LMFDB - Embedded newform 409.2.m.a.4.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [409,2,Mod(4,409)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(409, base_ring=CyclotomicField(102)) chi = DirichletCharacter(H, H._module([41])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("409.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 409 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	409.m (of order $102$, degree $32$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.26588144267$
Analytic rank:	$0$
Dimension:	$1056$
Relative dimension:	$33$ over $\Q(\zeta_{102})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{102}]$

Embedding invariants

Embedding label			4.20
Character	$\chi$	$=$	409.4
Dual form			409.2.m.a.307.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.689284 - 0.0853519i) q^{2} +(0.0642285 - 0.293276i) q^{3} +(-1.47177 + 0.370164i) q^{4} +(-0.212539 + 0.426836i) q^{5} +(0.0192400 - 0.207633i) q^{6} +(2.30590 - 1.33131i) q^{7} +(-2.27817 + 0.882566i) q^{8} +(2.64351 + 1.21621i) q^{9} +(-0.110069 + 0.312352i) q^{10} +(0.745889 - 0.0691168i) q^{11} +(0.0140310 + 0.455409i) q^{12} +(4.25511 + 0.394294i) q^{13} +(1.47579 - 1.11446i) q^{14} +(0.111530 + 0.0897477i) q^{15} +(1.17908 - 0.633151i) q^{16} +(-0.0479235 + 0.308729i) q^{17} +(1.92594 + 0.612684i) q^{18} +(2.03831 + 1.53926i) q^{19} +(0.154808 - 0.706877i) q^{20} +(-0.242337 - 0.761773i) q^{21} +(0.508230 - 0.111304i) q^{22} +(1.03588 - 6.67325i) q^{23} +(0.112513 + 0.724818i) q^{24} +(2.87616 + 3.80865i) q^{25} +(2.96664 - 0.0914011i) q^{26} +(1.06926 - 1.41592i) q^{27} +(-2.90094 + 2.81294i) q^{28} +(-4.87540 + 4.17699i) q^{29} +(0.0845359 + 0.0523424i) q^{30} -0.335442i q^{31} +(4.74685 - 3.36023i) q^{32} +(0.0276370 - 0.223191i) q^{33} +(-0.00668237 + 0.216892i) q^{34} +(0.0781580 + 1.26720i) q^{35} +(-4.34082 - 0.811441i) q^{36} +(-1.75221 + 0.0539851i) q^{37} +(1.53636 + 0.887016i) q^{38} +(0.388937 - 1.22260i) q^{39} +(0.107488 - 1.15998i) q^{40} +(-0.632865 - 1.79594i) q^{41} +(-0.232058 - 0.504394i) q^{42} +(-4.34384 + 3.28031i) q^{43} +(-1.07219 + 0.377825i) q^{44} +(-1.08097 + 0.869854i) q^{45} +(0.144441 - 4.68818i) q^{46} +(-0.0436263 + 0.0812425i) q^{47} +(-0.109958 - 0.386462i) q^{48} +(0.0447758 - 0.0775540i) q^{49} +(2.30757 + 2.37976i) q^{50} +(0.0874647 + 0.0338840i) q^{51} +(-6.40849 + 0.994781i) q^{52} +(-1.69990 - 2.94431i) q^{53} +(0.616169 - 1.06724i) q^{54} +(-0.129029 + 0.333062i) q^{55} +(-4.07825 + 5.06805i) q^{56} +(0.582347 - 0.498925i) q^{57} +(-3.00402 + 3.29526i) q^{58} +(-5.90951 - 1.68140i) q^{59} +(-0.197367 - 0.0908033i) q^{60} +(-6.85384 - 7.51830i) q^{61} +(-0.0286306 - 0.231215i) q^{62} +(7.71481 - 0.714883i) q^{63} +(1.00707 - 0.918064i) q^{64} +(-1.07268 + 1.73243i) q^{65} -0.156201i q^{66} +(-0.634132 - 0.895812i) q^{67} +(-0.0437480 - 0.472116i) q^{68} +(-1.89057 - 0.732412i) q^{69} +(0.162031 + 0.866787i) q^{70} +(-5.52319 - 0.340659i) q^{71} +(-7.09574 - 0.437650i) q^{72} +(-3.27817 - 3.17872i) q^{73} +(-1.20316 + 0.186766i) q^{74} +(1.30172 - 0.598885i) q^{75} +(-3.56970 - 1.51092i) q^{76} +(1.62793 - 1.15239i) q^{77} +(0.163737 - 0.875915i) q^{78} +(7.44673 + 3.70803i) q^{79} +(0.0196517 + 0.637842i) q^{80} +(5.33305 + 6.22476i) q^{81} +(-0.589511 - 1.18390i) q^{82} +(-1.18102 + 0.457530i) q^{83} +(0.638645 + 1.03145i) q^{84} +(-0.121591 - 0.0860724i) q^{85} +(-2.71416 + 2.63182i) q^{86} +(0.911872 + 1.69812i) q^{87} +(-1.63826 + 0.815756i) q^{88} +(2.58322 + 9.07906i) q^{89} +(-0.670852 + 0.691839i) q^{90} +(10.3368 - 4.75568i) q^{91} +(0.945625 + 10.2049i) q^{92} +(-0.0983771 - 0.0215449i) q^{93} +(-0.0231367 + 0.0597228i) q^{94} +(-1.09023 + 0.542872i) q^{95} +(-0.680592 - 1.60796i) q^{96} +(0.302048 + 4.89718i) q^{97} +(0.0242439 - 0.0572784i) q^{98} +(2.05582 + 0.724445i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1056 q - 33 q^{2} - 31 q^{3} + 29 q^{4} - 22 q^{5} - 44 q^{6} - 57 q^{7} - 22 q^{8} + 2 q^{9} - 30 q^{10} + 17 q^{11} + 67 q^{12} - 34 q^{13} - 68 q^{14} - 32 q^{15} + 21 q^{16} - 27 q^{17} + 22 q^{18}+ \cdots - 229 q^{99}+O(q^{100}) $ 1056 * q - 33 * q^2 - 31 * q^3 + 29 * q^4 - 22 * q^5 - 44 * q^6 - 57 * q^7 - 22 * q^8 + 2 * q^9 - 30 * q^10 + 17 * q^11 + 67 * q^12 - 34 * q^13 - 68 * q^14 - 32 * q^15 + 21 * q^16 - 27 * q^17 + 22 * q^18 - 34 * q^19 - 51 * q^20 - 108 * q^21 - 22 * q^22 - 32 * q^23 + 87 * q^24 - 112 * q^25 - 64 * q^26 - 82 * q^27 - 75 * q^28 - 19 * q^29 - 22 * q^30 + 52 * q^32 - 43 * q^33 - 48 * q^34 - 113 * q^35 + 22 * q^36 - 10 * q^37 - 57 * q^38 + 41 * q^39 - 225 * q^40 - 288 * q^41 - 173 * q^42 + 68 * q^43 - 34 * q^44 - 42 * q^45 + 17 * q^46 - 34 * q^47 + 68 * q^48 + 369 * q^49 - 40 * q^50 + 56 * q^51 + 8 * q^52 + 104 * q^53 + 128 * q^54 + 102 * q^55 - 138 * q^56 - 55 * q^57 - 34 * q^58 - 34 * q^59 - 254 * q^60 - 68 * q^61 + 25 * q^62 - 34 * q^63 + 98 * q^64 - 34 * q^65 - 40 * q^67 - 116 * q^68 - 38 * q^69 - 17 * q^70 + 21 * q^71 - 26 * q^72 - 31 * q^73 + 203 * q^74 + 23 * q^75 - 101 * q^76 + 19 * q^77 - 102 * q^78 - 34 * q^79 + 443 * q^80 - 265 * q^81 - 50 * q^82 + 26 * q^83 - 459 * q^84 + 84 * q^85 + 136 * q^86 - 188 * q^87 + 170 * q^88 - 80 * q^89 + 613 * q^90 - 152 * q^91 + 18 * q^92 + 56 * q^93 - 34 * q^94 - 34 * q^95 + 13 * q^96 - 31 * q^97 - 293 * q^98 - 229 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/409\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{41}{102}\right)$

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 $

$2$	0.689284	−	0.0853519i	0.487398	−	0.0603529i	0.124573	−	0.992210i	$-0.460244\pi$
$2$	0.689284	−	0.0853519i	0.487398	−	0.0603529i	0.362824	+	0.931858i	$0.381812\pi$
$3$	0.0642285	−	0.293276i	0.0370823	−	0.169323i	−0.954632	−	0.297790i	$-0.903751\pi$
$3$	0.0642285	−	0.293276i	0.0370823	−	0.169323i	0.991714	+	0.128467i	$0.0410055\pi$
$4$	−1.47177	+	0.370164i	−0.735883	+	0.185082i
$5$	−0.212539	+	0.426836i	−0.0950504	+	0.190887i	−0.937586	−	0.347754i	$-0.886944\pi$
$5$	−0.212539	+	0.426836i	−0.0950504	+	0.190887i	0.842535	+	0.538641i	$0.181062\pi$
$6$	0.0192400	−	0.207633i	0.00785470	−	0.0847657i
$7$	2.30590	−	1.33131i	0.871547	−	0.503188i	0.00368523	−	0.999993i	$-0.498827\pi$
$7$	2.30590	−	1.33131i	0.871547	−	0.503188i	0.867862	+	0.496805i	$0.165494\pi$
$8$	−2.27817	+	0.882566i	−0.805453	+	0.312034i
$9$	2.64351	+	1.21621i	0.881170	+	0.405403i
$10$	−0.110069	+	0.312352i	−0.0348067	+	0.0987744i
$11$	0.745889	−	0.0691168i	0.224894	−	0.0208395i	0.0207688	−	0.999784i	$-0.493389\pi$
$11$	0.745889	−	0.0691168i	0.224894	−	0.0208395i	0.204125	+	0.978945i	$0.434565\pi$
$12$	0.0140310	+	0.455409i	0.00405040	+	0.131465i
$13$	4.25511	+	0.394294i	1.18016	+	0.109358i	0.664400	−	0.747377i	$-0.268687\pi$
$13$	4.25511	+	0.394294i	1.18016	+	0.109358i	0.515757	+	0.856735i	$0.327511\pi$
$14$	1.47579	−	1.11446i	0.394421	−	0.297853i
$15$	0.111530	+	0.0897477i	0.0287969	+	0.0231728i
$16$	1.17908	−	0.633151i	0.294769	−	0.158288i
$17$	−0.0479235	+	0.308729i	−0.0116232	+	0.0748777i	−0.993268	−	0.115843i	$-0.963043\pi$
$17$	−0.0479235	+	0.308729i	−0.0116232	+	0.0748777i	0.981644	+	0.190720i	$0.0610824\pi$
$18$	1.92594	+	0.612684i	0.453947	+	0.144411i
$19$	2.03831	+	1.53926i	0.467621	+	0.353131i	0.809999	−	0.586431i	$-0.199468\pi$
$19$	2.03831	+	1.53926i	0.467621	+	0.353131i	−0.342378	+	0.939562i	$0.611232\pi$
$20$	0.154808	−	0.706877i	0.0346162	−	0.158063i
$21$	−0.242337	−	0.761773i	−0.0528824	−	0.166233i
$22$	0.508230	−	0.111304i	0.108355	−	0.0237301i
$23$	1.03588	−	6.67325i	0.215996	−	1.39147i	−0.593731	−	0.804663i	$-0.702346\pi$
$23$	1.03588	−	6.67325i	0.215996	−	1.39147i	0.809727	−	0.586806i	$-0.199615\pi$
$24$	0.112513	+	0.724818i	0.0229665	+	0.147953i
$25$	2.87616	+	3.80865i	0.575231	+	0.761729i
$26$	2.96664	−	0.0914011i	0.581805	−	0.0179252i
$27$	1.06926	−	1.41592i	0.205778	−	0.272494i
$28$	−2.90094	+	2.81294i	−0.548226	+	0.531595i
$29$	−4.87540	+	4.17699i	−0.905339	+	0.775647i	−0.975065	−	0.221919i	$-0.928768\pi$
$29$	−4.87540	+	4.17699i	−0.905339	+	0.775647i	0.0697258	+	0.997566i	$0.477788\pi$
$30$	0.0845359	+	0.0523424i	0.0154341	+	0.00955637i
$31$		−	0.335442i		−	0.0602471i	−0.999546	−	0.0301235i	$-0.990410\pi$
$31$		−	0.335442i		−	0.0602471i	0.999546	−	0.0301235i	$-0.00959007\pi$
$32$	4.74685	−	3.36023i	0.839133	−	0.594010i
$33$	0.0276370	−	0.223191i	0.00481098	−	0.0388525i
$34$	−0.00668237	+	0.216892i	−0.00114602	+	0.0371967i
$35$	0.0781580	+	1.26720i	0.0132111	+	0.214195i
$36$	−4.34082	−	0.811441i	−0.723471	−	0.135240i
$37$	−1.75221	+	0.0539851i	−0.288062	+	0.00887509i	−0.174505	−	0.984656i	$-0.555832\pi$
$37$	−1.75221	+	0.0539851i	−0.288062	+	0.00887509i	−0.113557	+	0.993531i	$0.536225\pi$
$38$	1.53636	+	0.887016i	0.249230	+	0.143893i
$39$	0.388937	−	1.22260i	0.0622797	−	0.195773i
$40$	0.107488	−	1.15998i	0.0169954	−	0.183409i
$41$	−0.632865	−	1.79594i	−0.0988369	−	0.280479i	0.883251	−	0.468900i	$-0.155349\pi$
$41$	−0.632865	−	1.79594i	−0.0988369	−	0.280479i	−0.982088	+	0.188421i	$0.939663\pi$
$42$	−0.232058	−	0.504394i	−0.0358074	−	0.0778297i
$43$	−4.34384	+	3.28031i	−0.662429	+	0.500243i	−0.879491	−	0.475915i	$-0.842117\pi$
$43$	−4.34384	+	3.28031i	−0.662429	+	0.500243i	0.217063	+	0.976158i	$0.430352\pi$
$44$	−1.07219	+	0.377825i	−0.161639	+	0.0569592i
$45$	−1.08097	+	0.869854i	−0.161142	+	0.129670i
$46$	0.144441	−	4.68818i	0.0212967	−	0.691235i
$47$	−0.0436263	+	0.0812425i	−0.00636355	+	0.0118504i	−0.884174	−	0.467158i	$-0.845278\pi$
$47$	−0.0436263	+	0.0812425i	−0.00636355	+	0.0118504i	0.877810	+	0.479008i	$0.159004\pi$
$48$	−0.109958	−	0.386462i	−0.0158710	−	0.0557809i
$49$	0.0447758	−	0.0775540i	0.00639654	−	0.0110791i
$50$	2.30757	+	2.37976i	0.326339	+	0.336548i
$51$	0.0874647	+	0.0338840i	0.0122475	+	0.00474471i
$52$	−6.40849	+	0.994781i	−0.888697	+	0.137951i
$53$	−1.69990	−	2.94431i	−0.233499	−	0.404432i	0.725337	−	0.688394i	$-0.241684\pi$
$53$	−1.69990	−	2.94431i	−0.233499	−	0.404432i	−0.958835	+	0.283963i	$0.908351\pi$
$54$	0.616169	−	1.06724i	0.0838500	−	0.145232i
