Properties

Label 1148.2.i.a.821.1
Level $1148$
Weight $2$
Character 1148.821
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 821.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1148.821
Dual form 1148.2.i.a.165.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{5} +(2.50000 - 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{3} +(1.50000 - 2.59808i) q^{5} +(2.50000 - 0.866025i) q^{7} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{11} -4.00000 q^{13} -3.00000 q^{15} +(3.50000 - 6.06218i) q^{19} +(-2.00000 - 1.73205i) q^{21} +(-3.00000 + 5.19615i) q^{23} +(-2.00000 - 3.46410i) q^{25} -5.00000 q^{27} +6.00000 q^{29} +(5.00000 + 8.66025i) q^{31} +(-1.50000 + 2.59808i) q^{33} +(1.50000 - 7.79423i) q^{35} +(-1.00000 + 1.73205i) q^{37} +(2.00000 + 3.46410i) q^{39} -1.00000 q^{41} -4.00000 q^{43} +(-3.00000 - 5.19615i) q^{45} +(-6.00000 + 10.3923i) q^{47} +(5.50000 - 4.33013i) q^{49} +(3.00000 + 5.19615i) q^{53} -9.00000 q^{55} -7.00000 q^{57} +(-3.00000 - 5.19615i) q^{59} +(6.50000 - 11.2583i) q^{61} +(1.00000 - 5.19615i) q^{63} +(-6.00000 + 10.3923i) q^{65} +(2.00000 + 3.46410i) q^{67} +6.00000 q^{69} -9.00000 q^{71} +(-7.00000 - 12.1244i) q^{73} +(-2.00000 + 3.46410i) q^{75} +(-6.00000 - 5.19615i) q^{77} +(0.500000 - 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +12.0000 q^{83} +(-3.00000 - 5.19615i) q^{87} +(6.00000 - 10.3923i) q^{89} +(-10.0000 + 3.46410i) q^{91} +(5.00000 - 8.66025i) q^{93} +(-10.5000 - 18.1865i) q^{95} +2.00000 q^{97} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{3} + 3q^{5} + 5q^{7} + 2q^{9} + O(q^{10}) \) \( 2q - q^{3} + 3q^{5} + 5q^{7} + 2q^{9} - 3q^{11} - 8q^{13} - 6q^{15} + 7q^{19} - 4q^{21} - 6q^{23} - 4q^{25} - 10q^{27} + 12q^{29} + 10q^{31} - 3q^{33} + 3q^{35} - 2q^{37} + 4q^{39} - 2q^{41} - 8q^{43} - 6q^{45} - 12q^{47} + 11q^{49} + 6q^{53} - 18q^{55} - 14q^{57} - 6q^{59} + 13q^{61} + 2q^{63} - 12q^{65} + 4q^{67} + 12q^{69} - 18q^{71} - 14q^{73} - 4q^{75} - 12q^{77} + q^{79} - q^{81} + 24q^{83} - 6q^{87} + 12q^{89} - 20q^{91} + 10q^{93} - 21q^{95} + 4q^{97} - 12q^{99} + O(q^{100}) \)

Character values

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

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

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 \(-0.259881\pi\)
−0.973494 + 0.228714i \(0.926548\pi\)
\(4\) 0 0
\(5\) 1.50000 2.59808i 0.670820 1.16190i −0.306851 0.951757i \(-0.599275\pi\)
0.977672 0.210138i \(-0.0673912\pi\)
\(6\) 0 0
\(7\) 2.50000 0.866025i 0.944911 0.327327i
\(8\) 0 0
\(9\) 1.00000 1.73205i 0.333333 0.577350i
\(10\) 0 0
\(11\) −1.50000 2.59808i −0.452267 0.783349i 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) 0 0
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 0 0
\(15\) −3.00000 −0.774597
\(16\) 0 0
\(17\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) 3.50000 6.06218i 0.802955 1.39076i −0.114708 0.993399i \(-0.536593\pi\)
0.917663 0.397360i \(-0.130073\pi\)
\(20\) 0 0
\(21\) −2.00000 1.73205i −0.436436 0.377964i
\(22\) 0 0
\(23\) −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i \(0.381789\pi\)
−0.988436 + 0.151642i \(0.951544\pi\)
\(24\) 0 0
\(25\) −2.00000 3.46410i −0.400000 0.692820i
\(26\) 0 0
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 5.00000 + 8.66025i 0.898027 + 1.55543i 0.830014 + 0.557743i \(0.188333\pi\)
0.0680129 + 0.997684i \(0.478334\pi\)
\(32\) 0 0
\(33\) −1.50000 + 2.59808i −0.261116 + 0.452267i
\(34\) 0 0
\(35\) 1.50000 7.79423i 0.253546 1.31747i
\(36\) 0 0
