LMFDB - Embedded newform 672.2.bs.a.659.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(155,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1, 4, 0]))

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

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

chi := DirichletCharacter("672.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bs (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			659.34
Character	$\chi$	$=$	672.659
Dual form			672.2.bs.a.155.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.838438 + 1.13887i) q^{2} +(0.990810 - 1.42067i) q^{3} +(-0.594043 + 1.90974i) q^{4} +(1.38677 + 3.34796i) q^{5} +(2.44869 - 0.0627400i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-2.67301 + 0.924664i) q^{8} +(-1.03659 - 2.81522i) q^{9} +O(q^{10})$	\(q+(0.838438 + 1.13887i) q^{2} +(0.990810 - 1.42067i) q^{3} +(-0.594043 + 1.90974i) q^{4} +(1.38677 + 3.34796i) q^{5} +(2.44869 - 0.0627400i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-2.67301 + 0.924664i) q^{8} +(-1.03659 - 2.81522i) q^{9} +(-2.65017 + 4.38641i) q^{10} +(0.378180 + 0.913007i) q^{11} +(2.12452 + 2.73613i) q^{12} +(4.13390 + 1.71232i) q^{13} +(0.212436 - 1.39817i) q^{14} +(6.13037 + 1.34705i) q^{15} +(-3.29423 - 2.26894i) q^{16} +3.26447 q^{17} +(2.33705 - 3.54093i) q^{18} +(-2.64793 + 6.39267i) q^{19} +(-7.21754 + 0.659543i) q^{20} +(-1.70517 + 0.303955i) q^{21} +(-0.722715 + 1.19620i) q^{22} +(-4.18817 - 4.18817i) q^{23} +(-1.33481 + 4.71363i) q^{24} +(-5.75018 + 5.75018i) q^{25} +(1.51592 + 6.14364i) q^{26} +(-5.02656 - 1.31670i) q^{27} +(1.77044 - 0.930340i) q^{28} +(8.17496 + 3.38618i) q^{29} +(3.60582 + 8.11110i) q^{30} -3.54789i q^{31} +(-0.177986 - 5.65405i) q^{32} +(1.67178 + 0.367349i) q^{33} +(2.73705 + 3.71780i) q^{34} +(1.38677 - 3.34796i) q^{35} +(5.99213 - 0.307261i) q^{36} +(-3.50173 + 1.45046i) q^{37} +(-9.50054 + 2.34421i) q^{38} +(6.52855 - 4.17632i) q^{39} +(-6.80260 - 7.66684i) q^{40} +(5.55858 - 5.55858i) q^{41} +(-1.77585 - 1.68712i) q^{42} +(-6.28829 + 2.60469i) q^{43} +(-1.96826 + 0.179861i) q^{44} +(7.98774 - 7.37454i) q^{45} +(1.25825 - 8.28130i) q^{46} -8.07759i q^{47} +(-6.48736 + 2.43192i) q^{48} +1.00000i q^{49} +(-11.3699 - 1.72753i) q^{50} +(3.23447 - 4.63772i) q^{51} +(-5.72580 + 6.87750i) q^{52} +(8.16987 - 3.38407i) q^{53} +(-2.71492 - 6.82856i) q^{54} +(-2.53226 + 2.53226i) q^{55} +(2.54394 + 1.23627i) q^{56} +(6.45826 + 10.0957i) q^{57} +(2.99779 + 12.1493i) q^{58} +(-2.98401 + 1.23602i) q^{59} +(-6.21422 + 10.9072i) q^{60} +(0.512237 - 1.23665i) q^{61} +(4.04058 - 2.97468i) q^{62} +(-1.25768 + 2.72364i) q^{63} +(6.28999 - 4.94328i) q^{64} +16.2147i q^{65} +(0.983326 + 2.21194i) q^{66} +(-2.07847 - 0.860932i) q^{67} +(-1.93923 + 6.23429i) q^{68} +(-10.0997 + 1.80032i) q^{69} +(4.97561 - 1.22771i) q^{70} +(5.42590 - 5.42590i) q^{71} +(5.37396 + 6.56663i) q^{72} +(-4.26813 - 4.26813i) q^{73} +(-4.58787 - 2.77189i) q^{74} +(2.47176 + 13.8664i) q^{75} +(-10.6354 - 8.85438i) q^{76} +(0.378180 - 0.913007i) q^{77} +(10.2301 + 3.93357i) q^{78} +14.7584 q^{79} +(3.02797 - 14.1754i) q^{80} +(-6.85095 + 5.83647i) q^{81} +(10.9910 + 1.66996i) q^{82} +(3.68658 + 1.52703i) q^{83} +(0.432469 - 3.43700i) q^{84} +(4.52707 + 10.9293i) q^{85} +(-8.23875 - 4.97766i) q^{86} +(12.9105 - 8.25884i) q^{87} +(-1.85511 - 2.09079i) q^{88} +(-7.82842 - 7.82842i) q^{89} +(15.0959 + 2.91389i) q^{90} +(-1.71232 - 4.13390i) q^{91} +(10.4863 - 5.51037i) q^{92} +(-5.04037 - 3.51528i) q^{93} +(9.19932 - 6.77256i) q^{94} -25.0745 q^{95} +(-8.20888 - 5.34923i) q^{96} +0.711404 q^{97} +(-1.13887 + 0.838438i) q^{98} +(2.17830 - 2.01108i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 16 q^{4}+O(q^{10}) $ 192 * q - 16 * q^4	$ 192 q - 16 q^{4} + 8 q^{10} + 16 q^{16} + 16 q^{22} + 24 q^{27} - 84 q^{30} + 40 q^{36} + 32 q^{37} + 24 q^{39} - 96 q^{46} - 72 q^{48} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 28 q^{60} - 16 q^{61} - 64 q^{64} - 12 q^{66} - 32 q^{67} + 56 q^{69} - 24 q^{70} + 60 q^{72} + 80 q^{75} - 56 q^{76} + 100 q^{78} - 32 q^{79} - 120 q^{82} - 56 q^{87} + 40 q^{88} + 60 q^{90} - 80 q^{93} + 216 q^{94} + 96 q^{96} - 64 q^{99}+O(q^{100}) $ 192 * q - 16 * q^4 + 8 * q^10 + 16 * q^16 + 16 * q^22 + 24 * q^27 - 84 * q^30 + 40 * q^36 + 32 * q^37 + 24 * q^39 - 96 * q^46 - 72 * q^48 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 28 * q^60 - 16 * q^61 - 64 * q^64 - 12 * q^66 - 32 * q^67 + 56 * q^69 - 24 * q^70 + 60 * q^72 + 80 * q^75 - 56 * q^76 + 100 * q^78 - 32 * q^79 - 120 * q^82 - 56 * q^87 + 40 * q^88 + 60 * q^90 - 80 * q^93 + 216 * q^94 + 96 * q^96 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$-1$	$e\left(\frac{7}{8}\right)$	$-1$	$1$

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 $

$2$	0.838438	+	1.13887i	0.592865	+	0.805302i
$2$	0.838438	+	1.13887i	0.592865	+	0.805302i
$3$	0.990810	−	1.42067i	0.572044	−	0.820223i
$3$	0.990810	−	1.42067i	0.572044	−	0.820223i
$4$	−0.594043	+	1.90974i	−0.297021	+	0.954871i
$5$	1.38677	+	3.34796i	0.620183	+	1.49725i	0.851489	+	0.524373i	$0.175700\pi$
$5$	1.38677	+	3.34796i	0.620183	+	1.49725i	−0.231306	+	0.972881i	$0.574300\pi$
$6$	2.44869	−	0.0627400i	0.999672	−	0.0256135i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	−2.67301	+	0.924664i	−0.945053	+	0.326918i
$9$	−1.03659	−	2.81522i	−0.345531	−	0.938407i
$10$	−2.65017	+	4.38641i	−0.838056	+	1.38710i
$11$	0.378180	+	0.913007i	0.114026	+	0.275282i	0.970582	−	0.240772i	$-0.0774005\pi$
$11$	0.378180	+	0.913007i	0.114026	+	0.275282i	−0.856556	+	0.516054i	$0.827400\pi$
$12$	2.12452	+	2.73613i	0.613297	+	0.789852i
$13$	4.13390	+	1.71232i	1.14654	+	0.474912i	0.873371	−	0.487055i	$-0.161929\pi$
$13$	4.13390	+	1.71232i	1.14654	+	0.474912i	0.273167	+	0.961967i	$0.411929\pi$
$14$	0.212436	−	1.39817i	0.0567760	−	0.373676i
$15$	6.13037	+	1.34705i	1.58285	+	0.347807i
$16$	−3.29423	−	2.26894i	−0.823557	−	0.567234i
$17$	3.26447			0.791749			0.395875	−	0.918305i	$-0.370441\pi$
$17$	3.26447			0.791749			0.395875	+	0.918305i	$0.370441\pi$
$18$	2.33705	−	3.54093i	0.550848	−	0.834606i
$19$	−2.64793	+	6.39267i	−0.607477	+	1.46658i	0.258258	+	0.966076i	$0.416852\pi$
$19$	−2.64793	+	6.39267i	−0.607477	+	1.46658i	−0.865735	+	0.500503i	$0.833148\pi$
$20$	−7.21754	+	0.659543i	−1.61389	+	0.147478i
$21$	−1.70517	+	0.303955i	−0.372099	+	0.0663285i
$22$	−0.722715	+	1.19620i	−0.154083	+	0.255030i
$23$	−4.18817	−	4.18817i	−0.873294	−	0.873294i	0.119536	−	0.992830i	$-0.461859\pi$
$23$	−4.18817	−	4.18817i	−0.873294	−	0.873294i	−0.992830	+	0.119536i	$0.961859\pi$
$24$	−1.33481	+	4.71363i	−0.272466	+	0.962165i
$25$	−5.75018	+	5.75018i	−1.15004	+	1.15004i
$26$	1.51592	+	6.14364i	0.297296	+	1.20487i
$27$	−5.02656	−	1.31670i	−0.967362	−	0.253398i
$28$	1.77044	−	0.930340i	0.334582	−	0.175818i
$29$	8.17496	+	3.38618i	1.51805	+	0.628798i	0.977200	−	0.212320i	$-0.0681019\pi$
$29$	8.17496	+	3.38618i	1.51805	+	0.628798i	0.540852	+	0.841118i	$0.318102\pi$
$30$	3.60582	+	8.11110i	0.658329	+	1.48088i
$31$		−	3.54789i		−	0.637219i	−0.947886	−	0.318610i	$-0.896784\pi$
$31$		−	3.54789i		−	0.637219i	0.947886	−	0.318610i	$-0.103216\pi$
$32$	−0.177986	−	5.65405i	−0.0314638	−	0.999505i
$33$	1.67178	+	0.367349i	0.291020	+	0.0639472i
$34$	2.73705	+	3.71780i	0.469401	+	0.637597i
$35$	1.38677	−	3.34796i	0.234407	−	0.565909i
$36$	5.99213	−	0.307261i	0.998688	−	0.0512102i
$37$	−3.50173	+	1.45046i	−0.575681	+	0.238455i	−0.651477	−	0.758669i	$-0.725850\pi$
$37$	−3.50173	+	1.45046i	−0.575681	+	0.238455i	0.0757960	+	0.997123i	$0.475850\pi$
$38$	−9.50054	+	2.34421i	−1.54119	+	0.380282i
$39$	6.52855	−	4.17632i	1.04540	−	0.668746i
$40$	−6.80260	−	7.66684i	−1.07558	−	1.21223i
$41$	5.55858	−	5.55858i	0.868104	−	0.868104i	−0.124158	−	0.992262i	$-0.539623\pi$
$41$	5.55858	−	5.55858i	0.868104	−	0.868104i	0.992262	+	0.124158i	$0.0396231\pi$
$42$	−1.77585	−	1.68712i	−0.274019	−	0.260328i
$43$	−6.28829	+	2.60469i	−0.958955	+	0.397212i	−0.806590	−	0.591112i	$-0.798689\pi$
$43$	−6.28829	+	2.60469i	−0.958955	+	0.397212i	−0.152366	+	0.988324i	$0.548689\pi$
$44$	−1.96826	+	0.179861i	−0.296727	+	0.0271151i
$45$	7.98774	−	7.37454i	1.19074	−	1.09933i
$46$	1.25825	−	8.28130i	0.185519	−	1.22101i
$47$		−	8.07759i		−	1.17824i	−0.808046	−	0.589119i	$-0.799475\pi$
$47$		−	8.07759i		−	1.17824i	0.808046	−	0.589119i	$-0.200525\pi$
$48$	−6.48736	+	2.43192i	−0.936369	+	0.351017i
$49$			1.00000i			0.142857i
$50$	−11.3699	−	1.72753i	−1.60794	−	0.244309i
$51$	3.23447	−	4.63772i	0.452916	−	0.649411i
$52$	−5.72580	+	6.87750i	−0.794026	+	0.953737i
$53$	8.16987	−	3.38407i	1.12222	−	0.464838i	0.257089	−	0.966388i	$-0.417237\pi$
$53$	8.16987	−	3.38407i	1.12222	−	0.464838i	0.865129	+	0.501550i	$0.167237\pi$
$54$	−2.71492	−	6.82856i	−0.369453	−	0.929249i
$55$	−2.53226	+	2.53226i	−0.341450	+	0.341450i
$56$	2.54394	+	1.23627i	0.339948	+	0.165203i
$57$	6.45826	+	10.0957i	0.855418	+	1.33721i
$58$	2.99779	+	12.1493i	0.393629	+	1.59528i
$59$	−2.98401	+	1.23602i	−0.388486	+	0.160916i	−0.568373	−	0.822771i	$-0.692427\pi$
$59$	−2.98401	+	1.23602i	−0.388486	+	0.160916i	0.179887	+	0.983687i	$0.442427\pi$
$60$	−6.21422	+	10.9072i	−0.802252	+	1.40811i
$61$	0.512237	−	1.23665i	0.0655852	−	0.158337i	−0.887689	−	0.460444i	$-0.847690\pi$
$61$	0.512237	−	1.23665i	0.0655852	−	0.158337i	0.953274	+	0.302108i	$0.0976902\pi$
