Properties

Label 731.2.j.a.135.11
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 135.11
Character \(\chi\) = 731.135
Dual form 731.2.j.a.509.11

$q$-expansion

\(f(q)\) \(=\) \(q-2.05109 q^{2} +(-2.62751 - 1.51699i) q^{3} +2.20698 q^{4} +(2.73044 + 1.57642i) q^{5} +(5.38926 + 3.11149i) q^{6} +(0.592018 - 0.341802i) q^{7} -0.424527 q^{8} +(3.10253 + 5.37374i) q^{9} +O(q^{10})\) \(q-2.05109 q^{2} +(-2.62751 - 1.51699i) q^{3} +2.20698 q^{4} +(2.73044 + 1.57642i) q^{5} +(5.38926 + 3.11149i) q^{6} +(0.592018 - 0.341802i) q^{7} -0.424527 q^{8} +(3.10253 + 5.37374i) q^{9} +(-5.60038 - 3.23338i) q^{10} +5.64679i q^{11} +(-5.79885 - 3.34797i) q^{12} +(2.15005 + 3.72399i) q^{13} +(-1.21428 + 0.701067i) q^{14} +(-4.78283 - 8.28411i) q^{15} -3.54321 q^{16} +(3.49409 + 2.18891i) q^{17} +(-6.36357 - 11.0220i) q^{18} +(0.516837 - 0.895188i) q^{19} +(6.02601 + 3.47912i) q^{20} -2.07404 q^{21} -11.5821i q^{22} +(-5.57224 - 3.21713i) q^{23} +(1.11545 + 0.644003i) q^{24} +(2.47020 + 4.27851i) q^{25} +(-4.40994 - 7.63825i) q^{26} -9.72411i q^{27} +(1.30657 - 0.754348i) q^{28} +(-5.65872 + 3.26706i) q^{29} +(9.81003 + 16.9915i) q^{30} +(-1.62115 - 0.935974i) q^{31} +8.11650 q^{32} +(8.56614 - 14.8370i) q^{33} +(-7.16670 - 4.48966i) q^{34} +2.15529 q^{35} +(6.84721 + 11.8597i) q^{36} +(-9.34986 - 5.39814i) q^{37} +(-1.06008 + 1.83611i) q^{38} -13.0464i q^{39} +(-1.15914 - 0.669232i) q^{40} +2.21300i q^{41} +4.25405 q^{42} +(-3.47316 + 5.56212i) q^{43} +12.4623i q^{44} +19.5636i q^{45} +(11.4292 + 6.59864i) q^{46} +5.35132 q^{47} +(9.30981 + 5.37502i) q^{48} +(-3.26634 + 5.65747i) q^{49} +(-5.06661 - 8.77562i) q^{50} +(-5.86018 - 11.0519i) q^{51} +(4.74510 + 8.21876i) q^{52} +(0.600594 - 1.04026i) q^{53} +19.9450i q^{54} +(-8.90171 + 15.4182i) q^{55} +(-0.251327 + 0.145104i) q^{56} +(-2.71599 + 1.56808i) q^{57} +(11.6066 - 6.70105i) q^{58} -8.40734 q^{59} +(-10.5556 - 18.2828i) q^{60} +(-9.40100 + 5.42767i) q^{61} +(3.32514 + 1.91977i) q^{62} +(3.67351 + 2.12090i) q^{63} -9.56126 q^{64} +13.5575i q^{65} +(-17.5699 + 30.4320i) q^{66} +(1.27484 - 2.20809i) q^{67} +(7.71137 + 4.83088i) q^{68} +(9.76073 + 16.9061i) q^{69} -4.42070 q^{70} +(6.92813 - 3.99996i) q^{71} +(-1.31711 - 2.28130i) q^{72} +(6.67168 - 3.85190i) q^{73} +(19.1774 + 11.0721i) q^{74} -14.9891i q^{75} +(1.14065 - 1.97566i) q^{76} +(1.93008 + 3.34300i) q^{77} +26.7594i q^{78} +(-10.9204 + 6.30489i) q^{79} +(-9.67452 - 5.58559i) q^{80} +(-5.44380 + 9.42894i) q^{81} -4.53907i q^{82} +(-0.172186 + 0.298235i) q^{83} -4.57736 q^{84} +(6.08975 + 11.4848i) q^{85} +(7.12377 - 11.4084i) q^{86} +19.8244 q^{87} -2.39721i q^{88} +(3.74679 - 6.48963i) q^{89} -40.1267i q^{90} +(2.54573 + 1.46978i) q^{91} +(-12.2978 - 7.10014i) q^{92} +(2.83973 + 4.91856i) q^{93} -10.9761 q^{94} +(2.82238 - 1.62950i) q^{95} +(-21.3262 - 12.3127i) q^{96} -9.03426i q^{97} +(6.69957 - 11.6040i) q^{98} +(-30.3444 + 17.5193i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.05109 −1.45034 −0.725170 0.688570i \(-0.758239\pi\)
−0.725170 + 0.688570i \(0.758239\pi\)
\(3\) −2.62751 1.51699i −1.51699 0.875836i −0.999801 0.0199662i \(-0.993644\pi\)
−0.517192 0.855870i \(-0.673023\pi\)
\(4\) 2.20698 1.10349
\(5\) 2.73044 + 1.57642i 1.22109 + 0.704996i 0.965150 0.261696i \(-0.0842819\pi\)
0.255939 + 0.966693i \(0.417615\pi\)
\(6\) 5.38926 + 3.11149i 2.20016 + 1.27026i
\(7\) 0.592018 0.341802i 0.223762 0.129189i −0.383929 0.923363i \(-0.625429\pi\)
0.607691 + 0.794174i \(0.292096\pi\)
\(8\) −0.424527 −0.150093
\(9\) 3.10253 + 5.37374i 1.03418 + 1.79125i
\(10\) −5.60038 3.23338i −1.77100 1.02249i
\(11\) 5.64679i 1.70257i 0.524703 + 0.851286i \(0.324176\pi\)
−0.524703 + 0.851286i \(0.675824\pi\)
\(12\) −5.79885 3.34797i −1.67398 0.966474i
\(13\) 2.15005 + 3.72399i 0.596316 + 1.03285i 0.993360 + 0.115050i \(0.0367028\pi\)
−0.397044 + 0.917800i \(0.629964\pi\)
\(14\) −1.21428 + 0.701067i −0.324531 + 0.187368i
\(15\) −4.78283 8.28411i −1.23492 2.13895i
\(16\) −3.54321 −0.885802
\(17\) 3.49409 + 2.18891i 0.847441 + 0.530890i
\(18\) −6.36357 11.0220i −1.49991 2.59792i
\(19\) 0.516837 0.895188i 0.118571 0.205370i −0.800631 0.599158i \(-0.795502\pi\)
0.919201 + 0.393788i \(0.128835\pi\)
\(20\) 6.02601 + 3.47912i 1.34746 + 0.777955i
\(21\) −2.07404 −0.452593
\(22\) 11.5821i 2.46931i
\(23\) −5.57224 3.21713i −1.16189 0.670819i −0.210136 0.977672i \(-0.567391\pi\)
−0.951757 + 0.306853i \(0.900724\pi\)
\(24\) 1.11545 + 0.644003i 0.227690 + 0.131457i
\(25\) 2.47020 + 4.27851i 0.494040 + 0.855703i
\(26\) −4.40994 7.63825i −0.864861 1.49798i
\(27\) 9.72411i 1.87141i
\(28\) 1.30657 0.754348i 0.246918 0.142558i
\(29\) −5.65872 + 3.26706i −1.05080 + 0.606678i −0.922873 0.385105i \(-0.874165\pi\)
−0.127925 + 0.991784i \(0.540832\pi\)
\(30\) 9.81003 + 16.9915i 1.79106 + 3.10220i
\(31\) −1.62115 0.935974i −0.291168 0.168106i 0.347301 0.937754i \(-0.387098\pi\)
−0.638468 + 0.769648i \(0.720432\pi\)
\(32\) 8.11650 1.43481
\(33\) 8.56614 14.8370i 1.49117 2.58279i
\(34\) −7.16670 4.48966i −1.22908 0.769971i
\(35\) 2.15529 0.364311
\(36\) 6.84721 + 11.8597i 1.14120 + 1.97662i
\(37\) −9.34986 5.39814i −1.53711 0.887449i −0.999006 0.0445691i \(-0.985809\pi\)
−0.538101 0.842880i \(-0.680858\pi\)
\(38\) −1.06008 + 1.83611i −0.171968 + 0.297857i
\(39\) 13.0464i 2.08910i
\(40\) −1.15914 0.669232i −0.183277 0.105815i
\(41\) 2.21300i 0.345613i 0.984956 + 0.172806i \(0.0552835\pi\)
−0.984956 + 0.172806i \(0.944716\pi\)
\(42\) 4.25405 0.656414
