Properties

Label 91.2.q.a.43.4
Level $91$
Weight $2$
Character 91.43
Analytic conductor $0.727$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.726638658394\)
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: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 43.4
Root \(-1.08105 - 0.911778i\) of defining polynomial
Character \(\chi\) \(=\) 91.43
Dual form 91.2.q.a.36.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.713220 + 0.411778i) q^{2} +(-1.33015 + 2.30388i) q^{3} +(-0.660878 - 1.14467i) q^{4} +3.16209i q^{5} +(-1.89737 + 1.09545i) q^{6} +(0.866025 - 0.500000i) q^{7} -2.73565i q^{8} +(-2.03858 - 3.53092i) q^{9} +O(q^{10})\) \(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} +(0.866025 - 0.500000i) q^{7} -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} +0.823556 q^{14} +(-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} +2.66029i q^{21} +(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} +(-1.14467 - 0.660878i) q^{28} +(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} +(1.58105 + 2.73845i) q^{35} +(-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} +(-1.09545 + 1.89737i) q^{42} +(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} +(0.500000 - 0.866025i) q^{49} +(-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} +(-1.36783 - 2.36914i) q^{56} +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} +(-3.53092 - 2.03858i) q^{63} -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} +2.60416i q^{70} +(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} +5.94270 q^{77} +(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} +(3.04517 - 1.75813i) q^{84} +(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} +(-1.86872 - 3.08348i) q^{91} +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} +(0.713220 - 0.411778i) q^{98} -24.2293i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 4q^{4} - 18q^{6} - 4q^{9} + O(q^{10}) \) \( 12q + 4q^{4} - 18q^{6} - 4q^{9} + 12q^{10} + 6q^{11} - 4q^{12} + 4q^{13} - 8q^{14} + 6q^{15} - 8q^{16} - 4q^{17} - 12q^{20} + 6q^{22} - 12q^{23} + 12q^{24} - 20q^{25} - 42q^{26} + 12q^{27} + 8q^{29} + 8q^{30} + 36q^{32} - 30q^{33} + 6q^{35} - 10q^{36} - 42q^{37} + 4q^{38} - 4q^{39} + 92q^{40} + 30q^{41} + 4q^{42} + 2q^{43} + 12q^{46} - 2q^{48} + 6q^{49} - 18q^{50} + 52q^{51} + 2q^{52} - 44q^{53} + 12q^{54} - 6q^{55} - 12q^{56} - 12q^{58} + 18q^{59} + 14q^{61} - 4q^{62} + 12q^{63} - 52q^{64} + 60q^{65} - 52q^{66} - 24q^{67} - 8q^{68} + 4q^{69} - 24q^{71} + 60q^{72} + 6q^{74} + 46q^{75} - 18q^{76} + 8q^{77} - 10q^{78} - 56q^{79} - 72q^{80} + 2q^{81} + 14q^{82} + 18q^{84} - 48q^{85} - 2q^{87} - 14q^{88} - 12q^{89} + 24q^{90} + 14q^{91} + 24q^{92} - 18q^{93} + 4q^{94} - 22q^{95} + 6q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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 \(0.445395\pi\)
−0.938667 + 0.344824i \(0.887939\pi\)
\(4\) −0.660878 1.14467i −0.330439 0.572337i
\(5\) 3.16209i 1.41413i 0.707148 + 0.707065i \(0.249981\pi\)
−0.707148 + 0.707065i \(0.750019\pi\)
\(6\) −1.89737 + 1.09545i −0.774600 + 0.447215i
\(7\) 0.866025 0.500000i 0.327327 0.188982i
\(8\) 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
\(14\) 0.823556 0.220105
\(15\) −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 0.654611 0.755966i \(-0.272832\pi\)
−0.981991 + 0.188927i \(0.939499\pi\)
\(18\) 3.35776i 0.791433i
\(19\) 1.69485 0.978524i 0.388826 0.224489i −0.292825 0.956166i \(-0.594595\pi\)
0.681651 + 0.731677i \(0.261262\pi\)
\(20\) 3.61956 2.08976i 0.809359 0.467284i
\(21\) 2.66029i 0.580523i
\(22\) 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
\(28\) −1.14467 0.660878i −0.216323 0.124894i
\(29\) 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 \(0.0329760\pi\)
−0.994639 + 0.103412i \(0.967024\pi\)
