Properties

Label 177.5.b.a.119.7
Level $177$
Weight $5$
Character 177.119
Analytic conductor $18.296$
Analytic rank $0$
Dimension $78$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 177.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.2964834658\)
Analytic rank: \(0\)
Dimension: \(78\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 119.7
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.72

$q$-expansion

\(f(q)\) \(=\) \(q-6.87418i q^{2} +(8.98827 + 0.459381i) q^{3} -31.2543 q^{4} +23.0718i q^{5} +(3.15787 - 61.7870i) q^{6} +23.0938 q^{7} +104.861i q^{8} +(80.5779 + 8.25808i) q^{9} +O(q^{10})\) \(q-6.87418i q^{2} +(8.98827 + 0.459381i) q^{3} -31.2543 q^{4} +23.0718i q^{5} +(3.15787 - 61.7870i) q^{6} +23.0938 q^{7} +104.861i q^{8} +(80.5779 + 8.25808i) q^{9} +158.600 q^{10} +26.5708i q^{11} +(-280.922 - 14.3576i) q^{12} +309.103 q^{13} -158.751i q^{14} +(-10.5987 + 207.375i) q^{15} +220.764 q^{16} +148.246i q^{17} +(56.7675 - 553.907i) q^{18} +30.3588 q^{19} -721.093i q^{20} +(207.573 + 10.6089i) q^{21} +182.653 q^{22} -899.995i q^{23} +(-48.1712 + 942.519i) q^{24} +92.6930 q^{25} -2124.83i q^{26} +(720.463 + 111.242i) q^{27} -721.782 q^{28} -161.427i q^{29} +(1425.54 + 72.8576i) q^{30} -275.870 q^{31} +160.205i q^{32} +(-12.2061 + 238.826i) q^{33} +1019.07 q^{34} +532.816i q^{35} +(-2518.41 - 258.101i) q^{36} +1786.76 q^{37} -208.692i q^{38} +(2778.30 + 141.996i) q^{39} -2419.33 q^{40} +1895.31i q^{41} +(72.9272 - 1426.90i) q^{42} -1301.72 q^{43} -830.454i q^{44} +(-190.529 + 1859.08i) q^{45} -6186.73 q^{46} -2728.57i q^{47} +(1984.29 + 101.415i) q^{48} -1867.68 q^{49} -637.188i q^{50} +(-68.1013 + 1332.47i) q^{51} -9660.81 q^{52} +1992.52i q^{53} +(764.696 - 4952.59i) q^{54} -613.037 q^{55} +2421.64i q^{56} +(272.873 + 13.9462i) q^{57} -1109.68 q^{58} +453.188i q^{59} +(331.257 - 6481.38i) q^{60} +4427.43 q^{61} +1896.38i q^{62} +(1860.85 + 190.711i) q^{63} +4633.50 q^{64} +7131.56i q^{65} +(1641.73 + 83.9072i) q^{66} -3928.08 q^{67} -4633.32i q^{68} +(413.441 - 8089.40i) q^{69} +3662.67 q^{70} -526.218i q^{71} +(-865.951 + 8449.48i) q^{72} -3454.42 q^{73} -12282.5i q^{74} +(833.149 + 42.5814i) q^{75} -948.843 q^{76} +613.622i q^{77} +(976.106 - 19098.5i) q^{78} +738.873 q^{79} +5093.42i q^{80} +(6424.61 + 1330.84i) q^{81} +13028.7 q^{82} +3710.55i q^{83} +(-6487.57 - 331.573i) q^{84} -3420.29 q^{85} +8948.25i q^{86} +(74.1566 - 1450.95i) q^{87} -2786.25 q^{88} -7525.97i q^{89} +(12779.6 + 1309.73i) q^{90} +7138.37 q^{91} +28128.7i q^{92} +(-2479.59 - 126.729i) q^{93} -18756.7 q^{94} +700.431i q^{95} +(-73.5952 + 1439.97i) q^{96} +607.333 q^{97} +12838.7i q^{98} +(-219.424 + 2141.02i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} + O(q^{10}) \) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} - 156q^{10} - 4q^{13} + 13q^{15} + 4948q^{16} + 22q^{18} + 812q^{19} - 173q^{21} - 1644q^{22} - 678q^{24} - 8238q^{25} + 777q^{27} - 3764q^{28} + 1374q^{30} + 4664q^{31} - 1042q^{33} + 3244q^{34} + 3648q^{36} - 3960q^{37} - 7078q^{39} - 1576q^{40} + 4934q^{42} - 1492q^{43} - 2063q^{45} - 2036q^{46} - 2620q^{48} + 24274q^{49} + 7300q^{51} + 8408q^{52} - 14766q^{54} + 9780q^{55} + 6939q^{57} - 3856q^{58} + 4712q^{60} - 212q^{61} - 7438q^{63} - 45760q^{64} + 3048q^{66} - 12972q^{67} + 21672q^{69} + 5828q^{70} - 866q^{72} - 5240q^{73} - 20922q^{75} + 12368q^{76} - 16508q^{78} - 14976q^{79} + 25524q^{81} - 14484q^{82} + 9540q^{84} + 11572q^{85} + 5695q^{87} + 62160q^{88} - 31672q^{90} + 8284q^{91} - 9590q^{93} - 10992q^{94} + 34102q^{96} - 55000q^{97} - 14254q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.87418i 1.71854i −0.511518 0.859272i \(-0.670917\pi\)
0.511518 0.859272i \(-0.329083\pi\)
\(3\) 8.98827 + 0.459381i 0.998696 + 0.0510423i
\(4\) −31.2543 −1.95340
\(5\) 23.0718i 0.922871i 0.887174 + 0.461436i \(0.152665\pi\)
−0.887174 + 0.461436i \(0.847335\pi\)
\(6\) 3.15787 61.7870i 0.0877185 1.71630i
\(7\) 23.0938 0.471303 0.235651 0.971838i \(-0.424278\pi\)
0.235651 + 0.971838i \(0.424278\pi\)
\(8\) 104.861i 1.63845i
\(9\) 80.5779 + 8.25808i 0.994789 + 0.101952i
\(10\) 158.600 1.58600
\(11\) 26.5708i 0.219594i 0.993954 + 0.109797i \(0.0350200\pi\)
−0.993954 + 0.109797i \(0.964980\pi\)
\(12\) −280.922 14.3576i −1.95085 0.0997059i
\(13\) 309.103 1.82901 0.914506 0.404572i \(-0.132580\pi\)
0.914506 + 0.404572i \(0.132580\pi\)
\(14\) 158.751i 0.809954i
\(15\) −10.5987 + 207.375i −0.0471055 + 0.921668i
\(16\) 220.764 0.862359
\(17\) 148.246i 0.512961i 0.966549 + 0.256480i \(0.0825629\pi\)
−0.966549 + 0.256480i \(0.917437\pi\)
\(18\) 56.7675 553.907i 0.175208 1.70959i
\(19\) 30.3588 0.0840963 0.0420482 0.999116i \(-0.486612\pi\)
0.0420482 + 0.999116i \(0.486612\pi\)
\(20\) 721.093i 1.80273i
\(21\) 207.573 + 10.6089i 0.470688 + 0.0240564i
\(22\) 182.653 0.377382
\(23\) 899.995i 1.70131i −0.525721 0.850657i \(-0.676204\pi\)
0.525721 0.850657i \(-0.323796\pi\)
\(24\) −48.1712 + 942.519i −0.0836305 + 1.63632i
\(25\) 92.6930 0.148309
