Properties

Label 117.4.l.a.4.2
Level 117117
Weight 44
Character 117.4
Analytic conductor 6.9036.903
Analytic rank 00
Dimension 8080
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] = [117,4,Mod(4,117)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 4, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("117.4"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: N N == 117=3213 117 = 3^{2} \cdot 13
Weight: k k == 4 4
Character orbit: [χ][\chi] == 117.l (of order 66, degree 22, 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: 6.903223470676.90322347067
Analytic rank: 00
Dimension: 8080
Relative dimension: 4040 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 4.2
Character χ\chi == 117.4
Dual form 117.4.l.a.88.39

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) == q5.36996iq2+(4.96560+1.53062i)q320.8364q4+(10.16625.86946i)q5+(8.21934+26.6651i)q6+(7.29194+4.21000i)q7+68.9311iq8+(22.314415.2009i)q9+(31.5187+54.5920i)q1064.0601iq11+(103.46531.8926i)q12+(3.50927+46.7406i)q13+(22.607539.1574i)q14+(59.4652+13.5848i)q15+203.465q16+(30.6034+53.0066i)q17+(81.6280119.828i)q18+(86.4378+49.9049i)q19+(211.827+122.299i)q20+(42.65289.74404i)q21344.000q22+(53.0925+91.9588i)q23+(105.507342.284i)q24+(6.40106+11.0870i)q25+(250.995+18.8446i)q26+(87.5379+109.636i)q27+(151.93887.7214i)q28144.612q29+(72.9500319.325i)q30+(94.2187+54.3972i)q31541.152iq32+(98.0514+318.097i)q33+(284.643164.339i)q34+(49.420885.5994i)q35+(464.953+316.732i)q36+(4.757862.74695i)q37+(267.987+464.167i)q38+(54.1163237.467i)q39+(404.588700.767i)q40+(57.725533.3278i)q41+(52.3251+229.043i)q42+(165.712+287.022i)q43+1334.78iq44+(316.074+23.5614i)q45+(493.815285.104i)q46+(181.062104.536i)q47+(1010.33+311.428i)q48+(136.052235.649i)q49+(59.536534.3734i)q50+(233.097216.368i)q51+(73.1207973.908i)q52303.187q53+(588.742+470.075i)q54+(375.998+651.247i)q55+(290.200+502.641i)q56+(352.831380.111i)q57+776.561iq58+665.165iq59+(1239.04283.060i)q60+(318.154+551.059i)q61+(292.110505.950i)q62+(226.71116.9000i)q631278.24q64+(310.018454.577i)q65+(1708.17526.532i)q66+(120.31069.4610i)q67+(637.6651104.47i)q68+(404.390375.367i)q69+(459.665+265.388i)q70+(303.653+175.314i)q71+(1047.81+1538.16i)q72497.163iq73+(14.7510+25.5495i)q74+(48.755045.2559i)q75+(1801.061039.84i)q76+(269.693467.122i)q77+(1275.19+290.602i)q78+(1.083361.87643i)q79+(2068.471194.23i)q80+(266.867678.397i)q81+(178.969309.983i)q82+(122.776+70.8847i)q83+(888.731+203.031i)q84718.500iq85+(1541.30+889.869i)q86+(718.087221.346i)q87+4415.73q88+(71.967741.5506i)q89+(126.524+1697.30i)q90+(222.367+326.056i)q91+(1106.261916.09i)q92+(551.114125.902i)q93+(561.355972.296i)q94+1171.66q95+(828.296+2687.15i)q96+(442.042255.213i)q97+(1265.42+730.592i)q98+(973.7691429.46i)q99+O(q100)q-5.36996i q^{2} +(-4.96560 + 1.53062i) q^{3} -20.8364 q^{4} +(-10.1662 - 5.86946i) q^{5} +(8.21934 + 26.6651i) q^{6} +(7.29194 + 4.21000i) q^{7} +68.9311i q^{8} +(22.3144 - 15.2009i) q^{9} +(-31.5187 + 54.5920i) q^{10} -64.0601i q^{11} +(103.465 - 31.8926i) q^{12} +(-3.50927 + 46.7406i) q^{13} +(22.6075 - 39.1574i) q^{14} +(59.4652 + 13.5848i) q^{15} +203.465 q^{16} +(30.6034 + 53.0066i) q^{17} +(-81.6280 - 119.828i) q^{18} +(-86.4378 + 49.9049i) q^{19} +(211.827 + 122.299i) q^{20} +(-42.6528 - 9.74404i) q^{21} -344.000 q^{22} +(53.0925 + 91.9588i) q^{23} +(-105.507 - 342.284i) q^{24} +(6.40106 + 11.0870i) q^{25} +(250.995 + 18.8446i) q^{26} +(-87.5379 + 109.636i) q^{27} +(-151.938 - 87.7214i) q^{28} -144.612 q^{29} +(72.9500 - 319.325i) q^{30} +(94.2187 + 54.3972i) q^{31} -541.152i q^{32} +(98.0514 + 318.097i) q^{33} +(284.643 - 164.339i) q^{34} +(-49.4208 - 85.5994i) q^{35} +(-464.953 + 316.732i) q^{36} +(-4.75786 - 2.74695i) q^{37} +(267.987 + 464.167i) q^{38} +(-54.1163 - 237.467i) q^{39} +(404.588 - 700.767i) q^{40} +(57.7255 - 33.3278i) q^{41} +(-52.3251 + 229.043i) q^{42} +(-165.712 + 287.022i) q^{43} +1334.78i q^{44} +(-316.074 + 23.5614i) q^{45} +(493.815 - 285.104i) q^{46} +(181.062 - 104.536i) q^{47} +(-1010.33 + 311.428i) q^{48} +(-136.052 - 235.649i) q^{49} +(59.5365 - 34.3734i) q^{50} +(-233.097 - 216.368i) q^{51} +(73.1207 - 973.908i) q^{52} -303.187 q^{53} +(588.742 + 470.075i) q^{54} +(-375.998 + 651.247i) q^{55} +(-290.200 + 502.641i) q^{56} +(352.831 - 380.111i) q^{57} +776.561i q^{58} +665.165i q^{59} +(-1239.04 - 283.060i) q^{60} +(-318.154 + 551.059i) q^{61} +(292.110 - 505.950i) q^{62} +(226.711 - 16.9000i) q^{63} -1278.24 q^{64} +(310.018 - 454.577i) q^{65} +(1708.17 - 526.532i) q^{66} +(120.310 - 69.4610i) q^{67} +(-637.665 - 1104.47i) q^{68} +(-404.390 - 375.367i) q^{69} +(-459.665 + 265.388i) q^{70} +(-303.653 + 175.314i) q^{71} +(1047.81 + 1538.16i) q^{72} -497.163i q^{73} +(-14.7510 + 25.5495i) q^{74} +(-48.7550 - 45.2559i) q^{75} +(1801.06 - 1039.84i) q^{76} +(269.693 - 467.122i) q^{77} +(-1275.19 + 290.602i) q^{78} +(-1.08336 - 1.87643i) q^{79} +(-2068.47 - 1194.23i) q^{80} +(266.867 - 678.397i) q^{81} +(-178.969 - 309.983i) q^{82} +(-122.776 + 70.8847i) q^{83} +(888.731 + 203.031i) q^{84} -718.500i q^{85} +(1541.30 + 889.869i) q^{86} +(718.087 - 221.346i) q^{87} +4415.73 q^{88} +(-71.9677 - 41.5506i) q^{89} +(126.524 + 1697.30i) q^{90} +(-222.367 + 326.056i) q^{91} +(-1106.26 - 1916.09i) q^{92} +(-551.114 - 125.902i) q^{93} +(-561.355 - 972.296i) q^{94} +1171.66 q^{95} +(828.296 + 2687.15i) q^{96} +(-442.042 - 255.213i) q^{97} +(-1265.42 + 730.592i) q^{98} +(-973.769 - 1429.46i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 80qq3306q4+42q63q717q910q10101q1213q13+126q1463q15+1102q16138q17168q1896q19387q20249q21+62q22+2331q99+O(q100) 80 q - q^{3} - 306 q^{4} + 42 q^{6} - 3 q^{7} - 17 q^{9} - 10 q^{10} - 101 q^{12} - 13 q^{13} + 126 q^{14} - 63 q^{15} + 1102 q^{16} - 138 q^{17} - 168 q^{18} - 96 q^{19} - 387 q^{20} - 249 q^{21} + 62 q^{22}+ \cdots - 2331 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/117Z)×\left(\mathbb{Z}/117\mathbb{Z}\right)^\times.

