Properties

Label 546.2.i.i.235.1
Level 546546
Weight 22
Character 546.235
Analytic conductor 4.3604.360
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [546,2,Mod(79,546)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(546, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("546.79"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 546=23713 546 = 2 \cdot 3 \cdot 7 \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 546.i (of order 33, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,-2,2,-2,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 4.359831950364.35983195036
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q(2,3)\Q(\sqrt{2}, \sqrt{-3})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x4+2x2+4 x^{4} + 2x^{2} + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 235.1
Root 0.707107+1.22474i-0.707107 + 1.22474i of defining polynomial
Character χ\chi == 546.235
Dual form 546.2.i.i.79.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(0.5000000.866025i)q2+(0.5000000.866025i)q3+(0.500000+0.866025i)q4+(0.292893+0.507306i)q51.00000q6+(1.621322.09077i)q7+1.00000q8+(0.5000000.866025i)q9+(0.2928930.507306i)q10+(0.2071070.358719i)q11+(0.500000+0.866025i)q12+1.00000q13+(2.621320.358719i)q14+0.585786q15+(0.5000000.866025i)q16+(1.207112.09077i)q17+(0.500000+0.866025i)q18+(1.08579+1.88064i)q190.585786q20+(1.000002.44949i)q210.414214q22+(0.7071071.22474i)q23+(0.5000000.866025i)q24+(2.328434.03295i)q25+(0.5000000.866025i)q261.00000q27+(1.00000+2.44949i)q281.82843q29+(0.2928930.507306i)q30+(4.242647.34847i)q31+(0.500000+0.866025i)q32+(0.2071070.358719i)q332.41421q34+(1.53553+0.210133i)q35+1.00000q36+(0.7071071.22474i)q37+(1.085791.88064i)q38+(0.5000000.866025i)q39+(0.292893+0.507306i)q409.89949q41+(1.62132+2.09077i)q42+6.48528q43+(0.207107+0.358719i)q44+(0.2928930.507306i)q45+(0.707107+1.22474i)q46+(0.5000000.866025i)q471.00000q48+(1.742646.77962i)q494.65685q50+(1.207112.09077i)q51+(0.500000+0.866025i)q52+(4.74264+8.21449i)q53+(0.500000+0.866025i)q54+0.242641q55+(1.621322.09077i)q56+2.17157q57+(0.914214+1.58346i)q58+(1.03553+1.79360i)q59+(0.292893+0.507306i)q60+(2.20711+3.82282i)q618.48528q62+(2.621320.358719i)q63+1.00000q64+(0.292893+0.507306i)q65+(0.207107+0.358719i)q66+(0.914214+1.58346i)q67+(1.20711+2.09077i)q681.41421q69+(0.5857861.43488i)q705.00000q71+(0.5000000.866025i)q72+(0.707107+1.22474i)q73+(0.707107+1.22474i)q74+(2.328434.03295i)q752.17157q76+(0.4142141.01461i)q771.00000q78+(5.82843+10.0951i)q79+(0.2928930.507306i)q80+(0.500000+0.866025i)q81+(4.94975+8.57321i)q82+7.65685q83+(2.62132+0.358719i)q84+1.41421q85+(3.242645.61642i)q86+(0.914214+1.58346i)q87+(0.2071070.358719i)q88+(1.292892.23936i)q890.585786q90+(1.621322.09077i)q91+1.41421q92+(4.242647.34847i)q93+(0.500000+0.866025i)q94+(0.636039+1.10165i)q95+(0.500000+0.866025i)q960.928932q97+(5.00000+4.89898i)q980.414214q99+O(q100)q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.292893 + 0.507306i) q^{5} -1.00000 q^{6} +(1.62132 - 2.09077i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.292893 - 0.507306i) q^{10} +(0.207107 - 0.358719i) q^{11} +(0.500000 + 0.866025i) q^{12} +1.00000 q^{13} +(-2.62132 - 0.358719i) q^{14} +0.585786 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.20711 - 2.09077i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(1.08579 + 1.88064i) q^{19} -0.585786 q^{20} +(-1.00000 - 2.44949i) q^{21} -0.414214 q^{22} +(-0.707107 - 1.22474i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.32843 - 4.03295i) q^{25} +(-0.500000 - 0.866025i) q^{26} -1.00000 q^{27} +(1.00000 + 2.44949i) q^{28} -1.82843 q^{29} +(-0.292893 - 0.507306i) q^{30} +(4.24264 - 7.34847i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.207107 - 0.358719i) q^{33} -2.41421 q^{34} +(1.53553 + 0.210133i) q^{35} +1.00000 q^{36} +(-0.707107 - 1.22474i) q^{37} +(1.08579 - 1.88064i) q^{38} +(0.500000 - 0.866025i) q^{39} +(0.292893 + 0.507306i) q^{40} -9.89949 q^{41} +(-1.62132 + 2.09077i) q^{42} +6.48528 q^{43} +(0.207107 + 0.358719i) q^{44} +(0.292893 - 0.507306i) q^{45} +(-0.707107 + 1.22474i) q^{46} +(-0.500000 - 0.866025i) q^{47} -1.00000 q^{48} +(-1.74264 - 6.77962i) q^{49} -4.65685 q^{50} +(-1.20711 - 2.09077i) q^{51} +(-0.500000 + 0.866025i) q^{52} +(-4.74264 + 8.21449i) q^{53} +(0.500000 + 0.866025i) q^{54} +0.242641 q^{55} +(1.62132 - 2.09077i) q^{56} +2.17157 q^{57} +(0.914214 + 1.58346i) q^{58} +(-1.03553 + 1.79360i) q^{59} +(-0.292893 + 0.507306i) q^{60} +(2.20711 + 3.82282i) q^{61} -8.48528 q^{62} +(-2.62132 - 0.358719i) q^{63} +1.00000 q^{64} +(0.292893 + 0.507306i) q^{65} +(-0.207107 + 0.358719i) q^{66} +(-0.914214 + 1.58346i) q^{67} +(1.20711 + 2.09077i) q^{68} -1.41421 q^{69} +(-0.585786 - 1.43488i) q^{70} -5.00000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-0.707107 + 1.22474i) q^{73} +(-0.707107 + 1.22474i) q^{74} +(-2.32843 - 4.03295i) q^{75} -2.17157 q^{76} +(-0.414214 - 1.01461i) q^{77} -1.00000 q^{78} +(5.82843 + 10.0951i) q^{79} +(0.292893 - 0.507306i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.94975 + 8.57321i) q^{82} +7.65685 q^{83} +(2.62132 + 0.358719i) q^{84} +1.41421 q^{85} +(-3.24264 - 5.61642i) q^{86} +(-0.914214 + 1.58346i) q^{87} +(0.207107 - 0.358719i) q^{88} +(-1.29289 - 2.23936i) q^{89} -0.585786 q^{90} +(1.62132 - 2.09077i) q^{91} +1.41421 q^{92} +(-4.24264 - 7.34847i) q^{93} +(-0.500000 + 0.866025i) q^{94} +(-0.636039 + 1.10165i) q^{95} +(0.500000 + 0.866025i) q^{96} -0.928932 q^{97} +(-5.00000 + 4.89898i) q^{98} -0.414214 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q2q2+2q32q4+4q54q62q7+4q82q9+4q102q11+2q12+4q132q14+8q152q16+2q172q18+10q198q20++4q99+O(q100) 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} + 4 q^{10} - 2 q^{11} + 2 q^{12} + 4 q^{13} - 2 q^{14} + 8 q^{15} - 2 q^{16} + 2 q^{17} - 2 q^{18} + 10 q^{19} - 8 q^{20}+ \cdots + 4 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/546Z)×\left(\mathbb{Z}/546\mathbb{Z}\right)^\times.

nn 157157 365365 379379
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\right) 11 11

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.500000 0.866025i −0.353553 0.612372i
33 0.500000 0.866025i 0.288675 0.500000i
44 −0.500000 + 0.866025i −0.250000 + 0.433013i
55 0.292893 + 0.507306i 0.130986 + 0.226874i 0.924057 0.382255i 0.124852π-0.124852\pi
−0.793071 + 0.609129i 0.791519π0.791519\pi
66 −1.00000 −0.408248
77 1.62132 2.09077i 0.612801 0.790237i
88 1.00000 0.353553
99 −0.500000 0.866025i −0.166667 0.288675i
1010 0.292893 0.507306i 0.0926210 0.160424i
1111 0.207107 0.358719i 0.0624450 0.108158i −0.833113 0.553103i 0.813444π-0.813444\pi
0.895558 + 0.444945i 0.146777π0.146777\pi
1212 0.500000 + 0.866025i 0.144338 + 0.250000i
1313 1.00000 0.277350
1414 −2.62132 0.358719i −0.700577 0.0958718i
1515 0.585786 0.151249
1616 −0.500000 0.866025i −0.125000 0.216506i
1717 1.20711 2.09077i 0.292766 0.507086i −0.681696 0.731635i 0.738758π-0.738758\pi
0.974463 + 0.224549i 0.0720908π0.0720908\pi
1818 −0.500000 + 0.866025i −0.117851 + 0.204124i
1919 1.08579 + 1.88064i 0.249096 + 0.431448i 0.963275 0.268515i 0.0865330π-0.0865330\pi
−0.714179 + 0.699963i 0.753200π0.753200\pi
2020 −0.585786 −0.130986
2121 −1.00000 2.44949i −0.218218 0.534522i
2222 −0.414214 −0.0883106
2323 −0.707107 1.22474i −0.147442 0.255377i 0.782839 0.622224i 0.213771π-0.213771\pi
−0.930281 + 0.366847i 0.880437π0.880437\pi
2424 0.500000 0.866025i 0.102062 0.176777i
2525 2.32843 4.03295i 0.465685 0.806591i
2626 −0.500000 0.866025i −0.0980581 0.169842i
2727 −1.00000 −0.192450
2828 1.00000 + 2.44949i 0.188982 + 0.462910i
2929 −1.82843 −0.339530 −0.169765 0.985485i 0.554301π-0.554301\pi
−0.169765 + 0.985485i 0.554301π0.554301\pi
3030 −0.292893 0.507306i −0.0534747 0.0926210i
