Properties

Label 59.7.d.a.10.24
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 / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [59,7,Mod(2,59)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage: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")
 
Copy content magma://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

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content 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 10.24
Character χ\chi == 59.10
Dual form 59.7.d.a.6.24

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(10.5943+4.22114i)q2+(28.73143.12473i)q3+(47.9565+45.4268i)q4+(38.9642+45.8722i)q5+(291.198154.383i)q6+(199.703+120.157i)q7+(9.84607+21.2819i)q8+(103.774+22.8424i)q9+(606.429+321.508i)q10+(2296.40124.507i)q11+(1235.911455.03i)q12+(673.0843057.85i)q13+(1608.51+2115.95i)q14+(1262.831196.22i)q15+(214.4003954.37i)q16+(7008.52+4216.89i)q17+(1002.99+680.041i)q18+(480.5381730.74i)q19+(3952.41+429.851i)q20+(5362.294076.31i)q21+(23803.111012.5i)q22+(310.190+210.314i)q23+(216.391642.226i)q24+(1941.79+11844.4i)q25+(5776.7935236.8i)q26+(17055.6+5746.71i)q27+(4118.70+14834.2i)q28+(15350.4+38526.7i)q29+(18428.27342.46i)q30+(6389.901774.15i)q31+(14899.744220.8i)q32+(65589.8+10752.9i)q33+(92050.1+15090.9i)q34+(13293.1+4478.98i)q35+(3938.98+5809.55i)q36+(27989.360497.8i)q37+(12396.616307.5i)q38+(9783.70+89959.6i)q39+(1359.89377.572i)q40+(20488.6+30218.4i)q41+(39602.865820.4i)q42+(136366.+7393.55i)q43+(104471.110289.i)q44+(5091.29+3870.30i)q45+(4173.99+918.765i)q46+(102528.+87088.1i)q47+(6196.33+114285.i)q48+(29664.255952.7i)q49+(29425.1+133679.i)q50+(214541.99257.4i)q51+(106630.177220.i)q52+(43037.481177.2i)q53+(156434.+132876.i)q54+(95188.8100490.i)q55+(590.890+5433.15i)q56+(19214.7+48225.1i)q57+472958.iq58+(165340.+121833.i)q59+114902.q60+(94618.637699.5i)q61+(75185.1+8176.88i)q62+(17979.3+17030.9i)q63+(180432.212421.i)q64+(166497.+88270.9i)q65+(649485.+390782.i)q66+(16577.3+35831.3i)q67+(527664.116148.i)q68+(9569.365073.36i)q69+(159737.8660.71i)q70+(180099.212029.i)q71+(535.635+2433.42i)q72+(195764.+257523.i)q73+(551895.522783.i)q74+(18779.9346375.i)q75+(101667.61171.1i)q76+(443638.300794.i)q77+(276081.+994354.i)q78+(485.92652.8476i)q79+(189749.+144244.i)q80+(542378.250931.i)q81+(344617.+233656.i)q82+(175853.+521914.i)q83+(71983.1439077.i)q84+(79643.5485804.i)q85+(1.47591e6497290.i)q86+(320654.1.15489e6i)q87+(19960.850097.7i)q88+(211510.+84273.1i)q89+(70275.5+19511.9i)q90+(233007.691539.i)q91+(24429.54005.01i)q92+(189135.+31007.0i)q93+(1.45382e6+489849.i)q94+(60669.2+89480.3i)q95+(566268.+1.22397e6i)q96+(25350.6+33348.1i)q97+(78086.5717994.i)q98+(235462.65375.8i)q99+O(q100)q+(10.5943 + 4.22114i) q^{2} +(-28.7314 - 3.12473i) q^{3} +(47.9565 + 45.4268i) q^{4} +(-38.9642 + 45.8722i) q^{5} +(-291.198 - 154.383i) q^{6} +(199.703 + 120.157i) q^{7} +(9.84607 + 21.2819i) q^{8} +(103.774 + 22.8424i) q^{9} +(-606.429 + 321.508i) q^{10} +(-2296.40 - 124.507i) q^{11} +(-1235.91 - 1455.03i) q^{12} +(-673.084 - 3057.85i) q^{13} +(1608.51 + 2115.95i) q^{14} +(1262.83 - 1196.22i) q^{15} +(-214.400 - 3954.37i) q^{16} +(-7008.52 + 4216.89i) q^{17} +(1002.99 + 680.041i) q^{18} +(480.538 - 1730.74i) q^{19} +(-3952.41 + 429.851i) q^{20} +(-5362.29 - 4076.31i) q^{21} +(-23803.1 - 11012.5i) q^{22} +(-310.190 + 210.314i) q^{23} +(-216.391 - 642.226i) q^{24} +(1941.79 + 11844.4i) q^{25} +(5776.79 - 35236.8i) q^{26} +(17055.6 + 5746.71i) q^{27} +(4118.70 + 14834.2i) q^{28} +(15350.4 + 38526.7i) q^{29} +(18428.2 - 7342.46i) q^{30} +(6389.90 - 1774.15i) q^{31} +(14899.7 - 44220.8i) q^{32} +(65589.8 + 10752.9i) q^{33} +(-92050.1 + 15090.9i) q^{34} +(-13293.1 + 4478.98i) q^{35} +(3938.98 + 5809.55i) q^{36} +(27989.3 - 60497.8i) q^{37} +(12396.6 - 16307.5i) q^{38} +(9783.70 + 89959.6i) q^{39} +(-1359.89 - 377.572i) q^{40} +(-20488.6 + 30218.4i) q^{41} +(-39602.8 - 65820.4i) q^{42} +(-136366. + 7393.55i) q^{43} +(-104471. - 110289. i) q^{44} +(-5091.29 + 3870.30i) q^{45} +(-4173.99 + 918.765i) q^{46} +(-102528. + 87088.1i) q^{47} +(-6196.33 + 114285. i) q^{48} +(-29664.2 - 55952.7i) q^{49} +(-29425.1 + 133679. i) q^{50} +(214541. - 99257.4i) q^{51} +(106630. - 177220. i) q^{52} +(43037.4 - 81177.2i) q^{53} +(156434. + 132876. i) q^{54} +(95188.8 - 100490. i) q^{55} +(-590.890 + 5433.15i) q^{56} +(-19214.7 + 48225.1i) q^{57} +472958. i q^{58} +(165340. + 121833. i) q^{59} +114902. q^{60} +(-94618.6 - 37699.5i) q^{61} +(75185.1 + 8176.88i) q^{62} +(17979.3 + 17030.9i) q^{63} +(180432. - 212421. i) q^{64} +(166497. + 88270.9i) q^{65} +(649485. + 390782. i) q^{66} +(16577.3 + 35831.3i) q^{67} +(-527664. - 116148. i) q^{68} +(9569.36 - 5073.36i) q^{69} +(-159737. - 8660.71i) q^{70} +(-180099. - 212029. i) q^{71} +(535.635 + 2433.42i) q^{72} +(195764. + 257523. i) q^{73} +(551895. - 522783. i) q^{74} +(-18779.9 - 346375. i) q^{75} +(101667. - 61171.1i) q^{76} +(-443638. - 300794. i) q^{77} +(-276081. + 994354. i) q^{78} +(485.926 - 52.8476i) q^{79} +(189749. + 144244. i) q^{80} +(-542378. - 250931. i) q^{81} +(-344617. + 233656. i) q^{82} +(175853. + 521914. i) q^{83} +(-71983.1 - 439077. i) q^{84} +(79643.5 - 485804. i) q^{85} +(-1.47591e6 - 497290. i) q^{86} +(-320654. - 1.15489e6i) q^{87} +(-19960.8 - 50097.7i) q^{88} +(-211510. + 84273.1i) q^{89} +(-70275.5 + 19511.9i) q^{90} +(233007. - 691539. i) q^{91} +(-24429.5 - 4005.01i) q^{92} +(-189135. + 31007.0i) q^{93} +(-1.45382e6 + 489849. i) q^{94} +(60669.2 + 89480.3i) q^{95} +(-566268. + 1.22397e6i) q^{96} +(-25350.6 + 33348.1i) q^{97} +(-78086.5 - 717994. i) q^{98} +(-235462. - 65375.8i) 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 10.5943 + 4.22114i 1.32428 + 0.527642i 0.921757 0.387767i 0.126754π-0.126754\pi
0.402524 + 0.915409i 0.368133π0.368133\pi
33 −28.7314 3.12473i −1.06413 0.115731i −0.440732 0.897639i 0.645281π-0.645281\pi
−0.623394 + 0.781908i 0.714247π0.714247\pi
44 47.9565 + 45.4268i 0.749320 + 0.709794i
55 −38.9642 + 45.8722i −0.311713 + 0.366977i −0.895602 0.444857i 0.853255π-0.853255\pi
0.583888 + 0.811834i 0.301531π0.301531\pi
66 −291.198 154.383i −1.34814 0.714738i
77 199.703 + 120.157i 0.582225 + 0.350313i 0.776000 0.630733i 0.217246π-0.217246\pi
−0.193775 + 0.981046i 0.562073π0.562073\pi
88 9.84607 + 21.2819i 0.0192306 + 0.0415663i
99 103.774 + 22.8424i 0.142351 + 0.0313338i
1010 −606.429 + 321.508i −0.606429 + 0.321508i
1111 −2296.40 124.507i −1.72532 0.0935441i −0.835395 0.549651i 0.814761π-0.814761\pi
−0.889925 + 0.456107i 0.849244π0.849244\pi
1212 −1235.91 1455.03i −0.715227 0.842030i
1313 −673.084 3057.85i −0.306365 1.39183i −0.838375 0.545093i 0.816494π-0.816494\pi
0.532010 0.846738i 0.321437π-0.321437\pi
1414 1608.51 + 2115.95i 0.586190 + 0.771120i
1515 1262.83 1196.22i 0.374173 0.354435i
1616 −214.400 3954.37i −0.0523437 0.965422i
1717 −7008.52 + 4216.89i −1.42653 + 0.858312i −0.998957 0.0456701i 0.985458π-0.985458\pi
−0.427570 + 0.903982i 0.640630π0.640630\pi
1818 1002.99 + 680.041i 0.171980 + 0.116605i
1919 480.538 1730.74i 0.0700596 0.252332i −0.920225 0.391391i 0.871994π-0.871994\pi
0.990284 + 0.139059i 0.0444078π0.0444078\pi
2020 −3952.41 + 429.851i −0.494051 + 0.0537313i
2121 −5362.29 4076.31i −0.579019 0.440159i
2222 −23803.1 11012.5i −2.23545 1.03423i
2323 −310.190 + 210.314i −0.0254943 + 0.0172856i −0.573868 0.818948i 0.694558π-0.694558\pi
0.548373 + 0.836234i 0.315247π0.315247\pi
2424 −216.391 642.226i −0.0156533 0.0464573i
2525 1941.79 + 11844.4i 0.124275 + 0.758043i
2626 5776.79 35236.8i 0.328675 2.00483i
2727 17055.6 + 5746.71i 0.866516 + 0.291963i
2828 4118.70 + 14834.2i 0.187623 + 0.675756i
2929 15350.4 + 38526.7i 0.629400 + 1.57967i 0.803735 + 0.594988i 0.202843π0.202843\pi
−0.174335 + 0.984686i 0.555778π0.555778\pi
3030 18428.2 7342.46i 0.682525 0.271943i
3131 6389.90 1774.15i 0.214491 0.0595531i −0.158621 0.987340i 0.550705π-0.550705\pi
0.373112 + 0.927786i 0.378291π0.378291\pi
3232 14899.7 44220.8i 0.454703 1.34951i
3333 65589.8 + 10752.9i 1.82513 + 0.299215i
3434 −92050.1 + 15090.9i −2.34200 + 0.383952i
3535 −13293.1 + 4478.98i −0.310044 + 0.104466i
3636 3938.98 + 5809.55i 0.0844259 + 0.124519i
3737 27989.3 60497.8i 0.552569 1.19436i −0.407141 0.913365i 0.633474π-0.633474\pi
0.959710 0.280993i 0.0906637π-0.0906637\pi
3838 12396.6 16307.5i 0.225919 0.297192i
3939 9783.70 + 89959.6i 0.164934 + 1.51654i
4040 −1359.89 377.572i −0.0212483 0.00589956i
4141 −20488.6 + 30218.4i −0.297276 + 0.438450i −0.946767 0.321920i 0.895672π-0.895672\pi
0.649491 + 0.760370i 0.274982π0.274982\pi
4242 −39602.8 65820.4i −0.534538 0.888409i
4343 −136366. + 7393.55i −1.71515 + 0.0929925i −0.885306 0.465010i 0.846051π-0.846051\pi
