Properties

Label 177.3.c.a.58.15
Level $177$
Weight $3$
Character 177.58
Analytic conductor $4.823$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(4.82290067918\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + 5962230 x^{6} + 6517782 x^{4} + 3428244 x^{2} + 570861\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{7}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.15
Root \(1.86235i\) of defining polynomial
Character \(\chi\) \(=\) 177.58
Dual form 177.3.c.a.58.6

$q$-expansion

\(f(q)\) \(=\) \(q+1.86235i q^{2} -1.73205 q^{3} +0.531642 q^{4} -9.04540 q^{5} -3.22569i q^{6} +1.29987 q^{7} +8.43952i q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+1.86235i q^{2} -1.73205 q^{3} +0.531642 q^{4} -9.04540 q^{5} -3.22569i q^{6} +1.29987 q^{7} +8.43952i q^{8} +3.00000 q^{9} -16.8457i q^{10} -12.8790i q^{11} -0.920831 q^{12} -23.5709i q^{13} +2.42081i q^{14} +15.6671 q^{15} -13.5908 q^{16} -10.1284 q^{17} +5.58706i q^{18} -23.3600 q^{19} -4.80892 q^{20} -2.25144 q^{21} +23.9853 q^{22} -9.25801i q^{23} -14.6177i q^{24} +56.8193 q^{25} +43.8973 q^{26} -5.19615 q^{27} +0.691065 q^{28} -25.9681 q^{29} +29.1777i q^{30} +28.4380i q^{31} +8.44722i q^{32} +22.3072i q^{33} -18.8627i q^{34} -11.7578 q^{35} +1.59493 q^{36} -22.3933i q^{37} -43.5046i q^{38} +40.8260i q^{39} -76.3388i q^{40} -44.4678 q^{41} -4.19297i q^{42} +42.8166i q^{43} -6.84704i q^{44} -27.1362 q^{45} +17.2417 q^{46} +30.6792i q^{47} +23.5399 q^{48} -47.3103 q^{49} +105.818i q^{50} +17.5430 q^{51} -12.5313i q^{52} +41.9742 q^{53} -9.67707i q^{54} +116.496i q^{55} +10.9703i q^{56} +40.4608 q^{57} -48.3618i q^{58} +(-2.69759 - 58.9383i) q^{59} +8.32929 q^{60} +31.9823i q^{61} -52.9616 q^{62} +3.89961 q^{63} -70.0949 q^{64} +213.208i q^{65} -41.5438 q^{66} -94.0998i q^{67} -5.38470 q^{68} +16.0353i q^{69} -21.8972i q^{70} +5.78244 q^{71} +25.3185i q^{72} -41.5942i q^{73} +41.7043 q^{74} -98.4139 q^{75} -12.4192 q^{76} -16.7411i q^{77} -76.0324 q^{78} -105.782 q^{79} +122.934 q^{80} +9.00000 q^{81} -82.8148i q^{82} +3.14451i q^{83} -1.19696 q^{84} +91.6157 q^{85} -79.7397 q^{86} +44.9781 q^{87} +108.693 q^{88} +21.8316i q^{89} -50.5372i q^{90} -30.6391i q^{91} -4.92194i q^{92} -49.2561i q^{93} -57.1355 q^{94} +211.301 q^{95} -14.6310i q^{96} +126.206i q^{97} -88.1085i q^{98} -38.6371i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 40q^{4} - 8q^{7} + 60q^{9} + O(q^{10}) \) \( 20q - 40q^{4} - 8q^{7} + 60q^{9} - 24q^{12} + 24q^{15} - 8q^{16} + 16q^{17} - 60q^{19} - 164q^{20} + 40q^{22} + 100q^{25} - 156q^{26} + 200q^{28} - 60q^{29} - 32q^{35} - 120q^{36} + 28q^{41} + 180q^{46} - 96q^{48} + 284q^{49} - 24q^{51} - 8q^{53} + 24q^{57} - 152q^{59} - 72q^{60} - 8q^{62} - 24q^{63} + 204q^{64} - 120q^{66} + 384q^{68} + 92q^{71} + 104q^{74} + 240q^{75} + 120q^{76} - 468q^{78} - 420q^{79} + 376q^{80} + 180q^{81} + 168q^{84} - 348q^{85} + 232q^{86} + 144q^{87} - 212q^{88} + 152q^{94} + 788q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.86235i 0.931176i 0.885001 + 0.465588i \(0.154157\pi\)
−0.885001 + 0.465588i \(0.845843\pi\)
\(3\) −1.73205 −0.577350
\(4\) 0.531642 0.132910
\(5\) −9.04540 −1.80908 −0.904540 0.426388i \(-0.859786\pi\)
−0.904540 + 0.426388i \(0.859786\pi\)
\(6\) 3.22569i 0.537615i
\(7\) 1.29987 0.185696 0.0928478 0.995680i \(-0.470403\pi\)
0.0928478 + 0.995680i \(0.470403\pi\)
\(8\) 8.43952i 1.05494i
\(9\) 3.00000 0.333333
\(10\) 16.8457i 1.68457i
\(11\) 12.8790i 1.17082i −0.810736 0.585411i \(-0.800933\pi\)
0.810736 0.585411i \(-0.199067\pi\)
\(12\) −0.920831 −0.0767359
\(13\) 23.5709i 1.81315i −0.422050 0.906573i \(-0.638689\pi\)
0.422050 0.906573i \(-0.361311\pi\)
\(14\) 2.42081i 0.172915i
\(15\) 15.6671 1.04447
\(16\) −13.5908 −0.849424
\(17\) −10.1284 −0.595790 −0.297895 0.954599i \(-0.596285\pi\)
−0.297895 + 0.954599i \(0.596285\pi\)
\(18\) 5.58706i 0.310392i
\(19\) −23.3600 −1.22948 −0.614738 0.788731i \(-0.710738\pi\)
−0.614738 + 0.788731i \(0.710738\pi\)
\(20\) −4.80892 −0.240446
\(21\) −2.25144 −0.107211
\(22\) 23.9853 1.09024
\(23\) 9.25801i 0.402522i −0.979538 0.201261i \(-0.935496\pi\)
0.979538 0.201261i \(-0.0645039\pi\)
\(24\) 14.6177i 0.609070i
\(25\) 56.8193 2.27277
\(26\) 43.8973 1.68836
\(27\) −5.19615 −0.192450
\(28\) 0.691065 0.0246809
\(29\) −25.9681 −0.895452 −0.447726 0.894171i \(-0.647766\pi\)
