Properties

Label 980.2.c.e.979.18
Level $980$
Weight $2$
Character 980.979
Analytic conductor $7.825$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

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 979.18
Character \(\chi\) \(=\) 980.979
Dual form 980.2.c.e.979.19

$q$-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} +(-3.13582 + 0.408241i) 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} +(2.33427 + 3.81460i) 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} +(-1.02122 - 7.84424i) 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} +(3.58134 - 5.21287i) 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} +(-1.13193 + 6.97988i) 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} +(-9.54221 + 5.83918i) 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} +(-8.79610 - 1.62129i) 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} +(10.2149 - 1.32984i) 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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 16 q^{4} - 64 q^{9} + O(q^{10}) \) \( 48 q + 16 q^{4} - 64 q^{9} + 16 q^{16} - 16 q^{25} - 48 q^{29} - 8 q^{30} + 176 q^{36} - 48 q^{44} - 32 q^{46} + 32 q^{50} + 24 q^{60} - 80 q^{64} - 16 q^{65} - 112 q^{74} - 48 q^{81} - 64 q^{85} - 112 q^{86} + O(q^{100}) \)

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
\(10\) −3.13582 + 0.408241i −0.991632 + 0.129097i
\(11\) 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 \(-0.854260\pi\)
−0.897002 + 0.442026i \(0.854260\pi\)
\(20\) 2.33427 + 3.81460i 0.521960 + 0.852970i
\(21\) 0 0
\(22\) −2.90618 + 1.29673i −0.619599 + 0.276464i
\(23\) 2.99226 0.623930 0.311965 0.950094i \(-0.399013\pi\)
0.311965 + 0.950094i \(0.399013\pi\)
\(24\) −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 \(0.649659\pi\)
\(30\) −1.02122 7.84424i −0.186448 1.43216i
\(31\) 1.49990 0.269391 0.134695 0.990887i \(-0.456994\pi\)
0.134695 + 0.990887i \(0.456994\pi\)
\(32\) −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 \(-0.871296\pi\)
0.919364 0.393408i \(-0.128704\pi\)
\(38\) 4.50627 + 10.0992i 0.731013 + 1.63831i
\(39\) 14.9244i 2.38982i
\(40\) 3.58134 5.21287i 0.566260 0.824226i
\(41\) 8.82927i 1.37890i −0.724333 0.689450i \(-0.757852\pi\)
0.724333 0.689450i \(-0.242148\pi\)
\(42\) 0 0
\(43\) −1.12695 −0.171858 −0.0859292 0.996301i \(-0.527386\pi\)
−0.0859292 + 0.996301i \(0.527386\pi\)
\(44\) 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
\(50\) −1.13193 + 6.97988i −0.160079 + 0.987104i
\(51\) 5.02172i 0.703182i
\(52\) 7.96997 8.88040i 1.10524 1.23149i
\(53\) 7.06264i 0.970129i −0.874478 0.485064i \(-0.838796\pi\)
0.874478 0.485064i \(-0.161204\pi\)
\(54\) −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 \(-0.766337\pi\)
−0.742450 + 0.669901i \(0.766337\pi\)
\(60\) −9.54221 + 5.83918i −1.23189 + 0.753835i
\(61\) 1.21986i 0.156187i 0.996946 + 0.0780935i \(0.0248833\pi\)
−0.996946 + 0.0780935i \(0.975117\pi\)
\(62\) −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 \(-0.521694\pi\)
−0.0681000 + 0.997678i \(0.521694\pi\)
\(68\) −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 \(-0.239189\pi\)
\(80\) −8.79610 1.62129i −0.983434 0.181266i
\(81\) −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 \(-0.921974\pi\)
