Properties

Label 39.4.j.c.10.2
Level $39$
Weight $4$
Character 39.10
Analytic conductor $2.301$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [39,4,Mod(4,39)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(39, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("39.4");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 39 = 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 39.j (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.30107449022\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 10.2
Root \(2.04224i\) of defining polynomial
Character \(\chi\) \(=\) 39.10
Dual form 39.4.j.c.4.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.76863 + 1.02112i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-1.91462 + 3.31622i) q^{4} -12.0825i q^{5} +(5.30590 + 3.06336i) q^{6} +(-25.7533 - 14.8686i) q^{7} -24.1582i q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\) \(q+(-1.76863 + 1.02112i) q^{2} +(-1.50000 - 2.59808i) q^{3} +(-1.91462 + 3.31622i) q^{4} -12.0825i q^{5} +(5.30590 + 3.06336i) q^{6} +(-25.7533 - 14.8686i) q^{7} -24.1582i q^{8} +(-4.50000 + 7.79423i) q^{9} +(12.3377 + 21.3694i) q^{10} +(24.3038 - 14.0318i) q^{11} +11.4877 q^{12} +(-40.9717 + 22.7667i) q^{13} +60.7308 q^{14} +(-31.3911 + 18.1237i) q^{15} +(9.35146 + 16.1972i) q^{16} +(-25.3278 + 43.8690i) q^{17} -18.3802i q^{18} +(91.0612 + 52.5742i) q^{19} +(40.0681 + 23.1333i) q^{20} +89.2119i q^{21} +(-28.6563 + 49.6342i) q^{22} +(-80.2961 - 139.077i) q^{23} +(-62.7648 + 36.2373i) q^{24} -20.9857 q^{25} +(49.2164 - 82.1030i) q^{26} +27.0000 q^{27} +(98.6155 - 56.9357i) q^{28} +(-70.0525 - 121.334i) q^{29} +(37.0130 - 64.1083i) q^{30} -223.593i q^{31} +(134.294 + 77.5348i) q^{32} +(-72.9113 - 42.0954i) q^{33} -103.451i q^{34} +(-179.650 + 311.163i) q^{35} +(-17.2316 - 29.8460i) q^{36} +(-197.759 + 114.176i) q^{37} -214.739 q^{38} +(120.607 + 72.2975i) q^{39} -291.890 q^{40} +(256.259 - 147.951i) q^{41} +(-91.0962 - 157.783i) q^{42} +(96.0517 - 166.366i) q^{43} +107.462i q^{44} +(94.1734 + 54.3710i) q^{45} +(284.029 + 163.984i) q^{46} +36.9300i q^{47} +(28.0544 - 48.5916i) q^{48} +(270.653 + 468.785i) q^{49} +(37.1160 - 21.4289i) q^{50} +151.967 q^{51} +(2.94589 - 179.461i) q^{52} +149.102 q^{53} +(-47.7531 + 27.5703i) q^{54} +(-169.538 - 293.649i) q^{55} +(-359.200 + 622.152i) q^{56} -315.445i q^{57} +(247.794 + 143.064i) q^{58} +(-380.070 - 219.433i) q^{59} -138.800i q^{60} +(-143.073 + 247.809i) q^{61} +(228.316 + 395.454i) q^{62} +(231.779 - 133.818i) q^{63} -466.313 q^{64} +(275.077 + 495.038i) q^{65} +171.938 q^{66} +(465.166 - 268.564i) q^{67} +(-96.9863 - 167.985i) q^{68} +(-240.888 + 417.231i) q^{69} -733.777i q^{70} +(88.9656 + 51.3643i) q^{71} +(188.294 + 108.712i) q^{72} -75.5209i q^{73} +(233.175 - 403.871i) q^{74} +(31.4786 + 54.5225i) q^{75} +(-348.696 + 201.319i) q^{76} -834.535 q^{77} +(-287.134 - 4.71337i) q^{78} +17.5526 q^{79} +(195.702 - 112.989i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(-302.152 + 523.342i) q^{82} -1463.08i q^{83} +(-295.847 - 170.807i) q^{84} +(530.045 + 306.022i) q^{85} +392.322i q^{86} +(-210.157 + 364.003i) q^{87} +(-338.983 - 587.135i) q^{88} +(-290.036 + 167.453i) q^{89} -222.078 q^{90} +(1393.66 + 22.8773i) q^{91} +614.946 q^{92} +(-580.912 + 335.390i) q^{93} +(-37.7100 - 65.3156i) q^{94} +(635.225 - 1100.24i) q^{95} -465.209i q^{96} +(-648.442 - 374.378i) q^{97} +(-957.374 - 552.740i) q^{98} +252.572i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 15 q^{3} + 30 q^{4} + 30 q^{7} - 45 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 15 q^{3} + 30 q^{4} + 30 q^{7} - 45 q^{9} + 40 q^{10} + 60 q^{11} - 180 q^{12} + 25 q^{13} - 60 q^{14} + 45 q^{15} - 250 q^{16} + 105 q^{17} + 180 q^{19} + 510 q^{20} - 290 q^{22} - 60 q^{23} - 960 q^{25} - 30 q^{26} + 270 q^{27} + 150 q^{28} - 495 q^{29} + 120 q^{30} + 1440 q^{32} - 180 q^{33} + 60 q^{35} + 270 q^{36} - 405 q^{37} - 1380 q^{38} + 345 q^{39} + 2000 q^{40} + 1065 q^{41} + 90 q^{42} - 370 q^{43} - 135 q^{45} - 390 q^{46} - 750 q^{48} + 775 q^{49} - 4320 q^{50} - 630 q^{51} + 2940 q^{52} + 330 q^{53} - 260 q^{55} - 2670 q^{56} + 2040 q^{58} + 780 q^{59} - 1375 q^{61} - 780 q^{62} - 270 q^{63} - 3140 q^{64} + 1605 q^{65} + 1740 q^{66} + 1590 q^{67} - 600 q^{68} - 180 q^{69} + 1620 q^{71} + 2190 q^{74} + 1440 q^{75} - 5190 q^{76} - 4320 q^{77} + 2340 q^{78} + 1100 q^{79} + 8430 q^{80} - 405 q^{81} - 2390 q^{82} - 450 q^{84} + 525 q^{85} - 1485 q^{87} + 3170 q^{88} + 2040 q^{89} - 720 q^{90} + 4770 q^{91} - 1740 q^{92} - 990 q^{93} - 3230 q^{94} - 1380 q^{95} - 3750 q^{97} + 180 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).

\(n\) \(14\) \(28\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.76863 + 1.02112i −0.625307 + 0.361021i −0.778932 0.627108i \(-0.784238\pi\)
0.153626 + 0.988129i \(0.450905\pi\)
\(3\) −1.50000 2.59808i −0.288675 0.500000i
\(4\) −1.91462 + 3.31622i −0.239328 + 0.414528i
\(5\) 12.0825i 1.08069i −0.841444 0.540344i \(-0.818294\pi\)
0.841444 0.540344i \(-0.181706\pi\)
\(6\) 5.30590 + 3.06336i 0.361021 + 0.208436i
\(7\) −25.7533 14.8686i −1.39055 0.802832i −0.397170 0.917745i \(-0.630008\pi\)
−0.993375 + 0.114914i \(0.963341\pi\)
\(8\) 24.1582i 1.06765i
\(9\) −4.50000 + 7.79423i −0.166667 + 0.288675i
\(10\) 12.3377 + 21.3694i 0.390151 + 0.675761i
\(11\) 24.3038 14.0318i 0.666169 0.384613i −0.128454 0.991715i \(-0.541002\pi\)
0.794624 + 0.607102i \(0.207668\pi\)
\(12\) 11.4877 0.276352
\(13\) −40.9717 + 22.7667i −0.874115 + 0.485719i
\(14\) 60.7308 1.15936
\(15\) −31.3911 + 18.1237i −0.540344 + 0.311968i
\(16\) 9.35146 + 16.1972i 0.146117 + 0.253081i
\(17\) −25.3278 + 43.8690i −0.361347 + 0.625871i −0.988183 0.153280i \(-0.951016\pi\)
0.626836 + 0.779151i \(0.284350\pi\)
\(18\) 18.3802i 0.240681i
\(19\) 91.0612 + 52.5742i 1.09952 + 0.634808i 0.936095 0.351748i \(-0.114413\pi\)
0.163425 + 0.986556i \(0.447746\pi\)
\(20\) 40.0681 + 23.1333i 0.447975 + 0.258639i
\(21\) 89.2119i 0.927030i
\(22\) −28.6563 + 49.6342i −0.277707 + 0.481002i
\(23\) −80.2961 139.077i −0.727951 1.26085i −0.957748 0.287610i \(-0.907139\pi\)
0.229796 0.973239i \(-0.426194\pi\)
\(24\) −62.7648 + 36.2373i −0.533826 + 0.308204i
\(25\) −20.9857 −0.167886
\(26\) 49.2164 82.1030i 0.371235 0.619297i
\(27\) 27.0000 0.192450
\(28\) 98.6155 56.9357i 0.665592 0.384280i
\(29\) −70.0525 121.334i −0.448566 0.776939i 0.549727 0.835344i \(-0.314732\pi\)
−0.998293 + 0.0584051i \(0.981398\pi\)
\(30\) 37.0130 64.1083i 0.225254 0.390151i
\(31\) 223.593i 1.29544i −0.761880 0.647718i \(-0.775724\pi\)
0.761880 0.647718i \(-0.224276\pi\)
\(32\) 134.294 + 77.5348i 0.741878 + 0.428323i
\(33\) −72.9113 42.0954i −0.384613 0.222056i
\(34\) 103.451i 0.521815i
\(35\) −179.650 + 311.163i −0.867610 + 1.50274i
\(36\) −17.2316 29.8460i −0.0797759 0.138176i
\(37\) −197.759 + 114.176i −0.878684 + 0.507308i −0.870224 0.492656i \(-0.836026\pi\)
−0.00845956 + 0.999964i \(0.502693\pi\)
\(38\) −214.739 −0.916716
\(39\) 120.607 + 72.2975i 0.495195 + 0.296843i
\(40\) −291.890 −1.15380
\(41\) 256.259 147.951i 0.976119 0.563563i 0.0750227 0.997182i \(-0.476097\pi\)
0.901096 + 0.433619i \(0.142764\pi\)
\(42\) −91.0962 157.783i −0.334677 0.579678i
\(43\) 96.0517 166.366i 0.340645 0.590015i −0.643907 0.765103i \(-0.722688\pi\)
0.984553 + 0.175088i \(0.0560211\pi\)
\(44\) 107.462i 0.368194i
\(45\) 94.1734 + 54.3710i 0.311968 + 0.180115i