−0.447726 + 0.894171i \(0.647766\pi\)
\(30\) 29.1777i 0.972589i
\(31\) 28.4380i 0.917355i 0.888603 + 0.458678i \(0.151677\pi\)
−0.888603 + 0.458678i \(0.848323\pi\)
\(32\) 8.44722i 0.263976i
\(33\) 22.3072i 0.675975i
\(34\) 18.8627i 0.554786i
\(35\) −11.7578 −0.335938
\(36\) 1.59493 0.0443035
\(37\) 22.3933i 0.605225i −0.953114 0.302613i \(-0.902141\pi\)
0.953114 0.302613i \(-0.0978588\pi\)
\(38\) 43.5046i 1.14486i
\(39\) 40.8260i 1.04682i
\(40\) 76.3388i 1.90847i
\(41\) −44.4678 −1.08458 −0.542290 0.840191i \(-0.682443\pi\)
−0.542290 + 0.840191i \(0.682443\pi\)
\(42\) 4.19297i 0.0998327i
\(43\) 42.8166i 0.995736i 0.867253 + 0.497868i \(0.165884\pi\)
−0.867253 + 0.497868i \(0.834116\pi\)
\(44\) 6.84704i 0.155615i
\(45\) −27.1362 −0.603027
\(46\) 17.2417 0.374819
\(47\) 30.6792i 0.652749i 0.945241 + 0.326374i \(0.105827\pi\)
−0.945241 + 0.326374i \(0.894173\pi\)
\(48\) 23.5399 0.490415
\(49\) −47.3103 −0.965517
\(50\) 105.818i 2.11635i
\(51\) 17.5430 0.343980
\(52\) 12.5313i 0.240986i
\(53\) 41.9742 0.791967 0.395983 0.918258i \(-0.370404\pi\)
0.395983 + 0.918258i \(0.370404\pi\)
\(54\) 9.67707i 0.179205i
\(55\) 116.496i 2.11811i
\(56\) 10.9703i 0.195898i
\(57\) 40.4608 0.709838
\(58\) 48.3618i 0.833824i
\(59\) −2.69759 58.9383i −0.0457219 0.998954i
\(60\) 8.32929 0.138821
\(61\) 31.9823i 0.524300i 0.965027 + 0.262150i \(0.0844315\pi\)
−0.965027 + 0.262150i \(0.915569\pi\)
\(62\) −52.9616 −0.854219
\(63\) 3.89961 0.0618985
\(64\) −70.0949 −1.09523
\(65\) 213.208i 3.28013i
\(66\) −41.5438 −0.629452
\(67\) 94.0998i 1.40447i −0.711943 0.702237i \(-0.752185\pi\)
0.711943 0.702237i \(-0.247815\pi\)
\(68\) −5.38470 −0.0791868
\(69\) 16.0353i 0.232396i
\(70\) 21.8972i 0.312818i
\(71\) 5.78244 0.0814428 0.0407214 0.999171i \(-0.487034\pi\)
0.0407214 + 0.999171i \(0.487034\pi\)
\(72\) 25.3185i 0.351647i
\(73\) 41.5942i 0.569783i −0.958560 0.284892i \(-0.908042\pi\)
0.958560 0.284892i \(-0.0919577\pi\)
\(74\) 41.7043 0.563571
\(75\) −98.4139 −1.31219
\(76\) −12.4192 −0.163410
\(77\) 16.7411i 0.217417i
\(78\) −76.0324 −0.974774
\(79\) −105.782 −1.33901 −0.669503 0.742809i \(-0.733493\pi\)
−0.669503 + 0.742809i \(0.733493\pi\)
\(80\) 122.934 1.53668
\(81\) 9.00000 0.111111
\(82\) 82.8148i 1.00994i
\(83\) 3.14451i 0.0378857i 0.999821 + 0.0189428i \(0.00603006\pi\)
−0.999821 + 0.0189428i \(0.993970\pi\)
\(84\) −1.19696 −0.0142495
\(85\) 91.6157 1.07783
\(86\) −79.7397 −0.927206
\(87\) 44.9781 0.516990
\(88\) 108.693 1.23515
\(89\) 21.8316i 0.245299i 0.992450 + 0.122649i \(0.0391391\pi\)
−0.992450 + 0.122649i \(0.960861\pi\)
\(90\) 50.5372i 0.561524i
\(91\) 30.6391i 0.336693i
\(92\) 4.92194i 0.0534994i
\(93\) 49.2561i 0.529635i
\(94\) −57.1355 −0.607824
\(95\) 211.301 2.22422
\(96\) 14.6310i 0.152406i
\(97\) 126.206i 1.30109i 0.759468 + 0.650544i \(0.225459\pi\)
−0.759468 + 0.650544i \(0.774541\pi\)
\(98\) 88.1085i 0.899067i
\(99\) 38.6371i 0.390274i
\(100\) 30.2075 0.302075
\(101\) 71.4450i 0.707376i −0.935363 0.353688i \(-0.884927\pi\)
0.935363 0.353688i \(-0.115073\pi\)
\(102\) 32.6712i 0.320306i
\(103\) 166.064i 1.61228i −0.591728 0.806138i \(-0.701554\pi\)
0.591728 0.806138i \(-0.298446\pi\)
\(104\) 198.927 1.91276
\(105\) 20.3652 0.193954
\(106\) 78.1708i 0.737461i
\(107\) 27.6484 0.258396 0.129198 0.991619i \(-0.458760\pi\)
0.129198 + 0.991619i \(0.458760\pi\)
\(108\) −2.76249 −0.0255786
\(109\) 110.232i 1.01130i 0.862738 + 0.505651i \(0.168748\pi\)
−0.862738 + 0.505651i \(0.831252\pi\)
\(110\) −216.957 −1.97234
\(111\) 38.7864i 0.349427i
\(112\) −17.6662 −0.157734
\(113\) 69.5553i 0.615534i −0.951462 0.307767i \(-0.900418\pi\)
0.951462 0.307767i \(-0.0995817\pi\)
\(114\) 75.3522i 0.660985i
\(115\) 83.7424i 0.728195i
\(116\) −13.8057 −0.119015
\(117\) 70.7127i 0.604382i
\(118\) 109.764 5.02387i 0.930203 0.0425752i
\(119\) −13.1656 −0.110636
\(120\) 132.223i 1.10186i
\(121\) −44.8699 −0.370826
\(122\) −59.5623 −0.488215
\(123\) 77.0205 0.626183
\(124\) 15.1188i 0.121926i
\(125\) −287.818 −2.30255
\(126\) 7.26244i 0.0576384i
\(127\) 218.788 1.72274 0.861370 0.507977i \(-0.169607\pi\)
0.861370 + 0.507977i \(0.169607\pi\)
\(128\) 96.7525i 0.755879i
\(129\) 74.1606i 0.574888i
\(130\) −397.069 −3.05438
\(131\) 245.998i 1.87785i −0.344127 0.938923i \(-0.611825\pi\)
0.344127 0.938923i \(-0.388175\pi\)
