Properties

Label 1148.2.i.c.165.1
Level $1148$
Weight $2$
Character 1148.165
Analytic conductor $9.167$
Analytic rank $0$
Dimension $2$
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.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.16682615204\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 165.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1148.165
Dual form 1148.2.i.c.821.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(2.00000 - 1.73205i) q^{7} +(1.00000 + 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{11} +2.00000 q^{13} +1.00000 q^{15} +(-0.500000 + 0.866025i) q^{17} +(1.50000 + 2.59808i) q^{19} +(-0.500000 - 2.59808i) q^{21} +(2.50000 + 4.33013i) q^{23} +(2.00000 - 3.46410i) q^{25} +5.00000 q^{27} -2.00000 q^{29} +(-2.50000 + 4.33013i) q^{31} +(1.50000 + 2.59808i) q^{33} +(2.50000 + 0.866025i) q^{35} +(-3.50000 - 6.06218i) q^{37} +(1.00000 - 1.73205i) q^{39} +1.00000 q^{41} +4.00000 q^{43} +(-1.00000 + 1.73205i) q^{45} +(1.50000 + 2.59808i) q^{47} +(1.00000 - 6.92820i) q^{49} +(0.500000 + 0.866025i) q^{51} +(1.50000 - 2.59808i) q^{53} -3.00000 q^{55} +3.00000 q^{57} +(-2.50000 + 4.33013i) q^{59} +(-1.50000 - 2.59808i) q^{61} +(5.00000 + 1.73205i) q^{63} +(1.00000 + 1.73205i) q^{65} +(6.50000 - 11.2583i) q^{67} +5.00000 q^{69} +(0.500000 - 0.866025i) q^{73} +(-2.00000 - 3.46410i) q^{75} +(1.50000 + 7.79423i) q^{77} +(5.50000 + 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{81} +4.00000 q^{83} -1.00000 q^{85} +(-1.00000 + 1.73205i) q^{87} +(-2.50000 - 4.33013i) q^{89} +(4.00000 - 3.46410i) q^{91} +(2.50000 + 4.33013i) q^{93} +(-1.50000 + 2.59808i) q^{95} +2.00000 q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{3} + q^{5} + 4q^{7} + 2q^{9} + O(q^{10}) \) \( 2q + q^{3} + q^{5} + 4q^{7} + 2q^{9} - 3q^{11} + 4q^{13} + 2q^{15} - q^{17} + 3q^{19} - q^{21} + 5q^{23} + 4q^{25} + 10q^{27} - 4q^{29} - 5q^{31} + 3q^{33} + 5q^{35} - 7q^{37} + 2q^{39} + 2q^{41} + 8q^{43} - 2q^{45} + 3q^{47} + 2q^{49} + q^{51} + 3q^{53} - 6q^{55} + 6q^{57} - 5q^{59} - 3q^{61} + 10q^{63} + 2q^{65} + 13q^{67} + 10q^{69} + q^{73} - 4q^{75} + 3q^{77} + 11q^{79} - q^{81} + 8q^{83} - 2q^{85} - 2q^{87} - 5q^{89} + 8q^{91} + 5q^{93} - 3q^{95} + 4q^{97} - 12q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(493\) \(575\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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 0
\(3\) 0.500000 0.866025i 0.288675 0.500000i −0.684819 0.728714i \(-0.740119\pi\)
0.973494 + 0.228714i \(0.0734519\pi\)
\(4\) 0 0
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i 0.955901 0.293691i \(-0.0948835\pi\)
−0.732294 + 0.680989i \(0.761550\pi\)
\(6\) 0 0
\(7\) 2.00000 1.73205i 0.755929 0.654654i
\(8\) 0 0
\(9\) 1.00000 + 1.73205i 0.333333 + 0.577350i
\(10\) 0 0
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 0 0
\(17\) −0.500000 + 0.866025i −0.121268 + 0.210042i −0.920268 0.391289i \(-0.872029\pi\)
0.799000 + 0.601331i \(0.205363\pi\)
\(18\) 0 0
\(19\) 1.50000 + 2.59808i 0.344124 + 0.596040i 0.985194 0.171442i \(-0.0548427\pi\)
−0.641071 + 0.767482i \(0.721509\pi\)
\(20\) 0 0
\(21\) −0.500000 2.59808i −0.109109 0.566947i
\(22\) 0 0
\(23\) 2.50000 + 4.33013i 0.521286 + 0.902894i 0.999694 + 0.0247559i \(0.00788087\pi\)
−0.478407 + 0.878138i \(0.658786\pi\)
\(24\) 0 0
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 0 0
\(31\) −2.50000 + 4.33013i −0.449013 + 0.777714i −0.998322 0.0579057i \(-0.981558\pi\)
0.549309 + 0.835619i \(0.314891\pi\)
\(32\) 0 0
\(33\) 1.50000 + 2.59808i 0.261116 + 0.452267i
\(34\) 0 0
\(35\) 2.50000 + 0.866025i 0.422577 + 0.146385i
\(36\) 0 0
\(37\) −3.50000 6.06218i −0.575396 0.996616i −0.995998 0.0893706i \(-0.971514\pi\)
0.420602 0.907245i \(-0.361819\pi\)
\(38\) 0 0
\(39\) 1.00000 1.73205i 0.160128 0.277350i
\(40\) 0 0
\(41\) 1.00000 0.156174
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) −1.00000 + 1.73205i −0.149071 + 0.258199i
\(46\) 0 0
\(47\) 1.50000 + 2.59808i 0.218797 + 0.378968i 0.954441 0.298401i \(-0.0964533\pi\)
−0.735643 + 0.677369i \(0.763120\pi\)