−0.829840 + 0.558002i 0.811568π0.811568\pi
4444 −104471. 110289.i −1.22642 1.29472i
4545 −5091.29 + 3870.30i −0.0558715 + 0.0424724i
4646 −4173.99 + 918.765i −0.0428823 + 0.00943911i
4747 −102528. + 87088.1i −0.987528 + 0.838813i −0.986924 0.161186i 0.948468π-0.948468\pi
−0.000603557 1.00000i 0.500192π0.500192\pi
4848 −6196.33 + 114285.i −0.0560287 + 1.03339i
4949 −29664.2 55952.7i −0.252142 0.475590i
5050 −29425.1 + 133679.i −0.235400 + 1.06944i
5151 214541. 99257.4i 1.61734 0.748260i
5252 106630. 177220.i 0.758347 1.26038i
5353 43037.4 81177.2i 0.289080 0.545263i −0.695856 0.718181i 0.744975π-0.744975\pi
0.984936 + 0.172918i 0.0553196π0.0553196\pi
5454 156434. + 132876.i 0.993459 + 0.843852i
5555 95188.8 100490.i 0.572134 0.603994i
5656 −590.890 + 5433.15i −0.00336467 + 0.0309376i
5757 −19214.7 + 48225.1i −0.103755 + 0.260405i
5858 472958.i 2.42403i
5959 165340. + 121833.i 0.805048 + 0.593210i
6060 114902. 0.531952
6161 −94618.6 37699.5i −0.416857 0.166091i 0.152273 0.988338i 0.451341π-0.451341\pi
−0.569130 + 0.822247i 0.692720π0.692720\pi
6262 75185.1 + 8176.88i 0.315469 + 0.0343093i
6363 17979.3 + 17030.9i 0.0719037 + 0.0681108i
6464 180432. 212421.i 0.688295 0.810323i
6565 166497. + 88270.9i 0.606269 + 0.321423i
6666 649485. + 390782.i 2.25911 + 1.35926i
6767 16577.3 + 35831.3i 0.0551176 + 0.119135i 0.933177 0.359416i 0.117024π-0.117024\pi
−0.878060 + 0.478551i 0.841162π0.841162\pi
6868 −527664. 116148.i −1.67815 0.369389i
6969 9569.36 5073.36i 0.0291297 0.0154436i
7070 −159737. 8660.71i −0.465707 0.0252499i
7171 −180099. 212029.i −0.503196 0.592408i 0.450652 0.892700i 0.351192π-0.351192\pi
−0.953847 + 0.300292i 0.902916π0.902916\pi
7272 535.635 + 2433.42i 0.00143507 + 0.00651957i
7373 195764. + 257523.i 0.503226 + 0.661983i 0.975636 0.219396i 0.0704087π-0.0704087\pi
−0.472409 + 0.881379i 0.656616π0.656616\pi
7474 551895. 522783.i 1.36195 1.29011i
7575 −18779.9 346375.i −0.0445153 0.821036i
7676 101667. 61171.1i 0.231601 0.139349i
7777 −443638. 300794.i −0.971754 0.658866i
7878 −276081. + 994354.i −0.581772 + 2.09535i
7979 485.926 52.8476i 0.000985573 0.000107188i −0.107626 0.994191i 0.534325π-0.534325\pi
0.108612 + 0.994084i 0.465359π0.465359\pi
8080 189749. + 144244.i 0.370604 + 0.281726i
8181 −542378. 250931.i −1.02058 0.472171i
8282 −344617. + 233656.i −0.625022 + 0.423775i
8383 175853. + 521914.i 0.307550 + 0.912777i 0.984291 + 0.176555i 0.0564954π0.0564954\pi
−0.676740 + 0.736222i 0.736608π0.736608\pi
8484 −71983.1 439077.i −0.121449 0.740804i
8585 79643.5 485804.i 0.129686 0.791050i
8686 −1.47591e6 497290.i −2.32040 0.781834i
8787 −320654. 1.15489e6i −0.486944 1.75381i
8888 −19960.8 50097.7i −0.0292907 0.0735140i
8989 −211510. + 84273.1i −0.300027 + 0.119542i −0.515294 0.857014i 0.672317π-0.672317\pi
0.215267 + 0.976555i 0.430938π0.430938\pi
9090 −70275.5 + 19511.9i −0.0963998 + 0.0267653i
9191 233007. 691539.i 0.309203 0.917683i
9292 −24429.5 4005.01i −0.0313726 0.00514328i
9393 −189135. + 31007.0i −0.235138 + 0.0385489i
9494 −1.45382e6 + 489849.i −1.75036 + 0.589764i
9595 60669.2 + 89480.3i 0.0707615 + 0.104365i
9696 −566268. + 1.22397e6i −0.640042 + 1.38343i
9797 −25350.6 + 33348.1i −0.0277762 + 0.0365390i −0.809772 0.586745i 0.800409π-0.800409\pi
0.781995 + 0.623284i 0.214202π0.214202\pi
9898 −78086.5 717994.i −0.0829656 0.762856i
9999 −235462. 65375.8i −0.242670 0.0673770i
100100 −444933. + 656227.i −0.444933 + 0.656227i
101101 −617819. 1.02682e6i −0.599649 0.996625i −0.996882 0.0789070i 0.974857π-0.974857\pi
0.397233 0.917718i 0.369971π-0.369971\pi
102102 2.69189e6 145950.i 2.53662 0.137532i
103103 501612. + 529545.i 0.459046 + 0.484609i 0.913890 0.405962i 0.133064π-0.133064\pi
−0.454844 + 0.890571i 0.650305π0.650305\pi
104104 58449.8 44432.4i 0.0519616 0.0395002i
105105 395927. 87150.0i 0.342016 0.0752835i
106106 798609. 678345.i 0.670528 0.569551i
107107 −19328.5 + 356493.i −0.0157778 + 0.291004i 0.979987 + 0.199063i 0.0637899π0.0637899\pi
−0.995764 + 0.0919411i 0.970693π0.970693\pi
108108 556874. + 1.05038e6i 0.442064 + 0.833822i
109109 351700. 1.59779e6i 0.271577 1.23379i −0.621332 0.783548i 0.713408π-0.713408\pi
0.892909 0.450238i 0.148661π-0.148661\pi
110110 1.43263e6 662807.i 1.07636 0.497977i
111111 −993211. + 1.65073e6i −0.726227 + 1.20700i
112112 432330. 815462.i 0.307724 0.580429i
113113 −1.29159e6 1.09708e6i −0.895134 0.760333i 0.0764393 0.997074i 0.475645π-0.475645\pi
−0.971573 + 0.236741i 0.923921π0.923921\pi
114114 −407130. + 429802.i −0.274801 + 0.290104i
115115 2438.73 22423.8i 0.00160351 0.0147440i
116116 −1.01399e6 + 2.54492e6i −0.649621 + 1.63043i
117117 332700.i 0.207728i
118118 1.23738e6 + 1.98865e6i 0.753108 + 1.21035i
119119 −1.90631e6 −1.13124
120120 37891.8 + 15097.5i 0.0219281 + 0.00873697i
121121 3.49678e6 + 380297.i 1.97384 + 0.214668i
122122 −843279. 798796.i −0.464399 0.439902i
123123 683090. 804196.i 0.367082 0.432162i
124124 387031. + 205191.i 0.202993 + 0.107620i
125125 −1.42480e6 857271.i −0.729495 0.438923i
126126 118587. + 256323.i 0.0592826 + 0.128137i
127127 −3.14148e6 691491.i −1.53364 0.337579i −0.633693 0.773585i 0.718462π-0.718462\pi
−0.899944 + 0.436006i 0.856393π0.856393\pi
128128 169631. 89932.9i 0.0808866 0.0428834i
129129 3.94109e6 + 213680.i 1.83589 + 0.0995392i
130130 1.39130e6 + 1.63797e6i 0.633274 + 0.745548i
131131 −466951. 2.12138e6i −0.207710 0.943636i −0.958943 0.283599i 0.908472π-0.908472\pi
0.751233 0.660037i 0.229459π-0.229459\pi
132132 2.65699e6 + 3.49521e6i 1.15523 + 1.51968i
133133 303927. 287895.i 0.129186 0.122371i
134134 24375.6 + 449581.i 0.0101307 + 0.186850i
135135 −928173. + 558463.i −0.377248 + 0.226983i
136136 −158750. 107635.i −0.0631098 0.0427895i
137137 358617. 1.29162e6i 0.139466 0.502312i −0.860508 0.509436i 0.829854π-0.829854\pi
0.999975 + 0.00712447i 0.00226781π0.00226781\pi
138138 122796. 13354.8i 0.0467246 0.00508161i
139139 3.06781e6 + 2.33209e6i 1.14231 + 0.868361i 0.992727 0.120389i 0.0384141π-0.0384141\pi
0.149582 + 0.988749i 0.452207π0.452207\pi
140140 −840959. 389069.i −0.306472 0.141789i
141141 3.21790e6 2.18179e6i 1.14793 0.778316i
142142 −1.01301e6 3.00651e6i −0.353793 1.05002i
143143 1.16495e6 + 7.10586e6i 0.398380 + 2.43001i
144144 68078.0 415257.i 0.0227992 0.139069i
145145 −2.36542e6 797002.i −0.775897 0.261430i
146146 986931. + 3.55461e6i 0.317123 + 1.14218i
147147 677458. + 1.70029e6i 0.213270 + 0.535268i
148148 4.09049e6 1.62980e6i 1.26180 0.502747i
149149 1.80975e6 502473.i 0.547090 0.151899i 0.0170238 0.999855i 0.494581π-0.494581\pi
0.530066 + 0.847956i 0.322167π0.322167\pi
150150 1.26314e6 3.74885e6i 0.374262 1.11077i
151151 −5.97961e6 980307.i −1.73677 0.284729i −0.791534 0.611125i 0.790717π-0.790717\pi
−0.945233 + 0.326396i 0.894166π0.894166\pi
152152 41565.0 6814.23i 0.0118358 0.00194038i
153153 −823625. + 277512.i −0.229962 + 0.0774831i
154154 −3.43032e6 5.05934e6i −0.939231 1.38526i
155155 −167593. + 362247.i −0.0450051 + 0.0972768i
156156 −3.61739e6 + 4.75859e6i −0.952843 + 1.25344i
157157 −408189. 3.75323e6i −0.105478 0.969854i −0.920585 0.390543i 0.872287π-0.872287\pi
0.815107 0.579311i 0.196678π-0.196678\pi
158158 5371.10 + 1491.28i 0.00136173 + 0.000378083i
159159 −1.49018e6 + 2.19785e6i −0.370722 + 0.546774i
160160 1.44795e6 + 2.40651e6i 0.353503 + 0.587526i
161161 −87216.6 + 4728.75i −0.0208988 + 0.00113310i
162162 −4.68688e6 4.94788e6i −1.10240 1.16379i
163163 −1.07036e6 + 813669.i −0.247155 + 0.187882i −0.721416 0.692502i 0.756508π-0.756508\pi
0.474261 + 0.880384i 0.342715π0.342715\pi
164164 −2.35529e6 + 518438.i −0.533964 + 0.117534i
165165 −3.04891e6 + 2.58977e6i −0.678723 + 0.576513i
166166 −340036. + 6.27159e6i −0.0743362 + 1.37105i
167167 1.19848e6 + 2.26058e6i 0.257325 + 0.485366i 0.978191 0.207708i 0.0666005π-0.0666005\pi
−0.720866 + 0.693075i 0.756256π0.756256\pi
168168 33954.2 154256.i 0.00716087 0.0325322i
169169 −4.51673e6 + 2.08966e6i −0.935759 + 0.432928i
170170 2.89441e6 4.81054e6i 0.589132 0.979145i
171171 89401.6 168629.i 0.0178796 0.0337244i
172172 −6.87550e6 5.84010e6i −1.35120 1.14772i
173173 3.28079e6 3.46348e6i 0.633636 0.668921i −0.327547 0.944835i 0.606222π-0.606222\pi
0.961182 + 0.275914i 0.0889805π0.0889805\pi
174174 1.47786e6 1.35887e7i 0.280535 2.57948i
175175 −1.03541e6 + 2.59869e6i −0.193197 + 0.484887i
176176 9.10751e6i 1.67056i
177177 −4.36976e6 4.01707e6i −0.788020 0.724419i
178178 −2.59651e6 −0.460395
179179 7.07717e6 + 2.81980e6i 1.23396 + 0.491654i 0.893695 0.448676i 0.148104π-0.148104\pi
0.340264 + 0.940330i 0.389484π0.389484\pi
180180 −419976. 45675.1i −0.0720123 0.00783181i