\(132\) 11.8594i 0.0898441i
\(133\) −30.3650 −0.228308
\(134\) 175.247 1.30781
\(135\) 47.0013 0.348158
\(136\) 85.4791i 0.628522i
\(137\) 250.848 1.83101 0.915504 0.402308i \(-0.131792\pi\)
0.915504 + 0.402308i \(0.131792\pi\)
\(138\) −29.8635 −0.216402
\(139\) −14.5923 −0.104981 −0.0524903 0.998621i \(-0.516716\pi\)
−0.0524903 + 0.998621i \(0.516716\pi\)
\(140\) −6.25096 −0.0446497
\(141\) 53.1379i 0.376865i
\(142\) 10.7689i 0.0758376i
\(143\) −303.571 −2.12287
\(144\) −40.7724 −0.283141
\(145\) 234.892 1.61995
\(146\) 77.4631 0.530569
\(147\) 81.9439 0.557442
\(148\) 11.9052i 0.0804408i
\(149\) 182.069i 1.22194i 0.791653 + 0.610971i \(0.209221\pi\)
−0.791653 + 0.610971i \(0.790779\pi\)
\(150\) 183.281i 1.22188i
\(151\) 31.7495i 0.210262i 0.994458 + 0.105131i \(0.0335262\pi\)
−0.994458 + 0.105131i \(0.966474\pi\)
\(152\) 197.147i 1.29702i
\(153\) −30.3853 −0.198597
\(154\) 31.1778 0.202453
\(155\) 257.233i 1.65957i
\(156\) 21.7048i 0.139133i
\(157\) 243.661i 1.55198i 0.630744 + 0.775991i \(0.282750\pi\)
−0.630744 + 0.775991i \(0.717250\pi\)
\(158\) 197.002i 1.24685i
\(159\) −72.7015 −0.457242
\(160\) 76.4085i 0.477553i
\(161\) 12.0342i 0.0747465i
\(162\) 16.7612i 0.103464i
\(163\) −9.01747 −0.0553219 −0.0276610 0.999617i \(-0.508806\pi\)
−0.0276610 + 0.999617i \(0.508806\pi\)
\(164\) −23.6410 −0.144152
\(165\) 201.777i 1.22289i
\(166\) −5.85619 −0.0352783
\(167\) −134.849 −0.807482 −0.403741 0.914873i \(-0.632290\pi\)
−0.403741 + 0.914873i \(0.632290\pi\)
\(168\) 19.0011i 0.113102i
\(169\) −386.587 −2.28750
\(170\) 170.621i 1.00365i
\(171\) −70.0801 −0.409825
\(172\) 22.7631i 0.132344i
\(173\) 273.027i 1.57819i 0.614271 + 0.789095i \(0.289450\pi\)
−0.614271 + 0.789095i \(0.710550\pi\)
\(174\) 83.7651i 0.481409i
\(175\) 73.8576 0.422044
\(176\) 175.036i 0.994525i
\(177\) 4.67237 + 102.084i 0.0263976 + 0.576746i
\(178\) −40.6581 −0.228417
\(179\) 110.268i 0.616025i −0.951382 0.308012i \(-0.900336\pi\)
0.951382 0.308012i \(-0.0996638\pi\)
\(180\) −14.4267 −0.0801486
\(181\) 21.7461 0.120144 0.0600721 0.998194i \(-0.480867\pi\)
0.0600721 + 0.998194i \(0.480867\pi\)
\(182\) 57.0607 0.313521
\(183\) 55.3949i 0.302705i
\(184\) 78.1331 0.424636
\(185\) 202.557i 1.09490i
\(186\) 91.7322 0.493184
\(187\) 130.445i 0.697564i
\(188\) 16.3104i 0.0867572i
\(189\) −6.75432 −0.0357371
\(190\) 393.517i 2.07114i
\(191\) 25.4664i 0.133332i 0.997775 + 0.0666660i \(0.0212362\pi\)
−0.997775 + 0.0666660i \(0.978764\pi\)
\(192\) 121.408 0.632333
\(193\) −140.722 −0.729130 −0.364565 0.931178i \(-0.618782\pi\)
−0.364565 + 0.931178i \(0.618782\pi\)
\(194\) −235.039 −1.21154
\(195\) 369.287i 1.89378i
\(196\) −25.1522 −0.128327
\(197\) −221.365 −1.12368 −0.561841 0.827245i \(-0.689907\pi\)
−0.561841 + 0.827245i \(0.689907\pi\)
\(198\) 71.9560 0.363414
\(199\) 282.321 1.41870 0.709348 0.704858i \(-0.248989\pi\)
0.709348 + 0.704858i \(0.248989\pi\)
\(200\) 479.527i 2.39764i
\(201\) 162.986i 0.810873i
\(202\) 133.056 0.658692
\(203\) −33.7551 −0.166282
\(204\) 9.32657 0.0457185
\(205\) 402.229 1.96209
\(206\) 309.270 1.50131
\(207\) 27.7740i 0.134174i
\(208\) 320.347i 1.54013i
\(209\) 300.855i 1.43950i
\(210\) 37.9271i 0.180605i
\(211\) 2.24194i 0.0106253i 0.999986 + 0.00531265i \(0.00169108\pi\)
−0.999986 + 0.00531265i \(0.998309\pi\)
\(212\) 22.3153 0.105261
\(213\) −10.0155 −0.0470210
\(214\) 51.4910i 0.240612i
\(215\) 387.294i 1.80137i
\(216\) 43.8530i 0.203023i
\(217\) 36.9657i 0.170349i
\(218\) −205.291 −0.941701
\(219\) 72.0433i 0.328965i
\(220\) 61.9343i 0.281519i
\(221\) 238.736i 1.08025i
\(222\) −72.2339 −0.325378
\(223\) −313.196 −1.40447 −0.702234 0.711946i \(-0.747814\pi\)
−0.702234 + 0.711946i \(0.747814\pi\)
\(224\) 10.9803i 0.0490191i
\(225\) 170.458 0.757591
\(226\) 129.537 0.573170
\(227\) 398.887i 1.75721i −0.477548 0.878605i \(-0.658474\pi\)
0.477548 0.878605i \(-0.341526\pi\)
\(228\) 21.5106 0.0943449
\(229\) 52.2219i 0.228043i 0.993478 + 0.114022i \(0.0363733\pi\)
−0.993478 + 0.114022i \(0.963627\pi\)
\(230\) −155.958 −0.678078
\(231\) 28.9964i 0.125525i
\(232\) 219.158i 0.944648i
\(233\) 420.216i 1.80350i −0.432255 0.901751i \(-0.642282\pi\)
0.432255 0.901751i \(-0.357718\pi\)
\(234\) 131.692 0.562786
\(235\) 277.506i 1.18088i
\(236\) −1.43415 31.3341i −0.00607692 0.132771i