$55$	−0.129029	+	0.333062i	−0.0173983	+	0.0449101i
$56$	−4.07825	+	5.06805i	−0.544979	+	0.677247i
$57$	0.582347	−	0.498925i	0.0771338	−	0.0660842i
$58$	−3.00402	+	3.29526i	−0.394448	+	0.432688i
$59$	−5.90951	−	1.68140i	−0.769353	−	0.218900i	−0.133854	−	0.991001i	$-0.542735\pi$
$59$	−5.90951	−	1.68140i	−0.769353	−	0.218900i	−0.635500	+	0.772101i	$0.719206\pi$
$60$	−0.197367	−	0.0908033i	−0.0254800	−	0.0117227i
$61$	−6.85384	−	7.51830i	−0.877544	−	0.962620i	0.122009	−	0.992529i	$-0.461066\pi$
$61$	−6.85384	−	7.51830i	−0.877544	−	0.962620i	−0.999553	+	0.0299092i	$0.990478\pi$
$62$	−0.0286306	−	0.231215i	−0.00363609	−	0.0293643i
$63$	7.71481	−	0.714883i	0.971975	−	0.0900668i
$64$	1.00707	−	0.918064i	0.125883	−	0.114758i
$65$	−1.07268	+	1.73243i	−0.133049	+	0.214882i
$66$		−	0.156201i		−	0.0192270i
$67$	−0.634132	−	0.895812i	−0.0774716	−	0.109441i	0.775625	−	0.631194i	$-0.217435\pi$
$67$	−0.634132	−	0.895812i	−0.0774716	−	0.109441i	−0.853096	+	0.521753i	$0.825278\pi$
$68$	−0.0437480	−	0.472116i	−0.00530522	−	0.0572525i
$69$	−1.89057	−	0.732412i	−0.227598	−	0.0881721i
$70$	0.162031	+	0.866787i	0.0193664	+	0.103601i
$71$	−5.52319	−	0.340659i	−0.655482	−	0.0404288i	−0.269594	−	0.962974i	$-0.586889\pi$
$71$	−5.52319	−	0.340659i	−0.655482	−	0.0404288i	−0.385888	+	0.922545i	$0.626105\pi$
$72$	−7.09574	−	0.437650i	−0.836241	−	0.0515776i
$73$	−3.27817	−	3.17872i	−0.383681	−	0.372042i	0.478979	−	0.877826i	$-0.341007\pi$
$73$	−3.27817	−	3.17872i	−0.383681	−	0.372042i	−0.862660	+	0.505785i	$0.831203\pi$
$74$	−1.20316	+	0.186766i	−0.139865	+	0.0217111i
$75$	1.30172	−	0.598885i	0.150309	−	0.0691533i
$76$	−3.56970	−	1.51092i	−0.409473	−	0.173315i
$77$	1.62793	−	1.15239i	0.185520	−	0.131327i
$78$	0.163737	−	0.875915i	0.0185395	−	0.0991778i
$79$	7.44673	+	3.70803i	0.837822	+	0.417186i	0.812829	−	0.582502i	$-0.197926\pi$
$79$	7.44673	+	3.70803i	0.837822	+	0.417186i	0.0249927	+	0.999688i	$0.492044\pi$
$80$	0.0196517	+	0.637842i	0.00219713	+	0.0713129i
$81$	5.33305	+	6.22476i	0.592561	+	0.691641i
$82$	−0.589511	−	1.18390i	−0.0651006	−	0.130740i
$83$	−1.18102	+	0.457530i	−0.129634	+	0.0502204i	−0.425185	−	0.905107i	$-0.639791\pi$
$83$	−1.18102	+	0.457530i	−0.129634	+	0.0502204i	0.295551	+	0.955327i	$0.404497\pi$
$84$	0.638645	+	1.03145i	0.0696819	+	0.112540i
$85$	−0.121591	−	0.0860724i	−0.0131884	−	0.00933586i
$86$	−2.71416	+	2.63182i	−0.292675	+	0.283797i
$87$	0.911872	+	1.69812i	0.0977629	+	0.182058i
$88$	−1.63826	+	0.815756i	−0.174639	+	0.0869598i
$89$	2.58322	+	9.07906i	0.273820	+	0.962379i	0.969716	+	0.244236i	$0.0785371\pi$
$89$	2.58322	+	9.07906i	0.273820	+	0.962379i	−0.695895	+	0.718143i	$0.744992\pi$
$90$	−0.670852	+	0.691839i	−0.0707141	+	0.0729263i
$91$	10.3368	−	4.75568i	1.08359	−	0.498530i
$92$	0.945625	+	10.2049i	0.0985882	+	1.06394i
$93$	−0.0983771	−	0.0215449i	−0.0102012	−	0.00223410i
$94$	−0.0231367	+	0.0597228i	−0.00238637	+	0.00615993i
$95$	−1.09023	+	0.542872i	−0.111856	+	0.0556975i
$96$	−0.680592	−	1.60796i	−0.0694626	−	0.164112i
$97$	0.302048	+	4.89718i	0.0306683	+	0.497233i	0.981978	+	0.188996i	$0.0605233\pi$
$97$	0.302048	+	4.89718i	0.0306683	+	0.497233i	−0.951310	+	0.308237i	$0.900261\pi$
$98$	0.0242439	−	0.0572784i	0.00244900	−	0.00578599i
$99$	2.05582	+	0.724445i	0.206618	+	0.0728094i
$100$	−5.64285	−	4.54079i	−0.564285	−	0.454079i
$101$	2.87398	−	3.35453i	0.285972	−	0.333788i	−0.597853	−	0.801606i	$-0.703979\pi$
$101$	2.87398	−	3.35453i	0.285972	−	0.333788i	0.883825	+	0.467818i	$0.154960\pi$
$102$	0.0631801	+	0.0158904i	0.00625576	+	0.00157339i
$103$	0.302111	−	0.606721i	0.0297679	−	0.0597820i	−0.879780	−	0.475381i	$-0.842310\pi$
$103$	0.302111	−	0.606721i	0.0297679	−	0.0597820i	0.909548	+	0.415599i	$0.136428\pi$
$104$	−10.0418	+	2.85715i	−0.984684	+	0.280167i
$105$	0.376658	+	0.0584682i	0.0367581	+	0.00570591i
$106$	−1.42301	−	1.88437i	−0.138215	−	0.183027i
$107$	−8.22638	−	10.2230i	−0.795274	−	0.988290i	−0.999955	−	0.00946145i	$-0.996988\pi$
$107$	−8.22638	−	10.2230i	−0.795274	−	0.988290i	0.204681	−	0.978829i	$-0.434384\pi$
$108$	−1.04957	+	2.47971i	−0.100995	+	0.238610i
$109$	3.17054	−	2.55133i	0.303683	−	0.244373i	−0.463060	−	0.886327i	$-0.653249\pi$
$109$	3.17054	−	2.55133i	0.303683	−	0.244373i	0.766743	+	0.641954i	$0.221876\pi$
$110$	−0.0605102	+	0.240587i	−0.00576942	+	0.0229391i
$111$	−0.0967094	+	0.517350i	−0.00917925	+	0.0491047i
$112$	1.87591	−	3.02970i	0.177257	−	0.286280i
$113$	7.29843	−	3.08916i	0.686578	−	0.290604i	−0.0184018	−	0.999831i	$-0.505858\pi$
$113$	7.29843	−	3.08916i	0.686578	−	0.290604i	0.704980	+	0.709227i	$0.250956\pi$
$114$	0.358819	−	0.393605i	0.0336064	−	0.0368645i
$115$	2.62822	+	1.86048i	0.245083	+	0.173491i
$116$	5.62928	−	7.95225i	0.522665	−	0.738348i
$117$	10.7689	+	6.21742i	0.995585	+	0.574801i
$118$	−4.21685	−	0.654576i	−0.388192	−	0.0602586i
$119$	0.300507	+	0.775698i	0.0275474	+	0.0711081i
$120$	−0.333292	−	0.106028i	−0.0304252	−	0.00967896i
$121$	−10.2611	+	1.91814i	−0.932830	+	0.174376i
$122$	−5.36594	−	4.59726i	−0.485810	−	0.416216i
$123$	−0.567355	+	0.0702537i	−0.0511566	+	0.00633456i
$124$	0.124168	+	0.493692i	0.0111507	+	0.0443348i
$125$	−4.58049	+	0.856243i	−0.409692	+	0.0765847i
$126$	5.25668	−	1.15123i	0.468303	−	0.102560i
$127$	−6.57784	−	4.35864i	−0.583689	−	0.386767i	0.225562	−	0.974229i	$-0.427578\pi$
$127$	−6.57784	−	4.35864i	−0.583689	−	0.386767i	−0.809252	+	0.587462i	$0.800127\pi$
$128$	−6.95196	+	8.11436i	−0.614472	+	0.717215i
$129$	0.683040	+	1.48463i	0.0601383	+	0.130715i
$130$	−0.591513	+	1.28569i	−0.0518791	+	0.112763i
$131$	−4.87709	−	5.69257i	−0.426114	−	0.497362i	0.504476	−	0.863426i	$-0.331686\pi$
$131$	−4.87709	−	5.69257i	−0.426114	−	0.497362i	−0.930590	+	0.366064i	$0.880705\pi$
$132$	0.0419420	+	0.338715i	0.00365058	+	0.0294813i
$133$	6.74938	+	0.835754i	0.585245	+	0.0724691i
$134$	−0.513557	−	0.563345i	−0.0443645	−	0.0486656i
$135$	0.377108	+	0.757336i	0.0324563	+	0.0651811i
$136$	−0.163296	−	0.745631i	−0.0140025	−	0.0639373i
$137$	−3.98797	−	11.3170i	−0.340716	−	0.966880i	−0.980189	−	0.198067i	$-0.936534\pi$
$137$	−3.98797	−	11.3170i	−0.340716	−	0.966880i	0.639473	−	0.768814i	$-0.279153\pi$
$138$	−1.36566	−	0.343476i	−0.116252	−	0.0292386i
$139$	10.3905	+	15.6808i	0.881311	+	1.33003i	0.943295	+	0.331955i	$0.107708\pi$
$139$	10.3905	+	15.6808i	0.881311	+	1.33003i	−0.0619838	+	0.998077i	$0.519743\pi$
$140$	−0.584101	−	1.83608i	−0.0493655	−	0.155177i
$141$	0.0210244	+	0.0180126i	0.00177058	+	0.00151694i
$142$	−3.83612	+	0.236604i	−0.321920	+	0.0198554i
$143$	3.20109			0.267689
$144$	3.88695	−	0.239739i	0.323912	−	0.0199782i
$145$	−0.746676	−	2.96877i	−0.0620080	−	0.246543i
$146$	−2.53090	−	1.91125i	−0.209459	−	0.158176i
$147$	−0.0198689	−	0.0181129i	−0.00163876	−	0.00149392i
$148$	2.55886	−	0.728059i	0.210337	−	0.0598461i
$149$	−4.31387	+	13.5604i	−0.353406	+	1.11091i	0.597615	+	0.801783i	$0.296115\pi$
$149$	−4.31387	+	13.5604i	−0.353406	+	1.11091i	−0.951021	+	0.309126i	$0.899963\pi$
$150$	0.846137	−	0.523906i	0.0690868	−	0.0427767i
$151$	−12.8657	−	20.7788i	−1.04700	−	1.69096i	−0.613134	−	0.789979i	$-0.710092\pi$
$151$	−12.8657	−	20.7788i	−1.04700	−	1.69096i	−0.433863	−	0.900979i	$-0.642850\pi$
$152$	−6.00212	−	1.70775i	−0.486836	−	0.138517i
$153$	−0.502164	+	0.757842i	−0.0405976	+	0.0612679i
$154$	1.02375	−	0.933268i	0.0824958	−	0.0752049i
$155$	0.143179	+	0.0712945i	0.0115004	+	0.00572651i
$156$	−0.119862	+	1.94335i	−0.00959662	+	0.155593i
$157$	−1.01273	+	0.356871i	−0.0808243	+	0.0284814i	−0.372462	−	0.928048i	$-0.621486\pi$
$157$	−1.01273	+	0.356871i	−0.0808243	+	0.0284814i	0.291637	+	0.956529i	$0.405800\pi$
$158$	5.44940	+	1.92029i	0.433531	+	0.152770i
$159$	−0.972677	+	0.309431i	−0.0771383	+	0.0245395i
$160$	0.425375	+	2.74031i	0.0336288	+	0.216640i
$161$	−6.49554	−	16.7669i	−0.511920	−	1.32142i
$162$	4.20728	+	3.83545i	0.330555	+	0.301341i
$163$	10.4756	−	2.63472i	0.820513	−	0.206367i	0.189243	−	0.981930i	$-0.439397\pi$
$163$	10.4756	−	2.63472i	0.820513	−	0.206367i	0.631270	+	0.775563i	$0.282534\pi$
$164$	1.59622	+	2.40894i	0.124644	+	0.188107i
$165$	0.0893919	+	0.0592332i	0.00695915	+	0.00461130i
$166$	−0.775008	+	0.416170i	−0.0601523	+	0.0323011i
$167$	7.32129	−	2.32907i	0.566539	−	0.180229i	−0.00618003	−	0.999981i	$-0.501967\pi$
$167$	7.32129	−	2.32907i	0.566539	−	0.180229i	0.572719	+	0.819752i	$0.305889\pi$
$168$	1.22440	+	1.52157i	0.0944645	+	0.117391i
$169$	5.17188	+	0.966792i	0.397837	+	0.0743686i
$170$	−0.0911571	−	0.0489503i	−0.00699143	−	0.00375432i
$171$	3.51624	+	6.54807i	0.268894	+	0.500743i
$172$	5.17886	−	6.43578i	0.394884	−	0.490724i
$173$	−3.11586	−	0.0959987i	−0.236895	−	0.00729865i	−0.0878693	−	0.996132i	$-0.528006\pi$
$173$	−3.11586	−	0.0959987i	−0.236895	−	0.00729865i	−0.149025	+	0.988833i	$0.547614\pi$
$174$	0.773477	+	1.09266i	0.0586371	+	0.0828342i
$175$	11.7026	+	4.95329i	0.884635	+	0.374434i
$176$	0.835699	−	0.553754i	0.0629932	−	0.0417408i
$177$	−0.872675	+	1.62513i	−0.0655942	+	0.122152i
$178$	2.55549	+	6.03757i	0.191542	+	0.452535i
$179$	−1.86172	−	0.999721i	−0.139151	−	0.0747227i	0.402040	−	0.915622i	$-0.368301\pi$
$179$	−1.86172	−	0.999721i	−0.139151	−	0.0747227i	−0.541192	+	0.840899i	$0.682027\pi$
$180$	1.26895	−	1.68036i	0.0945817	−	0.125246i
$181$	−13.0233	+	18.3975i	−0.968018	+	1.36748i	−0.0382753	+	0.999267i	$0.512186\pi$
$181$	−13.0233	+	18.3975i	−0.968018	+	1.36748i	−0.929742	+	0.368211i	$0.879970\pi$
$182$	6.71908	−	4.16028i	0.498051	−	0.308380i
$183$	−2.64515	+	1.52718i	−0.195535	+	0.112892i
$184$	3.52968	+	16.1170i	0.260211	+	1.18816i
$185$	0.349371	−	0.759381i	0.0256863	−	0.0558308i
$186$	−0.0696487	−	0.00645390i	−0.00510689	−	0.000473223i
$187$	−0.0144073	+	0.233590i	−0.00105357	+	0.0170818i
$188$	0.0341347	−	0.135719i	0.00248953	−	0.00989832i
$189$	0.580560	−	4.68848i	0.0422295	−	0.341037i
$190$	−0.705146	+	0.467247i	−0.0511567	+	0.0338977i
$191$	−2.95670	+	3.04920i	−0.213939	+	0.220632i	−0.816355	−	0.577550i	$-0.804009\pi$
