Properties

Label 59.7.d.a.10.7
Level 5959
Weight 77
Character 59.10
Analytic conductor 13.57313.573
Analytic rank 00
Dimension 812812
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [59,7,Mod(2,59)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(59, base_ring=CyclotomicField(58))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("59.2");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: N N == 59 59
Weight: k k == 7 7
Character orbit: [χ][\chi] == 59.d (of order 5858, degree 2828, 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: 13.573190933613.5731909336
Analytic rank: 00
Dimension: 812812
Relative dimension: 2929 over Q(ζ58)\Q(\zeta_{58})
Twist minimal: yes
Sato-Tate group: SU(2)[C58]\mathrm{SU}(2)[C_{58}]

Embedding invariants

Embedding label 10.7
Character χ\chi == 59.10
Dual form 59.7.d.a.6.7

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+(9.459703.76909i)q2+(5.39355+0.586583i)q3+(28.8162+27.2961i)q4+(148.963175.372i)q5+(48.810425.8777i)q6+(211.535+127.276i)q7+(103.934+224.649i)q8+(683.210150.386i)q9+(2070.14+1097.52i)q10+(2335.97+126.653i)q11+(139.410+164.126i)q12+(747.510+3395.97i)q13+(1521.342001.29i)q14+(906.308858.500i)q15+(273.9885053.41i)q16+(2007.561207.91i)q17+(5896.15+3997.69i)q18+(368.836+1328.43i)q19+(9079.53987.458i)q20+(1066.26+810.553i)q21+(21620.310002.6i)q22+(8643.175860.21i)q23+(428.796+1272.62i)q24+(6037.7736828.7i)q25+(5728.5034942.3i)q26+(7344.762474.74i)q27+(2621.48+9441.70i)q28+(3408.688555.15i)q29+(11809.2+4705.20i)q30+(29379.38157.12i)q31+(11396.6+33824.0i)q32+(12524.9+2053.35i)q33+(23543.7+3859.79i)q34+(53831.618138.0i)q35+(15582.622982.6i)q36+(6881.05+14873.1i)q37+(8496.0511176.4i)q38+(2039.71+18754.8i)q39+(54879.6+15237.2i)q40+(38748.057149.1i)q41+(7031.5011686.4i)q42+(9193.41498.452i)q43+(63856.7+67412.8i)q44+(128146.+97414.3i)q45+(103849.+22859.0i)q46+(109955.+93396.6i)q47+(1486.4827416.5i)q48+(26560.150097.6i)q49+(81695.4+371146.i)q50+(11536.45337.32i)q51+(71156.5+118263.i)q52+(58453.6+110255.i)q53+(60151.7+51093.3i)q54+(370184.390799.i)q55+(6606.90+60749.5i)q56+(2768.57+6948.59i)q57+93776.8iq58+(166722.119934.i)q59+49550.1q60+(232192.92513.7i)q61+(308664.33569.3i)q62+(125382.118768.i)q63+(25610.230150.7i)q64+(706911.+374780.i)q65+(110742.66631.5i)q66+(71156.1153801.i)q67+(90821.7+19991.4i)q68+(50054.826537.4i)q69+(577594.31316.2i)q70+(227058.267313.i)q71+(37224.6169113.i)q72+(176777.+232546.i)q73+(121151.114760.i)q74+(10961.8202179.i)q75+(46889.4+28212.4i)q76+(478020.+324106.i)q77+(51393.5185103.i)q78+(226702.24655.4i)q79+(927043.704720.i)q80+(424686.+196481.i)q81+(581945.+394568.i)q82+(65354.9193966.i)q83+(8600.70+52462.0i)q84+(87217.8532005.i)q85+(88845.729935.6i)q86+(13366.648142.1i)q87+(214334.+537939.i)q88+(1.02924e6+410086.i)q89+(1.57939e6438515.i)q90+(274102.+813506.i)q91+(409024.+67056.1i)q92+(163243.26762.4i)q93+(1.39216e6469074.i)q94+(178027.+262570.i)q95+(81308.8+175746.i)q96+(1.03603e61.36287e6i)q97+(62427.9+574015.i)q98+(1.57691e6437828.i)q99+O(q100)q+(-9.45970 - 3.76909i) q^{2} +(5.39355 + 0.586583i) q^{3} +(28.8162 + 27.2961i) q^{4} +(148.963 - 175.372i) q^{5} +(-48.8104 - 25.8777i) q^{6} +(211.535 + 127.276i) q^{7} +(103.934 + 224.649i) q^{8} +(-683.210 - 150.386i) q^{9} +(-2070.14 + 1097.52i) q^{10} +(2335.97 + 126.653i) q^{11} +(139.410 + 164.126i) q^{12} +(747.510 + 3395.97i) q^{13} +(-1521.34 - 2001.29i) q^{14} +(906.308 - 858.500i) q^{15} +(-273.988 - 5053.41i) q^{16} +(2007.56 - 1207.91i) q^{17} +(5896.15 + 3997.69i) q^{18} +(-368.836 + 1328.43i) q^{19} +(9079.53 - 987.458i) q^{20} +(1066.26 + 810.553i) q^{21} +(-21620.3 - 10002.6i) q^{22} +(8643.17 - 5860.21i) q^{23} +(428.796 + 1272.62i) q^{24} +(-6037.77 - 36828.7i) q^{25} +(5728.50 - 34942.3i) q^{26} +(-7344.76 - 2474.74i) q^{27} +(2621.48 + 9441.70i) q^{28} +(-3408.68 - 8555.15i) q^{29} +(-11809.2 + 4705.20i) q^{30} +(29379.3 - 8157.12i) q^{31} +(-11396.6 + 33824.0i) q^{32} +(12524.9 + 2053.35i) q^{33} +(-23543.7 + 3859.79i) q^{34} +(53831.6 - 18138.0i) q^{35} +(-15582.6 - 22982.6i) q^{36} +(-6881.05 + 14873.1i) q^{37} +(8496.05 - 11176.4i) q^{38} +(2039.71 + 18754.8i) q^{39} +(54879.6 + 15237.2i) q^{40} +(38748.0 - 57149.1i) q^{41} +(-7031.50 - 11686.4i) q^{42} +(9193.41 - 498.452i) q^{43} +(63856.7 + 67412.8i) q^{44} +(-128146. + 97414.3i) q^{45} +(-103849. + 22859.0i) q^{46} +(-109955. + 93396.6i) q^{47} +(1486.48 - 27416.5i) q^{48} +(-26560.1 - 50097.6i) q^{49} +(-81695.4 + 371146. i) q^{50} +(11536.4 - 5337.32i) q^{51} +(-71156.5 + 118263. i) q^{52} +(-58453.6 + 110255. i) q^{53} +(60151.7 + 51093.3i) q^{54} +(370184. - 390799. i) q^{55} +(-6606.90 + 60749.5i) q^{56} +(-2768.57 + 6948.59i) q^{57} +93776.8i q^{58} +(166722. - 119934. i) q^{59} +49550.1 q^{60} +(-232192. - 92513.7i) q^{61} +(-308664. - 33569.3i) q^{62} +(-125382. - 118768. i) q^{63} +(25610.2 - 30150.7i) q^{64} +(706911. + 374780. i) q^{65} +(-110742. - 66631.5i) q^{66} +(-71156.1 - 153801. i) q^{67} +(90821.7 + 19991.4i) q^{68} +(50054.8 - 26537.4i) q^{69} +(-577594. - 31316.2i) q^{70} +(-227058. - 267313. i) q^{71} +(-37224.6 - 169113. i) q^{72} +(176777. + 232546. i) q^{73} +(121151. - 114760. i) q^{74} +(-10961.8 - 202179. i) q^{75} +(-46889.4 + 28212.4i) q^{76} +(478020. + 324106. i) q^{77} +(51393.5 - 185103. i) q^{78} +(226702. - 24655.4i) q^{79} +(-927043. - 704720. i) q^{80} +(424686. + 196481. i) q^{81} +(-581945. + 394568. i) q^{82} +(-65354.9 - 193966. i) q^{83} +(8600.70 + 52462.0i) q^{84} +(87217.8 - 532005. i) q^{85} +(-88845.7 - 29935.6i) q^{86} +(-13366.6 - 48142.1i) q^{87} +(214334. + 537939. i) q^{88} +(-1.02924e6 + 410086. i) q^{89} +(1.57939e6 - 438515. i) q^{90} +(-274102. + 813506. i) q^{91} +(409024. + 67056.1i) q^{92} +(163243. - 26762.4i) q^{93} +(1.39216e6 - 469074. i) q^{94} +(178027. + 262570. i) q^{95} +(-81308.8 + 175746. i) q^{96} +(1.03603e6 - 1.36287e6i) q^{97} +(62427.9 + 574015. i) q^{98} +(-1.57691e6 - 437828. i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 812q29q239q3+869q4171q529q6435q729q87648q929q1029q11+1095q1229q1329q14569q1525051q169071q17++9513421q99+O(q100) 812 q - 29 q^{2} - 39 q^{3} + 869 q^{4} - 171 q^{5} - 29 q^{6} - 435 q^{7} - 29 q^{8} - 7648 q^{9} - 29 q^{10} - 29 q^{11} + 1095 q^{12} - 29 q^{13} - 29 q^{14} - 569 q^{15} - 25051 q^{16} - 9071 q^{17}+ \cdots + 9513421 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/59Z)×\left(\mathbb{Z}/59\mathbb{Z}\right)^\times.

