LMFDB - Embedded newform 256.2.m.a.101.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(5,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("256.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.m (of order $64$, degree $32$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$31$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			101.24
Character	$\chi$	$=$	256.101
Dual form			256.2.m.a.109.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.948164 - 1.04928i) q^{2} +(-0.796024 + 0.199394i) q^{3} +(-0.201971 - 1.98978i) q^{4} +(-2.23808 - 1.05853i) q^{5} +(-0.545542 + 1.02431i) q^{6} +(-0.443907 - 1.46337i) q^{7} +(-2.27933 - 1.67471i) q^{8} +(-2.05187 + 1.09675i) q^{9} +O(q^{10})$	\(q+(0.948164 - 1.04928i) q^{2} +(-0.796024 + 0.199394i) q^{3} +(-0.201971 - 1.98978i) q^{4} +(-2.23808 - 1.05853i) q^{5} +(-0.545542 + 1.02431i) q^{6} +(-0.443907 - 1.46337i) q^{7} +(-2.27933 - 1.67471i) q^{8} +(-2.05187 + 1.09675i) q^{9} +(-3.23276 + 1.34471i) q^{10} +(0.660502 - 0.0979762i) q^{11} +(0.557522 + 1.54364i) q^{12} +(1.50872 - 4.21660i) q^{13} +(-1.95638 - 0.921729i) q^{14} +(1.99263 + 0.396359i) q^{15} +(-3.91842 + 0.803752i) q^{16} +(0.516309 - 0.102700i) q^{17} +(-0.794714 + 3.19287i) q^{18} +(0.468480 + 0.424605i) q^{19} +(-1.65422 + 4.66707i) q^{20} +(0.645147 + 1.07636i) q^{21} +(0.523460 - 0.785948i) q^{22} +(4.23811 - 0.417417i) q^{23} +(2.14833 + 0.878626i) q^{24} +(0.716544 + 0.873111i) q^{25} +(-2.99387 - 5.58110i) q^{26} +(3.23876 - 2.93544i) q^{27} +(-2.82212 + 1.17883i) q^{28} +(-4.00444 - 5.39936i) q^{29} +(2.30523 - 1.71501i) q^{30} +(8.89857 + 3.68591i) q^{31} +(-2.87194 + 4.87360i) q^{32} +(-0.506240 + 0.209691i) q^{33} +(0.381785 - 0.639129i) q^{34} +(-0.555522 + 3.74502i) q^{35} +(2.59669 + 3.86124i) q^{36} +(0.280550 - 5.71072i) q^{37} +(0.889725 - 0.0889703i) q^{38} +(-0.360217 + 3.65735i) q^{39} +(3.32859 + 6.16088i) q^{40} +(-5.74742 + 7.00326i) q^{41} +(1.74111 + 0.343630i) q^{42} +(0.718329 - 2.86773i) q^{43} +(-0.328353 - 1.29446i) q^{44} +(5.75318 - 0.282636i) q^{45} +(3.58043 - 4.84273i) q^{46} +(8.21197 + 5.48706i) q^{47} +(2.95889 - 1.42111i) q^{48} +(3.87590 - 2.58979i) q^{49} +(1.59554 + 0.0759985i) q^{50} +(-0.390517 + 0.184701i) q^{51} +(-8.69481 - 2.15039i) q^{52} +(-1.78653 + 2.40886i) q^{53} +(-0.00921977 - 6.18165i) q^{54} +(-1.58197 - 0.479884i) q^{55} +(-1.43890 + 4.07891i) q^{56} +(-0.457585 - 0.244584i) q^{57} +(-9.46229 - 0.917707i) q^{58} +(-3.14890 - 8.80058i) q^{59} +(0.386213 - 4.04494i) q^{60} +(-1.95664 + 3.26446i) q^{61} +(12.3048 - 5.84223i) q^{62} +(2.51578 + 2.51578i) q^{63} +(2.39069 + 7.63443i) q^{64} +(-7.84005 + 7.84005i) q^{65} +(-0.259974 + 0.730008i) q^{66} +(2.51171 + 1.50546i) q^{67} +(-0.308630 - 1.00660i) q^{68} +(-3.29040 + 1.17733i) q^{69} +(3.40285 + 4.13379i) q^{70} +(1.19413 - 2.23407i) q^{71} +(6.51361 + 0.936437i) q^{72} +(0.217845 - 0.718140i) q^{73} +(-5.72613 - 5.70907i) q^{74} +(-0.744479 - 0.552143i) q^{75} +(0.750251 - 1.01793i) q^{76} +(-0.436577 - 0.923064i) q^{77} +(3.49603 + 3.84573i) q^{78} +(-8.34415 - 12.4879i) q^{79} +(9.62053 + 2.34891i) q^{80} +(1.88492 - 2.82099i) q^{81} +(1.89887 + 12.6709i) q^{82} +(0.259401 + 5.28023i) q^{83} +(2.01142 - 1.50109i) q^{84} +(-1.26425 - 0.316679i) q^{85} +(-2.32795 - 3.47280i) q^{86} +(4.26423 + 3.49956i) q^{87} +(-1.66958 - 0.882829i) q^{88} +(0.0896871 + 0.00883341i) q^{89} +(5.15840 - 6.30468i) q^{90} +(-6.84017 - 0.336036i) q^{91} +(-1.68654 - 8.34857i) q^{92} +(-7.81842 - 1.15975i) q^{93} +(13.5437 - 3.41401i) q^{94} +(-0.599037 - 1.44620i) q^{95} +(1.31437 - 4.45215i) q^{96} +(3.08962 - 7.45900i) q^{97} +(0.957573 - 6.52244i) q^{98} +(-1.24781 + 0.925437i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) $ 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{9}{64}\right)$	$1$

Coefficient data

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

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

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

$2$	0.948164	−	1.04928i	0.670453	−	0.741952i
$2$	0.948164	−	1.04928i	0.670453	−	0.741952i
$3$	−0.796024	+	0.199394i	−0.459585	+	0.115120i	−0.465856	−	0.884860i	$-0.654254\pi$
$3$	−0.796024	+	0.199394i	−0.459585	+	0.115120i	0.00627157	+	0.999980i	$0.498004\pi$
$4$	−0.201971	−	1.98978i	−0.100985	−	0.994888i
$5$	−2.23808	−	1.05853i	−1.00090	−	0.473390i	−0.144390	−	0.989521i	$-0.546122\pi$
$5$	−2.23808	−	1.05853i	−1.00090	−	0.473390i	−0.856510	+	0.516131i	$0.827372\pi$
$6$	−0.545542	+	1.02431i	−0.222717	+	0.418172i
$7$	−0.443907	−	1.46337i	−0.167781	−	0.553101i	0.832218	−	0.554449i	$-0.187071\pi$
$7$	−0.443907	−	1.46337i	−0.167781	−	0.553101i	−0.999999	+	0.00134814i	$0.999571\pi$
$8$	−2.27933	−	1.67471i	−0.805865	−	0.592099i
$9$	−2.05187	+	1.09675i	−0.683956	+	0.365582i
$10$	−3.23276	+	1.34471i	−1.02229	+	0.425234i
$11$	0.660502	−	0.0979762i	0.199149	−	0.0295409i	−0.0464108	−	0.998922i	$-0.514778\pi$
$11$	0.660502	−	0.0979762i	0.199149	−	0.0295409i	0.245560	+	0.969382i	$0.421028\pi$
$12$	0.557522	+	1.54364i	0.160943	+	0.445610i
$13$	1.50872	−	4.21660i	0.418445	−	1.16947i	−0.528740	−	0.848784i	$-0.677335\pi$
$13$	1.50872	−	4.21660i	0.418445	−	1.16947i	0.947184	−	0.320690i	$-0.103915\pi$
$14$	−1.95638	−	0.921729i	−0.522864	−	0.246342i
$15$	1.99263	+	0.396359i	0.514495	+	0.102339i
$16$	−3.91842	+	0.803752i	−0.979604	+	0.200938i
$17$	0.516309	−	0.102700i	0.125223	−	0.0249085i	−0.132081	−	0.991239i	$-0.542166\pi$
$17$	0.516309	−	0.102700i	0.125223	−	0.0249085i	0.257304	+	0.966330i	$0.417166\pi$
$18$	−0.794714	+	3.19287i	−0.187316	+	0.752568i
$19$	0.468480	+	0.424605i	0.107477	+	0.0974112i	0.723529	−	0.690294i	$-0.242519\pi$
$19$	0.468480	+	0.424605i	0.107477	+	0.0974112i	−0.616052	+	0.787705i	$0.711269\pi$
$20$	−1.65422	+	4.66707i	−0.369894	+	1.04359i
$21$	0.645147	+	1.07636i	0.140783	+	0.234882i
$22$	0.523460	−	0.785948i	0.111602	−	0.167565i
$23$	4.23811	−	0.417417i	0.883706	−	0.0870375i	0.354027	−	0.935235i	$-0.384812\pi$
$23$	4.23811	−	0.417417i	0.883706	−	0.0870375i	0.529679	+	0.848198i	$0.322312\pi$
$24$	2.14833	+	0.878626i	0.438526	+	0.179349i
$25$	0.716544	+	0.873111i	0.143309	+	0.174622i
$26$	−2.99387	−	5.58110i	−0.587146	−	1.09454i
$27$	3.23876	−	2.93544i	0.623300	−	0.564926i
$28$	−2.82212	+	1.17883i	−0.533330	+	0.222779i
$29$	−4.00444	−	5.39936i	−0.743605	−	1.00264i	−0.999356	−	0.0358924i	$-0.988573\pi$
$29$	−4.00444	−	5.39936i	−0.743605	−	1.00264i	0.255751	−	0.966743i	$-0.417677\pi$
$30$	2.30523	−	1.71501i	0.420876	−	0.313117i
$31$	8.89857	+	3.68591i	1.59823	+	0.662008i	0.991164	−	0.132643i	$-0.0423465\pi$
$31$	8.89857	+	3.68591i	1.59823	+	0.662008i	0.607066	+	0.794652i	$0.292346\pi$
$32$	−2.87194	+	4.87360i	−0.507692	+	0.861539i
$33$	−0.506240	+	0.209691i	−0.0881250	+	0.0365026i
$34$	0.381785	−	0.639129i	0.0654755	−	0.109610i
$35$	−0.555522	+	3.74502i	−0.0939003	+	0.633024i
$36$	2.59669	+	3.86124i	0.432782	+	0.643541i
$37$	0.280550	−	5.71072i	0.0461221	−	0.938837i	−0.858550	−	0.512729i	$-0.828634\pi$
$37$	0.280550	−	5.71072i	0.0461221	−	0.938837i	0.904672	−	0.426108i	$-0.140116\pi$
$38$	0.889725	−	0.0889703i	0.144332	−	0.0144329i
$39$	−0.360217	+	3.65735i	−0.0576809	+	0.585644i
$40$	3.32859	+	6.16088i	0.526296	+	0.974121i
$41$	−5.74742	+	7.00326i	−0.897597	+	1.09372i	0.0975409	+	0.995232i	$0.468902\pi$
$41$	−5.74742	+	7.00326i	−0.897597	+	1.09372i	−0.995138	+	0.0984934i	$0.968598\pi$
$42$	1.74111	+	0.343630i	0.268659	+	0.0530232i
$43$	0.718329	−	2.86773i	0.109544	−	0.437325i	−0.890293	−	0.455389i	$-0.849500\pi$
$43$	0.718329	−	2.86773i	0.109544	−	0.437325i	0.999837	+	0.0180641i	$0.00575029\pi$
$44$	−0.328353	−	1.29446i	−0.0495010	−	0.195148i
$45$	5.75318	−	0.282636i	0.857634	−	0.0421329i
$46$	3.58043	−	4.84273i	0.527906	−	0.714022i
$47$	8.21197	+	5.48706i	1.19784	+	0.800370i	0.984289	−	0.176562i	$-0.0564978\pi$
$47$	8.21197	+	5.48706i	1.19784	+	0.800370i	0.213549	+	0.976932i	$0.431498\pi$
$48$	2.95889	−	1.42111i	0.427079	−	0.205120i
$49$	3.87590	−	2.58979i	0.553700	−	0.369970i
$50$	1.59554	+	0.0759985i	0.225643	+	0.0107478i
$51$	−0.390517	+	0.184701i	−0.0546833	+	0.0258633i
$52$	−8.69481	−	2.15039i	−1.20575	−	0.298206i
$53$	−1.78653	+	2.40886i	−0.245399	+	0.330883i	−0.908684	−	0.417484i	$-0.862912\pi$
$53$	−1.78653	+	2.40886i	−0.245399	+	0.330883i	0.663285	+	0.748367i	$0.269162\pi$
$54$	−0.00921977	−	6.18165i	−0.00125465	−	0.841216i
$55$	−1.58197	−	0.479884i	−0.213312	−	0.0647076i
$56$	−1.43890	+	4.07891i	−0.192282	+	0.545068i
$57$	−0.457585	−	0.244584i	−0.0606086	−	0.0323960i
$58$	−9.46229	−	0.917707i	−1.24246	−	0.120501i
$59$	−3.14890	−	8.80058i	−0.409952	−	1.14574i	−0.952188	−	0.305512i	$-0.901172\pi$
$59$	−3.14890	−	8.80058i	−0.409952	−	1.14574i	0.542236	−	0.840226i	$-0.317578\pi$
$60$	0.386213	−	4.04494i	0.0498598	−	0.522200i
$61$	−1.95664	+	3.26446i	−0.250523	+	0.417972i	−0.957141	−	0.289624i	$-0.906470\pi$
$61$	−1.95664	+	3.26446i	−0.250523	+	0.417972i	0.706618	+	0.707595i	$0.250220\pi$
$62$	12.3048	−	5.84223i	1.56272	−	0.741964i
$63$	2.51578	+	2.51578i	0.316959	+	0.316959i
$64$	2.39069	+	7.63443i	0.298836	+	0.954304i
$65$	−7.84005	+	7.84005i	−0.972439	+	0.972439i
$66$	−0.259974	+	0.730008i	−0.0320005	+	0.0898578i
$67$	2.51171	+	1.50546i	0.306855	+	0.183922i	0.659238	−	0.751934i	$-0.270879\pi$
$67$	2.51171	+	1.50546i	0.306855	+	0.183922i	−0.352384	+	0.935856i	$0.614629\pi$
$68$	−0.308630	−	1.00660i	−0.0374269	−	0.122068i
$69$	−3.29040	+	1.17733i	−0.396118	+	0.141733i
