LMFDB - Embedded newform 475.2.n.b.39.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(39,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("475.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.n (of order $10$, 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:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.20
Character	$\chi$	$=$	475.39
Dual form			475.2.n.b.134.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11654 + 1.53678i) q^{2} +(-0.629163 - 0.204428i) q^{3} +(-0.497012 + 1.52965i) q^{4} +(-2.15934 + 0.580726i) q^{5} +(-0.388324 - 1.19514i) q^{6} +3.69899i q^{7} +(0.707528 - 0.229890i) q^{8} +(-2.07300 - 1.50612i) q^{9} +O(q^{10})$	\(q+(1.11654 + 1.53678i) q^{2} +(-0.629163 - 0.204428i) q^{3} +(-0.497012 + 1.52965i) q^{4} +(-2.15934 + 0.580726i) q^{5} +(-0.388324 - 1.19514i) q^{6} +3.69899i q^{7} +(0.707528 - 0.229890i) q^{8} +(-2.07300 - 1.50612i) q^{9} +(-3.30344 - 2.67004i) q^{10} +(0.469857 - 0.341371i) q^{11} +(0.625403 - 0.860794i) q^{12} +(-2.67718 + 3.68482i) q^{13} +(-5.68456 + 4.13007i) q^{14} +(1.47729 + 0.0760574i) q^{15} +(3.74566 + 2.72138i) q^{16} +(-7.77450 + 2.52609i) q^{17} -4.86739i q^{18} +(0.309017 + 0.951057i) q^{19} +(0.184914 - 3.59166i) q^{20} +(0.756176 - 2.32727i) q^{21} +(1.04923 + 0.340915i) q^{22} +(-0.509142 - 0.700774i) q^{23} -0.492146 q^{24} +(4.32551 - 2.50797i) q^{25} -8.65195 q^{26} +(2.16289 + 2.97697i) q^{27} +(-5.65815 - 1.83844i) q^{28} +(1.75147 - 5.39047i) q^{29} +(1.53257 + 2.35520i) q^{30} +(-0.438627 - 1.34996i) q^{31} +7.30693i q^{32} +(-0.365403 + 0.118727i) q^{33} +(-12.5626 - 9.12725i) q^{34} +(-2.14810 - 7.98739i) q^{35} +(3.33413 - 2.42239i) q^{36} +(0.489545 - 0.673800i) q^{37} +(-1.11654 + 1.53678i) q^{38} +(2.43766 - 1.77106i) q^{39} +(-1.39429 + 0.907291i) q^{40} +(8.66044 + 6.29218i) q^{41} +(4.42081 - 1.43641i) q^{42} +9.46284i q^{43} +(0.288652 + 0.888381i) q^{44} +(5.35095 + 2.04838i) q^{45} +(0.508461 - 1.56488i) q^{46} +(5.20080 + 1.68984i) q^{47} +(-1.80031 - 2.47791i) q^{48} -6.68256 q^{49} +(8.68382 + 3.84713i) q^{50} +5.40783 q^{51} +(-4.30588 - 5.92654i) q^{52} +(-3.88734 - 1.26307i) q^{53} +(-2.16000 + 6.64780i) q^{54} +(-0.816339 + 1.01000i) q^{55} +(0.850361 + 2.61714i) q^{56} -0.661541i q^{57} +(10.2396 - 3.32704i) q^{58} +(4.99226 + 3.62709i) q^{59} +(-0.850574 + 2.22194i) q^{60} +(-6.18275 + 4.49203i) q^{61} +(1.58485 - 2.18135i) q^{62} +(5.57113 - 7.66800i) q^{63} +(-3.73784 + 2.71570i) q^{64} +(3.64107 - 9.51150i) q^{65} +(-0.590443 - 0.428982i) q^{66} +(8.81945 - 2.86561i) q^{67} -13.1477i q^{68} +(0.177076 + 0.544984i) q^{69} +(9.87646 - 12.2194i) q^{70} +(2.96824 - 9.13530i) q^{71} +(-1.81294 - 0.589061i) q^{72} +(-2.90121 - 3.99317i) q^{73} +1.58208 q^{74} +(-3.23415 + 0.693670i) q^{75} -1.60836 q^{76} +(1.26273 + 1.73800i) q^{77} +(5.44349 + 1.76870i) q^{78} +(-2.43976 + 7.50881i) q^{79} +(-9.66854 - 3.70119i) q^{80} +(1.62320 + 4.99570i) q^{81} +20.3347i q^{82} +(3.35925 - 1.09149i) q^{83} +(3.18407 + 2.31336i) q^{84} +(15.3208 - 9.96954i) q^{85} +(-14.5423 + 10.5656i) q^{86} +(-2.20392 + 3.03344i) q^{87} +(0.253959 - 0.349545i) q^{88} +(5.31639 - 3.86258i) q^{89} +(2.82662 + 10.5104i) q^{90} +(-13.6301 - 9.90287i) q^{91} +(1.32498 - 0.430514i) q^{92} +0.939010i q^{93} +(3.20997 + 9.87927i) q^{94} +(-1.21958 - 1.87420i) q^{95} +(1.49374 - 4.59725i) q^{96} +(16.0424 + 5.21250i) q^{97} +(-7.46134 - 10.2697i) q^{98} -1.48816 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9}+O(q^{10}) $ 96 * q + 26 * q^4 - 4 * q^5 - 2 * q^6 + 28 * q^9	$ 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9} + 28 q^{10} - 15 q^{11} - 85 q^{12} + 10 q^{14} - 10 q^{15} - 42 q^{16} + 20 q^{17} - 24 q^{19} - 16 q^{21} - 35 q^{23} - 24 q^{24} - 8 q^{25} + 28 q^{26} + 15 q^{27} + 30 q^{28} + 28 q^{29} - 64 q^{30} - 8 q^{31} + 25 q^{33} - 8 q^{34} + 33 q^{35} - 42 q^{36} - 55 q^{37} - 6 q^{39} - 48 q^{40} - 27 q^{41} + 210 q^{42} - 4 q^{44} + 15 q^{45} + 10 q^{46} - 115 q^{48} - 150 q^{49} + 9 q^{50} + 60 q^{51} - 5 q^{52} + 40 q^{53} + 47 q^{54} + 33 q^{55} - 12 q^{56} + 60 q^{58} + 25 q^{59} + 170 q^{60} + 26 q^{61} - 110 q^{62} - 30 q^{63} + 62 q^{64} - 15 q^{65} - 41 q^{66} + 35 q^{67} + 14 q^{69} - 20 q^{70} - 38 q^{71} - 60 q^{73} + 6 q^{74} - 151 q^{75} - 104 q^{76} + 115 q^{78} + 8 q^{79} - 63 q^{80} - 67 q^{81} + 160 q^{83} + 18 q^{84} - 8 q^{85} - 10 q^{87} - 120 q^{88} + 76 q^{89} + 108 q^{90} - 8 q^{91} + 85 q^{92} + 58 q^{94} + q^{95} - 6 q^{96} - 10 q^{97} + 10 q^{98} - 112 q^{99}+O(q^{100}) $ 96 * q + 26 * q^4 - 4 * q^5 - 2 * q^6 + 28 * q^9 + 28 * q^10 - 15 * q^11 - 85 * q^12 + 10 * q^14 - 10 * q^15 - 42 * q^16 + 20 * q^17 - 24 * q^19 - 16 * q^21 - 35 * q^23 - 24 * q^24 - 8 * q^25 + 28 * q^26 + 15 * q^27 + 30 * q^28 + 28 * q^29 - 64 * q^30 - 8 * q^31 + 25 * q^33 - 8 * q^34 + 33 * q^35 - 42 * q^36 - 55 * q^37 - 6 * q^39 - 48 * q^40 - 27 * q^41 + 210 * q^42 - 4 * q^44 + 15 * q^45 + 10 * q^46 - 115 * q^48 - 150 * q^49 + 9 * q^50 + 60 * q^51 - 5 * q^52 + 40 * q^53 + 47 * q^54 + 33 * q^55 - 12 * q^56 + 60 * q^58 + 25 * q^59 + 170 * q^60 + 26 * q^61 - 110 * q^62 - 30 * q^63 + 62 * q^64 - 15 * q^65 - 41 * q^66 + 35 * q^67 + 14 * q^69 - 20 * q^70 - 38 * q^71 - 60 * q^73 + 6 * q^74 - 151 * q^75 - 104 * q^76 + 115 * q^78 + 8 * q^79 - 63 * q^80 - 67 * q^81 + 160 * q^83 + 18 * q^84 - 8 * q^85 - 10 * q^87 - 120 * q^88 + 76 * q^89 + 108 * q^90 - 8 * q^91 + 85 * q^92 + 58 * q^94 + q^95 - 6 * q^96 - 10 * q^97 + 10 * q^98 - 112 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	1.11654	+	1.53678i	0.789512	+	1.08667i	0.994169	+	0.107837i	$0.0343923\pi$
$2$	1.11654	+	1.53678i	0.789512	+	1.08667i	−0.204656	+	0.978834i	$0.565608\pi$
$3$	−0.629163	−	0.204428i	−0.363248	−	0.118026i	0.121706	−	0.992566i	$-0.461163\pi$
$3$	−0.629163	−	0.204428i	−0.363248	−	0.118026i	−0.484954	+	0.874540i	$0.661163\pi$
$4$	−0.497012	+	1.52965i	−0.248506	+	0.764823i
$5$	−2.15934	+	0.580726i	−0.965687	+	0.259709i
$5$	−2.15934	+	0.580726i	−0.965687	+	0.259709i
$6$	−0.388324	−	1.19514i	−0.158533	−	0.487914i
$7$			3.69899i			1.39809i	0.715078	+	0.699044i	$0.246391\pi$
$7$			3.69899i			1.39809i	−0.715078	+	0.699044i	$0.753609\pi$
$8$	0.707528	−	0.229890i	0.250149	−	0.0812783i
$9$	−2.07300	−	1.50612i	−0.690998	−	0.502040i
$10$	−3.30344	−	2.67004i	−1.04464	−	0.844340i
$11$	0.469857	−	0.341371i	0.141667	−	0.102927i	−0.514694	−	0.857374i	$-0.672095\pi$
$11$	0.469857	−	0.341371i	0.141667	−	0.102927i	0.656362	+	0.754446i	$0.272095\pi$
$12$	0.625403	−	0.860794i	0.180538	−	0.248490i
$13$	−2.67718	+	3.68482i	−0.742516	+	1.02199i	0.255954	+	0.966689i	$0.417610\pi$
$13$	−2.67718	+	3.68482i	−0.742516	+	1.02199i	−0.998470	+	0.0552966i	$0.982390\pi$
$14$	−5.68456	+	4.13007i	−1.51926	+	1.10381i
$15$	1.47729	+	0.0760574i	0.381436	+	0.0196379i
$16$	3.74566	+	2.72138i	0.936415	+	0.680346i
$17$	−7.77450	+	2.52609i	−1.88559	+	0.612666i	−0.902157	+	0.431408i	$0.858017\pi$
$17$	−7.77450	+	2.52609i	−1.88559	+	0.612666i	−0.983436	+	0.181258i	$0.941983\pi$
$18$		−	4.86739i		−	1.14725i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$19$	0.309017	+	0.951057i	0.0708934	+	0.218187i
$20$	0.184914	−	3.59166i	0.0413479	−	0.803119i
$21$	0.756176	−	2.32727i	0.165011	−	0.507852i
$22$	1.04923	+	0.340915i	0.223696	+	0.0726833i
$23$	−0.509142	−	0.700774i	−0.106163	−	0.146121i	0.752630	−	0.658444i	$-0.228785\pi$
$23$	−0.509142	−	0.700774i	−0.106163	−	0.146121i	−0.858793	+	0.512323i	$0.828785\pi$
$24$	−0.492146			−0.100459
$25$	4.32551	−	2.50797i	0.865103	−	0.501594i
$26$	−8.65195			−1.69679
$27$	2.16289	+	2.97697i	0.416249	+	0.572917i
$28$	−5.65815	−	1.83844i	−1.06929	−	0.347433i
$29$	1.75147	−	5.39047i	0.325240	−	1.00098i	−0.646093	−	0.763259i	$-0.723598\pi$
$29$	1.75147	−	5.39047i	0.325240	−	1.00098i	0.971332	−	0.237726i	$-0.0764020\pi$
$30$	1.53257	+	2.35520i	0.279808	+	0.429999i
$31$	−0.438627	−	1.34996i	−0.0787798	−	0.242459i	0.903909	−	0.427726i	$-0.140685\pi$
$31$	−0.438627	−	1.34996i	−0.0787798	−	0.242459i	−0.982688	+	0.185267i	$0.940685\pi$
$32$			7.30693i			1.29169i
$33$	−0.365403	+	0.118727i	−0.0636084	+	0.0206676i
$34$	−12.5626	−	9.12725i	−2.15446	−	1.56531i
$35$	−2.14810	−	7.98739i	−0.363096	−	1.35012i
$36$	3.33413	−	2.42239i	0.555689	−	0.403731i
$37$	0.489545	−	0.673800i	0.0804806	−	0.110772i	−0.766879	−	0.641792i	$-0.778191\pi$
$37$	0.489545	−	0.673800i	0.0804806	−	0.110772i	0.847359	+	0.531020i	$0.178191\pi$
$38$	−1.11654	+	1.53678i	−0.181127	+	0.249299i
$39$	2.43766	−	1.77106i	0.390338	−	0.283597i
$40$	−1.39429	+	0.907291i	−0.220457	+	0.143455i
$41$	8.66044	+	6.29218i	1.35253	+	0.982673i	0.998881	+	0.0472968i	$0.0150606\pi$
$41$	8.66044	+	6.29218i	1.35253	+	0.982673i	0.353653	+	0.935377i	$0.384939\pi$
$42$	4.42081	−	1.43641i	0.682146	−	0.221643i
$43$			9.46284i			1.44307i	0.692378	+	0.721535i	$0.256563\pi$
$43$			9.46284i			1.44307i	−0.692378	+	0.721535i	$0.743437\pi$
$44$	0.288652	+	0.888381i	0.0435160	+	0.133928i
$45$	5.35095	+	2.04838i	0.797672	+	0.305355i
$46$	0.508461	−	1.56488i	0.0749685	−	0.230729i
$47$	5.20080	+	1.68984i	0.758614	+	0.246489i	0.662684	−	0.748899i	$-0.269417\pi$
$47$	5.20080	+	1.68984i	0.758614	+	0.246489i	0.0959303	+	0.995388i	$0.469417\pi$
$48$	−1.80031	−	2.47791i	−0.259852	−	0.357656i
$49$	−6.68256			−0.954651
$50$	8.68382	+	3.84713i	1.22808	+	0.544067i
$51$	5.40783			0.757248
$52$	−4.30588	−	5.92654i	−0.597118	−	0.821863i