\(32\) −5.01684 + 2.89647i −0.886860 + 0.512029i
\(33\) −13.6913 + 7.90465i −2.38334 + 1.37602i
\(34\) 2.22331i 0.381294i
\(35\) 1.58105 + 2.73845i 0.267246 + 0.462883i
\(36\) −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 0.225782 0.974178i \(-0.427506\pi\)
−0.730772 + 0.682622i \(0.760840\pi\)
\(42\) −1.09545 + 1.89737i −0.169032 + 0.292771i
\(43\) 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 \(-0.989410\pi\)
0.999447 0.0332624i \(-0.0105897\pi\)
\(48\) −0.519487 0.899778i −0.0749815 0.129872i
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) −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
\(56\) −1.36783 2.36914i −0.182783 0.316590i
\(57\) 5.20632i 0.689594i
\(58\) 4.27822 2.47003i 0.561758 0.324331i
\(59\) 4.16200 2.40293i 0.541846 0.312835i −0.203981 0.978975i \(-0.565388\pi\)
0.745827 + 0.666140i \(0.232055\pi\)
\(60\) 11.1187i 1.43542i
\(61\) 0.578514 + 1.00201i 0.0740711 + 0.128295i 0.900682 0.434479i \(-0.143067\pi\)
−0.826611 + 0.562774i \(0.809734\pi\)
\(62\) −0.474182 + 0.821308i −0.0602212 + 0.104306i
\(63\) −3.53092 2.03858i −0.444854 0.256837i
\(64\) −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
\(70\) 2.60416i 0.311257i
\(71\) 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 \(-0.838435\pi\)
0.873927 0.486057i \(-0.161565\pi\)
\(74\) −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
\(77\) 5.94270 0.677233
\(78\) 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 \(-0.889520\pi\)
0.940369 0.340156i \(-0.110480\pi\)
\(84\) 3.04517 1.75813i 0.332255 0.191827i
\(85\) 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 0.654476 0.756083i \(-0.272889\pi\)
−0.327549 + 0.944834i \(0.606222\pi\)
\(90\) 10.6176 1.11919
\(91\) −1.86872 3.08348i −0.195895 0.323237i
\(92\) 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 −0.643065 0.765811i \(-0.722338\pi\)
0.341679 + 0.939817i \(0.389004\pi\)
\(98\) 0.713220 0.411778i 0.0720461 0.0415959i
\(99\) 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 \(0.397455\pi\)
−0.979779 + 0.200084i \(0.935879\pi\)
\(102\) 5.12223 + 2.95732i 0.507177 + 0.292819i
\(103\) −11.6450 −1.14741 −0.573706 0.819061i \(-0.694495\pi\)
−0.573706 + 0.819061i \(0.694495\pi\)
\(104\) −9.86130 + 0.209604i −0.966981 + 0.0205533i
\(105\) −8.41209 −0.820936
\(106\) 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
\(112\) 0.390549i 0.0369034i
\(113\) 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
\(119\) −2.33796 1.34982i −0.214320 0.123738i
\(120\) −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
\(126\) −1.67888 2.90791i −0.149567 0.259057i
\(127\) 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 \(-0.352657\pi\)
0.446537 + 0.894765i \(0.352657\pi\)
\(132\) 18.0965 + 10.4480i 1.57510 + 0.909383i
\(133\) 0.978524 1.69485i 0.0848488 0.146962i
\(134\) −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 \(0.164170\pi\)
−0.00784365 + 0.999969i \(0.502497\pi\)
\(140\) 2.08976 3.61956i 0.176617 0.305909i
\(141\) 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
\(147\) 1.33015 + 2.30388i 0.109709 + 0.190021i
\(148\) 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
\(154\) 4.23845 + 2.44707i 0.341544 + 0.197191i
\(155\) −3.64130 −0.292476
\(156\) −0.269413 12.6752i −0.0215703 1.01483i
\(157\) 6.50734 0.519342 0.259671 0.965697i \(-0.416386\pi\)
0.259671 + 0.965697i \(0.416386\pi\)
\(158\) −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
\(161\) 2.72941i 0.215108i
\(162\) 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 0.364097 0.931361i \(-0.381378\pi\)
−0.624534 + 0.780998i \(0.714711\pi\)
\(168\) 7.27763 0.561482
\(169\) −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 \(0.0116358\pi\)
−0.468015 + 0.883720i \(0.655031\pi\)
\(174\) 13.1420i 0.996293i