\(48\) 0 0
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 0 0
\(51\) 0.500000 + 0.866025i 0.0700140 + 0.121268i
\(52\) 0 0
\(53\) 1.50000 2.59808i 0.206041 0.356873i −0.744423 0.667708i \(-0.767275\pi\)
0.950464 + 0.310835i \(0.100609\pi\)
\(54\) 0 0
\(55\) −3.00000 −0.404520
\(56\) 0 0
\(57\) 3.00000 0.397360
\(58\) 0 0
\(59\) −2.50000 + 4.33013i −0.325472 + 0.563735i −0.981608 0.190909i \(-0.938857\pi\)
0.656136 + 0.754643i \(0.272190\pi\)
\(60\) 0 0
\(61\) −1.50000 2.59808i −0.192055 0.332650i 0.753876 0.657017i \(-0.228182\pi\)
−0.945931 + 0.324367i \(0.894849\pi\)
\(62\) 0 0
\(63\) 5.00000 + 1.73205i 0.629941 + 0.218218i
\(64\) 0 0
\(65\) 1.00000 + 1.73205i 0.124035 + 0.214834i
\(66\) 0 0
\(67\) 6.50000 11.2583i 0.794101 1.37542i −0.129307 0.991605i \(-0.541275\pi\)
0.923408 0.383819i \(-0.125391\pi\)
\(68\) 0 0
\(69\) 5.00000 0.601929
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 0.500000 0.866025i 0.0585206 0.101361i −0.835281 0.549823i \(-0.814695\pi\)
0.893801 + 0.448463i \(0.148028\pi\)
\(74\) 0 0
\(75\) −2.00000 3.46410i −0.230940 0.400000i
\(76\) 0 0
\(77\) 1.50000 + 7.79423i 0.170941 + 0.888235i
\(78\) 0 0
\(79\) 5.50000 + 9.52628i 0.618798 + 1.07179i 0.989705 + 0.143120i \(0.0457135\pi\)
−0.370907 + 0.928670i \(0.620953\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 4.00000 0.439057 0.219529 0.975606i \(-0.429548\pi\)
0.219529 + 0.975606i \(0.429548\pi\)
\(84\) 0 0
\(85\) −1.00000 −0.108465
\(86\) 0 0
\(87\) −1.00000 + 1.73205i −0.107211 + 0.185695i
\(88\) 0 0
\(89\) −2.50000 4.33013i −0.264999 0.458993i 0.702564 0.711621i \(-0.252038\pi\)
−0.967563 + 0.252628i \(0.918705\pi\)
\(90\) 0 0
\(91\) 4.00000 3.46410i 0.419314 0.363137i
\(92\) 0 0
\(93\) 2.50000 + 4.33013i 0.259238 + 0.449013i
\(94\) 0 0
\(95\) −1.50000 + 2.59808i −0.153897 + 0.266557i
\(96\) 0 0
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 0 0
\(99\) −6.00000 −0.603023
\(100\) 0 0
\(101\) 1.50000 2.59808i 0.149256 0.258518i −0.781697 0.623658i \(-0.785646\pi\)
0.930953 + 0.365140i \(0.118979\pi\)
\(102\) 0 0
\(103\) −3.50000 6.06218i −0.344865 0.597324i 0.640464 0.767988i \(-0.278742\pi\)
−0.985329 + 0.170664i \(0.945409\pi\)
\(104\) 0 0
\(105\) 2.00000 1.73205i 0.195180 0.169031i
\(106\) 0 0
\(107\) 0.500000 + 0.866025i 0.0483368 + 0.0837218i 0.889182 0.457555i \(-0.151275\pi\)
−0.840845 + 0.541276i \(0.817941\pi\)
\(108\) 0 0
\(109\) 3.50000 6.06218i 0.335239 0.580651i −0.648292 0.761392i \(-0.724516\pi\)
0.983531 + 0.180741i \(0.0578495\pi\)
\(110\) 0 0
\(111\) −7.00000 −0.664411
\(112\) 0 0
\(113\) −2.00000 −0.188144 −0.0940721 0.995565i \(-0.529988\pi\)
−0.0940721 + 0.995565i \(0.529988\pi\)
\(114\) 0 0
\(115\) −2.50000 + 4.33013i −0.233126 + 0.403786i
\(116\) 0 0
\(117\) 2.00000 + 3.46410i 0.184900 + 0.320256i
\(118\) 0 0
\(119\) 0.500000 + 2.59808i 0.0458349 + 0.238165i
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 0 0
\(123\) 0.500000 0.866025i 0.0450835 0.0780869i
\(124\) 0 0
\(125\) 9.00000 0.804984
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 2.00000 3.46410i 0.176090 0.304997i
\(130\) 0 0
\(131\) −3.50000 6.06218i −0.305796 0.529655i 0.671642 0.740876i \(-0.265589\pi\)
−0.977438 + 0.211221i \(0.932256\pi\)
\(132\) 0 0
\(133\) 7.50000 + 2.59808i 0.650332 + 0.225282i
\(134\) 0 0
\(135\) 2.50000 + 4.33013i 0.215166 + 0.372678i
\(136\) 0 0
\(137\) −2.50000 + 4.33013i −0.213589 + 0.369948i −0.952835 0.303488i \(-0.901849\pi\)
0.739246 + 0.673436i \(0.235182\pi\)
\(138\) 0 0
\(139\) −12.0000 −1.01783 −0.508913 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) 0 0
\(141\) 3.00000 0.252646
\(142\) 0 0
\(143\) −3.00000 + 5.19615i −0.250873 + 0.434524i
\(144\) 0 0
\(145\) −1.00000 1.73205i −0.0830455 0.143839i
\(146\) 0 0
\(147\) −5.50000 4.33013i −0.453632 0.357143i
\(148\) 0 0
\(149\) −10.5000 18.1865i −0.860194 1.48990i −0.871742 0.489966i \(-0.837009\pi\)
0.0115483 0.999933i \(-0.496324\pi\)
\(150\) 0 0
\(151\) −1.50000 + 2.59808i −0.122068 + 0.211428i −0.920583 0.390547i \(-0.872286\pi\)
