LMFDB - Embedded newform 225.2.w.a.77.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(2,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("225.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.w (of order $60$, degree $16$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$448$
Relative dimension:	$28$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			77.21
Character	$\chi$	$=$	225.77
Dual form			225.2.w.a.38.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.03530 - 0.397413i) q^{2} +(0.642595 + 1.60844i) q^{3} +(-0.572387 + 0.515379i) q^{4} +(-0.337136 + 2.21051i) q^{5} +(1.30449 + 1.40983i) q^{6} +(0.651331 - 2.43080i) q^{7} +(-1.39468 + 2.73721i) q^{8} +(-2.17414 + 2.06715i) q^{9} +O(q^{10})$	\(q+(1.03530 - 0.397413i) q^{2} +(0.642595 + 1.60844i) q^{3} +(-0.572387 + 0.515379i) q^{4} +(-0.337136 + 2.21051i) q^{5} +(1.30449 + 1.40983i) q^{6} +(0.651331 - 2.43080i) q^{7} +(-1.39468 + 2.73721i) q^{8} +(-2.17414 + 2.06715i) q^{9} +(0.529449 + 2.42251i) q^{10} +(0.992964 - 2.23023i) q^{11} +(-1.19677 - 0.589468i) q^{12} +(-0.0280741 + 0.0731355i) q^{13} +(-0.291712 - 2.77545i) q^{14} +(-3.77210 + 0.878200i) q^{15} +(-0.195083 + 1.85609i) q^{16} +(5.10587 + 2.60157i) q^{17} +(-1.42937 + 3.00415i) q^{18} +(1.99615 - 0.648587i) q^{19} +(-0.946277 - 1.43902i) q^{20} +(4.32834 - 0.514396i) q^{21} +(0.141688 - 2.70357i) q^{22} +(3.94298 - 4.86918i) q^{23} +(-5.29885 - 0.484335i) q^{24} +(-4.77268 - 1.49048i) q^{25} +0.0868740i q^{26} +(-4.72197 - 2.16863i) q^{27} +(0.879971 + 1.72704i) q^{28} +(5.33338 - 1.13364i) q^{29} +(-3.55624 + 2.40828i) q^{30} +(-2.55046 - 0.542118i) q^{31} +(-1.05454 - 3.93561i) q^{32} +(4.22527 + 0.163982i) q^{33} +(6.31999 + 0.664258i) q^{34} +(5.15372 + 2.25928i) q^{35} +(0.179084 - 2.30372i) q^{36} +(-1.17452 - 7.41562i) q^{37} +(1.80885 - 1.46478i) q^{38} +(-0.135674 + 0.00184113i) q^{39} +(-5.58043 - 4.00576i) q^{40} +(0.972306 + 2.18383i) q^{41} +(4.27669 - 2.25269i) q^{42} +(-2.31923 - 0.621435i) q^{43} +(0.581057 + 1.78831i) q^{44} +(-3.83647 - 5.50287i) q^{45} +(2.14708 - 6.60804i) q^{46} +(-5.09026 + 7.83831i) q^{47} +(-3.11076 + 0.878936i) q^{48} +(0.577613 + 0.333485i) q^{49} +(-5.53348 + 0.353634i) q^{50} +(-0.903455 + 9.88423i) q^{51} +(-0.0216233 - 0.0563306i) q^{52} +(-11.3074 + 5.76140i) q^{53} +(-5.75049 - 0.368602i) q^{54} +(4.59518 + 2.94684i) q^{55} +(5.74523 + 5.17303i) q^{56} +(2.32593 + 2.79390i) q^{57} +(5.07111 - 3.29322i) q^{58} +(8.91811 - 3.97060i) q^{59} +(1.70650 - 2.44673i) q^{60} +(-9.96634 - 4.43730i) q^{61} +(-2.85593 + 0.452335i) q^{62} +(3.60874 + 6.63131i) q^{63} +(-4.84981 - 6.67519i) q^{64} +(-0.152202 - 0.0867146i) q^{65} +(4.43957 - 1.50941i) q^{66} +(-2.63921 - 4.06402i) q^{67} +(-4.26333 + 1.14236i) q^{68} +(10.3655 + 3.21313i) q^{69} +(6.23350 + 0.290873i) q^{70} +(5.52847 + 1.79631i) q^{71} +(-2.62600 - 8.83411i) q^{72} +(-2.05016 + 12.9442i) q^{73} +(-4.16304 - 7.21060i) q^{74} +(-0.669555 - 8.63433i) q^{75} +(-0.808299 + 1.40002i) q^{76} +(-4.77451 - 3.86632i) q^{77} +(-0.139731 + 0.0558248i) q^{78} +(-1.55252 - 7.30404i) q^{79} +(-4.03713 - 1.05699i) q^{80} +(0.453788 - 8.98855i) q^{81} +(1.87451 + 1.87451i) q^{82} +(-1.34078 + 0.0702675i) q^{83} +(-2.21237 + 2.52517i) q^{84} +(-7.47216 + 10.4095i) q^{85} +(-2.64805 + 0.278322i) q^{86} +(5.25060 + 7.84993i) q^{87} +(4.71976 + 5.82842i) q^{88} +(6.60723 - 4.80043i) q^{89} +(-6.15880 - 4.17244i) q^{90} +(0.159492 + 0.115878i) q^{91} +(0.252563 + 4.81918i) q^{92} +(-0.766954 - 4.45062i) q^{93} +(-2.15488 + 10.1379i) q^{94} +(0.760734 + 4.63116i) q^{95} +(5.65253 - 4.22517i) q^{96} +(-16.1707 - 10.5014i) q^{97} +(0.730533 + 0.115705i) q^{98} +(2.45138 + 6.90145i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9}+O(q^{10}) $ 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9	$ 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} - 32 q^{10} - 18 q^{11} - 14 q^{12} - 8 q^{13} - 30 q^{14} - 14 q^{15} - 50 q^{16} - 56 q^{18} - 40 q^{19} - 48 q^{20} - 12 q^{21} - 48 q^{23} + 16 q^{25} - 38 q^{27} - 24 q^{28} - 30 q^{29} - 50 q^{30} - 6 q^{31} - 60 q^{32} - 8 q^{33} - 10 q^{34} + 4 q^{36} - 44 q^{37} - 60 q^{39} - 16 q^{40} - 18 q^{41} + 174 q^{42} - 8 q^{43} - 64 q^{45} - 24 q^{46} - 18 q^{47} - 100 q^{48} + 24 q^{50} - 32 q^{51} + 24 q^{52} - 150 q^{54} - 24 q^{55} - 18 q^{56} - 94 q^{57} - 4 q^{58} + 202 q^{60} - 6 q^{61} - 46 q^{63} - 40 q^{64} - 96 q^{65} + 12 q^{66} - 14 q^{67} + 288 q^{68} + 50 q^{69} - 28 q^{70} + 102 q^{72} - 32 q^{73} + 18 q^{75} - 32 q^{76} + 216 q^{77} + 182 q^{78} - 10 q^{79} - 32 q^{81} - 72 q^{82} + 36 q^{83} + 100 q^{84} - 32 q^{85} - 18 q^{86} + 48 q^{87} - 28 q^{88} + 106 q^{90} - 24 q^{91} + 30 q^{92} + 8 q^{93} - 130 q^{94} + 6 q^{95} - 60 q^{96} - 38 q^{97}+O(q^{100}) $ 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9 - 32 * q^10 - 18 * q^11 - 14 * q^12 - 8 * q^13 - 30 * q^14 - 14 * q^15 - 50 * q^16 - 56 * q^18 - 40 * q^19 - 48 * q^20 - 12 * q^21 - 48 * q^23 + 16 * q^25 - 38 * q^27 - 24 * q^28 - 30 * q^29 - 50 * q^30 - 6 * q^31 - 60 * q^32 - 8 * q^33 - 10 * q^34 + 4 * q^36 - 44 * q^37 - 60 * q^39 - 16 * q^40 - 18 * q^41 + 174 * q^42 - 8 * q^43 - 64 * q^45 - 24 * q^46 - 18 * q^47 - 100 * q^48 + 24 * q^50 - 32 * q^51 + 24 * q^52 - 150 * q^54 - 24 * q^55 - 18 * q^56 - 94 * q^57 - 4 * q^58 + 202 * q^60 - 6 * q^61 - 46 * q^63 - 40 * q^64 - 96 * q^65 + 12 * q^66 - 14 * q^67 + 288 * q^68 + 50 * q^69 - 28 * q^70 + 102 * q^72 - 32 * q^73 + 18 * q^75 - 32 * q^76 + 216 * q^77 + 182 * q^78 - 10 * q^79 - 32 * q^81 - 72 * q^82 + 36 * q^83 + 100 * q^84 - 32 * q^85 - 18 * q^86 + 48 * q^87 - 28 * q^88 + 106 * q^90 - 24 * q^91 + 30 * q^92 + 8 * q^93 - 130 * q^94 + 6 * q^95 - 60 * q^96 - 38 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{20}\right)$

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 $

$2$	1.03530	−	0.397413i	0.732066	−	0.281014i	0.0363582	−	0.999339i	$-0.488424\pi$
$2$	1.03530	−	0.397413i	0.732066	−	0.281014i	0.695708	+	0.718325i	$0.255091\pi$
$3$	0.642595	+	1.60844i	0.371003	+	0.928632i
$3$	0.642595	+	1.60844i	0.371003	+	0.928632i
$4$	−0.572387	+	0.515379i	−0.286193	+	0.257690i
$5$	−0.337136	+	2.21051i	−0.150772	+	0.988569i
$5$	−0.337136	+	2.21051i	−0.150772	+	0.988569i
$6$	1.30449	+	1.40983i	0.532557	+	0.575563i
$7$	0.651331	−	2.43080i	0.246180	−	0.918757i	−0.726607	−	0.687054i	$-0.758904\pi$
$7$	0.651331	−	2.43080i	0.246180	−	0.918757i	0.972787	−	0.231703i	$-0.0744297\pi$
$8$	−1.39468	+	2.73721i	−0.493094	+	0.967751i
$9$	−2.17414	+	2.06715i	−0.724714	+	0.689050i
$10$	0.529449	+	2.42251i	0.167427	+	0.766066i
$11$	0.992964	−	2.23023i	0.299390	−	0.672441i	−0.699729	−	0.714408i	$-0.746696\pi$
$11$	0.992964	−	2.23023i	0.299390	−	0.672441i	0.999119	+	0.0419676i	$0.0133626\pi$
$12$	−1.19677	−	0.589468i	−0.345477	−	0.170165i
$13$	−0.0280741	+	0.0731355i	−0.00778635	+	0.0202841i	−0.937419	−	0.348205i	$-0.886791\pi$
$13$	−0.0280741	+	0.0731355i	−0.00778635	+	0.0202841i	0.929632	+	0.368489i	$0.120125\pi$
$14$	−0.291712	−	2.77545i	−0.0779632	−	0.741770i
$15$	−3.77210	+	0.878200i	−0.973953	+	0.226750i
$16$	−0.195083	+	1.85609i	−0.0487707	+	0.464023i
$17$	5.10587	+	2.60157i	1.23836	+	0.630974i	0.945637	−	0.325225i	$-0.105440\pi$
$17$	5.10587	+	2.60157i	1.23836	+	0.630974i	0.292719	+	0.956199i	$0.405440\pi$
$18$	−1.42937	+	3.00415i	−0.336906	+	0.708084i
$19$	1.99615	−	0.648587i	0.457947	−	0.148796i	−0.0709536	−	0.997480i	$-0.522604\pi$
$19$	1.99615	−	0.648587i	0.457947	−	0.148796i	0.528901	+	0.848683i	$0.322604\pi$
$20$	−0.946277	−	1.43902i	−0.211594	−	0.321774i
$21$	4.32834	−	0.514396i	0.944520	−	0.112251i
$22$	0.141688	−	2.70357i	0.0302080	−	0.576403i
$23$	3.94298	−	4.86918i	0.822168	−	1.01529i	−0.177347	−	0.984148i	$-0.556751\pi$
$23$	3.94298	−	4.86918i	0.822168	−	1.01529i	0.999515	−	0.0311448i	$-0.00991531\pi$
$24$	−5.29885	−	0.484335i	−1.08162	−	0.0988644i
$25$	−4.77268	−	1.49048i	−0.954536	−	0.298096i
$26$			0.0868740i			0.0170374i
$27$	−4.72197	−	2.16863i	−0.908744	−	0.417353i
$28$	0.879971	+	1.72704i	0.166299	+	0.326380i
$29$	5.33338	−	1.13364i	0.990384	−	0.210513i	0.315892	−	0.948795i	$-0.397696\pi$
$29$	5.33338	−	1.13364i	0.990384	−	0.210513i	0.674491	+	0.738283i	$0.264363\pi$
$30$	−3.55624	+	2.40828i	−0.649278	+	0.439690i
$31$	−2.55046	−	0.542118i	−0.458077	−	0.0973672i	−0.0269068	−	0.999638i	$-0.508566\pi$
$31$	−2.55046	−	0.542118i	−0.458077	−	0.0973672i	−0.431170	+	0.902271i	$0.641899\pi$
$32$	−1.05454	−	3.93561i	−0.186419	−	0.695724i
$33$	4.22527	+	0.163982i	0.735524	+	0.0285457i
$34$	6.31999	+	0.664258i	1.08387	+	0.113919i
$35$	5.15372	+	2.25928i	0.871137	+	0.381888i
$36$	0.179084	−	2.30372i	0.0298473	−	0.383953i
$37$	−1.17452	−	7.41562i	−0.193090	−	1.21912i	−0.873696	−	0.486472i	$-0.838284\pi$
$37$	−1.17452	−	7.41562i	−0.193090	−	1.21912i	0.680607	−	0.732649i	$-0.261716\pi$
$38$	1.80885	−	1.46478i	0.293434	−	0.237618i
$39$	−0.135674	+	0.00184113i	−0.0217253	+	0.000294816i
$40$	−5.58043	−	4.00576i	−0.882344	−	0.633367i
$41$	0.972306	+	2.18383i	0.151849	+	0.341058i	0.973413	−	0.229059i	$-0.0735648\pi$
$41$	0.972306	+	2.18383i	0.151849	+	0.341058i	−0.821564	+	0.570116i	$0.806898\pi$
$42$	4.27669	−	2.25269i	0.659907	−	0.347598i
$43$	−2.31923	−	0.621435i	−0.353679	−	0.0947679i	0.0776054	−	0.996984i	$-0.475273\pi$
$43$	−2.31923	−	0.621435i	−0.353679	−	0.0947679i	−0.431284	+	0.902216i	$0.641939\pi$
$44$	0.581057	+	1.78831i	0.0875976	+	0.269598i
$45$	−3.83647	−	5.50287i	−0.571907	−	0.820319i
$46$	2.14708	−	6.60804i	0.316570	−	0.974302i
$47$	−5.09026	+	7.83831i	−0.742490	+	1.14333i	0.242404	+	0.970175i	$0.422064\pi$
$47$	−5.09026	+	7.83831i	−0.742490	+	1.14333i	−0.984894	+	0.173159i	$0.944603\pi$
$48$	−3.11076	+	0.878936i	−0.449000	+	0.126864i
$49$	0.577613	+	0.333485i	0.0825162	+	0.0476408i
$50$	−5.53348	+	0.353634i	−0.782552	+	0.0500115i
$51$	−0.903455	+	9.88423i	−0.126509	+	1.38407i
$52$	−0.0216233	−	0.0563306i	−0.00299861	−	0.00781165i
$53$	−11.3074	+	5.76140i	−1.55319	+	0.791389i	−0.999155	−	0.0411062i	$-0.986912\pi$
