Properties

Label 882.2.m.a.293.5
Level 882882
Weight 22
Character 882.293
Analytic conductor 7.0437.043
Analytic rank 00
Dimension 1616
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] = [882,2,Mod(293,882)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(882, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) 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("882.293"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 882=23272 882 = 2 \cdot 3^{2} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 882.m (of order 66, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [16,0,0,8,0,0,0,0,6,0,-12,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 7.042805458287.04280545828
Analytic rank: 00
Dimension: 1616
Relative dimension: 88 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x168x15+23x148x13131x12+380x11289x10880x9++6561 x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 32 3^{2}
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 293.5
Root 1.278661.16834i1.27866 - 1.16834i of defining polynomial
Character χ\chi == 882.293
Dual form 882.2.m.a.587.5

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+(0.8660250.500000i)q2+(1.71170+0.264701i)q3+(0.5000000.866025i)q4+(1.77612+3.07634i)q5+(1.35003+1.08509i)q61.00000iq8+(2.859870.906179i)q9+3.55225iq10+(2.61745+1.51119i)q11+(0.626615+1.61473i)q12+(0.888944+0.513232i)q13+(2.225895.73592i)q15+(0.5000000.866025i)q161.61841q17+(2.023632.21471i)q188.22889iq19+(1.77612+3.07634i)q20+(1.51119+2.61745i)q22+(2.908371.67915i)q23+(0.264701+1.71170i)q24+(3.809246.59779i)q25+1.02646q26+(4.65538+2.30812i)q27+(3.70319+2.13804i)q29+(0.9402836.08040i)q30+(5.183822.99288i)q31+(0.8660250.500000i)q32+(4.080293.27954i)q33+(1.40158+0.809204i)q34+(0.6451602.92981i)q365.84647q37+(4.114447.12643i)q38+(1.657460.643198i)q39+(3.07634+1.77612i)q40+(0.0472226+0.0817920i)q41+(3.05899+5.29833i)q43+3.02237iq44+(2.29177+10.4074i)q453.35830q46+(2.570234.45176i)q47+(1.08509+1.35003i)q48+(6.597793.80924i)q50+(2.770240.428394i)q51+(0.8889440.513232i)q523.18968iq53+(2.87762+4.32658i)q5410.7362iq55+(2.17819+14.0854i)q57+(2.13804+3.70319i)q58+(4.42036+7.65628i)q59+(3.854514.79564i)q60+(4.061952.34517i)q615.98576q621.00000q64+(3.15775+1.82313i)q65+(1.893864.88031i)q66+(0.1878380.325345i)q67+(0.809204+1.40158i)q68+(5.42275+2.10436i)q6913.9868iq71+(0.9061792.85987i)q721.31111iq73+(5.06319+2.92323i)q74+(8.26673+10.2852i)q75+(7.126434.11444i)q76+(1.75700+0.271706i)q78+(0.4620670.800324i)q79+3.55225q80+(7.357685.18310i)q81+0.0944452iq82+(5.432099.40866i)q83+(2.874504.97877i)q85+(5.29833+3.05899i)q86+(5.772834.63993i)q87+(1.51119+2.61745i)q884.70989q89+(3.21897+10.1590i)q90+(2.90837+1.67915i)q92+(9.66539+3.75077i)q93+(4.451762.57023i)q94+(25.3148+14.6155i)q95+(1.61473+0.626615i)q96+(13.3330+7.69782i)q97+(6.11615+6.69367i)q99+O(q100)q+(0.866025 - 0.500000i) q^{2} +(-1.71170 + 0.264701i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.77612 + 3.07634i) q^{5} +(-1.35003 + 1.08509i) q^{6} -1.00000i q^{8} +(2.85987 - 0.906179i) q^{9} +3.55225i q^{10} +(-2.61745 + 1.51119i) q^{11} +(-0.626615 + 1.61473i) q^{12} +(0.888944 + 0.513232i) q^{13} +(2.22589 - 5.73592i) q^{15} +(-0.500000 - 0.866025i) q^{16} -1.61841 q^{17} +(2.02363 - 2.21471i) q^{18} -8.22889i q^{19} +(1.77612 + 3.07634i) q^{20} +(-1.51119 + 2.61745i) q^{22} +(-2.90837 - 1.67915i) q^{23} +(0.264701 + 1.71170i) q^{24} +(-3.80924 - 6.59779i) q^{25} +1.02646 q^{26} +(-4.65538 + 2.30812i) q^{27} +(-3.70319 + 2.13804i) q^{29} +(-0.940283 - 6.08040i) q^{30} +(-5.18382 - 2.99288i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(4.08029 - 3.27954i) q^{33} +(-1.40158 + 0.809204i) q^{34} +(0.645160 - 2.92981i) q^{36} -5.84647 q^{37} +(-4.11444 - 7.12643i) q^{38} +(-1.65746 - 0.643198i) q^{39} +(3.07634 + 1.77612i) q^{40} +(-0.0472226 + 0.0817920i) q^{41} +(3.05899 + 5.29833i) q^{43} +3.02237i q^{44} +(-2.29177 + 10.4074i) q^{45} -3.35830 q^{46} +(-2.57023 - 4.45176i) q^{47} +(1.08509 + 1.35003i) q^{48} +(-6.59779 - 3.80924i) q^{50} +(2.77024 - 0.428394i) q^{51} +(0.888944 - 0.513232i) q^{52} -3.18968i q^{53} +(-2.87762 + 4.32658i) q^{54} -10.7362i q^{55} +(2.17819 + 14.0854i) q^{57} +(-2.13804 + 3.70319i) q^{58} +(-4.42036 + 7.65628i) q^{59} +(-3.85451 - 4.79564i) q^{60} +(4.06195 - 2.34517i) q^{61} -5.98576 q^{62} -1.00000 q^{64} +(-3.15775 + 1.82313i) q^{65} +(1.89386 - 4.88031i) q^{66} +(0.187838 - 0.325345i) q^{67} +(-0.809204 + 1.40158i) q^{68} +(5.42275 + 2.10436i) q^{69} -13.9868i q^{71} +(-0.906179 - 2.85987i) q^{72} -1.31111i q^{73} +(-5.06319 + 2.92323i) q^{74} +(8.26673 + 10.2852i) q^{75} +(-7.12643 - 4.11444i) q^{76} +(-1.75700 + 0.271706i) q^{78} +(-0.462067 - 0.800324i) q^{79} +3.55225 q^{80} +(7.35768 - 5.18310i) q^{81} +0.0944452i q^{82} +(-5.43209 - 9.40866i) q^{83} +(2.87450 - 4.97877i) q^{85} +(5.29833 + 3.05899i) q^{86} +(5.77283 - 4.63993i) q^{87} +(1.51119 + 2.61745i) q^{88} -4.70989 q^{89} +(3.21897 + 10.1590i) q^{90} +(-2.90837 + 1.67915i) q^{92} +(9.66539 + 3.75077i) q^{93} +(-4.45176 - 2.57023i) q^{94} +(25.3148 + 14.6155i) q^{95} +(1.61473 + 0.626615i) q^{96} +(-13.3330 + 7.69782i) q^{97} +(-6.11615 + 6.69367i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q+8q4+6q912q116q1318q158q1636q17+6q23+6q248q25+24q2636q27+6q29+18q306q3118q33+4q37+42q39++18q99+O(q100) 16 q + 8 q^{4} + 6 q^{9} - 12 q^{11} - 6 q^{13} - 18 q^{15} - 8 q^{16} - 36 q^{17} + 6 q^{23} + 6 q^{24} - 8 q^{25} + 24 q^{26} - 36 q^{27} + 6 q^{29} + 18 q^{30} - 6 q^{31} - 18 q^{33} + 4 q^{37} + 42 q^{39}+ \cdots + 18 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/882Z)×\left(\mathbb{Z}/882\mathbb{Z}\right)^\times.

