Properties

Label 177.3.c.a.58.11
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 58.11
Root \(0.537675i\) of defining polynomial
Character \(\chi\) \(=\) 177.58
Dual form 177.3.c.a.58.10

$q$-expansion

\(f(q)\) \(=\) \(q+0.537675i q^{2} -1.73205 q^{3} +3.71091 q^{4} -0.803210 q^{5} -0.931281i q^{6} +5.11098 q^{7} +4.14596i q^{8} +3.00000 q^{9} +O(q^{10})\) \(q+0.537675i q^{2} -1.73205 q^{3} +3.71091 q^{4} -0.803210 q^{5} -0.931281i q^{6} +5.11098 q^{7} +4.14596i q^{8} +3.00000 q^{9} -0.431866i q^{10} -17.7567i q^{11} -6.42748 q^{12} +24.6407i q^{13} +2.74805i q^{14} +1.39120 q^{15} +12.6144 q^{16} +18.2784 q^{17} +1.61303i q^{18} +28.5669 q^{19} -2.98064 q^{20} -8.85247 q^{21} +9.54732 q^{22} +11.8668i q^{23} -7.18102i q^{24} -24.3549 q^{25} -13.2487 q^{26} -5.19615 q^{27} +18.9664 q^{28} +9.01975 q^{29} +0.748014i q^{30} +4.94288i q^{31} +23.3663i q^{32} +30.7554i q^{33} +9.82784i q^{34} -4.10519 q^{35} +11.1327 q^{36} -39.7950i q^{37} +15.3597i q^{38} -42.6790i q^{39} -3.33008i q^{40} -38.0744 q^{41} -4.75976i q^{42} +19.2551i q^{43} -65.8933i q^{44} -2.40963 q^{45} -6.38050 q^{46} -65.6973i q^{47} -21.8488 q^{48} -22.8779 q^{49} -13.0950i q^{50} -31.6591 q^{51} +91.4394i q^{52} -40.1506 q^{53} -2.79384i q^{54} +14.2623i q^{55} +21.1899i q^{56} -49.4793 q^{57} +4.84970i q^{58} +(-53.3901 + 25.1097i) q^{59} +5.16261 q^{60} -110.438i q^{61} -2.65767 q^{62} +15.3329 q^{63} +37.8943 q^{64} -19.7917i q^{65} -16.5364 q^{66} +30.7950i q^{67} +67.8294 q^{68} -20.5539i q^{69} -2.20726i q^{70} -95.0078 q^{71} +12.4379i q^{72} -71.2671i q^{73} +21.3968 q^{74} +42.1838 q^{75} +106.009 q^{76} -90.7539i q^{77} +22.9474 q^{78} -13.3580 q^{79} -10.1320 q^{80} +9.00000 q^{81} -20.4717i q^{82} +142.514i q^{83} -32.8507 q^{84} -14.6814 q^{85} -10.3530 q^{86} -15.6227 q^{87} +73.6185 q^{88} +128.582i q^{89} -1.29560i q^{90} +125.938i q^{91} +44.0366i q^{92} -8.56133i q^{93} +35.3238 q^{94} -22.9452 q^{95} -40.4717i q^{96} +97.1513i q^{97} -12.3009i q^{98} -53.2700i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 40q^{4} - 8q^{7} + 60q^{9} + O(q^{10}) \) \( 20q - 40q^{4} - 8q^{7} + 60q^{9} - 24q^{12} + 24q^{15} - 8q^{16} + 16q^{17} - 60q^{19} - 164q^{20} + 40q^{22} + 100q^{25} - 156q^{26} + 200q^{28} - 60q^{29} - 32q^{35} - 120q^{36} + 28q^{41} + 180q^{46} - 96q^{48} + 284q^{49} - 24q^{51} - 8q^{53} + 24q^{57} - 152q^{59} - 72q^{60} - 8q^{62} - 24q^{63} + 204q^{64} - 120q^{66} + 384q^{68} + 92q^{71} + 104q^{74} + 240q^{75} + 120q^{76} - 468q^{78} - 420q^{79} + 376q^{80} + 180q^{81} + 168q^{84} - 348q^{85} + 232q^{86} + 144q^{87} - 212q^{88} + 152q^{94} + 788q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.537675i 0.268838i 0.990925 + 0.134419i \(0.0429168\pi\)
−0.990925 + 0.134419i \(0.957083\pi\)
\(3\) −1.73205 −0.577350
\(4\) 3.71091 0.927726
\(5\) −0.803210 −0.160642 −0.0803210 0.996769i \(-0.525595\pi\)
−0.0803210 + 0.996769i \(0.525595\pi\)
\(6\) 0.931281i 0.155214i
\(7\) 5.11098 0.730140 0.365070 0.930980i \(-0.381045\pi\)
0.365070 + 0.930980i \(0.381045\pi\)
\(8\) 4.14596i 0.518245i
\(9\) 3.00000 0.333333
\(10\) 0.431866i 0.0431866i
\(11\) 17.7567i 1.61424i −0.590386 0.807121i \(-0.701024\pi\)
0.590386 0.807121i \(-0.298976\pi\)
\(12\) −6.42748 −0.535623
\(13\) 24.6407i 1.89544i 0.319101 + 0.947721i \(0.396619\pi\)
−0.319101 + 0.947721i \(0.603381\pi\)
\(14\) 2.74805i 0.196289i
\(15\) 1.39120 0.0927467
\(16\) 12.6144 0.788402
\(17\) 18.2784 1.07520 0.537600 0.843200i \(-0.319331\pi\)
0.537600 + 0.843200i \(0.319331\pi\)
\(18\) 1.61303i 0.0896126i
\(19\) 28.5669 1.50352 0.751760 0.659437i \(-0.229205\pi\)
0.751760 + 0.659437i \(0.229205\pi\)
\(20\) −2.98064 −0.149032
\(21\) −8.85247 −0.421546
\(22\) 9.54732 0.433969
\(23\) 11.8668i 0.515949i 0.966152 + 0.257974i \(0.0830550\pi\)
−0.966152 + 0.257974i \(0.916945\pi\)
\(24\) 7.18102i 0.299209i
\(25\) −24.3549 −0.974194
\(26\) −13.2487 −0.509566
\(27\) −5.19615 −0.192450
\(28\) 18.9664 0.677370
\(29\) 9.01975 0.311026 0.155513 0.987834i \(-0.450297\pi\)
0.155513 + 0.987834i \(0.450297\pi\)
\(30\) 0.748014i 0.0249338i
\(31\) 4.94288i 0.159448i 0.996817 + 0.0797239i \(0.0254039\pi\)
−0.996817 + 0.0797239i \(0.974596\pi\)
\(32\) 23.3663i 0.730198i
\(33\) 30.7554i 0.931983i
\(34\) 9.82784i 0.289054i
