LMFDB - Embedded newform 475.2.p.g.107.3

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			107.3
Root			$-0.596975 + 0.159959i$ of defining polynomial
Character	$\chi$	$=$	475.107
Dual form			475.2.p.g.293.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.15988 + 0.578737i) q^{2} +(-0.0988601 + 0.368951i) q^{3} +(2.59808 + 1.50000i) q^{4} +(-0.427051 + 0.739674i) q^{6} +(1.22474 + 1.22474i) q^{7} +(1.58114 + 1.58114i) q^{8} +(2.47172 + 1.42705i) q^{9} +O(q^{10})$	\(q+(2.15988 + 0.578737i) q^{2} +(-0.0988601 + 0.368951i) 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} +(-1.79092 + 0.479877i) q^{13} +(1.93649 + 3.35410i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.171231 - 0.639042i) q^{17} +(4.51273 + 4.51273i) q^{18} +(4.33013 + 0.500000i) q^{19} +(-0.572949 + 0.330792i) q^{21} +(-4.00463 - 1.07304i) q^{22} +(-1.34486 - 5.01910i) q^{23} +(-0.739674 + 0.427051i) q^{24} -4.14590 q^{26} +(-1.58114 + 1.58114i) q^{27} +(1.34486 + 5.01910i) q^{28} +(0.330792 - 0.572949i) q^{29} -1.47935i q^{31} +(-1.73621 - 6.47963i) q^{32} +(0.183297 - 0.684072i) q^{33} +(0.739674 - 1.28115i) q^{34} +(4.28115 + 7.41517i) q^{36} +(-6.86474 + 6.86474i) q^{37} +(9.06317 + 3.58594i) q^{38} -0.708204i q^{39} +(3.92705 - 2.26728i) q^{41} +(-1.42894 + 0.382883i) q^{42} +(-3.10197 - 0.831171i) q^{43} +(-4.81710 - 2.78115i) q^{44} -11.6190i q^{46} +(3.74101 - 1.00240i) q^{47} +(0.368951 - 0.0988601i) q^{48} -4.00000i q^{49} +(0.218847 + 0.126351i) q^{51} +(-5.37277 - 1.43963i) q^{52} +(-13.0131 + 3.48685i) q^{53} +(-4.33013 + 2.50000i) q^{54} +3.87298i q^{56} +(-0.612552 + 1.54817i) q^{57} +(1.04606 - 1.04606i) q^{58} +(-7.13264 - 12.3541i) q^{59} +(4.78115 - 8.28120i) q^{61} +(0.856153 - 3.19521i) q^{62} +(1.27946 + 4.77501i) q^{63} -13.0000i q^{64} +(0.791796 - 1.37143i) q^{66} +(1.55291 + 5.79555i) q^{67} +(1.40343 - 1.40343i) q^{68} +1.98475 q^{69} +(3.35410 - 1.93649i) q^{71} +(1.65177 + 6.16451i) q^{72} +(-11.4671 - 3.07261i) q^{73} +(-18.7999 + 10.8541i) q^{74} +(10.5000 + 7.79423i) q^{76} +(-2.27080 - 2.27080i) q^{77} +(0.409864 - 1.52963i) q^{78} +(6.80185 + 11.7812i) q^{79} +(3.85410 + 6.67550i) q^{81} +(9.79410 - 2.62432i) 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} +(4.03459 - 15.0573i) q^{92} +(0.545807 + 0.146248i) q^{93} +8.66025 q^{94} +2.56231 q^{96} +(8.27055 + 2.21609i) q^{97} +(2.31495 - 8.63950i) 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 $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.15988	+	0.578737i	1.52726	+	0.409229i	0.922125	−	0.386892i	$-0.126451\pi$
$2$	2.15988	+	0.578737i	1.52726	+	0.409229i	0.605138	+	0.796121i	$0.293118\pi$
$3$	−0.0988601	+	0.368951i	−0.0570769	+	0.213014i	−0.988574	−	0.150734i	$-0.951836\pi$
$3$	−0.0988601	+	0.368951i	−0.0570769	+	0.213014i	0.931497	+	0.363748i	$0.118503\pi$
$4$	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	0.899608	−	0.436698i	$-0.143852\pi$
$7$	1.22474	+	1.22474i	0.462910	+	0.462910i	−0.436698	+	0.899608i	$0.643852\pi$
$8$	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
$13$	−1.79092	+	0.479877i	−0.496713	+	0.133094i	−0.498474	−	0.866905i	$-0.666106\pi$
$13$	−1.79092	+	0.479877i	−0.496713	+	0.133094i	0.00176097	+	0.999998i	$0.499439\pi$
$14$	1.93649	+	3.35410i	0.517549	+	0.896421i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.171231	−	0.639042i	0.0415295	−	0.154990i	−0.942047	−	0.335480i	$-0.891102\pi$
$17$	0.171231	−	0.639042i	0.0415295	−	0.154990i	0.983577	+	0.180490i	$0.0577682\pi$
$18$	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
$22$	−4.00463	−	1.07304i	−0.853790	−	0.228772i
$23$	−1.34486	−	5.01910i	−0.280423	−	1.04655i	−0.952119	−	0.305727i	$-0.901100\pi$
$23$	−1.34486	−	5.01910i	−0.280423	−	1.04655i	0.671696	−	0.740827i	$-0.265566\pi$
$24$	−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
$28$	1.34486	+	5.01910i	0.254155	+	0.948520i
$29$	0.330792	−	0.572949i	0.0614266	−	0.106394i	−0.833677	−	0.552253i	$-0.813768\pi$
$29$	0.330792	−	0.572949i	0.0614266	−	0.106394i	0.895103	+	0.445859i	$0.147102\pi$
$30$		0			0
$31$		−	1.47935i		−	0.265699i	−0.991136	−	0.132849i	$-0.957587\pi$
$31$		−	1.47935i		−	0.265699i	0.991136	−	0.132849i	$-0.0424127\pi$
$32$	−1.73621	−	6.47963i	−0.306922	−	1.14545i
$33$	0.183297	−	0.684072i	0.0319079	−	0.119082i
$34$	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	$0.955886\pi$
$38$	9.06317	+	3.58594i	1.47024	+	0.581717i
$39$		−	0.708204i		−	0.113403i
$40$		0			0
$41$	3.92705	−	2.26728i	0.613302	−	0.354090i	−0.160954	−	0.986962i	$-0.551457\pi$
$41$	3.92705	−	2.26728i	0.613302	−	0.354090i	0.774257	+	0.632872i	$0.218124\pi$
$42$	−1.42894	+	0.382883i	−0.220490	+	0.0590802i
$43$	−3.10197	−	0.831171i	−0.473046	−	0.126752i	0.0144165	−	0.999896i	$-0.495411\pi$
$43$	−3.10197	−	0.831171i	−0.473046	−	0.126752i	−0.487463	+	0.873144i	$0.662078\pi$
$44$	−4.81710	−	2.78115i	−0.726205	−	0.419275i
$45$		0			0
$46$		−	11.6190i		−	1.71312i
$47$	3.74101	−	1.00240i	0.545683	−	0.146215i	0.0245623	−	0.999698i	$-0.492181\pi$
$47$	3.74101	−	1.00240i	0.545683	−	0.146215i	0.521121	+	0.853483i	$0.325514\pi$
$48$	0.368951	−	0.0988601i	0.0532535	−	0.0142692i
$49$		−	4.00000i		−	0.571429i
$50$		0			0
$51$	0.218847	+	0.126351i	0.0306447	+	0.0176927i
$52$	−5.37277	−	1.43963i	−0.745070	−	0.199641i
$53$	−13.0131	+	3.48685i	−1.78748	+	0.478955i	−0.991915	−	0.126907i	$-0.959495\pi$
$53$	−13.0131	+	3.48685i	−1.78748	+	0.478955i	−0.795570	+	0.605862i	$0.792828\pi$
$54$	−4.33013	+	2.50000i	−0.589256	+	0.340207i
$55$		0			0
$56$			3.87298i			0.517549i
$57$	−0.612552	+	1.54817i	−0.0811345	+	0.205061i
$58$	1.04606	−	1.04606i	0.137354	−	0.137354i
$59$	−7.13264	−	12.3541i	−0.928591	−	1.60837i	−0.785681	−	0.618631i	$-0.787687\pi$
$59$	−7.13264	−	12.3541i	−0.928591	−	1.60837i	−0.142910	−	0.989736i	$-0.545646\pi$
$60$		0			0
$61$	4.78115	−	8.28120i	0.612164	−	1.06030i	−0.378711	−	0.925515i	$-0.623633\pi$
$61$	4.78115	−	8.28120i	0.612164	−	1.06030i	0.990875	−	0.134784i	$-0.0430341\pi$
$62$	0.856153	−	3.19521i	0.108732	−	0.405792i
$63$	1.27946	+	4.77501i	0.161197	+	0.601594i