\(46\) 284.029 + 163.984i 0.910386 + 0.525611i
\(47\) 36.9300i 0.114613i 0.998357 + 0.0573063i \(0.0182512\pi\)
−0.998357 + 0.0573063i \(0.981749\pi\)
\(48\) 28.0544 48.5916i 0.0843605 0.146117i
\(49\) 270.653 + 468.785i 0.789077 + 1.36672i
\(50\) 37.1160 21.4289i 0.104980 0.0606102i
\(51\) 151.967 0.417247
\(52\) 2.94589 179.461i 0.00785618 0.478591i
\(53\) 149.102 0.386429 0.193214 0.981157i \(-0.438109\pi\)
0.193214 + 0.981157i \(0.438109\pi\)
\(54\) −47.7531 + 27.5703i −0.120340 + 0.0694785i
\(55\) −169.538 293.649i −0.415647 0.719921i
\(56\) −359.200 + 622.152i −0.857144 + 1.48462i
\(57\) 315.445i 0.733013i
\(58\) 247.794 + 143.064i 0.560983 + 0.323884i
\(59\) −380.070 219.433i −0.838659 0.484200i 0.0181492 0.999835i \(-0.494223\pi\)
−0.856808 + 0.515635i \(0.827556\pi\)
\(60\) 138.800i 0.298650i
\(61\) −143.073 + 247.809i −0.300305 + 0.520143i −0.976205 0.216850i \(-0.930422\pi\)
0.675900 + 0.736993i \(0.263755\pi\)
\(62\) 228.316 + 395.454i 0.467679 + 0.810044i
\(63\) 231.779 133.818i 0.463515 0.267611i
\(64\) −466.313 −0.910768
\(65\) 275.077 + 495.038i 0.524910 + 0.944645i
\(66\) 171.938 0.320668
\(67\) 465.166 268.564i 0.848195 0.489706i −0.0118462 0.999930i \(-0.503771\pi\)
0.860042 + 0.510224i \(0.170438\pi\)
\(68\) −96.9863 167.985i −0.172961 0.299576i
\(69\) −240.888 + 417.231i −0.420283 + 0.727951i
\(70\) 733.777i 1.25290i
\(71\) 88.9656 + 51.3643i 0.148708 + 0.0858567i 0.572508 0.819899i \(-0.305971\pi\)
−0.423800 + 0.905756i \(0.639304\pi\)
\(72\) 188.294 + 108.712i 0.308204 + 0.177942i
\(73\) 75.5209i 0.121083i −0.998166 0.0605414i \(-0.980717\pi\)
0.998166 0.0605414i \(-0.0192827\pi\)
\(74\) 233.175 403.871i 0.366298 0.634446i
\(75\) 31.4786 + 54.5225i 0.0484644 + 0.0839428i
\(76\) −348.696 + 201.319i −0.526291 + 0.303854i
\(77\) −834.535 −1.23512
\(78\) −287.134 4.71337i −0.416815 0.00684211i
\(79\) 17.5526 0.0249978 0.0124989 0.999922i \(-0.496021\pi\)
0.0124989 + 0.999922i \(0.496021\pi\)
\(80\) 195.702 112.989i 0.273502 0.157906i
\(81\) −40.5000 70.1481i −0.0555556 0.0962250i
\(82\) −302.152 + 523.342i −0.406916 + 0.704799i
\(83\) 1463.08i 1.93487i −0.253122 0.967434i \(-0.581457\pi\)
0.253122 0.967434i \(-0.418543\pi\)
\(84\) −295.847 170.807i −0.384280 0.221864i
\(85\) 530.045 + 306.022i 0.676371 + 0.390503i
\(86\) 392.322i 0.491920i
\(87\) −210.157 + 364.003i −0.258980 + 0.448566i
\(88\) −338.983 587.135i −0.410633 0.711236i
\(89\) −290.036 + 167.453i −0.345436 + 0.199438i −0.662673 0.748909i \(-0.730578\pi\)
0.317237 + 0.948346i \(0.397245\pi\)
\(90\) −222.078 −0.260101
\(91\) 1393.66 + 22.8773i 1.60545 + 0.0263538i
\(92\) 614.946 0.696876
\(93\) −580.912 + 335.390i −0.647718 + 0.373960i
\(94\) −37.7100 65.3156i −0.0413776 0.0716680i
\(95\) 635.225 1100.24i 0.686029 1.18824i
\(96\) 465.209i 0.494585i
\(97\) −648.442 374.378i −0.678756 0.391880i 0.120630 0.992697i \(-0.461508\pi\)
−0.799386 + 0.600818i \(0.794842\pi\)
\(98\) −957.374 552.740i −0.986830 0.569747i
\(99\) 252.572i 0.256409i
\(100\) 40.1797 69.5933i 0.0401797 0.0695933i
\(101\) −392.001 678.966i −0.386194 0.668907i 0.605740 0.795662i \(-0.292877\pi\)
−0.991934 + 0.126755i \(0.959544\pi\)
\(102\) −268.774 + 155.176i −0.260907 + 0.150635i
\(103\) −396.040 −0.378864 −0.189432 0.981894i \(-0.560665\pi\)
−0.189432 + 0.981894i \(0.560665\pi\)
\(104\) 550.002 + 989.801i 0.518578 + 0.933250i
\(105\) 1077.90 1.00183
\(106\) −263.707 + 152.251i −0.241636 + 0.139509i
\(107\) 718.296 + 1244.12i 0.648974 + 1.12406i 0.983368 + 0.181623i \(0.0581351\pi\)
−0.334394 + 0.942433i \(0.608532\pi\)
\(108\) −51.6948 + 89.5380i −0.0460587 + 0.0797759i
\(109\) 1977.92i 1.73807i 0.494746 + 0.869037i \(0.335261\pi\)
−0.494746 + 0.869037i \(0.664739\pi\)
\(110\) 599.703 + 346.239i 0.519813 + 0.300114i
\(111\) 593.276 + 342.528i 0.507308 + 0.292895i
\(112\) 556.175i 0.469228i
\(113\) −61.2026 + 106.006i −0.0509509 + 0.0882496i −0.890376 0.455226i \(-0.849559\pi\)
0.839425 + 0.543475i \(0.182892\pi\)
\(114\) 322.108 + 557.907i 0.264633 + 0.458358i
\(115\) −1680.39 + 970.173i −1.36258 + 0.786688i
\(116\) 536.496 0.429417
\(117\) 6.92382 421.793i 0.00547100 0.333288i
\(118\) 896.273 0.699225
\(119\) 1304.55 753.180i 1.00494 0.580201i
\(120\) 437.835 + 758.353i 0.333073 + 0.576899i
\(121\) −271.718 + 470.629i −0.204146 + 0.353591i
\(122\) 584.379i 0.433665i
\(123\) −768.776 443.853i −0.563563 0.325373i
\(124\) 741.484 + 428.096i 0.536994 + 0.310034i
\(125\) 1256.75i 0.899256i
\(126\) −273.289 + 473.350i −0.193226 + 0.334677i
\(127\) 1154.80 + 2000.18i 0.806868 + 1.39754i 0.915022 + 0.403403i \(0.132173\pi\)
−0.108154 + 0.994134i \(0.534494\pi\)
\(128\) −249.616 + 144.116i −0.172369 + 0.0995170i
\(129\) −576.310 −0.393343
\(130\) −992.006 594.654i −0.669266 0.401190i
\(131\) −1444.26 −0.963250 −0.481625 0.876377i \(-0.659953\pi\)
−0.481625 + 0.876377i \(0.659953\pi\)
\(132\) 279.195 161.193i 0.184097 0.106289i
\(133\) −1563.41 2707.91i −1.01929 1.76546i
\(134\) −548.472 + 949.982i −0.353588 + 0.612433i
\(135\) 326.226i 0.207978i
\(136\) 1059.80 + 611.874i 0.668212 + 0.385792i
\(137\) 637.324 + 367.959i 0.397447 + 0.229466i 0.685382 0.728184i \(-0.259635\pi\)
−0.287935 + 0.957650i \(0.592969\pi\)
\(138\) 983.904i 0.606924i
\(139\) 752.571 1303.49i 0.459225 0.795400i −0.539696 0.841860i \(-0.681461\pi\)
0.998920 + 0.0464599i \(0.0147940\pi\)
\(140\) −687.923 1191.52i −0.415286 0.719297i
\(141\) 95.9469 55.3950i 0.0573063 0.0330858i
\(142\) −209.797 −0.123984
\(143\) −676.309 + 1128.22i −0.395495 + 0.659767i
\(144\) −168.326 −0.0974111
\(145\) −1466.02 + 846.406i −0.839629 + 0.484760i
\(146\) 77.1160 + 133.569i 0.0437134 + 0.0757139i
\(147\) 811.960 1406.36i 0.455574 0.789077i
\(148\) 874.415i 0.485652i
\(149\) 370.523 + 213.921i 0.203721 + 0.117618i 0.598390 0.801205i \(-0.295807\pi\)
−0.394669 + 0.918823i \(0.629141\pi\)
\(150\) −111.348 64.2868i −0.0606102 0.0349933i
\(151\) 1601.83i 0.863278i −0.902046 0.431639i \(-0.857935\pi\)
0.902046 0.431639i \(-0.142065\pi\)
\(152\) 1270.10 2199.87i 0.677753 1.17390i
\(153\) −227.950 394.821i −0.120449 0.208624i
\(154\) 1475.99 852.161i 0.772327 0.445903i
\(155\) −2701.55 −1.39996
\(156\) −470.672 + 261.538i −0.241563 + 0.134229i
\(157\) −730.346 −0.371261 −0.185631 0.982620i \(-0.559433\pi\)
−0.185631 + 0.982620i \(0.559433\pi\)
\(158\) −31.0442 + 17.9234i −0.0156313 + 0.00902473i
\(159\) −223.653 387.378i −0.111552 0.193214i
\(160\) 936.811 1622.60i 0.462884 0.801738i
\(161\) 4775.58i 2.33769i
\(162\) 143.259 + 82.7108i 0.0694785 + 0.0401134i
\(163\) −1644.03 949.180i −0.790001 0.456107i 0.0499619 0.998751i \(-0.484090\pi\)
−0.839963 + 0.542644i \(0.817423\pi\)
\(164\) 1133.08i 0.539505i
\(165\) −508.615 + 880.948i −0.239974 + 0.415647i
\(166\) 1493.98 + 2587.66i 0.698528 + 1.20989i
\(167\) 1236.25 713.751i 0.572839 0.330729i −0.185444 0.982655i \(-0.559372\pi\)
0.758282 + 0.651926i \(0.226039\pi\)
\(168\) 2155.20 0.989745
\(169\) 1160.36 1865.58i 0.528155 0.849148i
\(170\) −1249.94 −0.563919
\(171\) −819.551 + 473.168i −0.366507 + 0.211603i
\(172\) 367.806 + 637.058i 0.163052 + 0.282414i
\(173\) −1022.20 + 1770.50i −0.449227 + 0.778084i −0.998336 0.0576667i \(-0.981634\pi\)
0.549109 + 0.835751i \(0.314967\pi\)
\(174\) 858.385i 0.373988i
\(175\) 540.450 + 312.029i 0.233453 + 0.134784i
\(176\) 454.552 + 262.436i 0.194677 + 0.112397i
\(177\) 1316.60i 0.559106i
