Properties

Label 690.3.c.a.91.4
Level $690$
Weight $3$
Character 690.91
Analytic conductor $18.801$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 91.4
Character \(\chi\) \(=\) 690.91
Dual form 690.3.c.a.91.5

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} -1.73205 q^{3} +2.00000 q^{4} -2.23607i q^{5} +2.44949 q^{6} +5.52876i q^{7} -2.82843 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-1.41421 q^{2} -1.73205 q^{3} +2.00000 q^{4} -2.23607i q^{5} +2.44949 q^{6} +5.52876i q^{7} -2.82843 q^{8} +3.00000 q^{9} +3.16228i q^{10} +3.99843i q^{11} -3.46410 q^{12} +8.18275 q^{13} -7.81884i q^{14} +3.87298i q^{15} +4.00000 q^{16} -17.3987i q^{17} -4.24264 q^{18} +11.0934i q^{19} -4.47214i q^{20} -9.57609i q^{21} -5.65463i q^{22} +(-22.7880 + 3.11551i) q^{23} +4.89898 q^{24} -5.00000 q^{25} -11.5722 q^{26} -5.19615 q^{27} +11.0575i q^{28} +10.3250 q^{29} -5.47723i q^{30} -20.6672 q^{31} -5.65685 q^{32} -6.92548i q^{33} +24.6055i q^{34} +12.3627 q^{35} +6.00000 q^{36} +39.0577i q^{37} -15.6884i q^{38} -14.1729 q^{39} +6.32456i q^{40} +73.4079 q^{41} +13.5426i q^{42} -52.2098i q^{43} +7.99686i q^{44} -6.70820i q^{45} +(32.2271 - 4.40599i) q^{46} -74.9985 q^{47} -6.92820 q^{48} +18.4329 q^{49} +7.07107 q^{50} +30.1355i q^{51} +16.3655 q^{52} +18.2596i q^{53} +7.34847 q^{54} +8.94076 q^{55} -15.6377i q^{56} -19.2143i q^{57} -14.6017 q^{58} -6.77206 q^{59} +7.74597i q^{60} +115.117i q^{61} +29.2279 q^{62} +16.5863i q^{63} +8.00000 q^{64} -18.2972i q^{65} +9.79411i q^{66} +110.296i q^{67} -34.7974i q^{68} +(39.4700 - 5.39622i) q^{69} -17.4835 q^{70} +30.5113 q^{71} -8.48528 q^{72} -89.5707 q^{73} -55.2359i q^{74} +8.66025 q^{75} +22.1868i q^{76} -22.1063 q^{77} +20.0436 q^{78} +141.248i q^{79} -8.94427i q^{80} +9.00000 q^{81} -103.814 q^{82} +66.8139i q^{83} -19.1522i q^{84} -38.9047 q^{85} +73.8359i q^{86} -17.8834 q^{87} -11.3093i q^{88} +54.8986i q^{89} +9.48683i q^{90} +45.2404i q^{91} +(-45.5760 + 6.23102i) q^{92} +35.7967 q^{93} +106.064 q^{94} +24.8056 q^{95} +9.79796 q^{96} -8.89570i q^{97} -26.0680 q^{98} +11.9953i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 64q^{4} + 96q^{9} + O(q^{10}) \) \( 32q + 64q^{4} + 96q^{9} - 48q^{13} + 128q^{16} - 80q^{23} - 160q^{25} + 120q^{29} + 248q^{31} - 120q^{35} + 192q^{36} - 48q^{39} + 72q^{41} + 160q^{46} + 400q^{47} - 344q^{49} - 96q^{52} - 256q^{58} + 120q^{59} + 160q^{62} + 256q^{64} + 192q^{69} + 104q^{71} + 16q^{73} + 240q^{77} + 192q^{78} + 288q^{81} + 64q^{82} - 120q^{85} + 144q^{87} - 160q^{92} - 192q^{93} + 96q^{94} - 160q^{95} + 64q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −0.707107
\(3\) −1.73205 −0.577350
\(4\) 2.00000 0.500000
\(5\) 2.23607i 0.447214i
\(6\) 2.44949 0.408248
\(7\) 5.52876i 0.789822i 0.918719 + 0.394911i \(0.129225\pi\)
−0.918719 + 0.394911i \(0.870775\pi\)
\(8\) −2.82843 −0.353553
\(9\) 3.00000 0.333333
\(10\) 3.16228i 0.316228i
\(11\) 3.99843i 0.363493i 0.983345 + 0.181747i \(0.0581751\pi\)
−0.983345 + 0.181747i \(0.941825\pi\)
\(12\) −3.46410 −0.288675
\(13\) 8.18275 0.629442 0.314721 0.949184i \(-0.398089\pi\)
0.314721 + 0.949184i \(0.398089\pi\)
\(14\) 7.81884i 0.558489i
\(15\) 3.87298i 0.258199i
\(16\) 4.00000 0.250000
\(17\) 17.3987i 1.02345i −0.859148 0.511727i \(-0.829006\pi\)
0.859148 0.511727i \(-0.170994\pi\)
\(18\) −4.24264 −0.235702
\(19\) 11.0934i 0.583863i 0.956439 + 0.291932i \(0.0942980\pi\)
−0.956439 + 0.291932i \(0.905702\pi\)
\(20\) 4.47214i 0.223607i
\(21\) 9.57609i 0.456004i
\(22\) 5.65463i 0.257029i
\(23\) −22.7880 + 3.11551i −0.990783 + 0.135457i
\(24\) 4.89898 0.204124
\(25\) −5.00000 −0.200000
\(26\) −11.5722 −0.445083
\(27\) −5.19615 −0.192450
\(28\) 11.0575i 0.394911i
\(29\) 10.3250 0.356034 0.178017 0.984027i \(-0.443032\pi\)
0.178017 + 0.984027i \(0.443032\pi\)
\(30\) 5.47723i 0.182574i
\(31\) −20.6672 −0.666684 −0.333342 0.942806i \(-0.608176\pi\)
−0.333342 + 0.942806i \(0.608176\pi\)
\(32\) −5.65685 −0.176777
\(33\) 6.92548i 0.209863i
\(34\) 24.6055i 0.723691i
\(35\) 12.3627 0.353219
\(36\) 6.00000 0.166667
\(37\) 39.0577i 1.05561i 0.849365 + 0.527806i \(0.176985\pi\)
−0.849365 + 0.527806i \(0.823015\pi\)
\(38\) 15.6884i 0.412854i
\(39\) −14.1729 −0.363409
\(40\) 6.32456i 0.158114i
\(41\) 73.4079 1.79044 0.895218 0.445629i \(-0.147020\pi\)
0.895218 + 0.445629i \(0.147020\pi\)