0.798515 + 0.601975i \(0.205619\pi\)
\(152\) 0 0
\(153\) −2.00000 −0.161690
\(154\) 0 0
\(155\) −5.00000 −0.401610
\(156\) 0 0
\(157\) 1.50000 2.59808i 0.119713 0.207349i −0.799941 0.600079i \(-0.795136\pi\)
0.919654 + 0.392730i \(0.128469\pi\)
\(158\) 0 0
\(159\) −1.50000 2.59808i −0.118958 0.206041i
\(160\) 0 0
\(161\) 12.5000 + 4.33013i 0.985138 + 0.341262i
\(162\) 0 0
\(163\) 0.500000 + 0.866025i 0.0391630 + 0.0678323i 0.884943 0.465700i \(-0.154198\pi\)
−0.845780 + 0.533533i \(0.820864\pi\)
\(164\) 0 0
\(165\) −1.50000 + 2.59808i −0.116775 + 0.202260i
\(166\) 0 0
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) −3.00000 + 5.19615i −0.229416 + 0.397360i
\(172\) 0 0
\(173\) −5.50000 9.52628i −0.418157 0.724270i 0.577597 0.816322i \(-0.303991\pi\)
−0.995754 + 0.0920525i \(0.970657\pi\)
\(174\) 0 0
\(175\) −2.00000 10.3923i −0.151186 0.785584i
\(176\) 0 0
\(177\) 2.50000 + 4.33013i 0.187912 + 0.325472i
\(178\) 0 0
\(179\) −1.50000 + 2.59808i −0.112115 + 0.194189i −0.916623 0.399753i \(-0.869096\pi\)
0.804508 + 0.593942i \(0.202429\pi\)
\(180\) 0 0
\(181\) −22.0000 −1.63525 −0.817624 0.575753i \(-0.804709\pi\)
−0.817624 + 0.575753i \(0.804709\pi\)
\(182\) 0 0
\(183\) −3.00000 −0.221766
\(184\) 0 0
\(185\) 3.50000 6.06218i 0.257325 0.445700i
\(186\) 0 0
\(187\) −1.50000 2.59808i −0.109691 0.189990i
\(188\) 0 0
\(189\) 10.0000 8.66025i 0.727393 0.629941i
\(190\) 0 0
\(191\) 3.50000 + 6.06218i 0.253251 + 0.438644i 0.964419 0.264378i \(-0.0851668\pi\)
−0.711168 + 0.703022i \(0.751833\pi\)
\(192\) 0 0
\(193\) 3.50000 6.06218i 0.251936 0.436365i −0.712123 0.702055i \(-0.752266\pi\)
0.964059 + 0.265689i \(0.0855996\pi\)
\(194\) 0 0
\(195\) 2.00000 0.143223
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) −9.50000 + 16.4545i −0.673437 + 1.16643i 0.303486 + 0.952836i \(0.401849\pi\)
−0.976923 + 0.213591i \(0.931484\pi\)
\(200\) 0 0
\(201\) −6.50000 11.2583i −0.458475 0.794101i
\(202\) 0 0
\(203\) −4.00000 + 3.46410i −0.280745 + 0.243132i
\(204\) 0 0
\(205\) 0.500000 + 0.866025i 0.0349215 + 0.0604858i
\(206\) 0 0
\(207\) −5.00000 + 8.66025i −0.347524 + 0.601929i
\(208\) 0 0
\(209\) −9.00000 −0.622543
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 2.00000 + 3.46410i 0.136399 + 0.236250i
\(216\) 0 0
\(217\) 2.50000 + 12.9904i 0.169711 + 0.881845i
\(218\) 0 0
\(219\) −0.500000 0.866025i −0.0337869 0.0585206i
\(220\) 0 0
\(221\) −1.00000 + 1.73205i −0.0672673 + 0.116510i
\(222\) 0 0
\(223\) −12.0000 −0.803579 −0.401790 0.915732i \(-0.631612\pi\)
−0.401790 + 0.915732i \(0.631612\pi\)
\(224\) 0 0
\(225\) 8.00000 0.533333
\(226\) 0 0
\(227\) −13.5000 + 23.3827i −0.896026 + 1.55196i −0.0634974 + 0.997982i \(0.520225\pi\)
−0.832529 + 0.553981i \(0.813108\pi\)
\(228\) 0 0
\(229\) −0.500000 0.866025i −0.0330409 0.0572286i 0.849032 0.528341i \(-0.177186\pi\)
−0.882073 + 0.471113i \(0.843853\pi\)
\(230\) 0 0
\(231\) 7.50000 + 2.59808i 0.493464 + 0.170941i
\(232\) 0 0
\(233\) 13.5000 + 23.3827i 0.884414 + 1.53185i 0.846383 + 0.532574i \(0.178775\pi\)
0.0380310 + 0.999277i \(0.487891\pi\)
\(234\) 0 0
\(235\) −1.50000 + 2.59808i −0.0978492 + 0.169480i
\(236\) 0 0
\(237\) 11.0000 0.714527
\(238\) 0 0
\(239\) −16.0000 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 0 0
\(241\) −1.50000 + 2.59808i −0.0966235 + 0.167357i −0.910285 0.413982i \(-0.864138\pi\)
0.813662 + 0.581339i \(0.197471\pi\)
\(242\) 0 0
\(243\) 8.00000 + 13.8564i 0.513200 + 0.888889i
\(244\) 0 0
\(245\) 6.50000 2.59808i 0.415270 0.165985i
\(246\) 0 0
\(247\) 3.00000 + 5.19615i 0.190885 + 0.330623i
\(248\) 0 0
\(249\) 2.00000 3.46410i 0.126745 0.219529i
\(250\) 0 0
\(251\) −8.00000 −0.504956 −0.252478 0.967603i \(-0.581245\pi\)
−0.252478 + 0.967603i \(0.581245\pi\)
\(252\) 0 0
\(253\) −15.0000 −0.943042
\(254\) 0 0
\(255\) −0.500000 + 0.866025i −0.0313112 + 0.0542326i
\(256\) 0 0
\(257\) −0.500000 0.866025i −0.0311891 0.0540212i 0.850010 0.526767i \(-0.176596\pi\)
−0.881199 + 0.472746i \(0.843263\pi\)
\(258\) 0 0
\(259\) −17.5000 6.06218i −1.08740 0.376685i
\(260\) 0 0