$62$	4.04058	−	2.97468i	0.513154	−	0.377785i
$63$	−1.25768	+	2.72364i	−0.158453	+	0.343147i
$64$	6.28999	−	4.94328i	0.786249	−	0.617910i
$65$			16.2147i			2.01119i
$66$	0.983326	+	2.21194i	0.121039	+	0.272271i
$67$	−2.07847	−	0.860932i	−0.253926	−	0.105180i	0.252090	−	0.967704i	$-0.418882\pi$
$67$	−2.07847	−	0.860932i	−0.253926	−	0.105180i	−0.506016	+	0.862524i	$0.668882\pi$
$68$	−1.93923	+	6.23429i	−0.235166	+	0.756018i
$69$	−10.0997	+	1.80032i	−1.21586	+	0.216733i
$70$	4.97561	−	1.22771i	0.594699	−	0.146739i
$71$	5.42590	−	5.42590i	0.643936	−	0.643936i	−0.307585	−	0.951521i	$-0.599521\pi$
$71$	5.42590	−	5.42590i	0.643936	−	0.643936i	0.951521	+	0.307585i	$0.0995207\pi$
$72$	5.37396	+	6.56663i	0.633327	+	0.773884i
$73$	−4.26813	−	4.26813i	−0.499547	−	0.499547i	0.411750	−	0.911297i	$-0.364918\pi$
$73$	−4.26813	−	4.26813i	−0.499547	−	0.499547i	−0.911297	+	0.411750i	$0.864918\pi$
$74$	−4.58787	−	2.77189i	−0.533329	−	0.322225i
$75$	2.47176	+	13.8664i	0.285414	+	1.60116i
$76$	−10.6354	−	8.85438i	−1.21996	−	1.01567i
$77$	0.378180	−	0.913007i	0.0430976	−	0.104047i
$78$	10.2301	+	3.93357i	1.15833	+	0.445389i
$79$	14.7584			1.66045			0.830224	−	0.557429i	$-0.188212\pi$
$79$	14.7584			1.66045			0.830224	+	0.557429i	$0.188212\pi$
$80$	3.02797	−	14.1754i	0.338537	−	1.58486i
$81$	−6.85095	+	5.83647i	−0.761217	+	0.648497i
$82$	10.9910	+	1.66996i	1.21375	+	0.184417i
$83$	3.68658	+	1.52703i	0.404654	+	0.167613i	0.575721	−	0.817646i	$-0.304721\pi$
$83$	3.68658	+	1.52703i	0.404654	+	0.167613i	−0.171067	+	0.985259i	$0.554721\pi$
$84$	0.432469	−	3.43700i	0.0471862	−	0.375007i
$85$	4.52707	+	10.9293i	0.491029	+	1.18545i
$86$	−8.23875	−	4.97766i	−0.888407	−	0.536755i
$87$	12.9105	−	8.25884i	1.38415	−	0.885441i
$88$	−1.85511	−	2.09079i	−0.197755	−	0.222879i
$89$	−7.82842	−	7.82842i	−0.829811	−	0.829811i	0.157680	−	0.987490i	$-0.449599\pi$
$89$	−7.82842	−	7.82842i	−0.829811	−	0.829811i	−0.987490	+	0.157680i	$0.949599\pi$
$90$	15.0959	+	2.91389i	1.59124	+	0.307151i
$91$	−1.71232	−	4.13390i	−0.179500	−	0.433351i
$92$	10.4863	−	5.51037i	1.09327	−	0.574496i
$93$	−5.04037	−	3.51528i	−0.522662	−	0.364518i
$94$	9.19932	−	6.77256i	0.948837	−	0.698537i
$95$	−25.0745			−2.57259
$96$	−8.20888	−	5.34923i	−0.837815	−	0.545954i
$97$	0.711404			0.0722321			0.0361160	−	0.999348i	$-0.488501\pi$
$97$	0.711404			0.0722321			0.0361160	+	0.999348i	$0.488501\pi$
$98$	−1.13887	+	0.838438i	−0.115043	+	0.0846951i
$99$	2.17830	−	2.01108i	0.218927	−	0.202121i
$100$	−7.56550	−	14.3972i	−0.756550	−	1.43972i
$101$	−7.04511	−	17.0084i	−0.701015	−	1.69240i	−0.721317	−	0.692605i	$-0.756463\pi$
$101$	−7.04511	−	17.0084i	−0.701015	−	1.69240i	0.0203025	−	0.999794i	$-0.493537\pi$
$102$	7.99365	−	0.204813i	0.791490	−	0.0202795i
$103$	0.952773	+	0.952773i	0.0938795	+	0.0938795i	0.752487	−	0.658607i	$-0.228854\pi$
$103$	0.952773	+	0.952773i	0.0938795	+	0.0938795i	−0.658607	+	0.752487i	$0.728854\pi$
$104$	−12.6333	−	0.754578i	−1.23880	−	0.0739924i
$105$	−3.38231	−	5.28733i	−0.330080	−	0.515991i
$106$	10.7039	+	6.46707i	1.03966	+	0.628137i
$107$	5.51676	+	13.3186i	0.533325	+	1.28756i	0.929309	+	0.369303i	$0.120404\pi$
$107$	5.51676	+	13.3186i	0.533325	+	1.28756i	−0.395984	+	0.918258i	$0.629596\pi$
$108$	5.50054	−	8.81726i	0.529290	−	0.848441i
$109$	−7.83171	−	3.24400i	−0.750142	−	0.310719i	−0.0253425	−	0.999679i	$-0.508068\pi$
$109$	−7.83171	−	3.24400i	−0.750142	−	0.310719i	−0.724800	+	0.688960i	$0.758068\pi$
$110$	−5.00706	−	0.760769i	−0.477405	−	0.0725364i
$111$	−1.40892	+	6.41193i	−0.133729	+	0.608593i
$112$	0.724990	+	3.93375i	0.0685051	+	0.371704i
$113$	−5.19609			−0.488807			−0.244403	−	0.969674i	$-0.578592\pi$
$113$	−5.19609			−0.488807			−0.244403	+	0.969674i	$0.578592\pi$
$114$	−6.08288	+	15.8198i	−0.569713	+	1.48166i
$115$	8.21380	−	19.8299i	0.765940	−	1.84914i
$116$	−11.3230	+	13.6005i	−1.05131	+	1.26278i
$117$	0.535386	−	13.4128i	0.0494965	−	1.24002i
$118$	−3.90958	−	2.36207i	−0.359906	−	0.217447i
$119$	−2.30833	−	2.30833i	−0.211604	−	0.211604i
$120$	−17.6321	+	2.06784i	−1.60958	+	0.188767i
$121$	7.08761	−	7.08761i	0.644328	−	0.644328i
$122$	1.83786	−	0.453483i	0.166392	−	0.0410565i
$123$	−2.38940	−	13.4044i	−0.215445	−	1.20863i
$124$	6.77555	+	2.10760i	0.608462	+	0.189268i
$125$	−10.4857	−	4.34333i	−0.937872	−	0.388479i
$126$	−4.15636	+	0.851274i	−0.370278	+	0.0758375i
$127$		−	7.52117i		−	0.667395i	−0.942680	−	0.333698i	$-0.891704\pi$
$127$		−	7.52117i		−	0.667395i	0.942680	−	0.333698i	$-0.108296\pi$
$128$	10.9035	+	3.01884i	0.963744	+	0.266830i
$129$	−2.53009	+	11.5143i	−0.222762	+	1.01378i
$130$	−18.4665	+	13.5951i	−1.61961	+	1.19237i
$131$	4.09884	−	9.89548i	0.358118	−	0.864572i	−0.637447	−	0.770494i	$-0.720010\pi$
$131$	4.09884	−	9.89548i	0.358118	−	0.864572i	0.995565	−	0.0940782i	$-0.0299904\pi$
$132$	−1.69465	+	2.97446i	−0.147501	+	0.258893i
$133$	6.39267	−	2.64793i	0.554315	−	0.229605i
$134$	−0.762183	−	3.08895i	−0.0658426	−	0.266844i
$135$	−2.56244	−	18.6547i	−0.220540	−	1.60554i
$136$	−8.72596	+	3.01853i	−0.748245	+	0.258837i
$137$	1.32146	−	1.32146i	0.112900	−	0.112900i	−0.648400	−	0.761300i	$-0.724561\pi$
$137$	1.32146	−	1.32146i	0.112900	−	0.112900i	0.761300	+	0.648400i	$0.224561\pi$
$138$	−10.5183	−	9.99275i	−0.895375	−	0.850639i
$139$	2.81500	−	1.16601i	0.238766	−	0.0988999i	−0.260092	−	0.965584i	$-0.583753\pi$
$139$	2.81500	−	1.16601i	0.238766	−	0.0988999i	0.498858	+	0.866684i	$0.333753\pi$
$140$	5.56994	+	4.63721i	0.470746	+	0.391915i
$141$	−11.4756	−	8.00336i	−0.966418	−	0.674004i
$142$	10.7287	+	1.63010i	0.900330	+	0.136795i
$143$			4.42185i			0.369774i
$144$	−2.97279	+	11.6259i	−0.247732	+	0.968828i
$145$			32.0653i			2.66288i
$146$	1.28228	−	8.43940i	0.106122	−	0.698450i
$147$	1.42067	+	0.990810i	0.117175	+	0.0817206i
$148$	−0.689835	−	7.54904i	−0.0567041	−	0.620527i
$149$	0.128534	−	0.0532404i	0.0105299	−	0.00436162i	−0.377412	−	0.926045i	$-0.623186\pi$
$149$	0.128534	−	0.0532404i	0.0105299	−	0.00436162i	0.387942	+	0.921684i	$0.373186\pi$
$150$	−13.7196	+	14.4411i	−1.12020	+	1.17911i
$151$	−12.9375	+	12.9375i	−1.05284	+	1.05284i	−0.0543163	+	0.998524i	$0.517298\pi$
$151$	−12.9375	+	12.9375i	−1.05284	+	1.05284i	−0.998524	+	0.0543163i	$0.982702\pi$
$152$	1.16688	−	19.5361i	0.0946464	−	1.58459i
$153$	−3.38392	−	9.19020i	−0.273574	−	0.742984i
$154$	1.35688	−	0.334803i	0.109340	−	0.0269792i
$155$	11.8782	−	4.92010i	0.954079	−	0.395192i
$156$	4.09746	+	14.9487i	0.328059	+	1.19686i
$157$	0.666674	−	1.60949i	0.0532064	−	0.128452i	−0.895041	−	0.445983i	$-0.852854\pi$
$157$	0.666674	−	1.60949i	0.0532064	−	0.128452i	0.948248	+	0.317532i	$0.102854\pi$
$158$	12.3740	+	16.8079i	0.984423	+	1.33716i
$159$	3.28715	−	14.9596i	0.260688	−	1.18638i
$160$	18.6827	−	8.43677i	1.47700	−	0.666985i
$161$			5.92297i			0.466795i
$162$	−12.3911	−	2.90881i	−0.973535	−	0.228538i
$163$	−13.5676	−	5.61989i	−1.06270	−	0.440183i	−0.218289	−	0.975884i	$-0.570048\pi$
$163$	−13.5676	−	5.61989i	−1.06270	−	0.440183i	−0.844408	+	0.535701i	$0.820048\pi$
$164$	7.31342	+	13.9175i	0.571082	+	1.08677i
$165$	1.08851	+	6.10650i	0.0847407	+	0.475390i
$166$	1.35188	+	5.47884i	0.104926	+	0.425241i
$167$	−9.56742	+	9.56742i	−0.740349	+	0.740349i	−0.972645	−	0.232296i	$-0.925376\pi$
$167$	−9.56742	+	9.56742i	−0.740349	+	0.740349i	0.232296	+	0.972645i	$0.425376\pi$
$168$	4.27689	−	2.38919i	0.329969	−	0.184330i
$169$	4.96473	+	4.96473i	0.381902	+	0.381902i
$170$	−8.65138	+	14.3193i	−0.663530	+	1.09824i
$171$	20.7416	+	0.827922i	1.58615	+	0.0633128i
$172$	−1.23878	−	13.5563i	−0.0944563	−	1.03366i
$173$	−0.236859	+	0.571829i	−0.0180081	+	0.0434753i	−0.932628	−	0.360840i	$-0.882490\pi$
$173$	−0.236859	+	0.571829i	−0.0180081	+	0.0434753i	0.914620	+	0.404315i	$0.132490\pi$
$174$	20.2304	+	7.77879i	1.53366	+	0.589709i
$175$	8.13198			0.614720
$176$	0.825745	−	3.86572i	0.0622428	−	0.291390i
$177$	−1.20062	+	5.46395i	−0.0902440	+	0.410696i
$178$	2.35189	−	15.4792i	0.176282	−	1.16021i
$179$	15.9234	+	6.59567i	1.19017	+	0.492984i	0.887810	−	0.460210i	$-0.152226\pi$
$179$	15.9234	+	6.59567i	1.19017	+	0.492984i	0.302358	+	0.953194i	$0.402226\pi$
$180$	9.33841	+	19.6353i	0.696044	+	1.46353i
$181$	−6.36532	−	15.3672i	−0.473130	−	1.14224i	−0.962772	−	0.270314i	$-0.912872\pi$
$181$	−6.36532	−	15.3672i	−0.473130	−	1.14224i	0.489642	−	0.871924i	$-0.337128\pi$
$182$	3.27230	−	5.41613i	0.242559	−	0.401470i
$183$	−1.24934	−	1.95300i	−0.0923537	−	0.144370i
$184$	15.0677	+	7.32238i	1.11080	+	0.539813i
$185$	−9.71219	−	9.71219i	−0.714055	−	0.714055i
$186$	−0.222594	−	8.68766i	−0.0163214	−	0.637010i
$187$	1.23456	+	2.98048i	0.0902797	+	0.217954i
$188$	15.4261	+	4.79843i	1.12507	+	0.349962i
$189$	2.62327	+	4.48536i	0.190815	+	0.326262i
$190$	−21.0234	−	28.5565i	−1.52520	−	2.07171i
$191$	1.56310			0.113102			0.0565512	−	0.998400i	$-0.481990\pi$
$191$	1.56310			0.113102			0.0565512	+	0.998400i	$0.481990\pi$
$192$	−0.790568	−	13.8338i	−0.0570543	−	0.998371i
$193$	−22.4079			−1.61296			−0.806478	−	0.591264i	$-0.798629\pi$
$193$	−22.4079			−1.61296			−0.806478	+	0.591264i	$0.798629\pi$
$194$	0.596468	+	0.810195i	0.0428239	+	0.0581686i
$195$	23.0357	+	16.0657i	1.64962	+	1.15049i
$196$	−1.90974	−	0.594043i	−0.136410	−	0.0424316i
$197$	9.98215	+	24.0990i	0.711199	+	1.71699i	0.696984	+	0.717087i	$0.254525\pi$
$197$	9.98215	+	24.0990i	0.711199	+	1.71699i	0.0142153	+	0.999899i	$0.495475\pi$