\(178\) 341.979 592.325i 0.144002 0.249419i
\(179\) −1944.86 3368.59i −0.812098 1.40660i −0.911393 0.411537i \(-0.864992\pi\)
0.0992948 0.995058i \(-0.468341\pi\)
\(180\) −360.613 + 208.200i −0.149325 + 0.0862129i
\(181\) 2477.02 1.01721 0.508606 0.861000i \(-0.330161\pi\)
0.508606 + 0.861000i \(0.330161\pi\)
\(182\) −2488.24 + 1382.64i −1.01341 + 0.563121i
\(183\) 858.437 0.346762
\(184\) −3359.84 + 1939.81i −1.34615 + 0.777198i
\(185\) 1379.53 + 2389.41i 0.548242 + 0.949583i
\(186\) 684.947 1186.36i 0.270015 0.467679i
\(187\) 1421.58i 0.555914i
\(188\) −122.468 70.7070i −0.0475101 0.0274300i
\(189\) −695.338 401.454i −0.267611 0.154505i
\(190\) 2594.57i 0.990683i
\(191\) −1138.40 + 1971.78i −0.431267 + 0.746977i −0.996983 0.0776235i \(-0.975267\pi\)
0.565715 + 0.824601i \(0.308600\pi\)
\(192\) 699.470 + 1211.52i 0.262916 + 0.455384i
\(193\) 3396.92 1961.21i 1.26692 0.731456i 0.292515 0.956261i \(-0.405508\pi\)
0.974404 + 0.224805i \(0.0721744\pi\)
\(194\) 1529.14 0.565907
\(195\) 873.531 1457.23i 0.320794 0.535151i
\(196\) −2072.80 −0.755392
\(197\) 4384.88 2531.61i 1.58584 0.915584i 0.591855 0.806045i \(-0.298396\pi\)
0.993982 0.109539i \(-0.0349375\pi\)
\(198\) −257.907 446.708i −0.0925689 0.160334i
\(199\) 1635.03 2831.95i 0.582433 1.00880i −0.412757 0.910841i \(-0.635434\pi\)
0.995190 0.0979624i \(-0.0312325\pi\)
\(200\) 506.977i 0.179243i
\(201\) −1395.50 805.691i −0.489706 0.282732i
\(202\) 1386.61 + 800.561i 0.482979 + 0.278848i
\(203\) 4166.34i 1.44049i
\(204\) −290.959 + 503.956i −0.0998588 + 0.172961i
\(205\) −1787.61 3096.23i −0.609035 1.05488i
\(206\) 700.450 404.405i 0.236906 0.136778i
\(207\) 1445.33 0.485301
\(208\) −751.902 450.725i −0.250649 0.150251i
\(209\) 2950.84 0.976622
\(210\) −1906.41 + 1100.67i −0.626451 + 0.361682i
\(211\) 1406.09 + 2435.42i 0.458764 + 0.794602i 0.998896 0.0469781i \(-0.0149591\pi\)
−0.540132 + 0.841580i \(0.681626\pi\)
\(212\) −285.474 + 494.455i −0.0924831 + 0.160185i
\(213\) 308.186i 0.0991388i
\(214\) −2540.80 1466.93i −0.811616 0.468587i
\(215\) −2010.12 1160.54i −0.637622 0.368131i
\(216\) 652.271i 0.205470i
\(217\) −3324.53 + 5758.25i −1.04002 + 1.80136i
\(218\) −2019.69 3498.21i −0.627481 1.08683i
\(219\) −196.209 + 113.281i −0.0605414 + 0.0349536i
\(220\) 1298.41 0.397903
\(221\) 38.9700 2374.02i 0.0118616 0.722596i
\(222\) −1399.05 −0.422964
\(223\) 794.783 458.868i 0.238666 0.137794i −0.375897 0.926661i \(-0.622665\pi\)
0.614564 + 0.788867i \(0.289332\pi\)
\(224\) −2305.68 3993.55i −0.687743 1.19121i
\(225\) 94.4357 163.567i 0.0279809 0.0484644i
\(226\) 249.981i 0.0735774i
\(227\) −1157.35 668.194i −0.338396 0.195373i 0.321167 0.947023i \(-0.395925\pi\)
−0.659562 + 0.751650i \(0.729258\pi\)
\(228\) 1046.09 + 603.958i 0.303854 + 0.175430i
\(229\) 164.820i 0.0475617i 0.999717 + 0.0237808i \(0.00757039\pi\)
−0.999717 + 0.0237808i \(0.992430\pi\)
\(230\) 1981.33 3431.76i 0.568022 0.983843i
\(231\) 1251.80 + 2168.19i 0.356548 + 0.617559i
\(232\) −2931.22 + 1692.34i −0.829500 + 0.478912i
\(233\) 4243.42 1.19312 0.596558 0.802570i \(-0.296535\pi\)
0.596558 + 0.802570i \(0.296535\pi\)
\(234\) 418.456 + 753.067i 0.116903 + 0.210383i
\(235\) 446.205 0.123860
\(236\) 1455.38 840.264i 0.401429 0.231765i
\(237\) −26.3289 45.6031i −0.00721624 0.0124989i
\(238\) −1538.18 + 2664.20i −0.418929 + 0.725607i
\(239\) 2491.07i 0.674200i 0.941469 + 0.337100i \(0.109446\pi\)
−0.941469 + 0.337100i \(0.890554\pi\)
\(240\) −587.106 338.966i −0.157906 0.0911673i
\(241\) −2526.54 1458.70i −0.675306 0.389888i 0.122778 0.992434i \(-0.460820\pi\)
−0.798084 + 0.602546i \(0.794153\pi\)
\(242\) 1109.83i 0.294803i
\(243\) −121.500 + 210.444i −0.0320750 + 0.0555556i
\(244\) −547.861 948.922i −0.143743 0.248969i
\(245\) 5664.08 3270.16i 1.47700 0.852746i
\(246\) 1812.91 0.469866
\(247\) −4927.87 80.8921i −1.26944 0.0208382i
\(248\) −5401.60 −1.38307
\(249\) −3801.20 + 2194.62i −0.967434 + 0.558549i
\(250\) 1283.29 + 2222.73i 0.324650 + 0.562310i
\(251\) −656.939 + 1137.85i −0.165202 + 0.286138i −0.936727 0.350061i \(-0.886161\pi\)
0.771525 + 0.636199i \(0.219494\pi\)
\(252\) 1024.84i 0.256187i
\(253\) −3902.99 2253.39i −0.969878 0.559959i
\(254\) −4084.85 2358.39i −1.00908 0.582593i
\(255\) 1836.13i 0.450914i
\(256\) 2159.57 3740.49i 0.527239 0.913205i
\(257\) −493.791 855.271i −0.119851 0.207589i 0.799857 0.600190i \(-0.204909\pi\)
−0.919709 + 0.392601i \(0.871575\pi\)
\(258\) 1019.28 588.483i 0.245960 0.142005i
\(259\) 6790.57 1.62913
\(260\) −2168.33 35.5936i −0.517207 0.00849007i
\(261\) 1260.94 0.299044
\(262\) 2554.37 1474.77i 0.602326 0.347753i
\(263\) 3493.23 + 6050.44i 0.819017 + 1.41858i 0.906407 + 0.422405i \(0.138814\pi\)
−0.0873899 + 0.996174i \(0.527853\pi\)
\(264\) −1016.95 + 1761.41i −0.237079 + 0.410633i
\(265\) 1801.52i 0.417609i
\(266\) 5530.22 + 3192.87i 1.27473 + 0.735968i
\(267\) 870.109 + 502.358i 0.199438 + 0.115145i
\(268\) 2056.79i 0.468801i
\(269\) 2952.17 5113.31i 0.669134 1.15897i −0.309013 0.951058i \(-0.599999\pi\)
0.978147 0.207916i \(-0.0666681\pi\)
\(270\) 333.117 + 576.975i 0.0750846 + 0.130050i
\(271\) −1845.97 + 1065.77i −0.413781 + 0.238897i −0.692413 0.721501i \(-0.743452\pi\)
0.278632 + 0.960398i \(0.410119\pi\)
\(272\) −947.408 −0.211195
\(273\) −2031.06 3655.16i −0.450276 0.810331i
\(274\) −1502.92 −0.331368
\(275\) −510.032 + 294.467i −0.111840 + 0.0645710i
\(276\) −922.420 1597.68i −0.201171 0.348438i
\(277\) 2016.21 3492.17i 0.437336 0.757489i −0.560147 0.828393i \(-0.689255\pi\)
0.997483 + 0.0709046i \(0.0225886\pi\)
\(278\) 3073.86i 0.663159i
\(279\) 1742.74 + 1006.17i 0.373960 + 0.215906i
\(280\) 7517.12 + 4340.01i 1.60441 + 0.926305i
\(281\) 2298.29i 0.487916i −0.969786 0.243958i \(-0.921554\pi\)
0.969786 0.243958i \(-0.0784459\pi\)
\(282\) −113.130 + 195.947i −0.0238893 + 0.0413776i
\(283\) 3328.40 + 5764.96i 0.699127 + 1.21092i 0.968770 + 0.247963i \(0.0797611\pi\)
−0.269643 + 0.962960i \(0.586906\pi\)
\(284\) −340.671 + 196.687i −0.0711800 + 0.0410958i
\(285\) −3811.35 −0.792158
\(286\) 44.0914 2686.01i 0.00911601 0.555339i
\(287\) −8799.33 −1.80978
\(288\) −1208.65 + 697.813i −0.247293 + 0.142774i
\(289\) 1173.51 + 2032.57i 0.238857 + 0.413713i
\(290\) 1728.57 2993.96i 0.350017 0.606247i
\(291\) 2246.27i 0.452504i
\(292\) 250.444 + 144.594i 0.0501922 + 0.0289785i
\(293\) −6466.60 3733.49i −1.28936 0.744413i −0.310821 0.950468i \(-0.600604\pi\)
−0.978540 + 0.206055i \(0.933937\pi\)
\(294\) 3316.44i 0.657887i
\(295\) −2651.29 + 4592.18i −0.523269 + 0.906328i
\(296\) 2758.28 + 4777.49i 0.541628 + 0.938128i
\(297\) 656.202 378.858i 0.128204 0.0740188i
\(298\) −873.759 −0.169851
\(299\) 6456.18 + 3870.14i 1.24873 + 0.748548i
\(300\) −241.078 −0.0463955
\(301\) −4947.29 + 2856.32i −0.947365 + 0.546962i
\(302\) 1635.66 + 2833.05i 0.311662 + 0.539814i
\(303\) −1176.00 + 2036.90i −0.222969 + 0.386194i
\(304\) 1966.58i 0.371024i
\(305\) 2994.14 + 1728.67i 0.562112 + 0.324536i
\(306\) 806.321 + 465.529i 0.150635 + 0.0869691i
\(307\) 3965.99i 0.737299i −0.929568 0.368650i \(-0.879820\pi\)
0.929568 0.368650i \(-0.120180\pi\)
\(308\) 1597.82 2767.50i 0.295598 0.511991i
\(309\) 594.060 + 1028.94i 0.109369 + 0.189432i
\(310\) 4778.06 2758.61i 0.875405 0.505415i
\(311\) −7372.29 −1.34419 −0.672097 0.740463i \(-0.734606\pi\)
−0.672097 + 0.740463i \(0.734606\pi\)
\(312\) 1746.58 2913.65i 0.316925 0.528695i
\(313\) 8249.55 1.48975 0.744875 0.667204i \(-0.232509\pi\)
