Properties

Label 980.2.c.e.979.32
Level $980$
Weight $2$
Character 980.979
Analytic conductor $7.825$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.82533939809\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 979.32
Character \(\chi\) \(=\) 980.979
Dual form 980.2.c.e.979.29

$q$-expansion

\(f(q)\) \(=\) \(q+(0.576258 + 1.29148i) q^{2} +2.50150i q^{3} +(-1.33585 + 1.48845i) q^{4} +(0.639901 + 2.14255i) q^{5} +(-3.23064 + 1.44151i) q^{6} +(-2.69211 - 0.867500i) q^{8} -3.25749 q^{9} +O(q^{10})\) \(q+(0.576258 + 1.29148i) q^{2} +2.50150i q^{3} +(-1.33585 + 1.48845i) q^{4} +(0.639901 + 2.14255i) q^{5} +(-3.23064 + 1.44151i) q^{6} +(-2.69211 - 0.867500i) q^{8} -3.25749 q^{9} +(-2.39832 + 2.06108i) q^{10} -2.25026i q^{11} +(-3.72336 - 3.34164i) q^{12} -5.96620 q^{13} +(-5.35959 + 1.60071i) q^{15} +(-0.430987 - 3.97671i) q^{16} +2.00749 q^{17} +(-1.87716 - 4.20700i) q^{18} +7.81989 q^{19} +(-4.04390 - 1.90967i) q^{20} +(2.90618 - 1.29673i) q^{22} -2.99226 q^{23} +(2.17005 - 6.73430i) q^{24} +(-4.18105 + 2.74204i) q^{25} +(-3.43807 - 7.70524i) q^{26} -0.644123i q^{27} -4.87936 q^{29} +(-5.15579 - 5.99939i) q^{30} -1.49990 q^{31} +(4.88750 - 2.84822i) q^{32} +5.62903 q^{33} +(1.15683 + 2.59263i) q^{34} +(4.35154 - 4.84863i) q^{36} +4.78601i q^{37} +(4.50627 + 10.0992i) q^{38} -14.9244i q^{39} +(0.135982 - 6.32309i) q^{40} +8.82927i q^{41} +1.12695 q^{43} +(3.34941 + 3.00602i) q^{44} +(-2.08447 - 6.97935i) q^{45} +(-1.72431 - 3.86446i) q^{46} +9.56972i q^{47} +(9.94774 - 1.07811i) q^{48} +(-5.95066 - 3.81964i) q^{50} +5.02172i q^{51} +(7.96997 - 8.88040i) q^{52} +7.06264i q^{53} +(0.831874 - 0.371181i) q^{54} +(4.82131 - 1.43994i) q^{55} +19.5614i q^{57} +(-2.81177 - 6.30161i) q^{58} +11.4057 q^{59} +(4.77705 - 10.1158i) q^{60} -1.21986i q^{61} +(-0.864331 - 1.93710i) q^{62} +(6.49489 + 4.67081i) q^{64} +(-3.81777 - 12.7829i) q^{65} +(3.24377 + 7.26979i) q^{66} +1.11485 q^{67} +(-2.68171 + 2.98805i) q^{68} -7.48514i q^{69} -8.40090i q^{71} +(8.76953 + 2.82588i) q^{72} -5.88062 q^{73} +(-6.18105 + 2.75798i) q^{74} +(-6.85921 - 10.4589i) q^{75} +(-10.4462 + 11.6395i) q^{76} +(19.2746 - 8.60032i) q^{78} -12.1357i q^{79} +(8.24453 - 3.46811i) q^{80} -8.16121 q^{81} +(-11.4028 + 5.08793i) q^{82} -11.1319i q^{83} +(1.28459 + 4.30114i) q^{85} +(0.649414 + 1.45544i) q^{86} -12.2057i q^{87} +(-1.95210 + 6.05795i) q^{88} +4.57883i q^{89} +(7.81252 - 6.71396i) q^{90} +(3.99723 - 4.45385i) q^{92} -3.75201i q^{93} +(-12.3591 + 5.51462i) q^{94} +(5.00395 + 16.7545i) q^{95} +(7.12483 + 12.2261i) q^{96} -4.62008 q^{97} +7.33022i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 16q^{4} - 64q^{9} + O(q^{10}) \) \( 48q + 16q^{4} - 64q^{9} + 16q^{16} - 16q^{25} - 48q^{29} - 8q^{30} + 176q^{36} - 48q^{44} - 32q^{46} + 32q^{50} + 24q^{60} - 80q^{64} - 16q^{65} - 112q^{74} - 48q^{81} - 64q^{85} - 112q^{86} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\) \(491\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.576258 + 1.29148i 0.407476 + 0.913216i
\(3\) 2.50150i 1.44424i 0.691767 + 0.722120i \(0.256832\pi\)
−0.691767 + 0.722120i \(0.743168\pi\)
\(4\) −1.33585 + 1.48845i −0.667927 + 0.744227i
\(5\) 0.639901 + 2.14255i 0.286172 + 0.958178i
\(6\) −3.23064 + 1.44151i −1.31890 + 0.588493i
\(7\) 0 0
\(8\) −2.69211 0.867500i −0.951804 0.306708i
\(9\) −3.25749 −1.08583
\(10\) −2.39832 + 2.06108i −0.758415 + 0.651771i
\(11\) 2.25026i 0.678480i −0.940700 0.339240i \(-0.889830\pi\)
0.940700 0.339240i \(-0.110170\pi\)
\(12\) −3.72336 3.34164i −1.07484 0.964648i
\(13\) −5.96620 −1.65472 −0.827362 0.561668i \(-0.810160\pi\)
−0.827362 + 0.561668i \(0.810160\pi\)
\(14\) 0 0
\(15\) −5.35959 + 1.60071i −1.38384 + 0.413302i
\(16\) −0.430987 3.97671i −0.107747 0.994178i
\(17\) 2.00749 0.486887 0.243443 0.969915i \(-0.421723\pi\)
0.243443 + 0.969915i \(0.421723\pi\)
\(18\) −1.87716 4.20700i −0.442450 0.991599i
\(19\) 7.81989 1.79400 0.897002 0.442026i \(-0.145740\pi\)
0.897002 + 0.442026i \(0.145740\pi\)
\(20\) −4.04390 1.90967i −0.904244 0.427016i
\(21\) 0 0
\(22\) 2.90618 1.29673i 0.619599 0.276464i
\(23\) −2.99226 −0.623930 −0.311965 0.950094i \(-0.600987\pi\)
−0.311965 + 0.950094i \(0.600987\pi\)
\(24\) 2.17005 6.73430i 0.442960 1.37463i
\(25\) −4.18105 + 2.74204i −0.836211 + 0.548408i
\(26\) −3.43807 7.70524i −0.674260 1.51112i
\(27\) 0.644123i 0.123962i
\(28\) 0 0
\(29\) −4.87936 −0.906074 −0.453037 0.891492i \(-0.649659\pi\)
−0.453037 + 0.891492i \(0.649659\pi\)
\(30\) −5.15579 5.99939i −0.941315 1.09533i
\(31\) −1.49990 −0.269391 −0.134695 0.990887i \(-0.543006\pi\)
−0.134695 + 0.990887i \(0.543006\pi\)
\(32\) 4.88750 2.84822i 0.863996 0.503500i
\(33\) 5.62903 0.979888
\(34\) 1.15683 + 2.59263i 0.198395 + 0.444633i
\(35\) 0 0
\(36\) 4.35154 4.84863i 0.725256 0.808105i
\(37\) 4.78601i 0.786816i 0.919364 + 0.393408i \(0.128704\pi\)
−0.919364 + 0.393408i \(0.871296\pi\)
\(38\) 4.50627 + 10.0992i 0.731013 + 1.63831i
\(39\) 14.9244i 2.38982i
\(40\) 0.135982 6.32309i 0.0215006 0.999769i
\(41\) 8.82927i 1.37890i 0.724333 + 0.689450i \(0.242148\pi\)