nn 2828 9292
χ(n)\chi(n) e(16)e\left(\frac{1}{6}\right) e(13)e\left(\frac{1}{3}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 5.36996i 1.89857i −0.314422 0.949283i 0.601811π-0.601811\pi
0.314422 0.949283i 0.398189π-0.398189\pi
33 −4.96560 + 1.53062i −0.955631 + 0.294567i
44 −20.8364 −2.60455
55 −10.1662 5.86946i −0.909292 0.524980i −0.0290890 0.999577i 0.509261π-0.509261\pi
−0.880203 + 0.474597i 0.842594π0.842594\pi
66 8.21934 + 26.6651i 0.559255 + 1.81433i
77 7.29194 + 4.21000i 0.393728 + 0.227319i 0.683774 0.729694i 0.260337π-0.260337\pi
−0.290046 + 0.957013i 0.593671π0.593671\pi
88 68.9311i 3.04635i
99 22.3144 15.2009i 0.826460 0.562995i
1010 −31.5187 + 54.5920i −0.996710 + 1.72635i
1111 64.0601i 1.75589i −0.478757 0.877947i 0.658913π-0.658913\pi
0.478757 0.877947i 0.341087π-0.341087\pi
1212 103.465 31.8926i 2.48899 0.767216i
1313 −3.50927 + 46.7406i −0.0748690 + 0.997193i
1414 22.6075 39.1574i 0.431580 0.747518i
1515 59.4652 + 13.5848i 1.02359 + 0.233839i
1616 203.465 3.17915
1717 30.6034 + 53.0066i 0.436612 + 0.756234i 0.997426 0.0717079i 0.0228449π-0.0228449\pi
−0.560814 + 0.827942i 0.689512π0.689512\pi
1818 −81.6280 119.828i −1.06888 1.56909i
1919 −86.4378 + 49.9049i −1.04369 + 0.602577i −0.920878 0.389852i 0.872526π-0.872526\pi
−0.122817 + 0.992429i 0.539193π0.539193\pi
2020 211.827 + 122.299i 2.36830 + 1.36734i
2121 −42.6528 9.74404i −0.443219 0.101254i
2222 −344.000 −3.33368
2323 53.0925 + 91.9588i 0.481328 + 0.833684i 0.999770 0.0214281i 0.00682128π-0.00682128\pi
−0.518442 + 0.855113i 0.673488π0.673488\pi
2424 −105.507 342.284i −0.897356 2.91119i
2525 6.40106 + 11.0870i 0.0512085 + 0.0886957i
2626 250.995 + 18.8446i 1.89324 + 0.142144i
2727 −87.5379 + 109.636i −0.623951 + 0.781464i
2828 −151.938 87.7214i −1.02548 0.592064i
2929 −144.612 −0.925994 −0.462997 0.886360i 0.653226π-0.653226\pi
−0.462997 + 0.886360i 0.653226π0.653226\pi
3030 72.9500 319.325i 0.443960 1.94335i
3131 94.2187 + 54.3972i 0.545877 + 0.315162i 0.747457 0.664310i 0.231274π-0.231274\pi
−0.201581 + 0.979472i 0.564608π0.564608\pi
3232 541.152i 2.98947i
3333 98.0514 + 318.097i 0.517229 + 1.67799i
3434 284.643 164.339i 1.43576 0.828937i
3535 −49.4208 85.5994i −0.238676 0.413398i
3636 −464.953 + 316.732i −2.15256 + 1.46635i
3737 −4.75786 2.74695i −0.0211402 0.0122053i 0.489393 0.872064i 0.337219π-0.337219\pi
−0.510533 + 0.859858i 0.670552π0.670552\pi
3838 267.987 + 464.167i 1.14403 + 1.98152i
3939 −54.1163 237.467i −0.222193 0.975003i
4040 404.588 700.767i 1.59927 2.77003i
4141 57.7255 33.3278i 0.219883 0.126950i −0.386013 0.922493i 0.626148π-0.626148\pi
0.605896 + 0.795544i 0.292815π0.292815\pi
4242 −52.3251 + 229.043i −0.192236 + 0.841480i
4343 −165.712 + 287.022i −0.587696 + 1.01792i 0.406838 + 0.913500i 0.366631π0.366631\pi
−0.994533 + 0.104418i 0.966702π0.966702\pi
4444 1334.78i 4.57332i
4545 −316.074 + 23.5614i −1.04706 + 0.0780518i
4646 493.815 285.104i 1.58281 0.913833i
4747 181.062 104.536i 0.561928 0.324429i −0.191991 0.981397i 0.561494π-0.561494\pi
0.753919 + 0.656967i 0.228161π0.228161\pi
4848 −1010.33 + 311.428i −3.03809 + 0.936473i
4949 −136.052 235.649i −0.396652 0.687022i
5050 59.5365 34.3734i 0.168395 0.0972227i
5151 −233.097 216.368i −0.640002 0.594069i
5252 73.1207 973.908i 0.195000 2.59724i
5353 −303.187 −0.785773 −0.392887 0.919587i 0.628524π-0.628524\pi
−0.392887 + 0.919587i 0.628524π0.628524\pi
5454 588.742 + 470.075i 1.48366 + 1.18461i
5555 −375.998 + 651.247i −0.921810 + 1.59662i
5656 −290.200 + 502.641i −0.692493 + 1.19943i
5757 352.831 380.111i 0.819887 0.883280i
5858 776.561i 1.75806i
5959 665.165i 1.46775i 0.679286 + 0.733873i 0.262289π0.262289\pi
−0.679286 + 0.733873i 0.737711π0.737711\pi
6060 −1239.04 283.060i −2.66599 0.609048i
6161 −318.154 + 551.059i −0.667795 + 1.15665i 0.310725 + 0.950500i 0.399428π0.399428\pi
−0.978520 + 0.206154i 0.933905π0.933905\pi
6262 292.110 505.950i 0.598356 1.03638i
6363 226.711 16.9000i 0.453379 0.0337968i
6464 −1278.24 −2.49656
6565 310.018 454.577i 0.591585 0.867436i
6666 1708.17 526.532i 3.18577 0.981994i
6767 120.310 69.4610i 0.219376 0.126657i −0.386285 0.922379i 0.626242π-0.626242\pi
0.605661 + 0.795723i 0.292909π0.292909\pi
6868 −637.665 1104.47i −1.13718 1.96965i
6969 −404.390 375.367i −0.705548 0.654911i
7070 −459.665 + 265.388i −0.784864 + 0.453142i
7171 −303.653 + 175.314i −0.507564 + 0.293042i −0.731832 0.681485i 0.761334π-0.761334\pi
0.224268 + 0.974528i 0.428001π0.428001\pi
7272 1047.81 + 1538.16i 1.71508 + 2.51769i
7373 497.163i 0.797104i −0.917146 0.398552i 0.869513π-0.869513\pi
0.917146 0.398552i 0.130487π-0.130487\pi
7474 −14.7510 + 25.5495i −0.0231726 + 0.0401361i
7575 −48.7550 45.2559i −0.0750632 0.0696760i
7676 1801.06 1039.84i 2.71836 1.56945i
7777 269.693 467.122i 0.399148 0.691344i
7878 −1275.19 + 290.602i −1.85111 + 0.421849i
7979 −1.08336 1.87643i −0.00154288 0.00267235i 0.865253 0.501336i 0.167158π-0.167158\pi
−0.866796 + 0.498663i 0.833824π0.833824\pi
8080 −2068.47 1194.23i −2.89078 1.66899i
8181 266.867 678.397i 0.366073 0.930586i
8282 −178.969 309.983i −0.241022 0.417462i
8383 −122.776 + 70.8847i −0.162366 + 0.0937422i −0.578981 0.815341i 0.696550π-0.696550\pi
0.416615 + 0.909083i 0.363216π0.363216\pi
8484 888.731 + 203.031i 1.15439 + 0.263720i
8585 718.500i 0.916851i
8686 1541.30 + 889.869i 1.93259 + 1.11578i
8787 718.087 221.346i 0.884908 0.272767i
8888 4415.73 5.34907
8989 −71.9677 41.5506i −0.0857142 0.0494871i 0.456530 0.889708i 0.349092π-0.349092\pi
−0.542244 + 0.840221i 0.682425π0.682425\pi
9090 126.524 + 1697.30i 0.148187 + 1.98790i
9191 −222.367 + 326.056i −0.256159 + 0.375603i
9292 −1106.26 1916.09i −1.25364 2.17138i
9393 −551.114 125.902i −0.614493 0.140381i
9494 −561.355 972.296i −0.615951 1.06686i
9595 1171.66 1.26536
9696 828.296 + 2687.15i 0.880600 + 2.85683i
9797 −442.042 255.213i −0.462707 0.267144i 0.250475 0.968123i 0.419413π-0.419413\pi
−0.713182 + 0.700979i 0.752747π0.752747\pi
9898 −1265.42 + 730.592i −1.30436 + 0.753071i
9999 −973.769 1429.46i −0.988560 1.45118i
100100 −133.375 231.013i −0.133375 0.231013i
101101 −1407.17 −1.38632 −0.693161 0.720783i 0.743782π-0.743782\pi
−0.693161 + 0.720783i 0.743782π0.743782\pi
102102 −1161.88 + 1251.72i −1.12788 + 1.21509i
103103 −129.191 + 223.766i −0.123588 + 0.214061i −0.921180 0.389136i 0.872774π-0.872774\pi
0.797592 + 0.603197i 0.206107π0.206107\pi
104104 −3221.88 241.898i −3.03780 0.228077i
105105 376.424 + 349.408i 0.349859 + 0.324750i
106106 1628.10i 1.49184i
107107 1041.15 1803.33i 0.940675 1.62930i 0.176487 0.984303i 0.443527π-0.443527\pi
0.764188 0.644994i 0.223140π-0.223140\pi
108108 1823.98 2284.43i 1.62511 2.03536i
109109 1144.90i 1.00607i 0.864266 + 0.503035i 0.167783π0.167783\pi
−0.864266 + 0.503035i 0.832217π0.832217\pi
110110 3497.17 + 2019.09i 3.03129 + 1.75012i
111111 27.8302 + 6.35782i 0.0237975 + 0.00543655i
112112 1483.66 + 856.590i 1.25172 + 0.722680i
113113 −747.525 −0.622312 −0.311156 0.950359i 0.600716π-0.600716\pi
−0.311156 + 0.950359i 0.600716π0.600716\pi
114114 −2041.18 1894.69i −1.67697 1.55661i
115115 1246.50i 1.01075i
116116 3013.20 2.41180
117117 632.190 + 1096.33i 0.499539 + 0.866292i
118118 3571.91 2.78661
119119 515.361i 0.397000i
120120 −936.418 + 4099.00i −0.712357 + 3.11822i
121121 −2772.69 −2.08317
122122 2959.16 + 1708.47i 2.19598 + 1.26785i
123123 −235.630 + 253.848i −0.172732 + 0.186087i
124124 −1963.18 1133.44i −1.42176 0.820856i
125125 1317.08i 0.942427i
126126 −90.7522 1217.43i −0.0641654 0.860771i
127127 −1060.12 + 1836.18i −0.740711 + 1.28295i 0.211461 + 0.977387i 0.432178π0.432178\pi
−0.952172 + 0.305563i 0.901155π0.901155\pi
128128 2534.87i 1.75042i
129129 383.541 1678.88i 0.261775 1.14587i
130130 −2441.06 1664.78i −1.64688 1.12316i
131131 33.1785 57.4668i 0.0221284 0.0383274i −0.854749 0.519041i 0.826289π-0.826289\pi
0.876878 + 0.480714i 0.159622π0.159622\pi
132132 −2043.04 6628.01i −1.34715 4.37041i
133133 −840.399 −0.547908
134134 −373.002 646.059i −0.240466 0.416500i
135135 1533.43 600.784i 0.977607 0.383017i
136136 −3653.80 + 2109.52i −2.30376 + 1.33007i