nn 22
χ(n)\chi(n) e(758)e\left(\frac{7}{58}\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 −9.45970 3.76909i −1.18246 0.471136i −0.305732 0.952118i 0.598901π-0.598901\pi
−0.876731 + 0.480982i 0.840280π0.840280\pi
33 5.39355 + 0.586583i 0.199761 + 0.0217253i 0.207452 0.978245i 0.433483π-0.433483\pi
−0.00769147 + 0.999970i 0.502448π0.502448\pi
44 28.8162 + 27.2961i 0.450253 + 0.426502i
55 148.963 175.372i 1.19170 1.40298i 0.297852 0.954612i 0.403730π-0.403730\pi
0.893849 0.448368i 0.147994π-0.147994\pi
66 −48.8104 25.8777i −0.225974 0.119804i
77 211.535 + 127.276i 0.616720 + 0.371068i 0.789372 0.613915i 0.210406π-0.210406\pi
−0.172653 + 0.984983i 0.555234π0.555234\pi
88 103.934 + 224.649i 0.202996 + 0.438768i
99 −683.210 150.386i −0.937188 0.206291i
1010 −2070.14 + 1097.52i −2.07014 + 1.09752i
1111 2335.97 + 126.653i 1.75505 + 0.0951562i 0.903359 0.428885i 0.141093π-0.141093\pi
0.851693 + 0.524041i 0.175576π0.175576\pi
1212 139.410 + 164.126i 0.0806771 + 0.0949804i
1313 747.510 + 3395.97i 0.340241 + 1.54573i 0.767169 + 0.641445i 0.221665π0.221665\pi
−0.426928 + 0.904286i 0.640404π0.640404\pi
1414 −1521.34 2001.29i −0.554424 0.729333i
1515 906.308 858.500i 0.268536 0.254370i
1616 −273.988 5053.41i −0.0668916 1.23374i
1717 2007.56 1207.91i 0.408623 0.245860i −0.296372 0.955073i 0.595777π-0.595777\pi
0.704995 + 0.709212i 0.250949π0.250949\pi
1818 5896.15 + 3997.69i 1.01100 + 0.685474i
1919 −368.836 + 1328.43i −0.0537741 + 0.193677i −0.985558 0.169335i 0.945838π-0.945838\pi
0.931784 + 0.363012i 0.118252π0.118252\pi
2020 9079.53 987.458i 1.13494 0.123432i
2121 1066.26 + 810.553i 0.115135 + 0.0875233i
2222 −21620.3 10002.6i −2.03045 0.939387i
2323 8643.17 5860.21i 0.710378 0.481648i −0.151698 0.988427i 0.548474π-0.548474\pi
0.862076 + 0.506779i 0.169164π0.169164\pi
2424 428.796 + 1272.62i 0.0310183 + 0.0920589i
2525 −6037.77 36828.7i −0.386417 2.35704i
2626 5728.50 34942.3i 0.325927 1.98807i
2727 −7344.76 2474.74i −0.373152 0.125730i
2828 2621.48 + 9441.70i 0.119419 + 0.430107i
2929 −3408.68 8555.15i −0.139763 0.350779i 0.842388 0.538871i 0.181149π-0.181149\pi
−0.982151 + 0.188092i 0.939770π0.939770\pi
3030 −11809.2 + 4705.20i −0.437376 + 0.174267i
3131 29379.3 8157.12i 0.986180 0.273812i 0.263246 0.964729i 0.415207π-0.415207\pi
0.722934 + 0.690917i 0.242793π0.242793\pi
3232 −11396.6 + 33824.0i −0.347798 + 1.03223i
3333 12524.9 + 2053.35i 0.348524 + 0.0571375i
3434 −23543.7 + 3859.79i −0.599015 + 0.0982035i
3535 53831.6 18138.0i 1.25555 0.423043i
3636 −15582.6 22982.6i −0.333988 0.492596i
3737 −6881.05 + 14873.1i −0.135847 + 0.293628i −0.963545 0.267545i 0.913788π-0.913788\pi
0.827699 + 0.561173i 0.189650π0.189650\pi
3838 8496.05 11176.4i 0.154834 0.203681i
3939 2039.71 + 18754.8i 0.0343854 + 0.316169i
4040 54879.6 + 15237.2i 0.857493 + 0.238082i
4141 38748.0 57149.1i 0.562210 0.829197i −0.435259 0.900305i 0.643343π-0.643343\pi
0.997469 + 0.0711082i 0.0226536π0.0226536\pi
4242 −7031.50 11686.4i −0.0949074 0.157737i
4343 9193.41 498.452i 0.115630 0.00626929i 0.00376704 0.999993i 0.498801π-0.498801\pi
0.111863 + 0.993724i 0.464318π0.464318\pi
4444 63856.7 + 67412.8i 0.749633 + 0.791378i
4545 −128146. + 97414.3i −1.40627 + 1.06902i
4646 −103849. + 22859.0i −1.06692 + 0.234846i
4747 −109955. + 93396.6i −1.05906 + 0.899575i −0.995149 0.0983800i 0.968634π-0.968634\pi
−0.0639132 + 0.997955i 0.520358π0.520358\pi
4848 1486.48 27416.5i 0.0134411 0.247907i
4949 −26560.1 50097.6i −0.225757 0.425822i
5050 −81695.4 + 371146.i −0.653563 + 2.96917i
5151 11536.4 5337.32i 0.0869683 0.0402358i
5252 −71156.5 + 118263.i −0.506063 + 0.841084i
5353 −58453.6 + 110255.i −0.392630 + 0.740579i −0.998487 0.0549947i 0.982486π-0.982486\pi
0.605856 + 0.795574i 0.292831π0.292831\pi
5454 60151.7 + 51093.3i 0.382003 + 0.324476i
5555 370184. 390799.i 2.22500 2.34890i
5656 −6606.90 + 60749.5i −0.0376213 + 0.345922i
5757 −2768.57 + 6948.59i −0.0149497 + 0.0375208i
5858 93776.8i 0.480631i
5959 166722. 119934.i 0.811778 0.583966i
6060 49550.1 0.229399
6161 −232192. 92513.7i −1.02296 0.407583i −0.202495 0.979283i 0.564905π-0.564905\pi
−0.820463 + 0.571700i 0.806284π0.806284\pi
6262 −308664. 33569.3i −1.29512 0.140853i
6363 −125382. 118768.i −0.501434 0.474984i
6464 25610.2 30150.7i 0.0976952 0.115016i
6565 706911. + 374780.i 2.57410 + 1.36470i
6666 −110742. 66631.5i −0.385197 0.231765i
6767 −71156.1 153801.i −0.236585 0.511370i 0.752522 0.658567i 0.228837π-0.228837\pi
−0.989107 + 0.147197i 0.952975π0.952975\pi
6868 90821.7 + 19991.4i 0.288844 + 0.0635793i
6969 50054.8 26537.4i 0.152370 0.0807813i
7070 −577594. 31316.2i −1.68395 0.0913010i
7171 −227058. 267313.i −0.634398 0.746871i 0.347208 0.937788i 0.387130π-0.387130\pi
−0.981606 + 0.190917i 0.938854π0.938854\pi
7272 −37224.6 169113.i −0.0997314 0.453084i
7373 176777. + 232546.i 0.454420 + 0.597779i 0.965064 0.262013i 0.0843862π-0.0843862\pi
−0.510644 + 0.859792i 0.670593π0.670593\pi
7474 121151. 114760.i 0.298972 0.283202i
7575 −10961.8 202179.i −0.0259836 0.479240i
7676 −46889.4 + 28212.4i −0.106816 + 0.0642688i
7777 478020. + 324106.i 1.04707 + 0.709928i
7878 51393.5 185103.i 0.108299 0.390058i
7979 226702. 24655.4i 0.459806 0.0500069i 0.124715 0.992193i 0.460198π-0.460198\pi
0.335091 + 0.942186i 0.391233π0.391233\pi
8080 −927043. 704720.i −1.81063 1.37641i
8181 424686. + 196481.i 0.799121 + 0.369713i
8282 −581945. + 394568.i −1.05546 + 0.715617i
8383 −65354.9 193966.i −0.114299 0.339228i 0.875201 0.483760i 0.160729π-0.160729\pi
−0.989500 + 0.144531i 0.953833π0.953833\pi
8484 8600.70 + 52462.0i 0.0145110 + 0.0885129i
8585 87217.8 532005.i 0.142020 0.866281i
8686 −88845.7 29935.6i −0.139682 0.0470644i
8787 −13366.6 48142.1i −0.0202984 0.0731084i
8888 214334. + 537939.i 0.314517 + 0.789377i
8989 −1.02924e6 + 410086.i −1.45998 + 0.581708i −0.958912 0.283703i 0.908437π-0.908437\pi
−0.501064 + 0.865410i 0.667058π0.667058\pi
9090 1.57939e6 438515.i 2.16652 0.601530i
9191 −274102. + 813506.i −0.363738 + 1.07954i
9292 409024. + 67056.1i 0.525274 + 0.0861142i
9393 163243. 26762.4i 0.202949 0.0332718i
9494 1.39216e6 469074.i 1.67612 0.564752i
9595 178027. + 262570.i 0.207642 + 0.306249i
9696 −81308.8 + 175746.i −0.0919018 + 0.198642i
9797 1.03603e6 1.36287e6i 1.13516 1.49327i 0.291359 0.956614i 0.405892π-0.405892\pi
0.843798 0.536661i 0.180314π-0.180314\pi
9898 62427.9 + 574015.i 0.0663286 + 0.609881i
9999 −1.57691e6 437828.i −1.62518 0.451230i
100100 831297. 1.22607e6i 0.831297 1.22607i
101101 584527. + 971491.i 0.567336 + 0.942920i 0.999161 + 0.0409622i 0.0130423π0.0130423\pi
−0.431825 + 0.901958i 0.642130π0.642130\pi
102102 −129248. + 7007.62i −0.121793 + 0.00660344i
103103 −666331. 703437.i −0.609787 0.643744i 0.345850 0.938290i 0.387590π-0.387590\pi
−0.955638 + 0.294545i 0.904832π0.904832\pi
104104 −685211. + 520884.i −0.609150 + 0.463064i
105105 300982. 66251.2i 0.260000 0.0572303i
106106 968516. 822665.i 0.813184 0.690725i
107107 −19409.1 + 357980.i −0.0158436 + 0.292218i 0.979864 + 0.199665i 0.0639855π0.0639855\pi
−0.995708 + 0.0925530i 0.970497π0.970497\pi
108108 −144097. 271796.i −0.114389 0.215760i
109109 −441579. + 2.00611e6i −0.340980 + 1.54909i 0.424379 + 0.905485i 0.360492π0.360492\pi
−0.765359 + 0.643603i 0.777439π0.777439\pi
110110 −4.97479e6 + 2.30158e6i −3.73763 + 1.72921i
111111 −45837.6 + 76182.6i −0.0335160 + 0.0557041i
112112 585221. 1.10384e6i 0.416549 0.785695i
113113 64509.5 + 54794.9i 0.0447083 + 0.0379756i 0.669462 0.742846i 0.266525π-0.266525\pi
−0.624754 + 0.780822i 0.714801π0.714801\pi
114114 52379.7 55296.6i 0.0353548 0.0373236i
115115 259790. 2.38873e6i 0.170816 1.57063i
116116 135297. 339571.i 0.0866793 0.217549i
117117 2.43258e6i 1.51883i
118118 −2.02919e6 + 506151.i −1.23502 + 0.308059i
119119 578408. 0.343237
120120 287058. + 114374.i 0.166121 + 0.0661888i
121121 3.67956e6 + 400176.i 2.07702 + 0.225889i
122122 1.84777e6 + 1.75030e6i 1.01758 + 0.963904i
123123 242512. 285507.i 0.130322 0.153427i
124124 1.06926e6 + 566884.i 0.560812 + 0.297324i
125125 −4.27750e6 2.57369e6i −2.19008 1.31773i
126126 738429. + 1.59609e6i 0.369145 + 0.797895i
127127 2.50353e6 + 551068.i 1.22220 + 0.269026i 0.778785 0.627291i 0.215836π-0.215836\pi
0.443413 + 0.896317i 0.353768π0.353768\pi
128128 1.66231e6 881302.i 0.792652 0.420237i
129129 49877.5 + 2704.28i 0.0232346 + 0.00125974i
130130 −5.27458e6 6.20972e6i −2.40081 2.82645i
131131 525478. + 2.38727e6i 0.233744 + 1.06191i 0.936551 + 0.350530i 0.113999π0.113999\pi
−0.702807 + 0.711380i 0.748070π0.748070\pi
132132 304871. + 401051.i 0.132554 + 0.174372i
133133 −247099. + 234065.i −0.105031 + 0.0994904i
134134 93424.2 + 1.72311e6i 0.0388280 + 0.716140i
135135 −1.52810e6 + 919424.i −0.621082 + 0.373693i
136136 480010. + 325455.i 0.190824 + 0.129382i
137137 −627424. + 2.25978e6i −0.244005 + 0.878828i 0.735519 + 0.677504i 0.236938π0.236938\pi
−0.979525 + 0.201324i 0.935476π0.935476\pi
138138 −573525. + 62374.6i −0.218230 + 0.0237340i
139139 232756. + 176936.i 0.0866675 + 0.0658829i 0.647611 0.761971i 0.275768π-0.275768\pi
−0.560943 + 0.827854i 0.689561π0.689561\pi
