LMFDB - Embedded newform 475.2.l.c.301.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(101,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("475.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.l (of order $9$, degree $6$, 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:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 15 x^{16} - 14 x^{15} + 72 x^{14} - 51 x^{13} + 231 x^{12} - 93 x^{11} + 438 x^{10} + \cdots + 1 $ x^18 - 3x^17 + 15x^16 - 14x^15 + 72x^14 - 51x^13 + 231x^12 - 93x^11 + 438x^10 - 156x^9 + 582x^8 - 138x^7 + 437x^6 - 132x^5 + 198x^4 - 16x^3 + 15x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			301.3
Root			$0.816390 + 1.41403i$ of defining polynomial
Character	$\chi$	$=$	475.301
Dual form			475.2.l.c.101.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.484738 + 0.406743i) q^{2} +(1.80387 - 0.656554i) q^{3} +(-0.277766 - 1.57529i) q^{4} +(1.14145 + 0.415455i) q^{6} +(2.04448 + 3.54114i) q^{7} +(1.13887 - 1.97259i) q^{8} +(0.524744 - 0.440313i) q^{9} +O(q^{10})$	\(q+(0.484738 + 0.406743i) q^{2} +(1.80387 - 0.656554i) q^{3} +(-0.277766 - 1.57529i) q^{4} +(1.14145 + 0.415455i) q^{6} +(2.04448 + 3.54114i) q^{7} +(1.13887 - 1.97259i) q^{8} +(0.524744 - 0.440313i) q^{9} +(2.17413 - 3.76571i) q^{11} +(-1.53531 - 2.65924i) q^{12} +(1.45826 + 0.530764i) q^{13} +(-0.449299 + 2.54810i) q^{14} +(-1.65185 + 0.601224i) q^{16} +(-4.87326 - 4.08915i) q^{17} +0.433458 q^{18} +(0.708014 + 4.30101i) q^{19} +(6.01291 + 5.04543i) q^{21} +(2.58556 - 0.941068i) q^{22} +(0.583829 + 3.31106i) q^{23} +(0.759268 - 4.30602i) q^{24} +(0.490990 + 0.850420i) q^{26} +(-2.22197 + 3.84857i) q^{27} +(5.01042 - 4.20424i) q^{28} +(3.99325 - 3.35074i) q^{29} +(-3.28366 - 5.68747i) q^{31} +(-5.32603 - 1.93852i) q^{32} +(1.44946 - 8.22028i) q^{33} +(-0.699019 - 3.96434i) q^{34} +(-0.839375 - 0.704319i) q^{36} -0.180685 q^{37} +(-1.40621 + 2.37284i) q^{38} +2.97899 q^{39} +(-0.0242217 + 0.00881597i) q^{41} +(0.862490 + 4.89143i) q^{42} +(-0.793995 + 4.50297i) q^{43} +(-6.53598 - 2.37890i) q^{44} +(-1.06375 + 1.84246i) q^{46} +(1.09575 - 0.919441i) q^{47} +(-2.58498 + 2.16906i) q^{48} +(-4.85976 + 8.41736i) q^{49} +(-11.4755 - 4.17673i) q^{51} +(0.431051 - 2.44461i) q^{52} +(0.278010 + 1.57667i) q^{53} +(-2.64246 + 0.961776i) q^{54} +9.31361 q^{56} +(4.10101 + 7.29361i) q^{57} +3.29857 q^{58} +(7.31281 + 6.13617i) q^{59} +(-1.05793 - 5.99980i) q^{61} +(0.721625 - 4.09254i) q^{62} +(2.63203 + 0.957982i) q^{63} +(-0.0353865 - 0.0612913i) q^{64} +(4.04615 - 3.39513i) q^{66} +(-7.87159 + 6.60505i) q^{67} +(-5.08797 + 8.81262i) q^{68} +(3.22704 + 5.58940i) q^{69} +(-1.88710 + 10.7023i) q^{71} +(-0.270938 - 1.53657i) q^{72} +(-12.7987 + 4.65836i) q^{73} +(-0.0875850 - 0.0734926i) q^{74} +(6.57867 - 2.31000i) q^{76} +17.7799 q^{77} +(1.44403 + 1.21168i) q^{78} +(-16.2283 + 5.90661i) q^{79} +(-1.83820 + 10.4250i) q^{81} +(-0.0153270 - 0.00557858i) q^{82} +(-2.57831 - 4.46577i) q^{83} +(6.27783 - 10.8735i) q^{84} +(-2.21643 + 1.85981i) q^{86} +(5.00336 - 8.66608i) q^{87} +(-4.95213 - 8.57735i) q^{88} +(0.477195 + 0.173685i) q^{89} +(1.10187 + 6.24904i) q^{91} +(5.05370 - 1.83940i) q^{92} +(-9.65742 - 8.10354i) q^{93} +0.905127 q^{94} -10.8802 q^{96} +(-2.51273 - 2.10843i) q^{97} +(-5.77942 + 2.10354i) q^{98} +(-0.517226 - 2.93333i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9	$ 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9} + 18 q^{12} + 3 q^{13} - 12 q^{14} - 3 q^{16} - 24 q^{17} - 48 q^{18} - 21 q^{21} - 9 q^{22} + 9 q^{23} - 15 q^{24} + 3 q^{26} + 24 q^{27} + 12 q^{28} + 15 q^{29} - 18 q^{31} - 15 q^{32} + 33 q^{33} - 12 q^{34} + 75 q^{36} - 36 q^{37} + 33 q^{38} + 36 q^{39} - 30 q^{41} + 9 q^{42} + 36 q^{43} + 42 q^{44} + 9 q^{46} - 21 q^{47} - 33 q^{48} + 9 q^{49} - 45 q^{51} + 39 q^{52} + 12 q^{53} - 66 q^{54} - 72 q^{57} - 12 q^{58} + 18 q^{59} - 30 q^{61} + 24 q^{62} - 54 q^{63} + 36 q^{64} + 39 q^{66} - 51 q^{68} + 15 q^{69} - 12 q^{71} + 66 q^{72} - 24 q^{73} - 15 q^{74} - 33 q^{76} + 60 q^{77} + 48 q^{78} - 51 q^{79} + 27 q^{81} + 15 q^{82} + 48 q^{84} + 63 q^{86} + 15 q^{87} + 27 q^{88} - 54 q^{89} + 30 q^{91} + 42 q^{92} - 72 q^{93} + 30 q^{94} - 66 q^{96} - 27 q^{97} + 3 q^{98} - 93 q^{99}+O(q^{100}) $ 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9 + 18 * q^12 + 3 * q^13 - 12 * q^14 - 3 * q^16 - 24 * q^17 - 48 * q^18 - 21 * q^21 - 9 * q^22 + 9 * q^23 - 15 * q^24 + 3 * q^26 + 24 * q^27 + 12 * q^28 + 15 * q^29 - 18 * q^31 - 15 * q^32 + 33 * q^33 - 12 * q^34 + 75 * q^36 - 36 * q^37 + 33 * q^38 + 36 * q^39 - 30 * q^41 + 9 * q^42 + 36 * q^43 + 42 * q^44 + 9 * q^46 - 21 * q^47 - 33 * q^48 + 9 * q^49 - 45 * q^51 + 39 * q^52 + 12 * q^53 - 66 * q^54 - 72 * q^57 - 12 * q^58 + 18 * q^59 - 30 * q^61 + 24 * q^62 - 54 * q^63 + 36 * q^64 + 39 * q^66 - 51 * q^68 + 15 * q^69 - 12 * q^71 + 66 * q^72 - 24 * q^73 - 15 * q^74 - 33 * q^76 + 60 * q^77 + 48 * q^78 - 51 * q^79 + 27 * q^81 + 15 * q^82 + 48 * q^84 + 63 * q^86 + 15 * q^87 + 27 * q^88 - 54 * q^89 + 30 * q^91 + 42 * q^92 - 72 * q^93 + 30 * q^94 - 66 * q^96 - 27 * q^97 + 3 * q^98 - 93 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$	0.484738	+	0.406743i	0.342761	+	0.287611i	0.797876	−	0.602822i	$-0.205957\pi$
$2$	0.484738	+	0.406743i	0.342761	+	0.287611i	−0.455114	+	0.890433i	$0.650402\pi$
$3$	1.80387	−	0.656554i	1.04146	−	0.379062i	0.236029	−	0.971746i	$-0.424154\pi$
$3$	1.80387	−	0.656554i	1.04146	−	0.379062i	0.805435	+	0.592684i	$0.201932\pi$
$4$	−0.277766	−	1.57529i	−0.138883	−	0.787644i
$5$		0			0
$5$		0			0
$6$	1.14145	+	0.415455i	0.465996	+	0.169609i
$7$	2.04448	+	3.54114i	0.772739	+	1.33842i	0.936056	+	0.351850i	$0.114447\pi$
$7$	2.04448	+	3.54114i	0.772739	+	1.33842i	−0.163317	+	0.986574i	$0.552219\pi$
$8$	1.13887	−	1.97259i	0.402653	−	0.697415i
$9$	0.524744	−	0.440313i	0.174915	−	0.146771i
$10$		0			0
$11$	2.17413	−	3.76571i	0.655526	−	1.13540i	−0.326235	−	0.945289i	$-0.605780\pi$
$11$	2.17413	−	3.76571i	0.655526	−	1.13540i	0.981762	−	0.190116i	$-0.0608864\pi$
$12$	−1.53531	−	2.65924i	−0.443207	−	0.767657i
$13$	1.45826	+	0.530764i	0.404449	+	0.147207i	0.536231	−	0.844071i	$-0.319848\pi$
$13$	1.45826	+	0.530764i	0.404449	+	0.147207i	−0.131782	+	0.991279i	$0.542070\pi$
$14$	−0.449299	+	2.54810i	−0.120080	+	0.681008i
$15$		0			0
$16$	−1.65185	+	0.601224i	−0.412963	+	0.150306i
$17$	−4.87326	−	4.08915i	−1.18194	−	0.991765i	−0.999964	−	0.00846250i	$-0.997306\pi$
$17$	−4.87326	−	4.08915i	−1.18194	−	0.991765i	−0.181976	−	0.983303i	$-0.558249\pi$
$18$	0.433458			0.102167
$19$	0.708014	+	4.30101i	0.162429	+	0.986720i
$19$	0.708014	+	4.30101i	0.162429	+	0.986720i
$20$		0			0
$21$	6.01291	+	5.04543i	1.31213	+	1.10100i
$22$	2.58556	−	0.941068i	0.551244	−	0.200636i
$23$	0.583829	+	3.31106i	0.121737	+	0.690403i	0.983193	+	0.182571i	$0.0584419\pi$
$23$	0.583829	+	3.31106i	0.121737	+	0.690403i	−0.861456	+	0.507832i	$0.830447\pi$
$24$	0.759268	−	4.30602i	0.154985	−	0.878963i
$25$		0			0
$26$	0.490990	+	0.850420i	0.0962911	+	0.166781i
$27$	−2.22197	+	3.84857i	−0.427619	+	0.740658i
$28$	5.01042	−	4.20424i	0.946881	−	0.794527i
$29$	3.99325	−	3.35074i	0.741529	−	0.622216i	−0.191719	−	0.981450i	$-0.561406\pi$
$29$	3.99325	−	3.35074i	0.741529	−	0.622216i	0.933248	+	0.359233i	$0.116962\pi$
$30$		0			0
$31$	−3.28366	−	5.68747i	−0.589763	−	1.02150i	−0.994263	−	0.106961i	$-0.965888\pi$
$31$	−3.28366	−	5.68747i	−0.589763	−	1.02150i	0.404500	−	0.914538i	$-0.367445\pi$
$32$	−5.32603	−	1.93852i	−0.941518	−	0.342684i
$33$	1.44946	−	8.22028i	0.252318	−	1.43097i
$34$	−0.699019	−	3.96434i	−0.119881	−	0.679878i
$35$		0			0
$36$	−0.839375	−	0.704319i	−0.139896	−	0.117387i
$37$	−0.180685			−0.0297045			−0.0148522	−	0.999890i	$-0.504728\pi$
$37$	−0.180685			−0.0297045			−0.0148522	+	0.999890i	$0.504728\pi$
$38$	−1.40621	+	2.37284i	−0.228117	+	0.384926i
$39$	2.97899			0.477020
$40$		0			0
$41$	−0.0242217	+	0.00881597i	−0.00378279	+	0.00137682i	−0.343911	−	0.939002i	$-0.611752\pi$
$41$	−0.0242217	+	0.00881597i	−0.00378279	+	0.00137682i	0.340128	+	0.940379i	$0.389530\pi$
$42$	0.862490	+	4.89143i	0.133085	+	0.754763i
$43$	−0.793995	+	4.50297i	−0.121083	+	0.686696i	0.862474	+	0.506101i	$0.168914\pi$
$43$	−0.793995	+	4.50297i	−0.121083	+	0.686696i	−0.983557	+	0.180595i	$0.942198\pi$
$44$	−6.53598	−	2.37890i	−0.985336	−	0.358633i
$45$		0			0
$46$	−1.06375	+	1.84246i	−0.156841	+	0.271656i
$47$	1.09575	−	0.919441i	0.159831	−	0.134114i	−0.559365	−	0.828922i	$-0.688955\pi$
$47$	1.09575	−	0.919441i	0.159831	−	0.134114i	0.719196	+	0.694807i	$0.244510\pi$
$48$	−2.58498	+	2.16906i	−0.373110	+	0.313077i
$49$	−4.85976	+	8.41736i	−0.694252	+	1.20248i
$50$		0			0
$51$	−11.4755	−	4.17673i	−1.60689	−	0.584860i
