0.121815i	$-0.961128\pi$
$613$	−4.80036	−	17.9152i	−0.193885	−	0.723587i	0.798668	−	0.601772i	$-0.205538\pi$
$614$	−36.2283	+	20.9164i	−1.46205	+	0.844118i
$615$		0			0
$616$			7.18091i			0.289327i
$617$	7.40924	−	27.6517i	0.298285	−	1.11321i	−0.640289	−	0.768134i	$-0.721185\pi$
$617$	7.40924	−	27.6517i	0.298285	−	1.11321i	0.938573	−	0.345079i	$-0.112148\pi$
$618$	−2.14607	+	8.00926i	−0.0863278	+	0.322180i
$619$			12.5623i			0.504922i	0.967607	+	0.252461i	$0.0812399\pi$
$619$			12.5623i			0.504922i	−0.967607	+	0.252461i	$0.918760\pi$
$620$		0			0
$621$	10.0623	−	5.80948i	0.403786	−	0.233126i
$622$	5.20863	+	19.4389i	0.208847	+	0.779428i
$623$	−1.14305	+	4.26592i	−0.0457953	+	0.170911i
$624$	0.613323	+	0.354102i	0.0245526	+	0.0141754i
$625$		0			0
$626$		−	25.9808i		−	1.03840i
$627$	2.87047	−	1.13573i	0.114636	−	0.0453569i
$628$	−3.13817	+	3.13817i	−0.125227	+	0.125227i
$629$	−3.21140	+	5.56231i	−0.128047	+	0.221784i
$630$		0			0
$631$	−6.78115	−	11.7453i	−0.269953	−	0.467573i	0.698896	−	0.715223i	$-0.253675\pi$
$631$	−6.78115	−	11.7453i	−0.269953	−	0.467573i	−0.968850	+	0.247650i	$0.920342\pi$
$632$	−29.3823	+	7.87297i	−1.16877	+	0.313170i
$633$	−6.74975	−	1.80859i	−0.268279	−	0.0718850i
$634$			40.0000i			1.58860i
$635$		0			0
$636$	7.71885	+	13.3694i	0.306072	+	0.530133i
$637$	−7.16370	−	1.91951i	−0.283836	−	0.0760537i
$638$	1.93950	−	1.93950i	0.0767854	−	0.0767854i
$639$	−11.0539			−0.437285
$640$		0			0
$641$	−31.9058	−	18.4208i	−1.26020	−	0.727578i	−0.287088	−	0.957904i	$-0.592687\pi$
$641$	−31.9058	−	18.4208i	−1.26020	−	0.727578i	−0.973113	+	0.230326i	$0.926021\pi$
$642$	−0.899389	−	0.240991i	−0.0354961	−	0.00951114i
$643$	7.93837	+	29.6264i	0.313059	+	1.16835i	0.925783	+	0.378055i	$0.123407\pi$
$643$	7.93837	+	29.6264i	0.313059	+	1.16835i	−0.612724	+	0.790297i	$0.709926\pi$
$644$	−23.3827	−	13.5000i	−0.921407	−	0.531975i
$645$		0			0
$646$	3.84346	+	5.17772i	0.151219	+	0.203715i
$647$	−22.5132	−	22.5132i	−0.885086	−	0.885086i	0.108960	−	0.994046i	$-0.465248\pi$
$647$	−22.5132	−	22.5132i	−0.885086	−	0.885086i	−0.994046	+	0.108960i	$0.965248\pi$
$648$	16.6488	−	4.46102i	0.654025	−	0.175246i
$649$	−13.2246	+	22.9058i	−0.519113	+	0.899130i
$650$		0			0
$651$	0.489357	−	0.847591i	0.0191794	−	0.0332197i
$652$	−1.34486	+	5.01910i	−0.0526689	+	0.196563i
$653$	−6.48110	+	6.48110i	−0.253625	+	0.253625i	−0.822455	−	0.568830i	$-0.807396\pi$
$653$	−6.48110	+	6.48110i	−0.253625	+	0.253625i	0.568830	+	0.822455i	$0.307396\pi$
$654$	12.8825			0.503744
$655$		0			0
$656$	−3.92705	+	2.26728i	−0.153326	+	0.0885226i
$657$	23.9588	+	23.9588i	0.934723	+	0.934723i
$658$	10.6066	+	10.6066i	0.413488	+	0.413488i
$659$	−4.58283	−	7.93769i	−0.178522	−	0.309209i	0.762853	−	0.646572i	$-0.223798\pi$
$659$	−4.58283	−	7.93769i	−0.178522	−	0.309209i	−0.941374	+	0.337364i	$0.890465\pi$
$660$		0			0
$661$	9.21885	−	5.32250i	0.358572	−	0.207021i	−0.309882	−	0.950775i	$-0.600290\pi$
$661$	9.21885	−	5.32250i	0.358572	−	0.207021i	0.668454	+	0.743753i	$0.266956\pi$
$662$	22.4461	−	6.01441i	0.872392	−	0.233757i
$663$	−0.121266	−	0.452572i	−0.00470959	−	0.0175764i
$664$	−33.3775			−1.29530
$665$		0			0
$666$	−61.9574			−2.40080