\(42\) 13.5426i 0.322444i
\(43\) 52.2098i 1.21418i −0.794632 0.607091i \(-0.792336\pi\)
0.794632 0.607091i \(-0.207664\pi\)
\(44\) 7.99686i 0.181747i
\(45\) 6.70820i 0.149071i
\(46\) 32.2271 4.40599i 0.700590 0.0957825i
\(47\) −74.9985 −1.59571 −0.797857 0.602847i \(-0.794033\pi\)
−0.797857 + 0.602847i \(0.794033\pi\)
\(48\) −6.92820 −0.144338
\(49\) 18.4329 0.376181
\(50\) 7.07107 0.141421
\(51\) 30.1355i 0.590892i
\(52\) 16.3655 0.314721
\(53\) 18.2596i 0.344521i 0.985051 + 0.172260i \(0.0551071\pi\)
−0.985051 + 0.172260i \(0.944893\pi\)
\(54\) 7.34847 0.136083
\(55\) 8.94076 0.162559
\(56\) 15.6377i 0.279244i
\(57\) 19.2143i 0.337094i
\(58\) −14.6017 −0.251754
\(59\) −6.77206 −0.114781 −0.0573904 0.998352i \(-0.518278\pi\)
−0.0573904 + 0.998352i \(0.518278\pi\)
\(60\) 7.74597i 0.129099i
\(61\) 115.117i 1.88717i 0.331130 + 0.943585i \(0.392570\pi\)
−0.331130 + 0.943585i \(0.607430\pi\)
\(62\) 29.2279 0.471417
\(63\) 16.5863i 0.263274i
\(64\) 8.00000 0.125000
\(65\) 18.2972i 0.281495i
\(66\) 9.79411i 0.148396i
\(67\) 110.296i 1.64621i 0.567891 + 0.823104i \(0.307759\pi\)
−0.567891 + 0.823104i \(0.692241\pi\)
\(68\) 34.7974i 0.511727i
\(69\) 39.4700 5.39622i 0.572029 0.0782060i
\(70\) −17.4835 −0.249764
\(71\) 30.5113 0.429737 0.214868 0.976643i \(-0.431068\pi\)
0.214868 + 0.976643i \(0.431068\pi\)
\(72\) −8.48528 −0.117851
\(73\) −89.5707 −1.22700 −0.613498 0.789696i \(-0.710238\pi\)
−0.613498 + 0.789696i \(0.710238\pi\)
\(74\) 55.2359i 0.746431i
\(75\) 8.66025 0.115470
\(76\) 22.1868i 0.291932i
\(77\) −22.1063 −0.287095
\(78\) 20.0436 0.256969
\(79\) 141.248i 1.78795i 0.448113 + 0.893977i \(0.352096\pi\)
−0.448113 + 0.893977i \(0.647904\pi\)
\(80\) 8.94427i 0.111803i
\(81\) 9.00000 0.111111
\(82\) −103.814 −1.26603
\(83\) 66.8139i 0.804986i 0.915423 + 0.402493i \(0.131856\pi\)
−0.915423 + 0.402493i \(0.868144\pi\)
\(84\) 19.1522i 0.228002i
\(85\) −38.9047 −0.457703
\(86\) 73.8359i 0.858557i
\(87\) −17.8834 −0.205556
\(88\) 11.3093i 0.128514i
\(89\) 54.8986i 0.616838i 0.951251 + 0.308419i \(0.0997999\pi\)
−0.951251 + 0.308419i \(0.900200\pi\)
\(90\) 9.48683i 0.105409i
\(91\) 45.2404i 0.497148i
\(92\) −45.5760 + 6.23102i −0.495392 + 0.0677284i
\(93\) 35.7967 0.384910
\(94\) 106.064 1.12834
\(95\) 24.8056 0.261112
\(96\) 9.79796 0.102062
\(97\) 8.89570i 0.0917083i −0.998948 0.0458541i \(-0.985399\pi\)
0.998948 0.0458541i \(-0.0146009\pi\)
\(98\) −26.0680 −0.266000
\(99\) 11.9953i 0.121164i
\(100\) −10.0000 −0.100000
\(101\) −102.145 −1.01133 −0.505667 0.862729i \(-0.668754\pi\)
−0.505667 + 0.862729i \(0.668754\pi\)
\(102\) 42.6180i 0.417823i
\(103\) 178.032i 1.72847i 0.503092 + 0.864233i \(0.332196\pi\)
−0.503092 + 0.864233i \(0.667804\pi\)
\(104\) −23.1443 −0.222541
\(105\) −21.4128 −0.203931
\(106\) 25.8230i 0.243613i
\(107\) 5.45306i 0.0509632i 0.999675 + 0.0254816i \(0.00811192\pi\)
−0.999675 + 0.0254816i \(0.991888\pi\)
\(108\) −10.3923 −0.0962250
\(109\) 18.9658i 0.173998i 0.996208 + 0.0869989i \(0.0277277\pi\)
−0.996208 + 0.0869989i \(0.972272\pi\)
\(110\) −12.6441 −0.114947
\(111\) 67.6498i 0.609458i
\(112\) 22.1150i 0.197456i
\(113\) 55.6781i 0.492727i 0.969178 + 0.246363i \(0.0792357\pi\)
−0.969178 + 0.246363i \(0.920764\pi\)
\(114\) 27.1732i 0.238361i
\(115\) 6.96649 + 50.9555i 0.0605781 + 0.443092i
\(116\) 20.6500 0.178017
\(117\) 24.5482 0.209814
\(118\) 9.57714 0.0811622
\(119\) 96.1933 0.808347
\(120\) 10.9545i 0.0912871i
\(121\) 105.013 0.867873
\(122\) 162.801i 1.33443i
\(123\) −127.146 −1.03371
\(124\) −41.3344 −0.333342
\(125\) 11.1803i 0.0894427i
\(126\) 23.4565i 0.186163i
\(127\) −129.679 −1.02109 −0.510546 0.859850i \(-0.670557\pi\)
−0.510546 + 0.859850i \(0.670557\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 90.4301i 0.701008i
\(130\) 25.8761i 0.199047i
\(131\) 194.919 1.48793 0.743965 0.668218i \(-0.232943\pi\)
0.743965 + 0.668218i \(0.232943\pi\)
\(132\) 13.8510i 0.104932i
\(133\) −61.3327 −0.461148
\(134\) 155.982i 1.16404i
\(135\) 11.6190i 0.0860663i
\(136\) 49.2110i 0.361846i
\(137\) 115.467i 0.842825i 0.906869 + 0.421412i \(0.138466\pi\)
−0.906869 + 0.421412i \(0.861534\pi\)
\(138\) −55.8190 + 7.63140i −0.404486 + 0.0553000i
\(139\) −248.366 −1.78680 −0.893401 0.449260i \(-0.851688\pi\)
−0.893401 + 0.449260i \(0.851688\pi\)
\(140\) 24.7253 0.176610
