Properties

Label 690.3.g.a.461.19
Level $690$
Weight $3$
Character 690.461
Analytic conductor $18.801$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 690.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(56\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 461.19
Character \(\chi\) \(=\) 690.461
Dual form 690.3.g.a.461.20

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421i q^{2} +(-2.91669 - 0.702099i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(-0.992918 + 4.12482i) q^{6} -8.52828 q^{7} +2.82843i q^{8} +(8.01411 + 4.09561i) q^{9} +O(q^{10})\) \(q-1.41421i q^{2} +(-2.91669 - 0.702099i) q^{3} -2.00000 q^{4} -2.23607i q^{5} +(-0.992918 + 4.12482i) q^{6} -8.52828 q^{7} +2.82843i q^{8} +(8.01411 + 4.09561i) q^{9} -3.16228 q^{10} +11.2465i q^{11} +(5.83337 + 1.40420i) q^{12} +18.3730 q^{13} +12.0608i q^{14} +(-1.56994 + 6.52191i) q^{15} +4.00000 q^{16} -0.800569i q^{17} +(5.79206 - 11.3337i) q^{18} +13.2492 q^{19} +4.47214i q^{20} +(24.8743 + 5.98770i) q^{21} +15.9050 q^{22} -4.79583i q^{23} +(1.98584 - 8.24963i) q^{24} -5.00000 q^{25} -25.9833i q^{26} +(-20.4991 - 17.5723i) q^{27} +17.0566 q^{28} -10.9760i q^{29} +(9.22337 + 2.22023i) q^{30} -42.6501 q^{31} -5.65685i q^{32} +(7.89618 - 32.8026i) q^{33} -1.13218 q^{34} +19.0698i q^{35} +(-16.0282 - 8.19121i) q^{36} +42.8724 q^{37} -18.7371i q^{38} +(-53.5882 - 12.8996i) q^{39} +6.32456 q^{40} +59.2804i q^{41} +(8.46788 - 35.1776i) q^{42} +10.6963 q^{43} -22.4931i q^{44} +(9.15805 - 17.9201i) q^{45} -6.78233 q^{46} -65.8685i q^{47} +(-11.6667 - 2.80840i) q^{48} +23.7316 q^{49} +7.07107i q^{50} +(-0.562079 + 2.33501i) q^{51} -36.7459 q^{52} -68.3687i q^{53} +(-24.8510 + 28.9901i) q^{54} +25.1480 q^{55} -24.1216i q^{56} +(-38.6436 - 9.30223i) q^{57} -15.5224 q^{58} -54.6341i q^{59} +(3.13988 - 13.0438i) q^{60} +34.1922 q^{61} +60.3163i q^{62} +(-68.3466 - 34.9285i) q^{63} -8.00000 q^{64} -41.0832i q^{65} +(-46.3899 - 11.1669i) q^{66} +54.8459 q^{67} +1.60114i q^{68} +(-3.36715 + 13.9879i) q^{69} +26.9688 q^{70} +32.3338i q^{71} +(-11.5841 + 22.6673i) q^{72} -39.7792 q^{73} -60.6307i q^{74} +(14.5834 + 3.51050i) q^{75} -26.4983 q^{76} -95.9136i q^{77} +(-18.2429 + 75.7851i) q^{78} +14.3142 q^{79} -8.94427i q^{80} +(47.4520 + 65.6453i) q^{81} +83.8352 q^{82} -42.0770i q^{83} +(-49.7486 - 11.9754i) q^{84} -1.79013 q^{85} -15.1268i q^{86} +(-7.70625 + 32.0136i) q^{87} -31.8100 q^{88} -77.1399i q^{89} +(-25.3429 - 12.9514i) q^{90} -156.690 q^{91} +9.59166i q^{92} +(124.397 + 29.9446i) q^{93} -93.1521 q^{94} -29.6260i q^{95} +(-3.97167 + 16.4993i) q^{96} +139.910 q^{97} -33.5615i q^{98} +(-46.0614 + 90.1310i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q - 8q^{3} - 112q^{4} + 16q^{6} - 16q^{7} + O(q^{10}) \) \( 56q - 8q^{3} - 112q^{4} + 16q^{6} - 16q^{7} + 16q^{12} + 80q^{13} - 40q^{15} + 224q^{16} - 32q^{18} - 64q^{19} + 56q^{21} - 96q^{22} - 32q^{24} - 280q^{25} + 40q^{27} + 32q^{28} - 80q^{31} + 32q^{33} + 192q^{34} + 240q^{37} - 56q^{39} - 144q^{43} - 32q^{48} + 72q^{49} - 24q^{51} - 160q^{52} + 16q^{54} - 16q^{57} + 80q^{60} + 112q^{61} - 64q^{63} - 448q^{64} + 160q^{66} + 832q^{67} + 64q^{72} - 608q^{73} + 40q^{75} + 128q^{76} - 320q^{78} + 48q^{79} - 32q^{81} - 448q^{82} - 112q^{84} + 240q^{85} + 200q^{87} + 192q^{88} + 80q^{91} - 232q^{93} + 160q^{94} + 64q^{96} - 448q^{97} + 464q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.41421i 0.707107i
\(3\) −2.91669 0.702099i −0.972229 0.234033i
\(4\) −2.00000 −0.500000
\(5\) 2.23607i 0.447214i
\(6\) −0.992918 + 4.12482i −0.165486 + 0.687469i
\(7\) −8.52828 −1.21833 −0.609163 0.793045i \(-0.708494\pi\)
−0.609163 + 0.793045i \(0.708494\pi\)
\(8\) 2.82843i 0.353553i
\(9\) 8.01411 + 4.09561i 0.890457 + 0.455067i
\(10\) −3.16228 −0.316228
\(11\) 11.2465i 1.02241i 0.859458 + 0.511206i \(0.170801\pi\)
−0.859458 + 0.511206i \(0.829199\pi\)
\(12\) 5.83337 + 1.40420i 0.486114 + 0.117017i
\(13\) 18.3730 1.41331 0.706653 0.707561i \(-0.250204\pi\)
0.706653 + 0.707561i \(0.250204\pi\)
\(14\) 12.0608i 0.861486i
\(15\) −1.56994 + 6.52191i −0.104663 + 0.434794i
\(16\) 4.00000 0.250000
\(17\) 0.800569i 0.0470923i −0.999723 0.0235462i \(-0.992504\pi\)
0.999723 0.0235462i \(-0.00749567\pi\)
\(18\) 5.79206 11.3337i 0.321781 0.629648i
\(19\) 13.2492 0.697324 0.348662 0.937248i \(-0.386636\pi\)
0.348662 + 0.937248i \(0.386636\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 24.8743 + 5.98770i 1.18449 + 0.285129i
\(22\) 15.9050 0.722954
\(23\) 4.79583i 0.208514i
\(24\) 1.98584 8.24963i 0.0827432 0.343735i
\(25\) −5.00000 −0.200000
\(26\) 25.9833i 0.999358i
\(27\) −20.4991 17.5723i −0.759227 0.650826i
\(28\) 17.0566 0.609163
\(29\) 10.9760i 0.378483i −0.981931 0.189241i \(-0.939397\pi\)
0.981931 0.189241i \(-0.0606029\pi\)
\(30\) 9.22337 + 2.22023i 0.307446 + 0.0740078i
\(31\) −42.6501 −1.37581 −0.687905 0.725801i \(-0.741469\pi\)
−0.687905 + 0.725801i \(0.741469\pi\)
\(32\) 5.65685i 0.176777i
\(33\) 7.89618 32.8026i 0.239278 0.994018i
