Properties

Label 690.3.b.a.599.5
Level $690$
Weight $3$
Character 690.599
Analytic conductor $18.801$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $4$

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.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.8011382409\)
Analytic rank: \(0\)
Dimension: \(88\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 599.5
Character \(\chi\) \(=\) 690.599
Dual form 690.3.b.a.599.6

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +(-2.79936 - 1.07869i) q^{3} +2.00000 q^{4} +(4.72534 + 1.63438i) q^{5} +(3.95890 + 1.52550i) q^{6} +7.69411i q^{7} -2.82843 q^{8} +(6.67285 + 6.03929i) q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +(-2.79936 - 1.07869i) q^{3} +2.00000 q^{4} +(4.72534 + 1.63438i) q^{5} +(3.95890 + 1.52550i) q^{6} +7.69411i q^{7} -2.82843 q^{8} +(6.67285 + 6.03929i) q^{9} +(-6.68264 - 2.31136i) q^{10} -16.6679i q^{11} +(-5.59872 - 2.15738i) q^{12} -13.7877i q^{13} -10.8811i q^{14} +(-11.4649 - 9.67239i) q^{15} +4.00000 q^{16} -26.8740 q^{17} +(-9.43684 - 8.54085i) q^{18} +31.7201 q^{19} +(9.45067 + 3.26875i) q^{20} +(8.29957 - 21.5386i) q^{21} +23.5720i q^{22} -4.79583 q^{23} +(7.91779 + 3.05100i) q^{24} +(19.6576 + 15.4460i) q^{25} +19.4987i q^{26} +(-12.1652 - 24.1041i) q^{27} +15.3882i q^{28} +26.0495i q^{29} +(16.2139 + 13.6788i) q^{30} -7.68297 q^{31} -5.65685 q^{32} +(-17.9795 + 46.6596i) q^{33} +38.0055 q^{34} +(-12.5751 + 36.3573i) q^{35} +(13.3457 + 12.0786i) q^{36} +39.6223i q^{37} -44.8590 q^{38} +(-14.8726 + 38.5967i) q^{39} +(-13.3653 - 4.62272i) q^{40} -64.5050i q^{41} +(-11.7374 + 30.4602i) q^{42} -58.0405i q^{43} -33.3359i q^{44} +(21.6610 + 39.4436i) q^{45} +6.78233 q^{46} +72.2219 q^{47} +(-11.1974 - 4.31476i) q^{48} -10.1994 q^{49} +(-27.8001 - 21.8439i) q^{50} +(75.2299 + 28.9887i) q^{51} -27.5753i q^{52} +20.7097 q^{53} +(17.2042 + 34.0884i) q^{54} +(27.2417 - 78.7616i) q^{55} -21.7622i q^{56} +(-88.7961 - 34.2162i) q^{57} -36.8396i q^{58} +30.3283i q^{59} +(-22.9299 - 19.3448i) q^{60} -7.15931 q^{61} +10.8654 q^{62} +(-46.4670 + 51.3417i) q^{63} +8.00000 q^{64} +(22.5342 - 65.1514i) q^{65} +(25.4269 - 65.9866i) q^{66} -88.3837i q^{67} -53.7479 q^{68} +(13.4253 + 5.17322i) q^{69} +(17.7839 - 51.4170i) q^{70} -71.2117i q^{71} +(-18.8737 - 17.0817i) q^{72} +28.2401i q^{73} -56.0344i q^{74} +(-38.3674 - 64.4433i) q^{75} +63.4402 q^{76} +128.245 q^{77} +(21.0331 - 54.5839i) q^{78} -23.1310 q^{79} +(18.9013 + 6.53751i) q^{80} +(8.05390 + 80.5986i) q^{81} +91.2238i q^{82} +139.074 q^{83} +(16.5991 - 43.0772i) q^{84} +(-126.989 - 43.9222i) q^{85} +82.0817i q^{86} +(28.0994 - 72.9220i) q^{87} +47.1440i q^{88} -44.9943i q^{89} +(-30.6333 - 55.7817i) q^{90} +106.084 q^{91} -9.59166 q^{92} +(21.5074 + 8.28755i) q^{93} -102.137 q^{94} +(149.888 + 51.8426i) q^{95} +(15.8356 + 6.10200i) q^{96} +59.4001i q^{97} +14.4241 q^{98} +(100.663 - 111.223i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88q + 176q^{4} + 8q^{9} + O(q^{10}) \) \( 88q + 176q^{4} + 8q^{9} + 32q^{10} - 12q^{15} + 352q^{16} - 16q^{19} - 176q^{21} + 72q^{25} - 72q^{30} + 32q^{31} + 160q^{34} + 16q^{36} + 144q^{39} + 64q^{40} + 92q^{45} - 360q^{49} + 48q^{51} - 144q^{54} + 16q^{55} - 24q^{60} + 208q^{61} + 704q^{64} + 512q^{66} + 304q^{70} + 536q^{75} - 32q^{76} + 448q^{79} - 24q^{81} - 352q^{84} - 96q^{85} + 32q^{90} - 64q^{91} + 160q^{94} + 296q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −0.707107
\(3\) −2.79936 1.07869i −0.933121 0.359564i
\(4\) 2.00000 0.500000
\(5\) 4.72534 + 1.63438i 0.945067 + 0.326875i
\(6\) 3.95890 + 1.52550i 0.659816 + 0.254250i
\(7\) 7.69411i 1.09916i 0.835441 + 0.549580i \(0.185212\pi\)
−0.835441 + 0.549580i \(0.814788\pi\)
\(8\) −2.82843 −0.353553
\(9\) 6.67285 + 6.03929i 0.741428 + 0.671032i
\(10\) −6.68264 2.31136i −0.668264 0.231136i
\(11\) 16.6679i 1.51527i −0.652680 0.757633i \(-0.726356\pi\)
0.652680 0.757633i \(-0.273644\pi\)
\(12\) −5.59872 2.15738i −0.466560 0.179782i
\(13\) 13.7877i 1.06059i −0.847813 0.530295i \(-0.822081\pi\)
0.847813 0.530295i \(-0.177919\pi\)
\(14\) 10.8811i 0.777223i
\(15\) −11.4649 9.67239i −0.764329 0.644826i
\(16\) 4.00000 0.250000
\(17\) −26.8740 −1.58082 −0.790411 0.612578i \(-0.790133\pi\)
−0.790411 + 0.612578i \(0.790133\pi\)
\(18\) −9.43684 8.54085i −0.524269 0.474492i
\(19\) 31.7201 1.66948 0.834740 0.550644i \(-0.185618\pi\)
0.834740 + 0.550644i \(0.185618\pi\)
\(20\) 9.45067 + 3.26875i 0.472534 + 0.163438i
\(21\) 8.29957 21.5386i 0.395218 1.02565i
\(22\) 23.5720i 1.07146i
\(23\) −4.79583 −0.208514
\(24\) 7.91779 + 3.05100i 0.329908 + 0.127125i
\(25\) 19.6576 + 15.4460i 0.786305 + 0.617839i
\(26\) 19.4987i 0.749950i
\(27\) −12.1652 24.1041i −0.450563 0.892745i
\(28\) 15.3882i 0.549580i
\(29\) 26.0495i 0.898259i 0.893467 + 0.449129i \(0.148266\pi\)
−0.893467 + 0.449129i \(0.851734\pi\)
\(30\) 16.2139 + 13.6788i 0.540462 + 0.455961i
\(31\) −7.68297 −0.247838 −0.123919 0.992292i \(-0.539546\pi\)
−0.123919 + 0.992292i \(0.539546\pi\)
\(32\) −5.65685 −0.176777
\(33\) −17.9795 + 46.6596i −0.544835 + 1.41393i
\(34\) 38.0055 1.11781
\(35\) −12.5751 + 36.3573i −0.359288 + 1.03878i
\(36\) 13.3457 + 12.0786i 0.370714 + 0.335516i