\(35\) −4.10519 −0.117291
\(36\) 11.1327 0.309242
\(37\) 39.7950i 1.07554i −0.843091 0.537770i \(-0.819267\pi\)
0.843091 0.537770i \(-0.180733\pi\)
\(38\) 15.3597i 0.404203i
\(39\) 42.6790i 1.09433i
\(40\) 3.33008i 0.0832520i
\(41\) −38.0744 −0.928644 −0.464322 0.885667i \(-0.653702\pi\)
−0.464322 + 0.885667i \(0.653702\pi\)
\(42\) 4.75976i 0.113328i
\(43\) 19.2551i 0.447793i 0.974613 + 0.223896i \(0.0718778\pi\)
−0.974613 + 0.223896i \(0.928122\pi\)
\(44\) 65.8933i 1.49758i
\(45\) −2.40963 −0.0535473
\(46\) −6.38050 −0.138706
\(47\) 65.6973i 1.39782i −0.715212 0.698908i \(-0.753670\pi\)
0.715212 0.698908i \(-0.246330\pi\)
\(48\) −21.8488 −0.455184
\(49\) −22.8779 −0.466896
\(50\) 13.0950i 0.261900i
\(51\) −31.6591 −0.620767
\(52\) 91.4394i 1.75845i
\(53\) −40.1506 −0.757559 −0.378779 0.925487i \(-0.623656\pi\)
−0.378779 + 0.925487i \(0.623656\pi\)
\(54\) 2.79384i 0.0517378i
\(55\) 14.2623i 0.259315i
\(56\) 21.1899i 0.378392i
\(57\) −49.4793 −0.868058
\(58\) 4.84970i 0.0836155i
\(59\) −53.3901 + 25.1097i −0.904917 + 0.425589i
\(60\) 5.16261 0.0860435
\(61\) 110.438i 1.81047i −0.424916 0.905233i \(-0.639697\pi\)
0.424916 0.905233i \(-0.360303\pi\)
\(62\) −2.65767 −0.0428656
\(63\) 15.3329 0.243380
\(64\) 37.8943 0.592098
\(65\) 19.7917i 0.304487i
\(66\) −16.5364 −0.250552
\(67\) 30.7950i 0.459627i 0.973235 + 0.229814i \(0.0738117\pi\)
−0.973235 + 0.229814i \(0.926188\pi\)
\(68\) 67.8294 0.997491
\(69\) 20.5539i 0.297883i
\(70\) 2.20726i 0.0315323i
\(71\) −95.0078 −1.33814 −0.669069 0.743200i \(-0.733307\pi\)
−0.669069 + 0.743200i \(0.733307\pi\)
\(72\) 12.4379i 0.172748i
\(73\) 71.2671i 0.976262i −0.872770 0.488131i \(-0.837679\pi\)
0.872770 0.488131i \(-0.162321\pi\)
\(74\) 21.3968 0.289146
\(75\) 42.1838 0.562451
\(76\) 106.009 1.39486
\(77\) 90.7539i 1.17862i
\(78\) 22.9474 0.294198
\(79\) −13.3580 −0.169089 −0.0845446 0.996420i \(-0.526944\pi\)
−0.0845446 + 0.996420i \(0.526944\pi\)
\(80\) −10.1320 −0.126651
\(81\) 9.00000 0.111111
\(82\) 20.4717i 0.249654i
\(83\) 142.514i 1.71704i 0.512783 + 0.858518i \(0.328614\pi\)
−0.512783 + 0.858518i \(0.671386\pi\)
\(84\) −32.8507 −0.391080
\(85\) −14.6814 −0.172722
\(86\) −10.3530 −0.120384
\(87\) −15.6227 −0.179571
\(88\) 73.6185 0.836574
\(89\) 128.582i 1.44474i 0.691506 + 0.722371i \(0.256948\pi\)
−0.691506 + 0.722371i \(0.743052\pi\)
\(90\) 1.29560i 0.0143955i
\(91\) 125.938i 1.38394i
\(92\) 44.0366i 0.478659i
\(93\) 8.56133i 0.0920573i
\(94\) 35.3238 0.375786
\(95\) −22.9452 −0.241528
\(96\) 40.4717i 0.421580i
\(97\) 97.1513i 1.00156i 0.865575 + 0.500780i \(0.166953\pi\)
−0.865575 + 0.500780i \(0.833047\pi\)
\(98\) 12.3009i 0.125519i
\(99\) 53.2700i 0.538081i
\(100\) −90.3786 −0.903786
\(101\) 100.698i 0.997012i −0.866886 0.498506i \(-0.833882\pi\)
0.866886 0.498506i \(-0.166118\pi\)
\(102\) 17.0223i 0.166886i
\(103\) 118.731i 1.15273i −0.817194 0.576363i \(-0.804472\pi\)
0.817194 0.576363i \(-0.195528\pi\)
\(104\) −102.160 −0.982304
\(105\) 7.11039 0.0677180
\(106\) 21.5880i 0.203660i
\(107\) 158.040 1.47701 0.738503 0.674250i \(-0.235533\pi\)
0.738503 + 0.674250i \(0.235533\pi\)
\(108\) −19.2824 −0.178541
\(109\) 88.9732i 0.816268i 0.912922 + 0.408134i \(0.133820\pi\)
−0.912922 + 0.408134i \(0.866180\pi\)
\(110\) −7.66850 −0.0697137
\(111\) 68.9270i 0.620964i
\(112\) 64.4721 0.575644
\(113\) 158.257i 1.40050i −0.713895 0.700252i \(-0.753071\pi\)
0.713895 0.700252i \(-0.246929\pi\)
\(114\) 26.6038i 0.233367i
\(115\) 9.53155i 0.0828830i
\(116\) 33.4714 0.288547
\(117\) 73.9222i 0.631814i
\(118\) −13.5009 28.7065i −0.114414 0.243276i
\(119\) 93.4205 0.785046
\(120\) 5.76787i 0.0480655i
\(121\) −194.299 −1.60578
\(122\) 59.3800 0.486721
\(123\) 65.9468 0.536153
\(124\) 18.3426i 0.147924i
\(125\) 39.6423 0.317138
\(126\) 8.24414i 0.0654297i
\(127\) −101.633 −0.800259 −0.400129 0.916459i \(-0.631035\pi\)
−0.400129 + 0.916459i \(0.631035\pi\)
\(128\) 113.840i 0.889376i
\(129\) 33.3508i 0.258533i
\(130\) 10.6415 0.0818577
\(131\) 86.1937i 0.657967i 0.944336 + 0.328984i \(0.106706\pi\)
−0.944336 + 0.328984i \(0.893294\pi\)
\(132\) 114.131i 0.864625i
\(133\) 146.005 1.09778
\(134\) −16.5577 −0.123565
\(135\) 4.17360 0.0309156
\(136\) 75.7816i 0.557217i
\(137\) −174.098 −1.27079 −0.635395 0.772188i \(-0.719163\pi\)
