Properties

Label 936.2.m.h.181.11
Level $936$
Weight $2$
Character 936.181
Analytic conductor $7.474$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 936.m (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.47399762919\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \( x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{14} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 181.11
Root \(-0.0783900 - 1.17295i\) of defining polynomial
Character \(\chi\) \(=\) 936.181
Dual form 936.2.m.h.181.10

$q$-expansion

\(f(q)\) \(=\) \(q+(0.831254 + 1.14412i) q^{2} +(-0.618034 + 1.90211i) q^{4} -2.68999 q^{5} -4.15163i q^{7} +(-2.68999 + 0.874032i) q^{8} +O(q^{10})\) \(q+(0.831254 + 1.14412i) q^{2} +(-0.618034 + 1.90211i) q^{4} -2.68999 q^{5} -4.15163i q^{7} +(-2.68999 + 0.874032i) q^{8} +(-2.23607 - 3.07768i) q^{10} +4.35250 q^{11} +(-3.53159 - 0.726543i) q^{13} +(4.74998 - 3.45106i) q^{14} +(-3.23607 - 2.35114i) q^{16} +5.87130 q^{17} +5.71423 q^{19} +(1.66251 - 5.11667i) q^{20} +(3.61803 + 4.97980i) q^{22} +3.62866 q^{23} +2.23607 q^{25} +(-2.10439 - 4.64452i) q^{26} +(7.89688 + 2.56585i) q^{28} +3.08672i q^{29} -9.28334i q^{31} -5.65685i q^{32} +(4.88054 + 6.71749i) q^{34} +11.1679i q^{35} +2.69790 q^{37} +(4.74998 + 6.53779i) q^{38} +(7.23607 - 2.35114i) q^{40} -11.1074i q^{41} -3.80423i q^{43} +(-2.68999 + 8.27895i) q^{44} +(3.01634 + 4.15163i) q^{46} +4.91034i q^{47} -10.2361 q^{49} +(1.85874 + 2.55834i) q^{50} +(3.56461 - 6.26846i) q^{52} -1.17902i q^{53} -11.7082 q^{55} +(3.62866 + 11.1679i) q^{56} +(-3.53159 + 2.56585i) q^{58} +2.29753 q^{59} +7.05342i q^{61} +(10.6213 - 7.71681i) q^{62} +(6.47214 - 4.70228i) q^{64} +(9.49996 + 1.95440i) q^{65} -10.0795 q^{67} +(-3.62866 + 11.1679i) q^{68} +(-12.7774 + 9.28334i) q^{70} +2.08191i q^{71} -13.4350i q^{73} +(2.24264 + 3.08672i) q^{74} +(-3.53159 + 10.8691i) q^{76} -18.0700i q^{77} +10.9443 q^{79} +(8.70500 + 6.32456i) q^{80} +(12.7082 - 9.23305i) q^{82} -9.73249 q^{83} -15.7938 q^{85} +(4.35250 - 3.16228i) q^{86} +(-11.7082 + 3.80423i) q^{88} +12.1877i q^{89} +(-3.01634 + 14.6619i) q^{91} +(-2.24264 + 6.90212i) q^{92} +(-5.61803 + 4.08174i) q^{94} -15.3713 q^{95} -5.13170i q^{97} +(-8.50877 - 11.7113i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} - 16 q^{16} + 40 q^{22} + 80 q^{40} - 128 q^{49} + 40 q^{52} - 80 q^{55} + 32 q^{64} + 32 q^{79} + 96 q^{82} - 80 q^{88} - 72 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/936\mathbb{Z}\right)^\times\).

\(n\) \(145\) \(209\) \(469\) \(703\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.831254 + 1.14412i 0.587785 + 0.809017i
\(3\) 0 0
\(4\) −0.618034 + 1.90211i −0.309017 + 0.951057i
\(5\) −2.68999 −1.20300 −0.601501 0.798872i \(-0.705430\pi\)
−0.601501 + 0.798872i \(0.705430\pi\)
\(6\) 0 0
\(7\) 4.15163i 1.56917i −0.620021 0.784585i \(-0.712876\pi\)
0.620021 0.784585i \(-0.287124\pi\)
\(8\) −2.68999 + 0.874032i −0.951057 + 0.309017i
\(9\) 0 0
\(10\) −2.23607 3.07768i −0.707107 0.973249i
\(11\) 4.35250 1.31233 0.656164 0.754618i \(-0.272178\pi\)
0.656164 + 0.754618i \(0.272178\pi\)
\(12\) 0 0
\(13\) −3.53159 0.726543i −0.979487 0.201507i
\(14\) 4.74998 3.45106i 1.26949 0.922335i
\(15\) 0 0
\(16\) −3.23607 2.35114i −0.809017 0.587785i
\(17\) 5.87130 1.42400 0.711999 0.702180i \(-0.247790\pi\)
0.711999 + 0.702180i \(0.247790\pi\)
\(18\) 0 0
\(19\) 5.71423 1.31094 0.655468 0.755223i \(-0.272472\pi\)
0.655468 + 0.755223i \(0.272472\pi\)
\(20\) 1.66251 5.11667i 0.371748 1.14412i
\(21\) 0 0
\(22\) 3.61803 + 4.97980i 0.771367 + 1.06170i
\(23\) 3.62866 0.756628 0.378314 0.925677i \(-0.376504\pi\)
0.378314 + 0.925677i \(0.376504\pi\)
\(24\) 0 0
\(25\) 2.23607 0.447214
\(26\) −2.10439 4.64452i −0.412706 0.910864i
\(27\) 0 0
\(28\) 7.89688 + 2.56585i 1.49237 + 0.484900i
\(29\) 3.08672i 0.573190i 0.958052 + 0.286595i \(0.0925234\pi\)
−0.958052 + 0.286595i \(0.907477\pi\)
\(30\) 0 0
\(31\) 9.28334i 1.66734i −0.552266 0.833668i \(-0.686237\pi\)
0.552266 0.833668i \(-0.313763\pi\)
\(32\) 5.65685i 1.00000i
\(33\) 0 0
\(34\) 4.88054 + 6.71749i 0.837006 + 1.15204i
\(35\) 11.1679i 1.88771i
\(36\) 0 0
\(37\) 2.69790 0.443531 0.221766 0.975100i \(-0.428818\pi\)
0.221766 + 0.975100i \(0.428818\pi\)
\(38\) 4.74998 + 6.53779i 0.770548 + 1.06057i
\(39\) 0 0
\(40\) 7.23607 2.35114i 1.14412 0.371748i
\(41\) 11.1074i 1.73468i −0.497715 0.867340i \(-0.665828\pi\)
0.497715 0.867340i \(-0.334172\pi\)
\(42\) 0 0