\(34\) −1.13218 −0.0332993
\(35\) 19.0698i 0.544852i
\(36\) −16.0282 8.19121i −0.445229 0.227534i
\(37\) 42.8724 1.15871 0.579357 0.815074i \(-0.303304\pi\)
0.579357 + 0.815074i \(0.303304\pi\)
\(38\) 18.7371i 0.493083i
\(39\) −53.5882 12.8996i −1.37406 0.330760i
\(40\) 6.32456 0.158114
\(41\) 59.2804i 1.44586i 0.690919 + 0.722932i \(0.257206\pi\)
−0.690919 + 0.722932i \(0.742794\pi\)
\(42\) 8.46788 35.1776i 0.201616 0.837562i
\(43\) 10.6963 0.248750 0.124375 0.992235i \(-0.460307\pi\)
0.124375 + 0.992235i \(0.460307\pi\)
\(44\) 22.4931i 0.511206i
\(45\) 9.15805 17.9201i 0.203512 0.398224i
\(46\) −6.78233 −0.147442
\(47\) 65.8685i 1.40146i −0.713428 0.700729i \(-0.752858\pi\)
0.713428 0.700729i \(-0.247142\pi\)
\(48\) −11.6667 2.80840i −0.243057 0.0585083i
\(49\) 23.7316 0.484317
\(50\) 7.07107i 0.141421i
\(51\) −0.562079 + 2.33501i −0.0110212 + 0.0457845i
\(52\) −36.7459 −0.706653
\(53\) 68.3687i 1.28998i −0.764193 0.644988i \(-0.776862\pi\)
0.764193 0.644988i \(-0.223138\pi\)
\(54\) −24.8510 + 28.9901i −0.460203 + 0.536855i
\(55\) 25.1480 0.457237
\(56\) 24.1216i 0.430743i
\(57\) −38.6436 9.30223i −0.677959 0.163197i
\(58\) −15.5224 −0.267628
\(59\) 54.6341i 0.926002i −0.886358 0.463001i \(-0.846773\pi\)
0.886358 0.463001i \(-0.153227\pi\)
\(60\) 3.13988 13.0438i 0.0523314 0.217397i
\(61\) 34.1922 0.560528 0.280264 0.959923i \(-0.409578\pi\)
0.280264 + 0.959923i \(0.409578\pi\)
\(62\) 60.3163i 0.972844i
\(63\) −68.3466 34.9285i −1.08487 0.554420i
\(64\) −8.00000 −0.125000
\(65\) 41.0832i 0.632049i
\(66\) −46.3899 11.1669i −0.702877 0.169195i
\(67\) 54.8459 0.818595 0.409298 0.912401i \(-0.365774\pi\)
0.409298 + 0.912401i \(0.365774\pi\)
\(68\) 1.60114i 0.0235462i
\(69\) −3.36715 + 13.9879i −0.0487993 + 0.202724i
\(70\) 26.9688 0.385268
\(71\) 32.3338i 0.455405i 0.973731 + 0.227703i \(0.0731214\pi\)
−0.973731 + 0.227703i \(0.926879\pi\)
\(72\) −11.5841 + 22.6673i −0.160891 + 0.314824i
\(73\) −39.7792 −0.544920 −0.272460 0.962167i \(-0.587837\pi\)
−0.272460 + 0.962167i \(0.587837\pi\)
\(74\) 60.6307i 0.819334i
\(75\) 14.5834 + 3.51050i 0.194446 + 0.0468066i
\(76\) −26.4983 −0.348662
\(77\) 95.9136i 1.24563i
\(78\) −18.2429 + 75.7851i −0.233883 + 0.971604i
\(79\) 14.3142 0.181193 0.0905964 0.995888i \(-0.471123\pi\)
0.0905964 + 0.995888i \(0.471123\pi\)
\(80\) 8.94427i 0.111803i
\(81\) 47.4520 + 65.6453i 0.585827 + 0.810436i
\(82\) 83.8352 1.02238
\(83\) 42.0770i 0.506952i −0.967342 0.253476i \(-0.918426\pi\)
0.967342 0.253476i \(-0.0815738\pi\)
\(84\) −49.7486 11.9754i −0.592246 0.142564i
\(85\) −1.79013 −0.0210603
\(86\) 15.1268i 0.175893i
\(87\) −7.70625 + 32.0136i −0.0885775 + 0.367972i
\(88\) −31.8100 −0.361477
\(89\) 77.1399i 0.866740i −0.901216 0.433370i \(-0.857324\pi\)
0.901216 0.433370i \(-0.142676\pi\)
\(90\) −25.3429 12.9514i −0.281587 0.143905i
\(91\) −156.690 −1.72187
\(92\) 9.59166i 0.104257i
\(93\) 124.397 + 29.9446i 1.33760 + 0.321985i
\(94\) −93.1521 −0.990980
\(95\) 29.6260i 0.311853i
\(96\) −3.97167 + 16.4993i −0.0413716 + 0.171867i
\(97\) 139.910 1.44237 0.721187 0.692740i \(-0.243597\pi\)
0.721187 + 0.692740i \(0.243597\pi\)
\(98\) 33.5615i 0.342464i
\(99\) −46.0614 + 90.1310i −0.465266 + 0.910414i
\(100\) 10.0000 0.100000
\(101\) 185.003i 1.83171i −0.401504 0.915857i \(-0.631512\pi\)
0.401504 0.915857i \(-0.368488\pi\)
\(102\) 3.30220 + 0.794900i 0.0323745 + 0.00779313i
\(103\) −164.164 −1.59383 −0.796913 0.604093i \(-0.793535\pi\)
−0.796913 + 0.604093i \(0.793535\pi\)
\(104\) 51.9666i 0.499679i
\(105\) 13.3889 55.6207i 0.127513 0.529721i
\(106\) −96.6880 −0.912151
\(107\) 106.013i 0.990772i −0.868673 0.495386i \(-0.835027\pi\)
0.868673 0.495386i \(-0.164973\pi\)
\(108\) 40.9983 + 35.1446i 0.379614 + 0.325413i
\(109\) 58.8011 0.539459 0.269730 0.962936i \(-0.413066\pi\)
0.269730 + 0.962936i \(0.413066\pi\)
\(110\) 35.5647i 0.323315i
\(111\) −125.045 30.1007i −1.12653 0.271177i
\(112\) −34.1131 −0.304581
\(113\) 15.8528i 0.140290i −0.997537 0.0701450i \(-0.977654\pi\)
0.997537 0.0701450i \(-0.0223462\pi\)
\(114\) −13.1553 + 54.6504i −0.115398 + 0.479389i
\(115\) −10.7238 −0.0932505
\(116\) 21.9520i 0.189241i
\(117\) 147.243 + 75.2484i 1.25849 + 0.643149i
\(118\) −77.2643 −0.654782
\(119\) 6.82748i 0.0573738i
\(120\) −18.4467 4.44047i −0.153723 0.0370039i
\(121\) −5.48447 −0.0453262
\(122\) 48.3551i 0.396353i
\(123\) 41.6207 172.902i 0.338380 1.40571i
\(124\) 85.3002 0.687905
\(125\) 11.1803i 0.0894427i
\(126\) −49.3963 + 96.6567i −0.392034 + 0.767117i
\(127\) 201.548 1.58699 0.793495 0.608577i \(-0.208259\pi\)
0.793495 + 0.608577i \(0.208259\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) −31.1976 7.50983i −0.241842 0.0582158i
\(130\) −58.1004 −0.446926
\(131\) 137.815i 1.05202i 0.850477 + 0.526012i \(0.176313\pi\)
−0.850477 + 0.526012i \(0.823687\pi\)
\(132\) −15.7924 + 65.6052i −0.119639 + 0.497009i
\(133\) −112.993 −0.849568
\(134\) 77.5638i 0.578834i
\(135\) −39.2929 + 45.8374i −0.291058 + 0.339537i