$667$	0.889741	+	3.32056i	0.0344509	+	0.128573i
$668$	16.2798	−	4.36216i	0.629885	−	0.168777i
$669$	−5.57521	+	3.21885i	−0.215550	+	0.124448i
$670$		0			0
$671$	−8.86475	−	15.3542i	−0.342220	−	0.592742i
$672$	−3.13817	−	3.13817i	−0.121058	−	0.121058i
$673$	8.67656	+	8.67656i	0.334457	+	0.334457i	0.854276	−	0.519819i	$-0.174001\pi$
$673$	8.67656	+	8.67656i	0.334457	+	0.334457i	−0.519819	+	0.854276i	$0.674001\pi$
$674$	−38.9711	+	22.5000i	−1.50111	+	0.866668i
$675$		0			0
$676$	−28.6869			−1.10334
$677$	1.58114	−	1.58114i	0.0607681	−	0.0607681i	−0.676070	−	0.736838i	$-0.736318\pi$
$677$	1.58114	−	1.58114i	0.0607681	−	0.0607681i	0.736838	+	0.676070i	$0.236318\pi$
$678$	2.72481	−	10.1691i	0.104646	−	0.390543i
$679$	−7.41517	+	12.8435i	−0.284568	+	0.492887i
$680$		0			0
$681$	−2.57295	+	4.45648i	−0.0985956	+	0.170773i
$682$	−5.92424	+	1.58740i	−0.226851	+	0.0607845i
$683$	−15.9296	−	15.9296i	−0.609529	−	0.609529i	0.333294	−	0.942823i	$-0.391840\pi$
$683$	−15.9296	−	15.9296i	−0.609529	−	0.609529i	−0.942823	+	0.333294i	$0.891840\pi$
$684$	−14.8303	+	34.2492i	−0.567053	+	1.30955i
$685$		0			0
$686$	36.8951	+	21.3014i	1.40866	+	0.813292i
$687$	1.08746	+	4.05846i	0.0414892	+	0.154840i
$688$	3.10197	+	0.831171i	0.118262	+	0.0316881i
$689$	−21.6322	−	12.4894i	−0.824121	−	0.475807i
$690$		0			0
$691$	−9.56231			−0.363767			−0.181884	−	0.983320i	$-0.558219\pi$
$691$	−9.56231			−0.363767			−0.181884	+	0.983320i	$0.558219\pi$
$692$	−9.60505	+	9.60505i	−0.365129	+	0.365129i
$693$	−8.85335	−	2.37225i	−0.336311	−	0.0901142i
$694$	−25.2411	−	43.7188i	−0.958139	−	1.65954i
$695$		0			0
$696$		−	0.565061i		−	0.0214186i
$697$	2.89778	+	0.776457i	0.109761	+	0.0294104i
$698$	23.7586	−	6.36611i	0.899278	−	0.240961i
$699$	1.73205	+	3.00000i	0.0655122	+	0.113470i
$700$		0			0
$701$	2.07295	−	3.59045i	0.0782942	−	0.135610i	−0.824220	−	0.566270i	$-0.808386\pi$
$701$	2.07295	−	3.59045i	0.0782942	−	0.135610i	0.902514	+	0.430660i	$0.141719\pi$
$702$	6.55524	−	6.55524i	0.247412	−	0.247412i
$703$	26.2928	−	33.1576i	0.991652	−	1.25056i
$704$			24.1033i			0.908428i
$705$		0			0
$706$	−42.6246	−	24.6093i	−1.60420	−	0.926184i
$707$	−7.04180	+	26.2803i	−0.264834	+	0.988374i
$708$	4.23080	+	15.7896i	0.159003	+	0.593408i
$709$	−7.90215	+	4.56231i	−0.296771	+	0.171341i	−0.640992	−	0.767548i	$-0.721477\pi$
$709$	−7.90215	+	4.56231i	−0.296771	+	0.171341i	0.344220	+	0.938889i	$0.388143\pi$
$710$		0			0
$711$		−	38.8264i		−	1.45610i
$712$	1.47567	−	5.50728i	0.0553031	−	0.206394i
$713$	1.98952	−	7.42499i	0.0745081	−	0.278068i
$714$			0.978714i			0.0366274i
$715$		0			0
$716$	23.5623	−	13.6037i	0.880565	−	0.508394i
$717$	−2.35611	−	8.79314i	−0.0879907	−	0.328386i
$718$	−17.9285	+	66.9102i	−0.669087	+	2.49707i
$719$	33.0169	+	19.0623i	1.23132	+	0.710904i	0.967305	−	0.253614i	$-0.0816193\pi$
$719$	33.0169	+	19.0623i	1.23132	+	0.710904i	0.264016	+	0.964518i	$0.414953\pi$
$720$		0			0
$721$			16.8151i			0.626227i
$722$	−20.0592	−	37.4517i	−0.746525	−	1.39381i
$723$	−4.14205	+	4.14205i	−0.154044	+	0.154044i
$724$	−23.0036	+	39.8435i	−0.854923	+	1.48077i
$725$		0			0
$726$	3.22949	+	5.59364i	0.119858	+	0.207599i
