Properties

Label 637.2.q.h.589.4
Level $637$
Weight $2$
Character 637.589
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.58891012706304.1
Defining polynomial: \(x^{12} - 5 x^{10} - 2 x^{9} + 15 x^{8} + 2 x^{7} - 30 x^{6} + 4 x^{5} + 60 x^{4} - 16 x^{3} - 80 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 589.4
Root \(-1.08105 - 0.911778i\) of defining polynomial
Character \(\chi\) \(=\) 637.589
Dual form 637.2.q.h.491.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.713220 + 0.411778i) q^{2} +(1.33015 - 2.30388i) q^{3} +(-0.660878 - 1.14467i) q^{4} -3.16209i q^{5} +(1.89737 - 1.09545i) q^{6} -2.73565i q^{8} +(-2.03858 - 3.53092i) q^{9} +O(q^{10})\) \(q+(0.713220 + 0.411778i) q^{2} +(1.33015 - 2.30388i) q^{3} +(-0.660878 - 1.14467i) q^{4} -3.16209i q^{5} +(1.89737 - 1.09545i) q^{6} -2.73565i q^{8} +(-2.03858 - 3.53092i) q^{9} +(1.30208 - 2.25527i) q^{10} +(5.14653 + 2.97135i) q^{11} -3.51626 q^{12} +(0.0766193 + 3.60474i) q^{13} +(-7.28508 - 4.20604i) q^{15} +(-0.195274 + 0.338225i) q^{16} +(1.34982 + 2.33796i) q^{17} -3.35776i q^{18} +(-1.69485 + 0.978524i) q^{19} +(-3.61956 + 2.08976i) q^{20} +(2.44707 + 4.23845i) q^{22} +(-1.36471 + 2.36374i) q^{23} +(-6.30261 - 3.63882i) q^{24} -4.99883 q^{25} +(-1.42970 + 2.60252i) q^{26} -2.86554 q^{27} +(2.99923 - 5.19481i) q^{29} +(-3.46391 - 5.99967i) q^{30} -1.15155i q^{31} +(-5.01684 + 2.89647i) q^{32} +(13.6913 - 7.90465i) q^{33} +2.22331i q^{34} +(-2.69450 + 4.66701i) q^{36} +(-5.63310 - 3.25227i) q^{37} -1.61174 q^{38} +(8.40680 + 4.61830i) q^{39} -8.65038 q^{40} +(3.23351 + 1.86687i) q^{41} +(3.49562 + 6.05460i) q^{43} -7.85479i q^{44} +(-11.1651 + 6.44617i) q^{45} +(-1.94667 + 1.12391i) q^{46} +0.456071i q^{47} +(0.519487 + 0.899778i) q^{48} +(-3.56527 - 2.05841i) q^{50} +7.18184 q^{51} +(4.07561 - 2.46999i) q^{52} +0.399286 q^{53} +(-2.04376 - 1.17997i) q^{54} +(9.39568 - 16.2738i) q^{55} +5.20632i q^{57} +(4.27822 - 2.47003i) q^{58} +(-4.16200 + 2.40293i) q^{59} +11.1187i q^{60} +(-0.578514 - 1.00201i) q^{61} +(0.474182 - 0.821308i) q^{62} -3.98971 q^{64} +(11.3985 - 0.242277i) q^{65} +13.0199 q^{66} +(-5.43793 - 3.13959i) q^{67} +(1.78413 - 3.09021i) q^{68} +(3.63052 + 6.28825i) q^{69} +(3.90335 - 2.25360i) q^{71} +(-9.65936 + 5.57684i) q^{72} +8.30575i q^{73} +(-2.67843 - 4.63917i) q^{74} +(-6.64917 + 11.5167i) q^{75} +(2.24018 + 1.29337i) q^{76} +(4.09418 + 6.75560i) q^{78} -7.91410 q^{79} +(1.06950 + 0.617476i) q^{80} +(2.30414 - 3.99089i) q^{81} +(1.53747 + 2.66298i) q^{82} +6.19795i q^{83} +(7.39284 - 4.26826i) q^{85} +5.75769i q^{86} +(-7.97882 - 13.8197i) q^{87} +(8.12857 - 14.0791i) q^{88} +(-3.08423 - 1.78068i) q^{89} -10.6176 q^{90} +3.60762 q^{92} +(-2.65303 - 1.53173i) q^{93} +(-0.187800 + 0.325279i) q^{94} +(3.09418 + 5.35928i) q^{95} +15.4109i q^{96} +(2.96831 - 1.71375i) q^{97} -24.2293i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} + O(q^{10}) \) \( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} - 12 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{24} - 20 q^{25} + 42 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} + 30 q^{33} - 10 q^{36} - 42 q^{37} - 4 q^{38} - 4 q^{39} - 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 2 q^{48} - 18 q^{50} + 52 q^{51} - 2 q^{52} - 44 q^{53} - 12 q^{54} + 6 q^{55} - 12 q^{58} - 18 q^{59} - 14 q^{61} + 4 q^{62} - 52 q^{64} + 60 q^{65} + 52 q^{66} - 24 q^{67} + 8 q^{68} - 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} - 56 q^{79} + 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 2 q^{87} - 14 q^{88} + 12 q^{89} - 24 q^{90} + 24 q^{92} - 18 q^{93} - 4 q^{94} - 22 q^{95} - 6 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.713220 + 0.411778i 0.504323 + 0.291171i 0.730497 0.682916i \(-0.239288\pi\)
−0.226174 + 0.974087i \(0.572622\pi\)
\(3\) 1.33015 2.30388i 0.767960 1.33015i −0.170707 0.985322i \(-0.554605\pi\)
0.938667 0.344824i \(-0.112061\pi\)
\(4\) −0.660878 1.14467i −0.330439 0.572337i
\(5\) 3.16209i 1.41413i −0.707148 0.707065i \(-0.750019\pi\)
0.707148 0.707065i \(-0.249981\pi\)
\(6\) 1.89737 1.09545i 0.774600 0.447215i
\(7\) 0 0
\(8\) 2.73565i 0.967199i
\(9\) −2.03858 3.53092i −0.679526 1.17697i
\(10\) 1.30208 2.25527i 0.411754 0.713179i
\(11\) 5.14653 + 2.97135i 1.55174 + 0.895895i 0.998001 + 0.0632025i \(0.0201314\pi\)
0.553735 + 0.832693i \(0.313202\pi\)
\(12\) −3.51626 −1.01506
\(13\) 0.0766193 + 3.60474i 0.0212504 + 0.999774i
\(14\) 0 0
\(15\) −7.28508 4.20604i −1.88100 1.08600i
\(16\) −0.195274 + 0.338225i −0.0488186 + 0.0845563i
\(17\) 1.34982 + 2.33796i 0.327380 + 0.567038i 0.981991 0.188927i \(-0.0605010\pi\)
−0.654611 + 0.755966i \(0.727168\pi\)
\(18\) 3.35776i 0.791433i
\(19\) −1.69485 + 0.978524i −0.388826 + 0.224489i −0.681651 0.731677i \(-0.738738\pi\)
0.292825 + 0.956166i \(0.405405\pi\)
\(20\) −3.61956 + 2.08976i −0.809359 + 0.467284i
\(21\) 0 0
\(22\) 2.44707 + 4.23845i 0.521717 + 0.903641i
\(23\) −1.36471 + 2.36374i −0.284561 + 0.492874i −0.972503 0.232892i \(-0.925181\pi\)
0.687941 + 0.725766i \(0.258515\pi\)
\(24\) −6.30261 3.63882i −1.28652 0.742770i
\(25\) −4.99883 −0.999766
\(26\) −1.42970 + 2.60252i −0.280388 + 0.510397i
\(27\) −2.86554 −0.551474
\(28\) 0 0
\(29\) 2.99923 5.19481i 0.556942 0.964652i −0.440807 0.897602i \(-0.645308\pi\)
0.997750 0.0670505i \(-0.0213589\pi\)