$53$	−3.88734	−	1.26307i	−0.533967	−	0.173496i	0.0296075	−	0.999562i	$-0.490574\pi$
$53$	−3.88734	−	1.26307i	−0.533967	−	0.173496i	−0.563575	+	0.826065i	$0.690574\pi$
$54$	−2.16000	+	6.64780i	−0.293939	+	0.904651i
$55$	−0.816339	+	1.01000i	−0.110075	+	0.136188i
$56$	0.850361	+	2.61714i	0.113634	+	0.349730i
$57$		−	0.661541i		−	0.0876233i
$58$	10.2396	−	3.32704i	1.34452	−	0.436861i
$59$	4.99226	+	3.62709i	0.649937	+	0.472207i	0.863250	−	0.504777i	$-0.168425\pi$
$59$	4.99226	+	3.62709i	0.649937	+	0.472207i	−0.213313	+	0.976984i	$0.568425\pi$
$60$	−0.850574	+	2.22194i	−0.109809	+	0.286851i
$61$	−6.18275	+	4.49203i	−0.791620	+	0.575145i	−0.908444	−	0.418007i	$-0.862729\pi$
$61$	−6.18275	+	4.49203i	−0.791620	+	0.575145i	0.116824	+	0.993153i	$0.462729\pi$
$62$	1.58485	−	2.18135i	0.201276	−	0.277032i
$63$	5.57113	−	7.66800i	0.701896	−	0.966077i
$64$	−3.73784	+	2.71570i	−0.467230	+	0.339463i
$65$	3.64107	−	9.51150i	0.451620	−	1.17976i
$66$	−0.590443	−	0.428982i	−0.0726786	−	0.0528041i
$67$	8.81945	−	2.86561i	1.07747	−	0.350090i	0.284075	−	0.958802i	$-0.408313\pi$
$67$	8.81945	−	2.86561i	1.07747	−	0.350090i	0.793391	+	0.608712i	$0.208313\pi$
$68$		−	13.1477i		−	1.59440i
$69$	0.177076	+	0.544984i	0.0213174	+	0.0656083i
$70$	9.87646	−	12.2194i	1.18046	−	1.46050i
$71$	2.96824	−	9.13530i	0.352265	−	1.08416i	−0.605313	−	0.795988i	$-0.706952\pi$
$71$	2.96824	−	9.13530i	0.352265	−	1.08416i	0.957578	−	0.288174i	$-0.0930480\pi$
$72$	−1.81294	−	0.589061i	−0.213657	−	0.0694215i
$73$	−2.90121	−	3.99317i	−0.339561	−	0.467365i	0.604752	−	0.796413i	$-0.293272\pi$
$73$	−2.90121	−	3.99317i	−0.339561	−	0.467365i	−0.944313	+	0.329048i	$0.893272\pi$
$74$	1.58208			0.183913
$75$	−3.23415	+	0.693670i	−0.373448	+	0.0800981i
$76$	−1.60836			−0.184492
$77$	1.26273	+	1.73800i	0.143902	+	0.198063i
$78$	5.44349	+	1.76870i	0.616354	+	0.200265i
$79$	−2.43976	+	7.50881i	−0.274494	+	0.844807i	0.714858	+	0.699269i	$0.246491\pi$
$79$	−2.43976	+	7.50881i	−0.274494	+	0.844807i	−0.989353	+	0.145538i	$0.953509\pi$
$80$	−9.66854	−	3.70119i	−1.08098	−	0.413806i
$81$	1.62320	+	4.99570i	0.180356	+	0.555078i
$82$			20.3347i			2.24559i
$83$	3.35925	−	1.09149i	0.368726	−	0.119806i	−0.118792	−	0.992919i	$-0.537902\pi$
$83$	3.35925	−	1.09149i	0.368726	−	0.119806i	0.487518	+	0.873113i	$0.337902\pi$
$84$	3.18407	+	2.31336i	0.347411	+	0.252409i
$85$	15.3208	−	9.96954i	1.66178	−	1.08135i
$86$	−14.5423	+	10.5656i	−1.56814	+	1.13932i
$87$	−2.20392	+	3.03344i	−0.236285	+	0.325218i
$88$	0.253959	−	0.349545i	0.0270722	−	0.0372616i
$89$	5.31639	−	3.86258i	0.563536	−	0.409433i	−0.269216	−	0.963080i	$-0.586764\pi$
$89$	5.31639	−	3.86258i	0.563536	−	0.409433i	0.832751	+	0.553647i	$0.186764\pi$
$90$	2.82662	+	10.5104i	0.297952	+	1.10789i
$91$	−13.6301	−	9.90287i	−1.42883	−	1.03810i
$92$	1.32498	−	0.430514i	0.138139	−	0.0448841i
$93$			0.939010i			0.0973708i
$94$	3.20997	+	9.87927i	0.331083	+	1.01897i
$95$	−1.21958	−	1.87420i	−0.125126	−	0.192289i
$96$	1.49374	−	4.59725i	0.152454	−	0.469205i
$97$	16.0424	+	5.21250i	1.62886	+	0.529249i	0.974009	−	0.226508i	$-0.0727311\pi$
$97$	16.0424	+	5.21250i	1.62886	+	0.529249i	0.654852	+	0.755757i	$0.272731\pi$
$98$	−7.46134	−	10.2697i	−0.753709	−	1.03739i
$99$	−1.48816			−0.149566
$100$	1.68648	+	7.86300i	0.168648	+	0.786300i
$101$	−2.38075			−0.236893			−0.118447	−	0.992960i	$-0.537791\pi$
$101$	−2.38075			−0.236893			−0.118447	+	0.992960i	$0.537791\pi$
$102$	6.03805	+	8.31067i	0.597856	+	0.822878i
$103$	−4.21047	−	1.36807i	−0.414870	−	0.134800i	0.0941420	−	0.995559i	$-0.469989\pi$
$103$	−4.21047	−	1.36807i	−0.414870	−	0.134800i	−0.509012	+	0.860759i	$0.669989\pi$
$104$	−1.04708	+	3.22257i	−0.102674	+	0.315999i
$105$	−0.281336	+	5.46451i	−0.0274556	+	0.533281i
$106$	−2.39930	−	7.38427i	−0.233040	−	0.717224i
$107$			5.30227i			0.512590i	0.966599	+	0.256295i	$0.0825018\pi$
$107$			5.30227i			0.512590i	−0.966599	+	0.256295i	$0.917498\pi$
$108$	−5.62869	+	1.82887i	−0.541621	+	0.175983i
$109$	3.39432	+	2.46611i	0.325116	+	0.236211i	0.738356	−	0.674412i	$-0.235603\pi$
$109$	3.39432	+	2.46611i	0.325116	+	0.236211i	−0.413239	+	0.910623i	$0.635603\pi$
$110$	−2.46362	−	0.126838i	−0.234897	−	0.0120935i
$111$	−0.445747	+	0.323854i	−0.0423084	+	0.0307389i
$112$	−10.0664	+	13.8552i	−0.951183	+	1.30919i
$113$	−3.81871	+	5.25601i	−0.359234	+	0.494443i	−0.949935	−	0.312447i	$-0.898851\pi$
$113$	−3.81871	+	5.25601i	−0.359234	+	0.494443i	0.590701	+	0.806891i	$0.298851\pi$
$114$	1.01665	−	0.738637i	0.0952176	−	0.0691797i
$115$	1.50637	+	1.21754i	0.140470	+	0.113536i
$116$	7.37500	+	5.35825i	0.684752	+	0.497501i
$117$	11.0996	−	3.60647i	1.02615	−	0.333418i
$118$			11.7218i			1.07908i
$119$	−9.34398	−	28.7578i	−0.856561	−	2.63623i
$120$	1.06271	−	0.285802i	0.0970119	−	0.0260901i
$121$	−3.29496	+	10.1408i	−0.299541	+	0.921894i
$122$	−13.8066	−	4.48602i	−1.24999	−	0.406145i
$123$	−4.16254	−	5.72924i	−0.375323	−	0.516588i
$124$	2.28296			0.205016
$125$	−7.88382	+	7.92751i	−0.705150	+	0.709058i
$126$	18.0044			1.60396
$127$	−7.56739	−	10.4156i	−0.671498	−	0.924237i	0.328296	−	0.944575i	$-0.393526\pi$
$127$	−7.56739	−	10.4156i	−0.671498	−	0.924237i	−0.999793	+	0.0203379i	$0.993526\pi$
$128$	5.55170	+	1.80386i	0.490706	+	0.159440i
$129$	1.93446	−	5.95367i	0.170320	−	0.524191i
$130$	18.6825	−	5.02441i	1.63857	−	0.440670i
$131$	−4.48732	−	13.8105i	−0.392059	−	1.20663i	−0.931229	−	0.364435i	$-0.881262\pi$
$131$	−4.48732	−	13.8105i	−0.392059	−	1.20663i	0.539170	−	0.842197i	$-0.318738\pi$
$132$		−	0.617945i		−	0.0537852i
$133$	−3.51795	+	1.14305i	−0.305045	+	0.0991152i
$134$	14.2511	+	10.3540i	1.23111	+	0.894451i
$135$	−6.39923	−	5.17224i	−0.550758	−	0.445156i
$136$	−4.91995	+	3.57456i	−0.421882	+	0.306516i
$137$	3.49675	−	4.81286i	0.298747	−	0.411190i	−0.633083	−	0.774084i	$-0.718211\pi$
$137$	3.49675	−	4.81286i	0.298747	−	0.411190i	0.931831	+	0.362893i	$0.118211\pi$
$138$	−0.639810	+	0.880623i	−0.0544642	+	0.0749636i
$139$	−3.52230	+	2.55910i	−0.298758	+	0.217060i	−0.727058	−	0.686577i	$-0.759113\pi$
$139$	−3.52230	+	2.55910i	−0.298758	+	0.217060i	0.428300	+	0.903637i	$0.359113\pi$
$140$	13.2855	+	0.683994i	1.12283	+	0.0578081i
$141$	−2.92670	−	2.12637i	−0.246473	−	0.179073i
$142$	17.3531	−	5.63838i	1.45624	−	0.473162i
$143$			2.64525i			0.221207i
$144$	−3.66601	−	11.2828i	−0.305501	−	0.940236i
$145$	−0.651635	+	12.6570i	−0.0541154	+	1.05111i
$146$	2.89733	−	8.91706i	0.239785	−	0.737981i
$147$	4.20442	+	1.36610i	0.346775	+	0.112674i
$148$	0.787366	+	1.08372i	0.0647211	+	0.0890809i
$149$	−1.55161			−0.127113			−0.0635565	−	0.997978i	$-0.520244\pi$
$149$	−1.55161			−0.127113			−0.0635565	+	0.997978i	$0.520244\pi$
$150$	−4.67708	−	4.19569i	−0.381882	−	0.342576i
$151$	−22.8625			−1.86053			−0.930263	−	0.366893i	$-0.880421\pi$
$151$	−22.8625			−1.86053			−0.930263	+	0.366893i	$0.880421\pi$
$152$	0.437276	+	0.601859i	0.0354678	+	0.0488172i
$153$	19.9211	+	6.47275i	1.61052	+	0.523291i
$154$	−1.26104	+	3.88109i	−0.101618	+	0.312747i
$155$	1.73110	+	2.66029i	0.139045	+	0.213680i
$156$	1.49755	+	4.60900i	0.119900	+	0.369015i
$157$			18.5051i			1.47687i	0.674326	+	0.738433i	$0.264434\pi$
$157$			18.5051i			1.47687i	−0.674326	+	0.738433i	$0.735566\pi$
$158$	−14.2635	+	4.63449i	−1.13474	+	0.368700i
$159$	2.18756	+	1.58936i	0.173485	+	0.126044i
$160$	−4.24332	−	15.7781i	−0.335464	−	1.24737i
$161$	2.59216	−	1.88331i	0.204291	−	0.148426i
$162$	−5.86495	+	8.07241i	−0.460794	+	0.634228i
$163$	−5.96455	+	8.20950i	−0.467179	+	0.643017i	−0.975978	−	0.217868i	$-0.930090\pi$
$163$	−5.96455	+	8.20950i	−0.467179	+	0.643017i	0.508799	+	0.860885i	$0.330090\pi$
$164$	−13.9291	+	10.1201i	−1.08768	+	0.790248i
$165$	0.720082	−	0.468570i	0.0560583	−	0.0364781i
$166$	5.42811	+	3.94376i	0.421303	+	0.306095i
$167$	2.02501	−	0.657966i	0.156700	−	0.0509150i	−0.229617	−	0.973281i	$-0.573747\pi$
$167$	2.02501	−	0.657966i	0.156700	−	0.0509150i	0.386317	+	0.922366i	$0.373747\pi$
$168$		−	1.82045i		−	0.140451i
$169$	−2.39340	−	7.36612i	−0.184107	−	0.566625i
$170$	32.4273	+	12.4134i	2.48706	+	0.952067i
$171$	0.791814	−	2.43695i	0.0605515	−	0.186358i
$172$	−14.4748	−	4.70314i	−1.10369	−	0.358611i
$173$	−10.3911	−	14.3021i	−0.790020	−	1.08737i	−0.994106	−	0.108416i	$-0.965422\pi$
$173$	−10.3911	−	14.3021i	−0.790020	−	1.08737i	0.204086	−	0.978953i	$-0.434578\pi$
$174$	−7.12250			−0.539955
$175$	9.27698	+	16.0001i	0.701273	+	1.20949i
$176$	2.68893			0.202686
$177$	−2.39947	−	3.30259i	−0.180355	−	0.248238i
$178$	11.8719	+	3.85741i	0.889837	+	0.289125i
$179$	−2.63420	+	8.10724i	−0.196889	+	0.605964i	0.803060	+	0.595898i	$0.203204\pi$
$179$	−2.63420	+	8.10724i	−0.196889	+	0.605964i	−0.999949	+	0.0100652i	$0.996796\pi$
$180$	−5.79279	+	7.16698i	−0.431769	+	0.534195i
$181$	−1.61764	−	4.97859i	−0.120238	−	0.370056i	0.872765	−	0.488140i	$-0.162325\pi$
$181$	−1.61764	−	4.97859i	−0.120238	−	0.370056i	−0.993004	+	0.118085i	$0.962325\pi$
$182$		−	32.0035i		−	2.37226i
$183$	4.80825	−	1.56230i	0.355436	−	0.115488i
$184$	−0.521333	−	0.378770i	−0.0384332	−	0.0279233i
$185$	−0.665801	+	1.73926i	−0.0489506	+	0.127873i
$186$	−1.44306	+	1.04844i	−0.105810	+	0.0768755i
$187$	−2.79057	+	3.84089i	−0.204067	+	0.280874i
$188$	−5.16971	+	7.11550i	−0.377040	+	0.518951i
$189$	−11.0118	+	8.00053i	−0.800989	+	0.581953i
$190$	1.51854	−	3.96685i	0.110166	−	0.287785i
$191$	−20.6367	−	14.9935i	−1.49322	−	1.08489i	−0.972986	−	0.230865i	$-0.925845\pi$
