Properties

Label 21.8.g.b.17.4
Level 2121
Weight 88
Character 21.17
Analytic conductor 6.5606.560
Analytic rank 00
Dimension 3232
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [21,8,Mod(5,21)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(21, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("21.5");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: N N == 21=37 21 = 3 \cdot 7
Weight: k k == 8 8
Character orbit: [χ][\chi] == 21.g (of order 66, degree 22, 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: 6.560085535176.56008553517
Analytic rank: 00
Dimension: 3232
Relative dimension: 1616 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 17.4
Character χ\chi == 21.17
Dual form 21.8.g.b.5.4

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+(12.6634+7.31122i)q2+(9.88299+45.7092i)q3+(42.907874.3185i)q4+(269.104+466.101i)q5+(459.342506.577i)q6+(626.737+656.311i)q7616.838iq8+(1991.65+903.486i)q9+(6815.543934.95i)q10+(1644.13949.242i)q11+(3821.09+1226.79i)q12431.129iq13+(12735.13728.92i)q14+(18645.5+16907.0i)q15+(10002.0+17324.0i)q16+(10408.018027.1i)q17+(18615.526002.6i)q18+(23102.313338.1i)q19+46186.6q20+(23805.4+35133.9i)q21+27760.4q22+(26678.115402.6i)q23+(28195.26096.21i)q24+(105771.+183201.i)q25+(3152.08+5459.56i)q26+(60981.182107.6i)q27+(75668.018417.3i)q2840183.4iq29+(112505.350422.i)q30+(25132.1+14510.0i)q31+(184942.106777.i)q32+(27140.184533.3i)q33+304380.iq34+(137250.+468739.i)q35+(18311.7+186783.i)q36+(143496.248543.i)q37+(195036.+337812.i)q38+(19706.54260.84i)q39+(287509.165994.i)q40+309693.q41+(44585.3618961.i)q4247389.8q43+(141092.+81459.8i)q44+(957078.685181.i)q45+(225223.+390098.i)q46+(360027.+623585.i)q47+(693017.+628398.i)q48+(37945.1+822668.i)q493.09326e6iq50+(926866.+297577.i)q51+(32040.918498.8i)q52+(679694.+392422.i)q53+(1.37253e6+593916.i)q541.02178e6iq55+(404838.386595.i)q56+(837993.+924165.i)q57+(293790.+508859.i)q58+(494964.+857303.i)q59+(456462.+2.11115e6i)q60+(1.30273e6752131.i)q61424344.q62+(1.84121e6740896.i)q63+562144.q64+(200950.116018.i)q65+(274356.+1.26891e6i)q66+(997379.+1.72751e6i)q67+(893166.1.54701e6i)q68+(967698.+1.06721e6i)q69+(1.68900e66.93929e6i)q70+672836.iq71+(557305.+1.22853e6i)q72+(3.19678e61.84566e6i)q73+(3.63430e6+2.09827e6i)q74+(9.41930e63.02414e6i)q752.28924e6iq76+(407442.1.67399e6i)q77+(218400.+198036.i)q78+(626552.+1.08522e6i)q79+(5.38317e6+9.32393e6i)q80+(3.15039e63.59886e6i)q81+(3.92177e6+2.26423e6i)q824.44416e6q83+(1.58966e6+3.27670e6i)q84+1.12033e7q85+(600116.346477.i)q86+(1.83675e6397132.i)q87+(585529.+1.01417e6i)q88+(737221.1.27690e6i)q89+(1.71294e7+1.67931e6i)q90+(282955.270204.i)q912.64356e6iq92+(414861.+1.29217e6i)q93+(9.11834e65.26447e6i)q94+(1.24338e7+7.17867e6i)q95+(3.05288e69.50883e6i)q96+8.19557e6iq97+(5.53419e61.06952e7i)q98+(4.13217e6+405106.i)q99+O(q100)q+(-12.6634 + 7.31122i) q^{2} +(9.88299 + 45.7092i) q^{3} +(42.9078 - 74.3185i) q^{4} +(269.104 + 466.101i) q^{5} +(-459.342 - 506.577i) q^{6} +(626.737 + 656.311i) q^{7} -616.838i q^{8} +(-1991.65 + 903.486i) q^{9} +(-6815.54 - 3934.95i) q^{10} +(-1644.13 - 949.242i) q^{11} +(3821.09 + 1226.79i) q^{12} -431.129i q^{13} +(-12735.1 - 3728.92i) q^{14} +(-18645.5 + 16907.0i) q^{15} +(10002.0 + 17324.0i) q^{16} +(10408.0 - 18027.1i) q^{17} +(18615.5 - 26002.6i) q^{18} +(23102.3 - 13338.1i) q^{19} +46186.6 q^{20} +(-23805.4 + 35133.9i) q^{21} +27760.4 q^{22} +(26678.1 - 15402.6i) q^{23} +(28195.2 - 6096.21i) q^{24} +(-105771. + 183201. i) q^{25} +(3152.08 + 5459.56i) q^{26} +(-60981.1 - 82107.6i) q^{27} +(75668.0 - 18417.3i) q^{28} -40183.4i q^{29} +(112505. - 350422. i) q^{30} +(25132.1 + 14510.0i) q^{31} +(-184942. - 106777. i) q^{32} +(27140.1 - 84533.3i) q^{33} +304380. i q^{34} +(-137250. + 468739. i) q^{35} +(-18311.7 + 186783. i) q^{36} +(-143496. - 248543. i) q^{37} +(-195036. + 337812. i) q^{38} +(19706.5 - 4260.84i) q^{39} +(287509. - 165994. i) q^{40} +309693. q^{41} +(44585.3 - 618961. i) q^{42} -47389.8 q^{43} +(-141092. + 81459.8i) q^{44} +(-957078. - 685181. i) q^{45} +(-225223. + 390098. i) q^{46} +(360027. + 623585. i) q^{47} +(-693017. + 628398. i) q^{48} +(-37945.1 + 822668. i) q^{49} -3.09326e6i q^{50} +(926866. + 297577. i) q^{51} +(-32040.9 - 18498.8i) q^{52} +(679694. + 392422. i) q^{53} +(1.37253e6 + 593916. i) q^{54} -1.02178e6i q^{55} +(404838. - 386595. i) q^{56} +(837993. + 924165. i) q^{57} +(293790. + 508859. i) q^{58} +(-494964. + 857303. i) q^{59} +(456462. + 2.11115e6i) q^{60} +(1.30273e6 - 752131. i) q^{61} -424344. q^{62} +(-1.84121e6 - 740896. i) q^{63} +562144. q^{64} +(200950. - 116018. i) q^{65} +(274356. + 1.26891e6i) q^{66} +(-997379. + 1.72751e6i) q^{67} +(-893166. - 1.54701e6i) q^{68} +(967698. + 1.06721e6i) q^{69} +(-1.68900e6 - 6.93929e6i) q^{70} +672836. i q^{71} +(557305. + 1.22853e6i) q^{72} +(-3.19678e6 - 1.84566e6i) q^{73} +(3.63430e6 + 2.09827e6i) q^{74} +(-9.41930e6 - 3.02414e6i) q^{75} -2.28924e6i q^{76} +(-407442. - 1.67399e6i) q^{77} +(-218400. + 198036. i) q^{78} +(626552. + 1.08522e6i) q^{79} +(-5.38317e6 + 9.32393e6i) q^{80} +(3.15039e6 - 3.59886e6i) q^{81} +(-3.92177e6 + 2.26423e6i) q^{82} -4.44416e6 q^{83} +(1.58966e6 + 3.27670e6i) q^{84} +1.12033e7 q^{85} +(600116. - 346477. i) q^{86} +(1.83675e6 - 397132. i) q^{87} +(-585529. + 1.01417e6i) q^{88} +(-737221. - 1.27690e6i) q^{89} +(1.71294e7 + 1.67931e6i) q^{90} +(282955. - 270204. i) q^{91} -2.64356e6i q^{92} +(-414861. + 1.29217e6i) q^{93} +(-9.11834e6 - 5.26447e6i) q^{94} +(1.24338e7 + 7.17867e6i) q^{95} +(3.05288e6 - 9.50883e6i) q^{96} +8.19557e6i q^{97} +(-5.53419e6 - 1.06952e7i) q^{98} +(4.13217e6 + 405106. i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 32q84q3+1150q4+2464q73516q9630q103864q12+27576q1519594q16+33498q1847880q19+151788q21+105132q22211554q24331252q25++35642232q99+O(q100) 32 q - 84 q^{3} + 1150 q^{4} + 2464 q^{7} - 3516 q^{9} - 630 q^{10} - 3864 q^{12} + 27576 q^{15} - 19594 q^{16} + 33498 q^{18} - 47880 q^{19} + 151788 q^{21} + 105132 q^{22} - 211554 q^{24} - 331252 q^{25}+ \cdots + 35642232 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/21Z)×\left(\mathbb{Z}/21\mathbb{Z}\right)^\times.