137137 702.365 + 405.511i 0.438008 + 0.252884i 0.702752 0.711435i 0.251954π-0.251954\pi
−0.264744 + 0.964319i 0.585288π0.585288\pi
138138 −2015.70 + 2171.56i −1.24339 + 1.33953i
139139 1047.37 0.639111 0.319555 0.947568i 0.396466π-0.396466\pi
0.319555 + 0.947568i 0.396466π0.396466\pi
140140 1029.75 + 1783.59i 0.621644 + 1.07672i
141141 −739.078 + 796.222i −0.441430 + 0.475560i
142142 941.431 + 1630.61i 0.556360 + 0.963643i
143143 2994.21 + 224.804i 1.75097 + 0.131462i
144144 4540.22 3092.85i 2.62744 1.78984i
145145 1470.16 + 848.795i 0.841999 + 0.486128i
146146 −2669.75 −1.51335
147147 1036.27 + 961.894i 0.581427 + 0.539699i
148148 99.1369 + 57.2367i 0.0550608 + 0.0317894i
149149 525.616i 0.288994i −0.989505 0.144497i 0.953844π-0.953844\pi
0.989505 0.144497i 0.0461564π-0.0461564\pi
150150 −243.022 + 261.812i −0.132284 + 0.142513i
151151 −9.76002 + 5.63495i −0.00525999 + 0.00303686i −0.502628 0.864503i 0.667633π-0.667633\pi
0.497368 + 0.867540i 0.334300π0.334300\pi
152152 −3440.00 5958.25i −1.83566 3.17946i
153153 1488.64 + 717.614i 0.786599 + 0.379187i
154154 −2508.42 1448.24i −1.31256 0.757808i
155155 −638.564 1106.02i −0.330908 0.573149i
156156 1127.59 + 4947.96i 0.578715 + 2.53945i
157157 −775.103 + 1342.52i −0.394012 + 0.682449i −0.992975 0.118328i 0.962247π-0.962247\pi
0.598962 + 0.800777i 0.295580π0.295580\pi
158158 −10.0764 + 5.81759i −0.00507362 + 0.00292926i
159159 1505.51 464.064i 0.750909 0.231463i
160160 −3176.27 + 5501.46i −1.56941 + 2.71830i
161161 894.077i 0.437659i
162162 −3642.96 1433.07i −1.76678 0.695014i
163163 2085.51 1204.07i 1.00215 0.578589i 0.0932635 0.995641i 0.470270π-0.470270\pi
0.908883 + 0.417052i 0.136937π0.136937\pi
164164 −1202.79 + 694.433i −0.572697 + 0.330647i
165165 870.246 3809.34i 0.410597 1.79732i
166166 380.648 + 659.301i 0.177976 + 0.308263i
167167 736.874 425.434i 0.341443 0.197132i −0.319467 0.947597i 0.603504π-0.603504\pi
0.660910 + 0.750465i 0.270171π0.270171\pi
168168 671.667 2940.10i 0.308454 1.35020i
169169 −2172.37 328.051i −0.988789 0.149318i
170170 −3858.32 −1.74070
171171 −1170.21 + 2427.53i −0.523324 + 1.08560i
172172 3452.86 5980.52i 1.53069 2.65122i
173173 336.827 583.402i 0.148026 0.256389i −0.782472 0.622686i 0.786041π-0.786041\pi
0.930498 + 0.366297i 0.119375π0.119375\pi
174174 −1188.62 3856.10i −0.517867 1.68006i
175175 107.794i 0.0465626i
176176 13034.0i 5.58225i
177177 −1018.11 3302.94i −0.432350 1.40262i
178178 −223.125 + 386.464i −0.0939546 + 0.162734i
179179 −1893.72 + 3280.02i −0.790744 + 1.36961i 0.134762 + 0.990878i 0.456973π0.456973\pi
−0.925507 + 0.378732i 0.876360π0.876360\pi
180180 6585.85 490.936i 2.72711 0.203290i
181181 −2393.55 −0.982936 −0.491468 0.870896i 0.663540π-0.663540\pi
−0.491468 + 0.870896i 0.663540π0.663540\pi
182182 1750.90 + 1194.10i 0.713108 + 0.486334i
183183 736.367 3223.31i 0.297453 1.30204i
184184 −6338.82 + 3659.72i −2.53970 + 1.46629i
185185 32.2463 + 55.8522i 0.0128151 + 0.0221964i
186186 −676.089 + 2959.46i −0.266523 + 1.16666i
187187 3395.60 1960.45i 1.32787 0.766645i
188188 −3772.69 + 2178.16i −1.46357 + 0.844994i
189189 −1099.89 + 430.926i −0.423308 + 0.165848i
190190 6291.76i 2.40238i
191191 1517.89 2629.06i 0.575028 0.995978i −0.421010 0.907056i 0.638324π-0.638324\pi
0.996039 0.0889223i 0.0283423π-0.0283423\pi
192192 6347.23 1956.49i 2.38579 0.735405i
193193 −2227.05 + 1285.79i −0.830603 + 0.479549i −0.854059 0.520176i 0.825866π-0.825866\pi
0.0234564 + 0.999725i 0.492533π0.492533\pi
194194 −1370.48 + 2373.75i −0.507191 + 0.878480i
195195 −843.644 + 2731.77i −0.309818 + 1.00321i
196196 2834.83 + 4910.08i 1.03310 + 1.78939i
197197 −1272.74 734.815i −0.460298 0.265753i 0.251871 0.967761i 0.418954π-0.418954\pi
−0.712170 + 0.702007i 0.752287π0.752287\pi
198198 −7676.16 + 5229.10i −2.75516 + 1.87685i
199199 2440.78 + 4227.55i 0.869458 + 1.50595i 0.862551 + 0.505970i 0.168865π0.168865\pi
0.00690693 + 0.999976i 0.497801π0.497801\pi
200200 −764.236 + 441.232i −0.270198 + 0.155999i
201201 −491.093 + 529.064i −0.172334 + 0.185658i
202202 7556.43i 2.63202i
203203 −1054.50 608.818i −0.364589 0.210496i
204204 4856.91 + 4508.33i 1.66692 + 1.54728i
205205 −782.465 −0.266584
206206 1201.61 + 693.752i 0.406409 + 0.234641i
207207 2582.58 + 1244.96i 0.867159 + 0.418022i
208208 −714.016 + 9510.10i −0.238020 + 3.17023i
209209 3196.91 + 5537.21i 1.05806 + 1.83262i
210210 1876.31 2021.38i 0.616560 0.664231i
211211 2662.73 + 4611.98i 0.868766 + 1.50475i 0.863259 + 0.504762i 0.168420π0.168420\pi
0.00550699 + 0.999985i 0.498247π0.498247\pi
212212 6317.34 2.04659
213213 1239.48 1335.32i 0.398723 0.429552i
214214 −9683.82 5590.96i −3.09333 1.78593i
215215 3369.33 1945.28i 1.06877 0.617057i
216216 −7557.35 6034.08i −2.38061 1.90077i
217217 458.024 + 793.321i 0.143284 + 0.248176i
218218 6148.07 1.91009
219219 760.966 + 2468.72i 0.234801 + 0.761737i
220220 7834.46 13569.7i 2.40090 4.15849i
221221 −2584.95 + 1244.41i −0.786800 + 0.378768i
222222 34.1412 149.447i 0.0103217 0.0451812i
223223 4111.48i 1.23464i 0.786712 + 0.617320i 0.211782π0.211782\pi
−0.786712 + 0.617320i 0.788218π0.788218\pi
224224 2278.25 3946.05i 0.679563 1.17704i
225225 311.367 + 150.097i 0.0922570 + 0.0444733i
226226 4014.18i 1.18150i
227227 −3234.19 1867.26i −0.945641 0.545966i −0.0539166 0.998545i 0.517171π-0.517171\pi
−0.891724 + 0.452580i 0.850504π0.850504\pi
228228 −7351.73 + 7920.16i −2.13544 + 2.30055i
229229 2677.75 + 1546.00i 0.772711 + 0.446125i 0.833841 0.552005i 0.186137π-0.186137\pi
−0.0611296 + 0.998130i 0.519470π0.519470\pi
230230 −6693.63 −1.91898
231231 −624.204 + 2732.34i −0.177790 + 0.778245i
232232 9968.28i 2.82090i
233233 −2795.27 −0.785941 −0.392970 0.919551i 0.628553π-0.628553\pi
−0.392970 + 0.919551i 0.628553π0.628553\pi
234234 5887.27 3394.84i 1.64471 0.948407i
235235 −2454.28 −0.681276
236236 13859.7i 3.82283i
237237 8.25163 + 7.65942i 0.00226161 + 0.00209929i
238238 2767.46 0.753731
239239 −2951.04 1703.78i −0.798690 0.461124i 0.0443229 0.999017i 0.485887π-0.485887\pi
−0.843013 + 0.537893i 0.819220π0.819220\pi
240240 12099.1 + 2764.05i 3.25414 + 0.743410i
241241 −1938.89 1119.42i −0.518236 0.299203i 0.217977 0.975954i 0.430054π-0.430054\pi
−0.736212 + 0.676750i 0.763388π0.763388\pi
242242 14889.2i 3.95503i
243243 −286.791 + 3777.12i −0.0757106 + 0.997130i
244244 6629.20 11482.1i 1.73931 3.01257i
245245 3194.20i 0.832939i
246246 1363.15 + 1265.32i 0.353299 + 0.327943i
247247 −2029.25 4215.29i −0.522746 1.08588i
248248 −3749.66 + 6494.60i −0.960094 + 1.66293i
249249 501.159 539.908i 0.127549 0.137411i
250250 7072.67 1.78926
251251 −2861.54 4956.33i −0.719597 1.24638i −0.961160 0.275993i 0.910993π-0.910993\pi
0.241563 0.970385i 0.422340π-0.422340\pi
252252 −4723.85 + 352.135i −1.18085 + 0.0880255i
253253 5890.89 3401.11i 1.46386 0.845161i
254254 9860.20 + 5692.79i 2.43576 + 1.40629i
255255 1099.75 + 3567.79i 0.270074 + 0.876171i
256256 3386.24 0.826719
257257 −1330.60 2304.66i −0.322958 0.559380i 0.658139 0.752897i 0.271344π-0.271344\pi
−0.981097 + 0.193516i 0.938011π0.938011\pi
258258 −9015.52 2059.60i −2.17551 0.496996i
259259 −23.1294 40.0612i −0.00554899 0.00961113i
260260 −6459.67 + 9471.76i −1.54081 + 2.25928i
261261 −3226.94 + 2198.23i −0.765297 + 0.521330i
262262 −308.594 178.167i −0.0727672 0.0420122i
263263 −5541.11 −1.29916 −0.649581 0.760292i 0.725056π-0.725056\pi
−0.649581 + 0.760292i 0.725056π0.725056\pi
264264 −21926.8 + 6758.79i −5.11174 + 1.57566i
265265 3082.26 + 1779.55i 0.714498 + 0.412515i
266266 4512.91i 1.04024i
267267 420.961 + 96.1688i 0.0964884 + 0.0220428i
268268 −2506.83 + 1447.32i −0.571377 + 0.329885i
269269 −1403.73 2431.33i −0.318166 0.551080i 0.661939 0.749558i 0.269734π-0.269734\pi
−0.980106 + 0.198477i 0.936400π0.936400\pi
270270 −3226.19 8234.47i −0.727183 1.85605i
271271 1135.59 + 655.634i 0.254547 + 0.146963i 0.621845 0.783141i 0.286384π-0.286384\pi
−0.367297 + 0.930104i 0.619717π0.619717\pi
272272 6226.73 + 10785.0i 1.38805 + 2.40418i
273273 605.122 1959.42i 0.134153 0.434394i
274274 2177.57 3771.67i 0.480117 0.831587i