$191$	−20.6367	−	14.9935i	−1.49322	−	1.08489i	−0.520234	−	0.854024i	$-0.674155\pi$
$192$	2.90688	−	0.944502i	0.209786	−	0.0681635i
$193$		−	12.1241i		−	0.872712i	−0.899774	−	0.436356i	$-0.856269\pi$
$193$		−	12.1241i		−	0.872712i	0.899774	−	0.436356i	$-0.143731\pi$
$194$	9.90150	+	30.4737i	0.710886	+	2.18788i
$195$	−4.23524	+	5.23995i	−0.303292	+	0.375240i
$196$	3.32131	−	10.2219i	0.237237	−	0.730139i
$197$	20.2500	+	6.57964i	1.44276	+	0.468780i	0.922755	−	0.385386i	$-0.125932\pi$
$197$	20.2500	+	6.57964i	1.44276	+	0.468780i	0.520000	+	0.854166i	$0.325932\pi$
$198$	−1.66159	−	2.28698i	−0.118084	−	0.162528i
$199$	12.5767			0.891540			0.445770	−	0.895148i	$-0.352930\pi$
$199$	12.5767			0.891540			0.445770	+	0.895148i	$0.352930\pi$
$200$	2.48387	−	2.76885i	0.175636	−	0.195787i
$201$	−6.13468			−0.432707
$202$	−2.65820	−	3.65870i	−0.187030	−	0.257425i
$203$	19.9393	+	6.47868i	1.39947	+	0.454714i
$204$	−2.68776	+	8.27206i	−0.188181	+	0.579160i
$205$	−22.3549	−	8.55762i	−1.56133	−	0.597690i
$206$	−2.59874	−	7.99809i	−0.181063	−	0.557253i
$207$			2.21953i			0.154268i
$208$	−20.0556	+	6.51647i	−1.39061	+	0.451836i
$209$	0.469857	+	0.341371i	0.0325007	+	0.0236132i
$210$	−8.71189	+	5.66898i	−0.601177	+	0.391197i
$211$	−7.50476	+	5.45253i	−0.516649	+	0.375368i	−0.815340	−	0.578982i	$-0.803450\pi$
$211$	−7.50476	+	5.45253i	−0.516649	+	0.375368i	0.298691	+	0.954350i	$0.403450\pi$
$212$	3.86411	−	5.31849i	0.265388	−	0.365275i
$213$	−3.73502	+	5.14081i	−0.255919	+	0.352242i
$214$	−8.14845	+	5.92019i	−0.557016	+	0.404696i
$215$	−5.49532	−	20.4335i	−0.374778	−	1.39355i
$216$	2.21468	+	1.60906i	0.150690	+	0.109483i
$217$	4.99348	−	1.62248i	0.338980	−	0.110141i
$218$			7.96984i			0.539786i
$219$	1.00902	+	3.10544i	0.0681832	+	0.209846i
$220$	−1.13921	−	1.75069i	−0.0768052	−	0.118031i
$221$	11.5055	−	35.4104i	0.773947	−	2.38196i
$222$	−0.995387	−	0.323421i	−0.0668060	−	0.0217066i
$223$	−5.55911	−	7.65146i	−0.372266	−	0.512380i	0.581249	−	0.813726i	$-0.302564\pi$
$223$	−5.55911	−	7.65146i	−0.372266	−	0.512380i	−0.953515	+	0.301346i	$0.902564\pi$
$224$	−27.0283			−1.80590
$225$	−12.7441	−	1.31573i	−0.849605	−	0.0877150i
$226$	−12.3411			−0.820917
$227$	−6.57789	−	9.05369i	−0.436590	−	0.600915i	0.532860	−	0.846203i	$-0.321117\pi$
$227$	−6.57789	−	9.05369i	−0.436590	−	0.600915i	−0.969450	+	0.245289i	$0.921117\pi$
$228$	1.01192	+	0.328794i	0.0670163	+	0.0217749i
$229$	1.77068	−	5.44960i	0.117010	−	0.360120i	−0.875351	−	0.483488i	$-0.839370\pi$
$229$	1.77068	−	5.44960i	0.117010	−	0.360120i	0.992361	+	0.123368i	$0.0393696\pi$
$230$	−0.189173	+	3.67439i	−0.0124737	+	0.242282i
$231$	−0.439169	−	1.35162i	−0.0288952	−	0.0889302i
$232$		−	4.21655i		−	0.276830i
$233$	19.8095	−	6.43649i	1.29776	−	0.421668i	0.422959	−	0.906149i	$-0.360991\pi$
$233$	19.8095	−	6.43649i	1.29776	−	0.421668i	0.874802	+	0.484481i	$0.160991\pi$
$234$	17.9354	+	13.0309i	1.17248	+	0.851854i
$235$	−12.2116	−	0.628706i	−0.796599	−	0.0410123i
$236$	−8.02938	+	5.83368i	−0.522668	+	0.379741i
$237$	3.07001	−	4.22551i	0.199419	−	0.274476i
$238$	33.7616	−	46.4689i	2.18844	−	3.01213i
$239$	15.1207	−	10.9858i	0.978077	−	0.710614i	0.0207988	−	0.999784i	$-0.493379\pi$
$239$	15.1207	−	10.9858i	0.978077	−	0.710614i	0.957278	+	0.289169i	$0.0933790\pi$
$240$	5.32647	+	4.30517i	0.343822	+	0.277898i
$241$	22.2350	+	16.1546i	1.43228	+	1.04061i	0.989587	+	0.143939i	$0.0459769\pi$
$241$	22.2350	+	16.1546i	1.43228	+	1.04061i	0.442693	+	0.896673i	$0.354023\pi$
$242$	−19.2632	+	6.25900i	−1.23829	+	0.402344i
$243$		−	14.5141i		−	0.931082i
$244$	−3.79831	−	11.6900i	−0.243162	−	0.748376i
$245$	14.4299	−	3.88074i	0.921895	−	0.247931i
$246$	4.15697	−	12.7938i	0.265039	−	0.815706i
$247$	−4.33177	−	1.40748i	−0.275624	−	0.0895556i
$248$	−0.620682	−	0.854296i	−0.0394134	−	0.0542478i
$249$	−2.33665			−0.148079
$250$	−20.9855	−	3.26435i	−1.32724	−	0.206456i
$251$	−0.487130			−0.0307474			−0.0153737	−	0.999882i	$-0.504894\pi$
$251$	−0.487130			−0.0307474			−0.0153737	+	0.999882i	$0.504894\pi$
$252$	8.96040	+	12.3329i	0.564452	+	0.776902i
$253$	−0.478448	−	0.155457i	−0.0300798	−	0.00977351i
$254$	7.55727	−	23.2589i	0.474186	−	1.45939i
$255$	−11.6774	+	3.14047i	−0.731264	+	0.196664i
$256$	6.28201	+	19.3340i	0.392626	+	1.20838i
$257$			2.68019i			0.167186i	0.996500	+	0.0835928i	$0.0266395\pi$
$257$			2.68019i			0.167186i	−0.996500	+	0.0835928i	$0.973360\pi$
$258$	11.3094	−	3.67465i	0.704093	−	0.228774i
$259$	2.49238	+	1.81082i	0.154869	+	0.112519i
$260$	12.7396	+	10.2969i	0.790074	+	0.638585i
$261$	−11.7495	+	8.53649i	−0.727274	+	0.528396i
$262$	16.2135	−	22.3160i	1.00168	−	1.37869i
$263$	5.41495	−	7.45304i	0.333900	−	0.459574i	−0.608747	−	0.793364i	$-0.708328\pi$
$263$	5.41495	−	7.45304i	0.333900	−	0.459574i	0.942647	+	0.333790i	$0.108328\pi$
$264$	−0.231239	+	0.168005i	−0.0142318	+	0.0103400i
$265$	9.12759	+	0.469927i	0.560704	+	0.0288674i
$266$	−5.68456	−	4.13007i	−0.348542	−	0.253231i
$267$	−4.13449	+	1.34338i	−0.253027	+	0.0822134i
$268$			14.9149i			0.911071i
$269$	0.521685	+	1.60558i	0.0318077	+	0.0978940i	0.965700	−	0.259660i	$-0.0836106\pi$
$269$	0.521685	+	1.60558i	0.0318077	+	0.0978940i	−0.933892	+	0.357554i	$0.883611\pi$
$270$	0.803630	−	15.6092i	0.0489073	−	0.949948i
$271$	−6.38912	+	19.6637i	−0.388111	+	1.19448i	0.546087	+	0.837728i	$0.316117\pi$
$271$	−6.38912	+	19.6637i	−0.388111	+	1.19448i	−0.934198	+	0.356755i	$0.883883\pi$
$272$	−35.9951	−	11.6955i	−2.18252	−	0.709145i
$273$	6.55116	+	9.01690i	0.396494	+	0.545727i
$274$	11.3006			0.682693
$275$	1.17622	−	2.65500i	0.0709290	−	0.160102i
$276$	−0.921640			−0.0554762
$277$	−15.3770	−	21.1647i	−0.923916	−	1.27166i	−0.962186	−	0.272394i	$-0.912184\pi$
$277$	−15.3770	−	21.1647i	−0.923916	−	1.27166i	0.0382693	−	0.999267i	$-0.487816\pi$
$278$	−7.86557	−	2.55568i	−0.471745	−	0.153279i
$279$	−1.12392	+	3.45908i	−0.0672875	+	0.207090i
$280$	−3.35606	−	5.15748i	−0.200563	−	0.308218i
$281$	8.05513	+	24.7911i	0.480529	+	1.47892i	0.838354	+	0.545126i	$0.183518\pi$
$281$	8.05513	+	24.7911i	0.480529	+	1.47892i	−0.357825	+	0.933789i	$0.616482\pi$
$282$		−	6.87188i		−	0.409215i
$283$	−6.26152	+	2.03449i	−0.372209	+	0.120938i	−0.489147	−	0.872201i	$-0.662692\pi$
$283$	−6.26152	+	2.03449i	−0.372209	+	0.120938i	0.116938	+	0.993139i	$0.462692\pi$
$284$	12.4985	+	9.08071i	0.741651	+	0.538841i
$285$	0.384174	+	1.42849i	0.0227565	+	0.0846167i
$286$	−4.06518	+	2.95353i	−0.240379	+	0.174646i
$287$	−23.2747	+	32.0349i	−1.37386	+	1.89096i
$288$	11.0051	−	15.1472i	0.648482	−	0.892559i
$289$	40.3084	−	29.2858i	2.37108	−	1.72269i
$290$	−20.1786	+	13.1306i	−1.18493	+	0.771055i
$291$	−9.02772	−	6.55902i	−0.529214	−	0.384497i
$292$	7.55007	−	2.45317i	0.441834	−	0.143561i
$293$			19.7252i			1.15236i	0.817323	+	0.576179i	$0.195457\pi$
$293$			19.7252i			1.15236i	−0.817323	+	0.576179i	$0.804543\pi$
$294$	2.59500	+	7.98659i	0.151344	+	0.465787i
$295$	−12.8863	−	4.93299i	−0.750272	−	0.287210i
$296$	0.191467	−	0.589274i	0.0111288	−	0.0342509i
$297$	2.03250	+	0.660400i	0.117938	+	0.0383203i
$298$	−1.73243	−	2.38449i	−0.100357	−	0.138130i
$299$	3.94529			0.228162
$300$	0.546344	−	5.29187i	0.0315432	−	0.305526i
$301$	−35.0030			−2.01754
$302$	−25.5269	−	35.1348i	−1.46891	−	2.02178i
$303$	1.49788	+	0.486691i	0.0860510	+	0.0279596i
$304$	−1.43072	+	4.40329i	−0.0820572	+	0.252546i
$305$	10.7420	−	13.2903i	0.615087	−	0.761001i
$306$	12.2954	+	37.8415i	0.702884	+	2.16325i
$307$			26.1050i			1.48989i	0.667125	+	0.744946i	$0.267525\pi$
$307$			26.1050i			1.48989i	−0.667125	+	0.744946i	$0.732475\pi$
$308$	−3.28612	+	1.06772i	−0.187244	+	0.0608392i
$309$	2.36940	+	1.72147i	0.134791	+	0.0979312i
$310$	−2.15546	+	5.63065i	−0.122422	+	0.319799i
$311$	4.67229	−	3.39462i	0.264941	−	0.192491i	−0.447381	−	0.894343i	$-0.647643\pi$
$311$	4.67229	−	3.39462i	0.264941	−	0.192491i	0.712323	+	0.701852i	$0.247643\pi$
$312$	1.31756	−	1.81347i	0.0745924	−	0.102668i
$313$	10.2899	−	14.1629i	0.581621	−	0.800533i	−0.412251	−	0.911070i	$-0.635257\pi$
$313$	10.2899	−	14.1629i	0.581621	−	0.800533i	0.993872	+	0.110538i	$0.0352573\pi$
$314$	−28.4383	+	20.6617i	−1.60487	+	1.16600i
$315$	−7.57696	+	19.7931i	−0.426913	+	1.11522i
$316$	−10.2732	−	7.46393i	−0.577914	−	0.419879i
$317$	−22.8846	+	7.43566i	−1.28533	+	0.417628i	−0.870453	−	0.492251i	$-0.836174\pi$
$317$	−22.8846	+	7.43566i	−1.28533	+	0.417628i	−0.414874	+	0.909879i	$0.636174\pi$
$318$			5.13639i			0.288035i
$319$	−1.01721	−	3.13065i	−0.0569529	−	0.175283i
$320$	6.49420	−	8.03479i	0.363037	−	0.449158i
$321$	1.08393	−	3.33599i	0.0604991	−	0.186197i
$322$	5.78849	+	1.88079i	0.322580	+	0.104813i
$323$	−4.80490	−	6.61338i	−0.267352	−	0.367978i
$324$	−8.44841			−0.469356
$325$	−2.33875	+	22.6530i	−0.129730	+	1.25656i
$326$	−19.2759			−1.06759
$327$	−1.63144	−	2.24548i	−0.0902187	−	0.124175i
$328$	7.57401	+	2.46095i	0.418205	+	0.135883i
$329$	−6.25071	+	19.2377i	−0.344613	+	1.06061i
$330$	1.52409	+	0.583433i	0.0838984	+	0.0321169i
$331$	8.47750	+	26.0911i	0.465966	+	1.43409i	0.857764	+	0.514043i	$0.171853\pi$
$331$	8.47750	+	26.0911i	0.465966	+	1.43409i	−0.391799	+	0.920051i	$0.628147\pi$
$332$			5.68095i			0.311782i
$333$	−2.02965	+	0.659472i	−0.111224	+	0.0361389i
$334$	3.27216	+	2.37736i	0.179044	+	0.130083i
$335$	−17.3801	+	11.3095i	−0.949574	+	0.617905i
$336$	9.16578	−	6.65933i	0.500034	−	0.363296i