\(141\) 129.901 0.921285
\(142\) −43.1495 −0.303870
\(143\) 32.7181i 0.228798i
\(144\) 12.0000 0.0833333
\(145\) 23.0874i 0.159223i
\(146\) 126.672 0.867617
\(147\) −31.9266 −0.217188
\(148\) 78.1153i 0.527806i
\(149\) 224.035i 1.50359i −0.659397 0.751795i \(-0.729188\pi\)
0.659397 0.751795i \(-0.270812\pi\)
\(150\) −12.2474 −0.0816497
\(151\) 230.365 1.52560 0.762799 0.646636i \(-0.223825\pi\)
0.762799 + 0.646636i \(0.223825\pi\)
\(152\) 31.3769i 0.206427i
\(153\) 52.1962i 0.341151i
\(154\) 31.2631 0.203007
\(155\) 46.2133i 0.298150i
\(156\) −28.3459 −0.181704
\(157\) 11.2242i 0.0714920i 0.999361 + 0.0357460i \(0.0113807\pi\)
−0.999361 + 0.0357460i \(0.988619\pi\)
\(158\) 199.755i 1.26427i
\(159\) 31.6266i 0.198909i
\(160\) 12.6491i 0.0790569i
\(161\) −17.2249 125.989i −0.106987 0.782543i
\(162\) −12.7279 −0.0785674
\(163\) 67.5155 0.414206 0.207103 0.978319i \(-0.433597\pi\)
0.207103 + 0.978319i \(0.433597\pi\)
\(164\) 146.816 0.895218
\(165\) −15.4858 −0.0938536
\(166\) 94.4891i 0.569211i
\(167\) 28.5518 0.170969 0.0854845 0.996339i \(-0.472756\pi\)
0.0854845 + 0.996339i \(0.472756\pi\)
\(168\) 27.0853i 0.161222i
\(169\) −102.043 −0.603802
\(170\) 55.0196 0.323645
\(171\) 33.2802i 0.194621i
\(172\) 104.420i 0.607091i
\(173\) −40.7348 −0.235461 −0.117731 0.993046i \(-0.537562\pi\)
−0.117731 + 0.993046i \(0.537562\pi\)
\(174\) 25.2909 0.145350
\(175\) 27.6438i 0.157964i
\(176\) 15.9937i 0.0908734i
\(177\) 11.7296 0.0662687
\(178\) 77.6383i 0.436170i
\(179\) −283.716 −1.58500 −0.792502 0.609869i \(-0.791222\pi\)
−0.792502 + 0.609869i \(0.791222\pi\)
\(180\) 13.4164i 0.0745356i
\(181\) 23.5724i 0.130234i 0.997878 + 0.0651172i \(0.0207421\pi\)
−0.997878 + 0.0651172i \(0.979258\pi\)
\(182\) 63.9796i 0.351536i
\(183\) 199.389i 1.08956i
\(184\) 64.4542 8.81199i 0.350295 0.0478912i
\(185\) 87.3356 0.472084
\(186\) −50.6241 −0.272173
\(187\) 69.5675 0.372019
\(188\) −149.997 −0.797857
\(189\) 28.7283i 0.152001i
\(190\) −35.0804 −0.184634
\(191\) 39.2377i 0.205433i −0.994711 0.102717i \(-0.967247\pi\)
0.994711 0.102717i \(-0.0327535\pi\)
\(192\) −13.8564 −0.0721688
\(193\) 215.075 1.11438 0.557188 0.830386i \(-0.311880\pi\)
0.557188 + 0.830386i \(0.311880\pi\)
\(194\) 12.5804i 0.0648475i
\(195\) 31.6917i 0.162521i
\(196\) 36.8657 0.188090
\(197\) 195.426 0.992009 0.496005 0.868320i \(-0.334800\pi\)
0.496005 + 0.868320i \(0.334800\pi\)
\(198\) 16.9639i 0.0856762i
\(199\) 126.232i 0.634334i 0.948370 + 0.317167i \(0.102732\pi\)
−0.948370 + 0.317167i \(0.897268\pi\)
\(200\) 14.1421 0.0707107
\(201\) 191.038i 0.950438i
\(202\) 144.454 0.715121
\(203\) 57.0843i 0.281204i
\(204\) 60.2709i 0.295446i
\(205\) 164.145i 0.800707i
\(206\) 251.775i 1.22221i
\(207\) −68.3640 + 9.34652i −0.330261 + 0.0451523i
\(208\) 32.7310 0.157361
\(209\) −44.3562 −0.212231
\(210\) 30.2822 0.144201
\(211\) 248.669 1.17853 0.589263 0.807941i \(-0.299418\pi\)
0.589263 + 0.807941i \(0.299418\pi\)
\(212\) 36.5192i 0.172260i
\(213\) −52.8472 −0.248109
\(214\) 7.71179i 0.0360364i
\(215\) −116.745 −0.542999
\(216\) 14.6969 0.0680414
\(217\) 114.264i 0.526562i
\(218\) 26.8216i 0.123035i
\(219\) 155.141 0.708407
\(220\) 17.8815 0.0812796
\(221\) 142.369i 0.644205i
\(222\) 95.6713i 0.430952i
\(223\) −211.066 −0.946485 −0.473243 0.880932i \(-0.656917\pi\)
−0.473243 + 0.880932i \(0.656917\pi\)
\(224\) 31.2754i 0.139622i
\(225\) −15.0000 −0.0666667
\(226\) 78.7407i 0.348410i
\(227\) 273.698i 1.20572i −0.797848 0.602859i \(-0.794028\pi\)
0.797848 0.602859i \(-0.205972\pi\)
\(228\) 38.4287i 0.168547i
\(229\) 366.210i 1.59917i −0.600552 0.799586i \(-0.705052\pi\)
0.600552 0.799586i \(-0.294948\pi\)
\(230\) −9.85210 72.0620i −0.0428352 0.313313i
\(231\) 38.2893 0.165754
\(232\) −29.2035 −0.125877
\(233\) −232.825 −0.999249 −0.499624 0.866242i \(-0.666529\pi\)
−0.499624 + 0.866242i \(0.666529\pi\)
\(234\) −34.7165 −0.148361
\(235\) 167.702i 0.713625i
\(236\) −13.5441 −0.0573904
\(237\) 244.649i 1.03228i
\(238\) −136.038 −0.571588
\(239\) −103.855 −0.434541 −0.217270 0.976111i \(-0.569715\pi\)
−0.217270 + 0.976111i \(0.569715\pi\)
\(240\) 15.4919i 0.0645497i
\(241\) 206.595i 0.857243i 0.903484 + 0.428621i \(0.141001\pi\)
−0.903484 + 0.428621i \(0.858999\pi\)
\(242\) −148.510 −0.613679
\(243\) −15.5885 −0.0641500
\(244\) 230.235i 0.943585i
\(245\) 41.2171i 0.168233i