$70$	3.40285	+	4.13379i	0.406718	+	0.494083i
$71$	1.19413	−	2.23407i	0.141718	−	0.265135i	−0.801042	−	0.598608i	$-0.795721\pi$
$71$	1.19413	−	2.23407i	0.141718	−	0.265135i	0.942760	+	0.333473i	$0.108221\pi$
$72$	6.51361	+	0.936437i	0.767637	+	0.110360i
$73$	0.217845	−	0.718140i	0.0254969	−	0.0840520i	−0.943269	−	0.332031i	$-0.892266\pi$
$73$	0.217845	−	0.718140i	0.0254969	−	0.0840520i	0.968766	+	0.247979i	$0.0797663\pi$
$74$	−5.72613	−	5.70907i	−0.665649	−	0.663666i
$75$	−0.744479	−	0.552143i	−0.0859651	−	0.0637560i
$76$	0.750251	−	1.01793i	0.0860596	−	0.116764i
$77$	−0.436577	−	0.923064i	−0.0497525	−	0.105193i
$78$	3.49603	+	3.84573i	0.395847	+	0.435443i
$79$	−8.34415	−	12.4879i	−0.938790	−	1.40500i	−0.914183	−	0.405302i	$-0.867166\pi$
$79$	−8.34415	−	12.4879i	−0.938790	−	1.40500i	−0.0246074	−	0.999697i	$-0.507834\pi$
$80$	9.62053	+	2.34891i	1.07561	+	0.262616i
$81$	1.88492	−	2.82099i	0.209436	−	0.313443i
$82$	1.89887	+	12.6709i	0.209695	+	1.39926i
$83$	0.259401	+	5.28023i	0.0284730	+	0.579581i	0.970068	+	0.242833i	$0.0780768\pi$
$83$	0.259401	+	5.28023i	0.0284730	+	0.579581i	−0.941595	+	0.336747i	$0.890673\pi$
$84$	2.01142	−	1.50109i	0.219464	−	0.163783i
$85$	−1.26425	−	0.316679i	−0.137128	−	0.0343487i
$86$	−2.32795	−	3.47280i	−0.251030	−	0.374482i
$87$	4.26423	+	3.49956i	0.457173	+	0.375192i
$88$	−1.66958	−	0.882829i	−0.177978	−	0.0941099i
$89$	0.0896871	+	0.00883341i	0.00950681	+	0.000936339i	0.102769	−	0.994705i	$-0.467230\pi$
$89$	0.0896871	+	0.00883341i	0.00950681	+	0.000936339i	−0.0932626	+	0.995642i	$0.529730\pi$
$90$	5.15840	−	6.30468i	0.543743	−	0.664571i
$91$	−6.84017	−	0.336036i	−0.717044	−	0.0352261i
$92$	−1.68654	−	8.34857i	−0.175834	−	0.870399i
$93$	−7.81842	−	1.15975i	−0.810733	−	0.120261i
$94$	13.5437	−	3.41401i	1.39693	−	0.352128i
$95$	−0.599037	−	1.44620i	−0.0614599	−	0.148377i
$96$	1.31437	−	4.45215i	0.134147	−	0.454396i
$97$	3.08962	−	7.45900i	0.313703	−	0.757347i	−0.685858	−	0.727735i	$-0.740573\pi$
$97$	3.08962	−	7.45900i	0.313703	−	0.757347i	0.999561	−	0.0296115i	$-0.00942703\pi$
$98$	0.957573	−	6.52244i	0.0967295	−	0.658866i
$99$	−1.24781	+	0.925437i	−0.125409	+	0.0930099i
$100$	1.59257	−	1.60210i	0.159257	−	0.160210i
$101$	−0.607875	−	0.670686i	−0.0604858	−	0.0667358i	0.709957	−	0.704246i	$-0.248715\pi$
$101$	−0.607875	−	0.670686i	−0.0604858	−	0.0667358i	−0.770442	+	0.637510i	$0.779965\pi$
$102$	−0.176472	+	0.584888i	−0.0174733	+	0.0579125i
$103$	−5.11140	+	4.19482i	−0.503641	+	0.413328i	−0.851608	−	0.524179i	$-0.824372\pi$
$103$	−5.11140	+	4.19482i	−0.503641	+	0.413328i	0.347967	+	0.937507i	$0.386872\pi$
$104$	−10.5005	+	7.08435i	−1.02965	+	0.694677i
$105$	−0.304525	−	3.09190i	−0.0297186	−	0.301738i
$106$	0.833640	+	4.15857i	0.0809703	+	0.403916i
$107$	−9.90753	+	5.93835i	−0.957797	+	0.574082i	−0.905407	−	0.424545i	$-0.860434\pi$
$107$	−9.90753	+	5.93835i	−0.957797	+	0.574082i	−0.0523904	+	0.998627i	$0.516684\pi$
$108$	−6.49501	−	5.85154i	−0.624983	−	0.563065i
$109$	12.8532	−	14.1813i	1.23111	−	1.35833i	0.319337	−	0.947641i	$-0.396540\pi$
$109$	12.8532	−	14.1813i	1.23111	−	1.35833i	0.911777	−	0.410685i	$-0.134710\pi$
$110$	−2.00350	+	1.20491i	−0.191026	+	0.114884i
$111$	0.915358	+	4.60181i	0.0868819	+	0.436785i
$112$	2.91560	+	5.37729i	0.275498	+	0.508106i
$113$	−2.62167	+	13.1800i	−0.246626	+	1.23987i	0.636700	+	0.771111i	$0.280299\pi$
$113$	−2.62167	+	13.1800i	−0.246626	+	1.23987i	−0.883326	+	0.468759i	$0.844701\pi$
$114$	−0.690503	+	0.248228i	−0.0646715	+	0.0232487i
$115$	−9.92707	−	3.55196i	−0.925704	−	0.331222i
$116$	−9.93473	+	9.05844i	−0.922417	+	0.841055i
$117$	1.52884	+	10.3066i	0.141341	+	0.952844i
$118$	−12.2199	−	5.04032i	−1.12494	−	0.463999i
$119$	−0.379482	−	0.709960i	−0.0347870	−	0.0650820i
$120$	−3.87808	−	4.24051i	−0.354018	−	0.387104i
$121$	−10.0997	+	3.06370i	−0.918153	+	0.278519i
$122$	1.57011	+	5.14831i	0.142151	+	0.466106i
$123$	3.17868	−	6.72076i	0.286612	−	0.605991i
$124$	5.53688	−	18.4506i	0.497226	−	1.65691i
$125$	2.32836	+	9.29535i	0.208255	+	0.831401i
$126$	5.02513	−	0.254382i	0.447674	−	0.0226622i
$127$			7.26512i			0.644675i	0.946625	+	0.322338i	$0.104469\pi$
$127$			7.26512i			0.644675i	−0.946625	+	0.322338i	$0.895531\pi$
$128$	10.2774	+	4.73019i	0.908404	+	0.418094i
$129$			2.42601i			0.213598i
$130$	0.792744	+	15.6601i	0.0695282	+	1.37348i
$131$	3.57190	+	14.2598i	0.312079	+	1.24589i	0.899613	+	0.436689i	$0.143849\pi$
$131$	3.57190	+	14.2598i	0.312079	+	1.24589i	−0.587534	+	0.809199i	$0.699901\pi$
$132$	0.519484	+	0.964952i	0.0452153	+	0.0839883i
$133$	0.413392	−	0.874044i	0.0358456	−	0.0757892i
$134$	3.96117	−	1.20806i	0.342193	−	0.104361i
$135$	−10.3559	+	3.14142i	−0.891292	+	0.270370i
$136$	−1.34883	−	0.630581i	−0.115661	−	0.0540718i
$137$	−7.02010	−	13.1337i	−0.599768	−	1.12209i	−0.980336	−	0.197334i	$-0.936772\pi$
$137$	−7.02010	−	13.1337i	−0.599768	−	1.12209i	0.380568	−	0.924753i	$-0.375728\pi$
$138$	−1.88450	+	4.56885i	−0.160419	+	0.388926i
$139$	1.51323	+	10.2014i	0.128351	+	0.865270i	0.953724	+	0.300683i	$0.0972145\pi$
$139$	1.51323	+	10.2014i	0.128351	+	0.865270i	−0.825374	+	0.564587i	$0.809035\pi$
$140$	7.56395	+	0.348979i	0.639271	+	0.0294941i
$141$	−7.63101	−	2.73042i	−0.642647	−	0.229943i
$142$	−1.21192	−	3.37124i	−0.101702	−	0.282908i
$143$	0.583388	−	2.93289i	0.0487854	−	0.245261i
$144$	7.15856	−	5.94670i	0.596546	−	0.495558i
$145$	3.24685	+	16.3230i	0.269636	+	1.35555i
$146$	−0.546976	−	0.909495i	−0.0452680	−	0.0752704i
$147$	−2.56892	+	2.83437i	−0.211881	+	0.233775i
$148$	−11.4197	+	0.595167i	−0.938695	+	0.0489224i
$149$	−2.81252	+	1.68576i	−0.230411	+	0.138103i	−0.624650	−	0.780905i	$-0.714758\pi$
$149$	−2.81252	+	1.68576i	−0.230411	+	0.138103i	0.394239	+	0.919008i	$0.371008\pi$
$150$	−1.28524	+	0.257644i	−0.104939	+	0.0210365i
$151$	−0.792501	−	8.04640i	−0.0644928	−	0.654807i	−0.972033	−	0.234842i	$-0.924543\pi$
$151$	−0.792501	−	8.04640i	−0.0644928	−	0.654807i	0.907541	−	0.419964i	$-0.137957\pi$
$152$	−0.356729	−	1.75238i	−0.0289346	−	0.142137i
$153$	−0.946762	+	0.776987i	−0.0765412	+	0.0628157i
$154$	−1.38250	−	0.417125i	−0.111405	−	0.0336129i
$155$	−16.0140	−	17.6688i	−1.28628	−	1.41919i
$156$	7.35005	−	0.0219249i	0.588475	−	0.00175540i
$157$	19.2207	−	14.2550i	1.53398	−	1.13768i	0.590126	−	0.807311i	$-0.299078\pi$
$157$	19.2207	−	14.2550i	1.53398	−	1.13768i	0.943853	−	0.330366i	$-0.107172\pi$
$158$	−21.0149	−	3.08524i	−1.67186	−	0.245449i
$159$	0.941812	−	2.27374i	0.0746906	−	0.180319i
$160$	11.5865	−	7.86746i	0.915993	−	0.621977i
$161$	−2.49216	−	6.01661i	−0.196410	−	0.474175i
$162$	−1.17278	−	4.65257i	−0.0921426	−	0.365540i
$163$	6.04021	+	0.895981i	0.473106	+	0.0701786i	0.379026	−	0.925386i	$-0.376259\pi$
$163$	6.04021	+	0.895981i	0.473106	+	0.0701786i	0.0940799	+	0.995565i	$0.470009\pi$
$164$	15.0957	+	10.0216i	1.17878	+	0.782558i
$165$	1.35497	+	0.0665654i	0.105484	+	0.00518211i
$166$	5.78639	+	4.73434i	0.449111	+	0.367456i
$167$	−3.61663	−	0.356207i	−0.279863	−	0.0275641i	−0.0428884	−	0.999080i	$-0.513656\pi$
$167$	−3.61663	−	0.356207i	−0.279863	−	0.0275641i	−0.236975	+	0.971516i	$0.576156\pi$
$168$	0.332093	−	3.53382i	0.0256215	−	0.272640i
$169$	−5.45433	−	4.47625i	−0.419564	−	0.344327i
$170$	−1.53100	+	1.02629i	−0.117423	+	0.0787129i
$171$	−1.42694	−	0.357431i	−0.109121	−	0.0273334i
$172$	−5.85122	−	0.850116i	−0.446151	−	0.0648208i
$173$	0.236739	+	4.81894i	0.0179990	+	0.366377i	0.990852	+	0.134953i	$0.0430884\pi$
$173$	0.236739	+	4.81894i	0.0179990	+	0.366377i	−0.972853	+	0.231424i	$0.925662\pi$
$174$	7.71520	−	1.15620i	0.584888	−	0.0876516i
$175$	0.959603	−	1.43615i	0.0725392	−	0.108563i
$176$	−2.50937	+	0.914791i	−0.189151	+	0.0689550i
$177$	4.26138	+	6.37761i	0.320305	+	0.479370i
$178$	0.0943067	−	0.0857312i	0.00706859	−	0.00642583i
$179$	−7.24189	−	15.3117i	−0.541285	−	1.14445i	−0.970467	−	0.241232i	$-0.922448\pi$
$179$	−7.24189	−	15.3117i	−0.541285	−	1.14445i	0.429183	−	0.903218i	$-0.358802\pi$
$180$	−1.72436	−	11.3905i	−0.128526	−	0.848995i
$181$	−4.20645	−	3.11972i	−0.312663	−	0.231887i	0.427975	−	0.903790i	$-0.359227\pi$
$181$	−4.20645	−	3.11972i	−0.312663	−	0.231887i	−0.740639	+	0.671903i	$0.765477\pi$
$182$	−6.83819	+	6.85862i	−0.506881	+	0.508395i
$183$	0.906623	−	2.98873i	0.0670195	−	0.220934i
$184$	−10.3591	−	6.14617i	−0.763683	−	0.453101i
$185$	−6.67288	+	12.4841i	−0.490600	+	0.917848i
$186$	−8.63005	+	7.10406i	−0.632786	+	0.520895i
$187$	0.330961	−	0.118420i	0.0242023	−	0.00865971i
$188$	9.25944	−	17.4482i	0.675314	−	1.27254i
$189$	−5.73334	−	3.43643i	−0.417039	−	0.249964i
$190$	−2.08545	−	0.742681i	−0.151295	−	0.0538797i
$191$	13.2775	−	13.2775i	0.960726	−	0.960726i	−0.0385312	−	0.999257i	$-0.512268\pi$
$191$	13.2775	−	13.2775i	0.960726	−	0.960726i	0.999257	+	0.0385312i	$0.0122679\pi$
$192$	−3.42531	−	5.60051i	−0.247200	−	0.404182i
$193$	15.1468	+	15.1468i	1.09029	+	1.09029i	0.995497	+	0.0947949i	$0.0302195\pi$
$193$	15.1468	+	15.1468i	1.09029	+	1.09029i	0.0947949	+	0.995497i	$0.469780\pi$
$194$	−4.89710	−	10.3142i	−0.351592	−	0.740518i
$195$	4.67762	−	7.80413i	0.334971	−	0.558865i
$196$	−5.93592	−	7.18911i	−0.423995	−	0.513508i
$197$	−2.86446	−	8.00563i	−0.204084	−	0.570377i	0.795272	−	0.606253i	$-0.207328\pi$
$197$	−2.86446	−	8.00563i	−0.204084	−	0.570377i	−0.999356	+	0.0358754i	$0.988578\pi$
$198$	−0.212085	+	2.18676i	−0.0150722	+	0.155406i
$199$	15.5570	+	8.31538i	1.10281	+	0.589462i	0.919300	−	0.393557i	$-0.128755\pi$
$199$	15.5570	+	8.31538i	1.10281	+	0.589462i	0.183505	+	0.983019i	$0.441255\pi$