$53$	−11.3074	+	5.76140i	−1.55319	+	0.791389i	−0.554033	+	0.832495i	$0.686912\pi$
$54$	−5.75049	−	0.368602i	−0.782543	−	0.0501604i
$55$	4.59518	+	2.94684i	0.619614	+	0.397352i
$56$	5.74523	+	5.17303i	0.767738	+	0.691275i
$57$	2.32593	+	2.79390i	0.308077	+	0.370061i
$58$	5.07111	−	3.29322i	0.665869	−	0.432420i
$59$	8.91811	−	3.97060i	1.16104	−	0.516928i	0.266464	−	0.963845i	$-0.414145\pi$
$59$	8.91811	−	3.97060i	1.16104	−	0.516928i	0.894575	+	0.446917i	$0.147478\pi$
$60$	1.70650	−	2.44673i	0.220308	−	0.315872i
$61$	−9.96634	−	4.43730i	−1.27606	−	0.568138i	−0.346929	−	0.937891i	$-0.612775\pi$
$61$	−9.96634	−	4.43730i	−1.27606	−	0.568138i	−0.929130	+	0.369754i	$0.879442\pi$
$62$	−2.85593	+	0.452335i	−0.362704	+	0.0574466i
$63$	3.60874	+	6.63131i	0.454659	+	0.835466i
$64$	−4.84981	−	6.67519i	−0.606226	−	0.834399i
$65$	−0.152202	−	0.0867146i	−0.0188783	−	0.0107556i
$66$	4.43957	−	1.50941i	0.546474	−	0.185795i
$67$	−2.63921	−	4.06402i	−0.322430	−	0.496499i	0.639872	−	0.768482i	$-0.278987\pi$
$67$	−2.63921	−	4.06402i	−0.322430	−	0.496499i	−0.962302	+	0.271982i	$0.912321\pi$
$68$	−4.26333	+	1.14236i	−0.517004	+	0.138531i
$69$	10.3655	+	3.21313i	1.24786	+	0.386815i
$70$	6.23350	+	0.290873i	0.745045	+	0.0347660i
$71$	5.52847	+	1.79631i	0.656109	+	0.213183i	0.618106	−	0.786095i	$-0.287900\pi$
$71$	5.52847	+	1.79631i	0.656109	+	0.213183i	0.0380030	+	0.999278i	$0.487900\pi$
$72$	−2.62600	−	8.83411i	−0.309477	−	1.04111i
$73$	−2.05016	+	12.9442i	−0.239953	+	1.51501i	0.513835	+	0.857889i	$0.328224\pi$
$73$	−2.05016	+	12.9442i	−0.239953	+	1.51501i	−0.753789	+	0.657117i	$0.771776\pi$
$74$	−4.16304	−	7.21060i	−0.483944	−	0.838216i
$75$	−0.669555	−	8.63433i	−0.0773135	−	0.997007i
$76$	−0.808299	+	1.40002i	−0.0927183	+	0.160593i
$77$	−4.77451	−	3.86632i	−0.544106	−	0.440608i
$78$	−0.139731	+	0.0558248i	−0.0158215	+	0.00632092i
$79$	−1.55252	−	7.30404i	−0.174672	−	0.821769i	−0.975000	−	0.222206i	$-0.928674\pi$
$79$	−1.55252	−	7.30404i	−0.174672	−	0.821769i	0.800327	−	0.599563i	$-0.204659\pi$
$80$	−4.03713	−	1.05699i	−0.451365	−	0.118175i
$81$	0.453788	−	8.98855i	0.0504209	−	0.998728i
$82$	1.87451	+	1.87451i	0.207005	+	0.207005i
$83$	−1.34078	+	0.0702675i	−0.147170	+	0.00771286i	−0.125779	−	0.992058i	$-0.540143\pi$
$83$	−1.34078	+	0.0702675i	−0.147170	+	0.00771286i	−0.0213914	+	0.999771i	$0.506810\pi$
$84$	−2.21237	+	2.52517i	−0.241390	+	0.275518i
$85$	−7.47216	+	10.4095i	−0.810470	+	1.12907i
$86$	−2.64805	+	0.278322i	−0.285547	+	0.0300122i
$87$	5.25060	+	7.84993i	0.562924	+	0.841601i
$88$	4.71976	+	5.82842i	0.503128	+	0.621311i
$89$	6.60723	−	4.80043i	0.700365	−	0.508845i	−0.179686	−	0.983724i	$-0.557508\pi$
$89$	6.60723	−	4.80043i	0.700365	−	0.508845i	0.880051	+	0.474879i	$0.157508\pi$
$90$	−6.15880	−	4.17244i	−0.649194	−	0.439814i
$91$	0.159492	+	0.115878i	0.0167193	+	0.0121473i
$92$	0.252563	+	4.81918i	0.0263315	+	0.502434i
$93$	−0.766954	−	4.45062i	−0.0795294	−	0.461508i
$94$	−2.15488	+	10.1379i	−0.222259	+	1.04565i
$95$	0.760734	+	4.63116i	0.0780497	+	0.475147i
$96$	5.65253	−	4.22517i	0.576909	−	0.431229i
$97$	−16.1707	−	10.5014i	−1.64188	−	1.06625i	−0.932335	−	0.361597i	$-0.882232\pi$
$97$	−16.1707	−	10.5014i	−1.64188	−	1.06625i	−0.709550	−	0.704655i	$-0.751102\pi$
$98$	0.730533	+	0.115705i	0.0737950	+	0.0116880i
$99$	2.45138	+	6.90145i	0.246373	+	0.693622i
$100$	3.49998	−	1.60661i	0.349998	−	0.160661i
$101$	6.85621	−	3.95844i	0.682219	−	0.393879i	−0.118472	−	0.992957i	$-0.537800\pi$
$101$	6.85621	−	3.95844i	0.682219	−	0.393879i	0.800690	+	0.599078i	$0.204466\pi$
$102$	2.99278	+	10.5922i	0.296330	+	1.04878i
$103$	9.76545	+	0.511786i	0.962219	+	0.0504278i	0.526971	−	0.849883i	$-0.323328\pi$
$103$	9.76545	+	0.511786i	0.962219	+	0.0504278i	0.435248	+	0.900311i	$0.356661\pi$
$104$	−0.161033	−	0.178845i	−0.0157906	−	0.0175372i
$105$	−0.322160	+	9.74123i	−0.0314396	+	0.950647i
$106$	−9.41684	+	10.4585i	−0.914644	+	1.01582i
$107$	−8.05906	+	8.05906i	−0.779098	+	0.779098i	−0.979678	−	0.200579i	$-0.935718\pi$
$107$	−8.05906	+	8.05906i	−0.779098	+	0.779098i	0.200579	+	0.979678i	$0.435718\pi$
$108$	3.82046	−	1.19231i	0.367624	−	0.114730i
$109$	−0.0328738	+	0.0452469i	−0.00314874	+	0.00433387i	−0.810588	−	0.585616i	$-0.800853\pi$
$109$	−0.0328738	+	0.0452469i	−0.00314874	+	0.00433387i	0.807440	+	0.589950i	$0.200853\pi$
$110$	5.92850	+	1.22467i	0.565260	+	0.116768i
$111$	11.1728	−	6.65439i	1.06048	−	0.631606i
$112$	4.38472	+	1.68314i	0.414317	+	0.159042i
$113$	−9.71275	−	3.72838i	−0.913699	−	0.350736i	−0.144322	−	0.989531i	$-0.546100\pi$
$113$	−9.71275	−	3.72838i	−0.913699	−	0.350736i	−0.769377	+	0.638795i	$0.779433\pi$
$114$	3.51836	+	1.96816i	0.329524	+	0.184335i
$115$	9.43402	+	10.3576i	0.879727	+	0.965847i
$116$	−2.46850	+	3.39759i	−0.229194	+	0.315459i
$117$	−0.0901449	−	0.217040i	−0.00833390	−	0.0200654i
$118$	7.65493	−	7.65493i	0.704693	−	0.704693i
$119$	9.64952	−	10.7169i	0.884570	−	0.982414i
$120$	2.85706	−	11.5499i	0.260813	−	1.05435i
$121$	3.37247	+	3.74551i	0.306588	+	0.340501i
$122$	−12.0816	−	0.633168i	−1.09381	−	0.0573243i
$123$	−2.88776	+	2.96721i	−0.260381	+	0.267545i
$124$	1.73925	−	1.00415i	0.156189	−	0.0901758i
$125$	4.90376	−	10.0475i	0.438606	−	0.898680i
$126$	6.37149	+	5.43121i	0.567618	+	0.483851i
$127$	10.0760	+	1.59589i	0.894104	+	0.141612i	0.586545	−	0.809917i	$-0.300488\pi$
$127$	10.0760	+	1.59589i	0.894104	+	0.141612i	0.307559	+	0.951529i	$0.400488\pi$
$128$	−0.839583	−	0.545231i	−0.0742093	−	0.0481921i
$129$	−0.490785	−	4.12966i	−0.0432112	−	0.363596i
$130$	−0.192036	−	0.0292883i	−0.0168426	−	0.00256876i
$131$	−1.55120	+	7.29780i	−0.135529	+	0.637612i	0.856971	+	0.515364i	$0.172343\pi$
$131$	−1.55120	+	7.29780i	−0.135529	+	0.637612i	−0.992500	+	0.122247i	$0.960990\pi$
$132$	−2.50300	+	2.08375i	−0.217858	+	0.181367i
$133$	−0.276434	−	5.27468i	−0.0239699	−	0.457373i
$134$	−4.34746	−	3.15861i	−0.375563	−	0.272863i
$135$	6.38572	−	9.70683i	0.549595	−	0.835431i
$136$	−14.2421	+	10.3475i	−1.22125	+	0.887291i
$137$	5.43738	+	6.71461i	0.464547	+	0.573667i	0.954549	−	0.298054i	$-0.0963374\pi$
$137$	5.43738	+	6.71461i	0.464547	+	0.573667i	−0.490002	+	0.871721i	$0.663004\pi$
$138$	12.0083	−	0.792849i	1.02222	−	0.0674918i
$139$	12.4147	−	1.30484i	1.05300	−	0.110675i	0.437823	−	0.899061i	$-0.355750\pi$
$139$	12.4147	−	1.30484i	1.05300	−	0.110675i	0.615181	+	0.788386i	$0.289083\pi$
$140$	−4.11430	+	1.36293i	−0.347722	+	0.115189i
$141$	−15.8784	−	3.15050i	−1.33720	−	0.265320i
$142$	6.43749	−	0.337374i	0.540222	−	0.0283118i
$143$	0.135233	+	0.135233i	0.0113087	+	0.0113087i
$144$	−3.41268	−	4.43867i	−0.284390	−	0.369889i
$145$	0.707856	+	12.1717i	0.0587842	+	1.01080i
$146$	3.02168	+	14.2159i	0.250076	+	1.17651i
$147$	−0.165218	+	1.14335i	−0.0136270	+	0.0943020i
$148$	4.49414	+	3.63928i	0.369416	+	0.299147i
$149$	−5.76176	+	9.97966i	−0.472022	+	0.817566i	−0.999488	−	0.0320105i	$-0.989809\pi$
$149$	−5.76176	+	9.97966i	−0.472022	+	0.817566i	0.527466	+	0.849576i	$0.323142\pi$
$150$	−4.12459	−	8.67301i	−0.336771	−	0.708148i
$151$	5.11749	+	8.86375i	0.416455	+	0.721322i	0.995580	−	0.0939173i	$-0.0299389\pi$
$151$	5.11749	+	8.86375i	0.416455	+	0.721322i	−0.579125	+	0.815239i	$0.696606\pi$
$152$	−1.00866	+	6.36845i	−0.0818135	+	0.516550i
$153$	−16.4787	+	4.89841i	−1.33223	+	0.396013i
$154$	−6.47956	−	2.10534i	−0.522138	−	0.169653i
$155$	2.05821	−	5.45505i	0.165319	−	0.438160i
$156$	0.0767092	−	0.0709775i	0.00614165	−	0.00568275i
$157$	−6.84001	+	1.83277i	−0.545892	+	0.146271i	−0.521217	−	0.853424i	$-0.674522\pi$
$157$	−6.84001	+	1.83277i	−0.545892	+	0.146271i	−0.0246750	+	0.999696i	$0.507855\pi$
$158$	−4.51005	−	6.94486i	−0.358800	−	0.552504i
$159$	−16.5329	−	14.4850i	−1.31115	−	1.14873i
$160$	9.05521	−	1.00424i	0.715877	−	0.0793921i
$161$	−9.26781	−	12.7561i	−0.730406	−	1.00532i
$162$	−3.10237	−	9.48617i	−0.243745	−	0.745304i
$163$	−20.1209	+	3.18684i	−1.57599	+	0.249613i	−0.882310	−	0.470668i	$-0.844013\pi$
$163$	−20.1209	+	3.18684i	−1.57599	+	0.249613i	−0.693682	+	0.720281i	$0.744013\pi$
$164$	−1.68204	−	0.748891i	−0.131345	−	0.0584786i
$165$	−1.78697	+	9.28469i	−0.139116	+	0.722812i
$166$	−1.36018	+	0.605593i	−0.105571	+	0.0470031i
$167$	6.83161	−	4.43650i	0.528646	−	0.343307i	−0.252559	−	0.967582i	$-0.581272\pi$
$167$	6.83161	−	4.43650i	0.528646	−	0.343307i	0.781205	+	0.624275i	$0.214605\pi$
$168$	−4.62863	+	12.5650i	−0.357107	+	0.969411i
$169$	9.65632	+	8.69459i	0.742794	+	0.668815i
$170$	−3.59904	+	13.7464i	−0.276034	+	1.05430i
$171$	−2.99918	+	5.53645i	−0.229353	+	0.423383i
$172$	1.64777	−	0.839580i	0.125641	−	0.0640173i
$173$	−7.80211	−	20.3252i	−0.593184	−	1.54530i	−0.820603	−	0.571499i	$-0.806362\pi$
$173$	−7.80211	−	20.3252i	−0.593184	−	1.54530i	0.227419	−	0.973797i	$-0.426971\pi$
$174$	8.55560	+	6.04035i	0.648598	+	0.457918i
$175$	−6.73166	+	10.6306i	−0.508866	+	0.803601i
$176$	3.94580	+	2.27811i	0.297426	+	0.171719i
$177$	12.1172	+	11.7927i	0.910784	+	0.886396i
$178$	4.93269	−	7.59568i	0.369721	−	0.569320i
$179$	−3.03093	+	9.32825i	−0.226542	+	0.697226i	0.771589	+	0.636122i	$0.219462\pi$
$179$	−3.03093	+	9.32825i	−0.226542	+	0.697226i	−0.998131	+	0.0611045i	$0.980538\pi$
$180$	5.03200	+	1.17253i	0.375063	+	0.0873954i
$181$	−2.45627	−	7.55961i	−0.182573	−	0.561902i	0.817325	−	0.576177i	$-0.195456\pi$
$181$	−2.45627	−	7.55961i	−0.182573	−	0.561902i	−0.999898	+	0.0142750i	$0.995456\pi$
$182$	0.211173	+	0.0565838i	0.0156532	+	0.00419427i
$183$	0.732795	−	18.8816i	0.0541698	−	1.39577i
$184$	7.82878	+	17.5837i	0.577145	+	1.29629i
$185$	16.7883	−	0.0962102i	1.23430	−	0.00707351i
$186$	−2.56276	−	4.30292i	−0.187911	−	0.315505i
$187$	10.8721	−	8.80402i	0.795043	−	0.643814i
$188$	−1.12611	−	7.10995i	−0.0821297	−	0.518547i
$189$	−8.34708	+	10.0657i	−0.607161	+	0.732171i
$190$	2.62807	+	4.49230i	0.190660	+	0.325906i
$191$	−16.6413	−	1.74907i	−1.20412	−	0.126559i	−0.518864	−	0.854857i	$-0.673645\pi$
$191$	−16.6413	−	1.74907i	−1.20412	−	0.126559i	−0.685260	+	0.728298i	$0.740311\pi$