$198$	4.11672	+	0.794633i	0.292563	+	0.0564721i
$199$	14.1550	+	14.1550i	1.00342	+	1.00342i	0.999994	+	0.00342391i	$0.00108987\pi$
$199$	14.1550	+	14.1550i	1.00342	+	1.00342i	0.00342391	+	0.999994i	$0.498910\pi$
$200$	10.0533	−	20.6873i	0.710876	−	1.46281i
$201$	−3.28247	+	2.09980i	−0.231528	+	0.148108i
$202$	13.4634	−	22.2839i	0.947284	−	1.56789i
$203$	−3.38618	−	8.17496i	−0.237663	−	0.573770i
$204$	6.93544	+	8.93200i	0.485578	+	0.625365i
$205$	26.3184	+	10.9014i	1.83816	+	0.761389i
$206$	−0.286242	+	1.88393i	−0.0199434	+	0.131259i
$207$	−7.44920	+	16.1321i	−0.517755	+	1.12126i
$208$	−9.73287	−	15.0203i	−0.674853	−	1.04147i
$209$	−6.83795			−0.472991
$210$	3.18572	−	8.28511i	0.219835	−	0.571727i
$211$	3.87219	−	9.34829i	0.266573	−	0.643563i	−0.732745	−	0.680503i	$-0.761761\pi$
$211$	3.87219	−	9.34829i	0.266573	−	0.643563i	0.999317	+	0.0369403i	$0.0117611\pi$
$212$	1.60945	+	17.6126i	0.110537	+	1.20964i
$213$	−2.33237	−	13.0844i	−0.159811	−	0.896531i
$214$	−10.5427	+	17.4497i	−0.720685	+	1.19284i
$215$	−17.4408	−	17.4408i	−1.18945	−	1.18945i
$216$	14.6536	−	1.12833i	0.997049	−	0.0767733i
$217$	−2.50873	+	2.50873i	−0.170304	+	0.170304i
$218$	−2.87192	−	11.6392i	−0.194511	−	0.788305i
$219$	−10.2925	+	1.83469i	−0.695503	+	0.123977i
$220$	−3.33170	−	6.34024i	−0.224623	−	0.427459i
$221$	13.4950	+	5.58981i	0.907771	+	0.376011i
$222$	−8.48364	+	3.77143i	−0.569384	+	0.253122i
$223$		−	4.01245i		−	0.268693i	−0.990934	−	0.134347i	$-0.957106\pi$
$223$		−	4.01245i		−	0.268693i	0.990934	−	0.134347i	$-0.0428936\pi$
$224$	−3.87216	+	4.12387i	−0.258720	+	0.275538i
$225$	22.1486	+	10.2274i	1.47657	+	0.681829i
$226$	−4.35660	−	5.91766i	−0.289797	−	0.393637i
$227$	3.03414	−	7.32506i	0.201383	−	0.486181i	−0.790634	−	0.612290i	$-0.790249\pi$
$227$	3.03414	−	7.32506i	0.201383	−	0.486181i	0.992016	+	0.126108i	$0.0402487\pi$
$228$	−23.1168	+	6.33631i	−1.53094	+	0.419632i
$229$	−18.9882	+	7.86518i	−1.25478	+	0.519746i	−0.908303	−	0.418313i	$-0.862621\pi$
$229$	−18.9882	+	7.86518i	−1.25478	+	0.519746i	−0.346475	+	0.938059i	$0.612621\pi$
$230$	29.4704	−	7.27168i	1.94322	−	0.479480i
$231$	−0.922376	−	1.44188i	−0.0606879	−	0.0948691i
$232$	−24.9829	−	1.49221i	−1.64020	−	0.0979683i
$233$	−14.4363	+	14.4363i	−0.945756	+	0.945756i	−0.998603	−	0.0528463i	$-0.983171\pi$
$233$	−14.4363	+	14.4363i	−0.945756	+	0.945756i	0.0528463	+	0.998603i	$0.483171\pi$
$234$	15.7243	−	10.6361i	1.02793	−	0.695303i
$235$	27.0435	−	11.2018i	1.76412	−	0.730723i
$236$	−0.587846	−	6.43295i	−0.0382655	−	0.418749i
$237$	14.6228	−	20.9668i	0.949850	−	1.36194i
$238$	0.693491	−	4.56427i	0.0449523	−	0.295858i
$239$		−	14.8442i		−	0.960192i	−0.877216	−	0.480096i	$-0.840602\pi$
$239$		−	14.8442i		−	0.960192i	0.877216	−	0.480096i	$-0.159398\pi$
$240$	−17.1384	−	18.3469i	−1.10628	−	1.18429i
$241$			17.1188i			1.10272i	0.834267	+	0.551361i	$0.185891\pi$
$241$			17.1188i			1.10272i	−0.834267	+	0.551361i	$0.814109\pi$
$242$	14.0144	+	2.12933i	0.900879	+	0.136879i
$243$	1.50370	+	15.5158i	0.0964623	+	0.995337i
$244$	2.05739	+	1.71286i	0.131711	+	0.109655i
$245$	−3.34796	+	1.38677i	−0.213893	+	0.0885975i
$246$	13.2625	−	13.9600i	0.845584	−	0.890055i
$247$	−21.8926	+	21.8926i	−1.39299	+	1.39299i
$248$	3.28060	+	9.48354i	0.208318	+	0.602206i
$249$	5.82210	−	3.72440i	0.368960	−	0.236024i
$250$	−3.84515	−	15.5835i	−0.243189	−	0.985586i
$251$	−17.9903	+	7.45183i	−1.13554	+	0.470355i	−0.869660	−	0.493651i	$-0.835662\pi$
$251$	−17.9903	+	7.45183i	−1.13554	+	0.470355i	−0.265878	+	0.964007i	$0.585662\pi$
$252$	−4.45434	−	4.01981i	−0.280597	−	0.253224i
$253$	2.23995	−	5.40771i	0.140824	−	0.339980i
$254$	8.56562	−	6.30603i	0.537455	−	0.395676i
$255$	20.0124	+	4.39741i	1.25322	+	0.275376i
$256$	5.70386	+	14.9488i	0.356491	+	0.934299i
$257$		−	2.47735i		−	0.154533i	−0.997010	−	0.0772663i	$-0.975381\pi$
$257$		−	2.47735i		−	0.154533i	0.997010	−	0.0772663i	$-0.0246192\pi$
$258$	−15.2346	+	6.77261i	−0.948467	+	0.421644i
$259$	3.50173	+	1.45046i	0.217587	+	0.0901275i
$260$	−30.9660	−	9.63224i	−1.92043	−	0.597366i
$261$	1.05875	−	26.5244i	0.0655349	−	1.64182i
$262$	14.7063	−	3.62871i	0.908557	−	0.224182i
$263$	2.18068	−	2.18068i	0.134466	−	0.134466i	−0.636670	−	0.771136i	$-0.719689\pi$
$263$	2.18068	−	2.18068i	0.134466	−	0.134466i	0.771136	+	0.636670i	$0.219689\pi$
$264$	−4.80837	+	0.563912i	−0.295935	+	0.0347064i
$265$	22.6595	+	22.6595i	1.39196	+	1.39196i
$266$	8.37550	+	5.06028i	0.513535	+	0.310266i
$267$	−18.8780	+	3.36511i	−1.15532	+	0.205941i
$268$	2.87886	−	3.45792i	0.175854	−	0.211226i
$269$	−9.64403	+	23.2828i	−0.588007	+	1.41957i	0.297398	+	0.954754i	$0.403881\pi$
$269$	−9.64403	+	23.2828i	−0.588007	+	1.41957i	−0.885405	+	0.464821i	$0.846119\pi$
$270$	19.0968	−	18.5591i	1.16219	−	1.12947i
$271$	22.8488			1.38796			0.693982	−	0.719992i	$-0.255855\pi$
$271$	22.8488			1.38796			0.693982	+	0.719992i	$0.255855\pi$
$272$	−10.7539	−	7.40687i	−0.652051	−	0.449107i
$273$	−7.56948	−	1.66328i	−0.458126	−	0.100666i
$274$	2.61294	+	0.397007i	0.157853	+	0.0239841i
$275$	−7.42455	−	3.07535i	−0.447717	−	0.185451i
$276$	2.56150	−	20.3572i	0.154184	−	1.22536i
$277$	2.72624	+	6.58174i	0.163804	+	0.395458i	0.984375	−	0.176087i	$-0.0563441\pi$
$277$	2.72624	+	6.58174i	0.163804	+	0.395458i	−0.820570	+	0.571545i	$0.806344\pi$
$278$	3.68814	+	2.22829i	0.221200	+	0.133644i
$279$	−9.98809	+	3.67771i	−0.597971	+	0.220179i
$280$	−0.611117	+	10.2314i	−0.0365212	+	0.611445i
$281$	15.1287	+	15.1287i	0.902503	+	0.902503i	0.995652	−	0.0931495i	$-0.0296935\pi$
$281$	15.1287	+	15.1287i	0.902503	+	0.902503i	−0.0931495	+	0.995652i	$0.529693\pi$
$282$	−0.506788	−	19.7795i	−0.0301788	−	1.17785i
$283$	−2.62909	−	6.34718i	−0.156283	−	0.377301i	0.826272	−	0.563271i	$-0.190457\pi$
$283$	−2.62909	−	6.34718i	−0.156283	−	0.377301i	−0.982555	+	0.185970i	$0.940457\pi$
$284$	7.13885	+	13.5853i	0.423613	+	0.806138i
$285$	−24.8440	+	35.6225i	−1.47163	+	2.11010i
$286$	−5.03590	+	3.70745i	−0.297779	+	0.219226i
$287$	−7.86102			−0.464021
$288$	−15.7329	+	6.36202i	−0.927071	+	0.374886i
$289$	−6.34326			−0.373133
$290$	−36.5182	+	26.8848i	−2.14442	+	1.57873i
$291$	0.704866	−	1.01067i	0.0413200	−	0.0592464i
$292$	10.6865	−	5.61557i	0.625379	−	0.328627i
$293$	−0.523579	−	1.26403i	−0.0305878	−	0.0738455i	0.907848	−	0.419300i	$-0.137725\pi$
$293$	−0.523579	−	1.26403i	−0.0305878	−	0.0738455i	−0.938435	+	0.345455i	$0.887725\pi$
$294$	0.0627400	+	2.44869i	0.00365907	+	0.142810i
$295$	−8.27629	−	8.27629i	−0.481864	−	0.481864i
$296$	8.01898	−	7.11503i	0.466094	−	0.413553i
$297$	−0.698791	−	5.08724i	−0.0405480	−	0.295191i
$298$	0.168401	+	0.101744i	0.00975523	+	0.00589388i
$299$	−10.1420	−	24.4850i	−0.586527	−	1.41600i
$300$	−27.9496	−	3.51682i	−1.61367	−	0.203044i
$301$	6.28829	+	2.60469i	0.362451	+	0.150132i
$302$	−25.5814	−	3.88682i	−1.47205	−	0.223661i
$303$	−31.1436	−	6.84333i	−1.78916	−	0.393139i
$304$	23.2274	−	15.0509i	1.33219	−	0.863230i
$305$	4.85061			0.277745
$306$	7.62922	−	11.5593i	0.436133	−	0.660799i
$307$	−6.96234	+	16.8086i	−0.397362	+	0.959317i	0.590927	+	0.806725i	$0.298762\pi$
$307$	−6.96234	+	16.8086i	−0.397362	+	0.959317i	−0.988289	+	0.152592i	$0.951238\pi$
$308$	1.51895	+	1.26459i	0.0865504	+	0.0720568i
$309$	2.29759	−	0.409557i	0.130705	−	0.0232989i
$310$	15.5625	+	9.40248i	0.883889	+	0.534025i
$311$	−1.76390	−	1.76390i	−0.100021	−	0.100021i	0.655325	−	0.755347i	$-0.272532\pi$
$311$	−1.76390	−	1.76390i	−0.100021	−	0.100021i	−0.755347	+	0.655325i	$0.772532\pi$
$312$	−13.5892	+	17.2001i	−0.769337	+	0.973762i
$313$	4.77817	−	4.77817i	0.270078	−	0.270078i	−0.559053	−	0.829132i	$-0.688835\pi$
$313$	4.77817	−	4.77817i	0.270078	−	0.270078i	0.829132	+	0.559053i	$0.188835\pi$
$314$	2.39197	−	0.590207i	0.134987	−	0.0333073i
$315$	−10.8628	−	0.433598i	−0.612048	−	0.0244305i
$316$	−8.76711	+	28.1847i	−0.493189	+	1.58551i
$317$	2.08604	+	0.864065i	0.117164	+	0.0485308i	0.440495	−	0.897755i	$-0.354803\pi$
$317$	2.08604	+	0.864065i	0.117164	+	0.0485308i	−0.323332	+	0.946286i	$0.604803\pi$
$318$	19.7931	−	8.79910i	1.10994	−	0.493429i
$319$			8.74439i			0.489592i
$320$	25.2727	+	14.2035i	1.41279	+	0.793997i
$321$	24.3874	+	5.35875i	1.36117	+	0.299096i
$322$	−6.74548	+	4.96604i	−0.375911	+	0.276747i
$323$	−8.64408	+	20.8687i	−0.480970	+	1.16116i
$324$	−7.07640	−	16.5507i	−0.393133	−	0.919481i
$325$	−33.6168	+	13.9245i	−1.86472	+	0.772394i
$326$	−4.97529	−	20.1636i	−0.275556	−	1.11676i
$327$	−12.3684	+	7.91207i	−0.683973	+	0.437539i
$328$	−9.71833	+	19.9980i	−0.536605	+	1.10420i
$329$	−5.71172	+	5.71172i	−0.314897	+	0.314897i
$330$	−6.04185	+	6.35959i	−0.332593	+	0.350084i
$331$	−10.8342	+	4.48765i	−0.595499	+	0.246664i	−0.660014	−	0.751253i	$-0.729450\pi$
$331$	−10.8342	+	4.48765i	−0.595499	+	0.246664i	0.0645154	+	0.997917i	$0.479450\pi$
$332$	−5.10622	+	6.13329i	−0.280240	+	0.336608i
$333$	7.71324	+	8.35461i	0.422683	+	0.457830i
$334$	−18.9177	−	2.87434i	−1.03513	−	0.157277i
$335$		−	8.15256i		−	0.445422i
$336$	6.30688	+	2.86763i	0.344068	+	0.156442i
$337$		−	11.5608i		−	0.629755i	−0.949132	−	0.314878i	$-0.898037\pi$
$337$		−	11.5608i		−	0.629755i	0.949132	−	0.314878i	$-0.101963\pi$
$338$	−1.49155	+	9.81679i	−0.0811298	+	0.533963i
$339$	−5.14833	+	7.38191i	−0.279619	+	0.400930i
$340$	−23.5614	+	2.15305i	−1.27780	+	0.116766i