\(37\) −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i \(-0.885902\pi\)
0.772043 + 0.635571i \(0.219235\pi\)
\(38\) 0 0
\(39\) 2.00000 + 3.46410i 0.320256 + 0.554700i
\(40\) 0 0
\(41\) −1.00000 −0.156174
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) 0 0
\(45\) −3.00000 5.19615i −0.447214 0.774597i
\(46\) 0 0
\(47\) −6.00000 + 10.3923i −0.875190 + 1.51587i −0.0186297 + 0.999826i \(0.505930\pi\)
−0.856560 + 0.516047i \(0.827403\pi\)
\(48\) 0 0
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 3.00000 + 5.19615i 0.412082 + 0.713746i 0.995117 0.0987002i \(-0.0314685\pi\)
−0.583036 + 0.812447i \(0.698135\pi\)
\(54\) 0 0
\(55\) −9.00000 −1.21356
\(56\) 0 0
\(57\) −7.00000 −0.927173
\(58\) 0 0
\(59\) −3.00000 5.19615i −0.390567 0.676481i 0.601958 0.798528i \(-0.294388\pi\)
−0.992524 + 0.122047i \(0.961054\pi\)
\(60\) 0 0
\(61\) 6.50000 11.2583i 0.832240 1.44148i −0.0640184 0.997949i \(-0.520392\pi\)
0.896258 0.443533i \(-0.146275\pi\)
\(62\) 0 0
\(63\) 1.00000 5.19615i 0.125988 0.654654i
\(64\) 0 0
\(65\) −6.00000 + 10.3923i −0.744208 + 1.28901i
\(66\) 0 0
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) 0 0
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) −9.00000 −1.06810 −0.534052 0.845452i \(-0.679331\pi\)
−0.534052 + 0.845452i \(0.679331\pi\)
\(72\) 0 0
\(73\) −7.00000 12.1244i −0.819288 1.41905i −0.906208 0.422833i \(-0.861036\pi\)
0.0869195 0.996215i \(-0.472298\pi\)
\(74\) 0 0
\(75\) −2.00000 + 3.46410i −0.230940 + 0.400000i
\(76\) 0 0
\(77\) −6.00000 5.19615i −0.683763 0.592157i
\(78\) 0 0
\(79\) 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i \(-0.815418\pi\)
0.892781 + 0.450490i \(0.148751\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −3.00000 5.19615i −0.321634 0.557086i
\(88\) 0 0
\(89\) 6.00000 10.3923i 0.635999 1.10158i −0.350304 0.936636i \(-0.613922\pi\)
0.986303 0.164946i \(-0.0527450\pi\)
\(90\) 0 0
\(91\) −10.0000 + 3.46410i −1.04828 + 0.363137i
\(92\) 0 0
\(93\) 5.00000 8.66025i 0.518476 0.898027i
\(94\) 0 0
\(95\) −10.5000 18.1865i −1.07728 1.86590i
\(96\) 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
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) 0 0
\(103\) 2.00000 3.46410i 0.197066 0.341328i −0.750510 0.660859i \(-0.770192\pi\)
0.947576 + 0.319531i \(0.103525\pi\)
\(104\) 0 0
\(105\) −7.50000 + 2.59808i −0.731925 + 0.253546i
\(106\) 0 0
\(107\) −3.00000 + 5.19615i −0.290021 + 0.502331i −0.973814 0.227345i \(-0.926996\pi\)
0.683793 + 0.729676i \(0.260329\pi\)
\(108\) 0 0
\(109\) −4.00000 6.92820i −0.383131 0.663602i 0.608377 0.793648i \(-0.291821\pi\)
−0.991508 + 0.130046i \(0.958487\pi\)
\(110\) 0 0
\(111\) 2.00000 0.189832
\(112\) 0 0
\(113\) −3.00000 −0.282216 −0.141108 0.989994i \(-0.545067\pi\)
−0.141108 + 0.989994i \(0.545067\pi\)
\(114\) 0 0
\(115\) 9.00000 + 15.5885i 0.839254 + 1.45363i
\(116\) 0 0
\(117\) −4.00000 + 6.92820i −0.369800 + 0.640513i
\(118\) 0 0
\(119\) 0 0
\(120\) 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
\(125\) 3.00000 0.268328
\(126\) 0 0
\(127\) 14.0000 1.24230 0.621150 0.783692i \(-0.286666\pi\)
0.621150 + 0.783692i \(0.286666\pi\)
\(128\) 0 0
\(129\) 2.00000 + 3.46410i 0.176090 + 0.304997i
\(130\) 0 0
\(131\) −9.00000 + 15.5885i −0.786334 + 1.36197i 0.141865 + 0.989886i \(0.454690\pi\)
−0.928199 + 0.372084i \(0.878643\pi\)
\(132\) 0 0
\(133\) 3.50000 18.1865i 0.303488 1.57697i
\(134\) 0 0
\(135\) −7.50000 + 12.9904i −0.645497 + 1.11803i
\(136\) 0 0
