Properties

Label 74.8.c.a.47.2
Level 7474
Weight 88
Character 74.47
Analytic conductor 23.11623.116
Analytic rank 00
Dimension 2222
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [74,8,Mod(47,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.47");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: N N == 74=237 74 = 2 \cdot 37
Weight: k k == 8 8
Character orbit: [χ][\chi] == 74.c (of order 33, 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: 23.116491885823.1164918858
Analytic rank: 00
Dimension: 2222
Relative dimension: 1111 over Q(ζ3)\Q(\zeta_{3})
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 47.2
Character χ\chi == 74.47
Dual form 74.8.c.a.63.2

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+(4.00000+6.92820i)q2+(33.063357.2674i)q3+(32.000055.4256i)q4+(102.843+178.129i)q5+529.013q6+(87.2990+151.206i)q7+512.000q8+(1092.87+1892.90i)q91645.48q105682.10q11+(2116.05+3665.11i)q12+(6239.4810807.1i)q131396.78q14+(6800.6411779.1i)q15+(2048.00+3547.24i)q16+(10150.4+17581.0i)q17+(8742.9515143.2i)q18+(29257.4+50675.4i)q19+(6581.9311400.2i)q20+(5772.809998.77i)q21+(22728.439366.8i)q22+65697.1q23+(16928.429320.9i)q24+(17909.331019.8i)q25+99831.7q2683.4648q27+(5587.149677.21i)q28+177274.q29+(54405.1+94232.4i)q3095681.2q31+(16384.028377.9i)q32+(187869.+325399.i)q33+(81203.3140648.i)q34+(17956.1+31100.9i)q35+139887.q36+(274975.138999.i)q37468119.q38+(412596.+714638.i)q39+(52655.4+91201.9i)q40+(244216.+422995.i)q41+(46182.4+79990.2i)q42+761147.q43+(181827.+314934.i)q44449574.q45+(262788.+455163.i)q46423371.q47+270855.q48+(396529.686809.i)q49+(143274.+248158.i)q50+1.34243e6q51+(399327.+691655.i)q52+(327136.+566616.i)q53+(333.859578.261i)q54+(584363.1.01215e6i)q55+(44697.1+77417.7i)q56+(1.93470e63.35099e6i)q57+(709094.+1.22819e6i)q58+(91051.3+157706.i)q59870482.q60+(1.23526e6+2.13954e6i)q61+(382725.662898.i)q62381626.q63+262144.q64+(1.28337e62.22286e6i)q653.00591e6q66+(1.13014e61.95746e6i)q67+1.29925e6q68+(2.17217e63.76230e6i)q69+(143649.248807.i)q70+(1.36480e6+2.36390e6i)q71+(559549.+969167.i)q72+4.27107e6q73+(136883.+2.46108e6i)q742.36856e6q75+(1.87248e63.24322e6i)q76+(496042.859170.i)q77+(3.30077e65.71710e6i)q78+(756160.1.30971e6i)q79842487.q80+(2.39286e6+4.14456e6i)q813.90746e6q82+(3.15145e6+5.45848e6i)q83738918.q844.17558e6q85+(3.04459e6+5.27338e6i)q86+(5.86126e61.01520e7i)q872.90924e6q88+(550715.953866.i)q89+(1.79830e63.11474e6i)q90+(1.08940e61.88690e6i)q91+(2.10231e63.64130e6i)q92+(3.16354e6+5.47941e6i)q93+(1.69349e62.93320e6i)q94+(6.01782e6+1.04232e7i)q95+(1.08342e6+1.87654e6i)q96203177.q97+(3.17223e6+5.49447e6i)q98+(6.20980e61.07557e7i)q99+O(q100)q+(-4.00000 + 6.92820i) q^{2} +(-33.0633 - 57.2674i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(102.843 + 178.129i) q^{5} +529.013 q^{6} +(87.2990 + 151.206i) q^{7} +512.000 q^{8} +(-1092.87 + 1892.90i) q^{9} -1645.48 q^{10} -5682.10 q^{11} +(-2116.05 + 3665.11i) q^{12} +(-6239.48 - 10807.1i) q^{13} -1396.78 q^{14} +(6800.64 - 11779.1i) q^{15} +(-2048.00 + 3547.24i) q^{16} +(-10150.4 + 17581.0i) q^{17} +(-8742.95 - 15143.2i) q^{18} +(29257.4 + 50675.4i) q^{19} +(6581.93 - 11400.2i) q^{20} +(5772.80 - 9998.77i) q^{21} +(22728.4 - 39366.8i) q^{22} +65697.1 q^{23} +(-16928.4 - 29320.9i) q^{24} +(17909.3 - 31019.8i) q^{25} +99831.7 q^{26} -83.4648 q^{27} +(5587.14 - 9677.21i) q^{28} +177274. q^{29} +(54405.1 + 94232.4i) q^{30} -95681.2 q^{31} +(-16384.0 - 28377.9i) q^{32} +(187869. + 325399. i) q^{33} +(-81203.3 - 140648. i) q^{34} +(-17956.1 + 31100.9i) q^{35} +139887. q^{36} +(274975. - 138999. i) q^{37} -468119. q^{38} +(-412596. + 714638. i) q^{39} +(52655.4 + 91201.9i) q^{40} +(244216. + 422995. i) q^{41} +(46182.4 + 79990.2i) q^{42} +761147. q^{43} +(181827. + 314934. i) q^{44} -449574. q^{45} +(-262788. + 455163. i) q^{46} -423371. q^{47} +270855. q^{48} +(396529. - 686809. i) q^{49} +(143274. + 248158. i) q^{50} +1.34243e6 q^{51} +(-399327. + 691655. i) q^{52} +(-327136. + 566616. i) q^{53} +(333.859 - 578.261i) q^{54} +(-584363. - 1.01215e6i) q^{55} +(44697.1 + 77417.7i) q^{56} +(1.93470e6 - 3.35099e6i) q^{57} +(-709094. + 1.22819e6i) q^{58} +(-91051.3 + 157706. i) q^{59} -870482. q^{60} +(1.23526e6 + 2.13954e6i) q^{61} +(382725. - 662898. i) q^{62} -381626. q^{63} +262144. q^{64} +(1.28337e6 - 2.22286e6i) q^{65} -3.00591e6 q^{66} +(-1.13014e6 - 1.95746e6i) q^{67} +1.29925e6 q^{68} +(-2.17217e6 - 3.76230e6i) q^{69} +(-143649. - 248807. i) q^{70} +(1.36480e6 + 2.36390e6i) q^{71} +(-559549. + 969167. i) q^{72} +4.27107e6 q^{73} +(-136883. + 2.46108e6i) q^{74} -2.36856e6 q^{75} +(1.87248e6 - 3.24322e6i) q^{76} +(-496042. - 859170. i) q^{77} +(-3.30077e6 - 5.71710e6i) q^{78} +(-756160. - 1.30971e6i) q^{79} -842487. q^{80} +(2.39286e6 + 4.14456e6i) q^{81} -3.90746e6 q^{82} +(-3.15145e6 + 5.45848e6i) q^{83} -738918. q^{84} -4.17558e6 q^{85} +(-3.04459e6 + 5.27338e6i) q^{86} +(-5.86126e6 - 1.01520e7i) q^{87} -2.90924e6 q^{88} +(550715. - 953866. i) q^{89} +(1.79830e6 - 3.11474e6i) q^{90} +(1.08940e6 - 1.88690e6i) q^{91} +(-2.10231e6 - 3.64130e6i) q^{92} +(3.16354e6 + 5.47941e6i) q^{93} +(1.69349e6 - 2.93320e6i) q^{94} +(-6.01782e6 + 1.04232e7i) q^{95} +(-1.08342e6 + 1.87654e6i) q^{96} -203177. q^{97} +(3.17223e6 + 5.49447e6i) q^{98} +(6.20980e6 - 1.07557e7i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 22q88q2+40q3704q4+475q5640q6588q7+11264q88369q97600q104904q11+2560q122612q13+9408q143688q1545056q16+24651q17++13715284q99+O(q100) 22 q - 88 q^{2} + 40 q^{3} - 704 q^{4} + 475 q^{5} - 640 q^{6} - 588 q^{7} + 11264 q^{8} - 8369 q^{9} - 7600 q^{10} - 4904 q^{11} + 2560 q^{12} - 2612 q^{13} + 9408 q^{14} - 3688 q^{15} - 45056 q^{16} + 24651 q^{17}+ \cdots + 13715284 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/74Z)×\left(\mathbb{Z}/74\mathbb{Z}\right)^\times.