181181 6.50737e6 + 6.16411e6i 1.09741 + 1.03952i 0.999015 + 0.0443776i 0.0141305π0.0141305\pi
0.0983981 + 0.995147i 0.468628π0.468628\pi
182182 5.38761e6 6.34279e6i 0.893680 1.05212i
183183 2.60073e6 + 1.37882e6i 0.424367 + 0.224985i
184184 −7530.03 4530.67i −0.00120877 0.000727292i
185185 1.68459e6 + 3.64118e6i 0.266059 + 0.575078i
186186 −2.13462e6 469866.i −0.331728 0.0730190i
187187 1.66194e7 8.81105e6i 2.54150 1.34742i
188188 −8.87302e6 481081.i −1.33536 0.0724011i
189189 2.71555e6 + 3.19700e6i 0.402229 + 0.473540i
190190 265036. + 1.20407e6i 0.0386406 + 0.175546i
191191 −4.51237e6 5.93592e6i −0.647596 0.851898i 0.348758 0.937213i 0.386603π-0.386603\pi
−0.996354 + 0.0853148i 0.972810π0.972810\pi
192192 −5.84784e6 + 5.53937e6i −0.826212 + 0.782630i
193193 −181119. 3.34055e6i −0.0251938 0.464671i −0.983725 0.179683i 0.942493π-0.942493\pi
0.958531 0.284989i 0.0919899π-0.0919899\pi
194194 −409338. + 246290.i −0.0560630 + 0.0337320i
195195 −4.50786e6 3.05640e6i −0.607948 0.412199i
196196 1.11916e6 4.03085e6i 0.148636 0.535338i
197197 −3.76589e6 + 409565.i −0.492571 + 0.0535703i −0.351034 0.936363i 0.614170π-0.614170\pi
−0.141537 + 0.989933i 0.545204π0.545204\pi
198198 −2.21859e6 1.68653e6i −0.285812 0.217269i
199199 −2.48913e6 1.15159e6i −0.315855 0.146130i 0.255556 0.966794i 0.417742π-0.417742\pi
−0.571411 + 0.820664i 0.693604π0.693604\pi
200200 −232953. + 157946.i −0.0291191 + 0.0197433i
201201 −364327. 1.08128e6i −0.0448645 0.133153i
202202 −2.21097e6 1.34863e7i −0.268243 1.63621i
203203 −1.56374e6 + 9.53837e6i −0.186928 + 1.14021i
204204 1.47976e7 + 4.98589e6i 1.74301 + 0.587290i
205205 −587863. 2.11729e6i −0.0682361 0.245764i
206206 3.07892e6 + 7.72751e6i 0.352206 + 0.883971i
207207 −36993.7 + 14739.6i −0.00417077 + 0.00166179i
208208 −1.19476e7 + 3.31723e6i −1.32767 + 0.368625i
209209 −1.31900e6 + 3.91465e6i −0.144479 + 0.428799i
210210 4.56242e6 + 747971.i 0.492649 + 0.0807656i
211211 −1.46968e7 + 2.40942e6i −1.56450 + 0.256487i −0.880876 0.473347i 0.843046π-0.843046\pi
−0.683624 + 0.729834i 0.739597π0.739597\pi
212212 5.75154e6 1.93792e6i 0.603638 0.203389i
213213 4.51197e6 + 6.65466e6i 0.466904 + 0.688632i
214214 −1.70958e6 + 3.69519e6i −0.174440 + 0.377047i
215215 4.97423e6 6.54349e6i 0.500508 0.658406i
216216 45629.8 + 419559.i 0.00452780 + 0.0416325i
217217 1.48926e6 + 413491.i 0.145744 + 0.0404657i
218218 1.04705e7 1.54428e7i 1.01064 1.49058i
219219 −4.81988e6 8.01070e6i −0.458885 0.762672i
220220 9.12984e6 495005.i 0.857423 0.0464881i
221221 1.76120e7 + 1.85927e7i 1.63166 + 1.72253i
222222 −1.74903e7 + 1.32958e7i −1.59859 + 1.21522i
223223 −1.55989e7 + 3.43359e6i −1.40663 + 0.309623i −0.852466 0.522782i 0.824894π-0.824894\pi
−0.554167 + 0.832406i 0.686963π0.686963\pi
224224 8.28897e6 7.04072e6i 0.737491 0.626430i
225225 −69047.0 + 1.27350e6i −0.00606174 + 0.111802i
226226 −9.05245e6 1.70747e7i −0.784225 1.47921i
227227 −4.14116e6 + 1.88135e7i −0.354033 + 1.60839i 0.377112 + 0.926168i 0.376917π0.376917\pi
−0.731145 + 0.682222i 0.761014π0.761014\pi
228228 −3.11218e6 + 1.43985e6i −0.262579 + 0.121482i
229229 −2.61582e6 + 4.34753e6i −0.217822 + 0.362023i −0.946431 0.322907i 0.895340π-0.895340\pi
0.728609 + 0.684930i 0.240167π0.240167\pi
230230 120490. 227269.i 0.00990305 0.0186791i
231231 1.18064e7 + 1.00285e7i 0.957819 + 0.813578i
232232 −668780. + 706023.i −0.0535574 + 0.0565399i
233233 2.49159e6 2.29098e7i 0.196974 1.81114i −0.311695 0.950182i 0.600897π-0.600897\pi
0.508669 0.860962i 0.330138π-0.330138\pi
234234 1.40437e6 3.52471e6i 0.109606 0.275091i
235235 8.09650e6i 0.623870i
236236 2.39465e6 + 1.33535e7i 0.182182 + 1.01592i
237237 −14126.5 −0.00106118
238238 −2.01960e7 8.04681e6i −1.49808 0.596888i
239239 8.85710e6 + 963268.i 0.648781 + 0.0705592i 0.426592 0.904444i 0.359714π-0.359714\pi
0.222189 + 0.975004i 0.428680π0.428680\pi
240240 −5.00104e6 4.73724e6i −0.361765 0.342682i
241241 −6.80268e6 + 8.00874e6i −0.485992 + 0.572154i −0.949431 0.313975i 0.898339π-0.898339\pi
0.463439 + 0.886129i 0.346615π0.346615\pi
242242 3.54405e7 + 1.87893e7i 2.50065 + 1.32576i
243243 3.55693e6 + 2.14013e6i 0.247888 + 0.149149i
244244 −2.82501e6 6.10616e6i −0.194469 0.420338i
245245 3.72251e6 + 819387.i 0.253127 + 0.0557174i
246246 1.06315e7 5.63644e6i 0.714146 0.378616i
247247 −5.61580e6 304480.i −0.372667 0.0202054i
248248 100673. + 118521.i 0.00660019 + 0.00777035i
249249 −3.42167e6 1.55448e7i −0.221636 1.00690i
250250 −1.14760e7 1.50964e7i −0.734463 0.966170i
251251 −1.65384e7 + 1.56660e7i −1.04586 + 0.990688i −0.999966 0.00825862i 0.997371π-0.997371\pi
−0.0458906 + 0.998946i 0.514613π0.514613\pi
252252 88564.9 + 1.63348e6i 0.00553427 + 0.102074i
253253 738505. 444344.i 0.0456029 0.0274383i
254254 −3.03627e7 2.05864e7i −1.85285 1.25626i
255255 −3.80627e6 + 1.37090e7i −0.229551 + 0.826769i
256256 −1.55561e7 + 1.69183e6i −0.927214 + 0.100841i
257257 1.08757e7 + 8.26749e6i 0.640705 + 0.487051i 0.874366 0.485267i 0.161278π-0.161278\pi
−0.233661 + 0.972318i 0.575071π0.575071\pi
258258 4.08510e7 + 1.88997e7i 2.37872 + 1.10051i
259259 1.28588e7 8.71849e6i 0.740119 0.501813i
260260 3.97473e6 + 1.17966e7i 0.226145 + 0.671175i
261261 712933. + 4.34870e6i 0.0400984 + 0.244590i
262262 4.00764e6 2.44455e7i 0.222836 1.35924i
263263 9.76083e6 + 3.28881e6i 0.536561 + 0.180789i 0.574520 0.818491i 0.305189π-0.305189\pi
−0.0379583 + 0.999279i 0.512085π0.512085\pi
264264 416959. + 1.50175e6i 0.0226611 + 0.0816180i
265265 2.04686e6 + 5.13722e6i 0.109989 + 0.276052i
266266 4.43512e6 1.76711e6i 0.235646 0.0938900i
267267 6.34030e6 1.76038e6i 0.333101 0.0924851i
268268 −832711. + 2.47140e6i −0.0432603 + 0.128392i
269269 −7.74549e6 1.26981e6i −0.397917 0.0652351i −0.0404985 0.999180i 0.512895π-0.512895\pi
−0.357418 + 0.933944i 0.616343π0.616343\pi
270270 −1.21906e7 + 1.99855e6i −0.619349 + 0.101537i
271271 −5.31725e6 + 1.79159e6i −0.267165 + 0.0900183i −0.449696 0.893182i 0.648468π-0.648468\pi
0.182531 + 0.983200i 0.441571π0.441571\pi
272272 1.81778e7 + 2.68102e7i 0.903303 + 1.33227i
273273 −8.85548e6 + 1.91408e7i −0.435235 + 0.940746i
274274 9.25138e6 1.21700e7i 0.449733 0.591614i
275275 −2.98442e6 2.74413e7i −0.143503 1.31949i
276276 689379. + 191405.i 0.0327892 + 0.00910388i
277277 2.03828e6 3.00624e6i 0.0959013 0.141444i −0.776711 0.629857i 0.783114π-0.783114\pi
0.872613 + 0.488413i 0.162424π0.162424\pi
278278 2.26571e7 + 3.76563e7i 1.05455 + 1.75268i
279279 703630. 38149.7i 0.0323990 0.00175662i
280280 −226207. 238803.i −0.0103046 0.0108784i
281281 5.41384e6 4.11549e6i 0.243998 0.185482i −0.476027 0.879431i 0.657924π-0.657924\pi
0.720025 + 0.693948i 0.244130π0.244130\pi
282282 4.33009e7 9.53125e6i 1.93086 0.425014i
283283 1.11714e7 9.48907e6i 0.492888 0.418663i −0.366165 0.930550i 0.619329π-0.619329\pi
0.859053 + 0.511887i 0.171053π0.171053\pi
284284 994881. 1.83495e7i 0.0434326 0.801068i
285285 −1.46351e6 2.76047e6i −0.0632209 0.119247i
286286 −1.76531e7 + 8.01987e7i −0.754609 + 3.42822i
287287 −7.72260e6 + 3.57285e6i −0.326676 + 0.151137i
288288 2.55631e6 4.24862e6i 0.107013 0.177857i
289289 2.00310e7 3.77825e7i 0.829868 1.56530i
290290 −2.16956e7 1.84284e7i −0.889564 0.755603i
291291 832562. 878925.i 0.0337861 0.0356675i
292292 −2.31029e6 + 2.12428e7i −0.0927937 + 0.853224i
293293 9.05585e6 2.27285e7i 0.360020 0.903582i −0.631706 0.775208i 0.717645π-0.717645\pi
0.991726 0.128374i 0.0409757π-0.0409757\pi
294294 2.08730e7i 0.821377i
295295 −1.20311e7 + 2.83739e6i −0.468639 + 0.110523i
296296 1.56309e6 0.0602712
297297 −3.84511e7 1.53203e7i −1.46771 0.584787i
298298 2.12939e7 + 2.31585e6i 0.804649 + 0.0875109i
299299 851893. + 806956.i 0.0318692 + 0.0301881i
300300 1.48341e7 1.74640e7i 0.549410 0.646816i
301301 −2.81211e7 1.49089e7i −1.03118 0.546695i
302302 −5.92114e7 3.56263e7i −2.14973 1.29345i
303303 1.45423e7 + 3.14326e7i 0.522763 + 1.12993i
304304 −6.94702e6 1.52916e6i −0.247274 0.0544291i
305305 5.41609e6 2.87143e6i 0.190891 0.101204i
306306 −9.89711e6 536606.i −0.345417 0.0187280i
307307 −1.57903e6 1.85898e6i −0.0545728 0.0642481i 0.734198 0.678935i 0.237558π-0.237558\pi
−0.788771 + 0.614687i 0.789282π0.789282\pi
308308 −7.61121e6 3.45781e7i −0.260496 1.18345i
309309 −1.27573e7 1.67820e7i −0.432399 0.568811i
310310 −3.30462e6 + 3.13030e6i −0.110927 + 0.105075i
311311 2.61919e6 + 4.83082e7i 0.0870736 + 1.60598i 0.637067 + 0.770809i 0.280148π0.280148\pi
−0.549993 + 0.835169i 0.685370π0.685370\pi
312312 −1.81818e6 + 1.09396e6i −0.0598651 + 0.0360197i
313313 −5.97952e6 4.05422e6i −0.195000 0.132213i 0.459780 0.888033i 0.347928π-0.347928\pi
−0.654780 + 0.755820i 0.727239π0.727239\pi
314314 1.15184e7 4.14857e7i 0.372053 1.34001i