\(43\) −3.47316 + 5.56212i −0.529652 + 0.848215i
\(44\) 12.4623i 1.87877i
\(45\) 19.5636i 2.91636i
\(46\) 11.4292 + 6.59864i 1.68514 + 0.972916i
\(47\) 5.35132 0.780571 0.390285 0.920694i \(-0.372376\pi\)
0.390285 + 0.920694i \(0.372376\pi\)
\(48\) 9.30981 + 5.37502i 1.34376 + 0.775817i
\(49\) −3.26634 + 5.65747i −0.466620 + 0.808210i
\(50\) −5.06661 8.77562i −0.716526 1.24106i
\(51\) −5.86018 11.0519i −0.820589 1.54757i
\(52\) 4.74510 + 8.21876i 0.658028 + 1.13974i
\(53\) 0.600594 1.04026i 0.0824979 0.142891i −0.821824 0.569741i \(-0.807044\pi\)
0.904322 + 0.426850i \(0.140377\pi\)
\(54\) 19.9450i 2.71418i
\(55\) −8.90171 + 15.4182i −1.20031 + 2.07899i
\(56\) −0.251327 + 0.145104i −0.0335850 + 0.0193903i
\(57\) −2.71599 + 1.56808i −0.359741 + 0.207697i
\(58\) 11.6066 6.70105i 1.52401 0.879890i
\(59\) −8.40734 −1.09454 −0.547271 0.836955i \(-0.684333\pi\)
−0.547271 + 0.836955i \(0.684333\pi\)
\(60\) −10.5556 18.2828i −1.36272 2.36030i
\(61\) −9.40100 + 5.42767i −1.20367 + 0.694942i −0.961370 0.275259i \(-0.911236\pi\)
−0.242304 + 0.970200i \(0.577903\pi\)
\(62\) 3.32514 + 1.91977i 0.422293 + 0.243811i
\(63\) 3.67351 + 2.12090i 0.462819 + 0.267208i
\(64\) −9.56126 −1.19516
\(65\) 13.5575i 1.68160i
\(66\) −17.5699 + 30.4320i −2.16271 + 3.74592i
\(67\) 1.27484 2.20809i 0.155747 0.269761i −0.777584 0.628779i \(-0.783555\pi\)
0.933331 + 0.359018i \(0.116888\pi\)
\(68\) 7.71137 + 4.83088i 0.935141 + 0.585830i
\(69\) 9.76073 + 16.9061i 1.17505 + 2.03525i
\(70\) −4.42070 −0.528375
\(71\) 6.92813 3.99996i 0.822218 0.474708i −0.0289626 0.999580i \(-0.509220\pi\)
0.851181 + 0.524873i \(0.175887\pi\)
\(72\) −1.31711 2.28130i −0.155223 0.268853i
\(73\) 6.67168 3.85190i 0.780861 0.450830i −0.0558742 0.998438i \(-0.517795\pi\)
0.836735 + 0.547607i \(0.184461\pi\)
\(74\) 19.1774 + 11.0721i 2.22933 + 1.28710i
\(75\) 14.9891i 1.73079i
\(76\) 1.14065 1.97566i 0.130841 0.226623i
\(77\) 1.93008 + 3.34300i 0.219953 + 0.380970i
\(78\) 26.7594i 3.02991i
\(79\) −10.9204 + 6.30489i −1.22864 + 0.709355i −0.966745 0.255742i \(-0.917680\pi\)
−0.261894 + 0.965097i \(0.584347\pi\)
\(80\) −9.67452 5.58559i −1.08164 0.624487i
\(81\) −5.44380 + 9.42894i −0.604867 + 1.04766i
\(82\) 4.53907i 0.501256i
\(83\) −0.172186 + 0.298235i −0.0188999 + 0.0327356i −0.875321 0.483543i \(-0.839350\pi\)
0.856421 + 0.516278i \(0.172683\pi\)
\(84\) −4.57736 −0.499431
\(85\) 6.08975 + 11.4848i 0.660526 + 1.24571i
\(86\) 7.12377 11.4084i 0.768176 1.23020i
\(87\) 19.8244 2.12540
\(88\) 2.39721i 0.255544i
\(89\) 3.74679 6.48963i 0.397159 0.687899i −0.596215 0.802824i \(-0.703330\pi\)
0.993374 + 0.114926i \(0.0366629\pi\)
\(90\) 40.1267i 4.22972i
\(91\) 2.54573 + 1.46978i 0.266865 + 0.154075i
\(92\) −12.2978 7.10014i −1.28213 0.740241i
\(93\) 2.83973 + 4.91856i 0.294466 + 0.510031i
\(94\) −10.9761 −1.13209
\(95\) 2.82238 1.62950i 0.289570 0.167184i
\(96\) −21.3262 12.3127i −2.17659 1.25666i
\(97\) 9.03426i 0.917290i −0.888620 0.458645i \(-0.848335\pi\)
0.888620 0.458645i \(-0.151665\pi\)
\(98\) 6.69957 11.6040i 0.676759 1.17218i
\(99\) −30.3444 + 17.5193i −3.04973 + 1.76076i
\(100\) 5.45167 + 9.44257i 0.545167 + 0.944257i
\(101\) 3.36533 + 5.82892i 0.334863 + 0.579999i 0.983458 0.181134i \(-0.0579767\pi\)
−0.648596 + 0.761133i \(0.724643\pi\)
\(102\) 12.0198 + 22.6684i 1.19013 + 2.24451i
\(103\) −1.13465 1.96528i −0.111801 0.193645i 0.804696 0.593688i \(-0.202329\pi\)
−0.916496 + 0.400043i \(0.868995\pi\)
\(104\) −0.912752 1.58093i −0.0895027 0.155023i
\(105\) −5.66305 3.26956i −0.552657 0.319077i
\(106\) −1.23187 + 2.13367i −0.119650 + 0.207240i
\(107\) 18.3420i 1.77319i −0.462547 0.886595i \(-0.653064\pi\)
0.462547 0.886595i \(-0.346936\pi\)
\(108\) 21.4609i 2.06507i
\(109\) 1.63586 + 0.944467i 0.156687 + 0.0904635i 0.576294 0.817243i \(-0.304498\pi\)
−0.419606 + 0.907706i \(0.637832\pi\)
\(110\) 18.2582 31.6242i 1.74085 3.01525i
\(111\) 16.3779 + 28.3673i 1.55452 + 2.69251i
\(112\) −2.09764 + 1.21108i −0.198209 + 0.114436i
\(113\) 3.09468i 0.291123i 0.989349 + 0.145562i \(0.0464989\pi\)
−0.989349 + 0.145562i \(0.953501\pi\)
\(114\) 5.57074 3.21627i 0.521747 0.301231i
\(115\) −10.1431 17.5684i −0.945850 1.63826i
\(116\) −12.4887 + 7.21033i −1.15954 + 0.669462i
\(117\) −13.3412 + 23.1076i −1.23339 + 2.13630i
\(118\) 17.2442 1.58746
\(119\) 2.81674 + 0.101591i 0.258210 + 0.00931282i
\(120\) 2.03044 + 3.51683i 0.185353 + 0.321041i
\(121\) −20.8862 −1.89875
\(122\) 19.2823 11.1326i 1.74574 1.00790i
\(123\) 3.35711 5.81468i 0.302700 0.524292i
\(124\) −3.57785 2.06567i −0.321300 0.185503i
\(125\) 0.187906i 0.0168068i
\(126\) −7.53470 4.35016i −0.671244 0.387543i
\(127\) −15.8405 −1.40562 −0.702810 0.711378i \(-0.748072\pi\)
−0.702810 + 0.711378i \(0.748072\pi\)
\(128\) 3.37803 0.298578
\(129\) 17.5634 9.34575i 1.54638 0.822848i
\(130\) 27.8077i 2.43890i
\(131\) 9.64943i 0.843075i 0.906811 + 0.421537i \(0.138509\pi\)
−0.906811 + 0.421537i \(0.861491\pi\)
\(132\) 18.9053 32.7449i 1.64549 2.85007i
\(133\) 0.706623i 0.0612720i
\(134\) −2.61481 + 4.52899i −0.225886 + 0.391245i
\(135\) 15.3293 26.5511i 1.31933 2.28515i
\(136\) −1.48333 0.929252i −0.127195 0.0796827i
\(137\) 6.52067 0.557099 0.278549 0.960422i \(-0.410146\pi\)
0.278549 + 0.960422i \(0.410146\pi\)
\(138\) −20.0202 34.6759i −1.70423 2.95181i
\(139\) 5.47749 + 3.16243i 0.464594 + 0.268234i 0.713974 0.700172i \(-0.246893\pi\)
−0.249380 + 0.968406i \(0.580227\pi\)
\(140\) 4.75668 0.402013
\(141\) −14.0606 8.11791i −1.18412 0.683652i
\(142\) −14.2102 + 8.20428i −1.19250 + 0.688488i