$64$		−	13.0000i		−	1.62500i
$65$		0			0
$66$	0.791796	−	1.37143i	0.0974634	−	0.168811i
$67$	1.55291	+	5.79555i	0.189719	+	0.708040i	0.993571	+	0.113211i	$0.0361135\pi$
$67$	1.55291	+	5.79555i	0.189719	+	0.708040i	−0.803852	+	0.594829i	$0.797220\pi$
$68$	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	−0.287587	−	0.957754i	$-0.592853\pi$
$71$	3.35410	−	1.93649i	0.398059	−	0.229819i	0.685646	+	0.727935i	$0.259520\pi$
$72$	1.65177	+	6.16451i	0.194663	+	0.726494i
$73$	−11.4671	−	3.07261i	−1.34213	−	0.359622i	−0.484904	−	0.874567i	$-0.661145\pi$
$73$	−11.4671	−	3.07261i	−1.34213	−	0.359622i	−0.857223	+	0.514946i	$0.827812\pi$
$74$	−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
$78$	0.409864	−	1.52963i	0.0464079	−	0.173197i
$79$	6.80185	+	11.7812i	0.765268	+	1.32548i	0.940105	+	0.340886i	$0.110727\pi$
$79$	6.80185	+	11.7812i	0.765268	+	1.32548i	−0.174837	+	0.984597i	$0.555940\pi$
$80$		0			0
$81$	3.85410	+	6.67550i	0.428234	+	0.741722i
$82$	9.79410	−	2.62432i	1.08158	−	0.289808i
$83$	10.5549	−	10.5549i	1.15855	−	1.15855i	0.173762	−	0.984788i	$-0.444408\pi$
$83$	10.5549	−	10.5549i	1.15855	−	1.15855i	0.984788	−	0.173762i	$-0.0555925\pi$
$84$	−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	$-0.790185\pi$
$89$	1.27491	−	2.20820i	0.135140	−	0.234069i	0.925651	+	0.378379i	$0.123518\pi$
$90$		0			0
$91$	−2.78115	−	1.60570i	−0.291544	−	0.168323i
$92$	4.03459	−	15.0573i	0.420635	−	1.56983i
$93$	0.545807	+	0.146248i	0.0565975	+	0.0151653i
$94$	8.66025			0.893237
$95$		0			0
$96$	2.56231			0.261514
$97$	8.27055	+	2.21609i	0.839747	+	0.225010i	0.652962	−	0.757391i	$-0.273526\pi$
$97$	8.27055	+	2.21609i	0.839747	+	0.225010i	0.186786	+	0.982401i	$0.440193\pi$
$98$	2.31495	−	8.63950i	0.233845	−	0.872722i
$99$	−4.58283	−	2.64590i	−0.460592	−	0.265923i
$100$		0			0
$101$	−7.85410	+	13.6037i	−0.781512	+	1.35362i	0.149548	+	0.988754i	$0.452218\pi$
$101$	−7.85410	+	13.6037i	−0.781512	+	1.35362i	−0.931061	+	0.364865i	$0.881115\pi$
$102$	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	$0.233219\pi$
$108$	−6.47963	+	1.73621i	−0.623502	+	0.167067i
$109$	7.54153	+	13.0623i	0.722347	+	1.25114i	0.960057	+	0.279806i	$0.0902700\pi$
$109$	7.54153	+	13.0623i	0.722347	+	1.25114i	−0.237709	+	0.971336i	$0.576397\pi$
$110$		0			0
$111$	−1.85410	−	3.21140i	−0.175984	−	0.304812i
$112$	0.448288	−	1.67303i	0.0423592	−	0.158087i
$113$	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
$117$	−5.11148	−	1.36962i	−0.472557	−	0.126621i
$118$	−8.25585	−	30.8113i	−0.760013	−	2.83641i
$119$	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
$123$	0.448288	+	1.67303i	0.0404207	+	0.150852i
$124$	2.21902	−	3.84346i	0.199274	−	0.345153i
$125$		0			0
$126$			11.0539i			0.984759i
$127$	2.99254	+	11.1683i	0.265545	+	0.991029i	0.961916	+	0.273346i	$0.0881305\pi$
$127$	2.99254	+	11.1683i	0.265545	+	0.991029i	−0.696370	+	0.717683i	$0.745203\pi$
$128$	4.05116	−	15.1191i	0.358075	−	1.33635i
$129$	0.613323	−	1.06231i	0.0540000	−	0.0935308i
$130$		0			0
$131$	9.13525	+	15.8227i	0.798151	+	1.38244i	0.920819	+	0.389990i	$0.127522\pi$
$131$	9.13525	+	15.8227i	0.798151	+	1.38244i	−0.122668	+	0.992448i	$0.539145\pi$
$132$	1.50233	−	1.50233i	0.130761	−	0.130761i
$133$	4.69093	+	5.91567i	0.406755	+	0.512954i
$134$			13.4164i			1.15900i
$135$		0			0
$136$	1.28115	−	0.739674i	0.109858	−	0.0634265i
$137$	−3.74101	+	1.00240i	−0.319616	+	0.0856410i	−0.415060	−	0.909794i	$-0.636240\pi$
$137$	−3.74101	+	1.00240i	−0.319616	+	0.0856410i	0.0954440	+	0.995435i	$0.469573\pi$
$138$	4.28682	+	1.14865i	0.364918	+	0.0977796i
$139$	−2.11111	−	1.21885i	−0.179062	−	0.103381i	0.407790	−	0.913076i	$-0.366300\pi$
$139$	−2.11111	−	1.21885i	−0.179062	−	0.103381i	−0.586852	+	0.809694i	$0.699633\pi$
$140$		0			0
$141$			1.47935i			0.124584i
$142$	8.36516	−	2.24144i	0.701989	−	0.188097i
$143$	3.32056	−	0.889741i	0.277679	−	0.0744039i
$144$		−	2.85410i		−	0.237842i
$145$		0			0
$146$	−22.9894	−	13.2729i	−1.90261	−	1.09847i
$147$	1.47580	+	0.395440i	0.121722	+	0.0326154i
$148$	−28.1322	+	7.53800i	−2.31245	+	0.619620i
$149$	−8.40755	+	4.85410i	−0.688773	+	0.397664i	−0.803152	−	0.595774i	$-0.796846\pi$
$149$	−8.40755	+	4.85410i	−0.688773	+	0.397664i	0.114379	+	0.993437i	$0.463512\pi$
$150$		0			0
$151$			4.69075i			0.381728i	0.981617	+	0.190864i	$0.0611289\pi$
$151$			4.69075i			0.381728i	−0.981617	+	0.190864i	$0.938871\pi$
$152$	6.05596	+	7.63710i	0.491203	+	0.619451i
$153$	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
$157$	0.382883	−	1.42894i	0.0305574	−	0.114042i	−0.948963	−	0.315389i	$-0.897865\pi$
$157$	0.382883	−	1.42894i	0.0305574	−	0.114042i	0.979520	+	0.201347i	$0.0645318\pi$
$158$	7.87297	+	29.3823i	0.626340	+	2.33753i
$159$		−	5.14590i		−	0.408096i
$160$		0			0
$161$	4.50000	−	7.79423i	0.354650	−	0.614271i
$162$	4.46102	+	16.6488i	0.350491	+	1.30805i
$163$	−1.22474	+	1.22474i	−0.0959294	+	0.0959294i	−0.753443	−	0.657513i	$-0.771608\pi$
$163$	−1.22474	+	1.22474i	−0.0959294	+	0.0959294i	0.657513	+	0.753443i	$0.271608\pi$
$164$	13.6037			1.06227
$165$		0			0
$166$	28.9058	−	16.6888i	2.24352	−	1.29530i
$167$	1.45405	+	5.42660i	0.112518	+	0.419923i	0.999089	−	0.0426690i	$-0.0135861\pi$
$167$	1.45405	+	5.42660i	0.112518	+	0.419923i	−0.886571	+	0.462592i	$0.846919\pi$
$168$	−1.42894	−	0.382883i	−0.110245	−	0.0295401i
$169$	−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
$173$	−1.17190	+	4.37358i	−0.0890977	+	0.332517i	−0.996059	−	0.0886977i	$-0.971730\pi$
$173$	−1.17190	+	4.37358i	−0.0890977	+	0.332517i	0.906961	+	0.421215i	$0.138396\pi$
$174$	0.282530	+	0.489357i	0.0214186	+	0.0370980i
$175$		0			0
$176$	0.927051	+	1.60570i	0.0698791	+	0.121034i
$177$	5.26319	−	1.41027i	0.395606	−	0.106002i
$178$	4.03161	−	4.03161i	0.302182	−	0.302182i
$179$	9.06914			0.677859			0.338930	−	0.940812i	$-0.389935\pi$
$179$	9.06914			0.677859			0.338930	+	0.940812i	$0.389935\pi$
$180$		0			0
$181$	13.2812	+	7.66788i	0.987180	+	0.569949i	0.904430	−	0.426622i	$-0.140296\pi$
$181$	13.2812	+	7.66788i	0.987180	+	0.569949i	0.0827501	+	0.996570i	$0.473630\pi$