\(136\) 2.26435 0.0166496
\(137\) 12.5145i 0.0913465i −0.998956 0.0456733i \(-0.985457\pi\)
0.998956 0.0456733i \(-0.0145433\pi\)
\(138\) 19.7819 + 4.76187i 0.143347 + 0.0345063i
\(139\) 271.132 1.95059 0.975296 0.220900i \(-0.0708996\pi\)
0.975296 + 0.220900i \(0.0708996\pi\)
\(140\) 38.1396i 0.272426i
\(141\) −46.2462 + 192.118i −0.327987 + 1.36254i
\(142\) 45.7268 0.322020
\(143\) 206.632i 1.44498i
\(144\) 32.0565 + 16.3824i 0.222614 + 0.113767i
\(145\) −24.5431 −0.169263
\(146\) 56.2562i 0.385317i
\(147\) −69.2175 16.6619i −0.470867 0.113346i
\(148\) −85.7448 −0.579357
\(149\) 83.1004i 0.557721i 0.960332 + 0.278861i \(0.0899567\pi\)
−0.960332 + 0.278861i \(0.910043\pi\)
\(150\) 4.96459 20.6241i 0.0330973 0.137494i
\(151\) 170.027 1.12601 0.563003 0.826455i \(-0.309646\pi\)
0.563003 + 0.826455i \(0.309646\pi\)
\(152\) 37.4743i 0.246541i
\(153\) 3.27882 6.41585i 0.0214302 0.0419337i
\(154\) −135.642 −0.880794
\(155\) 95.3685i 0.615281i
\(156\) 107.176 + 25.7993i 0.687028 + 0.165380i
\(157\) 148.967 0.948833 0.474417 0.880300i \(-0.342659\pi\)
0.474417 + 0.880300i \(0.342659\pi\)
\(158\) 20.2434i 0.128123i
\(159\) −48.0016 + 199.410i −0.301897 + 1.25415i
\(160\) −12.6491 −0.0790569
\(161\) 40.9002i 0.254038i
\(162\) 92.8365 67.1073i 0.573065 0.414243i
\(163\) −233.872 −1.43480 −0.717398 0.696664i \(-0.754667\pi\)
−0.717398 + 0.696664i \(0.754667\pi\)
\(164\) 118.561i 0.722932i
\(165\) −73.3488 17.6564i −0.444538 0.107008i
\(166\) −59.5059 −0.358469
\(167\) 140.840i 0.843356i −0.906746 0.421678i \(-0.861441\pi\)
0.906746 0.421678i \(-0.138559\pi\)
\(168\) −16.9358 + 70.3552i −0.100808 + 0.418781i
\(169\) 168.566 0.997432
\(170\) 2.53162i 0.0148919i
\(171\) 106.180 + 54.2633i 0.620937 + 0.317330i
\(172\) −21.3925 −0.124375
\(173\) 112.577i 0.650735i −0.945588 0.325368i \(-0.894512\pi\)
0.945588 0.325368i \(-0.105488\pi\)
\(174\) 45.2740 + 10.8983i 0.260195 + 0.0626338i
\(175\) 42.6414 0.243665
\(176\) 44.9861i 0.255603i
\(177\) −38.3586 + 159.350i −0.216715 + 0.900285i
\(178\) −109.092 −0.612878
\(179\) 265.456i 1.48300i 0.670954 + 0.741499i \(0.265885\pi\)
−0.670954 + 0.741499i \(0.734115\pi\)
\(180\) −18.3161 + 35.8402i −0.101756 + 0.199112i
\(181\) −181.424 −1.00234 −0.501172 0.865348i \(-0.667098\pi\)
−0.501172 + 0.865348i \(0.667098\pi\)
\(182\) 221.593i 1.21754i
\(183\) −99.7279 24.0063i −0.544961 0.131182i
\(184\) 13.5647 0.0737210
\(185\) 95.8656i 0.518192i
\(186\) 42.3480 175.924i 0.227678 0.945827i
\(187\) 9.00363 0.0481477
\(188\) 131.737i 0.700729i
\(189\) 174.822 + 149.861i 0.924986 + 0.792918i
\(190\) −41.8975 −0.220513
\(191\) 192.654i 1.00866i −0.863511 0.504331i \(-0.831739\pi\)
0.863511 0.504331i \(-0.168261\pi\)
\(192\) 23.3335 + 5.61679i 0.121529 + 0.0292541i
\(193\) 204.556 1.05988 0.529938 0.848036i \(-0.322215\pi\)
0.529938 + 0.848036i \(0.322215\pi\)
\(194\) 197.863i 1.01991i
\(195\) −28.8445 + 119.827i −0.147920 + 0.614496i
\(196\) −47.4631 −0.242159
\(197\) 41.7064i 0.211708i −0.994382 0.105854i \(-0.966242\pi\)
0.994382 0.105854i \(-0.0337576\pi\)
\(198\) 127.464 + 65.1406i 0.643760 + 0.328993i
\(199\) −7.69267 −0.0386566 −0.0193283 0.999813i \(-0.506153\pi\)
−0.0193283 + 0.999813i \(0.506153\pi\)
\(200\) 14.1421i 0.0707107i
\(201\) −159.968 38.5073i −0.795862 0.191578i
\(202\) −261.634 −1.29522
\(203\) 93.6065i 0.461116i
\(204\) 1.12416 4.67002i 0.00551058 0.0228922i
\(205\) 132.555 0.646610
\(206\) 232.163i 1.12701i
\(207\) 19.6418 38.4343i 0.0948881 0.185673i
\(208\) 73.4919 0.353326
\(209\) 149.007i 0.712953i
\(210\) −78.6595 18.9348i −0.374569 0.0901655i
\(211\) 348.331 1.65086 0.825429 0.564507i \(-0.190934\pi\)
0.825429 + 0.564507i \(0.190934\pi\)
\(212\) 136.737i 0.644988i
\(213\) 22.7015 94.3074i 0.106580 0.442758i
\(214\) −149.924 −0.700581
\(215\) 23.9176i 0.111244i
\(216\) 49.7020 57.9803i 0.230102 0.268427i
\(217\) 363.732 1.67618
\(218\) 83.1573i 0.381455i
\(219\) 116.023 + 27.9289i 0.529787 + 0.127529i
\(220\) −50.2960 −0.228618
\(221\) 14.7088i 0.0665558i
\(222\) −42.5688 + 176.841i −0.191751 + 0.796580i
\(223\) 411.231 1.84409 0.922044 0.387086i \(-0.126518\pi\)
0.922044 + 0.387086i \(0.126518\pi\)
\(224\) 48.2432i 0.215372i
\(225\) −40.0706 20.4780i −0.178091 0.0910135i
\(226\) −22.4192 −0.0992000
\(227\) 97.7055i 0.430421i −0.976568 0.215210i \(-0.930956\pi\)
0.976568 0.215210i \(-0.0690437\pi\)
\(228\) 77.2873 + 18.6045i 0.338979 + 0.0815985i
\(229\) 88.0463 0.384482 0.192241 0.981348i \(-0.438425\pi\)
0.192241 + 0.981348i \(0.438425\pi\)
\(230\) 15.1658i 0.0659380i
\(231\) −67.3408 + 279.750i −0.291519 + 1.21104i
\(232\) 31.0448 0.133814
\(233\) 113.860i 0.488671i −0.969691 0.244336i \(-0.921430\pi\)
0.969691 0.244336i \(-0.0785699\pi\)
\(234\) 106.417 208.233i 0.454775 0.889885i
\(235\) −147.286 −0.626751
\(236\) 109.268i 0.463001i
\(237\) −41.7501 10.0500i −0.176161 0.0424051i
\(238\) 9.65551 0.0405694
\(239\) 88.4422i 0.370051i 0.982734 + 0.185026i \(0.0592368\pi\)
−0.982734 + 0.185026i \(0.940763\pi\)
