Properties

Label 731.2.j.a.135.1
Level 731
Weight 2
Character 731.135
Analytic conductor 5.837
Analytic rank 0
Dimension 128
CM no
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.j (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(64\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 135.1
Character \(\chi\) = 731.135
Dual form 731.2.j.a.509.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.78045 q^{2} +(-1.68248 - 0.971380i) q^{3} +5.73090 q^{4} +(1.18797 + 0.685872i) q^{5} +(4.67805 + 2.70087i) q^{6} +(-2.90625 + 1.67793i) q^{7} -10.3736 q^{8} +(0.387158 + 0.670578i) q^{9} +O(q^{10})\) \(q-2.78045 q^{2} +(-1.68248 - 0.971380i) q^{3} +5.73090 q^{4} +(1.18797 + 0.685872i) q^{5} +(4.67805 + 2.70087i) q^{6} +(-2.90625 + 1.67793i) q^{7} -10.3736 q^{8} +(0.387158 + 0.670578i) q^{9} +(-3.30308 - 1.90703i) q^{10} +1.06055i q^{11} +(-9.64212 - 5.56688i) q^{12} +(0.214061 + 0.370764i) q^{13} +(8.08069 - 4.66539i) q^{14} +(-1.33248 - 2.30793i) q^{15} +17.3814 q^{16} +(-2.41191 - 3.34405i) q^{17} +(-1.07647 - 1.86451i) q^{18} +(0.534156 - 0.925185i) q^{19} +(6.80811 + 3.93066i) q^{20} +6.51962 q^{21} -2.94881i q^{22} +(-0.430436 - 0.248512i) q^{23} +(17.4533 + 10.0767i) q^{24} +(-1.55916 - 2.70054i) q^{25} +(-0.595185 - 1.03089i) q^{26} +4.32397i q^{27} +(-16.6555 + 9.61603i) q^{28} +(-6.04418 + 3.48961i) q^{29} +(3.70491 + 6.41709i) q^{30} +(3.85505 + 2.22572i) q^{31} -27.5810 q^{32} +(1.03020 - 1.78435i) q^{33} +(6.70620 + 9.29797i) q^{34} -4.60337 q^{35} +(2.21877 + 3.84301i) q^{36} +(7.29863 + 4.21387i) q^{37} +(-1.48519 + 2.57243i) q^{38} -0.831738i q^{39} +(-12.3234 - 7.11495i) q^{40} -7.24987i q^{41} -18.1275 q^{42} +(2.42774 + 6.09148i) q^{43} +6.07791i q^{44} +1.06216i q^{45} +(1.19681 + 0.690976i) q^{46} +2.28042 q^{47} +(-29.2439 - 16.8840i) q^{48} +(2.13088 - 3.69079i) q^{49} +(4.33516 + 7.50872i) q^{50} +(0.809646 + 7.96918i) q^{51} +(1.22676 + 2.12481i) q^{52} +(1.38456 - 2.39813i) q^{53} -12.0226i q^{54} +(-0.727402 + 1.25990i) q^{55} +(30.1483 - 17.4061i) q^{56} +(-1.79741 + 1.03774i) q^{57} +(16.8055 - 9.70268i) q^{58} +1.12504 q^{59} +(-7.63634 - 13.2265i) q^{60} +(11.0503 - 6.37987i) q^{61} +(-10.7188 - 6.18849i) q^{62} +(-2.25036 - 1.29925i) q^{63} +41.9247 q^{64} +0.587273i q^{65} +(-2.86441 + 4.96131i) q^{66} +(6.15639 - 10.6632i) q^{67} +(-13.8224 - 19.1644i) q^{68} +(0.482800 + 0.836234i) q^{69} +12.7994 q^{70} +(-6.17942 + 3.56769i) q^{71} +(-4.01622 - 6.95629i) q^{72} +(7.77804 - 4.49065i) q^{73} +(-20.2935 - 11.7164i) q^{74} +6.05814i q^{75} +(3.06119 - 5.30214i) q^{76} +(-1.77953 - 3.08223i) q^{77} +2.31260i q^{78} +(-8.94632 + 5.16516i) q^{79} +(20.6485 + 11.9214i) q^{80} +(5.36169 - 9.28672i) q^{81} +20.1579i q^{82} +(4.18711 - 7.25229i) q^{83} +37.3633 q^{84} +(-0.571675 - 5.62688i) q^{85} +(-6.75021 - 16.9370i) q^{86} +13.5589 q^{87} -11.0017i q^{88} +(6.54312 - 11.3330i) q^{89} -2.95329i q^{90} +(-1.24423 - 0.718357i) q^{91} +(-2.46679 - 1.42420i) q^{92} +(-4.32403 - 7.48944i) q^{93} -6.34058 q^{94} +(1.26912 - 0.732725i) q^{95} +(46.4044 + 26.7916i) q^{96} -4.36956i q^{97} +(-5.92479 + 10.2620i) q^{98} +(-0.711181 + 0.410601i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q - 4q^{2} + 116q^{4} - 12q^{8} + 70q^{9} + O(q^{10}) \) \( 128q - 4q^{2} + 116q^{4} - 12q^{8} + 70q^{9} + 4q^{13} - 12q^{15} + 76q^{16} + 2q^{17} - 16q^{18} - 2q^{19} - 20q^{21} + 60q^{25} - 2q^{26} - 28q^{30} - 48q^{32} + 22q^{33} - 18q^{34} - 112q^{35} + 36q^{36} - 40q^{38} + 36q^{42} + 10q^{43} + 36q^{47} + 52q^{49} + 16q^{50} + 10q^{51} + 10q^{52} + 24q^{55} - 12q^{59} - 78q^{60} + 36q^{64} + 14q^{66} + 10q^{67} - q^{68} - 64q^{70} - 68q^{72} - 22q^{76} - 28q^{77} - 20q^{81} - 6q^{83} + 32q^{84} + 6q^{85} - 58q^{86} + 32q^{87} + 36q^{89} + 6q^{93} + 132q^{94} - 48q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.78045 −1.96607 −0.983037 0.183405i \(-0.941288\pi\)
−0.983037 + 0.183405i \(0.941288\pi\)
\(3\) −1.68248 0.971380i −0.971380 0.560827i −0.0717233 0.997425i \(-0.522850\pi\)
−0.899657 + 0.436598i \(0.856183\pi\)
\(4\) 5.73090 2.86545
\(5\) 1.18797 + 0.685872i 0.531274 + 0.306731i 0.741535 0.670914i \(-0.234098\pi\)
−0.210261 + 0.977645i \(0.567431\pi\)
\(6\) 4.67805 + 2.70087i 1.90981 + 1.10263i
\(7\) −2.90625 + 1.67793i −1.09846 + 0.634197i −0.935816 0.352488i \(-0.885336\pi\)
−0.162645 + 0.986685i \(0.552002\pi\)
\(8\) −10.3736 −3.66761
\(9\) 0.387158 + 0.670578i 0.129053 + 0.223526i
\(10\) −3.30308 1.90703i −1.04452 0.603057i
\(11\) 1.06055i 0.319768i 0.987136 + 0.159884i \(0.0511120\pi\)
−0.987136 + 0.159884i \(0.948888\pi\)
\(12\) −9.64212 5.56688i −2.78344 1.60702i
\(13\) 0.214061 + 0.370764i 0.0593698 + 0.102831i 0.894183 0.447702i \(-0.147758\pi\)
−0.834813 + 0.550534i \(0.814424\pi\)
\(14\) 8.08069 4.66539i 2.15966 1.24688i
\(15\) −1.33248 2.30793i −0.344046 0.595905i
\(16\) 17.3814 4.34535
\(17\) −2.41191 3.34405i −0.584974 0.811052i
\(18\) −1.07647 1.86451i −0.253727 0.439469i
\(19\) 0.534156 0.925185i 0.122544 0.212252i −0.798226 0.602358i \(-0.794228\pi\)
0.920770 + 0.390106i \(0.127561\pi\)
\(20\) 6.80811 + 3.93066i 1.52234 + 0.878923i
\(21\) 6.51962 1.42270
\(22\) 2.94881i 0.628687i
\(23\) −0.430436 0.248512i −0.0897521 0.0518184i 0.454452 0.890771i \(-0.349835\pi\)
−0.544204 + 0.838953i \(0.683168\pi\)
\(24\) 17.4533 + 10.0767i 3.56265 + 2.05689i
\(25\) −1.55916 2.70054i −0.311832 0.540109i
\(26\) −0.595185 1.03089i −0.116725 0.202174i
\(27\) 4.32397i 0.832148i
\(28\) −16.6555 + 9.61603i −3.14758 + 1.81726i
\(29\) −6.04418 + 3.48961i −1.12238 + 0.648004i −0.942006 0.335595i \(-0.891063\pi\)
