Properties

Label 1148.2.ba.a.113.10
Level $1148$
Weight $2$
Character 1148.113
Analytic conductor $9.167$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1148.ba (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(20\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 113.10
Character \(\chi\) \(=\) 1148.113
Dual form 1148.2.ba.a.701.11

$q$-expansion

\(f(q)\) \(=\) \(q+0.268055i q^{3} +(0.725265 + 2.23214i) q^{5} +(0.587785 + 0.809017i) q^{7} +2.92815 q^{9} +O(q^{10})\) \(q+0.268055i q^{3} +(0.725265 + 2.23214i) q^{5} +(0.587785 + 0.809017i) q^{7} +2.92815 q^{9} +(5.13064 + 1.66705i) q^{11} +(1.29047 - 1.77618i) q^{13} +(-0.598336 + 0.194411i) q^{15} +(-2.13726 - 0.694437i) q^{17} +(0.234325 + 0.322520i) q^{19} +(-0.216861 + 0.157559i) q^{21} +(-4.94523 - 3.59292i) q^{23} +(-0.411339 + 0.298855i) q^{25} +1.58907i q^{27} +(-0.796559 + 0.258818i) q^{29} +(-0.226552 + 0.697256i) q^{31} +(-0.446861 + 1.37530i) q^{33} +(-1.37954 + 1.89877i) q^{35} +(-1.56018 - 4.80173i) q^{37} +(0.476114 + 0.345917i) q^{39} +(5.06679 + 3.91505i) q^{41} +(6.26016 + 4.54827i) q^{43} +(2.12368 + 6.53602i) q^{45} +(-5.50692 + 7.57962i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(0.186148 - 0.572903i) q^{51} +(-0.775030 + 0.251822i) q^{53} +12.6613i q^{55} +(-0.0864533 + 0.0628120i) q^{57} +(0.625846 + 0.454704i) q^{59} +(4.04444 - 2.93846i) q^{61} +(1.72112 + 2.36892i) q^{63} +(4.90061 + 1.59230i) q^{65} +(3.57518 - 1.16165i) q^{67} +(0.963102 - 1.32560i) q^{69} +(0.416251 + 0.135248i) q^{71} -5.48431 q^{73} +(-0.0801097 - 0.110262i) q^{75} +(1.66705 + 5.13064i) q^{77} +5.94695i q^{79} +8.35848 q^{81} -4.84125 q^{83} -5.27430i q^{85} +(-0.0693775 - 0.213522i) q^{87} +(-3.57065 - 4.91458i) q^{89} +2.19548 q^{91} +(-0.186903 - 0.0607285i) q^{93} +(-0.549962 + 0.756958i) q^{95} +(-4.29839 + 1.39663i) q^{97} +(15.0233 + 4.88136i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 4q^{5} - 60q^{9} + O(q^{10}) \) \( 80q - 4q^{5} - 60q^{9} + 10q^{11} + 20q^{15} - 10q^{17} - 30q^{19} - 4q^{21} - 20q^{25} + 2q^{31} + 10q^{33} + 10q^{37} + 36q^{39} - 14q^{41} + 30q^{43} + 44q^{45} - 60q^{47} + 20q^{49} - 32q^{51} + 16q^{57} - 60q^{59} + 44q^{61} - 10q^{65} - 10q^{67} - 40q^{71} - 88q^{73} - 70q^{75} - 8q^{77} - 40q^{81} + 28q^{83} - 24q^{87} + 24q^{91} - 100q^{93} + 120q^{97} - 100q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times\).

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{7}{10}\right)\)

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 0
\(3\) 0.268055i 0.154762i 0.997002 + 0.0773809i \(0.0246558\pi\)
−0.997002 + 0.0773809i \(0.975344\pi\)
\(4\) 0 0
\(5\) 0.725265 + 2.23214i 0.324348 + 0.998242i 0.971734 + 0.236079i \(0.0758624\pi\)
−0.647385 + 0.762163i \(0.724138\pi\)
\(6\) 0 0
\(7\) 0.587785 + 0.809017i 0.222162 + 0.305780i
\(8\) 0 0
\(9\) 2.92815 0.976049
\(10\) 0 0
\(11\) 5.13064 + 1.66705i 1.54695 + 0.502633i 0.953283 0.302080i \(-0.0976808\pi\)
0.593664 + 0.804713i \(0.297681\pi\)
\(12\) 0 0
\(13\) 1.29047 1.77618i 0.357912 0.492623i −0.591654 0.806192i \(-0.701525\pi\)
0.949565 + 0.313569i \(0.101525\pi\)
\(14\) 0 0
\(15\) −0.598336 + 0.194411i −0.154490 + 0.0501967i
\(16\) 0 0
\(17\) −2.13726 0.694437i −0.518361 0.168426i 0.0381402 0.999272i \(-0.487857\pi\)
−0.556501 + 0.830847i \(0.687857\pi\)
\(18\) 0 0
\(19\) 0.234325 + 0.322520i 0.0537578 + 0.0739913i 0.835050 0.550175i \(-0.185439\pi\)
−0.781292 + 0.624166i \(0.785439\pi\)
\(20\) 0 0
\(21\) −0.216861 + 0.157559i −0.0473230 + 0.0343822i
\(22\) 0 0
\(23\) −4.94523 3.59292i −1.03115 0.749176i −0.0626134 0.998038i \(-0.519943\pi\)
−0.968539 + 0.248862i \(0.919943\pi\)
\(24\) 0 0
\(25\) −0.411339 + 0.298855i −0.0822677 + 0.0597710i
\(26\) 0 0
\(27\) 1.58907i 0.305817i
\(28\) 0 0
\(29\) −0.796559 + 0.258818i −0.147917 + 0.0480612i −0.382040 0.924146i \(-0.624778\pi\)
0.234123 + 0.972207i \(0.424778\pi\)
\(30\) 0 0
\(31\) −0.226552 + 0.697256i −0.0406900 + 0.125231i −0.969338 0.245731i \(-0.920972\pi\)
0.928648 + 0.370962i \(0.120972\pi\)
\(32\) 0 0
\(33\) −0.446861 + 1.37530i −0.0777885 + 0.239408i
\(34\) 0 0
\(35\) −1.37954 + 1.89877i −0.233184 + 0.320950i
\(36\) 0 0
\(37\) −1.56018 4.80173i −0.256491 0.789400i −0.993532 0.113551i \(-0.963777\pi\)
0.737041 0.675848i \(-0.236223\pi\)
\(38\) 0 0
\(39\) 0.476114 + 0.345917i 0.0762393 + 0.0553911i
\(40\) 0 0
\(41\) 5.06679 + 3.91505i 0.791300 + 0.611428i
