LMFDB - Embedded newform 418.2.j.a.177.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(23,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("418.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.j (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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			177.1
Character	$\chi$	$=$	418.177
Dual form			418.2.j.a.111.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(-2.02265 - 0.736184i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.505679 - 2.86785i) q^{5} +(2.02265 - 0.736184i) q^{6} +(1.62478 - 2.81421i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.25101 + 1.04972i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(-2.02265 - 0.736184i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.505679 - 2.86785i) q^{5} +(2.02265 - 0.736184i) q^{6} +(1.62478 - 2.81421i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.25101 + 1.04972i) q^{9} +(2.23079 + 1.87186i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.07623 + 1.86408i) q^{12} +(-3.31052 + 1.20493i) q^{13} +(0.564281 + 3.20020i) q^{14} +(-1.08845 + 6.17293i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(2.72527 - 2.28677i) q^{17} -1.63308 q^{18} +(-3.66468 + 2.36011i) q^{19} -2.91209 q^{20} +(-5.35814 + 4.49602i) q^{21} +(-0.939693 - 0.342020i) q^{22} +(0.484511 - 2.74780i) q^{23} +(-0.373771 - 2.11976i) q^{24} +(-3.27039 + 1.19032i) q^{25} +(1.76149 - 3.05099i) q^{26} +(1.47112 + 2.54805i) q^{27} +(-2.48931 - 2.08878i) q^{28} +(-7.69713 - 6.45866i) q^{29} +(-3.13408 - 5.42838i) q^{30} +(-1.80194 + 3.12106i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.373771 - 2.11976i) q^{33} +(-0.617768 + 3.50354i) q^{34} +(-8.89235 - 3.23655i) q^{35} +(1.25101 - 1.04972i) q^{36} +3.34865 q^{37} +(1.29025 - 4.16356i) q^{38} +7.58308 q^{39} +(2.23079 - 1.87186i) q^{40} +(-8.44150 - 3.07246i) q^{41} +(1.21459 - 6.88830i) q^{42} +(1.23938 + 7.02888i) q^{43} +(0.939693 - 0.342020i) q^{44} +(2.37784 - 4.11854i) q^{45} +(1.39509 + 2.41637i) q^{46} +(1.00493 + 0.843235i) q^{47} +(1.64888 + 1.38357i) q^{48} +(-1.77984 - 3.08278i) q^{49} +(1.74014 - 3.01401i) q^{50} +(-7.19575 + 2.61904i) q^{51} +(0.611760 + 3.46946i) q^{52} +(0.0301012 - 0.170712i) q^{53} +(-2.76480 - 1.00630i) q^{54} +(2.23079 - 1.87186i) q^{55} +3.24957 q^{56} +(9.14984 - 2.07580i) q^{57} +10.0479 q^{58} +(-7.10131 + 5.95870i) q^{59} +(5.89014 + 2.14384i) q^{60} +(-0.695487 + 3.94430i) q^{61} +(-0.625809 - 3.54914i) q^{62} +(4.98677 - 1.81504i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(5.12963 + 8.88478i) q^{65} +(1.64888 + 1.38357i) q^{66} +(6.94300 + 5.82587i) q^{67} +(-1.77879 - 3.08096i) q^{68} +(-3.00288 + 5.20114i) q^{69} +(8.89235 - 3.23655i) q^{70} +(-2.19794 - 12.4651i) q^{71} +(-0.283582 + 1.60827i) q^{72} +(-12.4814 - 4.54287i) q^{73} +(-2.56522 + 2.15247i) q^{74} +7.49115 q^{75} +(1.68789 + 4.01883i) q^{76} +3.24957 q^{77} +(-5.80898 + 4.87431i) q^{78} +(6.35375 + 2.31258i) q^{79} +(-0.505679 + 2.86785i) q^{80} +(-1.95047 - 11.0616i) q^{81} +(8.44150 - 3.07246i) q^{82} +(-1.23902 + 2.14604i) q^{83} +(3.49728 + 6.05747i) q^{84} +(-7.93623 - 6.65929i) q^{85} +(-5.46750 - 4.58778i) q^{86} +(10.8138 + 18.7301i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(7.46104 - 2.71560i) q^{89} +(0.825816 + 4.68343i) q^{90} +(-1.98796 + 11.2743i) q^{91} +(-2.62192 - 0.954300i) q^{92} +(5.94238 - 4.98625i) q^{93} -1.31184 q^{94} +(8.62160 + 9.31629i) q^{95} -2.15246 q^{96} +(3.91947 - 3.28883i) q^{97} +(3.34501 + 1.21748i) q^{98} +(-0.283582 + 1.60827i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{8}+O(q^{10}) $ 24 * q + 12 * q^8	$ 24 q + 12 q^{8} + 12 q^{11} - 3 q^{12} - 3 q^{13} + 3 q^{14} + 27 q^{15} - 6 q^{18} - 21 q^{19} - 18 q^{20} + 15 q^{21} + 9 q^{23} + 36 q^{25} - 21 q^{27} - 3 q^{28} - 9 q^{30} - 27 q^{31} - 9 q^{34} - 45 q^{35} + 18 q^{37} + 9 q^{38} + 36 q^{39} - 18 q^{41} + 39 q^{42} - 48 q^{43} + 36 q^{45} - 18 q^{46} - 9 q^{47} + 6 q^{49} + 3 q^{50} - 18 q^{51} - 3 q^{52} - 36 q^{53} - 45 q^{54} + 18 q^{58} + 9 q^{59} - 9 q^{60} + 15 q^{61} - 33 q^{62} + 87 q^{63} - 12 q^{64} - 36 q^{65} + 33 q^{67} + 9 q^{68} - 18 q^{69} + 45 q^{70} - 9 q^{71} - 3 q^{73} + 3 q^{74} + 42 q^{75} + 9 q^{76} + 12 q^{78} + 15 q^{79} - 108 q^{81} + 18 q^{82} + 36 q^{83} - 9 q^{84} - 99 q^{85} - 33 q^{86} + 63 q^{87} - 12 q^{88} - 27 q^{89} - 36 q^{90} - 21 q^{91} - 9 q^{92} - 21 q^{93} + 54 q^{94} + 18 q^{95} - 6 q^{96} + 45 q^{97} + 39 q^{98}+O(q^{100}) $ 24 * q + 12 * q^8 + 12 * q^11 - 3 * q^12 - 3 * q^13 + 3 * q^14 + 27 * q^15 - 6 * q^18 - 21 * q^19 - 18 * q^20 + 15 * q^21 + 9 * q^23 + 36 * q^25 - 21 * q^27 - 3 * q^28 - 9 * q^30 - 27 * q^31 - 9 * q^34 - 45 * q^35 + 18 * q^37 + 9 * q^38 + 36 * q^39 - 18 * q^41 + 39 * q^42 - 48 * q^43 + 36 * q^45 - 18 * q^46 - 9 * q^47 + 6 * q^49 + 3 * q^50 - 18 * q^51 - 3 * q^52 - 36 * q^53 - 45 * q^54 + 18 * q^58 + 9 * q^59 - 9 * q^60 + 15 * q^61 - 33 * q^62 + 87 * q^63 - 12 * q^64 - 36 * q^65 + 33 * q^67 + 9 * q^68 - 18 * q^69 + 45 * q^70 - 9 * q^71 - 3 * q^73 + 3 * q^74 + 42 * q^75 + 9 * q^76 + 12 * q^78 + 15 * q^79 - 108 * q^81 + 18 * q^82 + 36 * q^83 - 9 * q^84 - 99 * q^85 - 33 * q^86 + 63 * q^87 - 12 * q^88 - 27 * q^89 - 36 * q^90 - 21 * q^91 - 9 * q^92 - 21 * q^93 + 54 * q^94 + 18 * q^95 - 6 * q^96 + 45 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

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 $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	−2.02265	−	0.736184i	−1.16778	−	0.425036i	−0.315908	−	0.948790i	$-0.602309\pi$
$3$	−2.02265	−	0.736184i	−1.16778	−	0.425036i	−0.851870	+	0.523754i	$0.824531\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.505679	−	2.86785i	−0.226147	−	1.28254i	−0.860481	−	0.509483i	$-0.829837\pi$
$5$	−0.505679	−	2.86785i	−0.226147	−	1.28254i	0.634334	−	0.773059i	$-0.281274\pi$
$6$	2.02265	−	0.736184i	0.825743	−	0.300546i
$7$	1.62478	−	2.81421i	0.614110	−	1.06367i	−0.376429	−	0.926445i	$-0.622848\pi$
$7$	1.62478	−	2.81421i	0.614110	−	1.06367i	0.990540	−	0.137225i	$-0.0438184\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	1.25101	+	1.04972i	0.417004	+	0.349908i
$10$	2.23079	+	1.87186i	0.705438	+	0.591933i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	−1.07623	+	1.86408i	−0.310681	+	0.538115i
$13$	−3.31052	+	1.20493i	−0.918174	+	0.334188i	−0.757512	−	0.652821i	$-0.773585\pi$
$13$	−3.31052	+	1.20493i	−0.918174	+	0.334188i	−0.160662	+	0.987009i	$0.551363\pi$
$14$	0.564281	+	3.20020i	0.150811	+	0.855289i
$15$	−1.08845	+	6.17293i	−0.281038	+	1.59384i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	2.72527	−	2.28677i	0.660975	−	0.554624i	−0.249404	−	0.968400i	$-0.580235\pi$
$17$	2.72527	−	2.28677i	0.660975	−	0.554624i	0.910379	+	0.413776i	$0.135790\pi$
$18$	−1.63308			−0.384921
$19$	−3.66468	+	2.36011i	−0.840735	+	0.541447i
$19$	−3.66468	+	2.36011i	−0.840735	+	0.541447i
$20$	−2.91209			−0.651163
$21$	−5.35814	+	4.49602i	−1.16924	+	0.981111i
$22$	−0.939693	−	0.342020i	−0.200343	−	0.0729189i
$23$	0.484511	−	2.74780i	0.101027	−	0.572955i	−0.891705	−	0.452616i	$-0.850491\pi$
$23$	0.484511	−	2.74780i	0.101027	−	0.572955i	0.992733	−	0.120339i	$-0.0383982\pi$
$24$	−0.373771	−	2.11976i	−0.0762956	−	0.432694i
$25$	−3.27039	+	1.19032i	−0.654078	+	0.238065i
$26$	1.76149	−	3.05099i	0.345457	−	0.598349i
$27$	1.47112	+	2.54805i	0.283117	+	0.490373i
$28$	−2.48931	−	2.08878i	−0.470436	−	0.394743i
$29$	−7.69713	−	6.45866i	−1.42932	−	1.19934i	−0.946113	−	0.323836i	$-0.895027\pi$
$29$	−7.69713	−	6.45866i	−1.42932	−	1.19934i	−0.483207	−	0.875506i	$-0.660528\pi$
$30$	−3.13408	−	5.42838i	−0.572202	−	0.991083i
$31$	−1.80194	+	3.12106i	−0.323639	+	0.560559i	−0.981236	−	0.192811i	$-0.938240\pi$
$31$	−1.80194	+	3.12106i	−0.323639	+	0.560559i	0.657597	+	0.753370i	$0.271573\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	−0.373771	−	2.11976i	−0.0650651	−	0.369003i
$34$	−0.617768	+	3.50354i	−0.105946	+	0.600852i
$35$	−8.89235	−	3.23655i	−1.50308	−	0.547077i
$36$	1.25101	−	1.04972i	0.208502	−	0.174954i
$37$	3.34865			0.550515			0.275258	−	0.961371i	$-0.411237\pi$
$37$	3.34865			0.550515			0.275258	+	0.961371i	$0.411237\pi$
$38$	1.29025	−	4.16356i	0.209307	−	0.675419i
$39$	7.58308			1.21427
$40$	2.23079	−	1.87186i	0.352719	−	0.295966i
$41$	−8.44150	−	3.07246i	−1.31834	−	0.479837i	−0.415415	−	0.909632i	$-0.636364\pi$
$41$	−8.44150	−	3.07246i	−1.31834	−	0.479837i	−0.902926	+	0.429795i	$0.858586\pi$
$42$	1.21459	−	6.88830i	0.187416	−	1.06289i
$43$	1.23938	+	7.02888i	0.189004	+	1.07189i	0.920702	+	0.390266i	$0.127617\pi$
$43$	1.23938	+	7.02888i	0.189004	+	1.07189i	−0.731698	+	0.681628i	$0.761272\pi$
$44$	0.939693	−	0.342020i	0.141664	−	0.0515615i
$45$	2.37784	−	4.11854i	0.354468	−	0.613956i
$46$	1.39509	+	2.41637i	0.205695	+	0.356275i
$47$	1.00493	+	0.843235i	0.146584	+	0.122998i	0.713131	−	0.701031i	$-0.247277\pi$
$47$	1.00493	+	0.843235i	0.146584	+	0.122998i	−0.566547	+	0.824029i	$0.691721\pi$
$48$	1.64888	+	1.38357i	0.237995	+	0.199702i
$49$	−1.77984	−	3.08278i	−0.254263	−	0.440397i
$50$	1.74014	−	3.01401i	0.246093	−	0.426245i
$51$	−7.19575	+	2.61904i	−1.00761	+	0.366739i
$52$	0.611760	+	3.46946i	0.0848358	+	0.481128i
$53$	0.0301012	−	0.170712i	0.00413471	−	0.0234491i	−0.982671	−	0.185360i	$-0.940655\pi$
$53$	0.0301012	−	0.170712i	0.00413471	−	0.0234491i	0.986805	+	0.161911i	$0.0517658\pi$
$54$	−2.76480	−	1.00630i	−0.376241	−	0.136941i
$55$	2.23079	−	1.87186i	0.300800	−	0.252401i
$56$	3.24957			0.434242
