Properties

Label 968.2.o.d.493.5
Level 968968
Weight 22
Character 968.493
Analytic conductor 7.7307.730
Analytic rank 00
Dimension 4040
Inner twists 44

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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] = [968,2,Mod(245,968)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(968, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 8])) 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("968.245"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 968=23112 968 = 2^{3} \cdot 11^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 968.o (of order 1010, degree 44, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [40,-5,0,-1,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 7.729518915667.72951891566
Analytic rank: 00
Dimension: 4040
Relative dimension: 1010 over Q(ζ10)\Q(\zeta_{10})
Twist minimal: no (minimal twist has level 88)
Sato-Tate group: SU(2)[C10]\mathrm{SU}(2)[C_{10}]

Embedding invariants

Embedding label 493.5
Character χ\chi == 968.493
Dual form 968.2.o.d.269.5

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+(0.227030+1.39587i)q2+(0.510574+0.702745i)q3+(1.896910.633809i)q4+(3.49435+1.13538i)q5+(1.09686+0.553152i)q6+(0.9670030.702569i)q7+(1.315372.50396i)q8+(0.6938862.13556i)q9+(0.7915275.13543i)q10+(0.5231101.65665i)q12+(3.785691.23005i)q13+(1.200231.19031i)q14+(2.582011.87594i)q15+(3.19657+2.40456i)q16+(0.982622+3.02420i)q17+(2.82344+1.45341i)q18+(2.53106+3.48370i)q19+(7.34810+0.0610261i)q201.03827iq21+2.46096q23+(2.431240.354084i)q24+(6.876294.99592i)q25+(2.576455.00509i)q26+(4.333421.40801i)q27+(1.38903+1.94561i)q28+(2.257273.10687i)q29+(3.204763.17826i)q30+(2.827088.70085i)q31+(4.08218+3.91610i)q32+(4.44448+0.685031i)q34+(4.17673+1.35710i)q35+(2.66978+3.61119i)q36+(3.133114.31236i)q37+(5.43743+2.74213i)q38+(1.068473.28841i)q39+(1.75342+10.2431i)q40+(0.4312290.313306i)q41+(1.44929+0.235718i)q42+6.51729iq43+8.25022iq45+(0.558711+3.43518i)q46+(0.290335+0.210940i)q47+(0.0577087+3.47409i)q48+(1.721635.29862i)q49+(5.41254+10.7326i)q50+(1.62354+2.23461i)q51+(6.40153+4.73270i)q52+(2.30524+0.749017i)q53+(0.981589+6.36855i)q54+(3.03117+1.49719i)q56+(1.15586+3.55738i)q57+(3.82432+3.85621i)q58+(0.350132+0.481916i)q59+(3.70886+5.19500i)q60+(6.93255+2.25252i)q61+(11.5034+5.92159i)q62+(2.17137+1.57759i)q63+(4.539596.58727i)q64+14.6251q6511.2692iq67+(0.05281546.35945i)q68+(1.25650+1.72943i)q69+(2.84258+5.52207i)q70+(1.72651+5.31364i)q71+(4.434634.54652i)q72+(2.161441.57038i)q73+(5.30819+5.35246i)q74+(7.02172+2.28149i)q75+(2.593208.21250i)q76+(4.832770.744878i)q78+(3.5536910.9371i)q79+(13.90004.77305i)q80+(2.247851.63316i)q81+(0.339433+0.673070i)q82+(0.9537500.309892i)q83+(0.658065+1.96951i)q84+(6.867259.45196i)q85+(9.097311.47962i)q86+3.33584q87+13.6469q89+(11.51631.87305i)q90+(2.79658+3.84917i)q91+(4.668231.55978i)q92+(7.557912.45571i)q93+(0.2285310.453160i)q94+(12.79979.29955i)q95+(4.836270.869275i)q96+(1.83886+5.65943i)q97+(7.787061.20022i)q98+O(q100)q+(-0.227030 + 1.39587i) q^{2} +(0.510574 + 0.702745i) q^{3} +(-1.89691 - 0.633809i) q^{4} +(-3.49435 + 1.13538i) q^{5} +(-1.09686 + 0.553152i) q^{6} +(-0.967003 - 0.702569i) q^{7} +(1.31537 - 2.50396i) q^{8} +(0.693886 - 2.13556i) q^{9} +(-0.791527 - 5.13543i) q^{10} +(-0.523110 - 1.65665i) q^{12} +(-3.78569 - 1.23005i) q^{13} +(1.20023 - 1.19031i) q^{14} +(-2.58201 - 1.87594i) q^{15} +(3.19657 + 2.40456i) q^{16} +(0.982622 + 3.02420i) q^{17} +(2.82344 + 1.45341i) q^{18} +(2.53106 + 3.48370i) q^{19} +(7.34810 + 0.0610261i) q^{20} -1.03827i q^{21} +2.46096 q^{23} +(2.43124 - 0.354084i) q^{24} +(6.87629 - 4.99592i) q^{25} +(2.57645 - 5.00509i) q^{26} +(4.33342 - 1.40801i) q^{27} +(1.38903 + 1.94561i) q^{28} +(2.25727 - 3.10687i) q^{29} +(3.20476 - 3.17826i) q^{30} +(2.82708 - 8.70085i) q^{31} +(-4.08218 + 3.91610i) q^{32} +(-4.44448 + 0.685031i) q^{34} +(4.17673 + 1.35710i) q^{35} +(-2.66978 + 3.61119i) q^{36} +(3.13311 - 4.31236i) q^{37} +(-5.43743 + 2.74213i) q^{38} +(-1.06847 - 3.28841i) q^{39} +(-1.75342 + 10.2431i) q^{40} +(0.431229 - 0.313306i) q^{41} +(1.44929 + 0.235718i) q^{42} +6.51729i q^{43} +8.25022i q^{45} +(-0.558711 + 3.43518i) q^{46} +(-0.290335 + 0.210940i) q^{47} +(-0.0577087 + 3.47409i) q^{48} +(-1.72163 - 5.29862i) q^{49} +(5.41254 + 10.7326i) q^{50} +(-1.62354 + 2.23461i) q^{51} +(6.40153 + 4.73270i) q^{52} +(2.30524 + 0.749017i) q^{53} +(0.981589 + 6.36855i) q^{54} +(-3.03117 + 1.49719i) q^{56} +(-1.15586 + 3.55738i) q^{57} +(3.82432 + 3.85621i) q^{58} +(-0.350132 + 0.481916i) q^{59} +(3.70886 + 5.19500i) q^{60} +(-6.93255 + 2.25252i) q^{61} +(11.5034 + 5.92159i) q^{62} +(-2.17137 + 1.57759i) q^{63} +(-4.53959 - 6.58727i) q^{64} +14.6251 q^{65} -11.2692i q^{67} +(0.0528154 - 6.35945i) q^{68} +(1.25650 + 1.72943i) q^{69} +(-2.84258 + 5.52207i) q^{70} +(1.72651 + 5.31364i) q^{71} +(-4.43463 - 4.54652i) q^{72} +(-2.16144 - 1.57038i) q^{73} +(5.30819 + 5.35246i) q^{74} +(7.02172 + 2.28149i) q^{75} +(-2.59320 - 8.21250i) q^{76} +(4.83277 - 0.744878i) q^{78} +(3.55369 - 10.9371i) q^{79} +(-13.9000 - 4.77305i) q^{80} +(-2.24785 - 1.63316i) q^{81} +(0.339433 + 0.673070i) q^{82} +(0.953750 - 0.309892i) q^{83} +(-0.658065 + 1.96951i) q^{84} +(-6.86725 - 9.45196i) q^{85} +(-9.09731 - 1.47962i) q^{86} +3.33584 q^{87} +13.6469 q^{89} +(-11.5163 - 1.87305i) q^{90} +(2.79658 + 3.84917i) q^{91} +(-4.66823 - 1.55978i) q^{92} +(7.55791 - 2.45571i) q^{93} +(-0.228531 - 0.453160i) q^{94} +(-12.7997 - 9.29955i) q^{95} +(-4.83627 - 0.869275i) q^{96} +(-1.83886 + 5.65943i) q^{97} +(7.78706 - 1.20022i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 40q5q2q48q65q8+10q9+20q106q12+2q14+22q1525q164q1725q18+8q208q23+40q24+6q2520q26+18q28++144q98+O(q100) 40 q - 5 q^{2} - q^{4} - 8 q^{6} - 5 q^{8} + 10 q^{9} + 20 q^{10} - 6 q^{12} + 2 q^{14} + 22 q^{15} - 25 q^{16} - 4 q^{17} - 25 q^{18} + 8 q^{20} - 8 q^{23} + 40 q^{24} + 6 q^{25} - 20 q^{26} + 18 q^{28}+ \cdots + 144 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/968Z)×\left(\mathbb{Z}/968\mathbb{Z}\right)^\times.

