Properties

Label 177.3.c.a.58.17
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 58.17
Root \(2.96307i\) of defining polynomial
Character \(\chi\) \(=\) 177.58
Dual form 177.3.c.a.58.4

$q$-expansion

\(f(q)\) \(=\) \(q+2.96307i q^{2} +1.73205 q^{3} -4.77980 q^{4} +3.25089 q^{5} +5.13219i q^{6} +11.8224 q^{7} -2.31061i q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+2.96307i q^{2} +1.73205 q^{3} -4.77980 q^{4} +3.25089 q^{5} +5.13219i q^{6} +11.8224 q^{7} -2.31061i q^{8} +3.00000 q^{9} +9.63262i q^{10} -16.1383i q^{11} -8.27886 q^{12} +14.1300i q^{13} +35.0306i q^{14} +5.63070 q^{15} -12.2727 q^{16} -32.0002 q^{17} +8.88922i q^{18} +14.7891 q^{19} -15.5386 q^{20} +20.4770 q^{21} +47.8190 q^{22} -14.5859i q^{23} -4.00209i q^{24} -14.4317 q^{25} -41.8681 q^{26} +5.19615 q^{27} -56.5086 q^{28} -12.7940 q^{29} +16.6842i q^{30} +27.0884i q^{31} -45.6074i q^{32} -27.9523i q^{33} -94.8189i q^{34} +38.4332 q^{35} -14.3394 q^{36} -26.2136i q^{37} +43.8211i q^{38} +24.4738i q^{39} -7.51154i q^{40} -37.3257 q^{41} +60.6747i q^{42} -51.1308i q^{43} +77.1379i q^{44} +9.75266 q^{45} +43.2190 q^{46} +79.6198i q^{47} -21.2569 q^{48} +90.7685 q^{49} -42.7623i q^{50} -55.4260 q^{51} -67.5384i q^{52} +86.2911 q^{53} +15.3966i q^{54} -52.4638i q^{55} -27.3169i q^{56} +25.6154 q^{57} -37.9096i q^{58} +(-18.5829 - 55.9971i) q^{59} -26.9136 q^{60} +92.8151i q^{61} -80.2651 q^{62} +35.4671 q^{63} +86.0471 q^{64} +45.9349i q^{65} +82.8249 q^{66} -88.8299i q^{67} +152.955 q^{68} -25.2634i q^{69} +113.880i q^{70} -13.4604 q^{71} -6.93183i q^{72} -42.9424i q^{73} +77.6729 q^{74} -24.9965 q^{75} -70.6888 q^{76} -190.793i q^{77} -72.5177 q^{78} -1.74748 q^{79} -39.8972 q^{80} +9.00000 q^{81} -110.599i q^{82} +12.9404i q^{83} -97.8758 q^{84} -104.029 q^{85} +151.504 q^{86} -22.1599 q^{87} -37.2893 q^{88} -69.4234i q^{89} +28.8979i q^{90} +167.050i q^{91} +69.7175i q^{92} +46.9186i q^{93} -235.919 q^{94} +48.0776 q^{95} -78.9942i q^{96} -101.219i q^{97} +268.954i q^{98} -48.4149i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 40q^{4} - 8q^{7} + 60q^{9} + O(q^{10}) \) \( 20q - 40q^{4} - 8q^{7} + 60q^{9} - 24q^{12} + 24q^{15} - 8q^{16} + 16q^{17} - 60q^{19} - 164q^{20} + 40q^{22} + 100q^{25} - 156q^{26} + 200q^{28} - 60q^{29} - 32q^{35} - 120q^{36} + 28q^{41} + 180q^{46} - 96q^{48} + 284q^{49} - 24q^{51} - 8q^{53} + 24q^{57} - 152q^{59} - 72q^{60} - 8q^{62} - 24q^{63} + 204q^{64} - 120q^{66} + 384q^{68} + 92q^{71} + 104q^{74} + 240q^{75} + 120q^{76} - 468q^{78} - 420q^{79} + 376q^{80} + 180q^{81} + 168q^{84} - 348q^{85} + 232q^{86} + 144q^{87} - 212q^{88} + 152q^{94} + 788q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.96307i 1.48154i 0.671761 + 0.740768i \(0.265538\pi\)
−0.671761 + 0.740768i \(0.734462\pi\)
\(3\) 1.73205 0.577350
\(4\) −4.77980 −1.19495
\(5\) 3.25089 0.650178 0.325089 0.945683i \(-0.394606\pi\)
0.325089 + 0.945683i \(0.394606\pi\)
\(6\) 5.13219i 0.855366i
\(7\) 11.8224 1.68891 0.844455 0.535626i \(-0.179924\pi\)
0.844455 + 0.535626i \(0.179924\pi\)
\(8\) 2.31061i 0.288826i
\(9\) 3.00000 0.333333
\(10\) 9.63262i 0.963262i
\(11\) 16.1383i 1.46712i −0.679626 0.733559i \(-0.737858\pi\)
0.679626 0.733559i \(-0.262142\pi\)
\(12\) −8.27886 −0.689905
\(13\) 14.1300i 1.08692i 0.839435 + 0.543460i \(0.182886\pi\)
−0.839435 + 0.543460i \(0.817114\pi\)
\(14\) 35.0306i 2.50218i
\(15\) 5.63070 0.375380
\(16\) −12.2727 −0.767044
\(17\) −32.0002 −1.88236 −0.941182 0.337900i \(-0.890283\pi\)
−0.941182 + 0.337900i \(0.890283\pi\)
\(18\) 8.88922i 0.493846i
\(19\) 14.7891 0.778372 0.389186 0.921159i \(-0.372756\pi\)
0.389186 + 0.921159i \(0.372756\pi\)
\(20\) −15.5386 −0.776930
\(21\) 20.4770 0.975093
\(22\) 47.8190 2.17359
\(23\) 14.5859i 0.634168i −0.948398 0.317084i \(-0.897296\pi\)
0.948398 0.317084i \(-0.102704\pi\)
\(24\) 4.00209i 0.166754i
\(25\) −14.4317 −0.577269
\(26\) −41.8681 −1.61031
\(27\) 5.19615 0.192450
\(28\) −56.5086 −2.01816
\(29\) −12.7940 −0.441172 −0.220586 0.975367i \(-0.570797\pi\)
−0.220586 + 0.975367i \(0.570797\pi\)
\(30\) 16.6842i 0.556139i
\(31\) 27.0884i 0.873821i 0.899505 + 0.436910i \(0.143927\pi\)
−0.899505 + 0.436910i \(0.856073\pi\)
\(32\) 45.6074i 1.42523i
\(33\) 27.9523i 0.847041i
\(34\) 94.8189i 2.78879i