\(240\) −6.27977 + 26.0876i −0.0261657 + 0.108698i
\(241\) −297.884 −1.23603 −0.618017 0.786164i \(-0.712064\pi\)
−0.618017 + 0.786164i \(0.712064\pi\)
\(242\) 7.75622i 0.0320505i
\(243\) −92.3131 224.783i −0.379889 0.925032i
\(244\) −68.3844 −0.280264
\(245\) 53.0654i 0.216593i
\(246\) −244.521 58.8606i −0.993988 0.239271i
\(247\) 243.426 0.985532
\(248\) 120.633i 0.486422i
\(249\) −29.5422 + 122.725i −0.118643 + 0.492873i
\(250\) 15.8114 0.0632456
\(251\) 252.585i 1.00632i 0.864195 + 0.503158i \(0.167829\pi\)
−0.864195 + 0.503158i \(0.832171\pi\)
\(252\) 136.693 + 69.8569i 0.542433 + 0.277210i
\(253\) 53.9365 0.213188
\(254\) 285.032i 1.12217i
\(255\) 5.22124 + 1.25685i 0.0204754 + 0.00492881i
\(256\) 16.0000 0.0625000
\(257\) 108.572i 0.422460i 0.977436 + 0.211230i \(0.0677469\pi\)
−0.977436 + 0.211230i \(0.932253\pi\)
\(258\) −10.6205 + 44.1201i −0.0411648 + 0.171008i
\(259\) −365.628 −1.41169
\(260\) 82.1664i 0.316025i
\(261\) 44.9534 87.9630i 0.172235 0.337023i
\(262\) 194.900 0.743893
\(263\) 411.174i 1.56340i −0.623655 0.781700i \(-0.714353\pi\)
0.623655 0.781700i \(-0.285647\pi\)
\(264\) 92.7798 + 22.3338i 0.351439 + 0.0845976i
\(265\) −152.877 −0.576895
\(266\) 159.796i 0.600735i
\(267\) −54.1598 + 224.993i −0.202846 + 0.842670i
\(268\) −109.692 −0.409298
\(269\) 270.452i 1.00540i −0.864462 0.502698i \(-0.832341\pi\)
0.864462 0.502698i \(-0.167659\pi\)
\(270\) 64.8239 + 55.5685i 0.240089 + 0.205809i
\(271\) −138.939 −0.512689 −0.256345 0.966585i \(-0.582518\pi\)
−0.256345 + 0.966585i \(0.582518\pi\)
\(272\) 3.20228i 0.0117731i
\(273\) 457.015 + 110.012i 1.67405 + 0.402974i
\(274\) −17.6981 −0.0645917
\(275\) 56.2327i 0.204482i
\(276\) 6.73430 27.9759i 0.0243996 0.101362i
\(277\) −64.2222 −0.231849 −0.115925 0.993258i \(-0.536983\pi\)
−0.115925 + 0.993258i \(0.536983\pi\)
\(278\) 383.439i 1.37928i
\(279\) −341.803 174.678i −1.22510 0.626086i
\(280\) −53.9376 −0.192634
\(281\) 298.203i 1.06122i −0.847616 0.530611i \(-0.821963\pi\)
0.847616 0.530611i \(-0.178037\pi\)
\(282\) 271.695 + 65.4020i 0.963459 + 0.231922i
\(283\) −118.877 −0.420061 −0.210031 0.977695i \(-0.567356\pi\)
−0.210031 + 0.977695i \(0.567356\pi\)
\(284\) 64.6675i 0.227703i
\(285\) −20.8004 + 86.4098i −0.0729839 + 0.303192i
\(286\) 292.222 1.02176
\(287\) 505.560i 1.76153i
\(288\) 23.1682 45.3347i 0.0804453 0.157412i
\(289\) 288.359 0.997782
\(290\) 34.7092i 0.119687i
\(291\) −408.074 98.2309i −1.40232 0.337563i
\(292\) 79.5583 0.272460
\(293\) 338.920i 1.15672i 0.815781 + 0.578361i \(0.196308\pi\)
−0.815781 + 0.578361i \(0.803692\pi\)
\(294\) −23.5635 + 97.8883i −0.0801479 + 0.332953i
\(295\) −122.166 −0.414120
\(296\) 121.261i 0.409667i
\(297\) 197.627 230.544i 0.665412 0.776243i
\(298\) 117.522 0.394368
\(299\) 88.1137i 0.294695i
\(300\) −29.1669 7.02099i −0.0972229 0.0234033i
\(301\) −91.2207 −0.303059
\(302\) 240.455i 0.796207i
\(303\) −129.891 + 539.596i −0.428682 + 1.78085i
\(304\) 52.9966 0.174331
\(305\) 76.4561i 0.250676i
\(306\) −9.07338 4.63695i −0.0296516 0.0151534i
\(307\) 194.037 0.632042 0.316021 0.948752i \(-0.397653\pi\)
0.316021 + 0.948752i \(0.397653\pi\)
\(308\) 191.827i 0.622815i
\(309\) 478.815 + 115.260i 1.54956 + 0.373008i
\(310\) 134.871 0.435069
\(311\) 145.543i 0.467985i 0.972238 + 0.233992i \(0.0751791\pi\)
−0.972238 + 0.233992i \(0.924821\pi\)
\(312\) 36.4857 151.570i 0.116941 0.485802i
\(313\) −93.3372 −0.298202 −0.149101 0.988822i \(-0.547638\pi\)
−0.149101 + 0.988822i \(0.547638\pi\)
\(314\) 210.671i 0.670926i
\(315\) −78.1024 + 152.828i −0.247944 + 0.485167i
\(316\) −28.6285 −0.0905964
\(317\) 282.185i 0.890174i 0.895487 + 0.445087i \(0.146827\pi\)
−0.895487 + 0.445087i \(0.853173\pi\)
\(318\) 282.008 + 67.8845i 0.886819 + 0.213473i
\(319\) 123.442 0.386966
\(320\) 17.8885i 0.0559017i
\(321\) −74.4313 + 309.205i −0.231873 + 0.963257i
\(322\) 57.8416 0.179632
\(323\) 10.6069i 0.0328386i
\(324\) −94.9041 131.291i −0.292914 0.405218i
\(325\) −91.8648 −0.282661
\(326\) 330.745i 1.01455i
\(327\) −171.504 41.2842i −0.524478 0.126251i
\(328\) −167.670 −0.511190
\(329\) 561.745i 1.70743i
\(330\) −24.9699 + 103.731i −0.0756664 + 0.314336i
\(331\) −384.366 −1.16123 −0.580613 0.814179i \(-0.697187\pi\)
−0.580613 + 0.814179i \(0.697187\pi\)
\(332\) 84.1540i 0.253476i
\(333\) 343.584 + 175.588i 1.03178 + 0.527293i
\(334\) −199.178 −0.596343
\(335\) 122.639i 0.366087i
\(336\) 99.4973 + 23.9508i 0.296123 + 0.0712821i
\(337\) −267.563 −0.793954 −0.396977 0.917829i \(-0.629941\pi\)
−0.396977 + 0.917829i \(0.629941\pi\)
\(338\) 238.388i 0.705291i
\(339\) −11.1302 + 46.2376i −0.0328325 + 0.136394i
\(340\) 3.58025 0.0105302
\(341\) 479.666i 1.40664i
\(342\) 76.7400 150.162i 0.224386 0.439069i
\(343\) 215.496 0.628269
\(344\) 30.2536i 0.0879465i
\(345\) 31.2780 + 7.52918i 0.0906608 + 0.0218237i
\(346\) −159.208 −0.460139
\(347\) 518.074i 1.49301i 0.665380 + 0.746505i \(0.268270\pi\)
−0.665380 + 0.746505i \(0.731730\pi\)