$182$	−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
$187$	−0.317479	+	1.18485i	−0.0232164	+	0.0866447i
$188$	11.2230	+	3.00721i	0.818525	+	0.219323i
$189$	−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	$0.416762\pi$
$192$	4.79636	+	1.28518i	0.346148	+	0.0927500i
$193$	−2.14607	+	8.00926i	−0.154478	+	0.576519i	0.844672	+	0.535285i	$0.179796\pi$
$193$	−2.14607	+	8.00926i	−0.154478	+	0.576519i	−0.999150	+	0.0412344i	$0.986871\pi$
$194$	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	0.657941	−	0.753069i	$-0.271427\pi$
$197$	−1.33518	−	1.33518i	−0.0951276	−	0.0951276i	−0.753069	+	0.657941i	$0.771427\pi$
$198$	−8.36706	−	8.36706i	−0.594621	−	0.594621i
$199$	−18.2945	−	10.5623i	−1.29686	−	0.748742i	−0.316999	−	0.948426i	$-0.602675\pi$
$199$	−18.2945	−	10.5623i	−1.29686	−	0.748742i	−0.979860	+	0.199684i	$0.936008\pi$
$200$		0			0
$201$	−2.29180			−0.161651
$202$	−24.8369	+	24.8369i	−1.74751	+	1.74751i
$203$	1.10685	−	0.296580i	0.0776858	−	0.0208159i
$204$	0.379054	+	0.656541i	0.0265391	+	0.0459671i
$205$		0			0
$206$	−10.8541	−	18.7999i	−0.756241	−	1.30985i
$207$	3.83838	−	14.3250i	0.266786	−	0.995658i
$208$	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	−0.933765	−	0.357887i	$-0.883497\pi$
$211$	−15.8435	+	9.14723i	−1.09071	+	0.629721i	−0.156944	+	0.987608i	$0.550164\pi$
$212$	−39.0393	−	10.4605i	−2.68123	−	0.718433i
$213$	0.382883	+	1.42894i	0.0262347	+	0.0979094i
$214$	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
$218$	8.72912	+	32.5775i	0.591211	+	2.20643i
$219$	2.26728	−	3.92705i	0.153209	−	0.265366i
$220$		0			0
$221$			1.22665i			0.0825131i
$222$	−2.14607	−	8.00926i	−0.144035	−	0.537546i
$223$	4.36216	−	16.2798i	0.292112	−	1.09018i	−0.651372	−	0.758759i	$-0.725806\pi$
$223$	4.36216	−	16.2798i	0.292112	−	1.09018i	0.943484	−	0.331418i	$-0.107527\pi$
$224$	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	$0.397539\pi$
$228$	−3.91372	+	3.10345i	−0.259192	+	0.205531i
$229$			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
$232$	1.42894	−	0.382883i	0.0938145	−	0.0251375i
$233$	8.76011	+	2.34727i	0.573894	+	0.153774i	0.534082	−	0.845433i	$-0.320657\pi$
$233$	8.76011	+	2.34727i	0.573894	+	0.153774i	0.0398121	+	0.999207i	$0.487324\pi$
$234$	−10.2475	−	5.91641i	−0.669901	−	0.386768i
$235$		0			0
$236$		−	42.7959i		−	2.78577i
$237$	−5.01910	+	1.34486i	−0.326025	+	0.0873583i
$238$	2.47500	−	0.663174i	0.160430	−	0.0429872i
$239$		−	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	0.00699331	−	0.999976i	$-0.497774\pi$
$241$	−13.2812	−	7.66788i	−0.855514	−	0.493931i	−0.862508	+	0.506044i	$0.831107\pi$
$242$	−16.3336	−	4.37659i	−1.04997	−	0.281338i
$243$	−9.32358	+	2.49824i	−0.598108	+	0.160262i
$244$	24.8436	−	14.3435i	1.59045	−	0.918246i
$245$		0			0
$246$			3.87298i			0.246932i
$247$	−7.99487	+	1.18247i	−0.508701	+	0.0752385i
$248$	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	−0.749950	−	0.661494i	$-0.769923\pi$
$251$	3.13525	−	5.43042i	0.197896	−	0.342765i	0.947846	+	0.318729i	$0.103256\pi$
$252$	−3.83838	+	14.3250i	−0.241795	+	0.902391i
$253$	2.49351	+	9.30592i	0.156766	+	0.585058i
$254$			25.8541i			1.62223i
$255$		0			0
$256$	4.50000	−	7.79423i	0.281250	−	0.487139i
$257$	−6.67711	−	24.9193i	−0.416507	−	1.55442i	−0.781799	−	0.623531i	$-0.785697\pi$
$257$	−6.67711	−	24.9193i	−0.416507	−	1.55442i	0.365292	−	0.930893i	$-0.380969\pi$
$258$	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
$262$	10.5738	+	39.4620i	0.653253	+	2.43797i
$263$	12.5011	+	3.34967i	0.770853	+	0.206549i	0.622748	−	0.782422i	$-0.286016\pi$
$263$	12.5011	+	3.34967i	0.770853	+	0.206549i	0.148104	+	0.988972i	$0.452683\pi$
$264$	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
$268$	−4.65874	+	17.3867i	−0.284578	+	1.06206i
$269$	7.41517	+	12.8435i	0.452111	+	0.783080i	0.998517	−	0.0544410i	$-0.0173377\pi$
$269$	7.41517	+	12.8435i	0.452111	+	0.783080i	−0.546406	+	0.837521i	$0.684004\pi$
$270$		0			0
$271$	−0.281153	−	0.486971i	−0.0170788	−	0.0295814i	0.857360	−	0.514718i	$-0.172103\pi$
$271$	−0.281153	−	0.486971i	−0.0170788	−	0.0295814i	−0.874439	+	0.485136i	$0.838770\pi$
$272$	−0.639042	+	0.171231i	−0.0387476	+	0.0103824i
$273$	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	$-0.936880\pi$
$277$	−19.5959	−	19.5959i	−1.17740	−	1.17740i	−0.197001	−	0.980403i	$-0.563120\pi$
$278$	−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	0.359734	−	0.933055i	$-0.382867\pi$
$281$	−4.50000	−	2.59808i	−0.268447	−	0.154988i	−0.628182	+	0.778067i	$0.716201\pi$
$282$	−0.856153	+	3.19521i	−0.0509832	+	0.190272i
$283$	30.5672	+	8.19045i	1.81703	+	0.486871i	0.996414	−	0.0846102i	$-0.0269645\pi$
$283$	30.5672	+	8.19045i	1.81703	+	0.486871i	0.820615	+	0.571482i	$0.193631\pi$
$284$	11.6190			0.689458
$285$		0			0
$286$	7.68692			0.454537
$287$	7.58648	+	2.03279i	0.447816	+	0.119992i
$288$	4.95532	−	18.4935i	0.291995	−	1.08974i
$289$	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
$298$	−20.9685	+	5.61850i	−1.21467	+	0.325471i
$299$	4.81710	+	8.34346i	0.278580	+	0.482515i
$300$		0			0
$301$	−2.78115	−	4.81710i	−0.160303	−	0.277653i
$302$	−2.71471	+	10.1314i	−0.156214	+	0.582998i
$303$	−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
$307$	18.0707	+	4.84204i	1.03135	+	0.276350i	0.734525	−	0.678582i	$-0.237405\pi$
$307$	18.0707	+	4.84204i	1.03135	+	0.276350i	0.296826	+	0.954931i	$0.404072\pi$
$308$	−2.49351	−	9.30592i	−0.142081	−	0.530254i
$309$	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
$313$	3.00721	+	11.2230i	0.169977	+	0.634364i	0.997353	+	0.0727147i	$0.0231663\pi$
$313$	3.00721	+	11.2230i	0.169977	+	0.634364i	−0.827375	+	0.561649i	$0.810167\pi$
$314$	1.65396	−	2.86475i	0.0933384	−	0.161667i
$315$		0			0
$316$			40.8111i			2.29580i
$317$	4.62990	+	17.2790i	0.260041	+	0.970486i	0.965216	+	0.261453i	$0.0842016\pi$
$317$	4.62990	+	17.2790i	0.260041	+	0.970486i	−0.705175	+	0.709033i	$0.749132\pi$
$318$	2.97812	−	11.1145i	0.167005	−	0.623270i
$319$	−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