$200$	−0.171032	−	3.19011i	−0.0120938	−	0.225575i
$201$	−2.29957	−	0.697566i	−0.162199	−	0.0492025i
$202$	−1.28010	+	0.00190924i	−0.0900676	+	0.000134334i
$203$	−6.12364	+	8.25677i	−0.429795	+	0.579512i
$204$	0.446386	+	0.739737i	0.0312533	+	0.0517920i
$205$	20.2764	−	9.59001i	1.41616	−	0.669795i
$206$	−0.444913	+	9.34066i	−0.0309986	+	0.650795i
$207$	−8.23823	+	5.50461i	−0.572596	+	0.382597i
$208$	−2.52270	+	17.7350i	−0.174918	+	1.22970i
$209$	0.351033	+	0.234553i	0.0242815	+	0.0162244i
$210$	−3.53300	−	2.61209i	−0.243800	−	0.180252i
$211$	−1.28776	+	0.0632637i	−0.0886532	+	0.00435525i	−0.0933459	−	0.995634i	$-0.529756\pi$
$211$	−1.28776	+	0.0632637i	−0.0886532	+	0.00435525i	0.00469271	+	0.999989i	$0.498506\pi$
$212$	5.15392	+	3.06828i	0.353973	+	0.210730i
$213$	−0.505101	+	2.01647i	−0.0346089	+	0.138167i
$214$	−3.16299	+	16.0263i	−0.216217	+	1.09553i
$215$	−4.64326	+	5.65783i	−0.316668	+	0.385861i
$216$	−12.2982	+	1.26686i	−0.836789	+	0.0861986i
$217$	1.44369	−	14.6581i	0.0980043	−	0.995054i
$218$	−2.69322	−	26.9328i	−0.182408	−	1.82412i
$219$	−0.0302176	+	0.615094i	−0.00204192	+	0.0415642i
$220$	−0.635352	+	3.24468i	−0.0428354	+	0.218756i
$221$	0.345922	−	2.33202i	0.0232692	−	0.156868i
$222$	5.69649	+	3.40281i	0.382324	+	0.228382i
$223$	26.8319	−	11.1141i	1.79680	−	0.744257i	0.809141	−	0.587614i	$-0.199933\pi$
$223$	26.8319	−	11.1141i	1.79680	−	0.744257i	0.987655	−	0.156643i	$-0.0500672\pi$
$224$	8.40674	+	2.03928i	0.561699	+	0.136255i
$225$	−2.42783	−	1.00564i	−0.161856	−	0.0670428i
$226$	11.3437	+	15.2477i	0.754574	+	1.01426i
$227$	7.50035	+	10.1131i	0.497816	+	0.671227i	0.978638	−	0.205591i	$-0.0659118\pi$
$227$	7.50035	+	10.1131i	0.497816	+	0.671227i	−0.480822	+	0.876818i	$0.659662\pi$
$228$	−0.394249	+	0.959891i	−0.0261098	+	0.0635703i
$229$	−9.30988	+	8.43798i	−0.615214	+	0.557598i	−0.918559	−	0.395283i	$-0.870646\pi$
$229$	−9.30988	+	8.43798i	−0.615214	+	0.557598i	0.303345	+	0.952881i	$0.401896\pi$
$230$	−13.1395	+	7.04842i	−0.866392	+	0.464759i
$231$	0.531579	+	0.647731i	0.0349753	+	0.0426176i
$232$	0.0850735	+	19.0132i	0.00558535	+	1.24828i
$233$	22.6482	−	2.23066i	1.48374	−	0.146135i	0.676534	−	0.736411i	$-0.263481\pi$
$233$	22.6482	−	2.23066i	1.48374	−	0.146135i	0.807202	+	0.590276i	$0.200981\pi$
$234$	12.2641	+	8.16816i	0.801727	+	0.533969i
$235$	−12.5708	−	20.9731i	−0.820029	−	1.36814i
$236$	−16.8752	+	8.04306i	−1.09848	+	0.523559i
$237$	9.13216	+	8.27690i	0.593197	+	0.537643i
$238$	−1.10476	−	0.274977i	−0.0716108	−	0.0178241i
$239$	−0.128231	+	0.0255068i	−0.00829460	+	0.00164990i	−0.199236	−	0.979952i	$-0.563846\pi$
$239$	−0.128231	+	0.0255068i	−0.00829460	+	0.00164990i	0.190941	+	0.981601i	$0.438846\pi$
$240$	−8.12653	+	0.0484826i	−0.524565	+	0.00312954i
$241$	29.2024	+	5.80872i	1.88109	+	0.374172i	0.995854	−	0.0909657i	$-0.0289954\pi$
$241$	29.2024	+	5.80872i	1.88109	+	0.374172i	0.885238	+	0.465138i	$0.153995\pi$
$242$	−6.36147	+	13.5023i	−0.408931	+	0.867959i
$243$	−5.35568	+	14.9681i	−0.343567	+	0.960206i
$244$	6.89073	+	3.23396i	0.441134	+	0.207033i
$245$	−11.4160	+	1.69340i	−0.729338	+	0.108187i
$246$	−4.03804	−	9.70771i	−0.257456	−	0.618941i
$247$	2.49720	−	1.33478i	0.158893	−	0.0849300i
$248$	−14.1099	−	23.3039i	−0.895982	−	1.47980i
$249$	−1.25933	−	4.15147i	−0.0798071	−	0.263089i
$250$	11.9611	+	6.37041i	0.756485	+	0.402900i
$251$	26.1497	+	12.3679i	1.65055	+	0.780654i	0.999771	+	0.0213894i	$0.00680896\pi$
$251$	26.1497	+	12.3679i	1.65055	+	0.780654i	0.650782	+	0.759264i	$0.274441\pi$
$252$	4.49773	−	5.51395i	0.283330	−	0.347346i
$253$	2.75838	−	0.690938i	0.173418	−	0.0434389i
$254$	7.62314	+	6.88853i	0.478318	+	0.432225i
$255$	1.06952			0.0669760
$256$	14.7080	−	6.29887i	0.919248	−	0.393679i
$257$	−7.74855			−0.483341			−0.241671	−	0.970358i	$-0.577695\pi$
$257$	−7.74855			−0.483341			−0.241671	+	0.970358i	$0.577695\pi$
$258$	2.54556	+	2.30026i	0.158480	+	0.143208i
$259$	−8.48142	+	2.12448i	−0.527010	+	0.132009i
$260$	17.1834	+	14.0165i	1.06567	+	0.869266i
$261$	14.1383	+	6.68691i	0.875138	+	0.413909i
$262$	18.3493	+	9.77274i	1.13362	+	0.603762i
$263$	−3.76387	−	12.4078i	−0.232090	−	0.765099i	−0.993194	−	0.116469i	$-0.962842\pi$
$263$	−3.76387	−	12.4078i	−0.232090	−	0.765099i	0.761104	−	0.648630i	$-0.224658\pi$
$264$	1.50506	+	0.369849i	0.0926300	+	0.0227626i
$265$	6.54826	−	3.50012i	0.402257	−	0.215011i
$266$	−0.525152	−	1.26250i	−0.0321991	−	0.0774088i
$267$	−0.0731544	+	0.0108514i	−0.00447698	+	0.000664097i
$268$	2.48824	−	5.30181i	0.151994	−	0.323859i
$269$	6.27723	−	17.5437i	0.382729	−	1.06966i	−0.583532	−	0.812090i	$-0.698330\pi$
$269$	6.27723	−	17.5437i	0.382729	−	1.06966i	0.966261	−	0.257566i	$-0.0829204\pi$
$270$	−6.52284	+	13.8448i	−0.396968	+	0.842566i
$271$	−14.7047	−	2.92494i	−0.893244	−	0.177677i	−0.272933	−	0.962033i	$-0.587994\pi$
$271$	−14.7047	−	2.92494i	−0.893244	−	0.177677i	−0.620311	+	0.784356i	$0.712994\pi$
$272$	−1.94057	+	0.817407i	−0.117664	+	0.0495626i
$273$	5.51194	−	1.09639i	0.333598	−	0.0663567i
$274$	−20.4371	−	5.08685i	−1.23465	−	0.307308i
$275$	0.558823	+	0.506487i	0.0336983	+	0.0305423i
$276$	3.00718	+	6.30938i	0.181011	+	0.379780i
$277$	15.5423	+	25.9308i	0.933847	+	1.55803i	0.825859	+	0.563877i	$0.190691\pi$
$277$	15.5423	+	25.9308i	0.933847	+	1.55803i	0.107988	+	0.994152i	$0.465559\pi$
$278$	12.1389	+	8.08478i	0.728042	+	0.484893i
$279$	−22.3012	+	2.19647i	−1.33514	+	0.131499i
$280$	7.53805	−	7.60581i	0.450484	−	0.454534i
$281$	2.61284	+	3.18375i	0.155869	+	0.189927i	0.845090	−	0.534625i	$-0.179547\pi$
$281$	2.61284	+	3.18375i	0.155869	+	0.189927i	−0.689221	+	0.724551i	$0.742047\pi$
$282$	−10.1004	+	5.41817i	−0.601471	+	0.322647i
$283$	3.23318	−	2.93038i	0.192193	−	0.174193i	−0.569791	−	0.821790i	$-0.692976\pi$
$283$	3.23318	−	2.93038i	0.192193	−	0.174193i	0.761983	+	0.647597i	$0.224226\pi$
$284$	−4.68647	−	1.92484i	−0.278091	−	0.114218i
$285$	0.765212	+	1.03177i	0.0453272	+	0.0611167i
$286$	−2.52427	−	3.39300i	−0.149263	−	0.200632i
$287$	12.7997	+	5.30179i	0.755540	+	0.312955i
$288$	0.547741	−	13.1498i	0.0322760	−	0.774857i
$289$	−15.4499	+	6.39957i	−0.908819	+	0.376445i
$290$	20.2059	+	12.0700i	1.18653	+	0.708777i
$291$	−0.972134	+	6.55360i	−0.0569875	+	0.384179i
$292$	−1.47294	−	0.288420i	−0.0861971	−	0.0168785i
$293$	0.354575	−	7.21754i	0.0207145	−	0.421653i	−0.965934	−	0.258789i	$-0.916677\pi$
$293$	0.354575	−	7.21754i	0.0207145	−	0.421653i	0.986648	−	0.162864i	$-0.0520733\pi$
$294$	0.538283	+	5.38296i	0.0313933	+	0.313941i
$295$	−2.26822	+	23.0296i	−0.132061	+	1.34084i
$296$	−10.2033	+	12.5468i	−0.593053	+	0.729267i
$297$	1.85161	−	2.25619i	0.107441	−	0.130917i
$298$	−0.897899	+	4.54949i	−0.0520139	+	0.263545i
$299$	4.63405	−	18.5002i	0.267994	−	1.06989i
$300$	−0.948279	+	1.59286i	−0.0547489	+	0.0919640i
$301$	−4.51541	+	0.221828i	−0.260264	+	0.0127859i
$302$	−9.19433	−	6.79775i	−0.529074	−	0.391167i
$303$	0.617614	+	0.412676i	0.0354810	+	0.0237076i
$304$	−2.17698	−	1.28724i	−0.124858	−	0.0738282i
$305$	7.83467	−	5.23496i	0.448612	−	0.299753i
$306$	−0.0824093	+	1.73013i	−0.00471102	+	0.0989048i
$307$	3.11051	−	1.47116i	0.177526	−	0.0839637i	−0.336726	−	0.941603i	$-0.609320\pi$
$307$	3.11051	−	1.47116i	0.177526	−	0.0839637i	0.514252	+	0.857639i	$0.328070\pi$
$308$	−1.74851	+	1.05512i	−0.0996309	+	0.0601211i
$309$	3.23238	−	4.35836i	0.183884	−	0.247938i
$310$	−33.7234	+	0.0502976i	−1.91536	+	0.00285671i
$311$	−28.3738	−	8.60708i	−1.60893	−	0.488063i	−0.647258	−	0.762271i	$-0.724084\pi$
$311$	−28.3738	−	8.60708i	−1.60893	−	0.488063i	−0.961670	+	0.274208i	$0.911584\pi$
$312$	6.94605	−	7.73304i	0.393243	−	0.437797i
$313$	11.8508	+	6.33439i	0.669847	+	0.358041i	0.771004	−	0.636830i	$-0.219755\pi$
$313$	11.8508	+	6.33439i	0.669847	+	0.358041i	−0.101157	+	0.994870i	$0.532255\pi$
$314$	3.26687	−	33.6840i	0.184360	−	1.90090i
$315$	−2.96748	−	8.29355i	−0.167199	−	0.467289i
$316$	−23.1629	+	19.1252i	−1.30301	+	1.07588i
$317$	−17.0823	+	28.5000i	−0.959435	+	1.60072i	−0.171301	+	0.985219i	$0.554797\pi$
$317$	−17.0823	+	28.5000i	−0.959435	+	1.60072i	−0.788135	+	0.615502i	$0.788953\pi$
$318$	−1.49279	−	3.14410i	−0.0837115	−	0.176312i
$319$	−3.17394	−	3.17394i	−0.177707	−	0.177707i
$320$	2.73074	−	19.6171i	0.152653	−	1.09663i
$321$	6.70257	−	6.70257i	0.374101	−	0.374101i
$322$	−8.67607	−	3.08976i	−0.483499	−	0.172186i
$323$	0.285488	+	0.171115i	0.0158850	+	0.00952108i
$324$	−5.99383	−	3.18082i	−0.332990	−	0.176712i
$325$	4.76263	−	1.70410i	0.264183	−	0.0945262i
$326$	6.66725	−	5.48833i	0.369265	−	0.303970i
$327$	−7.40380	+	13.8515i	−0.409431	+	0.765992i
$328$	24.8287	−	6.33746i	1.37094	−	0.349928i
$329$	4.38423	−	14.4529i	0.241710	−	0.796812i
$330$	1.35458	−	1.35863i	0.0745671	−	0.0747899i
$331$	−6.98818	−	5.18279i	−0.384105	−	0.284872i	0.386367	−	0.922345i	$-0.373730\pi$
$331$	−6.98818	−	5.18279i	−0.384105	−	0.284872i	−0.770473	+	0.637473i	$0.779980\pi$
$332$	10.4541	−	1.58260i	0.573742	−	0.0868565i
$333$	5.68756	+	12.0253i	0.311676	+	0.658984i
$334$	−3.80292	+	3.45711i	−0.208087	+	0.189165i
$335$	−4.02783	−	6.02808i	−0.220064	−	0.329349i
$336$	−3.39308	−	3.69910i	−0.185108	−	0.201802i
$337$	−3.66031	+	5.47804i	−0.199390	+	0.298408i	−0.917668	−	0.397348i	$-0.869931\pi$
$337$	−3.66031	+	5.47804i	−0.199390	+	0.298408i	0.718278	+	0.695756i	$0.244931\pi$
$338$	−9.86843	+	1.47889i	−0.536772	+	0.0804410i
$339$	−0.541100	−	11.0144i	−0.0293885	−	0.598217i
$340$	−0.374778	+	2.57954i	−0.0203252	+	0.139895i