\(42\) 0 0
\(43\) 6.26016 + 4.54827i 0.954665 + 0.693605i 0.951906 0.306391i \(-0.0991217\pi\)
0.00275940 + 0.999996i \(0.499122\pi\)
\(44\) 0 0
\(45\) 2.12368 + 6.53602i 0.316580 + 0.974333i
\(46\) 0 0
\(47\) −5.50692 + 7.57962i −0.803267 + 1.10560i 0.189061 + 0.981965i \(0.439456\pi\)
−0.992328 + 0.123636i \(0.960544\pi\)
\(48\) 0 0
\(49\) −0.309017 + 0.951057i −0.0441453 + 0.135865i
\(50\) 0 0
\(51\) 0.186148 0.572903i 0.0260659 0.0802225i
\(52\) 0 0
\(53\) −0.775030 + 0.251822i −0.106459 + 0.0345905i −0.361762 0.932271i \(-0.617825\pi\)
0.255303 + 0.966861i \(0.417825\pi\)
\(54\) 0 0
\(55\) 12.6613i 1.70726i
\(56\) 0 0
\(57\) −0.0864533 + 0.0628120i −0.0114510 + 0.00831965i
\(58\) 0 0
\(59\) 0.625846 + 0.454704i 0.0814782 + 0.0591974i 0.627779 0.778392i \(-0.283964\pi\)
−0.546300 + 0.837589i \(0.683964\pi\)
\(60\) 0 0
\(61\) 4.04444 2.93846i 0.517837 0.376231i −0.297951 0.954581i \(-0.596303\pi\)
0.815788 + 0.578350i \(0.196303\pi\)
\(62\) 0 0
\(63\) 1.72112 + 2.36892i 0.216841 + 0.298456i
\(64\) 0 0
\(65\) 4.90061 + 1.59230i 0.607845 + 0.197501i
\(66\) 0 0
\(67\) 3.57518 1.16165i 0.436777 0.141918i −0.0823709 0.996602i \(-0.526249\pi\)
0.519148 + 0.854684i \(0.326249\pi\)
\(68\) 0 0
\(69\) 0.963102 1.32560i 0.115944 0.159583i
\(70\) 0 0
\(71\) 0.416251 + 0.135248i 0.0493999 + 0.0160510i 0.333613 0.942710i \(-0.391732\pi\)
−0.284213 + 0.958761i \(0.591732\pi\)
\(72\) 0 0
\(73\) −5.48431 −0.641890 −0.320945 0.947098i \(-0.604000\pi\)
−0.320945 + 0.947098i \(0.604000\pi\)
\(74\) 0 0
\(75\) −0.0801097 0.110262i −0.00925027 0.0127319i
\(76\) 0 0
\(77\) 1.66705 + 5.13064i 0.189978 + 0.584691i
\(78\) 0 0
\(79\) 5.94695i 0.669084i 0.942381 + 0.334542i \(0.108582\pi\)
−0.942381 + 0.334542i \(0.891418\pi\)
\(80\) 0 0
\(81\) 8.35848 0.928720
\(82\) 0 0
\(83\) −4.84125 −0.531396 −0.265698 0.964056i \(-0.585602\pi\)
−0.265698 + 0.964056i \(0.585602\pi\)
\(84\) 0 0
\(85\) 5.27430i 0.572078i
\(86\) 0 0
\(87\) −0.0693775 0.213522i −0.00743805 0.0228920i
\(88\) 0 0
\(89\) −3.57065 4.91458i −0.378488 0.520944i 0.576695 0.816959i \(-0.304342\pi\)
−0.955183 + 0.296015i \(0.904342\pi\)
\(90\) 0 0
\(91\) 2.19548 0.230149
\(92\) 0 0
\(93\) −0.186903 0.0607285i −0.0193809 0.00629725i
\(94\) 0 0
\(95\) −0.549962 + 0.756958i −0.0564249 + 0.0776622i
\(96\) 0 0
\(97\) −4.29839 + 1.39663i −0.436435 + 0.141806i −0.518990 0.854780i \(-0.673692\pi\)
0.0825551 + 0.996586i \(0.473692\pi\)
\(98\) 0 0
\(99\) 15.0233 + 4.88136i 1.50990 + 0.490595i
\(100\) 0 0
\(101\) −8.09357 11.1398i −0.805340 1.10846i −0.992026 0.126036i \(-0.959774\pi\)
0.186685 0.982420i \(-0.440226\pi\)
\(102\) 0 0
\(103\) −3.50643 + 2.54757i −0.345499 + 0.251020i −0.746978 0.664848i \(-0.768496\pi\)
0.401479 + 0.915868i \(0.368496\pi\)
\(104\) 0 0
\(105\) −0.508975 0.369792i −0.0496709 0.0360880i
\(106\) 0 0
\(107\) −14.3514 + 10.4269i −1.38741 + 1.00801i −0.391262 + 0.920279i \(0.627962\pi\)
−0.996144 + 0.0877308i \(0.972038\pi\)
\(108\) 0 0
\(109\) 11.0446i 1.05789i −0.848658 0.528943i \(-0.822589\pi\)
0.848658 0.528943i \(-0.177411\pi\)
\(110\) 0 0
\(111\) 1.28713 0.418214i 0.122169 0.0396951i
\(112\) 0 0
\(113\) 4.76483 14.6646i 0.448237 1.37953i −0.430657 0.902516i \(-0.641718\pi\)
0.878894 0.477017i \(-0.158282\pi\)
\(114\) 0 0
\(115\) 4.43329 13.6443i 0.413406 1.27233i
\(116\) 0 0
\(117\) 3.77868 5.20091i 0.349339 0.480825i
\(118\) 0 0
\(119\) −0.694437 2.13726i −0.0636590 0.195922i
\(120\) 0 0
\(121\) 14.6453 + 10.6404i 1.33139 + 0.967309i
\(122\) 0 0
\(123\) −1.04945 + 1.35818i −0.0946257 + 0.122463i
\(124\) 0 0
\(125\) 8.52843 + 6.19627i 0.762806 + 0.554211i
\(126\) 0 0
\(127\) −4.96524 15.2814i −0.440593 1.35601i −0.887245 0.461299i \(-0.847384\pi\)
0.446651 0.894708i \(-0.352616\pi\)
\(128\) 0 0
\(129\) −1.21919 + 1.67807i −0.107344 + 0.147746i
\(130\) 0 0
\(131\) −4.48979 + 13.8182i −0.392275 + 1.20730i 0.538788 + 0.842441i \(0.318882\pi\)
−0.931063 + 0.364857i \(0.881118\pi\)
\(132\) 0 0
\(133\) −0.123192 + 0.379146i −0.0106821 + 0.0328761i
\(134\) 0 0
\(135\) −3.54702 + 1.15250i −0.305279 + 0.0991912i
\(136\) 0 0
\(137\) 20.9508i 1.78995i 0.446115 + 0.894975i \(0.352807\pi\)
−0.446115 + 0.894975i \(0.647193\pi\)
\(138\) 0 0
\(139\) −5.65109 + 4.10576i −0.479320 + 0.348246i −0.801062 0.598581i \(-0.795731\pi\)
0.321743 + 0.946827i \(0.395731\pi\)
\(140\) 0 0
\(141\) −2.03176 1.47616i −0.171105 0.124315i