\(35\) 38.4332 1.09809
\(36\) −14.3394 −0.398317
\(37\) 26.2136i 0.708476i −0.935155 0.354238i \(-0.884740\pi\)
0.935155 0.354238i \(-0.115260\pi\)
\(38\) 43.8211i 1.15319i
\(39\) 24.4738i 0.627534i
\(40\) 7.51154i 0.187788i
\(41\) −37.3257 −0.910383 −0.455192 0.890394i \(-0.650429\pi\)
−0.455192 + 0.890394i \(0.650429\pi\)
\(42\) 60.6747i 1.44464i
\(43\) 51.1308i 1.18909i −0.804063 0.594544i \(-0.797332\pi\)
0.804063 0.594544i \(-0.202668\pi\)
\(44\) 77.1379i 1.75313i
\(45\) 9.75266 0.216726
\(46\) 43.2190 0.939542
\(47\) 79.6198i 1.69404i 0.531563 + 0.847019i \(0.321605\pi\)
−0.531563 + 0.847019i \(0.678395\pi\)
\(48\) −21.2569 −0.442853
\(49\) 90.7685 1.85242
\(50\) 42.7623i 0.855245i
\(51\) −55.4260 −1.08678
\(52\) 67.5384i 1.29882i
\(53\) 86.2911 1.62813 0.814067 0.580770i \(-0.197249\pi\)
0.814067 + 0.580770i \(0.197249\pi\)
\(54\) 15.3966i 0.285122i
\(55\) 52.4638i 0.953887i
\(56\) 27.3169i 0.487802i
\(57\) 25.6154 0.449393
\(58\) 37.9096i 0.653613i
\(59\) −18.5829 55.9971i −0.314965 0.949103i
\(60\) −26.9136 −0.448561
\(61\) 92.8151i 1.52156i 0.649010 + 0.760780i \(0.275183\pi\)
−0.649010 + 0.760780i \(0.724817\pi\)
\(62\) −80.2651 −1.29460
\(63\) 35.4671 0.562970
\(64\) 86.0471 1.34449
\(65\) 45.9349i 0.706691i
\(66\) 82.8249 1.25492
\(67\) 88.8299i 1.32582i −0.748700 0.662909i \(-0.769321\pi\)
0.748700 0.662909i \(-0.230679\pi\)
\(68\) 152.955 2.24933
\(69\) 25.2634i 0.366137i
\(70\) 113.880i 1.62686i
\(71\) −13.4604 −0.189583 −0.0947916 0.995497i \(-0.530218\pi\)
−0.0947916 + 0.995497i \(0.530218\pi\)
\(72\) 6.93183i 0.0962754i
\(73\) 42.9424i 0.588252i −0.955767 0.294126i \(-0.904972\pi\)
0.955767 0.294126i \(-0.0950285\pi\)
\(74\) 77.6729 1.04963
\(75\) −24.9965 −0.333286
\(76\) −70.6888 −0.930116
\(77\) 190.793i 2.47783i
\(78\) −72.5177 −0.929714
\(79\) −1.74748 −0.0221201 −0.0110600 0.999939i \(-0.503521\pi\)
−0.0110600 + 0.999939i \(0.503521\pi\)
\(80\) −39.8972 −0.498715
\(81\) 9.00000 0.111111
\(82\) 110.599i 1.34877i
\(83\) 12.9404i 0.155908i 0.996957 + 0.0779542i \(0.0248388\pi\)
−0.996957 + 0.0779542i \(0.975161\pi\)
\(84\) −97.8758 −1.16519
\(85\) −104.029 −1.22387
\(86\) 151.504 1.76168
\(87\) −22.1599 −0.254711
\(88\) −37.2893 −0.423742
\(89\) 69.4234i 0.780038i −0.920807 0.390019i \(-0.872468\pi\)
0.920807 0.390019i \(-0.127532\pi\)
\(90\) 28.8979i 0.321087i
\(91\) 167.050i 1.83571i
\(92\) 69.7175i 0.757799i
\(93\) 46.9186i 0.504501i
\(94\) −235.919 −2.50978
\(95\) 48.0776 0.506080
\(96\) 78.9942i 0.822857i
\(97\) 101.219i 1.04350i −0.853099 0.521748i \(-0.825280\pi\)
0.853099 0.521748i \(-0.174720\pi\)
\(98\) 268.954i 2.74443i
\(99\) 48.4149i 0.489039i
\(100\) 68.9808 0.689808
\(101\) 20.7851i 0.205793i 0.994692 + 0.102896i \(0.0328110\pi\)
−0.994692 + 0.102896i \(0.967189\pi\)
\(102\) 164.231i 1.61011i
\(103\) 69.7688i 0.677367i 0.940900 + 0.338683i \(0.109982\pi\)
−0.940900 + 0.338683i \(0.890018\pi\)
\(104\) 32.6488 0.313931
\(105\) 66.5683 0.633984
\(106\) 255.687i 2.41214i
\(107\) −80.8718 −0.755811 −0.377906 0.925844i \(-0.623356\pi\)
−0.377906 + 0.925844i \(0.623356\pi\)
\(108\) −24.8366 −0.229968
\(109\) 191.875i 1.76032i 0.474676 + 0.880160i \(0.342565\pi\)
−0.474676 + 0.880160i \(0.657435\pi\)
\(110\) 155.454 1.41322
\(111\) 45.4033i 0.409039i
\(112\) −145.092 −1.29547
\(113\) 83.6727i 0.740467i −0.928939 0.370233i \(-0.879278\pi\)
0.928939 0.370233i \(-0.120722\pi\)
\(114\) 75.9003i 0.665792i
\(115\) 47.4170i 0.412322i
\(116\) 61.1528 0.527179
\(117\) 42.3899i 0.362307i
\(118\) 165.924 55.0625i 1.40613 0.466632i
\(119\) −378.318 −3.17914
\(120\) 13.0104i 0.108420i
\(121\) −139.445 −1.15243
\(122\) −275.018 −2.25425
\(123\) −64.6500 −0.525610
\(124\) 129.477i 1.04417i
\(125\) −128.188 −1.02551
\(126\) 105.092i 0.834061i
\(127\) 67.6520 0.532693 0.266347 0.963877i \(-0.414183\pi\)
0.266347 + 0.963877i \(0.414183\pi\)
\(128\) 72.5345i 0.566676i
\(129\) 88.5612i 0.686521i
\(130\) −136.109 −1.04699
\(131\) 97.5354i 0.744545i 0.928123 + 0.372273i \(0.121421\pi\)
−0.928123 + 0.372273i \(0.878579\pi\)
\(132\) 133.607i 1.01217i
\(133\) 174.842 1.31460
\(134\) 263.209 1.96425
\(135\) 16.8921 0.125127
\(136\) 73.9400i 0.543676i
\(137\) −13.3827 −0.0976840 −0.0488420 0.998807i \(-0.515553\pi\)