0.970107 0.242677i \(-0.0780256\pi\)
\(90\) 10.2149 1.32984i 1.07675 0.140178i
\(91\) 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
\(100\) 9.66668 2.56034i 0.966668 0.256034i
\(101\) 0.111126i 0.0110574i 0.999985 + 0.00552872i \(0.00175986\pi\)
−0.999985 + 0.00552872i \(0.998240\pi\)
\(102\) 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 \(-0.749527\pi\)
−0.706056 + 0.708156i \(0.749527\pi\)
\(108\) 0.958748 + 0.860455i 0.0922555 + 0.0827973i
\(109\) 4.45913 0.427107 0.213553 0.976931i \(-0.431496\pi\)
0.213553 + 0.976931i \(0.431496\pi\)
\(110\) 0.918650 + 7.05641i 0.0875899 + 0.672802i
\(111\) 11.9722 1.13635
\(112\) 0 0
\(113\) 2.30454i 0.216793i −0.994108 0.108397i \(-0.965428\pi\)
0.994108 0.108397i \(-0.0345717\pi\)
\(114\) −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
\(120\) 13.0400 + 8.95873i 1.19038 + 0.817816i
\(121\) 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 \(-0.411554\pi\)
0.274300 + 0.961644i \(0.411554\pi\)
\(128\) 2.28954 11.0796i 0.202368 0.979309i
\(129\) 2.81907i 0.248205i
\(130\) 18.7089 2.43565i 1.64088 0.213620i
\(131\) 8.16897 0.713726 0.356863 0.934157i \(-0.383846\pi\)
0.356863 + 0.934157i \(0.383846\pi\)
\(132\) −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 \(0.0977597\pi\)
−0.953208 + 0.302316i \(0.902240\pi\)
\(138\) 9.66693 4.31337i 0.822904 0.367179i
\(139\) 14.4633 1.22676 0.613382 0.789787i \(-0.289809\pi\)
0.613382 + 0.789787i \(0.289809\pi\)
\(140\) 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 \(0.202077\pi\)
\(150\) −17.4602 2.83153i −1.42562 0.231193i
\(151\) 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
\(160\) 2.97495 + 12.2943i 0.235191 + 0.971949i
\(161\) 0 0
\(162\) 4.70296 + 10.5401i 0.369499 + 0.828105i
\(163\) −2.86934 −0.224744 −0.112372 0.993666i \(-0.535845\pi\)
−0.112372 + 0.993666i \(0.535845\pi\)
\(164\) 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
\(170\) −6.29511 + 0.819539i −0.482813 + 0.0628558i
\(171\) 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 \(-0.0501431\pi\)
\(180\) −7.60389 12.4260i −0.566760 0.926182i
\(181\) 5.33135i 0.396276i 0.980174 + 0.198138i \(0.0634894\pi\)
−0.980174 + 0.198138i \(0.936511\pi\)
\(182\) 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
\(190\) 24.5217 3.19240i 1.77899 0.231601i
\(191\) 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 \(-0.811037\pi\)
0.828907 0.559386i \(-0.188963\pi\)
\(194\) 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 \(0.120893\pi\)
−0.928740 + 0.370731i \(0.879107\pi\)
\(198\) 9.46685 4.22410i 0.672780 0.300193i
\(199\) −15.4520 −1.09536 −0.547681 0.836687i \(-0.684489\pi\)
−0.547681 + 0.836687i \(0.684489\pi\)
\(200\) −8.87713 11.0089i −0.627708 0.778449i
\(201\) 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
\(220\) 8.58385 5.25273i 0.578723 0.354139i
\(221\) −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 \(-0.911727\pi\)
0.961793 0.273778i \(-0.0882732\pi\)
\(230\) −9.38319 + 1.22157i −0.618709 + 0.0805477i
\(231\) 0 0
\(232\) −13.1358 4.23284i −0.862405 0.277900i
\(233\) 14.0909i 0.923124i 0.887108 + 0.461562i \(0.152711\pi\)
−0.887108 + 0.461562i \(0.847289\pi\)
\(234\) −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 \(-0.0865783\pi\)