$57$	9.14984	−	2.07580i	1.21193	−	0.274947i
$58$	10.0479			1.31935
$59$	−7.10131	+	5.95870i	−0.924511	+	0.775757i	−0.974824	−	0.222976i	$-0.928423\pi$
$59$	−7.10131	+	5.95870i	−0.924511	+	0.775757i	0.0503125	+	0.998734i	$0.483978\pi$
$60$	5.89014	+	2.14384i	0.760414	+	0.276768i
$61$	−0.695487	+	3.94430i	−0.0890480	+	0.505016i	0.907361	+	0.420351i	$0.138093\pi$
$61$	−0.695487	+	3.94430i	−0.0890480	+	0.505016i	−0.996409	+	0.0846651i	$0.973018\pi$
$62$	−0.625809	−	3.54914i	−0.0794778	−	0.450741i
$63$	4.98677	−	1.81504i	0.628274	−	0.228673i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	5.12963	+	8.88478i	0.636252	+	1.10202i
$66$	1.64888	+	1.38357i	0.202963	+	0.170306i
$67$	6.94300	+	5.82587i	0.848223	+	0.711744i	0.959398	−	0.282057i	$-0.0910169\pi$
$67$	6.94300	+	5.82587i	0.848223	+	0.711744i	−0.111175	+	0.993801i	$0.535461\pi$
$68$	−1.77879	−	3.08096i	−0.215710	−	0.373621i
$69$	−3.00288	+	5.20114i	−0.361505	+	0.626144i
$70$	8.89235	−	3.23655i	1.06284	−	0.386842i
$71$	−2.19794	−	12.4651i	−0.260848	−	1.47934i	−0.780604	−	0.625026i	$-0.785088\pi$
$71$	−2.19794	−	12.4651i	−0.260848	−	1.47934i	0.519756	−	0.854315i	$-0.326023\pi$
$72$	−0.283582	+	1.60827i	−0.0334204	+	0.189537i
$73$	−12.4814	−	4.54287i	−1.46084	−	0.531702i	−0.515244	−	0.857044i	$-0.672299\pi$
$73$	−12.4814	−	4.54287i	−1.46084	−	0.531702i	−0.945597	+	0.325342i	$0.894521\pi$
$74$	−2.56522	+	2.15247i	−0.298200	+	0.250220i
$75$	7.49115			0.865004
$76$	1.68789	+	4.01883i	0.193615	+	0.460992i
$77$	3.24957			0.370323
$78$	−5.80898	+	4.87431i	−0.657737	+	0.551907i
$79$	6.35375	+	2.31258i	0.714853	+	0.260185i	0.673739	−	0.738969i	$-0.264687\pi$
$79$	6.35375	+	2.31258i	0.714853	+	0.260185i	0.0411136	+	0.999154i	$0.486909\pi$
$80$	−0.505679	+	2.86785i	−0.0565367	+	0.320635i
$81$	−1.95047	−	11.0616i	−0.216719	−	1.22907i
$82$	8.44150	−	3.07246i	0.932208	−	0.339296i
$83$	−1.23902	+	2.14604i	−0.136000	+	0.235559i	−0.925979	−	0.377575i	$-0.876758\pi$
$83$	−1.23902	+	2.14604i	−0.136000	+	0.235559i	0.789979	+	0.613134i	$0.210091\pi$
$84$	3.49728	+	6.05747i	0.381585	+	0.660924i
$85$	−7.93623	−	6.65929i	−0.860805	−	0.722301i
$86$	−5.46750	−	4.58778i	−0.589575	−	0.494713i
$87$	10.8138	+	18.7301i	1.15936	+	2.00808i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	7.46104	−	2.71560i	0.790868	−	0.287853i	0.0851714	−	0.996366i	$-0.472856\pi$
$89$	7.46104	−	2.71560i	0.790868	−	0.287853i	0.705697	+	0.708514i	$0.250634\pi$
$90$	0.825816	+	4.68343i	0.0870486	+	0.493677i
$91$	−1.98796	+	11.2743i	−0.208394	+	1.18186i
$92$	−2.62192	−	0.954300i	−0.273354	−	0.0994927i
$93$	5.94238	−	4.98625i	0.616196	−	0.517050i
$94$	−1.31184			−0.135306
$95$	8.62160	+	9.31629i	0.884558	+	0.955831i
$96$	−2.15246			−0.219684
$97$	3.91947	−	3.28883i	0.397962	−	0.333930i	−0.421743	−	0.906715i	$-0.638582\pi$
$97$	3.91947	−	3.28883i	0.397962	−	0.333930i	0.819705	+	0.572785i	$0.194137\pi$
$98$	3.34501	+	1.21748i	0.337897	+	0.122985i
$99$	−0.283582	+	1.60827i	−0.0285010	+	0.161637i
$100$	0.604344	+	3.42740i	0.0604344	+	0.342740i
$101$	3.08174	−	1.12166i	0.306645	−	0.111610i	−0.184115	−	0.982905i	$-0.558942\pi$
$101$	3.08174	−	1.12166i	0.306645	−	0.111610i	0.490759	+	0.871295i	$0.336720\pi$
$102$	3.82878	−	6.63164i	0.379106	−	0.656630i
$103$	−0.262511	−	0.454682i	−0.0258659	−	0.0448011i	0.852803	−	0.522233i	$-0.174901\pi$
$103$	−0.262511	−	0.454682i	−0.0258659	−	0.0448011i	−0.878669	+	0.477432i	$0.841568\pi$
$104$	−2.69876	−	2.26453i	−0.264636	−	0.222056i
$105$	15.6034	+	13.0928i	1.52274	+	1.27773i
$106$	0.0866729	+	0.150122i	0.00841841	+	0.0145811i
$107$	5.20363	−	9.01295i	0.503054	−	0.871314i	−0.496940	−	0.867785i	$-0.665543\pi$
$107$	5.20363	−	9.01295i	0.503054	−	0.871314i	0.999994	−	0.00352960i	$-0.00112351\pi$
$108$	2.76480	−	1.00630i	0.266043	−	0.0968317i
$109$	−2.91635	−	16.5394i	−0.279335	−	1.58419i	−0.724845	−	0.688912i	$-0.758089\pi$
$109$	−2.91635	−	16.5394i	−0.279335	−	1.58419i	0.445510	−	0.895277i	$-0.353023\pi$
$110$	−0.505679	+	2.86785i	−0.0482146	+	0.273439i
$111$	−6.77315	−	2.46523i	−0.642879	−	0.233989i
$112$	−2.48931	+	2.08878i	−0.235218	+	0.197371i
$113$	13.0697			1.22949			0.614746	−	0.788725i	$-0.289258\pi$
$113$	13.0697			1.22949			0.614746	+	0.788725i	$0.289258\pi$
$114$	−5.67488	+	7.47156i	−0.531501	+	0.699776i
$115$	−8.12528			−0.757686
$116$	−7.69713	+	6.45866i	−0.714660	+	0.599671i
$117$	−5.40635	−	1.96775i	−0.499818	−	0.181919i
$118$	1.60974	−	9.12926i	0.148188	−	0.840417i
$119$	−2.00748	−	11.3850i	−0.184025	−	1.04366i
$120$	−5.89014	+	2.14384i	−0.537694	+	0.195705i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−2.00258	−	3.46856i	−0.181305	−	0.314029i
$123$	14.8123	+	12.4290i	1.33558	+	1.12069i
$124$	2.76074	+	2.31654i	0.247922	+	0.208031i
$125$	−2.21279	−	3.83266i	−0.197918	−	0.342803i
$126$	−2.65340	+	4.59583i	−0.236384	+	0.409429i
$127$	−15.4157	+	5.61086i	−1.36792	+	0.497883i	−0.918494	−	0.395434i	$-0.870594\pi$
$127$	−15.4157	+	5.61086i	−1.36792	+	0.497883i	−0.449428	+	0.893317i	$0.648372\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	2.66772	−	15.1294i	0.234879	−	1.33207i
$130$	−9.64055	−	3.50887i	−0.845532	−	0.307748i
$131$	−13.9200	+	11.6802i	−1.21619	+	1.02051i	−0.217179	+	0.976132i	$0.569685\pi$
$131$	−13.9200	+	11.6802i	−1.21619	+	1.02051i	−0.999015	+	0.0443758i	$0.985870\pi$
$132$	−2.15246			−0.187348
$133$	0.687541	+	14.1478i	0.0596173	+	1.22677i
$134$	−9.06345			−0.782963
$135$	6.56352	−	5.50744i	0.564898	−	0.474005i
$136$	3.34304	+	1.21677i	0.286663	+	0.104337i
$137$	1.22998	−	6.97554i	0.105084	−	0.595961i	−0.886103	−	0.463489i	$-0.846597\pi$
$137$	1.22998	−	6.97554i	0.105084	−	0.595961i	0.991187	−	0.132472i	$-0.0422915\pi$
$138$	−1.04289	−	5.91452i	−0.0887767	−	0.503478i
$139$	21.2818	−	7.74595i	1.80510	−	0.657003i	0.807342	−	0.590084i	$-0.200905\pi$
$139$	21.2818	−	7.74595i	1.80510	−	0.657003i	0.997758	−	0.0669186i	$-0.0213168\pi$
$140$	−4.73152	+	8.19523i	−0.399886	+	0.692623i
$141$	−1.41184	−	2.44538i	−0.118899	−	0.205938i
$142$	9.69616	+	8.13605i	0.813684	+	0.682762i
$143$	−2.69876	−	2.26453i	−0.225682	−	0.189370i
$144$	−0.816541	−	1.41429i	−0.0680451	−	0.117857i
$145$	−14.6302	+	25.3402i	−1.21497	+	2.10439i
$146$	12.4814	−	4.54287i	1.03297	−	0.375970i
$147$	1.33051	+	7.54568i	0.109738	+	0.622357i
$148$	0.581487	−	3.29778i	0.0477980	−	0.271076i
$149$	−2.04329	−	0.743696i	−0.167393	−	0.0609259i	0.256964	−	0.966421i	$-0.417278\pi$
$149$	−2.04329	−	0.743696i	−0.167393	−	0.0609259i	−0.424357	+	0.905495i	$0.639500\pi$
$150$	−5.73856	+	4.81522i	−0.468551	+	0.393161i
$151$	8.17643			0.665388			0.332694	−	0.943035i	$-0.392042\pi$
$151$	8.17643			0.665388			0.332694	+	0.943035i	$0.392042\pi$
$152$	−3.87626	−	1.99365i	−0.314406	−	0.161706i
$153$	5.80983			0.469697
$154$	−2.48931	+	2.08878i	−0.200595	+	0.168319i
$155$	9.86194	+	3.58945i	0.792130	+	0.288312i
$156$	1.31679	−	7.46788i	0.105427	−	0.597909i
$157$	−2.38739	−	13.5395i	−0.190534	−	1.08057i	−0.918636	−	0.395104i	$-0.870709\pi$
$157$	−2.38739	−	13.5395i	−0.190534	−	1.08057i	0.728102	−	0.685468i	$-0.240403\pi$
$158$	−6.35375	+	2.31258i	−0.505477	+	0.183979i
$159$	−0.186560	+	0.323131i	−0.0147952	+	0.0256260i
$160$	−1.45605	−	2.52195i	−0.115111	−	0.199377i
$161$	−6.94565	−	5.82809i	−0.547394	−	0.459318i
$162$	8.60443	+	7.21998i	0.676028	+	0.567255i
$163$	3.07801	+	5.33127i	0.241088	+	0.417577i	0.961025	−	0.276463i	$-0.0891624\pi$
$163$	3.07801	+	5.33127i	0.241088	+	0.417577i	−0.719936	+	0.694040i	$0.755829\pi$
$164$	−4.49163	+	7.77973i	−0.350737	+	0.607495i
$165$	−5.89014	+	2.14384i	−0.458547	+	0.166897i
$166$	−0.430307	−	2.44039i	−0.0333983	−	0.189411i
$167$	4.15640	−	23.5721i	0.321632	−	1.82406i	−0.210728	−	0.977545i	$-0.567583\pi$
$167$	4.15640	−	23.5721i	0.321632	−	1.82406i	0.532360	−	0.846518i	$-0.321305\pi$
$168$	−6.57274	−	2.39228i	−0.507098	−	0.184568i
$169$	−0.450874	+	0.378328i	−0.0346826	+	0.0291022i
$170$	10.3600			0.794577
$171$	−7.06203	−	0.894370i	−0.540047	−	0.0683942i
$172$	7.13731			0.544215
$173$	−8.10056	+	6.79718i	−0.615874	+	0.516780i	−0.896504	−	0.443036i	$-0.853901\pi$
$173$	−8.10056	+	6.79718i	−0.615874	+	0.516780i	0.280629	+	0.959816i	$0.409457\pi$
$174$	−20.3234	−	7.39710i	−1.54071	−	0.560772i
$175$	−1.96386	+	11.1376i	−0.148454	+	0.841922i
$176$	−0.173648	−	0.984808i	−0.0130892	−	0.0742327i
$177$	18.7502	−	6.82450i	1.40935	−	0.512961i
$178$	−3.96994	+	6.87613i	−0.297559	+	0.515388i
$179$	−2.32641	−	4.02947i	−0.173884	−	0.301176i	0.765890	−	0.642971i	$-0.222299\pi$
$179$	−2.32641	−	4.02947i	−0.173884	−	0.301176i	−0.939775	+	0.341795i	$0.888965\pi$
$180$	−3.64306	−	3.05689i	−0.271538	−	0.227847i
$181$	−18.7020	−	15.6928i	−1.39011	−	1.16644i	−0.965297	−	0.261154i	$-0.915897\pi$
$181$	−18.7020	−	15.6928i	−1.39011	−	1.16644i	−0.424809	−	0.905283i	$-0.639659\pi$
$182$	−5.72409	−	9.91441i	−0.424298	−	0.734905i
$183$	4.31046	−	7.46594i	0.318639	−	0.551898i
$184$	2.62192	−	0.954300i	0.193290	−	0.0703519i
$185$	−1.69334	−	9.60343i	−0.124497	−	0.706058i
$186$	−1.34703	+	7.63938i	−0.0987689	+	0.560146i
$187$	3.34304	+	1.21677i	0.244467	+	0.0889787i
$188$	1.00493	−	0.843235i	0.0732919	−	0.0614992i
$189$	9.56100			0.695460
$190$	−12.5929	−	1.59483i	−0.913587	−	0.115701i
$191$	−8.26922			−0.598340			−0.299170	−	0.954200i	$-0.596710\pi$
$191$	−8.26922			−0.598340			−0.299170	+	0.954200i	$0.596710\pi$
$192$	1.64888	−	1.38357i	0.118998	−	0.0998509i
$193$	13.4963	+	4.91224i	0.971482	+	0.353591i	0.778523	−	0.627616i	$-0.215969\pi$
$193$	13.4963	+	4.91224i	0.971482	+	0.353591i	0.192959	+	0.981207i	$0.438192\pi$
