Properties

Label 76.4.d.a.75.7
Level $76$
Weight $4$
Character 76.75
Analytic conductor $4.484$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [76,4,Mod(75,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.75");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 76.d (of order \(2\), degree \(1\), 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: \(4.48414516044\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 75.7
Character \(\chi\) \(=\) 76.75
Dual form 76.4.d.a.75.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.25296 - 1.71002i) q^{2} -8.24449 q^{3} +(2.15167 + 7.70521i) q^{4} -10.8316 q^{5} +(18.5745 + 14.0982i) q^{6} +8.32669i q^{7} +(8.32842 - 21.0389i) q^{8} +40.9716 q^{9} +O(q^{10})\) \(q+(-2.25296 - 1.71002i) q^{2} -8.24449 q^{3} +(2.15167 + 7.70521i) q^{4} -10.8316 q^{5} +(18.5745 + 14.0982i) q^{6} +8.32669i q^{7} +(8.32842 - 21.0389i) q^{8} +40.9716 q^{9} +(24.4032 + 18.5223i) q^{10} -53.9788i q^{11} +(-17.7394 - 63.5255i) q^{12} +43.7588i q^{13} +(14.2388 - 18.7597i) q^{14} +89.3011 q^{15} +(-54.7406 + 33.1582i) q^{16} +91.7057 q^{17} +(-92.3075 - 70.0622i) q^{18} +(54.7519 - 62.1388i) q^{19} +(-23.3061 - 83.4599i) q^{20} -68.6493i q^{21} +(-92.3047 + 121.612i) q^{22} +172.737i q^{23} +(-68.6636 + 173.455i) q^{24} -7.67618 q^{25} +(74.8283 - 98.5868i) q^{26} -115.189 q^{27} +(-64.1589 + 17.9163i) q^{28} +3.12725i q^{29} +(-201.192 - 152.707i) q^{30} +113.134 q^{31} +(180.030 + 18.9033i) q^{32} +445.027i q^{33} +(-206.609 - 156.818i) q^{34} -90.1914i q^{35} +(88.1575 + 315.695i) q^{36} +159.274i q^{37} +(-229.612 + 46.3695i) q^{38} -360.769i q^{39} +(-90.2102 + 227.886i) q^{40} -205.704i q^{41} +(-117.392 + 154.664i) q^{42} -28.4169i q^{43} +(415.918 - 116.145i) q^{44} -443.789 q^{45} +(295.384 - 389.170i) q^{46} -62.4555i q^{47} +(451.308 - 273.372i) q^{48} +273.666 q^{49} +(17.2941 + 13.1264i) q^{50} -756.067 q^{51} +(-337.171 + 94.1545i) q^{52} -650.269i q^{53} +(259.516 + 196.975i) q^{54} +584.677i q^{55} +(175.185 + 69.3482i) q^{56} +(-451.402 + 512.303i) q^{57} +(5.34765 - 7.04557i) q^{58} +792.302 q^{59} +(192.147 + 688.084i) q^{60} +30.4890 q^{61} +(-254.887 - 193.461i) q^{62} +341.158i q^{63} +(-373.275 - 350.442i) q^{64} -473.978i q^{65} +(761.005 - 1002.63i) q^{66} -278.499 q^{67} +(197.321 + 706.612i) q^{68} -1424.13i q^{69} +(-154.229 + 203.198i) q^{70} -74.0407 q^{71} +(341.229 - 862.000i) q^{72} +1117.76 q^{73} +(272.361 - 358.838i) q^{74} +63.2862 q^{75} +(596.601 + 288.173i) q^{76} +449.464 q^{77} +(-616.921 + 812.798i) q^{78} +51.9803 q^{79} +(592.929 - 359.157i) q^{80} -156.561 q^{81} +(-351.758 + 463.444i) q^{82} +1138.79i q^{83} +(528.957 - 147.711i) q^{84} -993.321 q^{85} +(-48.5934 + 64.0222i) q^{86} -25.7826i q^{87} +(-1135.66 - 449.558i) q^{88} +1036.42i q^{89} +(999.839 + 758.887i) q^{90} -364.365 q^{91} +(-1330.98 + 371.674i) q^{92} -932.733 q^{93} +(-106.800 + 140.710i) q^{94} +(-593.051 + 673.063i) q^{95} +(-1484.25 - 155.848i) q^{96} +145.329i q^{97} +(-616.560 - 467.974i) q^{98} -2211.60i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 10 q^{4} - 4 q^{5} - 6 q^{6} + 192 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + 10 q^{4} - 4 q^{5} - 6 q^{6} + 192 q^{9} - 134 q^{16} - 80 q^{17} - 300 q^{20} - 26 q^{24} + 496 q^{25} - 90 q^{26} + 254 q^{28} - 16 q^{30} - 556 q^{36} - 626 q^{38} - 850 q^{42} + 976 q^{44} - 612 q^{45} + 188 q^{49} + 354 q^{54} - 580 q^{57} + 2534 q^{58} - 948 q^{61} - 1068 q^{62} - 1634 q^{64} + 1244 q^{66} + 1630 q^{68} - 184 q^{73} + 2276 q^{74} + 1688 q^{76} + 308 q^{77} + 3376 q^{80} - 2284 q^{81} - 740 q^{82} + 684 q^{85} + 1810 q^{92} + 824 q^{93} - 5222 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.25296 1.71002i −0.796542 0.604583i
\(3\) −8.24449 −1.58665 −0.793326 0.608797i \(-0.791653\pi\)
−0.793326 + 0.608797i \(0.791653\pi\)
\(4\) 2.15167 + 7.70521i 0.268959 + 0.963152i
\(5\) −10.8316 −0.968809 −0.484404 0.874844i \(-0.660964\pi\)
−0.484404 + 0.874844i \(0.660964\pi\)
\(6\) 18.5745 + 14.0982i 1.26384 + 0.959263i
\(7\) 8.32669i 0.449599i 0.974405 + 0.224799i \(0.0721727\pi\)
−0.974405 + 0.224799i \(0.927827\pi\)
\(8\) 8.32842 21.0389i 0.368068 0.929799i
\(9\) 40.9716 1.51747
\(10\) 24.4032 + 18.5223i 0.771697 + 0.585725i
\(11\) 53.9788i 1.47956i −0.672846 0.739782i \(-0.734928\pi\)
0.672846 0.739782i \(-0.265072\pi\)
\(12\) −17.7394 63.5255i −0.426745 1.52819i
\(13\) 43.7588i 0.933577i 0.884369 + 0.466788i \(0.154589\pi\)
−0.884369 + 0.466788i \(0.845411\pi\)
\(14\) 14.2388 18.7597i 0.271820 0.358124i
\(15\) 89.3011 1.53716
\(16\) −54.7406 + 33.1582i −0.855322 + 0.518097i
\(17\) 91.7057 1.30835 0.654174 0.756344i \(-0.273017\pi\)
0.654174 + 0.756344i \(0.273017\pi\)
\(18\) −92.3075 70.0622i −1.20873 0.917435i
\(19\) 54.7519 62.1388i 0.661103 0.750296i
\(20\) −23.3061 83.4599i −0.260570 0.933110i
\(21\) 68.6493i 0.713357i
\(22\) −92.3047 + 121.612i −0.894519 + 1.17854i
\(23\) 172.737i 1.56601i 0.622017 + 0.783004i \(0.286314\pi\)
−0.622017 + 0.783004i \(0.713686\pi\)
\(24\) −68.6636 + 173.455i −0.583996 + 1.47527i
\(25\) −7.67618 −0.0614095
\(26\) 74.8283 98.5868i 0.564424 0.743633i
\(27\) −115.189 −0.821041
\(28\) −64.1589 + 17.9163i −0.433032 + 0.120924i
\(29\) 3.12725i 0.0200247i 0.999950 + 0.0100123i \(0.00318708\pi\)
−0.999950 + 0.0100123i \(0.996813\pi\)
\(30\) −201.192 152.707i −1.22442 0.929343i
\(31\) 113.134 0.655467 0.327734 0.944770i \(-0.393715\pi\)
0.327734 + 0.944770i \(0.393715\pi\)
\(32\) 180.030 + 18.9033i 0.994533 + 0.104427i
\(33\) 445.027i 2.34756i
\(34\) −206.609 156.818i −1.04215 0.791004i
\(35\) 90.1914i 0.435575i
\(36\) 88.1575 + 315.695i 0.408137 + 1.46155i
\(37\) 159.274i 0.707688i 0.935304 + 0.353844i \(0.115126\pi\)
−0.935304 + 0.353844i \(0.884874\pi\)
\(38\) −229.612 + 46.3695i −0.980212 + 0.197951i
\(39\) 360.769i 1.48126i
\(40\) −90.2102 + 227.886i −0.356587 + 0.900797i
\(41\) 205.704i 0.783551i −0.920061 0.391776i \(-0.871861\pi\)
0.920061 0.391776i \(-0.128139\pi\)
\(42\) −117.392 + 154.664i −0.431284 + 0.568219i
\(43\) 28.4169i 0.100780i −0.998730 0.0503899i \(-0.983954\pi\)
0.998730 0.0503899i \(-0.0160464\pi\)
\(44\) 415.918 116.145i 1.42505 0.397942i
\(45\) −443.789 −1.47014
\(46\) 295.384 389.170i 0.946782 1.24739i
\(47\) 62.4555i 0.193831i −0.995293 0.0969156i \(-0.969102\pi\)
0.995293 0.0969156i \(-0.0308977\pi\)
\(48\) 451.308 273.372i 1.35710 0.822040i
\(49\) 273.666 0.797861
\(50\) 17.2941 + 13.1264i 0.0489152 + 0.0371271i
\(51\) −756.067 −2.07589
\(52\) −337.171 + 94.1545i −0.899176 + 0.251094i
\(53\) 650.269i 1.68531i −0.538456 0.842654i \(-0.680992\pi\)
0.538456 0.842654i \(-0.319008\pi\)
\(54\) 259.516 + 196.975i 0.653994 + 0.496387i
\(55\) 584.677i 1.43342i
\(56\) 175.185 + 69.3482i 0.418037 + 0.165483i