nn 3939
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\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 −4.00000 + 6.92820i −0.353553 + 0.612372i
33 −33.0633 57.2674i −0.707005 1.22457i −0.965963 0.258680i 0.916713π-0.916713\pi
0.258958 0.965888i 0.416621π-0.416621\pi
44 −32.0000 55.4256i −0.250000 0.433013i
55 102.843 + 178.129i 0.367941 + 0.637292i 0.989243 0.146278i 0.0467295π-0.0467295\pi
−0.621303 + 0.783571i 0.713396π0.713396\pi
66 529.013 0.999856
77 87.2990 + 151.206i 0.0961981 + 0.166620i 0.910108 0.414371i 0.135998π-0.135998\pi
−0.813910 + 0.580991i 0.802665π0.802665\pi
88 512.000 0.353553
99 −1092.87 + 1892.90i −0.499711 + 0.865526i
1010 −1645.48 −0.520347
1111 −5682.10 −1.28717 −0.643583 0.765376i 0.722553π-0.722553\pi
−0.643583 + 0.765376i 0.722553π0.722553\pi
1212 −2116.05 + 3665.11i −0.353502 + 0.612284i
1313 −6239.48 10807.1i −0.787675 1.36429i −0.927388 0.374101i 0.877951π-0.877951\pi
0.139713 0.990192i 0.455382π-0.455382\pi
1414 −1396.78 −0.136045
1515 6800.64 11779.1i 0.520272 0.901138i
1616 −2048.00 + 3547.24i −0.125000 + 0.216506i
1717 −10150.4 + 17581.0i −0.501086 + 0.867907i 0.498913 + 0.866652i 0.333733π0.333733\pi
−0.999999 + 0.00125471i 0.999601π0.999601\pi
1818 −8742.95 15143.2i −0.353349 0.612019i
1919 29257.4 + 50675.4i 0.978586 + 1.69496i 0.667556 + 0.744560i 0.267340π0.267340\pi
0.311030 + 0.950400i 0.399326π0.399326\pi
2020 6581.93 11400.2i 0.183970 0.318646i
2121 5772.80 9998.77i 0.136025 0.235602i
2222 22728.4 39366.8i 0.455082 0.788225i
2323 65697.1 1.12590 0.562949 0.826492i 0.309667π-0.309667\pi
0.562949 + 0.826492i 0.309667π0.309667\pi
2424 −16928.4 29320.9i −0.249964 0.432950i
2525 17909.3 31019.8i 0.229239 0.397053i
2626 99831.7 1.11394
2727 −83.4648 −0.000816075
2828 5587.14 9677.21i 0.0480990 0.0833100i
2929 177274. 1.34974 0.674871 0.737936i 0.264199π-0.264199\pi
0.674871 + 0.737936i 0.264199π0.264199\pi
3030 54405.1 + 94232.4i 0.367888 + 0.637200i
3131 −95681.2 −0.576847 −0.288423 0.957503i 0.593131π-0.593131\pi
−0.288423 + 0.957503i 0.593131π0.593131\pi
3232 −16384.0 28377.9i −0.0883883 0.153093i
3333 187869. + 325399.i 0.910033 + 1.57622i
3434 −81203.3 140648.i −0.354321 0.613703i
3535 −17956.1 + 31100.9i −0.0707904 + 0.122613i
3636 139887. 0.499711
3737 274975. 138999.i 0.892456 0.451135i
3838 −468119. −1.38393
3939 −412596. + 714638.i −1.11378 + 1.92912i
4040 52655.4 + 91201.9i 0.130087 + 0.225317i
4141 244216. + 422995.i 0.553389 + 0.958498i 0.998027 + 0.0627876i 0.0199991π0.0199991\pi
−0.444638 + 0.895710i 0.646668π0.646668\pi
4242 46182.4 + 79990.2i 0.0961842 + 0.166596i
4343 761147. 1.45992 0.729959 0.683490i 0.239539π-0.239539\pi
0.729959 + 0.683490i 0.239539π0.239539\pi
4444 181827. + 314934.i 0.321792 + 0.557360i
4545 −449574. −0.735457
4646 −262788. + 455163.i −0.398065 + 0.689469i
4747 −423371. −0.594811 −0.297406 0.954751i 0.596121π-0.596121\pi
−0.297406 + 0.954751i 0.596121π0.596121\pi
4848 270855. 0.353502
4949 396529. 686809.i 0.481492 0.833968i
5050 143274. + 248158.i 0.162096 + 0.280759i
5151 1.34243e6 1.41708
5252 −399327. + 691655.i −0.393837 + 0.682146i
5353 −327136. + 566616.i −0.301830 + 0.522785i −0.976551 0.215288i 0.930931π-0.930931\pi
0.674720 + 0.738073i 0.264264π0.264264\pi
5454 333.859 578.261i 0.000288526 0.000499742i
5555 −584363. 1.01215e6i −0.473601 0.820302i
5656 44697.1 + 77417.7i 0.0340111 + 0.0589090i
5757 1.93470e6 3.35099e6i 1.38373 2.39669i
5858 −709094. + 1.22819e6i −0.477206 + 0.826545i
5959 −91051.3 + 157706.i −0.0577171 + 0.0999689i −0.893440 0.449182i 0.851715π-0.851715\pi
0.835723 + 0.549151i 0.185049π0.185049\pi
6060 −870482. −0.520272
6161 1.23526e6 + 2.13954e6i 0.696794 + 1.20688i 0.969572 + 0.244806i 0.0787241π0.0787241\pi
−0.272778 + 0.962077i 0.587943π0.587943\pi
6262 382725. 662898.i 0.203946 0.353245i
6363 −381626. −0.192285
6464 262144. 0.125000
6565 1.28337e6 2.22286e6i 0.579636 1.00396i
6666 −3.00591e6 −1.28698
6767 −1.13014e6 1.95746e6i −0.459060 0.795116i 0.539851 0.841760i 0.318480π-0.318480\pi
−0.998912 + 0.0466448i 0.985147π0.985147\pi
6868 1.29925e6 0.501086
6969 −2.17217e6 3.76230e6i −0.796015 1.37874i
7070 −143649. 248807.i −0.0500564 0.0867002i
7171 1.36480e6 + 2.36390e6i 0.452548 + 0.783836i 0.998544 0.0539518i 0.0171817π-0.0171817\pi
−0.545995 + 0.837788i 0.683848π0.683848\pi
7272 −559549. + 969167.i −0.176675 + 0.306010i
7373 4.27107e6 1.28501 0.642505 0.766281i 0.277895π-0.277895\pi
0.642505 + 0.766281i 0.277895π0.277895\pi
7474 −136883. + 2.46108e6i −0.0392679 + 0.706016i
7575 −2.36856e6 −0.648292
7676 1.87248e6 3.24322e6i 0.489293 0.847480i
7777 −496042. 859170.i −0.123823 0.214468i
7878 −3.30077e6 5.71710e6i −0.787561 1.36410i
7979 −756160. 1.30971e6i −0.172551 0.298868i 0.766760 0.641934i 0.221868π-0.221868\pi
−0.939311 + 0.343066i 0.888534π0.888534\pi
8080 −842487. −0.183970
8181 2.39286e6 + 4.14456e6i 0.500288 + 0.866525i
8282 −3.90746e6 −0.782610
8383 −3.15145e6 + 5.45848e6i −0.604975 + 1.04785i 0.387080 + 0.922046i 0.373484π0.373484\pi
−0.992055 + 0.125802i 0.959850π0.959850\pi
8484 −738918. −0.136025
8585 −4.17558e6 −0.737481
8686 −3.04459e6 + 5.27338e6i −0.516159 + 0.894014i
8787 −5.86126e6 1.01520e7i −0.954274 1.65285i
8888 −2.90924e6 −0.455082
8989 550715. 953866.i 0.0828060 0.143424i −0.821648 0.569995i 0.806945π-0.806945\pi
0.904454 + 0.426571i 0.140278π0.140278\pi
9090 1.79830e6 3.11474e6i 0.260023 0.450374i
9191 1.08940e6 1.88690e6i 0.151546 0.262485i
9292 −2.10231e6 3.64130e6i −0.281474 0.487528i
9393 3.16354e6 + 5.47941e6i 0.407833 + 0.706388i
9494 1.69349e6 2.93320e6i 0.210297 0.364246i
9595 −6.01782e6 + 1.04232e7i −0.720123 + 1.24729i
9696 −1.08342e6 + 1.87654e6i −0.124982 + 0.216475i
9797 −203177. −0.0226034 −0.0113017 0.999936i 0.503598π-0.503598\pi
−0.0113017 + 0.999936i 0.503598π0.503598\pi
9898 3.17223e6 + 5.49447e6i 0.340466 + 0.589705i
9999 6.20980e6 1.07557e7i 0.643212 1.11408i
100100 −2.29239e6 −0.229239
101101 7.19482e6 0.694856 0.347428 0.937707i 0.387055π-0.387055\pi
0.347428 + 0.937707i 0.387055π0.387055\pi
102102 −5.36970e6 + 9.30060e6i −0.501014 + 0.867782i
103103 −1.48628e7 −1.34020 −0.670101 0.742270i 0.733749π-0.733749\pi
−0.670101 + 0.742270i 0.733749π0.733749\pi
104104 −3.19462e6 5.53324e6i −0.278485 0.482350i
105105 2.37476e6 0.200197
106106 −2.61709e6 4.53293e6i −0.213426 0.369665i
107107 1.25379e7 + 2.17163e7i 0.989425 + 1.71373i 0.620327 + 0.784343i 0.287000π0.287000\pi
0.369097 + 0.929391i 0.379667π0.379667\pi
108108 2670.87 + 4626.09i 0.000204019 + 0.000353371i
109109 −163897. + 283879.i −0.0121221 + 0.0209962i −0.872023 0.489465i 0.837192π-0.837192\pi
0.859901 + 0.510461i 0.170525π0.170525\pi
110110 9.34980e6 0.669773
111111 −1.70517e7 1.11513e7i −1.18342 0.773918i
112112 −715154. −0.0480990
113113 9.09328e6 1.57500e7i 0.592852 1.02685i −0.400994 0.916081i 0.631335π-0.631335\pi
0.993846 0.110769i 0.0353314π-0.0353314\pi
114114 1.54776e7 + 2.68080e7i 0.978444 + 1.69472i
115115 6.75646e6 + 1.17025e7i 0.414264 + 0.717526i
116116 −5.67275e6 9.82550e6i −0.337436 0.584456i
117117 2.72757e7 1.57444
118118 −728411. 1.26164e6i −0.0408121 0.0706887i
119119 −3.54448e6 −0.192814
120120 3.48193e6 6.03088e6i 0.183944 0.318600i
121121 1.27991e7 0.656798
122122 −1.97642e7 −0.985415
123123 1.61492e7 2.79712e7i 0.782498 1.35533i
124124 3.06180e6 + 5.30319e6i 0.144212 + 0.249782i
125125 2.34365e7 1.07327
126126 1.52650e6 2.64398e6i 0.0679830 0.117750i
127127 −6.52628e6 + 1.13039e7i −0.282718 + 0.489681i −0.972053 0.234761i 0.924569π-0.924569\pi
0.689336 + 0.724442i 0.257903π0.257903\pi
128128 −1.04858e6 + 1.81619e6i −0.0441942 + 0.0765466i
129129 −2.51660e7 4.35889e7i −1.03217 1.78777i
130130 1.02670e7 + 1.77829e7i 0.409864 + 0.709906i
131131 5.33799e6 9.24567e6i 0.207457 0.359326i −0.743456 0.668785i 0.766815π-0.766815\pi
0.950913 + 0.309459i 0.100148π0.100148\pi
132132 1.20236e7 2.08256e7i 0.455016 0.788112i
133133 −5.10829e6 + 8.84782e6i −0.188276 + 0.326104i
134134 1.80822e7 0.649209
135135 −8583.73 14867.5i −0.000300267 0.000520078i
136136 −5.19701e6 + 9.00149e6i −0.177161 + 0.306851i
137137 −2.48718e7 −0.826391 −0.413195 0.910642i 0.635587π-0.635587\pi
−0.413195 + 0.910642i 0.635587π0.635587\pi