\(137\) 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i \(0.00465636\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(138\) 0 0
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) 0 0
\(141\) 12.0000 1.01058
\(142\) 0 0
\(143\) 6.00000 + 10.3923i 0.501745 + 0.869048i
\(144\) 0 0
\(145\) 9.00000 15.5885i 0.747409 1.29455i
\(146\) 0 0
\(147\) −6.50000 2.59808i −0.536111 0.214286i
\(148\) 0 0
\(149\) −9.00000 + 15.5885i −0.737309 + 1.27706i 0.216394 + 0.976306i \(0.430570\pi\)
−0.953703 + 0.300750i \(0.902763\pi\)
\(150\) 0 0
\(151\) 2.00000 + 3.46410i 0.162758 + 0.281905i 0.935857 0.352381i \(-0.114628\pi\)
−0.773099 + 0.634285i \(0.781294\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 30.0000 2.40966
\(156\) 0 0
\(157\) −7.00000 12.1244i −0.558661 0.967629i −0.997609 0.0691164i \(-0.977982\pi\)
0.438948 0.898513i \(-0.355351\pi\)
\(158\) 0 0
\(159\) 3.00000 5.19615i 0.237915 0.412082i
\(160\) 0 0
\(161\) −3.00000 + 15.5885i −0.236433 + 1.22854i
\(162\) 0 0
\(163\) −7.00000 + 12.1244i −0.548282 + 0.949653i 0.450110 + 0.892973i \(0.351385\pi\)
−0.998392 + 0.0566798i \(0.981949\pi\)
\(164\) 0 0
\(165\) 4.50000 + 7.79423i 0.350325 + 0.606780i
\(166\) 0 0
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) −7.00000 12.1244i −0.535303 0.927173i
\(172\) 0 0
\(173\) 10.5000 18.1865i 0.798300 1.38270i −0.122422 0.992478i \(-0.539066\pi\)
0.920722 0.390218i \(-0.127601\pi\)
\(174\) 0 0
\(175\) −8.00000 6.92820i −0.604743 0.523723i
\(176\) 0 0
\(177\) −3.00000 + 5.19615i −0.225494 + 0.390567i
\(178\) 0 0
\(179\) −1.50000 2.59808i −0.112115 0.194189i 0.804508 0.593942i \(-0.202429\pi\)
−0.916623 + 0.399753i \(0.869096\pi\)
\(180\) 0 0
\(181\) −4.00000 −0.297318 −0.148659 0.988889i \(-0.547496\pi\)
−0.148659 + 0.988889i \(0.547496\pi\)
\(182\) 0 0
\(183\) −13.0000 −0.960988
\(184\) 0 0
\(185\) 3.00000 + 5.19615i 0.220564 + 0.382029i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −12.5000 + 4.33013i −0.909241 + 0.314970i
\(190\) 0 0
\(191\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) 0 0
\(193\) −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i \(-0.998575\pi\)
0.496119 0.868255i \(-0.334758\pi\)
\(194\) 0 0
\(195\) 12.0000 0.859338
\(196\) 0 0
\(197\) 3.00000 0.213741 0.106871 0.994273i \(-0.465917\pi\)
0.106871 + 0.994273i \(0.465917\pi\)
\(198\) 0 0
\(199\) 8.00000 + 13.8564i 0.567105 + 0.982255i 0.996850 + 0.0793045i \(0.0252700\pi\)
−0.429745 + 0.902950i \(0.641397\pi\)
\(200\) 0 0
\(201\) 2.00000 3.46410i 0.141069 0.244339i
\(202\) 0 0
\(203\) 15.0000 5.19615i 1.05279 0.364698i
\(204\) 0 0
\(205\) −1.50000 + 2.59808i −0.104765 + 0.181458i
\(206\) 0 0
\(207\) 6.00000 + 10.3923i 0.417029 + 0.722315i
\(208\) 0 0
\(209\) −21.0000 −1.45260
\(210\) 0 0
\(211\) 23.0000 1.58339 0.791693 0.610920i \(-0.209200\pi\)
0.791693 + 0.610920i \(0.209200\pi\)
\(212\) 0 0
\(213\) 4.50000 + 7.79423i 0.308335 + 0.534052i
\(214\) 0 0
\(215\) −6.00000 + 10.3923i −0.409197 + 0.708749i
\(216\) 0 0
\(217\) 20.0000 + 17.3205i 1.35769 + 1.17579i
\(218\) 0 0
\(219\) −7.00000 + 12.1244i −0.473016 + 0.819288i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) 0 0
\(225\) −8.00000 −0.533333
\(226\) 0 0
\(227\) −10.5000 18.1865i −0.696909 1.20708i −0.969533 0.244962i \(-0.921225\pi\)
0.272623 0.962121i \(-0.412109\pi\)
\(228\) 0 0
\(229\) 2.00000 3.46410i 0.132164 0.228914i −0.792347 0.610071i \(-0.791141\pi\)
0.924510 + 0.381157i \(0.124474\pi\)
\(230\) 0 0
\(231\) −1.50000 + 7.79423i −0.0986928 + 0.512823i
\(232\) 0 0