$727$	24.1191	−	6.46270i	0.894529	−	0.239688i	0.217864	−	0.975979i	$-0.430091\pi$
$727$	24.1191	−	6.46270i	0.894529	−	0.239688i	0.676665	+	0.736291i	$0.263425\pi$
$728$	−6.93622	−	1.85856i	−0.257074	−	0.0688826i
$729$			19.4377i			0.719915i
$730$		0			0
$731$	−1.06231	−	1.83997i	−0.0392908	−	0.0680537i
$732$	−10.5841	−	2.83599i	−0.391198	−	0.104821i
$733$	−18.8812	+	18.8812i	−0.697392	+	0.697392i	−0.963847	−	0.266455i	$-0.914147\pi$
$733$	−18.8812	+	18.8812i	−0.697392	+	0.697392i	0.266455	+	0.963847i	$0.414147\pi$
$734$	−42.0378			−1.55164
$735$		0			0
$736$	−30.1869	−	17.4284i	−1.11270	−	0.642420i
$737$	10.7455	+	2.87926i	0.395817	+	0.106059i
$738$	7.49008	+	27.9534i	0.275714	+	1.02898i
$739$	−11.2583	−	6.50000i	−0.414144	−	0.239106i	0.278425	−	0.960458i	$-0.410188\pi$
$739$	−11.2583	−	6.50000i	−0.414144	−	0.239106i	−0.692569	+	0.721352i	$0.743521\pi$
$740$		0			0
$741$	0.354102	+	3.06661i	0.0130083	+	0.112655i
$742$	36.8950	+	36.8950i	1.35446	+	1.35446i
$743$	0.0538292	−	0.0144235i	0.00197480	−	0.000529147i	−0.257832	−	0.966190i	$-0.583008\pi$
$743$	0.0538292	−	0.0144235i	0.00197480	−	0.000529147i	0.259806	+	0.965661i	$0.416341\pi$
$744$	−0.631757	+	1.09424i	−0.0231613	+	0.0401166i
$745$		0			0
$746$	−17.0729	+	29.5712i	−0.625085	+	1.08268i
$747$	11.0264	−	41.1512i	0.403436	−	1.50564i
$748$	2.60211	−	2.60211i	0.0951425	−	0.0951425i
$749$	−1.88823			−0.0689944
$750$		0			0
$751$	22.6869	−	13.0983i	0.827857	−	0.477964i	−0.0252611	−	0.999681i	$-0.508042\pi$
$751$	22.6869	−	13.0983i	0.827857	−	0.477964i	0.853118	+	0.521717i	$0.174708\pi$
$752$	2.73861	+	2.73861i	0.0998669	+	0.0998669i
$753$	1.69361	+	1.69361i	0.0617185	+	0.0617185i
$754$	1.37143	+	2.37539i	0.0499446	+	0.0865065i
$755$		0			0
$756$	−10.0623	+	5.80948i	−0.365963	+	0.211289i
$757$	−18.4034	+	4.93117i	−0.668881	+	0.179226i	−0.577251	−	0.816567i	$-0.695875\pi$
$757$	−18.4034	+	4.93117i	−0.668881	+	0.179226i	−0.0916305	+	0.995793i	$0.529208\pi$
$758$	−15.7459	−	58.7646i	−0.571918	−	2.13443i
$759$	3.67994			0.133573
$760$		0			0
$761$	−12.0000			−0.435000			−0.217500	−	0.976060i	$-0.569790\pi$
$761$	−12.0000			−0.435000			−0.217500	+	0.976060i	$0.569790\pi$
$762$	2.55594	+	9.53889i	0.0925919	+	0.345558i
$763$	25.2344	−	6.76155i	0.913548	−	0.244784i
$764$	−18.5656	+	10.7188i	−0.671679	+	0.387794i
$765$		0			0
$766$	20.0623	+	34.7489i	0.724881	+	1.25553i
$767$	−18.7025	−	18.7025i	−0.675307	−	0.675307i
$768$	2.43082	+	2.43082i	0.0877145	+	0.0877145i
$769$	2.70599	−	1.56231i	0.0975806	−	0.0563382i	−0.450416	−	0.892819i	$-0.648724\pi$
$769$	2.70599	−	1.56231i	0.0975806	−	0.0563382i	0.547996	+	0.836481i	$0.315391\pi$
$770$		0			0
$771$	9.85410			0.354887
$772$	−17.5896	+	17.5896i	−0.633062	+	0.633062i
$773$	−13.3110	+	49.6771i	−0.478762	+	1.78676i	0.127883	+	0.991789i	$0.459182\pi$
$773$	−13.3110	+	49.6771i	−0.478762	+	1.78676i	−0.606644	+	0.794973i	$0.707485\pi$
$774$	10.2475	−	17.7492i	0.368339	−	0.637983i
$775$		0			0
$776$	9.57295	−	16.5808i	0.343649	−	0.595217i
$777$	6.20395	−	1.66234i	0.222565	−	0.0596362i
$778$	2.93159	+	2.93159i	0.105103	+	0.105103i
$779$	−18.1383	−	7.85410i	−0.649871	−	0.281402i
$780$		0			0
$781$	−6.21885	−	3.59045i	−0.222528	−	0.128477i