\(142\) 0 0
\(143\) 9.58191 6.96167i 0.801280 0.582164i
\(144\) 0 0
\(145\) −1.15543 1.59032i −0.0959535 0.132069i
\(146\) 0 0
\(147\) −0.254936 0.0828336i −0.0210267 0.00683200i
\(148\) 0 0
\(149\) 7.39980 2.40434i 0.606216 0.196971i 0.0102050 0.999948i \(-0.496752\pi\)
0.596011 + 0.802977i \(0.296752\pi\)
\(150\) 0 0
\(151\) 4.68258 6.44502i 0.381063 0.524489i −0.574803 0.818292i \(-0.694921\pi\)
0.955866 + 0.293804i \(0.0949212\pi\)
\(152\) 0 0
\(153\) −6.25820 2.03341i −0.505946 0.164392i
\(154\) 0 0
\(155\) −1.72068 −0.138208
\(156\) 0 0
\(157\) −5.64994 7.77648i −0.450914 0.620630i 0.521679 0.853142i \(-0.325306\pi\)
−0.972594 + 0.232511i \(0.925306\pi\)
\(158\) 0 0
\(159\) −0.0675024 0.207751i −0.00535328 0.0164757i
\(160\) 0 0
\(161\) 6.11264i 0.481744i
\(162\) 0 0
\(163\) −10.3496 −0.810646 −0.405323 0.914174i \(-0.632841\pi\)
−0.405323 + 0.914174i \(0.632841\pi\)
\(164\) 0 0
\(165\) −3.39394 −0.264218
\(166\) 0 0
\(167\) 4.73356i 0.366294i 0.983086 + 0.183147i \(0.0586284\pi\)
−0.983086 + 0.183147i \(0.941372\pi\)
\(168\) 0 0
\(169\) 2.52772 + 7.77952i 0.194440 + 0.598425i
\(170\) 0 0
\(171\) 0.686137 + 0.944387i 0.0524702 + 0.0722191i
\(172\) 0 0
\(173\) 7.05189 0.536145 0.268073 0.963399i \(-0.413613\pi\)
0.268073 + 0.963399i \(0.413613\pi\)
\(174\) 0 0
\(175\) −0.483558 0.157117i −0.0365535 0.0118770i
\(176\) 0 0
\(177\) −0.121886 + 0.167761i −0.00916150 + 0.0126097i
\(178\) 0 0
\(179\) −5.99974 + 1.94943i −0.448441 + 0.145707i −0.524527 0.851394i \(-0.675758\pi\)
0.0760856 + 0.997101i \(0.475758\pi\)
\(180\) 0 0
\(181\) −5.70107 1.85239i −0.423757 0.137687i 0.0893722 0.995998i \(-0.471514\pi\)
−0.513129 + 0.858311i \(0.671514\pi\)
\(182\) 0 0
\(183\) 0.787669 + 1.08413i 0.0582261 + 0.0801414i
\(184\) 0 0
\(185\) 9.58657 6.96505i 0.704819 0.512081i
\(186\) 0 0
\(187\) −9.80785 7.12582i −0.717221 0.521091i
\(188\) 0 0
\(189\) −1.28559 + 0.934033i −0.0935126 + 0.0679409i
\(190\) 0 0
\(191\) 5.58946i 0.404439i 0.979340 + 0.202219i \(0.0648154\pi\)
−0.979340 + 0.202219i \(0.935185\pi\)
\(192\) 0 0
\(193\) 5.35051 1.73849i 0.385138 0.125139i −0.110047 0.993926i \(-0.535100\pi\)
0.495185 + 0.868787i \(0.335100\pi\)
\(194\) 0 0
\(195\) −0.426825 + 1.31363i −0.0305656 + 0.0940713i
\(196\) 0 0
\(197\) 5.63619 17.3464i 0.401562 1.23588i −0.522170 0.852841i \(-0.674877\pi\)
0.923732 0.383039i \(-0.125123\pi\)
\(198\) 0 0
\(199\) 7.38976 10.1711i 0.523846 0.721013i −0.462331 0.886708i \(-0.652987\pi\)
0.986177 + 0.165695i \(0.0529867\pi\)
\(200\) 0 0
\(201\) 0.311385 + 0.958345i 0.0219634 + 0.0675965i
\(202\) 0 0
\(203\) −0.677594 0.492301i −0.0475578 0.0345527i
\(204\) 0 0
\(205\) −5.06415 + 14.1492i −0.353696 + 0.988225i
\(206\) 0 0
\(207\) −14.4804 10.5206i −1.00646 0.731232i
\(208\) 0 0
\(209\) 0.664580 + 2.04537i 0.0459700 + 0.141481i
\(210\) 0 0
\(211\) 7.36629 10.1388i 0.507116 0.697986i −0.476313 0.879276i \(-0.658027\pi\)
0.983430 + 0.181290i \(0.0580272\pi\)
\(212\) 0 0
\(213\) −0.0362540 + 0.111578i −0.00248408 + 0.00764523i
\(214\) 0 0
\(215\) −5.61209 + 17.2722i −0.382741 + 1.17796i
\(216\) 0 0
\(217\) −0.697256 + 0.226552i −0.0473328 + 0.0153794i
\(218\) 0 0
\(219\) 1.47010i 0.0993400i
\(220\) 0 0
\(221\) −3.99151 + 2.90000i −0.268498 + 0.195075i
\(222\) 0 0
\(223\) −16.5571 12.0294i −1.10874 0.805548i −0.126277 0.991995i \(-0.540303\pi\)
−0.982465 + 0.186447i \(0.940303\pi\)
\(224\) 0 0
\(225\) −1.20446 + 0.875091i −0.0802973 + 0.0583394i
\(226\) 0 0
\(227\) −14.8844 20.4866i −0.987913 1.35974i −0.932456 0.361284i \(-0.882339\pi\)
−0.0554567 0.998461i \(-0.517661\pi\)
\(228\) 0 0
\(229\) −16.1772 5.25628i −1.06902 0.347345i −0.278912 0.960317i \(-0.589974\pi\)
−0.790105 + 0.612972i \(0.789974\pi\)
\(230\) 0 0
\(231\) −1.37530 + 0.446861i −0.0904878 + 0.0294013i
\(232\) 0 0
\(233\) −2.05700 + 2.83121i −0.134758 + 0.185479i −0.871063 0.491171i \(-0.836569\pi\)
0.736305 + 0.676650i \(0.236569\pi\)
\(234\) 0 0
\(235\) −20.9127 6.79496i −1.36420 0.443254i
\(236\) 0 0
\(237\) −1.59411 −0.103549
\(238\) 0 0
\(239\) −11.5349 15.8765i −0.746133 1.02696i −0.998242 0.0592652i \(-0.981124\pi\)
0.252109 0.967699i \(-0.418876\pi\)
\(240\) 0 0
\(241\) −1.93700 5.96147i −0.124773 0.384012i 0.869087 0.494660i \(-0.164707\pi\)
−0.993860 + 0.110648i \(0.964707\pi\)
\(242\) 0 0
\(243\) 7.00775i 0.449547i
\(244\) 0 0
\(245\) −2.34701 −0.149945
\(246\) 0 0