$52$	0.431051	−	2.44461i	0.0597760	−	0.339006i
$53$	0.278010	+	1.57667i	0.0381876	+	0.216573i	0.997930	−	0.0643090i	$-0.0204843\pi$
$53$	0.278010	+	1.57667i	0.0381876	+	0.216573i	−0.959742	+	0.280882i	$0.909373\pi$
$54$	−2.64246	+	0.961776i	−0.359593	+	0.130881i
$55$		0			0
$56$	9.31361			1.24458
$57$	4.10101	+	7.29361i	0.543192	+	0.966063i
$58$	3.29857			0.433124
$59$	7.31281	+	6.13617i	0.952046	+	0.798862i	0.979641	−	0.200758i	$-0.0643403\pi$
$59$	7.31281	+	6.13617i	0.952046	+	0.798862i	−0.0275947	+	0.999619i	$0.508785\pi$
$60$		0			0
$61$	−1.05793	−	5.99980i	−0.135454	−	0.768195i	−0.974543	−	0.224201i	$-0.928023\pi$
$61$	−1.05793	−	5.99980i	−0.135454	−	0.768195i	0.839089	−	0.543994i	$-0.183088\pi$
$62$	0.721625	−	4.09254i	0.0916464	−	0.519753i
$63$	2.63203	+	0.957982i	0.331605	+	0.120694i
$64$	−0.0353865	−	0.0612913i	−0.00442332	−	0.00766141i
$65$		0			0
$66$	4.04615	−	3.39513i	0.498047	−	0.417911i
$67$	−7.87159	+	6.60505i	−0.961668	+	0.806935i	−0.981224	−	0.192874i	$-0.938219\pi$
$67$	−7.87159	+	6.60505i	−0.961668	+	0.806935i	0.0195559	+	0.999809i	$0.493775\pi$
$68$	−5.08797	+	8.81262i	−0.617007	+	1.06869i
$69$	3.22704	+	5.58940i	0.388490	+	0.672884i
$70$		0			0
$71$	−1.88710	+	10.7023i	−0.223957	+	1.27012i	0.640711	+	0.767782i	$0.278640\pi$
$71$	−1.88710	+	10.7023i	−0.223957	+	1.27012i	−0.864669	+	0.502343i	$0.832472\pi$
$72$	−0.270938	−	1.53657i	−0.0319303	−	0.181086i
$73$	−12.7987	+	4.65836i	−1.49798	+	0.545220i	−0.955536	−	0.294873i	$-0.904723\pi$
$73$	−12.7987	+	4.65836i	−1.49798	+	0.545220i	−0.542443	+	0.840093i	$0.682500\pi$
$74$	−0.0875850	−	0.0734926i	−0.0101816	−	0.00854334i
$75$		0			0
$76$	6.57867	−	2.31000i	0.754625	−	0.264975i
$77$	17.7799			2.02620
$78$	1.44403	+	1.21168i	0.163504	+	0.137196i
$79$	−16.2283	+	5.90661i	−1.82582	+	0.664545i	−0.831839	+	0.555016i	$0.812712\pi$
$79$	−16.2283	+	5.90661i	−1.82582	+	0.664545i	−0.993984	+	0.109529i	$0.965066\pi$
$80$		0			0
$81$	−1.83820	+	10.4250i	−0.204245	+	1.15833i
$82$	−0.0153270	−	0.00557858i	−0.00169259	−	0.000616051i
$83$	−2.57831	−	4.46577i	−0.283007	−	0.490182i	0.689117	−	0.724650i	$-0.257999\pi$
$83$	−2.57831	−	4.46577i	−0.283007	−	0.490182i	−0.972124	+	0.234468i	$0.924665\pi$
$84$	6.27783	−	10.8735i	0.684967	−	1.18640i
$85$		0			0
$86$	−2.21643	+	1.85981i	−0.239004	+	0.200548i
$87$	5.00336	−	8.66608i	0.536417	−	0.929101i
$88$	−4.95213	−	8.57735i	−0.527899	−	0.914348i
$89$	0.477195	+	0.173685i	0.0505826	+	0.0184106i	0.367188	−	0.930147i	$-0.380321\pi$
$89$	0.477195	+	0.173685i	0.0505826	+	0.0184106i	−0.316605	+	0.948557i	$0.602543\pi$
$90$		0			0
$91$	1.10187	+	6.24904i	0.115508	+	0.655077i
$92$	5.05370	−	1.83940i	0.526885	−	0.191770i
$93$	−9.65742	−	8.10354i	−1.00143	−	0.840298i
$94$	0.905127			0.0933567
$95$		0			0
$96$	−10.8802			−1.11046
$97$	−2.51273	−	2.10843i	−0.255129	−	0.214079i	0.506248	−	0.862388i	$-0.331032\pi$
$97$	−2.51273	−	2.10843i	−0.255129	−	0.214079i	−0.761377	+	0.648309i	$0.775476\pi$
$98$	−5.77942	+	2.10354i	−0.583809	+	0.212489i
$99$	−0.517226	−	2.93333i	−0.0519832	−	0.294811i
$100$		0			0
$101$	3.27996	+	1.19381i	0.326369	+	0.118788i	0.500008	−	0.866021i	$-0.333330\pi$
$101$	3.27996	+	1.19381i	0.326369	+	0.118788i	−0.173639	+	0.984809i	$0.555553\pi$
$102$	−3.86374	−	6.69220i	−0.382567	−	0.662626i
$103$	4.31572	−	7.47504i	0.425240	−	0.736537i	−0.571203	−	0.820809i	$-0.693523\pi$
$103$	4.31572	−	7.47504i	0.425240	−	0.736537i	0.996443	+	0.0842716i	$0.0268563\pi$
$104$	2.70776	−	2.27208i	0.265517	−	0.222796i
$105$		0			0
$106$	−0.506539	+	0.877351i	−0.0491994	+	0.0852159i
$107$	3.13732	+	5.43399i	0.303296	+	0.525324i	0.976880	−	0.213786i	$-0.0685796\pi$
$107$	3.13732	+	5.43399i	0.303296	+	0.525324i	−0.673584	+	0.739110i	$0.735246\pi$
$108$	6.67980	+	2.43125i	0.642764	+	0.233947i
$109$	1.71297	−	9.71476i	0.164073	−	0.930506i	−0.785942	−	0.618301i	$-0.787821\pi$
$109$	1.71297	−	9.71476i	0.164073	−	0.930506i	0.950015	−	0.312205i	$-0.101068\pi$
$110$		0			0
$111$	−0.325933	+	0.118630i	−0.0309361	+	0.0112598i
$112$	−5.50619	−	4.62024i	−0.520286	−	0.436571i
$113$	5.24756			0.493649			0.246825	−	0.969060i	$-0.420613\pi$
$113$	5.24756			0.493649			0.246825	+	0.969060i	$0.420613\pi$
$114$	−0.978713	+	5.20355i	−0.0916648	+	0.487357i
$115$		0			0
$116$	−6.38756	−	5.35980i	−0.593071	−	0.497645i
$117$	0.998916	−	0.363576i	0.0923499	−	0.0336126i
$118$	1.04895	+	5.94887i	0.0965634	+	0.547638i
$119$	4.51698	−	25.6171i	0.414071	−	2.34831i
$120$		0			0
$121$	−3.95372	−	6.84804i	−0.359429	−	0.622550i
$122$	1.92756	−	3.33863i	0.174513	−	0.302266i
$123$	−0.0379046	+	0.0318057i	−0.00341774	+	0.00286782i
$124$	−8.04731	+	6.75249i	−0.722669	+	0.606392i
$125$		0			0
$126$	0.886194	+	1.53493i	0.0789484	+	0.136743i
$127$	5.00719	+	1.82247i	0.444316	+	0.161718i	0.554482	−	0.832195i	$-0.312916\pi$
$127$	5.00719	+	1.82247i	0.444316	+	0.161718i	−0.110167	+	0.993913i	$0.535138\pi$
$128$	−1.96064	+	11.1194i	−0.173298	+	0.982822i
$129$	1.52418	+	8.64406i	0.134197	+	0.761067i
$130$		0			0
$131$	−1.31194	−	1.10085i	−0.114625	−	0.0961816i	0.583674	−	0.811988i	$-0.301615\pi$
$131$	−1.31194	−	1.10085i	−0.114625	−	0.0961816i	−0.698298	+	0.715807i	$0.746059\pi$
$132$	−13.3519			−1.16214
$133$	−13.7830	+	11.3005i	−1.19513	+	0.979877i
$134$	−6.50222			−0.561706
$135$		0			0
$136$	−13.6163	+	4.95591i	−1.16758	+	0.424966i
$137$	−0.997739	−	5.65846i	−0.0852426	−	0.483435i	−0.997304	−	0.0733811i	$-0.976621\pi$
$137$	−0.997739	−	5.65846i	−0.0852426	−	0.483435i	0.912061	−	0.410054i	$-0.134490\pi$
$138$	−0.709182	+	4.02197i	−0.0603695	+	0.342373i
$139$	16.5249	+	6.01458i	1.40162	+	0.510150i	0.928660	−	0.370932i	$-0.120962\pi$
$139$	16.5249	+	6.01458i	1.40162	+	0.510150i	0.472965	+	0.881081i	$0.343184\pi$
$140$		0			0
$141$	1.37292	−	2.37797i	0.115621	−	0.200261i
$142$	−5.26782	+	4.42023i	−0.442066	+	0.370937i
$143$	5.16916	−	4.33744i	0.432267	−	0.362715i
$144$	−0.602072	+	1.04282i	−0.0501727	+	0.0869016i
$145$		0			0
$146$	−8.09879	−	2.94772i	−0.670261	−	0.243955i
$147$	−3.23992	+	18.3745i	−0.267224	+	1.51550i
$148$	0.0501882	+	0.284631i	0.00412544	+	0.0233966i
$149$	−10.3558	+	3.76921i	−0.848381	+	0.308785i	−0.729380	−	0.684109i	$-0.760191\pi$
$149$	−10.3558	+	3.76921i	−0.848381	+	0.308785i	−0.119001	+	0.992894i	$0.537969\pi$
$150$		0			0
$151$	−2.37114			−0.192960			−0.0964802	−	0.995335i	$-0.530758\pi$
$151$	−2.37114			−0.192960			−0.0964802	+	0.995335i	$0.530758\pi$
$152$	9.29047	+	3.50170i	0.753557	+	0.284025i
$153$	−4.35772			−0.352301
$154$	8.61857	+	7.23184i	0.694504	+	0.582758i
$155$		0			0
$156$	−0.827461	−	4.69276i	−0.0662499	−	0.375722i
$157$	0.561125	−	3.18230i	0.0447827	−	0.253975i	−0.954195	−	0.299186i	$-0.903285\pi$
$157$	0.561125	−	3.18230i	0.0447827	−	0.253975i	0.998977	+	0.0452110i	$0.0143960\pi$
$158$	−10.2689	−	3.73759i	−0.816952	−	0.297346i
$159$	1.53666	+	2.66158i	0.121865	+	0.211077i
$160$		0			0
$161$	−10.5313	+	8.83679i	−0.829981	+	0.696437i
$162$	−5.13133	+	4.30570i	−0.403155	+	0.338288i
$163$	3.29087	−	5.69996i	0.257761	−	0.446455i	−0.707881	−	0.706332i	$-0.750349\pi$
$163$	3.29087	−	5.69996i	0.257761	−	0.446455i	0.965642	+	0.259877i	$0.0836819\pi$
$164$	0.0206156	+	0.0357074i	0.00160981	+	0.00278828i
$165$		0			0
$166$	0.566616	−	3.21344i	0.0439780	−	0.249411i
$167$	−2.75277	−	15.6118i	−0.213016	−	1.20807i	−0.884316	−	0.466888i	$-0.845375\pi$
$167$	−2.75277	−	15.6118i	−0.213016	−	1.20807i	0.671300	−	0.741185i	$-0.265736\pi$
$168$	16.8005	−	6.11489i	1.29619	−	0.471774i
$169$	−8.11376	−	6.80825i	−0.624135	−	0.523712i
$170$		0			0
$171$	2.26532	+	1.94518i	0.173233	+	0.148752i
$172$	7.31401			0.557688
$173$	1.45639	+	1.22206i	0.110728	+	0.0929114i	0.696470	−	0.717585i	$-0.254753\pi$
$173$	1.45639	+	1.22206i	0.110728	+	0.0929114i	−0.585743	+	0.810497i	$0.699197\pi$
$174$	5.95019	−	2.16569i	0.451083	−	0.164181i
$175$		0			0
$176$	−1.32731	+	7.52753i	−0.100050	+	0.567409i
$177$	17.2201	+	6.26759i	1.29434	+	0.471101i
$178$	0.160670	+	0.278288i	0.0120427	+	0.0208586i
$179$	7.14016	−	12.3671i	0.533681	−	0.924362i	−0.465545	−	0.885024i	$-0.654142\pi$
$179$	7.14016	−	12.3671i	0.533681	−	0.924362i	0.999226	−	0.0393383i	$-0.0125250\pi$
$180$		0			0
$181$	11.0202	−	9.24705i	0.819125	−	0.687328i	−0.133642	−	0.991030i	$-0.542667\pi$
$181$	11.0202	−	9.24705i	0.819125	−	0.687328i	0.952767	+	0.303702i	$0.0982227\pi$
$182$	−2.00763	+	3.47733i	−0.148816	+	0.257756i
$183$	−5.84755	−	10.1283i	−0.432263	−	0.748702i
$184$	7.19626	+	2.61922i	0.530515	+	0.193092i
$185$		0			0
$186$	−1.38526	−	7.85619i	−0.101572	−	0.576043i
$187$	−25.9937	+	9.46093i	−1.90085	+	0.691852i
$188$	−1.75274	−	1.47073i	−0.127832	−	0.107264i
$189$	−18.1711			−1.32175
$190$		0			0
$191$	24.1791			1.74954			0.874769	−	0.484540i	$-0.161013\pi$