−0.635395 + 0.772188i \(0.719163\pi\)
\(138\) 11.0513 0.0800822
\(139\) 166.414 1.19722 0.598612 0.801039i \(-0.295719\pi\)
0.598612 + 0.801039i \(0.295719\pi\)
\(140\) −15.2340 −0.108814
\(141\) 113.791i 0.807029i
\(142\) 51.0834i 0.359742i
\(143\) 437.537 3.05970
\(144\) 37.8433 0.262801
\(145\) −7.24475 −0.0499638
\(146\) 38.3186 0.262456
\(147\) 39.6257 0.269563
\(148\) 147.676i 0.997808i
\(149\) 27.1832i 0.182438i −0.995831 0.0912188i \(-0.970924\pi\)
0.995831 0.0912188i \(-0.0290763\pi\)
\(150\) 22.6812i 0.151208i
\(151\) 94.4601i 0.625563i −0.949825 0.312782i \(-0.898739\pi\)
0.949825 0.312782i \(-0.101261\pi\)
\(152\) 118.437i 0.779192i
\(153\) 54.8352 0.358400
\(154\) 48.7961 0.316858
\(155\) 3.97017i 0.0256140i
\(156\) 158.378i 1.01524i
\(157\) 13.0757i 0.0832847i −0.999133 0.0416424i \(-0.986741\pi\)
0.999133 0.0416424i \(-0.0132590\pi\)
\(158\) 7.18229i 0.0454575i
\(159\) 69.5429 0.437377
\(160\) 18.7681i 0.117300i
\(161\) 60.6511i 0.376715i
\(162\) 4.83908i 0.0298709i
\(163\) −31.6216 −0.193998 −0.0969989 0.995284i \(-0.530924\pi\)
−0.0969989 + 0.995284i \(0.530924\pi\)
\(164\) −141.290 −0.861527
\(165\) 24.7031i 0.149716i
\(166\) −76.6263 −0.461604
\(167\) 142.242 0.851751 0.425875 0.904782i \(-0.359966\pi\)
0.425875 + 0.904782i \(0.359966\pi\)
\(168\) 36.7020i 0.218464i
\(169\) −438.166 −2.59270
\(170\) 7.89382i 0.0464342i
\(171\) 85.7006 0.501173
\(172\) 71.4538i 0.415429i
\(173\) 202.500i 1.17052i 0.810845 + 0.585261i \(0.199008\pi\)
−0.810845 + 0.585261i \(0.800992\pi\)
\(174\) 8.39992i 0.0482754i
\(175\) −124.477 −0.711298
\(176\) 223.990i 1.27267i
\(177\) 92.4743 43.4913i 0.522454 0.245714i
\(178\) −69.1354 −0.388401
\(179\) 190.907i 1.06652i 0.845952 + 0.533259i \(0.179033\pi\)
−0.845952 + 0.533259i \(0.820967\pi\)
\(180\) −8.94191 −0.0496773
\(181\) −123.971 −0.684922 −0.342461 0.939532i \(-0.611261\pi\)
−0.342461 + 0.939532i \(0.611261\pi\)
\(182\) −67.7139 −0.372054
\(183\) 191.285i 1.04527i
\(184\) −49.1994 −0.267388
\(185\) 31.9637i 0.172777i
\(186\) 4.60321 0.0247485
\(187\) 324.563i 1.73563i
\(188\) 243.797i 1.29679i
\(189\) −26.5574 −0.140515
\(190\) 12.3371i 0.0649319i
\(191\) 125.336i 0.656211i −0.944641 0.328105i \(-0.893590\pi\)
0.944641 0.328105i \(-0.106410\pi\)
\(192\) −65.6348 −0.341848
\(193\) −108.008 −0.559626 −0.279813 0.960055i \(-0.590272\pi\)
−0.279813 + 0.960055i \(0.590272\pi\)
\(194\) −52.2358 −0.269257
\(195\) 34.2802i 0.175796i
\(196\) −84.8978 −0.433152
\(197\) −132.587 −0.673031 −0.336516 0.941678i \(-0.609248\pi\)
−0.336516 + 0.941678i \(0.609248\pi\)
\(198\) 28.6420 0.144656
\(199\) −229.429 −1.15291 −0.576455 0.817129i \(-0.695564\pi\)
−0.576455 + 0.817129i \(0.695564\pi\)
\(200\) 100.974i 0.504872i
\(201\) 53.3386i 0.265366i
\(202\) 54.1429 0.268034
\(203\) 46.0997 0.227092
\(204\) −117.484 −0.575902
\(205\) 30.5817 0.149179
\(206\) 63.8386 0.309896
\(207\) 35.6005i 0.171983i
\(208\) 310.829i 1.49437i
\(209\) 507.253i 2.42705i
\(210\) 3.82308i 0.0182052i
\(211\) 270.274i 1.28092i −0.767991 0.640461i \(-0.778743\pi\)
0.767991 0.640461i \(-0.221257\pi\)
\(212\) −148.995 −0.702807
\(213\) 164.558 0.772575
\(214\) 84.9741i 0.397075i
\(215\) 15.4659i 0.0719343i
\(216\) 21.5431i 0.0997364i
\(217\) 25.2630i 0.116419i
\(218\) −47.8387 −0.219444
\(219\) 123.438i 0.563645i
\(220\) 52.9261i 0.240573i
\(221\) 450.393i 2.03798i
\(222\) −37.0603 −0.166938
\(223\) 37.2371 0.166982 0.0834912 0.996509i \(-0.473393\pi\)
0.0834912 + 0.996509i \(0.473393\pi\)
\(224\) 119.425i 0.533146i
\(225\) −73.0646 −0.324731
\(226\) 85.0909 0.376508
\(227\) 157.805i 0.695175i −0.937648 0.347587i \(-0.887001\pi\)
0.937648 0.347587i \(-0.112999\pi\)
\(228\) −183.613 −0.805320
\(229\) 304.839i 1.33118i −0.746319 0.665588i \(-0.768181\pi\)
0.746319 0.665588i \(-0.231819\pi\)
\(230\) 5.12488 0.0222821
\(231\) 157.190i 0.680478i
\(232\) 37.3956i 0.161188i
\(233\) 163.385i 0.701221i 0.936521 + 0.350611i \(0.114026\pi\)
−0.936521 + 0.350611i \(0.885974\pi\)
\(234\) −39.7461 −0.169855
\(235\) 52.7687i 0.224548i
\(236\) −198.126 + 93.1798i −0.839515 + 0.394830i
\(237\) 23.1368 0.0976237
\(238\) 50.2299i 0.211050i
\(239\) −235.307 −0.984549 −0.492275 0.870440i \(-0.663834\pi\)
−0.492275 + 0.870440i \(0.663834\pi\)
\(240\) 17.5492 0.0731217
