Properties

Label 968.2.k.g.699.5
Level 968968
Weight 22
Character 968.699
Analytic conductor 7.7307.730
Analytic rank 00
Dimension 3232
Inner twists 1616

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [968,2,Mod(403,968)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(968, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 5, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("968.403");
 
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.k (of order 1010, degree 44, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 7.729518915667.72951891566
Analytic rank: 00
Dimension: 3232
Relative dimension: 88 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 699.5
Character χ\chi == 968.699
Dual form 968.2.k.g.475.5

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.4051501.35494i)q2+(0.3351060.243469i)q3+(1.671711.09791i)q4+(2.516260.817582i)q5+(0.465653+0.355406i)q6+(2.66220+1.93420i)q7+(2.16488+1.82024i)q8+(0.8740322.68999i)q9+(2.12723+3.07813i)q10+(0.292893+0.774923i)q12+(0.4212011.29632i)q13+(1.54213+4.39075i)q14+(0.644157+0.886607i)q15+(1.58921+3.67075i)q16+(5.22148+1.69656i)q17+(3.99889+0.0944070i)q18+(1.336691.83979i)q19+(3.30882+4.12937i)q20+1.36303q21+6.38741iq23+(1.168640.0828919i)q24+(1.61803+1.17557i)q25+(1.92709+0.0454952i)q26+(0.746033+2.29605i)q27+(6.573980.310574i)q28+(5.324403.86840i)q29+(1.462280.513584i)q30+(1.04227+0.338654i)q31+(5.617500.666071i)q32+(4.414216.38741i)q34+(8.280152.69038i)q35+(1.49223+5.45649i)q36+(2.84345+3.91367i)q37+(1.951242.55652i)q38+(0.174467+0.536955i)q39+(6.935612.81023i)q40+(5.90043+8.12124i)q41+(0.5522341.84683i)q42+6.43215iq43+7.48331iq45+(8.65453+2.58786i)q46+(0.3611601.61701i)q48+(1.183053.64105i)q49+(2.248371.71605i)q50+(1.336691.83979i)q51+(0.719116+2.62951i)q52+(7.11706+2.31247i)q53+(2.80875+1.94107i)q54+(2.242649.03316i)q56+(0.895864+0.291084i)q57+(3.084268.78150i)q58+(2.62335+1.90598i)q59+(0.1034322.18937i)q60+(2.033746.25920i)q61+(0.0365790+1.54941i)q62+(7.52983+5.47074i)q63+(1.373457.88122i)q64+3.60625iq656.07107q67+(6.866128.56884i)q68+(1.555132.14046i)q69+(0.29059712.3091i)q70+(6.074791.97382i)q71+(6.78861+4.23258i)q72+(0.5536740.762067i)q73+(6.454802.26707i)q74+(0.2559980.787881i)q75+(4.25447+1.60804i)q76+(0.656854+0.453939i)q78+(2.87614+8.85185i)q79+(0.99771810.5359i)q80+(6.05572+4.39974i)q81+(8.61321+11.2850i)q82+(4.32561+1.40548i)q83+(2.278601.49648i)q84+(11.75158.53797i)q85+(8.71516+2.60599i)q862.72607q8710.6569q89+(10.1394+3.03187i)q90+(3.62867+2.63638i)q91+(7.0127710.6779i)q92+(0.431722+0.140275i)q93+(4.86763+3.53654i)q95+(2.044631.14448i)q96+(2.31308+7.11893i)q97+(4.454083.07813i)q98+O(q100)q+(0.405150 - 1.35494i) q^{2} +(-0.335106 - 0.243469i) q^{3} +(-1.67171 - 1.09791i) q^{4} +(-2.51626 - 0.817582i) q^{5} +(-0.465653 + 0.355406i) q^{6} +(-2.66220 + 1.93420i) q^{7} +(-2.16488 + 1.82024i) q^{8} +(-0.874032 - 2.68999i) q^{9} +(-2.12723 + 3.07813i) q^{10} +(0.292893 + 0.774923i) q^{12} +(-0.421201 - 1.29632i) q^{13} +(1.54213 + 4.39075i) q^{14} +(0.644157 + 0.886607i) q^{15} +(1.58921 + 3.67075i) q^{16} +(5.22148 + 1.69656i) q^{17} +(-3.99889 + 0.0944070i) q^{18} +(1.33669 - 1.83979i) q^{19} +(3.30882 + 4.12937i) q^{20} +1.36303 q^{21} +6.38741i q^{23} +(1.16864 - 0.0828919i) q^{24} +(1.61803 + 1.17557i) q^{25} +(-1.92709 + 0.0454952i) q^{26} +(-0.746033 + 2.29605i) q^{27} +(6.57398 - 0.310574i) q^{28} +(5.32440 - 3.86840i) q^{29} +(1.46228 - 0.513584i) q^{30} +(-1.04227 + 0.338654i) q^{31} +(5.61750 - 0.666071i) q^{32} +(4.41421 - 6.38741i) q^{34} +(8.28015 - 2.69038i) q^{35} +(-1.49223 + 5.45649i) q^{36} +(2.84345 + 3.91367i) q^{37} +(-1.95124 - 2.55652i) q^{38} +(-0.174467 + 0.536955i) q^{39} +(6.93561 - 2.81023i) q^{40} +(-5.90043 + 8.12124i) q^{41} +(0.552234 - 1.84683i) q^{42} +6.43215i q^{43} +7.48331i q^{45} +(8.65453 + 2.58786i) q^{46} +(0.361160 - 1.61701i) q^{48} +(1.18305 - 3.64105i) q^{49} +(2.24837 - 1.71605i) q^{50} +(-1.33669 - 1.83979i) q^{51} +(-0.719116 + 2.62951i) q^{52} +(-7.11706 + 2.31247i) q^{53} +(2.80875 + 1.94107i) q^{54} +(2.24264 - 9.03316i) q^{56} +(-0.895864 + 0.291084i) q^{57} +(-3.08426 - 8.78150i) q^{58} +(-2.62335 + 1.90598i) q^{59} +(-0.103432 - 2.18937i) q^{60} +(2.03374 - 6.25920i) q^{61} +(0.0365790 + 1.54941i) q^{62} +(7.52983 + 5.47074i) q^{63} +(1.37345 - 7.88122i) q^{64} +3.60625i q^{65} -6.07107 q^{67} +(-6.86612 - 8.56884i) q^{68} +(1.55513 - 2.14046i) q^{69} +(-0.290597 - 12.3091i) q^{70} +(-6.07479 - 1.97382i) q^{71} +(6.78861 + 4.23258i) q^{72} +(-0.553674 - 0.762067i) q^{73} +(6.45480 - 2.26707i) q^{74} +(-0.255998 - 0.787881i) q^{75} +(-4.25447 + 1.60804i) q^{76} +(0.656854 + 0.453939i) q^{78} +(2.87614 + 8.85185i) q^{79} +(-0.997718 - 10.5359i) q^{80} +(-6.05572 + 4.39974i) q^{81} +(8.61321 + 11.2850i) q^{82} +(4.32561 + 1.40548i) q^{83} +(-2.27860 - 1.49648i) q^{84} +(-11.7515 - 8.53797i) q^{85} +(8.71516 + 2.60599i) q^{86} -2.72607 q^{87} -10.6569 q^{89} +(10.1394 + 3.03187i) q^{90} +(3.62867 + 2.63638i) q^{91} +(7.01277 - 10.6779i) q^{92} +(0.431722 + 0.140275i) q^{93} +(-4.86763 + 3.53654i) q^{95} +(-2.04463 - 1.14448i) q^{96} +(2.31308 + 7.11893i) q^{97} +(-4.45408 - 3.07813i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 32q+8q3+32q12+8q14+24q16+16q2524q26+8q27+96q34+16q36+8q38+24q4224q488q4964q5616q58+8q5956q60++8q97+O(q100) 32 q + 8 q^{3} + 32 q^{12} + 8 q^{14} + 24 q^{16} + 16 q^{25} - 24 q^{26} + 8 q^{27} + 96 q^{34} + 16 q^{36} + 8 q^{38} + 24 q^{42} - 24 q^{48} - 8 q^{49} - 64 q^{56} - 16 q^{58} + 8 q^{59} - 56 q^{60}+ \cdots + 8 q^{97}+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 1-1 e(910)e\left(\frac{9}{10}\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 0.405150 1.35494i 0.286484 0.958085i
33 −0.335106 0.243469i −0.193473 0.140567i 0.486831 0.873496i 0.338153π-0.338153\pi
−0.680305 + 0.732929i 0.738153π0.738153\pi
44 −1.67171 1.09791i −0.835853 0.548953i
55 −2.51626 0.817582i −1.12531 0.365634i −0.313515 0.949583i 0.601507π-0.601507\pi
−0.811790 + 0.583949i 0.801507π0.801507\pi
66 −0.465653 + 0.355406i −0.190102 + 0.145094i
77 −2.66220 + 1.93420i −1.00622 + 0.731059i −0.963412 0.268025i 0.913629π-0.913629\pi
−0.0428042 + 0.999083i 0.513629π0.513629\pi
88 −2.16488 + 1.82024i −0.765402 + 0.643552i
99 −0.874032 2.68999i −0.291344 0.896665i
1010 −2.12723 + 3.07813i −0.672691 + 0.973390i
1111 0 0
1212 0.292893 + 0.774923i 0.0845510 + 0.223701i
1313 −0.421201 1.29632i −0.116820 0.359535i 0.875502 0.483214i 0.160531π-0.160531\pi
−0.992322 + 0.123679i 0.960531π0.960531\pi
1414 1.54213 + 4.39075i 0.412151 + 1.17348i
1515 0.644157 + 0.886607i 0.166321 + 0.228921i
1616 1.58921 + 3.67075i 0.397302 + 0.917688i
1717 5.22148 + 1.69656i 1.26639 + 0.411476i 0.863769 0.503888i 0.168098π-0.168098\pi
0.402625 + 0.915365i 0.368098π0.368098\pi
1818 −3.99889 + 0.0944070i −0.942546 + 0.0222519i
1919 1.33669 1.83979i 0.306657 0.422077i −0.627678 0.778473i 0.715994π-0.715994\pi
0.934335 + 0.356396i 0.115994π0.115994\pi
2020 3.30882 + 4.12937i 0.739875 + 0.923356i
2121 1.36303 0.297439
2222 0 0
2323 6.38741i 1.33187i 0.746011 + 0.665933i 0.231967π0.231967\pi
−0.746011 + 0.665933i 0.768033π0.768033\pi
2424 1.16864 0.0828919i 0.238547 0.0169202i
2525 1.61803 + 1.17557i 0.323607 + 0.235114i
2626 −1.92709 + 0.0454952i −0.377933 + 0.00892235i
2727 −0.746033 + 2.29605i −0.143574 + 0.441876i
2828 6.57398 0.310574i 1.24237 0.0586930i
2929 5.32440 3.86840i 0.988715 0.718344i 0.0290761 0.999577i 0.490743π-0.490743\pi
0.959639 + 0.281233i 0.0907435π0.0907435\pi
3030 1.46228 0.513584i 0.266974 0.0937672i
3131 −1.04227 + 0.338654i −0.187197 + 0.0608240i −0.401115 0.916028i 0.631377π-0.631377\pi
0.213918 + 0.976852i 0.431377π0.431377\pi
3232 5.61750 0.666071i 0.993044 0.117746i
3333 0 0
3434 4.41421 6.38741i 0.757031 1.09543i
3535 8.28015 2.69038i 1.39960 0.454758i
3636 −1.49223 + 5.45649i −0.248706 + 0.909414i
3737 2.84345 + 3.91367i 0.467460 + 0.643404i 0.976035 0.217614i 0.0698275π-0.0698275\pi