$323$	1.06097	−	2.68152i	0.0590340	−	0.149204i
$324$			23.1246i			1.28470i
$325$		0			0
$326$	−3.35410	+	1.93649i	−0.185767	+	0.107252i
$327$	−5.56490	+	1.49111i	−0.307740	+	0.0824587i
$328$	9.79410	+	2.62432i	0.540789	+	0.144904i
$329$	5.80948	+	3.35410i	0.320287	+	0.184918i
$330$		0			0
$331$		−	10.3923i		−	0.571213i	−0.958347	−	0.285606i	$-0.907805\pi$
$331$		−	10.3923i		−	0.571213i	0.958347	−	0.285606i	$-0.0921950\pi$
$332$	43.2548	−	11.5901i	2.37391	−	0.636088i
$333$	−26.7641	+	7.17141i	−1.46666	+	0.392991i
$334$			12.5623i			0.687379i
$335$		0			0
$336$	0.572949	+	0.330792i	0.0312569	+	0.0180462i
$337$	19.4389	+	5.20863i	1.05890	+	0.283732i	0.745926	−	0.666028i	$-0.232007\pi$
$337$	19.4389	+	5.20863i	1.05890	+	0.283732i	0.312977	+	0.949761i	$0.398674\pi$
$338$	−20.6534	+	5.53406i	−1.12340	+	0.301013i
$339$	−4.07742	+	2.35410i	−0.221455	+	0.127857i
$340$		0			0
$341$			2.74286i			0.148534i
$342$	17.2843	+	21.7971i	0.934630	+	1.17865i
$343$	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
$347$	5.84318	−	21.8070i	0.313678	−	1.17066i	−0.611535	−	0.791217i	$-0.709448\pi$
$347$	5.84318	−	21.8070i	0.313678	−	1.17066i	0.925214	−	0.379446i	$-0.123886\pi$
$348$	0.196213	+	0.732277i	0.0105181	+	0.0392541i
$349$			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
$352$	3.21911	+	12.0139i	0.171579	+	0.640342i
$353$	−15.5643	+	15.5643i	−0.828405	+	0.828405i	−0.987296	−	0.158892i	$-0.949208\pi$
$353$	−15.5643	+	15.5643i	−0.828405	+	0.828405i	0.158892	+	0.987296i	$0.449208\pi$
$354$	12.1840			0.647573
$355$		0			0
$356$	6.62461	−	3.82472i	0.351104	−	0.202710i
$357$	0.113284	+	0.422780i	0.00599560	+	0.0223759i
$358$	19.5882	+	5.24864i	1.03527	+	0.277399i
$359$	26.8284	−	15.4894i	1.41595	−	0.817497i	0.420007	−	0.907521i	$-0.362028\pi$
$359$	26.8284	−	15.4894i	1.41595	−	0.817497i	0.995940	+	0.0900240i	$0.0286944\pi$
$360$		0			0
$361$	18.5000	+	4.33013i	0.973684	+	0.227901i
$362$	24.2480	+	24.2480i	1.27444	+	1.27444i
$363$	0.747610	−	2.79012i	0.0392394	−	0.146443i
$364$	−4.81710	−	8.34346i	−0.252485	−	0.437316i
$365$		0			0
$366$	4.08359	+	7.07299i	0.213453	+	0.369711i
$367$	18.1593	−	4.86576i	0.947906	−	0.253991i	0.248433	−	0.968649i	$-0.420085\pi$
$367$	18.1593	−	4.86576i	0.947906	−	0.253991i	0.699473	+	0.714659i	$0.253418\pi$
$368$	−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
$377$	−0.317479	+	1.18485i	−0.0163510	+	0.0610228i
$378$	−8.36516	−	2.24144i	−0.430258	−	0.115287i
$379$	−27.2074			−1.39755			−0.698775	−	0.715341i	$-0.746271\pi$
$379$	−27.2074			−1.39755			−0.698775	+	0.715341i	$0.746271\pi$
$380$		0			0
$381$	−4.41641			−0.226259
$382$	15.4343	+	4.13560i	0.789685	+	0.211595i
$383$	4.64432	−	17.3328i	0.237314	−	0.885667i	−0.739779	−	0.672850i	$-0.765070\pi$
$383$	4.64432	−	17.3328i	0.237314	−	0.885667i	0.977092	−	0.212816i	$-0.0682635\pi$
$384$	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	$-0.318366\pi$
$389$	1.60570	+	0.927051i	0.0814122	+	0.0470034i	−0.458741	+	0.888570i	$0.651700\pi$
$390$		0			0
$391$	−3.43769			−0.173852
$392$	6.32456	−	6.32456i	0.319438	−	0.319438i
$393$	−6.74092	+	1.80622i	−0.340034	+	0.0911119i
$394$	−2.11111	−	3.65654i	−0.106356	−	0.184214i
$395$		0			0
$396$	−7.93769	−	13.7485i	−0.398884	−	0.690888i
$397$	−5.69693	+	21.2612i	−0.285921	+	1.06707i	0.662243	+	0.749289i	$0.269605\pi$
$397$	−5.69693	+	21.2612i	−0.285921	+	1.06707i	−0.948164	+	0.317782i	$0.897062\pi$
$398$	−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	0.221409	−	0.975181i	$-0.428934\pi$
$401$	23.5623	−	13.6037i	1.17665	−	0.679337i	0.955236	+	0.295844i	$0.0956010\pi$
$402$	−4.94999	−	1.32635i	−0.246883	−	0.0661522i
$403$	0.709905	+	2.64940i	0.0353629	+	0.131976i
$404$	−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
$408$	0.146248	+	0.545807i	0.00724038	+	0.0270215i
$409$	−11.6190	+	20.1246i	−0.574520	+	0.995098i	0.421573	+	0.906794i	$0.361478\pi$
$409$	−11.6190	+	20.1246i	−0.574520	+	0.995098i	−0.996094	+	0.0883038i	$0.971855\pi$
$410$		0			0
$411$		−	1.47935i		−	0.0729709i
$412$	−7.53800	−	28.1322i	−0.371371	−	1.38597i
$413$	6.39495	−	23.8663i	0.314675	−	1.17438i
$414$	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
$418$	−16.8040	−	6.64870i	−0.821912	−	0.325199i
$419$		−	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	−0.996250	−	0.0865199i	$-0.972425\pi$
$421$	−29.1246	+	16.8151i	−1.41945	+	0.819518i	−0.423197	+	0.906038i	$0.639092\pi$
$422$	−39.5137	+	10.5877i	−1.92350	+	0.515400i
$423$	10.6772	+	2.86096i	0.519145	+	0.139104i
$424$	−26.0887	−	15.0623i	−1.26698	−	0.731490i
$425$		0			0
$426$			3.30792i			0.160269i
$427$	15.9980	−	4.28666i	0.774200	−	0.207446i
$428$	3.15907	−	0.846470i	0.152699	−	0.0409157i
$429$			1.31308i			0.0633962i
$430$		0			0
$431$	−21.9271	−	12.6596i	−1.05619	−	0.609791i	−0.131813	−	0.991275i	$-0.542080\pi$
$431$	−21.9271	−	12.6596i	−1.05619	−	0.609791i	−0.924376	+	0.381484i	$0.875413\pi$
$432$	2.15988	+	0.578737i	0.103917	+	0.0278445i
$433$	13.6433	−	3.65572i	0.655656	−	0.175683i	0.0843715	−	0.996434i	$-0.473112\pi$
$433$	13.6433	−	3.65572i	0.655656	−	0.175683i	0.571285	+	0.820752i	$0.306445\pi$
$434$	4.96188	−	2.86475i	0.238178	−	0.137512i
$435$		0			0
$436$			45.2492i			2.16704i
$437$	−3.31388	−	22.4058i	−0.158524	−	1.07181i
$438$	7.16978	−	7.16978i	0.342585	−	0.342585i
$439$	12.7377	+	22.0623i	0.607936	+	1.05298i	0.991580	+	0.129495i	$0.0413357\pi$
$439$	12.7377	+	22.0623i	0.607936	+	1.05298i	−0.383644	+	0.923481i	$0.625331\pi$
$440$		0			0
$441$	5.70820	−	9.88690i	0.271819	−	0.470805i
$442$	−0.709905	+	2.64940i	−0.0337667	+	0.126019i
$443$	−8.41164	−	31.3927i	−0.399649	−	1.49151i	−0.813715	−	0.581264i	$-0.802558\pi$
$443$	−8.41164	−	31.3927i	−0.399649	−	1.49151i	0.414066	−	0.910247i	$-0.364108\pi$
$444$		−	11.1246i		−	0.527951i
$445$		0			0
$446$	18.8435	−	32.6378i	0.892264	−	1.54545i
$447$	−0.959754	−	3.58185i	−0.0453948	−	0.169416i
$448$	15.9217	−	15.9217i	0.752229	−	0.752229i
$449$	−14.2653			−0.673221			−0.336610	−	0.941644i	$-0.609280\pi$
$449$	−14.2653			−0.673221			−0.336610	+	0.941644i	$0.609280\pi$
$450$		0			0