\(37\) 39.6223i 1.07087i 0.844575 + 0.535437i \(0.179853\pi\)
−0.844575 + 0.535437i \(0.820147\pi\)
\(38\) −44.8590 −1.18050
\(39\) −14.8726 + 38.5967i −0.381349 + 0.989658i
\(40\) −13.3653 4.62272i −0.334132 0.115568i
\(41\) 64.5050i 1.57329i −0.617404 0.786646i \(-0.711816\pi\)
0.617404 0.786646i \(-0.288184\pi\)
\(42\) −11.7374 + 30.4602i −0.279461 + 0.725243i
\(43\) 58.0405i 1.34978i −0.737919 0.674890i \(-0.764191\pi\)
0.737919 0.674890i \(-0.235809\pi\)
\(44\) 33.3359i 0.757633i
\(45\) 21.6610 + 39.4436i 0.481355 + 0.876526i
\(46\) 6.78233 0.147442
\(47\) 72.2219 1.53664 0.768318 0.640068i \(-0.221094\pi\)
0.768318 + 0.640068i \(0.221094\pi\)
\(48\) −11.1974 4.31476i −0.233280 0.0898909i
\(49\) −10.1994 −0.208151
\(50\) −27.8001 21.8439i −0.556001 0.436878i
\(51\) 75.2299 + 28.9887i 1.47510 + 0.568406i
\(52\) 27.5753i 0.530295i
\(53\) 20.7097 0.390749 0.195375 0.980729i \(-0.437408\pi\)
0.195375 + 0.980729i \(0.437408\pi\)
\(54\) 17.2042 + 34.0884i 0.318596 + 0.631266i
\(55\) 27.2417 78.7616i 0.495303 1.43203i
\(56\) 21.7622i 0.388611i
\(57\) −88.7961 34.2162i −1.55783 0.600284i
\(58\) 36.8396i 0.635165i
\(59\) 30.3283i 0.514039i 0.966406 + 0.257019i \(0.0827405\pi\)
−0.966406 + 0.257019i \(0.917260\pi\)
\(60\) −22.9299 19.3448i −0.382165 0.322413i
\(61\) −7.15931 −0.117366 −0.0586829 0.998277i \(-0.518690\pi\)
−0.0586829 + 0.998277i \(0.518690\pi\)
\(62\) 10.8654 0.175248
\(63\) −46.4670 + 51.3417i −0.737571 + 0.814947i
\(64\) 8.00000 0.125000
\(65\) 22.5342 65.1514i 0.346681 1.00233i
\(66\) 25.4269 65.9866i 0.385256 0.999797i
\(67\) 88.3837i 1.31916i −0.751635 0.659580i \(-0.770734\pi\)
0.751635 0.659580i \(-0.229266\pi\)
\(68\) −53.7479 −0.790411
\(69\) 13.4253 + 5.17322i 0.194569 + 0.0749742i
\(70\) 17.7839 51.4170i 0.254055 0.734528i
\(71\) 71.2117i 1.00298i −0.865163 0.501491i \(-0.832785\pi\)
0.865163 0.501491i \(-0.167215\pi\)
\(72\) −18.8737 17.0817i −0.262134 0.237246i
\(73\) 28.2401i 0.386850i 0.981115 + 0.193425i \(0.0619596\pi\)
−0.981115 + 0.193425i \(0.938040\pi\)
\(74\) 56.0344i 0.757222i
\(75\) −38.3674 64.4433i −0.511565 0.859245i
\(76\) 63.4402 0.834740
\(77\) 128.245 1.66552
\(78\) 21.0331 54.5839i 0.269655 0.699794i
\(79\) −23.1310 −0.292798 −0.146399 0.989226i \(-0.546768\pi\)
−0.146399 + 0.989226i \(0.546768\pi\)
\(80\) 18.9013 + 6.53751i 0.236267 + 0.0817189i
\(81\) 8.05390 + 80.5986i 0.0994309 + 0.995044i
\(82\) 91.2238i 1.11249i
\(83\) 139.074 1.67559 0.837793 0.545988i \(-0.183845\pi\)
0.837793 + 0.545988i \(0.183845\pi\)
\(84\) 16.5991 43.0772i 0.197609 0.512824i
\(85\) −126.989 43.9222i −1.49398 0.516732i
\(86\) 82.0817i 0.954438i
\(87\) 28.0994 72.9220i 0.322981 0.838184i
\(88\) 47.1440i 0.535728i
\(89\) 44.9943i 0.505554i −0.967525 0.252777i \(-0.918656\pi\)
0.967525 0.252777i \(-0.0813440\pi\)
\(90\) −30.6333 55.7817i −0.340370 0.619797i
\(91\) 106.084 1.16576
\(92\) −9.59166 −0.104257
\(93\) 21.5074 + 8.28755i 0.231262 + 0.0891134i
\(94\) −102.137 −1.08657
\(95\) 149.888 + 51.8426i 1.57777 + 0.545712i
\(96\) 15.8356 + 6.10200i 0.164954 + 0.0635625i
\(97\) 59.4001i 0.612372i 0.951972 + 0.306186i \(0.0990530\pi\)
−0.951972 + 0.306186i \(0.900947\pi\)
\(98\) 14.4241 0.147185
\(99\) 100.663 111.223i 1.01679 1.12346i
\(100\) 39.3152 + 30.8919i 0.393152 + 0.308919i
\(101\) 36.3941i 0.360338i −0.983636 0.180169i \(-0.942336\pi\)
0.983636 0.180169i \(-0.0576644\pi\)
\(102\) −106.391 40.9962i −1.04305 0.401924i
\(103\) 4.70396i 0.0456696i 0.999739 + 0.0228348i \(0.00726917\pi\)
−0.999739 + 0.0228348i \(0.992731\pi\)
\(104\) 38.9974i 0.374975i
\(105\) 74.4205 88.2126i 0.708767 0.840120i
\(106\) −29.2879 −0.276301
\(107\) 143.867 1.34455 0.672276 0.740301i \(-0.265317\pi\)
0.672276 + 0.740301i \(0.265317\pi\)
\(108\) −24.3304 48.2082i −0.225281 0.446372i
\(109\) 101.340 0.929721 0.464860 0.885384i \(-0.346105\pi\)
0.464860 + 0.885384i \(0.346105\pi\)
\(110\) −38.5256 + 111.386i −0.350232 + 1.01260i
\(111\) 42.7402 110.917i 0.385047 0.999254i
\(112\) 30.7765i 0.274790i
\(113\) 44.1938 0.391096 0.195548 0.980694i \(-0.437351\pi\)
0.195548 + 0.980694i \(0.437351\pi\)
\(114\) 125.577 + 48.3890i 1.10155 + 0.424465i
\(115\) −22.6619 7.83820i −0.197060 0.0681582i
\(116\) 52.0990i 0.449129i
\(117\) 83.2677 92.0030i 0.711690 0.786351i
\(118\) 42.8907i 0.363480i
\(119\) 206.771i 1.73757i
\(120\) 32.4277 + 27.3577i 0.270231 + 0.227980i
\(121\) −156.820 −1.29603
\(122\) 10.1248 0.0829902
\(123\) −69.5810 + 180.573i −0.565699 + 1.46807i
\(124\) −15.3659 −0.123919
\(125\) 67.6443 + 105.115i 0.541155 + 0.840923i
\(126\) 65.7143 72.6081i 0.521542 0.576255i
\(127\) 221.597i 1.74486i −0.488739 0.872430i \(-0.662543\pi\)
0.488739 0.872430i \(-0.337457\pi\)
\(128\) −11.3137 −0.0883883
\(129\) −62.6078 + 162.476i −0.485332 + 1.25951i
\(130\) −31.8682 + 92.1379i −0.245140 + 0.708753i
\(131\) 100.251i 0.765273i −0.923899 0.382637i \(-0.875016\pi\)
0.923899 0.382637i \(-0.124984\pi\)
\(132\) −35.9591 + 93.3191i −0.272417 + 0.706963i
\(133\) 244.058i 1.83502i
\(134\) 124.993i 0.932787i
\(135\) −18.0894 133.783i −0.133996 0.990982i
\(136\) 76.0110 0.558905
\(137\) −154.818 −1.13006 −0.565030 0.825070i \(-0.691136\pi\)
−0.565030 + 0.825070i \(0.691136\pi\)
\(138\) −18.9862 7.31604i −0.137581 0.0530148i