$341$	3.23925	−	1.34174i	0.175415	−	0.0726593i
$342$	16.4477	+	24.3161i	0.889388	+	1.31487i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	14.4002	−	12.7769i	0.776407	−	0.688886i
$345$	−20.0333	−	31.3167i	−1.07856	−	1.68603i
$346$	−0.849829	+	0.209692i	−0.0456871	+	0.0112731i
$347$	5.79074	−	2.39860i	0.310863	−	0.128764i	−0.221797	−	0.975093i	$-0.571192\pi$
$347$	5.79074	−	2.39860i	0.310863	−	0.128764i	0.532660	+	0.846329i	$0.321192\pi$
$348$	8.10289	+	29.5618i	0.434360	+	1.58468i
$349$	6.11567	−	14.7645i	0.327365	−	0.790328i	−0.671422	−	0.741075i	$-0.734316\pi$
$349$	6.11567	−	14.7645i	0.327365	−	0.790328i	0.998786	−	0.0492526i	$-0.0156839\pi$
$350$	6.81816	+	9.26125i	0.364446	+	0.495035i
$351$	−18.5247	−	14.0502i	−0.988776	−	0.749943i
$352$	5.09488	−	2.30075i	0.271558	−	0.122631i
$353$			1.67879i			0.0893530i	0.999002	+	0.0446765i	$0.0142257\pi$
$353$			1.67879i			0.0893530i	−0.999002	+	0.0446765i	$0.985774\pi$
$354$	−7.22937	+	3.21384i	−0.384237	+	0.170814i
$355$	25.6902	+	10.6412i	1.36349	+	0.564778i
$356$	19.6007	−	10.2998i	1.03883	−	0.545890i
$357$	−5.56648	+	0.992252i	−0.294609	+	0.0525155i
$358$	5.83915	+	23.6647i	0.308609	+	1.25072i
$359$	−15.6864	+	15.6864i	−0.827898	+	0.827898i	−0.987226	−	0.159328i	$-0.949067\pi$
$359$	−15.6864	+	15.6864i	−0.827898	+	0.827898i	0.159328	+	0.987226i	$0.449067\pi$
$360$	−14.5324	+	27.0982i	−0.765922	+	1.42820i
$361$	−20.4197	−	20.4197i	−1.07472	−	1.07472i
$362$	12.1643	−	20.1337i	0.639343	−	1.05821i
$363$	−3.04667	−	17.0916i	−0.159908	−	0.897077i
$364$	8.91188	−	0.814372i	0.467109	−	0.0426847i
$365$	8.37061	−	20.2084i	0.438138	−	1.05776i
$366$	1.17672	−	3.06030i	0.0615081	−	0.159965i
$367$	−9.05621			−0.472730			−0.236365	−	0.971664i	$-0.575956\pi$
$367$	−9.05621			−0.472730			−0.236365	+	0.971664i	$0.575956\pi$
$368$	4.29409	+	23.2995i	0.223845	+	1.21457i
$369$	−21.4106	−	9.88666i	−1.11459	−	0.514679i
$370$	2.91784	−	19.2040i	0.151691	−	0.998368i
$371$	−8.16987	−	3.38407i	−0.424158	−	0.175692i
$372$	9.70747	−	7.53757i	0.503309	−	0.390805i
$373$	4.22344	+	10.1963i	0.218681	+	0.527943i	0.994706	−	0.102759i	$-0.0327670\pi$
$373$	4.22344	+	10.1963i	0.218681	+	0.527943i	−0.776025	+	0.630702i	$0.782767\pi$
$374$	−2.35928	+	3.90495i	−0.121995	+	0.201920i
$375$	−16.5598	+	10.5933i	−0.855144	+	0.547037i
$376$	7.46906	+	21.5915i	0.385187	+	1.11350i
$377$	27.9963	+	27.9963i	1.44188	+	1.44188i
$378$	−2.90879	+	6.74826i	−0.149612	+	0.347093i
$379$	9.44144	+	22.7937i	0.484974	+	1.17083i	0.957219	+	0.289364i	$0.0934438\pi$
$379$	9.44144	+	22.7937i	0.484974	+	1.17083i	−0.472245	+	0.881467i	$0.656556\pi$
$380$	14.8953	−	47.8858i	0.764113	−	2.45649i
$381$	−10.6851	−	7.45204i	−0.547413	−	0.381780i
$382$	1.31057	+	1.78017i	0.0670544	+	0.0910815i
$383$	−17.3845			−0.888305			−0.444152	−	0.895951i	$-0.646495\pi$
$383$	−17.3845			−0.888305			−0.444152	+	0.895951i	$0.646495\pi$
$384$	15.0921	−	12.4992i	0.770164	−	0.637846i
$385$	3.58116			0.182513
$386$	−18.7876	−	25.5197i	−0.956266	−	1.29892i
$387$	13.8512	+	15.0029i	0.704095	+	0.762642i
$388$	−0.422604	+	1.35860i	−0.0214545	+	0.0689723i
$389$	6.73235	+	16.2533i	0.341344	+	0.824076i	0.997580	+	0.0695215i	$0.0221472\pi$
$389$	6.73235	+	16.2533i	0.341344	+	0.824076i	−0.656237	+	0.754555i	$0.727853\pi$
$390$	1.01731	+	39.7048i	0.0515136	+	2.01053i
$391$	−13.6721	−	13.6721i	−0.691430	−	0.691430i
$392$	−0.924664	−	2.67301i	−0.0467026	−	0.135008i
$393$	−9.99702	−	15.6276i	−0.504283	−	0.788310i
$394$	−19.0762	+	31.5739i	−0.961046	+	1.59067i
$395$	20.4665	+	49.4105i	1.02978	+	2.48611i
$396$	2.54663	+	5.35466i	0.127973	+	0.269082i
$397$	−27.7342	−	11.4879i	−1.39194	−	0.576560i	−0.444292	−	0.895882i	$-0.646545\pi$
$397$	−27.7342	−	11.4879i	−1.39194	−	0.576560i	−0.947646	+	0.319322i	$0.896545\pi$
$398$	−4.25258	+	27.9887i	−0.213162	+	1.40295i
$399$	2.57209	−	11.7055i	0.128766	−	0.586006i
$400$	31.9892	−	5.89560i	1.59946	−	0.294780i
$401$	15.1147			0.754793			0.377396	−	0.926052i	$-0.376819\pi$
$401$	15.1147			0.754793			0.377396	+	0.926052i	$0.376819\pi$
$402$	−5.14354	−	1.97775i	−0.256537	−	0.0986411i
$403$	6.07511	−	14.6666i	0.302623	−	0.730596i
$404$	36.6667	−	3.35063i	1.82424	−	0.166700i
$405$	−29.0410	−	14.8429i	−1.44306	−	0.737548i
$406$	6.47110	−	10.7106i	0.321155	−	0.531559i
$407$	−2.64857	−	2.64857i	−0.131285	−	0.131285i
$408$	−4.35743	+	15.3875i	−0.215725	+	0.761794i
$409$	−16.2376	+	16.2376i	−0.802896	+	0.802896i	−0.983547	−	0.180651i	$-0.942180\pi$
$409$	−16.2376	+	16.2376i	−0.802896	+	0.802896i	0.180651	+	0.983547i	$0.442180\pi$
$410$	9.65104	+	39.1133i	0.476631	+	1.93167i
$411$	−0.568041	−	3.18668i	−0.0280194	−	0.157187i
$412$	−2.38554	+	1.25356i	−0.117527	+	0.0617586i
$413$	2.98401	+	1.23602i	0.146834	+	0.0608205i
$414$	−24.6180	+	5.04207i	−1.20991	+	0.247804i
$415$			14.4602i			0.709821i
$416$	8.94576	−	23.6781i	0.438602	−	1.16091i
$417$	1.13262	−	5.15448i	0.0554645	−	0.252416i
$418$	−5.73320	−	7.78753i	−0.280420	−	0.380900i
$419$	0.582085	−	1.40528i	0.0284367	−	0.0686523i	−0.909023	−	0.416745i	$-0.863171\pi$
$419$	0.582085	−	1.40528i	0.0284367	−	0.0686523i	0.937460	+	0.348093i	$0.113171\pi$
$420$	12.1067	−	3.31844i	0.590745	−	0.161923i
$421$	23.5356	−	9.74876i	1.14705	−	0.475125i	0.273510	−	0.961869i	$-0.411815\pi$
$421$	23.5356	−	9.74876i	1.14705	−	0.475125i	0.873545	+	0.486744i	$0.161815\pi$
$422$	13.8931	−	3.42805i	0.676304	−	0.166875i
$423$	−22.7402	+	8.37317i	−1.10567	+	0.407117i
$424$	−18.7090	+	16.6000i	−0.908591	+	0.806170i
$425$	−18.7713	+	18.7713i	−0.910540	+	0.910540i
$426$	12.9459	−	13.6268i	0.627231	−	0.660218i
$427$	−1.23665	+	0.512237i	−0.0598456	+	0.0247889i
$428$	−28.7123	+	2.62375i	−1.38786	+	0.126824i
$429$	6.28198	+	4.38121i	0.303297	+	0.211527i
$430$	5.23975	−	34.4859i	0.252683	−	1.66306i
$431$		−	9.17873i		−	0.442124i	−0.975260	−	0.221062i	$-0.929048\pi$
$431$		−	9.17873i		−	0.442124i	0.975260	−	0.221062i	$-0.0709523\pi$
$432$	13.5711	+	15.7424i	0.652941	+	0.757409i
$433$			8.98199i			0.431647i	0.976432	+	0.215824i	$0.0692436\pi$
$433$			8.98199i			0.431647i	−0.976432	+	0.215824i	$0.930756\pi$
$434$	−4.96054	−	0.753699i	−0.238113	−	0.0361787i
$435$	45.5541	+	31.7706i	2.18415	+	1.52328i
$436$	10.8476	−	13.0295i	0.519505	−	0.623999i
$437$	37.8636	−	15.6836i	1.81126	−	0.750249i
$438$	−10.7191	−	10.1835i	−0.512178	−	0.486588i
$439$	3.95814	−	3.95814i	0.188912	−	0.188912i	−0.606314	−	0.795225i	$-0.707352\pi$
$439$	3.95814	−	3.95814i	0.188912	−	0.188912i	0.795225	+	0.606314i	$0.207352\pi$
$440$	4.42728	−	9.11027i	0.211062	−	0.434315i
$441$	2.81522	−	1.03659i	0.134058	−	0.0493615i
$442$	4.94866	+	20.0557i	0.235384	+	0.953953i
$443$	14.1315	−	5.85347i	0.671409	−	0.278107i	−0.0208216	−	0.999783i	$-0.506628\pi$
$443$	14.1315	−	5.85347i	0.671409	−	0.278107i	0.692230	+	0.721677i	$0.256628\pi$
$444$	−11.4082	−	6.49963i	−0.541408	−	0.308459i
$445$	15.3530	−	37.0655i	0.727803	−	1.75707i
$446$	4.56965	−	3.36419i	0.216379	−	0.159299i
$447$	0.0517155	−	0.235355i	0.00244606	−	0.0111319i
$448$	−7.94312	−	0.952271i	−0.375277	−	0.0449906i
$449$		−	9.01943i		−	0.425653i	−0.977090	−	0.212827i	$-0.931733\pi$
$449$		−	9.01943i		−	0.425653i	0.977090	−	0.212827i	$-0.0682670\pi$
$450$	6.92254	+	33.7994i	0.326332	+	1.59332i
$451$	7.17717	+	2.97288i	0.337960	+	0.139987i
$452$	3.08670	−	9.92318i	0.145186	−	0.466747i
$453$	5.56129	+	31.1985i	0.261292	+	1.46583i
$454$	10.8862	−	2.68613i	0.510916	−	0.126066i
$455$	11.4656	−	11.4656i	0.537513	−	0.537513i
$456$	−26.5982	−	21.0143i	−1.24557	−	0.984087i
$457$	−25.5762	−	25.5762i	−1.19640	−	1.19640i	−0.975236	−	0.221169i	$-0.929013\pi$
$457$	−25.5762	−	25.5762i	−1.19640	−	1.19640i	−0.221169	−	0.975236i	$-0.570987\pi$
$458$	−24.8779	−	15.0306i	−1.16247	−	0.702335i
$459$	−16.4090	−	4.29831i	−0.765908	−	0.200628i
$460$	32.9906	+	27.4660i	1.53819	+	1.28061i
$461$	9.68036	−	23.3705i	0.450860	−	1.08847i	−0.521136	−	0.853473i	$-0.674492\pi$
$461$	9.68036	−	23.3705i	0.450860	−	1.08847i	0.971996	−	0.234998i	$-0.0755083\pi$
$462$	0.868762	−	2.25940i	0.0404185	−	0.105117i
$463$	19.6379			0.912650			0.456325	−	0.889813i	$-0.349166\pi$
$463$	19.6379			0.912650			0.456325	+	0.889813i	$0.349166\pi$
$464$	−19.2471	−	29.7033i	−0.893526	−	1.37894i
$465$	4.77919	−	21.7498i	0.221629	−	1.00862i
$466$	−28.5451	−	4.33711i	−1.32233	−	0.200913i
$467$	19.9742	+	8.27358i	0.924295	+	0.382856i	0.793511	−	0.608555i	$-0.208251\pi$
$467$	19.9742	+	8.27358i	0.924295	+	0.382856i	0.130784	+	0.991411i	$0.458251\pi$
$468$	25.2970	+	8.99024i	1.16935	+	0.415574i
$469$	0.860932	+	2.07847i	0.0397541	+	0.0959750i
$470$	35.4316	+	21.4070i	1.63434	+	0.987429i
$471$	−1.62601	−	2.54182i	−0.0749225	−	0.117121i
$472$	6.83341	−	6.06311i	0.314533	−	0.279077i
$473$	−4.75621	−	4.75621i	−0.218691	−	0.218691i
$474$	36.1387	−	0.925942i	1.65990	−	0.0425299i
$475$	−21.5329	−	51.9850i	−0.987998	−	2.38524i
$476$	5.77955	−	3.03706i	0.264905	−	0.139204i
$477$	−17.9957	−	19.4921i	−0.823968	−	0.892482i
$478$	16.9056	−	12.4460i	0.773244	−	0.569265i
$479$	37.5509			1.71575			0.857873	−	0.513862i	$-0.171786\pi$
$479$	37.5509			1.71575			0.857873	+	0.513862i	$0.171786\pi$
$480$	6.52518	−	34.9012i	0.297833	−	1.59301i
$481$	−16.9595			−0.773285
$482$	−19.4961	+	14.3531i	−0.888023	+	0.653765i
$483$	8.41457	+	5.86853i	0.382876	+	0.267027i
$484$	9.32516	+	17.7459i	0.423871	+	0.806630i
$485$	0.986554	+	2.38175i	0.0447971	+	0.108150i