275275 710.231 410.052i 0.155740 0.0899167i
276276 8426.04 + 7821.31i 1.83764 + 1.70575i
277277 3519.80 6096.48i 0.763482 1.32239i −0.177564 0.984109i 0.556822π-0.556822\pi
0.941045 0.338280i 0.109845π-0.109845\pi
278278 5624.31i 1.21339i
279279 2929.32 218.364i 0.628580 0.0468569i
280280 5900.46 3406.63i 1.25936 0.727090i
281281 2519.54 1454.66i 0.534886 0.308817i −0.208118 0.978104i 0.566734π-0.566734\pi
0.743004 + 0.669287i 0.233400π0.233400\pi
282282 4275.68 + 3968.81i 0.902883 + 0.838083i
283283 −3080.02 5334.74i −0.646954 1.12056i −0.983847 0.179014i 0.942709π-0.942709\pi
0.336893 0.941543i 0.390624π-0.390624\pi
284284 6327.05 3652.93i 1.32198 0.763244i
285285 −5817.99 + 1793.36i −1.20922 + 0.372735i
286286 1207.19 16078.8i 0.249589 3.32433i
287287 561.241 0.115432
288288 −8225.98 12075.5i −1.68306 2.47068i
289289 583.369 1010.43i 0.118740 0.205664i
290290 4557.99 7894.68i 0.922947 1.59859i
291291 2585.64 + 590.690i 0.520869 + 0.118993i
292292 10359.1i 2.07610i
293293 6394.70i 1.27503i −0.770440 0.637513i 0.779963π-0.779963\pi
0.770440 0.637513i 0.220037π-0.220037\pi
294294 5165.33 5564.71i 1.02465 1.10388i
295295 3904.16 6762.20i 0.770538 1.33461i
296296 189.351 327.965i 0.0371817 0.0644006i
297297 7023.31 + 5607.68i 1.37217 + 1.09559i
298298 −2822.53 −0.548675
299299 −4484.53 + 2158.87i −0.867381 + 0.417560i
300300 1015.88 + 942.971i 0.195506 + 0.181475i
301301 −2416.73 + 1395.30i −0.462784 + 0.267188i
302302 30.2594 + 52.4109i 0.00576568 + 0.00998645i
303303 6987.44 2153.84i 1.32481 0.408365i
304304 −17587.1 + 10153.9i −3.31806 + 1.91568i
305305 6468.84 3734.78i 1.21444 0.701158i
306306 3853.55 7993.94i 0.719912 1.49341i
307307 6396.54i 1.18915i 0.804039 + 0.594576i 0.202680π0.202680\pi
−0.804039 + 0.594576i 0.797320π0.797320\pi
308308 −5619.44 + 9733.16i −1.03960 + 1.80064i
309309 299.013 1308.87i 0.0550494 0.240969i
310310 −5939.31 + 3429.06i −1.08816 + 0.628250i
311311 3896.83 6749.51i 0.710511 1.23064i −0.254154 0.967164i 0.581797π-0.581797\pi
0.964665 0.263478i 0.0848696π-0.0848696\pi
312312 16368.8 3730.30i 2.97020 0.676879i
313313 706.302 + 1223.35i 0.127548 + 0.220920i 0.922726 0.385456i 0.125956π-0.125956\pi
−0.795178 + 0.606376i 0.792623π0.792623\pi
314314 7209.26 + 4162.27i 1.29567 + 0.748058i
315315 −2403.98 1158.86i −0.429997 0.207284i
316316 22.5733 + 39.0982i 0.00401851 + 0.00696027i
317317 −4485.28 + 2589.58i −0.794695 + 0.458818i −0.841613 0.540081i 0.818393π-0.818393\pi
0.0469177 + 0.998899i 0.485060π0.485060\pi
318318 −2492.00 8084.51i −0.439448 1.42565i
319319 9263.87i 1.62595i
320320 12994.8 + 7502.57i 2.27010 + 1.31065i
321321 −2409.75 + 10548.2i −0.419000 + 1.83410i
322322 4801.16 0.830925
323323 −5290.58 3054.52i −0.911379 0.526185i
324324 −5560.56 + 14135.4i −0.953457 + 2.42376i
325325 −540.674 + 260.282i −0.0922807 + 0.0444242i
326326 −6465.80 11199.1i −1.09849 1.90264i
327327 −1752.40 5685.12i −0.296355 0.961431i
328328 2297.32 + 3979.08i 0.386733 + 0.669841i
329329 1760.39 0.294995
330330 −20456.0 4673.18i −3.41232 0.779547i
331331 −6152.62 3552.22i −1.02169 0.589872i −0.107096 0.994249i 0.534155π-0.534155\pi
−0.914592 + 0.404377i 0.867488π0.867488\pi
332332 2558.21 1476.98i 0.422892 0.244157i
333333 −147.925 + 11.0269i −0.0243431 + 0.00181463i
334334 −2284.56 3956.98i −0.374269 0.648252i
335335 −1630.79 −0.265969
336336 −8678.36 1982.58i −1.40906 0.321900i
337337 −1016.32 + 1760.32i −0.164281 + 0.284542i −0.936400 0.350936i 0.885864π-0.885864\pi
0.772119 + 0.635478i 0.219197π0.219197\pi
338338 −1761.62 + 11665.5i −0.283490 + 1.87728i
339339 3711.91 1144.17i 0.594700 0.183313i
340340 14971.0i 2.38799i
341341 3484.69 6035.66i 0.553391 0.958502i
342342 13035.7 + 6283.99i 2.06109 + 0.993566i
343343 5179.17i 0.815303i
344344 −19784.8 11422.7i −3.10094 1.79033i
345345 1907.91 + 6189.60i 0.297734 + 0.965904i
346346 −3132.84 1808.75i −0.486771 0.281037i
347347 5092.50 0.787837 0.393919 0.919145i 0.371119π-0.371119\pi
0.393919 + 0.919145i 0.371119π0.371119\pi
348348 −14962.4 + 4612.06i −2.30479 + 0.710437i
349349 4348.27i 0.666927i −0.942763 0.333463i 0.891783π-0.891783\pi
0.942763 0.333463i 0.108217π-0.108217\pi
350350 578.848 0.0884021
351351 −4817.27 4476.32i −0.732556 0.680707i
352352 −34666.2 −5.24920
353353 8976.19i 1.35341i 0.736253 + 0.676706i 0.236593π0.236593\pi
−0.736253 + 0.676706i 0.763407π0.763407\pi
354354 −17736.7 + 5467.22i −2.66297 + 0.820845i
355355 4116.00 0.615365
356356 1499.55 + 865.766i 0.223247 + 0.128892i
357357 −788.819 2559.08i −0.116943 0.379386i
358358 17613.6 + 10169.2i 2.60029 + 1.50128i
359359 1660.55i 0.244124i 0.992523 + 0.122062i 0.0389506π0.0389506\pi
−0.992523 + 0.122062i 0.961049π0.961049\pi
360360 −1624.12 21787.3i −0.237773 3.18970i
361361 1551.50 2687.28i 0.226199 0.391788i
362362 12853.3i 1.86617i
363363 13768.1 4243.93i 1.99074 0.613632i
364364 4633.34 6793.83i 0.667179 0.978279i
365365 −2918.08 + 5054.26i −0.418464 + 0.724800i
366366 −17309.1 3954.26i −2.47202 0.564733i
367367 699.079 0.0994322 0.0497161 0.998763i 0.484168π-0.484168\pi
0.0497161 + 0.998763i 0.484168π0.484168\pi
368368 10802.5 + 18710.4i 1.53021 + 2.65041i
369369 781.499 1621.17i 0.110253 0.228712i
370370 299.924 173.161i 0.0421413 0.0243303i
371371 −2210.82 1276.42i −0.309381 0.178621i
372372 11483.2 + 2623.35i 1.60048 + 0.365630i
373373 −2680.87 −0.372145 −0.186073 0.982536i 0.559576π-0.559576\pi
−0.186073 + 0.982536i 0.559576π0.559576\pi
374374 −10527.5 18234.3i −1.45553 2.52104i
375375 −2015.95 6540.10i −0.277608 0.900612i
376376 7205.80 + 12480.8i 0.988326 + 1.71183i
377377 507.484 6759.26i 0.0693282 0.923395i
378378 2314.06 + 5906.36i 0.314873 + 0.803678i
379379 4008.82 + 2314.50i 0.543323 + 0.313688i 0.746425 0.665470i 0.231769π-0.231769\pi
−0.203101 + 0.979158i 0.565102π0.565102\pi
380380 −24413.2 −3.29571
381381 2453.64 10740.4i 0.329932 1.44422i
382382 −14117.9 8150.98i −1.89093 1.09173i
383383 8757.77i 1.16841i 0.811606 + 0.584205i 0.198594π0.198594\pi
−0.811606 + 0.584205i 0.801406π0.801406\pi
384384 −3879.92 12587.2i −0.515615 1.67275i
385385 −5483.51 + 3165.90i −0.725884 + 0.419089i
386386 6904.61 + 11959.1i 0.910455 + 1.57695i
387387 665.211 + 8923.71i 0.0873761 + 1.17214i
388388 9210.58 + 5317.73i 1.20515 + 0.695791i
389389 −5694.49 9863.15i −0.742216 1.28556i −0.951484 0.307698i 0.900441π-0.900441\pi
0.209268 0.977858i 0.432892π-0.432892\pi
390390 14669.5 + 4530.33i 1.90466 + 0.588211i
391391 −3249.61 + 5628.50i −0.420307 + 0.727993i
392392 16243.5 9378.20i 2.09291 1.20834i
393393 −76.7915 + 336.141i −0.00985653 + 0.0431452i
394394 −3945.92 + 6834.54i −0.504550 + 0.873907i
395395 25.4349i 0.00323992i
396396 20289.9 + 29784.9i 2.57476 + 3.77967i
397397 339.920 196.253i 0.0429725 0.0248102i −0.478360 0.878164i 0.658769π-0.658769\pi
0.521332 + 0.853354i 0.325435π0.325435\pi
398398 22701.8 13106.9i 2.85914 1.65072i
399399 4173.09 1286.33i 0.523598 0.161396i
400400 1302.39 + 2255.81i 0.162799 + 0.281977i
401401 −10519.3 + 6073.31i −1.30999 + 0.756325i −0.982095 0.188388i 0.939674π-0.939674\pi
−0.327899 + 0.944713i 0.606341π0.606341\pi
402402 2841.05 + 2637.15i 0.352484 + 0.327187i
403403 −2873.20 + 4212.94i −0.355147 + 0.520749i
404404 29320.4 3.61075
405405 −6694.85 + 5330.35i −0.821407 + 0.653994i
406406 −3269.32 + 5662.64i −0.399640 + 0.692197i
407407 −175.970 + 304.789i −0.0214312 + 0.0371200i
408408 14914.5 16067.6i 1.80974 1.94967i
409409 4759.97i 0.575465i −0.957711 0.287733i 0.907099π-0.907099\pi
0.957711 0.287733i 0.0929014π-0.0929014\pi
410410 4201.80i 0.506127i
411411 −4108.35 938.553i −0.493065 0.112641i
412412 2691.89 4662.48i 0.321892 0.557534i
413413 −2800.34 + 4850.34i −0.333646 + 0.577892i
414414 6685.37 13868.4i 0.793642 1.64636i
415415 1664.22 0.196851
416416 25293.8 + 1899.05i 2.98108 + 0.223819i
417417 −5200.80 + 1603.11i −0.610754 + 0.188261i
418418 29734.6 17167.3i 3.47935 2.00880i
419419 2297.80 + 3979.90i 0.267911 + 0.464036i 0.968322 0.249704i 0.0803333π-0.0803333\pi
−0.700411 + 0.713740i 0.747000π0.747000\pi
420420 −7843.34 7280.42i −0.911228 0.845829i