140140 2.04632e6 + 946727.i 0.745742 + 0.345017i
141141 −647832. + 439241.i −0.231103 + 0.156692i
142142 1.14037e6 + 3.38451e6i 0.398274 + 1.18204i
143143 1.31605e6 + 8.02758e6i 0.450055 + 2.74521i
144144 −572771. + 3.49375e6i −0.191820 + 1.17005i
145145 −2.00810e6 676609.i −0.658692 0.221939i
146146 −795771. 2.86611e6i −0.255699 0.920946i
147147 −113866. 285783.i −0.0358463 0.0899673i
148148 −604265. + 240761.i −0.186398 + 0.0742679i
149149 1.41355e6 392471.i 0.427321 0.118645i −0.0472080 0.998885i 0.515032π-0.515032\pi
0.474529 + 0.880240i 0.342619π0.342619\pi
150150 −658336. + 1.95387e6i −0.195062 + 0.578925i
151151 −1.14944e6 188441.i −0.333853 0.0547325i −0.00747603 0.999972i 0.502380π-0.502380\pi
−0.326377 + 0.945240i 0.605828π0.605828\pi
152152 −336765. + 55209.9i −0.0958951 + 0.0157212i
153153 −1.55324e6 + 523348.i −0.433675 + 0.146122i
154154 −3.30034e6 4.86764e6i −0.903643 1.33277i
155155 2.94588e6 6.36743e6i 0.791080 1.70989i
156156 −453157. + 596118.i −0.119364 + 0.157021i
157157 −27097.5 249158.i −0.00700214 0.0643836i 0.990116 0.140254i 0.0447920π-0.0447920\pi
−0.997118 + 0.0758705i 0.975826π0.975826\pi
158158 −2.23746e6 621229.i −0.567263 0.157500i
159159 −379946. + 560379.i −0.0945215 + 0.139409i
160160 4.23412e6 + 7.03717e6i 1.03372 + 1.71806i
161161 2.57420e6 139569.i 0.616828 0.0334434i
162162 −3.27685e6 3.45933e6i −0.770746 0.813666i
163163 −930241. + 707151.i −0.214799 + 0.163286i −0.707041 0.707172i 0.749971π-0.749971\pi
0.492242 + 0.870458i 0.336177π0.336177\pi
164164 2.67652e6 589147.i 0.606791 0.133565i
165165 2.22584e6 1.89065e6i 0.495499 0.420881i
166166 −112839. + 2.08119e6i −0.0246680 + 0.454975i
167167 3.13331e6 + 5.91006e6i 0.672751 + 1.26894i 0.951225 + 0.308499i 0.0998268π0.0998268\pi
−0.278473 + 0.960444i 0.589828π0.589828\pi
168168 −71269.3 + 323780.i −0.0150305 + 0.0682844i
169169 −6.59316e6 + 3.05032e6i −1.36595 + 0.631953i
170170 −2.83023e6 + 4.70388e6i −0.576069 + 0.957435i
171171 451770. 852128.i 0.0903501 0.170418i
172172 278525. + 236581.i 0.0547367 + 0.0464938i
173173 6.26267e6 6.61142e6i 1.20954 1.27690i 0.259153 0.965836i 0.416557π-0.416557\pi
0.950390 0.311062i 0.100685π-0.100685\pi
174174 −55007.9 + 505789.i −0.0104419 + 0.0960112i
175175 3.41023e6 8.55903e6i 0.636311 1.59702i
176176 1.18393e7i 2.17165i
177177 969575. 549075.i 0.174848 0.0990174i
178178 1.12819e7 2.00043
179179 −4.03695e6 1.60847e6i −0.703873 0.280449i −0.00938793 0.999956i 0.502988π-0.502988\pi
−0.694485 + 0.719507i 0.744368π0.744368\pi
180180 −6.35173e6 690792.i −1.08912 0.118449i
181181 −981884. 930090.i −0.165586 0.156852i 0.600420 0.799685i 0.295000π-0.295000\pi
−0.766006 + 0.642833i 0.777759π0.777759\pi
182182 5.65910e6 6.66241e6i 0.938714 1.10514i
183183 −1.19807e6 635177.i −0.195492 0.103643i
184184 2.21481e6 + 1.33261e6i 0.355536 + 0.213919i
185185 1.58332e6 + 3.42229e6i 0.250065 + 0.540507i
186186 −1.64510e6 362115.i −0.255655 0.0562739i
187187 4.84260e6 2.56739e6i 0.740549 0.392614i
188188 −5.71785e6 310013.i −0.860517 0.0466559i
189189 −1.23870e6 1.45831e6i −0.183476 0.216005i
190190 −694431. 3.15483e6i −0.101244 0.459955i
191191 1.22540e6 + 1.61199e6i 0.175865 + 0.231347i 0.875577 0.483079i 0.160481π-0.160481\pi
−0.699712 + 0.714425i 0.746688π0.746688\pi
192192 155816. 147596.i 0.0220144 0.0208532i
193193 −189431. 3.49385e6i −0.0263499 0.485995i −0.981690 0.190486i 0.938994π-0.938994\pi
0.955340 0.295509i 0.0954892π-0.0954892\pi
194194 −1.49373e7 + 8.98747e6i −2.04582 + 1.23093i
195195 3.59292e6 + 2.43606e6i 0.484555 + 0.328537i
196196 602111. 2.16861e6i 0.0799666 0.288014i
197197 −6.24153e6 + 678807.i −0.816380 + 0.0887866i −0.506775 0.862079i 0.669162π-0.669162\pi
−0.309605 + 0.950865i 0.600197π0.600197\pi
198198 1.32669e7 + 1.00853e7i 1.70913 + 1.29925i
199199 −1.29818e7 6.00603e6i −1.64731 0.762129i −0.647315 0.762223i 0.724108π-0.724108\pi
−1.00000 9.41593e-5i 0.999970π0.999970\pi
200200 7.64602e6 5.18413e6i 0.955753 0.648017i
201201 −293566. 871273.i −0.0361508 0.107292i
202202 −1.86781e6 1.13932e7i −0.226610 1.38226i
203203 367813. 2.24356e6i 0.0439682 0.268194i
204204 478124. + 161099.i 0.0563184 + 0.0189759i
205205 −4.25036e6 1.53084e7i −0.493361 1.77692i
206206 3.65197e6 + 9.16576e6i 0.417759 + 1.04850i
207207 −6.78639e6 + 2.70395e6i −0.765117 + 0.304850i
208208 1.69564e7 4.70793e6i 1.88428 0.523167i
209209 −1.02984e6 + 3.05646e6i −0.112806 + 0.334796i
210210 −3.09691e6 507713.i −0.334403 0.0548227i
211211 −1.82835e7 + 2.99742e6i −1.94631 + 0.319081i −0.999991 0.00416867i 0.998673π-0.998673\pi
−0.946314 + 0.323249i 0.895225π0.895225\pi
212212 −4.69395e6 + 1.58158e6i −0.492642 + 0.165990i
213213 −1.06785e6 1.57496e6i −0.110502 0.162978i
214214 1.53286e6 3.31323e6i 0.156409 0.338073i
215215 1.28206e6 1.68652e6i 0.129001 0.169698i
216216 −207421. 1.90720e6i −0.0205822 0.189250i
217217 7.25295e6 + 2.01377e6i 0.709799 + 0.197075i
218218 1.17384e7 1.73129e7i 1.13303 1.67109i
219219 817048. + 1.35794e6i 0.0777885 + 0.129285i
220220 2.13346e7 1.15673e6i 2.00363 0.108633i
221221 5.60270e6 + 5.91470e6i 0.519064 + 0.547969i
222222 720749. 547899.i 0.0658757 0.0500774i
223223 5.44005e6 1.19745e6i 0.490556 0.107979i 0.0371975 0.999308i 0.488157π-0.488157\pi
0.453358 + 0.891328i 0.350226π0.350226\pi
224224 −6.71578e6 + 5.70443e6i −0.597520 + 0.507538i
225225 −1.41346e6 + 2.60698e7i −0.124090 + 2.28870i
226226 −403714. 761485.i −0.0349742 0.0659684i
227227 −3.07029e6 + 1.39485e7i −0.262484 + 1.19248i 0.642249 + 0.766496i 0.278002π0.278002\pi
−0.904733 + 0.425980i 0.859929π0.859929\pi
228228 −269449. + 124661.i −0.0227338 + 0.0105178i
229229 6.46613e6 1.07468e7i 0.538441 0.894895i −0.461529 0.887125i 0.652699π-0.652699\pi
0.999970 0.00777036i 0.00247341π-0.00247341\pi
230230 −1.14609e7 + 2.16175e7i −0.941962 + 1.77673i
231231 2.38811e6 + 2.02848e6i 0.193739 + 0.164564i
232232 1.56763e6 1.65493e6i 0.125539 0.132530i
233233 −146585. + 1.34783e6i −0.0115884 + 0.106553i −0.998504 0.0546870i 0.982584π-0.982584\pi
0.986915 + 0.161240i 0.0515494π0.0515494\pi
234234 −9.16860e6 + 2.30114e7i −0.715575 + 1.79596i
235235 3.31957e7i 2.55787i
236236 8.07804e6 + 1.09483e6i 0.614568 + 0.0832931i
237237 1.23719e6 0.0929377
238238 −5.47157e6 2.18007e6i −0.405864 0.161711i
239239 −1.66478e7 1.81056e6i −1.21945 0.132623i −0.524327 0.851517i 0.675683π-0.675683\pi
−0.695120 + 0.718894i 0.744649π0.744649\pi
240240 −4.58667e6 4.34473e6i −0.331791 0.314289i
241241 −2.04320e6 + 2.40544e6i −0.145969 + 0.171848i −0.830288 0.557335i 0.811824π-0.811824\pi
0.684319 + 0.729183i 0.260100π0.260100\pi
242242 −3.32992e7 1.76541e7i −2.34957 1.24566i
243243 7.01663e6 + 4.22177e6i 0.489001 + 0.294222i
244244 −4.16562e6 9.00384e6i −0.286754 0.619809i
245245 −1.27422e7 2.80477e6i −0.866455 0.190721i
246246 −3.37019e6 + 1.78676e6i −0.226386 + 0.120022i
247247 −4.78701e6 259544.i −0.317668 0.0172235i
248248 4.88599e6 + 5.75224e6i 0.320330 + 0.377122i
249249 −238717. 1.08450e6i −0.0154627 0.0702478i
250250 3.07634e7 + 4.04686e7i 1.96886 + 2.58999i
251251 1.27253e7 1.20540e7i 0.804721 0.762272i −0.170061 0.985434i 0.554396π-0.554396\pi
0.974781 + 0.223162i 0.0716378π0.0716378\pi
252252 −371120. 6.84490e6i −0.0231906 0.427726i
253253 2.09324e7 1.25946e7i 1.29258 0.777721i
254254 −2.16056e7 1.46490e7i −1.31846 0.893935i
255255 782479. 2.81823e6i 0.0471902 0.169964i
256256 −2.15636e7 + 2.34519e6i −1.28529 + 0.139784i
257257 1.05472e7 + 8.01781e6i 0.621355 + 0.472342i 0.867866 0.496798i 0.165491π-0.165491\pi
−0.246511 + 0.969140i 0.579284π0.579284\pi
258258 −461633. 213574.i −0.0268805 0.0124363i
259259 −3.34858e6 + 2.27039e6i −0.192735 + 0.130678i
260260 1.01404e7 + 3.00957e7i 0.576947 + 1.71232i
261261 1.04227e6 + 6.35758e6i 0.0586219 + 0.357578i
262262 4.02697e6 2.45634e7i 0.223911 1.36579i
263263 −1.02663e7 3.45913e6i −0.564350 0.190152i 0.0226432 0.999744i 0.492792π-0.492792\pi
−0.586993 + 0.809592i 0.699688π0.699688\pi
264264 840476. + 3.02712e6i 0.0456787 + 0.164520i
265265 1.06283e7 + 2.66751e7i 0.571120 + 1.43340i
266266 3.21970e6 1.28284e6i 0.171068 0.0681599i
267267 −5.79179e6 + 1.60808e6i −0.304284 + 0.0844840i
268268 2.14774e6 6.37425e6i 0.111577 0.331150i
269269 1.97941e7 + 3.24507e6i 1.01690 + 0.166712i 0.647105 0.762401i 0.275980π-0.275980\pi
0.369795 + 0.929113i 0.379428π0.379428\pi
270270 1.79207e7 2.93795e6i 0.910467 0.149263i
271271 −3.09532e7 + 1.04293e7i −1.55524 + 0.524022i −0.960114 0.279610i 0.909795π-0.909795\pi
−0.595127 + 0.803632i 0.702898π0.702898\pi
272272 −6.65412e6 9.81409e6i −0.330662 0.487690i
273273 −1.95557e6 + 4.22690e6i −0.0961138 + 0.207747i
274274 1.44525e7 1.90120e7i 0.702575 0.924221i
275275 −9.43960e6 8.67957e7i −0.453895 4.17350i
276276 2.16676e6 + 601597.i 0.103058 + 0.0286140i
277277 −1.63284e7 + 2.40825e7i −0.768251 + 1.13309i 0.219280 + 0.975662i 0.429629π0.429629\pi
−0.987531 + 0.157424i 0.949681π0.949681\pi
278278 −1.53491e6 2.55104e6i −0.0714413 0.118736i
279279 −2.12989e7 + 1.15480e6i −0.980721 + 0.0531732i
280280 9.66960e6 + 1.02081e7i 0.440488 + 0.465018i