\(348\) 15.4125 64.0271i 0.0442888 0.183986i
\(349\) −375.123 −1.07485 −0.537426 0.843311i \(-0.680603\pi\)
−0.537426 + 0.843311i \(0.680603\pi\)
\(350\) 60.3040i 0.172297i
\(351\) −376.630 322.855i −1.07302 0.919816i
\(352\) 63.6200 0.180739
\(353\) 101.654i 0.287970i 0.989580 + 0.143985i \(0.0459918\pi\)
−0.989580 + 0.143985i \(0.954008\pi\)
\(354\) 225.356 + 54.2472i 0.636598 + 0.153241i
\(355\) 72.3005 0.203663
\(356\) 154.280i 0.433370i
\(357\) 4.79357 19.9136i 0.0134274 0.0557804i
\(358\) 375.412 1.04864
\(359\) 147.915i 0.412019i 0.978550 + 0.206010i \(0.0660478\pi\)
−0.978550 + 0.206010i \(0.933952\pi\)
\(360\) 50.6857 + 25.9029i 0.140794 + 0.0719525i
\(361\) −185.460 −0.513739
\(362\) 256.573i 0.708764i
\(363\) 15.9965 + 3.85064i 0.0440674 + 0.0106078i
\(364\) 313.380 0.860933
\(365\) 88.9489i 0.243696i
\(366\) −33.9501 + 141.037i −0.0927597 + 0.385346i
\(367\) −398.761 −1.08654 −0.543271 0.839557i \(-0.682814\pi\)
−0.543271 + 0.839557i \(0.682814\pi\)
\(368\) 19.1833i 0.0521286i
\(369\) −242.789 + 475.080i −0.657966 + 1.28748i
\(370\) −135.574 −0.366417
\(371\) 583.068i 1.57161i
\(372\) −248.794 59.8892i −0.668801 0.160992i
\(373\) 349.777 0.937739 0.468869 0.883268i \(-0.344662\pi\)
0.468869 + 0.883268i \(0.344662\pi\)
\(374\) 12.7331i 0.0340456i
\(375\) 7.84971 32.6095i 0.0209326 0.0869588i
\(376\) 186.304 0.495490
\(377\) 201.662i 0.534912i
\(378\) 211.936 247.236i 0.560678 0.654064i
\(379\) −568.739 −1.50063 −0.750315 0.661080i \(-0.770098\pi\)
−0.750315 + 0.661080i \(0.770098\pi\)
\(380\) 59.2521i 0.155926i
\(381\) −587.851 141.507i −1.54292 0.371408i
\(382\) −272.454 −0.713231
\(383\) 116.352i 0.303791i −0.988397 0.151896i \(-0.951462\pi\)
0.988397 0.151896i \(-0.0485378\pi\)
\(384\) 7.94335 32.9985i 0.0206858 0.0859337i
\(385\) −214.469 −0.557063
\(386\) 289.286i 0.749445i
\(387\) 85.7210 + 43.8077i 0.221501 + 0.113198i
\(388\) −279.821 −0.721187
\(389\) 718.880i 1.84802i −0.382368 0.924010i \(-0.624891\pi\)
0.382368 0.924010i \(-0.375109\pi\)
\(390\) 169.461 + 40.7923i 0.434515 + 0.104596i
\(391\) −3.83939 −0.00981942
\(392\) 67.1230i 0.171232i
\(393\) 96.7599 401.963i 0.246208 1.02281i
\(394\) −58.9818 −0.149700
\(395\) 32.0076i 0.0810319i
\(396\) 92.1227 180.262i 0.232633 0.455207i
\(397\) −187.368 −0.471961 −0.235980 0.971758i \(-0.575830\pi\)
−0.235980 + 0.971758i \(0.575830\pi\)
\(398\) 10.8791i 0.0273344i
\(399\) 329.564 + 79.3320i 0.825974 + 0.198827i
\(400\) −20.0000 −0.0500000
\(401\) 95.8953i 0.239141i 0.992826 + 0.119570i \(0.0381517\pi\)
−0.992826 + 0.119570i \(0.961848\pi\)
\(402\) −54.4575 + 226.229i −0.135466 + 0.562759i
\(403\) −783.609 −1.94444
\(404\) 370.006i 0.915857i
\(405\) 146.787 106.106i 0.362438 0.261990i
\(406\) 132.380 0.326058
\(407\) 482.166i 1.18468i
\(408\) −6.60440 1.58980i −0.0161873 0.00389657i
\(409\) 678.263 1.65835 0.829173 0.558993i \(-0.188812\pi\)
0.829173 + 0.558993i \(0.188812\pi\)
\(410\) 187.461i 0.457222i
\(411\) −8.78640 + 36.5008i −0.0213781 + 0.0888097i
\(412\) 328.328 0.796913
\(413\) 465.935i 1.12817i
\(414\) −54.3544 27.7777i −0.131291 0.0670960i
\(415\) −94.0870 −0.226716
\(416\) 103.933i 0.249839i
\(417\) −790.808 190.362i −1.89642 0.456503i
\(418\) 210.728 0.504134
\(419\) 149.069i 0.355774i −0.984051 0.177887i \(-0.943074\pi\)
0.984051 0.177887i \(-0.0569262\pi\)
\(420\) −26.7778 + 111.241i −0.0637567 + 0.264860i
\(421\) −61.2688 −0.145532 −0.0727658 0.997349i \(-0.523183\pi\)
−0.0727658 + 0.997349i \(0.523183\pi\)
\(422\) 492.614i 1.16733i
\(423\) 269.771 527.877i 0.637757 1.24794i
\(424\) 193.376 0.456075
\(425\) 4.00285i 0.00941846i
\(426\) −133.371 32.1048i −0.313077 0.0753633i
\(427\) −291.601 −0.682906
\(428\) 212.025i 0.495386i
\(429\) 145.076 602.681i 0.338173 1.40485i
\(430\) −33.8245 −0.0786617
\(431\) 325.729i 0.755751i −0.925856 0.377875i \(-0.876655\pi\)
0.925856 0.377875i \(-0.123345\pi\)
\(432\) −81.9965 70.2892i −0.189807 0.162706i
\(433\) 406.666 0.939183 0.469592 0.882884i \(-0.344401\pi\)
0.469592 + 0.882884i \(0.344401\pi\)
\(434\) 514.395i 1.18524i
\(435\) 71.5845 + 17.2317i 0.164562 + 0.0396131i
\(436\) −117.602 −0.269730
\(437\) 63.5407i 0.145402i
\(438\) 39.4975 164.082i 0.0901769 0.374616i
\(439\) 583.212 1.32850 0.664250 0.747510i \(-0.268751\pi\)
0.664250 + 0.747510i \(0.268751\pi\)
\(440\) 71.1293i 0.161658i
\(441\) 190.187 + 97.1951i 0.431264 + 0.220397i
\(442\) −20.8014 −0.0470621
\(443\) 203.714i 0.459850i 0.973208 + 0.229925i \(0.0738482\pi\)
−0.973208 + 0.229925i \(0.926152\pi\)
\(444\) 250.091 + 60.2013i 0.563267 + 0.135589i
\(445\) −172.490 −0.387618
\(446\) 581.569i 1.30397i
\(447\) 58.3448 242.378i 0.130525 0.542232i
\(448\) 68.2262 0.152291
\(449\) 843.006i 1.87752i −0.344574 0.938759i \(-0.611977\pi\)
0.344574 0.938759i \(-0.388023\pi\)
\(450\) −28.9603 + 56.6683i −0.0643562 + 0.125930i
\(451\) −666.699 −1.47827
\(452\) 31.7055i 0.0701450i
\(453\) −495.915 119.376i −1.09474 0.263523i
\(454\) −138.176 −0.304353
\(455\) 350.369i 0.770042i