−0.508575 + 0.861018i 0.669827π0.669827\pi
3838 −1.95124 2.55652i −0.316534 0.414722i
3939 −0.174467 + 0.536955i −0.0279371 + 0.0859816i
4040 6.93561 2.81023i 1.09662 0.444336i
4141 −5.90043 + 8.12124i −0.921492 + 1.26832i 0.0415954 + 0.999135i 0.486756π0.486756\pi
−0.963087 + 0.269190i 0.913244π0.913244\pi
4242 0.552234 1.84683i 0.0852115 0.284971i
4343 6.43215i 0.980894i 0.871471 + 0.490447i 0.163166π0.163166\pi
−0.871471 + 0.490447i 0.836834π0.836834\pi
4444 0 0
4545 7.48331i 1.11555i
4646 8.65453 + 2.58786i 1.27604 + 0.381559i
4747 0 0 −0.809017 0.587785i 0.800000π-0.800000\pi
0.809017 + 0.587785i 0.200000π0.200000\pi
4848 0.361160 1.61701i 0.0521290 0.233396i
4949 1.18305 3.64105i 0.169007 0.520150i
5050 2.24837 1.71605i 0.317968 0.242686i
5151 −1.33669 1.83979i −0.187174 0.257623i
5252 −0.719116 + 2.62951i −0.0997234 + 0.364648i
5353 −7.11706 + 2.31247i −0.977603 + 0.317642i −0.753881 0.657011i 0.771821π-0.771821\pi
−0.223722 + 0.974653i 0.571821π0.571821\pi
5454 2.80875 + 1.94107i 0.382223 + 0.264147i
5555 0 0
5656 2.24264 9.03316i 0.299685 1.20711i
5757 −0.895864 + 0.291084i −0.118660 + 0.0385550i
5858 −3.08426 8.78150i −0.404983 1.15307i
5959 −2.62335 + 1.90598i −0.341531 + 0.248137i −0.745308 0.666721i 0.767697π-0.767697\pi
0.403776 + 0.914858i 0.367697π0.367697\pi
6060 −0.103432 2.18937i −0.0133531 0.282646i
6161 2.03374 6.25920i 0.260393 0.801409i −0.732325 0.680955i 0.761565π-0.761565\pi
0.992719 0.120454i 0.0384350π-0.0384350\pi
6262 0.0365790 + 1.54941i 0.00464554 + 0.196776i
6363 7.52983 + 5.47074i 0.948670 + 0.689249i
6464 1.37345 7.88122i 0.171681 0.985153i
6565 3.60625i 0.447300i
6666 0 0
6767 −6.07107 −0.741699 −0.370849 0.928693i 0.620933π-0.620933\pi
−0.370849 + 0.928693i 0.620933π0.620933\pi
6868 −6.86612 8.56884i −0.832639 1.03912i
6969 1.55513 2.14046i 0.187216 0.257681i
7070 −0.290597 12.3091i −0.0347329 1.47122i
7171 −6.07479 1.97382i −0.720945 0.234249i −0.0745119 0.997220i 0.523740π-0.523740\pi
−0.646433 + 0.762971i 0.723740π0.723740\pi
7272 6.78861 + 4.23258i 0.800046 + 0.498814i
7373 −0.553674 0.762067i −0.0648027 0.0891932i 0.775386 0.631488i 0.217556π-0.217556\pi
−0.840188 + 0.542295i 0.817556π0.817556\pi
7474 6.45480 2.26707i 0.750355 0.263541i
7575 −0.255998 0.787881i −0.0295601 0.0909767i
7676 −4.25447 + 1.60804i −0.488021 + 0.184455i
7777 0 0
7878 0.656854 + 0.453939i 0.0743741 + 0.0513985i
7979 2.87614 + 8.85185i 0.323591 + 0.995911i 0.972073 + 0.234680i 0.0754044π0.0754044\pi
−0.648482 + 0.761230i 0.724596π0.724596\pi
8080 −0.997718 10.5359i −0.111548 1.17795i
8181 −6.05572 + 4.39974i −0.672858 + 0.488860i
8282 8.61321 + 11.2850i 0.951170 + 1.24622i
8383 4.32561 + 1.40548i 0.474798 + 0.154271i 0.536634 0.843815i 0.319696π-0.319696\pi
−0.0618362 + 0.998086i 0.519696π0.519696\pi
8484 −2.27860 1.49648i −0.248615 0.163280i
8585 −11.7515 8.53797i −1.27463 0.926073i
8686 8.71516 + 2.60599i 0.939780 + 0.281011i
8787 −2.72607 −0.292265
8888 0 0
8989 −10.6569 −1.12962 −0.564812 0.825220i 0.691051π-0.691051\pi
−0.564812 + 0.825220i 0.691051π0.691051\pi
9090 10.1394 + 3.03187i 1.06879 + 0.319587i
9191 3.62867 + 2.63638i 0.380388 + 0.276368i
9292 7.01277 10.6779i 0.731132 1.11325i
9393 0.431722 + 0.140275i 0.0447675 + 0.0145458i
9494 0 0
9595 −4.86763 + 3.53654i −0.499409 + 0.362842i
9696 −2.04463 1.14448i −0.208679 0.116808i
9797 2.31308 + 7.11893i 0.234858 + 0.722817i 0.997140 + 0.0755731i 0.0240786π0.0240786\pi
−0.762283 + 0.647244i 0.775921π0.775921\pi
9898 −4.45408 3.07813i −0.449930 0.310938i
9999 0 0
100100 −1.41421 3.74166i −0.141421 0.374166i
101101 −5.33108 16.4074i −0.530462 1.63259i −0.753255 0.657729i 0.771517π-0.771517\pi
0.222792 0.974866i 0.428483π-0.428483\pi
102102 −3.03436 + 1.06574i −0.300447 + 0.105524i
103103 10.6191 + 14.6160i 1.04633 + 1.44015i 0.891946 + 0.452143i 0.149340π0.149340\pi
0.154387 + 0.988010i 0.450660π0.450660\pi
104104 3.27147 + 2.03970i 0.320794 + 0.200009i
105105 −3.42975 1.11439i −0.334709 0.108754i
106106 0.249777 + 10.5801i 0.0242605 + 1.02763i
107107 5.11741 7.04351i 0.494719 0.680922i −0.486531 0.873663i 0.661738π-0.661738\pi
0.981250 + 0.192741i 0.0617378π0.0617378\pi
108108 3.76800 3.01926i 0.362576 0.290528i
109109 2.72607 0.261110 0.130555 0.991441i 0.458324π-0.458324\pi
0.130555 + 0.991441i 0.458324π0.458324\pi
110110 0 0
111111 2.00378i 0.190191i
112112 −11.3308 6.69842i −1.07066 0.632941i
113113 −4.99291 3.62756i −0.469693 0.341252i 0.327629 0.944807i 0.393751π-0.393751\pi
−0.797322 + 0.603555i 0.793751π0.793751\pi
114114 0.0314409 + 1.33177i 0.00294471 + 0.124732i
115115 5.22223 16.0724i 0.486976 1.49876i
116116 −13.1480 + 0.621149i −1.22076 + 0.0576722i
117117 −3.11896 + 2.26606i −0.288348 + 0.209497i
118118 1.51963 + 4.32668i 0.139893 + 0.398303i
119119 −17.1821 + 5.58280i −1.57508 + 0.511774i
120120 −3.00836 0.746879i −0.274625 0.0681804i
121121 0 0
122122 −7.65685 5.29150i −0.693219 0.479070i
123123 3.95453 1.28491i 0.356568 0.115856i
124124 2.11418 + 0.578183i 0.189859 + 0.0519223i
125125 4.66540 + 6.42137i 0.417286 + 0.574345i
126126 10.4632 7.98597i 0.932138 0.711447i
127127 0.174467 0.536955i 0.0154815 0.0476470i −0.943017 0.332744i 0.892026π-0.892026\pi
0.958499 + 0.285097i 0.0920257π0.0920257\pi
128128 −10.1221 5.05401i −0.894676 0.446716i
129129 1.56603 2.15545i 0.137881 0.189777i
130130 4.88624 + 1.46107i 0.428552 + 0.128145i
131131 6.82233i 0.596070i −0.954555 0.298035i 0.903669π-0.903669\pi
0.954555 0.298035i 0.0963311π-0.0963311\pi
132132 0 0
133133 7.48331i 0.648886i
134134 −2.45969 + 8.22591i −0.212485 + 0.710611i
135135 3.75442 5.16752i 0.323129 0.444749i
136136 −14.3920 + 5.83149i −1.23411 + 0.500046i
137137 −2.67512 + 8.23316i −0.228551 + 0.703406i 0.769361 + 0.638814i 0.220575π0.220575\pi
−0.997912 + 0.0645922i 0.979425π0.979425\pi
138138 −2.27012 2.97431i −0.193246 0.253190i
139139 11.5715 + 15.9268i 0.981483 + 1.35090i 0.936027 + 0.351929i 0.114474π0.114474\pi
0.0454561 + 0.998966i 0.485526π0.485526\pi
140140 −16.7958 4.59329i −1.41950 0.388203i
141141 0 0
142142 −5.13560 + 7.43126i −0.430970 + 0.623617i
143143 0 0
144144 8.48528 7.48331i 0.707107 0.623610i
145145 −16.5603 + 5.38077i −1.37526 + 0.446848i
146146 −1.25687 + 0.441442i −0.104020 + 0.0365340i
147147 −1.28293 + 0.932102i −0.105814 + 0.0768785i
148148 −0.456572 9.66435i −0.0375300 0.794405i
149149 −6.52242 + 20.0739i −0.534337 + 1.64452i 0.210740 + 0.977542i 0.432413π0.432413\pi
−0.745077 + 0.666978i 0.767587π0.767587\pi
150150 −1.17125 + 0.0276512i −0.0956319 + 0.00225771i
151151 10.6488 + 7.73680i 0.866586 + 0.629612i 0.929669 0.368396i 0.120093π-0.120093\pi
−0.0630824 + 0.998008i 0.520093π0.520093\pi
152152 0.455092 + 6.41603i 0.0369128 + 0.520409i
153153 15.5286i 1.25541i
154154 0 0
155155 2.89949 0.232893
156156 0.881183 0.706082i 0.0705511 0.0565318i
157157 −0.266819 + 0.367244i −0.0212945 + 0.0293093i −0.819531 0.573034i 0.805766π-0.805766\pi
0.798237 + 0.602343i 0.205766π0.205766\pi
158158 13.1590 0.310661i 1.04687 0.0247149i
159159 2.94798 + 0.957857i 0.233790 + 0.0759630i
160160 −14.6797 2.91676i −1.16053 0.230590i
161161 −12.3545 17.0045i −0.973673 1.34015i
162162 3.50789 + 9.98767i 0.275606 + 0.784706i
163163 −3.96420 12.2006i −0.310500 0.955622i −0.977567 0.210624i 0.932451π-0.932451\pi
0.667067 0.744998i 0.267549π-0.267549\pi
164164 18.7801 7.09822i 1.46648 0.554278i
165165 0 0
166166 3.65685 5.29150i 0.283827 0.410700i
167167 6.76915 + 20.8333i 0.523813 + 1.61213i 0.766652 + 0.642063i 0.221921π0.221921\pi
−0.242840 + 0.970066i 0.578079π0.578079\pi
168168 −2.95081 + 2.48105i −0.227660 + 0.191417i
169169 9.01418 6.54918i 0.693398 0.503783i
170170 −16.3295 + 12.4634i −1.25242 + 0.955899i
171171 −6.11734 1.98764i −0.467805 0.151999i
172172 7.06189 10.7527i 0.538464 0.819884i
173173 −4.41087 3.20469i −0.335353 0.243648i 0.407346 0.913274i 0.366454π-0.366454\pi
−0.742698 + 0.669626i 0.766454π0.766454\pi
174174 −1.10447 + 3.69365i −0.0837295 + 0.280015i