\(143\) −21.0286 + 12.1409i −1.75850 + 1.01527i
\(144\) −10.9929 19.0403i −0.916076 1.58669i
\(145\) −20.6011 −1.71082
\(146\) −13.6842 + 7.90059i −1.13251 + 0.653858i
\(147\) 17.1647 9.91003i 1.41572 0.817366i
\(148\) −20.6349 11.9136i −1.69618 0.979290i
\(149\) 7.31218 12.6651i 0.599037 1.03756i −0.393926 0.919142i \(-0.628883\pi\)
0.992963 0.118421i \(-0.0377832\pi\)
\(150\) 30.7440i 2.51024i
\(151\) 8.08879 0.658256 0.329128 0.944285i \(-0.393245\pi\)
0.329128 + 0.944285i \(0.393245\pi\)
\(152\) −0.219411 + 0.380031i −0.0177966 + 0.0308246i
\(153\) −0.922139 + 25.5675i −0.0745505 + 2.06701i
\(154\) −3.95878 6.85680i −0.319007 0.552537i
\(155\) −2.95098 5.11124i −0.237028 0.410545i
\(156\) 28.7931i 2.30530i
\(157\) 1.27006 + 2.19980i 0.101362 + 0.175564i 0.912246 0.409643i \(-0.134347\pi\)
−0.810884 + 0.585207i \(0.801013\pi\)
\(158\) 22.3987 12.9319i 1.78195 1.02881i
\(159\) −3.15613 + 1.82219i −0.250297 + 0.144509i
\(160\) 22.1616 + 12.7950i 1.75203 + 1.01153i
\(161\) −4.39849 −0.346649
\(162\) 11.1657 19.3396i 0.877263 1.51946i
\(163\) −13.4548 + 7.76816i −1.05387 + 0.608449i −0.923729 0.383047i \(-0.874875\pi\)
−0.130136 + 0.991496i \(0.541541\pi\)
\(164\) 4.88404i 0.381380i
\(165\) 46.7786 27.0077i 3.64171 2.10254i
\(166\) 0.353170 0.611708i 0.0274113 0.0474777i
\(167\) 19.6637 + 11.3528i 1.52162 + 0.878508i 0.999674 + 0.0255293i \(0.00812711\pi\)
0.521946 + 0.852978i \(0.325206\pi\)
\(168\) 0.880486 0.0679310
\(169\) −2.74541 + 4.75519i −0.211186 + 0.365784i
\(170\) −12.4906 23.5565i −0.957988 1.80670i
\(171\) 6.41401 0.490492
\(172\) −7.66518 + 12.2755i −0.584465 + 0.935995i
\(173\) 18.2726i 1.38924i 0.719378 + 0.694619i \(0.244427\pi\)
−0.719378 + 0.694619i \(0.755573\pi\)
\(174\) −40.6617 −3.08256
\(175\) 2.92481 + 1.68864i 0.221095 + 0.127649i
\(176\) 20.0078i 1.50814i
\(177\) 22.0904 + 12.7539i 1.66041 + 0.958640i
\(178\) −7.68500 + 13.3108i −0.576015 + 0.997688i
\(179\) 4.61487 + 7.99320i 0.344932 + 0.597439i 0.985341 0.170594i \(-0.0545687\pi\)
−0.640410 + 0.768034i \(0.721235\pi\)
\(180\) 43.1763i 3.21817i
\(181\) −7.90234 + 4.56242i −0.587376 + 0.339122i −0.764059 0.645146i \(-0.776797\pi\)
0.176683 + 0.984268i \(0.443463\pi\)
\(182\) −5.22153 3.01465i −0.387046 0.223461i
\(183\) 32.9349 2.43462
\(184\) 2.36556 + 1.36576i 0.174392 + 0.100685i
\(185\) −17.0195 29.4786i −1.25130 2.16731i
\(186\) −5.82455 10.0884i −0.427076 0.739718i
\(187\) −12.3603 + 19.7304i −0.903877 + 1.44283i
\(188\) 11.8102 0.861350
\(189\) −3.32372 5.75685i −0.241765 0.418749i
\(190\) −5.78897 + 3.34226i −0.419976 + 0.242473i
\(191\) 6.14249 10.6391i 0.444455 0.769818i −0.553559 0.832810i \(-0.686731\pi\)
0.998014 + 0.0629917i \(0.0200641\pi\)
\(192\) 25.1223 + 14.5044i 1.81305 + 1.04676i
\(193\) 4.78107i 0.344149i 0.985084 + 0.172075i \(0.0550470\pi\)
−0.985084 + 0.172075i \(0.944953\pi\)
\(194\) 18.5301i 1.33038i
\(195\) 20.5666 35.6225i 1.47281 2.55098i
\(196\) −7.20874 + 12.4859i −0.514910 + 0.891850i
\(197\) 12.2357 7.06430i 0.871759 0.503310i 0.00382668 0.999993i \(-0.498782\pi\)
0.867932 + 0.496682i \(0.165449\pi\)
\(198\) 62.2391 35.9338i 4.42314 2.55370i
\(199\) 11.4273i 0.810061i 0.914303 + 0.405030i \(0.132739\pi\)
−0.914303 + 0.405030i \(0.867261\pi\)
\(200\) −1.04867 1.81634i −0.0741519 0.128435i
\(201\) −6.69931 + 3.86785i −0.472533 + 0.272817i
\(202\) −6.90260 11.9556i −0.485665 0.841196i
\(203\) −2.23338 + 3.86832i −0.156752 + 0.271503i
\(204\) −12.9333 24.3913i −0.905510 1.70773i
\(205\) −3.48862 + 6.04247i −0.243656 + 0.422024i
\(206\) 2.32728 + 4.03097i 0.162149 + 0.280851i
\(207\) 39.9250i 2.77498i
\(208\) −7.61807 13.1949i −0.528218 0.914901i
\(209\) 5.05494 + 2.91847i 0.349657 + 0.201875i
\(210\) 11.6154 + 6.70617i 0.801541 + 0.462770i
\(211\) 4.40660i 0.303363i −0.988429 0.151681i \(-0.951531\pi\)
0.988429 0.151681i \(-0.0484688\pi\)
\(212\) 1.32550 2.29583i 0.0910355 0.157678i
\(213\) −24.2716 −1.66306
\(214\) 37.6211i 2.57173i
\(215\) −18.2515 + 9.71187i −1.24474 + 0.662344i
\(216\) 4.12814i 0.280884i
\(217\) −1.27967 −0.0868697
\(218\) −3.35531 1.93719i −0.227250 0.131203i
\(219\) −23.3732 −1.57941
\(220\) −19.6459 + 34.0276i −1.32452 + 2.29414i
\(221\) −0.639041 + 17.7182i −0.0429865 + 1.19186i
\(222\) −33.5925 58.1840i −2.25458 3.90505i
\(223\) 13.2525 0.887451 0.443725 0.896163i \(-0.353657\pi\)
0.443725 + 0.896163i \(0.353657\pi\)
\(224\) 4.80511 2.77423i 0.321055 0.185361i
\(225\) −15.3277 + 26.5484i −1.02185 + 1.76990i
\(226\) 6.34748i 0.422228i
\(227\) 18.9287 + 10.9285i 1.25634 + 0.725350i 0.972362 0.233480i \(-0.0750112\pi\)
0.283982 + 0.958830i \(0.408345\pi\)
\(228\) −5.99412 + 3.46070i −0.396970 + 0.229191i
\(229\) 10.9778 + 19.0142i 0.725435 + 1.25649i 0.958795 + 0.284100i \(0.0916948\pi\)
−0.233359 + 0.972391i \(0.574972\pi\)
\(230\) 20.8044 + 36.0344i 1.37180 + 2.37604i
\(231\) 11.7117i 0.770572i
\(232\) 2.40228 1.38696i 0.157717 0.0910581i
\(233\) −8.51839 + 4.91810i −0.558058 + 0.322195i −0.752366 0.658745i \(-0.771087\pi\)
0.194307 + 0.980941i \(0.437754\pi\)
\(234\) 27.3640 47.3958i 1.78884 3.09836i
\(235\) 14.6115 + 8.43593i 0.953147 + 0.550299i
\(236\) −18.5548 −1.20781
\(237\) 38.2578 2.48511
\(238\) −5.77739 0.208372i −0.374492 0.0135068i
\(239\) −13.4913 + 23.3676i −0.872678 + 1.51152i −0.0134617 + 0.999909i \(0.504285\pi\)
−0.859216 + 0.511613i \(0.829048\pi\)
\(240\) 16.9466 + 29.3523i 1.09390 + 1.89469i
\(241\) 21.5038 12.4152i 1.38518 0.799734i 0.392412 0.919789i \(-0.371641\pi\)