$451$	−7.28115	+	4.20378i	−0.342856	+	0.197948i
$452$	9.57080	+	35.7187i	0.450172	+	1.68007i
$453$	−1.73065	−	0.463728i	−0.0813133	−	0.0217878i
$454$	−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	$-0.955681\pi$
$457$	−24.1375	−	24.1375i	−1.12911	−	1.12911i	−0.138783	−	0.990323i	$-0.544319\pi$
$458$	−6.36611	+	23.7586i	−0.297469	+	1.11017i
$459$	0.739674	+	1.28115i	0.0345250	+	0.0597991i
$460$		0			0
$461$	−1.71885	−	2.97713i	−0.0800547	−	0.138659i	0.823219	−	0.567725i	$-0.192176\pi$
$461$	−1.71885	−	2.97713i	−0.0800547	−	0.138659i	−0.903273	+	0.429066i	$0.858843\pi$
$462$	2.64940	−	0.709905i	0.123261	−	0.0330278i
$463$	−17.8351	+	17.8351i	−0.828868	+	0.828868i	−0.987360	−	0.158492i	$-0.949337\pi$
$463$	−17.8351	+	17.8351i	−0.828868	+	0.828868i	0.158492	+	0.987360i	$0.449337\pi$
$464$	−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	0.618735	−	0.785600i	$-0.287646\pi$
$467$	−3.60598	−	3.60598i	−0.166865	−	0.166865i	−0.785600	+	0.618735i	$0.787646\pi$
$468$	−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
$472$	8.25585	−	30.8113i	0.380006	−	1.41820i
$473$	5.75137	+	1.54108i	0.264448	+	0.0708588i
$474$	−11.6190			−0.533676
$475$		0			0
$476$	3.43769			0.157566
$477$	−37.1407	−	9.95181i	−1.70055	−	0.455662i
$478$	13.7929	−	51.4759i	0.630874	−	2.35445i
$479$	−22.6246	−	13.0623i	−1.03374	−	0.596832i	−0.115689	−	0.993286i	$-0.536907\pi$
$479$	−22.6246	−	13.0623i	−1.03374	−	0.596832i	−0.918055	+	0.396454i	$0.870241\pi$
$480$		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	$0.451626\pi$
$488$	20.6534	−	5.53406i	0.934935	−	0.250515i
$489$	−0.330792	−	0.572949i	−0.0149589	−	0.0259097i
$490$		0			0
$491$	−4.06231	−	7.03612i	−0.183329	−	0.317536i	0.759683	−	0.650294i	$-0.225354\pi$
$491$	−4.06231	−	7.03612i	−0.183329	−	0.317536i	−0.943012	+	0.332758i	$0.892021\pi$
$492$	−1.34486	+	5.01910i	−0.0606311	+	0.226278i
$493$	−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
$497$	6.47963	+	1.73621i	0.290651	+	0.0778797i
$498$	3.29970	+	12.3147i	0.147863	+	0.551833i
$499$	26.0887	−	15.0623i	1.16789	−	0.674281i	0.214708	−	0.976678i	$-0.431120\pi$
$499$	26.0887	−	15.0623i	1.16789	−	0.674281i	0.953182	+	0.302397i	$0.0977868\pi$
$500$		0			0
$501$	−2.14590			−0.0958717
$502$	9.91455	−	9.91455i	0.442508	−	0.442508i
$503$	−7.70174	−	28.7433i	−0.343403	−	1.28160i	−0.894466	−	0.447135i	$-0.852444\pi$
$503$	−7.70174	−	28.7433i	−0.343403	−	1.28160i	0.551063	−	0.834464i	$-0.314222\pi$
$504$	−5.52694	+	9.57295i	−0.246190	+	0.426413i
$505$		0			0
$506$			21.5427i			0.957691i
$507$	−0.945330	−	3.52802i	−0.0419836	−	0.156685i
$508$	−8.97763	+	33.5050i	−0.398318	+	1.48654i
$509$	16.1535	−	27.9787i	0.715992	−	1.24013i	−0.246584	−	0.969122i	$-0.579308\pi$
$509$	16.1535	−	27.9787i	0.715992	−	1.24013i	0.962576	−	0.271013i	$-0.0873587\pi$
$510$		0			0
$511$	−10.2812	−	17.8075i	−0.454811	−	0.787757i
$512$	−7.90569	+	7.90569i	−0.349386	+	0.349386i
$513$	−7.63710	+	6.05596i	−0.337186	+	0.267377i
$514$		−	57.6869i		−	2.54446i
$515$		0			0
$516$	3.18692	−	1.83997i	0.140296	−	0.0810001i
$517$	−6.93622	+	1.85856i	−0.305055	+	0.0817392i
$518$	−36.3185	−	9.73152i	−1.59574	−	0.427579i
$519$	−1.49778	−	0.864745i	−0.0657454	−	0.0379581i
$520$		0			0
$521$		−	28.5306i		−	1.24995i	−0.780646	−	0.624974i	$-0.785110\pi$
$521$		−	28.5306i		−	1.24995i	0.780646	−	0.624974i	$-0.214890\pi$
$522$	4.07834	−	1.09279i	0.178504	−	0.0478300i
$523$	−1.52963	+	0.409864i	−0.0668862	+	0.0179221i	−0.292107	−	0.956386i	$-0.594356\pi$
$523$	−1.52963	+	0.409864i	−0.0668862	+	0.0179221i	0.225221	+	0.974308i	$0.427690\pi$
$524$			54.8115i			2.39445i
$525$		0			0
$526$	25.0623	+	14.4697i	1.09277	+	0.630910i
$527$	−0.945365	−	0.253310i	−0.0411807	−	0.0110343i
$528$	−0.684072	+	0.183297i	−0.0297704	+	0.00797696i
$529$	−3.46410	+	2.00000i	−0.150613	+	0.0869565i
$530$		0			0
$531$		−	40.7146i		−	1.76686i
$532$	3.31388	+	22.4058i	0.143675	+	0.971413i
$533$	−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
$537$	−0.896575	+	3.34607i	−0.0386901	+	0.144393i
$538$	8.58287	+	32.0317i	0.370034	+	1.38099i
$539$			7.41641i			0.319447i
$540$		0			0
$541$	−12.2812	+	21.2716i	−0.528008	+	0.914537i	0.471459	+	0.881888i	$0.343728\pi$
$541$	−12.2812	+	21.2716i	−0.528008	+	0.914537i	−0.999467	+	0.0326487i	$0.989606\pi$
$542$	−0.325427	−	1.21451i	−0.0139783	−	0.0521677i
$543$	−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
$547$	0.366593	+	1.36814i	0.0156744	+	0.0584977i	0.973320	−	0.229452i	$-0.0736932\pi$
$547$	0.366593	+	1.36814i	0.0156744	+	0.0584977i	−0.957646	+	0.287949i	$0.907027\pi$
$548$	−11.2230	−	3.00721i	−0.479425	−	0.128461i
$549$	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
$553$	−6.09837	+	22.7594i	−0.259329	+	0.967830i
$554$	−30.9839	−	53.6656i	−1.31638	−	2.28003i
$555$		0			0
$556$	−3.65654	−	6.33332i	−0.155072	−	0.268592i
$557$	4.28682	−	1.14865i	0.181638	−	0.0486699i	−0.166853	−	0.985982i	$-0.553361\pi$
$557$	4.28682	−	1.14865i	0.181638	−	0.0486699i	0.348492	+	0.937312i	$0.386694\pi$
$558$	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
$567$	−3.45549	+	12.8961i	−0.145117	+	0.541584i
$568$	8.36516	+	2.24144i	0.350994	+	0.0940487i
$569$	−40.2461			−1.68720			−0.843601	−	0.536970i	$-0.819569\pi$
$569$	−40.2461			−1.68720			−0.843601	+	0.536970i	$0.819569\pi$
$570$		0			0
$571$	21.1246			0.884037			0.442019	−	0.897006i	$-0.354262\pi$
$571$	21.1246			0.884037			0.442019	+	0.897006i	$0.354262\pi$
$572$	9.96167	+	2.66922i	0.416518	+	0.111606i
$573$	−0.706444	+	2.63649i	−0.0295121	+	0.110141i
$574$	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	0.960912	−	0.276853i	$-0.0892914\pi$
$577$	16.4317	+	16.4317i	0.684060	+	0.684060i	−0.276853	+	0.960912i	$0.589291\pi$
$578$	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
$583$	24.1276	−	6.46497i	0.999262	−	0.267752i
$584$	−13.2729	−	22.9894i	−0.549237	−	0.951306i
$585$		0			0
$586$	6.34346	+	10.9872i	0.262046	+	0.453877i
$587$	−5.03699	+	18.7983i	−0.207899	+	0.775889i	0.780647	+	0.624972i	$0.214889\pi$