\(175\) −4.32911 + 2.49941i −0.327250 + 0.188938i
\(176\) −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 \(-0.510228\pi\)
−0.0321279 + 0.999484i \(0.510228\pi\)
\(182\) −0.0631003 2.96870i −0.00467730 0.220055i
\(183\) −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
\(189\) 2.48163 1.43277i 0.180512 0.104219i
\(190\) 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
\(196\) −1.32176 −0.0944111
\(197\) 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 \(-0.895838\pi\)
0.195106 0.980782i \(-0.437495\pi\)
\(200\) 13.6751i 0.966972i
\(201\) 14.4665 8.35223i 1.02039 0.589121i
\(202\) −9.50686 + 5.48879i −0.668901 + 0.386190i
\(203\) 5.99845i 0.421009i
\(204\) −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
\(210\) −5.99967 3.46391i −0.414017 0.239033i
\(211\) 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
\(217\) 0.575774 + 0.997270i 0.0390861 + 0.0676991i
\(218\) 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 −0.0429835 0.999076i \(-0.513686\pi\)
−0.886717 + 0.462313i \(0.847020\pi\)
\(224\) −2.89647 + 5.01684i −0.193529 + 0.335201i
\(225\) 10.1905 + 17.6505i 0.679366 + 1.17670i
\(226\) 4.75536i 0.316322i
\(227\) −14.1812 + 8.18751i −0.941239 + 0.543424i −0.890348 0.455280i \(-0.849539\pi\)
−0.0508902 + 0.998704i \(0.516206\pi\)
\(228\) 5.95954 3.44074i 0.394680 0.227869i
\(229\) 27.0104i 1.78490i −0.451148 0.892449i \(-0.648985\pi\)
0.451148 0.892449i \(-0.351015\pi\)
\(230\) −3.55392 6.15556i −0.234338 0.405886i
\(231\) −7.90465 + 13.6913i −0.520088 + 0.900819i
\(232\) −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
\(238\) −1.11165 1.92544i −0.0720578 0.124808i
\(239\) 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 −0.0432510 0.999064i \(-0.513772\pi\)
0.843589 + 0.536989i \(0.180438\pi\)
\(242\) 20.0253i 1.28727i
\(243\) 10.4280 + 18.0618i 0.668956 + 1.15867i
\(244\) 0.764654 1.32442i 0.0489519 0.0847872i
\(245\) 2.73845 + 1.58105i 0.174953 + 0.101009i
\(246\) 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 0.969341 0.245719i \(-0.0790239\pi\)
−0.697469 + 0.716615i \(0.745691\pi\)
\(252\) 5.38900i 0.339475i
\(253\) −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 −0.657912 0.753094i \(-0.728560\pi\)
0.981155 + 0.193222i \(0.0618936\pi\)
\(258\) −13.2650 7.65856i −0.825844 0.476801i
\(259\) −6.50454 −0.404172
\(260\) −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
\(266\) 1.39581 0.805869i 0.0855824 0.0494110i
\(267\) −8.20495 + 4.73713i −0.502135 + 0.289908i
\(268\) 8.29954i 0.506975i
\(269\) −6.46995 11.2063i −0.394480 0.683259i 0.598555 0.801082i \(-0.295742\pi\)
−0.993035 + 0.117823i \(0.962409\pi\)
\(270\) −3.73117 + 6.46257i −0.227072 + 0.393299i
\(271\) −15.3069 8.83745i −0.929829 0.536837i −0.0430712 0.999072i \(-0.513714\pi\)
−0.886757 + 0.462235i \(0.847048\pi\)
\(272\) 1.05434 0.0639289
\(273\) 9.58965 0.203830i 0.580392 0.0123363i
\(274\) −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
\(280\) 7.49145 4.32519i 0.447700 0.258480i
\(281\) 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 \(0.492333\pi\)
−0.877817 + 0.478996i \(0.841001\pi\)
\(284\) −5.15927 2.97871i −0.306146 0.176754i
\(285\) −16.4629 −0.975176
\(286\) 15.0910 9.14580i 0.892350 0.540802i
\(287\) −3.73374 −0.220396
\(288\) 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 0.484124 0.874999i \(-0.339138\pi\)
0.999834 + 0.0182359i \(0.00580499\pi\)
\(294\) 2.19090i 0.127776i
\(295\) 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
\(301\) 6.05460 + 3.49562i 0.348981 + 0.201484i
\(302\) −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 \(0.0646555\pi\)
−0.979442 + 0.201728i \(0.935344\pi\)
\(308\) −3.92740 6.80245i −0.223784 0.387606i
\(309\) 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 \(-0.282494\pi\)
