Properties

Label 690.3.g.a.461.17
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 461.17
Character \(\chi\) \(=\) 690.461
Dual form 690.3.g.a.461.18

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421i q^{2} +(-1.05752 + 2.80743i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(3.97030 + 1.49556i) q^{6} +11.9645 q^{7} +2.82843i q^{8} +(-6.76329 - 5.93784i) q^{9} +O(q^{10})\) \(q-1.41421i q^{2} +(-1.05752 + 2.80743i) q^{3} -2.00000 q^{4} +2.23607i q^{5} +(3.97030 + 1.49556i) q^{6} +11.9645 q^{7} +2.82843i q^{8} +(-6.76329 - 5.93784i) q^{9} +3.16228 q^{10} -12.8979i q^{11} +(2.11505 - 5.61485i) q^{12} +20.2679 q^{13} -16.9204i q^{14} +(-6.27760 - 2.36470i) q^{15} +4.00000 q^{16} -2.71211i q^{17} +(-8.39738 + 9.56473i) q^{18} -31.6020 q^{19} -4.47214i q^{20} +(-12.6528 + 33.5896i) q^{21} -18.2404 q^{22} +4.79583i q^{23} +(-7.94060 - 2.99113i) q^{24} -5.00000 q^{25} -28.6632i q^{26} +(23.8224 - 12.7080i) q^{27} -23.9291 q^{28} -32.1682i q^{29} +(-3.34418 + 8.87786i) q^{30} +30.5608 q^{31} -5.65685i q^{32} +(36.2099 + 13.6399i) q^{33} -3.83551 q^{34} +26.7535i q^{35} +(13.5266 + 11.8757i) q^{36} +26.7311 q^{37} +44.6920i q^{38} +(-21.4338 + 56.9008i) q^{39} -6.32456 q^{40} -17.8221i q^{41} +(47.5028 + 17.8937i) q^{42} +63.9371 q^{43} +25.7958i q^{44} +(13.2774 - 15.1232i) q^{45} +6.78233 q^{46} -2.85097i q^{47} +(-4.23010 + 11.2297i) q^{48} +94.1502 q^{49} +7.07107i q^{50} +(7.61406 + 2.86812i) q^{51} -40.5359 q^{52} +61.3108i q^{53} +(-17.9719 - 33.6899i) q^{54} +28.8406 q^{55} +33.8408i q^{56} +(33.4199 - 88.7203i) q^{57} -45.4927 q^{58} -63.3148i q^{59} +(12.5552 + 4.72939i) q^{60} -48.8150 q^{61} -43.2195i q^{62} +(-80.9196 - 71.0435i) q^{63} -8.00000 q^{64} +45.3205i q^{65} +(19.2897 - 51.2086i) q^{66} +84.5799 q^{67} +5.42423i q^{68} +(-13.4639 - 5.07171i) q^{69} +37.8352 q^{70} +56.5778i q^{71} +(16.7948 - 19.1295i) q^{72} +79.0816 q^{73} -37.8034i q^{74} +(5.28762 - 14.0371i) q^{75} +63.2040 q^{76} -154.318i q^{77} +(80.4698 + 30.3120i) q^{78} +74.6226 q^{79} +8.94427i q^{80} +(10.4841 + 80.3186i) q^{81} -25.2042 q^{82} +102.897i q^{83} +(25.3056 - 67.1791i) q^{84} +6.06447 q^{85} -90.4207i q^{86} +(90.3099 + 34.0186i) q^{87} +36.4808 q^{88} +127.899i q^{89} +(-21.3874 - 18.7771i) q^{90} +242.497 q^{91} -9.59166i q^{92} +(-32.3188 + 85.7973i) q^{93} -4.03188 q^{94} -70.6643i q^{95} +(15.8812 + 5.98226i) q^{96} -148.644 q^{97} -133.149i q^{98} +(-76.5858 + 87.2323i) 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
\(3\) −1.05752 + 2.80743i −0.352508 + 0.935809i
\(4\) −2.00000 −0.500000
\(5\) 2.23607i 0.447214i
\(6\) 3.97030 + 1.49556i 0.661717 + 0.249261i
\(7\) 11.9645 1.70922 0.854610 0.519270i \(-0.173796\pi\)
0.854610 + 0.519270i \(0.173796\pi\)
\(8\) 2.82843i 0.353553i
\(9\) −6.76329 5.93784i −0.751476 0.659760i
\(10\) 3.16228 0.316228
\(11\) 12.8979i 1.17254i −0.810117 0.586269i \(-0.800596\pi\)
0.810117 0.586269i \(-0.199404\pi\)
\(12\) 2.11505 5.61485i 0.176254 0.467904i
\(13\) 20.2679 1.55907 0.779536 0.626357i \(-0.215455\pi\)
0.779536 + 0.626357i \(0.215455\pi\)
\(14\) 16.9204i 1.20860i
\(15\) −6.27760 2.36470i −0.418506 0.157646i
\(16\) 4.00000 0.250000
\(17\) 2.71211i 0.159536i −0.996813 0.0797680i \(-0.974582\pi\)
0.996813 0.0797680i \(-0.0254180\pi\)
\(18\) −8.39738 + 9.56473i −0.466521 + 0.531374i
\(19\) −31.6020 −1.66326 −0.831632 0.555327i \(-0.812593\pi\)
−0.831632 + 0.555327i \(0.812593\pi\)
\(20\) 4.47214i 0.223607i
\(21\) −12.6528 + 33.5896i −0.602514 + 1.59950i
\(22\) −18.2404 −0.829109
\(23\) 4.79583i 0.208514i
\(24\) −7.94060 2.99113i −0.330858 0.124630i
\(25\) −5.00000 −0.200000
\(26\) 28.6632i 1.10243i
\(27\) 23.8224 12.7080i 0.882311 0.470667i
\(28\) −23.9291 −0.854610
\(29\) 32.1682i 1.10925i −0.832101 0.554624i \(-0.812862\pi\)
0.832101 0.554624i \(-0.187138\pi\)
\(30\) −3.34418 + 8.87786i −0.111473 + 0.295929i
\(31\) 30.5608 0.985833 0.492917 0.870077i \(-0.335931\pi\)
0.492917 + 0.870077i \(0.335931\pi\)
\(32\) 5.65685i 0.176777i
\(33\) 36.2099 + 13.6399i 1.09727 + 0.413329i
\(34\) −3.83551 −0.112809
\(35\) 26.7535i 0.764386i
\(36\) 13.5266 + 11.8757i 0.375738 + 0.329880i
\(37\) 26.7311 0.722461 0.361230 0.932477i \(-0.382357\pi\)
0.361230 + 0.932477i \(0.382357\pi\)
\(38\) 44.6920i 1.17611i
\(39\) −21.4338 + 56.9008i −0.549586 + 1.45899i
\(40\) −6.32456 −0.158114
\(41\) 17.8221i 0.434685i −0.976095 0.217343i \(-0.930261\pi\)
0.976095 0.217343i \(-0.0697389\pi\)
\(42\) 47.5028 + 17.8937i 1.13102 + 0.426042i
\(43\) 63.9371 1.48691 0.743454 0.668787i \(-0.233186\pi\)
0.743454 + 0.668787i \(0.233186\pi\)
\(44\) 25.7958i 0.586269i
\(45\) 13.2774 15.1232i 0.295054 0.336070i
\(46\) 6.78233 0.147442
\(47\) 2.85097i 0.0606589i −0.999540 0.0303294i \(-0.990344\pi\)
0.999540 0.0303294i \(-0.00965564\pi\)
\(48\) −4.23010 + 11.2297i −0.0881270 + 0.233952i
\(49\) 94.1502 1.92143