$587$	−5.03699	+	18.7983i	−0.207899	+	0.775889i	−0.988546	+	0.150918i	$0.951777\pi$
$588$	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
$592$	9.37740	+	2.51267i	0.385409	+	0.103270i
$593$	3.34967	+	12.5011i	0.137554	+	0.513360i	0.999974	+	0.00716635i	$0.00228114\pi$
$593$	3.34967	+	12.5011i	0.137554	+	0.513360i	−0.862420	+	0.506193i	$0.831052\pi$
$594$	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
$598$	5.57567	+	20.8087i	0.228006	+	0.850930i
$599$	−2.97713	+	5.15654i	−0.121642	+	0.210691i	−0.920415	−	0.390942i	$-0.872149\pi$
$599$	−2.97713	+	5.15654i	−0.121642	+	0.210691i	0.798773	+	0.601632i	$0.205483\pi$
$600$		0			0
$601$		−	31.1769i		−	1.27173i	−0.771799	−	0.635866i	$-0.780643\pi$
$601$		−	31.1769i		−	1.27173i	0.771799	−	0.635866i	$-0.219357\pi$
$602$	−3.21911	−	12.0139i	−0.131201	−	0.489650i
$603$	−4.43218	+	16.5411i	−0.180492	+	0.673606i
$604$	−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	$0.232359\pi$
$608$	−4.27820	−	28.9257i	−0.173504	−	1.17309i
$609$			0.437694i			0.0177363i
$610$		0			0
$611$	−6.21885	+	3.59045i	−0.251588	+	0.145254i
$612$	5.47167	−	1.46613i	0.221179	−	0.0592648i
$613$	−17.9152	−	4.80036i	−0.723587	−	0.193885i	−0.121815	−	0.992553i	$-0.538872\pi$
$613$	−17.9152	−	4.80036i	−0.723587	−	0.193885i	−0.601772	+	0.798668i	$0.705538\pi$
$614$	36.2283	+	20.9164i	1.46205	+	0.844118i
$615$		0			0
$616$		−	7.18091i		−	0.289327i
$617$	27.6517	−	7.40924i	1.11321	−	0.298285i	0.345079	−	0.938573i	$-0.387852\pi$
$617$	27.6517	−	7.40924i	1.11321	−	0.298285i	0.768134	+	0.640289i	$0.221185\pi$
$618$	8.00926	−	2.14607i	0.322180	−	0.0863278i
$619$			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
$622$	−19.4389	−	5.20863i	−0.779428	−	0.208847i
$623$	4.26592	−	1.14305i	0.170911	−	0.0457953i
$624$	−0.613323	+	0.354102i	−0.0245526	+	0.0141754i
$625$		0			0
$626$			25.9808i			1.03840i
$627$	1.13573	−	2.87047i	0.0453569	−	0.114636i
$628$	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	−0.968850	−	0.247650i	$-0.920342\pi$
$631$	−6.78115	+	11.7453i	−0.269953	+	0.467573i	0.698896	+	0.715223i	$0.253675\pi$
$632$	−7.87297	+	29.3823i	−0.313170	+	1.16877i
$633$	−1.80859	−	6.74975i	−0.0718850	−	0.268279i
$634$			40.0000i			1.58860i
$635$		0			0
$636$	7.71885	−	13.3694i	0.306072	−	0.530133i
$637$	1.91951	+	7.16370i	0.0760537	+	0.283836i
$638$	−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	−0.973113	−	0.230326i	$-0.926021\pi$
$641$	−31.9058	+	18.4208i	−1.26020	+	0.727578i	−0.287088	+	0.957904i	$0.592687\pi$
$642$	0.240991	+	0.899389i	0.00951114	+	0.0354961i
$643$	29.6264	+	7.93837i	1.16835	+	0.313059i	0.790297	−	0.612724i	$-0.209926\pi$
$643$	29.6264	+	7.93837i	1.16835	+	0.313059i	0.378055	+	0.925783i	$0.376593\pi$
$644$	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	0.994046	−	0.108960i	$-0.0347521\pi$
$647$	22.5132	+	22.5132i	0.885086	+	0.885086i	−0.108960	+	0.994046i	$0.534752\pi$
$648$	−4.46102	+	16.6488i	−0.175246	+	0.654025i
$649$	13.2246	+	22.9058i	0.519113	+	0.899130i
$650$		0			0
$651$	0.489357	+	0.847591i	0.0191794	+	0.0332197i
$652$	−5.01910	+	1.34486i	−0.196563	+	0.0526689i
$653$	6.48110	−	6.48110i	0.253625	−	0.253625i	−0.568830	−	0.822455i	$-0.692604\pi$
$653$	6.48110	−	6.48110i	0.253625	−	0.253625i	0.822455	+	0.568830i	$0.192604\pi$
$654$	−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	$-0.776202\pi$
$659$	4.58283	−	7.93769i	0.178522	−	0.309209i	0.941374	+	0.337364i	$0.109535\pi$
$660$		0			0
$661$	9.21885	+	5.32250i	0.358572	+	0.207021i	0.668454	−	0.743753i	$-0.266956\pi$
$661$	9.21885	+	5.32250i	0.358572	+	0.207021i	−0.309882	+	0.950775i	$0.600290\pi$
$662$	6.01441	−	22.4461i	0.233757	−	0.872392i
$663$	−0.452572	−	0.121266i	−0.0175764	−	0.00470959i
$664$	33.3775			1.29530
$665$		0			0
$666$	−61.9574			−2.40080
$667$	−3.32056	−	0.889741i	−0.128573	−	0.0344509i
$668$	−4.36216	+	16.2798i	−0.168777	+	0.629885i
$669$	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	$0.236318\pi$
$678$	−10.1691	+	2.72481i	−0.390543	+	0.104646i
$679$	7.41517	+	12.8435i	0.284568	+	0.492887i
$680$		0			0
$681$	−2.57295	−	4.45648i	−0.0985956	−	0.170773i
$682$	−1.58740	+	5.92424i	−0.0607845	+	0.226851i
$683$	−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
$687$	−4.05846	−	1.08746i	−0.154840	−	0.0414892i
$688$	0.831171	+	3.10197i	0.0316881	+	0.118262i
$689$	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
$693$	−2.37225	−	8.85335i	−0.0901142	−	0.336311i
$694$	25.2411	−	43.7188i	0.958139	−	1.65954i
$695$		0			0
$696$			0.565061i			0.0214186i
$697$	−0.776457	−	2.89778i	−0.0294104	−	0.109761i
$698$	−6.36611	+	23.7586i	−0.240961	+	0.899278i
$699$	−1.73205	+	3.00000i	−0.0655122	+	0.113470i
$700$		0			0
$701$	2.07295	+	3.59045i	0.0782942	+	0.135610i	0.902514	−	0.430660i	$-0.141719\pi$
$701$	2.07295	+	3.59045i	0.0782942	+	0.135610i	−0.824220	+	0.566270i	$0.808386\pi$
$702$	6.55524	−	6.55524i	0.247412	−	0.247412i
$703$	−33.1576	+	26.2928i	−1.25056	+	0.991652i
$704$			24.1033i			0.908428i
$705$		0			0
$706$	−42.6246	+	24.6093i	−1.60420	+	0.926184i
$707$	−26.2803	+	7.04180i	−0.988374	+	0.264834i
$708$	15.7896	+	4.23080i	0.593408	+	0.159003i
$709$	7.90215	+	4.56231i	0.296771	+	0.171341i	0.640992	−	0.767548i	$-0.278523\pi$
$709$	7.90215	+	4.56231i	0.296771	+	0.171341i	−0.344220	+	0.938889i	$0.611857\pi$
$710$		0			0
$711$			38.8264i			1.45610i
$712$	5.50728	−	1.47567i	0.206394	−	0.0553031i
$713$	−7.42499	+	1.98952i	−0.278068	+	0.0745081i
$714$			0.978714i			0.0366274i
$715$		0			0
$716$	23.5623	+	13.6037i	0.880565	+	0.508394i
$717$	8.79314	+	2.35611i	0.328386	+	0.0879907i
$718$	66.9102	−	17.9285i	2.49707	−	0.669087i
$719$	−33.0169	+	19.0623i	−1.23132	+	0.710904i	−0.967305	−	0.253614i	$-0.918381\pi$
$719$	−33.0169	+	19.0623i	−1.23132	+	0.710904i	−0.264016	+	0.964518i	$0.585047\pi$
$720$		0			0
$721$		−	16.8151i		−	0.626227i
$722$	37.4517	+	20.0592i	1.39381	+	0.746525i
$723$	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
$727$	6.46270	−	24.1191i	0.239688	−	0.894529i	−0.736291	−	0.676665i	$-0.763425\pi$
$727$	6.46270	−	24.1191i	0.239688	−	0.894529i	0.975979	−	0.217864i	$-0.0699088\pi$