\(139\) 188.794 1.35823 0.679114 0.734033i \(-0.262364\pi\)
0.679114 + 0.734033i \(0.262364\pi\)
\(140\) −25.1502 + 72.7146i −0.179644 + 0.519390i
\(141\) −202.175 77.9051i −1.43387 0.552519i
\(142\) 100.709i 0.709215i
\(143\) −229.812 −1.60708
\(144\) 26.6914 + 24.1572i 0.185357 + 0.167758i
\(145\) −42.5747 + 123.093i −0.293619 + 0.848915i
\(146\) 39.9375i 0.273544i
\(147\) 28.5518 + 11.0020i 0.194230 + 0.0748435i
\(148\) 79.2446i 0.535437i
\(149\) 47.2917i 0.317394i −0.987327 0.158697i \(-0.949271\pi\)
0.987327 0.158697i \(-0.0507293\pi\)
\(150\) 54.2596 + 91.1367i 0.361731 + 0.607578i
\(151\) 31.0861 0.205868 0.102934 0.994688i \(-0.467177\pi\)
0.102934 + 0.994688i \(0.467177\pi\)
\(152\) −89.7180 −0.590250
\(153\) −179.326 162.300i −1.17206 1.06078i
\(154\) −181.366 −1.17770
\(155\) −36.3046 12.5569i −0.234223 0.0810120i
\(156\) −29.7453 + 77.1933i −0.190675 + 0.494829i
\(157\) 47.1835i 0.300532i 0.988646 + 0.150266i \(0.0480130\pi\)
−0.988646 + 0.150266i \(0.951987\pi\)
\(158\) 32.7122 0.207039
\(159\) −57.9739 22.3394i −0.364616 0.140499i
\(160\) −26.7305 9.24543i −0.167066 0.0577840i
\(161\) 36.8997i 0.229191i
\(162\) −11.3899 113.984i −0.0703083 0.703603i
\(163\) 240.131i 1.47320i −0.676331 0.736598i \(-0.736431\pi\)
0.676331 0.736598i \(-0.263569\pi\)
\(164\) 129.010i 0.786646i
\(165\) −161.219 + 191.097i −0.977083 + 1.15816i
\(166\) −196.680 −1.18482
\(167\) 81.2198 0.486346 0.243173 0.969983i \(-0.421812\pi\)
0.243173 + 0.969983i \(0.421812\pi\)
\(168\) −23.4747 + 60.9204i −0.139731 + 0.362621i
\(169\) −21.0997 −0.124850
\(170\) 179.589 + 62.1154i 1.05641 + 0.365384i
\(171\) 211.664 + 191.567i 1.23780 + 1.12028i
\(172\) 116.081i 0.674890i
\(173\) −31.4683 −0.181898 −0.0909488 0.995856i \(-0.528990\pi\)
−0.0909488 + 0.995856i \(0.528990\pi\)
\(174\) −39.7385 + 103.127i −0.228382 + 0.592685i
\(175\) −118.843 + 151.248i −0.679103 + 0.864274i
\(176\) 66.6717i 0.378817i
\(177\) 32.7149 84.8999i 0.184830 0.479660i
\(178\) 63.6316i 0.357481i
\(179\) 100.597i 0.561996i 0.959708 + 0.280998i \(0.0906653\pi\)
−0.959708 + 0.280998i \(0.909335\pi\)
\(180\) 43.3220 + 78.8873i 0.240678 + 0.438263i
\(181\) 79.4785 0.439108 0.219554 0.975600i \(-0.429540\pi\)
0.219554 + 0.975600i \(0.429540\pi\)
\(182\) −150.025 −0.824315
\(183\) 20.0415 + 7.72269i 0.109516 + 0.0422005i
\(184\) 13.5647 0.0737210
\(185\) −64.7578 + 187.229i −0.350042 + 1.01205i
\(186\) −30.4161 11.7204i −0.163527 0.0630127i
\(187\) 447.933i 2.39537i
\(188\) 144.444 0.768318
\(189\) 185.460 93.6004i 0.981269 0.495240i
\(190\) −211.974 73.3166i −1.11565 0.385877i
\(191\) 181.244i 0.948921i 0.880277 + 0.474461i \(0.157357\pi\)
−0.880277 + 0.474461i \(0.842643\pi\)
\(192\) −22.3949 8.62953i −0.116640 0.0449455i
\(193\) 180.172i 0.933532i −0.884381 0.466766i \(-0.845419\pi\)
0.884381 0.466766i \(-0.154581\pi\)
\(194\) 84.0044i 0.433013i
\(195\) −133.360 + 158.075i −0.683896 + 0.810640i
\(196\) −20.3988 −0.104075
\(197\) 273.165 1.38663 0.693313 0.720637i \(-0.256150\pi\)
0.693313 + 0.720637i \(0.256150\pi\)
\(198\) −142.358 + 157.293i −0.718981 + 0.794407i
\(199\) −1.98578 −0.00997879 −0.00498939 0.999988i \(-0.501588\pi\)
−0.00498939 + 0.999988i \(0.501588\pi\)
\(200\) −55.6001 43.6878i −0.278001 0.218439i
\(201\) −95.3387 + 247.418i −0.474322 + 1.23093i
\(202\) 51.4691i 0.254797i
\(203\) −200.428 −0.987329
\(204\) 150.460 + 57.9774i 0.737548 + 0.284203i
\(205\) 105.426 304.808i 0.514271 1.48687i
\(206\) 6.65241i 0.0322933i
\(207\) −32.0019 28.9634i −0.154598 0.139920i
\(208\) 55.1507i 0.265147i
\(209\) 528.709i 2.52971i
\(210\) −105.246 + 124.751i −0.501174 + 0.594054i
\(211\) −216.942 −1.02816 −0.514081 0.857741i \(-0.671867\pi\)
−0.514081 + 0.857741i \(0.671867\pi\)
\(212\) 41.4194 0.195375
\(213\) −76.8154 + 199.347i −0.360636 + 0.935903i
\(214\) −203.459 −0.950742
\(215\) 94.8601 274.261i 0.441210 1.27563i
\(216\) 34.4084 + 68.1767i 0.159298 + 0.315633i
\(217\) 59.1136i 0.272413i
\(218\) −143.316 −0.657412
\(219\) 30.4623 79.0541i 0.139097 0.360978i
\(220\) 54.4834 157.523i 0.247652 0.716015i
\(221\) 370.529i 1.67660i
\(222\) −60.4438 + 156.861i −0.272269 + 0.706579i
\(223\) 256.080i 1.14834i 0.818736 + 0.574171i \(0.194675\pi\)
−0.818736 + 0.574171i \(0.805325\pi\)
\(224\) 43.5245i 0.194306i
\(225\) 37.8897 + 221.787i 0.168399 + 0.985719i
\(226\) −62.4995 −0.276547
\(227\) 215.303 0.948473 0.474237 0.880397i \(-0.342724\pi\)
0.474237 + 0.880397i \(0.342724\pi\)
\(228\) −177.592 68.4324i −0.778913 0.300142i
\(229\) −182.701 −0.797823 −0.398911 0.916989i \(-0.630612\pi\)
−0.398911 + 0.916989i \(0.630612\pi\)
\(230\) 32.0488 + 11.0849i 0.139343 + 0.0481952i
\(231\) −359.004 138.337i −1.55413 0.598860i
\(232\) 73.6791i 0.317582i
\(233\) 135.492 0.581512 0.290756 0.956797i \(-0.406093\pi\)
0.290756 + 0.956797i \(0.406093\pi\)
\(234\) −117.758 + 130.112i −0.503241 + 0.556034i
\(235\) 341.273 + 118.038i 1.45222 + 0.502289i
\(236\) 60.6566i 0.257019i
\(237\) 64.7521 + 24.9512i 0.273216 + 0.105279i
\(238\) 292.419i 1.22865i
\(239\) 301.405i 1.26111i 0.776145 + 0.630555i \(0.217173\pi\)
−0.776145 + 0.630555i \(0.782827\pi\)
\(240\) −45.8598 38.6896i −0.191082 0.161207i