\(240\) 4.05565 22.0034i 0.261791 1.42032i
\(241\) 25.7383i 1.65795i −0.559285 0.828975i \(-0.688924\pi\)
0.559285 0.828975i \(-0.311076\pi\)
\(242\) −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
\(250\) 14.2304 + 6.89165i 0.900011 + 0.435866i
\(251\) −4.80612 −0.303360 −0.151680 0.988430i \(-0.548468\pi\)
−0.151680 + 0.988430i \(0.548468\pi\)
\(252\) 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
\(260\) −13.9267 22.7586i −0.863699 1.41143i
\(261\) 15.8945 0.983844
\(262\) −4.70743 10.5501i −0.290826 0.651786i
\(263\) −15.7285 −0.969863 −0.484931 0.874552i \(-0.661155\pi\)
−0.484931 + 0.874552i \(0.661155\pi\)
\(264\) 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 \(-0.986479\pi\)
0.999098 0.0424642i \(-0.0135208\pi\)
\(270\) 0.262958 + 2.01985i 0.0160031 + 0.122924i
\(271\) −14.2313 −0.864492 −0.432246 0.901756i \(-0.642279\pi\)
−0.432246 + 0.901756i \(0.642279\pi\)
\(272\) −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 \(0.217467\pi\)
−0.775560 + 0.631273i \(0.782533\pi\)
\(278\) −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
\(290\) 15.3008 1.99196i 0.898492 0.116972i
\(291\) 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
\(300\) 6.40468 + 24.1812i 0.369775 + 1.39610i
\(301\) 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
\(310\) −4.70342 + 0.612323i −0.267136 + 0.0347776i
\(311\) 7.05694 0.400162 0.200081 0.979779i \(-0.435879\pi\)
0.200081 + 0.979779i \(0.435879\pi\)
\(312\) 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 \(0.216079\pi\)
−0.778307 + 0.627884i \(0.783921\pi\)
\(318\) −10.1809 22.8169i −0.570914 1.27951i
\(319\) 10.9798i 0.614753i
\(320\) 14.1635 10.9268i 0.791765 0.610826i
\(321\) 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
\(330\) −17.6516 + 2.29800i −0.971689 + 0.126501i
\(331\) 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 \(0.0695354\pi\)
−0.976234 + 0.216719i \(0.930465\pi\)
\(338\) −13.0208 29.1817i −0.708239 1.58727i
\(339\) 5.76482 0.313102
\(340\) 4.68602 + 7.65775i 0.254135 + 0.415300i
\(341\) 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 \(-0.679119\pi\)
−0.533489 + 0.845807i \(0.679119\pi\)
\(348\) 18.1676 + 16.3050i 0.973887 + 0.874042i
\(349\) 12.8850i 0.689719i −0.938654 0.344859i \(-0.887927\pi\)
0.938654 0.344859i \(-0.112073\pi\)
\(350\) 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 \(0.984707\pi\)
\(360\) −11.6662 + 16.9809i −0.614863 + 0.894971i
\(361\) 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
\(370\) 1.95385 + 15.0081i 0.101576 + 0.780232i
\(371\) 0 0
\(372\) −5.58469 5.01213i −0.289553 0.259867i
\(373\) 13.1871i 0.682803i −0.939918 0.341401i \(-0.889098\pi\)
0.939918 0.341401i \(-0.110902\pi\)
\(374\) −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 \(0.856309\pi\)
\(380\) −18.2538 29.8297i −0.936398 1.53023i
\(381\) 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 \(0.726918\pi\)
\(390\) 6.09277 + 46.8003i 0.308519 + 2.36982i
\(391\) 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
\(400\) −9.10233 + 17.8086i −0.455116 + 0.890432i
\(401\) −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 \(0.0269029\pi\)
−0.996430 + 0.0844172i \(0.973097\pi\)
\(410\) 3.60447 + 27.6870i 0.178012 + 1.36736i