\(43\) 3.80423i 0.580139i −0.957006 0.290070i \(-0.906322\pi\)
0.957006 0.290070i \(-0.0936784\pi\)
\(44\) −2.68999 + 8.27895i −0.405532 + 1.24810i
\(45\) 0 0
\(46\) 3.01634 + 4.15163i 0.444735 + 0.612125i
\(47\) 4.91034i 0.716247i 0.933674 + 0.358123i \(0.116583\pi\)
−0.933674 + 0.358123i \(0.883417\pi\)
\(48\) 0 0
\(49\) −10.2361 −1.46230
\(50\) 1.85874 + 2.55834i 0.262866 + 0.361803i
\(51\) 0 0
\(52\) 3.56461 6.26846i 0.494322 0.869279i
\(53\) 1.17902i 0.161951i −0.996716 0.0809757i \(-0.974196\pi\)
0.996716 0.0809757i \(-0.0258036\pi\)
\(54\) 0 0
\(55\) −11.7082 −1.57873
\(56\) 3.62866 + 11.1679i 0.484900 + 1.49237i
\(57\) 0 0
\(58\) −3.53159 + 2.56585i −0.463721 + 0.336913i
\(59\) 2.29753 0.299113 0.149556 0.988753i \(-0.452215\pi\)
0.149556 + 0.988753i \(0.452215\pi\)
\(60\) 0 0
\(61\) 7.05342i 0.903098i 0.892246 + 0.451549i \(0.149128\pi\)
−0.892246 + 0.451549i \(0.850872\pi\)
\(62\) 10.6213 7.71681i 1.34890 0.980036i
\(63\) 0 0
\(64\) 6.47214 4.70228i 0.809017 0.587785i
\(65\) 9.49996 + 1.95440i 1.17832 + 0.242413i
\(66\) 0 0
\(67\) −10.0795 −1.23141 −0.615705 0.787977i \(-0.711129\pi\)
−0.615705 + 0.787977i \(0.711129\pi\)
\(68\) −3.62866 + 11.1679i −0.440040 + 1.35430i
\(69\) 0 0
\(70\) −12.7774 + 9.28334i −1.52719 + 1.10957i
\(71\) 2.08191i 0.247078i 0.992340 + 0.123539i \(0.0394244\pi\)
−0.992340 + 0.123539i \(0.960576\pi\)
\(72\) 0 0
\(73\) 13.4350i 1.57244i −0.617944 0.786222i \(-0.712034\pi\)
0.617944 0.786222i \(-0.287966\pi\)
\(74\) 2.24264 + 3.08672i 0.260701 + 0.358824i
\(75\) 0 0
\(76\) −3.53159 + 10.8691i −0.405101 + 1.24677i
\(77\) 18.0700i 2.05927i
\(78\) 0 0
\(79\) 10.9443 1.23133 0.615663 0.788009i \(-0.288888\pi\)
0.615663 + 0.788009i \(0.288888\pi\)
\(80\) 8.70500 + 6.32456i 0.973249 + 0.707107i
\(81\) 0 0
\(82\) 12.7082 9.23305i 1.40339 1.01962i
\(83\) −9.73249 −1.06828 −0.534140 0.845396i \(-0.679364\pi\)
−0.534140 + 0.845396i \(0.679364\pi\)
\(84\) 0 0
\(85\) −15.7938 −1.71307
\(86\) 4.35250 3.16228i 0.469342 0.340997i
\(87\) 0 0
\(88\) −11.7082 + 3.80423i −1.24810 + 0.405532i
\(89\) 12.1877i 1.29190i 0.763381 + 0.645949i \(0.223538\pi\)
−0.763381 + 0.645949i \(0.776462\pi\)
\(90\) 0 0
\(91\) −3.01634 + 14.6619i −0.316198 + 1.53698i
\(92\) −2.24264 + 6.90212i −0.233811 + 0.719596i
\(93\) 0 0
\(94\) −5.61803 + 4.08174i −0.579456 + 0.420999i
\(95\) −15.3713 −1.57706
\(96\) 0 0
\(97\) 5.13170i 0.521045i −0.965468 0.260523i \(-0.916105\pi\)
0.965468 0.260523i \(-0.0838949\pi\)
\(98\) −8.50877 11.7113i −0.859516 1.18302i
\(99\) 0 0
\(100\) −1.38197 + 4.25325i −0.138197 + 0.425325i
\(101\) 14.9833i 1.49089i −0.666566 0.745446i \(-0.732237\pi\)
0.666566 0.745446i \(-0.267763\pi\)
\(102\) 0 0
\(103\) 1.70820 0.168314 0.0841572 0.996452i \(-0.473180\pi\)
0.0841572 + 0.996452i \(0.473180\pi\)
\(104\) 10.1350 1.13233i 0.993817 0.111034i
\(105\) 0 0
\(106\) 1.34895 0.980068i 0.131021 0.0951926i
\(107\) 4.99442i 0.482829i 0.970422 + 0.241415i \(0.0776114\pi\)
−0.970422 + 0.241415i \(0.922389\pi\)
\(108\) 0 0
\(109\) 8.73057 0.836237 0.418119 0.908392i \(-0.362690\pi\)
0.418119 + 0.908392i \(0.362690\pi\)
\(110\) −9.73249 13.3956i −0.927957 1.27722i
\(111\) 0 0
\(112\) −9.76108 + 13.4350i −0.922335 + 1.26949i
\(113\) 5.87130 0.552325 0.276163 0.961111i \(-0.410937\pi\)
0.276163 + 0.961111i \(0.410937\pi\)
\(114\) 0 0
\(115\) −9.76108 −0.910225
\(116\) −5.87130 1.90770i −0.545136 0.177126i
\(117\) 0 0
\(118\) 1.90983 + 2.62866i 0.175814 + 0.241987i
\(119\) 24.3755i 2.23450i
\(120\) 0 0
\(121\) 7.94427 0.722207
\(122\) −8.06998 + 5.86319i −0.730622 + 0.530828i
\(123\) 0 0
\(124\) 17.6580 + 5.73742i 1.58573 + 0.515235i
\(125\) 7.43496 0.665003
\(126\) 0 0
\(127\) −6.00000 −0.532414 −0.266207 0.963916i \(-0.585770\pi\)
−0.266207 + 0.963916i \(0.585770\pi\)
\(128\) 10.7600 + 3.49613i 0.951057 + 0.309017i
\(129\) 0 0
\(130\) 5.66081 + 12.4937i 0.496486 + 1.09577i
\(131\) 8.80982i 0.769718i −0.922975 0.384859i \(-0.874250\pi\)
0.922975 0.384859i \(-0.125750\pi\)
\(132\) 0 0
\(133\) 23.7234i 2.05708i
\(134\) −8.37864 11.5322i −0.723804 0.996231i
\(135\) 0 0
\(136\) −15.7938 + 5.13170i −1.35430 + 0.440040i
\(137\) 10.4397i 0.891922i 0.895052 + 0.445961i \(0.147138\pi\)
−0.895052 + 0.445961i \(0.852862\pi\)
\(138\) 0 0
\(139\) 14.3188i 1.21451i −0.794507 0.607254i \(-0.792271\pi\)
0.794507 0.607254i \(-0.207729\pi\)
\(140\) −21.2426 6.90212i −1.79532 0.583336i
\(141\) 0 0
\(142\) −2.38197 + 1.73060i −0.199890 + 0.145229i