\(233\) −3.00000 + 5.19615i −0.196537 + 0.340411i −0.947403 0.320043i \(-0.896303\pi\)
0.750867 + 0.660454i \(0.229636\pi\)
\(234\) 0 0
\(235\) 18.0000 + 31.1769i 1.17419 + 2.03376i
\(236\) 0 0
\(237\) −1.00000 −0.0649570
\(238\) 0 0
\(239\) −27.0000 −1.74648 −0.873242 0.487286i \(-0.837987\pi\)
−0.873242 + 0.487286i \(0.837987\pi\)
\(240\) 0 0
\(241\) 11.0000 + 19.0526i 0.708572 + 1.22728i 0.965387 + 0.260822i \(0.0839937\pi\)
−0.256814 + 0.966461i \(0.582673\pi\)
\(242\) 0 0
\(243\) −8.00000 + 13.8564i −0.513200 + 0.888889i
\(244\) 0 0
\(245\) −3.00000 20.7846i −0.191663 1.32788i
\(246\) 0 0
\(247\) −14.0000 + 24.2487i −0.890799 + 1.54291i
\(248\) 0 0
\(249\) −6.00000 10.3923i −0.380235 0.658586i
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 18.0000 1.13165
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3.00000 5.19615i 0.187135 0.324127i −0.757159 0.653231i \(-0.773413\pi\)
0.944294 + 0.329104i \(0.106747\pi\)
\(258\) 0 0
\(259\) −1.00000 + 5.19615i −0.0621370 + 0.322873i
\(260\) 0 0
\(261\) 6.00000 10.3923i 0.371391 0.643268i
\(262\) 0 0
\(263\) −6.00000 10.3923i −0.369976 0.640817i 0.619586 0.784929i \(-0.287301\pi\)
−0.989561 + 0.144112i \(0.953967\pi\)
\(264\) 0 0
\(265\) 18.0000 1.10573
\(266\) 0 0
\(267\) −12.0000 −0.734388
\(268\) 0 0
\(269\) 7.50000 + 12.9904i 0.457283 + 0.792038i 0.998816 0.0486418i \(-0.0154893\pi\)
−0.541533 + 0.840679i \(0.682156\pi\)
\(270\) 0 0
\(271\) −4.00000 + 6.92820i −0.242983 + 0.420858i −0.961563 0.274586i \(-0.911459\pi\)
0.718580 + 0.695444i \(0.244792\pi\)
\(272\) 0 0
\(273\) 8.00000 + 6.92820i 0.484182 + 0.419314i
\(274\) 0 0
\(275\) −6.00000 + 10.3923i −0.361814 + 0.626680i
\(276\) 0 0
\(277\) 6.50000 + 11.2583i 0.390547 + 0.676448i 0.992522 0.122068i \(-0.0389525\pi\)
−0.601975 + 0.798515i \(0.705619\pi\)
\(278\) 0 0
\(279\) 20.0000 1.19737
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) −13.0000 22.5167i −0.772770 1.33848i −0.936039 0.351895i \(-0.885537\pi\)
0.163270 0.986581i \(-0.447796\pi\)
\(284\) 0 0
\(285\) −10.5000 + 18.1865i −0.621966 + 1.07728i
\(286\) 0 0
\(287\) −2.50000 + 0.866025i −0.147570 + 0.0511199i
\(288\) 0 0
\(289\) 8.50000 14.7224i 0.500000 0.866025i
\(290\) 0 0
\(291\) −1.00000 1.73205i −0.0586210 0.101535i
\(292\) 0 0
\(293\) 12.0000 0.701047 0.350524 0.936554i \(-0.386004\pi\)
0.350524 + 0.936554i \(0.386004\pi\)
\(294\) 0 0
\(295\) −18.0000 −1.04800
\(296\) 0 0
\(297\) 7.50000 + 12.9904i 0.435194 + 0.753778i
\(298\) 0 0
\(299\) 12.0000 20.7846i 0.693978 1.20201i
\(300\) 0 0
\(301\) −10.0000 + 3.46410i −0.576390 + 0.199667i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −19.5000 33.7750i −1.11657 1.93395i
\(306\) 0 0
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 0 0
\(309\) −4.00000 −0.227552
\(310\) 0 0
\(311\) −6.00000 10.3923i −0.340229 0.589294i 0.644246 0.764818i \(-0.277171\pi\)
−0.984475 + 0.175525i \(0.943838\pi\)
\(312\) 0 0
\(313\) −10.0000 + 17.3205i −0.565233 + 0.979013i 0.431795 + 0.901972i \(0.357881\pi\)
−0.997028 + 0.0770410i \(0.975453\pi\)
\(314\) 0 0
\(315\) −12.0000 10.3923i −0.676123 0.585540i
\(316\) 0 0
\(317\) 9.00000 15.5885i 0.505490 0.875535i −0.494489 0.869184i \(-0.664645\pi\)
0.999980 0.00635137i \(-0.00202172\pi\)
\(318\) 0 0
\(319\) −9.00000 15.5885i −0.503903 0.872786i
\(320\) 0 0
\(321\) 6.00000 0.334887
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 8.00000 + 13.8564i 0.443760 + 0.768615i
\(326\) 0 0
\(327\) −4.00000 + 6.92820i −0.221201 + 0.383131i
\(328\) 0 0
\(329\) −6.00000 + 31.1769i −0.330791 + 1.71884i