\(456\) 26.3107 109.301i 0.0576988 0.239695i
\(457\) −209.735 −0.458938 −0.229469 0.973316i \(-0.573699\pi\)
−0.229469 + 0.973316i \(0.573699\pi\)
\(458\) 124.516i 0.271870i
\(459\) −14.0678 + 16.4110i −0.0306489 + 0.0357538i
\(460\) 21.4476 0.0466252
\(461\) 131.916i 0.286153i −0.989712 0.143076i \(-0.954301\pi\)
0.989712 0.143076i \(-0.0456995\pi\)
\(462\) 395.626 + 95.2343i 0.856333 + 0.206135i
\(463\) −483.695 −1.04470 −0.522349 0.852732i \(-0.674944\pi\)
−0.522349 + 0.852732i \(0.674944\pi\)
\(464\) 43.9040i 0.0946207i
\(465\) 66.9581 278.160i 0.143996 0.598193i
\(466\) −161.023 −0.345543
\(467\) 468.672i 1.00358i −0.864989 0.501790i \(-0.832675\pi\)
0.864989 0.501790i \(-0.167325\pi\)
\(468\) −294.486 150.497i −0.629244 0.321575i
\(469\) −467.741 −0.997316
\(470\) 208.294i 0.443180i
\(471\) −434.489 104.589i −0.922483 0.222058i
\(472\) 154.529 0.327391
\(473\) 120.296i 0.254325i
\(474\) −14.2129 + 59.0436i −0.0299849 + 0.124565i
\(475\) −66.2458 −0.139465
\(476\) 13.6550i 0.0286869i
\(477\) 280.011 547.915i 0.587026 1.14867i
\(478\) 125.076 0.261666
\(479\) 661.943i 1.38193i −0.722890 0.690964i \(-0.757187\pi\)
0.722890 0.690964i \(-0.242813\pi\)
\(480\) 36.8935 + 8.88093i 0.0768614 + 0.0185019i
\(481\) 787.693 1.63762
\(482\) 421.272i 0.874009i
\(483\) 28.7160 119.293i 0.0594534 0.246983i
\(484\) 10.9689 0.0226631
\(485\) 312.849i 0.645049i
\(486\) −317.891 + 130.551i −0.654096 + 0.268622i
\(487\) −26.7852 −0.0550003 −0.0275002 0.999622i \(-0.508755\pi\)
−0.0275002 + 0.999622i \(0.508755\pi\)
\(488\) 96.7102i 0.198177i
\(489\) 682.130 + 164.201i 1.39495 + 0.335790i
\(490\) −75.0458 −0.153155
\(491\) 616.828i 1.25627i 0.778105 + 0.628135i \(0.216181\pi\)
−0.778105 + 0.628135i \(0.783819\pi\)
\(492\) −83.2415 + 345.805i −0.169190 + 0.702855i
\(493\) −8.78705 −0.0178236
\(494\) 344.257i 0.696876i
\(495\) 201.539 + 102.996i 0.407149 + 0.208073i
\(496\) −170.600 −0.343952
\(497\) 275.751i 0.554832i
\(498\) 173.560 + 41.7790i 0.348514 + 0.0838936i
\(499\) 985.407 1.97476 0.987382 0.158359i \(-0.0506202\pi\)
0.987382 + 0.158359i \(0.0506202\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) −98.8839 + 410.787i −0.197373 + 0.819935i
\(502\) 357.209 0.711573
\(503\) 571.158i 1.13550i 0.823200 + 0.567752i \(0.192187\pi\)
−0.823200 + 0.567752i \(0.807813\pi\)
\(504\) 98.7926 193.313i 0.196017 0.383558i
\(505\) −413.680 −0.819168
\(506\) 76.2777i 0.150746i
\(507\) −491.654 118.350i −0.969732 0.233432i
\(508\) −403.095 −0.793495
\(509\) 885.134i 1.73897i 0.493962 + 0.869484i \(0.335548\pi\)
−0.493962 + 0.869484i \(0.664452\pi\)
\(510\) 1.77745 7.38395i 0.00348520 0.0144783i
\(511\) 339.248 0.663890
\(512\) 22.6274i 0.0441942i
\(513\) −271.596 232.818i −0.529427 0.453837i
\(514\) 153.544 0.298724
\(515\) 367.082i 0.712781i
\(516\) 62.3952 + 15.0197i 0.120921 + 0.0291079i
\(517\) 740.792 1.43287
\(518\) 517.076i 0.998216i
\(519\) −79.0404 + 328.352i −0.152294 + 0.632663i
\(520\) 116.201 0.223463
\(521\) 578.831i 1.11100i −0.831516 0.555500i \(-0.812527\pi\)
0.831516 0.555500i \(-0.187473\pi\)
\(522\) −124.398 63.5737i −0.238311 0.121789i
\(523\) −918.390 −1.75600 −0.878002 0.478657i \(-0.841124\pi\)
−0.878002 + 0.478657i \(0.841124\pi\)
\(524\) 275.630i 0.526012i
\(525\) −124.372 29.9385i −0.236898 0.0570257i
\(526\) −581.488 −1.10549
\(527\) 34.1443i 0.0647900i
\(528\) 31.5847 131.210i 0.0598196 0.248505i
\(529\) −23.0000 −0.0434783
\(530\) 216.201i 0.407926i
\(531\) 223.760 437.844i 0.421393 0.824565i
\(532\) 225.985 0.424784
\(533\) 1089.16i 2.04345i
\(534\) 318.188 + 76.5936i 0.595857 + 0.143434i
\(535\) −237.051 −0.443087
\(536\) 155.128i 0.289417i
\(537\) 186.377 774.253i 0.347070 1.44181i
\(538\) −382.476 −0.710922
\(539\) 266.898i 0.495172i
\(540\) 78.5857 91.6749i 0.145529 0.169768i
\(541\) 635.953 1.17551 0.587757 0.809037i \(-0.300011\pi\)
0.587757 + 0.809037i \(0.300011\pi\)
\(542\) 196.489i 0.362526i
\(543\) 529.158 + 127.378i 0.974507 + 0.234582i
\(544\) −4.52870 −0.00832482
\(545\) 131.483i 0.241254i
\(546\) 155.580 646.317i 0.284945 1.18373i
\(547\) −147.805 −0.270209 −0.135105 0.990831i \(-0.543137\pi\)
−0.135105 + 0.990831i \(0.543137\pi\)
\(548\) 25.0289i 0.0456733i
\(549\) 274.020 + 140.038i 0.499126 + 0.255078i
\(550\) −79.5250 −0.144591
\(551\) 145.423i 0.263925i
\(552\) −39.5639 9.52374i −0.0716736 0.0172531i
\(553\) −122.076 −0.220752
\(554\) 90.8239i 0.163942i
\(555\) −67.3072 + 279.610i −0.121274 + 0.503801i
\(556\) −542.265 −0.975296
\(557\) 301.911i 0.542031i −0.962575 0.271015i \(-0.912641\pi\)
0.962575 0.271015i \(-0.0873594\pi\)
\(558\) −247.032 + 483.382i −0.442709 + 0.866276i
\(559\) 196.522 0.351560
\(560\) 76.2793i 0.136213i
\(561\) −26.2608 6.32144i −0.0468106 0.0112682i
\(562\) −421.723 −0.750397
\(563\) 1059.79i 1.88240i −0.337855 0.941198i \(-0.609701\pi\)
0.337855 0.941198i \(-0.390299\pi\)
\(564\) 92.4924 384.235i 0.163994 0.681268i
\(565\) −35.4479 −0.0627396
\(566\) 168.118i 0.297028i