\(57\) −451.402 + 512.303i −1.04894 + 1.19046i
\(58\) 5.34765 7.04557i 0.0121066 0.0159505i
\(59\) 792.302 1.74829 0.874144 0.485667i \(-0.161423\pi\)
0.874144 + 0.485667i \(0.161423\pi\)
\(60\) 192.147 + 688.084i 0.413434 + 1.48052i
\(61\) 30.4890 0.0639953 0.0319976 0.999488i \(-0.489813\pi\)
0.0319976 + 0.999488i \(0.489813\pi\)
\(62\) −254.887 193.461i −0.522107 0.396284i
\(63\) 341.158i 0.682251i
\(64\) −373.275 350.442i −0.729052 0.684458i
\(65\) 473.978i 0.904457i
\(66\) 761.005 1002.63i 1.41929 1.86993i
\(67\) −278.499 −0.507822 −0.253911 0.967228i \(-0.581717\pi\)
−0.253911 + 0.967228i \(0.581717\pi\)
\(68\) 197.321 + 706.612i 0.351892 + 1.26014i
\(69\) 1424.13i 2.48471i
\(70\) −154.229 + 203.198i −0.263341 + 0.346954i
\(71\) −74.0407 −0.123761 −0.0618804 0.998084i \(-0.519710\pi\)
−0.0618804 + 0.998084i \(0.519710\pi\)
\(72\) 341.229 862.000i 0.558531 1.41094i
\(73\) 1117.76 1.79210 0.896052 0.443950i \(-0.146423\pi\)
0.896052 + 0.443950i \(0.146423\pi\)
\(74\) 272.361 358.838i 0.427856 0.563703i
\(75\) 63.2862 0.0974355
\(76\) 596.601 + 288.173i 0.900458 + 0.434943i
\(77\) 449.464 0.665211
\(78\) −616.921 + 812.798i −0.895546 + 1.17989i
\(79\) 51.9803 0.0740284 0.0370142 0.999315i \(-0.488215\pi\)
0.0370142 + 0.999315i \(0.488215\pi\)
\(80\) 592.929 359.157i 0.828644 0.501937i
\(81\) −156.561 −0.214761
\(82\) −351.758 + 463.444i −0.473722 + 0.624132i
\(83\) 1138.79i 1.50600i 0.658020 + 0.753001i \(0.271394\pi\)
−0.658020 + 0.753001i \(0.728606\pi\)
\(84\) 528.957 147.711i 0.687071 0.191864i
\(85\) −993.321 −1.26754
\(86\) −48.5934 + 64.0222i −0.0609298 + 0.0802754i
\(87\) 25.7826i 0.0317722i
\(88\) −1135.66 449.558i −1.37570 0.544580i
\(89\) 1036.42i 1.23439i 0.786810 + 0.617195i \(0.211731\pi\)
−0.786810 + 0.617195i \(0.788269\pi\)
\(90\) 999.839 + 758.887i 1.17103 + 0.888819i
\(91\) −364.365 −0.419735
\(92\) −1330.98 + 371.674i −1.50830 + 0.421192i
\(93\) −932.733 −1.04000
\(94\) −106.800 + 140.710i −0.117187 + 0.154395i
\(95\) −593.051 + 673.063i −0.640482 + 0.726893i
\(96\) −1484.25 155.848i −1.57798 0.165690i
\(97\) 145.329i 0.152123i 0.997103 + 0.0760616i \(0.0242346\pi\)
−0.997103 + 0.0760616i \(0.975765\pi\)
\(98\) −616.560 467.974i −0.635530 0.482373i
\(99\) 2211.60i 2.24519i
\(100\) −16.5166 59.1466i −0.0165166 0.0591466i
\(101\) −120.050 −0.118272 −0.0591359 0.998250i \(-0.518835\pi\)
−0.0591359 + 0.998250i \(0.518835\pi\)
\(102\) 1703.39 + 1292.89i 1.65354 + 1.25505i
\(103\) 467.567 0.447289 0.223644 0.974671i \(-0.428205\pi\)
0.223644 + 0.974671i \(0.428205\pi\)
\(104\) 920.638 + 364.441i 0.868039 + 0.343619i
\(105\) 743.582i 0.691107i
\(106\) −1111.97 + 1465.03i −1.01891 + 1.34242i
\(107\) −402.048 −0.363247 −0.181624 0.983368i \(-0.558135\pi\)
−0.181624 + 0.983368i \(0.558135\pi\)
\(108\) −247.849 887.554i −0.220826 0.790787i
\(109\) 1409.93i 1.23896i 0.785013 + 0.619479i \(0.212656\pi\)
−0.785013 + 0.619479i \(0.787344\pi\)
\(110\) 999.809 1317.26i 0.866618 1.14178i
\(111\) 1313.13i 1.12286i
\(112\) −276.098 455.808i −0.232936 0.384552i
\(113\) 2163.38i 1.80100i −0.434854 0.900501i \(-0.643200\pi\)
0.434854 0.900501i \(-0.356800\pi\)
\(114\) 1893.04 382.293i 1.55526 0.314079i
\(115\) 1871.02i 1.51716i
\(116\) −24.0961 + 6.72882i −0.0192868 + 0.00538582i
\(117\) 1792.87i 1.41667i
\(118\) −1785.03 1354.85i −1.39259 1.05699i
\(119\) 763.605i 0.588231i
\(120\) 743.737 1878.80i 0.565780 1.42925i
\(121\) −1582.71 −1.18911
\(122\) −68.6905 52.1367i −0.0509749 0.0386905i
\(123\) 1695.93i 1.24322i
\(124\) 243.428 + 871.722i 0.176294 + 0.631314i
\(125\) 1437.10 1.02830
\(126\) 583.386 768.615i 0.412478 0.543442i
\(127\) 1117.34 0.780695 0.390348 0.920668i \(-0.372355\pi\)
0.390348 + 0.920668i \(0.372355\pi\)
\(128\) 241.711 + 1427.84i 0.166909 + 0.985972i
\(129\) 234.283i 0.159903i
\(130\) −810.511 + 1067.85i −0.546819 + 0.720438i
\(131\) 1499.93i 1.00037i −0.865917 0.500187i \(-0.833264\pi\)
0.865917 0.500187i \(-0.166736\pi\)
\(132\) −3429.03 + 957.553i −2.26105 + 0.631396i
\(133\) 517.410 + 455.902i 0.337332 + 0.297231i
\(134\) 627.447 + 476.238i 0.404501 + 0.307020i
\(135\) 1247.68 0.795431
\(136\) 763.764 1929.39i 0.481560 1.21650i
\(137\) 845.590 0.527326 0.263663 0.964615i \(-0.415069\pi\)
0.263663 + 0.964615i \(0.415069\pi\)
\(138\) −2435.29 + 3208.51i −1.50221 + 1.97918i
\(139\) 1116.12i 0.681063i 0.940233 + 0.340532i \(0.110607\pi\)
−0.940233 + 0.340532i \(0.889393\pi\)
\(140\) 694.944 194.062i 0.419525 0.117152i
\(141\) 514.914i 0.307543i
\(142\) 166.811 + 126.611i 0.0985807 + 0.0748237i
\(143\) 2362.04 1.38129
\(144\) −2242.81 + 1358.54i −1.29792 + 0.786195i
\(145\) 33.8731i 0.0194001i
\(146\) −2518.26 1911.39i −1.42749 1.08348i
\(147\) −2256.24 −1.26593
\(148\) −1227.24 + 342.705i −0.681611 + 0.190339i
\(149\) 2000.12 1.09971 0.549854 0.835261i \(-0.314683\pi\)
0.549854 + 0.835261i \(0.314683\pi\)
\(150\) −142.581 108.221i −0.0776115 0.0589078i
\(151\) 2532.76 1.36499 0.682494 0.730891i \(-0.260895\pi\)
0.682494 + 0.730891i \(0.260895\pi\)
\(152\) −851.338 1669.44i −0.454294 0.890852i
\(153\) 3757.33 1.98537
\(154\) −1012.63 768.592i −0.529868 0.402175i
\(155\) −1225.42 −0.635022
\(156\) 2779.80 776.256i 1.42668 0.398399i
\(157\) 2373.98 1.20678 0.603389 0.797447i \(-0.293817\pi\)
0.603389 + 0.797447i \(0.293817\pi\)
\(158\) −117.110 88.8873i −0.0589667 0.0447563i
\(159\) 5361.13i 2.67400i
\(160\) −1950.01 204.753i −0.963512 0.101170i
\(161\) −1438.33 −0.704075
\(162\) 352.725 + 267.721i 0.171066 + 0.129841i
\(163\) 858.761i 0.412659i −0.978483 0.206329i \(-0.933848\pi\)
0.978483 0.206329i \(-0.0661518\pi\)
\(164\) 1585.00 442.608i 0.754679 0.210743i
\(165\) 4820.36i 2.27433i
\(166\) 1947.35 2565.64i 0.910503 1.19959i
\(167\) −3711.38 −1.71973 −0.859866 0.510520i \(-0.829453\pi\)
−0.859866 + 0.510520i \(0.829453\pi\)
\(168\) −1444.31 571.740i −0.663279 0.262564i
\(169\) 282.171 0.128435
\(170\) 2237.91 + 1698.60i 1.00965 + 0.766332i
\(171\) 2243.27 2545.93i 1.00320 1.13855i
\(172\) 218.958 61.1438i 0.0970663 0.0271057i
\(173\) 1139.19i 0.500642i 0.968163 + 0.250321i \(0.0805361\pi\)
−0.968163 + 0.250321i \(0.919464\pi\)
\(174\) −44.0887 + 58.0871i −0.0192089 + 0.0253079i
\(175\) 63.9172i 0.0276096i
\(176\) 1789.84 + 2954.83i 0.766558 + 1.26550i
\(177\) −6532.13 −2.77393
\(178\) 1772.30 2335.02i 0.746291 0.983244i
\(179\) 441.493 0.184350 0.0921752 0.995743i \(-0.470618\pi\)
0.0921752 + 0.995743i \(0.470618\pi\)
\(180\) −954.888 3419.49i −0.395406 1.41596i
\(181\) 3285.85i 1.34936i 0.738108 + 0.674682i \(0.235719\pi\)
−0.738108 + 0.674682i \(0.764281\pi\)
\(182\) 820.901 + 623.072i 0.334337 + 0.253765i
\(183\) −251.366 −0.101538
\(184\) 3634.21 + 1438.63i 1.45607 + 0.576397i
\(185\) 1725.19i 0.685614i
