Properties

Label 731.2.j.a.135.2
Level 731
Weight 2
Character 731.135
Analytic conductor 5.837
Analytic rank 0
Dimension 128
CM no
Inner twists 4

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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 135.2
Character \(\chi\) = 731.135
Dual form 731.2.j.a.509.2

$q$-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} +(-1.69008 - 3.76080i) 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} +(4.69918 + 10.4567i) 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} +(-9.68567 - 21.5528i) 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 0.899657 0.436598i \(-0.143817\pi\)
0.0717233 + 0.997425i \(0.477150\pi\)
\(4\) 5.73090 2.86545
\(5\) −1.18797 0.685872i −0.531274 0.306731i 0.210261 0.977645i \(-0.432569\pi\)
−0.741535 + 0.670914i \(0.765902\pi\)
\(6\) −4.67805 2.70087i −1.90981 1.10263i
\(7\) 2.90625 1.67793i 1.09846 0.634197i 0.162645 0.986685i \(-0.447998\pi\)
0.935816 + 0.352488i \(0.114664\pi\)
\(8\) −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 \(-0.948888\pi\)
0.987136 0.159884i \(-0.0511120\pi\)
\(12\) 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
\(17\) −1.69008 3.76080i −0.409904 0.912129i
\(18\) −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 0.544204 0.838953i \(-0.316832\pi\)
−0.454452 + 0.890771i \(0.650165\pi\)
\(24\) −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 0.180370 0.983599i \(-0.442271\pi\)
0.942006 + 0.335595i \(0.108937\pi\)
\(30\) 3.70491 + 6.41709i 0.676420 + 1.17159i
\(31\) −3.85505 2.22572i −0.692388 0.399750i 0.112118 0.993695i \(-0.464237\pi\)
−0.804506 + 0.593944i \(0.797570\pi\)
\(32\) −27.5810 −4.87567
\(33\) 1.03020 1.78435i 0.179334 0.310616i
\(34\) 4.69918 + 10.4567i 0.805902 + 1.79331i
\(35\) −4.60337 −0.778112
\(36\) 2.21877 + 3.84301i 0.369794 + 0.640502i
\(37\) −7.29863 4.21387i −1.19989 0.692755i −0.239357 0.970932i \(-0.576937\pi\)
−0.960530 + 0.278176i \(0.910270\pi\)
\(38\) −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 \(0.191556\pi\)
−0.824323 + 0.566120i \(0.808444\pi\)
\(42\) −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 −0.995839 0.0911264i \(-0.970953\pi\)
−0.419002 + 0.907985i \(0.637620\pi\)
\(62\) 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 \(-0.104303\pi\)
\(68\) −9.68567 21.5528i −1.17456 2.61366i
\(69\) 0.482800 + 0.836234i 0.0581223 + 0.100671i
\(70\) 12.7994 1.52983
\(71\) 6.17942 3.56769i 0.733362 0.423407i −0.0862889 0.996270i \(-0.527501\pi\)
0.819651 + 0.572863i \(0.194167\pi\)
\(72\) −4.01622 6.95629i −0.473316 0.819807i
\(73\) −7.77804 + 4.49065i −0.910350 + 0.525591i −0.880544 0.473965i \(-0.842822\pi\)
−0.0298066 + 0.999556i \(0.509489\pi\)
\(74\) 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 0.0963633 0.995346i \(-0.469279\pi\)
0.910177 + 0.414220i \(0.135946\pi\)
\(80\) −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 \(0.0712032\pi\)
−0.975085 + 0.221831i \(0.928797\pi\)
\(98\) −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 \(-0.795433\pi\)
0.800501 0.599331i \(-0.204567\pi\)
\(108\) 24.7802i 2.38448i
\(109\) −1.50889 0.871161i −0.144526 0.0834421i 0.425993 0.904726i \(-0.359925\pi\)
−0.570519 + 0.821284i \(0.693258\pi\)
\(110\) 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 \(0.248516\pi\)
−0.710395 + 0.703803i \(0.751484\pi\)
\(114\) −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
\(119\) −11.2221 8.09402i −1.02873 0.741978i
\(120\) 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 \(0.271134\pi\)
−0.658636 + 0.752461i \(0.728866\pi\)
\(132\) 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
\(136\) 17.5322 + 39.0130i 1.50337 + 3.34534i
\(137\) 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 \(0.0107920\pi\)
0.529069 + 0.848579i \(0.322541\pi\)
\(140\) −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
\(153\) 1.86758 2.58935i 0.150985 0.209337i
\(154\) 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 −0.848815 0.528690i \(-0.822683\pi\)
0.0334516 + 0.999440i \(0.489350\pi\)
\(164\) 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 0.155144 0.987892i \(-0.450416\pi\)
−0.777967 + 0.628305i \(0.783749\pi\)
\(168\) −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 \(0.0513138\pi\)
−0.987034 + 0.160510i \(0.948686\pi\)
\(174\) −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 −0.0115344 0.999933i \(-0.503672\pi\)
0.860201 + 0.509956i \(0.170338\pi\)