$341$	6.23865	+	1.56270i	0.337842	+	0.0846250i
$342$	−1.72802	+	1.15836i	−0.0934406	+	0.0626368i
$343$	−13.7850	−	11.3131i	−0.744323	−	0.610850i
$344$	−6.43992	+	5.33351i	−0.347217	+	0.287564i
$345$	8.61043	+	0.848053i	0.463570	+	0.0456576i
$346$	5.28088	+	4.32074i	0.283902	+	0.232284i
$347$	17.1420	+	0.842134i	0.920233	+	0.0452081i	0.503667	−	0.863898i	$-0.331984\pi$
$347$	17.1420	+	0.842134i	0.920233	+	0.0452081i	0.416565	+	0.909106i	$0.363234\pi$
$348$	6.10209	−	9.19166i	0.327106	−	0.492725i
$349$	−1.62681	−	0.241315i	−0.0870812	−	0.0129173i	0.103048	−	0.994676i	$-0.467141\pi$
$349$	−1.62681	−	0.241315i	−0.0870812	−	0.0129173i	−0.190129	+	0.981759i	$0.560891\pi$
$350$	−0.597057	−	2.36859i	−0.0319141	−	0.126607i
$351$	−7.49119	−	18.0853i	−0.399850	−	0.965324i
$352$	−1.41943	+	3.50040i	−0.0756556	+	0.186572i
$353$	9.77790	−	23.6059i	0.520425	−	1.25642i	−0.417214	−	0.908808i	$-0.636993\pi$
$353$	9.77790	−	23.6059i	0.520425	−	1.25642i	0.937639	−	0.347610i	$-0.113007\pi$
$354$	10.7324	+	1.57564i	0.570419	+	0.0837444i
$355$	−5.03740	+	3.73599i	−0.267357	+	0.198286i
$356$	−0.000537652	−	0.180241i	−2.84955e−5	−	0.00955277i
$357$	0.443638	+	0.489480i	0.0234798	+	0.0259060i
$358$	−22.9327	−	6.91924i	−1.21203	−	0.365693i
$359$	1.18609	−	0.973397i	0.0625993	−	0.0513739i	−0.602573	−	0.798063i	$-0.705858\pi$
$359$	1.18609	−	0.973397i	0.0625993	−	0.0513739i	0.665173	+	0.746690i	$0.268358\pi$
$360$	−13.5867	−	8.99070i	−0.716084	−	0.473851i
$361$	−1.82314	−	18.5107i	−0.0959548	−	0.974246i
$362$	−7.26186	+	1.45574i	−0.381675	+	0.0765118i
$363$	7.42871	−	4.45260i	0.389906	−	0.233701i
$364$	0.712876	+	13.6783i	0.0373649	+	0.716936i
$365$	−1.24773	+	1.37666i	−0.0653092	+	0.0720576i
$366$	−2.27639	−	3.78511i	−0.118989	−	0.197851i
$367$	0.381381	+	1.91733i	0.0199080	+	0.100084i	0.989462	−	0.144794i	$-0.0462520\pi$
$367$	0.381381	+	1.91733i	0.0199080	+	0.100084i	−0.969554	+	0.244878i	$0.921252\pi$
$368$	−16.2712	+	5.04200i	−0.848193	+	0.262832i
$369$	4.11216	−	20.6732i	0.214070	−	1.07620i
$370$	6.77229	+	18.8387i	0.352075	+	0.979376i
$371$	4.31810	+	1.54504i	0.224185	+	0.0802146i
$372$	−0.728558	+	15.7911i	−0.0377740	+	0.818733i
$373$	1.24346	+	8.38269i	0.0643837	+	0.434039i	0.997268	+	0.0738641i	$0.0235331\pi$
$373$	1.24346	+	8.38269i	0.0643837	+	0.434039i	−0.932885	+	0.360175i	$0.882717\pi$
$374$	0.189550	−	0.459552i	0.00980140	−	0.0237628i
$375$	−3.70687	−	6.93506i	−0.191422	−	0.358125i
$376$	−9.52854	−	26.2595i	−0.491397	−	1.35423i
$377$	−28.8085	+	8.73896i	−1.48371	+	0.450080i
$378$	−9.04192	+	2.75757i	−0.465066	+	0.141834i
$379$	−3.40602	+	7.20142i	−0.174955	+	0.369912i	−0.972344	−	0.233554i	$-0.924964\pi$
$379$	−3.40602	+	7.20142i	−0.174955	+	0.369912i	0.797388	+	0.603467i	$0.206214\pi$
$380$	−2.75663	+	1.48404i	−0.141412	+	0.0761296i
$381$	−1.44862	−	5.78321i	−0.0742150	−	0.296283i
$382$	−1.34255	−	26.5210i	−0.0686908	−	1.35693i
$383$			24.5256i			1.25320i	0.779340	+	0.626601i	$0.215554\pi$
$383$			24.5256i			1.25320i	−0.779340	+	0.626601i	$0.784446\pi$
$384$	−9.12424	−	1.71610i	−0.465620	−	0.0875742i
$385$			2.52802i			0.128840i
$386$	30.2549	−	1.53156i	1.53993	−	0.0779546i
$387$	1.67125	+	6.67202i	0.0849547	+	0.339158i
$388$	−15.4658	−	4.64115i	−0.785155	−	0.235619i
$389$	1.88806	−	3.99197i	0.0957284	−	0.202401i	−0.850443	−	0.526068i	$-0.823666\pi$
$389$	1.88806	−	3.99197i	0.0957284	−	0.202401i	0.946171	+	0.323667i	$0.104916\pi$
$390$	−3.75356	−	12.3077i	−0.190069	−	0.623225i
$391$	2.14530	−	0.650771i	0.108493	−	0.0329109i
$392$	−13.1716	−	0.588015i	−0.665267	−	0.0296992i
$393$	−5.68665	−	10.6390i	−0.286853	−	0.536665i
$394$	−11.1161	−	4.58503i	−0.560022	−	0.230991i
$395$	5.45602	+	36.7815i	0.274522	+	1.85068i
$396$	2.09343	+	2.29594i	0.105199	+	0.115376i
$397$	−21.6075	−	7.73128i	−1.08445	−	0.388022i	−0.266807	−	0.963750i	$-0.585969\pi$
$397$	−21.6075	−	7.73128i	−1.08445	−	0.388022i	−0.817641	+	0.575728i	$0.804719\pi$
$398$	23.4757	−	8.43927i	1.17673	−	0.423022i
$399$	−0.154791	+	0.778188i	−0.00774925	+	0.0389581i
$400$	−3.50948	−	2.84529i	−0.175474	−	0.142264i
$401$	−0.501582	−	2.52162i	−0.0250478	−	0.125924i	0.966238	−	0.257650i	$-0.0829481\pi$
$401$	−0.501582	−	2.52162i	−0.0250478	−	0.125924i	−0.991286	+	0.131726i	$0.957948\pi$
$402$	−2.91231	+	1.75148i	−0.145253	+	0.0873558i
$403$	28.9675	−	31.9607i	1.44297	−	1.59207i
$404$	−1.21174	+	1.34499i	−0.0602865	+	0.0669159i
$405$	−7.20471	+	4.31834i	−0.358005	+	0.214580i
$406$	2.85744	+	14.2542i	0.141812	+	0.707423i
$407$	−0.374211	−	3.79943i	−0.0185490	−	0.188331i
$408$	1.19944	+	0.233009i	0.0593810	+	0.0115357i
$409$	−18.4697	+	15.1577i	−0.913269	+	0.749500i	−0.968510	−	0.248973i	$-0.919907\pi$
$409$	−18.4697	+	15.1577i	−0.913269	+	0.749500i	0.0552418	+	0.998473i	$0.482407\pi$
$410$	9.16273	−	30.3685i	0.452515	−	1.49979i
$411$	8.20695	+	9.05497i	0.404819	+	0.446649i
$412$	9.37910	+	9.32331i	0.462075	+	0.459327i
$413$	−11.4807	+	8.51464i	−0.564926	+	0.418978i
$414$	−2.03532	+	13.8635i	−0.100031	+	0.681352i
$415$	5.00874	−	12.0922i	0.245869	−	0.593581i
$416$	16.2170	+	19.4627i	0.795106	+	0.954239i
$417$	−3.23866	−	7.81882i	−0.158598	−	0.382889i
$418$	0.578948	−	0.145937i	0.0283173	−	0.00713801i
$419$	16.2067	+	2.40404i	0.791750	+	0.117445i	0.530343	−	0.847783i	$-0.322063\pi$
$419$	16.2067	+	2.40404i	0.791750	+	0.117445i	0.261408	+	0.965229i	$0.415813\pi$
$420$	−6.09068	+	1.23041i	−0.297195	+	0.0600378i
$421$	−38.0996	−	1.87171i	−1.85686	−	0.0912218i	−0.910340	−	0.413861i	$-0.864180\pi$
$421$	−38.0996	−	1.87171i	−1.85686	−	0.0912218i	−0.946522	+	0.322639i	$0.895430\pi$
$422$	−1.15463	+	1.41121i	−0.0562064	+	0.0686964i
$423$	−22.8678	−	2.25228i	−1.11187	−	0.109510i
$424$	8.10624	−	2.49866i	0.393674	−	0.121346i
$425$	0.459627	+	0.377206i	0.0222952	+	0.0182972i
$426$	1.63693	+	2.44194i	0.0793093	+	0.118312i
$427$	5.64567	+	1.41417i	0.273213	+	0.0684364i
$428$	13.8170	+	18.5144i	0.667870	+	0.894927i
$429$	0.120409	+	2.45098i	0.00581339	+	0.118334i
$430$	1.53407	+	10.2366i	0.0739793	+	0.493654i
$431$	−13.8945	+	20.7945i	−0.669272	+	1.00164i	0.329083	+	0.944301i	$0.393261\pi$
$431$	−13.8945	+	20.7945i	−0.669272	+	1.00164i	−0.998355	+	0.0573356i	$0.981739\pi$
$432$	−10.3315	+	14.1055i	−0.497072	+	0.678649i
$433$	−5.53539	−	8.28430i	−0.266014	−	0.398118i	0.674283	−	0.738473i	$-0.264453\pi$
$433$	−5.53539	−	8.28430i	−0.266014	−	0.398118i	−0.940297	+	0.340355i	$0.889453\pi$
$434$	−14.0115	−	15.4131i	−0.672575	−	0.739852i
$435$	−5.83928	−	12.3461i	−0.279972	−	0.591951i
$436$	−30.8137	−	22.7108i	−1.47571	−	1.08765i
$437$	2.16270	+	1.60397i	0.103456	+	0.0767284i
$438$	0.616754	+	0.614917i	0.0294696	+	0.0293819i
$439$	6.53070	−	21.5288i	0.311693	−	1.02752i	−0.651487	−	0.758660i	$-0.725855\pi$
$439$	6.53070	−	21.5288i	0.311693	−	1.02752i	0.963181	−	0.268855i	$-0.0866454\pi$
$440$	2.80216	+	3.74315i	0.133588	+	0.178448i
$441$	−5.11248	+	9.56479i	−0.243452	+	0.455466i
$442$	−2.11894	−	2.57410i	−0.100788	−	0.122438i
$443$	34.7596	−	12.4372i	1.65148	−	0.590908i	0.663870	−	0.747848i	$-0.268913\pi$
$443$	34.7596	−	12.4372i	1.65148	−	0.590908i	0.987608	+	0.156940i	$0.0501628\pi$
$444$	8.97170	−	2.75079i	0.425778	−	0.130547i
$445$	−0.191376	−	0.114707i	−0.00907211	−	0.00543761i
$446$	13.7792	−	38.6921i	0.652464	−	1.83213i
$447$	1.90270	−	1.90270i	0.0899948	−	0.0899948i
$448$	10.1107	−	6.88744i	0.477687	−	0.325401i
$449$	−9.25895	−	9.25895i	−0.436957	−	0.436957i	0.454030	−	0.890987i	$-0.349986\pi$
$449$	−9.25895	−	9.25895i	−0.436957	−	0.436957i	−0.890987	+	0.454030i	$0.849986\pi$
$450$	−3.35718	+	1.59396i	−0.158259	+	0.0751400i
$451$	−3.11003	+	5.18877i	−0.146446	+	0.244330i
$452$	26.7548	+	2.55455i	1.25844	+	0.120156i
$453$	2.23525	+	6.24711i	0.105021	+	0.293515i
$454$	17.7230	+	1.71887i	0.831780	+	0.0806707i
$455$	14.9531	+	7.99262i	0.701014	+	0.374700i
$456$	0.633380	+	1.32381i	0.0296607	+	0.0619931i
$457$	−5.58733	−	1.69490i	−0.261364	−	0.0792840i	0.156883	−	0.987617i	$-0.449855\pi$
$457$	−5.58733	−	1.69490i	−0.261364	−	0.0792840i	−0.418247	+	0.908333i	$0.637355\pi$
$458$	0.0265024	+	17.7692i	0.00123837	+	0.830302i
$459$	1.37073	−	1.84822i	0.0639803	−	0.0862675i
$460$	−5.06263	+	20.4700i	−0.236046	+	0.954420i
$461$	−26.8547	+	12.7013i	−1.25075	+	0.591559i	−0.934109	−	0.356987i	$-0.883804\pi$
$461$	−26.8547	+	12.7013i	−1.25075	+	0.591559i	−0.316638	+	0.948546i	$0.602554\pi$
$462$	1.18367	+	0.0563806i	0.0550695	+	0.00262306i
$463$	−9.88912	+	6.60770i	−0.459586	+	0.307086i	−0.763725	−	0.645542i	$-0.776631\pi$
$463$	−9.88912	+	6.60770i	−0.459586	+	0.307086i	0.304138	+	0.952628i	$0.401631\pi$
$464$	20.0308	+	17.9383i	0.929906	+	0.832767i
$465$	16.2706	+	10.8717i	0.754532	+	0.504162i
$466$	19.1337	−	25.8793i	0.886350	−	1.19884i
$467$	−5.76850	+	0.283388i	−0.266934	+	0.0131136i	−0.182095	−	0.983281i	$-0.558288\pi$
$467$	−5.76850	+	0.283388i	−0.266934	+	0.0131136i	−0.0848395	+	0.996395i	$0.527038\pi$
$468$	20.1990	−	5.12367i	0.933700	−	0.236842i
$469$	1.08808	−	4.34385i	0.0502427	−	0.200580i
$470$	−33.9258	−	6.69568i	−1.56488	−	0.308849i
$471$	−12.4578	+	15.1799i	−0.574024	+	0.699451i
$472$	−7.56105	+	25.3329i	−0.348025	+	1.16604i
$473$	0.193488	−	1.96452i	0.00889660	−	0.0903287i
$474$	17.3436	−	1.73431i	0.796616	−	0.0796597i
$475$	−0.0350414	+	0.713284i	−0.00160781	+	0.0327277i
$476$	−1.33602	+	0.898475i	−0.0612363	+	0.0411815i
$477$	1.02382	−	6.90204i	0.0468775	−	0.316023i
$478$	−0.0948207	+	0.158735i	−0.00433700	+	0.00726038i
$479$	−29.6502	+	12.2815i	−1.35475	+	0.561157i	−0.937612	−	0.347684i	$-0.886968\pi$