$782$	1.98952	+	7.42499i	0.0711451	+	0.265517i
$783$	1.42894	+	0.382883i	0.0510662	+	0.0136831i
$784$	3.46410	+	2.00000i	0.123718	+	0.0714286i
$785$		0			0
$786$	−15.6049			−0.556608
$787$	−18.4729	+	18.4729i	−0.658487	+	0.658487i	−0.955022	−	0.296535i	$-0.904169\pi$
$787$	−18.4729	+	18.4729i	−0.658487	+	0.658487i	0.296535	+	0.955022i	$0.404169\pi$
$788$	−5.47167	−	1.46613i	−0.194920	−	0.0522287i
$789$	2.47172	+	4.28115i	0.0879957	+	0.152413i
$790$		0			0
$791$		−	21.3497i		−	0.759107i
$792$	11.4296	+	3.06256i	0.406134	+	0.108823i
$793$	17.1254	−	4.58873i	0.608140	−	0.162951i
$794$	24.6093	+	42.6246i	0.873352	+	1.51269i
$795$		0			0
$796$	−31.6869	+	54.8834i	−1.12311	+	1.94529i
$797$	−27.8473	+	27.8473i	−0.986400	+	0.986400i	−0.999909	−	0.0135084i	$-0.995700\pi$
$797$	−27.8473	+	27.8473i	−0.986400	+	0.986400i	0.0135084	+	0.999909i	$0.495700\pi$
$798$	0.943464	−	6.37894i	0.0333983	−	0.225812i
$799$		−	2.56231i		−	0.0906479i
$800$		0			0
$801$	6.30244	+	3.63871i	0.222686	+	0.128568i
$802$	15.7459	−	58.7646i	0.556008	−	2.07505i
$803$	5.69693	+	21.2612i	0.201040	+	0.750293i
$804$	5.95426	−	3.43769i	0.209991	−	0.121238i
$805$		0			0
$806$		−	6.13323i		−	0.216034i
$807$	−1.46613	+	5.47167i	−0.0516102	+	0.192612i
$808$	9.09092	−	33.9278i	0.319817	−	1.19357i
$809$		−	35.5623i		−	1.25030i	−0.780503	−	0.625152i	$-0.785037\pi$
$809$		−	35.5623i		−	1.25030i	0.780503	−	0.625152i	$-0.214963\pi$
$810$		0			0
$811$	16.7188	−	9.65263i	0.587078	−	0.338950i	−0.176863	−	0.984235i	$-0.556595\pi$
$811$	16.7188	−	9.65263i	0.587078	−	0.338950i	0.763941	+	0.645286i	$0.223262\pi$
$812$	−0.889741	−	3.32056i	−0.0312238	−	0.116529i
$813$	−0.0555896	+	0.207463i	−0.00194961	+	0.00727605i
$814$	−34.8569	−	20.1246i	−1.22173	−	0.705367i
$815$		0			0
$816$			0.252703i			0.00884637i
$817$	5.15006	+	13.0164i	0.180178	+	0.455385i
$818$	36.7423	−	36.7423i	1.28467	−	1.28467i
$819$	4.58283	−	7.93769i	0.160137	−	0.277365i
$820$		0			0
$821$	−17.5623	−	30.4188i	−0.612929	−	1.06162i	−0.990744	−	0.135743i	$-0.956658\pi$
$821$	−17.5623	−	30.4188i	−0.612929	−	1.06162i	0.377815	−	0.925881i	$-0.376675\pi$
$822$	3.19521	−	0.856153i	0.111446	−	0.0298618i
$823$	−9.06183	−	2.42811i	−0.315875	−	0.0846386i	0.0973981	−	0.995246i	$-0.468948\pi$
$823$	−9.06183	−	2.42811i	−0.315875	−	0.0846386i	−0.413274	+	0.910607i	$0.635615\pi$
$824$		−	21.7082i		−	0.756241i
$825$		0			0
$826$	27.6246	+	47.8472i	0.961183	+	1.66482i
$827$	17.4405	+	4.67317i	0.606465	+	0.162502i	0.548967	−	0.835844i	$-0.315021\pi$
$827$	17.4405	+	4.67317i	0.606465	+	0.162502i	0.0574979	+	0.998346i	$0.481688\pi$
$828$	−31.4599	+	31.4599i	−1.09331	+	1.09331i
$829$	51.9247			1.80342			0.901709	−	0.432344i	$-0.142313\pi$
$829$	51.9247			1.80342			0.901709	+	0.432344i	$0.142313\pi$
$830$		0			0
$831$	9.16718	+	5.29268i	0.318006	+	0.183601i
$832$	−23.2820	−	6.23840i	−0.807159	−	0.216278i
$833$	−0.684923	−	2.55617i	−0.0237312	−	0.0885659i
$834$	−1.80310	−	1.04102i	−0.0624362	−	0.0360476i
$835$		0			0
$836$	−19.4681	+	14.4513i	−0.673317	+	0.499808i
$837$	−2.33905	−	2.33905i	−0.0808496	−	0.0808496i
$838$	−67.8555	+	18.1818i	−2.34403	+	0.628081i
$839$	−15.9192	+	27.5729i	−0.549594	+	0.951924i	0.448709	+	0.893678i	$0.351884\pi$