\(241\) 71.2458 0.295626 0.147813 0.989015i \(-0.452777\pi\)
0.147813 + 0.989015i \(0.452777\pi\)
\(242\) 104.470i 0.431694i
\(243\) −15.5885 −0.0641500
\(244\) 409.826i 1.67962i
\(245\) 18.3758 0.0750031
\(246\) 35.4580i 0.144138i
\(247\) 703.909i 2.84983i
\(248\) −20.4930 −0.0826331
\(249\) 246.842i 0.991331i
\(250\) 21.3147i 0.0852587i
\(251\) 415.223 1.65427 0.827137 0.562001i \(-0.189968\pi\)
0.827137 + 0.562001i \(0.189968\pi\)
\(252\) 56.8991 0.225790
\(253\) 210.715 0.832866
\(254\) 54.6455i 0.215140i
\(255\) 25.4289 0.0997212
\(256\) 90.3680 0.353000
\(257\) 383.556 1.49244 0.746218 0.665701i \(-0.231868\pi\)
0.746218 + 0.665701i \(0.231868\pi\)
\(258\) 17.9319 0.0695035
\(259\) 203.391i 0.785295i
\(260\) 73.4450i 0.282481i
\(261\) 27.0593 0.103675
\(262\) −46.3442 −0.176886
\(263\) −176.978 −0.672921 −0.336460 0.941698i \(-0.609230\pi\)
−0.336460 + 0.941698i \(0.609230\pi\)
\(264\) −127.511 −0.482996
\(265\) 32.2494 0.121696
\(266\) 78.5031i 0.295124i
\(267\) 222.711i 0.834122i
\(268\) 114.277i 0.426408i
\(269\) 151.733i 0.564063i −0.959405 0.282031i \(-0.908992\pi\)
0.959405 0.282031i \(-0.0910082\pi\)
\(270\) 2.24404i 0.00831127i
\(271\) 316.355 1.16736 0.583680 0.811984i \(-0.301612\pi\)
0.583680 + 0.811984i \(0.301612\pi\)
\(272\) 230.572 0.847690
\(273\) 218.131i 0.799016i
\(274\) 93.6083i 0.341636i
\(275\) 432.461i 1.57259i
\(276\) 76.2737i 0.276354i
\(277\) 122.572 0.442499 0.221250 0.975217i \(-0.428986\pi\)
0.221250 + 0.975217i \(0.428986\pi\)
\(278\) 89.4768i 0.321859i
\(279\) 14.8287i 0.0531493i
\(280\) 17.0200i 0.0607856i
\(281\) −188.817 −0.671945 −0.335973 0.941872i \(-0.609065\pi\)
−0.335973 + 0.941872i \(0.609065\pi\)
\(282\) −61.1827 −0.216960
\(283\) 326.692i 1.15439i 0.816606 + 0.577195i \(0.195853\pi\)
−0.816606 + 0.577195i \(0.804147\pi\)
\(284\) −352.565 −1.24143
\(285\) 39.7422 0.139446
\(286\) 235.253i 0.822563i
\(287\) −194.597 −0.678039
\(288\) 70.0990i 0.243399i
\(289\) 45.0999 0.156055
\(290\) 3.89532i 0.0134322i
\(291\) 168.271i 0.578251i
\(292\) 264.466i 0.905704i
\(293\) 61.3922 0.209530 0.104765 0.994497i \(-0.466591\pi\)
0.104765 + 0.994497i \(0.466591\pi\)
\(294\) 21.3058i 0.0724686i
\(295\) 42.8834 20.1684i 0.145368 0.0683674i
\(296\) 164.989 0.557394
\(297\) 92.2663i 0.310661i
\(298\) 14.6157 0.0490461
\(299\) −292.407 −0.977950
\(300\) 156.540 0.521801
\(301\) 98.4124i 0.326951i
\(302\) 50.7888 0.168175
\(303\) 174.414i 0.575625i
\(304\) 360.355 1.18538
\(305\) 88.7052i 0.290837i
\(306\) 29.4835i 0.0963514i
\(307\) −274.766 −0.895003 −0.447501 0.894283i \(-0.647686\pi\)
−0.447501 + 0.894283i \(0.647686\pi\)
\(308\) 336.779i 1.09344i
\(309\) 205.648i 0.665526i
\(310\) 2.13466 0.00688601
\(311\) 488.255 1.56995 0.784976 0.619526i \(-0.212675\pi\)
0.784976 + 0.619526i \(0.212675\pi\)
\(312\) 176.946 0.567133
\(313\) 244.585i 0.781421i 0.920514 + 0.390711i \(0.127771\pi\)
−0.920514 + 0.390711i \(0.872229\pi\)
\(314\) 7.03048 0.0223901
\(315\) −12.3156 −0.0390970
\(316\) −49.5704 −0.156868
\(317\) −329.194 −1.03847 −0.519234 0.854632i \(-0.673783\pi\)
−0.519234 + 0.854632i \(0.673783\pi\)
\(318\) 37.3915i 0.117583i
\(319\) 160.161i 0.502071i
\(320\) −30.4370 −0.0951157
\(321\) −273.733 −0.852750
\(322\) −32.6106 −0.101275
\(323\) 522.157 1.61658
\(324\) 33.3981 0.103081
\(325\) 600.121i 1.84653i
\(326\) 17.0022i 0.0521539i
\(327\) 154.106i 0.471272i
\(328\) 157.855i 0.481265i
\(329\) 335.778i 1.02060i
\(330\) 13.2822 0.0402492
\(331\) 397.945 1.20225 0.601126 0.799154i \(-0.294719\pi\)
0.601126 + 0.799154i \(0.294719\pi\)
\(332\) 528.856i 1.59294i
\(333\) 119.385i 0.358514i
\(334\) 76.4802i 0.228983i
\(335\) 24.7349i 0.0738354i
\(336\) −111.669 −0.332348
\(337\) 120.588i 0.357829i 0.983865 + 0.178915i \(0.0572586\pi\)
−0.983865 + 0.178915i \(0.942741\pi\)
\(338\) 235.591i 0.697015i
\(339\) 274.109i 0.808582i
\(340\) −54.4812 −0.160239
\(341\) 87.7692 0.257388
\(342\) 46.0791i 0.134734i
\(343\) −367.366 −1.07104
\(344\) −79.8309 −0.232067
\(345\) 16.5091i 0.0478525i
\(346\) −108.879 −0.314680
\(347\) 170.990i 0.492767i −0.969172 0.246384i \(-0.920758\pi\)
0.969172 0.246384i \(-0.0792423\pi\)
\(348\) −57.9742 −0.166593
\(349\) 294.342i 0.843388i 0.906738 + 0.421694i \(0.138564\pi\)
−0.906738 + 0.421694i \(0.861436\pi\)
\(350\) 66.9283i 0.191224i