0.992767 + 0.120056i \(0.0383073\pi\)
\(242\) 42.8396 2.75383
\(243\) 3.34329 1.93025i 0.214472 0.123826i
\(244\) −20.7478 + 11.9787i −1.32824 + 0.766860i
\(245\) −17.8371 + 10.2983i −1.13957 + 0.657932i
\(246\) −6.88573 + 11.9264i −0.439018 + 0.760402i
\(247\) 4.44490 0.282822
\(248\) 0.688223 + 0.397346i 0.0437022 + 0.0252315i
\(249\) 0.904841 0.522410i 0.0573420 0.0331064i
\(250\) 0.385412i 0.0243756i
\(251\) −13.8052 23.9113i −0.871375 1.50926i −0.860575 0.509323i \(-0.829896\pi\)
−0.0107993 0.999942i \(-0.503438\pi\)
\(252\) 8.10734 + 4.68078i 0.510715 + 0.294861i
\(253\) 18.1665 31.4653i 1.14212 1.97820i
\(254\) 32.4904 2.03863
\(255\) 1.42156 39.4146i 0.0890217 2.46824i
\(256\) 12.1939 0.762118
\(257\) −8.67045 −0.540848 −0.270424 0.962741i \(-0.587164\pi\)
−0.270424 + 0.962741i \(0.587164\pi\)
\(258\) −36.0242 + 19.1690i −2.24277 + 1.19341i
\(259\) −7.38038 −0.458595
\(260\) 29.9211i 1.85563i
\(261\) −35.1127 20.2723i −2.17342 1.25483i
\(262\) 19.7919i 1.22275i
\(263\) −10.7482 + 18.6164i −0.662762 + 1.14794i 0.317125 + 0.948384i \(0.397282\pi\)
−0.979887 + 0.199553i \(0.936051\pi\)
\(264\) −3.63655 + 6.29869i −0.223814 + 0.387658i
\(265\) 3.27977 1.89358i 0.201475 0.116322i
\(266\) 1.44935i 0.0888653i
\(267\) −19.6894 + 11.3677i −1.20497 + 0.695692i
\(268\) 2.81354 4.87320i 0.171864 0.297678i
\(269\) 16.9628i 1.03424i 0.855912 + 0.517121i \(0.172996\pi\)
−0.855912 + 0.517121i \(0.827004\pi\)
\(270\) −31.4417 + 54.4587i −1.91348 + 3.31425i
\(271\) −14.4206 24.9772i −0.875990 1.51726i −0.855704 0.517465i \(-0.826876\pi\)
−0.0202859 0.999794i \(-0.506458\pi\)
\(272\) −12.3803 7.75578i −0.750665 0.470263i
\(273\) −4.45929 7.72372i −0.269889 0.467461i
\(274\) −13.3745 −0.807983
\(275\) −24.1599 + 13.9487i −1.45689 + 0.841138i
\(276\) 21.5417 + 37.3113i 1.29666 + 2.24588i
\(277\) 2.22666 + 1.28556i 0.133787 + 0.0772421i 0.565400 0.824817i \(-0.308722\pi\)
−0.431613 + 0.902059i \(0.642055\pi\)
\(278\) −11.2348 6.48643i −0.673820 0.389030i
\(279\) 11.6156i 0.695405i
\(280\) −0.914979 −0.0546804
\(281\) 6.86624 11.8927i 0.409606 0.709458i −0.585240 0.810860i \(-0.699000\pi\)
0.994845 + 0.101402i \(0.0323330\pi\)
\(282\) 28.8397 + 16.6506i 1.71738 + 0.991528i
\(283\) −5.18134 + 2.99145i −0.307999 + 0.177823i −0.646031 0.763311i \(-0.723572\pi\)
0.338032 + 0.941135i \(0.390239\pi\)
\(284\) 15.2902 8.82781i 0.907308 0.523834i
\(285\) −9.88778 −0.585702
\(286\) 43.1316 24.9020i 2.55042 1.47249i
\(287\) 0.756408 + 1.31014i 0.0446494 + 0.0773350i
\(288\) 25.1817 + 43.6160i 1.48385 + 2.57010i
\(289\) 7.41731 + 15.2965i 0.436312 + 0.899795i
\(290\) 42.2547 2.48128
\(291\) −13.7049 + 23.7376i −0.803396 + 1.39152i
\(292\) 14.7242 8.50104i 0.861671 0.497486i
\(293\) −25.6204 −1.49676 −0.748381 0.663269i \(-0.769168\pi\)
−0.748381 + 0.663269i \(0.769168\pi\)
\(294\) −35.2063 + 20.3264i −2.05328 + 1.18546i
\(295\) −22.9557 13.2535i −1.33653 0.771649i
\(296\) 3.96926 + 2.29166i 0.230709 + 0.133200i
\(297\) 54.9100 3.18620
\(298\) −14.9980 + 25.9772i −0.868808 + 1.50482i
\(299\) 27.6680i 1.60008i
\(300\) 33.0806i 1.90991i
\(301\) −0.155031 + 4.48001i −0.00893586 + 0.258223i
\(302\) −16.5908 −0.954696
\(303\) 20.4207i 1.17314i
\(304\) −1.83126 + 3.17184i −0.105030 + 0.181917i
\(305\) −34.2251 −1.95973
\(306\) 1.89139 52.4413i 0.108124 2.99787i
\(307\) 6.15036 10.6527i 0.351020 0.607984i −0.635409 0.772176i \(-0.719168\pi\)
0.986428 + 0.164192i \(0.0525017\pi\)
\(308\) 4.25965 + 7.37792i 0.242716 + 0.420396i
\(309\) 6.88505i 0.391677i
\(310\) 6.05272 + 10.4836i 0.343771 + 0.595430i
\(311\) 13.6346 + 7.87195i 0.773148 + 0.446377i 0.833997 0.551770i \(-0.186047\pi\)
−0.0608482 + 0.998147i \(0.519381\pi\)
\(312\) 5.53855i 0.313559i
\(313\) −3.95768 2.28497i −0.223702 0.129154i 0.383961 0.923349i \(-0.374560\pi\)
−0.607663 + 0.794195i \(0.707893\pi\)
\(314\) −2.60500 4.51200i −0.147009 0.254627i
\(315\) 6.68686 + 11.5820i 0.376762 + 0.652571i
\(316\) −24.1010 + 13.9147i −1.35579 + 0.782765i
\(317\) 2.36369i 0.132758i −0.997794 0.0663789i \(-0.978855\pi\)
0.997794 0.0663789i \(-0.0211446\pi\)
\(318\) 6.47351 3.73748i 0.363017 0.209588i
\(319\) −18.4484 31.9536i −1.03291 1.78906i
\(320\) −26.1065 15.0726i −1.45939 0.842582i
\(321\) −27.8247 + 48.1938i −1.55302 + 2.68991i
\(322\) 9.02170 0.502760
\(323\) 3.76536 1.99655i 0.209510 0.111091i
\(324\) −12.0143 + 20.8094i −0.667463 + 1.15608i
\(325\) −10.6221 + 18.3980i −0.589208 + 1.02054i
\(326\) 27.5971 15.9332i 1.52846 0.882459i
\(327\) −2.86550 4.96319i −0.158462 0.274465i
\(328\) 0.939478i 0.0518740i
\(329\) 3.16808 1.82909i 0.174662 0.100841i
\(330\) −95.9473 + 55.3952i −5.28172 + 3.04940i
\(331\) 5.50577 + 9.53628i 0.302625 + 0.524161i 0.976730 0.214474i \(-0.0688038\pi\)
−0.674105 + 0.738636i \(0.735470\pi\)
\(332\) −0.380011 + 0.658198i −0.0208558 + 0.0361233i
\(333\) 66.9916i 3.67112i
\(334\) −40.3320 23.2857i −2.20687 1.27414i
\(335\) 6.96175 4.01937i 0.380361 0.219602i
\(336\) 7.34877 0.400908
\(337\) −0.573538 + 0.331133i −0.0312426 + 0.0180379i −0.515540 0.856866i \(-0.672409\pi\)
0.484297 + 0.874903i \(0.339075\pi\)
\(338\) 5.63109 9.75334i 0.306291 0.530512i
\(339\) 4.69461 8.13130i 0.254976 0.441632i
\(340\) 13.4399 + 25.3468i 0.728883 + 1.37462i
\(341\) 5.28525 9.15432i 0.286212 0.495734i
\(342\) −13.1557 −0.711380
\(343\) 9.25099i 0.499507i
\(344\) 1.47445 2.36127i 0.0794969 0.127311i
\(345\) 61.5481i 3.31364i
\(346\) 37.4787i 2.01487i
\(347\) 16.3592 + 9.44498i 0.878207 + 0.507033i 0.870067 0.492934i \(-0.164075\pi\)