−0.180370 + 0.983599i \(0.557729\pi\)
\(30\) 3.70491 + 6.41709i 0.676420 + 1.17159i
\(31\) 3.85505 + 2.22572i 0.692388 + 0.399750i 0.804506 0.593944i \(-0.202430\pi\)
−0.112118 + 0.993695i \(0.535763\pi\)
\(32\) −27.5810 −4.87567
\(33\) 1.03020 1.78435i 0.179334 0.310616i
\(34\) 6.70620 + 9.29797i 1.15010 + 1.59459i
\(35\) −4.60337 −0.778112
\(36\) 2.21877 + 3.84301i 0.369794 + 0.640502i
\(37\) 7.29863 + 4.21387i 1.19989 + 0.692755i 0.960530 0.278176i \(-0.0897299\pi\)
0.239357 + 0.970932i \(0.423063\pi\)
\(38\) −1.48519 + 2.57243i −0.240930 + 0.417303i
\(39\) 0.831738i 0.133185i
\(40\) −12.3234 7.11495i −1.94851 1.12497i
\(41\) 7.24987i 1.13224i −0.824323 0.566120i \(-0.808444\pi\)
0.824323 0.566120i \(-0.191556\pi\)
\(42\) −18.1275 −2.79713
\(43\) 2.42774 + 6.09148i 0.370227 + 0.928941i
\(44\) 6.07791i 0.916279i
\(45\) 1.06216i 0.158338i
\(46\) 1.19681 + 0.690976i 0.176459 + 0.101879i
\(47\) 2.28042 0.332633 0.166316 0.986072i \(-0.446813\pi\)
0.166316 + 0.986072i \(0.446813\pi\)
\(48\) −29.2439 16.8840i −4.22099 2.43699i
\(49\) 2.13088 3.69079i 0.304411 0.527255i
\(50\) 4.33516 + 7.50872i 0.613085 + 1.06189i
\(51\) 0.809646 + 7.96918i 0.113373 + 1.11591i
\(52\) 1.22676 + 2.12481i 0.170121 + 0.294658i
\(53\) 1.38456 2.39813i 0.190184 0.329409i −0.755127 0.655579i \(-0.772425\pi\)
0.945311 + 0.326170i \(0.105758\pi\)
\(54\) 12.0226i 1.63607i
\(55\) −0.727402 + 1.25990i −0.0980828 + 0.169884i
\(56\) 30.1483 17.4061i 4.02873 2.32599i
\(57\) −1.79741 + 1.03774i −0.238073 + 0.137452i
\(58\) 16.8055 9.70268i 2.20668 1.27402i
\(59\) 1.12504 0.146468 0.0732339 0.997315i \(-0.476668\pi\)
0.0732339 + 0.997315i \(0.476668\pi\)
\(60\) −7.63634 13.2265i −0.985847 1.70754i
\(61\) 11.0503 6.37987i 1.41484 0.816859i 0.419002 0.907985i \(-0.362380\pi\)
0.995839 + 0.0911264i \(0.0290467\pi\)
\(62\) −10.7188 6.18849i −1.36129 0.785939i
\(63\) −2.25036 1.29925i −0.283519 0.163690i
\(64\) 41.9247 5.24059
\(65\) 0.587273i 0.0728423i
\(66\) −2.86441 + 4.96131i −0.352585 + 0.610694i
\(67\) 6.15639 10.6632i 0.752123 1.30272i −0.194669 0.980869i \(-0.562363\pi\)
0.946792 0.321846i \(-0.104303\pi\)
\(68\) −13.8224 19.1644i −1.67621 2.32403i
\(69\) 0.482800 + 0.836234i 0.0581223 + 0.100671i
\(70\) 12.7994 1.52983
\(71\) −6.17942 + 3.56769i −0.733362 + 0.423407i −0.819651 0.572863i \(-0.805833\pi\)
0.0862889 + 0.996270i \(0.472499\pi\)
\(72\) −4.01622 6.95629i −0.473316 0.819807i
\(73\) 7.77804 4.49065i 0.910350 0.525591i 0.0298066 0.999556i \(-0.490511\pi\)
0.880544 + 0.473965i \(0.157178\pi\)
\(74\) −20.2935 11.7164i −2.35907 1.36201i
\(75\) 6.05814i 0.699534i
\(76\) 3.06119 5.30214i 0.351143 0.608197i
\(77\) −1.77953 3.08223i −0.202796 0.351252i
\(78\) 2.31260i 0.261851i
\(79\) −8.94632 + 5.16516i −1.00654 + 0.581126i −0.910177 0.414220i \(-0.864054\pi\)
−0.0963633 + 0.995346i \(0.530721\pi\)
\(80\) 20.6485 + 11.9214i 2.30857 + 1.33286i
\(81\) 5.36169 9.28672i 0.595744 1.03186i
\(82\) 20.1579i 2.22607i
\(83\) 4.18711 7.25229i 0.459595 0.796042i −0.539344 0.842085i \(-0.681328\pi\)
0.998939 + 0.0460432i \(0.0146612\pi\)
\(84\) 37.3633 4.07667
\(85\) −0.571675 5.62688i −0.0620068 0.610321i
\(86\) −6.75021 16.9370i −0.727894 1.82637i
\(87\) 13.5589 1.45367
\(88\) 11.0017i 1.17278i
\(89\) 6.54312 11.3330i 0.693570 1.20130i −0.277091 0.960844i \(-0.589370\pi\)
0.970661 0.240454i \(-0.0772963\pi\)
\(90\) 2.95329i 0.311304i
\(91\) −1.24423 0.718357i −0.130431 0.0753042i
\(92\) −2.46679 1.42420i −0.257180 0.148483i
\(93\) −4.32403 7.48944i −0.448381 0.776619i
\(94\) −6.34058 −0.653981
\(95\) 1.26912 0.732725i 0.130209 0.0751760i
\(96\) 46.4044 + 26.7916i 4.73613 + 2.73441i
\(97\) 4.36956i 0.443661i −0.975085 0.221831i \(-0.928797\pi\)
0.975085 0.221831i \(-0.0712032\pi\)
\(98\) −5.92479 + 10.2620i −0.598495 + 1.03662i
\(99\) −0.711181 + 0.410601i −0.0714764 + 0.0412669i
\(100\) −8.93538 15.4765i −0.893538 1.54765i
\(101\) 8.77316 + 15.1956i 0.872962 + 1.51202i 0.858918 + 0.512114i \(0.171137\pi\)
0.0140446 + 0.999901i \(0.495529\pi\)
\(102\) −2.25118 22.1579i −0.222900 2.19396i
\(103\) −2.22292 3.85021i −0.219031 0.379372i 0.735481 0.677545i \(-0.236956\pi\)
−0.954512 + 0.298173i \(0.903623\pi\)
\(104\) −2.22058 3.84615i −0.217745 0.377146i
\(105\) 7.74508 + 4.47162i 0.755842 + 0.436386i
\(106\) −3.84971 + 6.66789i −0.373917 + 0.647642i
\(107\) 12.3991i 1.19866i 0.800501 + 0.599331i \(0.204567\pi\)
−0.800501 + 0.599331i \(0.795433\pi\)
\(108\) 24.7802i 2.38448i
\(109\) 1.50889 + 0.871161i 0.144526 + 0.0834421i 0.570519 0.821284i \(-0.306742\pi\)
−0.425993 + 0.904726i \(0.640075\pi\)
\(110\) 2.02250 3.50308i 0.192838 0.334005i
\(111\) −8.18653 14.1795i −0.777031 1.34586i
\(112\) −50.5148 + 29.1647i −4.77320 + 2.75581i
\(113\) 14.9631i 1.40761i −0.710395 0.703803i \(-0.751484\pi\)
0.710395 0.703803i \(-0.248516\pi\)
\(114\) 4.99761 2.88537i 0.468070 0.270240i
\(115\) −0.340895 0.590448i −0.0317886 0.0550596i
\(116\) −34.6386 + 19.9986i −3.21611 + 1.85682i
\(117\) −0.165751 + 0.287089i −0.0153237 + 0.0265414i
\(118\) −3.12812 −0.287967
\(119\) 12.6207 + 5.67166i 1.15694 + 0.519920i
\(120\) 13.8226 + 23.9415i 1.26183 + 2.18555i
\(121\) 9.87523 0.897749
\(122\) −30.7247 + 17.7389i −2.78168 + 1.60601i
\(123\) −7.04238 + 12.1978i −0.634990 + 1.09984i
\(124\) 22.0929 + 12.7554i 1.98400 + 1.14546i
\(125\) 11.1363i 0.996057i
\(126\) 6.25702 + 3.61249i 0.557419 + 0.321826i
\(127\) 13.5979 1.20662 0.603309 0.797508i \(-0.293849\pi\)
0.603309 + 0.797508i \(0.293849\pi\)
\(128\) −61.4075 −5.42771
\(129\) 1.83252 12.6070i 0.161344 1.10999i
\(130\) 1.63288i 0.143213i
\(131\) 17.2246i 1.50492i −0.658636 0.752461i \(-0.728866\pi\)