\(26\) 2124.83i 3.14324i
\(27\) 720.463 + 111.242i 0.988289 + 0.152595i
\(28\) −721.782 −0.920640
\(29\) 161.427i 0.191947i −0.995384 0.0959734i \(-0.969404\pi\)
0.995384 0.0959734i \(-0.0305964\pi\)
\(30\) 1425.54 + 72.8576i 1.58393 + 0.0809529i
\(31\) −275.870 −0.287065 −0.143533 0.989646i \(-0.545846\pi\)
−0.143533 + 0.989646i \(0.545846\pi\)
\(32\) 160.205i 0.156450i
\(33\) −12.2061 + 238.826i −0.0112086 + 0.219308i
\(34\) 1019.07 0.881546
\(35\) 532.816i 0.434952i
\(36\) −2518.41 258.101i −1.94322 0.199152i
\(37\) 1786.76 1.30516 0.652579 0.757721i \(-0.273687\pi\)
0.652579 + 0.757721i \(0.273687\pi\)
\(38\) 208.692i 0.144523i
\(39\) 2778.30 + 141.996i 1.82663 + 0.0933570i
\(40\) −2419.33 −1.51208
\(41\) 1895.31i 1.12749i 0.825950 + 0.563744i \(0.190639\pi\)
−0.825950 + 0.563744i \(0.809361\pi\)
\(42\) 72.9272 1426.90i 0.0413420 0.808899i
\(43\) −1301.72 −0.704012 −0.352006 0.935998i \(-0.614500\pi\)
−0.352006 + 0.935998i \(0.614500\pi\)
\(44\) 830.454i 0.428954i
\(45\) −190.529 + 1859.08i −0.0940882 + 0.918062i
\(46\) −6186.73 −2.92378
\(47\) 2728.57i 1.23520i −0.786490 0.617602i \(-0.788104\pi\)
0.786490 0.617602i \(-0.211896\pi\)
\(48\) 1984.29 + 101.415i 0.861235 + 0.0440168i
\(49\) −1867.68 −0.777874
\(50\) 637.188i 0.254875i
\(51\) −68.1013 + 1332.47i −0.0261827 + 0.512292i
\(52\) −9660.81 −3.57278
\(53\) 1992.52i 0.709333i 0.934993 + 0.354667i \(0.115406\pi\)
−0.934993 + 0.354667i \(0.884594\pi\)
\(54\) 764.696 4952.59i 0.262241 1.69842i
\(55\) −613.037 −0.202657
\(56\) 2421.64i 0.772207i
\(57\) 272.873 + 13.9462i 0.0839867 + 0.00429247i
\(58\) −1109.68 −0.329869
\(59\) 453.188i 0.130189i
\(60\) 331.257 6481.38i 0.0920157 1.80038i
\(61\) 4427.43 1.18985 0.594924 0.803782i \(-0.297182\pi\)
0.594924 + 0.803782i \(0.297182\pi\)
\(62\) 1896.38i 0.493334i
\(63\) 1860.85 + 190.711i 0.468847 + 0.0480501i
\(64\) 4633.50 1.13123
\(65\) 7131.56i 1.68794i
\(66\) 1641.73 + 83.9072i 0.376890 + 0.0192624i
\(67\) −3928.08 −0.875046 −0.437523 0.899207i \(-0.644144\pi\)
−0.437523 + 0.899207i \(0.644144\pi\)
\(68\) 4633.32i 1.00202i
\(69\) 413.441 8089.40i 0.0868391 1.69910i
\(70\) 3662.67 0.747484
\(71\) 526.218i 0.104388i −0.998637 0.0521938i \(-0.983379\pi\)
0.998637 0.0521938i \(-0.0166213\pi\)
\(72\) −865.951 + 8449.48i −0.167043 + 1.62992i
\(73\) −3454.42 −0.648231 −0.324115 0.946018i \(-0.605067\pi\)
−0.324115 + 0.946018i \(0.605067\pi\)
\(74\) 12282.5i 2.24297i
\(75\) 833.149 + 42.5814i 0.148115 + 0.00757003i
\(76\) −948.843 −0.164273
\(77\) 613.622i 0.103495i
\(78\) 976.106 19098.5i 0.160438 3.13914i
\(79\) 738.873 0.118390 0.0591951 0.998246i \(-0.481147\pi\)
0.0591951 + 0.998246i \(0.481147\pi\)
\(80\) 5093.42i 0.795846i
\(81\) 6424.61 + 1330.84i 0.979212 + 0.202841i
\(82\) 13028.7 1.93764
\(83\) 3710.55i 0.538619i 0.963054 + 0.269310i \(0.0867955\pi\)
−0.963054 + 0.269310i \(0.913204\pi\)
\(84\) −6487.57 331.573i −0.919440 0.0469916i
\(85\) −3420.29 −0.473397
\(86\) 8948.25i 1.20988i
\(87\) 74.1566 1450.95i 0.00979741 0.191697i
\(88\) −2786.25 −0.359794
\(89\) 7525.97i 0.950129i −0.879951 0.475064i \(-0.842425\pi\)
0.879951 0.475064i \(-0.157575\pi\)
\(90\) 12779.6 + 1309.73i 1.57773 + 0.161695i
\(91\) 7138.37 0.862018
\(92\) 28128.7i 3.32334i
\(93\) −2479.59 126.729i −0.286691 0.0146525i
\(94\) −18756.7 −2.12275
\(95\) 700.431i 0.0776101i
\(96\) −73.5952 + 1439.97i −0.00798559 + 0.156246i
\(97\) 607.333 0.0645481 0.0322740 0.999479i \(-0.489725\pi\)
0.0322740 + 0.999479i \(0.489725\pi\)
\(98\) 12838.7i 1.33681i
\(99\) −219.424 + 2141.02i −0.0223879 + 0.218450i
\(100\) −2897.06 −0.289706
\(101\) 11870.0i 1.16361i 0.813327 + 0.581807i \(0.197654\pi\)
−0.813327 + 0.581807i \(0.802346\pi\)
\(102\) 9159.65 + 468.140i 0.880397 + 0.0449962i
\(103\) −11295.9 −1.06475 −0.532375 0.846509i \(-0.678700\pi\)
−0.532375 + 0.846509i \(0.678700\pi\)
\(104\) 32412.9i 2.99675i
\(105\) −244.765 + 4789.09i −0.0222009 + 0.434385i
\(106\) 13696.9 1.21902
\(107\) 14375.5i 1.25561i 0.778369 + 0.627807i \(0.216047\pi\)
−0.778369 + 0.627807i \(0.783953\pi\)
\(108\) −22517.6 3476.79i −1.93052 0.298079i
\(109\) 14936.2 1.25715 0.628573 0.777750i \(-0.283639\pi\)
0.628573 + 0.777750i \(0.283639\pi\)
\(110\) 4214.12i 0.348275i
\(111\) 16059.9 + 820.804i 1.30346 + 0.0666183i
\(112\) 5098.28 0.406432
\(113\) 20530.9i 1.60787i −0.594718 0.803935i \(-0.702736\pi\)
0.594718 0.803935i \(-0.297264\pi\)
\(114\) 95.8690 1875.78i 0.00737681 0.144335i
\(115\) 20764.5 1.57009
\(116\) 5045.30i 0.374948i
\(117\) 24906.9 + 2552.60i 1.81948 + 0.186471i
\(118\) 3115.29 0.223735
\(119\) 3423.56i 0.241760i
\(120\) −21745.6 1111.39i −1.51011 0.0771802i
\(121\) 13935.0 0.951779
\(122\) 30434.9i 2.04481i
\(123\) −870.668 + 17035.5i −0.0575496 + 1.12602i
\(124\) 8622.12 0.560752
\(125\) 16558.5i 1.05974i
\(126\) 1310.98 12791.8i 0.0825762 0.805734i
\(127\) −23339.4 −1.44705 −0.723523 0.690300i \(-0.757478\pi\)
−0.723523 + 0.690300i \(0.757478\pi\)
\(128\) 29288.2i 1.78761i
\(129\) −11700.2 597.985i −0.703095 0.0359344i