421421 5888.64 3399.81i 0.681698 0.393578i −0.118797 0.992919i 0.537904π-0.537904\pi
0.800494 + 0.599340i 0.204570π0.204570\pi
422422 24766.1 14298.7i 2.85686 1.64941i
423423 2451.26 5084.97i 0.281759 0.584491i
424424 20899.0i 2.39374i
425425 −391.788 + 678.596i −0.0447165 + 0.0774512i
426426 −7170.60 6655.97i −0.815532 0.757002i
427427 −4639.92 + 2678.86i −0.525858 + 0.303604i
428428 −21694.0 + 37575.0i −2.45004 + 4.24359i
429429 −15212.1 + 3466.69i −1.71200 + 0.390148i
430430 −10446.1 18093.2i −1.17152 2.02914i
431431 −1238.01 714.766i −0.138359 0.0798818i 0.429223 0.903199i 0.358788π-0.358788\pi
−0.567582 + 0.823317i 0.692121π0.692121\pi
432432 −17810.9 + 22307.2i −1.98363 + 2.48439i
433433 −5071.03 8783.28i −0.562813 0.974821i −0.997249 0.0741185i 0.976386π-0.976386\pi
0.434436 0.900703i 0.356948π-0.356948\pi
434434 4260.10 2459.57i 0.471178 0.272035i
435435 −8599.39 1964.53i −0.947838 0.216534i
436436 23855.6i 2.62036i
437437 −9178.39 5299.15i −1.00472 0.580075i
438438 13256.9 4086.36i 1.44621 0.445785i
439439 7604.04 0.826700 0.413350 0.910572i 0.364359π-0.364359\pi
0.413350 + 0.910572i 0.364359π0.364359\pi
440440 −44891.2 25917.9i −4.86387 2.80816i
441441 −6617.98 3190.26i −0.714608 0.344483i
442442 6682.40 + 13881.1i 0.719116 + 1.49379i
443443 5480.82 + 9493.06i 0.587814 + 1.01812i 0.994518 + 0.104564i 0.0333448π0.0333448\pi
−0.406704 + 0.913560i 0.633322π0.633322\pi
444444 −579.882 132.474i −0.0619820 0.0141598i
445445 487.759 + 844.823i 0.0519595 + 0.0899965i
446446 22078.4 2.34405
447447 804.516 + 2610.00i 0.0851282 + 0.276172i
448448 −9320.84 5381.39i −0.982965 0.567515i
449449 −3552.85 + 2051.24i −0.373428 + 0.215599i −0.674955 0.737859i 0.735837π-0.735837\pi
0.301527 + 0.953458i 0.402504π0.402504\pi
450450 806.017 1672.03i 0.0844356 0.175156i
451451 −2134.98 3697.90i −0.222910 0.386091i
452452 15575.7 1.62084
453453 39.8394 42.9198i 0.00413205 0.00445154i
454454 −10027.1 + 17367.4i −1.03655 + 1.79536i
455455 4174.40 2009.57i 0.430108 0.207055i
456456 26201.5 + 24321.0i 2.69078 + 2.49767i
457457 13148.4i 1.34586i −0.739707 0.672929i 0.765036π-0.765036\pi
0.739707 0.672929i 0.234964π-0.234964\pi
458458 8301.96 14379.4i 0.846998 1.46704i
459459 −8490.40 1284.84i −0.863394 0.130657i
460460 25972.5i 2.63255i
461461 −569.224 328.642i −0.0575085 0.0332026i 0.470970 0.882149i 0.343904π-0.343904\pi
−0.528479 + 0.848947i 0.677237π0.677237\pi
462462 14672.5 + 3351.95i 1.47755 + 0.337547i
463463 5806.14 + 3352.18i 0.582795 + 0.336477i 0.762244 0.647290i 0.224098π-0.224098\pi
−0.179448 + 0.983767i 0.557431π0.557431\pi
464464 −29423.6 −2.94387
465465 4863.75 + 4514.68i 0.485056 + 0.450244i
466466 15010.5i 1.49216i
467467 −5159.32 −0.511231 −0.255616 0.966779i 0.582278π-0.582278\pi
−0.255616 + 0.966779i 0.582278π0.582278\pi
468468 −13172.6 22843.7i −1.30108 2.25630i
469469 1169.72 0.115166
470470 13179.4i 1.29345i
471471 1793.97 7852.79i 0.175503 0.768232i
472472 −45850.5 −4.47127
473473 18386.7 + 10615.6i 1.78736 + 1.03193i
474474 41.1307 44.3109i 0.00398565 0.00429381i
475475 −1106.59 638.888i −0.106892 0.0617141i
476476 10738.3i 1.03401i
477477 −6765.45 + 4608.71i −0.649410 + 0.442387i
478478 −9149.24 + 15847.0i −0.875474 + 1.51637i
479479 5030.03i 0.479808i 0.970797 + 0.239904i 0.0771159π0.0771159\pi
−0.970797 + 0.239904i 0.922884π0.922884\pi
480480 7351.47 32179.7i 0.699056 3.05999i
481481 145.091 212.746i 0.0137538 0.0201671i
482482 −6011.23 + 10411.7i −0.568058 + 0.983905i
483483 −1368.49 4439.63i −0.128920 0.418241i
484484 57773.0 5.42572
485485 2995.92 + 5189.09i 0.280491 + 0.485824i
486486 20283.0 + 1540.06i 1.89312 + 0.143742i
487487 −9594.76 + 5539.54i −0.892772 + 0.515442i −0.874848 0.484397i 0.839039π-0.839039\pi
−0.0179238 + 0.999839i 0.505706π0.505706\pi
488488 −37985.1 21930.7i −3.52358 2.03434i
489489 −8512.85 + 9171.05i −0.787248 + 0.848117i
490490 17152.7 1.58139
491491 −4565.93 7908.43i −0.419669 0.726889i 0.576237 0.817283i 0.304521π-0.304521\pi
−0.995906 + 0.0903942i 0.971187π0.971187\pi
492492 4909.68 5289.29i 0.449889 0.484674i
493493 −4425.62 7665.40i −0.404300 0.700268i
494494 −22635.9 + 10897.0i −2.06161 + 0.992468i
495495 1509.35 + 20247.7i 0.137051 + 1.83852i
496496 19170.2 + 11067.9i 1.73542 + 1.00195i
497497 −2952.29 −0.266456
498498 −2899.28 2691.20i −0.260883 0.242160i
499499 221.565 + 127.921i 0.0198770 + 0.0114760i 0.509906 0.860230i 0.329680π-0.329680\pi
−0.490029 + 0.871706i 0.663014π0.663014\pi
500500 27443.3i 2.45460i
501501 −3007.85 + 3240.41i −0.268225 + 0.288964i
502502 −26615.3 + 15366.3i −2.36633 + 1.36620i
503503 2257.49 + 3910.09i 0.200113 + 0.346605i 0.948565 0.316584i 0.102536π-0.102536\pi
−0.748452 + 0.663189i 0.769202π0.769202\pi
504504 1164.93 + 15627.4i 0.102957 + 1.38115i
505505 14305.6 + 8259.32i 1.26057 + 0.727792i
506506 −18263.8 31633.8i −1.60459 2.77924i
507507 11289.2 1696.09i 0.988902 0.148572i
508508 22089.1 38259.4i 1.92922 3.34151i
509509 8937.71 5160.19i 0.778305 0.449354i −0.0575246 0.998344i 0.518321π-0.518321\pi
0.835829 + 0.548990i 0.184987π0.184987\pi
510510 19158.9 5905.60i 1.66347 0.512754i
511511 2093.06 3625.28i 0.181197 0.313842i
512512 2095.01i 0.180834i
513513 2095.20 13845.3i 0.180322 1.19159i
514514 −12375.9 + 7145.24i −1.06202 + 0.613158i
515515 2626.77 1516.57i 0.224756 0.129763i
516516 −7991.63 + 34981.9i −0.681806 + 2.98448i
517517 −6696.60 11598.9i −0.569664 0.986687i
518518 −215.127 + 124.204i −0.0182474 + 0.0105351i
519519 −779.586 + 3412.50i −0.0659345 + 0.288616i
520520 31334.5 + 21369.9i 2.64251 + 1.80218i
521521 −17801.0 −1.49688 −0.748442 0.663200i 0.769198π-0.769198\pi
−0.748442 + 0.663200i 0.769198π0.769198\pi
522522 11804.4 + 17328.5i 0.989779 + 1.45297i
523523 1182.75 2048.59i 0.0988874 0.171278i −0.812337 0.583188i 0.801805π-0.801805\pi
0.911224 + 0.411910i 0.135138π0.135138\pi
524524 −691.321 + 1197.40i −0.0576345 + 0.0998259i
525525 −164.991 535.262i −0.0137158 0.0444966i
526526 29755.5i 2.46655i
527527 6658.94i 0.550414i
528528 19950.1 + 64721.7i 1.64435 + 5.33457i
529529 445.882 772.289i 0.0366468 0.0634741i
530530 9556.08 16551.6i 0.783188 1.35652i
531531 10111.1 + 14842.8i 0.826334 + 1.21303i
532532 17510.9 1.42706
533533 1355.19 + 2815.08i 0.110131 + 0.228770i
534534 516.422 2260.54i 0.0418498 0.183190i
535535 −21169.2 + 12222.0i −1.71070 + 0.987672i
536536 4788.02 + 8293.09i 0.385841 + 0.668297i
537537 4383.01 19185.8i 0.352218 1.54177i
538538 −13056.1 + 7537.96i −1.04626 + 0.604060i
539539 −15095.7 + 8715.49i −1.20634 + 0.696480i
540540 −31951.3 + 12518.2i −2.54623 + 0.997588i
541541 16139.3i 1.28259i 0.767294 + 0.641295i 0.221603π0.221603\pi
−0.767294 + 0.641295i 0.778397π0.778397\pi
542542 3520.73 6098.07i 0.279019 0.483274i
543543 11885.4 3663.61i 0.939324 0.289541i
544544 28684.6 16561.1i 2.26074 1.30524i
545545 6719.95 11639.3i 0.528167 0.914811i
546546 −10522.0 3249.48i −0.824726 0.254698i
547547 3851.87 + 6671.63i 0.301086 + 0.521496i 0.976382 0.216050i 0.0693175π-0.0693175\pi
−0.675296 + 0.737547i 0.735984π0.735984\pi
548548 −14634.8 8449.39i −1.14082 0.658650i
549549 1277.15 + 17132.8i 0.0992849 + 1.33189i
550550 −2201.96 3813.91i −0.170713 0.295683i
551551 12500.0 7216.86i 0.966455 0.557983i
552552 25874.4 27875.0i 1.99509 2.14935i
553553 18.2438i 0.00140290i
554554 −32737.8 18901.2i −2.51064 1.44952i
555555 −245.610 227.983i −0.0187848 0.0174367i
556556 −21823.4 −1.66460
557557 7014.78 + 4049.98i 0.533619 + 0.308085i 0.742489 0.669858i 0.233645π-0.233645\pi
−0.208870 + 0.977943i 0.566979π0.566979\pi
558558 −1172.60 15730.3i −0.0889610 1.19340i
559559 −12834.1 8752.74i −0.971062 0.662257i
560560 −10055.4 17416.5i −0.758785 1.31425i
561561 −13860.5 + 14932.2i −1.04312 + 1.12378i
562562 −7811.44 13529.8i −0.586309 1.01552i
563563 14995.5 1.12253 0.561265 0.827636i 0.310315π-0.310315\pi
0.561265 + 0.827636i 0.310315π0.310315\pi
564564 15399.7 16590.4i 1.14973 1.23862i
565565 7599.49 + 4387.56i 0.565863 + 0.326701i
566566 −28647.3 + 16539.5i −2.12745 + 1.22828i
567567 4802.03 3823.32i 0.355673 0.283182i
568568 −12084.6 20931.2i −0.892709 1.54622i