138138 3.47547e7 1.12574
139139 −1.98302e7 + 3.43469e7i −0.626290 + 1.08477i 0.362000 + 0.932178i 0.382094π0.382094\pi
−0.988290 + 0.152587i 0.951239π0.951239\pi
140140 2.29838e6 0.0707904
141141 1.39981e7 + 2.42454e7i 0.420534 + 0.728387i
142142 −2.18368e7 −0.640000
143143 3.54534e7 + 6.14071e7i 1.01387 + 1.75607i
144144 −4.47639e6 7.75334e6i −0.124928 0.216381i
145145 1.82313e7 + 3.15775e7i 0.496626 + 0.860181i
146146 −1.70843e7 + 2.95909e7i −0.454320 + 0.786905i
147147 −5.24423e7 −1.36167
148148 −1.65033e7 1.07927e7i −0.418461 0.273661i
149149 −1.90913e7 −0.472806 −0.236403 0.971655i 0.575969π-0.575969\pi
−0.236403 + 0.971655i 0.575969π0.575969\pi
150150 9.47426e6 1.64099e7i 0.229206 0.396996i
151151 −4.46190e6 7.72824e6i −0.105463 0.182668i 0.808464 0.588545i 0.200299π-0.200299\pi
−0.913927 + 0.405878i 0.866966π0.866966\pi
152152 1.49798e7 + 2.59458e7i 0.345982 + 0.599259i
153153 −2.21861e7 3.84275e7i −0.500797 0.867406i
154154 7.93668e6 0.175112
155155 −9.84010e6 1.70436e7i −0.212246 0.367620i
156156 5.28123e7 1.11378
157157 −3.82479e6 + 6.62473e6i −0.0788785 + 0.136622i −0.902766 0.430131i 0.858467π-0.858467\pi
0.823888 + 0.566753i 0.191801π0.191801\pi
158158 1.20986e7 0.244025
159159 4.32648e7 0.853582
160160 3.36995e6 5.83692e6i 0.0650434 0.112658i
161161 5.73530e6 + 9.93382e6i 0.108309 + 0.187597i
162162 −3.82858e7 −0.707515
163163 2.95512e7 5.11841e7i 0.534463 0.925718i −0.464726 0.885455i 0.653847π-0.653847\pi
0.999189 0.0402630i 0.0128196π-0.0128196\pi
164164 1.56298e7 2.70717e7i 0.276695 0.479249i
165165 −3.86420e7 + 6.69298e7i −0.669677 + 1.15991i
166166 −2.52116e7 4.36678e7i −0.427782 0.740940i
167167 −3.17445e6 5.49831e6i −0.0527425 0.0913527i 0.838449 0.544980i 0.183463π-0.183463\pi
−0.891191 + 0.453628i 0.850130π0.850130\pi
168168 2.95567e6 5.11937e6i 0.0480921 0.0832979i
169169 −4.64880e7 + 8.05197e7i −0.740863 + 1.28321i
170170 1.67023e7 2.89293e7i 0.260739 0.451613i
171171 −1.27898e8 −1.95604
172172 −2.43567e7 4.21870e7i −0.364980 0.632163i
173173 −7.37844e6 + 1.27798e7i −0.108344 + 0.187657i −0.915099 0.403228i 0.867888π-0.867888\pi
0.806756 + 0.590885i 0.201221π0.201221\pi
174174 9.37801e7 1.34955
175175 6.25386e6 0.0882094
176176 1.16369e7 2.01558e7i 0.160896 0.278680i
177177 1.20418e7 0.163225
178178 4.40572e6 + 7.63093e6i 0.0585527 + 0.101416i
179179 6.93955e7 0.904370 0.452185 0.891924i 0.350645π-0.350645\pi
0.452185 + 0.891924i 0.350645π0.350645\pi
180180 1.43864e7 + 2.49179e7i 0.183864 + 0.318462i
181181 5.13734e7 + 8.89814e7i 0.643967 + 1.11538i 0.984539 + 0.175165i 0.0560458π0.0560458\pi
−0.340573 + 0.940218i 0.610621π0.610621\pi
182182 8.71521e6 + 1.50952e7i 0.107159 + 0.185605i
183183 8.16837e7 1.41480e8i 0.985273 1.70654i
184184 3.36369e7 0.398065
185185 5.30389e7 + 3.46858e7i 0.615876 + 0.402764i
186186 −5.06166e7 −0.576764
187187 5.76757e7 9.98972e7i 0.644982 1.11714i
188188 1.35479e7 + 2.34656e7i 0.148703 + 0.257561i
189189 −7286.39 12620.4i −7.85048e−5 0.000135974i
190190 −4.81426e7 8.33854e7i −0.509204 0.881967i
191191 −1.41972e8 −1.47430 −0.737152 0.675727i 0.763830π-0.763830\pi
−0.737152 + 0.675727i 0.763830π0.763830\pi
192192 −8.66736e6 1.50123e7i −0.0883756 0.153071i
193193 −1.04565e8 −1.04698 −0.523488 0.852033i 0.675370π-0.675370\pi
−0.523488 + 0.852033i 0.675370π0.675370\pi
194194 812707. 1.40765e6i 0.00799149 0.0138417i
195195 −1.69730e8 −1.63922
196196 −5.07557e7 −0.481492
197197 6.87121e7 1.19013e8i 0.640326 1.10908i −0.345034 0.938590i 0.612133π-0.612133\pi
0.985360 0.170487i 0.0545342π-0.0545342\pi
198198 4.96784e7 + 8.60454e7i 0.454820 + 0.787771i
199199 −8.23840e7 −0.741066 −0.370533 0.928819i 0.620825π-0.620825\pi
−0.370533 + 0.928819i 0.620825π0.620825\pi
200200 9.16956e6 1.58821e7i 0.0810482 0.140380i
201201 −7.47323e7 + 1.29440e8i −0.649115 + 1.12430i
202202 −2.87793e7 + 4.98472e7i −0.245669 + 0.425511i
203203 1.54758e7 + 2.68049e7i 0.129843 + 0.224894i
204204 −4.29576e7 7.44048e7i −0.354270 0.613614i
205205 −5.02316e7 + 8.70037e7i −0.407229 + 0.705341i
206206 5.94512e7 1.02973e8i 0.473833 0.820703i
207207 −7.17983e7 + 1.24358e8i −0.562624 + 0.974493i
208208 5.11138e7 0.393837
209209 −1.66244e8 2.87943e8i −1.25960 2.18170i
210210 −9.49903e6 + 1.64528e7i −0.0707802 + 0.122595i
211211 −1.95531e8 −1.43294 −0.716468 0.697620i 0.754243π-0.754243\pi
−0.716468 + 0.697620i 0.754243π0.754243\pi
212212 4.18734e7 0.301830
213213 9.02497e7 1.56317e8i 0.639907 1.10835i
214214 −2.00607e8 −1.39926
215215 7.82783e7 + 1.35582e8i 0.537164 + 0.930395i
216216 −42734.0 −0.000288526
217217 −8.35287e6 1.44676e7i −0.0554915 0.0961142i
218218 −1.31118e6 2.27103e6i −0.00857165 0.0148465i
219219 −1.41216e8 2.44593e8i −0.908509 1.57358i
220220 −3.73992e7 + 6.47773e7i −0.236801 + 0.410151i
221221 2.53333e8 1.57877
222222 1.45465e8 7.35325e7i 0.892327 0.451070i
223223 1.42945e8 0.863181 0.431590 0.902070i 0.357953π-0.357953\pi
0.431590 + 0.902070i 0.357953π0.357953\pi
224224 2.86061e6 4.95473e6i 0.0170056 0.0294545i
225225 3.91450e7 + 6.78012e7i 0.229107 + 0.396824i
226226 7.27463e7 + 1.26000e8i 0.419210 + 0.726092i
227227 9.98211e7 + 1.72895e8i 0.566411 + 0.981053i 0.996917 + 0.0784648i 0.0250018π0.0250018\pi
−0.430506 + 0.902588i 0.641665π0.641665\pi
228228 −2.47641e8 −1.38373
229229 −1.15473e8 2.00004e8i −0.635411 1.10056i −0.986428 0.164194i 0.947498π-0.947498\pi
0.351017 0.936369i 0.385836π-0.385836\pi
230230 −1.08103e8 −0.585858
231231 −3.28016e7 + 5.68141e7i −0.175087 + 0.303259i
232232 9.07640e7 0.477206
233233 2.27221e8 1.17680 0.588399 0.808571i 0.299758π-0.299758\pi
0.588399 + 0.808571i 0.299758π0.299758\pi
234234 −1.09103e8 + 1.88972e8i −0.556649 + 0.964144i
235235 −4.35406e7 7.54146e7i −0.218855 0.379069i
236236 1.16546e7 0.0577171
237237 −5.00023e7 + 8.66066e7i −0.243989 + 0.422602i
238238 1.41779e7 2.45569e7i 0.0681701 0.118074i
239239 1.64265e6 2.84516e6i 0.00778311 0.0134807i −0.862108 0.506725i 0.830856π-0.830856\pi
0.869891 + 0.493244i 0.164189π0.164189\pi
240240 2.78554e7 + 4.82470e7i 0.130068 + 0.225284i
241241 1.64801e8 + 2.85444e8i 0.758405 + 1.31360i 0.943664 + 0.330906i 0.107354π0.107354\pi
−0.185259 + 0.982690i 0.559312π0.559312\pi
242242 −5.11966e7 + 8.86750e7i −0.232213 + 0.402205i
243243 1.58141e8 2.73908e8i 0.707005 1.22457i
244244 7.90567e7 1.36930e8i 0.348397 0.603441i
245245 1.63120e8 0.708642
246246 1.29194e8 + 2.23770e8i 0.553309 + 0.958360i
247247 3.65103e8 6.32376e8i 1.54161 2.67015i
248248 −4.89888e7 −0.203946
249249 4.16790e8 1.71088
250250 −9.37461e7 + 1.62373e8i −0.379457 + 0.657239i
251251 2.97593e8 1.18786 0.593929 0.804518i 0.297576π-0.297576\pi
0.593929 + 0.804518i 0.297576π0.297576\pi
252252 1.22120e7 + 2.11518e7i 0.0480713 + 0.0832619i
253253 −3.73298e8 −1.44922
254254 −5.22103e7 9.04308e7i −0.199912 0.346257i
255255 1.38059e8 + 2.39125e8i 0.521402 + 0.903095i
256256 −8.38861e6 1.45295e7i −0.0312500 0.0541266i
257257 −8.76073e7 + 1.51740e8i −0.321940 + 0.557616i −0.980888 0.194572i 0.937668π-0.937668\pi
0.658949 + 0.752188i 0.271001π0.271001\pi
258258 4.02657e8 1.45971
259259 4.50226e7 + 2.94434e7i 0.161021 + 0.105303i
260260 −1.64271e8 −0.579636
261261 −1.93737e8 + 3.35562e8i −0.674482 + 1.16824i
262262 4.27039e7 + 7.39654e7i 0.146694 + 0.254082i
263263 4.22487e7 + 7.31770e7i 0.143208 + 0.248044i 0.928703 0.370824i 0.120925π-0.120925\pi
−0.785495 + 0.618868i 0.787591π0.787591\pi
264264 9.61891e7 + 1.66604e8i 0.321745 + 0.557279i
265265 −1.34574e8 −0.444223
266266 −4.08663e7 7.07826e7i −0.133131 0.230590i
267267 −7.28339e7 −0.234177
268268 −7.23288e7 + 1.25277e8i −0.229530 + 0.397558i
269269 2.13687e8 0.669338 0.334669 0.942336i 0.391376π-0.391376\pi
0.334669 + 0.942336i 0.391376π0.391376\pi
270270 137340. 0.000424642
271271 −1.70568e8 + 2.95432e8i −0.520601 + 0.901707i 0.479112 + 0.877754i 0.340959π0.340959\pi
−0.999713 + 0.0239537i 0.992375π0.992375\pi
272272 −4.15761e7 7.20119e7i −0.125272 0.216977i
273273 −1.44077e8 −0.428574
274274 9.94872e7 1.72317e8i 0.292173 0.506059i
275275 −1.01762e8 + 1.76258e8i −0.295069 + 0.511074i
276276 −1.39019e8 + 2.40787e8i −0.398008 + 0.689369i
277277 2.50203e7 + 4.33364e7i 0.0707315 + 0.122511i 0.899222 0.437492i 0.144133π-0.144133\pi