175175 −6.58132 −0.497501
176176 0 0
177177 1.34315 0.100957
178178 −4.31762 + 14.4394i −0.323620 + 1.08228i
179179 −7.87005 5.71793i −0.588235 0.427378i 0.253448 0.967349i 0.418435π-0.418435\pi
−0.841684 + 0.539971i 0.818435π0.818435\pi
180180 8.21597 12.5099i 0.612382 0.932434i
181181 2.51626 + 0.817582i 0.187032 + 0.0607704i 0.401036 0.916063i 0.368650π-0.368650\pi
−0.214003 + 0.976833i 0.568650π0.568650\pi
182182 5.04229 3.84849i 0.373759 0.285269i
183183 −2.20544 + 1.60234i −0.163031 + 0.118449i
184184 −11.6266 13.8280i −0.857126 1.01941i
185185 −3.95511 12.1726i −0.290785 0.894945i
186186 0.364976 0.528123i 0.0267613 0.0387239i
187187 0 0
188188 0 0
189189 −2.45494 7.55553i −0.178571 0.549584i
190190 2.81967 + 8.02817i 0.204560 + 0.582425i
191191 −9.97496 13.7294i −0.721763 0.993421i −0.999463 0.0327535i 0.989572π-0.989572\pi
0.277701 0.960668i 0.410428π-0.410428\pi
192192 −2.37908 + 2.30665i −0.171695 + 0.166468i
193193 −12.2347 3.97529i −0.880672 0.286148i −0.166435 0.986052i 0.553226π-0.553226\pi
−0.714236 + 0.699905i 0.753226π0.753226\pi
194194 10.5828 0.249843i 0.759803 0.0179377i
195195 0.878009 1.20848i 0.0628755 0.0865408i
196196 −5.97524 + 4.78789i −0.426803 + 0.341992i
197197 10.4366 0.743574 0.371787 0.928318i 0.378745π-0.378745\pi
0.371787 + 0.928318i 0.378745π0.378745\pi
198198 0 0
199199 21.1660i 1.50042i 0.661200 + 0.750209i 0.270047π0.270047\pi
−0.661200 + 0.750209i 0.729953π0.729953\pi
200200 −5.64268 + 0.400237i −0.398998 + 0.0283010i
201201 2.03445 + 1.47811i 0.143499 + 0.104258i
202202 −24.3908 + 0.575827i −1.71613 + 0.0405150i
203203 −6.69234 + 20.5969i −0.469710 + 1.44562i
204204 0.214632 + 4.54315i 0.0150272 + 0.318084i
205205 21.4868 15.6111i 1.50070 1.09032i
206206 24.1060 8.46657i 1.67955 0.589894i
207207 17.1821 5.58280i 1.19424 0.388031i
208208 4.08910 3.60625i 0.283528 0.250049i
209209 0 0
210210 −2.89949 + 4.19560i −0.200084 + 0.289524i
211211 −8.65123 + 2.81095i −0.595575 + 0.193514i −0.591266 0.806477i 0.701372π-0.701372\pi
−0.00430905 + 0.999991i 0.501372π0.501372\pi
212212 14.4365 + 3.94808i 0.991503 + 0.271155i
213213 1.55513 + 2.14046i 0.106556 + 0.146662i
214214 −7.47020 9.78745i −0.510652 0.669056i
215215 5.25881 16.1850i 0.358648 1.10381i
216216 −2.56430 6.32865i −0.174478 0.430610i
217217 2.11970 2.91752i 0.143895 0.198054i
218218 1.10447 3.69365i 0.0748040 0.250166i
219219 0.390175i 0.0263656i
220220 0 0
221221 7.48331i 0.503382i
222222 −2.71500 0.811833i −0.182219 0.0544867i
223223 −2.46611 + 3.39431i −0.165143 + 0.227300i −0.883566 0.468307i 0.844864π-0.844864\pi
0.718423 + 0.695606i 0.244864π0.244864\pi
224224 −13.6666 + 12.6386i −0.913138 + 0.844451i
225225 1.74806 5.37999i 0.116538 0.358666i
226226 −6.93799 + 5.29537i −0.461508 + 0.352243i
227227 7.79079 + 10.7231i 0.517093 + 0.711717i 0.985095 0.172010i 0.0550262π-0.0550262\pi
−0.468002 + 0.883727i 0.655026π0.655026\pi
228228 1.81720 + 0.496967i 0.120347 + 0.0329124i
229229 9.63331 3.13005i 0.636587 0.206840i 0.0270964 0.999633i 0.491374π-0.491374\pi
0.609491 + 0.792793i 0.291374π0.291374\pi
230230 −19.6613 13.5875i −1.29643 0.895934i
231231 0 0
232232 −4.48528 + 18.0663i −0.294473 + 1.18611i
233233 −7.90907 + 2.56981i −0.518140 + 0.168354i −0.556401 0.830914i 0.687818π-0.687818\pi
0.0382609 + 0.999268i 0.487818π0.487818\pi
234234 1.80672 + 5.14408i 0.118109 + 0.336279i
235235 0 0
236236 6.47806 0.306043i 0.421686 0.0199217i
237237 1.19134 3.66656i 0.0773856 0.238168i
238238 0.603016 + 25.5425i 0.0390877 + 1.65568i
239239 4.41087 + 3.20469i 0.285316 + 0.207294i 0.721233 0.692693i 0.243576π-0.243576\pi
−0.435917 + 0.899987i 0.643576π0.643576\pi
240240 −2.23081 + 3.77354i −0.143998 + 0.243581i
241241 4.54822i 0.292977i −0.989212 0.146488i 0.953203π-0.953203\pi
0.989212 0.146488i 0.0467971π-0.0467971\pi
242242 0 0
243243 10.3431 0.663513
244244 −10.2718 + 8.23070i −0.657586 + 0.526917i
245245 −5.95372 + 8.19459i −0.380369 + 0.523533i
246246 −0.138787 5.87872i −0.00884872 0.374814i
247247 −2.94798 0.957857i −0.187576 0.0609470i
248248 1.63996 2.63033i 0.104138 0.167026i
249249 −1.10735 1.52413i −0.0701754 0.0965881i
250250 10.5907 3.71970i 0.669817 0.235255i
251251 5.69030 + 17.5130i 0.359169 + 1.10541i 0.953553 + 0.301227i 0.0973960π0.0973960\pi
−0.594384 + 0.804182i 0.702604π0.702604\pi
252252 −6.58132 17.4125i −0.414584 1.09689i
253253 0 0
254254 −0.656854 0.453939i −0.0412147 0.0284827i
255255 1.85927 + 5.72225i 0.116432 + 0.358341i
256256 −10.9488 + 11.6672i −0.684302 + 0.729199i
257257 −5.24670 + 3.81195i −0.327280 + 0.237783i −0.739276 0.673403i 0.764832π-0.764832\pi
0.411995 + 0.911186i 0.364832π0.364832\pi
258258 −2.28602 2.99515i −0.142322 0.186470i
259259 −15.1396 4.91917i −0.940732 0.305662i
260260 3.95932 6.02860i 0.245547 0.373878i
261261 −15.0597 10.9415i −0.932170 0.677261i
262262 −9.24382 2.76407i −0.571085 0.170765i
263263 −19.1794 −1.18265 −0.591325 0.806433i 0.701395π-0.701395\pi
−0.591325 + 0.806433i 0.701395π0.701395\pi
264264 0 0
265265 19.7990 1.21624
266266 10.1394 + 3.03187i 0.621688 + 0.185896i
267267 3.57117 + 2.59461i 0.218552 + 0.158788i
268268 10.1490 + 6.66546i 0.619952 + 0.407158i
269269 −13.0130 4.22819i −0.793418 0.257797i −0.115859 0.993266i 0.536962π-0.536962\pi
−0.677559 + 0.735469i 0.736962π0.736962\pi
270270 −5.48056 7.18063i −0.333536 0.436999i
271271 −10.1920 + 7.40494i −0.619122 + 0.449818i −0.852615 0.522540i 0.824984π-0.824984\pi
0.233493 + 0.972359i 0.424984π0.424984\pi
272272 2.07036 + 21.8629i 0.125534 + 1.32563i
273273 −0.574112 1.76693i −0.0347468 0.106940i
274274 10.0716 + 6.96028i 0.608447 + 0.420486i
275275 0 0
276276 −4.94975 + 1.87083i −0.297940 + 0.112611i
277277 −1.19134 3.66656i −0.0715805 0.220302i 0.908866 0.417088i 0.136949π-0.136949\pi
−0.980446 + 0.196786i 0.936949π0.936949\pi
278278 26.2680 9.22591i 1.57545 0.553334i
279279 1.82195 + 2.50770i 0.109077 + 0.150132i
280280 −13.0284 + 20.8962i −0.778597 + 1.24879i
281281 −6.11734 1.98764i −0.364930 0.118573i 0.120812 0.992675i 0.461450π-0.461450\pi
−0.485741 + 0.874103i 0.661450π0.661450\pi
282282 0 0
283283 1.10735 1.52413i 0.0658250 0.0906004i −0.774835 0.632163i 0.782167π-0.782167\pi
0.840660 + 0.541563i 0.182167π0.182167\pi
284284 7.98820 + 9.96919i 0.474012 + 0.591562i
285285 2.49221 0.147626
286286 0 0
287287 33.0329i 1.94987i
288288 −6.70161 14.5289i −0.394896 0.856123i
289289 10.6322 + 7.72475i 0.625424 + 0.454397i
290290 0.581193 + 24.6182i 0.0341289 + 1.44563i
291291 0.958109 2.94876i 0.0561653 0.172859i
292292 0.0889034 + 1.88183i 0.00520268 + 0.110126i
293293 −11.7515 + 8.53797i −0.686531 + 0.498794i −0.875518 0.483186i 0.839480π-0.839480\pi
0.188987 + 0.981980i 0.439480π0.439480\pi
294294 0.743161 + 2.11593i 0.0433420 + 0.123403i
295295 8.15932 2.65113i 0.475054 0.154354i
296296 −13.2796 3.29688i −0.771859 0.191627i
297297 0 0
298298 24.5563 + 16.9704i 1.42251 + 0.983070i
299299 8.28015 2.69038i 0.478853 0.155589i
300300 −0.437065 + 1.59817i −0.0252340 + 0.0922703i
301301 −12.4411 17.1237i −0.717091 0.986991i
302302 14.7972 11.2939i 0.851485 0.649889i
303303 −2.20821 + 6.79616i −0.126858 + 0.390429i
304304 8.87770 + 1.98284i 0.509171 + 0.113723i
305305 −10.2348 + 14.0870i −0.586044 + 0.806621i
306306 −21.0403 6.29141i −1.20279 0.359656i
307307 22.3509i 1.27563i 0.770188 + 0.637817i 0.220162π0.220162\pi
−0.770188 + 0.637817i 0.779838π0.779838\pi
308308 0 0
309309 7.48331i 0.425711i
310310 1.17473 3.92863i 0.0667202 0.223131i
311311 −8.79716 + 12.1083i −0.498841 + 0.686596i −0.981988 0.188943i 0.939494π-0.939494\pi
0.483147 + 0.875539i 0.339494π0.339494\pi
312312 −0.599686 1.48002i −0.0339505 0.0837895i
313313 2.41912 7.44528i 0.136737 0.420832i −0.859120 0.511775i 0.828988π-0.828988\pi
0.995856 + 0.0909431i 0.0289881π0.0289881\pi
314314 0.389491 + 0.510312i 0.0219803 + 0.0287986i
315315 −14.4742 19.9221i −0.815530 1.12248i
316316 4.91043 17.9554i 0.276233 1.01007i