\(186\) 2101.41 + 1594.99i 0.828403 + 0.628765i
\(187\) 4950.16i 1.93578i
\(188\) 481.233 134.384i 0.186689 0.0521327i
\(189\) 959.141i 0.369139i
\(190\) 2487.07 502.257i 0.949638 0.191776i
\(191\) 2470.17i 0.935785i −0.883785 0.467893i \(-0.845013\pi\)
0.883785 0.467893i \(-0.154987\pi\)
\(192\) 3077.46 + 2889.22i 1.15675 + 1.08600i
\(193\) 945.372i 0.352588i −0.984338 0.176294i \(-0.943589\pi\)
0.984338 0.176294i \(-0.0564109\pi\)
\(194\) 248.516 327.421i 0.0919710 0.121173i
\(195\) 3907.71i 1.43506i
\(196\) 588.840 + 2108.66i 0.214592 + 0.768461i
\(197\) −4310.10 −1.55879 −0.779396 0.626531i \(-0.784474\pi\)
−0.779396 + 0.626531i \(0.784474\pi\)
\(198\) −3781.87 + 4982.64i −1.35740 + 1.78839i
\(199\) 3934.47i 1.40155i −0.713385 0.700773i \(-0.752839\pi\)
0.713385 0.700773i \(-0.247161\pi\)
\(200\) −63.9305 + 161.499i −0.0226028 + 0.0570985i
\(201\) 2296.08 0.805737
\(202\) 270.469 + 205.288i 0.0942085 + 0.0715051i
\(203\) −26.0396 −0.00900307
\(204\) −1626.81 5825.66i −0.558330 1.99940i
\(205\) 2228.11i 0.759111i
\(206\) −1053.41 799.548i −0.356284 0.270423i
\(207\) 7077.32i 2.37637i
\(208\) −1450.96 2395.38i −0.483683 0.798509i
\(209\) −3354.18 2955.44i −1.11011 0.978144i
\(210\) 1271.54 1675.26i 0.417831 0.550496i
\(211\) −618.267 −0.201722 −0.100861 0.994901i \(-0.532160\pi\)
−0.100861 + 0.994901i \(0.532160\pi\)
\(212\) 5010.46 1399.17i 1.62321 0.453279i
\(213\) 610.428 0.196365
\(214\) 905.799 + 687.510i 0.289342 + 0.219613i
\(215\) 307.801i 0.0976364i
\(216\) −959.341 + 2423.45i −0.302199 + 0.763403i
\(217\) 942.032i 0.294697i
\(218\) 2411.00 3176.51i 0.749053 0.986882i
\(219\) −9215.34 −2.84345
\(220\) −4505.06 + 1258.03i −1.38060 + 0.385530i
\(221\) 4012.93i 1.22144i
\(222\) −2245.48 + 2958.43i −0.678859 + 0.894402i
\(223\) 2321.60 0.697157 0.348578 0.937280i \(-0.386665\pi\)
0.348578 + 0.937280i \(0.386665\pi\)
\(224\) −157.402 + 1499.05i −0.0469503 + 0.447141i
\(225\) −314.506 −0.0931868
\(226\) −3699.41 + 4874.00i −1.08886 + 1.43457i
\(227\) −2363.51 −0.691064 −0.345532 0.938407i \(-0.612301\pi\)
−0.345532 + 0.938407i \(0.612301\pi\)
\(228\) −4918.67 2375.84i −1.42871 0.690104i
\(229\) −211.020 −0.0608934 −0.0304467 0.999536i \(-0.509693\pi\)
−0.0304467 + 0.999536i \(0.509693\pi\)
\(230\) −3199.48 + 4215.34i −0.917250 + 1.20848i
\(231\) −3705.60 −1.05546
\(232\) 65.7940 + 26.0450i 0.0186189 + 0.00737043i
\(233\) −2572.64 −0.723343 −0.361672 0.932306i \(-0.617794\pi\)
−0.361672 + 0.932306i \(0.617794\pi\)
\(234\) 3065.84 4039.26i 0.856496 1.12844i
\(235\) 676.494i 0.187785i
\(236\) 1704.78 + 6104.86i 0.470218 + 1.68387i
\(237\) −428.551 −0.117457
\(238\) 1305.78 1720.37i 0.355635 0.468551i
\(239\) 4787.32i 1.29567i 0.761779 + 0.647837i \(0.224326\pi\)
−0.761779 + 0.647837i \(0.775674\pi\)
\(240\) −4888.40 + 2961.06i −1.31477 + 0.796399i
\(241\) 3421.02i 0.914386i −0.889368 0.457193i \(-0.848855\pi\)
0.889368 0.457193i \(-0.151145\pi\)
\(242\) 3565.78 + 2706.46i 0.947178 + 0.718917i
\(243\) 4400.86 1.16179
\(244\) 65.6023 + 234.924i 0.0172121 + 0.0616372i
\(245\) −2964.25 −0.772975
\(246\) 2900.07 3820.86i 0.751632 0.990280i
\(247\) 2719.12 + 2395.88i 0.700458 + 0.617190i
\(248\) 942.228 2380.22i 0.241256 0.609453i
\(249\) 9388.72i 2.38950i
\(250\) −3237.72 2457.46i −0.819087 0.621694i
\(251\) 30.6786i 0.00771481i −0.999993 0.00385740i \(-0.998772\pi\)
0.999993 0.00385740i \(-0.00122785\pi\)
\(252\) −2628.69 + 734.060i −0.657112 + 0.183498i
\(253\) 9324.14 2.31701
\(254\) −2517.33 1910.68i −0.621857 0.471995i
\(255\) 8189.42 2.01114
\(256\) 1897.07 3630.20i 0.463152 0.886279i
\(257\) 1378.16i 0.334504i 0.985914 + 0.167252i \(0.0534893\pi\)
−0.985914 + 0.167252i \(0.946511\pi\)
\(258\) 400.628 527.830i 0.0966744 0.127369i
\(259\) −1326.22 −0.318176
\(260\) 3652.10 1019.85i 0.871130 0.243262i
\(261\) 128.128i 0.0303868i
\(262\) −2564.90 + 3379.27i −0.604809 + 0.796841i
\(263\) 440.404i 0.103257i 0.998666 + 0.0516283i \(0.0164411\pi\)
−0.998666 + 0.0516283i \(0.983559\pi\)
\(264\) 9362.91 + 3706.38i 2.18275 + 0.864059i
\(265\) 7043.46i 1.63274i
\(266\) −386.105 1911.91i −0.0889985 0.440702i
\(267\) 8544.79i 1.95855i
\(268\) −599.238 2145.89i −0.136583 0.489109i
\(269\) 3105.10i 0.703797i −0.936038 0.351899i \(-0.885536\pi\)
0.936038 0.351899i \(-0.114464\pi\)
\(270\) −2810.98 2133.56i −0.633595 0.480904i
\(271\) 1143.66i 0.256355i 0.991751 + 0.128178i \(0.0409128\pi\)
−0.991751 + 0.128178i \(0.959087\pi\)
\(272\) −5020.03 + 3040.80i −1.11906 + 0.677850i
\(273\) 3004.01 0.665974
\(274\) −1905.08 1445.98i −0.420037 0.318812i
\(275\) 414.351i 0.0908593i
\(276\) 10973.2 3064.26i 2.39315 0.668286i
\(277\) −6934.06 −1.50407 −0.752035 0.659124i \(-0.770927\pi\)
−0.752035 + 0.659124i \(0.770927\pi\)
\(278\) 1908.58 2514.57i 0.411759 0.542496i
\(279\) 4635.29 0.994650
\(280\) −1897.53 751.152i −0.404997 0.160321i
\(281\) 5954.29i 1.26407i 0.774941 + 0.632034i \(0.217780\pi\)
−0.774941 + 0.632034i \(0.782220\pi\)
\(282\) 880.512 1160.08i 0.185935 0.244971i
\(283\) 460.810i 0.0967927i −0.998828 0.0483963i \(-0.984589\pi\)
0.998828 0.0483963i \(-0.0154111\pi\)
\(284\) −159.311 570.499i −0.0332866 0.119200i
\(285\) 4889.41 5549.06i 1.01622 1.15333i
\(286\) −5321.59 4039.14i −1.10025 0.835102i
\(287\) 1712.83 0.352284
\(288\) 7376.10 + 774.500i 1.50917 + 0.158465i
\(289\) 3496.94 0.711772
\(290\) −57.9237 + 76.3149i −0.0117290 + 0.0154530i
\(291\) 1198.17i 0.241367i
\(292\) 2405.05 + 8612.56i 0.482003 + 1.72607i
\(293\) 6752.13i 1.34629i −0.739509 0.673146i \(-0.764942\pi\)
0.739509 0.673146i \(-0.235058\pi\)
\(294\) 5083.22 + 3858.21i 1.00837 + 0.765359i
\(295\) −8581.91 −1.69376
\(296\) 3350.95 + 1326.50i 0.658008 + 0.260477i
\(297\) 6217.75i 1.21478i
\(298\) −4506.20 3420.25i −0.875963 0.664864i
\(299\) −7558.76 −1.46199
\(300\) 136.171 + 487.634i 0.0262062 + 0.0938452i
\(301\) 236.619 0.0453105
\(302\) −5706.21 4331.07i −1.08727 0.825248i
\(303\) 989.754 0.187656
\(304\) −936.743 + 5216.99i −0.176730 + 0.984259i
\(305\) −330.245 −0.0619992
\(306\) −8465.12 6425.11i −1.58143 1.20032i
\(307\) 3859.20 0.717447 0.358723 0.933444i \(-0.383212\pi\)
0.358723 + 0.933444i \(0.383212\pi\)
\(308\) 967.100 + 3463.22i 0.178914 + 0.640699i
\(309\) −3854.85 −0.709692
\(310\) 2760.83 + 2095.50i 0.505822 + 0.383924i
\(311\) 79.1103i 0.0144242i −0.999974 0.00721211i \(-0.997704\pi\)
0.999974 0.00721211i \(-0.00229571\pi\)
\(312\) −7590.19 3004.63i −1.37728 0.545205i
\(313\) 5303.24 0.957690 0.478845 0.877899i \(-0.341056\pi\)
0.478845 + 0.877899i \(0.341056\pi\)
\(314\) −5348.48 4059.55i −0.961249 0.729597i
\(315\) 3695.29i 0.660971i
\(316\) 111.845 + 400.519i 0.0199106 + 0.0713006i
\(317\) 7950.65i 1.40869i 0.709860 + 0.704343i \(0.248758\pi\)
