Properties

Label 177.4.d.c.176.19
Level $177$
Weight $4$
Character 177.176
Analytic conductor $10.443$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 177.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.4433380710\)
Analytic rank: \(0\)
Dimension: \(52\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 176.19
Character \(\chi\) \(=\) 177.176
Dual form 177.4.d.c.176.20

$q$-expansion

\(f(q)\) \(=\) \(q-2.52893 q^{2} +(0.100502 - 5.19518i) q^{3} -1.60453 q^{4} +17.9211i q^{5} +(-0.254162 + 13.1382i) q^{6} -4.91298 q^{7} +24.2892 q^{8} +(-26.9798 - 1.04425i) q^{9} +O(q^{10})\) \(q-2.52893 q^{2} +(0.100502 - 5.19518i) q^{3} -1.60453 q^{4} +17.9211i q^{5} +(-0.254162 + 13.1382i) q^{6} -4.91298 q^{7} +24.2892 q^{8} +(-26.9798 - 1.04425i) q^{9} -45.3212i q^{10} +38.0756 q^{11} +(-0.161258 + 8.33584i) q^{12} -51.2270i q^{13} +12.4246 q^{14} +(93.1035 + 1.80111i) q^{15} -48.5892 q^{16} -30.7171i q^{17} +(68.2299 + 2.64083i) q^{18} -45.5739 q^{19} -28.7550i q^{20} +(-0.493764 + 25.5238i) q^{21} -96.2904 q^{22} -137.131 q^{23} +(2.44110 - 126.187i) q^{24} -196.167 q^{25} +129.549i q^{26} +(-8.13658 + 140.060i) q^{27} +7.88305 q^{28} -12.5498i q^{29} +(-235.452 - 4.55486i) q^{30} -75.5324i q^{31} -71.4347 q^{32} +(3.82667 - 197.810i) q^{33} +77.6812i q^{34} -88.0462i q^{35} +(43.2900 + 1.67553i) q^{36} -152.739i q^{37} +115.253 q^{38} +(-266.133 - 5.14840i) q^{39} +435.289i q^{40} -272.870i q^{41} +(1.24869 - 64.5479i) q^{42} -364.987i q^{43} -61.0936 q^{44} +(18.7141 - 483.509i) q^{45} +346.793 q^{46} +430.845 q^{47} +(-4.88330 + 252.430i) q^{48} -318.863 q^{49} +496.092 q^{50} +(-159.581 - 3.08712i) q^{51} +82.1954i q^{52} -660.497i q^{53} +(20.5768 - 354.201i) q^{54} +682.358i q^{55} -119.332 q^{56} +(-4.58026 + 236.765i) q^{57} +31.7375i q^{58} +(-351.582 - 285.954i) q^{59} +(-149.388 - 2.88993i) q^{60} +251.217i q^{61} +191.016i q^{62} +(132.551 + 5.13038i) q^{63} +569.367 q^{64} +918.046 q^{65} +(-9.67736 + 500.246i) q^{66} -442.198i q^{67} +49.2865i q^{68} +(-13.7819 + 712.418i) q^{69} +222.662i q^{70} +639.306i q^{71} +(-655.316 - 25.3639i) q^{72} -36.1944i q^{73} +386.267i q^{74} +(-19.7151 + 1019.12i) q^{75} +73.1249 q^{76} -187.065 q^{77} +(673.032 + 13.0199i) q^{78} -485.902 q^{79} -870.774i q^{80} +(726.819 + 56.3473i) q^{81} +690.068i q^{82} -1376.64 q^{83} +(0.792260 - 40.9538i) q^{84} +550.485 q^{85} +923.025i q^{86} +(-65.1984 - 1.26128i) q^{87} +924.825 q^{88} +1250.69 q^{89} +(-47.3267 + 1222.76i) q^{90} +251.677i q^{91} +220.030 q^{92} +(-392.404 - 7.59114i) q^{93} -1089.58 q^{94} -816.736i q^{95} +(-7.17931 + 371.116i) q^{96} -1687.28i q^{97} +806.380 q^{98} +(-1027.27 - 39.7605i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q - 8q^{3} + 268q^{4} - 16q^{7} - 4q^{9} + O(q^{10}) \) \( 52q - 8q^{3} + 268q^{4} - 16q^{7} - 4q^{9} + 28q^{12} + 114q^{15} + 484q^{16} - 184q^{19} - 758q^{21} - 60q^{22} + 36q^{25} + 742q^{27} - 4q^{28} - 888q^{36} + 1402q^{45} - 660q^{46} - 488q^{48} - 924q^{49} - 1772q^{51} - 630q^{57} - 1880q^{60} - 212q^{63} + 7648q^{64} + 1316q^{66} - 1556q^{75} - 5680q^{76} + 3224q^{78} - 1504q^{79} - 276q^{81} + 1228q^{84} - 848q^{85} + 3598q^{87} + 5760q^{88} + 888q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.52893 −0.894110 −0.447055 0.894506i \(-0.647527\pi\)
−0.447055 + 0.894506i \(0.647527\pi\)
\(3\) 0.100502 5.19518i 0.0193416 0.999813i
\(4\) −1.60453 −0.200567
\(5\) 17.9211i 1.60291i 0.598052 + 0.801457i \(0.295942\pi\)
−0.598052 + 0.801457i \(0.704058\pi\)
\(6\) −0.254162 + 13.1382i −0.0172935 + 0.893943i
\(7\) −4.91298 −0.265276 −0.132638 0.991165i \(-0.542345\pi\)
−0.132638 + 0.991165i \(0.542345\pi\)
\(8\) 24.2892 1.07344
\(9\) −26.9798 1.04425i −0.999252 0.0386759i
\(10\) 45.3212i 1.43318i
\(11\) 38.0756 1.04366 0.521829 0.853050i \(-0.325250\pi\)
0.521829 + 0.853050i \(0.325250\pi\)
\(12\) −0.161258 + 8.33584i −0.00387927 + 0.200529i
\(13\) 51.2270i 1.09291i −0.837489 0.546454i \(-0.815977\pi\)
0.837489 0.546454i \(-0.184023\pi\)
\(14\) 12.4246 0.237186
\(15\) 93.1035 + 1.80111i 1.60261 + 0.0310029i
\(16\) −48.5892 −0.759206
\(17\) 30.7171i 0.438234i −0.975699 0.219117i \(-0.929682\pi\)
0.975699 0.219117i \(-0.0703177\pi\)
\(18\) 68.2299 + 2.64083i 0.893441 + 0.0345805i
\(19\) −45.5739 −0.550283 −0.275141 0.961404i \(-0.588725\pi\)
−0.275141 + 0.961404i \(0.588725\pi\)
\(20\) 28.7550i 0.321491i
\(21\) −0.493764 + 25.5238i −0.00513086 + 0.265227i
\(22\) −96.2904 −0.933145
\(23\) −137.131 −1.24320 −0.621602 0.783333i \(-0.713518\pi\)
−0.621602 + 0.783333i \(0.713518\pi\)
\(24\) 2.44110 126.187i 0.0207620 1.07324i
\(25\) −196.167 −1.56934
\(26\) 129.549i 0.977181i
\(27\) −8.13658 + 140.060i −0.0579958 + 0.998317i
\(28\) 7.88305 0.0532056
\(29\) 12.5498i 0.0803598i −0.999192 0.0401799i \(-0.987207\pi\)
0.999192 0.0401799i \(-0.0127931\pi\)
\(30\) −235.452 4.55486i −1.43291 0.0277200i
\(31\) 75.5324i 0.437614i −0.975768 0.218807i \(-0.929784\pi\)
0.975768 0.218807i \(-0.0702164\pi\)
\(32\) −71.4347 −0.394625