−0.0488420 + 0.998807i \(0.515553\pi\)
\(138\) 74.8574 0.542445
\(139\) 78.8449 0.567230 0.283615 0.958938i \(-0.408466\pi\)
0.283615 + 0.958938i \(0.408466\pi\)
\(140\) −183.703 −1.31217
\(141\) 137.905i 0.978053i
\(142\) 39.8842i 0.280874i
\(143\) 228.034 1.59464
\(144\) −36.8181 −0.255681
\(145\) −41.5919 −0.286840
\(146\) 127.241 0.871516
\(147\) 157.216 1.06949
\(148\) 125.296i 0.846594i
\(149\) 3.94936i 0.0265058i −0.999912 0.0132529i \(-0.995781\pi\)
0.999912 0.0132529i \(-0.00421865\pi\)
\(150\) 74.0664i 0.493776i
\(151\) 57.9839i 0.383999i −0.981395 0.192000i \(-0.938503\pi\)
0.981395 0.192000i \(-0.0614973\pi\)
\(152\) 34.1718i 0.224814i
\(153\) −96.0006 −0.627455
\(154\) 565.334 3.67100
\(155\) 88.0615i 0.568139i
\(156\) 116.980i 0.749872i
\(157\) 115.827i 0.737751i −0.929479 0.368876i \(-0.879743\pi\)
0.929479 0.368876i \(-0.120257\pi\)
\(158\) 5.17792i 0.0327717i
\(159\) 149.461 0.940004
\(160\) 148.264i 0.926652i
\(161\) 172.439i 1.07105i
\(162\) 26.6677i 0.164615i
\(163\) −249.112 −1.52830 −0.764149 0.645040i \(-0.776841\pi\)
−0.764149 + 0.645040i \(0.776841\pi\)
\(164\) 178.410 1.08786
\(165\) 90.8700i 0.550727i
\(166\) −38.3433 −0.230984
\(167\) 50.4157 0.301890 0.150945 0.988542i \(-0.451768\pi\)
0.150945 + 0.988542i \(0.451768\pi\)
\(168\) 47.3143i 0.281633i
\(169\) −30.6558 −0.181395
\(170\) 308.246i 1.81321i
\(171\) 44.3672 0.259457
\(172\) 244.395i 1.42090i
\(173\) 13.4190i 0.0775665i 0.999248 + 0.0387832i \(0.0123482\pi\)
−0.999248 + 0.0387832i \(0.987652\pi\)
\(174\) 65.6613i 0.377364i
\(175\) −170.617 −0.974956
\(176\) 198.060i 1.12534i
\(177\) −32.1866 96.9898i −0.181845 0.547965i
\(178\) 205.707 1.15565
\(179\) 103.685i 0.579247i −0.957141 0.289623i \(-0.906470\pi\)
0.957141 0.289623i \(-0.0935300\pi\)
\(180\) −46.6158 −0.258977
\(181\) 120.947 0.668214 0.334107 0.942535i \(-0.391565\pi\)
0.334107 + 0.942535i \(0.391565\pi\)
\(182\) −494.980 −2.71967
\(183\) 160.760i 0.878473i
\(184\) −33.7022 −0.183164
\(185\) 85.2175i 0.460635i
\(186\) −139.023 −0.747436
\(187\) 516.429i 2.76165i
\(188\) 380.567i 2.02429i
\(189\) 61.4309 0.325031
\(190\) 142.457i 0.749776i
\(191\) 226.707i 1.18695i 0.804854 + 0.593473i \(0.202244\pi\)
−0.804854 + 0.593473i \(0.797756\pi\)
\(192\) 149.038 0.776239
\(193\) 145.379 0.753261 0.376630 0.926364i \(-0.377083\pi\)
0.376630 + 0.926364i \(0.377083\pi\)
\(194\) 299.920 1.54598
\(195\) 79.5616i 0.408008i
\(196\) −433.856 −2.21355
\(197\) 95.2626 0.483567 0.241783 0.970330i \(-0.422268\pi\)
0.241783 + 0.970330i \(0.422268\pi\)
\(198\) 143.457 0.724530
\(199\) 119.091 0.598447 0.299224 0.954183i \(-0.403272\pi\)
0.299224 + 0.954183i \(0.403272\pi\)
\(200\) 33.3461i 0.166731i
\(201\) 153.858i 0.765462i
\(202\) −61.5877 −0.304890
\(203\) −151.255 −0.745101
\(204\) 264.925 1.29865
\(205\) −121.342 −0.591911
\(206\) −206.730 −1.00354
\(207\) 43.7576i 0.211389i
\(208\) 173.413i 0.833715i
\(209\) 238.670i 1.14196i
\(210\) 197.247i 0.939270i
\(211\) 129.974i 0.615990i 0.951388 + 0.307995i \(0.0996581\pi\)
−0.951388 + 0.307995i \(0.900342\pi\)
\(212\) −412.455 −1.94554
\(213\) −23.3141 −0.109456
\(214\) 239.629i 1.11976i
\(215\) 166.221i 0.773119i
\(216\) 12.0063i 0.0555846i
\(217\) 320.250i 1.47581i
\(218\) −568.540 −2.60798
\(219\) 74.3784i 0.339627i
\(220\) 250.767i 1.13985i
\(221\) 452.161i 2.04598i
\(222\) 134.533 0.606006
\(223\) −21.6836 −0.0972360 −0.0486180 0.998817i \(-0.515482\pi\)
−0.0486180 + 0.998817i \(0.515482\pi\)
\(224\) 539.187i 2.40709i
\(225\) −43.2952 −0.192423
\(226\) 247.928 1.09703
\(227\) 237.429i 1.04594i 0.852350 + 0.522972i \(0.175177\pi\)
−0.852350 + 0.522972i \(0.824823\pi\)
\(228\) −122.437 −0.537003
\(229\) 203.447i 0.888415i 0.895924 + 0.444208i \(0.146515\pi\)
−0.895924 + 0.444208i \(0.853485\pi\)
\(230\) 140.500 0.610869
\(231\) 330.463i 1.43058i
\(232\) 29.5620i 0.127422i
\(233\) 328.561i 1.41013i 0.709142 + 0.705066i \(0.249082\pi\)
−0.709142 + 0.705066i \(0.750918\pi\)
\(234\) −125.604 −0.536771
\(235\) 258.835i 1.10143i
\(236\) 88.8226 + 267.655i 0.376367 + 1.13413i
\(237\) −3.02673 −0.0127710
\(238\) 1120.98i 4.71002i
\(239\) 206.816 0.865339 0.432669 0.901553i \(-0.357572\pi\)
0.432669 + 0.901553i \(0.357572\pi\)
\(240\) −69.1039 −0.287933