nn 485485 727727 849849
χ(n)\chi(n) 1-1 11 e(35)e\left(\frac{3}{5}\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 −0.227030 + 1.39587i −0.160534 + 0.987030i
33 0.510574 + 0.702745i 0.294780 + 0.405730i 0.930559 0.366141i 0.119321π-0.119321\pi
−0.635779 + 0.771871i 0.719321π0.719321\pi
44 −1.89691 0.633809i −0.948457 0.316905i
55 −3.49435 + 1.13538i −1.56272 + 0.507759i −0.957533 0.288325i 0.906902π-0.906902\pi
−0.605187 + 0.796083i 0.706902π0.706902\pi
66 −1.09686 + 0.553152i −0.447790 + 0.225823i
77 −0.967003 0.702569i −0.365493 0.265546i 0.389847 0.920880i 0.372528π-0.372528\pi
−0.755339 + 0.655334i 0.772528π0.772528\pi
88 1.31537 2.50396i 0.465054 0.885282i
99 0.693886 2.13556i 0.231295 0.711854i
1010 −0.791527 5.13543i −0.250303 1.62396i
1111 0 0
1212 −0.523110 1.65665i −0.151009 0.478235i
1313 −3.78569 1.23005i −1.04996 0.341154i −0.267309 0.963611i 0.586134π-0.586134\pi
−0.782654 + 0.622457i 0.786134π0.786134\pi
1414 1.20023 1.19031i 0.320776 0.318123i
1515 −2.58201 1.87594i −0.666672 0.484366i
1616 3.19657 + 2.40456i 0.799143 + 0.601141i
1717 0.982622 + 3.02420i 0.238321 + 0.733476i 0.996664 + 0.0816201i 0.0260094π0.0260094\pi
−0.758343 + 0.651856i 0.773991π0.773991\pi
1818 2.82344 + 1.45341i 0.665491 + 0.342573i
1919 2.53106 + 3.48370i 0.580665 + 0.799216i 0.993768 0.111468i 0.0355552π-0.0355552\pi
−0.413103 + 0.910684i 0.635555π0.635555\pi
2020 7.34810 + 0.0610261i 1.64308 + 0.0136459i
2121 1.03827i 0.226569i
2222 0 0
2323 2.46096 0.513145 0.256573 0.966525i 0.417407π-0.417407\pi
0.256573 + 0.966525i 0.417407π0.417407\pi
2424 2.43124 0.354084i 0.496275 0.0722770i
2525 6.87629 4.99592i 1.37526 0.999184i
2626 2.57645 5.00509i 0.505284 0.981578i
2727 4.33342 1.40801i 0.833967 0.270972i
2828 1.38903 + 1.94561i 0.262501 + 0.367685i
2929 2.25727 3.10687i 0.419165 0.576931i −0.546259 0.837616i 0.683949π-0.683949\pi
0.965424 + 0.260686i 0.0839486π0.0839486\pi
3030 3.20476 3.17826i 0.585107 0.580268i
3131 2.82708 8.70085i 0.507758 1.56272i −0.288326 0.957532i 0.593099π-0.593099\pi
0.796084 0.605186i 0.206901π-0.206901\pi
3232 −4.08218 + 3.91610i −0.721634 + 0.692274i
3333 0 0
3434 −4.44448 + 0.685031i −0.762222 + 0.117482i
3535 4.17673 + 1.35710i 0.705996 + 0.229392i
3636 −2.66978 + 3.61119i −0.444964 + 0.601865i
3737 3.13311 4.31236i 0.515080 0.708947i −0.469685 0.882834i 0.655633π-0.655633\pi
0.984766 + 0.173887i 0.0556326π0.0556326\pi
3838 −5.43743 + 2.74213i −0.882067 + 0.444832i
3939 −1.06847 3.28841i −0.171092 0.526567i
4040 −1.75342 + 10.2431i −0.277240 + 1.61958i
4141 0.431229 0.313306i 0.0673466 0.0489302i −0.553603 0.832781i 0.686747π-0.686747\pi
0.620949 + 0.783851i 0.286747π0.286747\pi
4242 1.44929 + 0.235718i 0.223631 + 0.0363721i
4343 6.51729i 0.993878i 0.867785 + 0.496939i 0.165543π0.165543\pi
−0.867785 + 0.496939i 0.834457π0.834457\pi
4444 0 0
4545 8.25022i 1.22987i
4646 −0.558711 + 3.43518i −0.0823775 + 0.506490i
4747 −0.290335 + 0.210940i −0.0423497 + 0.0307688i −0.608759 0.793355i 0.708332π-0.708332\pi
0.566409 + 0.824124i 0.308332π0.308332\pi
4848 −0.0577087 + 3.47409i −0.00832953 + 0.501441i
4949 −1.72163 5.29862i −0.245947 0.756946i
5050 5.41254 + 10.7326i 0.765448 + 1.51782i
5151 −1.62354 + 2.23461i −0.227341 + 0.312908i
5252 6.40153 + 4.73270i 0.887732 + 0.656308i
5353 2.30524 + 0.749017i 0.316649 + 0.102885i 0.463029 0.886343i 0.346762π-0.346762\pi
−0.146381 + 0.989228i 0.546762π0.546762\pi
5454 0.981589 + 6.36855i 0.133577 + 0.866651i
5555 0 0
5656 −3.03117 + 1.49719i −0.405057 + 0.200071i
5757 −1.15586 + 3.55738i −0.153098 + 0.471186i
5858 3.82432 + 3.85621i 0.502158 + 0.506345i
5959 −0.350132 + 0.481916i −0.0455833 + 0.0627401i −0.831200 0.555973i 0.812346π-0.812346\pi
0.785617 + 0.618713i 0.212346π0.212346\pi
6060 3.70886 + 5.19500i 0.478812 + 0.670672i
6161 −6.93255 + 2.25252i −0.887622 + 0.288406i −0.717118 0.696951i 0.754539π-0.754539\pi
−0.170503 + 0.985357i 0.554539π0.554539\pi
6262 11.5034 + 5.92159i 1.46094 + 0.752042i
6363 −2.17137 + 1.57759i −0.273567 + 0.198758i
6464 −4.53959 6.58727i −0.567449 0.823409i
6565 14.6251 1.81402
6666 0 0
6767 11.2692i 1.37675i −0.725353 0.688377i 0.758323π-0.758323\pi
0.725353 0.688377i 0.241677π-0.241677\pi
6868 0.0528154 6.35945i 0.00640480 0.771196i
6969 1.25650 + 1.72943i 0.151265 + 0.208199i
7070 −2.84258 + 5.52207i −0.339753 + 0.660014i
7171 1.72651 + 5.31364i 0.204899 + 0.630613i 0.999718 + 0.0237665i 0.00756584π0.00756584\pi
−0.794819 + 0.606847i 0.792434π0.792434\pi
7272 −4.43463 4.54652i −0.522627 0.535813i
7373 −2.16144 1.57038i −0.252978 0.183799i 0.454068 0.890967i 0.349972π-0.349972\pi
−0.707045 + 0.707168i 0.749972π0.749972\pi
7474 5.30819 + 5.35246i 0.617064 + 0.622210i
7575 7.02172 + 2.28149i 0.810798 + 0.263444i
7676 −2.59320 8.21250i −0.297460 0.942038i
7777 0 0
7878 4.83277 0.744878i 0.547204 0.0843408i
7979 3.55369 10.9371i 0.399822 1.23053i −0.525320 0.850905i 0.676055π-0.676055\pi
0.925142 0.379621i 0.123945π-0.123945\pi
8080 −13.9000 4.77305i −1.55407 0.533644i
8181 −2.24785 1.63316i −0.249761 0.181462i
8282 0.339433 + 0.673070i 0.0374841 + 0.0743281i
8383 0.953750 0.309892i 0.104688 0.0340151i −0.256205 0.966623i 0.582472π-0.582472\pi
0.360892 + 0.932607i 0.382472π0.382472\pi
8484 −0.658065 + 1.96951i −0.0718008 + 0.214891i
8585 −6.86725 9.45196i −0.744858 1.02521i
8686 −9.09731 1.47962i −0.980988 0.159552i
8787 3.33584 0.357640
8888 0 0
8989 13.6469 1.44657 0.723283 0.690551i 0.242632π-0.242632\pi
0.723283 + 0.690551i 0.242632π0.242632\pi
9090 −11.5163 1.87305i −1.21392 0.197437i
9191 2.79658 + 3.84917i 0.293162 + 0.403502i
9292 −4.66823 1.55978i −0.486697 0.162618i
9393 7.55791 2.45571i 0.783719 0.254646i
9494 −0.228531 0.453160i −0.0235712 0.0467399i
9595 −12.7997 9.29955i −1.31323 0.954114i
9696 −4.83627 0.869275i −0.493600 0.0887200i
9797 −1.83886 + 5.65943i −0.186708 + 0.574628i −0.999974 0.00726443i 0.997688π-0.997688\pi
0.813266 + 0.581893i 0.197688π0.197688\pi
9898 7.78706 1.20022i 0.786612 0.121241i
9999 0 0
100100 −16.2102 + 5.11857i −1.62102 + 0.511857i
101101 5.68268 + 1.84641i 0.565448 + 0.183725i 0.577771 0.816199i 0.303923π-0.303923\pi
−0.0123233 + 0.999924i 0.503923π0.503923\pi
102102 −2.75064 2.77358i −0.272354 0.274625i
103103 3.17591 + 2.30743i 0.312932 + 0.227358i 0.733153 0.680063i 0.238048π-0.238048\pi
−0.420222 + 0.907421i 0.638048π0.638048\pi
104104 −8.05958 + 7.86124i −0.790307 + 0.770858i
105105 1.17883 + 3.62808i 0.115042 + 0.354064i
106106 −1.56889 + 3.04776i −0.152384 + 0.296025i
107107 −7.53003 10.3642i −0.727955 1.00194i −0.999222 0.0394404i 0.987442π-0.987442\pi
0.271266 0.962504i 0.412558π-0.412558\pi
108108 −9.11253 0.0756798i −0.876854 0.00728229i
109109 5.65346i 0.541504i 0.962649 + 0.270752i 0.0872723π0.0872723\pi
−0.962649 + 0.270752i 0.912728π0.912728\pi
110110 0 0
111111 4.63018 0.439477
112112 −1.40172 4.57103i −0.132450 0.431922i
113113 12.9433 9.40385i 1.21760 0.884640i 0.221704 0.975114i 0.428838π-0.428838\pi
0.995899 + 0.0904741i 0.0288382π0.0288382\pi
114114 −4.70323 2.42107i −0.440498 0.226754i
115115 −8.59945 + 2.79413i −0.801903 + 0.260554i
116116 −6.25101 + 4.46278i −0.580392 + 0.414359i
117117 −5.25368 + 7.23107i −0.485703 + 0.668513i
118118 −0.593202 0.598149i −0.0546086 0.0550641i
119119 1.17451 3.61477i 0.107667 0.331365i
120120 −8.09358 + 3.99768i −0.738839 + 0.364936i
121121 0 0
122122 −1.57033 10.1883i −0.142171 0.922408i
123123 0.440349 + 0.143078i 0.0397049 + 0.0129009i
124124 −10.8774 + 14.7129i −0.976819 + 1.32126i
125125 −7.55775 + 10.4024i −0.675986 + 0.930414i
126126 −1.70915 3.38911i −0.152263 0.301926i
127127 −2.86054 8.80385i −0.253832 0.781215i −0.994058 0.108856i 0.965281π-0.965281\pi
0.740225 0.672359i 0.234719π-0.234719\pi
128128 10.2256 4.84118i 0.903824 0.427904i
129129 −4.58000 + 3.32756i −0.403246 + 0.292976i
130130 −3.32034 + 20.4148i −0.291213 + 1.79049i
131131 13.3281i 1.16448i −0.813016 0.582241i 0.802176π-0.802176\pi
0.813016 0.582241i 0.197824π-0.197824\pi
132132 0 0
133133 5.14699i 0.446301i
134134 15.7304 + 2.55845i 1.35890 + 0.221016i
135135 −13.5438 + 9.84017i −1.16567 + 0.846907i
136136 8.86498 + 1.51751i 0.760166 + 0.130125i
137137 −3.00021 9.23371i −0.256325 0.788889i −0.993566 0.113258i 0.963871π-0.963871\pi
0.737240 0.675631i 0.236129π-0.236129\pi