0.744875 + 0.667204i \(0.232509\pi\)
\(314\) 1291.72 745.772i 0.232152 0.134033i
\(315\) −1616.85 2800.46i −0.289203 0.500915i
\(316\) −33.6067 + 58.2084i −0.00598267 + 0.0103623i
\(317\) 5575.26i 0.987817i 0.869514 + 0.493909i \(0.164432\pi\)
−0.869514 + 0.493909i \(0.835568\pi\)
\(318\) 791.120 + 456.753i 0.139509 + 0.0805455i
\(319\) −3405.08 1965.92i −0.597642 0.345049i
\(320\) 5634.21i 0.984256i
\(321\) 2154.89 3732.37i 0.374686 0.648974i
\(322\) −4876.44 8446.25i −0.843955 1.46177i
\(323\) −4612.76 + 2663.18i −0.794615 + 0.458771i
\(324\) 310.169 0.0531840
\(325\) 859.819 477.775i 0.146751 0.0815452i
\(326\) 3876.91 0.658657
\(327\) 5138.78 2966.88i 0.869037 0.501739i
\(328\) −3574.23 6190.74i −0.601688 1.04215i
\(329\) 549.099 951.068i 0.0920146 0.159374i
\(330\) 2077.43i 0.346542i
\(331\) −3600.38 2078.68i −0.597870 0.345180i 0.170333 0.985387i \(-0.445516\pi\)
−0.768203 + 0.640206i \(0.778849\pi\)
\(332\) 4851.91 + 2801.25i 0.802057 + 0.463068i
\(333\) 2055.17i 0.338206i
\(334\) −1457.65 + 2524.73i −0.238800 + 0.413614i
\(335\) −3244.91 5620.35i −0.529219 0.916634i
\(336\) −1444.98 + 834.262i −0.234614 + 0.135454i
\(337\) −3225.18 −0.521326 −0.260663 0.965430i \(-0.583941\pi\)
−0.260663 + 0.965430i \(0.583941\pi\)
\(338\) −147.264 + 4484.39i −0.0236986 + 0.721653i
\(339\) 367.215 0.0588330
\(340\) −2029.67 + 1171.83i −0.323749 + 0.186916i
\(341\) −3137.41 5434.15i −0.498241 0.862979i
\(342\) 966.324 1673.72i 0.152786 0.264633i
\(343\) 5897.11i 0.928321i
\(344\) −4019.11 2320.44i −0.629930 0.363690i
\(345\) 5041.17 + 2910.52i 0.786688 + 0.454195i
\(346\) 4175.15i 0.648721i
\(347\) −1645.25 + 2849.65i −0.254529 + 0.440856i −0.964767 0.263104i \(-0.915254\pi\)
0.710239 + 0.703961i \(0.248587\pi\)
\(348\) −804.744 1393.86i −0.123962 0.214709i
\(349\) −3889.77 + 2245.76i −0.596604 + 0.344449i −0.767704 0.640804i \(-0.778601\pi\)
0.171101 + 0.985254i \(0.445268\pi\)
\(350\) −1274.48 −0.194639
\(351\) −1106.24 + 614.700i −0.168224 + 0.0934766i
\(352\) 4351.81 0.658955
\(353\) −5107.71 + 2948.94i −0.770130 + 0.444635i −0.832921 0.553392i \(-0.813333\pi\)
0.0627907 + 0.998027i \(0.480000\pi\)
\(354\) −1344.41 2328.58i −0.201849 0.349613i
\(355\) 620.607 1074.92i 0.0927843 0.160707i
\(356\) 1282.43i 0.190924i
\(357\) −3913.64 2259.54i −0.580201 0.334979i
\(358\) 6879.49 + 3971.87i 1.01562 + 0.586369i
\(359\) 9277.20i 1.36388i −0.731410 0.681938i \(-0.761137\pi\)
0.731410 0.681938i \(-0.238863\pi\)
\(360\) 1313.51 2275.06i 0.192300 0.333073i
\(361\) 2098.59 + 3634.87i 0.305962 + 0.529942i
\(362\) −4380.94 + 2529.33i −0.636069 + 0.367234i
\(363\) 1630.31 0.235727
\(364\) −2744.21 + 4577.90i −0.395152 + 0.659195i
\(365\) −912.477 −0.130853
\(366\) −1518.26 + 876.568i −0.216833 + 0.125188i
\(367\) 3287.18 + 5693.56i 0.467546 + 0.809814i 0.999312 0.0370774i \(-0.0118048\pi\)
−0.531766 + 0.846891i \(0.678471\pi\)
\(368\) 1501.77 2601.14i 0.212732 0.368462i
\(369\) 2663.12i 0.375708i
\(370\) −4879.75 2817.33i −0.685638 0.395853i
\(371\) −3839.86 2216.94i −0.537347 0.310237i
\(372\) 2568.58i 0.357996i
\(373\) 2672.77 4629.38i 0.371021 0.642628i −0.618702 0.785626i \(-0.712341\pi\)
0.989723 + 0.142998i \(0.0456743\pi\)
\(374\) −1451.60 2514.25i −0.200697 0.347617i
\(375\) −3265.13 + 1885.12i −0.449628 + 0.259593i
\(376\) 892.162 0.122366
\(377\) 5632.55 + 3376.41i 0.769472 + 0.461258i
\(378\) 1639.73 0.223118
\(379\) 899.378 519.256i 0.121894 0.0703757i −0.437813 0.899066i \(-0.644247\pi\)
0.559707 + 0.828690i \(0.310914\pi\)
\(380\) 2432.43 + 4213.10i 0.328372 + 0.568756i
\(381\) 3464.41 6000.54i 0.465846 0.806868i
\(382\) 4649.80i 0.622786i
\(383\) 5844.97 + 3374.59i 0.779801 + 0.450219i 0.836360 0.548181i \(-0.184679\pi\)
−0.0565585 + 0.998399i \(0.518013\pi\)
\(384\) 748.849 + 432.348i 0.0995170 + 0.0574562i
\(385\) 10083.2i 1.33478i
\(386\) −4005.27 + 6937.33i −0.528142 + 0.914769i
\(387\) 864.465 + 1497.30i 0.113548 + 0.196672i
\(388\) 2483.04 1433.59i 0.324890 0.187575i
\(389\) 1246.11 0.162417 0.0812083 0.996697i \(-0.474122\pi\)
0.0812083 + 0.996697i \(0.474122\pi\)
\(390\) −56.9491 + 3469.29i −0.00739418 + 0.450447i
\(391\) 8134.89 1.05217
\(392\) 11325.0 6538.50i 1.45918 0.842459i
\(393\) 2166.39 + 3752.30i 0.278066 + 0.481625i
\(394\) −5170.17 + 8954.99i −0.661090 + 1.14504i
\(395\) 212.079i 0.0270148i
\(396\) −837.586 483.580i −0.106289 0.0613657i
\(397\) −7236.24 4177.85i −0.914802 0.528161i −0.0328293 0.999461i \(-0.510452\pi\)
−0.881973 + 0.471300i \(0.843785\pi\)
\(398\) 6678.25i 0.841082i
\(399\) −4690.24 + 8123.74i −0.588486 + 1.01929i
\(400\) −196.247 339.910i −0.0245309 0.0424887i
\(401\) 2843.73 1641.83i 0.354137 0.204461i −0.312369 0.949961i \(-0.601122\pi\)
0.666506 + 0.745500i \(0.267789\pi\)
\(402\) 3290.83 0.408288
\(403\) 5090.47 + 9160.98i 0.629217 + 1.13236i
\(404\) 3002.14 0.369708
\(405\) −847.561 + 489.339i −0.103989 + 0.0600382i
\(406\) −4254.34 7368.74i −0.520048 0.900749i
\(407\) −3204.18 + 5549.81i −0.390235 + 0.675906i
\(408\) 3671.24i 0.445474i
\(409\) 9464.72 + 5464.46i 1.14426 + 0.660636i 0.947481 0.319813i \(-0.103620\pi\)
0.196775 + 0.980449i \(0.436953\pi\)
\(410\) 6323.26 + 3650.74i 0.761667 + 0.439749i
\(411\) 2207.75i 0.264965i
\(412\) 758.267 1313.36i 0.0906726 0.157050i
\(413\) 6525.36 + 11302.3i 0.777462 + 1.34660i
\(414\) −2556.26 + 1475.86i −0.303462 + 0.175204i
\(415\) −17677.6 −2.09099
\(416\) −7267.47 119.297i −0.856531 0.0140601i
\(417\) −4515.43 −0.530267
\(418\) −5218.96 + 3013.17i −0.610688 + 0.352581i
\(419\) −3651.47 6324.53i −0.425742 0.737407i 0.570747 0.821126i \(-0.306654\pi\)
−0.996489 + 0.0837185i \(0.973320\pi\)
\(420\) −2063.77 + 3574.55i −0.239766 + 0.415286i
\(421\) 7580.99i 0.877612i −0.898582 0.438806i \(-0.855401\pi\)
0.898582 0.438806i \(-0.144599\pi\)
\(422\) −4973.71 2871.57i −0.573736 0.331247i
\(423\) −287.841 166.185i −0.0330858 0.0191021i
\(424\) 3602.03i 0.412571i
\(425\) 531.521 920.622i 0.0606649 0.105075i
\(426\) 314.695 + 545.068i 0.0357912 + 0.0619921i
\(427\) 7369.18 4254.60i 0.835175 0.482188i
\(428\) −5501.06 −0.621270
\(429\) 3945.67 + 64.7690i 0.444053 + 0.00728923i
\(430\) 4740.21 0.531612
\(431\) 8709.40 5028.37i 0.973357 0.561968i 0.0730993 0.997325i \(-0.476711\pi\)
0.900258 + 0.435357i \(0.143378\pi\)
\(432\) 252.490 + 437.325i 0.0281202 + 0.0487055i
\(433\) 1366.69 2367.18i 0.151683 0.262723i −0.780163 0.625576i \(-0.784864\pi\)
0.931846 + 0.362853i \(0.118197\pi\)
\(434\) 13579.0i 1.50187i
\(435\) 4398.05 + 2539.22i 0.484760 + 0.279876i
\(436\) −6559.22 3786.97i −0.720481 0.415970i
\(437\) 16886.0i 1.84844i
\(438\) 231.348 400.706i 0.0252380 0.0437134i
\(439\) 3372.12 + 5840.68i 0.366611 + 0.634989i 0.989033 0.147692i \(-0.0471846\pi\)
−0.622422 + 0.782682i \(0.713851\pi\)
\(440\) −7094.03 + 4095.74i −0.768624 + 0.443765i
\(441\) −4871.76 −0.526051
\(442\) 2355.24 + 4238.56i 0.253455 + 0.456126i
\(443\) 8655.69 0.928317 0.464158 0.885752i \(-0.346357\pi\)
0.464158 + 0.885752i \(0.346357\pi\)
\(444\) −2271.80 + 1311.62i −0.242826 + 0.140196i
\(445\) 2023.24 + 3504.35i 0.215530 + 0.373308i
\(446\) −937.120 + 1623.14i −0.0994931 + 0.172327i
\(447\) 1283.53i 0.135814i
\(448\) 12009.1 + 6933.45i 1.26646 + 0.731193i
\(449\) 5648.62 + 3261.23i 0.593708 + 0.342777i 0.766562 0.642170i \(-0.221966\pi\)
−0.172854 + 0.984947i \(0.555299\pi\)
\(450\) 385.721i 0.0404068i