315315 −1.48179e6 + 161155.i −0.0474084 + 0.00515598i
316316 25704.0 + 19539.7i 0.000814591 + 0.000619236i
317317 −1.43081e7 6.61965e6i −0.449165 0.207806i 0.182248 0.983253i 0.441663π-0.441663\pi
−0.631413 + 0.775447i 0.717525π0.717525\pi
318318 −2.50648e7 + 1.69944e7i −0.779441 + 0.528474i
319319 −3.04539e7 9.03839e7i −0.938146 2.78432i
320320 2.71383e6 + 1.65536e7i 0.0828196 + 0.505177i
321321 1.66928e6 1.01821e7i 0.0504677 0.307839i
322322 −943956. 318056.i −0.0282738 0.00952655i
323323 3.93049e6 + 1.41563e7i 0.116638 + 0.420091i
324324 −1.46116e7 3.66723e7i −0.429598 1.07821i
325325 3.49115e7 1.39100e7i 1.01699 0.405208i
326326 −1.47743e7 + 4.10207e6i −0.426437 + 0.118400i
327327 −1.50975e7 + 4.48077e7i −0.431779 + 1.28147i
328328 −844838. 138504.i −0.0239415 0.00392501i
329329 −3.09395e7 + 5.07227e6i −0.868811 + 0.142434i
330330 −4.32327e7 + 1.45668e7i −1.20301 + 0.405342i
331331 −8.36160e6 1.23324e7i −0.230571 0.340068i 0.694750 0.719251i 0.255515π-0.255515\pi
−0.925321 + 0.379184i 0.876205π0.876205\pi
332332 −1.52756e7 + 3.30176e7i −0.417430 + 0.902260i
333333 4.28647e6 5.63875e6i 0.116083 0.152704i
334334 3.15482e6 + 2.90081e7i 0.0846710 + 0.778537i
335335 −2.28958e6 635699.i −0.0609006 0.0169090i
336336 −1.49696e7 + 2.20784e7i −0.394631 + 0.582037i
337337 3.17314e6 + 5.27380e6i 0.0829086 + 0.137795i 0.895537 0.444987i 0.146792π-0.146792\pi
−0.812628 + 0.582782i 0.801964π0.801964\pi
338338 −5.66721e7 + 3.07267e6i −1.46764 + 0.0795731i
339339 3.36810e7 + 3.55566e7i 0.864541 + 0.912685i
340340 2.58879e7 1.96795e7i 0.658659 0.500700i
341341 −1.48947e7 + 3.27856e6i −0.375636 + 0.0826838i
342342 1.65895e6 1.40913e6i 0.0414720 0.0352266i
343343 2.28357e6 4.21179e7i 0.0565889 1.04372i
344344 −1.50002e6 2.82933e6i −0.0368486 0.0695039i
345345 −140136. + 636647.i −0.00341267 + 0.0155039i
346346 4.93773e7 2.28444e7i 1.19206 0.551507i
347347 9.66126e6 1.60571e7i 0.231231 0.384308i −0.719418 0.694577i 0.755591π-0.755591\pi
0.950649 + 0.310269i 0.100419π0.100419\pi
348348 3.70856e7 6.99508e7i 0.879969 1.65980i
349349 −1.40839e7 1.19630e7i −0.331320 0.281426i 0.466249 0.884654i 0.345605π-0.345605\pi
−0.797569 + 0.603228i 0.793881π0.793881\pi
350350 −2.19388e7 + 2.31606e7i −0.511693 + 0.540188i
351351 6.09272e6 5.60216e7i 0.140893 1.29549i
352352 −3.97215e7 + 9.96935e7i −0.910747 + 2.28580i
353353 1.75893e7i 0.399875i 0.979809 + 0.199938i 0.0640739π0.0640739\pi
−0.979809 + 0.199938i 0.935926π0.935926\pi
354354 −2.93377e7 6.10032e7i −0.661327 1.37513i
355355 1.67437e7 0.374253
356356 −1.39715e7 5.56676e6i −0.309666 0.123382i
357357 5.47711e7 + 5.95672e6i 1.20378 + 0.130919i
358358 6.30746e7 + 5.97474e7i 1.37469 + 1.30218i
359359 −6.97356e6 + 8.20991e6i −0.150720 + 0.177441i −0.832341 0.554264i 0.813000π-0.813000\pi
0.681621 + 0.731706i 0.261276π0.261276\pi
360360 −132497. 70245.3i −0.00283986 0.00150560i
361361 3.75470e7 + 2.25913e7i 0.798094 + 0.480197i
362362 4.29212e7 + 9.27727e7i 0.904787 + 1.95566i
363363 −9.92790e7 2.18530e7i −2.07557 0.456868i
364364 4.25886e7 2.25790e7i 0.883058 0.468168i
365365 −1.94409e7 1.05405e6i −0.399795 0.0216763i
366366 2.17326e7 + 2.55856e7i 0.443269 + 0.521857i
367367 −2.79190e6 1.26837e7i −0.0564809 0.256595i 0.939916 0.341405i 0.110903π-0.110903\pi
−0.996397 + 0.0848098i 0.972972π0.972972\pi
368368 898163. + 1.18151e6i 0.0180224 + 0.0237080i
369369 −2.81644e6 + 2.66787e6i −0.0560559 + 0.0530989i
370370 2.47704e6 + 4.56864e7i 0.0489022 + 0.901949i
371371 1.83487e7 1.10401e7i 0.359323 0.216197i
372372 −1.04788e7 7.10479e6i −0.203555 0.138014i
373373 −1.52767e7 + 5.50217e7i −0.294376 + 1.06025i 0.657422 + 0.753523i 0.271647π0.271647\pi
−0.951798 + 0.306725i 0.900767π0.900767\pi
374374 2.13263e8 2.31937e7i 4.07662 0.443359i
375375 3.82577e7 + 2.90827e7i 0.725478 + 0.551494i
376376 −2.86290e6 1.32452e6i −0.0538571 0.0249169i
377377 1.07477e8 7.28710e7i 2.00581 1.35998i
378378 1.52743e7 + 4.53325e7i 0.282804 + 0.839333i
379379 1.49758e7 + 9.13486e7i 0.275089 + 1.67797i 0.657093 + 0.753809i 0.271786π0.271786\pi
−0.382004 + 0.924161i 0.624766π0.624766\pi
380380 −1.15532e6 + 7.04717e6i −0.0210549 + 0.128429i
381381 8.80983e7 + 2.96838e7i 1.59292 + 0.536716i
382382 −2.27488e7 8.19339e7i −0.408102 1.46985i
383383 1.18972e7 + 2.98598e7i 0.211763 + 0.531485i 0.996038 0.0889285i 0.0283443π-0.0283443\pi
−0.784275 + 0.620413i 0.786965π0.786965\pi
384384 −5.15477e6 + 2.05385e6i −0.0910365 + 0.0362723i
385385 3.10841e7 8.63045e6i 0.544698 0.151235i
386386 1.21821e7 3.61552e7i 0.211817 0.628649i
387387 −1.43201e7 2.34766e6i −0.247066 0.0405045i
388388 −2.73062e6 + 447663.i −0.0467484 + 0.00766401i
389389 −6.53871e7 + 2.20315e7i −1.11082 + 0.374278i −0.814122 0.580693i 0.802781π-0.802781\pi
−0.296696 + 0.954972i 0.595885π0.595885\pi
390390 −3.48559e7 5.14086e7i −0.587601 0.866646i
391391 1.28710e6 2.78202e6i 0.0215319 0.0465405i
392392 898705. 1.18223e6i 0.0149197 0.0196265i
393393 6.78742e6 + 6.24093e7i 0.111822 + 1.02819i
394394 −4.16256e7 1.15573e7i −0.680569 0.188959i
395395 −16509.5 + 24349.6i −0.000267881 + 0.000395095i
396396 −8.32213e6 1.38315e7i −0.134014 0.222732i
397397 4.30266e7 2.33284e6i 0.687647 0.0372831i 0.292995 0.956114i 0.405348π-0.405348\pi
0.394652 + 0.918831i 0.370865π0.370865\pi
398398 −2.15094e7 2.27072e7i −0.341177 0.360176i
399399 −9.63184e6 + 7.32193e6i −0.151632 + 0.115268i
400400 4.64209e7 1.02180e7i 0.725326 0.159656i
401401 7.40951e7 6.29369e7i 1.14910 0.976051i 0.149177 0.988811i 0.452338π-0.452338\pi
0.999919 + 0.0127600i 0.00406174π0.00406174\pi
402402 704474. 1.29933e7i 0.0108439 0.200005i
403403 −9.72602e6 1.83452e7i −0.148600 0.280290i
404404 1.70169e7 7.73084e7i 0.258069 1.17242i
405405 3.26441e7 1.51028e7i 0.491405 0.227348i
406406 −5.68293e7 + 9.44511e7i −0.849170 + 1.41133i
407407 −7.18070e7 + 1.35442e8i −1.06508 + 2.00896i
408408 4.22478e6 + 3.58856e6i 0.0622047 + 0.0528372i
409409 −5.55750e7 + 5.86698e7i −0.812287 + 0.857521i −0.992005 0.126197i 0.959723π-0.959723\pi
0.179718 + 0.983718i 0.442481π0.442481\pi
410410 2.70940e6 2.49126e7i 0.0393117 0.361465i
411411 −1.43395e7 + 3.59895e7i −0.206543 + 0.518383i
412412 4.81818e7i 0.688955i
413413 1.83798e7 + 4.41972e7i 0.260910 + 0.627400i
414414 −454138. −0.00640010
415415 −3.07933e7 1.22692e7i −0.430836 0.171661i
416416 −1.45249e8 1.57968e7i −2.01760 0.219427i
417417 −8.08553e7 7.65902e7i −1.11506 1.05625i
418418 −3.04981e7 + 3.59051e7i −0.417584 + 0.491618i
419419 3.35946e7 + 1.78107e7i 0.456696 + 0.242125i 0.680842 0.732431i 0.261614π-0.261614\pi
−0.224145 + 0.974556i 0.571959π0.571959\pi
420420 2.29462e7 + 1.38063e7i 0.309715 + 0.186350i
421421 −1.61228e7 3.48489e7i −0.216070 0.467028i 0.768985 0.639267i 0.220762π-0.220762\pi
−0.985055 + 0.172239i 0.944900π0.944900\pi
422422 −1.65872e8 3.65112e7i −2.20717 0.485835i
423423 −1.26290e7 + 6.69549e6i −0.166859 + 0.0884629i
424424 2.15136e6 + 116643.i 0.0282238 + 0.00153025i
425425 −6.35557e7 7.48236e7i −0.827919 0.974702i
426426 1.97107e7 + 8.95468e7i 0.254961 + 1.15830i
427427 −1.43658e7 1.88978e7i −0.184521 0.242733i
428428 −1.71213e7 + 1.62181e7i −0.218376 + 0.206856i
429429 −1.12667e7 2.07802e8i −0.142700 2.63195i
430430 8.03192e7 4.83265e7i 1.01022 0.607827i
431431 −8.08601e7 5.48245e7i −1.00996 0.684767i −0.0603383 0.998178i 0.519218π-0.519218\pi
−0.949618 + 0.313411i 0.898528π0.898528\pi
432432 1.90679e7 6.86763e7i 0.236511 0.851836i
433433 −2.73632e7 + 2.97593e6i −0.337057 + 0.0366572i −0.275083 0.961421i 0.588705π-0.588705\pi
−0.0619746 + 0.998078i 0.519740π0.519740\pi
434434 1.40322e7 + 1.06670e7i 0.171655 + 0.130489i
435435 6.54714e7 + 3.02903e7i 0.795397 + 0.367990i
436436 8.94487e7 6.06477e7i 1.07923 0.731737i
437437 214941. + 637923.i 0.00257558 + 0.00764405i
438438 −1.72488e7 1.05213e8i −0.205275 1.25212i
439439 2.33574e6 1.42474e7i 0.0276078 0.168400i −0.969424 0.245392i 0.921083π-0.921083\pi
0.997032 + 0.0769920i 0.0245316π0.0245316\pi
440440 3.07585e6 + 1.03637e6i 0.0361083 + 0.0121663i
441441 −1.80028e6 6.48403e6i −0.0209906 0.0756013i
442442 1.08103e8 + 2.71318e8i 1.25190 + 3.14204i
443443 −5.67345e7 + 2.26051e7i −0.652583 + 0.260013i −0.672847 0.739782i 0.734929π-0.734929\pi
0.0202638 + 0.999795i 0.493549π0.493549\pi
444444 −1.22618e8 + 3.40448e7i −1.40090 + 0.388957i
445445 4.37550e6 1.29860e7i 0.0496533 0.147366i
446446 −1.79753e8 2.94690e7i −2.02615 0.332170i
447447 −5.35666e7 + 8.78181e6i −0.599752 + 0.0983244i
448448 6.15569e7 2.07409e7i 0.684609 0.230672i
449449 −8.57158e7 1.26421e8i −0.946939 1.39663i −0.917795 0.397055i 0.870032π-0.870032\pi
−0.0291445 0.999575i 0.509278π-0.509278\pi
450450 −6.10710e6 + 1.32003e7i −0.0670190 + 0.144859i