−0.724333 + 0.689450i \(0.757852\pi\)
\(42\) 0 0
\(43\) 1.12695 0.171858 0.0859292 0.996301i \(-0.472614\pi\)
0.0859292 + 0.996301i \(0.472614\pi\)
\(44\) 3.34941 + 3.00602i 0.504943 + 0.453175i
\(45\) −2.08447 6.97935i −0.310735 1.04042i
\(46\) −1.72431 3.86446i −0.254236 0.569783i
\(47\) 9.56972i 1.39589i 0.716153 + 0.697943i \(0.245901\pi\)
−0.716153 + 0.697943i \(0.754099\pi\)
\(48\) 9.94774 1.07811i 1.43583 0.155612i
\(49\) 0 0
\(50\) −5.95066 3.81964i −0.841551 0.540178i
\(51\) 5.02172i 0.703182i
\(52\) 7.96997 8.88040i 1.10524 1.23149i
\(53\) 7.06264i 0.970129i 0.874478 + 0.485064i \(0.161204\pi\)
−0.874478 + 0.485064i \(0.838796\pi\)
\(54\) 0.831874 0.371181i 0.113204 0.0505113i
\(55\) 4.82131 1.43994i 0.650105 0.194162i
\(56\) 0 0
\(57\) 19.5614i 2.59098i
\(58\) −2.81177 6.30161i −0.369203 0.827441i
\(59\) 11.4057 1.48490 0.742450 0.669901i \(-0.233663\pi\)
0.742450 + 0.669901i \(0.233663\pi\)
\(60\) 4.77705 10.1158i 0.616714 1.30595i
\(61\) 1.21986i 0.156187i −0.996946 0.0780935i \(-0.975117\pi\)
0.996946 0.0780935i \(-0.0248833\pi\)
\(62\) −0.864331 1.93710i −0.109770 0.246012i
\(63\) 0 0
\(64\) 6.49489 + 4.67081i 0.811861 + 0.583851i
\(65\) −3.81777 12.7829i −0.473536 1.58552i
\(66\) 3.24377 + 7.26979i 0.399281 + 0.894850i
\(67\) 1.11485 0.136200 0.0681000 0.997678i \(-0.478306\pi\)
0.0681000 + 0.997678i \(0.478306\pi\)
\(68\) −2.68171 + 2.98805i −0.325205 + 0.362354i
\(69\) 7.48514i 0.901105i
\(70\) 0 0
\(71\) 8.40090i 0.997003i −0.866889 0.498501i \(-0.833884\pi\)
0.866889 0.498501i \(-0.166116\pi\)
\(72\) 8.76953 + 2.82588i 1.03350 + 0.333033i
\(73\) −5.88062 −0.688274 −0.344137 0.938919i \(-0.611828\pi\)
−0.344137 + 0.938919i \(0.611828\pi\)
\(74\) −6.18105 + 2.75798i −0.718533 + 0.320608i
\(75\) −6.85921 10.4589i −0.792033 1.20769i
\(76\) −10.4462 + 11.6395i −1.19826 + 1.33515i
\(77\) 0 0
\(78\) 19.2746 8.60032i 2.18242 0.973794i
\(79\) 12.1357i 1.36537i −0.730711 0.682687i \(-0.760811\pi\)
0.730711 0.682687i \(-0.239189\pi\)
\(80\) 8.24453 3.46811i 0.921766 0.387747i
\(81\) −8.16121 −0.906801
\(82\) −11.4028 + 5.08793i −1.25923 + 0.561868i
\(83\) 11.1319i 1.22188i −0.791677 0.610940i \(-0.790792\pi\)
0.791677 0.610940i \(-0.209208\pi\)
\(84\) 0 0
\(85\) 1.28459 + 4.30114i 0.139334 + 0.466524i
\(86\) 0.649414 + 1.45544i 0.0700281 + 0.156944i
\(87\) 12.2057i 1.30859i
\(88\) −1.95210 + 6.05795i −0.208095 + 0.645780i
\(89\) 4.57883i 0.485355i 0.970107 + 0.242677i \(0.0780256\pi\)
−0.970107 + 0.242677i \(0.921974\pi\)
\(90\) 7.81252 6.71396i 0.823512 0.707714i
\(91\) 0 0
\(92\) 3.99723 4.45385i 0.416740 0.464345i
\(93\) 3.75201i 0.389065i
\(94\) −12.3591 + 5.51462i −1.27475 + 0.568790i
\(95\) 5.00395 + 16.7545i 0.513394 + 1.71898i
\(96\) 7.12483 + 12.2261i 0.727175 + 1.24782i
\(97\) −4.62008 −0.469098 −0.234549 0.972104i \(-0.575361\pi\)
−0.234549 + 0.972104i \(0.575361\pi\)
\(98\) 0 0
\(99\) 7.33022i 0.736715i
\(100\) 1.50388 9.88627i 0.150388 0.988627i
\(101\) 0.111126i 0.0110574i −0.999985 0.00552872i \(-0.998240\pi\)
0.999985 0.00552872i \(-0.00175986\pi\)
\(102\) −6.48547 + 2.89381i −0.642157 + 0.286530i
\(103\) 12.9119i 1.27224i 0.771588 + 0.636122i \(0.219463\pi\)
−0.771588 + 0.636122i \(0.780537\pi\)
\(104\) 16.0616 + 5.17567i 1.57497 + 0.507517i
\(105\) 0 0
\(106\) −9.12128 + 4.06990i −0.885937 + 0.395304i
\(107\) 14.6070 1.41211 0.706056 0.708156i \(-0.250473\pi\)
0.706056 + 0.708156i \(0.250473\pi\)
\(108\) 0.958748 + 0.860455i 0.0922555 + 0.0827973i
\(109\) 4.45913 0.427107 0.213553 0.976931i \(-0.431496\pi\)
0.213553 + 0.976931i \(0.431496\pi\)
\(110\) 4.63798 + 5.39685i 0.442214 + 0.514570i
\(111\) −11.9722 −1.13635
\(112\) 0 0
\(113\) 2.30454i 0.216793i 0.994108 + 0.108397i \(0.0345717\pi\)
−0.994108 + 0.108397i \(0.965428\pi\)
\(114\) −25.2632 + 11.2724i −2.36612 + 1.05576i
\(115\) −1.91475 6.41108i −0.178551 0.597836i
\(116\) 6.51811 7.26270i 0.605191 0.674324i
\(117\) 19.4349 1.79675
\(118\) 6.57265 + 14.7303i 0.605061 + 1.35604i
\(119\) 0 0
\(120\) 15.8172 + 0.340159i 1.44391 + 0.0310521i
\(121\) 5.93632 0.539665
\(122\) 1.57543 0.702953i 0.142632 0.0636424i
\(123\) −22.0864 −1.99146
\(124\) 2.00365 2.23254i 0.179933 0.200488i
\(125\) −8.55042 7.20349i −0.764773 0.644300i
\(126\) 0 0
\(127\) −6.18242 −0.548601 −0.274300 0.961644i \(-0.588446\pi\)
−0.274300 + 0.961644i \(0.588446\pi\)
\(128\) −2.28954 + 11.0796i −0.202368 + 0.979309i
\(129\) 2.81907i 0.248205i
\(130\) 14.3088 12.2968i 1.25497 1.07850i
\(131\) −8.16897 −0.713726 −0.356863 0.934157i \(-0.616154\pi\)
−0.356863 + 0.934157i \(0.616154\pi\)
\(132\) −7.51956 + 8.37855i −0.654494 + 0.729259i
\(133\) 0 0
\(134\) 0.642438 + 1.43980i 0.0554982 + 0.124380i
\(135\) 1.38007 0.412175i 0.118777 0.0354744i
\(136\) −5.40437 1.74149i −0.463421 0.149332i
\(137\) 7.07703i 0.604631i −0.953208 0.302316i \(-0.902240\pi\)
0.953208 0.302316i \(-0.0977597\pi\)
\(138\) 9.66693 4.31337i 0.822904 0.367179i
\(139\) −14.4633 −1.22676 −0.613382 0.789787i \(-0.710191\pi\)
−0.613382 + 0.789787i \(0.710191\pi\)
\(140\) 0 0
\(141\) −23.9386 −2.01600
\(142\) 10.8496 4.84108i 0.910479 0.406254i