$486$	−16.4097	+	14.7215i	−0.744357	+	0.667782i
$487$	26.4243	+	26.4243i	1.19740	+	1.19740i	0.974942	+	0.222458i	$0.0714081\pi$
$487$	26.4243	+	26.4243i	1.19740	+	1.19740i	0.222458	+	0.974942i	$0.428592\pi$
$488$	−0.225730	+	3.77922i	−0.0102183	+	0.171077i
$489$	−21.4269	+	13.7068i	−0.968958	+	0.619844i
$490$	−4.38641	−	2.65017i	−0.198158	−	0.119722i
$491$	−1.72521	−	4.16503i	−0.0778577	−	0.187965i	0.880158	−	0.474681i	$-0.157437\pi$
$491$	−1.72521	−	4.16503i	−0.0778577	−	0.187965i	−0.958016	+	0.286716i	$0.907437\pi$
$492$	27.0183	+	3.39964i	1.21808	+	0.153268i
$493$	26.6869	+	11.0541i	1.20192	+	0.497850i
$494$	−43.2883	−	6.57719i	−1.94763	−	0.295922i
$495$	9.75381	+	4.50396i	0.438401	+	0.202438i
$496$	−8.04993	+	11.6875i	−0.361452	+	0.524786i
$497$	−7.67338			−0.344198
$498$	9.12307	+	3.50792i	0.408815	+	0.157194i
$499$	−16.1323	+	38.9469i	−0.722183	+	1.74350i	−0.0551455	+	0.998478i	$0.517562\pi$
$499$	−16.1323	+	38.9469i	−0.722183	+	1.74350i	−0.667037	+	0.745025i	$0.732438\pi$
$500$	14.5236	−	17.4449i	0.649516	−	0.780160i
$501$	4.11263	+	23.0716i	0.183739	+	1.03076i
$502$	−23.5704	−	14.2407i	−1.05200	−	0.635593i
$503$	2.13440	+	2.13440i	0.0951684	+	0.0951684i	0.753088	−	0.657920i	$-0.228563\pi$
$503$	2.13440	+	2.13440i	0.0951684	+	0.0951684i	−0.657920	+	0.753088i	$0.728563\pi$
$504$	0.843342	−	8.44327i	0.0375655	−	0.376093i
$505$	47.1735	−	47.1735i	2.09919	−	2.09919i
$506$	8.03673	−	1.98303i	0.357276	−	0.0881563i
$507$	11.9723	−	2.13413i	0.531710	−	0.0947799i
$508$	14.3635	+	4.46789i	0.637276	+	0.198231i
$509$	−21.6049	−	8.94906i	−0.957622	−	0.396660i	−0.151532	−	0.988452i	$-0.548421\pi$
$509$	−21.6049	−	8.94906i	−0.957622	−	0.396660i	−0.806091	+	0.591792i	$0.798421\pi$
$510$	11.7711	+	26.4784i	0.521232	+	1.17248i
$511$			6.03605i			0.267019i
$512$	−12.2424	+	19.0296i	−0.541041	+	0.840996i
$513$	21.7272	−	28.6466i	0.959279	−	1.26478i
$514$	2.82137	−	2.07710i	0.124445	−	0.0916170i
$515$	−1.86857	+	4.51113i	−0.0823390	+	0.198784i
$516$	−20.4864	−	11.6718i	−0.901864	−	0.513823i
$517$	7.37490	−	3.05478i	0.324348	−	0.134349i
$518$	1.28410	+	5.20413i	0.0564200	+	0.228657i
$519$	0.577696	+	0.903071i	0.0253580	+	0.0396404i
$520$	−14.9932	−	43.3422i	−0.657495	−	1.90068i
$521$	−20.7497	+	20.7497i	−0.909062	+	0.909062i	−0.996197	−	0.0871345i	$-0.972229\pi$
$521$	−20.7497	+	20.7497i	−0.909062	+	0.909062i	0.0871345	+	0.996197i	$0.472229\pi$
$522$	31.0955	−	21.0333i	1.36101	−	0.920603i
$523$	−31.2842	+	12.9583i	−1.36796	+	0.566628i	−0.941235	−	0.337753i	$-0.890333\pi$
$523$	−31.2842	+	12.9583i	−1.36796	+	0.566628i	−0.426726	+	0.904381i	$0.640333\pi$
$524$	16.4629	+	13.7061i	0.719186	+	0.598752i
$525$	8.05724	−	11.5528i	0.351647	−	0.504207i
$526$	4.31187	+	0.655142i	0.188006	+	0.0285655i
$527$		−	11.5820i		−	0.504518i
$528$	−4.67375	−	5.00330i	−0.203399	−	0.217741i
$529$			12.0815i			0.525284i
$530$	−6.80759	+	44.8047i	−0.295703	+	1.94619i
$531$	6.57288	+	7.11942i	0.285239	+	0.308956i
$532$	1.25935	+	13.7813i	0.0545995	+	0.597497i
$533$	32.4967	−	13.4606i	1.40759	−	0.583042i
$534$	−19.6605	−	18.6782i	−0.850793	−	0.808284i
$535$	−36.9398	+	36.9398i	−1.59705	+	1.59705i
$536$	6.35186	+	0.379392i	0.274358	+	0.0163872i
$537$	25.1473	−	16.0868i	1.08519	−	0.694195i
$538$	−34.6019	+	8.53787i	−1.49179	+	0.368094i
$539$	−0.913007	+	0.378180i	−0.0393260	+	0.0162894i
$540$	37.1478	+	6.18808i	1.59859	+	0.266293i
$541$	−8.53807	+	20.6127i	−0.367080	+	0.886210i	0.627145	+	0.778902i	$0.284223\pi$
$541$	−8.53807	+	20.6127i	−0.367080	+	0.886210i	−0.994226	+	0.107308i	$0.965777\pi$
$542$	19.1573	+	26.0217i	0.822876	+	1.11773i
$543$	−28.1386	−	6.18301i	−1.20754	−	0.265338i
$544$	−0.581030	−	18.4575i	−0.0249115	−	0.791357i
$545$		−	30.7190i		−	1.31586i
$546$	−4.45229	−	10.0152i	−0.190540	−	0.428611i
$547$	−6.05859	−	2.50955i	−0.259046	−	0.107301i	0.249381	−	0.968406i	$-0.419773\pi$
$547$	−6.05859	−	2.50955i	−0.259046	−	0.107301i	−0.508427	+	0.861105i	$0.669773\pi$
$548$	1.73865	+	3.30866i	0.0742713	+	0.141339i
$549$	−4.01242	−	0.160160i	−0.171246	−	0.00683545i
$550$	−2.72261	−	11.0341i	−0.116092	−	0.470495i
$551$	−43.2935	+	43.2935i	−1.84436	+	1.84436i
$552$	25.3319	−	14.1511i	1.07820	−	0.602310i
$553$	−10.4358	−	10.4358i	−0.443774	−	0.443774i
$554$	−5.20995	+	8.62321i	−0.221349	+	0.366365i
$555$	−23.4207	+	4.17486i	−0.994155	+	0.177213i
$556$	0.554551	+	6.06859i	0.0235182	+	0.257366i
$557$	−4.79202	+	11.5690i	−0.203044	+	0.490192i	−0.992298	−	0.123875i	$-0.960468\pi$
$557$	−4.79202	+	11.5690i	−0.203044	+	0.490192i	0.789254	+	0.614068i	$0.210468\pi$
$558$	−12.5628	−	8.29158i	−0.531827	−	0.351011i
$559$	−30.4552			−1.28812
$560$	−12.1646	+	7.88245i	−0.514050	+	0.333094i
$561$	5.45748	+	1.19920i	0.230415	+	0.0506301i
$562$	−4.54512	+	29.9141i	−0.191724	+	1.26185i
$563$	−29.5106	−	12.2237i	−1.24373	−	0.515168i	−0.338848	−	0.940841i	$-0.610037\pi$
$563$	−29.5106	−	12.2237i	−1.24373	−	0.515168i	−0.904877	+	0.425673i	$0.860037\pi$
$564$	22.1013	−	17.1610i	0.930634	−	0.722610i
$565$	−7.20578	−	17.3963i	−0.303149	−	0.731868i
$566$	5.02428	−	8.31591i	0.211186	−	0.349544i
$567$	8.97137	+	0.717345i	0.376762	+	0.0301256i
$568$	−9.48637	+	19.5206i	−0.398039	+	0.819068i
$569$	−12.7889	−	12.7889i	−0.536140	−	0.536140i	0.386253	−	0.922393i	$-0.373769\pi$
$569$	−12.7889	−	12.7889i	−0.536140	−	0.536140i	−0.922393	+	0.386253i	$0.873769\pi$
$570$	−61.3995	+	1.57317i	−2.57174	+	0.0658930i
$571$	−1.27051	−	3.06727i	−0.0531690	−	0.128361i	0.895063	−	0.445940i	$-0.147130\pi$
$571$	−1.27051	−	3.06727i	−0.0531690	−	0.128361i	−0.948232	+	0.317578i	$0.897130\pi$
$572$	−8.44459	−	2.62677i	−0.353086	−	0.109831i
$573$	1.54874	−	2.22065i	0.0646995	−	0.0927691i
$574$	−6.59098	−	8.95266i	−0.275102	−	0.373677i
$575$	48.1654			2.00864
$576$	−20.4366	−	12.5836i	−0.851524	−	0.524315i
$577$	−10.9212			−0.454654			−0.227327	−	0.973818i	$-0.572999\pi$
$577$	−10.9212			−0.454654			−0.227327	+	0.973818i	$0.572999\pi$
$578$	−5.31843	−	7.22414i	−0.221218	−	0.300485i
$579$	−22.2020	+	31.8342i	−0.922682	+	1.32298i
$580$	−61.2364	−	19.0482i	−2.54271	−	0.790932i
$581$	−1.52703	−	3.68658i	−0.0633519	−	0.152945i
$582$	1.74200	−	0.0446335i	0.0722084	−	0.00185012i
$583$	6.17936	+	6.17936i	0.255923	+	0.255923i
$584$	15.3554	+	7.46218i	0.635409	+	0.308787i
$585$	45.6481	−	16.8081i	1.88732	−	0.694928i
$586$	1.00058	−	1.65610i	0.0413334	−	0.0684128i
$587$	−7.31821	−	17.6677i	−0.302055	−	0.729225i	−0.999916	−	0.0129917i	$-0.995865\pi$
$587$	−7.31821	−	17.6677i	−0.302055	−	0.729225i	0.697861	−	0.716234i	$-0.254135\pi$
$588$	−2.73613	+	2.12452i	−0.112836	+	0.0876139i
$589$	22.6805	+	9.39456i	0.934532	+	0.387096i
$590$	2.48645	−	16.3648i	0.102365	−	0.673727i
$591$	44.1271	+	9.69625i	1.81515	+	0.398850i
$592$	14.8265	+	3.16704i	0.609366	+	0.130165i
$593$	47.7117			1.95929			0.979643	−	0.200747i	$-0.0643369\pi$
$593$	47.7117			1.95929			0.979643	+	0.200747i	$0.0643369\pi$
$594$	5.20780	−	5.06116i	0.213679	−	0.207662i
$595$	4.52707	−	10.9293i	0.185592	−	0.448058i
$596$	0.0253209	+	0.277093i	0.00103719	+	0.0113502i
$597$	34.1343	−	6.08462i	1.39703	−	0.249027i
$598$	19.3817	−	32.0795i	0.792577	−	1.31183i
$599$	28.3161	+	28.3161i	1.15696	+	1.15696i	0.985125	+	0.171839i	$0.0549710\pi$
$599$	28.3161	+	28.3161i	1.15696	+	1.15696i	0.171839	+	0.985125i	$0.445029\pi$
$600$	−19.4288	−	34.7796i	−0.793178	−	1.41987i
$601$	8.26293	−	8.26293i	0.337052	−	0.337052i	−0.518205	−	0.855257i	$-0.673399\pi$
$601$	8.26293	−	8.26293i	0.337052	−	0.337052i	0.855257	+	0.518205i	$0.173399\pi$
$602$	2.30594	+	9.34541i	0.0939830	+	0.380891i
$603$	−0.269185	+	6.74380i	−0.0109621	+	0.274629i
$604$	−17.0219	−	32.3927i	−0.692610	−	1.31804i
$605$	33.5579	+	13.9002i	1.36432	+	0.565122i
$606$	−18.3184	−	41.2062i	−0.744133	−	1.67389i
$607$		−	35.3706i		−	1.43565i	−0.696224	−	0.717824i	$-0.745138\pi$
$607$		−	35.3706i		−	1.43565i	0.696224	−	0.717824i	$-0.254862\pi$
$608$	36.6158	+	13.8337i	1.48497	+	0.561032i
$609$	−14.9690	−	3.28920i	−0.606573	−	0.133285i
$610$	4.06693	+	5.52420i	0.164665	+	0.223668i
$611$	13.8314	−	33.3920i	0.559559	−	1.35090i
$612$	19.5611	−	1.00304i	0.790711	−	0.0405457i
$613$	−12.8226	+	5.31128i	−0.517899	+	0.214521i	−0.626294	−	0.779587i	$-0.715429\pi$
$613$	−12.8226	+	5.31128i	−0.517899	+	0.214521i	0.108395	+	0.994108i	$0.465429\pi$
$614$	−24.9803	+	6.16377i	−1.00812	+	0.248749i
$615$	41.5638	−	26.5884i	1.67601	−	1.07215i
$616$	−0.166655	+	2.79017i	−0.00671472	+	0.112419i
$617$	−25.5629	+	25.5629i	−1.02913	+	1.02913i	−0.0295625	+	0.999563i	$0.509411\pi$
$617$	−25.5629	+	25.5629i	−1.02913	+	1.02913i	−0.999563	+	0.0295625i	$0.990589\pi$
$618$	2.39282	+	2.27327i	0.0962533	+	0.0914442i
$619$	−0.472404	+	0.195676i	−0.0189875	+	0.00786489i	−0.392157	−	0.919898i	$-0.628271\pi$
$619$	−0.472404	+	0.195676i	−0.0189875	+	0.00786489i	0.373169	+	0.927763i	$0.378271\pi$
$620$	2.33998	+	25.6070i	0.0939759	+	1.02840i
$621$	15.5375	+	26.5666i	0.623500	+	1.06608i
$622$	0.529928	−	3.48776i	0.0212482	−	0.139847i
$623$			11.0711i			0.443552i
$624$	−30.9823	−	1.05511i	−1.24029	−	0.0422382i
$625$		−	0.469150i		−	0.0187660i
$626$	9.44792	+	1.43551i	0.377615	+	0.0573744i
$627$	−6.77511	+	9.71445i	−0.270572	+	0.387958i
$628$	2.67768	+	2.22928i	0.106851	+	0.0889581i
$629$	−11.4313	+	4.73499i	−0.455795	+	0.188796i
$630$	−8.61395	−	12.7348i	−0.343188	−	0.507367i
