Properties

Label 8.11.d.b.3.5
Level 88
Weight 1111
Character 8.3
Analytic conductor 5.0835.083
Analytic rank 00
Dimension 88
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [8,11,Mod(3,8)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 11, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("8.3"); S:= CuspForms(chi, 11); N := Newforms(S);
 
Level: N N == 8=23 8 = 2^{3}
Weight: k k == 11 11
Character orbit: [χ][\chi] == 8.d (of order 22, degree 11, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 5.082858021395.08285802139
Analytic rank: 00
Dimension: 88
Coefficient field: Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x83x7+5x651x5+30855x4121569x3+12144527x2+279415575x+3348211684 x^{8} - 3x^{7} + 5x^{6} - 51x^{5} + 30855x^{4} - 121569x^{3} + 12144527x^{2} + 279415575x + 3348211684 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 22833 2^{28}\cdot 3^{3}
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 3.5
Root 8.43092+11.1953i-8.43092 + 11.1953i of defining polynomial
Character χ\chi == 8.3
Dual form 8.11.d.b.3.6

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+(22.861822.3905i)q2+352.099q3+(21.32791023.78i)q4+3773.58iq5+(8049.627883.68i)q615618.2iq7+(22435.323883.0i)q8+64924.4q9+(84492.5+86271.1i)q10115158.q11+(7509.52360471.i)q12+546374.iq13+(349700.357061.i)q14+1.32867e6iq15+(1.04767e643670.1i)q161.50100e6q17+(1.48429e61.45369e6i)q18+3.45753e6q19+(3.86331e6+80482.6i)q205.49914e6iq21+(2.63273e6+2.57846e6i)q22+3.90931e6iq23+(7.89945e68.40917e6i)q244.47430e6q25+(1.22336e7+1.24911e7i)q26+2.06872e6q27+(1.59896e7333103.i)q281.57435e7iq29+(2.97497e7+3.03759e7i)q301.36335e7iq31+(2.49294e7+2.24594e7i)q324.05471e7q33+(3.43155e7+3.36081e7i)q34+5.89365e7q35+(1.38470e66.64682e7i)q367.96225e7iq37+(7.90455e77.74159e7i)q38+1.92377e8iq39+(9.01244e78.46616e7i)q401.01409e7q41+(1.23129e81.25721e8i)q42+4.09302e7q43+(2.45608e6+1.17897e8i)q44+2.44998e8iq45+(8.75315e7+8.93740e7i)q462.36040e8iq47+(3.68882e81.53762e7i)q48+3.85474e7q49+(1.02291e8+1.00182e8i)q505.28499e8q51+(5.59365e8+1.16530e7i)q52+3.09768e8iq53+(4.72948e74.63198e7i)q544.34559e8iq55+(3.73009e8+3.50399e8i)q56+1.21739e9q57+(3.52505e83.59925e8i)q586.26191e7q59+(1.36027e9+2.83378e7i)q601.02129e9iq61+(3.05262e83.11688e8i)q621.01400e9iq63+(6.70530e7+1.07165e9i)q642.06179e9q65+(9.26981e8+9.07871e8i)q66+6.25414e8q67+(3.20131e7+1.53669e9i)q68+1.37646e9iq69+(1.34740e91.31962e9i)q70+2.05543e9iq71+(1.45660e91.55059e9i)q72+2.44117e9q73+(1.78279e91.82032e9i)q741.57539e9q75+(7.37418e73.53974e9i)q76+1.79856e9iq77+(4.30743e9+4.39810e9i)q78+3.04489e9iq79+(1.64793e83.95346e9i)q803.10533e9q81+(2.31839e8+2.27059e8i)q82+2.75511e9q83+(5.62990e91.17285e8i)q845.66413e9iq85+(9.35741e89.16450e8i)q865.54325e9iq87+(2.58362e9+2.75032e9i)q88+2.51922e8q89+(5.48563e9+5.60110e9i)q90+8.53337e9q91+(4.00226e9+8.33773e7i)q924.80035e9iq93+(5.28506e95.39630e9i)q94+1.30473e10iq95+(8.77760e9+7.90793e9i)q961.56384e10q97+(8.81265e88.63097e8i)q987.47658e9q99+O(q100)q+(22.8618 - 22.3905i) q^{2} +352.099 q^{3} +(21.3279 - 1023.78i) q^{4} +3773.58i q^{5} +(8049.62 - 7883.68i) q^{6} -15618.2i q^{7} +(-22435.3 - 23883.0i) q^{8} +64924.4 q^{9} +(84492.5 + 86271.1i) q^{10} -115158. q^{11} +(7509.52 - 360471. i) q^{12} +546374. i q^{13} +(-349700. - 357061. i) q^{14} +1.32867e6i q^{15} +(-1.04767e6 - 43670.1i) q^{16} -1.50100e6 q^{17} +(1.48429e6 - 1.45369e6i) q^{18} +3.45753e6 q^{19} +(3.86331e6 + 80482.6i) q^{20} -5.49914e6i q^{21} +(-2.63273e6 + 2.57846e6i) q^{22} +3.90931e6i q^{23} +(-7.89945e6 - 8.40917e6i) q^{24} -4.47430e6 q^{25} +(1.22336e7 + 1.24911e7i) q^{26} +2.06872e6 q^{27} +(-1.59896e7 - 333103. i) q^{28} -1.57435e7i q^{29} +(2.97497e7 + 3.03759e7i) q^{30} -1.36335e7i q^{31} +(-2.49294e7 + 2.24594e7i) q^{32} -4.05471e7 q^{33} +(-3.43155e7 + 3.36081e7i) q^{34} +5.89365e7 q^{35} +(1.38470e6 - 6.64682e7i) q^{36} -7.96225e7i q^{37} +(7.90455e7 - 7.74159e7i) q^{38} +1.92377e8i q^{39} +(9.01244e7 - 8.46616e7i) q^{40} -1.01409e7 q^{41} +(-1.23129e8 - 1.25721e8i) q^{42} +4.09302e7 q^{43} +(-2.45608e6 + 1.17897e8i) q^{44} +2.44998e8i q^{45} +(8.75315e7 + 8.93740e7i) q^{46} -2.36040e8i q^{47} +(-3.68882e8 - 1.53762e7i) q^{48} +3.85474e7 q^{49} +(-1.02291e8 + 1.00182e8i) q^{50} -5.28499e8 q^{51} +(5.59365e8 + 1.16530e7i) q^{52} +3.09768e8i q^{53} +(4.72948e7 - 4.63198e7i) q^{54} -4.34559e8i q^{55} +(-3.73009e8 + 3.50399e8i) q^{56} +1.21739e9 q^{57} +(-3.52505e8 - 3.59925e8i) q^{58} -6.26191e7 q^{59} +(1.36027e9 + 2.83378e7i) q^{60} -1.02129e9i q^{61} +(-3.05262e8 - 3.11688e8i) q^{62} -1.01400e9i q^{63} +(-6.70530e7 + 1.07165e9i) q^{64} -2.06179e9 q^{65} +(-9.26981e8 + 9.07871e8i) q^{66} +6.25414e8 q^{67} +(-3.20131e7 + 1.53669e9i) q^{68} +1.37646e9i q^{69} +(1.34740e9 - 1.31962e9i) q^{70} +2.05543e9i q^{71} +(-1.45660e9 - 1.55059e9i) q^{72} +2.44117e9 q^{73} +(-1.78279e9 - 1.82032e9i) q^{74} -1.57539e9 q^{75} +(7.37418e7 - 3.53974e9i) q^{76} +1.79856e9i q^{77} +(4.30743e9 + 4.39810e9i) q^{78} +3.04489e9i q^{79} +(1.64793e8 - 3.95346e9i) q^{80} -3.10533e9 q^{81} +(-2.31839e8 + 2.27059e8i) q^{82} +2.75511e9 q^{83} +(-5.62990e9 - 1.17285e8i) q^{84} -5.66413e9i q^{85} +(9.35741e8 - 9.16450e8i) q^{86} -5.54325e9i q^{87} +(2.58362e9 + 2.75032e9i) q^{88} +2.51922e8 q^{89} +(5.48563e9 + 5.60110e9i) q^{90} +8.53337e9 q^{91} +(4.00226e9 + 8.33773e7i) q^{92} -4.80035e9i q^{93} +(-5.28506e9 - 5.39630e9i) q^{94} +1.30473e10i q^{95} +(-8.77760e9 + 7.90793e9i) q^{96} -1.56384e10 q^{97} +(8.81265e8 - 8.63097e8i) q^{98} -7.47658e9 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+42q2+480q3+212q45412q672q835496q9+9120q10+143328q11+180120q12400320q141987312q16370800q17+3067758q18+1753312q19+13646747232q99+O(q100) 8 q + 42 q^{2} + 480 q^{3} + 212 q^{4} - 5412 q^{6} - 72 q^{8} - 35496 q^{9} + 9120 q^{10} + 143328 q^{11} + 180120 q^{12} - 400320 q^{14} - 1987312 q^{16} - 370800 q^{17} + 3067758 q^{18} + 1753312 q^{19}+ \cdots - 13646747232 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/8Z)×\left(\mathbb{Z}/8\mathbb{Z}\right)^\times.