$191$	−2.95670	+	3.04920i	−0.213939	+	0.220632i	0.602416	+	0.798182i	$0.294205\pi$
$192$	−0.204564	−	0.354315i	−0.0147631	−	0.0255705i
$193$	0.0424202	−	0.149091i	0.00305347	−	0.0107318i	−0.960284	−	0.279025i	$-0.909989\pi$
$193$	0.0424202	−	0.149091i	0.00305347	−	0.0107318i	0.963337	+	0.268293i	$0.0864595\pi$
$194$	0.626180	+	3.34977i	0.0449571	+	0.240499i
$195$	0.439185	+	0.425862i	0.0314507	+	0.0304966i
$196$	−0.0371918	+	0.130716i	−0.00265656	+	0.00933683i
$197$	−7.64893	−	7.88822i	−0.544963	−	0.562012i	0.388149	−	0.921597i	$-0.373115\pi$
$197$	−7.64893	−	7.88822i	−0.544963	−	0.562012i	−0.933113	+	0.359584i	$0.882918\pi$
$198$	1.47888	+	0.323880i	0.105099	+	0.0230171i
$199$	12.5197	+	0.385729i	0.887500	+	0.0273436i	0.471344	−	0.881950i	$-0.343769\pi$
$199$	12.5197	+	0.385729i	0.887500	+	0.0273436i	0.416156	+	0.909293i	$0.363377\pi$
$200$	−9.91374	−	6.13833i	−0.701008	−	0.434046i
$201$	−0.303450	+	0.128439i	−0.0214037	+	0.00905941i
$202$	1.69468	−	2.55752i	0.119237	−	0.179947i
$203$	−5.68131	+	16.1224i	−0.398750	+	1.13157i
$204$	−0.141270	−	0.0174930i	−0.00989089	−	0.00122476i
$205$	0.901081	+	0.111578i	0.0629342	+	0.00779294i
$206$	0.156456	−	0.443989i	0.0109008	−	0.0309342i
$207$	10.8544	−	16.3810i	0.754435	−	1.13856i
$208$	5.26676	−	2.22923i	0.365184	−	0.154569i
$209$	1.62674	+	1.00724i	0.112524	+	0.0696721i
$210$	0.264615	+	0.00815270i	0.0182602	+	0.000562590i
$211$	21.8716	+	4.78996i	1.50571	+	0.329755i	0.889172	−	0.457573i	$-0.151281\pi$
$211$	21.8716	+	4.78996i	1.50571	+	0.329755i	0.616534	+	0.787328i	$0.288536\pi$
$212$	3.59173	+	3.70409i	0.246681	+	0.254398i
$213$	−0.454653	+	1.59794i	−0.0311523	+	0.109489i
$214$	−6.54286	−	6.34438i	−0.447261	−	0.433693i
$215$	−0.476921	−	2.55130i	−0.0325257	−	0.173997i
$216$	−1.18629	+	4.16939i	−0.0807171	+	0.283691i
$217$	−0.446577	−	0.773494i	−0.0303156	−	0.0525082i
$218$	1.96764	−	2.02920i	0.133266	−	0.137435i
$219$	−1.14280	+	0.757244i	−0.0772230	+	0.0511698i
$220$	0.0666128	−	0.537952i	0.00449104	−	0.0362687i
$221$	−0.325650	+	1.29478i	−0.0219056	+	0.0870963i
$222$	−0.0225035	+	0.364855i	−0.00151034	+	0.0244875i
$223$	20.6132	+	1.91010i	1.38036	+	0.127910i	0.756689	−	0.653775i	$-0.226816\pi$
$223$	20.6132	+	1.91010i	1.38036	+	0.127910i	0.623674	+	0.781684i	$0.285639\pi$
$224$	6.47225	−	14.0679i	0.432446	−	0.939950i
$225$	2.97104	+	13.5662i	0.198070	+	0.904413i
$226$	4.76703	−	2.75224i	0.317098	−	0.183077i
$227$	8.03863	−	4.97731i	0.533543	−	0.330356i	−0.233076	−	0.972459i	$-0.574879\pi$
$227$	8.03863	−	4.97731i	0.533543	−	0.330356i	0.766618	+	0.642103i	$0.221938\pi$
$228$	−0.672395	+	0.949864i	−0.0445304	+	0.0629063i
$229$	−4.16315	+	5.51290i	−0.275109	+	0.364303i	−0.914505	−	0.404575i	$-0.867420\pi$
$229$	−4.16315	+	5.51290i	−0.275109	+	0.364303i	0.639396	+	0.768877i	$0.279184\pi$
$230$	1.97039	+	1.05808i	0.129923	+	0.0697674i
$231$	−0.233408	−	0.551448i	−0.0153571	−	0.0362826i
$232$	7.42050	−	13.8187i	0.487180	−	0.907244i
$233$	4.87678	−	3.23147i	0.319489	−	0.211701i	−0.382384	−	0.924004i	$-0.624897\pi$
$233$	4.87678	−	3.23147i	0.319489	−	0.211701i	0.701872	+	0.712303i	$0.252348\pi$
$234$	7.95350	+	3.36643i	0.519936	+	0.220070i
$235$	−0.0254049	−	0.0358885i	−0.00165724	−	0.00234111i
$236$	9.31982	+	0.287141i	0.606668	+	0.0186913i
$237$	1.56577	−	1.94579i	0.101708	−	0.126392i
$238$	0.273342	+	0.509027i	0.0177181	+	0.0329953i
$239$	−4.01941	−	2.15838i	−0.259994	−	0.139614i	0.337918	−	0.941176i	$-0.390277\pi$
$239$	−4.01941	−	2.15838i	−0.259994	−	0.139614i	−0.597912	+	0.801562i	$0.704003\pi$
$240$	0.188326	+	0.0352043i	0.0121564	+	0.00227243i
$241$	−8.79148	−	10.9252i	−0.566309	−	0.703754i	0.411935	−	0.911213i	$-0.364853\pi$
$241$	−8.79148	−	10.9252i	−0.566309	−	0.703754i	−0.978244	+	0.207459i	$0.933481\pi$
$242$	−6.90912	+	2.19795i	−0.444135	+	0.141290i
$243$	6.85765	−	3.68248i	0.439919	−	0.236231i
$244$	12.8702	+	8.52814i	0.823933	+	0.545958i
$245$	0.0235862	+	0.0355952i	0.00150687	+	0.00227409i
$246$	−0.385072	+	0.0968496i	−0.0245513	+	0.00617490i
$247$	8.06634	+	7.35344i	0.513249	+	0.467888i
$248$	0.296049	+	0.764192i	0.0187992	+	0.0485262i
$249$	0.0583274	+	0.375752i	0.00369635	+	0.0238123i
$250$	−3.08418	+	0.981148i	−0.195061	+	0.0620533i
$251$	−21.9686	−	7.74142i	−1.38664	−	0.488634i	−0.468002	−	0.883727i	$-0.655026\pi$
$251$	−21.9686	−	7.74142i	−1.38664	−	0.488634i	−0.918641	+	0.395093i	$0.870712\pi$
$252$	−11.0898	+	3.90789i	−0.698590	+	0.246174i
$253$	0.311418	−	5.04910i	0.0195787	−	0.317434i
$254$	−4.90602	−	2.44291i	−0.307831	−	0.153282i
$255$	−0.0330526	+	0.0301314i	−0.00206983	+	0.00188690i
$256$	−5.60475	+	8.45841i	−0.350297	+	0.528651i
$257$	−29.9807	−	8.53023i	−1.87014	−	0.532101i	−0.999169	−	0.0407710i	$-0.987019\pi$
$257$	−29.9807	−	8.53023i	−1.87014	−	0.532101i	−0.870973	−	0.491330i	$-0.836511\pi$
$258$	0.597525	+	0.965036i	0.0372003	+	0.0600805i
$259$	−3.96855	+	2.45722i	−0.246594	+	0.152684i
$260$	0.937446	−	2.94680i	0.0581379	−	0.182753i
$261$	−17.9683	+	5.11241i	−1.11221	+	0.316450i
$262$	−3.84758	−	3.50753i	−0.237704	−	0.216696i
$263$	13.4131	+	10.1291i	0.827088	+	0.624588i	0.928948	−	0.370211i	$-0.120715\pi$
$263$	13.4131	+	10.1291i	0.827088	+	0.624588i	−0.101860	+	0.994799i	$0.532479\pi$
$264$	0.134019	+	0.532857i	0.00824829	+	0.0327951i
$265$	1.61803	−	0.0997967i	0.0993948	−	0.00613046i
$266$	4.72357			0.289621
$267$	2.82859	−	0.174461i	0.173107	−	0.0106769i
$268$	1.26489	+	1.08369i	0.0772656	+	0.0661971i
$269$	−6.26972	−	19.7085i	−0.382271	−	1.20165i	−0.930804	−	0.365518i	$-0.880892\pi$
$269$	−6.26972	−	19.7085i	−0.382271	−	1.20165i	0.548533	−	0.836129i	$-0.315187\pi$
$270$	0.324575	+	0.489833i	0.0197530	+	0.0298103i
$271$	24.8616	+	6.25296i	1.51024	+	0.379840i	0.908169	−	0.418604i	$-0.137481\pi$
$271$	24.8616	+	6.25296i	1.51024	+	0.379840i	0.602069	+	0.798444i	$0.294343\pi$
$272$	0.138966	+	0.394358i	0.00842607	+	0.0239114i
$273$	−0.730811	−	3.33698i	−0.0442307	−	0.201963i
$274$	−3.71478	−	7.46028i	−0.224418	−	0.450692i
$275$	2.40853	+	2.64204i	0.145240	+	0.159321i
$276$	3.05360	+	0.378117i	0.183805	+	0.0227600i
$277$	0.954258	+	7.70639i	0.0573358	+	0.463032i	0.993706	+	0.112018i	$0.0357316\pi$
$277$	0.954258	+	7.70639i	0.0573358	+	0.463032i	−0.936370	+	0.351014i	$0.885837\pi$
$278$	8.50040	+	9.92171i	0.509820	+	0.595065i
$279$	0.407967	−	0.886743i	0.0244243	−	0.0530879i
$280$	−1.29644	−	2.81790i	−0.0774772	−	0.168402i
$281$	−6.10139	+	7.12157i	−0.363978	+	0.424837i	−0.911080	−	0.412229i	$-0.864750\pi$
$281$	−6.10139	+	7.12157i	−0.363978	+	0.424837i	0.547102	+	0.837066i	$0.315731\pi$
$282$	0.0160292	+	0.0106214i	0.000954527	+	0.000632493i
$283$	−17.1918	+	3.76507i	−1.02195	+	0.223810i	−0.693305	−	0.720644i	$-0.743846\pi$
$283$	−17.1918	+	3.76507i	−1.02195	+	0.223810i	−0.328643	+	0.944454i	$0.606591\pi$
$284$	8.25494	−	1.54312i	0.489841	−	0.0915671i
$285$	0.0891874	+	0.354608i	0.00528301	+	0.0210052i
$286$	2.20646	−	0.273219i	0.130471	−	0.0161558i
$287$	−3.85028	−	3.29871i	−0.227275	−	0.194717i
$288$	16.6351	−	3.10964i	0.980232	−	0.183237i
$289$	16.1070	+	5.12400i	0.947470	+	0.301412i
$290$	−0.768062	−	1.98260i	−0.0451022	−	0.116422i
$291$	1.45563	+	0.225955i	0.0853303	+	0.0132457i
$292$	6.00135	+	3.46488i	0.351202	+	0.202767i
$293$	−16.9946	+	24.0075i	−0.992834	+	1.40253i	−0.0788026	+	0.996890i	$0.525110\pi$
$293$	−16.9946	+	24.0075i	−0.992834	+	1.40253i	−0.914031	+	0.405644i	$0.867047\pi$
$294$	−0.0152413	−	0.0107891i	−0.000888888	−	0.000629231i
$295$	1.97369	−	2.16503i	0.114912	−	0.126053i
$296$	3.94418	−	1.66943i	0.229251	−	0.0970337i
$297$	0.699681	−	1.13002i	0.0405996	−	0.0655707i
$298$	−1.81608	+	9.71515i	−0.105203	+	0.562784i
$299$	7.03902	−	27.9870i	0.407077	−	1.61853i
$300$	−1.69414	+	1.36327i	−0.0978111	+	0.0787083i
$301$	−5.64933	+	13.3471i	−0.325622	+	0.769312i
$302$	−10.6416	−	13.2244i	−0.612358	−	0.760979i
$303$	−0.799211	−	1.05833i	−0.0459135	−	0.0607993i
$304$	3.37792	+	0.524349i	0.193737	+	0.0300735i
$305$	4.66579	−	1.32753i	0.267162	−	0.0760143i
$306$	−0.281451	+	0.565229i	−0.0160895	+	0.0323120i
$307$	−0.172137	−	0.0432942i	−0.00982438	−	0.00247093i	0.238998	−	0.971020i	$-0.423181\pi$
$307$	−0.172137	−	0.0432942i	−0.00982438	−	0.00247093i	−0.248823	+	0.968549i	$0.580044\pi$
$308$	−1.96936	+	2.29864i	−0.112214	+	0.130977i
$309$	−0.158533	−	0.127571i	−0.00901862	−	0.00725726i
$310$	0.104776	+	0.0369216i	0.00595087	+	0.00209701i
$311$	2.54179	−	6.00521i	0.144131	−	0.340524i	−0.832963	−	0.553328i	$-0.813358\pi$
$311$	2.54179	−	6.00521i	0.144131	−	0.340524i	0.977095	+	0.212804i	$0.0682596\pi$
$312$	0.192962	+	3.12855i	0.0109243	+	0.177119i
$313$	−0.869844	−	2.05509i	−0.0491665	−	0.116160i	0.894489	−	0.447090i	$-0.147540\pi$
$313$	−0.869844	−	2.05509i	−0.0491665	−	0.116160i	−0.943655	+	0.330930i	$0.892638\pi$
$314$	−0.667596	+	0.332423i	−0.0376746	+	0.0187597i
$315$	−1.33456	+	3.44490i	−0.0751940	+	0.194098i
$316$	−12.3324	−	2.70084i	−0.693753	−	0.151934i
$317$	−0.715478	−	7.72124i	−0.0401853	−	0.433668i	−0.991931	−	0.126780i	$-0.959536\pi$
$317$	−0.715478	−	7.72124i	−0.0401853	−	0.433668i	0.951746	−	0.306888i	$-0.0992878\pi$
$318$	−0.644040	+	0.296306i	−0.0361160	+	0.0166160i
$319$	−3.34781	+	3.45254i	−0.187441	+	0.193305i
$320$	0.177821	+	0.624977i	0.00994052	+	0.0349373i
$321$	−3.52652	+	1.75600i	−0.196831	+	0.0980102i
$322$	−5.90836	−	11.0028i	−0.329260	−	0.613160i
$323$	−0.572898	+	0.555519i	−0.0318769	+	0.0309099i
$324$	−10.1532	−	7.18729i	−0.564066	−	0.399294i
$325$	10.7366	+	17.3403i	0.595562	+	0.961866i
$326$	6.99580	−	2.71019i	0.387461	−	0.150103i
$327$	−0.544604	−	1.09371i	−0.0301167	−	0.0604824i
$328$	3.02681	+	3.53290i	0.167127	+	0.195072i
$329$	0.00756122	+	0.245417i	0.000416864	+	0.0135303i
$330$	0.0666721	+	0.0331988i	0.00367018	+	0.00182753i
$331$	−0.430081	+	2.30073i	−0.0236394	+	0.126459i	−0.992757	−	0.120139i	$-0.961666\pi$
$331$	−0.430081	+	2.30073i	−0.0236394	+	0.126459i	0.969118	+	0.246599i	$0.0793129\pi$
$332$	1.56882	−	1.11055i	0.0861004	−	0.0609492i
$333$	−4.69765	−	1.98834i	−0.257430	−	0.108961i