\(33\) 3.82667 197.810i 0.0201860 1.04346i
\(34\) 77.6812i 0.391830i
\(35\) 88.0462i 0.425215i
\(36\) 43.2900 + 1.67553i 0.200417 + 0.00775710i
\(37\) 152.739i 0.678654i −0.940668 0.339327i \(-0.889801\pi\)
0.940668 0.339327i \(-0.110199\pi\)
\(38\) 115.253 0.492014
\(39\) −266.133 5.14840i −1.09270 0.0211386i
\(40\) 435.289i 1.72063i
\(41\) 272.870i 1.03939i −0.854351 0.519697i \(-0.826045\pi\)
0.854351 0.519697i \(-0.173955\pi\)
\(42\) 1.24869 64.5479i 0.00458756 0.237142i
\(43\) 364.987i 1.29442i −0.762313 0.647209i \(-0.775936\pi\)
0.762313 0.647209i \(-0.224064\pi\)
\(44\) −61.0936 −0.209323
\(45\) 18.7141 483.509i 0.0619942 1.60172i
\(46\) 346.793 1.11156
\(47\) 430.845 1.33713 0.668567 0.743652i \(-0.266908\pi\)
0.668567 + 0.743652i \(0.266908\pi\)
\(48\) −4.88330 + 252.430i −0.0146842 + 0.759064i
\(49\) −318.863 −0.929629
\(50\) 496.092 1.40316
\(51\) −159.581 3.08712i −0.438152 0.00847614i
\(52\) 82.1954i 0.219201i
\(53\) 660.497i 1.71181i −0.517129 0.855907i \(-0.672999\pi\)
0.517129 0.855907i \(-0.327001\pi\)
\(54\) 20.5768 354.201i 0.0518546 0.892605i
\(55\) 682.358i 1.67289i
\(56\) −119.332 −0.284758
\(57\) −4.58026 + 236.765i −0.0106433 + 0.550180i
\(58\) 31.7375i 0.0718506i
\(59\) −351.582 285.954i −0.775797 0.630983i
\(60\) −149.388 2.88993i −0.321431 0.00621815i
\(61\) 251.217i 0.527295i 0.964619 + 0.263648i \(0.0849256\pi\)
−0.964619 + 0.263648i \(0.915074\pi\)
\(62\) 191.016i 0.391275i
\(63\) 132.551 + 5.13038i 0.265078 + 0.0102598i
\(64\) 569.367 1.11204
\(65\) 918.046 1.75184
\(66\) −9.67736 + 500.246i −0.0180485 + 0.932971i
\(67\) 442.198i 0.806314i −0.915131 0.403157i \(-0.867913\pi\)
0.915131 0.403157i \(-0.132087\pi\)
\(68\) 49.2865i 0.0878952i
\(69\) −13.7819 + 712.418i −0.0240455 + 1.24297i
\(70\) 222.662i 0.380189i
\(71\) 639.306i 1.06862i 0.845290 + 0.534308i \(0.179428\pi\)
−0.845290 + 0.534308i \(0.820572\pi\)
\(72\) −655.316 25.3639i −1.07264 0.0415162i
\(73\) 36.1944i 0.0580305i −0.999579 0.0290153i \(-0.990763\pi\)
0.999579 0.0290153i \(-0.00923714\pi\)
\(74\) 386.267i 0.606792i
\(75\) −19.7151 + 1019.12i −0.0303534 + 1.56904i
\(76\) 73.1249 0.110368
\(77\) −187.065 −0.276858
\(78\) 673.032 + 13.0199i 0.976998 + 0.0189002i
\(79\) −485.902 −0.692003 −0.346001 0.938234i \(-0.612461\pi\)
−0.346001 + 0.938234i \(0.612461\pi\)
\(80\) 870.774i 1.21694i
\(81\) 726.819 + 56.3473i 0.997008 + 0.0772939i
\(82\) 690.068i 0.929332i
\(83\) −1376.64 −1.82056 −0.910278 0.413998i \(-0.864132\pi\)
−0.910278 + 0.413998i \(0.864132\pi\)
\(84\) 0.792260 40.9538i 0.00102908 0.0531956i
\(85\) 550.485 0.702452
\(86\) 923.025i 1.15735i
\(87\) −65.1984 1.26128i −0.0803448 0.00155429i
\(88\) 924.825 1.12030
\(89\) 1250.69 1.48959 0.744793 0.667295i \(-0.232548\pi\)
0.744793 + 0.667295i \(0.232548\pi\)
\(90\) −47.3267 + 1222.76i −0.0554296 + 1.43211i
\(91\) 251.677i 0.289923i
\(92\) 220.030 0.249345
\(93\) −392.404 7.59114i −0.437532 0.00846414i
\(94\) −1089.58 −1.19554
\(95\) 816.736i 0.882056i
\(96\) −7.17931 + 371.116i −0.00763266 + 0.394551i
\(97\) 1687.28i 1.76616i −0.469220 0.883081i \(-0.655465\pi\)
0.469220 0.883081i \(-0.344535\pi\)
\(98\) 806.380 0.831191
\(99\) −1027.27 39.7605i −1.04288 0.0403644i
\(100\) 314.756 0.314756
\(101\) 916.279 0.902704 0.451352 0.892346i \(-0.350942\pi\)
0.451352 + 0.892346i \(0.350942\pi\)
\(102\) 403.568 + 7.80710i 0.391757 + 0.00757860i
\(103\) 178.532i 0.170789i −0.996347 0.0853946i \(-0.972785\pi\)
0.996347 0.0853946i \(-0.0272151\pi\)
\(104\) 1244.26i 1.17317i
\(105\) −457.416 8.84880i −0.425136 0.00822433i
\(106\) 1670.35i 1.53055i
\(107\) 1657.49i 1.49753i 0.662834 + 0.748766i \(0.269354\pi\)
−0.662834 + 0.748766i \(0.730646\pi\)
\(108\) 13.0554 224.731i 0.0116320 0.200229i
\(109\) 116.077i 0.102002i −0.998699 0.0510009i \(-0.983759\pi\)
0.998699 0.0510009i \(-0.0162411\pi\)
\(110\) 1725.63i 1.49575i
\(111\) −793.509 15.3506i −0.678527 0.0131262i
\(112\) 238.718 0.201399
\(113\) 1038.47 0.864522 0.432261 0.901749i \(-0.357716\pi\)
0.432261 + 0.901749i \(0.357716\pi\)
\(114\) 11.5831 598.761i 0.00951632 0.491922i
\(115\) 2457.53i 1.99275i
\(116\) 20.1365i 0.0161175i
\(117\) −53.4938 + 1382.09i −0.0422692 + 1.09209i
\(118\) 889.124 + 723.155i 0.693648 + 0.564168i
\(119\) 150.912i 0.116253i
\(120\) 2261.41 + 43.7473i 1.72031 + 0.0332797i
\(121\) 118.753 0.0892212
\(122\) 635.309i 0.471460i
\(123\) −1417.61 27.4239i −1.03920 0.0201035i
\(124\) 121.194i 0.0877707i
\(125\) 1275.39i 0.912596i
\(126\) −335.213 12.9744i −0.237009 0.00917339i
\(127\) 1213.40 0.847813 0.423906 0.905706i \(-0.360659\pi\)
0.423906 + 0.905706i \(0.360659\pi\)
\(128\) −868.409 −0.599666
\(129\) −1896.17 36.6818i −1.29418 0.0250361i
\(130\) −2321.67 −1.56634
\(131\) −2467.88 −1.64595 −0.822975 0.568077i \(-0.807687\pi\)
−0.822975 + 0.568077i \(0.807687\pi\)
\(132\) −6.14001 + 317.392i −0.00404863 + 0.209284i
\(133\) 223.904 0.145977
\(134\) 1118.29i 0.720934i
\(135\) −2510.03 145.817i −1.60022 0.0929623i
\(136\) 746.091i 0.470418i