\(241\) −88.1708 −0.365854 −0.182927 0.983127i \(-0.558557\pi\)
−0.182927 + 0.983127i \(0.558557\pi\)
\(242\) 221.777 0.916434
\(243\) 64.3952 234.312i 0.265001 0.964248i
\(244\) −14.3186 −0.0586829
\(245\) −48.1956 16.6697i −0.196717 0.0680394i
\(246\) 98.4023 255.369i 0.400009 1.03808i
\(247\) 437.346i 1.77063i
\(248\) 21.7307 0.0876238
\(249\) −389.318 150.018i −1.56352 0.602480i
\(250\) −95.6636 148.656i −0.382654 0.594622i
\(251\) 176.705i 0.704003i −0.936000 0.352001i \(-0.885501\pi\)
0.936000 0.352001i \(-0.114499\pi\)
\(252\) −92.9340 + 102.683i −0.368786 + 0.407474i
\(253\) 79.9366i 0.315955i
\(254\) 313.386i 1.23380i
\(255\) 308.108 + 259.935i 1.20827 + 1.01935i
\(256\) 16.0000 0.0625000
\(257\) 257.023 1.00009 0.500044 0.866000i \(-0.333317\pi\)
0.500044 + 0.866000i \(0.333317\pi\)
\(258\) 88.5408 229.776i 0.343181 0.890606i
\(259\) −304.859 −1.17706
\(260\) 45.0685 130.303i 0.173340 0.501164i
\(261\) −157.321 + 173.824i −0.602761 + 0.665994i
\(262\) 141.776i 0.541130i
\(263\) 64.1622 0.243963 0.121981 0.992532i \(-0.461075\pi\)
0.121981 + 0.992532i \(0.461075\pi\)
\(264\) 50.8538 131.973i 0.192628 0.499898i
\(265\) 97.8603 + 33.8475i 0.369284 + 0.127726i
\(266\) 345.150i 1.29756i
\(267\) −48.5350 + 125.955i −0.181779 + 0.471743i
\(268\) 176.767i 0.659580i
\(269\) 417.123i 1.55064i 0.631568 + 0.775321i \(0.282412\pi\)
−0.631568 + 0.775321i \(0.717588\pi\)
\(270\) 25.5823 + 189.197i 0.0947494 + 0.700730i
\(271\) −375.668 −1.38623 −0.693115 0.720827i \(-0.743762\pi\)
−0.693115 + 0.720827i \(0.743762\pi\)
\(272\) −107.496 −0.395205
\(273\) −296.967 114.432i −1.08779 0.419164i
\(274\) 218.946 0.799074
\(275\) 257.452 327.652i 0.936190 1.19146i
\(276\) 26.8505 + 10.3464i 0.0972845 + 0.0374871i
\(277\) 361.975i 1.30677i 0.757027 + 0.653384i \(0.226651\pi\)
−0.757027 + 0.653384i \(0.773349\pi\)
\(278\) −266.995 −0.960412
\(279\) −51.2673 46.3997i −0.183754 0.166307i
\(280\) 35.5677 102.834i 0.127028 0.367264i
\(281\) 53.2019i 0.189330i −0.995509 0.0946652i \(-0.969822\pi\)
0.995509 0.0946652i \(-0.0301781\pi\)
\(282\) 285.919 + 110.174i 1.01390 + 0.390690i
\(283\) 262.727i 0.928363i −0.885740 0.464182i \(-0.846349\pi\)
0.885740 0.464182i \(-0.153651\pi\)
\(284\) 142.423i 0.501491i
\(285\) −363.669 306.809i −1.27603 1.07652i
\(286\) 325.003 1.13637
\(287\) 496.309 1.72930
\(288\) −37.7473 34.1634i −0.131067 0.118623i
\(289\) 433.210 1.49900
\(290\) 60.2097 174.079i 0.207620 0.600274i
\(291\) 64.0744 166.282i 0.220187 0.571417i
\(292\) 56.4801i 0.193425i
\(293\) −249.475 −0.851452 −0.425726 0.904852i \(-0.639981\pi\)
−0.425726 + 0.904852i \(0.639981\pi\)
\(294\) −40.3783 15.5592i −0.137341 0.0529223i
\(295\) −49.5679 + 143.311i −0.168027 + 0.485801i
\(296\) 112.069i 0.378611i
\(297\) −401.766 + 202.769i −1.35275 + 0.682723i
\(298\) 66.8806i 0.224432i
\(299\) 66.1233i 0.221148i
\(300\) −76.7347 128.887i −0.255782 0.429622i
\(301\) 446.570 1.48362
\(302\) −43.9624 −0.145571
\(303\) −39.2580 + 101.880i −0.129564 + 0.336239i
\(304\) 126.880 0.417370
\(305\) −33.8302 11.7010i −0.110919 0.0383640i
\(306\) 253.605 + 229.526i 0.828775 + 0.750086i
\(307\) 368.547i 1.20048i −0.799820 0.600240i \(-0.795072\pi\)
0.799820 0.600240i \(-0.204928\pi\)
\(308\) 256.490 0.832760
\(309\) 5.07412 13.1681i 0.0164211 0.0426152i
\(310\) 51.3425 + 17.7581i 0.165621 + 0.0572842i
\(311\) 446.781i 1.43660i 0.695735 + 0.718298i \(0.255079\pi\)
−0.695735 + 0.718298i \(0.744921\pi\)
\(312\) 42.0661 109.168i 0.134827 0.349897i
\(313\) 55.1749i 0.176278i 0.996108 + 0.0881388i \(0.0280919\pi\)
−0.996108 + 0.0881388i \(0.971908\pi\)
\(314\) 66.7276i 0.212508i
\(315\) −303.484 + 166.662i −0.963441 + 0.529086i
\(316\) −46.2621 −0.146399
\(317\) −296.868 −0.936492 −0.468246 0.883598i \(-0.655114\pi\)
−0.468246 + 0.883598i \(0.655114\pi\)
\(318\) 81.9875 + 31.5926i 0.257822 + 0.0993479i
\(319\) 434.191 1.36110
\(320\) 37.8027 + 13.0750i 0.118133 + 0.0408594i
\(321\) −402.736 155.188i −1.25463 0.483452i
\(322\) 52.1840i 0.162062i
\(323\) −852.445 −2.63915
\(324\) 16.1078 + 161.197i 0.0497154 + 0.497522i
\(325\) 212.964 271.033i 0.655273 0.833947i
\(326\) 339.596i 1.04171i
\(327\) −283.686 109.314i −0.867542 0.334294i
\(328\) 182.448i 0.556243i
\(329\) 555.684i 1.68901i
\(330\) 227.998 270.252i 0.690902 0.818945i
\(331\) −589.940 −1.78230 −0.891148 0.453712i \(-0.850100\pi\)
−0.891148 + 0.453712i \(0.850100\pi\)
\(332\) 278.147 0.837793
\(333\) −239.291 + 264.394i −0.718591 + 0.793975i
\(334\) −114.862 −0.343899
\(335\) 144.452 417.643i 0.431201 1.24669i
\(336\) 33.1983 86.1544i 0.0988044 0.256412i
\(337\) 58.6794i 0.174123i −0.996203 0.0870614i \(-0.972252\pi\)
0.996203 0.0870614i \(-0.0277476\pi\)
\(338\) 29.8395 0.0882825
\(339\) −123.715 47.6715i −0.364940 0.140624i
\(340\) −253.977 87.8444i −0.746991 0.258366i
\(341\) 128.059i 0.375540i
\(342\) −299.338 270.917i −0.875256 0.792154i
\(343\) 298.536i 0.870368i
\(344\) 164.163i 0.477219i
\(345\) 54.9839 + 46.3872i 0.159374 + 0.134456i
\(346\) 44.5029 0.128621
\(347\) 202.744 0.584277 0.292138 0.956376i \(-0.405633\pi\)
0.292138 + 0.956376i \(0.405633\pi\)
\(348\) 56.1987 145.844i 0.161491 0.419092i
\(349\) −201.859 −0.578391 −0.289196 0.957270i \(-0.593388\pi\)