\(247\) 0.875243 0.0556904
\(248\) 0 0
\(249\) 1.29772i 0.0822399i
\(250\) 0 0
\(251\) 3.06229 + 9.42475i 0.193290 + 0.594885i 0.999992 + 0.00392715i \(0.00125005\pi\)
−0.806702 + 0.590958i \(0.798750\pi\)
\(252\) 0 0
\(253\) −19.3827 26.6779i −1.21858 1.67723i
\(254\) 0 0
\(255\) 1.41380 0.0885359
\(256\) 0 0
\(257\) 20.2916 + 6.59315i 1.26576 + 0.411269i 0.863542 0.504277i \(-0.168241\pi\)
0.402214 + 0.915546i \(0.368241\pi\)
\(258\) 0 0
\(259\) 2.96763 4.08460i 0.184400 0.253804i
\(260\) 0 0
\(261\) −2.33244 + 0.757856i −0.144375 + 0.0469101i
\(262\) 0 0
\(263\) 18.6774 + 6.06864i 1.15170 + 0.374209i 0.821782 0.569802i \(-0.192980\pi\)
0.329914 + 0.944011i \(0.392980\pi\)
\(264\) 0 0
\(265\) −1.12420 1.54733i −0.0690593 0.0950520i
\(266\) 0 0
\(267\) 1.31738 0.957132i 0.0806223 0.0585755i
\(268\) 0 0
\(269\) 5.01337 + 3.64243i 0.305671 + 0.222083i 0.730037 0.683408i \(-0.239503\pi\)
−0.424366 + 0.905491i \(0.639503\pi\)
\(270\) 0 0
\(271\) −17.4513 + 12.6791i −1.06009 + 0.770202i −0.974105 0.226095i \(-0.927404\pi\)
−0.0859862 + 0.996296i \(0.527404\pi\)
\(272\) 0 0
\(273\) 0.588510i 0.0356182i
\(274\) 0 0
\(275\) −2.60864 + 0.847597i −0.157307 + 0.0511120i
\(276\) 0 0
\(277\) 8.63130 26.5644i 0.518604 1.59610i −0.258022 0.966139i \(-0.583071\pi\)
0.776627 0.629961i \(-0.216929\pi\)
\(278\) 0 0
\(279\) −0.663378 + 2.04167i −0.0397154 + 0.122231i
\(280\) 0 0
\(281\) 16.7505 23.0551i 0.999250 1.37535i 0.0734655 0.997298i \(-0.476594\pi\)
0.925784 0.378052i \(-0.123406\pi\)
\(282\) 0 0
\(283\) 4.28398 + 13.1847i 0.254656 + 0.783751i 0.993897 + 0.110310i \(0.0351844\pi\)
−0.739241 + 0.673441i \(0.764816\pi\)
\(284\) 0 0
\(285\) −0.202907 0.147420i −0.0120191 0.00873242i
\(286\) 0 0
\(287\) −0.189155 + 6.40033i −0.0111654 + 0.377800i
\(288\) 0 0
\(289\) −9.66766 7.02397i −0.568686 0.413174i
\(290\) 0 0
\(291\) −0.374374 1.15221i −0.0219462 0.0675435i
\(292\) 0 0
\(293\) 5.88596 8.10133i 0.343861 0.473285i −0.601703 0.798720i \(-0.705511\pi\)
0.945564 + 0.325435i \(0.105511\pi\)
\(294\) 0 0
\(295\) −0.561057 + 1.72675i −0.0326660 + 0.100536i
\(296\) 0 0
\(297\) −2.64906 + 8.15295i −0.153714 + 0.473082i
\(298\) 0 0
\(299\) −12.7633 + 4.14706i −0.738123 + 0.239831i
\(300\) 0 0
\(301\) 7.73798i 0.446010i
\(302\) 0 0
\(303\) 2.98609 2.16952i 0.171547 0.124636i
\(304\) 0 0
\(305\) 9.49232 + 6.89658i 0.543529 + 0.394897i
\(306\) 0 0
\(307\) 5.91481 4.29736i 0.337576 0.245263i −0.406062 0.913845i \(-0.633098\pi\)
0.743638 + 0.668582i \(0.233098\pi\)
\(308\) 0 0
\(309\) −0.682891 0.939918i −0.0388483 0.0534701i
\(310\) 0 0
\(311\) 26.1389 + 8.49305i 1.48220 + 0.481597i 0.934770 0.355253i \(-0.115605\pi\)
0.547432 + 0.836850i \(0.315605\pi\)
\(312\) 0 0
\(313\) 2.85284 0.926943i 0.161252 0.0523939i −0.227279 0.973830i \(-0.572983\pi\)
0.388531 + 0.921436i \(0.372983\pi\)
\(314\) 0 0
\(315\) −4.03948 + 5.55987i −0.227599 + 0.313263i
\(316\) 0 0
\(317\) 5.59992 + 1.81952i 0.314523 + 0.102195i 0.462025 0.886867i \(-0.347123\pi\)
−0.147502 + 0.989062i \(0.547123\pi\)
\(318\) 0 0
\(319\) −4.51832 −0.252977
\(320\) 0 0
\(321\) −2.79500 3.84698i −0.156001 0.214718i
\(322\) 0 0
\(323\) −0.276842 0.852033i −0.0154039 0.0474084i
\(324\) 0 0
\(325\) 1.11627i 0.0619198i
\(326\) 0 0
\(327\) 2.96058 0.163720
\(328\) 0 0
\(329\) −9.36893 −0.516526
\(330\) 0 0
\(331\) 23.6626i 1.30062i −0.759670 0.650308i \(-0.774640\pi\)
0.759670 0.650308i \(-0.225360\pi\)
\(332\) 0 0
\(333\) −4.56843 14.0602i −0.250348 0.770492i
\(334\) 0 0
\(335\) 5.18590 + 7.13778i 0.283336 + 0.389979i
\(336\) 0 0
\(337\) −11.4217 −0.622181 −0.311090 0.950380i \(-0.600694\pi\)
−0.311090 + 0.950380i \(0.600694\pi\)
\(338\) 0 0
\(339\) 3.93093 + 1.27724i 0.213499 + 0.0693700i
\(340\) 0 0
\(341\) −2.32471 + 3.19970i −0.125890 + 0.173273i
\(342\) 0 0
\(343\) −0.951057 + 0.309017i −0.0513522 + 0.0166853i
\(344\) 0 0
\(345\) 3.65742 + 1.18837i 0.196909 + 0.0639795i
\(346\) 0 0
\(347\) −9.10033 12.5255i −0.488531 0.672406i 0.491585 0.870830i \(-0.336418\pi\)
−0.980116 + 0.198424i \(0.936418\pi\)
\(348\) 0 0
\(349\) 0.727151 0.528306i 0.0389235 0.0282796i −0.568153 0.822923i \(-0.692342\pi\)
0.607077 + 0.794643i \(0.292342\pi\)
\(350\) 0 0
\(351\) 2.82247 + 2.05065i 0.150653 + 0.109455i
\(352\) 0 0
\(353\) 8.98026 6.52454i 0.477971 0.347266i −0.322569 0.946546i \(-0.604546\pi\)
0.800540 + 0.599280i \(0.204546\pi\)
\(354\) 0 0