0.658636 0.752461i \(-0.271134\pi\)
\(132\) 5.90396 10.2260i 0.513873 0.890055i
\(133\) 3.58510i 0.310867i
\(134\) −17.1175 + 29.6484i −1.47873 + 2.56124i
\(135\) −2.96569 + 5.13672i −0.255246 + 0.442099i
\(136\) 25.0201 + 34.6898i 2.14546 + 2.97462i
\(137\) 6.36482 0.543783 0.271892 0.962328i \(-0.412351\pi\)
0.271892 + 0.962328i \(0.412351\pi\)
\(138\) −1.34240 2.32511i −0.114273 0.197926i
\(139\) −18.0207 10.4042i −1.52849 0.882476i −0.999425 0.0338975i \(-0.989208\pi\)
−0.529069 0.848579i \(-0.677459\pi\)
\(140\) −26.3815 −2.22964
\(141\) −3.83675 2.21515i −0.323113 0.186549i
\(142\) 17.1816 9.91978i 1.44184 0.832449i
\(143\) −0.393214 + 0.227022i −0.0328822 + 0.0189845i
\(144\) 6.72936 + 11.6556i 0.560780 + 0.971299i
\(145\) −9.57370 −0.795053
\(146\) −21.6264 + 12.4860i −1.78982 + 1.03335i
\(147\) −7.17031 + 4.13978i −0.591397 + 0.341443i
\(148\) 41.8277 + 24.1492i 3.43822 + 1.98506i
\(149\) 3.57153 6.18607i 0.292591 0.506783i −0.681831 0.731510i \(-0.738816\pi\)
0.974422 + 0.224728i \(0.0721492\pi\)
\(150\) 16.8444i 1.37534i
\(151\) −12.2028 −0.993051 −0.496525 0.868022i \(-0.665391\pi\)
−0.496525 + 0.868022i \(0.665391\pi\)
\(152\) −5.54111 + 9.59748i −0.449443 + 0.778458i
\(153\) 1.30866 2.91205i 0.105799 0.235425i
\(154\) 4.94788 + 8.56998i 0.398712 + 0.690589i
\(155\) 3.05311 + 5.28815i 0.245232 + 0.424754i
\(156\) 4.76660i 0.381634i
\(157\) −0.997669 1.72801i −0.0796226 0.137910i 0.823465 0.567368i \(-0.192038\pi\)
−0.903087 + 0.429457i \(0.858705\pi\)
\(158\) 24.8748 14.3615i 1.97893 1.14254i
\(159\) −4.65900 + 2.68987i −0.369482 + 0.213321i
\(160\) −32.7652 18.9170i −2.59032 1.49552i
\(161\) 1.66794 0.131452
\(162\) −14.9079 + 25.8213i −1.17128 + 2.02871i
\(163\) 10.4099 6.01014i 0.815363 0.470750i −0.0334516 0.999440i \(-0.510650\pi\)
0.848815 + 0.528690i \(0.177317\pi\)
\(164\) 41.5483i 3.24438i
\(165\) 2.44768 1.41317i 0.190551 0.110015i
\(166\) −11.6421 + 20.1646i −0.903598 + 1.56508i
\(167\) 8.04864 + 4.64689i 0.622823 + 0.359587i 0.777967 0.628305i \(-0.216251\pi\)
−0.155144 + 0.987892i \(0.549584\pi\)
\(168\) −67.6318 −5.21790
\(169\) 6.40836 11.0996i 0.492950 0.853815i
\(170\) 1.58951 + 15.6453i 0.121910 + 1.19994i
\(171\) 0.827211 0.0632584
\(172\) 13.9131 + 34.9096i 1.06087 + 2.66183i
\(173\) 4.22235i 0.321019i −0.987034 0.160510i \(-0.948686\pi\)
0.987034 0.160510i \(-0.0513138\pi\)
\(174\) −37.7000 −2.85803
\(175\) 9.06263 + 5.23231i 0.685070 + 0.395525i
\(176\) 18.4339i 1.38950i
\(177\) −1.89286 1.09284i −0.142276 0.0821430i
\(178\) −18.1928 + 31.5109i −1.36361 + 2.36184i
\(179\) 7.63121 + 13.2176i 0.570384 + 0.987933i 0.996526 + 0.0832774i \(0.0265388\pi\)
−0.426143 + 0.904656i \(0.640128\pi\)
\(180\) 6.08716i 0.453710i
\(181\) −11.4176 + 6.59197i −0.848666 + 0.489978i −0.860201 0.509956i \(-0.829662\pi\)
0.0115344 + 0.999933i \(0.496328\pi\)
\(182\) 3.45952 + 1.99735i 0.256437 + 0.148054i
\(183\) −24.7891 −1.83246
\(184\) 4.46516 + 2.57796i 0.329176 + 0.190050i
\(185\) 5.78035 + 10.0119i 0.424979 + 0.736086i
\(186\) 12.0228 + 20.8240i 0.881551 + 1.52689i
\(187\) 3.54653 2.55795i 0.259348 0.187056i
\(188\) 13.0688 0.953142
\(189\) −7.25530 12.5666i −0.527746 0.914082i
\(190\) −3.52872 + 2.03731i −0.256000 + 0.147802i
\(191\) 5.59777 9.69562i 0.405040 0.701551i −0.589286 0.807925i \(-0.700591\pi\)
0.994326 + 0.106374i \(0.0339241\pi\)
\(192\) −70.5374 40.7248i −5.09060 2.93906i
\(193\) 3.52859i 0.253994i 0.991903 + 0.126997i \(0.0405338\pi\)
−0.991903 + 0.126997i \(0.959466\pi\)
\(194\) 12.1493i 0.872271i
\(195\) 0.570465 0.988075i 0.0408519 0.0707575i
\(196\) 12.2118 21.1515i 0.872274 1.51082i
\(197\) 21.4729 12.3974i 1.52988 0.883278i 0.530517 0.847674i \(-0.321998\pi\)
0.999366 0.0356042i \(-0.0113356\pi\)
\(198\) 1.97740 1.14165i 0.140528 0.0811339i
\(199\) 2.62518i 0.186094i 0.995662 + 0.0930472i \(0.0296607\pi\)
−0.995662 + 0.0930472i \(0.970339\pi\)
\(200\) 16.1741 + 28.0143i 1.14368 + 1.98091i
\(201\) −20.7160 + 11.9604i −1.46119 + 0.843621i
\(202\) −24.3933 42.2505i −1.71631 2.97273i
\(203\) 11.7106 20.2834i 0.821924 1.42361i
\(204\) 4.64000 + 45.6706i 0.324865 + 3.19758i
\(205\) 4.97249 8.61260i 0.347293 0.601530i
\(206\) 6.18071 + 10.7053i 0.430631 + 0.745874i
\(207\) 0.384854i 0.0267492i
\(208\) 3.72068 + 6.44440i 0.257983 + 0.446839i
\(209\) 0.981205 + 0.566499i 0.0678714 + 0.0391856i
\(210\) −21.5348 12.4331i −1.48604 0.857967i
\(211\) 2.59376i 0.178562i −0.996006 0.0892808i \(-0.971543\pi\)
0.996006 0.0892808i \(-0.0284569\pi\)
\(212\) 7.93479 13.7435i 0.544964 0.943905i
\(213\) 13.8623 0.949831
\(214\) 34.4750i 2.35666i
\(215\) −1.29390 + 8.90158i −0.0882434 + 0.607083i
\(216\) 44.8550i 3.05200i
\(217\) −14.9384 −1.01408
\(218\) −4.19540 2.42222i −0.284149 0.164053i
\(219\) −17.4485 −1.17906
\(220\) −4.16867 + 7.22034i −0.281051 + 0.486795i
\(221\) 0.723559 1.61008i 0.0486719 0.108306i
\(222\) 22.7622 + 39.4254i 1.52770 + 2.64606i
\(223\) −2.50665 −0.167858 −0.0839288 0.996472i \(-0.526747\pi\)
−0.0839288 + 0.996472i \(0.526747\pi\)
\(224\) 80.1573 46.2789i 5.35574 3.09214i
\(225\) 1.20728 2.09108i 0.0804855 0.139405i
\(226\) 41.6040i 2.76746i
\(227\) 10.3495 + 5.97529i 0.686921 + 0.396594i 0.802458 0.596709i \(-0.203525\pi\)
−0.115537 + 0.993303i \(0.536859\pi\)
\(228\) −10.3008 + 5.94716i −0.682187 + 0.393861i
\(229\) 7.68147 + 13.3047i 0.507606 + 0.879200i 0.999961 + 0.00880516i \(0.00280281\pi\)
−0.492355 + 0.870394i \(0.663864\pi\)
\(230\) 0.947842 + 1.64171i 0.0624989 + 0.108251i
\(231\) 6.91438i 0.454933i
\(232\) 62.6998 36.1997i 4.11644 2.37663i