$839$	−15.9192	+	27.5729i	−0.549594	+	0.951924i	−0.998302	+	0.0582459i	$0.981449\pi$
$840$		0			0
$841$	14.2812	−	24.7357i	0.492454	−	0.852955i
$842$	−19.4630	+	72.6371i	−0.670741	+	2.50324i
$843$	−1.40343	+	1.40343i	−0.0483368	+	0.0483368i
$844$	54.8834			1.88916
$845$		0			0
$846$	21.4058	−	12.3586i	0.735945	−	0.424898i
$847$	9.26190	+	9.26190i	0.318242	+	0.318242i
$848$	9.52624	+	9.52624i	0.327132	+	0.327132i
$849$	6.04374	+	10.4681i	0.207421	+	0.359263i
$850$		0			0
$851$	43.6869	−	25.2227i	1.49757	−	0.864621i
$852$	−4.28682	+	1.14865i	−0.146864	+	0.0393521i
$853$	−9.66612	−	36.0744i	−0.330962	−	1.23517i	−0.908181	−	0.418577i	$-0.862529\pi$
$853$	−9.66612	−	36.0744i	−0.330962	−	1.23517i	0.577220	−	0.816589i	$-0.304138\pi$
$854$	−37.0347			−1.26730
$855$		0			0
$856$	2.43769			0.0833187
$857$	−8.73875	−	32.6135i	−0.298510	−	1.11405i	−0.938390	−	0.345579i	$-0.887682\pi$
$857$	−8.73875	−	32.6135i	−0.298510	−	1.11405i	0.639880	−	0.768475i	$-0.278984\pi$
$858$	2.83609	−	0.759929i	0.0968227	−	0.0259436i
$859$	35.1280	−	20.2812i	1.19855	−	0.691984i	0.238319	−	0.971187i	$-0.423404\pi$
$859$	35.1280	−	20.2812i	1.19855	−	0.691984i	0.960232	+	0.279203i	$0.0900702\pi$
$860$		0			0
$861$	−1.50000	−	2.59808i	−0.0511199	−	0.0885422i
$862$	40.0331	+	40.0331i	1.36353	+	1.36353i
$863$	26.9188	+	26.9188i	0.916325	+	0.916325i	0.996760	−	0.0804345i	$-0.0256308\pi$
$863$	26.9188	+	26.9188i	0.916325	+	0.916325i	−0.0804345	+	0.996760i	$0.525631\pi$
$864$	−12.9904	+	7.50000i	−0.441942	+	0.255155i
$865$		0			0
$866$	31.5836			1.07325
$867$	−4.47333	+	4.47333i	−0.151922	+	0.151922i
$868$	−1.98952	+	7.42499i	−0.0675287	+	0.252021i
$869$	12.6113	−	21.8435i	0.427810	−	0.740989i
$870$		0			0
$871$	−5.56231	+	9.63420i	−0.188472	+	0.326442i
$872$	−32.5775	+	8.72912i	−1.10321	+	0.295605i
$873$	17.2801	+	17.2801i	0.584841	+	0.584841i
$874$	−5.80948	−	50.3115i	−0.196508	−	1.70181i
$875$		0			0
$876$	11.7812	+	6.80185i	0.398048	+	0.229813i
$877$	−0.549890	−	2.05222i	−0.0185685	−	0.0692985i	0.956020	−	0.293302i	$-0.0947540\pi$
$877$	−0.549890	−	2.05222i	−0.0185685	−	0.0692985i	−0.974588	+	0.224003i	$0.928087\pi$
$878$	55.0236	+	14.7435i	1.85696	+	0.497570i
$879$	1.87684	+	1.08359i	0.0633041	+	0.0365487i
$880$		0			0
$881$	44.5623			1.50134			0.750671	−	0.660676i	$-0.229730\pi$
$881$	44.5623			1.50134			0.750671	+	0.660676i	$0.229730\pi$
$882$	18.0509	−	18.0509i	0.607806	−	0.607806i
$883$	−16.7303	−	4.48288i	−0.563020	−	0.150861i	−0.0339267	−	0.999424i	$-0.510801\pi$
$883$	−16.7303	−	4.48288i	−0.563020	−	0.150861i	−0.529094	+	0.848563i	$0.677468\pi$
$884$	1.83997	+	3.18692i	0.0618848	+	0.107188i
$885$		0			0
$886$			72.6724i			2.44148i
$887$	−18.5473	−	4.96975i	−0.622759	−	0.166868i	−0.0663773	−	0.997795i	$-0.521144\pi$
$887$	−18.5473	−	4.96975i	−0.622759	−	0.166868i	−0.556382	+	0.830927i	$0.687811\pi$
$888$	−8.00926	+	2.14607i	−0.268773	+	0.0720176i
$889$	10.0133	+	17.3435i	0.335834	+	0.581681i
$890$		0			0
$891$	−7.14590	+	12.3771i	−0.239397	+	0.414647i
$892$	35.7529	−	35.7529i	1.19710	−	1.19710i
$893$	−2.47002	+	16.7003i	−0.0826561	+	0.558853i
$894$		−	8.29180i		−	0.277319i
$895$		0			0