\(246\) 179.812 0.730942
\(247\) 90.7746i 0.367508i
\(248\) 58.4557 0.235708
\(249\) 115.725i 0.464759i
\(250\) 15.8114i 0.0632456i
\(251\) 252.278i 1.00509i 0.864550 + 0.502547i \(0.167603\pi\)
−0.864550 + 0.502547i \(0.832397\pi\)
\(252\) 33.1725i 0.131637i
\(253\) −12.4571 91.1162i −0.0492377 0.360143i
\(254\) 183.393 0.722021
\(255\) 67.3850 0.264255
\(256\) 16.0000 0.0625000
\(257\) −161.467 −0.628277 −0.314139 0.949377i \(-0.601716\pi\)
−0.314139 + 0.949377i \(0.601716\pi\)
\(258\) 127.887i 0.495688i
\(259\) −215.940 −0.833746
\(260\) 36.5944i 0.140748i
\(261\) 30.9749 0.118678
\(262\) −275.657 −1.05213
\(263\) 271.077i 1.03071i −0.856977 0.515355i \(-0.827660\pi\)
0.856977 0.515355i \(-0.172340\pi\)
\(264\) 19.5882i 0.0741978i
\(265\) 40.8297 0.154074
\(266\) 86.7376 0.326081
\(267\) 95.0871i 0.356132i
\(268\) 220.592i 0.823104i
\(269\) −164.713 −0.612315 −0.306158 0.951981i \(-0.599043\pi\)
−0.306158 + 0.951981i \(0.599043\pi\)
\(270\) 16.4317i 0.0608581i
\(271\) 248.736 0.917845 0.458922 0.888476i \(-0.348236\pi\)
0.458922 + 0.888476i \(0.348236\pi\)
\(272\) 69.5949i 0.255864i
\(273\) 78.3587i 0.287028i
\(274\) 163.295i 0.595967i
\(275\) 19.9921i 0.0726987i
\(276\) 78.9400 10.7924i 0.286014 0.0391030i
\(277\) −134.521 −0.485636 −0.242818 0.970072i \(-0.578072\pi\)
−0.242818 + 0.970072i \(0.578072\pi\)
\(278\) 351.242 1.26346
\(279\) −62.0016 −0.222228
\(280\) −34.9669 −0.124882
\(281\) 244.802i 0.871182i 0.900145 + 0.435591i \(0.143461\pi\)
−0.900145 + 0.435591i \(0.856539\pi\)
\(282\) −183.708 −0.651447
\(283\) 413.193i 1.46005i −0.683423 0.730023i \(-0.739509\pi\)
0.683423 0.730023i \(-0.260491\pi\)
\(284\) 61.0226 0.214868
\(285\) −42.9646 −0.150753
\(286\) 46.2704i 0.161785i
\(287\) 405.854i 1.41413i
\(288\) −16.9706 −0.0589256
\(289\) −13.7155 −0.0474585
\(290\) 32.6505i 0.112588i
\(291\) 15.4078i 0.0529478i
\(292\) −179.141 −0.613498
\(293\) 59.2551i 0.202236i −0.994874 0.101118i \(-0.967758\pi\)
0.994874 0.101118i \(-0.0322419\pi\)
\(294\) 45.1511 0.153575
\(295\) 15.1428i 0.0513315i
\(296\) 110.472i 0.373215i
\(297\) 20.7764i 0.0699543i
\(298\) 316.833i 1.06320i
\(299\) −186.469 + 25.4934i −0.623641 + 0.0852623i
\(300\) 17.3205 0.0577350
\(301\) 288.655 0.958988
\(302\) −325.786 −1.07876
\(303\) 176.920 0.583894
\(304\) 44.3736i 0.145966i
\(305\) 257.410 0.843968
\(306\) 73.8165i 0.241230i
\(307\) 163.557 0.532760 0.266380 0.963868i \(-0.414172\pi\)
0.266380 + 0.963868i \(0.414172\pi\)
\(308\) −44.2127 −0.143548
\(309\) 308.360i 0.997930i
\(310\) 65.3555i 0.210824i
\(311\) 143.413 0.461134 0.230567 0.973056i \(-0.425942\pi\)
0.230567 + 0.973056i \(0.425942\pi\)
\(312\) 40.0871 0.128484
\(313\) 37.6949i 0.120431i 0.998185 + 0.0602155i \(0.0191788\pi\)
−0.998185 + 0.0602155i \(0.980821\pi\)
\(314\) 15.8735i 0.0505525i
\(315\) 37.0880 0.117740
\(316\) 282.497i 0.893977i
\(317\) −123.519 −0.389650 −0.194825 0.980838i \(-0.562414\pi\)
−0.194825 + 0.980838i \(0.562414\pi\)
\(318\) 44.7267i 0.140650i
\(319\) 41.2837i 0.129416i
\(320\) 17.8885i 0.0559017i
\(321\) 9.44497i 0.0294236i
\(322\) 24.3597 + 178.176i 0.0756511 + 0.553341i
\(323\) 193.011 0.597557
\(324\) 18.0000 0.0555556
\(325\) −40.9137 −0.125888
\(326\) −95.4814 −0.292888
\(327\) 32.8496i 0.100458i
\(328\) −207.629 −0.633015
\(329\) 414.649i 1.26033i
\(330\) 21.9003 0.0663645
\(331\) 139.163 0.420432 0.210216 0.977655i \(-0.432583\pi\)
0.210216 + 0.977655i \(0.432583\pi\)
\(332\) 133.628i 0.402493i
\(333\) 117.173i 0.351871i
\(334\) −40.3784 −0.120893
\(335\) 246.629 0.736206
\(336\) 38.3043i 0.114001i
\(337\) 441.284i 1.30945i −0.755868 0.654724i \(-0.772785\pi\)
0.755868 0.654724i \(-0.227215\pi\)
\(338\) 144.310 0.426953
\(339\) 96.4373i 0.284476i
\(340\) −77.8094 −0.228851
\(341\) 82.6364i 0.242335i
\(342\) 47.0653i 0.137618i
\(343\) 372.820i 1.08694i
\(344\) 147.672i 0.429278i
\(345\) −12.0663 88.2576i −0.0349748 0.255819i
\(346\) 57.6077 0.166496
\(347\) 229.795 0.662233 0.331116 0.943590i \(-0.392575\pi\)
0.331116 + 0.943590i \(0.392575\pi\)
\(348\) −35.7668 −0.102778
\(349\) −521.752 −1.49499 −0.747496 0.664266i \(-0.768744\pi\)
−0.747496 + 0.664266i \(0.768744\pi\)
\(350\) 39.0942i 0.111698i
\(351\) −42.5188 −0.121136
\(352\) 22.6185i 0.0642572i
\(353\) 214.638 0.608040 0.304020 0.952666i \(-0.401671\pi\)