\(30\) −3.46391 5.99967i −0.632421 1.09539i
\(31\) 1.15155i 0.206824i −0.994639 0.103412i \(-0.967024\pi\)
0.994639 0.103412i \(-0.0329760\pi\)
\(32\) −5.01684 + 2.89647i −0.886860 + 0.512029i
\(33\) 13.6913 7.90465i 2.38334 1.37602i
\(34\) 2.22331i 0.381294i
\(35\) 0 0
\(36\) −2.69450 + 4.66701i −0.449083 + 0.777835i
\(37\) −5.63310 3.25227i −0.926075 0.534670i −0.0405072 0.999179i \(-0.512897\pi\)
−0.885568 + 0.464509i \(0.846231\pi\)
\(38\) −1.61174 −0.261459
\(39\) 8.40680 + 4.61830i 1.34617 + 0.739521i
\(40\) −8.65038 −1.36775
\(41\) 3.23351 + 1.86687i 0.504990 + 0.291556i 0.730772 0.682622i \(-0.239160\pi\)
−0.225782 + 0.974178i \(0.572494\pi\)
\(42\) 0 0
\(43\) 3.49562 + 6.05460i 0.533078 + 0.923318i 0.999254 + 0.0386258i \(0.0122980\pi\)
−0.466176 + 0.884692i \(0.654369\pi\)
\(44\) 7.85479i 1.18415i
\(45\) −11.1651 + 6.44617i −1.66439 + 0.960938i
\(46\) −1.94667 + 1.12391i −0.287021 + 0.165712i
\(47\) 0.456071i 0.0665248i 0.999447 + 0.0332624i \(0.0105897\pi\)
−0.999447 + 0.0332624i \(0.989410\pi\)
\(48\) 0.519487 + 0.899778i 0.0749815 + 0.129872i
\(49\) 0 0
\(50\) −3.56527 2.05841i −0.504205 0.291103i
\(51\) 7.18184 1.00566
\(52\) 4.07561 2.46999i 0.565186 0.342527i
\(53\) 0.399286 0.0548462 0.0274231 0.999624i \(-0.491270\pi\)
0.0274231 + 0.999624i \(0.491270\pi\)
\(54\) −2.04376 1.17997i −0.278121 0.160573i
\(55\) 9.39568 16.2738i 1.26691 2.19436i
\(56\) 0 0
\(57\) 5.20632i 0.689594i
\(58\) 4.27822 2.47003i 0.561758 0.324331i
\(59\) −4.16200 + 2.40293i −0.541846 + 0.312835i −0.745827 0.666140i \(-0.767945\pi\)
0.203981 + 0.978975i \(0.434612\pi\)
\(60\) 11.1187i 1.43542i
\(61\) −0.578514 1.00201i −0.0740711 0.128295i 0.826611 0.562774i \(-0.190266\pi\)
−0.900682 + 0.434479i \(0.856933\pi\)
\(62\) 0.474182 0.821308i 0.0602212 0.104306i
\(63\) 0 0
\(64\) −3.98971 −0.498714
\(65\) 11.3985 0.242277i 1.41381 0.0300508i
\(66\) 13.0199 1.60263
\(67\) −5.43793 3.13959i −0.664349 0.383562i 0.129583 0.991569i \(-0.458636\pi\)
−0.793932 + 0.608007i \(0.791969\pi\)
\(68\) 1.78413 3.09021i 0.216358 0.374743i
\(69\) 3.63052 + 6.28825i 0.437063 + 0.757016i
\(70\) 0 0
\(71\) 3.90335 2.25360i 0.463242 0.267453i −0.250165 0.968203i \(-0.580485\pi\)
0.713406 + 0.700751i \(0.247151\pi\)
\(72\) −9.65936 + 5.57684i −1.13837 + 0.657236i
\(73\) 8.30575i 0.972115i 0.873927 + 0.486057i \(0.161565\pi\)
−0.873927 + 0.486057i \(0.838435\pi\)
\(74\) −2.67843 4.63917i −0.311361 0.539293i
\(75\) −6.64917 + 11.5167i −0.767780 + 1.32983i
\(76\) 2.24018 + 1.29337i 0.256966 + 0.148360i
\(77\) 0 0
\(78\) 4.09418 + 6.75560i 0.463575 + 0.764921i
\(79\) −7.91410 −0.890405 −0.445203 0.895430i \(-0.646868\pi\)
−0.445203 + 0.895430i \(0.646868\pi\)
\(80\) 1.06950 + 0.617476i 0.119574 + 0.0690359i
\(81\) 2.30414 3.99089i 0.256016 0.443432i
\(82\) 1.53747 + 2.66298i 0.169785 + 0.294077i
\(83\) 6.19795i 0.680313i 0.940369 + 0.340156i \(0.110480\pi\)
−0.940369 + 0.340156i \(0.889520\pi\)
\(84\) 0 0
\(85\) 7.39284 4.26826i 0.801866 0.462958i
\(86\) 5.75769i 0.620867i
\(87\) −7.97882 13.8197i −0.855419 1.48163i
\(88\) 8.12857 14.0791i 0.866509 1.50084i
\(89\) −3.08423 1.78068i −0.326928 0.188752i 0.327549 0.944834i \(-0.393778\pi\)
−0.654476 + 0.756083i \(0.727111\pi\)
\(90\) −10.6176 −1.11919
\(91\) 0 0
\(92\) 3.60762 0.376120
\(93\) −2.65303 1.53173i −0.275106 0.158833i
\(94\) −0.187800 + 0.325279i −0.0193701 + 0.0335500i
\(95\) 3.09418 + 5.35928i 0.317457 + 0.549851i
\(96\) 15.4109i 1.57287i
\(97\) 2.96831 1.71375i 0.301386 0.174005i −0.341679 0.939817i \(-0.610996\pi\)
0.643065 + 0.765811i \(0.277662\pi\)
\(98\) 0 0
\(99\) 24.2293i 2.43513i
\(100\) 3.30361 + 5.72203i 0.330361 + 0.572203i
\(101\) 6.66474 11.5437i 0.663167 1.14864i −0.316612 0.948555i \(-0.602545\pi\)
0.979779 0.200084i \(-0.0641214\pi\)
\(102\) 5.12223 + 2.95732i 0.507177 + 0.292819i
\(103\) 11.6450 1.14741 0.573706 0.819061i \(-0.305505\pi\)
0.573706 + 0.819061i \(0.305505\pi\)
\(104\) 9.86130 0.209604i 0.966981 0.0205533i
\(105\) 0 0
\(106\) 0.284779 + 0.164417i 0.0276602 + 0.0159696i
\(107\) −1.96483 + 3.40318i −0.189947 + 0.328998i −0.945232 0.326398i \(-0.894165\pi\)
0.755285 + 0.655396i \(0.227498\pi\)
\(108\) 1.89377 + 3.28011i 0.182228 + 0.315629i
\(109\) 11.2533i 1.07787i −0.842346 0.538936i \(-0.818826\pi\)
0.842346 0.538936i \(-0.181174\pi\)
\(110\) 13.4024 7.73787i 1.27787 0.737777i
\(111\) −14.9857 + 8.65199i −1.42238 + 0.821210i
\(112\) 0 0
\(113\) 2.88709 + 5.00059i 0.271595 + 0.470416i 0.969270 0.245998i \(-0.0791157\pi\)
−0.697676 + 0.716414i \(0.745782\pi\)
\(114\) −2.14385 + 3.71325i −0.200790 + 0.347778i
\(115\) 7.47437 + 4.31533i 0.696989 + 0.402407i
\(116\) −7.92849 −0.736142
\(117\) 12.5718 7.61907i 1.16227 0.704383i
\(118\) −3.95790 −0.364354
\(119\) 0 0
\(120\) −11.5063 + 19.9294i −1.05037 + 1.81930i
\(121\) 12.1578 + 21.0580i 1.10526 + 1.91436i
\(122\) 0.952877i 0.0862694i
\(123\) 8.60209 4.96642i 0.775625 0.447807i
\(124\) −1.31815 + 0.761033i −0.118373 + 0.0683428i
\(125\) 0.00370455i 0.000331345i
\(126\) 0 0
\(127\) 3.06558 5.30975i 0.272027 0.471164i −0.697354 0.716727i \(-0.745639\pi\)
0.969381 + 0.245563i \(0.0789728\pi\)
\(128\) 7.18812 + 4.15007i 0.635346 + 0.366817i
\(129\) 18.5988 1.63753
\(130\) 8.22942 + 4.52086i 0.721767 + 0.396506i
\(131\) −10.2217 −0.893073 −0.446537 0.894765i \(-0.647343\pi\)