$192$	7.62016	−	12.0901i	0.549938	−	0.872525i
$193$	−2.86891	−	10.7069i	−0.206509	−	0.770701i	−0.988984	−	0.148020i	$-0.952710\pi$
$193$	−2.86891	−	10.7069i	−0.206509	−	0.770701i	0.782476	−	0.622681i	$-0.213957\pi$
$194$	−20.9149	−	4.44559i	−1.50160	−	0.319175i
$195$	0.0416708	−	0.300529i	0.00298411	−	0.0215214i
$196$	−0.502490	+	0.106807i	−0.0358921	+	0.00762910i
$197$	−6.74976	−	13.2471i	−0.480900	−	0.943820i	−0.996224	−	0.0868242i	$-0.972328\pi$
$197$	−6.74976	−	13.2471i	−0.480900	−	0.943820i	0.515323	−	0.856996i	$-0.327672\pi$
$198$	5.28064	+	6.17084i	0.375278	+	0.438543i
$199$		−	2.33837i		−	0.165763i	−0.996559	−	0.0828814i	$-0.973588\pi$
$199$		−	2.33837i		−	0.165763i	0.996559	−	0.0828814i	$-0.0264123\pi$
$200$	10.7361	−	10.9851i	0.759159	−	0.776764i
$201$	4.84078	−	6.85652i	0.341442	−	0.483622i
$202$	5.52508	−	6.82291i	0.388743	−	0.480058i
$203$	0.718131	−	13.7028i	0.0504029	−	0.961745i
$204$	−4.57700	−	6.12322i	−0.320454	−	0.428711i
$205$	−5.15518	+	1.41304i	−0.360053	+	0.0986909i
$206$	10.3135	−	3.35107i	0.718578	−	0.233480i
$207$	1.49271	+	18.7370i	0.103751	+	1.30231i
$208$	−0.130269	−	0.0663755i	−0.00903255	−	0.00460231i
$209$	0.535600	−	5.09590i	0.0370483	−	0.352491i
$210$	3.53777	+	10.2131i	0.244129	+	0.704771i
$211$	−2.31952	−	22.0687i	−0.159682	−	1.51927i	−0.721733	−	0.692172i	$-0.756654\pi$
$211$	−2.31952	−	22.0687i	−0.159682	−	1.51927i	0.562051	−	0.827103i	$-0.310012\pi$
$212$	3.50289	−	9.12533i	0.240579	−	0.626730i
$213$	0.663320	+	10.0465i	0.0454499	+	0.688375i
$214$	−5.14074	+	11.5463i	−0.351414	+	0.789289i
$215$	2.15558	−	4.91715i	0.147009	−	0.335347i
$216$	12.5217	−	9.90051i	0.851991	−	0.673644i
$217$	−2.97898	+	5.84657i	−0.202226	+	0.396891i
$218$	−0.0160524	+	0.0599085i	−0.00108721	+	0.00405752i
$219$	−22.1374	+	5.02034i	−1.49591	+	0.339243i
$220$	−4.14896	+	0.681527i	−0.279723	+	0.0459485i
$221$	−0.333610	+	0.300384i	−0.0224410	+	0.0202060i
$222$	8.92265	−	11.3295i	0.598849	−	0.760386i
$223$	21.8333	−	8.38104i	1.46207	−	0.561236i	0.508142	−	0.861274i	$-0.330333\pi$
$223$	21.8333	−	8.38104i	1.46207	−	0.561236i	0.953927	+	0.300038i	$0.0969993\pi$
$224$	−10.2535			−0.685093
$225$	13.4575	−	6.62532i	0.897169	−	0.441688i
$226$	−11.5373			−0.767450
$227$	−5.63854	+	2.16443i	−0.374243	+	0.143659i	−0.538217	−	0.842806i	$-0.680902\pi$
$227$	−5.63854	+	2.16443i	−0.374243	+	0.143659i	0.163974	+	0.986465i	$0.447569\pi$
$228$	−2.77125	−	0.400455i	−0.183530	−	0.0265208i
$229$	−6.43761	+	5.79645i	−0.425410	+	0.383040i	−0.853841	−	0.520534i	$-0.825733\pi$
$229$	−6.43761	+	5.79645i	−0.425410	+	0.383040i	0.428432	+	0.903574i	$0.359066\pi$
$230$	13.8833	+	6.97394i	0.915435	+	0.459848i
$231$	3.15066	−	10.1640i	0.207298	−	0.668740i
$232$	−4.33533	+	16.1797i	−0.284628	+	1.06225i
$233$	−10.4578	+	20.5247i	−0.685116	+	1.34462i	0.242159	+	0.970236i	$0.422144\pi$
$233$	−10.4578	+	20.5247i	−0.685116	+	1.34462i	−0.927276	+	0.374380i	$0.877856\pi$
$234$	−0.179582	−	0.188876i	−0.0117396	−	0.0123472i
$235$	−15.6105	−	13.8946i	−1.01832	−	0.906385i
$236$	−3.05824	+	6.86893i	−0.199075	+	0.447129i
$237$	10.7505	−	7.19068i	0.698317	−	0.467085i
$238$	5.73109	−	14.9300i	0.371491	−	0.967768i
$239$	−0.489805	−	4.66018i	−0.0316829	−	0.301442i	−0.998876	−	0.0474000i	$-0.984906\pi$
$239$	−0.489805	−	4.66018i	−0.0316829	−	0.301442i	0.967193	−	0.254042i	$-0.0817602\pi$
$240$	−0.894145	−	7.17269i	−0.0577168	−	0.462995i
$241$	−1.11245	+	10.5843i	−0.0716593	+	0.681793i	0.898442	+	0.439092i	$0.144700\pi$
$241$	−1.11245	+	10.5843i	−0.0716593	+	0.681793i	−0.970101	+	0.242700i	$0.921967\pi$
$242$	4.98003	+	2.53745i	0.320128	+	0.163114i
$243$	14.7491	−	5.04611i	0.946157	−	0.323708i
$244$	7.99149	−	2.59659i	0.511603	−	0.166230i
$245$	−0.931906	+	1.16439i	−0.0595373	+	0.0743901i
$246$	−1.81048	+	4.21958i	−0.115432	+	0.269031i
$247$	−0.00860524	+	0.164198i	−0.000547538	+	0.0104476i
$248$	5.04097	−	6.22508i	0.320102	−	0.395293i
$249$	−0.974602	−	2.11141i	−0.0617629	−	0.133805i
$250$	1.08382	−	12.3510i	0.0685470	−	0.781147i
$251$		−	14.6220i		−	0.922931i	−0.887158	−	0.461466i	$-0.847324\pi$
$251$		−	14.6220i		−	0.922931i	0.887158	−	0.461466i	$-0.152676\pi$
$252$	−5.48323	−	1.93580i	−0.345411	−	0.121944i
$253$	−6.94416	−	13.6287i	−0.436576	−	0.856828i
$254$	11.0659	−	2.35214i	0.694338	−	0.147586i
$255$	−21.5446	−	5.32942i	−1.34917	−	0.333741i
$256$	15.0555	+	3.20014i	0.940967	+	0.200009i
$257$	4.81396	+	17.9660i	0.300287	+	1.12069i	0.936927	+	0.349525i	$0.113657\pi$
$257$	4.81396	+	17.9660i	0.300287	+	1.12069i	−0.636640	+	0.771161i	$0.719676\pi$
$258$	−2.14929	−	4.08038i	−0.133809	−	0.254033i
$259$	−18.7909	−	1.97500i	−1.16761	−	0.122721i
$260$	0.131809	−	0.0288074i	0.00817445	−	0.00178656i
$261$	−9.25211	+	13.4896i	−0.572691	+	0.834985i
$262$	1.29430	+	8.17186i	0.0799618	+	0.504859i
$263$	−13.8028	+	11.1773i	−0.851120	+	0.689224i	−0.952140	−	0.305661i	$-0.901123\pi$
$263$	−13.8028	+	11.1773i	−0.851120	+	0.689224i	0.101020	+	0.994884i	$0.467789\pi$
$264$	−6.34175	+	11.3368i	−0.390308	+	0.697729i
$265$	−8.92348	−	26.9374i	−0.548165	−	1.65475i
$266$	−2.38242	−	5.35101i	−0.146076	−	0.328091i
$267$	11.9670	+	7.54258i	0.732367	+	0.461598i
$268$	3.60516	+	0.965999i	0.220220	+	0.0590078i
$269$	2.10939	+	6.49203i	0.128612	+	0.395826i	0.994542	−	0.104339i	$-0.0332727\pi$
$269$	2.10939	+	6.49203i	0.128612	+	0.395826i	−0.865930	+	0.500165i	$0.833273\pi$
$270$	2.75349	−	12.5872i	0.167572	−	0.766034i
$271$	8.03831	−	24.7394i	0.488293	−	1.50281i	−0.338862	−	0.940836i	$-0.610042\pi$
$271$	8.03831	−	24.7394i	0.488293	−	1.50281i	0.827155	−	0.561974i	$-0.189958\pi$
$272$	−5.82482	+	8.96943i	−0.353181	+	0.543852i
$273$	−0.0838934	+	0.330996i	−0.00507746	+	0.0200328i
$274$	8.29778	+	4.79073i	0.501287	+	0.289418i
$275$	−8.06322	+	9.16419i	−0.486231	+	0.552622i
$276$	−7.58905	+	3.50301i	−0.456807	+	0.210857i
$277$	−4.61289	−	12.0170i	−0.277162	−	0.722030i	−0.999534	−	0.0305263i	$-0.990282\pi$
$277$	−4.61289	−	12.0170i	−0.277162	−	0.722030i	0.722372	−	0.691504i	$-0.243052\pi$
$278$	12.3344	−	6.28468i	0.739767	−	0.376930i
$279$	6.66571	−	4.09355i	0.399066	−	0.245074i
$280$	−13.3719	+	10.9558i	−0.799126	+	0.654737i
$281$	−2.22045	−	1.99931i	−0.132461	−	0.119269i	0.600237	−	0.799822i	$-0.295073\pi$
$281$	−2.22045	−	1.99931i	−0.132461	−	0.119269i	−0.732699	+	0.680553i	$0.761739\pi$
$282$	−17.6909	+	3.04859i	−1.05348	+	0.181541i
$283$	−5.98776	+	3.88850i	−0.355935	+	0.231147i	−0.710203	−	0.703997i	$-0.751397\pi$
$283$	−5.98776	+	3.88850i	−0.355935	+	0.231147i	0.354268	+	0.935144i	$0.384730\pi$
$284$	−4.09020	+	1.82108i	−0.242709	+	0.108061i
$285$	−6.96008	+	4.19955i	−0.412280	+	0.248760i
$286$	0.193749	+	0.0862628i	0.0114566	+	0.00510082i
$287$	5.94176	−	0.941083i	0.350731	−	0.0555503i
$288$	10.4282	+	6.37667i	0.614488	+	0.375749i
$289$	9.30939	+	12.8133i	0.547611	+	0.753722i
$290$	5.57002	+	12.3200i	0.327083	+	0.723454i
$291$	6.49958	−	32.7577i	0.381012	−	1.92029i
$292$	−5.49769	−	8.46570i	−0.321728	−	0.495418i
$293$	−2.94987	+	0.790416i	−0.172333	+	0.0461766i	−0.343954	−	0.938987i	$-0.611766\pi$
$293$	−2.94987	+	0.790416i	−0.172333	+	0.0461766i	0.171621	+	0.985163i	$0.445100\pi$
$294$	0.283333	+	1.24937i	0.0165243	+	0.0728646i
$295$	5.77042	+	21.0522i	0.335967	+	1.22571i
$296$	21.9362	+	7.12751i	1.27502	+	0.414278i
$297$	−9.52530	+	8.37773i	−0.552714	+	0.486125i
$298$	−1.99908	+	12.6217i	−0.115804	+	0.731157i
$299$	0.245414	+	0.425070i	0.0141927	+	0.0245824i
$300$	4.83320	+	4.59710i	0.279045	+	0.265414i
$301$	−3.02117	+	5.23282i	−0.174137	+	0.301615i
$302$	8.82069	+	7.14286i	0.507574	+	0.411025i
$303$	10.7727	+	8.48412i	0.618874	+	0.487400i
$304$	0.814422	+	3.83156i	0.0467103	+	0.219755i
$305$	13.1687	−	20.5347i	0.754037	−	1.17581i
$306$	−15.1137	+	11.6202i	−0.863992	+	0.664281i
$307$	19.5469	+	19.5469i	1.11560	+	1.11560i	0.992379	+	0.123224i	$0.0393235\pi$
$307$	19.5469	+	19.5469i	1.11560	+	1.11560i	0.123224	+	0.992379i	$0.460676\pi$
$308$	4.72548	−	0.247652i	0.269259	−	0.0141113i
$309$	5.45206	+	16.0360i	0.310157	+	0.912256i
$310$	−0.0370528	−	6.46556i	−0.00210446	−	0.367219i
$311$	−10.9971	+	1.15584i	−0.623587	+	0.0655416i	−0.411052	−	0.911612i	$-0.634839\pi$
$311$	−10.9971	+	1.15584i	−0.623587	+	0.0655416i	−0.212535	+	0.977154i	$0.568172\pi$
$312$	0.184183	−	0.373937i	0.0104273	−	0.0211700i
$313$	−3.41386	−	4.21576i	−0.192963	−	0.238289i	0.671477	−	0.741025i	$-0.265660\pi$
$313$	−3.41386	−	4.21576i	−0.192963	−	0.238289i	−0.864440	+	0.502736i	$0.832327\pi$
$314$	−6.35307	+	4.61578i	−0.358525	+	0.260483i
$315$	−15.8752	+	5.74150i	−0.894465	+	0.323497i
$316$	4.65299	+	3.38060i	0.261751	+	0.190174i
$317$	0.215478	+	4.11157i	0.0121025	+	0.230929i	0.997983	+	0.0634796i	$0.0202198\pi$
$317$	0.215478	+	4.11157i	0.0121025	+	0.230929i	−0.985881	+	0.167449i	$0.946447\pi$
$318$	−22.8730	−	8.42584i	−1.28265	−	0.472498i
$319$	2.76756	−	13.0203i	0.154954	−	0.728999i
$320$	16.3906	−	8.47009i	0.916263	−	0.473493i
$321$	−18.1412	−	7.78378i	−1.01254	−	0.434448i
$322$	−14.6644	−	9.52315i	−0.817213	−	0.530705i
$323$	11.8794	+	1.88151i	0.660988	+	0.104690i
$324$	4.37277	+	5.37880i	0.242932	+	0.298822i
$325$	0.242996	−	0.307208i	0.0134790	−	0.0170409i
$326$	−19.5646	+	11.2957i	−1.08359	+	0.625608i
$327$	−0.0939015	−	0.0238000i	−0.00519276	−	0.00131614i
$328$	−7.33368	−	0.384342i	−0.404935	−	0.0212217i
$329$	15.7379	+	17.4787i	0.867660	+	0.963634i
$330$	1.83981	+	10.3226i	0.101278	+	0.568240i
$331$	−9.43791	+	10.4819i	−0.518754	+	0.576135i	−0.944418	−	0.328746i	$-0.893374\pi$
$331$	−9.43791	+	10.4819i	−0.518754	+	0.576135i	0.425664	+	0.904881i	$0.360041\pi$
$332$	0.731232	−	0.731232i	0.0401316	−	0.0401316i
$333$	17.8828	+	13.6947i	0.979970	+	0.750465i
$334$	5.30962	−	7.30807i	0.290530	−	0.399880i
$335$	9.87332	−	4.46386i	0.539437	−	0.243887i
$336$	0.110382	+	8.13413i	0.00602182	+	0.443753i
$337$	2.50558	+	0.961801i	0.136487	+	0.0523926i	0.425653	−	0.904886i	$-0.360044\pi$
$337$	2.50558	+	0.961801i	0.136487	+	0.0523926i	−0.289165	+	0.957279i	$0.593378\pi$