nn 199199 785785
χ(n)\chi(n) 1-1 e(56)e\left(\frac{5}{6}\right)

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 0.866025 0.500000i 0.612372 0.353553i
33 −1.71170 + 0.264701i −0.988253 + 0.152825i
44 0.500000 0.866025i 0.250000 0.433013i
55 −1.77612 + 3.07634i −0.794307 + 1.37578i 0.128971 + 0.991648i 0.458833π0.458833\pi
−0.923278 + 0.384132i 0.874501π0.874501\pi
66 −1.35003 + 1.08509i −0.551147 + 0.442986i
77 0 0
88 1.00000i 0.353553i
99 2.85987 0.906179i 0.953289 0.302060i
1010 3.55225i 1.12332i
1111 −2.61745 + 1.51119i −0.789191 + 0.455639i −0.839678 0.543085i 0.817256π-0.817256\pi
0.0504869 + 0.998725i 0.483923π0.483923\pi
1212 −0.626615 + 1.61473i −0.180888 + 0.466132i
1313 0.888944 + 0.513232i 0.246549 + 0.142345i 0.618183 0.786034i 0.287869π-0.287869\pi
−0.371634 + 0.928379i 0.621202π0.621202\pi
1414 0 0
1515 2.22589 5.73592i 0.574723 1.48101i
1616 −0.500000 0.866025i −0.125000 0.216506i
1717 −1.61841 −0.392522 −0.196261 0.980552i 0.562880π-0.562880\pi
−0.196261 + 0.980552i 0.562880π0.562880\pi
1818 2.02363 2.21471i 0.476974 0.522012i
1919 8.22889i 1.88784i −0.330179 0.943918i 0.607109π-0.607109\pi
0.330179 0.943918i 0.392891π-0.392891\pi
2020 1.77612 + 3.07634i 0.397154 + 0.687890i
2121 0 0
2222 −1.51119 + 2.61745i −0.322186 + 0.558042i
2323 −2.90837 1.67915i −0.606438 0.350127i 0.165132 0.986271i 0.447195π-0.447195\pi
−0.771570 + 0.636144i 0.780528π0.780528\pi
2424 0.264701 + 1.71170i 0.0540318 + 0.349400i
2525 −3.80924 6.59779i −0.761848 1.31956i
2626 1.02646 0.201306
2727 −4.65538 + 2.30812i −0.895929 + 0.444198i
2828 0 0
2929 −3.70319 + 2.13804i −0.687666 + 0.397024i −0.802737 0.596333i 0.796624π-0.796624\pi
0.115071 + 0.993357i 0.463290π0.463290\pi
3030 −0.940283 6.08040i −0.171671 1.11012i
3131 −5.18382 2.99288i −0.931041 0.537537i −0.0439006 0.999036i 0.513978π-0.513978\pi
−0.887141 + 0.461499i 0.847312π0.847312\pi
3232 −0.866025 0.500000i −0.153093 0.0883883i
3333 4.08029 3.27954i 0.710287 0.570895i
3434 −1.40158 + 0.809204i −0.240369 + 0.138777i
3535 0 0
3636 0.645160 2.92981i 0.107527 0.488301i
3737 −5.84647 −0.961154 −0.480577 0.876953i 0.659573π-0.659573\pi
−0.480577 + 0.876953i 0.659573π0.659573\pi
3838 −4.11444 7.12643i −0.667451 1.15606i
3939 −1.65746 0.643198i −0.265407 0.102994i
4040 3.07634 + 1.77612i 0.486412 + 0.280830i
4141 −0.0472226 + 0.0817920i −0.00737493 + 0.0127738i −0.869689 0.493600i 0.835681π-0.835681\pi
0.862314 + 0.506373i 0.169014π0.169014\pi
4242 0 0
4343 3.05899 + 5.29833i 0.466492 + 0.807988i 0.999267 0.0382684i 0.0121842π-0.0121842\pi
−0.532775 + 0.846257i 0.678851π0.678851\pi
4444 3.02237i 0.455639i
4545 −2.29177 + 10.4074i −0.341637 + 1.55144i
4646 −3.35830 −0.495154
4747 −2.57023 4.45176i −0.374906 0.649356i 0.615407 0.788210i 0.288992π-0.288992\pi
−0.990313 + 0.138853i 0.955658π0.955658\pi
4848 1.08509 + 1.35003i 0.156619 + 0.194860i
4949 0 0
5050 −6.59779 3.80924i −0.933069 0.538708i
5151 2.77024 0.428394i 0.387911 0.0599871i
5252 0.888944 0.513232i 0.123274 0.0711725i
5353 3.18968i 0.438137i −0.975709 0.219068i 0.929698π-0.929698\pi
0.975709 0.219068i 0.0703018π-0.0703018\pi
5454 −2.87762 + 4.32658i −0.391594 + 0.588773i
5555 10.7362i 1.44767i
5656 0 0
5757 2.17819 + 14.0854i 0.288509 + 1.86566i
5858 −2.13804 + 3.70319i −0.280738 + 0.486253i
5959 −4.42036 + 7.65628i −0.575481 + 0.996763i 0.420508 + 0.907289i 0.361852π0.361852\pi
−0.995989 + 0.0894739i 0.971481π0.971481\pi
6060 −3.85451 4.79564i −0.497615 0.619115i
6161 4.06195 2.34517i 0.520080 0.300268i −0.216887 0.976197i 0.569590π-0.569590\pi
0.736967 + 0.675928i 0.236257π0.236257\pi
6262 −5.98576 −0.760192
6363 0 0
6464 −1.00000 −0.125000
6565 −3.15775 + 1.82313i −0.391671 + 0.226131i
6666 1.89386 4.88031i 0.233118 0.600725i
6767 0.187838 0.325345i 0.0229480 0.0397472i −0.854323 0.519742i 0.826028π-0.826028\pi
0.877271 + 0.479995i 0.159361π0.159361\pi
6868 −0.809204 + 1.40158i −0.0981304 + 0.169967i
6969 5.42275 + 2.10436i 0.652822 + 0.253335i
7070 0 0
7171 13.9868i 1.65993i −0.557815 0.829966i 0.688360π-0.688360\pi
0.557815 0.829966i 0.311640π-0.311640\pi
7272 −0.906179 2.85987i −0.106794 0.337039i
7373 1.31111i 0.153454i −0.997052 0.0767270i 0.975553π-0.975553\pi
0.997052 0.0767270i 0.0244470π-0.0244470\pi
7474 −5.06319 + 2.92323i −0.588584 + 0.339819i
7575 8.26673 + 10.2852i 0.954560 + 1.18763i
7676 −7.12643 4.11444i −0.817457 0.471959i
7777 0 0
7878 −1.75700 + 0.271706i −0.198942 + 0.0307646i
7979 −0.462067 0.800324i −0.0519866 0.0900434i 0.838861 0.544346i 0.183222π-0.183222\pi
−0.890848 + 0.454302i 0.849889π0.849889\pi
8080 3.55225 0.397154
8181 7.35768 5.18310i 0.817520 0.575900i
8282 0.0944452i 0.0104297i
8383 −5.43209 9.40866i −0.596250 1.03273i −0.993369 0.114968i 0.963323π-0.963323\pi
0.397119 0.917767i 0.370010π-0.370010\pi
8484 0 0
8585 2.87450 4.97877i 0.311783 0.540024i
8686 5.29833 + 3.05899i 0.571334 + 0.329860i
8787 5.77283 4.63993i 0.618913 0.497453i
8888 1.51119 + 2.61745i 0.161093 + 0.279021i
8989 −4.70989 −0.499247 −0.249624 0.968343i 0.580307π-0.580307\pi
−0.249624 + 0.968343i 0.580307π0.580307\pi
9090 3.21897 + 10.1590i 0.339310 + 1.07085i
9191 0 0
9292 −2.90837 + 1.67915i −0.303219 + 0.175063i
9393 9.66539 + 3.75077i 1.00225 + 0.388936i
9494 −4.45176 2.57023i −0.459164 0.265099i
9595 25.3148 + 14.6155i 2.59725 + 1.49952i
9696 1.61473 + 0.626615i 0.164803 + 0.0639536i
9797 −13.3330 + 7.69782i −1.35376 + 0.781595i −0.988774 0.149417i 0.952260π-0.952260\pi
−0.364988 + 0.931012i 0.618927π0.618927\pi
9898 0 0
9999 −6.11615 + 6.69367i −0.614697 + 0.672739i
100100 −7.61848 −0.761848
101101 6.85234 + 11.8686i 0.681833 + 1.18097i 0.974421 + 0.224731i 0.0721503π0.0721503\pi
−0.292588 + 0.956239i 0.594516π0.594516\pi
102102 2.18490 1.75612i 0.216337 0.173882i
103103 2.64014 + 1.52429i 0.260141 + 0.150192i 0.624399 0.781106i 0.285344π-0.285344\pi
−0.364258 + 0.931298i 0.618677π0.618677\pi
104104 0.513232 0.888944i 0.0503266 0.0871682i
105105 0 0
106106 −1.59484 2.76235i −0.154905 0.268303i
107107 13.1267i 1.26901i 0.772920 + 0.634504i 0.218796π0.218796\pi
−0.772920 + 0.634504i 0.781204π0.781204\pi
108108 −0.328801 + 5.18574i −0.0316389 + 0.498998i
109109 −10.5715 −1.01256 −0.506282 0.862368i 0.668980π-0.668980\pi
−0.506282 + 0.862368i 0.668980π0.668980\pi
110110 −5.36811 9.29783i −0.511829 0.886514i
111111 10.0074 1.54756i 0.949863 0.146888i
112112 0 0
113113 10.6520 + 6.14993i 1.00205 + 0.578537i 0.908856 0.417111i 0.136957π-0.136957\pi
0.0931992 + 0.995647i 0.470291π0.470291\pi
114114 8.92908 + 11.1092i 0.836285 + 1.04048i
115115 10.3313 5.96476i 0.963396 0.556217i
116116 4.27608i 0.397024i
117117 3.00734 + 0.662233i 0.278029 + 0.0612235i
118118 8.84071i 0.813853i
119119 0 0
120120 −5.73592 2.22589i −0.523616 0.203195i
121121 −0.932639 + 1.61538i −0.0847854 + 0.146853i
122122 2.34517 4.06195i 0.212322 0.367752i
123123 0.0591808 0.152504i 0.00533615 0.0137508i
124124 −5.18382 + 2.99288i −0.465521 + 0.268768i
125125 9.30148 0.831950
126126 0 0
127127 0.287164 0.0254817 0.0127408 0.999919i 0.495944π-0.495944\pi
0.0127408 + 0.999919i 0.495944π0.495944\pi
128128 −0.866025 + 0.500000i −0.0765466 + 0.0441942i
129129 −6.63857 8.25947i −0.584493 0.727206i
130130 −1.82313 + 3.15775i −0.159899 + 0.276953i
131131 −0.186474 + 0.322983i −0.0162923 + 0.0282192i −0.874057 0.485824i 0.838520π-0.838520\pi
0.857764 + 0.514043i 0.171853π0.171853\pi
132132 −0.800023 5.17341i −0.0696331 0.450287i
133133 0 0
134134 0.375675i 0.0324534i
135135 1.16798 18.4210i 0.100524 1.58543i
136136 1.61841i 0.138777i
137137 −6.11607 + 3.53111i −0.522531 + 0.301683i −0.737969 0.674834i 0.764215π-0.764215\pi
0.215439 + 0.976517i 0.430882π0.430882\pi
138138 5.74842 0.888944i 0.489338 0.0756720i