−0.446537 + 0.894765i \(0.647343\pi\)
\(132\) −18.0965 10.4480i −1.57510 0.909383i
\(133\) 0 0
\(134\) −2.58563 4.47844i −0.223364 0.386878i
\(135\) 9.06111i 0.779856i
\(136\) 6.39584 3.69264i 0.548439 0.316641i
\(137\) −17.2751 + 9.97376i −1.47591 + 0.852116i −0.999631 0.0271788i \(-0.991348\pi\)
−0.476278 + 0.879295i \(0.658014\pi\)
\(138\) 5.97987i 0.509041i
\(139\) −10.1637 17.6041i −0.862077 1.49316i −0.869921 0.493192i \(-0.835830\pi\)
0.00784365 0.999969i \(-0.497503\pi\)
\(140\) 0 0
\(141\) 1.05073 + 0.606641i 0.0884877 + 0.0510884i
\(142\) 3.71193 0.311498
\(143\) −10.3166 + 18.7795i −0.862718 + 1.57042i
\(144\) 1.59233 0.132694
\(145\) −16.4265 9.48383i −1.36414 0.787589i
\(146\) −3.42013 + 5.92383i −0.283052 + 0.490260i
\(147\) 0 0
\(148\) 8.59741i 0.706703i
\(149\) −9.28046 + 5.35808i −0.760285 + 0.438951i −0.829398 0.558658i \(-0.811316\pi\)
0.0691132 + 0.997609i \(0.477983\pi\)
\(150\) −9.48465 + 5.47597i −0.774418 + 0.447111i
\(151\) 8.74416i 0.711590i 0.934564 + 0.355795i \(0.115790\pi\)
−0.934564 + 0.355795i \(0.884210\pi\)
\(152\) 2.67690 + 4.63653i 0.217125 + 0.376072i
\(153\) 5.50343 9.53222i 0.444926 0.770634i
\(154\) 0 0
\(155\) −3.64130 −0.292476
\(156\) −0.269413 12.6752i −0.0215703 1.01483i
\(157\) −6.50734 −0.519342 −0.259671 0.965697i \(-0.583614\pi\)
−0.259671 + 0.965697i \(0.583614\pi\)
\(158\) −5.64449 3.25885i −0.449052 0.259260i
\(159\) 0.531109 0.919907i 0.0421197 0.0729534i
\(160\) 9.15891 + 15.8637i 0.724075 + 1.25414i
\(161\) 0 0
\(162\) 3.28672 1.89759i 0.258229 0.149089i
\(163\) 2.26264 1.30634i 0.177224 0.102320i −0.408764 0.912640i \(-0.634040\pi\)
0.585988 + 0.810320i \(0.300707\pi\)
\(164\) 4.93509i 0.385366i
\(165\) −24.9952 43.2930i −1.94588 3.37036i
\(166\) −2.55218 + 4.42050i −0.198087 + 0.343097i
\(167\) 3.36558 + 1.94312i 0.260436 + 0.150363i 0.624534 0.780998i \(-0.285289\pi\)
−0.364097 + 0.931361i \(0.618622\pi\)
\(168\) 0 0
\(169\) −12.9883 + 0.552385i −0.999097 + 0.0424911i
\(170\) 7.03030 0.539200
\(171\) 6.91018 + 3.98959i 0.528434 + 0.305092i
\(172\) 4.62036 8.00270i 0.352299 0.610200i
\(173\) −6.98838 12.1042i −0.531317 0.920267i −0.999332 0.0365470i \(-0.988364\pi\)
0.468015 0.883720i \(-0.344969\pi\)
\(174\) 13.1420i 0.996293i
\(175\) 0 0
\(176\) −2.00997 + 1.16046i −0.151507 + 0.0874727i
\(177\) 12.7850i 0.960979i
\(178\) −1.46649 2.54004i −0.109918 0.190384i
\(179\) −12.6422 + 21.8968i −0.944919 + 1.63665i −0.189005 + 0.981976i \(0.560526\pi\)
−0.755914 + 0.654671i \(0.772807\pi\)
\(180\) 14.7575 + 8.52026i 1.09996 + 0.635063i
\(181\) 0.864474 0.0642559 0.0321279 0.999484i \(-0.489772\pi\)
0.0321279 + 0.999484i \(0.489772\pi\)
\(182\) 0 0
\(183\) −3.07803 −0.227535
\(184\) 6.46638 + 3.73336i 0.476708 + 0.275227i
\(185\) −10.2840 + 17.8124i −0.756093 + 1.30959i
\(186\) −1.26146 2.18492i −0.0924950 0.160206i
\(187\) 16.0432i 1.17319i
\(188\) 0.522052 0.301407i 0.0380746 0.0219824i
\(189\) 0 0
\(190\) 5.09647i 0.369737i
\(191\) −7.33382 12.7026i −0.530657 0.919125i −0.999360 0.0357690i \(-0.988612\pi\)
0.468703 0.883356i \(-0.344721\pi\)
\(192\) −5.30690 + 9.19182i −0.382993 + 0.663363i
\(193\) 14.2859 + 8.24794i 1.02832 + 0.593700i 0.916503 0.400029i \(-0.131000\pi\)
0.111816 + 0.993729i \(0.464333\pi\)
\(194\) 2.82275 0.202661
\(195\) 14.6035 26.5831i 1.04578 1.90365i
\(196\) 0 0
\(197\) 9.53510 + 5.50509i 0.679348 + 0.392222i 0.799609 0.600521i \(-0.205040\pi\)
−0.120262 + 0.992742i \(0.538373\pi\)
\(198\) 9.97709 17.2808i 0.709041 1.22809i
\(199\) 10.6059 + 18.3699i 0.751829 + 1.30221i 0.946935 + 0.321425i \(0.104162\pi\)
−0.195106 + 0.980782i \(0.562505\pi\)
\(200\) 13.6751i 0.966972i
\(201\) −14.4665 + 8.35223i −1.02039 + 0.589121i
\(202\) 9.50686 5.48879i 0.668901 0.386190i
\(203\) 0 0
\(204\) −4.74632 8.22086i −0.332309 0.575576i
\(205\) 5.90322 10.2247i 0.412299 0.714122i
\(206\) 8.30542 + 4.79514i 0.578666 + 0.334093i
\(207\) 11.1282 0.773466
\(208\) −1.23417 0.677998i −0.0855746 0.0470107i
\(209\) −11.6301 −0.804474
\(210\) 0 0
\(211\) 8.96788 15.5328i 0.617375 1.06932i −0.372588 0.927997i \(-0.621530\pi\)
0.989963 0.141327i \(-0.0451370\pi\)
\(212\) −0.263879 0.457052i −0.0181233 0.0313905i
\(213\) 11.9905i 0.821572i
\(214\) −2.80271 + 1.61815i −0.191589 + 0.110614i
\(215\) 19.1452 11.0535i 1.30569 0.753842i
\(216\) 7.83913i 0.533385i
\(217\) 0 0
\(218\) 4.63387 8.02610i 0.313845 0.543596i
\(219\) 19.1355 + 11.0479i 1.29305 + 0.746545i
\(220\) −24.8376 −1.67455
\(221\) −8.32431 + 5.04488i −0.559953 + 0.339356i
\(222\) −14.2508 −0.956451
\(223\) 13.8834 + 8.01558i 0.929700 + 0.536763i 0.886717 0.462313i \(-0.152980\pi\)
0.0429835 + 0.999076i \(0.486314\pi\)
\(224\) 0 0
\(225\) 10.1905 + 17.6505i 0.679366 + 1.17670i
\(226\) 4.75536i 0.316322i
\(227\) 14.1812 8.18751i 0.941239 0.543424i 0.0508902 0.998704i \(-0.483794\pi\)
0.890348 + 0.455280i \(0.150461\pi\)
\(228\) 5.95954 3.44074i 0.394680 0.227869i
\(229\) 27.0104i 1.78490i 0.451148 + 0.892449i \(0.351015\pi\)
−0.451148 + 0.892449i \(0.648985\pi\)
\(230\) 3.55392 + 6.15556i 0.234338 + 0.405886i
\(231\) 0 0
\(232\) −14.2112 8.20484i −0.933011 0.538674i
\(233\) −11.5681 −0.757853 −0.378926 0.925427i \(-0.623707\pi\)
−0.378926 + 0.925427i \(0.623707\pi\)
\(234\) 12.1039 0.257269i 0.791254 0.0168182i
\(235\) 1.44214 0.0940747
\(236\) 5.50114 + 3.17609i 0.358094 + 0.206746i