−0.709860 + 0.704343i \(0.751242\pi\)
\(318\) 9167.64 12078.4i 1.61665 2.12995i
\(319\) 168.805 0.0296278
\(320\) 4043.17 + 3795.86i 0.706312 + 0.663109i
\(321\) 3314.68 0.576347
\(322\) 3240.50 + 2459.57i 0.560826 + 0.425672i
\(323\) 5021.06 5698.48i 0.864952 0.981647i
\(324\) −336.867 1206.33i −0.0577618 0.206847i
\(325\) 335.900i 0.0573304i
\(326\) −1468.50 + 1934.76i −0.249486 + 0.328700i
\(327\) 11624.1i 1.96580i
\(328\) −4327.80 1713.19i −0.728545 0.288400i
\(329\) 520.047 0.0871463
\(330\) −8242.91 + 10860.1i −1.37502 + 1.81160i
\(331\) −2166.70 −0.359796 −0.179898 0.983685i \(-0.557577\pi\)
−0.179898 + 0.983685i \(0.557577\pi\)
\(332\) −8774.60 + 2450.30i −1.45051 + 0.405053i
\(333\) 6525.71i 1.07389i
\(334\) 8361.60 + 6346.53i 1.36984 + 1.03972i
\(335\) 3016.59 0.491982
\(336\) 2276.29 + 3757.90i 0.369588 + 0.610150i
\(337\) 6552.73i 1.05920i 0.848248 + 0.529600i \(0.177658\pi\)
−0.848248 + 0.529600i \(0.822342\pi\)
\(338\) −635.720 482.517i −0.102304 0.0776494i
\(339\) 17835.9i 2.85757i
\(340\) −2137.30 7653.75i −0.340916 1.22083i
\(341\) 6106.84i 0.969806i
\(342\) −9407.59 + 1899.83i −1.48744 + 0.300384i
\(343\) 5134.79i 0.808316i
\(344\) −597.862 236.668i −0.0937050 0.0370938i
\(345\) 15425.6i 2.40721i
\(346\) 1948.04 2566.55i 0.302679 0.398782i
\(347\) 3764.47i 0.582383i 0.956665 + 0.291192i \(0.0940518\pi\)
−0.956665 + 0.291192i \(0.905948\pi\)
\(348\) 198.660 55.4756i 0.0306014 0.00854542i
\(349\) 4243.17 0.650808 0.325404 0.945575i \(-0.394500\pi\)
0.325404 + 0.945575i \(0.394500\pi\)
\(350\) −109.300 + 144.003i −0.0166923 + 0.0219922i
\(351\) 5040.52i 0.766504i
\(352\) 1020.38 9717.78i 0.154507 1.47148i
\(353\) 5116.61 0.771473 0.385736 0.922609i \(-0.373947\pi\)
0.385736 + 0.922609i \(0.373947\pi\)
\(354\) 14716.6 + 11170.1i 2.20955 + 1.67707i
\(355\) 801.980 0.119901
\(356\) −7985.87 + 2230.05i −1.18890 + 0.332000i
\(357\) 6295.53i 0.933319i
\(358\) −994.666 754.961i −0.146843 0.111455i
\(359\) 9232.77i 1.35734i −0.734441 0.678672i \(-0.762556\pi\)
0.734441 0.678672i \(-0.237444\pi\)
\(360\) −3696.06 + 9336.85i −0.541109 + 1.36693i
\(361\) −863.458 6804.43i −0.125887 0.992045i
\(362\) 5618.86 7402.89i 0.815803 1.07483i
\(363\) 13048.6 1.88671
\(364\) −783.995 2807.51i −0.112892 0.404268i
\(365\) −12107.1 −1.73621
\(366\) 566.318 + 429.841i 0.0808795 + 0.0613883i
\(367\) 386.149i 0.0549232i 0.999623 + 0.0274616i \(0.00874240\pi\)
−0.999623 + 0.0274616i \(0.991258\pi\)
\(368\) −5727.65 9455.74i −0.811344 1.33944i
\(369\) 8428.03i 1.18901i
\(370\) −2950.11 + 3886.79i −0.414511 + 0.546121i
\(371\) 5414.58 0.757712
\(372\) −2006.94 7186.90i −0.279717 1.00168i
\(373\) 5244.60i 0.728030i −0.931393 0.364015i \(-0.881406\pi\)
0.931393 0.364015i \(-0.118594\pi\)
\(374\) −8464.87 + 11152.5i −1.17034 + 1.54193i
\(375\) −11848.1 −1.63156
\(376\) −1314.00 520.156i −0.180224 0.0713430i
\(377\) −136.845 −0.0186946
\(378\) −1640.15 + 2160.91i −0.223175 + 0.294035i
\(379\) 6933.67 0.939733 0.469867 0.882737i \(-0.344302\pi\)
0.469867 + 0.882737i \(0.344302\pi\)
\(380\) −6462.15 3121.38i −0.872372 0.421377i
\(381\) −9211.93 −1.23869
\(382\) −4224.03 + 5565.19i −0.565760 + 0.745392i
\(383\) −14266.3 −1.90333 −0.951666 0.307135i \(-0.900630\pi\)
−0.951666 + 0.307135i \(0.900630\pi\)
\(384\) −1992.78 11771.8i −0.264827 1.56440i
\(385\) −4868.42 −0.644462
\(386\) −1616.60 + 2129.89i −0.213168 + 0.280851i
\(387\) 1164.29i 0.152930i
\(388\) −1119.79 + 312.701i −0.146518 + 0.0409149i
\(389\) 3977.48 0.518422 0.259211 0.965821i \(-0.416537\pi\)
0.259211 + 0.965821i \(0.416537\pi\)
\(390\) 6682.25 8803.91i 0.867613 1.14309i
\(391\) 15841.0i 2.04888i
\(392\) 2279.21 5757.65i 0.293667 0.741850i
\(393\) 12366.1i 1.58725i
\(394\) 9710.50 + 7370.35i 1.24164 + 0.942419i
\(395\) −563.031 −0.0717194
\(396\) 17040.8 4758.63i 2.16246 0.603864i
\(397\) 5351.99 0.676596 0.338298 0.941039i \(-0.390149\pi\)
0.338298 + 0.941039i \(0.390149\pi\)
\(398\) −6728.02 + 8864.22i −0.847350 + 1.11639i
\(399\) −4265.78 3758.68i −0.535229 0.471602i
\(400\) 420.199 254.528i 0.0525249 0.0318160i
\(401\) 392.753i 0.0489106i 0.999701 + 0.0244553i \(0.00778514\pi\)
−0.999701 + 0.0244553i \(0.992215\pi\)
\(402\) −5172.98 3926.34i −0.641803 0.487135i
\(403\) 4950.61i 0.611929i
\(404\) −258.309 925.014i −0.0318103 0.113914i
\(405\) 1695.80 0.208062
\(406\) 58.6663 + 44.5282i 0.00717132 + 0.00544310i
\(407\) 8597.41 1.04707
\(408\) −6296.84 + 15906.9i −0.764069 + 1.93016i
\(409\) 13687.4i 1.65476i −0.561642 0.827380i \(-0.689830\pi\)
0.561642 0.827380i \(-0.310170\pi\)
\(410\) 3810.11 5019.84i 0.458946 0.604664i
\(411\) −6971.46 −0.836683
\(412\) 1006.05 + 3602.70i 0.120302 + 0.430807i
\(413\) 6597.25i 0.786028i
\(414\) 12102.3 15944.9i 1.43671 1.89288i
\(415\) 12334.9i 1.45903i
\(416\) −827.186 + 7877.87i −0.0974907 + 0.928472i
\(417\) 9201.82i 1.08061i
\(418\) 2502.97 + 12394.2i 0.292881 + 1.45029i
\(419\) 8342.37i 0.972677i 0.873770 + 0.486338i \(0.161668\pi\)
−0.873770 + 0.486338i \(0.838332\pi\)
\(420\) −5729.46 + 1599.95i −0.665641 + 0.185879i
\(421\) 3217.13i 0.372430i 0.982509 + 0.186215i \(0.0596222\pi\)
−0.982509 + 0.186215i \(0.940378\pi\)
\(422\) 1392.93 + 1057.25i 0.160680 + 0.121958i
\(423\) 2558.90i 0.294133i
\(424\) −13681.0 5415.71i −1.56700 0.620307i
\(425\) −703.950 −0.0803449
\(426\) −1375.27 1043.84i −0.156413 0.118719i
\(427\) 253.872i 0.0287722i
\(428\) −865.076 3097.87i −0.0976987 0.349862i
\(429\) −19473.8 −2.19162
\(430\) 526.345 693.463i 0.0590293 0.0777715i
\(431\) 6540.79 0.730994 0.365497 0.930812i \(-0.380899\pi\)
0.365497 + 0.930812i \(0.380899\pi\)
\(432\) 6305.51 3819.45i 0.702254 0.425378i
\(433\) 2762.10i 0.306555i 0.988183 + 0.153277i \(0.0489828\pi\)
−0.988183 + 0.153277i \(0.951017\pi\)
\(434\) 1610.89 2122.36i 0.178169 0.234739i
\(435\) 279.267i 0.0307812i
\(436\) −10863.8 + 3033.70i −1.19330 + 0.333229i
\(437\) 10733.7 + 9457.69i 1.17497 + 1.03529i
\(438\) 20761.8 + 15758.4i 2.26492 + 1.71910i
\(439\) 8030.43 0.873055 0.436528 0.899691i \(-0.356208\pi\)
0.436528 + 0.899691i \(0.356208\pi\)
\(440\) 12301.0 + 4869.44i 1.33279 + 0.527594i
\(441\) 11212.5 1.21073
\(442\) 6862.18 9040.97i 0.738463 0.972930i
\(443\) 2090.03i 0.224154i −0.993700 0.112077i \(-0.964250\pi\)
0.993700 0.112077i \(-0.0357504\pi\)
\(444\) 10118.0 2825.43i 1.08148 0.302002i
\(445\) 11226.1i 1.19589i
\(446\) −5230.48 3969.98i −0.555315 0.421489i
\(447\) −16490.0 −1.74485
\(448\) 2918.02 3108.14i 0.307731 0.327781i
\(449\) 5954.95i 0.625905i −0.949769 0.312953i \(-0.898682\pi\)
0.949769 0.312953i \(-0.101318\pi\)
\(450\) 708.569 + 537.810i 0.0742273 + 0.0563392i
\(451\) −11103.7 −1.15931
\(452\) 16669.3 4654.88i 1.73464 0.484396i
\(453\) −20881.3 −2.16576
\(454\) 5324.89 + 4041.64i 0.550461 + 0.417805i