\(451\) 4152.03 7191.53i 0.433507 0.750856i
\(452\) −234.360 405.923i −0.0243879 0.0422411i
\(453\) −4161.67 + 2402.74i −0.431639 + 0.249207i
\(454\) 2729.23 0.282135
\(455\) 276.414 16838.9i 0.0284802 1.73499i
\(456\) −7620.59 −0.782602
\(457\) −1343.40 + 775.613i −0.137509 + 0.0793909i −0.567176 0.823596i \(-0.691964\pi\)
0.429667 + 0.902987i \(0.358631\pi\)
\(458\) −168.301 291.507i −0.0171708 0.0297406i
\(459\) −683.850 + 1184.46i −0.0695412 + 0.120449i
\(460\) 7430.06i 0.753105i
\(461\) −6725.77 3883.12i −0.679501 0.392310i 0.120166 0.992754i \(-0.461657\pi\)
−0.799667 + 0.600444i \(0.794991\pi\)
\(462\) −4427.96 2556.48i −0.445903 0.257442i
\(463\) 2004.52i 0.201205i 0.994927 + 0.100603i \(0.0320771\pi\)
−0.994927 + 0.100603i \(0.967923\pi\)
\(464\) 1310.19 2269.31i 0.131086 0.227048i
\(465\) 4052.33 + 7018.84i 0.404134 + 0.699980i
\(466\) −7505.06 + 4333.05i −0.746063 + 0.430739i
\(467\) −18674.3 −1.85042 −0.925209 0.379458i \(-0.876111\pi\)
−0.925209 + 0.379458i \(0.876111\pi\)
\(468\) 1385.50 + 830.535i 0.136848 + 0.0820331i
\(469\) −15972.7 −1.57261
\(470\) −789.173 + 455.629i −0.0774507 + 0.0447162i
\(471\) 1095.52 + 1897.50i 0.107174 + 0.185631i
\(472\) −5301.11 + 9181.80i −0.516957 + 0.895395i
\(473\) 5391.11i 0.524067i
\(474\) 93.1326 + 53.7701i 0.00902473 + 0.00521043i
\(475\) −1910.98 1103.31i −0.184594 0.106575i
\(476\) 5768.22i 0.555433i
\(477\) −670.959 + 1162.13i −0.0644048 + 0.111552i
\(478\) −2543.68 4405.79i −0.243400 0.421581i
\(479\) 8065.31 4656.51i 0.769340 0.444178i −0.0632994 0.997995i \(-0.520162\pi\)
0.832639 + 0.553816i \(0.186829\pi\)
\(480\) −5620.86 −0.534492
\(481\) 5503.09 9180.28i 0.521662 0.870239i
\(482\) 5958.03 0.563031
\(483\) 12407.3 7163.36i 1.16884 0.674833i
\(484\) −1040.47 1802.15i −0.0977155 0.169248i
\(485\) −4523.41 + 7834.77i −0.423500 + 0.733523i
\(486\) 496.265i 0.0463190i
\(487\) 3062.96 + 1768.40i 0.285002 + 0.164546i 0.635686 0.771948i \(-0.280717\pi\)
−0.350684 + 0.936494i \(0.614051\pi\)
\(488\) 5986.62 + 3456.38i 0.555331 + 0.320621i
\(489\) 5695.08i 0.526667i
\(490\) −6678.46 + 11567.4i −0.615718 + 1.06646i
\(491\) −1680.89 2911.39i −0.154496 0.267595i 0.778379 0.627794i \(-0.216042\pi\)
−0.932875 + 0.360199i \(0.882709\pi\)
\(492\) 2943.83 1699.62i 0.269752 0.155742i
\(493\) 7097.10 0.648351
\(494\) 8798.20 4888.88i 0.801315 0.445266i
\(495\) 3051.69 0.277098
\(496\) 3621.58 2090.92i 0.327851 0.189285i
\(497\) −1527.44 2645.60i −0.137857 0.238775i
\(498\) 4481.95 7762.97i 0.403295 0.698528i
\(499\) 4027.43i 0.361308i 0.983547 + 0.180654i \(0.0578214\pi\)
−0.983547 + 0.180654i \(0.942179\pi\)
\(500\) 4167.66 + 2406.20i 0.372767 + 0.215217i
\(501\) −3708.76 2141.25i −0.330729 0.190946i
\(502\) 2683.26i 0.238565i
\(503\) −883.336 + 1529.98i −0.0783022 + 0.135623i −0.902518 0.430653i \(-0.858283\pi\)
0.824215 + 0.566277i \(0.191617\pi\)
\(504\) −3232.80 5599.37i −0.285715 0.494872i
\(505\) −8203.57 + 4736.33i −0.722880 + 0.417355i
\(506\) 9203.96 0.808628
\(507\) −6587.45 216.327i −0.577039 0.0189496i
\(508\) −8844.05 −0.772424
\(509\) −5903.06 + 3408.13i −0.514044 + 0.296784i −0.734495 0.678615i \(-0.762581\pi\)
0.220450 + 0.975398i \(0.429247\pi\)
\(510\) 1874.91 + 3247.44i 0.162789 + 0.281959i
\(511\) −1122.89 + 1944.91i −0.0972091 + 0.168371i
\(512\) 6514.89i 0.562344i
\(513\) 2458.65 + 1419.50i 0.211603 + 0.122169i
\(514\) 1746.67 + 1008.44i 0.149888 + 0.0865378i
\(515\) 4785.13i 0.409433i
\(516\) 1103.42 1911.17i 0.0941380 0.163052i
\(517\) 518.194 + 897.538i 0.0440815 + 0.0763514i
\(518\) −12010.0 + 6933.99i −1.01871 + 0.588151i
\(519\) 6133.19 0.518723
\(520\) 11959.2 6645.37i 1.00855 0.560421i
\(521\) −5442.27 −0.457640 −0.228820 0.973469i \(-0.573487\pi\)
−0.228820 + 0.973469i \(0.573487\pi\)
\(522\) −2230.15 + 1287.58i −0.186994 + 0.107961i
\(523\) −10364.3 17951.4i −0.866535 1.50088i −0.865515 0.500883i \(-0.833009\pi\)
−0.00101984 0.999999i \(-0.500325\pi\)
\(524\) 2765.22 4789.49i 0.230532 0.399294i
\(525\) 1872.17i 0.155635i
\(526\) −12356.5 7134.01i −1.02427 0.591365i
\(527\) 9808.81 + 5663.12i 0.810775 + 0.468101i
\(528\) 1574.61i 0.129785i
\(529\) −6811.41 + 11797.7i −0.559827 + 0.969648i
\(530\) 1839.57 + 3186.22i 0.150765 + 0.261133i
\(531\) 3420.63 1974.90i 0.279553 0.161400i
\(532\) 11973.4 0.975775
\(533\) −7130.99 + 11896.0i −0.579508 + 0.966738i
\(534\) −2051.87 −0.166279
\(535\) 15032.1 8678.77i 1.21475 0.701339i
\(536\) −6488.01 11237.6i −0.522835 0.905577i
\(537\) −5834.58 + 10105.8i −0.468865 + 0.812098i
\(538\) 12058.1i 0.966285i
\(539\) 13155.8 + 7595.50i 1.05132 + 0.606979i
\(540\) 1081.84 + 624.600i 0.0862129 + 0.0497750i
\(541\) 8577.44i 0.681651i 0.940127 + 0.340825i \(0.110706\pi\)
−0.940127 + 0.340825i \(0.889294\pi\)
\(542\) 2176.56 3769.92i 0.172493 0.298767i
\(543\) −3715.53 6435.48i −0.293644 0.508606i
\(544\) −6802.75 + 3927.57i −0.536150 + 0.309546i
\(545\) 23898.1 1.87832
\(546\) 7324.56 + 4390.68i 0.574107 + 0.344146i
\(547\) 8723.99 0.681921 0.340961 0.940078i \(-0.389248\pi\)
0.340961 + 0.940078i \(0.389248\pi\)
\(548\) −2440.47 + 1409.01i −0.190240 + 0.109835i
\(549\) −1287.65 2230.28i −0.100102 0.173381i
\(550\) 601.373 1041.61i 0.0466230 0.0807533i
\(551\) 14731.8i 1.13901i
\(552\) 10079.5 + 5819.42i 0.777198 + 0.448716i
\(553\) −452.037 260.984i −0.0347606 0.0200690i
\(554\) 8235.17i 0.631550i
\(555\) 4138.58 7168.22i 0.316528 0.548242i
\(556\) 2881.78 + 4991.39i 0.219810 + 0.380723i
\(557\) −835.720 + 482.503i −0.0635738 + 0.0367043i −0.531450 0.847090i \(-0.678353\pi\)
0.467876 + 0.883794i \(0.345019\pi\)
\(558\) −4109.68 −0.311786
\(559\) −147.788 + 9003.09i −0.0111820 + 0.681199i
\(560\) −6719.95 −0.507089
\(561\) 3693.36 2132.37i 0.277957 0.160479i
\(562\) 2346.83 + 4064.83i 0.176148 + 0.305097i
\(563\) −7302.60 + 12648.5i −0.546657 + 0.946837i 0.451844 + 0.892097i \(0.350766\pi\)
−0.998501 + 0.0547402i \(0.982567\pi\)
\(564\) 424.242i 0.0316734i
\(565\) 1280.81 + 739.477i 0.0953702 + 0.0550620i
\(566\) −11773.4 6797.40i −0.874337 0.504799i
\(567\) 2408.72i 0.178407i
\(568\) 1240.87 2149.25i 0.0916650 0.158768i
\(569\) 3901.24 + 6757.15i 0.287432 + 0.497846i 0.973196 0.229977i \(-0.0738653\pi\)
−0.685764 + 0.727824i \(0.740532\pi\)
\(570\) 6740.89 3891.85i 0.495342 0.285986i
\(571\) −11988.2 −0.878618 −0.439309 0.898336i \(-0.644777\pi\)
−0.439309 + 0.898336i \(0.644777\pi\)
\(572\) −2446.56 4402.91i −0.178839 0.321844i
\(573\) 6830.43 0.497985
\(574\) 15562.8 8985.18i 1.13167 0.653370i
\(575\) 1685.07 + 2918.63i 0.122213 + 0.211678i
\(576\) 2098.41 3634.55i 0.151795 0.262916i
\(577\) 5576.90i 0.402374i −0.979553 0.201187i \(-0.935520\pi\)
0.979553 0.201187i \(-0.0644798\pi\)
\(578\) −4151.01 2396.58i −0.298718 0.172465i
\(579\) −10190.8 5883.63i −0.731456 0.422306i
\(580\) 6482.19i 0.464066i
\(581\) −21754.1 + 37679.1i −1.55337 + 2.69052i
\(582\) −2293.71 3972.83i −0.163363 0.282954i
\(583\) 3623.74 2092.17i 0.257427 0.148626i
\(584\) −1824.45 −0.129274
\(585\) −5096.29 83.6567i −0.360181 0.00591245i
\(586\) 15249.4 1.07499
\(587\) −23169.7 + 13377.0i −1.62916 + 0.940593i −0.644810 + 0.764343i \(0.723064\pi\)
−0.984345 + 0.176251i \(0.943603\pi\)
\(588\) 3109.19 + 5385.28i 0.218063 + 0.377696i
\(589\) 11755.2 20360.6i 0.822353 1.42436i
\(590\) 10829.2i 0.755644i
\(591\) −13154.6 7594.84i −0.915584 0.528612i
\(592\) −3698.66 2135.42i −0.256781 0.148252i
\(593\) 3589.40i 0.248565i −0.992247 0.124283i \(-0.960337\pi\)