\(355\) 1.02722i 0.0545192i
\(356\) 0 0
\(357\) 0.572903 0.186148i 0.0303213 0.00985198i
\(358\) 0 0
\(359\) −1.58197 + 4.86879i −0.0834929 + 0.256965i −0.984084 0.177702i \(-0.943134\pi\)
0.900591 + 0.434667i \(0.143134\pi\)
\(360\) 0 0
\(361\) 5.82221 17.9189i 0.306432 0.943101i
\(362\) 0 0
\(363\) −2.85222 + 3.92574i −0.149702 + 0.206048i
\(364\) 0 0
\(365\) −3.97758 12.2417i −0.208196 0.640761i
\(366\) 0 0
\(367\) 6.06146 + 4.40391i 0.316405 + 0.229882i 0.734640 0.678457i \(-0.237351\pi\)
−0.418235 + 0.908339i \(0.637351\pi\)
\(368\) 0 0
\(369\) 14.8363 + 11.4638i 0.772348 + 0.596783i
\(370\) 0 0
\(371\) −0.659280 0.478995i −0.0342281 0.0248682i
\(372\) 0 0
\(373\) −4.79750 14.7652i −0.248405 0.764512i −0.995058 0.0992981i \(-0.968340\pi\)
0.746653 0.665214i \(-0.231660\pi\)
\(374\) 0 0
\(375\) −1.66094 + 2.28609i −0.0857707 + 0.118053i
\(376\) 0 0
\(377\) −0.568229 + 1.74883i −0.0292653 + 0.0900692i
\(378\) 0 0
\(379\) 3.29566 10.1430i 0.169286 0.521010i −0.830040 0.557704i \(-0.811683\pi\)
0.999327 + 0.0366936i \(0.0116825\pi\)
\(380\) 0 0
\(381\) 4.09627 1.33096i 0.209858 0.0681870i
\(382\) 0 0
\(383\) 19.4885i 0.995817i 0.867230 + 0.497908i \(0.165898\pi\)
−0.867230 + 0.497908i \(0.834102\pi\)
\(384\) 0 0
\(385\) −10.2432 + 7.44215i −0.522044 + 0.379287i
\(386\) 0 0
\(387\) 18.3307 + 13.3180i 0.931800 + 0.676992i
\(388\) 0 0
\(389\) −17.2827 + 12.5566i −0.876266 + 0.636645i −0.932261 0.361786i \(-0.882167\pi\)
0.0559947 + 0.998431i \(0.482167\pi\)
\(390\) 0 0
\(391\) 8.07418 + 11.1132i 0.408329 + 0.562016i
\(392\) 0 0
\(393\) −3.70403 1.20351i −0.186844 0.0607092i
\(394\) 0 0
\(395\) −13.2744 + 4.31311i −0.667907 + 0.217016i
\(396\) 0 0
\(397\) 0.643695 0.885970i 0.0323061 0.0444656i −0.792558 0.609796i \(-0.791251\pi\)
0.824865 + 0.565330i \(0.191251\pi\)
\(398\) 0 0
\(399\) −0.101632 0.0330222i −0.00508796 0.00165318i
\(400\) 0 0
\(401\) −3.31994 −0.165790 −0.0828949 0.996558i \(-0.526417\pi\)
−0.0828949 + 0.996558i \(0.526417\pi\)
\(402\) 0 0
\(403\) 0.946092 + 1.30218i 0.0471282 + 0.0648664i
\(404\) 0 0
\(405\) 6.06211 + 18.6573i 0.301229 + 0.927087i
\(406\) 0 0
\(407\) 27.2368i 1.35008i
\(408\) 0 0
\(409\) 15.3385 0.758438 0.379219 0.925307i \(-0.376193\pi\)
0.379219 + 0.925307i \(0.376193\pi\)
\(410\) 0 0
\(411\) −5.61598 −0.277016
\(412\) 0 0
\(413\) 0.773588i 0.0380658i
\(414\) 0 0
\(415\) −3.51119 10.8063i −0.172358 0.530462i
\(416\) 0 0
\(417\) −1.10057 1.51481i −0.0538952 0.0741804i
\(418\) 0 0
\(419\) −34.3488 −1.67805 −0.839026 0.544092i \(-0.816874\pi\)
−0.839026 + 0.544092i \(0.816874\pi\)
\(420\) 0 0
\(421\) 10.9075 + 3.54407i 0.531601 + 0.172728i 0.562504 0.826795i \(-0.309838\pi\)
−0.0309027 + 0.999522i \(0.509838\pi\)
\(422\) 0 0
\(423\) −16.1251 + 22.1942i −0.784027 + 1.07912i
\(424\) 0 0
\(425\) 1.08667 0.353081i 0.0527114 0.0171270i
\(426\) 0 0
\(427\) 4.75452 + 1.54484i 0.230087 + 0.0747599i
\(428\) 0 0
\(429\) 1.86611 + 2.56848i 0.0900967 + 0.124007i
\(430\) 0 0
\(431\) −4.06821 + 2.95573i −0.195959 + 0.142373i −0.681438 0.731876i \(-0.738645\pi\)
0.485479 + 0.874248i \(0.338645\pi\)
\(432\) 0 0
\(433\) −26.9426 19.5749i −1.29478 0.940712i −0.294889 0.955532i \(-0.595283\pi\)
−0.999890 + 0.0148196i \(0.995283\pi\)
\(434\) 0 0
\(435\) 0.426293 0.309720i 0.0204392 0.0148499i
\(436\) 0 0
\(437\) 2.43685i 0.116570i
\(438\) 0 0
\(439\) 10.1951 3.31258i 0.486584 0.158101i −0.0554430 0.998462i \(-0.517657\pi\)
0.542027 + 0.840361i \(0.317657\pi\)
\(440\) 0 0
\(441\) −0.904847 + 2.78483i −0.0430880 + 0.132611i
\(442\) 0 0
\(443\) 2.60957 8.03143i 0.123984 0.381585i −0.869730 0.493527i \(-0.835707\pi\)
0.993715 + 0.111943i \(0.0357073\pi\)
\(444\) 0 0
\(445\) 8.38034 11.5345i 0.397266 0.546790i
\(446\) 0 0
\(447\) 0.644497 + 1.98356i 0.0304837 + 0.0938190i
\(448\) 0 0
\(449\) 8.30924 + 6.03702i 0.392137 + 0.284904i 0.766331 0.642446i \(-0.222080\pi\)
−0.374193 + 0.927351i \(0.622080\pi\)
\(450\) 0 0
\(451\) 19.4693 + 28.5333i 0.916775 + 1.34358i
\(452\) 0 0
\(453\) 1.72762 + 1.25519i 0.0811708 + 0.0589740i
\(454\) 0 0
\(455\) 1.59230 + 4.90061i 0.0746483 + 0.229744i
\(456\) 0 0
\(457\) −14.6659 + 20.1859i −0.686041 + 0.944254i −0.999987 0.00518651i \(-0.998349\pi\)
0.313946 + 0.949441i \(0.398349\pi\)
\(458\) 0 0
\(459\) 1.10351 3.39626i 0.0515074 0.158524i
\(460\) 0 0
\(461\) −2.83030 + 8.71077i −0.131820 + 0.405701i −0.995082 0.0990557i \(-0.968418\pi\)