\(237\) −10.5269 + 18.2331i −0.683796 + 1.18437i
\(238\) 0 0
\(239\) 14.6731i 0.949122i 0.880223 + 0.474561i \(0.157393\pi\)
−0.880223 + 0.474561i \(0.842607\pi\)
\(240\) 2.84518 1.64267i 0.183656 0.106034i
\(241\) −12.4246 + 7.17334i −0.800338 + 0.462076i −0.843589 0.536989i \(-0.819562\pi\)
0.0432510 + 0.999064i \(0.486228\pi\)
\(242\) 20.0253i 1.28727i
\(243\) −10.4280 18.0618i −0.668956 1.15867i
\(244\) −0.764654 + 1.32442i −0.0489519 + 0.0847872i
\(245\) 0 0
\(246\) 8.18025 0.521554
\(247\) −3.65718 6.03453i −0.232701 0.383968i
\(248\) −3.15024 −0.200040
\(249\) 14.2793 + 8.24417i 0.904916 + 0.522453i
\(250\) 0.00152545 0.00264216i 9.64781e−5 0.000167105i
\(251\) −4.30726 7.46040i −0.271872 0.470896i 0.697469 0.716615i \(-0.254309\pi\)
−0.969341 + 0.245719i \(0.920976\pi\)
\(252\) 0 0
\(253\) −14.0470 + 8.11004i −0.883128 + 0.509874i
\(254\) 4.37287 2.52468i 0.274378 0.158412i
\(255\) 22.7096i 1.42213i
\(256\) 7.40753 + 12.8302i 0.462970 + 0.801888i
\(257\) −5.18197 + 8.97544i −0.323243 + 0.559873i −0.981155 0.193222i \(-0.938106\pi\)
0.657912 + 0.753094i \(0.271440\pi\)
\(258\) 13.2650 + 7.65856i 0.825844 + 0.476801i
\(259\) 0 0
\(260\) −7.81035 12.8875i −0.484377 0.799247i
\(261\) −24.4566 −1.51383
\(262\) −7.29032 4.20907i −0.450397 0.260037i
\(263\) 11.0413 19.1241i 0.680835 1.17924i −0.293891 0.955839i \(-0.594950\pi\)
0.974726 0.223403i \(-0.0717165\pi\)
\(264\) −21.6244 37.4545i −1.33089 2.30517i
\(265\) 1.26258i 0.0775596i
\(266\) 0 0
\(267\) −8.20495 + 4.73713i −0.502135 + 0.289908i
\(268\) 8.29954i 0.506975i
\(269\) 6.46995 + 11.2063i 0.394480 + 0.683259i 0.993035 0.117823i \(-0.0375915\pi\)
−0.598555 + 0.801082i \(0.704258\pi\)
\(270\) −3.73117 + 6.46257i −0.227072 + 0.393299i
\(271\) 15.3069 + 8.83745i 0.929829 + 0.536837i 0.886757 0.462235i \(-0.152952\pi\)
0.0430712 + 0.999072i \(0.486286\pi\)
\(272\) −1.05434 −0.0639289
\(273\) 0 0
\(274\) −16.4279 −0.992446
\(275\) −25.7266 14.8533i −1.55137 0.895685i
\(276\) 4.79866 8.31152i 0.288845 0.500295i
\(277\) −9.00751 15.6015i −0.541209 0.937401i −0.998835 0.0482562i \(-0.984634\pi\)
0.457626 0.889145i \(-0.348700\pi\)
\(278\) 16.7408i 1.00405i
\(279\) −4.06602 + 2.34752i −0.243426 + 0.140542i
\(280\) 0 0
\(281\) 2.44178i 0.145665i −0.997344 0.0728323i \(-0.976796\pi\)
0.997344 0.0728323i \(-0.0232038\pi\)
\(282\) 0.499603 + 0.865337i 0.0297509 + 0.0515301i
\(283\) 14.3620 24.8757i 0.853732 1.47871i −0.0240853 0.999710i \(-0.507667\pi\)
0.877817 0.478996i \(-0.158999\pi\)
\(284\) −5.15927 2.97871i −0.306146 0.176754i
\(285\) 16.4629 0.975176
\(286\) −15.0910 + 9.14580i −0.892350 + 0.540802i
\(287\) 0 0
\(288\) 20.4544 + 11.8094i 1.20529 + 0.695873i
\(289\) 4.85596 8.41078i 0.285645 0.494752i
\(290\) −7.81046 13.5281i −0.458646 0.794399i
\(291\) 9.11818i 0.534517i
\(292\) 9.50738 5.48909i 0.556377 0.321225i
\(293\) −25.4013 + 14.6654i −1.48396 + 0.856763i −0.999834 0.0182359i \(-0.994195\pi\)
−0.484124 + 0.874999i \(0.660862\pi\)
\(294\) 0 0
\(295\) 7.59829 + 13.1606i 0.442390 + 0.766241i
\(296\) −8.89708 + 15.4102i −0.517132 + 0.895699i
\(297\) −14.7476 8.51453i −0.855742 0.494063i
\(298\) −8.82535 −0.511239
\(299\) −8.62523 4.73830i −0.498810 0.274023i
\(300\) 17.5772 1.01482
\(301\) 0 0
\(302\) −3.60065 + 6.23651i −0.207194 + 0.358871i
\(303\) −17.7302 30.7096i −1.01857 1.76422i
\(304\) 0.764323i 0.0438369i
\(305\) −3.16846 + 1.82931i −0.181426 + 0.104746i
\(306\) 7.85032 4.53238i 0.448773 0.259099i
\(307\) 7.06910i 0.403455i −0.979442 0.201728i \(-0.935344\pi\)
0.979442 0.201728i \(-0.0646555\pi\)
\(308\) 0 0
\(309\) 15.4895 26.8286i 0.881166 1.52623i
\(310\) −2.59705 1.49941i −0.147503 0.0851607i
\(311\) −22.2686 −1.26274 −0.631368 0.775483i \(-0.717506\pi\)
−0.631368 + 0.775483i \(0.717506\pi\)
\(312\) 12.6341 22.9981i 0.715264 1.30201i
\(313\) 28.0840 1.58740 0.793700 0.608309i \(-0.208152\pi\)
0.793700 + 0.608309i \(0.208152\pi\)
\(314\) −4.64117 2.67958i −0.261916 0.151217i
\(315\) 0 0
\(316\) 5.23025 + 9.05906i 0.294225 + 0.509612i
\(317\) 19.5155i 1.09610i 0.836446 + 0.548049i \(0.184629\pi\)
−0.836446 + 0.548049i \(0.815371\pi\)
\(318\) 0.757595 0.437398i 0.0424838 0.0245281i
\(319\) 30.8712 17.8235i 1.72845 0.997924i
\(320\) 12.6158i 0.705247i
\(321\) 5.22702 + 9.05346i 0.291744 + 0.505315i
\(322\) 0 0
\(323\) −4.57550 2.64167i −0.254588 0.146986i
\(324\) −6.09102 −0.338390
\(325\) −0.383007 18.0195i −0.0212454 0.999540i
\(326\) 2.15168 0.119171
\(327\) −25.9263 14.9686i −1.43373 0.827764i
\(328\) 5.10711 8.84577i 0.281993 0.488426i
\(329\) 0 0
\(330\) 41.1700i 2.26633i
\(331\) 13.5367 7.81539i 0.744042 0.429573i −0.0794953 0.996835i \(-0.525331\pi\)
0.823537 + 0.567263i \(0.191998\pi\)
\(332\) 7.09463 4.09609i 0.389368 0.224802i
\(333\) 26.5200i 1.45329i
\(334\) 1.60027 + 2.77174i 0.0875627 + 0.151663i
\(335\) −9.92767 + 17.1952i −0.542407 + 0.939476i
\(336\) 0 0
\(337\) 21.7501 1.18480 0.592401 0.805643i \(-0.298180\pi\)
0.592401 + 0.805643i \(0.298180\pi\)
\(338\) −9.49095 4.95431i −0.516240 0.269479i
\(339\) 15.3610 0.834295
\(340\) −9.77153 5.64160i −0.529936 0.305959i
\(341\) 3.42165 5.92647i 0.185293 0.320937i
\(342\) 3.28565 + 5.69092i 0.177668 + 0.307730i
\(343\) 0 0
\(344\) 16.5633 9.56281i 0.893032 0.515592i
\(345\) 19.8840 11.4800i 1.07052 0.618065i
\(346\) 11.5106i 0.618816i