$896$	23.4787	+	13.5554i	0.784369	+	0.452856i
$897$	−0.952437	+	3.55454i	−0.0318010	+	0.118683i
$898$	−8.25585	−	30.8113i	−0.275501	−	1.02818i
$899$	0.847591	−	0.489357i	0.0282687	−	0.0163210i
$900$		0			0
$901$		−	8.91296i		−	0.296934i
$902$	−4.86576	+	18.1593i	−0.162012	+	0.604637i
$903$	−0.549890	+	2.05222i	−0.0182992	+	0.0682935i
$904$			27.5623i			0.916709i
$905$		0			0
$906$	−3.46962	+	2.00319i	−0.115271	+	0.0665515i
$907$	−5.91508	−	22.0754i	−0.196407	−	0.733001i	−0.991898	−	0.127035i	$-0.959454\pi$
$907$	−5.91508	−	22.0754i	−0.196407	−	0.733001i	0.795491	−	0.605965i	$-0.207213\pi$
$908$	10.4605	−	39.0393i	0.347145	−	1.29556i
$909$	38.8264	+	22.4164i	1.28779	+	0.743505i
$910$		0			0
$911$		−	13.0386i		−	0.431990i	−0.976395	−	0.215995i	$-0.930701\pi$
$911$		−	13.0386i		−	0.431990i	0.976395	−	0.215995i	$-0.0692994\pi$
$912$	0.243601	−	1.64703i	0.00806644	−	0.0545387i
$913$	19.5698	−	19.5698i	0.647667	−	0.647667i
$914$	38.1648	−	66.1033i	1.26238	−	2.18650i
$915$		0			0
$916$	−16.5000	−	28.5788i	−0.545175	−	0.944271i
$917$	−30.5672	+	8.19045i	−1.00942	+	0.270472i
$918$	3.19521	+	0.856153i	0.105458	+	0.0282573i
$919$		−	46.5623i		−	1.53595i	−0.640481	−	0.767974i	$-0.721265\pi$
$919$		−	46.5623i		−	1.53595i	0.640481	−	0.767974i	$-0.278735\pi$
$920$		0			0
$921$	−3.57295	−	6.18853i	−0.117733	−	0.203919i
$922$	7.42499	+	1.98952i	0.244529	+	0.0655214i
$923$	5.07767	−	5.07767i	0.167133	−	0.167133i
$924$	−3.67994			−0.121061
$925$		0			0
$926$	−48.8435	−	28.1998i	−1.60510	−	0.926702i
$927$	26.7641	+	7.17141i	0.879047	+	0.235540i
$928$	−1.14865	−	4.28682i	−0.0377063	−	0.140722i
$929$	−33.3959	−	19.2812i	−1.09569	−	0.632594i	−0.160601	−	0.987019i	$-0.551343\pi$
$929$	−33.3959	−	19.2812i	−1.09569	−	0.632594i	−0.935084	+	0.354425i	$0.884677\pi$
$930$		0			0
$931$	2.00000	+	17.3205i	0.0655474	+	0.567657i
$932$	−19.2385	−	19.2385i	−0.630179	−	0.630179i
$933$	−3.32056	+	0.889741i	−0.108710	+	0.0291288i
$934$	5.70156	−	9.87539i	0.186561	−	0.323133i
$935$		0			0
$936$	−5.91641	+	10.2475i	−0.193384	+	0.334951i
$937$	8.13458	−	30.3587i	0.265745	−	0.991775i	−0.696047	−	0.717996i	$-0.745060\pi$
$937$	8.13458	−	30.3587i	0.265745	−	0.991775i	0.961793	−	0.273779i	$-0.0882737\pi$
$938$	16.4317	−	16.4317i	0.536513	−	0.536513i
$939$	4.43804			0.144830
$940$		0			0
$941$	6.62461	−	3.82472i	0.215956	−	0.124682i	−0.388120	−	0.921609i	$-0.626875\pi$
$941$	6.62461	−	3.82472i	0.215956	−	0.124682i	0.604076	+	0.796926i	$0.293542\pi$
$942$	−0.893439	−	0.893439i	−0.0291098	−	0.0291098i
$943$	−16.6611	−	16.6611i	−0.542559	−	0.542559i
$944$	7.13264	+	12.3541i	0.232148	+	0.402092i
$945$		0			0
$946$	11.5304	−	6.65707i	0.374885	−	0.216440i
$947$	−39.8731	+	10.6840i	−1.29570	+	0.347182i	−0.839823	−	0.542860i	$-0.817341\pi$
$947$	−39.8731	+	10.6840i	−1.29570	+	0.347182i	−0.455878	+	0.890042i	$0.650675\pi$
$948$	−4.03459	−	15.0573i	−0.131037	−	0.489038i
$949$	−22.0113			−0.714516
$950$		0			0
$951$	−6.83282			−0.221569
$952$	−0.663174	−	2.47500i	−0.0214936	−	0.0802151i
$953$	35.8264	−	9.59964i	1.16053	−	0.310963i	0.373352	−	0.927690i	$-0.378208\pi$
$953$	35.8264	−	9.59964i	1.16053	−	0.310963i	0.787177	+	0.616727i	$0.211542\pi$
