Properties

Label 936.2.m.h.181.5
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 181.5
Root \(0.752864 - 0.902863i\) of defining polynomial
Character \(\chi\) \(=\) 936.181
Dual form 936.2.m.h.181.8

$q$-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 \(-0.294570\pi\)
0.601501 + 0.798872i \(0.294570\pi\)
\(6\) 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 \(-0.727822\pi\)
−0.656164 + 0.754618i \(0.727822\pi\)
\(12\) 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 \(-0.752210\pi\)
−0.711999 + 0.702180i \(0.752210\pi\)
\(18\) 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 \(-0.623496\pi\)
−0.378314 + 0.925677i \(0.623496\pi\)
\(24\) 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 \(-0.907477\pi\)
0.958052 0.286595i \(-0.0925234\pi\)
\(30\) 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 \(0.334172\pi\)
−0.497715 + 0.867340i \(0.665828\pi\)
\(42\) 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 \(-0.883417\pi\)
0.933674 0.358123i \(-0.116583\pi\)
\(48\) 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 \(0.0258036\pi\)
−0.996716 + 0.0809757i \(0.974196\pi\)
\(54\) 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 \(-0.547785\pi\)
−0.149556 + 0.988753i \(0.547785\pi\)
\(60\) 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 \(-0.960576\pi\)
0.992340 0.123539i \(-0.0394244\pi\)
\(72\) 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 \(-0.320636\pi\)
0.534140 + 0.845396i \(0.320636\pi\)
\(84\) 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 \(-0.776462\pi\)
0.763381 0.645949i \(-0.223538\pi\)
\(90\) 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 \(0.267763\pi\)
−0.666566 + 0.745446i \(0.732237\pi\)
\(102\) 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 \(-0.922389\pi\)
0.970422 0.241415i \(-0.0776114\pi\)
\(108\) 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 \(-0.589063\pi\)
−0.276163 + 0.961111i \(0.589063\pi\)
\(114\) 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 \(0.125750\pi\)
−0.922975 + 0.384859i \(0.874250\pi\)
\(132\) 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 \(-0.852862\pi\)
0.895052 0.445961i \(-0.147138\pi\)
\(138\) 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 \(-0.508281\pi\)
−0.0260115 + 0.999662i \(0.508281\pi\)
\(150\) 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 \(-0.610763\pi\)
0.340992 0.940066i \(-0.389237\pi\)
\(168\) 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 \(0.0142714\pi\)
−0.998995 + 0.0448198i \(0.985729\pi\)
\(174\) 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 \(-0.752049\pi\)
0.711645 0.702539i \(-0.247951\pi\)
\(180\) 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 \(-0.312292\pi\)
0.556113 + 0.831107i \(0.312292\pi\)
\(192\) 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 \(-0.376623\pi\)
0.377968 + 0.925819i \(0.376623\pi\)
\(198\) 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 \(-0.510856\pi\)
−0.0340983 + 0.999418i \(0.510856\pi\)
\(228\) 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 \(-0.423599\pi\)
0.237722 + 0.971333i \(0.423599\pi\)
\(234\) 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 \(-0.926554\pi\)
0.973498 0.228695i \(-0.0734457\pi\)
\(240\) 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 \(-0.976290\pi\)
0.997227 0.0744193i \(-0.0237103\pi\)
\(252\) 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 \(-0.194562\pi\)
0.818941 + 0.573878i \(0.194562\pi\)
\(258\) 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 \(-0.571831\pi\)
−0.223753 + 0.974646i \(0.571831\pi\)
\(264\) 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 \(0.199619\pi\)
−0.809720 + 0.586817i \(0.800381\pi\)
\(270\) 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 \(0.0900576\pi\)
−0.960243 + 0.279165i \(0.909942\pi\)
\(282\) 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 \(-0.232794\pi\)
0.744278 + 0.667869i \(0.232794\pi\)
\(294\) 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 \(-0.599875\pi\)
−0.308644 + 0.951178i \(0.599875\pi\)
\(312\) 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 \(-0.369095\pi\)
0.399756 + 0.916622i \(0.369095\pi\)
