Properties

Label 22.6.c.b.15.2
Level 2222
Weight 66
Character 22.15
Analytic conductor 3.5283.528
Analytic rank 00
Dimension 1212
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [22,6,Mod(3,22)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(22, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("22.3");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 22=211 22 = 2 \cdot 11
Weight: k k == 6 6
Character orbit: [χ][\chi] == 22.c (of order 55, degree 44, 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: 3.528444035893.52844403589
Analytic rank: 00
Dimension: 1212
Relative dimension: 33 over Q(ζ5)\Q(\zeta_{5})
Coefficient field: Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x122x11+329x10+1365x9+52729x8+242031x7+7017903x6++93740681241 x^{12} - 2 x^{11} + 329 x^{10} + 1365 x^{9} + 52729 x^{8} + 242031 x^{7} + 7017903 x^{6} + \cdots + 93740681241 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 24112 2^{4}\cdot 11^{2}
Twist minimal: yes
Sato-Tate group: SU(2)[C5]\mathrm{SU}(2)[C_{5}]

Embedding invariants

Embedding label 15.2
Root 0.6699022.06175i-0.669902 - 2.06175i of defining polynomial
Character χ\chi == 22.15
Dual form 22.6.c.b.3.2

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+(3.236072.35114i)q2+(1.32178+4.06802i)q3+(4.94427+15.2169i)q4+(21.5825+15.6806i)q5+(13.841810.0567i)q6+(76.6137+235.793i)q7+(19.777160.8676i)q8+(181.789+132.078i)q9+106.710q10+(401.306+2.06892i)q1168.4378q12+(283.449205.938i)q13+(306.455943.171i)q14+(35.2616108.524i)q15+(207.108+150.473i)q16+(257.644+187.189i)q17+(277.750854.825i)q18+(202.192622.284i)q19+(345.320250.889i)q201060.48q21+(1303.52+936.832i)q22+3448.46q23+(221.470+160.907i)q24+(745.756+2295.20i)q25+(433.072+1332.86i)q26+(1618.47+1175.89i)q27+(3209.24+2331.65i)q28+(1270.413909.92i)q29+(141.046+434.096i)q30+(5668.58+4118.46i)q31+1024.00q32+(522.0221635.26i)q33+1273.86q34+(5350.883887.64i)q35+(1111.00+3419.30i)q36+(444.0601366.68i)q37+(2117.38+1538.37i)q38+(1212.42880.872i)q39+(527.601+1623.79i)q40+(2717.548363.72i)q41+(3431.77+2493.33i)q42+12877.7q43+(2015.656096.41i)q445994.52q45+(11159.58107.82i)q46+(6117.5418827.8i)q47+(338.3751041.41i)q48+(36131.4+26251.0i)q49+(7809.665674.05i)q50+(420.9411295.52i)q51+(1732.295331.43i)q52+(4973.19+3613.23i)q53+8002.17q54+(8628.746337.37i)q55+15867.3q56+(2264.21+1645.04i)q57+(5081.64+15639.7i)q58+(7700.42+23699.4i)q59+(1477.061073.15i)q60+(13593.5+9876.26i)q61+(8660.8226655.3i)q62+(17215.4+52983.6i)q63+(3313.732407.57i)q64+9346.76q65+(5534.01+4064.45i)q66+66822.5q67+(4122.302995.03i)q68+(4558.11+14028.4i)q69+(8175.42+25161.4i)q70+(11254.6+8176.95i)q71+(11634.58452.98i)q72+(17586.754126.3i)q73+(1776.24+5466.70i)q74+(8351.196067.49i)q75+10468.9q76+(31233.494466.6i)q775994.52q78+(46707.433934.9i)q79+(2110.416495.16i)q80+(14229.0+43792.4i)q81+(28458.4+20676.2i)q82+(52116.637865.0i)q83+(5243.2816137.2i)q84+(2625.368080.02i)q85+(41673.230277.4i)q86+17584.8q87+(7810.74+24467.5i)q8844688.3q89+(19398.7+14094.0i)q90+(26842.682613.0i)q91+(17050.1+52474.9i)q92+(24246.6+17616.2i)q93+(64063.7+46545.0i)q94+(5393.96+16600.9i)q95+(1353.50+4165.65i)q96+(119204.+86606.8i)q97+178644.q98+(73226.552627.5i)q99+O(q100)q+(-3.23607 - 2.35114i) q^{2} +(-1.32178 + 4.06802i) q^{3} +(4.94427 + 15.2169i) q^{4} +(-21.5825 + 15.6806i) q^{5} +(13.8418 - 10.0567i) q^{6} +(76.6137 + 235.793i) q^{7} +(19.7771 - 60.8676i) q^{8} +(181.789 + 132.078i) q^{9} +106.710 q^{10} +(-401.306 + 2.06892i) q^{11} -68.4378 q^{12} +(-283.449 - 205.938i) q^{13} +(306.455 - 943.171i) q^{14} +(-35.2616 - 108.524i) q^{15} +(-207.108 + 150.473i) q^{16} +(-257.644 + 187.189i) q^{17} +(-277.750 - 854.825i) q^{18} +(202.192 - 622.284i) q^{19} +(-345.320 - 250.889i) q^{20} -1060.48 q^{21} +(1303.52 + 936.832i) q^{22} +3448.46 q^{23} +(221.470 + 160.907i) q^{24} +(-745.756 + 2295.20i) q^{25} +(433.072 + 1332.86i) q^{26} +(-1618.47 + 1175.89i) q^{27} +(-3209.24 + 2331.65i) q^{28} +(-1270.41 - 3909.92i) q^{29} +(-141.046 + 434.096i) q^{30} +(5668.58 + 4118.46i) q^{31} +1024.00 q^{32} +(522.022 - 1635.26i) q^{33} +1273.86 q^{34} +(-5350.88 - 3887.64i) q^{35} +(-1111.00 + 3419.30i) q^{36} +(-444.060 - 1366.68i) q^{37} +(-2117.38 + 1538.37i) q^{38} +(1212.42 - 880.872i) q^{39} +(527.601 + 1623.79i) q^{40} +(2717.54 - 8363.72i) q^{41} +(3431.77 + 2493.33i) q^{42} +12877.7 q^{43} +(-2015.65 - 6096.41i) q^{44} -5994.52 q^{45} +(-11159.5 - 8107.82i) q^{46} +(6117.54 - 18827.8i) q^{47} +(-338.375 - 1041.41i) q^{48} +(-36131.4 + 26251.0i) q^{49} +(7809.66 - 5674.05i) q^{50} +(-420.941 - 1295.52i) q^{51} +(1732.29 - 5331.43i) q^{52} +(4973.19 + 3613.23i) q^{53} +8002.17 q^{54} +(8628.74 - 6337.37i) q^{55} +15867.3 q^{56} +(2264.21 + 1645.04i) q^{57} +(-5081.64 + 15639.7i) q^{58} +(7700.42 + 23699.4i) q^{59} +(1477.06 - 1073.15i) q^{60} +(-13593.5 + 9876.26i) q^{61} +(-8660.82 - 26655.3i) q^{62} +(-17215.4 + 52983.6i) q^{63} +(-3313.73 - 2407.57i) q^{64} +9346.76 q^{65} +(-5534.01 + 4064.45i) q^{66} +66822.5 q^{67} +(-4122.30 - 2995.03i) q^{68} +(-4558.11 + 14028.4i) q^{69} +(8175.42 + 25161.4i) q^{70} +(-11254.6 + 8176.95i) q^{71} +(11634.5 - 8452.98i) q^{72} +(-17586.7 - 54126.3i) q^{73} +(-1776.24 + 5466.70i) q^{74} +(-8351.19 - 6067.49i) q^{75} +10468.9 q^{76} +(-31233.4 - 94466.6i) q^{77} -5994.52 q^{78} +(-46707.4 - 33934.9i) q^{79} +(2110.41 - 6495.16i) q^{80} +(14229.0 + 43792.4i) q^{81} +(-28458.4 + 20676.2i) q^{82} +(52116.6 - 37865.0i) q^{83} +(-5243.28 - 16137.2i) q^{84} +(2625.36 - 8080.02i) q^{85} +(-41673.2 - 30277.4i) q^{86} +17584.8 q^{87} +(-7810.74 + 24467.5i) q^{88} -44688.3 q^{89} +(19398.7 + 14094.0i) q^{90} +(26842.6 - 82613.0i) q^{91} +(17050.1 + 52474.9i) q^{92} +(-24246.6 + 17616.2i) q^{93} +(-64063.7 + 46545.0i) q^{94} +(5393.96 + 16600.9i) q^{95} +(-1353.50 + 4165.65i) q^{96} +(119204. + 86606.8i) q^{97} +178644. q^{98} +(-73226.5 - 52627.5i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q12q248q4+44q5100q6326q7192q869q9+96q10+1011q11+800q12246q131304q14+112q15768q16+400q171416q18+199487q99+O(q100) 12 q - 12 q^{2} - 48 q^{4} + 44 q^{5} - 100 q^{6} - 326 q^{7} - 192 q^{8} - 69 q^{9} + 96 q^{10} + 1011 q^{11} + 800 q^{12} - 246 q^{13} - 1304 q^{14} + 112 q^{15} - 768 q^{16} + 400 q^{17} - 1416 q^{18}+ \cdots - 199487 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/22Z)×\left(\mathbb{Z}/22\mathbb{Z}\right)^\times.