\(330\) 0 0
\(331\) 14.0000 24.2487i 0.769510 1.33283i −0.168320 0.985732i \(-0.553834\pi\)
0.937829 0.347097i \(-0.112833\pi\)
\(332\) 0 0
\(333\) 2.00000 + 3.46410i 0.109599 + 0.189832i
\(334\) 0 0
\(335\) 12.0000 0.655630
\(336\) 0 0
\(337\) 23.0000 1.25289 0.626445 0.779466i \(-0.284509\pi\)
0.626445 + 0.779466i \(0.284509\pi\)
\(338\) 0 0
\(339\) 1.50000 + 2.59808i 0.0814688 + 0.141108i
\(340\) 0 0
\(341\) 15.0000 25.9808i 0.812296 1.40694i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) 0 0
\(345\) 9.00000 15.5885i 0.484544 0.839254i
\(346\) 0 0
\(347\) 7.50000 + 12.9904i 0.402621 + 0.697360i 0.994041 0.109003i \(-0.0347659\pi\)
−0.591420 + 0.806363i \(0.701433\pi\)
\(348\) 0 0
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) 20.0000 1.06752
\(352\) 0 0
\(353\) 7.50000 + 12.9904i 0.399185 + 0.691408i 0.993626 0.112731i \(-0.0359599\pi\)
−0.594441 + 0.804139i \(0.702627\pi\)
\(354\) 0 0
\(355\) −13.5000 + 23.3827i −0.716506 + 1.24102i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −18.0000 + 31.1769i −0.950004 + 1.64545i −0.204595 + 0.978847i \(0.565588\pi\)
−0.745409 + 0.666608i \(0.767746\pi\)
\(360\) 0 0
\(361\) −15.0000 25.9808i −0.789474 1.36741i
\(362\) 0 0
\(363\) −2.00000 −0.104973
\(364\) 0 0
\(365\) −42.0000 −2.19838
\(366\) 0 0
\(367\) 14.0000 + 24.2487i 0.730794 + 1.26577i 0.956544 + 0.291587i \(0.0941834\pi\)
−0.225750 + 0.974185i \(0.572483\pi\)
\(368\) 0 0
\(369\) −1.00000 + 1.73205i −0.0520579 + 0.0901670i
\(370\) 0 0
\(371\) 12.0000 + 10.3923i 0.623009 + 0.539542i
\(372\) 0 0
\(373\) −14.5000 + 25.1147i −0.750782 + 1.30039i 0.196663 + 0.980471i \(0.436990\pi\)
−0.947444 + 0.319921i \(0.896344\pi\)
\(374\) 0 0
\(375\) −1.50000 2.59808i −0.0774597 0.134164i
\(376\) 0 0
\(377\) −24.0000 −1.23606
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 0 0
\(381\) −7.00000 12.1244i −0.358621 0.621150i
\(382\) 0 0
\(383\) 13.5000 23.3827i 0.689818 1.19480i −0.282079 0.959391i \(-0.591024\pi\)
0.971897 0.235408i \(-0.0756427\pi\)
\(384\) 0 0
\(385\) −22.5000 + 7.79423i −1.14671 + 0.397231i
\(386\) 0 0
\(387\) −4.00000 + 6.92820i −0.203331 + 0.352180i
\(388\) 0 0
\(389\) −7.50000 12.9904i −0.380265 0.658638i 0.610835 0.791758i \(-0.290834\pi\)
−0.991100 + 0.133120i \(0.957501\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 18.0000 0.907980
\(394\) 0 0
\(395\) −1.50000 2.59808i −0.0754732 0.130723i
\(396\) 0 0
\(397\) −7.00000 + 12.1244i −0.351320 + 0.608504i −0.986481 0.163876i \(-0.947600\pi\)
0.635161 + 0.772380i \(0.280934\pi\)
\(398\) 0 0
\(399\) −17.5000 + 6.06218i −0.876096 + 0.303488i
\(400\) 0 0
\(401\) −13.5000 + 23.3827i −0.674158 + 1.16768i 0.302556 + 0.953131i \(0.402160\pi\)
−0.976714 + 0.214544i \(0.931173\pi\)
\(402\) 0 0
\(403\) −20.0000 34.6410i −0.996271 1.72559i
\(404\) 0 0
\(405\) −3.00000 −0.149071
\(406\) 0 0
\(407\) 6.00000 0.297409
\(408\) 0 0
\(409\) 15.5000 + 26.8468i 0.766426 + 1.32749i 0.939490 + 0.342578i \(0.111300\pi\)
−0.173064 + 0.984911i \(0.555367\pi\)
\(410\) 0 0
\(411\) 6.00000 10.3923i 0.295958 0.512615i
\(412\) 0 0
\(413\) −12.0000 10.3923i −0.590481 0.511372i
\(414\) 0 0
\(415\) 18.0000 31.1769i 0.883585 1.53041i
\(416\) 0 0
\(417\) −7.00000 12.1244i −0.342791 0.593732i
\(418\) 0 0
\(419\) −6.00000 −0.293119 −0.146560 0.989202i \(-0.546820\pi\)
−0.146560 + 0.989202i \(0.546820\pi\)
\(420\) 0 0
\(421\) 8.00000 0.389896 0.194948 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) 0 0