\(351\) 128.037i 0.364778i
\(352\) 414.908 1.17872
\(353\) 165.480i 0.468783i 0.972142 + 0.234391i \(0.0753098\pi\)
−0.972142 + 0.234391i \(0.924690\pi\)
\(354\) 23.3842 + 49.7212i 0.0660571 + 0.140455i
\(355\) 76.3112 0.214961
\(356\) 477.156i 1.34032i
\(357\) −161.809 −0.453247
\(358\) −102.646 −0.286720
\(359\) 231.500 0.644845 0.322423 0.946596i \(-0.395503\pi\)
0.322423 + 0.946596i \(0.395503\pi\)
\(360\) 9.99024i 0.0277507i
\(361\) 455.067 1.26057
\(362\) 66.6561i 0.184133i
\(363\) 336.536 0.927097
\(364\) 467.345i 1.28391i
\(365\) 57.2425i 0.156829i
\(366\) −102.849 −0.281009
\(367\) 23.9385i 0.0652276i −0.999468 0.0326138i \(-0.989617\pi\)
0.999468 0.0326138i \(-0.0103831\pi\)
\(368\) 149.693i 0.406775i
\(369\) −114.223 −0.309548
\(370\) −17.1861 −0.0464490
\(371\) −205.209 −0.553124
\(372\) 31.7703i 0.0854040i
\(373\) 279.182 0.748476 0.374238 0.927333i \(-0.377904\pi\)
0.374238 + 0.927333i \(0.377904\pi\)
\(374\) 174.510 0.466604
\(375\) −68.6625 −0.183100
\(376\) 272.379 0.724412
\(377\) 222.253i 0.589531i
\(378\) 14.2793i 0.0377758i
\(379\) 89.9356 0.237297 0.118649 0.992936i \(-0.462144\pi\)
0.118649 + 0.992936i \(0.462144\pi\)
\(380\) −85.1475 −0.224072
\(381\) 176.033 0.462030
\(382\) 67.3902 0.176414
\(383\) −143.916 −0.375761 −0.187880 0.982192i \(-0.560162\pi\)
−0.187880 + 0.982192i \(0.560162\pi\)
\(384\) 197.177i 0.513481i
\(385\) 72.8944i 0.189336i
\(386\) 58.0731i 0.150448i
\(387\) 57.7653i 0.149264i
\(388\) 360.519i 0.929173i
\(389\) −182.927 −0.470250 −0.235125 0.971965i \(-0.575550\pi\)
−0.235125 + 0.971965i \(0.575550\pi\)
\(390\) −18.4316 −0.0472605
\(391\) 216.907i 0.554748i
\(392\) 94.8510i 0.241967i
\(393\) 149.292i 0.379877i
\(394\) 71.2888i 0.180936i
\(395\) 10.7293 0.0271628
\(396\) 197.680i 0.499192i
\(397\) 170.243i 0.428823i 0.976743 + 0.214412i \(0.0687834\pi\)
−0.976743 + 0.214412i \(0.931217\pi\)
\(398\) 123.358i 0.309945i
\(399\) −252.888 −0.633803
\(400\) −307.223 −0.768057
\(401\) 512.169i 1.27723i −0.769527 0.638614i \(-0.779508\pi\)
0.769527 0.638614i \(-0.220492\pi\)
\(402\) 28.6788 0.0713404
\(403\) −121.796 −0.302224
\(404\) 373.682i 0.924954i
\(405\) −7.22889 −0.0178491
\(406\) 24.7867i 0.0610510i
\(407\) −706.627 −1.73618
\(408\) 131.258i 0.321710i
\(409\) 91.1229i 0.222794i −0.993776 0.111397i \(-0.964467\pi\)
0.993776 0.111397i \(-0.0355326\pi\)
\(410\) 16.4430i 0.0401050i
\(411\) 301.547 0.733690
\(412\) 440.598i 1.06941i
\(413\) −272.875 + 128.335i −0.660715 + 0.310739i
\(414\) −19.1415 −0.0462355
\(415\) 114.469i 0.275828i
\(416\) −575.763 −1.38405
\(417\) −288.238 −0.691218
\(418\) 272.737 0.652481
\(419\) 90.7750i 0.216647i 0.994116 + 0.108323i \(0.0345482\pi\)
−0.994116 + 0.108323i \(0.965452\pi\)
\(420\) 26.3860 0.0628238
\(421\) 504.157i 1.19752i 0.800927 + 0.598762i \(0.204340\pi\)
−0.800927 + 0.598762i \(0.795660\pi\)
\(422\) 145.320 0.344360
\(423\) 197.092i 0.465939i
\(424\) 166.463i 0.392601i
\(425\) −445.168 −1.04745
\(426\) 88.4790i 0.207697i
\(427\) 564.448i 1.32189i
\(428\) 586.470 1.37026
\(429\) −757.837 −1.76652
\(430\) 8.31562 0.0193387
\(431\) 335.908i 0.779369i −0.920948 0.389685i \(-0.872584\pi\)
0.920948 0.389685i \(-0.127416\pi\)
\(432\) −65.5465 −0.151728
\(433\) 165.667 0.382603 0.191302 0.981531i \(-0.438729\pi\)
0.191302 + 0.981531i \(0.438729\pi\)
\(434\) −13.5833 −0.0312979
\(435\) 12.5483 0.0288466
\(436\) 330.171i 0.757273i
\(437\) 338.998i 0.775739i
\(438\) −66.3697 −0.151529
\(439\) −159.958 −0.364369 −0.182185 0.983264i \(-0.558317\pi\)
−0.182185 + 0.983264i \(0.558317\pi\)
\(440\) −59.1311 −0.134389
\(441\) −68.6337 −0.155632
\(442\) −242.165 −0.547885
\(443\) 65.1418i 0.147047i −0.997293 0.0735235i \(-0.976576\pi\)
0.997293 0.0735235i \(-0.0234244\pi\)
\(444\) 255.781i 0.576084i
\(445\) 103.278i 0.232086i
\(446\) 20.0215i 0.0448912i
\(447\) 47.0827i 0.105330i
\(448\) 193.677 0.432314
\(449\) −371.170 −0.826658 −0.413329 0.910582i \(-0.635634\pi\)
−0.413329 + 0.910582i \(0.635634\pi\)
\(450\) 39.2850i 0.0873000i
\(451\) 676.074i 1.49906i
\(452\) 587.277i 1.29929i
\(453\) 163.610i 0.361169i
\(454\) 84.8477 0.186889
\(455\) 101.155i 0.222318i
\(456\) 205.139i 0.449867i
\(457\) 169.801i 0.371555i −0.982592 0.185777i \(-0.940520\pi\)
0.982592 0.185777i \(-0.0594803\pi\)