\(241\) −138.114 −0.573085 −0.286543 0.958068i \(-0.592506\pi\)
−0.286543 + 0.958068i \(0.592506\pi\)
\(242\) 413.185i 1.70737i
\(243\) 15.5885 0.0641500
\(244\) 443.638i 1.81819i
\(245\) 295.078 1.20440
\(246\) 191.563i 0.778710i
\(247\) 208.969i 0.846028i
\(248\) 62.5909 0.252382
\(249\) 22.4134i 0.0900137i
\(250\) 379.831i 1.51932i
\(251\) 439.750 1.75199 0.875996 0.482319i \(-0.160205\pi\)
0.875996 + 0.482319i \(0.160205\pi\)
\(252\) −169.526 −0.672722
\(253\) −235.391 −0.930399
\(254\) 200.458i 0.789204i
\(255\) −180.184 −0.706602
\(256\) 129.263 0.504936
\(257\) 258.065 1.00414 0.502072 0.864826i \(-0.332571\pi\)
0.502072 + 0.864826i \(0.332571\pi\)
\(258\) 262.413 1.01711
\(259\) 309.907i 1.19655i
\(260\) 219.560i 0.844461i
\(261\) −38.3820 −0.147057
\(262\) −289.005 −1.10307
\(263\) −238.300 −0.906084 −0.453042 0.891489i \(-0.649661\pi\)
−0.453042 + 0.891489i \(0.649661\pi\)
\(264\) −64.5870 −0.244648
\(265\) 280.523 1.05858
\(266\) 518.069i 1.94763i
\(267\) 120.245i 0.450355i
\(268\) 424.589i 1.58429i
\(269\) 320.536i 1.19158i 0.803138 + 0.595792i \(0.203162\pi\)
−0.803138 + 0.595792i \(0.796838\pi\)
\(270\) 50.0526i 0.185380i
\(271\) −56.4111 −0.208159 −0.104079 0.994569i \(-0.533190\pi\)
−0.104079 + 0.994569i \(0.533190\pi\)
\(272\) 392.729 1.44386
\(273\) 289.339i 1.05985i
\(274\) 39.6539i 0.144722i
\(275\) 232.904i 0.846922i
\(276\) 120.754i 0.437515i
\(277\) −238.376 −0.860562 −0.430281 0.902695i \(-0.641585\pi\)
−0.430281 + 0.902695i \(0.641585\pi\)
\(278\) 233.623i 0.840372i
\(279\) 81.2653i 0.291274i
\(280\) 88.8042i 0.317158i
\(281\) −161.899 −0.576154 −0.288077 0.957607i \(-0.593016\pi\)
−0.288077 + 0.957607i \(0.593016\pi\)
\(282\) −408.624 −1.44902
\(283\) 411.702i 1.45478i 0.686226 + 0.727388i \(0.259266\pi\)
−0.686226 + 0.727388i \(0.740734\pi\)
\(284\) 64.3381 0.226542
\(285\) 83.2728 0.292185
\(286\) 675.680i 2.36252i
\(287\) −441.278 −1.53756
\(288\) 136.822i 0.475077i
\(289\) 735.012 2.54329
\(290\) 123.240i 0.424965i
\(291\) 175.317i 0.602463i
\(292\) 205.256i 0.702932i
\(293\) 14.3590 0.0490069 0.0245034 0.999700i \(-0.492200\pi\)
0.0245034 + 0.999700i \(0.492200\pi\)
\(294\) 465.842i 1.58450i
\(295\) −60.4110 182.040i −0.204783 0.617086i
\(296\) −60.5695 −0.204627
\(297\) 83.8570i 0.282347i
\(298\) 11.7023 0.0392693
\(299\) 206.098 0.689290
\(300\) 119.478 0.398261
\(301\) 604.488i 2.00826i
\(302\) 171.811 0.568909
\(303\) 36.0008i 0.118815i
\(304\) −181.502 −0.597045
\(305\) 301.732i 0.989284i
\(306\) 284.457i 0.929597i
\(307\) −200.292 −0.652415 −0.326208 0.945298i \(-0.605771\pi\)
−0.326208 + 0.945298i \(0.605771\pi\)
\(308\) 911.953i 2.96089i
\(309\) 120.843i 0.391078i
\(310\) −260.933 −0.841718
\(311\) −175.394 −0.563969 −0.281984 0.959419i \(-0.590993\pi\)
−0.281984 + 0.959419i \(0.590993\pi\)
\(312\) 56.5494 0.181248
\(313\) 47.0884i 0.150442i 0.997167 + 0.0752210i \(0.0239662\pi\)
−0.997167 + 0.0752210i \(0.976034\pi\)
\(314\) 343.204 1.09301
\(315\) 115.300 0.366031
\(316\) 8.35263 0.0264324
\(317\) 204.197 0.644155 0.322077 0.946713i \(-0.395619\pi\)
0.322077 + 0.946713i \(0.395619\pi\)
\(318\) 442.863i 1.39265i
\(319\) 206.473i 0.647252i
\(320\) 279.730 0.874155
\(321\) −140.074 −0.436368
\(322\) 510.951 1.58680
\(323\) −473.253 −1.46518
\(324\) −43.0182 −0.132772
\(325\) 203.920i 0.627445i
\(326\) 738.138i 2.26423i
\(327\) 332.337i 1.01632i
\(328\) 86.2452i 0.262943i
\(329\) 941.295i 2.86108i
\(330\) 269.254 0.815922
\(331\) −540.983 −1.63439 −0.817195 0.576361i \(-0.804472\pi\)
−0.817195 + 0.576361i \(0.804472\pi\)
\(332\) 61.8525i 0.186303i
\(333\) 78.6409i 0.236159i
\(334\) 149.385i 0.447261i
\(335\) 288.776i 0.862018i
\(336\) −251.307 −0.747939
\(337\) 616.965i 1.83076i −0.402593 0.915379i \(-0.631891\pi\)
0.402593 0.915379i \(-0.368109\pi\)
\(338\) 90.8355i 0.268744i
\(339\) 144.925i 0.427509i
\(340\) 497.238 1.46247
\(341\) 437.161 1.28200
\(342\) 131.463i 0.384395i
\(343\) 493.803 1.43966
\(344\) −118.143 −0.343440
\(345\) 82.1286i 0.238054i
\(346\) −39.7615 −0.114918
\(347\) 47.1982i 0.136018i −0.997685 0.0680090i \(-0.978335\pi\)
0.997685 0.0680090i \(-0.0216647\pi\)
\(348\) 105.920 0.304367
\(349\) 36.9208i 0.105790i −0.998600 0.0528952i \(-0.983155\pi\)
0.998600 0.0528952i \(-0.0168449\pi\)