0.992247 0.124283i \(-0.0396629\pi\)
\(594\) −773.721 + 1340.12i −0.0534447 + 0.0925689i
\(595\) −9100.26 15762.1i −0.627016 1.08602i
\(596\) −1418.82 + 819.158i −0.0975122 + 0.0562987i
\(597\) −9810.18 −0.672536
\(598\) −15370.5 252.310i −1.05108 0.0172537i
\(599\) −7462.78 −0.509050 −0.254525 0.967066i \(-0.581919\pi\)
−0.254525 + 0.967066i \(0.581919\pi\)
\(600\) 1317.16 760.465i 0.0896216 0.0517431i
\(601\) 8255.52 + 14299.0i 0.560316 + 0.970495i 0.997469 + 0.0711081i \(0.0226535\pi\)
−0.437153 + 0.899387i \(0.644013\pi\)
\(602\) 5833.30 10103.6i 0.394929 0.684037i
\(603\) 4834.15i 0.326471i
\(604\) 5312.02 + 3066.90i 0.357853 + 0.206606i
\(605\) 5686.35 + 3283.02i 0.382121 + 0.220618i
\(606\) 4803.37i 0.321986i
\(607\) 5976.78 10352.1i 0.399654 0.692222i −0.594029 0.804444i \(-0.702464\pi\)
0.993683 + 0.112222i \(0.0357968\pi\)
\(608\) 8152.66 + 14120.8i 0.543806 + 0.941900i
\(609\) 10824.5 6249.51i 0.720246 0.415834i
\(610\) −7060.73 −0.468657
\(611\) −840.773 1513.08i −0.0556695 0.100185i
\(612\) 1745.75 0.115307
\(613\) 3962.63 2287.82i 0.261091 0.150741i −0.363741 0.931500i \(-0.618501\pi\)
0.624832 + 0.780759i \(0.285167\pi\)
\(614\) 4049.76 + 7014.38i 0.266181 + 0.461038i
\(615\) −5362.83 + 9288.70i −0.351627 + 0.609035i
\(616\) 20160.9i 1.31868i
\(617\) −16654.6 9615.51i −1.08669 0.627400i −0.153996 0.988071i \(-0.549214\pi\)
−0.932693 + 0.360671i \(0.882548\pi\)
\(618\) −2101.35 1213.21i −0.136778 0.0789687i
\(619\) 11715.6i 0.760727i −0.924837 0.380363i \(-0.875799\pi\)
0.924837 0.380363i \(-0.124201\pi\)
\(620\) 5172.45 8958.95i 0.335050 0.580323i
\(621\) −2167.99 3755.07i −0.140094 0.242650i
\(622\) 13038.9 7528.00i 0.840533 0.485282i
\(623\) 9959.17 0.640459
\(624\) −43.1652 + 2629.59i −0.00276922 + 0.168698i
\(625\) −17807.8 −1.13970
\(626\) −14590.4 + 8423.79i −0.931551 + 0.537831i
\(627\) −4426.26 7666.51i −0.281926 0.488311i
\(628\) 1398.34 2421.99i 0.0888531 0.153898i
\(629\) 11567.3i 0.733256i
\(630\) 5719.22 + 3302.00i 0.361682 + 0.208817i
\(631\) 7603.78 + 4390.04i 0.479717 + 0.276965i 0.720299 0.693664i \(-0.244005\pi\)
−0.240581 + 0.970629i \(0.577338\pi\)
\(632\) 424.040i 0.0266889i
\(633\) 4218.27 7306.25i 0.264867 0.458764i
\(634\) −5693.02 9860.60i −0.356623 0.617689i
\(635\) 24167.1 13952.9i 1.51030 0.871973i
\(636\) 1712.84 0.106790
\(637\) −21761.8 13045.0i −1.35359 0.811403i
\(638\) 8029.78 0.498279
\(639\) −800.691 + 462.279i −0.0495694 + 0.0286189i
\(640\) 1741.28 + 3015.98i 0.107547 + 0.186277i
\(641\) 12495.9 21643.5i 0.769980 1.33364i −0.167593 0.985856i \(-0.553599\pi\)
0.937573 0.347789i \(-0.113067\pi\)
\(642\) 8801.60i 0.541077i
\(643\) −2038.50 1176.93i −0.125024 0.0721827i 0.436184 0.899858i \(-0.356330\pi\)
−0.561208 + 0.827675i \(0.689663\pi\)
\(644\) −15836.9 9143.42i −0.969038 0.559474i
\(645\) 6963.24i 0.425081i
\(646\) 5438.85 9420.37i 0.331252 0.573745i
\(647\) −2955.40 5118.90i −0.179581 0.311043i 0.762156 0.647393i \(-0.224141\pi\)
−0.941737 + 0.336350i \(0.890807\pi\)
\(648\) −1694.65 + 978.407i −0.102735 + 0.0593140i
\(649\) −12316.2 −0.744918
\(650\) −1032.84 + 1722.99i −0.0623251 + 0.103971i
\(651\) 19947.2 1.20091
\(652\) 6295.38 3634.64i 0.378138 0.218318i
\(653\) −2962.17 5130.63i −0.177517 0.307469i 0.763512 0.645793i \(-0.223473\pi\)
−0.941029 + 0.338325i \(0.890140\pi\)
\(654\) −6059.08 + 10494.6i −0.362277 + 0.627481i
\(655\) 17450.2i 1.04097i
\(656\) 4792.79 + 2767.12i 0.285254 + 0.164692i
\(657\) 588.627 + 339.844i 0.0349536 + 0.0201805i
\(658\) 2242.79i 0.132877i
\(659\) 6419.77 11119.4i 0.379482 0.657282i −0.611505 0.791241i \(-0.709436\pi\)
0.990987 + 0.133958i \(0.0427688\pi\)
\(660\) −1947.61 3373.36i −0.114865 0.198952i
\(661\) 8890.18 5132.75i 0.523129 0.302028i −0.215085 0.976595i \(-0.569003\pi\)
0.738214 + 0.674567i \(0.235670\pi\)
\(662\) 8490.35 0.498469
\(663\) −6226.33 + 3459.78i −0.364722 + 0.202665i
\(664\) −35345.4 −2.06577
\(665\) −32718.2 + 18889.9i −1.90791 + 1.10153i
\(666\) 2098.57 + 3634.84i 0.122099 + 0.211482i
\(667\) −11249.9 + 19485.4i −0.653069 + 1.13115i
\(668\) 5466.25i 0.316610i
\(669\) −2384.35 1376.60i −0.137794 0.0795555i
\(670\) 11478.1 + 6626.89i 0.661848 + 0.382118i
\(671\) 8030.27i 0.462004i
\(672\) −6917.03 + 11980.6i −0.397069 + 0.687743i
\(673\) 4931.41 + 8541.45i 0.282454 + 0.489225i 0.971989 0.235028i \(-0.0755181\pi\)
−0.689534 + 0.724253i \(0.742185\pi\)
\(674\) 5704.17 3293.30i 0.325989 0.188210i
\(675\) −566.614 −0.0323096
\(676\) 3965.03 + 7419.88i 0.225593 + 0.422160i
\(677\) 32615.5 1.85158 0.925788 0.378043i \(-0.123403\pi\)
0.925788 + 0.378043i \(0.123403\pi\)
\(678\) −649.470 + 374.971i −0.0367887 + 0.0212400i
\(679\) 11133.0 + 19282.9i 0.629227 + 1.08985i
\(680\) 7392.93 12804.9i 0.416921 0.722128i
\(681\) 4009.17i 0.225597i
\(682\) 11097.9 + 6407.35i 0.623107 + 0.359751i
\(683\) 18729.9 + 10813.7i 1.04931 + 0.605820i 0.922456 0.386102i \(-0.126179\pi\)
0.126854 + 0.991921i \(0.459512\pi\)
\(684\) 3623.75i 0.202570i
\(685\) 4445.85 7700.44i 0.247981 0.429516i
\(686\) 6021.66 + 10429.8i 0.335143 + 0.580485i
\(687\) 428.215 247.230i 0.0237808 0.0137299i
\(688\) 3592.90 0.199096
\(689\) −6108.95 + 3394.56i −0.337783 + 0.187696i
\(690\) −11888.0 −0.655895
\(691\) −12326.3 + 7116.57i −0.678601 + 0.391790i −0.799328 0.600896i \(-0.794811\pi\)
0.120727 + 0.992686i \(0.461477\pi\)
\(692\) −3914.25 6779.67i −0.215025 0.372434i
\(693\) 3755.41 6504.56i 0.205853 0.356548i
\(694\) 6719.98i 0.367561i
\(695\) −15749.4 9092.90i −0.859579 0.496278i
\(696\) 8793.66 + 5077.02i 0.478912 + 0.276500i
\(697\) 14989.1i 0.814566i
\(698\) 4586.39 7943.86i 0.248707 0.430773i
\(699\) −6365.13 11024.7i −0.344423 0.596558i
\(700\) −2069.52 + 1194.84i −0.111743 + 0.0645151i
\(701\) 28747.0 1.54887 0.774437 0.632651i \(-0.218033\pi\)
0.774437 + 0.632651i \(0.218033\pi\)
\(702\) 1328.84 2216.78i 0.0714443 0.119184i
\(703\) −24010.8 −1.28817
\(704\) −11333.2 + 6543.21i −0.606726 + 0.350293i
\(705\) −669.307 1159.27i −0.0357554 0.0619302i
\(706\) 6022.45 10431.2i 0.321045 0.556066i
\(707\) 23314.1i 1.24019i
\(708\) −4366.14 2520.79i −0.231765 0.133810i
\(709\) 1575.00 + 909.324i 0.0834276 + 0.0481670i 0.541133 0.840937i \(-0.317995\pi\)
−0.457706 + 0.889104i \(0.651329\pi\)
\(710\) 2534.86i 0.133988i
\(711\) −78.9868 + 136.809i −0.00416630 + 0.00721624i
\(712\) 4045.35 + 7006.75i 0.212930 + 0.368805i
\(713\) −31096.6 + 17953.6i −1.63335 + 0.943014i
\(714\) 9229.06 0.483738
\(715\) 13631.7 + 8171.47i 0.713002 + 0.427407i
\(716\) 14894.7 0.777431
\(717\) 6471.98 3736.60i 0.337100 0.194625i
\(718\) 9473.15 + 16408.0i 0.492388 + 0.852841i
\(719\) 13070.9 22639.5i 0.677973 1.17428i −0.297617 0.954685i \(-0.596192\pi\)
0.975590 0.219599i \(-0.0704748\pi\)
\(720\) 2033.80i 0.105271i
\(721\) 10199.3 + 5888.58i 0.526827 + 0.304164i
\(722\) −7423.29 4285.84i −0.382640 0.220917i
\(723\) 8752.19i 0.450204i
\(724\) −4742.55 + 8214.34i −0.243447 + 0.421662i
\(725\) 1470.10 + 2546.29i 0.0753078 + 0.130437i
\(726\) −2883.42 + 1664.74i −0.147402 + 0.0851024i
\(727\) 1340.10 0.0683652 0.0341826 0.999416i \(-0.489117\pi\)
0.0341826 + 0.999416i \(0.489117\pi\)
\(728\) 552.674 33668.4i 0.0281366 1.71406i
\(729\) 729.000 0.0370370
\(730\) 1613.84 931.750i 0.0818231 0.0472406i
\(731\) 4865.56 + 8427.39i 0.246182 + 0.426400i
\(732\) −1643.58 + 2846.77i −0.0829898 + 0.143743i