\(130\) 49023.6 2.90080
\(131\) 1138.83i 0.0663614i −0.999449 0.0331807i \(-0.989436\pi\)
0.999449 0.0331807i \(-0.0105637\pi\)
\(132\) 381.495 7464.34i 0.0218948 0.428394i
\(133\) 701.100 0.0396348
\(134\) 27002.3i 1.50381i
\(135\) −2566.55 + 16622.4i −0.140826 + 0.912063i
\(136\) −15545.2 −0.840462
\(137\) 27914.4i 1.48726i −0.668591 0.743630i \(-0.733102\pi\)
0.668591 0.743630i \(-0.266898\pi\)
\(138\) −55608.0 2842.07i −2.91997 0.149237i
\(139\) −27635.8 −1.43035 −0.715175 0.698946i \(-0.753653\pi\)
−0.715175 + 0.698946i \(0.753653\pi\)
\(140\) 16652.8i 0.849632i
\(141\) 1253.45 24525.1i 0.0630477 1.23359i
\(142\) −3617.31 −0.179395
\(143\) 8213.13i 0.401640i
\(144\) 17788.7 + 1823.09i 0.857866 + 0.0879189i
\(145\) 3724.41 0.177142
\(146\) 23746.3i 1.11401i
\(147\) −16787.2 857.975i −0.776860 0.0397045i
\(148\) −55844.0 −2.54949
\(149\) 9243.56i 0.416358i −0.978091 0.208179i \(-0.933246\pi\)
0.978091 0.208179i \(-0.0667536\pi\)
\(150\) 292.712 5727.22i 0.0130094 0.254543i
\(151\) 5292.22 0.232105 0.116052 0.993243i \(-0.462976\pi\)
0.116052 + 0.993243i \(0.462976\pi\)
\(152\) 3183.45i 0.137788i
\(153\) −1224.22 + 11945.3i −0.0522972 + 0.510288i
\(154\) 4218.15 0.177861
\(155\) 6364.80i 0.264924i
\(156\) −86833.9 4437.99i −3.56813 0.182363i
\(157\) −26208.0 −1.06325 −0.531624 0.846981i \(-0.678418\pi\)
−0.531624 + 0.846981i \(0.678418\pi\)
\(158\) 5079.15i 0.203459i
\(159\) −915.325 + 17909.3i −0.0362060 + 0.708409i
\(160\) −3696.22 −0.144384
\(161\) 20784.3i 0.801834i
\(162\) 9148.42 44163.9i 0.348591 1.68282i
\(163\) −30024.1 −1.13004 −0.565021 0.825077i \(-0.691132\pi\)
−0.565021 + 0.825077i \(0.691132\pi\)
\(164\) 59236.5i 2.20243i
\(165\) −5510.14 281.617i −0.202393 0.0103441i
\(166\) 25507.0 0.925641
\(167\) 17501.5i 0.627541i −0.949499 0.313771i \(-0.898408\pi\)
0.949499 0.313771i \(-0.101592\pi\)
\(168\) −1112.46 + 21766.4i −0.0394153 + 0.771201i
\(169\) 66983.7 2.34528
\(170\) 23511.7i 0.813554i
\(171\) 2446.25 + 250.705i 0.0836582 + 0.00857376i
\(172\) 40684.4 1.37521
\(173\) 18255.7i 0.609966i −0.952358 0.304983i \(-0.901349\pi\)
0.952358 0.304983i \(-0.0986509\pi\)
\(174\) −9974.10 509.766i −0.329439 0.0168373i
\(175\) 2140.63 0.0698983
\(176\) 5865.89i 0.189369i
\(177\) −208.186 + 4073.37i −0.00664515 + 0.130019i
\(178\) −51734.9 −1.63284
\(179\) 10728.6i 0.334840i −0.985886 0.167420i \(-0.946456\pi\)
0.985886 0.167420i \(-0.0535437\pi\)
\(180\) 5954.84 58104.2i 0.183792 1.79334i
\(181\) −24990.8 −0.762821 −0.381410 0.924406i \(-0.624561\pi\)
−0.381410 + 0.924406i \(0.624561\pi\)
\(182\) 49070.4i 1.48142i
\(183\) 39794.9 + 2033.88i 1.18830 + 0.0607326i
\(184\) 94374.4 2.78752
\(185\) 41223.8i 1.20449i
\(186\) −871.160 + 17045.1i −0.0251809 + 0.492691i
\(187\) −3939.01 −0.112643
\(188\) 85279.6i 2.41284i
\(189\) 16638.2 + 2569.00i 0.465783 + 0.0719185i
\(190\) 4814.89 0.133376
\(191\) 55736.7i 1.52783i 0.645317 + 0.763915i \(0.276725\pi\)
−0.645317 + 0.763915i \(0.723275\pi\)
\(192\) 41647.2 + 2128.54i 1.12975 + 0.0577404i
\(193\) −60148.8 −1.61478 −0.807389 0.590020i \(-0.799120\pi\)
−0.807389 + 0.590020i \(0.799120\pi\)
\(194\) 4174.91i 0.110929i
\(195\) −3276.10 + 64100.3i −0.0861565 + 1.68574i
\(196\) 58372.9 1.51950
\(197\) 37142.7i 0.957064i 0.878070 + 0.478532i \(0.158831\pi\)
−0.878070 + 0.478532i \(0.841169\pi\)
\(198\) 14717.8 + 1508.36i 0.375415 + 0.0384747i
\(199\) −23649.3 −0.597189 −0.298594 0.954380i \(-0.596518\pi\)
−0.298594 + 0.954380i \(0.596518\pi\)
\(200\) 9719.88i 0.242997i
\(201\) −35306.6 1804.49i −0.873905 0.0446644i
\(202\) 81596.7 1.99972
\(203\) 3727.97i 0.0904650i
\(204\) 2128.46 41645.5i 0.0511452 1.00071i
\(205\) −43728.1 −1.04053
\(206\) 77650.3i 1.82982i
\(207\) 7432.23 72519.8i 0.173452 1.69245i
\(208\) 68238.8 1.57727
\(209\) 806.659i 0.0184670i
\(210\) 32921.1 + 1682.56i 0.746509 + 0.0381533i
\(211\) 20215.3 0.454062 0.227031 0.973888i \(-0.427098\pi\)
0.227031 + 0.973888i \(0.427098\pi\)
\(212\) 62274.8i 1.38561i
\(213\) 241.734 4729.79i 0.00532818 0.104251i
\(214\) 98820.0 2.15783
\(215\) 30033.0i 0.649713i
\(216\) −11664.9 + 75548.4i −0.250020 + 1.61926i
\(217\) −6370.89 −0.135295
\(218\) 102674.i 2.16046i
\(219\) −31049.3 1586.90i −0.647386 0.0330872i
\(220\) 19160.1 0.395869
\(221\) 45823.2i 0.938211i
\(222\) 5642.36 110399.i 0.114487 2.24005i
\(223\) −59089.4 −1.18823 −0.594114 0.804381i \(-0.702497\pi\)
−0.594114 + 0.804381i \(0.702497\pi\)
\(224\) 3699.75i 0.0737355i
\(225\) 7469.01 + 765.466i 0.147536 + 0.0151203i
\(226\) −141133. −2.76320
\(227\) 18810.9i 0.365055i 0.983201 + 0.182528i \(0.0584279\pi\)
−0.983201 + 0.182528i \(0.941572\pi\)
\(228\) −8528.46 435.881i −0.164059 0.00838490i
\(229\) −88005.3 −1.67818 −0.839089 0.543994i \(-0.816911\pi\)
−0.839089 + 0.543994i \(0.816911\pi\)
\(230\) 142739.i 2.69828i
\(231\) −281.887 + 5515.40i −0.00528263 + 0.103360i
\(232\) 16927.4 0.314496
\(233\) 6710.57i 0.123608i 0.998088 + 0.0618041i \(0.0196854\pi\)
−0.998088 + 0.0618041i \(0.980315\pi\)