\(347\) 7.97952 + 13.8209i 0.428363 + 0.741946i 0.996728 0.0808303i \(-0.0257572\pi\)
−0.568365 + 0.822777i \(0.692424\pi\)
\(348\) −10.5460 + 18.2663i −0.565327 + 0.979176i
\(349\) −5.90375 3.40853i −0.316021 0.182455i 0.333597 0.942716i \(-0.391738\pi\)
−0.649617 + 0.760261i \(0.725071\pi\)
\(350\) 0 0
\(351\) −0.219556 10.3295i −0.0117190 0.551349i
\(352\) −34.4257 −1.83490
\(353\) −12.1272 7.00163i −0.645465 0.372659i 0.141252 0.989974i \(-0.454887\pi\)
−0.786716 + 0.617314i \(0.788221\pi\)
\(354\) −5.26458 + 9.11852i −0.279809 + 0.484644i
\(355\) −7.12608 12.3427i −0.378213 0.655085i
\(356\) 4.70725i 0.249484i
\(357\) 0 0
\(358\) −18.0333 + 10.4115i −0.953088 + 0.550266i
\(359\) 5.41494i 0.285789i −0.989738 0.142895i \(-0.954359\pi\)
0.989738 0.142895i \(-0.0456410\pi\)
\(360\) 17.6345 + 30.5438i 0.929418 + 1.60980i
\(361\) −7.58498 + 13.1376i −0.399210 + 0.691451i
\(362\) 0.616561 + 0.355972i 0.0324057 + 0.0187094i
\(363\) 64.6867 3.39517
\(364\) 0 0
\(365\) 26.2636 1.37470
\(366\) −2.19531 1.26747i −0.114751 0.0662515i
\(367\) 15.0159 26.0083i 0.783822 1.35762i −0.145878 0.989303i \(-0.546601\pi\)
0.929700 0.368317i \(-0.120066\pi\)
\(368\) −0.532985 0.923157i −0.0277838 0.0481229i
\(369\) 15.2230i 0.792480i
\(370\) −14.6695 + 8.46943i −0.762630 + 0.440305i
\(371\) 0 0
\(372\) 4.04914i 0.209938i
\(373\) −10.7049 18.5414i −0.554278 0.960037i −0.997959 0.0638526i \(-0.979661\pi\)
0.443682 0.896184i \(-0.353672\pi\)
\(374\) −6.60622 + 11.4423i −0.341599 + 0.591668i
\(375\) −0.00853484 0.00492759i −0.000440737 0.000254460i
\(376\) 1.24765 0.0643427
\(377\) 18.9557 + 10.4134i 0.976270 + 0.536317i
\(378\) 0 0
\(379\) −8.20693 4.73827i −0.421562 0.243389i 0.274184 0.961677i \(-0.411592\pi\)
−0.695745 + 0.718289i \(0.744926\pi\)
\(380\) 4.08975 7.08366i 0.209800 0.363384i
\(381\) −8.15535 14.1255i −0.417811 0.723670i
\(382\) 12.0796i 0.618048i
\(383\) 4.70304 2.71530i 0.240314 0.138746i −0.375007 0.927022i \(-0.622360\pi\)
0.615321 + 0.788277i \(0.289026\pi\)
\(384\) 19.1225 11.0404i 0.975842 0.563402i
\(385\) 0 0
\(386\) 6.79264 + 11.7652i 0.345736 + 0.598833i
\(387\) 14.2522 24.6855i 0.724480 1.25484i
\(388\) −3.92338 2.26516i −0.199179 0.114996i
\(389\) 10.6422 0.539580 0.269790 0.962919i \(-0.413046\pi\)
0.269790 + 0.962919i \(0.413046\pi\)
\(390\) 21.3618 12.9462i 1.08170 0.655556i
\(391\) −7.36845 −0.372638
\(392\) 0 0
\(393\) −13.5963 + 23.5495i −0.685845 + 1.18792i
\(394\) 4.53375 + 7.85269i 0.228407 + 0.395613i
\(395\) 25.0251i 1.25915i
\(396\) −27.7346 + 16.0126i −1.39372 + 0.804663i
\(397\) −32.2035 + 18.5927i −1.61625 + 0.933140i −0.628367 + 0.777917i \(0.716276\pi\)
−0.987879 + 0.155223i \(0.950390\pi\)
\(398\) 17.4690i 0.875644i
\(399\) 0 0
\(400\) 0.976143 1.69073i 0.0488072 0.0845365i
\(401\) −0.776487 0.448305i −0.0387759 0.0223873i 0.480487 0.877002i \(-0.340460\pi\)
−0.519263 + 0.854615i \(0.673793\pi\)
\(402\) −13.7571 −0.686139
\(403\) 4.15103 0.0882308i 0.206777 0.00439509i
\(404\) −17.6183 −0.876545
\(405\) −12.6196 7.28590i −0.627071 0.362039i
\(406\) 0 0
\(407\) −19.3273 33.4758i −0.958016 1.65933i
\(408\) 19.6470i 0.972672i
\(409\) −21.2846 + 12.2886i −1.05245 + 0.607635i −0.923335 0.383995i \(-0.874548\pi\)
−0.129119 + 0.991629i \(0.541215\pi\)
\(410\) 8.42059 4.86163i 0.415863 0.240099i
\(411\) 53.0662i 2.61756i
\(412\) −7.69589 13.3297i −0.379149 0.656706i
\(413\) 0 0
\(414\) 7.93689 + 4.58237i 0.390077 + 0.225211i
\(415\) 19.5985 0.962052
\(416\) −10.8254 17.8624i −0.530759 0.875778i
\(417\) −54.0770 −2.64816
\(418\) −8.29486 4.78904i −0.405715 0.234239i
\(419\) −3.82279 + 6.62126i −0.186755 + 0.323470i −0.944167 0.329468i \(-0.893131\pi\)
0.757411 + 0.652938i \(0.226464\pi\)
\(420\) 0 0
\(421\) 25.0780i 1.22223i −0.791544 0.611113i \(-0.790722\pi\)
0.791544 0.611113i \(-0.209278\pi\)
\(422\) 12.7922 7.38555i 0.622712 0.359523i
\(423\) 1.61035 0.929736i 0.0782979 0.0452053i
\(424\) 1.09231i 0.0530471i
\(425\) −6.74753 11.6871i −0.327303 0.566906i
\(426\) 4.93741 8.55184i 0.239218 0.414338i
\(427\) 0 0
\(428\) 5.19405 0.251064
\(429\) 29.5432 + 48.7478i 1.42636 + 2.35356i
\(430\) 18.2063 0.877987
\(431\) 6.71520 + 3.87702i 0.323460 + 0.186750i 0.652934 0.757415i \(-0.273538\pi\)
−0.329474 + 0.944165i \(0.606871\pi\)
\(432\) 0.559567 0.969199i 0.0269222 0.0466306i
\(433\) −17.9880 31.1561i −0.864448 1.49727i −0.867594 0.497273i \(-0.834335\pi\)
0.00314644 0.999995i \(-0.498998\pi\)
\(434\) 0 0
\(435\) −43.6992 + 25.2298i −2.09522 + 1.20967i
\(436\) −12.8814 + 7.43707i −0.616907 + 0.356171i
\(437\) 5.34160i 0.255523i
\(438\) 9.09853 + 15.7591i 0.434745 + 0.753000i
\(439\) 14.1175 24.4523i 0.673792 1.16704i −0.303028 0.952982i \(-0.597998\pi\)
0.976820 0.214061i \(-0.0686691\pi\)
\(440\) −44.5194 25.7033i −2.12238 1.22536i
\(441\) 0 0
\(442\) −8.01444 + 0.170348i −0.381208 + 0.00810264i
\(443\) 28.7918 1.36794 0.683970 0.729511i \(-0.260252\pi\)
0.683970 + 0.729511i \(0.260252\pi\)
\(444\) 19.8074 + 11.4358i 0.940018 + 0.542720i
\(445\) −5.63068 + 9.75262i −0.266920 + 0.462319i
\(446\) 6.60128 + 11.4337i 0.312579 + 0.541404i
\(447\) 28.5081i 1.34839i
\(448\) 0 0
\(449\) −25.2795 + 14.5951i −1.19301 + 0.688785i −0.958988 0.283446i \(-0.908522\pi\)
−0.234023 + 0.972231i \(0.575189\pi\)
\(450\) 16.7849i 0.791247i
\(451\) 11.0942 + 19.2158i 0.522408 + 0.904836i