\(233\) 5.95032 3.43542i 0.389819 0.225062i −0.292263 0.956338i \(-0.594408\pi\)
0.682082 + 0.731276i \(0.261075\pi\)
\(234\) 0.460862 0.798236i 0.0301275 0.0521823i
\(235\) 2.70905 + 1.56407i 0.176719 + 0.102029i
\(236\) 6.44749 0.419696
\(237\) 20.0693 1.30364
\(238\) −35.0912 15.7698i −2.27463 1.02220i
\(239\) 0.799317 1.38446i 0.0517035 0.0895532i −0.839015 0.544108i \(-0.816868\pi\)
0.890719 + 0.454555i \(0.150202\pi\)
\(240\) −23.1605 40.1151i −1.49500 2.58942i
\(241\) 6.31839 3.64792i 0.407003 0.234983i −0.282498 0.959268i \(-0.591163\pi\)
0.689501 + 0.724285i \(0.257830\pi\)
\(242\) −27.4576 −1.76504
\(243\) −6.80787 + 3.93053i −0.436725 + 0.252143i
\(244\) 63.3279 36.5624i 4.05416 2.34067i
\(245\) 5.06281 2.92302i 0.323451 0.186745i
\(246\) 19.5810 33.9153i 1.24844 2.16236i
\(247\) 0.457367 0.0291016
\(248\) −39.9907 23.0886i −2.53941 1.46613i
\(249\) −14.0895 + 8.13455i −0.892883 + 0.515506i
\(250\) 30.9638i 1.95832i
\(251\) 9.28427 + 16.0808i 0.586018 + 1.01501i 0.994748 + 0.102357i \(0.0326385\pi\)
−0.408730 + 0.912655i \(0.634028\pi\)
\(252\) −12.8966 7.44585i −0.812409 0.469045i
\(253\) 0.263560 0.456499i 0.0165699 0.0286998i
\(254\) −37.8083 −2.37230
\(255\) −4.50401 + 10.0224i −0.282052 + 0.627629i
\(256\) 86.8912 5.43070
\(257\) −19.1102 −1.19206 −0.596030 0.802962i \(-0.703256\pi\)
−0.596030 + 0.802962i \(0.703256\pi\)
\(258\) −5.09522 + 35.0532i −0.317214 + 2.18232i
\(259\) −28.2822 −1.75737
\(260\) 3.36560i 0.208726i
\(261\) −4.68011 2.70206i −0.289691 0.167253i
\(262\) 47.8922i 2.95879i
\(263\) −10.4372 + 18.0777i −0.643584 + 1.11472i 0.341043 + 0.940048i \(0.389220\pi\)
−0.984627 + 0.174672i \(0.944113\pi\)
\(264\) −10.6868 + 18.5101i −0.657729 + 1.13922i
\(265\) 3.28962 1.89927i 0.202080 0.116671i
\(266\) 9.96818i 0.611189i
\(267\) −22.0173 + 12.7117i −1.34744 + 0.777944i
\(268\) 35.2817 61.1096i 2.15517 3.73286i
\(269\) 25.8522i 1.57624i 0.615523 + 0.788119i \(0.288945\pi\)
−0.615523 + 0.788119i \(0.711055\pi\)
\(270\) 8.24595 14.2824i 0.501832 0.869199i
\(271\) 11.6978 + 20.2612i 0.710592 + 1.23078i 0.964635 + 0.263588i \(0.0849059\pi\)
−0.254044 + 0.967193i \(0.581761\pi\)
\(272\) −41.9224 58.1243i −2.54192 3.52431i
\(273\) 1.39559 + 2.41724i 0.0844652 + 0.146298i
\(274\) −17.6971 −1.06912
\(275\) 2.86406 1.65357i 0.172709 0.0997138i
\(276\) 2.76688 + 4.79237i 0.166546 + 0.288467i
\(277\) −27.7210 16.0047i −1.66559 0.961629i −0.969971 0.243219i \(-0.921797\pi\)
−0.695620 0.718410i \(-0.744870\pi\)
\(278\) 50.1056 + 28.9285i 3.00513 + 1.73501i
\(279\) 3.44682i 0.206356i
\(280\) 47.7534 2.85381
\(281\) −3.25357 + 5.63534i −0.194091 + 0.336176i −0.946602 0.322404i \(-0.895509\pi\)
0.752511 + 0.658580i \(0.228843\pi\)
\(282\) 10.6679 + 6.15911i 0.635264 + 0.366770i
\(283\) −8.10886 + 4.68166i −0.482022 + 0.278296i −0.721259 0.692666i \(-0.756436\pi\)
0.239237 + 0.970961i \(0.423103\pi\)
\(284\) −35.4136 + 20.4461i −2.10141 + 1.21325i
\(285\) −2.84702 −0.168643
\(286\) 1.09331 0.631224i 0.0646489 0.0373250i
\(287\) 12.1648 + 21.0700i 0.718063 + 1.24372i
\(288\) −10.6782 18.4952i −0.629219 1.08984i
\(289\) −5.36537 + 16.1311i −0.315610 + 0.948889i
\(290\) 26.6192 1.56313
\(291\) −4.24450 + 7.35169i −0.248817 + 0.430964i
\(292\) 44.5752 25.7355i 2.60856 1.50605i
\(293\) −21.7770 −1.27222 −0.636112 0.771597i \(-0.719458\pi\)
−0.636112 + 0.771597i \(0.719458\pi\)
\(294\) 19.9367 11.5105i 1.16273 0.671303i
\(295\) 1.33651 + 0.771634i 0.0778145 + 0.0449262i
\(296\) −75.7129 43.7129i −4.40072 2.54076i
\(297\) −4.58579 −0.266094
\(298\) −9.93046 + 17.2001i −0.575256 + 0.996372i
\(299\) 0.212787i 0.0123058i
\(300\) 34.7186i 2.00448i
\(301\) −17.2767 13.6298i −0.995811 0.785609i
\(302\) 33.9293 1.95241
\(303\) 34.0883i 1.95832i
\(304\) 9.28438 16.0810i 0.532496 0.922310i
\(305\) 17.5031 1.00222
\(306\) −3.63865 + 8.09681i −0.208008 + 0.462864i
\(307\) −1.25920 + 2.18099i −0.0718661 + 0.124476i −0.899719 0.436469i \(-0.856229\pi\)
0.827853 + 0.560945i \(0.189562\pi\)
\(308\) −10.1983 17.6639i −0.581101 1.00650i
\(309\) 8.63719i 0.491353i
\(310\) −8.48903 14.7034i −0.482144 0.835098i
\(311\) 10.9160 + 6.30238i 0.618992 + 0.357375i 0.776477 0.630146i \(-0.217005\pi\)
−0.157484 + 0.987521i \(0.550338\pi\)
\(312\) 8.62809i 0.488470i
\(313\) 8.58998 + 4.95943i 0.485534 + 0.280323i 0.722720 0.691141i \(-0.242892\pi\)
−0.237186 + 0.971464i \(0.576225\pi\)
\(314\) 2.77397 + 4.80465i 0.156544 + 0.271142i
\(315\) −1.78223 3.08692i −0.100417 0.173928i
\(316\) −51.2705 + 29.6010i −2.88419 + 1.66519i
\(317\) 19.6627i 1.10436i 0.833723 + 0.552182i \(0.186205\pi\)
−0.833723 + 0.552182i \(0.813795\pi\)
\(318\) 12.9541 7.47906i 0.726430 0.419405i
\(319\) −3.70090 6.41016i −0.207211 0.358900i
\(320\) 49.8051 + 28.7550i 2.78419 + 1.60745i
\(321\) 12.0442 20.8612i 0.672242 1.16436i
\(322\) −4.63763 −0.258445
\(323\) −4.38220 + 0.445219i −0.243832 + 0.0247727i
\(324\) 30.7273 53.2213i 1.70707 2.95674i
\(325\) 0.667510 1.15616i 0.0370268 0.0641323i
\(326\) −28.9441 + 16.7109i −1.60307 + 0.925530i
\(327\) −1.69246 2.93142i −0.0935930 0.162108i
\(328\) 75.2071i 4.15262i
\(329\) −6.62747 + 3.82637i −0.365384 + 0.210955i
\(330\) −6.80564 + 3.92924i −0.374638 + 0.216297i
\(331\) −5.49425 9.51632i −0.301991 0.523064i 0.674596 0.738187i \(-0.264318\pi\)
−0.976587 + 0.215123i \(0.930985\pi\)
\(332\) 23.9959 41.5621i 1.31695 2.28102i
\(333\) 6.52573i 0.357608i
\(334\) −22.3788 12.9204i −1.22452 0.706975i
\(335\) 14.6272 8.44499i 0.799167 0.461399i
\(336\) 113.320 6.18212
\(337\) 18.3664 10.6039i 1.00048 0.577629i 0.0920919 0.995751i \(-0.470645\pi\)
0.908391 + 0.418121i \(0.137311\pi\)