0.631368 + 0.775483i \(0.282494\pi\)
\(312\) 12.6341 22.9981i 0.715264 1.30201i
\(313\) −28.0840 −1.58740 −0.793700 0.608309i \(-0.791848\pi\)
−0.793700 + 0.608309i \(0.791848\pi\)
\(314\) 4.64117 + 2.67958i 0.261916 + 0.151217i
\(315\) 6.44617 11.1651i 0.363200 0.629082i
\(316\) 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
\(322\) −1.12391 + 1.94667i −0.0626332 + 0.108484i
\(323\) −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
\(329\) −0.228035 0.394969i −0.0125720 0.0217753i
\(330\) 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
\(336\) −0.899778 0.519487i −0.0490869 0.0283403i
\(337\) 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
\(343\) 1.00000i 0.0539949i
\(344\) 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 0.649617 0.760261i \(-0.274929\pi\)
−0.333597 + 0.942716i \(0.608262\pi\)
\(350\) −4.11682 −0.220053
\(351\) −0.219556 10.3295i −0.0117190 0.551349i
\(352\) −34.4257 −1.83490
\(353\) 12.1272 + 7.00163i 0.645465 + 0.372659i 0.786716 0.617314i \(-0.211779\pi\)
−0.141252 + 0.989974i \(0.545113\pi\)
\(354\) −5.26458 + 9.11852i −0.279809 + 0.484644i
\(355\) 7.12608 + 12.3427i 0.378213 + 0.655085i
\(356\) 4.70725i 0.249484i
\(357\) 6.21965 3.59092i 0.329179 0.190052i
\(358\) −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
\(364\) −2.29459 + 4.17688i −0.120269 + 0.218928i
\(365\) 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 \(0.453399\pi\)
−0.929700 + 0.368317i \(0.879934\pi\)
\(368\) −0.532985 0.923157i −0.0277838 0.0481229i
\(369\) 15.2230i 0.792480i
\(370\) 14.6695 8.46943i 0.762630 0.440305i
\(371\) 0.345792 0.199643i 0.0179526 0.0103649i
\(372\) 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
\(378\) 2.35994 0.121382
\(379\) −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 −0.615321 0.788277i \(-0.710974\pi\)
0.375007 + 0.927022i \(0.377640\pi\)
\(384\) −19.1225 + 11.0404i −0.975842 + 0.563402i
\(385\) 18.7914i 0.957696i
\(386\) 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
\(392\) −2.36914 1.36783i −0.119660 0.0690856i
\(393\) −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 \(-0.283724\pi\)
0.987879 0.155223i \(-0.0496097\pi\)
\(398\) 17.4690i 0.875644i
\(399\) 2.60316 + 4.50880i 0.130321 + 0.225723i
\(400\) 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
\(406\) 2.47003 4.27822i 0.122586 0.212324i
\(407\) −19.3273 33.4758i −0.958016 1.65933i
\(408\) 19.6470i 0.972672i
\(409\) 21.2846 12.2886i 1.05245 0.607635i 0.129119 0.991629i \(-0.458785\pi\)
0.923335 + 0.383995i \(0.125452\pi\)
\(410\) 8.42059 4.86163i 0.415863 0.240099i
\(411\) 53.0662i 2.61756i
\(412\) 7.69589 + 13.3297i 0.379149 + 0.656706i
\(413\) 2.40293 4.16200i 0.118241 0.204799i
\(414\) 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 −0.757411 0.652938i \(-0.773536\pi\)
0.944167 + 0.329468i \(0.106869\pi\)
\(420\) 5.55936 + 9.62910i 0.271269 + 0.469852i
\(421\) 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
\(427\) 1.00201 + 0.578514i 0.0484909 + 0.0279962i
\(428\) 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 \(0.165665\pi\)
−0.00314644 + 0.999995i \(0.501002\pi\)
\(434\) 0.948365i 0.0455230i
\(435\) −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 \(0.402002\pi\)
−0.976820 + 0.214061i \(0.931331\pi\)
\(440\) 44.5194 + 25.7033i 2.12238 + 1.22536i
\(441\) −4.07715 −0.194150
\(442\) −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
\(448\) −3.45519 + 1.99486i −0.163243 + 0.0942481i
\(449\) −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
\(455\) 9.75026 5.90907i 0.457099 0.277022i
\(456\) 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 −0.874424 0.485163i \(-0.838760\pi\)
−0.0170480 + 0.999855i \(0.505427\pi\)
\(462\) −11.2755 + 6.50993i −0.524585 + 0.302869i