$631$	−8.71541	+	8.71541i	−0.346955	+	0.346955i	−0.858974	−	0.512019i	$-0.828898\pi$
$631$	−8.71541	+	8.71541i	−0.346955	+	0.346955i	0.512019	+	0.858974i	$0.328898\pi$
$632$	−39.4494	+	13.6466i	−1.56921	+	0.542831i
$633$	−9.44421	−	14.7635i	−0.375374	−	0.586796i
$634$	0.764958	+	3.10019i	0.0303803	+	0.123124i
$635$	25.1806	−	10.4301i	0.999260	−	0.413907i
$636$	26.6163	+	15.1643i	1.05541	+	0.601302i
$637$	−1.71232	+	4.13390i	−0.0678445	+	0.163791i
$638$	−9.95870	+	7.33163i	−0.394269	+	0.290262i
$639$	−20.8996	−	9.65067i	−0.826774	−	0.381775i
$640$	5.01371	+	40.6910i	0.198184	+	1.60845i
$641$			16.9518i			0.669555i	0.942297	+	0.334777i	$0.108661\pi$
$641$			16.9518i			0.669555i	−0.942297	+	0.334777i	$0.891339\pi$
$642$	14.3444	+	32.2670i	0.566129	+	1.27348i
$643$	10.3117	+	4.27126i	0.406656	+	0.168442i	0.576628	−	0.817006i	$-0.304368\pi$
$643$	10.3117	+	4.27126i	0.406656	+	0.168442i	−0.169973	+	0.985449i	$0.554368\pi$
$644$	−11.3113	−	3.51849i	−0.445729	−	0.138648i
$645$	−42.0582	+	7.49708i	−1.65604	+	0.295197i
$646$	−31.0142	+	7.65261i	−1.22024	+	0.301088i
$647$	1.75000	−	1.75000i	0.0687996	−	0.0687996i	−0.671870	−	0.740669i	$-0.734509\pi$
$647$	1.75000	−	1.75000i	0.0687996	−	0.0687996i	0.740669	+	0.671870i	$0.234509\pi$
$648$	12.9159	−	21.9358i	0.507385	−	0.861720i
$649$	−2.25699	−	2.25699i	−0.0885946	−	0.0885946i
$650$	−44.0438	−	26.6102i	−1.72754	−	1.04374i
$651$	1.07840	+	6.04976i	0.0422658	+	0.237109i
$652$	18.7923	−	22.5722i	0.735962	−	0.883994i
$653$	1.64313	−	3.96687i	0.0643007	−	0.155236i	−0.888463	−	0.458948i	$-0.848226\pi$
$653$	1.64313	−	3.96687i	0.0643007	−	0.155236i	0.952764	+	0.303713i	$0.0982263\pi$
$654$	−19.3809	−	7.45218i	−0.757855	−	0.291403i
$655$	38.8138			1.51658
$656$	−30.9233	+	5.69916i	−1.20735	+	0.222515i
$657$	−7.59142	+	16.4400i	−0.296170	+	0.641387i
$658$	−11.2938	−	1.71597i	−0.440279	−	0.0668956i
$659$	−19.7539	−	8.18233i	−0.769502	−	0.318738i	−0.0368314	−	0.999321i	$-0.511726\pi$
$659$	−19.7539	−	8.18233i	−0.769502	−	0.318738i	−0.732671	+	0.680583i	$0.761726\pi$
$660$	−12.3085	−	1.54874i	−0.479106	−	0.0602846i
$661$	5.48126	+	13.2329i	0.213196	+	0.514702i	0.993911	−	0.110186i	$-0.0351447\pi$
$661$	5.48126	+	13.2329i	0.213196	+	0.514702i	−0.780715	+	0.624888i	$0.785145\pi$
$662$	−14.1946	−	8.57606i	−0.551689	−	0.333318i
$663$	21.3122	−	13.6335i	0.827698	−	0.529479i
$664$	−11.2663	−	0.672925i	−0.437215	−	0.0261146i
$665$	17.7303	+	17.7303i	0.687553	+	0.687553i
$666$	−3.04772	+	15.7892i	−0.118097	+	0.611819i
$667$	−20.0562	−	48.4200i	−0.776580	−	1.87483i
$668$	−12.5879	−	23.9548i	−0.487039	−	0.926838i
$669$	−5.70036	−	3.97557i	−0.220389	−	0.153705i
$670$	9.28470	−	6.83542i	0.358699	−	0.264075i
$671$	1.32279			0.0510656
$672$	2.02208	+	9.58703i	0.0780033	+	0.369828i
$673$	−38.0370			−1.46622			−0.733110	−	0.680110i	$-0.761932\pi$
$673$	−38.0370			−1.46622			−0.733110	+	0.680110i	$0.761932\pi$
$674$	13.1662	−	9.69299i	0.507143	−	0.373360i
$675$	36.4748	−	21.3324i	1.40392	−	0.821083i
$676$	−12.4306	+	6.53209i	−0.478100	+	0.251234i
$677$	−14.4691	−	34.9314i	−0.556091	−	1.34252i	−0.912838	−	0.408321i	$-0.866114\pi$
$677$	−14.4691	−	34.9314i	−0.556091	−	1.34252i	0.356748	−	0.934201i	$-0.383886\pi$
$678$	−12.7236	+	0.326003i	−0.488646	+	0.0125201i
$679$	−0.503038	−	0.503038i	−0.0193048	−	0.0193048i
$680$	−22.2068	−	25.0282i	−0.851594	−	0.959786i
$681$	−7.40022	−	11.5682i	−0.283577	−	0.443296i
$682$	4.24397	+	2.56411i	0.162510	+	0.0981848i
$683$	−10.0282	−	24.2103i	−0.383719	−	0.926381i	−0.991240	−	0.132076i	$-0.957836\pi$
$683$	−10.0282	−	24.2103i	−0.383719	−	0.926381i	0.607520	−	0.794304i	$-0.292164\pi$
$684$	−13.9025	+	39.1193i	−0.531576	+	1.49576i
$685$	6.25677	+	2.59164i	0.239059	+	0.0990214i
$686$	1.39817	+	0.212436i	0.0533823	+	0.00811085i
$687$	−7.63992	+	34.7689i	−0.291481	+	1.32652i
$688$	26.6249	+	5.68727i	1.01507	+	0.216825i
$689$	39.5680			1.50742
$690$	18.8689	−	49.0724i	0.718326	−	1.86816i
$691$	1.18418	−	2.85887i	0.0450484	−	0.108757i	−0.899754	−	0.436398i	$-0.856254\pi$
$691$	1.18418	−	2.85887i	0.0450484	−	0.108757i	0.944802	+	0.327642i	$0.106254\pi$
$692$	−0.951340	−	0.792030i	−0.0361645	−	0.0301085i
$693$	−2.96234	−	0.118245i	−0.112530	−	0.00449174i
$694$	7.58687	+	4.58381i	0.287994	+	0.173999i
$695$	7.80753	+	7.80753i	0.296157	+	0.296157i
$696$	−26.8732	+	34.0138i	−1.01863	+	1.28929i
$697$	18.1458	−	18.1458i	0.687321	−	0.687321i
$698$	21.9425	−	5.41421i	0.830535	−	0.204931i
$699$	6.20557	+	34.8129i	0.234716	+	1.31675i
$700$	−4.83074	+	15.5300i	−0.182585	+	0.586978i
$701$	11.2618	+	4.66481i	0.425354	+	0.176187i	0.585083	−	0.810974i	$-0.301062\pi$
$701$	11.2618	+	4.66481i	0.425354	+	0.176187i	−0.159729	+	0.987161i	$0.551062\pi$
$702$	0.469472	−	32.8774i	0.0177191	−	1.24088i
$703$		−	26.2261i		−	0.989137i
$704$	6.89200	+	3.87336i	0.259752	+	0.145983i
$705$	10.8809	−	49.5186i	0.409800	−	1.86498i
$706$	−1.91192	+	1.40756i	−0.0719561	+	0.0529743i
$707$	−7.04511	+	17.0084i	−0.264959	+	0.639667i
$708$	−9.72152	−	5.53869i	−0.365357	−	0.208157i
$709$	39.5539	−	16.3838i	1.48548	−	0.615306i	0.515152	−	0.857099i	$-0.327736\pi$
$709$	39.5539	−	16.3838i	1.48548	−	0.615306i	0.970328	+	0.241793i	$0.0777356\pi$
$710$	9.42068	+	38.1798i	0.353552	+	1.43286i
$711$	−15.2984	−	41.5482i	−0.573736	−	1.55818i
$712$	28.1641	+	13.6868i	1.05549	+	0.512935i
$713$	−14.8591	+	14.8591i	−0.556479	+	0.556479i
$714$	−5.79719	−	5.50754i	−0.216954	−	0.206115i
$715$	−14.8042	+	6.13209i	−0.553645	+	0.229327i
$716$	−22.0552	+	26.4914i	−0.824241	+	0.990030i
$717$	−21.0887	−	14.7078i	−0.787571	−	0.549272i
$718$	−31.0169	−	4.71268i	−1.15754	−	0.175875i
$719$		−	45.1990i		−	1.68564i	−0.538196	−	0.842820i	$-0.680894\pi$
$719$		−	45.1990i		−	1.68564i	0.538196	−	0.842820i	$-0.319106\pi$
$720$	−43.0458	+	6.16973i	−1.60422	+	0.229932i
$721$		−	1.34743i		−	0.0501807i
$722$	6.13469	−	40.3760i	0.228309	−	1.50264i
$723$	24.3202	+	16.9615i	0.904477	+	0.630805i
$724$	33.1287	−	3.02732i	1.23122	−	0.112509i
$725$	−66.4786	+	27.5363i	−2.46895	+	1.02267i
$726$	16.9107	−	17.8000i	0.627613	−	0.660620i
$727$	−11.0717	+	11.0717i	−0.410628	+	0.410628i	−0.881957	−	0.471329i	$-0.843774\pi$
$727$	−11.0717	+	11.0717i	−0.410628	+	0.410628i	0.471329	+	0.881957i	$0.343774\pi$
$728$	8.39952	+	9.46665i	0.311307	+	0.350858i
$729$	23.5326	+	13.2369i	0.871578	+	0.490256i
$730$	30.0330	−	7.41051i	1.11157	−	0.274275i
$731$	−20.5279	+	8.50294i	−0.759252	+	0.314493i
$732$	4.47189	−	1.22575i	0.165286	−	0.0453049i
$733$	11.7736	−	28.4239i	0.434867	−	1.04986i	−0.542830	−	0.839843i	$-0.682647\pi$
$733$	11.7736	−	28.4239i	0.434867	−	1.04986i	0.977697	−	0.210020i	$-0.0673528\pi$
$734$	−7.59307	−	10.3138i	−0.280265	−	0.380690i
$735$	−1.34705	+	6.13037i	−0.0496868	+	0.226122i
$736$	−22.9347	+	24.4256i	−0.845384	+	0.900338i
$737$		−	2.22325i		−	0.0818944i
$738$	−6.69188	−	32.6732i	−0.246331	−	1.20272i
$739$	0.181978	+	0.0753778i	0.00669417	+	0.00277282i	0.386028	−	0.922487i	$-0.373847\pi$
$739$	0.181978	+	0.0753778i	0.00669417	+	0.00277282i	−0.379334	+	0.925260i	$0.623847\pi$
$740$	24.3172	−	12.7783i	0.893920	−	0.469741i
$741$	9.41069	+	52.7934i	0.345710	+	1.93942i
$742$	−2.99592	−	12.1417i	−0.109984	−	0.445737i
$743$	26.2149	−	26.2149i	0.961731	−	0.961731i	−0.0375636	−	0.999294i	$-0.511960\pi$
$743$	26.2149	−	26.2149i	0.961731	−	0.961731i	0.999294	+	0.0375636i	$0.0119597\pi$
$744$	16.7234	+	4.73574i	0.613110	+	0.173621i
$745$	0.356494	+	0.356494i	0.0130609	+	0.0130609i
$746$	−8.07113	+	13.3589i	−0.295505	+	0.489104i
$747$	0.477452	−	11.9614i	0.0174691	−	0.437646i
$748$	−6.42533	+	0.587150i	−0.234933	+	0.0214683i
$749$	5.51676	−	13.3186i	0.201578	−	0.486652i
$750$	−25.9488	−	9.97758i	−0.947515	−	0.364330i
$751$	12.6023			0.459865			0.229933	−	0.973207i	$-0.426149\pi$
$751$	12.6023			0.459865			0.229933	+	0.973207i	$0.426149\pi$
$752$	−18.3275	+	26.6094i	−0.668337	+	0.970346i
$753$	−7.23840	+	32.9416i	−0.263782	+	1.20046i
$754$	−8.41093	+	55.3572i	−0.306308	+	2.01599i
$755$	−61.2557	−	25.3729i	−2.22932	−	0.923415i
$756$	−10.1242	+	2.34527i	−0.368214	+	0.0852967i
$757$	−10.1135	−	24.4162i	−0.367583	−	0.887423i	−0.994145	−	0.108052i	$-0.965539\pi$
$757$	−10.1135	−	24.4162i	−0.367583	−	0.887423i	0.626563	−	0.779371i	$-0.284461\pi$
$758$	−18.0429	+	29.8636i	−0.655348	+	1.08470i
$759$	−5.46320	−	8.54023i	−0.198302	−	0.309991i
$760$	67.0244	−	23.1855i	2.43123	−	0.841026i
$761$	−20.1333	−	20.1333i	−0.729830	−	0.729830i	0.240756	−	0.970586i	$-0.422605\pi$
$761$	−20.1333	−	20.1333i	−0.729830	−	0.729830i	−0.970586	+	0.240756i	$0.922605\pi$
$762$	−0.471878	−	18.4170i	−0.0170943	−	0.667177i
$763$	3.24400	+	7.83171i	0.117441	+	0.283527i
$764$	−0.928551	+	2.98513i	−0.0335938	+	0.107998i
$765$	26.0757	−	24.0739i	0.942769	−	0.870395i
$766$	−14.5758	−	19.7986i	−0.526645	−	0.715353i
$767$	−14.4521			−0.521835
$768$	26.8887	+	6.70811i	0.970262	+	0.242058i
$769$	40.3656			1.45562			0.727810	−	0.685778i	$-0.240538\pi$
$769$	40.3656			1.45562			0.727810	+	0.685778i	$0.240538\pi$
$770$	3.00258	+	4.07847i	0.108206	+	0.146978i
$771$	−3.51948	−	2.45458i	−0.126751	−	0.0883995i
$772$	13.3112	−	42.7933i	0.479082	−	1.54016i
$773$	−13.0211	−	31.4357i	−0.468337	−	1.13066i	−0.964889	−	0.262658i	$-0.915401\pi$
$773$	−13.0211	−	31.4357i	−0.468337	−	1.13066i	0.496552	−	0.868007i	$-0.334599\pi$