$728$	−1.85856	−	6.93622i	−0.0688826	−	0.257074i
$729$			19.4377i			0.719915i
$730$		0			0
$731$	−1.06231	+	1.83997i	−0.0392908	+	0.0680537i
$732$	2.83599	+	10.5841i	0.104821	+	0.391198i
$733$	18.8812	−	18.8812i	0.697392	−	0.697392i	−0.266455	−	0.963847i	$-0.585853\pi$
$733$	18.8812	−	18.8812i	0.697392	−	0.697392i	0.963847	+	0.266455i	$0.0858525\pi$
$734$	42.0378			1.55164
$735$		0			0
$736$	−30.1869	+	17.4284i	−1.11270	+	0.642420i
$737$	−2.87926	−	10.7455i	−0.106059	−	0.395817i
$738$	27.9534	+	7.49008i	1.02898	+	0.275714i
$739$	11.2583	−	6.50000i	0.414144	−	0.239106i	−0.278425	−	0.960458i	$-0.589812\pi$
$739$	11.2583	−	6.50000i	0.414144	−	0.239106i	0.692569	+	0.721352i	$0.256479\pi$
$740$		0			0
$741$	0.354102	−	3.06661i	0.0130083	−	0.112655i
$742$	−36.8950	−	36.8950i	−1.35446	−	1.35446i
$743$	−0.0144235	+	0.0538292i	−0.000529147	+	0.00197480i	−0.966190	−	0.257832i	$-0.916992\pi$
$743$	−0.0144235	+	0.0538292i	−0.000529147	+	0.00197480i	0.965661	+	0.259806i	$0.0836587\pi$
$744$	0.631757	+	1.09424i	0.0231613	+	0.0401166i
$745$		0			0
$746$	−17.0729	−	29.5712i	−0.625085	−	1.08268i
$747$	41.1512	−	11.0264i	1.50564	−	0.403436i
$748$	−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	0.853118	−	0.521717i	$-0.174708\pi$
$751$	22.6869	+	13.0983i	0.827857	+	0.477964i	−0.0252611	+	0.999681i	$0.508042\pi$
$752$	−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
$757$	−4.93117	+	18.4034i	−0.179226	+	0.668881i	0.816567	+	0.577251i	$0.195875\pi$
$757$	−4.93117	+	18.4034i	−0.179226	+	0.668881i	−0.995793	+	0.0916305i	$0.970792\pi$
$758$	−58.7646	−	15.7459i	−2.13443	−	0.571918i
$759$	−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	$0.569790\pi$
$762$	−9.53889	−	2.55594i	−0.345558	−	0.0925919i
$763$	−6.76155	+	25.2344i	−0.244784	+	0.913548i
$764$	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	$-0.351276\pi$
$769$	−2.70599	−	1.56231i	−0.0975806	−	0.0563382i	−0.547996	+	0.836481i	$0.684609\pi$
$770$		0			0
$771$	9.85410			0.354887
$772$	−17.5896	+	17.5896i	−0.633062	+	0.633062i
$773$	49.6771	−	13.3110i	1.78676	−	0.478762i	0.794973	−	0.606644i	$-0.207485\pi$
$773$	49.6771	−	13.3110i	1.78676	−	0.478762i	0.991789	+	0.127883i	$0.0408181\pi$
$774$	−10.2475	−	17.7492i	−0.368339	−	0.637983i
$775$		0			0
$776$	9.57295	+	16.5808i	0.343649	+	0.595217i
$777$	1.66234	−	6.20395i	0.0596362	−	0.222565i
$778$	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
$782$	−7.42499	−	1.98952i	−0.265517	−	0.0711451i
$783$	0.382883	+	1.42894i	0.0136831	+	0.0510662i
$784$	−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	$0.404169\pi$
$788$	−1.46613	−	5.47167i	−0.0522287	−	0.194920i
$789$	−2.47172	+	4.28115i	−0.0879957	+	0.152413i
$790$		0			0
$791$			21.3497i			0.759107i
$792$	−3.06256	−	11.4296i	−0.108823	−	0.406134i
$793$	−4.58873	+	17.1254i	−0.162951	+	0.608140i
$794$	−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	$0.495700\pi$
$798$	−6.37894	+	0.943464i	−0.225812	+	0.0333983i
$799$		−	2.56231i		−	0.0906479i
$800$		0			0
$801$	6.30244	−	3.63871i	0.222686	−	0.128568i
$802$	58.7646	−	15.7459i	2.07505	−	0.556008i
$803$	21.2612	+	5.69693i	0.750293	+	0.201040i
$804$	−5.95426	−	3.43769i	−0.209991	−	0.121238i
$805$		0			0
$806$			6.13323i			0.216034i
$807$	−5.47167	+	1.46613i	−0.192612	+	0.0516102i
$808$	−33.9278	+	9.09092i	−1.19357	+	0.319817i
$809$		−	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	0.763941	−	0.645286i	$-0.223262\pi$
$811$	16.7188	+	9.65263i	0.587078	+	0.338950i	−0.176863	+	0.984235i	$0.556595\pi$
$812$	3.32056	+	0.889741i	0.116529	+	0.0312238i
$813$	0.207463	−	0.0555896i	0.00727605	−	0.00194961i
$814$	34.8569	−	20.1246i	1.22173	−	0.705367i
$815$		0			0
$816$		−	0.252703i		−	0.00884637i
$817$	−13.0164	−	5.15006i	−0.455385	−	0.180178i
$818$	−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	0.377815	+	0.925881i	$0.376675\pi$
$821$	−17.5623	+	30.4188i	−0.612929	+	1.06162i	−0.990744	+	0.135743i	$0.956658\pi$
$822$	0.856153	−	3.19521i	0.0298618	−	0.111446i
$823$	−2.42811	−	9.06183i	−0.0846386	−	0.315875i	0.910607	−	0.413274i	$-0.135615\pi$
$823$	−2.42811	−	9.06183i	−0.0846386	−	0.315875i	−0.995246	+	0.0973981i	$0.968948\pi$
$824$		−	21.7082i		−	0.756241i
$825$		0			0
$826$	27.6246	−	47.8472i	0.961183	−	1.66482i
$827$	−4.67317	−	17.4405i	−0.162502	−	0.606465i	−0.998346	−	0.0574979i	$-0.981688\pi$
$827$	−4.67317	−	17.4405i	−0.162502	−	0.606465i	0.835844	−	0.548967i	$-0.184979\pi$
$828$	31.4599	−	31.4599i	1.09331	−	1.09331i
$829$	−51.9247			−1.80342			−0.901709	−	0.432344i	$-0.857687\pi$
$829$	−51.9247			−1.80342			−0.901709	+	0.432344i	$0.857687\pi$
$830$		0			0
$831$	9.16718	−	5.29268i	0.318006	−	0.183601i
$832$	6.23840	+	23.2820i	0.216278	+	0.807159i
$833$	−2.55617	−	0.684923i	−0.0885659	−	0.0237312i
$834$	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
$838$	18.1818	−	67.8555i	0.628081	−	2.34403i
$839$	15.9192	+	27.5729i	0.549594	+	0.951924i	0.998302	+	0.0582459i	$0.0185507\pi$
$839$	15.9192	+	27.5729i	0.549594	+	0.951924i	−0.448709	+	0.893678i	$0.648116\pi$
$840$		0			0
$841$	14.2812	+	24.7357i	0.492454	+	0.852955i
$842$	−72.6371	+	19.4630i	−2.50324	+	0.670741i
$843$	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
$852$	−1.14865	+	4.28682i	−0.0393521	+	0.146864i
$853$	−36.0744	−	9.66612i	−1.23517	−	0.330962i	−0.418577	−	0.908181i	$-0.637471\pi$
$853$	−36.0744	−	9.66612i	−1.23517	−	0.330962i	−0.816589	+	0.577220i	$0.804138\pi$
$854$	37.0347			1.26730
$855$		0			0
$856$	2.43769			0.0833187
$857$	32.6135	+	8.73875i	1.11405	+	0.298510i	0.768475	−	0.639880i	$-0.221016\pi$
$857$	32.6135	+	8.73875i	1.11405	+	0.298510i	0.345579	+	0.938390i	$0.387682\pi$
$858$	−0.759929	+	2.83609i	−0.0259436	+	0.0968227i
$859$	−35.1280	−	20.2812i	−1.19855	−	0.691984i	−0.238319	−	0.971187i	$-0.576596\pi$
$859$	−35.1280	−	20.2812i	−1.19855	−	0.691984i	−0.960232	+	0.279203i	$0.909930\pi$
$860$		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
$868$	7.42499	−	1.98952i	0.252021	−	0.0675287i
$869$	−12.6113	−	21.8435i	−0.427810	−	0.740989i
$870$		0			0