\(350\) 505.551i 1.44443i
\(351\) 73.4214i 0.209178i
\(352\) −736.025 −2.09098
\(353\) 83.2316i 0.235784i 0.993026 + 0.117892i \(0.0376136\pi\)
−0.993026 + 0.117892i \(0.962386\pi\)
\(354\) 287.388 95.3711i 0.811830 0.269410i
\(355\) −43.7583 −0.123263
\(356\) 331.830i 0.932107i
\(357\) −655.266 −1.83548
\(358\) 307.227 0.858175
\(359\) 505.228 1.40732 0.703660 0.710537i \(-0.251548\pi\)
0.703660 + 0.710537i \(0.251548\pi\)
\(360\) 22.5346i 0.0625961i
\(361\) −142.284 −0.394137
\(362\) 358.374i 0.989983i
\(363\) −241.525 −0.665359
\(364\) 798.464i 2.19358i
\(365\) 139.601i 0.382468i
\(366\) −476.345 −1.30149
\(367\) 49.1101i 0.133815i 0.997759 + 0.0669075i \(0.0213132\pi\)
−0.997759 + 0.0669075i \(0.978687\pi\)
\(368\) 179.008i 0.486434i
\(369\) −111.977 −0.303461
\(370\) 252.506 0.682448
\(371\) 1020.17 2.74977
\(372\) 224.261i 0.602853i
\(373\) −583.281 −1.56376 −0.781879 0.623431i \(-0.785738\pi\)
−0.781879 + 0.623431i \(0.785738\pi\)
\(374\) −1530.22 −4.09149
\(375\) −222.028 −0.592076
\(376\) 183.970 0.489283
\(377\) 180.779i 0.479519i
\(378\) 182.024i 0.481545i
\(379\) 161.645 0.426504 0.213252 0.976997i \(-0.431594\pi\)
0.213252 + 0.976997i \(0.431594\pi\)
\(380\) −229.801 −0.604740
\(381\) 117.177 0.307550
\(382\) −671.749 −1.75851
\(383\) −167.234 −0.436642 −0.218321 0.975877i \(-0.570058\pi\)
−0.218321 + 0.975877i \(0.570058\pi\)
\(384\) 125.633i 0.327170i
\(385\) 620.247i 1.61103i
\(386\) 430.770i 1.11598i
\(387\) 153.392i 0.396363i
\(388\) 483.808i 1.24693i
\(389\) −327.884 −0.842889 −0.421445 0.906854i \(-0.638477\pi\)
−0.421445 + 0.906854i \(0.638477\pi\)
\(390\) −235.747 −0.604479
\(391\) 466.750i 1.19373i
\(392\) 209.731i 0.535027i
\(393\) 168.936i 0.429863i
\(394\) 282.270i 0.716421i
\(395\) −5.68088 −0.0143820
\(396\) 231.414i 0.584378i
\(397\) 691.182i 1.74101i −0.492156 0.870507i \(-0.663791\pi\)
0.492156 0.870507i \(-0.336209\pi\)
\(398\) 352.875i 0.886621i
\(399\) 302.835 0.758985
\(400\) 177.116 0.442791
\(401\) 102.992i 0.256838i 0.991720 + 0.128419i \(0.0409903\pi\)
−0.991720 + 0.128419i \(0.959010\pi\)
\(402\) 455.892 1.13406
\(403\) −382.759 −0.949774
\(404\) 99.3485i 0.245912i
\(405\) 29.2580 0.0722420
\(406\) 448.181i 1.10389i
\(407\) −423.043 −1.03942
\(408\) 128.068i 0.313892i
\(409\) 720.907i 1.76261i −0.472549 0.881304i \(-0.656666\pi\)
0.472549 0.881304i \(-0.343334\pi\)
\(410\) 359.544i 0.876937i
\(411\) −23.1795 −0.0563979
\(412\) 333.481i 0.809420i
\(413\) −219.694 662.019i −0.531947 1.60295i
\(414\) 129.657 0.313181
\(415\) 42.0678i 0.101368i
\(416\) 644.430 1.54911
\(417\) 136.563 0.327490
\(418\) 707.198 1.69186
\(419\) 642.761i 1.53404i −0.641626 0.767018i \(-0.721740\pi\)
0.641626 0.767018i \(-0.278260\pi\)
\(420\) −318.183 −0.757579
\(421\) 110.137i 0.261607i 0.991408 + 0.130804i \(0.0417557\pi\)
−0.991408 + 0.130804i \(0.958244\pi\)
\(422\) −385.122 −0.912612
\(423\) 238.859i 0.564679i
\(424\) 199.385i 0.470248i
\(425\) 461.818 1.08663
\(426\) 69.0814i 0.162163i
\(427\) 1097.29i 2.56978i
\(428\) 386.551 0.903157
\(429\) 394.966 0.920666
\(430\) 492.524 1.14540
\(431\) 209.550i 0.486194i −0.970002 0.243097i \(-0.921837\pi\)
0.970002 0.243097i \(-0.0781633\pi\)
\(432\) −63.7708 −0.147618
\(433\) −24.0985 −0.0556548 −0.0278274 0.999613i \(-0.508859\pi\)
−0.0278274 + 0.999613i \(0.508859\pi\)
\(434\) −948.923 −2.18646
\(435\) −72.0392 −0.165607
\(436\) 917.124i 2.10350i
\(437\) 215.711i 0.493618i
\(438\) 220.389 0.503170
\(439\) −552.406 −1.25833 −0.629164 0.777273i \(-0.716603\pi\)
−0.629164 + 0.777273i \(0.716603\pi\)
\(440\) −121.223 −0.275508
\(441\) 272.306 0.617473
\(442\) 1339.79 3.03119
\(443\) 406.654i 0.917955i 0.888448 + 0.458977i \(0.151784\pi\)
−0.888448 + 0.458977i \(0.848216\pi\)
\(444\) 217.019i 0.488781i
\(445\) 225.688i 0.507163i
\(446\) 64.2502i 0.144059i
\(447\) 6.84050i 0.0153031i
\(448\) 1017.28 2.27072
\(449\) −107.442 −0.239292 −0.119646 0.992817i \(-0.538176\pi\)
−0.119646 + 0.992817i \(0.538176\pi\)
\(450\) 128.287i 0.285082i
\(451\) 602.373i 1.33564i
\(452\) 399.939i 0.884821i
\(453\) 100.431i 0.221702i
\(454\) −703.521 −1.54961
\(455\) 543.060i 1.19354i
\(456\) 59.1872i 0.129797i
\(457\) 145.963i 0.319393i 0.987166 + 0.159697i \(0.0510516\pi\)
−0.987166 + 0.159697i \(0.948948\pi\)