\(234\) 17547.0 171214.i 0.320458 3.12686i
\(235\) 62952.9 1.13993
\(236\) 14164.1i 0.254310i
\(237\) 6641.19 + 339.424i 0.118236 + 0.00604291i
\(238\) 23534.2 0.415475
\(239\) 69891.0i 1.22356i 0.791028 + 0.611780i \(0.209546\pi\)
−0.791028 + 0.611780i \(0.790454\pi\)
\(240\) −2339.82 + 45781.0i −0.0406219 + 0.794809i
\(241\) −16723.6 −0.287935 −0.143968 0.989582i \(-0.545986\pi\)
−0.143968 + 0.989582i \(0.545986\pi\)
\(242\) 95791.6i 1.63567i
\(243\) 57134.7 + 14913.3i 0.967582 + 0.252558i
\(244\) −138376. −2.32424
\(245\) 43090.6i 0.717877i
\(246\) 117105. + 5985.13i 1.93511 + 0.0989016i
\(247\) 9383.99 0.153813
\(248\) 28928.0i 0.470343i
\(249\) −1704.56 + 33351.4i −0.0274924 + 0.537917i
\(250\) 113826. 1.82121
\(251\) 106808.i 1.69534i 0.530525 + 0.847669i \(0.321995\pi\)
−0.530525 + 0.847669i \(0.678005\pi\)
\(252\) −58159.7 5960.53i −0.915843 0.0938608i
\(253\) 23913.6 0.373598
\(254\) 160439.i 2.48681i
\(255\) −30742.5 1571.22i −0.472780 0.0241633i
\(256\) −127197. −1.94087
\(257\) 99904.2i 1.51258i 0.654238 + 0.756289i \(0.272989\pi\)
−0.654238 + 0.756289i \(0.727011\pi\)
\(258\) −4110.66 + 80429.3i −0.0617549 + 1.20830i
\(259\) 41263.1 0.615124
\(260\) 222892.i 3.29722i
\(261\) 1333.08 13007.5i 0.0195693 0.190947i
\(262\) −7828.51 −0.114045
\(263\) 134698.i 1.94737i −0.227888 0.973687i \(-0.573182\pi\)
0.227888 0.973687i \(-0.426818\pi\)
\(264\) −25043.5 1279.95i −0.359325 0.0183647i
\(265\) −45970.9 −0.654623
\(266\) 4819.49i 0.0681142i
\(267\) 3457.29 67645.4i 0.0484968 0.948890i
\(268\) 122770. 1.70931
\(269\) 40912.3i 0.565391i 0.959210 + 0.282696i \(0.0912286\pi\)
−0.959210 + 0.282696i \(0.908771\pi\)
\(270\) 114265. + 17642.9i 1.56742 + 0.242015i
\(271\) −84953.4 −1.15676 −0.578378 0.815769i \(-0.696314\pi\)
−0.578378 + 0.815769i \(0.696314\pi\)
\(272\) 32727.3i 0.442356i
\(273\) 64161.6 + 3279.23i 0.860894 + 0.0439994i
\(274\) −191889. −2.55592
\(275\) 2462.93i 0.0325677i
\(276\) −12921.8 + 252829.i −0.169631 + 3.31901i
\(277\) 73776.7 0.961523 0.480761 0.876851i \(-0.340360\pi\)
0.480761 + 0.876851i \(0.340360\pi\)
\(278\) 189973.i 2.45812i
\(279\) −22229.0 2278.15i −0.285569 0.0292668i
\(280\) −55871.6 −0.712648
\(281\) 121705.i 1.54133i −0.637241 0.770665i \(-0.719924\pi\)
0.637241 0.770665i \(-0.280076\pi\)
\(282\) −168590. 8616.45i −2.11999 0.108350i
\(283\) −16658.8 −0.208004 −0.104002 0.994577i \(-0.533165\pi\)
−0.104002 + 0.994577i \(0.533165\pi\)
\(284\) 16446.6i 0.203910i
\(285\) −321.765 + 6295.66i −0.00396140 + 0.0775089i
\(286\) 56458.5 0.690236
\(287\) 43769.9i 0.531388i
\(288\) −1322.99 + 12909.0i −0.0159504 + 0.155635i
\(289\) 61544.2 0.736871
\(290\) 25602.3i 0.304427i
\(291\) 5458.87 + 278.997i 0.0644639 + 0.00329469i
\(292\) 107966. 1.26625
\(293\) 56581.4i 0.659081i −0.944142 0.329540i \(-0.893106\pi\)
0.944142 0.329540i \(-0.106894\pi\)
\(294\) −5897.87 + 115398.i −0.0682340 + 1.33507i
\(295\) −10455.8 −0.120148
\(296\) 187362.i 2.13844i
\(297\) −2955.79 + 19143.3i −0.0335089 + 0.217022i
\(298\) −63541.9 −0.715529
\(299\) 278191.i 3.11172i
\(300\) −26039.5 1330.85i −0.289328 0.0147873i
\(301\) −30061.7 −0.331803
\(302\) 36379.7i 0.398882i
\(303\) −5452.86 + 106691.i −0.0593936 + 1.16210i
\(304\) 6702.12 0.0725213
\(305\) 102149.i 1.09808i
\(306\) 82114.3 + 8415.54i 0.876953 + 0.0898750i
\(307\) −55789.7 −0.591939 −0.295970 0.955197i \(-0.595643\pi\)
−0.295970 + 0.955197i \(0.595643\pi\)
\(308\) 19178.4i 0.202167i
\(309\) −101531. 5189.14i −1.06336 0.0543473i
\(310\) −43752.8 −0.455284
\(311\) 82190.7i 0.849771i 0.905247 + 0.424885i \(0.139686\pi\)
−0.905247 + 0.424885i \(0.860314\pi\)
\(312\) −14889.9 + 291335.i −0.152961 + 2.99284i
\(313\) −99391.8 −1.01452 −0.507261 0.861792i \(-0.669342\pi\)
−0.507261 + 0.861792i \(0.669342\pi\)
\(314\) 180158.i 1.82724i
\(315\) −4400.03 + 42933.2i −0.0443440 + 0.432685i
\(316\) −23093.0 −0.231263
\(317\) 23818.1i 0.237022i −0.992953 0.118511i \(-0.962188\pi\)
0.992953 0.118511i \(-0.0378122\pi\)
\(318\) 123112. + 6292.11i 1.21743 + 0.0622217i
\(319\) 4289.26 0.0421503
\(320\) 106903.i 1.04398i
\(321\) −6603.85 + 129211.i −0.0640895 + 1.25398i
\(322\) −142875. −1.37799
\(323\) 4500.56i 0.0431381i
\(324\) −200797. 41594.5i −1.91279 0.396228i
\(325\) 28651.7 0.271258
\(326\) 206391.i 1.94203i
\(327\) 134250. + 6861.39i 1.25551 + 0.0641677i
\(328\) −198744. −1.84734
\(329\) 63013.1i 0.582155i
\(330\) −1935.89 + 37877.7i −0.0177768 + 0.347821i
\(331\) 153951. 1.40516 0.702579 0.711606i \(-0.252032\pi\)
0.702579 + 0.711606i \(0.252032\pi\)
\(332\) 115971.i 1.05214i
\(333\) 143974. + 14755.2i 1.29836 + 0.133063i
\(334\) −120308. −1.07846
\(335\) 90627.8i 0.807555i
\(336\) 45824.7 + 2342.06i 0.405902 + 0.0207452i
\(337\) 162616. 1.43187 0.715935 0.698167i \(-0.246001\pi\)
0.715935 + 0.698167i \(0.246001\pi\)
\(338\) 460458.i 4.03048i
\(339\) 9431.50 184537.i 0.0820694 1.60577i
\(340\) 106899. 0.924731
\(341\) 7330.09i 0.0630377i
\(342\) 1723.39 16815.9i 0.0147344 0.143770i
\(343\) −98580.0 −0.837916