139139 12.6320 + 7.29308i 1.07143 + 0.618591i 0.928572 0.371152i 0.121037π-0.121037\pi
0.142858 + 0.989743i 0.454371π0.454371\pi
140140 0 0
141141 5.57785 + 6.93976i 0.469740 + 0.584434i
142142 −6.99341 12.1129i −0.586874 1.01650i
143143 −3.10236 −0.259432
144144 −2.21471 2.02363i −0.184559 0.168636i
145145 15.1897i 1.26144i
146146 −0.655556 1.13546i −0.0542542 0.0939710i
147147 0 0
148148 −2.92323 + 5.06319i −0.240288 + 0.416192i
149149 9.26832 + 5.35107i 0.759290 + 0.438376i 0.829041 0.559188i 0.188887π-0.188887\pi
−0.0697505 + 0.997564i 0.522220π0.522220\pi
150150 12.3018 + 4.77385i 1.00444 + 0.389783i
151151 −8.00065 13.8575i −0.651084 1.12771i −0.982860 0.184352i 0.940981π-0.940981\pi
0.331777 0.943358i 0.392352π-0.392352\pi
152152 −8.22889 −0.667451
153153 −4.62843 + 1.46657i −0.374187 + 0.118565i
154154 0 0
155155 18.4142 10.6315i 1.47907 0.853939i
156156 −1.38576 + 1.11381i −0.110949 + 0.0891759i
157157 9.98239 + 5.76334i 0.796681 + 0.459964i 0.842309 0.538994i 0.181196π-0.181196\pi
−0.0456280 + 0.998958i 0.514529π0.514529\pi
158158 −0.800324 0.462067i −0.0636703 0.0367601i
159159 0.844312 + 5.45980i 0.0669583 + 0.432990i
160160 3.07634 1.77612i 0.243206 0.140415i
161161 0 0
162162 3.78039 8.16754i 0.297015 0.641702i
163163 −2.74773 −0.215219 −0.107609 0.994193i 0.534320π-0.534320\pi
−0.107609 + 0.994193i 0.534320π0.534320\pi
164164 0.0472226 + 0.0817920i 0.00368747 + 0.00638688i
165165 2.84188 + 18.3772i 0.221240 + 1.43067i
166166 −9.40866 5.43209i −0.730254 0.421612i
167167 2.76946 4.79685i 0.214307 0.371191i −0.738751 0.673979i 0.764584π-0.764584\pi
0.953058 + 0.302788i 0.0979173π0.0979173\pi
168168 0 0
169169 −5.97319 10.3459i −0.459476 0.795835i
170170 5.74899i 0.440927i
171171 −7.45685 23.5335i −0.570239 1.79965i
172172 6.11799 0.466492
173173 5.60253 + 9.70387i 0.425953 + 0.737772i 0.996509 0.0834869i 0.0266057π-0.0266057\pi
−0.570556 + 0.821259i 0.693272π0.693272\pi
174174 2.67945 6.90471i 0.203129 0.523445i
175175 0 0
176176 2.61745 + 1.51119i 0.197298 + 0.113910i
177177 5.53972 14.2754i 0.416391 1.07300i
178178 −4.07888 + 2.35495i −0.305725 + 0.176511i
179179 2.74178i 0.204930i −0.994737 0.102465i 0.967327π-0.967327\pi
0.994737 0.102465i 0.0326730π-0.0326730\pi
180180 7.86719 + 7.18843i 0.586386 + 0.535794i
181181 22.2899i 1.65679i −0.560142 0.828397i 0.689253π-0.689253\pi
0.560142 0.828397i 0.310747π-0.310747\pi
182182 0 0
183183 −6.33210 + 5.08944i −0.468082 + 0.376222i
184184 −1.67915 + 2.90837i −0.123789 + 0.214408i
185185 10.3841 17.9857i 0.763451 1.32234i
186186 10.2459 1.58443i 0.751262 0.116176i
187187 4.23610 2.44571i 0.309774 0.178848i
188188 −5.14045 −0.374906
189189 0 0
190190 29.2311 2.12064
191191 −4.44499 + 2.56632i −0.321628 + 0.185692i −0.652118 0.758117i 0.726119π-0.726119\pi
0.330490 + 0.943810i 0.392786π0.392786\pi
192192 1.71170 0.264701i 0.123532 0.0191031i
193193 −7.99235 + 13.8432i −0.575302 + 0.996452i 0.420707 + 0.907197i 0.361782π0.361782\pi
−0.996009 + 0.0892557i 0.971551π0.971551\pi
194194 −7.69782 + 13.3330i −0.552671 + 0.957254i
195195 4.92256 3.95652i 0.352512 0.283332i
196196 0 0
197197 4.72572i 0.336694i 0.985728 + 0.168347i 0.0538428π0.0538428\pi
−0.985728 + 0.168347i 0.946157π0.946157\pi
198198 −1.94991 + 8.85496i −0.138574 + 0.629295i
199199 2.12095i 0.150350i −0.997170 0.0751749i 0.976048π-0.976048\pi
0.997170 0.0751749i 0.0239515π-0.0239515\pi
200200 −6.59779 + 3.80924i −0.466534 + 0.269354i
201201 −0.235404 + 0.606615i −0.0166041 + 0.0427873i
202202 11.8686 + 6.85234i 0.835072 + 0.482129i
203203 0 0
204204 1.01412 2.61329i 0.0710025 0.182967i
205205 −0.167747 0.290545i −0.0117159 0.0202926i
206206 3.04857 0.212404
207207 −9.83917 2.16664i −0.683870 0.150592i
208208 1.02646i 0.0711725i
209209 12.4354 + 21.5387i 0.860173 + 1.48986i
210210 0 0
211211 −13.8079 + 23.9160i −0.950578 + 1.64645i −0.206399 + 0.978468i 0.566174π0.566174\pi
−0.744179 + 0.667981i 0.767159π0.767159\pi
212212 −2.76235 1.59484i −0.189719 0.109534i
213213 3.70232 + 23.9413i 0.253679 + 1.64043i
214214 6.56336 + 11.3681i 0.448662 + 0.777105i
215215 −21.7326 −1.48215
216216 2.30812 + 4.65538i 0.157048 + 0.316759i
217217 0 0
218218 −9.15516 + 5.28574i −0.620066 + 0.357995i
219219 0.347052 + 2.24424i 0.0234516 + 0.151651i
220220 −9.29783 5.36811i −0.626860 0.361918i
221221 −1.43867 0.830619i −0.0967757 0.0558735i
222222 7.89291 6.34395i 0.529737 0.425778i
223223 17.6209 10.1734i 1.17998 0.681264i 0.223973 0.974595i 0.428097π-0.428097\pi
0.956011 + 0.293331i 0.0947638π0.0947638\pi
224224 0 0
225225 −16.8727 15.4170i −1.12485 1.02780i
226226 12.2999 0.818174
227227 2.08000 + 3.60266i 0.138054 + 0.239117i 0.926760 0.375654i 0.122582π-0.122582\pi
−0.788706 + 0.614771i 0.789248π0.789248\pi
228228 13.2874 + 5.15634i 0.879982 + 0.341487i
229229 −5.16986 2.98482i −0.341634 0.197242i 0.319361 0.947633i 0.396532π-0.396532\pi
−0.660994 + 0.750391i 0.729865π0.729865\pi
230230 5.96476 10.3313i 0.393305 0.681224i
231231 0 0
232232 2.13804 + 3.70319i 0.140369 + 0.243126i
233233 4.48720i 0.293966i 0.989139 + 0.146983i 0.0469563π0.0469563\pi
−0.989139 + 0.146983i 0.953044π0.953044\pi
234234 2.93555 0.930160i 0.191903 0.0608065i
235235 18.2602 1.19116
236236 4.42036 + 7.65628i 0.287741 + 0.498381i
237237 1.00277 + 1.24761i 0.0651368 + 0.0810409i
238238 0 0
239239 −3.02944 1.74905i −0.195958 0.113136i 0.398811 0.917033i 0.369423π-0.369423\pi
−0.594769 + 0.803897i 0.702756π0.702756\pi
240240 −6.08040 + 0.940283i −0.392488 + 0.0606950i
241241 10.0170 5.78332i 0.645252 0.372537i −0.141383 0.989955i 0.545155π-0.545155\pi
0.786635 + 0.617419i 0.211821π0.211821\pi
242242 1.86528i 0.119905i
243243 −11.2222 + 10.8195i −0.719905 + 0.694073i
244244 4.69034i 0.300268i
245245 0 0
246246 −0.0249997 0.161662i −0.00159392 0.0103072i
247247 4.22333 7.31502i 0.268724 0.465444i
248248 −2.99288 + 5.18382i −0.190048 + 0.329173i
249249 11.7886 + 14.6670i 0.747074 + 0.929482i
250250 8.05532 4.65074i 0.509463 0.294139i
251251 −26.7426 −1.68798 −0.843988 0.536361i 0.819798π-0.819798\pi
−0.843988 + 0.536361i 0.819798π0.819798\pi
252252 0 0
253253 10.1500 0.638127
254254 0.248691 0.143582i 0.0156043 0.00900913i
255255 −3.60240 + 9.28307i −0.225591 + 0.581328i
256256 −0.500000 + 0.866025i −0.0312500 + 0.0541266i
257257 −2.60614 + 4.51396i −0.162566 + 0.281573i −0.935788 0.352562i 0.885310π-0.885310\pi
0.773222 + 0.634135i 0.218644π0.218644\pi
258258 −9.87890 3.83362i −0.615034 0.238671i
259259 0 0
260260 3.64626i 0.226131i
261261 −8.65319 + 9.47026i −0.535619 + 0.586194i
262262 0.372949i 0.0230409i
263263 13.0228 7.51869i 0.803018 0.463622i −0.0415076 0.999138i 0.513216π-0.513216\pi
0.844525 + 0.535516i 0.179883π0.179883\pi
264264 −3.27954 4.08029i −0.201842 0.251124i
265265 9.81255 + 5.66528i 0.602780 + 0.348015i
266266 0 0
267267 8.06194 1.24671i 0.493383 0.0762975i
268268 −0.187838 0.325345i −0.0114740 0.0198736i
269269 −23.1313 −1.41034 −0.705170 0.709038i 0.749130π-0.749130\pi
−0.705170 + 0.709038i 0.749130π0.749130\pi
270270 −8.19902 16.5371i −0.498976 1.00641i
271271 9.91496i 0.602291i 0.953578 + 0.301146i 0.0973690π0.0973690\pi
−0.953578 + 0.301146i 0.902631π0.902631\pi
272272 0.809204 + 1.40158i 0.0490652 + 0.0849834i
273273 0 0
274274 −3.53111 + 6.11607i −0.213322 + 0.369485i
275275 19.9410 + 11.5129i 1.20249 + 0.694256i
276276 4.53380 3.64406i 0.272903 0.219346i
277277 4.29721 + 7.44299i 0.258195 + 0.447206i 0.965758 0.259443i 0.0835391π-0.0835391\pi
−0.707564 + 0.706650i 0.750206π0.750206\pi
278278 14.5862 0.874819
279279 −17.5371 3.86177i −1.04992 0.231198i
280280 0 0
281281 −17.9508 + 10.3639i −1.07085 + 0.618258i −0.928415 0.371545i 0.878828π-0.878828\pi
−0.142440 + 0.989803i 0.545495π0.545495\pi
282282 8.30045 + 3.22108i 0.494284 + 0.191813i