\(50\) 7.07107i 0.141421i
\(51\) 7.61406 + 2.86812i 0.149295 + 0.0562377i
\(52\) −40.5359 −0.779536
\(53\) 61.3108i 1.15681i 0.815750 + 0.578404i \(0.196324\pi\)
−0.815750 + 0.578404i \(0.803676\pi\)
\(54\) −17.9719 33.6899i −0.332812 0.623888i
\(55\) 28.8406 0.524375
\(56\) 33.8408i 0.604301i
\(57\) 33.4199 88.7203i 0.586314 1.55650i
\(58\) −45.4927 −0.784357
\(59\) 63.3148i 1.07313i −0.843858 0.536566i \(-0.819721\pi\)
0.843858 0.536566i \(-0.180279\pi\)
\(60\) 12.5552 + 4.72939i 0.209253 + 0.0788232i
\(61\) −48.8150 −0.800247 −0.400123 0.916461i \(-0.631033\pi\)
−0.400123 + 0.916461i \(0.631033\pi\)
\(62\) 43.2195i 0.697089i
\(63\) −80.9196 71.0435i −1.28444 1.12768i
\(64\) −8.00000 −0.125000
\(65\) 45.3205i 0.697239i
\(66\) 19.2897 51.2086i 0.292268 0.775888i
\(67\) 84.5799 1.26239 0.631194 0.775625i \(-0.282565\pi\)
0.631194 + 0.775625i \(0.282565\pi\)
\(68\) 5.42423i 0.0797680i
\(69\) −13.4639 5.07171i −0.195130 0.0735030i
\(70\) 37.8352 0.540503
\(71\) 56.5778i 0.796871i 0.917196 + 0.398435i \(0.130447\pi\)
−0.917196 + 0.398435i \(0.869553\pi\)
\(72\) 16.7948 19.1295i 0.233260 0.265687i
\(73\) 79.0816 1.08331 0.541655 0.840601i \(-0.317798\pi\)
0.541655 + 0.840601i \(0.317798\pi\)
\(74\) 37.8034i 0.510857i
\(75\) 5.28762 14.0371i 0.0705016 0.187162i
\(76\) 63.2040 0.831632
\(77\) 154.318i 2.00412i
\(78\) 80.4698 + 30.3120i 1.03166 + 0.388616i
\(79\) 74.6226 0.944590 0.472295 0.881441i \(-0.343426\pi\)
0.472295 + 0.881441i \(0.343426\pi\)
\(80\) 8.94427i 0.111803i
\(81\) 10.4841 + 80.3186i 0.129433 + 0.991588i
\(82\) −25.2042 −0.307369
\(83\) 102.897i 1.23972i 0.784711 + 0.619862i \(0.212811\pi\)
−0.784711 + 0.619862i \(0.787189\pi\)
\(84\) 25.3056 67.1791i 0.301257 0.799752i
\(85\) 6.06447 0.0713467
\(86\) 90.4207i 1.05140i
\(87\) 90.3099 + 34.0186i 1.03804 + 0.391019i
\(88\) 36.4808 0.414555
\(89\) 127.899i 1.43707i 0.695489 + 0.718536i \(0.255188\pi\)
−0.695489 + 0.718536i \(0.744812\pi\)
\(90\) −21.3874 18.7771i −0.237638 0.208634i
\(91\) 242.497 2.66480
\(92\) 9.59166i 0.104257i
\(93\) −32.3188 + 85.7973i −0.347514 + 0.922551i
\(94\) −4.03188 −0.0428923
\(95\) 70.6643i 0.743834i
\(96\) 15.8812 + 5.98226i 0.165429 + 0.0623152i
\(97\) −148.644 −1.53241 −0.766204 0.642597i \(-0.777857\pi\)
−0.766204 + 0.642597i \(0.777857\pi\)
\(98\) 133.149i 1.35866i
\(99\) −76.5858 + 87.2323i −0.773594 + 0.881134i
\(100\) 10.0000 0.100000
\(101\) 80.7538i 0.799542i −0.916615 0.399771i \(-0.869090\pi\)
0.916615 0.399771i \(-0.130910\pi\)
\(102\) 4.05614 10.7679i 0.0397661 0.105568i
\(103\) −136.026 −1.32064 −0.660319 0.750985i \(-0.729579\pi\)
−0.660319 + 0.750985i \(0.729579\pi\)
\(104\) 57.3264i 0.551215i
\(105\) −75.1085 28.2925i −0.715320 0.269452i
\(106\) 86.7066 0.817987
\(107\) 125.903i 1.17666i −0.808621 0.588330i \(-0.799786\pi\)
0.808621 0.588330i \(-0.200214\pi\)
\(108\) −47.6448 + 25.4160i −0.441155 + 0.235334i
\(109\) 89.7028 0.822961 0.411481 0.911419i \(-0.365012\pi\)
0.411481 + 0.911419i \(0.365012\pi\)
\(110\) 40.7868i 0.370789i
\(111\) −28.2687 + 75.0455i −0.254673 + 0.676085i
\(112\) 47.8582 0.427305
\(113\) 74.8993i 0.662825i −0.943486 0.331413i \(-0.892475\pi\)
0.943486 0.331413i \(-0.107525\pi\)
\(114\) −125.469 47.2629i −1.10061 0.414586i
\(115\) −10.7238 −0.0932505
\(116\) 64.3364i 0.554624i
\(117\) −137.078 120.348i −1.17161 1.02861i
\(118\) −89.5407 −0.758820
\(119\) 32.4492i 0.272682i
\(120\) 6.68837 17.7557i 0.0557364 0.147964i
\(121\) −45.3562 −0.374844
\(122\) 69.0349i 0.565860i
\(123\) 50.0342 + 18.8473i 0.406782 + 0.153230i
\(124\) −61.1217 −0.492917
\(125\) 11.1803i 0.0894427i
\(126\) −100.471 + 114.438i −0.797387 + 0.908235i
\(127\) 12.5296 0.0986580 0.0493290 0.998783i \(-0.484292\pi\)
0.0493290 + 0.998783i \(0.484292\pi\)
\(128\) 11.3137i 0.0883883i
\(129\) −67.6150 + 179.499i −0.524147 + 1.39146i
\(130\) 64.0929 0.493022
\(131\) 173.928i 1.32770i 0.747867 + 0.663849i \(0.231078\pi\)
−0.747867 + 0.663849i \(0.768922\pi\)
\(132\) −72.4199 27.2797i −0.548636 0.206664i
\(133\) −378.104 −2.84288
\(134\) 119.614i 0.892643i
\(135\) 28.4160 + 53.2685i 0.210489 + 0.394581i
\(136\) 7.67101 0.0564045
\(137\) 120.287i 0.878006i 0.898486 + 0.439003i \(0.144668\pi\)
−0.898486 + 0.439003i \(0.855332\pi\)
\(138\) −7.17248 + 19.0409i −0.0519745 + 0.137977i
\(139\) 75.7495 0.544960 0.272480 0.962161i \(-0.412156\pi\)
0.272480 + 0.962161i \(0.412156\pi\)
\(140\) 53.5070i 0.382193i
\(141\) 8.00388 + 3.01497i 0.0567651 + 0.0213827i
\(142\) 80.0131 0.563473
\(143\) 261.414i 1.82807i
\(144\) −27.0531 23.7514i −0.187869 0.164940i
\(145\) 71.9303 0.496071
\(146\) 111.838i 0.766016i
\(147\) −99.5661 + 264.320i −0.677320 + 1.79809i
\(148\) −53.4621 −0.361230
\(149\) 145.429i 0.976032i −0.872835 0.488016i \(-0.837721\pi\)
0.872835 0.488016i \(-0.162279\pi\)
\(150\) −19.8515 7.47782i −0.132343 0.0498522i