\(182\) −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
\(187\) −3.98852 + 1.79241i −0.291669 + 0.131074i
\(188\) 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 \(-0.959466\pi\)
0.991903 0.126997i \(-0.0405338\pi\)
\(194\) 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 \(0.678002\pi\)
−0.999366 + 0.0356042i \(0.988664\pi\)
\(198\) −1.97740 + 1.14165i −0.140528 + 0.0811339i
\(199\) 2.62518i 0.186094i −0.995662 0.0930472i \(-0.970339\pi\)
0.995662 0.0930472i \(-0.0296607\pi\)
\(200\) 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 \(0.0284569\pi\)
−0.996006 + 0.0892808i \(0.971543\pi\)
\(212\) 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
\(221\) 1.03259 1.43166i 0.0694596 0.0963039i
\(222\) 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 0.115537 0.993303i \(-0.463141\pi\)
−0.802458 + 0.596709i \(0.796475\pi\)
\(228\) 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 −0.682082 0.731276i \(-0.738925\pi\)
0.292263 + 0.956338i \(0.405592\pi\)
\(234\) 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
\(238\) 31.2026 + 22.5050i 2.02257 + 1.45878i
\(239\) 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 −0.689501 0.724285i \(-0.742170\pi\)
0.282498 + 0.959268i \(0.408837\pi\)
\(242\) −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
\(255\) −6.42767 + 8.91180i −0.402516 + 0.558078i
\(256\) 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 \(-0.711055\pi\)
0.615523 0.788119i \(-0.288945\pi\)
\(270\) 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 \(0.581761\pi\)
\(272\) −29.3759 65.3680i −1.78118 3.96352i
\(273\) 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 \(0.0782034\pi\)
0.695620 + 0.718410i \(0.255130\pi\)
\(278\) −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 −0.239237 0.970961i \(-0.576897\pi\)
0.721259 + 0.692666i \(0.243564\pi\)
\(284\) 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
\(289\) −11.2873 + 12.7121i −0.663957 + 0.747771i
\(290\) 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
\(306\) −5.19272 + 7.19957i −0.296848 + 0.411572i
\(307\) −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 0.157484 0.987521i \(-0.449662\pi\)
−0.776477 + 0.630146i \(0.782995\pi\)
\(312\) 8.62809i 0.488470i
\(313\) −8.58998 4.95943i −0.485534 0.280323i 0.237186 0.971464i \(-0.423775\pi\)
−0.722720 + 0.691141i \(0.757108\pi\)
\(314\) 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 \(-0.813795\pi\)
0.833723 0.552182i \(-0.186205\pi\)
\(318\) −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 −0.908391 0.418121i \(-0.862689\pi\)
−0.0920919 + 0.995751i \(0.529355\pi\)
\(338\) −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 0.403708 0.914888i \(-0.367721\pi\)
−0.590462 + 0.807065i \(0.701054\pi\)
\(348\) 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
\(357\) −11.0187 24.5190i −0.583170 1.29768i
\(358\) −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 \(-0.946531\pi\)
−0.637752 0.770241i \(-0.720136\pi\)
\(368\) 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 \(0.952046\pi\)
\(374\) 11.0899 4.98371i 0.573444 0.257702i
\(375\) −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 \(0.336123\pi\)
−0.492392 + 0.870374i \(0.663877\pi\)
\(380\) −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 0.900345 0.435178i \(-0.143314\pi\)
0.0732975 + 0.997310i \(0.476648\pi\)
\(398\) 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 −0.934327 0.356418i \(-0.883998\pi\)
−0.158496 + 0.987360i \(0.550665\pi\)
\(402\) −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 \(0.149255\pi\)
−0.892067 + 0.451904i \(0.850745\pi\)
\(420\) −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
\(425\) −7.52111 + 10.4278i −0.364827 + 0.505824i
\(426\) −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 \(0.0641028\pi\)
−0.979790 + 0.200027i \(0.935897\pi\)
\(432\) 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 −0.582437 0.812876i \(-0.697901\pi\)
0.412753 + 0.910843i \(0.364567\pi\)
\(440\) 7.54576 13.0696i 0.359730 0.623070i
\(441\) 3.29995 0.157140
\(442\) −2.87107 + 3.98066i −0.136563 + 0.189341i
\(443\) −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 0.912240 0.409655i \(-0.134351\pi\)
0.101349 + 0.994851i \(0.467684\pi\)
\(450\) −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
\(459\) −16.2616 + 7.30785i −0.759026 + 0.341101i
\(460\) −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
\(476\) −64.3130 46.3860i −2.94778 2.12610i