138138 −2.69932 + 1.36128i −0.229782 + 0.115880i
139139 13.0811 18.0046i 1.10953 1.52713i 0.287418 0.957805i 0.407203π-0.407203\pi
0.822110 0.569329i 0.192797π-0.192797\pi
140140 −7.06275 5.22155i −0.596912 0.441302i
141141 −0.296475 0.0963305i −0.0249677 0.00811249i
142142 −7.80913 + 1.20363i −0.655328 + 0.101006i
143143 0 0
144144 7.35315 5.15798i 0.612763 0.429832i
145145 −4.36021 + 13.4193i −0.362096 + 1.11442i
146146 2.68276 2.66057i 0.222027 0.220190i
147147 2.84456 3.91521i 0.234616 0.322921i
148148 −8.67646 + 6.19438i −0.713200 + 0.509175i
149149 11.9845 3.89401i 0.981811 0.319010i 0.226237 0.974072i 0.427358π-0.427358\pi
0.755575 + 0.655062i 0.227358π0.227358\pi
150150 −4.77881 + 9.28345i −0.390188 + 0.757990i
151151 −12.2699 + 8.91459i −0.998509 + 0.725459i −0.961768 0.273866i 0.911698π-0.911698\pi
−0.0367411 + 0.999325i 0.511698π0.511698\pi
152152 12.0523 1.75529i 0.977572 0.142373i
153153 7.14020 0.577251
154154 0 0
155155 33.6136i 2.69991i
156156 −0.0574296 + 6.91504i −0.00459805 + 0.553646i
157157 −0.897329 1.23507i −0.0716147 0.0985691i 0.771707 0.635978i 0.219403π-0.219403\pi
−0.843322 + 0.537409i 0.819403π0.819403\pi
158158 14.4601 + 7.44356i 1.15038 + 0.592178i
159159 0.650627 + 2.00242i 0.0515980 + 0.158802i
160160 9.81829 18.3190i 0.776204 1.44825i
161161 −2.37975 1.72899i −0.187551 0.136264i
162162 2.79000 2.76693i 0.219203 0.217390i
163163 −14.7758 4.80095i −1.15733 0.376039i −0.333430 0.942775i 0.608206π-0.608206\pi
−0.823900 + 0.566735i 0.808206π0.808206\pi
164164 −1.01658 + 0.320998i −0.0793816 + 0.0250657i
165165 0 0
166166 0.216040 + 1.40167i 0.0167679 + 0.108791i
167167 2.59371 7.98263i 0.200707 0.617714i −0.799155 0.601125i 0.794719π-0.794719\pi
0.999862 0.0165890i 0.00528067π-0.00528067\pi
168168 −2.59978 1.36571i −0.200578 0.105367i
169169 2.30125 + 1.67195i 0.177019 + 0.128612i
170170 14.7528 7.43992i 1.13149 0.570616i
171171 9.19593 2.98794i 0.703230 0.228493i
172172 4.13072 12.3628i 0.314965 0.942651i
173173 14.6137 + 20.1141i 1.11106 + 1.52925i 0.819843 + 0.572589i 0.194061π0.194061\pi
0.291219 + 0.956656i 0.405939π0.405939\pi
174174 −0.757336 + 4.65641i −0.0574135 + 0.353001i
175175 −10.1594 −0.767976
176176 0 0
177177 −0.517432 −0.0388926
178178 −3.09825 + 19.0493i −0.232224 + 1.42781i
179179 −9.69021 13.3374i −0.724280 0.996886i −0.999371 0.0354679i 0.988708π-0.988708\pi
0.275091 0.961418i 0.411292π-0.411292\pi
180180 5.22907 15.6500i 0.389752 1.16648i
181181 8.72980 2.83648i 0.648881 0.210834i 0.0339603 0.999423i 0.489188π-0.489188\pi
0.614921 + 0.788589i 0.289188π0.289188\pi
182182 −6.00785 + 3.02980i −0.445332 + 0.224583i
183183 −5.12253 3.72174i −0.378668 0.275119i
184184 3.23708 6.16213i 0.238641 0.454278i
185185 −6.05201 + 18.6262i −0.444952 + 1.36942i
186186 1.71199 + 11.1074i 0.125529 + 0.814434i
187187 0 0
188188 0.684436 0.216119i 0.0499176 0.0157621i
189189 −5.17965 1.68297i −0.376764 0.122418i
190190 15.8869 15.7555i 1.15256 1.14302i
191191 1.99813 + 1.45172i 0.144579 + 0.105043i 0.657724 0.753259i 0.271519π-0.271519\pi
−0.513144 + 0.858302i 0.671519π0.671519\pi
192192 2.31138 6.55347i 0.166809 0.472956i
193193 3.09207 + 9.51643i 0.222572 + 0.685007i 0.998529 + 0.0542210i 0.0172675π0.0172675\pi
−0.775957 + 0.630786i 0.782732π0.782732\pi
194194 −7.48236 3.85167i −0.537202 0.276534i
195195 7.46721 + 10.2777i 0.534738 + 0.736003i
196196 −0.0925364 + 11.1422i −0.00660974 + 0.795873i
197197 11.7936i 0.840260i 0.907464 + 0.420130i 0.138015π0.138015\pi
−0.907464 + 0.420130i 0.861985π0.861985\pi
198198 0 0
199199 −14.7867 −1.04820 −0.524101 0.851656i 0.675598π-0.675598\pi
−0.524101 + 0.851656i 0.675598π0.675598\pi
200200 −3.46467 23.7894i −0.244989 1.68217i
201201 7.91939 5.75378i 0.558591 0.405840i
202202 −3.86750 + 7.51310i −0.272116 + 0.528620i
203203 −4.36557 + 1.41846i −0.306403 + 0.0995565i
204204 4.49604 3.20985i 0.314786 0.224735i
205205 −1.15114 + 1.58441i −0.0803992 + 0.110660i
206206 −3.94191 + 3.90930i −0.274646 + 0.272374i
207207 1.70763 5.25553i 0.118688 0.365285i
208208 −9.14352 13.0349i −0.633989 0.903806i
209209 0 0
210210 −5.33196 + 0.821819i −0.367940 + 0.0567109i
211211 −8.08990 2.62857i −0.556932 0.180958i 0.0170085 0.999855i 0.494586π-0.494586\pi
−0.573940 + 0.818897i 0.694586π0.694586\pi
212212 −3.89810 2.88190i −0.267723 0.197930i
213213 −2.85263 + 3.92630i −0.195459 + 0.269026i
214214 16.1766 8.15797i 1.10581 0.557667i
215215 −7.39962 22.7737i −0.504650 1.55315i
216216 2.17446 12.7027i 0.147953 0.864312i
217217 −8.84673 + 6.42753i −0.600555 + 0.436329i
218218 −7.89151 1.28351i −0.534480 0.0869300i
219219 2.32074i 0.156821i
220220 0 0
221221 12.6574i 0.851427i
222222 −1.05119 + 6.46313i −0.0705512 + 0.433777i
223223 −4.06365 + 2.95241i −0.272122 + 0.197708i −0.715474 0.698639i 0.753789π-0.753789\pi
0.443352 + 0.896348i 0.353789π0.353789\pi
224224 6.69880 0.918863i 0.447583 0.0613941i
225225 −5.89773 18.1513i −0.393182 1.21009i
226226 10.1881 + 20.2021i 0.677699 + 1.34383i
227227 −10.6228 + 14.6211i −0.705062 + 0.970434i 0.294828 + 0.955550i 0.404738π0.404738\pi
−0.999889 + 0.0148837i 0.995262π0.995262\pi
228228 4.44727 6.01545i 0.294528 0.398383i
229229 −3.78767 1.23069i −0.250296 0.0813262i 0.181182 0.983450i 0.442008π-0.442008\pi
−0.431478 + 0.902123i 0.642008π0.642008\pi
230230 −1.94791 12.6381i −0.128442 0.833330i
231231 0 0
232232 −4.81031 9.73880i −0.315812 0.639383i
233233 −3.79638 + 11.6841i −0.248709 + 0.765448i 0.746295 + 0.665615i 0.231831π0.231831\pi
−0.995004 + 0.0998327i 0.968169π0.968169\pi
234234 −8.90091 8.97513i −0.581870 0.586723i
235235 0.775032 1.06674i 0.0505575 0.0695865i
236236 0.969613 0.692236i 0.0631165 0.0450607i
237237 9.50046 3.08689i 0.617121 0.200515i
238238 4.77911 + 2.46013i 0.309783 + 0.159466i
239239 16.9458 12.3118i 1.09613 0.796386i 0.115707 0.993283i 0.463087π-0.463087\pi
0.980424 + 0.196898i 0.0630866π0.0630866\pi
240240 −3.74276 12.2052i −0.241594 0.787841i
241241 −17.4490 −1.12399 −0.561996 0.827140i 0.689966π-0.689966\pi
−0.561996 + 0.827140i 0.689966π0.689966\pi
242242 0 0
243243 16.0828i 1.03171i
244244 14.5781 + 0.121072i 0.933268 + 0.00775082i
245245 12.0319 + 16.5605i 0.768692 + 1.05801i
246246 −0.299691 + 0.582187i −0.0191076 + 0.0371189i
247247 −5.29670 16.3016i −0.337021 1.03724i
248248 −18.0679 18.5237i −1.14731 1.17626i
249249 0.704736 + 0.512021i 0.0446608 + 0.0324480i
250250 −12.8045 12.9113i −0.809828 0.816582i
251251 5.66665 + 1.84121i 0.357676 + 0.116216i 0.482342 0.875983i 0.339786π-0.339786\pi
−0.124667 + 0.992199i 0.539786π0.539786\pi
252252 5.11879 1.61632i 0.322454 0.101819i
253253 0 0
254254 12.9385 1.99421i 0.811832 0.125128i
255255 3.13608 9.65186i 0.196389 0.604423i
256256 4.43614 + 15.3727i 0.277259 + 0.960795i
257257 11.4623 + 8.32787i 0.715000 + 0.519478i 0.884783 0.466003i 0.154307π-0.154307\pi
−0.169783 + 0.985482i 0.554307π0.554307\pi
258258 −3.60506 7.14855i −0.224441 0.445049i
259259 −6.05945 + 1.96884i −0.376516 + 0.122338i
260260 −27.7426 9.26953i −1.72052 0.574872i
261261 −5.06862 6.97635i −0.313740 0.431825i
262262 18.6043 + 3.02588i 1.14938 + 0.186939i
263263 −11.0152 −0.679225 −0.339612 0.940566i 0.610296π-0.610296\pi
−0.339612 + 0.940566i 0.610296π0.610296\pi
264264 0 0
265265 −8.90572 −0.547074
266266 7.18454 + 1.16852i 0.440512 + 0.0716466i
267267 6.96775 + 9.59029i 0.426419 + 0.586916i
268268 −7.14254 + 21.3768i −0.436300 + 1.30579i
269269 −2.36175 + 0.767379i −0.143998 + 0.0467879i −0.380129 0.924933i 0.624121π-0.624121\pi
0.236131 + 0.971721i 0.424121π0.424121\pi
270270 −10.6608 21.1395i −0.648793 1.28651i
271271 0.248958 + 0.180879i 0.0151231 + 0.0109876i 0.595321 0.803488i 0.297025π-0.297025\pi
−0.580198 + 0.814475i 0.697025π0.697025\pi
272272 −4.13086 + 12.0299i −0.250470 + 0.729417i
273273 −1.27712 + 3.93057i −0.0772949 + 0.237889i
274274 13.5702 2.09158i 0.819806 0.126357i
275275 0 0
276276 −1.28735 4.07696i −0.0774895 0.245404i
277277 2.37765 + 0.772546i 0.142859 + 0.0464178i 0.379574 0.925161i 0.376071π-0.376071\pi
−0.236715 + 0.971579i 0.576071π0.576071\pi
278278 22.1624 + 22.3472i 1.32921 + 1.34030i
279279 −16.6195 12.0748i −0.994985 0.722899i
280280 8.89208 8.67325i 0.531403 0.518326i
281281 0.384151 + 1.18230i 0.0229166 + 0.0705299i 0.961861 0.273540i 0.0881944π-0.0881944\pi