\(237\) 183.219 0.773076
\(238\) 24.5191i 0.103021i
\(239\) −157.064 −0.657171 −0.328585 0.944474i \(-0.606572\pi\)
−0.328585 + 0.944474i \(0.606572\pi\)
\(240\) −212.928 −0.887201
\(241\) 97.2511 0.403531 0.201766 0.979434i \(-0.435332\pi\)
0.201766 + 0.979434i \(0.435332\pi\)
\(242\) 83.5636i 0.345304i
\(243\) −15.5885 −0.0641500
\(244\) 17.0031i 0.0696849i
\(245\) 427.941 1.74670
\(246\) 143.439i 0.583087i
\(247\) 550.617i 2.22922i
\(248\) −240.003 −0.967754
\(249\) 5.44645i 0.0218733i
\(250\) 536.019i 2.14408i
\(251\) 298.241 1.18821 0.594105 0.804387i \(-0.297506\pi\)
0.594105 + 0.804387i \(0.297506\pi\)
\(252\) 2.07319 0.00822696
\(253\) −119.234 −0.471282
\(254\) 407.461i 1.60418i
\(255\) −158.683 −0.622287
\(256\) −100.192 −0.391376
\(257\) 398.043 1.54881 0.774403 0.632692i \(-0.218050\pi\)
0.774403 + 0.632692i \(0.218050\pi\)
\(258\) 138.113 0.535322
\(259\) 29.1084i 0.112388i
\(260\) 113.350i 0.435963i
\(261\) −77.9044 −0.298484
\(262\) 458.135 1.74861
\(263\) 205.829 0.782620 0.391310 0.920259i \(-0.372022\pi\)
0.391310 + 0.920259i \(0.372022\pi\)
\(264\) −188.262 −0.713112
\(265\) −379.674 −1.43273
\(266\) 56.5503i 0.212595i
\(267\) 37.8134i 0.141623i
\(268\) 50.0274i 0.186669i
\(269\) 161.097i 0.598874i −0.954116 0.299437i \(-0.903201\pi\)
0.954116 0.299437i \(-0.0967989\pi\)
\(270\) 87.5330i 0.324196i
\(271\) −222.809 −0.822173 −0.411086 0.911596i \(-0.634851\pi\)
−0.411086 + 0.911596i \(0.634851\pi\)
\(272\) 137.653 0.506079
\(273\) 53.0684i 0.194390i
\(274\) 467.168i 1.70499i
\(275\) 731.779i 2.66101i
\(276\) 8.52506i 0.0308879i
\(277\) −407.546 −1.47128 −0.735642 0.677371i \(-0.763119\pi\)
−0.735642 + 0.677371i \(0.763119\pi\)
\(278\) 27.1760i 0.0977555i
\(279\) 85.3140i 0.305785i
\(280\) 99.2304i 0.354394i
\(281\) −374.820 −1.33388 −0.666940 0.745112i \(-0.732396\pi\)
−0.666940 + 0.745112i \(0.732396\pi\)
\(282\) 98.9616 0.350928
\(283\) 361.855i 1.27864i −0.768941 0.639320i \(-0.779216\pi\)
0.768941 0.639320i \(-0.220784\pi\)
\(284\) 3.07419 0.0108246
\(285\) −365.984 −1.28415
\(286\) 565.356i 1.97677i
\(287\) −57.8023 −0.201402
\(288\) 25.3417i 0.0879919i
\(289\) −186.415 −0.645034
\(290\) 437.452i 1.50845i
\(291\) 218.595i 0.751184i
\(292\) 22.1132i 0.0757302i
\(293\) 299.087 1.02078 0.510388 0.859944i \(-0.329502\pi\)
0.510388 + 0.859944i \(0.329502\pi\)
\(294\) 152.608i 0.519076i
\(295\) 24.4008 + 533.121i 0.0827146 + 1.80719i
\(296\) 188.989 0.638476
\(297\) 66.9215i 0.225325i
\(298\) −339.078 −1.13784
\(299\) −218.219 −0.729831
\(300\) −52.3210 −0.174403
\(301\) 55.6560i 0.184904i
\(302\) −59.1288 −0.195791
\(303\) 123.746i 0.408404i
\(304\) 317.481 1.04435
\(305\) 289.293i 0.948500i
\(306\) 56.5881i 0.184929i
\(307\) 183.459 0.597585 0.298793 0.954318i \(-0.403416\pi\)
0.298793 + 0.954318i \(0.403416\pi\)
\(308\) 8.90026i 0.0288969i
\(309\) 287.632i 0.930848i
\(310\) 479.059 1.54535
\(311\) −198.361 −0.637816 −0.318908 0.947786i \(-0.603316\pi\)
−0.318908 + 0.947786i \(0.603316\pi\)
\(312\) −344.551 −1.10433
\(313\) 81.4573i 0.260247i 0.991498 + 0.130124i \(0.0415374\pi\)
−0.991498 + 0.130124i \(0.958463\pi\)
\(314\) −453.783 −1.44517
\(315\) −35.2735 −0.111979
\(316\) −56.2379 −0.177968
\(317\) −272.467 −0.859516 −0.429758 0.902944i \(-0.641401\pi\)
−0.429758 + 0.902944i \(0.641401\pi\)
\(318\) 135.396i 0.425773i
\(319\) 334.445i 1.04842i
\(320\) 634.036 1.98136
\(321\) −47.8884 −0.149185
\(322\) 22.4119 0.0696022
\(323\) 236.601 0.732509
\(324\) 4.78478 0.0147678
\(325\) 1339.28i 4.12087i
\(326\) 16.7937i 0.0515145i
\(327\) 190.927i 0.583876i
\(328\) 375.287i 1.14417i
\(329\) 39.8789i 0.121213i
\(330\) 375.781 1.13873
\(331\) −145.462 −0.439463 −0.219732 0.975560i \(-0.570518\pi\)
−0.219732 + 0.975560i \(0.570518\pi\)
\(332\) 1.67175i 0.00503541i
\(333\) 67.1800i 0.201742i
\(334\) 251.137i 0.751908i
\(335\) 851.170i 2.54081i
\(336\) 30.5988 0.0910679
\(337\) 174.373i 0.517427i −0.965954 0.258714i \(-0.916701\pi\)
0.965954 0.258714i \(-0.0832986\pi\)
\(338\) 719.961i 2.13006i
\(339\) 120.473i 0.355379i
\(340\) 48.7068 0.143255
\(341\) 366.255 1.07406
\(342\) 130.514i 0.381620i
\(343\) −125.191 −0.364988
\(344\) −361.352 −1.05044
\(345\) 145.046i 0.420423i
\(346\) −508.472 −1.46957
\(347\) 366.795i 1.05705i 0.848919 + 0.528524i \(0.177254\pi\)