$479$	−29.6502	+	12.2815i	−1.35475	+	0.561157i	−0.417142	+	0.908841i	$0.636968\pi$
$480$	−7.65441	+	8.57296i	−0.349374	+	0.391300i
$481$	−23.6566	−	9.79887i	−1.07865	−	0.446790i
$482$	33.7836	−	25.1338i	1.53880	−	1.14481i
$483$	3.18349	+	4.29245i	0.144854	+	0.195313i
$484$	8.13592	+	19.4773i	0.369815	+	0.885333i
$485$	−14.8104	+	13.4234i	−0.672506	+	0.609524i
$486$	10.6277	+	19.8118i	0.482081	+	0.898684i
$487$	7.20472	+	8.77898i	0.326477	+	0.397813i	0.910220	−	0.414125i	$-0.135912\pi$
$487$	7.20472	+	8.77898i	0.326477	+	0.397813i	−0.583743	+	0.811939i	$0.698412\pi$
$488$	9.92686	−	4.16398i	0.449368	−	0.188494i
$489$	−4.98681	+	0.491158i	−0.225511	+	0.0222109i
$490$	−9.04735	+	13.5841i	−0.408718	+	0.613668i
$491$	4.19432	+	6.99780i	0.189287	+	0.315806i	0.937712	−	0.347413i	$-0.112940\pi$
$491$	4.19432	+	6.99780i	0.189287	+	0.315806i	−0.748425	+	0.663219i	$0.769190\pi$
$492$	−14.0148	−	4.96747i	−0.631837	−	0.223951i
$493$	−2.62204	−	2.37648i	−0.118091	−	0.107031i
$494$	0.967197	−	3.88585i	0.0435162	−	0.174832i
$495$	3.77230	−	0.750356i	0.169552	−	0.0337260i
$496$	−37.8308	−	7.29067i	−1.69865	−	0.327361i
$497$	−3.79934	−	0.755737i	−0.170424	−	0.0338994i
$498$	−5.55010	−	2.61488i	−0.248706	−	0.117176i
$499$	−10.1020	+	28.2332i	−0.452228	+	1.26389i	0.471848	+	0.881680i	$0.343587\pi$
$499$	−10.1020	+	28.2332i	−0.452228	+	1.26389i	−0.924075	+	0.382211i	$0.875163\pi$
$500$	18.0254	−	6.51031i	0.806120	−	0.291150i
$501$	2.94995	−	0.437584i	0.131794	−	0.0195498i
$502$	37.7715	−	15.7115i	1.68583	−	0.701240i
$503$	35.6217	−	19.0402i	1.58829	−	0.848960i	0.589129	−	0.808039i	$-0.299471\pi$
$503$	35.6217	−	19.0402i	1.58829	−	0.848960i	0.999162	−	0.0409207i	$-0.0130291\pi$
$504$	−1.52109	−	9.94750i	−0.0677548	−	0.443097i
$505$	0.650529	+	2.14451i	0.0289481	+	0.0954292i
$506$	1.89041	−	3.54943i	0.0840389	−	0.157791i
$507$	5.23431	+	2.47565i	0.232464	+	0.109947i
$508$	14.4560	−	1.46734i	0.641380	−	0.0651027i
$509$	−27.0904	+	6.78579i	−1.20076	+	0.300775i	−0.791229	−	0.611520i	$-0.790558\pi$
$509$	−27.0904	+	6.78579i	−1.20076	+	0.300775i	−0.409533	+	0.912296i	$0.634308\pi$
$510$	1.01408	−	1.12222i	0.0449042	−	0.0496929i
$511$	−1.14761			−0.0507671
$512$	7.33629	−	21.4051i	0.324221	−	0.945981i
$513$	2.76370			0.122020
$514$	−7.34690	+	8.13039i	−0.324058	+	0.358616i
$515$	15.8801	−	3.97775i	0.699760	−	0.175281i
$516$	4.82722	−	0.489983i	0.212507	−	0.0215703i
$517$	5.96162	+	2.81964i	0.262192	+	0.124007i
$518$	−5.81260	+	10.9137i	−0.255391	+	0.479522i
$519$	−1.14932	−	3.78879i	−0.0504494	−	0.166309i
$520$	30.9999	−	4.74025i	1.35943	−	0.207874i
$521$	25.0629	−	13.3964i	1.09803	−	0.586908i	0.180096	−	0.983649i	$-0.442359\pi$
$521$	25.0629	−	13.3964i	1.09803	−	0.586908i	0.917930	+	0.396741i	$0.129859\pi$
$522$	20.4218	−	8.49471i	0.893840	−	0.371803i
$523$	−19.8601	+	2.94597i	−0.868421	+	0.128818i	−0.566049	−	0.824372i	$-0.691529\pi$
$523$	−19.8601	+	2.94597i	−0.868421	+	0.128818i	−0.302373	+	0.953190i	$0.597779\pi$
$524$	27.6525	−	9.98736i	1.20800	−	0.436300i
$525$	−0.477508	+	1.33455i	−0.0208402	+	0.0582444i
$526$	−16.5880	−	7.81529i	−0.723272	−	0.340763i
$527$	4.97296	+	0.989182i	0.216625	+	0.0430895i
$528$	1.81512	−	1.22855i	0.0789929	−	0.0534657i
$529$	−4.77076	+	0.948963i	−0.207424	+	0.0412593i
$530$	2.53623	−	10.1896i	0.110167	−	0.442610i
$531$	16.1131	+	14.6041i	0.699250	+	0.633763i
$532$	−1.82264	−	0.646026i	−0.0790216	−	0.0280088i
$533$	20.8587	+	34.8006i	0.903489	+	1.50738i
$534$	−0.0579762	+	0.0870483i	−0.00250888	+	0.00376695i
$535$	28.4598	−	2.80304i	1.23042	−	0.121186i
$536$	−3.20381	−	7.63784i	−0.138384	−	0.329904i
$537$	8.81778	+	10.7445i	0.380515	+	0.463659i
$538$	−12.4564	−	23.2208i	−0.537032	−	1.00112i
$539$	2.30630	−	2.09031i	0.0993394	−	0.0900360i
$540$	8.34231	+	19.9714i	0.358996	+	0.859432i
$541$	−6.08822	−	8.20901i	−0.261753	−	0.352933i	0.652706	−	0.757611i	$-0.273634\pi$
$541$	−6.08822	−	8.20901i	−0.261753	−	0.352933i	−0.914459	+	0.404678i	$0.867384\pi$
$542$	−17.0115	+	12.6560i	−0.730706	+	0.543620i
$543$	3.97049	+	1.64463i	0.170390	+	0.0705779i
$544$	−0.982289	+	2.81123i	−0.0421153	+	0.120531i
$545$	−43.7779	+	18.1334i	−1.87524	+	0.776750i
$546$	4.07580	−	6.82312i	0.174428	−	0.292003i
$547$	−5.60828	+	37.8080i	−0.239793	+	1.61655i	0.450332	+	0.892861i	$0.351306\pi$
$547$	−5.60828	+	37.8080i	−0.239793	+	1.61655i	−0.690124	+	0.723691i	$0.742444\pi$
$548$	−24.7152	+	16.6211i	−1.05578	+	0.710016i
$549$	0.434487	−	8.84418i	0.0185434	−	0.377461i
$550$	1.06130	−	0.106128i	0.0452541	−	0.00452530i
$551$	0.416598	−	4.22980i	0.0177477	−	0.180195i
$552$	9.47160	+	2.82696i	0.403138	+	0.120323i
$553$	−14.5704	+	17.7540i	−0.619594	+	0.754978i
$554$	41.9452	+	8.27841i	1.78208	+	0.351716i
$555$	2.82253	−	11.2682i	0.119810	−	0.478307i
$556$	19.9928	−	5.07137i	0.847885	−	0.215074i
$557$	14.6421	−	0.719318i	0.620404	−	0.0304785i	0.263561	−	0.964643i	$-0.415103\pi$
$557$	14.6421	−	0.719318i	0.620404	−	0.0304785i	0.356843	+	0.934164i	$0.383853\pi$
$558$	−18.8405	+	25.4828i	−0.797580	+	1.07877i
$559$	−11.0083	−	7.35551i	−0.465602	−	0.311105i
$560$	−0.833306	−	15.1211i	−0.0352136	−	0.638981i
$561$	−0.239841	+	0.160257i	−0.0101261	+	0.00676604i
$562$	5.81804	+	0.277124i	0.245419	+	0.0116898i
$563$	−28.9654	+	13.6996i	−1.22075	+	0.577370i	−0.925753	−	0.378129i	$-0.876567\pi$
$563$	−28.9654	+	13.6996i	−1.22075	+	0.577370i	−0.294993	+	0.955499i	$0.595317\pi$
$564$	−3.89168	+	15.7355i	−0.163869	+	0.662582i
$565$	19.8190	−	26.7228i	0.833790	−	1.12424i
$566$	−0.00920388	−	6.17099i	−0.000386868	−	0.259386i
$567$	−4.96487	−	1.50608i	−0.208505	−	0.0632493i
$568$	−6.46324	+	3.09235i	−0.271192	+	0.129752i
$569$	−25.5580	−	13.6611i	−1.07145	−	0.572701i	−0.161267	−	0.986911i	$-0.551558\pi$
$569$	−25.5580	−	13.6611i	−1.07145	−	0.572701i	−0.910182	+	0.414210i	$0.864058\pi$
$570$	1.80816	+	0.175365i	0.0757354	+	0.00734525i
$571$	7.37196	+	20.6032i	0.308507	+	0.862219i	0.991302	+	0.131609i	$0.0420142\pi$
$571$	7.37196	+	20.6032i	0.308507	+	0.862219i	−0.682795	+	0.730610i	$0.739236\pi$
$572$	−5.95362	−	0.568454i	−0.248933	−	0.0237683i
$573$	−7.92176	+	13.2167i	−0.330936	+	0.552134i
$574$	17.6992	−	8.40344i	0.738752	−	0.350753i
$575$	3.40124	+	3.40124i	0.141842	+	0.141842i
$576$	−13.2784	−	13.0429i	−0.553267	−	0.543453i
$577$	−0.293456	+	0.293456i	−0.0122167	+	0.0122167i	−0.713189	−	0.700972i	$-0.752750\pi$
$577$	−0.293456	+	0.293456i	−0.0122167	+	0.0122167i	0.700972	+	0.713189i	$0.252750\pi$
$578$	−7.93413	+	22.2791i	−0.330016	+	0.926689i
$579$	−15.0774	−	9.03705i	−0.626596	−	0.375567i
$580$	31.8234	−	9.75727i	1.32139	−	0.405149i
$581$	7.61176	−	2.72353i	0.315789	−	0.112991i
$582$	5.95481	+	7.23392i	0.246835	+	0.299856i
$583$	−0.943998	+	1.76610i	−0.0390964	+	0.0731442i
$584$	−1.69922	+	1.27205i	−0.0703142	+	0.0526378i
$585$	7.48820	−	24.6853i	0.309599	−	1.02061i
$586$	−7.23701	−	7.21546i	−0.298958	−	0.298068i
$587$	−1.46175	−	1.08411i	−0.0603329	−	0.0447459i	0.565113	−	0.825014i	$-0.308833\pi$
$587$	−1.46175	−	1.08411i	−0.0603329	−	0.0447459i	−0.625445	+	0.780268i	$0.715083\pi$
$588$	6.15860	+	4.53912i	0.253977	+	0.187190i
$589$	2.60374	+	5.50515i	0.107285	+	0.226836i
$590$	22.0138	+	24.2159i	0.906296	+	0.996951i
$591$	3.87645	+	5.80152i	0.159456	+	0.238643i
$592$	3.49070	+	22.6025i	0.143467	+	0.928956i
$593$	1.11596	−	1.67015i	0.0458270	−	0.0685850i	−0.807849	−	0.589390i	$-0.799368\pi$
$593$	1.11596	−	1.67015i	0.0458270	−	0.0685850i	0.853676	+	0.520805i	$0.174368\pi$
$594$	−0.611744	−	4.08209i	−0.0251002	−	0.167490i
$595$	0.0977940	+	1.99064i	0.00400916	+	0.0816084i
$596$	3.92233	+	5.25581i	0.160665	+	0.215286i
$597$	−14.0418	−	3.51728i	−0.574692	−	0.143953i
$598$	−15.0180	−	22.4036i	−0.614131	−	0.916151i
$599$	17.6497	+	14.4847i	0.721147	+	0.591830i	0.921723	−	0.387848i	$-0.126781\pi$
$599$	17.6497	+	14.4847i	0.721147	+	0.591830i	−0.200576	+	0.979678i	$0.564281\pi$
$600$	0.772234	+	2.50530i	0.0315263	+	0.102279i
$601$	38.7475	+	3.81629i	1.58054	+	0.155670i	0.849846	−	0.527032i	$-0.176695\pi$
$601$	38.7475	+	3.81629i	1.58054	+	0.155670i	0.730697	+	0.682701i	$0.239195\pi$
$602$	−4.04859	+	4.94825i	−0.165008	+	0.201676i
$603$	−6.80481	−	0.334299i	−0.277113	−	0.0136137i
$604$	−15.8505	+	3.20204i	−0.644946	+	0.130289i
$605$	25.8469	+	3.83403i	1.05083	+	0.155875i
$606$	1.01861	−	0.256764i	0.0413783	−	0.0104303i
$607$	3.31752	+	8.00920i	0.134654	+	0.325083i	0.976796	−	0.214173i	$-0.0687055\pi$
$607$	3.31752	+	8.00920i	0.134654	+	0.325083i	−0.842142	+	0.539256i	$0.818706\pi$
$608$	−3.41480	+	1.06374i	−0.138489	+	0.0431404i
$609$	3.22822	−	7.79361i	0.130814	−	0.315813i
$610$	1.93562	−	13.1843i	0.0783710	−	0.533818i
$611$	35.5263	−	26.3481i	1.43724	−	1.06593i
$612$	1.73725	+	1.72692i	0.0702241	+	0.0698064i
$613$	−14.0660	−	15.5194i	−0.568119	−	0.626822i	0.387344	−	0.921935i	$-0.373393\pi$
$613$	−14.0660	−	15.5194i	−0.568119	−	0.626822i	−0.955462	+	0.295113i	$0.904643\pi$
$614$	1.40562	−	4.65870i	0.0567260	−	0.188010i
$615$	−14.2283	+	11.6769i	−0.573740	+	0.470857i
$616$	−0.550762	+	2.83511i	−0.0221908	+	0.114230i
$617$	1.40953	+	14.3112i	0.0567454	+	0.576146i	0.980952	+	0.194252i	$0.0622280\pi$
$617$	1.40953	+	14.3112i	0.0567454	+	0.576146i	−0.924206	+	0.381894i	$0.875272\pi$
$618$	−1.50831	−	7.52410i	−0.0606730	−	0.302664i
$619$	−32.0338	+	19.2003i	−1.28755	+	0.771727i	−0.983496	−	0.180929i	$-0.942090\pi$
$619$	−32.0338	+	19.2003i	−1.28755	+	0.771727i	−0.304052	+	0.952655i	$0.598340\pi$
$620$	−31.9225	+	35.4329i	−1.28204	+	1.42302i