$334$	4.84766	−	2.23028i	0.265252	−	0.122035i
$335$	0.517143	−	0.0802754i	0.0282545	−	0.00438591i
$336$	−0.768052	−	0.744753i	−0.0419007	−	0.0406296i
$337$	3.98429	+	0.245742i	0.217038	+	0.0133864i	0.169715	−	0.985493i	$-0.445715\pi$
$337$	3.98429	+	0.245742i	0.217038	+	0.0133864i	0.0473230	+	0.998880i	$0.484931\pi$
$338$	3.64741	+	0.224965i	0.198393	+	0.0122365i
$339$	−0.437210	−	2.33887i	−0.0237460	−	0.127030i
$340$	0.210814	+	0.0816699i	0.0114330	+	0.00442917i
$341$	−0.0231846	−	0.250202i	−0.00125552	−	0.0135492i
$342$	2.98258	+	4.21336i	0.161279	+	0.227833i
$343$			18.3999i			0.993502i
$344$	7.00088	−	11.3068i	0.377462	−	0.609623i
$345$	0.714441	−	0.651299i	0.0384642	−	0.0350648i
$346$	−2.15591	+	0.199774i	−0.115902	+	0.0107399i
$347$	2.58110	+	20.8444i	0.138561	+	1.11899i	0.888954	+	0.457996i	$0.151433\pi$
$347$	2.58110	+	20.8444i	0.138561	+	1.11899i	−0.750394	+	0.660991i	$0.770136\pi$
$348$	−1.97065	−	2.16169i	−0.105638	−	0.115879i
$349$	−16.5156	−	7.59840i	−0.884061	−	0.406733i	−0.0768829	−	0.997040i	$-0.524497\pi$
$349$	−16.5156	−	7.59840i	−0.884061	−	0.406733i	−0.807179	+	0.590307i	$0.799007\pi$
$350$	8.48920	+	2.41539i	0.453767	+	0.129108i
$351$	5.10809	−	5.60331i	0.272650	−	0.299083i
$352$	3.30838	−	2.83444i	0.176337	−	0.151076i
$353$	−16.7973	+	20.8740i	−0.894028	+	1.11101i	0.0992278	+	0.995065i	$0.468363\pi$
$353$	−16.7973	+	20.8740i	−0.894028	+	1.11101i	−0.993255	+	0.115947i	$0.963010\pi$
$354$	−0.462813	+	1.19466i	−0.0245982	+	0.0634954i
$355$	1.31930	−	2.28509i	0.0700211	−	0.121280i
$356$	−7.16263	−	12.4060i	−0.379619	−	0.657519i
$357$	0.246795	−	0.0383096i	0.0130618	−	0.00202756i
$358$	−1.36858	−	0.530191i	−0.0723318	−	0.0280215i
$359$	−22.8985	−	23.6149i	−1.20854	−	1.24635i	−0.960713	−	0.277543i	$-0.910480\pi$
$359$	−22.8985	−	23.6149i	−1.20854	−	1.24635i	−0.247826	−	0.968805i	$-0.579716\pi$
$360$	1.69493	−	2.93570i	0.0893305	−	0.154725i
$361$	−3.41420	−	11.9997i	−0.179695	−	0.631562i
$362$	−7.40652	+	13.7927i	−0.389278	+	0.724928i
$363$	−0.0965127	+	3.13255i	−0.00506560	+	0.164416i
$364$	−13.4530	+	10.8255i	−0.705126	+	0.567413i
$365$	2.05353	−	0.723637i	0.107487	−	0.0378769i
$366$	−1.69291	+	1.27843i	−0.0884900	+	0.0668245i
$367$	−12.0432	−	26.1767i	−0.628648	−	1.36641i	−0.913106	−	0.407722i	$-0.866323\pi$
$367$	−12.0432	−	26.1767i	−0.628648	−	1.36641i	0.284458	−	0.958689i	$-0.408186\pi$
$368$	−3.00379	−	8.52415i	−0.156584	−	0.444352i
$369$	0.511251	−	5.51728i	0.0266147	−	0.287218i
$370$	0.176001	−	0.553249i	0.00914987	−	0.0287621i
$371$	−7.83957	−	4.52618i	−0.407010	−	0.234988i
$372$	0.152763	−	0.00470658i	0.00792040	−	0.000244025i
$373$	3.79949	+	0.710247i	0.196730	+	0.0367752i	0.281192	−	0.959651i	$-0.409270\pi$
$373$	3.79949	+	0.710247i	0.196730	+	0.0367752i	−0.0844622	+	0.996427i	$0.526917\pi$
$374$	0.0100066	+	0.162239i	0.000517428	+	0.00838919i
$375$	−0.0430826	+	1.39835i	−0.00222477	+	0.0722102i
$376$	0.0276861	−	0.223587i	0.00142780	−	0.0115306i
$377$	−22.3924	+	15.8512i	−1.15326	+	0.816379i
$378$		−	3.28125i		−	0.168769i
$379$	−23.7843	−	14.7266i	−1.22172	−	0.756456i	−0.244697	−	0.969600i	$-0.578689\pi$
$379$	−23.7843	−	14.7266i	−1.22172	−	0.756456i	−0.977021	+	0.213144i	$0.931630\pi$
$380$	1.40362	−	1.20255i	0.0720041	−	0.0616893i
$381$	−1.70077	+	1.64918i	−0.0871331	+	0.0844899i
$382$	−1.77775	+	2.35412i	−0.0909577	+	0.120447i
$383$	14.8383	−	0.457162i	0.758200	−	0.0233599i	0.350606	−	0.936523i	$-0.385976\pi$
$383$	14.8383	−	0.457162i	0.758200	−	0.0233599i	0.407594	+	0.913163i	$0.366368\pi$
$384$	1.93324	+	2.56002i	0.0986550	+	0.130640i
$385$	0.145882	+	0.939785i	0.00743482	+	0.0478959i
$386$	0.0165143	−	0.106387i	0.000840557	−	0.00541496i
$387$	−15.4725	+	3.38853i	−0.786512	+	0.172249i
$388$	−2.25730	−	7.09569i	−0.114597	−	0.360229i
$389$	1.53072	−	6.98948i	0.0776106	−	0.354381i	−0.921838	−	0.387575i	$-0.873313\pi$
$389$	1.53072	−	6.98948i	0.0776106	−	0.354381i	0.999449	+	0.0331937i	$0.0105678\pi$
$390$	0.339072	+	0.256055i	0.0171696	+	0.0129658i
$391$	2.01058	+	0.639612i	0.101679	+	0.0323466i
$392$	−0.0335602	+	0.216198i	−0.00169505	+	0.0109197i
$393$	−1.98274	+	1.06471i	−0.100016	+	0.0537076i
$394$	−5.94556	−	4.78437i	−0.299533	−	0.241033i
$395$	−3.16544	+	2.39043i	−0.159271	+	0.120276i
$396$	−3.29386	−	0.305221i	−0.165523	−	0.0153379i
$397$	0.982245	+	31.8811i	0.0492975	+	1.60007i	0.623814	+	0.781573i	$0.285582\pi$
$397$	0.982245	+	31.8811i	0.0492975	+	1.60007i	−0.574517	+	0.818493i	$0.694810\pi$
$398$	8.66257	−	0.802706i	0.434216	−	0.0402360i
$399$	0.678609	−	1.92575i	0.0339730	−	0.0964083i
$400$	5.80266	+	2.66965i	0.290133	+	0.133482i
$401$	−28.0501	+	10.8667i	−1.40075	+	0.542655i	−0.938866	−	0.344284i	$-0.888122\pi$
$401$	−28.0501	+	10.8667i	−1.40075	+	0.542655i	−0.461888	+	0.886938i	$0.652828\pi$
$402$	−0.198201	+	0.114431i	−0.00988535	+	0.00570731i
$403$	0.132263	−	1.42734i	0.00658848	−	0.0711010i
$404$	−2.98810	+	6.00092i	−0.148664	+	0.298557i
$405$	−3.79044	+	0.953333i	−0.188348	+	0.0473715i
$406$	−2.53996	+	11.5978i	−0.126056	+	0.575590i
$407$	−1.30322	+	0.161374i	−0.0645984	+	0.00799902i
$408$	−0.229164			−0.0113453
$409$	8.92845	+	18.1462i	0.441483	+	0.897269i
$409$	8.92845	+	18.1462i	0.441483	+	0.897269i
$410$	0.630624			0.0311443
$411$	−3.57516	+	0.442701i	−0.176350	+	0.0218368i
$412$	−0.220051	+	1.00478i	−0.0108411	+	0.0495021i
$413$	−15.8652	+	3.99026i	−0.780676	+	0.196348i
$414$	6.08364	−	12.2176i	0.298994	−	0.600462i
$415$	0.0557228	−	0.601345i	0.00273533	−	0.0295189i
$416$	21.5233	−	12.4265i	1.05527	−	0.609259i
$417$	5.26619	−	2.04013i	0.257886	−	0.0999057i
$418$	1.20726	+	0.555427i	0.0590490	+	0.0271668i
$419$	−6.58359	+	18.6829i	−0.321629	+	0.912718i	0.664580	+	0.747217i	$0.268610\pi$
$419$	−6.58359	+	18.6829i	−0.321629	+	0.912718i	−0.986210	+	0.165501i	$0.947076\pi$
$420$	−0.575996	+	0.0533739i	−0.0281057	+	0.00260438i
$421$	−0.123864	−	4.02028i	−0.00603674	−	0.195936i	−0.997731	−	0.0673215i	$-0.978555\pi$
$421$	−0.123864	−	4.02028i	−0.00603674	−	0.195936i	0.991695	−	0.128615i	$-0.0410531\pi$
$422$	15.4846	+	1.43486i	0.753779	+	0.0698479i
$423$	−0.214134	+	0.161707i	−0.0104116	+	0.00786245i
$424$	6.47119	+	5.20735i	0.314269	+	0.252891i
$425$	−1.31367	+	0.705428i	−0.0637225	+	0.0342183i
$426$	−0.176998	+	1.14024i	−0.00857559	+	0.0552448i
$427$	−25.8134	−	8.21185i	−1.24920	−	0.397399i
$428$	15.8915	+	12.0007i	0.768143	+	0.580075i
$429$	0.205601	−	0.938805i	0.00992653	−	0.0453259i
$430$	−0.546492	−	1.71787i	−0.0263542	−	0.0828428i
$431$	29.6884	−	6.50186i	1.43004	−	0.313183i	0.569258	−	0.822159i	$-0.307231\pi$
$431$	29.6884	−	6.50186i	1.43004	−	0.313183i	0.860781	+	0.508976i	$0.169976\pi$
$432$	0.364241	−	2.34648i	0.0175246	−	0.112895i
$433$	−3.47965	−	22.4163i	−0.167221	−	1.07726i	−0.912073	−	0.410028i	$-0.865519\pi$
$433$	−3.47965	−	22.4163i	−0.167221	−	1.07726i	0.744851	−	0.667230i	$-0.232520\pi$
$434$	−0.373838	−	0.495041i	−0.0179448	−	0.0237627i
$435$	−0.918628	+	0.0283026i	−0.0440448	+	0.00135701i
$436$	−3.72189	+	4.92857i	−0.178246	+	0.236036i
$437$	12.3833	−	12.0077i	0.592376	−	0.574406i
$438$	−0.723079	+	0.619496i	−0.0345501	+	0.0296007i
$439$	−15.3474	−	9.50273i	−0.732493	−	0.453541i	0.108839	−	0.994059i	$-0.465287\pi$
$439$	−15.3474	−	9.50273i	−0.732493	−	0.453541i	−0.841332	+	0.540519i	$0.818228\pi$
$440$		−	0.872648i		−	0.0416018i
$441$	0.212687	−	0.150558i	0.0101280	−	0.00716943i
$442$	−0.113954	+	0.920266i	−0.00542022	+	0.0437726i
$443$	−0.271211	+	8.80280i	−0.0128856	+	0.418234i	0.970963	+	0.239230i	$0.0768951\pi$
$443$	−0.271211	+	8.80280i	−0.0128856	+	0.418234i	−0.983848	+	0.179003i	$0.942713\pi$
$444$	−0.0491706	−	0.797216i	−0.00233353	−	0.0378342i
$445$	−4.42431	−	0.827046i	−0.209732	−	0.0392058i
$446$	14.3714	−	0.442778i	0.680505	−	0.0209662i
$447$	3.69986	+	2.13612i	0.174998	+	0.101035i
$448$	1.09997	−	3.45768i	0.0519686	−	0.163360i
$449$	−0.428204	+	4.62106i	−0.0202082	+	0.218081i	0.979642	+	0.200754i	$0.0643392\pi$
$449$	−0.428204	+	4.62106i	−0.0202082	+	0.218081i	−0.999850	+	0.0173271i	$0.994484\pi$
$450$	3.20579	+	9.09739i	0.151123	+	0.428855i
$451$	−0.596176	−	1.29583i	−0.0280728	−	0.0610182i
$452$	−9.59808	+	7.24814i	−0.451456	+	0.340924i
$453$	−6.92029	+	2.43861i	−0.325143	+	0.114576i
$454$	5.11608	−	4.11689i	0.240110	−	0.193215i
$455$	−0.167077	+	5.42288i	−0.00783270	+	0.254229i
$456$	−0.886349	+	1.65059i	−0.0415071	+	0.0772961i
$457$	−2.26103	−	7.94669i	−0.105766	−	0.371730i	0.890813	−	0.454370i	$-0.150136\pi$
$457$	−2.26103	−	7.94669i	−0.105766	−	0.371730i	−0.996580	+	0.0826396i	$0.973665\pi$
$458$	−2.39906	+	4.15529i	−0.112101	+	0.194164i
$459$	0.385893	+	0.397966i	0.0180120	+	0.0185754i
$460$	−4.55681	−	1.76532i	−0.212462	−	0.0823083i
$461$	−11.1978	+	1.73822i	−0.521534	+	0.0809571i	−0.408721	−	0.912659i	$-0.634025\pi$
$461$	−11.1978	+	1.73822i	−0.521534	+	0.0809571i	−0.112813	+	0.993616i	$0.535986\pi$
$462$	−0.207952	−	0.360183i	−0.00967479	−	0.0167572i
$463$	17.7552	−	30.7529i	0.825153	−	1.42921i	−0.0766493	−	0.997058i	$-0.524422\pi$
$463$	17.7552	−	30.7529i	0.825153	−	1.42921i	0.901802	−	0.432149i	$-0.142244\pi$
$464$	−3.10381	+	8.01186i	−0.144091	+	0.371941i
$465$	0.0301051	−	0.0374117i	0.00139609	−	0.00173493i
$466$	3.08568	−	2.64365i	0.142941	−	0.122465i
$467$	−18.5820	+	20.3835i	−0.859873	+	0.943236i	−0.998892	−	0.0470534i	$-0.985017\pi$
$467$	−18.5820	+	20.3835i	−0.859873	+	0.943236i	0.139019	+	0.990290i	$0.455605\pi$
$468$	−18.1508	−	5.16434i	−0.839019	−	0.238722i
$469$	−2.65485	−	1.22142i	−0.122589	−	0.0564001i
$470$	−0.0205744	−	0.0225690i	−0.000949025	−	0.00104103i
$471$	0.0396159	+	0.319929i	0.00182540	+	0.0147416i
$472$	14.9468	−	1.38503i	0.687982	−	0.0637509i
$473$	−3.01329	+	2.74698i	−0.138551	+	0.126306i
$474$	0.913183	−	1.47484i	0.0419439	−	0.0677417i
$475$			12.1904i			0.559333i
$476$	−0.729411	−	1.03041i	−0.0334325	−	0.0472287i
$477$	−0.912805	−	9.85073i	−0.0417944	−	0.451034i
$478$	−2.95474	−	1.14467i	−0.135147	−	0.0523561i
$479$	−0.809657	−	4.33128i	−0.0369942	−	0.197901i	0.959483	−	0.281767i	$-0.0909204\pi$