nn 1313
χ(n)\chi(n) e(15)e\left(\frac{1}{5}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −3.23607 2.35114i −0.572061 0.415627i
33 −1.32178 + 4.06802i −0.0847921 + 0.260963i −0.984459 0.175613i 0.943809π-0.943809\pi
0.899667 + 0.436577i 0.143809π0.143809\pi
44 4.94427 + 15.2169i 0.154508 + 0.475528i
55 −21.5825 + 15.6806i −0.386079 + 0.280503i −0.763847 0.645398i 0.776692π-0.776692\pi
0.377768 + 0.925900i 0.376692π0.376692\pi
66 13.8418 10.0567i 0.156970 0.114045i
77 76.6137 + 235.793i 0.590965 + 1.81880i 0.573867 + 0.818948i 0.305443π0.305443\pi
0.0170973 + 0.999854i 0.494557π0.494557\pi
88 19.7771 60.8676i 0.109254 0.336249i
99 181.789 + 132.078i 0.748105 + 0.543530i
1010 106.710 0.337445
1111 −401.306 + 2.06892i −0.999987 + 0.00515539i
1212 −68.4378 −0.137197
1313 −283.449 205.938i −0.465176 0.337970i 0.330382 0.943847i 0.392822π-0.392822\pi
−0.795558 + 0.605877i 0.792822π0.792822\pi
1414 306.455 943.171i 0.417875 1.28609i
1515 −35.2616 108.524i −0.0404645 0.124537i
1616 −207.108 + 150.473i −0.202254 + 0.146946i
1717 −257.644 + 187.189i −0.216221 + 0.157094i −0.690624 0.723214i 0.742664π-0.742664\pi
0.474403 + 0.880308i 0.342664π0.342664\pi
1818 −277.750 854.825i −0.202056 0.621865i
1919 202.192 622.284i 0.128493 0.395462i −0.866028 0.499995i 0.833335π-0.833335\pi
0.994521 + 0.104534i 0.0333350π0.0333350\pi
2020 −345.320 250.889i −0.193039 0.140251i
2121 −1060.48 −0.524750
2222 1303.52 + 936.832i 0.574197 + 0.412672i
2323 3448.46 1.35927 0.679635 0.733550i 0.262138π-0.262138\pi
0.679635 + 0.733550i 0.262138π0.262138\pi
2424 221.470 + 160.907i 0.0784849 + 0.0570226i
2525 −745.756 + 2295.20i −0.238642 + 0.734464i
2626 433.072 + 1332.86i 0.125640 + 0.386679i
2727 −1618.47 + 1175.89i −0.427264 + 0.310425i
2828 −3209.24 + 2331.65i −0.773583 + 0.562041i
2929 −1270.41 3909.92i −0.280510 0.863322i −0.987709 0.156307i 0.950041π-0.950041\pi
0.707198 0.707015i 0.249959π-0.249959\pi
3030 −141.046 + 434.096i −0.0286127 + 0.0880609i
3131 5668.58 + 4118.46i 1.05942 + 0.769717i 0.973982 0.226626i 0.0727696π-0.0727696\pi
0.0854424 + 0.996343i 0.472770π0.472770\pi
3232 1024.00 0.176777
3333 522.022 1635.26i 0.0834456 0.261397i
3434 1273.86 0.188984
3535 −5350.88 3887.64i −0.738338 0.536434i
3636 −1111.00 + 3419.30i −0.142875 + 0.439725i
3737 −444.060 1366.68i −0.0533258 0.164120i 0.920847 0.389924i 0.127499π-0.127499\pi
−0.974173 + 0.225805i 0.927499π0.927499\pi
3838 −2117.38 + 1538.37i −0.237871 + 0.172823i
3939 1212.42 880.872i 0.127641 0.0927366i
4040 527.601 + 1623.79i 0.0521382 + 0.160465i
4141 2717.54 8363.72i 0.252473 0.777033i −0.741844 0.670573i 0.766048π-0.766048\pi
0.994317 0.106460i 0.0339517π-0.0339517\pi
4242 3431.77 + 2493.33i 0.300189 + 0.218100i
4343 12877.7 1.06211 0.531054 0.847338i 0.321796π-0.321796\pi
0.531054 + 0.847338i 0.321796π0.321796\pi
4444 −2015.65 6096.41i −0.156958 0.474725i
4545 −5994.52 −0.441289
4646 −11159.5 8107.82i −0.777586 0.564950i
4747 6117.54 18827.8i 0.403954 1.24324i −0.517811 0.855495i 0.673253π-0.673253\pi
0.921765 0.387748i 0.126747π-0.126747\pi
4848 −338.375 1041.41i −0.0211980 0.0652408i
4949 −36131.4 + 26251.0i −2.14978 + 1.56191i
5050 7809.66 5674.05i 0.441781 0.320973i
5151 −420.941 1295.52i −0.0226619 0.0697461i
5252 1732.29 5331.43i 0.0888406 0.273423i
5353 4973.19 + 3613.23i 0.243190 + 0.176688i 0.702703 0.711483i 0.251976π-0.251976\pi
−0.459513 + 0.888171i 0.651976π0.651976\pi
5454 8002.17 0.373442
5555 8628.74 6337.37i 0.384628 0.282489i
5656 15867.3 0.676136
5757 2264.21 + 1645.04i 0.0923058 + 0.0670641i
5858 −5081.64 + 15639.7i −0.198351 + 0.610461i
5959 7700.42 + 23699.4i 0.287995 + 0.886356i 0.985485 + 0.169762i 0.0542999π0.0542999\pi
−0.697491 + 0.716594i 0.745700π0.745700\pi
6060 1477.06 1073.15i 0.0529687 0.0384840i
6161 −13593.5 + 9876.26i −0.467743 + 0.339835i −0.796561 0.604558i 0.793350π-0.793350\pi
0.328818 + 0.944393i 0.393350π0.393350\pi
6262 −8660.82 26655.3i −0.286141 0.880650i
6363 −17215.4 + 52983.6i −0.546470 + 1.68186i
6464 −3313.73 2407.57i −0.101127 0.0734732i
6565 9346.76 0.274396
6666 −5534.01 + 4064.45i −0.156380 + 0.114853i
6767 66822.5 1.81859 0.909297 0.416147i 0.136620π-0.136620\pi
0.909297 + 0.416147i 0.136620π0.136620\pi
6868 −4122.30 2995.03i −0.108110 0.0785469i
6969 −4558.11 + 14028.4i −0.115255 + 0.354720i
7070 8175.42 + 25161.4i 0.199418 + 0.613746i
7171 −11254.6 + 8176.95i −0.264963 + 0.192507i −0.712332 0.701843i 0.752361π-0.752361\pi
0.447369 + 0.894349i 0.352361π0.352361\pi
7272 11634.5 8452.98i 0.264495 0.192167i
7373 −17586.7 54126.3i −0.386258 1.18878i −0.935564 0.353158i 0.885108π-0.885108\pi
0.549306 0.835621i 0.314892π-0.314892\pi
7474 −1776.24 + 5466.70i −0.0377070 + 0.116050i
7575 −8351.19 6067.49i −0.171433 0.124554i
7676 10468.9 0.207906
7777 −31233.4 94466.6i −0.600333 1.81573i
7878 −5994.52 −0.111562
7979 −46707.4 33934.9i −0.842012 0.611758i 0.0809199 0.996721i 0.474214π-0.474214\pi
−0.922932 + 0.384963i 0.874214π0.874214\pi
8080 2110.41 6495.16i 0.0368673 0.113466i
8181 14229.0 + 43792.4i 0.240970 + 0.741628i
8282 −28458.4 + 20676.2i −0.467386 + 0.339576i
8383 52116.6 37865.0i 0.830388 0.603312i −0.0892810 0.996006i 0.528457π-0.528457\pi
0.919669 + 0.392694i 0.128457π0.128457\pi
8484 −5243.28 16137.2i −0.0810783 0.249533i
8585 2625.36 8080.02i 0.0394131 0.121301i
8686 −41673.2 30277.4i −0.607590 0.441440i
8787 17584.8 0.249081
8888 −7810.74 + 24467.5i −0.107519 + 0.336808i
8989 −44688.3 −0.598025 −0.299012 0.954249i 0.596657π-0.596657\pi
−0.299012 + 0.954249i 0.596657π0.596657\pi
9090 19398.7 + 14094.0i 0.252445 + 0.183412i
9191 26842.6 82613.0i 0.339798 1.04579i
9292 17050.1 + 52474.9i 0.210019 + 0.646372i
9393 −24246.6 + 17616.2i −0.290699 + 0.211205i
9494 −64063.7 + 46545.0i −0.747812 + 0.543317i
9595 5393.96 + 16600.9i 0.0613195 + 0.188722i
9696 −1353.50 + 4165.65i −0.0149893 + 0.0461322i
9797 119204. + 86606.8i 1.28636 + 0.934593i 0.999725 0.0234473i 0.00746418π-0.00746418\pi
0.286632 + 0.958041i 0.407464π0.407464\pi
9898 178644. 1.87898
9999 −73226.5 52627.5i −0.750897 0.539666i
100100 −38613.1 −0.386131
101101 72022.8 + 52327.6i 0.702533 + 0.510420i 0.880756 0.473570i 0.157035π-0.157035\pi
−0.178223 + 0.983990i 0.557035π0.557035\pi
102102 −1683.76 + 5182.09i −0.0160244 + 0.0493179i
103103 1714.96 + 5278.09i 0.0159279 + 0.0490212i 0.958705 0.284404i 0.0917956π-0.0917956\pi
−0.942777 + 0.333425i 0.891796π0.891796\pi
104104 −18140.8 + 13180.0i −0.164464 + 0.119490i
105105 22887.7 16628.9i 0.202595 0.147194i
106106 −7598.36 23385.3i −0.0656833 0.202152i
107107 −63253.1 + 194673.i −0.534099 + 1.64379i 0.211488 + 0.977381i 0.432169π0.432169\pi
−0.745587 + 0.666408i 0.767831π0.767831\pi
108108 −25895.6 18814.2i −0.213632 0.155213i
109109 −17153.0 −0.138285 −0.0691425 0.997607i 0.522026π-0.522026\pi
−0.0691425 + 0.997607i 0.522026π0.522026\pi
110110 −42823.2 + 220.773i −0.337441 + 0.00173966i
111111 6146.61 0.0473509
112112 −51347.8 37306.4i −0.386791 0.281020i
113113 −13340.1 + 41056.6i −0.0982795 + 0.302473i −0.988094 0.153848i 0.950833π-0.950833\pi
0.889815 + 0.456322i 0.150833π0.150833\pi
114114 −3459.40 10646.9i −0.0249309 0.0767295i
115115 −74426.4 + 54073.9i −0.524786 + 0.381279i
116116 53215.6 38663.4i 0.367193 0.266781i
117117 −24328.3 74874.7i −0.164303 0.505674i
118118 30801.7 94797.8i 0.203643 0.626748i
119119 −63877.0 46409.3i −0.413501 0.300426i
120120 −7302.98 −0.0462963
121121 161042. 1660.54i 0.999947 0.0103106i
122122 67210.0 0.408822
123123 30431.8 + 22110.0i 0.181369 + 0.131773i
124124 −34643.3 + 106621.i −0.202332 + 0.622714i
125125 −45656.6 140517.i −0.261354 0.804364i
126126 180282. 130983.i 1.01164 0.735000i
127127 −27072.1 + 19669.0i −0.148941 + 0.108212i −0.659760 0.751476i 0.729342π-0.729342\pi
0.510819 + 0.859688i 0.329342π0.329342\pi
128128 5062.93 + 15582.1i 0.0273135 + 0.0840623i
129129 −17021.5 + 52386.8i −0.0900583 + 0.277171i
130130 −30246.8 21975.6i −0.156971 0.114046i
131131 −291258. −1.48286 −0.741429 0.671031i 0.765852π-0.765852\pi
−0.741429 + 0.671031i 0.765852π0.765852\pi
132132 27464.5 141.592i 0.137195 0.000707302i
133133 162221. 0.795201
134134 −216242. 157109.i −1.04035 0.755857i
135135 16492.0 50757.2i 0.0778824 0.239697i
136136 6298.32 + 19384.2i 0.0291996 + 0.0898672i
137137 7972.17 5792.12i 0.0362890 0.0263655i −0.569493 0.821996i 0.692860π-0.692860\pi
0.605782 + 0.795631i 0.292860π0.292860\pi
138138 47733.1 34680.1i 0.213364 0.155018i
139139 −16414.0 50517.1i −0.0720573 0.221769i 0.908542 0.417794i 0.137197π-0.137197\pi