283283 2.04997 + 1.18355i 0.121858 + 0.0703547i 0.559690 0.828702i 0.310920π-0.310920\pi
−0.437832 + 0.899057i 0.644254π0.644254\pi
284284 −12.1129 6.99341i −0.718771 0.414983i
285285 −47.2003 18.3166i −2.79590 1.08498i
286286 −2.68672 + 1.55118i −0.158869 + 0.0917231i
287287 0 0
288288 −2.92981 0.645160i −0.172641 0.0380164i
289289 −14.3808 −0.845927
290290 −7.59485 13.1547i −0.445985 0.772468i
291291 20.7846 16.7057i 1.21841 0.979303i
292292 −1.13546 0.655556i −0.0664475 0.0383635i
293293 −8.83774 + 15.3074i −0.516306 + 0.894268i 0.483515 + 0.875336i 0.339360π0.339360\pi
−0.999821 + 0.0189321i 0.993973π0.993973\pi
294294 0 0
295295 −15.7022 27.1970i −0.914218 1.58347i
296296 5.84647i 0.339819i
297297 8.69723 13.0765i 0.504665 0.758777i
298298 10.7021 0.619958
299299 −1.72359 2.98534i −0.0996777 0.172647i
300300 13.0406 2.01662i 0.752898 0.116429i
301301 0 0
302302 −13.8575 8.00065i −0.797411 0.460386i
303303 −14.8708 18.5017i −0.854305 1.06290i
304304 −7.12643 + 4.11444i −0.408729 + 0.235980i
305305 16.6613i 0.954021i
306306 −3.27506 + 3.58430i −0.187223 + 0.204901i
307307 1.28155i 0.0731422i 0.999331 + 0.0365711i 0.0116435π0.0116435\pi
−0.999331 + 0.0365711i 0.988356π0.988356\pi
308308 0 0
309309 −4.92262 1.91028i −0.280038 0.108672i
310310 10.6315 18.4142i 0.603826 1.04586i
311311 6.26643 10.8538i 0.355336 0.615461i −0.631839 0.775100i 0.717700π-0.717700\pi
0.987175 + 0.159639i 0.0510330π0.0510330\pi
312312 −0.643198 + 1.65746i −0.0364139 + 0.0938354i
313313 −7.58105 + 4.37692i −0.428507 + 0.247398i −0.698710 0.715405i 0.746242π-0.746242\pi
0.270204 + 0.962803i 0.412909π0.412909\pi
314314 11.5267 0.650488
315315 0 0
316316 −0.924134 −0.0519866
317317 −11.8458 + 6.83920i −0.665329 + 0.384128i −0.794304 0.607520i 0.792164π-0.792164\pi
0.128976 + 0.991648i 0.458831π0.458831\pi
318318 3.46109 + 4.30617i 0.194089 + 0.241478i
319319 6.46195 11.1924i 0.361799 0.626655i
320320 1.77612 3.07634i 0.0992884 0.171973i
321321 −3.47465 22.4691i −0.193936 1.25410i
322322 0 0
323323 13.3177i 0.741017i
324324 −0.809858 8.96349i −0.0449921 0.497972i
325325 7.82009i 0.433781i
326326 −2.37960 + 1.37386i −0.131794 + 0.0760912i
327327 18.0952 2.79828i 1.00067 0.154745i
328328 0.0817920 + 0.0472226i 0.00451621 + 0.00260743i
329329 0 0
330330 11.6498 + 14.4942i 0.641298 + 0.797880i
331331 5.44858 + 9.43721i 0.299481 + 0.518716i 0.976017 0.217693i 0.0698532π-0.0698532\pi
−0.676536 + 0.736409i 0.736520π0.736520\pi
332332 −10.8642 −0.596250
333333 −16.7201 + 5.29795i −0.916257 + 0.290326i
334334 5.53892i 0.303076i
335335 0.667247 + 1.15570i 0.0364556 + 0.0631429i
336336 0 0
337337 12.8090 22.1858i 0.697749 1.20854i −0.271496 0.962440i 0.587518π-0.587518\pi
0.969245 0.246098i 0.0791484π-0.0791484\pi
338338 −10.3459 5.97319i −0.562741 0.324898i
339339 −19.8610 7.70727i −1.07870 0.418602i
340340 −2.87450 4.97877i −0.155891 0.270012i
341341 18.0912 0.979692
342342 −18.2246 16.6522i −0.985473 0.900448i
343343 0 0
344344 5.29833 3.05899i 0.285667 0.164930i
345345 −16.1052 + 12.9446i −0.867075 + 0.696914i
346346 9.70387 + 5.60253i 0.521683 + 0.301194i
347347 −14.5166 8.38116i −0.779291 0.449924i 0.0568878 0.998381i 0.481882π-0.481882\pi
−0.836179 + 0.548457i 0.815216π0.815216\pi
348348 −1.13188 7.31938i −0.0606752 0.392360i
349349 −14.4455 + 8.34010i −0.773249 + 0.446435i −0.834032 0.551716i 0.813973π-0.813973\pi
0.0607835 + 0.998151i 0.480640π0.480640\pi
350350 0 0
351351 −5.32298 0.337503i −0.284119 0.0180146i
352352 3.02237 0.161093
353353 17.9568 + 31.1021i 0.955746 + 1.65540i 0.732653 + 0.680603i 0.238282π0.238282\pi
0.223093 + 0.974797i 0.428385π0.428385\pi
354354 −2.34014 15.1327i −0.124377 0.804293i
355355 43.0282 + 24.8424i 2.28370 + 1.31850i
356356 −2.35495 + 4.07888i −0.124812 + 0.216180i
357357 0 0
358358 −1.37089 2.37445i −0.0724538 0.125494i
359359 28.5498i 1.50680i −0.657563 0.753399i 0.728413π-0.728413\pi
0.657563 0.753399i 0.271587π-0.271587\pi
360360 10.4074 + 2.29177i 0.548518 + 0.120787i
361361 −48.7146 −2.56393
362362 −11.1449 19.3036i −0.585765 1.01457i
363363 1.16881 3.01192i 0.0613467 0.158085i
364364 0 0
365365 4.03342 + 2.32870i 0.211119 + 0.121890i
366366 −2.93904 + 7.57364i −0.153626 + 0.395880i
367367 0.310665 0.179362i 0.0162166 0.00936264i −0.491870 0.870669i 0.663686π-0.663686\pi
0.508086 + 0.861306i 0.330353π0.330353\pi
368368 3.35830i 0.175063i
369369 −0.0609323 + 0.276706i −0.00317201 + 0.0144048i
370370 20.7681i 1.07968i
371371 0 0
372372 8.08095 6.49509i 0.418978 0.336755i
373373 −12.6854 + 21.9718i −0.656826 + 1.13766i 0.324606 + 0.945849i 0.394768π0.394768\pi
−0.981433 + 0.191807i 0.938565π0.938565\pi
374374 2.44571 4.23610i 0.126465 0.219044i
375375 −15.9214 + 2.46211i −0.822177 + 0.127143i
376376 −4.45176 + 2.57023i −0.229582 + 0.132549i
377377 −4.38924 −0.226057
378378 0 0
379379 26.9063 1.38209 0.691043 0.722814i 0.257152π-0.257152\pi
0.691043 + 0.722814i 0.257152π0.257152\pi
380380 25.3148 14.6155i 1.29862 0.749761i
381381 −0.491540 + 0.0760125i −0.0251823 + 0.00389424i
382382 −2.56632 + 4.44499i −0.131304 + 0.227426i
383383 6.28586 10.8874i 0.321192 0.556322i −0.659542 0.751668i 0.729250π-0.729250\pi
0.980734 + 0.195346i 0.0625830π0.0625830\pi
384384 1.35003 1.08509i 0.0688934 0.0553733i
385385 0 0
386386 15.9847i 0.813600i
387387 13.5496 + 12.3805i 0.688763 + 0.629338i
388388 15.3956i 0.781595i
389389 14.0805 8.12937i 0.713909 0.412175i −0.0985980 0.995127i 0.531436π-0.531436\pi
0.812507 + 0.582952i 0.198102π0.198102\pi
390390 2.28480 5.88772i 0.115695 0.298136i
391391 4.70694 + 2.71755i 0.238040 + 0.137432i
392392 0 0
393393 0.233695 0.602212i 0.0117884 0.0303776i
394394 2.36286 + 4.09259i 0.119039 + 0.206182i
395395 3.28275 0.165173
396396 2.73881 + 8.64358i 0.137630 + 0.434356i
397397 14.6938i 0.737463i −0.929536 0.368732i 0.879792π-0.879792\pi
0.929536 0.368732i 0.120208π-0.120208\pi
398398 −1.06047 1.83679i −0.0531567 0.0920701i
399399 0 0
400400 −3.80924 + 6.59779i −0.190462 + 0.329890i
401401 −14.4162 8.32318i −0.719909 0.415640i 0.0948099 0.995495i 0.469776π-0.469776\pi
−0.814719 + 0.579855i 0.803109π0.803109\pi
402402 0.0994416 + 0.643046i 0.00495969 + 0.0320722i
403403 −3.07208 5.32101i −0.153031 0.265058i
404404 13.7047 0.681833
405405 2.87682 + 31.8405i 0.142950 + 1.58217i
406406 0 0
407407 15.3028 8.83510i 0.758534 0.437940i
408408 −0.428394 2.77024i −0.0212087 0.137147i
409409 2.43254 + 1.40443i 0.120282 + 0.0694446i 0.558934 0.829212i 0.311211π-0.311211\pi
−0.438652 + 0.898657i 0.644544π0.644544\pi
410410 −0.290545 0.167747i −0.0143490 0.00828441i
411411 9.53421 7.66315i 0.470288 0.377995i
412412 2.64014 1.52429i 0.130070 0.0750962i
413413 0 0
414414 −9.60429 + 3.04322i −0.472025 + 0.149566i
415415 38.5923 1.89442
416416 −0.513232 0.888944i −0.0251633 0.0435841i
417417 −23.5527 9.13990i −1.15338 0.447583i
418418 21.5387 + 12.4354i 1.05349 + 0.608234i
419419 −7.47362 + 12.9447i −0.365110 + 0.632390i −0.988794 0.149287i 0.952302π-0.952302\pi
0.623684 + 0.781677i 0.285635π0.285635\pi
420420 0 0
421421 −7.80336 13.5158i −0.380312 0.658720i 0.610794 0.791789i 0.290850π-0.290850\pi
−0.991107 + 0.133069i 0.957517π0.957517\pi
422422 27.6159i 1.34432i
423423 −11.3846 10.4024i −0.553538 0.505780i
424424 −3.18968 −0.154905
425425 6.16490 + 10.6779i 0.299042 + 0.517955i
426426 15.1770 + 18.8826i 0.735326 + 0.914867i
427427 0 0
428428 11.3681 + 6.56336i 0.549496 + 0.317252i
429429 5.31032 0.821196i 0.256385 0.0396477i
430430 −18.8210 + 10.8663i −0.907629 + 0.524020i
431431 16.1758i 0.779163i −0.920992 0.389581i 0.872620π-0.872620\pi
0.920992 0.389581i 0.127380π-0.127380\pi
432432 4.32658 + 2.87762i 0.208163 + 0.138450i
433433 27.2499i 1.30955i 0.755824 + 0.654774i 0.227236π0.227236\pi
−0.755824 + 0.654774i 0.772764π0.772764\pi
434434 0 0