\(344\) 136500.i 1.15349i
\(345\) 186637. + 9538.81i 1.56805 + 0.0801413i
\(346\) −125493. −1.04825
\(347\) 38712.6i 0.321509i −0.986994 0.160754i \(-0.948607\pi\)
0.986994 0.160754i \(-0.0513927\pi\)
\(348\) −2317.71 + 45348.5i −0.0191382 + 0.374459i
\(349\) −132581. −1.08851 −0.544254 0.838920i \(-0.683187\pi\)
−0.544254 + 0.838920i \(0.683187\pi\)
\(350\) 14715.1i 0.120123i
\(351\) 222697. + 34385.2i 1.80759 + 0.279098i
\(352\) −4256.79 −0.0343555
\(353\) 93039.8i 0.746654i −0.927700 0.373327i \(-0.878217\pi\)
0.927700 0.373327i \(-0.121783\pi\)
\(354\) 28001.1 + 1431.11i 0.223444 + 0.0114200i
\(355\) 12140.8 0.0963363
\(356\) 235219.i 1.85598i
\(357\) −1572.72 + 30771.9i −0.0123400 + 0.241445i
\(358\) −73750.5 −0.575438
\(359\) 222462.i 1.72611i −0.505114 0.863053i \(-0.668550\pi\)
0.505114 0.863053i \(-0.331450\pi\)
\(360\) −194945. 19979.0i −1.50420 0.154159i
\(361\) −129399. −0.992928
\(362\) 171791.i 1.31094i
\(363\) 125251. + 6401.47i 0.950538 + 0.0485810i
\(364\) −223105. −1.68386
\(365\) 79699.6i 0.598233i
\(366\) 13981.2 273557.i 0.104372 2.04214i
\(367\) −103258. −0.766637 −0.383319 0.923616i \(-0.625219\pi\)
−0.383319 + 0.923616i \(0.625219\pi\)
\(368\) 198686.i 1.46714i
\(369\) −15651.6 + 152720.i −0.114949 + 1.12161i
\(370\) 283379. 2.06997
\(371\) 46014.8i 0.334311i
\(372\) 77498.0 + 3960.84i 0.560021 + 0.0286221i
\(373\) 139399. 1.00194 0.500972 0.865464i \(-0.332976\pi\)
0.500972 + 0.865464i \(0.332976\pi\)
\(374\) 27077.5i 0.193582i
\(375\) −7606.64 + 148832.i −0.0540917 + 1.05836i
\(376\) 286120. 2.02383
\(377\) 49897.6i 0.351073i
\(378\) 17659.8 114374.i 0.123595 0.800469i
\(379\) 54321.9 0.378178 0.189089 0.981960i \(-0.439447\pi\)
0.189089 + 0.981960i \(0.439447\pi\)
\(380\) 21891.5i 0.151603i
\(381\) −209781. 10721.7i −1.44516 0.0738606i
\(382\) 383144. 2.62564
\(383\) 35259.1i 0.240366i −0.992752 0.120183i \(-0.961652\pi\)
0.992752 0.120183i \(-0.0383482\pi\)
\(384\) 13454.5 263251.i 0.0912439 1.78528i
\(385\) −14157.4 −0.0955126
\(386\) 413474.i 2.77507i
\(387\) −104890. 10749.7i −0.700344 0.0717752i
\(388\) −18981.8 −0.126088
\(389\) 6941.86i 0.0458751i −0.999737 0.0229375i \(-0.992698\pi\)
0.999737 0.0229375i \(-0.00730189\pi\)
\(390\) 440637. + 22520.5i 2.89702 + 0.148064i
\(391\) 133420. 0.872708
\(392\) 195846.i 1.27451i
\(393\) 523.156 10236.1i 0.00338724 0.0662749i
\(394\) 255325. 1.64476
\(395\) 17047.1i 0.109259i
\(396\) 6857.96 66916.3i 0.0437325 0.426718i
\(397\) 187412. 1.18909 0.594546 0.804061i \(-0.297332\pi\)
0.594546 + 0.804061i \(0.297332\pi\)
\(398\) 162569.i 1.02630i
\(399\) 6301.68 + 322.072i 0.0395832 + 0.00202305i
\(400\) 20463.3 0.127895
\(401\) 235928.i 1.46721i −0.679578 0.733604i \(-0.737837\pi\)
0.679578 0.733604i \(-0.262163\pi\)
\(402\) −12404.4 + 242704.i −0.0767578 + 1.50185i
\(403\) −85272.1 −0.525046
\(404\) 370990.i 2.27300i
\(405\) −30704.8 + 148227.i −0.187196 + 0.903686i
\(406\) −25626.7 −0.155468
\(407\) 47475.8i 0.286605i
\(408\) −139724. 7141.17i −0.839367 0.0428992i
\(409\) 106205. 0.634890 0.317445 0.948277i \(-0.397175\pi\)
0.317445 + 0.948277i \(0.397175\pi\)
\(410\) 300595.i 1.78819i
\(411\) 12823.3 250902.i 0.0759133 1.48532i
\(412\) 353047. 2.07988
\(413\) 10465.8i 0.0613584i
\(414\) −498514. 51090.5i −2.90855 0.298085i
\(415\) −85609.0 −0.497076
\(416\) 49519.9i 0.286150i
\(417\) −248398. 12695.4i −1.42849 0.0730084i
\(418\) 5545.11 0.0317364
\(419\) 180870.i 1.03024i 0.857118 + 0.515120i \(0.172253\pi\)
−0.857118 + 0.515120i \(0.827747\pi\)
\(420\) 7649.98 149680.i 0.0433672 0.848525i
\(421\) 14021.8 0.0791117 0.0395558 0.999217i \(-0.487406\pi\)
0.0395558 + 0.999217i \(0.487406\pi\)
\(422\) 138964.i 0.780326i
\(423\) 22532.7 219862.i 0.125931 1.22877i
\(424\) −208937. −1.16221
\(425\) 13741.3i 0.0760766i
\(426\) −32513.4 1661.73i −0.179161 0.00915672i
\(427\) 102246. 0.560779
\(428\) 449298.i 2.45271i
\(429\) −3772.96 + 73821.8i −0.0205006 + 0.401116i
\(430\) −206452. −1.11656
\(431\) 74917.2i 0.403299i −0.979458 0.201649i \(-0.935370\pi\)
0.979458 0.201649i \(-0.0646301\pi\)
\(432\) 159052. + 24558.2i 0.852260 + 0.131592i
\(433\) −76413.8 −0.407564 −0.203782 0.979016i \(-0.565323\pi\)
−0.203782 + 0.979016i \(0.565323\pi\)
\(434\) 43794.6i 0.232510i
\(435\) 33476.0 + 1710.92i 0.176911 + 0.00904175i
\(436\) −466820. −2.45570
\(437\) 27322.8i 0.143074i
\(438\) −10908.6 + 213438.i −0.0568618 + 1.11256i
\(439\) 207056. 1.07438 0.537191 0.843460i \(-0.319485\pi\)
0.537191 + 0.843460i \(0.319485\pi\)
\(440\) 64283.6i 0.332044i
\(441\) −150493. 15423.4i −0.773821 0.0793055i
\(442\) 314997. 1.61236
\(443\) 383130.i 1.95226i −0.217179 0.976132i \(-0.569686\pi\)
0.217179 0.976132i \(-0.430314\pi\)
\(444\) −501941. 25653.7i −2.54617 0.130132i
\(445\) 173638. 0.876846
\(446\) 406191.i 2.04202i
\(447\) 4246.31 83083.6i 0.0212519 0.415815i
\(448\) 107005. 0.533150
\(449\) 125237.i 0.621214i −0.950538 0.310607i \(-0.899468\pi\)
0.950538 0.310607i \(-0.100532\pi\)