$871$	−5.56231	−	9.63420i	−0.188472	−	0.326442i
$872$	−8.72912	+	32.5775i	−0.295605	+	1.10321i
$873$	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
$877$	2.05222	+	0.549890i	0.0692985	+	0.0185685i	0.293302	−	0.956020i	$-0.405246\pi$
$877$	2.05222	+	0.549890i	0.0692985	+	0.0185685i	−0.224003	+	0.974588i	$0.571913\pi$
$878$	14.7435	+	55.0236i	0.497570	+	1.85696i
$879$	−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
$883$	−4.48288	−	16.7303i	−0.150861	−	0.563020i	−0.999424	−	0.0339267i	$-0.989199\pi$
$883$	−4.48288	−	16.7303i	−0.150861	−	0.563020i	0.848563	−	0.529094i	$-0.177468\pi$
$884$	−1.83997	+	3.18692i	−0.0618848	+	0.107188i
$885$		0			0
$886$		−	72.6724i		−	2.44148i
$887$	4.96975	+	18.5473i	0.166868	+	0.622759i	0.997795	+	0.0663773i	$0.0211441\pi$
$887$	4.96975	+	18.5473i	0.166868	+	0.622759i	−0.830927	+	0.556382i	$0.812189\pi$
$888$	2.14607	−	8.00926i	0.0720176	−	0.268773i
$889$	−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
$893$	16.7003	−	2.47002i	0.558853	−	0.0826561i
$894$		−	8.29180i		−	0.277319i
$895$		0			0
$896$	23.4787	−	13.5554i	0.784369	−	0.452856i
$897$	−3.55454	+	0.952437i	−0.118683	+	0.0318010i
$898$	−30.8113	−	8.25585i	−1.02818	−	0.275501i
$899$	−0.847591	−	0.489357i	−0.0282687	−	0.0163210i
$900$		0			0
$901$			8.91296i			0.296934i
$902$	−18.1593	+	4.86576i	−0.604637	+	0.162012i
$903$	2.05222	−	0.549890i	0.0682935	−	0.0182992i
$904$			27.5623i			0.916709i
$905$		0			0
$906$	−3.46962	−	2.00319i	−0.115271	−	0.0665515i
$907$	22.0754	+	5.91508i	0.733001	+	0.196407i	0.605965	−	0.795491i	$-0.292787\pi$
$907$	22.0754	+	5.91508i	0.733001	+	0.196407i	0.127035	+	0.991898i	$0.459454\pi$
$908$	−39.0393	+	10.4605i	−1.29556	+	0.347145i
$909$	−38.8264	+	22.4164i	−1.28779	+	0.743505i
$910$		0			0
$911$			13.0386i			0.431990i	0.976395	+	0.215995i	$0.0692994\pi$
$911$			13.0386i			0.431990i	−0.976395	+	0.215995i	$0.930701\pi$
$912$	1.64703	−	0.243601i	0.0545387	−	0.00806644i
$913$	−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
$917$	−8.19045	+	30.5672i	−0.270472	+	1.00942i
$918$	0.856153	+	3.19521i	0.0282573	+	0.105458i
$919$		−	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
$922$	−1.98952	−	7.42499i	−0.0655214	−	0.244529i
$923$	−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
$927$	−7.17141	−	26.7641i	−0.235540	−	0.879047i
$928$	−4.28682	−	1.14865i	−0.140722	−	0.0377063i
$929$	33.3959	−	19.2812i	1.09569	−	0.632594i	0.160601	−	0.987019i	$-0.448657\pi$
$929$	33.3959	−	19.2812i	1.09569	−	0.632594i	0.935084	+	0.354425i	$0.115323\pi$
$930$		0			0
$931$	2.00000	−	17.3205i	0.0655474	−	0.567657i
$932$	19.2385	+	19.2385i	0.630179	+	0.630179i
$933$	0.889741	−	3.32056i	0.0291288	−	0.108710i
$934$	−5.70156	−	9.87539i	−0.186561	−	0.323133i
$935$		0			0
$936$	−5.91641	−	10.2475i	−0.193384	−	0.334951i
$937$	30.3587	−	8.13458i	0.991775	−	0.265745i	0.273779	−	0.961793i	$-0.411726\pi$
$937$	30.3587	−	8.13458i	0.991775	−	0.265745i	0.717996	+	0.696047i	$0.245060\pi$
$938$	−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	0.604076	−	0.796926i	$-0.293542\pi$
$941$	6.62461	+	3.82472i	0.215956	+	0.124682i	−0.388120	+	0.921609i	$0.626875\pi$
$942$	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
$947$	−10.6840	+	39.8731i	−0.347182	+	1.29570i	0.542860	+	0.839823i	$0.317341\pi$
$947$	−10.6840	+	39.8731i	−0.347182	+	1.29570i	−0.890042	+	0.455878i	$0.849325\pi$
$948$	−15.0573	−	4.03459i	−0.489038	−	0.131037i
$949$	22.0113			0.714516
$950$		0			0
$951$	−6.83282			−0.221569
$952$	2.47500	+	0.663174i	0.0802151	+	0.0214936i
$953$	−9.59964	+	35.8264i	−0.310963	+	1.16053i	0.616727	+	0.787177i	$0.288458\pi$
$953$	−9.59964	+	35.8264i	−0.310963	+	1.16053i	−0.927690	+	0.373352i	$0.878208\pi$
$954$	−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
$963$	3.00544	−	0.805304i	0.0968488	−	0.0259506i
$964$	−23.0036	−	39.8435i	−0.740897	−	1.28327i
$965$		0			0
$966$	3.84346	+	6.65707i	0.123661	+	0.214188i
$967$	0.896575	−	3.34607i	0.0288319	−	0.107602i	−0.950010	−	0.312218i	$-0.898928\pi$
$967$	0.896575	−	3.34607i	0.0288319	−	0.107602i	0.978842	+	0.204616i	$0.0655946\pi$
$968$	−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	−0.587850	−	0.808970i	$-0.700025\pi$
$971$	−5.64590	+	3.25966i	−0.181185	+	0.104607i	0.406664	+	0.913578i	$0.366692\pi$
$972$	−27.9707	−	7.49473i	−0.897161	−	0.240394i
$973$	−1.09279	−	4.07834i	−0.0350332	−	0.130746i
$974$	−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	$-0.194774\pi$
$978$	−0.382883	−	1.42894i	−0.0122433	−	0.0456925i
$979$	−2.36381	+	4.09424i	−0.0755476	+	0.130852i
$980$		0			0
$981$			43.0486i			1.37443i
$982$	−4.70201	−	17.5482i	−0.150047	−	0.559984i
$983$	−8.69548	+	32.4520i	−0.277343	+	1.03506i	0.676912	+	0.736064i	$0.263318\pi$
$983$	−8.69548	+	32.4520i	−0.277343	+	1.03506i	−0.954255	+	0.298993i	$0.903349\pi$
$984$	−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
$988$	−22.5450	−	8.92017i	−0.717251	−	0.283788i
$989$			16.6869i			0.530613i
$990$		0			0
$991$	−11.3435	+	6.54915i	−0.360337	+	0.208041i	−0.669229	−	0.743057i	$-0.733375\pi$
$991$	−11.3435	+	6.54915i	−0.360337	+	0.208041i	0.308892	+	0.951097i	$0.400042\pi$
$992$	−9.58562	+	2.56846i	−0.304344	+	0.0815487i
$993$	3.83425	+	1.02738i	0.121676	+	0.0326030i
$994$	12.9904	+	7.50000i	0.412030	+	0.237886i
$995$		0			0
$996$			17.1047i			0.541982i
$997$	−53.7455	+	14.4011i	−1.70214	+	0.456086i	−0.973476	−	0.228788i	$-0.926524\pi$
$997$	−53.7455	+	14.4011i	−1.70214	+	0.456086i	−0.728661	+	0.684874i	$0.759857\pi$
$998$	65.0654	−	17.4342i	2.05961	−	0.551871i
$999$		−	21.7082i		−	0.686817i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.p.g.107.2	✓	16	5.4	even	2	inner
475.2.p.g.107.3	yes	16	1.1	even	1	trivial
475.2.p.g.293.2	yes	16	95.27	even	12	inner
475.2.p.g.293.3	yes	16	95.8	even	12	inner
475.2.p.g.407.2	yes	16	95.84	odd	6	inner
475.2.p.g.407.3	yes	16	19.8	odd	6	inner
475.2.p.g.468.2	yes	16	5.2	odd	4	inner
475.2.p.g.468.3	yes	16	5.3	odd	4	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)

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