451451 5.08124e7 6.68426e7i 0.553911 0.728657i
452452 −1.21030e7 1.11285e8i −0.131062 1.20509i
453453 1.68739e8 + 4.68502e7i 1.81519 + 0.503985i
454454 −1.23287e8 + 1.81834e8i −1.31749 + 1.94316i
455455 2.26435e7 + 3.76338e7i 0.240386 + 0.399525i
456456 −1.21551e6 + 65903.2i −0.0128193 + 0.000695043i
457457 7.42158e7 + 7.83486e7i 0.777585 + 0.820886i 0.987629 0.156806i 0.0501196π-0.0501196\pi
−0.210045 + 0.977692i 0.567361π0.567361\pi
458458 −4.60642e7 + 3.50171e7i −0.479476 + 0.364488i
459459 −1.43768e8 + 3.16457e7i −1.48670 + 0.327248i
460460 1.13559e6 964582.i 0.0116667 0.00990982i
461461 914273. 1.68628e7i 0.00933196 0.172118i −0.990152 0.139996i 0.955291π-0.955291\pi
0.999484 0.0321215i 0.0102264π-0.0102264\pi
462462 8.27489e7 + 1.56081e8i 0.839143 + 1.58279i
463463 1.66711e7 7.57375e7i 0.167966 0.763076i −0.815026 0.579425i 0.803277π-0.803277\pi
0.982991 0.183651i 0.0587918π-0.0587918\pi
464464 1.49058e8 6.89613e7i 1.49211 0.690322i
465465 5.94711e6 9.88418e6i 0.0591490 0.0983064i
466466 1.23102e8 2.32195e8i 1.21648 2.29453i
467467 9.43078e7 + 8.01057e7i 0.925970 + 0.786526i 0.977235 0.212159i 0.0680496π-0.0680496\pi
−0.0512654 + 0.998685i 0.516325π0.516325\pi
468468 1.51135e7 1.59551e7i 0.147444 0.155655i
469469 −994852. + 9.14751e6i −0.00964361 + 0.0886716i
470470 3.41764e7 8.57764e7i 0.329180 0.826179i
471471 1.09111e8i 1.04425i
472472 −964888. + 4.71833e6i −0.00917595 + 0.0448706i
473473 3.14072e8 2.96787
474474 −149659. 59629.8i −0.00140530 0.000559923i
475475 2.14328e7 + 2.33095e6i 0.199985 + 0.0217497i
476476 −9.14202e7 8.65978e7i −0.847659 0.802945i
477477 6.32044e6 7.44099e6i 0.0582361 0.0685608i
478478 8.97683e7 + 4.75921e7i 0.821938 + 0.435764i
479479 −7.52882e7 4.52994e7i −0.685047 0.412179i 0.130047 0.991508i 0.458487π-0.458487\pi
−0.815094 + 0.579329i 0.803315π0.803315\pi
480480 −3.40819e7 7.36668e7i −0.308177 0.666114i
481481 −2.03833e8 4.48669e7i −1.83163 0.403173i
482482 −1.05875e8 + 5.61315e7i −0.945483 + 0.501263i
483483 2.52063e6 + 136665.i 0.0223701 + 0.00121287i
484484 1.50417e8 + 1.77085e8i 1.32667 + 1.56187i
485485 −541986. 2.46227e6i −0.00475076 0.0215829i
486486 2.86492e7 + 3.76874e7i 0.249576 + 0.328312i
487487 −1.12404e8 + 1.06475e8i −0.973188 + 0.921853i −0.996964 0.0778648i 0.975190π-0.975190\pi
0.0237760 + 0.999717i 0.492431π0.492431\pi
488488 −129303. 2.38486e6i −0.00111263 0.0205212i
489489 3.32956e7 2.00333e7i 0.284747 0.171327i
490490 3.59785e7 + 2.43940e7i 0.305812 + 0.207346i
491491 −3.39440e7 + 1.22255e8i −0.286760 + 1.03282i 0.670101 + 0.742270i 0.266251π0.266251\pi
−0.956861 + 0.290546i 0.906163π0.906163\pi
492492 6.92907e7 7.53581e6i 0.581808 0.0632754i
493493 −2.70046e8 2.05284e8i −2.25371 1.71322i
494494 −5.82100e7 2.69308e7i −0.482855 0.223392i
495495 1.21735e7 8.25385e6i 0.100369 0.0680520i
496496 −8.38562e6 2.48876e7i −0.0687211 0.203957i
497497 −1.04895e7 6.39832e7i −0.0854448 0.521190i
498498 2.93667e7 1.79129e8i 0.237776 1.45037i
499499 6.75184e7 + 2.27496e7i 0.543401 + 0.183093i 0.577597 0.816322i 0.303991π-0.303991\pi
−0.0341962 + 0.999415i 0.510887π0.510887\pi
500500 −2.93851e7 1.05836e8i −0.235081 0.846685i
501501 −2.73704e7 6.86945e7i −0.217654 0.546271i
502502 −2.41340e8 + 9.61587e7i −1.90774 + 0.760112i
503503 −1.86222e8 + 5.17043e7i −1.46328 + 0.406277i −0.905726 0.423864i 0.860673π-0.860673\pi
−0.557553 + 0.830142i 0.688259π0.688259\pi
504504 −185425. + 550321.i −0.00144836 + 0.00429858i
505505 7.11754e7 + 1.16686e7i 0.552657 + 0.0906036i
506506 9.69955e6 1.59016e6i 0.0748687 0.0122741i
507507 1.36302e8 4.59254e7i 1.04587 0.352394i
508508 −1.19242e8 1.75869e8i −0.909574 1.34152i
509509 −5.35953e7 + 1.15844e8i −0.406419 + 0.878460i 0.591001 + 0.806671i 0.298733π0.298733\pi
−0.997420 + 0.0717889i 0.977129π0.977129\pi
510510 −9.81920e7 + 1.29169e8i −0.740228 + 0.973754i
511511 8.15136e6 + 7.49505e7i 0.0610896 + 0.561710i
512512 −1.83786e8 5.10280e7i −1.36931 0.380188i
513513 1.81420e7 2.67574e7i 0.134379 0.198195i
514514 8.03217e7 + 1.33496e8i 0.591485 + 0.983056i
515515 −4.38363e7 + 2.37673e6i −0.320931 + 0.0174004i
516516 1.79294e8 + 1.89279e8i 1.30502 + 1.37769i
517517 2.46289e8 1.87224e8i 1.78227 1.35484i
518518 1.73031e8 3.80871e7i 1.24490 0.274024i
519519 −1.05084e8 + 8.92592e7i −0.751683 + 0.638485i
520520 −239238. + 4.41249e6i −0.00170145 + 0.0313815i
521521 1.00678e8 + 1.89898e8i 0.711902 + 1.34279i 0.930253 + 0.366919i 0.119587π0.119587\pi
−0.218351 + 0.975870i 0.570068π0.570068\pi
522522 −1.08035e7 + 4.90806e7i −0.0759542 + 0.345063i
523523 1.87924e8 8.69427e7i 1.31364 0.607754i 0.367052 0.930201i 0.380367π-0.380367\pi
0.946588 + 0.322446i 0.104505π0.104505\pi
524524 7.39742e7 1.22946e8i 0.514146 0.854517i
525525 3.78691e7 7.14286e7i 0.261702 0.493622i
526526 8.95262e7 + 7.60442e7i 0.615167 + 0.522527i
527527 −3.73024e7 + 3.93796e7i −0.254862 + 0.269054i
528528 2.84585e7 2.61672e8i 0.193335 1.77768i
529529 −5.47417e7 + 1.37391e8i −0.369787 + 0.928095i
530530 6.30651e7i 0.423605i
531531 1.43750e7 + 1.64198e7i 0.0960119 + 0.109669i
532532 2.76534e7 0.183660
533533 1.06194e8 + 4.23115e7i 0.701323 + 0.279433i
534534 7.46015e7 + 8.11340e6i 0.489919 + 0.0532819i
535535 −1.56000e7 1.47771e7i −0.101874 0.0965000i
536536 −599338. + 705595.i −0.00389204 + 0.00458206i
537537 −1.94526e8 1.03131e8i −1.25619 0.665989i
538538 −7.66977e7 4.61475e7i −0.492533 0.296347i
539539 6.11544e7 + 1.32183e8i 0.390537 + 0.844131i
540540 −6.98811e7 1.53820e7i −0.443791 0.0976858i
541541 9.29603e7 4.92844e7i 0.587091 0.311256i −0.148253 0.988949i 0.547365π-0.547365\pi
0.735345 + 0.677693i 0.237020π0.237020\pi
542542 −6.38949e7 3.46428e6i −0.401299 0.0217578i
543543 −1.67705e8 1.97437e8i −1.04748 1.23319i
544544 8.20491e7 + 3.72753e8i 0.509656 + 2.31539i
545545 5.95903e7 + 7.83897e7i 0.368117 + 0.484250i
546546 −1.74613e8 + 1.65402e8i −1.07275 + 1.01616i
547547 −1.01695e6 1.87566e7i −0.00621353 0.114602i −0.999995 0.00325124i 0.998965π-0.998965\pi
0.993781 0.111351i 0.0355177π-0.0355177\pi
548548 7.58722e7 4.56508e7i 0.461043 0.277400i
549549 −8.95779e6 6.07353e6i −0.0541357 0.0367049i
550550 8.42158e7 3.03318e8i 0.506180 1.82310i
551551 7.40562e7 8.05410e6i 0.442697 0.0481462i
552552 202191. + 153702.i 0.00120211 + 0.000913823i
553553 103391. + 47833.8i 0.000611374 + 0.000282852i
554554 3.42838e7 2.32450e7i 0.201632 0.136710i
555555 −3.70229e7 1.09880e8i −0.216567 0.642746i
556556 4.11820e7 + 2.51199e8i 0.239598 + 1.46148i
557557 3.65666e7 2.23046e8i 0.211602 1.29071i −0.640752 0.767748i 0.721377π-0.721377\pi
0.852354 0.522965i 0.175174π-0.175174\pi
558558 7.61547e6 + 2.56595e6i 0.0438323 + 0.0147688i
559559 1.14394e8 + 4.12011e8i 0.654891 + 2.35870i
560560 2.05616e7 + 5.16057e7i 0.117083 + 0.293855i
561561 −5.05031e8 + 2.01223e8i −2.86042 + 1.13970i
562562 7.47276e7 2.07480e7i 0.420990 0.116887i
563563 5.69961e7 1.69159e8i 0.319389 0.947913i −0.660922 0.750455i 0.729835π-0.729835\pi
0.980311 0.197459i 0.0632689π-0.0632689\pi
564564 2.53431e8 + 4.15479e7i 1.41261 + 0.231586i
565565 1.00651e8 1.65009e7i 0.558050 0.0914877i
566566 1.58407e8 5.33736e7i 0.873627 0.294359i
567567 −7.81635e7 1.15282e8i −0.428800 0.632432i
568568 2.73912e6 5.92051e6i 0.0149474 0.0323083i
569569 −7.43850e7 + 9.78517e7i −0.403783 + 0.531168i −0.952378 0.304921i 0.901370π-0.901370\pi
0.548594 + 0.836089i 0.315163π0.315163\pi
570570 −3.85246e6 3.54228e7i −0.0208024 0.191275i
571571 −2.57875e8 7.15988e7i −1.38517 0.384589i −0.506587 0.862189i 0.669093π-0.669093\pi
−0.878578 + 0.477599i 0.841507π0.841507\pi
572572 −2.66930e8 + 3.93692e8i −1.42629 + 2.10363i
573573 1.11099e8 + 1.84647e8i 0.590533 + 0.981474i
574574 −9.68967e7 + 5.25358e6i −0.512358 + 0.0277792i
575575 −3.09337e6 3.26563e6i −0.0162715 0.0171776i
576576 2.35764e7 1.79223e7i 0.123370 0.0937834i
577577 3.18496e8 7.01063e7i 1.65797 0.364947i 0.715338 0.698778i 0.246273π-0.246273\pi
0.942633 + 0.333831i 0.108342π0.108342\pi
578578 3.71699e8 3.15724e8i 1.92490 1.63502i
579579 −5.23450e6 + 9.65447e7i −0.0269674 + 0.497385i
580580 −7.72319e7 1.45675e8i −0.395834 0.746622i
581581 −2.75934e7 + 1.25358e8i −0.140694 + 0.639180i
582582 1.25304e7 5.79720e6i 0.0635620 0.0294069i
583583 −1.08938e8 + 1.81057e8i −0.549762 + 0.913712i
584584 −3.55308e6 + 6.70181e6i −0.0178388 + 0.0336476i
585585 1.52617e7 + 1.29634e7i 0.0762315 + 0.0647516i
586586 1.91880e8 2.02565e8i 0.953535 1.00664i
587587 −1.23178e7 + 1.13260e8i −0.0609002 + 0.559968i 0.923447 + 0.383727i 0.125360π0.125360\pi
−0.984347 + 0.176242i 0.943606π0.943606\pi
588588 −4.47503e7 + 1.12315e8i −0.220122 + 0.552465i
589589 1.19118e7i 0.0582951i