nn 88 1010
χ(n)\chi(n) 1-1 e(16)e\left(\frac{1}{6}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −12.6634 + 7.31122i −1.11930 + 0.646226i −0.941221 0.337790i 0.890321π-0.890321\pi
−0.178076 + 0.984017i 0.556987π0.556987\pi
33 9.88299 + 45.7092i 0.211331 + 0.977414i
44 42.9078 74.3185i 0.335217 0.580613i
55 269.104 + 466.101i 0.962775 + 1.66758i 0.715478 + 0.698635i 0.246209π0.246209\pi
0.247297 + 0.968940i 0.420458π0.420458\pi
66 −459.342 506.577i −0.868174 0.957449i
77 626.737 + 656.311i 0.690625 + 0.723213i
88 616.838i 0.425948i
99 −1991.65 + 903.486i −0.910678 + 0.413117i
1010 −6815.54 3934.95i −2.15526 1.24434i
1111 −1644.13 949.242i −0.372446 0.215032i 0.302081 0.953282i 0.402319π-0.402319\pi
−0.674526 + 0.738251i 0.735652π0.735652\pi
1212 3821.09 + 1226.79i 0.638342 + 0.204944i
1313 431.129i 0.0544259i −0.999630 0.0272129i 0.991337π-0.991337\pi
0.999630 0.0272129i 0.00866322π-0.00866322\pi
1414 −12735.1 3728.92i −1.24037 0.363191i
1515 −18645.5 + 16907.0i −1.42645 + 1.29344i
1616 10002.0 + 17324.0i 0.610476 + 1.05738i
1717 10408.0 18027.1i 0.513801 0.889929i −0.486071 0.873919i 0.661570π-0.661570\pi
0.999872 0.0160095i 0.00509620π-0.00509620\pi
1818 18615.5 26002.6i 0.752352 1.05090i
1919 23102.3 13338.1i 0.772711 0.446125i −0.0611298 0.998130i 0.519470π-0.519470\pi
0.833841 + 0.552005i 0.186137π0.186137\pi
2020 46186.6 1.29096
2121 −23805.4 + 35133.9i −0.560929 + 0.827864i
2222 27760.4 0.555837
2323 26678.1 15402.6i 0.457201 0.263965i −0.253666 0.967292i 0.581636π-0.581636\pi
0.710866 + 0.703327i 0.248303π0.248303\pi
2424 28195.2 6096.21i 0.416328 0.0900162i
2525 −105771. + 183201.i −1.35387 + 2.34497i
2626 3152.08 + 5459.56i 0.0351714 + 0.0609187i
2727 −60981.1 82107.6i −0.596241 0.802805i
2828 75668.0 18417.3i 0.651417 0.158552i
2929 40183.4i 0.305952i −0.988230 0.152976i 0.951114π-0.951114\pi
0.988230 0.152976i 0.0488858π-0.0488858\pi
3030 112505. 350422.i 0.760763 2.36955i
3131 25132.1 + 14510.0i 0.151518 + 0.0874787i 0.573842 0.818966i 0.305452π-0.305452\pi
−0.422324 + 0.906445i 0.638786π0.638786\pi
3232 −184942. 106777.i −0.997726 0.576038i
3333 27140.1 84533.3i 0.131466 0.409477i
3434 304380.i 1.32813i
3535 −137250. + 468739.i −0.541097 + 1.84796i
3636 −18311.7 + 186783.i −0.0654139 + 0.667236i
3737 −143496. 248543.i −0.465730 0.806669i 0.533504 0.845798i 0.320875π-0.320875\pi
−0.999234 + 0.0391289i 0.987542π0.987542\pi
3838 −195036. + 337812.i −0.576596 + 0.998693i
3939 19706.5 4260.84i 0.0531966 0.0115019i
4040 287509. 165994.i 0.710300 0.410092i
4141 309693. 0.701759 0.350879 0.936421i 0.385883π-0.385883\pi
0.350879 + 0.936421i 0.385883π0.385883\pi
4242 44585.3 618961.i 0.0928581 1.28911i
4343 −47389.8 −0.0908961 −0.0454480 0.998967i 0.514472π-0.514472\pi
−0.0454480 + 0.998967i 0.514472π0.514472\pi
4444 −141092. + 81459.8i −0.249700 + 0.144165i
4545 −957078. 685181.i −1.56568 1.12089i
4646 −225223. + 390098.i −0.341162 + 0.590910i
4747 360027. + 623585.i 0.505816 + 0.876099i 0.999977 + 0.00672904i 0.00214194π0.00214194\pi
−0.494161 + 0.869370i 0.664525π0.664525\pi
4848 −693017. + 628398.i −0.904481 + 0.820145i
4949 −37945.1 + 822668.i −0.0460755 + 0.998938i
5050 3.09326e6i 3.49963i
5151 926866. + 297577.i 0.978411 + 0.314126i
5252 −32040.9 18498.8i −0.0316004 0.0182445i
5353 679694. + 392422.i 0.627116 + 0.362066i 0.779634 0.626235i 0.215405π-0.215405\pi
−0.152518 + 0.988301i 0.548738π0.548738\pi
5454 1.37253e6 + 593916.i 1.18617 + 0.513271i
5555 1.02178e6i 0.828108i
5656 404838. 386595.i 0.308051 0.294170i
5757 837993. + 924165.i 0.599347 + 0.660979i
5858 293790. + 508859.i 0.197715 + 0.342452i
5959 −494964. + 857303.i −0.313756 + 0.543441i −0.979172 0.203032i 0.934921π-0.934921\pi
0.665417 + 0.746472i 0.268254π0.268254\pi
6060 456462. + 2.11115e6i 0.272819 + 1.26180i
6161 1.30273e6 752131.i 0.734852 0.424267i −0.0853427 0.996352i 0.527199π-0.527199\pi
0.820194 + 0.572085i 0.193865π0.193865\pi
6262 −424344. −0.226124
6363 −1.84121e6 740896.i −0.927708 0.373306i
6464 562144. 0.268051
6565 200950. 116018.i 0.0907592 0.0523999i
6666 274356. + 1.26891e6i 0.117466 + 0.543283i
6767 −997379. + 1.72751e6i −0.405134 + 0.701712i −0.994337 0.106273i 0.966108π-0.966108\pi
0.589203 + 0.807985i 0.299442π0.299442\pi
6868 −893166. 1.54701e6i −0.344470 0.596639i
6969 967698. + 1.06721e6i 0.354624 + 0.391090i
7070 −1.68900e6 6.93929e6i −0.588553 2.41809i
7171 672836.i 0.223103i 0.993759 + 0.111551i 0.0355820π0.0355820\pi
−0.993759 + 0.111551i 0.964418π0.964418\pi
7272 557305. + 1.22853e6i 0.175966 + 0.387901i
7373 −3.19678e6 1.84566e6i −0.961795 0.555293i −0.0650703 0.997881i 0.520727π-0.520727\pi
−0.896725 + 0.442588i 0.854060π0.854060\pi
7474 3.63430e6 + 2.09827e6i 1.04258 + 0.601935i
7575 −9.41930e6 3.02414e6i −2.57813 0.827727i
7676 2.28924e6i 0.598195i
7777 −407442. 1.67399e6i −0.101706 0.417864i
7878 −218400. + 198036.i −0.0521100 + 0.0472511i
7979 626552. + 1.08522e6i 0.142976 + 0.247641i 0.928616 0.371043i 0.121000π-0.121000\pi
−0.785640 + 0.618684i 0.787666π0.787666\pi
8080 −5.38317e6 + 9.32393e6i −1.17550 + 2.03603i
8181 3.15039e6 3.59886e6i 0.658669 0.752433i
8282 −3.92177e6 + 2.26423e6i −0.785477 + 0.453495i
8383 −4.44416e6 −0.853133 −0.426566 0.904456i 0.640277π-0.640277\pi
−0.426566 + 0.904456i 0.640277π0.640277\pi
8484 1.58966e6 + 3.27670e6i 0.292636 + 0.603197i
8585 1.12033e7 1.97870
8686 600116. 346477.i 0.101740 0.0587395i
8787 1.83675e6 397132.i 0.299042 0.0646574i
8888 −585529. + 1.01417e6i −0.0915923 + 0.158642i
8989 −737221. 1.27690e6i −0.110849 0.191996i 0.805264 0.592917i 0.202024π-0.202024\pi
−0.916113 + 0.400920i 0.868690π0.868690\pi
9090 1.71294e7 + 1.67931e6i 2.47681 + 0.242819i
9191 282955. 270204.i 0.0393615 0.0375879i
9292 2.64356e6i 0.353942i
9393 −414861. + 1.29217e6i −0.0534825 + 0.166582i
9494 −9.11834e6 5.26447e6i −1.13232 0.653744i
9595 1.24338e7 + 7.17867e6i 1.48789 + 0.859036i
9696 3.05288e6 9.50883e6i 0.352177 1.09693i
9797 8.19557e6i 0.911755i 0.890043 + 0.455877i 0.150674π0.150674\pi
−0.890043 + 0.455877i 0.849326π0.849326\pi
9898 −5.53419e6 1.06952e7i −0.593968 1.14788i
9999 4.13217e6 + 405106.i 0.428011 + 0.0419610i
100100 9.07682e6 + 1.57215e7i 0.907682 + 1.57215i
101101 6.76207e6 1.17123e7i 0.653063 1.13114i −0.329313 0.944221i 0.606817π-0.606817\pi
0.982376 0.186917i 0.0598496π-0.0598496\pi
102102 −1.39129e7 + 3.00818e6i −1.29813 + 0.280675i
103103 8.19802e6 4.73313e6i 0.739228 0.426794i −0.0825603 0.996586i 0.526310π-0.526310\pi
0.821789 + 0.569792i 0.192976π0.192976\pi
104104 −265937. −0.0231826
105105 −2.27821e7 1.64105e6i −1.92057 0.138344i
106106 −1.14763e7 −0.935906
107107 −170692. + 98549.2i −0.0134701 + 0.00777696i −0.506720 0.862111i 0.669142π-0.669142\pi
0.493250 + 0.869888i 0.335809π0.335809\pi
108108 −8.71868e6 + 1.00897e6i −0.665990 + 0.0770714i
109109 924586. 1.60143e6i 0.0683840 0.118445i −0.829806 0.558052i 0.811549π-0.811549\pi
0.898190 + 0.439607i 0.144882π0.144882\pi
110110 7.47044e6 + 1.29392e7i 0.535145 + 0.926899i
111111 9.94251e6 9.01544e6i 0.690026 0.625686i
112112 −5.10131e6 + 1.74221e7i −0.343098 + 1.17175i
113113 1.54177e7i 1.00518i −0.864525 0.502590i 0.832380π-0.832380\pi
0.864525 0.502590i 0.167620π-0.167620\pi
114114 −1.73686e7 5.57632e6i −1.09799 0.352518i
115115 1.43583e7 + 8.28979e6i 0.880362 + 0.508277i
116116 −2.98637e6 1.72418e6i −0.177640 0.102561i
117117 389519. + 858659.i 0.0224842 + 0.0495645i
118118 1.44752e7i 0.811029i
119119 1.83545e7 4.46740e6i 0.998452 0.243019i
120120 1.04289e7 + 1.15013e7i 0.550938 + 0.607592i
121121 −7.94147e6 1.37550e7i −0.407523 0.705850i
122122 −1.09980e7 + 1.90491e7i −0.548345 + 0.949761i
123123 3.06069e6 + 1.41558e7i 0.148304 + 0.685909i
124124 2.15673e6 1.24519e6i 0.101583 0.0586488i
125125 −7.18062e7 −3.28834
126126 2.87328e7 4.07923e6i 1.27962 0.181669i
127127 −1.74020e7 −0.753853 −0.376926 0.926243i 0.623019π-0.623019\pi
−0.376926 + 0.926243i 0.623019π0.623019\pi
128128 1.65540e7 9.55744e6i 0.697698 0.402816i
129129 −468353. 2.16615e6i −0.0192092 0.0888432i
130130 −1.69647e6 + 2.93838e6i −0.0677244 + 0.117302i
131131 2.28229e7 + 3.95304e7i 0.886995 + 1.53632i 0.843410 + 0.537270i 0.180544π0.180544\pi
0.0435843 + 0.999050i 0.486122π0.486122\pi
132132 −5.11787e6 5.64415e6i −0.193678 0.213594i
133133 2.32330e7 + 6.80280e6i 0.856297 + 0.250730i
134134 2.91682e7i 1.04723i
135135 2.18602e7 5.05188e7i 0.764692 1.76720i
136136 −1.11198e7 6.42003e6i −0.379063 0.218852i
137137 −2.55140e7 1.47305e7i −0.847728 0.489436i 0.0121555 0.999926i 0.496131π-0.496131\pi
−0.859884 + 0.510490i 0.829464π0.829464\pi
138138 −2.00569e7 6.43943e6i −0.649662 0.208579i
139139 6.02035e7i 1.90138i 0.310136 + 0.950692i 0.399625π0.399625\pi