\(143\) −15.3713 3.16228i −1.28541 0.264443i
\(144\) 0 0
\(145\) 8.30327i 0.689549i
\(146\) 15.3713 11.1679i 1.27213 0.924260i
\(147\) 0 0
\(148\) −1.66739 + 5.13170i −0.137059 + 0.421823i
\(149\) 0.635021 0.0520230 0.0260115 0.999662i \(-0.491719\pi\)
0.0260115 + 0.999662i \(0.491719\pi\)
\(150\) 0 0
\(151\) 4.15163i 0.337855i 0.985628 + 0.168928i \(0.0540304\pi\)
−0.985628 + 0.168928i \(0.945970\pi\)
\(152\) −15.3713 + 4.99442i −1.24677 + 0.405101i
\(153\) 0 0
\(154\) 20.6743 15.0208i 1.66598 1.21041i
\(155\) 24.9721i 2.00581i
\(156\) 0 0
\(157\) 16.1150i 1.28611i 0.765818 + 0.643057i \(0.222334\pi\)
−0.765818 + 0.643057i \(0.777666\pi\)
\(158\) 9.09747 + 12.5216i 0.723756 + 0.996164i
\(159\) 0 0
\(160\) 15.2169i 1.20300i
\(161\) 15.0649i 1.18728i
\(162\) 0 0
\(163\) −10.0795 −0.789489 −0.394745 0.918791i \(-0.629167\pi\)
−0.394745 + 0.918791i \(0.629167\pi\)
\(164\) 21.1275 + 6.86474i 1.64978 + 0.536046i
\(165\) 0 0
\(166\) −8.09017 11.1352i −0.627919 0.864256i
\(167\) 24.2967i 1.88013i 0.340992 + 0.940066i \(0.389237\pi\)
−0.340992 + 0.940066i \(0.610763\pi\)
\(168\) 0 0
\(169\) 11.9443 + 5.13170i 0.918790 + 0.394746i
\(170\) −13.1286 18.0700i −1.00692 1.38591i
\(171\) 0 0
\(172\) 7.23607 + 2.35114i 0.551745 + 0.179273i
\(173\) 1.17902i 0.0896395i −0.998995 0.0448198i \(-0.985729\pi\)
0.998995 0.0448198i \(-0.0142714\pi\)
\(174\) 0 0
\(175\) 9.28334i 0.701754i
\(176\) −14.0850 10.2333i −1.06170 0.771367i
\(177\) 0 0
\(178\) −13.9443 + 10.1311i −1.04517 + 0.759359i
\(179\) 18.7987i 1.40508i 0.711645 + 0.702539i \(0.247951\pi\)
−0.711645 + 0.702539i \(0.752049\pi\)
\(180\) 0 0
\(181\) 13.2088i 0.981802i −0.871215 0.490901i \(-0.836668\pi\)
0.871215 0.490901i \(-0.163332\pi\)
\(182\) −19.2823 + 8.73668i −1.42930 + 0.647606i
\(183\) 0 0
\(184\) −9.76108 + 3.17157i −0.719596 + 0.233811i
\(185\) −7.25732 −0.533569
\(186\) 0 0
\(187\) 25.5548 1.86875
\(188\) −9.34003 3.03476i −0.681191 0.221332i
\(189\) 0 0
\(190\) −12.7774 17.5866i −0.926971 1.27587i
\(191\) −15.3713 −1.11223 −0.556113 0.831107i \(-0.687708\pi\)
−0.556113 + 0.831107i \(0.687708\pi\)
\(192\) 0 0
\(193\) 13.4350i 0.967070i −0.875325 0.483535i \(-0.839353\pi\)
0.875325 0.483535i \(-0.160647\pi\)
\(194\) 5.87130 4.26575i 0.421535 0.306263i
\(195\) 0 0
\(196\) 6.32624 19.4702i 0.451874 1.39073i
\(197\) −10.6101 −0.755936 −0.377968 0.925819i \(-0.623377\pi\)
−0.377968 + 0.925819i \(0.623377\pi\)
\(198\) 0 0
\(199\) 18.0000 1.27599 0.637993 0.770042i \(-0.279765\pi\)
0.637993 + 0.770042i \(0.279765\pi\)
\(200\) −6.01501 + 1.95440i −0.425325 + 0.138197i
\(201\) 0 0
\(202\) 17.1427 12.4549i 1.20616 0.876324i
\(203\) 12.8149 0.899433
\(204\) 0 0
\(205\) 29.8788i 2.08682i
\(206\) 1.41995 + 1.95440i 0.0989327 + 0.136169i
\(207\) 0 0
\(208\) 9.72027 + 10.6544i 0.673979 + 0.738750i
\(209\) 24.8712 1.72038
\(210\) 0 0
\(211\) 17.0130i 1.17122i 0.810591 + 0.585612i \(0.199146\pi\)
−0.810591 + 0.585612i \(0.800854\pi\)
\(212\) 2.24264 + 0.728677i 0.154025 + 0.0500457i
\(213\) 0 0
\(214\) −5.71423 + 4.15163i −0.390617 + 0.283800i
\(215\) 10.2333i 0.697908i
\(216\) 0 0
\(217\) −38.5410 −2.61633
\(218\) 7.25732 + 9.98885i 0.491528 + 0.676530i
\(219\) 0 0
\(220\) 7.23607 22.2703i 0.487856 1.50147i
\(221\) −20.7350 4.26575i −1.39479 0.286945i
\(222\) 0 0
\(223\) 9.28334i 0.621658i 0.950466 + 0.310829i \(0.100607\pi\)
−0.950466 + 0.310829i \(0.899393\pi\)
\(224\) −23.4852 −1.56917
\(225\) 0 0
\(226\) 4.88054 + 6.71749i 0.324649 + 0.446840i
\(227\) 1.02749 0.0681967 0.0340983 0.999418i \(-0.489144\pi\)
0.0340983 + 0.999418i \(0.489144\pi\)
\(228\) 0 0
\(229\) 18.4917 1.22196 0.610981 0.791645i \(-0.290775\pi\)
0.610981 + 0.791645i \(0.290775\pi\)
\(230\) −8.11393 11.1679i −0.535017 0.736388i
\(231\) 0 0
\(232\) −2.69790 8.30327i −0.177126 0.545136i
\(233\) −7.25732 −0.475443 −0.237722 0.971333i \(-0.576401\pi\)
−0.237722 + 0.971333i \(0.576401\pi\)
\(234\) 0 0
\(235\) 13.2088i 0.861646i
\(236\) −1.41995 + 4.37016i −0.0924309 + 0.284473i
\(237\) 0 0
\(238\) 27.8885 20.2622i 1.80775 1.31340i
\(239\) 7.07107i 0.457389i 0.973498 + 0.228695i \(0.0734457\pi\)
−0.973498 + 0.228695i \(0.926554\pi\)
\(240\) 0 0
\(241\) 18.5667i 1.19598i 0.801502 + 0.597992i \(0.204035\pi\)
−0.801502 + 0.597992i \(0.795965\pi\)
\(242\) 6.60371 + 9.08922i 0.424502 + 0.584277i
\(243\) 0 0
\(244\) −13.4164 4.35926i −0.858898 0.279073i
\(245\) 27.5350 1.75914
\(246\) 0 0