317317 −14.6658 + 4.76522i −0.823715 + 0.267641i −0.690396 0.723432i 0.742564π-0.742564\pi
−0.133319 + 0.991073i 0.542564π0.542564\pi
318318 2.49221 3.60625i 0.139756 0.202229i
319319 0 0
320320 −9.89949 + 18.7083i −0.553399 + 1.04583i
321321 −3.42975 + 1.11439i −0.191430 + 0.0621994i
322322 −28.0455 + 9.85021i −1.56292 + 0.548931i
323323 10.1008 7.33866i 0.562024 0.408334i
324324 14.9539 0.706466i 0.830771 0.0392481i
325325 0.842402 2.59265i 0.0467281 0.143814i
326326 −18.1371 + 0.428186i −1.00452 + 0.0237150i
327327 −0.913522 0.663713i −0.0505179 0.0367034i
328328 −2.00887 28.3217i −0.110921 1.56381i
329329 0 0
330330 0 0
331331 −18.0711 −0.993276 −0.496638 0.867958i 0.665432π-0.665432\pi
−0.496638 + 0.867958i 0.665432π0.665432\pi
332332 −5.68808 7.09866i −0.312174 0.389589i
333333 8.04249 11.0695i 0.440726 0.606607i
334334 30.9703 0.731157i 1.69462 0.0400071i
335335 15.2764 + 4.96360i 0.834638 + 0.271190i
336336 2.16615 + 5.00336i 0.118173 + 0.272956i
337337 11.2472 + 15.4804i 0.612673 + 0.843272i 0.996794 0.0800109i 0.0254955π-0.0254955\pi
−0.384121 + 0.923283i 0.625496π0.625496\pi
338338 −5.22163 14.8670i −0.284019 0.808660i
339339 0.789955 + 2.43123i 0.0429045 + 0.132046i
340340 10.2712 + 27.1750i 0.557034 + 1.47377i
341341 0 0
342342 −5.17157 + 7.48331i −0.279647 + 0.404651i
343343 −3.22507 9.92576i −0.174138 0.535941i
344344 −11.7081 13.9249i −0.631257 0.750778i
345345 −5.66312 + 4.11450i −0.304892 + 0.221517i
346346 −6.12921 + 4.67808i −0.329509 + 0.251495i
347347 3.95453 + 1.28491i 0.212291 + 0.0689774i 0.413232 0.910626i 0.364400π-0.364400\pi
−0.200941 + 0.979603i 0.564400π0.564400\pi
348348 4.55719 + 2.99297i 0.244291 + 0.160440i
349349 11.7515 + 8.53797i 0.629044 + 0.457027i 0.856069 0.516862i 0.172900π-0.172900\pi
−0.227025 + 0.973889i 0.572900π0.572900\pi
350350 −2.66642 + 8.91727i −0.142526 + 0.476648i
351351 3.29066 0.175642
352352 0 0
353353 1.82843 0.0973174 0.0486587 0.998815i 0.484505π-0.484505\pi
0.0486587 + 0.998815i 0.484505π0.484505\pi
354354 0.544176 1.81988i 0.0289226 0.0967254i
355355 13.6720 + 9.93327i 0.725633 + 0.527203i
356356 17.8151 + 11.7002i 0.944200 + 0.620110i
357357 7.11706 + 2.31247i 0.376675 + 0.122389i
358358 −10.9360 + 8.34681i −0.577985 + 0.441142i
359359 2.66220 1.93420i 0.140505 0.102083i −0.515312 0.857003i 0.672324π-0.672324\pi
0.655818 + 0.754919i 0.272324π0.272324\pi
360360 −13.6214 16.2005i −0.717913 0.853842i
361361 4.27322 + 13.1516i 0.224906 + 0.692190i
362362 2.12723 3.07813i 0.111805 0.161783i
363363 0 0
364364 −3.17157 8.39119i −0.166236 0.439818i
365365 0.770135 + 2.37023i 0.0403107 + 0.124064i
366366 1.27754 + 3.63742i 0.0667782 + 0.190131i
367367 −13.0852 18.0103i −0.683043 0.940128i 0.316922 0.948452i 0.397351π-0.397351\pi
−0.999965 + 0.00832319i 0.997351π0.997351\pi
368368 −23.4466 + 10.1509i −1.22224 + 0.529153i
369369 27.0032 + 8.77389i 1.40573 + 0.456750i
370370 −18.0955 + 0.427203i −0.940738 + 0.0222092i
371371 14.4742 19.9221i 0.751464 1.03430i
372372 −0.567704 0.708488i −0.0294341 0.0367334i
373373 0.233860 0.0121088 0.00605440 0.999982i 0.498073π-0.498073\pi
0.00605440 + 0.999982i 0.498073π0.498073\pi
374374 0 0
375375 3.28772i 0.169777i
376376 0 0
377377 −7.25734 5.27276i −0.373772 0.271561i
378378 −11.2319 + 0.265166i −0.577705 + 0.0136387i
379379 −4.96623 + 15.2845i −0.255098 + 0.785112i 0.738712 + 0.674021i 0.235434π0.235434\pi
−0.993810 + 0.111091i 0.964566π0.964566\pi
380380 12.0200 0.567863i 0.616615 0.0291307i
381381 −0.189197 + 0.137459i −0.00969283 + 0.00704226i
382382 −22.6438 + 7.95299i −1.15856 + 0.406910i
383383 6.93823 2.25437i 0.354527 0.115193i −0.126338 0.991987i 0.540323π-0.540323\pi
0.480865 + 0.876794i 0.340323π0.340323\pi
384384 2.16148 + 4.15804i 0.110303 + 0.212189i
385385 0 0
386386 −10.3431 + 14.9666i −0.526452 + 0.761781i
387387 17.3025 5.62191i 0.879533 0.285778i
388388 3.94912 14.4403i 0.200486 0.733095i
389389 −19.1495 26.3570i −0.970916 1.33635i −0.941583 0.336782i 0.890661π-0.890661\pi
−0.0293336 0.999570i 0.509339π-0.509339\pi
390390 −1.28168 1.67926i −0.0649005 0.0850327i
391391 −10.8366 + 33.3517i −0.548032 + 1.68667i
392392 4.06642 + 10.0359i 0.205385 + 0.506889i
393393 −1.66102 + 2.28620i −0.0837875 + 0.115324i
394394 4.22837 14.1409i 0.213022 0.712407i
395395 24.6250i 1.23902i
396396 0 0
397397 22.4499i 1.12673i −0.826208 0.563365i 0.809506π-0.809506\pi
0.826208 0.563365i 0.190494π-0.190494\pi
398398 28.6786 + 8.57541i 1.43753 + 0.429846i
399399 1.82195 2.50770i 0.0912117 0.125542i
400400 −1.74383 + 7.80763i −0.0871917 + 0.390381i
401401 −1.49207 + 4.59211i −0.0745102 + 0.229319i −0.981375 0.192104i 0.938469π-0.938469\pi
0.906864 + 0.421422i 0.138469π0.138469\pi
402402 2.82701 2.15769i 0.140998 0.107616i
403403 0.878009 + 1.20848i 0.0437367 + 0.0601985i
404404 −9.10174 + 33.2813i −0.452829 + 1.65581i
405405 18.8349 6.11983i 0.935914 0.304097i
406406 25.1961 + 17.4125i 1.25046 + 0.864169i
407407 0 0
408408 6.24264 + 1.54985i 0.309057 + 0.0767288i
409409 1.79173 0.582168i 0.0885952 0.0287863i −0.264384 0.964417i 0.585169π-0.585169\pi
0.352979 + 0.935631i 0.385169π0.385169\pi
410410 −12.4466 35.4380i −0.614695 1.75016i
411411 2.90096 2.10767i 0.143094 0.103964i
412412 −1.70511 36.0924i −0.0840048 1.77814i
413413 3.29734 10.1482i 0.162252 0.499359i
414414 −0.603016 25.5425i −0.0296366 1.25535i
415415 −9.73527 7.07309i −0.477886 0.347204i
416416 −3.22954 7.00155i −0.158341 0.343279i
417417 8.15447i 0.399326i
418418 0 0
419419 16.1421 0.788595 0.394297 0.918983i 0.370988π-0.370988\pi
0.394297 + 0.918983i 0.370988π0.370988\pi
420420 4.51004 + 5.62848i 0.220067 + 0.274642i
421421 4.39858 6.05413i 0.214374 0.295060i −0.688265 0.725460i 0.741627π-0.741627\pi
0.902639 + 0.430399i 0.141627π0.141627\pi
422422 0.303620 + 12.8607i 0.0147800 + 0.626050i
423423 0 0
424424 11.1983 17.9610i 0.543840 0.872263i
425425 6.45410 + 8.88331i 0.313070 + 0.430904i
426426 3.53025 1.23990i 0.171041 0.0600734i
427427 6.69234 + 20.5969i 0.323865 + 0.996753i
428428 −16.2879 + 6.15626i −0.787307 + 0.297574i
429429 0 0
430430 −19.7990 13.6827i −0.954792 0.659838i
431431 −0.667935 2.05569i −0.0321733 0.0990192i 0.933680 0.358108i 0.116578π-0.116578\pi
−0.965854 + 0.259088i 0.916578π0.916578\pi
432432 −9.61384 + 0.910405i −0.462546 + 0.0438019i
433433 14.0309 10.1940i 0.674282 0.489895i −0.197174 0.980369i 0.563176π-0.563176\pi
0.871456 + 0.490474i 0.163176π0.163176\pi
434434 −3.09426 4.05409i −0.148529 0.194603i
435435 6.85950 + 2.22879i 0.328888 + 0.106862i
436436 −4.55719 2.99297i −0.218250 0.143337i
437437 11.7515 + 8.53797i 0.562151 + 0.408427i
438438 0.528663 + 0.158080i 0.0252605 + 0.00755334i
439439 34.5035 1.64676 0.823380 0.567490i 0.192085π-0.192085\pi
0.823380 + 0.567490i 0.192085π0.192085\pi
440440 0 0
441441 −10.8284 −0.515639
442442 −10.1394 3.03187i −0.482283 0.144211i
443443 −21.3695 15.5259i −1.01530 0.737657i −0.0499842 0.998750i 0.515917π-0.515917\pi
−0.965314 + 0.261093i 0.915917π0.915917\pi
444444 −2.19997 + 3.34974i −0.104406 + 0.158972i
445445 26.8154 + 8.71285i 1.27117 + 0.413029i
446446 3.59993 + 4.71663i 0.170462 + 0.223339i
447447 7.07307 5.13889i 0.334545 0.243061i
448448 11.5875 + 23.6379i 0.547456 + 1.11679i
449449 4.93518 + 15.1889i 0.232905 + 0.716809i 0.997392 + 0.0721698i 0.0229923π0.0229923\pi
−0.764487 + 0.644639i 0.777008π0.777008\pi
450450 −6.58132 4.54822i −0.310246 0.214405i
451451 0 0
452452 4.36396 + 11.5460i 0.205263 + 0.543076i
453453 −1.68480 5.18529i −0.0791590 0.243626i
454454 17.6856 6.21156i 0.830024 0.291523i
455455 −6.97521 9.60056i −0.327003 0.450081i
456456 1.40960 2.26085i 0.0660105 0.105874i
457457 21.6281 + 7.02738i 1.01172 + 0.328727i 0.767539 0.641003i 0.221481π-0.221481\pi
0.244180 + 0.969730i 0.421481π0.421481\pi
458458 −0.338087 14.3207i −0.0157978 0.669161i
459459 −7.79079 + 10.7231i −0.363643 + 0.500511i
460460 −26.3760 + 21.1348i −1.22979 + 0.985414i
461461 −3.85525 −0.179557 −0.0897783 0.995962i 0.528616π-0.528616\pi