\(143\) 13.4255i 1.12270i
\(144\) 1.40394 + 12.9541i 0.116995 + 1.07951i
\(145\) −3.12230 10.4543i −0.259293 0.868180i
\(146\) −3.38875 7.59471i −0.280455 0.628543i
\(147\) 0 0
\(148\) −7.12376 6.39342i −0.585569 0.525536i
\(149\) 19.6566 1.61033 0.805164 0.593053i \(-0.202077\pi\)
0.805164 + 0.593053i \(0.202077\pi\)
\(150\) 9.55482 14.8856i 0.780148 1.21540i
\(151\) 17.4157i 1.41727i 0.705574 + 0.708636i \(0.250689\pi\)
−0.705574 + 0.708636i \(0.749311\pi\)
\(152\) −21.0520 6.78375i −1.70754 0.550235i
\(153\) −6.53938 −0.528677
\(154\) 0 0
\(155\) −0.959789 3.21362i −0.0770921 0.258124i
\(156\) 22.2143 + 19.9369i 1.77857 + 1.59623i
\(157\) −6.86058 −0.547534 −0.273767 0.961796i \(-0.588270\pi\)
−0.273767 + 0.961796i \(0.588270\pi\)
\(158\) 15.6731 6.99330i 1.24688 0.556357i
\(159\) −17.6672 −1.40110
\(160\) 9.22998 + 8.64913i 0.729694 + 0.683774i
\(161\) 0 0
\(162\) −4.70296 10.5401i −0.369499 0.828105i
\(163\) 2.86934 0.224744 0.112372 0.993666i \(-0.464155\pi\)
0.112372 + 0.993666i \(0.464155\pi\)
\(164\) −13.1420 11.7946i −1.02621 0.921005i
\(165\) 3.60202 + 12.0605i 0.280417 + 0.938908i
\(166\) 14.3766 6.41482i 1.11584 0.497886i
\(167\) 15.9389i 1.23339i 0.787204 + 0.616693i \(0.211528\pi\)
−0.787204 + 0.616693i \(0.788472\pi\)
\(168\) 0 0
\(169\) 22.5955 1.73811
\(170\) −4.81460 + 4.13759i −0.369263 + 0.317339i
\(171\) −25.4732 −1.94799
\(172\) −1.50544 + 1.67741i −0.114789 + 0.127902i
\(173\) −1.02406 −0.0778580 −0.0389290 0.999242i \(-0.512395\pi\)
−0.0389290 + 0.999242i \(0.512395\pi\)
\(174\) 15.7635 7.03363i 1.19502 0.533218i
\(175\) 0 0
\(176\) −8.94865 + 0.969834i −0.674530 + 0.0731040i
\(177\) 28.5314i 2.14455i
\(178\) −5.91348 + 2.63858i −0.443234 + 0.197770i
\(179\) 4.19778i 0.313757i −0.987618 0.156878i \(-0.949857\pi\)
0.987618 0.156878i \(-0.0501431\pi\)
\(180\) 13.1730 + 6.22076i 0.981857 + 0.463668i
\(181\) 5.33135i 0.396276i −0.980174 0.198138i \(-0.936511\pi\)
0.980174 0.198138i \(-0.0634894\pi\)
\(182\) 0 0
\(183\) 3.05148 0.225572
\(184\) 8.05550 + 2.59579i 0.593859 + 0.191364i
\(185\) −10.2543 + 3.06257i −0.753910 + 0.225165i
\(186\) 4.84565 2.16212i 0.355300 0.158535i
\(187\) 4.51737i 0.330343i
\(188\) −14.2441 12.7837i −1.03886 0.932350i
\(189\) 0 0
\(190\) −18.7546 + 16.1174i −1.36060 + 1.16928i
\(191\) 16.7444i 1.21158i 0.795624 + 0.605791i \(0.207143\pi\)
−0.795624 + 0.605791i \(0.792857\pi\)
\(192\) −11.6840 + 16.2470i −0.843221 + 1.17252i
\(193\) 15.5425i 1.11877i 0.828907 + 0.559386i \(0.188963\pi\)
−0.828907 + 0.559386i \(0.811037\pi\)
\(194\) −2.66235 5.96675i −0.191146 0.428387i
\(195\) 31.9764 9.55015i 2.28987 0.683900i
\(196\) 0 0
\(197\) 10.4069i 0.741463i −0.928740 0.370731i \(-0.879107\pi\)
0.928740 0.370731i \(-0.120893\pi\)
\(198\) −9.46685 + 4.22410i −0.672780 + 0.300193i
\(199\) 15.4520 1.09536 0.547681 0.836687i \(-0.315511\pi\)
0.547681 + 0.836687i \(0.315511\pi\)
\(200\) 13.6346 3.75480i 0.964110 0.265505i
\(201\) 2.78879i 0.196706i
\(202\) 0.143517 0.0640372i 0.0100978 0.00450564i
\(203\) 0 0
\(204\) −7.47460 6.70829i −0.523327 0.469674i
\(205\) −18.9172 + 5.64985i −1.32123 + 0.394603i
\(206\) −16.6755 + 7.44056i −1.16183 + 0.518409i
\(207\) 9.74728 0.677483
\(208\) 2.57135 + 23.7258i 0.178291 + 1.64509i
\(209\) 17.5968i 1.21720i
\(210\) 0 0
\(211\) 10.3988i 0.715879i −0.933745 0.357940i \(-0.883479\pi\)
0.933745 0.357940i \(-0.116521\pi\)
\(212\) −10.5124 9.43466i −0.721996 0.647975i
\(213\) 21.0148 1.43991
\(214\) 8.41740 + 18.8647i 0.575402 + 1.28956i
\(215\) 0.721137 + 2.41455i 0.0491811 + 0.164671i
\(216\) −0.558777 + 1.73405i −0.0380200 + 0.117987i
\(217\) 0 0
\(218\) 2.56960 + 5.75888i 0.174036 + 0.390041i
\(219\) 14.7104i 0.994034i
\(220\) −4.29727 + 9.09984i −0.289722 + 0.613511i
\(221\) −11.9771 −0.805664
\(222\) −6.89908 15.4619i −0.463036 1.03773i
\(223\) 11.3655i 0.761093i 0.924762 + 0.380547i \(0.124264\pi\)
−0.924762 + 0.380547i \(0.875736\pi\)
\(224\) 0 0
\(225\) 13.6198 8.93218i 0.907984 0.595479i
\(226\) −2.97628 + 1.32801i −0.197979 + 0.0883380i
\(227\) 6.17093i 0.409579i 0.978806 + 0.204790i \(0.0656510\pi\)
−0.978806 + 0.204790i \(0.934349\pi\)
\(228\) −29.1163 26.1312i −1.92827 1.73058i
\(229\) 8.28601i 0.547555i 0.961793 + 0.273778i \(0.0882732\pi\)
−0.961793 + 0.273778i \(0.911727\pi\)
\(230\) 7.17641 6.16730i 0.473198 0.406660i
\(231\) 0 0
\(232\) 13.1358 + 4.23284i 0.862405 + 0.277900i
\(233\) 14.0909i 0.923124i −0.887108 0.461562i \(-0.847289\pi\)
0.887108 0.461562i \(-0.152711\pi\)
\(234\) 11.1995 + 25.0998i 0.732133 + 1.64082i
\(235\) −20.5036 + 6.12367i −1.33751 + 0.399464i
\(236\) −15.2364 + 16.9769i −0.991806 + 1.10510i
\(237\) 30.3575 1.97193
\(238\) 0 0
\(239\) 8.30653i 0.537305i −0.963237 0.268652i \(-0.913422\pi\)
0.963237 0.268652i \(-0.0865783\pi\)
\(240\) 8.67548 + 20.6237i 0.560000 + 1.33125i
\(241\) 25.7383i 1.65795i 0.559285 + 0.828975i \(0.311076\pi\)
−0.559285 + 0.828975i \(0.688924\pi\)
\(242\) 3.42085 + 7.66665i 0.219900 + 0.492831i
\(243\) 22.3476i 1.43360i
\(244\) 1.81570 + 1.62955i 0.116239 + 0.104322i
\(245\) 0 0