435435 4.02072 + 26.0003i 0.192779 + 1.24662i
436436 −5.28574 + 9.15516i −0.253141 + 0.438453i
437437 −13.8175 + 23.9327i −0.660983 + 1.14486i
438438 1.42267 + 1.77004i 0.0679780 + 0.0845757i
439439 −28.6955 + 16.5674i −1.36956 + 0.790717i −0.990872 0.134806i 0.956959π-0.956959\pi
−0.378690 + 0.925523i 0.623625π0.623625\pi
440440 −10.7362 −0.511829
441441 0 0
442442 −1.66124 −0.0790171
443443 −19.2808 + 11.1318i −0.916060 + 0.528887i −0.882376 0.470545i 0.844057π-0.844057\pi
−0.0336837 + 0.999433i 0.510724π0.510724\pi
444444 3.66349 9.44047i 0.173861 0.448025i
445445 8.36535 14.4892i 0.396556 0.686855i
446446 10.1734 17.6209i 0.481727 0.834375i
447447 −17.2811 6.70612i −0.817366 0.317188i
448448 0 0
449449 6.80819i 0.321298i −0.987012 0.160649i 0.948641π-0.948641\pi
0.987012 0.160649i 0.0513588π-0.0513588\pi
450450 −22.3207 4.91513i −1.05221 0.231702i
451451 0.285448i 0.0134412i
452452 10.6520 6.14993i 0.501027 0.289268i
453453 17.3628 + 21.6022i 0.815778 + 1.01496i
454454 3.60266 + 2.08000i 0.169081 + 0.0976192i
455455 0 0
456456 14.0854 2.17819i 0.659611 0.102003i
457457 −7.61298 13.1861i −0.356120 0.616818i 0.631189 0.775629i 0.282567π-0.282567\pi
−0.987309 + 0.158811i 0.949234π0.949234\pi
458458 −5.96964 −0.278943
459459 7.53431 3.73548i 0.351671 0.174357i
460460 11.9295i 0.556217i
461461 −0.103381 0.179060i −0.00481492 0.00833968i 0.863608 0.504164i 0.168199π-0.168199\pi
−0.868423 + 0.495824i 0.834866π0.834866\pi
462462 0 0
463463 −7.60217 + 13.1673i −0.353303 + 0.611938i −0.986826 0.161785i 0.948275π-0.948275\pi
0.633523 + 0.773724i 0.281608π0.281608\pi
464464 3.70319 + 2.13804i 0.171916 + 0.0992560i
465465 −28.7056 + 23.0722i −1.33119 + 1.06995i
466466 2.24360 + 3.88603i 0.103933 + 0.180017i
467467 2.30849 0.106824 0.0534120 0.998573i 0.482990π-0.482990\pi
0.0534120 + 0.998573i 0.482990π0.482990\pi
468468 2.07718 2.27332i 0.0960178 0.105084i
469469 0 0
470470 15.8138 9.13009i 0.729435 0.421139i
471471 −18.6125 7.22278i −0.857617 0.332808i
472472 7.65628 + 4.42036i 0.352409 + 0.203463i
473473 −16.0135 9.24541i −0.736303 0.425105i
474474 1.49223 + 0.579076i 0.0685403 + 0.0265978i
475475 −54.2925 + 31.3458i −2.49111 + 1.43824i
476476 0 0
477477 −2.89042 9.12207i −0.132343 0.417671i
478478 −3.49809 −0.159999
479479 −6.21659 10.7674i −0.284043 0.491977i 0.688334 0.725394i 0.258343π-0.258343\pi
−0.972377 + 0.233417i 0.925009π0.925009\pi
480480 −4.79564 + 3.85451i −0.218890 + 0.175934i
481481 −5.19719 3.00060i −0.236971 0.136815i
482482 5.78332 10.0170i 0.263423 0.456262i
483483 0 0
484484 0.932639 + 1.61538i 0.0423927 + 0.0734263i
485485 54.6891i 2.48331i
486486 −4.30895 + 14.9811i −0.195458 + 0.679556i
487487 37.3007 1.69026 0.845128 0.534565i 0.179524π-0.179524\pi
0.845128 + 0.534565i 0.179524π0.179524\pi
488488 −2.34517 4.06195i −0.106161 0.183876i
489489 4.70330 0.727325i 0.212690 0.0328908i
490490 0 0
491491 −11.8191 6.82377i −0.533389 0.307952i 0.209006 0.977914i 0.432977π-0.432977\pi
−0.742396 + 0.669962i 0.766310π0.766310\pi
492492 −0.102482 0.127504i −0.00462023 0.00574832i
493493 5.99328 3.46022i 0.269924 0.155840i
494494 8.44666i 0.380033i
495495 −9.72893 30.7041i −0.437283 1.38005i
496496 5.98576i 0.268768i
497497 0 0
498498 17.5427 + 6.80766i 0.786109 + 0.305059i
499499 10.5010 18.1882i 0.470088 0.814216i −0.529327 0.848418i 0.677556π-0.677556\pi
0.999415 + 0.0342021i 0.0108890π0.0108890\pi
500500 4.65074 8.05532i 0.207987 0.360245i
501501 −3.47077 + 8.94386i −0.155063 + 0.399582i
502502 −23.1598 + 13.3713i −1.03367 + 0.596790i
503503 22.3018 0.994388 0.497194 0.867639i 0.334364π-0.334364\pi
0.497194 + 0.867639i 0.334364π0.334364\pi
504504 0 0
505505 −48.6824 −2.16634
506506 8.79018 5.07501i 0.390771 0.225612i
507507 12.9629 + 16.1280i 0.575702 + 0.716268i
508508 0.143582 0.248691i 0.00637042 0.0110339i
509509 10.9589 18.9814i 0.485746 0.841337i −0.514120 0.857719i 0.671881π-0.671881\pi
0.999866 + 0.0163813i 0.00521458π0.00521458\pi
510510 1.52176 + 9.84057i 0.0673847 + 0.435748i
511511 0 0
512512 1.00000i 0.0441942i
513513 18.9933 + 38.3086i 0.838573 + 1.69137i
514514 5.21227i 0.229904i
515515 −9.37844 + 5.41465i −0.413264 + 0.238598i
516516 −10.4722 + 1.61944i −0.461013 + 0.0712917i
517517 13.4549 + 7.76818i 0.591745 + 0.341644i
518518 0 0
519519 −12.1585 15.1272i −0.533699 0.664009i
520520 1.82313 + 3.15775i 0.0799495 + 0.138477i
521521 26.7678 1.17272 0.586358 0.810052i 0.300561π-0.300561\pi
0.586358 + 0.810052i 0.300561π0.300561\pi
522522 −2.75875 + 12.5281i −0.120747 + 0.548339i
523523 17.1561i 0.750184i 0.926988 + 0.375092i 0.122389π0.122389\pi
−0.926988 + 0.375092i 0.877611π0.877611\pi
524524 0.186474 + 0.322983i 0.00814617 + 0.0141096i
525525 0 0
526526 7.51869 13.0228i 0.327831 0.567819i
527527 8.38954 + 4.84370i 0.365454 + 0.210995i
528528 −4.88031 1.89386i −0.212388 0.0824198i
529529 −5.86091 10.1514i −0.254822 0.441365i
530530 11.3306 0.492168
531531 −5.70367 + 25.9016i −0.247518 + 1.12403i
532532 0 0
533533 −0.0839566 + 0.0484723i −0.00363656 + 0.00209957i
534534 6.35849 5.11065i 0.275159 0.221160i
535535 −40.3822 23.3147i −1.74588 1.00798i
536536 −0.325345 0.187838i −0.0140527 0.00811336i
537537 0.725752 + 4.69312i 0.0313185 + 0.202523i
538538 −20.0323 + 11.5657i −0.863654 + 0.498631i
539539 0 0
540540 −15.3691 10.2220i −0.661381 0.439886i
541541 28.8182 1.23899 0.619496 0.785000i 0.287337π-0.287337\pi
0.619496 + 0.785000i 0.287337π0.287337\pi
542542 4.95748 + 8.58661i 0.212942 + 0.368827i
543543 5.90015 + 38.1537i 0.253199 + 1.63733i
544544 1.40158 + 0.809204i 0.0600924 + 0.0346943i
545545 18.7763 32.5214i 0.804286 1.39306i
546546 0 0
547547 −16.4045 28.4135i −0.701407 1.21487i −0.967972 0.251056i 0.919222π-0.919222\pi
0.266565 0.963817i 0.414111π-0.414111\pi
548548 7.06222i 0.301683i
549549 9.49151 10.3877i 0.405088 0.443338i
550550 23.0259 0.981826
551551 17.5937 + 30.4732i 0.749516 + 1.29820i
552552 2.10436 5.42275i 0.0895676 0.230808i
553553 0 0
554554 7.44299 + 4.29721i 0.316223 + 0.182571i
555555 −13.0136 + 33.5349i −0.552397 + 1.42348i
556556 12.6320 7.29308i 0.535715 0.309295i
557557 46.2508i 1.95971i −0.199708 0.979855i 0.563999π-0.563999\pi
0.199708 0.979855i 0.436001π-0.436001\pi
558558 −17.1185 + 5.42417i −0.724683 + 0.229623i
559559 6.27990i 0.265611i
560560 0 0
561561 −6.60357 + 5.30764i −0.278803 + 0.224089i
562562 −10.3639 + 17.9508i −0.437174 + 0.757208i
563563 0.988637 1.71237i 0.0416661 0.0721678i −0.844440 0.535650i 0.820067π-0.820067\pi
0.886106 + 0.463482i 0.153400π0.153400\pi
564564 8.79894 1.36068i 0.370502 0.0572950i
565565 −37.8385 + 21.8461i −1.59188 + 0.919071i
566566 2.36710 0.0994966
567567 0 0
568568 −13.9868 −0.586874
569569 28.5702 16.4950i 1.19773 0.691508i 0.237679 0.971344i 0.423613π-0.423613\pi
0.960048 + 0.279836i 0.0902800π0.0902800\pi
570570 −50.0350 + 7.73748i −2.09573 + 0.324087i
571571 −7.40326 + 12.8228i −0.309817 + 0.536618i −0.978322 0.207089i 0.933601π-0.933601\pi
0.668505 + 0.743707i 0.266934π0.266934\pi
572572 −1.55118 + 2.68672i −0.0648580 + 0.112337i
573573 6.92921 5.56937i 0.289472 0.232664i
574574 0 0
575575 25.5851i 1.06697i
576576 −2.85987 + 0.906179i −0.119161 + 0.0377575i
577577 18.4180i 0.766752i 0.923592 + 0.383376i 0.125239π0.125239\pi
−0.923592 + 0.383376i 0.874761π0.874761\pi
578578 −12.4541 + 7.19038i −0.518022 + 0.299080i
579579 10.0163 25.8110i 0.416261 1.07267i
580580 −13.1547 7.59485i −0.546218 0.315359i
581581 0 0
582582 9.64714 24.8598i 0.399887 1.03047i
583583 4.82020 + 8.34884i 0.199632 + 0.345774i
584584 −1.31111 −0.0542542
585585 −7.37867 + 8.07539i −0.305070 + 0.333876i
586586 17.6755i 0.730167i
587587 −23.1065 40.0216i −0.953707 1.65187i −0.737301 0.675565i 0.763900π-0.763900\pi
−0.216406 0.976304i 0.569433π-0.569433\pi