\(247\) −20.1803 4.15163i −1.28404 0.264162i
\(248\) 8.11393 + 24.9721i 0.515235 + 1.58573i
\(249\) 0 0
\(250\) 6.18034 + 8.50651i 0.390879 + 0.537999i
\(251\) 2.35805i 0.148839i 0.997227 + 0.0744193i \(0.0237103\pi\)
−0.997227 + 0.0744193i \(0.976290\pi\)
\(252\) 0 0
\(253\) 15.7938 0.992945
\(254\) −4.98752 6.86474i −0.312945 0.430732i
\(255\) 0 0
\(256\) 4.94427 + 15.2169i 0.309017 + 0.951057i
\(257\) −26.2572 −1.63788 −0.818941 0.573878i \(-0.805438\pi\)
−0.818941 + 0.573878i \(0.805438\pi\)
\(258\) 0 0
\(259\) 11.2007i 0.695976i
\(260\) −9.58878 + 16.8621i −0.594671 + 1.04574i
\(261\) 0 0
\(262\) 10.0795 7.32320i 0.622715 0.452429i
\(263\) 7.25732 0.447506 0.223753 0.974646i \(-0.428169\pi\)
0.223753 + 0.974646i \(0.428169\pi\)
\(264\) 0 0
\(265\) 3.17157i 0.194828i
\(266\) 27.1425 19.7202i 1.66421 1.20912i
\(267\) 0 0
\(268\) 6.22949 19.1724i 0.380526 1.17114i
\(269\) 19.2490i 1.17363i −0.809720 0.586817i \(-0.800381\pi\)
0.809720 0.586817i \(-0.199619\pi\)
\(270\) 0 0
\(271\) 9.28334i 0.563923i 0.959426 + 0.281961i \(0.0909850\pi\)
−0.959426 + 0.281961i \(0.909015\pi\)
\(272\) −18.9999 13.8042i −1.15204 0.837006i
\(273\) 0 0
\(274\) −11.9443 + 8.67802i −0.721580 + 0.524258i
\(275\) 9.73249 0.586891
\(276\) 0 0
\(277\) 21.7153i 1.30475i −0.757898 0.652373i \(-0.773774\pi\)
0.757898 0.652373i \(-0.226226\pi\)
\(278\) 16.3825 11.9026i 0.982558 0.713870i
\(279\) 0 0
\(280\) −9.76108 30.0415i −0.583336 1.79532i
\(281\) 9.35931i 0.558330i −0.960243 0.279165i \(-0.909942\pi\)
0.960243 0.279165i \(-0.0900576\pi\)
\(282\) 0 0
\(283\) 12.3107i 0.731797i 0.930655 + 0.365899i \(0.119238\pi\)
−0.930655 + 0.365899i \(0.880762\pi\)
\(284\) −3.96004 1.28669i −0.234985 0.0763512i
\(285\) 0 0
\(286\) −9.15938 20.2153i −0.541606 1.19535i
\(287\) −46.1138 −2.72201
\(288\) 0 0
\(289\) 17.4721 1.02777
\(290\) 9.49996 6.90212i 0.557857 0.405307i
\(291\) 0 0
\(292\) 25.5548 + 8.30327i 1.49548 + 0.485912i
\(293\) −25.4800 −1.48856 −0.744278 0.667869i \(-0.767206\pi\)
−0.744278 + 0.667869i \(0.767206\pi\)
\(294\) 0 0
\(295\) −6.18034 −0.359833
\(296\) −7.25732 + 2.35805i −0.421823 + 0.137059i
\(297\) 0 0
\(298\) 0.527864 + 0.726543i 0.0305783 + 0.0420875i
\(299\) −12.8149 2.63638i −0.741108 0.152466i
\(300\) 0 0
\(301\) −15.7938 −0.910337
\(302\) −4.74998 + 3.45106i −0.273331 + 0.198586i
\(303\) 0 0
\(304\) −18.4917 13.4350i −1.06057 0.770548i
\(305\) 18.9737i 1.08643i
\(306\) 0 0
\(307\) −4.04684 −0.230966 −0.115483 0.993309i \(-0.536842\pi\)
−0.115483 + 0.993309i \(0.536842\pi\)
\(308\) 34.3712 + 11.1679i 1.95848 + 0.636349i
\(309\) 0 0
\(310\) −28.5712 + 20.7582i −1.62273 + 1.17898i
\(311\) 10.8860 0.617288 0.308644 0.951178i \(-0.400125\pi\)
0.308644 + 0.951178i \(0.400125\pi\)
\(312\) 0 0
\(313\) −2.47214 −0.139733 −0.0698667 0.997556i \(-0.522257\pi\)
−0.0698667 + 0.997556i \(0.522257\pi\)
\(314\) −18.4375 + 13.3956i −1.04049 + 0.755959i
\(315\) 0 0
\(316\) −6.76393 + 20.8172i −0.380501 + 1.17106i
\(317\) −14.2349 −0.799512 −0.399756 0.916622i \(-0.630905\pi\)
−0.399756 + 0.916622i \(0.630905\pi\)
\(318\) 0 0
\(319\) 13.4350i 0.752214i
\(320\) −17.4100 + 12.6491i −0.973249 + 0.707107i
\(321\) 0 0
\(322\) 17.2361 12.5227i 0.960529 0.697865i
\(323\) 33.5500 1.86677
\(324\) 0 0
\(325\) −7.89688 1.62460i −0.438040 0.0901165i
\(326\) −8.37864 11.5322i −0.464050 0.638710i
\(327\) 0 0
\(328\) 9.70820 + 29.8788i 0.536046 + 1.64978i
\(329\) 20.3859 1.12391
\(330\) 0 0
\(331\) 3.01634 0.165793 0.0828965 0.996558i \(-0.473583\pi\)
0.0828965 + 0.996558i \(0.473583\pi\)
\(332\) 6.01501 18.5123i 0.330117 1.01599i
\(333\) 0 0
\(334\) −27.7984 + 20.1967i −1.52106 + 1.10511i
\(335\) 27.1139 1.48139
\(336\) 0 0
\(337\) 14.4721 0.788347 0.394174 0.919036i \(-0.371031\pi\)
0.394174 + 0.919036i \(0.371031\pi\)
\(338\) 4.05742 + 17.9315i 0.220695 + 0.975343i
\(339\) 0 0
\(340\) 9.76108 30.0415i 0.529369 1.62923i
\(341\) 40.4057i 2.18809i
\(342\) 0 0
\(343\) 13.4350i 0.725420i
\(344\) 3.32502 + 10.2333i 0.179273 + 0.551745i
\(345\) 0 0
\(346\) 1.34895 0.980068i 0.0725199 0.0526888i
\(347\) 28.5092i 1.53045i −0.643761 0.765227i \(-0.722627\pi\)
0.643761 0.765227i \(-0.277373\pi\)
\(348\) 0 0
\(349\) −9.76108 −0.522499 −0.261249 0.965271i \(-0.584134\pi\)
−0.261249 + 0.965271i \(0.584134\pi\)
\(350\) 10.6213 7.71681i 0.567731 0.412481i
\(351\) 0 0
\(352\) 24.6215i 1.31233i
\(353\) 7.86629i 0.418680i 0.977843 + 0.209340i \(0.0671316\pi\)
−0.977843 + 0.209340i \(0.932868\pi\)