nn 55 77
χ(n)\chi(n) 1-1 1-1

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 22.8618 22.3905i 0.714433 0.699704i
33 352.099 1.44897 0.724483 0.689293i 0.242079π-0.242079\pi
0.724483 + 0.689293i 0.242079π0.242079\pi
44 21.3279 1023.78i 0.0208280 0.999783i
55 3773.58i 1.20755i 0.797156 + 0.603773i 0.206337π0.206337\pi
−0.797156 + 0.603773i 0.793663π0.793663\pi
66 8049.62 7883.68i 1.03519 1.01385i
77 15618.2i 0.929267i −0.885503 0.464633i 0.846186π-0.846186\pi
0.885503 0.464633i 0.153814π-0.153814\pi
88 −22435.3 23883.0i −0.684672 0.728851i
99 64924.4 1.09950
1010 84492.5 + 86271.1i 0.844925 + 0.862711i
1111 −115158. −0.715042 −0.357521 0.933905i 0.616378π-0.616378\pi
−0.357521 + 0.933905i 0.616378π0.616378\pi
1212 7509.52 360471.i 0.0301791 1.44865i
1313 546374.i 1.47154i 0.677230 + 0.735772i 0.263180π0.263180\pi
−0.677230 + 0.735772i 0.736820π0.736820\pi
1414 −349700. 357061.i −0.650212 0.663899i
1515 1.32867e6i 1.74969i
1616 −1.04767e6 43670.1i −0.999132 0.0416470i
1717 −1.50100e6 −1.05715 −0.528573 0.848888i 0.677273π-0.677273\pi
−0.528573 + 0.848888i 0.677273π0.677273\pi
1818 1.48429e6 1.45369e6i 0.785519 0.769325i
1919 3.45753e6 1.39636 0.698180 0.715922i 0.253993π-0.253993\pi
0.698180 + 0.715922i 0.253993π0.253993\pi
2020 3.86331e6 + 80482.6i 1.20728 + 0.0251508i
2121 5.49914e6i 1.34648i
2222 −2.63273e6 + 2.57846e6i −0.510850 + 0.500318i
2323 3.90931e6i 0.607380i 0.952771 + 0.303690i 0.0982188π0.0982188\pi
−0.952771 + 0.303690i 0.901781π0.901781\pi
2424 −7.89945e6 8.40917e6i −0.992066 1.05608i
2525 −4.47430e6 −0.458168
2626 1.22336e7 + 1.24911e7i 1.02965 + 1.05132i
2727 2.06872e6 0.144173
2828 −1.59896e7 333103.i −0.929065 0.0193548i
2929 1.57435e7i 0.767557i −0.923425 0.383778i 0.874623π-0.874623\pi
0.923425 0.383778i 0.125377π-0.125377\pi
3030 2.97497e7 + 3.03759e7i 1.22427 + 1.25004i
3131 1.36335e7i 0.476212i −0.971239 0.238106i 0.923473π-0.923473\pi
0.971239 0.238106i 0.0765265π-0.0765265\pi
3232 −2.49294e7 + 2.24594e7i −0.742953 + 0.669343i
3333 −4.05471e7 −1.03607
3434 −3.43155e7 + 3.36081e7i −0.755260 + 0.739690i
3535 5.89365e7 1.12213
3636 1.38470e6 6.64682e7i 0.0229004 1.09926i
3737 7.96225e7i 1.14823i −0.818776 0.574113i 0.805347π-0.805347\pi
0.818776 0.574113i 0.194653π-0.194653\pi
3838 7.90455e7 7.74159e7i 0.997606 0.977040i
3939 1.92377e8i 2.13222i
4040 9.01244e7 8.46616e7i 0.880122 0.826773i
4141 −1.01409e7 −0.0875298 −0.0437649 0.999042i 0.513935π-0.513935\pi
−0.0437649 + 0.999042i 0.513935π0.513935\pi
4242 −1.23129e8 1.25721e8i −0.942135 0.961966i
4343 4.09302e7 0.278421 0.139210 0.990263i 0.455544π-0.455544\pi
0.139210 + 0.990263i 0.455544π0.455544\pi
4444 −2.45608e6 + 1.17897e8i −0.0148929 + 0.714887i
4545 2.44998e8i 1.32770i
4646 8.75315e7 + 8.93740e7i 0.424987 + 0.433932i
4747 2.36040e8i 1.02919i −0.857433 0.514595i 0.827942π-0.827942\pi
0.857433 0.514595i 0.172058π-0.172058\pi
4848 −3.68882e8 1.53762e7i −1.44771 0.0603451i
4949 3.85474e7 0.136463
5050 −1.02291e8 + 1.00182e8i −0.327330 + 0.320582i
5151 −5.28499e8 −1.53177
5252 5.59365e8 + 1.16530e7i 1.47122 + 0.0306493i
5353 3.09768e8i 0.740725i 0.928887 + 0.370362i 0.120766π0.120766\pi
−0.928887 + 0.370362i 0.879234π0.879234\pi
5454 4.72948e7 4.63198e7i 0.103002 0.100878i
5555 4.34559e8i 0.863447i
5656 −3.73009e8 + 3.50399e8i −0.677297 + 0.636243i
5757 1.21739e9 2.02328
5858 −3.52505e8 3.59925e8i −0.537063 0.548368i
5959 −6.26191e7 −0.0875885 −0.0437942 0.999041i 0.513945π-0.513945\pi
−0.0437942 + 0.999041i 0.513945π0.513945\pi
6060 1.36027e9 + 2.83378e7i 1.74931 + 0.0364426i
6161 1.02129e9i 1.20921i −0.796527 0.604603i 0.793332π-0.793332\pi
0.796527 0.604603i 0.206668π-0.206668\pi
6262 −3.05262e8 3.11688e8i −0.333207 0.340221i
6363 1.01400e9i 1.02173i
6464 −6.70530e7 + 1.07165e9i −0.0624479 + 0.998048i
6565 −2.06179e9 −1.77696
6666 −9.26981e8 + 9.07871e8i −0.740203 + 0.724944i
6767 6.25414e8 0.463227 0.231613 0.972808i 0.425600π-0.425600\pi
0.231613 + 0.972808i 0.425600π0.425600\pi
6868 −3.20131e7 + 1.53669e9i −0.0220183 + 1.05692i
6969 1.37646e9i 0.880073i
7070 1.34740e9 1.31962e9i 0.801688 0.785161i
7171 2.05543e9i 1.13923i 0.821913 + 0.569614i 0.192907π0.192907\pi
−0.821913 + 0.569614i 0.807093π0.807093\pi
7272 −1.45660e9 1.55059e9i −0.752797 0.801372i
7373 2.44117e9 1.17756 0.588781 0.808292i 0.299608π-0.299608\pi
0.588781 + 0.808292i 0.299608π0.299608\pi
7474 −1.78279e9 1.82032e9i −0.803418 0.820330i
7575 −1.57539e9 −0.663870
7676 7.37418e7 3.53974e9i 0.0290834 1.39606i
7777 1.79856e9i 0.664465i
7878 4.30743e9 + 4.39810e9i 1.49192 + 1.52332i
7979 3.04489e9i 0.989548i 0.869022 + 0.494774i 0.164749π0.164749\pi
−0.869022 + 0.494774i 0.835251π0.835251\pi
8080 1.64793e8 3.95346e9i 0.0502907 1.20650i
8181 −3.10533e9 −0.890599
8282 −2.31839e8 + 2.27059e8i −0.0625341 + 0.0612450i
8383 2.75511e9 0.699438 0.349719 0.936855i 0.386277π-0.386277\pi
0.349719 + 0.936855i 0.386277π0.386277\pi
8484 −5.62990e9 1.17285e8i −1.34618 0.0280444i
8585 5.66413e9i 1.27655i
8686 9.35741e8 9.16450e8i 0.198913 0.194812i
8787 5.54325e9i 1.11216i
8888 2.58362e9 + 2.75032e9i 0.489570 + 0.521159i
8989 2.51922e8 0.0451145 0.0225573 0.999746i 0.492819π-0.492819\pi
0.0225573 + 0.999746i 0.492819π0.492819\pi
9090 5.48563e9 + 5.60110e9i 0.928996 + 0.948551i
9191 8.53337e9 1.36746
9292 4.00226e9 + 8.33773e7i 0.607249 + 0.0126505i
9393 4.80035e9i 0.690014i
9494 −5.28506e9 5.39630e9i −0.720129 0.735287i
9595 1.30473e10i 1.68617i
9696 −8.77760e9 + 7.90793e9i −1.07651 + 0.969855i
9797 −1.56384e10 −1.82110 −0.910549 0.413401i 0.864341π-0.864341\pi
−0.910549 + 0.413401i 0.864341π0.864341\pi
9898 8.81265e8 8.63097e8i 0.0974936 0.0954837i
9999 −7.47658e9 −0.786189
100100 −9.54274e7 + 4.58069e9i −0.00954274 + 0.458069i
101101 3.85788e9i 0.367064i −0.983014 0.183532i 0.941247π-0.941247\pi
0.983014 0.183532i 0.0587532π-0.0587532\pi
102102 −1.20825e10 + 1.18334e10i −1.09435 + 1.07178i
103103 9.28145e9i 0.800626i −0.916378 0.400313i 0.868901π-0.868901\pi
0.916378 0.400313i 0.131099π-0.131099\pi
104104 1.30490e10 1.22581e10i 1.07254 1.00752i
105105 2.07515e10 1.62593
106106 6.93586e9 + 7.08186e9i 0.518288 + 0.529198i
107107 −3.91137e9 −0.278875 −0.139438 0.990231i 0.544529π-0.544529\pi
−0.139438 + 0.990231i 0.544529π0.544529\pi
108108 4.41215e7 2.11791e9i 0.00300283 0.144142i
109109 1.09799e10i 0.713619i 0.934177 + 0.356809i 0.116135π0.116135\pi
−0.934177 + 0.356809i 0.883865π0.883865\pi
110110 −9.73002e9 9.93483e9i −0.604157 0.616875i
111111 2.80350e10i 1.66374i
112112 −6.82047e8 + 1.63626e10i −0.0387012 + 0.928461i
113113 2.02898e10 1.10125 0.550624 0.834753i 0.314390π-0.314390\pi
0.550624 + 0.834753i 0.314390π0.314390\pi
114114 2.78318e10 2.72580e10i 1.44550 1.41570i
115115 −1.47521e10 −0.733440
116116 −1.61178e10 3.35775e8i −0.767390 0.0159867i
117117 3.54730e10i 1.61796i
118118 −1.43159e9 + 1.40208e9i −0.0625761 + 0.0612860i
119119 2.34428e10i 0.982371i
120120 3.17327e10 2.98092e10i 1.27527 1.19797i
121121 −1.26760e10 −0.488714
122122 −2.28673e10 2.33486e10i −0.846087 0.863896i
123123 −3.57058e9 −0.126828
124124 −1.39577e10 2.90775e8i −0.476108 0.00991855i
125125 1.99672e10i 0.654287i
126126 −2.27040e10 2.31819e10i −0.714908 0.729957i
127127 6.26328e9i 0.189576i 0.995497 + 0.0947880i 0.0302173π0.0302173\pi
−0.995497 + 0.0947880i 0.969783π0.969783\pi
128128 2.24618e10 + 2.60012e10i 0.653724 + 0.756733i
129129 1.44115e10 0.403422
130130 −4.71362e10 + 4.61645e10i −1.26952 + 1.24334i
131131 −4.99170e9 −0.129387 −0.0646937 0.997905i 0.520607π-0.520607\pi
−0.0646937 + 0.997905i 0.520607π0.520607\pi
132132 −8.64784e8 + 4.15112e10i −0.0215793 + 1.03585i
133133 5.40003e10i 1.29759i
134134 1.42981e10 1.40034e10i 0.330944 0.324122i
135135 7.80649e9i 0.174095i
136136 3.36754e10 + 3.58483e10i 0.723798 + 0.770502i
137137 −5.31439e10 −1.10116 −0.550580 0.834782i 0.685594π-0.685594\pi
−0.550580 + 0.834782i 0.685594π0.685594\pi