−0.938944 + 0.344069i 0.888194π0.888194\pi
282282 0.201774 0.391971i 0.0120155 0.0233415i
283283 −8.11251 11.1659i −0.482239 0.663745i 0.496694 0.867926i 0.334547π-0.334547\pi
−0.978933 + 0.204181i 0.934547π0.934547\pi
284284 0.0927987 11.1738i 0.00550659 0.663043i
285285 13.7431i 0.814069i
286286 0 0
287287 −0.637118 −0.0376079
288288 5.53050 + 11.4351i 0.325888 + 0.673818i
289289 5.57305 4.04906i 0.327826 0.238180i
290290 −17.7418 9.13288i −1.04183 0.536301i
291291 −4.91602 + 1.59731i −0.288182 + 0.0936360i
292292 3.10475 + 4.34882i 0.181692 + 0.254495i
293293 8.74894 12.0419i 0.511118 0.703494i −0.472989 0.881068i 0.656825π-0.656825\pi
0.984107 + 0.177574i 0.0568250π0.0568250\pi
294294 4.81933 + 4.85952i 0.281069 + 0.283413i
295295 0.676325 2.08151i 0.0393772 0.121190i
296296 −6.67674 13.5175i −0.388078 0.785690i
297297 0 0
298298 2.71469 + 17.6129i 0.157258 + 1.02029i
299299 −9.31644 3.02709i −0.538784 0.175061i
300300 −11.8736 8.77823i −0.685521 0.506811i
301301 4.57885 6.30224i 0.263920 0.363255i
302302 −9.65800 19.1511i −0.555755 1.10202i
303303 1.60387 + 4.93621i 0.0921400 + 0.283578i
304304 −0.286078 + 17.2220i −0.0164077 + 0.987749i
305305 21.6673 15.7422i 1.24066 0.901395i
306306 −1.62104 + 9.96680i −0.0926686 + 0.569764i
307307 8.40361i 0.479619i −0.970820 0.239810i 0.922915π-0.922915\pi
0.970820 0.239810i 0.0770850π-0.0770850\pi
308308 0 0
309309 3.40997i 0.193986i
310310 −46.9203 7.63129i −2.66489 0.433428i
311311 −20.7482 + 15.0745i −1.17652 + 0.854795i −0.991775 0.127991i 0.959147π-0.959147\pi
−0.184749 + 0.982786i 0.559147π0.559147\pi
312312 −9.63947 1.65009i −0.545727 0.0934177i
313313 5.83498 + 17.9582i 0.329812 + 1.01506i 0.969221 + 0.246191i 0.0791791π0.0791791\pi
−0.639409 + 0.768867i 0.720821π0.720821\pi
314314 1.92772 0.972159i 0.108787 0.0548621i
315315 5.79635 7.97799i 0.326587 0.449509i
316316 −13.6731 + 18.4945i −0.769173 + 1.04040i
317317 −18.9857 6.16884i −1.06634 0.346476i −0.277282 0.960789i 0.589434π-0.589434\pi
−0.789063 + 0.614312i 0.789434π0.789434\pi
318318 −2.94284 + 0.453581i −0.165026 + 0.0254356i
319319 0 0
320320 23.3420 + 17.8640i 1.30486 + 0.998631i
321321 3.43875 10.5834i 0.191932 0.590707i
322322 2.95373 2.92930i 0.164605 0.163243i
323323 −8.04834 + 11.0776i −0.447822 + 0.616374i
324324 3.22886 + 4.52266i 0.179381 + 0.251259i
325325 −32.1768 + 10.4549i −1.78485 + 0.579931i
326326 10.0561 19.5352i 0.556953 1.08195i
327327 −3.97295 + 2.88651i −0.219704 + 0.159625i
328328 −0.217278 1.49189i −0.0119972 0.0823759i
329329 0.428955 0.0236490
330330 0 0
331331 18.8624i 1.03677i −0.855147 0.518386i 0.826533π-0.826533\pi
0.855147 0.518386i 0.173467π-0.173467\pi
332332 −2.00560 0.0166565i −0.110071 0.000914145i
333333 −7.03528 9.68324i −0.385531 0.530638i
334334 10.5539 + 5.43278i 0.577482 + 0.297269i
335335 12.7949 + 39.3786i 0.699059 + 2.15148i
336336 2.49659 3.31891i 0.136200 0.181061i
337337 17.2189 + 12.5102i 0.937972 + 0.681476i 0.947932 0.318474i 0.103170π-0.103170\pi
−0.00995978 + 0.999950i 0.503170π0.503170\pi
338338 −2.85628 + 2.83266i −0.155361 + 0.154076i
339339 13.2170 + 4.29447i 0.717850 + 0.233244i
340340 7.03585 + 22.2821i 0.381572 + 1.20842i
341341 0 0
342342 2.08303 + 13.5147i 0.112637 + 0.730791i
343343 −4.64336 + 14.2908i −0.250718 + 0.771631i
344344 16.3190 + 8.57267i 0.879862 + 0.462207i
345345 −6.35422 4.61661i −0.342100 0.248550i
346346 −31.3944 + 15.8324i −1.68778 + 0.851155i
347347 −5.18044 + 1.68323i −0.278100 + 0.0903603i −0.444747 0.895656i 0.646706π-0.646706\pi
0.166646 + 0.986017i 0.446706π0.446706\pi
348348 −6.32781 2.11429i −0.339206 0.113338i
349349 −6.00038 8.25881i −0.321193 0.442084i 0.617638 0.786462i 0.288090π-0.288090\pi
−0.938831 + 0.344379i 0.888090π0.888090\pi
350350 2.30648 14.1812i 0.123287 0.758016i
351351 −18.1369 −0.968077
352352 0 0
353353 5.11121 0.272042 0.136021 0.990706i 0.456569π-0.456569\pi
0.136021 + 0.990706i 0.456569π0.456569\pi
354354 0.117473 0.722269i 0.00624360 0.0383882i
355355 −12.0660 16.6075i −0.640399 0.881433i
356356 −25.8870 8.64952i −1.37201 0.458424i
357357 3.13994 1.02023i 0.166183 0.0539962i
358358 20.8173 10.4983i 1.10023 0.554852i
359359 16.9733 + 12.3318i 0.895815 + 0.650848i 0.937388 0.348288i 0.113237π-0.113237\pi
−0.0415725 + 0.999135i 0.513237π0.513237\pi
360360 20.6582 + 10.8521i 1.08878 + 0.571957i
361361 0.141394 0.435166i 0.00744178 0.0229035i
362362 1.97744 + 12.8296i 0.103932 + 0.674311i
363363 0 0
364364 −2.86524 9.07405i −0.150180 0.475609i
365365 9.33581 + 3.03339i 0.488659 + 0.158775i
366366 6.35803 6.30545i 0.332340 0.329591i
367367 25.5075 + 18.5323i 1.33148 + 0.967378i 0.999712 + 0.0240171i 0.00764560π0.00764560\pi
0.331769 + 0.943361i 0.392354π0.392354\pi
368368 7.86663 + 5.91753i 0.410077 + 0.308473i
369369 −0.369861 1.13831i −0.0192542 0.0592583i
370370 −24.6257 12.6765i −1.28023 0.659021i
371371 −1.70293 2.34389i −0.0884119 0.121689i
372372 −15.8932 0.131993i −0.824023 0.00684353i
373373 24.8244i 1.28536i −0.766136 0.642678i 0.777823π-0.777823\pi
0.766136 0.642678i 0.222177π-0.222177\pi
374374 0 0
375375 −11.1690 −0.576765
376376 0.146287 + 1.00445i 0.00754419 + 0.0518006i
377377 −12.3669 + 8.98510i −0.636929 + 0.462756i
378378 3.52515 6.84804i 0.181314 0.352225i
379379 33.9918 11.0446i 1.74604 0.567324i 0.750434 0.660945i 0.229844π-0.229844\pi
0.995608 + 0.0936215i 0.0298443π0.0298443\pi
380380 18.3859 + 25.7530i 0.943175 + 1.32110i
381381 4.72634 6.50525i 0.242138 0.333274i
382382 −2.48005 + 2.45954i −0.126891 + 0.125841i
383383 −5.88298 + 18.1060i −0.300606 + 0.925171i 0.680674 + 0.732586i 0.261687π0.261687\pi
−0.981280 + 0.192585i 0.938313π0.938313\pi
384384 8.62305 + 4.71422i 0.440043 + 0.240571i
385385 0 0
386386 −13.9857 + 2.15562i −0.711853 + 0.109718i
387387 13.9181 + 4.52226i 0.707496 + 0.229879i
388388 7.07516 9.56997i 0.359187 0.485842i
389389 19.1441 26.3496i 0.970643 1.33598i 0.0289221 0.999582i 0.490793π-0.490793\pi
0.941721 0.336394i 0.109207π-0.109207\pi
390390 −16.0417 + 8.08991i −0.812301 + 0.409648i
391391 2.41819 + 7.44243i 0.122293 + 0.376380i
392392 −15.5321 2.65879i −0.784490 0.134289i
393393 9.36627 6.80499i 0.472466 0.343266i
394394 −16.4624 2.67750i −0.829362 0.134891i
395395 42.2530i 2.12598i
396396 0 0
397397 13.0143i 0.653167i 0.945168 + 0.326584i 0.105897π0.105897\pi
−0.945168 + 0.326584i 0.894103π0.894103\pi
398398 3.35702 20.6403i 0.168272 1.03461i
399399 3.61702 2.62792i 0.181078 0.131561i
400400 33.9936 + 0.564674i 1.69968 + 0.0282337i
401401 6.35150 + 19.5479i 0.317179 + 0.976175i 0.974848 + 0.222869i 0.0715422π0.0715422\pi
−0.657670 + 0.753306i 0.728458π0.728458\pi
402402 6.23359 + 12.3607i 0.310903 + 0.616497i
403403 −21.4049 + 29.4613i −1.06625 + 1.46757i
404404 −9.60928 7.10422i −0.478080 0.353448i
405405 9.70901 + 3.15465i 0.482445 + 0.156756i
406406 −0.988874 6.41581i −0.0490770 0.318412i
407407 0 0
408408 3.45981 + 7.00462i 0.171286 + 0.346781i
409409 −3.04719 + 9.37828i −0.150674 + 0.463726i −0.997697 0.0678299i 0.978392π-0.978392\pi
0.847023 + 0.531556i 0.178392π0.178392\pi
410410 −1.95029 1.96655i −0.0963179 0.0971212i
411411 4.95711 6.82288i 0.244516 0.336548i
412412 −4.56196 6.38992i −0.224751 0.314809i
413413 0.677157 0.220022i 0.0333207 0.0108266i
414414 6.94836 + 3.57679i 0.341493 + 0.175790i
415415 −2.98089 + 2.16574i −0.146326 + 0.106312i
416416 20.2709 9.80387i 0.993861 0.480674i
417417 19.3316 0.946671
418418 0 0
419419 0.169087i 0.00826046i 0.999991 + 0.00413023i 0.00131470π0.00131470\pi
−0.999991 + 0.00413023i 0.998685π0.998685\pi
420420 0.0633616 7.62931i 0.00309173 0.372272i
421421 −13.8205 19.0223i −0.673569 0.927089i 0.326265 0.945278i 0.394210π-0.394210\pi
−0.999835 + 0.0181896i 0.994210π0.994210\pi
422422 5.50579 10.6957i 0.268018 0.520658i
423423 0.249017 + 0.766396i 0.0121076 + 0.0372635i
424424 4.90775 4.78697i 0.238341 0.232476i
425425 21.8655 + 15.8862i 1.06063 + 0.770593i
426426 −4.83299 4.87329i −0.234159 0.236112i
427427 8.28634 + 2.69240i 0.401004 + 0.130294i
428428 7.71490 + 24.4326i 0.372914 + 1.18099i
429429 0 0
430430 33.4691 5.15861i 1.61402 0.248770i
431431 2.25358 6.93580i 0.108551 0.334086i −0.881996 0.471256i 0.843801π-0.843801\pi
0.990547 + 0.137170i 0.0438008π0.0438008\pi
432432 17.2377 + 5.91917i 0.829351 + 0.284786i