$191$	24.1791			1.74954			0.874769	+	0.484540i	$0.161013\pi$
$192$	−0.104074	−	0.0873282i	−0.00751087	−	0.00630237i
$193$	−4.80540	+	1.74902i	−0.345900	+	0.125897i	−0.509128	−	0.860691i	$-0.670032\pi$
$193$	−4.80540	+	1.74902i	−0.345900	+	0.125897i	0.163227	+	0.986588i	$0.447810\pi$
$194$	−0.360425	−	2.04407i	−0.0258770	−	0.146756i
$195$		0			0
$196$	14.6096	+	5.31747i	1.04355	+	0.379819i
$197$	0.0321431	+	0.0556735i	0.00229010	+	0.00396658i	0.867168	−	0.498015i	$-0.165938\pi$
$197$	0.0321431	+	0.0556735i	0.00229010	+	0.00396658i	−0.864878	+	0.501982i	$0.832604\pi$
$198$	0.942395	−	1.63228i	0.0669731	−	0.116001i
$199$	−4.88735	+	4.10098i	−0.346455	+	0.290711i	−0.799365	−	0.600846i	$-0.794831\pi$
$199$	−4.88735	+	4.10098i	−0.346455	+	0.290711i	0.452910	+	0.891556i	$0.350386\pi$
$200$		0			0
$201$	−9.86274	+	17.0828i	−0.695664	+	1.20493i
$202$	1.10435	+	1.91279i	0.0777017	+	0.134583i
$203$	20.0295	+	7.29015i	1.40580	+	0.511668i
$204$	−3.39206	+	19.2373i	−0.237492	+	1.34688i
$205$		0			0
$206$	5.13241	−	1.86805i	0.357592	−	0.130153i
$207$	1.76426	+	1.48039i	0.122625	+	0.102894i
$208$	−2.72794			−0.189149
$209$	17.7357	+	6.68481i	1.22680	+	0.462398i
$210$		0			0
$211$	−4.52874	−	3.80006i	−0.311771	−	0.261607i	0.473453	−	0.880819i	$-0.343008\pi$
$211$	−4.52874	−	3.80006i	−0.311771	−	0.261607i	−0.785224	+	0.619212i	$0.787452\pi$
$212$	2.40649	−	0.875891i	0.165278	−	0.0601564i
$213$	3.62254	+	20.5445i	0.248212	+	1.40768i
$214$	−0.689464	+	3.91015i	−0.0471308	+	0.267292i
$215$		0			0
$216$	5.06110	+	8.76609i	0.344364	+	0.596457i
$217$	13.4267	−	23.2558i	0.911466	−	1.57870i
$218$	4.78176	−	4.01237i	0.323862	−	0.271752i
$219$	−20.0288	+	16.8061i	−1.35342	+	1.13565i
$220$		0			0
$221$	−4.93612	−	8.54961i	−0.332039	−	0.575109i
$222$	−0.206244	−	0.0750666i	−0.0138422	−	0.00503814i
$223$	5.09043	−	28.8693i	0.340881	−	1.93323i	−0.0179785	−	0.999838i	$-0.505723\pi$
$223$	5.09043	−	28.8693i	0.340881	−	1.93323i	0.358859	−	0.933392i	$-0.383166\pi$
$224$	−4.02439	−	22.8234i	−0.268891	−	1.52495i
$225$		0			0
$226$	2.54369	+	2.13441i	0.169204	+	0.141979i
$227$	−8.00202			−0.531113			−0.265557	−	0.964095i	$-0.585556\pi$
$227$	−8.00202			−0.531113			−0.265557	+	0.964095i	$0.585556\pi$
$228$	10.3504	−	8.48619i	0.685473	−	0.562012i
$229$	28.2694			1.86809			0.934047	−	0.357150i	$-0.116251\pi$
$229$	28.2694			1.86809			0.934047	+	0.357150i	$0.116251\pi$
$230$		0			0
$231$	32.0725	−	11.6734i	2.11022	−	0.768056i
$232$	−2.06181	−	11.6931i	−0.135365	−	0.767691i
$233$	1.18970	−	6.74715i	0.0779401	−	0.442020i	−0.920718	−	0.390229i	$-0.872396\pi$
$233$	1.18970	−	6.74715i	0.0779401	−	0.442020i	0.998658	−	0.0517912i	$-0.0164930\pi$
$234$	0.632095	+	0.230064i	0.0413213	+	0.0150397i
$235$		0			0
$236$	7.63499	−	13.2242i	0.496996	−	0.860821i
$237$	−25.3957	+	21.3095i	−1.64963	+	1.38420i
$238$	12.6091	−	10.5803i	0.817328	−	0.685820i
$239$	6.69674	−	11.5991i	0.433176	−	0.750283i	−0.563969	−	0.825796i	$-0.690726\pi$
$239$	6.69674	−	11.5991i	0.433176	−	0.750283i	0.997145	+	0.0755132i	$0.0240595\pi$
$240$		0			0
$241$	24.1069	+	8.77421i	1.55286	+	0.565196i	0.969087	−	0.246717i	$-0.0793520\pi$
$241$	24.1069	+	8.77421i	1.55286	+	0.565196i	0.583777	+	0.811914i	$0.301574\pi$
$242$	0.868879	−	4.92766i	0.0558536	−	0.316762i
$243$	1.21363	+	6.88283i	0.0778543	+	0.441534i
$244$	−9.15755	+	3.33308i	−0.586252	+	0.213378i
$245$		0			0
$246$	−0.0313106			−0.00199629
$247$	−1.25035	+	6.64779i	−0.0795581	+	0.422989i
$248$	−14.9587			−0.949879
$249$	−7.58296	−	6.36286i	−0.480551	−	0.403230i
$250$		0			0
$251$	−1.58376	−	8.98194i	−0.0999660	−	0.566935i	−0.993112	−	0.117168i	$-0.962618\pi$
$251$	−1.58376	−	8.98194i	−0.0999660	−	0.566935i	0.893146	−	0.449767i	$-0.148493\pi$
$252$	0.778008	−	4.41230i	0.0490099	−	0.277949i
$253$	13.7378	+	5.00015i	0.863688	+	0.314357i
$254$	1.68590	+	2.92006i	0.105783	+	0.183221i
$255$		0			0
$256$	−5.58156	+	4.68348i	−0.348847	+	0.292718i
$257$	18.9570	−	15.9068i	1.18250	−	0.992237i	0.182543	−	0.983198i	$-0.441567\pi$
$257$	18.9570	−	15.9068i	1.18250	−	0.992237i	0.999959	−	0.00903962i	$-0.00287744\pi$
$258$	−2.77709	+	4.81006i	−0.172894	+	0.299461i
$259$	−0.369407	−	0.639831i	−0.0229538	−	0.0397572i
$260$		0			0
$261$	0.620065	−	3.51656i	0.0383810	−	0.217670i
$262$	−0.188184	−	1.06725i	−0.0116261	−	0.0659347i
$263$	−13.7492	+	5.00428i	−0.847809	+	0.308577i	−0.729147	−	0.684357i	$-0.760083\pi$
$263$	−13.7492	+	5.00428i	−0.847809	+	0.308577i	−0.118662	+	0.992935i	$0.537861\pi$
$264$	−14.5645	−	12.2211i	−0.896382	−	0.752154i
$265$		0			0
$266$	−11.2775	−	0.128351i	−0.691469	−	0.00786969i
$267$	0.974832			0.0596587
$268$	12.5913	+	10.5654i	0.769136	+	0.645382i
$269$	−16.1661	+	5.88396i	−0.985662	+	0.358752i	−0.784039	−	0.620712i	$-0.786844\pi$
$269$	−16.1661	+	5.88396i	−0.985662	+	0.358752i	−0.201623	+	0.979463i	$0.564622\pi$
$270$		0			0
$271$	2.37389	−	13.4630i	0.144203	−	0.817819i	−0.823800	−	0.566881i	$-0.808150\pi$
$271$	2.37389	−	13.4630i	0.144203	−	0.817819i	0.968003	−	0.250938i	$-0.0807389\pi$
$272$	10.5084	+	3.82475i	0.637165	+	0.231909i
$273$	6.09047	+	10.5490i	0.368612	+	0.638455i
$274$	1.81790	−	3.14869i	0.109823	−	0.190220i
$275$		0			0
$276$	7.90854	−	6.63606i	0.476038	−	0.399444i
$277$	−6.72984	+	11.6564i	−0.404357	+	0.700367i	−0.994246	−	0.107117i	$-0.965838\pi$
$277$	−6.72984	+	11.6564i	−0.404357	+	0.700367i	0.589889	+	0.807484i	$0.299171\pi$
$278$	5.56386	+	9.63689i	0.333698	+	0.577982i
$279$	−4.22735	−	1.53863i	−0.253085	−	0.0921152i
$280$		0			0
$281$	−3.03476	−	17.2110i	−0.181039	−	1.02672i	−0.930940	−	0.365172i	$-0.881010\pi$
$281$	−3.03476	−	17.2110i	−0.181039	−	1.02672i	0.749901	−	0.661550i	$-0.230101\pi$
$282$	1.63273	−	0.594265i	0.0972276	−	0.0353880i
$283$	16.1126	+	13.5201i	0.957794	+	0.803684i	0.980593	−	0.196056i	$-0.0628133\pi$
$283$	16.1126	+	13.5201i	0.957794	+	0.803684i	−0.0227990	+	0.999740i	$0.507258\pi$
$284$	17.3833			1.03151
$285$		0			0
$286$	4.26991			0.252485
$287$	−0.0807392	−	0.0677483i	−0.00476589	−	0.00399905i
$288$	−3.64836	+	1.32789i	−0.214981	+	0.0782468i
$289$	4.07550	+	23.1133i	0.239735	+	1.35961i
$290$		0			0
$291$	−5.91693	−	2.15359i	−0.346857	−	0.126246i
$292$	10.8933	+	18.8678i	0.637483	+	1.10415i
$293$	−5.36574	+	9.29373i	−0.313470	+	0.542945i	−0.979111	−	0.203326i	$-0.934825\pi$
$293$	−5.36574	+	9.29373i	−0.313470	+	0.542945i	0.665641	+	0.746272i	$0.268158\pi$
$294$	−9.04422	+	7.58900i	−0.527470	+	0.442600i
$295$		0			0
$296$	−0.205778	+	0.356418i	−0.0119606	+	0.0207164i
$297$	9.66174	+	16.7346i	0.560631	+	0.971042i
$298$	−6.55295	−	2.38508i	−0.379602	−	0.138164i
$299$	−0.906014	+	5.13826i	−0.0523962	+	0.297153i
$300$		0			0
$301$	−17.5689	+	6.39457i	−1.01266	+	0.368577i
$302$	−1.14938	−	0.964444i	−0.0661394	−	0.0554975i
$303$	6.70042			0.384929
$304$	−3.75541	−	6.67896i	−0.215387	−	0.383064i
$305$		0			0
$306$	−2.11235	−	1.77248i	−0.120755	−	0.101326i
$307$	−2.54584	+	0.926610i	−0.145299	+	0.0528845i	−0.413646	−	0.910438i	$-0.635745\pi$
$307$	−2.54584	+	0.926610i	−0.145299	+	0.0528845i	0.268347	+	0.963322i	$0.413523\pi$
$308$	−4.93864	−	28.0084i	−0.281405	−	1.59593i
$309$	2.87721	−	16.3175i	0.163679	−	0.928269i
$310$		0			0
$311$	3.62852	+	6.28478i	0.205755	+	0.356377i	0.950373	−	0.311113i	$-0.100702\pi$
$311$	3.62852	+	6.28478i	0.205755	+	0.356377i	−0.744618	+	0.667491i	$0.767368\pi$
$312$	3.39269	−	5.87632i	0.192073	−	0.332681i
$313$	6.64853	−	5.57878i	0.375797	−	0.315331i	−0.435253	−	0.900308i	$-0.643341\pi$
$313$	6.64853	−	5.57878i	0.375797	−	0.315331i	0.811050	+	0.584977i	$0.198897\pi$
$314$	1.56638	−	1.31435i	0.0883958	−	0.0741729i
$315$		0			0
$316$	13.8123	+	23.9235i	0.777000	+	1.34580i
$317$	−30.0020	−	10.9198i	−1.68508	−	0.613319i	−0.691089	−	0.722770i	$-0.742869\pi$
$317$	−30.0020	−	10.9198i	−1.68508	−	0.613319i	−0.993992	+	0.109451i	$0.965091\pi$
$318$	−0.337701	+	1.91520i	−0.0189373	+	0.107399i
$319$	−3.93604	−	22.3224i	−0.220376	−	1.24981i
$320$		0			0
$321$	9.22702	+	7.74239i	0.515002	+	0.432138i
$322$	−8.69922			−0.484788
$323$	14.1372	−	23.8551i	0.786613	−	1.32734i
$324$	16.9329			0.940717
$325$		0			0
$326$	3.91363	−	1.42445i	0.216756	−	0.0788928i
$327$	−3.28829	−	18.6488i	−0.181843	−	1.03128i
$328$	−0.0101952	+	0.0578197i	−0.000562935	+	0.00319256i
$329$	5.49609	+	2.00041i	0.303009	+	0.110286i
$330$		0			0
$331$	−12.1500	+	21.0443i	−0.667822	+	1.15670i	0.310690	+	0.950511i	$0.399440\pi$
$331$	−12.1500	+	21.0443i	−0.667822	+	1.15670i	−0.978512	+	0.206190i	$0.933893\pi$
$332$	−6.31871	+	5.30202i	−0.346784	+	0.290986i
$333$	−0.0948136	+	0.0795580i	−0.00519575	+	0.00435975i
$334$	5.01560	−	8.68728i	0.274442	−	0.475347i
$335$		0			0
$336$	−12.9659	−	4.71919i	−0.707346	−	0.257453i
$337$	−4.92922	+	27.9550i	−0.268512	+	1.52280i	0.490334	+	0.871534i	$0.336875\pi$