\(261\) −2.00000 3.46410i −0.123797 0.214423i
\(262\) 0 0
\(263\) 12.5000 21.6506i 0.770783 1.33504i −0.166351 0.986067i \(-0.553199\pi\)
0.937134 0.348969i \(-0.113468\pi\)
\(264\) 0 0
\(265\) 3.00000 0.184289
\(266\) 0 0
\(267\) −5.00000 −0.305995
\(268\) 0 0
\(269\) 4.50000 7.79423i 0.274370 0.475223i −0.695606 0.718423i \(-0.744864\pi\)
0.969976 + 0.243201i \(0.0781974\pi\)
\(270\) 0 0
\(271\) −13.5000 23.3827i −0.820067 1.42040i −0.905632 0.424064i \(-0.860603\pi\)
0.0855654 0.996333i \(-0.472730\pi\)
\(272\) 0 0
\(273\) −1.00000 5.19615i −0.0605228 0.314485i
\(274\) 0 0
\(275\) 6.00000 + 10.3923i 0.361814 + 0.626680i
\(276\) 0 0
\(277\) 8.50000 14.7224i 0.510716 0.884585i −0.489207 0.872167i \(-0.662714\pi\)
0.999923 0.0124177i \(-0.00395278\pi\)
\(278\) 0 0
\(279\) −10.0000 −0.598684
\(280\) 0 0
\(281\) −22.0000 −1.31241 −0.656205 0.754583i \(-0.727839\pi\)
−0.656205 + 0.754583i \(0.727839\pi\)
\(282\) 0 0
\(283\) −4.50000 + 7.79423i −0.267497 + 0.463319i −0.968215 0.250120i \(-0.919530\pi\)
0.700718 + 0.713439i \(0.252863\pi\)
\(284\) 0 0
\(285\) 1.50000 + 2.59808i 0.0888523 + 0.153897i
\(286\) 0 0
\(287\) 2.00000 1.73205i 0.118056 0.102240i
\(288\) 0 0
\(289\) 8.00000 + 13.8564i 0.470588 + 0.815083i
\(290\) 0 0
\(291\) 1.00000 1.73205i 0.0586210 0.101535i
\(292\) 0 0
\(293\) −26.0000 −1.51894 −0.759468 0.650545i \(-0.774541\pi\)
−0.759468 + 0.650545i \(0.774541\pi\)
\(294\) 0 0
\(295\) −5.00000 −0.291111
\(296\) 0 0
\(297\) −7.50000 + 12.9904i −0.435194 + 0.753778i
\(298\) 0 0
\(299\) 5.00000 + 8.66025i 0.289157 + 0.500835i
\(300\) 0 0
\(301\) 8.00000 6.92820i 0.461112 0.399335i
\(302\) 0 0
\(303\) −1.50000 2.59808i −0.0861727 0.149256i
\(304\) 0 0
\(305\) 1.50000 2.59808i 0.0858898 0.148765i
\(306\) 0 0
\(307\) −16.0000 −0.913168 −0.456584 0.889680i \(-0.650927\pi\)
−0.456584 + 0.889680i \(0.650927\pi\)
\(308\) 0 0
\(309\) −7.00000 −0.398216
\(310\) 0 0
\(311\) 6.50000 11.2583i 0.368581 0.638401i −0.620763 0.783998i \(-0.713177\pi\)
0.989344 + 0.145597i \(0.0465103\pi\)
\(312\) 0 0
\(313\) −0.500000 0.866025i −0.0282617 0.0489506i 0.851549 0.524276i \(-0.175664\pi\)
−0.879810 + 0.475325i \(0.842331\pi\)
\(314\) 0 0
\(315\) 1.00000 + 5.19615i 0.0563436 + 0.292770i
\(316\) 0 0
\(317\) −2.50000 4.33013i −0.140414 0.243204i 0.787239 0.616649i \(-0.211510\pi\)
−0.927653 + 0.373444i \(0.878177\pi\)
\(318\) 0 0
\(319\) 3.00000 5.19615i 0.167968 0.290929i
\(320\) 0 0
\(321\) 1.00000 0.0558146
\(322\) 0 0
\(323\) −3.00000 −0.166924
\(324\) 0 0
\(325\) 4.00000 6.92820i 0.221880 0.384308i
\(326\) 0 0
\(327\) −3.50000 6.06218i −0.193550 0.335239i
\(328\) 0 0
\(329\) 7.50000 + 2.59808i 0.413488 + 0.143237i
\(330\) 0 0
\(331\) −10.5000 18.1865i −0.577132 0.999622i −0.995806 0.0914858i \(-0.970838\pi\)
0.418674 0.908137i \(-0.362495\pi\)
\(332\) 0 0
\(333\) 7.00000 12.1244i 0.383598 0.664411i
\(334\) 0 0
\(335\) 13.0000 0.710266
\(336\) 0 0
\(337\) −18.0000 −0.980522 −0.490261 0.871576i \(-0.663099\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) 0 0
\(339\) −1.00000 + 1.73205i −0.0543125 + 0.0940721i
\(340\) 0 0
\(341\) −7.50000 12.9904i −0.406148 0.703469i
\(342\) 0 0
\(343\) −10.0000 15.5885i −0.539949 0.841698i
\(344\) 0 0
\(345\) 2.50000 + 4.33013i 0.134595 + 0.233126i
\(346\) 0 0
\(347\) −3.50000 + 6.06218i −0.187890 + 0.325435i −0.944547 0.328378i \(-0.893498\pi\)
0.756657 + 0.653812i \(0.226831\pi\)
\(348\) 0 0
\(349\) −30.0000 −1.60586 −0.802932 0.596071i \(-0.796728\pi\)
−0.802932 + 0.596071i \(0.796728\pi\)
\(350\) 0 0
\(351\) 10.0000 0.533761
\(352\) 0 0
\(353\) 6.50000 11.2583i 0.345960 0.599220i −0.639568 0.768735i \(-0.720887\pi\)
0.985528 + 0.169514i \(0.0542199\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 2.50000 + 0.866025i 0.132314 + 0.0458349i
\(358\) 0 0
\(359\) 12.5000 + 21.6506i 0.659725 + 1.14268i 0.980687 + 0.195585i \(0.0626605\pi\)
−0.320962 + 0.947092i \(0.604006\pi\)
\(360\) 0 0
\(361\) 5.00000 8.66025i 0.263158 0.455803i
\(362\) 0 0
\(363\) 2.00000 0.104973
\(364\) 0 0
\(365\) 1.00000 0.0523424
\(366\) 0 0