138138 3.08197e10 + 3.14685e10i 0.615791 + 0.628753i
139139 3.24537e10 0.625446 0.312723 0.949844i 0.398759π-0.398759\pi
0.312723 + 0.949844i 0.398759π0.398759\pi
140140 1.25699e9 6.03379e10i 0.0233718 1.12189i
141141 8.31093e10i 1.49126i
142142 4.60221e10 + 4.69909e10i 0.797122 + 0.813901i
143143 6.29195e10i 1.05222i
144144 −6.80191e10 2.83525e9i −1.09855 0.0457909i
145145 5.94093e10 0.926860
146146 5.58097e10 5.46591e10i 0.841289 0.823946i
147147 1.35725e10 0.197730
148148 −8.15157e10 1.69818e9i −1.14798 0.0239153i
149149 9.33485e10i 1.27109i 0.772064 + 0.635544i 0.219224π0.219224\pi
−0.772064 + 0.635544i 0.780776π0.780776\pi
150150 −3.60164e10 + 3.52739e10i −0.474290 + 0.464513i
151151 1.79317e8i 0.00228422i −0.999999 0.00114211i 0.999636π-0.999636\pi
0.999999 0.00114211i 0.000363545π-0.000363545\pi
152152 −7.75708e10 8.25761e10i −0.956049 1.01774i
153153 −9.74513e10 −1.16233
154154 4.02708e10 + 4.11185e10i 0.464929 + 0.474716i
155155 5.14473e10 0.575048
156156 1.96952e11 + 4.10301e9i 2.13175 + 0.0444098i
157157 4.41399e10i 0.462736i −0.972866 0.231368i 0.925680π-0.925680\pi
0.972866 0.231368i 0.0743201π-0.0743201\pi
158158 6.81768e10 + 6.96119e10i 0.692391 + 0.706965i
159159 1.09069e11i 1.07328i
160160 −8.47525e10 9.40731e10i −0.808263 0.897151i
161161 6.10563e10 0.564419
162162 −7.09935e10 + 6.95299e10i −0.636273 + 0.623156i
163163 −1.06005e11 −0.921272 −0.460636 0.887589i 0.652379π-0.652379\pi
−0.460636 + 0.887589i 0.652379π0.652379\pi
164164 −2.16283e8 + 1.03820e10i −0.00182307 + 0.0875108i
165165 1.53008e11i 1.25110i
166166 6.29870e10 6.16885e10i 0.499701 0.489400i
167167 1.65219e11i 1.27198i 0.771699 + 0.635988i 0.219407π0.219407\pi
−0.771699 + 0.635988i 0.780593π0.780593\pi
168168 −1.31336e11 + 1.23375e11i −0.981380 + 0.921894i
169169 −1.60666e11 −1.16544
170170 −1.26823e11 1.29493e11i −0.893209 0.912011i
171171 2.24478e11 1.53530
172172 8.72956e8 4.19035e10i 0.00579896 0.278361i
173173 2.73295e11i 1.76361i 0.471617 + 0.881803i 0.343670π0.343670\pi
−0.471617 + 0.881803i 0.656330π0.656330\pi
174174 −1.24116e11 1.26729e11i −0.778185 0.794566i
175175 6.98805e10i 0.425761i
176176 1.20647e11 + 5.02897e9i 0.714422 + 0.0297794i
177177 −2.20481e10 −0.126913
178178 5.75941e9 5.64067e9i 0.0322313 0.0315668i
179179 −1.55618e11 −0.846824 −0.423412 0.905937i 0.639168π-0.639168\pi
−0.423412 + 0.905937i 0.639168π0.639168\pi
180180 2.50823e11 + 5.22528e9i 1.32741 + 0.0276533i
181181 1.55132e10i 0.0798562i −0.999203 0.0399281i 0.987287π-0.987287\pi
0.999203 0.0399281i 0.0127129π-0.0127129\pi
182182 1.95089e11 1.91067e11i 0.976956 0.956815i
183183 3.59595e11i 1.75210i
184184 9.33660e10 8.77067e10i 0.442690 0.415856i
185185 3.00462e11 1.38654
186186 −1.07482e11 1.09745e11i −0.482806 0.492969i
187187 1.72852e11 0.755904
188188 −2.41652e11 5.03423e9i −1.02897 0.0214360i
189189 3.23097e10i 0.133975i
190190 2.92135e11 + 2.98285e11i 1.17982 + 1.20466i
191191 2.19148e11i 0.862127i −0.902322 0.431063i 0.858139π-0.858139\pi
0.902322 0.431063i 0.141861π-0.141861\pi
192192 −2.36093e10 + 3.77325e11i −0.0904849 + 1.44614i
193193 1.83821e11 0.686451 0.343225 0.939253i 0.388481π-0.388481\pi
0.343225 + 0.939253i 0.388481π0.388481\pi
194194 −3.57522e11 + 3.50152e11i −1.30105 + 1.27423i
195195 −7.25952e11 −2.57475
196196 8.22135e8 3.94640e10i 0.00284225 0.136433i
197197 2.89571e10i 0.0975943i 0.998809 + 0.0487971i 0.0155388π0.0155388\pi
−0.998809 + 0.0487971i 0.984461π0.984461\pi
198198 −1.70928e11 + 1.67405e11i −0.561679 + 0.550100i
199199 3.25273e11i 1.04228i −0.853473 0.521138i 0.825508π-0.825508\pi
0.853473 0.521138i 0.174492π-0.174492\pi
200200 1.00382e11 + 1.06860e11i 0.313695 + 0.333937i
201201 2.20207e11 0.671199
202202 −8.63801e10 8.81983e10i −0.256836 0.262243i
203203 −2.45884e11 −0.713265
204204 −1.12718e10 + 5.41065e11i −0.0319037 + 1.53144i
205205 3.82674e10i 0.105696i
206206 −2.07817e11 2.12191e11i −0.560201 0.571993i
207207 2.53810e11i 0.667815i
208208 2.38602e10 5.72417e11i 0.0612854 1.47027i
209209 −3.98163e11 −0.998457
210210 4.74417e11 4.64636e11i 1.16162 1.13767i
211211 6.20459e11 1.48354 0.741772 0.670652i 0.233986π-0.233986\pi
0.741772 + 0.670652i 0.233986π0.233986\pi
212212 3.17133e11 + 6.60669e9i 0.740564 + 0.0154278i
213213 7.23713e11i 1.65070i
214214 −8.94211e10 + 8.75776e10i −0.199237 + 0.195130i
215215 1.54454e11i 0.336206i
216216 −4.64125e10 4.94073e10i −0.0987111 0.105080i
217217 −2.12931e11 −0.442528
218218 2.45846e11 + 2.51021e11i 0.499322 + 0.509832i
219219 8.59533e11 1.70625
220220 −4.44892e11 9.26824e9i −0.863260 0.0179839i
221221 8.20105e11i 1.55564i
222222 −6.27718e11 6.40931e11i −1.16412 1.18863i
223223 5.25673e11i 0.953217i 0.879116 + 0.476608i 0.158134π0.158134\pi
−0.879116 + 0.476608i 0.841866π0.841866\pi
224224 3.50776e11 + 3.89352e11i 0.621998 + 0.690402i
225225 −2.90491e11 −0.503756
226226 4.63862e11 4.54299e11i 0.786768 0.770548i
227227 −8.73761e11 −1.44965 −0.724825 0.688933i 0.758079π-0.758079\pi
−0.724825 + 0.688933i 0.758079π0.758079\pi
228228 2.59644e10 1.24634e12i 0.0421409 2.02284i
229229 8.30219e11i 1.31830i −0.752010 0.659151i 0.770916π-0.770916\pi
0.752010 0.659151i 0.229084π-0.229084\pi
230230 −3.37260e11 + 3.30307e11i −0.523994 + 0.513191i
231231 6.33272e11i 0.962787i
232232 −3.76001e11 + 3.53210e11i −0.559435 + 0.525525i
233233 8.33377e11 1.21356 0.606781 0.794869i 0.292460π-0.292460\pi
0.606781 + 0.794869i 0.292460π0.292460\pi
234234 7.94259e11 + 8.10978e11i 1.13210 + 1.15593i
235235 8.90716e11 1.24280
236236 −1.33553e9 + 6.41081e10i −0.00182429 + 0.0875695i
237237 1.07210e12i 1.43382i
238238 5.24898e11 + 5.35947e11i 0.687369 + 0.701838i
239239 9.19325e11i 1.17891i −0.807802 0.589454i 0.799343π-0.799343\pi
0.807802 0.589454i 0.200657π-0.200657\pi
240240 5.80232e10 1.39201e12i 0.0728695 1.74817i
241241 −1.56744e12 −1.92799 −0.963997 0.265912i 0.914327π-0.914327\pi
−0.963997 + 0.265912i 0.914327π0.914327\pi
242242 −2.89797e11 + 2.83822e11i −0.349153 + 0.341955i
243243 −1.21554e12 −1.43462
244244 −1.04558e12 2.17820e10i −1.20894 0.0251854i
245245 1.45462e11i 0.164785i
246246 −8.16302e10 + 7.99473e10i −0.0906098 + 0.0887418i
247247 1.88910e12i 2.05481i
248248 −3.25610e11 + 3.05873e11i −0.347087 + 0.326049i
249249 9.70072e11 1.01346
250250 4.47077e11 + 4.56488e11i 0.457807 + 0.467444i
251251 1.83947e12 1.84639 0.923195 0.384331i 0.125568π-0.125568\pi
0.923195 + 0.384331i 0.125568π0.125568\pi
252252 −1.03811e12 2.16265e10i −1.02151 0.0212806i
253253 4.50189e11i 0.434303i
254254 1.40238e11 + 1.43190e11i 0.132647 + 0.135439i
255255 1.99433e12i 1.84968i
256256 1.09570e12 + 9.15033e10i 0.996531 + 0.0832218i
257257 −4.69431e11 −0.418703 −0.209352 0.977840i 0.567135π-0.567135\pi
−0.209352 + 0.977840i 0.567135π0.567135\pi
258258 3.29473e11 3.22681e11i 0.288218 0.282276i
259259 −1.24356e12 −1.06701
260260 −4.39736e10 + 2.11081e12i −0.0370105 + 1.77657i
261261 1.02214e12i 0.843929i
262262 −1.14119e11 + 1.11767e11i −0.0924386 + 0.0905329i
263263 2.02740e12i 1.61124i −0.592433 0.805619i 0.701833π-0.701833\pi
0.592433 0.805619i 0.298167π-0.298167\pi
264264 9.09687e11 + 9.68385e11i 0.709369 + 0.755142i
265265 −1.16893e12 −0.894459
266266 −1.20910e12 1.23455e12i −0.907931 0.927042i
267267 8.87015e10 0.0653694
268268 1.33388e10 6.40285e11i 0.00964810 0.463126i
269269 1.54905e12i 1.09977i −0.835239 0.549886i 0.814671π-0.814671\pi
0.835239 0.549886i 0.185329π-0.185329\pi
270270 1.74792e11 + 1.78471e11i 0.121815 + 0.124379i
271271 2.74756e12i 1.87975i 0.341514 + 0.939877i 0.389060π0.389060\pi
−0.341514 + 0.939877i 0.610940π0.610940\pi
272272 1.57254e12 + 6.55486e10i 1.05623 + 0.0440270i
273273 3.00459e12 1.98140
274274 −1.21497e12 + 1.18992e12i −0.786705 + 0.770487i
275275 5.15253e11 0.327610
276276 1.40919e12 + 2.93570e10i 0.879882 + 0.0183302i
277277 3.44260e11i 0.211100i 0.994414 + 0.105550i 0.0336603π0.0336603\pi
−0.994414 + 0.105550i 0.966340π0.966340\pi