\(137\) 653.589i 0.407590i 0.979014 + 0.203795i \(0.0653276\pi\)
−0.979014 + 0.203795i \(0.934672\pi\)
\(138\) 34.8533 1801.65i 0.0214994 1.11135i
\(139\) −706.567 −0.431153 −0.215576 0.976487i \(-0.569163\pi\)
−0.215576 + 0.976487i \(0.569163\pi\)
\(140\) 141.273i 0.0852840i
\(141\) 43.3007 2238.32i 0.0258623 1.33688i
\(142\) 1616.76i 0.955460i
\(143\) 1950.50i 1.14062i
\(144\) 1310.93 + 50.7393i 0.758638 + 0.0293630i
\(145\) 224.906 0.128810
\(146\) 91.5329i 0.0518857i
\(147\) −32.0463 + 1656.55i −0.0179805 + 0.929455i
\(148\) 245.075i 0.136115i
\(149\) −1113.52 −0.612235 −0.306118 0.951994i \(-0.599030\pi\)
−0.306118 + 0.951994i \(0.599030\pi\)
\(150\) 49.8581 2577.29i 0.0271393 1.40290i
\(151\) 1135.35i 0.611879i −0.952051 0.305939i \(-0.901029\pi\)
0.952051 0.305939i \(-0.0989705\pi\)
\(152\) −1106.95 −0.590695
\(153\) −32.0763 + 828.740i −0.0169491 + 0.437906i
\(154\) 473.074 0.247541
\(155\) 1353.63 0.701457
\(156\) 427.020 + 8.26078i 0.219160 + 0.00423969i
\(157\) 1602.61i 0.814665i 0.913280 + 0.407332i \(0.133541\pi\)
−0.913280 + 0.407332i \(0.866459\pi\)
\(158\) 1228.81 0.618727
\(159\) −3431.40 66.3811i −1.71149 0.0331092i
\(160\) 1280.19i 0.632550i
\(161\) 673.720 0.329793
\(162\) −1838.07 142.498i −0.891436 0.0691093i
\(163\) 867.586 0.416899 0.208450 0.978033i \(-0.433158\pi\)
0.208450 + 0.978033i \(0.433158\pi\)
\(164\) 437.829i 0.208468i
\(165\) 3544.97 + 68.5782i 1.67258 + 0.0323564i
\(166\) 3481.43 1.62778
\(167\) 3842.95i 1.78070i 0.455277 + 0.890350i \(0.349540\pi\)
−0.455277 + 0.890350i \(0.650460\pi\)
\(168\) −11.9931 + 619.953i −0.00550767 + 0.284705i
\(169\) −427.204 −0.194449
\(170\) −1392.13 −0.628070
\(171\) 1229.58 + 47.5905i 0.549871 + 0.0212827i
\(172\) 585.633i 0.259617i
\(173\) 2410.10 1.05917 0.529586 0.848256i \(-0.322347\pi\)
0.529586 + 0.848256i \(0.322347\pi\)
\(174\) 164.882 + 3.18967i 0.0718371 + 0.00138970i
\(175\) 963.765 0.416307
\(176\) −1850.06 −0.792352
\(177\) −1520.91 + 1797.79i −0.645870 + 0.763448i
\(178\) −3162.91 −1.33185
\(179\) 1229.32 0.513318 0.256659 0.966502i \(-0.417378\pi\)
0.256659 + 0.966502i \(0.417378\pi\)
\(180\) −30.0274 + 775.805i −0.0124340 + 0.321251i
\(181\) −2553.60 −1.04866 −0.524329 0.851516i \(-0.675684\pi\)
−0.524329 + 0.851516i \(0.675684\pi\)
\(182\) 636.474i 0.259223i
\(183\) 1305.12 + 25.2477i 0.527197 + 0.0101987i
\(184\) −3330.78 −1.33450
\(185\) 2737.26 1.08782
\(186\) 992.362 + 19.1974i 0.391202 + 0.00756787i
\(187\) 1169.57i 0.457367i
\(188\) −691.306 −0.268184
\(189\) 39.9749 688.113i 0.0153849 0.264830i
\(190\) 2065.47i 0.788656i
\(191\) −3086.92 −1.16943 −0.584716 0.811238i \(-0.698794\pi\)
−0.584716 + 0.811238i \(0.698794\pi\)
\(192\) 57.2224 2957.96i 0.0215087 1.11184i
\(193\) −4387.11 −1.63622 −0.818111 0.575060i \(-0.804979\pi\)
−0.818111 + 0.575060i \(0.804979\pi\)
\(194\) 4267.02i 1.57914i
\(195\) 92.2652 4769.41i 0.0338833 1.75151i
\(196\) 511.626 0.186452
\(197\) 1321.27i 0.477852i −0.971038 0.238926i \(-0.923205\pi\)
0.971038 0.238926i \(-0.0767953\pi\)
\(198\) 2597.90 + 100.551i 0.932447 + 0.0360902i
\(199\) 2247.81 0.800718 0.400359 0.916358i \(-0.368885\pi\)
0.400359 + 0.916358i \(0.368885\pi\)
\(200\) −4764.73 −1.68459
\(201\) −2297.30 44.4416i −0.806163 0.0155954i
\(202\) −2317.20 −0.807117
\(203\) 61.6569i 0.0213176i
\(204\) 256.052 + 4.95338i 0.0878787 + 0.00170003i
\(205\) 4890.14 1.66606
\(206\) 451.494i 0.152704i
\(207\) 3699.75 + 143.199i 1.24227 + 0.0480820i
\(208\) 2489.08i 0.829743i
\(209\) −1735.26 −0.574307
\(210\) 1156.77 + 22.3780i 0.380118 + 0.00735346i
\(211\) 238.261i 0.0777372i −0.999244 0.0388686i \(-0.987625\pi\)
0.999244 0.0388686i \(-0.0123754\pi\)
\(212\) 1059.79i 0.343333i
\(213\) 3321.31 + 64.2514i 1.06842 + 0.0206687i
\(214\) 4191.68i 1.33896i
\(215\) 6540.98 2.07484
\(216\) −197.631 + 3401.94i −0.0622549 + 1.07163i
\(217\) 371.090i 0.116088i
\(218\) 293.551i 0.0912008i
\(219\) −188.036 3.63760i −0.0580197 0.00112240i
\(220\) 1094.87i 0.335527i
\(221\) −1573.54 −0.478950
\(222\) 2006.72 + 38.8205i 0.606678 + 0.0117363i
\(223\) 2110.45 0.633750 0.316875 0.948467i \(-0.397366\pi\)
0.316875 + 0.948467i \(0.397366\pi\)
\(224\) 350.958 0.104685
\(225\) 5292.54 + 204.847i 1.56816 + 0.0606955i
\(226\) −2626.21 −0.772978
\(227\) 2633.15 0.769904 0.384952 0.922937i \(-0.374218\pi\)
0.384952 + 0.922937i \(0.374218\pi\)
\(228\) 7.34918 379.897i 0.00213470 0.110348i
\(229\) 811.669i 0.234221i −0.993119 0.117110i \(-0.962637\pi\)
0.993119 0.117110i \(-0.0373631\pi\)
\(230\) 6214.92i 1.78174i
\(231\) −18.8004 + 971.836i −0.00535486 + 0.276806i
\(232\) 304.824i 0.0862614i
\(233\) −4623.35 −1.29994 −0.649970 0.759960i \(-0.725219\pi\)
−0.649970 + 0.759960i \(0.725219\pi\)
\(234\) 135.282 3495.21i 0.0377934 0.976450i
\(235\) 7721.24i 2.14331i
\(236\) 564.124 + 458.822i 0.155599 + 0.126554i
\(237\) −48.8340 + 2524.35i −0.0133844 + 0.691873i
\(238\) 381.646i 0.103943i
\(239\) 4107.24i 1.11161i −0.831312 0.555806i \(-0.812410\pi\)