\(458\) 163.905 0.357870
\(459\) −94.9774 −0.206922
\(460\) 35.3707i 0.0768928i
\(461\) −657.621 −1.42651 −0.713255 0.700905i \(-0.752780\pi\)
−0.713255 + 0.700905i \(0.752780\pi\)
\(462\) −84.5174 −0.182938
\(463\) 729.046i 1.57461i −0.616562 0.787306i \(-0.711475\pi\)
0.616562 0.787306i \(-0.288525\pi\)
\(464\) 113.779 0.245214
\(465\) 6.87654i 0.0147883i
\(466\) −87.8478 −0.188515
\(467\) 144.936i 0.310355i 0.987887 + 0.155178i \(0.0495950\pi\)
−0.987887 + 0.155178i \(0.950405\pi\)
\(468\) 274.318i 0.586150i
\(469\) 157.393i 0.335592i
\(470\) −28.3725 −0.0603669
\(471\) 22.6478i 0.0480844i
\(472\) −104.104 221.353i −0.220559 0.468969i
\(473\) 341.906 0.722846
\(474\) 12.4401i 0.0262449i
\(475\) −695.742 −1.46472
\(476\) 346.675 0.728308
\(477\) −120.452 −0.252520
\(478\) 126.519i 0.264684i
\(479\) −73.1977 −0.152814 −0.0764068 0.997077i \(-0.524345\pi\)
−0.0764068 + 0.997077i \(0.524345\pi\)
\(480\) 32.5072i 0.0677234i
\(481\) 980.578 2.03862
\(482\) 38.3071i 0.0794753i
\(483\) 105.051i 0.217496i
\(484\) −721.026 −1.48972
\(485\) 78.0328i 0.160892i
\(486\) 8.38153i 0.0172459i
\(487\) −54.7261 −0.112374 −0.0561869 0.998420i \(-0.517894\pi\)
−0.0561869 + 0.998420i \(0.517894\pi\)
\(488\) 457.873 0.938265
\(489\) 54.7703 0.112005
\(490\) 9.88020i 0.0201637i
\(491\) 588.790 1.19916 0.599582 0.800313i \(-0.295333\pi\)
0.599582 + 0.800313i \(0.295333\pi\)
\(492\) 244.722 0.497403
\(493\) 164.867 0.334415
\(494\) −378.474 −0.766143
\(495\) 42.7870i 0.0864384i
\(496\) 62.3517i 0.125709i
\(497\) −485.583 −0.977028
\(498\) 132.721 0.266507
\(499\) 368.842 0.739162 0.369581 0.929199i \(-0.379501\pi\)
0.369581 + 0.929199i \(0.379501\pi\)
\(500\) 147.109 0.294218
\(501\) −246.371 −0.491758
\(502\) 223.255i 0.444731i
\(503\) 74.8276i 0.148763i −0.997230 0.0743813i \(-0.976302\pi\)
0.997230 0.0743813i \(-0.0236982\pi\)
\(504\) 63.5698i 0.126131i
\(505\) 80.8818i 0.160162i
\(506\) 113.296i 0.223906i
\(507\) 758.925 1.49689
\(508\) −377.150 −0.742421
\(509\) 853.153i 1.67614i −0.545566 0.838068i \(-0.683685\pi\)
0.545566 0.838068i \(-0.316315\pi\)
\(510\) 13.6725i 0.0268088i
\(511\) 364.245i 0.712808i
\(512\) 503.949i 0.984276i
\(513\) −148.438 −0.289353
\(514\) 206.229i 0.401223i
\(515\) 95.3657i 0.185176i
\(516\) 123.762i 0.239848i
\(517\) −1166.57 −2.25641
\(518\) 109.359 0.211117
\(519\) 350.741i 0.675801i
\(520\) 82.0556 0.157799
\(521\) 168.377 0.323180 0.161590 0.986858i \(-0.448338\pi\)
0.161590 + 0.986858i \(0.448338\pi\)
\(522\) 14.5491i 0.0278718i
\(523\) −213.899 −0.408986 −0.204493 0.978868i \(-0.565554\pi\)
−0.204493 + 0.978868i \(0.565554\pi\)
\(524\) 319.857i 0.610413i
\(525\) 215.601 0.410668
\(526\) 95.1568i 0.180906i
\(527\) 90.3480i 0.171438i
\(528\) 387.963i 0.734778i
\(529\) 388.179 0.733797
\(530\) 17.3397i 0.0327164i
\(531\) −160.170 + 75.3292i −0.301639 + 0.141863i
\(532\) 541.810 1.01844
\(533\) 938.181i 1.76019i
\(534\) 119.746 0.224243
\(535\) −126.939 −0.237269
\(536\) −127.675 −0.238200
\(537\) 330.660i 0.615754i
\(538\) 81.5830 0.151641
\(539\) 406.235i 0.753684i
\(540\) 15.4878 0.0286812
\(541\) 236.317i 0.436816i −0.975858 0.218408i \(-0.929914\pi\)
0.975858 0.218408i \(-0.0700863\pi\)
\(542\) 170.096i 0.313831i
\(543\) 214.724 0.395440
\(544\) 427.099i 0.785109i
\(545\) 71.4641i 0.131127i
\(546\) 117.284 0.214806
\(547\) −466.310 −0.852487 −0.426243 0.904609i \(-0.640163\pi\)
−0.426243 + 0.904609i \(0.640163\pi\)
\(548\) −646.062 −1.17894
\(549\) 331.315i 0.603488i
\(550\) −232.524 −0.422770
\(551\) 257.666 0.467634
\(552\) 85.2159 0.154377
\(553\) −68.2726 −0.123459
\(554\) 65.9041i 0.118960i
\(555\) 55.3628i 0.0997528i
\(556\) 617.547 1.11070
\(557\) 1045.31 1.87668 0.938339 0.345717i \(-0.112364\pi\)
0.938339 + 0.345717i \(0.112364\pi\)
\(558\) −7.97300 −0.0142885
\(559\) −474.460 −0.848765
\(560\) −51.7846 −0.0924725
\(561\) 562.160i 1.00207i
\(562\) 101.522i 0.180644i
\(563\) 1039.19i 1.84581i 0.385026 + 0.922906i \(0.374192\pi\)
−0.385026 + 0.922906i \(0.625808\pi\)
\(564\) 422.268i 0.748702i
\(565\) 127.114i 0.224980i
\(566\) −175.654 −0.310343
\(567\) 45.9988 0.0811266
\(568\) 393.899i 0.693484i
\(569\) 206.318i 0.362597i 0.983428 + 0.181298i \(0.0580300\pi\)
−0.983428 + 0.181298i \(0.941970\pi\)
\(570\) 21.3684i 0.0374885i