\(458\) −602.829 −1.31622
\(459\) −166.278 −0.362261
\(460\) 226.644i 0.492704i
\(461\) −194.199 −0.421255 −0.210628 0.977566i \(-0.567551\pi\)
−0.210628 + 0.977566i \(0.567551\pi\)
\(462\) 979.186 2.11945
\(463\) 40.1621i 0.0867433i −0.999059 0.0433716i \(-0.986190\pi\)
0.999059 0.0433716i \(-0.0138100\pi\)
\(464\) 157.017 0.338399
\(465\) 152.527i 0.328015i
\(466\) −973.549 −2.08916
\(467\) 316.774i 0.678316i −0.940729 0.339158i \(-0.889858\pi\)
0.940729 0.339158i \(-0.110142\pi\)
\(468\) 202.615i 0.432939i
\(469\) 1050.18i 2.23919i
\(470\) −766.947 −1.63180
\(471\) 200.618i 0.425941i
\(472\) −129.387 + 42.9379i −0.274126 + 0.0909701i
\(473\) −825.164 −1.74453
\(474\) 8.96843i 0.0189207i
\(475\) −213.432 −0.449330
\(476\) 1808.29 3.79892
\(477\) 258.873 0.542712
\(478\) 612.811i 1.28203i
\(479\) 124.453 0.259818 0.129909 0.991526i \(-0.458532\pi\)
0.129909 + 0.991526i \(0.458532\pi\)
\(480\) 256.801i 0.535003i
\(481\) 370.397 0.770057
\(482\) 409.240i 0.849047i
\(483\) 298.674i 0.618372i
\(484\) 666.518 1.37710
\(485\) 329.052i 0.678458i
\(486\) 46.1897i 0.0950406i
\(487\) 97.3968 0.199993 0.0999967 0.994988i \(-0.468117\pi\)
0.0999967 + 0.994988i \(0.468117\pi\)
\(488\) 214.460 0.439466
\(489\) −431.475 −0.882363
\(490\) 874.339i 1.78436i
\(491\) 548.845 1.11781 0.558905 0.829231i \(-0.311221\pi\)
0.558905 + 0.829231i \(0.311221\pi\)
\(492\) 309.014 0.628078
\(493\) 409.410 0.830447
\(494\) −619.190 −1.25342
\(495\) 157.391i 0.317962i
\(496\) 332.448i 0.670259i
\(497\) −159.134 −0.320189
\(498\) −66.4126 −0.133359
\(499\) −184.851 −0.370443 −0.185221 0.982697i \(-0.559300\pi\)
−0.185221 + 0.982697i \(0.559300\pi\)
\(500\) 612.714 1.22543
\(501\) 87.3225 0.174296
\(502\) 1303.01i 2.59564i
\(503\) 244.747i 0.486574i 0.969954 + 0.243287i \(0.0782256\pi\)
−0.969954 + 0.243287i \(0.921774\pi\)
\(504\) 81.9507i 0.162601i
\(505\) 67.5699i 0.133802i
\(506\) 697.480i 1.37842i
\(507\) −53.0975 −0.104729
\(508\) −323.363 −0.636542
\(509\) 66.3400i 0.130334i −0.997874 0.0651670i \(-0.979242\pi\)
0.997874 0.0651670i \(-0.0207580\pi\)
\(510\) 533.897i 1.04686i
\(511\) 507.681i 0.993504i
\(512\) 673.155i 1.31476i
\(513\) 76.8462 0.149798
\(514\) 764.666i 1.48768i
\(515\) 226.810i 0.440409i
\(516\) 423.305i 0.820358i
\(517\) 1284.93 2.48535
\(518\) 918.278 1.77274
\(519\) 23.2424i 0.0447830i
\(520\) 106.138 0.204111
\(521\) −762.537 −1.46360 −0.731802 0.681518i \(-0.761320\pi\)
−0.731802 + 0.681518i \(0.761320\pi\)
\(522\) 113.729i 0.217871i
\(523\) 402.292 0.769201 0.384600 0.923083i \(-0.374339\pi\)
0.384600 + 0.923083i \(0.374339\pi\)
\(524\) 466.200i 0.889694i
\(525\) −295.518 −0.562891
\(526\) 706.100i 1.34240i
\(527\) 866.835i 1.64485i
\(528\) 343.051i 0.649717i
\(529\) 316.253 0.597831
\(530\) 831.210i 1.56832i
\(531\) −55.7487 167.991i −0.104988 0.316368i
\(532\) −835.709 −1.57088
\(533\) 527.411i 0.989514i
\(534\) 356.294 0.667218
\(535\) −262.905 −0.491411
\(536\) −205.251 −0.382931
\(537\) 179.588i 0.334428i
\(538\) −949.773 −1.76538
\(539\) 1464.85i 2.71772i
\(540\) −80.7409 −0.149520
\(541\) 479.860i 0.886987i 0.896278 + 0.443494i \(0.146261\pi\)
−0.896278 + 0.443494i \(0.853739\pi\)
\(542\) 167.150i 0.308395i
\(543\) 209.486 0.385793
\(544\) 1459.44i 2.68280i
\(545\) 623.764i 1.14452i
\(546\) −857.331 −1.57020
\(547\) 670.600 1.22596 0.612980 0.790098i \(-0.289971\pi\)
0.612980 + 0.790098i \(0.289971\pi\)
\(548\) 63.9667 0.116728
\(549\) 278.445i 0.507186i
\(550\) −690.110 −1.25475
\(551\) −189.211 −0.343396
\(552\) −58.3740 −0.105750
\(553\) −20.6594 −0.0373588
\(554\) 706.324i 1.27495i
\(555\) 147.601i 0.265948i
\(556\) −376.863 −0.677812
\(557\) 719.857 1.29238 0.646191 0.763176i \(-0.276361\pi\)
0.646191 + 0.763176i \(0.276361\pi\)
\(558\) −240.795 −0.431533
\(559\) 722.476 1.29244
\(560\) −471.679 −0.842284
\(561\) 894.480i 1.59444i
\(562\) 479.719i 0.853593i
\(563\) 622.327i 1.10538i 0.833388 + 0.552688i \(0.186398\pi\)
−0.833388 + 0.552688i \(0.813602\pi\)
\(564\) 659.161i 1.16872i
\(565\) 272.011i 0.481435i
\(566\) −1219.90 −2.15530
\(567\) 106.401 0.187657
\(568\) 31.1017i 0.0547566i
\(569\) 540.853i 0.950532i 0.879842 + 0.475266i \(0.157648\pi\)
−0.879842 + 0.475266i \(0.842352\pi\)
\(570\) 246.743i 0.432883i