−0.848919 + 0.528524i \(0.822746\pi\)
\(348\) 23.9122 0.0687134
\(349\) 208.270i 0.596763i −0.954447 0.298382i \(-0.903553\pi\)
0.954447 0.298382i \(-0.0964468\pi\)
\(350\) 137.549i 0.392997i
\(351\) 122.478i 0.348940i
\(352\) 108.792 0.309069
\(353\) 174.980i 0.495695i −0.968799 0.247847i \(-0.920277\pi\)
0.968799 0.247847i \(-0.0797231\pi\)
\(354\) −190.117 + 8.70160i −0.537053 + 0.0245808i
\(355\) −52.3045 −0.147337
\(356\) 11.6066i 0.0326028i
\(357\) 22.8035 0.0638755
\(358\) 205.359 0.573628
\(359\) 203.293 0.566275 0.283137 0.959079i \(-0.408625\pi\)
0.283137 + 0.959079i \(0.408625\pi\)
\(360\) 229.016i 0.636157i
\(361\) 184.691 0.511610
\(362\) 40.4989i 0.111876i
\(363\) 77.7169 0.214096
\(364\) 16.2890i 0.0447500i
\(365\) 376.236i 1.03078i
\(366\) 103.165 0.281871
\(367\) 514.435i 1.40173i −0.713293 0.700866i \(-0.752797\pi\)
0.713293 0.700866i \(-0.247203\pi\)
\(368\) 125.824i 0.341912i
\(369\) −133.403 −0.361527
\(370\) −377.232 −1.01955
\(371\) 54.5610 0.147065
\(372\) 26.1866i 0.0703941i
\(373\) 631.405 1.69278 0.846388 0.532567i \(-0.178773\pi\)
0.846388 + 0.532567i \(0.178773\pi\)
\(374\) −242.934 −0.649556
\(375\) 498.516 1.32938
\(376\) −258.918 −0.688611
\(377\) 612.092i 1.62359i
\(378\) 12.5789i 0.0332776i
\(379\) 196.674 0.518930 0.259465 0.965753i \(-0.416454\pi\)
0.259465 + 0.965753i \(0.416454\pi\)
\(380\) 112.336 0.295622
\(381\) −378.952 −0.994625
\(382\) −47.4275 −0.124156
\(383\) −127.877 −0.333883 −0.166941 0.985967i \(-0.553389\pi\)
−0.166941 + 0.985967i \(0.553389\pi\)
\(384\) 167.580i 0.436407i
\(385\) 151.430i 0.393324i
\(386\) 262.074i 0.678949i
\(387\) 128.450i 0.331912i
\(388\) 67.0962i 0.172928i
\(389\) 188.964 0.485770 0.242885 0.970055i \(-0.421906\pi\)
0.242885 + 0.970055i \(0.421906\pi\)
\(390\) 687.743 1.76344
\(391\) 93.7691i 0.239819i
\(392\) 399.276i 1.01856i
\(393\) 426.081i 1.08417i
\(394\) 412.261i 1.04635i
\(395\) 956.836 2.42237
\(396\) 20.5411i 0.0518715i
\(397\) 507.775i 1.27903i 0.768779 + 0.639515i \(0.220865\pi\)
−0.768779 + 0.639515i \(0.779135\pi\)
\(398\) 525.780i 1.32106i
\(399\) 52.5937 0.131814
\(400\) −772.219 −1.93055
\(401\) 427.106i 1.06510i −0.846398 0.532551i \(-0.821233\pi\)
0.846398 0.532551i \(-0.178767\pi\)
\(402\) −303.537 −0.755066
\(403\) 670.309 1.66330
\(404\) 37.9832i 0.0940177i
\(405\) −81.4086 −0.201009
\(406\) 62.8640i 0.154837i
\(407\) −288.405 −0.708611
\(408\) 148.054i 0.362878i
\(409\) 154.410i 0.377530i 0.982022 + 0.188765i \(0.0604485\pi\)
−0.982022 + 0.188765i \(0.939551\pi\)
\(410\) 749.093i 1.82706i
\(411\) −434.482 −1.05713
\(412\) 88.2868i 0.214288i
\(413\) −3.50652 76.6121i −0.00849035 0.185501i
\(414\) 51.7250 0.124940
\(415\) 28.4434i 0.0685383i
\(416\) 199.108 0.478626
\(417\) 25.2746 0.0606106
\(418\) −560.298 −1.34043
\(419\) 381.674i 0.910917i 0.890257 + 0.455458i \(0.150525\pi\)
−0.890257 + 0.455458i \(0.849475\pi\)
\(420\) 10.8270 0.0257785
\(421\) 223.524i 0.530935i −0.964120 0.265468i \(-0.914474\pi\)
0.964120 0.265468i \(-0.0855263\pi\)
\(422\) −4.17528 −0.00989403
\(423\) 92.0376i 0.217583i
\(424\) 354.242i 0.835477i
\(425\) −575.490 −1.35410
\(426\) 18.6524i 0.0437849i
\(427\) 41.5728i 0.0973601i
\(428\) 14.6990 0.0343435
\(429\) 525.800 1.22564
\(430\) 721.278 1.67739
\(431\) 59.8456i 0.138853i 0.997587 + 0.0694264i \(0.0221169\pi\)
−0.997587 + 0.0694264i \(0.977883\pi\)
\(432\) 70.6198 0.163472
\(433\) 654.088 1.51060 0.755298 0.655381i \(-0.227492\pi\)
0.755298 + 0.655381i \(0.227492\pi\)
\(434\) −68.8431 −0.158625
\(435\) −406.845 −0.935276
\(436\) 58.6039i 0.134413i
\(437\) 216.267i 0.494891i
\(438\) −134.170 −0.306324
\(439\) 308.578 0.702910 0.351455 0.936205i \(-0.385687\pi\)
0.351455 + 0.936205i \(0.385687\pi\)
\(440\) −983.171 −2.23448
\(441\) −141.931 −0.321839
\(442\) −444.611 −1.00591
\(443\) 94.0704i 0.212348i −0.994348 0.106174i \(-0.966140\pi\)
0.994348 0.106174i \(-0.0338601\pi\)
\(444\) 20.6205i 0.0464425i
\(445\) 197.476i 0.443765i
\(446\) 583.282i 1.30781i
\(447\) 315.354i 0.705489i
\(448\) −91.1141 −0.203380
\(449\) −447.832 −0.997399 −0.498699 0.866775i \(-0.666189\pi\)
−0.498699 + 0.866775i \(0.666189\pi\)
\(450\) 317.453i 0.705451i
\(451\) 572.703i 1.26985i
\(452\) 36.9785i 0.0818109i
\(453\) 54.9918i 0.121395i
\(454\) 742.868 1.63627
\(455\) 277.143i 0.609105i
\(456\) 341.469i 0.748836i