590590 −1.39437e8 2.07248e7i −0.678926 0.100910i
591591 1.09479e8 0.530357
592592 −2.45232e8 9.77092e7i −1.18198 0.470945i
593593 −9.92700e7 1.07963e7i −0.476052 0.0517737i −0.133052 0.991109i 0.542478π-0.542478\pi
−0.343000 + 0.939335i 0.611443π0.611443\pi
594594 −3.42691e8 3.24614e8i −1.63510 1.54885i
595595 7.42780e7 8.74468e7i 0.352622 0.415138i
596596 1.09615e8 + 5.81141e7i 0.517762 + 0.274500i
597597 6.79177e7 + 4.08647e7i 0.319198 + 0.192055i
598598 5.61890e6 + 1.21450e7i 0.0262753 + 0.0567931i
599599 1.36976e8 + 3.01507e7i 0.637330 + 0.140287i 0.521870 0.853025i 0.325235π-0.325235\pi
0.115460 + 0.993312i 0.463166π0.463166\pi
600600 7.18661e6 3.81010e6i 0.0332713 0.0176394i
601601 −9.49834e7 5.14985e6i −0.437547 0.0237231i −0.165950 0.986134i 0.553069π-0.553069\pi
−0.271597 + 0.962411i 0.587552π0.587552\pi
602602 −2.34990e8 2.76651e8i −1.07711 1.26807i
603603 901822. + 4.09702e6i 0.00411309 + 0.0186860i
604604 −2.42229e8 3.18646e8i −1.09930 1.44610i
605605 −1.53694e8 + 1.45587e8i −0.694050 + 0.657439i
606606 2.13832e7 + 3.94390e8i 0.0960849 + 1.77218i
607607 2.21199e8 1.33091e8i 0.989046 0.595089i 0.0734965 0.997295i 0.476584π-0.476584\pi
0.915549 + 0.402207i 0.131757π0.131757\pi
608608 −6.93749e7 4.70374e7i −0.308668 0.209282i
609609 7.47331e7 2.69164e8i 0.330873 1.19170i
610610 6.95002e7 7.55860e6i 0.306194 0.0333006i
611611 3.35313e8 + 2.54898e8i 1.47003 + 1.11749i
612612 −5.21046e7 2.41062e7i −0.227312 0.105166i
613613 9.21279e7 6.24643e7i 0.399954 0.271175i −0.344584 0.938755i 0.611980π-0.611980\pi
0.744538 + 0.667580i 0.232670π0.232670\pi
614614 −8.88167e6 2.63598e7i −0.0383698 0.113877i
615615 1.02742e7 + 6.26697e7i 0.0441694 + 0.269421i
616616 2.03339e6 1.24031e7i 0.00869917 0.0530626i
617617 3.23742e8 + 1.09081e8i 1.37830 + 0.464402i 0.908320 0.418276i 0.137366π-0.137366\pi
0.469977 + 0.882678i 0.344262π0.344262\pi
618618 −6.43154e7 2.31643e8i −0.272489 0.981418i
619619 6.47185e7 + 1.62431e8i 0.272871 + 0.684853i 0.999999 0.00164844i 0.000524714π-0.000524714\pi
−0.727128 + 0.686502i 0.759145π0.759145\pi
620620 −2.44929e7 + 9.75886e6i −0.102770 + 0.0409472i
621621 −6.49910e6 + 1.80446e6i −0.0271380 + 0.00753483i
622622 −1.76167e8 + 5.22845e8i −0.732071 + 2.17271i
623623 −5.23652e7 8.58483e6i −0.216560 0.0355032i
624624 3.53636e8 5.79757e7i 1.45547 0.238612i
625625 −8.28817e7 + 2.79261e7i −0.339483 + 0.114385i
626626 −4.62352e7 6.81918e7i −0.188473 0.277977i
627627 5.01289e7 1.08352e8i 0.203369 0.439576i
628628 1.50922e8 1.98535e8i 0.609360 0.801599i
629629 5.89491e7 + 5.42028e8i 0.236878 + 2.17806i
630630 −1.63787e7 4.54753e6i −0.0655026 0.0181867i
631631 −6.47033e7 + 9.54302e7i −0.257536 + 0.379838i −0.934373 0.356295i 0.884040π-0.884040\pi
0.676837 + 0.736133i 0.263350π0.263350\pi
632632 5909.16 + 9821.10i 2.34085e−5 + 3.89053e-5i
633633 4.29789e8 2.33025e7i 1.69451 0.0918736i
634634 −1.23642e8 1.30527e8i −0.485173 0.512191i
635635 1.54125e8 1.17163e8i 0.601939 0.457582i
636636 −1.71305e8 + 3.77072e7i −0.665886 + 0.146573i
637637 −1.51129e8 + 1.28370e8i −0.584693 + 0.496643i
638638 5.88866e7 1.08610e9i 0.226754 4.18223i
639639 −1.38463e7 2.61170e7i −0.0530680 0.100097i
640640 −2.48413e6 + 1.12855e7i −0.00947621 + 0.0430509i
641641 −4.39473e8 + 2.03322e8i −1.66862 + 0.771988i −0.669037 + 0.743229i 0.733293π0.733293\pi
−0.999586 + 0.0287590i 0.990844π0.990844\pi
642642 6.06650e7 1.00826e8i 0.229262 0.381037i
643643 9.66264e7 1.82257e8i 0.363465 0.685568i −0.632572 0.774501i 0.718001π-0.718001\pi
0.996038 + 0.0889330i 0.0283457π0.0283457\pi
644644 −4.39742e6 3.73520e6i −0.0164642 0.0139848i
645645 −1.63363e8 + 1.72461e8i −0.608801 + 0.642704i
646646 −1.81152e7 + 1.66567e8i −0.0671965 + 0.617861i
647647 −6.52358e7 + 1.63729e8i −0.240865 + 0.604525i −0.998860 0.0477353i 0.984800π-0.984800\pi
0.757995 + 0.652260i 0.226179π0.226179\pi
648648 1.40135e7i 0.0515018i
649649 −3.64518e8 3.00363e8i −1.33347 1.09878i
650650 4.28577e8 1.56059
651651 −4.14965e7 1.65337e7i −0.150407 0.0599277i
652652 −8.82933e7 9.60247e6i −0.318555 0.0346450i
653653 −1.03388e8 9.79341e7i −0.371304 0.351718i 0.479182 0.877716i 0.340933π-0.340933\pi
−0.850486 + 0.525998i 0.823692π0.823692\pi
654654 −3.49086e8 + 4.10976e8i −1.24796 + 1.46921i
655655 1.15507e8 + 6.12377e7i 0.411039 + 0.217919i
656656 1.23887e8 + 7.45406e7i 0.438849 + 0.264047i
657657 1.44327e7 + 3.11958e7i 0.0508923 + 0.110002i
658658 −3.49191e8 7.68628e7i −1.22570 0.269798i
659659 3.60381e7 1.91062e7i 0.125923 0.0667603i −0.404256 0.914646i 0.632469π-0.632469\pi
0.530179 + 0.847886i 0.322125π0.322125\pi
660660 −2.63860e8 1.43061e7i −0.917786 0.0497609i
661661 −1.38681e8 1.63268e8i −0.480190 0.565323i 0.467714 0.883880i 0.345078π-0.345078\pi
−0.947904 + 0.318557i 0.896802π0.896802\pi
662662 −3.65280e7 1.65948e8i −0.125908 0.572004i
663663 −4.47919e8 5.89227e8i −1.53695 2.02182i
664664 −9.37587e6 + 8.88130e6i −0.0320264 + 0.0303370i
665665 1.36410e6 + 2.51594e7i 0.00463854 + 0.0855529i
666666 6.92139e7 4.16446e7i 0.234299 0.140973i
667667 −1.28642e7 8.72217e6i −0.0433517 0.0293932i
668668 −4.52158e7 + 1.62852e8i −0.151691 + 0.546342i
669669 4.58909e8 4.99094e7i 1.53267 0.166688i
670670 −2.15730e7 1.63994e7i −0.0717277 0.0545259i
671671 2.12588e8 + 9.83538e7i 0.703675 + 0.325555i
672672 −2.60154e8 + 1.76389e8i −0.857281 + 0.581251i
673673 7.72978e7 + 2.29412e8i 0.253584 + 0.752610i 0.996528 + 0.0832569i 0.0265322π0.0265322\pi
−0.742944 + 0.669353i 0.766571π0.766571\pi
674674 1.13556e7 + 6.92662e7i 0.0370878 + 0.226226i
675675 −3.49479e7 + 2.13173e8i −0.113635 + 0.693140i
676676 −3.11533e8 1.04968e8i −1.00847 0.339794i
677677 1.54431e7 + 5.56209e7i 0.0497700 + 0.179255i 0.984257 0.176741i 0.0565554π-0.0565554\pi
−0.934487 + 0.355996i 0.884142π0.884142\pi
678678 2.06736e8 + 5.18868e8i 0.663325 + 1.66482i
679679 −9.06962e6 + 3.61367e6i −0.0289721 + 0.0115435i
680680 1.11230e7 3.08829e6i 0.0353749 0.00982180i
681681 1.77768e8 5.27597e8i 0.562876 1.67056i
682682 −1.71637e8 2.81385e7i −0.541076 0.0887049i
683683 2.36683e8 3.88022e7i 0.742855 0.121785i 0.221543 0.975151i 0.428891π-0.428891\pi
0.521313 + 0.853366i 0.325442π0.325442\pi
684684 1.19477e7 4.02564e6i 0.0373349 0.0125796i
685685 4.52762e7 + 6.67774e7i 0.140864 + 0.207758i
686686 2.01978e8 4.36569e8i 0.625651 1.35232i
687687 8.87411e7 1.16737e8i 0.273687 0.360029i
688688 5.84737e7 + 5.37656e8i 0.179554 + 1.65097i
689689 −2.77196e8 7.69630e7i −0.847479 0.235301i
690690 −4.17201e6 + 6.15326e6i −0.0126998 + 0.0187309i
691691 −2.63644e8 4.38180e8i −0.799069 1.32806i −0.941075 0.338197i 0.890183π-0.890183\pi
0.142007 0.989866i 0.454644π-0.454644\pi
692692 3.14670e8 1.70609e7i 0.949592 0.0514854i
693693 −3.91672e7 4.13483e7i −0.117685 0.124239i
694694 1.70133e8 1.29332e8i 0.508992 0.386926i
695695 −2.26512e8 + 4.98591e7i −0.674742 + 0.148522i
696696 2.14211e7 1.81953e7i 0.0635353 0.0539673i
697697 1.61671e7 2.98184e8i 0.0477456 0.880616i
698698 −9.87114e7 1.86189e8i −0.290269 0.547506i
699699 −1.43174e8 + 6.50445e8i −0.419210 + 1.90449i
700700 −1.67705e8 + 7.75886e7i −0.488936 + 0.226206i
701701 −1.72452e8 + 2.86617e8i −0.500626 + 0.832047i −0.999398 0.0346860i 0.988957π-0.988957\pi
0.498772 + 0.866733i 0.333784π0.333784\pi
702702 3.01023e8 5.67789e8i 0.870138 1.64125i
703703 −9.12563e7 7.75138e7i −0.262662 0.223107i
704704 −4.40793e8 + 4.65340e8i −1.26333 + 1.33368i
705705 −2.52994e7 + 2.32624e8i −0.0722009 + 0.663876i
706706 −7.42468e7 + 1.86345e8i −0.210991 + 0.529547i
707707 2.79296e8i 0.790325i
708708 −2.70755e7 3.91149e8i −0.0762916 1.10215i
709709 −1.14471e8 −0.321187 −0.160594 0.987021i 0.551341π-0.551341\pi
−0.160594 + 0.987021i 0.551341π0.551341\pi
710710 1.77387e8 + 7.06772e7i 0.495616 + 0.197472i
711711 51633.6 + 5615.49i 0.000143656 + 1.56235e-5i
712712 −3.87603e6 3.67157e6i −0.0107386 0.0101721i
713713 −1.60895e6 + 1.89421e6i −0.00443890 + 0.00522587i
714714 5.55115e8 + 2.94303e8i 1.52506 + 0.808538i
715715 −3.71352e8 2.23435e8i −1.01594 0.611271i
716716 2.11302e8 + 4.56721e8i 0.575657 + 1.24426i
717717 −2.51467e8 5.53521e7i −0.682219 0.150168i
718718 −1.08535e8 + 5.75415e7i −0.293222 + 0.155456i
719719 −3.27531e8 1.77582e7i −0.881182 0.0477763i −0.392007 0.919962i 0.628219π-0.628219\pi
−0.489174 + 0.872186i 0.662702π0.662702\pi
720720 1.63962e7 + 1.93030e7i 0.0439283 + 0.0517164i
721721 3.65447e7 + 1.66024e8i 0.0975032 + 0.442961i
722722 3.02422e8 + 3.97829e8i 0.803529 + 1.05702i
723723 2.20476e8 2.08846e8i 0.583373 0.552600i
724724 3.20549e7 + 5.91218e8i 0.0844655 + 1.55787i
725725 −4.26519e8 + 2.56628e8i −1.11924 + 0.673426i
726726 −9.59543e8 6.50586e8i −2.50758 1.70018i