$774$	−5.47300	+	28.3537i	−0.196723	+	1.01915i
$775$	20.4010	+	20.4010i	0.732824	+	0.732824i
$776$	−1.90159	+	0.657809i	−0.0682631	+	0.0236140i
$777$	5.53018	−	3.53766i	0.198394	−	0.126913i
$778$	−12.8657	+	21.2947i	−0.461259	+	0.763451i
$779$	20.8154	+	50.2529i	0.745790	+	1.80050i
$780$	−44.3656	+	34.4486i	−1.58854	+	1.23346i
$781$	7.00586	+	2.90192i	0.250689	+	0.103839i
$782$	4.10752	−	27.0340i	0.146885	−	0.966734i
$783$	−36.6334	−	27.7848i	−1.30917	−	0.992947i
$784$	2.26894	−	3.29423i	0.0810334	−	0.117651i
$785$	6.31305			0.225322
$786$	9.41594	−	24.4881i	0.335855	−	0.873461i
$787$	−5.73151	+	13.8371i	−0.204306	+	0.493239i	−0.992508	−	0.122178i	$-0.961012\pi$
$787$	−5.73151	+	13.8371i	−0.204306	+	0.493239i	0.788202	+	0.615417i	$0.211012\pi$
$788$	−51.9528	+	4.74747i	−1.85074	+	0.169122i
$789$	−0.937382	−	5.25866i	−0.0333717	−	0.187213i
$790$	−39.1122	+	64.7363i	−1.39155	+	2.30322i
$791$	3.67419	+	3.67419i	0.130639	+	0.130639i
$792$	−3.96305	+	7.38983i	−0.140821	+	0.262586i
$793$	4.23507	−	4.23507i	0.150392	−	0.150392i
$794$	−10.1702	−	41.2175i	−0.360928	−	1.46275i
$795$	54.6428	−	9.74035i	1.93798	−	0.345455i
$796$	−35.4410	+	18.6237i	−1.25617	+	0.660098i
$797$	−25.6987	−	10.6448i	−0.910296	−	0.377057i	−0.122126	−	0.992515i	$-0.538971\pi$
$797$	−25.6987	−	10.6448i	−0.910296	−	0.377057i	−0.788170	+	0.615457i	$0.788971\pi$
$798$	15.4875	−	6.88503i	0.548252	−	0.243727i
$799$		−	26.3690i		−	0.932869i
$800$	33.5352	+	31.4883i	1.18565	+	1.11328i
$801$	−13.9239	+	30.1536i	−0.491975	+	1.06543i
$802$	12.6728	+	17.2137i	0.447490	+	0.607836i
$803$	2.28271	−	5.51096i	0.0805552	−	0.194477i
$804$	−2.06015	−	7.51604i	−0.0726558	−	0.265070i
$805$	−19.8299	+	8.21380i	−0.698911	+	0.289498i
$806$	21.7969	−	5.37830i	0.767765	−	0.189442i
$807$	23.5217	+	36.7697i	0.828001	+	1.29436i
$808$	34.5587	+	38.9493i	1.21577	+	1.37023i
$809$	18.4526	−	18.4526i	0.648757	−	0.648757i	−0.303935	−	0.952693i	$-0.598301\pi$
$809$	18.4526	−	18.4526i	0.648757	−	0.648757i	0.952693	+	0.303935i	$0.0983006\pi$
$810$	−7.44500	−	45.5187i	−0.261591	−	1.59936i
$811$	−24.2158	+	10.0305i	−0.850333	+	0.352220i	−0.764919	−	0.644126i	$-0.777221\pi$
$811$	−24.2158	+	10.0305i	−0.850333	+	0.352220i	−0.0854138	+	0.996346i	$0.527221\pi$
$812$	17.6236	−	1.61045i	0.618467	−	0.0565158i
$813$	22.6388	−	32.4605i	0.793977	−	1.13844i
$814$	0.795710	−	5.23703i	0.0278896	−	0.183558i
$815$		−	53.2173i		−	1.86412i
$816$	−21.1778	+	7.93891i	−0.741370	+	0.277917i
$817$		−	47.0960i		−	1.64768i
$818$	−32.1067	−	4.87826i	−1.12258	−	0.170564i
$819$	−9.86288	+	9.10573i	−0.344637	+	0.318180i
$820$	−36.4532	+	43.7854i	−1.27300	+	1.52905i
$821$	−35.4541	+	14.6856i	−1.23736	+	0.512530i	−0.902888	−	0.429877i	$-0.858557\pi$
$821$	−35.4541	+	14.6856i	−1.23736	+	0.512530i	−0.334469	+	0.942407i	$0.608557\pi$
$822$	3.15294	−	3.31875i	0.109971	−	0.115755i
$823$	0.0338137	−	0.0338137i	0.00117867	−	0.00117867i	−0.706517	−	0.707696i	$-0.749735\pi$
$823$	0.0338137	−	0.0338137i	0.00117867	−	0.00117867i	0.707696	+	0.706517i	$0.249735\pi$
$824$	−3.42777	−	1.66578i	−0.119412	−	0.0580302i
$825$	−11.7254	+	7.50074i	−0.408225	+	0.261142i
$826$	1.09425	+	4.43473i	0.0380738	+	0.154304i
$827$	−21.8273	+	9.04116i	−0.759009	+	0.314392i	−0.728412	−	0.685140i	$-0.759741\pi$
$827$	−21.8273	+	9.04116i	−0.759009	+	0.314392i	−0.0305977	+	0.999532i	$0.509741\pi$
$828$	−26.3829	−	23.8092i	−0.916869	−	0.827426i
$829$	17.5433	−	42.3533i	0.609304	−	1.47099i	−0.254455	−	0.967085i	$-0.581896\pi$
$829$	17.5433	−	42.3533i	0.609304	−	1.47099i	0.863759	−	0.503905i	$-0.168104\pi$
$830$	−16.4682	+	12.1239i	−0.571620	+	0.420828i
$831$	12.0517	+	2.64816i	0.418067	+	0.0918637i
$832$	34.4667	−	9.66456i	1.19492	−	0.335058i
$833$			3.26447i			0.113107i
$834$	6.81991	−	3.03181i	0.236154	−	0.104983i
$835$	−45.2992	−	18.7635i	−1.56764	−	0.649339i
$836$	4.06203	−	13.0587i	0.140488	−	0.451645i
$837$	−4.67149	+	17.8337i	−0.161470	+	0.616422i
$838$	2.08847	−	0.515320i	0.0721450	−	0.0178014i
$839$	7.35162	−	7.35162i	0.253806	−	0.253806i	−0.568723	−	0.822529i	$-0.692562\pi$
$839$	7.35162	−	7.35162i	0.253806	−	0.253806i	0.822529	+	0.568723i	$0.192562\pi$
$840$	13.9300	+	11.0056i	0.480630	+	0.379729i
$841$	34.8577	+	34.8577i	1.20199	+	1.20199i
$842$	30.8357	+	18.6302i	1.06267	+	0.642039i
$843$	36.4825	−	6.50319i	1.25652	−	0.223982i
$844$	15.5526	+	12.9482i	0.535342	+	0.445694i
$845$	−9.73677	+	23.5066i	−0.334955	+	0.808653i
$846$	−28.6022	−	18.8777i	−0.983364	−	0.649030i
$847$	−10.0234			−0.344408
$848$	−34.5916	−	7.38901i	−1.18788	−	0.253740i
$849$	−11.6222	−	2.55379i	−0.398872	−	0.0876458i
$850$	−37.1165	−	5.63945i	−1.27309	−	0.193432i
$851$	20.7406	+	8.59105i	0.710980	+	0.294497i
$852$	26.3734	+	3.31850i	0.903538	+	0.113690i
$853$	−12.9501	−	31.2644i	−0.443404	−	1.07047i	−0.974746	−	0.223315i	$-0.928312\pi$
$853$	−12.9501	−	31.2644i	−0.443404	−	1.07047i	0.531342	−	0.847157i	$-0.321688\pi$
$854$	−1.62022	−	0.978901i	−0.0554429	−	0.0334973i
$855$	25.9920	+	70.5902i	0.888908	+	2.41414i
$856$	−27.0616	−	30.4997i	−0.924947	−	1.04246i
$857$	0.0339928	+	0.0339928i	0.00116117	+	0.00116117i	0.707687	−	0.706526i	$-0.249739\pi$
$857$	0.0339928	+	0.0339928i	0.00116117	+	0.00116117i	−0.706526	+	0.707687i	$0.749739\pi$
$858$	0.277427	+	10.8277i	0.00947120	+	0.369652i
$859$	−9.52933	−	23.0058i	−0.325137	−	0.784949i	−0.998940	−	0.0460382i	$-0.985340\pi$
$859$	−9.52933	−	23.0058i	−0.325137	−	0.784949i	0.673803	−	0.738911i	$-0.264660\pi$
$860$	43.6681	−	22.9469i	1.48907	−	0.782482i
$861$	−7.78877	+	11.1679i	−0.265441	+	0.380601i
$862$	10.4534	−	7.69580i	0.356043	−	0.262120i
$863$	7.78546			0.265020			0.132510	−	0.991182i	$-0.457696\pi$
$863$	7.78546			0.265020			0.132510	+	0.991182i	$0.457696\pi$
$864$	−6.55002	+	28.6548i	−0.222836	+	0.974856i
$865$	−2.24293			−0.0762619
$866$	−10.2293	+	7.53085i	−0.347606	+	0.255909i
$867$	−6.28496	+	9.01166i	−0.213449	+	0.306052i
$868$	−3.30074	−	6.28133i	−0.112034	−	0.213202i
$869$	5.58133	+	13.4745i	0.189334	+	0.457092i
$870$	2.01178	+	78.5179i	0.0682057	+	2.66200i
$871$	−7.11802	−	7.11802i	−0.241185	−	0.241185i
$872$	23.9339	+	1.42955i	0.810503	+	0.0484108i
$873$	−0.737435	−	2.00276i	−0.0249584	−	0.0677831i
$874$	49.6078	+	29.9719i	1.67801	+	1.01381i
$875$	4.34333	+	10.4857i	0.146831	+	0.354482i
$876$	2.61040	−	20.7459i	0.0881973	−	0.700939i
$877$	43.6551	+	18.0825i	1.47413	+	0.610603i	0.967796	−	0.251736i	$-0.0810015\pi$
$877$	43.6551	+	18.0825i	1.47413	+	0.610603i	0.506331	+	0.862339i	$0.331002\pi$
$878$	7.82645	+	1.18914i	0.264130	+	0.0401316i
$879$	−2.31453	−	0.508583i	−0.0780673	−	0.0171541i
$880$	14.0874	−	2.59631i	0.474886	−	0.0875215i
$881$	6.59425			0.222166			0.111083	−	0.993811i	$-0.464568\pi$
$881$	6.59425			0.222166			0.111083	+	0.993811i	$0.464568\pi$
$882$	3.54093	+	2.33705i	0.119229	+	0.0786925i
$883$	3.08349	−	7.44420i	0.103768	−	0.250517i	−0.863465	−	0.504409i	$-0.831711\pi$
$883$	3.08349	−	7.44420i	0.103768	−	0.250517i	0.967233	+	0.253891i	$0.0817106\pi$
$884$	−18.6917	+	22.4514i	−0.628669	+	0.755121i
$885$	−19.9581	+	3.55763i	−0.670884	+	0.119588i
$886$	18.5147	+	11.1862i	0.622015	+	0.375807i
$887$	−11.0165	−	11.0165i	−0.369898	−	0.369898i	0.497542	−	0.867440i	$-0.334236\pi$
$887$	−11.0165	−	11.0165i	−0.369898	−	0.369898i	−0.867440	+	0.497542i	$0.834236\pi$
$888$	−2.16282	−	18.4419i	−0.0725793	−	0.618871i
$889$	−5.31827	+	5.31827i	−0.178369	+	0.178369i
$890$	55.0852	−	13.5920i	1.84646	−	0.455606i
$891$	−7.91964	−	4.04773i	−0.265318	−	0.135604i
$892$	7.66274	+	2.38357i	0.256568	+	0.0798077i
$893$	51.6374	+	21.3889i	1.72798	+	0.715753i
$894$	0.311398	−	0.138433i	0.0104147	−	0.00462990i
$895$			62.4575i			2.08772i
$896$	−5.57531	−	9.84459i	−0.186258	−	0.328885i
$897$	−44.8338	−	9.85152i	−1.49696	−	0.328933i
$898$	10.2719	−	7.56224i	0.342779	−	0.252355i
$899$	12.0138	−	29.0038i	0.400682	−	0.967332i
$900$	−32.6890	+	36.2226i	−1.08963	+	1.20742i
$901$	26.6703	−	11.0472i	0.888515	−	0.368035i
$902$	2.63189	+	10.6664i	0.0876324	+	0.355153i
$903$	9.93090	−	6.35281i	0.330480	−	0.211408i
$904$	13.8892	−	4.80463i	0.461948	−	0.159800i
$905$	42.6217	−	42.6217i	1.41679	−	1.41679i
$906$	−30.8682	+	32.4916i	−1.02553	+	1.07946i
$907$	11.4597	−	4.74676i	0.380513	−	0.157614i	−0.184224	−	0.982884i	$-0.558977\pi$
$907$	11.4597	−	4.74676i	0.380513	−	0.157614i	0.564738	+	0.825270i	$0.308977\pi$
$908$	12.1866	+	10.1458i	0.404425	+	0.336701i
$909$	−40.5795	+	37.4643i	−1.34594	+	1.24261i
$910$	22.6709	+	3.44460i	0.751533	+	0.114187i
$911$		−	20.2458i		−	0.670774i	−0.942080	−	0.335387i	$-0.891133\pi$
$911$		−	20.2458i		−	0.670774i	0.942080	−	0.335387i	$-0.108867\pi$
$912$	1.63162	−	47.9111i	0.0540285	−	1.58649i
$913$			3.94336i			0.130506i
$914$	7.68386	−	50.5720i	0.254160	−	1.67277i
$915$	4.80603	−	6.89110i	0.158882	−	0.227813i
$916$	−3.74065	−	40.9349i	−0.123595	−	1.35253i
$917$	−9.89548	+	4.09884i	−0.326778	+	0.135356i
$918$	−8.86275	−	22.2916i	−0.292514	−	0.735733i
$919$	21.5980	−	21.5980i	0.712453	−	0.712453i	−0.254595	−	0.967048i	$-0.581942\pi$
$919$	21.5980	−	21.5980i	0.712453	−	0.712453i	0.967048	+	0.254595i	$0.0819420\pi$
$920$	−3.61962	+	60.6005i	−0.119335	+	1.99794i
$921$	16.9811	+	26.5453i	0.559545	+	0.874697i
$922$	34.7323	−	8.57003i	1.14385	−	0.282239i
$923$	31.7210	−	13.1393i	1.04411	−	0.432485i
$924$	3.30156	−	0.904958i	0.108613	−	0.0297709i