0.831312 0.555806i \(-0.187590\pi\)
\(240\) −4523.83 87.5143i −1.21672 0.0235376i
\(241\) −1369.49 −0.366045 −0.183023 0.983109i \(-0.558588\pi\)
−0.183023 + 0.983109i \(0.558588\pi\)
\(242\) −300.319 −0.0797736
\(243\) 365.781 3770.29i 0.0965632 0.995327i
\(244\) 403.086i 0.105758i
\(245\) 5714.38i 1.49012i
\(246\) 3585.03 + 69.3530i 0.929159 + 0.0179748i
\(247\) 2334.61i 0.601409i
\(248\) 1834.62i 0.469752i
\(249\) −138.355 + 7151.91i −0.0352124 + 1.82022i
\(250\) 3225.37i 0.815962i
\(251\) 581.170i 0.146148i 0.997327 + 0.0730740i \(0.0232809\pi\)
−0.997327 + 0.0730740i \(0.976719\pi\)
\(252\) −212.683 8.23187i −0.0531658 0.00205777i
\(253\) −5221.33 −1.29748
\(254\) −3068.61 −0.758038
\(255\) 55.3247 2859.87i 0.0135865 0.702321i
\(256\) −2358.79 −0.575877
\(257\) 1366.48i 0.331667i −0.986154 0.165834i \(-0.946969\pi\)
0.986154 0.165834i \(-0.0530315\pi\)
\(258\) 4795.28 + 92.7656i 1.15714 + 0.0223850i
\(259\) 750.406i 0.180031i
\(260\) −1473.03 −0.351360
\(261\) −13.1051 + 338.591i −0.00310799 + 0.0802997i
\(262\) 6241.08 1.47166
\(263\) 3753.52i 0.880046i −0.897986 0.440023i \(-0.854970\pi\)
0.897986 0.440023i \(-0.145030\pi\)
\(264\) 92.9465 4804.63i 0.0216684 1.12009i
\(265\) 11836.8 2.74389
\(266\) −566.237 −0.130520
\(267\) 125.697 6497.58i 0.0288110 1.48931i
\(268\) 709.521i 0.161720i
\(269\) −2795.74 −0.633678 −0.316839 0.948479i \(-0.602621\pi\)
−0.316839 + 0.948479i \(0.602621\pi\)
\(270\) 6347.69 + 368.760i 1.43077 + 0.0831185i
\(271\) −8440.91 −1.89206 −0.946031 0.324076i \(-0.894946\pi\)
−0.946031 + 0.324076i \(0.894946\pi\)
\(272\) 1492.52i 0.332710i
\(273\) 1307.51 + 25.2940i 0.289868 + 0.00560756i
\(274\) 1652.88i 0.364431i
\(275\) −7469.18 −1.63785
\(276\) 22.1135 1143.10i 0.00482273 0.249299i
\(277\) 2260.98 0.490430 0.245215 0.969469i \(-0.421141\pi\)
0.245215 + 0.969469i \(0.421141\pi\)
\(278\) 1786.86 0.385498
\(279\) −78.8747 + 2037.85i −0.0169251 + 0.437286i
\(280\) 2138.57i 0.456443i
\(281\) 6580.58i 1.39703i 0.715597 + 0.698513i \(0.246155\pi\)
−0.715597 + 0.698513i \(0.753845\pi\)
\(282\) −109.504 + 5660.54i −0.0231237 + 1.19532i
\(283\) 5314.23i 1.11625i 0.829758 + 0.558124i \(0.188479\pi\)
−0.829758 + 0.558124i \(0.811521\pi\)
\(284\) 1025.79i 0.214329i
\(285\) −4243.09 82.0834i −0.881891 0.0170604i
\(286\) 4932.67i 1.01984i
\(287\) 1340.61i 0.275726i
\(288\) 1927.29 + 74.5957i 0.394330 + 0.0152625i
\(289\) 3969.46 0.807951
\(290\) −568.771 −0.115170
\(291\) −8765.74 169.575i −1.76583 0.0341604i
\(292\) 58.0750i 0.0116390i
\(293\) 3526.60i 0.703161i 0.936158 + 0.351580i \(0.114356\pi\)
−0.936158 + 0.351580i \(0.885644\pi\)
\(294\) 81.0426 4189.29i 0.0160765 0.831035i
\(295\) 5124.61 6300.74i 1.01141 1.24354i
\(296\) 3709.91i 0.728494i
\(297\) −309.805 + 5332.87i −0.0605277 + 1.04190i
\(298\) 2816.01 0.547406
\(299\) 7024.78i 1.35871i
\(300\) 31.6336 1635.22i 0.00608788 0.314697i
\(301\) 1793.17i 0.343378i
\(302\) 2871.22i 0.547087i
\(303\) 92.0876 4760.23i 0.0174597 0.902535i
\(304\) 2214.40 0.417778
\(305\) −4502.09 −0.845209
\(306\) 81.1185 2095.82i 0.0151544 0.391537i
\(307\) −6528.33 −1.21365 −0.606827 0.794834i \(-0.707558\pi\)
−0.606827 + 0.794834i \(0.707558\pi\)
\(308\) 300.152 0.0555284
\(309\) −927.506 17.9428i −0.170757 0.00330333i
\(310\) −3423.22 −0.627180
\(311\) 4105.29i 0.748519i −0.927324 0.374260i \(-0.877897\pi\)
0.927324 0.374260i \(-0.122103\pi\)
\(312\) −6464.16 125.050i −1.17295 0.0226910i
\(313\) 5568.41i 1.00558i 0.864410 + 0.502788i \(0.167692\pi\)
−0.864410 + 0.502788i \(0.832308\pi\)
\(314\) 4052.89i 0.728400i
\(315\) −91.9423 + 2375.47i −0.0164456 + 0.424897i
\(316\) 779.645 0.138793
\(317\) 6372.94i 1.12915i 0.825382 + 0.564574i \(0.190960\pi\)
−0.825382 + 0.564574i \(0.809040\pi\)
\(318\) 8677.75 + 167.873i 1.53027 + 0.0296033i
\(319\) 477.841i 0.0838682i
\(320\) 10203.7i 1.78251i
\(321\) 8610.98 + 166.581i 1.49725 + 0.0289646i
\(322\) −1703.79 −0.294871
\(323\) 1399.90i 0.241153i
\(324\) −1166.21 90.4111i −0.199967 0.0155026i
\(325\) 10049.0i 1.71514i
\(326\) −2194.06 −0.372754
\(327\) −603.042 11.6660i −0.101983 0.00197287i
\(328\) 6627.78i 1.11573i
\(329\) −2116.74 −0.354710
\(330\) −8964.98 173.429i −1.49547 0.0289302i
\(331\) 7783.40 1.29249 0.646246 0.763129i \(-0.276338\pi\)
0.646246 + 0.763129i \(0.276338\pi\)
\(332\) 2208.87 0.365143
\(333\) −159.498 + 4120.88i −0.0262476 + 0.678146i
\(334\) 9718.55i 1.59214i
\(335\) 7924.68 1.29245
\(336\) 23.9916 1240.18i 0.00389538 0.201362i
\(337\) 607.505i 0.0981986i −0.998794 0.0490993i \(-0.984365\pi\)
0.998794 0.0490993i \(-0.0156351\pi\)
\(338\) 1080.37 0.173859
\(339\) 104.368 5395.04i 0.0167212 0.864360i
\(340\) −883.271 −0.140888
\(341\) 2875.94i 0.456719i
\(342\) −3109.50 120.353i −0.491646 0.0190291i
\(343\) 3251.72 0.511885
\(344\) 8865.22i 1.38948i
\(345\) −12767.3 246.987i −1.99238 0.0385429i
\(346\) −6094.97 −0.947017
\(347\) 8204.92 1.26935 0.634673 0.772780i \(-0.281135\pi\)
0.634673 + 0.772780i \(0.281135\pi\)
\(348\) 104.613 + 2.02376i 0.0161145 + 0.000311738i