\(733\) 32517.1i 1.63854i 0.573409 + 0.819269i \(0.305620\pi\)
−0.573409 + 0.819269i \(0.694380\pi\)
\(734\) −11627.6 6713.22i −0.584719 0.337588i
\(735\) −16992.2 9810.47i −0.852746 0.492333i
\(736\) 24903.0i 1.24719i
\(737\) 7536.86 13054.2i 0.376694 0.652454i
\(738\) −2719.37 4710.08i −0.135639 0.234933i
\(739\) −19200.2 + 11085.3i −0.955741 + 0.551797i −0.894860 0.446348i \(-0.852724\pi\)
−0.0608813 + 0.998145i \(0.519391\pi\)
\(740\) −10565.1 −0.524838
\(741\) 7181.64 + 12924.3i 0.356038 + 0.640738i
\(742\) 9055.07 0.448008
\(743\) 26316.6 15193.9i 1.29941 0.750216i 0.319110 0.947718i \(-0.396616\pi\)
0.980303 + 0.197502i \(0.0632828\pi\)
\(744\) 8102.40 + 14033.8i 0.399259 + 0.691536i
\(745\) 2584.70 4476.83i 0.127109 0.220159i
\(746\) 10916.9i 0.535786i
\(747\) 11403.6 + 6583.87i 0.558549 + 0.322478i
\(748\) −4714.27 2721.78i −0.230442 0.133046i
\(749\) 42720.3i 2.08407i
\(750\) 3849.88 6668.18i 0.187437 0.324650i
\(751\) −8449.17 14634.4i −0.410539 0.711074i 0.584410 0.811459i \(-0.301326\pi\)
−0.994949 + 0.100385i \(0.967993\pi\)
\(752\) −598.163 + 345.350i −0.0290063 + 0.0167468i
\(753\) 3941.63 0.190758
\(754\) −13409.6 220.122i −0.647680 0.0106318i
\(755\) −19354.0 −0.932934
\(756\) 2662.62 1537.26i 0.128093 0.0739547i
\(757\) −16462.9 28514.6i −0.790428 1.36906i −0.925702 0.378253i \(-0.876525\pi\)
0.135275 0.990808i \(-0.456808\pi\)
\(758\) −1060.45 + 1836.75i −0.0508142 + 0.0880128i
\(759\) 13520.4i 0.646585i
\(760\) −26579.9 15345.9i −1.26862 0.732440i
\(761\) 14542.3 + 8396.01i 0.692718 + 0.399941i 0.804630 0.593777i \(-0.202364\pi\)
−0.111911 + 0.993718i \(0.535697\pi\)
\(762\) 14150.3i 0.672720i
\(763\) 29409.0 50937.8i 1.39538 2.41687i
\(764\) −4359.23 7550.41i −0.206429 0.357545i
\(765\) −4770.41 + 2754.20i −0.225457 + 0.130168i
\(766\) −13783.5 −0.650153
\(767\) 20567.9 + 337.626i 0.968270 + 0.0158944i
\(768\) −12957.4 −0.608804
\(769\) 1335.04 770.783i 0.0626042 0.0361445i −0.468371 0.883532i \(-0.655159\pi\)
0.530975 + 0.847387i \(0.321826\pi\)
\(770\) −10296.2 17833.5i −0.481882 0.834645i
\(771\) −1481.37 + 2565.81i −0.0691963 + 0.119851i
\(772\) 15019.9i 0.700231i
\(773\) −32970.6 19035.6i −1.53411 0.885721i −0.999166 0.0408357i \(-0.986998\pi\)
−0.534948 0.844885i \(-0.679669\pi\)
\(774\) −3057.85 1765.45i −0.142005 0.0819867i
\(775\) 4692.26i 0.217485i
\(776\) −9044.30 + 15665.2i −0.418391 + 0.724674i
\(777\) −10185.9 17642.4i −0.470290 0.814566i
\(778\) −2203.91 + 1272.43i −0.101560 + 0.0586358i
\(779\) 31113.6 1.43102
\(780\) 3160.02 + 5686.87i 0.145060 + 0.261055i
\(781\) 2882.93 0.132086
\(782\) −14387.6 + 8306.71i −0.657930 + 0.379856i
\(783\) −1891.42 3276.03i −0.0863266 0.149522i
\(784\) −5062.01 + 8767.66i −0.230595 + 0.399401i
\(785\) 8824.38i 0.401217i
\(786\) −7663.11 4424.30i −0.347753 0.200775i
\(787\) −17363.6 10024.9i −0.786463 0.454065i 0.0522528 0.998634i \(-0.483360\pi\)
−0.838716 + 0.544569i \(0.816693\pi\)
\(788\) 19388.3i 0.876498i
\(789\) 10479.7 18151.3i 0.472860 0.819017i
\(790\) 216.558 + 375.090i 0.00975291 + 0.0168925i
\(791\) 3152.33 1820.00i 0.141699 0.0818100i
\(792\) 6101.69 0.273755
\(793\) 220.136 13410.5i 0.00985781 0.600529i
\(794\) 17064.4 0.762709
\(795\) −4680.48 + 2702.28i −0.208804 + 0.120553i
\(796\) 6260.93 + 10844.2i 0.278785 + 0.482869i
\(797\) −11200.9 + 19400.6i −0.497813 + 0.862238i −0.999997 0.00252302i \(-0.999197\pi\)
0.502183 + 0.864761i \(0.332530\pi\)
\(798\) 19157.2i 0.849823i
\(799\) −1620.08 935.355i −0.0717327 0.0414149i
\(800\) −2818.26 1627.12i −0.124551 0.0719093i
\(801\) 3014.15i 0.132958i
\(802\) −3353.01 + 5807.59i −0.147630 + 0.255702i
\(803\) −1059.69 1835.44i −0.0465700 0.0806617i
\(804\) 5343.70 3085.19i 0.234400 0.135331i
\(805\) 57700.7 2.52631
\(806\) −18357.7 11004.4i −0.802259 0.480911i
\(807\) −17713.0 −0.772649
\(808\) −16402.6 + 9470.04i −0.714159 + 0.412320i
\(809\) 20983.2 + 36343.9i 0.911903 + 1.57946i 0.811373 + 0.584528i \(0.198720\pi\)
0.100530 + 0.994934i \(0.467946\pi\)
\(810\) 999.350 1730.92i 0.0433501 0.0750846i
\(811\) 13029.1i 0.564133i 0.959395 + 0.282067i \(0.0910199\pi\)
−0.959395 + 0.282067i \(0.908980\pi\)
\(812\) −13816.5 7976.97i −0.597124 0.344750i
\(813\) 5537.91 + 3197.31i 0.238897 + 0.137927i
\(814\) 13087.4i 0.563532i
\(815\) −11468.4 + 19863.9i −0.492909 + 0.853744i
\(816\) 1421.11 + 2461.44i 0.0609667 + 0.105597i
\(817\) 17493.2 10099.7i 0.749092 0.432489i
\(818\) −22319.5 −0.954014
\(819\) −6449.80 + 10759.6i −0.275182 + 0.459060i
\(820\) 13690.4 0.583036
\(821\) −7706.01 + 4449.07i −0.327578 + 0.189127i −0.654765 0.755832i \(-0.727233\pi\)
0.327187 + 0.944960i \(0.393899\pi\)
\(822\) 2254.39 + 3904.71i 0.0956578 + 0.165684i
\(823\) 11361.8 19679.2i 0.481224 0.833504i −0.518544 0.855051i \(-0.673526\pi\)
0.999768 + 0.0215466i \(0.00685902\pi\)
\(824\) 9567.61i 0.404494i
\(825\) 1530.09 + 883.401i 0.0645710 + 0.0372801i
\(826\) −23081.9 13326.4i −0.972304 0.561360i
\(827\) 19073.3i 0.801989i 0.916081 + 0.400994i \(0.131335\pi\)
−0.916081 + 0.400994i \(0.868665\pi\)
\(828\) −2767.26 + 4793.03i −0.116146 + 0.201171i
\(829\) 21251.9 + 36809.4i 0.890361 + 1.54215i 0.839443 + 0.543448i \(0.182881\pi\)
0.0509178 + 0.998703i \(0.483785\pi\)
\(830\) 31265.2 18051.0i 1.30751 0.754891i
\(831\) −12097.2 −0.504992
\(832\) 19105.6 10616.4i 0.796116 0.442377i
\(833\) −27420.2 −1.14052
\(834\) 7986.13 4610.80i 0.331579 0.191437i
\(835\) −8623.86 14937.0i −0.357414 0.619060i
\(836\) −5649.74 + 9785.65i −0.233733 + 0.404837i
\(837\) 6037.01i 0.249307i
\(838\) 12916.2 + 7457.19i 0.532439 + 0.307404i
\(839\) 16824.5 + 9713.62i 0.692307 + 0.399704i 0.804476 0.593985i \(-0.202446\pi\)
−0.112168 + 0.993689i \(0.535780\pi\)
\(840\) 26040.1i 1.06960i
\(841\) 2379.80 4121.94i 0.0975768 0.169008i
\(842\) 7741.11 + 13408.0i 0.316836 + 0.548777i
\(843\) −5971.13 + 3447.43i −0.243958 + 0.140849i
\(844\) −10768.5 −0.439180
\(845\) −22540.8 14020.0i −0.917664 0.570770i
\(846\) 678.780 0.0275850
\(847\) 13995.2 8080.15i 0.567747 0.327789i
\(848\) 1394.32 + 2415.03i 0.0564637 + 0.0977979i
\(849\) 9985.20 17294.9i 0.403641 0.699127i
\(850\) 2170.99i 0.0876052i
\(851\) 31758.5 + 18335.8i 1.27928 + 0.738592i
\(852\) 1022.01 + 590.060i 0.0410958 + 0.0237267i
\(853\) 26851.8i 1.07783i 0.842361 + 0.538914i \(0.181165\pi\)
−0.842361 + 0.538914i \(0.818835\pi\)
\(854\) −8688.92 + 15049.7i −0.348160 + 0.603031i
\(855\) 5717.03 + 9902.18i 0.228676 + 0.396079i
\(856\) 30055.8 17352.7i 1.20010 0.692878i
\(857\) −41539.4 −1.65573 −0.827864 0.560929i \(-0.810444\pi\)
−0.827864 + 0.560929i \(0.810444\pi\)
\(858\) −7044.58 + 3914.46i −0.280301 + 0.155754i
\(859\) −11936.2 −0.474107 −0.237054 0.971497i \(-0.576182\pi\)
−0.237054 + 0.971497i \(0.576182\pi\)
\(860\) 7697.22 4443.99i 0.305201 0.176208i
\(861\) 13199.0 + 22861.3i 0.522439 + 0.904892i
\(862\) −10269.2 + 17786.7i −0.405765 + 0.702805i
\(863\) 41128.6i 1.62229i −0.584848 0.811143i \(-0.698846\pi\)
0.584848 0.811143i \(-0.301154\pi\)
\(864\) 3625.94 + 2093.44i 0.142774 + 0.0824309i
\(865\) 21392.0 + 12350.7i 0.840866 + 0.485474i
\(866\) 5582.22i 0.219043i
\(867\) 3520.52 6097.72i 0.137904 0.238857i
\(868\) −12730.4 22049.7i −0.497810 0.862232i
\(869\) 426.595 246.295i 0.0166528 0.00961448i
\(870\) −10371.4 −0.404165
\(871\) −12944.3 + 21593.8i −0.503561 + 0.840044i
\(872\) 47782.9 1.85566
\(873\) 5835.98 3369.40i 0.226252 0.130627i
\(874\) 17242.7 + 29865.2i 0.667325 + 1.15584i