569569 22982.6 1.69329 0.846643 0.532161i 0.178620π-0.178620\pi
0.846643 + 0.532161i 0.178620π0.178620\pi
570570 9630.27 + 31242.4i 0.707662 + 2.29579i
571571 3053.73 5289.21i 0.223808 0.387647i −0.732153 0.681140i 0.761484π-0.761484\pi
0.955961 + 0.293493i 0.0948178π0.0948178\pi
572572 −62388.6 4684.12i −4.56049 0.342400i
573573 −3513.14 + 15378.1i −0.256132 + 1.12117i
574574 3013.84i 0.219155i
575575 −679.696 + 1177.27i −0.0492961 + 0.0853834i
576576 −28523.2 + 19430.3i −2.06331 + 1.40555i
577577 6485.30i 0.467914i 0.972247 + 0.233957i 0.0751676π0.0751676\pi
−0.972247 + 0.233957i 0.924832π0.924832\pi
578578 −5425.94 3132.67i −0.390466 0.225436i
579579 9090.58 9793.45i 0.652490 0.702940i
580580 −30632.8 17685.9i −2.19303 1.26615i
581581 −1193.70 −0.0852375
582582 3171.98 13884.8i 0.225916 0.988904i
583583 19422.2i 1.37974i
584584 34270.0 2.42826
585585 7.91227 14856.2i 0.000559200 1.04996i
586586 −34339.3 −2.42072
587587 18389.1i 1.29302i −0.762907 0.646508i 0.776229π-0.776229\pi
0.762907 0.646508i 0.223771π-0.223771\pi
588588 −21592.1 20042.4i −1.51436 1.40567i
589589 −10858.7 −0.759638
590590 −36312.7 20965.1i −2.53385 1.46292i
591591 7444.62 + 1700.73i 0.518157 + 0.118373i
592592 −968.061 558.910i −0.0672079 0.0388025i
593593 8897.54i 0.616152i −0.951362 0.308076i 0.900315π-0.900315\pi
0.951362 0.308076i 0.0996851π-0.0996851\pi
594594 30113.0 37714.9i 2.08005 2.60515i
595595 3024.89 5239.26i 0.208417 0.360989i
596596 10952.0i 0.752701i
597597 −18590.7 17256.4i −1.27448 1.18301i
598598 11593.0 + 24081.7i 0.792765 + 1.64678i
599599 3417.69 5919.62i 0.233127 0.403788i −0.725600 0.688117i 0.758437π-0.758437\pi
0.958727 + 0.284329i 0.0917708π0.0917708\pi
600600 3119.54 3360.73i 0.212258 0.228669i
601601 −16844.9 −1.14329 −0.571644 0.820502i 0.693694π-0.693694\pi
−0.571644 + 0.820502i 0.693694π0.693694\pi
602602 7492.70 + 12977.7i 0.507275 + 0.878626i
603603 1628.78 3378.80i 0.109998 0.228184i
604604 203.364 117.412i 0.0136999 0.00790966i
605605 28187.8 + 16274.2i 1.89421 + 1.09362i
606606 −11566.0 37522.3i −0.775308 2.51524i
607607 10593.7 0.708375 0.354187 0.935175i 0.384758π-0.384758\pi
0.354187 + 0.935175i 0.384758π0.384758\pi
608608 27006.1 + 46776.0i 1.80139 + 3.12010i
609609 6168.11 + 1409.11i 0.410418 + 0.0937601i
610610 −20055.6 34737.4i −1.33119 2.30570i
611611 4250.69 + 8829.80i 0.281448 + 0.584641i
612612 −31018.0 14952.5i −2.04874 0.987613i
613613 13031.2 + 7523.54i 0.858603 + 0.495715i 0.863544 0.504273i 0.168240π-0.168240\pi
−0.00494128 + 0.999988i 0.501573π0.501573\pi
614614 34349.1 2.25768
615615 3885.41 1197.65i 0.254756 0.0785269i
616616 32199.2 + 18590.2i 2.10608 + 1.21594i
617617 22615.3i 1.47562i 0.675009 + 0.737810i 0.264140π0.264140\pi
−0.675009 + 0.737810i 0.735860π0.735860\pi
618618 −7028.60 1605.69i −0.457495 0.104515i
619619 −15814.0 + 9130.21i −1.02685 + 0.592850i −0.916080 0.400996i 0.868664π-0.868664\pi
−0.110767 + 0.993846i 0.535331π0.535331\pi
620620 13305.4 + 23045.6i 0.861867 + 1.49280i
621621 −14729.6 2229.02i −0.951819 0.144038i
622622 −36244.6 20925.8i −2.33646 1.34895i
623623 −349.856 605.969i −0.0224987 0.0389689i
624624 −11010.8 48316.3i −0.706386 3.09968i
625625 8530.69 14775.6i 0.545964 0.945637i
626626 6569.34 3792.81i 0.419431 0.242158i
627627 −24349.9 22602.4i −1.55095 1.43964i
628628 16150.4 27973.3i 1.02623 1.77748i
629629 336.264i 0.0213159i
630630 −6223.04 + 12909.3i −0.393543 + 0.816378i
631631 12091.5 6981.04i 0.762846 0.440429i −0.0674708 0.997721i 0.521493π-0.521493\pi
0.830317 + 0.557292i 0.188160π0.188160\pi
632632 129.345 74.6771i 0.00814091 0.00470015i
633633 −20281.2 18825.6i −1.27347 1.18207i
634634 13905.9 + 24085.8i 0.871095 + 1.50878i
635635 21554.8 12444.6i 1.34705 0.777717i
636636 −31369.4 + 9669.43i −1.95578 + 0.602858i
637637 11491.8 5532.19i 0.714791 0.344103i
638638 49746.6 3.08697
639639 −4110.92 + 8527.83i −0.254500 + 0.527944i
640640 14878.3 25770.0i 0.918934 1.59164i
641641 −15169.9 + 26275.0i −0.934748 + 1.61903i −0.159665 + 0.987171i 0.551041π0.551041\pi
−0.775083 + 0.631860i 0.782292π0.782292\pi
642642 56643.6 + 12940.3i 3.48216 + 0.795500i
643643 11875.9i 0.728366i −0.931327 0.364183i 0.881348π-0.881348\pi
0.931327 0.364183i 0.118652π-0.118652\pi
644644 18629.4i 1.13991i
645645 −13753.3 + 14816.7i −0.839589 + 0.904505i
646646 −16402.6 + 28410.2i −0.998997 + 1.73031i
647647 −6511.05 + 11277.5i −0.395635 + 0.685260i −0.993182 0.116574i 0.962809π-0.962809\pi
0.597547 + 0.801834i 0.296142π0.296142\pi
648648 46762.7 + 18395.5i 2.83489 + 1.11519i
649649 42610.5 2.57721
650650 1397.70 + 2903.40i 0.0843423 + 0.175201i
651651 −3488.64 3238.26i −0.210031 0.194958i
652652 −43454.6 + 25088.5i −2.61014 + 1.50697i
653653 5187.04 + 8984.22i 0.310849 + 0.538407i 0.978547 0.206026i 0.0660532π-0.0660532\pi
−0.667697 + 0.744433i 0.732720π0.732720\pi
654654 −30528.9 + 9410.33i −1.82534 + 0.562650i
655655 −674.598 + 389.479i −0.0402423 + 0.0232339i
656656 11745.1 6781.06i 0.699041 0.403591i
657657 −7557.31 11093.9i −0.448765 0.658775i
658658 9453.22i 0.560068i
659659 1295.81 2244.40i 0.0765971 0.132670i −0.825183 0.564866i 0.808928π-0.808928\pi
0.901780 + 0.432196i 0.142261π0.142261\pi
660660 −18132.8 + 79373.2i −1.06942 + 4.68121i
661661 17856.5 10309.5i 1.05074 0.606645i 0.127884 0.991789i 0.459182π-0.459182\pi
0.922856 + 0.385144i 0.125848π0.125848\pi
662662 −19075.3 + 33039.3i −1.11991 + 1.93974i
663663 10931.2 10135.8i 0.640318 0.593728i
664664 −4886.16 8463.08i −0.285572 0.494625i
665665 8543.66 + 4932.69i 0.498209 + 0.287641i
666666 59.2142 + 794.351i 0.00344520 + 0.0462170i
667667 −7677.82 13298.4i −0.445707 0.771987i
668668 −15353.8 + 8864.53i −0.889307 + 0.513442i
669669 −6293.09 20416.0i −0.363685 1.17986i
670670 8757.29i 0.504960i
671671 35300.9 + 20381.0i 2.03096 + 1.17258i
672672 −5273.01 + 23081.6i −0.302694 + 1.32499i
673673 −17596.4 −1.00786 −0.503932 0.863744i 0.668114π-0.668114\pi
−0.503932 + 0.863744i 0.668114π0.668114\pi
674674 9452.84 + 5457.60i 0.540222 + 0.311897i
675675 −1775.87 268.741i −0.101264 0.0153242i
676676 45264.4 + 6835.41i 2.57536 + 0.388906i
677677 −644.287 1115.94i −0.0365760 0.0633515i 0.847158 0.531341i 0.178312π-0.178312\pi
−0.883734 + 0.467990i 0.844978π0.844978\pi
678678 −6144.16 19932.8i −0.348031 1.12908i
679679 −2148.90 3722.00i −0.121454 0.210364i
680680 49527.0 2.79305
681681 18917.7 + 4321.76i 1.06451 + 0.243187i
682682 −32411.2 18712.6i −1.81978 1.05065i
683683 11888.3 6863.70i 0.666021 0.384527i −0.128546 0.991704i 0.541031π-0.541031\pi
0.794567 + 0.607176i 0.207698π0.207698\pi
684684 24383.1 50581.1i 1.36303 2.82751i
685685 −4760.25 8245.00i −0.265518 0.459891i
686686 −27811.9 −1.54791
687687 −15663.0 3578.22i −0.869841 0.198715i
688688 −33716.8 + 58399.2i −1.86837 + 3.23611i
689689 1063.97 14171.2i 0.0588301 0.783568i
690690 33237.9 10245.4i 1.83383 0.565268i
691691 15077.3i 0.830056i 0.909809 + 0.415028i 0.136228π0.136228\pi
−0.909809 + 0.415028i 0.863772π0.863772\pi
692692 −7018.28 + 12156.0i −0.385542 + 0.667778i
693693 −1082.61 14523.1i −0.0593436 0.796087i
694694 27346.5i 1.49576i
695695 −10647.7 6147.47i −0.581138 0.335520i
696696 15257.6 + 49498.5i 0.830946 + 2.69574i
697697 3533.19 + 2039.89i 0.192007 + 0.110855i
698698 −23350.0 −1.26620
699699 13880.2 4278.49i 0.751069 0.231512i
700700 2246.04i 0.121275i
701701 9756.56 0.525678 0.262839 0.964840i 0.415341π-0.415341\pi
0.262839 + 0.964840i 0.415341π0.415341\pi
702702 −24037.6 + 25868.5i −1.29237 + 1.39081i
703703 548.346 0.0294186
704704 81884.1i 4.38370i
705705 12187.0 3756.57i 0.651048 0.200682i
706706 48201.8 2.56954
707707 −10261.0 5924.18i −0.545833 0.315137i
708708 21213.8 + 68821.6i 1.12608 + 3.65321i
709709 7601.62 + 4388.80i 0.402659 + 0.232475i 0.687630 0.726061i 0.258651π-0.258651\pi
−0.284972 + 0.958536i 0.591984π0.591984\pi
710710 22102.7i 1.16831i
711711 −52.6980 25.4035i −0.00277965 0.00133995i
712712 2864.13 4960.81i 0.150755 0.261116i
713713 11552.3i 0.606785i
714714 −13742.1 + 4235.93i −0.720289 + 0.222025i
715715 −29120.2 19859.8i −1.52313 1.03876i