\(477\) 2.14418 0.0981752
\(478\) −2.22246 + 3.84942i −0.101653 + 0.176068i
\(479\) −5.93134 3.42446i −0.271010 0.156468i 0.358337 0.933592i \(-0.383344\pi\)
−0.629346 + 0.777125i \(0.716677\pi\)
\(480\) 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 0.420290 0.907390i \(-0.361928\pi\)
0.995968 + 0.0897130i \(0.0285950\pi\)
\(488\) 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
\(493\) −23.3389 16.8333i −1.05113 0.758132i
\(494\) −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 −0.999846 0.0175654i \(-0.994408\pi\)
−0.484711 + 0.874675i \(0.661075\pi\)
\(500\) 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 −0.753184 0.657810i \(-0.771483\pi\)
0.193088 + 0.981182i \(0.438150\pi\)
\(504\) −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 \(0.793566\pi\)
\(510\) 17.8718 24.7788i 0.791377 1.09722i
\(511\) −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 0.561959 0.827165i \(-0.310048\pi\)
−0.435366 + 0.900253i \(0.643381\pi\)
\(522\) −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 0.396984 0.917825i \(-0.370057\pi\)
0.993352 + 0.115114i \(0.0367235\pi\)
\(542\) −32.5252 56.3353i −1.39708 2.41981i
\(543\) 25.6132 1.09917
\(544\) 46.6140 + 103.727i 1.99856 + 4.44724i
\(545\) 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 0.982927 0.183995i \(-0.0589030\pi\)
0.332119 + 0.943237i \(0.392236\pi\)
\(548\) 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 0.422479 0.906373i \(-0.361160\pi\)
−0.573702 + 0.819064i \(0.694493\pi\)
\(572\) 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 \(0.650219\pi\)
\(578\) 31.3837 35.3454i 1.30539 1.47017i
\(579\) 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
\(595\) 7.78006 + 17.3124i 0.318951 + 0.709738i
\(596\) 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 \(-0.823708\pi\)
0.850512 0.525956i \(-0.176292\pi\)
\(602\) −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 0.753861 0.657034i \(-0.228189\pi\)
−0.192077 + 0.981380i \(0.561522\pi\)
\(608\) −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
\(612\) 10.7029 14.8393i 0.432640 0.599844i
\(613\) 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 0.0338032 0.999429i \(-0.489238\pi\)
0.882432 + 0.470440i \(0.155905\pi\)
\(618\) 24.0153i 0.966036i
\(619\) 11.2905 6.51858i 0.453804 0.262004i −0.255631 0.966774i \(-0.582283\pi\)
0.709435 + 0.704770i \(0.248950\pi\)
\(620\) 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 \(0.168543\pi\)
−0.863063 + 0.505097i \(0.831457\pi\)
\(642\) −33.4883 + 58.0034i −1.32168 + 2.28921i
\(643\) 47.0244i 1.85446i 0.374491 + 0.927231i \(0.377817\pi\)
−0.374491 + 0.927231i \(0.622183\pi\)
\(644\) 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 \(-0.621424\pi\)
0.372281 0.928120i \(-0.378576\pi\)
\(654\) 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
\(663\) 3.12800 1.40570i 0.121481 0.0545929i
\(664\) −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 −0.299034 0.954242i \(-0.596664\pi\)
0.676881 + 0.736092i \(0.263331\pi\)
\(674\) 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 \(-0.804887\pi\)
0.817946 0.575295i \(-0.195113\pi\)
\(678\) 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 0.114548 0.993418i \(-0.463458\pi\)
−0.803051 + 0.595911i \(0.796791\pi\)
\(684\) 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 0.697241 0.716837i \(-0.254411\pi\)
−0.272178 + 0.962247i \(0.587744\pi\)
\(692\) 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
\(697\) 27.2653 12.2529i 1.03275 0.464110i
\(698\) −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 \(-0.697743\pi\)
0.582034 0.813164i \(-0.302257\pi\)
\(710\) 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
\(714\) 30.6368 + 68.1738i 1.14656 + 2.55134i
\(715\) −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 0.866063 0.499934i \(-0.166643\pi\)
7.56518e−5 1.00000i \(0.499976\pi\)
\(720\) 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
\(731\) 18.8058 19.4253i 0.695556 0.718471i
\(732\) −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 0.837735 0.546076i \(-0.183879\pi\)
−0.0540483 + 0.998538i \(0.517213\pi\)
\(744\) 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
\(748\) −22.8578 + 10.2721i −0.835764 + 0.375587i
\(749\) −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 −0.163855 0.986484i \(-0.552393\pi\)
−0.936248 + 0.351340i \(0.885726\pi\)
\(752\) 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