\(423\) 12.0000 + 20.7846i 0.583460 + 1.01058i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 6.50000 33.7750i 0.314557 1.63449i
\(428\) 0 0
\(429\) 6.00000 10.3923i 0.289683 0.501745i
\(430\) 0 0
\(431\) −9.00000 15.5885i −0.433515 0.750870i 0.563658 0.826008i \(-0.309393\pi\)
−0.997173 + 0.0751385i \(0.976060\pi\)
\(432\) 0 0
\(433\) 23.0000 1.10531 0.552655 0.833410i \(-0.313615\pi\)
0.552655 + 0.833410i \(0.313615\pi\)
\(434\) 0 0
\(435\) −18.0000 −0.863034
\(436\) 0 0
\(437\) 21.0000 + 36.3731i 1.00457 + 1.73996i
\(438\) 0 0
\(439\) 0.500000 0.866025i 0.0238637 0.0413331i −0.853847 0.520524i \(-0.825737\pi\)
0.877711 + 0.479191i \(0.159070\pi\)
\(440\) 0 0
\(441\) −2.00000 13.8564i −0.0952381 0.659829i
\(442\) 0 0
\(443\) −9.00000 + 15.5885i −0.427603 + 0.740630i −0.996660 0.0816684i \(-0.973975\pi\)
0.569057 + 0.822298i \(0.307309\pi\)
\(444\) 0 0
\(445\) −18.0000 31.1769i −0.853282 1.47793i
\(446\) 0 0
\(447\) 18.0000 0.851371
\(448\) 0 0
\(449\) 9.00000 0.424736 0.212368 0.977190i \(-0.431882\pi\)
0.212368 + 0.977190i \(0.431882\pi\)
\(450\) 0 0
\(451\) 1.50000 + 2.59808i 0.0706322 + 0.122339i
\(452\) 0 0
\(453\) 2.00000 3.46410i 0.0939682 0.162758i
\(454\) 0 0
\(455\) −6.00000 + 31.1769i −0.281284 + 1.46160i
\(456\) 0 0
\(457\) 8.00000 13.8564i 0.374224 0.648175i −0.615986 0.787757i \(-0.711242\pi\)
0.990211 + 0.139581i \(0.0445757\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 27.0000 1.25752 0.628758 0.777601i \(-0.283564\pi\)
0.628758 + 0.777601i \(0.283564\pi\)
\(462\) 0 0
\(463\) −1.00000 −0.0464739 −0.0232370 0.999730i \(-0.507397\pi\)
−0.0232370 + 0.999730i \(0.507397\pi\)
\(464\) 0 0
\(465\) −15.0000 25.9808i −0.695608 1.20483i
\(466\) 0 0
\(467\) −15.0000 + 25.9808i −0.694117 + 1.20225i 0.276360 + 0.961054i \(0.410872\pi\)
−0.970477 + 0.241192i \(0.922462\pi\)
\(468\) 0 0
\(469\) 8.00000 + 6.92820i 0.369406 + 0.319915i
\(470\) 0 0
\(471\) −7.00000 + 12.1244i −0.322543 + 0.558661i
\(472\) 0 0
\(473\) 6.00000 + 10.3923i 0.275880 + 0.477839i
\(474\) 0 0
\(475\) −28.0000 −1.28473
\(476\) 0 0
\(477\) 12.0000 0.549442
\(478\) 0 0
\(479\) −10.5000 18.1865i −0.479757 0.830964i 0.519973 0.854183i \(-0.325942\pi\)
−0.999730 + 0.0232187i \(0.992609\pi\)
\(480\) 0 0
\(481\) 4.00000 6.92820i 0.182384 0.315899i
\(482\) 0 0
\(483\) 15.0000 5.19615i 0.682524 0.236433i
\(484\) 0 0
\(485\) 3.00000 5.19615i 0.136223 0.235945i
\(486\) 0 0
\(487\) −4.00000 6.92820i −0.181257 0.313947i 0.761052 0.648691i \(-0.224683\pi\)
−0.942309 + 0.334744i \(0.891350\pi\)
\(488\) 0 0
\(489\) 14.0000 0.633102
\(490\) 0 0
\(491\) −42.0000 −1.89543 −0.947717 0.319113i \(-0.896615\pi\)
−0.947717 + 0.319113i \(0.896615\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) −9.00000 + 15.5885i −0.404520 + 0.700649i
\(496\) 0 0
\(497\) −22.5000 + 7.79423i −1.00926 + 0.349619i
\(498\) 0 0
\(499\) 2.00000 3.46410i 0.0895323 0.155074i −0.817781 0.575529i \(-0.804796\pi\)
0.907314 + 0.420455i \(0.138129\pi\)
\(500\) 0 0
\(501\) −6.00000 10.3923i −0.268060 0.464294i
\(502\) 0 0
\(503\) 9.00000 0.401290 0.200645 0.979664i \(-0.435696\pi\)
0.200645 + 0.979664i \(0.435696\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.50000 2.59808i −0.0666173 0.115385i
\(508\) 0 0
\(509\) 9.00000 15.5885i 0.398918 0.690946i −0.594675 0.803966i \(-0.702719\pi\)
0.993593 + 0.113020i \(0.0360525\pi\)
\(510\) 0 0
\(511\) −28.0000 24.2487i −1.23865 1.07270i
\(512\) 0 0
\(513\) −17.5000 + 30.3109i −0.772644 + 1.33826i
\(514\) 0 0
\(515\) −6.00000 10.3923i −0.264392 0.457940i
\(516\) 0 0