433433 −1.89173 1.37442i −0.0909105 0.0660504i 0.541401 0.840764i 0.317894π-0.317894\pi
−0.632312 + 0.774714i 0.717894π0.717894\pi
434434 −6.96353 13.8081i −0.334260 0.662812i
435435 −11.6566 + 3.78746i −0.558891 + 0.181595i
436436 3.58322 10.7241i 0.171605 0.513593i
437437 6.22883 + 8.57325i 0.297965 + 0.410114i
438438 3.23945 + 0.526877i 0.154787 + 0.0251752i
439439 1.21401 0.0579413 0.0289707 0.999580i 0.490777π-0.490777\pi
0.0289707 + 0.999580i 0.490777π0.490777\pi
440440 0 0
441441 −12.5102 −0.595722
442442 17.6681 + 2.87360i 0.840384 + 0.136683i
443443 2.71484 + 3.73666i 0.128986 + 0.177534i 0.868625 0.495469i 0.165004π-0.165004\pi
−0.739639 + 0.673003i 0.765004π0.765004\pi
444444 −8.78305 2.93465i −0.416825 0.139272i
445445 −47.6870 + 15.4944i −2.26058 + 0.734507i
446446 −3.19862 6.34262i −0.151459 0.300332i
447447 8.85550 + 6.43389i 0.418851 + 0.304313i
448448 −0.238214 + 9.55928i −0.0112546 + 0.451634i
449449 1.81356 5.58157i 0.0855872 0.263410i −0.899099 0.437745i 0.855777π-0.855777\pi
0.984687 + 0.174334i 0.0557774π0.0557774\pi
450450 26.6759 4.11157i 1.25751 0.193821i
451451 0 0
452452 −30.5126 + 9.63473i −1.43519 + 0.453180i
453453 −12.5294 4.07104i −0.588682 0.191274i
454454 −17.9974 18.1475i −0.844661 0.851705i
455455 −14.1425 10.2751i −0.663012 0.481706i
456456 7.38713 + 7.57351i 0.345934 + 0.354662i
457457 7.57010 + 23.2984i 0.354115 + 1.08985i 0.956521 + 0.291663i 0.0942086π0.0942086\pi
−0.602407 + 0.798189i 0.705791π0.705791\pi
458458 2.57780 5.00770i 0.120453 0.233994i
459459 8.51622 + 11.7216i 0.397503 + 0.547116i
460460 18.0834 + 0.150183i 0.843141 + 0.00700231i
461461 6.59878i 0.307336i 0.988123 + 0.153668i 0.0491086π0.0491086\pi
−0.988123 + 0.153668i 0.950891π0.950891\pi
462462 0 0
463463 −14.4202 −0.670163 −0.335081 0.942189i 0.608764π-0.608764\pi
−0.335081 + 0.942189i 0.608764π0.608764\pi
464464 14.6862 4.50357i 0.681789 0.209073i
465465 −23.6218 + 17.1622i −1.09544 + 0.795880i
466466 −15.4475 7.95189i −0.715594 0.368364i
467467 −5.22015 + 1.69613i −0.241560 + 0.0784876i −0.427295 0.904112i 0.640533π-0.640533\pi
0.185735 + 0.982600i 0.440533π0.440533\pi
468468 14.5489 10.3869i 0.672523 0.480134i
469469 −7.91740 + 10.8974i −0.365592 + 0.503194i
470470 1.31308 + 1.32403i 0.0605677 + 0.0610728i
471471 0.409785 1.26119i 0.0188819 0.0581125i
472472 0.746141 + 1.51061i 0.0343439 + 0.0695316i
473473 0 0
474474 2.15201 + 13.9622i 0.0988450 + 0.641307i
475475 34.8086 + 11.3100i 1.59713 + 0.518938i
476476 −4.51902 + 6.11249i −0.207129 + 0.280166i
477477 3.19914 4.40324i 0.146479 0.201611i
478478 13.3385 + 26.4493i 0.610090 + 1.20976i
479479 9.22841 + 28.4021i 0.421657 + 1.29773i 0.906160 + 0.422936i 0.139001π0.139001\pi
−0.484503 + 0.874790i 0.660999π0.660999\pi
480480 17.8866 2.45347i 0.816407 0.111985i
481481 −17.1654 + 12.4714i −0.782675 + 0.568647i
482482 3.96145 24.3566i 0.180439 1.10941i
483483 2.55514i 0.116263i
484484 0 0
485485 21.8638i 0.992786i
486486 22.4495 + 3.65127i 1.01833 + 0.165625i
487487 2.40887 1.75015i 0.109156 0.0793068i −0.531868 0.846827i 0.678510π-0.678510\pi
0.641024 + 0.767520i 0.278510π0.278510\pi
488488 −3.47867 + 20.3217i −0.157472 + 0.919920i
489489 −4.17030 12.8349i −0.188588 0.580413i
490490 −25.8480 + 13.0353i −1.16769 + 0.588875i
491491 1.75193 2.41132i 0.0790633 0.108821i −0.767654 0.640865i 0.778576π-0.778576\pi
0.846717 + 0.532044i 0.178576π0.178576\pi
492492 −0.744620 0.550504i −0.0335701 0.0248186i
493493 11.6138 + 3.77356i 0.523061 + 0.169953i
494494 23.9574 3.69257i 1.07789 0.166136i
495495 0 0
496496 29.9587 21.0150i 1.34519 0.943601i
497497 2.06366 6.35130i 0.0925678 0.284895i
498498 −0.874711 + 0.867477i −0.0391967 + 0.0388726i
499499 −8.93099 + 12.2925i −0.399806 + 0.550286i −0.960695 0.277605i 0.910459π-0.910459\pi
0.560889 + 0.827891i 0.310459π0.310459\pi
500500 20.9295 14.9422i 0.935996 0.668236i
501501 6.93404 2.25300i 0.309790 0.100657i
502502 −3.85659 + 7.49191i −0.172128 + 0.334380i
503503 26.6342 19.3508i 1.18756 0.862812i 0.194554 0.980892i 0.437674π-0.437674\pi
0.993004 + 0.118080i 0.0376740π0.0376740\pi
504504 1.09406 + 7.51213i 0.0487333 + 0.334617i
505505 −21.9536 −0.976924
506506 0 0
507507 2.47085i 0.109734i
508508 −0.153752 + 18.5132i −0.00682166 + 0.821390i
509509 7.92281 + 10.9048i 0.351172 + 0.483347i 0.947663 0.319273i 0.103439π-0.103439\pi
−0.596490 + 0.802620i 0.703439π0.703439\pi
510510 12.7608 + 6.56882i 0.565056 + 0.290872i
511511 0.986821 + 3.03712i 0.0436544 + 0.134354i
512512 −22.4655 + 2.70222i −0.992844 + 0.119422i
513513 15.8732 + 11.5326i 0.700820 + 0.509176i
514514 −14.2269 + 14.1093i −0.627523 + 0.622333i
515515 −13.7176 4.45710i −0.604468 0.196403i
516516 10.7969 3.40926i 0.475307 0.150084i
517517 0 0
518518 −1.37256 8.90520i −0.0603070 0.391272i
519519 −6.67368 + 20.5395i −0.292942 + 0.901583i
520520 19.2375 36.6206i 0.843619 1.60592i
521521 −7.52914 5.47024i −0.329857 0.239655i 0.410513 0.911855i 0.365350π-0.365350\pi
−0.740370 + 0.672199i 0.765350π0.765350\pi
522522 10.8888 5.49130i 0.476591 0.240348i
523523 13.6298 4.42859i 0.595989 0.193649i 0.00453848 0.999990i 0.498555π-0.498555\pi
0.591451 + 0.806341i 0.298555π0.298555\pi
524524 −8.44748 + 25.2823i −0.369030 + 1.10446i
525525 −5.18711 7.13945i −0.226384 0.311591i
526526 2.50077 15.3758i 0.109039 0.670415i
527527 29.0911 1.26723
528528 0 0
529529 −16.9437 −0.736682
530530 2.02186 12.4312i 0.0878242 0.539978i
531531 0.786209 + 1.08212i 0.0341186 + 0.0469602i
532532 −3.26221 + 9.76340i −0.141435 + 0.423297i
533533 −2.01788 + 0.655649i −0.0874041 + 0.0283993i
534534 −14.9687 + 7.54880i −0.647759 + 0.326669i
535535 38.0799 + 27.6666i 1.64634 + 1.19613i
536536 −28.2176 14.8232i −1.21882 0.640266i
537537 4.42524 13.6195i 0.190963 0.587725i
538538 −0.534975 3.47092i −0.0230644 0.149642i
539539 0 0
540540 31.9283 10.0818i 1.37398 0.433850i
541541 −21.9923 7.14572i −0.945521 0.307218i −0.204627 0.978840i 0.565598π-0.565598\pi
−0.740894 + 0.671622i 0.765598π0.765598\pi
542542 −0.309004 + 0.306448i −0.0132729 + 0.0131631i
543543 6.45054 + 4.68659i 0.276819 + 0.201121i
544544 −15.8543 8.49729i −0.679747 0.364318i
545545 −6.41884 19.7552i −0.274953 0.846219i
546546 −5.19663 2.67505i −0.222395 0.114482i
547547 5.31444 + 7.31470i 0.227229 + 0.312754i 0.907374 0.420323i 0.138083π-0.138083\pi
−0.680145 + 0.733077i 0.738083π0.738083\pi
548548 −0.161260 + 19.4171i −0.00688867 + 0.829458i
549549 16.3679i 0.698564i
550550 0 0
551551 16.5367 0.704487
552552 5.98318 0.871385i 0.254661 0.0370886i
553553 −11.1205 + 8.07954i −0.472893 + 0.343577i
554554 −1.61817 + 3.14351i −0.0687496 + 0.133555i
555555 −16.1794 + 5.25702i −0.686779 + 0.223148i
556556 −36.2253 + 25.8623i −1.53630 + 1.09681i
557557 −16.3446 + 22.4964i −0.692542 + 0.953203i 0.307456 + 0.951562i 0.400522π0.400522\pi
−0.999999 + 0.00164059i 0.999478π0.999478\pi
558558 20.6280 20.4574i 0.873253 0.866030i
559559 8.01658 24.6725i 0.339065 1.04353i
560560 10.0880 + 14.3813i 0.426295 + 0.607720i
561561 0 0
562562 −1.73755 + 0.267809i −0.0732940 + 0.0112969i
563563 −33.6052 10.9190i −1.41629 0.460181i −0.501869 0.864943i 0.667354π-0.667354\pi
−0.914422 + 0.404762i 0.867354π0.867354\pi
564564 0.501332 + 0.370639i 0.0211099 + 0.0156067i
565565 −34.5514 + 47.5559i −1.45359 + 2.00069i
566566 17.4280 8.78903i 0.732552 0.369430i
567567 1.02627 + 3.15853i 0.0430993 + 0.132646i
568568 15.5761 + 2.66632i 0.653560 + 0.111876i
569569 26.4592 19.2237i 1.10923 0.805901i 0.126686 0.991943i 0.459566π-0.459566\pi
0.982542 + 0.186042i 0.0595660π0.0595660\pi
570570 19.1836 + 3.12009i 0.803511 + 0.130686i
571571 32.0987i 1.34329i −0.740874 0.671644i 0.765588π-0.765588\pi
0.740874 0.671644i 0.234412π-0.234412\pi
572572 0 0
573573 2.14539i 0.0896249i
574574 0.144645 0.889335i 0.00603736 0.0371201i
575575 16.9223 12.2948i 0.705708 0.512727i
576576 −17.2175 + 5.12376i −0.717395 + 0.213490i
577577 6.54916 + 20.1562i 0.272645 + 0.839116i 0.989833 + 0.142236i 0.0454290π0.0454290\pi
−0.717188 + 0.696880i 0.754571π0.754571\pi
578578 4.38671 + 8.69851i 0.182463 + 0.361811i
579579 −5.10889 + 7.03178i −0.212318 + 0.292231i
580580 16.7762 22.6918i 0.696596 0.942226i
581581 −1.14000 0.370408i −0.0472952 0.0153671i
582582 −1.11356 7.22476i −0.0461584 0.299476i
583583 0 0