\(457\) 351.865i 0.769946i 0.922928 + 0.384973i \(0.125789\pi\)
−0.922928 + 0.384973i \(0.874211\pi\)
\(458\) −97.2555 −0.212348
\(459\) 52.6289 0.114660
\(460\) 44.5210i 0.0967847i
\(461\) −350.814 −0.760984 −0.380492 0.924784i \(-0.624245\pi\)
−0.380492 + 0.924784i \(0.624245\pi\)
\(462\) −54.0015 −0.116886
\(463\) 321.469i 0.694318i −0.937806 0.347159i \(-0.887146\pi\)
0.937806 0.347159i \(-0.112854\pi\)
\(464\) 352.927 0.760619
\(465\) 445.541i 0.958153i
\(466\) 782.591 1.67938
\(467\) 631.306i 1.35183i −0.736978 0.675916i \(-0.763748\pi\)
0.736978 0.675916i \(-0.236252\pi\)
\(468\) 37.5938i 0.0803287i
\(469\) 122.317i 0.260805i
\(470\) 516.814 1.09960
\(471\) 422.033i 0.896037i
\(472\) 497.411 22.7664i 1.05384 0.0482338i
\(473\) 551.438 1.16583
\(474\) 341.218i 0.719870i
\(475\) −1327.30 −2.79432
\(476\) −6.99940 −0.0147046
\(477\) 125.923 0.263989
\(478\) 292.508i 0.611942i
\(479\) −134.615 −0.281032 −0.140516 0.990078i \(-0.544876\pi\)
−0.140516 + 0.990078i \(0.544876\pi\)
\(480\) 132.343i 0.275715i
\(481\) −527.831 −1.09736
\(482\) 181.116i 0.375759i
\(483\) 20.8438i 0.0431549i
\(484\) −23.8547 −0.0492866
\(485\) 1141.58i 2.35377i
\(486\) 29.0312i 0.0597350i
\(487\) −739.718 −1.51893 −0.759464 0.650549i \(-0.774539\pi\)
−0.759464 + 0.650549i \(0.774539\pi\)
\(488\) −269.915 −0.553104
\(489\) 15.6187 0.0319401
\(490\) 796.977i 1.62648i
\(491\) −424.454 −0.864469 −0.432234 0.901761i \(-0.642275\pi\)
−0.432234 + 0.901761i \(0.642275\pi\)
\(492\) 40.9473 0.0832263
\(493\) 263.016 0.533502
\(494\) −1025.44 −2.07580
\(495\) 349.489i 0.706037i
\(496\) 386.495i 0.779224i
\(497\) 7.51641 0.0151236
\(498\) 10.1432 0.0203679
\(499\) 10.2031 0.0204471 0.0102236 0.999948i \(-0.496746\pi\)
0.0102236 + 0.999948i \(0.496746\pi\)
\(500\) −153.016 −0.306033
\(501\) 233.566 0.466200
\(502\) 555.429i 1.10643i
\(503\) 188.722i 0.375193i 0.982246 + 0.187596i \(0.0600697\pi\)
−0.982246 + 0.187596i \(0.939930\pi\)
\(504\) 32.9108i 0.0652992i
\(505\) 646.249i 1.27970i
\(506\) 222.056i 0.438847i
\(507\) 669.588 1.32069
\(508\) 116.317 0.228970
\(509\) 939.054i 1.84490i 0.386116 + 0.922450i \(0.373816\pi\)
−0.386116 + 0.922450i \(0.626184\pi\)
\(510\) 295.524i 0.579459i
\(511\) 54.0670i 0.105806i
\(512\) 573.603i 1.12032i
\(513\) 121.382 0.236613
\(514\) 741.297i 1.44221i
\(515\) 1502.12i 2.91674i
\(516\) 39.4269i 0.0764087i
\(517\) 395.119 0.764253
\(518\) 54.2101 0.104653
\(519\) 472.896i 0.911168i
\(520\) −1799.37 −3.46033
\(521\) −7.53069 −0.0144543 −0.00722715 0.999974i \(-0.502300\pi\)
−0.00722715 + 0.999974i \(0.502300\pi\)
\(522\) 145.085i 0.277941i
\(523\) −843.214 −1.61226 −0.806132 0.591736i \(-0.798443\pi\)
−0.806132 + 0.591736i \(0.798443\pi\)
\(524\) 130.783i 0.249585i
\(525\) −127.925 −0.243667
\(526\) 383.326i 0.728757i
\(527\) 288.032i 0.546551i
\(528\) 303.172i 0.574189i
\(529\) 443.289 0.837976
\(530\) 707.087i 1.33413i
\(531\) −8.09278 176.815i −0.0152406 0.332985i
\(532\) −16.1433 −0.0303445
\(533\) 1048.15i 1.96650i
\(534\) 70.4220 0.131876
\(535\) −250.091 −0.467459
\(536\) 794.156 1.48164
\(537\) 190.991i 0.355662i
\(538\) 300.020 0.557658
\(539\) 609.312i 1.13045i
\(540\) 24.9879 0.0462738
\(541\) 895.843i 1.65590i −0.560800 0.827951i \(-0.689506\pi\)
0.560800 0.827951i \(-0.310494\pi\)
\(542\) 414.949i 0.765588i
\(543\) −37.6654 −0.0693653
\(544\) 85.5571i 0.157274i
\(545\) 997.092i 1.82953i
\(546\) −98.8321 −0.181011
\(547\) 217.435 0.397504 0.198752 0.980050i \(-0.436311\pi\)
0.198752 + 0.980050i \(0.436311\pi\)
\(548\) 133.361 0.243360
\(549\) 95.9468i 0.174767i
\(550\) 1362.83 2.47787
\(551\) 606.616 1.10094
\(552\) −135.330 −0.245164
\(553\) −137.502 −0.248648
\(554\) 758.994i 1.37002i
\(555\) 350.838i 0.632141i
\(556\) −7.75788 −0.0139530
\(557\) −946.289 −1.69890 −0.849451 0.527667i \(-0.823067\pi\)
−0.849451 + 0.527667i \(0.823067\pi\)
\(558\) −158.885 −0.284740
\(559\) 1009.23 1.80541
\(560\) 159.798 0.285354
\(561\) 225.937i 0.402739i
\(562\) 698.047i 1.24208i
\(563\) 273.838i 0.486391i −0.969977 0.243195i \(-0.921804\pi\)
0.969977 0.243195i \(-0.0781956\pi\)
\(564\) 28.2504i 0.0500893i
\(565\) 629.156i 1.11355i
\(566\) 673.902 1.19064
\(567\) 11.6988 0.0206328
\(568\) 48.8010i 0.0859173i
\(569\) 652.571i 1.14687i 0.819250 + 0.573437i \(0.194390\pi\)