\(455\) 3946.67 0.406643
\(456\) 7018.85 + 13763.7i 0.720806 + 1.41347i
\(457\) −9073.80 −0.928785 −0.464392 0.885630i \(-0.653727\pi\)
−0.464392 + 0.885630i \(0.653727\pi\)
\(458\) 475.420 + 360.848i 0.0485042 + 0.0368151i
\(459\) −10563.5 −1.07421
\(460\) 14416.6 4025.83i 1.46126 0.408055i
\(461\) 7334.64 0.741016 0.370508 0.928829i \(-0.379184\pi\)
0.370508 + 0.928829i \(0.379184\pi\)
\(462\) 8348.58 + 6336.65i 0.840717 + 0.638112i
\(463\) 14521.0i 1.45756i −0.684749 0.728779i \(-0.740088\pi\)
0.684749 0.728779i \(-0.259912\pi\)
\(464\) −103.694 171.187i −0.0103747 0.0171275i
\(465\) 10103.0 1.00756
\(466\) 5796.05 + 4399.26i 0.576174 + 0.437321i
\(467\) 6164.98i 0.610881i 0.952211 + 0.305441i \(0.0988037\pi\)
−0.952211 + 0.305441i \(0.901196\pi\)
\(468\) −13814.4 + 3857.66i −1.36447 + 0.381027i
\(469\) 2318.97i 0.228316i
\(470\) 1156.82 1524.11i 0.113532 0.149579i
\(471\) −19572.2 −1.91474
\(472\) 6598.63 16669.2i 0.643488 1.62556i
\(473\) −1533.91 −0.149110
\(474\) 965.510 + 732.831i 0.0935597 + 0.0710127i
\(475\) −420.286 + 476.989i −0.0405980 + 0.0460752i
\(476\) −5883.74 + 1643.03i −0.566556 + 0.158210i
\(477\) 26642.6i 2.55740i
\(478\) 8186.41 10785.7i 0.783342 1.03206i
\(479\) 12691.5i 1.21062i 0.795988 + 0.605312i \(0.206952\pi\)
−0.795988 + 0.605312i \(0.793048\pi\)
\(480\) 16076.8 + 1688.09i 1.52876 + 0.160522i
\(481\) −6969.63 −0.660681
\(482\) −5850.00 + 7707.42i −0.552822 + 0.728347i
\(483\) 11858.3 1.11712
\(484\) −3405.47 12195.1i −0.319822 1.14529i
\(485\) 1574.15i 0.147378i
\(486\) −9914.97 7525.55i −0.925416 0.702399i
\(487\) 11817.4 1.09958 0.549792 0.835301i \(-0.314707\pi\)
0.549792 + 0.835301i \(0.314707\pi\)
\(488\) 253.925 641.456i 0.0235546 0.0595027i
\(489\) 7080.05i 0.654746i
\(490\) 6678.34 + 5068.92i 0.615707 + 0.467327i
\(491\) 6262.42i 0.575599i 0.957691 + 0.287800i \(0.0929237\pi\)
−0.957691 + 0.287800i \(0.907076\pi\)
\(492\) −13067.5 + 3649.08i −1.19741 + 0.334376i
\(493\) 286.787i 0.0261992i
\(494\) −2029.07 10047.6i −0.184802 0.915103i
\(495\) 23955.2i 2.17516i
\(496\) −6193.03 + 3751.32i −0.560635 + 0.339595i
\(497\) 616.514i 0.0556427i
\(498\) −16054.9 + 21152.4i −1.44465 + 1.90334i
\(499\) 2958.80i 0.265439i −0.991154 0.132719i \(-0.957629\pi\)
0.991154 0.132719i \(-0.0423709\pi\)
\(500\) 3092.16 + 11073.1i 0.276571 + 0.990412i
\(501\) 30598.4 2.72862
\(502\) −52.4610 + 69.1177i −0.00466424 + 0.00614517i
\(503\) 7221.67i 0.640156i −0.947391 0.320078i \(-0.896291\pi\)
0.947391 0.320078i \(-0.103709\pi\)
\(504\) 7177.60 + 2841.31i 0.634357 + 0.251115i
\(505\) 1300.34 0.114583
\(506\) −21006.9 15944.4i −1.84560 1.40082i
\(507\) −2326.35 −0.203781
\(508\) 2404.16 + 8609.38i 0.209975 + 0.751928i
\(509\) 16729.8i 1.45685i 0.685125 + 0.728426i \(0.259748\pi\)
−0.685125 + 0.728426i \(0.740252\pi\)
\(510\) −18450.5 14004.1i −1.60196 1.21590i
\(511\) 9307.21i 0.805728i
\(512\) −10481.7 + 4934.68i −0.904749 + 0.425945i
\(513\) −6306.81 + 7157.69i −0.542792 + 0.616023i
\(514\) 2356.68 3104.95i 0.202235 0.266446i
\(515\) −5064.50 −0.433337
\(516\) −1805.20 + 504.100i −0.154011 + 0.0430073i
\(517\) −3371.27 −0.286786
\(518\) 2987.93 + 2267.87i 0.253440 + 0.192364i
\(519\) 9392.04i 0.794345i
\(520\) −9972.00 3947.49i −0.840963 0.332902i
\(521\) 10904.0i 0.916914i −0.888717 0.458457i \(-0.848402\pi\)
0.888717 0.458457i \(-0.151598\pi\)
\(522\) 219.102 288.668i 0.0183713 0.0242044i
\(523\) 2809.15 0.234867 0.117434 0.993081i \(-0.462533\pi\)
0.117434 + 0.993081i \(0.462533\pi\)
\(524\) 11557.2 3227.35i 0.963512 0.269060i
\(525\) 526.964i 0.0438069i
\(526\) 753.099 992.213i 0.0624271 0.0822482i
\(527\) 10375.0 0.857578
\(528\) −14756.3 24361.1i −1.21626 2.00792i
\(529\) −17671.1 −1.45238
\(530\) 12044.4 15868.6i 0.987127 1.30055i
\(531\) 32461.9 2.65297
\(532\) −2399.52 + 4967.71i −0.195550 + 0.404845i
\(533\) 9001.36 0.731505
\(534\) −14611.7 + 19251.1i −1.18411 + 1.56007i
\(535\) 4354.83 0.351917
\(536\) −2319.46 + 5859.32i −0.186913 + 0.472172i
\(537\) −3639.88 −0.292500
\(538\) −5309.78 + 6995.68i −0.425504 + 0.560604i
\(539\) 14772.2i 1.18049i
\(540\) 2684.60 + 9613.64i 0.213939 + 0.766121i
\(541\) 276.064 0.0219389 0.0109694 0.999940i \(-0.496508\pi\)
0.0109694 + 0.999940i \(0.496508\pi\)
\(542\) 1955.68 2576.62i 0.154988 0.204198i
\(543\) 27090.1i 2.14097i
\(544\) 16509.7 + 1733.54i 1.30119 + 0.136627i
\(545\) 15271.8i 1.20031i
\(546\) −6767.91 5136.91i −0.530476 0.402636i
\(547\) −906.625 −0.0708674 −0.0354337 0.999372i \(-0.511281\pi\)
−0.0354337 + 0.999372i \(0.511281\pi\)
\(548\) 1819.43 + 6515.45i 0.141829 + 0.507895i
\(549\) 1249.18 0.0971107
\(550\) 708.548 933.517i 0.0549320 0.0723732i
\(551\) 194.323 + 171.223i 0.0150244 + 0.0132384i
\(552\) −29962.2 11860.8i −2.31028 0.914542i
\(553\) 432.824i 0.0332831i
\(554\) 15622.2 + 11857.4i 1.19805 + 0.909334i
\(555\) 14223.3i 1.08783i
\(556\) −8599.92 + 2401.52i −0.655967 + 0.183178i
\(557\) 14545.7 1.10650 0.553252 0.833014i \(-0.313387\pi\)
0.553252 + 0.833014i \(0.313387\pi\)
\(558\) −10443.1 7926.42i −0.792281 0.601348i
\(559\) 1243.49 0.0940857
\(560\) 2990.58 + 4937.13i 0.225670 + 0.372557i
\(561\) 40811.6i 3.07142i
\(562\) 10181.9 13414.8i 0.764234 1.00688i
\(563\) −448.637 −0.0335840 −0.0167920 0.999859i \(-0.505345\pi\)
−0.0167920 + 0.999859i \(0.505345\pi\)
\(564\) −3967.52 + 1107.93i −0.296210 + 0.0827165i
\(565\) 23432.8i 1.74483i
\(566\) −787.994 + 1038.19i −0.0585192 + 0.0770995i
\(567\) 1303.63i 0.0965562i
\(568\) −616.642 + 1557.74i −0.0455524 + 0.115073i
\(569\) 11035.3i 0.813045i −0.913641 0.406523i \(-0.866741\pi\)
0.913641 0.406523i \(-0.133259\pi\)
\(570\) −20504.6 + 4140.85i −1.50675 + 0.304283i
\(571\) 8153.77i 0.597592i −0.954317 0.298796i \(-0.903415\pi\)
0.954317 0.298796i \(-0.0965849\pi\)
\(572\) 5082.35 + 18200.1i 0.371510 + 1.33039i
\(573\) 20365.3i 1.48477i
\(574\) −3858.95 2928.98i −0.280609 0.212985i
\(575\) 1325.96i 0.0961677i
\(576\) −15293.7 14358.2i −1.10631 1.03864i
\(577\) −4525.76 −0.326534 −0.163267 0.986582i \(-0.552203\pi\)
−0.163267 + 0.986582i \(0.552203\pi\)
\(578\) −7878.46 5979.83i −0.566957 0.430325i
\(579\) 7794.11i 0.559434i
\(580\) 261.000 72.8839i 0.0186852 0.00521783i
\(581\) −9482.32 −0.677096
\(582\) −2048.88 + 2699.42i −0.145926 + 0.192259i
\(583\) −35100.7 −2.49352
\(584\) 9309.15 23516.4i 0.659615 1.66630i
\(585\) 19419.6i 1.37248i
\(586\) −11546.3 + 15212.3i −0.813946 + 1.07238i
\(587\) 7894.03i 0.555062i −0.960717 0.277531i \(-0.910484\pi\)
0.960717 0.277531i \(-0.0895161\pi\)
\(588\) −4854.69 17384.8i −0.340483 1.21928i
\(589\) 6194.31 7030.01i 0.433331 0.491794i
\(590\) 19334.7 + 14675.2i 1.34915 + 1.02402i
\(591\) 35534.6 2.47326
\(592\) −5281.23 8718.75i −0.366651 0.605301i