\(349\) 12249.4i 1.87878i −0.342854 0.939389i \(-0.611394\pi\)
0.342854 0.939389i \(-0.388606\pi\)
\(350\) −2437.29 −0.372225
\(351\) 7174.85 + 416.813i 1.09107 + 0.0633841i
\(352\) −2719.92 −0.411853
\(353\) 10546.0 1.59010 0.795051 0.606542i \(-0.207444\pi\)
0.795051 + 0.606542i \(0.207444\pi\)
\(354\) 3846.28 4546.48i 0.577479 0.682606i
\(355\) −11457.1 −1.71290
\(356\) −2006.78 −0.298761
\(357\) 784.017 + 15.1670i 0.116231 + 0.00224852i
\(358\) −3108.87 −0.458963
\(359\) 4715.89i 0.693301i −0.937994 0.346651i \(-0.887319\pi\)
0.937994 0.346651i \(-0.112681\pi\)
\(360\) 454.550 11744.0i 0.0665470 1.71934i
\(361\) −4782.02 −0.697189
\(362\) 6457.85 0.937617
\(363\) 11.9349 616.946i 0.00172568 0.0892045i
\(364\) 403.825i 0.0581488i
\(365\) 648.644 0.0930180
\(366\) −3300.54 63.8496i −0.471372 0.00911878i
\(367\) 3339.88i 0.475042i −0.971382 0.237521i \(-0.923665\pi\)
0.971382 0.237521i \(-0.0763348\pi\)
\(368\) 6663.06 0.943848
\(369\) −284.944 + 7361.98i −0.0401995 + 1.03862i
\(370\) −6922.33 −0.972635
\(371\) 3245.01i 0.454104i
\(372\) 629.626 + 12.1802i 0.0877543 + 0.00169762i
\(373\) 8644.93 1.20005 0.600023 0.799982i \(-0.295158\pi\)
0.600023 + 0.799982i \(0.295158\pi\)
\(374\) 2957.76i 0.408936i
\(375\) −6625.89 128.179i −0.912425 0.0176510i
\(376\) 10464.9 1.43533
\(377\) −642.887 −0.0878260
\(378\) −101.094 + 1740.19i −0.0137558 + 0.236787i
\(379\) −10504.2 −1.42365 −0.711825 0.702356i \(-0.752131\pi\)
−0.711825 + 0.702356i \(0.752131\pi\)
\(380\) 1310.48i 0.176911i
\(381\) 121.949 6303.85i 0.0163980 0.847654i
\(382\) 7806.59 1.04560
\(383\) 3695.29i 0.493004i −0.969142 0.246502i \(-0.920719\pi\)
0.969142 0.246502i \(-0.0792812\pi\)
\(384\) −87.2766 + 4511.54i −0.0115985 + 0.599554i
\(385\) 3352.42i 0.443779i
\(386\) 11094.7 1.46296
\(387\) −381.137 + 9847.27i −0.0500628 + 1.29345i
\(388\) 2707.30i 0.354233i
\(389\) 12641.4i 1.64767i −0.566832 0.823833i \(-0.691831\pi\)
0.566832 0.823833i \(-0.308169\pi\)
\(390\) −233.332 + 12061.5i −0.0302954 + 1.56604i
\(391\) 4212.25i 0.544815i
\(392\) −7744.90 −0.997900
\(393\) −248.026 + 12821.1i −0.0318353 + 1.64564i
\(394\) 3341.40i 0.427252i
\(395\) 8707.91i 1.10922i
\(396\) 1648.29 + 63.7970i 0.209166 + 0.00809575i
\(397\) 13140.9i 1.66127i −0.556821 0.830633i \(-0.687979\pi\)
0.556821 0.830633i \(-0.312021\pi\)
\(398\) −5684.54 −0.715931
\(399\) 22.5027 1163.22i 0.00282342 0.145950i
\(400\) 9531.60 1.19145
\(401\) −4936.62 −0.614770 −0.307385 0.951585i \(-0.599454\pi\)
−0.307385 + 0.951585i \(0.599454\pi\)
\(402\) 5809.69 + 112.390i 0.720799 + 0.0139440i
\(403\) −3869.30 −0.478272
\(404\) −1470.20 −0.181052
\(405\) −1009.81 + 13025.4i −0.123896 + 1.59812i
\(406\) 155.926i 0.0190603i
\(407\) 5815.65i 0.708282i
\(408\) −3876.08 74.9835i −0.470330 0.00909862i
\(409\) 5911.21i 0.714647i −0.933981 0.357323i \(-0.883689\pi\)
0.933981 0.357323i \(-0.116311\pi\)
\(410\) −12366.8 −1.48964
\(411\) 3395.51 + 65.6868i 0.407514 + 0.00788344i
\(412\) 286.460i 0.0342546i
\(413\) 1727.31 + 1404.89i 0.205800 + 0.167385i
\(414\) −9356.40 362.138i −1.11073 0.0429907i
\(415\) 24671.0i 2.91820i
\(416\) 3659.39i 0.431289i
\(417\) −71.0113 + 3670.74i −0.00833918 + 0.431072i
\(418\) 4388.33 0.513494
\(419\) −14149.6 −1.64976 −0.824882 0.565304i \(-0.808759\pi\)
−0.824882 + 0.565304i \(0.808759\pi\)
\(420\) 733.939 + 14.1982i 0.0852680 + 0.00164953i
\(421\) 4735.46i 0.548200i 0.961701 + 0.274100i \(0.0883799\pi\)
−0.961701 + 0.274100i \(0.911620\pi\)
\(422\) 602.544i 0.0695057i
\(423\) −11624.1 449.910i −1.33613 0.0517148i
\(424\) 16042.9i 1.83753i
\(425\) 6025.67i 0.687737i
\(426\) −8399.35 162.487i −0.955281 0.0184801i
\(427\) 1234.22i 0.139879i
\(428\) 2659.50i 0.300355i
\(429\) −10133.2 196.029i −1.14041 0.0220614i
\(430\) −16541.6 −1.85514
\(431\) 10921.4 1.22057 0.610287 0.792180i \(-0.291054\pi\)
0.610287 + 0.792180i \(0.291054\pi\)
\(432\) 395.350 6805.40i 0.0440308 0.757929i
\(433\) 1855.12 0.205893 0.102946 0.994687i \(-0.467173\pi\)
0.102946 + 0.994687i \(0.467173\pi\)
\(434\) 938.458i 0.103796i
\(435\) 22.6035 1168.43i 0.00249139 0.128786i
\(436\) 186.250i 0.0204581i
\(437\) 6249.58 0.684114
\(438\) 475.530 + 9.19921i 0.0518760 + 0.00100355i
\(439\) 9335.14 1.01490 0.507451 0.861681i \(-0.330588\pi\)
0.507451 + 0.861681i \(0.330588\pi\)
\(440\) 16573.9i 1.79575i
\(441\) 8602.85 + 332.972i 0.928933 + 0.0359542i
\(442\) 3979.37 0.428234
\(443\) −2399.08 −0.257300 −0.128650 0.991690i \(-0.541064\pi\)
−0.128650 + 0.991690i \(0.541064\pi\)
\(444\) 1273.21 + 24.6305i 0.136090 + 0.00263268i
\(445\) 22413.8i 2.38768i
\(446\) −5337.17 −0.566642
\(447\) −111.911 + 5784.94i −0.0118416 + 0.612121i
\(448\) −2797.29 −0.294999
\(449\) 8641.91i 0.908323i −0.890919 0.454162i \(-0.849939\pi\)
0.890919 0.454162i \(-0.150061\pi\)
\(450\) −13384.5 518.044i −1.40211 0.0542685i
\(451\) 10389.7i 1.08477i
\(452\) −1666.26 −0.173394
\(453\) −5898.36 114.105i −0.611764 0.0118347i
\(454\) −6659.04 −0.688379
\(455\) −4510.34 −0.464721