\(318\) 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 \(0.277373\pi\)
−0.643761 + 0.765227i \(0.722627\pi\)
\(348\) 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 \(-0.932868\pi\)
0.977843 0.209340i \(-0.0671316\pi\)
\(354\) 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 \(0.112720\pi\)
−0.937951 + 0.346767i \(0.887280\pi\)
\(360\) 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 \(-0.863955\pi\)
0.910047 0.414505i \(-0.136045\pi\)
\(384\) 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 \(-0.904836\pi\)
0.955641 0.294534i \(-0.0951643\pi\)
\(390\) 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 \(-0.801931\pi\)
0.812567 0.582868i \(-0.198069\pi\)
\(402\) 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 \(-0.880730\pi\)
0.930619 0.365990i \(-0.119270\pi\)
\(420\) 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 \(-0.832979\pi\)
0.865468 0.500963i \(-0.167021\pi\)
\(432\) 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 \(-0.991083\pi\)
0.999608 0.0280086i \(-0.00891656\pi\)
\(444\) 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 \(-0.712002\pi\)
0.617865 0.786284i \(-0.287998\pi\)
\(450\) 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 \(-0.695030\pi\)
−0.575082 + 0.818096i \(0.695030\pi\)
\(462\) 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 \(0.0456223\pi\)
−0.989746 + 0.142837i \(0.954378\pi\)
\(468\) 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 \(0.0757013\pi\)
−0.971853 + 0.235587i \(0.924299\pi\)
\(480\) 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 \(-0.799091\pi\)
0.807336 0.590092i \(-0.200909\pi\)
\(492\) 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 \(-0.639228\pi\)
−0.423582 + 0.905858i \(0.639228\pi\)
\(504\) 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 \(-0.708924\pi\)
−0.610233 + 0.792222i \(0.708924\pi\)
\(510\) 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 \(-0.683400\pi\)
−0.544814 + 0.838557i \(0.683400\pi\)
\(522\) 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 \(-0.523455\pi\)
−0.0736186 + 0.997286i \(0.523455\pi\)
\(558\) 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 \(0.147090\pi\)
−0.895120 + 0.445825i \(0.852910\pi\)
\(564\) 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 \(-0.470029\pi\)
0.0940162 + 0.995571i \(0.470029\pi\)
\(570\) 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 \(-0.673225\pi\)
−0.517736 + 0.855540i \(0.673225\pi\)
\(588\) 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 \(0.114731\pi\)
−0.935742 + 0.352685i \(0.885269\pi\)
\(594\) 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 \(-0.693608\pi\)
−0.571421 + 0.820657i \(0.693608\pi\)
\(600\) 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 \(0.0419671\pi\)
−0.991321 + 0.131462i \(0.958033\pi\)
\(618\) 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 \(-0.316180\pi\)
0.545922 + 0.837836i \(0.316180\pi\)
\(642\) 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 \(-0.396656\pi\)
0.318992 + 0.947758i \(0.396656\pi\)
\(648\) 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 \(-0.735291\pi\)
0.673689 0.739015i \(-0.264709\pi\)
\(654\) 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 \(0.00903651\pi\)
−0.999597 + 0.0283852i \(0.990963\pi\)
\(660\) 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 \(0.222653\pi\)
−0.765173 + 0.643824i \(0.777347\pi\)
\(678\) 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 \(-0.659354\pi\)
−0.479974 + 0.877283i \(0.659354\pi\)
\(684\) 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 \(0.0327876\pi\)
−0.994700 + 0.102823i \(0.967212\pi\)
\(702\) 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 \(-0.331276\pi\)
0.505588 + 0.862775i \(0.331276\pi\)
\(720\) 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 \(-0.980604\pi\)
0.998144 0.0608977i \(-0.0193963\pi\)
\(744\) 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 \(0.0773062\pi\)
−0.970653 + 0.240484i \(0.922694\pi\)
\(762\) 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 \(-0.268071\pi\)
0.665846 + 0.746089i \(0.268071\pi\)
\(774\) 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