\(411\) −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 \(-0.626118\pi\)
−0.385925 + 0.922530i \(0.626118\pi\)
\(420\) 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
\(430\) 3.53391 0.460068i 0.170420 0.0221865i
\(431\) 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 \(-0.570973\pi\)
−0.221127 + 0.975245i \(0.570973\pi\)
\(440\) −11.7303 8.05897i −0.559221 0.384196i
\(441\) 0 0
\(442\) 6.90187 + 15.4682i 0.328288 + 0.735745i
\(443\) −27.3290 −1.29844 −0.649221 0.760600i \(-0.724905\pi\)
−0.649221 + 0.760600i \(0.724905\pi\)
\(444\) −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 \(0.232187\pi\)
\(450\) 3.68726 22.7369i 0.173819 1.07183i
\(451\) −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 \(-0.844095\pi\)
0.882432 0.470439i \(-0.155905\pi\)
\(458\) −10.7012 + 4.77488i −0.500036 + 0.223115i
\(459\) 1.29307i 0.0603553i
\(460\) 6.98476 + 11.4143i 0.325666 + 0.532194i
\(461\) 1.57753i 0.0734730i −0.999325 0.0367365i \(-0.988304\pi\)
0.999325 0.0367365i \(-0.0116962\pi\)
\(462\) 0 0
\(463\) 27.7330 1.28886 0.644431 0.764663i \(-0.277094\pi\)
0.644431 + 0.764663i \(0.277094\pi\)
\(464\) 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
\(470\) −3.90675 30.0089i −0.180205 1.38421i
\(471\) 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 \(-0.422552\pi\)
0.240916 + 0.970546i \(0.422552\pi\)
\(480\) −30.7542 + 7.44184i −1.40373 + 0.339672i
\(481\) 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 \(-0.366285\pi\)
0.407830 + 0.913058i \(0.366285\pi\)
\(488\) −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 \(0.953285\pi\)
\(500\) 0.700054 22.3497i 0.0313074 0.999510i
\(501\) −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 \(-0.848886\pi\)
0.889412 0.457107i \(-0.151114\pi\)
\(510\) −2.05008 15.7472i −0.0907789 0.697298i
\(511\) 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
\(520\) −21.3670 + 31.1010i −0.937005 + 1.36387i
\(521\) 5.87937i 0.257580i 0.991672 + 0.128790i \(0.0411093\pi\)
−0.991672 + 0.128790i \(0.958891\pi\)
\(522\) −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
\(530\) 2.88326 + 22.1471i 0.125241 + 0.962011i
\(531\) 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
\(540\) 2.45707 1.50356i 0.105736 0.0647029i
\(541\) 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 \(-0.706951\pi\)
−0.605310 + 0.795990i \(0.706951\pi\)
\(548\) −10.5338 9.45388i −0.449983 0.403850i
\(549\) 3.97369i 0.169593i
\(550\) 15.7066 + 2.54715i 0.669730 + 0.108611i
\(551\) 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 \(0.200113\pi\)
−0.808808 + 0.588072i \(0.799887\pi\)
\(558\) 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 \(0.424201\pi\)
\(570\) 7.98579 + 61.3410i 0.334488 + 2.56929i
\(571\) 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
\(580\) −11.3898 18.6128i −0.472934 0.772854i
\(581\) 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
\(590\) 35.7663 4.65629i 1.47248 0.191697i
\(591\) −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 \(0.891217\pi\)
\(600\) 27.5388 22.2061i 1.12427 0.906561i
\(601\) 17.5151i 0.714458i −0.934017 0.357229i \(-0.883722\pi\)
0.934017 0.357229i \(-0.116278\pi\)
\(602\) 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
\(610\) −0.497997 3.82525i −0.0201633 0.154880i