−0.289196 + 0.957270i \(0.593388\pi\)
\(350\) 168.069 213.897i 0.480198 0.611134i
\(351\) −332.339 + 167.730i −0.946836 + 0.477862i
\(352\) 94.2881i 0.267864i
\(353\) 212.494 0.601965 0.300982 0.953630i \(-0.402685\pi\)
0.300982 + 0.953630i \(0.402685\pi\)
\(354\) −46.2658 + 120.067i −0.130694 + 0.339171i
\(355\) 116.387 336.499i 0.327850 0.947885i
\(356\) 89.9887i 0.252777i
\(357\) −223.042 + 578.828i −0.624768 + 1.62137i
\(358\) 142.266i 0.397391i
\(359\) 663.928i 1.84938i 0.380720 + 0.924690i \(0.375676\pi\)
−0.380720 + 0.924690i \(0.624324\pi\)
\(360\) −61.2665 111.563i −0.170185 0.309899i
\(361\) 645.166 1.78716
\(362\) −112.400 −0.310496
\(363\) 438.996 + 169.160i 1.20935 + 0.466006i
\(364\) 212.168 0.582878
\(365\) −46.1549 + 133.444i −0.126452 + 0.365599i
\(366\) −28.3430 10.9215i −0.0774398 0.0298402i
\(367\) 630.396i 1.71770i −0.512227 0.858850i \(-0.671179\pi\)
0.512227 0.858850i \(-0.328821\pi\)
\(368\) −19.1833 −0.0521286
\(369\) 389.565 430.432i 1.05573 1.16648i
\(370\) 91.5814 264.781i 0.247517 0.715626i
\(371\) 159.343i 0.429495i
\(372\) 43.0148 + 16.5751i 0.115631 + 0.0445567i
\(373\) 383.897i 1.02921i 0.857426 + 0.514607i \(0.172062\pi\)
−0.857426 + 0.514607i \(0.827938\pi\)
\(374\) 633.473i 1.69378i
\(375\) −75.9740 367.223i −0.202597 0.979262i
\(376\) −204.274 −0.543283
\(377\) 359.162 0.952684
\(378\) −262.280 + 132.371i −0.693862 + 0.350188i
\(379\) 210.581 0.555621 0.277811 0.960636i \(-0.410391\pi\)
0.277811 + 0.960636i \(0.410391\pi\)
\(380\) 299.777 + 103.685i 0.788886 + 0.272856i
\(381\) −239.035 + 620.331i −0.627388 + 1.62816i
\(382\) 256.318i 0.670989i
\(383\) −566.239 −1.47843 −0.739216 0.673469i \(-0.764804\pi\)
−0.739216 + 0.673469i \(0.764804\pi\)
\(384\) 31.6712 + 12.2040i 0.0824770 + 0.0317812i
\(385\) 606.001 + 209.601i 1.57403 + 0.544417i
\(386\) 254.801i 0.660107i
\(387\) 350.524 387.296i 0.905746 1.00076i
\(388\) 118.800i 0.306186i
\(389\) 120.478i 0.309713i −0.987937 0.154856i \(-0.950509\pi\)
0.987937 0.154856i \(-0.0494915\pi\)
\(390\) 188.599 223.551i 0.483587 0.573209i
\(391\) 128.883 0.329624
\(392\) 28.8482 0.0735924
\(393\) −108.140 + 280.638i −0.275164 + 0.714092i
\(394\) −386.314 −0.980492
\(395\) −109.302 37.8048i −0.276714 0.0957085i
\(396\) 201.325 222.445i 0.508397 0.561731i
\(397\) 214.516i 0.540342i 0.962812 + 0.270171i \(0.0870802\pi\)
−0.962812 + 0.270171i \(0.912920\pi\)
\(398\) 2.80831 0.00705607
\(399\) 263.263 683.207i 0.659808 1.71230i
\(400\) 78.6305 + 61.7839i 0.196576 + 0.154460i
\(401\) 630.643i 1.57268i −0.617796 0.786338i \(-0.711974\pi\)
0.617796 0.786338i \(-0.288026\pi\)
\(402\) 134.829 349.902i 0.335396 0.870402i
\(403\) 105.930i 0.262854i
\(404\) 72.7883i 0.180169i
\(405\) −93.6711 + 394.019i −0.231287 + 0.972886i
\(406\) 283.448 0.698147
\(407\) 660.422 1.62266
\(408\) −212.782 81.9924i −0.521525 0.200962i
\(409\) −464.370 −1.13538 −0.567689 0.823243i \(-0.692163\pi\)
−0.567689 + 0.823243i \(0.692163\pi\)
\(410\) −149.094 + 431.063i −0.363644 + 1.05137i
\(411\) 433.393 + 167.001i 1.05448 + 0.406329i
\(412\) 9.40793i 0.0228348i
\(413\) −233.349 −0.565011
\(414\) 45.2575 + 40.9605i 0.109318 + 0.0989383i
\(415\) 657.170 + 227.299i 1.58354 + 0.547708i
\(416\) 77.9948i 0.187488i
\(417\) −528.502 203.650i −1.26739 0.488369i
\(418\) 747.707i 1.78877i
\(419\) 586.065i 1.39872i −0.714769 0.699361i \(-0.753468\pi\)
0.714769 0.699361i \(-0.246532\pi\)
\(420\) 148.841 176.425i 0.354383 0.420060i
\(421\) −228.330 −0.542353 −0.271176 0.962530i \(-0.587413\pi\)
−0.271176 + 0.962530i \(0.587413\pi\)
\(422\) 306.803 0.727021
\(423\) 481.926 + 436.169i 1.13931 + 1.03113i
\(424\) −58.5759 −0.138151
\(425\) −528.278 415.094i −1.24301 0.976692i
\(426\) 108.633 281.920i 0.255008 0.661783i
\(427\) 55.0846i 0.129004i
\(428\) 287.734 0.672276
\(429\) 643.327 + 247.896i 1.49960 + 0.577846i
\(430\) −134.152 + 387.864i −0.311982 + 0.902009i
\(431\) 562.763i 1.30571i −0.757481 0.652857i \(-0.773570\pi\)
0.757481 0.652857i \(-0.226430\pi\)
\(432\) −48.6608 96.4164i −0.112641 0.223186i
\(433\) 402.222i 0.928919i −0.885594 0.464459i \(-0.846249\pi\)
0.885594 0.464459i \(-0.153751\pi\)
\(434\) 83.5993i 0.192625i
\(435\) 251.961 298.656i 0.579221 0.686566i
\(436\) 202.679 0.464860
\(437\) −152.124 −0.348111
\(438\) −43.0802 + 111.799i −0.0983566 + 0.255250i
\(439\) −146.580 −0.333896 −0.166948 0.985966i \(-0.553391\pi\)
−0.166948 + 0.985966i \(0.553391\pi\)
\(440\) −77.0511 + 222.771i −0.175116 + 0.506299i
\(441\) −68.0590 61.5971i −0.154329 0.139676i
\(442\) 524.007i 1.18554i
\(443\) −784.192 −1.77019 −0.885093 0.465414i \(-0.845905\pi\)
−0.885093 + 0.465414i \(0.845905\pi\)
\(444\) 85.4805 221.834i 0.192524 0.499627i
\(445\) 73.5377 212.613i 0.165253 0.477783i
\(446\) 362.152i 0.812000i
\(447\) −51.0131 + 132.387i −0.114123 + 0.296167i
\(448\) 61.5529i 0.137395i
\(449\) 579.670i 1.29103i −0.763750 0.645513i \(-0.776644\pi\)
0.763750 0.645513i \(-0.223356\pi\)
\(450\) −53.5841 313.654i −0.119076 0.697009i
\(451\) −1075.16 −2.38396
\(452\) 88.3877 0.195548
\(453\) −87.0212 33.5323i −0.192100 0.0740227i
\(454\) −304.485 −0.670672
\(455\) 501.282 + 173.381i 1.10172 + 0.381057i
\(456\) 251.153 + 96.7780i 0.550775 + 0.212233i