\(456\) −111.251 + 5750.82i −0.0114250 + 0.590585i
\(457\) 14348.7i 1.46872i 0.678762 + 0.734359i \(0.262517\pi\)
−0.678762 + 0.734359i \(0.737483\pi\)
\(458\) 2052.65i 0.209419i
\(459\) 4302.23 + 249.932i 0.437497 + 0.0254157i
\(460\) 3943.19i 0.399679i
\(461\) 8909.98i 0.900172i −0.892985 0.450086i \(-0.851393\pi\)
0.892985 0.450086i \(-0.148607\pi\)
\(462\) 47.5447 2457.70i 0.00478784 0.247495i
\(463\) 13537.1i 1.35880i 0.733769 + 0.679400i \(0.237760\pi\)
−0.733769 + 0.679400i \(0.762240\pi\)
\(464\) 609.784i 0.0610097i
\(465\) 136.042 7032.33i 0.0135673 0.701326i
\(466\) 11692.1 1.16229
\(467\) 10252.9 1.01595 0.507976 0.861371i \(-0.330394\pi\)
0.507976 + 0.861371i \(0.330394\pi\)
\(468\) 85.8325 2217.62i 0.00847780 0.219037i
\(469\) 2172.51i 0.213896i
\(470\) 19526.4i 1.91636i
\(471\) 8325.86 + 161.065i 0.814512 + 0.0157569i
\(472\) −8539.62 6945.57i −0.832771 0.677322i
\(473\) 13897.1i 1.35093i
\(474\) 123.498 6383.89i 0.0119671 0.618611i
\(475\) 8940.10 0.863578
\(476\) 242.144i 0.0233165i
\(477\) −689.723 + 17820.1i −0.0662060 + 1.71053i
\(478\) 10386.9i 0.993905i
\(479\) 9800.56i 0.934862i 0.884029 + 0.467431i \(0.154820\pi\)
−0.884029 + 0.467431i \(0.845180\pi\)
\(480\) −6650.82 128.661i −0.632431 0.0122345i
\(481\) −7824.38 −0.741707
\(482\) 3463.35 0.327285
\(483\) 67.7101 3500.10i 0.00637871 0.329731i
\(484\) −190.544 −0.0178948
\(485\) 30238.0 2.83101
\(486\) −925.033 + 9534.79i −0.0863382 + 0.889932i
\(487\) −1932.83 −0.179846 −0.0899229 0.995949i \(-0.528662\pi\)
−0.0899229 + 0.995949i \(0.528662\pi\)
\(488\) 6101.84i 0.566019i
\(489\) 87.1939 4507.26i 0.00806349 0.416821i
\(490\) 14451.2i 1.33233i
\(491\) 10380.0i 0.954061i 0.878887 + 0.477031i \(0.158287\pi\)
−0.878887 + 0.477031i \(0.841713\pi\)
\(492\) 2274.60 + 44.0026i 0.208429 + 0.00403209i
\(493\) −385.492 −0.0352164
\(494\) 5904.07i 0.537726i
\(495\) 712.552 18409.9i 0.0647007 1.67164i
\(496\) 3670.06i 0.332239i
\(497\) 3140.90i 0.283478i
\(498\) 349.890 18086.6i 0.0314838 1.62747i
\(499\) −8109.16 −0.727487 −0.363743 0.931499i \(-0.618501\pi\)
−0.363743 + 0.931499i \(0.618501\pi\)
\(500\) 2046.41i 0.183036i
\(501\) 19964.8 + 386.224i 1.78037 + 0.0344415i
\(502\) 1469.74i 0.130672i
\(503\) −3825.79 −0.339132 −0.169566 0.985519i \(-0.554237\pi\)
−0.169566 + 0.985519i \(0.554237\pi\)
\(504\) 3219.56 + 124.613i 0.284545 + 0.0110133i
\(505\) 16420.8i 1.44696i
\(506\) 13204.4 1.16009
\(507\) −42.9348 + 2219.40i −0.00376095 + 0.194413i
\(508\) −1946.95 −0.170043
\(509\) 19008.0 1.65524 0.827618 0.561291i \(-0.189695\pi\)
0.827618 + 0.561291i \(0.189695\pi\)
\(510\) −139.912 + 7232.39i −0.0121479 + 0.627952i
\(511\) 177.822i 0.0153941i
\(512\) 12912.5 1.11456
\(513\) 370.816 6383.08i 0.0319141 0.549357i
\(514\) 3455.72i 0.296547i
\(515\) 3199.50 0.273760
\(516\) 3042.47 + 58.8572i 0.259568 + 0.00502140i
\(517\) 16404.7 1.39551
\(518\) 1897.72i 0.160967i
\(519\) 242.220 12520.9i 0.0204861 1.05897i
\(520\) 22298.5 1.88049
\(521\) 18365.1i 1.54432i 0.635428 + 0.772160i \(0.280824\pi\)
−0.635428 + 0.772160i \(0.719176\pi\)
\(522\) 33.1418 856.270i 0.00277889 0.0717968i
\(523\) 13117.1 1.09669 0.548346 0.836252i \(-0.315258\pi\)
0.548346 + 0.836252i \(0.315258\pi\)
\(524\) 3959.79 0.330123
\(525\) 96.8601 5006.93i 0.00805204 0.416230i
\(526\) 9492.38i 0.786858i
\(527\) −2320.13 −0.191777
\(528\) −185.935 + 9611.42i −0.0153253 + 0.792203i
\(529\) 6637.78 0.545556
\(530\) −29934.5 −2.45334
\(531\) 9186.99 + 8082.11i 0.750813 + 0.660515i
\(532\) −359.261 −0.0292781
\(533\) −13978.3 −1.13596
\(534\) −317.878 + 16431.9i −0.0257602 + 1.33161i
\(535\) −29704.2 −2.40042
\(536\) 10740.6i 0.865529i
\(537\) 123.549 6386.55i 0.00992838 0.513222i
\(538\) 7070.22 0.566578
\(539\) −12140.9 −0.970214
\(540\) 4027.43 + 233.968i 0.320950 + 0.0186451i
\(541\) 1040.15i 0.0826605i −0.999146 0.0413303i \(-0.986840\pi\)
0.999146 0.0413303i \(-0.0131596\pi\)
\(542\) 21346.4 1.69171
\(543\) −256.641 + 13266.4i −0.0202827 + 1.04846i
\(544\) 2194.26i 0.172938i
\(545\) 2080.24 0.163500
\(546\) −3306.60 63.9667i −0.259174 0.00501378i
\(547\) 270.011 0.0211057 0.0105529 0.999944i \(-0.496641\pi\)
0.0105529 + 0.999944i \(0.496641\pi\)
\(548\) 1048.70i 0.0817490i
\(549\) 262.333 6777.78i 0.0203936 0.526901i
\(550\) 18889.0 1.46442
\(551\) 571.943i 0.0442206i
\(552\) −334.750 + 17304.0i −0.0258114 + 1.33425i
\(553\) 2387.23 0.183572
\(554\) −5717.86 −0.438499
\(555\) 275.100 14220.6i 0.0210402 1.08762i
\(556\) 1133.71 0.0864749
\(557\) 19341.3i 1.47130i −0.677359 0.735652i \(-0.736876\pi\)
0.677359 0.735652i \(-0.263124\pi\)
\(558\) 199.468 5153.57i 0.0151329 0.390982i
\(559\) −18697.2 −1.41468
\(560\) 4278.10i 0.322826i
\(561\) −6076.14 117.544i −0.457281 0.00884619i
\(562\) 16641.8i 1.24910i
\(563\) −24978.5 −1.86983 −0.934917 0.354866i \(-0.884527\pi\)
−0.934917 + 0.354866i \(0.884527\pi\)
\(564\) −69.4774 + 3591.46i −0.00518711 + 0.268134i
\(565\) 18610.5i 1.38576i
\(566\) 13439.3i 0.998048i
\(567\) −3570.85 276.833i −0.264483 0.0205042i