$954$	74.4598	−	42.9894i	2.41072	−	1.39183i
$955$		0			0
$956$	35.7492	+	61.9195i	1.15621	+	2.00262i
$957$	0.331306	+	0.331306i	0.0107096	+	0.0107096i
$958$	−41.3066	−	41.3066i	−1.33456	−	1.33456i
$959$	5.80948	−	3.35410i	0.187598	−	0.108310i
$960$		0			0
$961$	28.8115			0.929404
$962$	28.4605	−	28.4605i	0.917603	−	0.917603i
$963$	−0.805304	+	3.00544i	−0.0259506	+	0.0968488i
$964$	23.0036	−	39.8435i	0.740897	−	1.28327i
$965$		0			0
$966$	3.84346	−	6.65707i	0.123661	−	0.214188i
$967$	3.34607	−	0.896575i	0.107602	−	0.0288319i	−0.204616	−	0.978842i	$-0.565595\pi$
$967$	3.34607	−	0.896575i	0.107602	−	0.0288319i	0.312218	+	0.950010i	$0.398928\pi$
$968$	−11.9571	−	11.9571i	−0.384314	−	0.384314i
$969$	−0.884460	+	0.656541i	−0.0284129	+	0.0210911i
$970$		0			0
$971$	−5.64590	−	3.25966i	−0.181185	−	0.104607i	0.406664	−	0.913578i	$-0.366692\pi$
$971$	−5.64590	−	3.25966i	−0.181185	−	0.104607i	−0.587850	+	0.808970i	$0.700025\pi$
$972$	7.49473	+	27.9707i	0.240394	+	0.897161i
$973$	−4.07834	−	1.09279i	−0.130746	−	0.0350332i
$974$	50.5901	+	29.2082i	1.62101	+	0.935891i
$975$		0			0
$976$	−9.56231			−0.306082
$977$	43.5404	−	43.5404i	1.39298	−	1.39298i	0.574423	−	0.818559i	$-0.305226\pi$
$977$	43.5404	−	43.5404i	1.39298	−	1.39298i	0.818559	−	0.574423i	$-0.194774\pi$
$978$	−1.42894	−	0.382883i	−0.0456925	−	0.0122433i
$979$	2.36381	+	4.09424i	0.0755476	+	0.130852i
$980$		0			0
$981$		−	43.0486i		−	1.37443i
$982$	17.5482	+	4.70201i	0.559984	+	0.150047i
$983$	32.4520	−	8.69548i	1.03506	−	0.277343i	0.298993	−	0.954255i	$-0.403349\pi$
$983$	32.4520	−	8.69548i	1.03506	−	0.277343i	0.736064	+	0.676912i	$0.236682\pi$
$984$	1.93649	+	3.35410i	0.0617331	+	0.106925i
$985$		0			0
$986$	−0.489357	+	0.847591i	−0.0155843	+	0.0269928i
$987$	−1.81182	+	1.81182i	−0.0576710	+	0.0576710i
$988$	−8.92017	−	22.5450i	−0.283788	−	0.717251i
$989$			16.6869i			0.530613i
$990$		0			0
$991$	−11.3435	−	6.54915i	−0.360337	−	0.208041i	0.308892	−	0.951097i	$-0.400042\pi$
$991$	−11.3435	−	6.54915i	−0.360337	−	0.208041i	−0.669229	+	0.743057i	$0.733375\pi$
$992$	−2.56846	+	9.58562i	−0.0815487	+	0.304344i
$993$	1.02738	+	3.83425i	0.0326030	+	0.121676i
$994$	−12.9904	+	7.50000i	−0.412030	+	0.237886i
$995$		0			0
$996$		−	17.1047i		−	0.541982i
$997$	−14.4011	+	53.7455i	−0.456086	+	1.70214i	0.228788	+	0.973476i	$0.426524\pi$
$997$	−14.4011	+	53.7455i	−0.456086	+	1.70214i	−0.684874	+	0.728661i	$0.740143\pi$
$998$	−17.4342	+	65.0654i	−0.551871	+	2.05961i
$999$		−	21.7082i		−	0.686817i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.p.g.407.2	yes	16
5.2	odd	4	inner	475.2.p.g.293.3	yes	16
5.3	odd	4	inner	475.2.p.g.293.2	yes	16
5.4	even	2	inner	475.2.p.g.407.3	yes	16
19.12	odd	6	inner	475.2.p.g.107.2	✓	16
95.12	even	12	inner	475.2.p.g.468.3	yes	16
95.69	odd	6	inner	475.2.p.g.107.3	yes	16
95.88	even	12	inner	475.2.p.g.468.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.p.g.107.2	✓	16	19.12	odd	6	inner
475.2.p.g.107.3	yes	16	95.69	odd	6	inner
475.2.p.g.293.2	yes	16	5.3	odd	4	inner
475.2.p.g.293.3	yes	16	5.2	odd	4	inner
475.2.p.g.407.2	yes	16	1.1	even	1	trivial
475.2.p.g.407.3	yes	16	5.4	even	2	inner
475.2.p.g.468.2	yes	16	95.88	even	12	inner