$338$	13.4525	+	5.16394i	0.731720	+	0.280881i
$339$	−0.244511	−	18.0182i	−0.0132800	−	0.978614i
$340$	−1.08786	−	9.80924i	−0.0589976	−	0.531981i
$341$	−3.74157	+	5.14983i	−0.202617	+	0.278879i
$342$	−0.904782	+	6.92379i	−0.0489250	+	0.374396i
$343$	13.6431	−	13.6431i	0.736661	−	0.736661i
$344$	4.93558	−	5.48151i	0.266108	−	0.295543i
$345$	−10.5972	+	21.8298i	−0.570535	+	1.17527i
$346$	−16.1550	−	17.9420i	−0.868499	−	0.964565i
$347$	16.6889	+	0.874630i	0.895909	+	0.0469526i	0.494730	−	0.869047i	$-0.335267\pi$
$347$	16.6889	+	0.874630i	0.895909	+	0.0469526i	0.401179	+	0.916000i	$0.368600\pi$
$348$	−7.05106	−	1.78714i	−0.377977	−	0.0958010i
$349$	−24.6896	+	14.2546i	−1.32161	+	0.763030i	−0.983985	−	0.178252i	$-0.942956\pi$
$349$	−24.6896	+	14.2546i	−1.32161	+	0.763030i	−0.337621	+	0.941282i	$0.609622\pi$
$350$	−2.74451	+	13.6811i	−0.146700	+	0.731287i
$351$	0.291169	−	0.284462i	0.0155415	−	0.0151834i
$352$	−9.82444	−	1.55604i	−0.523645	−	0.0829372i
$353$	18.5093	+	12.0201i	0.985151	+	0.639765i	0.933378	−	0.358894i	$-0.116846\pi$
$353$	18.5093	+	12.0201i	0.985151	+	0.639765i	0.0517731	+	0.998659i	$0.483513\pi$
$354$	17.2315	+	7.39345i	0.915844	+	0.392958i
$355$	−5.83460	+	11.6151i	−0.309668	+	0.616467i
$356$	−1.30785	+	6.15293i	−0.0693157	+	0.326105i
$357$	23.4382	+	8.63403i	1.24048	+	0.456961i
$358$	0.569256	+	10.8620i	0.0300861	+	0.574077i
$359$	10.0097	+	7.27249i	0.528293	+	0.383827i	0.819719	−	0.572766i	$-0.194130\pi$
$359$	10.0097	+	7.27249i	0.528293	+	0.383827i	−0.291426	+	0.956593i	$0.594130\pi$
$360$	20.4132	−	2.82649i	1.07587	−	0.148969i
$361$	−11.8074	+	8.57857i	−0.621441	+	0.451504i
$362$	−5.54726	−	6.85029i	−0.291557	−	0.360043i
$363$	−3.85728	+	7.83126i	−0.202455	+	0.411035i
$364$	−0.151012	+	0.0158720i	−0.00791520	+	0.000831921i
$365$	−27.9221	−	8.89586i	−1.46151	−	0.465630i
$366$	−6.74515	−	19.8393i	−0.352574	−	1.03702i
$367$	−4.26161	+	0.223342i	−0.222454	+	0.0116583i	−0.163238	−	0.986587i	$-0.552194\pi$
$367$	−4.26161	+	0.223342i	−0.222454	+	0.0116583i	−0.0592169	+	0.998245i	$0.518860\pi$
$368$	8.26842	+	8.26842i	0.431021	+	0.431021i
$369$	−6.62824	−	2.73807i	−0.345052	−	0.142538i
$370$	17.3426	−	6.77148i	0.901599	−	0.352033i
$371$	6.63996	+	31.2386i	0.344730	+	1.62183i
$372$	2.73275	+	2.15220i	0.141687	+	0.111587i
$373$	1.38476	+	1.12136i	0.0717002	+	0.0580617i	0.664501	−	0.747288i	$-0.268644\pi$
$373$	1.38476	+	1.12136i	0.0717002	+	0.0580617i	−0.592800	+	0.805349i	$0.701978\pi$
$374$	7.75698	−	13.4355i	0.401104	−	0.694732i
$375$	19.3120	+	1.43089i	0.997266	+	0.0738908i
$376$	−14.3558	−	24.8651i	−0.740346	−	1.28232i
$377$	−0.0668201	+	0.421885i	−0.00344141	+	0.0217282i
$378$	−4.64147	+	13.7382i	−0.238732	+	0.706618i
$379$	20.1539	+	6.54841i	1.03524	+	0.336369i	0.776859	−	0.629674i	$-0.216812\pi$
$379$	20.1539	+	6.54841i	1.03524	+	0.336369i	0.258379	+	0.966044i	$0.416812\pi$
$380$	−2.82224	−	2.25875i	−0.144778	−	0.115871i
$381$	3.90793	+	17.2322i	0.200209	+	0.882832i
$382$	−17.9238	+	4.80267i	−0.917062	+	0.245726i
$383$	13.3710	+	20.5895i	0.683224	+	1.05207i	0.994800	+	0.101852i	$0.0324767\pi$
$383$	13.3710	+	20.5895i	0.683224	+	1.05207i	−0.311575	+	0.950221i	$0.600857\pi$
$384$	0.337459	−	1.70078i	0.0172209	−	0.0867925i
$385$	10.1562	−	9.25060i	0.517607	−	0.471454i
$386$	−7.22525	−	9.94471i	−0.367756	−	0.506172i
$387$	6.32692	−	3.44310i	0.321616	−	0.175022i
$388$	14.6681	−	2.32319i	0.744658	−	0.117942i
$389$	−27.0261	−	12.0328i	−1.37028	−	0.610087i	−0.416097	−	0.909320i	$-0.636602\pi$
$389$	−27.0261	−	12.0328i	−1.37028	−	0.610087i	−0.954180	+	0.299233i	$0.903269\pi$
$390$	−0.0762927	−	0.327698i	−0.00386323	−	0.0165936i
$391$	32.7999	−	14.6034i	1.65876	−	0.738528i
$392$	−1.71841	+	1.11595i	−0.0867927	+	0.0563638i
$393$	−12.7348	+	2.19453i	−0.642388	+	0.110700i
$394$	−12.2526	−	11.0323i	−0.617277	−	0.555799i
$395$	16.6690	−	0.969406i	0.838711	−	0.0487761i
$396$	−4.96000	−	2.68691i	−0.249249	−	0.135022i
$397$	19.3203	−	9.84417i	0.969656	−	0.494065i	0.103931	−	0.994584i	$-0.466858\pi$
$397$	19.3203	−	9.84417i	0.969656	−	0.494065i	0.865725	+	0.500520i	$0.166858\pi$
$398$	−0.929300	−	2.42091i	−0.0465816	−	0.121349i
$399$	8.30636	−	3.83411i	0.415838	−	0.191946i
$400$	3.69754	−	8.56775i	0.184877	−	0.428388i
$401$	26.7982	+	15.4719i	1.33824	+	0.772631i	0.986546	−	0.163485i	$-0.0522736\pi$
$401$	26.7982	+	15.4719i	1.33824	+	0.772631i	0.351691	+	0.936116i	$0.385607\pi$
$402$	2.28678	−	9.02233i	0.114054	−	0.449993i
$403$	0.111250	−	0.171310i	0.00554176	−	0.00853356i
$404$	−1.88431	+	5.79930i	−0.0937478	+	0.288526i
$405$	19.7163	+	4.03346i	0.979709	+	0.200424i
$406$	−4.70218	−	14.4718i	−0.233365	−	0.718225i
$407$	−17.7048	−	4.74399i	−0.877595	−	0.235151i
$408$	−25.7952	−	16.2583i	−1.27705	−	0.804905i
$409$	5.78882	+	13.0019i	0.286238	+	0.642902i	0.998242	−	0.0592740i	$-0.0188786\pi$
$409$	5.78882	+	13.0019i	0.286238	+	0.642902i	−0.712003	+	0.702176i	$0.752212\pi$
$410$	−4.77558	+	3.51165i	−0.235849	+	0.173428i
$411$	−7.30599	+	13.0605i	−0.360378	+	0.644225i
$412$	−5.85338	+	4.73997i	−0.288375	+	0.233522i
$413$	−3.84309	−	24.2643i	−0.189106	−	1.19397i
$414$	8.99174	+	18.8052i	0.441920	+	0.924223i
$415$	0.296699	−	2.98750i	0.0145644	−	0.146651i
$416$	0.317438	+	0.0333641i	0.0155637	+	0.00163581i
$417$	10.0764	+	19.1298i	0.493444	+	0.936792i
$418$	−1.47067	−	5.48862i	−0.0719329	−	0.268457i
$419$	−11.9439	−	2.53876i	−0.583499	−	0.124026i	−0.0933013	−	0.995638i	$-0.529742\pi$
$419$	−11.9439	−	2.53876i	−0.583499	−	0.124026i	−0.490197	+	0.871611i	$0.663075\pi$
$420$	−4.83603	−	5.74179i	−0.235974	−	0.280170i
$421$	24.5669	−	5.22186i	1.19732	−	0.254498i	0.434236	−	0.900799i	$-0.357018\pi$
$421$	24.5669	−	5.22186i	1.19732	−	0.254498i	0.763083	+	0.646301i	$0.223685\pi$
$422$	−11.1718	−	21.9259i	−0.543835	−	1.06734i
$423$	−5.13601	−	27.5639i	−0.249721	−	1.34020i
$424$		−	38.9860i		−	1.89333i
$425$	−20.4911	−	20.0267i	−0.993964	−	0.971436i
$426$	4.67935	+	10.1375i	0.226715	+	0.491164i
$427$	−17.2776	+	21.3360i	−0.836121	+	1.03252i
$428$	0.459426	−	8.76636i	0.0222072	−	0.423738i
$429$	−0.130613	+	0.304413i	−0.00630607	+	0.0146972i
$430$	0.277522	−	5.94737i	0.0133833	−	0.286808i
$431$	−17.4861	+	5.68157i	−0.842275	+	0.273672i	−0.698207	−	0.715896i	$-0.746018\pi$
$431$	−17.4861	+	5.68157i	−0.842275	+	0.273672i	−0.144068	+	0.989568i	$0.546018\pi$
$432$	4.94635	−	8.34135i	0.237981	−	0.401323i
$433$	−28.8691	−	14.7095i	−1.38736	−	0.706895i	−0.408755	−	0.912644i	$-0.634037\pi$
$433$	−28.8691	−	14.7095i	−1.38736	−	0.706895i	−0.978605	+	0.205749i	$0.934037\pi$
$434$	−0.760621	+	7.23683i	−0.0365110	+	0.347379i
$435$	−19.1225	+	8.96000i	−0.916853	+	0.429599i
$436$	−0.00450279	−	0.0428412i	−0.000215645	−	0.00205172i
$437$	4.71268	−	12.2770i	0.225438	−	0.587286i
$438$	−20.9236	+	13.9952i	−0.999769	+	0.668718i
$439$	5.63755	−	12.6621i	0.269066	−	0.604331i	−0.727593	−	0.686009i	$-0.759361\pi$
$439$	5.63755	−	12.6621i	0.269066	−	0.604331i	0.996659	+	0.0816777i	$0.0260278\pi$
$440$	−14.4750	+	8.46809i	−0.690066	+	0.403700i
$441$	−1.94518	+	0.468969i	−0.0926275	+	0.0223318i
$442$	−0.226009	+	0.443567i	−0.0107501	+	0.0210984i
$443$	−8.86899	+	33.0995i	−0.421379	+	1.57261i	0.350327	+	0.936627i	$0.386070\pi$
$443$	−8.86899	+	33.0995i	−0.421379	+	1.57261i	−0.771706	+	0.635979i	$0.780596\pi$
$444$	−2.96564	+	9.56712i	−0.140743	+	0.454035i
$445$	8.38386	+	16.2237i	0.397433	+	0.769078i
$446$	19.2733	−	17.3537i	0.912616	−	0.821723i
$447$	−19.7541	−	2.85455i	−0.934339	−	0.135015i
$448$	−19.3849	+	7.44117i	−0.915851	+	0.351562i
$449$	27.6968			1.30709			0.653546	−	0.756887i	$-0.273281\pi$
$449$	27.6968			1.30709			0.653546	+	0.756887i	$0.273281\pi$
$450$	11.2996	−	12.2074i	0.532666	−	0.575461i
$451$	5.83592			0.274803
$452$	7.48098	−	2.87168i	0.351876	−	0.135072i
$453$	−10.9683	+	13.9270i	−0.515336	+	0.654346i
$454$	−4.97739	+	4.48166i	−0.233601	+	0.210335i
$455$	−0.309920	+	0.313492i	−0.0145293	+	0.0146967i
$456$	−10.8914	+	2.46997i	−0.510038	+	0.115667i
$457$	6.54536	−	24.4276i	0.306179	−	1.14268i	−0.625747	−	0.780026i	$-0.715206\pi$
$457$	6.54536	−	24.4276i	0.306179	−	1.14268i	0.931926	−	0.362649i	$-0.118128\pi$
$458$	−4.36126	+	8.55945i	−0.203788	+	0.399957i
$459$	−18.4679	−	23.3573i	−0.862010	−	1.09023i
$460$	−10.7380	−	1.06643i	−0.500661	−	0.0497224i
$461$	10.2589	−	23.0420i	0.477806	−	1.07317i	−0.500449	−	0.865766i	$-0.666832\pi$
$461$	10.2589	−	23.0420i	0.477806	−	1.07317i	0.978255	−	0.207405i	$-0.0665017\pi$
$462$	−0.777434	−	11.7748i	−0.0361695	−	0.547816i
$463$	4.73354	−	12.3313i	0.219986	−	0.573083i	−0.778526	−	0.627612i	$-0.784032\pi$
$463$	4.73354	−	12.3313i	0.219986	−	0.573083i	0.998512	+	0.0545289i	$0.0173657\pi$
$464$	1.06370	+	10.1204i	0.0493808	+	0.469827i
$465$	10.0967	−	0.194892i	0.468223	−	0.00903788i
$466$	−2.67020	+	25.4052i	−0.123694	+	1.17687i
$467$	−26.1256	−	13.3117i	−1.20895	−	0.615990i	−0.270938	−	0.962597i	$-0.587334\pi$
$467$	−26.1256	−	13.3117i	−1.20895	−	0.615990i	−0.938011	+	0.346606i	$0.887334\pi$
$468$	0.163456	+	0.0777721i	0.00755575	+	0.00359502i
$469$	−11.5978	+	3.76836i	−0.535538	+	0.174007i
$470$	−21.6834	−	8.18123i	−1.00018	−	0.377372i
$471$	−7.34326	−	9.82399i	−0.338360	−	0.452666i
$472$	−1.56953	+	29.9485i	−0.0722437	+	1.37849i
$473$	−3.68885	+	4.55535i	−0.169614	+	0.209455i
$474$	8.27224	−	11.7169i	0.379957	−	0.538174i
$475$	−10.4937	+	0.120278i	−0.481483	+	0.00551875i
$476$			11.1074i			0.509105i
$477$	12.6742	−	35.9001i	0.580311	−	1.64375i
$478$	−2.35911	−	4.63002i	−0.107903	−	0.211772i
$479$	−18.0407	+	3.83468i	−0.824302	+	0.175211i	−0.600705	−	0.799471i	$-0.705113\pi$
$479$	−18.0407	+	3.83468i	−0.824302	+	0.175211i	−0.223597	+	0.974682i	$0.571780\pi$
$480$	7.43409	+	13.9194i	0.339318	+	0.635332i
$481$	0.575319	+	0.122288i	0.0262323	+	0.00557584i
$482$	3.05461	+	11.4000i	0.139134	+	0.519254i
$483$	14.5619	−	23.1037i	0.662587	−	1.05125i
$484$	−3.86072	−	0.405778i	−0.175487	−	0.0184444i
$485$	28.6651	−	32.2050i	1.30161	−	1.46235i
$486$	13.2643	−	11.0857i	0.601683	−	0.502859i