\(571\) 144.089i 0.252345i 0.992008 + 0.126173i \(0.0402693\pi\)
−0.992008 + 0.126173i \(0.959731\pi\)
\(572\) 1623.66 2.83857
\(573\) 217.089i 0.378863i
\(574\) 104.630i 0.182283i
\(575\) 289.015i 0.502634i
\(576\) 113.683 0.197366
\(577\) −596.647 −1.03405 −0.517025 0.855970i \(-0.672961\pi\)
−0.517025 + 0.855970i \(0.672961\pi\)
\(578\) 24.2491i 0.0419535i
\(579\) 187.075 0.323100
\(580\) −26.8846 −0.0463527
\(581\) 728.386i 1.25368i
\(582\) 90.4751 0.155456
\(583\) 712.941i 1.22288i
\(584\) 295.471 0.505943
\(585\) 59.3750i 0.101496i
\(586\) 33.0091i 0.0563295i
\(587\) 177.665i 0.302666i −0.988483 0.151333i \(-0.951643\pi\)
0.988483 0.151333i \(-0.0483566\pi\)
\(588\) 147.047 0.250080
\(589\) 141.203i 0.239733i
\(590\) 10.8440 + 23.0574i 0.0183797 + 0.0390803i
\(591\) 229.648 0.388575
\(592\) 501.992i 0.847959i
\(593\) −297.828 −0.502240 −0.251120 0.967956i \(-0.580799\pi\)
−0.251120 + 0.967956i \(0.580799\pi\)
\(594\) −49.6093 −0.0835174
\(595\) −75.0362 −0.126111
\(596\) 100.874i 0.169252i
\(597\) 397.383 0.665632
\(598\) 157.220i 0.262910i
\(599\) −665.978 −1.11182 −0.555908 0.831244i \(-0.687629\pi\)
−0.555908 + 0.831244i \(0.687629\pi\)
\(600\) 174.893i 0.291488i
\(601\) 892.749i 1.48544i −0.669603 0.742720i \(-0.733536\pi\)
0.669603 0.742720i \(-0.266464\pi\)
\(602\) −52.9139 −0.0878968
\(603\) 92.3851i 0.153209i
\(604\) 350.532i 0.580351i
\(605\) 156.063 0.257955
\(606\) −93.7783 −0.154750
\(607\) −507.085 −0.835395 −0.417697 0.908586i \(-0.637163\pi\)
−0.417697 + 0.908586i \(0.637163\pi\)
\(608\) 667.503i 1.09787i
\(609\) −79.8471 −0.131112
\(610\) −47.6946 −0.0781879
\(611\) 1618.83 2.64948
\(612\) 203.488 0.332497
\(613\) 16.5526i 0.0270026i −0.999909 0.0135013i \(-0.995702\pi\)
0.999909 0.0135013i \(-0.00429774\pi\)
\(614\) 147.735i 0.240610i
\(615\) −52.9691 −0.0861286
\(616\) 376.262 0.610816
\(617\) −357.976 −0.580188 −0.290094 0.956998i \(-0.593687\pi\)
−0.290094 + 0.956998i \(0.593687\pi\)
\(618\) −110.572 −0.178919
\(619\) −484.085 −0.782044 −0.391022 0.920381i \(-0.627878\pi\)
−0.391022 + 0.920381i \(0.627878\pi\)
\(620\) 14.7329i 0.0237628i
\(621\) 61.6618i 0.0992944i
\(622\) 262.523i 0.422062i
\(623\) 657.180i 1.05486i
\(624\) 538.372i 0.862775i
\(625\) 577.030 0.923248
\(626\) −131.507 −0.210076
\(627\) 878.587i 1.40126i
\(628\) 48.5227i 0.0772654i
\(629\) 727.389i 1.15642i
\(630\) 6.62177i 0.0105108i
\(631\) 517.329 0.819856 0.409928 0.912118i \(-0.365554\pi\)
0.409928 + 0.912118i \(0.365554\pi\)
\(632\) 55.3820i 0.0876297i
\(633\) 468.129i 0.739540i
\(634\) 177.000i 0.279179i
\(635\) 81.6325 0.128555
\(636\) 258.067 0.405766
\(637\) 563.729i 0.884974i
\(638\) 86.1145 0.134976
\(639\) −285.023 −0.446046
\(640\) 91.4375i 0.142871i
\(641\) −412.313 −0.643234 −0.321617 0.946870i \(-0.604226\pi\)
−0.321617 + 0.946870i \(0.604226\pi\)
\(642\) 147.179i 0.229251i
\(643\) 77.3753 0.120335 0.0601674 0.998188i \(-0.480837\pi\)
0.0601674 + 0.998188i \(0.480837\pi\)
\(644\) 225.070i 0.349488i
\(645\) 26.7877i 0.0415313i
\(646\) 280.751i 0.434599i
\(647\) 1058.14 1.63546 0.817728 0.575605i \(-0.195233\pi\)
0.817728 + 0.575605i \(0.195233\pi\)
\(648\) 37.3137i 0.0575828i
\(649\) 445.865 + 948.030i 0.687003 + 1.46075i
\(650\) 322.671 0.496416
\(651\) 43.7567i 0.0672147i
\(652\) −117.345 −0.179977
\(653\) −399.017 −0.611052 −0.305526 0.952184i \(-0.598832\pi\)
−0.305526 + 0.952184i \(0.598832\pi\)
\(654\) 82.8591 0.126696
\(655\) 69.2316i 0.105697i
\(656\) −480.287 −0.732145
\(657\) 213.801i 0.325421i
\(658\) 180.539 0.274376
\(659\) 309.391i 0.469486i −0.972057 0.234743i \(-0.924575\pi\)
0.972057 0.234743i \(-0.0754249\pi\)
\(660\) 91.6708i 0.138895i
\(661\) 646.215 0.977633 0.488816 0.872387i \(-0.337429\pi\)
0.488816 + 0.872387i \(0.337429\pi\)
\(662\) 213.965i 0.323210i
\(663\) 780.104i 1.17663i
\(664\) −590.858 −0.889846
\(665\) −117.272 −0.176349
\(666\) 64.1904 0.0963820
\(667\) 107.036i 0.160473i
\(668\) 527.848 0.790191
\(669\) −64.4965 −0.0964073
\(670\) 13.2993 0.0198497
\(671\) −1961.02 −2.92253
\(672\) 206.850i 0.307812i
\(673\) 940.573i 1.39758i 0.715326 + 0.698791i \(0.246278\pi\)
−0.715326 + 0.698791i \(0.753722\pi\)
\(674\) −64.8374 −0.0961979
\(675\) 126.552 0.187484
\(676\) −1625.99 −2.40531
\(677\) 1185.19 1.75065 0.875327 0.483531i \(-0.160646\pi\)