\(568\) 15528.2i 1.14709i
\(569\) −3828.07 −0.282041 −0.141020 0.990007i \(-0.545038\pi\)
−0.141020 + 0.990007i \(0.545038\pi\)
\(570\) 10730.5 + 207.583i 0.788508 + 0.0152538i
\(571\) 19204.9i 1.40753i 0.710432 + 0.703765i \(0.248499\pi\)
−0.710432 + 0.703765i \(0.751501\pi\)
\(572\) 3129.64i 0.228771i
\(573\) −310.241 + 16037.1i −0.0226187 + 1.16921i
\(574\) 3390.29i 0.246530i
\(575\) 26900.5 1.95100
\(576\) −15361.4 594.561i −1.11121 0.0430093i
\(577\) −12909.8 −0.931445 −0.465723 0.884931i \(-0.654206\pi\)
−0.465723 + 0.884931i \(0.654206\pi\)
\(578\) −10038.5 −0.722397
\(579\) −440.912 + 22791.8i −0.0316471 + 1.63592i
\(580\) −360.869 −0.0258350
\(581\) 6763.42 0.482950
\(582\) 22167.9 + 428.843i 1.57885 + 0.0305431i
\(583\) 25148.8i 1.78655i
\(584\) 879.130i 0.0622923i
\(585\) −24768.7 958.669i −1.75053 0.0677540i
\(586\) 8918.51i 0.628703i
\(587\) 4715.16 0.331543 0.165771 0.986164i \(-0.446989\pi\)
0.165771 + 0.986164i \(0.446989\pi\)
\(588\) 51.4193 2657.99i 0.00360628 0.186418i
\(589\) 3442.31i 0.240811i
\(590\) −12959.8 + 15934.1i −0.904313 + 1.11186i
\(591\) −6864.25 132.790i −0.477763 0.00924241i
\(592\) 7421.48i 0.515238i
\(593\) 15022.0i 1.04027i 0.854084 + 0.520135i \(0.174118\pi\)
−0.854084 + 0.520135i \(0.825882\pi\)
\(594\) 783.475 13486.4i 0.0541185 0.931574i
\(595\) −2704.52 −0.186344
\(596\) 1786.68 0.122794
\(597\) 225.909 11677.8i 0.0154872 0.800569i
\(598\) 17765.2i 1.21484i
\(599\) 20568.7i 1.40303i 0.712655 + 0.701515i \(0.247493\pi\)
−0.712655 + 0.701515i \(0.752507\pi\)
\(600\) −478.864 + 24753.6i −0.0325825 + 1.68427i
\(601\) 12269.7i 0.832764i −0.909190 0.416382i \(-0.863298\pi\)
0.909190 0.416382i \(-0.136702\pi\)
\(602\) 4534.81i 0.307018i
\(603\) −461.765 + 11930.4i −0.0311849 + 0.805711i
\(604\) 1821.71i 0.122722i
\(605\) 2128.20i 0.143014i
\(606\) −232.883 + 12038.3i −0.0156109 + 0.806966i
\(607\) −11719.7 −0.783673 −0.391837 0.920035i \(-0.628160\pi\)
−0.391837 + 0.920035i \(0.628160\pi\)
\(608\) 3255.56 0.217155
\(609\) 320.319 + 6.19662i 0.0213136 + 0.000412315i
\(610\) 11385.4 0.755710
\(611\) 22070.9i 1.46136i
\(612\) 51.4675 1329.74i 0.00339943 0.0878294i
\(613\) 331.561i 0.0218460i 0.999940 + 0.0109230i \(0.00347697\pi\)
−0.999940 + 0.0109230i \(0.996523\pi\)
\(614\) 16509.7 1.08514
\(615\) 491.467 25405.1i 0.0322242 1.66575i
\(616\) −4543.65 −0.297190
\(617\) 22795.3i 1.48736i 0.668533 + 0.743682i \(0.266923\pi\)
−0.668533 + 0.743682i \(0.733077\pi\)
\(618\) 2345.59 + 45.3760i 0.152676 + 0.00295354i
\(619\) −14271.8 −0.926708 −0.463354 0.886173i \(-0.653354\pi\)
−0.463354 + 0.886173i \(0.653354\pi\)
\(620\) −2171.94 −0.140689
\(621\) 1115.77 19206.5i 0.0721006 1.24111i
\(622\) 10382.0i 0.669259i
\(623\) −6144.64 −0.395152
\(624\) 12931.2 + 250.157i 0.829588 + 0.0160485i
\(625\) −1664.40 −0.106522
\(626\) 14082.1i 0.899096i
\(627\) −174.396 + 9014.97i −0.0111080 + 0.574199i
\(628\) 2571.44i 0.163395i
\(629\) −4691.70 −0.297409
\(630\) 232.515 6007.39i 0.0147042 0.379905i
\(631\) −5033.55 −0.317563 −0.158782 0.987314i \(-0.550757\pi\)
−0.158782 + 0.987314i \(0.550757\pi\)
\(632\) −11802.1 −0.742823
\(633\) −1237.81 23.9456i −0.0777227 0.00150356i
\(634\) 16116.7i 1.00958i
\(635\) 21745.6i 1.35897i
\(636\) 5505.79 + 106.511i 0.343269 + 0.00664060i
\(637\) 16334.4i 1.01600i
\(638\) 1208.42i 0.0749874i
\(639\) 667.595 17248.4i 0.0413297 1.06782i
\(640\) 15562.9i 0.961213i
\(641\) 15611.3i 0.961948i −0.876735 0.480974i \(-0.840283\pi\)
0.876735 0.480974i \(-0.159717\pi\)
\(642\) −21776.5 421.271i −1.33871 0.0258976i
\(643\) 23418.0 1.43626 0.718130 0.695909i \(-0.244998\pi\)
0.718130 + 0.695909i \(0.244998\pi\)
\(644\) −1081.01 −0.0661454
\(645\) 657.380 33981.6i 0.0401307 2.07445i
\(646\) 3540.24i 0.215617i
\(647\) 17281.7i 1.05010i −0.851072 0.525048i \(-0.824047\pi\)
0.851072 0.525048i \(-0.175953\pi\)
\(648\) 17653.8 + 1368.63i 1.07023 + 0.0829703i
\(649\) −13386.7 10887.9i −0.809666 0.658530i
\(650\) 25413.3i 1.53352i
\(651\) 1927.88 + 37.2952i 0.116067 + 0.00224533i
\(652\) −1392.07 −0.0836161
\(653\) 2766.26i 0.165777i 0.996559 + 0.0828884i \(0.0264145\pi\)
−0.996559 + 0.0828884i \(0.973585\pi\)
\(654\) 1525.05 + 29.5024i 0.0911837 + 0.00176397i
\(655\) 44227.2i 2.63832i
\(656\) 13258.5i 0.789114i
\(657\) −37.7959 + 976.517i −0.00224438 + 0.0579871i
\(658\) 5353.07 0.317150
\(659\) 14505.0 0.857412 0.428706 0.903444i \(-0.358970\pi\)
0.428706 + 0.903444i \(0.358970\pi\)
\(660\) −5688.03 110.036i −0.335464 0.00648961i
\(661\) 2069.11 0.121754 0.0608769 0.998145i \(-0.480610\pi\)
0.0608769 + 0.998145i \(0.480610\pi\)
\(662\) −19683.7 −1.15563
\(663\) −158.144 + 8174.84i −0.00926365 + 0.478860i
\(664\) −33437.5 −1.95426
\(665\) 4012.61i 0.233989i
\(666\) 403.359 10421.4i 0.0234682 0.606338i
\(667\) 1720.96i 0.0999037i
\(668\) 6166.15i 0.357149i
\(669\) 212.104 10964.2i 0.0122577 0.633631i
\(670\) −20040.9 −1.15560
\(671\) 9565.24i 0.550316i
\(672\) 35.2719 1823.29i 0.00202476 0.104665i