$337$	−4.92922	+	27.9550i	−0.268512	+	1.52280i	−0.758846	+	0.651270i	$0.774236\pi$
$338$	−1.16384	−	6.60044i	−0.0633043	−	0.359016i
$339$	9.46591	−	3.44531i	0.514118	−	0.187124i
$340$		0			0
$341$	−28.5565			−1.54642
$342$	0.306894	+	1.86431i	0.0165949	+	0.100810i
$343$	−11.1200			−0.600424
$344$	7.97824	+	6.69454i	0.430158	+	0.360945i
$345$		0			0
$346$	0.208905	+	1.18476i	0.0112308	+	0.0636929i
$347$	5.40071	−	30.6289i	0.289925	−	1.64425i	−0.397217	−	0.917725i	$-0.630024\pi$
$347$	5.40071	−	30.6289i	0.289925	−	1.64425i	0.687142	−	0.726523i	$-0.258865\pi$
$348$	−15.0413	−	5.47460i	−0.806300	−	0.293469i
$349$	−8.73989	−	15.1379i	−0.467836	−	0.810315i	0.531489	−	0.847065i	$-0.321633\pi$
$349$	−8.73989	−	15.1379i	−0.467836	−	0.810315i	−0.999324	+	0.0367503i	$0.988299\pi$
$350$		0			0
$351$	−5.28290	+	4.43288i	−0.281981	+	0.236610i
$352$	−18.8794	+	15.8417i	−1.00627	+	0.844365i
$353$	−4.41270	+	7.64303i	−0.234865	+	0.406797i	−0.959233	−	0.282615i	$-0.908798\pi$
$353$	−4.41270	+	7.64303i	−0.234865	+	0.406797i	0.724369	+	0.689413i	$0.242131\pi$
$354$	5.79792	+	10.0423i	0.308156	+	0.533742i
$355$		0			0
$356$	0.141055	−	0.799964i	0.00747591	−	0.0423980i
$357$	−8.67096	−	49.1755i	−0.458916	−	2.60264i
$358$	8.49136	−	3.09060i	0.448782	−	0.163343i
$359$	15.2610	+	12.8055i	0.805443	+	0.675847i	0.949515	−	0.313720i	$-0.101575\pi$
$359$	15.2610	+	12.8055i	0.805443	+	0.675847i	−0.144073	+	0.989567i	$0.546020\pi$
$360$		0			0
$361$	−17.9974	+	6.09035i	−0.947233	+	0.320545i
$362$	9.10309			0.478448
$363$	−11.6281	−	9.75714i	−0.610317	−	0.512117i
$364$	9.53797	−	3.47154i	0.499925	−	0.181958i
$365$		0			0
$366$	1.28507	−	7.28800i	0.0671718	−	0.380950i
$367$	7.94641	+	2.89226i	0.414799	+	0.150975i	0.540985	−	0.841032i	$-0.318051\pi$
$367$	7.94641	+	2.89226i	0.414799	+	0.150975i	−0.126186	+	0.992007i	$0.540274\pi$
$368$	−2.95509	−	5.11836i	−0.154044	−	0.266813i
$369$	−0.00882841	+	0.0152912i	−0.000459589	+	0.000796031i
$370$		0			0
$371$	−5.01483	+	4.20794i	−0.260357	+	0.218465i
$372$	−10.0829	+	17.4641i	−0.522774	+	0.905471i
$373$	−3.56895	−	6.18160i	−0.184793	−	0.320071i	0.758714	−	0.651424i	$-0.225828\pi$
$373$	−3.56895	−	6.18160i	−0.184793	−	0.320071i	−0.943507	+	0.331353i	$0.892495\pi$
$374$	−16.4483	−	5.98669i	−0.850522	−	0.309565i
$375$		0			0
$376$	−0.565760	−	3.20859i	−0.0291769	−	0.165470i
$377$	7.60166	−	2.76678i	0.391505	−	0.142496i
$378$	−8.80822	−	7.39097i	−0.453046	−	0.380151i
$379$	6.11358			0.314033			0.157017	−	0.987596i	$-0.449812\pi$
$379$	6.11358			0.314033			0.157017	+	0.987596i	$0.449812\pi$
$380$		0			0
$381$	10.2289			0.524040
$382$	11.7205	+	9.83469i	0.599674	+	0.503186i
$383$	0.492206	−	0.179148i	0.0251505	−	0.00915404i	−0.329414	−	0.944185i	$-0.606851\pi$
$383$	0.492206	−	0.179148i	0.0251505	−	0.00915404i	0.354565	+	0.935031i	$0.384629\pi$
$384$	3.76372	+	21.3451i	0.192067	+	1.08926i
$385$		0			0
$386$	−3.04076	−	1.10675i	−0.154771	−	0.0563319i
$387$	1.56607	+	2.71251i	0.0796078	+	0.137885i
$388$	−2.62343	+	4.54392i	−0.133185	+	0.230683i
$389$	−1.91233	+	1.60464i	−0.0969590	+	0.0813583i	−0.689979	−	0.723830i	$-0.742380\pi$
$389$	−1.91233	+	1.60464i	−0.0969590	+	0.0813583i	0.593020	+	0.805188i	$0.297936\pi$
$390$		0			0
$391$	10.6943	−	18.5230i	0.540832	−	0.936749i
$392$	11.0693	+	19.1726i	0.559085	+	0.968364i
$393$	−3.08933	−	1.12443i	−0.155836	−	0.0567198i
$394$	−0.00706385	+	0.0400611i	−0.000355872	+	0.00201825i
$395$		0			0
$396$	−4.47718	+	1.62956i	−0.224987	+	0.0818884i
$397$	2.21214	+	1.85621i	0.111024	+	0.0931604i	0.696610	−	0.717450i	$-0.254691\pi$
$397$	2.21214	+	1.85621i	0.111024	+	0.0931604i	−0.585586	+	0.810611i	$0.699135\pi$
$398$	−4.03713			−0.202363
$399$	−17.4433	+	29.4339i	−0.873255	+	1.47354i
$400$		0			0
$401$	−13.2096	−	11.0842i	−0.659658	−	0.553519i	0.250326	−	0.968162i	$-0.419462\pi$
$401$	−13.2096	−	11.0842i	−0.659658	−	0.553519i	−0.909984	+	0.414643i	$0.863907\pi$
$402$	−11.7291	+	4.26906i	−0.584997	+	0.212921i
$403$	−1.76973	−	10.0367i	−0.0881567	−	0.499962i
$404$	0.969531	−	5.49848i	0.0482360	−	0.273560i
$405$		0			0
$406$	6.74385	+	11.6807i	0.334692	+	0.579703i
$407$	−0.392834	+	0.680409i	−0.0194721	+	0.0337266i
$408$	−21.3081	+	17.8796i	−1.05491	+	0.885173i
$409$	−20.0017	+	16.7834i	−0.989019	+	0.829886i	−0.985425	−	0.170108i	$-0.945588\pi$
$409$	−20.0017	+	16.7834i	−0.989019	+	0.829886i	−0.00359375	+	0.999994i	$0.501144\pi$
$410$		0			0
$411$	−5.51488	−	9.55205i	−0.272029	−	0.471168i
$412$	−12.9741	−	4.72218i	−0.639188	−	0.232645i
$413$	−6.77817	+	38.4409i	−0.333532	+	1.89155i
$414$	0.253065	+	1.43520i	0.0124375	+	0.0705364i
$415$		0			0
$416$	−6.73785	−	5.65373i	−0.330350	−	0.277197i
$417$	33.7577			1.65312
$418$	5.87816	+	10.4543i	0.287510	+	0.511334i
$419$	−0.112702			−0.00550586			−0.00275293	−	0.999996i	$-0.500876\pi$
$419$	−0.112702			−0.00550586			−0.00275293	+	0.999996i	$0.500876\pi$
$420$		0			0
$421$	−18.9996	+	6.91529i	−0.925985	+	0.337031i	−0.760617	−	0.649201i	$-0.775103\pi$
$421$	−18.9996	+	6.91529i	−0.925985	+	0.337031i	−0.165368	+	0.986232i	$0.552881\pi$
$422$	−0.649600	−	3.68407i	−0.0316221	−	0.179338i
$423$	0.170145	−	0.964943i	0.00827275	−	0.0469171i
$424$	3.42674	+	1.24723i	0.166417	+	0.0605710i
$425$		0			0
$426$	−6.60034	+	11.4321i	−0.319787	+	0.553888i
$427$	19.0832	−	16.0127i	0.923500	−	0.774909i
$428$	7.68866	−	6.45156i	0.371646	−	0.311848i
$429$	6.47672	−	11.2180i	0.312699	−	0.541610i
$430$		0			0
$431$	38.1011	+	13.8677i	1.83526	+	0.667982i	0.991306	+	0.131573i	$0.0420028\pi$
$431$	38.1011	+	13.8677i	1.83526	+	0.667982i	0.843958	+	0.536409i	$0.180219\pi$
$432$	1.35651	−	7.69317i	0.0652653	−	0.370138i
$433$	3.95457	+	22.4275i	0.190044	+	1.07779i	0.919301	+	0.393555i	$0.128755\pi$
$433$	3.95457	+	22.4275i	0.190044	+	1.07779i	−0.729257	+	0.684240i	$0.760134\pi$
$434$	15.9676	−	5.81172i	0.766468	−	0.278972i
$435$		0			0
$436$	−15.7794			−0.755694
$437$	−13.8275	+	4.85533i	−0.661461	+	0.232262i
$438$	−16.5445			−0.790526
$439$	−25.0285	−	21.0014i	−1.19455	−	1.00234i	−0.999769	−	0.0214950i	$-0.993157\pi$
$439$	−25.0285	−	21.0014i	−1.19455	−	1.00234i	−0.194777	−	0.980848i	$-0.562398\pi$
$440$		0			0
$441$	1.15614	+	6.55677i	0.0550541	+	0.312227i
$442$	1.08477	−	6.15205i	0.0515974	−	0.292623i
$443$	−13.0384	−	4.74560i	−0.619475	−	0.225470i	0.0131689	−	0.999913i	$-0.495808\pi$
$443$	−13.0384	−	4.74560i	−0.619475	−	0.225470i	−0.632644	+	0.774443i	$0.718030\pi$
$444$	0.277409	+	0.480486i	0.0131652	+	0.0228029i
$445$		0			0
$446$	14.2099	−	11.9235i	0.672859	−	0.564596i
$447$	−16.2058	+	13.5983i	−0.766510	+	0.643178i
$448$	0.144694	−	0.250617i	0.00683614	−	0.0118405i
$449$	3.00375	+	5.20265i	0.141756	+	0.245528i	0.928158	−	0.372187i	$-0.121392\pi$
$449$	3.00375	+	5.20265i	0.141756	+	0.245528i	−0.786402	+	0.617715i	$0.788059\pi$
$450$		0			0
$451$	−0.0194628	+	0.110379i	−0.000916467	+	0.00519754i
$452$	−1.45759	−	8.26642i	−0.0685594	−	0.388820i
$453$	−4.27722	+	1.55678i	−0.200961	+	0.0731439i
$454$	−3.87889	−	3.25477i	−0.182045	−	0.152754i
$455$		0			0
$456$	19.0578	+	0.216899i	0.892465	+	0.0101572i
$457$	23.9751			1.12151			0.560754	−	0.827982i	$-0.310511\pi$
$457$	23.9751			1.12151			0.560754	+	0.827982i	$0.310511\pi$
$458$	13.7032	+	11.4984i	0.640311	+	0.537285i
$459$	26.5657	−	9.66912i	1.23998	−	0.451316i
$460$		0			0
$461$	−6.26625	+	35.5376i	−0.291848	+	1.65515i	0.387896	+	0.921703i	$0.373202\pi$
$461$	−6.26625	+	35.5376i	−0.291848	+	1.65515i	−0.679744	+	0.733450i	$0.737909\pi$
$462$	20.2949	+	7.38673i	0.944203	+	0.343662i
$463$	3.52141	+	6.09926i	0.163654	+	0.283457i	0.936176	−	0.351531i	$-0.114339\pi$
$463$	3.52141	+	6.09926i	0.163654	+	0.283457i	−0.772523	+	0.634987i	$0.781005\pi$
$464$	−4.58171	+	7.93576i	−0.212701	+	0.368408i
$465$		0			0
$466$	3.32105	−	2.78669i	0.153845	−	0.129091i
$467$	19.8650	−	34.4072i	0.919244	−	1.59218i	0.118678	−	0.992933i	$-0.462134\pi$
$467$	19.8650	−	34.4072i	0.919244	−	1.59218i	0.800566	−	0.599245i	$-0.204532\pi$
$468$	−0.850201	−	1.47259i	−0.0393006	−	0.0680706i
$469$	−39.4826	−	14.3705i	−1.82314	−	0.663568i
$470$		0			0
$471$	−1.07716	−	6.10886i	−0.0496327	−	0.281481i
$472$	20.4325	−	7.43683i	0.940483	−	0.342308i
$473$	15.2306	+	12.7800i	0.700305	+	0.587626i
$474$	−20.9777			−0.963539
$475$		0			0
$476$	−41.6089			−1.90714
$477$	0.840113	+	0.704938i	0.0384661	+	0.0322769i
$478$	7.96402	−	2.89867i	0.364266	−	0.132582i
$479$	−6.30401	−	35.7518i	−0.288038	−	1.63354i	−0.694229	−	0.719754i	$-0.744255\pi$
$479$	−6.30401	−	35.7518i	−0.288038	−	1.63354i	0.406192	−	0.913788i	$-0.366857\pi$
$480$		0			0
$481$	−0.263486	−	0.0959012i	−0.0120139	−	0.00437272i
$482$	8.11670	+	14.0585i	0.369705	+	0.640349i
$483$	−13.1952	+	22.8548i	−0.600403	+	1.03993i