\(367\) 13.5000 23.3827i 0.704694 1.22057i −0.262108 0.965039i \(-0.584418\pi\)
0.966802 0.255528i \(-0.0822492\pi\)
\(368\) 0 0
\(369\) 1.00000 + 1.73205i 0.0520579 + 0.0901670i
\(370\) 0 0
\(371\) −1.50000 7.79423i −0.0778761 0.404656i
\(372\) 0 0
\(373\) −9.50000 16.4545i −0.491891 0.851981i 0.508065 0.861319i \(-0.330361\pi\)
−0.999956 + 0.00933789i \(0.997028\pi\)
\(374\) 0 0
\(375\) 4.50000 7.79423i 0.232379 0.402492i
\(376\) 0 0
\(377\) −4.00000 −0.206010
\(378\) 0 0
\(379\) −4.00000 −0.205466 −0.102733 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −4.50000 7.79423i −0.229939 0.398266i 0.727851 0.685736i \(-0.240519\pi\)
−0.957790 + 0.287469i \(0.907186\pi\)
\(384\) 0 0
\(385\) −6.00000 + 5.19615i −0.305788 + 0.264820i
\(386\) 0 0
\(387\) 4.00000 + 6.92820i 0.203331 + 0.352180i
\(388\) 0 0
\(389\) 12.5000 21.6506i 0.633775 1.09773i −0.352998 0.935624i \(-0.614838\pi\)
0.986773 0.162107i \(-0.0518289\pi\)
\(390\) 0 0
\(391\) −5.00000 −0.252861
\(392\) 0 0
\(393\) −7.00000 −0.353103
\(394\) 0 0
\(395\) −5.50000 + 9.52628i −0.276735 + 0.479319i
\(396\) 0 0
\(397\) 7.50000 + 12.9904i 0.376414 + 0.651969i 0.990538 0.137241i \(-0.0438236\pi\)
−0.614123 + 0.789210i \(0.710490\pi\)
\(398\) 0 0
\(399\) 6.00000 5.19615i 0.300376 0.260133i
\(400\) 0 0
\(401\) 6.50000 + 11.2583i 0.324595 + 0.562214i 0.981430 0.191820i \(-0.0614388\pi\)
−0.656836 + 0.754034i \(0.728105\pi\)
\(402\) 0 0
\(403\) −5.00000 + 8.66025i −0.249068 + 0.431398i
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) 21.0000 1.04093
\(408\) 0 0
\(409\) 4.50000 7.79423i 0.222511 0.385400i −0.733059 0.680165i \(-0.761908\pi\)
0.955570 + 0.294765i \(0.0952414\pi\)
\(410\) 0 0
\(411\) 2.50000 + 4.33013i 0.123316 + 0.213589i
\(412\) 0 0
\(413\) 2.50000 + 12.9904i 0.123017 + 0.639215i
\(414\) 0 0
\(415\) 2.00000 + 3.46410i 0.0981761 + 0.170046i
\(416\) 0 0
\(417\) −6.00000 + 10.3923i −0.293821 + 0.508913i
\(418\) 0 0
\(419\) −24.0000 −1.17248 −0.586238 0.810139i \(-0.699392\pi\)
−0.586238 + 0.810139i \(0.699392\pi\)
\(420\) 0 0
\(421\) 6.00000 0.292422 0.146211 0.989253i \(-0.453292\pi\)
0.146211 + 0.989253i \(0.453292\pi\)
\(422\) 0 0
\(423\) −3.00000 + 5.19615i −0.145865 + 0.252646i
\(424\) 0 0
\(425\) 2.00000 + 3.46410i 0.0970143 + 0.168034i
\(426\) 0 0
\(427\) −7.50000 2.59808i −0.362950 0.125730i
\(428\) 0 0
\(429\) 3.00000 + 5.19615i 0.144841 + 0.250873i
\(430\) 0 0
\(431\) 9.50000 16.4545i 0.457599 0.792585i −0.541235 0.840872i \(-0.682043\pi\)
0.998833 + 0.0482871i \(0.0153762\pi\)
\(432\) 0 0
\(433\) 6.00000 0.288342 0.144171 0.989553i \(-0.453949\pi\)
0.144171 + 0.989553i \(0.453949\pi\)
\(434\) 0 0
\(435\) −2.00000 −0.0958927
\(436\) 0 0
\(437\) −7.50000 + 12.9904i −0.358774 + 0.621414i
\(438\) 0 0
\(439\) 17.5000 + 30.3109i 0.835229 + 1.44666i 0.893843 + 0.448379i \(0.147999\pi\)
−0.0586141 + 0.998281i \(0.518668\pi\)
\(440\) 0 0
\(441\) 13.0000 5.19615i 0.619048 0.247436i
\(442\) 0 0
\(443\) 4.50000 + 7.79423i 0.213801 + 0.370315i 0.952901 0.303281i \(-0.0980821\pi\)
−0.739100 + 0.673596i \(0.764749\pi\)
\(444\) 0 0
\(445\) 2.50000 4.33013i 0.118511 0.205268i
\(446\) 0 0
\(447\) −21.0000 −0.993266
\(448\) 0 0
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 0 0
\(451\) −1.50000 + 2.59808i −0.0706322 + 0.122339i
\(452\) 0 0
\(453\) 1.50000 + 2.59808i 0.0704761 + 0.122068i
\(454\) 0 0
\(455\) 5.00000 + 1.73205i 0.234404 + 0.0811998i
\(456\) 0 0
\(457\) 1.50000 + 2.59808i 0.0701670 + 0.121533i 0.898974 0.438001i \(-0.144313\pi\)
−0.828807 + 0.559534i \(0.810980\pi\)
\(458\) 0 0
\(459\) −2.50000 + 4.33013i −0.116690 + 0.202113i
\(460\) 0 0
\(461\) 26.0000 1.21094 0.605470 0.795868i \(-0.292985\pi\)
0.605470 + 0.795868i \(0.292985\pi\)
\(462\) 0 0
\(463\) 32.0000 1.48717 0.743583 0.668644i \(-0.233125\pi\)
0.743583 + 0.668644i \(0.233125\pi\)
\(464\) 0 0
\(465\) −2.50000 + 4.33013i −0.115935 + 0.200805i
\(466\) 0 0
\(467\) 16.5000 + 28.5788i 0.763529 + 1.32247i 0.941021 + 0.338349i \(0.109868\pi\)
−0.177492 + 0.984122i \(0.556798\pi\)
\(468\) 0 0
\(469\) −6.50000 33.7750i −0.300142 1.55958i