$479$	−0.809657	−	4.33128i	−0.0369942	−	0.197901i	−0.996477	+	0.0838655i	$0.973273\pi$
$480$	0.830989	+	0.0512536i	0.0379293	+	0.00233940i
$481$	−7.47715	−	0.461175i	−0.340929	−	0.0210278i
$482$	−6.99232	−	6.78020i	−0.318491	−	0.308830i
$483$	−5.33454	+	0.828074i	−0.242730	+	0.0376786i
$484$	14.3920	−	6.62135i	0.654180	−	0.300971i
$485$	−2.15449	−	0.911917i	−0.0978303	−	0.0414080i
$486$	4.41256	−	3.12359i	0.200158	−	0.141689i
$487$	1.50079	−	8.02854i	0.0680075	−	0.363808i	−0.931992	−	0.362480i	$-0.881930\pi$
$487$	1.50079	−	8.02854i	0.0680075	−	0.363808i	0.999999	−	0.00132809i	$-0.000422745\pi$
$488$	22.2496	+	11.0790i	1.00719	+	0.501521i
$489$	−0.0998687	−	3.24147i	−0.00451622	−	0.146584i
$490$	0.0192957	+	0.0225221i	0.000871692	+	0.00101744i
$491$	−6.90154	−	13.8602i	−0.311462	−	0.625500i	0.683021	−	0.730399i	$-0.260666\pi$
$491$	−6.90154	−	13.8602i	−0.311462	−	0.625500i	−0.994483	+	0.104899i	$0.966548\pi$
$492$	0.809008	−	0.313411i	0.0364729	−	0.0141297i
$493$	−1.05591	−	1.70535i	−0.0475558	−	0.0768052i
$494$	6.18763	+	4.38013i	0.278395	+	0.197071i
$495$	−0.746162	+	0.723527i	−0.0335375	+	0.0325201i
$496$	−0.212385	−	0.395512i	−0.00953638	−	0.0177590i
$497$	−13.1894	+	6.56756i	−0.591627	+	0.294595i
$498$	0.0722753	+	0.254021i	0.00323873	+	0.0113830i
$499$	3.61380	−	3.72685i	0.161776	−	0.166837i	−0.632161	−	0.774837i	$-0.717832\pi$
$499$	3.61380	−	3.72685i	0.161776	−	0.166837i	0.793937	+	0.608000i	$0.208028\pi$
$500$	6.42447	−	2.95572i	0.287311	−	0.132184i
$501$	−0.212826	−	2.29675i	−0.00950835	−	0.102611i
$502$	−15.8033	−	3.46098i	−0.705337	−	0.154471i
$503$	−12.8894	+	33.2713i	−0.574708	+	1.48349i	0.277728	+	0.960660i	$0.410419\pi$
$503$	−12.8894	+	33.2713i	−0.574708	+	1.48349i	−0.852436	+	0.522832i	$0.824875\pi$
$504$	−16.9447	+	8.43745i	−0.754777	+	0.375834i
$505$	0.820999	+	1.93969i	0.0365340	+	0.0863149i
$506$	−0.216295	−	3.50685i	−0.00961548	−	0.155898i
$507$	0.615719	−	1.45469i	0.0273451	−	0.0646052i
$508$	11.2945	+	3.98001i	0.501111	+	0.176585i
$509$	25.2260	+	20.2993i	1.11812	+	0.899749i	0.995691	−	0.0927287i	$-0.0295589\pi$
$509$	25.2260	+	20.2993i	1.11812	+	0.899749i	0.122429	+	0.992477i	$0.460931\pi$
$510$	−0.0202109	+	0.0235902i	−0.000894952	+	0.00104459i
$511$	−11.7910	−	2.96555i	−0.521603	−	0.131188i
$512$	6.38425	−	12.8213i	0.282147	−	0.566627i
$513$	4.35895	−	1.24023i	0.192453	−	0.0547575i
$514$	−21.3933	−	3.32085i	−0.943616	−	0.146476i
$515$	0.194760	+	0.257904i	0.00858216	+	0.0113646i
$516$	−1.55483	−	1.93220i	−0.0684477	−	0.0850602i
$517$	−0.0269252	+	0.0636132i	−0.00118417	+	0.00279770i
$518$	−2.52573	+	2.03245i	−0.110974	+	0.0893007i
$519$	−0.228281	+	0.907643i	−0.0100204	+	0.0398411i
$520$	0.914750	−	4.89348i	0.0401144	−	0.214593i
$521$	13.5188	−	21.8336i	0.592268	−	0.956546i	−0.406805	−	0.913515i	$-0.633357\pi$
$521$	13.5188	−	21.8336i	0.592268	−	0.956546i	0.999074	−	0.0430314i	$-0.0137015\pi$
$522$	−11.9489	+	5.05753i	−0.522988	+	0.221362i
$523$	−13.1304	+	14.4033i	−0.574151	+	0.629814i	−0.955632	−	0.294563i	$-0.904826\pi$
$523$	−13.1304	+	14.4033i	−0.574151	+	0.629814i	0.381481	+	0.924377i	$0.375414\pi$
$524$	9.28513	+	6.57280i	0.405623	+	0.287134i
$525$	2.20432	−	3.11396i	0.0962046	−	0.135904i
$526$	10.1100	+	5.83700i	0.440816	+	0.254505i
$527$	0.103560	+	0.0160756i	0.00451116	+	0.000700262i
$528$	−0.108727	−	0.280658i	−0.00473175	−	0.0122141i
$529$	−21.5416	−	6.85288i	−0.936592	−	0.297951i
$530$	1.10677	−	0.206890i	0.0480748	−	0.00898674i
$531$	−13.5769	−	11.6320i	−0.589189	−	0.504786i
$532$	−10.2429	+	1.26834i	−0.444085	+	0.0549896i
$533$	−1.98478	−	7.89147i	−0.0859705	−	0.341817i
$534$	1.93481	−	0.361679i	0.0837275	−	0.0156514i
$535$	6.11195	−	1.33854i	0.264243	−	0.0578701i
$536$	2.23527	+	1.48114i	0.0965490	+	0.0639757i
$537$	−0.412770	+	0.481787i	−0.0178123	+	0.0207906i
$538$	−6.00377	−	13.0496i	−0.258841	−	0.562609i
$539$	0.0280375	−	0.0609414i	0.00120766	−	0.00262493i
$540$	−0.835354	−	0.975029i	−0.0359479	−	0.0419586i
$541$	−3.25652	−	26.2990i	−0.140009	−	1.13068i	−0.885656	−	0.464342i	$-0.846291\pi$
$541$	−3.25652	−	26.2990i	−0.140009	−	1.13068i	0.745647	−	0.666341i	$-0.232141\pi$
$542$	17.6704	+	2.18808i	0.759011	+	0.0939859i
$543$	4.55909	+	5.00108i	0.195649	+	0.214617i
$544$	0.809913	+	1.62652i	0.0347247	+	0.0697366i
$545$	0.415134	+	1.89556i	0.0177824	+	0.0811968i
$546$	−0.788554	−	2.23775i	−0.0337470	−	0.0957671i
$547$	6.65278	+	1.67324i	0.284452	+	0.0715426i	0.383503	−	0.923540i	$-0.374718\pi$
$547$	6.65278	+	1.67324i	0.284452	+	0.0715426i	−0.0990503	+	0.995082i	$0.531580\pi$
$548$	10.0585	+	15.1798i	0.429679	+	0.648451i
$549$	−8.97437	−	28.2104i	−0.383017	−	1.20399i
$550$	1.88567	+	1.61554i	0.0804051	+	0.0688869i
$551$	−16.3671	+	1.00949i	−0.697261	+	0.0430056i
$552$	4.95344			0.210833
$553$	22.1079	−	1.36357i	0.940125	−	0.0579849i
$554$	1.31551	+	5.23045i	0.0558907	+	0.222220i
$555$	−0.200269	−	0.151236i	−0.00850095	−	0.00641962i
$556$	−21.0969	−	19.2323i	−0.894707	−	0.815633i
$557$	43.5423	−	12.3889i	1.84495	−	0.524933i	0.844996	−	0.534773i	$-0.179603\pi$
$557$	43.5423	−	12.3889i	1.84495	−	0.524933i	0.999952	+	0.00984017i	$0.00313228\pi$
$558$	0.205520	−	0.646039i	0.00870035	−	0.0273490i
$559$	−19.7769	+	12.2454i	−0.836475	+	0.517923i
$560$	0.894481	+	1.44464i	0.0377987	+	0.0610470i
$561$	0.0675809	+	0.0192284i	0.00285327	+	0.000811825i
$562$	−3.59775	+	5.42955i	−0.151762	+	0.229032i
$563$	5.53751	−	5.04811i	0.233378	−	0.212752i	−0.548555	−	0.836114i	$-0.684822\pi$
$563$	5.53751	−	5.04811i	0.233378	−	0.212752i	0.781933	+	0.623362i	$0.214234\pi$
$564$	−0.0376107	−	0.0187279i	−0.00158370	−	0.000788587i
$565$	−0.232637	+	3.77180i	−0.00978710	+	0.158681i
$566$	−11.5287	+	4.06255i	−0.484587	+	0.170762i
$567$	20.5846	+	7.25372i	0.864471	+	0.304628i
$568$	12.8834	−	4.09850i	0.540575	−	0.171969i
$569$	1.53815	+	9.90895i	0.0644828	+	0.415405i	0.998332	+	0.0577375i	$0.0183886\pi$
$569$	1.53815	+	9.90895i	0.0644828	+	0.415405i	−0.933849	+	0.357667i	$0.883572\pi$
$570$	0.0917419	+	0.236813i	0.00384265	+	0.00991902i
$571$	18.2784	+	16.6630i	0.764928	+	0.697324i	0.958919	−	0.283679i	$-0.0915551\pi$
$571$	18.2784	+	16.6630i	0.764928	+	0.697324i	−0.193991	+	0.981003i	$0.562143\pi$
$572$	−4.71126	+	1.18493i	−0.196988	+	0.0495444i
$573$	0.704353	+	1.06297i	0.0294248	+	0.0444064i
$574$	−2.93549	−	1.94512i	−0.122525	−	0.0811879i
$575$	28.3954	−	15.2480i	1.18417	−	0.635886i
$576$	3.77875	−	1.20211i	0.157448	−	0.0500878i
$577$	22.5744	+	28.0534i	0.939787	+	1.16788i	0.985628	+	0.168928i	$0.0540304\pi$
$577$	22.5744	+	28.0534i	0.939787	+	1.16788i	−0.0458419	+	0.998949i	$0.514597\pi$
$578$	11.5396	+	2.15713i	0.479986	+	0.0897249i
$579$	−0.0410004	−	0.0220167i	−0.00170392	−	0.000914985i
$580$	2.19786	+	4.09294i	0.0912613	+	0.169950i
$581$	−2.11420	+	2.62732i	−0.0877117	+	0.109000i
$582$	1.02263	+	0.0315068i	0.0423892	+	0.00130600i
$583$	−1.47143	−	2.07863i	−0.0609406	−	0.0860882i
$584$	10.2736	+	4.34846i	0.425126	+	0.179941i
$585$	−4.94263	+	3.27511i	−0.204353	+	0.135409i
$586$	−9.66500	+	17.9985i	−0.399258	+	0.743512i
$587$	8.14081	+	19.2334i	0.336007	+	0.793848i	0.998978	+	0.0452030i	$0.0143935\pi$
$587$	8.14081	+	19.2334i	0.336007	+	0.793848i	−0.662971	+	0.748645i	$0.730705\pi$
$588$	0.0359470	+	0.0193031i	0.00148243	+	0.000796048i
$589$	0.516333	−	0.683735i	0.0212751	−	0.0281728i
$590$	1.17564	−	1.66078i	0.0484004	−	0.0683732i
$591$	−2.80471	+	1.73660i	−0.115370	+	0.0714342i
$592$	−2.03181	+	1.17307i	−0.0835070	+	0.0482128i
$593$	4.05594	+	18.5200i	0.166558	+	0.760525i	0.983075	+	0.183204i	$0.0586469\pi$
$593$	4.05594	+	18.5200i	0.166558	+	0.760525i	−0.816517	+	0.577321i	$0.804098\pi$
$594$	0.385830	−	0.838627i	0.0158308	−	0.0344093i
$595$	−0.394965	−	0.0365989i	−0.0161920	−	0.00150041i
$596$	1.32944	−	21.5545i	0.0544559	−	0.882909i
$597$	0.917248	−	3.64696i	0.0375405	−	0.149260i
$598$	2.46314	−	19.8918i	0.100725	−	0.813436i
$599$	24.0127	−	15.9114i	0.981133	−	0.650122i	0.0439767	−	0.999033i	$-0.485997\pi$
$599$	24.0127	−	15.9114i	0.981133	−	0.650122i	0.937156	+	0.348910i	$0.113448\pi$
$600$	−2.43697	+	2.51321i	−0.0994889	+	0.102601i
$601$	−0.876141	−	1.51752i	−0.0357385	−	0.0619010i	0.847603	−	0.530631i	$-0.178045\pi$
$601$	−0.876141	−	1.51752i	−0.0357385	−	0.0619010i	−0.883341	+	0.468730i	$0.844712\pi$
$602$	−2.75479	+	9.68210i	−0.112277	+	0.394613i
$603$	−0.586842	−	3.13932i	−0.0238980	−	0.127843i
$604$	26.6269	+	25.8192i	1.08343	+	1.05057i
$605$	1.36216	−	4.78750i	0.0553797	−	0.194640i
$606$	−0.641214	−	0.661274i	−0.0260475	−	0.0268624i
$607$	40.2847	+	8.82250i	1.63511	+	0.358094i	0.934641	−	0.355592i	$-0.115721\pi$
$607$	40.2847	+	8.82250i	1.63511	+	0.358094i	0.700466	+	0.713686i	$0.252975\pi$
$608$	14.8479	+	0.457458i	0.602160	+	0.0185524i
$609$	4.36341	+	2.70171i	0.176814	+	0.109479i
$610$	3.10275	−	1.31328i	0.125627	−	0.0531732i
$611$	−0.217668	+	0.328495i	−0.00880592	+	0.0132895i
$612$	0.458543	−	1.30125i	0.0185355	−	0.0525999i
$613$	26.8158	+	3.32052i	1.08308	+	0.134115i	0.644521	−	0.764587i	$-0.277057\pi$
$613$	26.8158	+	3.32052i	1.08308	+	0.134115i	0.438561	+	0.898701i	$0.355488\pi$
$614$	−0.122347	−	0.0151498i	−0.00493751	−	0.000611396i
$615$	0.0905982	−	0.257099i	0.00365327	−	0.0103672i
$616$	−2.69163	+	4.06208i	−0.108449	+	0.163666i
$617$	36.8323	−	15.5898i	1.48281	−	0.627621i	0.510202	−	0.860055i	$-0.329571\pi$
$617$	36.8323	−	15.5898i	1.48281	−	0.627621i	0.972612	+	0.232434i	$0.0746688\pi$
$618$	−0.120163	−	0.0744015i	−0.00483365	−	0.00299287i
$619$	20.7942	+	0.640661i	0.835788	+	0.0257503i	0.445868	−	0.895099i	$-0.352895\pi$
$619$	20.7942	+	0.640661i	0.835788	+	0.0257503i	0.389919	+	0.920849i	$0.372503\pi$
$620$	−0.237116	−	0.0519292i	−0.00952281	−	0.00208553i
$621$	−8.34119	−	8.60214i	−0.334720	−	0.345192i
$622$	1.23946	−	4.35624i	0.0496977	−	0.174669i
$623$	18.0437	+	17.4963i	0.722905	+	0.700976i
$624$	−0.315503	−	1.68779i	−0.0126302	−	0.0675659i
$625$	−5.92241	+	20.8151i	−0.236897	+	0.832605i