\(354\) 0 0
\(355\) 5.60034i 0.297235i
\(356\) −23.1825 7.53244i −1.22867 0.399218i
\(357\) 0 0
\(358\) −21.5080 + 15.6265i −1.13673 + 0.825885i
\(359\) 13.1406i 0.693533i −0.937951 0.346767i \(-0.887280\pi\)
0.937951 0.346767i \(-0.112720\pi\)
\(360\) 0 0
\(361\) 13.6525 0.718551
\(362\) 15.1125 10.9799i 0.794294 0.577089i
\(363\) 0 0
\(364\) −26.0243 14.7990i −1.36405 0.775676i
\(365\) 36.1400i 1.89165i
\(366\) 0 0
\(367\) −9.12461 −0.476301 −0.238150 0.971228i \(-0.576541\pi\)
−0.238150 + 0.971228i \(0.576541\pi\)
\(368\) −11.7426 8.53149i −0.612125 0.444735i
\(369\) 0 0
\(370\) −6.03268 8.30327i −0.313624 0.431666i
\(371\) −4.89487 −0.254129
\(372\) 0 0
\(373\) 0.343027i 0.0177613i 0.999961 + 0.00888063i \(0.00282683\pi\)
−0.999961 + 0.00888063i \(0.997173\pi\)
\(374\) 21.2426 + 29.2379i 1.09843 + 1.51185i
\(375\) 0 0
\(376\) −4.29180 13.2088i −0.221332 0.681191i
\(377\) 2.24264 10.9010i 0.115502 0.561432i
\(378\) 0 0
\(379\) 18.8101 0.966210 0.483105 0.875563i \(-0.339509\pi\)
0.483105 + 0.875563i \(0.339509\pi\)
\(380\) 9.49996 29.2379i 0.487338 1.49987i
\(381\) 0 0
\(382\) −12.7774 17.5866i −0.653750 0.899809i
\(383\) 16.2241i 0.829010i 0.910047 + 0.414505i \(0.136045\pi\)
−0.910047 + 0.414505i \(0.863955\pi\)
\(384\) 0 0
\(385\) 48.6082i 2.47730i
\(386\) 15.3713 11.1679i 0.782376 0.568430i
\(387\) 0 0
\(388\) 9.76108 + 3.17157i 0.495544 + 0.161012i
\(389\) 11.6182i 0.589067i 0.955641 + 0.294534i \(0.0951643\pi\)
−0.955641 + 0.294534i \(0.904836\pi\)
\(390\) 0 0
\(391\) 21.3050 1.07744
\(392\) 27.5350 8.94665i 1.39073 0.451874i
\(393\) 0 0
\(394\) −8.81966 12.1392i −0.444328 0.611565i
\(395\) −29.4400 −1.48129
\(396\) 0 0
\(397\) 24.5243 1.23084 0.615420 0.788199i \(-0.288986\pi\)
0.615420 + 0.788199i \(0.288986\pi\)
\(398\) 14.9626 + 20.5942i 0.750006 + 1.03229i
\(399\) 0 0
\(400\) −7.23607 5.25731i −0.361803 0.262866i
\(401\) 23.3438i 1.16574i 0.812567 + 0.582868i \(0.198069\pi\)
−0.812567 + 0.582868i \(0.801931\pi\)
\(402\) 0 0
\(403\) −6.74474 + 32.7849i −0.335979 + 1.63313i
\(404\) 28.4999 + 9.26017i 1.41792 + 0.460711i
\(405\) 0 0
\(406\) 10.6525 + 14.6619i 0.528673 + 0.727657i
\(407\) 11.7426 0.582059
\(408\) 0 0
\(409\) 15.3951i 0.761239i 0.924732 + 0.380620i \(0.124289\pi\)
−0.924732 + 0.380620i \(0.875711\pi\)
\(410\) −34.1850 + 24.8369i −1.68828 + 1.22660i
\(411\) 0 0
\(412\) −1.05573 + 3.24920i −0.0520120 + 0.160076i
\(413\) 9.53850i 0.469359i
\(414\) 0 0
\(415\) 26.1803 1.28514
\(416\) −4.10995 + 19.9777i −0.201507 + 0.979487i
\(417\) 0 0
\(418\) 20.6743 + 28.4557i 1.01121 + 1.39182i
\(419\) 14.9833i 0.731981i 0.930619 + 0.365990i \(0.119270\pi\)
−0.930619 + 0.365990i \(0.880730\pi\)
\(420\) 0 0
\(421\) −15.7938 −0.769741 −0.384870 0.922971i \(-0.625754\pi\)
−0.384870 + 0.922971i \(0.625754\pi\)
\(422\) −19.4650 + 14.1421i −0.947540 + 0.688428i
\(423\) 0 0
\(424\) 1.03050 + 3.17157i 0.0500457 + 0.154025i
\(425\) 13.1286 0.636832
\(426\) 0 0
\(427\) 29.2832 1.41711
\(428\) −9.49996 3.08672i −0.459198 0.149202i
\(429\) 0 0
\(430\) −11.7082 + 8.50651i −0.564620 + 0.410220i
\(431\) 20.8005i 1.00193i 0.865468 + 0.500963i \(0.167021\pi\)
−0.865468 + 0.500963i \(0.832979\pi\)
\(432\) 0 0
\(433\) 14.1803 0.681464 0.340732 0.940161i \(-0.389325\pi\)
0.340732 + 0.940161i \(0.389325\pi\)
\(434\) −32.0374 44.0957i −1.53784 2.11666i
\(435\) 0 0
\(436\) −5.39579 + 16.6065i −0.258412 + 0.795309i
\(437\) 20.7350 0.991891
\(438\) 0 0
\(439\) 24.1803 1.15406 0.577032 0.816721i \(-0.304211\pi\)
0.577032 + 0.816721i \(0.304211\pi\)
\(440\) 31.4950 10.2333i 1.50147 0.487856i
\(441\) 0 0
\(442\) −12.3555 27.2693i −0.587693 1.29707i
\(443\) 1.17902i 0.0560171i 0.999608 + 0.0280086i \(0.00891656\pi\)
−0.999608 + 0.0280086i \(0.991083\pi\)
\(444\) 0 0
\(445\) 32.7849i 1.55416i
\(446\) −10.6213 + 7.71681i −0.502932 + 0.365402i
\(447\) 0 0
\(448\) −19.5222 26.8699i −0.922335 1.26949i
\(449\) 33.3221i 1.57257i 0.617865 + 0.786284i \(0.287998\pi\)
−0.617865 + 0.786284i \(0.712002\pi\)
\(450\) 0 0
\(451\) 48.3449i 2.27647i
\(452\) −3.62866 + 11.1679i −0.170678 + 0.525293i
\(453\) 0 0
\(454\) 0.854102 + 1.17557i 0.0400850 + 0.0551723i
\(455\) 8.11393 39.4404i 0.380387 1.84899i
\(456\) 0 0
\(457\) 38.3448i 1.79369i 0.442342 + 0.896847i \(0.354148\pi\)
−0.442342 + 0.896847i \(0.645852\pi\)
\(458\) 15.3713 + 21.1567i 0.718252 + 0.988589i
\(459\) 0 0
\(460\) 6.03268 18.5667i 0.281275 0.865676i