−0.819250 + 0.573437i \(0.805610\pi\)
\(570\) 681.591i 1.19577i
\(571\) 373.051i 0.653329i −0.945140 0.326664i \(-0.894075\pi\)
0.945140 0.326664i \(-0.105925\pi\)
\(572\) −161.391 −0.282152
\(573\) 44.1091i 0.0769793i
\(574\) 107.648i 0.187541i
\(575\) 526.033i 0.914841i
\(576\) −210.285 −0.365077
\(577\) −565.048 −0.979286 −0.489643 0.871923i \(-0.662873\pi\)
−0.489643 + 0.871923i \(0.662873\pi\)
\(578\) 347.170i 0.600641i
\(579\) 243.738 0.420963
\(580\) 124.878 0.215308
\(581\) 4.08745i 0.00703520i
\(582\) 407.100 0.699485
\(583\) 540.588i 0.927253i
\(584\) 351.035 0.601087
\(585\) 639.624i 1.09338i
\(586\) 557.006i 0.950523i
\(587\) 34.5560i 0.0588688i −0.999567 0.0294344i \(-0.990629\pi\)
0.999567 0.0294344i \(-0.00937062\pi\)
\(588\) 43.5648 0.0740898
\(589\) 664.313i 1.12787i
\(590\) −992.859 + 45.4429i −1.68281 + 0.0770219i
\(591\) 383.416 0.648758
\(592\) 304.343i 0.514093i
\(593\) 179.049 0.301937 0.150968 0.988539i \(-0.451761\pi\)
0.150968 + 0.988539i \(0.451761\pi\)
\(594\) −124.631 −0.209817
\(595\) 119.088 0.200149
\(596\) 96.7958i 0.162409i
\(597\) −488.993 −0.819085
\(598\) 406.402i 0.679601i
\(599\) 41.4253 0.0691575 0.0345787 0.999402i \(-0.488991\pi\)
0.0345787 + 0.999402i \(0.488991\pi\)
\(600\) 830.566i 1.38428i
\(601\) 107.487i 0.178847i −0.995994 0.0894236i \(-0.971498\pi\)
0.995994 0.0894236i \(-0.0285025\pi\)
\(602\) −103.651 −0.172178
\(603\) 282.299i 0.468158i
\(604\) 16.8794i 0.0279460i
\(605\) 405.866 0.670853
\(606\) −230.459 −0.380296
\(607\) 594.804 0.979908 0.489954 0.871748i \(-0.337014\pi\)
0.489954 + 0.871748i \(0.337014\pi\)
\(608\) 197.327i 0.324552i
\(609\) 58.4656 0.0960027
\(610\) 538.765 0.883221
\(611\) 723.136 1.18353
\(612\) −16.1541 −0.0263956
\(613\) 898.671i 1.46602i −0.680217 0.733011i \(-0.738115\pi\)
0.680217 0.733011i \(-0.261885\pi\)
\(614\) 341.665i 0.556457i
\(615\) −696.682 −1.13282
\(616\) 141.287 0.229361
\(617\) 479.889 0.777778 0.388889 0.921285i \(-0.372859\pi\)
0.388889 + 0.921285i \(0.372859\pi\)
\(618\) −535.672 −0.866783
\(619\) −622.793 −1.00613 −0.503064 0.864249i \(-0.667794\pi\)
−0.503064 + 0.864249i \(0.667794\pi\)
\(620\) 136.756i 0.220574i
\(621\) 48.1060i 0.0774654i
\(622\) 369.418i 0.593920i
\(623\) 28.3782i 0.0455509i
\(624\) 554.857i 0.889194i
\(625\) 1182.95 1.89272
\(626\) −151.702 −0.242336
\(627\) 521.096i 0.831095i
\(628\) 129.540i 0.206275i
\(629\) 226.809i 0.360587i
\(630\) 65.6917i 0.104273i
\(631\) 739.694 1.17226 0.586128 0.810218i \(-0.300652\pi\)
0.586128 + 0.810218i \(0.300652\pi\)
\(632\) 892.745i 1.41257i
\(633\) 3.88315i 0.00613452i
\(634\) 507.429i 0.800361i
\(635\) −1979.03 −3.11658
\(636\) −38.6512 −0.0607723
\(637\) 1115.15i 1.75062i
\(638\) −622.854 −0.976260
\(639\) 17.3473 0.0271476
\(640\) 875.165i 1.36745i
\(641\) 509.503 0.794857 0.397428 0.917633i \(-0.369903\pi\)
0.397428 + 0.917633i \(0.369903\pi\)
\(642\) 89.1851i 0.138918i
\(643\) −1038.83 −1.61560 −0.807802 0.589454i \(-0.799343\pi\)
−0.807802 + 0.589454i \(0.799343\pi\)
\(644\) 6.39788i 0.00993460i
\(645\) 670.812i 1.04002i
\(646\) 440.634i 0.682095i
\(647\) 113.373 0.175228 0.0876142 0.996154i \(-0.472076\pi\)
0.0876142 + 0.996154i \(0.472076\pi\)
\(648\) 75.9556i 0.117216i
\(649\) −759.069 + 34.7424i −1.16960 + 0.0535322i
\(650\) 2494.21 3.83725
\(651\) 64.0264i 0.0983509i
\(652\) −4.79407 −0.00735286
\(653\) −196.978 −0.301652 −0.150826 0.988560i \(-0.548193\pi\)
−0.150826 + 0.988560i \(0.548193\pi\)
\(654\) 355.574 0.543691
\(655\) 2225.15i 3.39717i
\(656\) 604.353 0.921269
\(657\) 124.783i 0.189928i
\(658\) −74.2686 −0.112870
\(659\) 12.7484i 0.0193451i −0.999953 0.00967254i \(-0.996921\pi\)
0.999953 0.00967254i \(-0.00307891\pi\)
\(660\) 107.273i 0.162535i
\(661\) −617.452 −0.934118 −0.467059 0.884226i \(-0.654686\pi\)
−0.467059 + 0.884226i \(0.654686\pi\)
\(662\) 270.902i 0.409218i
\(663\) 413.503i 0.623685i
\(664\) −26.5382 −0.0399671
\(665\) 274.663 0.413028
\(666\) 125.113 0.187857
\(667\) 240.413i 0.360439i
\(668\) −71.6917 −0.107323
\(669\) 542.472 0.810870
\(670\) −1585.18 −2.36594
\(671\) 411.901 0.613862
\(672\) 19.0184i 0.0283012i
\(673\) 525.509i 0.780845i 0.920636 + 0.390423i \(0.127671\pi\)
−0.920636 + 0.390423i \(0.872329\pi\)
\(674\) 324.744 0.481816
\(675\) −295.242 −0.437395
\(676\) −205.526 −0.304032