278278 7.41951e11 7.26655e11i 0.446839 0.437627i
279279 8.85149e11i 0.523595i
280280 −1.32226e12 1.40758e12i −0.768293 0.817868i
281281 −5.16881e11 −0.295025 −0.147513 0.989060i 0.547127π-0.547127\pi
−0.147513 + 0.989060i 0.547127π0.547127\pi
282282 −1.86086e12 1.90003e12i −1.04344 1.06541i
283283 9.80974e11 0.540413 0.270206 0.962802i 0.412908π-0.412908\pi
0.270206 + 0.962802i 0.412908π0.412908\pi
284284 2.10430e12 + 4.38379e10i 1.13898 + 0.0237279i
285285 4.59392e12i 2.44320i
286286 −1.40880e12 1.43846e12i −0.736240 0.751737i
287287 1.58382e11i 0.0813385i
288288 −1.61853e12 + 1.45817e12i −0.816878 + 0.735943i
289289 2.36996e11 0.117558
290290 1.35821e12 1.33021e12i 0.662179 0.648528i
291291 −5.50625e12 −2.63871
292292 5.20651e10 2.49922e12i 0.0245263 1.17731i
293293 3.78962e12i 1.75492i 0.479648 + 0.877461i 0.340764π0.340764\pi
−0.479648 + 0.877461i 0.659236π0.659236\pi
294294 3.10292e11 3.03895e11i 0.141265 0.138353i
295295 2.36298e11i 0.105767i
296296 −1.90162e12 + 1.78636e12i −0.836885 + 0.786158i
297297 −2.38230e11 −0.103090
298298 2.09012e12 + 2.13412e12i 0.889386 + 0.908107i
299299 −2.13594e12 −0.893787
300300 −3.35999e10 + 1.61285e12i −0.0138271 + 0.663726i
301301 6.39256e11i 0.258727i
302302 −4.01501e9 4.09952e9i −0.00159828 0.00163192i
303303 1.35836e12i 0.531864i
304304 −3.62234e12 1.50990e11i −1.39515 0.0581543i
305305 3.85393e12 1.46017
306306 −2.22792e12 + 2.18199e12i −0.830408 + 0.813289i
307307 4.74199e12 1.73888 0.869438 0.494041i 0.164481π-0.164481\pi
0.869438 + 0.494041i 0.164481π0.164481\pi
308308 1.84133e12 + 3.83596e10i 0.664321 + 0.0138395i
309309 3.26798e12i 1.16008i
310310 1.17618e12 1.15193e12i 0.410833 0.402363i
311311 1.77863e12i 0.611340i −0.952138 0.305670i 0.901120π-0.901120\pi
0.952138 0.305670i 0.0988804π-0.0988804\pi
312312 4.59455e12 4.31605e12i 1.55407 1.45987i
313313 −2.19482e12 −0.730595 −0.365297 0.930891i 0.619033π-0.619033\pi
−0.365297 + 0.930891i 0.619033π0.619033\pi
314314 −9.88316e11 1.00912e12i −0.323778 0.330594i
315315 3.82642e12 1.23379
316316 3.11730e12 + 6.49412e10i 0.989333 + 0.0206103i
317317 2.30472e12i 0.719981i −0.932956 0.359991i 0.882780π-0.882780\pi
0.932956 0.359991i 0.117220π-0.117220\pi
318318 2.44211e12 + 2.49351e12i 0.750981 + 0.766789i
319319 1.81299e12i 0.548836i
320320 −4.04395e12 2.53030e11i −1.20519 0.0754088i
321321 −1.37719e12 −0.404080
322322 1.39586e12 1.36708e12i 0.403239 0.394926i
323323 −5.18974e12 −1.47616
324324 −6.62301e10 + 3.17917e12i −0.0185494 + 0.890406i
325325 2.44464e12i 0.674215i
326326 −2.42347e12 + 2.37351e12i −0.658187 + 0.644618i
327327 3.86601e12i 1.03401i
328328 2.27514e11 + 2.42194e11i 0.0599292 + 0.0637962i
329329 −3.68651e12 −0.956393
330330 −3.42592e12 3.49804e12i −0.875403 0.893830i
331331 3.59393e12 0.904544 0.452272 0.891880i 0.350614π-0.350614\pi
0.452272 + 0.891880i 0.350614π0.350614\pi
332332 5.87608e10 2.82062e12i 0.0145679 0.699286i
333333 5.16944e12i 1.26247i
334334 3.69935e12 + 3.77722e12i 0.890006 + 0.908740i
335335 2.36005e12i 0.559368i
336336 −2.40148e11 + 5.76127e12i −0.0560767 + 1.34531i
337337 −1.56362e12 −0.359734 −0.179867 0.983691i 0.557567π-0.557567\pi
−0.179867 + 0.983691i 0.557567π0.557567\pi
338338 −3.67312e12 + 3.59739e12i −0.832629 + 0.815464i
339339 7.14401e12 1.59567
340340 −5.79881e12 1.20804e11i −1.27628 0.0265881i
341341 1.57001e12i 0.340512i
342342 5.13198e12 5.02618e12i 1.09687 1.07426i
343343 5.01379e12i 1.05608i
344344 −9.18284e11 9.77537e11i −0.190627 0.202927i
345345 −5.19419e12 −1.06273
346346 6.11923e12 + 6.24804e12i 1.23400 + 1.25998i
347347 −1.77379e10 −0.00352578 −0.00176289 0.999998i 0.500561π-0.500561\pi
−0.00176289 + 0.999998i 0.500561π0.500561\pi
348348 −5.67506e12 1.18226e11i −1.11192 0.0231642i
349349 1.94015e12i 0.374722i −0.982291 0.187361i 0.940007π-0.940007\pi
0.982291 0.187361i 0.0599934π-0.0599934\pi
350350 1.56466e12 + 1.59760e12i 0.297907 + 0.304177i
351351 1.13030e12i 0.212157i
352352 2.87082e12 2.58639e12i 0.531243 0.478609i
353353 4.41804e12 0.806038 0.403019 0.915192i 0.367961π-0.367961\pi
0.403019 + 0.915192i 0.367961π0.367961\pi
354354 −5.04060e11 + 4.93669e11i −0.0906705 + 0.0888013i
355355 −7.75633e12 −1.37567
356356 5.37297e9 2.57912e11i 0.000939647 0.0451047i
357357 8.25419e12i 1.42342i
358358 −3.55770e12 + 3.48436e12i −0.604999 + 0.592527i
359359 4.43076e12i 0.743029i 0.928427 + 0.371515i 0.121161π0.121161\pi
−0.928427 + 0.371515i 0.878839π0.878839\pi
360360 5.85128e12 5.49660e12i 0.967694 0.909038i
361361 5.82343e12 0.949824
362362 −3.47349e11 3.54660e11i −0.0558757 0.0570519i
363363 −4.46320e12 −0.708130
364364 1.81999e11 8.73627e12i 0.0284814 1.36716i
365365 9.21196e12i 1.42196i
366366 −8.05153e12 8.22101e12i −1.22595 1.25176i
367367 2.67602e12i 0.401939i −0.979598 0.200969i 0.935591π-0.935591\pi
0.979598 0.200969i 0.0644092π-0.0644092\pi
368368 1.70720e11 4.09565e12i 0.0252956 0.606853i
369369 −6.58390e11 −0.0962390
370370 6.86912e12 6.72751e12i 0.990586 0.970165i
371371 4.83801e12 0.688331
372372 −4.91449e12 1.02381e11i −0.689865 0.0143716i
373373 9.92009e12i 1.37395i −0.726680 0.686976i 0.758938π-0.758938\pi
0.726680 0.686976i 0.241062π-0.241062\pi
374374 3.95172e12 3.87025e12i 0.540043 0.528909i
375375 7.03044e12i 0.948039i
376376 −5.63734e12 + 5.29563e12i −0.750127 + 0.704658i
377377 8.60182e12 1.12949
378378 −7.23431e11 7.38659e11i −0.0937429 0.0957161i
379379 6.20132e11 0.0793028 0.0396514 0.999214i 0.487375π-0.487375\pi
0.0396514 + 0.999214i 0.487375π0.487375\pi
380380 1.33575e13 + 2.78271e11i 1.68580 + 0.0351196i
381381 2.20529e12i 0.274689i
382382 −4.90685e12 5.01013e12i −0.603234 0.615931i
383383 5.18547e12i 0.629207i −0.949223 0.314604i 0.898128π-0.898128\pi
0.949223 0.314604i 0.101872π-0.101872\pi
384384 7.90876e12 + 9.15497e12i 0.947223 + 1.09648i
385385 −6.78703e12 −0.802373
386386 4.20250e12 4.11586e12i 0.490423 0.480313i
387387 2.65737e12 0.306124
388388 −3.33534e11 + 1.60102e13i −0.0379299 + 1.82070i
389389 1.84987e12i 0.207679i 0.994594 + 0.103840i 0.0331129π0.0331129\pi
−0.994594 + 0.103840i 0.966887π0.966887\pi
390390 −1.65966e13 + 1.62545e13i −1.83948 + 1.80156i
391391 5.86786e12i 0.642090i
392392 −8.64824e11 9.20628e11i −0.0934324 0.0994612i
393393 −1.75757e12 −0.187478
394394 6.48366e11 + 6.62013e11i 0.0682871 + 0.0697245i
395395 −1.14902e13 −1.19493
396396 −1.59460e11 + 7.65436e12i −0.0163748 + 0.786019i
397397 6.84533e12i 0.694132i 0.937841 + 0.347066i 0.112822π0.112822\pi
−0.937841 + 0.347066i 0.887178π0.887178\pi
398398 −7.28303e12 7.43634e12i −0.729285 0.744636i
399399 1.90134e13i 1.88017i
400400 4.68757e12 + 1.95393e11i 0.457771 + 0.0190813i
401401 −1.07383e13 −1.03565 −0.517825 0.855486i 0.673258π-0.673258\pi
−0.517825 + 0.855486i 0.673258π0.673258\pi
402402 5.03435e12 4.93056e12i 0.479527 0.469641i
403403 7.44901e12 0.700766
404404 −3.94962e12 8.22805e10i −0.366985 0.00764523i
405405 1.17182e13i 1.07544i
406406 −5.62137e12 + 5.50548e12i −0.509580 + 0.499075i
407407 9.16919e12i 0.821030i
408408 1.18570e13 + 1.26221e13i 1.04876 + 1.11643i
409409 1.79443e13 1.56787 0.783936 0.620841i 0.213209π-0.213209\pi
0.783936 + 0.620841i 0.213209π0.213209\pi
410410 −8.56828e11 8.74863e11i −0.0739561 0.0755129i
411411 −1.87119e13 −1.59554
412412 −9.50214e12 1.97954e11i −0.800452 0.0166755i
413413 9.77997e11i 0.0813931i
414414 5.68293e12 + 5.80255e12i 0.467273 + 0.477109i
415415 1.03967e13i 0.844604i
416416 −1.22712e13 1.36208e13i −0.984968 1.09329i
417417 1.14269e13 0.906250
418418 −9.10274e12 + 8.91508e12i −0.713330 + 0.698625i
419419 1.01675e13 0.787303 0.393652 0.919260i 0.371212π-0.371212\pi
0.393652 + 0.919260i 0.371212π0.371212\pi
420420 4.42585e11 2.12449e13i 0.0338649 1.62558i
421421 1.38694e13i 1.04869i 0.851505 + 0.524346i 0.175690π0.175690\pi
−0.851505 + 0.524346i 0.824310π0.824310\pi
422422 1.41848e13 1.38924e13i 1.05989 1.03804i
423423 1.53247e13i 1.13160i