\(461\) 24.6951 1.15016 0.575082 0.818096i \(-0.304970\pi\)
0.575082 + 0.818096i \(0.304970\pi\)
\(462\) 0 0
\(463\) 4.15163i 0.192943i −0.995336 0.0964714i \(-0.969244\pi\)
0.995336 0.0964714i \(-0.0307556\pi\)
\(464\) 7.25732 9.98885i 0.336913 0.463721i
\(465\) 0 0
\(466\) −6.03268 8.30327i −0.279458 0.384641i
\(467\) 6.17345i 0.285673i −0.989746 0.142837i \(-0.954378\pi\)
0.989746 0.142837i \(-0.0456223\pi\)
\(468\) 0 0
\(469\) 41.8465i 1.93229i
\(470\) 15.1125 10.9799i 0.697087 0.506463i
\(471\) 0 0
\(472\) −6.18034 + 2.00811i −0.284473 + 0.0924309i
\(473\) 16.5579i 0.761333i
\(474\) 0 0
\(475\) 12.7774 0.586268
\(476\) 46.3649 + 15.0649i 2.12513 + 0.690497i
\(477\) 0 0
\(478\) −8.09017 + 5.87785i −0.370036 + 0.268847i
\(479\) 10.3122i 0.471174i −0.971853 0.235587i \(-0.924299\pi\)
0.971853 0.235587i \(-0.0757013\pi\)
\(480\) 0 0
\(481\) −9.52786 1.96014i −0.434433 0.0893745i
\(482\) −21.2426 + 15.4336i −0.967572 + 0.702982i
\(483\) 0 0
\(484\) −4.90983 + 15.1109i −0.223174 + 0.686859i
\(485\) 13.8042i 0.626819i
\(486\) 0 0
\(487\) 17.5866i 0.796925i 0.917185 + 0.398463i \(0.130456\pi\)
−0.917185 + 0.398463i \(0.869544\pi\)
\(488\) −6.16492 18.9737i −0.279073 0.858898i
\(489\) 0 0
\(490\) 22.8885 + 31.5034i 1.03400 + 1.42318i
\(491\) 26.1511i 1.18018i 0.807336 + 0.590092i \(0.200909\pi\)
−0.807336 + 0.590092i \(0.799091\pi\)
\(492\) 0 0
\(493\) 18.1231i 0.816222i
\(494\) −12.0250 26.5398i −0.541031 1.19408i
\(495\) 0 0
\(496\) −21.8264 + 30.0415i −0.980036 + 1.34890i
\(497\) 8.64335 0.387707
\(498\) 0 0
\(499\) −39.3628 −1.76212 −0.881059 0.473006i \(-0.843169\pi\)
−0.881059 + 0.473006i \(0.843169\pi\)
\(500\) −4.59506 + 14.1421i −0.205497 + 0.632456i
\(501\) 0 0
\(502\) −2.69790 + 1.96014i −0.120413 + 0.0874851i
\(503\) 18.9999 0.847164 0.423582 0.905858i \(-0.360772\pi\)
0.423582 + 0.905858i \(0.360772\pi\)
\(504\) 0 0
\(505\) 40.3049i 1.79355i
\(506\) 13.1286 + 18.0700i 0.583638 + 0.803309i
\(507\) 0 0
\(508\) 3.70820 11.4127i 0.164525 0.506356i
\(509\) 27.5350 1.22047 0.610233 0.792222i \(-0.291076\pi\)
0.610233 + 0.792222i \(0.291076\pi\)
\(510\) 0 0
\(511\) −55.7771 −2.46743
\(512\) −13.3001 + 18.3060i −0.587785 + 0.809017i
\(513\) 0 0
\(514\) −21.8264 30.0415i −0.962723 1.32507i
\(515\) −4.59506 −0.202482
\(516\) 0 0
\(517\) 21.3723i 0.939951i
\(518\) 12.8149 9.31061i 0.563057 0.409085i
\(519\) 0 0
\(520\) −27.2630 + 3.04596i −1.19556 + 0.133574i
\(521\) 24.8712 1.08963 0.544814 0.838557i \(-0.316600\pi\)
0.544814 + 0.838557i \(0.316600\pi\)
\(522\) 0 0
\(523\) 21.9273i 0.958814i −0.877593 0.479407i \(-0.840852\pi\)
0.877593 0.479407i \(-0.159148\pi\)
\(524\) 16.7573 + 5.44477i 0.732045 + 0.237856i
\(525\) 0 0
\(526\) 6.03268 + 8.30327i 0.263037 + 0.362040i
\(527\) 54.5052i 2.37429i
\(528\) 0 0
\(529\) −9.83282 −0.427514
\(530\) −3.62866 + 2.63638i −0.157619 + 0.114517i
\(531\) 0 0
\(532\) 45.1246 + 14.6619i 1.95640 + 0.635673i
\(533\) −8.06998 + 39.2267i −0.349550 + 1.69910i
\(534\) 0 0
\(535\) 13.4350i 0.580844i
\(536\) 27.1139 8.80982i 1.17114 0.380526i
\(537\) 0 0
\(538\) 22.0232 16.0008i 0.949489 0.689844i
\(539\) −44.5525 −1.91901
\(540\) 0 0
\(541\) −41.3486 −1.77771 −0.888857 0.458184i \(-0.848500\pi\)
−0.888857 + 0.458184i \(0.848500\pi\)
\(542\) −10.6213 + 7.71681i −0.456223 + 0.331465i
\(543\) 0 0
\(544\) 33.2131i 1.42400i
\(545\) −23.4852 −1.00600
\(546\) 0 0
\(547\) 0.212002i 0.00906456i 0.999990 + 0.00453228i \(0.00144267\pi\)
−0.999990 + 0.00453228i \(0.998557\pi\)
\(548\) −19.8574 6.45207i −0.848268 0.275619i
\(549\) 0 0
\(550\) 8.09017 + 11.1352i 0.344966 + 0.474805i
\(551\) 17.6383i 0.751415i
\(552\) 0 0
\(553\) 45.4366i 1.93216i
\(554\) 24.8450 18.0509i 1.05556 0.766910i
\(555\) 0 0
\(556\) 27.2361 + 8.84953i 1.15507 + 0.375304i
\(557\) 3.47492 0.147237 0.0736186 0.997286i \(-0.476545\pi\)
0.0736186 + 0.997286i \(0.476545\pi\)
\(558\) 0 0
\(559\) −2.76393 + 13.4350i −0.116902 + 0.568239i
\(560\) 26.2572 36.1400i 1.10957 1.52719i
\(561\) 0 0
\(562\) 10.7082 7.77997i 0.451698 0.328178i
\(563\) 21.1567i 0.891649i −0.895120 0.445825i \(-0.852910\pi\)
0.895120 0.445825i \(-0.147090\pi\)
\(564\) 0 0
\(565\) −15.7938 −0.664448
\(566\) −14.0850 + 10.2333i −0.592036 + 0.430140i
\(567\) 0 0
\(568\) −1.81966 5.60034i −0.0763512 0.234985i
\(569\) −4.48527 −0.188032 −0.0940162 0.995571i \(-0.529971\pi\)
−0.0940162 + 0.995571i \(0.529971\pi\)
\(570\) 0 0
\(571\) 5.81234i 0.243239i −0.992577 0.121619i \(-0.961191\pi\)