\(593\) 6425.46 0.444961 0.222481 0.974937i \(-0.428585\pi\)
0.222481 + 0.974937i \(0.428585\pi\)
\(594\) 10632.5 14008.4i 0.734437 0.967626i
\(595\) 8271.07i 0.569884i
\(596\) 4303.61 + 15411.4i 0.295776 + 1.05918i
\(597\) 32437.7i 2.22377i
\(598\) 17029.6 + 12925.6i 1.16454 + 0.883893i
\(599\) −12953.7 −0.883595 −0.441797 0.897115i \(-0.645659\pi\)
−0.441797 + 0.897115i \(0.645659\pi\)
\(600\) 527.074 1331.48i 0.0358629 0.0905954i
\(601\) 3637.72i 0.246898i 0.992351 + 0.123449i \(0.0393955\pi\)
−0.992351 + 0.123449i \(0.960605\pi\)
\(602\) −533.092 404.622i −0.0360917 0.0273940i
\(603\) −11410.5 −0.770603
\(604\) 5449.67 + 19515.5i 0.367126 + 1.31469i
\(605\) 17143.3 1.15202
\(606\) −2229.88 1692.50i −0.149476 0.113454i
\(607\) −23243.7 −1.55426 −0.777129 0.629342i \(-0.783325\pi\)
−0.777129 + 0.629342i \(0.783325\pi\)
\(608\) 11031.6 10151.8i 0.735839 0.677156i
\(609\) 214.683 0.0142847
\(610\) 744.029 + 564.725i 0.0493850 + 0.0374837i
\(611\) 2732.97 0.180956
\(612\) 8084.55 + 28951.0i 0.533984 + 1.91222i
\(613\) 4530.37 0.298499 0.149250 0.988800i \(-0.452314\pi\)
0.149250 + 0.988800i \(0.452314\pi\)
\(614\) −8694.63 6599.30i −0.571477 0.433756i
\(615\) 18369.6i 1.20445i
\(616\) 3743.33 9456.26i 0.244843 0.618512i
\(617\) −27590.3 −1.80024 −0.900118 0.435647i \(-0.856520\pi\)
−0.900118 + 0.435647i \(0.856520\pi\)
\(618\) 8684.83 + 6591.87i 0.565299 + 0.429067i
\(619\) 1523.57i 0.0989300i −0.998776 0.0494650i \(-0.984248\pi\)
0.998776 0.0494650i \(-0.0157516\pi\)
\(620\) −2636.71 9442.16i −0.170795 0.611623i
\(621\) 19897.4i 1.28576i
\(622\) −135.280 + 178.233i −0.00872064 + 0.0114895i
\(623\) −8629.98 −0.554980
\(624\) 11962.4 + 19748.7i 0.767437 + 1.26696i
\(625\) −14606.6 −0.934819
\(626\) −11948.0 9068.64i −0.762841 0.579003i
\(627\) 27653.5 + 24366.1i 1.76136 + 1.55197i
\(628\) 5108.02 + 18292.0i 0.324574 + 1.16231i
\(629\) 14606.3i 0.925902i
\(630\) −6319.01 + 8325.34i −0.399612 + 0.526491i
\(631\) 2083.59i 0.131453i 0.997838 + 0.0657263i \(0.0209364\pi\)
−0.997838 + 0.0657263i \(0.979064\pi\)
\(632\) 432.914 1093.61i 0.0272475 0.0688315i
\(633\) 5097.30 0.320062
\(634\) 13595.8 17912.5i 0.851667 1.12208i
\(635\) −12102.6 −0.756344
\(636\) −41308.7 + 11535.4i −2.57546 + 0.719196i
\(637\) 11975.3i 0.744864i
\(638\) −380.311 288.660i −0.0235998 0.0179125i
\(639\) −3033.57 −0.187803
\(640\) −2618.12 15465.8i −0.161703 0.955219i
\(641\) 1554.43i 0.0957818i −0.998853 0.0478909i \(-0.984750\pi\)
0.998853 0.0478909i \(-0.0152500\pi\)
\(642\) −7467.85 5668.17i −0.459085 0.348450i
\(643\) 21731.9i 1.33285i 0.745573 + 0.666424i \(0.232176\pi\)
−0.745573 + 0.666424i \(0.767824\pi\)
\(644\) −3094.81 11082.6i −0.189367 0.678131i
\(645\) 2537.66i 0.154915i
\(646\) −21056.8 + 4252.35i −1.28246 + 0.258988i
\(647\) 7401.82i 0.449761i −0.974386 0.224881i \(-0.927801\pi\)
0.974386 0.224881i \(-0.0721992\pi\)
\(648\) −1303.90 + 3293.87i −0.0790465 + 0.199684i
\(649\) 42767.5i 2.58671i
\(650\) −574.396 + 756.770i −0.0346610 + 0.0456661i
\(651\) 7766.57i 0.467582i
\(652\) 6616.94 1847.77i 0.397453 0.110988i
\(653\) −10373.7 −0.621676 −0.310838 0.950463i \(-0.600610\pi\)
−0.310838 + 0.950463i \(0.600610\pi\)
\(654\) −19877.5 + 26188.7i −1.18849 + 1.56584i
\(655\) 16246.6i 0.969172i
\(656\) 6820.78 + 11260.4i 0.405955 + 0.670189i
\(657\) 45796.3 2.71946
\(658\) −1171.65 889.291i −0.0694157 0.0526872i
\(659\) 24282.1 1.43535 0.717676 0.696377i \(-0.245206\pi\)
0.717676 + 0.696377i \(0.245206\pi\)
\(660\) 37141.9 10371.8i 2.19053 0.611702i
\(661\) 1182.15i 0.0695618i −0.999395 0.0347809i \(-0.988927\pi\)
0.999395 0.0347809i \(-0.0110733\pi\)
\(662\) 4881.49 + 3705.10i 0.286593 + 0.217527i
\(663\) 33084.5i 1.93800i
\(664\) 23958.9 + 9484.30i 1.40028 + 0.554310i
\(665\) −5604.39 4938.15i −0.326810 0.287960i
\(666\) 11159.1 14702.2i 0.649258 0.855401i
\(667\) −540.192 −0.0313588
\(668\) −7985.68 28597.0i −0.462537 1.65636i
\(669\) −19140.4 −1.10615
\(670\) −6796.27 5158.43i −0.391885 0.297444i
\(671\) 1645.76i 0.0946852i
\(672\) 1297.70 12358.9i 0.0744938 0.709457i
\(673\) 11178.7i 0.640278i 0.947371 + 0.320139i \(0.103730\pi\)
−0.947371 + 0.320139i \(0.896270\pi\)
\(674\) 11205.3 14763.1i 0.640374 0.843697i
\(675\) 884.210 0.0504197
\(676\) 607.139 + 2174.19i 0.0345437 + 0.123702i
\(677\) 15827.8i 0.898538i −0.893397 0.449269i \(-0.851685\pi\)
0.893397 0.449269i \(-0.148315\pi\)
\(678\) 30499.8 40183.7i 1.72764 2.27617i
\(679\) −1210.11 −0.0683944
\(680\) −8272.79 + 20898.4i −0.466540 + 1.17856i
\(681\) 19485.9 1.09648
\(682\) −10442.8 + 13758.5i −0.586328 + 0.772491i
\(683\) 17273.7 0.967728 0.483864 0.875143i \(-0.339233\pi\)
0.483864 + 0.875143i \(0.339233\pi\)
\(684\) 24443.7 + 11806.9i 1.36642 + 0.660012i
\(685\) −9159.11 −0.510878
\(686\) 8780.58 11568.5i 0.488694 0.643858i
\(687\) 1739.75 0.0966167
\(688\) 942.253 + 1555.56i 0.0522137 + 0.0861993i
\(689\) 28455.0 1.57336
\(690\) 26378.1 34753.3i 1.45536 1.91744i
\(691\) 21595.1i 1.18888i 0.804141 + 0.594439i \(0.202626\pi\)
−0.804141 + 0.594439i \(0.797374\pi\)
\(692\) −8777.70 + 2451.16i −0.482194 + 0.134652i
\(693\) 18415.3 1.00944
\(694\) 6437.31 8481.20i 0.352099 0.463893i
\(695\) 12089.3i 0.659820i
\(696\) −542.438 214.728i −0.0295418 0.0116943i
\(697\) 18864.3i 1.02516i
\(698\) −9559.71 7255.91i −0.518396 0.393467i
\(699\) 21210.1 1.14769
\(700\) 492.495 137.529i 0.0265923 0.00742586i
\(701\) 16705.4 0.900076 0.450038 0.893009i \(-0.351410\pi\)
0.450038 + 0.893009i \(0.351410\pi\)
\(702\) −8619.38 + 11356.1i −0.463415 + 0.610553i
\(703\) 9897.08 + 8720.55i 0.530975 + 0.467854i
\(704\) −18916.5 + 20148.9i −1.01270 + 1.07868i
\(705\) 5577.35i 0.297950i
\(706\) −11527.5 8749.50i −0.614510 0.466419i
\(707\) 999.622i 0.0531749i
\(708\) −14055.0 50331.4i −0.746073 2.67171i
\(709\) −12352.1 −0.654293 −0.327146 0.944974i \(-0.606087\pi\)
−0.327146 + 0.944974i \(0.606087\pi\)
\(710\) −1806.83 1371.40i −0.0955059 0.0724898i
\(711\) 2129.72 0.112336
\(712\) 21805.3 + 8631.78i 1.14773 + 0.454339i
\(713\) 19542.5i 1.02647i
\(714\) −10765.5 + 14183.6i −0.564269 + 0.743428i
\(715\) −25584.7 −1.33820
\(716\) 949.948 + 3401.79i 0.0495827 + 0.177557i
\(717\) 39469.0i 2.05578i
\(718\) −15788.2 + 20801.1i −0.820627 + 1.08118i
\(719\) 17034.4i 0.883553i 0.897125 + 0.441776i \(0.145652\pi\)
−0.897125 + 0.441776i \(0.854348\pi\)
\(720\) 24293.3 14715.2i 1.25744 0.761672i
\(721\) 3893.28i 0.201100i
\(722\) −9690.37 + 16806.7i −0.499499 + 0.866314i
\(723\) 28204.5i 1.45081i
\(724\) −25318.1 + 7070.06i −1.29964 + 0.362924i
\(725\) 24.0053i 0.00122970i
\(726\) −29398.0 22313.4i −1.50284 1.14067i
\(727\) 36743.0i 1.87445i −0.348731 0.937223i \(-0.613387\pi\)
0.348731 0.937223i \(-0.386613\pi\)
\(728\) −3034.59 + 7665.87i −0.154491 + 0.390269i