\(571\) 783.357i 1.37190i 0.727647 + 0.685952i \(0.240614\pi\)
−0.727647 + 0.685952i \(0.759386\pi\)
\(572\) −1089.96 −1.90552
\(573\) 392.668i 0.685284i
\(574\) 1307.54i 2.27794i
\(575\) 210.499i 0.366085i
\(576\) 258.141 0.448162
\(577\) −1080.41 −1.87246 −0.936229 0.351390i \(-0.885709\pi\)
−0.936229 + 0.351390i \(0.885709\pi\)
\(578\) 2177.89i 3.76798i
\(579\) 251.804 0.434895
\(580\) 198.801 0.342760
\(581\) 152.986i 0.263315i
\(582\) 519.476 0.892571
\(583\) 1392.59i 2.38867i
\(584\) −99.2231 −0.169903
\(585\) 137.805i 0.235564i
\(586\) 42.5468i 0.0726055i
\(587\) 817.508i 1.39269i 0.717708 + 0.696344i \(0.245191\pi\)
−0.717708 + 0.696344i \(0.754809\pi\)
\(588\) −751.460 −1.27799
\(589\) 400.613i 0.680158i
\(590\) 539.399 179.002i 0.914235 0.303393i
\(591\) 165.000 0.279187
\(592\) 321.712i 0.543432i
\(593\) 1049.16 1.76924 0.884621 0.466310i \(-0.154417\pi\)
0.884621 + 0.466310i \(0.154417\pi\)
\(594\) 248.475 0.418307
\(595\) −1229.87 −2.06701
\(596\) 18.8772i 0.0316731i
\(597\) 206.272 0.345514
\(598\) 610.682i 1.02121i
\(599\) −209.961 −0.350520 −0.175260 0.984522i \(-0.556077\pi\)
−0.175260 + 0.984522i \(0.556077\pi\)
\(600\) 57.7571i 0.0962619i
\(601\) 60.2370i 0.100228i −0.998744 0.0501139i \(-0.984042\pi\)
0.998744 0.0501139i \(-0.0159584\pi\)
\(602\) 1791.14 2.97532
\(603\) 266.490i 0.441940i
\(604\) 277.152i 0.458860i
\(605\) −453.319 −0.749287
\(606\) −106.673 −0.176028
\(607\) 839.696 1.38335 0.691677 0.722207i \(-0.256872\pi\)
0.691677 + 0.722207i \(0.256872\pi\)
\(608\) 674.490i 1.10936i
\(609\) −261.982 −0.430184
\(610\) −894.053 −1.46566
\(611\) −1125.02 −1.84128
\(612\) 458.864 0.749777
\(613\) 14.7095i 0.0239960i −0.999928 0.0119980i \(-0.996181\pi\)
0.999928 0.0119980i \(-0.00381917\pi\)
\(614\) 593.478i 0.966577i
\(615\) −210.170 −0.341740
\(616\) −440.848 −0.715663
\(617\) −126.319 −0.204730 −0.102365 0.994747i \(-0.532641\pi\)
−0.102365 + 0.994747i \(0.532641\pi\)
\(618\) −358.067 −0.579396
\(619\) −957.437 −1.54675 −0.773374 0.633950i \(-0.781432\pi\)
−0.773374 + 0.633950i \(0.781432\pi\)
\(620\) 420.917i 0.678898i
\(621\) 75.7903i 0.122046i
\(622\) 519.706i 0.835540i
\(623\) 820.749i 1.31741i
\(624\) 300.360i 0.481346i
\(625\) −55.9320 −0.0894912
\(626\) −139.526 −0.222885
\(627\) 413.389i 0.659313i
\(628\) 553.630i 0.881576i
\(629\) 838.841i 1.33361i
\(630\) 341.641i 0.542288i
\(631\) 854.136 1.35362 0.676811 0.736157i \(-0.263361\pi\)
0.676811 + 0.736157i \(0.263361\pi\)
\(632\) 4.03776i 0.00638886i
\(633\) 225.122i 0.355642i
\(634\) 605.051i 0.954339i
\(635\) 219.929 0.346345
\(636\) −714.392 −1.12326
\(637\) 1282.56i 2.01343i
\(638\) −611.796 −0.958927
\(639\) −40.3812 −0.0631944
\(640\) 235.801i 0.368440i
\(641\) −196.567 −0.306657 −0.153329 0.988175i \(-0.548999\pi\)
−0.153329 + 0.988175i \(0.548999\pi\)
\(642\) 415.050i 0.646495i
\(643\) −185.202 −0.288028 −0.144014 0.989576i \(-0.546001\pi\)
−0.144014 + 0.989576i \(0.546001\pi\)
\(644\) 824.226i 1.27985i
\(645\) 287.902i 0.446360i
\(646\) 1402.28i 2.17072i
\(647\) 103.318 0.159688 0.0798440 0.996807i \(-0.474558\pi\)
0.0798440 + 0.996807i \(0.474558\pi\)
\(648\) 20.7955i 0.0320918i
\(649\) −903.698 + 299.897i −1.39245 + 0.462090i
\(650\) 604.229 0.929583
\(651\) 554.689i 0.852057i
\(652\) 1190.71 1.82624
\(653\) −387.091 −0.592789 −0.296394 0.955066i \(-0.595784\pi\)
−0.296394 + 0.955066i \(0.595784\pi\)
\(654\) −984.739 −1.50572
\(655\) 317.077i 0.484086i
\(656\) 458.087 0.698304
\(657\) 128.827i 0.196084i
\(658\) −2789.12 −4.23879
\(659\) 388.451i 0.589456i −0.955581 0.294728i \(-0.904771\pi\)
0.955581 0.294728i \(-0.0952290\pi\)
\(660\) 434.340i 0.658092i
\(661\) 699.132 1.05769 0.528844 0.848719i \(-0.322626\pi\)
0.528844 + 0.848719i \(0.322626\pi\)
\(662\) 1602.97i 2.42141i
\(663\) 783.167i 1.18125i
\(664\) 29.9002 0.0450304
\(665\) 568.391 0.854724
\(666\) 233.019 0.349878
\(667\) 186.611i 0.279777i
\(668\) −240.977 −0.360744
\(669\) −37.5572 −0.0561392
\(670\) 855.664 1.27711
\(671\) 1497.88 2.23231
\(672\) 933.900i 1.38973i
\(673\) 982.617i 1.46005i −0.683418 0.730027i \(-0.739507\pi\)
0.683418 0.730027i \(-0.260493\pi\)
\(674\) 1828.11 2.71233
\(675\) −74.9895 −0.111095
\(676\) 146.529 0.216759
\(677\) −176.203 −0.260270 −0.130135 0.991496i \(-0.541541\pi\)