424424 7.39818e12 6.94974e12i 0.539878 0.507153i
425425 6.71591e12 0.484351
426426 1.62043e13 + 1.65454e13i 1.15500 + 1.17931i
427427 −1.59507e13 −1.12368
428428 −8.34212e10 + 4.00437e12i −0.00580842 + 0.278815i
429429 2.21539e13i 1.52462i
430430 3.45830e12 + 3.53109e12i 0.235245 + 0.240197i
431431 3.51756e11i 0.0236513i −0.999930 0.0118257i 0.996236π-0.996236\pi
0.999930 0.0118257i 0.00376431π-0.00376431\pi
432432 −2.16733e12 9.03412e10i −0.144048 0.00600437i
433433 −1.73769e13 −1.14165 −0.570823 0.821073i 0.693376π-0.693376\pi
−0.570823 + 0.821073i 0.693376π0.693376\pi
434434 −4.86800e12 + 4.76764e12i −0.316156 + 0.309639i
435435 2.09179e13 1.34299
436436 1.12410e13 + 2.34178e11i 0.713464 + 0.0148633i
437437 1.35165e13i 0.848122i
438438 1.96505e13 1.92454e13i 1.21900 1.19387i
439439 1.05808e13i 0.648928i −0.945898 0.324464i 0.894816π-0.894816\pi
0.945898 0.324464i 0.105184π-0.105184\pi
440440 −1.03786e13 + 9.74949e12i −0.629324 + 0.591178i
441441 2.50267e12 0.150041
442442 −1.83626e13 1.87491e13i −1.08849 1.11140i
443443 2.18951e13 1.28330 0.641651 0.766996i 0.278250π-0.278250\pi
0.641651 + 0.766996i 0.278250π0.278250\pi
444444 −2.87016e13 5.97927e11i −1.66338 0.0346524i
445445 9.50649e11i 0.0544779i
446446 1.17701e13 + 1.20179e13i 0.666970 + 0.681009i
447447 3.28679e13i 1.84176i
448448 1.67372e13 + 1.04725e12i 0.927453 + 0.0580308i
449449 −3.53942e13 −1.93954 −0.969772 0.244011i 0.921537π-0.921537\pi
−0.969772 + 0.244011i 0.921537π0.921537\pi
450450 −6.64117e12 + 6.50426e12i −0.359900 + 0.352480i
451451 1.16780e12 0.0625875
452452 4.32739e11 2.07722e13i 0.0229368 1.10101i
453453 6.31374e10i 0.00330975i
454454 −1.99758e13 + 1.95640e13i −1.03568 + 1.01433i
455455 3.22014e13i 1.65127i
456456 −2.73126e13 2.90749e13i −1.38528 1.47467i
457457 −1.93883e13 −0.972653 −0.486326 0.873777i 0.661663π-0.661663\pi
−0.486326 + 0.873777i 0.661663π0.661663\pi
458458 −1.85890e13 1.89803e13i −0.922422 0.941839i
459459 −3.10514e12 −0.152412
460460 −3.14631e11 + 1.51029e13i −0.0152761 + 0.733281i
461461 1.69421e13i 0.813696i −0.913496 0.406848i 0.866628π-0.866628\pi
0.913496 0.406848i 0.133372π-0.133372\pi
462462 1.41793e13 + 1.44778e13i 0.673666 + 0.687847i
463463 4.19900e13i 1.97352i 0.162198 + 0.986758i 0.448142π0.448142\pi
−0.162198 + 0.986758i 0.551858π0.551858\pi
464464 −6.87518e11 + 1.64939e13i −0.0319664 + 0.766891i
465465 1.81145e13 0.833224
466466 1.90525e13 1.86598e13i 0.867009 0.849135i
467467 9.55773e12 0.430299 0.215150 0.976581i 0.430976π-0.430976\pi
0.215150 + 0.976581i 0.430976π0.430976\pi
468468 3.63165e13 + 7.56564e11i 1.61761 + 0.0336990i
469469 9.76783e12i 0.430461i
470470 2.03634e13 1.99436e13i 0.887894 0.869589i
471471 1.55416e13i 0.670488i
472472 1.40488e12 + 1.49553e12i 0.0599694 + 0.0638390i
473473 −4.71346e12 −0.199083
474474 2.40050e13 + 2.45103e13i 1.00325 + 1.02437i
475475 −1.54700e13 −0.639768
476476 2.40003e13 + 4.99987e11i 0.982158 + 0.0204608i
477477 2.01115e13i 0.814427i
478478 −2.05842e13 2.10175e13i −0.824886 0.842250i
479479 4.05634e13i 1.60863i −0.594201 0.804317i 0.702532π-0.702532\pi
0.594201 0.804317i 0.297468π-0.297468\pi
480480 −2.98412e13 3.31230e13i −1.17114 1.29994i
481481 4.35036e13 1.68966
482482 −3.58346e13 + 3.50958e13i −1.37742 + 1.34903i
483483 2.14978e13 0.817823
484484 −2.70352e11 + 1.29774e13i −0.0101790 + 0.488608i
485485 5.90127e13i 2.19906i
486486 −2.77894e13 + 2.72165e13i −1.02494 + 1.00381i
487487 5.27934e13i 1.92723i −0.267286 0.963617i 0.586127π-0.586127\pi
0.267286 0.963617i 0.413873π-0.413873\pi
488488 −2.43915e13 + 2.29130e13i −0.881331 + 0.827910i
489489 −3.73242e13 −1.33489
490490 3.25697e12 + 3.32553e12i 0.115301 + 0.117728i
491491 −2.41468e13 −0.846158 −0.423079 0.906093i 0.639051π-0.639051\pi
−0.423079 + 0.906093i 0.639051π0.639051\pi
492492 −7.61531e10 + 3.65549e12i −0.00264157 + 0.126800i
493493 2.36309e13i 0.811419i
494494 4.22980e13 + 4.31884e13i 1.43776 + 1.46802i
495495 2.82135e13i 0.949360i
496496 −5.95377e11 + 1.42834e13i −0.0198328 + 0.475799i
497497 3.21021e13 1.05865
498498 2.21776e13 2.17204e13i 0.724050 0.709123i
499499 2.21286e11 0.00715238 0.00357619 0.999994i 0.498862π-0.498862\pi
0.00357619 + 0.999994i 0.498862π0.498862\pi
500500 2.04420e13 + 4.25859e11i 0.654145 + 0.0136275i
501501 5.81735e13i 1.84305i
502502 4.20536e13 4.11867e13i 1.31912 1.29193i
503503 9.04543e12i 0.280924i 0.990086 + 0.140462i 0.0448588π0.0448588\pi
−0.990086 + 0.140462i 0.955141π0.955141\pi
504504 −2.42174e13 + 2.27495e13i −0.744689 + 0.699550i
505505 1.45580e13 0.443247
506506 −1.00800e13 1.02922e13i −0.303883 0.310280i
507507 −5.65702e13 −1.68868
508508 6.41221e12 + 1.33583e11i 0.189535 + 0.00394849i
509509 2.24139e13i 0.656036i −0.944671 0.328018i 0.893619π-0.893619\pi
0.944671 0.328018i 0.106381π-0.106381\pi
510510 −4.46542e13 4.55941e13i −1.29423 1.32147i
511511 3.81267e13i 1.09427i
512512 2.70985e13 2.24413e13i 0.770185 0.637821i
513513 7.15266e12 0.201317
514514 −1.07321e13 + 1.05108e13i −0.299135 + 0.292968i
515515 3.50243e13 0.966793
516516 3.07367e11 1.47542e13i 0.00840249 0.403335i
517517 2.71819e13i 0.735915i
518518 −2.84301e13 + 2.78440e13i −0.762305 + 0.746590i
519519 9.62269e13i 2.55540i
520520 4.62569e13 + 4.92416e13i 1.21663 + 1.29514i
521521 2.19502e12 0.0571807 0.0285904 0.999591i 0.490898π-0.490898\pi
0.0285904 + 0.999591i 0.490898π0.490898\pi
522522 −2.28862e13 2.33679e13i −0.590501 0.602930i
523523 −2.91933e13 −0.746062 −0.373031 0.927819i 0.621681π-0.621681\pi
−0.373031 + 0.927819i 0.621681π0.621681\pi
524524 −1.06462e11 + 5.11039e12i −0.00269488 + 0.129359i
525525 2.46048e13i 0.616913i
526526 −4.53945e13 4.63500e13i −1.12739 1.15112i
527527 2.04639e13i 0.503425i
528528 4.24798e13 + 1.77069e12i 1.03517 + 0.0431493i
529529 2.61438e13 0.631089
530530 −2.67240e13 + 2.61731e13i −0.639031 + 0.625857i
531531 −4.06551e12 −0.0963036
532532 −5.52843e13 1.15171e12i −1.29731 0.0270263i
533533 5.54070e12i 0.128804i
534534 2.02788e12 1.98607e12i 0.0467020 0.0457392i
535535 1.47599e13i 0.336755i
536536 −1.40314e13 1.49368e13i −0.317158 0.337623i
537537 −5.47927e13 −1.22702
538538 −3.46840e13 3.54141e13i −0.769516 0.785714i
539539 −4.43905e12 −0.0975768
540540 7.99211e12 + 1.66496e11i 0.174058 + 0.00362606i
541541 4.86387e12i 0.104953i 0.998622 + 0.0524766i 0.0167115π0.0167115\pi
−0.998622 + 0.0524766i 0.983288π0.983288\pi
542542 6.15194e13 + 6.28143e13i 1.31527 + 1.34296i
543543 5.46218e12i 0.115709i
544544 3.74189e13 3.37115e13i 0.785410 0.707593i
545545 −4.14336e13 −0.861728
546546 6.86904e13 6.72743e13i 1.41557 1.38639i
547547 3.29297e13 0.672436 0.336218 0.941784i 0.390852π-0.390852\pi
0.336218 + 0.941784i 0.390852π0.390852\pi
548548 −1.13345e12 + 5.44076e13i −0.0229350 + 1.10092i
549549 6.63067e13i 1.32952i
550550 1.17796e13 1.15368e13i 0.234055 0.229230i
551551 5.44335e13i 1.07179i
552552 3.28740e13 3.08814e13i 0.641442 0.602562i
553553 4.75557e13 0.919554
554554 7.70817e12 + 7.87043e12i 0.147708 + 0.150817i
555555 1.05792e14 2.00904
556556 6.92169e11 3.32254e13i 0.0130268 0.625311i
557557 4.29354e13i 0.800828i 0.916334 + 0.400414i 0.131134π0.131134\pi
−0.916334 + 0.400414i 0.868866π0.868866\pi
558558 −1.98190e13 2.02361e13i −0.366362 0.374073i
559559 2.23632e13i 0.409709i
560560 −6.17458e13 2.57376e12i −1.12116 0.0467335i
561561 6.08610e13 1.09528
562562 −1.18169e13 + 1.15732e13i −0.210776 + 0.206430i
563563 −1.01247e14 −1.78994 −0.894970 0.446126i 0.852803π-0.852803\pi
−0.894970 + 0.446126i 0.852803π0.852803\pi
564564 −8.50854e13 1.77255e12i −1.49094 0.0310600i
565565 7.65652e13i 1.32981i
566566 2.24269e13 2.19645e13i 0.386088 0.378129i
567567 4.84996e13i 0.827604i
568568 4.90898e13 4.61142e13i 0.830327 0.779997i
569569 −3.75395e12 −0.0629401 −0.0314701 0.999505i 0.510019π-0.510019\pi
−0.0314701 + 0.999505i 0.510019π0.510019\pi
570570 1.02860e14 + 1.05026e14i 1.70952 + 1.74550i
571571 −4.82773e13 −0.795358 −0.397679 0.917525i 0.630184π-0.630184\pi