$484$	−9.68943	+	8.13040i	−0.440429	+	0.369564i
$485$		0			0
$486$	−2.21125	+	3.83000i	−0.100305	+	0.173733i
$487$	−1.26752	−	2.19541i	−0.0574368	−	0.0994835i	0.835877	−	0.548916i	$-0.184959\pi$
$487$	−1.26752	−	2.19541i	−0.0574368	−	0.0994835i	−0.893314	+	0.449433i	$0.851626\pi$
$488$	−13.0400	−	4.74616i	−0.590292	−	0.214849i
$489$	2.19397	−	12.4426i	0.0992147	−	0.562675i
$490$		0			0
$491$	34.1243	−	12.4202i	1.54001	−	0.560516i	0.573959	−	0.818884i	$-0.305407\pi$
$491$	34.1243	−	12.4202i	1.54001	−	0.560516i	0.966047	+	0.258367i	$0.0831845\pi$
$492$	0.0606317	+	0.0508761i	0.00273349	+	0.00229367i
$493$	−33.1619			−1.49354
$494$	−3.31004	+	2.71386i	−0.148926	+	0.122102i
$495$		0			0
$496$	8.84356	+	7.42063i	0.397088	+	0.333196i
$497$	−41.7563	+	15.1980i	−1.87303	+	0.681725i
$498$	−1.08770	−	6.16864i	−0.0487409	−	0.276423i
$499$	−3.11167	+	17.6471i	−0.139297	+	0.789994i	0.832473	+	0.554066i	$0.186924\pi$
$499$	−3.11167	+	17.6471i	−0.139297	+	0.789994i	−0.971770	+	0.235929i	$0.924187\pi$
$500$		0			0
$501$	−15.2156	−	26.3542i	−0.679783	−	1.17742i
$502$	2.88564	−	4.99807i	0.128792	−	0.223075i
$503$	15.7096	−	13.1819i	0.700457	−	0.587753i	−0.221447	−	0.975173i	$-0.571078\pi$
$503$	15.7096	−	13.1819i	0.700457	−	0.587753i	0.921904	+	0.387419i	$0.126633\pi$
$504$	4.88726	−	4.10090i	0.217696	−	0.182669i
$505$		0			0
$506$	4.62546	+	8.01153i	0.205627	+	0.356156i
$507$	−19.1061	−	6.95407i	−0.848534	−	0.308841i
$508$	1.48008	−	8.39397i	0.0656681	−	0.372422i
$509$	−2.67442	−	15.1674i	−0.118542	−	0.672283i	−0.984936	−	0.172922i	$-0.944679\pi$
$509$	−2.67442	−	15.1674i	−0.118542	−	0.672283i	0.866394	−	0.499361i	$-0.166432\pi$
$510$		0			0
$511$	−42.6626	−	35.7982i	−1.88728	−	1.58362i
$512$	17.9712			0.794223
$513$	−18.1260	−	6.83190i	−0.800280	−	0.301636i
$514$	15.6591			0.690695
$515$		0			0
$516$	13.1935	−	4.80205i	0.580812	−	0.211398i
$517$	−1.08005	−	6.12526i	−0.0475004	−	0.269388i
$518$	0.0811817	−	0.460404i	0.00356692	−	0.0202290i
$519$	3.42949	+	1.24823i	0.150538	+	0.0547913i
$520$		0			0
$521$	1.17999	−	2.04381i	0.0516965	−	0.0895409i	−0.839019	−	0.544102i	$-0.816870\pi$
$521$	1.17999	−	2.04381i	0.0516965	−	0.0895409i	0.890716	+	0.454561i	$0.150204\pi$
$522$	1.73091	−	1.45240i	0.0757597	−	0.0635700i
$523$	−14.5909	+	12.2432i	−0.638014	+	0.535358i	−0.903408	−	0.428783i	$-0.858943\pi$
$523$	−14.5909	+	12.2432i	−0.638014	+	0.535358i	0.265393	+	0.964140i	$0.414498\pi$
$524$	−1.36974	+	2.37246i	−0.0598374	+	0.103641i
$525$		0			0
$526$	−8.70019	−	3.16661i	−0.379346	−	0.138071i
$527$	−7.25478	+	41.1439i	−0.316023	+	1.79226i
$528$	2.54795	+	14.4501i	0.110885	+	0.628861i
$529$	10.9907	−	4.00028i	0.477856	−	0.173925i
$530$		0			0
$531$	6.53919			0.283777
$532$	21.6300	+	18.5732i	0.937777	+	0.805252i
$533$	−0.0400008			−0.00173263
$534$	0.472538	+	0.396506i	0.0204487	+	0.0171585i
$535$		0			0
$536$	4.06429	+	23.0497i	0.175551	+	0.995597i
$537$	4.76022	−	26.9966i	0.205419	−	1.16499i
$538$	−10.2296	−	3.72326i	−0.441028	−	0.160521i
$539$	21.1316	+	36.6009i	0.910200	+	1.57651i
$540$		0			0
$541$	−3.83099	+	3.21458i	−0.164707	+	0.138206i	−0.721416	−	0.692502i	$-0.756508\pi$
$541$	−3.83099	+	3.21458i	−0.164707	+	0.138206i	0.556709	+	0.830708i	$0.312064\pi$
$542$	6.62670	−	5.56046i	0.284641	−	0.238842i
$543$	13.8078	−	23.9158i	0.592550	−	1.02633i
$544$	18.0282	+	31.2258i	0.772955	+	1.33880i
$545$		0			0
$546$	−1.33846	+	7.59076i	−0.0572806	+	0.324854i
$547$	0.426450	+	2.41852i	0.0182337	+	0.103408i	0.992566	−	0.121705i	$-0.0388360\pi$
$547$	0.426450	+	2.41852i	0.0182337	+	0.103408i	−0.974333	+	0.225113i	$0.927725\pi$
$548$	−8.63656	+	3.14345i	−0.368936	+	0.134282i
$549$	−3.19693	−	2.68254i	−0.136442	−	0.114488i
$550$		0			0
$551$	17.2388	+	14.8027i	0.734400	+	0.630615i
$552$	14.7008			0.625706
$553$	−54.0944	−	45.3906i	−2.30033	−	1.93020i
$554$	−8.00339	+	2.91299i	−0.340031	+	0.123761i
$555$		0			0
$556$	4.88463	−	27.7021i	0.207155	−	1.17483i
$557$	−4.38265	−	1.59515i	−0.185699	−	0.0675889i	0.247497	−	0.968889i	$-0.420392\pi$
$557$	−4.38265	−	1.59515i	−0.185699	−	0.0675889i	−0.433196	+	0.901300i	$0.642614\pi$
$558$	−1.42333	−	2.46528i	−0.0602543	−	0.104363i
$559$	−3.54786	+	6.14508i	−0.150059	+	0.259909i
$560$		0			0
$561$	−40.6776	+	34.1326i	−1.71741	+	1.44108i
$562$	5.52939	−	9.57719i	0.233243	−	0.403989i
$563$	17.3165	+	29.9930i	0.729803	+	1.26406i	0.956966	+	0.290199i	$0.0937215\pi$
$563$	17.3165	+	29.9930i	0.729803	+	1.26406i	−0.227163	+	0.973857i	$0.572945\pi$
$564$	−4.12733	−	1.50223i	−0.173792	−	0.0632552i
$565$		0			0
$566$	2.31118	+	13.1074i	0.0971463	+	0.550944i
$567$	−40.6744	+	14.8043i	−1.70816	+	0.621720i
$568$	18.9620	+	15.9110i	0.795628	+	0.667611i
$569$	−20.6116			−0.864081			−0.432041	−	0.901854i	$-0.642206\pi$
$569$	−20.6116			−0.864081			−0.432041	+	0.901854i	$0.642206\pi$
$570$		0			0
$571$	11.1132			0.465071			0.232536	−	0.972588i	$-0.425298\pi$
$571$	11.1132			0.465071			0.232536	+	0.972588i	$0.425298\pi$
$572$	−8.26853	−	6.93812i	−0.345725	−	0.290097i
$573$	43.6159	−	15.8749i	1.82208	−	0.663183i
$574$	−0.0115812	−	0.0656803i	−0.000483390	−	0.00274144i
$575$		0			0
$576$	−0.0455562	−	0.0165811i	−0.00189818	−	0.000690879i
$577$	−14.3527	−	24.8596i	−0.597510	−	1.03492i	−0.993187	−	0.116528i	$-0.962823\pi$
$577$	−14.3527	−	24.8596i	−0.597510	−	1.03492i	0.395677	−	0.918390i	$-0.370510\pi$
$578$	−7.42564	+	12.8616i	−0.308866	+	0.534971i
$579$	−7.51998	+	6.31001i	−0.312520	+	0.262235i
$580$		0			0
$581$	10.5426	−	18.2603i	0.437381	−	0.757566i
$582$	−1.99220	−	3.45060i	−0.0825795	−	0.143032i
$583$	6.54172	+	2.38099i	0.270930	+	0.0986106i
$584$	−5.38713	+	30.5519i	−0.222921	+	1.26425i
$585$		0			0
$586$	−6.38114	+	2.32254i	−0.263602	+	0.0959434i
$587$	−1.37306	−	1.15213i	−0.0566723	−	0.0475537i	0.614012	−	0.789297i	$-0.289555\pi$
$587$	−1.37306	−	1.15213i	−0.0566723	−	0.0475537i	−0.670684	+	0.741743i	$0.733999\pi$
$588$	29.8451			1.23079
$589$	22.1370	−	18.1499i	0.912139	−	0.747852i
$590$		0			0
$591$	0.0945347	+	0.0793240i	0.00388864	+	0.00326295i
$592$	0.298465	−	0.108632i	0.0122668	−	0.00446476i
$593$	−0.291962	−	1.65580i	−0.0119894	−	0.0679955i	0.978226	−	0.207542i	$-0.0665465\pi$
$593$	−0.291962	−	1.65580i	−0.0119894	−	0.0679955i	−0.990215	+	0.139547i	$0.955435\pi$
$594$	−2.12329	+	12.0418i	−0.0871195	+	0.494079i
$595$		0			0
$596$	8.81407	+	15.2664i	0.361039	+	0.625337i
$597$	−6.12363	+	10.6064i	−0.250623	+	0.434093i
$598$	−2.52913	+	2.12220i	−0.103424	+	0.0867830i
$599$	−1.65586	+	1.38943i	−0.0676568	+	0.0567708i	−0.675989	−	0.736912i	$-0.736283\pi$
$599$	−1.65586	+	1.38943i	−0.0676568	+	0.0567708i	0.608332	+	0.793683i	$0.291839\pi$
$600$		0			0
$601$	−2.21602	−	3.83826i	−0.0903934	−	0.156566i	0.817283	−	0.576236i	$-0.195479\pi$
$601$	−2.21602	−	3.83826i	−0.0903934	−	0.156566i	−0.907677	+	0.419670i	$0.862146\pi$
$602$	−11.1173	−	4.04636i	−0.453106	−	0.164917i
$603$	−1.22228	+	6.93192i	−0.0497753	+	0.282290i
$604$	0.658620	+	3.73522i	0.0267989	+	0.151984i
$605$		0			0
$606$	3.24795	+	2.72535i	0.131939	+	0.110710i
$607$	−29.9817			−1.21692			−0.608460	−	0.793585i	$-0.708212\pi$
$607$	−29.9817			−1.21692			−0.608460	+	0.793585i	$0.708212\pi$
$608$	4.56668	−	24.2798i	0.185203	−	0.984676i
$609$	40.9170			1.65804
$610$		0			0
$611$	2.08589	−	0.759203i	0.0843862	−	0.0307141i
$612$	1.21043	+	6.86467i	0.0489286	+	0.277488i
$613$	−3.44456	+	19.5351i	−0.139124	+	0.789013i	0.832774	+	0.553613i	$0.186751\pi$
$613$	−3.44456	+	19.5351i	−0.139124	+	0.789013i	−0.971898	+	0.235400i	$0.924360\pi$
$614$	−1.61096	−	0.586341i	−0.0650130	−	0.0236628i
$615$		0			0
$616$	20.2490	−	35.0724i	0.815857	−	1.41311i
$617$	−16.1011	+	13.5104i	−0.648206	+	0.543909i	−0.906526	−	0.422150i	$-0.861275\pi$
$617$	−16.1011	+	13.5104i	−0.648206	+	0.543909i	0.258320	+	0.966059i	$0.416831\pi$
$618$	8.03173	−	6.73942i	0.323083	−	0.271099i
$619$	−10.1316	+	17.5484i	−0.407223	+	0.705331i	−0.994577	−	0.103999i	$-0.966836\pi$
$619$	−10.1316	+	17.5484i	−0.407223	+	0.705331i	0.587354	+	0.809330i	$0.300169\pi$
$620$		0			0
$621$	−14.0401	−	5.11018i	−0.563410	−	0.205064i
$622$	−0.797413	+	4.52235i	−0.0319733	+	0.181330i
$623$	0.360573	+	2.04491i	0.0144460	+	0.0819275i
$624$	−4.92084	+	1.79104i	−0.196991	+	0.0716990i
$625$		0			0
$626$	5.49193			0.219501
$627$	36.3818	+	0.414065i	1.45295	+	0.0165362i
$628$	−5.16890			−0.206261
$629$	0.880527	+	0.738850i	0.0351089	+	0.0294599i
$630$		0			0
$631$	6.98027	+	39.5871i	0.277880	+	1.57594i	0.729661	+	0.683809i	$0.239678\pi$
$631$	6.98027	+	39.5871i	0.277880	+	1.57594i	−0.451781	+	0.892129i	$0.649211\pi$
$632$	−6.83066	+	38.7386i	−0.271709	+	1.54094i
$633$	−10.6642	−	3.88145i	−0.423863	−	0.154274i
$634$	−10.1015	−	17.4964i	−0.401183	−	0.694870i
$635$		0			0
$636$	3.76592	−	3.15998i	0.149329	−	0.125302i