281281 1.43466e7 1.09060e7i 0.646591 0.491526i −0.229729 0.973255i 0.573784π-0.573784\pi
0.876320 + 0.481729i 0.159991π0.159991\pi
282282 7.78384e6 1.71335e6i 0.347094 0.0764011i
283283 −2.29835e7 + 1.95224e7i −1.01405 + 0.861338i −0.990379 0.138382i 0.955810π-0.955810\pi
−0.0236664 + 0.999720i 0.507534π0.507534\pi
284284 753678. 1.39008e7i 0.0329026 0.606853i
285285 806177. + 1.52061e6i 0.0348254 + 0.0656876i
286286 1.78072e7 8.08988e7i 0.761197 3.45815i
287287 1.54703e7 7.15732e6i 0.654414 0.302764i
288288 1.28729e7 2.13950e7i 0.538890 0.895643i
289289 −8.73498e6 + 1.64759e7i −0.361883 + 0.682584i
290290 1.64459e7 + 1.39692e7i 0.674315 + 0.572768i
291291 6.38730e6 6.74299e6i 0.259202 0.273636i
292292 −1.25358e6 + 1.15264e7i −0.0503503 + 0.462963i
293293 −1.48469e6 + 3.72630e6i −0.0590246 + 0.148141i −0.955531 0.294889i 0.904717π-0.904717\pi
0.896507 + 0.443030i 0.146097π0.146097\pi
294294 3.13260e6i 0.123271i
295295 3.80223e6 4.71042e7i 0.148106 1.83482i
296296 −4.05641e6 −0.156411
297297 −1.68437e7 6.71115e6i −0.642938 0.256170i
298298 −1.48511e7 1.61515e6i −0.561188 0.0610329i
299299 2.63620e7 + 2.49714e7i 0.986198 + 0.934176i
300300 5.20283e6 6.12525e6i 0.192698 0.226861i
301301 2.00817e6 + 1.06466e6i 0.0736378 + 0.0390403i
302302 1.01631e7 + 6.11494e6i 0.368983 + 0.222009i
303303 2.58281e6 + 5.58266e6i 0.0928464 + 0.200684i
304304 6.81415e6 + 1.49991e6i 0.242544 + 0.0533881i
305305 −5.08123e7 + 2.69390e7i −1.79089 + 0.949471i
306306 1.66657e7 + 903590.i 0.581648 + 0.0315360i
307307 −9.24274e6 1.08814e7i −0.319437 0.376070i 0.578884 0.815410i 0.303488π-0.303488\pi
−0.898321 + 0.439339i 0.855213π0.855213\pi
308308 4.92788e6 + 2.23876e7i 0.168658 + 0.766223i
309309 −3.18126e6 4.18488e6i −0.107826 0.141843i
310310 −5.18666e7 + 4.91306e7i −1.74102 + 1.64918i
311311 103657. + 1.91183e6i 0.00344600 + 0.0635578i 0.999751 0.0223326i 0.00710927π-0.00710927\pi
−0.996305 + 0.0858904i 0.972627π0.972627\pi
312312 −4.00126e6 + 2.40748e6i −0.131745 + 0.0792681i
313313 2.18286e7 + 1.48001e7i 0.711857 + 0.482651i 0.862577 0.505926i 0.168849π-0.168849\pi
−0.150720 + 0.988576i 0.548159π0.548159\pi
314314 −682763. + 2.45909e6i −0.0220537 + 0.0794302i
315315 −3.95060e7 + 4.29653e6i −1.26395 + 0.137463i
316316 7.20569e6 + 5.47762e6i 0.228357 + 0.173593i
317317 2.30483e7 + 1.06633e7i 0.723537 + 0.334744i 0.746857 0.664984i 0.231562π-0.231562\pi
−0.0233204 + 0.999728i 0.507424π0.507424\pi
318318 5.70629e6 3.86896e6i 0.177449 0.120313i
319319 −6.87906e6 2.04163e7i −0.211913 0.628935i
320320 −1.47263e6 8.98265e6i −0.0449411 0.274129i
321321 −314669. + 1.91940e6i −0.00951348 + 0.0580296i
322322 −2.48772e7 8.38210e6i −0.745132 0.251064i
323323 864161. + 3.11243e6i 0.0256441 + 0.0923616i
324324 6.87466e6 + 1.72541e7i 0.202123 + 0.507291i
325325 1.20556e8 4.80339e7i 3.51187 1.39926i
326326 1.14651e7 3.18328e6i 0.330922 0.0918801i
327327 −3.55843e6 + 1.05610e7i −0.101769 + 0.302039i
328328 1.68657e7 + 2.76500e6i 0.477951 + 0.0783562i
329329 −3.51465e7 + 5.76197e6i −0.986948 + 0.161802i
330330 −2.81818e7 + 9.49557e6i −0.784201 + 0.264228i
331331 2.98301e7 + 4.39961e7i 0.822566 + 1.21319i 0.974407 + 0.224790i 0.0721695π0.0721695\pi
−0.151841 + 0.988405i 0.548520π0.548520\pi
332332 3.41126e6 7.37331e6i 0.0932180 0.201487i
333333 6.93791e6 9.12667e6i 0.187887 0.247161i
334334 −7.36468e6 6.77171e7i −0.197658 1.81744i
335335 −3.75721e7 1.04318e7i −0.999381 0.277477i
336336 3.80392e6 5.61036e6i 0.100280 0.147902i
337337 6.89836e6 + 1.14652e7i 0.180242 + 0.299565i 0.933785 0.357834i 0.116484π-0.116484\pi
−0.753543 + 0.657398i 0.771657π0.771657\pi
338338 7.38662e7 4.00491e6i 1.91292 0.103715i
339339 315793. + 333379.i 0.00810594 + 0.00855734i
340340 1.70350e7 1.29496e7i 0.433416 0.329474i
341341 6.96624e7 1.53339e7i 1.75685 0.386712i
342342 −7.48535e6 + 6.35812e6i −0.187126 + 0.158946i
343343 2.33029e6 4.29796e7i 0.0577467 1.06507i
344344 1.06748e6 + 2.01349e6i 0.0262232 + 0.0494622i
345345 2.80237e6 1.27313e7i 0.0682447 0.310039i
346346 −8.41620e7 + 3.89375e7i −2.03183 + 0.940026i
347347 3.31515e7 5.50982e7i 0.793441 1.31871i −0.150504 0.988609i 0.548090π-0.548090\pi
0.943946 0.330101i 0.107083π-0.107083\pi
348348 928919. 1.75213e6i 0.0220415 0.0415746i
349349 −1.39635e7 1.18607e7i −0.328487 0.279019i 0.467932 0.883764i 0.344999π-0.344999\pi
−0.796419 + 0.604745i 0.793275π0.793275\pi
350350 −6.45195e7 + 6.81124e7i −1.50483 + 1.58863i
351351 2.91386e6 2.67925e7i 0.0673824 0.619571i
352352 −3.09061e7 + 7.75686e7i −0.708625 + 1.77852i
353353 6.40645e6i 0.145644i 0.997345 + 0.0728221i 0.0232005π0.0232005\pi
−0.997345 + 0.0728221i 0.976799π0.976799\pi
354354 −1.12414e7 + 1.53966e6i −0.253402 + 0.0347069i
355355 −8.07026e7 −1.80386
356356 −4.08525e7 1.62771e7i −0.905458 0.360768i
357357 3.11967e6 + 339285.i 0.0685653 + 0.00745692i
358358 3.21259e7 + 3.04312e7i 0.700174 + 0.663240i
359359 2.21315e6 2.60552e6i 0.0478329 0.0563132i −0.737725 0.675101i 0.764100π-0.764100\pi
0.785558 + 0.618788i 0.212376π0.212376\pi
360360 −3.52028e7 1.86633e7i −0.754518 0.400020i
361361 3.86829e7 + 2.32747e7i 0.822238 + 0.494724i
362362 5.78274e6 + 1.24992e7i 0.121901 + 0.263485i
363363 1.96111e7 + 4.31674e6i 0.409999 + 0.0902476i
364364 −3.01042e7 + 1.59602e7i −0.624198 + 0.330929i
365365 6.71154e7 + 3.63889e6i 1.38021 + 0.0748326i
366366 8.93935e6 + 1.05242e7i 0.182332 + 0.214658i
367367 1.92169e7 + 8.73031e7i 0.388763 + 1.76617i 0.611456 + 0.791278i 0.290584π0.290584\pi
−0.222694 + 0.974888i 0.571485π0.571485\pi
368368 −3.19822e7 4.20718e7i −0.641748 0.844205i
369369 −3.50675e7 + 3.32177e7i −0.697952 + 0.661135i
370370 −2.07882e6 3.83415e7i −0.0410403 0.756944i
371371 −2.63979e7 + 1.58831e7i −0.516948 + 0.311037i
372372 5.43456e6 + 3.68473e6i 0.105569 + 0.0715775i
373373 2.38903e7 8.60452e7i 0.460358 1.65806i −0.260879 0.965371i 0.584012π-0.584012\pi
0.721237 0.692688i 0.243574π-0.243574\pi
374374 −5.54863e7 + 6.03450e6i −1.06065 + 0.115352i
375375 −2.15612e7 1.63904e7i −0.408864 0.310811i
376376 −3.24095e7 1.49942e7i −0.609690 0.282073i
377377 2.65050e7 1.79709e7i 0.494657 0.335386i
378378 6.22121e6 + 1.84639e7i 0.115186 + 0.341860i
379379 4.77257e6 + 2.91114e7i 0.0876667 + 0.534743i 0.993749 + 0.111641i 0.0356106π0.0356106\pi
−0.906082 + 0.423102i 0.860941π0.860941\pi
380380 −2.03709e6 + 1.24257e7i −0.0371245 + 0.226449i
381381 1.31797e7 + 4.44074e6i 0.238303 + 0.0802935i
382382 −5.51622e6 1.98676e7i −0.0989581 0.356415i
383383 −1.10105e7 2.76343e7i −0.195980 0.491872i 0.797841 0.602868i 0.205975π-0.205975\pi
−0.993821 + 0.110996i 0.964596π0.964596\pi
384384 9.48271e6 3.77826e6i 0.167471 0.0667264i
385385 1.28046e8 3.55519e7i 2.24380 0.622989i
386386 −1.13767e7 + 3.37647e7i −0.197812 + 0.587085i
387387 −6.35599e6 1.04201e6i −0.109661 0.0179779i
388388 6.70555e7 1.09932e7i 1.14799 0.188204i
389389 −5.93430e7 + 1.99950e7i −1.00814 + 0.339682i −0.774454 0.632631i 0.781975π-0.781975\pi
−0.233685 + 0.972312i 0.575079π0.575079\pi
390390 −2.48062e7 3.65864e7i −0.418183 0.616774i
391391 1.02731e7 2.22049e7i 0.171858 0.371466i
392392 8.49390e6 1.11735e7i 0.141010 0.185495i
393393 1.43386e6 + 1.31841e7i 0.0236226 + 0.217206i
394394 6.16015e7 + 1.71036e7i 1.00717 + 0.279639i
395395 2.94463e7 4.34301e7i 0.477793 0.704692i
396396 −3.34896e7 5.56602e7i −0.539293 0.896312i
397397 −1.20169e8 + 6.51538e6i −1.92053 + 0.104128i −0.975110 0.221723i 0.928832π-0.928832\pi
−0.945421 + 0.325851i 0.894349π0.894349\pi
398398 1.00167e8 + 1.05745e8i 1.58882 + 1.67730i
399399 −1.47004e6 + 1.11750e6i −0.0231425 + 0.0175925i
400400 −1.84457e8 + 4.06020e7i −2.88213 + 0.634405i
401401 −1.29376e7 + 1.09893e7i −0.200642 + 0.170427i −0.742075 0.670317i 0.766158π-0.766158\pi
0.541432 + 0.840744i 0.317882π0.317882\pi
402402 −506859. + 9.34846e6i −0.00780205 + 0.143900i
403403 4.96627e7 + 9.36737e7i 0.758778 + 1.43121i
404404 −9.67413e6 + 4.39500e7i −0.146713 + 0.666523i
405405 9.77196e7 4.52099e7i 1.47101 0.680563i
406406 −1.19356e7 + 1.98371e7i −0.178347 + 0.296414i
407407 −1.79577e7 + 3.38718e7i −0.266359 + 0.502406i
408408 2.39805e6 + 2.03692e6i 0.0353084 + 0.0299912i
409409 2.10183e7 2.21888e7i 0.307205 0.324313i −0.554052 0.832482i 0.686919π-0.686919\pi
0.861257 + 0.508170i 0.169678π0.169678\pi
410410 −1.74917e7 + 1.60833e8i −0.253793 + 2.33359i
411411 −4.70959e6 + 1.18202e7i −0.0678356 + 0.170254i
412412 3.84586e7i 0.549923i
413413 5.05323e7 4.15049e6i 0.717331 0.0589182i
414414 7.43886e7 1.04835
415415 −4.37518e7 1.74323e7i −0.612141 0.243899i
416416 −1.23384e8 1.34189e7i −1.71388 0.186396i
417417 1.15159e6 + 1.09085e6i 0.0158815 + 0.0150437i
418418 2.12621e7 2.50316e7i 0.291123 0.342737i
419419 −4.10143e7 2.17444e7i −0.557562 0.295601i 0.165698 0.986177i 0.447012π-0.447012\pi
−0.723260 + 0.690576i 0.757357π0.757357\pi
420420 1.04816e7 + 6.30655e6i 0.141475 + 0.0851224i
421421 −2.67639e7 5.78492e7i −0.358677 0.775267i −0.999968 0.00796959i 0.997463π-0.997463\pi
0.641292 0.767297i 0.278399π-0.278399\pi
422422 1.84254e8 + 4.05573e7i 2.45176 + 0.539674i
423423 8.91679e7 4.72738e7i 1.17811 0.624597i
424424 −3.08441e7 1.67232e6i −0.404645 0.0219392i