475.2.p.g.468.3	yes	16	95.12	even	12	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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.578737 - 2.15988i) q^{2} +(0.368951 - 0.0988601i) q^{3} +(-2.59808 + 1.50000i) q^{4} +(-0.427051 - 0.739674i) q^{6} +(-1.22474 - 1.22474i) q^{7} +(1.58114 + 1.58114i) q^{8} +(-2.47172 + 1.42705i) q^{9} +O(q^{10})\)	\(q+(-0.578737 - 2.15988i) q^{2} +(0.368951 - 0.0988601i) q^{3} +(-2.59808 + 1.50000i) q^{4} +(-0.427051 - 0.739674i) q^{6} +(-1.22474 - 1.22474i) q^{7} +(1.58114 + 1.58114i) q^{8} +(-2.47172 + 1.42705i) q^{9} -1.85410 q^{11} +(-0.810272 + 0.810272i) q^{12} +(0.479877 - 1.79092i) q^{13} +(-1.93649 + 3.35410i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.639042 - 0.171231i) q^{17} +(4.51273 + 4.51273i) q^{18} +(-4.33013 + 0.500000i) q^{19} +(-0.572949 - 0.330792i) q^{21} +(1.07304 + 4.00463i) q^{22} +(-5.01910 - 1.34486i) q^{23} +(0.739674 + 0.427051i) q^{24} -4.14590 q^{26} +(-1.58114 + 1.58114i) q^{27} +(5.01910 + 1.34486i) q^{28} +(-0.330792 - 0.572949i) q^{29} +1.47935i q^{31} +(6.47963 + 1.73621i) q^{32} +(-0.684072 + 0.183297i) q^{33} +(-0.739674 - 1.28115i) q^{34} +(4.28115 - 7.41517i) q^{36} +(-6.86474 + 6.86474i) q^{37} +(3.58594 + 9.06317i) q^{38} -0.708204i q^{39} +(3.92705 + 2.26728i) q^{41} +(-0.382883 + 1.42894i) q^{42} +(-0.831171 - 3.10197i) q^{43} +(4.81710 - 2.78115i) q^{44} +11.6190i q^{46} +(1.00240 - 3.74101i) q^{47} +(-0.0988601 + 0.368951i) q^{48} -4.00000i q^{49} +(0.218847 - 0.126351i) q^{51} +(1.43963 + 5.37277i) q^{52} +(3.48685 - 13.0131i) q^{53} +(4.33013 + 2.50000i) q^{54} -3.87298i q^{56} +(-1.54817 + 0.612552i) q^{57} +(-1.04606 + 1.04606i) q^{58} +(7.13264 - 12.3541i) q^{59} +(4.78115 + 8.28120i) q^{61} +(3.19521 - 0.856153i) q^{62} +(4.77501 + 1.27946i) q^{63} -13.0000i q^{64} +(0.791796 + 1.37143i) q^{66} +(-5.79555 - 1.55291i) q^{67} +(-1.40343 + 1.40343i) q^{68} -1.98475 q^{69} +(3.35410 + 1.93649i) q^{71} +(-6.16451 - 1.65177i) q^{72} +(-3.07261 - 11.4671i) q^{73} +(18.7999 + 10.8541i) q^{74} +(10.5000 - 7.79423i) q^{76} +(2.27080 + 2.27080i) q^{77} +(-1.52963 + 0.409864i) q^{78} +(-6.80185 + 11.7812i) q^{79} +(3.85410 - 6.67550i) q^{81} +(2.62432 - 9.79410i) q^{82} +(-10.5549 + 10.5549i) q^{83} +1.98475 q^{84} +(-6.21885 + 3.59045i) q^{86} +(-0.178688 - 0.178688i) q^{87} +(-2.93159 - 2.93159i) q^{88} +(-1.27491 - 2.20820i) q^{89} +(-2.78115 + 1.60570i) q^{91} +(15.0573 - 4.03459i) q^{92} +(0.146248 + 0.545807i) q^{93} -8.66025 q^{94} +2.56231 q^{96} +(-2.21609 - 8.27055i) q^{97} +(-8.63950 + 2.31495i) q^{98} +(4.58283 - 2.64590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 20 q^{6}+O(q^{10}) \) 16 * q + 20 * q^6	\( 16 q + 20 q^{6} + 24 q^{11} - 8 q^{16} - 36 q^{21} - 120 q^{26} - 12 q^{36} + 36 q^{41} + 84 q^{51} - 4 q^{61} + 120 q^{66} + 168 q^{76} + 8 q^{81} - 180 q^{86} + 36 q^{91} - 120 q^{96}+O(q^{100}) \) 16 * q + 20 * q^6 + 24 * q^11 - 8 * q^16 - 36 * q^21 - 120 * q^26 - 12 * q^36 + 36 * q^41 + 84 * q^51 - 4 * q^61 + 120 * q^66 + 168 * q^76 + 8 * q^81 - 180 * q^86 + 36 * q^91 - 120 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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