0.992577 0.121619i \(-0.0388087\pi\)
\(572\) 15.5150 27.2835i 0.648713 1.14078i
\(573\) 0 0
\(574\) −38.3323 52.7598i −1.59996 2.20215i
\(575\) 8.11393 0.338374
\(576\) 0 0
\(577\) 14.6464i 0.609738i −0.952394 0.304869i \(-0.901387\pi\)
0.952394 0.304869i \(-0.0986126\pi\)
\(578\) 14.5238 + 19.9903i 0.604110 + 0.831486i
\(579\) 0 0
\(580\) 15.7938 + 5.13170i 0.655800 + 0.213082i
\(581\) 40.4057i 1.67631i
\(582\) 0 0
\(583\) 5.13170i 0.212533i
\(584\) 11.7426 + 36.1400i 0.485912 + 1.49548i
\(585\) 0 0
\(586\) −21.1803 29.1522i −0.874952 1.20427i
\(587\) 25.0875 1.03547 0.517736 0.855540i \(-0.326775\pi\)
0.517736 + 0.855540i \(0.326775\pi\)
\(588\) 0 0
\(589\) 53.0472i 2.18577i
\(590\) −5.13743 7.07107i −0.211505 0.291111i
\(591\) 0 0
\(592\) −8.73057 6.34313i −0.358824 0.260701i
\(593\) 17.1769i 0.705370i −0.935742 0.352685i \(-0.885269\pi\)
0.935742 0.352685i \(-0.114731\pi\)
\(594\) 0 0
\(595\) 65.5699i 2.68810i
\(596\) −0.392465 + 1.20788i −0.0160760 + 0.0494768i
\(597\) 0 0
\(598\) −7.63614 16.8534i −0.312265 0.689186i
\(599\) 27.9705 1.14284 0.571421 0.820657i \(-0.306392\pi\)
0.571421 + 0.820657i \(0.306392\pi\)
\(600\) 0 0
\(601\) −7.41641 −0.302522 −0.151261 0.988494i \(-0.548333\pi\)
−0.151261 + 0.988494i \(0.548333\pi\)
\(602\) −13.1286 18.0700i −0.535083 0.736478i
\(603\) 0 0
\(604\) −7.89688 2.56585i −0.321319 0.104403i
\(605\) −21.3700 −0.868816
\(606\) 0 0
\(607\) 2.29180 0.0930211 0.0465106 0.998918i \(-0.485190\pi\)
0.0465106 + 0.998918i \(0.485190\pi\)
\(608\) 32.3246i 1.31094i
\(609\) 0 0
\(610\) 21.7082 15.7719i 0.878939 0.638587i
\(611\) 3.56757 17.3413i 0.144329 0.701555i
\(612\) 0 0
\(613\) 34.2854 1.38477 0.692387 0.721526i \(-0.256559\pi\)
0.692387 + 0.721526i \(0.256559\pi\)
\(614\) −3.36395 4.63009i −0.135758 0.186855i
\(615\) 0 0
\(616\) 15.7938 + 48.6082i 0.636349 + 1.95848i
\(617\) 6.53089i 0.262924i −0.991321 0.131462i \(-0.958033\pi\)
0.991321 0.131462i \(-0.0419671\pi\)
\(618\) 0 0
\(619\) 32.2996 1.29823 0.649115 0.760691i \(-0.275140\pi\)
0.649115 + 0.760691i \(0.275140\pi\)
\(620\) −47.4998 15.4336i −1.90764 0.619829i
\(621\) 0 0
\(622\) 9.04902 + 12.4549i 0.362833 + 0.499396i
\(623\) 50.5990 2.02721
\(624\) 0 0
\(625\) −31.1803 −1.24721
\(626\) −2.05497 2.82843i −0.0821332 0.113047i
\(627\) 0 0
\(628\) −30.6525 9.95959i −1.22317 0.397431i
\(629\) 15.8401 0.631588
\(630\) 0 0
\(631\) 7.32320i 0.291532i 0.989319 + 0.145766i \(0.0465647\pi\)
−0.989319 + 0.145766i \(0.953435\pi\)
\(632\) −29.4400 + 9.56564i −1.17106 + 0.380501i
\(633\) 0 0
\(634\) −11.8328 16.2865i −0.469941 0.646818i
\(635\) 16.1400 0.640495
\(636\) 0 0
\(637\) 36.1496 + 7.43694i 1.43230 + 0.294662i
\(638\) −15.3713 + 11.1679i −0.608554 + 0.442140i
\(639\) 0 0
\(640\) −28.9443 9.40456i −1.14412 0.371748i
\(641\) −27.6433 −1.09184 −0.545922 0.837836i \(-0.683820\pi\)
−0.545922 + 0.837836i \(0.683820\pi\)
\(642\) 0 0
\(643\) −38.9691 −1.53679 −0.768396 0.639974i \(-0.778945\pi\)
−0.768396 + 0.639974i \(0.778945\pi\)
\(644\) 28.6551 + 9.31061i 1.12917 + 0.366889i
\(645\) 0 0
\(646\) 27.8885 + 38.3853i 1.09726 + 1.51025i
\(647\) −16.2279 −0.637983 −0.318992 0.947758i \(-0.603344\pi\)
−0.318992 + 0.947758i \(0.603344\pi\)
\(648\) 0 0
\(649\) 10.0000 0.392534
\(650\) −4.70557 10.3855i −0.184568 0.407351i
\(651\) 0 0
\(652\) 6.22949 19.1724i 0.243966 0.750849i
\(653\) 37.7694i 1.47803i 0.673689 + 0.739015i \(0.264709\pi\)
−0.673689 + 0.739015i \(0.735291\pi\)
\(654\) 0 0
\(655\) 23.6984i 0.925972i
\(656\) −26.1150 + 35.9442i −1.01962 + 1.40339i
\(657\) 0 0
\(658\) 16.9459 + 23.3240i 0.660620 + 0.909265i
\(659\) 1.45735i 0.0567704i −0.999597 0.0283852i \(-0.990963\pi\)
0.999597 0.0283852i \(-0.00903651\pi\)
\(660\) 0 0
\(661\) 23.4938 0.913804 0.456902 0.889517i \(-0.348959\pi\)
0.456902 + 0.889517i \(0.348959\pi\)
\(662\) 2.50734 + 3.45106i 0.0974507 + 0.134129i
\(663\) 0 0
\(664\) 26.1803 8.50651i 1.01599 0.330117i
\(665\) 63.8158i 2.47467i
\(666\) 0 0
\(667\) 11.2007i 0.433692i
\(668\) −46.2150 15.0162i −1.78811 0.580993i
\(669\) 0 0
\(670\) 22.5385 + 31.0216i 0.870738 + 1.19847i
\(671\) 30.7000i 1.18516i
\(672\) 0 0
\(673\) 18.6525 0.719000 0.359500 0.933145i \(-0.382947\pi\)
0.359500 + 0.933145i \(0.382947\pi\)
\(674\) 12.0300 + 16.5579i 0.463379 + 0.637787i
\(675\) 0 0
\(676\) −17.1430 + 19.5478i −0.659348 + 0.751838i
\(677\) 33.5036i 1.28765i −0.765173 0.643824i \(-0.777347\pi\)
0.765173 0.643824i \(-0.222653\pi\)