$626$	−0.774975	−	1.34230i	−0.0309742	−	0.0536490i
$627$	0.399882	−	0.412392i	0.0159698	−	0.0164694i
$628$	1.35839	−	0.900104i	0.0542058	−	0.0359181i
$629$	0.0673055	−	0.543545i	0.00268365	−	0.0216726i
$630$	−0.625864	+	2.48842i	−0.0249350	+	0.0991412i
$631$	3.01952	−	48.9563i	0.120205	−	1.94892i	−0.155861	−	0.987779i	$-0.549815\pi$
$631$	3.01952	−	48.9563i	0.120205	−	1.94892i	0.276066	−	0.961139i	$-0.410969\pi$
$632$	−20.2375	−	1.87528i	−0.805003	−	0.0745945i
$633$	2.80957	−	6.10678i	0.111670	−	0.242723i
$634$	−1.15219	−	5.26106i	−0.0457593	−	0.208944i
$635$	3.25847	−	1.88128i	0.129309	−	0.0746563i
$636$	1.31701	−	0.815460i	0.0522229	−	0.0323351i
$637$	0.221105	−	0.312346i	0.00876051	−	0.0123756i
$638$	−2.01291	+	2.66552i	−0.0796919	+	0.105529i
$639$	−14.1863	−	7.61788i	−0.561201	−	0.301359i
$640$	−1.98594	−	4.69197i	−0.0785012	−	0.185466i
$641$	21.6866	−	40.3856i	0.856570	−	1.59514i	0.0540291	−	0.998539i	$-0.482794\pi$
$641$	21.6866	−	40.3856i	0.856570	−	1.59514i	0.802541	−	0.596597i	$-0.203481\pi$
$642$	−2.28090	+	1.51138i	−0.0900198	+	0.0596493i
$643$	18.0310	+	7.63185i	0.711072	+	0.300971i	0.715101	−	0.699021i	$-0.246381\pi$
$643$	18.0310	+	7.63185i	0.711072	+	0.300971i	−0.00402929	+	0.999992i	$0.501283\pi$
$644$	15.7664	+	22.2726i	0.621284	+	0.877662i
$645$	−0.778868	−	0.0239967i	−0.0306679	−	0.000944868i
$646$	−0.347475	+	0.431808i	−0.0136712	+	0.0169893i
$647$	5.71528	+	10.6432i	0.224691	+	0.418428i	0.968156	−	0.250347i	$-0.0805447\pi$
$647$	5.71528	+	10.6432i	0.224691	+	0.418428i	−0.743465	+	0.668774i	$0.766819\pi$
$648$	−17.6433	−	9.47427i	−0.693096	−	0.372185i
$649$	−4.52405	−	0.845692i	−0.177585	−	0.0331963i
$650$	8.88063	+	11.0360i	0.348327	+	0.432867i
$651$	−0.255530	+	0.0812901i	−0.0100150	+	0.00318601i
$652$	−14.4424	+	7.75539i	−0.565607	+	0.303725i
$653$	25.8560	+	17.1328i	1.01182	+	0.670457i	0.944920	−	0.327302i	$-0.106140\pi$
$653$	25.8560	+	17.1328i	1.01182	+	0.670457i	0.0669020	+	0.997760i	$0.478689\pi$
$654$	−0.468737	−	0.707396i	−0.0183291	−	0.0276614i
$655$	3.46637	−	0.871826i	0.135442	−	0.0340651i
$656$	−1.88330	−	1.71685i	−0.0735304	−	0.0670318i
$657$	−4.79988	−	12.3899i	−0.187261	−	0.483377i
$658$	0.0261586	+	0.168517i	0.00101977	+	0.00656947i
$659$	−11.7024	+	3.72279i	−0.455860	+	0.145019i	−0.522283	−	0.852772i	$-0.674920\pi$
$659$	−11.7024	+	3.72279i	−0.455860	+	0.145019i	0.0664234	+	0.997792i	$0.478841\pi$
$660$	−0.153490	−	0.0540878i	−0.00597459	−	0.00210536i
$661$	−20.1710	+	7.10800i	−0.784563	+	0.276469i	−0.694524	−	0.719469i	$-0.744385\pi$
$661$	−20.1710	+	7.10800i	−0.784563	+	0.276469i	−0.0900382	+	0.995938i	$0.528699\pi$
$662$	−0.100076	+	1.62256i	−0.00388958	+	0.0630627i
$663$	0.358812	+	0.178667i	0.0139351	+	0.00693886i
$664$	2.28676	−	2.08466i	0.0887435	−	0.0809004i
$665$	−1.79124	+	2.70325i	−0.0694612	+	0.104827i
$666$	−3.40772	−	0.969581i	−0.132047	−	0.0375705i
$667$	22.8238	+	36.8617i	0.883740	+	1.42729i
$668$	−9.91309	+	6.13793i	−0.383549	+	0.237484i
$669$	1.88414	−	5.92269i	0.0728451	−	0.228984i
$670$	0.349607	−	0.0994717i	0.0135065	−	0.00384293i
$671$	−5.63184	−	5.13410i	−0.217415	−	0.198200i
$672$	−3.71007	−	2.80172i	−0.143119	−	0.108079i
$673$	2.51330	+	9.99283i	0.0968805	+	0.385195i	0.998920	−	0.0464578i	$-0.0147933\pi$
$673$	2.51330	+	9.99283i	0.0968805	+	0.385195i	−0.902040	+	0.431653i	$0.857931\pi$
$674$	2.76728	−	0.170680i	0.106592	−	0.00657435i
$675$	8.46810			0.325937
$676$	−7.96967	+	0.491552i	−0.306526	+	0.0189059i
$677$	20.9068	+	17.9119i	0.803514	+	0.688408i	0.953869	−	0.300224i	$-0.0970613\pi$
$677$	20.9068	+	17.9119i	0.803514	+	0.688408i	−0.150355	+	0.988632i	$0.548042\pi$
$678$	−0.500989	−	1.57483i	−0.0192404	−	0.0604809i
$679$	7.21616	+	10.8903i	0.276931	+	0.417930i
$680$	0.352969	+	0.0887752i	0.0135357	+	0.00340437i
$681$	−0.943418	−	2.67723i	−0.0361518	−	0.102591i
$682$	−0.0373360	−	0.170482i	−0.00142967	−	0.00652808i
$683$	−3.12056	−	6.26692i	−0.119405	−	0.239797i	0.827395	−	0.561621i	$-0.189822\pi$
$683$	−3.12056	−	6.26692i	−0.119405	−	0.239797i	−0.946800	+	0.321823i	$0.895704\pi$
$684$	−7.59894	−	8.33564i	−0.290553	−	0.318721i
$685$	5.67812	+	0.703104i	0.216950	+	0.0268642i
$686$	1.57047	+	12.6828i	0.0599607	+	0.484230i
$687$	1.34941	+	1.57504i	0.0514832	+	0.0600915i
$688$	−3.04478	+	6.61805i	−0.116081	+	0.252311i
$689$	−6.07233	−	13.1986i	−0.231337	−	0.502827i
$690$	0.436863	−	0.509909i	0.0166311	−	0.0194119i
$691$	−6.88645	−	4.56313i	−0.261973	−	0.173590i	0.414517	−	0.910042i	$-0.363951\pi$
$691$	−6.88645	−	4.56313i	−0.261973	−	0.173590i	−0.676490	+	0.736452i	$0.736500\pi$
$692$	4.62136	−	1.01209i	0.175678	−	0.0384740i
$693$	5.70498	−	1.06645i	0.216714	−	0.0405109i
$694$	3.55822	+	14.1474i	0.135068	+	0.537029i
$695$	−8.90154	+	1.10225i	−0.337655	+	0.0418107i
$696$	−3.57610	−	3.06381i	−0.135552	−	0.116134i
$697$	0.584787	−	0.109316i	0.0221504	−	0.00414063i
$698$	−12.0325	−	3.82781i	−0.455437	−	0.144885i
$699$	−0.634486	−	1.63780i	−0.0239985	−	0.0619472i
$700$	−19.0570	−	2.95820i	−0.720289	−	0.111809i
$701$	22.0671	+	12.7404i	0.833461	+	0.481199i	0.855036	−	0.518568i	$-0.173535\pi$
$701$	22.0671	+	12.7404i	0.833461	+	0.481199i	−0.0215751	+	0.999767i	$0.506868\pi$
$702$	3.04268	−	4.29826i	0.114838	−	0.162227i
$703$	−3.65466	−	2.58708i	−0.137838	−	0.0975735i
$704$	0.687707	−	0.754379i	0.0259189	−	0.0284317i
$705$	−0.0121570	+	0.00514560i	−0.000457858	+	0.000193795i
$706$	−9.79645	+	15.8218i	−0.368694	+	0.595461i
$707$	2.16119	−	11.5614i	0.0812800	−	0.434809i
$708$	0.682809	−	2.71484i	0.0256615	−	0.102030i
$709$	−2.34663	+	1.88832i	−0.0881294	+	0.0709174i	−0.669985	−	0.742375i	$-0.733699\pi$
$709$	−2.34663	+	1.88832i	−0.0881294	+	0.0709174i	0.581856	+	0.813292i	$0.302327\pi$
$710$	0.714335	−	1.68768i	0.0268085	−	0.0633376i
$711$	15.1758	+	18.8590i	0.569135	+	0.707267i
$712$	−13.8979	−	18.4038i	−0.520845	−	0.689710i
$713$	−2.23849	−	0.347477i	−0.0838320	−	0.0130131i
$714$	0.166842	−	0.0474706i	0.00624390	−	0.00177654i
$715$	−0.680358	+	1.36634i	−0.0254439	+	0.0510983i
$716$	3.11007	+	0.782215i	0.116229	+	0.0292327i
$717$	−0.891162	+	1.04017i	−0.0332810	+	0.0388458i
$718$	−17.7992	−	14.3230i	−0.664260	−	0.534528i
$719$	−23.2645	−	8.19808i	−0.867618	−	0.305737i	−0.138697	−	0.990335i	$-0.544292\pi$
$719$	−23.2645	−	8.19808i	−0.867618	−	0.305737i	−0.728921	+	0.684598i	$0.759978\pi$
$720$	−0.723799	+	1.71004i	−0.0269744	+	0.0637295i
$721$	−0.111097	−	1.80124i	−0.00413746	−	0.0670817i
$722$	−3.37755	−	7.97979i	−0.125700	−	0.296977i
$723$	−3.76877	+	1.87662i	−0.140162	+	0.0697924i
$724$	12.3572	−	31.8976i	0.459252	−	1.18547i
$725$	−29.9311	−	6.55501i	−1.11161	−	0.243447i
$726$	0.200844	+	2.16745i	0.00745402	+	0.0804417i
$727$	4.63819	−	2.13390i	0.172021	−	0.0791421i	−0.330073	−	0.943956i	$-0.607073\pi$
$727$	4.63819	−	2.13390i	0.172021	−	0.0791421i	0.502093	+	0.864813i	$0.332563\pi$
$728$	−19.3517	+	19.9571i	−0.717222	+	0.739660i
$729$	6.09004	+	21.4043i	0.225557	+	0.792750i
$730$	1.35370	−	0.674065i	0.0501029	−	0.0249483i
$731$	−0.804554	−	1.49827i	−0.0297575	−	0.0554155i
$732$	3.32774	−	3.22679i	0.122997	−	0.119266i
$733$	1.31227	+	0.928940i	0.0484700	+	0.0343112i	0.601754	−	0.798681i	$-0.294469\pi$
$733$	1.31227	+	0.928940i	0.0484700	+	0.0343112i	−0.553284	+	0.832993i	$0.686626\pi$
$734$	−10.5354	−	17.0152i	−0.388869	−	0.628044i
$735$	0.0119541	−	0.00463105i	0.000440935	−	0.000170819i
$736$	−17.5065	−	35.1578i	−0.645298	−	1.29593i
$737$	−0.534908	−	0.624347i	−0.0197036	−	0.0229981i
$738$	−0.118513	−	3.84661i	−0.00436252	−	0.141596i
$739$	−28.3105	−	14.0969i	−1.04142	−	0.518564i	−0.158141	−	0.987417i	$-0.550550\pi$
$739$	−28.3105	−	14.0969i	−1.04142	−	0.518564i	−0.883277	+	0.468852i	$0.844668\pi$
$740$	−0.233097	+	1.24696i	−0.00856880	+	0.0458390i
$741$	2.67468	−	1.89336i	0.0982567	−	0.0695545i
$742$	−5.79001	−	2.45070i	−0.212558	−	0.0899681i
$743$	5.59254	−	2.57297i	0.205170	−	0.0943933i	−0.312702	−	0.949851i	$-0.601234\pi$
$743$	5.59254	−	2.57297i	0.205170	−	0.0943933i	0.517872	+	0.855458i	$0.326724\pi$
$744$	0.243134	−	0.0377414i	0.00891373	−	0.00138367i
$745$	−4.87119	−	4.72343i	−0.178467	−	0.173053i
$746$	2.67955	+	0.165269i	0.0981052	+	0.00605092i
$747$	−3.67849	−	0.226882i	−0.134589	−	0.00830116i
$748$	−0.0652622	−	0.349122i	−0.00238622	−	0.0127652i
$749$	−32.5791	−	12.6212i	−1.19041	−	0.461169i
$750$	0.0896553	+	0.967535i	0.00327375	+	0.0353294i
$751$	−13.1320	−	18.5510i	−0.479193	−	0.676936i	0.503113	−	0.864221i	$-0.332188\pi$
$751$	−13.1320	−	18.5510i	−0.479193	−	0.676936i	−0.982306	+	0.187285i	$0.940031\pi$
$752$			0.123413i			0.00450042i
$753$	−3.68138	+	5.94564i	−0.134157	+	0.216671i
$754$	−14.0818	+	12.8372i	−0.512828	+	0.467504i
$755$	11.6036	−	1.07523i	0.422299	−	0.0391318i
$756$	0.881059	+	7.11525i	0.0320438	+	0.258779i
$757$	33.1078	+	36.3176i	1.20332	+	1.31998i	0.934145	+	0.356894i	$0.116164\pi$
$757$	33.1078	+	36.3176i	1.20332	+	1.31998i	0.269180	+	0.963090i	$0.413247\pi$
$758$	−17.6511	−	8.12079i	−0.641117	−	0.294961i
$759$	−1.46078	−	0.415628i	−0.0530230	−	0.0150863i
$760$	2.00461	−	2.19896i	0.0727150	−	0.0797645i
$761$	−5.37898	+	4.60843i	−0.194988	+	0.167056i	−0.742728	−	0.669593i	$-0.766469\pi$
$761$	−5.37898	+	4.60843i	−0.194988	+	0.167056i	0.547740	+	0.836648i	$0.315488\pi$
$762$	−1.03155	+	1.28192i	−0.0373692	+	0.0464389i
$763$	3.91434	−	10.1041i	0.141709	−	0.365792i
$764$	3.22287	−	5.58217i	0.116599	−	0.201956i
$765$	−0.216745	−	0.375413i	−0.00783643	−	0.0135731i
$766$	10.1888	−	1.58159i	0.368135	−	0.0571451i
$767$	−24.4827	−	9.48465i	−0.884019	−	0.342471i
$768$	2.12067	+	2.18701i	0.0765230	+	0.0789169i
$769$	−11.7790	+	20.4018i	−0.424761	+	0.735708i	−0.996398	−	0.0847985i	$-0.972975\pi$
$769$	−11.7790	+	20.4018i	−0.424761	+	0.735708i	0.571637	+	0.820507i	$0.306309\pi$
$770$	0.180766	+	0.635328i	0.00651437	+	0.0228956i
$771$	−4.42733	+	8.24473i	−0.159446	+	0.296927i
$772$	−0.00724428	+	0.235130i	−0.000260727	+	0.00846252i
$773$	−21.3819	+	17.2060i	−0.769055	+	0.618856i	−0.929768	−	0.368145i	$-0.879993\pi$