\(338\) −17.8181 + 30.8619i −0.969177 + 1.67866i
\(339\) −14.5348 + 25.1750i −0.789422 + 1.36732i
\(340\) −3.27621 32.2471i −0.177677 1.74884i
\(341\) −2.36048 + 4.08848i −0.127827 + 0.221403i
\(342\) −2.30002 −0.124371
\(343\) 9.18916i 0.496168i
\(344\) −25.1843 63.1904i −1.35785 3.40700i
\(345\) 1.32456i 0.0713117i
\(346\) 11.7400i 0.631148i
\(347\) 3.47884 + 2.00851i 0.186754 + 0.107822i 0.590462 0.807065i \(-0.298946\pi\)
−0.403708 + 0.914888i \(0.632279\pi\)
\(348\) 77.7050 4.16542
\(349\) 7.15030 12.3847i 0.382747 0.662937i −0.608707 0.793395i \(-0.708311\pi\)
0.991454 + 0.130458i \(0.0416448\pi\)
\(350\) −25.1982 14.5482i −1.34690 0.777633i
\(351\) −1.60317 + 0.925592i −0.0855710 + 0.0494045i
\(352\) 29.2510i 1.55908i
\(353\) 4.54259 + 7.86800i 0.241778 + 0.418772i 0.961221 0.275780i \(-0.0889361\pi\)
−0.719443 + 0.694552i \(0.755603\pi\)
\(354\) 5.26299 + 3.03859i 0.279725 + 0.161499i
\(355\) −9.78791 −0.519488
\(356\) 37.4980 64.9484i 1.98739 3.44226i
\(357\) −15.7247 21.8019i −0.832241 1.15388i
\(358\) −21.2182 36.7510i −1.12142 1.94235i
\(359\) −7.92961 13.7345i −0.418509 0.724878i 0.577281 0.816546i \(-0.304114\pi\)
−0.995790 + 0.0916671i \(0.970780\pi\)
\(360\) 11.0184i 0.580723i
\(361\) 8.92936 + 15.4661i 0.469966 + 0.814005i
\(362\) 31.7462 18.3287i 1.66854 0.963333i
\(363\) −16.6149 9.59260i −0.872055 0.503481i
\(364\) −7.13056 4.11683i −0.373743 0.215781i
\(365\) 12.3201 0.644861
\(366\) 68.9249 3.60276
\(367\) 31.1052 + 17.9586i 1.62368 + 0.937431i 0.985925 + 0.167189i \(0.0534690\pi\)
0.637752 + 0.770241i \(0.279864\pi\)
\(368\) −7.48158 4.31949i −0.390005 0.225169i
\(369\) 4.86160 2.80685i 0.253085 0.146119i
\(370\) −16.0720 27.8375i −0.835541 1.44720i
\(371\) 9.29278i 0.482457i
\(372\) −24.7806 42.9212i −1.28481 2.22536i
\(373\) −7.03696 12.1884i −0.364360 0.631090i 0.624313 0.781174i \(-0.285379\pi\)
−0.988673 + 0.150084i \(0.952046\pi\)
\(374\) −9.86096 + 7.11226i −0.509898 + 0.367766i
\(375\) −10.8175 + 18.7365i −0.558615 + 0.967550i
\(376\) −23.6561 −1.21997
\(377\) −2.58764 1.49398i −0.133270 0.0769437i
\(378\) 20.1730 + 34.9407i 1.03759 + 1.79715i
\(379\) 33.8887i 1.74075i −0.492392 0.870374i \(-0.663877\pi\)
0.492392 0.870374i \(-0.336123\pi\)
\(380\) 7.27318 4.19917i 0.373106 0.215413i
\(381\) −22.8782 13.2087i −1.17208 0.676703i
\(382\) −15.5643 + 26.9582i −0.796340 + 1.37930i
\(383\) 8.18485 0.418226 0.209113 0.977891i \(-0.432942\pi\)
0.209113 + 0.977891i \(0.432942\pi\)
\(384\) 103.317 + 59.6501i 5.27237 + 3.04400i
\(385\) 4.88211i 0.248815i
\(386\) 9.81107i 0.499370i
\(387\) −3.14489 + 3.98635i −0.159864 + 0.202638i
\(388\) 25.0415i 1.27129i
\(389\) 18.5706 0.941566 0.470783 0.882249i \(-0.343971\pi\)
0.470783 + 0.882249i \(0.343971\pi\)
\(390\) −1.58615 + 2.74729i −0.0803179 + 0.139115i
\(391\) 0.207135 + 2.03879i 0.0104753 + 0.103106i
\(392\) −22.1048 + 38.2867i −1.11646 + 1.93377i
\(393\) −16.7317 + 28.9801i −0.844001 + 1.46185i
\(394\) −59.7044 + 34.4704i −3.00786 + 1.73659i
\(395\) −14.1706 −0.712998
\(396\) −4.07571 + 2.35311i −0.204812 + 0.118248i
\(397\) −19.3997 11.2004i −0.973642 0.562133i −0.0732975 0.997310i \(-0.523352\pi\)
−0.900345 + 0.435178i \(0.856686\pi\)
\(398\) 7.29919i 0.365876i
\(399\) 3.48249 6.03185i 0.174343 0.301970i
\(400\) −27.1004 46.9392i −1.35502 2.34696i
\(401\) 21.8838 12.6346i 1.09282 0.630942i 0.158496 0.987360i \(-0.449335\pi\)
0.934327 + 0.356418i \(0.116002\pi\)
\(402\) 57.5998 33.2553i 2.87282 1.65862i
\(403\) 1.90575i 0.0949324i
\(404\) 50.2781 + 87.0842i 2.50143 + 4.33260i
\(405\) 12.7390 7.35487i 0.633006 0.365466i
\(406\) −32.5608 + 56.3969i −1.61596 + 2.79893i
\(407\) −4.46902 + 7.74056i −0.221521 + 0.383685i
\(408\) −8.39892 82.6689i −0.415809 4.09272i
\(409\) −32.2577 −1.59504 −0.797521 0.603291i \(-0.793856\pi\)
−0.797521 + 0.603291i \(0.793856\pi\)
\(410\) −13.8257 + 23.9469i −0.682805 + 1.18265i
\(411\) −10.7087 6.18266i −0.528220 0.304968i
\(412\) −12.7393 22.0652i −0.627621 1.08707i
\(413\) −3.26965 + 1.88774i −0.160889 + 0.0928894i
\(414\) 1.07007i 0.0525910i
\(415\) 9.94828 5.74364i 0.488342 0.281944i
\(416\) −5.90401 10.2260i −0.289468 0.501373i
\(417\) 20.2129 + 35.0099i 0.989832 + 1.71444i
\(418\) −2.72819 1.57512i −0.133440 0.0770417i
\(419\) 18.5005i 0.903808i −0.892067 0.451904i \(-0.850745\pi\)
0.892067 0.451904i \(-0.149255\pi\)
\(420\) 44.3863 + 25.6264i 2.16583 + 1.25044i
\(421\) −4.20258 7.27907i −0.204821 0.354760i 0.745255 0.666780i \(-0.232328\pi\)
−0.950076 + 0.312020i \(0.898995\pi\)
\(422\) 7.21181i 0.351066i
\(423\) 0.882882 + 1.52920i 0.0429272 + 0.0743520i
\(424\) −14.3629 + 24.8772i −0.697523 + 1.20814i
\(425\) −5.27020 + 11.7274i −0.255642 + 0.568861i
\(426\) −38.5435 −1.86744
\(427\) −21.4099 + 37.0831i −1.03610 + 1.79458i
\(428\) 71.0578i 3.43471i
\(429\) 0.882099 0.0425882
\(430\) 3.59763 24.7504i 0.173493 1.19357i
\(431\) 8.30532i 0.400053i −0.979790 0.200027i \(-0.935897\pi\)
0.979790 0.200027i \(-0.0641028\pi\)
\(432\) 75.1567i 3.61598i
\(433\) −10.9246 + 18.9220i −0.525004 + 0.909334i 0.474572 + 0.880217i \(0.342603\pi\)
−0.999576 + 0.0291174i \(0.990730\pi\)
\(434\) 41.5353 1.99376
\(435\) 16.1076 + 9.29970i 0.772298 + 0.445887i
\(436\) 8.64732 + 4.99253i 0.414132 + 0.239099i
\(437\) −0.459840 + 0.265489i −0.0219971 + 0.0127000i
\(438\) 48.5147 2.31812
\(439\) 3.55527 2.05264i 0.169684 0.0979670i −0.412753 0.910843i \(-0.635433\pi\)
0.582437 + 0.812876i \(0.302099\pi\)
\(440\) 7.54576 13.0696i 0.359730 0.623070i
\(441\) 3.29995 0.157140
\(442\) −2.01182 + 4.47675i −0.0956925 + 0.212937i
\(443\) −2.63062 4.55637i −0.124984 0.216479i 0.796742 0.604319i \(-0.206555\pi\)