0.863262 + 0.504757i \(0.168418\pi\)
\(462\) 0 0
\(463\) 1.53349 0.498261i 0.0712673 0.0231561i −0.273166 0.961967i \(-0.588071\pi\)
0.344434 + 0.938811i \(0.388071\pi\)
\(464\) 0 0
\(465\) 0.461237i 0.0213894i
\(466\) 0 0
\(467\) 22.1091 16.0632i 1.02309 0.743315i 0.0561720 0.998421i \(-0.482110\pi\)
0.966913 + 0.255106i \(0.0821105\pi\)
\(468\) 0 0
\(469\) 3.04123 + 2.20958i 0.140431 + 0.102029i
\(470\) 0 0
\(471\) 2.08453 1.51450i 0.0960499 0.0697843i
\(472\) 0 0
\(473\) 24.5364 + 33.7715i 1.12819 + 1.55282i
\(474\) 0 0
\(475\) −0.192774 0.0626360i −0.00884506 0.00287394i
\(476\) 0 0
\(477\) −2.26940 + 0.737373i −0.103909 + 0.0337620i
\(478\) 0 0
\(479\) 4.84871 6.67368i 0.221543 0.304928i −0.683749 0.729717i \(-0.739652\pi\)
0.905292 + 0.424789i \(0.139652\pi\)
\(480\) 0 0
\(481\) −10.5421 3.42533i −0.480678 0.156182i
\(482\) 0 0
\(483\) 1.63853 0.0745555
\(484\) 0 0
\(485\) −6.23494 8.58166i −0.283114 0.389673i
\(486\) 0 0
\(487\) −8.59539 26.4539i −0.389494 1.19874i −0.933167 0.359443i \(-0.882967\pi\)
0.543673 0.839297i \(-0.317033\pi\)
\(488\) 0 0
\(489\) 2.77427i 0.125457i
\(490\) 0 0
\(491\) −4.08168 −0.184204 −0.0921018 0.995750i \(-0.529359\pi\)
−0.0921018 + 0.995750i \(0.529359\pi\)
\(492\) 0 0
\(493\) 1.88219 0.0847694
\(494\) 0 0
\(495\) 37.0743i 1.66636i
\(496\) 0 0
\(497\) 0.135248 + 0.416251i 0.00606671 + 0.0186714i
\(498\) 0 0
\(499\) 23.0488 + 31.7240i 1.03181 + 1.42016i 0.903582 + 0.428414i \(0.140928\pi\)
0.128224 + 0.991745i \(0.459072\pi\)
\(500\) 0 0
\(501\) −1.26886 −0.0566883
\(502\) 0 0
\(503\) 36.0120 + 11.7010i 1.60570 + 0.521723i 0.968507 0.248985i \(-0.0800969\pi\)
0.637189 + 0.770707i \(0.280097\pi\)
\(504\) 0 0
\(505\) 18.9957 26.1453i 0.845296 1.16345i
\(506\) 0 0
\(507\) −2.08534 + 0.677569i −0.0926133 + 0.0300919i
\(508\) 0 0
\(509\) −34.7148 11.2795i −1.53871 0.499956i −0.587688 0.809088i \(-0.699962\pi\)
−0.951019 + 0.309132i \(0.899962\pi\)
\(510\) 0 0
\(511\) −3.22359 4.43690i −0.142603 0.196277i
\(512\) 0 0
\(513\) −0.512508 + 0.372359i −0.0226278 + 0.0164400i
\(514\) 0 0
\(515\) −8.22963 5.97917i −0.362641 0.263474i
\(516\) 0 0
\(517\) −40.8896 + 29.7080i −1.79832 + 1.30656i
\(518\) 0 0
\(519\) 1.89030i 0.0829748i
\(520\) 0 0
\(521\) −17.4368 + 5.66557i −0.763922 + 0.248213i −0.664961 0.746878i \(-0.731552\pi\)
−0.0989608 + 0.995091i \(0.531552\pi\)
\(522\) 0 0
\(523\) −7.59764 + 23.3831i −0.332222 + 1.02247i 0.635853 + 0.771811i \(0.280649\pi\)
−0.968074 + 0.250663i \(0.919351\pi\)
\(524\) 0 0
\(525\) 0.0421161 0.129620i 0.00183810 0.00565709i
\(526\) 0 0
\(527\) 0.968401 1.33289i 0.0421842 0.0580616i
\(528\) 0 0
\(529\) 4.43885 + 13.6614i 0.192993 + 0.593973i
\(530\) 0 0
\(531\) 1.83257 + 1.33144i 0.0795267 + 0.0577796i
\(532\) 0 0
\(533\) 13.4924 3.94728i 0.584419 0.170976i
\(534\) 0 0
\(535\) −33.6829 24.4721i −1.45624 1.05802i
\(536\) 0 0
\(537\) −0.522556 1.60826i −0.0225499 0.0694016i
\(538\) 0 0
\(539\) −3.17091 + 4.36438i −0.136581 + 0.187987i
\(540\) 0 0
\(541\) −5.37077 + 16.5295i −0.230907 + 0.710660i 0.766731 + 0.641969i \(0.221882\pi\)
−0.997638 + 0.0686909i \(0.978118\pi\)
\(542\) 0 0
\(543\) 0.496543 1.52820i 0.0213087 0.0655814i
\(544\) 0 0
\(545\) 24.6532 8.01030i 1.05603 0.343123i
\(546\) 0 0
\(547\) 1.75938i 0.0752256i −0.999292 0.0376128i \(-0.988025\pi\)
0.999292 0.0376128i \(-0.0119754\pi\)
\(548\) 0 0
\(549\) 11.8427 8.60423i 0.505434 0.367219i
\(550\) 0 0
\(551\) −0.270128 0.196259i −0.0115078 0.00836092i
\(552\) 0 0
\(553\) −4.81118 + 3.49553i −0.204592 + 0.148645i
\(554\) 0 0
\(555\) 1.86702 + 2.56973i 0.0792506 + 0.109079i
\(556\) 0 0
\(557\) −0.536030 0.174167i −0.0227123 0.00737967i 0.297639 0.954679i \(-0.403801\pi\)
−0.320351 + 0.947299i \(0.603801\pi\)
\(558\) 0 0
\(559\) 16.1571 5.24976i 0.683372 0.222041i
\(560\) 0 0
\(561\) 1.91011 2.62905i 0.0806450 0.110998i
\(562\) 0 0
\(563\) 35.3769 + 11.4946i 1.49096 + 0.484441i 0.937366 0.348347i \(-0.113257\pi\)
0.553592 + 0.832788i \(0.313257\pi\)
\(564\) 0 0
\(565\) 36.1892 1.52249
\(566\) 0 0
\(567\) 4.91299 + 6.76215i 0.206326 + 0.283984i
\(568\) 0 0
\(569\) 2.46796 + 7.59559i 0.103462 + 0.318424i 0.989366 0.145444i \(-0.0464612\pi\)
−0.885904 + 0.463868i \(0.846461\pi\)
\(570\) 0 0
\(571\) 5.04634i 0.211183i 0.994410 + 0.105591i \(0.0336735\pi\)
−0.994410 + 0.105591i \(0.966326\pi\)
\(572\) 0 0
\(573\) −1.49828 −0.0625917