\(450\) 5261.95 51343.3i 0.0259849 0.253547i
\(451\) −50359.9 −0.247589
\(452\) 641679.i 3.14081i
\(453\) 47567.9 + 2431.14i 0.231802 + 0.0118472i
\(454\) 129310. 0.627364
\(455\) 164695.i 0.795531i
\(456\) −1462.42 + 28613.7i −0.00703302 + 0.137608i
\(457\) 18503.6 0.0885982 0.0442991 0.999018i \(-0.485895\pi\)
0.0442991 + 0.999018i \(0.485895\pi\)
\(458\) 604964.i 2.88402i
\(459\) −16491.1 + 106805.i −0.0782753 + 0.506953i
\(460\) −648980. −3.06701
\(461\) 134584.i 0.633272i 0.948547 + 0.316636i \(0.102553\pi\)
−0.948547 + 0.316636i \(0.897447\pi\)
\(462\) 37913.9 + 1937.74i 0.177629 + 0.00907844i
\(463\) −207903. −0.969838 −0.484919 0.874559i \(-0.661151\pi\)
−0.484919 + 0.874559i \(0.661151\pi\)
\(464\) 35637.3i 0.165527i
\(465\) 2923.87 57208.6i 0.0135224 0.264579i
\(466\) 46129.7 0.212426
\(467\) 297233.i 1.36290i −0.731865 0.681449i \(-0.761350\pi\)
0.731865 0.681449i \(-0.238650\pi\)
\(468\) −778448. 79779.7i −3.55417 0.364251i
\(469\) −90714.4 −0.412411
\(470\) 432750.i 1.95903i
\(471\) −235564. 12039.5i −1.06186 0.0542707i
\(472\) −47521.7 −0.213308
\(473\) 34587.8i 0.154597i
\(474\) 2333.26 45652.7i 0.0103850 0.203194i
\(475\) 2814.05 0.0124722
\(476\) 107001.i 0.472252i
\(477\) −16454.4 + 160553.i −0.0723177 + 0.705637i
\(478\) 480443. 2.10274
\(479\) 74164.6i 0.323240i 0.986853 + 0.161620i \(0.0516719\pi\)
−0.986853 + 0.161620i \(0.948328\pi\)
\(480\) −33222.6 1697.97i −0.144195 0.00736967i
\(481\) 552293. 2.38715
\(482\) 114961.i 0.494830i
\(483\) 9547.93 186815.i 0.0409275 0.800788i
\(484\) −435529. −1.85920
\(485\) 14012.3i 0.0595696i
\(486\) 102517. 392754.i 0.434032 1.66283i
\(487\) −5375.18 −0.0226639 −0.0113320 0.999936i \(-0.503607\pi\)
−0.0113320 + 0.999936i \(0.503607\pi\)
\(488\) 464264.i 1.94951i
\(489\) −269864. 13792.5i −1.12857 0.0576800i
\(490\) −296212. −1.23370
\(491\) 321129.i 1.33204i −0.745934 0.666020i \(-0.767997\pi\)
0.745934 0.666020i \(-0.232003\pi\)
\(492\) 27212.1 532434.i 0.112417 2.19956i
\(493\) 23930.9 0.0984611
\(494\) 64507.2i 0.264335i
\(495\) −49397.2 5062.51i −0.201601 0.0206612i
\(496\) −60902.1 −0.247553
\(497\) 12152.4i 0.0491981i
\(498\) 229264. + 11717.4i 0.924435 + 0.0472469i
\(499\) −166114. −0.667122 −0.333561 0.942729i \(-0.608250\pi\)
−0.333561 + 0.942729i \(0.608250\pi\)
\(500\) 517523.i 2.07009i
\(501\) 8039.86 157308.i 0.0320312 0.626723i
\(502\) 734217. 2.91351
\(503\) 208387.i 0.823635i 0.911266 + 0.411817i \(0.135106\pi\)
−0.911266 + 0.411817i \(0.864894\pi\)
\(504\) −19998.1 + 195131.i −0.0787278 + 0.768183i
\(505\) −273863. −1.07387
\(506\) 164387.i 0.642045i
\(507\) 602067. + 30771.0i 2.34223 + 0.119709i
\(508\) 729457. 2.82665
\(509\) 258742.i 0.998690i 0.866403 + 0.499345i \(0.166426\pi\)
−0.866403 + 0.499345i \(0.833574\pi\)
\(510\) −10800.8 + 211329.i −0.0415257 + 0.812493i
\(511\) −79775.8 −0.305513
\(512\) 405760.i 1.54785i
\(513\) 21872.4 + 3377.17i 0.0831115 + 0.0128327i
\(514\) 686759. 2.59943
\(515\) 260617.i 0.982627i
\(516\) 365682. + 18689.6i 1.37342 + 0.0701942i
\(517\) 72500.3 0.271243
\(518\) 283650.i 1.05712i
\(519\) 8386.32 164087.i 0.0311341 0.609171i
\(520\) −747822. −2.76561
\(521\) 3325.78i 0.0122523i −0.999981 0.00612615i \(-0.998050\pi\)
0.999981 0.00612615i \(-0.00195003\pi\)
\(522\) −89415.7 9163.82i −0.328150 0.0336307i
\(523\) 152454. 0.557359 0.278680 0.960384i \(-0.410103\pi\)
0.278680 + 0.960384i \(0.410103\pi\)
\(524\) 35593.3i 0.129630i
\(525\) 19240.6 + 983.367i 0.0698072 + 0.00356777i
\(526\) −925938. −3.34665
\(527\) 40896.5i 0.147253i
\(528\) −2694.68 + 52724.1i −0.00966582 + 0.189122i
\(529\) −530150. −1.89447
\(530\) 316012.i 1.12500i
\(531\) −3742.46 + 36516.9i −0.0132730 + 0.129511i
\(532\) −21912.4 −0.0774225
\(533\) 585845.i 2.06219i
\(534\) −465007. 23766.0i −1.63071 0.0833439i
\(535\) −331669. −1.15877
\(536\) 411903.i 1.43372i
\(537\) 4928.53 96431.7i 0.0170910 0.334404i
\(538\) 281238. 0.971650
\(539\) 49625.7i 0.170816i
\(540\) 80215.7 519521.i 0.275088 1.78162i
\(541\) 12862.5 0.0439473 0.0219736 0.999759i \(-0.493005\pi\)
0.0219736 + 0.999759i \(0.493005\pi\)
\(542\) 583985.i 1.98794i
\(543\) −224624. 11480.3i −0.761826 0.0389362i
\(544\) −23749.7 −0.0802529
\(545\) 344604.i 1.16018i
\(546\) 22542.0 441058.i 0.0756150 1.47949i
\(547\) 194890. 0.651352 0.325676 0.945481i \(-0.394408\pi\)
0.325676 + 0.945481i \(0.394408\pi\)
\(548\) 872446.i 2.90521i
\(549\) 356753. + 36562.0i 1.18365 + 0.121307i
\(550\) 16930.6 0.0559690
\(551\) 4900.73i 0.0161420i
\(552\) 848262. + 43353.8i 2.78389 + 0.142282i
\(553\) 17063.4 0.0557976
\(554\) 507154.i 1.65242i
\(555\) −18937.4 + 370530.i −0.0614801 + 1.20292i
\(556\) 863738. 2.79404
\(557\) 417151.i 1.34457i 0.740293 + 0.672284i \(0.234687\pi\)
−0.740293 + 0.672284i \(0.765313\pi\)
\(558\) −15660.4 + 152806.i −0.0502962 + 0.490764i
\(559\) −402365. −1.28765
\(560\) 117626.i 0.375084i
\(561\) −35404.9 1809.51i −0.112496 0.00574956i
\(562\) −836622. −2.64884
\(563\) 595171.i 1.87770i −0.344333 0.938848i \(-0.611895\pi\)