\(151\) −88.0585 −0.583169 −0.291584 0.956545i \(-0.594182\pi\)
−0.291584 + 0.956545i \(0.594182\pi\)
\(152\) 89.3840i 0.588053i
\(153\) −16.1041 + 18.3428i −0.105256 + 0.119888i
\(154\) −218.238 −1.41713
\(155\) 68.3361i 0.440878i
\(156\) 42.8677 113.802i 0.274793 0.729497i
\(157\) 221.115 1.40837 0.704187 0.710014i \(-0.251312\pi\)
0.704187 + 0.710014i \(0.251312\pi\)
\(158\) 105.532i 0.667926i
\(159\) −172.126 64.8377i −1.08255 0.407784i
\(160\) 12.6491 0.0790569
\(161\) 57.3799i 0.356397i
\(162\) 113.588 14.8267i 0.701159 0.0915230i
\(163\) −101.135 −0.620463 −0.310232 0.950661i \(-0.600407\pi\)
−0.310232 + 0.950661i \(0.600407\pi\)
\(164\) 35.6442i 0.217343i
\(165\) −30.4996 + 80.9679i −0.184846 + 0.490715i
\(166\) 145.518 0.876617
\(167\) 113.469i 0.679456i −0.940524 0.339728i \(-0.889665\pi\)
0.940524 0.339728i \(-0.110335\pi\)
\(168\) −95.0056 35.7875i −0.565510 0.213021i
\(169\) 241.790 1.43071
\(170\) 8.57645i 0.0504497i
\(171\) 213.733 + 187.648i 1.24990 + 1.09736i
\(172\) −127.874 −0.743454
\(173\) 269.411i 1.55729i 0.627467 + 0.778643i \(0.284092\pi\)
−0.627467 + 0.778643i \(0.715908\pi\)
\(174\) 48.1096 127.717i 0.276492 0.734008i
\(175\) −59.8227 −0.341844
\(176\) 51.5917i 0.293134i
\(177\) 177.752 + 66.9570i 1.00425 + 0.378288i
\(178\) 180.877 1.01616
\(179\) 179.383i 1.00214i −0.865407 0.501069i \(-0.832940\pi\)
0.865407 0.501069i \(-0.167060\pi\)
\(180\) −26.5548 + 30.2463i −0.147527 + 0.168035i
\(181\) −221.212 −1.22217 −0.611083 0.791567i \(-0.709266\pi\)
−0.611083 + 0.791567i \(0.709266\pi\)
\(182\) 342.942i 1.88430i
\(183\) 51.6231 137.045i 0.282093 0.748878i
\(184\) −13.5647 −0.0737210
\(185\) 59.7724i 0.323094i
\(186\) 121.336 + 45.7057i 0.652342 + 0.245730i
\(187\) −34.9806 −0.187062
\(188\) 5.70193i 0.0303294i
\(189\) 285.024 152.046i 1.50806 0.804474i
\(190\) −99.9343 −0.525970
\(191\) 42.3868i 0.221920i −0.993825 0.110960i \(-0.964607\pi\)
0.993825 0.110960i \(-0.0353926\pi\)
\(192\) 8.46019 22.4594i 0.0440635 0.116976i
\(193\) −56.1826 −0.291102 −0.145551 0.989351i \(-0.546495\pi\)
−0.145551 + 0.989351i \(0.546495\pi\)
\(194\) 210.214i 1.08358i
\(195\) −127.234 47.9275i −0.652482 0.245782i
\(196\) −188.300 −0.960716
\(197\) 114.289i 0.580149i 0.957004 + 0.290075i \(0.0936801\pi\)
−0.957004 + 0.290075i \(0.906320\pi\)
\(198\) 123.365 + 108.309i 0.623056 + 0.547013i
\(199\) −185.324 −0.931275 −0.465638 0.884975i \(-0.654175\pi\)
−0.465638 + 0.884975i \(0.654175\pi\)
\(200\) 14.1421i 0.0707107i
\(201\) −89.4453 + 237.452i −0.445002 + 1.18135i
\(202\) −114.203 −0.565362
\(203\) 384.878i 1.89595i
\(204\) −15.2281 5.73625i −0.0746476 0.0281189i
\(205\) 39.8514 0.194397
\(206\) 192.369i 0.933832i
\(207\) 28.4769 32.4356i 0.137570 0.156694i
\(208\) 81.0718 0.389768
\(209\) 407.600i 1.95024i
\(210\) −40.0116 + 106.220i −0.190532 + 0.505807i
\(211\) 196.309 0.930374 0.465187 0.885212i \(-0.345987\pi\)
0.465187 + 0.885212i \(0.345987\pi\)
\(212\) 122.622i 0.578404i
\(213\) −158.838 59.8324i −0.745719 0.280903i
\(214\) −178.053 −0.832025
\(215\) 142.968i 0.664966i
\(216\) 35.9437 + 67.3799i 0.166406 + 0.311944i
\(217\) 365.646 1.68501
\(218\) 126.859i 0.581921i
\(219\) −83.6307 + 222.016i −0.381875 + 1.01377i
\(220\) −57.6812 −0.262187
\(221\) 54.9690i 0.248728i
\(222\) 106.130 + 39.9780i 0.478064 + 0.180081i
\(223\) −128.398 −0.575774 −0.287887 0.957664i \(-0.592953\pi\)
−0.287887 + 0.957664i \(0.592953\pi\)
\(224\) 67.6817i 0.302150i
\(225\) 33.8164 + 29.6892i 0.150295 + 0.131952i
\(226\) −105.924 −0.468688
\(227\) 272.176i 1.19901i −0.800370 0.599507i \(-0.795363\pi\)
0.800370 0.599507i \(-0.204637\pi\)
\(228\) −66.8398 + 177.441i −0.293157 + 0.778248i
\(229\) 107.101 0.467692 0.233846 0.972274i \(-0.424869\pi\)
0.233846 + 0.972274i \(0.424869\pi\)
\(230\) 15.1658i 0.0659380i
\(231\) 433.235 + 163.195i 1.87548 + 0.706470i
\(232\) 90.9854 0.392179
\(233\) 80.1887i 0.344158i 0.985083 + 0.172079i \(0.0550484\pi\)
−0.985083 + 0.172079i \(0.944952\pi\)
\(234\) −170.198 + 193.857i −0.727340 + 0.828451i
\(235\) 6.37496 0.0271275
\(236\) 126.630i 0.536566i
\(237\) −78.9152 + 209.497i −0.332976 + 0.883956i
\(238\) −45.8901 −0.192815
\(239\) 171.517i 0.717643i −0.933406 0.358821i \(-0.883179\pi\)
0.933406 0.358821i \(-0.116821\pi\)
\(240\) −25.1104 9.45878i −0.104627 0.0394116i
\(241\) −429.769 −1.78327 −0.891637 0.452751i \(-0.850443\pi\)
−0.891637 + 0.452751i \(0.850443\pi\)
\(242\) 64.1433i 0.265055i
\(243\) −236.576 55.5056i −0.973563 0.228418i
\(244\) 97.6301 0.400123
\(245\) 210.526i 0.859291i
\(246\) 26.6541 70.7590i 0.108350 0.287638i
\(247\) −640.508 −2.59315
\(248\) 86.4391i 0.348545i
\(249\) −288.876 108.816i −1.16014 0.437013i
\(250\) −15.8114 −0.0632456
\(251\) 475.569i 1.89470i −0.320206 0.947348i \(-0.603752\pi\)
0.320206 0.947348i \(-0.396248\pi\)
\(252\) 161.839 + 142.087i 0.642219 + 0.563838i