3131 4.24264 7.34847i 0.762001 1.31982i −0.179817 0.983700i 0.557551π-0.557551\pi
0.941818 0.336124i 0.109116π-0.109116\pi
3232 −0.500000 + 0.866025i −0.0883883 + 0.153093i
3333 −0.207107 0.358719i −0.0360527 0.0624450i
3434 −2.41421 −0.414034
3535 1.53553 + 0.210133i 0.259553 + 0.0355190i
3636 1.00000 0.166667
3737 −0.707107 1.22474i −0.116248 0.201347i 0.802030 0.597284i 0.203753π-0.203753\pi
−0.918278 + 0.395937i 0.870420π0.870420\pi
3838 1.08579 1.88064i 0.176138 0.305080i
3939 0.500000 0.866025i 0.0800641 0.138675i
4040 0.292893 + 0.507306i 0.0463105 + 0.0802121i
4141 −9.89949 −1.54604 −0.773021 0.634381i 0.781255π-0.781255\pi
−0.773021 + 0.634381i 0.781255π0.781255\pi
4242 −1.62132 + 2.09077i −0.250175 + 0.322613i
4343 6.48528 0.988996 0.494498 0.869179i 0.335352π-0.335352\pi
0.494498 + 0.869179i 0.335352π0.335352\pi
4444 0.207107 + 0.358719i 0.0312225 + 0.0540790i
4545 0.292893 0.507306i 0.0436619 0.0756247i
4646 −0.707107 + 1.22474i −0.104257 + 0.180579i
4747 −0.500000 0.866025i −0.0729325 0.126323i 0.827253 0.561830i 0.189902π-0.189902\pi
−0.900185 + 0.435507i 0.856569π0.856569\pi
4848 −1.00000 −0.144338
4949 −1.74264 6.77962i −0.248949 0.968517i
5050 −4.65685 −0.658579
5151 −1.20711 2.09077i −0.169029 0.292766i
5252 −0.500000 + 0.866025i −0.0693375 + 0.120096i
5353 −4.74264 + 8.21449i −0.651452 + 1.12835i 0.331319 + 0.943519i 0.392506π0.392506\pi
−0.982771 + 0.184829i 0.940827π0.940827\pi
5454 0.500000 + 0.866025i 0.0680414 + 0.117851i
5555 0.242641 0.0327177
5656 1.62132 2.09077i 0.216658 0.279391i
5757 2.17157 0.287632
5858 0.914214 + 1.58346i 0.120042 + 0.207919i
5959 −1.03553 + 1.79360i −0.134815 + 0.233506i −0.925527 0.378682i 0.876377π-0.876377\pi
0.790712 + 0.612189i 0.209711π0.209711\pi
6060 −0.292893 + 0.507306i −0.0378124 + 0.0654929i
6161 2.20711 + 3.82282i 0.282591 + 0.489462i 0.972022 0.234889i 0.0754727π-0.0754727\pi
−0.689431 + 0.724351i 0.742139π0.742139\pi
6262 −8.48528 −1.07763
6363 −2.62132 0.358719i −0.330255 0.0451944i
6464 1.00000 0.125000
6565 0.292893 + 0.507306i 0.0363289 + 0.0629236i
6666 −0.207107 + 0.358719i −0.0254931 + 0.0441553i
6767 −0.914214 + 1.58346i −0.111689 + 0.193451i −0.916451 0.400146i 0.868959π-0.868959\pi
0.804762 + 0.593597i 0.202293π0.202293\pi
6868 1.20711 + 2.09077i 0.146383 + 0.253543i
6969 −1.41421 −0.170251
7070 −0.585786 1.43488i −0.0700149 0.171501i
7171 −5.00000 −0.593391 −0.296695 0.954972i 0.595885π-0.595885\pi
−0.296695 + 0.954972i 0.595885π0.595885\pi
7272 −0.500000 0.866025i −0.0589256 0.102062i
7373 −0.707107 + 1.22474i −0.0827606 + 0.143346i −0.904435 0.426612i 0.859707π-0.859707\pi
0.821674 + 0.569958i 0.193040π0.193040\pi
7474 −0.707107 + 1.22474i −0.0821995 + 0.142374i
7575 −2.32843 4.03295i −0.268864 0.465685i
7676 −2.17157 −0.249096
7777 −0.414214 1.01461i −0.0472040 0.115626i
7878 −1.00000 −0.113228
7979 5.82843 + 10.0951i 0.655749 + 1.13579i 0.981705 + 0.190406i 0.0609805π0.0609805\pi
−0.325956 + 0.945385i 0.605686π0.605686\pi
8080 0.292893 0.507306i 0.0327465 0.0567185i
8181 −0.500000 + 0.866025i −0.0555556 + 0.0962250i
8282 4.94975 + 8.57321i 0.546608 + 0.946753i
8383 7.65685 0.840449 0.420224 0.907420i 0.361951π-0.361951\pi
0.420224 + 0.907420i 0.361951π0.361951\pi
8484 2.62132 + 0.358719i 0.286009 + 0.0391395i
8585 1.41421 0.153393
8686 −3.24264 5.61642i −0.349663 0.605634i
8787 −0.914214 + 1.58346i −0.0980140 + 0.169765i
8888 0.207107 0.358719i 0.0220777 0.0382396i
8989 −1.29289 2.23936i −0.137046 0.237371i 0.789331 0.613968i 0.210428π-0.210428\pi
−0.926377 + 0.376597i 0.877094π0.877094\pi
9090 −0.585786 −0.0617473
9191 1.62132 2.09077i 0.169961 0.219172i
9292 1.41421 0.147442
9393 −4.24264 7.34847i −0.439941 0.762001i
9494 −0.500000 + 0.866025i −0.0515711 + 0.0893237i
9595 −0.636039 + 1.10165i −0.0652562 + 0.113027i
9696 0.500000 + 0.866025i 0.0510310 + 0.0883883i
9797 −0.928932 −0.0943188 −0.0471594 0.998887i 0.515017π-0.515017\pi
−0.0471594 + 0.998887i 0.515017π0.515017\pi
9898 −5.00000 + 4.89898i −0.505076 + 0.494872i
9999 −0.414214 −0.0416300
100100 2.32843 + 4.03295i 0.232843 + 0.403295i
101101 7.41421 12.8418i 0.737742 1.27781i −0.215768 0.976445i 0.569226π-0.569226\pi
0.953510 0.301362i 0.0974412π-0.0974412\pi
102102 −1.20711 + 2.09077i −0.119521 + 0.207017i
103103 8.41421 + 14.5738i 0.829077 + 1.43600i 0.898763 + 0.438435i 0.144467π0.144467\pi
−0.0696860 + 0.997569i 0.522200π0.522200\pi
104104 1.00000 0.0980581
105105 0.949747 1.22474i 0.0926859 0.119523i
106106 9.48528 0.921292
107107 9.65685 + 16.7262i 0.933563 + 1.61698i 0.777176 + 0.629283i 0.216651π0.216651\pi
0.156387 + 0.987696i 0.450015π0.450015\pi
108108 0.500000 0.866025i 0.0481125 0.0833333i
109109 4.82843 8.36308i 0.462479 0.801038i −0.536604 0.843834i 0.680293π-0.680293\pi
0.999084 + 0.0427961i 0.0136266π0.0136266\pi
110110 −0.121320 0.210133i −0.0115674 0.0200354i
111111 −1.41421 −0.134231
112112 −2.62132 0.358719i −0.247691 0.0338958i
113113 4.89949 0.460906 0.230453 0.973083i 0.425979π-0.425979\pi
0.230453 + 0.973083i 0.425979π0.425979\pi
114114 −1.08579 1.88064i −0.101693 0.176138i
115115 0.414214 0.717439i 0.0386256 0.0669015i
116116 0.914214 1.58346i 0.0848826 0.147021i
117117 −0.500000 0.866025i −0.0462250 0.0800641i
118118 2.07107 0.190657
119119 −2.41421 5.91359i −0.221311 0.542098i
120120 0.585786 0.0534747
121121 5.41421 + 9.37769i 0.492201 + 0.852518i
122122 2.20711 3.82282i 0.199822 0.346102i
123123 −4.94975 + 8.57321i −0.446304 + 0.773021i
124124 4.24264 + 7.34847i 0.381000 + 0.659912i
125125 5.65685 0.505964
126126 1.00000 + 2.44949i 0.0890871 + 0.218218i
127127 −7.89949 −0.700967 −0.350483 0.936569i 0.613983π-0.613983\pi
−0.350483 + 0.936569i 0.613983π0.613983\pi
128128 −0.500000 0.866025i −0.0441942 0.0765466i
129129 3.24264 5.61642i 0.285499 0.494498i
130130 0.292893 0.507306i 0.0256884 0.0444937i
131131 4.77817 + 8.27604i 0.417471 + 0.723081i 0.995684 0.0928046i 0.0295832π-0.0295832\pi
−0.578213 + 0.815886i 0.696250π0.696250\pi
132132 0.414214 0.0360527
133133 5.69239 + 0.778985i 0.493593 + 0.0675466i
134134 1.82843 0.157952
135135 −0.292893 0.507306i −0.0252082 0.0436619i
136136 1.20711 2.09077i 0.103509 0.179282i
137137 −5.53553 + 9.58783i −0.472933 + 0.819143i −0.999520 0.0309777i 0.990138π-0.990138\pi
0.526587 + 0.850121i 0.323471π0.323471\pi
138138 0.707107 + 1.22474i 0.0601929 + 0.104257i
139139 −13.0711 −1.10867 −0.554337 0.832292i 0.687028π-0.687028\pi
−0.554337 + 0.832292i 0.687028π0.687028\pi
140140 −0.949747 + 1.22474i −0.0802683 + 0.103510i
141141 −1.00000 −0.0842152
142142 2.50000 + 4.33013i 0.209795 + 0.363376i
143143 0.207107 0.358719i 0.0173191 0.0299976i
144144 −0.500000 + 0.866025i −0.0416667 + 0.0721688i
145145 −0.535534 0.927572i −0.0444737 0.0770307i
146146 1.41421 0.117041
147147 −6.74264 1.88064i −0.556124 0.155112i
148148 1.41421 0.116248
149149 2.46447 + 4.26858i 0.201897 + 0.349696i 0.949140 0.314856i 0.101956π-0.101956\pi
−0.747243 + 0.664551i 0.768623π0.768623\pi
150150 −2.32843 + 4.03295i −0.190115 + 0.329289i
151151 −2.03553 + 3.52565i −0.165649 + 0.286913i −0.936886 0.349636i 0.886305π-0.886305\pi
0.771236 + 0.636549i 0.219639π0.219639\pi
152152 1.08579 + 1.88064i 0.0880689 + 0.152540i
153153 −2.41421 −0.195178
154154 −0.671573 + 0.866025i −0.0541169 + 0.0697863i
155155 4.97056 0.399245
156156 0.500000 + 0.866025i 0.0400320 + 0.0693375i
157157 −4.86396 + 8.42463i −0.388186 + 0.672358i −0.992206 0.124611i 0.960232π-0.960232\pi
0.604019 + 0.796970i 0.293565π0.293565\pi
158158 5.82843 10.0951i 0.463685 0.803126i
159159 4.74264 + 8.21449i 0.376116 + 0.651452i
160160 −0.585786 −0.0463105
161161 −3.70711 0.507306i −0.292161 0.0399813i
162162 1.00000 0.0785674