−0.397679 + 0.917525i 0.630184π0.630184\pi
572572 −6.44156e13 1.34194e12i −1.05199 0.0219156i
573573 7.71618e13i 1.24919i
574574 3.54626e12 + 3.62090e12i 0.0569129 + 0.0581109i
575575 1.74914e13i 0.278283i
576576 −4.35337e12 + 6.95760e13i −0.0686615 + 1.09735i
577577 −3.01929e13 −0.472091 −0.236046 0.971742i 0.575851π-0.575851\pi
−0.236046 + 0.971742i 0.575851π0.575851\pi
578578 5.41816e12 5.30646e12i 0.0839871 0.0822556i
579579 6.47232e13 0.994644
580580 1.26707e12 6.08219e13i 0.0193047 0.926659i
581581 4.30299e13i 0.649964i
582582 −1.25883e14 + 1.23288e14i −1.88518 + 1.84631i
583583 3.56723e13i 0.529649i
584584 −5.47685e13 5.83025e13i −0.806244 0.858268i
585585 −1.33860e14 −1.95377
586586 8.48516e13 + 8.66377e13i 1.22793 + 1.25377i
587587 5.82710e13 0.836107 0.418053 0.908422i 0.362712π-0.362712\pi
0.418053 + 0.908422i 0.362712π0.362712\pi
588588 2.89473e11 1.38952e13i 0.00411833 0.197687i
589589 4.71383e13i 0.664963i
590590 −5.29085e12 5.40222e12i −0.0740057 0.0755635i
591591 1.01958e13i 0.141411i
592592 −3.47712e12 + 8.34178e13i −0.0478202 + 1.14723i
593593 −3.13152e13 −0.427052 −0.213526 0.976937i 0.568495π-0.568495\pi
−0.213526 + 0.976937i 0.568495π0.568495\pi
594594 −5.44639e12 + 5.33411e12i −0.0736506 + 0.0721323i
595595 −8.84635e13 −1.18626
596596 9.55681e13 + 1.99093e12i 1.27081 + 0.0264743i
597597 1.14528e14i 1.51022i
598598 −4.88316e13 + 4.78249e13i −0.638550 + 0.625386i
599599 7.34955e13i 0.953074i 0.879154 + 0.476537i 0.158108π0.158108\pi
−0.879154 + 0.476537i 0.841892π0.841892\pi
600600 3.53445e13 + 3.76251e13i 0.454533 + 0.483862i
601601 1.07112e14 1.36605 0.683024 0.730396i 0.260665π-0.260665\pi
0.683024 + 0.730396i 0.260665π0.260665\pi
602602 −1.43133e13 1.46146e13i −0.181033 0.184843i
603603 4.06046e13 0.509318
604604 −1.83581e11 3.82446e9i −0.00228372 4.75757e-5i
605605 4.78339e13i 0.590145i
606606 −3.04143e13 3.10545e13i −0.372147 0.379981i
607607 1.36295e13i 0.165401i 0.996574 + 0.0827004i 0.0263545π0.0263545\pi
−0.996574 + 0.0827004i 0.973646π0.973646\pi
608608 −8.61940e13 + 7.76541e13i −1.03743 + 0.934645i
609609 −8.65756e13 −1.03350
610610 8.81079e13 8.62915e13i 1.04319 1.02169i
611611 1.28966e14 1.51450
612612 −2.07843e12 + 9.97685e13i −0.0242091 + 1.16208i
613613 1.16805e14i 1.34946i 0.738066 + 0.674729i 0.235739π0.235739\pi
−0.738066 + 0.674729i 0.764261π0.764261\pi
614614 1.08411e14 1.06176e14i 1.24231 1.21670i
615615 1.34739e13i 0.153150i
616616 4.29551e13 4.03514e13i 0.484296 0.454941i
617617 4.22466e13 0.472461 0.236230 0.971697i 0.424088π-0.424088\pi
0.236230 + 0.971697i 0.424088π0.424088\pi
618618 −7.31719e13 7.47122e13i −0.811712 0.828798i
619619 1.04957e14 1.15493 0.577466 0.816415i 0.304042π-0.304042\pi
0.577466 + 0.816415i 0.304042π0.304042\pi
620620 1.09726e12 5.26706e13i 0.0119771 0.574923i
621621 8.08727e12i 0.0875677i
622622 −3.98244e13 4.06627e13i −0.427757 0.436761i
623623 3.93457e12i 0.0419234i
624624 8.40113e12 2.01547e14i 0.0888004 2.13037i
625625 −1.19042e14 −1.24825
626626 −5.01776e13 + 4.91431e13i −0.521961 + 0.511200i
627627 −1.40193e14 −1.44673
628628 −4.51895e13 9.41411e11i −0.462635 0.00963787i
629629 1.19513e14i 1.21384i
630630 8.74790e13 8.56756e13i 0.881457 0.863285i
631631 2.87613e12i 0.0287516i −0.999897 0.0143758i 0.995424π-0.995424\pi
0.999897 0.0143758i 0.00457612π-0.00457612\pi
632632 7.27212e13 6.83133e13i 0.721233 0.677516i
633633 2.18463e14 2.14960
634634 −5.16038e13 5.26901e13i −0.503774 0.514378i
635635 −2.36350e13 −0.228922
636636 1.11662e14 + 2.32621e12i 1.07305 + 0.0223544i
637637 2.10613e13i 0.200811i
638638 4.05938e13 + 4.14483e13i 0.384023 + 0.392106i
639639 1.33447e14i 1.25258i
640640 −9.81175e13 + 8.47614e13i −0.913791 + 0.789402i
641641 −3.00941e13 −0.278094 −0.139047 0.990286i 0.544404π-0.544404\pi
−0.139047 + 0.990286i 0.544404π0.544404\pi
642642 −3.14850e13 + 3.08359e13i −0.288688 + 0.282737i
643643 −1.66359e14 −1.51353 −0.756764 0.653689i 0.773221π-0.773221\pi
−0.756764 + 0.653689i 0.773221π0.773221\pi
644644 1.30220e12 6.25081e13i 0.0117557 0.564296i
645645 5.43829e13i 0.487151i
646646 −1.18647e14 + 1.16201e14i −1.05461 + 1.03287i
647647 1.73339e14i 1.52889i −0.644690 0.764444i 0.723013π-0.723013\pi
0.644690 0.764444i 0.276987π-0.276987\pi
648648 6.96691e13 + 7.41645e13i 0.609768 + 0.649114i
649649 7.21111e12 0.0626295
650650 −5.47368e13 5.58890e13i −0.471751 0.481681i
651651 −7.49728e13 −0.641207
652652 −2.26086e12 + 1.08525e14i −0.0191883 + 0.921072i
653653 1.89861e14i 1.59908i 0.600612 + 0.799541i 0.294924π0.294924\pi
−0.600612 + 0.799541i 0.705076π0.705076\pi
654654 8.65620e13 + 8.83841e13i 0.723500 + 0.738730i
655655 1.88366e13i 0.156241i
656656 1.06242e13 + 4.42852e11i 0.0874538 + 0.00364535i
657657 1.58492e14 1.29473
658658 −8.42805e13 + 8.25430e13i −0.683278 + 0.669192i
659659 −9.80342e13 −0.788771 −0.394385 0.918945i 0.629042π-0.629042\pi
−0.394385 + 0.918945i 0.629042π0.629042\pi
660660 −1.56646e14 3.26333e12i −1.25083 0.0260580i
661661 1.54197e14i 1.22199i −0.791634 0.610996i 0.790769π-0.790769\pi
0.791634 0.610996i 0.209231π-0.209231\pi
662662 8.21638e13 8.04700e13i 0.646236 0.632913i
663663 2.88758e14i 2.25406i
664664 −6.18119e13 6.58004e13i −0.478886 0.509786i
665665 2.03775e14 1.56690
666666 −1.15747e14 1.18183e14i −0.883359 0.901953i
667667 6.15461e13 0.466199
668668 1.69148e14 + 3.52378e12i 1.27170 + 0.0264927i
669669 1.85089e14i 1.38118i
670670 5.28428e13 + 5.39551e13i 0.391392 + 0.399631i
671671 1.17610e14i 0.864634i
672672 1.23508e14 + 1.37090e14i 0.901254 + 1.00037i
673673 −6.70067e13 −0.485336 −0.242668 0.970109i 0.578023π-0.578023\pi
−0.242668 + 0.970109i 0.578023π0.578023\pi
674674 −3.57472e13 + 3.50103e13i −0.257006 + 0.251707i
675675 −9.25608e12 −0.0660554
676676 −3.42666e12 + 1.64486e14i −0.0242738 + 1.16519i
677677 1.71430e14i 1.20543i −0.797956 0.602715i 0.794085π-0.794085\pi
0.797956 0.602715i 0.205915π-0.205915\pi
678678 1.63325e14 1.59958e14i 1.14000 1.11650i
679679 2.44243e14i 1.69229i
680680 −1.35276e14 + 1.27077e14i −0.930417 + 0.874020i
681681 −3.07650e14 −2.10049
682682 3.51535e13 + 3.58934e13i 0.238257 + 0.243273i
683683 5.05521e13 0.340123 0.170061 0.985433i 0.445603π-0.445603\pi
0.170061 + 0.985433i 0.445603π0.445603\pi
684684 4.78764e12 2.29816e14i 0.0319773 1.53497i
685685 2.00543e14i 1.32970i
686686 −1.12262e14 1.14625e14i −0.738942 0.754496i
687687 2.92319e14i 1.91017i
688688 −4.28812e13 1.78743e12i −0.278179 0.0115954i
689689 −1.69249e14 −1.09001
690690 −1.18749e14 + 1.16301e14i −0.759248 + 0.743596i
691691 5.33777e13 0.338821 0.169410 0.985546i 0.445814π-0.445814\pi
0.169410 + 0.985546i 0.445814π0.445814\pi
692692 2.79794e14 + 5.82881e12i 1.76322 + 0.0367324i
693693 1.16771e14i 0.730580i
694694 −4.05521e11 + 3.97161e11i −0.00251893 + 0.00246700i
695695 1.22467e14i 0.755256i
696696 −1.32389e14 + 1.24365e14i −0.810601 + 0.761467i
697697 1.52214e13 0.0925317
698698 −4.34411e13 4.43555e13i −0.262195 0.267714i
699699 2.93431e14 1.75841
700700 7.15421e13 + 1.49040e12i 0.425668 + 0.00886775i
701701 3.55178e13i 0.209824i −0.994481 0.104912i 0.966544π-0.966544\pi
0.994481 0.104912i 0.0334561π-0.0334561\pi
702702 2.53079e13 + 2.58406e13i 0.148447 + 0.151572i
703703 2.75297e14i 1.60334i
704704 7.72170e12 1.23409e14i 0.0446529 0.713647i
705705 3.13620e14 1.80077
706706 1.01004e14 9.89222e13i 0.575860 0.563988i
707707 −6.02531e13 −0.341101
708708 −4.70240e11 + 2.25724e13i −0.00264334 + 0.126885i
709709 2.13491e14i 1.19165i −0.803115 0.595824i 0.796826π-0.796826\pi
0.803115 0.595824i 0.203174π-0.203174\pi
710710 −1.77324e14 + 1.73668e14i −0.982824 + 0.962562i
711711 1.97688e14i 1.08801i
712712 −5.65196e12 6.01666e12i −0.0308887 0.0328818i
713713 5.32977e13 0.289242
714714 1.84816e14 + 1.88706e14i 0.995974 + 1.01694i
715715 2.37432e14 1.27060
716716 −3.31899e12 + 1.59318e14i −0.0176377 + 0.846641i
717717 3.23693e14i 1.70820i