−0.310136 + 0.950692i 0.600375π0.600375\pi
140140 2.89468e7 + 3.03128e7i 0.891565 + 0.933636i
141141 −2.49454e7 + 2.26194e7i −0.749417 + 0.679539i
142142 −4.91925e6 8.52039e6i −0.144175 0.249718i
143143 −409246. + 708834.i −0.0117033 + 0.0202707i
144144 −3.55726e7 2.54668e7i −0.992767 0.710731i
145145 1.87295e7 1.08135e7i 0.510199 0.294563i
146146 5.39761e7 1.43538
147147 −3.79785e7 + 6.39599e6i −0.986114 + 0.166072i
148148 −2.46284e7 −0.624484
149149 −9.02712e6 + 5.21181e6i −0.223562 + 0.129073i −0.607598 0.794244i 0.707867π-0.707867\pi
0.384037 + 0.923318i 0.374534π0.374534\pi
150150 1.41391e8 3.05707e7i 3.42059 0.739582i
151151 1.90839e7 3.30543e7i 0.451074 0.781283i −0.547379 0.836885i 0.684374π-0.684374\pi
0.998453 + 0.0556021i 0.0177078π0.0177078\pi
152152 −8.22746e6 1.42504e7i −0.190026 0.329135i
153153 −4.44179e6 + 4.53072e7i −0.100262 + 1.02270i
154154 1.73985e7 + 1.82195e7i 0.383874 + 0.401988i
155155 1.56188e7i 0.336889i
156156 528905. 1.64738e6i 0.0111543 0.0347423i
157157 −4.74464e7 2.73932e7i −0.978486 0.564929i −0.0766733 0.997056i 0.524430π-0.524430\pi
−0.901813 + 0.432127i 0.857763π0.857763\pi
158158 −1.58686e7 9.16171e6i −0.320065 0.184789i
159159 −1.12198e7 + 3.49465e7i −0.221359 + 0.689468i
160160 1.14936e8i 2.21838i
161161 2.68290e7 + 7.85573e6i 0.506657 + 0.148353i
162162 −1.35826e7 + 6.86071e7i −0.251004 + 1.26785i
163163 3.01449e7 + 5.22125e7i 0.545202 + 0.944317i 0.998594 + 0.0530060i 0.0168802π0.0168802\pi
−0.453393 + 0.891311i 0.649786π0.649786\pi
164164 1.32883e7 2.30159e7i 0.235242 0.407451i
165165 4.67046e7 1.00982e7i 0.809405 0.175005i
166166 5.62782e7 3.24922e7i 0.954909 0.551317i
167167 3.16225e7 0.525398 0.262699 0.964878i 0.415387π-0.415387\pi
0.262699 + 0.964878i 0.415387π0.415387\pi
168168 2.16719e7 + 1.46841e7i 0.352627 + 0.238926i
169169 6.25626e7 0.997038
170170 −1.41872e8 + 8.19097e7i −2.21475 + 1.27869i
171171 −3.39609e7 + 4.74375e7i −0.519389 + 0.725496i
172172 −2.03339e6 + 3.52194e6i −0.0304699 + 0.0527755i
173173 1.77562e6 + 3.07546e6i 0.0260729 + 0.0451595i 0.878767 0.477250i 0.158366π-0.158366\pi
−0.852695 + 0.522410i 0.825033π0.825033\pi
174174 −2.03560e7 + 1.84579e7i −0.292934 + 0.265620i
175175 −1.86528e8 + 4.54001e7i −2.63093 + 0.640358i
176176 3.79774e7i 0.525087i
177177 −4.40783e7 1.41517e7i −0.597473 0.191823i
178178 1.86714e7 + 1.07800e7i 0.248146 + 0.143267i
179179 −7.62456e7 4.40204e7i −0.993641 0.573679i −0.0872803 0.996184i 0.527818π-0.527818\pi
−0.906361 + 0.422505i 0.861151π0.861151\pi
180180 −9.19877e7 + 4.17290e7i −1.17564 + 0.533315i
181181 1.12564e8i 1.41099i −0.708714 0.705496i 0.750724π-0.750724\pi
0.708714 0.705496i 0.249276π-0.249276\pi
182182 −1.60765e6 + 5.49045e6i −0.0197670 + 0.0675084i
183183 4.72541e7 + 5.21133e7i 0.569982 + 0.628594i
184184 −9.50090e6 1.64560e7i −0.112435 0.194744i
185185 7.72308e7 1.33768e8i 0.896787 1.55328i
186186 −4.19379e6 1.93964e7i −0.0477872 0.221017i
187187 −3.42242e7 + 1.97593e7i −0.382726 + 0.220967i
188188 6.17919e7 0.678233
189189 1.56690e7 9.14824e7i 0.168821 0.985647i
190190 −2.09939e8 −2.22053
191191 7.36326e7 4.25118e7i 0.764633 0.441461i −0.0663235 0.997798i 0.521127π-0.521127\pi
0.830957 + 0.556337i 0.187794π0.187794\pi
192192 5.55566e6 + 2.56951e7i 0.0566476 + 0.261997i
193193 9.02429e7 1.56305e8i 0.903571 1.56503i 0.0807470 0.996735i 0.474269π-0.474269\pi
0.822824 0.568296i 0.192397π-0.192397\pi
194194 −5.99196e7 1.03784e8i −0.589200 1.02052i
195195 7.28909e6 + 8.03864e6i 0.0703967 + 0.0776357i
196196 5.95113e7 + 3.81189e7i 0.564551 + 0.361613i
197197 2.09911e8i 1.95616i 0.208239 + 0.978078i 0.433227π0.433227\pi
−0.208239 + 0.978078i 0.566773π0.566773\pi
198198 −5.52892e7 + 2.50812e7i −0.506188 + 0.229625i
199199 1.26959e8 + 7.32997e7i 1.14203 + 0.659350i 0.946932 0.321434i 0.104165π-0.104165\pi
0.195096 + 0.980784i 0.437498π0.437498\pi
200200 1.13005e8 + 6.52437e7i 0.998836 + 0.576678i
201201 −8.88202e7 2.85164e7i −0.771481 0.247690i
202202 1.97756e8i 1.68811i
203203 2.63728e7 2.51844e7i 0.221269 0.211298i
204204 6.18853e7 5.61149e7i 0.510366 0.462778i
205205 8.33396e7 + 1.44348e8i 0.675636 + 1.17024i
206206 −6.92099e7 + 1.19875e8i −0.551611 + 0.955418i
207207 −3.92174e7 + 5.47799e7i −0.307314 + 0.429264i
208208 7.46890e6 4.31217e6i 0.0575486 0.0332257i
209209 −5.06443e7 −0.383724
210210 3.00497e8 1.45784e8i 2.23909 1.08628i
211211 1.44961e8 1.06233 0.531167 0.847267i 0.321754π-0.321754\pi
0.531167 + 0.847267i 0.321754π0.321754\pi
212212 5.83284e7 3.36759e7i 0.420440 0.242741i
213213 −3.07548e7 + 6.64963e6i −0.218064 + 0.0471486i
214214 1.44103e6 2.49594e6i 0.0100514 0.0174095i
215215 −1.27528e7 2.20885e7i −0.0875125 0.151576i
216216 −5.06471e7 + 3.76155e7i −0.341953 + 0.253968i
217217 6.22812e6 + 2.55884e7i 0.0413760 + 0.169994i
218218 2.70394e7i 0.176766i
219219 5.27699e7 1.64363e8i 0.339494 1.05742i
220220 −7.59370e7 4.38423e7i −0.480811 0.277596i
221221 −7.77202e6 4.48718e6i −0.0484352 0.0279640i
222222 −5.99921e7 + 1.86858e8i −0.368009 + 1.14624i
223223 1.90116e8i 1.14803i −0.818846 0.574013i 0.805386π-0.805386\pi
0.818846 0.574013i 0.194614π-0.194614\pi
224224 −4.58316e7 1.88300e8i −0.272456 1.11939i
225225 4.51398e7 4.60436e8i 0.264193 2.69482i
226226 1.12722e8 + 1.95240e8i 0.649575 + 1.12510i
227227 −2.24577e7 + 3.88979e7i −0.127431 + 0.220717i −0.922681 0.385565i 0.874006π-0.874006\pi
0.795250 + 0.606282i 0.207340π0.207340\pi
228228 1.04639e8 2.26245e7i 0.584685 0.126417i
229229 −7.11671e7 + 4.10883e7i −0.391611 + 0.226097i −0.682858 0.730551i 0.739263π-0.739263\pi
0.291247 + 0.956648i 0.405930π0.405930\pi
230230 −2.42434e8 −1.31385
231231 7.24898e7 3.51678e7i 0.386932 0.187717i
232232 −2.47867e7 −0.130320
233233 3.15260e7 1.82015e7i 0.163276 0.0942676i −0.416135 0.909303i 0.636616π-0.636616\pi
0.579412 + 0.815035i 0.303282π0.303282\pi
234234 −1.12105e7 8.02569e6i −0.0571964 0.0409474i
235235 −1.93769e8 + 3.35618e8i −0.973974 + 1.68697i
236236 4.24756e7 + 7.35700e7i 0.210353 + 0.364341i
237237 −4.34123e7 + 3.93644e7i −0.211833 + 0.192081i
238238 −1.99768e8 + 1.90766e8i −0.960519 + 0.917236i
239239 1.04151e8i 0.493482i 0.969081 + 0.246741i 0.0793597π0.0793597\pi
−0.969081 + 0.246741i 0.920640π0.920640\pi
240240 −4.79391e8 1.53912e8i −2.23846 0.718676i
241241 −2.43431e8 1.40545e8i −1.12025 0.646778i −0.178787 0.983888i 0.557217π-0.557217\pi
−0.941465 + 0.337110i 0.890551π0.890551\pi
242242 2.01132e8 + 1.16124e8i 0.912278 + 0.526704i
243243 1.95636e8 + 1.08434e8i 0.874636 + 0.484780i
244244 1.29089e8i 0.568886i
245245 −3.93658e8 + 2.03697e8i −1.71016 + 0.884918i
246246 −1.42255e8 1.56883e8i −0.609249 0.671899i
247247 −5.75044e6 9.96006e6i −0.0242807 0.0420555i
248248 8.95034e6 1.55024e7i 0.0372614 0.0645386i
249249 −4.39216e7 2.03139e8i −0.180294 0.833864i
250250 9.09311e8 5.24991e8i 3.68063 2.12501i
251251 3.23864e8 1.29272 0.646360 0.763033i 0.276290π-0.276290\pi
0.646360 + 0.763033i 0.276290π0.276290\pi
252252 −1.34065e8 + 1.05046e8i −0.527730 + 0.413501i
253253 −5.84831e7 −0.227043
254254 2.20369e8 1.27230e8i 0.843785 0.487160i
255255 1.10722e8 + 5.12093e8i 0.418161 + 1.93401i
256256 −1.75730e8 + 3.04374e8i −0.654646 + 1.13388i
257257 1.00340e8 + 1.73794e8i 0.368729 + 0.638657i 0.989367 0.145440i 0.0464597π-0.0464597\pi
−0.620638 + 0.784097i 0.713126π0.713126\pi
258258 2.17681e7 + 2.40066e7i 0.0789136 + 0.0870284i
259259 7.31870e7 2.49949e8i 0.261749 0.893928i
260260 1.99124e7i 0.0702614i
261261 3.63052e7 + 8.00314e7i 0.126394 + 0.278624i
262262 −5.78031e8 3.33726e8i −1.98562 1.14640i
263263 −3.72853e8 2.15267e8i −1.26384 0.729679i −0.290025 0.957019i 0.593664π-0.593664\pi
−0.973815 + 0.227340i 0.926997π0.926997\pi
264264 −5.21434e7 1.67410e7i −0.174416 0.0559975i
265265 4.22408e8i 1.39435i
266266 −3.43945e8 + 8.37149e7i −1.12048 + 0.272720i
267267 5.10802e7 4.63174e7i 0.164234 0.148920i
268268 8.55907e7 + 1.48247e8i 0.271616 + 0.470452i
269269 1.21334e8 2.10157e8i 0.380058 0.658280i −0.611012 0.791621i 0.709237π-0.709237\pi
0.991070 + 0.133342i 0.0425707π0.0425707\pi
270270 9.25293e7 + 7.99565e8i 0.286092 + 2.47218i
271271 −1.27614e8 + 7.36782e7i −0.389500 + 0.224878i −0.681943 0.731405i 0.738865π-0.738865\pi
0.292444 + 0.956283i 0.405532π0.405532\pi
272272 4.16403e8 1.25465
273273 1.51473e7 + 1.02632e7i 0.0450572 + 0.0305290i
274274 4.30792e8 1.26515
275275 3.47804e8 2.00805e8i 1.00849 0.582250i
276276 1.20835e8 2.61263e7i 0.345948 0.0747991i
277277 2.57551e8 4.46092e8i 0.728089 1.26109i −0.229602 0.973285i 0.573742π-0.573742\pi
0.957690 0.287802i 0.0929244π-0.0929244\pi
278278 −4.40161e8 7.62381e8i −1.22872 2.12821i
279279 −6.31641e7 6.19242e6i −0.174123 0.0170705i
280280 2.89136e8 + 8.46612e7i 0.787135 + 0.230479i