$487$	−1.29525	−	8.17789i	−0.0586934	−	0.370576i	−0.999500	−	0.0316307i	$-0.989930\pi$
$487$	−1.29525	−	8.17789i	−0.0586934	−	0.370576i	0.940806	−	0.338945i	$-0.110070\pi$
$488$	26.0457	−	21.0914i	1.17903	−	0.954762i
$489$	−18.0554	−	30.3154i	−0.816496	−	1.37091i
$490$	−0.502056	+	1.57584i	−0.0226806	+	0.0711892i
$491$	−2.92812	−	6.57666i	−0.132144	−	0.296800i	0.835340	−	0.549734i	$-0.185271\pi$
$491$	−2.92812	−	6.57666i	−0.132144	−	0.296800i	−0.967484	+	0.252934i	$0.918604\pi$
$492$	0.123675	−	3.18669i	0.00557571	−	0.143667i
$493$	30.1808	+	8.08692i	1.35927	+	0.364217i
$494$	0.0563454	+	0.173413i	0.00253510	+	0.00780223i
$495$	−16.0821	+	3.09207i	−0.722839	+	0.138978i
$496$	1.50377	−	4.62813i	0.0675213	−	0.207809i
$497$	7.96734	−	12.2686i	0.357384	−	0.550323i
$498$	−1.84811	−	1.79862i	−0.0828156	−	0.0805981i
$499$	10.2532	+	5.91969i	0.458996	+	0.265002i	0.711622	−	0.702562i	$-0.247961\pi$
$499$	10.2532	+	5.91969i	0.458996	+	0.265002i	−0.252626	+	0.967564i	$0.581294\pi$
$500$	2.37145	+	8.27837i	0.106054	+	0.370220i
$501$	11.5258	+	8.13735i	0.514935	+	0.363550i
$502$	−5.81097	−	15.1381i	−0.259356	−	0.675646i
$503$	20.6249	−	10.5089i	0.919621	−	0.468570i	0.0709429	−	0.997480i	$-0.477399\pi$
$503$	20.6249	−	10.5089i	0.919621	−	0.468570i	0.848678	+	0.528910i	$0.177399\pi$
$504$	−23.1844	+	0.629349i	−1.03271	+	0.0280334i
$505$	6.43867	+	16.4902i	0.286517	+	0.733806i
$506$	−12.6055	−	11.3500i	−0.560382	−	0.504571i
$507$	−7.77960	+	21.1187i	−0.345504	+	0.937914i
$508$	−6.58988	+	4.27952i	−0.292379	+	0.189873i
$509$	23.1755	−	10.3184i	1.02723	−	0.457354i	0.177252	−	0.984165i	$-0.443279\pi$
$509$	23.1755	−	10.3184i	1.02723	−	0.457354i	0.849982	+	0.526811i	$0.176612\pi$
$510$	−24.4230	+	3.04457i	−1.08147	+	0.134816i
$511$	30.1295	+	13.4145i	1.33285	+	0.593423i
$512$	18.8362	−	2.98336i	0.832450	−	0.131847i
$513$	−10.8323	−	1.26629i	−0.478258	−	0.0559082i
$514$	12.1238	+	16.6870i	0.534758	+	0.736031i
$515$	−4.42359	+	21.4141i	−0.194927	+	0.943616i
$516$	2.40926	+	2.11082i	0.106062	+	0.0929237i
$517$	12.4268	+	19.1356i	0.546531	+	0.841583i
$518$	−20.2391	+	5.42304i	−0.889254	+	0.238275i
$519$	27.6782	−	25.6101i	1.21494	−	1.12416i
$520$	0.449629	−	0.295670i	0.0197175	−	0.0129660i
$521$	4.24963	+	1.38079i	0.186179	+	0.0604934i	0.400623	−	0.916243i	$-0.368794\pi$
$521$	4.24963	+	1.38079i	0.186179	+	0.0604934i	−0.214443	+	0.976736i	$0.568794\pi$
$522$	−4.21774	+	17.6427i	−0.184605	+	0.772198i
$523$	−6.97403	+	44.0323i	−0.304953	+	1.92540i	0.0682899	+	0.997666i	$0.478246\pi$
$523$	−6.97403	+	44.0323i	−0.304953	+	1.92540i	−0.373243	+	0.927734i	$0.621754\pi$
$524$	−2.87325	−	4.97662i	−0.125519	−	0.217404i
$525$	−21.4245	−	3.99626i	−0.935040	−	0.174411i
$526$	−9.84803	+	17.0573i	−0.429395	+	0.743733i
$527$	−11.6120	−	9.40320i	−0.505826	−	0.409610i
$528$	−1.12864	+	7.81048i	−0.0491179	+	0.339908i
$529$	−3.37981	−	15.9007i	−0.146948	−	0.691336i
$530$	−19.9437	−	24.3419i	−0.866301	−	1.05734i
$531$	−11.1814	+	27.0677i	−0.485232	+	1.17464i
$532$	2.87669	+	2.87669i	0.124720	+	0.124720i
$533$	−0.187012	+	0.00980091i	−0.00810041	+	0.000424524i
$534$	15.3869	+	3.05298i	0.665856	+	0.132115i
$535$	−15.0976	−	20.5316i	−0.652726	−	0.887658i
$536$	14.8049	−	1.55606i	0.639476	−	0.0672117i
$537$	−16.9516	+	1.11923i	−0.731514	+	0.0482982i
$538$	4.76387	+	5.88288i	0.205385	+	0.253629i
$539$	1.31730	−	0.957074i	0.0567401	−	0.0412241i
$540$	1.34760	+	8.84713i	0.0579914	+	0.380720i
$541$	21.4770	+	15.6039i	0.923368	+	0.670866i	0.944360	−	0.328914i	$-0.106682\pi$
$541$	21.4770	+	15.6039i	0.923368	+	0.670866i	−0.0209921	+	0.999780i	$0.506682\pi$
$542$	−1.50972	−	28.8072i	−0.0648480	−	1.23737i
$543$	10.5808	−	8.80853i	0.454065	−	0.378010i
$544$	4.85440	−	22.8382i	0.208131	−	0.979178i
$545$	−0.0889357	−	0.0879222i	−0.00380959	−	0.00376617i
$546$	0.0446877	+	0.376020i	0.00191246	+	0.0160922i
$547$	5.68331	+	3.69078i	0.243001	+	0.157807i	0.660394	−	0.750920i	$-0.270389\pi$
$547$	5.68331	+	3.69078i	0.243001	+	0.157807i	−0.417393	+	0.908726i	$0.637056\pi$
$548$	−6.57285	−	1.04104i	−0.280778	−	0.0444709i
$549$	30.8408	−	10.9546i	1.31625	−	0.467530i
$550$	−4.70586	+	12.6921i	−0.200658	+	0.541193i
$551$	9.91094	−	5.72208i	0.422220	−	0.243769i
$552$	−23.2516	+	23.8913i	−0.989653	+	1.01688i
$553$	−18.7659	−	0.983479i	−0.798007	−	0.0418218i
$554$	−9.55142	−	10.6079i	−0.405801	−	0.450688i
$555$	10.9428	+	26.9410i	0.464496	+	1.14358i
$556$	−6.43354	+	7.14517i	−0.272843	+	0.303023i
$557$	−4.04978	+	4.04978i	−0.171595	+	0.171595i	−0.787680	−	0.616085i	$-0.788718\pi$
$557$	−4.04978	+	4.04978i	−0.171595	+	0.171595i	0.616085	+	0.787680i	$0.288718\pi$
$558$	5.27416	−	6.88708i	0.223273	−	0.291553i
$559$	0.110559	−	0.152171i	0.00467615	−	0.00643617i
$560$	−5.19883	+	9.12501i	−0.219691	+	0.385602i
$561$	21.1470	+	11.8296i	0.892829	+	0.499446i
$562$	−3.09338	−	1.18744i	−0.130486	−	0.0500891i
$563$	5.09051	+	1.95406i	0.214539	+	0.0823540i	0.463264	−	0.886220i	$-0.346678\pi$
$563$	5.09051	+	1.95406i	0.214539	+	0.0823540i	−0.248725	+	0.968574i	$0.580011\pi$
$564$	10.7123	−	6.38009i	0.451068	−	0.268650i
$565$	11.5161	−	20.2131i	0.484487	−	0.850373i
$566$	−4.65377	+	6.40537i	−0.195613	+	0.269238i
$567$	−21.5538	−	6.95759i	−0.905175	−	0.292191i
$568$	−12.6273	+	12.6273i	−0.529831	+	0.529831i
$569$	−26.0647	+	28.9478i	−1.09269	+	1.21355i	−0.117293	+	0.993097i	$0.537422\pi$
$569$	−26.0647	+	28.9478i	−1.09269	+	1.21355i	−0.975397	+	0.220458i	$0.929245\pi$
$570$	−5.53680	+	7.11382i	−0.231911	+	0.297965i
$571$	10.5410	+	11.7070i	0.441127	+	0.489921i	0.922175	−	0.386773i	$-0.126410\pi$
$571$	10.5410	+	11.7070i	0.441127	+	0.489921i	−0.481048	+	0.876694i	$0.659744\pi$
$572$	−0.147101	−	0.00770926i	−0.00615062	−	0.000322340i
$573$	−7.88036	−	27.8905i	−0.329207	−	1.16514i
$574$	5.77749	−	3.33564i	0.241148	−	0.139227i
$575$	−26.0760	+	17.3621i	−1.08744	+	0.724048i
$576$	24.3428	+	4.48753i	1.01428	+	0.186981i
$577$	−11.6182	−	1.84015i	−0.483673	−	0.0766063i	−0.0901640	−	0.995927i	$-0.528739\pi$
$577$	−11.6182	−	1.84015i	−0.483673	−	0.0766063i	−0.393509	+	0.919321i	$0.628739\pi$
$578$	14.7302	+	9.56588i	0.612694	+	0.397888i
$579$	15.3779	−	11.4947i	0.639082	−	0.477703i
$580$	−6.67819	−	6.60208i	−0.277297	−	0.274136i
$581$	−0.702488	+	3.30495i	−0.0291441	+	0.137112i
$582$	−6.28934	−	36.4969i	−0.260701	−	1.51285i
$583$	1.62144	+	30.9389i	0.0671532	+	1.28136i
$584$	−32.5718	−	23.6648i	−1.34783	−	0.979255i
$585$	0.510160	−	0.126094i	0.0210925	−	0.00521334i
$586$	−2.73987	+	1.99063i	−0.113183	+	0.0822323i
$587$	2.76822	+	3.41846i	0.114256	+	0.141095i	0.831066	−	0.556175i	$-0.187731\pi$
$587$	2.76822	+	3.41846i	0.114256	+	0.141095i	−0.716809	+	0.697270i	$0.754398\pi$
$588$	−0.494691	−	0.739589i	−0.0204007	−	0.0305001i
$589$	−5.44271	+	0.572052i	−0.224263	+	0.0235710i
$590$	14.3405	+	19.5020i	0.590390	+	0.802885i
$591$	16.9698	−	19.3691i	0.698046	−	0.796739i
$592$	13.9932	−	0.733352i	0.575117	−	0.0301406i
$593$	−13.2498	−	13.2498i	−0.544103	−	0.544103i	0.380626	−	0.924729i	$-0.375708\pi$
$593$	−13.2498	−	13.2498i	−0.544103	−	0.544103i	−0.924729	+	0.380626i	$0.875708\pi$
$594$	−6.53210	+	12.4589i	−0.268015	+	0.511196i
$595$	20.4365	+	24.9434i	0.837816	+	1.02258i
$596$	−1.84536	−	8.68172i	−0.0755887	−	0.355617i
$597$	3.76112	−	1.50263i	0.153933	−	0.0614984i
$598$	0.423005	+	0.342543i	0.0172980	+	0.0140076i
$599$	−8.89838	+	15.4124i	−0.363578	+	0.629735i	−0.988547	−	0.150914i	$-0.951778\pi$
$599$	−8.89838	+	15.4124i	−0.363578	+	0.629735i	0.624969	+	0.780650i	$0.285112\pi$
$600$	24.5678	+	10.2094i	1.00298	+	0.416798i
$601$	13.7336	+	23.7874i	0.560207	+	0.970307i	0.997478	+	0.0709770i	$0.0226117\pi$
$601$	13.7336	+	23.7874i	0.560207	+	0.970307i	−0.437271	+	0.899330i	$0.644055\pi$
$602$	−1.04822	+	6.61817i	−0.0427221	+	0.269737i
$603$	14.1389	+	3.38013i	0.575783	+	0.137649i
$604$	−7.49737	−	2.43604i	−0.305064	−	0.0991212i
$605$	−9.41646	+	6.19213i	−0.382833	+	0.251746i
$606$	14.5246	+	4.50238i	0.590022	+	0.182897i
$607$	−13.6149	+	3.64809i	−0.552610	+	0.148071i	−0.524309	−	0.851528i	$-0.675676\pi$
$607$	−13.6149	+	3.64809i	−0.552610	+	0.148071i	−0.0283011	+	0.999599i	$0.509010\pi$
$608$	−4.65761	−	7.17209i	−0.188891	−	0.290866i
$609$	22.5015	−	7.65026i	0.911807	−	0.310004i
$610$	5.47275	−	26.4929i	0.221585	−	1.07267i
$611$	−0.430354	−	0.592332i	−0.0174103	−	0.0239632i
$612$	6.90766	−	11.2966i	0.279226	−	0.456637i
$613$	−27.0483	+	4.28402i	−1.09247	+	0.173030i	−0.676568	−	0.736380i	$-0.736534\pi$
$613$	−27.0483	+	4.28402i	−1.09247	+	0.173030i	−0.415901	+	0.909410i	$0.636534\pi$
$614$	28.0051	+	12.4687i	1.13019	+	0.503195i
$615$	−5.58548	−	7.38377i	−0.225228	−	0.297742i
$616$	17.2419	−	7.67657i	0.694694	−	0.309298i
$617$	−9.22424	+	5.99029i	−0.371354	+	0.241160i	−0.716800	−	0.697278i	$-0.754394\pi$
$617$	−9.22424	+	5.99029i	−0.371354	+	0.241160i	0.345447	+	0.938438i	$0.387727\pi$
$618$	12.0174	+	14.4353i	0.483412	+	0.580673i
$619$	−3.64901	−	3.28558i	−0.146666	−	0.132059i	0.592532	−	0.805547i	$-0.298128\pi$
$619$	−3.64901	−	3.28558i	−0.146666	−	0.132059i	−0.739198	+	0.673488i	$0.764795\pi$
$620$	1.63333	+	4.18315i	0.0655960	+	0.168000i
$621$	−29.1781	+	14.4413i	−1.17088	+	0.579507i
$622$	−10.9259	+	5.56702i	−0.438088	+	0.223217i
$623$	−7.36541	−	19.1875i	−0.295089	−	0.768732i
$624$	0.0230504	−	0.252183i	0.000922755	−	0.0100954i
$625$	20.5569	+	14.2272i	0.822277	+	0.569087i
$626$	−5.20976	−	3.00786i	−0.208224	−	0.120218i
$627$	8.54061	−	2.41312i	0.341079	−	0.0963708i
$628$	2.97055	−	4.57425i	0.118538	−	0.182533i
$629$	13.2953	−	40.9188i	0.530119	−	1.63154i
$630$	−14.1538	+	12.2532i	−0.563900	+	0.488178i
$631$	−2.72168	−	8.37647i	−0.108348	−	0.333462i	0.882153	−	0.470962i	$-0.156093\pi$
$631$	−2.72168	−	8.37647i	−0.108348	−	0.333462i	−0.990502	+	0.137500i	$0.956093\pi$
$632$	22.1580	+	5.93722i	0.881398	+	0.236170i
$633$	34.0057	−	17.9121i	1.35160	−	0.711941i
$634$	1.85708	+	4.17107i	0.0737540	+	0.165654i
$635$	−6.92472	+	21.7351i	−0.274799	+	0.862532i
$636$	16.9285	−	0.229723i	0.671257	−	0.00910910i