−0.828491 + 0.560003i 0.810800π0.810800\pi
278278 −1.58642e8 2.74775e8i −0.442854 0.767045i
279279 1.04567e8 1.81115e8i 0.288257 0.499276i
280280 −9.19353e6 + 1.59237e7i −0.0250282 + 0.0433501i
281281 −1.90644e8 + 3.30205e8i −0.512568 + 0.887793i 0.487326 + 0.873220i 0.337972π0.337972\pi
−0.999894 + 0.0145732i 0.995361π0.995361\pi
282282 −2.23969e8 −0.594725
283283 1.17189e8 + 2.02978e8i 0.307352 + 0.532349i 0.977782 0.209623i 0.0672238π-0.0672238\pi
−0.670430 + 0.741972i 0.733890π0.733890\pi
284284 8.73472e7 1.51290e8i 0.226274 0.391918i
285285 7.95878e8 2.03652
286286 −5.67254e8 −1.43383
287287 −4.26396e7 + 7.38540e7i −0.106470 + 0.184411i
288288 7.16223e7 0.176675
289289 −892401. 1.54568e6i −0.00217479 0.00376685i
290290 −2.91700e8 −0.702335
291291 6.71770e6 + 1.16354e7i 0.0159807 + 0.0276794i
292292 −1.36674e8 2.36727e8i −0.321253 0.556426i
293293 2.52263e8 + 4.36932e8i 0.585891 + 1.01479i 0.994764 + 0.102201i 0.0325886π0.0325886\pi
−0.408873 + 0.912591i 0.634078π0.634078\pi
294294 2.09769e8 3.63331e8i 0.481422 0.833848i
295295 −3.74558e7 −0.0849459
296296 1.40787e8 7.11677e7i 0.315531 0.159500i
297297 474255. 0.00105042
298298 7.63651e7 1.32268e8i 0.167162 0.289534i
299299 −4.09916e8 7.09996e8i −0.886841 1.53605i
300300 7.57940e7 + 1.31279e8i 0.162073 + 0.280719i
301301 6.64474e7 + 1.15090e8i 0.140441 + 0.243252i
302302 7.13905e7 0.149147
303303 −2.37885e8 4.12028e8i −0.491267 0.850899i
304304 −2.39677e8 −0.489293
305305 −2.54075e8 + 4.40071e8i −0.512758 + 0.888123i
306306 3.54978e8 0.708234
307307 −1.90308e8 −0.375381 −0.187691 0.982228i 0.560100π-0.560100\pi
−0.187691 + 0.982228i 0.560100π0.560100\pi
308308 −3.17467e7 + 5.49869e7i −0.0619115 + 0.107234i
309309 4.91414e8 + 8.51154e8i 0.947530 + 1.64117i
310310 1.57442e8 0.300161
311311 3.02378e8 5.23735e8i 0.570019 0.987302i −0.426544 0.904467i 0.640269π-0.640269\pi
0.996563 0.0828351i 0.0263975π-0.0263975\pi
312312 −2.11249e8 + 3.65895e8i −0.393781 + 0.682048i
313313 2.37570e7 4.11484e7i 0.0437912 0.0758486i −0.843299 0.537445i 0.819390π-0.819390\pi
0.887090 + 0.461596i 0.152723π0.152723\pi
314314 −3.05983e7 5.29978e7i −0.0557755 0.0966060i
315315 −3.92474e7 6.79785e7i −0.0707496 0.122542i
316316 −4.83942e7 + 8.38212e7i −0.0862757 + 0.149434i
317317 5.49685e8 9.52083e8i 0.969185 1.67868i 0.271261 0.962506i 0.412559π-0.412559\pi
0.697924 0.716172i 0.254107π-0.254107\pi
318318 −1.73059e8 + 2.99747e8i −0.301787 + 0.522710i
319319 −1.00729e9 −1.73734
320320 2.69596e7 + 4.66954e7i 0.0459926 + 0.0796616i
321321 8.29092e8 1.43603e9i 1.39906 2.42324i
322322 −9.17647e7 −0.153172
323323 −1.18790e9 −1.96142
324324 1.53143e8 2.65252e8i 0.250144 0.433262i
325325 −4.46979e8 −0.722263
326326 2.36409e8 + 4.09473e8i 0.377923 + 0.654581i
327327 2.16760e7 0.0342816
328328 1.25039e8 + 2.16573e8i 0.195653 + 0.338880i
329329 −3.69599e7 6.40165e7i −0.0572197 0.0991074i
330330 −3.09136e8 5.35439e8i −0.473533 0.820183i
331331 −6.01124e7 + 1.04118e8i −0.0911100 + 0.157807i −0.907978 0.419017i 0.862375π-0.862375\pi
0.816868 + 0.576824i 0.195708π0.195708\pi
332332 4.03386e8 0.604975
333333 −3.73987e7 + 6.72409e8i −0.0555011 + 0.997881i
334334 5.07912e7 0.0745892
335335 2.32453e8 4.02620e8i 0.337814 0.585111i
336336 2.36454e7 + 4.09550e7i 0.0340062 + 0.0589005i
337337 −4.60562e8 7.97718e8i −0.655517 1.13539i −0.981764 0.190104i 0.939117π-0.939117\pi
0.326247 0.945285i 0.394216π-0.394216\pi
338338 −3.71904e8 6.44157e8i −0.523869 0.907368i
339339 −1.20262e9 −1.67660
340340 1.33619e8 + 2.31434e8i 0.184370 + 0.319338i
341341 5.43670e8 0.742498
342342 5.11593e8 8.86105e8i 0.691565 1.19783i
343343 2.82256e8 0.377670
344344 3.89707e8 0.516159
345345 4.46783e8 7.73850e8i 0.585773 1.01459i
346346 −5.90275e7 1.02239e8i −0.0766105 0.132693i
347347 8.20647e8 1.05439 0.527197 0.849743i 0.323243π-0.323243\pi
0.527197 + 0.849743i 0.323243π0.323243\pi
348348 −3.75120e8 + 6.49727e8i −0.477137 + 0.826426i
349349 2.85785e8 4.94993e8i 0.359873 0.623319i −0.628066 0.778160i 0.716153π-0.716153\pi
0.987939 + 0.154841i 0.0494865π0.0494865\pi
350350 −2.50154e7 + 4.33280e7i −0.0311867 + 0.0540170i
351351 520777. + 902012.i 0.000642801 + 0.00111336i
352352 9.30956e7 + 1.61246e8i 0.113771 + 0.197056i
353353 3.99070e8 6.91209e8i 0.482878 0.836369i −0.516929 0.856028i 0.672925π-0.672925\pi
0.999807 + 0.0196593i 0.00625814π0.00625814\pi
354354 −4.81674e7 + 8.34284e7i −0.0577087 + 0.0999545i
355355 −2.80719e8 + 4.86220e8i −0.333022 + 0.576811i
356356 −7.04915e7 −0.0828060
357357 1.17193e8 + 2.02983e8i 0.136320 + 0.236114i
358358 −2.77582e8 + 4.80786e8i −0.319743 + 0.553811i
359359 −9.18116e8 −1.04729 −0.523645 0.851936i 0.675428π-0.675428\pi
−0.523645 + 0.851936i 0.675428π0.675428\pi
360360 −2.30182e8 −0.260023
361361 −1.26506e9 + 2.19115e9i −1.41526 + 2.45130i
362362 −8.21975e8 −0.910706
363363 −4.23182e8 7.32973e8i −0.464359 0.804294i
364364 −1.39443e8 −0.151546
365365 4.39248e8 + 7.60800e8i 0.472808 + 0.818928i
366366 6.53470e8 + 1.13184e9i 0.696693 + 1.20671i
367367 −1.25225e8 2.16896e8i −0.132239 0.229045i 0.792300 0.610132i 0.208883π-0.208883\pi
−0.924539 + 0.381086i 0.875550π0.875550\pi
368368 −1.34548e8 + 2.33043e8i −0.140737 + 0.243764i
369369 −1.06758e9 −1.10614
370370 −4.52466e8 + 2.28721e8i −0.464387 + 0.234747i
371371 −1.14235e8 −0.116142
372372 2.02466e8 3.50682e8i 0.203917 0.353194i
373373 8.92411e8 + 1.54570e9i 0.890398 + 1.54221i 0.839399 + 0.543516i 0.182907π0.182907\pi
0.0509994 + 0.998699i 0.483759π0.483759\pi
374374 4.61406e8 + 7.99178e8i 0.456071 + 0.789938i
375375 −7.74889e8 1.34215e9i −0.758805 1.31429i
376376 −2.16766e8 −0.210297
377377 −1.10610e9 1.91581e9i −1.06316 1.84144i
378378 116582. 0.000111023
379379 −2.24696e8 + 3.89184e8i −0.212011 + 0.367213i −0.952344 0.305027i 0.901334π-0.901334\pi
0.740333 + 0.672240i 0.234668π0.234668\pi
380380 7.70282e8 0.720123
381381 8.63123e8 0.799531
382382 5.67889e8 9.83613e8i 0.521245 0.902823i
383383 4.14759e8 + 7.18384e8i 0.377225 + 0.653372i 0.990657 0.136375i 0.0435451π-0.0435451\pi
−0.613433 + 0.789747i 0.710212π0.710212\pi
384384 1.38678e8 0.124982
385385 1.02029e8 1.76719e8i 0.0911191 0.157823i
386386 4.18261e8 7.24450e8i 0.370162 0.641140i
387387 −8.31833e8 + 1.44078e9i −0.729538 + 1.26360i
388388 6.50166e6 + 1.12612e7i 0.00565084 + 0.00978754i
389389 6.35425e8 + 1.10059e9i 0.547319 + 0.947984i 0.998457 + 0.0555301i 0.0176849π0.0176849\pi
−0.451138 + 0.892454i 0.648982π0.648982\pi
390390 6.78920e8 1.17592e9i 0.579552 1.00381i
391391 −6.66853e8 + 1.15502e9i −0.564172 + 0.977174i
392392 2.03023e8 3.51646e8i 0.170233 0.294852i
393393 −7.05967e8 −0.586693
394394 5.49697e8 + 9.52102e8i 0.452779 + 0.784236i
395395 1.55531e8 2.69387e8i 0.126978 0.219931i
396396 −7.94854e8 −0.643212
397397 −9.52444e8 −0.763963 −0.381982 0.924170i 0.624758π-0.624758\pi
−0.381982 + 0.924170i 0.624758π0.624758\pi
398398 3.29536e8 5.70773e8i 0.262007 0.453809i
399399 6.75589e8 0.532448
400400 7.33565e7 + 1.27057e8i 0.0573097 + 0.0992634i
401401 −7.29454e8 −0.564928 −0.282464 0.959278i 0.591152π-0.591152\pi
−0.282464 + 0.959278i 0.591152π0.591152\pi
402402 −5.97858e8 1.03552e9i −0.458994 0.795001i
403403 5.97001e8 + 1.03404e9i 0.454368 + 0.786988i
404404 −2.30234e8 3.98777e8i −0.173714 0.300882i
405405 −4.92177e8 + 8.52475e8i −0.368153 + 0.637660i
406406 −2.47613e8 −0.183625
407407 −1.56243e9 + 7.89809e8i −1.14874 + 0.580686i
408408 6.87322e8 0.501014
409409 5.49737e8 9.52173e8i 0.397304 0.688152i −0.596088 0.802919i 0.703279π-0.703279\pi
0.993392 + 0.114768i 0.0366124π0.0366124\pi
410410 −4.01853e8 6.96030e8i −0.287954 0.498752i
411411 8.22345e8 + 1.42434e9i 0.584262 + 1.01197i
412412 4.75610e8 + 8.23780e8i 0.335051 + 0.580325i
413413 −3.17948e7 −0.0222091
414414 −5.74387e8 9.94867e8i −0.397835 0.689071i
415415 −1.29641e9 −0.890380
416416 −2.04455e8 + 3.54127e8i −0.139243 + 0.241175i
417417 2.62261e9 1.77116
418418 2.65990e9 1.78135
419419 5.02986e7 8.71197e7i 0.0334046 0.0578585i −0.848840 0.528650i 0.822698π-0.822698\pi
0.882244 + 0.470792i 0.156032π0.156032\pi
420420 −7.59922e7 1.31622e8i −0.0500492 0.0866877i
421421 −2.50820e8 −0.163823 −0.0819116 0.996640i 0.526103π-0.526103\pi