\(452\) 3.81603 6.60955i 0.179491 0.310887i
\(453\) 20.1455 + 11.6310i 0.946518 + 0.546473i
\(454\) 13.4858 0.632918
\(455\) 0 0
\(456\) 14.2427 0.666974
\(457\) −27.4399 15.8424i −1.28358 0.741077i −0.306081 0.952006i \(-0.599018\pi\)
−0.977501 + 0.210929i \(0.932351\pi\)
\(458\) −11.1223 + 19.2644i −0.519711 + 0.900165i
\(459\) −3.86797 6.69952i −0.180541 0.312707i
\(460\) 11.4076i 0.531883i
\(461\) 19.1407 11.0509i 0.891471 0.514691i 0.0170480 0.999855i \(-0.494573\pi\)
0.874424 + 0.485163i \(0.161240\pi\)
\(462\) 0 0
\(463\) 38.8811i 1.80696i 0.428632 + 0.903479i \(0.358996\pi\)
−0.428632 + 0.903479i \(0.641004\pi\)
\(464\) 1.17134 + 2.02883i 0.0543783 + 0.0941860i
\(465\) −4.84346 + 8.38913i −0.224610 + 0.389036i
\(466\) −8.25062 4.76350i −0.382202 0.220665i
\(467\) 13.2823 0.614632 0.307316 0.951607i \(-0.400569\pi\)
0.307316 + 0.951607i \(0.400569\pi\)
\(468\) −17.0298 9.35538i −0.787203 0.432453i
\(469\) 0 0
\(470\) 1.02856 + 0.593841i 0.0474440 + 0.0273918i
\(471\) −8.65571 + 14.9921i −0.398834 + 0.690801i
\(472\) 6.57358 + 11.3858i 0.302574 + 0.524073i
\(473\) 41.5469i 1.91033i
\(474\) −15.0160 + 8.66949i −0.689708 + 0.398203i
\(475\) 8.47228 4.89147i 0.388735 0.224436i
\(476\) 0 0
\(477\) −0.813975 1.40985i −0.0372694 0.0645524i
\(478\) −6.04205 + 10.4651i −0.276357 + 0.478664i
\(479\) −5.74618 3.31756i −0.262550 0.151583i 0.362947 0.931810i \(-0.381770\pi\)
−0.625497 + 0.780226i \(0.715104\pi\)
\(480\) 48.7307 2.22424
\(481\) 11.2920 20.5550i 0.514870 0.937228i
\(482\) −11.8153 −0.538172
\(483\) 0 0
\(484\) 16.0697 27.8335i 0.730439 1.26516i
\(485\) −5.41905 9.38607i −0.246066 0.426200i
\(486\) 17.1761i 0.779123i
\(487\) 28.9860 16.7351i 1.31348 0.758338i 0.330809 0.943698i \(-0.392678\pi\)
0.982671 + 0.185359i \(0.0593449\pi\)
\(488\) −2.74116 + 1.58261i −0.124087 + 0.0716415i
\(489\) 6.95047i 0.314311i
\(490\) 0 0
\(491\) −18.6643 + 32.3276i −0.842310 + 1.45892i 0.0456264 + 0.998959i \(0.485472\pi\)
−0.887937 + 0.459966i \(0.847862\pi\)
\(492\) −11.3699 6.56439i −0.512593 0.295946i
\(493\) 16.1937 0.729327
\(494\) −0.123490 5.80989i −0.00555609 0.261399i
\(495\) −76.6152 −3.44360
\(496\) 0.389483 + 0.224868i 0.0174883 + 0.0100969i
\(497\) 0 0
\(498\) 6.78954 + 11.7598i 0.304246 + 0.526970i
\(499\) 34.1327i 1.52799i 0.645223 + 0.763994i \(0.276764\pi\)
−0.645223 + 0.763994i \(0.723236\pi\)
\(500\) −0.00424050 + 0.00244826i −0.000189641 + 0.000109489i
\(501\) 8.95342 5.16926i 0.400009 0.230946i
\(502\) 7.09454i 0.316645i
\(503\) 7.65447 + 13.2579i 0.341296 + 0.591142i 0.984674 0.174407i \(-0.0558008\pi\)
−0.643378 + 0.765549i \(0.722467\pi\)
\(504\) 0 0
\(505\) −36.5022 21.0745i −1.62433 0.937805i
\(506\) −13.3581 −0.593842
\(507\) −16.0037 + 30.6581i −0.710747 + 1.36158i
\(508\) −8.10390 −0.359553
\(509\) 16.0189 + 9.24851i 0.710025 + 0.409933i 0.811070 0.584949i \(-0.198885\pi\)
−0.101046 + 0.994882i \(0.532219\pi\)
\(510\) 9.35133 16.1970i 0.414084 0.717214i
\(511\) 0 0
\(512\) 4.39924i 0.194421i
\(513\) 4.85668 2.80400i 0.214427 0.123800i
\(514\) −7.39178 + 4.26765i −0.326037 + 0.188238i
\(515\) 36.8224i 1.62259i
\(516\) −12.2915 21.2895i −0.541104 0.937219i
\(517\) −1.35515 + 2.34718i −0.0595992 + 0.103229i
\(518\) 0 0
\(519\) −37.1823 −1.63212
\(520\) −0.662786 31.1824i −0.0290651 1.36744i
\(521\) −23.5865 −1.03334 −0.516671 0.856184i \(-0.672829\pi\)
−0.516671 + 0.856184i \(0.672829\pi\)
\(522\) −17.4430 10.0707i −0.763457 0.440782i
\(523\) 6.15294 10.6572i 0.269049 0.466007i −0.699567 0.714567i \(-0.746624\pi\)
0.968617 + 0.248560i \(0.0799572\pi\)
\(524\) 6.75529 + 11.7005i 0.295106 + 0.511139i
\(525\) 0 0
\(526\) 15.7498 9.09312i 0.686722 0.396479i
\(527\) 2.69227 1.55438i 0.117277 0.0677101i
\(528\) 6.17431i 0.268702i
\(529\) 7.77515 + 13.4670i 0.338050 + 0.585520i
\(530\) 0.519902 0.900497i 0.0225831 0.0391151i
\(531\) 16.9691 + 9.79712i 0.736397 + 0.425159i
\(532\) 0 0
\(533\) −6.48183 + 11.7990i −0.280759 + 0.511072i
\(534\) −7.80259 −0.337651
\(535\) 10.7612 + 6.21297i 0.465246 + 0.268610i
\(536\) −8.58883 + 14.8763i −0.370981 + 0.642558i
\(537\) 33.6318 + 58.2520i 1.45132 + 2.51376i
\(538\) 10.6567i 0.459444i
\(539\) 0 0
\(540\) 10.3720 5.98829i 0.446341 0.257695i
\(541\) 19.4411i 0.835838i −0.908484 0.417919i \(-0.862760\pi\)
0.908484 0.417919i \(-0.137240\pi\)
\(542\) 7.27813 + 12.6061i 0.312623 + 0.541478i
\(543\) 1.14988 1.99165i 0.0493460 0.0854697i
\(544\) −13.5437 7.81944i −0.580680 0.335256i
\(545\) −35.5841 −1.52425
\(546\) 0 0
\(547\) 40.2163 1.71953 0.859763 0.510693i \(-0.170611\pi\)
0.859763 + 0.510693i \(0.170611\pi\)
\(548\) 22.8334 + 13.1829i 0.975395 + 0.563145i
\(549\) −2.35869 + 4.08537i −0.100666 + 0.174359i
\(550\) −12.2325 21.1873i −0.521595 0.903429i
\(551\) 11.7393i 0.500109i
\(552\) 17.2024 9.93184i 0.732185 0.422727i
\(553\) 0 0
\(554\) 14.8364i 0.630337i
\(555\) 27.3584 + 47.3861i 1.16130 + 2.01143i
\(556\) −13.4340 + 23.2683i −0.569727 + 0.986797i
\(557\) 6.89702 + 3.98199i 0.292236 + 0.168722i 0.638950 0.769248i \(-0.279369\pi\)
−0.346714 + 0.937971i \(0.612703\pi\)
\(558\) −3.86663 −0.163687
\(559\) −21.5574 + 13.0647i −0.911781 + 0.552578i
\(560\) 0 0
\(561\) 36.9615 + 21.3397i 1.56052 + 0.900965i
\(562\) 1.00547 1.74153i 0.0424133 0.0734620i
\(563\) 0.711981 + 1.23319i 0.0300064 + 0.0519726i 0.880639 0.473789i \(-0.157114\pi\)