\(457\) 72.8841i 0.159484i 0.996816 + 0.0797419i \(0.0254096\pi\)
−0.996816 + 0.0797419i \(0.974590\pi\)
\(458\) 258.379 0.564146
\(459\) 326.927 + 647.773i 0.712259 + 1.41127i
\(460\) −45.3238 15.6764i −0.0985301 0.0340791i
\(461\) 188.695i 0.409316i 0.978834 + 0.204658i \(0.0656082\pi\)
−0.978834 + 0.204658i \(0.934392\pi\)
\(462\) 507.708 + 195.638i 1.09894 + 0.423458i
\(463\) 553.814i 1.19614i 0.801443 + 0.598072i \(0.204066\pi\)
−0.801443 + 0.598072i \(0.795934\pi\)
\(464\) 104.198i 0.224565i
\(465\) 88.0847 + 74.3127i 0.189430 + 0.159812i
\(466\) −191.615 −0.411191
\(467\) −425.497 −0.911129 −0.455565 0.890203i \(-0.650563\pi\)
−0.455565 + 0.890203i \(0.650563\pi\)
\(468\) 166.535 184.006i 0.355845 0.393175i
\(469\) 680.034 1.44997
\(470\) −482.633 166.931i −1.02688 0.355172i
\(471\) 50.8964 132.084i 0.108060 0.280432i
\(472\) 85.7814i 0.181740i
\(473\) −967.416 −2.04528
\(474\) −91.5734 35.2864i −0.193193 0.0744438i
\(475\) 623.542 + 489.948i 1.31272 + 1.03147i
\(476\) 413.543i 0.868787i
\(477\) 138.193 + 125.072i 0.289712 + 0.262205i
\(478\) 426.251i 0.891739i
\(479\) 166.558i 0.347720i −0.984770 0.173860i \(-0.944376\pi\)
0.984770 0.173860i \(-0.0556240\pi\)
\(480\) 64.8555 + 54.7153i 0.135116 + 0.113990i
\(481\) 546.299 1.13576
\(482\) 124.692 0.258698
\(483\) −39.8033 + 103.296i −0.0824086 + 0.213862i
\(484\) −313.640 −0.648016
\(485\) −97.0822 + 280.686i −0.200169 + 0.578733i
\(486\) −91.0686 + 331.368i −0.187384 + 0.681826i
\(487\) 332.759i 0.683284i −0.939830 0.341642i \(-0.889017\pi\)
0.939830 0.341642i \(-0.110983\pi\)
\(488\) 20.2496 0.0414951
\(489\) −259.027 + 672.213i −0.529708 + 1.37467i
\(490\) 68.1588 + 23.5745i 0.139100 + 0.0481111i
\(491\) 499.918i 1.01816i 0.860719 + 0.509081i \(0.170015\pi\)
−0.860719 + 0.509081i \(0.829985\pi\)
\(492\) −139.162 + 361.146i −0.282849 + 0.734036i
\(493\) 700.053i 1.41999i
\(494\) 618.501i 1.25203i
\(495\) 657.444 361.044i 1.32817 0.729382i
\(496\) −30.7319 −0.0619594
\(497\) 547.911 1.10244
\(498\) 550.578 + 212.157i 1.10558 + 0.426018i
\(499\) −29.1297 −0.0583761 −0.0291881 0.999574i \(-0.509292\pi\)
−0.0291881 + 0.999574i \(0.509292\pi\)
\(500\) 135.289 + 210.231i 0.270577 + 0.420462i
\(501\) −227.364 87.6111i −0.453820 0.174872i
\(502\) 249.898i 0.497805i
\(503\) 445.761 0.886204 0.443102 0.896471i \(-0.353878\pi\)
0.443102 + 0.896471i \(0.353878\pi\)
\(504\) 131.429 145.216i 0.260771 0.288127i
\(505\) 59.4817 171.975i 0.117786 0.340544i
\(506\) 113.047i 0.223414i
\(507\) 59.0657 + 22.7601i 0.116500 + 0.0448916i
\(508\) 443.194i 0.872430i
\(509\) 208.350i 0.409333i 0.978832 + 0.204666i \(0.0656110\pi\)
−0.978832 + 0.204666i \(0.934389\pi\)
\(510\) −435.731 367.604i −0.854374 0.720793i
\(511\) −217.282 −0.425210
\(512\) −22.6274 −0.0441942
\(513\) −385.881 764.585i −0.752206 1.49042i
\(514\) −363.485 −0.707169
\(515\) −7.68805 + 22.2278i −0.0149283 + 0.0431608i
\(516\) −125.216 + 324.953i −0.242666 + 0.629754i
\(517\) 1203.79i 2.32841i
\(518\) 431.135 0.832307
\(519\) 88.0912 + 33.9446i 0.169732 + 0.0654038i
\(520\) −63.7365 + 184.276i −0.122570 + 0.354377i
\(521\) 823.005i 1.57966i −0.613324 0.789832i \(-0.710168\pi\)
0.613324 0.789832i \(-0.289832\pi\)
\(522\) 222.485 245.825i 0.426216 0.470929i
\(523\) 293.166i 0.560546i 0.959920 + 0.280273i \(0.0904250\pi\)
−0.959920 + 0.280273i \(0.909575\pi\)
\(524\) 200.502i 0.382637i
\(525\) 495.834 295.203i 0.944447 0.562291i
\(526\) −90.7391 −0.172508
\(527\) 206.472 0.391787
\(528\) −71.9182 + 186.638i −0.136209 + 0.353482i
\(529\) 23.0000 0.0434783
\(530\) −138.395 47.8676i −0.261123 0.0903161i
\(531\) −183.161 + 202.376i −0.344937 + 0.381123i
\(532\) 488.116i 0.917512i
\(533\) −889.373 −1.66862
\(534\) 68.6388 178.128i 0.128537 0.333573i
\(535\) 679.820 + 235.133i 1.27069 + 0.439501i
\(536\) 249.987i 0.466393i
\(537\) 108.513 281.608i 0.202073 0.524410i
\(538\) 589.900i 1.09647i
\(539\) 170.003i 0.315404i
\(540\) −36.1789 267.565i −0.0669979 0.495491i
\(541\) 572.496 1.05822 0.529109 0.848554i \(-0.322526\pi\)
0.529109 + 0.848554i \(0.322526\pi\)
\(542\) 531.275 0.980212
\(543\) −222.489 85.7327i −0.409740 0.157887i
\(544\) 152.022 0.279452
\(545\) 478.864 + 165.627i 0.878649 + 0.303903i
\(546\) 419.975 + 161.831i 0.769185 + 0.296394i
\(547\) 168.725i 0.308456i −0.988035 0.154228i \(-0.950711\pi\)
0.988035 0.154228i \(-0.0492890\pi\)
\(548\) −309.637 −0.565030
\(549\) −47.7730 43.2372i −0.0870183 0.0787563i
\(550\) −364.093 + 463.370i −0.661987 + 0.842490i
\(551\) 826.293i 1.49962i
\(552\) −37.9724 14.6321i −0.0687906 0.0265074i
\(553\) 177.973i 0.321832i
\(554\) 511.909i 0.924024i
\(555\) 383.243 454.267i 0.690527 0.818500i
\(556\) 377.587 0.679114
\(557\) −990.965 −1.77911 −0.889555 0.456828i \(-0.848986\pi\)
−0.889555 + 0.456828i \(0.848986\pi\)
\(558\) 72.5029 + 65.6190i 0.129934 + 0.117597i
\(559\) −800.243 −1.43156
\(560\) −50.3003 + 145.429i −0.0898220 + 0.259695i
\(561\) 483.182 1253.93i 0.861286 2.23516i
\(562\) 75.2388i 0.133877i
\(563\) 790.012 1.40322 0.701609 0.712562i \(-0.252465\pi\)
0.701609 + 0.712562i \(0.252465\pi\)
\(564\) −404.350 155.810i −0.716933 0.276259i
\(565\) 208.831 + 72.2294i 0.369612 + 0.127840i
\(566\) 371.552i 0.656452i