−0.921727 + 0.387840i \(0.873221\pi\)
\(444\) −46.9162 81.2612i −2.22654 3.85649i
\(445\) 15.5460 8.97549i 0.736951 0.425479i
\(446\) 6.96961 0.330021
\(447\) −12.0180 + 6.93862i −0.568434 + 0.328186i
\(448\) −121.844 + 70.3466i −5.75658 + 3.32356i
\(449\) −21.4776 12.4001i −1.01359 0.585196i −0.101349 0.994851i \(-0.532316\pi\)
−0.912240 + 0.409655i \(0.865649\pi\)
\(450\) −3.35679 + 5.81413i −0.158241 + 0.274081i
\(451\) 7.68885 0.362054
\(452\) 85.7517i 4.03342i
\(453\) 20.5310 + 11.8536i 0.964630 + 0.556929i
\(454\) −28.7763 16.6140i −1.35054 0.779733i
\(455\) −0.985401 1.70677i −0.0461963 0.0800144i
\(456\) 18.6456 10.7650i 0.873160 0.504119i
\(457\) 11.4128 0.533868 0.266934 0.963715i \(-0.413989\pi\)
0.266934 + 0.963715i \(0.413989\pi\)
\(458\) −21.3580 36.9931i −0.997992 1.72857i
\(459\) 14.4596 10.4290i 0.674915 0.486785i
\(460\) −1.95364 3.38380i −0.0910888 0.157770i
\(461\) 15.3235 26.5411i 0.713686 1.23614i −0.249778 0.968303i \(-0.580358\pi\)
0.963464 0.267838i \(-0.0863091\pi\)
\(462\) 19.2251i 0.894432i
\(463\) −4.39635 + 7.61471i −0.204316 + 0.353885i −0.949915 0.312510i \(-0.898830\pi\)
0.745599 + 0.666395i \(0.232164\pi\)
\(464\) −105.056 + 60.6543i −4.87712 + 2.81581i
\(465\) 11.8629i 0.550130i
\(466\) −16.5446 + 9.55201i −0.766412 + 0.442488i
\(467\) 8.92365 15.4562i 0.412937 0.715228i −0.582272 0.812994i \(-0.697836\pi\)
0.995209 + 0.0977656i \(0.0311695\pi\)
\(468\) −0.949901 + 1.64528i −0.0439092 + 0.0760530i
\(469\) 41.3199i 1.90798i
\(470\) −7.53239 4.34883i −0.347443 0.200596i
\(471\) 3.87646i 0.178618i
\(472\) −11.6707 −0.537187
\(473\) −6.46031 + 2.57474i −0.297046 + 0.118387i
\(474\) −55.8018 −2.56306
\(475\) −3.33134 −0.152852
\(476\) 72.3280 + 32.5037i 3.31515 + 1.48980i
\(477\) 2.14418 0.0981752
\(478\) −2.22246 + 3.84942i −0.101653 + 0.176068i
\(479\) 5.93134 + 3.42446i 0.271010 + 0.156468i 0.629346 0.777125i \(-0.283323\pi\)
−0.358337 + 0.933592i \(0.616656\pi\)
\(480\) 36.7512 + 63.6550i 1.67746 + 2.90544i
\(481\) 3.60809i 0.164515i
\(482\) −17.5680 + 10.1429i −0.800198 + 0.461995i
\(483\) −2.80628 1.62021i −0.127690 0.0737219i
\(484\) 56.5940 2.57245
\(485\) 2.99696 5.19088i 0.136085 0.235706i
\(486\) 18.9289 10.9286i 0.858634 0.495733i
\(487\) −31.2541 + 18.0446i −1.41626 + 0.817677i −0.995968 0.0897130i \(-0.971405\pi\)
−0.420290 + 0.907390i \(0.638072\pi\)
\(488\) −114.631 + 66.1821i −5.18909 + 2.99592i
\(489\) −23.3525 −1.05604
\(490\) −14.0769 + 8.12730i −0.635929 + 0.367154i
\(491\) 16.5630 + 28.6879i 0.747476 + 1.29467i 0.949029 + 0.315188i \(0.102068\pi\)
−0.201554 + 0.979477i \(0.564599\pi\)
\(492\) −40.3592 + 69.9042i −1.81953 + 3.15152i
\(493\) 26.2475 + 11.7954i 1.18213 + 0.531239i
\(494\) −1.27169 −0.0572159
\(495\) −1.12648 −0.0506314
\(496\) 67.0063 + 38.6861i 3.00867 + 1.73706i
\(497\) 11.9726 20.7372i 0.537046 0.930192i
\(498\) 39.1750 22.6177i 1.75547 1.01352i
\(499\) 33.1625 19.1464i 1.48456 0.857109i 0.484711 0.874675i \(-0.338925\pi\)
0.999846 + 0.0175654i \(0.00559154\pi\)
\(500\) 63.8208i 2.85415i
\(501\) −9.02778 15.6366i −0.403332 0.698591i
\(502\) −25.8144 44.7119i −1.15216 1.99559i
\(503\) 12.5617 7.25248i 0.560097 0.323372i −0.193088 0.981182i \(-0.561850\pi\)
0.753184 + 0.657810i \(0.228517\pi\)
\(504\) 23.3443 + 13.4778i 1.03984 + 0.600350i
\(505\) 24.0691i 1.07106i
\(506\) −0.732815 + 1.26927i −0.0325776 + 0.0564260i
\(507\) −21.5639 + 12.4499i −0.957684 + 0.552919i
\(508\) 77.9282 3.45750
\(509\) 2.81128 + 4.86928i 0.124608 + 0.215827i 0.921580 0.388189i \(-0.126899\pi\)
−0.796972 + 0.604017i \(0.793566\pi\)
\(510\) 12.5232 27.8668i 0.554535 1.23396i
\(511\) −15.0700 + 26.1020i −0.666656 + 1.15468i
\(512\) −118.781 −5.24945
\(513\) 4.00047 + 2.30967i 0.176625 + 0.101975i
\(514\) 53.1349 2.34368
\(515\) 6.09855i 0.268734i
\(516\) 10.5020 72.2497i 0.462323 3.18062i
\(517\) 2.41849i 0.106365i
\(518\) 78.6373 3.45513
\(519\) −4.10151 + 7.10402i −0.180036 + 0.311832i
\(520\) 6.09212i 0.267157i
\(521\) −2.88953 1.66827i −0.126593 0.0730884i 0.435366 0.900253i \(-0.356619\pi\)
−0.561959 + 0.827165i \(0.689952\pi\)
\(522\) 13.0128 + 7.51295i 0.569555 + 0.328833i
\(523\) −7.69278 13.3243i −0.336382 0.582630i 0.647367 0.762178i \(-0.275870\pi\)
−0.983749 + 0.179548i \(0.942537\pi\)
\(524\) 98.7126i 4.31228i
\(525\) −10.1651 17.6065i −0.443642 0.768411i
\(526\) 29.0200 50.2642i 1.26533 2.19162i
\(527\) −1.85514 18.2597i −0.0808110 0.795406i
\(528\) 17.9063 31.0146i 0.779271 1.34974i
\(529\) −11.3765 19.7046i −0.494630 0.856724i
\(530\) −9.14663 + 5.28081i −0.397304 + 0.229384i
\(531\) 0.435569 + 0.754427i 0.0189021 + 0.0327393i
\(532\) 20.5458i 0.890775i
\(533\) 2.68799 1.55191i 0.116430 0.0672209i
\(534\) 61.2181 35.3443i 2.64917 1.52950i
\(535\) −8.50417 + 14.7297i −0.367667 + 0.636819i
\(536\) −63.8638 + 110.615i −2.75850 + 4.77786i
\(537\) 29.6512i 1.27954i
\(538\) 71.8808i 3.09900i
\(539\) 3.91426 + 2.25990i 0.168599 + 0.0973408i
\(540\) −16.9961 + 29.4381i −0.731394 + 1.26681i
\(541\) −32.3384 + 18.6706i −1.39034 + 0.802711i −0.993352 0.115114i \(-0.963277\pi\)
−0.396984 + 0.917825i \(0.629943\pi\)
\(542\) −32.5252 56.3353i −1.39708 2.41981i
\(543\) 25.6132 1.09917
\(544\) 66.5229 + 92.2322i 2.85214 + 3.95442i
\(545\) 1.19501 + 2.06982i 0.0511886 + 0.0886612i
\(546\) −3.88038 6.72102i −0.166065 0.287633i
\(547\) −30.7563 17.7572i −1.31505 0.759242i −0.332119 0.943237i \(-0.607764\pi\)
−0.982927 + 0.183995i \(0.941097\pi\)
\(548\) 36.4762 1.55818
\(549\) 8.55640 + 4.94004i 0.365178 + 0.210836i
\(550\) −7.96338 + 4.59766i −0.339560 + 0.196045i
\(551\) 7.45598i 0.317635i