163163 9.32843 + 16.1573i 0.730659 + 1.26554i 0.956602 + 0.291398i 0.0941203π0.0941203\pi
−0.225943 + 0.974140i 0.572546π0.572546\pi
164164 4.94975 8.57321i 0.386510 0.669456i
165165 0.121320 0.210133i 0.00944478 0.0163588i
166166 −3.82843 6.63103i −0.297144 0.514668i
167167 −0.656854 −0.0508289 −0.0254145 0.999677i 0.508091π-0.508091\pi
−0.0254145 + 0.999677i 0.508091π0.508091\pi
168168 −1.00000 2.44949i −0.0771517 0.188982i
169169 1.00000 0.0769231
170170 −0.707107 1.22474i −0.0542326 0.0939336i
171171 1.08579 1.88064i 0.0830322 0.143816i
172172 −3.24264 + 5.61642i −0.247249 + 0.428248i
173173 −2.74264 4.75039i −0.208519 0.361166i 0.742729 0.669592i 0.233531π-0.233531\pi
−0.951248 + 0.308426i 0.900198π0.900198\pi
174174 1.82843 0.138613
175175 −4.65685 11.4069i −0.352025 0.862282i
176176 −0.414214 −0.0312225
177177 1.03553 + 1.79360i 0.0778355 + 0.134815i
178178 −1.29289 + 2.23936i −0.0969064 + 0.167847i
179179 −9.82843 + 17.0233i −0.734611 + 1.27238i 0.220283 + 0.975436i 0.429302π0.429302\pi
−0.954894 + 0.296948i 0.904031π0.904031\pi
180180 0.292893 + 0.507306i 0.0218310 + 0.0378124i
181181 2.89949 0.215518 0.107759 0.994177i 0.465633π-0.465633\pi
0.107759 + 0.994177i 0.465633π0.465633\pi
182182 −2.62132 0.358719i −0.194305 0.0265901i
183183 4.41421 0.326308
184184 −0.707107 1.22474i −0.0521286 0.0902894i
185185 0.414214 0.717439i 0.0304536 0.0527472i
186186 −4.24264 + 7.34847i −0.311086 + 0.538816i
187187 −0.500000 0.866025i −0.0365636 0.0633300i
188188 1.00000 0.0729325
189189 −1.62132 + 2.09077i −0.117934 + 0.152081i
190190 1.27208 0.0922862
191191 5.17157 + 8.95743i 0.374202 + 0.648137i 0.990207 0.139605i 0.0445834π-0.0445834\pi
−0.616005 + 0.787742i 0.711250π0.711250\pi
192192 0.500000 0.866025i 0.0360844 0.0625000i
193193 1.46447 2.53653i 0.105415 0.182583i −0.808493 0.588506i 0.799716π-0.799716\pi
0.913908 + 0.405922i 0.133050π0.133050\pi
194194 0.464466 + 0.804479i 0.0333467 + 0.0577582i
195195 0.585786 0.0419490
196196 6.74264 + 1.88064i 0.481617 + 0.134331i
197197 −15.5563 −1.10834 −0.554172 0.832402i 0.686965π-0.686965\pi
−0.554172 + 0.832402i 0.686965π0.686965\pi
198198 0.207107 + 0.358719i 0.0147184 + 0.0254931i
199199 −1.36396 + 2.36245i −0.0966886 + 0.167470i −0.910312 0.413923i 0.864158π-0.864158\pi
0.813623 + 0.581392i 0.197492π0.197492\pi
200200 2.32843 4.03295i 0.164645 0.285173i
201201 0.914214 + 1.58346i 0.0644837 + 0.111689i
202202 −14.8284 −1.04332
203203 −2.96447 + 3.82282i −0.208065 + 0.268309i
204204 2.41421 0.169029
205205 −2.89949 5.02207i −0.202510 0.350757i
206206 8.41421 14.5738i 0.586246 1.01541i
207207 −0.707107 + 1.22474i −0.0491473 + 0.0851257i
208208 −0.500000 0.866025i −0.0346688 0.0600481i
209209 0.899495 0.0622194
210210 −1.53553 0.210133i −0.105962 0.0145006i
211211 −12.9289 −0.890064 −0.445032 0.895515i 0.646808π-0.646808\pi
−0.445032 + 0.895515i 0.646808π0.646808\pi
212212 −4.74264 8.21449i −0.325726 0.564174i
213213 −2.50000 + 4.33013i −0.171297 + 0.296695i
214214 9.65685 16.7262i 0.660129 1.14338i
215215 1.89949 + 3.29002i 0.129544 + 0.224378i
216216 −1.00000 −0.0680414
217217 −8.48528 20.7846i −0.576018 1.41095i
218218 −9.65685 −0.654045
219219 0.707107 + 1.22474i 0.0477818 + 0.0827606i
220220 −0.121320 + 0.210133i −0.00817942 + 0.0141672i
221221 1.20711 2.09077i 0.0811988 0.140640i
222222 0.707107 + 1.22474i 0.0474579 + 0.0821995i
223223 −7.92893 −0.530961 −0.265480 0.964116i 0.585531π-0.585531\pi
−0.265480 + 0.964116i 0.585531π0.585531\pi
224224 1.00000 + 2.44949i 0.0668153 + 0.163663i
225225 −4.65685 −0.310457
226226 −2.44975 4.24309i −0.162955 0.282246i
227227 10.5858 18.3351i 0.702603 1.21694i −0.264946 0.964263i 0.585354π-0.585354\pi
0.967550 0.252681i 0.0813125π-0.0813125\pi
228228 −1.08579 + 1.88064i −0.0719080 + 0.124548i
229229 −13.2426 22.9369i −0.875098 1.51571i −0.856658 0.515885i 0.827463π-0.827463\pi
−0.0184404 0.999830i 0.505870π-0.505870\pi
230230 −0.828427 −0.0546249
231231 −1.08579 0.148586i −0.0714395 0.00977627i
232232 −1.82843 −0.120042
233233 8.86396 + 15.3528i 0.580697 + 1.00580i 0.995397 + 0.0958390i 0.0305534π0.0305534\pi
−0.414699 + 0.909958i 0.636113π0.636113\pi
234234 −0.500000 + 0.866025i −0.0326860 + 0.0566139i
235235 0.292893 0.507306i 0.0191062 0.0330930i
236236 −1.03553 1.79360i −0.0674075 0.116753i
237237 11.6569 0.757194
238238 −3.91421 + 5.04757i −0.253721 + 0.327185i
239239 4.51472 0.292033 0.146016 0.989282i 0.453355π-0.453355\pi
0.146016 + 0.989282i 0.453355π0.453355\pi
240240 −0.292893 0.507306i −0.0189062 0.0327465i
241241 1.07107 1.85514i 0.0689935 0.119500i −0.829465 0.558559i 0.811355π-0.811355\pi
0.898459 + 0.439058i 0.144688π0.144688\pi
242242 5.41421 9.37769i 0.348039 0.602821i
243243 0.500000 + 0.866025i 0.0320750 + 0.0555556i
244244 −4.41421 −0.282591
245245 2.92893 2.86976i 0.187123 0.183342i
246246 9.89949 0.631169
247247 1.08579 + 1.88064i 0.0690869 + 0.119662i
248248 4.24264 7.34847i 0.269408 0.466628i
249249 3.82843 6.63103i 0.242617 0.420224i
250250 −2.82843 4.89898i −0.178885 0.309839i
251251 24.8284 1.56716 0.783578 0.621293i 0.213392π-0.213392\pi
0.783578 + 0.621293i 0.213392π0.213392\pi
252252 1.62132 2.09077i 0.102134 0.131706i
253253 −0.585786 −0.0368281
254254 3.94975 + 6.84116i 0.247829 + 0.429253i
255255 0.707107 1.22474i 0.0442807 0.0766965i
256256 −0.500000 + 0.866025i −0.0312500 + 0.0541266i
257257 −13.2426 22.9369i −0.826053 1.43077i −0.901112 0.433587i 0.857248π-0.857248\pi
0.0750585 0.997179i 0.476086π-0.476086\pi
258258 −6.48528 −0.403756
259259 −3.70711 0.507306i −0.230348 0.0315225i
260260 −0.585786 −0.0363289
261261 0.914214 + 1.58346i 0.0565884 + 0.0980140i
262262 4.77817 8.27604i 0.295197 0.511296i
263263 −10.2929 + 17.8278i −0.634687 + 1.09931i 0.351894 + 0.936040i 0.385538π0.385538\pi
−0.986581 + 0.163270i 0.947796π0.947796\pi
264264 −0.207107 0.358719i −0.0127465 0.0220777i
265265 −5.55635 −0.341324
266266 −2.17157 5.31925i −0.133148 0.326144i
267267 −2.58579 −0.158248
268268 −0.914214 1.58346i −0.0558445 0.0967255i
269269 4.57107 7.91732i 0.278703 0.482728i −0.692360 0.721552i 0.743429π-0.743429\pi
0.971063 + 0.238825i 0.0767622π0.0767622\pi
270270 −0.292893 + 0.507306i −0.0178249 + 0.0308737i
271271 −13.1066 22.7013i −0.796169 1.37901i −0.922094 0.386966i 0.873523π-0.873523\pi
0.125925 0.992040i 0.459810π-0.459810\pi
272272 −2.41421 −0.146383
273273 −1.00000 2.44949i −0.0605228 0.148250i
274274 11.0711 0.668828
275275 −0.964466 1.67050i −0.0581595 0.100735i
276276 0.707107 1.22474i 0.0425628 0.0737210i
277277 −9.03553 + 15.6500i −0.542893 + 0.940318i 0.455844 + 0.890060i 0.349338π0.349338\pi
−0.998736 + 0.0502577i 0.983996π0.983996\pi
278278 6.53553 + 11.3199i 0.391975 + 0.678921i
279279 −8.48528 −0.508001
280280 1.53553 + 0.210133i 0.0917657 + 0.0125578i
281281 0.686292 0.0409407 0.0204704 0.999790i 0.493484π-0.493484\pi
0.0204704 + 0.999790i 0.493484π0.493484\pi
282282 0.500000 + 0.866025i 0.0297746 + 0.0515711i
283283 7.87868 13.6463i 0.468339 0.811187i −0.531006 0.847368i 0.678186π-0.678186\pi
0.999345 + 0.0361811i 0.0115193π0.0115193\pi
284284 2.50000 4.33013i 0.148348 0.256946i
285285 0.636039 + 1.10165i 0.0376757 + 0.0652562i
286286 −0.414214 −0.0244930
287287 −16.0503 + 20.6976i −0.947416 + 1.22174i
288288 1.00000 0.0589256
289289 5.58579 + 9.67487i 0.328576 + 0.569110i
290290 −0.535534 + 0.927572i −0.0314476 + 0.0544689i
291291 −0.464466 + 0.804479i −0.0272275 + 0.0471594i
292292 −0.707107 1.22474i −0.0413803 0.0716728i
293293 −9.89949 −0.578335 −0.289167 0.957279i 0.593378π-0.593378\pi
−0.289167 + 0.957279i 0.593378π0.593378\pi
294294 1.74264 + 6.77962i 0.101633 + 0.395395i
295295 −1.21320 −0.0706354
296296 −0.707107 1.22474i −0.0410997 0.0711868i
297297 −0.207107 + 0.358719i −0.0120176 + 0.0208150i