−0.130135 + 0.991496i \(0.541541\pi\)
\(678\) 429.425 0.633370
\(679\) 1196.65i 1.76237i
\(680\) 240.371i 0.353486i
\(681\) 411.240i 0.603876i
\(682\) 1295.34i 1.89933i
\(683\) 793.332i 1.16154i −0.814068 0.580770i \(-0.802752\pi\)
0.814068 0.580770i \(-0.197248\pi\)
\(684\) −212.066 −0.310039
\(685\) −43.5057 −0.0635120
\(686\) 1463.17i 2.13291i
\(687\) 352.381i 0.512927i
\(688\) 627.513i 0.912083i
\(689\) 1219.29i 1.76965i
\(690\) 243.353 0.352686
\(691\) 977.811i 1.41507i 0.706680 + 0.707533i \(0.250192\pi\)
−0.706680 + 0.707533i \(0.749808\pi\)
\(692\) 64.1402i 0.0926881i
\(693\) 572.379i 0.825944i
\(694\) 139.852 0.201516
\(695\) 256.316 0.368800
\(696\) 51.2028i 0.0735672i
\(697\) 1194.43 1.71367
\(698\) 109.399 0.156732
\(699\) 569.084i 0.814140i
\(700\) 815.517 1.16502
\(701\) 940.284i 1.34135i 0.741753 + 0.670674i \(0.233995\pi\)
−0.741753 + 0.670674i \(0.766005\pi\)
\(702\) −217.553 −0.309905
\(703\) 387.675i 0.551458i
\(704\) 1388.65i 1.97252i
\(705\) 448.315i 0.635908i
\(706\) −246.621 −0.349322
\(707\) 245.729i 0.347566i
\(708\) 153.845 + 463.592i 0.217296 + 0.654791i
\(709\) 1249.95 1.76298 0.881488 0.472207i \(-0.156542\pi\)
0.881488 + 0.472207i \(0.156542\pi\)
\(710\) 129.659i 0.182618i
\(711\) −5.24245 −0.00737335
\(712\) −160.410 −0.225296
\(713\) 395.108 0.554149
\(714\) 1941.60i 2.71933i
\(715\) 741.311 1.03680
\(716\) 495.595i 0.692171i
\(717\) 358.216 0.499603
\(718\) 1497.03i 2.08500i
\(719\) 711.393i 0.989420i −0.869058 0.494710i \(-0.835274\pi\)
0.869058 0.494710i \(-0.164726\pi\)
\(720\) −119.692 −0.166238
\(721\) 824.832i 1.14401i
\(722\) 421.597i 0.583929i
\(723\) −239.220 −0.330871
\(724\) −578.101 −0.798483
\(725\) 184.640 0.254675
\(726\) 715.657i 0.985753i
\(727\) −729.102 −1.00289 −0.501446 0.865189i \(-0.667198\pi\)
−0.501446 + 0.865189i \(0.667198\pi\)
\(728\) 385.987 0.530202
\(729\) 27.0000 0.0370370
\(730\) 413.647 0.566640
\(731\) 1636.20i 2.23830i
\(732\) 768.403i 1.04973i
\(733\) −1330.92 −1.81572 −0.907861 0.419271i \(-0.862286\pi\)
−0.907861 + 0.419271i \(0.862286\pi\)
\(734\) −145.517 −0.198252
\(735\) 511.091 0.695361
\(736\) −665.222 −0.903835
\(737\) −1433.56 −1.94513
\(738\) 331.796i 0.449589i
\(739\) 1212.71i 1.64101i −0.571640 0.820505i \(-0.693693\pi\)
0.571640 0.820505i \(-0.306307\pi\)
\(740\) 407.323i 0.550436i
\(741\) 361.945i 0.488454i
\(742\) 3022.83i 4.07389i
\(743\) 1031.43 1.38820 0.694100 0.719878i \(-0.255802\pi\)
0.694100 + 0.719878i \(0.255802\pi\)
\(744\) 108.411 0.145713
\(745\) 12.8389i 0.0172335i
\(746\) 1728.31i 2.31676i
\(747\) 38.8212i 0.0519695i
\(748\) 2468.43i 3.30003i
\(749\) −956.096 −1.27650
\(750\) 657.886i 0.877182i
\(751\) 673.571i 0.896899i −0.893808 0.448450i \(-0.851976\pi\)
0.893808 0.448450i \(-0.148024\pi\)
\(752\) 977.149i 1.29940i
\(753\) 761.669 1.01151
\(754\) 535.661 0.710425
\(755\) 188.499i 0.249668i
\(756\) −293.627 −0.388396
\(757\) −142.288 −0.187962 −0.0939812 0.995574i \(-0.529959\pi\)
−0.0939812 + 0.995574i \(0.529959\pi\)
\(758\) 478.966i 0.631881i
\(759\) −407.709 −0.537166
\(760\) 111.089i 0.146169i
\(761\) 585.282 0.769096 0.384548 0.923105i \(-0.374357\pi\)
0.384548 + 0.923105i \(0.374357\pi\)
\(762\) 347.203i 0.455647i
\(763\) 2268.42i 2.97302i
\(764\) 1083.61i 1.41834i
\(765\) −312.087 −0.407957
\(766\) 495.526i 0.646901i
\(767\) 791.237 262.576i 1.03160 0.342341i
\(768\) 223.891 0.291525
\(769\) 545.480i 0.709337i 0.934992 + 0.354668i \(0.115406\pi\)
−0.934992 + 0.354668i \(0.884594\pi\)
\(770\) 1837.84 2.38680
\(771\) 446.982 0.579743
\(772\) −694.885 −0.900110
\(773\) 119.861i 0.155060i 0.996990 + 0.0775299i \(0.0247033\pi\)
−0.996990 + 0.0775299i \(0.975297\pi\)
\(774\) 454.513 0.587226
\(775\) 390.933i 0.504430i
\(776\) −233.878 −0.301389
\(777\) 536.775i 0.690830i
\(778\) 971.544i 1.24877i
\(779\) −552.012 −0.708617
\(780\) 380.289i 0.487550i
\(781\) 217.228i 0.278141i
\(782\) −1383.01 −1.76856
\(783\) −66.4796 −0.0849037
\(784\) −1113.97 −1.42089
\(785\) 376.540i 0.479669i
\(786\) −500.570 −0.636858
\(787\) 1312.72 1.66800 0.834001 0.551763i \(-0.186045\pi\)
0.834001 + 0.551763i \(0.186045\pi\)
\(788\) −455.336 −0.577838
\(789\) −412.748 −0.523128
\(790\) 16.8329i 0.0213074i
\(791\) 989.210i 1.25058i