\(552\) −5.00836 8.67474i −0.213170 0.369221i
\(553\) 17.3335 30.0226i 0.737097 1.27669i
\(554\) 77.0767 + 44.5003i 3.27468 + 1.89064i
\(555\) 22.4597i 0.953359i
\(556\) −103.275 59.6257i −4.37982 2.52869i
\(557\) −36.3617 −1.54070 −0.770348 0.637624i \(-0.779917\pi\)
−0.770348 + 0.637624i \(0.779917\pi\)
\(558\) 9.58370i 0.405710i
\(559\) −1.73882 + 2.20407i −0.0735441 + 0.0932220i
\(560\) −80.0131 −3.38117
\(561\) −8.45172 + 0.858670i −0.356832 + 0.0362531i
\(562\) 9.04638 15.6688i 0.381598 0.660948i
\(563\) 39.6244 1.66997 0.834984 0.550274i \(-0.185477\pi\)
0.834984 + 0.550274i \(0.185477\pi\)
\(564\) −21.9880 12.6948i −0.925863 0.534547i
\(565\) 10.2627 17.7756i 0.431757 0.747824i
\(566\) 22.5463 13.0171i 0.947691 0.547150i
\(567\) 35.9861i 1.51127i
\(568\) 64.1027 37.0097i 2.68969 1.55289i
\(569\) −2.63292 + 4.56036i −0.110378 + 0.191180i −0.915923 0.401355i \(-0.868539\pi\)
0.805545 + 0.592535i \(0.201873\pi\)
\(570\) 7.91599 0.331564
\(571\) 3.61357 + 2.08630i 0.151223 + 0.0873088i 0.573702 0.819064i \(-0.305507\pi\)
−0.422479 + 0.906373i \(0.638840\pi\)
\(572\) −2.25347 + 1.30104i −0.0942223 + 0.0543993i
\(573\) −18.8363 + 10.8751i −0.786896 + 0.454315i
\(574\) −33.8235 58.5840i −1.41177 2.44525i
\(575\) 1.54988i 0.0646345i
\(576\) 16.2315 + 28.1138i 0.676312 + 1.17141i
\(577\) 13.0688 + 22.6358i 0.544061 + 0.942342i 0.998665 + 0.0516482i \(0.0164475\pi\)
−0.454604 + 0.890694i \(0.650219\pi\)
\(578\) 14.9181 44.8517i 0.620513 1.86559i
\(579\) 3.42760 5.93678i 0.142446 0.246724i
\(580\) −54.8659 −2.27818
\(581\) 28.1027i 1.16589i
\(582\) 11.8016 20.4410i 0.489193 0.847307i
\(583\) 2.54334 + 1.46840i 0.105334 + 0.0608148i
\(584\) −80.6861 + 46.5841i −3.33881 + 1.92766i
\(585\) −0.393812 + 0.227368i −0.0162821 + 0.00940050i
\(586\) 60.5497 2.50129
\(587\) 8.32686 + 14.4226i 0.343686 + 0.595282i 0.985114 0.171901i \(-0.0549909\pi\)
−0.641428 + 0.767183i \(0.721658\pi\)
\(588\) −41.0923 + 23.7247i −1.69462 + 0.978389i
\(589\) 4.11840 2.37776i 0.169696 0.0979738i
\(590\) −3.71609 2.14549i −0.152989 0.0883284i
\(591\) −48.1704 −1.98146
\(592\) 126.860 + 73.2429i 5.21393 + 3.01027i
\(593\) 12.0397 + 20.8534i 0.494412 + 0.856346i 0.999979 0.00644065i \(-0.00205014\pi\)
−0.505567 + 0.862787i \(0.668717\pi\)
\(594\) 12.7505 0.523161
\(595\) 11.1029 + 15.3939i 0.455176 + 0.631089i
\(596\) 20.4681 35.4517i 0.838405 1.45216i
\(597\) 2.55005 4.41682i 0.104367 0.180768i
\(598\) 0.591643i 0.0241941i
\(599\) −0.741295 + 1.28396i −0.0302885 + 0.0524612i −0.880772 0.473540i \(-0.842976\pi\)
0.850484 + 0.526001i \(0.176309\pi\)
\(600\) 62.8446i 2.56562i
\(601\) 25.7879i 1.05191i 0.850512 + 0.525956i \(0.176292\pi\)
−0.850512 + 0.525956i \(0.823708\pi\)
\(602\) 48.0369 + 37.8970i 1.95784 + 1.54457i
\(603\) 9.53399 0.388254
\(604\) −69.9331 −2.84554
\(605\) 11.7314 + 6.77315i 0.476951 + 0.275368i
\(606\) 94.7808i 3.85021i
\(607\) −13.8409 7.99103i −0.561784 0.324346i 0.192077 0.981380i \(-0.438478\pi\)
−0.753861 + 0.657034i \(0.771811\pi\)
\(608\) −14.7325 + 25.5175i −0.597483 + 1.03487i
\(609\) −39.4057 + 22.7509i −1.59680 + 0.921914i
\(610\) −48.6665 −1.97045
\(611\) 0.488147 + 0.845496i 0.0197483 + 0.0342051i
\(612\) 7.49977 16.6887i 0.303160 0.674600i
\(613\) 15.8431 0.639898 0.319949 0.947435i \(-0.396334\pi\)
0.319949 + 0.947435i \(0.396334\pi\)
\(614\) 3.50113 6.06414i 0.141294 0.244729i
\(615\) −16.7322 + 9.66035i −0.674708 + 0.389543i
\(616\) 18.4600 + 31.9737i 0.743776 + 1.28826i
\(617\) −22.7588 + 13.1398i −0.916235 + 0.528989i −0.882432 0.470440i \(-0.844095\pi\)
−0.0338032 + 0.999429i \(0.510762\pi\)
\(618\) 24.0153i 0.966036i
\(619\) −11.2905 + 6.51858i −0.453804 + 0.262004i −0.709435 0.704770i \(-0.751050\pi\)
0.255631 + 0.966774i \(0.417717\pi\)
\(620\) 17.4971 + 30.3058i 0.702700 + 1.21711i
\(621\) 1.07456 1.86119i 0.0431206 0.0746870i
\(622\) −30.3515 17.5235i −1.21699 0.702627i
\(623\) 43.9155i 1.75944i
\(624\) 14.4568i 0.578734i
\(625\) −0.157750 + 0.273232i −0.00631002 + 0.0109293i
\(626\) −23.8840 13.7894i −0.954597 0.551137i
\(627\) −1.10057 1.90625i −0.0439526 0.0761281i
\(628\) −5.71754 9.90307i −0.228155 0.395175i
\(629\) −3.51226 34.5705i −0.140043 1.37842i
\(630\) 4.95541 + 8.58302i 0.197428 + 0.341956i
\(631\) −7.00329 12.1301i −0.278797 0.482890i 0.692289 0.721620i \(-0.256602\pi\)
−0.971086 + 0.238730i \(0.923269\pi\)
\(632\) 92.8054 53.5812i 3.69160 2.13135i
\(633\) −2.51952 + 4.36394i −0.100142 + 0.173451i
\(634\) 54.6710i 2.17126i
\(635\) 16.1538 + 9.32642i 0.641045 + 0.370108i
\(636\) −26.7002 + 15.4154i −1.05873 + 0.611260i
\(637\) 1.82455 0.0722912
\(638\) 10.2902 + 17.8231i 0.407392 + 0.705624i
\(639\) −4.78483 2.76252i −0.189285 0.109284i
\(640\) −72.9500 42.1177i −2.88360 1.66485i
\(641\) 25.5761i 1.01019i −0.863063 0.505097i \(-0.831457\pi\)
0.863063 0.505097i \(-0.168543\pi\)
\(642\) −33.4883 + 58.0034i −1.32168 + 2.28921i
\(643\) 47.0244i 1.85446i −0.374491 0.927231i \(-0.622183\pi\)
0.374491 0.927231i \(-0.377817\pi\)
\(644\) 9.55881 0.376670
\(645\) 10.8238 13.7199i 0.426186 0.540219i
\(646\) 12.1845 1.23791i 0.479393 0.0487049i
\(647\) −24.6397 −0.968685 −0.484343 0.874878i \(-0.660941\pi\)
−0.484343 + 0.874878i \(0.660941\pi\)
\(648\) −55.6199 + 96.3365i −2.18496 + 3.78446i
\(649\) 1.19316i 0.0468357i
\(650\) −1.85598 + 3.21465i −0.0727974 + 0.126089i
\(651\) 25.1335 + 14.5108i 0.985059 + 0.568724i
\(652\) 59.6579 34.4435i 2.33638 1.34891i
\(653\) 47.4341i 1.85624i 0.372281 + 0.928120i \(0.378576\pi\)
−0.372281 + 0.928120i \(0.621424\pi\)
\(654\) 4.70579 + 8.15066i 0.184011 + 0.318716i
\(655\) 11.8139 20.4623i 0.461607 0.799527i