$637$	−0.0406056	+	0.0328818i	−0.00160885	+	0.00130282i
$638$	−2.30921	−	14.5798i	−0.0914226	−	0.577220i
$639$	−15.7329	+	7.52274i	−0.622385	+	0.297595i
$640$	1.48829	−	1.67209i	0.0588299	−	0.0660950i
$641$	−33.0459	−	3.47327i	−1.30523	−	0.137186i	−0.573743	−	0.819036i	$-0.694509\pi$
$641$	−33.0459	−	3.47327i	−1.30523	−	0.137186i	−0.731492	+	0.681850i	$0.761176\pi$
$642$	−21.8749	−	0.848965i	−0.863334	−	0.0335060i
$643$	−5.86068	−	21.8724i	−0.231123	−	0.862562i	−0.979858	−	0.199693i	$-0.936005\pi$
$643$	−5.86068	−	21.8724i	−0.231123	−	0.862562i	0.748736	−	0.662869i	$-0.230661\pi$
$644$	11.8790	+	2.52495i	0.468097	+	0.0994971i
$645$	9.29410	+	0.307373i	0.365955	+	0.0121028i
$646$	13.0465	−	2.77311i	0.513306	−	0.109107i
$647$	2.77041	+	5.43724i	0.108916	+	0.213760i	0.939031	−	0.343832i	$-0.111725\pi$
$647$	2.77041	+	5.43724i	0.108916	+	0.213760i	−0.830115	+	0.557592i	$0.811725\pi$
$648$	23.9707	+	13.7783i	0.941658	+	0.541262i
$649$		−	23.8321i		−	0.935493i
$650$	0.129484	−	0.414622i	0.00507879	−	0.0162628i
$651$	−11.3181	−	1.03452i	−0.443592	−	0.0405460i
$652$	9.87451	−	12.1940i	0.386716	−	0.477554i
$653$	−1.50181	+	28.6563i	−0.0587705	+	1.12141i	0.796975	+	0.604012i	$0.206432\pi$
$653$	−1.50181	+	28.6563i	−0.0587705	+	1.12141i	−0.855746	+	0.517397i	$0.826901\pi$
$654$	−0.106674	+	0.0126776i	−0.00417130	+	0.000495734i
$655$	−15.6089	−	5.88928i	−0.609889	−	0.230113i
$656$	−4.24307	+	1.37866i	−0.165664	+	0.0538276i
$657$	−22.3003	−	32.3806i	−0.870017	−	1.26329i
$658$	23.2397	+	11.8412i	0.905978	+	0.461619i
$659$	−3.01974	+	28.7309i	−0.117632	+	1.11920i	0.763330	+	0.646009i	$0.223563\pi$
$659$	−3.01974	+	28.7309i	−0.117632	+	1.11920i	−0.880962	+	0.473187i	$0.843104\pi$
$660$	−3.76230	−	6.23540i	−0.146447	−	0.242713i
$661$	5.01797	+	47.7428i	0.195177	+	1.85698i	0.453929	+	0.891038i	$0.350022\pi$
$661$	5.01797	+	47.7428i	0.195177	+	1.85698i	−0.258753	+	0.965944i	$0.583312\pi$
$662$	−5.60541	+	14.6026i	−0.217860	+	0.567546i
$663$	−0.697525	−	0.343565i	−0.0270896	−	0.0133430i
$664$	1.67763	−	3.76801i	0.0651045	−	0.146227i
$665$	11.7529	+	1.16722i	0.455759	+	0.0452630i
$666$	23.9564	+	7.07124i	0.928293	+	0.274005i
$667$	15.5095	−	30.4391i	0.600530	−	1.17861i
$668$	−1.62384	+	6.06026i	−0.0628284	+	0.234479i
$669$	27.5104	+	29.7320i	1.06361	+	1.14950i
$670$	8.44782	−	8.54521i	0.326368	−	0.330130i
$671$	−19.7924	+	17.8212i	−0.764078	+	0.687979i
$672$	−6.58888	−	16.4922i	−0.254171	−	0.636199i
$673$	−37.9677	+	14.5744i	−1.46355	+	0.561803i	−0.954309	−	0.298822i	$-0.903406\pi$
$673$	−37.9677	+	14.5744i	−1.46355	+	0.561803i	−0.509239	+	0.860625i	$0.670073\pi$
$674$	2.97625			0.114641
$675$	19.3042	+	17.3882i	0.743017	+	0.669272i
$676$	−10.0082			−0.384929
$677$	23.3420	−	8.96016i	0.897106	−	0.344367i	0.134260	−	0.990946i	$-0.457134\pi$
$677$	23.3420	−	8.96016i	0.897106	−	0.344367i	0.762847	+	0.646579i	$0.223801\pi$
$678$	−7.41381	−	18.5570i	−0.284726	−	0.712678i
$679$	−36.0592	+	32.4679i	−1.38383	+	1.24600i
$680$	−18.0717	−	34.9708i	−0.693018	−	1.34107i
$681$	−7.10466	−	7.67839i	−0.272251	−	0.294236i
$682$	−1.82702	+	6.81855i	−0.0699604	+	0.261096i
$683$	−15.4432	+	30.3089i	−0.590916	+	1.15974i	0.381036	+	0.924560i	$0.375567\pi$
$683$	−15.4432	+	30.3089i	−0.590916	+	1.15974i	−0.971952	+	0.235178i	$0.924433\pi$
$684$	−1.13668	−	4.71471i	−0.0434622	−	0.180271i
$685$	−16.6758	+	9.75563i	−0.637150	+	0.372744i
$686$	8.70274	−	19.5467i	0.332272	−	0.746296i
$687$	−13.4600	−	6.62973i	−0.513532	−	0.252940i
$688$	1.60588	−	4.18346i	0.0612236	−	0.159493i
$689$	−0.103918	−	0.988717i	−0.00395897	−	0.0376671i
$690$	−2.29584	+	26.8118i	−0.0874011	+	1.02071i
$691$	1.49865	−	14.2587i	0.0570111	−	0.542425i	−0.928321	−	0.371779i	$-0.878748\pi$
$691$	1.49865	−	14.2587i	0.0570111	−	0.542425i	0.985332	−	0.170646i	$-0.0545854\pi$
$692$	14.9410	+	7.61282i	0.567972	+	0.289396i
$693$	18.3727	−	1.46369i	0.697922	−	0.0556010i
$694$	17.6256	−	5.72690i	0.669058	−	0.217390i
$695$	−1.30109	+	27.8828i	−0.0493533	+	1.05765i
$696$	−28.8099	+	3.42388i	−1.09203	+	0.129782i
$697$	−0.716933	+	13.6799i	−0.0271558	+	0.518163i
$698$	−19.8962	+	24.5697i	−0.753081	+	0.929977i
$699$	−39.7328	−	3.63172i	−1.50283	−	0.137364i
$700$	−1.62570	−	9.55419i	−0.0614456	−	0.361115i
$701$		−	25.6509i		−	0.968822i	−0.874841	−	0.484411i	$-0.839034\pi$
$701$		−	25.6509i		−	0.968822i	0.874841	−	0.484411i	$-0.160966\pi$
$702$	0.188398	−	0.410217i	0.00711061	−	0.0154826i
$703$	−7.15419	−	14.0409i	−0.269825	−	0.529562i
$704$	−19.7029	+	4.18799i	−0.742582	+	0.157841i
$705$	12.3174	−	34.0372i	0.463899	−	1.28191i
$706$	23.9396	+	5.08852i	0.900978	+	0.191509i
$707$	−5.15651	−	19.2443i	−0.193930	−	0.723758i
$708$	−13.0135	−	0.505052i	−0.489075	−	0.0189810i
$709$	2.42249	+	0.254614i	0.0909787	+	0.00956224i	0.149908	−	0.988700i	$-0.452102\pi$
$709$	2.42249	+	0.254614i	0.0909787	+	0.00956224i	−0.0589297	+	0.998262i	$0.518769\pi$
$710$	−1.42454	+	14.3439i	−0.0534620	+	0.538315i
$711$	18.4740	+	12.6707i	0.692827	+	0.475190i
$712$	3.92484	+	24.7805i	0.147090	+	0.928688i
$713$	−12.6961	+	10.2811i	−0.475472	+	0.385030i
$714$	27.6967	−	0.375851i	1.03652	−	0.0140659i
$715$	−0.344525	+	0.253341i	−0.0128845	+	0.00947441i
$716$	−3.07272	−	6.90144i	−0.114833	−	0.257919i
$717$	7.18087	−	3.78243i	0.268174	−	0.141258i
$718$	13.2532	+	3.55119i	0.494606	+	0.132529i
$719$	2.53963	+	7.81619i	0.0947123	+	0.291495i	0.987179	−	0.159620i	$-0.0510267\pi$
$719$	2.53963	+	7.81619i	0.0947123	+	0.291495i	−0.892466	+	0.451114i	$0.851027\pi$
$720$	10.9622	−	6.04731i	0.408539	−	0.225370i
$721$	7.60460	−	23.4045i	0.283210	−	0.871631i
$722$	−8.81492	+	13.5738i	−0.328057	+	0.505164i
$723$	−17.7390	+	5.01209i	−0.659720	+	0.186402i
$724$	5.30200	+	3.06111i	0.197047	+	0.113765i
$725$	−27.1442	−	2.53878i	−1.00811	−	0.0942881i
$726$	−0.881188	+	9.64062i	−0.0327039	+	0.357797i
$727$	6.77599	+	17.6521i	0.251308	+	0.654679i	0.999966	−	0.00827742i	$-0.00263481\pi$
$727$	6.77599	+	17.6521i	0.251308	+	0.654679i	−0.748658	+	0.662956i	$0.769301\pi$
$728$	−0.539624	+	0.274952i	−0.0199998	+	0.0101904i
$729$	17.5941	+	20.4804i	0.651633	+	0.758535i
$730$	−32.4430	+	1.88676i	−1.20077	+	0.0698320i
$731$	−10.2250	−	9.20659i	−0.378184	−	0.340518i
$732$	9.31175	+	11.1852i	0.344172	+	0.413419i
$733$	8.64845	−	5.61637i	0.319438	−	0.207445i	−0.374952	−	0.927044i	$-0.622341\pi$
$733$	8.64845	−	5.61637i	0.319438	−	0.207445i	0.694390	+	0.719599i	$0.255674\pi$
$734$	−4.32328	+	1.92485i	−0.159575	+	0.0710474i
$735$	−2.47168	−	0.750681i	−0.0911695	−	0.0276893i
$736$	−23.3212	−	10.3833i	−0.859631	−	0.382732i
$737$	−11.6844	+	1.85062i	−0.430399	+	0.0681685i
$738$	−7.95035	−	0.200559i	−0.292656	−	0.00738269i
$739$	−3.28609	−	4.52292i	−0.120881	−	0.166378i	0.744288	−	0.667859i	$-0.232789\pi$
$739$	−3.28609	−	4.52292i	−0.120881	−	0.166378i	−0.865169	+	0.501480i	$0.832789\pi$
$740$	−9.55978	+	8.70738i	−0.351425	+	0.320090i
$741$	−0.269631	+	0.0916717i	−0.00990516	+	0.00336764i
$742$	19.2890	+	29.7024i	0.708120	+	1.09041i
$743$	25.9901	−	6.96402i	0.953484	−	0.255485i	0.251644	−	0.967820i	$-0.419029\pi$
$743$	25.9901	−	6.96402i	0.953484	−	0.255485i	0.701840	+	0.712335i	$0.252362\pi$
$744$	13.2520	+	4.10788i	0.485841	+	0.150602i
$745$	−20.1176	−	16.1009i	−0.737052	−	0.589892i
$746$	1.87928	+	0.610615i	0.0688054	+	0.0223562i
$747$	2.76980	−	2.92437i	0.101342	−	0.106997i
$748$	−1.68561	+	10.6425i	−0.0616321	+	0.389129i
$749$	14.3409	+	24.8391i	0.524003	+	0.907600i
$750$	20.5623	−	6.19344i	0.750829	−	0.226153i
$751$	14.9521	−	25.8979i	0.545611	−	0.945026i	−0.452957	−	0.891532i	$-0.649631\pi$
$751$	14.9521	−	25.8979i	0.545611	−	0.945026i	0.998568	−	0.0534937i	$-0.0170357\pi$
$752$	−13.5556	−	10.9771i	−0.494321	−	0.400293i
$753$	23.5185	−	9.39602i	0.857063	−	0.342410i
$754$	0.0984843	+	0.463332i	0.00358659	+	0.0168736i
$755$	−21.3187	+	8.32395i	−0.775866	+	0.302940i
$756$	−0.409888	−	10.0634i	−0.0149075	−	0.366001i
$757$	−9.07256	−	9.07256i	−0.329748	−	0.329748i	0.522743	−	0.852491i	$-0.324909\pi$
$757$	−9.07256	−	9.07256i	−0.329748	−	0.329748i	−0.852491	+	0.522743i	$0.824909\pi$
$758$	23.4678	−	1.22989i	0.852387	−	0.0446717i
$759$	17.4586	−	19.9270i	0.633707	−	0.723303i
$760$	−13.7375	−	4.37669i	−0.498310	−	0.158759i
$761$	3.27543	−	0.344261i	0.118734	−	0.0124795i	−0.0449750	−	0.998988i	$-0.514321\pi$
$761$	3.27543	−	0.344261i	0.118734	−	0.0124795i	0.163709	+	0.986509i	$0.447654\pi$
$762$	10.8942	+	16.2874i	0.394654	+	0.590030i
$763$	0.0885746	+	0.109381i	0.00320662	+	0.00395984i
$764$	10.4267	−	7.57544i	0.377225	−	0.274070i
$765$	−5.27240	−	38.0778i	−0.190624	−	1.37670i
$766$	22.0255	+	16.0024i	0.795812	+	0.578191i
$767$	0.0400239	+	0.763702i	0.00144518	+	0.0275757i
$768$	4.52736	+	26.2722i	0.163367	+	0.948016i
$769$	5.90756	−	27.7929i	0.213032	−	1.00224i	−0.733515	−	0.679673i	$-0.762122\pi$
$769$	5.90756	−	27.7929i	0.213032	−	1.00224i	0.946548	−	0.322564i	$-0.104545\pi$
$770$	6.83835	−	13.6133i	0.246437	−	0.490590i
$771$	−25.8037	+	19.2878i	−0.929297	+	0.694633i
$772$	7.16025	+	4.64992i	0.257703	+	0.167354i
$773$	−9.64385	−	1.52744i	−0.346865	−	0.0549381i	−0.0194288	−	0.999811i	$-0.506185\pi$
$773$	−9.64385	−	1.52744i	−0.346865	−	0.0549381i	−0.327437	+	0.944873i	$0.606185\pi$
$774$	5.18191	−	6.07903i	0.186260	−	0.218506i
$775$	11.3645	+	6.38877i	0.408226	+	0.229492i
$776$	51.2974	−	29.6166i	1.84147	−	1.06317i
$777$	−8.89828	−	31.4931i	−0.319224	−	1.12981i
$778$	−32.7620	−	1.71699i	−1.17458	−	0.0615569i
$779$	3.35727	+	3.72863i	0.120287	+	0.133592i
$780$	0.131035	+	0.193495i	0.00469180	+	0.00692824i
$781$	9.49576	−	10.5461i	0.339785	−	0.377369i
$782$	28.1540	−	28.1540i	1.00679	−	1.00679i
$783$	−27.6425	−	6.21309i	−0.987864	−	0.222038i
$784$	−0.731661	+	1.00705i	−0.0261308	+	0.0359659i
$785$	−1.74535	−	15.7378i	−0.0622942	−	0.561705i
$786$	−12.3122	+	7.33299i	−0.439162	+	0.261559i
$787$	−1.45142	−	0.557146i	−0.0517374	−	0.0198601i	0.332362	−	0.943152i	$-0.392155\pi$
$787$	−1.45142	−	0.557146i	−0.0517374	−	0.0198601i	−0.384099	+	0.923292i	$0.625488\pi$