\(246\) −12.7275 28.5242i −0.811473 1.81864i
\(247\) −46.6550 −2.96858
\(248\) 4.03790 + 1.30117i 0.256407 + 0.0826241i
\(249\) 27.8463 1.76469
\(250\) 4.37594 15.1938i 0.276759 0.960939i
\(251\) 4.80612 0.303360 0.151680 0.988430i \(-0.451532\pi\)
0.151680 + 0.988430i \(0.451532\pi\)
\(252\) 0 0
\(253\) 6.73338i 0.423324i
\(254\) −3.56267 7.98448i −0.223541 0.500991i
\(255\) −10.7593 + 3.21340i −0.673774 + 0.201231i
\(256\) −15.6285 + 3.42782i −0.976781 + 0.214239i
\(257\) 21.4125 1.33567 0.667837 0.744307i \(-0.267220\pi\)
0.667837 + 0.744307i \(0.267220\pi\)
\(258\) −3.64078 + 1.62451i −0.226665 + 0.101138i
\(259\) 0 0
\(260\) 24.1267 + 11.3935i 1.49627 + 0.706594i
\(261\) 15.8945 0.983844
\(262\) −4.70743 10.5501i −0.290826 0.651786i
\(263\) 15.7285 0.969863 0.484931 0.874552i \(-0.338845\pi\)
0.484931 + 0.874552i \(0.338845\pi\)
\(264\) −15.1540 4.88318i −0.932662 0.300539i
\(265\) −15.1321 + 4.51939i −0.929556 + 0.277624i
\(266\) 0 0
\(267\) −11.4539 −0.700969
\(268\) −1.48927 + 1.65940i −0.0909717 + 0.101364i
\(269\) 1.39293i 0.0849284i 0.999098 + 0.0424642i \(0.0135208\pi\)
−0.999098 + 0.0424642i \(0.986479\pi\)
\(270\) 1.32759 + 1.54481i 0.0807946 + 0.0940144i
\(271\) 14.2313 0.864492 0.432246 0.901756i \(-0.357721\pi\)
0.432246 + 0.901756i \(0.357721\pi\)
\(272\) −0.865200 7.98320i −0.0524604 0.484052i
\(273\) 0 0
\(274\) 9.13986 4.07819i 0.552159 0.246373i
\(275\) 6.17031 + 9.40847i 0.372084 + 0.567352i
\(276\) 11.1413 + 9.99906i 0.670627 + 0.601873i
\(277\) 21.0130i 1.26255i −0.775560 0.631273i \(-0.782533\pi\)
0.775560 0.631273i \(-0.217467\pi\)
\(278\) −8.33460 18.6791i −0.499876 1.12030i
\(279\) 4.88593 0.292513
\(280\) 0 0
\(281\) 3.92163 0.233945 0.116972 0.993135i \(-0.462681\pi\)
0.116972 + 0.993135i \(0.462681\pi\)
\(282\) −13.7948 30.9163i −0.821469 1.84104i
\(283\) 1.20399i 0.0715696i −0.999360 0.0357848i \(-0.988607\pi\)
0.999360 0.0357848i \(-0.0113931\pi\)
\(284\) 12.5043 + 11.2224i 0.741996 + 0.665925i
\(285\) −41.9114 + 12.5174i −2.48262 + 0.741465i
\(286\) −17.3388 + 7.73655i −1.02527 + 0.457472i
\(287\) 0 0
\(288\) −15.9210 + 9.27807i −0.938154 + 0.546716i
\(289\) −12.9700 −0.762941
\(290\) 11.7023 10.0568i 0.687181 0.590553i
\(291\) 11.5571i 0.677490i
\(292\) 7.85565 8.75302i 0.459717 0.512232i
\(293\) 14.4715 0.845433 0.422716 0.906262i \(-0.361077\pi\)
0.422716 + 0.906262i \(0.361077\pi\)
\(294\) 0 0
\(295\) 7.29854 + 24.4374i 0.424937 + 1.42280i
\(296\) 4.15187 12.8845i 0.241322 0.748894i
\(297\) −1.44945 −0.0841054
\(298\) 11.3272 + 25.3861i 0.656169 + 1.47058i
\(299\) 17.8524 1.03243
\(300\) 24.7305 + 3.76196i 1.42782 + 0.217197i
\(301\) 0 0
\(302\) −22.4921 + 10.0359i −1.29428 + 0.577504i
\(303\) 0.277982 0.0159696
\(304\) −3.37027 31.0974i −0.193298 1.78356i
\(305\) 2.61361 0.780589i 0.149655 0.0446964i
\(306\) −3.76837 8.44549i −0.215423 0.482797i
\(307\) 24.7976i 1.41527i −0.706576 0.707637i \(-0.749761\pi\)
0.706576 0.707637i \(-0.250239\pi\)
\(308\) 0 0
\(309\) −32.2990 −1.83743
\(310\) 3.59725 3.09142i 0.204310 0.175581i
\(311\) −7.05694 −0.400162 −0.200081 0.979779i \(-0.564121\pi\)
−0.200081 + 0.979779i \(0.564121\pi\)
\(312\) −12.9469 + 40.1782i −0.732976 + 2.27464i
\(313\) −32.5746 −1.84123 −0.920613 0.390477i \(-0.872310\pi\)
−0.920613 + 0.390477i \(0.872310\pi\)
\(314\) −3.95346 8.86032i −0.223107 0.500017i
\(315\) 0 0
\(316\) 18.0634 + 16.2115i 1.01615 + 0.911971i
\(317\) 22.3583i 1.25577i −0.778307 0.627884i \(-0.783921\pi\)
0.778307 0.627884i \(-0.216079\pi\)
\(318\) −10.1809 22.8169i −0.570914 1.27951i
\(319\) 10.9798i 0.614753i
\(320\) −5.85136 + 16.9045i −0.327101 + 0.944989i
\(321\) 36.5394i 2.03943i
\(322\) 0 0
\(323\) 15.6983 0.873478
\(324\) 10.9022 12.1476i 0.605677 0.674866i
\(325\) 24.9450 16.3595i 1.38370 0.907464i
\(326\) 1.65348 + 3.70570i 0.0915777 + 0.205240i
\(327\) 11.1545i 0.616845i
\(328\) 7.65939 23.7693i 0.422919 1.31244i
\(329\) 0 0
\(330\) −13.5002 + 11.6019i −0.743163 + 0.638663i
\(331\) 24.2144i 1.33094i 0.746424 + 0.665471i \(0.231769\pi\)
−0.746424 + 0.665471i \(0.768231\pi\)
\(332\) 16.5692 + 14.8705i 0.909356 + 0.816127i
\(333\) 15.5904i 0.854350i
\(334\) −20.5848 + 9.18489i −1.12635 + 0.502575i
\(335\) 0.713390 + 2.38861i 0.0389767 + 0.130504i
\(336\) 0 0
\(337\) 7.95685i 0.433437i −0.976234 0.216719i \(-0.930465\pi\)
0.976234 0.216719i \(-0.0695354\pi\)
\(338\) 13.0208 + 29.1817i 0.708239 + 1.58727i
\(339\) −5.76482 −0.313102
\(340\) −8.11808 3.83365i −0.440265 0.207909i
\(341\) 3.37518i 0.182776i
\(342\) −14.6791 32.8982i −0.793757 1.77893i
\(343\) 0 0
\(344\) −3.03387 0.977630i −0.163576 0.0527103i
\(345\) 16.0373 4.78975i 0.863420 0.257871i
\(346\) −0.590124 1.32256i −0.0317252 0.0711012i
\(347\) 19.8756 1.06698 0.533489 0.845807i \(-0.320881\pi\)
0.533489 + 0.845807i \(0.320881\pi\)
\(348\) 18.1676 + 16.3050i 0.973887 + 0.874042i
\(349\) 12.8850i 0.689719i 0.938654 + 0.344859i \(0.112073\pi\)
−0.938654 + 0.344859i \(0.887927\pi\)
\(350\) 0 0
\(351\) 3.84297i 0.205122i
\(352\) −6.40925 10.9982i −0.341614 0.586204i