−0.850632 + 0.525761i \(0.823781\pi\)
\(564\) 1.60366i 0.0675263i
\(565\) 15.8123 9.12924i 0.665229 0.384070i
\(566\) 20.4865 11.8279i 0.861113 0.497164i
\(567\) 0 0
\(568\) −6.16506 10.6782i −0.258680 0.448047i
\(569\) −9.25946 + 16.0379i −0.388177 + 0.672342i −0.992204 0.124622i \(-0.960228\pi\)
0.604028 + 0.796963i \(0.293562\pi\)
\(570\) 11.7417 + 6.77904i 0.491804 + 0.283943i
\(571\) −4.35766 −0.182362 −0.0911812 0.995834i \(-0.529064\pi\)
−0.0911812 + 0.995834i \(0.529064\pi\)
\(572\) 28.3145 0.601828i 1.18389 0.0251637i
\(573\) −39.0202 −1.63009
\(574\) 0 0
\(575\) 6.82194 11.8159i 0.284494 0.492759i
\(576\) 8.13334 + 14.0874i 0.338889 + 0.586973i
\(577\) 9.56416i 0.398161i 0.979983 + 0.199081i \(0.0637955\pi\)
−0.979983 + 0.199081i \(0.936204\pi\)
\(578\) 6.92674 3.99916i 0.288115 0.166343i
\(579\) 38.0046 21.9419i 1.57942 0.911876i
\(580\) 25.0706i 1.04100i
\(581\) 0 0
\(582\) 3.75466 6.50327i 0.155636 0.269569i
\(583\) 2.05494 + 1.18642i 0.0851068 + 0.0491364i
\(584\) 22.7216 0.940228
\(585\) −24.0922 39.7533i −0.996090 1.64360i
\(586\) −24.1556 −0.997859
\(587\) 2.04428 + 1.18027i 0.0843765 + 0.0487148i 0.541595 0.840640i \(-0.317821\pi\)
−0.457218 + 0.889355i \(0.651154\pi\)
\(588\) 0 0
\(589\) 1.12682 + 1.95171i 0.0464297 + 0.0804186i
\(590\) 12.5152i 0.515244i
\(591\) 25.3661 14.6452i 1.04342 0.602421i
\(592\) 2.20000 1.27017i 0.0904194 0.0522037i
\(593\) 40.4292i 1.66023i 0.557594 + 0.830114i \(0.311725\pi\)
−0.557594 + 0.830114i \(0.688275\pi\)
\(594\) −7.01219 12.1455i −0.287714 0.498335i
\(595\) 0 0
\(596\) 12.2665 + 7.08207i 0.502455 + 0.290093i
\(597\) 56.4294 2.30950
\(598\) −4.20056 6.93114i −0.171774 0.283435i
\(599\) −38.5873 −1.57663 −0.788316 0.615270i \(-0.789047\pi\)
−0.788316 + 0.615270i \(0.789047\pi\)
\(600\) 31.5057 + 18.1898i 1.28621 + 0.742596i
\(601\) 4.08115 7.06877i 0.166474 0.288341i −0.770704 0.637193i \(-0.780095\pi\)
0.937178 + 0.348852i \(0.113429\pi\)
\(602\) 0 0
\(603\) 25.6012i 1.04256i
\(604\) 10.0092 5.77882i 0.407269 0.235137i
\(605\) 66.5872 38.4442i 2.70716 1.56298i
\(606\) 29.2036i 1.18631i
\(607\) 3.79263 + 6.56902i 0.153938 + 0.266628i 0.932672 0.360726i \(-0.117471\pi\)
−0.778734 + 0.627354i \(0.784138\pi\)
\(608\) 5.66853 9.81819i 0.229889 0.398180i
\(609\) 0 0
\(610\) −3.01308 −0.121996
\(611\) −1.64402 + 0.0349438i −0.0665098 + 0.00141368i
\(612\) −14.5484 −0.588083
\(613\) −13.4908 7.78892i −0.544889 0.314592i 0.202169 0.979351i \(-0.435201\pi\)
−0.747058 + 0.664759i \(0.768534\pi\)
\(614\) 2.91090 5.04183i 0.117474 0.203472i
\(615\) −15.7043 27.2006i −0.633258 1.09683i
\(616\) 0 0
\(617\) 20.6709 11.9343i 0.832177 0.480458i −0.0224202 0.999749i \(-0.507137\pi\)
0.854598 + 0.519291i \(0.173804\pi\)
\(618\) 22.0948 12.7565i 0.888785 0.513140i
\(619\) 19.4963i 0.783622i −0.920046 0.391811i \(-0.871849\pi\)
0.920046 0.391811i \(-0.128151\pi\)
\(620\) 2.40646 + 4.16810i 0.0966456 + 0.167395i
\(621\) 3.91063 6.77341i 0.156928 0.271807i
\(622\) −15.8824 9.16972i −0.636827 0.367672i
\(623\) 0 0
\(624\) −3.20366 + 1.94155i −0.128249 + 0.0777244i
\(625\) −25.0059 −1.00023
\(626\) 20.0301 + 11.5644i 0.800562 + 0.462205i
\(627\) −15.4698 + 26.7945i −0.617804 + 1.07007i
\(628\) 4.30055 + 7.44878i 0.171611 + 0.297239i
\(629\) 17.5599i 0.700161i
\(630\) 0 0
\(631\) −22.2239 + 12.8309i −0.884718 + 0.510792i −0.872211 0.489130i \(-0.837314\pi\)
−0.0125066 + 0.999922i \(0.503981\pi\)
\(632\) 21.6502i 0.861199i
\(633\) −23.8572 41.3219i −0.948238 1.64240i
\(634\) −8.03604 + 13.9188i −0.319152 + 0.552788i
\(635\) −16.7899 9.69366i −0.666287 0.384681i
\(636\) −1.40399 −0.0556719
\(637\) 0 0
\(638\) 29.3573 1.16227
\(639\) −15.9145 9.18826i −0.629569 0.363482i
\(640\) 13.1229 22.7295i 0.518728 0.898463i
\(641\) −0.553020 0.957859i −0.0218430 0.0378332i 0.854897 0.518797i \(-0.173620\pi\)
−0.876740 + 0.480964i \(0.840287\pi\)
\(642\) 8.60949i 0.339789i
\(643\) −10.9437 + 6.31833i −0.431576 + 0.249171i −0.700018 0.714125i \(-0.746825\pi\)
0.268442 + 0.963296i \(0.413491\pi\)
\(644\) 0 0
\(645\) 58.8110i 2.31568i
\(646\) −2.17556 3.76818i −0.0855962 0.148257i
\(647\) −12.8574 + 22.2697i −0.505477 + 0.875512i 0.494503 + 0.869176i \(0.335350\pi\)
−0.999980 + 0.00633579i \(0.997983\pi\)
\(648\) −10.9177 6.30332i −0.428887 0.247618i
\(649\) −28.5598 −1.12107
\(650\) 7.14685 13.0096i 0.280323 0.510277i
\(651\) 0 0
\(652\) −2.99066 1.72666i −0.117123 0.0676211i
\(653\) −12.6303 + 21.8764i −0.494263 + 0.856089i −0.999978 0.00661158i \(-0.997895\pi\)
0.505715 + 0.862701i \(0.331229\pi\)
\(654\) −12.3275 21.3518i −0.482041 0.834920i
\(655\) 32.3219i 1.26292i
\(656\) −1.26285 + 0.729104i −0.0493058 + 0.0284667i
\(657\) 29.3269 16.9319i 1.14415 0.660577i
\(658\) 0 0
\(659\) −11.4882 19.8982i −0.447517 0.775123i 0.550707 0.834699i \(-0.314358\pi\)
−0.998224 + 0.0595764i \(0.981025\pi\)
\(660\) −33.0376 + 57.2228i −1.28599 + 2.22739i
\(661\) −26.3554 15.2163i −1.02511 0.591845i −0.109528 0.993984i \(-0.534934\pi\)
−0.915579 + 0.402138i \(0.868267\pi\)
\(662\) 12.8728 0.500316
\(663\) 0.550267 + 25.8886i 0.0213706 + 1.00543i
\(664\) 16.9554 0.657998
\(665\) 0 0
\(666\) −10.9204 + 18.9146i −0.423155 + 0.732926i
\(667\) 8.18613 + 14.1788i 0.316968 + 0.549005i
\(668\) 5.13665i 0.198743i
\(669\) 36.9339 21.3238i 1.42795 0.824425i