−0.0819116 + 0.996640i 0.526103π0.526103\pi
422422 7.82124e8 1.35468e9i 0.506620 0.877491i
423423 4.62689e8 8.01402e8i 0.297234 0.514824i
424424 −1.67494e8 + 2.90107e8i −0.106713 + 0.184832i
425425 3.63573e8 + 6.29728e8i 0.229737 + 0.397916i
426426 7.21998e8 + 1.25054e9i 0.452483 + 0.783723i
427427 −2.15674e8 + 3.73559e8i −0.134060 + 0.232199i
428428 8.02428e8 1.38985e9i 0.494712 0.856867i
429429 2.34442e9 4.06065e9i 1.43362 2.48310i
430430 −1.25245e9 −0.759664
431431 5.20141e8 + 9.00910e8i 0.312932 + 0.542015i 0.978996 0.203880i 0.0653554π-0.0653554\pi
−0.666064 + 0.745895i 0.732022π0.732022\pi
432432 170936. 296070.i 0.000102009 0.000176685i
433433 2.78932e9 1.65117 0.825584 0.564279i 0.190846π-0.190846\pi
0.825584 + 0.564279i 0.190846π0.190846\pi
434434 1.33646e8 0.0784769
435435 1.20557e9 2.08811e9i 0.702233 1.21630i
436436 2.09789e7 0.0121221
437437 1.92213e9 + 3.32923e9i 1.10179 + 1.90835i
438438 2.25945e9 1.28483
439439 −9.89247e8 1.71343e9i −0.558057 0.966584i −0.997659 0.0683906i 0.978214π-0.978214\pi
0.439601 0.898193i 0.355120π-0.355120\pi
440440 −2.99194e8 5.18219e8i −0.167443 0.290020i
441441 8.66709e8 + 1.50118e9i 0.481214 + 0.833487i
442442 −1.01333e9 + 1.75514e9i −0.558180 + 0.966796i
443443 −3.63514e7 −0.0198659 −0.00993296 0.999951i 0.503162π-0.503162\pi
−0.00993296 + 0.999951i 0.503162π0.503162\pi
444444 −7.24127e7 + 1.30194e9i −0.0392622 + 0.705914i
445445 2.26548e8 0.121871
446446 −5.71780e8 + 9.90351e8i −0.305180 + 0.528588i
447447 6.31222e8 + 1.09331e9i 0.334276 + 0.578984i
448448 2.28849e7 + 3.96378e7i 0.0120248 + 0.0208275i
449449 1.43180e8 + 2.47996e8i 0.0746485 + 0.129295i 0.900933 0.433957i 0.142883π-0.142883\pi
−0.826285 + 0.563252i 0.809550π0.809550\pi
450450 −6.26320e8 −0.324006
451451 −1.38766e9 2.40350e9i −0.712304 1.23375i
452452 −1.16394e9 −0.592852
453453 −2.95051e8 + 5.11043e8i −0.149126 + 0.258294i
454454 −1.59714e9 −0.801026
455455 4.48148e8 0.223039
456456 9.90565e8 1.71571e9i 0.489222 0.847358i
457457 4.09367e8 + 7.09044e8i 0.200635 + 0.347510i 0.948733 0.316078i 0.102366π-0.102366\pi
−0.748098 + 0.663588i 0.769033π0.769033\pi
458458 1.84756e9 0.898606
459459 847202. 1.46740e6i 0.000408924 0.000708277i
460460 4.32414e8 7.48963e8i 0.207132 0.358763i
461461 −3.51653e7 + 6.09081e7i −0.0167171 + 0.0289549i −0.874263 0.485453i 0.838655π-0.838655\pi
0.857546 + 0.514408i 0.171988π0.171988\pi
462462 −2.62413e8 4.54513e8i −0.123805 0.214437i
463463 −4.79035e8 8.29713e8i −0.224302 0.388503i 0.731808 0.681511i 0.238677π-0.238677\pi
−0.956110 + 0.293008i 0.905344π0.905344\pi
464464 −3.63056e8 + 6.28832e8i −0.168718 + 0.292228i
465465 −6.50693e8 + 1.12703e9i −0.300117 + 0.519818i
466466 −9.08882e8 + 1.57423e9i −0.416061 + 0.720639i
467467 −1.12248e9 −0.510000 −0.255000 0.966941i 0.582075π-0.582075\pi
−0.255000 + 0.966941i 0.582075π0.582075\pi
468468 −8.72824e8 1.51178e9i −0.393610 0.681753i
469469 1.97320e8 3.41768e8i 0.0883214 0.152977i
470470 6.96650e8 0.309508
471471 5.05841e8 0.223070
472472 −4.66183e7 + 8.07452e7i −0.0204061 + 0.0353443i
473473 −4.32491e9 −1.87916
474474 −4.00019e8 6.92853e8i −0.172527 0.298825i
475475 2.09592e9 0.897320
476476 1.13424e8 + 1.96455e8i 0.0482035 + 0.0834909i
477477 −7.15033e8 1.23847e9i −0.301656 0.522484i
478478 1.31412e7 + 2.27613e7i 0.00550349 + 0.00953232i
479479 −1.25400e9 + 2.17200e9i −0.521344 + 0.902995i 0.478347 + 0.878171i 0.341236π0.341236\pi
−0.999692 + 0.0248243i 0.992097π0.992097\pi
480480 −4.45687e8 −0.183944
481481 −3.21788e9 2.10439e9i −1.31845 0.862223i
482482 −2.63682e9 −1.07255
483483 3.79256e8 6.56891e8i 0.153150 0.265264i
484484 −4.09572e8 7.09400e8i −0.164200 0.284402i
485485 −2.08952e7 3.61916e7i −0.00831670 0.0144050i
486486 1.26513e9 + 2.19126e9i 0.499928 + 0.865900i
487487 −1.85017e9 −0.725874 −0.362937 0.931814i 0.618226π-0.618226\pi
−0.362937 + 0.931814i 0.618226π0.618226\pi
488488 6.32454e8 + 1.09544e9i 0.246354 + 0.426697i
489489 −3.90824e9 −1.51147
490490 −6.52482e8 + 1.13013e9i −0.250543 + 0.433953i
491491 1.44884e9 0.552375 0.276188 0.961104i 0.410929π-0.410929\pi
0.276188 + 0.961104i 0.410929π0.410929\pi
492492 −2.06710e9 −0.782498
493493 −1.79940e9 + 3.11665e9i −0.676337 + 1.17145i
494494 2.92082e9 + 5.05901e9i 1.09009 + 1.88808i
495495 2.55453e9 0.946656
496496 1.95955e8 3.39404e8i 0.0721058 0.124891i
497497 −2.38291e8 + 4.12733e8i −0.0870685 + 0.150807i
498498 −1.66716e9 + 2.88761e9i −0.604888 + 1.04770i
499499 −1.86563e9 3.23137e9i −0.672163 1.16422i −0.977290 0.211908i 0.932032π-0.932032\pi
0.305127 0.952312i 0.401301π-0.401301\pi
500500 −7.49968e8 1.29898e9i −0.268317 0.464738i
501501 −2.09916e8 + 3.63585e8i −0.0745784 + 0.129174i
502502 −1.19037e9 + 2.06178e9i −0.419971 + 0.727411i
503503 2.63972e9 4.57213e9i 0.924847 1.60188i 0.133039 0.991111i 0.457526π-0.457526\pi
0.791807 0.610771i 0.209140π-0.209140\pi
504504 −1.95392e8 −0.0679830
505505 7.39934e8 + 1.28160e9i 0.255666 + 0.442827i
506506 1.49319e9 2.58628e9i 0.512376 0.887461i
507507 6.14820e9 2.09517
508508 8.35364e8 0.282718
509509 5.86626e8 1.01607e9i 0.197174 0.341515i −0.750437 0.660942i 0.770157π-0.770157\pi
0.947611 + 0.319427i 0.103490π0.103490\pi
510510 −2.20894e9 −0.737374
511511 3.72860e8 + 6.45813e8i 0.123616 + 0.214108i
512512 1.34218e8 0.0441942
513513 −2.44197e6 4.22961e6i −0.000798599 0.00138321i
514514 −7.00859e8 1.21392e9i −0.227646 0.394294i
515515 −1.52853e9 2.64749e9i −0.493115 0.854101i
516516 −1.61063e9 + 2.78969e9i −0.516085 + 0.893885i
517517 2.40564e9 0.765621
518518 −3.84080e8 + 1.94152e8i −0.121414 + 0.0613745i
519519 9.75823e8 0.306398
520520 6.57085e8 1.13811e9i 0.204932 0.354953i
521521 −1.03976e9 1.80091e9i −0.322106 0.557904i 0.658816 0.752304i 0.271057π-0.271057\pi
−0.980922 + 0.194400i 0.937724π0.937724\pi
522522 −1.54989e9 2.68449e9i −0.476931 0.826068i
523523 2.29797e9 + 3.98020e9i 0.702406 + 1.21660i 0.967620 + 0.252413i 0.0812241π0.0812241\pi
−0.265214 + 0.964190i 0.585443π0.585443\pi
524524 −6.83263e8 −0.207457
525525 −2.06773e8 3.58142e8i −0.0623644 0.108018i
526526 −6.75980e8 −0.202527
527527 9.71203e8 1.68217e9i 0.289050 0.500649i
528528 −1.53903e9 −0.455016
529529 9.11286e8 0.267646
530530 5.38296e8 9.32356e8i 0.157056 0.272030i
531531 −1.99014e8 3.44703e8i −0.0576838 0.0999112i
532532 6.53862e8 0.188276
533533 3.04756e9 5.27853e9i 0.871781 1.50997i
534534 2.91335e8 5.04608e8i 0.0827940 0.143403i
535535 −2.57887e9 + 4.46673e9i −0.728100 + 1.26111i
536536 −5.78631e8 1.00222e9i −0.162302 0.281116i
537537 −2.29445e9 3.97410e9i −0.639394 1.10746i
538538 −8.54748e8 + 1.48047e9i −0.236647 + 0.409884i
539539 −2.25312e9 + 3.90252e9i −0.619760 + 1.07346i
540540 −549359. + 951518.i −0.000150134 + 0.000260039i
541541 −5.95661e9 −1.61737 −0.808684 0.588244i 0.799820π-0.799820\pi
−0.808684 + 0.588244i 0.799820π0.799820\pi
542542 −1.36454e9 2.36346e9i −0.368121 0.637603i
543543 3.39715e9 5.88404e9i 0.910575 1.57716i
544544 6.65217e8 0.177161
545545 −6.74226e7 −0.0178409
546546 5.76308e8 9.98195e8i 0.151524 0.262447i
547547 6.55369e9 1.71210 0.856052 0.516890i 0.172910π-0.172910\pi
0.856052 + 0.516890i 0.172910π0.172910\pi
548548 7.95898e8 + 1.37854e9i 0.206598 + 0.357838i
549549 −5.39991e9 −1.39278
550550 −8.14100e8 1.41006e9i −0.208645 0.361384i
551551 5.18657e9 + 8.98340e9i 1.32084 + 2.28776i
552552 −1.11215e9 1.92630e9i −0.281434 0.487458i
553553 1.32024e8 2.28672e8i 0.0331982 0.0575010i
554554 −4.00325e8 −0.100029
555555 2.32722e8 4.18423e9i 0.0577847 1.03894i
556556 2.53826e9 0.626290
557557 −6.06102e8 + 1.04980e9i −0.148611 + 0.257403i −0.930715 0.365746i 0.880814π-0.880814\pi
0.782103 + 0.623149i 0.214147π0.214147\pi
558558 8.36536e8 + 1.44892e9i 0.203828 + 0.353041i
559559 −4.74916e9 8.22579e9i −1.14994 1.99176i
560560 −7.35483e7 1.27389e8i −0.0176976 0.0306531i
561561 −7.62781e9 −1.82402
562562 −1.52515e9 2.64164e9i −0.362440 0.627765i
563563 2.22115e9 0.524563 0.262282 0.964991i 0.415525π-0.415525\pi
0.262282 + 0.964991i 0.415525π0.415525\pi
564564 8.95877e8 1.55170e9i 0.210267 0.364193i
565565 3.74071e9 0.872538
566566 −1.87503e9 −0.434661
567567 −4.17789e8 + 7.23632e8i −0.0962535 + 0.166716i
568568 6.98778e8 + 1.21032e9i 0.160000 + 0.277128i