\(470\) 0 0
\(471\) −1.50000 2.59808i −0.0691164 0.119713i
\(472\) 0 0
\(473\) −6.00000 + 10.3923i −0.275880 + 0.477839i
\(474\) 0 0
\(475\) 12.0000 0.550598
\(476\) 0 0
\(477\) 6.00000 0.274721
\(478\) 0 0
\(479\) −9.50000 + 16.4545i −0.434066 + 0.751825i −0.997219 0.0745283i \(-0.976255\pi\)
0.563153 + 0.826353i \(0.309588\pi\)
\(480\) 0 0
\(481\) −7.00000 12.1244i −0.319173 0.552823i
\(482\) 0 0
\(483\) 10.0000 8.66025i 0.455016 0.394055i
\(484\) 0 0
\(485\) 1.00000 + 1.73205i 0.0454077 + 0.0786484i
\(486\) 0 0
\(487\) 5.50000 9.52628i 0.249229 0.431677i −0.714083 0.700061i \(-0.753156\pi\)
0.963312 + 0.268384i \(0.0864896\pi\)
\(488\) 0 0
\(489\) 1.00000 0.0452216
\(490\) 0 0
\(491\) 36.0000 1.62466 0.812329 0.583200i \(-0.198200\pi\)
0.812329 + 0.583200i \(0.198200\pi\)
\(492\) 0 0
\(493\) 1.00000 1.73205i 0.0450377 0.0780076i
\(494\) 0 0
\(495\) −3.00000 5.19615i −0.134840 0.233550i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 3.50000 + 6.06218i 0.156682 + 0.271380i 0.933670 0.358134i \(-0.116587\pi\)
−0.776989 + 0.629515i \(0.783254\pi\)
\(500\) 0 0
\(501\) −4.00000 + 6.92820i −0.178707 + 0.309529i
\(502\) 0 0
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 0 0
\(505\) 3.00000 0.133498
\(506\) 0 0
\(507\) −4.50000 + 7.79423i −0.199852 + 0.346154i
\(508\) 0 0
\(509\) 5.50000 + 9.52628i 0.243783 + 0.422245i 0.961789 0.273792i \(-0.0882781\pi\)
−0.718006 + 0.696037i \(0.754945\pi\)
\(510\) 0 0
\(511\) −0.500000 2.59808i −0.0221187 0.114932i
\(512\) 0 0
\(513\) 7.50000 + 12.9904i 0.331133 + 0.573539i
\(514\) 0 0
\(515\) 3.50000 6.06218i 0.154228 0.267131i
\(516\) 0 0
\(517\) −9.00000 −0.395820
\(518\) 0 0
\(519\) −11.0000 −0.482846
\(520\) 0 0
\(521\) −6.50000 + 11.2583i −0.284770 + 0.493236i −0.972553 0.232680i \(-0.925251\pi\)
0.687783 + 0.725916i \(0.258584\pi\)
\(522\) 0 0
\(523\) −5.50000 9.52628i −0.240498 0.416555i 0.720358 0.693602i \(-0.243977\pi\)
−0.960856 + 0.277047i \(0.910644\pi\)
\(524\) 0 0
\(525\) −10.0000 3.46410i −0.436436 0.151186i
\(526\) 0 0
\(527\) −2.50000 4.33013i −0.108902 0.188623i
\(528\) 0 0
\(529\) −1.00000 + 1.73205i −0.0434783 + 0.0753066i
\(530\) 0 0
\(531\) −10.0000 −0.433963
\(532\) 0 0
\(533\) 2.00000 0.0866296
\(534\) 0 0
\(535\) −0.500000 + 0.866025i −0.0216169 + 0.0374415i
\(536\) 0 0
\(537\) 1.50000 + 2.59808i 0.0647298 + 0.112115i
\(538\) 0 0
\(539\) 16.5000 + 12.9904i 0.710705 + 0.559535i
\(540\) 0 0
\(541\) 0.500000 + 0.866025i 0.0214967 + 0.0372333i 0.876574 0.481268i \(-0.159824\pi\)
−0.855077 + 0.518501i \(0.826490\pi\)
\(542\) 0 0
\(543\) −11.0000 + 19.0526i −0.472055 + 0.817624i
\(544\) 0 0
\(545\) 7.00000 0.299847
\(546\) 0 0
\(547\) 4.00000 0.171028 0.0855138 0.996337i \(-0.472747\pi\)
0.0855138 + 0.996337i \(0.472747\pi\)
\(548\) 0 0
\(549\) 3.00000 5.19615i 0.128037 0.221766i
\(550\) 0 0
\(551\) −3.00000 5.19615i −0.127804 0.221364i
\(552\) 0 0
\(553\) 27.5000 + 9.52628i 1.16942 + 0.405099i
\(554\) 0 0
\(555\) −3.50000 6.06218i −0.148567 0.257325i
\(556\) 0 0
\(557\) 1.50000 2.59808i 0.0635570 0.110084i −0.832496 0.554031i \(-0.813089\pi\)
0.896053 + 0.443947i \(0.146422\pi\)
\(558\) 0 0
\(559\) 8.00000 0.338364
\(560\) 0 0
\(561\) −3.00000 −0.126660
\(562\) 0 0
\(563\) 10.5000 18.1865i 0.442522 0.766471i −0.555354 0.831614i \(-0.687417\pi\)
0.997876 + 0.0651433i \(0.0207504\pi\)
\(564\) 0 0
\(565\) −1.00000 1.73205i −0.0420703 0.0728679i
\(566\) 0 0
\(567\) 0.500000 + 2.59808i 0.0209980 + 0.109109i
\(568\) 0 0
\(569\) 22.5000 + 38.9711i 0.943249 + 1.63376i 0.759220 + 0.650835i \(0.225581\pi\)
0.184030 + 0.982921i \(0.441086\pi\)
\(570\) 0 0
\(571\) 2.50000 4.33013i 0.104622 0.181210i −0.808962 0.587861i \(-0.799970\pi\)
0.913584 + 0.406651i \(0.133303\pi\)
\(572\) 0 0
\(573\) 7.00000 0.292429
\(574\) 0 0
\(575\) 20.0000 0.834058
\(576\) 0 0
\(577\) −8.50000 + 14.7224i −0.353860 + 0.612903i −0.986922 0.161198i \(-0.948464\pi\)
0.633062 + 0.774101i \(0.281798\pi\)
\(578\) 0 0
\(579\) −3.50000 6.06218i −0.145455 0.251936i
\(580\) 0 0