$194$	−0.888473	+	5.03878i	−0.0637886	+	0.361763i
$195$	−3.83461	−	21.7471i	−0.274602	−	1.55735i
$196$	−3.34501	+	1.21748i	−0.238929	+	0.0869632i
$197$	3.98362	−	6.89984i	0.283821	−	0.491593i	−0.688501	−	0.725235i	$-0.741731\pi$
$197$	3.98362	−	6.89984i	0.283821	−	0.491593i	0.972323	+	0.233642i	$0.0750644\pi$
$198$	−0.816541	−	1.41429i	−0.0580290	−	0.100509i
$199$	−10.6929	−	8.97244i	−0.758003	−	0.636040i	0.179604	−	0.983739i	$-0.442519\pi$
$199$	−10.6929	−	8.97244i	−0.758003	−	0.636040i	−0.937606	+	0.347699i	$0.886963\pi$
$200$	−2.66605	−	2.23708i	−0.188518	−	0.158185i
$201$	−9.75435	−	16.8950i	−0.688019	−	1.19168i
$202$	−1.63976	+	2.84015i	−0.115373	+	0.199832i
$203$	−30.6822	+	11.1674i	−2.15347	+	0.783797i
$204$	1.32972	+	7.54122i	0.0930991	+	0.527991i
$205$	−4.54265	+	25.7626i	−0.317272	+	1.79934i
$206$	0.493359	+	0.179568i	0.0343739	+	0.0125111i
$207$	3.49056	−	2.92893i	0.242611	−	0.203575i
$208$	3.52299			0.244275
$209$	−3.87626	−	1.99365i	−0.268126	−	0.137903i
$210$	−20.3688			−1.40558
$211$	14.2704	−	11.9743i	0.982416	−	0.824345i	−0.00203575	−	0.999998i	$-0.500648\pi$
$211$	14.2704	−	11.9743i	0.982416	−	0.824345i	0.984452	+	0.175653i	$0.0562036\pi$
$212$	−0.162892	−	0.0592877i	−0.0111874	−	0.00407190i
$213$	−4.73098	+	26.8307i	−0.324161	+	1.83841i
$214$	1.80720	+	10.2491i	0.123538	+	0.700617i
$215$	19.5310	−	7.10872i	1.33201	−	0.484811i
$216$	−1.47112	+	2.54805i	−0.100097	+	0.173373i
$217$	5.85554	+	10.1421i	0.397500	+	0.688490i
$218$	12.8654	+	10.7953i	0.871354	+	0.731153i
$219$	21.9012	+	18.3773i	1.47994	+	1.24182i
$220$	−1.45605	−	2.52195i	−0.0981666	−	0.170030i
$221$	−6.26666	+	10.8542i	−0.421541	+	0.730131i
$222$	6.77315	−	2.46523i	0.454584	−	0.165455i
$223$	−2.97931	−	16.8965i	−0.199509	−	1.13147i	−0.905849	−	0.423601i	$-0.860766\pi$
$223$	−2.97931	−	16.8965i	−0.199509	−	1.13147i	0.706339	−	0.707873i	$-0.250345\pi$
$224$	0.564281	−	3.20020i	0.0377026	−	0.213822i
$225$	−5.34081	−	1.94390i	−0.356054	−	0.129593i
$226$	−10.0120	+	8.40103i	−0.665986	+	0.558828i
$227$	−0.720276			−0.0478064			−0.0239032	−	0.999714i	$-0.507609\pi$
$227$	−0.720276			−0.0478064			−0.0239032	+	0.999714i	$0.507609\pi$
$228$	−0.455416	−	9.37129i	−0.0301606	−	0.620629i
$229$	−13.1209			−0.867056			−0.433528	−	0.901140i	$-0.642731\pi$
$229$	−13.1209			−0.867056			−0.433528	+	0.901140i	$0.642731\pi$
$230$	6.22433	−	5.22283i	0.410420	−	0.344383i
$231$	−6.57274	−	2.39228i	−0.432454	−	0.157401i
$232$	1.74480	−	9.89523i	0.114552	−	0.649654i
$233$	−0.543594	−	3.08287i	−0.0356120	−	0.201966i	0.961811	−	0.273716i	$-0.0882527\pi$
$233$	−0.543594	−	3.08287i	−0.0356120	−	0.201966i	−0.997423	+	0.0717500i	$0.977142\pi$
$234$	5.40635	−	1.96775i	0.353424	−	0.128636i
$235$	1.91010	−	3.30839i	0.124601	−	0.215816i
$236$	4.63505	+	8.02814i	0.301716	+	0.522587i
$237$	−11.1489	−	9.35506i	−0.724201	−	0.607677i
$238$	8.85594	+	7.43102i	0.574046	+	0.481681i
$239$	−8.20473	−	14.2110i	−0.530720	−	0.919234i	−0.999357	−	0.0358434i	$-0.988588\pi$
$239$	−8.20473	−	14.2110i	−0.530720	−	0.919234i	0.468637	−	0.883391i	$-0.344745\pi$
$240$	3.13408	−	5.42838i	0.202304	−	0.350401i
$241$	−10.9079	+	3.97015i	−0.702639	+	0.255740i	−0.668537	−	0.743679i	$-0.733079\pi$
$241$	−10.9079	+	3.97015i	−0.702639	+	0.255740i	−0.0341019	+	0.999418i	$0.510857\pi$
$242$	−0.173648	−	0.984808i	−0.0111625	−	0.0633058i
$243$	−2.66556	+	15.1171i	−0.170996	+	0.969764i
$244$	3.76361	+	1.36984i	0.240941	+	0.0876952i
$245$	−7.94092	+	6.66322i	−0.507327	+	0.425698i
$246$	−19.3361			−1.23282
$247$	9.28823	−	12.2289i	0.590996	−	0.778106i
$248$	−3.60389			−0.228847
$249$	4.08599	−	3.42855i	0.258939	−	0.217275i
$250$	4.15868	+	1.51364i	0.263018	+	0.0957307i
$251$	3.06589	−	17.3875i	0.193517	−	1.09749i	−0.720998	−	0.692937i	$-0.756316\pi$
$251$	3.06589	−	17.3875i	0.193517	−	1.09749i	0.914515	−	0.404552i	$-0.132573\pi$
$252$	−0.921517	−	5.22619i	−0.0580501	−	0.329219i
$253$	2.62192	−	0.954300i	0.164839	−	0.0599963i
$254$	8.20252	−	14.2072i	0.514672	−	0.891438i
$255$	11.1498	+	19.3119i	0.698225	+	1.20936i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−5.50745	−	4.62130i	−0.343545	−	0.288269i	0.454647	−	0.890672i	$-0.349766\pi$
$257$	−5.50745	−	4.62130i	−0.343545	−	0.288269i	−0.798192	+	0.602403i	$0.794210\pi$
$258$	7.68139	+	13.3046i	0.478222	+	0.828305i
$259$	5.44084	−	9.42380i	0.338077	−	0.585567i
$260$	9.64055	−	3.50887i	0.597881	−	0.217611i
$261$	−2.84940	−	16.1597i	−0.176373	−	1.00026i
$262$	3.15540	−	17.8952i	0.194941	−	1.10557i
$263$	2.43577	+	0.886549i	0.150196	+	0.0546669i	0.416024	−	0.909354i	$-0.363423\pi$
$263$	2.43577	+	0.886549i	0.150196	+	0.0546669i	−0.265828	+	0.964020i	$0.585645\pi$
$264$	1.64888	−	1.38357i	0.101482	−	0.0851531i
$265$	−0.504799			−0.0310095
$266$	−9.62074	−	10.3959i	−0.589886	−	0.637415i
$267$	−17.0903			−1.04591
$268$	6.94300	−	5.82587i	0.424111	−	0.355872i
$269$	29.7961	+	10.8449i	1.81670	+	0.661224i	0.995947	+	0.0899393i	$0.0286673\pi$
$269$	29.7961	+	10.8449i	1.81670	+	0.661224i	0.820752	+	0.571285i	$0.193555\pi$
$270$	−1.48783	+	8.43789i	−0.0905464	+	0.513514i
$271$	4.90191	+	27.8001i	0.297770	+	1.68874i	0.655727	+	0.754998i	$0.272362\pi$
$271$	4.90191	+	27.8001i	0.297770	+	1.68874i	−0.357957	+	0.933738i	$0.616527\pi$
$272$	−3.34304	+	1.21677i	−0.202701	+	0.0737773i
$273$	12.3209	−	21.3404i	0.745693	−	1.29158i
$274$	3.54158	+	6.13419i	0.213954	+	0.370580i
$275$	−2.66605	−	2.23708i	−0.160769	−	0.134901i
$276$	4.60068	+	3.86043i	0.276929	+	0.232371i
$277$	3.06472	+	5.30825i	0.184141	+	0.318942i	0.943287	−	0.331979i	$-0.107716\pi$
$277$	3.06472	+	5.30825i	0.184141	+	0.318942i	−0.759146	+	0.650921i	$0.774383\pi$
$278$	−11.3238	+	19.6134i	−0.679157	+	1.17634i
$279$	−5.53051	+	2.01294i	−0.331103	+	0.120512i
$280$	−1.64324	−	9.31927i	−0.0982023	−	0.556933i
$281$	−5.42802	+	30.7839i	−0.323809	+	1.83641i	0.194108	+	0.980980i	$0.437819\pi$
$281$	−5.42802	+	30.7839i	−0.323809	+	1.83641i	−0.517917	+	0.855431i	$0.673292\pi$
$282$	2.65340	+	0.965757i	0.158007	+	0.0575100i
$283$	−18.4494	+	15.4809i	−1.09671	+	0.920246i	−0.997199	−	0.0747914i	$-0.976171\pi$
$283$	−18.4494	+	15.4809i	−1.09671	+	0.920246i	−0.0995067	+	0.995037i	$0.531726\pi$
$284$	−12.6574			−0.751081
$285$	−10.5800	−	25.1907i	−0.626704	−	1.49217i
$286$	3.52299			0.208318
$287$	−22.3621	+	18.7641i	−1.32000	+	1.10761i
$288$	1.53459	+	0.558547i	0.0904269	+	0.0329127i
$289$	−0.754255	+	4.27759i	−0.0443679	+	0.251623i
$290$	−5.08101	−	28.8158i	−0.298367	−	1.69212i
$291$	−10.3489	+	3.76669i	−0.606664	+	0.220808i
$292$	−6.64123	+	11.5029i	−0.388648	+	0.673159i
$293$	−10.2762	−	17.7989i	−0.600342	−	1.03982i	−0.992769	−	0.120040i	$-0.961698\pi$
$293$	−10.2762	−	17.7989i	−0.600342	−	1.03982i	0.392427	−	0.919783i	$-0.371636\pi$
$294$	−5.86949	−	4.92509i	−0.342316	−	0.287237i
$295$	20.6797	+	17.3523i	1.20402	+	1.01029i
$296$	1.67433	+	2.90002i	0.0973182	+	0.168560i
$297$	−1.47112	+	2.54805i	−0.0853629	+	0.147853i
$298$	2.04329	−	0.743696i	0.118364	−	0.0430811i
$299$	1.70692	+	9.68045i	0.0987140	+	0.559835i
$300$	1.30083	−	7.37735i	0.0751032	−	0.425931i
$301$	21.7945	+	7.93253i	1.25621	+	0.457224i
$302$	−6.26351	+	5.25571i	−0.360424	+	0.302432i
$303$	−7.05903			−0.405531
$304$	4.25088	−	0.964387i	0.243805	−	0.0553114i
$305$	11.6634			0.667842
$306$	−4.45059	+	3.73449i	−0.254423	+	0.213486i
$307$	−14.7104	−	5.35416i	−0.839569	−	0.305578i	−0.113789	−	0.993505i	$-0.536299\pi$
$307$	−14.7104	−	5.35416i	−0.839569	−	0.305578i	−0.725780	+	0.687927i	$0.758521\pi$
$308$	0.564281	−	3.20020i	0.0321529	−	0.182348i
$309$	0.196238	+	1.11292i	0.0111636	+	0.0633117i
$310$	−9.86194	+	3.58945i	−0.560120	+	0.203867i
$311$	2.23233	−	3.86650i	0.126584	−	0.219249i	−0.795767	−	0.605603i	$-0.792932\pi$
$311$	2.23233	−	3.86650i	0.126584	−	0.219249i	0.922351	+	0.386353i	$0.126265\pi$
$312$	3.79154	+	6.56714i	0.214654	+	0.371791i
$313$	−5.80646	−	4.87220i	−0.328201	−	0.275393i	0.463766	−	0.885958i	$-0.346498\pi$
$313$	−5.80646	−	4.87220i	−0.328201	−	0.275393i	−0.791966	+	0.610565i	$0.790942\pi$
$314$	10.5319	+	8.83730i	0.594349	+	0.498718i
$315$	−7.72695	−	13.3835i	−0.435365	−	0.754074i
$316$	3.38076	−	5.85565i	0.190183	−	0.329406i
$317$	23.4816	−	8.54661i	1.31886	−	0.480026i	0.415767	−	0.909471i	$-0.363513\pi$
$317$	23.4816	−	8.54661i	1.31886	−	0.480026i	0.903093	+	0.429446i	$0.141291\pi$
$318$	−0.0647915	−	0.367451i	−0.00363333	−	0.0206056i
$319$	1.74480	−	9.89523i	0.0976899	−	0.554027i
$320$	2.73647	+	0.995994i	0.152973	+	0.0556778i
$321$	−17.1603	+	14.3992i	−0.957795	+	0.803685i
$322$	9.06690			0.505279
$323$	−4.59019	+	14.8122i	−0.255405	+	0.824174i
$324$	−11.2323			−0.624016
$325$	9.39244	−	7.88120i	0.520999	−	0.437170i
$326$	−5.78476	−	2.10548i	−0.320388	−	0.116612i
$327$	−6.27732	+	35.6004i	−0.347136	+	1.96871i
$328$	−1.55993	−	8.84678i	−0.0861325	−	0.488482i
$329$	4.00583	−	1.45800i	0.220849	−	0.0803823i
$330$	3.13408	−	5.42838i	0.172525	−	0.298823i
$331$	0.157129	+	0.272155i	0.00863658	+	0.0149590i	0.870311	−	0.492502i	$-0.163918\pi$
$331$	0.157129	+	0.272155i	0.00863658	+	0.0149590i	−0.861675	+	0.507461i	$0.830584\pi$
$332$	1.89829	+	1.59285i	0.104182	+	0.0874191i
$333$	4.18921	+	3.51516i	0.229567	+	0.192630i
$334$	11.9679	+	20.7289i	0.654852	+	1.13424i
$335$	13.1968	−	22.8575i	0.721018	−	1.24884i
$336$	6.57274	−	2.39228i	0.358572	−	0.130510i
$337$	−2.61052	−	14.8050i	−0.142204	−	0.806478i	−0.969570	−	0.244815i	$-0.921273\pi$
$337$	−2.61052	−	14.8050i	−0.142204	−	0.806478i	0.827366	−	0.561663i	$-0.189838\pi$