718718 9.92071e13 + 1.01295e14i 0.519901 + 0.530844i
719719 2.65916e14i 1.38389i 0.721952 + 0.691943i 0.243245π0.243245\pi
−0.721952 + 0.691943i 0.756755π0.756755\pi
720720 1.06991e13 2.56676e14i 0.0552947 1.32655i
721721 −1.44959e14 −0.743995
722722 1.33134e14 1.30390e14i 0.678585 0.664596i
723723 −5.51893e14 −2.79360
724724 −1.58821e13 3.30864e11i −0.0798389 0.00166325i
725725 7.04410e13i 0.351670i
726726 −1.02037e14 + 9.99334e13i −0.505911 + 0.495482i
727727 1.56999e14i 0.773082i 0.922272 + 0.386541i 0.126330π0.126330\pi
−0.922272 + 0.386541i 0.873670π0.873670\pi
728728 −1.91449e14 2.03802e14i −0.936260 0.996672i
729729 −2.44622e14 −1.18812
730730 2.06261e14 + 2.10602e14i 0.994953 + 1.01590i
731731 −6.14361e13 −0.294332
732732 −3.68146e14 7.66941e12i −1.75172 0.0364927i
733733 2.64144e14i 1.24831i 0.781302 + 0.624153i 0.214556π0.214556\pi
−0.781302 + 0.624153i 0.785444π0.785444\pi
734734 −5.99176e13 6.11789e13i −0.281238 0.287158i
735735 5.12169e13i 0.238768i
736736 −8.78008e13 9.74566e13i −0.406546 0.451255i
737737 −7.20216e13 −0.331227
738738 −1.50520e13 + 1.47417e13i −0.0687563 + 0.0673389i
739739 2.68052e14 1.21618 0.608089 0.793869i 0.291936π-0.291936\pi
0.608089 + 0.793869i 0.291936π0.291936\pi
740740 6.40822e12 3.07606e14i 0.0288788 1.38623i
741741 6.65150e14i 2.97734i
742742 1.10606e14 1.08326e14i 0.491766 0.481628i
743743 9.68880e13i 0.427884i 0.976846 + 0.213942i 0.0686303π0.0686303\pi
−0.976846 + 0.213942i 0.931370π0.931370\pi
744744 −1.14647e14 + 1.07697e14i −0.502918 + 0.472434i
745745 −3.52258e14 −1.53490
746746 −2.22116e14 2.26792e14i −0.961360 0.981596i
747747 1.78874e14 0.769032
748748 3.68657e12 1.76962e14i 0.0157440 0.755740i
749749 6.10885e13i 0.259149i
750750 1.57415e14 + 1.60729e14i 0.663347 + 0.677310i
751751 2.13814e13i 0.0895026i −0.998998 0.0447513i 0.985750π-0.985750\pi
0.998998 0.0447513i 0.0142495π-0.0142495\pi
752752 −1.03079e13 + 2.47291e14i −0.0428627 + 1.02830i
753753 6.47674e14 2.67536
754754 1.96653e14 1.92599e14i 0.806947 0.790311i
755755 6.76669e11 0.00275830
756756 −3.30779e13 6.89098e11i −0.133946 0.00279043i
757757 3.45330e14i 1.38917i −0.719412 0.694584i 0.755589π-0.755589\pi
0.719412 0.694584i 0.244411π-0.244411\pi
758758 1.41774e13 1.38851e13i 0.0566565 0.0554885i
759759 1.58511e14i 0.629290i
760760 3.11608e14 2.92720e14i 1.22897 1.15447i
761761 1.01279e14 0.396822 0.198411 0.980119i 0.436422π-0.436422\pi
0.198411 + 0.980119i 0.436422π0.436422\pi
762762 4.93777e13 + 5.04170e13i 0.192201 + 0.196247i
763763 1.71486e14 0.663142
764764 −2.24359e14 4.67397e12i −0.861940 0.0179564i
765765 3.67740e14i 1.40357i
766766 −1.16105e14 1.18549e14i −0.440259 0.449526i
767767 3.42135e13i 0.128890i
768768 3.85794e14 + 3.22182e13i 1.44394 + 0.120585i
769769 −2.20211e14 −0.818854 −0.409427 0.912343i 0.634271π-0.634271\pi
−0.409427 + 0.912343i 0.634271π0.634271\pi
770770 −1.55164e14 + 1.51965e14i −0.573241 + 0.561424i
771771 −1.65286e14 −0.606687
772772 3.92052e12 1.88192e14i 0.0142974 0.686302i
773773 1.15285e14i 0.417709i 0.977947 + 0.208855i 0.0669735π0.0669735\pi
−0.977947 + 0.208855i 0.933026π0.933026\pi
774774 6.07524e13 5.95000e13i 0.218705 0.214196i
775775 6.10005e13i 0.218185i
776776 3.50853e14 + 3.73492e14i 1.24686 + 1.32731i
777777 −4.37855e14 −1.54606
778778 4.14196e13 + 4.22915e13i 0.145314 + 0.148373i
779779 −3.50623e13 −0.122223
780780 −1.54830e13 + 7.43214e14i −0.0536269 + 2.57419i
781781 2.36700e14i 0.814596i
782782 −1.31384e14 1.34150e14i −0.449273 0.458730i
783783 3.25689e13i 0.110661i
784784 −4.03848e13 1.68337e12i −0.136345 0.00568328i
785785 1.66566e14 0.558775
786786 −4.01813e13 + 3.93529e13i −0.133940 + 0.131179i
787787 2.91930e14 0.966953 0.483476 0.875357i 0.339374π-0.339374\pi
0.483476 + 0.875357i 0.339374π0.339374\pi
788788 2.96457e13 + 6.17595e11i 0.0975731 + 0.00203270i
789789 7.13843e14i 2.33463i
790790 −2.62686e14 + 2.57271e14i −0.853694 + 0.836094i
791791 3.16890e14i 1.02335i
792792 1.67740e14 + 1.78563e14i 0.538282 + 0.573015i
793793 5.58007e14 1.77940
794794 1.53271e14 + 1.56497e14i 0.485687 + 0.495910i
795795 −4.11580e14 −1.29604
796796 −3.33007e14 6.93739e12i −1.04205 0.0217085i
797797 3.56212e14i 1.10769i 0.832621 + 0.553843i 0.186839π0.186839\pi
−0.832621 + 0.553843i 0.813161π0.813161\pi
798798 −4.25721e14 4.34682e14i −1.31556 1.34325i
799799 3.54295e14i 1.08800i
800800 1.11542e14 1.00490e14i 0.340398 0.306672i
801801 1.63559e13 0.0496035
802802 −2.45497e14 + 2.40436e14i −0.739903 + 0.724649i
803803 −2.81121e14 −0.842007
804804 4.69656e12 2.25443e14i 0.0139798 0.671054i
805805 2.30401e14i 0.681562i
806806 1.70298e14 1.66787e14i 0.500650 0.490329i
807807 5.45417e14i 1.59353i
808808 −9.21378e13 + 8.65529e13i −0.267535 + 0.251319i
809809 −2.42201e14 −0.698930 −0.349465 0.936949i 0.613637π-0.613637\pi
−0.349465 + 0.936949i 0.613637π0.613637\pi
810810 −2.62377e14 2.67900e14i −0.752490 0.768329i
811811 −4.06752e14 −1.15938 −0.579689 0.814838i 0.696826π-0.696826\pi
−0.579689 + 0.814838i 0.696826π0.696826\pi
812812 −5.24420e12 + 2.51731e14i −0.0148559 + 0.713110i
813813 9.67412e14i 2.72370i
814814 2.05303e14 + 2.09625e14i 0.574478 + 0.586570i
815815 4.00018e14i 1.11248i
816816 5.53690e14 + 2.30796e13i 1.53044 + 0.0637936i
817817 1.41517e14 0.388776
818818 4.10241e14 4.01783e14i 1.12014 1.09705i
819819 5.54024e14 1.50352
820820 −3.91773e13 8.16163e11i −0.105673 0.00220144i
821821 4.04166e14i 1.08354i 0.840528 + 0.541768i 0.182245π0.182245\pi
−0.840528 + 0.541768i 0.817755π0.817755\pi
822822 −4.27788e14 + 4.18969e14i −1.13991 + 1.11641i
823823 1.42442e14i 0.377259i 0.982048 + 0.188630i 0.0604045π0.0604045\pi
−0.982048 + 0.188630i 0.939595π0.939595\pi
824824 −2.21669e14 + 2.08232e14i −0.583537 + 0.548166i
825825 1.81420e14 0.474695
826826 2.18979e13 + 2.23588e13i 0.0569511 + 0.0581499i
827827 −3.85554e13 −0.0996684 −0.0498342 0.998758i 0.515869π-0.515869\pi
−0.0498342 + 0.998758i 0.515869π0.515869\pi
828828 2.59845e14 + 5.41322e12i 0.667670 + 0.0139093i
829829 2.35400e14i 0.601221i −0.953747 0.300610i 0.902810π-0.902810\pi
0.953747 0.300610i 0.0971904π-0.0971904\pi
830830 2.32787e14 + 2.37687e14i 0.590973 + 0.603412i
831831 1.21214e14i 0.305877i
832832 −5.85519e14 3.66360e13i −1.46867 0.0918949i
833833 −5.78595e13 −0.144261
834834 2.61240e14 2.55854e14i 0.647455 0.634107i
835835 −6.23469e14 −1.53597
836836 −8.49198e12 + 4.07630e14i −0.0207959 + 0.998241i
837837 2.82040e13i 0.0686568i
838838 2.32447e14 2.27655e14i 0.562475 0.550879i
839839 5.54263e14i 1.33323i −0.745401 0.666616i 0.767742π-0.767742\pi
0.745401 0.666616i 0.232258π-0.232258\pi
840840 −4.65566e14 4.95607e14i −1.11323 1.18506i
841841 1.72850e14 0.410857
842842 3.10544e14 + 3.17081e14i 0.733774 + 0.749220i
843843 −1.81993e14 −0.427481
844844 1.32331e13 6.35212e14i 0.0308993 1.48322i
845845 6.06286e14i 1.40732i
846846 −3.43129e14 3.50352e14i −0.791782 0.808449i
847847 1.97976e14i 0.454146i
848848 1.35276e13 3.24533e14i 0.0308490 0.740082i
849849 3.45400e14 0.783039
850850 1.53538e14 1.50373e14i 0.346036 0.338902i
851851 3.11269e14 0.697410
852852 7.40921e14 + 1.54353e13i 1.65034 + 0.0343808i
853853 2.17078e14i 0.480696i 0.970687 + 0.240348i 0.0772615π0.0772615\pi
−0.970687 + 0.240348i 0.922738π0.922738\pi
854854 −3.64663e14 + 3.57145e14i −0.802790 + 0.786240i
855855 8.47086e14i 1.85395i
856856 8.77528e13 + 9.34151e13i 0.190938 + 0.203258i
857857 7.39171e14 1.59897 0.799485 0.600685i 0.205106π-0.205106\pi
0.799485 + 0.600685i 0.205106π0.205106\pi
858858 −4.96037e14 5.06478e14i −1.06679 1.08924i
859859 3.16235e14 0.676152 0.338076 0.941119i 0.390224π-0.390224\pi
0.338076 + 0.941119i 0.390224π0.390224\pi
860860 1.58126e14 + 3.29417e12i 0.336133 + 0.00700251i
861861 5.57661e13i 0.117857i
862862 −7.87601e12 8.04180e12i −0.0165489 0.0168973i
863863 3.17121e14i 0.662478i −0.943547 0.331239i 0.892533π-0.892533\pi
0.943547 0.331239i 0.107467π-0.107467\pi