−0.980599 + 0.196025i 0.937197π0.937197\pi
140140 32701.7 100645.i 0.141010 0.433984i
141141 68505.9 + 49772.5i 0.290189 + 0.210834i
142142 55645.8 0.231586
143143 114176. + 82057.8i 0.466912 + 0.335567i
144144 −57524.3 −0.231177
145145 88728.4 + 64465.0i 0.350464 + 0.254627i
146146 −70346.8 + 216505.i −0.273125 + 0.840594i
147147 −59031.8 181681.i −0.225316 0.693453i
148148 18601.0 13514.4i 0.0698043 0.0507158i
149149 −207374. + 150666.i −0.765223 + 0.555967i −0.900508 0.434840i 0.856805π-0.856805\pi
0.135285 + 0.990807i 0.456805π0.456805\pi
150150 12759.5 + 39269.6i 0.0463025 + 0.142505i
151151 61189.6 188322.i 0.218391 0.672139i −0.780504 0.625150i 0.785038π-0.785038\pi
0.998895 0.0469885i 0.0149624π-0.0149624\pi
152152 −33878.1 24613.9i −0.118935 0.0864115i
153153 −71560.5 −0.247141
154154 −121031. + 379135.i −0.411239 + 1.28822i
155155 −186922. −0.624929
156156 19398.7 + 14094.0i 0.0638205 + 0.0463683i
157157 170781. 525610.i 0.552955 1.70182i −0.148327 0.988938i 0.547389π-0.547389\pi
0.701282 0.712884i 0.252611π-0.252611\pi
158158 71362.6 + 219632.i 0.227420 + 0.699926i
159159 −21272.1 + 15455.1i −0.0667296 + 0.0484819i
160160 −22100.5 + 16056.9i −0.0682498 + 0.0495864i
161161 264200. + 813123.i 0.803281 + 2.47224i
162162 56916.1 175170.i 0.170391 0.524410i
163163 116271. + 84475.8i 0.342770 + 0.249037i 0.745830 0.666137i 0.232053π-0.232053\pi
−0.403060 + 0.915174i 0.632053π0.632053\pi
164164 140706. 0.408511
165165 14375.2 + 43478.5i 0.0411060 + 0.124327i
166166 −257679. −0.725786
167167 357081. + 259435.i 0.990776 + 0.719841i 0.960091 0.279688i 0.0902310π-0.0902310\pi
0.0306854 + 0.999529i 0.490231π0.490231\pi
168168 −20973.1 + 64548.6i −0.0573310 + 0.176447i
169169 −76802.8 236375.i −0.206852 0.636626i
170170 −27493.1 + 19974.9i −0.0729628 + 0.0530105i
171171 118946. 86419.5i 0.311072 0.226007i
172172 63671.0 + 195959.i 0.164105 + 0.505062i
173173 161154. 495982.i 0.409380 1.25994i −0.507803 0.861473i 0.669542π-0.669542\pi
0.917182 0.398468i 0.130458π-0.130458\pi
174174 −56905.7 41344.4i −0.142489 0.103525i
175175 −598327. −1.47687
176176 82802.6 60814.3i 0.201494 0.147987i
177177 −106588. −0.255726
178178 144615. + 105069.i 0.342107 + 0.248555i
179179 −110943. + 341446.i −0.258801 + 0.796507i 0.734256 + 0.678872i 0.237531π0.237531\pi
−0.993057 + 0.117634i 0.962469π0.962469\pi
180180 −29638.6 91218.1i −0.0681829 0.209846i
181181 324312. 235627.i 0.735812 0.534599i −0.155585 0.987823i 0.549726π-0.549726\pi
0.891397 + 0.453224i 0.149726π0.149726\pi
182182 −281099. + 204231.i −0.629044 + 0.457027i
183183 −22209.2 68352.9i −0.0490236 0.150879i
184184 68200.6 209900.i 0.148506 0.457054i
185185 31014.2 + 22533.1i 0.0666240 + 0.0484052i
186186 119882. 0.254080
187187 103007. 75653.3i 0.215408 0.158206i
188188 316748. 0.653611
189189 −401263. 291535.i −0.817099 0.593658i
190190 21575.8 66403.6i 0.0433595 0.133447i
191191 −112279. 345560.i −0.222698 0.685394i −0.998517 0.0544387i 0.982663π-0.982663\pi
0.775819 0.630955i 0.217337π-0.217337\pi
192192 14174.0 10298.0i 0.0277486 0.0201605i
193193 226270. 164395.i 0.437254 0.317683i −0.347289 0.937758i 0.612898π-0.612898\pi
0.784543 + 0.620075i 0.212898π0.212898\pi
194194 −182128. 560531.i −0.347433 1.06929i
195195 −12354.4 + 38022.8i −0.0232666 + 0.0716073i
196196 −578103. 420016.i −1.07489 0.780955i
197197 −983666. −1.80585 −0.902926 0.429796i 0.858586π-0.858586\pi
−0.902926 + 0.429796i 0.858586π0.858586\pi
198198 113231. + 342472.i 0.205259 + 0.620815i
199199 −345412. −0.618308 −0.309154 0.951012i 0.600046π-0.600046\pi
−0.309154 + 0.951012i 0.600046π0.600046\pi
200200 124954. + 90784.7i 0.220890 + 0.160486i
201201 −88324.6 + 271835.i −0.154203 + 0.474587i
202202 −110041. 338672.i −0.189748 0.583983i
203203 824600. 599107.i 1.40444 1.02039i
204204 17632.6 12810.8i 0.0296648 0.0215527i
205205 72496.8 + 223122.i 0.120485 + 0.370816i
206206 6859.82 21112.4i 0.0112628 0.0346632i
207207 626894. + 455465.i 1.01688 + 0.738804i
208208 89692.8 0.143747
209209 −79853.5 + 250145.i −0.126453 + 0.396119i
210210 −113163. −0.177074
211211 487700. + 354335.i 0.754131 + 0.547908i 0.897105 0.441818i 0.145666π-0.145666\pi
−0.142973 + 0.989727i 0.545666π0.545666\pi
212212 −30393.4 + 93541.4i −0.0464451 + 0.142943i
213213 −18387.9 56592.1i −0.0277704 0.0854686i
214214 662395. 481258.i 0.988741 0.718362i
215215 −277933. + 201930.i −0.410057 + 0.297924i
216216 39564.9 + 121768.i 0.0577000 + 0.177582i
217217 −536813. + 1.65214e6i −0.773880 + 2.38176i
218218 55508.4 + 40329.2i 0.0791075 + 0.0574750i
219219 243432. 0.342979
220220 139098. + 99969.0i 0.193760 + 0.139254i
221221 111578. 0.153674
222222 −19890.8 14451.5i −0.0270876 0.0196803i
223223 52180.4 160595.i 0.0702660 0.216257i −0.909757 0.415142i 0.863732π-0.863732\pi
0.980023 + 0.198885i 0.0637320π0.0637320\pi
224224 78452.5 + 241452.i 0.104469 + 0.321522i
225225 −438715. + 318745.i −0.577732 + 0.419747i
226226 139699. 101498.i 0.181938 0.132186i
227227 76550.7 + 235599.i 0.0986017 + 0.303465i 0.988176 0.153326i 0.0489986π-0.0489986\pi
−0.889574 + 0.456791i 0.848999π0.848999\pi
228228 −13837.6 + 42587.7i −0.0176288 + 0.0542560i
229229 −1.00001e6 726549.i −1.26013 0.915537i −0.261365 0.965240i 0.584173π-0.584173\pi
−0.998764 + 0.0497030i 0.984173π0.984173\pi
230230 367984. 0.458680
231231 425575. 2194.04i 0.524743 0.00270529i
232232 −263113. −0.320938
233233 261056. + 189668.i 0.315024 + 0.228879i 0.734049 0.679096i 0.237628π-0.237628\pi
−0.419025 + 0.907975i 0.637628π0.637628\pi
234234 −97313.1 + 299499.i −0.116180 + 0.357565i
235235 163200. + 502278.i 0.192775 + 0.593300i
236236 −322559. + 234353.i −0.376990 + 0.273899i
237237 199785. 145152.i 0.231042 0.167862i
238238 97595.3 + 300367.i 0.111683 + 0.343725i
239239 214684. 660728.i 0.243111 0.748218i −0.752831 0.658214i 0.771312π-0.771312\pi
0.995941 0.0900036i 0.0286879π-0.0286879\pi
240240 23632.9 + 17170.3i 0.0264844 + 0.0192420i
241241 1.18914e6 1.31884 0.659419 0.751776i 0.270802π-0.270802\pi
0.659419 + 0.751776i 0.270802π0.270802\pi
242242 −525048. 373260.i −0.576316 0.409707i
243243 −683087. −0.742097
244244 −217496. 158020.i −0.233871 0.169917i
245245 368174. 1.13312e6i 0.391867 1.20604i
246246 −46495.6 143099.i −0.0489862 0.150764i
247247 −185463. + 134747.i −0.193426 + 0.140532i
248248 362789. 263582.i 0.374563 0.272136i
249249 85148.6 + 262060.i 0.0870320 + 0.267857i
250250 −182626. + 562066.i −0.184805 + 0.568771i
251251 −311952. 226647.i −0.312539 0.227073i 0.420446 0.907317i 0.361874π-0.361874\pi
−0.732985 + 0.680245i 0.761874π0.761874\pi
252252 −891364. −0.884207
253253 −1.38389e6 + 7134.59i −1.35925 + 0.00700757i
254254 133852. 0.130179
255255 29399.5 + 21360.0i 0.0283132 + 0.0205708i
256256 20251.7 62328.4i 0.0193136 0.0594410i
257257 −453253. 1.39497e6i −0.428063 1.31744i −0.900030 0.435827i 0.856456π-0.856456\pi
0.471967 0.881616i 0.343544π-0.343544\pi
258258 178252. 129507.i 0.166719 0.121128i
259259 288231. 209412.i 0.266988 0.193978i
260260 46212.9 + 142229.i 0.0423965 + 0.130483i
261261 285466. 878575.i 0.259390 0.798321i
262262 942530. + 684788.i 0.848286 + 0.616316i
263263 961837. 0.857456 0.428728 0.903434i 0.358962π-0.358962\pi
0.428728 + 0.903434i 0.358962π0.358962\pi
264264 −89210.0 64114.8i −0.0787778 0.0566172i
265265 −163991. −0.143452
266266 −524957. 381404.i −0.454904 0.330507i
267267 59068.1 181793.i 0.0507078 0.156063i
268268 330389. + 1.01683e6i 0.280988 + 0.864793i
269269 −113828. + 82700.9i −0.0959110 + 0.0696834i −0.634707 0.772753i 0.718879π-0.718879\pi
0.538796 + 0.842436i 0.318879π0.318879\pi
270270 −172707. + 125479.i −0.144178 + 0.104752i
271271 −479460. 1.47563e6i −0.396578 1.22054i −0.927726 0.373263i 0.878239π-0.878239\pi
0.531147 0.847280i 0.321761π-0.321761\pi
272272 25193.3 77536.9i 0.0206473 0.0635457i
273273 300591. + 218392.i 0.244101 + 0.177350i
274274 −39416.6 −0.0317177
275275 294528. 922621.i 0.234852 0.735685i
276276 −236005. −0.186487
277277 240429. + 174682.i 0.188272 + 0.136788i 0.677929 0.735128i 0.262878π-0.262878\pi
−0.489656 + 0.871915i 0.662878π0.662878\pi
278278 −65656.0 + 202069.i −0.0509522 + 0.156815i
279279 486530. + 1.49739e6i 0.374196 + 1.15166i
280280 −342456. + 248809.i −0.261042 + 0.189658i
281281 −357871. + 260009.i −0.270372 + 0.196437i −0.714707 0.699424i 0.753440π-0.753440\pi
0.444335 + 0.895861i 0.353440π0.353440\pi
282282 −104668. 322134.i −0.0783773 0.241220i