$338$	0.102205	−	0.579632i	0.00555921	−	0.0315278i
$339$	−26.4354	−	9.62170i	−1.43577	−	0.522579i
$340$	−7.93623	+	6.65929i	−0.430403	+	0.361151i
$341$	−3.60389			−0.195162
$342$	5.98472	−	3.85426i	0.323616	−	0.208414i
$343$	11.1795			0.603638
$344$	−5.46750	+	4.58778i	−0.294788	+	0.247356i
$345$	16.4346	+	5.98170i	0.884809	+	0.322044i
$346$	1.83625	−	10.4139i	0.0987173	−	0.559854i
$347$	−3.21284	−	18.2209i	−0.172474	−	0.978151i	−0.941019	−	0.338354i	$-0.890130\pi$
$347$	−3.21284	−	18.2209i	−0.172474	−	0.978151i	0.768544	−	0.639796i	$-0.220981\pi$
$348$	20.3234	−	7.39710i	1.08945	−	0.396526i
$349$	−5.67865	+	9.83572i	−0.303971	+	0.526494i	−0.977032	−	0.213094i	$-0.931646\pi$
$349$	−5.67865	+	9.83572i	−0.303971	+	0.526494i	0.673060	+	0.739588i	$0.264979\pi$
$350$	−5.65470	−	9.79422i	−0.302256	−	0.523523i
$351$	−7.94040	−	6.66279i	−0.423827	−	0.355633i
$352$	0.766044	+	0.642788i	0.0408303	+	0.0342607i
$353$	16.6323	+	28.8080i	0.885247	+	1.53329i	0.845430	+	0.534086i	$0.179344\pi$
$353$	16.6323	+	28.8080i	0.885247	+	1.53329i	0.0398167	+	0.999207i	$0.487323\pi$
$354$	−9.97675	+	17.2802i	−0.530259	+	0.918435i
$355$	−34.6367	+	12.6067i	−1.83833	+	0.669096i
$356$	−1.37874	−	7.81925i	−0.0730733	−	0.414419i
$357$	−4.32102	+	24.5057i	−0.228693	+	1.29698i
$358$	4.37223	+	1.59136i	0.231079	+	0.0841060i
$359$	−16.7615	+	14.0646i	−0.884639	+	0.742300i	−0.967127	−	0.254292i	$-0.918158\pi$
$359$	−16.7615	+	14.0646i	−0.884639	+	0.742300i	0.0824889	+	0.996592i	$0.473713\pi$
$360$	4.75568			0.250646
$361$	7.85973	−	17.2981i	0.413670	−	0.910427i
$362$	24.4137			1.28315
$363$	1.64888	−	1.38357i	0.0865437	−	0.0726188i
$364$	10.7578	+	3.91551i	0.563860	+	0.205228i
$365$	−6.71666	+	38.0921i	−0.351566	+	1.99383i
$366$	1.49701	+	8.48995i	0.0782499	+	0.443777i
$367$	31.9195	−	11.6178i	1.66618	−	0.606442i	0.674868	−	0.737938i	$-0.264200\pi$
$367$	31.9195	−	11.6178i	1.66618	−	0.606442i	0.991317	+	0.131497i	$0.0419783\pi$
$368$	−1.39509	+	2.41637i	−0.0727243	+	0.125962i
$369$	−7.33520	−	12.7049i	−0.381855	−	0.661392i
$370$	7.47015	+	6.26820i	0.388354	+	0.325868i
$371$	−0.431512	−	0.362081i	−0.0224030	−	0.0187983i
$372$	−3.87861	−	6.71795i	−0.201097	−	0.348310i
$373$	7.10714	−	12.3099i	0.367994	−	0.637384i	−0.621258	−	0.783606i	$-0.713378\pi$
$373$	7.10714	−	12.3099i	0.367994	−	0.637384i	0.989252	+	0.146222i	$0.0467115\pi$
$374$	−3.34304	+	1.21677i	−0.172864	+	0.0629175i
$375$	1.65415	+	9.38115i	0.0854199	+	0.484440i
$376$	−0.227799	+	1.29191i	−0.0117478	+	0.0666252i
$377$	33.2638	+	12.1070i	1.71317	+	0.623543i
$378$	−7.32415	+	6.14569i	−0.376714	+	0.316100i
$379$	−23.0870			−1.18590			−0.592949	−	0.805240i	$-0.702036\pi$
$379$	−23.0870			−1.18590			−0.592949	+	0.805240i	$0.702036\pi$
$380$	10.6719	−	6.87287i	0.547456	−	0.352571i
$381$	35.3112			1.80905
$382$	6.33459	−	5.31535i	0.324106	−	0.271957i
$383$	21.3408	+	7.76741i	1.09046	+	0.396896i	0.823792	−	0.566892i	$-0.191854\pi$
$383$	21.3408	+	7.76741i	1.09046	+	0.396896i	0.266671	+	0.963788i	$0.414076\pi$
$384$	−0.373771	+	2.11976i	−0.0190739	+	0.108173i
$385$	−1.64324	−	9.31927i	−0.0837472	−	0.474954i
$386$	−13.4963	+	4.91224i	−0.686942	+	0.250026i
$387$	−5.82791	+	10.0942i	−0.296249	+	0.513118i
$388$	−2.55825	−	4.43103i	−0.129876	−	0.224951i
$389$	8.84713	+	7.42363i	0.448567	+	0.376393i	0.838904	−	0.544279i	$-0.183197\pi$
$389$	8.84713	+	7.42363i	0.448567	+	0.376393i	−0.390337	+	0.920672i	$0.627641\pi$
$390$	16.9163	+	14.1944i	0.856589	+	0.718763i
$391$	−4.96316	−	8.59645i	−0.250998	−	0.434741i
$392$	1.77984	−	3.08278i	0.0898957	−	0.155704i
$393$	36.7540	−	13.3774i	1.85400	−	0.674800i
$394$	1.38350	+	7.84620i	0.0696996	+	0.395286i
$395$	3.41916	−	19.3910i	0.172037	−	0.975668i
$396$	1.53459	+	0.558547i	0.0771163	+	0.0280680i
$397$	11.5884	−	9.72379i	0.581603	−	0.488023i	−0.303870	−	0.952713i	$-0.598279\pi$
$397$	11.5884	−	9.72379i	0.581603	−	0.488023i	0.885473	+	0.464691i	$0.153834\pi$
$398$	13.9586			0.699684
$399$	9.02476	−	29.1223i	0.451803	−	1.45794i
$400$	3.48028			0.174014
$401$	1.21109	−	1.01622i	0.0604788	−	0.0507477i	−0.612047	−	0.790821i	$-0.709654\pi$
$401$	1.21109	−	1.01622i	0.0604788	−	0.0507477i	0.672526	+	0.740074i	$0.265209\pi$
$402$	18.3322	+	6.67237i	0.914326	+	0.332788i
$403$	2.20472	−	12.5036i	0.109825	−	0.622847i
$404$	−0.569483	−	3.22970i	−0.0283328	−	0.160683i
$405$	−30.7368	+	11.1873i	−1.52733	+	0.555901i
$406$	16.3256	−	28.2768i	0.810228	−	1.40336i
$407$	1.67433	+	2.90002i	0.0829933	+	0.143749i
$408$	−5.86603	−	4.92218i	−0.290412	−	0.243684i
$409$	16.7666	+	14.0689i	0.829056	+	0.695661i	0.955074	−	0.296367i	$-0.0957752\pi$
$409$	16.7666	+	14.0689i	0.829056	+	0.695661i	−0.126018	+	0.992028i	$0.540220\pi$
$410$	−13.0800	−	22.6553i	−0.645977	−	1.11886i
$411$	−7.62310	+	13.2036i	−0.376020	+	0.651285i
$412$	−0.493359	+	0.179568i	−0.0243060	+	0.00884667i
$413$	5.23094	+	29.6662i	0.257398	+	1.45978i
$414$	−0.791246	+	4.48738i	−0.0388876	+	0.220543i
$415$	6.78108	+	2.46811i	0.332870	+	0.121155i
$416$	−2.69876	+	2.26453i	−0.132318	+	0.111028i
$417$	−48.7481			−2.38721
$418$	4.25088	−	0.964387i	0.207917	−	0.0471697i
$419$	−6.84641			−0.334469			−0.167234	−	0.985917i	$-0.553484\pi$
$419$	−6.84641			−0.334469			−0.167234	+	0.985917i	$0.553484\pi$
$420$	15.6034	−	13.0928i	0.761368	−	0.638864i
$421$	−0.389345	−	0.141710i	−0.0189755	−	0.00690653i	0.332515	−	0.943098i	$-0.392103\pi$
$421$	−0.389345	−	0.141710i	−0.0189755	−	0.00690653i	−0.351490	+	0.936191i	$0.614325\pi$
$422$	−3.23484	+	18.3457i	−0.157470	+	0.893055i
$423$	0.372014	+	2.10980i	0.0180879	+	0.102582i
$424$	0.162892	−	0.0592877i	0.00791072	−	0.00287927i
$425$	−6.19069	+	10.7226i	−0.300293	+	0.520122i
$426$	−13.6223	−	23.5945i	−0.660003	−	1.14316i
$427$	9.97008	+	8.36589i	0.482486	+	0.404854i
$428$	−7.97242	−	6.68965i	−0.385361	−	0.323357i
$429$	3.79154	+	6.56714i	0.183057	+	0.317065i
$430$	−10.3923	+	17.9999i	−0.501159	+	0.868033i
$431$	1.46749	−	0.534123i	0.0706865	−	0.0257278i	−0.306435	−	0.951892i	$-0.599136\pi$
$431$	1.46749	−	0.534123i	0.0706865	−	0.0257278i	0.377121	+	0.926164i	$0.376914\pi$
$432$	−0.510914	−	2.89754i	−0.0245814	−	0.139408i
$433$	6.71866	−	38.1034i	0.322878	−	1.83113i	−0.201307	−	0.979528i	$-0.564519\pi$
$433$	6.71866	−	38.1034i	0.322878	−	1.83113i	0.524185	−	0.851604i	$-0.324370\pi$
$434$	−11.0048	−	4.00543i	−0.528248	−	0.192267i
$435$	48.2468	−	40.4839i	2.31326	−	1.94105i
$436$	−16.7946			−0.804314
$437$	4.70954	+	11.2133i	0.225288	+	0.536405i
$438$	−28.5899			−1.36608
$439$	1.04516	−	0.876992i	0.0498827	−	0.0418566i	−0.617505	−	0.786567i	$-0.711857\pi$
$439$	1.04516	−	0.876992i	0.0498827	−	0.0418566i	0.667388	+	0.744710i	$0.267412\pi$
$440$	2.73647	+	0.995994i	0.130456	+	0.0474821i
$441$	1.00946	−	5.72494i	0.0480696	−	0.272616i
$442$	−2.17639	−	12.3429i	−0.103520	−	0.587093i
$443$	25.8899	−	9.42316i	1.23007	−	0.447708i	0.356447	−	0.934316i	$-0.383988\pi$
$443$	25.8899	−	9.42316i	1.23007	−	0.447708i	0.873621	+	0.486607i	$0.161766\pi$
$444$	−3.60392	+	6.24217i	−0.171034	+	0.296240i
$445$	−11.5608	−	20.0239i	−0.548035	−	0.949225i
$446$	13.1432	+	11.0284i	0.622347	+	0.522211i
$447$	3.58536	+	3.00847i	0.169582	+	0.142296i
$448$	1.62478	+	2.81421i	0.0767638	+	0.132959i
$449$	2.17968	−	3.77532i	0.102866	−	0.178169i	−0.809999	−	0.586432i	$-0.800532\pi$
$449$	2.17968	−	3.77532i	0.102866	−	0.178169i	0.912864	+	0.408263i	$0.133865\pi$
$450$	5.34081	−	1.94390i	0.251768	−	0.0916362i
$451$	−1.55993	−	8.84678i	−0.0734541	−	0.416579i
$452$	2.26953	−	12.8711i	0.106750	−	0.605407i
$453$	−16.5380	−	6.01936i	−0.777025	−	0.282814i
$454$	0.551763	−	0.462984i	0.0258955	−	0.0217289i
$455$	33.3381			1.56292
$456$	6.37262	+	6.88609i	0.298425	+	0.322471i
$457$	19.8226			0.927263			0.463631	−	0.886028i	$-0.346546\pi$
$457$	19.8226			0.927263			0.463631	+	0.886028i	$0.346546\pi$
$458$	10.0512	−	8.43397i	0.469663	−	0.394094i
$459$	9.83601	+	3.58001i	0.459106	+	0.167101i
$460$	−1.41094	+	8.00184i	−0.0657854	+	0.373088i
$461$	−1.51915	−	8.61550i	−0.0707537	−	0.401264i	−0.999531	−	0.0306257i	$-0.990250\pi$
$461$	−1.51915	−	8.61550i	−0.0707537	−	0.401264i	0.928777	−	0.370638i	$-0.120861\pi$
$462$	6.57274	−	2.39228i	0.305791	−	0.111299i
$463$	−8.31385	+	14.4000i	−0.386378	+	0.669226i	−0.991959	−	0.126558i	$-0.959607\pi$
$463$	−8.31385	+	14.4000i	−0.386378	+	0.669226i	0.605582	+	0.795783i	$0.292941\pi$
$464$	5.02394	+	8.70172i	0.233231	+	0.403967i
$465$	−17.3048	−	14.5204i	−0.802489	−	0.673368i
$466$	2.39805	+	2.01220i	0.111088	+	0.0932135i
$467$	−7.36619	−	12.7586i	−0.340867	−	0.590398i	0.643727	−	0.765255i	$-0.277387\pi$
$467$	−7.36619	−	12.7586i	−0.340867	−	0.590398i	−0.984594	+	0.174857i	$0.944054\pi$
$468$	−2.87666	+	4.98252i	−0.132974	+	0.230317i
$469$	27.6761	−	10.0733i	1.27796	−	0.465141i
$470$	0.663371	+	3.76216i	0.0305990	+	0.173536i
$471$	−5.13875	+	29.1433i	−0.236781	+	1.34285i
$472$	−8.71104	−	3.17056i	−0.400958	−	0.145937i
$473$	−5.46750	+	4.58778i	−0.251396	+	0.210946i
$474$	14.5539			0.668482
$475$	9.17563	−	12.0806i	0.421007	−	0.554298i
$476$	−11.5606			−0.529880
$477$	0.216858	−	0.181965i	0.00992923	−	0.00833162i
$478$	15.4199	+	5.61237i	0.705288	+	0.256704i
$479$	−3.92400	+	22.2541i	−0.179292	+	1.01682i	0.753780	+	0.657127i	$0.228228\pi$
$479$	−3.92400	+	22.2541i	−0.179292	+	1.01682i	−0.933072	+	0.359689i	$0.882883\pi$
$480$	1.08845	+	6.17293i	0.0496809	+	0.281754i
$481$	−11.0858	+	4.03490i	−0.505469	+	0.183976i
$482$	5.80397	−	10.0528i	0.264364	−	0.457891i
$483$	9.75807	+	16.9015i	0.444007	+	0.769043i
$484$	0.766044	+	0.642788i	0.0348202	+	0.0292176i