\(670\) −14.1612 + 8.17600i −0.547096 + 0.315866i
\(671\) 6.87586i 0.265440i
\(672\) 0 0
\(673\) 5.41933 9.38656i 0.208900 0.361825i −0.742468 0.669881i \(-0.766345\pi\)
0.951368 + 0.308056i \(0.0996784\pi\)
\(674\) 15.5126 + 8.95620i 0.597523 + 0.344980i
\(675\) 14.3244 0.551345
\(676\) 9.21595 + 14.5023i 0.354460 + 0.557779i
\(677\) 18.1209 0.696442 0.348221 0.937412i \(-0.386786\pi\)
0.348221 + 0.937412i \(0.386786\pi\)
\(678\) 10.9558 + 6.32532i 0.420754 + 0.242923i
\(679\) 0 0
\(680\) −11.6765 20.2242i −0.447772 0.775564i
\(681\) 43.5624i 1.66931i
\(682\) 4.88078 2.81792i 0.186895 0.107904i
\(683\) 32.7662 18.9176i 1.25376 0.723861i 0.281909 0.959441i \(-0.409032\pi\)
0.971855 + 0.235580i \(0.0756990\pi\)
\(684\) 10.5465i 0.403257i
\(685\) 31.5380 + 54.6254i 1.20500 + 2.08713i
\(686\) 0 0
\(687\) 62.2288 + 35.9278i 2.37418 + 1.37073i
\(688\) −2.73042 −0.104096
\(689\) 0.0305930 + 1.43932i 0.00116550 + 0.0548338i
\(690\) 18.9089 0.719850
\(691\) −26.0034 15.0131i −0.989216 0.571124i −0.0841761 0.996451i \(-0.526826\pi\)
−0.905040 + 0.425327i \(0.860159\pi\)
\(692\) −9.23693 + 15.9988i −0.351135 + 0.608184i
\(693\) 0 0
\(694\) 13.1432i 0.498907i
\(695\) −55.6658 + 32.1387i −2.11152 + 1.21909i
\(696\) −37.8059 + 21.8273i −1.43303 + 0.827360i
\(697\) 10.0798i 0.381798i
\(698\) −2.80712 4.86207i −0.106251 0.184032i
\(699\) −15.3873 + 26.6516i −0.582001 + 1.00805i
\(700\) 0 0
\(701\) 0.116177 0.00438796 0.00219398 0.999998i \(-0.499302\pi\)
0.00219398 + 0.999998i \(0.499302\pi\)
\(702\) 4.09688 7.45764i 0.154627 0.281470i
\(703\) 12.7297 0.480110
\(704\) −20.5332 11.8548i −0.773873 0.446796i
\(705\) 1.91825 3.32251i 0.0722456 0.125133i
\(706\) −5.76624 9.98741i −0.217015 0.375881i
\(707\) 0 0
\(708\) 14.6347 8.44932i 0.550004 0.317545i
\(709\) 5.82829 3.36497i 0.218886 0.126374i −0.386548 0.922269i \(-0.626333\pi\)
0.605434 + 0.795895i \(0.292999\pi\)
\(710\) 11.7375i 0.440499i
\(711\) 16.1335 + 27.9440i 0.605053 + 1.04798i
\(712\) −4.87132 + 8.43738i −0.182561 + 0.316204i
\(713\) 2.72196 + 1.57153i 0.101938 + 0.0588541i
\(714\) 0 0
\(715\) 59.3826 + 32.6221i 2.22078 + 1.22000i
\(716\) 33.4197 1.24895
\(717\) 33.8050 + 19.5173i 1.26247 + 0.728888i
\(718\) 2.22975 3.86204i 0.0832136 0.144130i
\(719\) −23.4039 40.5367i −0.872818 1.51177i −0.859069 0.511860i \(-0.828957\pi\)
−0.0137492 0.999905i \(-0.504377\pi\)
\(720\) 5.03509i 0.187647i
\(721\) 0 0
\(722\) −10.8195 + 6.24666i −0.402661 + 0.232476i
\(723\) 38.1664i 1.41942i
\(724\) −0.571312 0.989541i −0.0212326 0.0367760i
\(725\) −14.9926 + 25.9680i −0.556812 + 0.964426i
\(726\) 46.1359 + 26.6366i 1.71226 + 0.988576i
\(727\) −13.3362 −0.494611 −0.247305 0.968938i \(-0.579545\pi\)
−0.247305 + 0.968938i \(0.579545\pi\)
\(728\) 0 0
\(729\) −41.6582 −1.54290
\(730\) 18.7317 + 10.8148i 0.693291 + 0.400272i
\(731\) −9.43694 + 16.3453i −0.349038 + 0.604551i
\(732\) 2.03420 + 3.52334i 0.0751863 + 0.130226i
\(733\) 29.4612i 1.08817i 0.839029 + 0.544087i \(0.183124\pi\)
−0.839029 + 0.544087i \(0.816876\pi\)
\(734\) 21.4193 12.3664i 0.790599 0.456453i
\(735\) 0 0
\(736\) 15.8113i 0.582814i
\(737\) −18.6576 32.3160i −0.687263 1.19037i
\(738\) 6.26851 10.8574i 0.230747 0.399666i
\(739\) −10.4184 6.01509i −0.383249 0.221269i 0.295982 0.955193i \(-0.404353\pi\)
−0.679231 + 0.733925i \(0.737686\pi\)
\(740\) 27.1858 0.999370
\(741\) −18.7674 + 0.398904i −0.689438 + 0.0146541i
\(742\) 0 0
\(743\) −18.9509 10.9413i −0.695242 0.401398i 0.110331 0.993895i \(-0.464809\pi\)
−0.805573 + 0.592497i \(0.798142\pi\)
\(744\) −4.19027 + 7.25777i −0.153623 + 0.266083i
\(745\) 16.9427 + 29.3457i 0.620734 + 1.07514i
\(746\) 17.6321i 0.645558i
\(747\) 21.8844 12.6350i 0.800710 0.462290i
\(748\) 18.3642 10.6026i 0.671461 0.387668i
\(749\) 0 0
\(750\) −0.00405815 0.00702892i −0.000148183 0.000256660i
\(751\) 17.3746 30.0937i 0.634008 1.09813i −0.352717 0.935730i \(-0.614742\pi\)
0.986724 0.162403i \(-0.0519245\pi\)
\(752\) −0.154255 0.0890590i −0.00562509 0.00324765i
\(753\) −22.9172 −0.835147
\(754\) 9.23160 + 15.2326i 0.336195 + 0.554739i
\(755\) 27.6498 1.00628
\(756\) 0 0
\(757\) −21.9632 + 38.0413i −0.798265 + 1.38264i 0.122481 + 0.992471i \(0.460915\pi\)
−0.920745 + 0.390164i \(0.872418\pi\)
\(758\) −3.90223 6.75887i −0.141736 0.245493i
\(759\) 43.1502i 1.56625i
\(760\) 14.6611 8.46461i 0.531815 0.307044i
\(761\) −0.122449 + 0.0706957i −0.00443876 + 0.00256272i −0.502218 0.864741i \(-0.667482\pi\)
0.497779 + 0.867304i \(0.334149\pi\)
\(762\) 13.4328i 0.486618i
\(763\) 0 0
\(764\) −9.69352 + 16.7897i −0.350699 + 0.607429i
\(765\) −30.1418 17.4024i −1.08978 0.629183i
\(766\) 4.47241 0.161595
\(767\) −8.98082 14.8188i −0.324279 0.535076i
\(768\) 39.4124 1.42217
\(769\) −11.8200 6.82429i −0.426241 0.246090i 0.271503 0.962438i \(-0.412479\pi\)
−0.697744 + 0.716347i \(0.745813\pi\)
\(770\) 0 0
\(771\) 13.7856 + 23.8773i 0.496475 + 0.859920i
\(772\) 21.8035i 0.784726i
\(773\) −15.2328 + 8.79469i −0.547887 + 0.316323i −0.748269 0.663395i \(-0.769115\pi\)
0.200382 + 0.979718i \(0.435782\pi\)
\(774\) 20.3299 11.7375i 0.730744 0.421895i
\(775\) 5.75639i 0.206776i
\(776\) −4.68824 8.12026i −0.168298 0.291500i
\(777\) 0 0
\(778\) 7.59022 + 4.38221i 0.272123 + 0.157110i
\(779\) −7.30711 −0.261804
\(780\) −40.0801 + 0.851909i −1.43510 + 0.0305032i
\(781\)