283283 −382775. + 1.17806e6i −0.284104 + 0.874384i 0.702561 + 0.711623i 0.252040π0.252040\pi
−0.986666 + 0.162760i 0.947960π0.947960\pi
284284 −180074. 130831.i −0.132481 0.0962533i
285285 −74662.4 −0.0544490
286286 −176552. 533988.i −0.127631 0.386026i
287287 2.18030e6 1.56247
288288 186152. + 135248.i 0.132247 + 0.0960834i
289289 −407419. + 1.25391e6i −0.286944 + 0.883123i
290290 −135565. 417226.i −0.0946570 0.291324i
291291 −509879. + 370449.i −0.352968 + 0.256446i
292292 736681. 535230.i 0.505618 0.367353i
293293 −387305. 1.19200e6i −0.263562 0.811162i −0.992021 0.126072i 0.959763π-0.959763\pi
0.728459 0.685090i 0.240237π-0.240237\pi
294294 −236127. + 726725.i −0.159323 + 0.490345i
295295 −537815. 390746.i −0.359814 0.261420i
296296 −91968.5 −0.0610112
297297 647070. 475240.i 0.425657 0.312624i
298298 1.02531e6 0.668829
299299 −977464. 710170.i −0.632300 0.459393i
300300 51037.9 157079.i 0.0327408 0.100766i
301301 986611. + 3.03648e6i 0.627668 + 1.93176i
302302 −640786. + 465558.i −0.404292 + 0.293735i
303303 −308068. + 223824.i −0.192770 + 0.140056i
304304 51761.2 + 159305.i 0.0321233 + 0.0988654i
305305 138516. 426308.i 0.0852610 0.262406i
306306 231575. + 168249.i 0.141380 + 0.102718i
307307 −1.58831e6 −0.961809 −0.480905 0.876773i 0.659692π-0.659692\pi
−0.480905 + 0.876773i 0.659692π0.659692\pi
308308 1.28306e6 942344.i 0.770675 0.566021i
309309 −23738.1 −0.0141433
310310 604892. + 439480.i 0.357498 + 0.259737i
311311 −713092. + 2.19467e6i −0.418066 + 1.28667i 0.491414 + 0.870926i 0.336480π0.336480\pi
−0.909480 + 0.415748i 0.863520π0.863520\pi
312312 −29638.5 91218.0i −0.0172373 0.0530510i
313313 −1.52449e6 + 1.10761e6i −0.879558 + 0.639036i −0.933134 0.359528i 0.882938π-0.882938\pi
0.0535769 + 0.998564i 0.482938π0.482938\pi
314314 −1.78844e6 + 1.29938e6i −1.02365 + 0.743723i
315315 −459263. 1.41347e6i −0.260786 0.802618i
316316 285450. 878526.i 0.160810 0.494922i
317317 1.16948e6 + 849674.i 0.653647 + 0.474902i 0.864511 0.502613i 0.167628π-0.167628\pi
−0.210865 + 0.977515i 0.567628π0.567628\pi
318318 105175. 0.0583238
319319 517913. + 1.56645e6i 0.284957 + 0.861865i
320320 109271. 0.0596525
321321 −708326. 514629.i −0.383681 0.278761i
322322 1.05680e6 3.25249e6i 0.568005 1.74814i
323323 64391.2 + 198176.i 0.0343416 + 0.105693i
324324 −596033. + 433043.i −0.315433 + 0.229176i
325325 684053. 496993.i 0.359237 0.261001i
326326 −177646. 546739.i −0.0925789 0.284929i
327327 22672.5 69778.9i 0.0117255 0.0360873i
328328 −455334. 330820.i −0.233693 0.169788i
329329 4.90816e6 2.49994
330330 55704.7 174497.i 0.0281583 0.0882072i
331331 2.78136e6 1.39536 0.697682 0.716407i 0.254215π-0.254215\pi
0.697682 + 0.716407i 0.254215π0.254215\pi
332332 833866. + 605839.i 0.415194 + 0.301656i
333333 99782.1 307098.i 0.0493108 0.151763i
334334 −545571. 1.67910e6i −0.267600 0.823587i
335335 −1.44220e6 + 1.04782e6i −0.702121 + 0.510121i
336336 219633. 159573.i 0.106133 0.0771101i
337337 240197. + 739250.i 0.115211 + 0.354582i 0.991991 0.126309i 0.0403132π-0.0403132\pi
−0.876780 + 0.480891i 0.840313π0.840313\pi
338338 −307211. + 945499.i −0.146267 + 0.450162i
339339 −149386. 108536.i −0.0706011 0.0512947i
340340 135933. 0.0637718
341341 −2.28336e6 1.64104e6i −1.06338 0.764245i
342342 −588103. −0.271887
343343 −5.58686e6 4.05909e6i −2.56409 1.86292i
344344 254684. 783837.i 0.116039 0.357133i
345345 −121598. 374241.i −0.0550022 0.169279i
346346 −1.68763e6 + 1.22613e6i −0.757856 + 0.550615i
347347 −717707. + 521445.i −0.319981 + 0.232480i −0.736167 0.676800i 0.763366π-0.763366\pi
0.416187 + 0.909279i 0.363366π0.363366\pi
348348 86944.2 + 267587.i 0.0384851 + 0.118445i
349349 964120. 2.96726e6i 0.423709 1.30404i −0.480516 0.876986i 0.659551π-0.659551\pi
0.904225 0.427056i 0.140449π-0.140449\pi
350350 1.93623e6 + 1.40675e6i 0.844862 + 0.613828i
351351 700915. 0.303667
352352 −410938. + 2118.57i −0.176774 + 0.000911353i
353353 −2.74141e6 −1.17095 −0.585474 0.810691i 0.699092π-0.699092\pi
−0.585474 + 0.810691i 0.699092π0.699092\pi
354354 344926. + 250603.i 0.146291 + 0.106287i
355355 114683. 352958.i 0.0482978 0.148645i
356356 −220951. 680018.i −0.0923999 0.284378i
357357 273225. 198510.i 0.113462 0.0824349i
358358 1.16181e6 844101.i 0.479100 0.348086i
359359 23033.4 + 70889.4i 0.00943238 + 0.0290299i 0.955662 0.294466i 0.0951418π-0.0951418\pi
−0.946230 + 0.323496i 0.895142π0.895142\pi
360360 −118554. + 364872.i −0.0482126 + 0.148383i
361361 1.65685e6 + 1.20377e6i 0.669138 + 0.486157i
362362 −1.60349e6 −0.643123
363363 −206107. + 657318.i −0.0820969 + 0.261824i
364364 1.38983e6 0.549805
365365 1.22830e6 + 892409.i 0.482582 + 0.350616i
366366 −88836.8 + 273411.i −0.0346649 + 0.106688i
367367 −619573. 1.90685e6i −0.240119 0.739012i −0.996401 0.0847653i 0.972986π-0.972986\pi
0.756282 0.654246i 0.227014π-0.227014\pi
368368 −714206. + 518901.i −0.274918 + 0.199740i
369369 1.59868e6 1.16151e6i 0.611217 0.444075i
370370 −47385.4 145837.i −0.0179945 0.0553815i
371371 −470960. + 1.44947e6i −0.177643 + 0.546730i
372372 −387945. 281859.i −0.145349 0.105602i
373373 1.18585e6 0.441325 0.220662 0.975350i 0.429178π-0.429178\pi
0.220662 + 0.975350i 0.429178π0.429178\pi
374374 −511209. + 2635.52i −0.188982 + 0.000974286i
375375 631972. 0.232070
376376 −1.02502e6 744720.i −0.373906 0.271659i
377377 −445104. + 1.36989e6i −0.161290 + 0.496401i
378378 613076. + 1.88685e6i 0.220691 + 0.679217i
379379 852348. 619267.i 0.304803 0.221452i −0.424860 0.905259i 0.639677π-0.639677\pi
0.729663 + 0.683807i 0.239677π0.239677\pi
380380 −225945. + 164159.i −0.0802683 + 0.0583183i
381381 −44230.7 136128.i −0.0156103 0.0480435i
382382 −449117. + 1.38224e6i −0.157471 + 0.484647i
383383 −2.59766e6 1.88731e6i −0.904867 0.657425i 0.0348442 0.999393i 0.488907π-0.488907\pi
−0.939712 + 0.341968i 0.888907π0.888907\pi
384384 −70080.4 −0.0242532
385385 2.15539e6 + 1.54907e6i 0.741094 + 0.532621i
386386 −1.11874e6 −0.382174
387387 2.34104e6 + 1.70086e6i 0.794567 + 0.577287i
388388 −728510. + 2.24212e6i −0.245672 + 0.756102i
389389 1.02564e6 + 3.15659e6i 0.343653 + 1.05766i 0.962301 + 0.271987i 0.0876808π0.0876808\pi
−0.618648 + 0.785669i 0.712319π0.712319\pi
390390 129376. 93997.5i 0.0430719 0.0312935i
391391 −888476. + 645516.i −0.293903 + 0.213533i
392392 883263. + 2.71840e6i 0.290319 + 0.893509i
393393 384978. 1.18484e6i 0.125735 0.386972i
394394 3.18321e6 + 2.31274e6i 1.03306 + 0.750561i
395395 1.54018e6 0.496683
396396 438776. 1.37449e6i 0.140606 0.440456i
397397 1.28321e6 0.408621 0.204311 0.978906i 0.434505π-0.434505\pi
0.204311 + 0.978906i 0.434505π0.434505\pi
398398 1.11778e6 + 812113.i 0.353710 + 0.256986i
399399 −214420. + 659916.i −0.0674268 + 0.207518i
400400 −190913. 587571.i −0.0596605 0.183616i
401401 832356. 604742.i 0.258493 0.187806i −0.450990 0.892529i 0.648929π-0.648929\pi
0.709482 + 0.704723i 0.248929π0.248929\pi
402402 924947. 672013.i 0.285464 0.207402i
403403 −758607. 2.33475e6i −0.232677 0.716107i
404404 −440164. + 1.35469e6i −0.134172 + 0.412938i
405405 −993788. 722029.i −0.301062 0.218734i
406406 −4.07705e6 −1.22753
407407 181032. + 547537.i 0.0541712 + 0.163843i
408408 −87180.4 −0.0259280
409409 −1.65183e6 1.20012e6i −0.488266 0.354746i 0.316251 0.948675i 0.397576π-0.397576\pi
−0.804517 + 0.593930i 0.797576π0.797576\pi
410410 289987. 892489.i 0.0851960 0.262206i
411411 13025.0 + 40086.8i 0.00380341 + 0.0117057i
412412 −71837.0 + 52192.6i −0.0208500 + 0.0151484i
413413 −4.99820e6 + 3.63141e6i −1.44191 + 1.04761i
414414 −957809. 2.94783e6i −0.274649 0.845283i
415415 −531061. + 1.63444e6i −0.151365 + 0.465852i
416416 −290252. 210880.i −0.0822322 0.0597452i
417417 227200. 0.0639836
418418 846537. 621738.i 0.236976 0.174047i
419419 797311. 0.221867 0.110933 0.993828i 0.464616π-0.464616\pi
0.110933 + 0.993828i 0.464616π0.464616\pi
420420 366203. + 266062.i 0.101297 + 0.0735969i
421421 980563. 3.01786e6i 0.269631 0.829839i −0.720959 0.692978i 0.756298π-0.756298\pi
0.990590 0.136862i 0.0437016π-0.0437016\pi
422422 −745140. 2.29330e6i −0.203684 0.626875i
423423 3.59884e6 2.61471e6i 0.977940 0.710515i
424424 318284. 231247.i 0.0859806 0.0624685i
425425 −237497. 730942.i −0.0637803 0.196296i
426426 −73551.5 + 226368.i −0.0196367 + 0.0604354i
427427 −3.37020e6 2.44859e6i −0.894512 0.649901i
428428 −3.27506e6 −0.864191
429429 −484728. + 356008.i −0.127161 + 0.0933934i
430430 1.37418e6 0.358403
431431 5.49188e6 + 3.99008e6i 1.42406 + 1.03464i 0.991085 + 0.133233i 0.0425358π0.0425358\pi