$485$	−11.4139	−	9.57737i	−0.518277	−	0.434886i
$486$	−7.67517	−	13.2938i	−0.348153	−	0.603018i
$487$	−7.85455	+	13.6045i	−0.355923	+	0.616478i	−0.987276	−	0.159019i	$-0.949167\pi$
$487$	−7.85455	+	13.6045i	−0.355923	+	0.616478i	0.631352	+	0.775496i	$0.282500\pi$
$488$	−3.76361	+	1.36984i	−0.170371	+	0.0620099i
$489$	−2.30094	−	13.0493i	−0.104052	−	0.590108i
$490$	1.80006	−	10.2086i	0.0813184	−	0.461180i
$491$	−31.8837	−	11.6047i	−1.43889	−	0.523713i	−0.499424	−	0.866357i	$-0.666455\pi$
$491$	−31.8837	−	11.6047i	−1.43889	−	0.523713i	−0.939465	+	0.342644i	$0.888677\pi$
$492$	14.8123	−	12.4290i	0.667791	−	0.560343i
$493$	−35.7462			−1.60993
$494$	0.745390	+	15.3382i	0.0335367	+	0.690100i
$495$	4.75568			0.213752
$496$	2.76074	−	2.31654i	0.123961	−	0.104016i
$497$	−38.6507	−	14.0677i	−1.73372	−	0.631023i
$498$	−0.926218	+	5.25284i	−0.0415048	+	0.235385i
$499$	−2.68031	−	15.2008i	−0.119987	−	0.680482i	−0.984159	−	0.177286i	$-0.943268\pi$
$499$	−2.68031	−	15.2008i	−0.119987	−	0.680482i	0.864172	−	0.503196i	$-0.167843\pi$
$500$	−4.15868	+	1.51364i	−0.185982	+	0.0676918i
$501$	−25.7603	+	44.6182i	−1.15089	+	1.99339i
$502$	8.82787	+	15.2903i	0.394007	+	0.682440i
$503$	−20.2184	−	16.9653i	−0.901496	−	0.756445i	0.0689864	−	0.997618i	$-0.478023\pi$
$503$	−20.2184	−	16.9653i	−0.901496	−	0.756445i	−0.970482	+	0.241173i	$0.922468\pi$
$504$	4.06525	+	3.41115i	0.181081	+	0.151945i
$505$	−4.77513	−	8.27077i	−0.212490	−	0.368044i
$506$	−1.39509	+	2.41637i	−0.0620195	+	0.107421i
$507$	1.19048	−	0.433299i	0.0528710	−	0.0192435i
$508$	2.84871	+	16.1558i	0.126391	+	0.716798i
$509$	−6.95259	+	39.4301i	−0.308168	+	1.74771i	0.300035	+	0.953928i	$0.403002\pi$
$509$	−6.95259	+	39.4301i	−0.308168	+	1.74771i	−0.608203	+	0.793781i	$0.708109\pi$
$510$	−20.9547	−	7.62688i	−0.927889	−	0.337724i
$511$	−33.0642	+	27.7441i	−1.46267	+	1.22733i
$512$	−1.00000			−0.0441942
$513$	−11.4049	−	5.86578i	−0.503537	−	0.258981i
$514$	7.18947			0.317114
$515$	−1.17121	+	0.982764i	−0.0516098	+	0.0433058i
$516$	−14.4363	−	5.25438i	−0.635522	−	0.231311i
$517$	−0.227799	+	1.29191i	−0.0100186	+	0.0568182i
$518$	1.88958	+	10.7164i	0.0830235	+	0.470850i
$519$	21.3886	−	7.78481i	0.938854	−	0.341715i
$520$	−5.12963	+	8.88478i	−0.224949	+	0.389623i
$521$	−18.7242	−	32.4313i	−0.820323	−	1.42084i	−0.905442	−	0.424470i	$-0.860461\pi$
$521$	−18.7242	−	32.4313i	−0.820323	−	1.42084i	0.0851195	−	0.996371i	$-0.472873\pi$
$522$	12.5700	+	10.5475i	0.550175	+	0.461652i
$523$	−17.5497	−	14.7260i	−0.767397	−	0.643922i	0.172644	−	0.984984i	$-0.444769\pi$
$523$	−17.5497	−	14.7260i	−0.767397	−	0.643922i	−0.940041	+	0.341062i	$0.889213\pi$
$524$	9.08562	+	15.7367i	0.396907	+	0.687463i
$525$	12.1715	−	21.0817i	0.531208	−	0.920079i
$526$	−2.43577	+	0.886549i	−0.106205	+	0.0386554i
$527$	2.22637	+	12.6264i	0.0969822	+	0.550013i
$528$	−0.373771	+	2.11976i	−0.0162663	+	0.0922507i
$529$	14.2973	+	5.20379i	0.621621	+	0.226252i
$530$	0.386698	−	0.324478i	0.0167971	−	0.0140944i
$531$	−15.1388			−0.656969
$532$	14.0523	+	1.77965i	0.609244	+	0.0771577i
$533$	31.6479			1.37082
$534$	13.0919	−	10.9854i	0.566542	−	0.475385i
$535$	−28.4791	−	10.3656i	−1.23126	−	0.448142i
$536$	−1.57385	+	8.92575i	−0.0679800	+	0.385534i
$537$	1.73909	+	9.86287i	0.0750473	+	0.425614i
$538$	−29.7961	+	10.8449i	−1.28460	+	0.467556i
$539$	1.77984	−	3.08278i	0.0766633	−	0.132785i
$540$	−4.28403	−	7.42016i	−0.184355	−	0.319313i
$541$	−15.8172	−	13.2722i	−0.680035	−	0.570617i	0.235982	−	0.971757i	$-0.424169\pi$
$541$	−15.8172	−	13.2722i	−0.680035	−	0.570617i	−0.916016	+	0.401141i	$0.868614\pi$
$542$	−21.6246	−	18.1452i	−0.928858	−	0.779405i
$543$	26.2747	+	45.5092i	1.12756	+	1.95298i
$544$	1.77879	−	3.08096i	0.0762651	−	0.132095i
$545$	−45.9578	+	16.7273i	−1.96862	+	0.716518i
$546$	4.27899	+	24.2674i	0.183124	+	1.03855i
$547$	−2.03677	+	11.5511i	−0.0870859	+	0.493889i	0.909801	+	0.415045i	$0.136234\pi$
$547$	−2.03677	+	11.5511i	−0.0870859	+	0.493889i	−0.996887	+	0.0788442i	$0.974877\pi$
$548$	−6.65598	−	2.42258i	−0.284330	−	0.103488i
$549$	−5.01050	+	4.20431i	−0.213843	+	0.179435i
$550$	3.48028			0.148399
$551$	43.4506	+	5.50280i	1.85106	+	0.234427i
$552$	−6.00576			−0.255622
$553$	16.8315	−	14.1233i	0.715750	−	0.600585i
$554$	−5.75979	−	2.09639i	−0.244710	−	0.0890672i
$555$	−3.64486	+	20.6710i	−0.154715	+	0.877435i
$556$	−3.93272	−	22.3036i	−0.166785	−	0.945882i
$557$	12.6554	−	4.60618i	0.536225	−	0.195170i	−0.0596908	−	0.998217i	$-0.519011\pi$
$557$	12.6554	−	4.60618i	0.536225	−	0.195170i	0.595916	+	0.803047i	$0.296789\pi$
$558$	2.94272	−	5.09695i	0.124575	−	0.215771i
$559$	−12.5723	−	21.7759i	−0.531753	−	0.921022i
$560$	7.24911	+	6.08272i	0.306331	+	0.257042i
$561$	−5.86603	−	4.92218i	−0.247664	−	0.207815i
$562$	−15.6294	−	27.0709i	−0.659285	−	1.14192i
$563$	−11.0442	+	19.1292i	−0.465459	+	0.806198i	−0.999222	−	0.0394358i	$-0.987444\pi$
$563$	−11.0442	+	19.1292i	−0.465459	+	0.806198i	0.533763	+	0.845634i	$0.320777\pi$
$564$	−2.65340	+	0.965757i	−0.111728	+	0.0406657i
$565$	−6.60907	−	37.4819i	−0.278046	−	1.57688i
$566$	4.18215	−	23.7182i	0.175789	−	0.996948i
$567$	−34.2989	−	12.4838i	−1.44042	−	0.524269i
$568$	9.69616	−	8.13605i	0.406842	−	0.341381i
$569$	−14.7776			−0.619508			−0.309754	−	0.950817i	$-0.600247\pi$
$569$	−14.7776			−0.619508			−0.309754	+	0.950817i	$0.600247\pi$
$570$	24.2970	+	12.4965i	1.01769	+	0.523421i
$571$	2.49931			0.104593			0.0522964	−	0.998632i	$-0.483346\pi$
$571$	2.49931			0.104593			0.0522964	+	0.998632i	$0.483346\pi$
$572$	−2.69876	+	2.26453i	−0.112841	+	0.0946848i
$573$	16.7257	+	6.08767i	0.698728	+	0.254316i
$574$	5.06909	−	28.7482i	0.211580	−	1.19993i
$575$	1.68623	+	9.56310i	0.0703207	+	0.398809i
$576$	−1.53459	+	0.558547i	−0.0639414	+	0.0232728i
$577$	−8.79537	+	15.2340i	−0.366156	+	0.634201i	−0.988961	−	0.148176i	$-0.952660\pi$
$577$	−8.79537	+	15.2340i	−0.366156	+	0.634201i	0.622805	+	0.782377i	$0.285993\pi$
$578$	−2.17179	−	3.76165i	−0.0903346	−	0.156464i
$579$	−23.6819	−	19.8715i	−0.984186	−	0.825830i
$580$	22.4147	+	18.8082i	0.930721	+	0.780968i
$581$	4.02627	+	6.97371i	0.167038	+	0.289318i
$582$	5.50654	−	9.53761i	0.228253	−	0.395347i
$583$	0.162892	−	0.0592877i	0.00674628	−	0.00245545i
$584$	−2.30647	−	13.0807i	−0.0954426	−	0.541282i
$585$	−2.90934	+	16.4997i	−0.120286	+	0.682177i
$586$	19.3129	+	7.02933i	0.797810	+	0.290379i
$587$	−10.6737	+	8.95629i	−0.440550	+	0.369666i	−0.835915	−	0.548858i	$-0.815063\pi$
$587$	−10.6737	+	8.95629i	−0.440550	+	0.369666i	0.395365	+	0.918524i	$0.370618\pi$
$588$	7.66208			0.315979
$589$	−0.762508	−	15.6905i	−0.0314186	−	0.646515i
$590$	−26.9954			−1.11138
$591$	−13.1370	+	11.0233i	−0.540385	+	0.453437i
$592$	−3.14670	−	1.14531i	−0.129329	−	0.0470718i
$593$	1.51015	−	8.56449i	0.0620145	−	0.351702i	−0.937973	−	0.346708i	$-0.887299\pi$
$593$	1.51015	−	8.56449i	0.0620145	−	0.351702i	0.999988	−	0.00499339i	$-0.00158945\pi$
$594$	−0.510914	−	2.89754i	−0.0209631	−	0.118887i
$595$	−31.6353	+	11.5143i	−1.29692	+	0.472040i
$596$	−1.08721	+	1.88310i	−0.0445339	+	0.0771349i
$597$	15.0227	+	26.0201i	0.614838	+	1.06493i
$598$	−7.53005	−	6.31847i	−0.307927	−	0.258381i
$599$	0.553443	+	0.464394i	0.0226131	+	0.0189746i	0.654024	−	0.756474i	$-0.273079\pi$
$599$	0.553443	+	0.464394i	0.0226131	+	0.0189746i	−0.631411	+	0.775448i	$0.717524\pi$
$600$	3.74558	+	6.48753i	0.152913	+	0.264852i
$601$	−19.3695	+	33.5489i	−0.790097	+	1.36849i	0.135809	+	0.990735i	$0.456637\pi$
$601$	−19.3695	+	33.5489i	−0.790097	+	1.36849i	−0.925906	+	0.377754i	$0.876697\pi$
$602$	−21.7945	+	7.93253i	−0.888276	+	0.323306i
$603$	2.57023	+	14.5765i	0.104668	+	0.593600i
$604$	1.41982	−	8.05221i	0.0577717	−	0.327640i
$605$	2.73647	+	0.995994i	0.111253	+	0.0404929i
$606$	5.40753	−	4.53746i	0.219666	−	0.184322i
$607$	19.9762			0.810810			0.405405	−	0.914137i	$-0.367131\pi$
$607$	19.9762			0.810810			0.405405	+	0.914137i	$0.367131\pi$
$608$	−2.63646	+	3.47117i	−0.106923	+	0.140775i
$609$	70.2805			2.84791
$610$	−8.93466	+	7.49707i	−0.361754	+	0.303547i
$611$	−4.34288	−	1.58068i	−0.175694	−	0.0639474i
$612$	1.00887	−	5.72156i	0.0407810	−	0.231280i
$613$	0.271372	+	1.53903i	0.0109606	+	0.0621608i	0.989797	−	0.142481i	$-0.0455081\pi$
$613$	0.271372	+	1.53903i	0.0109606	+	0.0621608i	−0.978837	+	0.204642i	$0.934397\pi$
$614$	14.7104	−	5.35416i	0.593665	−	0.216076i
$615$	28.1542	−	48.7646i	1.13529	−	1.96638i
$616$	1.62478	+	2.81421i	0.0654644	+	0.113388i
$617$	−23.4195	−	19.6513i	−0.942832	−	0.791130i	0.0352437	−	0.999379i	$-0.488779\pi$
$617$	−23.4195	−	19.6513i	−0.942832	−	0.791130i	−0.978076	+	0.208249i	$0.933224\pi$
$618$	−0.865697	−	0.726406i	−0.0348234	−	0.0292203i
$619$	−7.72494	−	13.3800i	−0.310492	−	0.537787i	0.667977	−	0.744182i	$-0.267160\pi$
$619$	−7.72494	−	13.3800i	−0.310492	−	0.537787i	−0.978469	+	0.206394i	$0.933827\pi$
$620$	5.24743	−	9.08881i	0.210742	−	0.365015i
$621$	7.71430	−	2.80778i	0.309564	−	0.112672i
$622$	0.775279	+	4.39682i	0.0310858	+	0.176297i
$623$	4.48032	−	25.4092i	0.179500	−	1.01800i
$624$	−7.12577	−	2.59357i	−0.285259	−	0.103826i
$625$	−23.2028	+	19.4694i	−0.928111	+	0.778777i
$626$	7.57980			0.302950
$627$	6.37262	+	6.88609i	0.254498	+	0.275004i
$628$	−13.7484			−0.548621
$629$	9.12598	−	7.65761i	0.363877	−	0.305329i
$630$	14.5219	+	5.28555i	0.578567	+	0.210581i
$631$	2.06282	−	11.6988i	0.0821196	−	0.465724i	−0.915821	−	0.401586i	$-0.868459\pi$
$631$	2.06282	−	11.6988i	0.0821196	−	0.465724i	0.997941	−	0.0641378i	$-0.0204297\pi$