\(567\) −404.684 559.841i −0.713729 0.987375i
\(568\) −91.4537 −0.161010
\(569\) 149.837i 0.263335i 0.991294 + 0.131667i \(0.0420330\pi\)
−0.991294 + 0.131667i \(0.957967\pi\)
\(570\) 122.202 + 29.4162i 0.214389 + 0.0516074i
\(571\) 1037.30 1.81665 0.908323 0.418271i \(-0.137364\pi\)
0.908323 + 0.418271i \(0.137364\pi\)
\(572\) 413.264i 0.722490i
\(573\) −135.262 + 561.912i −0.236060 + 0.980649i
\(574\) −714.970 −1.24559
\(575\) 23.9792i 0.0417029i
\(576\) −64.1129 32.7648i −0.111307 0.0568834i
\(577\) 580.551 1.00615 0.503077 0.864242i \(-0.332201\pi\)
0.503077 + 0.864242i \(0.332201\pi\)
\(578\) 407.801i 0.705539i
\(579\) −596.626 143.619i −1.03044 0.248046i
\(580\) 49.0862 0.0846314
\(581\) 358.844i 0.617632i
\(582\) −138.919 + 577.104i −0.238693 + 0.991588i
\(583\) 768.911 1.31889
\(584\) 112.512i 0.192658i
\(585\) 168.261 329.245i 0.287625 0.562813i
\(586\) 479.305 0.817926
\(587\) 1007.65i 1.71662i −0.513136 0.858308i \(-0.671516\pi\)
0.513136 0.858308i \(-0.328484\pi\)
\(588\) 138.435 + 33.3238i 0.235434 + 0.0566732i
\(589\) −565.078 −0.959385
\(590\) 172.768i 0.292827i
\(591\) −29.2820 + 121.644i −0.0495466 + 0.205828i
\(592\) 171.490 0.289678
\(593\) 181.266i 0.305677i 0.988251 + 0.152838i \(0.0488414\pi\)
−0.988251 + 0.152838i \(0.951159\pi\)
\(594\) −326.039 279.487i −0.548887 0.470517i
\(595\) 15.2667 0.0256583
\(596\) 166.201i 0.278861i
\(597\) 22.4371 + 5.40101i 0.0375831 + 0.00904693i
\(598\) −124.612 −0.208381
\(599\) 75.2652i 0.125651i −0.998025 0.0628257i \(-0.979989\pi\)
0.998025 0.0628257i \(-0.0200112\pi\)
\(600\) −9.92918 + 41.2482i −0.0165486 + 0.0687469i
\(601\) −206.231 −0.343146 −0.171573 0.985171i \(-0.554885\pi\)
−0.171573 + 0.985171i \(0.554885\pi\)
\(602\) 129.006i 0.214295i
\(603\) 439.541 + 224.627i 0.728924 + 0.372516i
\(604\) −340.054 −0.563003
\(605\) 12.2637i 0.0202705i
\(606\) 763.104 + 183.693i 1.25925 + 0.303124i
\(607\) 649.464 1.06996 0.534978 0.844866i \(-0.320320\pi\)
0.534978 + 0.844866i \(0.320320\pi\)
\(608\) 74.9486i 0.123271i
\(609\) 65.7210 273.021i 0.107916 0.448310i
\(610\) −108.125 −0.177255
\(611\) 1210.20i 1.98069i
\(612\) −6.55763 + 12.8317i −0.0107151 + 0.0209668i
\(613\) 230.058 0.375299 0.187650 0.982236i \(-0.439913\pi\)
0.187650 + 0.982236i \(0.439913\pi\)
\(614\) 274.410i 0.446921i
\(615\) −386.622 93.0668i −0.628653 0.151328i
\(616\) 271.285 0.440397
\(617\) 486.305i 0.788176i 0.919073 + 0.394088i \(0.128940\pi\)
−0.919073 + 0.394088i \(0.871060\pi\)
\(618\) 163.002 677.147i 0.263757 1.09571i
\(619\) −176.546 −0.285211 −0.142605 0.989780i \(-0.545548\pi\)
−0.142605 + 0.989780i \(0.545548\pi\)
\(620\) 190.737i 0.307640i
\(621\) −84.2738 + 98.3104i −0.135707 + 0.158310i
\(622\) 205.829 0.330915
\(623\) 657.870i 1.05597i
\(624\) −214.353 51.5986i −0.343514 0.0826900i
\(625\) 25.0000 0.0400000
\(626\) 131.999i 0.210861i
\(627\) 104.618 434.607i 0.166855 0.693153i
\(628\) −297.934 −0.474417
\(629\) 34.3223i 0.0545665i
\(630\) 216.131 + 110.454i 0.343065 + 0.175323i
\(631\) −594.149 −0.941599 −0.470800 0.882240i \(-0.656035\pi\)
−0.470800 + 0.882240i \(0.656035\pi\)
\(632\) 40.4868i 0.0640613i
\(633\) −1015.97 244.563i −1.60501 0.386355i
\(634\) 399.070 0.629448
\(635\) 450.674i 0.709724i
\(636\) 96.0033 398.820i 0.150949 0.627076i
\(637\) 436.019 0.684488
\(638\) 174.573i 0.273626i
\(639\) −132.426 + 259.126i −0.207240 + 0.405519i
\(640\) 25.2982 0.0395285
\(641\) 457.503i 0.713734i 0.934155 + 0.356867i \(0.116155\pi\)
−0.934155 + 0.356867i \(0.883845\pi\)
\(642\) 437.282 + 105.262i 0.681125 + 0.163959i
\(643\) −713.769 −1.11006 −0.555030 0.831830i \(-0.687293\pi\)
−0.555030 + 0.831830i \(0.687293\pi\)
\(644\) 81.8004i 0.127019i
\(645\) −16.7925 + 69.7600i −0.0260349 + 0.108155i
\(646\) −15.0004 −0.0232204
\(647\) 784.509i 1.21253i −0.795261 0.606267i \(-0.792666\pi\)
0.795261 0.606267i \(-0.207334\pi\)
\(648\) −185.673 + 134.215i −0.286532 + 0.207121i
\(649\) 614.444 0.946755
\(650\) 129.917i 0.199872i
\(651\) −1060.89 255.376i −1.62963 0.392282i
\(652\) 467.743 0.717398
\(653\) 400.746i 0.613700i −0.951758 0.306850i \(-0.900725\pi\)
0.951758 0.306850i \(-0.0992750\pi\)
\(654\) −58.3847 + 242.544i −0.0892732 + 0.370862i
\(655\) 308.164 0.470479
\(656\) 237.122i 0.361466i
\(657\) −318.795 162.920i −0.485228 0.247975i
\(658\) 794.427 1.20734
\(659\) 1057.28i 1.60437i 0.597073 + 0.802187i \(0.296330\pi\)
−0.597073 + 0.802187i \(0.703670\pi\)
\(660\) 146.698 + 35.3128i 0.222269 + 0.0535042i
\(661\) −266.071 −0.402528 −0.201264 0.979537i \(-0.564505\pi\)
−0.201264 + 0.979537i \(0.564505\pi\)
\(662\) 543.576i 0.821111i
\(663\) −10.3271 + 42.9010i −0.0155763 + 0.0647075i
\(664\) 119.012 0.179234
\(665\) 252.659i 0.379938i
\(666\) 248.320 485.901i 0.372852 0.729582i
\(667\) −52.6391 −0.0789192
\(668\) 281.681i 0.421678i
\(669\) −1199.43 288.725i −1.79287 0.431577i
\(670\) −173.438 −0.258863
\(671\) 384.544i 0.573091i
\(672\) 33.8715 140.710i 0.0504041 0.209390i
\(673\) −10.7379 −0.0159552 −0.00797761 0.999968i \(-0.502539\pi\)