\(611\) 57.0948i 2.30981i
\(612\) 8.73565 9.73356i 0.353118 0.393456i
\(613\) 21.7127i 0.876966i 0.898739 + 0.438483i \(0.144484\pi\)
−0.898739 + 0.438483i \(0.855516\pi\)
\(614\) −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 \(-0.969512\pi\)
0.995416 0.0956353i \(-0.0304883\pi\)
\(618\) 18.6126 + 41.7136i 0.748707 + 1.67797i
\(619\) 31.5652 1.26871 0.634357 0.773040i \(-0.281265\pi\)
0.634357 + 0.773040i \(0.281265\pi\)
\(620\) 3.50119 + 5.72153i 0.140611 + 0.229782i
\(621\) 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
\(640\) −22.2736 11.9953i −0.880441 0.474156i
\(641\) 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
\(650\) 6.75333 41.6433i 0.264887 1.63339i
\(651\) 0 0
\(652\) 3.83302 4.27088i 0.150113 0.167260i
\(653\) 18.0725i 0.707230i 0.935391 + 0.353615i \(0.115048\pi\)
−0.935391 + 0.353615i \(0.884952\pi\)
\(654\) 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 \(-0.0836660\pi\)
\(660\) 13.1397 + 21.4725i 0.511462 + 0.835816i
\(661\) 18.4115i 0.716123i −0.933698 0.358062i \(-0.883438\pi\)
0.933698 0.358062i \(-0.116562\pi\)
\(662\) 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
\(670\) 3.49595 0.455126i 0.135060 0.0175831i
\(671\) 2.74500 0.105970
\(672\) 0 0
\(673\) 43.5683i 1.67944i −0.543023 0.839718i \(-0.682720\pi\)
0.543023 0.839718i \(-0.317280\pi\)
\(674\) 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
\(680\) 7.18950 10.4648i 0.275705 0.401305i
\(681\) −15.4366 −0.591531
\(682\) −4.35898 + 1.94497i −0.166914 + 0.0744768i
\(683\) 0.937655 0.0358784 0.0179392 0.999839i \(-0.494289\pi\)
0.0179392 + 0.999839i \(0.494289\pi\)
\(684\) −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
\(690\) −3.05574 23.4720i −0.116330 0.893565i
\(691\) 8.12642 0.309144 0.154572 0.987982i \(-0.450600\pi\)
0.154572 + 0.987982i \(0.450600\pi\)
\(692\) 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 \(0.367733\pi\)
\(710\) 3.42959 + 26.3437i 0.128710 + 0.988660i
\(711\) 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 \(-0.667263\pi\)
−0.501623 + 0.865087i \(0.667263\pi\)
\(720\) 28.6533 + 5.28134i 1.06784 + 0.196824i
\(721\) 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
\(730\) 18.4405 2.40071i 0.682515 0.0888543i
\(731\) −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 \(0.695830\pi\)
\(740\) 18.2567 11.1719i 0.671131 0.410686i
\(741\) 116.707i 4.28735i
\(742\) 0 0
\(743\) −34.9014 −1.28041 −0.640204 0.768205i \(-0.721150\pi\)
−0.640204 + 0.768205i \(0.721150\pi\)
\(744\) −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
\(750\) −17.2395 + 35.5974i −0.629496 + 1.29983i
\(751\) 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 \(-0.546415\pi\)
0.145301 0.989388i \(-0.453585\pi\)
\(758\) 21.9364 9.78798i 0.796765 0.355516i
\(759\) 16.8435 0.611382
\(760\) −28.0057 + 40.7640i −1.01587 + 1.47867i
\(761\) 25.8142i 0.935765i −0.883791 0.467883i \(-0.845017\pi\)
0.883791 0.467883i \(-0.154983\pi\)
\(762\) 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 \(-0.742513\pi\)
0.690281 0.723542i \(-0.257487\pi\)
\(770\) 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
\(780\) 56.9307 34.8377i 2.03845 1.24739i
\(781\) −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 &min