$337$	−1.52436	+	2.09811i	−0.0830373	+	0.114291i	−0.848515	−	0.529172i	$-0.822503\pi$
$337$	−1.52436	+	2.09811i	−0.0830373	+	0.114291i	0.765478	+	0.643463i	$0.222503\pi$
$338$	8.64781	−	11.9027i	0.470379	−	0.647421i
$339$	3.47707	−	2.52624i	0.188848	−	0.137206i
$340$	7.63522	+	28.3904i	0.414078	+	1.53969i
$341$	−0.666929	−	0.484552i	−0.0361162	−	0.0262400i
$342$	4.62916	−	1.50411i	0.250316	−	0.0813327i
$343$			1.17421i			0.0634012i
$344$	2.17541	+	6.69522i	0.117290	+	0.360982i
$345$	−0.698854	−	1.07397i	−0.0376250	−	0.0578208i
$346$	10.3772	−	31.9377i	0.557881	−	1.71698i
$347$	−22.8002	−	7.40822i	−1.22398	−	0.397694i	−0.375448	−	0.926844i	$-0.622511\pi$
$347$	−22.8002	−	7.40822i	−1.22398	−	0.397694i	−0.848529	+	0.529150i	$0.822511\pi$
$348$	−3.54471	−	4.87887i	−0.190016	−	0.261535i
$349$	16.5020			0.883330			0.441665	−	0.897180i	$-0.354388\pi$
$349$	16.5020			0.883330			0.441665	+	0.897180i	$0.354388\pi$
$350$	−14.2305	+	32.1214i	−0.760653	+	1.71696i
$351$	−16.7600			−0.894585
$352$	2.49438	+	3.43321i	0.132951	+	0.182991i
$353$	−10.7056	−	3.47847i	−0.569803	−	0.185140i	0.00992440	−	0.999951i	$-0.496841\pi$
$353$	−10.7056	−	3.47847i	−0.569803	−	0.185140i	−0.579727	+	0.814811i	$0.696841\pi$
$354$	2.39626	−	7.37494i	0.127360	−	0.391973i
$355$	−1.10434	+	21.4500i	−0.0586121	+	1.13845i
$356$	3.26607	+	10.0519i	0.173101	+	0.532751i
$357$			20.0035i			1.05870i
$358$	−15.4003	+	5.00385i	−0.813929	+	0.264462i
$359$	2.91584	+	2.11848i	0.153892	+	0.111809i	0.662067	−	0.749445i	$-0.269680\pi$
$359$	2.91584	+	2.11848i	0.153892	+	0.111809i	−0.508175	+	0.861254i	$0.669680\pi$
$360$	4.25685	+	0.219161i	0.224356	+	0.0115508i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	5.84486	−	8.04476i	0.307199	−	0.422823i
$363$	4.14613	−	5.70666i	0.217615	−	0.299522i
$364$	21.9222	−	15.9274i	1.14904	−	0.834824i
$365$	8.58363	+	6.93781i	0.449288	+	0.363142i
$366$	7.76951	+	5.64488i	0.406119	+	0.295063i
$367$	35.4939	−	11.5327i	1.85276	−	0.602000i	0.856449	−	0.516231i	$-0.172666\pi$
$367$	35.4939	−	11.5327i	1.85276	−	0.602000i	0.996315	−	0.0857681i	$-0.0273344\pi$
$368$		−	4.01043i		−	0.209058i
$369$	−8.47628	−	26.0873i	−0.441258	−	1.35805i
$370$	−3.41625	+	0.918756i	−0.177603	+	0.0477638i
$371$	4.67210	−	14.3792i	0.242563	−	0.746533i
$372$	−1.43635	−	0.466699i	−0.0744714	−	0.0241972i
$373$	20.2203	+	27.8308i	1.04697	+	1.44103i	0.891409	+	0.453200i	$0.149718\pi$
$373$	20.2203	+	27.8308i	1.04697	+	1.44103i	0.155558	+	0.987827i	$0.450282\pi$
$374$	−9.01840			−0.466330
$375$	6.58081	−	3.37603i	0.339832	−	0.174337i
$376$	4.06819			0.209801
$377$	15.1739	+	20.8851i	0.781496	+	1.07564i
$378$	−24.5902	−	7.98983i	−1.26478	−	0.410953i
$379$	−5.78893	+	17.8165i	−0.297357	+	0.915172i	0.685062	+	0.728485i	$0.259775\pi$
$379$	−5.78893	+	17.8165i	−0.297357	+	0.915172i	−0.982419	+	0.186687i	$0.940225\pi$
$380$	3.47301	−	0.934019i	0.178162	−	0.0479142i
$381$	2.63189	+	8.10011i	0.134836	+	0.414981i
$382$		−	48.4549i		−	2.47917i
$383$	−1.76651	+	0.573975i	−0.0902646	+	0.0293287i	−0.353801	−	0.935321i	$-0.615111\pi$
$383$	−1.76651	+	0.573975i	−0.0902646	+	0.0293287i	0.263537	+	0.964649i	$0.415111\pi$
$384$	−3.12417	−	2.26984i	−0.159430	−	0.115832i
$385$	−3.73597	−	3.01964i	−0.190403	−	0.153895i
$386$	18.6321	−	13.5370i	0.948350	−	0.689017i
$387$	14.2522	−	19.6164i	0.724478	−	0.997159i
$388$	−15.9465	+	21.9485i	−0.809563	+	1.11427i
$389$	−3.82390	+	2.77822i	−0.193879	+	0.140862i	−0.680490	−	0.732757i	$-0.738233\pi$
$389$	−3.82390	+	2.77822i	−0.193879	+	0.140862i	0.486611	+	0.873619i	$0.338233\pi$
$390$	−12.7815	−	0.658045i	−0.647215	−	0.0333214i
$391$	5.72854	+	4.16203i	0.289705	+	0.210483i
$392$	−4.72810	+	1.53625i	−0.238805	+	0.0775925i
$393$			9.60641i			0.484579i
$394$	12.4985	+	38.4664i	0.629664	+	1.93791i
$395$	0.907714	−	17.6309i	0.0456720	−	0.887108i
$396$	0.739632	−	2.27635i	0.0371679	−	0.114391i
$397$	22.3714	+	7.26892i	1.12279	+	0.364816i	0.810832	−	0.585280i	$-0.199015\pi$
$397$	22.3714	+	7.26892i	1.12279	+	0.364816i	0.311958	+	0.950096i	$0.399015\pi$
$398$	14.0424	+	19.3277i	0.703881	+	0.968810i
$399$	2.44704			0.122505
$400$	23.0271	+	2.37736i	1.15135	+	0.118868i
$401$	29.6809			1.48219			0.741097	−	0.671398i	$-0.234306\pi$
$401$	29.6809			1.48219			0.741097	+	0.671398i	$0.234306\pi$
$402$	−6.84961	−	9.42768i	−0.341627	−	0.470210i
$403$	6.14863	+	1.99781i	0.306285	+	0.0995181i
$404$	1.18326	−	3.64170i	0.0588694	−	0.181181i
$405$	−6.40618	−	9.84480i	−0.318326	−	0.489192i
$406$	12.3067	+	37.8761i	0.610771	+	1.87976i
$407$		−	0.483707i		−	0.0239764i
$408$	3.82619	−	1.24320i	0.189425	−	0.0615478i
$409$	−30.7494	−	22.3408i	−1.52046	−	1.10468i	−0.961258	−	0.275650i	$-0.911107\pi$
$409$	−30.7494	−	22.3408i	−1.52046	−	1.10468i	−0.559203	−	0.829030i	$-0.688893\pi$
$410$	−11.8089	−	43.9096i	−0.583199	−	2.16854i
$411$	−3.18391	+	2.31324i	−0.157051	+	0.114104i
$412$	4.18531	−	5.76059i	0.206195	−	0.283804i
$413$	−13.4166	+	18.4664i	−0.660187	+	0.908670i
$414$	−3.41094	+	2.47819i	−0.167638	+	0.121796i
$415$	−6.61992	+	4.30770i	−0.324959	+	0.211457i
$416$	−26.9247	−	19.5619i	−1.32009	−	0.959103i
$417$	2.73925	−	0.890037i	0.134142	−	0.0435853i
$418$			1.10322i			0.0539604i
$419$	−1.34457	−	4.13816i	−0.0656865	−	0.202162i	0.912826	−	0.408348i	$-0.133895\pi$
$419$	−1.34457	−	4.13816i	−0.0656865	−	0.202162i	−0.978513	+	0.206186i	$0.933895\pi$
$420$	−8.21893	−	3.14627i	−0.401043	−	0.153522i
$421$	0.0476210	−	0.146562i	0.00232091	−	0.00714302i	−0.949889	−	0.312586i	$-0.898805\pi$
$421$	0.0476210	−	0.146562i	0.00232091	−	0.00714302i	0.952210	+	0.305443i	$0.0988046\pi$
$422$	−16.7587	−	5.44524i	−0.815802	−	0.265070i
$423$	−8.23612	−	11.3360i	−0.400454	−	0.551178i
$424$	−3.04077			−0.147673
$425$	−27.2933	+	30.4248i	−1.32392	+	1.47582i
$426$	−12.0706			−0.584823
$427$	−16.6160	−	22.8700i	−0.804104	−	1.10675i
$428$	−8.11060	−	2.63529i	−0.392040	−	0.127382i
$429$	0.540762	−	1.66430i	0.0261083	−	0.0803530i
$430$	25.2661	−	31.2599i	1.21844	−	1.50749i
$431$	−5.61018	−	17.2664i	−0.270233	−	0.831691i	−0.990441	−	0.137933i	$-0.955954\pi$
$431$	−5.61018	−	17.2664i	−0.270233	−	0.831691i	0.720209	−	0.693757i	$-0.244046\pi$
$432$			17.0368i			0.819682i
$433$	−16.5856	+	5.38898i	−0.797052	+	0.258978i	−0.679104	−	0.734042i	$-0.737632\pi$
$433$	−16.5856	+	5.38898i	−0.797052	+	0.258978i	−0.117948	+	0.993020i	$0.537632\pi$
$434$	8.06882	+	5.86234i	0.387316	+	0.281401i
$435$	2.99742	−	7.83010i	0.143715	−	0.375425i
$436$	−5.45930	+	3.96641i	−0.261453	+	0.189957i
$437$	0.509142	−	0.700774i	0.0243556	−	0.0335225i
$438$	−3.64578	+	5.01799i	−0.174202	+	0.239769i
$439$	−0.0702552	+	0.0510434i	−0.00335310	+	0.00243617i	−0.589461	−	0.807797i	$-0.700660\pi$
$439$	−0.0702552	+	0.0510434i	−0.00335310	+	0.00243617i	0.586107	+	0.810233i	$0.300660\pi$
$440$	−0.345395	+	0.902269i	−0.0164661	+	0.0430140i
$441$	13.8529	+	10.0647i	0.659663	+	0.479273i
$442$	67.2646	−	21.8556i	3.19945	−	1.03956i
$443$			3.48688i			0.165667i	0.996563	+	0.0828334i	$0.0263969\pi$
$443$			3.48688i			0.165667i	−0.996563	+	0.0828334i	$0.973603\pi$
$444$	−0.273840	−	0.842794i	−0.0129959	−	0.0399972i
$445$	−9.23679	+	11.4280i	−0.437866	+	0.541739i
$446$	5.55168	−	17.0863i	0.262879	−	0.809060i
$447$	0.976216	+	0.317192i	0.0461735	+	0.0150027i
$448$	−10.0454	−	13.8263i	−0.474599	−	0.653229i
$449$	23.7196			1.11939			0.559697	−	0.828697i	$-0.310917\pi$
$449$	23.7196			1.11939			0.559697	+	0.828697i	$0.310917\pi$
$450$	−12.2073	−	21.0540i	−0.575456	−	0.992493i
$451$	6.21714			0.292754
$452$	−6.14188	−	8.45357i	−0.288890	−	0.397623i
$453$	14.3843	+	4.67373i	0.675831	+	0.219591i
$454$	6.56910	−	20.2176i	0.308303	−	0.948859i
$455$	35.1830	+	13.4683i	1.64940	+	0.631404i
$456$	−0.152082	−	0.468059i	−0.00712187	−	0.0219189i
$457$		−	10.2781i		−	0.480791i	−0.970675	−	0.240395i	$-0.922723\pi$
$457$		−	10.2781i		−	0.480791i	0.970675	−	0.240395i	$-0.0772771\pi$
$458$	10.3519	−	3.36354i	0.483713	−	0.157168i
$459$	−24.3355	−	17.6808i	−1.13588	−	0.825267i
$460$	−2.61108	+	1.69908i	−0.121742	+	0.0792200i
$461$	−10.9961	+	7.98911i	−0.512138	+	0.372090i	−0.813634	−	0.581377i	$-0.802514\pi$
$461$	−10.9961	+	7.98911i	−0.512138	+	0.372090i	0.301496	+	0.953467i	$0.402514\pi$
$462$	1.58680	−	2.18405i	0.0738247	−	0.101611i
$463$	22.7510	−	31.3141i	1.05733	−	1.45529i	0.175054	−	0.984559i	$-0.443990\pi$
$463$	22.7510	−	31.3141i	1.05733	−	1.45529i	0.882276	−	0.470732i	$-0.156010\pi$
$464$	21.2299	−	15.4245i	0.985575	−	0.716062i
$465$	−0.545308	−	2.02764i	−0.0252880	−	0.0940297i
$466$	32.0095	+	23.2563i	1.48281	+	1.07733i
$467$	−11.9552	+	3.88449i	−0.553223	+	0.179753i	−0.572269	−	0.820066i	$-0.693937\pi$
$467$	−11.9552	+	3.88449i	−0.553223	+	0.179753i	0.0190469	+	0.999819i	$0.493937\pi$
$468$			18.7708i			0.867683i
$469$	10.5999	+	32.6231i	0.489457	+	1.50639i
$470$	−12.6686	−	19.4686i	−0.584358	−	0.898020i
$471$	3.78295	−	11.6427i	0.174309	−	0.536468i
$472$	4.36600	+	1.41860i	0.200961	+	0.0652963i
$473$	3.23034	+	4.44619i	0.148531	+	0.204436i
$474$	9.92149			0.455709
$475$	3.72188	+	3.33880i	0.170772	+	0.153195i
$476$	48.6333			2.22911
$477$	6.15610	+	8.47314i	0.281868	+	0.387958i
$478$	33.7657	+	10.9711i	1.54441	+	0.501808i
$479$	5.63004	−	17.3275i	0.257243	−	0.791713i	−0.736136	−	0.676834i	$-0.763352\pi$
$479$	5.63004	−	17.3275i	0.257243	−	0.791713i	0.993379	−	0.114880i	$-0.0366483\pi$
$480$	−0.555746	+	10.7945i	−0.0253662	+	0.492698i
$481$	1.17224	+	3.60777i	0.0534493	+	0.164500i
