LMFDB - Embedded newform 287.2.h.d.78.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(57,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("287.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.h (of order $5$, 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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			78.6
Character	$\chi$	$=$	287.78
Dual form			287.2.h.d.92.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.178644 - 0.129793i) q^{2} +1.96598 q^{3} +(-0.602966 + 1.85574i) q^{4} +(0.495330 - 1.52447i) q^{5} +(0.351211 - 0.255170i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.269617 + 0.829796i) q^{8} +0.865075 q^{9} +O(q^{10})$	\(q+(0.178644 - 0.129793i) q^{2} +1.96598 q^{3} +(-0.602966 + 1.85574i) q^{4} +(0.495330 - 1.52447i) q^{5} +(0.351211 - 0.255170i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.269617 + 0.829796i) q^{8} +0.865075 q^{9} +(-0.109377 - 0.336628i) q^{10} +(1.10323 + 3.39538i) q^{11} +(-1.18542 + 3.64835i) q^{12} +(3.74181 - 2.71858i) q^{13} +0.220817 q^{14} +(0.973809 - 2.99708i) q^{15} +(-3.00131 - 2.18058i) q^{16} +(-1.09928 - 3.38324i) q^{17} +(0.154541 - 0.112280i) q^{18} +(0.931695 + 0.676916i) q^{19} +(2.53035 + 1.83841i) q^{20} +(1.59051 + 1.15557i) q^{21} +(0.637781 + 0.463375i) q^{22} +(-6.11239 + 4.44091i) q^{23} +(0.530062 + 1.63136i) q^{24} +(1.96643 + 1.42869i) q^{25} +(0.315601 - 0.971319i) q^{26} -4.19722 q^{27} +(-1.57859 + 1.14691i) q^{28} +(-0.755486 + 2.32515i) q^{29} +(-0.215033 - 0.661804i) q^{30} +(-2.63600 - 8.11277i) q^{31} -2.56419 q^{32} +(2.16892 + 6.67525i) q^{33} +(-0.635500 - 0.461718i) q^{34} +(1.29679 - 0.942174i) q^{35} +(-0.521611 + 1.60535i) q^{36} +(3.37179 - 10.3773i) q^{37} +0.254301 q^{38} +(7.35632 - 5.34468i) q^{39} +1.39855 q^{40} +(3.69015 - 5.23286i) q^{41} +0.434121 q^{42} +(-4.23145 + 3.07433i) q^{43} -6.96615 q^{44} +(0.428498 - 1.31878i) q^{45} +(-0.515546 + 1.58669i) q^{46} +(-2.41514 + 1.75470i) q^{47} +(-5.90050 - 4.28697i) q^{48} +(0.309017 + 0.951057i) q^{49} +0.536725 q^{50} +(-2.16116 - 6.65138i) q^{51} +(2.78880 + 8.58304i) q^{52} +(-2.46761 + 7.59452i) q^{53} +(-0.749810 + 0.544769i) q^{54} +5.72262 q^{55} +(-0.269617 + 0.829796i) q^{56} +(1.83169 + 1.33080i) q^{57} +(0.166824 + 0.513431i) q^{58} +(-5.76999 + 4.19215i) q^{59} +(4.97462 + 3.61427i) q^{60} +(-9.61371 - 6.98477i) q^{61} +(-1.52389 - 1.10717i) q^{62} +(0.699860 + 0.508478i) q^{63} +(5.54453 - 4.02834i) q^{64} +(-2.29097 - 7.05087i) q^{65} +(1.25386 + 0.910985i) q^{66} +(-0.0768576 + 0.236543i) q^{67} +6.94124 q^{68} +(-12.0168 + 8.73074i) q^{69} +(0.109377 - 0.336628i) q^{70} +(-2.30406 - 7.09116i) q^{71} +(0.233239 + 0.717836i) q^{72} +6.37980 q^{73} +(-0.744548 - 2.29148i) q^{74} +(3.86596 + 2.80878i) q^{75} +(-1.81796 + 1.32083i) q^{76} +(-1.10323 + 3.39538i) q^{77} +(0.620465 - 1.90959i) q^{78} +4.03319 q^{79} +(-4.81086 + 3.49529i) q^{80} -10.8469 q^{81} +(-0.0199632 - 1.41378i) q^{82} -10.7389 q^{83} +(-3.10347 + 2.25480i) q^{84} -5.70215 q^{85} +(-0.356900 + 1.09842i) q^{86} +(-1.48527 + 4.57119i) q^{87} +(-2.52002 + 1.83091i) q^{88} +(3.07461 + 2.23383i) q^{89} +(-0.0946194 - 0.291209i) q^{90} +4.62513 q^{91} +(-4.55561 - 14.0207i) q^{92} +(-5.18232 - 15.9495i) q^{93} +(-0.203704 + 0.626935i) q^{94} +(1.49344 - 1.08504i) q^{95} -5.04114 q^{96} +(-4.52491 + 13.9263i) q^{97} +(0.178644 + 0.129793i) q^{98} +(0.954373 + 2.93726i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 2 q^{2} - 10 q^{3} - 14 q^{4} - q^{5} + 9 q^{6} + 10 q^{7} + 3 q^{8} + 22 q^{9}+O(q^{10}) $ 40 * q - 2 * q^2 - 10 * q^3 - 14 * q^4 - q^5 + 9 * q^6 + 10 * q^7 + 3 * q^8 + 22 * q^9	\( 40 q - 2 q^{2} - 10 q^{3} - 14 q^{4} - q^{5} + 9 q^{6} + 10 q^{7} + 3 q^{8} + 22 q^{9} + 10 q^{10} + 5 q^{11} - 17 q^{12} + 3 q^{13} - 8 q^{14} + 23 q^{15} - 18 q^{16} + 11 q^{17} - 38 q^{18} - 2 q^{19} + 31 q^{20} + 4 q^{22} + 2 q^{23} + 10 q^{24} - 21 q^{25} - 7 q^{26} - 52 q^{27} + 14 q^{28} - 11 q^{29} - 18 q^{30} - 3 q^{31} + 44 q^{32} - 51 q^{33} + 29 q^{34} - 9 q^{35} + 35 q^{36} + 11 q^{37} + 52 q^{38} - 5 q^{39} - 32 q^{40} + 29 q^{41} + 6 q^{42} - 32 q^{43} - 92 q^{44} - 56 q^{45} + 26 q^{46} + 29 q^{47} + 11 q^{48} - 10 q^{49} - 24 q^{50} - 4 q^{51} + 3 q^{52} + 30 q^{53} + 58 q^{54} - 100 q^{55} - 3 q^{56} - 49 q^{57} + 25 q^{58} + 5 q^{59} - 91 q^{60} + 22 q^{61} - 34 q^{62} + 13 q^{63} - 9 q^{64} + 21 q^{65} + 29 q^{66} + 9 q^{67} - 20 q^{68} + 30 q^{69} - 10 q^{70} + 34 q^{71} - 37 q^{72} - 20 q^{73} - 58 q^{74} + 41 q^{75} - 37 q^{76} - 5 q^{77} + 63 q^{78} + 66 q^{79} + 22 q^{80} + 96 q^{81} + 76 q^{82} - 22 q^{83} - 38 q^{84} - 26 q^{85} + 3 q^{86} + 49 q^{87} - 19 q^{89} - q^{90} + 22 q^{91} - 2 q^{92} - 39 q^{93} + 66 q^{94} + 71 q^{95} - 302 q^{96} + 47 q^{97} - 2 q^{98} + 28 q^{99}+O(q^{100}) \) 40 * q - 2 * q^2 - 10 * q^3 - 14 * q^4 - q^5 + 9 * q^6 + 10 * q^7 + 3 * q^8 + 22 * q^9 + 10 * q^10 + 5 * q^11 - 17 * q^12 + 3 * q^13 - 8 * q^14 + 23 * q^15 - 18 * q^16 + 11 * q^17 - 38 * q^18 - 2 * q^19 + 31 * q^20 + 4 * q^22 + 2 * q^23 + 10 * q^24 - 21 * q^25 - 7 * q^26 - 52 * q^27 + 14 * q^28 - 11 * q^29 - 18 * q^30 - 3 * q^31 + 44 * q^32 - 51 * q^33 + 29 * q^34 - 9 * q^35 + 35 * q^36 + 11 * q^37 + 52 * q^38 - 5 * q^39 - 32 * q^40 + 29 * q^41 + 6 * q^42 - 32 * q^43 - 92 * q^44 - 56 * q^45 + 26 * q^46 + 29 * q^47 + 11 * q^48 - 10 * q^49 - 24 * q^50 - 4 * q^51 + 3 * q^52 + 30 * q^53 + 58 * q^54 - 100 * q^55 - 3 * q^56 - 49 * q^57 + 25 * q^58 + 5 * q^59 - 91 * q^60 + 22 * q^61 - 34 * q^62 + 13 * q^63 - 9 * q^64 + 21 * q^65 + 29 * q^66 + 9 * q^67 - 20 * q^68 + 30 * q^69 - 10 * q^70 + 34 * q^71 - 37 * q^72 - 20 * q^73 - 58 * q^74 + 41 * q^75 - 37 * q^76 - 5 * q^77 + 63 * q^78 + 66 * q^79 + 22 * q^80 + 96 * q^81 + 76 * q^82 - 22 * q^83 - 38 * q^84 - 26 * q^85 + 3 * q^86 + 49 * q^87 - 19 * q^89 - q^90 + 22 * q^91 - 2 * q^92 - 39 * q^93 + 66 * q^94 + 71 * q^95 - 302 * q^96 + 47 * q^97 - 2 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	0.178644	−	0.129793i	0.126321	−	0.0917773i	−0.522831	−	0.852436i	$-0.675124\pi$
$2$	0.178644	−	0.129793i	0.126321	−	0.0917773i	0.649152	+	0.760659i	$0.275124\pi$
$3$	1.96598			1.13506			0.567529	−	0.823353i	$-0.307899\pi$
$3$	1.96598			1.13506			0.567529	+	0.823353i	$0.307899\pi$
$4$	−0.602966	+	1.85574i	−0.301483	+	0.927870i
$5$	0.495330	−	1.52447i	0.221518	−	0.681764i	−0.777108	−	0.629367i	$-0.783314\pi$
$5$	0.495330	−	1.52447i	0.221518	−	0.681764i	0.998626	−	0.0523963i	$-0.0166859\pi$
$6$	0.351211	−	0.255170i	0.143381	−	0.104173i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$7$	0.809017	+	0.587785i	0.305780	+	0.222162i
$8$	0.269617	+	0.829796i	0.0953241	+	0.293377i
$9$	0.865075			0.288358
$10$	−0.109377	−	0.336628i	−0.0345881	−	0.106451i
$11$	1.10323	+	3.39538i	0.332635	+	1.02375i	0.967875	+	0.251431i	$0.0809011\pi$
$11$	1.10323	+	3.39538i	0.332635	+	1.02375i	−0.635240	+	0.772315i	$0.719099\pi$
$12$	−1.18542	+	3.64835i	−0.342201	+	1.05319i
$13$	3.74181	−	2.71858i	1.03779	−	0.753999i	0.0679378	−	0.997690i	$-0.478358\pi$
$13$	3.74181	−	2.71858i	1.03779	−	0.753999i	0.969853	+	0.243690i	$0.0783580\pi$
$14$	0.220817			0.0590157
$15$	0.973809	−	2.99708i	0.251436	−	0.773842i
$16$	−3.00131	−	2.18058i	−0.750326	−	0.545144i
$17$	−1.09928	−	3.38324i	−0.266615	−	0.820556i	−0.991317	−	0.131494i	$-0.958023\pi$
$17$	−1.09928	−	3.38324i	−0.266615	−	0.820556i	0.724702	−	0.689062i	$-0.241977\pi$
$18$	0.154541	−	0.112280i	0.0364256	−	0.0264647i
$19$	0.931695	+	0.676916i	0.213746	+	0.155295i	0.689507	−	0.724279i	$-0.257827\pi$
$19$	0.931695	+	0.676916i	0.213746	+	0.155295i	−0.475761	+	0.879574i	$0.657827\pi$
$20$	2.53035	+	1.83841i	0.565804	+	0.411081i
$21$	1.59051	+	1.15557i	0.347078	+	0.252167i
$22$	0.637781	+	0.463375i	0.135975	+	0.0987918i
$23$	−6.11239	+	4.44091i	−1.27452	+	0.925994i	−0.999373	−	0.0354071i	$-0.988727\pi$
$23$	−6.11239	+	4.44091i	−1.27452	+	0.925994i	−0.275149	+	0.961402i	$0.588727\pi$
$24$	0.530062	+	1.63136i	0.108198	+	0.333000i
$25$	1.96643	+	1.42869i	0.393286	+	0.285739i
$26$	0.315601	−	0.971319i	0.0618944	−	0.190491i
$27$	−4.19722			−0.807755
$28$	−1.57859	+	1.14691i	−0.298325	+	0.216746i
$29$	−0.755486	+	2.32515i	−0.140290	+	0.431769i	−0.996375	−	0.0850660i	$-0.972890\pi$
$29$	−0.755486	+	2.32515i	−0.140290	+	0.431769i	0.856085	+	0.516835i	$0.172890\pi$
$30$	−0.215033	−	0.661804i	−0.0392595	−	0.120828i
$31$	−2.63600	−	8.11277i	−0.473439	−	1.45710i	−0.848051	−	0.529915i	$-0.822224\pi$
$31$	−2.63600	−	8.11277i	−0.473439	−	1.45710i	0.374612	−	0.927182i	$-0.377776\pi$
$32$	−2.56419			−0.453289
$33$	2.16892	+	6.67525i	0.377560	+	1.16201i
$34$	−0.635500	−	0.461718i	−0.108987	−	0.0791840i
$35$	1.29679	−	0.942174i	0.219198	−	0.159257i
$36$	−0.521611	+	1.60535i	−0.0869351	+	0.267559i
$37$	3.37179	−	10.3773i	0.554319	−	1.70602i	−0.143415	−	0.989663i	$-0.545808\pi$
$37$	3.37179	−	10.3773i	0.554319	−	1.70602i	0.697734	−	0.716357i	$-0.254192\pi$
$38$	0.254301			0.0412531
$39$	7.35632	−	5.34468i	1.17795	−	0.855833i
$40$	1.39855			0.221130
$41$	3.69015	−	5.23286i	0.576304	−	0.817235i
$41$	3.69015	−	5.23286i	0.576304	−	0.817235i
$42$	0.434121			0.0669863
$43$	−4.23145	+	3.07433i	−0.645291	+	0.468831i	−0.861664	−	0.507480i	$-0.830577\pi$
$43$	−4.23145	+	3.07433i	−0.645291	+	0.468831i	0.216373	+	0.976311i	$0.430577\pi$
$44$	−6.96615			−1.05019
$45$	0.428498	−	1.31878i	0.0638767	−	0.196592i
$46$	−0.515546	+	1.58669i	−0.0760132	+	0.233944i