\(729\) −32055.7 −1.62860
\(730\) 27276.9 + 20703.4i 1.38296 + 1.04968i
\(731\) 2605.99i 0.131855i
\(732\) −540.857 1936.83i −0.0273096 0.0977968i
\(733\) −14324.5 −0.721810 −0.360905 0.932603i \(-0.617532\pi\)
−0.360905 + 0.932603i \(0.617532\pi\)
\(734\) 660.322 869.979i 0.0332056 0.0437487i
\(735\) 24438.7 1.22644
\(736\) −3265.31 + 31097.8i −0.163534 + 1.55745i
\(737\) 15033.0i 0.751355i
\(738\) −14412.1 + 18988.0i −0.718857 + 0.947099i
\(739\) 22582.8i 1.12412i 0.827098 + 0.562058i \(0.189990\pi\)
−0.827098 + 0.562058i \(0.810010\pi\)
\(740\) 13293.0 3712.05i 0.660351 0.184402i
\(741\) −22417.7 19752.8i −1.11138 0.979266i
\(742\) −12198.9 9259.04i −0.603550 0.458100i
\(743\) −10461.2 −0.516533 −0.258266 0.966074i \(-0.583151\pi\)
−0.258266 + 0.966074i \(0.583151\pi\)
\(744\) −7768.19 + 19623.7i −0.382790 + 0.966990i
\(745\) −21664.5 −1.06541
\(746\) −8968.37 + 11815.9i −0.440155 + 0.579907i
\(747\) 46657.9i 2.28531i
\(748\) 38142.0 10651.1i 1.86445 0.520647i
\(749\) 3347.73i 0.163316i
\(750\) 26693.4 + 20260.5i 1.29961 + 0.986413i
\(751\) −20249.7 −0.983919 −0.491959 0.870618i \(-0.663719\pi\)
−0.491959 + 0.870618i \(0.663719\pi\)
\(752\) 2070.91 + 3418.85i 0.100423 + 0.165788i
\(753\) 252.929i 0.0122407i
\(754\) 308.305 + 234.007i 0.0148910 + 0.0113024i
\(755\) −27433.9 −1.32241
\(756\) 7390.39 2063.76i 0.355537 0.0992833i
\(757\) 13523.4 0.649293 0.324647 0.945835i \(-0.394755\pi\)
0.324647 + 0.945835i \(0.394755\pi\)
\(758\) −15621.3 11856.7i −0.748537 0.568147i
\(759\) −76872.8 −3.67629
\(760\) 9221.36 + 18082.7i 0.440124 + 0.863065i
\(761\) 5278.02 0.251417 0.125708 0.992067i \(-0.459880\pi\)
0.125708 + 0.992067i \(0.459880\pi\)
\(762\) 20754.1 + 15752.6i 0.986671 + 0.748892i
\(763\) −11740.0 −0.557034
\(764\) 19033.2 5314.99i 0.901303 0.251688i
\(765\) −40697.9 −1.92345
\(766\) 32141.5 + 24395.7i 1.51608 + 1.15072i
\(767\) 34670.2i 1.63216i
\(768\) −15640.4 + 29929.1i −0.734861 + 1.40622i
\(769\) −16532.4 −0.775260 −0.387630 0.921815i \(-0.626706\pi\)
−0.387630 + 0.921815i \(0.626706\pi\)
\(770\) 10968.4 + 8325.09i 0.513341 + 0.389631i
\(771\) 11362.2i 0.530741i
\(772\) 7284.30 2034.13i 0.339595 0.0948316i
\(773\) 16507.8i 0.768106i 0.923311 + 0.384053i \(0.125472\pi\)
−0.923311 + 0.384053i \(0.874528\pi\)
\(774\) −1990.95 + 2623.09i −0.0924590 + 0.121815i
\(775\) −868.438 −0.0402519
\(776\) 3057.57 + 1210.36i 0.141444 + 0.0559916i
\(777\) 10934.0 0.504834
\(778\) −8961.11 6801.56i −0.412945 0.313429i
\(779\) −12782.2 11262.7i −0.587895 0.518008i
\(780\) −30109.7 + 8408.10i −1.38218 + 0.385972i
\(781\) 3996.63i 0.183112i
\(782\) 27088.4 35689.1i 1.23872 1.63202i
\(783\) 360.224i 0.0164411i
\(784\) −14980.7 + 9074.28i −0.682428 + 0.413369i
\(785\) −25714.0 −1.16914
\(786\) 21146.3 27860.4i 0.959622 1.26431i
\(787\) 6081.09 0.275435 0.137718 0.990472i \(-0.456023\pi\)
0.137718 + 0.990472i \(0.456023\pi\)
\(788\) −9273.93 33210.3i −0.419251 1.50135i
\(789\) 3630.91i 0.163832i
\(790\) 1268.49 + 962.793i 0.0571275 + 0.0433603i
\(791\) 18013.8 0.809728
\(792\) −46529.7 18419.1i −2.08758 0.826382i
\(793\) 1334.16i 0.0597445i
\(794\) −12057.8 9152.00i −0.538937 0.409058i
\(795\) 58069.7i 2.59059i
\(796\) 30316.0 8465.70i 1.34990 0.376958i
\(797\) 9391.19i 0.417381i −0.977982 0.208691i \(-0.933080\pi\)
0.977982 0.208691i \(-0.0669202\pi\)
\(798\) 3183.23 + 15762.7i 0.141210 + 0.699241i
\(799\) 5727.53i 0.253599i
\(800\) −1381.94 145.105i −0.0610737 0.00641281i
\(801\) 42464.0i 1.87315i
\(802\) 671.615 884.857i 0.0295705 0.0389593i
\(803\) 60335.1i 2.65153i
\(804\) 4940.41 + 17691.8i 0.216710 + 0.776047i
\(805\) 15579.4 0.682114
\(806\) 8465.63 11153.5i 0.369962 0.487427i
\(807\) 25600.0i 1.11668i
\(808\) −999.830 + 2525.73i −0.0435320 + 0.109969i
\(809\) −4772.24 −0.207396 −0.103698 0.994609i \(-0.533067\pi\)
−0.103698 + 0.994609i \(0.533067\pi\)
\(810\) −3820.58 2899.85i −0.165730 0.125791i
\(811\) −5522.21 −0.239101 −0.119551 0.992828i \(-0.538145\pi\)
−0.119551 + 0.992828i \(0.538145\pi\)
\(812\) −56.0287 200.641i −0.00242146 0.00867132i
\(813\) 9428.88i 0.406747i
\(814\) −19369.6 14701.7i −0.834036 0.633041i
\(815\) 9301.77i 0.399788i
\(816\) 41387.6 25069.8i 1.77556 1.07551i
\(817\) −1765.79 1555.88i −0.0756147 0.0666258i
\(818\) −23405.7 + 30837.1i −1.00044 + 1.31809i
\(819\) −14928.6 −0.636934
\(820\) −17168.1 + 4794.16i −0.731139 + 0.204170i
\(821\) 9804.95 0.416803 0.208401 0.978043i \(-0.433174\pi\)
0.208401 + 0.978043i \(0.433174\pi\)
\(822\) 15706.4 + 11921.3i 0.666454 + 0.505844i
\(823\) 7930.93i 0.335911i −0.985795 0.167955i \(-0.946284\pi\)
0.985795 0.167955i \(-0.0537165\pi\)
\(824\) 3894.09 9837.12i 0.164633 0.415889i
\(825\) 3416.11i 0.144162i
\(826\) 11281.4 14863.4i 0.475219 0.626105i
\(827\) 22575.7 0.949255 0.474627 0.880187i \(-0.342583\pi\)
0.474627 + 0.880187i \(0.342583\pi\)
\(828\) −54532.2 + 15228.1i −2.28880 + 0.639145i
\(829\) 24785.4i 1.03840i 0.854654 + 0.519199i \(0.173770\pi\)
−0.854654 + 0.519199i \(0.826230\pi\)
\(830\) −21092.9 + 27790.1i −0.882103 + 1.16218i
\(831\) 57167.8 2.38644
\(832\) 15334.9 16334.0i 0.638994 0.680626i
\(833\) 25096.8 1.04388
\(834\) −15735.3 + 20731.3i −0.653319 + 0.860752i
\(835\) 40200.2 1.66609
\(836\) 15555.2 32203.8i 0.643527 1.33229i
\(837\) −13031.8 −0.538165
\(838\) 14265.6 18795.0i 0.588064 0.774778i
\(839\) 15875.5 0.653258 0.326629 0.945153i \(-0.394087\pi\)
0.326629 + 0.945153i \(0.394087\pi\)
\(840\) 15644.2 + 6192.87i 0.642590 + 0.254374i
\(841\) 24379.2 0.999599
\(842\) 5501.35 7248.06i 0.225165 0.296656i
\(843\) 49090.1i 2.00564i
\(844\) −1330.31 4763.88i −0.0542549 0.194289i
\(845\) −3056.37 −0.124429
\(846\) −4375.77 + 5765.11i −0.177828 + 0.234289i
\(847\) 13178.7i 0.534623i
\(848\) 21561.7 + 35596.1i 0.873152 + 1.44148i
\(849\) 3799.15i 0.153576i
\(850\) 1585.97 + 1203.77i 0.0639981 + 0.0485751i
\(851\) −27512.5 −1.10825
\(852\) 1313.44 + 4703.48i 0.0528143 + 0.189130i
\(853\) −17536.1 −0.703897 −0.351948 0.936019i \(-0.614481\pi\)
−0.351948 + 0.936019i \(0.614481\pi\)
\(854\) 434.126 571.964i 0.0173952 0.0229183i
\(855\) −24298.3 + 27576.5i −0.971910 + 1.10304i
\(856\) −3348.43 + 8458.67i −0.133700 + 0.337747i
\(857\) 43551.9i 1.73594i 0.496613 + 0.867972i \(0.334577\pi\)
−0.496613 + 0.867972i \(0.665423\pi\)
\(858\) 43873.8 + 33300.6i 1.74572 + 1.32502i
\(859\) 8655.89i 0.343813i −0.985113 0.171906i \(-0.945007\pi\)
0.985113 0.171906i \(-0.0549927\pi\)
\(860\) −2371.67 + 662.286i −0.0940387 + 0.0262602i
\(861\) −14121.4 −0.558952
\(862\) −14736.1 11184.9i −0.582268 0.441947i
\(863\) 45399.0 1.79073 0.895364 0.445334i \(-0.146915\pi\)
0.895364 + 0.445334i \(0.146915\pi\)
\(864\) −20737.4 2177.45i −0.816552 0.0857389i
\(865\) 12339.3i 0.485026i
\(866\) 4723.25 6222.91i 0.185338 0.244184i