298298 2.46447 4.26858i 0.142763 0.247272i
299299 −0.707107 1.22474i −0.0408930 0.0708288i
300300 4.65685 0.268864
301301 10.5147 13.5592i 0.606058 0.781541i
302302 4.07107 0.234264
303303 −7.41421 12.8418i −0.425935 0.737742i
304304 1.08579 1.88064i 0.0622741 0.107862i
305305 −1.29289 + 2.23936i −0.0740309 + 0.128225i
306306 1.20711 + 2.09077i 0.0690057 + 0.119521i
307307 −28.1127 −1.60448 −0.802238 0.597004i 0.796358π-0.796358\pi
−0.802238 + 0.597004i 0.796358π0.796358\pi
308308 1.08579 + 0.148586i 0.0618684 + 0.00846650i
309309 16.8284 0.957336
310310 −2.48528 4.30463i −0.141154 0.244487i
311311 4.05025 7.01524i 0.229669 0.397798i −0.728041 0.685533i 0.759569π-0.759569\pi
0.957710 + 0.287735i 0.0929024π0.0929024\pi
312312 0.500000 0.866025i 0.0283069 0.0490290i
313313 −1.75736 3.04384i −0.0993318 0.172048i 0.812076 0.583551i 0.198337π-0.198337\pi
−0.911408 + 0.411503i 0.865004π0.865004\pi
314314 9.72792 0.548978
315315 −0.585786 1.43488i −0.0330053 0.0808462i
316316 −11.6569 −0.655749
317317 −14.8995 25.8067i −0.836839 1.44945i −0.892524 0.450999i 0.851068π-0.851068\pi
0.0556853 0.998448i 0.482266π-0.482266\pi
318318 4.74264 8.21449i 0.265954 0.460646i
319319 −0.378680 + 0.655892i −0.0212020 + 0.0367229i
320320 0.292893 + 0.507306i 0.0163732 + 0.0283593i
321321 19.3137 1.07799
322322 1.41421 + 3.46410i 0.0788110 + 0.193047i
323323 5.24264 0.291708
324324 −0.500000 0.866025i −0.0277778 0.0481125i
325325 2.32843 4.03295i 0.129158 0.223708i
326326 9.32843 16.1573i 0.516654 0.894871i
327327 −4.82843 8.36308i −0.267013 0.462479i
328328 −9.89949 −0.546608
329329 −2.62132 0.358719i −0.144518 0.0197768i
330330 −0.242641 −0.0133569
331331 11.2426 + 19.4728i 0.617951 + 1.07032i 0.989859 + 0.142053i 0.0453705π0.0453705\pi
−0.371908 + 0.928270i 0.621296π0.621296\pi
332332 −3.82843 + 6.63103i −0.210112 + 0.363925i
333333 −0.707107 + 1.22474i −0.0387492 + 0.0671156i
334334 0.328427 + 0.568852i 0.0179707 + 0.0311262i
335335 −1.07107 −0.0585187
336336 −1.62132 + 2.09077i −0.0884503 + 0.114061i
337337 −20.3137 −1.10656 −0.553279 0.832996i 0.686624π-0.686624\pi
−0.553279 + 0.832996i 0.686624π0.686624\pi
338338 −0.500000 0.866025i −0.0271964 0.0471056i
339339 2.44975 4.24309i 0.133052 0.230453i
340340 −0.707107 + 1.22474i −0.0383482 + 0.0664211i
341341 −1.75736 3.04384i −0.0951663 0.164833i
342342 −2.17157 −0.117425
343343 −17.0000 7.34847i −0.917914 0.396780i
344344 6.48528 0.349663
345345 −0.414214 0.717439i −0.0223005 0.0386256i
346346 −2.74264 + 4.75039i −0.147445 + 0.255383i
347347 4.36396 7.55860i 0.234270 0.405767i −0.724790 0.688969i 0.758063π-0.758063\pi
0.959060 + 0.283202i 0.0913968π0.0913968\pi
348348 −0.914214 1.58346i −0.0490070 0.0848826i
349349 −6.72792 −0.360137 −0.180069 0.983654i 0.557632π-0.557632\pi
−0.180069 + 0.983654i 0.557632π0.557632\pi
350350 −7.55025 + 9.73641i −0.403578 + 0.520433i
351351 −1.00000 −0.0533761
352352 0.207107 + 0.358719i 0.0110388 + 0.0191198i
353353 −6.31371 + 10.9357i −0.336045 + 0.582047i −0.983685 0.179900i 0.942423π-0.942423\pi
0.647640 + 0.761946i 0.275756π0.275756\pi
354354 1.03553 1.79360i 0.0550380 0.0953286i
355355 −1.46447 2.53653i −0.0777258 0.134625i
356356 2.58579 0.137046
357357 −6.32843 0.866025i −0.334936 0.0458349i
358358 19.6569 1.03890
359359 0.414214 + 0.717439i 0.0218614 + 0.0378650i 0.876749 0.480948i 0.159707π-0.159707\pi
−0.854888 + 0.518813i 0.826374π0.826374\pi
360360 0.292893 0.507306i 0.0154368 0.0267374i
361361 7.14214 12.3705i 0.375902 0.651081i
362362 −1.44975 2.51104i −0.0761970 0.131977i
363363 10.8284 0.568345
364364 1.00000 + 2.44949i 0.0524142 + 0.128388i
365365 −0.828427 −0.0433619
366366 −2.20711 3.82282i −0.115367 0.199822i
367367 −6.31371 + 10.9357i −0.329573 + 0.570837i −0.982427 0.186647i 0.940238π-0.940238\pi
0.652854 + 0.757484i 0.273571π0.273571\pi
368368 −0.707107 + 1.22474i −0.0368605 + 0.0638442i
369369 4.94975 + 8.57321i 0.257674 + 0.446304i
370370 −0.828427 −0.0430679
371371 9.48528 + 23.2341i 0.492451 + 1.20625i
372372 8.48528 0.439941
373373 2.79289 + 4.83743i 0.144611 + 0.250473i 0.929228 0.369508i 0.120474π-0.120474\pi
−0.784617 + 0.619981i 0.787140π0.787140\pi
374374 −0.500000 + 0.866025i −0.0258544 + 0.0447811i
375375 2.82843 4.89898i 0.146059 0.252982i
376376 −0.500000 0.866025i −0.0257855 0.0446619i
377377 −1.82843 −0.0941688
378378 2.62132 + 0.358719i 0.134826 + 0.0184505i
379379 18.6274 0.956826 0.478413 0.878135i 0.341212π-0.341212\pi
0.478413 + 0.878135i 0.341212π0.341212\pi
380380 −0.636039 1.10165i −0.0326281 0.0565135i
381381 −3.94975 + 6.84116i −0.202352 + 0.350483i
382382 5.17157 8.95743i 0.264601 0.458302i
383383 −5.58579 9.67487i −0.285420 0.494363i 0.687291 0.726382i 0.258800π-0.258800\pi
−0.972711 + 0.232020i 0.925467π0.925467\pi
384384 −1.00000 −0.0510310
385385 0.393398 0.507306i 0.0200494 0.0258547i
386386 −2.92893 −0.149079
387387 −3.24264 5.61642i −0.164833 0.285499i
388388 0.464466 0.804479i 0.0235797 0.0408412i
389389 2.25736 3.90986i 0.114453 0.198238i −0.803108 0.595833i 0.796822π-0.796822\pi
0.917561 + 0.397595i 0.130155π0.130155\pi
390390 −0.292893 0.507306i −0.0148312 0.0256884i
391391 −3.41421 −0.172664
392392 −1.74264 6.77962i −0.0880166 0.342422i
393393 9.55635 0.482054
394394 7.77817 + 13.4722i 0.391859 + 0.678719i
395395 −3.41421 + 5.91359i −0.171788 + 0.297545i
396396 0.207107 0.358719i 0.0104075 0.0180263i
397397 4.77817 + 8.27604i 0.239810 + 0.415363i 0.960660 0.277729i 0.0895816π-0.0895816\pi
−0.720850 + 0.693091i 0.756248π0.756248\pi
398398 2.72792 0.136738
399399 3.52082 4.54026i 0.176261 0.227297i
400400 −4.65685 −0.232843
401401 −9.94975 17.2335i −0.496867 0.860598i 0.503127 0.864213i 0.332183π-0.332183\pi
−0.999993 + 0.00361428i 0.998850π0.998850\pi
402402 0.914214 1.58346i 0.0455968 0.0789760i
403403 4.24264 7.34847i 0.211341 0.366053i
404404 7.41421 + 12.8418i 0.368871 + 0.638903i
405405 −0.585786 −0.0291080
406406 4.79289 + 0.655892i 0.237867 + 0.0325514i
407407 −0.585786 −0.0290364
408408 −1.20711 2.09077i −0.0597607 0.103509i
409409 −16.2929 + 28.2201i −0.805632 + 1.39540i 0.110232 + 0.993906i 0.464841π0.464841\pi
−0.915864 + 0.401489i 0.868493π0.868493\pi
410410 −2.89949 + 5.02207i −0.143196 + 0.248022i
411411 5.53553 + 9.58783i 0.273048 + 0.472933i
412412 −16.8284 −0.829077
413413 2.07107 + 5.07306i 0.101911 + 0.249629i
414414 1.41421 0.0695048
415415 2.24264 + 3.88437i 0.110087 + 0.190676i
416416 −0.500000 + 0.866025i −0.0245145 + 0.0424604i
417417 −6.53553 + 11.3199i −0.320046 + 0.554337i
418418 −0.449747 0.778985i −0.0219979 0.0381014i
419419 27.4558 1.34131 0.670653 0.741771i 0.266014π-0.266014\pi
0.670653 + 0.741771i 0.266014π0.266014\pi
420420 0.585786 + 1.43488i 0.0285835 + 0.0700149i
421421 1.07107 0.0522007 0.0261003 0.999659i 0.491691π-0.491691\pi
0.0261003 + 0.999659i 0.491691π0.491691\pi
422422 6.46447 + 11.1968i 0.314685 + 0.545051i
423423 −0.500000 + 0.866025i −0.0243108 + 0.0421076i
424424 −4.74264 + 8.21449i −0.230323 + 0.398931i
425425 −5.62132 9.73641i −0.272674 0.472285i
426426 5.00000 0.242251
427427 11.5711 + 1.58346i 0.559963 + 0.0766292i
428428 −19.3137 −0.933563
429429 −0.207107 0.358719i −0.00999921 0.0173191i
430430 1.89949 3.29002i 0.0916018 0.158659i
431431 −15.2426 + 26.4010i −0.734212 + 1.27169i 0.220856 + 0.975306i 0.429115π0.429115\pi
−0.955068 + 0.296386i 0.904218π0.904218\pi
432432 0.500000 + 0.866025i 0.0240563 + 0.0416667i
433433 29.9706 1.44029 0.720147 0.693822i 0.244074π-0.244074\pi
0.720147 + 0.693822i 0.244074π0.244074\pi
434434 −13.7574 + 17.7408i −0.660374 + 0.851584i
435435 −1.07107 −0.0513538
436436 4.82843 + 8.36308i 0.231240 + 0.400519i
437437 1.53553 2.65962i 0.0734545 0.127227i
438438 0.707107 1.22474i 0.0337869 0.0585206i