0.432974 + 0.901406i 0.357464π0.357464\pi
432432 158260. 487073.i 0.0408000 0.125570i
433433 −823285. 2.53381e6i −0.211023 0.649463i −0.999412 0.0342855i 0.989084π-0.989084\pi
0.788389 0.615177i 0.210916π-0.210916\pi
434434 5.62158e6 4.08432e6i 1.43263 1.04087i
435435 −379524. + 275740.i −0.0961648 + 0.0698678i
436436 −84809.3 261016.i −0.0213662 0.0657584i
437437 697252. 2.14592e6i 0.174657 0.537539i
438438 −787764. 572344.i −0.196205 0.142551i
439439 −2.51318e6 −0.622390 −0.311195 0.950346i 0.600729π-0.600729\pi
−0.311195 + 0.950346i 0.600729π0.600729\pi
440440 −215089. 650546.i −0.0529647 0.160194i
441441 −1.00355e7 −2.45721
442442 −361075. 262337.i −0.0879108 0.0638709i
443443 −796545. + 2.45151e6i −0.192842 + 0.593505i 0.807153 + 0.590342i 0.201007π0.201007\pi
−0.999995 + 0.00316367i 0.998993π0.998993\pi
444444 30390.5 + 93532.3i 0.00731611 + 0.0225167i
445445 964485. 700739.i 0.230885 0.167748i
446446 −546440. + 397012.i −0.130079 + 0.0945076i
447447 −338809. 1.04275e6i −0.0802021 0.246837i
448448 313810. 965807.i 0.0738706 0.227350i
449449 −1.83008e6 1.32963e6i −0.428405 0.311255i 0.352606 0.935772i 0.385296π-0.385296\pi
−0.781011 + 0.624517i 0.785296π0.785296\pi
450450 2.16913e6 0.504957
451451 −1.07326e6 + 3.36203e6i −0.248464 + 0.778325i
452452 −690712. −0.159020
453453 685219. + 497840.i 0.156886 + 0.113984i
454454 306203. 942395.i 0.0697220 0.214582i
455455 716090. + 2.20390e6i 0.162158 + 0.499072i
456456 144909. 105283.i 0.0326350 0.0237107i
457457 6.57114e6 4.77422e6i 1.47181 1.06933i 0.491720 0.870753i 0.336368π-0.336368\pi
0.980085 0.198576i 0.0636318π-0.0636318\pi
458458 1.52788e6 + 4.70232e6i 0.340349 + 1.04749i
459459 196876. 605921.i 0.0436175 0.134241i
460460 −1.19082e6 865183.i −0.262393 0.190640i
461461 −696701. −0.152684 −0.0763421 0.997082i 0.524324π-0.524324\pi
−0.0763421 + 0.997082i 0.524324π0.524324\pi
462462 −1.38235e6 993488.i −0.301310 0.216550i
463463 1.94210e6 0.421036 0.210518 0.977590i 0.432485π-0.432485\pi
0.210518 + 0.977590i 0.432485π0.432485\pi
464464 851450. + 618615.i 0.183596 + 0.133391i
465465 247069. 760401.i 0.0529891 0.163084i
466466 −398858. 1.22756e6i −0.0850852 0.261865i
467467 1.02824e6 747060.i 0.218174 0.158512i −0.473331 0.880885i 0.656948π-0.656948\pi
0.691504 + 0.722372i 0.256948π0.256948\pi
468468 1.01908e6 740402.i 0.215076 0.156262i
469469 5.11952e6 + 1.57563e7i 1.07473 + 3.30766i
470470 652800. 2.00911e6i 0.136312 0.419527i
471471 1.91245e6 + 1.38948e6i 0.397227 + 0.288602i
472472 1.59482e6 0.329501
473473 −5.16792e6 + 26643.0i −1.06209 + 0.00547558i
474474 −987790. −0.201938
475475 1.27748e6 + 928143.i 0.259788 + 0.188747i
476476 390381. 1.20147e6i 0.0789717 0.243050i
477477 426846. + 1.31370e6i 0.0858964 + 0.264362i
478478 −2.24820e6 + 1.63341e6i −0.450054 + 0.326983i
479479 4.34813e6 3.15910e6i 0.865892 0.629108i −0.0635892 0.997976i 0.520255π-0.520255\pi
0.929482 + 0.368868i 0.120255π0.120255\pi
480480 −36107.9 111129.i −0.00715318 0.0220152i
481481 −155582. + 478832.i −0.0306617 + 0.0943671i
482482 −3.84815e6 2.79584e6i −0.754456 0.548145i
483483 −3.65701e6 −0.713277
484484 821506. + 2.44236e6i 0.159403 + 0.473910i
485485 −3.93076e6 −0.758792
486486 2.21052e6 + 1.60603e6i 0.424525 + 0.308435i
487487 −1.27362e6 + 3.91980e6i −0.243342 + 0.748931i 0.752562 + 0.658521i 0.228818π0.228818\pi
−0.995905 + 0.0904096i 0.971182π0.971182\pi
488488 332305. + 1.02273e6i 0.0631665 + 0.194406i
489489 −497334. + 361334.i −0.0940536 + 0.0683340i
490490 −3.85557e6 + 2.80124e6i −0.725435 + 0.527059i
491491 −301095. 926675.i −0.0563637 0.173470i 0.918911 0.394464i 0.129070π-0.129070\pi
−0.975275 + 0.220994i 0.929070π0.929070\pi
492492 −185982. + 572395.i −0.0346385 + 0.106606i
493493 1.05921e6 + 769560.i 0.196275 + 0.142602i
494494 916980. 0.169061
495495 2.40564e6 12402.2i 0.441283 0.00227502i
496496 −1.79373e6 −0.327380
497497 −2.79032e6 2.02729e6i −0.506715 0.368150i
498498 340594. 1.04824e6i 0.0615409 0.189404i
499499 −1.74115e6 5.35872e6i −0.313030 0.963406i −0.976558 0.215255i 0.930942π-0.930942\pi
0.663528 0.748151i 0.269058π-0.269058\pi
500500 1.91249e6 1.38950e6i 0.342116 0.248562i
501501 −1.52737e6 + 1.10970e6i −0.271862 + 0.197519i
502502 476621. + 1.46689e6i 0.0844138 + 0.259799i
503503 391597. 1.20521e6i 0.0690111 0.212394i −0.910603 0.413282i 0.864382π-0.864382\pi
0.979614 + 0.200887i 0.0643825π0.0643825\pi
504504 2.88452e6 + 2.09572e6i 0.505821 + 0.367500i
505505 −2.37496e6 −0.414407
506506 4.49514e6 + 3.23063e6i 0.780489 + 0.560933i
507507 1.06309e6 0.183675
508508 −433154. 314705.i −0.0744703 0.0541058i
509509 567484. 1.74654e6i 0.0970865 0.298802i −0.890705 0.454581i 0.849789π-0.849789\pi
0.987792 + 0.155780i 0.0497889π0.0497889\pi
510510 −44918.4 138245.i −0.00764714 0.0235355i
511511 1.14152e7 8.29363e6i 1.93389 1.40505i
512512 −212079. + 154084.i −0.0357538 + 0.0259767i
513513 404494. + 1.24490e6i 0.0678607 + 0.208854i
514514 −1.81301e6 + 5.57988e6i −0.302687 + 0.931573i
515515 −119777. 87022.7i −0.0199000 0.0144582i
516516 −881324. −0.145717
517517 −2.41605e6 + 7.56839e6i −0.397539 + 1.24531i
518518 −1.42509e6 −0.233356
519519 1.80465e6 + 1.31116e6i 0.294086 + 0.213666i
520520 184852. 568915.i 0.0299789 0.0922655i
521521 −3.50060e6 1.07738e7i −0.565000 1.73889i −0.667950 0.744206i 0.732828π-0.732828\pi
0.102950 0.994687i 0.467172π-0.467172\pi
522522 −2.98944e6 + 2.17196e6i −0.480191 + 0.348879i
523523 −2.61689e6 + 1.90128e6i −0.418342 + 0.303943i −0.776970 0.629537i 0.783244π-0.783244\pi
0.358629 + 0.933480i 0.383244π0.383244\pi
524524 −1.44006e6 4.43204e6i −0.229114 0.705141i
525525 790856. 2.43400e6i 0.125227 0.385410i
526526 −3.11257e6 2.26141e6i −0.490518 0.356382i
527527 −2.23141e6 −0.349987
528528 137947. + 417225.i 0.0215341 + 0.0651307i
529529 5.45556e6 0.847617
530530 530687. + 385567.i 0.0820633 + 0.0596225i
531531 −1.73032e6 + 5.32536e6i −0.266311 + 0.819621i
532532 802063. + 2.46850e6i 0.122865 + 0.378141i
533533 −2.49269e6 + 1.81105e6i −0.380058 + 0.276129i
534534 −618569. + 449417.i −0.0938718 + 0.0682018i
535535 −1.68743e6 5.19337e6i −0.254883 0.784449i
536536 1.32155e6 4.06733e6i 0.198689 0.611501i
537537 −1.24237e6 902632.i −0.185915 0.135075i
538538 562796. 0.0838293
539539 1.44455e7 1.06095e7i 2.14170 1.57297i
540540 853908. 0.126016
541541 −2.57354e6 1.86979e6i −0.378040 0.274662i 0.382497 0.923957i 0.375064π-0.375064\pi
−0.760537 + 0.649295i 0.775064π0.775064\pi
542542 −1.91784e6 + 5.90250e6i −0.280423 + 0.863054i
543543 529864. + 1.63075e6i 0.0771196 + 0.237350i
544544 −263827. + 191682.i −0.0382228 + 0.0277705i
545545 370205. 268970.i 0.0533889 0.0387893i
546546 −459262. 1.41346e6i −0.0659294 0.202910i
547547 −1.70754e6 + 5.25527e6i −0.244007 + 0.750977i 0.751791 + 0.659402i 0.229190π0.229190\pi
−0.995798 + 0.0915756i 0.970810π0.970810\pi
548548 127555. + 92673.9i 0.0181445 + 0.0131828i
549549 −3.77559e6 −0.534631
550550 −3.12232e6 + 2.29319e6i −0.440120 + 0.323246i
551551 −2.68995e6 −0.377455
552552 763730. + 554882.i 0.106682 + 0.0775091i
553553 4.42318e6 1.36132e7i 0.615067 1.89298i
554554 −367342. 1.13056e6i −0.0508506 0.156502i
555555 −132659. + 96382.4i −0.0182812 + 0.0132821i
556556 687559. 499541.i 0.0943242 0.0685305i
557557 −692564. 2.13149e6i −0.0945849 0.291102i 0.892560 0.450928i 0.148907π-0.148907\pi
−0.987145 + 0.159826i 0.948907π0.948907\pi
558558 1.94612e6 5.98955e6i 0.264597 0.814345i
559559 −3.65018e6 2.65201e6i −0.494066 0.358960i
560560 1.69320e6 0.228159
561561 171607. + 519031.i 0.0230211 + 0.0696283i
562562 1.76941e6 0.236314
563563 3.52631e6 + 2.56201e6i 0.468867 + 0.340652i 0.797000 0.603980i 0.206419π-0.206419\pi
−0.328133 + 0.944632i 0.606419π0.606419\pi
564564 −418671. + 1.28854e6i −0.0554211 + 0.170569i
565565 −355879. 1.09528e6i −0.0469009 0.144346i
566566 4.00848e6 2.91233e6i 0.525943 0.382120i
567567 −9.23580e6 + 6.71020e6i −1.20647 + 0.876552i
568568 275128. + 846758.i 0.0357820 + 0.110126i
569569 901504. 2.77454e6i 0.116731 0.359262i −0.875573 0.483086i 0.839516π-0.839516\pi
0.992304 + 0.123824i 0.0395159π0.0395159\pi
570570 241613. + 175542.i 0.0311482 + 0.0226305i
571571 −4.46777e6 −0.573457 −0.286728 0.958012i 0.592568π-0.592568\pi
−0.286728 + 0.958012i 0.592568π0.592568\pi
572572 −684148. + 2.14312e6i −0.0874299 + 0.273878i
573573 1.55415e6 0.197746
574574 −7.05561e6 5.12620e6i −0.893830 0.649406i
575575 −2.57171e6 + 7.91491e6i −0.324379 + 0.998336i
576576 −284416. 875341.i −0.0357188 0.109931i