281281 3.74214e8i 1.00612i −0.864253 0.503058i 0.832208π-0.832208\pi
0.864253 0.503058i 0.167792π-0.167792\pi
282282 1.50518e8 4.68820e8i 0.399684 1.24490i
283283 −3.25535e8 1.87948e8i −0.853778 0.492929i 0.00814601 0.999967i 0.497407π-0.497407\pi
−0.861924 + 0.507038i 0.830740π0.830740\pi
284284 5.00042e7 + 2.88699e7i 0.129536 + 0.0747879i
285285 −2.05248e8 + 6.39286e8i −0.525195 + 1.63583i
286286 1.19683e7i 0.0302519i
287287 1.94096e8 + 2.03255e8i 0.484652 + 0.507522i
288288 4.64812e8 + 4.55689e7i 1.14658 + 0.112407i
289289 −1.14821e7 1.98876e7i −0.0279820 0.0484663i
290290 −1.58120e8 + 2.73872e8i −0.380709 + 0.659408i
291291 −3.74613e8 + 8.09968e7i −0.891162 + 0.192682i
292292 −2.74334e8 + 1.58387e8i −0.644821 + 0.372288i
293293 −1.82974e7 −0.0424964 −0.0212482 0.999774i 0.506764π-0.506764\pi
−0.0212482 + 0.999774i 0.506764π0.506764\pi
294294 4.34174e8 3.58664e8i 0.996434 0.823137i
295295 −5.32787e8 −1.20830
296296 −1.53311e8 + 8.85140e7i −0.343599 + 0.198377i
297297 2.23212e7 + 1.92882e8i 0.0494389 + 0.427212i
298298 7.62093e7 1.31998e8i 0.166821 0.288943i
299299 −6.64050e6 1.15017e7i −0.0143665 0.0248835i
300300 −6.28911e8 + 5.70269e8i −1.34482 + 1.21943i
301301 −2.97009e7 3.11024e7i −0.0627751 0.0657373i
302302 5.58106e8i 1.16598i
303303 6.02187e8 + 1.93336e8i 1.24360 + 0.399268i
304304 4.62140e8 + 2.66817e8i 0.943443 + 0.544697i
305305 7.01139e8 + 4.04803e8i 1.41499 + 0.816947i
306306 −2.75003e8 6.06218e8i −0.548671 1.20950i
307307 6.99449e8i 1.37966i −0.723972 0.689830i 0.757685π-0.757685\pi
0.723972 0.689830i 0.242315π-0.242315\pi
308308 −1.41891e8 4.15467e7i −0.276711 0.0810231i
309309 2.97368e8 + 3.27947e8i 0.573376 + 0.632338i
310310 −1.14193e8 1.97787e8i −0.217707 0.377079i
311311 −2.11777e8 + 3.66808e8i −0.399224 + 0.691476i −0.993630 0.112689i 0.964054π-0.964054\pi
0.594406 + 0.804165i 0.297387π0.297387\pi
312312 −2.62825e6 1.21557e7i −0.00489921 0.0226590i
313313 2.91296e8 1.68180e8i 0.536944 0.310005i −0.206895 0.978363i 0.566336π-0.566336\pi
0.743840 + 0.668358i 0.233003π0.233003\pi
314314 8.01111e8 1.46029
315315 −1.50144e8 1.05757e9i −0.270658 1.90643i
316316 1.07536e8 0.191712
317317 −5.98493e8 + 3.45540e8i −1.05524 + 0.609244i −0.924112 0.382121i 0.875194π-0.875194\pi
−0.131129 + 0.991365i 0.541860π0.541860\pi
318318 −1.13420e8 5.24573e8i −0.197786 0.914768i
319319 −3.81438e7 + 6.60669e7i −0.0657894 + 0.113951i
320320 1.51275e8 + 2.62016e8i 0.258073 + 0.446995i
321321 −6.19155e6 6.82823e6i −0.0104480 0.0115223i
322322 −3.97181e8 + 9.66723e7i −0.662969 + 0.161364i
323323 5.55290e8i 0.916877i
324324 −1.32286e8 3.88552e8i −0.216075 0.634661i
325325 7.89833e7 + 4.56010e7i 0.127627 + 0.0736856i
326326 −7.63474e8 4.40792e8i −1.22049 0.704647i
327327 8.23377e7 + 2.64351e7i 0.130221 + 0.0418085i
328328 1.91031e8i 0.298913i
329329 −1.83624e8 + 6.27114e8i −0.284278 + 0.970869i
330330 −5.17609e8 + 4.69345e8i −0.792872 + 0.718942i
331331 4.28091e8 + 7.41475e8i 0.648840 + 1.12382i 0.983400 + 0.181450i 0.0580789π0.0580789\pi
−0.334560 + 0.942374i 0.608588π0.608588\pi
332332 −1.90689e8 + 3.30284e8i −0.285985 + 0.495340i
333333 5.10350e8 + 3.65364e8i 0.757379 + 0.542214i
334334 −4.00448e8 + 2.31199e8i −0.588077 + 0.339526i
335335 −1.07359e9 −1.56021
336336 −8.46764e8 6.09945e7i −1.21780 0.0877210i
337337 −8.30714e8 −1.18235 −0.591176 0.806542i 0.701336π-0.701336\pi
−0.591176 + 0.806542i 0.701336π0.701336\pi
338338 −7.92256e8 + 4.57409e8i −1.11598 + 0.644312i
339339 7.04729e8 1.52373e8i 0.982478 0.212426i
340340 4.80709e8 8.32612e8i 0.663293 1.14886i
341341 −2.75470e7 4.77129e7i −0.0376214 0.0651621i
342342 8.32351e7 8.49015e8i 0.112516 1.14769i
343343 −5.63708e8 + 4.90693e8i −0.754266 + 0.656569i
344344 2.92318e7i 0.0387170i
345345 −2.37016e8 + 7.38235e8i −0.310749 + 0.967894i
346346 −4.49708e7 2.59639e7i −0.0583666 0.0336979i
347347 9.93989e7 + 5.73880e7i 0.127711 + 0.0737340i 0.562495 0.826801i 0.309842π-0.309842\pi
−0.434783 + 0.900535i 0.643175π0.643175\pi
348348 4.92966e7 1.53545e8i 0.0627032 0.195302i
349349 2.74148e8i 0.345220i −0.984990 0.172610i 0.944780π-0.944780\pi
0.984990 0.172610i 0.0552200π-0.0552200\pi
350350 2.03014e9 1.93866e9i 2.53098 2.41693i
351351 −3.53990e7 + 2.62907e7i −0.0436934 + 0.0324510i
352352 2.02713e8 + 3.51110e8i 0.247733 + 0.429085i
353353 6.24059e8 1.08090e9i 0.755117 1.30790i −0.190199 0.981746i 0.560913π-0.560913\pi
0.945316 0.326155i 0.105753π-0.105753\pi
354354 6.61647e8 1.43058e8i 0.792711 0.171396i
355355 −3.13610e8 + 1.81063e8i −0.372041 + 0.214798i
356356 −1.26530e8 −0.148634
357357 3.85598e8 + 7.94815e8i 0.448535 + 0.924544i
358358 1.28737e9 1.48291
359359 −5.32474e8 + 3.07424e8i −0.607391 + 0.350677i −0.771943 0.635691i 0.780715π-0.780715\pi
0.164553 + 0.986368i 0.447382π0.447382\pi
360360 −4.22646e8 + 5.90362e8i −0.477439 + 0.666899i
361361 −9.11257e7 + 1.57834e8i −0.101945 + 0.176574i
362362 8.22980e8 + 1.42544e9i 0.911820 + 1.57932i
363363 5.50245e8 4.98938e8i 0.603786 0.547487i
364364 −7.94022e6 3.26226e7i −0.00862934 0.0354539i
365365 1.98670e9i 2.13849i
366366 −9.79410e8 3.14447e8i −1.04419 0.335246i
367367 4.65901e8 + 2.68988e8i 0.491997 + 0.284055i 0.725403 0.688325i 0.241654π-0.241654\pi
−0.233406 + 0.972379i 0.574987π0.574987\pi
368368 5.33670e8 + 3.08114e8i 0.558220 + 0.322288i
369369 −6.16801e8 + 2.79803e8i −0.639077 + 0.289908i
370370 2.25860e9i 2.31811i
371371 1.68439e8 + 6.92036e8i 0.171251 + 0.703590i
372372 7.82314e7 + 8.62760e7i 0.0787917 + 0.0868940i
373373 5.39544e8 + 9.34518e8i 0.538327 + 0.932409i 0.998994 + 0.0448366i 0.0142767π0.0142767\pi
−0.460668 + 0.887573i 0.652390π0.652390\pi
374374 2.88930e8 5.00441e8i 0.285589 0.494655i
375375 −7.09661e8 3.28220e9i −0.694930 3.21407i
376376 3.84651e8 2.22079e8i 0.373173 0.215451i
377377 −1.73242e7 −0.0166517
378378 4.70425e8 + 1.27304e9i 0.447990 + 1.21233i
379379 1.22890e9 1.15952 0.579761 0.814787i 0.303146π-0.303146\pi
0.579761 + 0.814787i 0.303146π0.303146\pi
380380 1.06702e9 6.16042e8i 0.997535 0.575927i
381381 −1.71984e8 7.95431e8i −0.159313 0.736827i
382382 −6.21626e8 + 1.07669e9i −0.570568 + 0.988253i
383383 −5.18994e8 8.98924e8i −0.472027 0.817574i 0.527461 0.849579i 0.323144π-0.323144\pi
−0.999488 + 0.0320050i 0.989811π0.989811\pi
384384 6.00465e8 + 6.62212e8i 0.541164 + 0.596812i
385385 6.70604e8 6.40386e8i 0.598899 0.571912i
386386 2.63914e9i 2.33565i
387387 9.43840e7 4.28160e7i 0.0827771 0.0375507i
388388 6.09083e8 + 3.51654e8i 0.529377 + 0.305636i
389389 −4.61824e8 2.66634e8i −0.397790 0.229664i 0.287740 0.957708i 0.407096π-0.407096\pi
−0.685530 + 0.728045i 0.740429π0.740429\pi
390390 −1.51077e8 4.85044e7i −0.128965 0.0414052i
391391 6.41238e8i 0.542501i
392392 5.07453e8 + 2.34060e7i 0.425495 + 0.0196257i
393393 −1.58134e9 + 1.43389e9i −1.31417 + 1.19163i
394394 −1.53471e9 2.65819e9i −1.26412 2.18952i
395395 −3.37215e8 + 5.84073e8i −0.275307 + 0.476845i
396396 2.07409e8 2.89715e8i 0.167840 0.234443i
397397 −9.29738e8 + 5.36785e8i −0.745751 + 0.430560i −0.824157 0.566362i 0.808350π-0.808350\pi
0.0784055 + 0.996922i 0.475017π0.475017\pi
398398 −2.14364e9 −1.70436
399399 −8.13386e7 + 1.12919e9i −0.0641049 + 0.889944i
400400 −4.23171e9 −3.30602
401401 1.98658e9 1.14695e9i 1.53851 0.888262i 0.539588 0.841929i 0.318580π-0.318580\pi
0.998926 0.0463328i 0.0147535π-0.0147535\pi
402402 1.33325e9 2.88269e8i 1.02358 0.221313i
403403 6.25569e6 1.08352e7i 0.00476111 0.00824648i
404404 −5.80291e8 1.00509e9i −0.437836 0.758354i
405405 2.52522e9 + 4.99935e8i 1.88889 + 0.373957i
406406 −1.49841e8 + 5.11738e8i −0.111119 + 0.379495i
407407 5.44851e8i 0.400587i
408408 1.83557e8 5.71727e8i 0.133801 0.416752i
409409 1.47920e9 + 8.54019e8i 1.06905 + 0.617214i 0.927921 0.372777i 0.121594π-0.121594\pi
0.141126 + 0.989992i 0.454928π0.454928\pi
410410 −2.11072e9 1.21863e9i −1.51247 0.873228i
411411 4.21165e8 1.31180e9i 0.299230 0.932015i
412412 8.12353e8i 0.572274i
413413 −8.72869e8 + 2.12453e8i −0.609711 + 0.148401i
414414 9.61182e7 9.80426e8i 0.0665740 0.679069i
415415 −1.19594e9 2.07143e9i −0.821375 1.42266i
416416 −4.60345e7 + 7.97340e7i −0.0313514 + 0.0543021i
417417 −2.75185e9 + 5.94991e8i −1.85844 + 0.401822i
418418 6.41330e8 3.70272e8i 0.429501 0.247973i
419419 −1.93716e9 −1.28652 −0.643261 0.765647i 0.722419π-0.722419\pi
−0.643261 + 0.765647i 0.722419π0.722419\pi
420420 −1.09949e9 + 1.62272e9i −0.724134 + 1.06874i
421421 2.15401e9 1.40689 0.703447 0.710748i 0.251643π-0.251643\pi
0.703447 + 0.710748i 0.251643π0.251643\pi
422422 −1.83569e9 + 1.05984e9i −1.18907 + 0.686509i
423423 −1.28045e9 9.16686e8i −0.822567 0.588883i
424424 2.42061e8 4.19261e8i 0.154221 0.267119i
425425 2.20173e9 + 3.81350e9i 1.39124 + 2.40970i