439439 −8.29289 14.3637i −0.395798 0.685543i 0.597405 0.801940i 0.296199π-0.296199\pi
−0.993203 + 0.116397i 0.962865π0.962865\pi
440440 0.242641 0.0115674
441441 −5.00000 + 4.89898i −0.238095 + 0.233285i
442442 −2.41421 −0.114832
443443 16.8492 + 29.1837i 0.800532 + 1.38656i 0.919267 + 0.393636i 0.128783π0.128783\pi
−0.118735 + 0.992926i 0.537884π0.537884\pi
444444 0.707107 1.22474i 0.0335578 0.0581238i
445445 0.757359 1.31178i 0.0359023 0.0621846i
446446 3.96447 + 6.86666i 0.187723 + 0.325146i
447447 4.92893 0.233130
448448 1.62132 2.09077i 0.0766002 0.0987796i
449449 24.9706 1.17843 0.589217 0.807975i 0.299436π-0.299436\pi
0.589217 + 0.807975i 0.299436π0.299436\pi
450450 2.32843 + 4.03295i 0.109763 + 0.190115i
451451 −2.05025 + 3.55114i −0.0965426 + 0.167217i
452452 −2.44975 + 4.24309i −0.115226 + 0.199578i
453453 2.03553 + 3.52565i 0.0956377 + 0.165649i
454454 −21.1716 −0.993631
455455 1.53553 + 0.210133i 0.0719869 + 0.00985119i
456456 2.17157 0.101693
457457 1.53553 + 2.65962i 0.0718292 + 0.124412i 0.899703 0.436503i 0.143783π-0.143783\pi
−0.827874 + 0.560914i 0.810450π0.810450\pi
458458 −13.2426 + 22.9369i −0.618788 + 1.07177i
459459 −1.20711 + 2.09077i −0.0563429 + 0.0975888i
460460 0.414214 + 0.717439i 0.0193128 + 0.0334508i
461461 −4.48528 −0.208900 −0.104450 0.994530i 0.533308π-0.533308\pi
−0.104450 + 0.994530i 0.533308π0.533308\pi
462462 0.414214 + 1.01461i 0.0192710 + 0.0472040i
463463 −20.9706 −0.974585 −0.487292 0.873239i 0.662015π-0.662015\pi
−0.487292 + 0.873239i 0.662015π0.662015\pi
464464 0.914214 + 1.58346i 0.0424413 + 0.0735105i
465465 2.48528 4.30463i 0.115252 0.199623i
466466 8.86396 15.3528i 0.410615 0.711206i
467467 5.70711 + 9.88500i 0.264093 + 0.457423i 0.967326 0.253537i 0.0815939π-0.0815939\pi
−0.703232 + 0.710960i 0.748261π0.748261\pi
468468 1.00000 0.0462250
469469 1.82843 + 4.47871i 0.0844289 + 0.206808i
470470 −0.585786 −0.0270203
471471 4.86396 + 8.42463i 0.224119 + 0.388186i
472472 −1.03553 + 1.79360i −0.0476643 + 0.0825570i
473473 1.34315 2.32640i 0.0617579 0.106968i
474474 −5.82843 10.0951i −0.267709 0.463685i
475475 10.1127 0.464002
476476 6.32843 + 0.866025i 0.290063 + 0.0396942i
477477 9.48528 0.434301
478478 −2.25736 3.90986i −0.103249 0.178833i
479479 16.0563 27.8104i 0.733633 1.27069i −0.221687 0.975118i 0.571156π-0.571156\pi
0.955320 0.295572i 0.0955103π-0.0955103\pi
480480 −0.292893 + 0.507306i −0.0133687 + 0.0231552i
481481 −0.707107 1.22474i −0.0322413 0.0558436i
482482 −2.14214 −0.0975716
483483 −2.29289 + 2.95680i −0.104330 + 0.134539i
484484 −10.8284 −0.492201
485485 −0.272078 0.471253i −0.0123544 0.0213985i
486486 0.500000 0.866025i 0.0226805 0.0392837i
487487 −8.10660 + 14.0410i −0.367345 + 0.636261i −0.989150 0.146912i 0.953067π-0.953067\pi
0.621804 + 0.783173i 0.286400π0.286400\pi
488488 2.20711 + 3.82282i 0.0999110 + 0.173051i
489489 18.6569 0.843692
490490 −3.94975 1.10165i −0.178431 0.0497676i
491491 23.6569 1.06762 0.533809 0.845605i 0.320760π-0.320760\pi
0.533809 + 0.845605i 0.320760π0.320760\pi
492492 −4.94975 8.57321i −0.223152 0.386510i
493493 −2.20711 + 3.82282i −0.0994031 + 0.172171i
494494 1.08579 1.88064i 0.0488518 0.0846139i
495495 −0.121320 0.210133i −0.00545294 0.00944478i
496496 −8.48528 −0.381000
497497 −8.10660 + 10.4539i −0.363631 + 0.468919i
498498 −7.65685 −0.343112
499499 −1.82843 3.16693i −0.0818516 0.141771i 0.822194 0.569208i 0.192750π-0.192750\pi
−0.904045 + 0.427437i 0.859417π0.859417\pi
500500 −2.82843 + 4.89898i −0.126491 + 0.219089i
501501 −0.328427 + 0.568852i −0.0146730 + 0.0254145i
502502 −12.4142 21.5020i −0.554073 0.959683i
503503 26.1421 1.16562 0.582810 0.812608i 0.301953π-0.301953\pi
0.582810 + 0.812608i 0.301953π0.301953\pi
504504 −2.62132 0.358719i −0.116763 0.0159786i
505505 8.68629 0.386535
506506 0.292893 + 0.507306i 0.0130207 + 0.0225525i
507507 0.500000 0.866025i 0.0222058 0.0384615i
508508 3.94975 6.84116i 0.175242 0.303528i
509509 −5.31371 9.20361i −0.235526 0.407943i 0.723899 0.689906i 0.242348π-0.242348\pi
−0.959425 + 0.281963i 0.909015π0.909015\pi
510510 −1.41421 −0.0626224
511511 1.41421 + 3.46410i 0.0625611 + 0.153243i
512512 1.00000 0.0441942
513513 −1.08579 1.88064i −0.0479386 0.0830322i
514514 −13.2426 + 22.9369i −0.584108 + 1.01170i
515515 −4.92893 + 8.53716i −0.217195 + 0.376192i
516516 3.24264 + 5.61642i 0.142749 + 0.247249i
517517 −0.414214 −0.0182171
518518 1.41421 + 3.46410i 0.0621370 + 0.152204i
519519 −5.48528 −0.240777
520520 0.292893 + 0.507306i 0.0128442 + 0.0222468i
521521 −20.3137 + 35.1844i −0.889960 + 1.54146i −0.0500384 + 0.998747i 0.515934π0.515934\pi
−0.839921 + 0.542708i 0.817399π0.817399\pi
522522 0.914214 1.58346i 0.0400140 0.0693064i
523523 8.41421 + 14.5738i 0.367928 + 0.637270i 0.989241 0.146292i 0.0467340π-0.0467340\pi
−0.621314 + 0.783562i 0.713401π0.713401\pi
524524 −9.55635 −0.417471
525525 −12.2071 1.67050i −0.532762 0.0729068i
526526 20.5858 0.897583
527527 −10.2426 17.7408i −0.446176 0.772800i
528528 −0.207107 + 0.358719i −0.00901317 + 0.0156113i
529529 10.5000 18.1865i 0.456522 0.790719i
530530 2.77817 + 4.81194i 0.120676 + 0.209017i
531531 2.07107 0.0898767
532532 −3.52082 + 4.54026i −0.152647 + 0.196845i
533533 −9.89949 −0.428795
534534 1.29289 + 2.23936i 0.0559490 + 0.0969064i
535535 −5.65685 + 9.79796i −0.244567 + 0.423603i
536536 −0.914214 + 1.58346i −0.0394880 + 0.0683952i
537537 9.82843 + 17.0233i 0.424128 + 0.734611i
538538 −9.14214 −0.394145
539539 −2.79289 0.778985i −0.120298 0.0335533i
540540 0.585786 0.0252082
541541 −11.5355 19.9801i −0.495951 0.859013i 0.504038 0.863682i 0.331847π-0.331847\pi
−0.999989 + 0.00466870i 0.998514π0.998514\pi
542542 −13.1066 + 22.7013i −0.562977 + 0.975104i
543543 1.44975 2.51104i 0.0622146 0.107759i
544544 1.20711 + 2.09077i 0.0517543 + 0.0896410i
545545 5.65685 0.242313
546546 −1.62132 + 2.09077i −0.0693861 + 0.0894767i
547547 −30.8701 −1.31991 −0.659954 0.751306i 0.729424π-0.729424\pi
−0.659954 + 0.751306i 0.729424π0.729424\pi
548548 −5.53553 9.58783i −0.236466 0.409572i
549549 2.20711 3.82282i 0.0941970 0.163154i
550550 −0.964466 + 1.67050i −0.0411250 + 0.0712305i
551551 −1.98528 3.43861i −0.0845758 0.146490i
552552 −1.41421 −0.0601929
553553 30.5563 + 4.18154i 1.29939 + 0.177817i
554554 18.0711 0.767766
555555 −0.414214 0.717439i −0.0175824 0.0304536i
556556 6.53553 11.3199i 0.277168 0.480070i
557557 16.3137 28.2562i 0.691234 1.19725i −0.280200 0.959942i 0.590401π-0.590401\pi
0.971434 0.237311i 0.0762660π-0.0762660\pi
558558 4.24264 + 7.34847i 0.179605 + 0.311086i
559559 6.48528 0.274298
560560 −0.585786 1.43488i −0.0247540 0.0606347i
561561 −1.00000 −0.0422200
562562 −0.343146 0.594346i −0.0144747 0.0250710i
563563 16.3848 28.3793i 0.690536 1.19604i −0.281126 0.959671i 0.590708π-0.590708\pi
0.971662 0.236373i 0.0759586π-0.0759586\pi
564564 0.500000 0.866025i 0.0210538 0.0364662i
565565 1.43503 + 2.48554i 0.0603721 + 0.104568i
566566 −15.7574 −0.662331
567567 1.00000 + 2.44949i 0.0419961 + 0.102869i
568568 −5.00000 −0.209795
569569 −11.8640 20.5490i −0.497363 0.861458i 0.502632 0.864500i 0.332365π-0.332365\pi
−0.999995 + 0.00304214i 0.999032π0.999032\pi
570570 0.636039 1.10165i 0.0266407 0.0461431i
571571 15.6569 27.1185i 0.655219 1.13487i −0.326620 0.945156i 0.605910π-0.605910\pi
0.981839 0.189717i 0.0607570π-0.0607570\pi
572572 0.207107 + 0.358719i 0.00865957 + 0.0149988i
573573 10.3431 0.432091
574574 25.9497 + 3.55114i 1.08312 + 0.148222i
575575 −6.58579 −0.274646
576576 −0.500000 0.866025i −0.0208333 0.0360844i
577577 −8.17157 + 14.1536i −0.340187 + 0.589221i −0.984467 0.175568i 0.943824π-0.943824\pi
0.644280 + 0.764790i 0.277157π0.277157\pi
578578 5.58579 9.67487i 0.232338 0.402421i
579579 −1.46447 2.53653i −0.0608611 0.105415i
580580 1.07107 0.0444737