\(463\) 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 \(-0.599431\pi\)
−0.307316 + 0.951607i \(0.599431\pi\)
\(468\) 17.0298 + 9.35538i 0.787203 + 0.432453i
\(469\) −6.27918 −0.289946
\(470\) 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
\(476\) 3.56827i 0.163551i
\(477\) −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 0.625497 0.780226i \(-0.284896\pi\)
−0.362947 + 0.931810i \(0.618230\pi\)
\(480\) 48.7307 2.22424
\(481\) −11.2920 + 20.5550i −0.514870 + 0.937228i
\(482\) 11.8153 0.538172
\(483\) −6.28825 3.63052i −0.286125 0.165194i
\(484\) 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
\(490\) 1.30208 + 2.25527i 0.0588220 + 0.101883i
\(491\) −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
\(497\) 2.25360 3.90335i 0.101088 0.175089i
\(498\) 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 0.643378 0.765549i \(-0.277533\pi\)
−0.984674 + 0.174407i \(0.944199\pi\)
\(504\) −5.57684 + 9.65936i −0.248412 + 0.430262i
\(505\) −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 0.101046 0.994882i \(-0.467781\pi\)
−0.811070 + 0.584949i \(0.801115\pi\)
\(510\) −9.35133 + 16.1970i −0.414084 + 0.717214i
\(511\) −4.15288 7.19299i −0.183712 0.318199i
\(512\) 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
\(518\) −4.63917 2.67843i −0.203833 0.117683i
\(519\) −37.1823 −1.63212
\(520\) −0.662786 31.1824i −0.0290651 1.36744i
\(521\) 23.5865 1.03334 0.516671 0.856184i \(-0.327171\pi\)
0.516671 + 0.856184i \(0.327171\pi\)
\(522\) −17.4430 10.0707i −0.763457 0.440782i
\(523\) −6.15294 + 10.6572i −0.269049 + 0.466007i −0.968617 0.248560i \(-0.920043\pi\)
0.699567 + 0.714567i \(0.253376\pi\)
\(524\) −6.75529 11.7005i −0.295106 0.511139i
\(525\) 13.2983i 0.580387i
\(526\) 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
\(532\) −2.58674 −0.112149
\(533\) −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
\(539\) 5.14653 2.97135i 0.221677 0.127985i
\(540\) 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
\(546\) 6.92347 + 3.80343i 0.296297 + 0.162772i
\(547\) 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
\(553\) −6.85381 + 3.95705i −0.291454 + 0.168271i
\(554\) 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
\(560\) −1.23495 −0.0521862
\(561\) 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 0.850632 0.525761i \(-0.176219\pi\)
−0.880639 + 0.473789i \(0.842886\pi\)
\(564\) 1.60366i 0.0675263i
\(565\) −15.8123 + 9.12924i −0.665229 + 0.384070i
\(566\) −20.4865 + 11.8279i −0.861113 + 0.497164i
\(567\) 4.60828i 0.193530i
\(568\) −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
\(574\) −2.66298 1.53747i −0.111151 0.0641729i
\(575\) 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 \(-0.936204\pi\)
0.979983 0.199081i \(-0.0637955\pi\)
\(578\) 6.92674 3.99916i 0.288115 0.166343i
\(579\) −38.0046 + 21.9419i −1.57942 + 0.911876i
\(580\) 25.0706i 1.04100i
\(581\) −3.09897 5.36758i −0.128567 0.222685i
\(582\) 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 0.457218 0.889355i \(-0.348846\pi\)
−0.541595 + 0.840640i \(0.682179\pi\)
\(588\) 1.75813 3.04517i 0.0725040 0.125581i
\(589\) 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 \(-0.688275\pi\)
0.557594 0.830114i \(-0.311725\pi\)
\(594\) 7.01219 + 12.1455i 0.287714 + 0.498335i
\(595\) 4.26826 7.39284i 0.174982 0.303077i
\(596\) 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 −0.937178 0.348852i \(-0.886571\pi\)
0.770704 + 0.637193i \(0.219905\pi\)
\(602\) 2.87884 + 4.98630i 0.117333 + 0.203226i
\(603\) 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 0.778734 0.627354i \(-0.215862\pi\)
−0.932672 + 0.360726i \(0.882529\pi\)
\(608\) −5.66853 + 9.81819i −0.229889 + 0.398180i
\(609\) 13.8197 + 7.97882i 0.560003 + 0.323318i
\(610\) −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