0.304020 + 0.952666i \(0.401671\pi\)
\(354\) −16.5881 −0.0468590
\(355\) 68.2254i 0.192184i
\(356\) 109.797i 0.308419i
\(357\) −166.612 −0.466699
\(358\) 401.235 1.12077
\(359\) 597.409i 1.66409i 0.554707 + 0.832045i \(0.312830\pi\)
−0.554707 + 0.832045i \(0.687170\pi\)
\(360\) 18.9737i 0.0527046i
\(361\) 237.936 0.659104
\(362\) 33.3364i 0.0920896i
\(363\) −181.887 −0.501066
\(364\) 90.4809i 0.248574i
\(365\) 200.286i 0.548729i
\(366\) 281.979i 0.770434i
\(367\) 99.3937i 0.270828i 0.990789 + 0.135414i \(0.0432364\pi\)
−0.990789 + 0.135414i \(0.956764\pi\)
\(368\) −91.1521 + 12.4620i −0.247696 + 0.0338642i
\(369\) 220.224 0.596812
\(370\) −123.511 −0.333814
\(371\) −100.953 −0.272110
\(372\) 71.5933 0.192455
\(373\) 59.2285i 0.158790i 0.996843 + 0.0793948i \(0.0252988\pi\)
−0.996843 + 0.0793948i \(0.974701\pi\)
\(374\) −98.3833 −0.263057
\(375\) 19.3649i 0.0516398i
\(376\) 212.128 0.564170
\(377\) 84.4868 0.224103
\(378\) 40.6279i 0.107481i
\(379\) 127.161i 0.335517i −0.985828 0.167759i \(-0.946347\pi\)
0.985828 0.167759i \(-0.0536529\pi\)
\(380\) 49.6112 0.130556
\(381\) 224.610 0.589528
\(382\) 55.4905i 0.145263i
\(383\) 354.837i 0.926466i 0.886236 + 0.463233i \(0.153311\pi\)
−0.886236 + 0.463233i \(0.846689\pi\)
\(384\) 19.5959 0.0510310
\(385\) 49.4313i 0.128393i
\(386\) −304.161 −0.787983
\(387\) 156.630i 0.404727i
\(388\) 17.7914i 0.0458541i
\(389\) 188.718i 0.485136i 0.970134 + 0.242568i \(0.0779897\pi\)
−0.970134 + 0.242568i \(0.922010\pi\)
\(390\) 44.8188i 0.114920i
\(391\) 54.2058 + 396.482i 0.138634 + 1.01402i
\(392\) −52.1360 −0.133000
\(393\) −337.609 −0.859057
\(394\) −276.374 −0.701457
\(395\) 315.841 0.799597
\(396\) 23.9906i 0.0605822i
\(397\) 110.983 0.279553 0.139777 0.990183i \(-0.455362\pi\)
0.139777 + 0.990183i \(0.455362\pi\)
\(398\) 178.520i 0.448542i
\(399\) 106.231 0.266244
\(400\) −20.0000 −0.0500000
\(401\) 493.947i 1.23179i 0.787829 + 0.615894i \(0.211205\pi\)
−0.787829 + 0.615894i \(0.788795\pi\)
\(402\) 270.169i 0.672061i
\(403\) −169.115 −0.419639
\(404\) −204.289 −0.505667
\(405\) 20.1246i 0.0496904i
\(406\) 80.7294i 0.198841i
\(407\) −156.169 −0.383708
\(408\) 85.2360i 0.208912i
\(409\) 65.1665 0.159331 0.0796656 0.996822i \(-0.474615\pi\)
0.0796656 + 0.996822i \(0.474615\pi\)
\(410\) 232.136i 0.566185i
\(411\) 199.995i 0.486605i
\(412\) 356.064i 0.864233i
\(413\) 37.4411i 0.0906564i
\(414\) 96.6814 13.2180i 0.233530 0.0319275i
\(415\) 149.400 0.360001
\(416\) −46.2886 −0.111271
\(417\) 430.182 1.03161
\(418\) 62.7291 0.150070
\(419\) 330.658i 0.789161i 0.918861 + 0.394580i \(0.129110\pi\)
−0.918861 + 0.394580i \(0.870890\pi\)
\(420\) −42.8256 −0.101966
\(421\) 775.522i 1.84209i −0.389451 0.921047i \(-0.627335\pi\)
0.389451 0.921047i \(-0.372665\pi\)
\(422\) −351.671 −0.833344
\(423\) −224.996 −0.531904
\(424\) 51.6460i 0.121807i
\(425\) 86.9936i 0.204691i
\(426\) 74.7372 0.175439
\(427\) −636.456 −1.49053
\(428\) 10.9061i 0.0254816i
\(429\) 56.6695i 0.132097i
\(430\) 165.102 0.383958
\(431\) 10.8609i 0.0251993i −0.999921 0.0125996i \(-0.995989\pi\)
0.999921 0.0125996i \(-0.00401069\pi\)
\(432\) −20.7846 −0.0481125
\(433\) 693.229i 1.60099i −0.599338 0.800496i \(-0.704570\pi\)
0.599338 0.800496i \(-0.295430\pi\)
\(434\) 161.594i 0.372336i
\(435\) 39.9885i 0.0919276i
\(436\) 37.9315i 0.0869989i
\(437\) −34.5616 252.797i −0.0790883 0.578482i
\(438\) −219.403 −0.500919
\(439\) −631.383 −1.43823 −0.719115 0.694891i \(-0.755453\pi\)
−0.719115 + 0.694891i \(0.755453\pi\)
\(440\) −25.2883 −0.0574734
\(441\) 55.2986 0.125394
\(442\) 201.341i 0.455522i
\(443\) −12.4244 −0.0280460 −0.0140230 0.999902i \(-0.504464\pi\)
−0.0140230 + 0.999902i \(0.504464\pi\)
\(444\) 135.300i 0.304729i
\(445\) 122.757 0.275858
\(446\) 298.493 0.669266
\(447\) 388.040i 0.868098i
\(448\) 44.2300i 0.0987278i
\(449\) −712.745 −1.58740 −0.793702 0.608306i \(-0.791849\pi\)
−0.793702 + 0.608306i \(0.791849\pi\)
\(450\) 21.2132 0.0471405
\(451\) 293.516i 0.650812i
\(452\) 111.356i 0.246363i
\(453\) −399.004 −0.880804
\(454\) 387.067i 0.852571i
\(455\) 101.161 0.222331
\(456\) 54.3464i 0.119181i
\(457\) 345.010i 0.754946i 0.926021 + 0.377473i \(0.123207\pi\)
−0.926021 + 0.377473i \(0.876793\pi\)
\(458\) 517.900i 1.13079i
\(459\) 90.4064i 0.196964i
\(460\) 13.9330 + 101.911i 0.0302891 + 0.221546i