588588 0 0
589589 −24.6281 + 42.6571i −1.01478 + 1.75765i
590590 −27.1970 15.7022i −1.11968 0.646450i
591591 −1.25090 8.08904i −0.0514552 0.332738i
592592 2.92323 + 5.06319i 0.120144 + 0.208096i
593593 13.6093 0.558867 0.279434 0.960165i 0.409853π-0.409853\pi
0.279434 + 0.960165i 0.409853π0.409853\pi
594594 0.993759 15.6732i 0.0407744 0.643080i
595595 0 0
596596 9.26832 5.35107i 0.379645 0.219188i
597597 0.561416 + 3.63043i 0.0229772 + 0.148584i
598598 −2.98534 1.72359i −0.122080 0.0704827i
599599 −20.4214 11.7903i −0.834396 0.481739i 0.0209595 0.999780i 0.493328π-0.493328\pi
−0.855355 + 0.518042i 0.826661π0.826661\pi
600600 10.2852 8.26673i 0.419890 0.337488i
601601 31.0765 17.9420i 1.26764 0.731871i 0.293097 0.956083i 0.405314π-0.405314\pi
0.974540 + 0.224212i 0.0719808π0.0719808\pi
602602 0 0
603603 0.242371 1.10066i 0.00987010 0.0448222i
604604 −16.0013 −0.651084
605605 −3.31297 5.73823i −0.134691 0.233292i
606606 −22.1294 8.58755i −0.898943 0.348846i
607607 −16.8502 9.72845i −0.683928 0.394866i 0.117406 0.993084i 0.462542π-0.462542\pi
−0.801333 + 0.598218i 0.795876π0.795876\pi
608608 −4.11444 + 7.12643i −0.166863 + 0.289015i
609609 0 0
610610 8.33063 + 14.4291i 0.337297 + 0.584216i
611611 5.27649i 0.213464i
612612 −1.04413 + 4.74162i −0.0422065 + 0.191669i
613613 42.2421 1.70614 0.853071 0.521795i 0.174738π-0.174738\pi
0.853071 + 0.521795i 0.174738π0.174738\pi
614614 0.640777 + 1.10986i 0.0258597 + 0.0447902i
615615 0.364040 + 0.452926i 0.0146795 + 0.0182637i
616616 0 0
617617 9.63660 + 5.56369i 0.387955 + 0.223986i 0.681274 0.732029i 0.261426π-0.261426\pi
−0.293319 + 0.956015i 0.594760π0.594760\pi
618618 −5.21826 + 0.806960i −0.209909 + 0.0324607i
619619 8.71387 5.03096i 0.350240 0.202211i −0.314551 0.949241i 0.601854π-0.601854\pi
0.664791 + 0.747029i 0.268521π0.268521\pi
620620 21.2629i 0.853939i
621621 17.4153 + 1.10421i 0.698851 + 0.0443105i
622622 12.5329i 0.502522i
623623 0 0
624624 0.271706 + 1.75700i 0.0108769 + 0.0703365i
625625 2.52560 4.37447i 0.101024 0.174979i
626626 −4.37692 + 7.58105i −0.174937 + 0.303000i
627627 −26.9870 33.5762i −1.07776 1.34091i
628628 9.98239 5.76334i 0.398341 0.229982i
629629 9.46198 0.377274
630630 0 0
631631 10.3528 0.412139 0.206070 0.978537i 0.433933π-0.433933\pi
0.206070 + 0.978537i 0.433933π0.433933\pi
632632 −0.800324 + 0.462067i −0.0318352 + 0.0183800i
633633 17.3045 44.5922i 0.687793 1.77238i
634634 −6.83920 + 11.8458i −0.271619 + 0.470459i
635635 −0.510039 + 0.883413i −0.0202403 + 0.0350572i
636636 5.15048 + 1.99870i 0.204230 + 0.0792538i
637637 0 0
638638 12.9239i 0.511662i
639639 −12.6746 40.0005i −0.501398 1.58239i
640640 3.55225i 0.140415i
641641 23.0678 13.3182i 0.911123 0.526037i 0.0303310 0.999540i 0.490344π-0.490344\pi
0.880792 + 0.473503i 0.157011π0.157011\pi
642642 −14.2437 17.7215i −0.562153 0.699410i
643643 −40.0493 23.1225i −1.57939 0.911861i −0.994944 0.100429i 0.967979π-0.967979\pi
−0.584446 0.811433i 0.698688π-0.698688\pi
644644 0 0
645645 37.1998 5.75264i 1.46474 0.226510i
646646 6.65885 + 11.5335i 0.261989 + 0.453778i
647647 −31.4063 −1.23471 −0.617355 0.786684i 0.711796π-0.711796\pi
−0.617355 + 0.786684i 0.711796π0.711796\pi
648648 −5.18310 7.35768i −0.203611 0.289037i
649649 26.7199i 1.04885i
650650 −3.91005 6.77240i −0.153365 0.265635i
651651 0 0
652652 −1.37386 + 2.37960i −0.0538046 + 0.0931923i
653653 −39.9639 23.0732i −1.56391 0.902924i −0.996855 0.0792429i 0.974750π-0.974750\pi
−0.567054 0.823681i 0.691917π-0.691917\pi
654654 14.2718 11.4710i 0.558072 0.448552i
655655 −0.662404 1.14732i −0.0258823 0.0448294i
656656 0.0944452 0.00368747
657657 −1.18810 3.74960i −0.0463522 0.146286i
658658 0 0
659659 1.18052 0.681575i 0.0459867 0.0265504i −0.476830 0.878995i 0.658214π-0.658214\pi
0.522817 + 0.852445i 0.324881π0.324881\pi
660660 17.3361 + 6.72747i 0.674806 + 0.261866i
661661 −6.23888 3.60202i −0.242664 0.140102i 0.373736 0.927535i 0.378076π-0.378076\pi
−0.616401 + 0.787433i 0.711410π0.711410\pi
662662 9.43721 + 5.44858i 0.366788 + 0.211765i
663663 2.68245 + 1.04096i 0.104178 + 0.0404274i
664664 −9.40866 + 5.43209i −0.365127 + 0.210806i
665665 0 0
666666 −11.8311 + 12.9482i −0.458445 + 0.501733i
667667 14.3604 0.556035
668668 −2.76946 4.79685i −0.107154 0.185596i
669669 −27.4689 + 22.0782i −1.06201 + 0.853593i
670670 1.15570 + 0.667247i 0.0446488 + 0.0257780i
671671 −7.08797 + 12.2767i −0.273628 + 0.473938i
672672 0 0
673673 19.4709 + 33.7246i 0.750548 + 1.29999i 0.947558 + 0.319585i 0.103544π0.103544\pi
−0.197010 + 0.980402i 0.563123π0.563123\pi
674674 25.6180i 0.986767i
675675 32.9620 + 21.9231i 1.26871 + 0.843820i
676676 −11.9464 −0.459476
677677 1.20505 + 2.08722i 0.0463140 + 0.0802182i 0.888253 0.459354i 0.151919π-0.151919\pi
−0.841939 + 0.539573i 0.818586π0.818586\pi
678678 −21.0537 + 3.25578i −0.808563 + 0.125037i
679679 0 0
680680 −4.97877 2.87450i −0.190927 0.110232i
681681 −4.51397 5.61612i −0.172976 0.215210i
682682 15.6674 9.04559i 0.599937 0.346374i
683683 28.3251i 1.08383i 0.840433 + 0.541915i 0.182300π0.182300\pi
−0.840433 + 0.541915i 0.817700π0.817700\pi
684684 −24.1091 5.30895i −0.921833 0.202993i
685685 25.0868i 0.958517i
686686 0 0
687687 9.63935 + 3.74066i 0.367764 + 0.142715i
688688 3.05899 5.29833i 0.116623 0.201997i
689689 1.63705 2.83545i 0.0623666 0.108022i
690690 −7.47522 + 19.2630i −0.284577 + 0.733328i
691691 2.95334 1.70511i 0.112350 0.0648655i −0.442772 0.896634i 0.646005π-0.646005\pi
0.555122 + 0.831769i 0.312672π0.312672\pi
692692 11.2051 0.425953
693693 0 0
694694 −16.7623 −0.636289
695695 −44.8719 + 25.9068i −1.70209 + 0.982702i
696696 −4.63993 5.77283i −0.175876 0.218819i
697697 0.0764255 0.132373i 0.00289482 0.00501398i
698698 −8.34010 + 14.4455i −0.315678 + 0.546769i
699699 −1.18776 7.68076i −0.0449254 0.290513i
700700 0 0
701701 51.4943i 1.94491i −0.233087 0.972456i 0.574883π-0.574883\pi
0.233087 0.972456i 0.425117π-0.425117\pi
702702 −4.77858 + 2.36920i −0.180356 + 0.0894198i
703703 48.1099i 1.81450i
704704 2.61745 1.51119i 0.0986488 0.0569549i
705705 −31.2560 + 4.83348i −1.17717 + 0.182039i
706706 31.1021 + 17.9568i 1.17054 + 0.675814i
707707 0 0
708708 −9.59297 11.9352i −0.360526 0.448553i
709709 −5.04218 8.73331i −0.189363 0.327986i 0.755675 0.654947i 0.227309π-0.227309\pi
−0.945038 + 0.326960i 0.893976π0.893976\pi
710710 49.6847 1.86463
711711 −2.04669 1.87010i −0.0767567 0.0701344i
712712 4.70989i 0.176511i
713713 10.0510 + 17.4088i 0.376412 + 0.651965i
714714 0 0
715715 5.51017 9.54389i 0.206069 0.356921i
716716 −2.37445 1.37089i −0.0887375 0.0512326i
717717 5.64848 + 2.19196i 0.210946 + 0.0818602i
718718 −14.2749 24.7248i −0.532734 0.922722i
719719 −31.9168 −1.19030 −0.595148 0.803616i 0.702907π-0.702907\pi
−0.595148 + 0.803616i 0.702907π0.702907\pi
720720 10.1590 3.21897i 0.378602 0.119964i
721721 0 0
722722 −42.1881 + 24.3573i −1.57008 + 0.906485i
723723 −15.6153 + 12.5508i −0.580740 + 0.466771i
724724 −19.3036 11.1449i −0.717413 0.414198i
725725 28.2127 + 16.2886i 1.04779 + 0.604943i
726726 −0.493741 3.19281i −0.0183244 0.118496i
727727 17.9336 10.3540i 0.665120 0.384007i −0.129105 0.991631i 0.541210π-0.541210\pi
0.794225 + 0.607624i 0.207877π0.207877\pi
728728 0 0
729729 16.3452 21.4904i 0.605377 0.795939i
730730 4.65739 0.172378
731731 −4.95070 8.57487i −0.183108 0.317153i
732732 1.24154 + 8.02848i 0.0458885 + 0.296741i
733733 7.69996 + 4.44558i 0.284405 + 0.164201i 0.635416 0.772170i 0.280829π-0.280829\pi
−0.351011 + 0.936371i 0.614162π0.614162\pi
734734 0.179362 0.310665i 0.00662038 0.0114668i
735735 0 0
736736 1.67915 + 2.90837i 0.0618943 + 0.107204i
737737 1.13543i 0.0418241i
738738 0.0855843 + 0.270101i 0.00315040 + 0.00994255i
739739 32.7763 1.20570 0.602848 0.797856i 0.294032π-0.294032\pi