\(678\) 0 0
\(679\) −21.3050 −0.817609
\(680\) 42.4851 13.8042i 1.62923 0.529369i
\(681\) 0 0
\(682\) 46.2291 33.5874i 1.77020 1.28613i
\(683\) 25.0875 0.959947 0.479974 0.877283i \(-0.340646\pi\)
0.479974 + 0.877283i \(0.340646\pi\)
\(684\) 0 0
\(685\) 28.0827i 1.07298i
\(686\) −15.3713 + 11.1679i −0.586877 + 0.426391i
\(687\) 0 0
\(688\) −8.94427 + 12.3107i −0.340997 + 0.469342i
\(689\) −0.856611 + 4.16383i −0.0326343 + 0.158629i
\(690\) 0 0
\(691\) −1.34895 −0.0513164 −0.0256582 0.999671i \(-0.508168\pi\)
−0.0256582 + 0.999671i \(0.508168\pi\)
\(692\) 2.24264 + 0.728677i 0.0852522 + 0.0277001i
\(693\) 0 0
\(694\) 32.6180 23.6984i 1.23816 0.899578i
\(695\) 38.5176i 1.46106i
\(696\) 0 0
\(697\) 65.2147i 2.47018i
\(698\) −8.11393 11.1679i −0.307117 0.422710i
\(699\) 0 0
\(700\) 17.6580 + 5.73742i 0.667408 + 0.216854i
\(701\) 5.44477i 0.205646i −0.994700 0.102823i \(-0.967212\pi\)
0.994700 0.102823i \(-0.0327876\pi\)
\(702\) 0 0
\(703\) 15.4164 0.581441
\(704\) 28.1700 20.4667i 1.06170 0.771367i
\(705\) 0 0
\(706\) −9.00000 + 6.53888i −0.338719 + 0.246094i
\(707\) −62.2051 −2.33946
\(708\) 0 0
\(709\) 15.7938 0.593147 0.296573 0.955010i \(-0.404156\pi\)
0.296573 + 0.955010i \(0.404156\pi\)
\(710\) 6.40747 4.65530i 0.240468 0.174710i
\(711\) 0 0
\(712\) −10.6525 32.7849i −0.399218 1.22867i
\(713\) 33.6861i 1.26155i
\(714\) 0 0
\(715\) 41.3486 + 8.50651i 1.54635 + 0.318125i
\(716\) −35.7572 11.6182i −1.33631 0.434193i
\(717\) 0 0
\(718\) 15.0344 10.9232i 0.561080 0.407649i
\(719\) −27.1139 −1.01118 −0.505588 0.862775i \(-0.668724\pi\)
−0.505588 + 0.862775i \(0.668724\pi\)
\(720\) 0 0
\(721\) 7.09184i 0.264114i
\(722\) 11.3487 + 15.6201i 0.422354 + 0.581320i
\(723\) 0 0
\(724\) 25.1246 + 8.16348i 0.933749 + 0.303393i
\(725\) 6.90212i 0.256338i
\(726\) 0 0
\(727\) 22.3607 0.829312 0.414656 0.909978i \(-0.363902\pi\)
0.414656 + 0.909978i \(0.363902\pi\)
\(728\) −4.70102 42.0767i −0.174231 1.55947i
\(729\) 0 0
\(730\) −41.3486 + 30.0415i −1.53038 + 1.11189i
\(731\) 22.3357i 0.826117i
\(732\) 0 0
\(733\) 24.9179 0.920365 0.460183 0.887824i \(-0.347784\pi\)
0.460183 + 0.887824i \(0.347784\pi\)
\(734\) −7.58487 10.4397i −0.279963 0.385335i
\(735\) 0 0
\(736\) 20.5268i 0.756628i
\(737\) −43.8711 −1.61601
\(738\) 0 0
\(739\) −29.6017 −1.08892 −0.544458 0.838788i \(-0.683264\pi\)
−0.544458 + 0.838788i \(0.683264\pi\)
\(740\) 4.48527 13.8042i 0.164882 0.507454i
\(741\) 0 0
\(742\) −4.06888 5.60034i −0.149373 0.205595i
\(743\) 3.31990i 0.121795i 0.998144 + 0.0608977i \(0.0193963\pi\)
−0.998144 + 0.0608977i \(0.980604\pi\)
\(744\) 0 0
\(745\) −1.70820 −0.0625837
\(746\) −0.392465 + 0.285142i −0.0143692 + 0.0104398i
\(747\) 0 0
\(748\) −15.7938 + 48.6082i −0.577477 + 1.77729i
\(749\) 20.7350 0.757641
\(750\) 0 0
\(751\) 12.5410 0.457628 0.228814 0.973470i \(-0.426515\pi\)
0.228814 + 0.973470i \(0.426515\pi\)
\(752\) 11.5449 15.8902i 0.420999 0.579456i
\(753\) 0 0
\(754\) 14.3363 6.49569i 0.522099 0.236559i
\(755\) 11.1679i 0.406440i
\(756\) 0 0
\(757\) 5.25731i 0.191080i −0.995426 0.0955401i \(-0.969542\pi\)
0.995426 0.0955401i \(-0.0304578\pi\)
\(758\) 15.6360 + 21.5211i 0.567924 + 0.781680i
\(759\) 0 0
\(760\) 41.3486 13.4350i 1.49987 0.487338i
\(761\) 13.2681i 0.480968i −0.970653 0.240484i \(-0.922694\pi\)
0.970653 0.240484i \(-0.0773062\pi\)
\(762\) 0 0
\(763\) 36.2461i 1.31220i
\(764\) 9.49996 29.2379i 0.343696 1.05779i
\(765\) 0 0
\(766\) −18.5623 + 13.4863i −0.670683 + 0.487280i
\(767\) −8.11393 1.66925i −0.292977 0.0602732i
\(768\) 0 0
\(769\) 46.6480i 1.68217i −0.540902 0.841086i \(-0.681917\pi\)
0.540902 0.841086i \(-0.318083\pi\)
\(770\) −55.6137 + 40.4057i −2.00418 + 1.45612i
\(771\) 0 0
\(772\) 25.5548 + 8.30327i 0.919739 + 0.298841i
\(773\) −37.0249 −1.33169 −0.665846 0.746089i \(-0.731929\pi\)
−0.665846 + 0.746089i \(0.731929\pi\)
\(774\) 0 0
\(775\) 20.7582i 0.745656i
\(776\) 4.48527 + 13.8042i 0.161012 + 0.495544i
\(777\) 0 0
\(778\) −13.2927 + 9.65769i −0.476565 + 0.346245i
\(779\) 63.4702i 2.27405i
\(780\) 0 0
\(781\) 9.06154i 0.324247i
\(782\) 17.7098 + 24.3755i 0.633302 + 0.871665i
\(783\) 0 0
\(784\) 33.1246 + 24.0664i 1.18302 + 0.859516i
\(785\) 43.3491i 1.54720i
\(786\) 0 0
\(787\) −5.07735 −0.180988 −0.0904940 0.995897i \(-0.528845\pi\)
−0.0904940 + 0.995897i \(0.528845\pi\)
\(788\) 6.55738 20.1815i 0.233597 0.718938i
\(789\) 0 0
\(790\) −24.4721 33.6830i −0.870680 1.19839i
\(791\) 24.3755i