−0.0897783 + 0.995962i 0.528616π0.528616\pi
462462 0 0
463463 22.2619i 1.03460i −0.855804 0.517300i 0.826937π-0.826937\pi
0.855804 0.517300i 0.173063π-0.173063\pi
464464 22.6615 + 13.3968i 1.05203 + 0.621933i
465465 −0.971638 0.705936i −0.0450586 0.0327370i
466466 0.277573 + 11.7574i 0.0128583 + 0.544653i
467467 11.1466 34.3056i 0.515802 1.58747i −0.266016 0.963969i 0.585708π-0.585708\pi
0.781818 0.623506i 0.214292π-0.214292\pi
468468 7.70190 0.363861i 0.356020 0.0168195i
469469 16.1624 11.7427i 0.746310 0.542226i
470470 0 0
471471 0.178825 0.0581038i 0.00823982 0.00267728i
472472 2.20992 8.90135i 0.101720 0.409718i
473473 0 0
474474 −4.48528 3.09969i −0.206016 0.142373i
475475 4.32561 1.40548i 0.198473 0.0644877i
476476 34.8528 + 9.53150i 1.59748 + 0.436876i
477477 12.4411 + 17.1237i 0.569637 + 0.784039i
478478 6.12921 4.67808i 0.280344 0.213970i
479479 8.45395 26.0186i 0.386271 1.18882i −0.549283 0.835636i 0.685099π-0.685099\pi
0.935554 0.353184i 0.114901π-0.114901\pi
480480 4.20910 + 4.55146i 0.192118 + 0.207745i
481481 3.87572 5.33447i 0.176718 0.243231i
482482 −6.16255 1.84271i −0.280696 0.0839332i
483483 8.70626i 0.396149i
484484 0 0
485485 19.8042i 0.899262i
486486 4.19053 14.0143i 0.190086 0.635702i
487487 15.6619 21.5567i 0.709706 0.976827i −0.290097 0.956997i 0.593688π-0.593688\pi
0.999803 0.0198298i 0.00631245π-0.00631245\pi
488488 6.99045 + 17.2523i 0.316443 + 0.780977i
489489 −1.64203 + 5.05364i −0.0742550 + 0.228533i
490490 8.69100 + 11.3869i 0.392619 + 0.514410i
491491 −15.1229 20.8149i −0.682487 0.939362i 0.317474 0.948267i 0.397166π-0.397166\pi
−0.999960 + 0.00890465i 0.997166π0.997166\pi
492492 −8.02153 2.19372i −0.361638 0.0989004i
493493 34.3642 11.1656i 1.54768 0.502873i
494494 −2.49221 + 3.60625i −0.112130 + 0.162253i
495495 0 0
496496 −2.89949 3.28772i −0.130191 0.147623i
497497 19.9900 6.49516i 0.896676 0.291348i
498498 −2.51375 + 0.882884i −0.112644 + 0.0395630i
499499 −14.9549 + 10.8654i −0.669474 + 0.486401i −0.869849 0.493318i 0.835784π-0.835784\pi
0.200375 + 0.979719i 0.435784π0.435784\pi
500500 −0.749123 15.8568i −0.0335018 0.709139i
501501 2.80387 8.62944i 0.125268 0.385535i
502502 26.0344 0.614628i 1.16197 0.0274322i
503503 −3.11896 2.26606i −0.139068 0.101038i 0.516076 0.856543i 0.327392π-0.327392\pi
−0.655144 + 0.755504i 0.727392π0.727392\pi
504504 −26.2593 + 1.86258i −1.16968 + 0.0829660i
505505 45.6438i 2.03112i
506506 0 0
507507 −4.61522 −0.204969
508508 −0.881183 + 0.706082i −0.0390962 + 0.0313273i
509509 −20.9714 + 28.8647i −0.929542 + 1.27940i 0.0304965 + 0.999535i 0.490291π0.490291\pi
−0.960038 + 0.279869i 0.909709π0.909709\pi
510510 8.50657 0.200826i 0.376677 0.00889271i
511511 2.94798 + 0.957857i 0.130411 + 0.0423731i
512512 11.3724 + 19.5619i 0.502592 + 0.864524i
513513 3.22705 + 4.44165i 0.142478 + 0.196104i
514514 3.03925 + 8.65336i 0.134056 + 0.381683i
515515 −14.7707 45.4595i −0.650875 2.00319i
516516 −4.98442 + 1.88393i −0.219427 + 0.0829356i
517517 0 0
518518 −12.7990 + 18.5203i −0.562355 + 0.813733i
519519 0.697869 + 2.14782i 0.0306330 + 0.0942788i
520520 −6.56425 7.80712i −0.287861 0.342365i
521521 16.2715 11.8219i 0.712868 0.517929i −0.171230 0.985231i 0.554774π-0.554774\pi
0.884098 + 0.467302i 0.154774π0.154774\pi
522522 −20.9264 + 15.9719i −0.915926 + 0.699073i
523523 16.1892 + 5.26019i 0.707905 + 0.230012i 0.640771 0.767732i 0.278615π-0.278615\pi
0.0671335 + 0.997744i 0.478615π0.478615\pi
524524 −7.49027 + 11.4049i −0.327214 + 0.498227i
525525 2.20544 + 1.60234i 0.0962532 + 0.0699320i
526526 −7.77052 + 25.9868i −0.338811 + 1.13308i
527527 −6.01673 −0.262093
528528 0 0
529529 −17.7990 −0.773869
530530 8.02156 26.8264i 0.348434 1.16526i
531531 7.41996 + 5.39092i 0.321999 + 0.233946i
532532 8.21597 12.5099i 0.356208 0.542373i
533533 13.0130 + 4.22819i 0.563656 + 0.183143i
534534 4.96239 3.78751i 0.214744 0.163902i
535535 −18.6354 + 13.5394i −0.805678 + 0.585359i
536536 13.1432 11.0508i 0.567698 0.477322i
537537 1.24516 + 3.83222i 0.0537328 + 0.165373i
538538 −11.0011 + 15.9188i −0.474293 + 0.686307i
539539 0 0
540540 −11.9497 + 4.51658i −0.514235 + 0.194363i
541541 5.33108 + 16.4074i 0.229201 + 0.705408i 0.997838 + 0.0657228i 0.0209353π0.0209353\pi
−0.768637 + 0.639685i 0.779065π0.779065\pi
542542 5.90393 + 16.8097i 0.253595 + 0.722037i
543543 −0.644157 0.886607i −0.0276434 0.0380479i
544544 30.4617 + 6.05256i 1.30603 + 0.259501i
545545 −6.85950 2.22879i −0.293829 0.0954707i
546546 −2.62669 + 0.0620116i −0.112412 + 0.00265385i
547547 −24.2504 + 33.3778i −1.03687 + 1.42713i −0.137210 + 0.990542i 0.543813π0.543813\pi
−0.899661 + 0.436589i 0.856187π0.856187\pi
548548 13.5112 10.8264i 0.577171 0.462481i
549549 −18.6148 −0.794459
550550 0 0
551551 14.9666i 0.637600i
552552 0.529464 + 7.46456i 0.0225355 + 0.317713i
553553 −24.7781 18.0023i −1.05367 0.765538i
554554 −5.45062 + 0.128680i −0.231575 + 0.00546709i
555555 −1.63826 + 5.04204i −0.0695402 + 0.214023i
556556 −1.85804 39.3294i −0.0787983 1.66794i
557557 −19.2813 + 14.0087i −0.816977 + 0.593568i −0.915845 0.401532i 0.868478π-0.868478\pi
0.0988682 + 0.995101i 0.468478π0.468478\pi
558558 4.13594 1.45263i 0.175088 0.0614949i
559559 8.33815 2.70923i 0.352666 0.114588i
560560 23.0346 + 26.1188i 0.973390 + 1.10372i
561561 0 0
562562 −5.17157 + 7.48331i −0.218150 + 0.315665i
563563 −11.1851 + 3.63426i −0.471396 + 0.153166i −0.535075 0.844805i 0.679717π-0.679717\pi
0.0636788 + 0.997970i 0.479717π0.479717\pi
564564 0 0
565565 9.59762 + 13.2100i 0.403775 + 0.555749i
566566 −1.61646 2.11789i −0.0679450 0.0890216i
567567 7.61155 23.4259i 0.319655 0.983797i
568568 16.7440 6.78449i 0.702564 0.284671i
569569 −1.56603 + 2.15545i −0.0656513 + 0.0903612i −0.840580 0.541687i 0.817786π-0.817786\pi
0.774929 + 0.632049i 0.217786π0.217786\pi
570570 1.00972 3.37679i 0.0422925 0.141438i
571571 21.9607i 0.919028i 0.888170 + 0.459514i 0.151976π0.151976\pi
−0.888170 + 0.459514i 0.848024π0.848024\pi
572572 0 0
573573 7.02938i 0.293656i
574574 −44.7576 13.3833i −1.86814 0.558608i
575575 −7.50885 + 10.3350i −0.313141 + 0.431001i
576576 −22.4009 + 3.19387i −0.933370 + 0.133078i
577577 −9.77341 + 30.0795i −0.406872 + 1.25222i 0.512449 + 0.858717i 0.328738π0.328738\pi
−0.919322 + 0.393507i 0.871262π0.871262\pi
578578 14.7742 11.2763i 0.614525 0.469032i
579579 3.13205 + 4.31090i 0.130164 + 0.179155i
580580 33.5915 + 9.18657i 1.39481 + 0.381452i
581581 −14.2341 + 4.62494i −0.590530 + 0.191875i
582582 −3.60720 2.49287i −0.149523 0.103333i
583583 0 0
584584 2.58579 + 0.641967i 0.107001 + 0.0265648i
585585 9.70080 3.15198i 0.401079 0.130318i
586586 6.80729 + 19.3817i 0.281206 + 0.800651i
587587 24.5005 17.8006i 1.01124 0.734711i 0.0467739 0.998906i 0.485106π-0.485106\pi
0.964470 + 0.264194i 0.0851060π0.0851060\pi
588588 3.16804 0.149668i 0.130648 0.00617219i
589589 −0.770135 + 2.37023i −0.0317329 + 0.0976637i
590590 −0.286356 12.1295i −0.0117891 0.499362i
591591 −3.49735 2.54097i −0.143862 0.104522i
592592 −9.84728 + 16.6572i −0.404721 + 0.684608i
593593 1.88393i 0.0773639i −0.999252 0.0386819i 0.987684π-0.987684\pi
0.999252 0.0386819i 0.0123159π-0.0123159\pi
594594 0 0
595595 47.7990 1.95957
596596 32.9428 26.3967i 1.34939 1.08125i
597597 5.15326 7.09285i 0.210909 0.290291i
598598 −0.290597 12.3091i −0.0118834 0.503356i
599599 0 0 0.309017 0.951057i 0.400000π-0.400000\pi
−0.309017 + 0.951057i 0.600000π0.600000\pi
600600 1.98834 + 1.23969i 0.0811736 + 0.0506103i
601601 −19.2673 26.5192i −0.785930 1.08174i −0.994603 0.103754i 0.966915π-0.966915\pi
0.208673 0.977985i 0.433085π-0.433085\pi
602602 −28.2420 + 9.91921i −1.15106 + 0.404277i
603603 5.30631 + 16.3311i 0.216090 + 0.665055i
604604 −9.30739 24.6250i −0.378712 1.00198i
605605 0 0
606606 8.31371 + 5.74544i 0.337721 + 0.233393i
607607 −8.97735 27.6295i −0.364380 1.12145i −0.950369 0.311126i 0.899294π-0.899294\pi
0.585989 0.810319i 0.300706π-0.300706\pi
608608 6.28342 11.2254i 0.254826 0.455249i