584584 −6.77526 + 3.34652i −0.280362 + 0.138480i
585585 10.1482 31.2328i 0.419575 1.29132i
586586 14.8226 + 14.9463i 0.612318 + 0.617424i
587587 −3.97489 + 5.47096i −0.164061 + 0.225811i −0.883130 0.469128i 0.844568π-0.844568\pi
0.719069 + 0.694939i 0.244568π0.244568\pi
588588 −7.87739 + 5.62390i −0.324858 + 0.231926i
589589 37.4667 12.1737i 1.54379 0.501607i
590590 2.75198 + 1.41663i 0.113297 + 0.0583217i
591591 −8.28790 + 6.02151i −0.340919 + 0.247692i
592592 20.3846 6.25099i 0.837800 0.256914i
593593 −8.93648 −0.366977 −0.183489 0.983022i 0.558739π-0.558739\pi
−0.183489 + 0.983022i 0.558739π0.558739\pi
594594 0 0
595595 13.9648i 0.572500i
596596 −25.2017 0.209301i −1.03230 0.00857329i
597597 −7.54971 10.3913i −0.308989 0.425287i
598598 6.34055 12.3173i 0.259284 0.503692i
599599 −1.75023 5.38664i −0.0715123 0.220092i 0.908912 0.416987i 0.136914π-0.136914\pi
−0.980425 + 0.196895i 0.936914π0.936914\pi
600600 14.9489 14.5811i 0.610288 0.595269i
601601 −27.7733 20.1785i −1.13290 0.823099i −0.146784 0.989169i 0.546892π-0.546892\pi
−0.986114 + 0.166070i 0.946892π0.946892\pi
602602 7.75758 + 7.82228i 0.316176 + 0.318812i
603603 −24.0661 7.81956i −0.980048 0.318437i
604604 28.9251 9.13346i 1.17694 0.371635i
605605 0 0
606606 −7.25444 + 1.11813i −0.294691 + 0.0454210i
607607 12.4984 38.4660i 0.507293 1.56129i −0.289588 0.957151i 0.593518π-0.593518\pi
0.796881 0.604136i 0.206482π-0.206482\pi
608608 −23.9747 4.30924i −0.972304 0.174763i
609609 −3.22577 2.34366i −0.130715 0.0949698i
610610 17.0550 + 33.8187i 0.690535 + 1.36928i
611611 1.35858 0.441431i 0.0549625 0.0178584i
612612 −13.5443 4.52552i −0.547498 0.182933i
613613 8.52308 + 11.7310i 0.344244 + 0.473811i 0.945675 0.325114i 0.105403π-0.105403\pi
−0.601431 + 0.798925i 0.705403π0.705403\pi
614614 11.7304 + 1.90787i 0.473399 + 0.0769954i
615615 −1.70118 −0.0685982
616616 0 0
617617 −17.5018 −0.704595 −0.352297 0.935888i 0.614599π-0.614599\pi
−0.352297 + 0.935888i 0.614599π0.614599\pi
618618 −4.75988 0.774166i −0.191471 0.0311415i
619619 16.5014 + 22.7122i 0.663245 + 0.912879i 0.999583 0.0288623i 0.00918843π-0.00918843\pi
−0.336338 + 0.941741i 0.609188π0.609188\pi
620620 21.3046 63.7621i 0.855614 2.56075i
621621 10.6644 3.46506i 0.427946 0.139048i
622622 −16.3316 32.3842i −0.654836 1.29849i
623623 −13.1966 9.58787i −0.528710 0.384130i
624624 4.49175 13.0808i 0.179814 0.523653i
625625 1.46621 4.51254i 0.0586486 0.180502i
626626 −26.3921 + 4.06783i −1.05484 + 0.162583i
627627 0 0
628628 0.919360 + 2.91155i 0.0366864 + 0.116184i
629629 16.1201 + 5.23774i 0.642750 + 0.208842i
630630 9.82030 + 9.90220i 0.391250 + 0.394513i
631631 −14.5008 10.5355i −0.577268 0.419410i 0.260470 0.965482i 0.416123π-0.416123\pi
−0.837738 + 0.546072i 0.816123π0.816123\pi
632632 −22.7117 23.2847i −0.903423 0.926216i
633633 −2.28328 7.02722i −0.0907523 0.279307i
634634 12.9212 25.1011i 0.513168 0.996893i
635635 19.9915 + 27.5159i 0.793337 + 1.09193i
636636 0.0349708 4.21080i 0.00138668 0.166969i
637637 22.1767i 0.878671i
638638 0 0
639639 12.5456 0.496297
640640 −30.2352 + 28.5267i −1.19515 + 1.12762i
641641 −2.86764 + 2.08347i −0.113265 + 0.0822919i −0.642976 0.765886i 0.722300π-0.722300\pi
0.529711 + 0.848178i 0.322300π0.322300\pi
642642 13.9924 + 7.20280i 0.552234 + 0.284272i
643643 −14.8746 + 4.83306i −0.586598 + 0.190597i −0.587254 0.809403i 0.699791π-0.699791\pi
0.000656291 1.00000i 0.499791π0.499791\pi
644644 3.41834 + 4.78806i 0.134701 + 0.188676i
645645 12.2261 16.8277i 0.481400 0.662591i
646646 −13.6357 13.7494i −0.536489 0.540963i
647647 −8.57099 + 26.3788i −0.336960 + 1.03706i 0.628788 + 0.777577i 0.283551π0.283551\pi
−0.965748 + 0.259481i 0.916449π0.916449\pi
648648 −7.04611 + 3.48030i −0.276797 + 0.136719i
649649 0 0
650650 −7.28856 47.2882i −0.285881 1.85480i
651651 −9.03383 2.93527i −0.354064 0.115042i
652652 24.9856 + 18.4720i 0.978510 + 0.723421i
653653 2.60741 3.58879i 0.102036 0.140440i −0.754946 0.655787i 0.772337π-0.772337\pi
0.856982 + 0.515347i 0.172337π0.172337\pi
654654 −3.12723 6.20105i −0.122284 0.242480i
655655 15.1325 + 46.5731i 0.591276 + 1.81976i
656656 2.13182 + 0.0354120i 0.0832335 + 0.00138261i
657657 −4.85344 + 3.52623i −0.189351 + 0.137571i
658658 −0.0973855 + 0.598765i −0.00379648 + 0.0233423i
659659 14.0037i 0.545506i −0.962084 0.272753i 0.912066π-0.912066\pi
0.962084 0.272753i 0.0879341π-0.0879341\pi
660660 0 0
661661 33.4719i 1.30191i 0.759118 + 0.650953i 0.225631π0.225631\pi
−0.759118 + 0.650953i 0.774369π0.774369\pi
662662 26.3295 + 4.28233i 1.02332 + 0.166437i
663663 8.89491 6.46253i 0.345450 0.250984i
664664 0.478581 2.79577i 0.0185725 0.108497i
665665 5.84380 + 17.9854i 0.226613 + 0.697443i
666666 15.1138 7.62197i 0.585647 0.295345i
667667 5.55505 7.64587i 0.215092 0.296049i
668668 −9.97951 + 13.4984i −0.386119 + 0.522270i
669669 −4.14959 1.34828i −0.160432 0.0521277i
670670 −57.8723 + 8.91989i −2.23580 + 0.344605i
671671 0 0
672672 4.06597 + 4.23841i 0.156848 + 0.163500i
673673 0.312128 0.960631i 0.0120317 0.0370296i −0.944860 0.327473i 0.893803π-0.893803\pi
0.956892 + 0.290444i 0.0938029π0.0938029\pi
674674 −21.3719 + 21.1951i −0.823215 + 0.816406i
675675 22.7635 31.3313i 0.876168 1.20594i
676676 −3.30557 4.63011i −0.127137 0.178081i
677677 −29.7611 + 9.66997i −1.14381 + 0.371647i −0.818809 0.574066i 0.805365π-0.805365\pi
−0.325003 + 0.945713i 0.605365π0.605365\pi
678678 −8.99519 + 17.4743i −0.345458 + 0.671096i
679679 5.75432 4.18076i 0.220831 0.160443i
680680 −32.7003 + 4.76244i −1.25400 + 0.182631i
681681 −15.6986 −0.601573
682682 0 0
683683 12.2698i 0.469491i −0.972057 0.234745i 0.924574π-0.924574\pi
0.972057 0.234745i 0.0754256π-0.0754256\pi
684684 −19.3377 0.160600i −0.739395 0.00614069i
685685 20.9676 + 28.8594i 0.801130 + 1.10266i
686686 −18.8939 9.72598i −0.721374 0.371340i
687687 −1.06903 3.29013i −0.0407859 0.125526i
688688 −15.6713 + 20.8330i −0.597461 + 0.794251i
689689 −7.80559 5.67110i −0.297369 0.216052i
690690 7.88680 7.82157i 0.300245 0.297762i
691691 9.98898 + 3.24562i 0.379999 + 0.123469i 0.492787 0.870150i 0.335978π-0.335978\pi
−0.112788 + 0.993619i 0.535978π0.535978\pi
692692 −14.9725 47.4170i −0.569170 1.80252i
693693 0 0
694694 −1.17345 7.61337i −0.0445437 0.288999i
695695 −25.2679 + 77.7666i −0.958466 + 2.94986i
696696 4.38787 8.35280i 0.166322 0.316612i
697697 1.37124 + 0.996261i 0.0519392 + 0.0377361i
698698 12.8905 6.50076i 0.487913 0.246057i
699699 −10.1492 + 3.29769i −0.383880 + 0.124730i
700700 19.2715 + 6.43910i 0.728393 + 0.243375i
701701 3.40536 + 4.68708i 0.128619 + 0.177028i 0.868470 0.495742i 0.165104π-0.165104\pi
−0.739851 + 0.672771i 0.765104π0.765104\pi
702702 4.11762 25.3168i 0.155410 0.955521i
703703 22.9531 0.865691
704704 0 0
705705 1.14536 0.0431367
706706 −1.16040 + 7.13459i −0.0436721 + 0.268514i
707707 −4.19793 5.77796i −0.157880 0.217303i
708708 0.981525 + 0.327953i 0.0368880 + 0.0123252i
709709 43.3278 14.0781i 1.62721 0.528713i 0.653583 0.756855i 0.273265π-0.273265\pi
0.973628 + 0.228142i 0.0732650π0.0732650\pi
710710 25.9212 13.0722i 0.972807 0.490592i
711711 −20.8911 15.1783i −0.783477 0.569230i
712712 17.9507 34.1712i 0.672732 1.28062i
713713 6.95732 21.4124i 0.260554 0.801902i
714714 0.711247 + 4.61457i 0.0266177 + 0.172696i
715715 0 0
716716 9.92812 + 31.4417i 0.371031 + 1.17503i
717717 17.3042 + 5.62246i 0.646236 + 0.209975i
718718 −21.0671 + 20.8928i −0.786216 + 0.779713i
719719 −2.37119 1.72277i −0.0884304 0.0642485i 0.542692 0.839932i 0.317405π-0.317405\pi
−0.631122 + 0.775684i 0.717405π0.717405\pi
720720 −19.8382 + 26.3724i −0.739326 + 0.982842i
721721 −1.44998 4.46259i −0.0540002 0.166195i
722722 0.575335 + 0.296163i 0.0214117 + 0.0110221i
723723 −8.90903 12.2622i −0.331331 0.456037i
724724 −18.3575 0.152459i −0.682250 0.00566611i
725725 32.6409i 1.21225i
726726 0 0
727727 −24.5751 −0.911438 −0.455719 0.890124i 0.650618π-0.650618\pi
−0.455719 + 0.890124i 0.650618π0.650618\pi
728728 13.3167 1.93943i 0.493550 0.0718802i
729729 4.55856 3.31199i 0.168836 0.122666i
730730 −6.35373 + 12.3429i −0.235162 + 0.456832i
731731 −19.7096 + 6.40404i −0.728986 + 0.236862i
732732 7.35813 + 10.3065i 0.271964 + 0.380940i
733733 −12.2285 + 16.8312i −0.451672 + 0.621673i −0.972756 0.231833i 0.925528π-0.925528\pi
0.521084 + 0.853505i 0.325528π0.325528\pi