$482$			52.2076i			2.37799i
$483$	−2.01589	+	0.655003i	−0.0917262	+	0.0298037i
$484$	−13.8742	−	10.0802i	−0.630647	−	0.458192i
$485$	−37.6681	−	1.93931i	−1.71042	−	0.0880597i
$486$	22.3051	−	16.2056i	1.01178	−	0.735101i
$487$	−2.91029	+	4.00567i	−0.131878	+	0.181514i	−0.869849	−	0.493318i	$-0.835784\pi$
$487$	−2.91029	+	4.00567i	−0.131878	+	0.181514i	0.737971	+	0.674832i	$0.235784\pi$
$488$	−3.34180	+	4.59959i	−0.151276	+	0.208214i
$489$	5.43092	−	3.94580i	0.245595	−	0.178435i
$490$	22.0754	+	17.8427i	0.997267	+	0.806051i
$491$	26.8120	+	19.4801i	1.21001	+	0.879123i	0.995232	−	0.0975398i	$-0.0310973\pi$
$491$	26.8120	+	19.4801i	1.21001	+	0.879123i	0.214778	+	0.976663i	$0.431097\pi$
$492$	10.8325	−	3.51971i	0.488369	−	0.158681i
$493$			46.3325i			2.08671i
$494$	−2.67360	−	8.22849i	−0.120291	−	0.370217i
$495$	3.21344	−	0.864212i	0.144433	−	0.0388435i
$496$	2.03080	−	6.25015i	0.0911855	−	0.280640i
$497$	33.7914	+	10.9795i	1.51575	+	0.492498i
$498$	−2.60896	−	3.59092i	−0.116910	−	0.160913i
$499$	18.4622			0.826482			0.413241	−	0.910622i	$-0.364397\pi$
$499$	18.4622			0.826482			0.413241	+	0.910622i	$0.364397\pi$
$500$	−8.20793	−	15.9995i	−0.367070	−	0.715520i
$501$	−1.40857			−0.0629303
$502$	−0.543900	−	0.748614i	−0.0242755	−	0.0334123i
$503$	−30.6021	−	9.94323i	−1.36448	−	0.443347i	−0.466945	−	0.884287i	$-0.654645\pi$
$503$	−30.6021	−	9.94323i	−1.36448	−	0.443347i	−0.897537	+	0.440940i	$0.854645\pi$
$504$	2.17893	−	6.70607i	0.0970574	−	0.298712i
$505$	5.14085	−	1.38256i	0.228765	−	0.0615233i
$506$	−0.295302	−	0.908845i	−0.0131278	−	0.0404031i
$507$			5.12377i			0.227555i
$508$	19.6933	−	6.39874i	0.873749	−	0.283898i
$509$	−1.16600	−	0.847148i	−0.0516820	−	0.0375492i	0.561644	−	0.827379i	$-0.310169\pi$
$509$	−1.16600	−	0.847148i	−0.0516820	−	0.0375492i	−0.613326	+	0.789830i	$0.710169\pi$
$510$	−17.8644	−	14.4391i	−0.791051	−	0.639375i
$511$	14.7707	−	10.7315i	0.653418	−	0.474736i
$512$	−15.8359	+	21.7962i	−0.699852	+	0.963264i
$513$	−2.16289	+	2.97697i	−0.0954941	+	0.131436i
$514$	−4.11887	+	2.99254i	−0.181676	+	0.131995i
$515$	9.88632	+	0.508990i	0.435643	+	0.0224288i
$516$	8.14555	+	5.91809i	0.358588	+	0.260529i
$517$	3.02050	−	0.981418i	0.132841	−	0.0431627i
$518$			5.85211i			0.257127i
$519$	3.61395	+	11.1226i	0.158635	+	0.488227i
$520$	0.389566	−	7.56670i	0.0170836	−	0.331822i
$521$	10.0341	−	30.8816i	0.439600	−	1.35295i	−0.448699	−	0.893683i	$-0.648112\pi$
$521$	10.0341	−	30.8816i	0.439600	−	1.35295i	0.888299	−	0.459266i	$-0.151888\pi$
$522$	−26.2375	−	8.52508i	−1.14838	−	0.373133i
$523$	−8.01785	−	11.0356i	−0.350596	−	0.482554i	0.596903	−	0.802314i	$-0.296398\pi$
$523$	−8.01785	−	11.0356i	−0.350596	−	0.482554i	−0.947499	+	0.319760i	$0.896398\pi$
$524$	23.3555			1.02029
$525$	−2.56588	−	11.9631i	−0.111984	−	0.522113i
$526$	17.4997			0.763024
$527$	6.82021	+	9.38722i	0.297093	+	0.408914i
$528$	−1.69178	−	0.549691i	−0.0736251	−	0.0239222i
$529$	6.87553	−	21.1607i	0.298936	−	0.920031i
$530$	9.46914	+	14.5518i	0.411313	+	0.632091i
$531$	−4.88611	−	15.0379i	−0.212039	−	0.652589i
$532$		−	5.94933i		−	0.257936i
$533$	−46.3711	+	15.0669i	−2.00856	+	0.652619i
$534$	−6.68080	−	4.85389i	−0.289107	−	0.210048i
$535$	−3.07917	−	11.4494i	−0.133124	−	0.495001i
$536$	5.58123	−	4.05500i	0.241072	−	0.175149i
$537$	3.31469	−	4.56227i	0.143039	−	0.196877i
$538$	−1.88495	+	2.59441i	−0.0812660	+	0.111853i
$539$	−3.13985	+	2.28123i	−0.135243	+	0.0982597i
$540$	11.0922	−	7.21788i	0.477332	−	0.310608i
$541$	9.52519	+	6.92046i	0.409520	+	0.297534i	0.773407	−	0.633909i	$-0.218551\pi$
$541$	9.52519	+	6.92046i	0.409520	+	0.297534i	−0.363887	+	0.931443i	$0.618551\pi$
$542$	−37.3525	+	12.1366i	−1.60443	+	0.521310i
$543$			3.46304i			0.148613i
$544$	−18.4579	−	56.8077i	−0.791377	−	2.43561i
$545$	−8.76162	−	3.35402i	−0.375307	−	0.143670i
$546$	−6.54240	+	20.1354i	−0.279989	+	0.861717i
$547$	18.0262	+	5.85706i	0.770744	+	0.250430i	0.667883	−	0.744266i	$-0.267200\pi$
$547$	18.0262	+	5.85706i	0.770744	+	0.250430i	0.102860	+	0.994696i	$0.467200\pi$
$548$	5.62405	+	7.74083i	0.240247	+	0.330672i
$549$	19.5823			0.835754
$550$	5.39346	−	1.15680i	0.229978	−	0.0493262i
$551$	5.66787			0.241460
$552$	0.250572	+	0.344883i	0.0106651	+	0.0146792i
$553$	−27.7750	−	9.02466i	−1.18111	−	0.383767i
$554$	15.3565	−	47.2624i	0.652434	−	2.00799i
$555$	0.774449	−	0.958168i	0.0328735	−	0.0406720i
$556$	−2.16389	−	6.65977i	−0.0917694	−	0.282437i
$557$			25.1504i			1.06566i	0.846223	+	0.532828i	$0.178871\pi$
$557$			25.1504i			1.06566i	−0.846223	+	0.532828i	$0.821129\pi$
$558$	−6.57076	+	2.13497i	−0.278162	+	0.0903804i
$559$	−34.8689	−	25.3337i	−1.47480	−	1.07150i
$560$	13.6907	−	35.7639i	0.578537	−	1.51130i
$561$	2.54091	−	1.84608i	0.107277	−	0.0779415i
$562$	−29.1048	+	40.0593i	−1.22771	+	1.68980i
$563$	−12.3262	+	16.9655i	−0.519486	+	0.715011i	−0.985483	−	0.169776i	$-0.945696\pi$
$563$	−12.3262	+	16.9655i	−0.519486	+	0.715011i	0.465997	+	0.884786i	$0.345696\pi$
$564$	4.70720	−	3.41998i	0.198209	−	0.144007i
$565$	5.19360	−	13.5671i	0.218497	−	0.570774i
$566$	−10.1178	−	7.35102i	−0.425283	−	0.308986i
$567$	−18.4791	+	6.00422i	−0.776048	+	0.252153i
$568$		−	7.14585i		−	0.299833i
$569$	3.91906	+	12.0616i	0.164295	+	0.505649i	0.998984	−	0.0450734i	$-0.0143522\pi$
$569$	3.91906	+	12.0616i	0.164295	+	0.505649i	−0.834688	+	0.550723i	$0.814352\pi$
$570$	−1.76634	+	2.18536i	−0.0739839	+	0.0915347i
$571$	−6.33901	+	19.5095i	−0.265279	+	0.816445i	0.726350	+	0.687325i	$0.241215\pi$
$571$	−6.33901	+	19.5095i	−0.265279	+	0.816445i	−0.991629	+	0.129120i	$0.958785\pi$
$572$	−4.04630	−	1.31472i	−0.169184	−	0.0549713i
$573$	9.91879	+	13.6520i	0.414363	+	0.570322i
$574$	−75.2179			−3.13954
$575$	−3.95982	−	1.75429i	−0.165136	−	0.0731591i
$576$	11.8387			0.493279
$577$	4.07627	+	5.61051i	0.169697	+	0.233569i	0.885392	−	0.464845i	$-0.153890\pi$
$577$	4.07627	+	5.61051i	0.169697	+	0.233569i	−0.715695	+	0.698413i	$0.753890\pi$
$578$	90.0118	+	29.2466i	3.74400	+	1.21650i
$579$	−2.47850	+	7.62804i	−0.103003	+	0.317010i
$580$	−19.0368	−	7.28745i	−0.790462	−	0.302595i
$581$	4.03740	+	12.4259i	0.167500	+	0.515511i
$582$		−	21.1971i		−	0.878647i
$583$	−2.25767	+	0.733562i	−0.0935032	+	0.0303810i
$584$	−2.97067	−	2.15832i	−0.122927	−	0.0893120i
$585$	−21.8734	+	14.2334i	−0.904353	+	0.588479i
$586$	−30.3134	+	22.0240i	−1.25223	+	0.909801i
$587$	24.4703	−	33.6805i	1.01000	−	1.39014i	0.0910157	−	0.995849i	$-0.470989\pi$
$587$	24.4703	−	33.6805i	1.01000	−	1.39014i	0.918984	−	0.394296i	$-0.129011\pi$
$588$	−4.17930	+	5.75231i	−0.172351	+	0.237221i
$589$	1.14834	−	0.834319i	0.0473166	−	0.0343775i
$590$	−6.80717	−	25.3114i	−0.280247	−	1.04205i
$591$	−11.3955	−	8.27933i	−0.468749	−	0.340566i
$592$	3.66734	−	1.19159i	0.150727	−	0.0489740i
$593$			19.7900i			0.812678i	0.913722	+	0.406339i	$0.133195\pi$
$593$			19.7900i			0.812678i	−0.913722	+	0.406339i	$0.866805\pi$
$594$	1.25448	+	3.86088i	0.0514718	+	0.158414i
$595$	36.8773	+	56.6717i	1.51182	+	2.32331i
$596$	0.771169	−	2.37341i	0.0315883	−	0.0972188i
$597$	−7.91281	−	2.57103i	−0.323850	−	0.105225i
$598$	4.40507	+	6.06306i	0.180137	+	0.247937i
$599$	26.4293			1.07987			0.539935	−	0.841706i	$-0.318449\pi$
$599$	26.4293			1.07987			0.539935	+	0.841706i	$0.318449\pi$
$600$	−2.12879	+	1.23429i	−0.0869073	+	0.0503897i
$601$	3.90904			0.159453			0.0797265	−	0.996817i	$-0.474595\pi$
$601$	3.90904			0.159453			0.0797265	+	0.996817i	$0.474595\pi$
$602$	−39.0822	−	53.7920i	−1.59287	−	2.19240i
$603$	−22.5986	−	7.34274i	−0.920287	−	0.299019i
$604$	11.3629	−	34.9716i	0.462352	−	1.42297i
$605$	1.22589	−	23.8110i	0.0498395	−	0.968054i
$606$	0.924503	+	2.84533i	0.0375554	+	0.115584i
$607$		−	18.8108i		−	0.763508i	−0.924264	−	0.381754i	$-0.875320\pi$
$607$		−	18.8108i		−	0.763508i	0.924264	−	0.381754i	$-0.124680\pi$
$608$	−6.94930	+	2.25796i	−0.281831	+	0.0915725i
$609$	−11.2207	−	8.15229i	−0.454684	−	0.330347i
$610$	32.4182	+	1.66903i	1.31258	+	0.0675770i
$611$	−20.1502	+	14.6400i	−0.815191	+	0.592271i
$612$	−19.8020	+	27.2552i	−0.800450	+	1.10172i
$613$	−9.36869	+	12.8949i	−0.378398	+	0.520820i	−0.955159	−	0.296093i	$-0.904316\pi$
$613$	−9.36869	+	12.8949i	−0.378398	+	0.520820i	0.576761	+	0.816913i	$0.304316\pi$
$614$	−40.1178	+	29.1473i	−1.61902	+	1.17629i
$615$	12.3155	+	9.95410i	0.496607	+	0.401388i
$616$	1.29297	+	0.939395i	0.0520951	+	0.0378493i
$617$	37.5908	−	12.2140i	1.51335	−	0.491717i	0.569470	−	0.822012i	$-0.307148\pi$
$617$	37.5908	−	12.2140i	1.51335	−	0.491717i	0.943878	+	0.330295i	$0.107148\pi$
$618$			5.56335i			0.223791i
$619$	−12.6246	−	38.8545i	−0.507425	−	1.56169i	−0.796656	−	0.604434i	$-0.793399\pi$
$619$	−12.6246	−	38.8545i	−0.507425	−	1.56169i	0.289231	−	0.957259i	$-0.406601\pi$
$620$	−4.92969	+	1.32577i	−0.197981	+	0.0532443i
$621$	0.984960	−	3.03140i	0.0395251	−	0.121646i
$622$	10.4336	+	3.39008i	0.418349	+	0.135930i
$623$	14.2877	+	19.6653i	0.572423	+	0.787873i
$624$	13.9504			0.558463
$625$	12.4201	−	21.6965i	0.496806	−	0.867862i
$626$	33.2544			1.32911
$627$	−0.225831	−	0.310830i	−0.00901883	−	0.0124134i
$628$	−28.3062	−	9.19725i	−1.12954	−	0.367010i
$629$	−2.10388	+	6.47509i	−0.0838874	+	0.258179i
$630$	−38.8777	+	10.4556i	−1.54893	+	0.416563i
$631$	1.24641	+	3.83606i	0.0496189	+	0.152711i	0.972796	−	0.231664i	$-0.0744169\pi$
$631$	1.24641	+	3.83606i	0.0496189	+	0.152711i	−0.923177	+	0.384375i	$0.874417\pi$