581581 12.4142 16.0087i 0.515028 0.664154i
582582 0.928932 0.0385055
583583 1.96447 + 3.40256i 0.0813599 + 0.140919i
584584 −0.707107 + 1.22474i −0.0292603 + 0.0506803i
585585 0.292893 0.507306i 0.0121096 0.0209745i
586586 4.94975 + 8.57321i 0.204472 + 0.354156i
587587 −1.58579 −0.0654524 −0.0327262 0.999464i 0.510419π-0.510419\pi
−0.0327262 + 0.999464i 0.510419π0.510419\pi
588588 5.00000 4.89898i 0.206197 0.202031i
589589 18.4264 0.759247
590590 0.606602 + 1.05066i 0.0249734 + 0.0432552i
591591 −7.77817 + 13.4722i −0.319951 + 0.554172i
592592 −0.707107 + 1.22474i −0.0290619 + 0.0503367i
593593 17.1924 + 29.7781i 0.706007 + 1.22284i 0.966327 + 0.257317i 0.0828385π0.0828385\pi
−0.260320 + 0.965522i 0.583828π0.583828\pi
594594 0.414214 0.0169954
595595 2.29289 2.95680i 0.0939995 0.121217i
596596 −4.92893 −0.201897
597597 1.36396 + 2.36245i 0.0558232 + 0.0966886i
598598 −0.707107 + 1.22474i −0.0289157 + 0.0500835i
599599 −0.778175 + 1.34784i −0.0317954 + 0.0550712i −0.881485 0.472212i 0.843456π-0.843456\pi
0.849690 + 0.527283i 0.176789π0.176789\pi
600600 −2.32843 4.03295i −0.0950576 0.164645i
601601 1.20101 0.0489902 0.0244951 0.999700i 0.492202π-0.492202\pi
0.0244951 + 0.999700i 0.492202π0.492202\pi
602602 −17.0000 2.32640i −0.692868 0.0948169i
603603 1.82843 0.0744593
604604 −2.03553 3.52565i −0.0828247 0.143457i
605605 −3.17157 + 5.49333i −0.128943 + 0.223335i
606606 −7.41421 + 12.8418i −0.301182 + 0.521662i
607607 −17.2635 29.9012i −0.700702 1.21365i −0.968220 0.250099i 0.919537π-0.919537\pi
0.267518 0.963553i 0.413796π-0.413796\pi
608608 −2.17157 −0.0880689
609609 1.82843 + 4.47871i 0.0740916 + 0.181487i
610610 2.58579 0.104695
611611 −0.500000 0.866025i −0.0202278 0.0350356i
612612 1.20711 2.09077i 0.0487944 0.0845144i
613613 3.89949 6.75412i 0.157499 0.272796i −0.776467 0.630158i 0.782990π-0.782990\pi
0.933966 + 0.357361i 0.116324π0.116324\pi
614614 14.0563 + 24.3463i 0.567268 + 0.982537i
615615 −5.79899 −0.233838
616616 −0.414214 1.01461i −0.0166891 0.0408799i
617617 −24.1421 −0.971926 −0.485963 0.873979i 0.661531π-0.661531\pi
−0.485963 + 0.873979i 0.661531π0.661531\pi
618618 −8.41421 14.5738i −0.338469 0.586246i
619619 −10.4142 + 18.0379i −0.418583 + 0.725006i −0.995797 0.0915862i 0.970806π-0.970806\pi
0.577215 + 0.816593i 0.304140π0.304140\pi
620620 −2.48528 + 4.30463i −0.0998113 + 0.172878i
621621 0.707107 + 1.22474i 0.0283752 + 0.0491473i
622622 −8.10051 −0.324801
623623 −6.77817 0.927572i −0.271562 0.0371624i
624624 −1.00000 −0.0400320
625625 −9.98528 17.2950i −0.399411 0.691801i
626626 −1.75736 + 3.04384i −0.0702382 + 0.121656i
627627 0.449747 0.778985i 0.0179612 0.0311097i
628628 −4.86396 8.42463i −0.194093 0.336179i
629629 −3.41421 −0.136134
630630 −0.949747 + 1.22474i −0.0378388 + 0.0487950i
631631 32.6274 1.29888 0.649438 0.760414i 0.275004π-0.275004\pi
0.649438 + 0.760414i 0.275004π0.275004\pi
632632 5.82843 + 10.0951i 0.231842 + 0.401563i
633633 −6.46447 + 11.1968i −0.256939 + 0.445032i
634634 −14.8995 + 25.8067i −0.591735 + 1.02491i
635635 −2.31371 4.00746i −0.0918167 0.159031i
636636 −9.48528 −0.376116
637637 −1.74264 6.77962i −0.0690459 0.268618i
638638 0.757359 0.0299841
639639 2.50000 + 4.33013i 0.0988985 + 0.171297i
640640 0.292893 0.507306i 0.0115776 0.0200530i
641641 −15.8995 + 27.5387i −0.627992 + 1.08771i 0.359962 + 0.932967i 0.382790π0.382790\pi
−0.987954 + 0.154748i 0.950544π0.950544\pi
642642 −9.65685 16.7262i −0.381126 0.660129i
643643 −2.51472 −0.0991708 −0.0495854 0.998770i 0.515790π-0.515790\pi
−0.0495854 + 0.998770i 0.515790π0.515790\pi
644644 2.29289 2.95680i 0.0903527 0.116514i
645645 3.79899 0.149585
646646 −2.62132 4.54026i −0.103134 0.178634i
647647 4.51472 7.81972i 0.177492 0.307425i −0.763529 0.645774i 0.776535π-0.776535\pi
0.941021 + 0.338349i 0.109868π0.109868\pi
648648 −0.500000 + 0.866025i −0.0196419 + 0.0340207i
649649 0.428932 + 0.742932i 0.0168371 + 0.0291626i
650650 −4.65685 −0.182657
651651 −22.2426 3.04384i −0.871758 0.119297i
652652 −18.6569 −0.730659
653653 −11.0711 19.1757i −0.433244 0.750401i 0.563906 0.825839i 0.309298π-0.309298\pi
−0.997151 + 0.0754376i 0.975965π0.975965\pi
654654 −4.82843 + 8.36308i −0.188806 + 0.327022i
655655 −2.79899 + 4.84799i −0.109366 + 0.189427i
656656 4.94975 + 8.57321i 0.193255 + 0.334728i
657657 1.41421 0.0551737
658658 1.00000 + 2.44949i 0.0389841 + 0.0954911i
659659 10.5858 0.412364 0.206182 0.978514i 0.433896π-0.433896\pi
0.206182 + 0.978514i 0.433896π0.433896\pi
660660 0.121320 + 0.210133i 0.00472239 + 0.00817942i
661661 −20.1213 + 34.8511i −0.782629 + 1.35555i 0.147777 + 0.989021i 0.452788π0.452788\pi
−0.930405 + 0.366532i 0.880545π0.880545\pi
662662 11.2426 19.4728i 0.436958 0.756833i
663663 −1.20711 2.09077i −0.0468801 0.0811988i
664664 7.65685 0.297144
665665 1.27208 + 3.11594i 0.0493291 + 0.120831i
666666 1.41421 0.0547997
667667 1.29289 + 2.23936i 0.0500610 + 0.0867082i
668668 0.328427 0.568852i 0.0127072 0.0220096i
669669 −3.96447 + 6.86666i −0.153275 + 0.265480i
670670 0.535534 + 0.927572i 0.0206895 + 0.0358352i
671671 1.82843 0.0705856
672672 2.62132 + 0.358719i 0.101120 + 0.0138379i
673673 42.1421 1.62446 0.812230 0.583337i 0.198253π-0.198253\pi
0.812230 + 0.583337i 0.198253π0.198253\pi
674674 10.1569 + 17.5922i 0.391227 + 0.677626i
675675 −2.32843 + 4.03295i −0.0896212 + 0.155228i
676676 −0.500000 + 0.866025i −0.0192308 + 0.0333087i
677677 −7.50000 12.9904i −0.288248 0.499261i 0.685143 0.728408i 0.259740π-0.259740\pi
−0.973392 + 0.229147i 0.926406π0.926406\pi
678678 −4.89949 −0.188164
679679 −1.50610 + 1.94218i −0.0577987 + 0.0745342i
680680 1.41421 0.0542326
681681 −10.5858 18.3351i −0.405648 0.702603i
682682 −1.75736 + 3.04384i −0.0672928 + 0.116554i
683683 7.07107 12.2474i 0.270567 0.468636i −0.698440 0.715668i 0.746122π-0.746122\pi
0.969007 + 0.247033i 0.0794555π0.0794555\pi
684684 1.08579 + 1.88064i 0.0415161 + 0.0719080i
685685 −6.48528 −0.247790
686686 2.13604 + 18.3967i 0.0815543 + 0.702388i
687687 −26.4853 −1.01048
688688 −3.24264 5.61642i −0.123625 0.214124i
689689 −4.74264 + 8.21449i −0.180680 + 0.312947i
690690 −0.414214 + 0.717439i −0.0157688 + 0.0273124i
691691 10.3284 + 17.8894i 0.392912 + 0.680543i 0.992832 0.119516i 0.0381344π-0.0381344\pi
−0.599920 + 0.800060i 0.704801π0.704801\pi
692692 5.48528 0.208519
693693 −0.671573 + 0.866025i −0.0255109 + 0.0328976i
694694 −8.72792 −0.331307
695695 −3.82843 6.63103i −0.145221 0.251529i
696696 −0.914214 + 1.58346i −0.0346532 + 0.0600211i
697697 −11.9497 + 20.6976i −0.452629 + 0.783976i
698698 3.36396 + 5.82655i 0.127328 + 0.220538i
699699 17.7279 0.670532
700700 12.2071 + 1.67050i 0.461385 + 0.0631391i
701701 −29.1716 −1.10180 −0.550898 0.834573i 0.685715π-0.685715\pi
−0.550898 + 0.834573i 0.685715π0.685715\pi
702702 0.500000 + 0.866025i 0.0188713 + 0.0326860i
703703 1.53553 2.65962i 0.0579138 0.100310i
704704 0.207107 0.358719i 0.00780563 0.0135197i
705705 −0.292893 0.507306i −0.0110310 0.0191062i
706706 12.6274 0.475239
707707 −14.8284 36.3221i −0.557680 1.36603i
708708 −2.07107 −0.0778355
709709 18.4350 + 31.9304i 0.692342 + 1.19917i 0.971069 + 0.238801i 0.0767544π0.0767544\pi
−0.278726 + 0.960371i 0.589912π0.589912\pi
710710 −1.46447 + 2.53653i −0.0549604 + 0.0951943i
711711 5.82843 10.0951i 0.218583 0.378597i
712712 −1.29289 2.23936i −0.0484532 0.0839234i
713713 −12.0000 −0.449404
714714 2.41421 + 5.91359i 0.0903497 + 0.221311i
715715 0.242641 0.00907425
716716 −9.82843 17.0233i −0.367306 0.636192i
717717 2.25736 3.90986i 0.0843026 0.146016i
718718 0.414214 0.717439i 0.0154583 0.0267746i
719719 −4.65685 8.06591i −0.173671 0.300808i 0.766029 0.642806i 0.222230π-0.222230\pi
−0.939701 + 0.341998i 0.888896π0.888896\pi
720720 −0.585786 −0.0218310