\(574\) 0 0
\(575\) 3.10793 0.129610
\(576\) 0 0
\(577\) 39.2379i 1.63349i −0.576996 0.816747i \(-0.695775\pi\)
0.576996 0.816747i \(-0.304225\pi\)
\(578\) 0 0
\(579\) 0.466010 + 1.43423i 0.0193667 + 0.0596047i
\(580\) 0 0
\(581\) −2.84562 3.91665i −0.118056 0.162490i
\(582\) 0 0
\(583\) −4.39620 −0.182072
\(584\) 0 0
\(585\) 14.3497 + 4.66250i 0.593287 + 0.192771i
\(586\) 0 0
\(587\) −3.64847 + 5.02169i −0.150589 + 0.207267i −0.877646 0.479309i \(-0.840887\pi\)
0.727058 + 0.686576i \(0.240887\pi\)
\(588\) 0 0
\(589\) −0.277966 + 0.0903166i −0.0114534 + 0.00372143i
\(590\) 0 0
\(591\) 4.64980 + 1.51081i 0.191267 + 0.0621464i
\(592\) 0 0
\(593\) 8.95699 + 12.3282i 0.367820 + 0.506260i 0.952307 0.305143i \(-0.0987042\pi\)
−0.584487 + 0.811403i \(0.698704\pi\)
\(594\) 0 0
\(595\) 4.26700 3.10016i 0.174930 0.127094i
\(596\) 0 0
\(597\) 2.72643 + 1.98087i 0.111585 + 0.0810714i
\(598\) 0 0
\(599\) 7.28459 5.29256i 0.297640 0.216248i −0.428935 0.903335i \(-0.641111\pi\)
0.726575 + 0.687087i \(0.241111\pi\)
\(600\) 0 0
\(601\) 45.5966i 1.85992i 0.367655 + 0.929962i \(0.380161\pi\)
−0.367655 + 0.929962i \(0.619839\pi\)
\(602\) 0 0
\(603\) 10.4686 3.40147i 0.426316 0.138518i
\(604\) 0 0
\(605\) −13.1291 + 40.4073i −0.533775 + 1.64279i
\(606\) 0 0
\(607\) −11.8922 + 36.6003i −0.482688 + 1.48556i 0.352615 + 0.935769i \(0.385293\pi\)
−0.835302 + 0.549791i \(0.814707\pi\)
\(608\) 0 0
\(609\) 0.131964 0.181633i 0.00534744 0.00736012i
\(610\) 0 0
\(611\) 6.35626 + 19.5625i 0.257147 + 0.791416i
\(612\) 0 0
\(613\) 12.3274 + 8.95636i 0.497898 + 0.361744i 0.808213 0.588890i \(-0.200435\pi\)
−0.310316 + 0.950634i \(0.600435\pi\)
\(614\) 0 0
\(615\) −3.79277 1.35747i −0.152939 0.0547386i
\(616\) 0 0
\(617\) −11.9743 8.69981i −0.482066 0.350241i 0.320059 0.947398i \(-0.396297\pi\)
−0.802125 + 0.597156i \(0.796297\pi\)
\(618\) 0 0
\(619\) −14.4967 44.6162i −0.582671 1.79328i −0.608429 0.793608i \(-0.708200\pi\)
0.0257586 0.999668i \(-0.491800\pi\)
\(620\) 0 0
\(621\) 5.70941 7.85833i 0.229111 0.315344i
\(622\) 0 0
\(623\) 1.87720 5.77743i 0.0752085 0.231468i
\(624\) 0 0
\(625\) −8.43113 + 25.9483i −0.337245 + 1.03793i
\(626\) 0 0
\(627\) −0.548272 + 0.178144i −0.0218959 + 0.00711440i
\(628\) 0 0
\(629\) 11.3460i 0.452394i
\(630\) 0 0
\(631\) 0.217394 0.157946i 0.00865431 0.00628773i −0.583450 0.812149i \(-0.698297\pi\)
0.592104 + 0.805862i \(0.298297\pi\)
\(632\) 0 0
\(633\) 2.71777 + 1.97457i 0.108022 + 0.0784822i
\(634\) 0 0
\(635\) 30.5091 22.1662i 1.21072 0.879638i
\(636\) 0 0
\(637\) 1.29047 + 1.77618i 0.0511303 + 0.0703748i
\(638\) 0 0
\(639\) 1.21884 + 0.396027i 0.0482168 + 0.0156666i
\(640\) 0 0
\(641\) 36.7902 11.9539i 1.45313 0.472149i 0.527164 0.849764i \(-0.323255\pi\)
0.925963 + 0.377614i \(0.123255\pi\)
\(642\) 0 0
\(643\) −0.647437 + 0.891121i −0.0255324 + 0.0351424i −0.821592 0.570075i \(-0.806914\pi\)
0.796060 + 0.605218i \(0.206914\pi\)
\(644\) 0 0
\(645\) −4.62991 1.50435i −0.182303 0.0592337i
\(646\) 0 0
\(647\) 20.7824 0.817042 0.408521 0.912749i \(-0.366045\pi\)
0.408521 + 0.912749i \(0.366045\pi\)
\(648\) 0 0
\(649\) 2.45298 + 3.37624i 0.0962879 + 0.132529i
\(650\) 0 0
\(651\) −0.0607285 0.186903i −0.00238014 0.00732531i
\(652\) 0 0
\(653\) 1.53742i 0.0601637i −0.999547 0.0300819i \(-0.990423\pi\)
0.999547 0.0300819i \(-0.00957680\pi\)
\(654\) 0 0
\(655\) −34.1003 −1.33241
\(656\) 0 0
\(657\) −16.0589 −0.626516
\(658\) 0 0
\(659\) 40.7164i 1.58608i 0.609167 + 0.793042i \(0.291504\pi\)
−0.609167 + 0.793042i \(0.708496\pi\)
\(660\) 0 0
\(661\) −10.2305 31.4864i −0.397922 1.22468i −0.926662 0.375895i \(-0.877335\pi\)
0.528740 0.848784i \(-0.322665\pi\)
\(662\) 0 0
\(663\) −0.777361 1.06995i −0.0301902 0.0415533i
\(664\) 0 0
\(665\) −0.935651 −0.0362830
\(666\) 0 0
\(667\) 4.86908 + 1.58206i 0.188532 + 0.0612576i
\(668\) 0 0
\(669\) 3.22455 4.43821i 0.124668 0.171591i
\(670\) 0 0
\(671\) 25.6491 8.33390i 0.990172 0.321727i
\(672\) 0 0
\(673\) 12.9855 + 4.21925i 0.500555 + 0.162640i 0.548403 0.836214i \(-0.315236\pi\)
−0.0478475 + 0.998855i \(0.515236\pi\)
\(674\) 0 0
\(675\) −0.474902 0.653646i −0.0182790 0.0251589i
\(676\) 0 0
\(677\) −39.8643 + 28.9631i −1.53211 + 1.11314i −0.577058 + 0.816703i \(0.695799\pi\)
−0.955052 + 0.296439i \(0.904201\pi\)
\(678\) 0 0
\(679\) −3.65643 2.65655i −0.140321 0.101949i
\(680\) 0 0
\(681\) 5.49155 3.98984i 0.210437 0.152891i
\(682\) 0 0