716716 39458.4 68343.9i 2.05954 3.56722i
717717 17261.5 + 3943.40i 0.899085 + 0.205396i
718718 8917.07 0.463485
719719 −14737.9 25526.8i −0.764439 1.32405i −0.940542 0.339676i 0.889683π-0.889683\pi
0.176103 0.984372i 0.443651π-0.443651\pi
720720 −64310.1 + 4793.94i −3.32874 + 0.248138i
721721 −1884.11 + 1087.79i −0.0973203 + 0.0561879i
722722 −14430.6 8331.49i −0.743836 0.429454i
723723 11341.2 + 2590.89i 0.583377 + 0.133273i
724724 49873.1 2.56011
725725 −925.671 1603.31i −0.0474187 0.0821316i
726726 −22789.7 73934.1i −1.16502 3.77955i
727727 10788.1 + 18685.5i 0.550354 + 0.953242i 0.998249 + 0.0591553i 0.0188407π0.0188407\pi
−0.447894 + 0.894086i 0.647826π0.647826\pi
728728 −22475.4 15328.0i −1.14422 0.780350i
729729 −4357.23 19194.7i −0.221370 0.975190i
730730 27141.2 + 15670.0i 1.37608 + 0.794481i
731731 −20285.4 −1.02638
732732 −15343.3 + 67162.4i −0.774731 + 3.39125i
733733 −10580.0 6108.38i −0.533127 0.307801i 0.209162 0.977881i 0.432926π-0.432926\pi
−0.742289 + 0.670080i 0.766260π0.766260\pi
734734 3754.02i 0.188779i
735735 −4889.10 15861.1i −0.245356 0.795982i
736736 49763.7 28731.1i 2.49228 1.43892i
737737 −4449.68 7707.06i −0.222396 0.385201i
738738 −8705.60 4196.62i −0.434224 0.209322i
739739 −31979.8 18463.5i −1.59187 0.919068i −0.992986 0.118235i 0.962276π-0.962276\pi
−0.598888 0.800833i 0.704390π-0.704390\pi
740740 −671.897 1163.76i −0.0333776 0.0578117i
741741 16528.4 + 17825.4i 0.819417 + 0.883716i
742742 −6854.32 + 11872.0i −0.339124 + 0.587380i
743743 −15838.7 + 9144.46i −0.782052 + 0.451518i −0.837157 0.546963i 0.815784π-0.815784\pi
0.0551050 + 0.998481i 0.482451π0.482451\pi
744744 8678.57 37988.9i 0.427650 1.87196i
745745 −3085.08 + 5343.51i −0.151716 + 0.262780i
746746 14396.2i 0.706542i
747747 −1662.16 + 3448.05i −0.0814129 + 0.168886i
748748 −70752.3 + 40848.9i −3.45850 + 1.99677i
749749 15184.1 8766.53i 0.740739 0.427666i
750750 −35120.1 + 10825.5i −1.70987 + 0.527057i
751751 1937.61 + 3356.04i 0.0941470 + 0.163067i 0.909252 0.416245i 0.136654π-0.136654\pi
−0.815105 + 0.579313i 0.803321π0.803321\pi
752752 36839.9 21269.5i 1.78645 1.03141i
753753 21795.5 + 20231.3i 1.05481 + 0.979108i
754754 −36297.0 2725.16i −1.75313 0.131624i
755755 132.296 0.00637716
756756 22917.8 8978.97i 1.10253 0.431960i
757757 −456.389 + 790.489i −0.0219125 + 0.0379535i −0.876774 0.480903i 0.840309π-0.840309\pi
0.854861 + 0.518857i 0.173642π0.173642\pi
758758 12428.7 21527.2i 0.595557 1.03154i
759759 −24046.0 + 25905.2i −1.14995 + 1.23887i
760760 80763.7i 3.85475i
761761 31894.5i 1.51929i 0.650341 + 0.759643i 0.274626π0.274626\pi
−0.650341 + 0.759643i 0.725374π0.725374\pi
762762 −57675.3 13176.0i −2.74194 0.626397i
763763 −4820.03 + 8348.54i −0.228698 + 0.396117i
764764 −31627.3 + 54780.1i −1.49769 + 2.59408i
765765 −10921.8 16032.9i −0.516182 0.757741i
766766 47028.8 2.21830
767767 −31090.2 2334.24i −1.46363 0.109889i
768768 −16814.7 + 5183.04i −0.790038 + 0.243524i
769769 7296.61 4212.70i 0.342162 0.197547i −0.319066 0.947733i 0.603369π-0.603369\pi
0.661228 + 0.750185i 0.270036π0.270036\pi
770770 17000.8 + 29446.2i 0.795669 + 1.37814i
771771 10134.8 + 9407.39i 0.473404 + 0.439428i
772772 46403.7 26791.2i 2.16335 1.24901i
773773 13965.8 8063.17i 0.649826 0.375177i −0.138563 0.990354i 0.544248π-0.544248\pi
0.788390 + 0.615176i 0.210915π0.210915\pi
774774 47920.0 3572.15i 2.22538 0.165889i
775775 1392.80i 0.0645558i
776776 17592.1 30470.4i 0.813815 1.40957i
777777 176.170 + 163.526i 0.00813391 + 0.00755014i
778778 −52964.7 + 30579.2i −2.44071 + 1.40915i
779779 −3326.44 + 5761.57i −0.152994 + 0.264993i
780780 17578.5 56920.3i 0.806939 2.61291i
781781 11230.7 + 19452.1i 0.514551 + 0.891228i
782782 30224.8 + 17450.3i 1.38214 + 0.797981i
783783 12659.0 15854.7i 0.577775 0.723630i
784784 −27681.8 47946.4i −1.26102 2.18415i
785785 15759.7 9098.86i 0.716545 0.413697i
786786 1805.06 + 412.367i 0.0819140 + 0.0187133i
787787 27615.0i 1.25078i 0.780310 + 0.625392i 0.215061π0.215061\pi
−0.780310 + 0.625392i 0.784939π0.784939\pi
788788 26519.3 + 15310.9i 1.19887 + 0.692169i
789789 27515.0 8481.32i 1.24152 0.382691i
790790 136.584 0.00615121
791791 −5450.90 3147.08i −0.245021 0.141463i
792792 98534.5 67122.9i 4.42080 3.01150i
793793 −24640.4 16804.5i −1.10341 0.752518i
794794 −1053.87 1825.35i −0.0471038 0.0815861i
795795 −18029.1 4118.75i −0.804310 0.183745i
796796 −50857.1 88087.1i −2.26455 3.92232i
797797 11813.1 0.525019 0.262510 0.964929i 0.415450π-0.415450\pi
0.262510 + 0.964929i 0.415450π0.415450\pi
798798 −6907.53 22409.3i −0.306421 0.994086i
799799 11082.2 + 6398.32i 0.490689 + 0.283299i
800800 5999.73 3463.95i 0.265153 0.153086i
801801 −2237.52 + 166.794i −0.0987004 + 0.00735754i
802802 32613.4 + 56488.0i 1.43593 + 2.48711i
803803 −31848.3 −1.39963
804804 10232.6 11023.8i 0.448852 0.483557i
805805 5247.75 9089.37i 0.229763 0.397960i
806806 22623.3 + 15428.9i 0.988676 + 0.674269i
807807 10691.8 + 9924.44i 0.466380 + 0.432908i
808808 96997.7i 4.22323i
809809 10156.8 17592.1i 0.441402 0.764532i −0.556391 0.830920i 0.687814π-0.687814\pi
0.997794 + 0.0663888i 0.0211478π0.0211478\pi
810810 28623.8 + 35951.1i 1.24165 + 1.55950i
811811 3849.49i 0.166676i 0.996521 + 0.0833378i 0.0265581π0.0265581\pi
−0.996521 + 0.0833378i 0.973442π0.973442\pi
812812 21972.1 + 12685.6i 0.949592 + 0.548247i
813813 −6642.42 1517.46i −0.286543 0.0654609i
814814 1636.70 + 944.952i 0.0704748 + 0.0406886i
815815 −28269.0 −1.21499
816816 −47427.2 44023.3i −2.03466 1.88863i
817817 33079.5i 1.41653i
818818 −25560.8 −1.09256
819819 −5.67525 + 10655.9i −0.000242136 + 0.454637i
820820 16303.8 0.694332
821821 504.340i 0.0214392i 0.999943 + 0.0107196i 0.00341222π0.00341222\pi
−0.999943 + 0.0107196i 0.996588π0.996588\pi
822822 −5039.99 + 22061.6i −0.213856 + 0.936117i
823823 30422.7 1.28854 0.644270 0.764798i 0.277161π-0.277161\pi
0.644270 + 0.764798i 0.277161π0.277161\pi
824824 −15424.4 8905.30i −0.652106 0.376494i
825825 −2899.09 + 3123.25i −0.122344 + 0.131803i
826826 26046.1 + 15037.7i 1.09717 + 0.633450i
827827 7861.80i 0.330570i −0.986246 0.165285i 0.947146π-0.947146\pi
0.986246 0.165285i 0.0528544π-0.0528544\pi
828828 −53811.8 25940.5i −2.25856 1.08876i
829829 −15744.2 + 27269.8i −0.659613 + 1.14248i 0.321103 + 0.947044i 0.395946π0.395946\pi
−0.980716 + 0.195439i 0.937387π0.937387\pi
830830 8936.78i 0.373735i
831831 −8146.58 + 35660.2i −0.340074 + 1.48861i
832832 4485.69 59745.7i 0.186915 2.48955i
833833 8327.28 14423.3i 0.346366 0.599924i
834834 8608.66 + 27928.1i 0.357426 + 1.15956i
835835 −9988.27 −0.413962
836836 −66612.3 115376.i −2.75578 4.77315i
837837 −14211.6 + 5567.97i −0.586888 + 0.229937i
838838 21371.9 12339.1i 0.881003 0.508647i
839839 28133.5 + 16242.9i 1.15766 + 0.668375i 0.950742 0.309984i 0.100324π-0.100324\pi
0.206917 + 0.978358i 0.433657π0.433657\pi
840840 −24085.1 + 25947.3i −0.989303 + 1.06580i
841841 −3476.30 −0.142536
842842 −18256.8 31621.7i −0.747235 1.29425i
843843 −10284.5 + 11079.7i −0.420186 + 0.452675i
844844 −55481.7 96097.1i −2.26275 3.91919i
845845 20159.3 + 16085.7i 0.820710 + 0.654868i
846846 −27306.1 13163.1i −1.10969 0.534938i
847847 −20218.3 11673.0i −0.820200 0.473543i
848848 −61688.2 −2.49809
849849 23459.6 + 21775.9i 0.948328 + 0.880267i
850850 3644.03 + 2103.88i 0.147046 + 0.0848972i
851851 583.370i 0.0234990i
852852 −25826.4 + 27823.3i −1.03850 + 1.11879i
853853 38754.7 22375.1i 1.55561 0.898133i 0.557944 0.829879i 0.311591π-0.311591\pi
0.997668 0.0682538i 0.0217428π-0.0217428\pi
854854 14385.4 + 24916.2i 0.576413 + 0.998377i
855855 26144.9 17810.2i 1.04577 0.712394i
856856 124306. + 71767.9i 4.96341 + 2.86563i
857857 459.332 + 795.586i 0.0183086 + 0.0317114i 0.875035 0.484060i 0.160839π-0.160839\pi
−0.856726 + 0.515772i 0.827505π0.827505\pi
858858 18616.0 + 81688.5i 0.740722 + 3.25035i
859859 −14789.9 + 25616.8i −0.587455 + 1.01750i 0.407109 + 0.913379i 0.366537π0.366537\pi
−0.994564 + 0.104123i 0.966797π0.966797\pi
860860 −70204.9 + 40532.8i −2.78368 + 1.60716i
861861 −2786.90 + 859.044i −0.110310 + 0.0340025i