0.875327 + 0.483531i \(0.160646\pi\)
\(678\) −147.382 −0.217377
\(679\) 496.538i 0.731278i
\(680\) 60.8685i 0.0895125i
\(681\) 273.326i 0.401359i
\(682\) 47.1913i 0.0691955i
\(683\) 126.072i 0.184586i 0.995732 + 0.0922928i \(0.0294196\pi\)
−0.995732 + 0.0922928i \(0.970580\pi\)
\(684\) 318.027 0.464952
\(685\) 139.837 0.204142
\(686\) 197.524i 0.287936i
\(687\) 527.997i 0.768555i
\(688\) 242.892i 0.353041i
\(689\) 989.341i 1.43591i
\(690\) −8.87655 −0.0128646
\(691\) 1168.97i 1.69171i −0.533410 0.845857i \(-0.679090\pi\)
0.533410 0.845857i \(-0.320910\pi\)
\(692\) 751.459i 1.08592i
\(693\) 272.262i 0.392874i
\(694\) 91.9372 0.132474
\(695\) −133.665 −0.192324
\(696\) 64.7710i 0.0930618i
\(697\) −695.939 −0.998478
\(698\) −158.261 −0.226734
\(699\) 282.990i 0.404850i
\(700\) −461.923 −0.659890
\(701\) 747.168i 1.06586i 0.846159 + 0.532930i \(0.178909\pi\)
−0.846159 + 0.532930i \(0.821091\pi\)
\(702\) 68.8423 0.0980660
\(703\) 1136.82i 1.61710i
\(704\) 672.876i 0.955789i
\(705\) 91.3981i 0.129643i
\(706\) −88.9747 −0.126027
\(707\) 514.666i 0.727958i
\(708\) 343.164 161.392i 0.484694 0.227955i
\(709\) 1148.98 1.62056 0.810282 0.586040i \(-0.199314\pi\)
0.810282 + 0.586040i \(0.199314\pi\)
\(710\) 41.0307i 0.0577897i
\(711\) −40.0741 −0.0563630
\(712\) −533.096 −0.748731
\(713\) −58.6563 −0.0822669
\(714\) 87.0007i 0.121850i
\(715\) −351.434 −0.491516
\(716\) 708.437i 0.989437i
\(717\) 407.564 0.568430
\(718\) 124.472i 0.173359i
\(719\) 392.721i 0.546204i 0.961985 + 0.273102i \(0.0880496\pi\)
−0.961985 + 0.273102i \(0.911950\pi\)
\(720\) −30.3961 −0.0422168
\(721\) 606.830i 0.841650i
\(722\) 244.678i 0.338889i
\(723\) −123.401 −0.170680
\(724\) −460.044 −0.635421
\(725\) −219.675 −0.303000
\(726\) 180.947i 0.249239i
\(727\) 1029.86 1.41658 0.708292 0.705920i \(-0.249466\pi\)
0.708292 + 0.705920i \(0.249466\pi\)
\(728\) −522.135 −0.717219
\(729\) 27.0000 0.0370370
\(730\) −30.7779 −0.0421615
\(731\) 351.952i 0.481467i
\(732\) 709.840i 0.969727i
\(733\) −679.097 −0.926462 −0.463231 0.886238i \(-0.653310\pi\)
−0.463231 + 0.886238i \(0.653310\pi\)
\(734\) 12.8712 0.0175356
\(735\) −31.8278 −0.0433031
\(736\) −277.284 −0.376745
\(737\) 546.817 0.741950
\(738\) 61.4150i 0.0832181i
\(739\) 297.353i 0.402372i −0.979553 0.201186i \(-0.935521\pi\)
0.979553 0.201186i \(-0.0644795\pi\)
\(740\) 118.614i 0.160290i
\(741\) 1219.21i 1.64535i
\(742\) 110.336i 0.148701i
\(743\) 592.272 0.797136 0.398568 0.917139i \(-0.369507\pi\)
0.398568 + 0.917139i \(0.369507\pi\)
\(744\) 35.4950 0.0477083
\(745\) 21.8338i 0.0293071i
\(746\) 150.109i 0.201219i
\(747\) 427.542i 0.572345i
\(748\) 1204.42i 1.61019i
\(749\) 807.737 1.07842
\(750\) 36.9181i 0.0492242i
\(751\) 546.455i 0.727637i −0.931470 0.363818i \(-0.881473\pi\)
0.931470 0.363818i \(-0.118527\pi\)
\(752\) 828.735i 1.10204i
\(753\) −719.187 −0.955095
\(754\) −119.500 −0.158488
\(755\) 75.8712i 0.100492i
\(756\) −98.5521 −0.130360
\(757\) −392.628 −0.518663 −0.259331 0.965788i \(-0.583502\pi\)
−0.259331 + 0.965788i \(0.583502\pi\)
\(758\) 48.3561i 0.0637944i
\(759\) −364.969 −0.480856
\(760\) 95.1300i 0.125171i
\(761\) −526.584 −0.691963 −0.345982 0.938241i \(-0.612454\pi\)
−0.345982 + 0.938241i \(0.612454\pi\)
\(762\) 94.6488i 0.124211i
\(763\) 454.740i 0.595989i
\(764\) 465.111i 0.608784i
\(765\) −44.0442 −0.0575741
\(766\) 77.3803i 0.101019i
\(767\) −618.722 1315.57i −0.806678 1.71522i
\(768\) −156.522 −0.203805
\(769\) 1298.20i 1.68817i 0.536212 + 0.844084i \(0.319855\pi\)
−0.536212 + 0.844084i \(0.680145\pi\)
\(770\) −39.1935 −0.0509007
\(771\) −664.339 −0.861659
\(772\) −400.807 −0.519179
\(773\) 1105.65i 1.43034i 0.698951 + 0.715170i \(0.253651\pi\)
−0.698951 + 0.715170i \(0.746349\pi\)
\(774\) −31.0590 −0.0401279
\(775\) 120.383i 0.155333i
\(776\) −402.786 −0.519054
\(777\) 352.284i 0.453390i
\(778\) 98.3554i 0.126421i
\(779\) −1087.67 −1.39623
\(780\) 127.211i 0.163090i
\(781\) 1687.02i 2.16008i
\(782\) −116.625 −0.149137
\(783\) −46.8680 −0.0598570
\(784\) −288.592 −0.368102
\(785\) 10.5025i 0.0133790i
\(786\) 80.2705 0.102125
\(787\) 597.635 0.759384 0.379692 0.925113i \(-0.376030\pi\)
0.379692 + 0.925113i \(0.376030\pi\)
\(788\) −492.018 −0.624389
\(789\) 306.535 0.388511
\(790\) 5.76889i 0.00730239i
\(791\) 808.848i 1.02256i