609609 7.25734 5.27276i 0.294082 0.213663i
610610 14.9404 + 19.5749i 0.604919 + 0.792564i
611611 0 0
612612 −17.0489 + 25.9593i −0.689162 + 1.04934i
613613 21.6760 + 15.7485i 0.875484 + 0.636077i 0.932053 0.362322i 0.118016π-0.118016\pi
−0.0565685 + 0.998399i 0.518016π0.518016\pi
614614 30.2841 + 9.05547i 1.22217 + 0.365449i
615615 −11.0011 −0.443609
616616 0 0
617617 33.1127 1.33307 0.666534 0.745475i 0.267777π-0.267777\pi
0.666534 + 0.745475i 0.267777π0.267777\pi
618618 −10.1394 3.03187i −0.407867 0.121960i
619619 −25.5058 18.5311i −1.02516 0.744826i −0.0578297 0.998326i 0.518418π-0.518418\pi
−0.967335 + 0.253501i 0.918418π0.918418\pi
620620 −4.84711 3.18337i −0.194664 0.127847i
621621 −14.6658 4.76522i −0.588520 0.191222i
622622 12.8418 + 16.8253i 0.514907 + 0.674632i
623623 28.3707 20.6125i 1.13665 0.825822i
624624 −2.24829 + 0.212907i −0.0900037 + 0.00852311i
625625 −9.57953 29.4828i −0.383181 1.17931i
626626 −9.10777 6.29420i −0.364020 0.251567i
627627 0 0
628628 0.849242 0.320983i 0.0338885 0.0128086i
629629 8.20722 + 25.2592i 0.327243 + 1.00715i
630630 −32.8574 + 11.5402i −1.30907 + 0.459774i
631631 6.86469 + 9.44844i 0.273279 + 0.376136i 0.923493 0.383615i 0.125321π-0.125321\pi
−0.650214 + 0.759751i 0.725321π0.725321\pi
632632 −22.3390 13.9280i −0.888598 0.554025i
633633 3.58346 + 1.16434i 0.142430 + 0.0462782i
634634 0.514706 + 21.8019i 0.0204416 + 0.865864i
635635 −0.878009 + 1.20848i −0.0348427 + 0.0479569i
636636 −3.87652 4.83786i −0.153714 0.191834i
637637 −5.21828 −0.206756
638638 0 0
639639 18.0663i 0.714693i
640640 21.3378 + 20.9929i 0.843449 + 0.829815i
641641 14.4235 + 10.4793i 0.569694 + 0.413907i 0.834994 0.550259i 0.185471π-0.185471\pi
−0.265300 + 0.964166i 0.585471π0.585471\pi
642642 0.120369 + 5.09859i 0.00475059 + 0.201225i
643643 0.190115 0.585112i 0.00749739 0.0230746i −0.947238 0.320532i 0.896138π-0.896138\pi
0.954735 + 0.297457i 0.0961385π0.0961385\pi
644644 1.98377 + 41.9907i 0.0781713 + 1.65467i
645645 −5.70279 + 4.14332i −0.224547 + 0.163143i
646646 −5.85108 16.6592i −0.230208 0.655448i
647647 −22.3934 + 7.27607i −0.880377 + 0.286052i −0.714114 0.700030i 0.753170π-0.753170\pi
−0.166263 + 0.986081i 0.553170π0.553170\pi
648648 5.10135 20.5478i 0.200400 0.807193i
649649 0 0
650650 −3.17157 2.19181i −0.124399 0.0859699i
651651 −1.42065 + 0.461597i −0.0556796 + 0.0180914i
652652 −6.76807 + 24.7481i −0.265058 + 0.969210i
653653 −21.5051 29.5992i −0.841558 1.15830i −0.985660 0.168742i 0.946030π-0.946030\pi
0.144103 0.989563i 0.453970π-0.453970\pi
654654 −1.26940 + 0.968861i −0.0496375 + 0.0378855i
655655 −5.57781 + 17.1667i −0.217943 + 0.670760i
656656 −39.1881 8.75266i −1.53004 0.341734i
657657 −1.56603 + 2.15545i −0.0610965 + 0.0840922i
658658 0 0
659659 10.9804i 0.427735i −0.976863 0.213867i 0.931394π-0.931394\pi
0.976863 0.213867i 0.0686060π-0.0686060\pi
660660 0 0
661661 12.3209i 0.479227i 0.970868 + 0.239613i 0.0770207π0.0770207\pi
−0.970868 + 0.239613i 0.922979π0.922979\pi
662662 −7.32149 + 24.4852i −0.284558 + 0.951642i
663663 −1.82195 + 2.50770i −0.0707588 + 0.0973911i
664664 −11.9228 + 4.83096i −0.462693 + 0.187478i
665665 6.11822 18.8300i 0.237255 0.730194i
666666 −11.7401 15.3819i −0.454920 0.596036i
667667 24.7091 + 34.0091i 0.956738 + 1.31684i
668668 11.5570 42.2591i 0.447152 1.63505i
669669 1.65282 0.537032i 0.0639015 0.0207629i
670670 12.9146 18.6875i 0.498934 0.721962i
671671 0 0
672672 7.65685 0.907878i 0.295370 0.0350222i
673673 36.3966 11.8260i 1.40299 0.455858i 0.492831 0.870125i 0.335962π-0.335962\pi
0.910156 + 0.414267i 0.135962π0.135962\pi
674674 25.5318 8.96732i 0.983447 0.345408i
675675 −3.90628 + 2.83808i −0.150353 + 0.109238i
676676 −22.2594 + 1.05160i −0.856132 + 0.0404462i
677677 −0.770135 + 2.37023i −0.0295987 + 0.0910954i −0.964765 0.263115i 0.915250π-0.915250\pi
0.935166 + 0.354210i 0.115250π0.115250\pi
678678 3.61422 0.0853256i 0.138803 0.00327691i
679679 −19.9273 14.4780i −0.764740 0.555616i
680680 40.9818 2.90686i 1.57158 0.111473i
681681 5.49019i 0.210384i
682682 0 0
683683 −36.4264 −1.39382 −0.696909 0.717160i 0.745442π-0.745442\pi
−0.696909 + 0.717160i 0.745442π0.745442\pi
684684 8.04415 + 10.0390i 0.307576 + 0.383851i
685685 13.4626 18.5296i 0.514378 0.707981i
686686 −14.7554 + 0.348350i −0.563364 + 0.0133001i
687687 −3.99025 1.29651i −0.152238 0.0494650i
688688 −23.6108 + 10.2220i −0.900155 + 0.389711i
689689 5.99542 + 8.25199i 0.228407 + 0.314376i
690690 3.28047 + 9.34016i 0.124885 + 0.355574i
691691 −2.70617 8.32874i −0.102948 0.316840i 0.886296 0.463120i 0.153270π-0.153270\pi
−0.989243 + 0.146280i 0.953270π0.953270\pi
692692 3.85525 + 10.2000i 0.146554 + 0.387747i
693693 0 0
694694 3.34315 4.83756i 0.126904 0.183631i
695695 −16.0954 49.5367i −0.610535 1.87903i
696696 5.90163 4.96210i 0.223701 0.188088i
697697 −44.5871 + 32.3944i −1.68886 + 1.22703i
698698 16.3295 12.4634i 0.618082 0.471746i
699699 3.27604 + 1.06445i 0.123911 + 0.0402612i
700700 11.0020 + 7.22566i 0.415838 + 0.273104i
701701 −21.1084 15.3361i −0.797253 0.579238i 0.112854 0.993612i 0.464001π-0.464001\pi
−0.910107 + 0.414374i 0.864001π0.864001\pi
702702 1.33321 4.45863i 0.0503188 0.168280i
703703 11.0011 0.414916
704704 0 0
705705 0 0
706706 0.740787 2.47740i 0.0278799 0.0932383i
707707 45.9275 + 33.3683i 1.72728 + 1.25494i
708708 −2.24535 1.47465i −0.0843853 0.0554206i
709709 −43.9975 14.2957i −1.65236 0.536885i −0.673111 0.739542i 0.735042π-0.735042\pi
−0.979250 + 0.202657i 0.935042π0.935042\pi
710710 18.9982 14.5002i 0.712988 0.544183i
711711 21.2976 15.4736i 0.798722 0.580305i
712712 23.0709 19.3980i 0.864617 0.726972i
713713 −2.16312 6.65740i −0.0810094 0.249321i
714714 6.01673 8.70626i 0.225170 0.325824i
715715 0 0
716716 6.87868 + 18.1993i 0.257068 + 0.680139i
717717 −0.697869 2.14782i −0.0260624 0.0802118i
718718 −1.54213 4.39075i −0.0575517 0.163861i
719719 2.99975 + 4.12880i 0.111872 + 0.153978i 0.861281 0.508129i 0.169663π-0.169663\pi
−0.749410 + 0.662107i 0.769663π0.769663\pi
720720 −27.4694 + 11.8925i −1.02372 + 0.443209i
721721 −56.5404 18.3711i −2.10567 0.684175i
722722 19.5509 0.461564i 0.727609 0.0171776i
723723 −1.10735 + 1.52413i −0.0411827 + 0.0566832i
724724 −3.30882 4.12937i −0.122971 0.153467i
725725 13.1626 0.488848
726726 0 0
727727 8.57922i 0.318186i 0.987264 + 0.159093i 0.0508569π0.0508569\pi
−0.987264 + 0.159093i 0.949143π0.949143\pi
728728 −12.6545 + 0.897588i −0.469007 + 0.0332668i
729729 14.7011 + 10.6810i 0.544486 + 0.395592i
730730 3.52354 0.0831847i 0.130412 0.00307881i
731731 −10.9125 + 33.5853i −0.403615 + 1.24220i
732732 5.44607 0.257288i 0.201292 0.00950965i
733733 −22.2111 + 16.1373i −0.820386 + 0.596045i −0.916823 0.399294i 0.869255π-0.869255\pi
0.0964371 + 0.995339i 0.469255π0.469255\pi
734734 −29.7043 + 10.4328i −1.09640 + 0.385081i
735735 3.99025 1.29651i 0.147183 0.0478225i
736736 4.25447 + 35.8813i 0.156822 + 1.32260i
737737 0 0
738738 22.8284 33.0329i 0.840326 1.21596i
739739 −45.3553 + 14.7368i −1.66842 + 0.542103i −0.982611 0.185678i 0.940552π-0.940552\pi
−0.685810 + 0.727781i 0.740552π0.740552\pi
740740 −6.75254 + 24.6913i −0.248228 + 0.907670i
741741 0.754677 + 1.03872i 0.0277238 + 0.0381585i
742742 −21.1289 27.6831i −0.775666 1.01628i
743743 −7.78602 + 23.9629i −0.285641 + 0.879114i 0.700564 + 0.713589i 0.252932π0.252932\pi
−0.986206 + 0.165524i 0.947068π0.947068\pi
744744 −1.18996 + 0.482159i −0.0436261 + 0.0176768i
745745 32.8242 45.1786i 1.20258 1.65522i
746746 0.0947483 0.316865i 0.00346898 0.0116013i
747747 12.8643i 0.470680i
748748 0 0
749749 28.6493i 1.04682i
750750 −4.45465 1.33202i −0.162661 0.0486385i
751751 −4.28806 + 5.90201i −0.156474 + 0.215367i −0.880055 0.474871i 0.842495π-0.842495\pi
0.723582 + 0.690239i 0.242495π0.242495\pi
752752 0 0
753753 2.35700 7.25410i 0.0858939 0.264354i
754754 −10.0846 + 7.69697i −0.367258 + 0.280307i
755755 −20.4696 28.1741i −0.744967 1.02536i
756756 −4.19131 + 15.3259i −0.152437 + 0.557398i