862862 −3838.26 + 6648.06i −0.151661 + 0.262684i
863863 39382.6i 1.55342i −0.629861 0.776708i 0.716888π-0.716888\pi
0.629861 0.776708i 0.283112π-0.283112\pi
864864 59329.9 + 47371.3i 2.33616 + 1.86528i
865865 −6848.50 + 3953.99i −0.269198 + 0.155421i
866866 −47165.8 + 27231.2i −1.85076 + 1.06854i
867867 −1350.21 + 5910.29i −0.0528898 + 0.231515i
868868 −9543.59 16530.0i −0.373192 0.646388i
869869 −120.204 + 69.4001i −0.00469236 + 0.00270913i
870870 −10549.5 + 46178.4i −0.411104 + 1.79953i
871871 2824.45 + 5867.12i 0.109877 + 0.228243i
872872 −78919.2 −3.06484
873873 −13743.4 + 1024.49i −0.532810 + 0.0397178i
874874 −28456.2 + 49287.6i −1.10131 + 1.90753i
875875 −5544.91 + 9604.07i −0.214231 + 0.371059i
876876 −15855.8 51439.2i −0.611551 1.98398i
877877 20348.5i 0.783488i −0.920074 0.391744i 0.871872π-0.871872\pi
0.920074 0.391744i 0.128128π-0.128128\pi
878878 40833.4i 1.56954i
879879 9787.84 + 31753.6i 0.375581 + 1.21845i
880880 −76502.6 + 132506.i −2.93057 + 5.07590i
881881 −24802.5 + 42959.1i −0.948486 + 1.64283i −0.199868 + 0.979823i 0.564051π0.564051\pi
−0.748617 + 0.663002i 0.769282π0.769282\pi
882882 −17131.5 + 35538.3i −0.654024 + 1.35673i
883883 18405.7 0.701475 0.350737 0.936474i 0.385931π-0.385931\pi
0.350737 + 0.936474i 0.385931π0.385931\pi
884884 53861.2 25929.0i 2.04926 0.986522i
885885 −9036.16 + 39554.1i −0.343217 + 1.50237i
886886 50977.3 29431.8i 1.93298 1.11600i
887887 7683.33 + 13307.9i 0.290847 + 0.503761i 0.974010 0.226504i 0.0727297π-0.0727297\pi
−0.683163 + 0.730265i 0.739396π0.739396\pi
888888 −438.251 + 1918.37i −0.0165617 + 0.0724957i
889889 −15460.6 + 8926.20i −0.583277 + 0.336755i
890890 4536.66 2619.24i 0.170864 0.0986486i
891891 −43458.2 17095.5i −1.63401 0.642786i
892892 85668.5i 3.21569i
893893 −10433.7 + 18071.8i −0.390988 + 0.677210i
894894 14015.6 4320.22i 0.524330 0.161622i
895895 38503.9 22230.2i 1.43804 0.830250i
896896 −10671.8 + 18484.1i −0.397902 + 0.689187i
897897 18964.0 17584.2i 0.705897 0.654535i
898898 11015.0 + 19078.6i 0.409328 + 0.708978i
899899 −13625.2 7866.50i −0.505478 0.291838i
900900 −6487.78 3127.50i −0.240288 0.115833i
901901 −9278.55 16070.9i −0.343078 0.594229i
902902 −19857.6 + 11464.8i −0.733020 + 0.423209i
903903 9864.85 10627.6i 0.363546 0.391655i
904904 51527.7i 1.89578i
905905 24333.3 + 14048.9i 0.893776 + 0.516022i
906906 −230.477 213.936i −0.00845154 0.00784498i
907907 11289.2 0.413286 0.206643 0.978416i 0.433746π-0.433746\pi
0.206643 + 0.978416i 0.433746π0.433746\pi
908908 67388.9 + 38907.0i 2.46297 + 1.42200i
909909 −31400.2 + 21390.2i −1.14574 + 0.780492i
910910 −10791.3 22416.3i −0.393108 0.816588i
911911 −14294.1 24758.0i −0.519850 0.900406i −0.999734 0.0230743i 0.992655π-0.992655\pi
0.479884 0.877332i 0.340679π-0.340679\pi
912912 71788.9 77339.5i 2.60654 2.80808i
913913 4540.88 + 7865.03i 0.164601 + 0.285098i
914914 −70606.4 −2.55520
915915 −26405.2 + 28446.8i −0.954019 + 1.02778i
916916 −55794.8 32213.2i −2.01257 1.16196i
917917 483.870 279.363i 0.0174251 0.0100604i
918918 −6899.56 + 45593.1i −0.248060 + 1.63921i
919919 −25711.9 44534.3i −0.922913 1.59853i −0.794883 0.606763i 0.792468π-0.792468\pi
−0.128030 0.991770i 0.540865π-0.540865\pi
920920 85922.3 3.07910
921921 −9790.65 31762.7i −0.350285 1.13639i
922922 −1764.79 + 3056.71i −0.0630373 + 0.109184i
923923 −7128.70 14808.2i −0.254219 0.528079i
924924 13006.2 56932.2i 0.463065 2.02698i
925925 70.3337i 0.00250006i
926926 18001.0 31178.7i 0.638824 1.10648i
927927 518.606 + 6957.03i 0.0183746 + 0.246493i
928928 78257.2i 2.76823i
929929 −620.371 358.171i −0.0219093 0.0126493i 0.489005 0.872281i 0.337360π-0.337360\pi
−0.510915 + 0.859631i 0.670693π0.670693\pi
930930 24243.7 26118.1i 0.854818 0.920912i
931931 23520.0 + 13579.3i 0.827968 + 0.478028i
932932 58243.4 2.04703
933933 −9019.21 + 39479.9i −0.316480 + 1.38533i
934934 27705.3i 0.970606i
935935 −46027.2 −1.60989
936936 −75571.5 + 43577.6i −2.63903 + 1.52177i
937937 10269.7 0.358053 0.179027 0.983844i 0.442705π-0.442705\pi
0.179027 + 0.983844i 0.442705π0.442705\pi
938938 6281.36i 0.218650i
939939 −5379.69 4993.60i −0.186965 0.173546i
940940 51138.5 1.77442
941941 15117.0 + 8727.78i 0.523697 + 0.302357i 0.738446 0.674313i 0.235560π-0.235560\pi
−0.214749 + 0.976669i 0.568893π0.568893\pi
942942 −42169.1 9633.56i −1.45854 0.333204i
943943 6129.57 + 3538.91i 0.211672 + 0.122209i
944944 135338.i 4.66618i
945945 13711.0 + 2074.87i 0.471978 + 0.0714240i
946946 57005.1 98735.7i 1.95919 3.39342i
947947 22499.0i 0.772038i 0.922491 + 0.386019i 0.126150π0.126150\pi
−0.922491 + 0.386019i 0.873850π0.873850\pi
948948 −171.935 159.595i −0.00589048 0.00546772i
949949 23237.7 + 1744.68i 0.794867 + 0.0596784i
950950 −3430.80 + 5942.33i −0.117168 + 0.202942i
951951 18308.5 19724.1i 0.624283 0.672551i
952952 −35524.4 −1.20940
953953 17997.1 + 31171.9i 0.611734 + 1.05955i 0.990948 + 0.134246i 0.0428611π0.0428611\pi
−0.379214 + 0.925309i 0.623806π0.623806\pi
954954 24748.6 + 36330.2i 0.839900 + 1.23295i
955955 −30862.3 + 17818.3i −1.04574 + 0.603757i
956956 61489.1 + 35500.8i 2.08023 + 1.20102i
957957 −14179.4 46000.7i −0.478951 1.55381i
958958 27011.0 0.910947
959959 3414.40 + 5913.91i 0.114971 + 0.199135i
960960 −76010.7 17364.7i −2.55545 0.583795i
961961 −8977.39 15549.3i −0.301346 0.521946i
962962 −1142.44 779.132i −0.0382886 0.0261125i
963963 −4179.45 56066.8i −0.139856 1.87614i
964964 40399.5 + 23324.7i 1.34977 + 0.779292i
965965 30187.5 1.00701
966966 −23840.6 + 7348.73i −0.794058 + 0.244763i
967967 −253.944 146.615i −0.00844498 0.00487571i 0.495772 0.868453i 0.334885π-0.334885\pi
−0.504217 + 0.863577i 0.668219π0.668219\pi
968968 191125.i 6.34606i
969969 30946.2 + 7069.67i 1.02594 + 0.234376i
970970 27865.2 16088.0i 0.922369 0.532530i
971971 −2773.93 4804.59i −0.0916784 0.158792i 0.816539 0.577290i 0.195890π-0.195890\pi
−0.908217 + 0.418498i 0.862557π0.862557\pi
972972 5975.71 78701.8i 0.197192 2.59708i
973973 7637.32 + 4409.41i 0.251635 + 0.145282i
974974 29747.1 + 51523.4i 0.978601 + 1.69499i
975975 2286.38 2120.02i 0.0751003 0.0696360i
976976 −64733.4 + 112122.i −2.12302 + 3.67717i
977977 −38408.3 + 22175.0i −1.25772 + 0.726143i −0.972630 0.232358i 0.925356π-0.925356\pi
−0.285087 + 0.958502i 0.592022π0.592022\pi
978978 49248.1 + 45713.6i 1.61021 + 1.49464i
979979 −2661.73 + 4610.26i −0.0868942 + 0.150505i
980980 66555.7i 2.16943i
981981 17403.5 + 25547.8i 0.566412 + 0.831477i
982982 −42467.9 + 24518.9i −1.38005 + 0.796770i
983983 7906.47 4564.80i 0.256538 0.148113i −0.366216 0.930530i 0.619347π-0.619347\pi
0.622754 + 0.782417i 0.286014π0.286014\pi
984984 −17498.0 16242.2i −0.566887 0.526202i
985985 8625.93 + 14940.5i 0.279030 + 0.483295i
986986 −41162.9 + 23765.4i −1.32951 + 0.767590i
987987 −8741.40 + 2694.48i −0.281907 + 0.0868960i
988988 42282.4 + 87831.6i 1.36152 + 2.82823i
989989 −35192.3 −1.13150
990990 108729. 8105.13i 3.49055 0.260200i
991991 −23742.5 + 41123.3i −0.761056 + 1.31819i 0.181251 + 0.983437i 0.441985π0.441985\pi
−0.942307 + 0.334751i 0.891348π0.891348\pi
992992 29437.1 50986.6i 0.942168 1.63188i
993993 35988.6 + 8221.60i 1.15011 + 0.262744i
994994 15853.7i 0.505884i
995995 57304.2i 1.82579i
996996 −10442.4 + 11249.8i −0.332208 + 0.357894i
997997 −12692.9 + 21984.7i −0.403198 + 0.698359i −0.994110 0.108377i 0.965435π-0.965435\pi
0.590912 + 0.806736i 0.298768π0.298768\pi
998998 686.928 1189.79i 0.0217879 0.0377377i
999999 717.659 281.172i 0.0227285 0.00890479i
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 117.4.l.a.4.2 80
3.2 odd 2 351.4.l.a.199.39 80
9.2 odd 6 351.4.r.a.316.39 80
9.7 even 3 117.4.r.a.43.2 yes 80
13.10 even 6 117.4.r.a.49.2 yes 80
39.23 odd 6 351.4.r.a.10.39 80
117.88 even 6 inner 117.4.l.a.88.39 yes 80
117.101 odd 6 351.4.l.a.127.2 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
117.4.l.a.4.2 80 1.1 even 1 trivial
117.4.l.a.88.39 yes 80 117.88 even 6 inner
117.4.r.a.43.2 yes 80 9.7 even 3
117.4.r.a.49.2 yes 80 13.10 even 6
351.4.l.a.127.2 80 117.101 odd 6
351.4.l.a.199.39 80 3.2 odd 2
351.4.r.a.10.39 80 39.23 odd 6
351.4.r.a.316.39 80 9.2 odd 6