0.00814030 + 0.999967i \(0.497409\pi\)
\(348\) 43.7521 2.34536
\(349\) 14.8419 25.7069i 0.794467 1.37606i −0.128710 0.991682i \(-0.541084\pi\)
0.923177 0.384375i \(-0.125583\pi\)
\(350\) −5.99905 3.46355i −0.320662 0.185135i
\(351\) 36.2125 20.9073i 1.93288 1.11595i
\(352\) 45.8322i 2.44286i
\(353\) −0.314242 0.544283i −0.0167254 0.0289692i 0.857542 0.514415i \(-0.171991\pi\)
−0.874267 + 0.485445i \(0.838657\pi\)
\(354\) −45.3093 26.1594i −2.40816 1.39035i
\(355\) 25.2225 1.33867
\(356\) 8.26907 14.3224i 0.438260 0.759088i
\(357\) −7.24689 4.53990i −0.383546 0.240277i
\(358\) −9.46553 16.3948i −0.500269 0.866491i
\(359\) 13.8906 + 24.0592i 0.733119 + 1.26980i 0.955544 + 0.294849i \(0.0952693\pi\)
−0.222425 + 0.974950i \(0.571397\pi\)
\(360\) 8.30525i 0.437725i
\(361\) 8.96576 + 15.5292i 0.471882 + 0.817324i
\(362\) 16.2084 9.35793i 0.851895 0.491842i
\(363\) 54.8787 + 31.6842i 2.88039 + 1.66299i
\(364\) 5.61837 + 3.24377i 0.294483 + 0.170020i
\(365\) 24.2888 1.27134
\(366\) −67.5525 −3.53103
\(367\) −23.0272 13.2947i −1.20201 0.693980i −0.241007 0.970523i \(-0.577478\pi\)
−0.961001 + 0.276544i \(0.910811\pi\)
\(368\) 19.7436 + 11.3990i 1.02921 + 0.594213i
\(369\) −11.8921 + 6.86591i −0.619078 + 0.357425i
\(370\) 34.9085 + 60.4633i 1.81481 + 3.14334i
\(371\) 0.821136i 0.0426313i
\(372\) 6.26722 + 10.8551i 0.324940 + 0.562813i
\(373\) 2.44220 + 4.23002i 0.126452 + 0.219022i 0.922300 0.386475i \(-0.126308\pi\)
−0.795847 + 0.605497i \(0.792974\pi\)
\(374\) 25.3522 40.4688i 1.31093 2.09259i
\(375\) −0.285052 + 0.493724i −0.0147200 + 0.0254958i
\(376\) −2.27178 −0.117158
\(377\) −24.3330 14.0487i −1.25322 0.723544i
\(378\) 6.81725 + 11.8078i 0.350641 + 0.607329i
\(379\) 3.43324i 0.176354i 0.996105 + 0.0881769i \(0.0281041\pi\)
−0.996105 + 0.0881769i \(0.971896\pi\)
\(380\) 6.22893 3.59628i 0.319538 0.184485i
\(381\) 41.6211 + 24.0300i 2.13231 + 1.23109i
\(382\) −12.5988 + 21.8218i −0.644611 + 1.11650i
\(383\) −14.0869 −0.719805 −0.359902 0.932990i \(-0.617190\pi\)
−0.359902 + 0.932990i \(0.617190\pi\)
\(384\) −8.87579 5.12444i −0.452941 0.261505i
\(385\) 12.1705i 0.620265i
\(386\) 9.80642i 0.499134i
\(387\) −40.6650 1.40722i −2.06712 0.0715329i
\(388\) 19.9384i 1.01222i
\(389\) 3.55992 0.180495 0.0902476 0.995919i \(-0.471234\pi\)
0.0902476 + 0.995919i \(0.471234\pi\)
\(390\) −42.1841 + 73.0650i −2.13607 + 3.69979i
\(391\) −12.4279 23.4381i −0.628504 1.18532i
\(392\) 1.38665 2.40175i 0.0700364 0.121307i
\(393\) 14.6381 25.3540i 0.738395 1.27894i
\(394\) −25.0966 + 14.4895i −1.26435 + 0.729971i
\(395\) −39.7566 −2.00037
\(396\) −66.9693 + 38.6648i −3.36534 + 1.94298i
\(397\) −1.11273 0.642434i −0.0558462 0.0322428i 0.471817 0.881697i \(-0.343598\pi\)
−0.527663 + 0.849454i \(0.676932\pi\)
\(398\) 23.4385i 1.17486i
\(399\) −1.07194 + 1.85666i −0.0536642 + 0.0929491i
\(400\) −8.75244 15.1597i −0.437622 0.757983i
\(401\) 9.42298 5.44036i 0.470561 0.271679i −0.245913 0.969292i \(-0.579088\pi\)
0.716475 + 0.697613i \(0.245755\pi\)
\(402\) 13.7409 7.93331i 0.685333 0.395677i
\(403\) 8.04956i 0.400977i
\(404\) 7.42720 + 12.8643i 0.369517 + 0.640022i
\(405\) −29.7279 + 17.1634i −1.47719 + 0.852858i
\(406\) 4.58086 7.93428i 0.227344 0.393772i
\(407\) 30.4822 52.7967i 1.51095 2.61703i
\(408\) 2.48780 + 4.69182i 0.123165 + 0.232280i
\(409\) −12.2819 −0.607301 −0.303650 0.952784i \(-0.598205\pi\)
−0.303650 + 0.952784i \(0.598205\pi\)
\(410\) 7.15548 12.3937i 0.353384 0.612079i
\(411\) −17.1331 9.89181i −0.845114 0.487927i
\(412\) −2.50415 4.33732i −0.123371 0.213685i
\(413\) −4.97730 + 2.87364i −0.244917 + 0.141403i
\(414\) 81.8899i 4.02467i
\(415\) −0.940288 + 0.542875i −0.0461569 + 0.0266487i
\(416\) 17.4509 + 30.2258i 0.855599 + 1.48194i
\(417\) −9.59476 16.6186i −0.469857 0.813817i
\(418\) −10.3681 5.98605i −0.507122 0.292787i
\(419\) 9.71694i 0.474704i 0.971424 + 0.237352i \(0.0762794\pi\)
−0.971424 + 0.237352i \(0.923721\pi\)
\(420\) −12.4982 7.21584i −0.609850 0.352097i
\(421\) 15.9832 + 27.6836i 0.778971 + 1.34922i 0.932535 + 0.361079i \(0.117592\pi\)
−0.153564 + 0.988139i \(0.549075\pi\)
\(422\) 9.03834i 0.439979i
\(423\) 16.6026 + 28.7566i 0.807248 + 1.39819i
\(424\) −0.254968 + 0.441618i −0.0123823 + 0.0214469i
\(425\) −0.734197 + 20.3566i −0.0356138 + 0.987438i
\(426\) 49.7833 2.41201
\(427\) −3.71037 + 6.42655i −0.179558 + 0.311003i
\(428\) 40.4804i 1.95669i
\(429\) 73.6704 3.55684
\(430\) 37.4355 19.9199i 1.80530 0.960624i
\(431\) 6.73660i 0.324491i 0.986750 + 0.162245i \(0.0518736\pi\)
−0.986750 + 0.162245i \(0.948126\pi\)
\(432\) 34.4545i 1.65770i
\(433\) 8.06048 13.9612i 0.387362 0.670931i −0.604732 0.796429i \(-0.706720\pi\)
0.992094 + 0.125498i \(0.0400530\pi\)
\(434\) 2.62472 0.125991
\(435\) 54.1294 + 31.2516i 2.59531 + 1.49840i
\(436\) 3.61031 + 2.08442i 0.172903 + 0.0998254i
\(437\) −5.75988 + 3.32547i −0.275532 + 0.159079i
\(438\) 47.9405 2.29069
\(439\) 24.1934 13.9681i 1.15469 0.666659i 0.204662 0.978833i \(-0.434390\pi\)
0.950025 + 0.312173i \(0.101057\pi\)
\(440\) 3.77901 6.54544i 0.180157 0.312042i
\(441\) −40.5357 −1.93027
\(442\) 1.31073 36.3417i 0.0623451 1.72860i
\(443\) 8.61247 + 14.9172i 0.409191 + 0.708739i 0.994799 0.101855i \(-0.0324777\pi\)
−0.585609 + 0.810594i \(0.699144\pi\)
\(444\) 36.1456 + 62.6060i 1.71539 + 2.97115i
\(445\) 20.4608 11.8130i 0.969933 0.559991i
\(446\) −27.1820 −1.28711
\(447\) −38.4256 + 22.1850i −1.81747 + 1.04932i
\(448\) −5.66044 + 3.26806i −0.267431 + 0.154401i