721721 44.1127 + 6.03668i 1.64284 + 0.224818i
722722 −14.2843 −0.531606
723723 −1.07107 1.85514i −0.0398334 0.0689935i
724724 −1.44975 + 2.51104i −0.0538794 + 0.0933219i
725725 −4.25736 + 7.37396i −0.158114 + 0.273862i
726726 −5.41421 9.37769i −0.200940 0.348039i
727727 −50.4264 −1.87021 −0.935106 0.354368i 0.884696π-0.884696\pi
−0.935106 + 0.354368i 0.884696π0.884696\pi
728728 1.62132 2.09077i 0.0600901 0.0774891i
729729 1.00000 0.0370370
730730 0.414214 + 0.717439i 0.0153307 + 0.0265536i
731731 7.82843 13.5592i 0.289545 0.501506i
732732 −2.20711 + 3.82282i −0.0815770 + 0.141296i
733733 14.2929 + 24.7560i 0.527920 + 0.914384i 0.999470 + 0.0325451i 0.0103613π0.0103613\pi
−0.471550 + 0.881839i 0.656305π0.656305\pi
734734 12.6274 0.466086
735735 −1.02082 3.97141i −0.0376533 0.146488i
736736 1.41421 0.0521286
737737 0.378680 + 0.655892i 0.0139488 + 0.0241601i
738738 4.94975 8.57321i 0.182203 0.315584i
739739 15.0000 25.9808i 0.551784 0.955718i −0.446362 0.894852i 0.647281π-0.647281\pi
0.998146 0.0608653i 0.0193860π-0.0193860\pi
740740 0.414214 + 0.717439i 0.0152268 + 0.0263736i
741741 2.17157 0.0797747
742742 15.3787 19.8315i 0.564569 0.728039i
743743 12.1716 0.446532 0.223266 0.974758i 0.428328π-0.428328\pi
0.223266 + 0.974758i 0.428328π0.428328\pi
744744 −4.24264 7.34847i −0.155543 0.269408i
745745 −1.44365 + 2.50048i −0.0528913 + 0.0916104i
746746 2.79289 4.83743i 0.102255 0.177111i
747747 −3.82843 6.63103i −0.140075 0.242617i
748748 1.00000 0.0365636
749749 50.6274 + 6.92820i 1.84989 + 0.253151i
750750 −5.65685 −0.206559
751751 9.65685 + 16.7262i 0.352384 + 0.610346i 0.986667 0.162755i 0.0520379π-0.0520379\pi
−0.634283 + 0.773101i 0.718705π0.718705\pi
752752 −0.500000 + 0.866025i −0.0182331 + 0.0315807i
753753 12.4142 21.5020i 0.452399 0.783578i
754754 0.914214 + 1.58346i 0.0332937 + 0.0576664i
755755 −2.38478 −0.0867909
756756 −1.00000 2.44949i −0.0363696 0.0890871i
757757 −30.7574 −1.11790 −0.558948 0.829203i 0.688795π-0.688795\pi
−0.558948 + 0.829203i 0.688795π0.688795\pi
758758 −9.31371 16.1318i −0.338289 0.585934i
759759 −0.292893 + 0.507306i −0.0106314 + 0.0184140i
760760 −0.636039 + 1.10165i −0.0230716 + 0.0399611i
761761 −21.5563 37.3367i −0.781417 1.35345i −0.931116 0.364722i 0.881164π-0.881164\pi
0.149699 0.988732i 0.452169π-0.452169\pi
762762 7.89949 0.286169
763763 −9.65685 23.6544i −0.349602 0.856346i
764764 −10.3431 −0.374202
765765 −0.707107 1.22474i −0.0255655 0.0442807i
766766 −5.58579 + 9.67487i −0.201823 + 0.349567i
767767 −1.03553 + 1.79360i −0.0373910 + 0.0647630i
768768 0.500000 + 0.866025i 0.0180422 + 0.0312500i
769769 9.89949 0.356985 0.178492 0.983941i 0.442878π-0.442878\pi
0.178492 + 0.983941i 0.442878π0.442878\pi
770770 −0.636039 0.0870399i −0.0229213 0.00313670i
771771 −26.4853 −0.953844
772772 1.46447 + 2.53653i 0.0527073 + 0.0912917i
773773 −9.48528 + 16.4290i −0.341162 + 0.590910i −0.984649 0.174547i 0.944154π-0.944154\pi
0.643487 + 0.765457i 0.277487π0.277487\pi
774774 −3.24264 + 5.61642i −0.116554 + 0.201878i
775775 −19.7574 34.2208i −0.709705 1.22925i
776776 −0.928932 −0.0333467
777777 −2.29289 + 2.95680i −0.0822571 + 0.106074i
778778 −4.51472 −0.161861
779779 −10.7487 18.6174i −0.385113 0.667036i
780780 −0.292893 + 0.507306i −0.0104873 + 0.0181645i
781781 −1.03553 + 1.79360i −0.0370543 + 0.0641800i
782782 1.70711 + 2.95680i 0.0610460 + 0.105735i
783783 1.82843 0.0653427
784784 −5.00000 + 4.89898i −0.178571 + 0.174964i
785785 −5.69848 −0.203388
786786 −4.77817 8.27604i −0.170432 0.295197i
787787 13.1569 22.7883i 0.468991 0.812317i −0.530380 0.847760i 0.677951π-0.677951\pi
0.999372 + 0.0354431i 0.0112843π0.0112843\pi
788788 7.77817 13.4722i 0.277086 0.479927i
789789 10.2929 + 17.8278i 0.366437 + 0.634687i
790790 6.82843 0.242945
791791 7.94365 10.2437i 0.282444 0.364225i
792792 −0.414214 −0.0147184
793793 2.20711 + 3.82282i 0.0783767 + 0.135752i
794794 4.77817 8.27604i 0.169571 0.293706i
795795 −2.77817 + 4.81194i −0.0985317 + 0.170662i
796796 −1.36396 2.36245i −0.0483443 0.0837348i
797797 34.3431 1.21650 0.608248 0.793747i 0.291872π-0.291872\pi
0.608248 + 0.793747i 0.291872π0.291872\pi
798798 −5.69239 0.778985i −0.201508 0.0275758i
799799 −2.41421 −0.0854087
800800 2.32843 + 4.03295i 0.0823223 + 0.142586i
801801 −1.29289 + 2.23936i −0.0456821 + 0.0791238i
802802 −9.94975 + 17.2335i −0.351338 + 0.608535i
803803 0.292893 + 0.507306i 0.0103360 + 0.0179024i
804804 −1.82843 −0.0644837
805805 −0.828427 2.02922i −0.0291982 0.0715207i
806806 −8.48528 −0.298881
807807 −4.57107 7.91732i −0.160909 0.278703i
808808 7.41421 12.8418i 0.260831 0.451773i
809809 8.79289 15.2297i 0.309142 0.535449i −0.669033 0.743233i 0.733292π-0.733292\pi
0.978175 + 0.207783i 0.0666249π0.0666249\pi
810810 0.292893 + 0.507306i 0.0102912 + 0.0178249i
811811 55.4558 1.94732 0.973659 0.228009i 0.0732216π-0.0732216\pi
0.973659 + 0.228009i 0.0732216π0.0732216\pi
812812 −1.82843 4.47871i −0.0641652 0.157172i
813813 −26.2132 −0.919337
814814 0.292893 + 0.507306i 0.0102659 + 0.0177811i
815815 −5.46447 + 9.46473i −0.191412 + 0.331535i
816816 −1.20711 + 2.09077i −0.0422572 + 0.0731916i
817817 7.04163 + 12.1965i 0.246355 + 0.426700i
818818 32.5858 1.13934
819819 −2.62132 0.358719i −0.0915963 0.0125347i
820820 5.79899 0.202510
821821 −23.9497 41.4822i −0.835852 1.44774i −0.893335 0.449392i 0.851641π-0.851641\pi
0.0574829 0.998346i 0.481693π-0.481693\pi
822822 5.53553 9.58783i 0.193074 0.334414i
823823 21.9203 37.9671i 0.764094 1.32345i −0.176630 0.984277i 0.556520π-0.556520\pi
0.940724 0.339172i 0.110147π-0.110147\pi
824824 8.41421 + 14.5738i 0.293123 + 0.507704i
825825 −1.92893 −0.0671568
826826 3.35786 4.33013i 0.116835 0.150664i
827827 46.3553 1.61193 0.805967 0.591961i 0.201646π-0.201646\pi
0.805967 + 0.591961i 0.201646π0.201646\pi
828828 −0.707107 1.22474i −0.0245737 0.0425628i
829829 13.3492 23.1216i 0.463638 0.803045i −0.535501 0.844535i 0.679877π-0.679877\pi
0.999139 + 0.0414897i 0.0132104π0.0132104\pi
830830 2.24264 3.88437i 0.0778432 0.134828i
831831 9.03553 + 15.6500i 0.313439 + 0.542893i
832832 1.00000 0.0346688
833833 −16.2782 4.54026i −0.564005 0.157311i
834834 13.0711 0.452614
835835 −0.192388 0.333226i −0.00665787 0.0115318i
836836 −0.449747 + 0.778985i −0.0155548 + 0.0269418i
837837 −4.24264 + 7.34847i −0.146647 + 0.254000i
838838 −13.7279 23.7775i −0.474223 0.821379i
839839 −31.8284 −1.09884 −0.549420 0.835547i 0.685151π-0.685151\pi
−0.549420 + 0.835547i 0.685151π0.685151\pi
840840 0.949747 1.22474i 0.0327694 0.0422577i
841841 −25.6569 −0.884719
842842 −0.535534 0.927572i −0.0184557 0.0319662i
843843 0.343146 0.594346i 0.0118186 0.0204704i
844844 6.46447 11.1968i 0.222516 0.385409i
845845 0.292893 + 0.507306i 0.0100758 + 0.0174519i
846846 1.00000 0.0343807
847847 28.3848 + 3.88437i 0.975312 + 0.133468i
848848 9.48528 0.325726
849849 −7.87868 13.6463i −0.270396 0.468339i
850850 −5.62132 + 9.73641i −0.192810 + 0.333956i
851851 −1.00000 + 1.73205i −0.0342796 + 0.0593739i
852852 −2.50000 4.33013i −0.0856486 0.148348i
853853 6.72792 0.230360 0.115180 0.993345i 0.463256π-0.463256\pi
0.115180 + 0.993345i 0.463256π0.463256\pi
854854 −4.41421 10.8126i −0.151051 0.369999i
855855 1.27208 0.0435041
856856 9.65685 + 16.7262i 0.330064 + 0.571688i
857857 −10.2782 + 17.8023i −0.351096 + 0.608116i −0.986442 0.164112i 0.947524π-0.947524\pi
0.635346 + 0.772228i 0.280858π0.280858\pi
858858 −0.207107 + 0.358719i −0.00707051 + 0.0122465i
859859 5.89949 + 10.2182i 0.201288 + 0.348641i 0.948944 0.315445i 0.102154π-0.102154\pi
−0.747656 + 0.664087i 0.768821π0.768821\pi
860860 −3.79899 −0.129544
861861 9.89949 + 24.2487i 0.337374 + 0.826394i
862862 30.4853 1.03833
863863 −19.6569 34.0467i −0.669127 1.15896i −0.978149 0.207907i 0.933335π-0.933335\pi