569569 −5.04048e9 −1.14704 −0.573520 0.819192i 0.694423π-0.694423\pi
−0.573520 + 0.819192i 0.694423π0.694423\pi
570570 −3.18351e9 + 5.51400e9i −0.720019 + 1.24711i
571571 −1.59482e9 + 2.76231e9i −0.358497 + 0.620935i −0.987710 0.156298i 0.950044π-0.950044\pi
0.629213 + 0.777233i 0.283377π0.283377\pi
572572 2.26902e9 3.93005e9i 0.506934 0.878036i
573573 4.69408e9 + 8.13038e9i 1.04234 + 1.80539i
574574 −3.41117e8 5.90832e8i −0.0752856 0.130398i
575575 1.17659e9 2.03791e9i 0.258100 0.447042i
576576 −2.86489e8 + 4.96214e8i −0.0624639 + 0.108191i
577577 4.53197e9 7.84960e9i 0.982136 1.70111i 0.328106 0.944641i 0.393590π-0.393590\pi
0.654030 0.756469i 0.273077π-0.273077\pi
578578 1.42784e7 0.00307562
579579 3.45728e9 + 5.98818e9i 0.740217 + 1.28209i
580580 1.16680e9 2.02096e9i 0.248313 0.430090i
581581 −1.10048e9 −0.232790
582582 −1.07483e8 −0.0226001
583583 1.85882e9 3.21957e9i 0.388506 0.672912i
584584 2.18679e9 0.454320
585585 2.80511e9 + 4.85859e9i 0.579301 + 1.00338i
586586 −4.03621e9 −0.828575
587587 1.43883e8 + 2.49212e8i 0.0293613 + 0.0508553i 0.880333 0.474357i 0.157319π-0.157319\pi
−0.850971 + 0.525212i 0.823986π0.823986\pi
588588 1.67815e9 + 2.90665e9i 0.340417 + 0.589620i
589589 −2.79939e9 4.84868e9i −0.564494 0.977732i
590590 1.49823e8 2.59502e8i 0.0300329 0.0520185i
591591 −9.08740e9 −1.81085
592592 −7.00839e7 + 1.26007e9i −0.0138833 + 0.249614i
593593 −6.45832e9 −1.27183 −0.635913 0.771761i 0.719376π-0.719376\pi
−0.635913 + 0.771761i 0.719376π0.719376\pi
594594 −1.89702e6 + 3.28574e6i −0.000371381 + 0.000643251i
595595 −3.64524e8 6.31374e8i −0.0709442 0.122879i
596596 6.10921e8 + 1.05815e9i 0.118202 + 0.204731i
597597 2.72389e9 + 4.71792e9i 0.523937 + 0.907486i
598598 6.55866e9 1.25418
599599 2.16097e9 + 3.74292e9i 0.410824 + 0.711568i 0.994980 0.100073i 0.0319077π-0.0319077\pi
−0.584156 + 0.811641i 0.698574π0.698574\pi
600600 −1.21270e9 −0.229206
601601 2.83309e9 4.90706e9i 0.532354 0.922064i −0.466933 0.884293i 0.654641π-0.654641\pi
0.999286 0.0377708i 0.0120257π-0.0120257\pi
602602 −1.06316e9 −0.198614
603603 4.94037e9 0.917590
604604 −2.85562e8 + 4.94608e8i −0.0527316 + 0.0913338i
605605 1.31630e9 + 2.27989e9i 0.241663 + 0.418573i
606606 3.80615e9 0.694756
607607 −3.16656e8 + 5.48463e8i −0.0574681 + 0.0995376i −0.893328 0.449405i 0.851636π-0.851636\pi
0.835860 + 0.548942i 0.184969π0.184969\pi
608608 9.58708e8 1.66053e9i 0.172991 0.299629i
609609 1.02336e9 1.77252e9i 0.183599 0.318002i
610610 −2.03260e9 3.52057e9i −0.362575 0.627998i
611611 2.64162e9 + 4.57542e9i 0.468518 + 0.811496i
612612 −1.41991e9 + 2.45936e9i −0.250399 + 0.433703i
613613 1.99594e9 3.45707e9i 0.349974 0.606172i −0.636271 0.771466i 0.719524π-0.719524\pi
0.986244 + 0.165294i 0.0528572π0.0528572\pi
614614 7.61232e8 1.31849e9i 0.132717 0.229873i
615615 6.64330e9 1.15165
616616 −2.53974e8 4.39895e8i −0.0437780 0.0758258i
617617 1.33468e9 2.31173e9i 0.228759 0.396222i −0.728682 0.684853i 0.759867π-0.759867\pi
0.957441 + 0.288630i 0.0931999π0.0931999\pi
618618 −7.86262e9 −1.34001
619619 −5.70698e9 −0.967139 −0.483569 0.875306i 0.660660π-0.660660\pi
−0.483569 + 0.875306i 0.660660π0.660660\pi
620620 −6.29766e8 + 1.09079e9i −0.106123 + 0.183810i
621621 −5.48339e6 −0.000918817
622622 2.41903e9 + 4.18988e9i 0.403064 + 0.698128i
623623 1.92307e8 0.0318631
624624 −1.68999e9 2.92716e9i −0.278445 0.482281i
625625 1.01111e9 + 1.75129e9i 0.165660 + 0.286932i
626626 1.90056e8 + 3.29187e8i 0.0309651 + 0.0536331i
627627 −1.09932e10 + 1.90407e10i −1.78109 + 3.08494i
628628 4.89573e8 0.0788785
629629 −3.47354e8 + 6.24524e9i −0.0556538 + 1.00063i
630630 6.27958e8 0.100055
631631 5.21371e9 9.03041e9i 0.826121 1.43088i −0.0749377 0.997188i 0.523876π-0.523876\pi
0.901059 0.433696i 0.142791π-0.142791\pi
632632 −3.87154e8 6.70570e8i −0.0610062 0.105666i
633633 6.46491e9 + 1.11975e10i 1.01309 + 1.75473i
634634 4.39748e9 + 7.61666e9i 0.685317 + 1.18700i
635635 −2.68472e9 −0.416094
636636 −1.38447e9 2.39798e9i −0.213395 0.369612i
637637 −9.89655e9 −1.51704
638638 4.02915e9 6.97869e9i 0.614244 1.06390i
639639 −5.96619e9 −0.904574
640640 −4.31353e8 −0.0650434
641641 2.30437e9 3.99129e9i 0.345581 0.598563i −0.639878 0.768476i 0.721015π-0.721015\pi
0.985459 + 0.169913i 0.0543486π0.0543486\pi
642642 6.63274e9 + 1.14882e10i 0.989282 + 1.71349i
643643 4.40952e9 0.654113 0.327057 0.945005i 0.393943π-0.393943\pi
0.327057 + 0.945005i 0.393943π0.393943\pi
644644 3.67059e8 6.35765e8i 0.0541546 0.0937985i
645645 5.17628e9 8.96559e9i 0.759555 1.31559i
646646 4.75160e9 8.23002e9i 0.693468 1.20112i
647647 5.97464e9 + 1.03484e10i 0.867255 + 1.50213i 0.864791 + 0.502132i 0.167451π0.167451\pi
0.00246394 + 0.999997i 0.499216π0.499216\pi
648648 1.22515e9 + 2.12202e9i 0.176879 + 0.306363i
649649 5.17363e8 8.96099e8i 0.0742915 0.128677i
650650 1.78792e9 3.09676e9i 0.255358 0.442294i
651651 −5.52348e8 + 9.56694e8i −0.0784656 + 0.135906i
652652 −3.78255e9 −0.534463
653653 −1.84460e9 3.19495e9i −0.259243 0.449022i 0.706796 0.707417i 0.250140π-0.250140\pi
−0.966039 + 0.258395i 0.916806π0.916806\pi
654654 −8.67039e7 + 1.50176e8i −0.0121204 + 0.0209931i
655655 2.19589e9 0.305328
656656 −2.00062e9 −0.276695
657657 −4.66772e9 + 8.08473e9i −0.642135 + 1.11221i
658658 5.91359e8 0.0809208
659659 3.59404e9 + 6.22507e9i 0.489198 + 0.847316i 0.999923 0.0124287i 0.00395627π-0.00395627\pi
−0.510725 + 0.859744i 0.670623π0.670623\pi
660660 4.94617e9 0.669677
661661 4.20354e9 + 7.28075e9i 0.566122 + 0.980553i 0.996944 + 0.0781157i 0.0248904π0.0248904\pi
−0.430822 + 0.902437i 0.641776π0.641776\pi
662662 −4.80899e8 8.32941e8i −0.0644245 0.111586i
663663 −8.37605e9 1.45077e10i −1.11620 1.93331i
664664 −1.61354e9 + 2.79474e9i −0.213891 + 0.370470i
665665 −2.10140e9 −0.277098
666666 −4.50899e9 2.94874e9i −0.591452 0.386791i
667667 1.16464e10 1.51967
668668 −2.03165e8 + 3.51892e8i −0.0263712 + 0.0456763i
669669 −4.72624e9 8.18608e9i −0.610273 1.05702i
670670 1.85962e9 + 3.22096e9i 0.238871 + 0.413736i
671671 −7.01888e9 1.21571e10i −0.896890 1.55346i
672672 −3.78326e8 −0.0480921
673673 1.38835e9 + 2.40469e9i 0.175568 + 0.304092i 0.940358 0.340187i 0.110491π-0.110491\pi
−0.764790 + 0.644280i 0.777157π0.777157\pi
674674 7.36900e9 0.927041
675675 −1.49479e6 + 2.58906e6i −0.000187076 + 0.000324025i
676676 5.95047e9 0.740863
677677 −6.79466e8 −0.0841603 −0.0420801 0.999114i 0.513398π-0.513398\pi
−0.0420801 + 0.999114i 0.513398π0.513398\pi
678678 4.81047e9 8.33198e9i 0.592766 1.02670i
679679 −1.77371e7 3.07216e7i −0.00217440 0.00376617i
680680 −2.13790e9 −0.260739
681681 6.60083e9 1.14330e10i 0.800910 1.38722i
682682 −2.17468e9 + 3.76666e9i −0.262513 + 0.454685i
683683 −7.55881e9 + 1.30922e10i −0.907781 + 1.57232i −0.0906398 + 0.995884i 0.528891π0.528891\pi
−0.817141 + 0.576438i 0.804442π0.804442\pi
684684 4.09274e9 + 7.08884e9i 0.489010 + 0.846991i
685685 −2.55788e9 4.43038e9i −0.304063 0.526652i
686686 −1.12902e9 + 1.95552e9i −0.133527 + 0.231275i
687687 −7.63581e9 + 1.32256e10i −0.898477 + 1.55621i
688688 −1.55883e9 + 2.69997e9i −0.182490 + 0.316082i
689689 8.16464e9 0.950976
690690 3.57426e9 + 6.19080e9i 0.414204 + 0.717423i
691691 3.67767e9 6.36992e9i 0.424033 0.734447i −0.572296 0.820047i 0.693947π-0.693947\pi
0.996330 + 0.0855996i 0.0272806π0.0272806\pi
692692 9.44440e8 0.108344
693693 2.16844e9 0.247503
694694 −3.28259e9 + 5.68561e9i −0.372785 + 0.645682i
695695 −8.15756e9 −0.921750
696696 −3.00096e9 5.19782e9i −0.337387 0.584371i
697697 −9.91557e9 −1.10918
698698 2.28628e9 + 3.95995e9i 0.254469 + 0.440753i
699699 −7.51267e9 1.30123e10i −0.832002 1.44107i
700700 −2.00123e8 3.46624e8i −0.0220523 0.0381958i
701701 5.90179e9 1.02222e10i 0.647099 1.12081i −0.336713 0.941607i 0.609315π-0.609315\pi
0.983812 0.179201i 0.0573513π-0.0573513\pi
702702 −8.33243e6 −0.000909058
703703 1.50889e10 + 9.86768e9i 1.63800 + 1.07120i
704704 −1.48953e9 −0.160896
705705 −2.87920e9 + 4.98692e9i −0.309464 + 0.536007i
706706 3.19256e9 + 5.52967e9i 0.341446 + 0.591402i
707707 6.28101e8 + 1.08790e9i 0.0668438 + 0.115777i
708708 −3.85339e8 6.67427e8i −0.0408062 0.0706785i
709709 8.55548e9 0.901535 0.450767 0.892641i 0.351150π-0.351150\pi
0.450767 + 0.892641i 0.351150π0.351150\pi