426426 3.40843e8 3.09062e8i 0.213610 0.193692i
427427 1.31010e9 + 3.83607e8i 0.814342 + 0.238446i
428428 1.69141e7i 0.0104279i
429429 −3.64448e7 1.17009e7i −0.0222861 0.00715513i
430430 3.22987e8 + 1.86477e8i 0.195905 + 0.113106i
431431 2.52692e9 + 1.45892e9i 1.52027 + 0.877729i 0.999714 + 0.0239018i 0.00760891π0.00760891\pi
0.520557 + 0.853827i 0.325724π0.325724\pi
432432 8.12500e8 1.87768e9i 0.484876 1.12054i
433433 1.75910e9i 1.04132i −0.853765 0.520659i 0.825686π-0.825686\pi
0.853765 0.520659i 0.174314π-0.174314\pi
434434 −2.65952e8 2.78502e8i −0.156167 0.163536i
435435 6.79380e8 + 7.49242e8i 0.395731 + 0.436425i
436436 −7.93439e7 1.37428e8i −0.0458470 0.0794093i
437437 4.10883e8 7.11669e8i 0.235523 0.407937i
438438 5.33446e8 + 2.46720e9i 0.303341 + 1.40296i
439439 −1.10932e9 + 6.40468e8i −0.625795 + 0.361303i −0.779122 0.626873i 0.784335π-0.784335\pi
0.153327 + 0.988176i 0.451001π0.451001\pi
440440 −6.30272e8 −0.352731
441441 −6.67696e8 1.67275e9i −0.370718 0.928745i
442442 1.31227e8 0.0722844
443443 1.15271e9 6.65519e8i 0.629953 0.363703i −0.150781 0.988567i 0.548179π-0.548179\pi
0.780734 + 0.624864i 0.214845π0.214845\pi
444444 −2.43403e8 1.12575e9i −0.131973 0.610379i
445445 3.96778e8 6.87239e8i 0.213446 0.369699i
446446 1.38998e9 + 2.40751e9i 0.741884 + 1.28498i
447447 −3.27442e8 3.61114e8i −0.173404 0.191235i
448448 3.52316e8 + 3.68941e8i 0.185123 + 0.193858i
449449 9.16466e8i 0.477809i 0.971043 + 0.238905i 0.0767883π0.0767883\pi
−0.971043 + 0.238905i 0.923212π0.923212\pi
450450 2.79472e9 + 6.16071e9i 1.44576 + 3.18704i
451451 −5.09177e8 2.93974e8i −0.261367 0.150900i
452452 −1.14582e9 6.61539e8i −0.583621 0.336954i
453453 1.69949e9 + 5.45633e8i 0.858963 + 0.275776i
454454 6.56773e8i 0.329397i
455455 2.02087e8 + 5.91726e7i 0.100577 + 0.0294497i
456456 5.70060e8 5.16906e8i 0.281542 0.255291i
457457 −3.22049e8 5.57805e8i −0.157839 0.273386i 0.776250 0.630425i 0.217119π-0.217119\pi
−0.934089 + 0.357040i 0.883786π0.883786\pi
458458 6.00811e8 1.04064e9i 0.292219 0.506139i
459459 −2.11485e9 + 2.44740e8i −1.02079 + 0.118130i
460460 1.23217e9 7.11393e8i 0.590225 0.340767i
461461 1.81792e9 0.864215 0.432108 0.901822i 0.357770π-0.357770\pi
0.432108 + 0.901822i 0.357770π0.357770\pi
462462 −6.60848e8 + 9.75333e8i −0.311785 + 0.460157i
463463 −1.41455e9 −0.662348 −0.331174 0.943570i 0.607445π-0.607445\pi
−0.331174 + 0.943570i 0.607445π0.607445\pi
464464 6.96139e8 4.01916e8i 0.323507 0.186777i
465465 −7.13923e8 + 1.54361e8i −0.329280 + 0.0711953i
466466 −2.66151e8 + 4.60987e8i −0.121836 + 0.211027i
467467 −2.04006e9 3.53349e9i −0.926902 1.60544i −0.788473 0.615069i 0.789128π-0.789128\pi
−0.138429 0.990372i 0.544205π-0.544205\pi
468468 8.05277e7 + 7.89471e6i 0.0363149 + 0.00356021i
469469 −1.75888e9 + 4.28104e8i −0.787283 + 0.191622i
470470 5.66676e9i 2.51763i
471471 7.83207e8 2.43946e9i 0.345385 1.07577i
472472 5.28817e8 + 3.05313e8i 0.231477 + 0.133644i
473473 7.79152e7 + 4.49844e7i 0.0338539 + 0.0195455i
474474 2.61945e8 8.15883e8i 0.112976 0.351887i
475475 5.64315e9i 2.41598i
476476 4.55539e8 1.55576e9i 0.193598 0.661179i
477477 −1.70826e9 1.67473e8i −0.720676 0.0706531i
478478 −7.61471e8 1.31891e9i −0.318901 0.552353i
479479 515988. 893717.i 0.000214519 0.000371557i −0.865918 0.500186i 0.833265π-0.833265\pi
0.866133 + 0.499814i 0.166598π0.166598\pi
480480 5.25362e9 1.13591e9i 2.16828 0.468813i
481481 −1.07154e8 + 6.18654e7i −0.0439037 + 0.0253478i
482482 4.11021e9 1.67186
483483 −9.39282e7 + 1.30397e9i −0.0379298 + 0.526565i
484484 −1.36300e9 −0.546435
485485 −3.81997e9 + 2.20546e9i −1.52042 + 0.877815i
486486 −3.27021e9 + 5.71926e7i −1.29226 + 0.0226002i
487487 4.79628e8 8.30739e8i 0.188171 0.325922i −0.756469 0.654029i 0.773077π-0.773077\pi
0.944640 + 0.328107i 0.106411π0.106411\pi
488488 −4.63943e8 8.03573e8i −0.180716 0.313009i
489489 −2.08867e9 + 1.89391e9i −0.807771 + 0.732452i
490490 3.49578e9 5.45762e9i 1.34232 2.09564i
491491 6.85759e8i 0.261449i −0.991419 0.130724i 0.958270π-0.958270\pi
0.991419 0.130724i 0.0417303π-0.0417303\pi
492492 1.18337e9 + 3.79928e8i 0.447962 + 0.143822i
493493 −7.24391e8 4.18228e8i −0.272276 0.157199i
494494 1.45640e8 + 8.40855e7i 0.0543547 + 0.0313817i
495495 9.23162e8 + 2.03503e9i 0.342105 + 0.754140i
496496 5.80520e8i 0.213615i
497497 −4.41590e8 + 4.21691e8i −0.161351 + 0.154080i
498498 2.04139e9 + 2.25131e9i 0.740668 + 0.816831i
499499 1.49005e9 + 2.58084e9i 0.536844 + 0.929841i 0.999072 + 0.0430800i 0.0137170π0.0137170\pi
−0.462227 + 0.886761i 0.652950π0.652950\pi
500500 −3.08105e9 + 5.33653e9i −1.10231 + 1.90926i
501501 3.12525e8 + 1.44544e9i 0.111033 + 0.513532i
502502 −4.10122e9 + 2.36784e9i −1.44694 + 0.835390i
503503 −2.90478e9 −1.01771 −0.508856 0.860852i 0.669931π-0.669931\pi
−0.508856 + 0.860852i 0.669931π0.669931\pi
504504 −4.57013e8 + 1.13573e9i −0.159009 + 0.395155i
505505 7.27880e9 2.51501
506506 7.40595e8 4.27583e8i 0.254129 0.146721i
507507 6.18306e8 + 2.85969e9i 0.210705 + 0.974519i
508508 −7.46682e8 + 1.29329e9i −0.252704 + 0.437697i
509509 −2.50540e8 4.33948e8i −0.0842102 0.145856i 0.820844 0.571152i 0.193503π-0.193503\pi
−0.905054 + 0.425296i 0.860170π0.860170\pi
510510 −5.14614e9 5.67532e9i −1.71785 1.89450i
511511 −7.92211e8 3.25483e9i −0.262644 1.07908i
512512 2.69250e9i 0.886567i
513513 −2.50396e9 1.08350e9i −0.818874 0.354339i
514514 −2.54129e9 1.46721e9i −0.825435 0.476565i
515515 4.41224e9 + 2.54741e9i 1.42342 + 0.821813i
516516 −1.81081e8 5.81373e7i −0.0580228 0.0186286i
517517 1.36701e9i 0.435066i
518518 9.00636e8 + 3.70029e9i 0.284705 + 1.16972i
519519 −1.23028e8 + 1.11557e8i −0.0386296 + 0.0350276i
520520 −7.15646e7 1.23954e8i −0.0223196 0.0386587i
521521 −2.31309e9 + 4.00639e9i −0.716573 + 1.24114i 0.245777 + 0.969327i 0.420957π0.420957\pi
−0.962350 + 0.271814i 0.912376π0.912376\pi
522522 −1.04487e9 7.48035e8i −0.321527 0.230184i
523523 −3.91578e9 + 2.26078e9i −1.19691 + 0.691037i −0.959865 0.280461i 0.909513π-0.909513\pi
−0.237046 + 0.971498i 0.576179π0.576179\pi
524524 3.91712e9 1.18934
525525 −3.91865e9 8.07733e9i −1.18189 2.43618i
526526 6.29545e9 1.88615
527527 5.23148e8 3.02040e8i 0.155700 0.0898932i
528528 1.73591e9 3.75330e8i 0.513227 0.110967i
529529 −1.22793e9 + 2.12684e9i −0.360645 + 0.624656i
530530 −3.08832e9 5.34913e9i −0.901066 1.56069i
531531 2.11235e8 2.15464e9i 0.0612259 0.624517i
532532 1.50245e9 1.43475e9i 0.432623 0.413128i
533533 1.33518e8i 0.0381939i
534534 −3.08213e8 + 9.59994e8i −0.0875905 + 0.272819i
535535 −9.18678e7 5.30399e7i −0.0259373 0.0149749i
536536 1.06560e9 + 6.15222e8i 0.298893 + 0.172566i
537537 1.25860e9 3.92018e9i 0.350734 1.09244i
538538 3.54840e9i 0.982414i
539539 8.43298e8 1.31656e9i 0.231964 0.362142i
540540 −2.81651e9 3.79227e9i −0.769721 1.03639i
541541 −5.49428e8 9.51638e8i −0.149183 0.258393i 0.781742 0.623601i 0.214331π-0.214331\pi
−0.930926 + 0.365208i 0.880998π0.880998\pi
542542 1.07735e9 1.86603e9i 0.290644 0.503410i
543543 5.14520e9 1.11247e9i 1.37912 0.298187i
544544 −3.84975e9 + 2.22265e9i −1.02526 + 0.591937i
545545 9.95238e8 0.263354
546546 −2.66852e8 1.92220e7i −0.0701611 0.00505388i
547547 −4.60429e9 −1.20284 −0.601419 0.798934i 0.705398π-0.705398\pi
−0.601419 + 0.798934i 0.705398π0.705398\pi
548548 −2.18950e9 + 1.26411e9i −0.568346 + 0.328135i
549549 −1.91504e9 + 2.67498e9i −0.493942 + 0.689950i
550550 −2.93626e9 + 5.08574e9i −0.752531 + 1.30342i
551551 −5.35971e8 9.28328e8i −0.136493 0.236413i
552552 6.58295e8 5.96913e8i 0.166584 0.151051i
553553 −3.19558e8 + 1.09136e9i −0.0803549 + 0.274429i
554554 7.53205e9i 1.88204i
555555 6.87768e9 + 2.20813e9i 1.70772 + 0.548276i
556556 4.47423e9 + 2.58320e9i 1.10397 + 0.637377i
557557 −3.59243e9 2.07409e9i −0.880837 0.508551i −0.00990238 0.999951i 0.503152π-0.503152\pi
−0.870934 + 0.491400i 0.836485π0.836485\pi
558558 8.45146e8 3.83389e8i 0.205926 0.0934157i
559559 2.04311e7i 0.00494710i
560560 −9.49323e9 + 2.31061e9i −2.28431 + 0.555993i
561561 −1.24142e9 1.36908e9i −0.296858 0.327384i
562562 2.73596e9 + 4.73882e9i 0.650179 + 1.12614i
563563 3.29882e9 5.71373e9i 0.779075 1.34940i −0.153400 0.988164i 0.549022π-0.549022\pi
0.932475 0.361234i 0.117644π-0.117644\pi
564564 6.10689e8 + 2.82446e9i 0.143332 + 0.662915i
565565 7.18620e9 4.14895e9i 1.67621 0.967763i
566566 5.49650e9 1.27417
567567 4.33644e9 1.87902e8i 0.999063 0.0432902i
568568 4.15031e8 0.0950301
569569 9.40776e8 5.43157e8i 0.214089 0.123604i −0.389122 0.921186i 0.627221π-0.627221\pi
0.603210 + 0.797582i 0.293888π0.293888\pi
570570 −2.07483e9 9.59615e9i −0.469267 2.17038i
571571 7.54394e8 1.30665e9i 0.169579 0.293719i −0.768693 0.639618i 0.779093π-0.779093\pi
0.938272 + 0.345899i 0.112426π0.112426\pi