727727 9.71038e7 3.49736e8i 0.252716 0.910201i −0.722943 0.690908i 0.757211π-0.757211\pi
0.975659 0.219293i 0.0703751π-0.0703751\pi
728728 1.70115e7 1.85011e6i 0.0440908 0.00479516i
729729 2.51317e8 + 1.91046e8i 0.648694 + 0.493124i
730730 −2.01512e8 9.32296e7i −0.518004 0.239654i
731731 9.24547e8 6.26858e8i 2.36688 1.60479i
732732 6.20864e7 + 1.84266e8i 0.158294 + 0.469799i
733733 −8.52302e7 5.19881e8i −0.216412 1.32005i −0.841821 0.539757i 0.818516π-0.818516\pi
0.625409 0.780297i 0.284932π-0.284932\pi
734734 2.39616e7 1.46160e8i 0.0605938 0.369606i
735735 −1.04393e8 3.51740e7i −0.262911 0.0885849i
736736 4.67850e6 + 1.68504e7i 0.0117347 + 0.0422647i
737737 −3.36069e7 8.43470e7i −0.0839511 0.210701i
738738 −4.10995e7 + 1.63755e7i −0.102251 + 0.0407405i
739739 −4.88107e8 + 1.35522e8i −1.20943 + 0.335798i −0.812999 0.582265i 0.802166π-0.802166\pi
−0.396435 + 0.918063i 0.629753π0.629753\pi
740740 −8.46201e7 + 2.51143e8i −0.208823 + 0.619764i
741741 1.60398e8 + 2.62960e7i 0.394226 + 0.0646301i
742742 2.40993e8 3.95088e7i 0.589919 0.0967124i
743743 4.33184e8 1.45957e8i 1.05610 0.355842i 0.262914 0.964819i 0.415316π-0.415316\pi
0.793188 + 0.608977i 0.208420π0.208420\pi
744744 −2.52212e6 3.71985e6i −0.00612417 0.00903248i
745745 −4.74657e7 + 1.02595e8i −0.114792 + 0.248118i
746746 −3.94099e8 + 5.18429e8i −0.949268 + 1.24874i
747747 6.32723e6 + 5.81779e7i 0.0151793 + 0.139571i
748748 1.19727e9 + 3.32419e8i 2.86079 + 0.794295i
749749 −4.66952e7 + 6.88703e7i −0.111129 + 0.163903i
750750 2.82549e8 + 4.69600e8i 0.669746 + 1.11313i
751751 2.04890e8 1.11088e7i 0.483728 0.0262269i 0.189337 0.981912i 0.439366π-0.439366\pi
0.294391 + 0.955685i 0.404883π0.404883\pi
752752 3.66361e8 + 3.86762e8i 0.861500 + 0.909474i
753753 5.24123e8 3.98428e8i 1.22758 0.933179i
754754 1.44623e9 3.18340e8i 3.37384 0.742639i
755755 2.77959e8 2.36101e8i 0.645863 0.548601i
756756 −1.50009e7 + 2.76676e8i −0.0347178 + 0.640333i
757757 −1.95816e8 3.69347e8i −0.451398 0.851427i −0.999883 0.0152668i 0.995140π-0.995140\pi
0.548486 0.836160i 0.315205π-0.315205\pi
758758 −2.26937e8 + 1.03098e9i −0.521072 + 2.36725i
759759 −2.26068e7 + 1.04590e7i −0.0517027 + 0.0239202i
760760 −1.30696e6 + 2.17219e6i −0.00297729 + 0.00494830i
761761 −8.91031e7 + 1.68066e8i −0.202180 + 0.381352i −0.963781 0.266694i 0.914069π-0.914069\pi
0.761601 + 0.648046i 0.224414π0.224414\pi
762762 8.08037e8 + 6.86352e8i 1.82627 + 1.55125i
763763 2.62222e8 2.76824e8i 0.590330 0.623204i
764764 5.32524e7 4.89648e8i 0.119415 1.09800i
765765 1.93618e7 4.85945e7i 0.0432476 0.108543i
766766 3.66562e8i 0.815570i
767767 2.61259e8 5.87589e8i 0.579009 1.30223i
768768 4.52235e8 0.998344
769769 1.18087e8 + 4.70503e7i 0.259672 + 0.103463i 0.496341 0.868128i 0.334677π-0.334677\pi
−0.236670 + 0.971590i 0.576056π0.576056\pi
770770 3.65743e8 + 3.97769e7i 0.801131 + 0.0871282i
771771 −2.86641e8 2.71520e8i −0.625424 0.592433i
772772 1.43065e8 1.68429e8i 0.310943 0.366070i
773773 −2.59275e8 1.37459e8i −0.561335 0.297601i 0.163477 0.986547i 0.447729π-0.447729\pi
−0.724813 + 0.688946i 0.758074π0.758074\pi
774774 −1.41801e8 8.53189e7i −0.305814 0.184002i
775775 3.34216e7 + 7.22397e7i 0.0717997 + 0.155192i
776776 −959316. 211161.i −0.00205294 0.000451887i
777777 −3.96695e8 + 2.10314e8i −0.845655 + 0.448338i
778778 −7.85725e8 4.26008e7i −1.66852 0.0904646i
779779 4.24547e7 + 4.99816e7i 0.0898077 + 0.105730i
780780 −7.73384e7 3.51352e8i −0.162971 0.740387i
781781 3.87181e8 + 5.09328e8i 0.812757 + 1.06916i
782782 2.53792e7 2.40404e7i 0.0530710 0.0502715i
783783 4.04096e7 + 7.45311e8i 0.0841781 + 1.55257i
784784 −2.14897e8 + 1.29300e8i −0.445947 + 0.268317i
785785 1.88074e8 + 1.27517e8i 0.388793 + 0.263608i
786786 −1.91531e8 + 6.89831e8i −0.394431 + 1.42061i
787787 −5.38061e8 + 5.85177e7i −1.10384 + 0.120050i −0.641848 0.766832i 0.721832π-0.721832\pi
−0.461995 + 0.886882i 0.652866π0.652866\pi
788788 −1.99204e8 1.51431e8i −0.407117 0.309482i
789789 −2.70166e8 1.24992e8i −0.550046 0.254479i
790790 −277689. + 188278.i −0.000563218 + 0.000381871i
791791 −1.26111e8 3.74284e8i −0.254814 0.756262i
792792 −927055. 5.65479e6i −0.00186608 0.0113826i
793793 −5.15932e7 + 3.14705e8i −0.103460 + 0.631079i
794794 4.65682e8 + 1.56907e8i 0.930311 + 0.313458i
795795 −4.27566e7 1.53995e8i −0.0850946 0.306483i
796796 −6.70566e7 1.68299e8i −0.132954 0.333690i
797797 −7.40962e8 + 2.95226e8i −1.46359 + 0.583150i −0.959803 0.280675i 0.909442π-0.909442\pi
−0.503792 + 0.863825i 0.668062π0.668062\pi
798798 −1.32949e8 + 3.69131e7i −0.261623 + 0.0726393i
799799 3.51329e8 1.04271e9i 0.688770 2.04420i
800800 5.52702e8 + 9.06109e7i 1.07950 + 0.176974i
801801 −2.38742e7 + 3.91397e6i −0.0464548 + 0.00761588i
802802 1.05065e9 3.54004e8i 2.03673 0.686255i
803803 −4.17488e8 6.15749e8i −0.806302 1.18921i
804804 3.16474e7 6.84048e7i 0.0608934 0.131619i
805805 3.18141e6 4.18507e6i 0.00609862 0.00802259i
806806 −2.56023e7 2.35409e8i −0.0488960 0.449591i
807807 2.18571e8 + 6.06860e7i 0.415884 + 0.115470i
808808 1.57697e7 2.32586e7i 0.0298944 0.0440909i
809809 −1.33199e8 2.21379e8i −0.251569 0.418110i 0.705179 0.709029i 0.250867π-0.250867\pi
−0.956748 + 0.290919i 0.906039π0.906039\pi
810810 4.09590e8 2.22073e7i 0.770716 0.0417870i
811811 2.32880e7 + 2.45848e7i 0.0436586 + 0.0460898i 0.747459 0.664308i 0.231274π-0.231274\pi
−0.703800 + 0.710398i 0.748515π0.748515\pi
812812 −5.08289e8 + 3.86391e8i −0.949385 + 0.721704i
813813 1.58370e8 3.48600e7i 0.294715 0.0648717i
814814 −1.33246e9 + 1.13180e9i −2.47048 + 2.09845i
815815 4.38106e6 8.08039e7i 0.00809294 0.149265i
816816 −4.38498e8 8.27095e8i −0.807044 1.52225i
817817 −5.27328e7 + 2.39567e8i −0.0966974 + 0.439301i
818818 −8.36429e8 + 3.86973e8i −1.52816 + 0.707003i
819819 3.99764e7 6.64413e7i 0.0727699 0.120945i
820820 6.79899e7 1.28243e8i 0.123311 0.232590i
821821 −2.82431e8 2.39899e8i −0.510368 0.433511i 0.354837 0.934928i 0.384536π-0.384536\pi
−0.865206 + 0.501417i 0.832812π0.832812\pi
822822 −3.03833e8 + 3.20753e8i −0.547041 + 0.577504i
823823 5.88678e7 5.41281e8i 0.105604 0.971009i −0.814721 0.579853i 0.803110π-0.803110\pi
0.920325 0.391156i 0.127925π-0.127925\pi
824824 −6.33084e6 + 1.58892e7i −0.0113157 + 0.0284001i
825825 7.97753e8i 1.42071i
826826 8.15779e6 + 5.45820e8i 0.0144755 + 0.968522i
827827 −2.67270e8 −0.472534 −0.236267 0.971688i 0.575924π-0.575924\pi
−0.236267 + 0.971688i 0.575924π0.575924\pi
828828 −2.44366e6 973643.i −0.00430477 0.00171518i
829829 9.71543e8 + 1.05662e8i 1.70529 + 0.185462i 0.908240 0.418450i 0.137426π-0.137426\pi
0.797051 + 0.603911i 0.206392π0.206392\pi
830830 −2.74442e8 2.59965e8i −0.479973 0.454654i
831831 −6.79563e7 + 8.00044e7i −0.118420 + 0.139415i
832832 −7.71000e8 4.08758e8i −1.33870 0.709735i
833833 4.43849e8 + 2.67055e8i 0.767892 + 0.462025i
834834 −5.33304e8 1.15272e9i −0.919340 1.98712i
835835 −1.50395e8 3.31045e7i −0.258330 0.0568627i
836836 −2.41085e8 + 1.27815e8i −0.412620 + 0.218757i
837837 1.19179e8 + 6.46171e6i 0.203247 + 0.0110197i
838838 2.80728e8 + 3.30499e8i 0.477039 + 0.561614i
839839 −2.08852e8 9.48824e8i −0.353633 1.60657i −0.732263 0.681022i 0.761536π-0.761536\pi
0.378630 0.925548i 0.376395π-0.376395\pi
840840 5.75304e6 + 7.56800e6i 0.00970643 + 0.0127686i
841841 −8.16830e8 + 7.73742e8i −1.37323 + 1.30079i
842842 −2.37073e7 4.37255e8i −0.0397141 0.732484i
843843 −1.68407e8 + 1.01327e8i −0.281111 + 0.169139i
844844 −8.14260e8 5.52082e8i −1.35436 0.918282i
845845 8.01333e7 2.88614e8i 0.132814 0.478352i
846846 −1.62058e8 + 1.76248e7i −0.267645 + 0.0291081i
847847 6.52622e8 + 4.96110e8i 1.07402 + 0.816447i
848848 −3.30232e8 1.52781e8i −0.541541 0.250543i
849849 −3.50621e8 + 2.37727e8i −0.572947 + 0.388468i
850850 −3.57485e8 1.06098e9i −0.582104 1.72762i
851851 4.04154e6 + 2.46523e7i 0.00655781 + 0.0400009i
852852 −8.59216e7 + 5.24099e8i −0.138926 + 0.847411i
853853 −1.57117e7 5.29387e6i −0.0253148 0.00852956i 0.306616 0.951833i 0.400803π-0.400803\pi
−0.331930 + 0.943304i 0.607700π0.607700\pi
854854 −7.24242e7 2.60848e8i −0.116281 0.418807i
855855 4.25193e6 + 1.06715e7i 0.00680280 + 0.0170738i
856856 −7.77716e6 + 3.09871e6i −0.0123994 + 0.00494036i
857857 −5.17119e8 + 1.43577e8i −0.821576 + 0.228109i −0.652786 0.757543i 0.726400π-0.726400\pi
−0.168790 + 0.985652i 0.553986π0.553986\pi
858858 7.57797e8 2.24906e9i 1.19975 3.56073i
859859 8.64885e8 + 1.41791e8i 1.36452 + 0.223701i 0.799147 0.601136i 0.205285π-0.205285\pi
0.565370 + 0.824837i 0.308733π0.308733\pi
860860 5.35797e8 8.78394e7i 0.842373 0.138100i
861861 2.33045e8 7.85221e7i 0.365116 0.123022i
862862 −6.25231e8 9.22146e8i −0.976154 1.43972i
863863 −2.20524e8 + 4.76654e8i −0.343102 + 0.741602i −0.999923 0.0124446i 0.996039π-0.996039\pi