$47$	−2.41514	+	1.75470i	−0.352284	+	0.255950i	−0.749827	−	0.661634i	$-0.769863\pi$
$47$	−2.41514	+	1.75470i	−0.352284	+	0.255950i	0.397542	+	0.917584i	$0.369863\pi$
$48$	−5.90050	−	4.28697i	−0.851664	−	0.618770i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	0.536725			0.0759044
$51$	−2.16116	−	6.65138i	−0.302623	−	0.931379i
$52$	2.78880	+	8.58304i	0.386737	+	1.19025i
$53$	−2.46761	+	7.59452i	−0.338952	+	1.04319i	0.625790	+	0.779991i	$0.284777\pi$
$53$	−2.46761	+	7.59452i	−0.338952	+	1.04319i	−0.964742	+	0.263196i	$0.915223\pi$
$54$	−0.749810	+	0.544769i	−0.102036	+	0.0741336i
$55$	5.72262			0.771637
$56$	−0.269617	+	0.829796i	−0.0360291	+	0.110886i
$57$	1.83169	+	1.33080i	0.242614	+	0.176269i
$58$	0.166824	+	0.513431i	0.0219050	+	0.0674168i
$59$	−5.76999	+	4.19215i	−0.751189	+	0.545771i	−0.896195	−	0.443660i	$-0.853680\pi$
$59$	−5.76999	+	4.19215i	−0.751189	+	0.545771i	0.145006	+	0.989431i	$0.453680\pi$
$60$	4.97462	+	3.61427i	0.642221	+	0.466601i
$61$	−9.61371	−	6.98477i	−1.23091	−	0.894308i	−0.233951	−	0.972248i	$-0.575165\pi$
$61$	−9.61371	−	6.98477i	−1.23091	−	0.894308i	−0.996958	+	0.0779408i	$0.975165\pi$
$62$	−1.52389	−	1.10717i	−0.193534	−	0.140610i
$63$	0.699860	+	0.508478i	0.0881741	+	0.0640622i
$64$	5.54453	−	4.02834i	0.693067	−	0.503542i
$65$	−2.29097	−	7.05087i	−0.284159	−	0.874553i
$66$	1.25386	+	0.910985i	0.154340	+	0.112135i
$67$	−0.0768576	+	0.236543i	−0.00938964	+	0.0288984i	−0.955642	−	0.294532i	$-0.904836\pi$
$67$	−0.0768576	+	0.236543i	−0.00938964	+	0.0288984i	0.946252	+	0.323431i	$0.104836\pi$
$68$	6.94124			0.841749
$69$	−12.0168	+	8.73074i	−1.44666	+	1.05106i
$70$	0.109377	−	0.336628i	0.0130731	−	0.0402348i
$71$	−2.30406	−	7.09116i	−0.273441	−	0.841566i	−0.989628	−	0.143656i	$-0.954114\pi$
$71$	−2.30406	−	7.09116i	−0.273441	−	0.841566i	0.716186	−	0.697909i	$-0.245886\pi$
$72$	0.233239	+	0.717836i	0.0274875	+	0.0845977i
$73$	6.37980			0.746699			0.373350	−	0.927691i	$-0.378209\pi$
$73$	6.37980			0.746699			0.373350	+	0.927691i	$0.378209\pi$
$74$	−0.744548	−	2.29148i	−0.0865519	−	0.266379i
$75$	3.86596	+	2.80878i	0.446402	+	0.324330i
$76$	−1.81796	+	1.32083i	−0.208534	+	0.151509i
$77$	−1.10323	+	3.39538i	−0.125724	+	0.386939i
$78$	0.620465	−	1.90959i	0.0702538	−	0.216219i
$79$	4.03319			0.453770			0.226885	−	0.973922i	$-0.427146\pi$
$79$	4.03319			0.453770			0.226885	+	0.973922i	$0.427146\pi$
$80$	−4.81086	+	3.49529i	−0.537871	+	0.390786i
$81$	−10.8469			−1.20521
$82$	−0.0199632	−	1.41378i	−0.00220457	−	0.156125i
$83$	−10.7389			−1.17875			−0.589375	−	0.807860i	$-0.700626\pi$
$83$	−10.7389			−1.17875			−0.589375	+	0.807860i	$0.700626\pi$
$84$	−3.10347	+	2.25480i	−0.338616	+	0.246019i
$85$	−5.70215			−0.618485
$86$	−0.356900	+	1.09842i	−0.0384855	+	0.118446i
$87$	−1.48527	+	4.57119i	−0.159238	+	0.490083i
$88$	−2.52002	+	1.83091i	−0.268636	+	0.195175i
$89$	3.07461	+	2.23383i	0.325908	+	0.236786i	0.738692	−	0.674043i	$-0.235444\pi$
$89$	3.07461	+	2.23383i	0.325908	+	0.236786i	−0.412784	+	0.910829i	$0.635444\pi$
$90$	−0.0946194	−	0.291209i	−0.00997376	−	0.0306961i
$91$	4.62513			0.484845
$92$	−4.55561	−	14.0207i	−0.474955	−	1.46176i
$93$	−5.18232	−	15.9495i	−0.537381	−	1.65389i
$94$	−0.203704	+	0.626935i	−0.0210104	+	0.0646635i
$95$	1.49344	−	1.08504i	0.153223	−	0.111323i
$96$	−5.04114			−0.514509
$97$	−4.52491	+	13.9263i	−0.459435	+	1.41400i	0.406413	+	0.913690i	$0.366780\pi$
$97$	−4.52491	+	13.9263i	−0.459435	+	1.41400i	−0.865848	+	0.500307i	$0.833220\pi$
$98$	0.178644	+	0.129793i	0.0180458	+	0.0131110i
$99$	0.954373	+	2.93726i	0.0959181	+	0.295205i
$100$	−3.83697	+	2.78772i	−0.383697	+	0.278772i
$101$	11.3459	+	8.24325i	1.12896	+	0.820234i	0.985542	−	0.169429i	$-0.0541922\pi$
$101$	11.3459	+	8.24325i	1.12896	+	0.820234i	0.143413	+	0.989663i	$0.454192\pi$
$102$	−1.24938	−	0.907728i	−0.123707	−	0.0898785i
$103$	8.09359	+	5.88034i	0.797485	+	0.579407i	0.910175	−	0.414223i	$-0.135947\pi$
$103$	8.09359	+	5.88034i	0.797485	+	0.579407i	−0.112690	+	0.993630i	$0.535947\pi$
$104$	3.26473	+	2.37196i	0.320133	+	0.232590i
$105$	2.54947	−	1.85230i	0.248802	−	0.180765i
$106$	0.544889	+	1.67700i	0.0529243	+	0.162884i
$107$	−1.66295	−	1.20821i	−0.160764	−	0.116802i	0.504495	−	0.863415i	$-0.331679\pi$
$107$	−1.66295	−	1.20821i	−0.160764	−	0.116802i	−0.665259	+	0.746613i	$0.731679\pi$
$108$	2.53078	−	7.78895i	0.243525	−	0.749492i
$109$	4.54143			0.434990			0.217495	−	0.976061i	$-0.430211\pi$
$109$	4.54143			0.434990			0.217495	+	0.976061i	$0.430211\pi$
$110$	1.02231	−	0.742754i	0.0974737	−	0.0708188i
$111$	6.62887	−	20.4016i	0.629185	−	1.93643i
$112$	−1.14640	−	3.52825i	−0.108324	−	0.333388i
$113$	−4.00664	−	12.3312i	−0.376913	−	1.16002i	−0.942179	−	0.335111i	$-0.891226\pi$
$113$	−4.00664	−	12.3312i	−0.376913	−	1.16002i	0.565265	−	0.824909i	$-0.308774\pi$
$114$	0.499950			0.0468246
$115$	3.74239	+	11.5179i	0.348979	+	1.07405i
$116$	−3.85933	−	2.80397i	−0.358330	−	0.260342i
$117$	3.23694	−	2.35178i	0.299256	−	0.217422i
$118$	−0.486667	+	1.49781i	−0.0448013	+	0.137884i
$119$	1.09928	−	3.38324i	0.100771	−	0.310141i
$120$	2.74952			0.250996
$121$	−1.41231	+	1.02610i	−0.128392	+	0.0932821i
$122$	−2.62401			−0.237566
$123$	7.25475	−	10.2877i	0.654139	−	0.927610i
$124$	16.6446			1.49473
$125$	9.63599	−	7.00096i	0.861869	−	0.626185i
$126$	0.191023			0.0170177
$127$	−5.37230	+	16.5342i	−0.476715	+	1.46718i	0.366917	+	0.930254i	$0.380413\pi$
$127$	−5.37230	+	16.5342i	−0.476715	+	1.46718i	−0.843631	+	0.536923i	$0.819587\pi$
$128$	2.05241	−	6.31666i	0.181409	−	0.558319i
$129$	−8.31895	+	6.04407i	−0.732443	+	0.532151i
$130$	−1.32442	−	0.962248i	−0.116159	−	0.0843947i
$131$	−0.598030	−	1.84055i	−0.0522501	−	0.160809i	0.921527	−	0.388315i	$-0.126943\pi$
$131$	−0.598030	−	1.84055i	−0.0522501	−	0.160809i	−0.973777	+	0.227506i	$0.926943\pi$
$132$	−13.6953			−1.19202
$133$	0.355876	+	1.09527i	0.0308583	+	0.0949722i
$134$	0.0169714	+	0.0522327i	0.00146611	+	0.00451222i
$135$	−2.07901	+	6.39853i	−0.178933	+	0.550698i
$136$	2.51101	−	1.82436i	0.215318	−	0.156437i
$137$	13.9009			1.18764			0.593819	−	0.804599i	$-0.297619\pi$
$137$	13.9009			1.18764			0.593819	+	0.804599i	$0.297619\pi$
$138$	−1.01355	+	3.11940i	−0.0862794	+	0.265541i
$139$	8.92846	+	6.48691i	0.757302	+	0.550212i	0.898082	−	0.439829i	$-0.144961\pi$
$139$	8.92846	+	6.48691i	0.757302	+	0.550212i	−0.140780	+	0.990041i	$0.544961\pi$
$140$	0.966508	+	2.97461i	0.0816849	+	0.251400i
$141$	−4.74812	+	3.44971i	−0.399864	+	0.290518i
$142$	−1.33199	−	0.967746i	−0.111778	−	0.0812114i
$143$	13.3587	+	9.70565i	1.11711	+	0.811627i
$144$	−2.59635	−	1.88636i	−0.216363	−	0.157197i
$145$	3.17040	+	2.30343i	0.263287	+	0.191290i
$146$	1.13972	−	0.828052i	0.0943235	−	0.0685300i
$147$	0.607521	+	1.86976i	0.0501075	+	0.154215i
$148$	17.2245	+	12.5143i	1.41585	+	1.02867i
$149$	2.57716	−	7.93168i	0.211129	−	0.649788i	−0.788277	−	0.615321i	$-0.789027\pi$
$149$	2.57716	−	7.93168i	0.211129	−	0.649788i	0.999406	−	0.0344674i	$-0.0109735\pi$
$150$	1.05519			0.0861560
$151$	11.6849	−	8.48959i	0.950905	−	0.690873i	−0.000115780	−	1.00000i	$-0.500037\pi$
$151$	11.6849	−	8.48959i	0.950905	−	0.690873i	0.951021	+	0.309127i	$0.100037\pi$
$152$	−0.310501	+	0.955625i	−0.0251850	+	0.0775114i
$153$	−0.950960	−	2.92675i	−0.0768806	−	0.236614i
$154$	0.243611	+	0.749756i	0.0196307	+	0.0604171i
$155$	−13.6734			−1.09827
$156$	5.48272	+	16.8741i	0.438969	+	1.35101i
$157$	14.9037	+	10.8281i	1.18944	+	0.864180i	0.993205	−	0.116377i	$-0.0371281\pi$
$157$	14.9037	+	10.8281i	1.18944	+	0.864180i	0.196236	+	0.980557i	$0.437128\pi$
$158$	0.720507	−	0.523479i	0.0573205	−	0.0416458i
$159$	−4.85127	+	14.9307i	−0.384731	+	1.18408i
$160$	−1.27012	+	3.90903i	−0.100412	+	0.309036i
$161$	−7.55533			−0.595444
$162$	−1.93773	+	1.40784i	−0.152243	+	0.110611i
$163$	10.3969			0.814347			0.407173	−	0.913351i	$-0.366514\pi$
$163$	10.3969			0.814347			0.407173	+	0.913351i	$0.366514\pi$
$164$	7.48579	+	10.0032i	0.584542	+	0.781118i
$165$	11.2505			0.875854
$166$	−1.91845	+	1.39383i	−0.148900	+	0.108182i
$167$	−5.70631			−0.441567			−0.220784	−	0.975323i	$-0.570861\pi$
$167$	−5.70631			−0.441567			−0.220784	+	0.975323i	$0.570861\pi$
$168$	−0.530062	+	1.63136i	−0.0408952	+	0.125862i
$169$	2.59322	−	7.98110i	0.199478	−	0.613931i
$170$	−1.01866	+	0.740098i	−0.0781275	+	0.0567629i
$171$	0.805986	+	0.585583i	0.0616353	+	0.0447806i
$172$	−3.15373	−	9.70620i	−0.240470	−	0.740090i
$173$	−0.774003			−0.0588464			−0.0294232	−	0.999567i	$-0.509367\pi$
$173$	−0.774003			−0.0588464			−0.0294232	+	0.999567i	$0.509367\pi$
$174$	0.327972	+	1.00939i	0.0248635	+	0.0765220i
$175$	0.751109	+	2.31168i	0.0567785	+	0.174746i
$176$	4.09277	−	12.5962i	0.308504	−	0.949477i
$177$	−11.3437	+	8.24167i	−0.852644	+	0.619482i
$178$	0.839197			0.0629004
$179$	−5.62710	+	17.3184i	−0.420589	+	1.29444i	0.486565	+	0.873644i	$0.338250\pi$
$179$	−5.62710	+	17.3184i	−0.420589	+	1.29444i	−0.907155	+	0.420797i	$0.861750\pi$
$180$	2.18894	+	1.59036i	0.163154	+	0.118538i
$181$	−3.46262	−	10.6569i	−0.257375	−	0.792118i	−0.993353	−	0.115112i	$-0.963277\pi$
$181$	−3.46262	−	10.6569i	−0.257375	−	0.792118i	0.735978	−	0.677006i	$-0.236723\pi$
$182$	0.826253	−	0.600308i	0.0612460	−	0.0444978i
$183$	−18.9003	−	13.7319i	−1.39715	−	1.01509i
$184$	−5.33306	−	3.87469i	−0.393158	−	0.285646i
$185$	−14.1497	−	10.2804i	−1.04031	−	0.755830i
$186$	−2.99593	−	2.17667i	−0.219672	−	0.159601i