572572 3.51197e7 + 6.08290e7i 0.00784629 + 0.0135902i
573573 2.67089e9 + 2.94554e9i 0.593082 + 0.654069i
574574 −3.94396e9 1.15482e9i −0.870443 0.254872i
575575 6.51660e9i 1.42950i
576576 −1.11959e9 + 5.07889e8i −0.244108 + 0.110736i
577577 6.90685e8 + 3.98767e8i 0.149680 + 0.0864180i 0.572970 0.819577i 0.305791π-0.305791\pi
−0.423289 + 0.905995i 0.639125π0.639125\pi
578578 2.90805e8 + 1.67896e8i 0.0626404 + 0.0361654i
579579 8.03645e9 + 2.58016e9i 1.72064 + 0.552423i
580580 1.85594e9i 0.394971i
581581 −2.78532e9 2.91675e9i −0.589194 0.616997i
582582 4.15168e9 3.76457e9i 0.872959 0.791562i
583583 −7.45006e8 1.29039e9i −0.155711 0.269700i
584584 −1.13847e9 + 1.97190e9i −0.236526 + 0.409675i
585585 −2.95401e8 + 4.12624e8i −0.0610052 + 0.0852136i
586586 2.31707e8 1.33776e8i 0.0475661 0.0274623i
587587 3.14642e9 0.642072 0.321036 0.947067i 0.395969π-0.395969\pi
0.321036 + 0.947067i 0.395969π0.395969\pi
588588 −1.15423e9 + 3.09694e9i −0.234139 + 0.628221i
589589 7.74145e8 0.156106
590590 6.74689e9 3.89532e9i 1.35245 0.780838i
591591 −9.59485e9 + 2.07455e9i −1.91197 + 0.413397i
592592 2.87051e9 4.97187e9i 0.568635 0.984904i
593593 −1.02329e9 1.77240e9i −0.201516 0.349035i 0.747501 0.664260i 0.231253π-0.231253\pi
−0.949017 + 0.315225i 0.897920π0.897920\pi
594594 −1.69286e9 2.27934e9i −0.331413 0.446229i
595595 7.02151e9 + 7.35284e9i 1.36654 + 1.43102i
596596 8.94509e8i 0.173070i
597597 −2.09573e9 + 6.52760e9i −0.403112 + 1.25558i
598598 1.68183e8 + 9.71003e7i 0.0321608 + 0.0185680i
599599 −4.71997e8 2.72508e8i −0.0897316 0.0518066i 0.454463 0.890766i 0.349831π-0.349831\pi
−0.544194 + 0.838959i 0.683165π0.683165\pi
600600 −1.86540e9 + 5.81019e9i −0.352568 + 1.09815i
601601 1.21229e9i 0.227796i 0.993492 + 0.113898i 0.0363336π0.0363336\pi
−0.993492 + 0.113898i 0.963666π0.963666\pi
602602 6.03511e8 + 1.76713e8i 0.112745 + 0.0330126i
603603 4.25650e8 4.34172e9i 0.0790573 0.806402i
604604 −1.63770e9 2.83657e9i −0.302415 0.523799i
605605 4.27416e9 7.40306e9i 0.784705 1.35915i
606606 −9.03925e9 + 1.95442e9i −1.64998 + 0.356750i
607607 1.38049e9 7.97028e8i 0.250538 0.144648i −0.369473 0.929242i 0.620462π-0.620462\pi
0.620011 + 0.784593i 0.287128π0.287128\pi
608608 −5.69679e9 −1.02794
609609 1.41180e9 + 9.56582e8i 0.253287 + 0.171617i
610610 −1.18384e10 −2.11173
611611 2.68846e8 1.55218e8i 0.0476825 0.0275295i
612612 3.17658e9 + 2.27414e9i 0.560182 + 0.401040i
613613 8.48511e8 1.46966e9i 0.148780 0.257695i −0.781997 0.623283i 0.785799π-0.785799\pi
0.930777 + 0.365587i 0.119132π0.119132\pi
614614 5.11383e9 + 8.85741e9i 0.891572 + 1.54425i
615615 −5.77440e9 + 5.23598e9i −1.00102 + 0.907684i
616616 −1.03258e9 + 2.51326e8i −0.177988 + 0.0433216i
617617 1.19915e9i 0.205530i −0.994706 0.102765i 0.967231π-0.967231\pi
0.994706 0.102765i 0.0327690π-0.0327690\pi
618618 −6.16338e9 1.97880e9i −1.05041 0.337243i
619619 −5.24316e9 3.02714e9i −0.888538 0.512997i −0.0150737 0.999886i 0.504798π-0.504798\pi
−0.873464 + 0.486889i 0.838132π0.838132\pi
620620 1.16077e9 + 6.70169e8i 0.195602 + 0.112931i
621621 −2.89153e9 1.25121e9i −0.484514 0.209656i
622622 6.19338e9i 1.03196i
623623 3.76003e8 1.28413e9i 0.0622992 0.212765i
624624 2.70921e8 + 2.98780e8i 0.0446371 + 0.0492272i
625625 −1.10600e10 1.91564e10i −1.81206 3.13859i
626626 −2.45920e9 + 4.25946e9i −0.400667 + 0.693975i
627627 −5.00518e8 2.31491e9i −0.0810929 0.375057i
628628 −4.07164e9 + 2.35076e9i −0.656011 + 0.378748i
629629 −5.97402e9 −0.957170
630630 9.63345e9 + 1.22947e10i 1.53493 + 1.95896i
631631 −4.25664e8 −0.0674472 −0.0337236 0.999431i 0.510737π-0.510737\pi
−0.0337236 + 0.999431i 0.510737π0.510737\pi
632632 6.69405e8 3.86481e8i 0.105482 0.0609002i
633633 1.43264e9 + 6.62603e9i 0.224505 + 1.03834i
634634 5.05264e9 8.75143e9i 0.787419 1.36385i
635635 −4.68295e9 8.11110e9i −0.725791 1.25711i
636636 2.11576e9 + 2.33332e9i 0.326111 + 0.359646i
637637 3.54676e8 + 1.63592e7i 0.0543681 + 0.00250770i
638638 1.11551e9i 0.170060i
639639 −6.07898e8 1.34006e9i −0.0921675 0.203175i
640640 8.90947e9 + 5.14389e9i 1.34345 + 0.775642i
641641 −7.45438e9 4.30379e9i −1.11791 0.645428i −0.177046 0.984203i 0.556654π-0.556654\pi
−0.940868 + 0.338775i 0.889988π0.889988\pi
642642 1.28329e8 + 4.12009e7i 0.0191404 + 0.00614517i
643643 2.22868e9i 0.330605i 0.986243 + 0.165303i 0.0528601π0.0528601\pi
−0.986243 + 0.165303i 0.947140π0.947140\pi
644644 1.73500e9 1.65682e9i 0.255976 0.244441i
645645 8.83609e8 8.01218e8i 0.129659 0.117569i
646646 4.05985e9 + 7.03186e9i 0.592510 + 1.02626i
647647 2.39282e9 4.14449e9i 0.347333 0.601598i −0.638442 0.769670i 0.720421π-0.720421\pi
0.985775 + 0.168072i 0.0537542π0.0537542\pi
648648 −2.21992e9 1.94328e9i −0.320497 0.280559i
649649 1.62757e9 9.39681e8i 0.233714 0.134935i
650650 −1.33360e9 −0.190470
651651 −1.10807e9 + 5.37573e8i −0.157411 + 0.0763667i
652652 5.17381e9 0.731044
653653 3.97133e9 2.29285e9i 0.558136 0.322240i −0.194261 0.980950i 0.562231π-0.562231\pi
0.752397 + 0.658710i 0.228897π0.228897\pi
654654 −1.23595e9 + 2.67230e8i −0.172774 + 0.0373563i
655655 −1.22834e10 + 2.12756e10i −1.70795 + 2.95826i
656656 3.09756e9 + 5.36514e9i 0.428407 + 0.742023i
657657 8.03441e9 + 7.87670e8i 1.10529 + 0.108359i
658658 −2.25966e9 9.28390e9i −0.309210 1.27040i
659659 1.15059e10i 1.56610i 0.621956 + 0.783052i 0.286338π0.286338\pi
−0.621956 + 0.783052i 0.713662π0.713662\pi
660660 1.25351e9 3.90431e9i 0.169716 0.528616i
661661 3.44053e9 + 1.98639e9i 0.463361 + 0.267522i 0.713457 0.700699i 0.247129π-0.247129\pi
−0.250095 + 0.968221i 0.580462π0.580462\pi
662662 −1.08422e10 6.25973e9i −1.45249 0.838595i
663663 1.28294e8 3.99599e8i 0.0170966 0.0532509i
664664 2.74133e9i 0.363390i
665665 3.08129e9 + 1.26596e10i 0.406310 + 1.66934i
666666 −9.13402e9 8.95474e8i −1.19813 0.117461i
667667 −6.18928e8 1.07202e9i −0.0807607 0.139882i
668668 1.35685e9 2.35014e9i 0.176123 0.305053i
669669 8.69004e9 1.87891e9i 1.12210 0.242614i
670670 1.35953e10 7.84928e9i 1.74634 1.00825i
671671 −2.85582e9 −0.364923
672672 8.15410e9 3.95589e9i 1.03653 0.502866i
673673 2.68753e9 0.339861 0.169931 0.985456i 0.445646π-0.445646\pi
0.169931 + 0.985456i 0.445646π0.445646\pi
674674 1.05197e10 6.07353e9i 1.32340 0.764068i
675675 2.14922e10 2.48718e9i 2.68979 0.311275i
676676 2.68443e9 4.64956e9i 0.334224 0.578893i
677677 3.78037e9 + 6.54778e9i 0.468245 + 0.811025i 0.999341 0.0362869i 0.0115530π-0.0115530\pi
−0.531096 + 0.847312i 0.678220π0.678220\pi
678678 −7.81023e9 + 7.08198e9i −0.962410 + 0.872672i
679679 −5.37884e9 + 5.13646e9i −0.659393 + 0.629680i
680680 6.91062e9i 0.842822i
681681 −1.99994e9 6.42096e8i −0.242662 0.0779085i
682682 6.97679e8 + 4.02805e8i 0.0842190 + 0.0486239i
683683 1.22736e10 + 7.08616e9i 1.47401 + 0.851018i 0.999571 0.0292726i 0.00931909π-0.00931909\pi
0.474435 + 0.880291i 0.342652π0.342652\pi
684684 2.06829e9 + 4.55936e9i 0.247124 + 0.544763i
685685 1.58561e10i 1.88487i
686686 3.55090e9 1.03352e10i 0.419956 1.22232i
687687 −2.58146e9 2.84691e9i −0.303750 0.334985i
688688 −4.73995e8 8.20983e8i −0.0554899 0.0961113i
689689 1.69184e8 2.93036e8i 0.0197057 0.0341313i
690690 −2.39597e9 1.10814e10i −0.277658 1.28418i
691691 −7.55947e9 + 4.36446e9i −0.871602 + 0.503219i −0.867880 0.496774i 0.834518π-0.834518\pi
−0.00372142 + 0.999993i 0.501185π0.501185\pi
692692 3.04752e8 0.0349603
693693 2.32391e9 + 2.96589e9i 0.265248 + 0.338523i
694694 −1.67830e9 −0.190596
695695 −2.80609e10 + 1.62010e10i −3.17070 + 1.83061i
696696 −2.44967e8 1.13298e9i −0.0275407 0.127376i
697697 3.22327e9 5.58288e9i 0.360564 0.624515i
698698 2.00436e9 + 3.47165e9i 0.223090 + 0.386404i
699699 1.14355e9 + 1.26114e9i 0.126644 + 0.139667i
700700 −4.62942e9 + 1.58105e10i −0.510134 + 1.74221i
701701 1.45093e9i 0.159086i −0.996831 0.0795432i 0.974654π-0.974654\pi
0.996831 0.0795432i 0.0253461π-0.0253461\pi
702702 2.56054e8 5.91739e8i 0.0279352 0.0645581i
703703 −6.63018e9 3.82794e9i −0.719750 0.415548i
704704 −9.24240e8 5.33610e8i −0.0998344 0.0576394i
705705 −1.72558e10 5.54012e9i −1.85470 0.595466i
706706 1.82505e10i 1.95191i
707707 1.19249e10 2.90248e9i 1.26908 0.308888i
708708 −2.94303e9 + 2.66862e9i −0.311658 + 0.282598i
709709 7.91772e9 + 1.37139e10i 0.834331 + 1.44510i 0.894574 + 0.446920i 0.147479π0.147479\pi
−0.0602432 + 0.998184i 0.519188π0.519188\pi
710710 2.64758e9 4.58574e9i 0.277616 0.480845i
711711 −2.22835e9 1.59530e9i −0.232510 0.166456i
712712 −7.87643e8 + 4.54746e8i −0.0817805 + 0.0472160i
713713 8.93968e8 0.0923652
714714 −1.06940e10 7.24587e9i −1.09951 0.744984i
715715 −4.40518e8 −0.0450705
716716 −6.54307e9 + 3.77764e9i −0.666171 + 0.384614i
717717 −4.76066e9 + 1.02932e9i −0.482336 + 0.104288i
718718 4.49529e9 7.78607e9i 0.453234 0.785024i