$632$	1.17413	+	6.65880i	0.0467042	+	0.264873i
$633$	−37.6794	+	13.7142i	−1.49762	+	0.545089i
$634$	−12.4943	+	21.6408i	−0.496212	+	0.859465i
$635$	23.8865	+	41.3726i	0.947907	+	1.64182i
$636$	0.285826	+	0.239837i	0.0113337	+	0.00951014i
$637$	9.60675	+	8.06102i	0.380633	+	0.319389i
$638$	5.02394	+	8.70172i	0.198900	+	0.344504i
$639$	10.3353	−	17.9013i	0.408859	−	0.708164i
$640$	−2.73647	+	0.995994i	−0.108169	+	0.0393701i
$641$	4.56063	+	25.8646i	0.180134	+	1.02159i	0.932049	+	0.362332i	$0.118019\pi$
$641$	4.56063	+	25.8646i	0.180134	+	1.02159i	−0.751915	+	0.659260i	$0.770870\pi$
$642$	3.88993	−	22.0609i	0.153523	−	0.870673i
$643$	3.42653	+	1.24715i	0.135129	+	0.0491829i	0.408699	−	0.912669i	$-0.365982\pi$
$643$	3.42653	+	1.24715i	0.135129	+	0.0491829i	−0.273570	+	0.961852i	$0.588205\pi$
$644$	−6.94565	+	5.82809i	−0.273697	+	0.229659i
$645$	−44.7378			−1.76155
$646$	−6.00483	−	14.2973i	−0.236257	−	0.562521i
$647$	9.63780			0.378901			0.189451	−	0.981890i	$-0.439329\pi$
$647$	9.63780			0.378901			0.189451	+	0.981890i	$0.439329\pi$
$648$	8.60443	−	7.21998i	0.338014	−	0.283627i
$649$	−8.71104	−	3.17056i	−0.341938	−	0.124455i
$650$	−2.12909	+	12.0747i	−0.0835099	+	0.473608i
$651$	−4.37726	−	24.8247i	−0.171558	−	0.972955i
$652$	5.78476	−	2.10548i	0.226549	−	0.0824570i
$653$	13.9507	−	24.1634i	0.545935	−	0.945587i	−0.452613	−	0.891707i	$-0.649508\pi$
$653$	13.9507	−	24.1634i	0.545935	−	0.945587i	0.998547	−	0.0538795i	$-0.0171587\pi$
$654$	−18.0748	−	31.3065i	−0.706781	−	1.22418i
$655$	40.5362	+	34.0139i	1.58388	+	1.32903i
$656$	6.88158	+	5.77433i	0.268680	+	0.225450i
$657$	−10.8457	−	18.7852i	−0.423130	−	0.732882i
$658$	−2.13146	+	3.69179i	−0.0830929	+	0.143921i
$659$	10.8820	−	3.96073i	0.423903	−	0.154288i	−0.121255	−	0.992621i	$-0.538692\pi$
$659$	10.8820	−	3.96073i	0.423903	−	0.154288i	0.545158	+	0.838333i	$0.316470\pi$
$660$	1.08845	+	6.17293i	0.0423680	+	0.240281i
$661$	2.85857	−	16.2118i	0.111186	−	0.630565i	−0.877383	−	0.479791i	$-0.840712\pi$
$661$	2.85857	−	16.2118i	0.111186	−	0.630565i	0.988568	−	0.150774i	$-0.0481765\pi$
$662$	−0.295305	−	0.107482i	−0.0114774	−	0.00417742i
$663$	20.6659	−	17.3408i	0.802599	−	0.673460i
$664$	−2.47804			−0.0961665
$665$	40.2262	−	9.12603i	1.55991	−	0.353892i
$666$	−5.46862			−0.211905
$667$	−21.4764	+	18.0209i	−0.831570	+	0.697770i
$668$	−22.4922	−	8.18650i	−0.870250	−	0.316745i
$669$	−6.41285	+	36.3691i	−0.247935	+	1.40611i
$670$	4.58320	+	25.9926i	0.177064	+	1.00418i
$671$	−3.76361	+	1.36984i	−0.145293	+	0.0528822i
$672$	−3.49728	+	6.05747i	−0.134911	+	0.233672i
$673$	−7.32332	−	12.6844i	−0.282293	−	0.488946i	0.689656	−	0.724137i	$-0.257762\pi$
$673$	−7.32332	−	12.6844i	−0.282293	−	0.488946i	−0.971949	+	0.235191i	$0.924428\pi$
$674$	11.5162	+	9.66326i	0.443588	+	0.372215i
$675$	−7.84414	−	6.58202i	−0.301921	−	0.253342i
$676$	0.294287	+	0.509720i	0.0113187	+	0.0196046i
$677$	−12.9083	+	22.3579i	−0.496107	+	0.859283i	−0.999990	−	0.00448925i	$-0.998571\pi$
$677$	−12.9083	+	22.3579i	−0.496107	+	0.859283i	0.503883	+	0.863772i	$0.331904\pi$
$678$	26.4354	−	9.62170i	1.01525	−	0.369519i
$679$	−2.88715	−	16.3738i	−0.110799	−	0.628371i
$680$	1.79900	−	10.2026i	0.0689884	−	0.391253i
$681$	1.45687	+	0.530256i	0.0558272	+	0.0203195i
$682$	2.76074	−	2.31654i	0.105714	−	0.0887047i
$683$	−4.79403			−0.183439			−0.0917193	−	0.995785i	$-0.529236\pi$
$683$	−4.79403			−0.183439			−0.0917193	+	0.995785i	$0.529236\pi$
$684$	−2.10709	+	6.79943i	−0.0805666	+	0.259983i
$685$	−20.6268			−0.788109
$686$	−8.56402	+	7.18606i	−0.326976	+	0.274365i
$687$	26.5391	+	9.65943i	1.01253	+	0.368530i
$688$	1.23938	−	7.02888i	0.0472510	−	0.267974i
$689$	0.106046	+	0.601417i	0.00404003	+	0.0229121i
$690$	−16.4346	+	5.98170i	−0.625654	+	0.227720i
$691$	15.3400	−	26.5697i	0.583562	−	1.01076i	−0.411491	−	0.911414i	$-0.634992\pi$
$691$	15.3400	−	26.5697i	0.583562	−	1.01076i	0.995053	−	0.0993451i	$-0.0316748\pi$
$692$	5.28727	+	9.15781i	0.200992	+	0.348128i
$693$	4.06525	+	3.41115i	0.154426	+	0.129579i
$694$	14.1734	+	11.8929i	0.538014	+	0.451447i
$695$	−32.9760	−	57.1161i	−1.25085	−	2.16654i
$696$	−10.8138	+	18.7301i	−0.409897	+	0.709963i
$697$	−30.0314	+	10.9305i	−1.13752	+	0.414023i
$698$	−1.97218	−	11.1848i	−0.0746480	−	0.423350i
$699$	−1.17006	+	6.63576i	−0.0442559	+	0.250987i
$700$	10.6274	+	3.86804i	0.401676	+	0.146198i
$701$	−3.25005	+	2.72711i	−0.122753	+	0.103002i	−0.702097	−	0.712081i	$-0.747753\pi$
$701$	−3.25005	+	2.72711i	−0.122753	+	0.103002i	0.579345	+	0.815083i	$0.303308\pi$
$702$	10.3655			0.391219
$703$	−12.2717	+	7.90320i	−0.462837	+	0.298075i
$704$	−1.00000			−0.0376889
$705$	−6.29905	+	5.28553i	−0.237236	+	0.199065i
$706$	−31.2585	−	11.3772i	−1.17643	−	0.428185i
$707$	1.85057	−	10.4951i	0.0695979	−	0.394709i
$708$	−3.46489	−	19.6504i	−0.130219	−	0.738506i
$709$	9.97425	−	3.63033i	0.374591	−	0.136340i	−0.147862	−	0.989008i	$-0.547239\pi$
$709$	9.97425	−	3.63033i	0.374591	−	0.136340i	0.522453	+	0.852668i	$0.325017\pi$
$710$	18.4298	−	31.9214i	0.691659	−	1.19799i
$711$	5.52105	+	9.56275i	0.207056	+	0.358631i
$712$	6.08229	+	5.10365i	0.227944	+	0.191267i
$713$	7.70298	+	6.46357i	0.288479	+	0.242062i
$714$	−12.4419	−	21.5500i	−0.465626	−	0.806487i
$715$	−5.12963	+	8.88478i	−0.191837	+	0.332272i
$716$	−4.37223	+	1.59136i	−0.163398	+	0.0594719i
$717$	6.13338	+	34.7841i	0.229055	+	1.29904i
$718$	3.79953	−	21.5482i	0.141797	−	0.804171i
$719$	46.0118	+	16.7469i	1.71595	+	0.624556i	0.997477	−	0.0709964i	$-0.0226179\pi$
$719$	46.0118	+	16.7469i	1.71595	+	0.624556i	0.718476	+	0.695552i	$0.244840\pi$
$720$	−3.64306	+	3.05689i	−0.135769	+	0.113924i
$721$	−1.70609			−0.0635382
$722$	5.09811	+	18.3033i	0.189732	+	0.681177i
$723$	24.9856			0.929225
$724$	−18.7020	+	15.6928i	−0.695053	+	0.583219i
$725$	32.8605	+	11.9602i	1.22041	+	0.444192i
$726$	−0.373771	+	2.11976i	−0.0138719	+	0.0786716i
$727$	4.89783	+	27.7770i	0.181650	+	1.03019i	0.930184	+	0.367094i	$0.119647\pi$
$727$	4.89783	+	27.7770i	0.181650	+	1.03019i	−0.748534	+	0.663097i	$0.769242\pi$
$728$	−10.7578	+	3.91551i	−0.398709	+	0.145118i
$729$	−0.327946	+	0.568020i	−0.0121462	+	0.0210378i
$730$	−19.3399	−	33.4976i	−0.715800	−	1.23980i
$731$	19.4511	+	16.3214i	0.719425	+	0.603669i
$732$	−6.60401	−	5.54142i	−0.244091	−	0.204817i
$733$	−9.58788	−	16.6067i	−0.354136	−	0.613382i	0.632833	−	0.774288i	$-0.281892\pi$
$733$	−9.58788	−	16.6067i	−0.354136	−	0.613382i	−0.986970	+	0.160906i	$0.948558\pi$
$734$	−16.9840	+	29.4172i	−0.626891	+	1.08581i
$735$	20.9671	−	7.63139i	0.773382	−	0.281488i
$736$	−0.484511	−	2.74780i	−0.0178593	−	0.101285i
$737$	−1.57385	+	8.92575i	−0.0579736	+	0.328784i
$738$	13.7857	+	5.01757i	0.507457	+	0.184699i
$739$	15.3618	−	12.8900i	0.565091	−	0.474168i	−0.314922	−	0.949118i	$-0.601978\pi$
$739$	15.3618	−	12.8900i	0.565091	−	0.474168i	0.880013	+	0.474950i	$0.157534\pi$
$740$	−9.75158			−0.358475
$741$	−27.7896	+	17.8969i	−1.02087	+	0.657460i
$742$	0.563298			0.0206793
$743$	−10.9809	+	9.21407i	−0.402850	+	0.338031i	−0.821594	−	0.570073i	$-0.806915\pi$
$743$	−10.9809	+	9.21407i	−0.402850	+	0.338031i	0.418744	+	0.908104i	$0.362470\pi$
$744$	7.28941	+	2.65313i	0.267243	+	0.0972684i
$745$	−1.09956	+	6.23591i	−0.0402848	+	0.228466i
$746$	2.46828	+	13.9983i	0.0903703	+	0.512515i
$747$	−3.80278	+	1.38410i	−0.139137	+	0.0506416i
$748$	1.77879	−	3.08096i	0.0650391	−	0.112651i
$749$	−16.9095	−	29.2882i	−0.617861	−	1.07017i
$750$	−7.29724	−	6.12311i	−0.266457	−	0.223584i
$751$	20.7712	+	17.4291i	0.757951	+	0.635997i	0.937593	−	0.347736i	$-0.113049\pi$
$751$	20.7712	+	17.4291i	0.757951	+	0.635997i	−0.179641	+	0.983732i	$0.557494\pi$
$752$	−0.655921	−	1.13609i	−0.0239190	−	0.0414289i
$753$	−19.0016	+	32.9118i	−0.692458	+	1.19937i
$754$	−33.2638	+	12.1070i	−1.21139	+	0.440912i
$755$	−4.13465	−	23.4488i	−0.150475	−	0.853388i
$756$	1.66025	−	9.41574i	0.0603827	−	0.342447i
$757$	27.4905	+	10.0057i	0.999158	+	0.363664i	0.789260	−	0.614059i	$-0.210464\pi$
$757$	27.4905	+	10.0057i	0.999158	+	0.363664i	0.209898	+	0.977723i	$0.432687\pi$
$758$	17.6856	−	14.8400i	0.642372	−	0.539014i
$759$	−6.00576			−0.217995
$760$	−3.75734	+	12.1247i	−0.136293	+	0.439808i
$761$	45.9854			1.66697			0.833484	−	0.552543i	$-0.186343\pi$
$761$	45.9854			1.66697			0.833484	+	0.552543i	$0.186343\pi$
$762$	−27.0499	+	22.6976i	−0.979916	+	0.822247i
$763$	−51.2838	−	18.6658i	−1.85660	−	0.675746i
$764$	−1.43593	+	8.14359i	−0.0519503	+	0.294625i
$765$	−2.93791	−	16.6617i	−0.106220	−	0.602406i
$766$	−21.3408	+	7.76741i	−0.771074	+	0.280648i
$767$	16.3292	−	28.2830i	0.589614	−	1.02124i
$768$	−1.07623	−	1.86408i	−0.0388351	−	0.0672644i
$769$	34.2845	+	28.7681i	1.23633	+	1.03740i	0.997802	+	0.0662682i	$0.0211093\pi$
$769$	34.2845	+	28.7681i	1.23633	+	1.03740i	0.238528	+	0.971136i	$0.423335\pi$
$770$	7.24911	+	6.08272i	0.261240	+	0.219206i
$771$	7.73752	+	13.4018i	0.278660	+	0.482653i
$772$	7.18121	−	12.4382i	0.258457	−	0.447661i
$773$	14.9246	−	5.43211i	0.536801	−	0.195380i	−0.0593715	−	0.998236i	$-0.518910\pi$
$773$	14.9246	−	5.43211i	0.536801	−	0.195380i	0.596173	+	0.802856i	$0.296687\pi$
$774$	−2.02401	−	11.4787i	−0.0727515	−	0.412595i
$775$	2.17799	−	12.3520i	0.0782356	−	0.443696i
$776$	4.80795	+	1.74995i	0.172595	+	0.0628195i
$777$	−17.9426	+	15.0556i	−0.643686	+	0.540117i
$778$	−11.5491			−0.414056
$779$	38.1867	−	8.66334i	1.36818	−	0.310396i
$780$	−22.0826			−0.790685
$781$	9.69616	−	8.13605i	0.346956	−	0.291131i
$782$	9.32770	+	3.39500i	0.333558	+	0.121405i
$783$	5.13361	−	29.1141i	0.183460	−	1.04045i