577577 −7.50325e6 + 5.45143e6i −0.938231 + 0.681665i −0.947994 0.318288i 0.896892π-0.896892\pi
0.00976340 + 0.999952i 0.496892π0.496892\pi
578578 4.26655e6 3.09983e6i 0.531199 0.385939i
579579 369682. + 1.13776e6i 0.0458281 + 0.141044i
580580 −542260. + 1.66890e6i −0.0669326 + 0.205997i
581581 1.29211e7 + 9.38775e6i 1.58804 + 1.15378i
582582 2.52098e6 0.308505
583583 −2.00325e6 1.43972e6i −0.244097 0.175432i
584584 −3.64235e6 −0.441926
585585 1.69914e6 + 1.23450e6i 0.205277 + 0.149142i
586586 −1.54922e6 + 4.76800e6i −0.186367 + 0.573578i
587587 1.03915e6 + 3.19818e6i 0.124476 + 0.383096i 0.993805 0.111136i 0.0354491π-0.0354491\pi
−0.869330 + 0.494233i 0.835449π0.835449\pi
588588 2.47276e6 1.79656e6i 0.294943 0.214289i
589589 3.70899e6 2.69474e6i 0.440522 0.320058i
590590 821709. + 2.52896e6i 0.0971824 + 0.299097i
591591 1.30019e6 4.00157e6i 0.153122 0.471261i
592592 297616. + 216231.i 0.0349022 + 0.0253579i
593593 2.54991e6 0.297775 0.148887 0.988854i 0.452431π-0.452431\pi
0.148887 + 0.988854i 0.452431π0.452431\pi
594594 −3.21132e6 + 16555.8i −0.373437 + 0.00192524i
595595 2.10635e6 0.243915
596596 −3.31798e6 2.41065e6i −0.382611 0.277983i
597597 456559. 1.40514e6i 0.0524277 0.161356i
598598 1.49343e6 + 4.59631e6i 0.170778 + 0.525602i
599599 −9.68867e6 + 7.03923e6i −1.10331 + 0.801601i −0.981597 0.190964i 0.938839π-0.938839\pi
−0.121712 + 0.992565i 0.538839π0.538839\pi
600600 −534476. + 388320.i −0.0606108 + 0.0440363i
601601 2.97646e6 + 9.16059e6i 0.336135 + 1.03452i 0.966160 + 0.257942i 0.0830444π0.0830444\pi
−0.630026 + 0.776574i 0.716956π0.716956\pi
602602 3.94644e6 1.21459e7i 0.443828 1.36596i
603603 1.21476e7 + 8.82577e6i 1.36050 + 0.988461i
604604 3.16822e6 0.353364
605605 −3.44966e6 + 2.56108e6i −0.383166 + 0.284469i
606606 1.52317e6 0.168487
607607 −1.17375e6 852777.i −0.129301 0.0939429i 0.521255 0.853401i 0.325464π-0.325464\pi
−0.650556 + 0.759458i 0.725464π0.725464\pi
608608 207045. 637218.i 0.0227146 0.0699084i
609609 1.34724e6 + 4.14637e6i 0.147198 + 0.453028i
610610 −1.45056e6 + 1.05389e6i −0.157838 + 0.114676i
611611 −5.61138e6 + 4.07691e6i −0.608088 + 0.441802i
612612 −353815. 1.08893e6i −0.0381854 0.117523i
613613 −4.04623e6 + 1.24530e7i −0.434910 + 1.33852i 0.458268 + 0.888814i 0.348470π0.348470\pi
−0.893179 + 0.449702i 0.851530π0.851530\pi
614614 5.13988e6 + 3.73434e6i 0.550214 + 0.399754i
615615 −1.00349e6 −0.106986
616616 −6.36766e6 + 32828.2i −0.676127 + 0.00348574i
617617 2.37821e6 0.251500 0.125750 0.992062i 0.459866π-0.459866\pi
0.125750 + 0.992062i 0.459866π0.459866\pi
618618 76818.3 + 55811.7i 0.00809083 + 0.00587833i
619619 4.79961e6 1.47717e7i 0.503477 1.54954i −0.299840 0.953990i 0.596933π-0.596933\pi
0.803317 0.595552i 0.203067π-0.203067\pi
620620 −924192. 2.84437e6i −0.0965569 0.297171i
621621 −5.58124e6 + 4.05501e6i −0.580767 + 0.421952i
622622 7.46760e6 5.42553e6i 0.773936 0.562297i
623623 −3.42374e6 1.05372e7i −0.353412 1.08769i
624624 −118554. + 364872.i −0.0121886 + 0.0375127i
625625 −2.91253e6 2.11608e6i −0.298243 0.216686i
626626 7.53750e6 0.768761
627627 −912044. 655481.i −0.0926503 0.0665873i
628628 8.84254e6 0.894701
629629 370236. + 268992.i 0.0373123 + 0.0271090i
630630 −1.83705e6 + 5.65386e6i −0.184404 + 0.567536i
631631 1.62176e6 + 4.99126e6i 0.162149 + 0.499042i 0.998815 0.0486710i 0.0154986π-0.0154986\pi
−0.836666 + 0.547713i 0.815499π0.815499\pi
632632 −2.98928e6 + 2.17184e6i −0.297696 + 0.216289i
633633 −2.08607e6 + 1.51562e6i −0.206928 + 0.150342i
634634 −1.78680e6 5.49920e6i −0.176544 0.543346i
635635 275861. 849013.i 0.0271491 0.0835565i
636636 −340354. 247282.i −0.0333648 0.0242409i
637637 1.56475e7 1.52791
638638 2.00694e6 6.28682e6i 0.195201 0.611476i
639639 −3.12596e6 −0.302853
640640 −353607. 256911.i −0.0341249 0.0247932i
641641 2.76367e6 8.50572e6i 0.265670 0.817647i −0.725869 0.687833i 0.758562π-0.758562\pi
0.991538 0.129814i 0.0414379π-0.0414379\pi
642642 1.08223e6 + 3.33075e6i 0.103629 + 0.318937i
643643 −2.41405e6 + 1.75391e6i −0.230260 + 0.167294i −0.696933 0.717136i 0.745453π-0.745453\pi
0.466673 + 0.884430i 0.345453π0.345453\pi
644644 −1.10669e7 + 8.04060e6i −1.05151 + 0.763966i
645645 −454090. 1.39754e6i −0.0429776 0.132272i
646646 257565. 792703.i 0.0242832 0.0747359i
647647 −7.28511e6 5.29294e6i −0.684188 0.497092i 0.190556 0.981676i 0.438971π-0.438971\pi
−0.874745 + 0.484584i 0.838971π0.838971\pi
648648 2.94695e6 0.275699
649649 −3.13926e6 9.49481e6i −0.292560 0.884860i
650650 −3.38214e6 −0.313985
651651 −6.01139e6 4.36753e6i −0.555933 0.403909i
652652 −710585. + 2.18696e6i −0.0654632 + 0.201475i
653653 593661. + 1.82710e6i 0.0544823 + 0.167679i 0.974595 0.223974i 0.0719032π-0.0719032\pi
−0.920113 + 0.391654i 0.871903π0.871903\pi
654654 −237430. + 172503.i −0.0217066 + 0.0157707i
655655 6.28607e6 4.56709e6i 0.572500 0.415946i
656656 695689. + 2.14111e6i 0.0631184 + 0.194258i
657657 3.95180e6 1.21624e7i 0.357176 1.09927i
658658 −1.58831e7 1.15398e7i −1.43012 1.03904i
659659 −1.90140e7 −1.70554 −0.852768 0.522290i 0.825078π-0.825078\pi
−0.852768 + 0.522290i 0.825078π0.825078\pi
660660 −590532. + 433716.i −0.0527696 + 0.0387566i
661661 4.96738e6 0.442205 0.221103 0.975251i 0.429034π-0.429034\pi
0.221103 + 0.975251i 0.429034π0.429034\pi
662662 −9.00068e6 6.53938e6i −0.798234 0.579951i
663663 −147482. + 453903.i −0.0130303 + 0.0401032i
664664 −1.27403e6 3.92107e6i −0.112140 0.345132i
665665 −3.50112e6 + 2.54371e6i −0.307011 + 0.223056i
666666 −1.04493e6 + 759187.i −0.0912856 + 0.0663229i
667667 −4.38096e6 1.34832e7i −0.381290 1.17349i
668668 −2.18229e6 + 6.71638e6i −0.189221 + 0.582364i
669669 584331. + 424542.i 0.0504770 + 0.0366737i
670670 7.13061e6 0.613676
671671 5.43473e6 3.99153e6i 0.465985 0.342242i
672672 −1.08593e6 −0.0927635
673673 2.18225e6 + 1.58550e6i 0.185724 + 0.134936i 0.676762 0.736202i 0.263383π-0.263383\pi
−0.491038 + 0.871138i 0.663383π0.663383\pi
674674 960788. 2.95700e6i 0.0814662 0.250727i
675675 −1.49192e6 4.59164e6i −0.126033 0.387890i
676676 3.21716e6 2.33740e6i 0.270773 0.196728i
677677 1.58486e7 1.15147e7i 1.32898 0.965562i 0.329209 0.944257i 0.393218π-0.393218\pi
0.999773 0.0213049i 0.00678209π-0.00678209\pi
678678 228242. + 702457.i 0.0190687 + 0.0586875i
679679 −1.12886e7 + 3.47427e7i −0.939649 + 2.89194i
680680 −439889. 319598.i −0.0364814 0.0265053i
681681 −1.05960e6 −0.0875539
682682 3.53079e6 + 1.06790e7i 0.290677 + 0.879164i
683683 1.93523e7 1.58738 0.793689 0.608324i 0.208158π-0.208158\pi
0.793689 + 0.608324i 0.208158π0.208158\pi
684684 1.90314e6 + 1.38271e6i 0.155536 + 0.113003i
685685 −81235.3 + 250016.i −0.00661482 + 0.0203583i
686686 8.53597e6 + 2.62710e7i 0.692536 + 2.13141i
687687 4.27740e6 3.10771e6i 0.345771 0.251217i
688688 −2.66709e6 + 1.93775e6i −0.214816 + 0.156073i
689689 −665545. 2.04834e6i −0.0534108 0.164382i
690690 −486394. + 1.49697e6i −0.0388924 + 0.119699i
691691 −6.10065e6 4.43238e6i −0.486050 0.353136i 0.317613 0.948220i 0.397119π-0.397119\pi
−0.803663 + 0.595084i 0.797119π0.797119\pi
692692 8.34409e6 0.662390
693693 6.79904e6 2.12983e7i 0.537792 1.68466i
694694 3.54854e6 0.279673
695695 1.14639e6 + 832903.i 0.0900267 + 0.0654083i
696696 347777. 1.07035e6i 0.0272131 0.0837532i
697697 865441. + 2.66355e6i 0.0674770 + 0.207673i
698698 −1.00964e7 + 7.33546e6i −0.784382 + 0.569887i
699699 −1.11663e6 + 811281.i −0.0864405 + 0.0628027i
700700 −2.95829e6 9.10468e6i −0.228190 0.702295i
701701 −1.27831e6 + 3.93422e6i −0.0982517 + 0.302388i −0.988087 0.153893i 0.950819π-0.950819\pi
0.889836 + 0.456281i 0.150819π0.150819\pi
702702 −2.26821e6 1.64795e6i −0.173716 0.126212i
703703 −940245. −0.0717551
704704 1.33480e6 + 959316.i 0.101505 + 0.0729508i
705705 −2.25899e6 −0.171175
706706 8.87140e6 + 6.44545e6i 0.669855 + 0.486678i
707707 −6.82054e6 + 2.09915e7i −0.513181 + 1.57941i
708708 −527000. 1.62194e6i −0.0395119 0.121605i
709709 −6.87829e6 + 4.99737e6i −0.513884 + 0.373358i −0.814295 0.580451i 0.802876π-0.802876\pi
0.300411 + 0.953810i 0.402876π0.402876\pi
710710 −1.20097e6 + 872559.i −0.0894104 + 0.0649605i
711711 −4.00887e6 1.23380e7i −0.297405 0.915318i
712712 −883805. + 2.72007e6i −0.0653366 + 0.201085i
713713 1.95479e7 + 1.42024e7i 1.44004 + 1.04625i
714714 −1.35090e6 −0.0991693
715715 −3.75091e6 + 19337.7i −0.274392 + 0.00141462i
716716 −5.74428e6 −0.418748
717717 2.40409e6 + 1.74667e6i 0.174644 + 0.126886i
718718 92133.4 283558.i 0.00666970 0.0205272i
719719 756187. + 2.32730e6i 0.0545516 + 0.167892i 0.974620 0.223865i 0.0718674π-0.0718674\pi