$187$	10.2746	−	7.46495i	0.751355	−	0.545891i
$188$	−1.80002	−	5.53990i	−0.131280	−	0.404039i
$189$	−3.39562	−	2.46706i	−0.246995	−	0.179452i
$190$	0.125963	−	0.387674i	0.00913831	−	0.0281248i
$191$	21.3851			1.54737			0.773686	−	0.633570i	$-0.218411\pi$
$191$	21.3851			1.54737			0.773686	+	0.633570i	$0.218411\pi$
$192$	10.9004	−	7.91963i	0.786671	−	0.571550i
$193$	−2.27053	+	6.98797i	−0.163436	+	0.503005i	−0.998918	−	0.0465138i	$-0.985189\pi$
$193$	−2.27053	+	6.98797i	−0.163436	+	0.503005i	0.835481	+	0.549519i	$0.185189\pi$
$194$	0.999176	+	3.07515i	0.0717367	+	0.220783i
$195$	−4.50399	−	13.8619i	−0.322538	−	0.992669i
$196$	−1.95124			−0.139374
$197$	4.78044	+	14.7127i	0.340592	+	1.04823i	0.963901	+	0.266259i	$0.0857877\pi$
$197$	4.78044	+	14.7127i	0.340592	+	1.04823i	−0.623309	+	0.781975i	$0.714212\pi$
$198$	0.551728	+	0.400854i	0.0392096	+	0.0284874i
$199$	−0.801940	+	0.582643i	−0.0568480	+	0.0413025i	−0.615846	−	0.787866i	$-0.711186\pi$
$199$	−0.801940	+	0.582643i	−0.0568480	+	0.0413025i	0.558998	+	0.829169i	$0.311186\pi$
$200$	−0.655342	+	2.01694i	−0.0463397	+	0.142619i
$201$	−0.151100	+	0.465039i	−0.0106578	+	0.0328013i
$202$	3.09679			0.217889
$203$	−1.97789	+	1.43702i	−0.138820	+	0.100859i
$204$	13.6463			0.955434
$205$	−6.14950	−	8.21751i	−0.429499	−	0.573936i
$206$	2.20910			0.153915
$207$	−5.28768	+	3.84172i	−0.367519	+	0.267018i
$208$	−17.1584			−1.18972
$209$	−1.27052	+	3.91025i	−0.0878835	+	0.270478i
$210$	0.215033	−	0.661804i	0.0148387	−	0.0456688i
$211$	−6.53244	+	4.74610i	−0.449712	+	0.326735i	−0.789482	−	0.613774i	$-0.789651\pi$
$211$	−6.53244	+	4.74610i	−0.449712	+	0.326735i	0.339770	+	0.940508i	$0.389651\pi$
$212$	−12.6056	−	9.15848i	−0.865754	−	0.629007i
$213$	−4.52973	−	13.9411i	−0.310372	−	0.955226i
$214$	−0.453893			−0.0310275
$215$	2.59076	+	7.97354i	0.176688	+	0.543791i
$216$	−1.13164	−	3.48284i	−0.0769985	−	0.236977i
$217$	2.63600	−	8.11277i	0.178943	−	0.550731i
$218$	0.811301	−	0.589445i	0.0549483	−	0.0399222i
$219$	12.5426			0.847547
$220$	−3.45054	+	10.6197i	−0.232636	+	0.715979i
$221$	−13.3109	−	9.67095i	−0.895389	−	0.650538i
$222$	−1.46377	−	4.50501i	−0.0982415	−	0.302356i
$223$	6.73441	−	4.89283i	0.450969	−	0.327648i	−0.339009	−	0.940783i	$-0.610092\pi$
$223$	6.73441	−	4.89283i	0.450969	−	0.327648i	0.789978	+	0.613135i	$0.210092\pi$
$224$	−2.07447	−	1.50719i	−0.138606	−	0.100704i
$225$	1.70111	+	1.23593i	0.113407	+	0.0823951i
$226$	−2.31626	−	1.68286i	−0.154076	−	0.111942i
$227$	−8.73260	−	6.34461i	−0.579603	−	0.421106i	0.258978	−	0.965883i	$-0.416614\pi$
$227$	−8.73260	−	6.34461i	−0.579603	−	0.421106i	−0.838581	+	0.544777i	$0.816614\pi$
$228$	−3.57407	+	2.59672i	−0.236699	+	0.171972i
$229$	−3.78937	−	11.6625i	−0.250408	−	0.770678i	−0.994700	−	0.102823i	$-0.967213\pi$
$229$	−3.78937	−	11.6625i	−0.250408	−	0.770678i	0.744291	−	0.667855i	$-0.232787\pi$
$230$	2.16349	+	1.57187i	0.142657	+	0.103646i
$231$	−2.16892	+	6.67525i	−0.142704	+	0.439199i
$232$	−2.13309			−0.140044
$233$	−16.7213	+	12.1487i	−1.09545	+	0.795889i	−0.980311	−	0.197461i	$-0.936730\pi$
$233$	−16.7213	+	12.1487i	−1.09545	+	0.795889i	−0.115136	+	0.993350i	$0.536730\pi$
$234$	0.273018	−	0.840264i	0.0178478	−	0.0549297i
$235$	1.47870	+	4.55097i	0.0964597	+	0.296872i
$236$	−4.30042	−	13.2353i	−0.279933	−	0.861546i
$237$	7.92917			0.515055
$238$	−0.242739	−	0.747075i	−0.0157345	−	0.0484257i
$239$	11.0253	+	8.01034i	0.713166	+	0.518146i	0.884194	−	0.467121i	$-0.154709\pi$
$239$	11.0253	+	8.01034i	0.713166	+	0.518146i	−0.171027	+	0.985266i	$0.554709\pi$
$240$	−9.45805	+	6.87168i	−0.610515	+	0.443565i
$241$	−6.68802	+	20.5836i	−0.430813	+	1.32591i	0.466503	+	0.884519i	$0.345514\pi$
$241$	−6.68802	+	20.5836i	−0.430813	+	1.32591i	−0.897317	+	0.441387i	$0.854486\pi$
$242$	−0.119121	+	0.366615i	−0.00765736	+	0.0235669i
$243$	−8.73306			−0.560226
$244$	18.7586	−	13.6290i	1.20090	−	0.872504i
$245$	1.60292			0.102407
$246$	−0.0392472	−	2.77945i	−0.00250231	−	0.177211i
$247$	5.32648			0.338916
$248$	6.02124	−	4.37468i	0.382349	−	0.277793i
$249$	−21.1125			−1.33795
$250$	0.812742	−	2.50136i	0.0514023	−	0.158200i
$251$	0.0748315	−	0.230308i	0.00472332	−	0.0145369i	−0.948667	−	0.316276i	$-0.897567\pi$
$251$	0.0748315	−	0.230308i	0.00472332	−	0.0145369i	0.953390	+	0.301740i	$0.0975673\pi$
$252$	−1.36560	+	0.992163i	−0.0860244	+	0.0625004i
$253$	−21.8219	−	15.8546i	−1.37193	−	0.996768i
$254$	1.18629	+	3.65104i	0.0744347	+	0.229086i
$255$	−11.2103			−0.702017
$256$	3.78244	+	11.6412i	0.236403	+	0.727572i
$257$	−3.54894	−	10.9225i	−0.221377	−	0.681328i	−0.998639	−	0.0521514i	$-0.983392\pi$
$257$	−3.54894	−	10.9225i	−0.221377	−	0.681328i	0.777262	−	0.629177i	$-0.216608\pi$
$258$	−0.701657	+	2.15948i	−0.0436833	+	0.134443i
$259$	8.82747	−	6.41353i	0.548512	−	0.398517i
$260$	14.4660			0.897141
$261$	−0.653552	+	2.01143i	−0.0404538	+	0.124504i
$262$	−0.345724	−	0.251183i	−0.0213589	−	0.0155182i
$263$	6.15201	+	18.9339i	0.379349	+	1.16752i	0.940497	+	0.339801i	$0.110360\pi$
$263$	6.15201	+	18.9339i	0.379349	+	1.16752i	−0.561148	+	0.827716i	$0.689640\pi$
$264$	−4.95432	+	3.59952i	−0.304917	+	0.221535i
$265$	10.3553	+	7.52359i	0.636123	+	0.462171i
$266$	0.205734	+	0.149474i	0.0126143	+	0.00916486i
$267$	6.04461	+	4.39167i	0.369924	+	0.268766i
$268$	−0.392620	−	0.285255i	−0.0239831	−	0.0174247i
$269$	−2.03048	+	1.47523i	−0.123801	+	0.0899463i	−0.647962	−	0.761672i	$-0.724379\pi$
$269$	−2.03048	+	1.47523i	−0.123801	+	0.0899463i	0.524162	+	0.851619i	$0.324379\pi$
$270$	0.459080	+	1.41290i	0.0279387	+	0.0859865i
$271$	−8.24233	−	5.98840i	−0.500686	−	0.363770i	0.308593	−	0.951194i	$-0.400142\pi$
$271$	−8.24233	−	5.98840i	−0.500686	−	0.363770i	−0.809279	+	0.587425i	$0.800142\pi$
$272$	−4.07813	+	12.5512i	−0.247273	+	0.761028i
$273$	9.09291			0.550328
$274$	2.48333	−	1.80424i	0.150023	−	0.108998i
$275$	−2.68154	+	8.25294i	−0.161703	+	0.497671i
$276$	−8.95624	−	27.5645i	−0.539102	−	1.65919i
$277$	−9.12220	−	28.0753i	−0.548100	−	1.68688i	−0.713503	−	0.700653i	$-0.752892\pi$
$277$	−9.12220	−	28.0753i	−0.548100	−	1.68688i	0.165402	−	0.986226i	$-0.447108\pi$
$278$	2.43697			0.146160
$279$	−2.28034	−	7.01815i	−0.136520	−	0.420166i
$280$	1.13145	+	0.822046i	0.0676171	+	0.0491267i
$281$	−0.508748	+	0.369627i	−0.0303494	+	0.0220501i	−0.602857	−	0.797850i	$-0.705971\pi$
$281$	−0.508748	+	0.369627i	−0.0303494	+	0.0220501i	0.572507	+	0.819900i	$0.305971\pi$
$282$	−0.400477	+	1.23254i	−0.0238481	+	0.0733968i
$283$	0.584944	−	1.80027i	0.0347713	−	0.107015i	−0.932164	−	0.362035i	$-0.882082\pi$
$283$	0.584944	−	1.80027i	0.0347713	−	0.107015i	0.966936	+	0.255020i	$0.0820820\pi$
$284$	14.5486			0.863301
$285$	2.93606	−	2.13317i	0.173917	−	0.126358i
$286$	3.64618			0.215603
$287$	6.06119	−	2.06446i	0.357781	−	0.121861i
$288$	−2.21821			−0.130710
$289$	3.51540	−	2.55409i	0.206788	−	0.150241i
$290$	0.865343			0.0508147
$291$	−8.89589	+	27.3787i	−0.521486	+	1.60497i
$292$	−3.84680	+	11.8392i	−0.225117	+	0.692839i
$293$	−20.8022	+	15.1137i	−1.21528	+	0.882950i	−0.995699	−	0.0926453i	$-0.970468\pi$
$293$	−20.8022	+	15.1137i	−1.21528	+	0.882950i	−0.219577	+	0.975595i	$0.570468\pi$
$294$	0.351211	+	0.255170i	0.0204831	+	0.0148818i
$295$	3.53275	+	10.8727i	0.205685	+	0.633032i
$296$	9.52015			0.553347
$297$	−4.63048	−	14.2512i	−0.268688	−	0.826936i
$298$	−0.569079	−	1.75145i	−0.0329659	−	0.101459i
$299$	−10.7984	+	33.2341i	−0.624488	+	1.92198i
$300$	−7.54341	+	5.48061i	−0.435519	+	0.316423i
$301$	−5.23037			−0.301473
$302$	0.985558	−	3.03323i	0.0567125	−	0.174543i
$303$	22.3057	+	16.2061i	1.28143	+	0.931014i
$304$	−1.32023	−	4.06326i	−0.0757206	−	0.233044i
$305$	−15.4100	+	11.1960i	−0.882376	+	0.641083i
$306$	−0.549755	−	0.399420i	−0.0314274	−	0.0228334i
$307$	8.16780	+	5.93425i	0.466161	+	0.338686i	0.795943	−	0.605371i	$-0.206975\pi$
$307$	8.16780	+	5.93425i	0.466161	+	0.338686i	−0.329782	+	0.944057i	$0.606975\pi$
$308$	−5.63573	−	4.09460i	−0.321126	−	0.233311i
$309$	15.9118	+	11.5606i	0.905193	+	0.657661i
$310$	−2.44267	+	1.77470i	−0.138734	+	0.100796i
$311$	−6.40932	−	19.7259i	−0.363439	−	1.11855i	−0.950953	−	0.309337i	$-0.899893\pi$
$311$	−6.40932	−	19.7259i	−0.363439	−	1.11855i	0.587513	−	0.809214i	$-0.300107\pi$
$312$	6.41838	+	4.66323i	0.363369	+	0.264003i
$313$	1.53000	−	4.70886i	0.0864808	−	0.266161i	−0.898459	−	0.439057i	$-0.855313\pi$
$313$	1.53000	−	4.70886i	0.0864808	−	0.266161i	0.984940	+	0.172896i	$0.0553126\pi$
$314$	4.06787			0.229563
$315$	1.12182	−	0.815051i	0.0632075	−	0.0459229i
$316$	−2.43188	+	7.48456i	−0.136804	+	0.421039i
$317$	−3.16842	−	9.75138i	−0.177956	−	0.547692i	0.821800	−	0.569776i	$-0.192970\pi$
$317$	−3.16842	−	9.75138i	−0.177956	−	0.547692i	−0.999756	+	0.0220836i	$0.992970\pi$
$318$	1.07124	+	3.29694i	0.0600722	+	0.184883i
$319$	−8.72823			−0.488687
$320$	−3.39471	−	10.4478i	−0.189770	−	0.584052i
$321$	−3.26933	−	2.37531i	−0.182476	−	0.132577i
$322$	−1.34972	+	0.980627i	−0.0752168	+	0.0546482i
$323$	1.26597	−	3.89627i	0.0704407	−	0.216794i
$324$	6.54030	−	20.1290i	0.363350	−	1.11828i
$325$	11.2420			0.623595
$326$	1.85734	−	1.34944i	0.102869	−	0.0747386i
$327$	8.92836			0.493739
$328$	5.33713	+	1.65120i	0.294694	+	0.0911723i
$329$	−2.98528			−0.164584
$330$	2.00985	−	1.46024i	0.110638	−	0.0803835i
$331$	−17.4184			−0.957399			−0.478700	−	0.877979i	$-0.658892\pi$
$331$	−17.4184			−0.957399			−0.478700	+	0.877979i	$0.658892\pi$