0.656821 + 0.754047i 0.271901π0.271901\pi
864864 5.08248e8 6.68589e8i 0.788015 1.03662i
865865 3.10444e7 + 2.85449e8i 0.0479662 + 0.441041i
866866 −3.02455e8 8.39762e7i −0.465701 0.129301i
867867 −6.93579e8 + 1.02295e9i −1.06424 + 1.56963i
868868 5.26361e7 + 8.74819e7i 0.0804868 + 0.133770i
869869 −1.12246e6 + 60858.0i −0.00171046 + 9.27382e-5i
870870 5.65761e8 + 5.97267e8i 0.859163 + 0.907007i
871871 9.84089e7 7.48085e7i 0.148929 0.113213i
872872 3.74669e7 8.24708e6i 0.0565064 0.0124380i
873873 −3.39248e6 + 2.88160e6i −0.00509888 + 0.00433102i
874874 −415617. + 7.66561e6i −0.000622529 + 0.0114819i
875875 −1.81529e8 3.42399e8i −0.270970 0.511104i
876876 1.32756e8 6.03117e8i 0.197489 0.897199i
877877 8.06173e8 3.72975e8i 1.19517 0.552944i 0.281563 0.959543i 0.409147π-0.409147\pi
0.913607 + 0.406598i 0.133285π0.133285\pi
878878 8.48857e7 1.41081e8i 0.125415 0.208442i
879879 −3.31208e8 + 6.24724e8i −0.487679 + 0.919860i
880880 −4.17781e8 3.54866e8i −0.613057 0.520735i
881881 −6.57946e8 + 6.94585e8i −0.962193 + 1.01578i 0.0376707 + 0.999290i 0.488006π0.488006\pi
−0.999864 + 0.0164850i 0.994752π0.994752\pi
882882 8.29733e6 7.62927e7i 0.0120930 0.111193i
883883 2.24960e8 5.64607e8i 0.326756 0.820095i −0.670204 0.742177i 0.733793π-0.733793\pi
0.996960 0.0779181i 0.0248273π-0.0248273\pi
884884 1.69170e9i 2.44887i
885885 3.54536e8 4.39284e7i 0.511482 0.0633746i
886886 −6.96478e8 −1.00140
887887 5.56244e8 + 2.21628e8i 0.797066 + 0.317580i 0.732880 0.680358i 0.238176π-0.238176\pi
0.0641858 + 0.997938i 0.479555π0.479555\pi
888888 −4.49099e7 4.88425e6i −0.0641362 0.00697523i
889889 −5.44275e8 5.15565e8i −0.774663 0.733800i
890890 1.01171e8 1.19108e8i 0.143511 0.168955i
891891 1.21428e9 + 6.43768e8i 1.71666 + 0.910115i
892892 −9.04048e8 5.43948e8i −1.27379 0.766412i
893893 1.01459e8 + 2.19299e8i 0.142473 + 0.307951i
894894 −6.04568e8 1.33075e8i −0.846121 0.186245i
895895 −4.05107e8 + 2.14774e8i −0.565067 + 0.299580i
896896 4.46820e7 + 2.42259e6i 0.0621168 + 0.00336787i
897897 −2.19546e7 2.58469e7i −0.0304192 0.0358122i
898898 −3.74453e8 1.70116e9i −0.517093 2.34918i
899899 1.66440e8 + 2.18948e8i 0.229075 + 0.301343i
900900 −6.11621e7 + 5.79359e7i −0.0838987 + 0.0794731i
901901 4.06864e7 + 7.50416e8i 0.0556256 + 1.02595i
902902 8.20471e8 4.93661e8i 1.11800 0.672681i
903903 7.61373e8 + 5.16224e8i 1.03403 + 0.701092i
904904 1.06310e7 3.82894e7i 0.0143903 0.0518290i
905905 −5.36316e8 + 5.83278e7i −0.723560 + 0.0786919i
906906 1.58991e9 + 1.20862e9i 2.13790 + 1.62519i
907907 −8.09770e7 3.74640e7i −0.108528 0.0502102i 0.364874 0.931057i 0.381112π-0.381112\pi
−0.473402 + 0.880847i 0.656974π0.656974\pi
908908 −1.05323e9 + 7.14108e8i −1.40691 + 0.953908i
909909 −4.06584e7 1.20670e8i −0.0541326 0.160660i
910910 8.10336e7 + 4.94283e8i 0.107533 + 0.655921i
911911 −3.27091e7 + 1.99517e8i −0.0432627 + 0.263891i −0.999597 0.0283838i 0.990964π-0.990964\pi
0.956334 + 0.292275i 0.0944122π0.0944122\pi
912912 1.94820e8 + 6.56424e7i 0.256831 + 0.0865366i
913913 −3.38848e8 1.22042e9i −0.445238 1.60360i
914914 4.55540e8 + 1.14332e9i 0.596607 + 1.49737i
915915 −1.64584e8 + 6.55764e7i −0.214845 + 0.0856021i
916916 −3.22940e8 + 8.96638e7i −0.420180 + 0.116662i
917917 1.61648e8 4.79754e8i 0.209634 0.622172i
918918 −1.65670e9 2.71602e8i −2.14148 0.351078i
919919 −4.35014e8 + 7.13170e7i −0.560476 + 0.0918854i −0.435360 0.900257i 0.643379π-0.643379\pi
−0.125117 + 0.992142i 0.539930π0.539930\pi
920920 501233. 168885.i 0.000643689 0.000216884i
921921 3.95591e7 + 5.83452e7i 0.0506369 + 0.0746838i
922922 8.08661e7 1.74789e8i 0.103175 0.223009i
923923 −5.27132e8 + 6.93430e8i −0.670370 + 0.881856i
924924 1.10634e8 + 1.01726e9i 0.140240 + 1.28948i
925925 7.70911e8 + 2.14042e8i 0.974045 + 0.270442i
926926 4.96316e8 7.32011e8i 0.625065 0.921902i
927927 3.99582e7 + 6.64110e7i 0.0501610 + 0.0833682i
928928 1.93240e9 1.04771e8i 2.41798 0.131099i
929929 −6.26676e8 6.61573e8i −0.781620 0.825146i 0.206562 0.978434i 0.433773π-0.433773\pi
−0.988182 + 0.153287i 0.951014π0.951014\pi
930930 1.04728e8 7.96119e7i 0.130200 0.0989758i
931931 −1.11095e8 + 2.44538e7i −0.137671 + 0.0303038i
932932 1.16021e9 9.85488e8i 1.43314 1.21732i
933933 7.56969e7 1.39615e9i 0.0932037 1.71904i
934934 6.60983e8 + 1.24675e9i 0.811241 + 1.53016i
935935 −2.43379e8 + 1.10568e9i −0.297748 + 1.35268i
936936 7.08050e6 3.27579e6i 0.00863448 0.00399474i
937937 −2.68055e8 + 4.45511e8i −0.325840 + 0.541551i −0.975868 0.218359i 0.929930π-0.929930\pi
0.650028 + 0.759910i 0.274757π0.274757\pi
938938 −4.91526e7 + 9.27116e7i −0.0595577 + 0.112338i
939939 1.59132e8 + 1.35168e8i 0.192203 + 0.163259i
940940 3.67798e8 3.88280e8i 0.442819 0.467478i
941941 1.53162e8 1.40830e9i 0.183816 1.69016i −0.431688 0.902023i 0.642082π-0.642082\pi
0.615503 0.788134i 0.288953π-0.288953\pi
942942 −4.60573e8 + 1.15595e9i −0.550993 + 1.38289i
943943 1.36825e7i 0.0163166i
944944 4.46323e8 6.79936e8i 0.530558 0.808262i
945945 −2.52462e8 −0.299159
946946 3.32735e9 + 1.32574e9i 3.93030 + 1.56597i
947947 1.52582e9 + 1.65943e8i 1.79661 + 0.195393i 0.944620 0.328167i 0.106431π-0.106431\pi
0.851989 + 0.523560i 0.175396π0.175396\pi
948948 −677456. 641721.i −0.000795163 0.000753218i
949949 6.55701e8 7.71951e8i 0.767198 0.903215i
950950 2.17225e8 + 1.15165e8i 0.253360 + 0.134323i
951951 3.90409e8 + 2.34901e8i 0.453918 + 0.273114i
952952 −1.87697e7 4.05700e7i −0.0217544 0.0470213i
953953 1.59630e9 + 3.51373e8i 1.84432 + 0.405966i 0.992944 0.118587i 0.0378364π-0.0378364\pi
0.851378 + 0.524553i 0.175767π0.175767\pi
954954 9.83698e7 5.21523e7i 0.113296 0.0600660i
955955 4.48114e8 + 2.42960e7i 0.514492 + 0.0278949i
956956 3.80997e8 + 4.48545e8i 0.436062 + 0.513372i
957957 5.92558e8 + 2.69202e9i 0.676075 + 3.07144i
958958 −6.06407e8 7.97715e8i −0.689712 0.907301i
959959 2.26815e8 2.14850e8i 0.257167 0.243602i
960960 −2.62466e7 4.84090e8i −0.0296660 0.547157i
961961 −7.22781e8 + 4.34883e8i −0.814397 + 0.490007i
962962 −1.97006e9 1.33574e9i −2.21287 1.50036i
963963 −1.01489e7 + 3.65531e7i −0.0113643 + 0.0409304i
964964 −6.90044e8 + 7.50468e7i −0.770275 + 0.0837724i
965965 1.60295e8 + 1.21853e8i 0.178377 + 0.135599i
966966 2.61273e7 + 1.20878e7i 0.0289844 + 0.0134096i
967967 3.48363e8 2.36196e8i 0.385259 0.261212i −0.353148 0.935568i 0.614889π-0.614889\pi
0.738407 + 0.674355i 0.235578π0.235578\pi
968968 2.63360e7 + 7.81626e7i 0.0290352 + 0.0861733i
969969 −6.86937e7 4.19013e8i −0.0754998 0.460528i
970970 4.65163e6 2.83737e7i 0.00509671 0.0310886i
971971 −9.88421e8 3.33038e8i −1.07965 0.363777i −0.277395 0.960756i 0.589471π-0.589471\pi
−0.802257 + 0.596978i 0.796368π0.796368\pi
972972 7.33584e7 + 2.64213e8i 0.0798823 + 0.287710i
973973 3.32433e8 + 8.34344e8i 0.360883 + 0.905747i
974974 −1.64029e9 + 6.53550e8i −1.77518 + 0.707298i
975975 −1.04652e9 + 2.90565e8i −1.12911 + 0.313495i
976976 −1.28791e8 + 3.82240e8i −0.138528 + 0.411137i
977977 −7.75896e8 1.27202e8i −0.831993 0.136398i −0.269292 0.963059i 0.586790π-0.586790\pi
−0.562701 + 0.826660i 0.690238π0.690238\pi
978978 4.37305e8 7.16925e7i 0.467485 0.0766403i
979979 4.96203e8 1.67190e8i 0.528824 0.178182i
980980 1.41297e8 + 2.08397e8i 0.150125 + 0.221418i
981981 7.29945e7 1.57775e8i 0.0773184 0.167121i
982982 −8.75668e8 + 1.15192e9i −0.924709 + 1.21643i
983983 −8.40129e7 7.72486e8i −0.0884475 0.813261i −0.951396 0.307970i 0.900350π-0.900350\pi
0.862949 0.505292i 0.168615π-0.168615\pi
984984 2.38406e7 + 6.61931e6i 0.0250226 + 0.00694748i
985985 1.27947e8 1.88708e8i 0.133882 0.197461i
986986 −1.99441e9 3.31473e9i −2.08058 3.45794i
987987 9.04784e8 4.90560e7i 0.941008 0.0510200i
988988 −2.55483e8 2.69710e8i −0.264905 0.279657i
989989 4.07444e7 3.09731e7i 0.0421191 0.0320181i
990990 1.63810e8 3.60573e7i 0.168824 0.0371610i
991991 −7.93753e8 + 6.74220e8i −0.815576 + 0.692757i −0.954717 0.297516i 0.903842π-0.903842\pi
0.139141 + 0.990273i 0.455566π0.455566\pi
992992 1.67535e7 3.09001e8i 0.0171621 0.316537i
993993 2.01705e8 + 3.80456e8i 0.206001 + 0.388559i
994994 1.58953e8 7.22131e8i 0.161849 0.735287i
995995 1.49813e8 6.93108e7i 0.152083 0.0703609i
996996 5.42060e8 9.00911e8i 0.548617 0.911809i
997997 −3.87452e8 + 7.30813e8i −0.390961 + 0.737430i −0.998377 0.0569539i 0.981861π-0.981861\pi
0.607416 + 0.794384i 0.292206π0.292206\pi
998998 6.19277e8 + 5.26019e8i 0.623008 + 0.529188i
999999 8.25038e8 8.70982e8i 0.827518 0.873600i
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.10.24 yes 812
59.6 odd 58 inner 59.7.d.a.6.24 812
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
59.7.d.a.6.24 812 59.6 odd 58 inner
59.7.d.a.10.24 yes 812 1.1 even 1 trivial