0.344333 0.938848i \(-0.388105\pi\)
\(564\) −39175.8 + 766516.i −0.123157 + 2.40970i
\(565\) 473684. 1.48386
\(566\) 114516.i 0.357463i
\(567\) 148369. + 30734.1i 0.461505 + 0.0955994i
\(568\) 55179.7 0.171034
\(569\) 272434.i 0.841465i 0.907185 + 0.420733i \(0.138227\pi\)
−0.907185 + 0.420733i \(0.861773\pi\)
\(570\) 43277.5 + 2211.87i 0.133203 + 0.00680784i
\(571\) 136619. 0.419025 0.209512 0.977806i \(-0.432812\pi\)
0.209512 + 0.977806i \(0.432812\pi\)
\(572\) 256696.i 0.784561i
\(573\) −25604.4 + 500977.i −0.0779840 + 1.52584i
\(574\) 300882. 0.913214
\(575\) 83423.2i 0.252320i
\(576\) 373358. + 38263.8i 1.12533 + 0.115330i
\(577\) 183983. 0.552619 0.276310 0.961069i \(-0.410888\pi\)
0.276310 + 0.961069i \(0.410888\pi\)
\(578\) 423066.i 1.26635i
\(579\) −540634. 27631.2i −1.61267 0.0824220i
\(580\) −116404. −0.346029
\(581\) 85690.8i 0.253853i
\(582\) 1917.88 37525.3i 0.00566206 0.110784i
\(583\) −52942.9 −0.155765
\(584\) 362234.i 1.06210i
\(585\) −58893.0 + 574646.i −0.172088 + 1.67915i
\(586\) −388951. −1.13266
\(587\) 128452.i 0.372791i 0.982475 + 0.186396i \(0.0596807\pi\)
−0.982475 + 0.186396i \(0.940319\pi\)
\(588\) 524672. + 26815.4i 1.51751 + 0.0775586i
\(589\) −8375.07 −0.0241411
\(590\) 71875.3i 0.206479i
\(591\) −17062.6 + 333848.i −0.0488508 + 0.955816i
\(592\) 394452. 1.12551
\(593\) 467110.i 1.32834i −0.747581 0.664171i \(-0.768785\pi\)
0.747581 0.664171i \(-0.231215\pi\)
\(594\) 131594. + 20318.6i 0.372962 + 0.0575866i
\(595\) −78987.6 −0.223113
\(596\) 288901.i 0.813311i
\(597\) −212566. 10864.0i −0.596410 0.0304819i
\(598\) −1.91234e6 −5.34764
\(599\) 491820.i 1.37073i −0.728199 0.685366i \(-0.759642\pi\)
0.728199 0.685366i \(-0.240358\pi\)
\(600\) −4465.13 + 87364.9i −0.0124031 + 0.242680i
\(601\) 546800. 1.51384 0.756920 0.653508i \(-0.226703\pi\)
0.756920 + 0.653508i \(0.226703\pi\)
\(602\) 206649.i 0.570218i
\(603\) −316517. 32438.4i −0.870486 0.0892124i
\(604\) −165405. −0.453392
\(605\) 321505.i 0.878369i
\(606\) 733413. + 37484.0i 1.99712 + 0.102070i
\(607\) −603563. −1.63812 −0.819059 0.573709i \(-0.805504\pi\)
−0.819059 + 0.573709i \(0.805504\pi\)
\(608\) 4863.63i 0.0131569i
\(609\) 1712.56 33508.0i 0.00461754 0.0903470i
\(610\) 702188. 1.88709
\(611\) 843408.i 2.25920i
\(612\) 38262.3 373343.i 0.102157 0.996794i
\(613\) 372913. 0.992399 0.496200 0.868208i \(-0.334728\pi\)
0.496200 + 0.868208i \(0.334728\pi\)
\(614\) 383508.i 1.01727i
\(615\) −393040. 20087.9i −1.03917 0.0531109i
\(616\) −64345.1 −0.169572
\(617\) 559864.i 1.47066i 0.677709 + 0.735330i \(0.262973\pi\)
−0.677709 + 0.735330i \(0.737027\pi\)
\(618\) −35671.1 + 697941.i −0.0933983 + 1.82744i
\(619\) 385336. 1.00568 0.502838 0.864381i \(-0.332289\pi\)
0.502838 + 0.864381i \(0.332289\pi\)
\(620\) 198928.i 0.517502i
\(621\) 100117. 648413.i 0.259612 1.68139i
\(622\) 564993. 1.46037
\(623\) 173803.i 0.447798i
\(624\) 613349. + 31347.6i 1.57521 + 0.0805073i
\(625\) −324100. −0.829696
\(626\) 683237.i 1.74350i
\(627\) −370.564 + 7250.46i −0.000942601 + 0.0184430i
\(628\) 819113. 2.07694
\(629\) 264880.i 0.669495i
\(630\) 295130. + 30246.6i 0.743589 + 0.0762072i
\(631\) 791453. 1.98777 0.993886 0.110415i \(-0.0352179\pi\)
0.993886 + 0.110415i \(0.0352179\pi\)
\(632\) 77479.0i 0.193977i
\(633\) 181701. + 9286.53i 0.453470 + 0.0231764i
\(634\) −163730. −0.407334
\(635\) 538482.i 1.33544i
\(636\) 28607.9 559743.i 0.0707247 1.38380i
\(637\) −577304. −1.42274
\(638\) 29485.1i 0.0724372i
\(639\) 4345.55 42401.5i 0.0106425 0.103844i
\(640\) 675732. 1.64974
\(641\) 571714.i 1.39144i −0.718315 0.695718i \(-0.755087\pi\)
0.718315 0.695718i \(-0.244913\pi\)
\(642\) 888220. + 45396.0i 2.15502 + 0.110141i
\(643\) 100352. 0.242718 0.121359 0.992609i \(-0.461275\pi\)
0.121359 + 0.992609i \(0.461275\pi\)
\(644\) 649600.i 1.56630i
\(645\) 13796.6 269944.i 0.0331629 0.648866i
\(646\) 30937.6 0.0741348
\(647\) 7039.72i 0.0168169i 0.999965 + 0.00840847i \(0.00267653\pi\)
−0.999965 + 0.00840847i \(0.997323\pi\)
\(648\) −139553. + 673691.i −0.332345 + 1.60439i
\(649\) −12041.6 −0.0285887
\(650\) 196957.i 0.466170i
\(651\) −57263.2 2926.66i −0.135118 0.00690575i
\(652\) 938383. 2.20742
\(653\) 699199.i 1.63974i 0.572551 + 0.819869i \(0.305954\pi\)
−0.572551 + 0.819869i \(0.694046\pi\)
\(654\) 47166.4 922860.i 0.110275 2.15765i
\(655\) 26274.8 0.0612431
\(656\) 418415.i 0.972299i
\(657\) −278350. 28526.9i −0.644853 0.0660882i
\(658\) −433163. −1.00046
\(659\) 440423.i 1.01414i 0.861904 + 0.507072i \(0.169272\pi\)
−0.861904 + 0.507072i \(0.830728\pi\)
\(660\) 172216. + 8801.77i 0.395353 + 0.0202061i
\(661\) −410057. −0.938515 −0.469257 0.883061i \(-0.655478\pi\)
−0.469257 + 0.883061i \(0.655478\pi\)
\(662\) 1.05828e6i 2.41483i
\(663\) −21050.3 + 411871.i −0.0478885 + 0.936988i
\(664\) −389092. −0.882503
\(665\) 16175.6i 0.0365778i
\(666\) 101430. 989700.i 0.228675 2.23128i
\(667\) −145284. −0.326562
\(668\) 546998.i 1.22584i
\(669\) −531111. 27144.6i −1.18668 0.0606499i
\(670\) −622992. −1.38782