$332$	6.47521	−	19.9286i	0.355373	−	1.09373i
$333$	2.91685	−	8.97715i	0.159843	−	0.491945i
$334$	−1.01940	+	0.740637i	−0.0557791	+	0.0405259i
$335$	0.322533	+	0.234334i	0.0176219	+	0.0128030i
$336$	−2.25379	−	6.93646i	−0.122954	−	0.378415i
$337$	−28.6661			−1.56154			−0.780770	−	0.624819i	$-0.785173\pi$
$337$	−28.6661			−1.56154			−0.780770	+	0.624819i	$0.785173\pi$
$338$	−0.572625	−	1.76236i	−0.0311467	−	0.0958597i
$339$	−7.87698	−	24.2429i	−0.427819	−	1.31669i
$340$	3.43821	−	10.5817i	0.186463	−	0.573874i
$341$	24.6378	−	17.9004i	1.33421	−	0.969363i
$342$	0.219989			0.0118957
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	−3.69194	−	2.68235i	−0.199056	−	0.144623i
$345$	7.35745	+	22.6439i	0.396112	+	1.21911i
$346$	−0.138271	+	0.100460i	−0.00743351	+	0.00540076i
$347$	−17.0973	−	12.4219i	−0.917833	−	0.666845i	0.0251506	−	0.999684i	$-0.491993\pi$
$347$	−17.0973	−	12.4219i	−0.917833	−	0.666845i	−0.942984	+	0.332839i	$0.891993\pi$
$348$	−7.58737	−	5.51255i	−0.406726	−	0.295504i
$349$	9.64039	+	7.00416i	0.516039	+	0.374924i	0.815109	−	0.579307i	$-0.196677\pi$
$349$	9.64039	+	7.00416i	0.516039	+	0.374924i	−0.299071	+	0.954231i	$0.596677\pi$
$350$	0.434220	+	0.315479i	0.0232100	+	0.0168631i
$351$	−15.7052	+	11.4105i	−0.838281	+	0.609047i
$352$	−2.82888	−	8.70639i	−0.150780	−	0.464052i
$353$	−12.9206	−	9.38735i	−0.687693	−	0.499638i	0.188208	−	0.982129i	$-0.439732\pi$
$353$	−12.9206	−	9.38735i	−0.687693	−	0.499638i	−0.875901	+	0.482491i	$0.839732\pi$
$354$	−0.956777	+	2.94466i	−0.0508521	+	0.156507i
$355$	−11.9515			−0.634321
$356$	−5.99930	+	4.35874i	−0.317962	+	0.231013i
$357$	2.16116	−	6.65138i	0.114381	−	0.352028i
$358$	1.24256	+	3.82420i	0.0656712	+	0.202115i
$359$	6.46369	+	19.8932i	0.341140	+	1.04992i	0.963618	+	0.267284i	$0.0861263\pi$
$359$	6.46369	+	19.8932i	0.341140	+	1.04992i	−0.622477	+	0.782638i	$0.713874\pi$
$360$	1.20985			0.0637647
$361$	−5.46148	−	16.8087i	−0.287446	−	0.884669i
$362$	−2.00176	−	1.45436i	−0.105210	−	0.0764397i
$363$	−2.77657	+	2.01730i	−0.145732	+	0.105881i
$364$	−2.78880	+	8.58304i	−0.146173	+	0.449873i
$365$	3.16011	−	9.72581i	0.165408	−	0.509072i
$366$	−5.15874			−0.269652
$367$	4.66873	−	3.39203i	0.243706	−	0.177063i	−0.459227	−	0.888319i	$-0.651874\pi$
$367$	4.66873	−	3.39203i	0.243706	−	0.177063i	0.702933	+	0.711256i	$0.251874\pi$
$368$	28.0289			1.46111
$369$	3.19225	−	4.52681i	0.166182	−	0.235657i
$370$	−3.86209			−0.200781
$371$	−6.46029	+	4.69367i	−0.335401	+	0.243683i
$372$	32.7230			1.69661
$373$	6.50272	−	20.0133i	0.336698	−	1.03625i	−0.629182	−	0.777258i	$-0.716610\pi$
$373$	6.50272	−	20.0133i	0.336698	−	1.03625i	0.965880	−	0.258991i	$-0.0833901\pi$
$374$	0.866608	−	2.66714i	0.0448112	−	0.137915i
$375$	18.9442	−	13.7637i	0.978272	−	0.710756i
$376$	−2.10721	−	1.53098i	−0.108671	−	0.0789541i
$377$	3.49422	+	10.7541i	0.179961	+	0.553864i
$378$	−0.926816			−0.0476703
$379$	7.69505	+	23.6829i	0.395268	+	1.21651i	0.928752	+	0.370701i	$0.120882\pi$
$379$	7.69505	+	23.6829i	0.395268	+	1.21651i	−0.533484	+	0.845810i	$0.679118\pi$
$380$	1.11307	+	3.42567i	0.0570992	+	0.175733i
$381$	−10.5618	+	32.5060i	−0.541099	+	1.66533i
$382$	3.82033	−	2.77563i	0.195465	−	0.142014i
$383$	−24.5054			−1.25217			−0.626083	−	0.779756i	$-0.715343\pi$
$383$	−24.5054			−1.25217			−0.626083	+	0.779756i	$0.715343\pi$
$384$	4.03499	−	12.4184i	0.205910	−	0.633725i
$385$	4.62969	+	3.36367i	0.235951	+	0.171428i
$386$	0.501370	+	1.54306i	0.0255191	+	0.0785396i
$387$	−3.66052	+	2.65953i	−0.186075	+	0.135191i
$388$	−23.1151	−	16.7941i	−1.17349	−	0.852592i
$389$	20.0701	+	14.5818i	1.01759	+	0.739325i	0.965788	−	0.259332i	$-0.0835025\pi$
$389$	20.0701	+	14.5818i	1.01759	+	0.739325i	0.0518051	+	0.998657i	$0.483503\pi$
$390$	−2.60378	−	1.89176i	−0.131848	−	0.0957929i
$391$	21.7439	+	15.7979i	1.09964	+	0.798933i
$392$	−0.705867	+	0.512842i	−0.0356517	+	0.0259024i
$393$	−1.17571	−	3.61848i	−0.0593069	−	0.182528i
$394$	2.76360	+	2.00787i	0.139228	+	0.101155i
$395$	1.99776	−	6.14848i	0.100518	−	0.309364i
$396$	−6.02624			−0.302830
$397$	7.89520	−	5.73620i	0.396249	−	0.287892i	−0.371763	−	0.928328i	$-0.621246\pi$
$397$	7.89520	−	5.73620i	0.396249	−	0.287892i	0.768011	+	0.640436i	$0.221246\pi$
$398$	−0.0676392	+	0.208172i	−0.00339045	+	0.0104347i
$399$	0.699645	+	2.15328i	0.0350260	+	0.107799i
$400$	−2.78648	−	8.57589i	−0.139324	−	0.428795i
$401$	9.85090			0.491930			0.245965	−	0.969279i	$-0.420895\pi$
$401$	9.85090			0.491930			0.245965	+	0.969279i	$0.420895\pi$
$402$	0.0333655	+	0.102688i	0.00166412	+	0.00512163i
$403$	−31.9186	−	23.1903i	−1.58998	−	1.15519i
$404$	−22.1385	+	16.0846i	−1.10143	+	0.800237i
$405$	−5.37278	+	16.5357i	−0.266976	+	0.821667i
$406$	−0.166824	+	0.513431i	−0.00827933	+	0.0254811i
$407$	38.9548			1.93092
$408$	4.93660	−	3.58665i	0.244398	−	0.177566i
$409$	−30.7727			−1.52161			−0.760807	−	0.648978i	$-0.775197\pi$
$409$	−30.7727			−1.52161			−0.760807	+	0.648978i	$0.775197\pi$
$410$	−2.16515	−	0.669852i	−0.106929	−	0.0330817i
$411$	27.3290			1.34804
$412$	−15.7925	+	11.4740i	−0.778043	+	0.565281i
$413$	−7.13210			−0.350948
$414$	−0.445986	+	1.37260i	−0.0219190	+	0.0674598i
$415$	−5.31931	+	16.3712i	−0.261115	+	0.803629i
$416$	−9.59470	+	6.97096i	−0.470419	+	0.341779i
$417$	17.5532	+	12.7531i	0.859582	+	0.624523i
$418$	0.280551	+	0.863448i	0.0137222	+	0.0422326i
$419$	23.4042			1.14337			0.571685	−	0.820473i	$-0.306290\pi$
$419$	23.4042			1.14337			0.571685	+	0.820473i	$0.306290\pi$
$420$	1.90014	+	5.84802i	0.0927171	+	0.285354i
$421$	5.92704	+	18.2416i	0.288866	+	0.889040i	0.985213	+	0.171334i	$0.0548077\pi$
$421$	5.92704	+	18.2416i	0.288866	+	0.889040i	−0.696347	+	0.717706i	$0.745192\pi$
$422$	−0.550975	+	1.69573i	−0.0268210	+	0.0825467i
$423$	−2.08928	+	1.51795i	−0.101584	+	0.0738052i
$424$	−6.96721			−0.338358
$425$	2.67196	−	8.22343i	0.129609	−	0.398895i
$426$	−2.61866	−	1.90257i	−0.126874	−	0.0921797i
$427$	−3.67211	−	11.3016i	−0.177706	−	0.546922i
$428$	3.24482	−	2.35750i	0.156844	−	0.113954i
$429$	26.2629	+	19.0811i	1.26798	+	0.921245i
$430$	1.49773	+	1.08817i	0.0722270	+	0.0524760i
$431$	25.5366	+	18.5534i	1.23005	+	0.893686i	0.996894	−	0.0787522i	$-0.0250936\pi$
$431$	25.5366	+	18.5534i	1.23005	+	0.893686i	0.233159	+	0.972439i	$0.425094\pi$
$432$	12.5971	+	9.15236i	0.606080	+	0.440343i
$433$	−15.9089	+	11.5585i	−0.764534	+	0.555466i	−0.900298	−	0.435275i	$-0.856651\pi$
$433$	−15.9089	+	11.5585i	−0.764534	+	0.555466i	0.135764	+	0.990741i	$0.456651\pi$
$434$	−0.582072	−	1.79143i	−0.0279404	−	0.0859916i
$435$	6.23294	+	4.52850i	0.298847	+	0.217125i
$436$	−2.73833	+	8.42771i	−0.131142	+	0.403614i
$437$	−8.70101			−0.416226
$438$	2.24066	−	1.62793i	0.107063	−	0.0777856i
$439$	9.24140	−	28.4421i	0.441068	−	1.35747i	−0.445670	−	0.895197i	$-0.647035\pi$
$439$	9.24140	−	28.4421i	0.441068	−	1.35747i	0.886739	−	0.462271i	$-0.152965\pi$
$440$	1.54292	+	4.74861i	0.0735556	+	0.226381i
$441$	0.267323	+	0.822735i	0.0127297	+	0.0391779i
$442$	−3.63314			−0.172811
$443$	−5.92482	−	18.2347i	−0.281497	−	0.866358i	−0.987427	−	0.158077i	$-0.949471\pi$
$443$	−5.92482	−	18.2347i	−0.281497	−	0.866358i	0.705930	−	0.708282i	$-0.250529\pi$
$444$	33.8630	+	24.6029i	1.60707	+	1.16760i
$445$	4.92836	−	3.58066i	0.233627	−	0.169740i
$446$	0.568010	−	1.74815i	0.0268960	−	0.0827775i
$447$	5.06664	−	15.5935i	0.239644	−	0.737548i
$448$	6.85342			0.323794
$449$	−15.8562	+	11.5202i	−0.748299	+	0.543671i	−0.895299	−	0.445466i	$-0.853038\pi$
$449$	−15.8562	+	11.5202i	−0.748299	+	0.543671i	0.147000	+	0.989136i	$0.453038\pi$
$450$	0.464308			0.0218877
$451$	21.8386	+	6.75642i	1.02834	+	0.318148i
$452$	25.2993			1.18998
$453$	22.9723	−	16.6904i	1.07933	−	0.784181i
$454$	−2.38351			−0.111864
$455$	2.29097	−	7.05087i	0.107402	−	0.330550i
$456$	−0.610439	+	1.87874i	−0.0285864	+	0.0879800i
$457$	7.72315	−	5.61120i	0.361274	−	0.262481i	−0.392309	−	0.919833i	$-0.628324\pi$
$457$	7.72315	−	5.61120i	0.361274	−	0.262481i	0.753583	+	0.657353i	$0.228324\pi$
$458$	−2.19065	−	1.59160i	−0.102363	−	0.0743707i
$459$	4.61392	+	14.2002i	0.215359	+	0.662808i
$460$	−23.6307			−1.10179
$461$	5.25764	+	16.1813i	0.244873	+	0.753640i	0.995657	+	0.0930934i	$0.0296755\pi$
$461$	5.25764	+	16.1813i	0.244873	+	0.753640i	−0.750785	+	0.660547i	$0.770324\pi$
$462$	0.478933	+	1.47401i	0.0222820	+	0.0685769i
$463$	6.39676	−	19.6872i	0.297282	−	0.914941i	−0.685163	−	0.728390i	$-0.740269\pi$
$463$	6.39676	−	19.6872i	0.297282	−	0.914941i	0.982445	−	0.186551i	$-0.0597310\pi$
$464$	7.33760	−	5.33108i	0.340640	−	0.247489i
$465$	−26.8816			−1.24660
$466$	−1.41035	+	4.34060i	−0.0653330	+	0.201074i
$467$	10.1553	+	7.37828i	0.469933	+	0.341426i	0.797415	−	0.603431i	$-0.206200\pi$
$467$	10.1553	+	7.37828i	0.469933	+	0.341426i	−0.327482	+	0.944857i	$0.606200\pi$
$468$	2.41252	+	7.42497i	0.111519	+	0.343219i
$469$	−0.201216	+	0.146192i	−0.00929128	+	0.00675051i
$470$	0.854844	+	0.621080i	0.0394310	+	0.0286483i
$471$	29.3003	+	21.2879i	1.35009	+	0.980895i
$472$	−5.03432	−	3.65764i	−0.231723	−	0.168357i
$473$	−15.1068	−	10.9757i	−0.694610	−	0.504664i
$474$	1.41650	−	1.02915i	0.0650621	−	0.0472704i
$475$	0.865006	+	2.66221i	0.0396892	+	0.122151i
$476$	5.61558	+	4.07996i	0.257390	+	0.187005i
$477$	−2.13467	+	6.56983i	−0.0977397	+	0.300812i
$478$	3.00929			0.137642
$479$	0.212807	−	0.154613i	0.00972340	−	0.00706447i	−0.582913	−	0.812535i	$-0.698087\pi$
$479$	0.212807	−	0.154613i	0.00972340	−	0.00706447i	0.592636	+	0.805470i	$0.298087\pi$