\(875\) −18686.1 + 32365.4i −0.721951 + 1.25046i
\(876\) 867.564i 0.0334615i
\(877\) −5548.50 3203.43i −0.213637 0.123343i 0.389364 0.921084i \(-0.372695\pi\)
−0.603001 + 0.797741i \(0.706028\pi\)
\(878\) −11928.1 6886.68i −0.458489 0.264709i
\(879\) 22401.0i 0.859574i
\(880\) 3170.87 5492.10i 0.121466 0.210385i
\(881\) −1469.04 2544.45i −0.0561783 0.0973037i 0.836569 0.547862i \(-0.184558\pi\)
−0.892747 + 0.450559i \(0.851225\pi\)
\(882\) 8616.36 4974.66i 0.328943 0.189916i
\(883\) −3022.06 −0.115176 −0.0575881 0.998340i \(-0.518341\pi\)
−0.0575881 + 0.998340i \(0.518341\pi\)
\(884\) 7798.16 + 4674.58i 0.296697 + 0.177854i
\(885\) 15907.8 0.604219
\(886\) −15308.8 + 8838.51i −0.580483 + 0.335142i
\(887\) 5030.22 + 8712.59i 0.190415 + 0.329809i 0.945388 0.325948i \(-0.105683\pi\)
−0.754973 + 0.655756i \(0.772350\pi\)
\(888\) 8274.85 14332.5i 0.312709 0.541628i
\(889\) 68681.5i 2.59112i
\(890\) −7156.74 4131.94i −0.269544 0.155621i
\(891\) −1968.61 1136.57i −0.0740188 0.0427348i
\(892\) 3514.24i 0.131912i
\(893\) −1941.57 + 3362.89i −0.0727570 + 0.126019i
\(894\) 1310.64 + 2270.09i 0.0490317 + 0.0849254i
\(895\) −40700.9 + 23498.7i −1.52009 + 0.877624i
\(896\) 8571.24 0.319582
\(897\) 370.637 22578.9i 0.0137962 0.840453i
\(898\) −13320.5 −0.494999
\(899\) −27129.5 + 15663.2i −1.00647 + 0.581088i
\(900\) 361.617 + 626.339i 0.0133932 + 0.0231978i
\(901\) −3776.42 + 6540.95i −0.139635 + 0.241854i
\(902\) 16958.9i 0.626020i
\(903\) 14841.9 + 8568.96i 0.546962 + 0.315788i
\(904\) 2560.91 + 1478.54i 0.0942197 + 0.0543978i
\(905\) 29928.4i 1.09929i
\(906\) 4906.99 8499.15i 0.179938 0.311662i
\(907\) −21579.3 37376.5i −0.789999 1.36832i −0.925967 0.377606i \(-0.876748\pi\)
0.135967 0.990713i \(-0.456586\pi\)
\(908\) 4431.76 2558.68i 0.161975 0.0935163i
\(909\) 7056.02 0.257462
\(910\) 16705.7 + 30064.1i 0.608558 + 1.09518i
\(911\) −32665.9 −1.18800 −0.594001 0.804464i \(-0.702453\pi\)
−0.594001 + 0.804464i \(0.702453\pi\)
\(912\) 5109.33 2949.87i 0.185512 0.107105i
\(913\) −20529.7 35558.4i −0.744176 1.28895i
\(914\) 1583.99 2743.55i 0.0573235 0.0992873i
\(915\) 10372.0i 0.374741i
\(916\) −546.581 315.568i −0.0197156 0.0113828i
\(917\) 37194.4 + 21474.2i 1.33944 + 0.773327i
\(918\) 2793.18i 0.100423i
\(919\) −9494.97 + 16445.8i −0.340816 + 0.590311i −0.984585 0.174909i \(-0.944037\pi\)
0.643768 + 0.765221i \(0.277370\pi\)
\(920\) 23437.6 + 40595.2i 0.839909 + 1.45476i
\(921\) −10303.9 + 5948.98i −0.368650 + 0.212840i
\(922\) 15860.6 0.566529
\(923\) −4814.47 79.0305i −0.171690 0.00281833i
\(924\) −9586.91 −0.341327
\(925\) 4150.10 2396.06i 0.147518 0.0851698i
\(926\) −2046.86 3545.27i −0.0726393 0.125815i
\(927\) 1782.18 3086.83i 0.0631440 0.109369i
\(928\) 21726.0i 0.768525i
\(929\) −4846.98 2798.40i −0.171178 0.0988295i 0.411963 0.911200i \(-0.364843\pi\)
−0.583141 + 0.812371i \(0.698177\pi\)
\(930\) −14334.2 8275.84i −0.505415 0.291802i
\(931\) 56917.6i 2.00365i
\(932\) −8124.55 + 14072.1i −0.285546 + 0.494579i
\(933\) 11058.4 + 19153.8i 0.388035 + 0.672097i
\(934\) 33028.1 19068.8i 1.15708 0.668040i
\(935\) 17176.1 0.600770
\(936\) −10189.7 167.267i −0.355836 0.00584112i
\(937\) 40294.4 1.40487 0.702433 0.711750i \(-0.252097\pi\)
0.702433 + 0.711750i \(0.252097\pi\)
\(938\) 28249.9 16310.1i 0.983360 0.567743i
\(939\) −12374.3 21432.9i −0.430054 0.744875i
\(940\) −854.314 + 1479.72i −0.0296432 + 0.0513436i
\(941\) 43648.8i 1.51213i −0.654499 0.756063i \(-0.727120\pi\)
0.654499 0.756063i \(-0.272880\pi\)
\(942\) −3875.15 2237.32i −0.134033 0.0773840i
\(943\) −41153.1 23759.8i −1.42113 0.820492i
\(944\) 8208.10i 0.282999i
\(945\) −4850.54 + 8401.39i −0.166972 + 0.289203i
\(946\) 5504.98 + 9534.90i 0.189199 + 0.327702i
\(947\) −9081.62 + 5243.28i −0.311629 + 0.179919i −0.647655 0.761933i \(-0.724250\pi\)
0.336026 + 0.941853i \(0.390917\pi\)
\(948\) 201.640 0.00690819
\(949\) 1719.36 + 3094.22i 0.0588122 + 0.105840i
\(950\) 4506.44 0.153903
\(951\) 14485.0 8362.90i 0.493909 0.285158i
\(952\) −18195.5 31515.5i −0.619452 1.07292i
\(953\) 16529.4 28629.7i 0.561846 0.973145i −0.435490 0.900194i \(-0.643425\pi\)
0.997335 0.0729517i \(-0.0232419\pi\)
\(954\) 2740.52i 0.0930059i
\(955\) 23823.9 + 13754.7i 0.807249 + 0.466065i
\(956\) −8260.93 4769.45i −0.279475 0.161355i
\(957\) 11795.5i 0.398428i
\(958\) −9509.73 + 16471.3i −0.320715 + 0.555495i
\(959\) −10942.1 18952.3i −0.368445 0.638166i
\(960\) 14638.1 8451.31i 0.492128 0.284130i
\(961\) −20202.8 −0.678152
\(962\) −358.769 + 21855.9i −0.0120241 + 0.732497i
\(963\) −12929.3 −0.432650
\(964\) 9674.74 5585.71i 0.323239 0.186622i
\(965\) −23696.2 41043.1i −0.790476 1.36914i
\(966\) −14629.3 + 25338.7i −0.487258 + 0.843955i
\(967\) 53634.9i 1.78364i 0.452389 + 0.891821i \(0.350572\pi\)
−0.452389 + 0.891821i \(0.649428\pi\)
\(968\) 11369.5 + 6564.21i 0.377511 + 0.217956i
\(969\) 13838.3 + 7989.53i 0.458771 + 0.264872i
\(970\) 18475.8i 0.611569i
\(971\) 2043.40 3539.27i 0.0675344 0.116973i −0.830281 0.557345i \(-0.811820\pi\)
0.897815 + 0.440372i \(0.145153\pi\)
\(972\) −465.253 805.842i −0.0153529 0.0265920i
\(973\) −38762.3 + 22379.4i −1.27715 + 0.737360i
\(974\) −7223.00 −0.237618
\(975\) −2531.02 1517.21i −0.0831361 0.0498356i
\(976\) −5351.76 −0.175518
\(977\) −12454.3 + 7190.48i −0.407827 + 0.235459i −0.689856 0.723947i \(-0.742326\pi\)
0.282028 + 0.959406i \(0.408993\pi\)
\(978\) −5815.37 10072.5i −0.190138 0.329329i
\(979\) −4699.32 + 8139.46i −0.153413 + 0.265718i
\(980\) 25044.5i 0.816343i
\(981\) −15416.3 8900.63i −0.501739 0.289679i
\(982\) 5945.76 + 3432.79i 0.193215 + 0.111553i
\(983\) 12916.5i 0.419099i −0.977798 0.209549i \(-0.932800\pi\)
0.977798 0.209549i \(-0.0671997\pi\)
\(984\) −10722.7 + 18572.2i −0.347385 + 0.601688i
\(985\) −30588.1 52980.1i −0.989460 1.71379i
\(986\) −12552.2 + 7247.00i −0.405418 + 0.234068i
\(987\) −3294.59 −0.106249
\(988\) 9703.27 16187.0i 0.312451 0.521233i
\(989\) −30850.3 −0.991893
\(990\) −5397.33 + 3116.15i −0.173271 + 0.100038i
\(991\) 2919.49 + 5056.71i 0.0935829 + 0.162090i 0.909016 0.416761i \(-0.136835\pi\)
−0.815433 + 0.578851i \(0.803501\pi\)
\(992\) 17336.2 30027.2i 0.554865 0.961055i
\(993\) 12472.1i 0.398580i
\(994\) 5402.95 + 3119.40i 0.172406 + 0.0995385i
\(995\) −34217.0 19755.2i −1.09020 0.629428i
\(996\) 16807.5i 0.534705i
\(997\) −22145.1 + 38356.4i −0.703452 + 1.21841i 0.263796 + 0.964579i \(0.415026\pi\)
−0.967247 + 0.253835i \(0.918308\pi\)
\(998\) −4112.50 7123.05i −0.130440 0.225928i
\(999\) −5339.48 + 3082.75i −0.169103 + 0.0976315i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 39.4.j.c.10.2 yes 10
3.2 odd 2 117.4.q.e.10.4 10
4.3 odd 2 624.4.bv.h.49.2 10
13.2 odd 12 507.4.a.r.1.4 10
13.3 even 3 507.4.b.i.337.4 10
13.4 even 6 inner 39.4.j.c.4.2 10
13.10 even 6 507.4.b.i.337.7 10
13.11 odd 12 507.4.a.r.1.7 10
39.2 even 12 1521.4.a.bk.1.7 10
39.11 even 12 1521.4.a.bk.1.4 10
39.17 odd 6 117.4.q.e.82.4 10
52.43 odd 6 624.4.bv.h.433.4 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
39.4.j.c.4.2 10 13.4 even 6 inner
39.4.j.c.10.2 yes 10 1.1 even 1 trivial
117.4.q.e.10.4 10 3.2 odd 2
117.4.q.e.82.4 10 39.17 odd 6
507.4.a.r.1.4 10 13.2 odd 12
507.4.a.r.1.7 10 13.11 odd 12
507.4.b.i.337.4 10 13.3 even 3
507.4.b.i.337.7 10 13.10 even 6
624.4.bv.h.49.2 10 4.3 odd 2
624.4.bv.h.433.4 10 52.43 odd 6
1521.4.a.bk.1.4 10 39.11 even 12
1521.4.a.bk.1.7 10 39.2 even 12