0.602848 + 0.797856i 0.294032π0.294032\pi
740740 −10.3841 17.9857i −0.381726 0.661168i
741741 −5.29280 + 13.6391i −0.194436 + 0.501044i
742742 0 0
743743 −6.68055 3.85702i −0.245086 0.141500i 0.372426 0.928062i 0.378526π-0.378526\pi
−0.617512 + 0.786562i 0.711859π0.711859\pi
744744 3.75077 9.66539i 0.137510 0.354350i
745745 −32.9234 + 19.0083i −1.20622 + 0.696411i
746746 25.3708i 0.928893i
747747 −24.0610 21.9851i −0.880346 0.804392i
748748 4.89143i 0.178848i
749749 0 0
750750 −12.5573 + 10.0929i −0.458527 + 0.368542i
751751 −15.3804 + 26.6397i −0.561239 + 0.972095i 0.436149 + 0.899874i 0.356342π0.356342\pi
−0.997389 + 0.0722207i 0.976991π0.976991\pi
752752 −2.57023 + 4.45176i −0.0937265 + 0.162339i
753753 45.7754 7.07878i 1.66815 0.257965i
754754 −3.80120 + 2.19462i −0.138431 + 0.0799234i
755755 56.8406 2.06864
756756 0 0
757757 46.4611 1.68866 0.844328 0.535827i 0.180000π-0.180000\pi
0.844328 + 0.535827i 0.180000π0.180000\pi
758758 23.3016 13.4532i 0.846351 0.488641i
759759 −17.3738 + 2.68672i −0.630631 + 0.0975217i
760760 14.6155 25.3148i 0.530161 0.918266i
761761 18.5959 32.2090i 0.674099 1.16757i −0.302632 0.953107i 0.597865π-0.597865\pi
0.976731 0.214467i 0.0688013π-0.0688013\pi
762762 −0.387680 + 0.311599i −0.0140442 + 0.0112880i
763763 0 0
764764 5.13264i 0.185692i
765765 3.70902 16.8434i 0.134100 0.608976i
766766 12.5717i 0.454235i
767767 −7.85890 + 4.53734i −0.283768 + 0.163834i
768768 0.626615 1.61473i 0.0226110 0.0582666i
769769 12.2312 + 7.06166i 0.441067 + 0.254650i 0.704050 0.710150i 0.251373π-0.251373\pi
−0.262983 + 0.964800i 0.584706π0.584706\pi
770770 0 0
771771 3.26609 8.41642i 0.117625 0.303110i
772772 7.99235 + 13.8432i 0.287651 + 0.498226i
773773 30.9455 1.11303 0.556517 0.830836i 0.312138π-0.312138\pi
0.556517 + 0.830836i 0.312138π0.312138\pi
774774 17.9245 + 3.94708i 0.644284 + 0.141875i
775775 45.6024i 1.63809i
776776 7.69782 + 13.3330i 0.276336 + 0.478627i
777777 0 0
778778 8.12937 14.0805i 0.291452 0.504810i
779779 0.673057 + 0.388590i 0.0241148 + 0.0139227i
780780 −0.965167 6.24132i −0.0345585 0.223475i
781781 21.1367 + 36.6098i 0.756330 + 1.31000i
782782 5.43510 0.194359
783783 12.3049 18.5008i 0.439742 0.661165i
784784 0 0
785785 −35.4599 + 20.4728i −1.26562 + 0.730706i
786786 −0.0987198 0.638378i −0.00352122 0.0227702i
787787 15.8704 + 9.16280i 0.565720 + 0.326619i 0.755438 0.655220i 0.227424π-0.227424\pi
−0.189718 + 0.981839i 0.560757π0.560757\pi
788788 4.09259 + 2.36286i 0.145793 + 0.0841734i
789789 −20.3009 + 16.3169i −0.722732 + 0.580898i
790790 2.84295 1.64138i 0.101148 0.0583976i
791791 0 0
792792 6.69367 + 6.11615i 0.237849 + 0.217328i
793793 4.81447 0.170967
794794 −7.34692 12.7252i −0.260733 0.451602i
795795 −18.2958 7.09990i −0.648885 0.251807i
796796 −1.83679 1.06047i −0.0651034 0.0375875i
797797 1.07681 1.86508i 0.0381424 0.0660646i −0.846324 0.532668i 0.821189π-0.821189\pi
0.884466 + 0.466604i 0.154523π0.154523\pi
798798 0 0
799799 4.15968 + 7.20477i 0.147159 + 0.254886i
800800 7.61848i 0.269354i
801801 −13.4697 + 4.26800i −0.475927 + 0.150802i
802802 −16.6464 −0.587804
803803 1.98133 + 3.43177i 0.0699197 + 0.121104i
804804 0.407642 + 0.507173i 0.0143764 + 0.0178866i
805805 0 0
806806 −5.32101 3.07208i −0.187424 0.108210i
807807 39.5940 6.12287i 1.39377 0.215535i
808808 11.8686 6.85234i 0.417536 0.241064i
809809 19.6468i 0.690746i 0.938465 + 0.345373i 0.112248π0.112248\pi
−0.938465 + 0.345373i 0.887752π0.887752\pi
810810 18.4117 + 26.1363i 0.646920 + 0.918336i
811811 12.3340i 0.433105i −0.976271 0.216552i 0.930519π-0.930519\pi
0.976271 0.216552i 0.0694812π-0.0694812\pi
812812 0 0
813813 −2.62450 16.9715i −0.0920452 0.595216i
814814 8.83510 15.3028i 0.309670 0.536364i
815815 4.88030 8.45293i 0.170950 0.296093i
816816 −1.75612 2.18490i −0.0614765 0.0764868i
817817 43.5994 25.1721i 1.52535 0.880661i
818818 2.80886 0.0982095
819819 0 0
820820 −0.335493 −0.0117159
821821 19.3763 11.1869i 0.676238 0.390426i −0.122198 0.992506i 0.538994π-0.538994\pi
0.798436 + 0.602079i 0.205661π0.205661\pi
822822 4.42529 11.4036i 0.154350 0.397746i
823823 −13.5033 + 23.3883i −0.470694 + 0.815266i −0.999438 0.0335154i 0.989330π-0.989330\pi
0.528744 + 0.848781i 0.322663π0.322663\pi
824824 1.52429 2.64014i 0.0531010 0.0919737i
825825 −37.1805 14.4283i −1.29446 0.502330i
826826 0 0
827827 26.3189i 0.915196i 0.889159 + 0.457598i 0.151290π0.151290\pi
−0.889159 + 0.457598i 0.848710π0.848710\pi
828828 −6.79595 + 7.43765i −0.236176 + 0.258476i
829829 33.3351i 1.15778i −0.815407 0.578888i 0.803487π-0.803487\pi
0.815407 0.578888i 0.196513π-0.196513\pi
830830 33.4219 19.2962i 1.16009 0.669779i
831831 −9.32573 11.6027i −0.323506 0.402494i
832832 −0.888944 0.513232i −0.0308186 0.0177931i
833833 0 0
834834 −24.9672 + 3.86096i −0.864543 + 0.133694i
835835 9.83781 + 17.0396i 0.340452 + 0.589679i
836836 24.8707 0.860173
837837 31.0406 + 1.96812i 1.07292 + 0.0680283i
838838 14.9472i 0.516344i
839839 18.6896 + 32.3713i 0.645236 + 1.11758i 0.984247 + 0.176799i 0.0565743π0.0565743\pi
−0.339011 + 0.940782i 0.610092π0.610092\pi
840840 0 0
841841 −5.35758 + 9.27960i −0.184744 + 0.319986i
842842 −13.5158 7.80336i −0.465786 0.268922i
843843 27.9831 22.4915i 0.963790 0.774649i
844844 13.8079 + 23.9160i 0.475289 + 0.823224i
845845 42.4365 1.45986
846846 −15.0605 3.31641i −0.517792 0.114021i
847847 0 0
848848 −2.76235 + 1.59484i −0.0948594 + 0.0547671i
849849 −3.82223 1.48326i −0.131178 0.0509053i
850850 10.6779 + 6.16490i 0.366250 + 0.211454i
851851 17.0037 + 9.81710i 0.582880 + 0.336526i
852852 22.5850 + 8.76436i 0.773748 + 0.300262i
853853 4.65798 2.68929i 0.159486 0.0920795i −0.418133 0.908386i 0.637315π-0.637315\pi
0.577619 + 0.816306i 0.303982π0.303982\pi
854854 0 0
855855 85.6414 + 18.8587i 2.92887 + 0.644954i
856856 13.1267 0.448662
857857 −22.7000 39.3176i −0.775418 1.34306i −0.934559 0.355807i 0.884206π-0.884206\pi
0.159142 0.987256i 0.449127π-0.449127\pi
858858 4.18827 3.36633i 0.142985 0.114925i
859859 3.36261 + 1.94141i 0.114731 + 0.0662399i 0.556267 0.831003i 0.312233π-0.312233\pi
−0.441536 + 0.897243i 0.645566π0.645566\pi
860860 −10.8663 + 18.8210i −0.370538 + 0.641791i
861861 0 0
862862 −8.08792 14.0087i −0.275476 0.477138i
863863 23.4788i 0.799228i 0.916684 + 0.399614i 0.130856π0.130856\pi
−0.916684 + 0.399614i 0.869144π0.869144\pi
864864 5.18574 + 0.328801i 0.176422 + 0.0111860i
865865 −39.8032 −1.35335
866866 13.6250 + 23.5991i 0.462995 + 0.801931i
867867 24.6156 3.80660i 0.835990 0.129279i
868868 0 0
869869 2.41887 + 1.39654i 0.0820547 + 0.0473743i
870870 16.4822 + 20.5065i 0.558798 + 0.695237i
871871 0.333955 0.192809i 0.0113156 0.00653308i
872872 10.5715i 0.357995i
873873 −31.1550 + 34.0968i −1.05444 + 1.15400i
874874 27.6351i 0.934770i
875875 0 0
876876 2.11709 + 0.821562i 0.0715299 + 0.0277580i
877877 −16.4796 + 28.5434i −0.556475 + 0.963843i 0.441312 + 0.897354i 0.354513π0.354513\pi
−0.997787 + 0.0664896i 0.978820π0.978820\pi
878878 −16.5674 + 28.6955i −0.559121 + 0.968427i
879879 11.0757 28.5411i 0.373575 0.962668i
880880 −9.29783 + 5.36811i −0.313430 + 0.180959i
881881 −7.44403 −0.250796 −0.125398 0.992107i 0.540021π-0.540021\pi
−0.125398 + 0.992107i 0.540021π0.540021\pi
882882 0 0
883883 −28.2839 −0.951828 −0.475914 0.879492i 0.657883π-0.657883\pi
−0.475914 + 0.879492i 0.657883π0.657883\pi
884884 −1.43867 + 0.830619i −0.0483879 + 0.0279368i
885885 34.0766 + 42.3969i 1.14547 + 1.42516i
886886 −11.1318 + 19.2808i −0.373980 + 0.647752i
887887 −6.06377 + 10.5028i −0.203602 + 0.352648i −0.949686 0.313203i 0.898598π-0.898598\pi
0.746085 + 0.665851i 0.231931π0.231931\pi
888888 −1.54756 10.0074i −0.0519329 0.335827i
889889 0 0
890890 16.7307i 0.560814i
891891 −11.4257 + 24.6853i −0.382776 + 0.826989i