$773$	−21.3819	+	17.2060i	−0.769055	+	0.618856i	0.160714	+	0.987001i	$0.448620\pi$
$774$	−10.3757	+	3.65627i	−0.372948	+	0.131422i
$775$	1.27758	−	0.964783i	0.0458920	−	0.0346560i
$776$	−5.01020	−	10.8900i	−0.179856	−	0.390928i
$777$	0.465751	+	1.32171i	0.0167087	+	0.0474159i
$778$	0.458536	−	4.94839i	0.0164393	−	0.177408i
$779$	1.47445	−	4.63483i	0.0528275	−	0.166060i
$780$	−0.804017	−	0.464199i	−0.0287884	−	0.0166210i
$781$	−4.14323	+	0.127652i	−0.148256	+	0.00456773i
$782$	1.44045	+	0.269268i	0.0515105	+	0.00962899i
$783$	0.701244	+	11.3695i	0.0250604	+	0.406311i
$784$	0.00369075	−	0.119792i	0.000131813	−	0.00427828i
$785$	0.0629185	−	0.508117i	0.00224566	−	0.0181355i
$786$	−1.27580	+	0.903119i	−0.0455062	+	0.0322132i
$787$			27.8026i			0.991056i	0.868592	+	0.495528i	$0.165025\pi$
$787$			27.8026i			0.991056i	−0.868592	+	0.495528i	$0.834975\pi$
$788$	14.1774	+	8.77825i	0.505048	+	0.312712i
$789$	3.83213	−	3.28317i	0.136428	−	0.116884i
$790$	−1.97786	+	1.91786i	−0.0703691	+	0.0682345i
$791$	12.7168	−	16.8398i	0.452157	−	0.598753i
$792$	−5.32288	+	0.163996i	−0.189140	+	0.00582735i
$793$	−26.1994	−	34.6937i	−0.930369	−	1.23201i
$794$	3.39816	+	21.8913i	0.120596	+	0.776893i
$795$	0.0746557	−	0.480940i	0.00264776	−	0.0170572i
$796$	−18.5689	+	4.06665i	−0.658157	+	0.144139i
$797$	3.28264	+	10.3188i	0.116277	+	0.365510i	0.993392	−	0.114771i	$-0.0366133\pi$
$797$	3.28264	+	10.3188i	0.116277	+	0.365510i	−0.877115	+	0.480280i	$0.840535\pi$
$798$	0.303388	−	1.38531i	0.0107398	−	0.0490395i
$799$	−0.0229912	−	0.0173621i	−0.000813369	−	0.000614228i
$800$	26.4506	+	8.41455i	0.935171	+	0.297499i
$801$	−4.21327	+	27.1423i	−0.148869	+	0.959027i
$802$	−18.4070	+	9.88434i	−0.649973	+	0.349028i
$803$	−2.66485	−	2.14440i	−0.0940406	−	0.0756742i
$804$	0.399063	−	0.301359i	0.0140739	−	0.0106281i
$805$	8.53728	+	0.791096i	0.300900	+	0.0278825i
$806$	−0.0306597	−	0.995134i	−0.00107994	−	0.0350521i
$807$	−6.18272	+	0.572914i	−0.217642	+	0.0201675i
$808$	−3.58682	+	10.1786i	−0.126184	+	0.358083i
$809$	19.7444	+	9.08385i	0.694175	+	0.319371i	0.733341	−	0.679862i	$-0.237960\pi$
$809$	19.7444	+	9.08385i	0.694175	+	0.319371i	−0.0391654	+	0.999233i	$0.512470\pi$
$810$	−2.53132	+	0.980638i	−0.0889415	+	0.0344561i
$811$	18.1337	−	10.4695i	0.636760	−	0.367633i	−0.146605	−	0.989195i	$-0.546835\pi$
$811$	18.1337	−	10.4695i	0.636760	−	0.367633i	0.783365	+	0.621562i	$0.213501\pi$
$812$	2.39363	−	25.8314i	0.0840000	−	0.906504i
$813$	3.43067	−	6.88971i	0.120319	−	0.241633i
$814$	−0.884518	+	0.222465i	−0.0310024	+	0.00779741i
$815$	−1.10188	+	5.03135i	−0.0385973	+	0.176241i
$816$	0.124581	−	0.0154265i	0.00436122	−	0.000540036i
$817$	−13.9034			−0.486417
$818$	7.70305	+	11.7458i	0.269331	+	0.410682i
$819$	33.1093			1.15693
$820$	−1.36748	+	0.169331i	−0.0477545	+	0.00591329i
$821$	6.64741	−	30.3530i	0.231996	−	1.05933i	−0.704787	−	0.709419i	$-0.748958\pi$
$821$	6.64741	−	30.3530i	0.231996	−	1.05933i	0.936784	−	0.349909i	$-0.113788\pi$
$822$	−2.42652	+	0.610294i	−0.0846345	+	0.0212864i
$823$	12.7891	−	25.6840i	0.445800	−	0.895286i	−0.552299	−	0.833646i	$-0.686249\pi$
$823$	12.7891	−	25.6840i	0.445800	−	0.895286i	0.998098	−	0.0616402i	$-0.0196331\pi$
$824$	−0.152788	+	1.64885i	−0.00532262	+	0.0574402i
$825$	0.929543	−	0.536672i	0.0323625	−	0.0186845i
$826$	−10.5951	+	4.10455i	−0.368649	+	0.142815i
$827$	−26.1108	−	12.0129i	−0.907960	−	0.417728i	−0.0919486	−	0.995764i	$-0.529310\pi$
$827$	−26.1108	−	12.0129i	−0.907960	−	0.417728i	−0.816011	+	0.578036i	$0.803819\pi$
$828$	−9.91153	+	28.1269i	−0.344449	+	0.977476i
$829$	38.4177	−	3.55993i	1.33430	−	0.123641i	0.598656	−	0.801007i	$-0.295702\pi$
$829$	38.4177	−	3.55993i	1.33430	−	0.123641i	0.735647	+	0.677365i	$0.236878\pi$
$830$	−0.0129171	−	0.419254i	−0.000448358	−	0.0145525i
$831$	2.32139	+	0.215109i	0.0805282	+	0.00746204i
$832$	4.64718	−	3.50938i	0.161112	−	0.121666i
$833$	0.0217973	+	0.0175402i	0.000755232	+	0.000607733i
$834$	3.45577	−	1.85571i	0.119664	−	0.0642580i
$835$	−0.561930	+	3.62001i	−0.0194464	+	0.125276i
$836$	−2.76703	−	0.880256i	−0.0956997	−	0.0304443i
$837$	−0.474959	−	0.358673i	−0.0164170	−	0.0123975i
$838$	−2.94335	+	13.4397i	−0.101676	+	0.464268i
$839$	1.96824	+	6.18704i	0.0679512	+	0.213600i	0.980914	−	0.194443i	$-0.0622898\pi$
$839$	1.96824	+	6.18704i	0.0679512	+	0.213600i	−0.912963	+	0.408043i	$0.866211\pi$
$840$	−0.909692	+	0.199226i	−0.0313874	+	0.00687394i
$841$	1.87395	−	12.0722i	0.0646190	−	0.416282i
$842$	−0.428516	−	2.76054i	−0.0147676	−	0.0951346i
$843$	1.69670	+	2.24680i	0.0584376	+	0.0773839i
$844$	−33.9630	+	1.04639i	−1.16906	+	0.0360182i
$845$	−1.51189	+	2.00206i	−0.0520105	+	0.0688731i
$846$	−0.133797	+	0.129739i	−0.00460005	+	0.00446051i
$847$	−21.1075	+	18.0838i	−0.725262	+	0.621366i
$848$	−3.86850	−	2.39527i	−0.132845	−	0.0822540i
$849$			5.28378i			0.181339i
$850$	−0.845285	+	0.598365i	−0.0289930	+	0.0205237i
$851$	−1.45483	+	11.7489i	−0.0498708	+	0.402746i
$852$	0.0776432	−	2.52009i	0.00266001	−	0.0863369i
$853$	−3.25568	−	52.7853i	−0.111472	−	1.80733i	−0.479525	−	0.877528i	$-0.659191\pi$
$853$	−3.25568	−	52.7853i	−0.111472	−	1.80733i	0.368053	−	0.929805i	$-0.380025\pi$
$854$	−18.4937	−	3.45707i	−0.632841	−	0.118299i
$855$	−3.54229	+	0.109137i	−0.121144	+	0.00373240i
$856$	27.7635	+	16.0293i	0.948936	+	0.547869i
$857$	2.26567	−	7.12198i	0.0773937	−	0.243282i	−0.906450	−	0.422314i	$-0.861218\pi$
$857$	2.26567	−	7.12198i	0.0773937	−	0.243282i	0.983843	+	0.179032i	$0.0572964\pi$
$858$	0.0615891	−	0.664652i	0.00210262	−	0.0226908i
$859$	−9.63165	−	27.3326i	−0.328628	−	0.932578i	−0.984140	−	0.177393i	$-0.943234\pi$
$859$	−9.63165	−	27.3326i	−0.328628	−	0.932578i	0.655512	−	0.755185i	$-0.272453\pi$
$860$	1.64632	+	3.57838i	0.0561389	+	0.122022i
$861$	−1.21473	+	0.917323i	−0.0413980	+	0.0312623i
$862$	19.9088	−	7.01559i	0.678096	−	0.238952i
$863$	15.5176	−	12.4870i	0.528226	−	0.425062i	−0.325687	−	0.945478i	$-0.605596\pi$
$863$	15.5176	−	12.4870i	0.528226	−	0.425062i	0.853913	+	0.520416i	$0.174223\pi$
$864$	0.317775	−	10.3141i	0.0108109	−	0.350894i
$865$	0.703219	−	1.30956i	0.0239102	−	0.0445264i
$866$	−4.31174	−	15.1542i	−0.146519	−	0.514961i
$867$	2.53728	−	4.39469i	0.0861705	−	0.149252i
$868$	0.943576	+	0.973095i	0.0320271	+	0.0330290i
$869$	5.81072	+	2.25108i	0.197115	+	0.0763628i
$870$	−0.630780	+	0.0979152i	−0.0213854	+	0.00331964i
$871$	−2.34509	−	4.06182i	−0.0794604	−	0.137629i
$872$	−4.97131	+	8.61055i	−0.168350	+	0.291590i
$873$	−5.15752	+	13.3131i	−0.174556	+	0.450580i
$874$	7.51076	−	9.33366i	0.254055	−	0.315716i
$875$	−9.42223	+	8.07247i	−0.318529	+	0.272899i
$876$	1.40162	−	1.53751i	0.0473565	−	0.0519476i
$877$	−27.6702	−	7.87285i	−0.934356	−	0.265847i	−0.227965	−	0.973669i	$-0.573207\pi$
$877$	−27.6702	−	7.87285i	−0.934356	−	0.265847i	−0.706391	+	0.707822i	$0.749678\pi$
$878$	−11.3898	−	5.24015i	−0.384388	−	0.176846i
$879$	5.94930	+	6.52607i	0.200665	+	0.220119i
$880$	0.0587436	+	0.474401i	0.00198025	+	0.0159921i
$881$	−48.3118	+	4.47675i	−1.62767	+	0.150826i	−0.866997	−	0.498313i	$-0.833953\pi$
$881$	−48.3118	+	4.47675i	−1.62767	+	0.150826i	−0.760670	+	0.649139i	$0.775129\pi$
$882$	0.133751	−	0.121931i	0.00450364	−	0.00410561i
$883$	1.29856	−	2.09725i	0.0437000	−	0.0705779i	−0.827634	−	0.561267i	$-0.810314\pi$
$883$	1.29856	−	2.09725i	0.0437000	−	0.0705779i	0.871334	+	0.490690i	$0.163255\pi$
$884$		−	2.02616i		−	0.0681470i
$885$	−0.508185	−	0.717892i	−0.0170825	−	0.0241317i
$886$	0.564394	+	6.09078i	0.0189612	+	0.204624i
$887$	14.9198	+	5.77998i	0.500959	+	0.194073i	0.598444	−	0.801164i	$-0.295786\pi$
$887$	14.9198	+	5.77998i	0.500959	+	0.194073i	−0.0974851	+	0.995237i	$0.531080\pi$
$888$	−0.236275	−	1.26396i	−0.00792888	−	0.0424157i
$889$	−20.9705	−	1.29342i	−0.703329	−	0.0433799i
$890$	−3.12019	−	0.192447i	−0.104589	−	0.00645084i
$891$	4.40810	+	4.27438i	0.147677	+	0.143197i
$892$	−31.0449	+	4.81906i	−1.03946	+	0.161354i
$893$	−0.213978	+	0.0984454i	−0.00716049	+	0.00329435i
$894$	2.73258	+	1.15660i	0.0913911	+	0.0386826i
$895$	0.822405	−	0.582169i	0.0274900	−	0.0194597i
$896$	−5.22777	+	27.9661i	−0.174648	+	0.934282i
$897$	−7.75582	−	3.86194i	−0.258959	−	0.128946i
$898$	0.0992617	+	3.22177i	0.00331240	+	0.107512i
$899$	1.40114	+	1.63541i	0.0467305	+	0.0545441i
$900$	−9.39440	−	18.8665i	−0.313147	−	0.628883i
$901$	0.990457	−	0.383705i	0.0329969	−	0.0127831i
$902$	−0.521537	−	0.842310i	−0.0173653	−	0.0280459i
$903$	3.55153	+	2.51407i	0.118187	+	0.0836632i
$904$	−13.9006	+	13.4790i	−0.462328	+	0.448304i
$905$	−5.08476	−	9.46903i	−0.169023	−	0.314761i
$906$	−4.56190	+	2.27156i	−0.151559	+	0.0754675i
$907$	−8.45431	−	29.7138i	−0.280721	−	0.986631i	−0.966041	−	0.258389i	$-0.916808\pi$
$907$	−8.45431	−	29.7138i	−0.280721	−	0.986631i	0.685320	−	0.728242i	$-0.259662\pi$
$908$	−9.98856	+	10.3010i	−0.331482	+	0.341852i
$909$	11.6772	−	5.37236i	0.387308	−	0.178190i
$910$	0.347689	+	3.75217i	0.0115258	+	0.124383i
$911$	22.9324	+	5.02226i	0.759783	+	0.166395i	0.576984	−	0.816755i	$-0.304229\pi$
$911$	22.9324	+	5.02226i	0.759783	+	0.166395i	0.182799	+	0.983150i	$0.441484\pi$
$912$	0.370738	−	0.956984i	0.0122764	−	0.0316889i
$913$	−0.849287	+	0.422895i	−0.0281073	+	0.0139958i
$914$	−2.23676	−	5.28454i	−0.0739853	−	0.174797i
$915$	−0.0896569	−	1.45363i	−0.00296397	−	0.0480556i
$916$	4.08650	−	9.65475i	0.135022	−	0.319002i
$917$	−18.8247	−	6.63355i	−0.621645	−	0.219059i
$918$	0.299957	+	0.241375i	0.00990007	+	0.00796655i
$919$	−30.5679	+	35.6790i	−1.00834	+	1.17694i	−0.0241742	+	0.999708i	$0.507696\pi$
$919$	−30.5679	+	35.6790i	−1.00834	+	1.17694i	−0.984169	+	0.177235i	$0.943285\pi$
$920$	−7.62952	−	1.91890i	−0.251538	−	0.0632643i
$921$	−0.0237533	+	0.0477030i	−0.000782697	+	0.00157187i
$922$	−7.57011	+	2.15388i	−0.249308	+	0.0709344i
$923$	−23.3675	−	3.62730i	−0.769150	−	0.119394i
$924$	0.547648	+	0.725204i	0.0180163	+	0.0238575i
$925$	−5.24525	−	6.51829i	−0.172463	−	0.214320i
$926$	9.61355	−	22.7129i	0.315921	−	0.746392i