425425 −5.66070e7 6.66430e7i −0.737401 0.868136i
426426 4.16536e6 + 1.89234e7i 0.0538795 + 0.244777i
427427 −3.73419e7 4.91224e7i −0.479637 0.630951i
428428 −1.03308e7 + 9.78583e6i −0.131765 + 0.124815i
429429 2.38936e6 + 4.40691e7i 0.0302628 + 0.558164i
430430 −1.84846e7 + 1.11218e7i −0.232490 + 0.139884i
431431 −6.99048e6 4.73967e6i −0.0873123 0.0591992i 0.516750 0.856136i 0.327142π-0.327142\pi
−0.604062 + 0.796937i 0.706452π0.706452\pi
432432 −1.04935e7 + 3.77941e7i −0.130157 + 0.468784i
433433 6.72471e6 731357.i 0.0828343 0.00900877i −0.0666080 0.997779i 0.521218π-0.521218\pi
0.149442 + 0.988770i 0.452252π0.452252\pi
434434 −6.10207e7 4.63867e7i −0.746462 0.567446i
435435 −1.04339e7 4.82724e6i −0.126759 0.0586451i
436436 −6.74838e7 + 4.57551e7i −0.814217 + 0.552053i
437437 4.59696e6 + 1.36433e7i 0.0550841 + 0.163484i
438438 −2.61082e6 1.59253e7i −0.0310709 0.189524i
439439 −8.00907e6 + 4.88532e7i −0.0946648 + 0.577430i 0.896315 + 0.443418i 0.146234π0.146234\pi
−0.990980 + 0.134012i 0.957214π0.957214\pi
440440 1.26267e8 + 4.25444e7i 1.48229 + 0.499442i
441441 1.06121e7 + 3.82214e7i 0.123733 + 0.445647i
442442 −3.07069e7 7.70684e7i −0.355606 0.892503i
443443 −7.75975e7 + 3.09177e7i −0.892559 + 0.355628i −0.770909 0.636945i 0.780198π-0.780198\pi
−0.121650 + 0.992573i 0.538818π0.538818\pi
444444 −3.40036e6 + 944104.i −0.0388486 + 0.0107863i
445445 −8.14003e7 + 2.41587e8i −0.923732 + 2.74154i
446446 −5.59745e7 9.17656e6i −0.630937 0.103437i
447447 7.85429e6 1.28765e6i 0.0879396 0.0144170i
448448 9.25492e6 3.11834e6i 0.102929 0.0346809i
449449 6.53533e6 + 9.63888e6i 0.0721985 + 0.106485i 0.862074 0.506782i 0.169165π-0.169165\pi
−0.789876 + 0.613267i 0.789855π0.789855\pi
450450 1.11630e8 2.41285e8i 1.22502 2.64784i
451451 9.77525e7 1.28591e8i 1.06561 1.40179i
452452 363229. + 3.33984e6i 0.00393338 + 0.0361668i
453453 −6.08902e6 1.69061e6i −0.0655018 0.0181865i
454454 8.16172e7 1.20376e8i 0.872196 1.28639i
455455 1.01836e8 + 1.69252e8i 1.08110 + 1.79680i
456456 −1.84874e6 + 100236.i −0.0194976 + 0.00105713i
457457 −1.12094e8 1.18337e8i −1.17445 1.23985i −0.965062 0.262022i 0.915611π-0.915611\pi
−0.209390 0.977832i 0.567148π-0.567148\pi
458458 −1.01673e8 + 7.72900e7i −1.05830 + 0.804501i
459459 −1.77343e7 + 3.90362e6i −0.183390 + 0.0403673i
460460 7.26892e7 6.17427e7i 0.746786 0.634326i
461461 −6.49420e6 + 1.19778e8i −0.0662862 + 1.22258i 0.756411 + 0.654097i 0.226951π0.226951\pi
−0.822697 + 0.568480i 0.807532π0.807532\pi
462462 −1.49453e7 2.81898e7i −0.151558 0.285868i
463463 −1.48288e7 + 6.73680e7i −0.149404 + 0.678751i 0.841055 + 0.540949i 0.181935π0.181935\pi
−0.990460 + 0.137802i 0.955996π0.955996\pi
464464 −4.22988e7 + 1.95695e7i −0.423422 + 0.195896i
465465 1.96238e7 3.26150e7i 0.195175 0.324383i
466466 6.46673e6 1.21976e7i 0.0639039 0.120536i
467467 −6.00793e7 5.10319e7i −0.589895 0.501061i 0.301998 0.953309i 0.402346π-0.402346\pi
−0.891892 + 0.452248i 0.850622π0.850622\pi
468468 6.64000e7 7.00976e7i 0.647784 0.683857i
469469 4.52327e6 4.15908e7i 0.0438464 0.403161i
470470 1.25118e8 3.14021e8i 1.20510 3.02458i
471471 1.35974e6i 0.0130135i
472472 4.42712e7 + 2.49888e7i 0.421013 + 0.237640i
473473 2.15387e7 0.203534
474474 −1.17035e7 4.66309e6i −0.109895 0.0437863i
475475 5.11513e7 + 5.56304e6i 0.477283 + 0.0519077i
476476 1.66675e7 + 1.57883e7i 0.154543 + 0.146391i
477477 5.65169e7 6.65369e7i 0.520743 0.613066i
478478 1.50659e8 + 7.98743e7i 1.37947 + 0.731347i
479479 −6.60547e7 3.97438e7i −0.601031 0.361628i 0.182291 0.983245i 0.441649π-0.441649\pi
−0.783322 + 0.621616i 0.786476π0.786476\pi
480480 1.87091e7 + 4.04390e7i 0.169172 + 0.365659i
481481 −5.56524e7 1.22500e7i −0.500090 0.110078i
482482 2.83944e7 1.50537e7i 0.253566 0.134432i
483483 1.39659e7 + 757210.i 0.123945 + 0.00672009i
484484 9.51076e7 + 1.11969e8i 0.838840 + 0.987559i
485485 −8.46806e7 3.84708e8i −0.742264 3.37214i
486486 −5.04630e7 6.63830e7i −0.439607 0.578293i
487487 7.57682e7 7.17714e7i 0.655994 0.621390i −0.285517 0.958374i 0.592165π-0.592165\pi
0.941511 + 0.336983i 0.109407π0.109407\pi
488488 −3.34945e6 6.17771e7i −0.0288214 0.531579i
489489 −5.43210e6 + 3.26839e6i −0.0464560 + 0.0279516i
490490 1.09966e8 + 7.45587e7i 0.934695 + 0.633739i
491491 −1.14430e7 + 4.12138e7i −0.0966705 + 0.348176i −0.996028 0.0890379i 0.971621π-0.971621\pi
0.899358 + 0.437213i 0.144035π0.144035\pi
492492 1.47815e7 1.60759e6i 0.124115 0.0134983i
493493 −1.71770e7 1.30576e7i −0.143353 0.108974i
494494 4.43055e7 + 2.04979e7i 0.367516 + 0.170031i
495495 −3.11684e8 + 2.11327e8i −2.56980 + 1.74237i
496496 −4.92709e7 1.46231e8i −0.403780 1.19838i
497497 −1.40080e7 8.54452e7i −0.114106 0.696015i
498498 −1.82939e6 + 1.11588e7i −0.0148122 + 0.0903504i
499499 −8.86727e7 2.98773e7i −0.713655 0.240458i −0.0610260 0.998136i 0.519437π-0.519437\pi
−0.652629 + 0.757678i 0.726334π0.726334\pi
500500 −5.30095e7 1.90923e8i −0.424076 1.52738i
501501 1.34329e7 + 3.37141e7i 0.106821 + 0.268101i
502502 −1.65810e8 + 6.60646e7i −1.31069 + 0.522225i
503503 2.04116e8 5.66725e7i 1.60388 0.445316i 0.653635 0.756810i 0.273243π-0.273243\pi
0.950248 + 0.311494i 0.100829π0.100829\pi
504504 1.36498e7 4.05111e7i 0.106619 0.316433i
505505 2.57446e8 + 4.22060e7i 1.99899 + 0.327718i
506506 −2.45485e8 + 4.02452e7i −1.89484 + 0.310644i
507507 −3.73498e7 + 1.25846e7i −0.286592 + 0.0965640i
508508 5.71001e7 + 8.42164e7i 0.435558 + 0.642400i
509509 −8.76380e7 + 1.89426e8i −0.664567 + 1.43644i 0.222562 + 0.974918i 0.428558π0.428558\pi
−0.887130 + 0.461520i 0.847304π0.847304\pi
510510 −1.80242e7 + 2.37104e7i −0.135877 + 0.178743i
511511 7.79689e6 + 7.16912e7i 0.0584331 + 0.537283i
512512 9.67990e7 + 2.68761e7i 0.721209 + 0.200243i
513513 5.99652e6 8.84421e6i 0.0444168 0.0655099i
514514 −6.95539e7 1.15600e8i −0.512192 0.851269i
515515 −2.22622e8 + 1.20702e7i −1.62984 + 0.0883676i
516516 1.36346e6 + 1.43939e6i 0.00992417 + 0.0104768i
517517 −2.68681e8 + 2.04246e8i −1.94431 + 1.47803i
518518 4.02339e7 8.85614e6i 0.289469 0.0637170i
519519 3.76561e7 3.19854e7i 0.269360 0.228797i
520520 −1.07222e7 + 1.97759e8i −0.0762560 + 1.40646i
521521 4.75358e7 + 8.96620e7i 0.336130 + 0.634009i 0.992748 0.120215i 0.0383583π-0.0383583\pi
−0.656618 + 0.754224i 0.728013π0.728013\pi
522522 1.41027e7 6.40693e7i 0.0991496 0.450441i
523523 1.55666e7 7.20187e6i 0.108815 0.0503432i −0.364726 0.931115i 0.618837π-0.618837\pi
0.473541 + 0.880772i 0.342975π0.342975\pi
524524 −5.00210e7 + 8.31356e7i −0.347663 + 0.577821i
525525 2.34138e7 4.41631e7i 0.161806 0.305198i
526526 8.40787e7 + 7.14171e7i 0.577735 + 0.490733i
527527 4.91277e7 5.18635e7i 0.335656 0.354348i
528528 6.94476e6 6.38560e7i 0.0471797 0.433811i
529529 −1.44315e7 + 3.62203e7i −0.0974865 + 0.244673i
530530 2.92397e8i 1.96402i
531531 −1.31943e8 + 5.68676e7i −0.881256 + 0.379823i
532532 −1.35095e7 −0.0897233
533533 2.23041e8 + 8.88677e7i 1.47300 + 0.586898i
534534 6.08496e7 + 6.61780e6i 0.399608 + 0.0434600i
535535 5.98886e7 + 5.67295e7i 0.391096 + 0.370466i
536536 2.71558e7 3.19703e7i 0.176347 0.207612i
537537 −2.08300e7 1.10433e7i −0.134513 0.0713145i
538538 −1.75015e8 1.05303e8i −1.12390 0.676229i
539539 −5.56986e7 1.20391e8i −0.355695 0.768823i
540540 −6.91306e7 1.52168e7i −0.439025 0.0966367i
541541 −1.62917e8 + 8.63731e7i −1.02890 + 0.545490i −0.895262 0.445540i 0.853012π-0.853012\pi
−0.133641 + 0.991030i 0.542667π0.542667\pi
542542 3.32117e8 + 1.80069e7i 2.08590 + 0.113094i
543543 −4.75026e6 5.59244e6i −0.0296700 0.0349303i
544544 1.79769e7 + 8.16699e7i 0.111665 + 0.507301i
545545 2.86038e8 + 3.76277e8i 1.76699 + 2.32444i
546546 3.44307e7 3.26145e7i 0.211528 0.200370i
547547 −2.93103e6 5.40596e7i −0.0179084 0.330302i −0.993736 0.111758i 0.964352π-0.964352\pi
0.975827 0.218544i 0.0701308π-0.0701308\pi
548548 −7.97632e7 + 4.79919e7i −0.484686 + 0.291626i
549549 1.44723e8 + 9.81247e7i 0.874623 + 0.593009i
550550 −2.37845e8 + 8.56640e8i −1.42957 + 5.14885i
551551 1.26222e7 1.37274e6i 0.0754534 0.00820605i
552552 1.11640e7 + 8.48665e6i 0.0663747 + 0.0504567i
553553 5.10935e7 + 2.36384e7i 0.302127 + 0.139779i
554554 2.45231e8 1.66270e8i 1.44227 0.977881i
555555 6.53225e6 + 1.93870e7i 0.0382106 + 0.113405i
556556 1.87746e6 + 1.14520e7i 0.0109231 + 0.0666279i
557557 −2.55375e7 + 1.55772e8i −0.147779 + 0.901413i 0.804000 + 0.594629i 0.202701π0.202701\pi
−0.951779 + 0.306784i 0.900747π0.900747\pi
558558 2.05834e8 + 6.93536e7i 1.18472 + 0.399178i
559559 8.56490e6 + 3.08480e7i 0.0490328 + 0.176600i
560560 −1.06408e8 2.67063e8i −0.605912 1.52072i
561561 2.76248e7 1.10067e7i 0.156463 0.0623404i
562562 −1.76820e8 + 4.90939e7i −0.996146 + 0.276578i
563563 −2.34801e7 + 6.96864e7i −0.131575 + 0.390501i −0.993108 0.117200i 0.962608π-0.962608\pi
0.861533 + 0.507701i 0.169505π0.169505\pi
564564 −3.06576e7 5.02607e6i −0.170884 0.0280150i
565565 1.92190e7 3.15080e6i 0.106558 0.0174693i
566566 2.90999e8 9.80489e7i 1.60488 0.540746i
567567 6.48285e7 + 9.56149e7i 0.355645 + 0.524537i
568568 3.64528e7 7.87914e7i 0.198923 0.429965i
569569 5.30527e7 6.97896e7i 0.287985 0.378838i −0.629237 0.777213i 0.716633π-0.716633\pi