$784$	0.618133	+	3.50561i	0.0220762	+	0.125200i
$785$	−37.6221	+	13.6933i	−1.34279	+	0.488736i
$786$	−19.5564	+	33.8727i	−0.697554	+	1.20820i
$787$	−23.0245	−	39.8797i	−0.820736	−	1.42156i	−0.905135	−	0.425125i	$-0.860230\pi$
$787$	−23.0245	−	39.8797i	−0.820736	−	1.42156i	0.0843983	−	0.996432i	$-0.473103\pi$
$788$	−6.10326	−	5.12125i	−0.217420	−	0.182437i
$789$	−4.27405	−	3.58636i	−0.152160	−	0.127678i
$790$	9.84508	+	17.0522i	0.350272	+	0.606689i
$791$	21.2354	−	36.7808i	0.755044	−	1.30778i
$792$	−1.53459	+	0.558547i	−0.0545294	+	0.0198471i
$793$	−2.45019	−	13.8957i	−0.0870089	−	0.493452i
$794$	−2.62687	+	14.8977i	−0.0932240	+	0.528700i
$795$	1.02103	+	0.371625i	0.0362122	+	0.0131802i
$796$	−10.6929	+	8.97244i	−0.379001	+	0.318020i
$797$	15.8003			0.559675			0.279837	−	0.960047i	$-0.409719\pi$
$797$	15.8003			0.559675			0.279837	+	0.960047i	$0.409719\pi$
$798$	11.8061	+	28.1100i	0.417930	+	0.995082i
$799$	4.66699			0.165106
$800$	−2.66605	+	2.23708i	−0.0942590	+	0.0790927i
$801$	12.1845	+	4.43479i	0.430518	+	0.156696i
$802$	−0.274531	+	1.55694i	−0.00969403	+	0.0549776i
$803$	−2.30647	−	13.0807i	−0.0813937	−	0.461607i
$804$	−18.3322	+	6.67237i	−0.646526	+	0.235316i
$805$	−13.2018	+	22.8662i	−0.465303	+	0.805928i
$806$	6.34823	+	10.9954i	0.223607	+	0.387298i
$807$	−52.2832	−	43.8708i	−1.84046	−	1.54433i
$808$	2.51226	+	2.10803i	0.0883809	+	0.0741604i
$809$	7.40206	+	12.8207i	0.260243	+	0.450754i	0.966306	−	0.257395i	$-0.0828641\pi$
$809$	7.40206	+	12.8207i	0.260243	+	0.450754i	−0.706064	+	0.708148i	$0.749531\pi$
$810$	16.3547	−	28.3272i	0.574647	−	0.995317i
$811$	−11.5336	+	4.19788i	−0.404999	+	0.147407i	−0.536484	−	0.843911i	$-0.680248\pi$
$811$	−11.5336	+	4.19788i	−0.404999	+	0.147407i	0.131485	+	0.991318i	$0.458025\pi$
$812$	5.66983	+	32.1552i	0.198972	+	1.12843i
$813$	10.5512	−	59.8386i	0.370045	−	2.09863i
$814$	−3.14670	−	1.14531i	−0.110292	−	0.0401430i
$815$	13.7328	−	11.5232i	0.481039	−	0.403639i
$816$	7.65756			0.268068
$817$	−21.1309	−	22.8335i	−0.739276	−	0.798843i
$818$	−21.8873			−0.765271
$819$	−14.3218	+	12.0174i	−0.500445	+	0.419923i
$820$	24.5824	+	8.94727i	0.858456	+	0.312452i
$821$	3.53566	−	20.0517i	0.123395	−	0.699810i	−0.858853	−	0.512223i	$-0.828822\pi$
$821$	3.53566	−	20.0517i	0.123395	−	0.699810i	0.982248	−	0.187587i	$-0.0600667\pi$
$822$	−2.64747	−	15.0146i	−0.0923413	−	0.523693i
$823$	−30.8816	+	11.2400i	−1.07647	+	0.391802i	−0.818591	−	0.574377i	$-0.805244\pi$
$823$	−30.8816	+	11.2400i	−1.07647	+	0.391802i	−0.257875	+	0.966178i	$0.583022\pi$
$824$	0.262511	−	0.454682i	0.00914499	−	0.0158396i
$825$	3.74558	+	6.48753i	0.130404	+	0.225867i
$826$	−23.0762	−	19.3632i	−0.802923	−	0.673732i
$827$	−14.5673	−	12.2234i	−0.506554	−	0.425049i	0.353361	−	0.935487i	$-0.385039\pi$
$827$	−14.5673	−	12.2234i	−0.506554	−	0.425049i	−0.859914	+	0.510438i	$0.829483\pi$
$828$	−2.27830	−	3.94613i	−0.0791764	−	0.137138i
$829$	20.7764	−	35.9857i	0.721593	−	1.24984i	−0.238767	−	0.971077i	$-0.576743\pi$
$829$	20.7764	−	35.9857i	0.721593	−	1.24984i	0.960361	−	0.278760i	$-0.0899233\pi$
$830$	−6.78108	+	2.46811i	−0.235375	+	0.0856694i
$831$	−2.29101	−	12.9929i	−0.0794741	−	0.450720i
$832$	0.611760	−	3.46946i	0.0212090	−	0.120282i
$833$	−11.9002	−	4.33131i	−0.412316	−	0.150071i
$834$	37.3432	−	31.3347i	1.29309	−	1.08503i
$835$	−69.7030			−2.41217
$836$	−2.63646	+	3.47117i	−0.0911840	+	0.120053i
$837$	−10.6035			−0.366510
$838$	5.24465	−	4.40079i	0.181174	−	0.152023i
$839$	25.2100	+	9.17570i	0.870347	+	0.316780i	0.738308	−	0.674464i	$-0.235625\pi$
$839$	25.2100	+	9.17570i	0.870347	+	0.316780i	0.132039	+	0.991244i	$0.457847\pi$
$840$	−3.53701	+	20.0594i	−0.122038	+	0.692113i
$841$	12.4957	+	70.8667i	0.430887	+	2.44368i
$842$	0.389345	−	0.141710i	0.0134177	−	0.00488365i
$843$	33.6416	−	58.2690i	1.15868	−	2.00689i
$844$	−9.31436	−	16.1329i	−0.320613	−	0.555319i
$845$	1.31299	+	1.10173i	0.0451681	+	0.0379005i
$846$	−1.64113	−	1.37707i	−0.0564232	−	0.0473447i
$847$	1.62478	+	2.81421i	0.0558282	+	0.0966973i
$848$	−0.0866729	+	0.150122i	−0.00297636	+	0.00515520i
$849$	48.7136	−	17.7303i	1.67185	−	0.608502i
$850$	−2.15000	−	12.1933i	−0.0737446	−	0.418226i
$851$	1.62246	−	9.20142i	0.0556172	−	0.315421i
$852$	25.6016	+	9.31821i	0.877096	+	0.319237i
$853$	27.4627	−	23.0439i	0.940304	−	0.789009i	−0.0373338	−	0.999303i	$-0.511886\pi$
$853$	27.4627	−	23.0439i	0.940304	−	0.789009i	0.977638	+	0.210294i	$0.0674420\pi$
$854$	−13.0150			−0.445364
$855$	1.00620	+	20.7051i	0.0344114	+	0.708100i
$856$	10.4073			0.355713
$857$	−28.2525	+	23.7066i	−0.965086	+	0.809803i	−0.981773	−	0.190058i	$-0.939133\pi$
$857$	−28.2525	+	23.7066i	−0.965086	+	0.809803i	0.0166871	+	0.999861i	$0.494688\pi$
$858$	−7.12577	−	2.59357i	−0.243270	−	0.0885429i
$859$	6.74523	−	38.2541i	0.230144	−	1.30521i	−0.622459	−	0.782653i	$-0.713866\pi$
$859$	6.74523	−	38.2541i	0.230144	−	1.30521i	0.852603	−	0.522560i	$-0.175023\pi$
$860$	−3.60919	−	20.4687i	−0.123072	−	0.697978i
$861$	59.0446	−	21.4905i	2.01223	−	0.732394i
$862$	−0.780835	+	1.35245i	−0.0265953	+	0.0460645i
$863$	−19.2289	−	33.3054i	−0.654559	−	1.13373i	−0.982004	−	0.188860i	$-0.939521\pi$
$863$	−19.2289	−	33.3054i	−0.654559	−	1.13373i	0.327445	−	0.944870i	$-0.393812\pi$
$864$	2.25388	+	1.89123i	0.0766787	+	0.0643411i
$865$	23.5896	+	19.7940i	0.802070	+	0.673016i
$866$	19.3456	+	33.5076i	0.657390	+	1.13863i
$867$	4.67469	−	8.09680i	0.158761	−	0.274982i
$868$	11.0048	−	4.00543i	0.373528	−	0.135953i
$869$	1.17413	+	6.65880i	0.0398295	+	0.225884i
$870$	−10.9367	+	62.0249i	−0.370788	+	2.10284i
$871$	−30.0048	−	10.9208i	−1.01667	−	0.370038i
$872$	12.8654	−	10.7953i	0.435677	−	0.365576i
$873$	8.35568			0.282797
$874$	−10.8155	−	5.56265i	−0.365839	−	0.188159i
$875$	−14.3812			−0.486173
$876$	21.9012	−	18.3773i	0.739972	−	0.620910i
$877$	41.9766	+	15.2782i	1.41745	+	0.515909i	0.933307	−	0.359081i	$-0.116910\pi$
$877$	41.9766	+	15.2782i	1.41745	+	0.515909i	0.484142	+	0.874990i	$0.339132\pi$
$878$	−0.236918	+	1.34363i	−0.00799560	+	0.0453453i
$879$	7.68188	+	43.5661i	0.259104	+	1.46945i
$880$	−2.73647	+	0.995994i	−0.0922464	+	0.0335749i
$881$	17.5526	−	30.4020i	0.591362	−	1.02427i	−0.402687	−	0.915338i	$-0.631924\pi$
$881$	17.5526	−	30.4020i	0.591362	−	1.02427i	0.994049	−	0.108931i	$-0.0347429\pi$
$882$	2.90663	+	5.03443i	0.0978713	+	0.169518i
$883$	29.2053	+	24.5062i	0.982837	+	0.824698i	0.984515	−	0.175301i	$-0.0560897\pi$
$883$	29.2053	+	24.5062i	0.982837	+	0.824698i	−0.00167816	+	0.999999i	$0.500534\pi$
$884$	9.60108	+	8.05627i	0.322919	+	0.270962i
$885$	−29.0532	−	50.3217i	−0.976613	−	1.69154i
$886$	−13.7757	+	23.8603i	−0.462805	+	0.801602i
$887$	15.2934	−	5.56635i	0.513503	−	0.186900i	−0.0722543	−	0.997386i	$-0.523019\pi$
$887$	15.2934	−	5.56635i	0.513503	−	0.186900i	0.585757	+	0.810486i	$0.300797\pi$
$888$	−1.25163	−	7.09833i	−0.0420019	−	0.238205i
$889$	−9.25706	+	52.4994i	−0.310472	+	1.76077i
$890$	21.7272	+	7.90806i	0.728298	+	0.265079i
$891$	8.60443	−	7.21998i	0.288259	−	0.241878i
$892$	−17.1572			−0.574465
$893$	−5.67287	−	0.718440i	−0.189835	−	0.0240417i
$894$	−4.68035			−0.156534
$895$	−10.3795	+	8.70942i	−0.346948	+	0.291124i
$896$	−3.05359	−	1.11142i	−0.102013	−	0.0371299i
$897$	3.67409	−	20.8368i	0.122674	−	0.695720i
$898$	0.756996	+	4.29314i	0.0252613	+	0.143264i
$899$	34.0276	−	12.3851i	1.13489	−	0.413065i
$900$	−2.84179	+	4.92212i	−0.0947263	+	0.164071i
$901$	−0.308346	−	0.534071i	−0.0102725	−	0.0177925i
$902$	6.88158	+	5.77433i	0.229131	+	0.192264i
$903$	−38.2427	−	32.0895i	−1.27264	−	1.06787i
$904$	6.53484	+	11.3187i	0.217346	+	0.376454i
$905$	−35.5474	+	61.5700i	−1.18164	+	2.04665i
$906$	16.5380	−	6.01936i	0.549440	−	0.199980i
$907$	3.47862	+	19.7282i	0.115506	+	0.655065i	0.986499	+	0.163770i	$0.0523654\pi$
$907$	3.47862	+	19.7282i	0.115506	+	0.655065i	−0.870993	+	0.491296i	$0.836523\pi$
$908$	−0.125075	+	0.709333i	−0.00415075	+	0.0235401i
$909$	5.03273	+	1.83176i	0.166925	+	0.0607558i
$910$	−25.5385	+	21.4293i	−0.846593	+	0.710376i
$911$	9.49307			0.314519			0.157260	−	0.987557i	$-0.449734\pi$
$911$	9.49307			0.314519			0.157260	+	0.987557i	$0.449734\pi$
$912$	−9.30800	−	1.17881i	−0.308219	−	0.0390343i
$913$	−2.47804			−0.0820111
$914$	−15.1850	+	12.7417i	−0.502275	+	0.421459i
$915$	−23.5909	−	8.58639i	−0.779892	−	0.283857i
$916$	−2.27843	+	12.9216i	−0.0752813	+	0.426942i
$917$	10.2537	+	58.1516i	0.338607	+	1.92033i
$918$	−9.83601	+	3.58001i	−0.324637	+	0.118158i
$919$	18.8900	−	32.7184i	0.623122	−	1.07928i	−0.365778	−	0.930702i	$-0.619197\pi$
$919$	18.8900	−	32.7184i	0.623122	−	1.07928i	0.988901	−	0.148578i	$-0.0474695\pi$
$920$	−4.06264	−	7.03670i	−0.133941	−	0.231993i
$921$	25.8124	+	21.6592i	0.850548	+	0.713695i
$922$	6.70167	+	5.62337i	0.220708	+	0.185196i
$923$	22.2960	+	38.6178i	0.733881	+	1.27112i
$924$	−3.49728	+	6.05747i	−0.115052	+	0.199276i
$925$	−10.9514	+	3.98598i	−0.360080	+	0.131058i
$926$	−2.88737	−	16.3751i	−0.0948849	−	0.538119i
$927$	0.148886	−	0.844377i	0.00489007	−	0.0277330i
$928$	−9.44192	−	3.43658i	−0.309946	−	0.112811i
$929$	1.29710	−	1.08839i	0.0425563	−	0.0357090i	−0.621261	−	0.783603i	$-0.713379\pi$
$929$	1.29710	−	1.08839i	0.0425563	−	0.0357090i	0.663818	+	0.747894i	$0.268935\pi$
$930$	22.5898			0.740747
$931$	13.7983	+	7.09676i	0.452220	+	0.232587i
$932$	−3.13043			−0.102541
$933$	−7.36167	+	6.17718i	−0.241010	+	0.202232i
$934$	13.8439	+	5.03877i	0.452986	+	0.164874i
$935$	1.79900	−	10.2026i	0.0588335	−	0.333661i
$936$	−0.999054	−	5.66592i	−0.0326551	−	0.185196i