\(449\) 3.42380 + 1.97673i 0.161579 + 0.0932877i 0.578609 0.815605i \(-0.303596\pi\)
−0.417030 + 0.908893i \(0.636929\pi\)
\(450\) 31.4386 54.4533i 1.48203 2.56695i
\(451\) −12.4964 −0.588431
\(452\) 6.82989i 0.321251i
\(453\) −21.2534 12.2706i −0.998570 0.576525i
\(454\) −38.8245 22.4154i −1.82213 1.05200i
\(455\) 4.63398 + 8.02629i 0.217244 + 0.376278i
\(456\) 1.15301 0.665690i 0.0539946 0.0311738i
\(457\) 9.76598 0.456833 0.228417 0.973563i \(-0.426645\pi\)
0.228417 + 0.973563i \(0.426645\pi\)
\(458\) −22.5165 38.9998i −1.05213 1.82234i
\(459\) 21.2852 33.9769i 0.993510 1.58591i
\(460\) −22.3856 38.7730i −1.04373 1.80780i
\(461\) −7.82345 + 13.5506i −0.364374 + 0.631115i −0.988676 0.150069i \(-0.952050\pi\)
0.624301 + 0.781184i \(0.285384\pi\)
\(462\) 24.0217i 1.11759i
\(463\) −2.46855 + 4.27565i −0.114723 + 0.198706i −0.917669 0.397346i \(-0.869931\pi\)
0.802946 + 0.596052i \(0.203265\pi\)
\(464\) 20.0500 11.5759i 0.930799 0.537397i
\(465\) 17.9064i 0.830391i
\(466\) 17.4720 10.0875i 0.809375 0.467293i
\(467\) −1.76541 + 3.05777i −0.0816932 + 0.141497i −0.903977 0.427580i \(-0.859366\pi\)
0.822284 + 0.569077i \(0.192699\pi\)
\(468\) −29.4437 + 50.9979i −1.36103 + 2.35738i
\(469\) 1.74297i 0.0804829i
\(470\) −29.9694 17.3029i −1.38239 0.798122i
\(471\) 7.70667i 0.355105i
\(472\) 3.56914 0.164283
\(473\) −31.4081 19.6122i −1.44415 0.901770i
\(474\) −78.4703 −3.60426
\(475\) 5.10676 0.234314
\(476\) 6.21647 + 0.224209i 0.284932 + 0.0102766i
\(477\) 7.45345 0.341270
\(478\) 27.6718 47.9290i 1.26568 2.19222i
\(479\) 27.3058 + 15.7650i 1.24763 + 0.720322i 0.970637 0.240549i \(-0.0773274\pi\)
0.276997 + 0.960871i \(0.410661\pi\)
\(480\) −38.8199 67.2380i −1.77188 3.06898i
\(481\) 46.4251i 2.11680i
\(482\) −44.1062 + 25.4647i −2.00898 + 1.15989i
\(483\) 11.5571 + 6.67247i 0.525864 + 0.303608i
\(484\) −46.0954 −2.09525
\(485\) 14.2418 24.6675i 0.646686 1.12009i
\(486\) −6.85740 + 3.95912i −0.311058 + 0.179589i
\(487\) 7.94990 4.58988i 0.360244 0.207987i −0.308944 0.951080i \(-0.599975\pi\)
0.669188 + 0.743093i \(0.266642\pi\)
\(488\) 3.99097 2.30419i 0.180663 0.104306i
\(489\) 47.1370 2.13161
\(490\) 36.5855 21.1227i 1.65277 0.954225i
\(491\) 16.3000 + 28.2324i 0.735609 + 1.27411i 0.954456 + 0.298353i \(0.0964371\pi\)
−0.218847 + 0.975759i \(0.570230\pi\)
\(492\) 7.40906 12.8329i 0.334026 0.578550i
\(493\) −26.9234 0.971042i −1.21257 0.0437335i
\(494\) −9.11689 −0.410188
\(495\) −110.471 −4.96532
\(496\) 5.74409 + 3.31635i 0.257917 + 0.148909i
\(497\) 2.73439 4.73610i 0.122654 0.212443i
\(498\) −1.85591 + 1.07151i −0.0831654 + 0.0480155i
\(499\) 3.75431 2.16755i 0.168066 0.0970330i −0.413608 0.910455i \(-0.635731\pi\)
0.581674 + 0.813422i \(0.302398\pi\)
\(500\) 0.414704i 0.0185461i
\(501\) −34.4443 59.6593i −1.53886 2.66538i
\(502\) 28.3157 + 49.0442i 1.26379 + 2.18895i
\(503\) 12.9062 7.45139i 0.575459 0.332241i −0.183868 0.982951i \(-0.558862\pi\)
0.759327 + 0.650710i \(0.225529\pi\)
\(504\) −1.55950 0.900379i −0.0694657 0.0401061i
\(505\) 21.2207i 0.944308i
\(506\) −37.2611 + 64.5381i −1.65646 + 2.86907i
\(507\) 14.4272 8.32954i 0.640734 0.369928i
\(508\) −34.9597 −1.55108
\(509\) 20.5180 + 35.5382i 0.909443 + 1.57520i 0.814840 + 0.579687i \(0.196825\pi\)
0.0946035 + 0.995515i \(0.469842\pi\)
\(510\) −2.91575 + 80.8430i −0.129112 + 3.57979i
\(511\) 2.63317 4.56078i 0.116485 0.201757i
\(512\) −31.7668 −1.40391
\(513\) −8.70490 5.02578i −0.384331 0.221893i
\(514\) 17.7839 0.784413
\(515\) 7.15477i 0.315277i
\(516\) 38.7621 20.6258i 1.70641 0.908002i
\(517\) 30.2178i 1.32898i
\(518\) 15.1378 0.665118
\(519\) 27.7193 48.0113i 1.21674 2.10746i
\(520\) 5.75553i 0.252396i
\(521\) −6.21683 3.58929i −0.272364 0.157249i 0.357597 0.933876i \(-0.383596\pi\)
−0.629961 + 0.776626i \(0.716929\pi\)
\(522\) 72.0194 + 41.5804i 3.15220 + 1.81992i
\(523\) −1.92374 3.33201i −0.0841192 0.145699i 0.820896 0.571077i \(-0.193474\pi\)
−0.905016 + 0.425379i \(0.860141\pi\)
\(524\) 21.2961i 0.930323i
\(525\) −5.12330 8.87382i −0.223599 0.387285i
\(526\) 22.0455 38.1840i 0.961230 1.66490i
\(527\) −3.61569 6.81894i −0.157502 0.297038i
\(528\) −30.3516 + 52.5705i −1.32088 + 2.28784i
\(529\) 9.19990 + 15.9347i 0.399996 + 0.692813i
\(530\) −6.72711 + 3.88390i −0.292207 + 0.168706i
\(531\) −26.0840 45.1789i −1.13195 1.96060i
\(532\) 1.55950i 0.0676129i
\(533\) −8.24120 + 4.75806i −0.356966 + 0.206095i
\(534\) 40.3848 23.3162i 1.74762 1.00899i
\(535\) 28.9147 50.0818i 1.25009 2.16522i
\(536\) −0.541204 + 0.937392i −0.0233764 + 0.0404892i
\(537\) 28.0029i 1.20841i
\(538\) 34.7923i 1.50000i
\(539\) −31.9466 18.4444i −1.37604 0.794454i
\(540\) 33.8313 58.5976i 1.45587 2.52164i
\(541\) −12.8839 + 7.43849i −0.553920 + 0.319806i −0.750702 0.660641i \(-0.770284\pi\)
0.196782 + 0.980447i \(0.436951\pi\)
\(542\) 29.5780 + 51.2306i 1.27048 + 2.20054i
\(543\) 27.6846 1.18806
\(544\) 28.3598 + 17.7663i 1.21591 + 0.761725i
\(545\) 2.97775 + 5.15762i 0.127553 + 0.220928i
\(546\) 9.14641 + 15.8421i 0.391430 + 0.677977i
\(547\) 38.4238 + 22.1840i 1.64288 + 0.948520i 0.979801 + 0.199974i \(0.0640856\pi\)
0.663083 + 0.748546i \(0.269248\pi\)
\(548\) 14.3910 0.614752
\(549\) −58.3338 33.6790i −2.48962 1.43739i
\(550\) 49.5541 28.6101i 2.11299 1.21994i
\(551\) 6.75416i 0.287737i
\(552\) −4.14369 7.17708i −0.176367 0.305477i
\(553\) −4.31004 + 7.46521i −0.183282 + 0.317453i
\(554\) −4.56709 2.63681i −0.194037 0.112027i
\(555\) 103.274i 4.38372i
\(556\) 12.0887 + 6.97940i 0.512674 + 0.295993i