\(517\) 36.0000 1.58328
\(518\) 0 0
\(519\) −21.0000 −0.921798
\(520\) 0 0
\(521\) −15.0000 25.9808i −0.657162 1.13824i −0.981347 0.192244i \(-0.938423\pi\)
0.324185 0.945994i \(-0.394910\pi\)
\(522\) 0 0
\(523\) −19.0000 + 32.9090i −0.830812 + 1.43901i 0.0665832 + 0.997781i \(0.478790\pi\)
−0.897395 + 0.441228i \(0.854543\pi\)
\(524\) 0 0
\(525\) −2.00000 + 10.3923i −0.0872872 + 0.453557i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 0 0
\(531\) −12.0000 −0.520756
\(532\) 0 0
\(533\) 4.00000 0.173259
\(534\) 0 0
\(535\) 9.00000 + 15.5885i 0.389104 + 0.673948i
\(536\) 0 0
\(537\) −1.50000 + 2.59808i −0.0647298 + 0.112115i
\(538\) 0 0
\(539\) −19.5000 7.79423i −0.839924 0.335721i
\(540\) 0 0
\(541\) −7.00000 + 12.1244i −0.300954 + 0.521267i −0.976352 0.216186i \(-0.930638\pi\)
0.675399 + 0.737453i \(0.263972\pi\)
\(542\) 0 0
\(543\) 2.00000 + 3.46410i 0.0858282 + 0.148659i
\(544\) 0 0
\(545\) −24.0000 −1.02805
\(546\) 0 0
\(547\) 20.0000 0.855138 0.427569 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) 0 0
\(549\) −13.0000 22.5167i −0.554826 0.960988i
\(550\) 0 0
\(551\) 21.0000 36.3731i 0.894630 1.54954i
\(552\) 0 0
\(553\) 0.500000 2.59808i 0.0212622 0.110481i
\(554\) 0 0
\(555\) 3.00000 5.19615i 0.127343 0.220564i
\(556\) 0 0
\(557\) 6.00000 + 10.3923i 0.254228 + 0.440336i 0.964686 0.263404i \(-0.0848453\pi\)
−0.710457 + 0.703740i \(0.751512\pi\)
\(558\) 0 0
\(559\) 16.0000 0.676728
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 7.50000 + 12.9904i 0.316087 + 0.547479i 0.979668 0.200625i \(-0.0642974\pi\)
−0.663581 + 0.748105i \(0.730964\pi\)
\(564\) 0 0
\(565\) −4.50000 + 7.79423i −0.189316 + 0.327906i
\(566\) 0 0
\(567\) −2.00000 1.73205i −0.0839921 0.0727393i
\(568\) 0 0
\(569\) −15.0000 + 25.9808i −0.628833 + 1.08917i 0.358954 + 0.933355i \(0.383134\pi\)
−0.987786 + 0.155815i \(0.950200\pi\)
\(570\) 0 0
\(571\) −2.50000 4.33013i −0.104622 0.181210i 0.808962 0.587861i \(-0.200030\pi\)
−0.913584 + 0.406651i \(0.866697\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 24.0000 1.00087
\(576\) 0 0
\(577\) −10.0000 17.3205i −0.416305 0.721062i 0.579259 0.815144i \(-0.303342\pi\)
−0.995565 + 0.0940813i \(0.970009\pi\)
\(578\) 0 0
\(579\) −7.00000 + 12.1244i −0.290910 + 0.503871i
\(580\) 0 0
\(581\) 30.0000 10.3923i 1.24461 0.431145i
\(582\) 0 0
\(583\) 9.00000 15.5885i 0.372742 0.645608i
\(584\) 0 0
\(585\) 12.0000 + 20.7846i 0.496139 + 0.859338i
\(586\) 0 0
\(587\) −33.0000 −1.36206 −0.681028 0.732257i \(-0.738467\pi\)
−0.681028 + 0.732257i \(0.738467\pi\)
\(588\) 0 0
\(589\) 70.0000 2.88430
\(590\) 0 0
\(591\) −1.50000 2.59808i −0.0617018 0.106871i
\(592\) 0 0
\(593\) 3.00000 5.19615i 0.123195 0.213380i −0.797831 0.602881i \(-0.794019\pi\)
0.921026 + 0.389501i \(0.127353\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 8.00000 13.8564i 0.327418 0.567105i
\(598\) 0 0
\(599\) 15.0000 + 25.9808i 0.612883 + 1.06155i 0.990752 + 0.135686i \(0.0433238\pi\)
−0.377869 + 0.925859i \(0.623343\pi\)
\(600\) 0 0
\(601\) −34.0000 −1.38689 −0.693444 0.720510i \(-0.743908\pi\)
−0.693444 + 0.720510i \(0.743908\pi\)
\(602\) 0 0
\(603\) 8.00000 0.325785
\(604\) 0 0
\(605\) −3.00000 5.19615i −0.121967 0.211254i
\(606\) 0 0
\(607\) 14.0000 24.2487i 0.568242 0.984225i −0.428497 0.903543i \(-0.640957\pi\)
0.996740 0.0806818i \(-0.0257098\pi\)
\(608\) 0 0
\(609\) −12.0000 10.3923i −0.486265 0.421117i
\(610\) 0 0
\(611\) 24.0000 41.5692i 0.970936 1.68171i
\(612\) 0 0