$480$	−2.49703	+	7.68507i	−0.113973	+	0.350774i
$481$	−15.5950	−	47.9964i	−0.711070	−	2.18845i
$482$	1.47683	+	4.54520i	0.0672676	+	0.207028i
$483$	−14.8536			−0.675864
$484$	−1.05261	−	3.23959i	−0.0478457	−	0.147254i
$485$	18.9888	+	13.7962i	0.862238	+	0.626453i
$486$	−1.56011	+	1.13349i	−0.0707682	+	0.0514161i
$487$	−3.46524	+	10.6649i	−0.157025	+	0.483274i	−0.998360	−	0.0572399i	$-0.981770\pi$
$487$	−3.46524	+	10.6649i	−0.157025	+	0.483274i	0.841335	+	0.540514i	$0.181770\pi$
$488$	3.20391	−	9.86063i	0.145034	−	0.446370i
$489$	20.4401			0.924331
$490$	0.286353	−	0.208048i	0.0129361	−	0.00939864i
$491$	−37.9630			−1.71324			−0.856622	−	0.515944i	$-0.827441\pi$
$491$	−37.9630			−1.71324			−0.856622	+	0.515944i	$0.827441\pi$
$492$	14.7169	+	19.6661i	0.663489	+	0.886615i
$493$	8.69702			0.391694
$494$	0.951545	−	0.691338i	0.0428120	−	0.0311048i
$495$	4.95049			0.222508
$496$	−9.77908	+	30.0969i	−0.439093	+	1.35139i
$497$	2.30406	−	7.09116i	0.103351	−	0.318082i
$498$	−3.77163	+	2.74025i	−0.169011	+	0.122793i
$499$	15.1883	+	11.0350i	0.679922	+	0.493992i	0.873332	−	0.487126i	$-0.161955\pi$
$499$	15.1883	+	11.0350i	0.679922	+	0.493992i	−0.193410	+	0.981118i	$0.561955\pi$
$500$	7.18177	+	22.1032i	0.321179	+	0.988487i
$501$	−11.2185			−0.501205
$502$	−0.0165240	−	0.0508557i	−0.000737503	−	0.00226980i
$503$	−9.71252	−	29.8921i	−0.433060	−	1.33282i	−0.895062	−	0.445942i	$-0.852869\pi$
$503$	−9.71252	−	29.8921i	−0.433060	−	1.33282i	0.462002	−	0.886879i	$-0.347131\pi$
$504$	−0.233239	+	0.717836i	−0.0103893	+	0.0319749i
$505$	18.1865	−	13.2133i	0.809290	−	0.587984i
$506$	−5.95617			−0.264784
$507$	5.09821	−	15.6907i	0.226419	−	0.696847i
$508$	−27.4439	−	19.9392i	−1.21763	−	0.884658i
$509$	−3.34191	−	10.2853i	−0.148128	−	0.455890i	0.849272	−	0.527955i	$-0.177041\pi$
$509$	−3.34191	−	10.2853i	−0.148128	−	0.455890i	−0.997400	+	0.0720652i	$0.977041\pi$
$510$	−2.00266	+	1.45502i	−0.0886793	+	0.0644293i
$511$	5.16137	+	3.74995i	0.228325	+	0.165888i
$512$	12.9332	+	9.39651i	0.571572	+	0.415271i
$513$	−3.91053	−	2.84117i	−0.172654	−	0.125440i
$514$	−2.05166	−	1.49062i	−0.0904950	−	0.0657484i
$515$	12.9734	−	9.42573i	0.571676	−	0.415347i
$516$	−6.20018	−	19.0822i	−0.272948	−	0.840046i
$517$	−8.62233	−	6.26449i	−0.379209	−	0.275512i
$518$	0.744548	−	2.29148i	0.0327136	−	0.100682i
$519$	−1.52167			−0.0667941
$520$	5.23310	−	3.80207i	0.229487	−	0.166732i
$521$	4.30502	−	13.2495i	0.188606	−	0.580470i	−0.811386	−	0.584511i	$-0.801286\pi$
$521$	4.30502	−	13.2495i	0.188606	−	0.580470i	0.999992	+	0.00404107i	$0.00128632\pi$
$522$	0.144315	+	0.444156i	0.00631650	+	0.0194402i
$523$	5.61397	+	17.2780i	0.245482	+	0.755515i	0.995557	+	0.0941625i	$0.0300173\pi$
$523$	5.61397	+	17.2780i	0.245482	+	0.755515i	−0.750075	+	0.661353i	$0.769983\pi$
$524$	3.77617			0.164963
$525$	1.47666	+	4.54471i	0.0644469	+	0.198347i
$526$	3.55651	+	2.58396i	0.155071	+	0.112666i
$527$	−24.5497	+	17.8364i	−1.06940	+	0.776967i
$528$	8.04629	−	24.7639i	0.350170	−	1.07771i
$529$	10.5322	−	32.4149i	0.457924	−	1.40934i
$530$	2.82643			0.122772
$531$	−4.99148	+	3.62652i	−0.216612	+	0.157378i
$532$	−2.24712			−0.0974251
$533$	−0.418140	−	29.6123i	−0.0181117	−	1.28265i
$534$	1.64984			0.0713957
$535$	−2.66558	+	1.93666i	−0.115243	+	0.0837291i
$536$	−0.217005			−0.00937318
$537$	−11.0628	+	34.0477i	−0.477394	+	1.46927i
$538$	−0.171260	+	0.527083i	−0.00738353	+	0.0227242i
$539$	−2.88828	+	2.09846i	−0.124407	+	0.0903871i
$540$	−10.6204	−	7.71620i	−0.457031	−	0.332052i
$541$	3.75705	+	11.5630i	0.161528	+	0.497133i	0.998764	−	0.0497099i	$-0.0158297\pi$
$541$	3.75705	+	11.5630i	0.161528	+	0.497133i	−0.837236	+	0.546842i	$0.815830\pi$
$542$	−2.24970			−0.0966328
$543$	−6.80744	−	20.9512i	−0.292135	−	0.899100i
$544$	2.81876	+	8.67526i	0.120853	+	0.371949i
$545$	2.24951	−	6.92328i	0.0963584	−	0.296561i
$546$	1.62440	−	1.18019i	0.0695178	−	0.0505076i
$547$	−16.8301			−0.719605			−0.359803	−	0.933028i	$-0.617156\pi$
$547$	−16.8301			−0.719605			−0.359803	+	0.933028i	$0.617156\pi$
$548$	−8.38180	+	25.7965i	−0.358053	+	1.10197i
$549$	−8.31657	−	6.04234i	−0.354943	−	0.257881i
$550$	0.592129	+	1.82239i	0.0252485	+	0.0777068i
$551$	−2.27781	+	1.65493i	−0.0970380	+	0.0705022i
$552$	−10.4847	−	7.61757i	−0.446258	−	0.324225i
$553$	3.26292	+	2.37065i	0.138754	+	0.100810i
$554$	−5.27360	−	3.83149i	−0.224054	−	0.162784i
$555$	−27.8181	−	20.2110i	−1.18081	−	0.857911i
$556$	−17.4216	+	12.6575i	−0.738839	+	0.536798i
$557$	−10.5655	−	32.5171i	−0.447673	−	1.37779i	−0.879526	−	0.475851i	$-0.842140\pi$
$557$	−10.5655	−	32.5171i	−0.447673	−	1.37779i	0.431853	−	0.901944i	$-0.357860\pi$
$558$	−1.31827	−	0.957782i	−0.0558070	−	0.0405462i
$559$	−7.47547	+	23.0071i	−0.316179	+	0.973098i
$560$	−5.94655			−0.251288
$561$	20.1997	−	14.6759i	0.852832	−	0.619619i
$562$	−0.0429101	+	0.132064i	−0.00181005	+	0.00557077i
$563$	−7.32096	−	22.5316i	−0.308542	−	0.949594i	−0.978332	−	0.207043i	$-0.933616\pi$
$563$	−7.32096	−	22.5316i	−0.308542	−	0.949594i	0.669790	−	0.742551i	$-0.266384\pi$
$564$	−3.53881	−	10.8913i	−0.149011	−	0.458608i
$565$	−20.7831			−0.874353
$566$	−0.129165	−	0.397530i	−0.00542923	−	0.0167094i
$567$	−8.77530	−	6.37563i	−0.368528	−	0.267751i
$568$	5.26300	−	3.82380i	0.220831	−	0.160443i
$569$	10.7029	−	32.9401i	0.448688	−	1.38092i	−0.429700	−	0.902972i	$-0.641381\pi$
$569$	10.7029	−	32.9401i	0.448688	−	1.38092i	0.878388	−	0.477949i	$-0.158619\pi$
$570$	0.247641	−	0.762159i	0.0103725	−	0.0319233i
$571$	−18.3188			−0.766616			−0.383308	−	0.923621i	$-0.625215\pi$
$571$	−18.3188			−0.766616			−0.383308	+	0.923621i	$0.625215\pi$
$572$	−26.0660	+	18.9381i	−1.08987	+	0.791840i
$573$	42.0427			1.75636
$574$	0.814846	−	1.15550i	0.0340110	−	0.0482297i
$575$	−18.3643			−0.765844
$576$	4.79644	−	3.48481i	0.199851	−	0.145201i
$577$	25.2111			1.04955			0.524777	−	0.851240i	$-0.324149\pi$
$577$	25.2111			1.04955			0.524777	+	0.851240i	$0.324149\pi$
$578$	0.296505	−	0.912547i	0.0123330	−	0.0379570i
$579$	−4.46381	+	13.7382i	−0.185510	+	0.570940i
$580$	−6.18621	+	4.49455i	−0.256868	+	0.186626i
$581$	−8.68797	−	6.31218i	−0.360438	−	0.261873i
$582$	1.96436	+	6.04568i	0.0814253	+	0.250601i
$583$	−28.5086			−1.18071
$584$	1.72010	+	5.29393i	0.0711784	+	0.219065i
$585$	−1.98186	−	6.09953i	−0.0819397	−	0.252185i
$586$	−1.75455	+	5.39994i	−0.0724797	+	0.223070i
$587$	21.4965	−	15.6181i	0.887256	−	0.644629i	−0.0479053	−	0.998852i	$-0.515255\pi$
$587$	21.4965	−	15.6181i	0.887256	−	0.644629i	0.935161	+	0.354223i	$0.115255\pi$
$588$	−3.83610			−0.158198
$589$	3.03572	−	9.34298i	0.125085	−	0.384971i
$590$	2.04230	+	1.48382i	0.0840802	+	0.0610878i
$591$	9.39824	+	28.9248i	0.386592	+	1.18981i
$592$	−32.7483	+	23.7930i	−1.34595	+	0.977888i
$593$	14.2878	+	10.3807i	0.586731	+	0.426285i	0.841144	−	0.540811i	$-0.181882\pi$
$593$	14.2878	+	10.3807i	0.586731	+	0.426285i	−0.254413	+	0.967096i	$0.581882\pi$
$594$	−2.67691	−	1.94489i	−0.109835	−	0.0797996i
$595$	−4.61314	−	3.35164i	−0.189120	−	0.137404i
$596$	13.1652	+	9.56507i	0.539267	+	0.391800i
$597$	−1.57660	+	1.14546i	−0.0645258	+	0.0468808i
$598$	2.38447	+	7.33864i	0.0975082	+	0.300099i
$599$	−9.66370	−	7.02109i	−0.394848	−	0.286874i	0.372591	−	0.927996i	$-0.378469\pi$
$599$	−9.66370	−	7.02109i	−0.394848	−	0.286874i	−0.767439	+	0.641122i	$0.778469\pi$
$600$	−1.28839	+	3.96525i	−0.0525982	+	0.161881i
$601$	2.03802			0.0831324			0.0415662	−	0.999136i	$-0.486765\pi$
$601$	2.03802			0.0831324			0.0415662	+	0.999136i	$0.486765\pi$
$602$	−0.934375	+	0.678863i	−0.0380823	+	0.0276684i
$603$	−0.0664875	+	0.204628i	−0.00270758	+	0.00833308i
$604$	8.70885	+	26.8031i	0.354358	+	1.09060i
$605$	0.864704	+	2.66128i	0.0351552	+	0.108197i
$606$	6.08822			0.247317
$607$	−3.44226	−	10.5942i	−0.139717	−	0.430005i	0.856577	−	0.516020i	$-0.172587\pi$
$607$	−3.44226	−	10.5942i	−0.139717	−	0.430005i	−0.996294	+	0.0860147i	$0.972587\pi$
$608$	−2.38904	−	1.73574i	−0.0968884	−	0.0703936i
$609$	−3.88849	+	2.82515i	−0.157569	+	0.114481i
$610$	−1.29975	+	4.00022i	−0.0526253	+	0.161964i
$611$	−4.26669	+	13.1315i	−0.172612	+	0.531244i
$612$	6.00469			0.242725
$613$	−12.3235	+	8.95355i	−0.497741	+	0.361630i	−0.808154	−	0.588972i	$-0.799533\pi$
$613$	−12.3235	+	8.95355i	−0.497741	+	0.361630i	0.310412	+	0.950602i	$0.399533\pi$
$614$	2.22935			0.0899694
$615$	−12.0898	−	16.1555i	−0.487507	−	0.651451i
$616$	−3.11492			−0.125504
$617$	−33.5563	+	24.3801i	−1.35093	+	0.981506i	−0.351962	+	0.936014i	$0.614485\pi$
$617$	−33.5563	+	24.3801i	−1.35093	+	0.981506i	−0.998965	+	0.0454916i	$0.985515\pi$
$618$	4.34304			0.174703
$619$	1.86984	−	5.75478i	0.0751552	−	0.231304i	−0.906421	−	0.422376i	$-0.861196\pi$
$619$	1.86984	−	5.75478i	0.0751552	−	0.231304i	0.981576	+	0.191072i	$0.0611963\pi$
$620$	8.24458	−	25.3742i	0.331110	−	1.01905i
$621$	25.6551	−	18.6395i	1.02950	−	0.747977i
$622$	−3.70526	−	2.69203i	−0.148568	−	0.107941i
$623$	1.17440	+	3.61442i	0.0470512	+	0.144809i
$624$	−33.7330			−1.35040
$625$	−2.14421	−	6.59919i	−0.0857683	−	0.263968i
$626$	−0.337850	−	1.03980i	−0.0135032	−	0.0415586i
$627$	−2.49781	+	7.68747i	−0.0997529	+	0.307008i
$628$	−29.0806	+	21.1283i	−1.16044	+	0.843111i
$629$	−38.8155			−1.54767
$630$	0.0946194	−	0.291209i	0.00376973	−	0.0116020i
$631$	17.1367	+	12.4505i	0.682201	+	0.495648i	0.874087	−	0.485769i	$-0.161460\pi$
$631$	17.1367	+	12.4505i	0.682201	+	0.495648i	−0.191886	+	0.981417i	$0.561460\pi$