$621$	12.5009	−	13.7926i	0.501645	−	0.553479i
$622$	−35.9342	+	21.6110i	−1.44083	+	0.866524i
$623$	−0.0268862	−	0.135166i	−0.00107717	−	0.00541532i
$624$	−1.52812	−	14.6205i	−0.0611737	−	0.585289i
$625$	5.73014	−	28.8073i	0.229205	−	1.15229i
$626$	17.8830	−	6.42876i	0.714750	−	0.256945i
$627$	−0.326199	−	0.116716i	−0.0130271	−	0.00466119i
$628$	−32.2464	−	35.3658i	−1.28677	−	1.41125i
$629$	−0.441642	−	2.97731i	−0.0176094	−	0.118713i
$630$	−11.5159	−	4.74993i	−0.458805	−	0.189242i
$631$	−3.66805	−	6.86244i	−0.146023	−	0.273189i	0.798268	−	0.602303i	$-0.205750\pi$
$631$	−3.66805	−	6.86244i	−0.146023	−	0.273189i	−0.944290	+	0.329114i	$0.893250\pi$
$632$	−1.89455	+	42.4381i	−0.0753610	+	1.68810i
$633$	1.01248	−	0.307131i	0.0402423	−	0.0122074i
$634$	13.7077	+	44.9468i	0.544402	+	1.78506i
$635$	7.69037	−	16.2599i	0.305183	−	0.645255i
$636$	−4.71444	−	1.41477i	−0.186940	−	0.0560992i
$637$	−5.07246	−	20.2504i	−0.200978	−	0.802350i
$638$	−6.33977	+	0.320932i	−0.250994	+	0.0127058i
$639$			5.89367i			0.233150i
$640$	−17.9946	−	21.4655i	−0.711299	−	0.848500i
$641$		−	35.5495i		−	1.40412i	−0.712117	−	0.702061i	$-0.752264\pi$
$641$		−	35.5495i		−	1.40412i	0.712117	−	0.702061i	$-0.247736\pi$
$642$	−0.677727	−	13.3880i	−0.0267478	−	0.528382i
$643$	−9.47568	−	37.8290i	−0.373684	−	1.49183i	−0.806980	−	0.590579i	$-0.798899\pi$
$643$	−9.47568	−	37.8290i	−0.373684	−	1.49183i	0.433295	−	0.901252i	$-0.357351\pi$
$644$	−11.4684	+	6.17402i	−0.451917	+	0.243290i
$645$	2.56801	−	5.42961i	0.101115	−	0.213791i
$646$	0.450236	−	0.137311i	0.0177143	−	0.00540244i
$647$	19.9538	−	6.05291i	0.784464	−	0.237964i	0.127452	−	0.991845i	$-0.459320\pi$
$647$	19.9538	−	6.05291i	0.784464	−	0.237964i	0.657012	+	0.753880i	$0.271820\pi$
$648$	−9.02069	+	3.27326i	−0.354366	+	0.128586i
$649$	−2.94210	−	5.50428i	−0.115488	−	0.216062i
$650$	2.72768	−	6.61308i	0.106988	−	0.259386i
$651$	1.77351	+	11.9560i	0.0695094	+	0.468594i
$652$	0.562856	−	12.1996i	0.0220431	−	0.477774i
$653$	4.17358	+	1.49333i	0.163325	+	0.0584385i	0.417283	−	0.908777i	$-0.362982\pi$
$653$	4.17358	+	1.49333i	0.163325	+	0.0584385i	−0.253958	+	0.967215i	$0.581732\pi$
$654$	7.51410	+	20.9022i	0.293825	+	0.817340i
$655$	7.10031	−	35.6956i	0.277432	−	1.39474i
$656$	16.8919	−	32.0612i	0.659518	−	1.25178i
$657$	0.340627	+	1.71245i	0.0132891	+	0.0668090i
$658$	−11.0081	−	18.3040i	−0.429141	−	0.713563i
$659$	31.1774	−	34.3990i	1.21450	−	1.33999i	0.290843	−	0.956771i	$-0.406064\pi$
$659$	31.1774	−	34.3990i	1.21450	−	1.33999i	0.923656	−	0.383223i	$-0.125186\pi$
$660$	−0.141214	−	2.70953i	−0.00549674	−	0.105468i
$661$	0.183825	−	0.110180i	0.00714995	−	0.00428552i	−0.510523	−	0.859864i	$-0.670548\pi$
$661$	0.183825	−	0.110180i	0.00714995	−	0.00428552i	0.517673	+	0.855578i	$0.326798\pi$
$662$	−12.0641	+	2.41842i	−0.468886	+	0.0939944i
$663$	0.189627	+	1.92532i	0.00736451	+	0.0747731i
$664$	8.25160	−	12.4698i	0.320224	−	0.483923i
$665$	−1.85041	+	1.51859i	−0.0717557	+	0.0588884i
$666$	18.0107	+	5.43415i	0.697899	+	0.210569i
$667$	−19.2250	−	21.2115i	−0.744395	−	0.821313i
$668$	0.0216808	+	7.26823i	0.000838856	+	0.281216i
$669$	−19.1428	+	14.1972i	−0.740101	+	0.548897i
$670$	−10.1442	−	1.48929i	−0.391904	−	0.0575362i
$671$	−0.972527	+	2.34789i	−0.0375440	+	0.0906392i
$672$	−7.09859	+	0.0529377i	−0.273834	+	0.00204212i
$673$	8.95585	+	21.6213i	0.345223	+	0.833442i	0.997170	+	0.0751773i	$0.0239523\pi$
$673$	8.95585	+	21.6213i	0.345223	+	0.833442i	−0.651947	+	0.758264i	$0.726048\pi$
$674$	2.27742	+	9.03477i	0.0877228	+	0.348006i
$675$	4.88369	+	0.724426i	0.187973	+	0.0278832i
$676$	−7.80512	+	11.7570i	−0.300197	+	0.452191i
$677$	−6.86586	−	0.337298i	−0.263876	−	0.0129634i	−0.0833004	−	0.996524i	$-0.526546\pi$
$677$	−6.86586	−	0.337298i	−0.263876	−	0.0129634i	−0.180576	+	0.983561i	$0.557796\pi$
$678$	−12.0702	−	9.87564i	−0.463552	−	0.379272i
$679$	−12.2868	−	1.21014i	−0.471523	−	0.0464409i
$680$	2.35131	+	2.83907i	0.0901684	+	0.108874i
$681$	−7.98694	−	6.55471i	−0.306060	−	0.251177i
$682$	7.55497	−	5.06438i	0.289295	−	0.193925i
$683$	46.9245	+	11.7540i	1.79552	+	0.449753i	0.989790	−	0.142534i	$-0.0455252\pi$
$683$	46.9245	+	11.7540i	1.79552	+	0.449753i	0.805726	+	0.592288i	$0.201775\pi$
$684$	−0.423006	+	2.91149i	−0.0161740	+	0.111323i
$685$	1.80911	+	36.8253i	0.0691225	+	1.40702i
$686$	−24.9411	+	3.73768i	−0.952255	+	0.142705i
$687$	5.72841	−	8.57317i	0.218552	−	0.327087i
$688$	−0.509767	+	11.8143i	−0.0194347	+	0.450417i
$689$	7.46182	+	11.1674i	0.284273	+	0.425444i
$690$	9.05394	−	8.23064i	0.344678	−	0.313335i
$691$	3.82486	+	8.08699i	0.145505	+	0.307644i	0.963558	−	0.267498i	$-0.0861969\pi$
$691$	3.82486	+	8.08699i	0.145505	+	0.307644i	−0.818054	+	0.575142i	$0.804947\pi$
$692$	9.54080	−	1.44434i	0.362687	−	0.0549057i
$693$	1.90816	+	1.41519i	0.0724852	+	0.0537587i
$694$	17.1371	−	17.1883i	0.650515	−	0.652459i
$695$	7.41176	−	24.4333i	0.281144	−	0.926808i
$696$	−3.85883	−	15.1180i	−0.146269	−	0.573046i
$697$	−2.24821	+	4.20611i	−0.0851571	+	0.159318i
$698$	−1.79569	+	1.47817i	−0.0679678	+	0.0559496i
$699$	−17.5838	+	6.29158i	−0.665079	+	0.237969i
$700$	−3.05142	−	1.61933i	−0.115333	−	0.0612051i
$701$	24.5169	+	14.6949i	0.925990	+	0.555017i	0.895766	−	0.444526i	$-0.146628\pi$
$701$	24.5169	+	14.6949i	0.925990	+	0.555017i	0.0302243	+	0.999543i	$0.490378\pi$
$702$	−26.0794	−	9.28752i	−0.984305	−	0.350535i
$703$	2.55624	−	2.55624i	0.0964103	−	0.0964103i
$704$	2.32705	+	4.80833i	0.0877040	+	0.181221i
$705$	14.1886	+	14.1886i	0.534373	+	0.534373i
$706$	−15.4982	−	32.6421i	−0.583281	−	1.22850i
$707$	−0.711620	+	1.18727i	−0.0267632	+	0.0446517i
$708$	11.8293	−	9.76728i	0.444574	−	0.367077i
$709$	−14.4167	−	40.2920i	−0.541430	−	1.51320i	−0.831129	−	0.556079i	$-0.812305\pi$
$709$	−14.4167	−	40.2920i	−0.541430	−	1.51320i	0.289699	−	0.957118i	$-0.406445\pi$
$710$	−0.856186	+	8.82797i	−0.0321321	+	0.331308i
$711$	30.8171	+	16.4721i	1.15573	+	0.617752i
$712$	−0.189633	−	0.170334i	−0.00710680	−	0.00638354i
$713$	39.2516	+	11.9068i	1.46998	+	0.445915i
$714$	0.934242	−	0.00139340i	0.0349631	−	5.21466e-5i
$715$	−4.41023	+	5.94651i	−0.164933	+	0.222387i
$716$	−29.0042	+	17.5023i	−1.08394	+	0.654090i
$717$	0.0969895	−	0.0458726i	0.00362214	−	0.00171314i
$718$	0.103241	−	2.16748i	0.00385292	−	0.0808895i
$719$	−27.7029	+	18.5105i	−1.03315	+	0.690326i	−0.951913	−	0.306369i	$-0.900886\pi$
$719$	−27.7029	+	18.5105i	−1.03315	+	0.690326i	−0.0812329	+	0.996695i	$0.525886\pi$
$720$	−22.3162	+	5.73162i	−0.831676	+	0.213605i
$721$	8.40755	+	5.61774i	0.313113	+	0.209216i
$722$	−21.1515	−	15.6382i	−0.787177	−	0.581992i
$723$	−24.4040	+	1.19889i	−0.907596	+	0.0445873i
$724$	−5.35796	+	8.99999i	−0.199127	+	0.334482i
$725$	1.84488	−	7.36519i	0.0685173	−	0.273536i
$726$	2.37162	−	12.0166i	0.0880190	−	0.445977i
$727$	9.54877	−	11.6352i	0.354144	−	0.431526i	−0.565216	−	0.824943i	$-0.691207\pi$
$727$	9.54877	−	11.6352i	0.354144	−	0.431526i	0.919360	+	0.393417i	$0.128707\pi$
$728$	15.0282	+	12.2212i	0.556983	+	0.452949i
$729$	0.281054	−	2.85359i	0.0104094	−	0.105688i
$730$	0.261445	+	2.61452i	0.00967652	+	0.0967675i
$731$	0.0763632	−	1.55441i	0.00282439	−	0.0574919i
$732$	−6.13002	−	1.20034i	−0.226572	−	0.0443658i
$733$	−0.376154	+	2.53582i	−0.0138936	+	0.0936628i	−0.995014	−	0.0997345i	$-0.968201\pi$
$733$	−0.376154	+	2.53582i	−0.0138936	+	0.0936628i	0.981121	+	0.193397i	$0.0619506\pi$
$734$	2.37343	+	1.41777i	0.0876049	+	0.0523309i
$735$	8.74972	−	3.62425i	0.322738	−	0.133683i
$736$	−10.1373	+	21.8536i	−0.373664	+	0.805535i
$737$	1.80649	+	0.748273i	0.0665430	+	0.0275630i
$738$	−17.7930	−	23.9164i	−0.654968	−	0.880375i
$739$	17.5080	+	23.6069i	0.644043	+	0.868392i	0.997756	−	0.0669623i	$-0.0213307\pi$
$739$	17.5080	+	23.6069i	0.644043	+	0.868392i	−0.353712	+	0.935354i	$0.615081\pi$
$740$	26.1882	+	10.7561i	0.962699	+	0.395403i
$741$	−1.72168	+	1.56044i	−0.0632476	+	0.0573243i
$742$	5.71545	−	3.06594i	0.209821	−	0.112554i
$743$	−7.56435	−	9.21718i	−0.277509	−	0.338146i	0.615540	−	0.788106i	$-0.288938\pi$
$743$	−7.56435	−	9.21718i	−0.277509	−	0.338146i	−0.893049	+	0.449960i	$0.851438\pi$
$744$	15.8785	+	15.7371i	0.582135	+	0.576948i
$745$	8.07908	−	0.795720i	0.295995	−	0.0291529i
$746$	9.97478	+	6.64344i	0.365203	+	0.243233i
$747$	−6.32333	−	10.5498i	−0.231358	−	0.385998i
$748$	−0.302473	−	0.634621i	−0.0110595	−	0.0232040i
$749$	13.0880	+	11.8623i	0.478225	+	0.433438i
$750$	−10.7915	−	2.68604i	−0.394051	−	0.0980803i
$751$	38.5430	−	7.66667i	1.40645	−	0.279761i	0.567235	−	0.823556i	$-0.308013\pi$
$751$	38.5430	−	7.66667i	1.40645	−	0.279761i	0.839218	+	0.543795i	$0.183013\pi$
$752$	−36.5881	−	14.9002i	−1.33423	−	0.543354i
$753$	−23.2819	−	4.63105i	−0.848438	−	0.168765i
$754$	−18.1456	+	38.5141i	−0.660823	+	1.40260i
$755$	−6.74370	+	18.8474i	−0.245428	+	0.685926i
$756$	−5.67977	+	12.1021i	−0.206571	+	0.440150i
$757$	−46.1043	+	6.83893i	−1.67569	+	0.248565i	−0.915843	−	0.401537i	$-0.868476\pi$
$757$	−46.1043	+	6.83893i	−1.67569	+	0.248565i	−0.759847	+	0.650102i	$0.774726\pi$
$758$	4.32683	+	10.4020i	0.157158	+	0.377817i
$759$	−2.05797	+	1.10001i	−0.0746995	+	0.0399277i
$760$	−1.05657	+	4.29959i	−0.0383257	+	0.155962i
$761$	−6.53191	−	21.5328i	−0.236782	−	0.780564i	−0.992127	−	0.125237i	$-0.960031\pi$
$761$	−6.53191	−	21.5328i	−0.236782	−	0.780564i	0.755345	−	0.655327i	$-0.227469\pi$
$762$	−7.44173	−	3.96343i	−0.269585	−	0.143580i
$763$	−26.4581	−	12.5138i	−0.957849	−	0.453029i
$764$	−29.1009	−	23.7376i	−1.05283	−	0.858796i