\(353\) −8.34671 −0.444250 −0.222125 0.975018i \(-0.571299\pi\)
−0.222125 + 0.975018i \(0.571299\pi\)
\(354\) −36.8479 + 16.4415i −1.95844 + 0.873854i
\(355\) 17.9994 5.37574i 0.955306 0.285315i
\(356\) −6.81537 6.11665i −0.361214 0.324182i
\(357\) 0 0
\(358\) 5.42136 2.41900i 0.286528 0.127848i
\(359\) 1.81996i 0.0960538i 0.998846 + 0.0480269i \(0.0152933\pi\)
−0.998846 + 0.0480269i \(0.984707\pi\)
\(360\) −0.442961 + 20.5974i −0.0233461 + 1.08558i
\(361\) 42.1506 2.21845
\(362\) 6.88534 3.07223i 0.361886 0.161473i
\(363\) 14.8497i 0.779406i
\(364\) 0 0
\(365\) −3.76301 12.5995i −0.196965 0.659489i
\(366\) 1.75844 + 3.94093i 0.0919149 + 0.205996i
\(367\) 1.06984i 0.0558451i 0.999610 + 0.0279226i \(0.00888918\pi\)
−0.999610 + 0.0279226i \(0.991111\pi\)
\(368\) 1.28963 + 11.8994i 0.0672264 + 0.620298i
\(369\) 28.7613i 1.49725i
\(370\) −9.86437 11.4784i −0.512824 0.596733i
\(371\) 0 0
\(372\) 5.58469 + 5.01213i 0.289553 + 0.259867i
\(373\) 13.1871i 0.682803i 0.939918 + 0.341401i \(0.110902\pi\)
−0.939918 + 0.341401i \(0.889098\pi\)
\(374\) 5.83411 2.60317i 0.301675 0.134607i
\(375\) 18.0195 21.3889i 0.930524 1.10452i
\(376\) 8.30173 25.7627i 0.428129 1.32861i
\(377\) 29.1112 1.49930
\(378\) 0 0
\(379\) 16.9854i 0.872483i 0.899830 + 0.436241i \(0.143691\pi\)
−0.899830 + 0.436241i \(0.856309\pi\)
\(380\) −31.6229 14.9334i −1.62222 0.766069i
\(381\) 15.4653i 0.792312i
\(382\) −21.6251 + 9.64908i −1.10644 + 0.493690i
\(383\) 4.67572i 0.238918i 0.992839 + 0.119459i \(0.0381160\pi\)
−0.992839 + 0.119459i \(0.961884\pi\)
\(384\) −27.7157 5.72727i −1.41436 0.292269i
\(385\) 0 0
\(386\) −20.0728 + 8.95648i −1.02168 + 0.455873i
\(387\) −3.67104 −0.186609
\(388\) 6.17175 6.87677i 0.313323 0.349115i
\(389\) −25.7985 −1.30803 −0.654017 0.756480i \(-0.726918\pi\)
−0.654017 + 0.756480i \(0.726918\pi\)
\(390\) 30.7605 + 35.7936i 1.55762 + 1.81248i
\(391\) −6.00693 −0.303783
\(392\) 0 0
\(393\) 20.4347i 1.03079i
\(394\) 13.4404 5.99707i 0.677116 0.302128i
\(395\) 26.0014 7.76565i 1.30827 0.390732i
\(396\) −10.9107 9.79211i −0.548283 0.492072i
\(397\) 26.6167 1.33586 0.667928 0.744226i \(-0.267182\pi\)
0.667928 + 0.744226i \(0.267182\pi\)
\(398\) 8.90433 + 19.9560i 0.446334 + 1.00030i
\(399\) 0 0
\(400\) 12.7063 + 15.4451i 0.635314 + 0.772254i
\(401\) −9.02978 −0.450926 −0.225463 0.974252i \(-0.572389\pi\)
−0.225463 + 0.974252i \(0.572389\pi\)
\(402\) −3.60167 + 1.60706i −0.179635 + 0.0801528i
\(403\) 8.94872 0.445767
\(404\) 0.165406 + 0.148448i 0.00822925 + 0.00738557i
\(405\) −5.22236 17.4858i −0.259501 0.868877i
\(406\) 0 0
\(407\) 10.7698 0.533839
\(408\) 4.35634 13.5190i 0.215671 0.669291i
\(409\) 3.41447i 0.168834i −0.996430 0.0844172i \(-0.973097\pi\)
0.996430 0.0844172i \(-0.0269029\pi\)
\(410\) −18.1979 21.1754i −0.898728 1.04578i
\(411\) 17.7032 0.873233
\(412\) −19.2187 17.2484i −0.946838 0.849766i
\(413\) 0 0
\(414\) 5.61695 + 12.5884i 0.276058 + 0.618688i
\(415\) 23.8506 7.12328i 1.17078 0.349668i
\(416\) −29.1598 + 16.9931i −1.42967 + 0.833153i
\(417\) 36.1800i 1.77174i
\(418\) 22.7260 10.1403i 1.11156 0.495978i
\(419\) 15.7994 0.771850 0.385925 0.922530i \(-0.373882\pi\)
0.385925 + 0.922530i \(0.373882\pi\)
\(420\) 0 0
\(421\) 20.8340 1.01538 0.507692 0.861538i \(-0.330499\pi\)
0.507692 + 0.861538i \(0.330499\pi\)
\(422\) 13.4298 5.99236i 0.653753 0.291703i
\(423\) 31.1733i 1.51570i
\(424\) 6.12684 19.0134i 0.297546 0.923372i
\(425\) −8.39341 + 5.50461i −0.407140 + 0.267013i
\(426\) 12.1100 + 27.1403i 0.586729 + 1.31495i
\(427\) 0 0
\(428\) −19.5128 + 21.7418i −0.943188 + 1.05093i
\(429\) −33.5839 −1.62145
\(430\) −2.70279 + 2.32274i −0.130340 + 0.112012i
\(431\) 27.5487i 1.32697i −0.748188 0.663487i \(-0.769076\pi\)
0.748188 0.663487i \(-0.230924\pi\)
\(432\) −2.56149 + 0.277609i −0.123240 + 0.0133565i
\(433\) 2.28113 0.109624 0.0548121 0.998497i \(-0.482544\pi\)
0.0548121 + 0.998497i \(0.482544\pi\)
\(434\) 0 0
\(435\) 26.1514 7.81044i 1.25386 0.374482i
\(436\) −5.95674 + 6.63720i −0.285276 + 0.317864i
\(437\) −23.3992 −1.11933
\(438\) 18.9982 8.47695i 0.907768 0.405045i
\(439\) 9.26625 0.442254 0.221127 0.975245i \(-0.429027\pi\)
0.221127 + 0.975245i \(0.429027\pi\)
\(440\) −14.2286 0.305995i −0.678323 0.0145877i
\(441\) 0 0
\(442\) −6.90187 15.4682i −0.328288 0.735745i
\(443\) 27.3290 1.29844 0.649221 0.760600i \(-0.275095\pi\)
0.649221 + 0.760600i \(0.275095\pi\)
\(444\) 15.9931 17.8201i 0.759000 0.845703i
\(445\) −9.81037 + 2.92999i −0.465056 + 0.138895i
\(446\) −14.6784 + 6.54948i −0.695042 + 0.310127i
\(447\) 49.1708i 2.32570i
\(448\) 0 0
\(449\) 31.5958 1.49110 0.745549 0.666451i \(-0.232187\pi\)
0.745549 + 0.666451i \(0.232187\pi\)
\(450\) 19.3842 + 12.4425i 0.913782 + 0.586543i
\(451\) 19.8682 0.935556
\(452\) −3.43021 3.07854i −0.161343 0.144802i
\(453\) −43.5654 −2.04688
\(454\) −7.96965 + 3.55605i −0.374034 + 0.166893i
\(455\) 0 0
\(456\) 16.9695 52.6615i 0.794672 2.46610i
\(457\) 20.1137i 0.940879i 0.882432 + 0.470439i \(0.155905\pi\)
−0.882432 + 0.470439i \(0.844095\pi\)
\(458\) −10.7012 + 4.77488i −0.500036 + 0.223115i
\(459\) 1.29307i 0.0603553i