\(461\) −208.968 −0.453293 −0.226646 0.973977i \(-0.572776\pi\)
−0.226646 + 0.973977i \(0.572776\pi\)
\(462\) −54.1492 −0.117206
\(463\) 743.406 1.60563 0.802814 0.596229i \(-0.203335\pi\)
0.802814 + 0.596229i \(0.203335\pi\)
\(464\) 41.2999 0.0890085
\(465\) 80.0438i 0.172137i
\(466\) 329.264 0.706575
\(467\) 409.810i 0.877536i −0.898600 0.438768i \(-0.855415\pi\)
0.898600 0.438768i \(-0.144585\pi\)
\(468\) 49.0965 0.104907
\(469\) −609.799 −1.30021
\(470\) 237.166i 0.504609i
\(471\) 19.4410i 0.0412759i
\(472\) 19.1543 0.0405811
\(473\) 208.757 0.441347
\(474\) 345.986i 0.729929i
\(475\) 55.4670i 0.116773i
\(476\) 192.387 0.404173
\(477\) 54.7788i 0.114840i
\(478\) 146.873 0.307267
\(479\) 219.384i 0.458004i −0.973426 0.229002i \(-0.926454\pi\)
0.973426 0.229002i \(-0.0735462\pi\)
\(480\) 21.9089i 0.0456435i
\(481\) 319.599i 0.664447i
\(482\) 292.170i 0.606162i
\(483\) 29.8344 + 218.220i 0.0617689 + 0.451801i
\(484\) 210.025 0.433936
\(485\) −19.8914 −0.0410132
\(486\) 22.0454 0.0453609
\(487\) 47.9454 0.0984506 0.0492253 0.998788i \(-0.484325\pi\)
0.0492253 + 0.998788i \(0.484325\pi\)
\(488\) 325.601i 0.667216i
\(489\) −116.940 −0.239142
\(490\) 58.2898i 0.118959i
\(491\) −734.556 −1.49604 −0.748020 0.663676i \(-0.768995\pi\)
−0.748020 + 0.663676i \(0.768995\pi\)
\(492\) −254.292 −0.516854
\(493\) 179.641i 0.364384i
\(494\) 128.375i 0.259868i
\(495\) 26.8223 0.0541864
\(496\) −82.6689 −0.166671
\(497\) 168.690i 0.339416i
\(498\) 163.660i 0.328634i
\(499\) −391.502 −0.784574 −0.392287 0.919843i \(-0.628316\pi\)
−0.392287 + 0.919843i \(0.628316\pi\)
\(500\) 22.3607i 0.0447214i
\(501\) −49.4532 −0.0987090
\(502\) 356.776i 0.710708i
\(503\) 336.866i 0.669713i 0.942269 + 0.334856i \(0.108688\pi\)
−0.942269 + 0.334856i \(0.891312\pi\)
\(504\) 46.9131i 0.0930815i
\(505\) 228.403i 0.452282i
\(506\) 17.6170 + 128.858i 0.0348163 + 0.254660i
\(507\) 176.743 0.348605
\(508\) −259.358 −0.510546
\(509\) 345.754 0.679281 0.339641 0.940555i \(-0.389695\pi\)
0.339641 + 0.940555i \(0.389695\pi\)
\(510\) −95.2967 −0.186856
\(511\) 495.215i 0.969109i
\(512\) −22.6274 −0.0441942
\(513\) 57.6430i 0.112365i
\(514\) 228.349 0.444259
\(515\) 398.092 0.772993
\(516\) 180.860i 0.350504i
\(517\) 299.876i 0.580031i
\(518\) 305.386 0.589548
\(519\) 70.5548 0.135944
\(520\) 51.7523i 0.0995236i
\(521\) 217.945i 0.418320i −0.977881 0.209160i \(-0.932927\pi\)
0.977881 0.209160i \(-0.0670729\pi\)
\(522\) −43.8052 −0.0839180
\(523\) 106.244i 0.203144i 0.994828 + 0.101572i \(0.0323873\pi\)
−0.994828 + 0.101572i \(0.967613\pi\)
\(524\) 389.838 0.743965
\(525\) 47.8804i 0.0912008i
\(526\) 383.360i 0.728822i
\(527\) 359.583i 0.682321i
\(528\) 27.7019i 0.0524658i
\(529\) 509.587 141.992i 0.963303 0.268417i
\(530\) −57.7419 −0.108947
\(531\) −20.3162 −0.0382602
\(532\) −122.665 −0.230574
\(533\) 600.678 1.12698
\(534\) 134.473i 0.251823i
\(535\) 12.1934 0.0227914
\(536\) 311.964i 0.582022i
\(537\) 491.410 0.915103
\(538\) 232.939 0.432972
\(539\) 73.7024i 0.136739i
\(540\) 23.2379i 0.0430331i
\(541\) 547.119 1.01131 0.505656 0.862735i \(-0.331251\pi\)
0.505656 + 0.862735i \(0.331251\pi\)
\(542\) −351.766 −0.649014
\(543\) 40.8286i 0.0751908i
\(544\) 98.4220i 0.180923i
\(545\) 42.4087 0.0778142
\(546\) 110.816i 0.202960i
\(547\) −58.9612 −0.107790 −0.0538951 0.998547i \(-0.517164\pi\)
−0.0538951 + 0.998547i \(0.517164\pi\)
\(548\) 230.934i 0.421412i
\(549\) 345.352i 0.629057i
\(550\) 28.2732i 0.0514057i
\(551\) 114.539i 0.207875i
\(552\) −111.638 + 15.2628i −0.202243 + 0.0276500i
\(553\) −780.928 −1.41217
\(554\) 190.242 0.343397
\(555\) −151.270 −0.272558
\(556\) −496.731 −0.893401
\(557\) 1000.83i 1.79682i 0.439157 + 0.898410i \(0.355277\pi\)
−0.439157 + 0.898410i \(0.644723\pi\)
\(558\) 87.6836 0.157139
\(559\) 427.220i 0.764258i
\(560\) 49.4507 0.0883048
\(561\) −120.494 −0.214785
\(562\) 346.202i 0.616019i
\(563\) 308.329i 0.547653i 0.961779 + 0.273827i \(0.0882895\pi\)
−0.961779 + 0.273827i \(0.911711\pi\)
\(564\) 259.802 0.460643
\(565\) 124.500 0.220354
\(566\) 584.343i 1.03241i
\(567\) 49.7588i 0.0877580i
\(568\) −86.2991 −0.151935
\(569\) 871.925i 1.53238i 0.642613 + 0.766191i \(0.277850\pi\)
−0.642613 + 0.766191i \(0.722150\pi\)
\(570\) 60.7611 0.106598
\(571\) 86.2852i 0.151112i 0.997142 + 0.0755562i \(0.0240732\pi\)
−0.997142 + 0.0755562i \(0.975927\pi\)