$765$	2.94140	−	0.736781i	0.106346	−	0.0266384i
$766$	25.7342	+	23.2543i	0.929815	+	0.840213i
$767$	−41.8594			−1.51145
$768$	−10.4519	+	7.94673i	−0.377152	+	0.286753i
$769$	−7.77115			−0.280235			−0.140117	−	0.990135i	$-0.544748\pi$
$769$	−7.77115			−0.280235			−0.140117	+	0.990135i	$0.544748\pi$
$770$	2.65260	+	2.39698i	0.0955930	+	0.0863811i
$771$	6.16803	−	1.54501i	0.222136	−	0.0556423i
$772$	27.0796	−	33.1980i	0.974615	−	1.19482i
$773$	9.73811	+	4.60578i	0.350255	+	0.165658i	0.594583	−	0.804034i	$-0.297317\pi$
$773$	9.73811	+	4.60578i	0.350255	+	0.165658i	−0.244328	+	0.969693i	$0.578567\pi$
$774$	8.58543	+	4.57256i	0.308597	+	0.164357i
$775$	3.15801	+	10.4106i	0.113439	+	0.373958i
$776$	−19.5339	+	11.8273i	−0.701227	+	0.424576i
$777$	6.32781	−	3.38228i	0.227009	−	0.121339i
$778$	−2.39849	−	5.76614i	−0.0859902	−	0.206726i
$779$	−5.66617	+	0.840498i	−0.203012	+	0.0301139i
$780$	−16.4732	−	7.73120i	−0.589836	−	0.276821i
$781$	0.569842	−	1.59260i	0.0203906	−	0.0569878i
$782$	1.35126	−	2.86806i	0.0483210	−	0.102562i
$783$	−28.8189	−	5.73244i	−1.02990	−	0.204861i
$784$	−13.1058	+	13.2631i	−0.468065	+	0.473684i
$785$	−58.1069	+	11.5582i	−2.07392	+	0.412529i
$786$	−16.5551	−	4.12061i	−0.590501	−	0.146977i
$787$	−24.0344	−	21.7835i	−0.856733	−	0.776498i	0.119588	−	0.992824i	$-0.461843\pi$
$787$	−24.0344	−	21.7835i	−0.856733	−	0.776498i	−0.976321	+	0.216326i	$0.930593\pi$
$788$	−15.3509	+	7.31653i	−0.546852	+	0.260641i
$789$	5.47017	+	9.12643i	0.194743	+	0.324910i
$790$	43.7672	+	29.1500i	1.55717	+	1.03711i
$791$	20.4510	−	2.01424i	0.727152	−	0.0716183i
$792$	4.39400	−	0.0196607i	0.156134	−	0.000698614i
$793$	10.8129	+	13.1756i	0.383977	+	0.467878i
$794$	−28.5997	+	15.3417i	−1.01497	+	0.544458i
$795$	−4.51468	+	4.09186i	−0.160119	+	0.145123i
$796$	13.4037	−	32.6344i	0.475081	−	1.15670i
$797$	−10.4129	−	14.0401i	−0.368842	−	0.497327i	0.579325	−	0.815096i	$-0.303316\pi$
$797$	−10.4129	−	14.0401i	−0.368842	−	0.497327i	−0.948168	+	0.317770i	$0.897066\pi$
$798$	0.669768	+	0.900268i	0.0237095	+	0.0318692i
$799$	4.80344	+	1.98965i	0.169933	+	0.0703887i
$800$	−6.31306	+	0.984624i	−0.223201	+	0.0348117i
$801$	−0.193714	+	0.0802389i	−0.00684455	+	0.00283510i
$802$	−3.12147	−	1.86461i	−0.110223	−	0.0658418i
$803$	0.0735267	−	0.495677i	0.00259470	−	0.0174920i
$804$	−0.923554	+	4.71651i	−0.0325713	+	0.166338i
$805$	−0.791123	+	16.1037i	−0.0278834	+	0.567580i
$806$	−6.06974	−	60.6989i	−0.213798	−	2.13803i
$807$	−1.49873	+	15.2168i	−0.0527577	+	0.535658i
$808$	0.262342	+	2.54673i	0.00922915	+	0.0895936i
$809$	−17.5434	+	21.3767i	−0.616793	+	0.751565i	−0.983921	−	0.178606i	$-0.942841\pi$
$809$	−17.5434	+	21.3767i	−0.616793	+	0.751565i	0.367128	+	0.930171i	$0.380341\pi$
$810$	−2.30011	+	11.6542i	−0.0808176	+	0.409488i
$811$	−11.5167	+	45.9773i	−0.404407	+	1.61448i	0.335683	+	0.941975i	$0.391033\pi$
$811$	−11.5167	+	45.9773i	−0.404407	+	1.61448i	−0.740090	+	0.672508i	$0.765217\pi$
$812$	17.6659	+	10.5170i	0.619952	+	0.369076i
$813$	12.2885	−	0.603694i	0.430976	−	0.0211725i
$814$	−4.34147	−	3.20983i	−0.152169	−	0.112504i
$815$	−12.5701	−	8.39904i	−0.440310	−	0.294206i
$816$	1.38175	−	1.03761i	0.0483711	−	0.0363237i
$817$	1.55418	−	1.03847i	0.0543737	−	0.0363314i
$818$	−1.60766	+	33.7519i	−0.0562107	+	1.18011i
$819$	14.4037	−	6.81242i	0.503304	−	0.238045i
$820$	−23.1772	−	38.4085i	−0.809383	−	1.34128i
$821$	20.9170	−	28.2033i	0.730008	−	0.984302i	−0.269763	−	0.962927i	$-0.586945\pi$
$821$	20.9170	−	28.2033i	0.730008	−	0.984302i	0.999772	−	0.0213755i	$-0.00680456\pi$
$822$	17.2827	−	0.0257767i	0.602804	−	0.000899067i
$823$	−19.5204	−	5.92146i	−0.680440	−	0.206409i	−0.0689008	−	0.997624i	$-0.521949\pi$
$823$	−19.5204	−	5.92146i	−0.680440	−	0.206409i	−0.611539	+	0.791214i	$0.709449\pi$
$824$	18.6757	−	1.00126i	0.650598	−	0.0348806i
$825$	−0.545827	−	0.291750i	−0.0190032	−	0.0101574i
$826$	−1.95132	+	20.1197i	−0.0678952	+	0.700053i
$827$	7.35962	+	20.5688i	0.255919	+	0.715246i	0.998942	+	0.0459804i	$0.0146412\pi$
$827$	7.35962	+	20.5688i	0.255919	+	0.715246i	−0.743023	+	0.669266i	$0.766609\pi$
$828$	12.6168	+	15.2805i	0.438465	+	0.531033i
$829$	−0.593919	+	0.990894i	−0.0206277	+	0.0344152i	−0.867870	−	0.496792i	$-0.834511\pi$
$829$	−0.593919	+	0.990894i	−0.0206277	+	0.0344152i	0.847242	+	0.531207i	$0.178261\pi$
$830$	−7.93894	−	16.7209i	−0.275565	−	0.580391i
$831$	−17.5425	−	17.5425i	−0.608542	−	0.608542i
$832$	35.7982	+	1.43766i	1.24108	+	0.0498419i
$833$	1.73519	−	1.73519i	0.0601208	−	0.0601208i
$834$	−11.2749	−	4.01526i	−0.390418	−	0.139037i
$835$	7.71726	+	4.62555i	0.267067	+	0.160074i
$836$	0.395809	−	0.745850i	0.0136893	−	0.0257958i
$837$	39.6401	−	14.1835i	1.37016	−	0.490252i
$838$	17.8891	−	14.7259i	0.617970	−	0.508699i
$839$	14.9821	−	28.0295i	0.517238	−	0.967684i	−0.478729	−	0.877963i	$-0.658902\pi$
$839$	14.9821	−	28.0295i	0.517238	−	0.967684i	0.995967	−	0.0897216i	$-0.0285977\pi$
$840$	−4.48392	+	7.55745i	−0.154710	+	0.260757i
$841$	−4.69929	+	15.4915i	−0.162044	+	0.534189i
$842$	−38.0886	+	38.2024i	−1.31262	+	1.31654i
$843$	−2.71470	−	2.01336i	−0.0934992	−	0.0693438i
$844$	0.385971	+	2.54958i	0.0132857	+	0.0877602i
$845$	7.46896	+	15.7918i	0.256940	+	0.543254i
$846$	−24.0457	+	21.8591i	−0.826707	+	0.751532i
$847$	8.96665	+	13.4195i	0.308098	+	0.461101i
$848$	5.06425	−	10.8749i	0.173907	−	0.373444i
$849$	−1.98939	+	2.97733i	−0.0682757	+	0.102182i
$850$	0.831596	−	0.124624i	0.0285235	−	0.00427455i
$851$	−1.19475	−	24.3197i	−0.0409556	−	0.833670i
$852$	4.11435	+	0.597768i	0.140955	+	0.0204792i
$853$	19.0437	+	4.77019i	0.652042	+	0.163328i	0.554867	−	0.831939i	$-0.312769\pi$
$853$	19.0437	+	4.77019i	0.652042	+	0.163328i	0.0971754	+	0.995267i	$0.469019\pi$
$854$	6.83688	−	4.58302i	0.233953	−	0.156828i
$855$	2.81526	+	2.31042i	0.0962799	+	0.0790148i
$856$	32.5275	+	3.05679i	1.11177	+	0.104479i
$857$	25.8406	+	2.54508i	0.882698	+	0.0869382i	0.529200	−	0.848497i	$-0.322492\pi$
$857$	25.8406	+	2.54508i	0.882698	+	0.0869382i	0.353498	+	0.935435i	$0.384992\pi$
$858$	2.68592	+	2.19758i	0.0916959	+	0.0750243i
$859$	42.6230	+	2.09393i	1.45428	+	0.0714441i	0.760778	−	0.649012i	$-0.224818\pi$
$859$	42.6230	+	2.09393i	1.45428	+	0.0714441i	0.693500	+	0.720456i	$0.256068\pi$
$860$	12.1956	+	8.09634i	0.415867	+	0.276083i
$861$	−11.2460	−	1.66818i	−0.383262	−	0.0568516i
$862$	8.64502	+	34.2958i	0.294451	+	1.16812i
$863$	−13.6132	−	32.8651i	−0.463397	−	1.11874i	−0.966993	−	0.254801i	$-0.917990\pi$
$863$	−13.6132	−	32.8651i	−0.463397	−	1.11874i	0.503596	−	0.863939i	$-0.332010\pi$
$864$	5.00464	+	24.2149i	0.170261	+	0.823806i
$865$	4.57117	−	11.0358i	0.155424	−	0.375227i
$866$	−13.9410	−	2.04671i	−0.473734	−	0.0695499i
$867$	11.0225	−	8.17483i	0.374343	−	0.277632i
$868$	−29.4578	+	0.0878715i	−0.999865	+	0.00298255i
$869$	−6.73484	−	7.43076i	−0.228464	−	0.252071i
$870$	−18.4911	−	5.57911i	−0.626907	−	0.189150i
$871$	10.1374	−	8.31956i	0.343493	−	0.281898i
$872$	−53.0464	+	10.7985i	−1.79638	+	0.365685i
$873$	1.84114	+	18.6934i	0.0623131	+	0.632676i
$874$	3.73361	−	0.748452i	0.126291	−	0.0253168i
$875$	12.5689	−	7.53353i	0.424907	−	0.254680i
$876$	1.23000	−	0.0641046i	0.0415579	−	0.00216589i
$877$	18.4319	−	20.3365i	0.622401	−	0.686714i	−0.345392	−	0.938458i	$-0.612254\pi$
$877$	18.4319	−	20.3365i	0.622401	−	0.686714i	0.967794	+	0.251744i	$0.0810042\pi$
$878$	−16.3976	−	27.2654i	−0.553391	−	0.920162i
$879$	1.15688	+	5.81604i	0.0390207	+	0.196170i
$880$	6.58451	+	0.608877i	0.221964	+	0.0205252i
$881$	10.1227	−	50.8903i	0.341043	−	1.71454i	−0.305955	−	0.952046i	$-0.598976\pi$
$881$	10.1227	−	50.8903i	0.341043	−	1.71454i	0.646998	−	0.762492i	$-0.276024\pi$
$882$	5.18865	+	14.4334i	0.174711	+	0.485998i
$883$	−25.8901	−	9.26364i	−0.871272	−	0.311746i	−0.136975	−	0.990574i	$-0.543738\pi$
$883$	−25.8901	−	9.26364i	−0.871272	−	0.311746i	−0.734297	+	0.678828i	$0.762488\pi$
$884$	−4.71005	−	0.217308i	−0.158416	−	0.00730887i
$885$	−2.78640	−	18.7844i	−0.0936639	−	0.631431i
$886$	19.9077	−	48.2650i	0.668813	−	1.62149i
$887$	10.6630	+	19.9490i	0.358028	+	0.669822i	0.994869	−	0.101172i	$-0.0322594\pi$
$887$	10.6630	+	19.9490i	0.358028	+	0.669822i	−0.636841	+	0.770995i	$0.719759\pi$
$888$	5.62030	−	12.0220i	0.188605	−	0.403432i
$889$	10.6315	−	3.22504i	0.356570	−	0.108164i
$890$	−0.301815	+	0.0920465i	−0.0101169	+	0.00308541i
$891$	0.968605	−	2.04794i	0.0324495	−	0.0686087i
$892$	−27.5339	−	51.1447i	−0.921903	−	1.71245i
$893$	1.51731	+	6.05742i	0.0507747	+	0.202704i
$894$	−0.192391	−	3.80054i	−0.00643452	−	0.127109i
$895$			41.9346i			1.40172i
$896$	2.35979	−	17.1394i	0.0788350	−	0.572587i
$897$			15.6506i			0.522558i
$898$	−18.4942	+	0.936215i	−0.617160	+	0.0312419i
$899$	−15.7322	−	62.8065i	−0.524699	−	2.09471i
$900$	−1.51065	+	5.03395i	−0.0503550	+	0.167798i
$901$	−0.675013	+	1.42720i	−0.0224879	+	0.0475468i
$902$	2.49565	+	8.18310i	0.0830960	+	0.272467i
$903$	3.55015	−	1.07693i	0.118141	−	0.0358378i
$904$	28.0483	−	25.6511i	0.932874	−	0.853141i
$905$	6.11206	+	11.4349i	0.203172	+	0.380107i
$906$	8.67434	+	3.57788i	0.288186	+	0.118867i
$907$	−2.30685	−	15.5515i	−0.0765978	−	0.516380i	−0.993185	−	0.116546i	$-0.962818\pi$
$907$	−2.30685	−	15.5515i	−0.0765978	−	0.516380i	0.916588	−	0.399834i	$-0.130932\pi$
$908$	18.6079	−	16.9666i	0.617523	−	0.563055i
$909$	1.98285	+	0.709475i	0.0657670	+	0.0235318i
$910$	22.5645	−	8.11169i	0.748006	−	0.268900i
$911$	2.60321	−	13.0872i	0.0862481	−	0.433599i	−0.913400	−	0.407064i	$-0.866553\pi$