\(460\) 12.1004 + 5.71425i 0.564185 + 0.266428i
\(461\) 1.57753i 0.0734730i 0.999325 + 0.0367365i \(0.0116962\pi\)
−0.999325 + 0.0367365i \(0.988304\pi\)
\(462\) 0 0
\(463\) −27.7330 −1.28886 −0.644431 0.764663i \(-0.722906\pi\)
−0.644431 + 0.764663i \(0.722906\pi\)
\(464\) 2.10294 + 19.4038i 0.0976265 + 0.900799i
\(465\) 8.03887 2.40091i 0.372794 0.111340i
\(466\) 18.1981 8.11998i 0.843012 0.376151i
\(467\) 9.24121i 0.427632i 0.976874 + 0.213816i \(0.0685893\pi\)
−0.976874 + 0.213816i \(0.931411\pi\)
\(468\) −25.9621 + 28.9279i −1.20010 + 1.33719i
\(469\) 0 0
\(470\) −19.7240 22.9512i −0.909799 1.05866i
\(471\) 17.1617i 0.790771i
\(472\) −30.7055 9.89448i −1.41333 0.455430i
\(473\) 2.53594i 0.116603i
\(474\) 17.4937 + 39.2061i 0.803513 + 1.80080i
\(475\) −32.6954 + 21.4424i −1.50017 + 0.983847i
\(476\) 0 0
\(477\) 23.0065i 1.05340i
\(478\) 10.7277 4.78670i 0.490675 0.218939i
\(479\) −10.5454 −0.481833 −0.240916 0.970546i \(-0.577448\pi\)
−0.240916 + 0.970546i \(0.577448\pi\)
\(480\) −21.6358 + 23.0888i −0.987534 + 1.05385i
\(481\) 28.5543i 1.30196i
\(482\) −33.2406 + 14.8319i −1.51407 + 0.675575i
\(483\) 0 0
\(484\) −7.93005 + 8.83593i −0.360457 + 0.401633i
\(485\) −2.95639 9.89875i −0.134243 0.449479i
\(486\) 28.8616 12.8780i 1.30919 0.584158i
\(487\) −18.0001 −0.815661 −0.407830 0.913058i \(-0.633715\pi\)
−0.407830 + 0.913058i \(0.633715\pi\)
\(488\) −1.05823 + 3.28399i −0.0479037 + 0.148659i
\(489\) 7.17765i 0.324584i
\(490\) 0 0
\(491\) 0.704833i 0.0318086i −0.999874 0.0159043i \(-0.994937\pi\)
0.999874 0.0159043i \(-0.00506272\pi\)
\(492\) 29.5042 32.8746i 1.33015 1.48210i
\(493\) −9.79524 −0.441156
\(494\) −26.8853 60.2541i −1.20963 2.71096i
\(495\) −15.7054 + 4.69061i −0.705904 + 0.210827i
\(496\) 0.646439 + 5.96469i 0.0290259 + 0.267822i
\(497\) 0 0
\(498\) 16.0467 + 35.9630i 0.719068 + 1.61154i
\(499\) 6.53324i 0.292468i 0.989250 + 0.146234i \(0.0467153\pi\)
−0.989250 + 0.146234i \(0.953285\pi\)
\(500\) 22.1442 3.10409i 0.990318 0.138819i
\(501\) −39.8710 −1.78131
\(502\) 2.76956 + 6.20702i 0.123612 + 0.277033i
\(503\) 29.3454i 1.30845i −0.756301 0.654224i \(-0.772995\pi\)
0.756301 0.654224i \(-0.227005\pi\)
\(504\) 0 0
\(505\) 0.238093 0.0711096i 0.0105950 0.00316433i
\(506\) −8.69604 + 3.88016i −0.386586 + 0.172494i
\(507\) 56.5226i 2.51026i
\(508\) 8.25881 9.20224i 0.366425 0.408283i
\(509\) 20.6256i 0.914213i 0.889412 + 0.457107i \(0.151114\pi\)
−0.889412 + 0.457107i \(0.848886\pi\)
\(510\) −10.3502 12.0437i −0.458314 0.533304i
\(511\) 0 0
\(512\) −13.4330 18.2086i −0.593661 0.804715i
\(513\) 5.03697i 0.222388i
\(514\) 12.3391 + 27.6539i 0.544255 + 1.21976i
\(515\) −27.6643 + 8.26231i −1.21904 + 0.364081i
\(516\) −4.19605 3.76586i −0.184721 0.165783i
\(517\) 21.5344 0.947081
\(518\) 0 0
\(519\) 2.56169i 0.112446i
\(520\) −0.811295 + 37.7248i −0.0355776 + 1.65434i
\(521\) 5.87937i 0.257580i −0.991672 0.128790i \(-0.958891\pi\)
0.991672 0.128790i \(-0.0411093\pi\)
\(522\) 9.15932 + 20.5274i 0.400892 + 0.898462i
\(523\) 23.1425i 1.01195i −0.862548 0.505975i \(-0.831133\pi\)
0.862548 0.505975i \(-0.168867\pi\)
\(524\) 10.9125 12.1591i 0.476717 0.531174i
\(525\) 0 0
\(526\) 9.06369 + 20.3131i 0.395196 + 0.885694i
\(527\) −3.01104 −0.131163
\(528\) −2.42604 22.3850i −0.105580 0.974184i
\(529\) −14.0464 −0.610711
\(530\) −14.5567 16.9385i −0.632302 0.735761i
\(531\) −37.1541 −1.61235
\(532\) 0 0
\(533\) 52.6771i 2.28170i
\(534\) −6.60042 14.7926i −0.285628 0.640136i
\(535\) 9.34703 + 31.2963i 0.404107 + 1.35306i
\(536\) −3.00129 0.967129i −0.129636 0.0417736i
\(537\) 10.5007 0.453141
\(538\) −1.79894 + 0.802686i −0.0775580 + 0.0346062i
\(539\) 0 0
\(540\) −1.23007 + 2.60477i −0.0529336 + 0.112092i
\(541\) 1.76517 0.0758907 0.0379453 0.999280i \(-0.487919\pi\)
0.0379453 + 0.999280i \(0.487919\pi\)
\(542\) 8.20092 + 18.3795i 0.352260 + 0.789468i
\(543\) 13.3364 0.572318
\(544\) 9.81158 5.71777i 0.420668 0.245147i
\(545\) 2.85340 + 9.55391i 0.122226 + 0.409244i
\(546\) 0 0
\(547\) 28.3140 1.21062 0.605310 0.795990i \(-0.293049\pi\)
0.605310 + 0.795990i \(0.293049\pi\)
\(548\) 10.5338 + 9.45388i 0.449983 + 0.403850i
\(549\) 3.97369i 0.169593i
\(550\) −8.59519 + 13.3906i −0.366500 + 0.570975i
\(551\) −38.1560 −1.62550
\(552\) −6.49336 + 20.1508i −0.276376 + 0.857676i
\(553\) 0 0
\(554\) 27.1379 12.1089i 1.15298 0.514457i
\(555\) −7.66102 25.6511i −0.325192 1.08883i
\(556\) 19.3209 21.5280i 0.819388 0.912990i
\(557\) 27.7580i 1.17614i −0.808808 0.588072i \(-0.799887\pi\)
0.808808 0.588072i \(-0.200113\pi\)
\(558\) 2.81555 + 6.31009i 0.119192 + 0.267127i
\(559\) −6.72361 −0.284378
\(560\) 0 0
\(561\) 11.3002 0.477095
\(562\) 2.25987 + 5.06472i 0.0953269 + 0.213642i
\(563\) 35.5787i 1.49947i −0.661741 0.749733i \(-0.730182\pi\)
0.661741 0.749733i \(-0.269818\pi\)
\(564\) 31.9785 35.6315i 1.34654 1.50036i
\(565\) −4.93761 + 1.47468i −0.207727 + 0.0620402i
\(566\) 1.55493 0.693807i 0.0653585 0.0291629i
\(567\) 0 0
\(568\) −7.28778 + 22.6161i −0.305788 + 0.948951i
\(569\) 11.2535 0.471770 0.235885 0.971781i \(-0.424201\pi\)