\(572\) 65.4363i 0.114399i
\(573\) 67.9617i 0.118607i
\(574\) 573.964i 0.999938i
\(575\) 113.940 15.5775i 0.198157 0.0270914i
\(576\) 24.0000 0.0416667
\(577\) 316.305 0.548189 0.274094 0.961703i \(-0.411622\pi\)
0.274094 + 0.961703i \(0.411622\pi\)
\(578\) 19.3967 0.0335582
\(579\) −372.520 −0.643385
\(580\) 46.1747i 0.0796116i
\(581\) −369.398 −0.635796
\(582\) 21.7899i 0.0374397i
\(583\) −73.0097 −0.125231
\(584\) 253.344 0.433809
\(585\) 54.8916i 0.0938317i
\(586\) 83.7994i 0.143002i
\(587\) 2.18581 0.00372369 0.00186185 0.999998i \(-0.499407\pi\)
0.00186185 + 0.999998i \(0.499407\pi\)
\(588\) −63.8533 −0.108594
\(589\) 229.270i 0.389253i
\(590\) 21.4151i 0.0362969i
\(591\) −338.487 −0.572737
\(592\) 156.231i 0.263903i
\(593\) 19.9467 0.0336369 0.0168185 0.999859i \(-0.494646\pi\)
0.0168185 + 0.999859i \(0.494646\pi\)
\(594\) 29.3823i 0.0494652i
\(595\) 215.095i 0.361504i
\(596\) 448.070i 0.751795i
\(597\) 218.641i 0.366233i
\(598\) 263.706 36.0531i 0.440981 0.0602895i
\(599\) −455.182 −0.759903 −0.379952 0.925006i \(-0.624059\pi\)
−0.379952 + 0.925006i \(0.624059\pi\)
\(600\) −24.4949 −0.0408248
\(601\) 374.525 0.623169 0.311584 0.950218i \(-0.399140\pi\)
0.311584 + 0.950218i \(0.399140\pi\)
\(602\) −408.220 −0.678107
\(603\) 330.888i 0.548736i
\(604\) 460.730 0.762799
\(605\) 234.815i 0.388124i
\(606\) −250.202 −0.412875
\(607\) 613.993 1.01152 0.505760 0.862674i \(-0.331212\pi\)
0.505760 + 0.862674i \(0.331212\pi\)
\(608\) 62.7538i 0.103213i
\(609\) 98.8729i 0.162353i
\(610\) −364.033 −0.596776
\(611\) −613.694 −1.00441
\(612\) 104.392i 0.170576i
\(613\) 633.738i 1.03383i 0.856037 + 0.516915i \(0.172920\pi\)
−0.856037 + 0.516915i \(0.827080\pi\)
\(614\) −231.305 −0.376718
\(615\) 284.307i 0.462288i
\(616\) 62.5261 0.101503
\(617\) 209.518i 0.339575i 0.985481 + 0.169788i \(0.0543082\pi\)
−0.985481 + 0.169788i \(0.945692\pi\)
\(618\) 436.087i 0.705643i
\(619\) 82.5461i 0.133354i −0.997775 0.0666770i \(-0.978760\pi\)
0.997775 0.0666770i \(-0.0212397\pi\)
\(620\) 92.4266i 0.149075i
\(621\) 118.410 16.1887i 0.190676 0.0260687i
\(622\) −202.816 −0.326071
\(623\) −303.521 −0.487192
\(624\) −56.6918 −0.0908522
\(625\) 25.0000 0.0400000
\(626\) 53.3086i 0.0851575i
\(627\) 76.8271 0.122531
\(628\) 22.4485i 0.0357460i
\(629\) 679.553 1.08037
\(630\) −52.4504 −0.0832546
\(631\) 382.762i 0.606596i −0.952896 0.303298i \(-0.901912\pi\)
0.952896 0.303298i \(-0.0980877\pi\)
\(632\) 399.511i 0.632137i
\(633\) −430.707 −0.680422
\(634\) 174.682 0.275524
\(635\) 289.971i 0.456646i
\(636\) 63.2531i 0.0994546i
\(637\) 150.831 0.236784
\(638\) 58.3840i 0.0915109i
\(639\) 91.5340 0.143246
\(640\) 25.2982i 0.0395285i
\(641\) 336.338i 0.524708i −0.964972 0.262354i \(-0.915501\pi\)
0.964972 0.262354i \(-0.0844988\pi\)
\(642\) 13.3572i 0.0208056i
\(643\) 135.912i 0.211371i −0.994400 0.105686i \(-0.966296\pi\)
0.994400 0.105686i \(-0.0337037\pi\)
\(644\) −34.4498 251.979i −0.0534934 0.391271i
\(645\) 202.208 0.313501
\(646\) −272.959 −0.422537
\(647\) −586.820 −0.906986 −0.453493 0.891260i \(-0.649822\pi\)
−0.453493 + 0.891260i \(0.649822\pi\)
\(648\) −25.4558 −0.0392837
\(649\) 27.0776i 0.0417220i
\(650\) 57.8608 0.0890166
\(651\) 197.911i 0.304011i
\(652\) 135.031 0.207103
\(653\) −99.3991 −0.152219 −0.0761095 0.997099i \(-0.524250\pi\)
−0.0761095 + 0.997099i \(0.524250\pi\)
\(654\) 46.4564i 0.0710343i
\(655\) 435.852i 0.665423i
\(656\) 293.631 0.447609
\(657\) −268.712 −0.408999
\(658\) 586.402i 0.891188i
\(659\) 838.897i 1.27299i −0.771283 0.636493i \(-0.780385\pi\)
0.771283 0.636493i \(-0.219615\pi\)
\(660\) −30.9717 −0.0469268
\(661\) 1079.24i 1.63274i −0.577529 0.816370i \(-0.695983\pi\)
0.577529 0.816370i \(-0.304017\pi\)
\(662\) −196.806 −0.297290
\(663\) 246.591i 0.371932i
\(664\) 188.978i 0.284606i
\(665\) 137.144i 0.206232i
\(666\) 165.708i 0.248810i
\(667\) −235.286 + 32.1676i −0.352752 + 0.0482272i
\(668\) 57.1037 0.0854845
\(669\) 365.577 0.546453
\(670\) −348.786 −0.520576
\(671\) −460.289 −0.685974
\(672\) 54.1705i 0.0806109i
\(673\) 175.116 0.260202 0.130101 0.991501i \(-0.458470\pi\)
0.130101 + 0.991501i \(0.458470\pi\)
\(674\) 624.070i 0.925919i
\(675\) 25.9808 0.0384900
\(676\) −204.085 −0.301901
\(677\) 708.732i 1.04687i −0.852065 0.523435i \(-0.824650\pi\)
0.852065 0.523435i \(-0.175350\pi\)