\(253\) 61.8562 0.244491
\(254\) 17.7195i 0.0697618i
\(255\) −6.41332 + 17.0255i −0.0251503 + 0.0667669i
\(256\) 16.0000 0.0625000
\(257\) 321.762i 1.25199i 0.779827 + 0.625996i \(0.215307\pi\)
−0.779827 + 0.625996i \(0.784693\pi\)
\(258\) 253.849 + 95.6220i 0.983912 + 0.370628i
\(259\) 319.825 1.23484
\(260\) 90.6410i 0.348619i
\(261\) −191.010 + 217.563i −0.731838 + 0.833574i
\(262\) 245.972 0.938824
\(263\) 360.215i 1.36964i −0.728713 0.684819i \(-0.759881\pi\)
0.728713 0.684819i \(-0.240119\pi\)
\(264\) −38.5793 + 102.417i −0.146134 + 0.387944i
\(265\) −137.095 −0.517340
\(266\) 534.719i 2.01022i
\(267\) −359.068 135.257i −1.34483 0.506580i
\(268\) −169.160 −0.631194
\(269\) 23.2136i 0.0862960i 0.999069 + 0.0431480i \(0.0137387\pi\)
−0.999069 + 0.0431480i \(0.986261\pi\)
\(270\) 75.3330 40.1863i 0.279011 0.148838i
\(271\) −339.304 −1.25204 −0.626022 0.779806i \(-0.715318\pi\)
−0.626022 + 0.779806i \(0.715318\pi\)
\(272\) 10.8485i 0.0398840i
\(273\) −256.446 + 680.791i −0.939363 + 2.49374i
\(274\) 170.111 0.620844
\(275\) 64.4896i 0.234508i
\(276\) 26.9279 + 10.1434i 0.0975648 + 0.0367515i
\(277\) −330.334 −1.19254 −0.596271 0.802784i \(-0.703351\pi\)
−0.596271 + 0.802784i \(0.703351\pi\)
\(278\) 107.126i 0.385345i
\(279\) −206.692 181.465i −0.740830 0.650414i
\(280\) −75.6704 −0.270251
\(281\) 263.092i 0.936272i 0.883657 + 0.468136i \(0.155074\pi\)
−0.883657 + 0.468136i \(0.844926\pi\)
\(282\) 4.26381 11.3192i 0.0151199 0.0401390i
\(283\) 292.248 1.03268 0.516339 0.856384i \(-0.327294\pi\)
0.516339 + 0.856384i \(0.327294\pi\)
\(284\) 113.156i 0.398435i
\(285\) 198.385 + 74.7291i 0.696087 + 0.262208i
\(286\) −369.696 −1.29264
\(287\) 213.233i 0.742972i
\(288\) −33.5895 + 38.2589i −0.116630 + 0.132843i
\(289\) 281.644 0.974548
\(290\) 101.725i 0.350775i
\(291\) 157.194 417.306i 0.540186 1.43404i
\(292\) −158.163 −0.541655
\(293\) 541.886i 1.84944i 0.380650 + 0.924719i \(0.375700\pi\)
−0.380650 + 0.924719i \(0.624300\pi\)
\(294\) 373.805 + 140.808i 1.27144 + 0.478938i
\(295\) 141.576 0.479920
\(296\) 75.6068i 0.255428i
\(297\) −163.907 307.259i −0.551875 1.03454i
\(298\) −205.667 −0.690159
\(299\) 97.2017i 0.325089i
\(300\) −10.5752 + 28.0743i −0.0352508 + 0.0935809i
\(301\) 764.978 2.54145
\(302\) 124.534i 0.412363i
\(303\) 226.710 + 85.3990i 0.748219 + 0.281845i
\(304\) −126.408 −0.415816
\(305\) 109.154i 0.357881i
\(306\) 25.9406 + 22.7746i 0.0847733 + 0.0744269i
\(307\) −166.121 −0.541109 −0.270555 0.962705i \(-0.587207\pi\)
−0.270555 + 0.962705i \(0.587207\pi\)
\(308\) 308.635i 1.00206i
\(309\) 143.850 381.882i 0.465535 1.23586i
\(310\) 96.6418 0.311748
\(311\) 181.875i 0.584807i 0.956295 + 0.292403i \(0.0944550\pi\)
−0.956295 + 0.292403i \(0.905545\pi\)
\(312\) −160.940 60.6241i −0.515832 0.194308i
\(313\) 377.507 1.20609 0.603047 0.797706i \(-0.293953\pi\)
0.603047 + 0.797706i \(0.293953\pi\)
\(314\) 312.704i 0.995871i
\(315\) 158.858 180.942i 0.504312 0.574418i
\(316\) −149.245 −0.472295
\(317\) 153.129i 0.483058i −0.970394 0.241529i \(-0.922351\pi\)
0.970394 0.241529i \(-0.0776488\pi\)
\(318\) −91.6943 + 243.422i −0.288347 + 0.765480i
\(319\) −414.903 −1.30064
\(320\) 17.8885i 0.0559017i
\(321\) 353.462 + 133.145i 1.10113 + 0.414782i
\(322\) 81.1475 0.252011
\(323\) 85.7082i 0.265351i
\(324\) −20.9681 160.637i −0.0647165 0.495794i
\(325\) −101.340 −0.311815
\(326\) 143.027i 0.438734i
\(327\) −94.8628 + 251.834i −0.290100 + 0.770134i
\(328\) 50.4085 0.153684
\(329\) 34.1105i 0.103679i
\(330\) 114.506 + 43.1330i 0.346988 + 0.130706i
\(331\) −159.551 −0.482028 −0.241014 0.970522i \(-0.577480\pi\)
−0.241014 + 0.970522i \(0.577480\pi\)
\(332\) 205.794i 0.619862i
\(333\) −180.790 158.725i −0.542912 0.476651i
\(334\) −160.470 −0.480448
\(335\) 189.127i 0.564557i
\(336\) −50.6112 + 134.358i −0.150628 + 0.399876i
\(337\) −110.341 −0.327422 −0.163711 0.986508i \(-0.552347\pi\)
−0.163711 + 0.986508i \(0.552347\pi\)
\(338\) 341.942i 1.01166i
\(339\) 210.274 + 79.2078i 0.620278 + 0.233651i
\(340\) −12.1289 −0.0356733
\(341\) 394.171i 1.15593i
\(342\) 265.374 302.265i 0.775947 0.883815i
\(343\) 540.201 1.57493
\(344\) 180.841i 0.525702i
\(345\) 11.3407 30.1063i 0.0328715 0.0872646i
\(346\) 381.004 1.10117
\(347\) 345.104i 0.994537i −0.867597 0.497269i \(-0.834336\pi\)
0.867597 0.497269i \(-0.165664\pi\)
\(348\) −180.620 68.0373i −0.519022 0.195509i
\(349\) −414.181 −1.18677 −0.593383 0.804920i \(-0.702208\pi\)
−0.593383 + 0.804920i \(0.702208\pi\)
\(350\) 84.6021i 0.241720i
\(351\) 482.831 257.565i 1.37559 0.733805i
\(352\) −72.9616 −0.207277
\(353\) 151.503i 0.429187i −0.976703 0.214594i \(-0.931157\pi\)
0.976703 0.214594i \(-0.0688427\pi\)
\(354\) 94.6915 251.379i 0.267490 0.710110i
\(355\) −126.512 −0.356371
\(356\) 255.799i 0.718536i
\(357\) 91.0987 + 34.3158i 0.255178 + 0.0961227i
\(358\) −253.686 −0.708619