757757 −27.2471 + 8.85313i −0.990314 + 0.321772i −0.758988 0.651104i 0.774306π-0.774306\pi
−0.231325 + 0.972876i 0.574306π0.574306\pi
758758 18.6975 + 12.9214i 0.679122 + 0.469328i
759759 0 0
760760 4.10051 16.5165i 0.148741 0.599116i
761761 7.01320 2.27873i 0.254228 0.0826038i −0.179130 0.983825i 0.557328π-0.557328\pi
0.433359 + 0.901222i 0.357328π0.357328\pi
762762 0.109596 + 0.312041i 0.00397023 + 0.0113041i
763763 −7.25734 + 5.27276i −0.262733 + 0.190887i
764764 1.60168 + 33.9030i 0.0579467 + 1.22657i
765765 −12.6959 + 39.0740i −0.459021 + 1.41272i
766766 −0.243501 10.3142i −0.00879806 0.372668i
767767 3.57572 + 2.59791i 0.129112 + 0.0938052i
768768 6.50961 1.24404i 0.234895 0.0448904i
769769 2.82590i 0.101905i 0.998701 + 0.0509523i 0.0162256π0.0162256\pi
−0.998701 + 0.0509523i 0.983774π0.983774\pi
770770 0 0
771771 2.68629 0.0967444
772772 16.0883 + 20.0780i 0.579031 + 0.722624i
773773 −5.15326 + 7.09285i −0.185350 + 0.255112i −0.891573 0.452877i 0.850398π-0.850398\pi
0.706223 + 0.707989i 0.250398π0.250398\pi
774774 −0.607240 25.7214i −0.0218268 0.924538i
775775 −2.08454 0.677307i −0.0748788 0.0243296i
776776 −17.9657 11.2013i −0.644931 0.402103i
777777 3.87572 + 5.33447i 0.139041 + 0.191373i
778778 −43.4704 + 15.2678i −1.55849 + 0.547376i
779779 7.05437 + 21.7111i 0.252749 + 0.777882i
780780 −2.79457 + 1.05625i −0.100062 + 0.0378197i
781781 0 0
782782 40.7990 + 28.1954i 1.45897 + 1.00826i
783783 4.90988 + 15.1111i 0.175465 + 0.540025i
784784 15.2455 1.44371i 0.544482 0.0515610i
785785 0.971638 0.705936i 0.0346792 0.0251959i
786786 2.42470 + 3.17684i 0.0864860 + 0.113314i
787787 31.3289 + 10.1794i 1.11675 + 0.362855i 0.808528 0.588458i 0.200265π-0.200265\pi
0.308226 + 0.951313i 0.400265π0.400265\pi
788788 −17.4469 11.4584i −0.621519 0.408187i
789789 6.42711 + 4.66957i 0.228811 + 0.166241i
790790 −33.3654 9.97683i −1.18709 0.354960i
791791 20.3085 0.722088
792792 0 0
793793 −8.97056 −0.318554
794794 −30.4183 9.09560i −1.07950 0.322791i
795795 −6.63476 4.82043i −0.235311 0.170963i
796796 23.2383 35.3834i 0.823659 1.25413i
797797 41.9130 + 13.6183i 1.48463 + 0.482387i 0.935493 0.353344i 0.114955π-0.114955\pi
0.549140 + 0.835731i 0.314955π0.314955\pi
798798 −2.65961 3.48463i −0.0941493 0.123354i
799799 0 0
800800 9.87233 + 5.52605i 0.349039 + 0.195375i
801801 9.31443 + 28.6669i 0.329109 + 1.01289i
802802 5.61750 + 3.88215i 0.198361 + 0.137083i
803803 0 0
804804 −1.77817 4.70461i −0.0627114 0.165919i
805805 17.1846 + 52.8887i 0.605677 + 1.86408i
806806 1.99313 0.700033i 0.0702051 0.0246576i
807807 3.33131 + 4.58515i 0.117268 + 0.161405i
808808 41.4065 + 25.8162i 1.45668 + 0.908211i
809809 0.895864 + 0.291084i 0.0314969 + 0.0102340i 0.324723 0.945809i 0.394729π-0.394729\pi
−0.293226 + 0.956043i 0.594729π0.594729\pi
810810 −0.661022 27.9996i −0.0232260 0.983804i
811811 −3.32205 + 4.57240i −0.116653 + 0.160559i −0.863350 0.504605i 0.831638π-0.831638\pi
0.746698 + 0.665164i 0.231638π0.231638\pi
812812 33.8011 27.0844i 1.18618 0.950477i
813813 5.21828 0.183013
814814 0 0
815815 33.9408i 1.18890i
816816 4.62915 7.83046i 0.162053 0.274121i
817817 11.8338 + 8.59778i 0.414013 + 0.300798i
818818 −0.0628817 2.66354i −0.00219861 0.0931286i
819819 3.92028 12.0654i 0.136986 0.421599i
820820 −53.0591 + 2.50667i −1.85290 + 0.0875366i
821821 −17.2651 + 12.5438i −0.602556 + 0.437783i −0.846785 0.531935i 0.821465π-0.821465\pi
0.244229 + 0.969718i 0.421465π0.421465\pi
822822 −1.68044 4.78454i −0.0586120 0.166880i
823823 34.1854 11.1075i 1.19163 0.387183i 0.354953 0.934884i 0.384497π-0.384497\pi
0.836674 + 0.547701i 0.184497π0.184497\pi
824824 −49.5937 12.3125i −1.72768 0.428927i
825825 0 0
826826 −12.4142 8.57922i −0.431946 0.298509i
827827 −48.2602 + 15.6807i −1.67817 + 0.545271i −0.984556 0.175072i 0.943984π-0.943984\pi
−0.693617 + 0.720344i 0.743984π0.743984\pi
828828 −34.8528 9.53150i −1.21122 0.331243i
829829 24.6153 + 33.8801i 0.854925 + 1.17670i 0.982756 + 0.184908i 0.0591986π0.0591986\pi
−0.127831 + 0.991796i 0.540801π0.540801\pi
830830 −13.5278 + 10.3250i −0.469558 + 0.358386i
831831 −0.493468 + 1.51874i −0.0171182 + 0.0526844i
832832 −10.7951 + 1.53915i −0.374253 + 0.0533603i
833833 12.3545 17.0045i 0.428059 0.589173i
834834 −11.0488 3.30378i −0.382588 0.114401i
835835 57.9563i 2.00566i
836836 0 0
837837 2.64575i 0.0914505i
838838 6.53999 21.8716i 0.225920 0.755541i
839839 −31.9679 + 44.0000i −1.10365 + 1.51905i −0.273203 + 0.961956i 0.588083π0.588083\pi
−0.830451 + 0.557092i 0.811917π0.811917\pi
840840 9.45347 3.83044i 0.326176 0.132163i
841841 4.42318 13.6131i 0.152523 0.469419i
842842 −6.42088 8.41263i −0.221278 0.289918i
843843 1.56603 + 2.15545i 0.0539368 + 0.0742377i
844844 17.5485 + 4.79914i 0.604043 + 0.165193i
845845 −28.0365 + 9.10961i −0.964485 + 0.313380i
846846 0 0
847847 0 0
848848 −19.7990 22.4499i −0.679900 0.770934i
849849 −0.742158 + 0.241142i −0.0254708 + 0.00827596i
850850 14.6512 5.14583i 0.502532 0.176500i
851851 −24.9982 + 18.1623i −0.856928 + 0.622595i
852852 −0.249708 5.28561i −0.00855485 0.181082i
853853 17.9547 55.2589i 0.614758 1.89203i 0.209579 0.977792i 0.432791π-0.432791\pi
0.405179 0.914237i 0.367209π-0.367209\pi
854854 30.6189 0.722860i 1.04776 0.0247358i
855855 13.7678 + 10.0029i 0.470847 + 0.342090i
856856 1.74229 + 24.5633i 0.0595501 + 0.839557i
857857 21.9607i 0.750165i −0.926992 0.375082i 0.877614π-0.877614\pi
0.926992 0.375082i 0.122386π-0.122386\pi
858858 0 0
859859 −49.2426 −1.68014 −0.840069 0.542480i 0.817485π-0.817485\pi
−0.840069 + 0.542480i 0.817485π0.817485\pi
860860 −26.5607 + 21.2828i −0.905714 + 0.725739i
861861 −8.04249 + 11.0695i −0.274087 + 0.377249i
862862 −3.05595 + 0.0721457i −0.104086 + 0.00245729i
863863 −14.2341 4.62494i −0.484535 0.157435i 0.0565554 0.998399i 0.481988π-0.481988\pi
−0.541090 + 0.840965i 0.681988π0.681988\pi
864864 −2.66151 + 13.3950i −0.0905463 + 0.455707i
865865 8.47881 + 11.6701i 0.288288 + 0.396794i
866866 −8.12767 23.1411i −0.276189 0.786367i
867867 −1.68218 5.17722i −0.0571298 0.175828i
868868 −6.74668 + 2.55000i −0.228997 + 0.0865528i
869869 0 0
870870 5.79899 8.39119i 0.196604 0.284488i
871871 2.55714 + 7.87007i 0.0866454 + 0.266667i
872872 −5.90163 + 4.96210i −0.199854 + 0.168038i
873873 17.1282 12.4443i 0.579700 0.421177i
874874 16.3295 12.4634i 0.552355 0.421581i
875875 −24.8404 8.07115i −0.839760 0.272855i
876876 0.428376 0.652259i 0.0144735 0.0220378i
877877 23.6922 + 17.2134i 0.800029 + 0.581255i 0.910923 0.412577i 0.135371π-0.135371\pi
−0.110893 + 0.993832i 0.535371π0.535371\pi
878878 13.9791 46.7500i 0.471771 1.57774i
879879 6.01673 0.202939
880880 0 0
881881 6.51472 0.219486 0.109743 0.993960i 0.464997π-0.464997\pi
0.109743 + 0.993960i 0.464997π0.464997\pi
882882 −4.38714 + 14.6718i −0.147723 + 0.494026i
883883 3.51368 + 2.55284i 0.118245 + 0.0859098i 0.645336 0.763899i 0.276717π-0.276717\pi
−0.527091 + 0.849809i 0.676717π0.676717\pi
884884 −8.21597 + 12.5099i −0.276333 + 0.420754i
885885 −3.37970 1.09813i −0.113607 0.0369133i
886886 −29.6945 + 22.6641i −0.997605 + 0.761414i
887887 37.6492 27.3537i 1.26414 0.918448i 0.265182 0.964198i 0.414568π-0.414568\pi
0.998953 + 0.0457503i 0.0145679π0.0145679\pi
888888 3.64737 + 4.33796i 0.122398 + 0.145572i
889889 0.574112 + 1.76693i 0.0192551 + 0.0592611i
890890 22.6696 32.8032i 0.759888 1.09956i
891891 0 0
892892 7.84924 2.96673i 0.262812 0.0993336i
893893 0 0
894894 −4.09721 11.6656i −0.137031 0.390156i
895895 15.1282 + 20.8222i 0.505681 + 0.696010i
896896 36.7225 6.12339i 1.22681 0.204568i
897897 −3.42975 1.11439i −0.114516 0.0372085i
898898 22.5795 0.533064i 0.753488 0.0177886i
899899 −4.23940 + 5.83504i −0.141392 + 0.194609i
900900 −8.82897 + 7.07455i −0.294299 + 0.235818i
901901 −41.0848 −1.36873
902902 0 0
903903 8.76725i 0.291756i
904904 17.4121 1.23505i 0.579118 0.0410770i
905905 −5.66312 4.11450i −0.188248 0.136771i
906906 −7.70834 + 0.181981i −0.256093 + 0.00604591i