$637$	−11.5544	+	9.69532i	−0.457803	+	0.384143i
$638$	7.17154	−	12.4215i	0.283924	−	0.491771i
$639$	3.72210	+	6.44686i	0.147244	+	0.255034i
$640$		0			0
$641$	0.606201	−	3.43794i	0.0239435	−	0.135790i	−0.970493	−	0.241130i	$-0.922482\pi$
$641$	0.606201	−	3.43794i	0.0239435	−	0.135790i	0.994436	+	0.105340i	$0.0335930\pi$
$642$	1.32352	+	7.50606i	0.0522352	+	0.296241i
$643$	34.0072	−	12.3776i	1.34111	−	0.488125i	0.430949	−	0.902376i	$-0.358179\pi$
$643$	34.0072	−	12.3776i	1.34111	−	0.488125i	0.910162	+	0.414252i	$0.135957\pi$
$644$	16.8457	+	14.1352i	0.663814	+	0.557006i
$645$		0			0
$646$	16.5557	−	5.81330i	0.651377	−	0.228721i
$647$	21.1005			0.829545			0.414772	−	0.909925i	$-0.363861\pi$
$647$	21.1005			0.829545			0.414772	+	0.909925i	$0.363861\pi$
$648$	18.4707	+	15.4987i	0.725597	+	0.608848i
$649$	39.0061	−	14.1971i	1.53112	−	0.557283i
$650$		0			0
$651$	8.95137	−	50.7657i	0.350832	−	1.98967i
$652$	−9.89317	−	3.60082i	−0.387446	−	0.141019i
$653$	−8.38024	−	14.5150i	−0.327944	−	0.568016i	0.654160	−	0.756356i	$-0.273022\pi$
$653$	−8.38024	−	14.5150i	−0.327944	−	0.568016i	−0.982104	+	0.188341i	$0.939689\pi$
$654$	5.99132	−	10.3773i	0.234279	−	0.405784i
$655$		0			0
$656$	0.0347102	−	0.0291253i	0.00135521	−	0.00113715i
$657$	−4.66493	+	8.07989i	−0.181996	+	0.315227i
$658$	1.85051	+	3.20518i	0.0721404	+	0.124951i
$659$	−34.8179	−	12.6727i	−1.35631	−	0.493658i	−0.441401	−	0.897310i	$-0.645518\pi$
$659$	−34.8179	−	12.6727i	−1.35631	−	0.493658i	−0.914913	+	0.403652i	$0.867741\pi$
$660$		0			0
$661$	3.76649	+	21.3608i	0.146500	+	0.830841i	0.966151	+	0.257978i	$0.0830561\pi$
$661$	3.76649	+	21.3608i	0.146500	+	0.830841i	−0.819651	+	0.572863i	$0.805833\pi$
$662$	−14.4492	+	5.25908i	−0.561584	+	0.204400i
$663$	−14.5174	−	12.1815i	−0.563809	−	0.473092i
$664$	−11.7455			−0.455814
$665$		0			0
$666$	−0.0783194			−0.00303482
$667$	13.4259	+	11.2656i	0.519851	+	0.436207i
$668$	−23.8284	+	8.67282i	−0.921948	+	0.335561i
$669$	−9.77178	−	55.4185i	−0.377799	−	2.14260i
$670$		0			0
$671$	−24.8936	−	9.06052i	−0.961006	−	0.349777i
$672$	−22.2443	−	38.5282i	−0.858092	−	1.48626i
$673$	−2.69790	+	4.67290i	−0.103996	+	0.180127i	−0.913328	−	0.407225i	$-0.866496\pi$
$673$	−2.69790	+	4.67290i	−0.103996	+	0.180127i	0.809331	+	0.587352i	$0.199830\pi$
$674$	−13.7599	+	11.5459i	−0.530011	+	0.444732i
$675$		0			0
$676$	−8.47123	+	14.6726i	−0.325817	+	0.564331i
$677$	−15.4611	−	26.7794i	−0.594217	−	1.02921i	−0.993657	−	0.112455i	$-0.964129\pi$
$677$	−15.4611	−	26.7794i	−0.594217	−	1.02921i	0.399440	−	0.916759i	$-0.369205\pi$
$678$	5.98984	+	2.18012i	0.230039	+	0.0837272i
$679$	2.32902	−	13.2086i	0.0893798	−	0.506898i
$680$		0			0
$681$	−14.4346	+	5.25376i	−0.553135	+	0.201325i
$682$	−13.8424	−	11.6152i	−0.530053	−	0.444767i
$683$	21.3136			0.815542			0.407771	−	0.913084i	$-0.366306\pi$
$683$	21.3136			0.815542			0.407771	+	0.913084i	$0.366306\pi$
$684$	2.43500	−	4.10883i	0.0931045	−	0.157105i
$685$		0			0
$686$	−5.39029	−	4.52299i	−0.205802	−	0.172689i
$687$	50.9943	−	18.5604i	1.94555	−	0.708123i
$688$	−1.39573	−	7.91560i	−0.0532118	−	0.301779i
$689$	−0.431429	+	2.44676i	−0.0164362	+	0.0932141i
$690$		0			0
$691$	3.81597	+	6.60946i	0.145166	+	0.251436i	0.929435	−	0.368986i	$-0.120295\pi$
$691$	3.81597	+	6.60946i	0.145166	+	0.251436i	−0.784269	+	0.620421i	$0.786962\pi$
$692$	1.52056	−	2.63368i	0.0578029	−	0.100118i
$693$	9.32988	−	7.82870i	0.354413	−	0.297388i
$694$	15.0760	−	12.6503i	0.572279	−	0.480199i
$695$		0			0
$696$	−11.3964	−	19.7392i	−0.431980	−	0.748211i
$697$	0.154089	+	0.0560837i	0.00583652	+	0.00212432i
$698$	1.92070	−	10.8928i	0.0726995	−	0.412299i
$699$	−2.28380	−	12.9521i	−0.0863812	−	0.489892i
$700$		0			0
$701$	12.1942	+	10.2321i	0.460568	+	0.386463i	0.843340	−	0.537380i	$-0.180586\pi$
$701$	12.1942	+	10.2321i	0.460568	+	0.386463i	−0.382772	+	0.923843i	$0.625030\pi$
$702$	−4.36387			−0.164704
$703$	−0.127928	−	0.777130i	−0.00482488	−	0.0293100i
$704$	−0.307740			−0.0115984
$705$		0			0
$706$	−5.24776	+	1.91003i	−0.197502	+	0.0718848i
$707$	2.47837	+	14.0555i	0.0932085	+	0.528612i
$708$	5.09012	−	28.8675i	0.191298	−	1.08491i
$709$	37.3356	+	13.5890i	1.40217	+	0.510347i	0.928821	−	0.370530i	$-0.120824\pi$
$709$	37.3356	+	13.5890i	1.40217	+	0.510347i	0.473346	+	0.880877i	$0.343046\pi$
$710$		0			0
$711$	−5.91494	+	10.2450i	−0.221827	+	0.384216i
$712$	0.886075	−	0.743505i	0.0332071	−	0.0278640i
$713$	16.9144	−	14.1929i	0.633450	−	0.531528i
$714$	15.7987	−	27.3641i	0.591250	−	1.02407i
$715$		0			0
$716$	−21.4651	−	7.81265i	−0.802187	−	0.291972i
$717$	4.46460	−	25.3200i	0.166734	−	0.945593i
$718$	2.18903	+	12.4146i	0.0816938	+	0.463308i
$719$	7.66940	−	2.79143i	0.286020	−	0.104103i	−0.195026	−	0.980798i	$-0.562479\pi$
$719$	7.66940	−	2.79143i	0.286020	−	0.104103i	0.481046	+	0.876695i	$0.340257\pi$
$720$		0			0
$721$	35.2935			1.31440
$722$	−11.2012	−	4.36811i	−0.416867	−	0.162564i
$723$	49.2465			1.83150
$724$	−17.6278	−	14.7915i	−0.655132	−	0.549721i
$725$		0			0
$726$	−1.66793	−	9.45931i	−0.0619028	−	0.351068i
$727$	0.272620	−	1.54611i	0.0101109	−	0.0573419i	−0.979335	−	0.202246i	$-0.935176\pi$
$727$	0.272620	−	1.54611i	0.0101109	−	0.0573419i	0.989446	+	0.144904i	$0.0462872\pi$
$728$	13.5817	+	4.94333i	0.503370	+	0.183212i
$729$	−9.17050	−	15.8838i	−0.339648	−	0.588288i
$730$		0			0
$731$	22.2827	−	18.6974i	0.824154	−	0.691548i
$732$	−14.3307	+	12.0249i	−0.529677	+	0.444452i
$733$	2.20731	−	3.82317i	0.0815288	−	0.141212i	−0.822378	−	0.568941i	$-0.807353\pi$
$733$	2.20731	−	3.82317i	0.0815288	−	0.141212i	0.903907	+	0.427729i	$0.140686\pi$
$734$	2.67552	+	4.63414i	0.0987553	+	0.171049i
$735$		0			0
$736$	3.30905	−	18.7665i	0.121973	−	0.691744i
$737$	7.75881	+	44.0024i	0.285799	+	1.62085i
$738$	−0.0104991	+	0.00382135i	−0.000386476	+	0.000140666i
$739$	−7.78848	−	6.53531i	−0.286504	−	0.240405i	0.488197	−	0.872734i	$-0.337655\pi$
$739$	−7.78848	−	6.53531i	−0.286504	−	0.240405i	−0.774700	+	0.632328i	$0.782099\pi$
$740$		0			0
$741$	2.10916	+	12.8127i	0.0774821	+	0.470685i
$742$	−4.14243			−0.152073
$743$	−5.39641	−	4.52813i	−0.197975	−	0.166121i	0.538411	−	0.842682i	$-0.319025\pi$
$743$	−5.39641	−	4.52813i	−0.197975	−	0.166121i	−0.736386	+	0.676562i	$0.763469\pi$
$744$	−26.9835	+	9.82121i	−0.989265	+	0.360063i
$745$		0			0
$746$	0.784320	−	4.44810i	0.0287160	−	0.162857i
$747$	−3.31929	−	1.20812i	−0.121447	−	0.0442029i
$748$	22.1239	+	38.3196i	0.808928	+	1.40110i
$749$	−12.8283	+	22.2193i	−0.468737	+	0.811877i
$750$		0			0
$751$	19.7520	−	16.5739i	0.720760	−	0.604789i	−0.206835	−	0.978376i	$-0.566316\pi$
$751$	19.7520	−	16.5739i	0.720760	−	0.604789i	0.927595	+	0.373586i	$0.121872\pi$
$752$	−1.25722	+	2.17757i	−0.0458461	+	0.0794078i
$753$	−8.75402	−	15.1624i	−0.319014	−	0.552549i
$754$	4.81018	+	1.75076i	0.175176	+	0.0637590i
$755$		0			0
$756$	5.04731	+	28.6247i	0.183569	+	1.04107i
$757$	18.0947	−	6.58595i	0.657665	−	0.239370i	0.00843696	−	0.999964i	$-0.497314\pi$
$757$	18.0947	−	6.58595i	0.657665	−	0.239370i	0.649228	+	0.760594i	$0.275092\pi$
$758$	2.96348	+	2.48666i	0.107639	+	0.0903195i
$759$	28.0641			1.01866
$760$		0			0
$761$	30.9500			1.12194			0.560969	−	0.827837i	$-0.310429\pi$
$761$	30.9500			1.12194			0.560969	+	0.827837i	$0.310429\pi$
$762$	4.95831	+	4.16052i	0.179621	+	0.150720i
$763$	37.9034	−	13.7957i	1.37220	−	0.499439i
$764$	−6.71612	−	38.0890i	−0.242981	−	1.37801i
$765$		0			0
$766$	0.311458	+	0.113361i	0.0112534	+	0.00409592i
$767$	7.40713	+	12.8295i	0.267456	+	0.463247i
$768$	−6.99343	+	12.1130i	−0.252354	+	0.437090i
$769$	−22.7690	+	19.1055i	−0.821071	+	0.688960i	−0.953223	−	0.302269i	$-0.902256\pi$
$769$	−22.7690	+	19.1055i	−0.821071	+	0.688960i	0.132152	+	0.991230i	$0.457811\pi$
$770$		0			0
$771$	23.7522	−	41.1400i	0.855414	−	1.48162i
$772$	4.08999	+	7.08407i	0.147202	+	0.254961i
$773$	−11.6190	−	4.22899i	−0.417908	−	0.152106i	0.124503	−	0.992219i	$-0.460266\pi$
$773$	−11.6190	−	4.22899i	−0.417908	−	0.152106i	−0.542411	+	0.840113i	$0.682488\pi$
$774$	−0.344163	+	1.95185i	−0.0123707	+	0.0701577i
$775$		0			0
$776$	−7.02075	+	2.55534i	−0.252030	+	0.0917315i
$777$	−1.08645	−	0.911636i	−0.0389760	−	0.0327048i
$778$	−1.57965			−0.0566333
$779$	−0.0550669	−	0.0979360i	−0.00197298	−	0.00350892i
$780$		0			0
$781$	36.1988	+	30.3744i	1.29530	+	1.08688i
$782$	12.7180	−	4.62899i	0.454796	−	0.165532i
$783$	4.02265	+	22.8136i	0.143758	+	0.815291i
$784$	2.96688	−	16.8260i	0.105960	−	0.600929i
$785$		0			0
$786$	−1.04016	−	1.80162i	−0.0371014	−	0.0642616i
$787$	21.9353	−	37.9930i	0.781909	−	1.35431i	−0.148920	−	0.988849i	$-0.547580\pi$
$787$	21.9353	−	37.9930i	0.781909	−	1.35431i	0.930829	−	0.365456i	$-0.119087\pi$
$788$	0.0787736	−	0.0660989i	0.00280619	−	0.00235468i