710710 −2.24575e9 3.88976e9i −0.235482 0.407867i
711711 3.30553e9 0.344904
712712 2.81966e8 4.88379e8i 0.0292763 0.0507081i
713713 −6.28598e9 −0.649470
714714 −1.87508e9 −0.192786
715715 −7.29224e9 + 1.26305e10i −0.746088 + 1.29226i
716716 −2.22066e9 3.84629e9i −0.226092 0.391604i
717717 −2.17246e8 −0.0220108
718718 3.67246e9 6.36090e9i 0.370273 0.641332i
719719 5.48147e8 9.49419e8i 0.0549979 0.0952592i −0.837216 0.546873i 0.815818π-0.815818\pi
0.892214 + 0.451614i 0.149151π0.149151\pi
720720 9.20728e8 1.59475e9i 0.0919321 0.159231i
721721 −1.29751e9 2.24735e9i −0.128925 0.223304i
722722 −1.01205e10 1.75292e10i −1.00074 1.73333i
723723 1.08978e10 1.88755e10i 1.07239 1.85744i
724724 3.28790e9 5.69481e9i 0.321983 0.557691i
725725 3.17484e9 5.49899e9i 0.309413 0.535920i
726726 6.77092e9 0.656703
727727 −4.04479e9 7.00578e9i −0.390414 0.676217i 0.602090 0.798428i 0.294335π-0.294335\pi
−0.992504 + 0.122211i 0.961001π0.961001\pi
728728 5.57774e8 9.66092e8i 0.0535794 0.0928023i
729729 −1.04483e10 −0.998845
730730 −7.02797e9 −0.668652
731731 −7.72595e9 + 1.33817e10i −0.731545 + 1.26707i
732732 −1.04555e10 −0.985273
733733 −6.38475e9 1.10587e10i −0.598798 1.03715i −0.992999 0.118124i 0.962312π-0.962312\pi
0.394201 0.919024i 0.371021π-0.371021\pi
734734 2.00360e9 0.187015
735735 −5.39331e9 9.34148e9i −0.501013 0.867781i
736736 −1.07638e9 1.86435e9i −0.0995162 0.172367i
737737 6.42156e9 + 1.11225e10i 0.590887 + 1.02345i
738738 4.27034e9 7.39644e9i 0.391079 0.677369i
739739 −1.90123e10 −1.73292 −0.866459 0.499247i 0.833610π-0.833610\pi
−0.866459 + 0.499247i 0.833610π0.833610\pi
740740 2.25238e8 4.04966e9i 0.0204329 0.367373i
741741 −4.82861e10 −4.35971
742742 4.56938e8 7.91441e8i 0.0410624 0.0711221i
743743 7.78857e9 + 1.34902e10i 0.696621 + 1.20658i 0.969631 + 0.244572i 0.0786476π0.0786476\pi
−0.273010 + 0.962011i 0.588019π0.588019\pi
744744 1.61973e9 + 2.80546e9i 0.144191 + 0.249746i
745745 −1.96340e9 3.40071e9i −0.173965 0.301316i
746746 −1.42786e10 −1.25921
747747 −6.88825e9 1.19308e10i −0.604626 1.04724i
748748 −7.38249e9 −0.644982
749749 −2.18910e9 + 3.79163e9i −0.190361 + 0.329716i
750750 1.23982e10 1.07311
751751 6.04137e9 0.520470 0.260235 0.965545i 0.416200π-0.416200\pi
0.260235 + 0.965545i 0.416200π0.416200\pi
752752 8.67065e8 1.50180e9i 0.0743514 0.128780i
753753 −9.83941e9 1.70424e10i −0.839821 1.45461i
754754 1.76975e10 1.50353
755755 9.17748e8 1.58959e9i 0.0776084 0.134422i
756756 −466329. + 807706.i −3.92524e−5 + 6.79872e-5i
757757 1.80052e9 3.11859e9i 0.150856 0.261290i −0.780686 0.624923i 0.785130π-0.785130\pi
0.931542 + 0.363633i 0.118464π0.118464\pi
758758 −1.79757e9 3.11347e9i −0.149914 0.259659i
759759 1.23425e10 + 2.13778e10i 1.02460 + 1.77467i
760760 −3.08113e9 + 5.33667e9i −0.254602 + 0.440984i
761761 −5.92131e9 + 1.02560e10i −0.487048 + 0.843591i −0.999889 0.0148920i 0.995260π-0.995260\pi
0.512841 + 0.858483i 0.328593π0.328593\pi
762762 −3.45249e9 + 5.97989e9i −0.282677 + 0.489611i
763763 −5.72323e7 −0.00466451
764764 4.54311e9 + 7.86891e9i 0.368576 + 0.638392i
765765 4.56336e9 7.90397e9i 0.368527 0.638308i
766766 −6.63615e9 −0.533476
767767 2.27245e9 0.181849
768768 −5.54711e8 + 9.60787e8i −0.0441878 + 0.0765355i
769769 2.27682e10 1.80546 0.902729 0.430210i 0.141561π-0.141561\pi
0.902729 + 0.430210i 0.141561π0.141561\pi
770770 8.16229e8 + 1.41375e9i 0.0644309 + 0.111598i
771771 1.15864e10 0.910451
772772 3.34609e9 + 5.79560e9i 0.261744 + 0.453354i
773773 1.09428e10 + 1.89535e10i 0.852117 + 1.47591i 0.879294 + 0.476280i 0.158015π0.158015\pi
−0.0271763 + 0.999631i 0.508652π0.508652\pi
774774 −6.65467e9 1.15262e10i −0.515861 0.893498i
775775 −1.71358e9 + 2.96801e9i −0.132236 + 0.229039i
776776 −1.04027e8 −0.00799149
777777 1.97549e8 3.55182e9i 0.0151078 0.271630i
778778 −1.01668e10 −0.774026
779779 −1.42903e10 + 2.47515e10i −1.08308 + 1.87594i
780780 5.43136e9 + 9.40739e9i 0.409805 + 0.709803i
781781 −7.75494e9 1.34319e10i −0.582505 1.00893i
782782 −5.33482e9 9.24018e9i −0.398930 0.690967i
783783 −1.47961e7 −0.00110149
784784 1.62418e9 + 2.81317e9i 0.120373 + 0.208492i
785785 −1.57341e9 −0.116091
786786 2.82387e9 4.89109e9i 0.207427 0.359274i
787787 1.03415e10 0.756263 0.378131 0.925752i 0.376567π-0.376567\pi
0.378131 + 0.925752i 0.376567π0.376567\pi
788788 −8.79515e9 −0.640326
789789 2.79377e9 4.83895e9i 0.202498 0.350737i
790790 1.24425e9 + 2.15510e9i 0.0897867 + 0.155515i
791791 3.17534e9 0.228125
792792 3.17942e9 5.50691e9i 0.227410 0.393885i
793793 1.54148e10 2.66992e10i 1.09769 1.90126i
794794 3.80977e9 6.59872e9i 0.270102 0.467830i
795795 4.44947e9 + 7.70670e9i 0.314068 + 0.543981i
796796 2.63629e9 + 4.56618e9i 0.185267 + 0.320891i
797797 −7.23480e9 + 1.25310e10i −0.506201 + 0.876765i 0.493774 + 0.869590i 0.335617π0.335617\pi
−0.999974 + 0.00717472i 0.997716π0.997716\pi
798798 −2.70236e9 + 4.68062e9i −0.188249 + 0.326057i
799799 4.29739e9 7.44331e9i 0.298052 0.516241i
800800 −1.17370e9 −0.0810482
801801 1.20372e9 + 2.08490e9i 0.0827582 + 0.143341i
802802 2.91782e9 5.05381e9i 0.199732 0.345946i
803803 −2.42687e10 −1.65402
804804 9.56573e9 0.649115
805805 −1.17967e9 + 2.04324e9i −0.0797028 + 0.138049i
806806 −9.55202e9 −0.642573
807807 −7.06521e9 1.22373e10i −0.473225 0.819649i
808808 3.68375e9 0.245669
809809 −8.54214e9 1.47954e10i −0.567214 0.982443i −0.996840 0.0794360i 0.974688π-0.974688\pi
0.429626 0.903007i 0.358645π-0.358645\pi
810810 −3.93741e9 6.81980e9i −0.260324 0.450894i
811811 6.49416e9 + 1.12482e10i 0.427514 + 0.740476i 0.996652 0.0817667i 0.0260562π-0.0260562\pi
−0.569138 + 0.822242i 0.692723π0.692723\pi
812812 9.90452e8 1.71551e9i 0.0649213 0.112447i
813813 2.25582e10 1.47227
814814 7.77781e8 1.39841e10i 0.0505443 0.908760i
815815 1.21565e10 0.786604
816816 −2.74929e9 + 4.76191e9i −0.177135 + 0.306807i
817817 2.22692e10 + 3.85714e10i 1.42866 + 2.47450i
818818 4.39790e9 + 7.61738e9i 0.280937 + 0.486597i
819819 2.38115e9 + 4.12427e9i 0.151458 + 0.262333i
820820 6.42965e9 0.407229
821821 −7.95300e9 1.37750e10i −0.501568 0.868741i −0.999998 0.00181136i 0.999423π-0.999423\pi
0.498430 0.866930i 0.333910π-0.333910\pi
822822 −1.31575e10 −0.826271
823823 1.19682e10 2.07296e10i 0.748395 1.29626i −0.200197 0.979756i 0.564158π-0.564158\pi
0.948592 0.316503i 0.102509π-0.102509\pi
824824 −7.60976e9 −0.473833
825825 1.34584e10 0.834460
826826 1.27179e8 2.20281e8i 0.00785210 0.0136002i
827827 −2.37341e9 4.11087e9i −0.145916 0.252735i 0.783798 0.621016i 0.213280π-0.213280\pi
−0.929714 + 0.368281i 0.879946π0.879946\pi
828828 9.19019e9 0.562624
829829 −1.15292e10 + 1.99691e10i −0.702840 + 1.21736i 0.264625 + 0.964351i 0.414752π0.414752\pi
−0.967465 + 0.253004i 0.918581π0.918581\pi
830830 5.18566e9 8.98182e9i 0.314797 0.545244i
831831 1.65451e9 2.86569e9i 0.100015 0.173231i
832832 −1.63564e9 2.83302e9i −0.0984593 0.170537i
833833 8.04987e9 + 1.39428e10i 0.482538 + 0.835780i
834834 −1.04904e10 + 1.81700e10i −0.626199 + 1.08461i
835835 6.52937e8 1.13092e9i 0.0388123 0.0672248i
836836 −1.06396e10 + 1.84283e10i −0.629801 + 1.09085i
837837 7.98600e6 0.000470750
838838 4.02389e8 + 6.96958e8i 0.0236207 + 0.0409122i
839839 3.10277e9 5.37416e9i 0.181377 0.314155i −0.760972 0.648784i 0.775278π-0.775278\pi
0.942350 + 0.334629i 0.108611π0.108611\pi
840840 1.21588e9 0.0707802
841841 1.41760e10 0.821805
842842 1.00328e9 1.73773e9i 0.0579202 0.100321i
843843 2.52133e10 1.44955
844844 6.25699e9 + 1.08374e10i 0.358234 + 0.620480i
845845 −1.91238e10 −1.09038
846846 3.70152e9 + 6.41121e9i 0.210176 + 0.364036i
847847 1.11735e9 + 1.93531e9i 0.0631827 + 0.109436i
848848 −1.33995e9 2.32086e9i −0.0754575 0.130696i
849849 7.74935e9 1.34223e10i 0.434598 0.752747i
850850 −5.81717e9 −0.324897
851851 1.80650e10 9.13186e9i 1.00481 0.507932i
852852 −1.15520e10 −0.639907
853853 −9.63221e9 + 1.66835e10i −0.531379 + 0.920375i 0.467950 + 0.883755i 0.344993π0.344993\pi
−0.999329 + 0.0366204i 0.988341π0.988341\pi
854854 −1.72539e9 2.98847e9i −0.0947950 0.164190i
855855 −1.31534e10 2.27823e10i −0.719708 1.24657i
856856 6.41942e9 + 1.11188e10i 0.349814 + 0.605896i
857857 −5.42608e9 −0.294479 −0.147239 0.989101i 0.547039π-0.547039\pi
−0.147239 + 0.989101i 0.547039π0.547039\pi