$632$	1.08742	+	3.34673i	0.0432552	+	0.133126i
$633$	−12.8426	+	9.33073i	−0.510449	+	0.370863i
$634$	−1.83168	−	1.33079i	−0.0727453	−	0.0528525i
$635$	22.5449	+	16.3798i	0.894667	+	0.650013i
$636$	−24.7823	−	18.0054i	−0.982681	−	0.713960i
$637$	3.74181	+	2.71858i	0.148256	+	0.107714i
$638$	−1.55925	+	1.13286i	−0.0617312	+	0.0448504i
$639$	−1.99318	−	6.13438i	−0.0788490	−	0.242672i
$640$	−8.61293	−	6.25766i	−0.340456	−	0.247356i
$641$	−11.6921	+	35.9847i	−0.461811	+	1.42131i	0.401138	+	0.916018i	$0.368615\pi$
$641$	−11.6921	+	35.9847i	−0.461811	+	1.42131i	−0.862949	+	0.505291i	$0.831385\pi$
$642$	−0.892345			−0.0352180
$643$	27.8106	−	20.2056i	1.09674	−	0.796830i	0.116217	−	0.993224i	$-0.462923\pi$
$643$	27.8106	−	20.2056i	1.09674	−	0.796830i	0.980525	+	0.196394i	$0.0629232\pi$
$644$	4.55561	−	14.0207i	0.179516	−	0.552494i
$645$	5.09338	+	15.6758i	0.200552	+	0.617234i
$646$	−0.279548	−	0.860361i	−0.0109987	−	0.0338504i
$647$	15.9584			0.627391			0.313695	−	0.949524i	$-0.398433\pi$
$647$	15.9584			0.627391			0.313695	+	0.949524i	$0.398433\pi$
$648$	−2.92450	−	9.00069i	−0.114885	−	0.353581i
$649$	−20.5995	−	14.9664i	−0.808602	−	0.587484i
$650$	2.00832	−	1.45913i	0.0787729	−	0.0572319i
$651$	5.18232	−	15.9495i	0.203111	−	0.625112i
$652$	−6.26897	+	19.2939i	−0.245512	+	0.755608i
$653$	34.5559			1.35228			0.676139	−	0.736775i	$-0.263652\pi$
$653$	34.5559			1.35228			0.676139	+	0.736775i	$0.263652\pi$
$654$	1.59500	−	1.15884i	0.0623695	−	0.0453141i
$655$	−3.10208			−0.121208
$656$	−22.4859	+	7.65876i	−0.877927	+	0.299025i
$657$	5.51900			0.215317
$658$	−0.533303	+	0.387467i	−0.0207903	+	0.0151051i
$659$	−15.1335			−0.589516			−0.294758	−	0.955572i	$-0.595239\pi$
$659$	−15.1335			−0.589516			−0.294758	+	0.955572i	$0.595239\pi$
$660$	−6.78370	+	20.8781i	−0.264055	+	0.812678i
$661$	−6.01134	+	18.5010i	−0.233814	+	0.719606i	0.763462	+	0.645852i	$0.223498\pi$
$661$	−6.01134	+	18.5010i	−0.233814	+	0.719606i	−0.997276	+	0.0737537i	$0.976502\pi$
$662$	−3.11169	+	2.26078i	−0.120939	+	0.0878675i
$663$	−26.1690	−	19.0129i	−1.01632	−	0.738399i
$664$	−2.89540	−	8.91112i	−0.112363	−	0.345818i
$665$	1.84599			0.0715843
$666$	−0.644089	−	1.98230i	−0.0249580	−	0.0768127i
$667$	−5.70795	−	17.5673i	−0.221013	−	0.680207i
$668$	3.44071	−	10.5894i	0.133125	−	0.409717i
$669$	13.2397	−	9.61921i	0.511877	−	0.371900i
$670$	0.0880336			0.00340103
$671$	13.1098	−	40.3480i	0.506100	−	1.55762i
$672$	−4.07837	−	2.96311i	−0.157326	−	0.114304i
$673$	1.00064	+	3.07965i	0.0385717	+	0.118712i	0.968488	−	0.249059i	$-0.0801212\pi$
$673$	1.00064	+	3.07965i	0.0385717	+	0.118712i	−0.929917	+	0.367770i	$0.880121\pi$
$674$	−5.12103	+	3.72065i	−0.197255	+	0.143314i
$675$	−8.25353	−	5.99654i	−0.317679	−	0.230807i
$676$	13.2472	+	9.62467i	0.509508	+	0.370180i
$677$	40.5245	+	29.4428i	1.55748	+	1.13158i	0.938036	+	0.346537i	$0.112643\pi$
$677$	40.5245	+	29.4428i	1.55748	+	1.13158i	0.619446	+	0.785039i	$0.287357\pi$
$678$	−4.55373	−	3.30847i	−0.174885	−	0.127061i
$679$	−11.8464	+	8.60690i	−0.454622	+	0.330302i
$680$	−1.53740	−	4.73163i	−0.0589565	−	0.181450i
$681$	−17.1681	−	12.4734i	−0.657884	−	0.477980i
$682$	2.07806	−	6.39562i	0.0795732	−	0.244901i
$683$	23.6749			0.905896			0.452948	−	0.891537i	$-0.350372\pi$
$683$	23.6749			0.905896			0.452948	+	0.891537i	$0.350372\pi$
$684$	−1.57267	+	1.14261i	−0.0601326	+	0.0436889i
$685$	6.88556	−	21.1916i	0.263084	−	0.809689i
$686$	0.0682361	+	0.210009i	0.00260527	+	0.00801818i
$687$	−7.44982	−	22.9282i	−0.284228	−	0.874765i
$688$	19.4037			0.739759
$689$	11.4130	+	35.1256i	0.434801	+	1.33818i
$690$	4.25338	+	3.09026i	0.161924	+	0.117644i
$691$	20.2864	−	14.7389i	0.771729	−	0.560694i	−0.130756	−	0.991415i	$-0.541741\pi$
$691$	20.2864	−	14.7389i	0.771729	−	0.560694i	0.902485	+	0.430721i	$0.141741\pi$
$692$	0.466698	−	1.43635i	0.0177412	−	0.0546018i
$693$	−0.954373	+	2.93726i	−0.0362536	+	0.111577i
$694$	−4.66662			−0.177143
$695$	14.3116	−	10.3980i	0.542871	−	0.394419i
$696$	−4.19361			−0.158958
$697$	−21.7605	−	6.73227i	−0.824239	−	0.255003i
$698$	2.63129			0.0995958
$699$	−32.8737	+	23.8841i	−1.24340	+	0.903381i
$700$	−4.74276			−0.179259
$701$	8.82535	−	27.1616i	0.333329	−	1.02588i	−0.634210	−	0.773161i	$-0.718675\pi$
$701$	8.82535	−	27.1616i	0.333329	−	1.02588i	0.967539	−	0.252721i	$-0.0813253\pi$
$702$	−1.32465	+	4.07684i	−0.0499955	+	0.153870i
$703$	10.1661	−	7.38607i	0.383420	−	0.278571i
$704$	19.7946	+	14.3816i	0.746038	+	0.542028i
$705$	2.90709	+	8.94711i	0.109487	+	0.336968i
$706$	−3.52660			−0.132725
$707$	4.33373	+	13.3379i	0.162987	+	0.501622i
$708$	−8.45453	−	26.0204i	−0.317741	−	0.977906i
$709$	−10.4491	+	32.1592i	−0.392426	+	1.20776i	0.538522	+	0.842611i	$0.318983\pi$
$709$	−10.4491	+	32.1592i	−0.392426	+	1.20776i	−0.930948	+	0.365152i	$0.881017\pi$
$710$	−2.13507	+	1.55122i	−0.0801279	+	0.0582163i
$711$	3.48901			0.130848
$712$	−1.02466	+	3.15358i	−0.0384007	+	0.118185i
$713$	52.1404	+	37.8822i	1.95267	+	1.41870i
$714$	−0.477221	−	1.46873i	−0.0178595	−	0.0549660i
$715$	21.4129	−	15.5574i	0.800798	−	0.581814i
$716$	−28.7456	−	20.8849i	−1.07427	−	0.780504i
$717$	21.6755	+	15.7482i	0.809485	+	0.588126i
$718$	3.73669	+	2.71487i	0.139452	+	0.101318i
$719$	−7.83796	−	5.69461i	−0.292306	−	0.212373i	0.431961	−	0.901892i	$-0.357822\pi$
$719$	−7.83796	−	5.69461i	−0.292306	−	0.212373i	−0.724267	+	0.689519i	$0.757822\pi$
$720$	−4.16175	+	3.02369i	−0.155099	+	0.112686i
$721$	3.09148	+	9.51459i	0.115133	+	0.354342i
$722$	−3.15731	−	2.29392i	−0.117503	−	0.0853709i
$723$	−13.1485	+	40.4669i	−0.488998	+	1.50498i
$724$	21.8642			0.812576
$725$	−4.80753	+	3.49288i	−0.178547	+	0.129722i
$726$	−0.234188	+	0.720758i	−0.00869155	+	0.0267498i
$727$	−9.50638	−	29.2576i	−0.352572	−	1.08511i	−0.957404	−	0.288752i	$-0.906760\pi$
$727$	−9.50638	−	29.2576i	−0.352572	−	1.08511i	0.604832	−	0.796353i	$-0.293240\pi$
$728$	1.24701	+	3.83792i	0.0462174	+	0.142243i
$729$	15.3716			0.569318
$730$	−0.697804	−	2.14762i	−0.0258269	−	0.0794870i
$731$	15.0528	+	10.9365i	0.556746	+	0.404500i
$732$	36.8791	−	26.7942i	1.36309	−	0.990344i
$733$	−3.36988	+	10.3714i	−0.124469	+	0.383077i	−0.993804	−	0.111146i	$-0.964548\pi$
$733$	−3.36988	+	10.3714i	−0.124469	+	0.383077i	0.869335	+	0.494224i	$0.164548\pi$
$734$	0.393781	−	1.21193i	0.0145347	−	0.0447333i
$735$	3.15131			0.116238
$736$	15.6733	−	11.3873i	0.577726	−	0.419743i
$737$	−0.887945			−0.0327079
$738$	−0.0172697	−	1.22302i	−0.000635705	−	0.0450200i
$739$	−19.3088			−0.710286			−0.355143	−	0.934812i	$-0.615568\pi$
$739$	−19.3088			−0.710286			−0.355143	+	0.934812i	$0.615568\pi$
$740$	27.6096	−	20.0595i	1.01495	−	0.737402i
$741$	10.4717			0.384689
$742$	−0.544889	+	1.67700i	−0.0200035	+	0.0615645i
$743$	−2.42828	+	7.47347i	−0.0890849	+	0.274175i	−0.985667	−	0.168702i	$-0.946042\pi$
$743$	−2.42828	+	7.47347i	−0.0890849	+	0.274175i	0.896582	+	0.442877i	$0.146042\pi$
$744$	11.8376	−	8.60054i	0.433988	−	0.315311i
$745$	−10.8151	−	7.85760i	−0.396233	−	0.287880i
$746$	−1.43591	−	4.41927i	−0.0525723	−	0.161801i
$747$	−9.28997			−0.339902
$748$	7.65775	+	23.5681i	0.279995	+	0.861737i
$749$	−0.635191	−	1.95492i	−0.0232094	−	0.0714311i
$750$	1.59783	−	4.91763i	0.0583447	−	0.179566i
$751$	30.7490	−	22.3405i	1.12205	−	0.815215i	0.137529	−	0.990498i	$-0.456084\pi$
$751$	30.7490	−	22.3405i	1.12205	−	0.815215i	0.984518	+	0.175282i	$0.0560839\pi$
$752$	11.0748			0.403858
$753$	0.147117	−	0.452780i	0.00536124	−	0.0165002i
$754$	2.02003	+	1.46764i	0.0735651	+	0.0534481i
$755$	−7.15423	−	22.0185i	−0.260369	−	0.801334i
$756$	6.62567	−	4.81383i	0.240973	−	0.175077i
$757$	−33.6550	−	24.4518i	−1.22321	−	0.888715i	−0.226849	−	0.973930i	$-0.572842\pi$
$757$	−33.6550	−	24.4518i	−1.22321	−	0.888715i	−0.996363	+	0.0852148i	$0.972842\pi$
$758$	4.44855	+	3.23206i	0.161579	+	0.117394i
$759$	−42.9015	−	31.1697i	−1.55723	−	1.13139i
$760$	1.30302	+	0.946700i	0.0472655	+	0.0343404i
$761$	1.14534	−	0.832136i	0.0415184	−	0.0301649i	−0.566833	−	0.823833i	$-0.691831\pi$
$761$	1.14534	−	0.832136i	0.0415184	−	0.0301649i	0.608351	+	0.793668i	$0.291831\pi$
$762$	2.33223	+	7.17786i	0.0844877	+	0.260026i
$763$	3.67410	+	2.66939i	0.133011	+	0.0966383i
$764$	−12.8945	+	39.6852i	−0.466506	+	1.43576i
$765$	−4.93279			−0.178345
$766$	−4.37775	+	3.18062i	−0.158174	+	0.114920i
$767$	−10.1935	+	31.3724i	−0.368066	+	1.13279i
$768$	7.43620	+	22.8863i	0.268331	+	0.825837i
$769$	12.9060	+	39.7205i	0.465401	+	1.43236i	0.858477	+	0.512852i	$0.171411\pi$
$769$	12.9060	+	39.7205i	0.465401	+	1.43236i	−0.393076	+	0.919506i	$0.628589\pi$
$770$	1.26365			0.0455387
$771$	−6.97715	−	21.4734i	−0.251276	−	0.773347i
$772$	−11.5988	−	8.42702i	−0.417450	−	0.303295i
$773$	−28.7344	+	20.8768i	−1.03350	+	0.750885i	−0.969007	−	0.247033i	$-0.920545\pi$
$773$	−28.7344	+	20.8768i	−1.03350	+	0.750885i	−0.0644977	+	0.997918i	$0.520545\pi$
$774$	−0.308745	+	0.950219i	−0.0110976	+	0.0341549i
$775$	6.40716	−	19.7192i	0.230152	−	0.708335i
$776$	−12.7759			−0.458630
$777$	17.3546	−	12.6089i	0.622594	−	0.452341i
$778$	5.47801			0.196396
$779$	6.98030	−	2.37751i	0.250095	−	0.0851831i
$780$	28.4398			1.01831
$781$	21.5353	−	15.6463i	0.770593	−	0.559868i
$782$	5.93488			0.212231
$783$	3.17094	−	9.75915i	0.113320	−	0.348763i
$784$	1.14640	−	3.52825i	0.0409427	−	0.126009i
$785$	23.8894	−	17.3567i	0.852650	−	0.619486i
$786$	−0.679687	−	0.493821i	−0.0242436	−	0.0176140i