$789$	−21.5161	+	18.0541i	−0.765993	+	0.642744i
$790$		0			0
$791$	10.7285	+	18.5823i	0.381462	+	0.660712i
$792$	−6.37532	−	2.32043i	−0.226537	−	0.0824527i
$793$	1.64174	−	9.31078i	0.0583000	−	0.330636i
$794$	0.317309	+	1.79955i	0.0112609	+	0.0638636i
$795$		0			0
$796$	7.81776	+	6.55988i	0.277093	+	0.232509i
$797$	5.08657			0.180176			0.0900879	−	0.995934i	$-0.471285\pi$
$797$	5.08657			0.180176			0.0900879	+	0.995934i	$0.471285\pi$
$798$	−20.4274	+	7.17278i	−0.723123	+	0.253914i
$799$	−9.09960			−0.321921
$800$		0			0
$801$	0.326881	−	0.118975i	0.0115498	−	0.00420378i
$802$	−1.89479	−	10.7459i	−0.0669073	−	0.379450i
$803$	−10.2841	+	58.3242i	−0.362919	+	2.05822i
$804$	29.6498	+	10.7916i	1.04567	+	0.380592i
$805$		0			0
$806$	3.22449	−	5.58498i	0.113578	−	0.196722i
$807$	−25.2983	+	21.2278i	−0.890542	+	0.747254i
$808$	6.09036	−	5.11042i	0.214258	−	0.179784i
$809$	−15.1064	+	26.1650i	−0.531112	+	0.919914i	0.468228	+	0.883608i	$0.344892\pi$
$809$	−15.1064	+	26.1650i	−0.531112	+	0.919914i	−0.999341	+	0.0363062i	$0.988441\pi$
$810$		0			0
$811$	−3.43739	−	1.25111i	−0.120703	−	0.0439323i	0.280963	−	0.959719i	$-0.409346\pi$
$811$	−3.43739	−	1.25111i	−0.120703	−	0.0439323i	−0.401666	+	0.915786i	$0.631569\pi$
$812$	5.92057	−	33.5772i	0.207771	−	1.17833i
$813$	−4.55700	−	25.8441i	−0.159821	−	0.906391i
$814$	−0.467173	+	0.170037i	−0.0163744	+	0.00595980i
$815$		0			0
$816$	21.4669			0.751493
$817$	−19.9295	−	0.226820i	−0.697244	−	0.00793541i
$818$	−16.5221			−0.577682
$819$	3.32973	+	2.79398i	0.116350	+	0.0976295i
$820$		0			0
$821$	−3.37413	−	19.1357i	−0.117758	−	0.667839i	−0.985348	−	0.170558i	$-0.945443\pi$
$821$	−3.37413	−	19.1357i	−0.117758	−	0.667839i	0.867589	−	0.497281i	$-0.165668\pi$
$822$	1.21196	−	6.87338i	0.0422720	−	0.239737i
$823$	−4.92429	−	1.79230i	−0.171650	−	0.0624755i	0.254766	−	0.967003i	$-0.418002\pi$
$823$	−4.92429	−	1.79230i	−0.171650	−	0.0624755i	−0.426416	+	0.904527i	$0.640224\pi$
$824$	−9.83012	−	17.0263i	−0.342448	−	0.593138i
$825$		0			0
$826$	−18.9212	+	15.8768i	−0.658353	+	0.552424i
$827$	−43.8018	+	36.7541i	−1.52314	+	1.27806i	−0.692187	+	0.721718i	$0.743353\pi$
$827$	−43.8018	+	36.7541i	−1.52314	+	1.27806i	−0.830950	+	0.556346i	$0.812203\pi$
$828$	1.84199	−	3.19042i	0.0640136	−	0.110875i
$829$	7.34286	+	12.7182i	0.255028	+	0.441722i	0.964903	−	0.262606i	$-0.0845819\pi$
$829$	7.34286	+	12.7182i	0.255028	+	0.441722i	−0.709875	+	0.704328i	$0.751249\pi$
$830$		0			0
$831$	−4.48667	+	25.4452i	−0.155641	+	0.882683i
$832$	−0.0190716	−	0.108161i	−0.000661190	−	0.00374979i
$833$	58.1028	−	21.1477i	2.01314	−	0.732724i
$834$	16.3636	+	13.7307i	0.566626	+	0.475456i
$835$		0			0
$836$	5.60413	−	29.7956i	0.193823	−	1.03050i
$837$	29.1848			1.00878
$838$	−0.0546310	−	0.0458408i	−0.00188720	−	0.00158354i
$839$	−19.6431	+	7.14950i	−0.678155	+	0.246828i	−0.658055	−	0.752970i	$-0.728621\pi$
$839$	−19.6431	+	7.14950i	−0.678155	+	0.246828i	−0.0200999	+	0.999798i	$0.506398\pi$
$840$		0			0
$841$	−0.317165	+	1.79873i	−0.0109367	+	0.0620252i
$842$	−12.0226	−	4.37586i	−0.414326	−	0.150802i
$843$	−16.7743	−	29.0539i	−0.577736	−	1.00067i
$844$	−4.72826	+	8.18959i	−0.162753	+	0.281897i
$845$		0			0
$846$	0.474960	−	0.398539i	0.0163295	−	0.0137020i
$847$	16.1666	−	28.0013i	0.555490	−	0.962137i
$848$	−1.40716	−	2.43728i	−0.0483222	−	0.0836965i
$849$	37.9416	+	13.8096i	1.30215	+	0.473945i
$850$		0			0
$851$	−0.105489	−	0.598259i	−0.00361612	−	0.0205081i
$852$	31.3572	−	11.4131i	1.07428	−	0.391006i
$853$	−16.4723	−	13.8219i	−0.564000	−	0.473253i	0.315648	−	0.948876i	$-0.397778\pi$
$853$	−16.4723	−	13.8219i	−0.564000	−	0.473253i	−0.879649	+	0.475624i	$0.842222\pi$
$854$	15.7634			0.539413
$855$		0			0
$856$	14.2920			0.488492
$857$	38.9182	+	32.6562i	1.32942	+	1.11552i	0.984213	+	0.176990i	$0.0566359\pi$
$857$	38.9182	+	32.6562i	1.32942	+	1.11552i	0.345208	+	0.938526i	$0.387808\pi$
$858$	7.70236	−	2.80343i	0.262954	−	0.0957075i
$859$	−1.25062	−	7.09262i	−0.0426706	−	0.241997i	0.956011	−	0.293331i	$-0.0947638\pi$
$859$	−1.25062	−	7.09262i	−0.0426706	−	0.241997i	−0.998682	+	0.0513340i	$0.983653\pi$
$860$		0			0
$861$	−0.190123	−	0.0691992i	−0.00647939	−	0.00235830i
$862$	12.8285	+	22.2195i	0.436939	+	0.756801i
$863$	9.02344	−	15.6291i	0.307161	−	0.532019i	−0.670579	−	0.741838i	$-0.733954\pi$
$863$	9.02344	−	15.6291i	0.307161	−	0.532019i	0.977740	+	0.209819i	$0.0672875\pi$
$864$	19.2948	−	16.1903i	0.656423	−	0.550804i
$865$		0			0
$866$	−7.20529	+	12.4799i	−0.244846	+	0.424085i
$867$	22.5268	+	39.0176i	0.765051	+	1.32511i
$868$	−40.3640	−	14.6913i	−1.37004	−	0.498655i
$869$	−13.0399	+	73.9527i	−0.442347	+	2.50867i
$870$		0			0
$871$	−14.9846	+	5.45393i	−0.507732	+	0.184799i
$872$	−17.2124	−	14.4429i	−0.582884	−	0.489098i
$873$	−2.24691			−0.0760464
$874$	−8.67761	−	3.27070i	−0.293524	−	0.110633i
$875$		0			0
$876$	32.0378	+	26.8829i	1.08246	+	0.908289i
$877$	−22.3078	+	8.11936i	−0.753280	+	0.274171i	−0.689985	−	0.723824i	$-0.742383\pi$
$877$	−22.3078	+	8.11936i	−0.753280	+	0.274171i	−0.0632945	+	0.997995i	$0.520161\pi$
$878$	−3.59008	−	20.3604i	−0.121159	−	0.687129i
$879$	−3.57724	+	20.2876i	−0.120657	+	0.684282i
$880$		0			0
$881$	−16.7038	−	28.9318i	−0.562765	−	0.974737i	−0.997254	−	0.0740599i	$-0.976404\pi$
$881$	−16.7038	−	28.9318i	−0.562765	−	0.974737i	0.434489	−	0.900677i	$-0.356929\pi$
$882$	−2.10650	+	3.64857i	−0.0709296	+	0.122854i
$883$	−32.5424	+	27.3063i	−1.09514	+	0.918931i	−0.997089	−	0.0762507i	$-0.975705\pi$
$883$	−32.5424	+	27.3063i	−1.09514	+	0.918931i	−0.0980503	+	0.995181i	$0.531261\pi$
$884$	−12.0970	+	10.1506i	−0.406866	+	0.341401i
$885$		0			0
$886$	−4.38998	−	7.60367i	−0.147484	−	0.255450i
$887$	−8.82015	−	3.21027i	−0.296152	−	0.107790i	0.189671	−	0.981848i	$-0.439258\pi$
$887$	−8.82015	−	3.21027i	−0.296152	−	0.107790i	−0.485823	+	0.874057i	$0.661480\pi$
$888$	−0.137189	+	0.778035i	−0.00460375	+	0.0261092i
$889$	3.78347	+	21.4571i	0.126893	+	0.719648i
$890$		0			0
$891$	35.2609	+	29.5874i	1.18128	+	0.991215i
$892$	−46.8914			−1.57004
$893$	4.73033	+	4.06185i	0.158295	+	0.135924i
$894$	−13.3866			−0.447715
$895$		0			0
$896$	−43.3837	+	15.7904i	−1.44935	+	0.527519i
$897$	1.73922	+	9.86360i	0.0580708	+	0.329336i
$898$	−0.660111	+	3.74368i	−0.0220282	+	0.124928i
$899$	−32.1697	−	11.7088i	−1.07292	−	0.390511i
$900$		0			0
$901$	5.09244	−	8.82036i	0.169654	−	0.293849i
$902$	−0.0543303	+	0.0455885i	−0.00180900	+	0.00151793i
$903$	−27.4936	+	23.0699i	−0.914931	+	0.767719i
$904$	5.97631	−	10.3513i	0.198769	−	0.344278i
$905$		0			0
$906$	−2.70654	−	0.985100i	−0.0899188	−	0.0327278i
$907$	1.34450	−	7.62501i	0.0446432	−	0.253184i	−0.954316	−	0.298800i	$-0.903414\pi$
$907$	1.34450	−	7.62501i	0.0446432	−	0.253184i	0.998959	+	0.0456153i	$0.0145248\pi$
$908$	2.22269	+	12.6055i	0.0737625	+	0.418328i
$909$	2.24679	−	0.817765i	0.0745214	−	0.0271236i
$910$		0			0
$911$	−31.8865			−1.05645			−0.528223	−	0.849106i	$-0.677142\pi$
$911$	−31.8865			−1.05645			−0.528223	+	0.849106i	$0.677142\pi$
$912$	−11.1594	−	9.58233i	−0.369523	−	0.317303i
$913$	−22.4224			−0.742073
$914$	11.6216	+	9.75172i	0.384410	+	0.322558i
$915$		0			0
$916$	−7.85227	−	44.5324i	−0.259446	−	1.47139i
$917$	1.21602	−	6.89642i	0.0401567	−	0.227740i
$918$	16.8102	+	6.11843i	0.554821	+	0.201938i
$919$	9.68427	+	16.7736i	0.319455	+	0.553311i	0.980374	−	0.197145i	$-0.0631670\pi$
$919$	9.68427	+	16.7736i	0.319455	+	0.553311i	−0.660920	+	0.750457i	$0.729834\pi$
$920$		0			0
$921$	−3.98399	+	3.34297i	−0.131277	+	0.110154i
$922$	−17.4922	+	14.6777i	−0.576075	+	0.483384i
$923$	−8.43225	+	14.6051i	−0.277551	+	0.480733i
$924$	−27.2977	−	47.2810i	−0.898028	−	1.55543i
$925$		0			0
$926$	−0.773873	+	4.38885i	−0.0254311	+	0.144227i
$927$	−1.02671	−	5.82275i	−0.0337215	−	0.191244i
$928$	−27.7636	+	10.1051i	−0.911386	+	0.331717i
$929$	18.6717	+	15.6674i	0.612600	+	0.514032i	0.895468	−	0.445127i	$-0.146841\pi$
$929$	18.6717	+	15.6674i	0.612600	+	0.514032i	−0.282868	+	0.959159i	$0.591286\pi$
$930$		0			0
$931$	−39.6439	−	14.9423i	−1.29928	−	0.489714i
$932$	−10.9592			−0.358979
$933$	10.6717	+	8.95460i	0.349375	+	0.293161i
$934$	23.6243	−	8.59853i	0.773009	−	0.281352i
$935$		0			0
$936$	0.420455	−	2.38452i	0.0137430	−	0.0779404i
$937$	17.5551	+	6.38953i	0.573499	+	0.208737i	0.612457	−	0.790504i	$-0.290181\pi$
$937$	17.5551	+	6.38953i	0.573499	+	0.208737i	−0.0389573	+	0.999241i	$0.512404\pi$
$938$	−13.2936	−	23.0252i	−0.434052	−	0.751801i
$939$	8.33030	−	14.4285i	0.271849	−	0.470856i
$940$		0			0
$941$	−17.9348	+	15.0491i	−0.584659	+	0.490587i	−0.886473	−	0.462779i	$-0.846852\pi$
$941$	−17.9348	+	15.0491i	−0.584659	+	0.490587i	0.301814	+	0.953367i	$0.402408\pi$
$942$	1.96260	−	3.39932i	0.0639449	−	0.110756i