0.309021 0.951055i 0.399998π-0.399998\pi
864864 0.500000 0.866025i 0.0170103 0.0294628i
865865 1.60660 2.78272i 0.0546261 0.0946152i
866866 −14.9853 25.9553i −0.509221 0.881996i
867867 11.1716 0.379407
868868 22.2426 + 3.04384i 0.754964 + 0.103315i
869869 4.82843 0.163793
870870 0.535534 + 0.927572i 0.0181563 + 0.0314476i
871871 −0.914214 + 1.58346i −0.0309769 + 0.0536536i
872872 4.82843 8.36308i 0.163511 0.283210i
873873 0.464466 + 0.804479i 0.0157198 + 0.0272275i
874874 −3.07107 −0.103880
875875 9.17157 11.8272i 0.310056 0.399832i
876876 −1.41421 −0.0477818
877877 20.0208 + 34.6771i 0.676055 + 1.17096i 0.976159 + 0.217055i 0.0696451π0.0696451\pi
−0.300104 + 0.953906i 0.597022π0.597022\pi
878878 −8.29289 + 14.3637i −0.279872 + 0.484752i
879879 −4.94975 + 8.57321i −0.166951 + 0.289167i
880880 −0.121320 0.210133i −0.00408971 0.00708358i
881881 18.4853 0.622785 0.311392 0.950281i 0.399205π-0.399205\pi
0.311392 + 0.950281i 0.399205π0.399205\pi
882882 6.74264 + 1.88064i 0.227037 + 0.0633244i
883883 −9.75736 −0.328361 −0.164181 0.986430i 0.552498π-0.552498\pi
−0.164181 + 0.986430i 0.552498π0.552498\pi
884884 1.20711 + 2.09077i 0.0405994 + 0.0703202i
885885 −0.606602 + 1.05066i −0.0203907 + 0.0353177i
886886 16.8492 29.1837i 0.566061 0.980447i
887887 −24.4558 42.3588i −0.821147 1.42227i −0.904829 0.425776i 0.860001π-0.860001\pi
0.0836819 0.996493i 0.473332π-0.473332\pi
888888 −1.41421 −0.0474579
889889 −12.8076 + 16.5160i −0.429554 + 0.553930i
890890 −1.51472 −0.0507735
891891 0.207107 + 0.358719i 0.00693834 + 0.0120176i
892892 3.96447 6.86666i 0.132740 0.229913i
893893 1.08579 1.88064i 0.0363345 0.0629331i
894894 −2.46447 4.26858i −0.0824241 0.142763i
895895 −11.5147 −0.384895
896896 −2.62132 0.358719i −0.0875722 0.0119840i
897897 −1.41421 −0.0472192
898898 −12.4853 21.6251i −0.416639 0.721640i
899899 −7.75736 + 13.4361i −0.258722 + 0.448120i
900900 2.32843 4.03295i 0.0776142 0.134432i
901901 11.4497 + 19.8315i 0.381446 + 0.660685i
902902 4.10051 0.136532
903903 −6.48528 15.8856i −0.215817 0.528641i
904904 4.89949 0.162955
905905 0.849242 + 1.47093i 0.0282298 + 0.0488954i
906906 2.03553 3.52565i 0.0676261 0.117132i
907907 −27.1924 + 47.0986i −0.902908 + 1.56388i −0.0792080 + 0.996858i 0.525239π0.525239\pi
−0.823700 + 0.567025i 0.808094π0.808094\pi
908908 10.5858 + 18.3351i 0.351302 + 0.608472i
909909 −14.8284 −0.491828
910910 −0.585786 1.43488i −0.0194186 0.0475657i
911911 −4.34315 −0.143895 −0.0719474 0.997408i 0.522921π-0.522921\pi
−0.0719474 + 0.997408i 0.522921π0.522921\pi
912912 −1.08579 1.88064i −0.0359540 0.0622741i
913913 1.58579 2.74666i 0.0524819 0.0909013i
914914 1.53553 2.65962i 0.0507909 0.0879725i
915915 1.29289 + 2.23936i 0.0427417 + 0.0740309i
916916 26.4853 0.875098
917917 25.0503 + 3.42805i 0.827232 + 0.113204i
918918 2.41421 0.0796809
919919 −0.899495 1.55797i −0.0296716 0.0513927i 0.850808 0.525476i 0.176113π-0.176113\pi
−0.880480 + 0.474083i 0.842779π0.842779\pi
920920 0.414214 0.717439i 0.0136562 0.0236533i
921921 −14.0563 + 24.3463i −0.463172 + 0.802238i
922922 2.24264 + 3.88437i 0.0738574 + 0.127925i
923923 −5.00000 −0.164577
924924 0.671573 0.866025i 0.0220931 0.0284901i
925925 −6.58579 −0.216539
926926 10.4853 + 18.1610i 0.344568 + 0.596809i
927927 8.41421 14.5738i 0.276359 0.478668i
928928 0.914214 1.58346i 0.0300105 0.0519798i
929929 −17.3431 30.0392i −0.569010 0.985554i −0.996664 0.0816120i 0.973993π-0.973993\pi
0.427654 0.903942i 0.359340π-0.359340\pi
930930 −4.97056 −0.162991
931931 10.8579 10.6385i 0.355852 0.348662i
932932 −17.7279 −0.580697
933933 −4.05025 7.01524i −0.132599 0.229669i
934934 5.70711 9.88500i 0.186742 0.323447i
935935 0.292893 0.507306i 0.00957863 0.0165907i
936936 −0.500000 0.866025i −0.0163430 0.0283069i
937937 42.6569 1.39354 0.696769 0.717295i 0.254620π-0.254620\pi
0.696769 + 0.717295i 0.254620π0.254620\pi
938938 2.96447 3.82282i 0.0967932 0.124820i
939939 −3.51472 −0.114699
940940 0.292893 + 0.507306i 0.00955312 + 0.0165465i
941941 6.48528 11.2328i 0.211414 0.366180i −0.740743 0.671788i 0.765526π-0.765526\pi
0.952157 + 0.305608i 0.0988598π0.0988598\pi
942942 4.86396 8.42463i 0.158476 0.274489i
943943 7.00000 + 12.1244i 0.227951 + 0.394823i
944944 2.07107 0.0674075
945945 −1.53553 0.210133i −0.0499509 0.00683563i
946946 −2.68629 −0.0873389
947947 −4.20711 7.28692i −0.136713 0.236793i 0.789538 0.613702i 0.210320π-0.210320\pi
−0.926250 + 0.376909i 0.876987π0.876987\pi
948948 −5.82843 + 10.0951i −0.189299 + 0.327875i
949949 −0.707107 + 1.22474i −0.0229537 + 0.0397569i
950950 −5.05635 8.75785i −0.164050 0.284142i
951951 −29.7990 −0.966298
952952 −2.41421 5.91359i −0.0782451 0.191661i
953953 −41.5858 −1.34710 −0.673548 0.739144i 0.735230π-0.735230\pi
−0.673548 + 0.739144i 0.735230π0.735230\pi
954954 −4.74264 8.21449i −0.153549 0.265954i
955955 −3.02944 + 5.24714i −0.0980303 + 0.169793i
956956 −2.25736 + 3.90986i −0.0730082 + 0.126454i
957957 0.378680 + 0.655892i 0.0122410 + 0.0212020i
958958 −32.1127 −1.03751
959959 11.0711 + 27.1185i 0.357503 + 0.875701i
960960 0.585786 0.0189062
961961 −20.5000 35.5070i −0.661290 1.14539i
962962 −0.707107 + 1.22474i −0.0227980 + 0.0394874i
963963 9.65685 16.7262i 0.311188 0.538993i
964964 1.07107 + 1.85514i 0.0344968 + 0.0597502i
965965 1.71573 0.0552313
966966 3.70711 + 0.507306i 0.119274 + 0.0163223i
967967 −13.5858 −0.436889 −0.218445 0.975849i 0.570098π-0.570098\pi
−0.218445 + 0.975849i 0.570098π0.570098\pi
968968 5.41421 + 9.37769i 0.174019 + 0.301410i
969969 2.62132 4.54026i 0.0842089 0.145854i
970970 −0.272078 + 0.471253i −0.00873590 + 0.0151310i
971971 16.2635 + 28.1691i 0.521919 + 0.903990i 0.999675 + 0.0254978i 0.00811707π0.00811707\pi
−0.477756 + 0.878493i 0.658550π0.658550\pi
972972 −1.00000 −0.0320750
973973 −21.1924 + 27.3286i −0.679397 + 0.876115i
974974 16.2132 0.519505
975975 −2.32843 4.03295i −0.0745693 0.129158i
976976 2.20711 3.82282i 0.0706478 0.122366i
977977 −21.5858 + 37.3877i −0.690590 + 1.19614i 0.281054 + 0.959692i 0.409316π0.409316\pi
−0.971645 + 0.236446i 0.924017π0.924017\pi
978978 −9.32843 16.1573i −0.298290 0.516654i
979979 −1.07107 −0.0342315
980980 1.02082 + 3.97141i 0.0326087 + 0.126862i
981981 −9.65685 −0.308320
982982 −11.8284 20.4874i −0.377460 0.653780i
983983 14.7426 25.5350i 0.470217 0.814440i −0.529203 0.848495i 0.677509π-0.677509\pi
0.999420 + 0.0340553i 0.0108422π0.0108422\pi
984984 −4.94975 + 8.57321i −0.157792 + 0.273304i
985985 −4.55635 7.89183i −0.145177 0.251455i
986986 4.41421 0.140577
987987 −1.62132 + 2.09077i −0.0516072 + 0.0665500i
988988 −2.17157 −0.0690869
989989 −4.58579 7.94282i −0.145820 0.252567i
990990 −0.121320 + 0.210133i −0.00385581 + 0.00667847i
991991 0.343146 0.594346i 0.0109004 0.0188800i −0.860524 0.509410i 0.829864π-0.829864\pi
0.871424 + 0.490530i 0.163197π0.163197\pi
992992 4.24264 + 7.34847i 0.134704 + 0.233314i
993993 22.4853 0.713549
994994 13.1066 + 1.79360i 0.415716 + 0.0568895i
995995 −1.59798 −0.0506594
996996 3.82843 + 6.63103i 0.121308 + 0.210112i
997997 −26.2487 + 45.4641i −0.831306 + 1.43986i 0.0656972 + 0.997840i 0.479073π0.479073\pi
−0.897003 + 0.442024i 0.854260π0.854260\pi
998998 −1.82843 + 3.16693i −0.0578778 + 0.100247i
999999 0.707107 + 1.22474i 0.0223719 + 0.0387492i
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 546.2.i.i.235.1 yes 4
3.2 odd 2 1638.2.j.m.235.2 4
7.2 even 3 inner 546.2.i.i.79.1 4
7.3 odd 6 3822.2.a.bu.1.1 2
7.4 even 3 3822.2.a.bn.1.2 2
21.2 odd 6 1638.2.j.m.1171.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
546.2.i.i.79.1 4 7.2 even 3 inner
546.2.i.i.235.1 yes 4 1.1 even 1 trivial
1638.2.j.m.235.2 4 3.2 odd 2
1638.2.j.m.1171.2 4 21.2 odd 6
3822.2.a.bn.1.2 2 7.4 even 3
3822.2.a.bu.1.1 2 7.3 odd 6