\(359\) 307.489i 0.856517i 0.903656 + 0.428258i \(0.140873\pi\)
−0.903656 + 0.428258i \(0.859127\pi\)
\(360\) 42.7748 + 37.5542i 0.118819 + 0.104317i
\(361\) 637.687 1.76645
\(362\) 312.841i 0.864202i
\(363\) 47.9652 127.334i 0.132136 0.350783i
\(364\) −484.993 −1.33240
\(365\) 176.832i 0.484471i
\(366\) −193.810 73.0061i −0.529537 0.199470i
\(367\) −599.959 −1.63476 −0.817382 0.576095i \(-0.804576\pi\)
−0.817382 + 0.576095i \(0.804576\pi\)
\(368\) 19.1833i 0.0521286i
\(369\) −105.825 + 120.536i −0.286788 + 0.326655i
\(370\) 84.5310 0.228462
\(371\) 733.556i 1.97724i
\(372\) 64.6376 171.595i 0.173757 0.461276i
\(373\) 361.365 0.968807 0.484404 0.874845i \(-0.339037\pi\)
0.484404 + 0.874845i \(0.339037\pi\)
\(374\) 49.4700i 0.132273i
\(375\) 31.3880 + 11.8235i 0.0837013 + 0.0315293i
\(376\) 8.06375 0.0214461
\(377\) 651.983i 1.72940i
\(378\) −215.025 403.085i −0.568849 1.06636i
\(379\) 520.151 1.37243 0.686215 0.727399i \(-0.259271\pi\)
0.686215 + 0.727399i \(0.259271\pi\)
\(380\) 141.329i 0.371917i
\(381\) −13.2503 + 35.1758i −0.0347777 + 0.0923250i
\(382\) −59.9440 −0.156921
\(383\) 133.204i 0.347791i −0.984764 0.173895i \(-0.944365\pi\)
0.984764 0.173895i \(-0.0556354\pi\)
\(384\) −31.7624 11.9645i −0.0827146 0.0311576i
\(385\) 345.065 0.896272
\(386\) 79.4542i 0.205840i
\(387\) −432.425 379.648i −1.11738 0.981003i
\(388\) 297.287 0.766204
\(389\) 8.66553i 0.0222764i 0.999938 + 0.0111382i \(0.00354548\pi\)
−0.999938 + 0.0111382i \(0.996455\pi\)
\(390\) −67.7798 + 179.936i −0.173794 + 0.461374i
\(391\) 13.0068 0.0332656
\(392\) 266.297i 0.679329i
\(393\) −488.291 183.933i −1.24247 0.468024i
\(394\) 161.630 0.410228
\(395\) 166.861i 0.422433i
\(396\) 153.172 174.465i 0.386797 0.440567i
\(397\) −551.873 −1.39011 −0.695054 0.718957i \(-0.744620\pi\)
−0.695054 + 0.718957i \(0.744620\pi\)
\(398\) 262.087i 0.658511i
\(399\) 399.854 1061.50i 1.00214 2.66040i
\(400\) −20.0000 −0.0500000
\(401\) 554.382i 1.38250i 0.722616 + 0.691249i \(0.242939\pi\)
−0.722616 + 0.691249i \(0.757061\pi\)
\(402\) 335.808 + 126.495i 0.835343 + 0.314664i
\(403\) 619.405 1.53699
\(404\) 161.508i 0.399771i
\(405\) −179.598 + 23.4431i −0.443452 + 0.0578842i
\(406\) −544.299 −1.34064
\(407\) 344.775i 0.847112i
\(408\) −8.11228 + 21.5358i −0.0198830 + 0.0527838i
\(409\) −43.0172 −0.105176 −0.0525882 0.998616i \(-0.516747\pi\)
−0.0525882 + 0.998616i \(0.516747\pi\)
\(410\) 56.3584i 0.137459i
\(411\) −337.697 127.206i −0.821646 0.309504i
\(412\) 272.051 0.660319
\(413\) 757.533i 1.83422i
\(414\) −45.8708 40.2724i −0.110799 0.0972763i
\(415\) −230.085 −0.554422
\(416\) 114.653i 0.275608i
\(417\) −80.1069 + 212.661i −0.192103 + 0.509978i
\(418\) 576.434 1.37903
\(419\) 115.812i 0.276402i −0.990404 0.138201i \(-0.955868\pi\)
0.990404 0.138201i \(-0.0441319\pi\)
\(420\) 150.217 + 56.5850i 0.357660 + 0.134726i
\(421\) 67.9898 0.161496 0.0807480 0.996735i \(-0.474269\pi\)
0.0807480 + 0.996735i \(0.474269\pi\)
\(422\) 277.623i 0.657874i
\(423\) −16.9286 + 19.2819i −0.0400203 + 0.0455837i
\(424\) −173.413 −0.408994
\(425\) 13.5606i 0.0319072i
\(426\) −84.6158 + 224.631i −0.198629 + 0.527303i
\(427\) −584.050 −1.36780
\(428\) 251.805i 0.588330i
\(429\) 733.901 + 276.452i 1.71073 + 0.644410i
\(430\) 202.187 0.470202
\(431\) 299.480i 0.694849i −0.937708 0.347424i \(-0.887056\pi\)
0.937708 0.347424i \(-0.112944\pi\)
\(432\) 95.2896 50.8321i 0.220578 0.117667i
\(433\) −75.7013 −0.174830 −0.0874149 0.996172i \(-0.527861\pi\)
−0.0874149 + 0.996172i \(0.527861\pi\)
\(434\) 517.102i 1.19148i
\(435\) −76.0680 + 201.939i −0.174869 + 0.464228i
\(436\) −179.406 −0.411481
\(437\) 151.558i 0.346814i
\(438\) 313.978 + 118.272i 0.716844 + 0.270027i
\(439\) −348.819 −0.794575 −0.397288 0.917694i \(-0.630049\pi\)
−0.397288 + 0.917694i \(0.630049\pi\)
\(440\) 81.5736i 0.185394i
\(441\) −636.765 559.049i −1.44391 1.26768i
\(442\) −77.7378 −0.175877
\(443\) 199.180i 0.449616i −0.974403 0.224808i \(-0.927825\pi\)
0.974403 0.224808i \(-0.0721755\pi\)
\(444\) 56.5375 150.091i 0.127337 0.338043i
\(445\) −285.992 −0.642678
\(446\) 181.582i 0.407134i
\(447\) 408.281 + 153.794i 0.913379 + 0.344059i
\(448\) −95.7163 −0.213652
\(449\) 246.727i 0.549503i −0.961515 0.274752i \(-0.911404\pi\)
0.961515 0.274752i \(-0.0885957\pi\)
\(450\) 41.9869 47.8237i 0.0933042 0.106275i
\(451\) −229.868 −0.509685
\(452\) 149.799i 0.331413i
\(453\) 93.1240 247.218i 0.205572 0.545735i
\(454\) −384.915 −0.847830
\(455\) 542.239i 1.19173i
\(456\) 250.939 + 94.5257i 0.550305 + 0.207293i
\(457\) −825.255 −1.80581 −0.902905 0.429841i \(-0.858570\pi\)
−0.902905 + 0.429841i \(0.858570\pi\)
\(458\) 151.464i 0.330708i
\(459\) −34.4656 64.6090i −0.0750884 0.140760i
\(460\) 21.4476 0.0466252
\(461\) 811.399i 1.76009i −0.474895 0.880043i \(-0.657514\pi\)
0.474895 0.880043i \(-0.342486\pi\)