$943$	−0.0433315	−	0.0750524i	−0.00141107	−	0.00244404i
$944$	−15.7689	−	5.73940i	−0.513233	−	0.186802i
$945$		0			0
$946$	2.18468	+	12.3899i	0.0710299	+	0.402831i
$947$	37.3038	−	13.5775i	1.21221	−	0.441208i	0.344740	−	0.938698i	$-0.387967\pi$
$947$	37.3038	−	13.5775i	1.21221	−	0.441208i	0.867470	+	0.497490i	$0.165745\pi$
$948$	40.6226	+	34.0864i	1.31936	+	1.10708i
$949$	−21.1364			−0.686117
$950$		0			0
$951$	−61.2892			−1.98744
$952$	−45.3877	−	38.0848i	−1.47102	−	1.23433i
$953$	−46.8875	+	17.0657i	−1.51884	+	0.552811i	−0.960857	−	0.277045i	$-0.910645\pi$
$953$	−46.8875	+	17.0657i	−1.51884	+	0.552811i	−0.557978	+	0.829856i	$0.688423\pi$
$954$	0.120506	+	0.683421i	0.00390151	+	0.0221266i
$955$		0			0
$956$	−20.1320	−	7.32746i	−0.651116	−	0.236987i
$957$	−21.7560	−	37.6824i	−0.703271	−	1.21810i
$958$	11.4860	−	19.8944i	0.371097	−	0.642758i
$959$	17.9975	−	15.1017i	0.581170	−	0.487660i
$960$		0			0
$961$	−6.06485	+	10.5046i	−0.195640	+	0.338859i
$962$	−0.0887147	−	0.153658i	−0.00286028	−	0.00495414i
$963$	4.03895	+	1.47006i	0.130153	+	0.0473719i
$964$	7.12582	−	40.4125i	0.229507	−	1.30160i
$965$		0			0
$966$	−15.6922	+	5.71151i	−0.504890	+	0.183765i
$967$	41.2501	+	34.6130i	1.32651	+	1.11308i	0.984879	+	0.173246i	$0.0554255\pi$
$967$	41.2501	+	34.6130i	1.32651	+	1.11308i	0.341636	+	0.939832i	$0.389019\pi$
$968$	−18.0112			−0.578901
$969$	9.83939	−	52.3134i	0.316087	−	1.68055i
$970$		0			0
$971$	−18.3652	−	15.4102i	−0.589367	−	0.494537i	0.298641	−	0.954365i	$-0.403467\pi$
$971$	−18.3652	−	15.4102i	−0.589367	−	0.494537i	−0.888008	+	0.459828i	$0.847911\pi$
$972$	10.5053	−	3.82363i	0.336959	−	0.122643i
$973$	12.4864	+	70.8136i	0.400294	+	2.27018i
$974$	0.278553	−	1.57975i	0.00892542	−	0.0506186i
$975$		0			0
$976$	5.35476	+	9.27472i	0.171402	+	0.296876i
$977$	−26.3233	+	45.5933i	−0.842157	+	1.45866i	0.0459104	+	0.998946i	$0.485381\pi$
$977$	−26.3233	+	45.5933i	−0.842157	+	1.45866i	−0.888067	+	0.459713i	$0.847952\pi$
$978$	6.12445	−	5.13903i	0.195838	−	0.164328i
$979$	1.69153	−	1.41937i	0.0540617	−	0.0453631i
$980$		0			0
$981$	−3.37866	−	5.85201i	−0.107872	−	0.186840i
$982$	21.5932	+	7.85927i	0.689065	+	0.250799i
$983$	7.12467	−	40.4060i	0.227242	−	1.28875i	−0.631112	−	0.775692i	$-0.717401\pi$
$983$	7.12467	−	40.4060i	0.227242	−	1.28875i	0.858353	−	0.513059i	$-0.171488\pi$
$984$	0.0195710	+	0.110993i	0.000623902	+	0.00353832i
$985$		0			0
$986$	−16.0748	−	13.4884i	−0.511926	−	0.429557i
$987$	11.2276			0.357379
$988$	10.8195	+	0.123138i	0.344214	+	0.00391753i
$989$	−15.3731			−0.488837
$990$		0			0
$991$	−26.7308	+	9.72922i	−0.849133	+	0.309059i	−0.729687	−	0.683782i	$-0.760334\pi$
$991$	−26.7308	+	9.72922i	−0.849133	+	0.309059i	−0.119446	+	0.992841i	$0.538112\pi$
$992$	6.46362	+	36.6570i	0.205220	+	1.16386i
$993$	−8.10017	+	45.9383i	−0.257051	+	1.45781i
$994$	−26.4226	−	9.61703i	−0.838073	−	0.305034i
$995$		0			0
$996$	−7.91705	+	13.7127i	−0.250861	+	0.434504i
$997$	26.9547	−	22.6177i	0.853664	−	0.716309i	−0.106929	−	0.994267i	$-0.534102\pi$
$997$	26.9547	−	22.6177i	0.853664	−	0.716309i	0.960593	+	0.277957i	$0.0896574\pi$
$998$	−8.68620	+	7.28859i	−0.274957	+	0.230716i
$999$	0.401478	−	0.695381i	0.0127022	−	0.0220009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.l.c.301.3		18
5.2	odd	4		475.2.u.b.149.3		36
5.3	odd	4		475.2.u.b.149.4		36
5.4	even	2		95.2.k.a.16.1	yes	18
15.14	odd	2		855.2.bs.c.586.3		18
19.5	even	9		9025.2.a.cc.1.8		9
19.6	even	9	inner	475.2.l.c.101.3		18
19.14	odd	18		9025.2.a.cf.1.2		9
95.14	odd	18		1805.2.a.s.1.8		9
95.24	even	18		1805.2.a.v.1.2		9
95.44	even	18		95.2.k.a.6.1	✓	18
95.63	odd	36		475.2.u.b.424.3		36
95.82	odd	36		475.2.u.b.424.4		36
285.44	odd	18		855.2.bs.c.766.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.k.a.6.1	✓	18	95.44	even	18
95.2.k.a.16.1	yes	18	5.4	even	2
475.2.l.c.101.3		18	19.6	even	9	inner
475.2.l.c.301.3		18	1.1	even	1	trivial
475.2.u.b.149.3		36	5.2	odd	4
475.2.u.b.149.4		36	5.3	odd	4
475.2.u.b.424.3		36	95.63	odd	36
475.2.u.b.424.4		36	95.82	odd	36
855.2.bs.c.586.3		18	15.14	odd	2
855.2.bs.c.766.3		18	285.44	odd	18
1805.2.a.s.1.8		9	95.14	odd	18
1805.2.a.v.1.2		9	95.24	even	18
9025.2.a.cc.1.8		9	19.5	even	9
9025.2.a.cf.1.2		9	19.14	odd	18

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.l (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.484738 + 0.406743i) q^{2} +(1.80387 - 0.656554i) q^{3} +(-0.277766 - 1.57529i) q^{4} +(1.14145 + 0.415455i) q^{6} +(2.04448 + 3.54114i) q^{7} +(1.13887 - 1.97259i) q^{8} +(0.524744 - 0.440313i) q^{9} +O(q^{10})\)	\(q+(0.484738 + 0.406743i) q^{2} +(1.80387 - 0.656554i) q^{3} +(-0.277766 - 1.57529i) q^{4} +(1.14145 + 0.415455i) q^{6} +(2.04448 + 3.54114i) q^{7} +(1.13887 - 1.97259i) q^{8} +(0.524744 - 0.440313i) q^{9} +(2.17413 - 3.76571i) q^{11} +(-1.53531 - 2.65924i) q^{12} +(1.45826 + 0.530764i) q^{13} +(-0.449299 + 2.54810i) q^{14} +(-1.65185 + 0.601224i) q^{16} +(-4.87326 - 4.08915i) q^{17} +0.433458 q^{18} +(0.708014 + 4.30101i) q^{19} +(6.01291 + 5.04543i) q^{21} +(2.58556 - 0.941068i) q^{22} +(0.583829 + 3.31106i) q^{23} +(0.759268 - 4.30602i) q^{24} +(0.490990 + 0.850420i) q^{26} +(-2.22197 + 3.84857i) q^{27} +(5.01042 - 4.20424i) q^{28} +(3.99325 - 3.35074i) q^{29} +(-3.28366 - 5.68747i) q^{31} +(-5.32603 - 1.93852i) q^{32} +(1.44946 - 8.22028i) q^{33} +(-0.699019 - 3.96434i) q^{34} +(-0.839375 - 0.704319i) q^{36} -0.180685 q^{37} +(-1.40621 + 2.37284i) q^{38} +2.97899 q^{39} +(-0.0242217 + 0.00881597i) q^{41} +(0.862490 + 4.89143i) q^{42} +(-0.793995 + 4.50297i) q^{43} +(-6.53598 - 2.37890i) q^{44} +(-1.06375 + 1.84246i) q^{46} +(1.09575 - 0.919441i) q^{47} +(-2.58498 + 2.16906i) q^{48} +(-4.85976 + 8.41736i) q^{49} +(-11.4755 - 4.17673i) q^{51} +(0.431051 - 2.44461i) q^{52} +(0.278010 + 1.57667i) q^{53} +(-2.64246 + 0.961776i) q^{54} +9.31361 q^{56} +(4.10101 + 7.29361i) q^{57} +3.29857 q^{58} +(7.31281 + 6.13617i) q^{59} +(-1.05793 - 5.99980i) q^{61} +(0.721625 - 4.09254i) q^{62} +(2.63203 + 0.957982i) q^{63} +(-0.0353865 - 0.0612913i) q^{64} +(4.04615 - 3.39513i) q^{66} +(-7.87159 + 6.60505i) q^{67} +(-5.08797 + 8.81262i) q^{68} +(3.22704 + 5.58940i) q^{69} +(-1.88710 + 10.7023i) q^{71} +(-0.270938 - 1.53657i) q^{72} +(-12.7987 + 4.65836i) q^{73} +(-0.0875850 - 0.0734926i) q^{74} +(6.57867 - 2.31000i) q^{76} +17.7799 q^{77} +(1.44403 + 1.21168i) q^{78} +(-16.2283 + 5.90661i) q^{79} +(-1.83820 + 10.4250i) q^{81} +(-0.0153270 - 0.00557858i) q^{82} +(-2.57831 - 4.46577i) q^{83} +(6.27783 - 10.8735i) q^{84} +(-2.21643 + 1.85981i) q^{86} +(5.00336 - 8.66608i) q^{87} +(-4.95213 - 8.57735i) q^{88} +(0.477195 + 0.173685i) q^{89} +(1.10187 + 6.24904i) q^{91} +(5.05370 - 1.83940i) q^{92} +(-9.65742 - 8.10354i) q^{93} +0.905127 q^{94} -10.8802 q^{96} +(-2.51273 - 2.10843i) q^{97} +(-5.77942 + 2.10354i) q^{98} +(-0.517226 - 2.93333i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9	\( 18 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 6 q^{6} + 6 q^{8} + 3 q^{9} + 18 q^{12} + 3 q^{13} - 12 q^{14} - 3 q^{16} - 24 q^{17} - 48 q^{18} - 21 q^{21} - 9 q^{22} + 9 q^{23} - 15 q^{24} + 3 q^{26} + 24 q^{27} + 12 q^{28} + 15 q^{29} - 18 q^{31} - 15 q^{32} + 33 q^{33} - 12 q^{34} + 75 q^{36} - 36 q^{37} + 33 q^{38} + 36 q^{39} - 30 q^{41} + 9 q^{42} + 36 q^{43} + 42 q^{44} + 9 q^{46} - 21 q^{47} - 33 q^{48} + 9 q^{49} - 45 q^{51} + 39 q^{52} + 12 q^{53} - 66 q^{54} - 72 q^{57} - 12 q^{58} + 18 q^{59} - 30 q^{61} + 24 q^{62} - 54 q^{63} + 36 q^{64} + 39 q^{66} - 51 q^{68} + 15 q^{69} - 12 q^{71} + 66 q^{72} - 24 q^{73} - 15 q^{74} - 33 q^{76} + 60 q^{77} + 48 q^{78} - 51 q^{79} + 27 q^{81} + 15 q^{82} + 48 q^{84} + 63 q^{86} + 15 q^{87} + 27 q^{88} - 54 q^{89} + 30 q^{91} + 42 q^{92} - 72 q^{93} + 30 q^{94} - 66 q^{96} - 27 q^{97} + 3 q^{98} - 93 q^{99}+O(q^{100}) \) 18 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 6 * q^6 + 6 * q^8 + 3 * q^9 + 18 * q^12 + 3 * q^13 - 12 * q^14 - 3 * q^16 - 24 * q^17 - 48 * q^18 - 21 * q^21 - 9 * q^22 + 9 * q^23 - 15 * q^24 + 3 * q^26 + 24 * q^27 + 12 * q^28 + 15 * q^29 - 18 * q^31 - 15 * q^32 + 33 * q^33 - 12 * q^34 + 75 * q^36 - 36 * q^37 + 33 * q^38 + 36 * q^39 - 30 * q^41 + 9 * q^42 + 36 * q^43 + 42 * q^44 + 9 * q^46 - 21 * q^47 - 33 * q^48 + 9 * q^49 - 45 * q^51 + 39 * q^52 + 12 * q^53 - 66 * q^54 - 72 * q^57 - 12 * q^58 + 18 * q^59 - 30 * q^61 + 24 * q^62 - 54 * q^63 + 36 * q^64 + 39 * q^66 - 51 * q^68 + 15 * q^69 - 12 * q^71 + 66 * q^72 - 24 * q^73 - 15 * q^74 - 33 * q^76 + 60 * q^77 + 48 * q^78 - 51 * q^79 + 27 * q^81 + 15 * q^82 + 48 * q^84 + 63 * q^86 + 15 * q^87 + 27 * q^88 - 54 * q^89 + 30 * q^91 + 42 * q^92 - 72 * q^93 + 30 * q^94 - 66 * q^96 - 27 * q^97 + 3 * q^98 - 93 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more