\(567\) −620.135 + 61.9676i −1.09371 + 0.109290i
\(568\) 201.417i 0.354608i
\(569\) 133.372i 0.234398i −0.993108 0.117199i \(-0.962609\pi\)
0.993108 0.117199i \(-0.0373915\pi\)
\(570\) 514.306 + 433.894i 0.902291 + 0.761218i
\(571\) 1030.36 1.80449 0.902244 0.431227i \(-0.141919\pi\)
0.902244 + 0.431227i \(0.141919\pi\)
\(572\) −459.624 −0.803538
\(573\) 195.506 507.367i 0.341198 0.885458i
\(574\) −701.887 −1.22280
\(575\) −94.2746 74.0763i −0.163956 0.128828i
\(576\) 53.3828 + 48.3143i 0.0926785 + 0.0838791i
\(577\) 967.625i 1.67699i 0.544907 + 0.838497i \(0.316565\pi\)
−0.544907 + 0.838497i \(0.683435\pi\)
\(578\) −612.651 −1.05995
\(579\) −194.349 + 504.365i −0.335664 + 0.871098i
\(580\) −85.1494 + 246.185i −0.146809 + 0.424458i
\(581\) 1070.05i 1.84174i
\(582\) −90.6148 + 235.159i −0.155696 + 0.404053i
\(583\) 345.188i 0.592089i
\(584\) 79.8750i 0.136772i
\(585\) 543.836 298.654i 0.929634 0.510520i
\(586\) 352.811 0.602067
\(587\) −947.013 −1.61331 −0.806655 0.591023i \(-0.798724\pi\)
−0.806655 + 0.591023i \(0.798724\pi\)
\(588\) 57.1036 + 22.0040i 0.0971149 + 0.0374217i
\(589\) −243.705 −0.413760
\(590\) 70.0996 202.673i 0.118813 0.343514i
\(591\) −764.688 294.661i −1.29389 0.498580i
\(592\) 158.489i 0.267718i
\(593\) −579.653 −0.977492 −0.488746 0.872426i \(-0.662546\pi\)
−0.488746 + 0.872426i \(0.662546\pi\)
\(594\) 568.182 286.758i 0.956536 0.482758i
\(595\) 337.942 977.064i 0.567970 1.64212i
\(596\) 94.5834i 0.158697i
\(597\) 5.55891 + 2.14204i 0.00931141 + 0.00358801i
\(598\) 93.5125i 0.156375i
\(599\) 537.808i 0.897843i −0.893571 0.448922i \(-0.851808\pi\)
0.893571 0.448922i \(-0.148192\pi\)
\(600\) 108.519 + 182.273i 0.180865 + 0.303789i
\(601\) 29.8675 0.0496964 0.0248482 0.999691i \(-0.492090\pi\)
0.0248482 + 0.999691i \(0.492090\pi\)
\(602\) −631.546 −1.04908
\(603\) 533.775 589.771i 0.885199 0.978062i
\(604\) 62.1722 0.102934
\(605\) −741.027 256.303i −1.22484 0.423641i
\(606\) 55.5192 144.081i 0.0916159 0.237757i
\(607\) 828.617i 1.36510i 0.730838 + 0.682551i \(0.239130\pi\)
−0.730838 + 0.682551i \(0.760870\pi\)
\(608\) −179.436 −0.295125
\(609\) 561.070 + 216.200i 0.921297 + 0.355008i
\(610\) 47.8431 + 16.5477i 0.0784313 + 0.0271274i
\(611\) 995.771i 1.62974i
\(612\) −358.652 324.599i −0.586032 0.530391i
\(613\) 255.509i 0.416817i −0.978042 0.208409i \(-0.933172\pi\)
0.978042 0.208409i \(-0.0668284\pi\)
\(614\) 521.204i 0.848867i
\(615\) −623.918 + 739.546i −1.01450 + 1.20251i
\(616\) −362.732 −0.588850
\(617\) 591.174 0.958142 0.479071 0.877776i \(-0.340974\pi\)
0.479071 + 0.877776i \(0.340974\pi\)
\(618\) −7.17589 + 18.6225i −0.0116115 + 0.0301335i
\(619\) −1201.44 −1.94094 −0.970472 0.241215i \(-0.922454\pi\)
−0.970472 + 0.241215i \(0.922454\pi\)
\(620\) −72.6092 25.1137i −0.117112 0.0405060i
\(621\) 58.3422 + 115.599i 0.0939488 + 0.186150i
\(622\) 631.844i 1.01583i
\(623\) 346.192 0.555685
\(624\) −59.4905 + 154.387i −0.0953374 + 0.247414i
\(625\) 147.844 + 607.262i 0.236551 + 0.971619i
\(626\) 78.0291i 0.124647i
\(627\) −570.313 + 1480.05i −0.909591 + 2.36052i
\(628\) 94.3670i 0.150266i
\(629\) 1064.81i 1.69286i
\(630\) 429.191 235.696i 0.681256 0.374120i
\(631\) 129.923 0.205900 0.102950 0.994687i \(-0.467172\pi\)
0.102950 + 0.994687i \(0.467172\pi\)
\(632\) 65.4245 0.103520
\(633\) 607.300 + 234.014i 0.959400 + 0.369690i
\(634\) 419.835 0.662200
\(635\) 362.174 1047.12i 0.570352 1.64901i
\(636\) −115.948 44.6787i −0.182308 0.0702496i
\(637\) 140.626i 0.220763i
\(638\) −614.039 −0.962444
\(639\) 430.068 475.185i 0.673033 0.743639i
\(640\) −53.4611 18.4909i −0.0835329 0.0288920i
\(641\) 395.927i 0.617670i 0.951116 + 0.308835i \(0.0999391\pi\)
−0.951116 + 0.308835i \(0.900061\pi\)
\(642\) 569.555 + 219.469i 0.887157 + 0.341852i
\(643\) 787.933i 1.22540i 0.790315 + 0.612701i \(0.209917\pi\)
−0.790315 + 0.612701i \(0.790083\pi\)
\(644\) 73.7993i 0.114595i
\(645\) −561.391 + 665.431i −0.870373 + 1.03168i
\(646\) 1205.54 1.86616
\(647\) −752.984 −1.16381 −0.581904 0.813257i \(-0.697692\pi\)
−0.581904 + 0.813257i \(0.697692\pi\)
\(648\) −22.7799 227.967i −0.0351541 0.351801i
\(649\) 505.510 0.778906
\(650\) −301.176 + 383.298i −0.463348 + 0.589689i
\(651\) −63.7653 + 165.480i −0.0979498 + 0.254194i
\(652\) 480.262i 0.736598i
\(653\) 36.4462 0.0558135 0.0279067 0.999611i \(-0.491116\pi\)
0.0279067 + 0.999611i \(0.491116\pi\)
\(654\) 401.193 + 154.593i 0.613445 + 0.236381i
\(655\) 163.848 473.719i 0.250149 0.723235i
\(656\) 258.020i 0.393323i
\(657\) −170.550 + 188.442i −0.259589 + 0.286822i
\(658\) 785.855i 1.19431i
\(659\) 683.468i 1.03713i 0.855038 + 0.518565i \(0.173533\pi\)
−0.855038 + 0.518565i \(0.826467\pi\)
\(660\) −322.438 + 382.194i −0.488542 + 0.579081i
\(661\) −499.832 −0.756176 −0.378088 0.925770i \(-0.623418\pi\)
−0.378088 + 0.925770i \(0.623418\pi\)
\(662\) 834.302 1.26027
\(663\) 399.686 1037.25i 0.602845 1.56447i
\(664\) −393.360 −0.592409
\(665\) −398.883 + 1153.26i −0.599824 + 1.73422i
\(666\) 338.408 373.909i 0.508120 0.561425i
\(667\) 124.929i 0.187300i
\(668\) 162.440 0.243173
\(669\) 276.231 716.861i 0.412902 1.07154i
\(670\) −204.286 + 590.636i −0.304905 + 0.881546i
\(671\) 119.331i 0.177840i
\(672\) −46.9495 + 121.841i −0.0698653 + 0.181311i