−0.920069 + 0.391757i 0.871867π0.871867\pi
720720 1.24152e6 902014.i 0.0892526 0.0648458i
721721 −1.11315e6 + 808748.i −0.0797470 + 0.0579396i
722722 −2.53144e6 7.79098e6i −0.180728 0.556223i
723723 −1.57178e6 + 4.83745e6i −0.111827 + 0.344168i
724724 5.18899e6 + 3.77003e6i 0.367906 + 0.267299i
725725 9.92147e6 0.701021
726726 2.21242e6 1.64254e6i 0.155785 0.115658i
727727 1.95778e7 1.37381 0.686907 0.726745i 0.258968π-0.258968\pi
0.686907 + 0.726745i 0.258968π0.258968\pi
728728 −4.49759e6 3.26769e6i −0.314522 0.228514i
729729 −2.55476e6 + 7.86274e6i −0.178046 + 0.547968i
730730 −1.87667e6 5.77579e6i −0.130341 0.401148i
731731 −3.31787e6 + 2.41057e6i −0.229650 + 0.166850i
732732 930311. 675910.i 0.0641727 0.0466242i
733733 6.86146e6 + 2.11174e7i 0.471690 + 1.45171i 0.850371 + 0.526184i 0.176378π0.176378\pi
−0.378681 + 0.925527i 0.623622π0.623622\pi
734734 −2.47829e6 + 7.62740e6i −0.169790 + 0.522560i
735735 4.12292e6 + 2.99548e6i 0.281505 + 0.204526i
736736 3.53123e6 0.240287
737737 −2.68163e7 + 138250.i −1.81857 + 0.00937556i
738738 −7.90431e6 −0.534224
739739 −1.63436e7 1.18743e7i −1.10087 0.799828i −0.119667 0.992814i 0.538183π-0.538183\pi
−0.981201 + 0.192986i 0.938183π0.938183\pi
740740 −189542. + 583350.i −0.0127241 + 0.0391606i
741741 −303011. 932572.i −0.0202728 0.0623931i
742742 4.93196e6 3.58328e6i 0.328859 0.238930i
743743 1.08677e7 7.89582e6i 0.722211 0.524717i −0.164879 0.986314i 0.552723π-0.552723\pi
0.887090 + 0.461597i 0.152723π0.152723\pi
744744 592728. + 1.82423e6i 0.0392575 + 0.120822i
745745 2.11311e6 6.50348e6i 0.139486 0.429294i
746746 −3.83750e6 2.78810e6i −0.252465 0.183426i
747747 1.44754e7 0.949136
748748 1.66050e6 + 1.19340e6i 0.108514 + 0.0779885i
749749 −5.07485e7 −3.30536
750750 −2.04510e6 1.48585e6i −0.132758 0.0964546i
751751 5.07534e6 1.56203e7i 0.328371 1.01062i −0.641525 0.767102i 0.721698π-0.721698\pi
0.969896 0.243520i 0.0783022π-0.0783022\pi
752752 1.56609e6 + 4.81993e6i 0.100989 + 0.310811i
753753 1.33433e6 969450.i 0.0857585 0.0623072i
754754 4.66119e6 3.38655e6i 0.298585 0.216935i
755755 1.63238e6 + 5.02395e6i 0.104221 + 0.320758i
756756 2.45230e6 7.54741e6i 0.156052 0.480279i
757757 −9.57374e6 6.95573e6i −0.607214 0.441167i 0.241218 0.970471i 0.422453π-0.422453\pi
−0.848432 + 0.529304i 0.822453π0.822453\pi
758758 −4.21424e6 −0.266407
759759 1.80017e6 5.63912e6i 0.113425 0.355309i
760760 1.11713e6 0.0701571
761761 1.99372e7 + 1.44852e7i 1.24797 + 0.906701i 0.998102 0.0615795i 0.0196138π-0.0196138\pi
0.249865 + 0.968281i 0.419614π0.419614\pi
762762 −176923. + 544512.i −0.0110381 + 0.0339719i
763763 −1.31416e6 4.04456e6i −0.0817215 0.251513i
764764 4.70322e6 3.41709e6i 0.291516 0.211798i
765765 1.54445e6 1.12211e6i 0.0954160 0.0693238i
766766 3.96887e6 + 1.22149e7i 0.244396 + 0.752175i
767767 2.69794e6 8.30340e6i 0.165594 0.509645i
768768 226785. + 164769.i 0.0138743 + 0.0100803i
769769 3.87154e6 0.236085 0.118042 0.993009i 0.462338π-0.462338\pi
0.118042 + 0.993009i 0.462338π0.462338\pi
770770 −3.33290e6 1.00805e7i −0.202580 0.612710i
771771 6.27386e6 0.380101
772772 3.62032e6 + 2.63032e6i 0.218627 + 0.158842i
773773 3.88671e6 1.19621e7i 0.233956 0.720041i −0.763303 0.646041i 0.776423π-0.776423\pi
0.997258 0.0740003i 0.0235766π-0.0235766\pi
774774 −3.57679e6 1.10082e7i −0.214605 0.660487i
775775 −1.36801e7 + 9.93915e6i −0.818152 + 0.594422i
776776 7.62906e6 5.54284e6i 0.454796 0.330429i
777777 470914. + 1.44933e6i 0.0279827 + 0.0861219i
778778 4.10255e6 1.26264e7i 0.242999 0.747876i
779779 −4.65514e6 3.38216e6i −0.274846 0.199687i
780780 −639672. −0.0376462
781781 4.49963e6 3.30475e6i 0.263967 0.193870i
782782 4.39287e6 0.256880
783783 6.65376e6 + 4.83424e6i 0.387849 + 0.281789i
784784 3.53305e6 1.08736e7i 0.205286 0.631806i
785785 4.55599e6 + 1.40219e7i 0.263881 + 0.812143i
786786 −4.03155e6 + 2.92909e6i −0.232764 + 0.169113i
787787 −1.07082e7 + 7.77996e6i −0.616282 + 0.447755i −0.851621 0.524158i 0.824380π-0.824380\pi
0.235339 + 0.971913i 0.424380π0.424380\pi
788788 −4.86351e6 1.49684e7i −0.279020 0.858734i
789789 −1.27133e6 + 3.91277e6i −0.0727055 + 0.223765i
790790 −4.98413e6 3.62118e6i −0.284133 0.206435i
791791 −1.07029e7 −0.608219
792792 −4.65152e6 + 3.41630e6i −0.263501 + 0.193528i
793793 5.88697e6 0.332437
794794 −4.15255e6 3.01701e6i −0.233757 0.169834i
795795 216760. 667119.i 0.0121636 0.0374357i
796796 −1.70781e6 5.25611e6i −0.0955339 0.294023i
797797 8.07740e6 5.86857e6i 0.450428 0.327255i −0.339337 0.940665i 0.610203π-0.610203\pi
0.789765 + 0.613410i 0.210203π0.210203\pi
798798 2.24543e6 1.63140e6i 0.124823 0.0906889i
799799 1.94822e6 + 5.99602e6i 0.107962 + 0.332274i
800800 −763654. + 2.35028e6i −0.0421863 + 0.129836i
801801 −8.12387e6 5.90234e6i −0.447385 0.325044i
802802 −4.11539e6 −0.225931
803803 7.16963e6 + 2.16848e7i 0.392381 + 1.18677i
804804 −4.57319e6 −0.249505
805805 −1.84523e7 1.34064e7i −1.00360 0.729159i
806806 −3.03443e6 + 9.33900e6i −0.164528 + 0.506364i
807807 −185973. 572366.i −0.0100523 0.0309379i
808808 4.60946e6 3.34897e6i 0.248383 0.180461i
809809 −2.04173e7 + 1.48340e7i −1.09680 + 0.796870i −0.980534 0.196348i 0.937092π-0.937092\pi
−0.116263 + 0.993218i 0.537092π0.537092\pi
810810 1.51837e6 + 4.67307e6i 0.0813141 + 0.250259i
811811 927407. 2.85427e6i 0.0495129 0.152385i −0.923243 0.384216i 0.874472π-0.874472\pi
0.972756 + 0.231831i 0.0744717π0.0744717\pi
812812 1.31936e7 + 9.58572e6i 0.702220 + 0.510193i
813813 6.63661e6 0.352144
814814 701506. 2.19750e6i 0.0371082 0.116243i
815815 −3.83405e6 −0.202192
816816 282122. + 204973.i 0.0148324 + 0.0107764i
817817 2.60378e6 8.01360e6i 0.136474 0.420023i
818818 2.52377e6 + 7.76736e6i 0.131876 + 0.405873i
819819 1.57910e7 1.14729e7i 0.822623 0.597671i
820820 −3.03679e6 + 2.20635e6i −0.157717 + 0.114588i
821821 −5.01417e6 1.54320e7i −0.259622 0.799033i −0.992884 0.119087i 0.962003π-0.962003\pi
0.733262 0.679946i 0.237997π-0.237997\pi
822822 52100.0 160347.i 0.00268942 0.00827717i
823823 3.05087e6 + 2.21658e6i 0.157009 + 0.114073i 0.663516 0.748162i 0.269064π-0.269064\pi
−0.506507 + 0.862236i 0.669064π0.669064\pi
824824 355182. 0.0182235
825825 3.36394e6 + 2.41764e6i 0.172073 + 0.123668i
826826 2.47125e7 1.26028
827827 2.45796e7 + 1.78581e7i 1.24972 + 0.907972i 0.998205 0.0598821i 0.0190725π-0.0190725\pi
0.251511 + 0.967854i 0.419072π0.419072\pi
828828 −3.83124e6 + 1.17913e7i −0.194206 + 0.597705i
829829 −6.08855e6 1.87386e7i −0.307700 0.947004i −0.978656 0.205506i 0.934116π-0.934116\pi
0.670956 0.741497i 0.265884π-0.265884\pi
830830 5.56135e6 4.04055e6i 0.280211 0.203585i
831831 −1.02840e6 + 747177.i −0.0516606 + 0.0375336i
832832 443466. + 1.36485e6i 0.0222102 + 0.0683558i
833833 4.39514e6 1.35268e7i 0.219462 0.675435i
834834 −735235. 534180.i −0.0366025 0.0265933i
835835 −1.17748e7 −0.584435
836836 −4.20124e6 + 21659.3i −0.207904 + 0.00107184i
837837 −1.40173e7 −0.691593
838838 −2.58015e6 1.87459e6i −0.126921 0.0922138i
839839 −905404. + 2.78655e6i −0.0444056 + 0.136666i −0.970801 0.239885i 0.922890π-0.922890\pi
0.926396 + 0.376551i 0.122890π0.122890\pi
840840 −559508. 1.72199e6i −0.0273595 0.0842039i
841841 2.92033e6 2.12174e6i 0.142378 0.103443i
842842 −1.02686e7 + 7.46056e6i −0.499149 + 0.362653i
843843 −584693. 1.79950e6i −0.0283374 0.0872134i
844844 −2.98056e6 + 9.17322e6i −0.144026 + 0.443267i
845845 5.36409e6 + 3.89724e6i 0.258437 + 0.187765i
846846 −1.77937e7 −0.854751
847847 1.27296e7 + 3.78454e7i 0.609686 + 1.81261i
848848 −1.57368e6 −0.0751498
849849 −4.28643e6 3.11427e6i −0.204092 0.148282i
850850 −949990. + 2.92377e6i −0.0450995 + 0.138802i
851851 −1.53132e6 4.71293e6i −0.0724842 0.223083i
852852 770241. 559613.i 0.0363520 0.0264112i
853853 −2.17005e7 + 1.57663e7i −1.02117 + 0.741921i −0.966522 0.256585i 0.917403π-0.917403\pi
−0.0546451 + 0.998506i 0.517403π0.517403\pi
854854 5.14921e6 + 1.58476e7i 0.241599 + 0.743567i
855855 −1.21205e6 + 3.73029e6i −0.0567027 + 0.174513i
856856 1.05983e7 + 7.70013e6i 0.494370 + 0.359181i
857857 −2.33342e7 −1.08528 −0.542639 0.839966i 0.682575π-0.682575\pi
−0.542639 + 0.839966i 0.682575π0.682575\pi
858858 2.40564e6 12402.2i 0.111561 0.000575147i
859859 2.92630e7 1.35312 0.676559 0.736389i 0.263471π-0.263471\pi
0.676559 + 0.736389i 0.263471π0.263471\pi
860860 −4.44693e6 3.23089e6i −0.205029 0.148962i
861861 −2.88188e6 + 8.86951e6i −0.132485 + 0.407748i
862862 −8.39085e6 2.58244e7i −0.384625 1.18375i
863863 2.81459e7 2.04492e7i 1.28644 0.934650i 0.286709 0.958018i 0.407439π-0.407439\pi