\(581\) 8.00000 6.92820i 0.331896 0.287430i
\(582\) 0 0
\(583\) 4.50000 + 7.79423i 0.186371 + 0.322804i
\(584\) 0 0
\(585\) −2.00000 + 3.46410i −0.0826898 + 0.143223i
\(586\) 0 0
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 0 0
\(589\) −15.0000 −0.618064
\(590\) 0 0
\(591\) 3.00000 5.19615i 0.123404 0.213741i
\(592\) 0 0
\(593\) −4.50000 7.79423i −0.184793 0.320071i 0.758714 0.651424i \(-0.225828\pi\)
−0.943507 + 0.331353i \(0.892495\pi\)
\(594\) 0 0
\(595\) −2.00000 + 1.73205i −0.0819920 + 0.0710072i
\(596\) 0 0
\(597\) 9.50000 + 16.4545i 0.388809 + 0.673437i
\(598\) 0 0
\(599\) −8.50000 + 14.7224i −0.347301 + 0.601542i −0.985769 0.168106i \(-0.946235\pi\)
0.638468 + 0.769648i \(0.279568\pi\)
\(600\) 0 0
\(601\) 42.0000 1.71322 0.856608 0.515968i \(-0.172568\pi\)
0.856608 + 0.515968i \(0.172568\pi\)
\(602\) 0 0
\(603\) 26.0000 1.05880
\(604\) 0 0
\(605\) −1.00000 + 1.73205i −0.0406558 + 0.0704179i
\(606\) 0 0
\(607\) −11.5000 19.9186i −0.466771 0.808470i 0.532509 0.846424i \(-0.321249\pi\)
−0.999279 + 0.0379540i \(0.987916\pi\)
\(608\) 0 0
\(609\) 1.00000 + 5.19615i 0.0405220 + 0.210559i
\(610\) 0 0
\(611\) 3.00000 + 5.19615i 0.121367 + 0.210214i
\(612\) 0 0
\(613\) 14.5000 25.1147i 0.585649 1.01437i −0.409145 0.912470i \(-0.634173\pi\)
0.994794 0.101905i \(-0.0324938\pi\)
\(614\) 0 0
\(615\) 1.00000 0.0403239
\(616\) 0 0
\(617\) 22.0000 0.885687 0.442843 0.896599i \(-0.353970\pi\)
0.442843 + 0.896599i \(0.353970\pi\)
\(618\) 0 0
\(619\) −0.500000 + 0.866025i −0.0200967 + 0.0348085i −0.875899 0.482495i \(-0.839731\pi\)
0.855802 + 0.517303i \(0.173064\pi\)
\(620\) 0 0
\(621\) 12.5000 + 21.6506i 0.501608 + 0.868810i
\(622\) 0 0
\(623\) −12.5000 4.33013i −0.500802 0.173483i
\(624\) 0 0
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) 0 0
\(627\) −4.50000 + 7.79423i −0.179713 + 0.311272i
\(628\) 0 0
\(629\) 7.00000 0.279108
\(630\) 0 0
\(631\) 40.0000 1.59237 0.796187 0.605050i \(-0.206847\pi\)
0.796187 + 0.605050i \(0.206847\pi\)
\(632\) 0 0
\(633\) 2.00000 3.46410i 0.0794929 0.137686i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 2.00000 13.8564i 0.0792429 0.549011i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 17.5000 30.3109i 0.691208 1.19721i −0.280234 0.959932i \(-0.590412\pi\)
0.971442 0.237276i \(-0.0762547\pi\)
\(642\) 0 0
\(643\) −20.0000 −0.788723 −0.394362 0.918955i \(-0.629034\pi\)
−0.394362 + 0.918955i \(0.629034\pi\)
\(644\) 0 0
\(645\) 4.00000 0.157500
\(646\) 0 0
\(647\) −4.50000 + 7.79423i −0.176913 + 0.306423i −0.940822 0.338902i \(-0.889945\pi\)
0.763908 + 0.645325i \(0.223278\pi\)
\(648\) 0 0
\(649\) −7.50000 12.9904i −0.294401 0.509917i
\(650\) 0 0
\(651\) 12.5000 + 4.33013i 0.489914 + 0.169711i
\(652\) 0 0
\(653\) 21.5000 + 37.2391i 0.841360 + 1.45728i 0.888745 + 0.458402i \(0.151578\pi\)
−0.0473852 + 0.998877i \(0.515089\pi\)
\(654\) 0 0
\(655\) 3.50000 6.06218i 0.136756 0.236869i
\(656\) 0 0
\(657\) 2.00000 0.0780274
\(658\) 0 0
\(659\) −24.0000 −0.934907 −0.467454 0.884018i \(-0.654829\pi\)
−0.467454 + 0.884018i \(0.654829\pi\)
\(660\) 0 0
\(661\) 22.5000 38.9711i 0.875149 1.51580i 0.0185442 0.999828i \(-0.494097\pi\)
0.856604 0.515974i \(-0.172570\pi\)
\(662\) 0 0
\(663\) 1.00000 + 1.73205i 0.0388368 + 0.0672673i
\(664\) 0 0
\(665\) 1.50000 + 7.79423i 0.0581675 + 0.302247i
\(666\) 0 0
\(667\) −5.00000 8.66025i −0.193601 0.335326i
\(668\) 0 0
\(669\) −6.00000 + 10.3923i −0.231973 + 0.401790i
\(670\) 0 0
\(671\) 9.00000 0.347441
\(672\) 0 0
\(673\) −34.0000 −1.31060 −0.655302 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) 0 0
\(675\) 10.0000 17.3205i 0.384900 0.666667i
\(676\) 0 0
\(677\) −13.5000 23.3827i −0.518847 0.898670i −0.999760 0.0219013i \(-0.993028\pi\)
0.480913 0.876768i \(-0.340305\pi\)
\(678\) 0 0
\(679\) 4.00000 3.46410i 0.153506 0.132940i
\(680\) 0 0
\(681\) 13.5000 + 23.3827i 0.517321 + 0.896026i
\(682\) 0 0
\(683\) 2.50000 4.33013i 0.0956598 0.165688i −0.814224 0.580551i \(-0.802837\pi\)
0.909884 + 0.414863i \(0.136171\pi\)
\(684\) 0 0
\(685\) −5.00000 −0.191040
\(686\) 0 0