0.235885 + 0.971781i \(0.424201\pi\)
\(570\) −40.3177 46.9146i −1.68872 1.96504i
\(571\) 0.667681i 0.0279416i −0.999902 0.0139708i \(-0.995553\pi\)
0.999902 0.0139708i \(-0.00444718\pi\)
\(572\) −19.9832 17.9345i −0.835541 0.749880i
\(573\) −41.8861 −1.74982
\(574\) 0 0
\(575\) 12.5108 8.20491i 0.521737 0.342168i
\(576\) −21.1571 15.2151i −0.881544 0.633964i
\(577\) 32.2214 1.34139 0.670696 0.741732i \(-0.265995\pi\)
0.670696 + 0.741732i \(0.265995\pi\)
\(578\) −7.47406 16.7505i −0.310880 0.696730i
\(579\) −38.8795 −1.61578
\(580\) 19.7316 + 9.31799i 0.819312 + 0.386908i
\(581\) 0 0
\(582\) 14.9258 6.65987i 0.618695 0.276061i
\(583\) 15.8928 0.658213
\(584\) 15.8313 + 5.10143i 0.655102 + 0.211099i
\(585\) 12.4364 + 41.6402i 0.514181 + 1.72161i
\(586\) 8.33930 + 18.6897i 0.344493 + 0.772063i
\(587\) 5.94377i 0.245326i 0.992448 + 0.122663i \(0.0391434\pi\)
−0.992448 + 0.122663i \(0.960857\pi\)
\(588\) 0 0
\(589\) −11.7291 −0.483288
\(590\) −27.3546 + 23.5082i −1.12617 + 0.967816i
\(591\) 26.0329 1.07085
\(592\) 19.0326 2.06271i 0.782235 0.0847768i
\(593\) 32.3521 1.32854 0.664270 0.747493i \(-0.268743\pi\)
0.664270 + 0.747493i \(0.268743\pi\)
\(594\) −0.835255 1.87194i −0.0342709 0.0768064i
\(595\) 0 0
\(596\) −26.2583 + 29.2579i −1.07558 + 1.19845i
\(597\) 38.6531i 1.58197i
\(598\) 10.2876 + 23.0561i 0.420691 + 0.942834i
\(599\) 16.4047i 0.670277i 0.942169 + 0.335139i \(0.108783\pi\)
−0.942169 + 0.335139i \(0.891217\pi\)
\(600\) 9.39263 + 34.1069i 0.383453 + 1.39241i
\(601\) 17.5151i 0.714458i 0.934017 + 0.357229i \(0.116278\pi\)
−0.934017 + 0.357229i \(0.883722\pi\)
\(602\) 0 0
\(603\) −3.63160 −0.147890
\(604\) −25.9225 23.2649i −1.05477 0.946634i
\(605\) 3.79865 + 12.7189i 0.154437 + 0.517095i
\(606\) 0.160189 + 0.359008i 0.00650723 + 0.0145837i
\(607\) 2.77165i 0.112498i 0.998417 + 0.0562489i \(0.0179140\pi\)
−0.998417 + 0.0562489i \(0.982086\pi\)
\(608\) 38.2197 22.2728i 1.55001 0.903281i
\(609\) 0 0
\(610\) 2.51423 + 2.92561i 0.101798 + 0.118455i
\(611\) 57.0948i 2.30981i
\(612\) 8.73565 9.73356i 0.353118 0.393456i
\(613\) 21.7127i 0.876966i −0.898739 0.438483i \(-0.855516\pi\)
0.898739 0.438483i \(-0.144484\pi\)
\(614\) 32.0257 14.2898i 1.29245 0.576690i
\(615\) −14.1331 47.3213i −0.569902 1.90818i
\(616\) 0 0
\(617\) 4.75106i 0.191271i 0.995416 + 0.0956353i \(0.0304883\pi\)
−0.995416 + 0.0956353i \(0.969512\pi\)
\(618\) −18.6126 41.7136i −0.748707 1.67797i
\(619\) −31.5652 −1.26871 −0.634357 0.773040i \(-0.718735\pi\)
−0.634357 + 0.773040i \(0.718735\pi\)
\(620\) 6.06546 + 2.86433i 0.243595 + 0.115034i
\(621\) 1.92739i 0.0773434i
\(622\) −4.06662 9.11391i −0.163056 0.365435i
\(623\) 0 0
\(624\) −59.3502 + 6.43223i −2.37591 + 0.257495i
\(625\) 9.96243 22.9292i 0.398497 0.917169i
\(626\) −18.7714 42.0695i −0.750255 1.68144i
\(627\) 44.0184 1.75792
\(628\) 9.16474 10.2117i 0.365713 0.407490i
\(629\) 9.60786i 0.383090i
\(630\) 0 0
\(631\) 13.2126i 0.525986i −0.964798 0.262993i \(-0.915290\pi\)
0.964798 0.262993i \(-0.0847096\pi\)
\(632\) −10.5277 + 32.6706i −0.418771 + 1.29957i
\(633\) 26.0125 1.03390
\(634\) 28.8754 12.8841i 1.14679 0.511695i
\(635\) −3.95613 13.2461i −0.156994 0.525657i
\(636\) 23.6008 26.2968i 0.935832 1.04274i
\(637\) 0 0
\(638\) −14.1803 + 6.32722i −0.561402 + 0.250497i
\(639\) 27.3659i 1.08258i
\(640\) −25.2037 + 2.18441i −0.996265 + 0.0863463i
\(641\) 14.2989 0.564773 0.282386 0.959301i \(-0.408874\pi\)
0.282386 + 0.959301i \(0.408874\pi\)
\(642\) −47.1900 + 21.0561i −1.86244 + 0.831018i
\(643\) 8.53718i 0.336673i −0.985730 0.168337i \(-0.946160\pi\)
0.985730 0.168337i \(-0.0538396\pi\)
\(644\) 0 0
\(645\) −6.04000 + 1.80392i −0.237825 + 0.0710294i
\(646\) 9.04627 + 20.2741i 0.355921 + 0.797674i
\(647\) 23.8661i 0.938275i −0.883125 0.469137i \(-0.844565\pi\)
0.883125 0.469137i \(-0.155435\pi\)
\(648\) 21.9709 + 7.07985i 0.863097 + 0.278123i
\(649\) 25.6659i 1.00748i
\(650\) 35.5028 + 22.7887i 1.39253 + 0.893846i
\(651\) 0 0
\(652\) −3.83302 + 4.27088i −0.150113 + 0.167260i
\(653\) 18.0725i 0.707230i −0.935391 0.353615i \(-0.884952\pi\)
0.935391 0.353615i \(-0.115048\pi\)
\(654\) −14.4058 + 6.42786i −0.563313 + 0.251349i
\(655\) −5.22733 17.5024i −0.204249 0.683877i
\(656\) 35.1115 3.80530i 1.37087 0.148572i
\(657\) 19.1561 0.747350
\(658\) 0 0
\(659\) 13.3401i 0.519657i −0.965655 0.259828i \(-0.916334\pi\)
0.965655 0.259828i \(-0.0836660\pi\)
\(660\) −22.7632 10.7496i −0.886058 0.418428i
\(661\) 18.4115i 0.716123i 0.933698 + 0.358062i \(0.116562\pi\)
−0.933698 + 0.358062i \(0.883438\pi\)
\(662\) −31.2724 + 13.9537i −1.21544 + 0.542327i
\(663\) 29.9606i 1.16357i
\(664\) −9.65688 + 29.9682i −0.374760 + 1.16299i
\(665\) 0 0
\(666\) 20.1348 8.98410i 0.780206 0.348127i
\(667\) 14.6003 0.565327
\(668\) −23.7243 21.2920i −0.917919 0.823812i
\(669\) −28.4309 −1.09920
\(670\) −2.67376 + 2.29779i −0.103296 + 0.0887713i
\(671\) −2.74500 −0.105970
\(672\) 0 0
\(673\) 43.5683i 1.67944i 0.543023 + 0.839718i \(0.317280\pi\)
−0.543023 + 0.839718i \(0.682720\pi\)
\(674\) 10.2761 4.58520i 0.395822 0.176615i