719719 7.47727e8 + 1.29510e9i 0.0750225 + 0.129943i 0.901096 0.433619i 0.142764π-0.142764\pi
−0.826074 + 0.563562i 0.809430π0.809430\pi
720720 2.29737e9 2.34337e10i 0.229386 2.33979i
721721 8.24440e9 + 2.41402e9i 0.819192 + 0.239866i
722722 2.66496e9i 0.263518i
723723 4.01836e9 1.25160e10i 0.395426 1.23163i
724724 −8.36559e9 4.82987e9i −0.819241 0.472989i
725725 7.36165e9 + 4.25025e9i 0.717450 + 0.414220i
726726 −3.32012e9 + 1.03412e10i −0.322015 + 1.00298i
727727 1.76815e10i 1.70667i −0.521364 0.853334i 0.674577π-0.674577\pi
0.521364 0.853334i 0.325423π-0.325423\pi
728728 −1.66672e8 1.74537e8i −0.0160105 0.0167660i
729729 −3.02297e9 + 1.00140e10i −0.288993 + 0.957331i
730730 1.45252e10 + 2.51584e10i 1.38195 + 2.39360i
731731 −4.93231e8 + 8.54302e8i −0.0467025 + 0.0808910i
732732 5.90056e9 1.27579e9i 0.556038 0.120224i
733733 −2.58930e9 + 1.49494e9i −0.242839 + 0.140203i −0.616481 0.787370i 0.711442π-0.711442\pi
0.373642 + 0.927573i 0.378109π0.378109\pi
734734 −7.86652e9 −0.734254
735735 −1.32013e10 1.59806e10i −1.22634 1.48453i
736736 −6.57854e9 −0.608215
737737 3.27965e9 1.89351e9i 0.301781 0.174233i
738738 5.76510e9 8.05283e9i 0.527970 0.737482i
739739 5.30209e9 9.18349e9i 0.483272 0.837052i −0.516544 0.856261i 0.672782π-0.672782\pi
0.999815 + 0.0192094i 0.00611491π0.00611491\pi
740740 −6.62761e9 1.14794e10i −0.601237 1.04137i
741741 3.98434e8 3.61283e8i 0.0359744 0.0326200i
742742 −7.19263e9 7.53203e9i −0.646359 0.676860i
743743 6.92790e9i 0.619642i 0.950795 + 0.309821i 0.100269π0.100269\pi
−0.950795 + 0.309821i 0.899731π0.899731\pi
744744 7.97060e8 + 2.55902e8i 0.0709554 + 0.0227808i
745745 −4.85846e9 2.80503e9i −0.430479 0.248537i
746746 −1.36649e10 7.88945e9i −1.20510 0.695762i
747747 8.85123e9 4.01524e9i 0.776929 0.352443i
748748 3.39132e9i 0.296287i
749749 −1.71658e8 5.02628e7i −0.0149272 0.00437079i
750750 3.29836e10 + 3.63754e10i 2.85485 + 3.14842i
751751 3.62072e9 + 6.27127e9i 0.311929 + 0.540276i 0.978780 0.204915i 0.0656916π-0.0656916\pi
−0.666851 + 0.745191i 0.732358π0.732358\pi
752752 −7.20201e9 + 1.24742e10i −0.617577 + 1.06968i
753753 3.20074e9 + 1.48035e10i 0.273192 + 1.26352i
754754 2.19384e8 1.26661e8i 0.0186382 0.0107608i
755755 2.05422e10 1.73713
756756 −6.12651e9 5.08981e9i −0.515688 0.428425i
757757 −1.94667e10 −1.63101 −0.815507 0.578747i 0.803542π-0.803542\pi
−0.815507 + 0.578747i 0.803542π0.803542\pi
758758 −1.55620e10 + 8.98475e9i −1.29785 + 0.749314i
759759 −5.77988e8 2.67321e9i −0.0479814 0.221915i
760760 4.42808e9 7.66966e9i 0.365904 0.633765i
761761 −8.19400e9 1.41924e10i −0.673984 1.16737i −0.976765 0.214315i 0.931248π-0.931248\pi
0.302780 0.953060i 0.402085π-0.402085\pi
762762 7.99347e9 + 8.81545e9i 0.654475 + 0.721776i
763763 1.63051e9 3.96859e8i 0.132888 0.0323445i
764764 7.29635e9i 0.591942i
765765 −2.23131e10 + 1.01220e10i −1.80196 + 0.817433i
766766 1.31445e10 + 7.58896e9i 1.05668 + 0.610072i
767767 3.69608e8 + 2.13393e8i 0.0295772 + 0.0170764i
768768 −1.56494e10 5.02436e9i −1.24662 0.400236i
769769 1.90743e10i 1.51254i 0.654259 + 0.756270i 0.272980π0.272980\pi
−0.654259 + 0.756270i 0.727020π0.727020\pi
770770 −3.81013e9 + 1.30124e10i −0.300761 + 1.02716i
771771 −6.95230e9 + 6.30405e9i −0.546309 + 0.495369i
772772 −7.74425e9 1.34134e10i −0.605785 1.04925i
773773 −2.93621e9 + 5.08567e9i −0.228644 + 0.396023i −0.957406 0.288744i 0.906762π-0.906762\pi
0.728763 + 0.684766i 0.240096π0.240096\pi
774774 −8.82185e8 + 1.23226e9i −0.0683859 + 0.0955231i
775775 −5.31651e9 + 3.06949e9i −0.410271 + 0.236870i
776776 5.05534e9 0.388360
777777 1.21483e10 + 8.75071e8i 0.929054 + 0.0669221i
778778 7.79769e9 0.593660
779779 7.15462e9 4.13072e9i 0.542257 0.313072i
780780 9.10178e8 1.96794e8i 0.0686745 0.0148484i
781781 6.38684e8 1.10623e9i 0.0479742 0.0830937i
782782 4.68823e9 + 8.12025e9i 0.350579 + 0.607220i
783783 −3.29936e9 + 2.45043e9i −0.245620 + 0.182421i
784784 −1.46315e10 + 7.57100e9i −1.08438 + 0.561109i
785785 2.94865e10i 2.17560i
786786 9.54167e9 2.97195e10i 0.700883 2.18304i
787787 1.02364e10 + 5.91001e9i 0.748579 + 0.432192i 0.825180 0.564870i 0.191074π-0.191074\pi
−0.0766013 + 0.997062i 0.524407π0.524407\pi
788788 1.56003e10 + 9.00682e9i 1.13577 + 0.655737i
789789 6.15475e9 1.91703e10i 0.446109 1.38950i
790790 9.86181e9i 0.711642i
791791 1.01188e10 9.66282e9i 0.726960 0.694203i
792792 2.49885e8 2.54888e9i 0.0178732 0.182310i
793793 −3.24266e8 5.61644e8i −0.0230911 0.0399950i
794794 7.84910e9 1.35950e10i 0.556478 0.963848i
795795 −1.93079e10 + 4.17466e9i −1.36286 + 0.294670i
796796 1.08950e10 6.29026e9i 0.765655 0.442051i
797797 1.19819e9 0.0838345 0.0419173 0.999121i 0.486653π-0.486653\pi
0.0419173 + 0.999121i 0.486653π0.486653\pi
798798 −7.22575e9 1.48941e10i −0.503353 1.03754i
799799 1.49886e10 1.03955
800800 3.91231e10 2.25878e10i 2.70159 1.55976i
801801 2.62195e9 + 1.87708e9i 0.180265 + 0.129053i
802802 −1.67713e10 + 2.90487e10i −1.14804 + 1.98846i
803803 3.50396e9 + 6.06903e9i 0.238811 + 0.413633i
804804 −5.93037e9 + 5.37741e9i −0.402426 + 0.364902i
805805 3.55822e9 + 1.46190e10i 0.240407 + 0.987719i
806806 1.82947e8i 0.0123070i
807807 1.08052e10 + 3.46910e9i 0.723730 + 0.232359i
808808 −7.22457e9 4.17110e9i −0.481806 0.278171i
809809 −1.38749e10 8.01065e9i −0.921316 0.531922i −0.0372616 0.999306i 0.511863π-0.511863\pi
−0.884055 + 0.467383i 0.845197π0.845197\pi
810810 −3.56330e10 + 1.21315e10i −2.35589 + 0.802081i
811811 1.85573e10i 1.22164i −0.791770 0.610819i 0.790840π-0.790840\pi
0.791770 0.610819i 0.209160π-0.209160\pi
812812 −7.40069e8 3.04060e9i −0.0485094 0.199303i
813813 −4.62898e9 5.10498e9i −0.302112 0.333179i
814814 −3.98352e9 6.89966e9i −0.258870 0.448376i
815815 −1.62242e10 + 2.81012e10i −1.04981 + 1.81833i
816816 4.11531e9 + 1.90334e10i 0.265147 + 1.22631i
817817 −1.09481e9 + 6.32090e8i −0.0702364 + 0.0405510i
818818 −2.49757e10 −1.59544
819819 −3.19422e8 + 7.93799e8i −0.0203175 + 0.0504913i
820820 1.43037e10 0.905939
821821 −1.22520e10 + 7.07369e9i −0.772690 + 0.446113i −0.833834 0.552016i 0.813859π-0.813859\pi
0.0611431 + 0.998129i 0.480525π0.480525\pi
822822 4.25751e9 + 1.96911e10i 0.267365 + 1.23657i
823823 2.52111e9 4.36670e9i 0.157650 0.273057i −0.776371 0.630276i 0.782942π-0.782942\pi
0.934021 + 0.357219i 0.116275π0.116275\pi
824824 −2.91957e9 5.05685e9i −0.181792 0.314873i
825825 1.26160e10 + 1.39133e10i 0.782225 + 0.862662i
826826 9.50020e9 9.07211e9i 0.586547 0.560116i
827827 2.69970e10i 1.65976i −0.557941 0.829881i 0.688408π-0.688408\pi
0.557941 0.829881i 0.311592π-0.311592\pi
828828 2.38842e9 + 5.26506e9i 0.146219 + 0.322327i
829829 −2.29907e10 1.32737e10i −1.40156 0.809191i −0.407007 0.913425i 0.633428π-0.633428\pi
−0.994553 + 0.104234i 0.966761π0.966761\pi
830830 3.02894e10 + 1.74876e10i 1.83873 + 1.06159i
831831 2.29358e10 + 7.36372e9i 1.38647 + 0.445137i
832832 2.42356e8i 0.0145889i
833833 1.44354e10 + 9.24634e9i 0.865310 + 0.554259i
834834 3.04977e10 2.76540e10i 1.82048 1.65073i
835835 8.50973e9 + 1.47393e10i 0.505840 + 0.876141i
836836 −2.17304e9 + 3.76381e9i −0.128631 + 0.222795i
837837 −3.41199e8 2.94837e9i −0.0201126 0.173798i
838838 2.45311e10 1.41630e10i 1.44000 0.831385i
839839 −1.50756e10 −0.881266 −0.440633 0.897687i 0.645246π-0.645246\pi
−0.440633 + 0.897687i 0.645246π0.645246\pi
840840 −1.01226e9 + 1.40529e10i −0.0589272 + 0.818064i
841841 1.56352e10 0.906393
842842 −2.72771e10 + 1.57485e10i −1.57473 + 0.909172i
843843 1.71050e10 3.69836e9i 0.983392 0.212624i
844844 6.21994e9 1.07733e10i 0.356113 0.616806i
845845 1.68358e10 + 2.91605e10i 0.959923 + 1.66264i
846846 2.29169e10 + 2.24671e9i 1.30125 + 0.127571i
847847 4.05036e9 1.38328e10i 0.229035 0.782203i
848848 1.57001e10i 0.884130i
849849 5.37367e9 1.67374e10i 0.301366 0.938666i
850850 −5.57627e10 3.21946e10i −3.11442 1.79811i
851851 −7.65640e9 4.42043e9i −0.425864 0.245873i
852852 −8.25429e8 + 2.57097e9i −0.0457237 + 0.142416i
853853 1.92731e10i 1.06324i 0.846984 + 0.531618i 0.178416π0.178416\pi
−0.846984 + 0.531618i 0.821584π0.821584\pi
854854 −1.93950e10 + 4.72065e9i −1.06558 + 0.259358i
855855 −3.12497e10 3.06363e9i −1.70987 0.167631i
856856 6.07889e7 + 1.05289e8i 0.00331258 + 0.00573756i
857857 −6.08570e9 + 1.05407e10i −0.330277 + 0.572056i −0.982566 0.185914i 0.940475π-0.940475\pi
0.652289 + 0.757970i 0.273809π0.273809\pi
858858 5.47062e8 1.18283e8i 0.0295686 0.00639318i
859859 1.81238e10 1.04638e10i 0.975603 0.563264i 0.0746630 0.997209i 0.476212π-0.476212\pi
0.900940 + 0.433944i 0.142879π0.142879\pi
860860 −2.18877e9 −0.117343
861861 −7.37236e9 + 1.08807e10i −0.393637 + 0.580961i
862862 −4.26659e10 −2.26885
863863 1.03063e10 5.95032e9i 0.545838 0.315140i −0.201604 0.979467i 0.564615π-0.564615\pi