\(687\) −1.00000 −0.0381524
\(688\) 0 0
\(689\) 3.00000 5.19615i 0.114291 0.197958i
\(690\) 0 0
\(691\) 5.50000 + 9.52628i 0.209230 + 0.362397i 0.951472 0.307735i \(-0.0995710\pi\)
−0.742242 + 0.670132i \(0.766238\pi\)
\(692\) 0 0
\(693\) −12.0000 + 10.3923i −0.455842 + 0.394771i
\(694\) 0 0
\(695\) −6.00000 10.3923i −0.227593 0.394203i
\(696\) 0 0
\(697\) −0.500000 + 0.866025i −0.0189389 + 0.0328031i
\(698\) 0 0
\(699\) 27.0000 1.02123
\(700\) 0 0
\(701\) −14.0000 −0.528773 −0.264386 0.964417i \(-0.585169\pi\)
−0.264386 + 0.964417i \(0.585169\pi\)
\(702\) 0 0
\(703\) 10.5000 18.1865i 0.396015 0.685918i
\(704\) 0 0
\(705\) 1.50000 + 2.59808i 0.0564933 + 0.0978492i
\(706\) 0 0
\(707\) −1.50000 7.79423i −0.0564133 0.293132i
\(708\) 0 0
\(709\) −2.50000 4.33013i −0.0938895 0.162621i 0.815255 0.579102i \(-0.196597\pi\)
−0.909145 + 0.416481i \(0.863263\pi\)
\(710\) 0 0
\(711\) −11.0000 + 19.0526i −0.412532 + 0.714527i
\(712\) 0 0
\(713\) −25.0000 −0.936257
\(714\) 0 0
\(715\) −6.00000 −0.224387
\(716\) 0 0
\(717\) −8.00000 + 13.8564i −0.298765 + 0.517477i
\(718\) 0 0
\(719\) −22.5000 38.9711i −0.839108 1.45338i −0.890641 0.454707i \(-0.849744\pi\)
0.0515326 0.998671i \(-0.483589\pi\)
\(720\) 0 0
\(721\) −17.5000 6.06218i −0.651734 0.225767i
\(722\) 0 0
\(723\) 1.50000 + 2.59808i 0.0557856 + 0.0966235i
\(724\) 0 0
\(725\) −4.00000 + 6.92820i −0.148556 + 0.257307i
\(726\) 0 0
\(727\) 32.0000 1.18681 0.593407 0.804902i \(-0.297782\pi\)
0.593407 + 0.804902i \(0.297782\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −2.00000 + 3.46410i −0.0739727 + 0.128124i
\(732\) 0 0
\(733\) −3.50000 6.06218i −0.129275 0.223912i 0.794121 0.607760i \(-0.207932\pi\)
−0.923396 + 0.383849i \(0.874598\pi\)
\(734\) 0 0
\(735\) 1.00000 6.92820i 0.0368856 0.255551i
\(736\) 0 0
\(737\) 19.5000 + 33.7750i 0.718292 + 1.24412i
\(738\) 0 0
\(739\) 11.5000 19.9186i 0.423034 0.732717i −0.573200 0.819415i \(-0.694298\pi\)
0.996235 + 0.0866983i \(0.0276316\pi\)
\(740\) 0 0
\(741\) 6.00000 0.220416
\(742\) 0 0
\(743\) 36.0000 1.32071 0.660356 0.750953i \(-0.270405\pi\)
0.660356 + 0.750953i \(0.270405\pi\)
\(744\) 0 0
\(745\) 10.5000 18.1865i 0.384690 0.666303i
\(746\) 0 0
\(747\) 4.00000 + 6.92820i 0.146352 + 0.253490i
\(748\) 0 0
\(749\) 2.50000 + 0.866025i 0.0913480 + 0.0316439i
\(750\) 0 0
\(751\) 11.5000 + 19.9186i 0.419641 + 0.726839i 0.995903 0.0904254i \(-0.0288227\pi\)
−0.576262 + 0.817265i \(0.695489\pi\)
\(752\) 0 0
\(753\) −4.00000 + 6.92820i −0.145768 + 0.252478i
\(754\) 0 0
\(755\) −3.00000 −0.109181
\(756\) 0 0
\(757\) −34.0000 −1.23575 −0.617876 0.786276i \(-0.712006\pi\)
−0.617876 + 0.786276i \(0.712006\pi\)
\(758\) 0 0
\(759\) −7.50000 + 12.9904i −0.272233 + 0.471521i
\(760\) 0 0
\(761\) 6.50000 + 11.2583i 0.235625 + 0.408114i 0.959454 0.281865i \(-0.0909530\pi\)
−0.723829 + 0.689979i \(0.757620\pi\)
\(762\) 0 0
\(763\) −3.50000 18.1865i −0.126709 0.658397i
\(764\) 0 0
\(765\) −1.00000 1.73205i −0.0361551 0.0626224i
\(766\) 0 0
\(767\) −5.00000 + 8.66025i −0.180540 + 0.312704i
\(768\) 0 0
\(769\) 2.00000 0.0721218 0.0360609 0.999350i \(-0.488519\pi\)
0.0360609 + 0.999350i \(0.488519\pi\)
\(770\) 0 0
\(771\) −1.00000 −0.0360141
\(772\) 0 0
\(773\) 1.50000 2.59808i 0.0539513 0.0934463i −0.837788 0.545995i \(-0.816152\pi\)
0.891740 + 0.452549i \(0.149485\pi\)
\(774\) 0 0
\(775\) 10.0000 + 17.3205i 0.359211 + 0.622171i
\(776\) 0 0
\(777\) −14.0000 + 12.1244i −0.502247 + 0.434959i
\(778\) 0 0
\(779\) 1.50000 + 2.59808i 0.0537431 + 0.0930857i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −10.0000 −0.357371
\(784\) 0 0
\(785\) 3.00000 0.107075
\(786\) 0 0
\(787\) 5.50000 9.52628i 0.196054 0.339575i −0.751192 0.660084i \(-0.770521\pi\)
0.947245 + 0.320509i \(0.103854\pi\)
\(788\) 0 0
\(789\) −12.5000 21.6506i −0.445012 0.770783i
\(790\) 0 0
\(791\) −4.00000 + 3.46410i −0.142224 + 0.123169i
\(792\) 0 0
\(793\) −3.00000 5.19615i −0.106533 0.184521i
\(794\) 0 0
\(795\) 1.50000 2.59808i 0.0531995 0.0921443i
\(796\) 0 0
\(797\) −34.0000 −1.20434 −0.602171 0.798367i \(-0.705697\pi\)