858858 1.87553e10 + 3.24852e10i 1.01372 + 1.75582i
859859 −4.57327e9 −0.246179 −0.123089 0.992396i 0.539280π-0.539280\pi
−0.123089 + 0.992396i 0.539280π0.539280\pi
860860 5.00981e9 8.67725e9i 0.268582 0.465198i
861861 5.63924e9 0.301099
862862 −8.32225e9 −0.442553
863863 2.71067e9 4.69503e9i 0.143562 0.248657i −0.785274 0.619149i 0.787478π-0.787478\pi
0.928836 + 0.370492i 0.120811π0.120811\pi
864864 1.36749e6 + 2.36856e6i 7.21315e−5 + 0.000124935i
865865 −3.03527e9 −0.159456
866866 −1.11573e10 + 1.93250e10i −0.583776 + 1.01113i
867867 −5.90115e7 + 1.02211e8i −0.00307518 + 0.00532636i
868868 −5.34584e8 + 9.25926e8i −0.0277458 + 0.0480571i
869869 4.29658e9 + 7.44189e9i 0.222103 + 0.384693i
870870 9.64459e9 + 1.67049e10i 0.496554 + 0.860056i
871871 −1.41030e10 + 2.44270e10i −0.723180 + 1.25258i
872872 −8.39155e7 + 1.45346e8i −0.00428582 + 0.00742327i
873873 2.22046e8 3.84594e8i 0.0112952 0.0195638i
874874 −3.07541e10 −1.55816
875875 2.04598e9 + 3.54375e9i 0.103246 + 0.178828i
876876 −9.03782e9 + 1.56540e10i −0.454254 + 0.786792i
877877 2.34576e10 1.17431 0.587157 0.809473i 0.300247π-0.300247\pi
0.587157 + 0.809473i 0.300247π0.300247\pi
878878 1.58279e10 0.789212
879879 1.66813e10 2.88929e10i 0.828455 1.43493i
880880 4.78710e9 0.236801
881881 −6.52963e9 1.13096e10i −0.321716 0.557228i 0.659126 0.752032i 0.270926π-0.270926\pi
−0.980842 + 0.194804i 0.937593π0.937593\pi
882882 −1.38673e10 −0.680539
883883 4.44035e9 + 7.69091e9i 0.217048 + 0.375937i 0.953904 0.300112i 0.0970240π-0.0970240\pi
−0.736857 + 0.676049i 0.763691π0.763691\pi
884884 −8.10667e9 1.40412e10i −0.394693 0.683628i
885885 1.23842e9 + 2.14500e9i 0.0600572 + 0.104022i
886886 1.45406e8 2.51850e8i 0.00702366 0.0121653i
887887 −3.97795e9 −0.191393 −0.0956966 0.995411i 0.530508π-0.530508\pi
−0.0956966 + 0.995411i 0.530508π0.530508\pi
888888 −8.73048e9 5.70946e9i −0.418401 0.273621i
889889 −2.27895e9 −0.108788
890890 −9.06191e8 + 1.56957e9i −0.0430878 + 0.0746303i
891891 −1.35965e10 2.35498e10i −0.643955 1.11536i
892892 −4.57424e9 7.92281e9i −0.215795 0.373768i
893893 −1.23868e10 2.14545e10i −0.582074 1.00818i
894894 −1.00995e10 −0.472738
895895 7.13682e9 + 1.23613e10i 0.332755 + 0.576348i
896896 −3.66159e8 −0.0170056
897897 −2.71064e10 + 4.69496e10i −1.25400 + 2.17199i
898898 −2.29089e9 −0.105569
899899 −1.69617e10 −0.778595
900900 2.50528e9 4.33927e9i 0.114553 0.198412i
901901 −6.64113e9 1.15028e10i −0.302486 0.523921i
902902 2.22026e10 1.00735
903903 4.39394e9 7.61053e9i 0.198585 0.343960i
904904 4.65576e9 8.06402e9i 0.209605 0.363046i
905905 −1.05668e10 + 1.83022e10i −0.473883 + 0.820790i
906906 −2.36041e9 4.08834e9i −0.105448 0.182641i
907907 3.17776e9 + 5.50404e9i 0.141415 + 0.244938i 0.928030 0.372506i 0.121501π-0.121501\pi
−0.786615 + 0.617444i 0.788168π0.788168\pi
908908 6.38855e9 1.10653e10i 0.283205 0.490526i
909909 −7.86299e9 + 1.36191e10i −0.347228 + 0.601416i
910910 −1.79259e9 + 3.10486e9i −0.0788563 + 0.136583i
911911 1.98980e10 0.871956 0.435978 0.899957i 0.356403π-0.356403\pi
0.435978 + 0.899957i 0.356403π0.356403\pi
912912 7.92452e9 + 1.37257e10i 0.345932 + 0.599172i
913913 1.79069e10 3.10156e10i 0.778704 1.34875i
914914 −6.54987e9 −0.283740
915915 3.36023e10 1.45009
916916 −7.39024e9 + 1.28003e10i −0.317705 + 0.550282i
917917 1.86401e9 0.0798279
918918 6.77761e6 + 1.17392e7i 0.000289153 + 0.000500827i
919919 3.28479e10 1.39606 0.698030 0.716069i 0.254060π-0.254060\pi
0.698030 + 0.716069i 0.254060π0.254060\pi
920920 3.45931e9 + 5.99170e9i 0.146464 + 0.253684i
921921 6.29222e9 + 1.08984e10i 0.265396 + 0.459680i
922922 −2.81322e8 4.87264e8i −0.0118208 0.0204742i
923923 1.70313e10 2.94991e10i 0.712921 1.23482i
924924 4.19861e9 0.175087
925925 6.12868e8 1.10190e10i 0.0254607 0.457770i
926926 7.66456e9 0.317211
927927 1.62431e10 2.81339e10i 0.669715 1.15998i
928928 −2.90445e9 5.03065e9i −0.119302 0.206636i
929929 −7.58708e8 1.31412e9i −0.0310470 0.0537750i 0.850084 0.526646i 0.176551π-0.176551\pi
−0.881131 + 0.472871i 0.843217π0.843217\pi
930930 −5.20555e9 9.01627e9i −0.212215 0.367567i
931931 4.64057e10 1.88472
932932 −7.27106e9 1.25938e10i −0.294199 0.509568i
933933 −3.99905e10 −1.61202
934934 4.48993e9 7.77678e9i 0.180312 0.312310i
935935 2.37261e10 0.949260
936936 1.39652e10 0.556649
937937 −1.48859e10 + 2.57831e10i −0.591133 + 1.02387i 0.402947 + 0.915223i 0.367986π0.367986\pi
−0.994080 + 0.108650i 0.965347π0.965347\pi
938938 1.57856e9 + 2.73414e9i 0.0624527 + 0.108171i
939939 −3.14195e9 −0.123842
940940 −2.78660e9 + 4.82653e9i −0.109428 + 0.189534i
941941 2.21399e9 3.83474e9i 0.0866187 0.150028i −0.819461 0.573135i 0.805727π-0.805727\pi
0.906080 + 0.423107i 0.139060π0.139060\pi
942942 −2.02336e9 + 3.50457e9i −0.0788671 + 0.136602i
943943 1.60443e10 + 2.77895e10i 0.623060 + 1.07917i
944944 −3.72946e8 6.45962e8i −0.0144293 0.0249922i
945945 1.49870e6 2.59583e6i 5.77703e−5 0.000100061i
946946 1.72997e10 2.99639e10i 0.664383 1.15075i
947947 −1.18430e8 + 2.05127e8i −0.00453146 + 0.00784871i −0.868282 0.496071i 0.834776π-0.834776\pi
0.863751 + 0.503919i 0.168109π0.168109\pi
948948 6.40030e9 0.243989
949949 −2.66493e10 4.61579e10i −1.01217 1.75313i
950950 −8.38368e9 + 1.45210e10i −0.317250 + 0.549494i
951951 −7.26977e10 −2.74087
952952 −1.81478e9 −0.0681701
953953 1.67505e9 2.90127e9i 0.0626906 0.108583i −0.832977 0.553308i 0.813365π-0.813365\pi
0.895667 + 0.444725i 0.146699π0.146699\pi
954954 1.14405e10 0.426606
955955 −1.46008e10 2.52893e10i −0.542457 0.939563i
956956 −2.10260e8 −0.00778311
957957 3.33043e10 + 5.76847e10i 1.22831 + 2.12750i
958958 −1.00320e10 1.73760e10i −0.368646 0.638514i
959959 −2.17128e9 3.76078e9i −0.0794972 0.137693i
960960 1.78275e9 3.08781e9i 0.0650340 0.112642i
961961 −1.83577e10 −0.667248
962962 2.74512e10 1.38765e10i 0.994142 0.502538i
963963 −5.48093e10 −1.97771
964964 1.05473e10 1.82684e10i 0.379202 0.656798i
965965 −1.07538e10 1.86261e10i −0.385226 0.667230i
966966 3.03405e9 + 5.25513e9i 0.108294 + 0.187570i
967967 −2.05488e10 3.55915e10i −0.730790 1.26577i −0.956546 0.291582i 0.905818π-0.905818\pi
0.225755 0.974184i 0.427515π-0.427515\pi
968968 6.55316e9 0.232213
969969 3.92760e10 + 6.80280e10i 1.38674 + 2.40190i
970970 3.34324e8 0.0117616
971971 −2.07609e10 + 3.59590e10i −0.727745 + 1.26049i 0.230089 + 0.973170i 0.426098π0.426098\pi
−0.957834 + 0.287322i 0.907235π0.907235\pi
972972 −2.02420e10 −0.707005
973973 −6.92463e9 −0.240991
974974 7.40069e9 1.28184e10i 0.256635 0.444505i
975975 1.47786e10 + 2.55973e10i 0.510643 + 0.884460i
976976 −1.01193e10 −0.348397
977977 2.79759e10 4.84557e10i 0.959739 1.66232i 0.236609 0.971605i 0.423964π-0.423964\pi
0.723130 0.690712i 0.242703π-0.242703\pi
978978 1.56330e10 2.70771e10i 0.534386 0.925584i
979979 −3.12922e9 + 5.41997e9i −0.106585 + 0.184611i
980980 −5.21985e9 9.04105e9i −0.177161 0.306851i
981981 −3.58237e8 6.20484e8i −0.0121151 0.0209840i
982982 −5.79535e9 + 1.00378e10i −0.195294 + 0.338259i
983983 −2.41878e10 + 4.18945e10i −0.812194 + 1.40676i 0.0991319 + 0.995074i 0.468393π0.468393\pi
−0.911326 + 0.411686i 0.864940π0.864940\pi
984984 8.26839e9 1.43213e10i 0.276655 0.479180i
985985 2.82661e10 0.942409
986986 −1.43952e10 2.49332e10i −0.478243 0.828341i
987987 −2.44404e9 + 4.23320e9i −0.0809092 + 0.140139i
988988 −4.67331e10 −1.54161
989989 5.00051e10 1.64372
990990 −1.02181e10 + 1.76983e10i −0.334693 + 0.579706i
991991 −3.30034e9 −0.107721 −0.0538606 0.998548i 0.517153π-0.517153\pi
−0.0538606 + 0.998548i 0.517153π0.517153\pi
992992 1.56764e9 + 2.71523e9i 0.0509865 + 0.0883113i
993993 7.95006e9 0.257661
994994 −1.90633e9 3.30186e9i −0.0615667 0.106637i
995995 −8.47259e9 1.46749e10i −0.272669 0.472276i
996996 −1.33373e10 2.31009e10i −0.427720 0.740833i
997997 1.15607e10 2.00238e10i 0.369447 0.639901i −0.620032 0.784576i 0.712880π-0.712880\pi
0.989479 + 0.144675i 0.0462138π0.0462138\pi
998998 2.98501e10 0.950581
999999 −2.29507e7 + 1.16015e7i −0.000728310 + 0.000368160i
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 74.8.c.a.47.2 22
37.26 even 3 inner 74.8.c.a.63.2 yes 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.8.c.a.47.2 22 1.1 even 1 trivial
74.8.c.a.63.2 yes 22 37.26 even 3 inner