\(462\) 230.792 612.687i 0.499550 1.32616i
\(463\) 177.948 0.384338 0.192169 0.981362i \(-0.438448\pi\)
0.192169 + 0.981362i \(0.438448\pi\)
\(464\) 128.673i 0.277312i
\(465\) −191.849 72.2671i −0.412578 0.155413i
\(466\) 113.404 0.243356
\(467\) 168.607i 0.361042i −0.983571 0.180521i \(-0.942222\pi\)
0.983571 0.180521i \(-0.0577784\pi\)
\(468\) 274.156 + 240.696i 0.585803 + 0.514307i
\(469\) 1011.96 2.15770
\(470\) 9.01555i 0.0191820i
\(471\) −233.834 + 620.764i −0.496463 + 1.31797i
\(472\) 179.081 0.379410
\(473\) 824.655i 1.74346i
\(474\) 296.274 + 111.603i 0.625051 + 0.235449i
\(475\) 158.010 0.332653
\(476\) 64.8984i 0.136341i
\(477\) 364.054 414.663i 0.763216 0.869314i
\(478\) −242.561 −0.507450
\(479\) 77.6858i 0.162183i 0.996707 + 0.0810917i \(0.0258407\pi\)
−0.996707 + 0.0810917i \(0.974159\pi\)
\(480\) −13.3767 + 35.5114i −0.0278682 + 0.0739822i
\(481\) 541.783 1.12637
\(482\) 607.785i 1.26096i
\(483\) −161.090 60.6806i −0.333519 0.125633i
\(484\) 90.7124 0.187422
\(485\) 332.377i 0.685314i
\(486\) −78.4968 + 334.569i −0.161516 + 0.688413i
\(487\) 890.670 1.82889 0.914446 0.404708i \(-0.132627\pi\)
0.914446 + 0.404708i \(0.132627\pi\)
\(488\) 138.070i 0.282930i
\(489\) 106.953 283.930i 0.218718 0.580635i
\(490\) 297.729 0.607610
\(491\) 383.262i 0.780574i −0.920693 0.390287i \(-0.872376\pi\)
0.920693 0.390287i \(-0.127624\pi\)
\(492\) −100.068 37.6946i −0.203391 0.0766150i
\(493\) −87.2438 −0.176965
\(494\) 905.815i 1.83363i
\(495\) −195.057 171.251i −0.394055 0.345962i
\(496\) 122.243 0.246458
\(497\) 676.928i 1.36203i
\(498\) −153.889 + 408.532i −0.309015 + 0.820346i
\(499\) −658.924 −1.32049 −0.660245 0.751050i \(-0.729547\pi\)
−0.660245 + 0.751050i \(0.729547\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) 318.556 + 119.996i 0.635841 + 0.239514i
\(502\) −672.556 −1.33975
\(503\) 131.526i 0.261484i −0.991416 0.130742i \(-0.958264\pi\)
0.991416 0.130742i \(-0.0417359\pi\)
\(504\) 200.941 228.875i 0.398693 0.454117i
\(505\) 180.571 0.357566
\(506\) 87.4779i 0.172881i
\(507\) −255.698 + 678.807i −0.504336 + 1.33887i
\(508\) −25.0591 −0.0493290
\(509\) 440.534i 0.865489i −0.901517 0.432744i \(-0.857545\pi\)
0.901517 0.432744i \(-0.142455\pi\)
\(510\) 24.0778 + 9.06981i 0.0472113 + 0.0177839i
\(511\) 946.175 1.85161
\(512\) 22.6274i 0.0441942i
\(513\) −752.836 + 401.599i −1.46752 + 0.782844i
\(514\) 455.040 0.885292
\(515\) 304.163i 0.590607i
\(516\) 135.230 358.997i 0.262074 0.695731i
\(517\) −36.7715 −0.0711248
\(518\) 452.300i 0.873167i
\(519\) −756.350 284.908i −1.45732 0.548956i
\(520\) −128.186 −0.246511
\(521\) 843.155i 1.61834i 0.587575 + 0.809170i \(0.300083\pi\)
−0.587575 + 0.809170i \(0.699917\pi\)
\(522\) 307.680 + 270.129i 0.589426 + 0.517488i
\(523\) 233.277 0.446037 0.223018 0.974814i \(-0.428409\pi\)
0.223018 + 0.974814i \(0.428409\pi\)
\(524\) 347.857i 0.663849i
\(525\) 63.2639 167.948i 0.120503 0.319901i
\(526\) −509.421 −0.968480
\(527\) 82.8844i 0.157276i
\(528\) 144.840 + 54.5594i 0.274318 + 0.103332i
\(529\) −23.0000 −0.0434783
\(530\) 193.882i 0.365815i
\(531\) −375.954 + 428.216i −0.708010 + 0.806434i
\(532\) 756.207 1.42144
\(533\) 361.217i 0.677706i
\(534\) −191.282 + 507.799i −0.358206 + 0.950935i
\(535\) 281.527 0.526219
\(536\) 239.228i 0.446321i
\(537\) 503.604 + 189.702i 0.937810 + 0.353262i
\(538\) 32.8290 0.0610205
\(539\) 1214.34i 2.25295i
\(540\) −56.8320 106.537i −0.105244 0.197291i
\(541\) −432.754 −0.799916 −0.399958 0.916534i \(-0.630975\pi\)
−0.399958 + 0.916534i \(0.630975\pi\)
\(542\) 479.848i 0.885328i
\(543\) 233.937 621.037i 0.430823 1.14371i
\(544\) −15.3420 −0.0282023
\(545\) 200.582i 0.368039i
\(546\) 962.785 + 362.669i 1.76334 + 0.664230i
\(547\) −287.768 −0.526084 −0.263042 0.964784i \(-0.584726\pi\)
−0.263042 + 0.964784i \(0.584726\pi\)
\(548\) 240.574i 0.439003i
\(549\) 330.150 + 289.856i 0.601366 + 0.527971i
\(550\) 91.2020 0.165822
\(551\) 1016.58i 1.84497i
\(552\) 14.3450 38.0818i 0.0259872 0.0689887i
\(553\) 892.825 1.61451
\(554\) 467.163i 0.843254i
\(555\) −167.807 63.2108i −0.302354 0.113893i
\(556\) −151.499 −0.272480
\(557\) 285.062i 0.511780i 0.966706 + 0.255890i \(0.0823685\pi\)
−0.966706 + 0.255890i \(0.917631\pi\)
\(558\) −256.631 + 292.306i −0.459912 + 0.523846i
\(559\) 1295.87 2.31820
\(560\) 107.014i 0.191097i
\(561\) 36.9928 98.2054i 0.0659409 0.175054i
\(562\) 372.069 0.662044
\(563\) 142.443i 0.253007i −0.991966 0.126504i \(-0.959624\pi\)
0.991966 0.126504i \(-0.0403756\pi\)
\(564\) −16.0078 6.02993i −0.0283826 0.0106914i
\(565\) 167.480 0.296424
\(566\) 413.301i 0.730214i
\(567\) 125.437 + 960.976i 0.221229 + 1.69484i
\(568\) −160.026 −0.281736
\(569\) 262.892i 0.462025i 0.972951 + 0.231013i \(0.0742039\pi\)
−0.972951 + 0.231013i \(0.925796\pi\)
\(570\) 105.683 280.558i 0.185409 0.492208i
\(571\) 120.906 0.211744 0.105872 0.994380i \(-0.466237\pi\)