864864 −5.15720e13 + 4.64623e13i −0.107114 + 0.0965011i
865865 −1.03130e15 −2.12964
866866 −3.97267e14 + 3.89077e14i −0.815630 + 0.798815i
867867 8.34458e13 0.170337
868868 −4.54137e12 + 2.17994e14i −0.00921698 + 0.442432i
869869 3.50645e14i 0.707569i
870870 4.78222e14 4.68363e14i 0.959475 0.939695i
871871 3.41710e14i 0.681658i
872872 2.62233e14 2.46338e14i 0.520122 0.488595i
873873 −1.01531e15 −2.00230
874874 3.02643e14 + 3.09013e14i 0.593435 + 0.605926i
875875 3.11852e14 0.608007
876876 1.83320e13 8.79971e14i 0.0355378 1.70588i
877877 5.34325e14i 1.02993i 0.857211 + 0.514965i 0.172195π0.172195\pi
−0.857211 + 0.514965i 0.827805π0.827805\pi
878878 −2.36910e14 2.41897e14i −0.454058 0.463616i
879879 1.33432e15i 2.54282i
880880 −1.89772e13 + 4.55273e14i −0.0359600 + 0.862698i
881881 −1.20104e13 −0.0226297 −0.0113148 0.999936i 0.503602π-0.503602\pi
−0.0113148 + 0.999936i 0.503602π0.503602\pi
882882 5.72156e13 5.60361e13i 0.107194 0.104984i
883883 6.89886e14 1.28521 0.642605 0.766198i 0.277854π-0.277854\pi
0.642605 + 0.766198i 0.277854π0.277854\pi
884884 −8.39605e14 1.74911e13i −1.55530 0.0324008i
885885 8.32003e13i 0.153253i
886886 5.00563e14 4.90244e14i 0.916833 0.897932i
887887 7.40300e13i 0.134831i 0.997725 + 0.0674154i 0.0214753π0.0214753\pi
−0.997725 + 0.0674154i 0.978525π0.978525\pi
888888 −6.69559e14 + 6.28974e14i −1.21262 + 1.13912i
889889 9.78211e13 0.176167
890890 2.12855e13 + 2.17336e13i 0.0381184 + 0.0389208i
891891 3.57604e14 0.636816
892892 5.38173e14 + 1.12115e13i 0.953010 + 0.0198536i
893893 8.16114e14i 1.43712i
894894 7.35929e14 + 7.51420e14i 1.28869 + 1.31582i
895895 5.87236e14i 1.02258i
896896 4.06091e14 3.50812e14i 0.703207 0.607484i
897897 −7.52063e14 −1.29507
898898 −8.09176e14 + 7.92494e14i −1.38567 + 1.35711i
899899 −2.14639e14 −0.365519
900900 −6.19557e12 + 2.97399e14i −0.0104922 + 0.503647i
901901 4.64960e14i 0.783054i
902902 2.66982e13 2.61478e13i 0.0447146 0.0437927i
903903 2.25081e14i 0.374887i
904904 −4.55208e14 4.84581e14i −0.753994 0.802646i
905905 5.85404e13 0.0964301
906906 −1.41368e12 1.44344e12i −0.00231585 0.00236459i
907907 −1.10129e15 −1.79418 −0.897088 0.441852i 0.854322π-0.854322\pi
−0.897088 + 0.441852i 0.854322π0.854322\pi
908908 −1.86355e13 + 8.94537e14i −0.0301933 + 1.44934i
909909 2.50471e14i 0.403587i
910910 7.21006e14 + 7.36183e14i 1.15540 + 1.17972i
911911 5.75678e14i 0.917461i −0.888575 0.458730i 0.848304π-0.848304\pi
0.888575 0.458730i 0.151696π-0.151696\pi
912912 −1.27542e15 5.31635e13i −2.02152 0.0842635i
913913 −3.17274e14 −0.500128
914914 −4.43251e14 + 4.34114e14i −0.694895 + 0.680569i
915915 1.35696e15 2.11574
916916 −8.49960e14 1.77068e13i −1.31802 0.0274576i
917917 7.79613e13i 0.120235i
918918 −7.09893e13 + 6.95258e13i −0.108888 + 0.106643i
919919 2.49831e14i 0.381126i −0.981675 0.190563i 0.938969π-0.938969\pi
0.981675 0.190563i 0.0610314π-0.0610314\pi
920920 3.30968e14 + 3.52324e14i 0.502166 + 0.534569i
921921 1.66965e15 2.51957
922922 −3.79342e14 3.87327e14i −0.569346 0.581331i
923923 −1.12303e15 −1.67642
924924 6.48330e14 + 1.35064e13i 0.962578 + 0.0200530i
925925 3.56255e14i 0.526081i
926926 9.40178e14 + 9.59968e14i 1.38088 + 1.40994i
927927 6.02593e14i 0.880289i
928928 3.53589e14 + 3.92475e14i 0.513759 + 0.570259i
929929 −5.75740e14 −0.832046 −0.416023 0.909354i 0.636576π-0.636576\pi
−0.416023 + 0.909354i 0.636576π0.636576\pi
930930 4.14131e14 4.05594e14i 0.595283 0.583011i
931931 1.33279e14 0.190552
932932 1.77742e13 8.53193e14i 0.0252761 1.21330i
933933 6.26252e14i 0.885811i
934934 2.18507e14 2.14003e14i 0.307420 0.301082i
935935 6.52272e14i 0.912789i
936936 8.47201e14 7.95849e14i 1.17925 1.10777i
937937 4.19947e14 0.581428 0.290714 0.956810i 0.406107π-0.406107\pi
0.290714 + 0.956810i 0.406107π0.406107\pi
938938 −2.18707e14 2.23311e14i −0.301196 0.307536i
939939 −7.72792e14 −1.05861
940940 1.89971e13 9.11895e14i 0.0258850 1.24253i
941941 4.76423e14i 0.645721i −0.946447 0.322860i 0.895356π-0.895356\pi
0.946447 0.322860i 0.104644π-0.104644\pi
942942 −3.47985e14 3.55310e14i −0.469143 0.479019i
943943 3.96438e13i 0.0531639i
944944 6.56039e13 + 2.73458e12i 0.0875125 + 0.00364780i
945945 1.21923e14 0.161781
946946 −1.07758e14 + 1.05537e14i −0.142231 + 0.139299i
947947 7.31112e14 0.959918 0.479959 0.877291i 0.340652π-0.340652\pi
0.479959 + 0.877291i 0.340652π0.340652\pi
948948 1.09760e15 + 2.28657e13i 1.43351 + 0.0298637i
949949 1.33379e15i 1.73283i
950950 −3.53673e14 + 3.46382e14i −0.457071 + 0.447649i
951951 8.11488e14i 1.04323i
952952 5.59885e14 5.25948e14i 0.716002 0.672602i
953953 4.33318e14 0.551242 0.275621 0.961266i 0.411116π-0.411116\pi
0.275621 + 0.961266i 0.411116π0.411116\pi
954954 4.50307e14 + 4.59786e14i 0.569858 + 0.581853i
955955 8.26974e14 1.04106
956956 −9.41185e14 1.96073e13i −1.17865 0.0245543i
957957 6.38352e14i 0.795244i
958958 −9.08237e14 9.27355e14i −1.12557 1.14926i
959959 8.30012e14i 1.02327i
960960 −1.42387e15 8.90915e13i −1.74628 0.109265i
961961 6.33755e14 0.773222
962962 9.94573e14 9.74070e14i 1.20715 1.18226i
963963 −2.53943e14 −0.306623
964964 −3.34302e13 + 1.60471e15i −0.0401563 + 1.92758i
965965 6.93665e14i 0.828921i
966966 4.91480e14 4.81348e14i 0.584279 0.572234i
967967 1.28203e15i 1.51623i 0.652120 + 0.758115i 0.273880π0.273880\pi
−0.652120 + 0.758115i 0.726120π0.726120\pi
968968 2.84390e14 + 3.02741e14i 0.334609 + 0.356200i
969969 −1.82730e15 −2.13890
970970 −1.32133e15 1.34914e15i −1.53869 1.57108i
971971 −1.03910e15 −1.20381 −0.601907 0.798566i 0.705592π-0.705592\pi
−0.601907 + 0.798566i 0.705592π0.705592\pi
972972 −2.59249e13 + 1.24444e15i −0.0298803 + 1.43431i
973973 5.06868e14i 0.581207i
974974 −1.18207e15 1.20695e15i −1.34849 1.37688i
975975 8.60755e14i 0.976914i
976976 −4.45998e13 + 1.06997e15i −0.0503598 + 1.20816i
977977 −8.98564e13 −0.100943 −0.0504715 0.998726i 0.516072π-0.516072\pi
−0.0504715 + 0.998726i 0.516072π0.516072\pi
978978 −8.53299e14 + 8.35708e14i −0.953690 + 0.934029i
979979 −2.90109e13 −0.0322588
980980 1.48921e14 + 3.10240e12i 0.164750 + 0.00343215i
981981 7.12864e14i 0.784624i
982982 −5.52040e14 + 5.40659e14i −0.604523 + 0.592060i
983983 5.65525e14i 0.616147i 0.951363 + 0.308073i 0.0996842π0.0996842\pi
−0.951363 + 0.308073i 0.900316π0.900316\pi
984984 8.01073e13 + 8.52763e13i 0.0868353 + 0.0924384i
985985 −1.09272e14 −0.117850
986986 5.29108e14 + 5.40246e14i 0.567754 + 0.579705i
987987 −1.29802e15 −1.38578
988988 1.93402e15 + 4.02906e13i 2.05436 + 0.0427975i
989989 1.60009e14i 0.169107i
990990 −6.31716e14 6.45013e14i −0.664271 0.678254i
991991 1.22093e15i 1.27739i −0.769461 0.638693i 0.779475π-0.779475\pi
0.769461 0.638693i 0.220525π-0.220525\pi
992992 3.06201e14 + 3.39876e14i 0.318749 + 0.353803i
993993 1.26542e15 1.31065
994994 7.33912e14 7.18782e14i 0.756332 0.740739i
995995 1.22744e15 1.25860
996996 2.06896e13 9.93138e14i 0.0211084 1.01324i
997997 4.49639e14i 0.456445i −0.973609 0.228222i 0.926709π-0.926709\pi
0.973609 0.228222i 0.0732913π-0.0732913\pi
998998 5.05900e12 4.95470e12i 0.00510989 0.00500455i
999999 1.64717e14i 0.165543i
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 8.11.d.b.3.5 8
3.2 odd 2 72.11.b.b.19.4 8
4.3 odd 2 32.11.d.b.15.2 8
8.3 odd 2 inner 8.11.d.b.3.6 yes 8
8.5 even 2 32.11.d.b.15.1 8
12.11 even 2 288.11.b.b.271.2 8
16.3 odd 4 256.11.c.m.255.2 16
16.5 even 4 256.11.c.m.255.1 16
16.11 odd 4 256.11.c.m.255.15 16
16.13 even 4 256.11.c.m.255.16 16
24.5 odd 2 288.11.b.b.271.7 8
24.11 even 2 72.11.b.b.19.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8.11.d.b.3.5 8 1.1 even 1 trivial
8.11.d.b.3.6 yes 8 8.3 odd 2 inner
32.11.d.b.15.1 8 8.5 even 2
32.11.d.b.15.2 8 4.3 odd 2
72.11.b.b.19.3 8 24.11 even 2
72.11.b.b.19.4 8 3.2 odd 2
256.11.c.m.255.1 16 16.5 even 4
256.11.c.m.255.2 16 16.3 odd 4
256.11.c.m.255.15 16 16.11 odd 4
256.11.c.m.255.16 16 16.13 even 4
288.11.b.b.271.2 8 12.11 even 2
288.11.b.b.271.7 8 24.5 odd 2