0.917223 + 0.398375i 0.130426π0.130426\pi
570570 −1.89487e6 1.74231e7i −0.0102319 0.0940807i
571571 −2.62521e8 7.28887e7i −1.41012 0.391518i −0.522715 0.852507i 0.675081π-0.675081\pi
−0.887406 + 0.460989i 0.847495π0.847495\pi
572572 −1.81198e8 + 2.67247e8i −0.968202 + 1.42799i
573573 5.66371e6 + 9.41316e6i 0.0301049 + 0.0500347i
574574 −1.73321e8 + 9.39718e6i −0.916463 + 0.0496892i
575575 −2.68010e8 2.82934e8i −1.40977 1.48827i
576576 −2.20314e7 + 1.67478e7i −0.115285 + 0.0876377i
577577 3.08124e7 6.78233e6i 0.160398 0.0353062i −0.134045 0.990975i 0.542797π-0.542797\pi
0.294443 + 0.955669i 0.404866π0.404866\pi
578578 1.44729e8 1.22934e8i 0.749503 0.636634i
579579 1.02773e6 1.89553e7i 0.00529472 0.0976553i
580580 −3.93971e7 7.43108e7i −0.201920 0.380862i
581581 1.08625e7 4.93488e7i 0.0553861 0.251622i
582582 −8.58369e7 + 3.97124e7i −0.435417 + 0.201445i
583583 −1.50510e8 + 2.50150e8i −0.759557 + 1.26239i
584584 −3.38683e7 + 6.38823e7i −0.170041 + 0.320732i
585585 −4.26607e8 3.62363e8i −2.13089 1.80999i
586586 2.80895e7 2.96537e7i 0.139589 0.147362i
587587 2.21567e6 2.03727e7i 0.0109544 0.100724i −0.987384 0.158342i 0.949385π-0.949385\pi
0.998339 + 0.0576180i 0.0183505π0.0183505\pi
588588 4.51958e6 1.13433e7i 0.0222314 0.0557966i
589589 4.20369e7i 0.205724i
590590 −2.13508e8 + 4.31261e8i −1.03958 + 2.09983i
591591 −3.40621e7 −0.165010
592592 7.70454e7 + 3.06977e7i 0.371348 + 0.147959i
593593 −1.40038e8 1.52300e7i −0.671554 0.0730359i −0.234012 0.972234i 0.575185π-0.575185\pi
−0.437542 + 0.899198i 0.644151π0.644151\pi
594594 1.34042e8 + 1.26971e8i 0.639559 + 0.605822i
595595 8.61612e7 1.01437e8i 0.409036 0.481554i
596596 5.14462e7 + 2.72751e7i 0.243005 + 0.128833i
597597 −6.64950e7 4.00087e7i −0.312512 0.188032i
598598 −1.55257e8 3.35582e8i −0.726018 1.56926i
599599 2.73628e8 + 6.02300e7i 1.27315 + 0.280242i 0.799604 0.600527i 0.205043π-0.205043\pi
0.473546 + 0.880769i 0.342974π0.342974\pi
600600 4.42801e7 2.34758e7i 0.205000 0.108684i
601601 1.91502e8 + 1.03829e7i 0.882166 + 0.0478296i 0.489653 0.871917i 0.337123π-0.337123\pi
0.392512 + 0.919747i 0.371606π0.371606\pi
602602 −1.49839e7 1.76404e7i −0.0686806 0.0808571i
603603 2.54850e7 + 1.15779e8i 0.116234 + 0.528056i
604604 −2.79788e7 3.68055e7i −0.126975 0.167033i
605605 6.18297e8 5.85682e8i 2.79210 2.64482i
606606 −3.39110e6 6.25451e7i −0.0152378 0.281045i
607607 −1.17484e7 + 7.06879e6i −0.0525307 + 0.0316067i −0.541577 0.840651i 0.682173π-0.682173\pi
0.489046 + 0.872258i 0.337345π0.337345\pi
608608 −4.07293e7 2.76151e7i −0.181216 0.122867i
609609 3.29985e6 1.18850e7i 0.0146097 0.0526195i
610610 5.82204e8 6.33185e7i 2.56499 0.278960i
611611 −3.99365e8 3.03589e8i −1.75084 1.33095i
612612 −5.90439e7 2.73166e7i −0.257585 0.119171i
613613 −2.09897e8 + 1.42314e8i −0.911224 + 0.617825i −0.924124 0.382092i 0.875204π-0.875204\pi
0.0129008 + 0.999917i 0.495893π0.495893\pi
614614 4.64206e7 + 1.37771e8i 0.200542 + 0.595188i
615615 −1.39449e7 8.50599e7i −0.0599499 0.365678i
616616 −2.31276e7 + 1.41072e8i −0.0989440 + 0.603532i
617617 8.52456e7 + 2.87226e7i 0.362925 + 0.122284i 0.494855 0.868975i 0.335221π-0.335221\pi
−0.131931 + 0.991259i 0.542118π0.542118\pi
618618 1.43206e7 + 5.15781e7i 0.0606730 + 0.218525i
619619 −5.92801e7 1.48782e8i −0.249941 0.627303i 0.749455 0.662055i 0.230315π-0.230315\pi
−0.999396 + 0.0347513i 0.988936π0.988936\pi
620620 2.58695e8 1.03074e8i 1.08546 0.432487i
621621 −7.79844e7 + 2.16523e7i −0.325636 + 0.0904125i
622622 6.22531e6 1.84761e7i 0.0258696 0.0767783i
623623 −2.69914e8 4.42501e7i −1.11625 0.183000i
624624 9.42169e7 1.54461e7i 0.387771 0.0635718i
625625 −5.35935e8 + 1.80578e8i −2.19519 + 0.739646i
626626 −1.50709e8 2.22279e8i −0.614350 0.906098i
627627 −7.34737e6 + 1.58811e7i −0.0298078 + 0.0644284i
628628 6.02020e6 7.91944e6i 0.0243070 0.0319754i
629629 4.15129e6 + 3.81705e7i 0.0166813 + 0.153382i
630630 3.89909e8 + 1.08258e8i 1.55934 + 0.432949i
631631 4.30097e7 6.34345e7i 0.171190 0.252486i −0.732410 0.680864i 0.761604π-0.761604\pi
0.903600 + 0.428378i 0.140915π0.140915\pi
632632 2.91008e7 + 4.83660e7i 0.115280 + 0.191597i
633633 −1.00371e8 + 5.44195e6i −0.395728 + 0.0214557i
634634 −1.77839e8 1.87742e8i −0.697846 0.736707i
635635 4.69575e8 3.56961e8i 1.83393 1.39412i
636636 −2.62448e7 + 5.77691e6i −0.102017 + 0.0224556i
637637 1.50276e8 1.27646e8i 0.581395 0.493841i
638638 −1.18771e7 + 2.19060e8i −0.0457350 + 0.843532i
639639 1.14928e8 + 2.16778e8i 0.440478 + 0.830829i
640640 9.30664e7 4.22805e8i 0.355020 1.61287i
641641 4.66628e7 2.15885e7i 0.177173 0.0819688i −0.329298 0.944226i 0.606812π-0.606812\pi
0.506470 + 0.862257i 0.330950π0.330950\pi
642642 1.02111e7 1.69709e7i 0.0385892 0.0641357i
643643 1.08227e8 2.04138e8i 0.407103 0.767877i −0.592178 0.805807i 0.701732π-0.701732\pi
0.999280 + 0.0379301i 0.0120764π0.0120764\pi
644644 7.79882e7 + 6.62438e7i 0.291992 + 0.248021i
645645 7.90414e6 8.34430e6i 0.0294561 0.0310964i
646646 3.55631e6 3.26997e7i 0.0131917 0.121296i
647647 6.20488e7 1.55731e8i 0.229097 0.574991i −0.768822 0.639463i 0.779157π-0.779157\pi
0.997920 + 0.0644715i 0.0205362π0.0205362\pi
648648 1.15826e8i 0.425679i
649649 4.04649e8 2.59048e8i 1.48028 0.947644i
650650 −1.32147e9 −4.81190
651651 3.79379e7 + 1.51158e7i 0.137509 + 0.0547885i
652652 −4.61085e7 5.01460e6i −0.166356 0.0180923i
653653 3.86347e8 + 3.65968e8i 1.38752 + 1.31433i 0.896409 + 0.443229i 0.146167π0.146167\pi
0.491109 + 0.871098i 0.336592π0.336592\pi
654654 7.34672e7 8.64923e7i 0.262640 0.309203i
655655 4.96938e8 + 2.63460e8i 1.76839 + 0.937542i
656656 −2.99414e8 1.80152e8i −1.06062 0.638156i
657657 −8.58042e7 1.85463e8i −0.302561 0.653974i
658658 3.54193e8 + 7.79637e7i 1.24326 + 0.273662i
659659 1.50085e8 7.95702e7i 0.524423 0.278032i −0.185093 0.982721i 0.559259π-0.559259\pi
0.709516 + 0.704690i 0.248914π0.248914\pi
660660 1.15748e8 + 6.27566e6i 0.402606 + 0.0218287i
661661 1.24435e8 + 1.46497e8i 0.430863 + 0.507251i 0.934156 0.356864i 0.116154π-0.116154\pi
−0.503293 + 0.864116i 0.667878π0.667878\pi
662662 −1.16359e8 5.28623e8i −0.401074 1.82210i
663663 2.67490e7 + 3.51877e7i 0.0917839 + 0.120740i
664664 3.67818e7 3.48416e7i 0.125640 0.119013i
665665 4.23995e6 + 7.82013e7i 0.0144177 + 0.265919i
666666 −1.00030e8 + 6.01859e7i −0.338615 + 0.203738i
667667 −7.95968e7 5.39680e7i −0.268237 0.181869i
668668 −7.10316e7 + 2.55833e8i −0.238299 + 0.858275i
669669 3.00436e7 3.26743e6i 0.100340 0.0109126i
670670 3.16102e8 + 2.40295e8i 1.05100 + 0.798951i
671671 −5.30677e8 2.45517e8i −1.75656 0.812671i
672672 −3.95680e7 + 2.68277e7i −0.130387 + 0.0884049i
673673 −5.46342e7 1.62149e8i −0.179234 0.531946i 0.819946 0.572441i 0.194003π-0.194003\pi
−0.999180 + 0.0404943i 0.987107π0.987107\pi
674674 −2.20432e7 1.34458e8i −0.0719938 0.439143i
675675 −4.67955e7 + 2.85440e8i −0.152157 + 0.928119i
676676 −2.73252e8 9.20692e7i −0.884550 0.298040i
677677 1.26383e8 + 4.55190e8i 0.407307 + 1.46699i 0.828486 + 0.560010i 0.189203π0.189203\pi
−0.421179 + 0.906977i 0.638384π0.638384\pi
678678 −1.73077e6 4.34392e6i −0.00555330 0.0139377i
679679 3.92617e8 1.56433e8i 1.25418 0.499711i
680680 1.28579e8 3.56999e7i 0.408926 0.113538i
681681 −2.47417e7 + 7.34308e7i −0.0783409 + 0.232508i
682682 −7.16780e8 1.17510e8i −2.25961 0.370444i
683683 −1.19474e8 + 1.95868e7i −0.374983 + 0.0614754i −0.346327 0.938114i 0.612571π-0.612571\pi
−0.0286564 + 0.999589i 0.509123π0.509123\pi
684684 3.62781e7 1.22235e7i 0.113364 0.0381969i
685685 3.02840e8 + 4.46655e8i 0.942196 + 1.38964i
686686 −1.84038e8 + 3.97791e8i −0.570078 + 1.23220i
687687 4.11793e7 5.41704e7i 0.127001 0.167067i
688688 −5.03777e6 4.63215e7i −0.0154694 0.142239i
689689 −4.18118e8 1.16090e8i −1.27833 0.354925i
690690 −7.44951e7 + 1.09872e8i −0.226767 + 0.334457i
691691 −6.04738e7 1.00508e8i −0.183288 0.304627i 0.751567 0.659657i 0.229298π-0.229298\pi
−0.934855 + 0.355030i 0.884471π0.884471\pi
692692 3.60933e8 1.95692e7i 1.08920 0.0590547i
693693 −2.77847e8 2.93320e8i −0.834846 0.881336i
694694 −5.21273e8 + 3.96262e8i −1.55951 + 1.18551i
695695 6.57017e7 1.44620e7i 0.195714 0.0430800i
696696 9.42584e6 8.00638e6i 0.0279571 0.0237470i
697697 8.75815e6 1.61535e8i 0.0258651 0.477054i
698698 8.73864e7 + 1.64828e8i 0.256967 + 0.484692i
699699 −1.58123e6 + 7.18359e6i −0.00462980 + 0.0210334i
700700 3.31898e8 1.53552e8i 0.967633 0.447675i
701701 −2.04076e8 + 3.39178e8i −0.592432 + 0.984630i 0.405090 + 0.914277i 0.367240π0.367240\pi
−0.997522 + 0.0703534i 0.977587π0.977587\pi
702702 −1.28547e8 + 2.42466e8i −0.371580 + 0.700874i
703703 −1.72199e7 1.46267e7i −0.0495639 0.0420999i
704704 6.36435e7 6.71876e7i 0.182405 0.192562i
705705 −1.94720e7 + 1.79042e8i −0.0555705 + 0.510962i
706706 2.41465e7 6.06031e7i 0.0686183 0.172219i
707707 2.79901e8i 0.792037i
708708 4.29271e7 + 1.06434e7i 0.120957 + 0.0299904i
709709 −5.18262e8 −1.45416 −0.727078 0.686555i 0.759122π-0.759122\pi
−0.727078 + 0.686555i 0.759122π0.759122\pi
710710 7.63422e8 + 3.04175e8i 2.13300 + 0.849863i
711711 −1.58593e8 1.72480e7i −0.441241 0.0479878i
712712 −1.99098e8 1.88596e8i −0.551604 0.522507i