$788$	10.6908	+	4.10380i	0.380843	+	0.146192i
$789$	−26.8477	−	15.0185i	−0.955803	−	0.534673i
$790$	16.8722	−	7.62813i	0.600285	−	0.271397i
$791$	−15.3892	+	21.1814i	−0.547176	+	0.753123i
$792$	−22.3096	−	2.91536i	−0.792738	−	0.103593i
$793$	0.604320	−	0.604320i	0.0214600	−	0.0214600i
$794$	16.0900	−	17.8698i	0.571013	−	0.634174i
$795$	37.5929	−	31.6627i	1.33328	−	1.12296i
$796$	1.20515	+	1.33845i	0.0427153	+	0.0474402i
$797$	11.2870	+	0.591526i	0.399805	+	0.0209529i	0.251179	−	0.967941i	$-0.419182\pi$
$797$	11.2870	+	0.591526i	0.399805	+	0.0209529i	0.148626	+	0.988893i	$0.452515\pi$
$798$	7.07582	−	7.27051i	0.250481	−	0.257373i
$799$	−46.3821	+	26.7787i	−1.64088	+	0.947363i
$800$	−0.832958	+	20.3552i	−0.0294495	+	0.719664i
$801$	−4.44184	+	24.0950i	−0.156945	+	0.851353i
$802$	33.8928	+	5.36809i	1.19680	+	0.189554i
$803$	26.8329	+	17.4255i	0.946912	+	0.614932i
$804$	0.762909	+	6.41942i	0.0269057	+	0.226395i
$805$	31.3218	−	16.1860i	1.10395	−	0.570483i
$806$	0.0470959	−	0.221569i	0.00165888	−	0.00780444i
$807$	−9.08654	+	7.56457i	−0.319861	+	0.266285i
$808$	1.27286	+	24.2877i	0.0447792	+	0.854437i
$809$	12.7934	+	9.29496i	0.449793	+	0.326793i	0.789514	−	0.613733i	$-0.210333\pi$
$809$	12.7934	+	9.29496i	0.449793	+	0.326793i	−0.339721	+	0.940526i	$0.610333\pi$
$810$	22.0152	−	3.65967i	0.773534	−	0.128588i
$811$	−28.2443	+	20.5207i	−0.991790	+	0.720577i	−0.960312	−	0.278927i	$-0.910021\pi$
$811$	−28.2443	+	20.5207i	−0.991790	+	0.720577i	−0.0314775	+	0.999504i	$0.510021\pi$
$812$	6.65107	+	8.21339i	0.233407	+	0.288233i
$813$	44.9571	−	2.96829i	1.57672	−	0.104103i
$814$	−20.2151	+	2.12469i	−0.708538	+	0.0744704i
$815$	−0.261049	−	45.5518i	−0.00914413	−	1.59561i
$816$	−18.1698	−	3.60514i	−0.636069	−	0.126205i
$817$	−5.03257	+	0.263746i	−0.176067	+	0.00922730i
$818$	11.1603	+	11.1603i	0.390210	+	0.390210i
$819$	−0.586296	+	0.0777593i	−0.0204868	+	0.00271713i
$820$	2.22250	−	3.46568i	0.0776132	−	0.121027i
$821$	−4.23894	−	19.9427i	−0.147940	−	0.696004i	−0.988119	−	0.153694i	$-0.950883\pi$
$821$	−4.23894	−	19.9427i	−0.147940	−	0.696004i	0.840178	−	0.542310i	$-0.182450\pi$
$822$	−2.37347	+	16.4250i	−0.0827842	+	0.572886i
$823$	14.0564	+	11.3827i	0.489976	+	0.396774i	0.842220	−	0.539133i	$-0.181248\pi$
$823$	14.0564	+	11.3827i	0.489976	+	0.396774i	−0.352245	+	0.935908i	$0.614582\pi$
$824$	−15.0206	+	26.0164i	−0.523266	+	0.906323i
$825$	−19.9214	−	7.08032i	−0.693575	−	0.246505i
$826$	−13.6217	−	23.5935i	−0.473960	−	0.820923i
$827$	−2.04739	+	12.9267i	−0.0711949	+	0.449507i	0.926179	+	0.377084i	$0.123073\pi$
$827$	−2.04739	+	12.9267i	−0.0711949	+	0.449507i	−0.997374	+	0.0724230i	$0.976927\pi$
$828$	−10.5111	−	9.95550i	−0.365285	−	0.345977i
$829$	6.38932	+	2.07602i	0.221910	+	0.0721030i	0.417862	−	0.908511i	$-0.362780\pi$
$829$	6.38932	+	2.07602i	0.221910	+	0.0721030i	−0.195952	+	0.980614i	$0.562780\pi$
$830$	−0.880100	−	3.21086i	−0.0305487	−	0.111451i
$831$	16.3643	−	15.1416i	0.567673	−	0.525256i
$832$	0.624348	−	0.167293i	0.0216454	−	0.00579986i
$833$	2.08163	+	3.20544i	0.0721243	+	0.111062i
$834$	18.0345	+	15.8006i	0.624485	+	0.547129i
$835$	7.50373	+	16.5970i	0.259677	+	0.574364i
$836$	2.31975	+	3.19286i	0.0802302	+	0.110427i
$837$	10.8676	+	8.09088i	0.375638	+	0.279662i
$838$	−13.3744	+	2.11830i	−0.462013	+	0.0731756i
$839$	24.5111	+	10.9131i	0.846218	+	0.376761i	0.783592	−	0.621276i	$-0.213386\pi$
$839$	24.5111	+	10.9131i	0.846218	+	0.376761i	0.0626268	+	0.998037i	$0.480052\pi$
$840$	−26.2145	−	14.4677i	−0.904487	−	0.499184i
$841$	0.666958	−	0.296949i	0.0229986	−	0.0102396i
$842$	23.3588	−	15.1694i	0.804999	−	0.522772i
$843$	1.78891	−	4.85621i	0.0616132	−	0.167257i
$844$	12.7014	+	11.4364i	0.437201	+	0.393658i
$845$	−22.4749	+	18.4141i	−0.773162	+	0.633464i
$846$	−16.2716	−	26.4957i	−0.559428	−	0.910942i
$847$	11.3012	−	5.75824i	0.388314	−	0.197856i
$848$	−8.48779	−	22.1115i	−0.291472	−	0.759311i
$849$	−10.1021	−	7.13221i	−0.346704	−	0.244777i
$850$	−29.1732	−	12.5901i	−1.00063	−	0.431838i
$851$	−40.7391	−	23.5207i	−1.39652	−	0.806280i
$852$	−5.55743	−	5.40862i	−0.190394	−	0.185296i
$853$	−16.4376	+	25.3117i	−0.562814	+	0.866657i	−0.999456	−	0.0329780i	$-0.989501\pi$
$853$	−16.4376	+	25.3117i	−0.562814	+	0.866657i	0.436642	+	0.899635i	$0.356168\pi$
$854$	−9.40821	+	28.9555i	−0.321942	+	0.990836i
$855$	−11.2272	−	8.49624i	−0.383963	−	0.290565i
$856$	−10.8196	−	33.2992i	−0.369805	−	1.13814i
$857$	4.09627	+	1.09759i	0.139926	+	0.0374931i	0.328102	−	0.944642i	$-0.393591\pi$
$857$	4.09627	+	1.09759i	0.139926	+	0.0374931i	−0.188176	+	0.982135i	$0.560258\pi$
$858$	−0.0142458	+	0.367066i	−0.000486344	+	0.0125314i
$859$	−19.3205	−	43.3946i	−0.659207	−	1.48060i	−0.864878	−	0.501982i	$-0.832604\pi$
$859$	−19.3205	−	43.3946i	−0.659207	−	1.48060i	0.205671	−	0.978621i	$-0.434062\pi$
$860$	1.30037	+	3.92545i	0.0443424	+	0.133857i
$861$	5.33182	+	8.95222i	0.181708	+	0.305091i
$862$	−15.8454	+	12.8313i	−0.539695	+	0.437037i
$863$	−2.64928	−	16.7269i	−0.0901824	−	0.569389i	−0.990859	−	0.134900i	$-0.956929\pi$
$863$	−2.64928	−	16.7269i	−0.0901824	−	0.569389i	0.900677	−	0.434490i	$-0.143071\pi$
$864$	−3.55535	+	20.8707i	−0.120956	+	0.710037i
$865$	47.5593	−	10.3943i	1.61707	−	0.353416i
$866$	−35.7339	−	3.75578i	−1.21429	−	0.127627i
$867$	−14.6272	+	23.2073i	−0.496765	+	0.788162i
$868$	−1.30807	−	4.88180i	−0.0443990	−	0.165699i
$869$	−17.8313	−	3.79016i	−0.604886	−	0.128573i
$870$	−16.2366	+	16.8758i	−0.550474	+	0.572143i
$871$	0.371318	−	0.0789260i	0.0125816	−	0.00267431i
$872$	−0.0780021	−	0.153088i	−0.00264148	−	0.00518421i
$873$	56.8653	−	10.5958i	1.92460	−	0.358612i
$874$		−	14.5832i		−	0.493284i
$875$	−21.2296	−	18.4644i	−0.717692	−	0.624209i
$876$	10.0838	−	14.2827i	0.340699	−	0.482568i
$877$	−26.2459	+	32.4110i	−0.886263	+	1.09444i	0.108688	+	0.994076i	$0.465335\pi$
$877$	−26.2459	+	32.4110i	−0.886263	+	1.09444i	−0.994950	+	0.100367i	$0.967998\pi$
$878$	0.804434	−	15.3495i	0.0271483	−	0.518021i
$879$	−3.16691	−	4.23677i	−0.106817	−	0.142903i
$880$	−6.36605	+	7.95419i	−0.214600	+	0.268136i
$881$	22.1224	−	7.18801i	0.745323	−	0.242170i	0.0883555	−	0.996089i	$-0.471839\pi$
$881$	22.1224	−	7.18801i	0.745323	−	0.242170i	0.656968	+	0.753919i	$0.271839\pi$
$882$	−1.82746	+	1.25856i	−0.0615339	+	0.0423780i
$883$	29.2404	+	14.8987i	0.984019	+	0.501383i	0.870508	−	0.492154i	$-0.163790\pi$
$883$	29.2404	+	14.8987i	0.984019	+	0.501383i	0.113511	+	0.993537i	$0.463790\pi$
$884$	0.0361423	−	0.343871i	0.00121560	−	0.0115656i
$885$	−30.1531	+	22.8094i	−1.01358	+	0.766729i
$886$	3.97215	+	37.7925i	0.133447	+	1.26966i
$887$	−3.64313	+	9.49067i	−0.122324	+	0.318665i	−0.981046	−	0.193777i	$-0.937926\pi$
$887$	−3.64313	+	9.49067i	−0.122324	+	0.318665i	0.858721	+	0.512443i	$0.171259\pi$
$888$	2.63196	+	39.8632i	0.0883229	+	1.33772i
$889$	10.4421	−	23.4534i	0.350218	−	0.786602i
$890$	15.1273	+	13.4645i	0.507069	+	0.451332i
$891$	−19.5960	−	9.93736i	−0.656490	−	0.332914i
$892$	−8.17770	+	16.0496i	−0.273810	+	0.537382i
$893$	−5.07707	+	18.9479i	−0.169898	+	0.634067i
$894$	−21.5858	+	4.89526i	−0.721939	+	0.163722i
$895$	−19.5983	−	9.84478i	−0.655100	−	0.329075i
$896$	−1.87220	+	1.68573i	−0.0625457	+	0.0563164i
$897$	−0.525996	+	0.667881i	−0.0175625	+	0.0222999i
$898$	28.6744	−	11.0071i	0.956877	−	0.367311i
$899$	−14.2172			−0.474169
$900$	−4.28836	+	10.7280i	−0.142945	+	0.357599i
$901$	−72.7227			−2.42274
$902$	6.04192	−	2.31927i	0.201174	−	0.0772234i
$903$	−10.3580	−	1.49678i	−0.344694	−	0.0498096i
$904$	23.7516	−	21.3860i	0.789965	−	0.711288i
$905$	17.5387	−	2.88098i	0.583005	−	0.0957670i
$906$	−5.82070	+	18.7775i	−0.193380	+	0.623841i
$907$	10.8354	−	40.4383i	0.359784	−	1.34273i	−0.514573	−	0.857447i	$-0.672049\pi$
$907$	10.8354	−	40.4383i	0.359784	−	1.34273i	0.874356	−	0.485284i	$-0.161284\pi$
$908$	2.11192	−	4.14488i	0.0700866	−	0.137553i
$909$	−6.72370	+	22.7790i	−0.223011	+	0.755532i
$910$	−0.196273	+	0.447724i	−0.00650639	+	0.0148419i
$911$	18.8701	−	42.3829i	0.625193	−	1.40421i	−0.271883	−	0.962330i	$-0.587646\pi$
$911$	18.8701	−	42.3829i	0.625193	−	1.40421i	0.897076	−	0.441876i	$-0.145687\pi$
$912$	−5.63947	+	3.77209i	−0.186742	+	0.124906i
$913$	−1.17464	+	3.06003i	−0.0388748	+	0.101272i
$914$	−2.93147	−	27.8911i	−0.0969643	−	0.922554i
$915$	41.4909	+	7.98552i	1.37165	+	0.263993i
$916$	0.697432	−	6.63562i	0.0230438	−	0.219247i
$917$	16.7292	+	8.52393i	0.552446	+	0.281485i
$918$	−28.4023	−	16.8423i	−0.937416	−	0.555880i
$919$	−37.0383	+	12.0345i	−1.22178	+	0.396981i	−0.847731	−	0.530427i	$-0.822032\pi$
$919$	−37.0383	+	12.0345i	−1.22178	+	0.396981i	−0.374051	+	0.927408i	$0.622032\pi$
$920$	−41.5083	+	11.3775i	−1.36849	+	0.375104i
$921$	−18.8793	+	44.0008i	−0.622093	+	1.44988i
$922$	1.46387	−	27.9323i	0.0482100	−	0.919902i
$923$	−0.286581	+	0.353898i	−0.00943292	+	0.0116487i
$924$	3.43491	+	7.44150i	0.113000	+	0.244808i
$925$	−5.44725	+	37.1430i	−0.179104	+	1.22125i
$926$		−	14.6477i		−	0.481354i
$927$	−22.2894	+	19.0740i	−0.732081	+	0.626471i
$928$	−10.0859	−	19.7946i	−0.331084	−	0.649790i
$929$	11.9452	−	2.53902i	0.391908	−	0.0833026i	−0.00774289	−	0.999970i	$-0.502465\pi$
$929$	11.9452	−	2.53902i	0.391908	−	0.0833026i	0.399651	+	0.916667i	$0.369131\pi$
$930$	10.3756	−	4.21433i	0.340230	−	0.138193i
$931$	1.36930	+	0.291053i	0.0448768	+	0.00953887i
$932$	−4.59206	−	17.1378i	−0.150418	−	0.561367i
$933$	−8.92576	−	16.9454i	−0.292216	−	0.554766i
$934$	−32.3380	−	3.39886i	−1.05813	−	0.111214i
$935$	15.7960	+	27.0009i	0.516584	+	0.883024i
$936$	0.719809	+	0.0559558i	0.0235277	+	0.00182897i
$937$	−7.75367	−	48.9547i	−0.253301	−	1.59928i	−0.706395	−	0.707818i	$-0.749680\pi$
$937$	−7.75367	−	48.9547i	−0.253301	−	1.59928i	0.453093	−	0.891463i	$-0.350320\pi$
$938$	−10.5096	+	8.51051i	−0.343151	+	0.277878i
$939$	4.58706	−	8.20001i	0.149693	−	0.267597i
$940$	16.0962	−	0.0922444i	0.525002	−	0.00300868i
$941$	−9.92413	−	22.2900i	−0.323517	−	0.726632i	0.676434	−	0.736503i	$-0.263524\pi$
$941$	−9.92413	−	22.2900i	−0.323517	−	0.726632i	−0.999951	+	0.00987150i	$0.996858\pi$