\(867\) −28830.5 −1.12934
\(868\) −7258.56 + 2026.94i −0.283838 + 0.0792615i
\(869\) 2805.83i 0.109530i
\(870\) 477.551 629.177i 0.0186098 0.0245185i
\(871\) 12186.8i 0.474090i
\(872\) 29663.4 + 11742.5i 1.15198 + 0.456020i
\(873\) 5954.37i 0.230842i
\(874\) −8009.74 39662.6i −0.309993 1.53502i
\(875\) 11966.3i 0.462324i
\(876\) −19828.4 71006.1i −0.764771 2.73867i
\(877\) 28095.8i 1.08179i −0.841091 0.540894i \(-0.818086\pi\)
0.841091 0.540894i \(-0.181914\pi\)
\(878\) −18092.2 13732.2i −0.695425 0.527834i
\(879\) 55667.9i 2.13610i
\(880\) −19386.8 32005.6i −0.742648 1.22603i
\(881\) −36114.4 −1.38107 −0.690535 0.723299i \(-0.742625\pi\)
−0.690535 + 0.723299i \(0.742625\pi\)
\(882\) −25261.4 19173.7i −0.964396 0.731985i
\(883\) 44273.4i 1.68734i 0.536865 + 0.843668i \(0.319608\pi\)
−0.536865 + 0.843668i \(0.680392\pi\)
\(884\) −30920.5 + 8634.51i −1.17643 + 0.328518i
\(885\) 70753.5 2.68740
\(886\) −3573.99 + 4708.76i −0.135520 + 0.178548i
\(887\) 11620.8 0.439897 0.219949 0.975511i \(-0.429411\pi\)
0.219949 + 0.975511i \(0.429411\pi\)
\(888\) −27626.9 10936.3i −1.04403 0.413287i
\(889\) 9303.78i 0.351000i
\(890\) −19196.9 + 25292.1i −0.723014 + 0.952575i
\(891\) 8450.95i 0.317752i
\(892\) 4995.33 + 17888.4i 0.187507 + 0.671468i
\(893\) −3880.91 3419.56i −0.145431 0.128142i
\(894\) 37151.3 + 28198.2i 1.38985 + 1.05491i
\(895\) −4782.08 −0.178600
\(896\) −11889.2 + 2012.65i −0.443292 + 0.0750423i
\(897\) 62318.1 2.31967
\(898\) −10183.1 + 13416.3i −0.378411 + 0.498560i
\(899\) 353.798i 0.0131255i
\(900\) −676.713 2423.33i −0.0250634 0.0897531i
\(901\) 59633.4i 2.20497i
\(902\) 25016.1 + 18987.5i 0.923443 + 0.700902i
\(903\) −1950.80 −0.0718921
\(904\) −45515.2 18017.5i −1.67457 0.662891i
\(905\) 35591.0i 1.30728i
\(906\) 47044.8 + 35707.4i 1.72512 + 1.30938i
\(907\) −10361.0 −0.379308 −0.189654 0.981851i \(-0.560737\pi\)
−0.189654 + 0.981851i \(0.560737\pi\)
\(908\) −5085.49 18211.3i −0.185868 0.665599i
\(909\) −4918.66 −0.179474
\(910\) −8891.69 6748.87i −0.323908 0.245849i
\(911\) 23464.4 0.853357 0.426679 0.904403i \(-0.359684\pi\)
0.426679 + 0.904403i \(0.359684\pi\)
\(912\) 7722.97 43011.4i 0.280409 1.56168i
\(913\) 61470.3 2.22823
\(914\) 20442.9 + 15516.4i 0.739816 + 0.561527i
\(915\) 2722.70 0.0983712
\(916\) −454.046 1625.95i −0.0163778 0.0586496i
\(917\) 12489.4 0.449767
\(918\) 23799.1 + 18063.7i 0.855651 + 0.649447i
\(919\) 1012.80i 0.0363539i 0.999835 + 0.0181769i \(0.00578622\pi\)
−0.999835 + 0.0181769i \(0.994214\pi\)
\(920\) −39364.3 15582.7i −1.41066 0.558418i
\(921\) −31817.1 −1.13834
\(922\) −16524.7 12542.4i −0.590250 0.448005i
\(923\) 3239.93i 0.115540i
\(924\) −7973.25 28552.5i −0.283875 1.01657i
\(925\) 1222.62i 0.0434587i
\(926\) −24831.2 + 32715.3i −0.881215 + 1.16101i
\(927\) 19157.0 0.678746
\(928\) −59.1154 + 562.997i −0.00209112 + 0.0199152i
\(929\) 1877.93 0.0663217 0.0331608 0.999450i \(-0.489443\pi\)
0.0331608 + 0.999450i \(0.489443\pi\)
\(930\) −22761.7 17276.3i −0.802564 0.609153i
\(931\) 14983.8 17005.3i 0.527468 0.598631i
\(932\) −5535.47 19822.7i −0.194550 0.696689i
\(933\) 652.224i 0.0228862i
\(934\) 10542.2 13889.5i 0.369328 0.486593i
\(935\) 53618.2i 1.87540i
\(936\) 37720.0 + 14931.8i 1.31722 + 0.521431i
\(937\) 54015.7 1.88326 0.941631 0.336648i \(-0.109293\pi\)
0.941631 + 0.336648i \(0.109293\pi\)
\(938\) −3965.49 + 5224.56i −0.138036 + 0.181863i
\(939\) −43722.5 −1.51952
\(940\) −5212.53 + 1455.59i −0.180866 + 0.0505066i
\(941\) 41323.2i 1.43156i −0.698326 0.715780i \(-0.746072\pi\)
0.698326 0.715780i \(-0.253928\pi\)
\(942\) 44095.5 + 33468.9i 1.52517 + 1.15762i
\(943\) 35532.8 1.22705
\(944\) −43371.1 + 26271.3i −1.49535 + 0.905782i
\(945\) 10389.0i 0.357625i
\(946\) 3455.84 + 2623.01i 0.118773 + 0.0901496i
\(947\) 55668.4i 1.91022i −0.296251 0.955110i \(-0.595737\pi\)
0.296251 0.955110i \(-0.404263\pi\)
\(948\) −922.102 3302.08i −0.0315912 0.113129i
\(949\) 48911.7i 1.67307i
\(950\) 1762.55 355.941i 0.0601943 0.0121561i
\(951\) 65549.1i 2.23509i
\(952\) 16065.4 + 6359.62i 0.546937 + 0.216509i
\(953\) 40561.9i 1.37873i 0.724415 + 0.689364i \(0.242110\pi\)
−0.724415 + 0.689364i \(0.757890\pi\)
\(954\) −45559.3 + 60024.7i −1.54616 + 2.03708i
\(955\) 26755.9i 0.906597i
\(956\) −36887.3 + 10300.7i −1.24793 + 0.348483i
\(957\) −1391.71 −0.0470090
\(958\) 21702.7 28593.5i 0.731923 0.964314i
\(959\) 7040.97i 0.237085i
\(960\) −33333.9 31294.9i −1.12067 1.05212i
\(961\) −16991.7 −0.570363
\(962\) 15702.3 + 11918.2i 0.526260 + 0.399436i
\(963\) −16472.6 −0.551216
\(964\) 26359.7 7360.91i 0.880692 0.245932i
\(965\) 10239.9i 0.341590i
\(966\) −26716.3 20277.9i −0.889836 0.675393i
\(967\) 19719.9i 0.655791i −0.944714 0.327895i \(-0.893661\pi\)
0.944714 0.327895i \(-0.106339\pi\)
\(968\) −13181.5 + 33298.5i −0.437674 + 1.10563i
\(969\) −41396.1 + 46981.1i −1.37238 + 1.55753i
\(970\) −2691.83 + 3546.50i −0.0891024 + 0.117393i
\(971\) −35347.2 −1.16822 −0.584112 0.811673i \(-0.698557\pi\)
−0.584112 + 0.811673i \(0.698557\pi\)
\(972\) 9469.21 + 33909.6i 0.312474 + 1.11898i
\(973\) −9293.56 −0.306205
\(974\) −26624.2 20208.0i −0.875866 0.664790i
\(975\) 2769.33i 0.0909635i
\(976\) −1668.98 + 1010.96i −0.0547366 + 0.0331557i
\(977\) 12096.3i 0.396107i 0.980191 + 0.198053i \(0.0634619\pi\)
−0.980191 + 0.198053i \(0.936538\pi\)
\(978\) 12107.0 15951.1i 0.395848 0.521533i
\(979\) 55944.9 1.82636
\(980\) −6378.09 22840.2i −0.207899 0.744492i
\(981\) 57766.9i 1.88008i
\(982\) 10708.9 14109.0i 0.347997 0.458489i
\(983\) 37920.1 1.23038 0.615190 0.788379i \(-0.289079\pi\)
0.615190 + 0.788379i \(0.289079\pi\)
\(984\) 35680.5 + 14124.4i 1.15595 + 0.457591i
\(985\) 46685.4 1.51017
\(986\) 490.410 646.119i 0.0158396 0.0208688i
\(987\) −4287.52 −0.138271
\(988\) −12610.1 + 26106.5i −0.406053 + 0.840646i
\(989\) 4908.65 0.157822
\(990\) 40963.8 53970.1i 1.31506 1.73261i
\(991\) −44836.0 −1.43720 −0.718599 0.695425i \(-0.755216\pi\)
−0.718599 + 0.695425i \(0.755216\pi\)
\(992\) 20367.5 + 2138.61i 0.651883 + 0.0684485i
\(993\) 17863.3 0.570872
\(994\) −1054.25 + 1388.98i −0.0336406 + 0.0443218i
\(995\) 42616.7i 1.35783i
\(996\) 72342.1 20201.4i 2.30145 0.642678i
\(997\) −41630.7 −1.32242 −0.661212 0.750199i \(-0.729958\pi\)
−0.661212 + 0.750199i \(0.729958\pi\)
\(998\) −5059.60 + 6666.06i −0.160480 + 0.211433i
\(999\) 18346.6i 0.581041i
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 76.4.d.a.75.7 28
4.3 odd 2 inner 76.4.d.a.75.21 yes 28
19.18 odd 2 inner 76.4.d.a.75.22 yes 28
76.75 even 2 inner 76.4.d.a.75.8 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.4.d.a.75.7 28 1.1 even 1 trivial
76.4.d.a.75.8 yes 28 76.75 even 2 inner
76.4.d.a.75.21 yes 28 4.3 odd 2 inner
76.4.d.a.75.22 yes 28 19.18 odd 2 inner