734734 −31.6597 + 31.3978i −1.16858 + 1.15891i
735735 −5.49464 + 16.9108i −0.202673 + 0.623763i
736736 −10.0461 + 9.63735i −0.370303 + 0.355237i
737737 0 0
738738 1.67291 0.257847i 0.0615807 0.00949147i
739739 −2.61653 0.850163i −0.0962507 0.0312737i 0.260496 0.965475i 0.416114π-0.416114\pi
−0.356746 + 0.934201i 0.616114π0.616114\pi
740740 23.2856 31.4964i 0.855995 1.15783i
741741 8.75148 12.0454i 0.321494 0.442498i
742742 3.65838 1.84494i 0.134303 0.0677300i
743743 −13.8990 42.7766i −0.509903 1.56932i −0.792368 0.610043i 0.791152π-0.791152\pi
0.282465 0.959278i 0.408848π-0.408848\pi
744744 3.79247 22.1549i 0.139039 0.812237i
745745 −37.4570 + 27.2141i −1.37232 + 0.997046i
746746 34.6516 + 5.63587i 1.26869 + 0.206344i
747747 2.25182i 0.0823899i
748748 0 0
749749 15.3126i 0.559509i
750750 2.53570 15.5905i 0.0925905 0.569284i
751751 28.5391 20.7349i 1.04141 0.756626i 0.0708463 0.997487i 0.477430π-0.477430\pi
0.970559 + 0.240862i 0.0774300π0.0774300\pi
752752 −1.43530 0.0238420i −0.0523398 0.000869427i
753753 1.59935 + 4.92229i 0.0582835 + 0.179378i
754754 −9.73438 19.3025i −0.354505 0.702957i
755755 32.7538 45.0817i 1.19203 1.64069i
756756 8.75867 + 6.47536i 0.318550 + 0.235507i
757757 44.5991 + 14.4911i 1.62098 + 0.526689i 0.972173 0.234263i 0.0752677π-0.0752677\pi
0.648808 + 0.760952i 0.275268π0.275268\pi
758758 7.69970 + 49.9557i 0.279666 + 1.81447i
759759 0 0
760760 −40.1221 + 19.8176i −1.45538 + 0.718860i
761761 −1.36665 + 4.20610i −0.0495409 + 0.152471i −0.972767 0.231787i 0.925543π-0.925543\pi
0.923226 + 0.384258i 0.125543π0.125543\pi
762762 8.00748 + 8.07425i 0.290080 + 0.292499i
763763 3.97195 5.46691i 0.143794 0.197916i
764764 −2.87016 4.02023i −0.103839 0.145447i
765765 −24.9503 + 8.10685i −0.902081 + 0.293104i
766766 −23.9380 12.3225i −0.864914 0.445229i
767767 1.91827 1.39371i 0.0692648 0.0503238i
768768 −8.53813 + 10.9664i −0.308093 + 0.395716i
769769 −53.6158 −1.93344 −0.966718 0.255844i 0.917647π-0.917647\pi
−0.966718 + 0.255844i 0.917647π0.917647\pi
770770 0 0
771771 12.3071i 0.443229i
772772 0.166197 20.0116i 0.00598156 0.720234i
773773 −25.2658 34.7754i −0.908749 1.25079i −0.967592 0.252518i 0.918741π-0.918741\pi
0.0588433 0.998267i 0.481259π-0.481259\pi
774774 −9.47232 + 18.4012i −0.340475 + 0.661416i
775775 −24.0289 73.9534i −0.863144 2.65648i
776776 11.7522 + 12.0487i 0.421879 + 0.432523i
777777 −4.47739 3.25302i −0.160626 0.116701i
778778 32.4343 + 32.7048i 1.16283 + 1.17252i
779779 2.18293 + 0.709277i 0.0782116 + 0.0254125i
780780 −7.65054 24.2288i −0.273933 0.867529i
781781 0 0
782782 −10.9377 + 1.68583i −0.391131 + 0.0602852i
783783 5.40719 16.6416i 0.193237 0.594723i
784784 7.23758 21.0772i 0.258485 0.752757i
785785 4.53786 + 3.29694i 0.161963 + 0.117673i
786786 7.37247 + 14.6190i 0.262967 + 0.521444i
787787 14.4914 4.70853i 0.516562 0.167841i −0.0391226 0.999234i 0.512456π-0.512456\pi
0.555684 + 0.831393i 0.312456π0.312456\pi
788788 7.47490 22.3715i 0.266282 0.796951i
789789 −5.62407 7.74086i −0.200222 0.275582i
790790 −58.9798 9.59270i −2.09841 0.341293i
791791 −19.1230 −0.679937
792792 0 0
793793 29.0152 1.03036
794794 −18.1662 2.95463i −0.644696 0.104856i
795795 −4.54703 6.25845i −0.161267 0.221964i
796796 28.0491 + 9.37194i 0.994174 + 0.332180i
797797 30.7264 9.98362i 1.08839 0.353638i 0.290764 0.956795i 0.406091π-0.406091\pi
0.797623 + 0.603157i 0.206091π0.206091\pi
798798 2.84707 + 5.64552i 0.100785 + 0.199849i
799799 −0.923216 0.670755i −0.0326610 0.0237296i
800800 −8.50577 + 47.3225i −0.300724 + 1.67310i
801801 9.46938 29.1438i 0.334584 1.02974i
802802 −28.7283 + 4.42792i −1.01443 + 0.156355i
803803 0 0
804804 −18.6692 + 5.89504i −0.658412 + 0.207902i
805805 10.2788 + 3.33977i 0.362279 + 0.117711i
806806 −36.2647 36.5671i −1.27737 1.28802i
807807 −1.74512 1.26790i −0.0614312 0.0446324i
808808 12.0982 11.8005i 0.425612 0.415138i
809809 −15.5606 47.8907i −0.547082 1.68375i −0.715987 0.698113i 0.754023π-0.754023\pi
0.168905 0.985632i 0.445977π-0.445977\pi
810810 −6.60772 + 12.8363i −0.232172 + 0.451023i
811811 −25.6617 35.3204i −0.901106 1.24027i −0.970114 0.242649i 0.921984π-0.921984\pi
0.0690084 0.997616i 0.478016π-0.478016\pi
812812 9.18016 + 0.0762414i 0.322160 + 0.00267555i
813813 0.267306i 0.00937483i
814814 0 0
815815 57.0827 1.99952
816816 −10.5630 + 3.23919i −0.369780 + 0.113394i
817817 −22.7043 + 16.4957i −0.794323 + 0.577110i
818818 −12.3991 6.38263i −0.433523 0.223164i
819819 10.1606 3.30139i 0.355042 0.115360i
820820 3.18783 2.27589i 0.111324 0.0794774i
821821 −11.1672 + 15.3703i −0.389736 + 0.536426i −0.958131 0.286330i 0.907565π-0.907565\pi
0.568395 + 0.822756i 0.307565π0.307565\pi
822822 8.39845 + 8.46849i 0.292930 + 0.295373i
823823 −4.08288 + 12.5658i −0.142320 + 0.438017i −0.996657 0.0817036i 0.973964π-0.973964\pi
0.854336 + 0.519720i 0.173964π0.173964\pi
824824 9.95521 4.91720i 0.346806 0.171299i
825825 0 0
826826 0.153387 + 0.995176i 0.00533702 + 0.0346266i
827827 −16.8815 5.48515i −0.587029 0.190737i 0.000418135 1.00000i 0.499867π-0.499867\pi
−0.587447 + 0.809263i 0.699867π0.699867\pi
828828 −6.57022 + 8.88699i −0.228331 + 0.308844i
829829 5.03360 6.92816i 0.174824 0.240625i −0.712609 0.701562i 0.752486π-0.752486\pi
0.887433 + 0.460937i 0.152486π0.152486\pi
830830 −2.34635 4.65263i −0.0814429 0.161495i
831831 0.671065 + 2.06533i 0.0232790 + 0.0716454i
832832 9.08285 + 30.5213i 0.314891 + 1.05814i
833833 14.3324 10.4131i 0.496588 0.360792i
834834 −4.38885 + 26.9844i −0.151973 + 0.934393i
835835 30.8389i 1.06723i
836836 0 0
837837 41.6850i 1.44084i
838838 −0.236024 0.0383879i −0.00815333 0.00132609i
839839 30.7967 22.3751i 1.06322 0.772474i 0.0885383 0.996073i 0.471780π-0.471780\pi
0.974681 + 0.223598i 0.0717804π0.0717804\pi
840840 10.6352 + 1.82053i 0.366948 + 0.0628141i
841841 4.40414 + 13.5546i 0.151867 + 0.467398i
842842 29.6903 14.9730i 1.02320 0.516004i
843843 −0.634715 + 0.873611i −0.0218608 + 0.0300888i
844844 13.6798 + 10.1136i 0.470879 + 0.348125i
845845 −9.93967 3.22959i −0.341935 0.111101i
846846 −1.12633 + 0.173601i −0.0387239 + 0.00596853i
847847 0 0
848848 5.56779 + 7.93737i 0.191199 + 0.272571i
849849 3.70476 11.4021i 0.127147 0.391318i
850850 −27.1392 + 26.9147i −0.930866 + 0.923168i
851851 7.71046 10.6125i 0.264311 0.363793i
852852 7.89972 5.63984i 0.270640 0.193218i
853853 32.5718 10.5832i 1.11524 0.362362i 0.307288 0.951616i 0.400578π-0.400578\pi
0.807948 + 0.589254i 0.200578π0.200578\pi
854854 −5.63949 + 10.9554i −0.192979 + 0.374887i
855855 −28.7413 + 20.8818i −0.982933 + 0.714142i
856856 −35.8563 + 5.22208i −1.22554 + 0.178487i
857857 52.8215 1.80435 0.902174 0.431371i 0.141970π-0.141970\pi
0.902174 + 0.431371i 0.141970π0.141970\pi
858858 0 0
859859 8.91497i 0.304175i −0.988367 0.152087i 0.951400π-0.951400\pi
0.988367 0.152087i 0.0485995π-0.0485995\pi
860860 −0.397725 + 47.8897i −0.0135623 + 1.63303i
861861 −0.325296 0.447732i −0.0110861 0.0152587i
862862 9.16985 + 4.72034i 0.312326 + 0.160775i
863863 −0.324037 0.997282i −0.0110303 0.0339479i 0.945390 0.325942i 0.105681π-0.105681\pi
−0.956420 + 0.291994i 0.905681π0.905681\pi
864864 −12.1759 + 22.7178i −0.414232 + 0.772876i
865865 −73.9027 53.6934i −2.51277 1.82563i
866866 2.34799 2.32857i 0.0797880 0.0791281i
867867 5.69091 + 1.84909i 0.193273 + 0.0627984i
868868 20.8553 6.58533i 0.707876 0.223521i
869869 0 0
870870 −2.64041 17.1310i −0.0895182 0.580794i
871871 −13.8617 + 42.6618i −0.469685 + 1.44554i
872872 14.1560 + 7.43641i 0.479383 + 0.251829i
873873 10.8101 + 7.85400i 0.365867 + 0.265818i
874874 −13.3813 + 6.74826i −0.452629 + 0.228263i
875875 14.6167 4.74926i 0.494136 0.160554i
876876 −1.47091 + 4.40224i −0.0496973 + 0.148738i
877877 −7.10243 9.77565i −0.239832 0.330100i 0.672086 0.740473i 0.265399π-0.265399\pi
−0.911918 + 0.410373i 0.865399π0.865399\pi
878878 −0.275616 + 1.69460i −0.00930158 + 0.0571899i
879879 12.9294 0.436096
880880 0 0
881881 11.8356 0.398752 0.199376 0.979923i 0.436109π-0.436109\pi
0.199376 + 0.979923i 0.436109π0.436109\pi
882882 2.84018 17.4626i 0.0956338 0.587995i
883883 30.0534 + 41.3650i 1.01138 + 1.39204i 0.918075 + 0.396406i 0.129743π0.129743\pi
0.0933036 + 0.995638i 0.470257π0.470257\pi
884884 −8.02236 + 24.0100i −0.269821 + 0.807542i
885885 1.80809 0.587484i 0.0607783 0.0197481i