892892 20.3469i 0.681264i
893893 −36.6331 + 21.1501i −1.22588 + 0.707761i
894894 −18.3189 + 2.83286i −0.612676 + 0.0947451i
895895 8.43465 + 4.86975i 0.281939 + 0.162778i
896896 0 0
897897 3.74050 + 4.65379i 0.124892 + 0.155385i
898898 −3.40409 5.89606i −0.113596 0.196754i
899899 25.5956 0.853660
900900 −21.7878 + 6.90370i −0.726261 + 0.230123i
901901 5.16221i 0.171978i
902902 −0.142724 0.247206i −0.00475220 0.00823105i
903903 0 0
904904 6.14993 10.6520i 0.204544 0.354280i
905905 68.5712 + 39.5896i 2.27938 + 1.31600i
906906 25.8378 + 10.0267i 0.858403 + 0.333113i
907907 23.0890 + 39.9913i 0.766657 + 1.32789i 0.939366 + 0.342916i 0.111415π0.111415\pi
−0.172709 + 0.984973i 0.555252π0.555252\pi
908908 4.16000 0.138054
909909 30.3518 + 27.7332i 1.00671 + 0.919851i
910910 0 0
911911 −12.7284 + 7.34874i −0.421710 + 0.243475i −0.695809 0.718227i 0.744954π-0.744954\pi
0.274098 + 0.961702i 0.411621π0.411621\pi
912912 11.1092 8.92908i 0.367864 0.295672i
913913 28.4365 + 16.4178i 0.941110 + 0.543350i
914914 −13.1861 7.61298i −0.436156 0.251815i
915915 −4.41025 28.5192i −0.145798 0.942814i
916916 −5.16986 + 2.98482i −0.170817 + 0.0986212i
917917 0 0
918918 4.65716 7.00218i 0.153709 0.231106i
919919 25.8691 0.853342 0.426671 0.904407i 0.359686π-0.359686\pi
0.426671 + 0.904407i 0.359686π0.359686\pi
920920 −5.96476 10.3313i −0.196652 0.340612i
921921 −0.339228 2.19364i −0.0111780 0.0722830i
922922 −0.179060 0.103381i −0.00589704 0.00340466i
923923 7.17849 12.4335i 0.236283 0.409254i
924924 0 0
925925 22.2706 + 38.5738i 0.732253 + 1.26830i
926926 15.2043i 0.499645i
927927 8.93173 + 1.96682i 0.293357 + 0.0645987i
928928 4.27608 0.140369
929929 6.59673 + 11.4259i 0.216432 + 0.374870i 0.953714 0.300714i 0.0972248π-0.0972248\pi
−0.737283 + 0.675584i 0.763892π0.763892\pi
930930 −13.3237 + 34.3339i −0.436900 + 1.12585i
931931 0 0
932932 3.88603 + 2.24360i 0.127291 + 0.0734915i
933933 −7.85327 + 20.2372i −0.257105 + 0.662535i
934934 1.99921 1.15424i 0.0654161 0.0377680i
935935 17.3756i 0.568242i
936936 0.662233 3.00734i 0.0216458 0.0982981i
937937 8.86021i 0.289451i −0.989472 0.144725i 0.953770π-0.953770\pi
0.989472 0.144725i 0.0462298π-0.0462298\pi
938938 0 0
939939 11.8180 9.49871i 0.385664 0.309979i
940940 9.13009 15.8138i 0.297791 0.515788i
941941 −2.05919 + 3.56663i −0.0671278 + 0.116269i −0.897636 0.440738i 0.854717π-0.854717\pi
0.830508 + 0.557007i 0.188050π0.188050\pi
942942 −19.7303 + 3.05112i −0.642847 + 0.0994108i
943943 0.274682 0.158588i 0.00894488 0.00516433i
944944 8.84071 0.287741
945945 0 0
946946 −18.4908 −0.601189
947947 21.4498 12.3840i 0.697024 0.402427i −0.109214 0.994018i 0.534833π-0.534833\pi
0.806238 + 0.591591i 0.201500π0.201500\pi
948948 1.58184 0.244619i 0.0513759 0.00794485i
949949 0.672905 1.16550i 0.0218434 0.0378339i
950950 −31.3458 + 54.2925i −1.01699 + 1.76148i
951951 18.4662 14.8423i 0.598809 0.481294i
952952 0 0
953953 9.62625i 0.311825i −0.987771 0.155912i 0.950168π-0.950168\pi
0.987771 0.155912i 0.0498317π-0.0498317\pi
954954 −7.06422 6.45474i −0.228713 0.208980i
955955 18.2324i 0.589987i
956956 −3.02944 + 1.74905i −0.0979790 + 0.0565682i
957957 −8.09830 + 20.8686i −0.261781 + 0.674586i
958958 −10.7674 6.21659i −0.347880 0.200849i
959959 0 0
960960 −2.22589 + 5.73592i −0.0718404 + 0.185126i
961961 2.41465 + 4.18230i 0.0778920 + 0.134913i
962962 −6.00119 −0.193486
963963 11.8952 + 37.5407i 0.383316 + 1.20973i
964964 11.5666i 0.372537i
965965 −28.3908 49.1744i −0.913933 1.58298i
966966 0 0
967967 5.05558 8.75652i 0.162576 0.281591i −0.773216 0.634143i 0.781353π-0.781353\pi
0.935792 + 0.352553i 0.114686π0.114686\pi
968968 1.61538 + 0.932639i 0.0519202 + 0.0299762i
969969 −3.52520 22.7960i −0.113246 0.732312i
970970 −27.3446 47.3622i −0.877981 1.52071i
971971 −25.3149 −0.812392 −0.406196 0.913786i 0.633145π-0.633145\pi
−0.406196 + 0.913786i 0.633145π0.633145\pi
972972 3.75888 + 15.1285i 0.120566 + 0.485246i
973973 0 0
974974 32.3033 18.6503i 1.03507 0.597595i
975975 2.06998 + 13.3857i 0.0662926 + 0.428685i
976976 −4.06195 2.34517i −0.130020 0.0750671i
977977 −7.84008 4.52647i −0.250826 0.144815i 0.369316 0.929304i 0.379592π-0.379592\pi
−0.620143 + 0.784489i 0.712925π0.712925\pi
978978 3.70951 2.98153i 0.118617 0.0953388i
979979 12.3279 7.11752i 0.394001 0.227477i
980980 0 0
981981 −30.2330 + 9.57964i −0.965266 + 0.305855i
982982 −13.6475 −0.435511
983983 3.19651 + 5.53653i 0.101953 + 0.176588i 0.912489 0.409101i 0.134158π-0.134158\pi
−0.810536 + 0.585688i 0.800824π0.800824\pi
984984 −0.152504 0.0591808i −0.00486164 0.00188661i
985985 −14.5379 8.39347i −0.463216 0.267438i
986986 3.46022 5.99328i 0.110196 0.190865i
987987 0 0
988988 −4.22333 7.31502i −0.134362 0.232722i
989989 20.5460i 0.653326i
990990 −23.7776 21.7261i −0.755701 0.690501i
991991 −13.8446 −0.439788 −0.219894 0.975524i 0.570571π-0.570571\pi
−0.219894 + 0.975524i 0.570571π0.570571\pi
992992 2.99288 + 5.18382i 0.0950240 + 0.164586i
993993 −11.8244 14.7115i −0.375236 0.466855i
994994 0 0
995995 6.52475 + 3.76706i 0.206848 + 0.119424i
996996 18.5963 2.87576i 0.589246 0.0911219i
997997 −5.99391 + 3.46059i −0.189829 + 0.109598i −0.591903 0.806010i 0.701623π-0.701623\pi
0.402073 + 0.915607i 0.368290π0.368290\pi
998998 21.0019i 0.664804i
999999 27.2176 13.4944i 0.861125 0.426942i
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 882.2.m.a.293.5 16
3.2 odd 2 2646.2.m.a.881.4 16
7.2 even 3 126.2.t.a.59.4 yes 16
7.3 odd 6 126.2.l.a.5.6 16
7.4 even 3 882.2.l.b.509.7 16
7.5 odd 6 882.2.t.a.815.1 16
7.6 odd 2 882.2.m.b.293.8 16
9.2 odd 6 882.2.m.b.587.8 16
9.7 even 3 2646.2.m.b.1763.1 16
21.2 odd 6 378.2.t.a.17.5 16
21.5 even 6 2646.2.t.b.2285.8 16
21.11 odd 6 2646.2.l.a.1097.4 16
21.17 even 6 378.2.l.a.341.1 16
21.20 even 2 2646.2.m.b.881.1 16
28.3 even 6 1008.2.ca.c.257.7 16
28.23 odd 6 1008.2.df.c.689.3 16
63.2 odd 6 126.2.l.a.101.2 yes 16
63.11 odd 6 882.2.t.a.803.1 16
63.16 even 3 378.2.l.a.143.5 16
63.20 even 6 inner 882.2.m.a.587.5 16
63.23 odd 6 1134.2.k.a.647.4 16
63.25 even 3 2646.2.t.b.1979.8 16
63.31 odd 6 1134.2.k.a.971.4 16
63.34 odd 6 2646.2.m.a.1763.4 16
63.38 even 6 126.2.t.a.47.4 yes 16
63.47 even 6 882.2.l.b.227.3 16
63.52 odd 6 378.2.t.a.89.5 16
63.58 even 3 1134.2.k.b.647.5 16
63.59 even 6 1134.2.k.b.971.5 16
63.61 odd 6 2646.2.l.a.521.8 16
84.23 even 6 3024.2.df.c.17.1 16
84.59 odd 6 3024.2.ca.c.2609.1 16
252.79 odd 6 3024.2.ca.c.2033.1 16
252.115 even 6 3024.2.df.c.1601.1 16
252.191 even 6 1008.2.ca.c.353.7 16
252.227 odd 6 1008.2.df.c.929.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
126.2.l.a.5.6 16 7.3 odd 6
126.2.l.a.101.2 yes 16 63.2 odd 6
126.2.t.a.47.4 yes 16 63.38 even 6
126.2.t.a.59.4 yes 16 7.2 even 3
378.2.l.a.143.5 16 63.16 even 3
378.2.l.a.341.1 16 21.17 even 6
378.2.t.a.17.5 16 21.2 odd 6
378.2.t.a.89.5 16 63.52 odd 6
882.2.l.b.227.3 16 63.47 even 6
882.2.l.b.509.7 16 7.4 even 3
882.2.m.a.293.5 16 1.1 even 1 trivial
882.2.m.a.587.5 16 63.20 even 6 inner
882.2.m.b.293.8 16 7.6 odd 2
882.2.m.b.587.8 16 9.2 odd 6
882.2.t.a.803.1 16 63.11 odd 6
882.2.t.a.815.1 16 7.5 odd 6
1008.2.ca.c.257.7 16 28.3 even 6
1008.2.ca.c.353.7 16 252.191 even 6
1008.2.df.c.689.3 16 28.23 odd 6
1008.2.df.c.929.3 16 252.227 odd 6
1134.2.k.a.647.4 16 63.23 odd 6
1134.2.k.a.971.4 16 63.31 odd 6
1134.2.k.b.647.5 16 63.58 even 3
1134.2.k.b.971.5 16 63.59 even 6
2646.2.l.a.521.8 16 63.61 odd 6
2646.2.l.a.1097.4 16 21.11 odd 6
2646.2.m.a.881.4 16 3.2 odd 2
2646.2.m.a.1763.4 16 63.34 odd 6
2646.2.m.b.881.1 16 21.20 even 2
2646.2.m.b.1763.1 16 9.7 even 3
2646.2.t.b.1979.8 16 63.25 even 3
2646.2.t.b.2285.8 16 21.5 even 6
3024.2.ca.c.2033.1 16 252.79 odd 6
3024.2.ca.c.2609.1 16 84.59 odd 6
3024.2.df.c.17.1 16 84.23 even 6
3024.2.df.c.1601.1 16 252.115 even 6