\(683\) 4.72624i 0.180844i 0.995904 + 0.0904222i \(0.0288217\pi\)
−0.995904 + 0.0904222i \(0.971178\pi\)
\(684\) 0 0
\(685\) −46.7651 + 15.1949i −1.78680 + 0.580568i
\(686\) 0 0
\(687\) 1.40897 4.33637i 0.0537557 0.165443i
\(688\) 0 0
\(689\) −0.552871 + 1.70156i −0.0210627 + 0.0648243i
\(690\) 0 0
\(691\) 30.7958 42.3868i 1.17153 1.61247i 0.518737 0.854934i \(-0.326402\pi\)
0.652792 0.757538i \(-0.273598\pi\)
\(692\) 0 0
\(693\) 4.88136 + 15.0233i 0.185427 + 0.570687i
\(694\) 0 0
\(695\) −13.2632 9.63625i −0.503100 0.365524i
\(696\) 0 0
\(697\) −8.11029 11.8860i −0.307199 0.450216i
\(698\) 0 0
\(699\) −0.758921 0.551389i −0.0287050 0.0208554i
\(700\) 0 0
\(701\) 10.2511 + 31.5497i 0.387180 + 1.19162i 0.934886 + 0.354947i \(0.115501\pi\)
−0.547707 + 0.836671i \(0.684499\pi\)
\(702\) 0 0
\(703\) 1.18307 1.62835i 0.0446203 0.0614145i
\(704\) 0 0
\(705\) 1.82142 5.60577i 0.0685988 0.211125i
\(706\) 0 0
\(707\) 4.25504 13.0957i 0.160027 0.492513i
\(708\) 0 0
\(709\) 5.95914 1.93624i 0.223800 0.0727171i −0.194970 0.980809i \(-0.562461\pi\)
0.418771 + 0.908092i \(0.362461\pi\)
\(710\) 0 0
\(711\) 17.4135i 0.653059i
\(712\) 0 0
\(713\) 3.62554 2.63411i 0.135777 0.0986481i
\(714\) 0 0
\(715\) 22.4888 + 16.3391i 0.841034 + 0.611047i
\(716\) 0 0
\(717\) 4.25577 3.09200i 0.158935 0.115473i
\(718\) 0 0
\(719\) −15.0800 20.7558i −0.562387 0.774060i 0.429240 0.903190i \(-0.358781\pi\)
−0.991628 + 0.129131i \(0.958781\pi\)
\(720\) 0 0
\(721\) −4.12206 1.33934i −0.153514 0.0498796i
\(722\) 0 0
\(723\) 1.59800 0.519223i 0.0594304 0.0193101i
\(724\) 0 0
\(725\) 0.250307 0.344517i 0.00929615 0.0127951i
\(726\) 0 0
\(727\) 32.5765 + 10.5848i 1.20820 + 0.392567i 0.842770 0.538274i \(-0.180923\pi\)
0.365426 + 0.930840i \(0.380923\pi\)
\(728\) 0 0
\(729\) 23.1970 0.859147
\(730\) 0 0
\(731\) −10.2211 14.0681i −0.378040 0.520328i
\(732\) 0 0
\(733\) −4.32088 13.2983i −0.159595 0.491184i 0.839002 0.544128i \(-0.183140\pi\)
−0.998597 + 0.0529440i \(0.983140\pi\)
\(734\) 0 0
\(735\) 0.629128i 0.0232057i
\(736\) 0 0
\(737\) 20.2795 0.747004
\(738\) 0 0
\(739\) −26.1333 −0.961329 −0.480665 0.876904i \(-0.659605\pi\)
−0.480665 + 0.876904i \(0.659605\pi\)
\(740\) 0 0
\(741\) 0.234614i 0.00861874i
\(742\) 0 0
\(743\) 1.40117 + 4.31237i 0.0514041 + 0.158206i 0.973463 0.228843i \(-0.0734944\pi\)
−0.922059 + 0.387049i \(0.873494\pi\)
\(744\) 0 0
\(745\) 10.7336 + 14.7736i 0.393250 + 0.541262i
\(746\) 0 0
\(747\) −14.1759 −0.518669
\(748\) 0 0
\(749\) −16.8711 5.48176i −0.616458 0.200299i
\(750\) 0 0
\(751\) −19.6864 + 27.0961i −0.718369 + 0.988750i 0.281208 + 0.959647i \(0.409265\pi\)
−0.999576 + 0.0291028i \(0.990735\pi\)
\(752\) 0 0
\(753\) −2.52635 + 0.820862i −0.0920655 + 0.0299139i
\(754\) 0 0
\(755\) 17.7823 + 5.77781i 0.647164 + 0.210276i
\(756\) 0 0
\(757\) 3.08577 + 4.24719i 0.112154 + 0.154367i 0.861404 0.507921i \(-0.169586\pi\)
−0.749250 + 0.662288i \(0.769586\pi\)
\(758\) 0 0
\(759\) 7.15116 5.19562i 0.259571 0.188589i
\(760\) 0 0
\(761\) 41.1565 + 29.9019i 1.49192 + 1.08394i 0.973464 + 0.228841i \(0.0734935\pi\)
0.518457 + 0.855104i \(0.326507\pi\)
\(762\) 0 0
\(763\) 8.93531 6.49188i 0.323480 0.235022i
\(764\) 0 0
\(765\) 15.4439i 0.558376i
\(766\) 0 0
\(767\) 1.61527 0.524833i 0.0583241 0.0189506i
\(768\) 0 0
\(769\) 2.61771 8.05648i 0.0943970 0.290524i −0.892699 0.450653i \(-0.851191\pi\)
0.987096 + 0.160129i \(0.0511911\pi\)
\(770\) 0 0
\(771\) −1.76733 + 5.43928i −0.0636488 + 0.195891i
\(772\) 0 0
\(773\) −19.5562 + 26.9168i −0.703388 + 0.968130i 0.296527 + 0.955025i \(0.404172\pi\)
−0.999914 + 0.0131053i \(0.995828\pi\)
\(774\) 0 0
\(775\) −0.115189 0.354514i −0.00413770 0.0127345i
\(776\) 0 0
\(777\) 1.09490 + 0.795490i 0.0392792 + 0.0285380i
\(778\) 0 0
\(779\) −0.0754078 + 2.55154i −0.00270177 + 0.0914183i
\(780\) 0 0
\(781\) 1.91017 + 1.38782i 0.0683513 + 0.0496601i
\(782\) 0 0
\(783\) −0.411280 1.26579i −0.0146979 0.0452356i
\(784\) 0 0
\(785\) 13.2605 18.2514i 0.473286 0.651422i
\(786\) 0 0
\(787\) 9.11987 28.0681i 0.325088 1.00052i −0.646313 0.763073i \(-0.723690\pi\)
0.971401 0.237446i \(-0.0763102\pi\)
\(788\) 0 0
\(789\) −1.62673 + 5.00657i −0.0579132 + 0.178238i
\(790\) 0 0
\(791\) 14.6646 4.76483i 0.521414 0.169418i
\(792\) 0 0
\(793\) 10.9756i 0.389756i
\(794\) 0 0
\(795\) 0.414771 0.301349i 0.0147104 0.0106877i
\(796\) 0 0
\(797\) 24.2755 + 17.6372i 0.859883