\(616\) 16.2571i 0.655019i
\(617\) 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 \(0.128151\pi\)
−0.920046 + 0.391811i \(0.871849\pi\)
\(620\) 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
\(623\) 3.56136 0.142683
\(624\) −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
\(630\) 9.19508 5.30878i 0.366341 0.211507i
\(631\) −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
\(637\) −3.16010 1.73601i −0.125208 0.0687834i
\(638\) 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 −0.268442 0.963296i \(-0.586509\pi\)
0.700018 + 0.714125i \(0.253175\pi\)
\(644\) 3.12429 1.80381i 0.123114 0.0710801i
\(645\) 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 \(-0.664650\pi\)
0.999980 0.00633579i \(-0.00201676\pi\)
\(648\) −10.9177 6.30332i −0.428887 0.247618i
\(649\) 28.5598 1.12107
\(650\) −7.14685 + 13.0096i −0.280323 + 0.510277i
\(651\) −3.06345 −0.120066
\(652\) −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
\(658\) 0.375600i 0.0146424i
\(659\) −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 0.915579 0.402138i \(-0.131733\pi\)
0.109528 + 0.993984i \(0.465066\pi\)
\(662\) 12.8728 0.500316
\(663\) −0.550267 25.8886i −0.0213706 1.00543i
\(664\) −16.9554 −0.657998
\(665\) 5.35928 + 3.09418i 0.207824 + 0.119987i
\(666\) −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
\(672\) −7.70546 13.3462i −0.297245 0.514843i
\(673\) 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 \(-0.613214\pi\)
−0.348221 + 0.937412i \(0.613214\pi\)
\(678\) −10.9558 6.32532i −0.420754 0.242923i
\(679\) −1.71375 + 2.96831i −0.0657679 + 0.113913i
\(680\) −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
\(686\) 0.411778 0.713220i 0.0157218 0.0272309i
\(687\) 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 0.905040 0.425327i \(-0.139841\pi\)
0.0841761 + 0.996451i \(0.473174\pi\)
\(692\) 9.23693 15.9988i 0.351135 0.608184i
\(693\) −12.1146 20.9832i −0.460197 0.797085i
\(694\) 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
\(700\) 5.72203 + 3.30361i 0.216272 + 0.124865i
\(701\) 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
\(707\) 13.3295i 0.501307i
\(708\) 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
\(714\) 5.91465 0.221350
\(715\) 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 \(0.171043\pi\)
0.0137492 + 0.999905i \(0.495623\pi\)
\(720\) 5.03509i 0.187647i
\(721\) −10.0848 + 5.82248i −0.375579 + 0.216840i
\(722\) −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 \(-0.420455\pi\)
0.247305 + 0.968938i \(0.420455\pi\)
\(728\) −8.43534 + 5.11217i −0.312634 + 0.189470i
\(729\) −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 \(-0.816876\pi\)
0.839029 0.544087i \(-0.183124\pi\)
\(734\) −21.4193 + 12.3664i −0.790599 + 0.456453i
\(735\) −7.28508 + 4.20604i −0.268714 + 0.155142i
\(736\) 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
\(742\) 0.328834 0.0120719
\(743\) −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
\(749\) 3.92966i 0.143587i
\(750\) −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
\(756\) −3.28011 1.89377i −0.119297 0.0688759i
\(757\) −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 −0.497779 0.867304i \(-0.665851\pi\)
0.502218 + 0.864741i \(0.332518\pi\)
\(762\) 13.4328i 0.486618i
\(763\) −5.62666 9.74566i −0.203699 0.352817i
\(764\) −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 0.697744 0.716347i \(-0.254187\pi\)
−0.271503 + 0.962438i \(0.587521\pi\)
\(770\) −7.73787 + 13.4024i −0.278853 + 0.482988i
\(771\) 13.7856 + 23.8773i 0.496475 + 0.859920i
\(772\) 21.8035i 0.784726i
\(773\) 15.2328 8.79469i 0.547887 0.316323i −0.200382 0.979718i \(-0.564218\pi\)
0.748269 + 0.663395i \(0.230885\pi\)
\(774\) 20.3299 11.7375i 0.730744 0.421895i
\(775\) 5.75639i 0.206776i
\(776\)