0.747442 + 0.664328i 0.231282π0.231282\pi
864864 2.51082e9 + 2.16965e10i 0.132440 + 1.14444i
865865 −9.55652e8 + 1.65524e9i −0.0502046 + 0.0869569i
866866 1.28612e10 + 2.22762e10i 0.672928 + 1.16554i
867867 7.95567e8 7.21386e8i 0.0414582 0.0375925i
868868 2.16893e9 + 6.35079e8i 0.112571 + 0.0329616i
869869 2.37900e9i 0.122977i
870870 −1.40811e10 4.52085e9i −0.724970 0.232757i
871871 7.44780e8 + 4.29999e8i 0.0381913 + 0.0220498i
872872 −9.87823e8 5.70320e8i −0.0504512 0.0291280i
873873 −7.40459e9 1.63227e10i −0.376661 0.830315i
874874 1.20162e10i 0.608804i
875875 −4.50036e10 4.71272e10i −2.27101 2.37817i
876876 −9.95095e9 1.09742e10i −0.500150 0.551581i
877877 1.30463e10 + 2.25968e10i 0.653112 + 1.13122i 0.982363 + 0.186981i 0.0598704π0.0598704\pi
−0.329251 + 0.944242i 0.606796π0.606796\pi
878878 9.36520e9 1.62210e10i 0.466967 0.808811i
879879 −1.80833e8 8.36358e8i −0.00898083 0.0415366i
880880 1.77013e10 1.02199e10i 0.875621 0.505540i
881881 −2.60616e10 −1.28406 −0.642031 0.766678i 0.721908π-0.721908\pi
−0.642031 + 0.766678i 0.721908π0.721908\pi
882882 2.06852e10 + 1.63011e10i 1.01512 + 0.799974i
883883 −7.75021e9 −0.378836 −0.189418 0.981897i 0.560660π-0.560660\pi
−0.189418 + 0.981897i 0.560660π0.560660\pi
884884 −6.66960e8 + 3.85070e8i −0.0324726 + 0.0187481i
885885 −5.26553e9 2.43532e10i −0.255353 1.18101i
886886 −9.73151e9 + 1.68555e10i −0.470070 + 0.814185i
887887 −3.45188e9 5.97884e9i −0.166082 0.287663i 0.770957 0.636887i 0.219778π-0.219778\pi
−0.937039 + 0.349224i 0.886445π0.886445\pi
888888 −5.56107e9 6.13292e9i −0.266510 0.293915i
889889 −1.09065e10 1.14211e10i −0.520629 0.545197i
890890 1.16037e10i 0.551737i
891891 −8.59586e9 + 2.92653e9i −0.407115 + 0.138606i
892892 −1.41291e10 8.15746e9i −0.666559 0.384838i
893893 1.66349e10 + 9.60416e9i 0.781700 + 0.451315i
894894 6.78671e9 + 2.17892e9i 0.317671 + 0.101991i
895895 4.73843e10i 2.20929i
896896 1.66476e10 + 4.87455e9i 0.773169 + 0.226390i
897897 4.60104e8 4.17203e8i 0.0212854 0.0193007i
898898 −6.70049e9 1.16056e10i −0.308773 0.534810i
899899 5.83063e8 1.00989e9i 0.0267643 0.0463572i
900900 −3.22820e10 2.31110e10i −1.47609 1.05675i
901901 1.41485e10 8.16862e9i 0.644425 0.372059i
902902 8.59722e9 0.390063
903903 1.12813e9 1.66499e9i 0.0509862 0.0752496i
904904 −9.51021e9 −0.428155
905905 5.24662e10 3.02914e10i 2.35293 1.35847i
906906 −2.55105e10 + 5.51576e9i −1.13965 + 0.246409i
907907 −1.82417e10 + 3.15956e10i −0.811784 + 1.40605i 0.0998298 + 0.995005i 0.468170π0.468170\pi
−0.911614 + 0.411047i 0.865163π0.865163\pi
908908 1.92722e9 + 3.33805e9i 0.0854342 + 0.147976i
909909 −2.88584e9 + 2.94362e10i −0.127438 + 1.29989i
910910 −2.99173e9 + 7.28175e8i −0.131607 + 0.0320325i
911911 2.78042e8i 0.0121842i −0.999981 0.00609209i 0.998061π-0.998061\pi
0.999981 0.00609209i 0.00193918π-0.00193918\pi
912912 −7.62863e9 + 2.37610e10i −0.333016 + 1.03725i
913913 7.30680e9 + 4.21858e9i 0.317746 + 0.183451i
914914 8.15647e9 + 4.70914e9i 0.353338 + 0.204000i
915915 −1.15738e10 + 3.60491e10i −0.499463 + 1.55568i
916916 7.05204e9i 0.303166i
917917 −1.16403e10 + 3.97541e10i −0.498507 + 1.70251i
918918 2.49919e10 1.85614e10i 1.06623 0.791883i
919919 −1.20510e10 2.08729e10i −0.512174 0.887112i −0.999900 0.0141152i 0.995507π-0.995507\pi
0.487726 0.872997i 0.337827π-0.337827\pi
920920 5.11346e9 8.85677e9i 0.216500 0.374988i
921921 3.19712e10 6.91265e9i 1.34850 0.291565i
922922 −2.30211e10 + 1.32912e10i −0.967314 + 0.558479i
923923 2.90079e8 0.0121426
924924 4.96759e8 6.89631e9i 0.0207154 0.287584i
925925 6.07111e10 2.52216
926926 1.79131e10 1.03421e10i 0.741364 0.428027i
927927 −1.20513e10 + 1.68335e10i −0.496883 + 0.694059i
928928 −4.29065e9 + 7.43162e9i −0.176240 + 0.305257i
929929 −9.45594e8 1.63782e9i −0.0386945 0.0670209i 0.846030 0.533136i 0.178987π-0.178987\pi
−0.884724 + 0.466115i 0.845653π0.845653\pi
930930 7.91213e9 7.17438e9i 0.322554 0.292478i
931931 1.00962e10 + 1.95116e10i 0.410048 + 0.792446i
932932 3.12395e9i 0.126401i
933933 −1.88595e10 6.05497e9i −0.760227 0.244077i
934934 5.16682e10 + 2.98306e10i 2.07496 + 1.19798i
935935 −1.84197e10 1.06346e10i −0.736957 0.425482i
936936 5.29654e8 2.40270e8i 0.0211119 0.00957712i
937937 3.00074e9i 0.119163i 0.998223 + 0.0595813i 0.0189766π0.0189766\pi
−0.998223 + 0.0595813i 0.981023π0.981023\pi
938938 1.91434e10 1.82808e10i 0.757373 0.723245i
939939 1.05662e10 + 1.16528e10i 0.416476 + 0.459303i
940940 1.66284e10 + 2.88013e10i 0.652986 + 1.13101i
941941 −8.56893e7 + 1.48418e8i −0.00335246 + 0.00580662i −0.867697 0.497094i 0.834400π-0.834400\pi
0.864344 + 0.502901i 0.167734π0.167734\pi
942942 7.91737e9 + 3.66181e10i 0.308605 + 1.42731i
943943 8.26201e9 4.77007e9i 0.320845 0.185240i
944944 −1.98026e10 −0.766161
945945 4.68567e10 1.73149e10i 1.80618 0.667435i
946946 −1.31556e9 −0.0505234
947947 −1.86765e10 + 1.07829e10i −0.714613 + 0.412582i −0.812767 0.582589i 0.802040π-0.802040\pi
0.0981536 + 0.995171i 0.468706π0.468706\pi
948948 1.06278e9 + 4.91537e9i 0.0405147 + 0.187382i
949949 −7.95718e8 + 1.37822e9i −0.0302223 + 0.0523466i
950950 −4.12583e10 7.14615e10i −1.56127 2.70420i
951951 −2.17093e10 2.39417e10i −0.818490 0.902656i
952952 −2.75566e9 1.13217e10i −0.103513 0.425288i
953953 2.27050e10i 0.849760i 0.905250 + 0.424880i 0.139684π0.139684\pi
−0.905250 + 0.424880i 0.860316π0.860316\pi
954954 2.28568e10 1.03687e10i 0.852309 0.386638i
955955 3.96296e10 + 2.28802e10i 1.47234 + 0.850056i
956956 7.74035e9 + 4.46890e9i 0.286522 + 0.165424i
957957 −3.39684e9 1.09058e9i −0.125280 0.0402222i
958958 1.50900e7i 0.000554510i
959959 −6.32276e9 2.59773e10i −0.231495 0.951105i
960960 −1.04815e10 + 9.50415e9i −0.382361 + 0.346708i
961961 −1.33352e10 2.30973e10i −0.484695 0.839516i
962962 9.04623e8 1.56685e9i 0.0327608 0.0567434i
963963 2.50922e8 3.50494e8i 0.00905412 0.0126470i
964964 −2.08902e10 + 1.20609e10i −0.751056 + 0.433622i
965965 9.71388e10 3.47974
966966 −8.34415e9 1.71994e10i −0.297826 0.613894i
967967 −3.81459e10 −1.35661 −0.678306 0.734780i 0.737285π-0.737285\pi
−0.678306 + 0.734780i 0.737285π0.737285\pi
968968 −8.48463e9 + 4.89860e9i −0.300655 + 0.173583i
969969 2.53818e10 5.48793e9i 0.896169 0.193765i
970970 3.22492e10 5.58572e10i 1.13453 1.96507i
971971 −1.40228e10 2.42883e10i −0.491551 0.851391i 0.508402 0.861120i 0.330236π-0.330236\pi
−0.999953 + 0.00972902i 0.996903π0.996903\pi
972972 1.64530e10 9.88672e9i 0.574663 0.345319i
973973 −3.95122e10 + 3.77317e10i −1.37511 + 1.31314i
974974 1.40266e10i 0.486404i
975975 −1.30379e9 + 4.06093e9i −0.0450498 + 0.140317i
976976 2.60599e10 + 1.50457e10i 0.897219 + 0.518010i
977977 −2.09543e10 1.20980e10i −0.718857 0.415032i 0.0954746 0.995432i 0.469563π-0.469563\pi
−0.814332 + 0.580399i 0.802896π0.802896\pi
978978 1.26028e10 3.92541e10i 0.430806 1.34183i
979979 2.79920e9i 0.0953443i
980980 −1.75256e9 + 3.79963e10i −0.0594814 + 1.28958i
981981 −3.94584e8 + 4.02484e9i −0.0133444 + 0.136115i
982982 5.01373e9 + 8.68404e9i 0.168955 + 0.292639i
983983 7.54203e9 1.30632e10i 0.253251 0.438643i −0.711168 0.703022i 0.751834π-0.751834\pi
0.964419 + 0.264379i 0.0851669π0.0851669\pi
984984 8.73184e9 1.88795e9i 0.292162 0.0631696i
985985 −9.78398e10 + 5.64878e10i −3.26204 + 1.88334i
986986 1.22310e10 0.406343
987987 −3.04796e10 2.19552e9i −1.00902 0.0726821i
988988 −9.86956e8 −0.0325573
989989 −1.26427e9 + 7.29925e8i −0.0415577 + 0.0239934i
990990 −2.65689e10 1.90209e10i −0.870263 0.623029i
991991 1.84469e10 3.19510e10i 0.602096 1.04286i −0.390408 0.920642i 0.627666π-0.627666\pi
0.992503 0.122218i 0.0390008π-0.0390008\pi
992992 −3.09866e9 5.36704e9i −0.100782 0.174560i
993993 −2.96614e10 + 2.68956e10i −0.961321 + 0.871685i
994994 2.50895e9 8.56860e9i 0.0810289 0.276731i
995995 7.89009e10i 2.53922i
996996 −1.69816e10 5.45206e9i −0.544590 0.174845i
997997 −3.57225e10 2.06244e10i −1.14158 0.659094i −0.194762 0.980850i 0.562394π-0.562394\pi
−0.946823 + 0.321756i 0.895727π0.895727\pi
998998 −3.77381e10 2.17881e10i −1.20178 0.693846i
999999 −1.16567e10 + 2.69386e10i −0.369910 + 0.854860i
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 21.8.g.b.17.4 yes 32
3.2 odd 2 inner 21.8.g.b.17.13 yes 32
7.3 odd 6 147.8.c.b.146.31 32
7.4 even 3 147.8.c.b.146.1 32
7.5 odd 6 inner 21.8.g.b.5.13 yes 32
21.5 even 6 inner 21.8.g.b.5.4 32
21.11 odd 6 147.8.c.b.146.32 32
21.17 even 6 147.8.c.b.146.2 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.8.g.b.5.4 32 21.5 even 6 inner
21.8.g.b.5.13 yes 32 7.5 odd 6 inner
21.8.g.b.17.4 yes 32 1.1 even 1 trivial
21.8.g.b.17.13 yes 32 3.2 odd 2 inner
147.8.c.b.146.1 32 7.4 even 3
147.8.c.b.146.2 32 21.17 even 6
147.8.c.b.146.31 32 7.3 odd 6
147.8.c.b.146.32 32 21.11 odd 6