\(656\) 126.013i 4.91998i
\(657\) 6.02266 + 3.47719i 0.234966 + 0.135658i
\(658\) 18.4273 10.6390i 0.718372 0.414752i
\(659\) −14.6409 25.3588i −0.570328 0.987837i −0.996532 0.0832098i \(-0.973483\pi\)
0.426204 0.904627i \(-0.359850\pi\)
\(660\) 14.0274 8.09872i 0.546015 0.315242i
\(661\) 28.9918 1.12765 0.563826 0.825894i \(-0.309329\pi\)
0.563826 + 0.825894i \(0.309329\pi\)
\(662\) 15.2765 + 26.4596i 0.593737 + 1.02838i
\(663\) −2.78137 + 2.00608i −0.108020 + 0.0779096i
\(664\) −43.4353 + 75.2322i −1.68562 + 2.91958i
\(665\) −2.45892 + 4.25897i −0.0953528 + 0.165156i
\(666\) 18.1445i 0.703084i
\(667\) 3.46884 0.134314
\(668\) 46.1260 + 26.6308i 1.78467 + 1.03038i
\(669\) 4.21738 + 2.43491i 0.163054 + 0.0941390i
\(670\) −40.6701 + 23.4809i −1.57122 + 0.907145i
\(671\) 6.76617 + 11.7194i 0.261205 + 0.452421i
\(672\) −179.817 −6.93661
\(673\) −9.80220 + 5.65930i −0.377847 + 0.218150i −0.676881 0.736092i \(-0.736669\pi\)
0.299034 + 0.954242i \(0.403336\pi\)
\(674\) −51.0669 + 29.4835i −1.96702 + 1.13566i
\(675\) 11.6771 6.74176i 0.449450 0.259490i
\(676\) 36.7256 63.6107i 1.41252 2.44656i
\(677\) 29.9375i 1.15059i 0.817946 + 0.575295i \(0.195113\pi\)
−0.817946 + 0.575295i \(0.804887\pi\)
\(678\) 40.4133 69.9979i 1.55206 2.68825i
\(679\) 7.33180 + 12.6990i 0.281369 + 0.487345i
\(680\) 5.93031 + 58.3709i 0.227417 + 2.23842i
\(681\) −11.6086 20.1066i −0.444841 0.770487i
\(682\) 6.56320 11.3678i 0.251318 0.435296i
\(683\) 17.9935 + 10.3886i 0.688502 + 0.397507i 0.803051 0.595911i \(-0.203209\pi\)
−0.114548 + 0.993418i \(0.536542\pi\)
\(684\) 4.74067 0.181264
\(685\) 7.56119 + 4.36545i 0.288898 + 0.166795i
\(686\) 25.5500i 0.975503i
\(687\) 29.8465i 1.13872i
\(688\) 42.1975 + 105.878i 1.60877 + 4.03658i
\(689\) 1.18552 0.0451648
\(690\) 3.68286i 0.140204i
\(691\) −11.1736 6.45107i −0.425063 0.245410i 0.272178 0.962247i \(-0.412256\pi\)
−0.697241 + 0.716837i \(0.745589\pi\)
\(692\) 24.1979i 0.919865i
\(693\) 1.37792 2.38662i 0.0523427 0.0906602i
\(694\) −9.67274 5.58456i −0.367172 0.211987i
\(695\) −14.2720 24.7198i −0.541366 0.937674i
\(696\) −140.655 −5.33151
\(697\) −24.2440 + 17.4861i −0.918305 + 0.662331i
\(698\) −19.8811 + 34.4350i −0.752509 + 1.30338i
\(699\) −13.3484 −0.504883
\(700\) 51.9370 + 29.9858i 1.96303 + 1.13336i
\(701\) 14.4726 + 25.0673i 0.546624 + 0.946780i 0.998503 + 0.0547008i \(0.0174205\pi\)
−0.451879 + 0.892079i \(0.649246\pi\)
\(702\) 4.45754 2.57356i 0.168239 0.0971329i
\(703\) 7.79721 4.50172i 0.294077 0.169786i
\(704\) 44.4632i 1.67577i
\(705\) −3.03862 5.26304i −0.114441 0.198218i
\(706\) −12.6305 21.8766i −0.475353 0.823336i
\(707\) −50.9941 29.4414i −1.91783 1.10726i
\(708\) −10.8478 6.26297i −0.407684 0.235377i
\(709\) 43.3043i 1.62633i 0.582034 + 0.813164i \(0.302257\pi\)
−0.582034 + 0.813164i \(0.697743\pi\)
\(710\) 27.2148 1.02135
\(711\) −6.92729 3.99947i −0.259794 0.149992i
\(712\) −67.8756 + 117.564i −2.54374 + 4.40590i
\(713\) −1.10624 1.91606i −0.0414289 0.0717569i
\(714\) 43.7218 + 60.6192i 1.63625 + 2.26862i
\(715\) −0.622833 −0.0232926
\(716\) 43.7337 + 75.7490i 1.63441 + 2.83087i
\(717\) −2.68967 + 1.55288i −0.100448 + 0.0579934i
\(718\) 22.0479 + 38.1880i 0.822820 + 1.42517i
\(719\) −23.2248 13.4088i −0.866139 0.500066i −7.56518e−5 1.00000i \(-0.500024\pi\)
−0.866063 + 0.499934i \(0.833357\pi\)
\(720\) 18.4619i 0.688035i
\(721\) 12.9207 + 7.45979i 0.481193 + 0.277817i
\(722\) −24.8276 43.0027i −0.923988 1.60039i
\(723\) −14.1741 −0.527139
\(724\) −65.4333 + 37.7779i −2.43181 + 1.40401i
\(725\) 18.8477 + 10.8817i 0.699985 + 0.404137i
\(726\) 46.1968 + 26.6718i 1.71453 + 0.989882i
\(727\) −11.7441 −0.435563 −0.217782 0.975998i \(-0.569882\pi\)
−0.217782 + 0.975998i \(0.569882\pi\)
\(728\) 12.9071 + 7.45193i 0.478370 + 0.276187i
\(729\) −16.8980 −0.625852
\(730\) −34.2553 −1.26784
\(731\) 14.5147 22.8106i 0.536846 0.843680i
\(732\) −142.064 −5.25084
\(733\) 51.9958 1.92051 0.960254 0.279127i \(-0.0900451\pi\)
0.960254 + 0.279127i \(0.0900451\pi\)
\(734\) −86.4864 49.9329i −3.19227 1.84306i
\(735\) −11.3574 −0.418926
\(736\) 11.8718 + 6.85421i 0.437602 + 0.252650i
\(737\) 11.3088 + 6.52916i 0.416566 + 0.240505i
\(738\) −13.5174 + 7.80430i −0.497584 + 0.287280i
\(739\) 16.7365 0.615660 0.307830 0.951441i \(-0.400397\pi\)
0.307830 + 0.951441i \(0.400397\pi\)
\(740\) 33.1266 + 57.3769i 1.21776 + 2.10922i
\(741\) −0.769511 0.444277i −0.0282687 0.0163209i
\(742\) 25.8381i 0.948547i
\(743\) −21.3618 12.3332i −0.783687 0.452462i 0.0540483 0.998538i \(-0.482787\pi\)
−0.837735 + 0.546076i \(0.816121\pi\)
\(744\) 44.8557 + 77.6923i 1.64449 + 2.84834i
\(745\) 8.48570 4.89922i 0.310892 0.179494i
\(746\) 19.5659 + 33.8891i 0.716359 + 1.24077i
\(747\) 6.48430 0.237248
\(748\) 20.3248 14.6594i 0.743149 0.536000i
\(749\) −20.8047 36.0348i −0.760188 1.31668i
\(750\) 30.0776 52.0959i 1.09828 1.90228i
\(751\) 30.1476 + 17.4057i 1.10010 + 0.635145i 0.936248 0.351340i \(-0.114274\pi\)
0.163855 + 0.986484i \(0.447607\pi\)
\(752\) 39.6368 1.44541
\(753\) 36.0742i 1.31462i
\(754\) 7.19481 + 4.15393i 0.262020 + 0.151277i
\(755\) −14.4965 8.36957i −0.527582 0.304600i
\(756\) −41.5794 72.0177i −1.51223 2.61926i
\(757\) −19.2336 33.3136i −0.699057 1.21080i −0.968794 0.247868i \(-0.920270\pi\)
0.269737 0.962934i \(-0.413063\pi\)
\(758\) 94.2259i 3.42244i
\(759\) −0.886868 + 0.512033i −0.0321913 + 0.0185856i
\(760\) −13.1653 + 7.60098i −0.477555 + 0.275717i
\(761\) 1.28052 + 2.21792i 0.0464188 + 0.0803997i 0.888301 0.459261i \(-0.151886\pi\)
−0.841882 + 0.539661i \(0.818552\pi\)
\(762\) 63.6116 + 36.7262i 2.30441 + 1.33045i
\(763\)