713713 2.06128e8 2.42672e8i 0.568680 0.669501i
714714 −2.82324e7 1.49678e7i −0.0775626 0.0411211i
715715 1.60386e9 + 9.65010e8i 4.38781 + 2.64006i
716716 −7.24245e7 1.56543e8i −0.197309 0.426476i
717717 −8.87286e7 1.95306e7i −0.240717 0.0529857i
718718 −3.07561e7 + 1.63059e7i −0.0830918 + 0.0440525i
719719 3.28781e8 + 1.78260e7i 0.884547 + 0.0479587i 0.490812 0.871265i 0.336700π-0.336700\pi
0.393735 + 0.919224i 0.371183π0.371183\pi
720720 5.27385e8 + 6.20886e8i 1.41296 + 1.66347i
721721 −5.14213e7 2.33609e8i −0.137195 0.623282i
722722 −2.78204e8 3.65971e8i −0.739183 0.972379i
723723 −1.24311e7 + 1.17753e7i −0.0328923 + 0.0311572i
724724 −2.90629e6 5.36033e7i −0.00765813 0.141246i
725725 −2.94495e8 + 1.77192e8i −0.772793 + 0.464974i
726726 −1.69245e8 1.14751e8i −0.442290 0.299880i
727727 1.02660e8 3.69749e8i 0.267177 0.962285i −0.701235 0.712930i 0.747368π-0.747368\pi
0.968412 0.249355i 0.0802186π-0.0802186\pi
728728 −2.11242e8 + 2.29740e7i −0.547503 + 0.0595445i
729729 −2.36198e8 1.79553e8i −0.609669 0.463459i
730730 −6.21177e8 2.87387e8i −1.59679 0.738751i
731731 1.78543e7 1.21055e7i 0.0457078 0.0309907i
732732 −1.71860e7 5.10061e7i −0.0438168 0.130044i
733733 −2.58514e6 1.57687e7i −0.00656406 0.0400390i 0.983341 0.181768i 0.0581820π-0.0581820\pi
−0.989905 + 0.141729i 0.954734π0.954734\pi
734734 1.47267e8 8.98292e8i 0.372408 2.27159i
735735 −6.70804e7 2.26020e7i −0.168940 0.0569226i
736736 9.97128e7 + 3.59133e8i 0.250102 + 0.900786i
737737 −1.46739e8 3.68288e8i −0.366559 0.919994i
738738 4.56928e8 1.82057e8i 1.13679 0.452937i
739739 2.71850e8 7.54788e7i 0.673591 0.187022i 0.0861421 0.996283i 0.472546π-0.472546\pi
0.587449 + 0.809261i 0.300132π0.300132\pi
740740 −4.77901e7 + 1.41836e8i −0.117935 + 0.350018i
741741 −2.56667e7 4.20785e6i −0.0630835 0.0103420i
742742 3.09580e8 5.07531e7i 0.757813 0.124237i
743743 −2.80039e8 + 9.43562e7i −0.682735 + 0.230040i −0.639233 0.769013i 0.720748π-0.720748\pi
−0.0435021 + 0.999053i 0.513852π0.513852\pi
744744 2.29787e7 + 3.38910e7i 0.0557964 + 0.0822935i
745745 1.41738e8 3.06362e8i 0.342782 0.740911i
746746 −5.50307e8 + 7.23917e8i −1.32553 + 1.74370i
747747 1.54813e7 + 1.42348e8i 0.0371403 + 0.341500i
748748 2.09625e8 + 5.82021e7i 0.500886 + 0.139070i
749749 −4.96681e7 + 7.32550e7i −0.118204 + 0.174338i
750750 1.42186e8 + 2.36314e8i 0.337033 + 0.560153i
751751 −4.78560e8 + 2.59468e7i −1.12984 + 0.0612581i −0.609562 0.792739i 0.708655π-0.708655\pi
−0.520278 + 0.853997i 0.674172π0.674172\pi
752752 5.02098e8 + 5.30058e8i 1.18069 + 1.24644i
753753 7.57049e7 5.75494e7i 0.177312 0.134789i
754754 −3.18463e8 + 7.00991e7i −0.742926 + 0.163530i
755755 −2.04271e8 + 1.73510e8i −0.474642 + 0.403165i
756756 4.11162e6 7.58345e7i 0.00951586 0.175510i
757757 −2.65975e8 5.01681e8i −0.613130 1.15649i −0.974569 0.224090i 0.928059π-0.928059\pi
0.361439 0.932396i 0.382286π-0.382286\pi
758758 6.45763e7 2.93373e8i 0.148274 0.673616i
759759 1.20288e8 5.56511e7i 0.275104 0.127276i
760760 −4.04832e7 + 6.72835e7i −0.0922218 + 0.153274i
761761 −2.29926e8 + 4.33686e8i −0.521716 + 0.984061i 0.472967 + 0.881080i 0.343183π0.343183\pi
−0.994683 + 0.102981i 0.967162π0.967162\pi
762762 −1.07938e8 9.16834e7i −0.243955 0.207217i
763763 −3.48740e8 + 3.68160e8i −0.785106 + 0.828826i
764764 −8.68968e6 + 7.99003e7i −0.0194861 + 0.179171i
765765 −1.39594e8 + 3.50355e8i −0.311805 + 0.782571i
766766 3.02912e8i 0.673953i
767767 5.31920e8 + 4.76532e8i 1.17885 + 1.05610i
768768 −1.17680e8 −0.259788
769769 5.18949e8 + 2.06768e8i 1.14116 + 0.454679i 0.862673 0.505762i 0.168789π-0.168789\pi
0.278484 + 0.960441i 0.410168π0.410168\pi
770770 −1.34528e9 1.46308e8i −2.94673 0.320476i
771771 5.21839e7 + 4.94313e7i 0.113861 + 0.107855i
772772 8.99099e7 1.05850e8i 0.195414 0.230059i
773773 −1.27058e7 6.73620e6i −0.0275083 0.0145840i 0.454598 0.890697i 0.349783π-0.349783\pi
−0.482106 + 0.876113i 0.660128π0.660128\pi
774774 5.61984e7 + 3.38134e7i 0.121199 + 0.0729233i
775775 −4.77802e8 1.03275e9i −1.02646 2.21866i
776776 4.13846e8 + 9.10945e7i 0.885633 + 0.194943i
777777 −1.93925e7 + 1.02812e7i −0.0413400 + 0.0219171i
778778 6.36729e8 + 3.45225e7i 1.35212 + 0.0733100i
779779 6.16268e7 + 7.25527e7i 0.130364 + 0.153476i
780780 3.70392e7 + 1.68271e8i 0.0780508 + 0.354588i
781781 −4.96546e8 6.53195e8i −1.04233 1.37116i
782782 −1.80873e8 + 1.71332e8i −0.378227 + 0.358276i
783783 3.86421e6 + 7.12711e7i 0.00804961 + 0.148466i
784784 −2.45887e8 + 1.47945e8i −0.510254 + 0.307010i
785785 −4.77319e7 3.23631e7i −0.0986734 0.0669022i
786786 3.61282e7 1.30122e8i 0.0744009 0.267968i
787787 −7.99727e8 + 8.69755e7i −1.64066 + 0.178432i −0.881403 0.472364i 0.843401π-0.843401\pi
−0.759252 + 0.650796i 0.774435π0.774435\pi
788788 −1.98386e8 1.50809e8i −0.405445 0.308211i
789789 −5.33429e7 2.46791e7i −0.108604 0.0502455i
790790 −4.42245e8 + 2.99850e8i −0.896978 + 0.608166i
791791 6.67192e6 + 1.98015e7i 0.0134810 + 0.0400101i
792792 −6.55370e7 3.99758e8i −0.131920 0.804677i
793793 1.40608e8 8.57672e8i 0.281962 1.71989i
794794 1.16132e9 + 3.91295e8i 2.32001 + 0.781704i
795795 4.16772e7 + 1.50108e8i 0.0829463 + 0.298745i
796796 −2.10145e8 5.27425e8i −0.416659 1.04573i
797797 −3.42358e8 + 1.36408e8i −0.676247 + 0.269441i −0.682873 0.730537i 0.739270π-0.739270\pi
0.00662680 + 0.999978i 0.497891π0.497891\pi
798798 1.81181e7 5.03046e6i 0.0356536 0.00989917i
799799 −1.07927e8 + 3.20316e8i −0.211587 + 0.627968i
800800 1.31451e9 + 2.15502e8i 2.56739 + 0.420903i
801801 7.64857e8 1.25392e8i 1.48827 0.243990i
802802 1.63806e8 5.51927e7i 0.317546 0.106994i
803803 3.83494e8 + 5.65612e8i 0.740649 + 1.09238i
804804 1.53229e7 3.31200e7i 0.0294832 0.0637268i
805805 3.58983e8 4.72234e8i 0.688154 0.905252i
806806 −1.16729e8 1.07331e9i −0.222933 2.04984i
807807 1.04857e8 + 2.91133e7i 0.199515 + 0.0553950i
808808 −1.57493e8 + 2.32284e8i −0.298556 + 0.440338i
809809 −1.84958e8 3.07403e8i −0.349324 0.580581i 0.631524 0.775357i 0.282430π-0.282430\pi
−0.980848 + 0.194775i 0.937602π0.937602\pi
810810 −1.09480e9 + 5.93582e7i −2.06006 + 0.111693i
811811 2.60112e8 + 2.74597e8i 0.487638 + 0.514794i 0.922654 0.385629i 0.126016π-0.126016\pi
−0.435015 + 0.900423i 0.643257π0.643257\pi
812812 7.18394e7 5.46109e7i 0.134182 0.102003i
813813 −1.73065e8 + 3.80945e7i −0.322061 + 0.0708910i
814814 2.97540e8 2.52733e8i 0.551661 0.468585i
815815 −1.45564e7 + 2.68478e8i −0.0268895 + 0.495947i
816816 −3.01325e7 5.68360e7i −0.0554581 0.104605i
817817 −2.72871e6 + 1.23966e7i −0.00500370 + 0.0227320i
818818 −2.82459e8 + 1.30679e8i −0.516054 + 0.238752i
819819 3.09609e8 5.14575e8i 0.563589 0.936692i
820820 2.95382e8 5.57149e8i 0.535725 1.01048i
821821 7.08741e8 + 6.02010e8i 1.28073 + 1.08786i 0.991432 + 0.130624i 0.0416980π0.0416980\pi
0.289299 + 0.957239i 0.406578π0.406578\pi
822822 8.91026e7 9.40645e7i 0.160426 0.169360i
823823 −5.33633e7 + 4.90668e8i −0.0957290 + 0.880213i 0.843548 + 0.537054i 0.180463π0.180463\pi
−0.939277 + 0.343160i 0.888503π0.888503\pi
824824 8.87723e7 2.22802e8i 0.158670 0.398233i
825825 4.73674e8i 0.843563i
826826 −4.93664e8 1.51199e8i −0.875975 0.268292i
827827 −9.66722e8 −1.70917 −0.854585 0.519312i 0.826188π-0.826188\pi
−0.854585 + 0.519312i 0.826188π0.826188\pi
828828 −2.69365e8 1.07325e8i −0.474516 0.189064i
829829 1.08854e8 + 1.18386e7i 0.191064 + 0.0207795i 0.203151 0.979147i 0.434882π-0.434882\pi
−0.0120865 + 0.999927i 0.503847π0.503847\pi
830830 3.48175e8 + 3.29809e8i 0.608924 + 0.576804i
831831 −1.02194e8 + 1.20312e8i −0.178083 + 0.209656i
832832 1.21535e8 + 6.44336e7i 0.211023 + 0.111877i
833833 −1.13834e8 6.84919e7i −0.196942 0.118496i
834834 −6.78222e6 1.46595e7i −0.0116916 0.0252710i
835835 1.50321e9 + 3.30881e8i 2.58202 + 0.568346i
836836 −1.13106e8 + 5.99649e7i −0.193582 + 0.102631i
837837 −2.35970e8 1.27939e7i −0.402422 0.0218187i
838838 3.06026e8 + 3.60282e8i 0.520028 + 0.612224i
839839 −8.84721e7 4.01933e8i −0.149803 0.680562i −0.990323 0.138781i 0.955681π-0.955681\pi
0.840520 0.541780i 0.182250π-0.182250\pi
840840 4.61655e7 + 6.07297e7i 0.0778897 + 0.102462i
841841 3.70268e8 3.50736e8i 0.622483 0.589647i
842842 3.51396e7 + 6.48112e8i 0.0588655 + 1.08571i
843843 8.37763e7 5.04065e7i 0.139842 0.0841403i
844844 −6.08678e8 4.12694e8i −1.01242 0.686437i
845845 −4.47192e8 + 1.61064e9i −0.741181 + 2.66949i
846846 −1.02168e9 + 1.11115e8i −1.68735 + 0.183510i
847847 7.27422e8 + 5.52972e8i 1.19712 + 0.910024i
848848 5.73181e8 + 2.65182e8i 0.939948 + 0.434866i
849849 −1.35414e8 + 9.18131e7i −0.221279 + 0.150031i
850850 2.84302e8 + 8.43780e8i 0.462939 + 1.37395i
851851 2.76857e7 + 1.68875e8i 0.0449228 + 0.274017i
852852 1.22190e7 7.45323e7i 0.0197567 0.120511i
853853 −3.28674e7 1.10743e7i −0.0529565 0.0178431i 0.292699 0.956205i 0.405447π-0.405447\pi
−0.345655 + 0.938362i 0.612343π0.612343\pi
854854 1.68096e8 + 6.05428e8i 0.269889 + 0.972051i
855855 −8.21430e7 2.06163e8i −0.131423 0.329847i
856856 −8.24373e7 + 3.28460e7i −0.131432 + 0.0523674i
857857 −6.49859e8 + 1.80432e8i −1.03247 + 0.286663i −0.742127 0.670260i 0.766183π-0.766183\pi
−0.290342 + 0.956923i 0.593769π0.593769\pi
