Properties

Label 980.2.c.e.979.30
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 979.30
Character \(\chi\) \(=\) 980.979
Dual form 980.2.c.e.979.31

$q$-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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 16 q^{4} - 64 q^{9} + O(q^{10}) \) \( 48 q + 16 q^{4} - 64 q^{9} + 16 q^{16} - 16 q^{25} - 48 q^{29} - 8 q^{30} + 176 q^{36} - 48 q^{44} - 32 q^{46} + 32 q^{50} + 24 q^{60} - 80 q^{64} - 16 q^{65} - 112 q^{74} - 48 q^{81} - 64 q^{85} - 112 q^{86} + O(q^{100}) \)

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
\(10\) 2.39832 + 2.06108i 0.758415 + 0.651771i
\(11\) 2.25026i 0.678480i 0.940700 + 0.339240i \(0.110170\pi\)
−0.940700 + 0.339240i \(0.889830\pi\)
\(12\) 3.72336 3.34164i 1.07484 0.964648i
\(13\) 5.96620 1.65472 0.827362 0.561668i \(-0.189840\pi\)
0.827362 + 0.561668i \(0.189840\pi\)
\(14\) 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 \(-0.578277\pi\)
−0.243443 + 0.969915i \(0.578277\pi\)
\(18\) −1.87716 + 4.20700i −0.442450 + 0.991599i
\(19\) −7.81989 −1.79400 −0.897002 0.442026i \(-0.854260\pi\)
−0.897002 + 0.442026i \(0.854260\pi\)
\(20\) 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 \(-0.456994\pi\)
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
\(40\) −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 \(-0.838796\pi\)
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 \(0.766337\pi\)
\(60\) 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 \(0.166116\pi\)
−0.866889 + 0.498501i \(0.833884\pi\)
\(72\) 8.76953 2.82588i 1.03350 0.333033i
\(73\) 5.88062 0.688274 0.344137 0.938919i \(-0.388172\pi\)
0.344137 + 0.938919i \(0.388172\pi\)
\(74\) −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 \(0.239189\pi\)
−0.730711 + 0.682687i \(0.760811\pi\)
\(80\) −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 \(-0.424639\pi\)
0.234549 + 0.972104i \(0.424639\pi\)
\(98\) 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 \(-0.965428\pi\)
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
\(120\) 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 \(-0.383846\pi\)
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 \(0.202077\pi\)
\(150\) −9.55482 14.8856i −0.780148 1.21540i
\(151\) 17.4157i 1.41727i −0.705574 0.708636i \(-0.749311\pi\)
0.705574 0.708636i \(-0.250689\pi\)
\(152\) 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 \(-0.411730\pi\)
0.273767 + 0.961796i \(0.411730\pi\)
\(158\) 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 \(-0.487605\pi\)
0.0389290 + 0.999242i \(0.487605\pi\)
\(174\) −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 \(0.0501431\pi\)
−0.987618 + 0.156878i \(0.949857\pi\)
\(180\) −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 \(-0.792857\pi\)
0.795624 0.605791i \(-0.207143\pi\)
\(192\) 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 \(0.684489\pi\)
\(200\) 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 \(0.116521\pi\)
−0.933745 + 0.357940i \(0.883479\pi\)
\(212\) −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 \(0.152711\pi\)
−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 \(0.0865783\pi\)
−0.963237 + 0.268652i \(0.913422\pi\)
\(240\) 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 \(-0.548468\pi\)
−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 \(-0.732780\pi\)
−0.667837 + 0.744307i \(0.732780\pi\)
\(258\) 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 \(-0.642279\pi\)
−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
\(290\) −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 \(-0.638923\pi\)
−0.422716 + 0.906262i \(0.638923\pi\)
\(294\) 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 \(-0.435879\pi\)
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 \(-0.127690\pi\)
0.920613 + 0.390477i \(0.127690\pi\)
\(314\) 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
\(320\) 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 \(-0.768231\pi\)
0.746424 0.665471i \(-0.231769\pi\)
\(332\) −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
\(340\) −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 \(-0.428701\pi\)
0.222125 + 0.975018i \(0.428701\pi\)
\(354\) −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 \(-0.984707\pi\)
0.998846 0.0480269i \(-0.0152933\pi\)
\(360\) 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 \(-0.889098\pi\)
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 \(-0.856309\pi\)
0.899830 0.436241i \(-0.143691\pi\)
\(380\) −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 \(-0.732818\pi\)
−0.667928 + 0.744226i \(0.732818\pi\)
\(398\) −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 \(-0.626118\pi\)
−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
\(430\) 2.70279 + 2.32274i 0.130340 + 0.112012i
\(431\) 27.5487i 1.32697i 0.748188 + 0.663487i \(0.230924\pi\)
−0.748188 + 0.663487i \(0.769076\pi\)
\(432\) 2.56149 + 0.277609i 0.123240 + 0.0133565i
\(433\) −2.28113 −0.109624 −0.0548121 0.998497i \(-0.517456\pi\)
−0.0548121 + 0.998497i \(0.517456\pi\)
\(434\) 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 \(0.570973\pi\)
\(440\) 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 \(-0.844095\pi\)
0.882432 0.470439i \(-0.155905\pi\)
\(458\) 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 \(-0.422552\pi\)
0.240916 + 0.970546i \(0.422552\pi\)
\(480\) −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 \(0.00506272\pi\)
−0.999874 + 0.0159043i \(0.994937\pi\)
\(492\) 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 \(-0.953285\pi\)
0.989250 0.146234i \(-0.0467153\pi\)
\(500\) −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 \(0.200113\pi\)
−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 \(0.424201\pi\)
\(570\) 40.3177 46.9146i 1.68872 1.96504i
\(571\) 0.667681i 0.0279416i 0.999902 + 0.0139708i \(0.00444718\pi\)
−0.999902 + 0.0139708i \(0.995553\pi\)
\(572\) 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 \(-0.734005\pi\)
−0.670696 + 0.741732i \(0.734005\pi\)
\(578\) −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 \(-0.731257\pi\)
−0.664270 + 0.747493i \(0.731257\pi\)
\(594\) 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 \(-0.891217\pi\)
0.942169 0.335139i \(-0.108783\pi\)
\(600\) −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 \(0.144484\pi\)
−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 \(0.281265\pi\)
\(620\) 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 \(0.0847096\pi\)
−0.964798 + 0.262993i \(0.915290\pi\)
\(632\) −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 \(0.115048\pi\)
−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 \(0.0836660\pi\)
−0.965655 + 0.259828i \(0.916334\pi\)
\(660\) −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 \(-0.682720\pi\)
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 \(-0.579316\pi\)
−0.246609 + 0.969115i \(0.579316\pi\)
\(678\) 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 \(-0.450600\pi\)
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 \(0.367733\pi\)
\(710\) −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 \(-0.667263\pi\)
−0.501623 + 0.865087i \(0.667263\pi\)
\(720\) 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 \(-0.401668\pi\)
0.304030 + 0.952663i \(0.401668\pi\)
\(734\) 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 \(-0.695830\pi\)
0.577137 0.816647i \(-0.304170\pi\)
\(740\) −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 \(0.111600\pi\)
−0.939166 + 0.343463i \(0.888400\pi\)
\(752\) −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
\(760\) 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 \(-0.156462\pi\)
0.881607 + 0.471983i \(0.156462\pi\)
\(774\) −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