$787$	−3.79656	−	11.6846i	−0.135333	−	0.416511i	0.860309	−	0.509773i	$-0.170271\pi$
$787$	−3.79656	−	11.6846i	−0.135333	−	0.416511i	−0.995642	+	0.0932620i	$0.970271\pi$
$788$	−30.1853			−1.07531
$789$	12.0947	+	37.2237i	0.430584	+	1.32520i
$790$	−0.441139	−	1.35769i	−0.0156950	−	0.0483043i
$791$	4.00664	−	12.3312i	0.142460	−	0.438446i
$792$	−2.18001	+	1.58387i	−0.0774633	+	0.0562804i
$793$	−54.9613			−1.95173
$794$	0.665916	−	2.04948i	0.0236325	−	0.0727333i
$795$	20.3584	+	14.7912i	0.722037	+	0.524591i
$796$	−0.597692	−	1.83951i	−0.0211846	−	0.0651996i
$797$	0.106711	−	0.0775301i	0.00377990	−	0.00274626i	−0.585894	−	0.810388i	$-0.699256\pi$
$797$	0.106711	−	0.0775301i	0.00377990	−	0.00274626i	0.589674	+	0.807642i	$0.299256\pi$
$798$	0.404468	+	0.293863i	0.0143180	+	0.0104027i
$799$	8.59150	+	6.24209i	0.303945	+	0.220829i
$800$	−5.04229	−	3.66344i	−0.178272	−	0.129522i
$801$	2.65976	+	1.93243i	0.0939782	+	0.0682791i
$802$	1.75981	−	1.27857i	0.0621410	−	0.0451480i
$803$	7.03836	+	21.6618i	0.248378	+	0.764430i
$804$	−0.771883	−	0.560806i	−0.0272222	−	0.0197781i
$805$	−3.74239	+	11.5179i	−0.131902	+	0.405952i
$806$	−8.71201			−0.306868
$807$	−3.99188	+	2.90027i	−0.140521	+	0.102094i
$808$	−3.78118	+	11.6373i	−0.133021	+	0.409398i
$809$	2.87087	+	8.83563i	0.100934	+	0.310644i	0.988755	−	0.149546i	$-0.0477812\pi$
$809$	2.87087	+	8.83563i	0.100934	+	0.310644i	−0.887820	+	0.460190i	$0.847781\pi$
$810$	1.18640	+	3.65136i	0.0416858	+	0.128296i
$811$	−28.3957			−0.997108			−0.498554	−	0.866859i	$-0.666136\pi$
$811$	−28.3957			−0.997108			−0.498554	+	0.866859i	$0.666136\pi$
$812$	−1.47413	−	4.53692i	−0.0517320	−	0.159215i
$813$	−16.2043	−	11.7731i	−0.568308	−	0.412900i
$814$	6.95905	−	5.05605i	0.243915	−	0.177214i
$815$	5.14989	−	15.8497i	0.180393	−	0.555192i
$816$	−8.01752	+	24.6754i	−0.280669	+	0.863812i
$817$	−6.02349			−0.210735
$818$	−5.49738	+	3.99408i	−0.192211	+	0.139650i
$819$	4.00108			0.139809
$820$	18.9575	−	6.45698i	0.662025	−	0.225487i
$821$	36.1000			1.25990			0.629950	−	0.776636i	$-0.283075\pi$
$821$	36.1000			1.25990			0.629950	+	0.776636i	$0.283075\pi$
$822$	4.88217	−	3.54710i	0.170285	−	0.123719i
$823$	−53.2320			−1.85555			−0.927775	−	0.373139i	$-0.878281\pi$
$823$	−53.2320			−1.85555			−0.927775	+	0.373139i	$0.878281\pi$
$824$	−2.69731	+	8.30147i	−0.0939653	+	0.289195i
$825$	−5.27186	+	16.2251i	−0.183543	+	0.564886i
$826$	−1.27411	+	0.925695i	−0.0443320	+	0.0322091i
$827$	8.43409	+	6.12772i	0.293282	+	0.213082i	0.724690	−	0.689075i	$-0.241983\pi$
$827$	8.43409	+	6.12772i	0.293282	+	0.213082i	−0.431408	+	0.902157i	$0.641983\pi$
$828$	−3.94094	−	12.1290i	−0.136957	−	0.421511i
$829$	44.3771			1.54128			0.770641	−	0.637270i	$-0.219936\pi$
$829$	44.3771			1.54128			0.770641	+	0.637270i	$0.219936\pi$
$830$	1.17459	+	3.61502i	0.0407707	+	0.125479i
$831$	−17.9341	−	55.1954i	−0.622126	−	1.91471i
$832$	9.79521	−	30.1465i	0.339588	−	1.04514i
$833$	2.87795	−	2.09096i	0.0997152	−	0.0724474i
$834$	4.79104			0.165900
$835$	−2.82651	+	8.69909i	−0.0978153	+	0.301045i
$836$	−6.49033	−	4.71550i	−0.224473	−	0.163089i
$837$	11.0639	+	34.0511i	0.382423	+	1.17698i
$838$	4.18103	−	3.03769i	0.144431	−	0.104935i
$839$	−39.3858	−	28.6155i	−1.35975	−	0.987917i	−0.998461	−	0.0554629i	$-0.982337\pi$
$839$	−39.3858	−	28.6155i	−1.35975	−	0.987917i	−0.361290	−	0.932454i	$-0.617663\pi$
$840$	2.22441	+	1.61613i	0.0767493	+	0.0557617i
$841$	18.6259	+	13.5325i	0.642274	+	0.466639i
$842$	3.42646	+	2.48947i	0.118083	+	0.0857927i
$843$	−1.00019	+	0.726679i	−0.0344483	+	0.0250282i
$844$	−4.86868	−	14.9842i	−0.167587	−	0.515779i
$845$	−10.8824	−	7.90656i	−0.374368	−	0.271994i
$846$	−0.176219	+	0.542346i	−0.00605853	+	0.0186462i
$847$	−1.74571			−0.0599834
$848$	23.9665	−	17.4127i	0.823012	−	0.597953i
$849$	1.14999	−	3.53930i	0.0394675	−	0.121468i
$850$	−0.590012	−	1.81587i	−0.0202372	−	0.0622838i
$851$	25.4750	+	78.4040i	0.873272	+	2.68766i
$852$	28.6023			0.979897
$853$	15.6601	+	48.1969i	0.536192	+	1.65023i	0.741059	+	0.671440i	$0.234324\pi$
$853$	15.6601	+	48.1969i	0.536192	+	1.65023i	−0.204866	+	0.978790i	$0.565676\pi$
$854$	−2.12287	−	1.54235i	−0.0726430	−	0.0527782i
$855$	1.29193	−	0.938644i	0.0441832	−	0.0321010i
$856$	0.554204	−	1.70566i	0.0189423	−	0.0582984i
$857$	−13.9917	+	43.0622i	−0.477949	+	1.47098i	0.363990	+	0.931403i	$0.381414\pi$
$857$	−13.9917	+	43.0622i	−0.477949	+	1.47098i	−0.841939	+	0.539573i	$0.818586\pi$
$858$	7.16831			0.244722
$859$	12.9118	−	9.38095i	0.440544	−	0.320074i	−0.345307	−	0.938490i	$-0.612225\pi$
$859$	12.9118	−	9.38095i	0.440544	−	0.320074i	0.785851	+	0.618416i	$0.212225\pi$
$860$	−16.3589			−0.557835
$861$	11.9162	−	4.05868i	0.406102	−	0.138320i
$862$	6.97006			0.237401
$863$	12.3313	−	8.95923i	0.419763	−	0.304976i	−0.357779	−	0.933806i	$-0.616466\pi$
$863$	12.3313	−	8.95923i	0.419763	−	0.304976i	0.777543	+	0.628830i	$0.216466\pi$
$864$	10.7625			0.366146
$865$	−0.383387	+	1.17994i	−0.0130356	+	0.0401193i
$866$	−1.34183	+	4.12972i	−0.0455972	+	0.140334i
$867$	6.91121	−	5.02129i	0.234717	−	0.170532i
$868$	13.4658	+	9.78345i	0.457058	+	0.332072i
$869$	4.44952	+	13.6942i	0.150940	+	0.464545i
$870$	1.70125			0.0576776
$871$	0.355476	+	1.09404i	0.0120449	+	0.0370702i
$872$	1.22445	+	3.76846i	0.0414650	+	0.127616i
$873$	−3.91439	+	12.0472i	−0.132482	+	0.407738i
$874$	−1.55439	+	1.12933i	−0.0525779	+	0.0382001i
$875$	11.9107			0.402656
$876$	−7.56274	+	23.2757i	−0.255521	+	0.786413i
$877$	−36.2680	−	26.3502i	−1.22468	−	0.889784i	−0.228203	−	0.973614i	$-0.573285\pi$
$877$	−36.2680	−	26.3502i	−1.22468	−	0.889784i	−0.996480	+	0.0838295i	$0.973285\pi$
$878$	−2.04066	−	6.28049i	−0.0688688	−	0.211956i
$879$	−40.8967	+	29.7132i	−1.37941	+	1.00220i
$880$	−17.1753	−	12.4786i	−0.578980	−	0.420654i
$881$	−19.4543	−	14.1344i	−0.655432	−	0.476200i	0.209685	−	0.977769i	$-0.432756\pi$
$881$	−19.4543	−	14.1344i	−0.655432	−	0.476200i	−0.865117	+	0.501569i	$0.832756\pi$
$882$	0.154541	+	0.112280i	0.00520366	+	0.00378068i
$883$	19.0152	+	13.8154i	0.639914	+	0.464924i	0.859821	−	0.510596i	$-0.170575\pi$
$883$	19.0152	+	13.8154i	0.639914	+	0.464924i	−0.219907	+	0.975521i	$0.570575\pi$
$884$	25.9728	−	18.8703i	0.873559	−	0.634678i
$885$	6.94531	+	21.3755i	0.233464	+	0.718528i
$886$	−3.42517	−	2.48853i	−0.115071	−	0.0836039i
$887$	2.31681	−	7.13042i	0.0777910	−	0.239416i	−0.904597	−	0.426267i	$-0.859828\pi$
$887$	2.31681	−	7.13042i	0.0777910	−	0.239416i	0.982388	+	0.186851i	$0.0598283\pi$
$888$	18.7164			0.628082
$889$	−14.0649	+	10.2187i	−0.471720	+	0.342725i
$890$	0.415680	−	1.27933i	0.0139336	−	0.0428832i
$891$	−11.9665	−	36.8292i	−0.400894	−	1.23383i
$892$	5.01920	+	15.4475i	0.168055	+	0.517221i
$893$	−3.43796			−0.115047
$894$	−1.11880	−	3.44331i	−0.0374182	−	0.115161i
$895$	23.6142	+	17.1567i	0.789335	+	0.573485i
$896$	5.37327	−	3.90391i	0.179508	−	0.130420i
$897$	−21.2295	+	65.3375i	−0.708831	+	2.18156i
$898$	−1.33738	+	4.11603i	−0.0446289	+	0.137354i
$899$	20.8548			0.695548
$900$	−3.31927	+	2.41159i	−0.110642	+	0.0803863i
$901$	28.4067			0.946364
$902$	4.77828	−	1.62750i	0.159099	−	0.0541897i
$903$	−10.2828			−0.342190
$904$	9.15211	−	6.64940i	0.304395	−	0.221156i
$905$	−17.9612			−0.597050
$906$	1.93759	−	5.96328i	0.0643720	−	0.198117i
$907$	16.4279	−	50.5599i	0.545480	−	1.67882i	−0.174365	−	0.984681i	$-0.555787\pi$
$907$	16.4279	−	50.5599i	0.545480	−	1.67882i	0.719845	−	0.694134i	$-0.244213\pi$
$908$	17.0394	−	12.3799i	0.565472	−	0.410840i
$909$	9.81502	+	7.13103i	0.325544	+	0.236521i
$910$	−0.505884	−	1.55695i	−0.0167699	−	0.0516124i
$911$	−16.9600			−0.561910			−0.280955	−	0.959721i	$-0.590651\pi$
$911$	−16.9600			−0.561910			−0.280955	+	0.959721i	$0.590651\pi$
$912$	−2.59555	−	7.98829i	−0.0859474	−	0.264519i
$913$	−11.8475	−	36.4627i	−0.392093	−	1.20674i
$914$	0.651405	−	2.00482i	0.0215466	−	0.0663135i
$915$	−30.2958	+	22.0112i	−1.00155	+	0.727667i
$916$	23.9274			0.790583
$917$	0.598030	−	1.84055i	0.0197487	−	0.0607802i
$918$	2.66733	+	1.93793i	0.0880351	+	0.0639613i
$919$	−13.8099	−	42.5026i	−0.455547	−	1.40203i	−0.870491	−	0.492184i	$-0.836199\pi$
$919$	−13.8099	−	42.5026i	−0.455547	−	1.40203i	0.414944	−	0.909847i	$-0.363801\pi$
$920$	−8.54848	+	6.21084i	−0.281835	+	0.204765i
$921$	16.0577	+	11.6666i	0.529120	+	0.384428i
$922$	3.03947	+	2.20830i	0.100100	+	0.0727266i
$923$	−27.8992	−	20.2700i	−0.918315	−	0.667195i
$924$	−11.0797	−	8.04990i	−0.364496	−	0.264822i
$925$	21.4564	−	15.5890i	0.705482	−	0.512562i
$926$	−1.41251	−	4.34726i	−0.0464179	−	0.142860i
$927$	7.00156	+	5.08693i	0.229961	+	0.167077i
$928$	1.93721	−	5.96211i	0.0635920	−	0.195716i
$929$	24.3199			0.797910			0.398955	−	0.916971i	$-0.369373\pi$
$929$	24.3199			0.797910			0.398955	+	0.916971i	$0.369373\pi$
$930$	−4.80224	+	3.48903i	−0.157472	+	0.114410i
$931$	−0.355876	+	1.09527i	−0.0116634	+	0.0358961i
$932$	−12.4625	−	38.3556i	−0.408222	−	1.25638i
$933$	−12.6006	−	38.7806i	−0.412525	−	1.26962i
$934$	2.77184			0.0906974
$935$	−6.29076	−	19.3610i	−0.205730	−	0.633172i
$936$	2.82423	+	2.05192i	0.0923129	+	0.0670692i
$937$	−22.4996	+	16.3469i	−0.735031	+	0.534031i	−0.891151	−	0.453707i	$-0.850101\pi$
$937$	−22.4996	+	16.3469i	−0.735031	+	0.534031i	0.156120	+	0.987738i	$0.450101\pi$
$938$	−0.0169714	+	0.0522327i	−0.000554137	+	0.00170546i
$939$	3.00795	−	9.25753i	0.0981608	−	0.302108i
$940$	−9.33701			−0.304540