\(557\) −2.14157 −0.0907413 −0.0453706 0.998970i \(-0.514447\pi\)
−0.0453706 + 0.998970i \(0.514447\pi\)
\(558\) 23.8246i 1.00857i
\(559\) −28.1807 0.975200i −1.19192 0.0412466i
\(560\) −7.63665 −0.322707
\(561\) 62.4077 33.0912i 2.63486 1.39711i
\(562\) −14.0833 + 24.3930i −0.594068 + 1.02896i
\(563\) 21.7581 0.916993 0.458496 0.888696i \(-0.348388\pi\)
0.458496 + 0.888696i \(0.348388\pi\)
\(564\) −31.0315 17.9160i −1.30666 0.754401i
\(565\) −4.87852 + 8.44984i −0.205241 + 0.355488i
\(566\) 10.6274 6.13574i 0.446703 0.257904i
\(567\) 7.44280i 0.312568i
\(568\) −2.94118 + 1.69809i −0.123409 + 0.0712502i
\(569\) −5.01506 + 8.68634i −0.210242 + 0.364150i −0.951790 0.306749i \(-0.900759\pi\)
0.741548 + 0.670900i \(0.234092\pi\)
\(570\) 20.2807 0.849467
\(571\) −8.22999 4.75159i −0.344414 0.198848i 0.317808 0.948155i \(-0.397053\pi\)
−0.662222 + 0.749307i \(0.730387\pi\)
\(572\) −46.4096 + 26.7946i −1.94048 + 1.12034i
\(573\) −32.2789 + 18.6362i −1.34847 + 0.778539i
\(574\) −1.55146 2.68721i −0.0647568 0.112162i
\(575\) 31.7879i 1.32565i
\(576\) −29.6641 51.3797i −1.23600 2.14082i
\(577\) −4.82932 8.36462i −0.201047 0.348224i 0.747819 0.663903i \(-0.231101\pi\)
−0.948866 + 0.315679i \(0.897768\pi\)
\(578\) −15.2136 31.3746i −0.632802 1.30501i
\(579\) 7.25285 12.5623i 0.301418 0.522072i
\(580\) −45.4660 −1.88787
\(581\) 0.235414i 0.00976662i
\(582\) 28.1100 48.6880i 1.16520 2.01818i
\(583\) 5.87413 + 3.39143i 0.243281 + 0.140459i
\(584\) −2.83231 + 1.63523i −0.117202 + 0.0676664i
\(585\) −72.8546 + 42.0626i −3.01217 + 1.73907i
\(586\) 52.5498 2.17081
\(587\) 3.64827 + 6.31899i 0.150580 + 0.260813i 0.931441 0.363893i \(-0.118552\pi\)
−0.780861 + 0.624705i \(0.785219\pi\)
\(588\) 37.8820 21.8712i 1.56223 0.901953i
\(589\) −1.67574 + 0.967492i −0.0690479 + 0.0398648i
\(590\) 47.0843 + 27.1841i 1.93843 + 1.11915i
\(591\) −42.8659 −1.76327
\(592\) 33.1285 + 19.1268i 1.36157 + 0.786105i
\(593\) −18.6934 32.3779i −0.767645 1.32960i −0.938837 0.344362i \(-0.888095\pi\)
0.171192 0.985238i \(-0.445238\pi\)
\(594\) −112.625 −4.62108
\(595\) 7.53078 + 4.71775i 0.308732 + 0.193409i
\(596\) 16.1378 27.9515i 0.661030 1.14494i
\(597\) 17.3351 30.0254i 0.709480 1.22886i
\(598\) 56.7495i 2.32066i
\(599\) −5.43494 + 9.41359i −0.222066 + 0.384629i −0.955435 0.295201i \(-0.904613\pi\)
0.733369 + 0.679830i \(0.237947\pi\)
\(600\) 6.36327i 0.259779i
\(601\) 18.0742i 0.737262i 0.929576 + 0.368631i \(0.120173\pi\)
−0.929576 + 0.368631i \(0.879827\pi\)
\(602\) 0.317984 9.18890i 0.0129600 0.374512i
\(603\) 15.8209 0.644278
\(604\) 17.8518 0.726378
\(605\) −57.0286 32.9255i −2.31854 1.33861i
\(606\) 41.8847i 1.70145i
\(607\) −1.52330 0.879479i −0.0618290 0.0356970i 0.468767 0.883322i \(-0.344698\pi\)
−0.530596 + 0.847625i \(0.678032\pi\)
\(608\) 4.19491 7.26579i 0.170126 0.294667i
\(609\) 11.7364 6.77603i 0.475584 0.274579i
\(610\) 70.1989 2.84227
\(611\) 11.5056 + 19.9283i 0.465467 + 0.806212i
\(612\) −2.03514 + 56.4269i −0.0822656 + 2.28092i
\(613\) −18.3114 −0.739590 −0.369795 0.929113i \(-0.620572\pi\)
−0.369795 + 0.929113i \(0.620572\pi\)
\(614\) −12.6150 + 21.8497i −0.509098 + 0.881784i
\(615\) 18.3328 10.5844i 0.739248 0.426805i
\(616\) −0.819371 1.41919i −0.0330134 0.0571809i
\(617\) 34.0339 19.6495i 1.37015 0.791058i 0.379206 0.925312i \(-0.376197\pi\)
0.990947 + 0.134254i \(0.0428638\pi\)
\(618\) 14.1219i 0.568064i
\(619\) 14.1554 8.17264i 0.568955 0.328486i −0.187777 0.982212i \(-0.560128\pi\)
0.756732 + 0.653725i \(0.226795\pi\)
\(620\) −6.51273 11.2804i −0.261558 0.453031i
\(621\) −31.2838 + 54.1851i −1.25537 + 2.17437i
\(622\) −27.9659 16.1461i −1.12133 0.647399i
\(623\) 5.12263i 0.205234i
\(624\) 46.2262i 1.85053i
\(625\) 12.6472 21.9056i 0.505889 0.876225i
\(626\) 8.11757 + 4.68668i 0.324443 + 0.187318i
\(627\) −8.85459 15.3366i −0.353618 0.612485i
\(628\) 2.80299 + 4.85492i 0.111851 + 0.193732i
\(629\) −20.8532 39.3276i −0.831470 1.56810i
\(630\) −13.7154 23.7557i −0.546433 0.946450i
\(631\) −0.0315464 0.0546400i −0.00125584 0.00217518i 0.865397 0.501087i \(-0.167066\pi\)
−0.866653 + 0.498912i \(0.833733\pi\)
\(632\) 4.63599 2.67659i 0.184410 0.106469i
\(633\) −6.68478 + 11.5784i −0.265696 + 0.460199i
\(634\) 4.84814i 0.192544i
\(635\) −43.2516 24.9713i −1.71639 0.990957i
\(636\) −6.96551 + 4.02154i −0.276200 + 0.159464i
\(637\) −28.0912 −1.11301
\(638\) 37.8394 + 65.5398i 1.49808 + 2.59474i
\(639\) 42.9895 + 24.8200i 1.70064 + 0.981864i
\(640\) 9.22350 + 5.32519i 0.364591 + 0.210497i
\(641\) 4.39253i 0.173494i −0.996230 0.0867472i \(-0.972353\pi\)
0.996230 0.0867472i \(-0.0276472\pi\)
\(642\) 57.0710 98.8499i 2.25241 3.90129i
\(643\) 49.9514i 1.96989i 0.172863 + 0.984946i \(0.444698\pi\)
−0.172863 + 0.984946i \(0.555302\pi\)
\(644\) −9.70736 −0.382523
\(645\) 62.6888 + 2.16936i 2.46837 + 0.0854183i
\(646\) −7.72310 + 4.09511i −0.303861 + 0.161120i
\(647\) −9.31517 −0.366217 −0.183109 0.983093i \(-0.558616\pi\)
−0.183109 + 0.983093i \(0.558616\pi\)
\(648\) 2.31104 4.00284i 0.0907862 0.157246i
\(649\) 47.4745i 1.86354i
\(650\) 21.7869 37.7360i 0.854552 1.48013i
\(651\) 3.36234 + 1.94125i 0.131781 + 0.0760836i
\(652\) −29.6945 + 17.1441i −1.16293 + 0.671417i
\(653\) 7.95187i 0.311181i −0.987822 0.155590i \(-0.950272\pi\)
0.987822 0.155590i \(-0.0497280\pi\)
\(654\) 5.87740 + 10.1800i 0.229824 + 0.398068i
\(655\) −15.2116 + 26.3472i −0.594365 + 1.02947i
\(656\) 7.84113i 0.306145i
\(657\) 41.3982 + 23.9013i 1.61510 + 0.932477i