$632$			5.87357i			0.233638i
$633$	5.83637	−	1.89635i	0.231975	−	0.0753732i
$634$	−36.9785	−	26.8665i	−1.46861	−	1.06700i
$635$	22.3892	+	18.0963i	0.888489	+	0.718130i
$636$	−3.51840	+	2.55627i	−0.139514	+	0.101363i
$637$	17.8904	−	24.6240i	0.708844	−	0.975640i
$638$	3.67538	−	5.05873i	0.145510	−	0.200277i
$639$	−19.9120	+	14.4669i	−0.787707	+	0.572302i
$640$	−13.0356	−	0.671127i	−0.515276	−	0.0265286i
$641$	−3.44100	−	2.50003i	−0.135911	−	0.0987453i	0.517752	−	0.855531i	$-0.326769\pi$
$641$	−3.44100	−	2.50003i	−0.135911	−	0.0987453i	−0.653664	+	0.756785i	$0.726769\pi$
$642$	6.33695	−	2.05900i	0.250100	−	0.0812623i
$643$		−	35.6857i		−	1.40731i	−0.710544	−	0.703653i	$-0.751551\pi$
$643$		−	35.6857i		−	1.40731i	0.710544	−	0.703653i	$-0.248449\pi$
$644$	1.59247	+	4.90111i	0.0627520	+	0.193131i
$645$	−0.719719	+	13.9794i	−0.0283389	+	0.550439i
$646$	4.79848	−	14.7682i	0.188794	−	0.581047i
$647$	34.7958	+	11.3058i	1.36796	+	0.444478i	0.898694	−	0.438577i	$-0.144517\pi$
$647$	34.7958	+	11.3058i	1.36796	+	0.444478i	0.469269	+	0.883055i	$0.344517\pi$
$648$	2.29692	+	3.16144i	0.0902316	+	0.124193i
$649$	3.58384			0.140678
$650$	−37.4241	+	21.6989i	−1.46790	+	0.851099i
$651$	−3.47339			−0.136133
$652$	−9.59317	−	13.2039i	−0.375697	−	0.517103i
$653$	−23.1083	−	7.50833i	−0.904296	−	0.293824i	−0.180287	−	0.983614i	$-0.557703\pi$
$653$	−23.1083	−	7.50833i	−0.904296	−	0.293824i	−0.724009	+	0.689790i	$0.757703\pi$
$654$	1.62926	−	5.01433i	0.0637089	−	0.196076i
$655$	17.7098	+	27.2158i	0.691979	+	1.06341i
$656$	15.3157	+	47.1368i	0.597976	+	1.84038i
$657$			12.6474i			0.493421i
$658$	−36.5434	+	11.8737i	−1.42461	+	0.462884i
$659$	28.4302	+	20.6557i	1.10748	+	0.804634i	0.982265	−	0.187496i	$-0.0600370\pi$
$659$	28.4302	+	20.6557i	1.10748	+	0.804634i	0.125218	+	0.992129i	$0.460037\pi$
$660$	0.358857	+	1.33435i	0.0139685	+	0.0519397i
$661$	−17.6060	+	12.7915i	−0.684794	+	0.497532i	−0.874945	−	0.484223i	$-0.839102\pi$
$661$	−17.6060	+	12.7915i	−0.684794	+	0.497532i	0.190151	+	0.981755i	$0.439102\pi$
$662$	−30.6309	+	42.1598i	−1.19050	+	1.63859i
$663$	−14.4777	+	19.9269i	−0.562268	+	0.773896i
$664$	2.12584	−	1.54452i	0.0824987	−	0.0599388i
$665$	6.93266	−	4.51121i	0.268837	−	0.174937i
$666$	−3.27965	−	2.38280i	−0.127084	−	0.0923317i
$667$	−4.66924	+	1.51713i	−0.180794	+	0.0587435i
$668$			3.42457i			0.132501i
$669$	1.93342	+	5.95045i	0.0747503	+	0.230058i
$670$	−36.7858	−	14.0819i	−1.42116	−	0.544031i
$671$	−1.37156	+	4.22123i	−0.0529485	+	0.162959i
$672$	17.0052	+	5.52532i	0.655990	+	0.213144i
$673$	8.09455	+	11.1412i	0.312022	+	0.429461i	0.936010	−	0.351972i	$-0.114489\pi$
$673$	8.09455	+	11.1412i	0.312022	+	0.429461i	−0.623989	+	0.781433i	$0.714489\pi$
$674$	−4.92634			−0.189756
$675$	16.8218	+	7.45244i	0.647470	+	0.286844i
$676$	12.4571			0.479119
$677$	−17.6389	−	24.2779i	−0.677919	−	0.933076i	0.321987	−	0.946744i	$-0.395649\pi$
$677$	−17.6389	−	24.2779i	−0.677919	−	0.933076i	−0.999907	+	0.0136682i	$0.995649\pi$
$678$	7.76456	+	2.52286i	0.298196	+	0.0968898i
$679$	−19.2810	+	59.3408i	−0.739937	+	2.27729i
$680$	8.54802	−	10.5758i	0.327802	−	0.405565i
$681$	2.28774	+	7.04095i	0.0876665	+	0.269810i
$682$		−	1.56595i		−	0.0599632i
$683$	−36.1990	+	11.7618i	−1.38512	+	0.450052i	−0.904348	−	0.426796i	$-0.859642\pi$
$683$	−36.1990	+	11.7618i	−1.38512	+	0.450052i	−0.480768	+	0.876848i	$0.659642\pi$
$684$	3.33413	+	2.42239i	0.127484	+	0.0926223i
$685$	−4.75572	+	12.4233i	−0.181707	+	0.474669i
$686$	−1.80450	+	1.31105i	−0.0688962	+	0.0500560i
$687$	−2.22810	+	3.06671i	−0.0850072	+	0.117002i
$688$	−25.7520	+	35.4446i	−0.981786	+	1.35131i
$689$	15.0613	−	10.9427i	0.573790	−	0.416883i
$690$	0.870168	−	2.27312i	0.0331267	−	0.0865362i
$691$	−27.9763	−	20.3260i	−1.06427	−	0.773237i	−0.0893956	−	0.995996i	$-0.528494\pi$
$691$	−27.9763	−	20.3260i	−1.06427	−	0.773237i	−0.974873	+	0.222759i	$0.928494\pi$
$692$	27.0416	−	8.78636i	1.02797	−	0.334007i
$693$		−	5.50469i		−	0.209106i
$694$	−14.0724	−	43.3105i	−0.534182	−	1.64404i
$695$	6.11971	−	7.57146i	0.232134	−	0.287202i
$696$	−0.861979	+	2.65290i	−0.0326732	+	0.100558i
$697$	−83.2252	−	27.0415i	−3.15238	−	1.02427i
$698$	18.4251	+	25.3599i	0.697400	+	0.959888i
$699$	−13.7792			−0.521177
$700$	−29.0852	+	6.23827i	−1.09932	+	0.235784i
$701$	19.3937			0.732491			0.366245	−	0.930518i	$-0.380643\pi$
$701$	19.3937			0.732491			0.366245	+	0.930518i	$0.380643\pi$
$702$	−18.7132	−	25.7566i	−0.706286	−	0.972119i
$703$	0.792100	+	0.257369i	0.0298746	+	0.00970685i
$704$	−0.829190	+	2.55198i	−0.0312513	+	0.0961815i
$705$	7.55458	+	2.89195i	0.284522	+	0.108917i
$706$	−6.60759	−	20.3361i	−0.248680	−	0.765358i
$707$		−	8.80638i		−	0.331198i
$708$	6.24435	−	2.02891i	0.234677	−	0.0762513i
$709$	15.3321	+	11.1394i	0.575810	+	0.418351i	0.837211	−	0.546880i	$-0.184184\pi$
$709$	15.3321	+	11.1394i	0.575810	+	0.418351i	−0.261401	+	0.965230i	$0.584184\pi$
$710$	−34.1970	+	22.2526i	−1.28339	+	0.835126i
$711$	16.3668	−	11.8912i	0.613802	−	0.445953i
$712$	2.87352	−	3.95507i	0.107690	−	0.148222i
$713$	−0.722690	+	0.994698i	−0.0270650	+	0.0372517i
$714$	−30.7411	+	22.3347i	−1.15046	+	0.835856i
$715$	−1.53617	−	5.71201i	−0.0574494	−	0.213617i
$716$	−11.0920	−	8.05879i	−0.414526	−	0.301171i
$717$	−11.7592	+	3.82079i	−0.439155	+	0.142690i
$718$			6.84639i			0.255505i
$719$	−4.45249	−	13.7034i	−0.166050	−	0.511049i	0.833062	−	0.553179i	$-0.186586\pi$
$719$	−4.45249	−	13.7034i	−0.166050	−	0.511049i	−0.999112	+	0.0421302i	$0.986586\pi$
$720$	14.4684	+	22.2345i	0.539206	+	0.828632i
$721$	5.06047	−	15.5745i	0.188462	−	0.580025i
$722$	−1.80660	−	0.586999i	−0.0672346	−	0.0218459i
$723$	−10.6870	−	14.7093i	−0.397453	−	0.547046i
$724$	8.41947			0.312907
$725$	−5.94314	−	27.7092i	−0.220723	−	1.02909i
$726$	13.3992			0.497292
$727$	28.7629	+	39.5888i	1.06676	+	1.46827i	0.873315	+	0.487156i	$0.161966\pi$
$727$	28.7629	+	39.5888i	1.06676	+	1.46827i	0.193443	+	0.981111i	$0.438034\pi$
$728$	−11.9203	−	3.87313i	−0.441795	−	0.143548i
$729$	1.90252	−	5.85535i	0.0704636	−	0.216865i
$730$	−1.07795	+	20.9375i	−0.0398968	+	0.774933i
$731$	−23.9040	−	73.5688i	−0.884120	−	2.72104i
$732$			8.13140i			0.300545i
$733$	3.87474	−	1.25898i	0.143117	−	0.0465014i	−0.236583	−	0.971611i	$-0.576027\pi$
$733$	3.87474	−	1.25898i	0.143117	−	0.0465014i	0.379699	+	0.925110i	$0.376027\pi$
$734$	57.3535	+	41.6697i	2.11696	+	1.53806i
$735$	−9.87211	−	0.508258i	−0.364138	−	0.0187474i
$736$	5.12050	−	3.72026i	0.188744	−	0.137131i
$737$	3.16564	−	4.35714i	0.116608	−	0.160497i
$738$	30.6265	−	42.1537i	1.12738	−	1.55170i
$739$	24.6479	−	17.9078i	0.906689	−	0.658748i	−0.0334859	−	0.999439i	$-0.510661\pi$
$739$	24.6479	−	17.9078i	0.906689	−	0.658748i	0.940175	+	0.340691i	$0.110661\pi$
$740$	−2.32954	−	1.88287i	−0.0856354	−	0.0692157i
$741$	2.43766	+	1.77106i	0.0895497	+	0.0650617i
$742$	27.3144	−	8.87498i	1.00274	−	0.325811i
$743$			32.1613i			1.17988i	0.807445	+	0.589942i	$0.200850\pi$
$743$			32.1613i			1.17988i	−0.807445	+	0.589942i	$0.799150\pi$
$744$	0.215869	+	0.664376i	0.00791414	+	0.0243572i
$745$	3.35046	−	0.901061i	0.122751	−	0.0330123i
$746$	−20.1933	+	62.1484i	−0.739328	+	2.27542i
$747$	−8.60762	−	2.79679i	−0.314936	−	0.102329i
$748$	−4.48825	−	6.17755i	−0.164107	−	0.225874i
$749$	−19.6131			−0.716646
$750$	12.5360	+	6.34382i	0.457748	+	0.231643i
$751$	45.3016			1.65308			0.826539	−	0.562880i	$-0.190307\pi$
$751$	45.3016			1.65308			0.826539	+	0.562880i	$0.190307\pi$
$752$	14.8817	+	20.4829i	0.542680	+	0.746935i
$753$	0.306485	+	0.0995829i	0.0111689	+	0.00362900i
$754$	−15.1536	+	46.6381i	−0.551862	+	1.69846i
$755$	49.3680	−	13.2769i	1.79669	−	0.483195i
$756$	−6.76498	−	20.8205i	−0.246040	−	0.757234i
$757$		−	9.41621i		−	0.342238i	−0.985250	−	0.171119i	$-0.945262\pi$
$757$		−	9.41621i		−	0.342238i	0.985250	−	0.171119i	$-0.0547383\pi$
$758$	−33.8437	+	10.9965i	−1.22926	+	0.399410i
$759$	0.269242	+	0.195616i	0.00977287	+	0.00710041i
$760$	−1.29374	−	1.04568i	−0.0469291	−	0.0379309i
$761$	−41.9918	+	30.5088i	−1.52220	+	1.10594i	−0.561820	+	0.827260i	$0.689899\pi$
$761$	−41.9918	+	30.5088i	−1.52220	+	1.10594i	−0.960383	+	0.278685i	$0.910101\pi$
$762$	−9.50952	+	13.0887i	−0.344494	+	0.474155i
$763$	−9.12214	+	12.5556i	−0.330244	+	0.454542i
$764$	33.1914	−	24.1149i	1.20082	−	0.872448i
$765$	−46.7753	−	2.40819i	−1.69117	−	0.0870683i
$766$	−2.85446	−	2.07388i	−0.103136	−	0.0749325i
$767$	−26.7304	+	8.68522i	−0.965178	+	0.313605i
$768$		−	13.4485i		−	0.485280i
$769$	2.99698	+	9.22376i	0.108074	+	0.332617i	0.990440	−	0.137947i	$-0.0440504\pi$
$769$	2.99698	+	9.22376i	0.108074	+	0.332617i	−0.882366	+	0.470564i	$0.844050\pi$
$770$	0.469172	−	9.11292i	0.0169078	−	0.328407i
$771$	0.547905	−	1.68628i	0.0197323	−	0.0607298i
$772$	18.5456	+	6.02582i	0.667470	+	0.216874i
$773$	−31.3713	−	43.1789i	−1.12835	−	1.55304i	−0.791168	−	0.611598i	$-0.790527\pi$
$773$	−31.3713	−	43.1789i	−1.12835	−	1.55304i	−0.337180	−	0.941440i	$-0.609473\pi$
$774$	46.0593			1.65557
$775$	−5.28294	−	4.73919i	−0.189769	−	0.170237i
$776$	12.5488			0.450474
$777$	−1.19793	−	1.64881i	−0.0429756	−	0.0591509i
$778$	−8.53906	−	2.77451i	−0.306140	−	0.0994710i
$779$	−3.30799	+	10.1810i	−0.118521	+	0.364771i
$780$	−5.91030	−	9.08273i	−0.211623	−	0.325214i
$781$	−1.72388	−	5.30556i	−0.0616853	−	0.189848i
$782$			13.4506i			0.480992i
$783$	19.8355	−	6.44494i	0.708862	−	0.230323i
$784$	−25.0306	−	18.1858i	−0.893950	−	0.649493i