$942$	−11.5066	−	7.25244i	−0.374907	−	0.236297i
$943$	14.4673	+	3.87649i	0.471119	+	0.126236i
$944$	5.63002	+	17.3274i	0.183242	+	0.563959i
$945$	−19.4362	−	21.8448i	−0.632258	−	0.710611i
$946$	−2.00870	+	6.18214i	−0.0653085	+	0.200999i
$947$	20.2299	−	31.1514i	0.657384	−	1.01228i	−0.340030	−	0.940415i	$-0.610437\pi$
$947$	20.2299	−	31.1514i	0.657384	−	1.01228i	0.997414	−	0.0718684i	$-0.0228962\pi$
$948$	−2.44749	+	9.65641i	−0.0794907	+	0.313626i
$949$	−0.889125	−	0.513337i	−0.0288622	−	0.0166636i
$950$	−10.8163	+	4.29485i	−0.350926	+	0.139343i
$951$	−6.47474	+	2.98866i	−0.209958	+	0.0969140i
$952$	15.8764	+	41.3594i	0.514557	+	1.34047i
$953$	8.86706	−	4.51799i	0.287232	−	0.146352i	−0.304438	−	0.952532i	$-0.598469\pi$
$953$	8.86706	−	4.51799i	0.287232	−	0.146352i	0.591670	+	0.806180i	$0.298469\pi$
$954$	−1.14565	−	42.2042i	−0.0370918	−	1.36641i
$955$	9.47672	−	36.1961i	0.306660	−	1.17128i
$956$	2.68212	+	2.41499i	0.0867460	+	0.0781064i
$957$	22.7208	−	3.91537i	0.734460	−	0.126566i
$958$	−17.1536	+	11.1397i	−0.554207	+	0.359906i
$959$	19.8634	−	8.84376i	0.641423	−	0.285580i
$960$	24.1561	+	20.9204i	0.779636	+	0.675204i
$961$	−22.1089	−	9.84353i	−0.713192	−	0.317533i
$962$	0.644225	−	0.102035i	0.0207706	−	0.00328975i
$963$	0.862261	−	34.1808i	0.0277860	−	1.10146i
$964$	−4.81816	−	6.63163i	−0.155182	−	0.213590i
$965$	24.6349	−	2.73206i	0.793027	−	0.0879481i
$966$	5.89414	−	29.7063i	0.189641	−	0.955783i
$967$	−21.2194	−	32.6750i	−0.682369	−	1.05076i	−0.994902	−	0.100849i	$-0.967844\pi$
$967$	−21.2194	−	32.6750i	−0.682369	−	1.05076i	0.312533	−	0.949907i	$-0.398823\pi$
$968$	−14.9558	+	4.00739i	−0.480697	+	0.128802i
$969$	4.60736	+	20.3163i	0.148010	+	0.652655i
$970$	16.8781	−	44.7336i	0.541925	−	1.43631i
$971$	−0.613375	−	0.199297i	−0.0196841	−	0.00639576i	0.299158	−	0.954203i	$-0.403294\pi$
$971$	−0.613375	−	0.199297i	−0.0196841	−	0.00639576i	−0.318843	+	0.947808i	$0.603294\pi$
$972$	−5.84154	+	10.4897i	−0.187367	+	0.336458i
$973$	4.91430	−	31.0276i	0.157545	−	0.994701i
$974$	−4.59097	−	7.95180i	−0.147104	−	0.254792i
$975$	0.650273	+	0.193433i	0.0208254	+	0.00619481i
$976$	10.1803	−	17.6328i	0.325863	−	0.564411i
$977$	17.8333	+	14.4411i	0.570537	+	0.462012i	0.870658	−	0.491889i	$-0.163694\pi$
$977$	17.8333	+	14.4411i	0.570537	+	0.462012i	−0.300121	+	0.953901i	$0.597027\pi$
$978$	−30.7405	−	24.2100i	−0.982973	−	0.774150i
$979$	−4.14535	−	19.5023i	−0.132486	−	0.623297i
$980$	−0.0666913	−	1.14676i	−0.00213038	−	0.0366321i
$981$	−0.0220598	−	0.166328i	−0.000704316	−	0.00531046i
$982$	−5.64512	−	5.64512i	−0.180143	−	0.180143i
$983$	−10.5847	+	0.554719i	−0.337598	+	0.0176928i	−0.220382	−	0.975414i	$-0.570730\pi$
$983$	−10.5847	+	0.554719i	−0.337598	+	0.0176928i	−0.117216	+	0.993106i	$0.537397\pi$
$984$	−4.09440	−	12.0427i	−0.130525	−	0.383909i
$985$	31.5585	−	10.4543i	1.00554	−	0.333102i
$986$	34.4600	−	3.62189i	1.09743	−	0.115344i
$987$	−18.0003	+	36.5452i	−0.572957	+	1.16325i
$988$	−0.0796986	−	0.0984195i	−0.00253555	−	0.00313114i
$989$	−12.1705	+	8.84241i	−0.387000	+	0.281172i
$990$	−15.4210	+	9.59247i	−0.490111	+	0.304869i
$991$	10.0219	+	7.28132i	0.318356	+	0.231299i	0.735473	−	0.677554i	$-0.236960\pi$
$991$	10.0219	+	7.28132i	0.318356	+	0.231299i	−0.417118	+	0.908852i	$0.636960\pi$
$992$	0.556010	+	10.6093i	0.0176533	+	0.336846i
$993$	−22.9242	−	8.44469i	−0.727477	−	0.267984i
$994$	3.37285	−	15.8680i	0.106980	−	0.503302i
$995$	5.16899	+	0.788349i	0.163868	+	0.0249923i
$996$	1.64603	+	0.706254i	0.0521564	+	0.0223785i
$997$	27.5296	+	17.8779i	0.871871	+	0.566200i	0.901216	−	0.433370i	$-0.142676\pi$
$997$	27.5296	+	17.8779i	0.871871	+	0.566200i	−0.0293453	+	0.999569i	$0.509342\pi$
$998$	12.9677	+	2.05388i	0.410485	+	0.0650144i
$999$	−10.5357	+	37.5635i	−0.333335	+	1.18846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.w.a.77.21	yes	448
3.2	odd	2		675.2.bd.a.152.8		448
9.2	odd	6	inner	225.2.w.a.2.21	✓	448
9.7	even	3		675.2.bd.a.602.8		448
25.13	odd	20	inner	225.2.w.a.113.21	yes	448
75.38	even	20		675.2.bd.a.638.8		448
225.38	even	60	inner	225.2.w.a.38.21	yes	448
225.88	odd	60		675.2.bd.a.413.8		448

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.w.a.2.21	✓	448	9.2	odd	6	inner
225.2.w.a.38.21	yes	448	225.38	even	60	inner
225.2.w.a.77.21	yes	448	1.1	even	1	trivial
225.2.w.a.113.21	yes	448	25.13	odd	20	inner
675.2.bd.a.152.8		448	3.2	odd	2
675.2.bd.a.413.8		448	225.88	odd	60
675.2.bd.a.602.8		448	9.7	even	3
675.2.bd.a.638.8		448	75.38	even	20

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.w (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.03530 - 0.397413i) q^{2} +(0.642595 + 1.60844i) q^{3} +(-0.572387 + 0.515379i) q^{4} +(-0.337136 + 2.21051i) q^{5} +(1.30449 + 1.40983i) q^{6} +(0.651331 - 2.43080i) q^{7} +(-1.39468 + 2.73721i) q^{8} +(-2.17414 + 2.06715i) q^{9} +O(q^{10})\)	\(q+(1.03530 - 0.397413i) q^{2} +(0.642595 + 1.60844i) q^{3} +(-0.572387 + 0.515379i) q^{4} +(-0.337136 + 2.21051i) q^{5} +(1.30449 + 1.40983i) q^{6} +(0.651331 - 2.43080i) q^{7} +(-1.39468 + 2.73721i) q^{8} +(-2.17414 + 2.06715i) q^{9} +(0.529449 + 2.42251i) q^{10} +(0.992964 - 2.23023i) q^{11} +(-1.19677 - 0.589468i) q^{12} +(-0.0280741 + 0.0731355i) q^{13} +(-0.291712 - 2.77545i) q^{14} +(-3.77210 + 0.878200i) q^{15} +(-0.195083 + 1.85609i) q^{16} +(5.10587 + 2.60157i) q^{17} +(-1.42937 + 3.00415i) q^{18} +(1.99615 - 0.648587i) q^{19} +(-0.946277 - 1.43902i) q^{20} +(4.32834 - 0.514396i) q^{21} +(0.141688 - 2.70357i) q^{22} +(3.94298 - 4.86918i) q^{23} +(-5.29885 - 0.484335i) q^{24} +(-4.77268 - 1.49048i) q^{25} +0.0868740i q^{26} +(-4.72197 - 2.16863i) q^{27} +(0.879971 + 1.72704i) q^{28} +(5.33338 - 1.13364i) q^{29} +(-3.55624 + 2.40828i) q^{30} +(-2.55046 - 0.542118i) q^{31} +(-1.05454 - 3.93561i) q^{32} +(4.22527 + 0.163982i) q^{33} +(6.31999 + 0.664258i) q^{34} +(5.15372 + 2.25928i) q^{35} +(0.179084 - 2.30372i) q^{36} +(-1.17452 - 7.41562i) q^{37} +(1.80885 - 1.46478i) q^{38} +(-0.135674 + 0.00184113i) q^{39} +(-5.58043 - 4.00576i) q^{40} +(0.972306 + 2.18383i) q^{41} +(4.27669 - 2.25269i) q^{42} +(-2.31923 - 0.621435i) q^{43} +(0.581057 + 1.78831i) q^{44} +(-3.83647 - 5.50287i) q^{45} +(2.14708 - 6.60804i) q^{46} +(-5.09026 + 7.83831i) q^{47} +(-3.11076 + 0.878936i) q^{48} +(0.577613 + 0.333485i) q^{49} +(-5.53348 + 0.353634i) q^{50} +(-0.903455 + 9.88423i) q^{51} +(-0.0216233 - 0.0563306i) q^{52} +(-11.3074 + 5.76140i) q^{53} +(-5.75049 - 0.368602i) q^{54} +(4.59518 + 2.94684i) q^{55} +(5.74523 + 5.17303i) q^{56} +(2.32593 + 2.79390i) q^{57} +(5.07111 - 3.29322i) q^{58} +(8.91811 - 3.97060i) q^{59} +(1.70650 - 2.44673i) q^{60} +(-9.96634 - 4.43730i) q^{61} +(-2.85593 + 0.452335i) q^{62} +(3.60874 + 6.63131i) q^{63} +(-4.84981 - 6.67519i) q^{64} +(-0.152202 - 0.0867146i) q^{65} +(4.43957 - 1.50941i) q^{66} +(-2.63921 - 4.06402i) q^{67} +(-4.26333 + 1.14236i) q^{68} +(10.3655 + 3.21313i) q^{69} +(6.23350 + 0.290873i) q^{70} +(5.52847 + 1.79631i) q^{71} +(-2.62600 - 8.83411i) q^{72} +(-2.05016 + 12.9442i) q^{73} +(-4.16304 - 7.21060i) q^{74} +(-0.669555 - 8.63433i) q^{75} +(-0.808299 + 1.40002i) q^{76} +(-4.77451 - 3.86632i) q^{77} +(-0.139731 + 0.0558248i) q^{78} +(-1.55252 - 7.30404i) q^{79} +(-4.03713 - 1.05699i) q^{80} +(0.453788 - 8.98855i) q^{81} +(1.87451 + 1.87451i) q^{82} +(-1.34078 + 0.0702675i) q^{83} +(-2.21237 + 2.52517i) q^{84} +(-7.47216 + 10.4095i) q^{85} +(-2.64805 + 0.278322i) q^{86} +(5.25060 + 7.84993i) q^{87} +(4.71976 + 5.82842i) q^{88} +(6.60723 - 4.80043i) q^{89} +(-6.15880 - 4.17244i) q^{90} +(0.159492 + 0.115878i) q^{91} +(0.252563 + 4.81918i) q^{92} +(-0.766954 - 4.45062i) q^{93} +(-2.15488 + 10.1379i) q^{94} +(0.760734 + 4.63116i) q^{95} +(5.65253 - 4.22517i) q^{96} +(-16.1707 - 10.5014i) q^{97} +(0.730533 + 0.115705i) q^{98} +(2.45138 + 6.90145i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9}+O(q^{10}) \) 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9	\( 448 q - 24 q^{2} - 14 q^{3} - 10 q^{4} - 24 q^{5} - 12 q^{6} - 8 q^{7} - 20 q^{9} - 32 q^{10} - 18 q^{11} - 14 q^{12} - 8 q^{13} - 30 q^{14} - 14 q^{15} - 50 q^{16} - 56 q^{18} - 40 q^{19} - 48 q^{20} - 12 q^{21} - 48 q^{23} + 16 q^{25} - 38 q^{27} - 24 q^{28} - 30 q^{29} - 50 q^{30} - 6 q^{31} - 60 q^{32} - 8 q^{33} - 10 q^{34} + 4 q^{36} - 44 q^{37} - 60 q^{39} - 16 q^{40} - 18 q^{41} + 174 q^{42} - 8 q^{43} - 64 q^{45} - 24 q^{46} - 18 q^{47} - 100 q^{48} + 24 q^{50} - 32 q^{51} + 24 q^{52} - 150 q^{54} - 24 q^{55} - 18 q^{56} - 94 q^{57} - 4 q^{58} + 202 q^{60} - 6 q^{61} - 46 q^{63} - 40 q^{64} - 96 q^{65} + 12 q^{66} - 14 q^{67} + 288 q^{68} + 50 q^{69} - 28 q^{70} + 102 q^{72} - 32 q^{73} + 18 q^{75} - 32 q^{76} + 216 q^{77} + 182 q^{78} - 10 q^{79} - 32 q^{81} - 72 q^{82} + 36 q^{83} + 100 q^{84} - 32 q^{85} - 18 q^{86} + 48 q^{87} - 28 q^{88} + 106 q^{90} - 24 q^{91} + 30 q^{92} + 8 q^{93} - 130 q^{94} + 6 q^{95} - 60 q^{96} - 38 q^{97}+O(q^{100}) \) 448 * q - 24 * q^2 - 14 * q^3 - 10 * q^4 - 24 * q^5 - 12 * q^6 - 8 * q^7 - 20 * q^9 - 32 * q^10 - 18 * q^11 - 14 * q^12 - 8 * q^13 - 30 * q^14 - 14 * q^15 - 50 * q^16 - 56 * q^18 - 40 * q^19 - 48 * q^20 - 12 * q^21 - 48 * q^23 + 16 * q^25 - 38 * q^27 - 24 * q^28 - 30 * q^29 - 50 * q^30 - 6 * q^31 - 60 * q^32 - 8 * q^33 - 10 * q^34 + 4 * q^36 - 44 * q^37 - 60 * q^39 - 16 * q^40 - 18 * q^41 + 174 * q^42 - 8 * q^43 - 64 * q^45 - 24 * q^46 - 18 * q^47 - 100 * q^48 + 24 * q^50 - 32 * q^51 + 24 * q^52 - 150 * q^54 - 24 * q^55 - 18 * q^56 - 94 * q^57 - 4 * q^58 + 202 * q^60 - 6 * q^61 - 46 * q^63 - 40 * q^64 - 96 * q^65 + 12 * q^66 - 14 * q^67 + 288 * q^68 + 50 * q^69 - 28 * q^70 + 102 * q^72 - 32 * q^73 + 18 * q^75 - 32 * q^76 + 216 * q^77 + 182 * q^78 - 10 * q^79 - 32 * q^81 - 72 * q^82 + 36 * q^83 + 100 * q^84 - 32 * q^85 - 18 * q^86 + 48 * q^87 - 28 * q^88 + 106 * q^90 - 24 * q^91 + 30 * q^92 + 8 * q^93 - 130 * q^94 + 6 * q^95 - 60 * q^96 - 38 * q^97

Introduction

L-functions

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