\(658\) −6.49802 + 3.75163i −0.253319 + 0.146254i
\(659\) 1.51551 + 2.62494i 0.0590359 + 0.102253i 0.894033 0.448001i \(-0.147864\pi\)
−0.834997 + 0.550255i \(0.814531\pi\)
\(660\) 103.239 59.6052i 4.01858 2.32013i
\(661\) 18.9832 0.738362 0.369181 0.929357i \(-0.379638\pi\)
0.369181 + 0.929357i \(0.379638\pi\)
\(662\) −11.2928 19.5598i −0.438909 0.760213i
\(663\) 28.5575 45.5854i 1.10908 1.77039i
\(664\) 0.0730976 0.126609i 0.00283674 0.00491337i
\(665\) 1.11393 1.92939i 0.0431965 0.0748186i
\(666\) 137.406i 5.32437i
\(667\) 42.0423 1.62789
\(668\) 43.3972 + 25.0554i 1.67909 + 0.969423i
\(669\) −34.8209 20.1039i −1.34626 0.777261i
\(670\) −14.2792 + 8.24409i −0.551653 + 0.318497i
\(671\) −30.6489 53.0854i −1.18319 2.04934i
\(672\) −16.8340 −0.649384
\(673\) 20.7134 11.9589i 0.798444 0.460982i −0.0444829 0.999010i \(-0.514164\pi\)
0.842927 + 0.538028i \(0.180831\pi\)
\(674\) 1.17638 0.679183i 0.0453125 0.0261612i
\(675\) 41.6047 24.0205i 1.60137 0.924549i
\(676\) −6.05906 + 10.4946i −0.233041 + 0.403638i
\(677\) 3.83828i 0.147517i −0.997276 0.0737586i \(-0.976501\pi\)
0.997276 0.0737586i \(-0.0234994\pi\)
\(678\) −9.62907 + 16.6780i −0.369802 + 0.640516i
\(679\) −3.08793 5.34844i −0.118504 0.205254i
\(680\) −2.58526 4.87562i −0.0991402 0.186972i
\(681\) −33.1569 57.4294i −1.27058 2.20070i
\(682\) −10.8405 + 18.7763i −0.415105 + 0.718983i
\(683\) −11.1382 6.43062i −0.426190 0.246061i 0.271532 0.962429i \(-0.412470\pi\)
−0.697722 + 0.716368i \(0.745803\pi\)
\(684\) 14.1556 0.541252
\(685\) 17.8043 + 10.2793i 0.680268 + 0.392753i
\(686\) 18.9746i 0.724455i
\(687\) 66.6131i 2.54145i
\(688\) 12.3061 19.7077i 0.469167 0.751351i
\(689\) 5.16522 0.196779
\(690\) 126.241i 4.80590i
\(691\) 16.7418 + 9.66589i 0.636888 + 0.367708i 0.783415 0.621499i \(-0.213476\pi\)
−0.146526 + 0.989207i \(0.546809\pi\)
\(692\) 40.3271i 1.53301i
\(693\) −11.9763 + 20.7435i −0.454941 + 0.787981i
\(694\) −33.5542 19.3725i −1.27370 0.735371i
\(695\) 9.97063 + 17.2696i 0.378208 + 0.655075i
\(696\) −8.41600 −0.319008
\(697\) −4.84407 + 7.73243i −0.183482 + 0.292887i
\(698\) −30.4420 + 52.7271i −1.15225 + 1.99575i
\(699\) 29.8429 1.12876
\(700\) 6.45498 + 3.72678i 0.243975 + 0.140859i
\(701\) 12.6225 + 21.8627i 0.476744 + 0.825744i 0.999645 0.0266490i \(-0.00848366\pi\)
−0.522901 + 0.852393i \(0.675150\pi\)
\(702\) −74.2751 + 42.8828i −2.80333 + 1.61851i
\(703\) −9.66470 + 5.57992i −0.364511 + 0.210451i
\(704\) 53.9904i 2.03484i
\(705\) −25.5945 44.3309i −0.963944 1.66960i
\(706\) 0.644539 + 1.11637i 0.0242575 + 0.0420153i
\(707\) 3.98467 + 2.30055i 0.149859 + 0.0865211i
\(708\) 48.7529 + 28.1475i 1.83225 + 1.05785i
\(709\) 14.2535i 0.535303i −0.963516 0.267652i \(-0.913752\pi\)
0.963516 0.267652i \(-0.0862476\pi\)
\(710\) −51.7336 −1.94153
\(711\) −67.7616 39.1222i −2.54126 1.46720i
\(712\) −1.59061 + 2.75502i −0.0596107 + 0.103249i
\(713\) 6.02231 + 10.4309i 0.225537 + 0.390642i
\(714\) 14.8640 + 9.31175i 0.556272 + 0.348484i
\(715\) −76.5564 −2.86305
\(716\) 10.1849 + 17.6408i 0.380628 + 0.659267i
\(717\) 70.8968 40.9323i 2.64769 1.52864i
\(718\) −28.4909 49.3477i −1.06327 1.84164i
\(719\) 13.1423 + 7.58774i 0.490127 + 0.282975i 0.724627 0.689141i \(-0.242012\pi\)
−0.234500 + 0.972116i \(0.575345\pi\)
\(720\) 69.3178i 2.58332i
\(721\) −1.34347 0.775653i −0.0500335 0.0288868i
\(722\) −18.3896 31.8517i −0.684390 1.18540i
\(723\) −75.3351 −2.80174
\(724\) −17.4403 + 10.0691i −0.648162 + 0.374217i
\(725\) −27.9563 16.1406i −1.03827 0.599447i
\(726\) −112.561 64.9873i −4.17754 2.41190i
\(727\) 24.9894 0.926804 0.463402 0.886148i \(-0.346629\pi\)
0.463402 + 0.886148i \(0.346629\pi\)
\(728\) −1.08073 0.623961i −0.0400546 0.0231255i
\(729\) 20.9501 0.775930
\(730\) −49.8186 −1.84387
\(731\) −24.3105 + 11.8321i −0.899157 + 0.437626i
\(732\) 72.6866 2.68657
\(733\) −42.9208 −1.58532 −0.792659 0.609666i \(-0.791304\pi\)
−0.792659 + 0.609666i \(0.791304\pi\)
\(734\) 47.2308 + 27.2687i 1.74332 + 1.00651i
\(735\) 62.4895 2.30496
\(736\) −45.2271 26.1119i −1.66709 0.962496i
\(737\) 12.4686 + 7.19876i 0.459287 + 0.265170i
\(738\) 24.3918 14.0826i 0.897874 0.518388i
\(739\) 32.2619 1.18677 0.593386 0.804918i \(-0.297791\pi\)
0.593386 + 0.804918i \(0.297791\pi\)
\(740\) −37.5616 65.0586i −1.38079 2.39160i
\(741\) −11.6790 6.74287i −0.429039 0.247706i
\(742\) 1.68423i 0.0618299i
\(743\) −37.7905 21.8184i −1.38640 0.800438i −0.393492 0.919328i \(-0.628733\pi\)
−0.992907 + 0.118890i \(0.962066\pi\)
\(744\) −1.20554 2.08806i −0.0441973 0.0765519i
\(745\) 39.9309 23.0541i 1.46296 0.844638i
\(746\) −5.00918 8.67615i −0.183399 0.317656i
\(747\) −2.13685 −0.0781833
\(748\) −27.2790 + 43.5445i −0.997418 + 1.59214i
\(749\) −6.26933 10.8588i −0.229076 0.396772i
\(750\) 0.584667 1.01267i 0.0213490 0.0369776i
\(751\) −28.9263 16.7006i −1.05554 0.609415i −0.131343 0.991337i \(-0.541929\pi\)
−0.924194 + 0.381922i \(0.875262\pi\)
\(752\) −18.9609 −0.691431
\(753\) 83.7693i 3.05272i
\(754\) 49.9093 + 28.8151i 1.81759 + 1.04939i
\(755\) 22.0860 + 12.7513i 0.803790 + 0.464068i
\(756\) −7.33536 12.7052i −0.266785 0.462084i
\(757\) −21.7888 37.7392i −0.791926 1.37166i −0.924773 0.380519i \(-0.875745\pi\)
0.132847 0.991137i \(-0.457588\pi\)
\(758\) 7.04189i 0.255773i
\(759\) −95.4651 + 55.1168i −3.46516 + 2.00061i
\(760\) −1.19818 + 0.691768i −0.0434624 + 0.0250931i
\(761\) 5.72496 + 9.91593i 0.207530 + 0.359452i 0.950936 0.309388i \(-0.100124\pi\)
−0.743406 + 0.668840i \(0.766791\pi\)
\(762\) −85.3687 49.2876i −3.09258 1.78550i