$785$	−10.7464	−	39.9588i	−0.383555	−	1.42619i
$786$	−14.7630	+	10.7259i	−0.526578	+	0.382581i
$787$	−15.1298	+	20.8243i	−0.539318	+	0.742307i	−0.988515	−	0.151125i	$-0.951710\pi$
$787$	−15.1298	+	20.8243i	−0.539318	+	0.742307i	0.449197	+	0.893433i	$0.351710\pi$
$788$	−20.1290	+	27.7052i	−0.717067	+	0.986958i
$789$	−4.93050	+	3.58221i	−0.175530	+	0.127530i
$790$	28.1084	−	18.2906i	1.00005	−	0.650752i
$791$	−19.4419	−	14.1254i	−0.691276	−	0.502241i
$792$	−1.05291	+	0.342112i	−0.0374137	+	0.0121564i
$793$		−	34.8083i		−	1.23608i
$794$	13.8078	+	42.4961i	0.490021	+	1.50813i
$795$	−5.64668	−	2.16159i	−0.200267	−	0.0766638i
$796$	−6.25078	+	19.2379i	−0.221553	+	0.681870i
$797$	−23.1107	−	7.50914i	−0.818625	−	0.265987i	−0.130378	−	0.991464i	$-0.541619\pi$
$797$	−23.1107	−	7.50914i	−0.818625	−	0.265987i	−0.688246	+	0.725477i	$0.741619\pi$
$798$	2.73221	+	3.76057i	0.0967193	+	0.133123i
$799$	−44.7022			−1.58145
$800$	18.3256	+	31.6062i	0.647907	+	1.11745i
$801$	−16.8383			−0.594954
$802$	33.1399	+	45.6131i	1.17021	+	1.61066i
$803$	−2.72631	−	0.885831i	−0.0962093	−	0.0312603i
$804$	3.04901	−	9.38389i	0.107530	−	0.330944i
$805$	−4.50367	+	5.57205i	−0.158733	+	0.196389i
$806$	3.79498	+	11.6798i	0.133673	+	0.411402i
$807$		−	1.11682i		−	0.0393139i
$808$	−1.68445	+	0.547310i	−0.0592586	+	0.0192543i
$809$	4.67716	+	3.39816i	0.164440	+	0.119473i	0.666962	−	0.745092i	$-0.267594\pi$
$809$	4.67716	+	3.39816i	0.164440	+	0.119473i	−0.502522	+	0.864565i	$0.667594\pi$
$810$	7.97657	−	20.8370i	0.280268	−	0.732138i
$811$	30.0403	−	21.8255i	1.05486	−	0.766398i	0.0817261	−	0.996655i	$-0.473957\pi$
$811$	30.0403	−	21.8255i	1.05486	−	0.766398i	0.973130	+	0.230257i	$0.0739567\pi$
$812$	−19.8202	+	27.2801i	−0.695551	+	0.957344i
$813$	8.03959	−	11.0655i	0.281961	−	0.388086i
$814$	0.743353	−	0.540077i	0.0260545	−	0.0189297i
$815$	8.11203	−	21.1909i	0.284152	−	0.742284i
$816$	20.2559	+	14.7168i	0.709098	+	0.515190i
$817$	−8.99970	+	2.92418i	−0.314859	+	0.102304i
$818$		−	72.1996i		−	2.52440i
$819$	13.3403	+	41.0572i	0.466148	+	1.43466i
$820$	24.2008	−	29.9418i	0.845128	−	1.04561i
$821$	2.90136	−	8.92948i	0.101258	−	0.311641i	−0.887576	−	0.460662i	$-0.847612\pi$
$821$	2.90136	−	8.92948i	0.101258	−	0.311641i	0.988834	+	0.149021i	$0.0476121\pi$
$822$	−7.10991	−	2.31015i	−0.247987	−	0.0805757i
$823$	20.6322	+	28.3978i	0.719193	+	0.989884i	0.999550	+	0.0299883i	$0.00954699\pi$
$823$	20.6322	+	28.3978i	0.719193	+	0.989884i	−0.280357	+	0.959896i	$0.590453\pi$
$824$	−3.29353			−0.114736
$825$	−1.28279	+	1.42997i	−0.0446611	+	0.0497853i
$826$	−43.3589			−1.50865
$827$	−11.4323	−	15.7352i	−0.397540	−	0.547166i	0.562585	−	0.826740i	$-0.309807\pi$
$827$	−11.4323	−	15.7352i	−0.397540	−	0.547166i	−0.960124	+	0.279573i	$0.909807\pi$
$828$	−3.39509	−	1.10313i	−0.117988	−	0.0383365i
$829$	1.49917	−	4.61398i	0.0520684	−	0.160250i	−0.921641	−	0.388043i	$-0.873151\pi$
$829$	1.49917	−	4.61398i	0.0520684	−	0.160250i	0.973709	+	0.227793i	$0.0731511\pi$
$830$	−14.0114	−	5.36367i	−0.486343	−	0.186176i
$831$	5.34802	+	16.4595i	0.185521	+	0.570974i
$832$		−	21.0437i		−	0.729559i
$833$	51.9535	−	16.8807i	1.80008	−	0.584883i
$834$	4.42628	+	3.21588i	0.153269	+	0.111357i
$835$	−3.99060	+	2.59675i	−0.138100	+	0.0898643i
$836$	−0.755702	+	0.549050i	−0.0261365	+	0.0189893i
$837$	3.07007	−	4.22559i	0.106117	−	0.146058i
$838$	4.85819	−	6.68672i	0.167823	−	0.230989i
$839$	5.66281	−	4.11427i	0.195502	−	0.142040i	−0.485728	−	0.874110i	$-0.661445\pi$
$839$	5.66281	−	4.11427i	0.195502	−	0.142040i	0.681230	+	0.732070i	$0.261445\pi$
$840$	1.05718	+	3.93097i	0.0364762	+	0.135631i
$841$	−2.52801	−	1.83671i	−0.0871729	−	0.0633348i
$842$	0.278406	−	0.0904595i	0.00959449	−	0.00311744i
$843$		−	17.2444i		−	0.593927i
$844$	−4.61048	−	14.1896i	−0.158699	−	0.488426i
$845$	9.44586	+	14.5161i	0.324947	+	0.499368i
$846$	8.22511	−	25.3143i	0.282785	−	0.870323i
$847$	−37.5109	−	12.1880i	−1.28889	−	0.418785i
$848$	−11.1234	−	15.3100i	−0.381978	−	0.525747i
$849$	4.35543			0.149478
$850$	−77.2305	−	7.97344i	−2.64898	−	0.273487i
$851$	−0.721429			−0.0247303
$852$	−6.00727	−	8.26829i	−0.205806	−	0.283267i
$853$	13.0131	+	4.22821i	0.445560	+	0.144771i	0.523199	−	0.852210i	$-0.324738\pi$
$853$	13.0131	+	4.22821i	0.445560	+	0.144771i	−0.0776393	+	0.996982i	$0.524738\pi$
$854$	16.5938	−	51.0704i	0.567827	−	1.74759i
$855$	−0.294595	+	5.72204i	−0.0100749	+	0.195690i
$856$	1.21894	+	3.75151i	0.0416624	+	0.128224i
$857$		−	2.18798i		−	0.0747401i	−0.999301	−	0.0373701i	$-0.988102\pi$
$857$		−	2.18798i		−	0.0747401i	0.999301	−	0.0373701i	$-0.0118980\pi$
$858$	3.16145	−	1.02722i	0.107930	−	0.0350686i
$859$	−29.8308	−	21.6733i	−1.01781	−	0.739484i	−0.0519791	−	0.998648i	$-0.516553\pi$
$859$	−29.8308	−	21.6733i	−1.01781	−	0.739484i	−0.965833	+	0.259164i	$0.916553\pi$
$860$	33.9873	+	1.74981i	1.15896	+	0.0596679i
$861$	21.1924	−	15.3972i	0.722236	−	0.524735i
$862$	20.2707	−	27.9002i	0.690422	−	0.950284i
$863$	13.7398	−	18.9112i	0.467707	−	0.643744i	−0.508377	−	0.861134i	$-0.669755\pi$
$863$	13.7398	−	18.9112i	0.467707	−	0.643744i	0.976085	+	0.217391i	$0.0697545\pi$
$864$	−21.7525	+	15.8041i	−0.740034	+	0.537666i
$865$	30.7435	+	24.8488i	1.04531	+	0.844883i
$866$	−26.8001	−	19.4714i	−0.910706	−	0.661666i
$867$	−31.3474	+	10.1854i	−1.06461	+	0.345914i
$868$			8.44465i			0.286630i
$869$	1.41695	+	4.36093i	0.0480668	+	0.147935i
$870$	15.3799	−	4.13622i	0.521428	−	0.140231i
$871$	−13.0520	+	40.1698i	−0.442249	+	1.36110i
$872$	2.96851	+	0.964527i	0.100526	+	0.0326630i
$873$	−25.4052	−	34.9673i	−0.859836	−	1.18346i
$874$	1.64541			0.0556570
$875$	−29.3238	−	29.1622i	−0.991326	−	0.985862i
$876$	−5.25172			−0.177439
$877$	−0.788360	−	1.08508i	−0.0266210	−	0.0366407i	0.795499	−	0.605955i	$-0.207209\pi$
$877$	−0.788360	−	1.08508i	−0.0266210	−	0.0366407i	−0.822120	+	0.569314i	$0.807209\pi$
$878$	−0.156885	−	0.0509751i	−0.00529462	−	0.00172033i
$879$	4.03238	−	12.4104i	0.136009	−	0.418592i
$880$	−5.80632	+	1.56153i	−0.195731	+	0.0526392i
$881$	−2.96410	−	9.12257i	−0.0998632	−	0.307347i	0.888627	−	0.458630i	$-0.151660\pi$
$881$	−2.96410	−	9.12257i	−0.0998632	−	0.307347i	−0.988491	+	0.151283i	$0.951660\pi$
$882$			32.5266i			1.09523i
$883$	−28.3996	+	9.22758i	−0.955722	+	0.310533i	−0.745038	−	0.667021i	$-0.767569\pi$
$883$	−28.3996	+	9.22758i	−0.955722	+	0.310533i	−0.210683	+	0.977554i	$0.567569\pi$
$884$	48.4470	+	35.1988i	1.62945	+	1.18386i
$885$	7.09918	+	5.73798i	0.238636	+	0.192880i
$886$	−5.35859	+	3.89324i	−0.180025	+	0.130796i
$887$	7.11542	−	9.79354i	0.238913	−	0.328835i	−0.672677	−	0.739936i	$-0.734856\pi$
$887$	7.11542	−	9.79354i	0.238913	−	0.328835i	0.911590	+	0.411101i	$0.134856\pi$
$888$	−0.240928	+	0.331608i	−0.00808500	+	0.0111281i
$889$	38.5273	−	27.9917i	1.29217	−	0.938813i
$890$	−27.8756	−	1.43515i	−0.934392	−	0.0481065i
$891$	2.46806	+	1.79315i	0.0826832	+	0.0600729i
$892$	14.4670	−	4.70060i	0.484390	−	0.157388i
$893$			5.46844i			0.182994i
$894$	0.602528	+	1.85439i	0.0201516	+	0.0620201i
$895$	0.980056	−	19.0361i	0.0327597	−	0.636305i
$896$	−6.67246	+	20.5357i	−0.222911	+	0.686050i
$897$	−2.48223	−	0.806526i	−0.0828793	−	0.0269291i
$898$	26.4838	+	36.4518i	0.883776	+	1.21641i
$899$	−8.04514			−0.268320
$900$	8.34655	−	18.8400i	0.278218	−	0.628000i
$901$	33.4127			1.11314
$902$	6.94168	+	9.55441i	0.231133	+	0.318127i
$903$	22.0226	+	7.15557i	0.732866	+	0.238123i
$904$	−1.49354	+	4.59665i	−0.0496745	+	0.152882i
$905$	6.38424	+	9.81107i	0.212219	+	0.326131i
$906$	8.87807	+	27.3239i	0.294954	+	0.907776i
$907$		−	14.3762i		−	0.477355i	−0.971099	−	0.238678i	$-0.923286\pi$
$907$		−	14.3762i		−	0.477355i	0.971099	−	0.238678i	$-0.0767139\pi$
$908$	17.1182	−	5.56205i	0.568088	−	0.184583i
$909$	4.93528	+	3.58569i	0.163693	+	0.118930i
$910$	18.5853	+	69.1065i	0.616096	+	2.29086i
$911$	7.55566	−	5.48951i	0.250330	−	0.181875i	−0.455543	−	0.890214i	$-0.650555\pi$
$911$	7.55566	−	5.48951i	0.250330	−	0.181875i	0.705873	+	0.708338i	$0.250555\pi$
$912$	1.80031	−	2.47791i	0.0596141	−	0.0820518i
$913$	1.20577	−	1.65960i	0.0399051	−	0.0549246i
$914$	15.7953	−	11.4759i	0.522461	−	0.379590i
$915$	−9.47539	+	6.16581i	−0.313247	+	0.203835i
$916$	7.45591	+	5.41704i	0.246350	+	0.178984i
$917$	51.0851	−	16.5986i	1.68698	−	0.548133i
$918$		−	57.1396i		−	1.88589i
$919$	−10.7526	−	33.0932i	−0.354697	−	1.09164i	−0.956185	−	0.292763i	$-0.905425\pi$
$919$	−10.7526	−	33.0932i	−0.354697	−	1.09164i	0.601488	−	0.798882i	$-0.294575\pi$
$920$	1.34570	+	0.515143i	0.0443663	+	0.0169838i
$921$	5.33658	−	16.4243i	0.175846	−	0.541199i
$922$	−24.5551	−	7.97843i	−0.808678	−	0.262755i
$923$	25.7155	+	35.3943i	0.846434	+	1.16502i
$924$	2.28578			0.0751965
$925$	0.427660	−	4.14230i	0.0140614	−	0.136198i
$926$	73.5255			2.41620
$927$	6.66782	+	9.17747i	0.219000	+	0.301428i
$928$	39.3878	+	12.7979i	1.29297	+	0.420110i
$929$	−8.97582	+	27.6247i	−0.294487	+	0.906339i	0.688906	+	0.724851i	$0.258091\pi$
$929$	−8.97582	+	27.6247i	−0.294487	+	0.906339i	−0.983393	+	0.181488i	$0.941909\pi$
$930$	2.50719	−	3.10196i	0.0822141	−	0.101717i
$931$	−2.06502	−	6.35549i	−0.0676785	−	0.208293i
$932$			33.5005i			1.09734i
$933$	−3.63359	+	1.18062i	−0.118958	+	0.0386519i
$934$	−19.3181	−	14.0354i	−0.632108	−	0.459253i
$935$	3.79529	−	9.91435i	0.124119	−	0.324234i
$936$	7.02416	−	5.10335i	0.229592	−	0.166808i
$937$	−17.0726	+	23.4984i	−0.557738	+	0.767661i	−0.991037	−	0.133590i	$-0.957350\pi$