907907 −10.3566 + 31.8744i −0.343886 + 1.05837i 0.618292 + 0.785949i 0.287825π0.287825\pi
−0.962178 + 0.272423i 0.912175π0.912175\pi
908908 −1.25097 26.4794i −0.0415148 0.878751i
909909 −39.4762 + 28.6811i −1.30934 + 0.951293i
910910 −15.8342 + 5.56131i −0.524897 + 0.184355i
911911 −42.7023 + 13.8748i −1.41479 + 0.459694i −0.913943 0.405842i 0.866978π-0.866978\pi
−0.500848 + 0.865535i 0.666978π0.666978\pi
912912 −2.49221 2.82590i −0.0825253 0.0935749i
913913 0 0
914914 18.2843 26.4575i 0.604790 0.875137i
915915 6.85950 2.22879i 0.226768 0.0736814i
916916 −19.5406 5.34393i −0.645639 0.176569i
917917 13.1957 + 18.1624i 0.435762 + 0.599775i
918918 11.3727 + 14.9005i 0.375354 + 0.491789i
919919 7.29255 22.4442i 0.240559 0.740365i −0.755776 0.654830i 0.772740π-0.772740\pi
0.996335 0.0855346i 0.0272598π-0.0272598\pi
920920 17.9501 + 44.3005i 0.591796 + 1.46055i
921921 5.44175 7.48992i 0.179312 0.246801i
922922 −1.56195 + 5.22361i −0.0514402 + 0.172031i
923923 8.70626i 0.286570i
924924 0 0
925925 9.67513i 0.318116i
926926 −30.1635 9.01942i −0.991234 0.296396i
927927 30.0354 41.3402i 0.986492 1.35779i
928928 27.3332 25.2772i 0.897256 0.829764i
929929 10.6565 32.7975i 0.349630 1.07605i −0.609429 0.792841i 0.708601π-0.708601\pi
0.959058 0.283209i 0.0913989π-0.0913989\pi
930930 −1.35016 + 1.03050i −0.0442734 + 0.0337913i
931931 −5.11741 7.04351i −0.167716 0.230842i
932932 16.0431 + 4.38743i 0.525508 + 0.143715i
933933 5.89596 1.91571i 0.193025 0.0627177i
934934 −41.9659 29.0018i −1.37317 0.948969i
935935 0 0
936936 2.62742 10.5830i 0.0858798 0.345916i
937937 −20.7322 + 6.73630i −0.677291 + 0.220065i −0.627409 0.778690i 0.715885π-0.715885\pi
−0.0498823 + 0.998755i 0.515885π0.515885\pi
938938 −9.36237 26.6565i −0.305692 0.870367i
939939 −2.62335 + 1.90598i −0.0856098 + 0.0621992i
940940 0 0
941941 −4.56094 + 14.0371i −0.148683 + 0.457598i −0.997466 0.0711426i 0.977335π-0.977335\pi
0.848784 + 0.528740i 0.177335π0.177335\pi
942942 −0.00627597 0.265837i −0.000204482 0.00866145i
943943 −51.8737 37.6884i −1.68924 1.22730i
944944 −11.1654 6.60068i −0.363403 0.214834i
945945 21.0188i 0.683741i
946946 0 0
947947 24.4142 0.793355 0.396678 0.917958i 0.370163π-0.370163\pi
0.396678 + 0.917958i 0.370163π0.370163\pi
948948 −6.01710 + 4.82143i −0.195426 + 0.156593i
949949 −0.754677 + 1.03872i −0.0244979 + 0.0337184i
950950 −0.151810 6.43036i −0.00492537 0.208628i
951951 6.07479 + 1.97382i 0.196988 + 0.0640054i
952952 27.0352 43.3617i 0.876216 1.40536i
953953 21.4820 + 29.5674i 0.695870 + 0.957783i 0.999987 + 0.00514842i 0.00163880π0.00163880\pi
−0.304116 + 0.952635i 0.598361π0.598361\pi
954954 28.2420 9.91921i 0.914368 0.321146i
955955 13.8747 + 42.7020i 0.448975 + 1.38180i
956956 −3.85525 10.2000i −0.124688 0.329892i
957957 0 0
958958 −31.8284 21.9960i −1.02833 0.710659i
959959 −8.80289 27.0925i −0.284260 0.874863i
960960 7.87226 3.85904i 0.254076 0.124550i
961961 −24.1079 + 17.5154i −0.777674 + 0.565013i
962962 −5.65762 7.41262i −0.182409 0.238992i
963963 −23.4198 7.60955i −0.754692 0.245214i
964964 −4.99351 + 7.60329i −0.160830 + 0.244885i
965965 27.5355 + 20.0057i 0.886399 + 0.644007i
966966 11.7964 + 3.52734i 0.379544 + 0.113490i
967967 −3.85525 −0.123976 −0.0619882 0.998077i 0.519744π-0.519744\pi
−0.0619882 + 0.998077i 0.519744π0.519744\pi
968968 0 0
969969 −5.17157 −0.166135
970970 −26.8334 8.02367i −0.861569 0.257624i
971971 −26.5686 19.3032i −0.852628 0.619470i 0.0732417 0.997314i 0.476666π-0.476666\pi
−0.925869 + 0.377844i 0.876666π0.876666\pi
972972 −17.2907 11.3558i −0.554600 0.364237i
973973 −61.6113 20.0187i −1.97517 0.641771i
974974 −22.8626 29.9545i −0.732564 0.959805i
975975 −0.913522 + 0.663713i −0.0292561 + 0.0212558i
976976 26.2080 2.48183i 0.838898 0.0794414i
977977 −14.0996 43.3943i −0.451088 1.38831i −0.875667 0.482915i 0.839578π-0.839578\pi
0.424580 0.905391i 0.360422π-0.360422\pi
978978 6.18209 + 4.27232i 0.197681 + 0.136614i
979979 0 0
980980 18.9497 7.16233i 0.605327 0.228792i
981981 −2.38267 7.33311i −0.0760729 0.234128i
982982 −34.3299 + 12.0574i −1.09551 + 0.384768i
983983 −10.5086 14.4638i −0.335172 0.461325i 0.607851 0.794051i 0.292032π-0.292032\pi
−0.943024 + 0.332726i 0.892032π0.892032\pi
984984 −6.22227 + 9.97988i −0.198359 + 0.318147i
985985 −26.2611 8.53275i −0.836748 0.271876i
986986 −1.20603 51.0850i −0.0384079 1.62688i
987987 0 0
988988 3.87652 + 4.83786i 0.123329 + 0.153913i
989989 −41.0848 −1.30642
990990 0 0
991991 29.9333i 0.950861i 0.879753 + 0.475431i 0.157708π0.157708\pi
−0.879753 + 0.475431i 0.842292π0.842292\pi
992992 −5.62938 + 2.59661i −0.178733 + 0.0824425i
993993 6.05572 + 4.39974i 0.192172 + 0.139621i
994994 −0.701563 29.7168i −0.0222522 0.942558i
995995 17.3050 53.2592i 0.548604 1.68843i
996996 0.177807 + 3.76367i 0.00563403 + 0.119256i
997997 44.9898 32.6870i 1.42484 1.03521i 0.433893 0.900964i 0.357140π-0.357140\pi
0.990948 0.134243i 0.0428604π-0.0428604\pi
998998 8.66292 + 24.6651i 0.274220 + 0.780759i
999999 −11.1073 + 3.60898i −0.351420 + 0.114183i
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.k.g.699.5 32
8.3 odd 2 inner 968.2.k.g.699.7 32
11.2 odd 10 inner 968.2.k.g.475.7 32
11.3 even 5 88.2.g.b.43.1 8
11.4 even 5 inner 968.2.k.g.723.8 32
11.5 even 5 inner 968.2.k.g.403.6 32
11.6 odd 10 inner 968.2.k.g.403.3 32
11.7 odd 10 inner 968.2.k.g.723.1 32
11.8 odd 10 88.2.g.b.43.8 yes 8
11.9 even 5 inner 968.2.k.g.475.2 32
11.10 odd 2 inner 968.2.k.g.699.4 32
33.8 even 10 792.2.h.g.307.1 8
33.14 odd 10 792.2.h.g.307.8 8
44.3 odd 10 352.2.g.b.175.1 8
44.19 even 10 352.2.g.b.175.2 8
88.3 odd 10 88.2.g.b.43.7 yes 8
88.19 even 10 88.2.g.b.43.2 yes 8
88.27 odd 10 inner 968.2.k.g.403.1 32
88.35 even 10 inner 968.2.k.g.475.5 32
88.43 even 2 inner 968.2.k.g.699.2 32
88.51 even 10 inner 968.2.k.g.723.6 32
88.59 odd 10 inner 968.2.k.g.723.3 32
88.69 even 10 352.2.g.b.175.4 8
88.75 odd 10 inner 968.2.k.g.475.4 32
88.83 even 10 inner 968.2.k.g.403.8 32
88.85 odd 10 352.2.g.b.175.3 8
132.47 even 10 3168.2.h.g.2287.5 8
132.107 odd 10 3168.2.h.g.2287.8 8
176.3 odd 20 2816.2.e.o.2815.6 16
176.19 even 20 2816.2.e.o.2815.5 16
176.69 even 20 2816.2.e.o.2815.7 16
176.85 odd 20 2816.2.e.o.2815.8 16
176.91 odd 20 2816.2.e.o.2815.12 16
176.107 even 20 2816.2.e.o.2815.11 16
176.157 even 20 2816.2.e.o.2815.9 16
176.173 odd 20 2816.2.e.o.2815.10 16
264.107 odd 10 792.2.h.g.307.7 8
264.173 even 10 3168.2.h.g.2287.1 8
264.179 even 10 792.2.h.g.307.2 8
264.245 odd 10 3168.2.h.g.2287.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
88.2.g.b.43.1 8 11.3 even 5
88.2.g.b.43.2 yes 8 88.19 even 10
88.2.g.b.43.7 yes 8 88.3 odd 10
88.2.g.b.43.8 yes 8 11.8 odd 10
352.2.g.b.175.1 8 44.3 odd 10
352.2.g.b.175.2 8 44.19 even 10
352.2.g.b.175.3 8 88.85 odd 10
352.2.g.b.175.4 8 88.69 even 10
792.2.h.g.307.1 8 33.8 even 10
792.2.h.g.307.2 8 264.179 even 10
792.2.h.g.307.7 8 264.107 odd 10
792.2.h.g.307.8 8 33.14 odd 10
968.2.k.g.403.1 32 88.27 odd 10 inner
968.2.k.g.403.3 32 11.6 odd 10 inner
968.2.k.g.403.6 32 11.5 even 5 inner
968.2.k.g.403.8 32 88.83 even 10 inner
968.2.k.g.475.2 32 11.9 even 5 inner
968.2.k.g.475.4 32 88.75 odd 10 inner
968.2.k.g.475.5 32 88.35 even 10 inner
968.2.k.g.475.7 32 11.2 odd 10 inner
968.2.k.g.699.2 32 88.43 even 2 inner
968.2.k.g.699.4 32 11.10 odd 2 inner
968.2.k.g.699.5 32 1.1 even 1 trivial
968.2.k.g.699.7 32 8.3 odd 2 inner
968.2.k.g.723.1 32 11.7 odd 10 inner
968.2.k.g.723.3 32 88.59 odd 10 inner
968.2.k.g.723.6 32 88.51 even 10 inner
968.2.k.g.723.8 32 11.4 even 5 inner
2816.2.e.o.2815.5 16 176.19 even 20
2816.2.e.o.2815.6 16 176.3 odd 20
2816.2.e.o.2815.7 16 176.69 even 20
2816.2.e.o.2815.8 16 176.85 odd 20
2816.2.e.o.2815.9 16 176.157 even 20
2816.2.e.o.2815.10 16 176.173 odd 20
2816.2.e.o.2815.11 16 176.107 even 20
2816.2.e.o.2815.12 16 176.91 odd 20
3168.2.h.g.2287.1 8 264.173 even 10
3168.2.h.g.2287.4 8 264.245 odd 10
3168.2.h.g.2287.5 8 132.47 even 10
3168.2.h.g.2287.8 8 132.107 odd 10