\(671\) 117640.i 0.261283i
\(672\) −1699.60 + 33254.3i −0.00376363 + 0.0736393i
\(673\) −488999. −1.07964 −0.539819 0.841781i \(-0.681507\pi\)
−0.539819 + 0.841781i \(0.681507\pi\)
\(674\) 1.11785e6i 2.46073i
\(675\) 66781.8 + 10311.3i 0.146572 + 0.0226312i
\(676\) −2.09353e6 −4.58127
\(677\) 781793.i 1.70575i −0.522119 0.852873i \(-0.674858\pi\)
0.522119 0.852873i \(-0.325142\pi\)
\(678\) −1.26854e6 64833.8i −2.75959 0.141040i
\(679\) 14025.6 0.0304217
\(680\) 358655.i 0.775638i
\(681\) −8641.38 + 169078.i −0.0186333 + 0.364579i
\(682\) −50388.4 −0.108333
\(683\) 839447.i 1.79950i 0.436406 + 0.899750i \(0.356251\pi\)
−0.436406 + 0.899750i \(0.643749\pi\)
\(684\) −76455.8 7835.63i −0.163417 0.0167479i
\(685\) 644035. 1.37255
\(686\) 677657.i 1.44000i
\(687\) −791016. 40428.0i −1.67599 0.0856582i
\(688\) −287373. −0.607112
\(689\) 615893.i 1.29738i
\(690\) 65571.5 1.28297e6i 0.137726 2.69476i
\(691\) −347890. −0.728595 −0.364297 0.931283i \(-0.618691\pi\)
−0.364297 + 0.931283i \(0.618691\pi\)
\(692\) 570569.i 1.19151i
\(693\) −5067.34 + 49444.4i −0.0105515 + 0.102956i
\(694\) −266117. −0.552527
\(695\) 637607.i 1.32003i
\(696\) 152148. + 7776.13i 0.314086 + 0.0160526i
\(697\) −280971. −0.578357
\(698\) 911388.i 1.87065i
\(699\) −3082.71 + 60316.4i −0.00630926 + 0.123447i
\(700\) −66904.1 −0.136539
\(701\) 87614.4i 0.178295i 0.996018 + 0.0891476i \(0.0284143\pi\)
−0.996018 + 0.0891476i \(0.971586\pi\)
\(702\) 236370. 1.53086e6i 0.479643 3.10643i
\(703\) 54243.9 0.109759
\(704\) 123116.i 0.248410i
\(705\) 565838. + 28919.4i 1.13845 + 0.0581850i
\(706\) −639573. −1.28316
\(707\) 274124.i 0.548414i
\(708\) 6506.71 127311.i 0.0129806 0.253979i
\(709\) 342766. 0.681876 0.340938 0.940086i \(-0.389255\pi\)
0.340938 + 0.940086i \(0.389255\pi\)
\(710\) 83457.9i 0.165558i
\(711\) 59536.9 + 6101.67i 0.117773 + 0.0120701i
\(712\) 789181. 1.55674
\(713\) 248281.i 0.488388i
\(714\) 211531. + 10811.1i 0.414933 + 0.0212068i
\(715\) −189491. −0.370662
\(716\) 335316.i 0.654076i
\(717\) −32106.6 + 628199.i −0.0624534 + 1.22197i
\(718\) −1.52924e6 −2.96639
\(719\) 124920.i 0.241643i −0.992674 0.120821i \(-0.961447\pi\)
0.992674 0.120821i \(-0.0385529\pi\)
\(720\) −42061.9 + 410417.i −0.0811378 + 0.791700i
\(721\) −260866. −0.501819
\(722\) 889514.i 1.70639i
\(723\) −150316. 7682.50i −0.287560 0.0146969i
\(724\) 781070. 1.49009
\(725\) 14963.2i 0.0284674i
\(726\) 44004.9 861001.i 0.0834886 1.63354i
\(727\) 795417. 1.50496 0.752482 0.658612i \(-0.228856\pi\)
0.752482 + 0.658612i \(0.228856\pi\)
\(728\) 748537.i 1.41238i
\(729\) 506692. + 160291.i 0.953429 + 0.301616i
\(730\) −547870. −1.02809
\(731\) 192974.i 0.361131i
\(732\) −1.24376e6 63567.4i −2.32122 0.118635i
\(733\) −456048. −0.848795 −0.424398 0.905476i \(-0.639514\pi\)
−0.424398 + 0.905476i \(0.639514\pi\)
\(734\) 709811.i 1.31750i
\(735\) 19795.0 387310.i 0.0366421 0.716942i
\(736\) 144184. 0.266171
\(737\) 104372.i 0.192155i
\(738\) 1.04982e6 + 107592.i 1.92754 + 0.197545i
\(739\) −623496. −1.14168 −0.570840 0.821061i \(-0.693383\pi\)
−0.570840 + 0.821061i \(0.693383\pi\)
\(740\) 1.28842e6i 2.35285i
\(741\) 84345.8 + 4310.83i 0.153613 + 0.00785099i
\(742\) 316314. 0.574528
\(743\) 814960.i 1.47625i −0.674666 0.738123i \(-0.735712\pi\)
0.674666 0.738123i \(-0.264288\pi\)
\(744\) 13289.0 260012.i 0.0240074 0.469730i
\(745\) 213265. 0.384244
\(746\) 958257.i 1.72189i
\(747\) −30642.0 + 298988.i −0.0549131 + 0.535813i
\(748\) 123111. 0.220036
\(749\) 331986.i 0.591774i
\(750\) 1.02310e6 + 52289.4i 1.81884 + 0.0929589i
\(751\) 502089. 0.890226 0.445113 0.895474i \(-0.353163\pi\)
0.445113 + 0.895474i \(0.353163\pi\)
\(752\) 602369.i 1.06519i
\(753\) −49065.6 + 960019.i −0.0865340 + 1.69313i
\(754\) −343005. −0.603334
\(755\) 122101.i 0.214203i
\(756\) −520017. 80292.3i −0.909859 0.140485i
\(757\) −815505. −1.42310 −0.711549 0.702636i \(-0.752006\pi\)
−0.711549 + 0.702636i \(0.752006\pi\)
\(758\) 373418.i 0.649916i
\(759\) 214942. + 10985.5i 0.373111 + 0.0190693i
\(760\) −73447.9 −0.127161
\(761\) 246488.i 0.425625i 0.977093 + 0.212812i \(0.0682623\pi\)
−0.977093 + 0.212812i \(0.931738\pi\)
\(762\) −73702.7 + 1.44207e6i −0.126933 + 2.48357i
\(763\) 344933. 0.592496
\(764\) 1.74201e6i 2.98446i
\(765\) −275600. 28245.0i −0.470930 0.0482636i
\(766\) −242377. −0.413080
\(767\) 140082.i 0.238117i
\(768\) −1.14328e6 58431.7i −1.93834 0.0990663i
\(769\) 620106. 1.04861 0.524304 0.851531i \(-0.324326\pi\)
0.524304 + 0.851531i \(0.324326\pi\)
\(770\) 97320.2i 0.164143i
\(771\) −45894.1 + 897966.i −0.0772055 + 1.51061i
\(772\) 1.87991e6 3.15430
\(773\) 401136.i 0.671324i 0.941982 + 0.335662i \(0.108960\pi\)
−0.941982 + 0.335662i \(0.891040\pi\)
\(774\) −73895.4 + 721031.i −0.123349 + 1.20357i
\(775\) −25571.2 −0.0425743
\(776\) 63685.5i 0.105759i
\(777\) 370884. + 18955.5i 0.614322 + 0.0313974i
\(778\) −47719.6 −0.0788384
\(779\) 57539.2i 0.0948176i
\(780\) 102392. 2.00341e6i 0.168298 3.29292i
\(781\) 13982.0 0.0229229
\(782\) 917156.i 1.49979i