\(677\) −373.054 −0.551040 −0.275520 0.961295i \(-0.588850\pi\)
−0.275520 + 0.961295i \(0.588850\pi\)
\(678\) −224.364 −0.330920
\(679\) 164.051i 0.241606i
\(680\) 773.192i 1.13705i
\(681\) 690.892i 1.01453i
\(682\) 682.095i 1.00014i
\(683\) 602.186i 0.881679i −0.897586 0.440839i \(-0.854681\pi\)
0.897586 0.440839i \(-0.145319\pi\)
\(684\) −37.2575 −0.0544701
\(685\) −2269.02 −3.31244
\(686\) 233.149i 0.339868i
\(687\) 90.4509i 0.131661i
\(688\) 581.912i 0.845802i
\(689\) 989.370i 1.43595i
\(690\) 270.127 0.391488
\(691\) 1077.20i 1.55889i −0.626469 0.779447i \(-0.715500\pi\)
0.626469 0.779447i \(-0.284500\pi\)
\(692\) 145.153i 0.209758i
\(693\) 50.2232i 0.0724722i
\(694\) −683.103 −0.984298
\(695\) 131.993 0.189918
\(696\) 379.593i 0.545393i
\(697\) 450.389 0.646182
\(698\) 387.873 0.555692
\(699\) 727.836i 1.04125i
\(700\) 39.2658 0.0560940
\(701\) 228.502i 0.325965i −0.986629 0.162983i \(-0.947889\pi\)
0.986629 0.162983i \(-0.0521115\pi\)
\(702\) −228.097 −0.324925
\(703\) 523.109i 0.744109i
\(704\) 902.755i 1.28232i
\(705\) 480.654i 0.681779i
\(706\) 325.875 0.461579
\(707\) 92.8691i 0.131357i
\(708\) 2.48403 + 54.2722i 0.00350851 + 0.0766557i
\(709\) −162.647 −0.229403 −0.114701 0.993400i \(-0.536591\pi\)
−0.114701 + 0.993400i \(0.536591\pi\)
\(710\) 97.4094i 0.137196i
\(711\) −317.345 −0.446335
\(712\) −184.248 −0.258775
\(713\) 263.279 0.369256
\(714\) 42.4682i 0.0594793i
\(715\) 2745.92 3.84045
\(716\) 58.6233i 0.0818762i
\(717\) 272.042 0.379418
\(718\) 378.603i 0.527302i
\(719\) 719.737i 1.00102i −0.865729 0.500512i \(-0.833145\pi\)
0.865729 0.500512i \(-0.166855\pi\)
\(720\) 368.802 0.512226
\(721\) 215.862i 0.299392i
\(722\) 343.961i 0.476400i
\(723\) −168.444 −0.232979
\(724\) 11.5611 0.0159684
\(725\) −1475.49 −2.03516
\(726\) 144.736i 0.199361i
\(727\) −484.589 −0.666559 −0.333280 0.942828i \(-0.608155\pi\)
−0.333280 + 0.942828i \(0.608155\pi\)
\(728\) 258.579 0.355191
\(729\) 27.0000 0.0370370
\(730\) −700.685 −0.959842
\(731\) 433.665i 0.593250i
\(732\) 29.4503i 0.0402326i
\(733\) 1164.71 1.58896 0.794480 0.607290i \(-0.207743\pi\)
0.794480 + 0.607290i \(0.207743\pi\)
\(734\) 958.060 1.30526
\(735\) −741.216 −1.00846
\(736\) 78.2044 0.106256
\(737\) −1211.92 −1.64439
\(738\) 248.444i 0.336645i
\(739\) 157.927i 0.213703i 0.994275 + 0.106852i \(0.0340770\pi\)
−0.994275 + 0.106852i \(0.965923\pi\)
\(740\) 107.688i 0.145524i
\(741\) 953.696i 1.28704i
\(742\) 101.612i 0.136943i
\(743\) 700.568 0.942891 0.471445 0.881895i \(-0.343732\pi\)
0.471445 + 0.881895i \(0.343732\pi\)
\(744\) 415.697 0.558733
\(745\) 1646.89i 2.21059i
\(746\) 1175.90i 1.57627i
\(747\) 9.43354i 0.0126286i
\(748\) 69.3498i 0.0927136i
\(749\) 35.9393 0.0479830
\(750\) 928.413i 1.23788i
\(751\) 984.786i 1.31130i −0.755065 0.655650i \(-0.772395\pi\)
0.755065 0.655650i \(-0.227605\pi\)
\(752\) 416.955i 0.554461i
\(753\) −516.568 −0.686013
\(754\) −1139.93 −1.51184
\(755\) 287.187i 0.380381i
\(756\) −3.59088 −0.00474984
\(757\) −288.319 −0.380870 −0.190435 0.981700i \(-0.560990\pi\)
−0.190435 + 0.981700i \(0.560990\pi\)
\(758\) 366.277i 0.483215i
\(759\) 206.520 0.272095
\(760\) 1783.28i 2.34642i
\(761\) −462.140 −0.607280 −0.303640 0.952787i \(-0.598202\pi\)
−0.303640 + 0.952787i \(0.598202\pi\)
\(762\) 705.743i 0.926171i
\(763\) 143.287i 0.187794i
\(764\) 13.5390i 0.0177212i
\(765\) 274.847 0.359277
\(766\) 238.152i 0.310904i
\(767\) −1389.23 + 63.5846i −1.81125 + 0.0829005i
\(768\) 173.538 0.225961
\(769\) 569.738i 0.740881i −0.928856 0.370441i \(-0.879207\pi\)
0.928856 0.370441i \(-0.120793\pi\)
\(770\) −282.016 −0.366254
\(771\) −689.431 −0.894204
\(772\) −74.8138 −0.0969090
\(773\) 401.753i 0.519732i −0.965645 0.259866i \(-0.916322\pi\)
0.965645 0.259866i \(-0.0836784\pi\)
\(774\) −239.219 −0.309069
\(775\) 1615.83i 2.08494i
\(776\) −1065.11 −1.37257
\(777\) 50.4172i 0.0648870i
\(778\) 351.918i 0.452337i
\(779\) 1038.77 1.33347
\(780\) 196.329i 0.251703i
\(781\) 74.4723i 0.0953551i
\(782\) −174.631 −0.223313
\(783\) 134.934 0.172330
\(784\) 642.985 0.820134
\(785\) 2204.01i 2.80766i
\(786\) −793.513 −1.00956
\(787\) 454.102 0.577004 0.288502 0.957479i \(-0.406843\pi\)
0.288502 + 0.957479i \(0.406843\pi\)
\(788\) −117.687 −0.149349
\(789\) −356.506 −0.451846
\(790\) 1781.97i 2.25565i
\(791\) 90.4128i 0.114302i
\(792\)