0.105872 + 0.994380i \(0.466237\pi\)
\(572\) 522.828i 0.914036i
\(573\) 118.998 + 44.8250i 0.207675 + 0.0782287i
\(574\) −301.557 −0.525361
\(575\) 23.9792i 0.0417029i
\(576\) 54.1063 + 47.5027i 0.0939345 + 0.0824700i
\(577\) −223.738 −0.387762 −0.193881 0.981025i \(-0.562107\pi\)
−0.193881 + 0.981025i \(0.562107\pi\)
\(578\) 398.305i 0.689110i
\(579\) 59.4145 157.729i 0.102616 0.272416i
\(580\) −143.861 −0.248035
\(581\) 1231.12i 2.11896i
\(582\) −590.160 222.306i −1.01402 0.381969i
\(583\) 790.782 1.35640
\(584\) 223.677i 0.383008i
\(585\) 269.106 306.516i 0.460010 0.523958i
\(586\) 766.342 1.30775
\(587\) 593.776i 1.01154i −0.862667 0.505772i \(-0.831208\pi\)
0.862667 0.505772i \(-0.168792\pi\)
\(588\) 199.132 528.640i 0.338660 0.899047i
\(589\) −965.784 −1.63970
\(590\) 200.219i 0.339354i
\(591\) −320.859 120.864i −0.542909 0.204507i
\(592\) 106.924 0.180615
\(593\) 707.402i 1.19292i 0.802643 + 0.596460i \(0.203427\pi\)
−0.802643 + 0.596460i \(0.796573\pi\)
\(594\) −434.530 + 231.799i −0.731532 + 0.390235i
\(595\) 72.5586 0.121947
\(596\) 290.858i 0.488016i
\(597\) 195.984 520.283i 0.328282 0.871496i
\(598\) 137.464 0.229873
\(599\) 89.8222i 0.149954i 0.997185 + 0.0749768i \(0.0238883\pi\)
−0.997185 + 0.0749768i \(0.976112\pi\)
\(600\) 39.7030 + 14.9556i 0.0661717 + 0.0249261i
\(601\) −1122.70 −1.86806 −0.934029 0.357197i \(-0.883732\pi\)
−0.934029 + 0.357197i \(0.883732\pi\)
\(602\) 1081.84i 1.79708i
\(603\) −572.038 502.222i −0.948654 0.832873i
\(604\) 176.117 0.291584
\(605\) 101.419i 0.167636i
\(606\) 120.772 320.617i 0.199295 0.529070i
\(607\) −335.109 −0.552074 −0.276037 0.961147i \(-0.589021\pi\)
−0.276037 + 0.961147i \(0.589021\pi\)
\(608\) 178.768i 0.294026i
\(609\) 1080.52 + 407.017i 1.77425 + 0.668337i
\(610\) −154.367 −0.253060
\(611\) 57.7832i 0.0945716i
\(612\) 32.2082 36.6856i 0.0526278 0.0599438i
\(613\) 927.809 1.51356 0.756778 0.653672i \(-0.226773\pi\)
0.756778 + 0.653672i \(0.226773\pi\)
\(614\) 234.930i 0.382622i
\(615\) −42.1438 + 111.880i −0.0685265 + 0.181918i
\(616\) 436.476 0.708565
\(617\) 823.595i 1.33484i 0.744682 + 0.667419i \(0.232601\pi\)
−0.744682 + 0.667419i \(0.767399\pi\)
\(618\) −540.063 203.435i −0.873888 0.329183i
\(619\) 610.174 0.985742 0.492871 0.870103i \(-0.335948\pi\)
0.492871 + 0.870103i \(0.335948\pi\)
\(620\) 136.672i 0.220439i
\(621\) 60.9455 + 114.248i 0.0981409 + 0.183975i
\(622\) 257.210 0.413521
\(623\) 1530.26i 2.45627i
\(624\) −85.7354 + 227.603i −0.137396 + 0.364749i
\(625\) 25.0000 0.0400000
\(626\) 533.876i 0.852837i
\(627\) −1144.31 431.047i −1.82505 0.687475i
\(628\) −442.230 −0.704187
\(629\) 72.4976i 0.115259i
\(630\) −255.890 224.659i −0.406175 0.356602i
\(631\) −564.071 −0.893932 −0.446966 0.894551i \(-0.647495\pi\)
−0.446966 + 0.894551i \(0.647495\pi\)
\(632\) 211.065i 0.333963i
\(633\) −207.601 + 551.123i −0.327964 + 0.870653i
\(634\) −216.557 −0.341573
\(635\) 28.0170i 0.0441212i
\(636\) 344.251 + 129.675i 0.541276 + 0.203892i
\(637\) 1908.23 2.99565
\(638\) 586.761i 0.919688i
\(639\) 335.950 382.652i 0.525744 0.598829i
\(640\) −25.2982 −0.0395285
\(641\) 711.513i 1.11001i −0.831849 0.555003i \(-0.812717\pi\)
0.831849 0.555003i \(-0.187283\pi\)
\(642\) 188.296 499.871i 0.293295 0.778616i
\(643\) 1104.71 1.71805 0.859027 0.511930i \(-0.171069\pi\)
0.859027 + 0.511930i \(0.171069\pi\)
\(644\) 114.760i 0.178198i
\(645\) −401.371 151.192i −0.622281 0.234406i
\(646\) 121.210 0.187631
\(647\) 1047.39i 1.61884i 0.587228 + 0.809422i \(0.300219\pi\)
−0.587228 + 0.809422i \(0.699781\pi\)
\(648\) −227.175 + 29.6534i −0.350579 + 0.0457615i
\(649\) −816.629 −1.25829
\(650\) 143.316i 0.220486i
\(651\) −386.680 + 1026.53i −0.593978 + 1.57684i
\(652\) 202.271 0.310232
\(653\) 400.037i 0.612615i −0.951933 0.306307i \(-0.900906\pi\)
0.951933 0.306307i \(-0.0990935\pi\)
\(654\) 356.147 + 134.156i 0.544567 + 0.205132i
\(655\) −388.916 −0.593765
\(656\) 71.2884i 0.108671i
\(657\) −534.852 469.574i −0.814081 0.714725i
\(658\) −48.2395 −0.0733124
\(659\) 53.4238i 0.0810680i 0.999178 + 0.0405340i \(0.0129059\pi\)
−0.999178 + 0.0405340i \(0.987094\pi\)
\(660\) 60.9993 161.936i 0.0924231 0.245357i
\(661\) −748.518 −1.13240 −0.566201 0.824267i \(-0.691588\pi\)
−0.566201 + 0.824267i \(0.691588\pi\)
\(662\) 225.640i 0.340845i
\(663\) 154.321 + 58.1310i 0.232762 + 0.0876787i
\(664\) −291.037 −0.438309
\(665\) 845.465i 1.27138i
\(666\) −224.471 + 255.675i −0.337043 + 0.383897i
\(667\) 154.273 0.231294
\(668\) 226.938i 0.339728i
\(669\) 135.783 360.467i 0.202965 0.538814i
\(670\) 267.465 0.399202
\(671\) 629.612i 0.938319i
\(672\) 190.011 + 71.5750i 0.282755 + 0.106510i
\(673\) −59.5933 −0.0885487 −0.0442743 0.999019i \(-0.514098\pi\)
−0.0442743 + 0.999019i \(0.514098\pi\)
\(674\) 156.046i 0.231523i
\(675\) −119.112 + 63.5401i −0.176462 + 0.0941335i