$937$	−17.0726	+	23.4984i	−0.557738	+	0.767661i	0.433299	+	0.901250i	$0.357350\pi$
$938$	−38.2994	+	52.7147i	−1.25052	+	1.72120i
$939$	−9.36932	+	6.80721i	−0.305756	+	0.222145i
$940$	7.03102	−	18.3670i	0.229327	−	0.599065i
$941$	5.94547	+	4.31964i	0.193817	+	0.140816i	0.680461	−	0.732784i	$-0.261779\pi$
$941$	5.94547	+	4.31964i	0.193817	+	0.140816i	−0.486645	+	0.873600i	$0.661779\pi$
$942$	22.1162	−	7.18598i	0.720583	−	0.234132i
$943$		−	9.27262i		−	0.301958i
$944$	8.82863	+	27.1717i	0.287347	+	0.884364i
$945$	19.1321	−	23.6707i	0.622367	−	0.770008i
$946$	−3.22602	+	9.92868i	−0.104887	+	0.322809i
$947$	11.7201	+	3.80810i	0.380853	+	0.123747i	0.493186	−	0.869924i	$-0.335832\pi$
$947$	11.7201	+	3.80810i	0.380853	+	0.123747i	−0.112333	+	0.993671i	$0.535832\pi$
$948$	4.93770	+	6.79616i	0.160369	+	0.220729i
$949$	22.4812			0.729769
$950$	−0.975393	+	9.44763i	−0.0316459	+	0.306522i
$951$	15.9182			0.516183
$952$	−13.2223	−	18.1989i	−0.428536	−	0.589829i
$953$	−21.0130	−	6.82755i	−0.680679	−	0.221166i	−0.0517863	−	0.998658i	$-0.516491\pi$
$953$	−21.0130	−	6.82755i	−0.680679	−	0.221166i	−0.628893	+	0.777492i	$0.716491\pi$
$954$	−6.14787	+	18.9212i	−0.199044	+	0.612596i
$955$	53.2688	+	20.3917i	1.72374	+	0.659860i
$956$	9.28926	+	28.5894i	0.300436	+	0.924647i
$957$			2.17764i			0.0703930i
$958$	32.9148	−	10.6947i	1.06343	−	0.345529i
$959$	17.8027	+	12.9345i	0.574881	+	0.417675i
$960$	−5.72844	+	3.72760i	−0.184885	+	0.120308i
$961$	23.4495	−	17.0371i	0.756437	−	0.549583i
$962$	−4.23552	+	5.82969i	−0.136558	+	0.187957i
$963$	7.98585	−	10.9916i	0.257341	−	0.354199i
$964$	−35.7619	+	25.9826i	−1.15181	+	0.836842i
$965$	7.04078	+	26.1801i	0.226651	+	0.842767i
$966$	−3.25742	−	2.36665i	−0.104806	−	0.0761458i
$967$	25.8376	−	8.39513i	0.830880	−	0.269969i	0.137464	−	0.990507i	$-0.456105\pi$
$967$	25.8376	−	8.39513i	0.830880	−	0.269969i	0.693416	+	0.720538i	$0.256105\pi$
$968$			7.93240i			0.254957i
$969$	1.67111	+	5.14315i	0.0536838	+	0.165222i
$970$	−39.0776	−	60.0531i	−1.25471	−	1.92819i
$971$	10.3160	−	31.7493i	0.331055	−	1.01888i	−0.637577	−	0.770386i	$-0.720063\pi$
$971$	10.3160	−	31.7493i	0.331055	−	1.01888i	0.968633	−	0.248497i	$-0.0799366\pi$
$972$	22.2015	+	7.21370i	0.712113	+	0.231380i
$973$	−9.46610	−	13.0290i	−0.303469	−	0.417689i
$974$	−9.40530			−0.301365
$975$	6.10236	−	13.7744i	0.195432	−	0.441132i
$976$	−35.3830			−1.13258
$977$	−18.3448	−	25.2495i	−0.586904	−	0.807804i	0.407527	−	0.913193i	$-0.366391\pi$
$977$	−18.3448	−	25.2495i	−0.586904	−	0.807804i	−0.994431	+	0.105389i	$0.966391\pi$
$978$	12.1277	+	3.94052i	0.387800	+	0.126004i
$979$	1.17937	−	3.62972i	0.0376928	−	0.116006i
$980$	−1.23570	+	24.0015i	−0.0394729	+	0.766698i
$981$	−3.32214	−	10.2245i	−0.106068	−	0.326443i
$982$			62.9545i			2.00896i
$983$	34.0805	−	11.0734i	1.08700	−	0.353188i	0.289914	−	0.957053i	$-0.406373\pi$
$983$	34.0805	−	11.0734i	1.08700	−	0.353188i	0.797087	+	0.603865i	$0.206373\pi$
$984$	−4.26221	−	3.09667i	−0.135874	−	0.0987184i
$985$	−47.5477	−	2.44796i	−1.51500	−	0.0779984i
$986$	−71.2031	+	51.7321i	−2.26757	+	1.64749i
$987$	7.86544	−	10.8258i	0.250360	−	0.344590i
$988$	4.30588	−	5.92654i	0.136988	−	0.188548i
$989$	6.63131	−	4.81793i	0.210863	−	0.153201i
$990$	4.91604	+	3.97344i	0.156242	+	0.126284i
$991$	−12.8954	−	9.36904i	−0.409635	−	0.297617i	0.363819	−	0.931470i	$-0.381473\pi$
$991$	−12.8954	−	9.36904i	−0.409635	−	0.297617i	−0.773454	+	0.633852i	$0.781473\pi$
$992$	9.86403	−	3.20502i	0.313183	−	0.101759i
$993$		−	18.1486i		−	0.575927i
$994$	20.8563	+	64.1892i	0.661523	+	2.03596i
$995$	−27.1574	+	7.30363i	−0.860948	+	0.231541i
$996$	1.16134	−	3.57424i	0.0367985	−	0.113254i
$997$	−32.2472	−	10.4777i	−1.02128	−	0.331833i	−0.249941	−	0.968261i	$-0.580411\pi$
$997$	−32.2472	−	10.4777i	−1.02128	−	0.331833i	−0.771336	+	0.636428i	$0.780411\pi$
$998$	20.6138	+	28.3724i	0.652518	+	0.898114i
$999$	3.06471			0.0969632

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.n.b.39.20	✓	96
25.9	even	10	inner	475.2.n.b.134.20	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.n.b.39.20	✓	96	1.1	even	1	trivial
475.2.n.b.134.20	yes	96	25.9	even	10	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.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11654 + 1.53678i) q^{2} +(-0.629163 - 0.204428i) q^{3} +(-0.497012 + 1.52965i) q^{4} +(-2.15934 + 0.580726i) q^{5} +(-0.388324 - 1.19514i) q^{6} +3.69899i q^{7} +(0.707528 - 0.229890i) q^{8} +(-2.07300 - 1.50612i) q^{9} +O(q^{10})\)	\(q+(1.11654 + 1.53678i) q^{2} +(-0.629163 - 0.204428i) q^{3} +(-0.497012 + 1.52965i) q^{4} +(-2.15934 + 0.580726i) q^{5} +(-0.388324 - 1.19514i) q^{6} +3.69899i q^{7} +(0.707528 - 0.229890i) q^{8} +(-2.07300 - 1.50612i) q^{9} +(-3.30344 - 2.67004i) q^{10} +(0.469857 - 0.341371i) q^{11} +(0.625403 - 0.860794i) q^{12} +(-2.67718 + 3.68482i) q^{13} +(-5.68456 + 4.13007i) q^{14} +(1.47729 + 0.0760574i) q^{15} +(3.74566 + 2.72138i) q^{16} +(-7.77450 + 2.52609i) q^{17} -4.86739i q^{18} +(0.309017 + 0.951057i) q^{19} +(0.184914 - 3.59166i) q^{20} +(0.756176 - 2.32727i) q^{21} +(1.04923 + 0.340915i) q^{22} +(-0.509142 - 0.700774i) q^{23} -0.492146 q^{24} +(4.32551 - 2.50797i) q^{25} -8.65195 q^{26} +(2.16289 + 2.97697i) q^{27} +(-5.65815 - 1.83844i) q^{28} +(1.75147 - 5.39047i) q^{29} +(1.53257 + 2.35520i) q^{30} +(-0.438627 - 1.34996i) q^{31} +7.30693i q^{32} +(-0.365403 + 0.118727i) q^{33} +(-12.5626 - 9.12725i) q^{34} +(-2.14810 - 7.98739i) q^{35} +(3.33413 - 2.42239i) q^{36} +(0.489545 - 0.673800i) q^{37} +(-1.11654 + 1.53678i) q^{38} +(2.43766 - 1.77106i) q^{39} +(-1.39429 + 0.907291i) q^{40} +(8.66044 + 6.29218i) q^{41} +(4.42081 - 1.43641i) q^{42} +9.46284i q^{43} +(0.288652 + 0.888381i) q^{44} +(5.35095 + 2.04838i) q^{45} +(0.508461 - 1.56488i) q^{46} +(5.20080 + 1.68984i) q^{47} +(-1.80031 - 2.47791i) q^{48} -6.68256 q^{49} +(8.68382 + 3.84713i) q^{50} +5.40783 q^{51} +(-4.30588 - 5.92654i) q^{52} +(-3.88734 - 1.26307i) q^{53} +(-2.16000 + 6.64780i) q^{54} +(-0.816339 + 1.01000i) q^{55} +(0.850361 + 2.61714i) q^{56} -0.661541i q^{57} +(10.2396 - 3.32704i) q^{58} +(4.99226 + 3.62709i) q^{59} +(-0.850574 + 2.22194i) q^{60} +(-6.18275 + 4.49203i) q^{61} +(1.58485 - 2.18135i) q^{62} +(5.57113 - 7.66800i) q^{63} +(-3.73784 + 2.71570i) q^{64} +(3.64107 - 9.51150i) q^{65} +(-0.590443 - 0.428982i) q^{66} +(8.81945 - 2.86561i) q^{67} -13.1477i q^{68} +(0.177076 + 0.544984i) q^{69} +(9.87646 - 12.2194i) q^{70} +(2.96824 - 9.13530i) q^{71} +(-1.81294 - 0.589061i) q^{72} +(-2.90121 - 3.99317i) q^{73} +1.58208 q^{74} +(-3.23415 + 0.693670i) q^{75} -1.60836 q^{76} +(1.26273 + 1.73800i) q^{77} +(5.44349 + 1.76870i) q^{78} +(-2.43976 + 7.50881i) q^{79} +(-9.66854 - 3.70119i) q^{80} +(1.62320 + 4.99570i) q^{81} +20.3347i q^{82} +(3.35925 - 1.09149i) q^{83} +(3.18407 + 2.31336i) q^{84} +(15.3208 - 9.96954i) q^{85} +(-14.5423 + 10.5656i) q^{86} +(-2.20392 + 3.03344i) q^{87} +(0.253959 - 0.349545i) q^{88} +(5.31639 - 3.86258i) q^{89} +(2.82662 + 10.5104i) q^{90} +(-13.6301 - 9.90287i) q^{91} +(1.32498 - 0.430514i) q^{92} +0.939010i q^{93} +(3.20997 + 9.87927i) q^{94} +(-1.21958 - 1.87420i) q^{95} +(1.49374 - 4.59725i) q^{96} +(16.0424 + 5.21250i) q^{97} +(-7.46134 - 10.2697i) q^{98} -1.48816 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9}+O(q^{10}) \) 96 * q + 26 * q^4 - 4 * q^5 - 2 * q^6 + 28 * q^9	\( 96 q + 26 q^{4} - 4 q^{5} - 2 q^{6} + 28 q^{9} + 28 q^{10} - 15 q^{11} - 85 q^{12} + 10 q^{14} - 10 q^{15} - 42 q^{16} + 20 q^{17} - 24 q^{19} - 16 q^{21} - 35 q^{23} - 24 q^{24} - 8 q^{25} + 28 q^{26} + 15 q^{27} + 30 q^{28} + 28 q^{29} - 64 q^{30} - 8 q^{31} + 25 q^{33} - 8 q^{34} + 33 q^{35} - 42 q^{36} - 55 q^{37} - 6 q^{39} - 48 q^{40} - 27 q^{41} + 210 q^{42} - 4 q^{44} + 15 q^{45} + 10 q^{46} - 115 q^{48} - 150 q^{49} + 9 q^{50} + 60 q^{51} - 5 q^{52} + 40 q^{53} + 47 q^{54} + 33 q^{55} - 12 q^{56} + 60 q^{58} + 25 q^{59} + 170 q^{60} + 26 q^{61} - 110 q^{62} - 30 q^{63} + 62 q^{64} - 15 q^{65} - 41 q^{66} + 35 q^{67} + 14 q^{69} - 20 q^{70} - 38 q^{71} - 60 q^{73} + 6 q^{74} - 151 q^{75} - 104 q^{76} + 115 q^{78} + 8 q^{79} - 63 q^{80} - 67 q^{81} + 160 q^{83} + 18 q^{84} - 8 q^{85} - 10 q^{87} - 120 q^{88} + 76 q^{89} + 108 q^{90} - 8 q^{91} + 85 q^{92} + 58 q^{94} + q^{95} - 6 q^{96} - 10 q^{97} + 10 q^{98} - 112 q^{99}+O(q^{100}) \) 96 * q + 26 * q^4 - 4 * q^5 - 2 * q^6 + 28 * q^9 + 28 * q^10 - 15 * q^11 - 85 * q^12 + 10 * q^14 - 10 * q^15 - 42 * q^16 + 20 * q^17 - 24 * q^19 - 16 * q^21 - 35 * q^23 - 24 * q^24 - 8 * q^25 + 28 * q^26 + 15 * q^27 + 30 * q^28 + 28 * q^29 - 64 * q^30 - 8 * q^31 + 25 * q^33 - 8 * q^34 + 33 * q^35 - 42 * q^36 - 55 * q^37 - 6 * q^39 - 48 * q^40 - 27 * q^41 + 210 * q^42 - 4 * q^44 + 15 * q^45 + 10 * q^46 - 115 * q^48 - 150 * q^49 + 9 * q^50 + 60 * q^51 - 5 * q^52 + 40 * q^53 + 47 * q^54 + 33 * q^55 - 12 * q^56 + 60 * q^58 + 25 * q^59 + 170 * q^60 + 26 * q^61 - 110 * q^62 - 30 * q^63 + 62 * q^64 - 15 * q^65 - 41 * q^66 + 35 * q^67 + 14 * q^69 - 20 * q^70 - 38 * q^71 - 60 * q^73 + 6 * q^74 - 151 * q^75 - 104 * q^76 + 115 * q^78 + 8 * q^79 - 63 * q^80 - 67 * q^81 + 160 * q^83 + 18 * q^84 - 8 * q^85 - 10 * q^87 - 120 * q^88 + 76 * q^89 + 108 * q^90 - 8 * q^91 + 85 * q^92 + 58 * q^94 + q^95 - 6 * q^96 - 10 * q^97 + 10 * q^98 - 112 * q^99

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