\(673\) 19658.6i 1.12598i −0.826465 0.562988i \(-0.809652\pi\)
0.826465 0.562988i \(-0.190348\pi\)
\(674\) 1536.34i 0.0878004i
\(675\) 1596.13 27475.1i 0.0910148 1.56669i
\(676\) 685.464 0.0390000
\(677\) 6768.57i 0.384250i −0.981370 0.192125i \(-0.938462\pi\)
0.981370 0.192125i \(-0.0615379\pi\)
\(678\) −263.939 + 13643.6i −0.0149506 + 0.772834i
\(679\) 8289.60i 0.468521i
\(680\) 13370.8 0.754040
\(681\) 264.636 13679.7i 0.0148912 0.769760i
\(682\) 7273.05i 0.408357i
\(683\) −27264.9 −1.52747 −0.763734 0.645531i \(-0.776636\pi\)
−0.763734 + 0.645531i \(0.776636\pi\)
\(684\) −1972.89 76.3606i −0.110286 0.00426860i
\(685\) −11713.1 −0.653332
\(686\) −8223.36 −0.457681
\(687\) −4216.76 81.5741i −0.234177 0.00453020i
\(688\) 17734.4i 0.982730i
\(689\) −33835.3 −1.87086
\(690\) 32287.6 + 624.611i 1.78141 + 0.0344616i
\(691\) 5793.00i 0.318923i 0.987204 + 0.159462i \(0.0509758\pi\)
−0.987204 + 0.159462i \(0.949024\pi\)
\(692\) −3867.09 −0.212435
\(693\) 5046.98 + 195.343i 0.276650 + 0.0107077i
\(694\) −20749.6 −1.13494
\(695\) 12662.5i 0.691101i
\(696\) −1583.61 30.6353i −0.0862453 0.00166843i
\(697\) −8381.76 −0.455498
\(698\) 30977.7i 1.67983i
\(699\) −464.655 + 24019.2i −0.0251429 + 1.29970i
\(700\) −1546.39 −0.0834974
\(701\) 1161.05 0.0625565 0.0312783 0.999511i \(-0.490042\pi\)
0.0312783 + 0.999511i \(0.490042\pi\)
\(702\) −18144.7 1054.09i −0.975536 0.0566724i
\(703\) 6960.93i 0.373452i
\(704\) 21679.0 1.16059
\(705\) 40113.2 + 775.998i 2.14291 + 0.0414550i
\(706\) −26670.0 −1.42173
\(707\) −4501.66 −0.239466
\(708\) 2440.36 2884.61i 0.129540 0.153122i
\(709\) 2589.53 0.137167 0.0685837 0.997645i \(-0.478152\pi\)
0.0685837 + 0.997645i \(0.478152\pi\)
\(710\) 28974.1 1.53152
\(711\) 13109.5 + 507.403i 0.691485 + 0.0267638i
\(712\) 30378.3 1.59898
\(713\) 10357.8i 0.544043i
\(714\) −1982.72 38.3561i −0.103924 0.00201042i
\(715\) 34955.2 1.82832
\(716\) −1972.49 −0.102954
\(717\) −21337.9 412.785i −1.11141 0.0215003i
\(718\) 11926.1i 0.619888i
\(719\) −25261.8 −1.31030 −0.655152 0.755497i \(-0.727395\pi\)
−0.655152 + 0.755497i \(0.727395\pi\)
\(720\) −909.305 + 23493.3i −0.0470664 + 1.21603i
\(721\) 877.125i 0.0453063i
\(722\) 12093.4 0.623364
\(723\) −137.637 + 7114.77i −0.00707989 + 0.365977i
\(724\) 4097.33 0.210326
\(725\) 2461.85i 0.126112i
\(726\) −30.1826 + 1560.21i −0.00154295 + 0.0797587i
\(727\) −6751.37 −0.344422 −0.172211 0.985060i \(-0.555091\pi\)
−0.172211 + 0.985060i \(0.555091\pi\)
\(728\) 6113.03i 0.311214i
\(729\) −19550.6 2279.22i −0.993273 0.115796i
\(730\) −1640.37 −0.0831684
\(731\) −11211.3 −0.567258
\(732\) −2094.10 40.5108i −0.105738 0.00204552i
\(733\) 5684.58 0.286446 0.143223 0.989690i \(-0.454253\pi\)
0.143223 + 0.989690i \(0.454253\pi\)
\(734\) 8446.31i 0.424740i
\(735\) −29687.2 574.305i −1.48984 0.0288212i
\(736\) 9795.88 0.490599
\(737\) 16837.0i 0.841516i
\(738\) 720.603 18617.9i 0.0359428 0.928637i
\(739\) 22799.0i 1.13488i −0.823416 0.567438i \(-0.807935\pi\)
0.823416 0.567438i \(-0.192065\pi\)
\(740\) −4392.03 −0.218181
\(741\) 12128.7 + 234.633i 0.601296 + 0.0116322i
\(742\) 8206.39i 0.406019i
\(743\) 4680.60i 0.231110i −0.993301 0.115555i \(-0.963135\pi\)
0.993301 0.115555i \(-0.0368646\pi\)
\(744\) −9531.17 184.382i −0.469664 0.00908573i
\(745\) 19955.5i 0.981361i
\(746\) −21862.4 −1.07297
\(747\) 37141.5 + 1437.56i 1.81919 + 0.0704117i
\(748\) 1876.62i 0.0917325i
\(749\) 8143.24i 0.397260i
\(750\) 16756.4 + 324.156i 0.815809 + 0.0157820i
\(751\) 24749.5i 1.20256i −0.799039 0.601279i \(-0.794658\pi\)
0.799039 0.601279i \(-0.205342\pi\)
\(752\) −20934.4 −1.01516
\(753\) 3019.28 + 58.4086i 0.146121 + 0.00282673i
\(754\) 1625.81 0.0785261
\(755\) 20346.8 0.980790
\(756\) −64.1411 + 1104.10i −0.00308570 + 0.0531160i
\(757\) 24788.0 1.19014 0.595069 0.803675i \(-0.297125\pi\)
0.595069 + 0.803675i \(0.297125\pi\)
\(758\) 26564.3 1.27290
\(759\) −524.753 + 27125.8i −0.0250953 + 1.29724i
\(760\) 19837.8i 0.946834i
\(761\) 21981.9i 1.04710i 0.851995 + 0.523549i \(0.175392\pi\)
−0.851995 + 0.523549i \(0.824608\pi\)
\(762\) −308.401 + 15942.0i −0.0146616 + 0.757896i
\(763\) 570.286i 0.0270586i
\(764\) 4953.06 0.234549
\(765\) −14852.0 574.843i −0.701927 0.0271680i
\(766\) 9345.12i 0.440800i
\(767\) −14648.5 + 18010.5i −0.689606 + 0.847875i
\(768\) −237.063 + 12254.4i −0.0111384 + 0.575769i
\(769\) 33444.5i 1.56832i −0.620556 0.784162i \(-0.713093\pi\)
0.620556 0.784162i \(-0.286907\pi\)
\(770\) 8478.01i 0.396787i
\(771\) −7099.09 137.333i −0.331605 0.00641497i
\(772\) 7039.26 0.328172
\(773\) 25499.6 1.18649 0.593246 0.805021i \(-0.297846\pi\)
0.593246 + 0.805021i \(0.297846\pi\)
\(774\) 963.868 24903.0i 0.0447617 1.15649i
\(775\) 14817.0i 0.686762i
\(776\) 40982.7i 1.89587i
\(777\) 3898.50 + 75.4171i 0.179997 + 0.00348208i
\(778\) 31969.1i 1.47320i
\(779\) 12435.8i 0.571960i
\(780\) −148.043 + 7652.68i −0.00679586 + 0.351295i
\(781\) 24342.0i 1.11527i
\(782\) 10652.5i 0.487124i
\(783\) 1757.72 + 102.112i 0.0802246 + 0.00466053i
\(784\)