\(676\) −483.579 −0.715354
\(677\) 991.775i 1.46496i 0.680791 + 0.732478i \(0.261636\pi\)
−0.680791 + 0.732478i \(0.738364\pi\)
\(678\) 112.017 297.373i 0.165216 0.438603i
\(679\) −1778.45 −2.61922
\(680\) 17.1529i 0.0252249i
\(681\) 764.114 + 287.833i 1.12205 + 0.422662i
\(682\) −557.442 −0.817364
\(683\) 514.441i 0.753208i 0.926374 + 0.376604i \(0.122908\pi\)
−0.926374 + 0.376604i \(0.877092\pi\)
\(684\) −427.467 375.296i −0.624952 0.548678i
\(685\) −268.970 −0.392656
\(686\) 763.960i 1.11364i
\(687\) −113.262 + 300.679i −0.164865 + 0.437670i
\(688\) 255.748 0.371727
\(689\) 1242.64i 1.80355i
\(690\) −42.5767 16.0381i −0.0617054 0.0232437i
\(691\) −85.8481 −0.124238 −0.0621188 0.998069i \(-0.519786\pi\)
−0.0621188 + 0.998069i \(0.519786\pi\)
\(692\) 538.821i 0.778643i
\(693\) −916.313 + 1043.69i −1.32224 + 1.50605i
\(694\) −488.051 −0.703244
\(695\) 169.381i 0.243714i
\(696\) −96.2193 + 255.435i −0.138246 + 0.367004i
\(697\) −48.3355 −0.0693479
\(698\) 585.741i 0.839170i
\(699\) −225.124 84.8015i −0.322066 0.121318i
\(700\) 119.645 0.170922
\(701\) 847.483i 1.20896i 0.796619 + 0.604481i \(0.206620\pi\)
−0.796619 + 0.604481i \(0.793380\pi\)
\(702\) −364.252 682.826i −0.518878 0.972687i
\(703\) −844.755 −1.20164
\(704\) 103.183i 0.146567i
\(705\) −6.74167 + 17.8972i −0.00956265 + 0.0253861i
\(706\) −214.258 −0.303481
\(707\) 966.182i 1.36659i
\(708\) −355.504 133.914i −0.502124 0.189144i
\(709\) −434.828 −0.613297 −0.306649 0.951823i \(-0.599208\pi\)
−0.306649 + 0.951823i \(0.599208\pi\)
\(710\) 178.915i 0.251993i
\(711\) −504.694 443.097i −0.709837 0.623203i
\(712\) −361.754 −0.508082
\(713\) 146.565i 0.205560i
\(714\) 48.5299 128.833i 0.0679690 0.180438i
\(715\) 584.540 0.817538
\(716\) 358.766i 0.501069i
\(717\) 481.520 + 181.383i 0.671576 + 0.252975i
\(718\) 434.856 0.605649
\(719\) 1036.78i 1.44198i 0.692947 + 0.720988i \(0.256312\pi\)
−0.692947 + 0.720988i \(0.743688\pi\)
\(720\) 53.1097 60.4927i 0.0737634 0.0840176i
\(721\) −1627.48 −2.25726
\(722\) 901.826i 1.24907i
\(723\) 454.491 1206.54i 0.628618 1.66880i
\(724\) 442.424 0.611083
\(725\) 160.841i 0.221850i
\(726\) −180.078 67.8331i −0.248041 0.0934340i
\(727\) −371.369 −0.510823 −0.255412 0.966832i \(-0.582211\pi\)
−0.255412 + 0.966832i \(0.582211\pi\)
\(728\) 685.884i 0.942148i
\(729\) 406.013 605.471i 0.556945 0.830550i
\(730\) 250.078 0.342573
\(731\) 173.405i 0.237215i
\(732\) −103.246 + 274.089i −0.141047 + 0.374439i
\(733\) −524.689 −0.715810 −0.357905 0.933758i \(-0.616509\pi\)
−0.357905 + 0.933758i \(0.616509\pi\)
\(734\) 848.470i 1.15595i
\(735\) −591.037 222.637i −0.804132 0.302907i
\(736\) 27.1293 0.0368605
\(737\) 1090.90i 1.48020i
\(738\) 170.463 + 149.659i 0.230980 + 0.202790i
\(739\) 439.493 0.594713 0.297357 0.954766i \(-0.403895\pi\)
0.297357 + 0.954766i \(0.403895\pi\)
\(740\) 119.545i 0.161547i
\(741\) 677.352 1798.18i 0.914106 2.42669i
\(742\) 1037.40 1.39812
\(743\) 1233.57i 1.66025i 0.557577 + 0.830125i \(0.311731\pi\)
−0.557577 + 0.830125i \(0.688269\pi\)
\(744\) −242.671 91.4114i −0.326171 0.122865i
\(745\) 325.189 0.436495
\(746\) 511.047i 0.685050i
\(747\) 610.987 695.923i 0.817921 0.931623i
\(748\) 69.9612 0.0935310
\(749\) 1506.37i 2.01117i
\(750\) 16.7209 44.3893i 0.0222946 0.0591857i
\(751\) −80.5428 −0.107247 −0.0536237 0.998561i \(-0.517077\pi\)
−0.0536237 + 0.998561i \(0.517077\pi\)
\(752\) 11.4039i 0.0151647i
\(753\) 1335.12 + 502.925i 1.77307 + 0.667895i
\(754\) −922.044 −1.22287
\(755\) 196.905i 0.260801i
\(756\) −570.048 + 304.091i −0.754032 + 0.402237i
\(757\) 1135.47 1.49996 0.749982 0.661459i \(-0.230062\pi\)
0.749982 + 0.661459i \(0.230062\pi\)
\(758\) 735.605i 0.970455i
\(759\) −65.4144 + 173.657i −0.0861850 + 0.228797i
\(760\) 199.869 0.262985
\(761\) 398.257i 0.523334i −0.965158 0.261667i \(-0.915728\pi\)
0.965158 0.261667i \(-0.0842722\pi\)
\(762\) 49.7462 + 18.7388i 0.0652837 + 0.0245916i
\(763\) 1073.25 1.40662
\(764\) 84.7736i 0.110960i
\(765\) −41.0157 36.0099i −0.0536153 0.0470717i
\(766\) −188.379 −0.245925
\(767\) 1283.26i 1.67309i
\(768\) −16.9204 + 44.9188i −0.0220318 + 0.0584880i
\(769\) 52.7698 0.0686213 0.0343107 0.999411i \(-0.489076\pi\)
0.0343107 + 0.999411i \(0.489076\pi\)
\(770\) 487.995i 0.633760i
\(771\) −903.322 340.271i −1.17162 0.441337i
\(772\) 112.365 0.145551
\(773\) 267.888i 0.346556i −0.984873 0.173278i \(-0.944564\pi\)
0.984873 0.173278i \(-0.0554359\pi\)
\(774\) −536.904 + 611.541i −0.693674 + 0.790104i
\(775\) −152.804 −0.197167
\(776\) 420.428i 0.541788i
\(777\) −338.222 + 897.884i −0.435293 + 1.15558i
\(778\) 12.2549 0.0157518
\(779\) 563.214i 0.722996i
\(780\) 254.468 + 95.8550i 0.326241 + 0.122891i
\(781\) 729.736 0.934361
\(782\) 18.3944i 0.0235223i
\(783\) −408.794 766.324i −0.522087 0.978702i
\(784\) 376.601 0.480358
\(785\) 494.428i 0.629844i
\(786\) −260.121 + 690.548i −0.330943