$925$	11.7951	−	28.4760i	0.387822	−	0.936285i
$926$	16.4651	+	22.3650i	0.541078	+	0.734958i
$927$	1.69463	−	3.66991i	0.0556590	−	0.120536i
$928$	17.6906	−	46.8244i	0.580723	−	1.53708i
$929$		−	42.1602i		−	1.38323i	−0.722266	−	0.691615i	$-0.756899\pi$
$929$		−	42.1602i		−	1.38323i	0.722266	−	0.691615i	$-0.243101\pi$
$930$	28.7773	−	12.7930i	0.943643	−	0.419500i
$931$	−6.39267	−	2.64793i	−0.209511	−	0.0867824i
$932$	−18.9939	−	36.1455i	−0.622165	−	1.18398i
$933$	−4.25360	+	0.758224i	−0.139256	+	0.0248232i
$934$	7.32460	+	29.6849i	0.239668	+	0.971318i
$935$	−8.26649	+	8.26649i	−0.270343	+	0.270343i
$936$	10.9713	+	36.3477i	0.358607	+	1.18806i
$937$	−31.0132	−	31.0132i	−1.01316	−	1.01316i	−0.999912	−	0.0132456i	$-0.995784\pi$
$937$	−31.0132	−	31.0132i	−1.01316	−	1.01316i	−0.0132456	−	0.999912i	$-0.504216\pi$
$938$	−1.64527	+	2.72316i	−0.0537199	+	0.0889143i
$939$	−2.05394	−	11.5225i	−0.0670276	−	0.376021i
$940$	5.32752	+	58.3004i	0.173764	+	1.90155i
$941$	−20.5184	+	49.5358i	−0.668881	+	1.61482i	0.114604	+	0.993411i	$0.463440\pi$
$941$	−20.5184	+	49.5358i	−0.668881	+	1.61482i	−0.783485	+	0.621411i	$0.786560\pi$
$942$	1.53150	−	3.98297i	0.0498988	−	0.129772i
$943$	−46.5605			−1.51622
$944$	12.6345	+	2.69881i	0.411217	+	0.0878388i
$945$	−11.3789	+	15.0028i	−0.370157	+	0.488040i
$946$	1.42891	−	9.40449i	0.0464579	−	0.305766i
$947$	−35.7872	−	14.8235i	−1.16293	−	0.481700i	−0.284078	−	0.958801i	$-0.591688\pi$
$947$	−35.7872	−	14.8235i	−1.16293	−	0.481700i	−0.878848	+	0.477101i	$0.841688\pi$
$948$	31.3546	+	40.3808i	1.01835	+	1.31151i
$949$	−10.3356	−	24.9524i	−0.335509	−	0.809990i
$950$	41.1501	−	68.1094i	1.33509	−	2.20976i
$951$	3.29442	−	2.10744i	0.106829	−	0.0683385i
$952$	8.30461	+	4.03576i	0.269154	+	0.130800i
$953$	−12.2847	−	12.2847i	−0.397939	−	0.397939i	0.479566	−	0.877506i	$-0.340794\pi$
$953$	−12.2847	−	12.2847i	−0.397939	−	0.397939i	−0.877506	+	0.479566i	$0.840794\pi$
$954$	7.11062	−	36.8377i	0.230215	−	1.19266i
$955$	2.16767	+	5.23321i	0.0701441	+	0.169343i
$956$	28.3486	+	8.81809i	0.916859	+	0.285197i
$957$	12.4229	+	8.66402i	0.401574	+	0.280068i
$958$	31.4841	+	42.7656i	1.01721	+	1.38169i
$959$	−1.86883			−0.0603477
$960$	45.2188	−	21.8311i	1.45943	−	0.704597i
$961$	18.4125			0.593952
$962$	−14.2195	−	19.3146i	−0.458454	−	0.622728i
$963$	31.7763	−	29.3369i	1.02398	−	0.945368i
$964$	−32.6926	−	10.1693i	−1.05296	−	0.327532i
$965$	−31.0746	−	75.0208i	−1.00033	−	2.41500i
$966$	0.371607	+	14.5035i	0.0119563	+	0.466642i
$967$	4.53023	+	4.53023i	0.145682	+	0.145682i	0.776186	−	0.630504i	$-0.217152\pi$
$967$	4.53023	+	4.53023i	0.145682	+	0.145682i	−0.630504	+	0.776186i	$0.717152\pi$
$968$	−12.3916	+	25.4989i	−0.398282	+	0.819567i
$969$	21.0828	+	32.9572i	0.677277	+	1.05874i
$970$	−1.88534	+	3.12051i	−0.0605345	+	0.100193i
$971$	−2.84384	−	6.86563i	−0.0912631	−	0.220329i	0.871656	−	0.490117i	$-0.163046\pi$
$971$	−2.84384	−	6.86563i	−0.0912631	−	0.220329i	−0.962920	+	0.269789i	$0.913046\pi$
$972$	−30.5244	−	6.34535i	−0.979069	−	0.203527i
$973$	−2.81500	−	1.16601i	−0.0902449	−	0.0373807i
$974$	−7.93867	+	52.2490i	−0.254371	+	1.67417i
$975$	−13.5257	+	61.5548i	−0.433170	+	1.97133i
$976$	−4.49330	+	2.91157i	−0.143827	+	0.0931970i
$977$	3.95302			0.126468			0.0632341	−	0.997999i	$-0.479859\pi$
$977$	3.95302			0.126468			0.0632341	+	0.997999i	$0.479859\pi$
$978$	−33.5754	−	12.9101i	−1.07362	−	0.412820i
$979$	4.18685	−	10.1080i	0.133812	−	0.323052i
$980$	−0.659543	−	7.21754i	−0.0210683	−	0.230556i
$981$	−1.01429	+	25.4107i	−0.0323839	+	0.811302i
$982$	3.29694	−	5.45691i	0.105210	−	0.174137i
$983$	42.3045	+	42.3045i	1.34930	+	1.34930i	0.886418	+	0.462885i	$0.153186\pi$
$983$	42.3045	+	42.3045i	1.34930	+	1.34930i	0.462885	+	0.886418i	$0.346814\pi$
$984$	18.7814	+	33.6207i	0.598731	+	1.07179i
$985$	−66.8397	+	66.8397i	−2.12969	+	2.12969i
$986$	9.78617	+	39.6610i	0.311655	+	1.26306i
$987$	2.45523	+	13.7737i	0.0781508	+	0.438421i
$988$	−28.8040	−	54.8143i	−0.916379	−	1.74387i
$989$	37.2453	+	15.4275i	1.18433	+	0.490567i
$990$	3.04855	+	14.8846i	0.0968893	+	0.473064i
$991$			1.95693i			0.0621639i	0.999517	+	0.0310819i	$0.00989528\pi$
$991$			1.95693i			0.0621639i	−0.999517	+	0.0310819i	$0.990105\pi$
$992$	−20.0599	+	0.631475i	−0.636904	+	0.0200493i
$993$	−4.35912	+	19.8381i	−0.138333	+	0.629544i
$994$	−6.43366	−	8.73897i	−0.204063	−	0.277183i
$995$	−27.7606	+	67.0199i	−0.880069	+	2.12467i
$996$	3.65407	+	13.3312i	0.115784	+	0.422414i
$997$	−16.0593	+	6.65197i	−0.508602	+	0.210670i	−0.622202	−	0.782857i	$-0.713762\pi$
$997$	−16.0593	+	6.65197i	−0.508602	+	0.210670i	0.113600	+	0.993527i	$0.463762\pi$
$998$	−57.8814	+	14.2820i	−1.83220	+	0.452088i
$999$	19.5115	−	2.68013i	0.617316	−	0.0847955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bs.a.659.34	yes	192
3.2	odd	2	inner	672.2.bs.a.659.15	yes	192
32.27	odd	8	inner	672.2.bs.a.155.15	✓	192
96.59	even	8	inner	672.2.bs.a.155.34	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.bs.a.155.15	✓	192	32.27	odd	8	inner
672.2.bs.a.155.34	yes	192	96.59	even	8	inner
672.2.bs.a.659.15	yes	192	3.2	odd	2	inner
672.2.bs.a.659.34	yes	192	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bs (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.838438 + 1.13887i) q^{2} +(0.990810 - 1.42067i) q^{3} +(-0.594043 + 1.90974i) q^{4} +(1.38677 + 3.34796i) q^{5} +(2.44869 - 0.0627400i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-2.67301 + 0.924664i) q^{8} +(-1.03659 - 2.81522i) q^{9} +O(q^{10})\)	\(q+(0.838438 + 1.13887i) q^{2} +(0.990810 - 1.42067i) q^{3} +(-0.594043 + 1.90974i) q^{4} +(1.38677 + 3.34796i) q^{5} +(2.44869 - 0.0627400i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-2.67301 + 0.924664i) q^{8} +(-1.03659 - 2.81522i) q^{9} +(-2.65017 + 4.38641i) q^{10} +(0.378180 + 0.913007i) q^{11} +(2.12452 + 2.73613i) q^{12} +(4.13390 + 1.71232i) q^{13} +(0.212436 - 1.39817i) q^{14} +(6.13037 + 1.34705i) q^{15} +(-3.29423 - 2.26894i) q^{16} +3.26447 q^{17} +(2.33705 - 3.54093i) q^{18} +(-2.64793 + 6.39267i) q^{19} +(-7.21754 + 0.659543i) q^{20} +(-1.70517 + 0.303955i) q^{21} +(-0.722715 + 1.19620i) q^{22} +(-4.18817 - 4.18817i) q^{23} +(-1.33481 + 4.71363i) q^{24} +(-5.75018 + 5.75018i) q^{25} +(1.51592 + 6.14364i) q^{26} +(-5.02656 - 1.31670i) q^{27} +(1.77044 - 0.930340i) q^{28} +(8.17496 + 3.38618i) q^{29} +(3.60582 + 8.11110i) q^{30} -3.54789i q^{31} +(-0.177986 - 5.65405i) q^{32} +(1.67178 + 0.367349i) q^{33} +(2.73705 + 3.71780i) q^{34} +(1.38677 - 3.34796i) q^{35} +(5.99213 - 0.307261i) q^{36} +(-3.50173 + 1.45046i) q^{37} +(-9.50054 + 2.34421i) q^{38} +(6.52855 - 4.17632i) q^{39} +(-6.80260 - 7.66684i) q^{40} +(5.55858 - 5.55858i) q^{41} +(-1.77585 - 1.68712i) q^{42} +(-6.28829 + 2.60469i) q^{43} +(-1.96826 + 0.179861i) q^{44} +(7.98774 - 7.37454i) q^{45} +(1.25825 - 8.28130i) q^{46} -8.07759i q^{47} +(-6.48736 + 2.43192i) q^{48} +1.00000i q^{49} +(-11.3699 - 1.72753i) q^{50} +(3.23447 - 4.63772i) q^{51} +(-5.72580 + 6.87750i) q^{52} +(8.16987 - 3.38407i) q^{53} +(-2.71492 - 6.82856i) q^{54} +(-2.53226 + 2.53226i) q^{55} +(2.54394 + 1.23627i) q^{56} +(6.45826 + 10.0957i) q^{57} +(2.99779 + 12.1493i) q^{58} +(-2.98401 + 1.23602i) q^{59} +(-6.21422 + 10.9072i) q^{60} +(0.512237 - 1.23665i) q^{61} +(4.04058 - 2.97468i) q^{62} +(-1.25768 + 2.72364i) q^{63} +(6.28999 - 4.94328i) q^{64} +16.2147i q^{65} +(0.983326 + 2.21194i) q^{66} +(-2.07847 - 0.860932i) q^{67} +(-1.93923 + 6.23429i) q^{68} +(-10.0997 + 1.80032i) q^{69} +(4.97561 - 1.22771i) q^{70} +(5.42590 - 5.42590i) q^{71} +(5.37396 + 6.56663i) q^{72} +(-4.26813 - 4.26813i) q^{73} +(-4.58787 - 2.77189i) q^{74} +(2.47176 + 13.8664i) q^{75} +(-10.6354 - 8.85438i) q^{76} +(0.378180 - 0.913007i) q^{77} +(10.2301 + 3.93357i) q^{78} +14.7584 q^{79} +(3.02797 - 14.1754i) q^{80} +(-6.85095 + 5.83647i) q^{81} +(10.9910 + 1.66996i) q^{82} +(3.68658 + 1.52703i) q^{83} +(0.432469 - 3.43700i) q^{84} +(4.52707 + 10.9293i) q^{85} +(-8.23875 - 4.97766i) q^{86} +(12.9105 - 8.25884i) q^{87} +(-1.85511 - 2.09079i) q^{88} +(-7.82842 - 7.82842i) q^{89} +(15.0959 + 2.91389i) q^{90} +(-1.71232 - 4.13390i) q^{91} +(10.4863 - 5.51037i) q^{92} +(-5.04037 - 3.51528i) q^{93} +(9.19932 - 6.77256i) q^{94} -25.0745 q^{95} +(-8.20888 - 5.34923i) q^{96} +0.711404 q^{97} +(-1.13887 + 0.838438i) q^{98} +(2.17830 - 2.01108i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 16 q^{4}+O(q^{10}) \) 192 * q - 16 * q^4	\( 192 q - 16 q^{4} + 8 q^{10} + 16 q^{16} + 16 q^{22} + 24 q^{27} - 84 q^{30} + 40 q^{36} + 32 q^{37} + 24 q^{39} - 96 q^{46} - 72 q^{48} + 16 q^{52} - 32 q^{55} - 72 q^{58} - 28 q^{60} - 16 q^{61} - 64 q^{64} - 12 q^{66} - 32 q^{67} + 56 q^{69} - 24 q^{70} + 60 q^{72} + 80 q^{75} - 56 q^{76} + 100 q^{78} - 32 q^{79} - 120 q^{82} - 56 q^{87} + 40 q^{88} + 60 q^{90} - 80 q^{93} + 216 q^{94} + 96 q^{96} - 64 q^{99}+O(q^{100}) \) 192 * q - 16 * q^4 + 8 * q^10 + 16 * q^16 + 16 * q^22 + 24 * q^27 - 84 * q^30 + 40 * q^36 + 32 * q^37 + 24 * q^39 - 96 * q^46 - 72 * q^48 + 16 * q^52 - 32 * q^55 - 72 * q^58 - 28 * q^60 - 16 * q^61 - 64 * q^64 - 12 * q^66 - 32 * q^67 + 56 * q^69 - 24 * q^70 + 60 * q^72 + 80 * q^75 - 56 * q^76 + 100 * q^78 - 32 * q^79 - 120 * q^82 - 56 * q^87 + 40 * q^88 + 60 * q^90 - 80 * q^93 + 216 * q^94 + 96 * q^96 - 64 * q^99

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