$927$	1.53653	−	1.23644i	0.0504664	−	0.0406102i
$928$	−9.10719	+	36.2100i	−0.298958	+	1.18865i
$929$	−0.849255	+	4.54311i	−0.0278632	+	0.149055i	−0.994075	−	0.108693i	$-0.965333\pi$
$929$	−0.849255	+	4.54311i	−0.0278632	+	0.149055i	0.966212	+	0.257748i	$0.0829804\pi$
$930$	0.0175578	−	0.0283569i	0.000575744	−	0.000929858i
$931$	0.210643	−	0.0891576i	0.00690355	−	0.00292202i
$932$	−5.98131	+	6.56118i	−0.195924	+	0.214919i
$933$	−1.59793	−	1.13115i	−0.0523139	−	0.0370322i
$934$	−11.0685	+	15.6360i	−0.362173	+	0.511627i
$935$	−0.0966423	−	0.0557965i	−0.00316054	−	0.00182474i
$936$	−30.0206	−	4.66006i	−0.981254	−	0.152319i
$937$	12.4794	+	32.2130i	0.407683	+	1.05235i	0.973675	+	0.227941i	$0.0731993\pi$
$937$	12.4794	+	32.2130i	0.407683	+	1.05235i	−0.565992	+	0.824411i	$0.691507\pi$
$938$	−1.93420	−	0.615312i	−0.0631537	−	0.0200906i
$939$	−0.658577	+	0.123109i	−0.0214918	+	0.00401752i
$940$	0.0506748	+	0.0434155i	0.00165283	+	0.00141606i
$941$	21.6208	−	2.67723i	0.704817	−	0.0872752i	0.237529	−	0.971380i	$-0.423663\pi$
$941$	21.6208	−	2.67723i	0.704817	−	0.0872752i	0.467288	+	0.884105i	$0.345231\pi$
$942$	0.0546132	+	0.217141i	0.00177939	+	0.00707484i
$943$	−12.6403	+	2.36289i	−0.411626	+	0.0769462i
$944$	−8.03236	+	1.75911i	−0.261431	+	0.0572543i
$945$	1.87782	+	1.24429i	0.0610856	+	0.0404768i
$946$	−1.84256	+	2.15064i	−0.0599067	+	0.0699234i
$947$	14.9371	+	32.4668i	0.485390	+	1.05503i	0.982315	+	0.187235i	$0.0599527\pi$
$947$	14.9371	+	32.4668i	0.485390	+	1.05503i	−0.496925	+	0.867794i	$0.665538\pi$
$948$	−1.58418	+	3.44333i	−0.0514519	+	0.111834i
$949$	−12.6956	−	14.8184i	−0.412118	−	0.481026i
$950$	1.04047	+	8.40264i	0.0337574	+	0.272618i
$951$	−2.31041	−	0.286091i	−0.0749202	−	0.00927713i
$952$	−1.36921	−	1.50195i	−0.0443763	−	0.0486785i
$953$	−10.3949	−	20.8758i	−0.336725	−	0.676235i	0.660489	−	0.750836i	$-0.270349\pi$
$953$	−10.3949	−	20.8758i	−0.336725	−	0.676235i	−0.997213	+	0.0746014i	$0.976232\pi$
$954$	−1.46996	−	6.71204i	−0.0475917	−	0.217310i
$955$	−0.673093	−	1.91010i	−0.0217808	−	0.0618094i
$956$	6.71459	+	1.68879i	0.217165	+	0.0546192i
$957$	0.797524	+	1.20358i	0.0257803	+	0.0389063i
$958$	−0.927767	−	2.91638i	−0.0299748	−	0.0942239i
$959$	−24.2624	−	20.7867i	−0.783473	−	0.671238i
$960$	0.194712	−	0.0120094i	0.00628431	−	0.000387603i
$961$	30.8875			0.996370
$962$	−5.19324	+	0.320308i	−0.167437	+	0.0103272i
$963$	−9.31328	−	37.0295i	−0.300116	−	1.19326i
$964$	16.9831	+	12.8251i	0.546990	+	0.413067i
$965$	0.0546216	+	0.0497942i	0.00175833	+	0.00160293i
$966$	−3.60634	+	1.02609i	−0.116032	+	0.0330139i
$967$	8.03508	−	25.2578i	0.258391	−	0.812236i	−0.732876	−	0.680362i	$-0.761822\pi$
$967$	8.03508	−	25.2578i	0.258391	−	0.812236i	0.991267	−	0.131873i	$-0.0420992\pi$
$968$	21.6837	−	13.4260i	0.696940	−	0.431527i
$969$	0.126124	+	0.203697i	0.00405169	+	0.00654370i
$970$	−1.56289	−	0.444680i	−0.0501814	−	0.0142778i
$971$	−10.6177	+	16.0236i	−0.340737	+	0.514223i	−0.963329	−	0.268323i	$-0.913531\pi$
$971$	−10.6177	+	16.0236i	−0.340737	+	0.514223i	0.622592	+	0.782546i	$0.286080\pi$
$972$	−8.72974	+	7.95821i	−0.280006	+	0.255260i
$973$	44.8355	+	22.3254i	1.43736	+	0.715721i
$974$	0.349223	−	5.66204i	0.0111898	−	0.181424i
$975$	5.77509	−	2.03506i	0.184951	−	0.0651742i
$976$	−12.8414	−	4.52514i	−0.411044	−	0.144846i
$977$	44.8518	−	14.2684i	1.43494	−	0.456486i	0.517951	−	0.855410i	$-0.326695\pi$
$977$	44.8518	−	14.2684i	1.43494	−	0.456486i	0.916984	+	0.398924i	$0.130616\pi$
$978$	−0.345504	−	2.22577i	−0.0110480	−	0.0711724i
$979$	2.55431	+	6.59343i	0.0816360	+	0.210727i
$980$	−0.0478895	−	0.0436570i	−0.00152977	−	0.00139457i
$981$	11.4843	−	2.88842i	0.366665	−	0.0922201i
$982$	−5.94011	−	8.96453i	−0.189557	−	0.286070i
$983$	26.1935	+	17.3565i	0.835444	+	0.553586i	0.895731	−	0.444596i	$-0.146653\pi$
$983$	26.1935	+	17.3565i	0.835444	+	0.553586i	−0.0602870	+	0.998181i	$0.519202\pi$
$984$	1.23052	−	0.660777i	0.0392277	−	0.0210648i
$985$	4.99267	−	1.58828i	0.159080	−	0.0506069i
$986$	−0.873377	−	1.08535i	−0.0278140	−	0.0345645i
$987$	0.0724607	+	0.0135452i	0.00230645	+	0.000431150i
$988$	−14.5937	−	7.83667i	−0.464289	−	0.249318i
$989$	17.3907	+	32.3855i	0.552991	+	1.02980i
$990$	−0.452564	+	0.562402i	−0.0143834	+	0.0178743i
$991$	−17.5350	−	0.540246i	−0.557016	−	0.0171615i	−0.248933	−	0.968521i	$-0.580080\pi$
$991$	−17.5350	−	0.540246i	−0.557016	−	0.0171615i	−0.308084	+	0.951359i	$0.599688\pi$
$992$	−1.12716	−	1.59229i	−0.0357874	−	0.0505553i
$993$	0.647125	+	0.273905i	0.0205359	+	0.00869210i
$994$	−8.53072	+	5.65266i	−0.270578	+	0.179291i
$995$	−2.82557	+	5.26189i	−0.0895767	+	0.166813i
$996$	−0.224934	−	0.531428i	−0.00712731	−	0.0168389i
$997$	−48.3530	−	25.9650i	−1.53135	−	0.822320i	−0.531658	−	0.846959i	$-0.678431\pi$
$997$	−48.3530	−	25.9650i	−1.53135	−	0.822320i	−0.999696	+	0.0246388i	$0.992156\pi$
$998$	2.17284	−	2.87730i	0.0687800	−	0.0910795i
$999$	−1.79712	+	2.53872i	−0.0568585	+	0.0803216i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	409.2.m.a.4.20	✓	1056
409.307	even	102	inner	409.2.m.a.307.20	yes	1056

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
409.2.m.a.4.20	✓	1056	1.1	even	1	trivial
409.2.m.a.307.20	yes	1056	409.307	even	102	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 409 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	409.m (of order \(102\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(0.689284 - 0.0853519i) q^{2} +(0.0642285 - 0.293276i) q^{3} +(-1.47177 + 0.370164i) q^{4} +(-0.212539 + 0.426836i) q^{5} +(0.0192400 - 0.207633i) q^{6} +(2.30590 - 1.33131i) q^{7} +(-2.27817 + 0.882566i) q^{8} +(2.64351 + 1.21621i) q^{9} +(-0.110069 + 0.312352i) q^{10} +(0.745889 - 0.0691168i) q^{11} +(0.0140310 + 0.455409i) q^{12} +(4.25511 + 0.394294i) q^{13} +(1.47579 - 1.11446i) q^{14} +(0.111530 + 0.0897477i) q^{15} +(1.17908 - 0.633151i) q^{16} +(-0.0479235 + 0.308729i) q^{17} +(1.92594 + 0.612684i) q^{18} +(2.03831 + 1.53926i) q^{19} +(0.154808 - 0.706877i) q^{20} +(-0.242337 - 0.761773i) q^{21} +(0.508230 - 0.111304i) q^{22} +(1.03588 - 6.67325i) q^{23} +(0.112513 + 0.724818i) q^{24} +(2.87616 + 3.80865i) q^{25} +(2.96664 - 0.0914011i) q^{26} +(1.06926 - 1.41592i) q^{27} +(-2.90094 + 2.81294i) q^{28} +(-4.87540 + 4.17699i) q^{29} +(0.0845359 + 0.0523424i) q^{30} -0.335442i q^{31} +(4.74685 - 3.36023i) q^{32} +(0.0276370 - 0.223191i) q^{33} +(-0.00668237 + 0.216892i) q^{34} +(0.0781580 + 1.26720i) q^{35} +(-4.34082 - 0.811441i) q^{36} +(-1.75221 + 0.0539851i) q^{37} +(1.53636 + 0.887016i) q^{38} +(0.388937 - 1.22260i) q^{39} +(0.107488 - 1.15998i) q^{40} +(-0.632865 - 1.79594i) q^{41} +(-0.232058 - 0.504394i) q^{42} +(-4.34384 + 3.28031i) q^{43} +(-1.07219 + 0.377825i) q^{44} +(-1.08097 + 0.869854i) q^{45} +(0.144441 - 4.68818i) q^{46} +(-0.0436263 + 0.0812425i) q^{47} +(-0.109958 - 0.386462i) q^{48} +(0.0447758 - 0.0775540i) q^{49} +(2.30757 + 2.37976i) q^{50} +(0.0874647 + 0.0338840i) q^{51} +(-6.40849 + 0.994781i) q^{52} +(-1.69990 - 2.94431i) q^{53} +(0.616169 - 1.06724i) q^{54} +(-0.129029 + 0.333062i) q^{55} +(-4.07825 + 5.06805i) q^{56} +(0.582347 - 0.498925i) q^{57} +(-3.00402 + 3.29526i) q^{58} +(-5.90951 - 1.68140i) q^{59} +(-0.197367 - 0.0908033i) q^{60} +(-6.85384 - 7.51830i) q^{61} +(-0.0286306 - 0.231215i) q^{62} +(7.71481 - 0.714883i) q^{63} +(1.00707 - 0.918064i) q^{64} +(-1.07268 + 1.73243i) q^{65} -0.156201i q^{66} +(-0.634132 - 0.895812i) q^{67} +(-0.0437480 - 0.472116i) q^{68} +(-1.89057 - 0.732412i) q^{69} +(0.162031 + 0.866787i) q^{70} +(-5.52319 - 0.340659i) q^{71} +(-7.09574 - 0.437650i) q^{72} +(-3.27817 - 3.17872i) q^{73} +(-1.20316 + 0.186766i) q^{74} +(1.30172 - 0.598885i) q^{75} +(-3.56970 - 1.51092i) q^{76} +(1.62793 - 1.15239i) q^{77} +(0.163737 - 0.875915i) q^{78} +(7.44673 + 3.70803i) q^{79} +(0.0196517 + 0.637842i) q^{80} +(5.33305 + 6.22476i) q^{81} +(-0.589511 - 1.18390i) q^{82} +(-1.18102 + 0.457530i) q^{83} +(0.638645 + 1.03145i) q^{84} +(-0.121591 - 0.0860724i) q^{85} +(-2.71416 + 2.63182i) q^{86} +(0.911872 + 1.69812i) q^{87} +(-1.63826 + 0.815756i) q^{88} +(2.58322 + 9.07906i) q^{89} +(-0.670852 + 0.691839i) q^{90} +(10.3368 - 4.75568i) q^{91} +(0.945625 + 10.2049i) q^{92} +(-0.0983771 - 0.0215449i) q^{93} +(-0.0231367 + 0.0597228i) q^{94} +(-1.09023 + 0.542872i) q^{95} +(-0.680592 - 1.60796i) q^{96} +(0.302048 + 4.89718i) q^{97} +(0.0242439 - 0.0572784i) q^{98} +(2.05582 + 0.724445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1056 q - 33 q^{2} - 31 q^{3} + 29 q^{4} - 22 q^{5} - 44 q^{6} - 57 q^{7} - 22 q^{8} + 2 q^{9} - 30 q^{10} + 17 q^{11} + 67 q^{12} - 34 q^{13} - 68 q^{14} - 32 q^{15} + 21 q^{16} - 27 q^{17} + 22 q^{18}+ \cdots - 229 q^{99}+O(q^{100}) \) 1056 * q - 33 * q^2 - 31 * q^3 + 29 * q^4 - 22 * q^5 - 44 * q^6 - 57 * q^7 - 22 * q^8 + 2 * q^9 - 30 * q^10 + 17 * q^11 + 67 * q^12 - 34 * q^13 - 68 * q^14 - 32 * q^15 + 21 * q^16 - 27 * q^17 + 22 * q^18 - 34 * q^19 - 51 * q^20 - 108 * q^21 - 22 * q^22 - 32 * q^23 + 87 * q^24 - 112 * q^25 - 64 * q^26 - 82 * q^27 - 75 * q^28 - 19 * q^29 - 22 * q^30 + 52 * q^32 - 43 * q^33 - 48 * q^34 - 113 * q^35 + 22 * q^36 - 10 * q^37 - 57 * q^38 + 41 * q^39 - 225 * q^40 - 288 * q^41 - 173 * q^42 + 68 * q^43 - 34 * q^44 - 42 * q^45 + 17 * q^46 - 34 * q^47 + 68 * q^48 + 369 * q^49 - 40 * q^50 + 56 * q^51 + 8 * q^52 + 104 * q^53 + 128 * q^54 + 102 * q^55 - 138 * q^56 - 55 * q^57 - 34 * q^58 - 34 * q^59 - 254 * q^60 - 68 * q^61 + 25 * q^62 - 34 * q^63 + 98 * q^64 - 34 * q^65 - 40 * q^67 - 116 * q^68 - 38 * q^69 - 17 * q^70 + 21 * q^71 - 26 * q^72 - 31 * q^73 + 203 * q^74 + 23 * q^75 - 101 * q^76 + 19 * q^77 - 102 * q^78 - 34 * q^79 + 443 * q^80 - 265 * q^81 - 50 * q^82 + 26 * q^83 - 459 * q^84 + 84 * q^85 + 136 * q^86 - 188 * q^87 + 170 * q^88 - 80 * q^89 + 613 * q^90 - 152 * q^91 + 18 * q^92 + 56 * q^93 - 34 * q^94 - 34 * q^95 + 13 * q^96 - 31 * q^97 - 293 * q^98 - 229 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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