\(675\) 1.76621 + 2.69311i 0.0679815 + 0.103658i
\(676\) −30.1843 + 33.6323i −1.16093 + 1.29355i
\(677\) 12.8331 0.493218 0.246609 0.969115i \(-0.420684\pi\)
0.246609 + 0.969115i \(0.420684\pi\)
\(678\) −3.32202 7.44516i −0.127581 0.285930i
\(679\) 0 0
\(680\) 0.272982 12.6935i 0.0104684 0.486774i
\(681\) −15.4366 −0.591531
\(682\) −4.35898 + 1.94497i −0.166914 + 0.0744768i
\(683\) −0.937655 −0.0358784 −0.0179392 0.999839i \(-0.505711\pi\)
−0.0179392 + 0.999839i \(0.505711\pi\)
\(684\) 34.0285 37.9157i 1.30111 1.44974i
\(685\) 15.1629 4.52860i 0.579345 0.173029i
\(686\) 0 0
\(687\) −20.7274 −0.790801
\(688\) −0.485701 4.48156i −0.0185172 0.170858i
\(689\) 42.1371i 1.60530i
\(690\) 15.4275 + 17.9518i 0.587315 + 0.683412i
\(691\) −8.12642 −0.309144 −0.154572 0.987982i \(-0.549400\pi\)
−0.154572 + 0.987982i \(0.549400\pi\)
\(692\) 1.36800 1.52427i 0.0520035 0.0579440i
\(693\) 0 0
\(694\) 11.4535 + 25.6690i 0.434767 + 0.974381i
\(695\) −9.25509 30.9884i −0.351066 1.17546i
\(696\) −10.5884 + 32.8591i −0.401354 + 1.24552i
\(697\) 17.7246i 0.671369i
\(698\) −16.6408 + 7.42508i −0.629862 + 0.281044i
\(699\) 35.2483 1.33321
\(700\) 0 0
\(701\) −27.4244 −1.03580 −0.517902 0.855440i \(-0.673287\pi\)
−0.517902 + 0.855440i \(0.673287\pi\)
\(702\) −4.96312 + 2.21454i −0.187321 + 0.0835824i
\(703\) 37.4261i 1.41155i
\(704\) 10.5105 14.6152i 0.396131 0.550831i
\(705\) −15.3183 51.2898i −0.576922 1.93168i
\(706\) −4.80985 10.7796i −0.181021 0.405697i
\(707\) 0 0
\(708\) −42.4677 38.1139i −1.59603 1.43241i
\(709\) 21.4972 0.807346 0.403673 0.914903i \(-0.367733\pi\)
0.403673 + 0.914903i \(0.367733\pi\)
\(710\) 17.3149 + 20.1480i 0.649818 + 0.756142i
\(711\) 39.5320i 1.48257i
\(712\) 3.97213 12.3267i 0.148862 0.461963i
\(713\) 4.48811 0.168081
\(714\) 0 0
\(715\) −28.7648 + 8.59099i −1.07574 + 0.321285i
\(716\) 6.24820 + 5.60762i 0.233506 + 0.209567i
\(717\) 20.7788 0.775998
\(718\) −2.35045 + 1.04877i −0.0877178 + 0.0391396i
\(719\) 26.9012 1.00325 0.501623 0.865087i \(-0.332737\pi\)
0.501623 + 0.865087i \(0.332737\pi\)
\(720\) −26.8565 + 11.2974i −1.00088 + 0.421028i
\(721\) 0 0
\(722\) 24.2896 + 54.4368i 0.903966 + 2.02593i
\(723\) −64.3844 −2.39448
\(724\) 7.93547 + 7.12191i 0.294919 + 0.264684i
\(725\) 20.4009 13.3794i 0.757669 0.496898i
\(726\) −19.1781 + 8.55724i −0.711766 + 0.317589i
\(727\) 14.8535i 0.550886i −0.961317 0.275443i \(-0.911175\pi\)
0.961317 0.275443i \(-0.0888245\pi\)
\(728\) 0 0
\(729\) 31.4189 1.16366
\(730\) 14.1036 12.1204i 0.521998 0.448597i
\(731\) 2.26234 0.0836756
\(732\) −4.07633 + 4.54198i −0.150665 + 0.167876i
\(733\) −16.4626 −0.608059 −0.304030 0.952663i \(-0.598332\pi\)
−0.304030 + 0.952663i \(0.598332\pi\)
\(734\) −1.38168 + 0.616503i −0.0509987 + 0.0227555i
\(735\) 0 0
\(736\) −14.6247 + 8.52264i −0.539073 + 0.314149i
\(737\) 2.50870i 0.0924090i
\(738\) 37.1447 16.5739i 1.36732 0.610094i
\(739\) 44.4004i 1.63329i 0.577137 + 0.816647i \(0.304170\pi\)
−0.577137 + 0.816647i \(0.695830\pi\)
\(740\) 9.13973 19.3542i 0.335983 0.711474i
\(741\) 116.707i 4.28735i
\(742\) 0 0
\(743\) 34.9014 1.28041 0.640204 0.768205i \(-0.278850\pi\)
0.640204 + 0.768205i \(0.278850\pi\)
\(744\) −3.25487 + 10.1008i −0.119329 + 0.370314i
\(745\) 12.5782 + 42.1152i 0.460831 + 1.54298i
\(746\) −17.0309 + 7.59917i −0.623546 + 0.278226i
\(747\) 36.2620i 1.32676i
\(748\) 6.72390 + 6.03455i 0.245850 + 0.220645i
\(749\) 0 0
\(750\) 38.0072 + 10.9464i 1.38783 + 0.399706i
\(751\) 18.8248i 0.686927i −0.939166 0.343463i \(-0.888400\pi\)
0.939166 0.343463i \(-0.111600\pi\)
\(752\) 38.0560 4.12442i 1.38776 0.150402i
\(753\) 12.0225i 0.438124i
\(754\) 16.7756 + 37.5966i 0.610930 + 1.36919i
\(755\) −37.3141 + 11.1443i −1.35800 + 0.405584i
\(756\) 0 0
\(757\) 54.4433i 1.97878i 0.145301 + 0.989388i \(0.453585\pi\)
−0.145301 + 0.989388i \(0.546415\pi\)
\(758\) −21.9364 + 9.78798i −0.796765 + 0.355516i
\(759\) −16.8435 −0.611382
\(760\) 1.06336 49.4459i 0.0385722 1.79359i
\(761\) 25.8142i 0.935765i 0.883791 + 0.467883i \(0.154983\pi\)
−0.883791 + 0.467883i \(0.845017\pi\)
\(762\) 19.9732 8.91200i 0.723552 0.322848i
\(763\) 0 0
\(764\) −24.9232 22.3681i −0.901691 0.809248i
\(765\) −4.18455 14.0110i −0.151293 0.506567i
\(766\) −6.03861 + 2.69442i −0.218184 + 0.0973533i
\(767\) −68.0489 −2.45710
\(768\) −8.57469 39.0947i −0.309412 1.41071i
\(769\) 40.1288i 1.44708i 0.690281 + 0.723542i \(0.257487\pi\)
−0.690281 + 0.723542i \(0.742513\pi\)
\(770\) 0 0
\(771\) 53.5633i 1.92904i
\(772\) −23.1343 20.7625i −0.832620 0.747259i
\(773\) −49.0224 −1.76321 −0.881607 0.471983i \(-0.843538\pi\)
−0.881607 + 0.471983i \(0.843538\pi\)
\(774\) −2.11546 4.74108i −0.0760388 0.170415i
\(775\) 6.27118 4.11280i 0.225267 0.147736i
\(776\) 12.4377 + 4.00792i 0.446489 + 0.143876i
\(777\) 0 0
\(778\) −14.8666 33.3183i −0.532992 1.19452i
\(779\) 69.0439i 2.47375i
\(780\) −28.5008 + 60.3529i −1.02049 + 2.16098i
\(781\) −18.9042 −0.676446
\(782\) −3.46154 7.75784i −0.123784 0.277420i
\(783\) 3.14291i 0.112318i
\(784\) 0 0
\(785\) −4.39009 14.6992i −0.156689 0.524635i
\(786\) 26.3910 11.7756i 0.941336 0.420023i