−0.00797761 + 0.999968i \(0.502539\pi\)
\(674\) 378.391i 0.561410i
\(675\) 102.496 + 87.8615i 0.151845 + 0.130165i
\(676\) −337.132 −0.498716
\(677\) 245.177i 0.362152i 0.983469 + 0.181076i \(0.0579581\pi\)
−0.983469 + 0.181076i \(0.942042\pi\)
\(678\) 65.3898 + 15.7405i 0.0964451 + 0.0232161i
\(679\) −1193.19 −1.75728
\(680\) 5.06324i 0.00744595i
\(681\) −68.5990 + 284.976i −0.100733 + 0.418467i
\(682\) −678.349 −0.994647
\(683\) 965.369i 1.41342i 0.707501 + 0.706712i \(0.249822\pi\)
−0.707501 + 0.706712i \(0.750178\pi\)
\(684\) −212.361 108.527i −0.310469 0.158665i
\(685\) −27.9832 −0.0408514
\(686\) 304.758i 0.444253i
\(687\) −256.803 61.8172i −0.373804 0.0899814i
\(688\) 42.7850 0.0621875
\(689\) 1256.14i 1.82313i
\(690\) 10.6479 44.2337i 0.0154317 0.0641069i
\(691\) −143.140 −0.207148 −0.103574 0.994622i \(-0.533028\pi\)
−0.103574 + 0.994622i \(0.533028\pi\)
\(692\) 225.154i 0.325368i
\(693\) 392.824 768.662i 0.566846 1.10918i
\(694\) 732.668 1.05572
\(695\) 606.270i 0.872332i
\(696\) −90.5480 21.7966i −0.130098 0.0313169i
\(697\) 47.4581 0.0680891
\(698\) 530.504i 0.760034i
\(699\) −79.9413 + 332.095i −0.114365 + 0.475100i
\(700\) −85.2828 −0.121833
\(701\) 880.642i 1.25627i 0.778106 + 0.628133i \(0.216181\pi\)
−0.778106 + 0.628133i \(0.783819\pi\)
\(702\) −456.586 + 532.635i −0.650408 + 0.758739i
\(703\) 568.023 0.807999
\(704\) 89.9723i 0.127801i
\(705\) 429.588 + 103.410i 0.609345 + 0.146680i
\(706\) 143.760 0.203626
\(707\) 1577.76i 2.23163i
\(708\) 76.7171 318.701i 0.108357 0.450143i
\(709\) 384.075 0.541713 0.270857 0.962620i \(-0.412693\pi\)
0.270857 + 0.962620i \(0.412693\pi\)
\(710\) 102.248i 0.144012i
\(711\) 114.716 + 58.6255i 0.161344 + 0.0824549i
\(712\) 218.184 0.306439
\(713\) 204.543i 0.286876i
\(714\) −28.1621 6.77913i −0.0394427 0.00949458i
\(715\) 462.044 0.646215
\(716\) 530.913i 0.741499i
\(717\) 62.0952 257.958i 0.0866042 0.359774i
\(718\) 209.183 0.291342
\(719\) 366.200i 0.509318i 0.967031 + 0.254659i \(0.0819632\pi\)
−0.967031 + 0.254659i \(0.918037\pi\)
\(720\) 36.6322 71.6804i 0.0508781 0.0995561i
\(721\) 1400.04 1.94180
\(722\) 262.280i 0.363268i
\(723\) 868.835 + 209.144i 1.20171 + 0.289273i
\(724\) 362.848 0.501172
\(725\) 54.8800i 0.0756966i
\(726\) 5.44563 22.6224i 0.00750087 0.0311604i
\(727\) 46.5086 0.0639733 0.0319867 0.999488i \(-0.489817\pi\)
0.0319867 + 0.999488i \(0.489817\pi\)
\(728\) 443.186i 0.608772i
\(729\) 111.429 + 720.434i 0.152851 + 0.988249i
\(730\) 125.793 0.172319
\(731\) 8.56309i 0.0117142i
\(732\) 199.456 + 48.0126i 0.272481 + 0.0655910i
\(733\) −1189.43 −1.62269 −0.811344 0.584569i \(-0.801264\pi\)
−0.811344 + 0.584569i \(0.801264\pi\)
\(734\) 563.933i 0.768301i
\(735\) −37.2572 + 154.775i −0.0506900 + 0.210578i
\(736\) −27.1293 −0.0368605
\(737\) 616.826i 0.836942i
\(738\) 671.865 + 343.356i 0.910386 + 0.465252i
\(739\) 91.0727 0.123238 0.0616189 0.998100i \(-0.480374\pi\)
0.0616189 + 0.998100i \(0.480374\pi\)
\(740\) 191.731i 0.259096i
\(741\) −709.998 170.910i −0.958163 0.230647i
\(742\) 824.582 1.11130
\(743\) 1075.51i 1.44753i 0.690048 + 0.723764i \(0.257589\pi\)
−0.690048 + 0.723764i \(0.742411\pi\)
\(744\) −84.6961 + 351.848i −0.113839 + 0.472913i
\(745\) 185.818 0.249420
\(746\) 494.659i 0.663081i
\(747\) 172.331 337.210i 0.230697 0.451419i
\(748\) −18.0073 −0.0240739
\(749\) 904.105i 1.20708i
\(750\) −46.1169 11.1012i −0.0614891 0.0148016i
\(751\) 848.304 1.12957 0.564783 0.825240i \(-0.308960\pi\)
0.564783 + 0.825240i \(0.308960\pi\)
\(752\) 263.474i 0.350364i
\(753\) 177.340 736.712i 0.235511 0.978369i
\(754\) −285.193 −0.378240
\(755\) 380.192i 0.503566i
\(756\) −349.645 299.723i −0.462493 0.396459i
\(757\) 244.126 0.322491 0.161245 0.986914i \(-0.448449\pi\)
0.161245 + 0.986914i \(0.448449\pi\)
\(758\) 804.318i 1.06111i
\(759\) −157.316 37.8688i −0.207267 0.0498930i
\(760\) 83.7951 0.110257
\(761\) 926.253i 1.21715i −0.793495 0.608576i \(-0.791741\pi\)
0.793495 0.608576i \(-0.208259\pi\)
\(762\) −200.120 + 831.348i −0.262625 + 1.09101i
\(763\) −501.472 −0.657237
\(764\) 385.309i 0.504331i
\(765\) −14.3463 7.33165i −0.0187533 0.00958386i
\(766\) −164.547 −0.214813
\(767\) 1003.79i 1.30872i
\(768\) −46.6670 11.2336i −0.0607643 0.0146271i
\(769\) 39.9471 0.0519468 0.0259734 0.999663i \(-0.491731\pi\)
0.0259734 + 0.999663i \(0.491731\pi\)
\(770\) 303.305i 0.393903i
\(771\) 76.2284 316.671i 0.0988696 0.410728i
\(772\) −409.112 −0.529938
\(773\) 697.995i 0.902969i 0.892279 + 0.451485i \(0.149105\pi\)
−0.892279 + 0.451485i \(0.850895\pi\)
\(774\) 61.9534 121.228i 0.0800431 0.156625i
\(775\) 213.250 0.275162
\(776\) 395.726i 0.509956i
\(777\) 1066.42 + 256.707i 1.37249 + 0.330382i
\(778\) −1016.65 −1.30675
\(779\) 785.416i 1.00824i
\(780\) 57.6890 239.654i 0.0739602 0.307248i
\(781\) −363.643 −0.465612
\(782\) 5.42972i 0.00694338i
\(783\) −192.874 + 224.999i −0.246327 + 0.287355i
\(784\) 94.9262 0.121079
\(785\) 333.100i 0.424331i
\(786\) −568.462 136.839i