$941$	9.27208	−	6.73656i	0.302261	−	0.219606i	−0.426308	−	0.904578i	$-0.640186\pi$
$941$	9.27208	−	6.73656i	0.302261	−	0.219606i	0.728569	+	0.684973i	$0.240186\pi$
$942$	7.99735			0.260568
$943$	0.683049	+	48.3729i	0.0222431	+	1.57524i
$944$	26.4588			0.861161
$945$	−5.44292	+	3.95451i	−0.177058	+	0.128640i
$946$	−4.12331			−0.134060
$947$	5.60982	−	17.2652i	0.182294	−	0.561045i	−0.817597	−	0.575791i	$-0.804694\pi$
$947$	5.60982	−	17.2652i	0.182294	−	0.561045i	0.999891	+	0.0147464i	$0.00469411\pi$
$948$	−4.78102	+	14.7145i	−0.155280	+	0.477904i
$949$	23.8720	−	17.3440i	0.774917	−	0.563011i
$950$	0.500064	+	0.363318i	0.0162242	+	0.0117876i
$951$	−6.22904	−	19.1710i	−0.201991	−	0.621663i
$952$	3.10378			0.100594
$953$	13.2656	+	40.8274i	0.429716	+	1.32253i	0.898406	+	0.439166i	$0.144726\pi$
$953$	13.2656	+	40.8274i	0.429716	+	1.32253i	−0.468690	+	0.883363i	$0.655274\pi$
$954$	0.471370	+	1.45073i	0.0152612	+	0.0469690i
$955$	10.5927	−	32.6009i	0.342771	−	1.05494i
$956$	−21.5130	+	15.6301i	−0.695779	+	0.505513i
$957$	−17.1595			−0.554688
$958$	0.0179491	−	0.0552416i	0.000579909	−	0.00178478i
$959$	11.2461	+	8.17077i	0.363156	+	0.263848i
$960$	−6.67392	−	20.5402i	−0.215400	−	0.662933i
$961$	−33.7890	+	24.5492i	−1.08997	+	0.791909i
$962$	−9.01554	−	6.55017i	−0.290673	−	0.211186i
$963$	−1.43858	−	1.04519i	−0.0463575	−	0.0336807i
$964$	−34.1652	−	24.8224i	−1.10039	−	0.799477i
$965$	9.52828	+	6.92270i	0.306726	+	0.222850i
$966$	−2.65352	+	1.92789i	−0.0853755	+	0.0620289i
$967$	12.5125	+	38.5095i	0.402375	+	1.23838i	0.923067	+	0.384638i	$0.125674\pi$
$967$	12.5125	+	38.5095i	0.402375	+	1.23838i	−0.520692	+	0.853744i	$0.674326\pi$
$968$	−1.23224	−	0.895275i	−0.0396057	−	0.0287752i
$969$	2.48888	−	7.65998i	0.0799543	−	0.246074i
$970$	5.18289			0.166413
$971$	10.3321	−	7.50668i	0.331572	−	0.240901i	−0.409526	−	0.912299i	$-0.634306\pi$
$971$	10.3321	−	7.50668i	0.331572	−	0.240901i	0.741097	+	0.671398i	$0.234306\pi$
$972$	5.26574	−	16.2063i	0.168899	−	0.519817i
$973$	3.41037	+	10.4960i	0.109331	+	0.336487i
$974$	0.765183	+	2.35499i	0.0245180	+	0.0754588i
$975$	22.1016			0.707817
$976$	13.6229	+	41.9268i	0.436057	+	1.34205i
$977$	−2.62039	−	1.90382i	−0.0838337	−	0.0609087i	0.545079	−	0.838385i	$-0.316500\pi$
$977$	−2.62039	−	1.90382i	−0.0838337	−	0.0609087i	−0.628913	+	0.777476i	$0.716500\pi$
$978$	3.65150	−	2.65297i	0.116762	−	0.0848327i
$979$	−4.19272	+	12.9039i	−0.134000	+	0.412410i
$980$	−0.966508	+	2.97461i	−0.0308740	+	0.0950203i
$981$	3.92868			0.125433
$982$	−6.78187	+	4.92732i	−0.216418	+	0.157237i
$983$	0.0704190			0.00224602			0.00112301	−	0.999999i	$-0.499643\pi$
$983$	0.0704190			0.00224602			0.00112301	+	0.999999i	$0.499643\pi$
$984$	10.4927	+	3.24623i	0.334495	+	0.103486i
$985$	24.7969			0.790096
$986$	1.55367	−	1.12881i	0.0494790	−	0.0359486i
$987$	−5.86899			−0.186812
$988$	−3.21169	+	9.88455i	−0.102177	+	0.314470i
$989$	12.2115	−	37.5830i	0.388302	−	1.19507i
$990$	0.884377	−	0.642538i	0.0281074	−	0.0204212i
$991$	35.6319	+	25.8881i	1.13189	+	0.822363i	0.985968	−	0.166933i	$-0.0533865\pi$
$991$	35.6319	+	25.8881i	1.13189	+	0.822363i	0.145918	+	0.989297i	$0.453386\pi$
$992$	6.75920	+	20.8027i	0.214605	+	0.660485i
$993$	−34.2441			−1.08670
$994$	−0.508774	−	1.56585i	−0.0161373	−	0.0496656i
$995$	0.490997	+	1.51113i	0.0155657	+	0.0479062i
$996$	12.7301	−	39.1793i	0.403369	−	1.24144i
$997$	27.8850	−	20.2596i	0.883127	−	0.641629i	−0.0509499	−	0.998701i	$-0.516225\pi$
$997$	27.8850	−	20.2596i	0.883127	−	0.641629i	0.934077	+	0.357072i	$0.116225\pi$
$998$	4.14556			0.131225
$999$	−14.1522	+	43.5558i	−0.447754	+	1.37805i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.h.d.78.6	✓	40
41.10	even	5	inner	287.2.h.d.92.6	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.h.d.78.6	✓	40	1.1	even	1	trivial
287.2.h.d.92.6	yes	40	41.10	even	5	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.178644 - 0.129793i) q^{2} +1.96598 q^{3} +(-0.602966 + 1.85574i) q^{4} +(0.495330 - 1.52447i) q^{5} +(0.351211 - 0.255170i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.269617 + 0.829796i) q^{8} +0.865075 q^{9} +O(q^{10})\)	\(q+(0.178644 - 0.129793i) q^{2} +1.96598 q^{3} +(-0.602966 + 1.85574i) q^{4} +(0.495330 - 1.52447i) q^{5} +(0.351211 - 0.255170i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.269617 + 0.829796i) q^{8} +0.865075 q^{9} +(-0.109377 - 0.336628i) q^{10} +(1.10323 + 3.39538i) q^{11} +(-1.18542 + 3.64835i) q^{12} +(3.74181 - 2.71858i) q^{13} +0.220817 q^{14} +(0.973809 - 2.99708i) q^{15} +(-3.00131 - 2.18058i) q^{16} +(-1.09928 - 3.38324i) q^{17} +(0.154541 - 0.112280i) q^{18} +(0.931695 + 0.676916i) q^{19} +(2.53035 + 1.83841i) q^{20} +(1.59051 + 1.15557i) q^{21} +(0.637781 + 0.463375i) q^{22} +(-6.11239 + 4.44091i) q^{23} +(0.530062 + 1.63136i) q^{24} +(1.96643 + 1.42869i) q^{25} +(0.315601 - 0.971319i) q^{26} -4.19722 q^{27} +(-1.57859 + 1.14691i) q^{28} +(-0.755486 + 2.32515i) q^{29} +(-0.215033 - 0.661804i) q^{30} +(-2.63600 - 8.11277i) q^{31} -2.56419 q^{32} +(2.16892 + 6.67525i) q^{33} +(-0.635500 - 0.461718i) q^{34} +(1.29679 - 0.942174i) q^{35} +(-0.521611 + 1.60535i) q^{36} +(3.37179 - 10.3773i) q^{37} +0.254301 q^{38} +(7.35632 - 5.34468i) q^{39} +1.39855 q^{40} +(3.69015 - 5.23286i) q^{41} +0.434121 q^{42} +(-4.23145 + 3.07433i) q^{43} -6.96615 q^{44} +(0.428498 - 1.31878i) q^{45} +(-0.515546 + 1.58669i) q^{46} +(-2.41514 + 1.75470i) q^{47} +(-5.90050 - 4.28697i) q^{48} +(0.309017 + 0.951057i) q^{49} +0.536725 q^{50} +(-2.16116 - 6.65138i) q^{51} +(2.78880 + 8.58304i) q^{52} +(-2.46761 + 7.59452i) q^{53} +(-0.749810 + 0.544769i) q^{54} +5.72262 q^{55} +(-0.269617 + 0.829796i) q^{56} +(1.83169 + 1.33080i) q^{57} +(0.166824 + 0.513431i) q^{58} +(-5.76999 + 4.19215i) q^{59} +(4.97462 + 3.61427i) q^{60} +(-9.61371 - 6.98477i) q^{61} +(-1.52389 - 1.10717i) q^{62} +(0.699860 + 0.508478i) q^{63} +(5.54453 - 4.02834i) q^{64} +(-2.29097 - 7.05087i) q^{65} +(1.25386 + 0.910985i) q^{66} +(-0.0768576 + 0.236543i) q^{67} +6.94124 q^{68} +(-12.0168 + 8.73074i) q^{69} +(0.109377 - 0.336628i) q^{70} +(-2.30406 - 7.09116i) q^{71} +(0.233239 + 0.717836i) q^{72} +6.37980 q^{73} +(-0.744548 - 2.29148i) q^{74} +(3.86596 + 2.80878i) q^{75} +(-1.81796 + 1.32083i) q^{76} +(-1.10323 + 3.39538i) q^{77} +(0.620465 - 1.90959i) q^{78} +4.03319 q^{79} +(-4.81086 + 3.49529i) q^{80} -10.8469 q^{81} +(-0.0199632 - 1.41378i) q^{82} -10.7389 q^{83} +(-3.10347 + 2.25480i) q^{84} -5.70215 q^{85} +(-0.356900 + 1.09842i) q^{86} +(-1.48527 + 4.57119i) q^{87} +(-2.52002 + 1.83091i) q^{88} +(3.07461 + 2.23383i) q^{89} +(-0.0946194 - 0.291209i) q^{90} +4.62513 q^{91} +(-4.55561 - 14.0207i) q^{92} +(-5.18232 - 15.9495i) q^{93} +(-0.203704 + 0.626935i) q^{94} +(1.49344 - 1.08504i) q^{95} -5.04114 q^{96} +(-4.52491 + 13.9263i) q^{97} +(0.178644 + 0.129793i) q^{98} +(0.954373 + 2.93726i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 2 q^{2} - 10 q^{3} - 14 q^{4} - q^{5} + 9 q^{6} + 10 q^{7} + 3 q^{8} + 22 q^{9}+O(q^{10}) \) 40 * q - 2 * q^2 - 10 * q^3 - 14 * q^4 - q^5 + 9 * q^6 + 10 * q^7 + 3 * q^8 + 22 * q^9	\( 40 q - 2 q^{2} - 10 q^{3} - 14 q^{4} - q^{5} + 9 q^{6} + 10 q^{7} + 3 q^{8} + 22 q^{9} + 10 q^{10} + 5 q^{11} - 17 q^{12} + 3 q^{13} - 8 q^{14} + 23 q^{15} - 18 q^{16} + 11 q^{17} - 38 q^{18} - 2 q^{19} + 31 q^{20} + 4 q^{22} + 2 q^{23} + 10 q^{24} - 21 q^{25} - 7 q^{26} - 52 q^{27} + 14 q^{28} - 11 q^{29} - 18 q^{30} - 3 q^{31} + 44 q^{32} - 51 q^{33} + 29 q^{34} - 9 q^{35} + 35 q^{36} + 11 q^{37} + 52 q^{38} - 5 q^{39} - 32 q^{40} + 29 q^{41} + 6 q^{42} - 32 q^{43} - 92 q^{44} - 56 q^{45} + 26 q^{46} + 29 q^{47} + 11 q^{48} - 10 q^{49} - 24 q^{50} - 4 q^{51} + 3 q^{52} + 30 q^{53} + 58 q^{54} - 100 q^{55} - 3 q^{56} - 49 q^{57} + 25 q^{58} + 5 q^{59} - 91 q^{60} + 22 q^{61} - 34 q^{62} + 13 q^{63} - 9 q^{64} + 21 q^{65} + 29 q^{66} + 9 q^{67} - 20 q^{68} + 30 q^{69} - 10 q^{70} + 34 q^{71} - 37 q^{72} - 20 q^{73} - 58 q^{74} + 41 q^{75} - 37 q^{76} - 5 q^{77} + 63 q^{78} + 66 q^{79} + 22 q^{80} + 96 q^{81} + 76 q^{82} - 22 q^{83} - 38 q^{84} - 26 q^{85} + 3 q^{86} + 49 q^{87} - 19 q^{89} - q^{90} + 22 q^{91} - 2 q^{92} - 39 q^{93} + 66 q^{94} + 71 q^{95} - 302 q^{96} + 47 q^{97} - 2 q^{98} + 28 q^{99}+O(q^{100}) \) 40 * q - 2 * q^2 - 10 * q^3 - 14 * q^4 - q^5 + 9 * q^6 + 10 * q^7 + 3 * q^8 + 22 * q^9 + 10 * q^10 + 5 * q^11 - 17 * q^12 + 3 * q^13 - 8 * q^14 + 23 * q^15 - 18 * q^16 + 11 * q^17 - 38 * q^18 - 2 * q^19 + 31 * q^20 + 4 * q^22 + 2 * q^23 + 10 * q^24 - 21 * q^25 - 7 * q^26 - 52 * q^27 + 14 * q^28 - 11 * q^29 - 18 * q^30 - 3 * q^31 + 44 * q^32 - 51 * q^33 + 29 * q^34 - 9 * q^35 + 35 * q^36 + 11 * q^37 + 52 * q^38 - 5 * q^39 - 32 * q^40 + 29 * q^41 + 6 * q^42 - 32 * q^43 - 92 * q^44 - 56 * q^45 + 26 * q^46 + 29 * q^47 + 11 * q^48 - 10 * q^49 - 24 * q^50 - 4 * q^51 + 3 * q^52 + 30 * q^53 + 58 * q^54 - 100 * q^55 - 3 * q^56 - 49 * q^57 + 25 * q^58 + 5 * q^59 - 91 * q^60 + 22 * q^61 - 34 * q^62 + 13 * q^63 - 9 * q^64 + 21 * q^65 + 29 * q^66 + 9 * q^67 - 20 * q^68 + 30 * q^69 - 10 * q^70 + 34 * q^71 - 37 * q^72 - 20 * q^73 - 58 * q^74 + 41 * q^75 - 37 * q^76 - 5 * q^77 + 63 * q^78 + 66 * q^79 + 22 * q^80 + 96 * q^81 + 76 * q^82 - 22 * q^83 - 38 * q^84 - 26 * q^85 + 3 * q^86 + 49 * q^87 - 19 * q^89 - q^90 + 22 * q^91 - 2 * q^92 - 39 * q^93 + 66 * q^94 + 71 * q^95 - 302 * q^96 + 47 * q^97 - 2 * q^98 + 28 * q^99

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