$937$	33.5474	−	12.2103i	1.09595	−	0.398892i	0.270125	−	0.962825i	$-0.412935\pi$
$937$	33.5474	−	12.2103i	1.09595	−	0.398892i	0.825820	+	0.563934i	$0.190713\pi$
$938$	−14.7261	+	25.5064i	−0.480826	+	0.832814i
$939$	8.15761	+	14.1294i	0.266213	+	0.461095i
$940$	−2.92644	−	2.45558i	−0.0954501	−	0.0800921i
$941$	−13.1069	−	10.9980i	−0.427274	−	0.358525i	0.403648	−	0.914914i	$-0.367742\pi$
$941$	−13.1069	−	10.9980i	−0.427274	−	0.358525i	−0.830922	+	0.556389i	$0.812186\pi$
$942$	−14.7964	−	25.6282i	−0.482094	−	0.835011i
$943$	−12.5325	+	21.7069i	−0.408114	+	0.706874i
$944$	8.71104	−	3.17056i	0.283520	−	0.103193i
$945$	−4.83480	−	27.4195i	−0.157276	−	0.891957i
$946$	1.23938	−	7.02888i	0.0402958	−	0.228529i
$947$	5.17899	+	1.88500i	0.168295	+	0.0612542i	0.424793	−	0.905290i	$-0.360347\pi$
$947$	5.17899	+	1.88500i	0.168295	+	0.0612542i	−0.256499	+	0.966545i	$0.582569\pi$
$948$	−11.1489	+	9.35506i	−0.362100	+	0.303838i
$949$	46.7939			1.51899
$950$	0.736354	+	15.1523i	0.0238905	+	0.491605i
$951$	−53.7870			−1.74416
$952$	8.85594	−	7.43102i	0.287023	−	0.240841i
$953$	−5.89253	−	2.14471i	−0.190878	−	0.0694738i	0.244813	−	0.969570i	$-0.421274\pi$
$953$	−5.89253	−	2.14471i	−0.190878	−	0.0694738i	−0.435690	+	0.900097i	$0.643496\pi$
$954$	−0.0491577	+	0.278787i	−0.00159154	+	0.00902606i
$955$	4.18157	+	23.7149i	0.135313	+	0.767395i
$956$	−15.4199	+	5.61237i	−0.498714	+	0.181517i
$957$	−10.8138	+	18.7301i	−0.349562	+	0.605458i
$958$	−11.2987	−	19.5699i	−0.365045	−	0.632276i
$959$	−17.6322	−	14.7952i	−0.569373	−	0.477760i
$960$	−4.80169	−	4.02909i	−0.154974	−	0.130038i
$961$	9.00599	+	15.5988i	0.290516	+	0.503188i
$962$	5.89863	−	10.2167i	0.190179	−	0.329400i
$963$	15.9709	−	5.81294i	0.514656	−	0.187319i
$964$	2.01570	+	11.4316i	0.0649212	+	0.368187i
$965$	7.26278	−	41.1893i	0.233797	−	1.32593i
$966$	−18.3392	−	6.67491i	−0.590053	−	0.214762i
$967$	−16.7506	+	14.0555i	−0.538664	+	0.451993i	−0.871081	−	0.491140i	$-0.836580\pi$
$967$	−16.7506	+	14.0555i	−0.538664	+	0.451993i	0.332417	+	0.943133i	$0.392136\pi$
$968$	−1.00000			−0.0321412
$969$	20.1889	−	26.5807i	0.648560	−	0.853896i
$970$	14.8997			0.478402
$971$	−19.6412	+	16.4809i	−0.630315	+	0.528897i	−0.901027	−	0.433763i	$-0.857185\pi$
$971$	−19.6412	+	16.4809i	−0.630315	+	0.528897i	0.270712	+	0.962660i	$0.412741\pi$
$972$	14.4246	+	5.25012i	0.462669	+	0.168398i
$973$	12.7796	−	72.4769i	0.409696	−	2.32350i
$974$	−2.72786	−	15.4704i	−0.0874061	−	0.495705i
$975$	−24.7996	+	9.02633i	−0.794224	+	0.289074i
$976$	2.00258	−	3.46856i	0.0641009	−	0.111026i
$977$	25.5527	+	44.2586i	0.817504	+	1.41596i	0.907516	+	0.420018i	$0.137976\pi$
$977$	25.5527	+	44.2586i	0.817504	+	1.41596i	−0.0900111	+	0.995941i	$0.528690\pi$
$978$	10.1505	+	8.51731i	0.324578	+	0.272353i
$979$	6.08229	+	5.10365i	0.194391	+	0.163113i
$980$	5.18307	+	8.97733i	0.165567	+	0.286770i
$981$	13.7134	−	23.7524i	0.437837	−	0.758355i
$982$	31.8837	−	11.6047i	1.01745	−	0.370321i
$983$	9.15254	+	51.9066i	0.291921	+	1.65556i	0.679461	+	0.733711i	$0.262213\pi$
$983$	9.15254	+	51.9066i	0.291921	+	1.65556i	−0.387541	+	0.921853i	$0.626675\pi$
$984$	−3.35768	+	19.0423i	−0.107039	+	0.607048i
$985$	−21.8021	−	7.93533i	−0.694674	−	0.252841i
$986$	27.3832	−	22.9772i	0.872058	−	0.731744i
$987$	−9.17575			−0.292067
$988$	−10.4302	−	11.2706i	−0.331830	−	0.358567i
$989$	19.9144			0.633242
$990$	−3.64306	+	3.05689i	−0.115784	+	0.0971545i
$991$	14.5201	+	5.28489i	0.461246	+	0.167880i	0.562183	−	0.827013i	$-0.309962\pi$
$991$	14.5201	+	5.28489i	0.461246	+	0.167880i	−0.100937	+	0.994893i	$0.532184\pi$
$992$	−0.625809	+	3.54914i	−0.0198695	+	0.112685i
$993$	−0.117460	−	0.666150i	−0.00372749	−	0.0211396i
$994$	38.6507	−	14.0677i	1.22593	−	0.446200i
$995$	−20.3244	+	35.2029i	−0.644328	+	1.11601i
$996$	−2.66694	−	4.61927i	−0.0845051	−	0.146367i
$997$	33.7435	+	28.3142i	1.06867	+	0.896718i	0.994931	−	0.100559i	$-0.0320633\pi$
$997$	33.7435	+	28.3142i	1.06867	+	0.896718i	0.0737362	+	0.997278i	$0.476508\pi$
$998$	11.8241	+	9.92163i	0.374287	+	0.314064i
$999$	4.92626	+	8.53254i	0.155860	+	0.269958i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.j.a.177.1	yes	24
19.4	even	9		7942.2.a.bt.1.10		12
19.15	odd	18		7942.2.a.bx.1.3		12
19.16	even	9	inner	418.2.j.a.111.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.j.a.111.1	✓	24	19.16	even	9	inner
418.2.j.a.177.1	yes	24	1.1	even	1	trivial
7942.2.a.bt.1.10		12	19.4	even	9
7942.2.a.bx.1.3		12	19.15	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.j (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-2.02265 - 0.736184i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.505679 - 2.86785i) q^{5} +(2.02265 - 0.736184i) q^{6} +(1.62478 - 2.81421i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.25101 + 1.04972i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-2.02265 - 0.736184i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.505679 - 2.86785i) q^{5} +(2.02265 - 0.736184i) q^{6} +(1.62478 - 2.81421i) q^{7} +(0.500000 + 0.866025i) q^{8} +(1.25101 + 1.04972i) q^{9} +(2.23079 + 1.87186i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.07623 + 1.86408i) q^{12} +(-3.31052 + 1.20493i) q^{13} +(0.564281 + 3.20020i) q^{14} +(-1.08845 + 6.17293i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(2.72527 - 2.28677i) q^{17} -1.63308 q^{18} +(-3.66468 + 2.36011i) q^{19} -2.91209 q^{20} +(-5.35814 + 4.49602i) q^{21} +(-0.939693 - 0.342020i) q^{22} +(0.484511 - 2.74780i) q^{23} +(-0.373771 - 2.11976i) q^{24} +(-3.27039 + 1.19032i) q^{25} +(1.76149 - 3.05099i) q^{26} +(1.47112 + 2.54805i) q^{27} +(-2.48931 - 2.08878i) q^{28} +(-7.69713 - 6.45866i) q^{29} +(-3.13408 - 5.42838i) q^{30} +(-1.80194 + 3.12106i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.373771 - 2.11976i) q^{33} +(-0.617768 + 3.50354i) q^{34} +(-8.89235 - 3.23655i) q^{35} +(1.25101 - 1.04972i) q^{36} +3.34865 q^{37} +(1.29025 - 4.16356i) q^{38} +7.58308 q^{39} +(2.23079 - 1.87186i) q^{40} +(-8.44150 - 3.07246i) q^{41} +(1.21459 - 6.88830i) q^{42} +(1.23938 + 7.02888i) q^{43} +(0.939693 - 0.342020i) q^{44} +(2.37784 - 4.11854i) q^{45} +(1.39509 + 2.41637i) q^{46} +(1.00493 + 0.843235i) q^{47} +(1.64888 + 1.38357i) q^{48} +(-1.77984 - 3.08278i) q^{49} +(1.74014 - 3.01401i) q^{50} +(-7.19575 + 2.61904i) q^{51} +(0.611760 + 3.46946i) q^{52} +(0.0301012 - 0.170712i) q^{53} +(-2.76480 - 1.00630i) q^{54} +(2.23079 - 1.87186i) q^{55} +3.24957 q^{56} +(9.14984 - 2.07580i) q^{57} +10.0479 q^{58} +(-7.10131 + 5.95870i) q^{59} +(5.89014 + 2.14384i) q^{60} +(-0.695487 + 3.94430i) q^{61} +(-0.625809 - 3.54914i) q^{62} +(4.98677 - 1.81504i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(5.12963 + 8.88478i) q^{65} +(1.64888 + 1.38357i) q^{66} +(6.94300 + 5.82587i) q^{67} +(-1.77879 - 3.08096i) q^{68} +(-3.00288 + 5.20114i) q^{69} +(8.89235 - 3.23655i) q^{70} +(-2.19794 - 12.4651i) q^{71} +(-0.283582 + 1.60827i) q^{72} +(-12.4814 - 4.54287i) q^{73} +(-2.56522 + 2.15247i) q^{74} +7.49115 q^{75} +(1.68789 + 4.01883i) q^{76} +3.24957 q^{77} +(-5.80898 + 4.87431i) q^{78} +(6.35375 + 2.31258i) q^{79} +(-0.505679 + 2.86785i) q^{80} +(-1.95047 - 11.0616i) q^{81} +(8.44150 - 3.07246i) q^{82} +(-1.23902 + 2.14604i) q^{83} +(3.49728 + 6.05747i) q^{84} +(-7.93623 - 6.65929i) q^{85} +(-5.46750 - 4.58778i) q^{86} +(10.8138 + 18.7301i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(7.46104 - 2.71560i) q^{89} +(0.825816 + 4.68343i) q^{90} +(-1.98796 + 11.2743i) q^{91} +(-2.62192 - 0.954300i) q^{92} +(5.94238 - 4.98625i) q^{93} -1.31184 q^{94} +(8.62160 + 9.31629i) q^{95} -2.15246 q^{96} +(3.91947 - 3.28883i) q^{97} +(3.34501 + 1.21748i) q^{98} +(-0.283582 + 1.60827i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{8}+O(q^{10}) \) 24 * q + 12 * q^8	\( 24 q + 12 q^{8} + 12 q^{11} - 3 q^{12} - 3 q^{13} + 3 q^{14} + 27 q^{15} - 6 q^{18} - 21 q^{19} - 18 q^{20} + 15 q^{21} + 9 q^{23} + 36 q^{25} - 21 q^{27} - 3 q^{28} - 9 q^{30} - 27 q^{31} - 9 q^{34} - 45 q^{35} + 18 q^{37} + 9 q^{38} + 36 q^{39} - 18 q^{41} + 39 q^{42} - 48 q^{43} + 36 q^{45} - 18 q^{46} - 9 q^{47} + 6 q^{49} + 3 q^{50} - 18 q^{51} - 3 q^{52} - 36 q^{53} - 45 q^{54} + 18 q^{58} + 9 q^{59} - 9 q^{60} + 15 q^{61} - 33 q^{62} + 87 q^{63} - 12 q^{64} - 36 q^{65} + 33 q^{67} + 9 q^{68} - 18 q^{69} + 45 q^{70} - 9 q^{71} - 3 q^{73} + 3 q^{74} + 42 q^{75} + 9 q^{76} + 12 q^{78} + 15 q^{79} - 108 q^{81} + 18 q^{82} + 36 q^{83} - 9 q^{84} - 99 q^{85} - 33 q^{86} + 63 q^{87} - 12 q^{88} - 27 q^{89} - 36 q^{90} - 21 q^{91} - 9 q^{92} - 21 q^{93} + 54 q^{94} + 18 q^{95} - 6 q^{96} + 45 q^{97} + 39 q^{98}+O(q^{100}) \) 24 * q + 12 * q^8 + 12 * q^11 - 3 * q^12 - 3 * q^13 + 3 * q^14 + 27 * q^15 - 6 * q^18 - 21 * q^19 - 18 * q^20 + 15 * q^21 + 9 * q^23 + 36 * q^25 - 21 * q^27 - 3 * q^28 - 9 * q^30 - 27 * q^31 - 9 * q^34 - 45 * q^35 + 18 * q^37 + 9 * q^38 + 36 * q^39 - 18 * q^41 + 39 * q^42 - 48 * q^43 + 36 * q^45 - 18 * q^46 - 9 * q^47 + 6 * q^49 + 3 * q^50 - 18 * q^51 - 3 * q^52 - 36 * q^53 - 45 * q^54 + 18 * q^58 + 9 * q^59 - 9 * q^60 + 15 * q^61 - 33 * q^62 + 87 * q^63 - 12 * q^64 - 36 * q^65 + 33 * q^67 + 9 * q^68 - 18 * q^69 + 45 * q^70 - 9 * q^71 - 3 * q^73 + 3 * q^74 + 42 * q^75 + 9 * q^76 + 12 * q^78 + 15 * q^79 - 108 * q^81 + 18 * q^82 + 36 * q^83 - 9 * q^84 - 99 * q^85 - 33 * q^86 + 63 * q^87 - 12 * q^88 - 27 * q^89 - 36 * q^90 - 21 * q^91 - 9 * q^92 - 21 * q^93 + 54 * q^94 + 18 * q^95 - 6 * q^96 + 45 * q^97 + 39 * q^98

Introduction

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