0.999727 + 0.0233677i 0.00743883π0.00743883\pi
864864 −1.65732e6 + 1.20411e6i −0.0755302 + 0.0548759i
865865 4.29918e6 + 1.32315e7i 0.195364 + 0.601269i
866866 −3.29314e6 + 1.01352e7i −0.149216 + 0.459240i
867867 −4.56240e6 3.31478e6i −0.206132 0.149764i
868868 −2.77946e7 −1.25216
869869 1.88142e7 + 1.35217e7i 0.845155 + 0.607409i
870870 1.87647e6 0.0840511
871871 −1.89408e7 1.37613e7i −0.845966 0.614630i
872872 −339237. + 1.04406e6i −0.0151082 + 0.0464982i
873873 1.02312e7 + 3.14884e7i 0.454351 + 1.39835i
874874 −7.30172e6 + 5.30501e6i −0.323330 + 0.234913i
875875 2.96349e7 2.15310e7i 1.30853 0.950701i
876876 1.20360e6 + 3.70429e6i 0.0529932 + 0.163096i
877877 7.02553e6 2.16224e7i 0.308447 0.949302i −0.669922 0.742432i 0.733672π-0.733672\pi
0.978368 0.206870i 0.0663277π-0.0663277\pi
878878 8.13282e6 + 5.90884e6i 0.356045 + 0.258682i
879879 5.36101e6 0.234032
880880 −833481. + 2.61091e6i −0.0362818 + 0.113654i
881881 −1.22248e6 −0.0530642 −0.0265321 0.999648i 0.508446π-0.508446\pi
−0.0265321 + 0.999648i 0.508446π0.508446\pi
882882 3.24755e7 + 2.35949e7i 1.40567 + 1.02128i
883883 −3.32947e6 + 1.02471e7i −0.143705 + 0.442280i −0.996842 0.0794073i 0.974697π-0.974697\pi
0.853137 + 0.521687i 0.174697π0.174697\pi
884884 551674. + 1.69788e6i 0.0237439 + 0.0730762i
885885 2.30043e6 1.67136e6i 0.0987305 0.0717319i
886886 8.34152e6 6.06047e6i 0.356994 0.259371i
887887 −2.16403e6 6.66018e6i −0.0923535 0.284235i 0.894201 0.447665i 0.147744π-0.147744\pi
−0.986555 + 0.163430i 0.947744π0.947744\pi
888888 121562. 374129.i 0.00517327 0.0159217i
889889 −6.71192e6 4.87649e6i −0.284834 0.206944i
890890 −4.76868e6 −0.201801
891891 −5.80080e6 1.75447e7i −0.244790 0.740376i
892892 2.70175e6 0.113693
893893 −1.04793e7 7.61368e6i −0.439749 0.319497i
894894 −1.35523e6 + 4.17098e6i −0.0567114 + 0.174540i
895895 −2.95966e6 9.10889e6i −0.123505 0.380109i
896896 −3.28626e6 + 2.38761e6i −0.136751 + 0.0993557i
897897 4.18097e6 3.03765e6i 0.173499 0.126054i
898898 2.79612e6 + 8.60557e6i 0.115708 + 0.356114i
899899 8.90145e6 2.73958e7i 0.367334 1.13054i
900900 −7.01945e6 5.09993e6i −0.288866 0.209874i
901901 −1.95767e6 −0.0803393
902902 1.13778e7 8.35638e6i 0.465629 0.341981i
903903 −1.36565e7 −0.557341
904904 2.23519e6 + 1.62396e6i 0.0909690 + 0.0660928i
905905 −3.30470e6 + 1.01708e7i −0.134125 + 0.412795i
906906 −1.04692e6 3.22209e6i −0.0423734 0.130412i
907907 −584594. + 424732.i −0.0235959 + 0.0171434i −0.599521 0.800359i 0.704642π-0.704642\pi
0.575925 + 0.817503i 0.304642π0.304642\pi
908908 −3.20660e6 + 2.32973e6i −0.129071 + 0.0937758i
909909 6.18167e6 + 1.90252e7i 0.248140 + 0.763695i
910910 2.86436e6 8.81560e6i 0.114663 0.352897i
911911 −1.07649e7 7.82115e6i −0.429748 0.312230i 0.351800 0.936075i 0.385570π-0.385570\pi
−0.781548 + 0.623845i 0.785570π0.785570\pi
912912 −716470. −0.0285240
913913 −2.08364e7 + 1.53033e7i −0.827267 + 0.607585i
914914 −3.24895e7 −1.28641
915915 1.55114e6 + 1.12697e6i 0.0612490 + 0.0445000i
916916 6.11151e6 1.88093e7i 0.240663 0.740685i
917917 −2.23144e7 6.86765e7i −0.876316 2.69702i
918918 −2.06171e6 + 1.49792e6i −0.0807460 + 0.0586654i
919919 −3.87440e6 + 2.81491e6i −0.151327 + 0.109945i −0.660872 0.750498i 0.729813π-0.729813\pi
0.509546 + 0.860444i 0.329813π0.329813\pi
920920 1.81941e6 + 5.59958e6i 0.0708699 + 0.218115i
921921 2.09939e6 6.46127e6i 0.0815539 0.250997i
922922 2.25457e6 + 1.63804e6i 0.0873447 + 0.0634596i
923923 4.87406e6 0.188316
924924 2.13755e6 + 6.46509e6i 0.0823637 + 0.249112i
925925 3.46795e6 0.133266
926926 −6.28477e6 4.56615e6i −0.240858 0.174994i
927927 −385358. + 1.18601e6i −0.0147287 + 0.0453303i
928928 −1.30090e6 4.00376e6i −0.0495877 0.152615i
929929 1.48761e7 1.08081e7i 0.565522 0.410876i −0.267954 0.963432i 0.586347π-0.586347\pi
0.833476 + 0.552556i 0.186347π0.186347\pi
930930 −2.58734e6 + 1.87981e6i −0.0980949 + 0.0712702i
931931 9.03009e6 + 2.77917e7i 0.341443 + 1.05085i
932932 −1.59543e6 + 4.91024e6i −0.0601643 + 0.185167i
933933 −7.98541e6 5.80174e6i −0.300326 0.218200i
934934 −5.08390e6 −0.190691
935935 −1.03686e6 + 3.24799e6i −0.0387873 + 0.121503i
936936 −5.03859e6 −0.187983
937937 1.20080e7 + 8.72431e6i 0.446808 + 0.324625i 0.788334 0.615247i 0.210944π-0.210944\pi
−0.341526 + 0.939872i 0.610944π0.610944\pi
938938 2.04781e7 6.30251e7i 0.759945 2.33887i
939939 −2.49073e6 7.66567e6i −0.0921854 0.283718i
940940 −6.83621e6 + 4.96680e6i −0.252346 + 0.183340i
941941 9.28589e6 6.74660e6i 0.341861 0.248377i −0.403586 0.914942i 0.632236π-0.632236\pi
0.745447 + 0.666565i 0.232236π0.232236\pi
942942 −2.92197e6 8.99290e6i −0.107287 0.330196i
943943 9.37132e6 2.88420e7i 0.343180 1.05620i
944944 −5.16095e6 3.74965e6i −0.188495 0.136950i
945945 1.32317e7 0.481988
946946 1.67864e7 + 1.20643e7i 0.609858 + 0.438302i
947947 −4.57615e7 −1.65816 −0.829078 0.559133i 0.811134π-0.811134\pi
−0.829078 + 0.559133i 0.811134π0.811134\pi
948948 3.19656e6 + 2.32243e6i 0.115521 + 0.0839310i
949949 −6.16172e6 + 1.89638e7i −0.222094 + 0.683534i
950950 −1.95181e6 6.00707e6i −0.0701665 0.215950i
951951 −5.00227e6 + 3.63436e6i −0.179356 + 0.130310i
952952 −4.08813e6 + 2.97020e6i −0.146195 + 0.106217i
953953 3.04751e6 + 9.37927e6i 0.108696 + 0.334531i 0.990580 0.136935i 0.0437250π-0.0437250\pi
−0.881884 + 0.471466i 0.843725π0.843725\pi
954954 1.70738e6 5.25478e6i 0.0607379 0.186932i
955955 7.84185e6 + 5.69744e6i 0.278234 + 0.202149i
956956 1.11157e7 0.393361
957957 −7.05690e6 + 36381.5i −0.249077 + 0.00128411i
958958 −2.14983e7 −0.756818
959959 1.97652e6 + 1.43602e6i 0.0693991 + 0.0504214i
960960 −144432. + 444515.i −0.00505806 + 0.0155671i
961961 6.32415e6 + 1.94637e7i 0.220899 + 0.679857i
962962 1.62928e6 1.18374e6i 0.0567619 0.0412399i
963963 −3.72107e7 + 2.70352e7i −1.29301 + 0.939427i
964964 5.87945e6 + 1.80951e7i 0.203772 + 0.627145i
965965 −2.30566e6 + 7.09609e6i −0.0797034 + 0.245302i
966966 1.18343e7 + 8.59815e6i 0.408038 + 0.296457i
967967 −1.16954e7 −0.402206 −0.201103 0.979570i 0.564453π-0.564453\pi
−0.201103 + 0.979570i 0.564453π0.564453\pi
968968 3.08388e6 9.83511e6i 0.105781 0.337358i
969969 −891293. −0.0304938
970970 1.27202e7 + 9.24178e6i 0.434075 + 0.315374i
971971 −1.03326e7 + 3.18005e7i −0.351691 + 1.08239i 0.606212 + 0.795303i 0.292688π0.292688\pi
−0.957903 + 0.287091i 0.907312π0.907312\pi
972972 −3.37737e6 1.03945e7i −0.114660 0.352888i
973973 1.06540e7 7.74061e6i 0.360771 0.262116i
974974 1.33375e7 9.69028e6i 0.450482 0.327295i
975975 1.11761e6 + 3.43965e6i 0.0376512 + 0.115879i
976976 1.32922e6 4.09091e6i 0.0446655 0.137466i
977977 9.59962e6 + 6.97453e6i 0.321749 + 0.233765i 0.736922 0.675978i 0.236279π-0.236279\pi
−0.415172 + 0.909743i 0.636279π0.636279\pi
978978 2.45895e6 0.0822059
979979 1.79337e7 92456.5i 0.598017 0.00308305i
980980 1.90630e7 0.634054
981981 −3.11824e6 2.26554e6i −0.103452 0.0751620i
982982 −1.20438e6 + 3.70670e6i −0.0398552 + 0.122662i
983983 1.57967e7 + 4.86174e7i 0.521415 + 1.60475i 0.771297 + 0.636475i 0.219608π0.219608\pi
−0.249882 + 0.968276i 0.580392π0.580392\pi
984984 1.94763e6 1.41504e6i 0.0641238 0.0465887i
985985 2.12300e7 1.54245e7i 0.697202 0.506547i
986986 −1.61833e6 4.98070e6i −0.0530120 0.163154i
987987 −6.48750e6 + 1.99665e7i −0.211975 + 0.652391i
988988 −2.96741e6 2.15595e6i −0.0967130 0.0702661i
989989 4.44084e7 1.44369
990990 −7.81397e6 5.61586e6i −0.253387 0.182108i
991991 −9.95092e6 −0.321869 −0.160934 0.986965i 0.551451π-0.551451\pi
−0.160934 + 0.986965i 0.551451π0.551451\pi
992992 5.80462e6 + 4.21731e6i 0.187282 + 0.136068i
993993 −3.67635e6 + 1.13146e7i −0.118316 + 0.364139i
994994 4.26324e6 + 1.31209e7i 0.136859 + 0.421209i
995995 7.45485e6 5.41627e6i 0.238716 0.173437i
996996 −3.56675e6 + 2.59140e6i −0.113926 + 0.0827724i
997997 1.73606e6 + 5.34306e6i 0.0553131 + 0.170236i 0.974896 0.222659i 0.0714736π-0.0714736\pi
−0.919583 + 0.392895i 0.871474π0.871474\pi
998998 −6.96461e6 + 2.14349e7i −0.221345 + 0.681231i
999999 2.32576e6 + 1.68976e6i 0.0737311 + 0.0535688i
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 22.6.c.b.15.2 yes 12
3.2 odd 2 198.6.f.e.37.2 12
11.3 even 5 inner 22.6.c.b.3.2 12
11.5 even 5 242.6.a.p.1.3 6
11.6 odd 10 242.6.a.o.1.3 6
33.14 odd 10 198.6.f.e.91.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
22.6.c.b.3.2 12 11.3 even 5 inner
22.6.c.b.15.2 yes 12 1.1 even 1 trivial
198.6.f.e.37.2 12 3.2 odd 2
198.6.f.e.91.2 12 33.14 odd 10
242.6.a.o.1.3 6 11.6 odd 10
242.6.a.p.1.3 6 11.5 even 5