\(673\) 61.0956i 0.0907810i −0.998969 0.0453905i \(-0.985547\pi\)
0.998969 0.0453905i \(-0.0144532\pi\)
\(674\) 82.9852i 0.123123i
\(675\) 133.172 661.733i 0.197293 0.980345i
\(676\) −42.1994 −0.0624252
\(677\) −905.990 −1.33824 −0.669121 0.743153i \(-0.733329\pi\)
−0.669121 + 0.743153i \(0.733329\pi\)
\(678\) 174.959 + 67.4177i 0.258051 + 0.0994361i
\(679\) −457.031 −0.673095
\(680\) 359.178 + 124.231i 0.528203 + 0.182692i
\(681\) −602.712 232.246i −0.885040 0.341036i
\(682\) 181.103i 0.265547i
\(683\) 244.248 0.357611 0.178806 0.983884i \(-0.442777\pi\)
0.178806 + 0.983884i \(0.442777\pi\)
\(684\) 423.327 + 383.134i 0.618900 + 0.560138i
\(685\) −731.569 253.032i −1.06798 0.369389i
\(686\) 422.194i 0.615443i
\(687\) 511.447 + 197.078i 0.744465 + 0.286868i
\(688\) 232.162i 0.337445i
\(689\) 285.538i 0.414424i
\(690\) −77.7590 65.6014i −0.112694 0.0950744i
\(691\) 919.272 1.33035 0.665175 0.746688i \(-0.268357\pi\)
0.665175 + 0.746688i \(0.268357\pi\)
\(692\) −62.9366 −0.0909488
\(693\) 855.760 + 774.509i 1.23486 + 1.11762i
\(694\) −286.723 −0.413146
\(695\) 892.114 + 308.560i 1.28362 + 0.443971i
\(696\) −79.4770 + 206.255i −0.114191 + 0.296343i
\(697\) 1733.50i 2.48709i
\(698\) 285.471 0.408984
\(699\) −379.292 146.154i −0.542621 0.209091i
\(700\) −237.686 + 302.496i −0.339552 + 0.432137i
\(701\) 310.828i 0.443407i 0.975114 + 0.221703i \(0.0711617\pi\)
−0.975114 + 0.221703i \(0.928838\pi\)
\(702\) 469.999 237.206i 0.669514 0.337900i
\(703\) 1256.82i 1.78780i
\(704\) 133.343i 0.189408i
\(705\) −828.020 698.559i −1.17450 0.990863i
\(706\) −300.511 −0.425653
\(707\) 280.021 0.396069
\(708\) 65.4297 169.800i 0.0924149 0.239830i
\(709\) −479.118 −0.675766 −0.337883 0.941188i \(-0.609711\pi\)
−0.337883 + 0.941188i \(0.609711\pi\)
\(710\) −164.596 + 475.882i −0.231825 + 0.670256i
\(711\) −154.350 139.695i −0.217089 0.196477i
\(712\) 127.263i 0.178740i
\(713\) 36.8462 0.0516777
\(714\) 315.429 818.586i 0.441778 1.14648i
\(715\) −1085.94 375.599i −1.51880 0.525314i
\(716\) 201.194i 0.280998i
\(717\) 325.123 843.742i 0.453449 1.17677i
\(718\) 938.935i 1.30771i
\(719\) 1121.51i 1.55982i 0.625895 + 0.779908i \(0.284734\pi\)
−0.625895 + 0.779908i \(0.715266\pi\)
\(720\) 86.6440 + 157.775i 0.120339 + 0.219131i
\(721\) −36.1928 −0.0501981
\(722\) −912.402 −1.26372
\(723\) 246.822 + 95.1090i 0.341386 + 0.131548i
\(724\) 158.957 0.219554
\(725\) −402.360 + 512.071i −0.554979 + 0.706305i
\(726\) −620.834 239.229i −0.855143 0.329516i
\(727\) 552.754i 0.760322i 0.924920 + 0.380161i \(0.124131\pi\)
−0.924920 + 0.380161i \(0.875869\pi\)
\(728\) −300.050 −0.412157
\(729\) −433.016 + 586.462i −0.593986 + 0.804475i
\(730\) 65.2729 188.718i 0.0894150 0.258518i
\(731\) 1559.78i 2.13376i
\(732\) 40.0830 + 15.4454i 0.0547582 + 0.0211002i
\(733\) 73.2361i 0.0999128i −0.998751 0.0499564i \(-0.984092\pi\)
0.998751 0.0499564i \(-0.0159082\pi\)
\(734\) 891.514i 1.21460i
\(735\) 116.935 + 98.6525i 0.159096 + 0.134221i
\(736\) 27.1293 0.0368605
\(737\) −1473.17 −1.99888
\(738\) −550.927 + 608.723i −0.746514 + 0.824828i
\(739\) −503.948 −0.681933 −0.340966 0.940075i \(-0.610754\pi\)
−0.340966 + 0.940075i \(0.610754\pi\)
\(740\) −129.516 + 374.458i −0.175021 + 0.506024i
\(741\) −471.762 + 1224.29i −0.636655 + 1.65221i
\(742\) 225.345i 0.303699i
\(743\) −310.256 −0.417572 −0.208786 0.977961i \(-0.566951\pi\)
−0.208786 + 0.977961i \(0.566951\pi\)
\(744\) −60.8321 23.4407i −0.0817636 0.0315063i
\(745\) 77.2925 223.469i 0.103748 0.299959i
\(746\) 542.912i 0.727764i
\(747\) 928.018 + 839.907i 1.24233 + 1.12437i
\(748\) 895.867i 1.19768i
\(749\) 1106.93i 1.47788i
\(750\) 107.443 + 519.332i 0.143258 + 0.692443i
\(751\) 413.103 0.550070 0.275035 0.961434i \(-0.411311\pi\)
0.275035 + 0.961434i \(0.411311\pi\)
\(752\) 288.888 0.384159
\(753\) −190.610 + 494.660i −0.253134 + 0.656919i
\(754\) −507.932 −0.673649
\(755\) 146.892 + 50.8064i 0.194559 + 0.0672933i
\(756\) 370.920 187.201i 0.490634 0.247620i
\(757\) 941.341i 1.24351i 0.783210 + 0.621757i \(0.213581\pi\)
−0.783210 + 0.621757i \(0.786419\pi\)
\(758\) −297.806 −0.392884
\(759\) 86.2269 223.771i 0.113606 0.294824i
\(760\) −423.948 146.633i −0.557826 0.192938i
\(761\) 27.9347i 0.0367079i 0.999832 + 0.0183539i \(0.00584256\pi\)
−0.999832 + 0.0183539i \(0.994157\pi\)
\(762\) 338.046 877.280i 0.443631 1.15129i
\(763\) 779.718i 1.02191i
\(764\) 362.488i 0.474461i
\(765\) −582.117 1060.01i −0.760937 1.38563i
\(766\) 800.783 1.04541
\(767\) 418.156 0.545184
\(768\) −44.7898 17.2591i −0.0583200 0.0224727i
\(769\) −699.658 −0.909829 −0.454914 0.890535i \(-0.650330\pi\)
−0.454914 + 0.890535i \(0.650330\pi\)
\(770\) −857.014 296.420i −1.11301 0.384961i
\(771\) −719.499 277.248i −0.933203 0.359595i
\(772\) 360.343i 0.466766i
\(773\) 1255.17 1.62376 0.811881 0.583823i \(-0.198444\pi\)
0.811881 + 0.583823i \(0.198444\pi\)
\(774\) −495.715 + 547.719i −0.640459 + 0.707647i
\(775\) −151.029 118.671i −0.194876 0.153124i
\(776\) 168.009i 0.216506i
\(777\) 853.409 + 328.848i 1.09834 + 0.423228i
\(778\) 170.382i 0.219000i
\(779\) 2046.11i 2.62658i
\(780\) −266.719 + 316.149i −0.341948 + 0.405320i
\(781\) −1186.95 −1.51978
\(782\) −182.268 −0.233079
\(783\) 627.900 316.897i 0.801916