$911$	2.60321	−	13.0872i	0.0862481	−	0.433599i	0.999648	−	0.0265349i	$-0.00844732\pi$
$912$	1.98959	+	0.590598i	0.0658820	+	0.0195567i
$913$	0.688672	+	3.46219i	0.0227917	+	0.114582i
$914$	−7.07613	+	4.25563i	−0.234058	+	0.140764i
$915$	−5.19277	+	5.72934i	−0.171668	+	0.189406i
$916$	18.6700	+	16.8203i	0.616875	+	0.555760i
$917$	19.2818	−	11.5571i	0.636741	−	0.381648i
$918$	−0.639617	−	3.19070i	−0.0211105	−	0.105309i
$919$	5.28276	+	53.6368i	0.174262	+	1.76931i	0.542954	+	0.839763i	$0.317306\pi$
$919$	5.28276	+	53.6368i	0.174262	+	1.76931i	−0.368692	+	0.929552i	$0.620194\pi$
$920$	16.6786	+	24.7211i	0.549876	+	0.815029i
$921$	−2.18270	+	1.79130i	−0.0719225	+	0.0590253i
$922$	−12.1354	+	40.2210i	−0.399659	+	1.32461i
$923$	−7.61855	−	8.40577i	−0.250768	−	0.276679i
$924$	1.18148	−	1.18855i	0.0388677	−	0.0391003i
$925$	5.18712	−	3.84703i	0.170551	−	0.126490i
$926$	−2.44319	+	16.6416i	−0.0802882	+	0.546878i
$927$	5.88727	−	14.2131i	0.193363	−	0.466820i
$928$	37.8148	−	4.00938i	1.24133	−	0.131614i
$929$	−6.77096	−	16.3465i	−0.222148	−	0.536313i	0.773033	−	0.634365i	$-0.218739\pi$
$929$	−6.77096	−	16.3465i	−0.222148	−	0.536313i	−0.995181	+	0.0980529i	$0.968739\pi$
$930$	26.8346	−	6.76427i	0.879942	−	0.221809i
$931$	2.91542	+	0.432462i	0.0955491	+	0.0141734i
$932$	−9.01279	−	44.6144i	−0.295224	−	1.46139i
$933$	24.3024	+	1.19390i	0.795625	+	0.0390865i
$934$	−5.17213	+	6.32146i	−0.169237	+	0.206844i
$935$	−0.866069	−	0.0853003i	−0.0283235	−	0.00278962i
$936$	13.7758	−	26.0525i	0.450277	−	0.851552i
$937$	27.8304	+	22.8398i	0.909180	+	0.746145i	0.967690	−	0.252142i	$-0.0811350\pi$
$937$	27.8304	+	22.8398i	0.909180	+	0.746145i	−0.0585103	+	0.998287i	$0.518635\pi$
$938$	−3.52623	−	5.26037i	−0.115135	−	0.171757i
$939$	−10.6966	−	2.67935i	−0.349069	−	0.0874373i
$940$	−39.1929	+	29.2490i	−1.27833	+	0.953998i
$941$	0.280072	+	5.70101i	0.00913010	+	0.185847i	0.999028	+	0.0440689i	$0.0140321\pi$
$941$	0.280072	+	5.70101i	0.00913010	+	0.185847i	−0.989898	+	0.141779i	$0.954718\pi$
$942$	4.11587	+	27.4647i	0.134102	+	0.894847i
$943$	−21.4349	+	32.0796i	−0.698017	+	1.04466i
$944$	19.4122	+	31.9534i	0.631813	+	1.03999i
$945$	9.19410	+	13.7599i	0.299084	+	0.447611i
$946$	−1.87787	−	2.06571i	−0.0610548	−	0.0671620i
$947$	−15.9692	−	33.7640i	−0.518929	−	1.09718i	−0.977966	−	0.208765i	$-0.933056\pi$
$947$	−15.9692	−	33.7640i	−0.518929	−	1.09718i	0.459037	−	0.888417i	$-0.348194\pi$
$948$	14.6248	−	19.8426i	0.474990	−	0.644459i
$949$	−2.69944	−	2.00204i	−0.0876276	−	0.0649890i
$950$	0.715208	+	0.713078i	0.0232044	+	0.0231353i
$951$	7.91517	−	26.0928i	0.256667	−	0.846118i
$952$	−0.324014	+	2.25376i	−0.0105013	+	0.0730447i
$953$	0.831413	−	1.55546i	0.0269321	−	0.0503865i	−0.868095	−	0.496398i	$-0.834656\pi$
$953$	0.831413	−	1.55546i	0.0269321	−	0.0503865i	0.895027	+	0.446011i	$0.147156\pi$
$954$	−6.27141	−	7.61853i	−0.203044	−	0.246659i
$955$	−43.7708	+	15.6614i	−1.41639	+	0.506792i
$956$	0.0766519	+	0.250000i	0.00247910	+	0.00808559i
$957$	3.15940	+	1.89367i	0.102129	+	0.0612137i
$958$	−15.2265	+	42.7562i	−0.491947	+	1.38139i
$959$	−16.1031	+	16.1031i	−0.519997	+	0.519997i
$960$	1.73779	+	16.1602i	0.0560869	+	0.521568i
$961$	43.6782	+	43.6782i	1.40898	+	1.40898i
$962$	−32.7120	+	15.5314i	−1.05468	+	0.500752i
$963$	13.8161	−	23.0507i	0.445217	−	0.742800i
$964$	5.66002	−	59.2794i	0.182297	−	1.90926i
$965$	−17.8664	−	49.9332i	−0.575139	−	1.60741i
$966$	7.52245	+	0.729569i	0.242031	+	0.0234735i
$967$	23.5082	+	12.5654i	0.755972	+	0.404076i	0.803892	−	0.594775i	$-0.202759\pi$
$967$	23.5082	+	12.5654i	0.755972	+	0.404076i	−0.0479194	+	0.998851i	$0.515259\pi$
$968$	28.1513	+	9.93084i	0.904818	+	0.319189i
$969$	−0.261374	−	0.0792870i	−0.00839655	−	0.00254707i
$970$	0.0421607	+	28.2678i	0.00135370	+	0.907625i
$971$	−20.0179	+	26.9910i	−0.642405	+	0.866183i	−0.997645	−	0.0685919i	$-0.978149\pi$
$971$	−20.0179	+	26.9910i	−0.642405	+	0.866183i	0.355239	+	0.934775i	$0.384399\pi$
$972$	30.8649	+	7.63349i	0.989993	+	0.244844i
$973$	14.2566	−	6.74288i	0.457046	−	0.216167i
$974$	16.0428	+	0.764151i	0.514046	+	0.0244850i
$975$	−3.45138	+	2.30614i	−0.110533	+	0.0738556i
$976$	5.04312	−	14.3642i	0.161426	−	0.459786i
$977$	−23.7465	−	15.8669i	−0.759718	−	0.507627i	0.114344	−	0.993441i	$-0.463523\pi$
$977$	−23.7465	−	15.8669i	−0.759718	−	0.507627i	−0.874062	+	0.485814i	$0.838523\pi$
$978$	−4.21295	+	5.69825i	−0.134715	+	0.182210i
$979$	0.0601039	−	0.00295272i	0.00192093	−	9.43692e-5i
$980$	5.67517	+	22.3732i	0.181287	+	0.714685i
$981$	−10.8198	+	43.1949i	−0.345449	+	1.37911i
$982$	11.3195	+	2.23405i	0.361221	+	0.0712915i
$983$	−21.3543	+	26.0203i	−0.681096	+	0.829917i	−0.992740	−	0.120282i	$-0.961620\pi$
$983$	−21.3543	+	26.0203i	−0.681096	+	0.829917i	0.311644	+	0.950199i	$0.399120\pi$
$984$	−18.5006	+	9.99546i	−0.589778	+	0.318644i
$985$	−2.06333	+	20.9494i	−0.0657432	+	0.667502i
$986$	−4.97972	+	0.497960i	−0.158586	+	0.0158583i
$987$	−0.608142	+	12.3790i	−0.0193574	+	0.394029i
$988$	−3.16027	−	4.69928i	−0.100542	−	0.149504i
$989$	1.84731	−	12.4536i	0.0587412	−	0.396001i
$990$	2.78942	−	4.66965i	0.0886537	−	0.148411i
$991$	3.23047	−	1.33811i	0.102619	−	0.0425063i	−0.330783	−	0.943707i	$-0.607313\pi$
$991$	3.23047	−	1.33811i	0.102619	−	0.0425063i	0.433402	+	0.901200i	$0.357313\pi$
$992$	−43.5198	+	32.7823i	−1.38175	+	1.04084i
$993$	6.59618	+	2.73223i	0.209323	+	0.0867046i
$994$	−4.39538	+	3.27001i	−0.139413	+	0.103718i
$995$	−26.0157	−	35.0781i	−0.824753	−	1.11205i
$996$	−8.00614	+	3.34427i	−0.253684	+	0.105967i
$997$	5.73454	−	5.19749i	0.181615	−	0.164606i	−0.575689	−	0.817669i	$-0.695266\pi$
$997$	5.73454	−	5.19749i	0.181615	−	0.164606i	0.757304	+	0.653063i	$0.226516\pi$
$998$	20.0461	+	37.3695i	0.634549	+	1.18291i
$999$	−15.8549	−	19.3192i	−0.501626	−	0.611233i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.101.24	✓	992
256.109	even	64	inner	256.2.m.a.109.24	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.101.24	✓	992	1.1	even	1	trivial
256.2.m.a.109.24	yes	992	256.109	even	64	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.m (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(0.948164 - 1.04928i) q^{2} +(-0.796024 + 0.199394i) q^{3} +(-0.201971 - 1.98978i) q^{4} +(-2.23808 - 1.05853i) q^{5} +(-0.545542 + 1.02431i) q^{6} +(-0.443907 - 1.46337i) q^{7} +(-2.27933 - 1.67471i) q^{8} +(-2.05187 + 1.09675i) q^{9} +O(q^{10})\)	\(q+(0.948164 - 1.04928i) q^{2} +(-0.796024 + 0.199394i) q^{3} +(-0.201971 - 1.98978i) q^{4} +(-2.23808 - 1.05853i) q^{5} +(-0.545542 + 1.02431i) q^{6} +(-0.443907 - 1.46337i) q^{7} +(-2.27933 - 1.67471i) q^{8} +(-2.05187 + 1.09675i) q^{9} +(-3.23276 + 1.34471i) q^{10} +(0.660502 - 0.0979762i) q^{11} +(0.557522 + 1.54364i) q^{12} +(1.50872 - 4.21660i) q^{13} +(-1.95638 - 0.921729i) q^{14} +(1.99263 + 0.396359i) q^{15} +(-3.91842 + 0.803752i) q^{16} +(0.516309 - 0.102700i) q^{17} +(-0.794714 + 3.19287i) q^{18} +(0.468480 + 0.424605i) q^{19} +(-1.65422 + 4.66707i) q^{20} +(0.645147 + 1.07636i) q^{21} +(0.523460 - 0.785948i) q^{22} +(4.23811 - 0.417417i) q^{23} +(2.14833 + 0.878626i) q^{24} +(0.716544 + 0.873111i) q^{25} +(-2.99387 - 5.58110i) q^{26} +(3.23876 - 2.93544i) q^{27} +(-2.82212 + 1.17883i) q^{28} +(-4.00444 - 5.39936i) q^{29} +(2.30523 - 1.71501i) q^{30} +(8.89857 + 3.68591i) q^{31} +(-2.87194 + 4.87360i) q^{32} +(-0.506240 + 0.209691i) q^{33} +(0.381785 - 0.639129i) q^{34} +(-0.555522 + 3.74502i) q^{35} +(2.59669 + 3.86124i) q^{36} +(0.280550 - 5.71072i) q^{37} +(0.889725 - 0.0889703i) q^{38} +(-0.360217 + 3.65735i) q^{39} +(3.32859 + 6.16088i) q^{40} +(-5.74742 + 7.00326i) q^{41} +(1.74111 + 0.343630i) q^{42} +(0.718329 - 2.86773i) q^{43} +(-0.328353 - 1.29446i) q^{44} +(5.75318 - 0.282636i) q^{45} +(3.58043 - 4.84273i) q^{46} +(8.21197 + 5.48706i) q^{47} +(2.95889 - 1.42111i) q^{48} +(3.87590 - 2.58979i) q^{49} +(1.59554 + 0.0759985i) q^{50} +(-0.390517 + 0.184701i) q^{51} +(-8.69481 - 2.15039i) q^{52} +(-1.78653 + 2.40886i) q^{53} +(-0.00921977 - 6.18165i) q^{54} +(-1.58197 - 0.479884i) q^{55} +(-1.43890 + 4.07891i) q^{56} +(-0.457585 - 0.244584i) q^{57} +(-9.46229 - 0.917707i) q^{58} +(-3.14890 - 8.80058i) q^{59} +(0.386213 - 4.04494i) q^{60} +(-1.95664 + 3.26446i) q^{61} +(12.3048 - 5.84223i) q^{62} +(2.51578 + 2.51578i) q^{63} +(2.39069 + 7.63443i) q^{64} +(-7.84005 + 7.84005i) q^{65} +(-0.259974 + 0.730008i) q^{66} +(2.51171 + 1.50546i) q^{67} +(-0.308630 - 1.00660i) q^{68} +(-3.29040 + 1.17733i) q^{69} +(3.40285 + 4.13379i) q^{70} +(1.19413 - 2.23407i) q^{71} +(6.51361 + 0.936437i) q^{72} +(0.217845 - 0.718140i) q^{73} +(-5.72613 - 5.70907i) q^{74} +(-0.744479 - 0.552143i) q^{75} +(0.750251 - 1.01793i) q^{76} +(-0.436577 - 0.923064i) q^{77} +(3.49603 + 3.84573i) q^{78} +(-8.34415 - 12.4879i) q^{79} +(9.62053 + 2.34891i) q^{80} +(1.88492 - 2.82099i) q^{81} +(1.89887 + 12.6709i) q^{82} +(0.259401 + 5.28023i) q^{83} +(2.01142 - 1.50109i) q^{84} +(-1.26425 - 0.316679i) q^{85} +(-2.32795 - 3.47280i) q^{86} +(4.26423 + 3.49956i) q^{87} +(-1.66958 - 0.882829i) q^{88} +(0.0896871 + 0.00883341i) q^{89} +(5.15840 - 6.30468i) q^{90} +(-6.84017 - 0.336036i) q^{91} +(-1.68654 - 8.34857i) q^{92} +(-7.81842 - 1.15975i) q^{93} +(13.5437 - 3.41401i) q^{94} +(-0.599037 - 1.44620i) q^{95} +(1.31437 - 4.45215i) q^{96} +(3.08962 - 7.45900i) q^{97} +(0.957573 - 6.52244i) q^{98} +(-1.24781 + 0.925437i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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