858858 1.43498e8 4.25886e8i 0.227187 0.674266i
859859 5.35714e8 + 8.78258e7i 0.845188 + 0.138562i 0.568791 0.822482i 0.307411π-0.307411\pi
0.276397 + 0.961044i 0.410860π0.410860\pi
860860 8.29797e7 1.36038e7i 0.130460 0.0213878i
861861 8.76381e7 2.95287e7i 0.137304 0.0462631i
862862 4.82637e7 + 7.11836e7i 0.0753526 + 0.111137i
863863 1.18062e8 2.55187e8i 0.183687 0.397033i −0.793755 0.608238i 0.791877π-0.791877\pi
0.977442 + 0.211205i 0.0677388π0.0677388\pi
864864 1.67411e8 2.20225e8i 0.259563 0.341449i
865865 −2.26557e8 2.08315e9i −0.350049 3.21865i
866866 −6.63703e7 1.84276e7i −0.102193 0.0283737i
867867 −5.67770e7 + 8.37398e7i −0.0871195 + 0.128492i
868868 1.54034e8 + 2.56007e8i 0.235536 + 0.391465i
869869 5.32693e8 2.88818e7i 0.811742 0.0440114i
870870 8.05074e7 + 8.49906e7i 0.122258 + 0.129066i
871871 4.69115e8 3.56612e8i 0.709945 0.539686i
872872 −4.96567e8 + 1.09303e8i −0.748908 + 0.164847i
873873 −9.12781e8 + 7.75323e8i −1.37190 + 1.16531i
874874 7.93692e6 1.46388e8i 0.0118882 0.219266i
875875 −5.77271e8 1.08885e9i −0.861699 1.62534i
876876 −1.35224e7 + 6.14330e7i −0.0201160 + 0.0913881i
877877 −5.34710e8 + 2.47383e8i −0.792720 + 0.366751i −0.774090 0.633075i 0.781792π-0.781792\pi
−0.0186294 + 0.999826i 0.505930π0.505930\pi
878878 2.59895e8 4.31949e8i 0.383986 0.638189i
879879 −1.01935e7 + 1.92270e7i −0.0150092 + 0.0283104i
880880 −2.07629e9 1.76362e9i −3.04678 2.58796i
881881 −1.67363e8 + 1.76683e8i −0.244755 + 0.258385i −0.836786 0.547531i 0.815568π-0.815568\pi
0.592030 + 0.805916i 0.298327π0.298327\pi
882882 4.36724e7 4.01561e8i 0.0636505 0.585256i
883883 2.42020e8 6.07424e8i 0.351535 0.882288i −0.641783 0.766886i 0.721805π-0.721805\pi
0.993319 0.115402i 0.0368155π-0.0368155\pi
884884 3.23371e8i 0.468107i
885885 4.81380e7 2.51828e8i 0.0694478 0.363308i
886886 8.50581e8 1.22297
887887 −2.25955e8 9.00286e7i −0.323780 0.129006i 0.202584 0.979265i 0.435066π-0.435066\pi
−0.526365 + 0.850259i 0.676445π0.676445\pi
888888 −2.18785e7 2.37943e6i −0.0312448 0.00339808i
889889 4.59446e8 + 4.35210e8i 0.653926 + 0.619432i
890890 1.68059e9 1.97854e9i 2.38392 2.80656i
891891 9.67170e8 + 5.12761e8i 1.36732 + 0.724906i
892892 1.89447e8 + 1.13987e8i 0.266928 + 0.160605i
893893 −8.35154e7 1.80515e8i −0.117277 0.253490i
894894 −7.91525e7 1.74228e7i −0.110778 0.0243840i
895895 −8.83436e8 + 4.68368e8i −1.23227 + 0.653308i
896896 4.63806e8 + 2.51468e7i 0.644781 + 0.0349590i
897897 1.27537e8 + 1.50148e8i 0.176709 + 0.208037i
898898 −2.54924e7 1.15813e8i −0.0352032 0.159930i
899899 −1.69930e8 2.23539e8i −0.233879 0.307663i
900900 −7.52335e8 + 7.12649e8i −1.03201 + 0.977571i
901901 1.58291e7 + 2.91951e8i 0.0216413 + 0.399150i
902902 −1.40938e9 + 8.47997e8i −1.92048 + 1.15551i
903903 1.02066e7 + 6.92027e6i 0.0138618 + 0.00939853i
904904 −5.60491e6 + 2.01871e7i −0.00758688 + 0.0273255i
905905 −3.09376e8 + 3.36467e7i −0.417389 + 0.0453938i
906906 5.12283e7 + 3.89427e7i 0.0688851 + 0.0523651i
907907 4.54546e8 + 2.10295e8i 0.609194 + 0.281843i 0.700132 0.714013i 0.253124π-0.253124\pi
−0.0909381 + 0.995857i 0.528987π0.528987\pi
908908 −4.69214e8 + 3.18135e8i −0.626778 + 0.424966i
909909 −2.53256e8 7.51637e8i −0.337185 1.00073i
910910 −3.25408e8 1.98490e9i −0.431821 2.63399i
911911 4.51327e7 2.75297e8i 0.0596947 0.364122i −0.940039 0.341066i 0.889212π-0.889212\pi
0.999734 0.0230559i 0.00733957π-0.00733957\pi
912912 3.58726e7 + 1.20869e7i 0.0472910 + 0.0159342i
913913 −1.28101e8 4.61378e8i −0.168322 0.606240i
914914 6.14358e8 + 1.54192e9i 0.804606 + 2.01941i
915915 −2.89860e8 + 1.15491e8i −0.378378 + 0.150759i
916916 4.79675e8 1.33181e8i 0.624109 0.173283i
917917 −1.92686e8 + 5.71872e8i −0.249886 + 0.741636i
918918 1.82475e8 + 2.99152e7i 0.235871 + 0.0386691i
919919 3.21735e8 5.27457e7i 0.414525 0.0679580i 0.0490892 0.998794i 0.484368π-0.484368\pi
0.365436 + 0.930836i 0.380920π0.380920\pi
920920 5.63627e8 1.89908e8i 0.723816 0.243882i
921921 −4.34683e7 6.41109e7i −0.0556408 0.0820641i
922922 5.12889e8 1.10859e9i 0.654381 1.41442i
923923 7.38061e8 9.70902e8i 0.938614 1.23473i
924924 1.34466e7 + 1.23639e8i 0.0170449 + 0.156726i
925925 5.89305e8 + 1.63620e8i 0.744586 + 0.206733i
926926 3.94192e8 5.81390e8i 0.496449 0.732208i
927927 3.49457e8 + 5.80802e8i 0.438687 + 0.729103i
928928 3.28217e8 1.77954e7i 0.410693 0.0222671i
929929 −4.62155e8 4.87892e8i −0.576422 0.608522i 0.370951 0.928652i 0.379032π-0.379032\pi
−0.947373 + 0.320131i 0.896273π0.896273\pi
930930 −3.08564e8 + 2.34564e8i −0.383616 + 0.291617i
931931 7.63474e7 1.68053e7i 0.0946118 0.0208256i
932932 −4.10145e7 + 3.48380e7i −0.0506629 + 0.0430334i
933933 −562373. + 1.03724e7i −0.000692436 + 0.0127712i
934934 3.75989e8 + 7.09190e8i 0.461460 + 0.870407i
935935 2.71119e8 1.23170e9i 0.331684 1.50686i
936936 5.46477e8 2.52827e8i 0.666414 0.308316i
937937 2.52074e8 4.18950e8i 0.306414 0.509264i −0.664941 0.746896i 0.731543π-0.731543\pi
0.971355 + 0.237632i 0.0763711π0.0763711\pi
938938 −1.99548e8 + 3.76388e8i −0.241791 + 0.456066i
939939 1.09052e8 + 9.26296e7i 0.131715 + 0.111880i
940940 −9.06114e8 + 9.56573e8i −1.09094 + 1.15169i
941941 −1.30601e8 + 1.20085e9i −0.156739 + 1.44119i 0.606505 + 0.795079i 0.292571π0.292571\pi
−0.763244 + 0.646110i 0.776395π0.776395\pi
942942 −5.12498e6 + 1.28627e7i −0.00613111 + 0.0153879i
943943 7.21021e8i 0.859830i
944944 −6.51757e8 8.09655e8i −0.774765 0.962464i
945945 −4.40266e8 −0.521699
946946 −2.03750e8 8.11813e7i −0.240671 0.0958921i
947947 9.34765e8 + 1.01662e8i 1.10066 + 0.119704i 0.640371 0.768066i 0.278781π-0.278781\pi
0.460288 + 0.887770i 0.347746π0.347746\pi
948948 3.56511e7 + 3.37706e7i 0.0418455 + 0.0396381i
949949 −6.57578e8 + 7.74161e8i −0.769394 + 0.905800i
950950 −4.62909e8 2.45419e8i −0.539914 0.286244i
951951 1.18057e8 + 7.10326e7i 0.137262 + 0.0825878i
952952 6.01162e7 + 1.29939e8i 0.0696756 + 0.150601i
953953 −4.10586e8 9.03768e7i −0.474379 0.104419i −0.0286555 0.999589i 0.509123π-0.509123\pi
−0.445724 + 0.895171i 0.647054π0.647054\pi
954954 −7.85417e8 + 4.16402e8i −0.904597 + 0.479587i
955955 4.65239e8 + 2.52245e7i 0.534153 + 0.0289609i
956956 −4.30305e8 5.06594e8i −0.492496 0.579811i
957957 −2.51267e7 1.14152e8i −0.0286681 0.130241i
958958 4.75059e8 + 6.24930e8i 0.540321 + 0.710779i
959959 −4.20338e8 + 3.98165e8i −0.476588 + 0.451448i
960960 −2.67363e6 4.93122e7i −0.00302195 0.0557366i
961961 3.61404e7 2.17449e7i 0.0407214 0.0245012i
962962 4.80284e8 + 3.25640e8i 0.539476 + 0.365774i
963963 6.70957e7 2.41657e8i 0.0751304 0.270595i
964964 −1.24536e8 + 1.35442e7i −0.139016 + 0.0151189i
965965 −6.40942e8 4.87232e8i −0.713242 0.542193i
966966 −1.29259e8 5.98018e7i −0.143394 0.0663411i
967967 −5.42251e8 + 3.67656e8i −0.599682 + 0.406595i −0.822910 0.568172i 0.807651π-0.807651\pi
0.223228 + 0.974766i 0.428341π0.428341\pi
968968 2.92531e8 + 8.68202e8i 0.322512 + 0.957183i
969969 2.83519e6 + 1.72939e7i 0.00311610 + 0.0190074i
970970 −6.48945e8 + 3.95839e9i −0.711038 + 4.33714i
971971 9.61287e7 + 3.23895e7i 0.105001 + 0.0353791i 0.371312 0.928508i 0.378908π-0.378908\pi
−0.266310 + 0.963887i 0.585805π0.585805\pi
972972 8.69546e7 + 3.13182e8i 0.0946877 + 0.341034i
973973 2.67162e7 + 6.70525e7i 0.0290025 + 0.0727908i
974974 −9.87257e8 + 3.93359e8i −1.06845 + 0.425708i
975975 6.78401e8 1.88357e8i 0.731935 0.203221i
976976 −4.03892e8 + 1.19871e9i −0.434426 + 1.28933i
977977 3.08389e8 + 5.05578e7i 0.330686 + 0.0542132i 0.324838 0.945770i 0.394690π-0.394690\pi
0.00584792 + 0.999983i 0.498139π0.498139\pi
978978 6.37049e7 1.04439e7i 0.0681015 0.0111647i
979979 −2.45621e9 + 8.27594e8i −2.61769 + 0.882002i
980980 −2.90622e8 4.28635e8i −0.308781 0.455418i
981981 6.03383e8 1.30419e9i 0.639125 1.38145i
982982 2.63585e8 3.46741e8i 0.278347 0.366160i
983983 1.41891e8 + 1.30467e9i 0.149381 + 1.37353i 0.793482 + 0.608593i 0.208266π0.208266\pi
−0.644102 + 0.764940i 0.722769π0.722769\pi
984984 8.93442e7 + 2.48063e7i 0.0937737 + 0.0260361i
985985 −8.10711e8 + 1.19571e9i −0.848315 + 1.25117i
986986 1.13274e8 + 1.88263e8i 0.118168 + 0.196397i
987987 −1.92944e8 + 1.04611e7i −0.200669 + 0.0108799i
988988 −1.30859e8 1.38146e8i −0.135685 0.143241i
989989 7.65392e7 5.81836e7i 0.0791216 0.0601466i
990990 3.74495e9 8.24327e8i 3.85959 0.849559i
991991 1.22225e9 1.03819e9i 1.25585 1.06673i 0.261007 0.965337i 0.415945π-0.415945\pi
0.994846 0.101395i 0.0323306π-0.0323306\pi
992992 −5.89185e7 + 1.08669e9i −0.0603555 + 1.11319i
993993 1.35083e8 + 2.54793e8i 0.137960 + 0.260219i
994994 −1.89539e8 + 8.61084e8i −0.192992 + 0.876771i
995995 −2.98710e9 + 1.38198e9i −3.03236 + 1.40292i
996996 2.27238e7 3.77673e7i 0.0229987 0.0382241i
997997 1.21298e8 2.28791e8i 0.122396 0.230863i −0.814741 0.579825i 0.803121π-0.803121\pi
0.937137 + 0.348962i 0.113466π0.113466\pi
998998 7.26207e8 + 6.16845e8i 0.730581 + 0.620561i
999999 8.73467e7 9.22108e7i 0.0876093 0.0924880i
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 59.7.d.a.10.7 yes 812
59.6 odd 58 inner 59.7.d.a.6.7 812
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
59.7.d.a.6.7 812 59.6 odd 58 inner
59.7.d.a.10.7 yes 812 1.1 even 1 trivial