\(678\) 136.383i 0.201155i
\(679\) 49.1822 0.0724332
\(680\) 110.039 0.161822
\(681\) 474.059i 0.696121i
\(682\) 116.865i 0.171357i
\(683\) 1323.41 1.93764 0.968819 0.247768i \(-0.0796970\pi\)
0.968819 + 0.247768i \(0.0796970\pi\)
\(684\) 66.5604i 0.0973106i
\(685\) 258.192 0.376923
\(686\) 527.247i 0.768581i
\(687\) 634.295i 0.923282i
\(688\) 208.839i 0.303546i
\(689\) 149.414i 0.216856i
\(690\) 17.0643 + 124.815i 0.0247309 + 0.180891i
\(691\) 1044.51 1.51159 0.755794 0.654809i \(-0.227251\pi\)
0.755794 + 0.654809i \(0.227251\pi\)
\(692\) −81.4696 −0.117731
\(693\) −66.3190 −0.0956984
\(694\) −324.979 −0.468269
\(695\) 555.362i 0.799082i
\(696\) 50.5819 0.0726751
\(697\) 1277.20i 1.83243i
\(698\) 737.869 1.05712
\(699\) 403.265 0.576916
\(700\) 55.2876i 0.0789822i
\(701\) 745.468i 1.06344i −0.846922 0.531718i \(-0.821547\pi\)
0.846922 0.531718i \(-0.178453\pi\)
\(702\) 60.1307 0.0856562
\(703\) −433.282 −0.616333
\(704\) 31.9874i 0.0454367i
\(705\) 290.468i 0.412011i
\(706\) −303.544 −0.429949
\(707\) 564.733i 0.798774i
\(708\) 23.4591 0.0331343
\(709\) 831.513i 1.17280i −0.810023 0.586398i \(-0.800545\pi\)
0.810023 0.586398i \(-0.199455\pi\)
\(710\) 96.4853i 0.135895i
\(711\) 423.745i 0.595984i
\(712\) 155.277i 0.218085i
\(713\) 470.965 64.3889i 0.660540 0.0903070i
\(714\) 235.624 0.330006
\(715\) 73.1600 0.102322
\(716\) −567.431 −0.792502
\(717\) 179.883 0.250882
\(718\) 844.863i 1.17669i
\(719\) 1233.84 1.71605 0.858027 0.513605i \(-0.171690\pi\)
0.858027 + 0.513605i \(0.171690\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) −984.295 −1.36518
\(722\) −336.493 −0.466057
\(723\) 357.834i 0.494929i
\(724\) 47.1448i 0.0651172i
\(725\) −51.6249 −0.0712068
\(726\) 257.227 0.354307
\(727\) 250.846i 0.345042i −0.985006 0.172521i \(-0.944809\pi\)
0.985006 0.172521i \(-0.0551913\pi\)
\(728\) 127.959i 0.175768i
\(729\) 27.0000 0.0370370
\(730\) 283.247i 0.388010i
\(731\) −908.384 −1.24266
\(732\) 398.778i 0.544779i
\(733\) 1346.25i 1.83662i −0.395857 0.918312i \(-0.629552\pi\)
0.395857 0.918312i \(-0.370448\pi\)
\(734\) 140.564i 0.191504i
\(735\) 71.3901i 0.0971294i
\(736\) 128.908 17.6240i 0.175147 0.0239456i
\(737\) −441.010 −0.598385
\(738\) −311.443 −0.422010
\(739\) −192.468 −0.260444 −0.130222 0.991485i \(-0.541569\pi\)
−0.130222 + 0.991485i \(0.541569\pi\)
\(740\) 174.671 0.236042
\(741\) 157.226i 0.212181i
\(742\) 142.769 0.192411
\(743\) 1291.03i 1.73759i −0.495171 0.868796i \(-0.664894\pi\)
0.495171 0.868796i \(-0.335106\pi\)
\(744\) −101.248 −0.136086
\(745\) −500.957 −0.672426
\(746\) 83.7617i 0.112281i
\(747\) 200.442i 0.268329i
\(748\) 139.135 0.186009
\(749\) −30.1486 −0.0402518
\(750\) 27.3861i 0.0365148i
\(751\) 43.3403i 0.0577101i 0.999584 + 0.0288550i \(0.00918612\pi\)
−0.999584 + 0.0288550i \(0.990814\pi\)
\(752\) −299.994 −0.398928
\(753\) 436.959i 0.580291i
\(754\) −119.482 −0.158465
\(755\) 515.112i 0.682268i
\(756\) 57.4565i 0.0760007i
\(757\) 1237.39i 1.63460i 0.576211 + 0.817301i \(0.304531\pi\)
−0.576211 + 0.817301i \(0.695469\pi\)
\(758\) 179.833i 0.237247i
\(759\) 21.5764 + 157.818i 0.0284274 + 0.207929i
\(760\) −70.1609 −0.0923169
\(761\) −505.115 −0.663751 −0.331876 0.943323i \(-0.607681\pi\)
−0.331876 + 0.943323i \(0.607681\pi\)
\(762\) −317.647 −0.416859
\(763\) −104.857 −0.137427
\(764\) 78.4754i 0.102717i
\(765\) −116.714 −0.152568
\(766\) 501.815i 0.655110i
\(767\) −55.4141 −0.0722478
\(768\) −27.7128 −0.0360844
\(769\) 1237.03i 1.60862i −0.594208 0.804311i \(-0.702534\pi\)
0.594208 0.804311i \(-0.297466\pi\)
\(770\) 69.9064i 0.0907875i
\(771\) 279.669 0.362736
\(772\) 430.149 0.557188
\(773\) 1016.69i 1.31526i 0.753342 + 0.657629i \(0.228441\pi\)
−0.753342 + 0.657629i \(0.771559\pi\)
\(774\) 221.508i 0.286186i
\(775\) 103.336 0.133337
\(776\) 25.1608i 0.0324238i
\(777\) 374.020 0.481364
\(778\) 266.887i 0.343043i
\(779\) 814.343i 1.04537i
\(780\) 63.3833i 0.0812607i
\(781\) 121.997i 0.156207i
\(782\) −76.6586 560.711i −0.0980290 0.717021i
\(783\) −53.6502 −0.0685188
\(784\) 73.7314 0.0940452
\(785\) 25.0982 0.0319722
\(786\) 477.452 0.607445
\(787\) 654.021i 0.831030i −0.909586 0.415515i \(-0.863601\pi\)
0.909586 0.415515i \(-0.136399\pi\)
\(788\) 390.852 0.496005
\(789\) 469.519i 0.595081i
\(790\) −446.666 −0.565401
\(791\) −307.831 −0.389167
\(792\)