886886 −5.83224 + 2.94124i −0.195938 + 0.0988127i
887887 13.7419 + 9.98405i 0.461407 + 0.335232i 0.794083 0.607810i 0.207952π-0.207952\pi
−0.332676 + 0.943041i 0.607952π0.607952\pi
888888 6.09041 11.5938i 0.204381 0.389061i
889889 −3.41915 + 10.5231i −0.114675 + 0.352932i
890890 −10.8019 70.0826i −0.362080 2.34917i
891891 0 0
892892 9.57966 3.02490i 0.320751 0.101281i
893893 −1.46971 0.477537i −0.0491819 0.0159802i
894894 −10.9914 + 10.9004i −0.367606 + 0.364566i
895895 49.0041 + 35.6035i 1.63802 + 1.19009i
896896 −13.2894 2.50276i −0.443969 0.0836113i
897897 −2.62946 8.09264i −0.0877951 0.270205i
898898 7.37942 + 3.79868i 0.246254 + 0.126764i
899899 −20.6509 28.4235i −0.688746 0.947978i
900900 −0.316999 + 38.1696i −0.0105666 + 1.27232i
901901 7.70750i 0.256774i
902902 0 0
903903 6.76671 0.225182
904904 −6.52158 44.7790i −0.216904 1.48933i
905905 −27.2845 + 19.8233i −0.906966 + 0.658950i
906906 8.52720 16.5652i 0.283297 0.550340i
907907 13.6986 4.45094i 0.454855 0.147791i −0.0726243 0.997359i 0.523137π-0.523137\pi
0.527479 + 0.849568i 0.323137π0.323137\pi
908908 29.4176 21.0021i 0.976256 0.696978i
909909 7.88626 10.8545i 0.261571 0.360021i
910910 17.5536 17.4084i 0.581895 0.577082i
911911 −12.3572 + 38.0317i −0.409414 + 1.26005i 0.507739 + 0.861511i 0.330481π0.330481\pi
−0.917153 + 0.398535i 0.869519π0.869519\pi
912912 −12.2487 + 8.59207i −0.405596 + 0.284512i
913913 0 0
914914 −34.2402 + 5.27746i −1.13256 + 0.174563i
915915 22.1255 + 7.18901i 0.731446 + 0.237661i
916916 6.40487 + 4.73517i 0.211623 + 0.156455i
917917 −9.36391 + 12.8883i −0.309224 + 0.425610i
918918 −18.2953 + 9.22641i −0.603833 + 0.304517i
919919 2.18755 + 6.73259i 0.0721607 + 0.222088i 0.980632 0.195860i 0.0627497π-0.0627497\pi
−0.908471 + 0.417947i 0.862750π0.862750\pi
920920 −4.31510 + 25.2080i −0.142265 + 0.831082i
921921 5.90560 4.29067i 0.194596 0.141382i
922922 −9.21105 1.49812i −0.303350 0.0493380i
923923 22.2395i 0.732022i
924924 0 0
925925 45.3058i 1.48965i
926926 3.27381 20.1287i 0.107584 0.661471i
927927 7.13138 5.18125i 0.234225 0.170175i
928928 2.95220 + 21.5225i 0.0969107 + 0.706510i
929929 −11.8469 36.4610i −0.388684 1.19625i −0.933772 0.357867i 0.883504π-0.883504\pi
0.545089 0.838378i 0.316496π-0.316496\pi
930930 −18.5934 36.8694i −0.609703 1.20899i
931931 14.1013 19.4088i 0.462151 0.636097i
932932 14.6069 19.7575i 0.478464 0.647178i
933933 −21.1870 6.88409i −0.693632 0.225375i
934934 −1.18245 7.67174i −0.0386909 0.251027i
935935 0 0
936936 11.1957 + 22.6665i 0.365944 + 0.740879i
937937 17.9279 55.1764i 0.585679 1.80253i −0.0108493 0.999941i 0.503454π-0.503454\pi
0.596528 0.802592i 0.296546π-0.296546\pi
938938 −13.4138 13.5257i −0.437977 0.441630i
939939 −9.64086 + 13.2695i −0.314618 + 0.433034i
940940 −2.14628 + 1.53229i −0.0700039 + 0.0499779i
941941 10.4977 3.41092i 0.342216 0.111193i −0.132867 0.991134i 0.542418π-0.542418\pi
0.475083 + 0.879941i 0.342418π0.342418\pi
942942 1.66742 + 0.858334i 0.0543276 + 0.0279660i
943943 1.06124 0.771033i 0.0345586 0.0251083i
944944 −2.27802 + 0.698562i −0.0741432 + 0.0227363i
945945 20.0103 0.650936
946946 0 0
947947 15.5478i 0.505235i −0.967566 0.252617i 0.918709π-0.918709\pi
0.967566 0.252617i 0.0812914π-0.0812914\pi
948948 −19.9781 0.165918i −0.648857 0.00538877i
949949 6.25092 + 8.60365i 0.202913 + 0.279286i
950950 −23.6899 + 46.0206i −0.768602 + 1.49311i
951951 −5.35850 16.4918i −0.173761 0.534783i
952952 −7.50630 7.69569i −0.243281 0.249419i
953953 6.33105 + 4.59978i 0.205083 + 0.149001i 0.685586 0.727992i 0.259546π-0.259546\pi
−0.480503 + 0.876993i 0.659546π0.659546\pi
954954 5.42006 + 5.46526i 0.175481 + 0.176944i
955955 −8.63041 2.80419i −0.279274 0.0907415i
956956 −39.9480 + 12.6141i −1.29201 + 0.407969i
957957 0 0
958958 −41.7408 + 6.43354i −1.34858 + 0.207858i
959959 −3.58610 + 11.0369i −0.115801 + 0.356399i
960960 −0.636059 + 25.5244i −0.0205287 + 0.823796i
961961 −42.6329 30.9746i −1.37525 0.999180i
962962 −13.5114 26.7921i −0.435625 0.863811i
963963 −27.3584 + 8.88927i −0.881611 + 0.286453i
964964 33.0993 + 11.0594i 1.06606 + 0.356198i
965965 −21.6096 29.7430i −0.695637 0.957462i
966966 3.56665 + 0.580093i 0.114755 + 0.0186642i
967967 47.0564 1.51323 0.756615 0.653860i 0.226852π-0.226852\pi
0.756615 + 0.653860i 0.226852π0.226852\pi
968968 0 0
969969 −11.8940 −0.382090
970970 30.5191 + 4.96375i 0.979910 + 0.159376i
971971 −22.7992 31.3804i −0.731662 1.00705i −0.999055 0.0434585i 0.986162π-0.986162\pi
0.267394 0.963587i 0.413838π-0.413838\pi
972972 −10.1934 + 30.5077i −0.326954 + 0.978534i
973973 −25.2990 + 8.22014i −0.811049 + 0.263526i
974974 1.89610 + 3.75981i 0.0607549 + 0.120472i
975975 −23.7757 17.2741i −0.761433 0.553213i
976976 −27.5767 9.46941i −0.882709 0.303108i
977977 −12.0635 + 37.1276i −0.385945 + 1.18782i 0.549847 + 0.835265i 0.314686π0.314686\pi
−0.935792 + 0.352552i 0.885314π0.885314\pi
978978 18.8626 2.90731i 0.603160 0.0929654i
979979 0 0
980980 −12.3273 39.0399i −0.393782 1.24708i
981981 12.0733 + 3.92286i 0.385471 + 0.125247i
982982 2.96815 + 2.99291i 0.0947176 + 0.0955075i
983983 −4.54996 3.30574i −0.145121 0.105437i 0.512856 0.858475i 0.328588π-0.328588\pi
−0.657977 + 0.753038i 0.728588π0.728588\pi
984984 0.937484 0.914413i 0.0298859 0.0291504i
985985 −13.3903 41.2110i −0.426649 1.31309i
986986 −7.90410 + 15.3547i −0.251718 + 0.488994i
987987 0.219013 + 0.301446i 0.00697127 + 0.00959513i
988988 −0.284694 + 34.2798i −0.00905733 + 1.09058i
989989 16.0388i 0.510004i
990990 0 0
991991 7.34032 0.233173 0.116586 0.993181i 0.462805π-0.462805\pi
0.116586 + 0.993181i 0.462805π0.462805\pi
992992 22.5327 + 46.5895i 0.715414 + 1.47922i
993993 13.2555 9.63066i 0.420650 0.305620i
994994 8.39708 + 4.32254i 0.266339 + 0.137103i
995995 51.6699 16.7886i 1.63804 0.532233i
996996 −1.01230 1.41793i −0.0320760 0.0449287i
997997 33.4680 46.0647i 1.05994 1.45888i 0.180081 0.983652i 0.442364π-0.442364\pi
0.879861 0.475232i 0.157636π-0.157636\pi
998998 −15.1311 15.2573i −0.478966 0.482960i
999999 7.50522 23.0987i 0.237455 0.730811i
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 968.2.o.d.493.5 40
8.5 even 2 inner 968.2.o.d.493.4 40
11.2 odd 10 88.2.o.a.69.4 yes 40
11.3 even 5 968.2.o.i.565.8 40
11.4 even 5 968.2.c.i.485.2 20
11.5 even 5 inner 968.2.o.d.269.4 40
11.6 odd 10 968.2.o.j.269.7 40
11.7 odd 10 968.2.c.h.485.19 20
11.8 odd 10 88.2.o.a.37.3 40
11.9 even 5 968.2.o.i.245.7 40
11.10 odd 2 968.2.o.j.493.6 40
33.2 even 10 792.2.br.b.685.7 40
33.8 even 10 792.2.br.b.37.8 40
44.7 even 10 3872.2.c.h.1937.14 20
44.15 odd 10 3872.2.c.i.1937.14 20
44.19 even 10 352.2.w.a.81.7 40
44.35 even 10 352.2.w.a.113.4 40
88.5 even 10 inner 968.2.o.d.269.5 40
88.13 odd 10 88.2.o.a.69.3 yes 40
88.19 even 10 352.2.w.a.81.4 40
88.21 odd 2 968.2.o.j.493.7 40
88.29 odd 10 968.2.c.h.485.20 20
88.35 even 10 352.2.w.a.113.7 40
88.37 even 10 968.2.c.i.485.1 20
88.51 even 10 3872.2.c.h.1937.7 20
88.53 even 10 968.2.o.i.245.8 40
88.59 odd 10 3872.2.c.i.1937.7 20
88.61 odd 10 968.2.o.j.269.6 40
88.69 even 10 968.2.o.i.565.7 40
88.85 odd 10 88.2.o.a.37.4 yes 40
264.101 even 10 792.2.br.b.685.8 40
264.173 even 10 792.2.br.b.37.7 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
88.2.o.a.37.3 40 11.8 odd 10
88.2.o.a.37.4 yes 40 88.85 odd 10
88.2.o.a.69.3 yes 40 88.13 odd 10
88.2.o.a.69.4 yes 40 11.2 odd 10
352.2.w.a.81.4 40 88.19 even 10
352.2.w.a.81.7 40 44.19 even 10
352.2.w.a.113.4 40 44.35 even 10
352.2.w.a.113.7 40 88.35 even 10
792.2.br.b.37.7 40 264.173 even 10
792.2.br.b.37.8 40 33.8 even 10
792.2.br.b.685.7 40 33.2 even 10
792.2.br.b.685.8 40 264.101 even 10
968.2.c.h.485.19 20 11.7 odd 10
968.2.c.h.485.20 20 88.29 odd 10
968.2.c.i.485.1 20 88.37 even 10
968.2.c.i.485.2 20 11.4 even 5
968.2.o.d.269.4 40 11.5 even 5 inner
968.2.o.d.269.5 40 88.5 even 10 inner
968.2.o.d.493.4 40 8.5 even 2 inner
968.2.o.d.493.5 40 1.1 even 1 trivial
968.2.o.i.245.7 40 11.9 even 5
968.2.o.i.245.8 40 88.53 even 10
968.2.o.i.565.7 40 88.69 even 10
968.2.o.i.565.8 40 11.3 even 5
968.2.o.j.269.6 40 88.61 odd 10
968.2.o.j.269.7 40 11.6 odd 10
968.2.o.j.493.6 40 11.10 odd 2
968.2.o.j.493.7 40 88.21 odd 2
3872.2.c.h.1937.7 20 88.51 even 10
3872.2.c.h.1937.14 20 44.7 even 10
3872.2.c.i.1937.7 20 88.59 odd 10
3872.2.c.i.1937.14 20 44.15 odd 10