\(613\) 3.50000 + 6.06218i 0.141364 + 0.244849i 0.928010 0.372554i \(-0.121518\pi\)
−0.786647 + 0.617403i \(0.788185\pi\)
\(614\) 0 0
\(615\) 3.00000 0.120972
\(616\) 0 0
\(617\) −27.0000 −1.08698 −0.543490 0.839416i \(-0.682897\pi\)
−0.543490 + 0.839416i \(0.682897\pi\)
\(618\) 0 0
\(619\) −22.0000 38.1051i −0.884255 1.53157i −0.846566 0.532284i \(-0.821334\pi\)
−0.0376891 0.999290i \(-0.512000\pi\)
\(620\) 0 0
\(621\) 15.0000 25.9808i 0.601929 1.04257i
\(622\) 0 0
\(623\) 6.00000 31.1769i 0.240385 1.24908i
\(624\) 0 0
\(625\) 14.5000 25.1147i 0.580000 1.00459i
\(626\) 0 0
\(627\) 10.5000 + 18.1865i 0.419330 + 0.726300i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) 0 0
\(633\) −11.5000 19.9186i −0.457084 0.791693i
\(634\) 0 0
\(635\) 21.0000 36.3731i 0.833360 1.44342i
\(636\) 0 0
\(637\) −22.0000 + 17.3205i −0.871672 + 0.686264i
\(638\) 0 0
\(639\) −9.00000 + 15.5885i −0.356034 + 0.616670i
\(640\) 0 0
\(641\) −6.00000 10.3923i −0.236986 0.410471i 0.722862 0.690992i \(-0.242826\pi\)
−0.959848 + 0.280521i \(0.909493\pi\)
\(642\) 0 0
\(643\) 5.00000 0.197181 0.0985904 0.995128i \(-0.468567\pi\)
0.0985904 + 0.995128i \(0.468567\pi\)
\(644\) 0 0
\(645\) 12.0000 0.472500
\(646\) 0 0
\(647\) 6.00000 + 10.3923i 0.235884 + 0.408564i 0.959529 0.281609i \(-0.0908680\pi\)
−0.723645 + 0.690172i \(0.757535\pi\)
\(648\) 0 0
\(649\) −9.00000 + 15.5885i −0.353281 + 0.611900i
\(650\) 0 0
\(651\) 5.00000 25.9808i 0.195965 1.01827i
\(652\) 0 0
\(653\) −18.0000 + 31.1769i −0.704394 + 1.22005i 0.262515 + 0.964928i \(0.415448\pi\)
−0.966910 + 0.255119i \(0.917885\pi\)
\(654\) 0 0
\(655\) 27.0000 + 46.7654i 1.05498 + 1.82727i
\(656\) 0 0
\(657\) −28.0000 −1.09238
\(658\) 0 0
\(659\) −48.0000 −1.86981 −0.934907 0.354892i \(-0.884518\pi\)
−0.934907 + 0.354892i \(0.884518\pi\)
\(660\) 0 0
\(661\) 15.5000 + 26.8468i 0.602880 + 1.04422i 0.992383 + 0.123194i \(0.0393136\pi\)
−0.389503 + 0.921025i \(0.627353\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −42.0000 36.3731i −1.62869 1.41049i
\(666\) 0 0
\(667\) −18.0000 + 31.1769i −0.696963 + 1.20717i
\(668\) 0 0
\(669\) −4.00000 6.92820i −0.154649 0.267860i
\(670\) 0 0
\(671\) −39.0000 −1.50558
\(672\) 0 0
\(673\) −22.0000 −0.848038 −0.424019 0.905653i \(-0.639381\pi\)
−0.424019 + 0.905653i \(0.639381\pi\)
\(674\) 0 0
\(675\) 10.0000 + 17.3205i 0.384900 + 0.666667i
\(676\) 0 0
\(677\) 7.50000 12.9904i 0.288248 0.499261i −0.685143 0.728408i \(-0.740260\pi\)
0.973392 + 0.229147i \(0.0735938\pi\)
\(678\) 0 0
\(679\) 5.00000 1.73205i 0.191882 0.0664700i
\(680\) 0 0
\(681\) −10.5000 + 18.1865i −0.402361 + 0.696909i
\(682\) 0 0
\(683\) −6.00000 10.3923i −0.229584 0.397650i 0.728101 0.685470i \(-0.240403\pi\)
−0.957685 + 0.287819i \(0.907070\pi\)
\(684\) 0 0
\(685\) 36.0000 1.37549
\(686\) 0 0
\(687\) −4.00000 −0.152610
\(688\) 0 0
\(689\) −12.0000 20.7846i −0.457164 0.791831i
\(690\) 0 0
\(691\) 0.500000 0.866025i 0.0190209 0.0329452i −0.856358 0.516382i \(-0.827278\pi\)
0.875379 + 0.483437i \(0.160612\pi\)
\(692\) 0 0
\(693\) −15.0000 + 5.19615i −0.569803 + 0.197386i
\(694\) 0 0
\(695\) 21.0000 36.3731i 0.796575 1.37971i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 6.00000 0.226941
\(700\) 0 0
\(701\) 15.0000 0.566542 0.283271 0.959040i \(-0.408580\pi\)
0.283271 + 0.959040i \(0.408580\pi\)
\(702\) 0 0
\(703\) 7.00000 + 12.1244i 0.264010 + 0.457279i
\(704\) 0 0
\(705\) 18.0000 31.1769i 0.677919 1.17419i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 5.00000 8.66025i 0.187779 0.325243i −0.756730 0.653727i \(-0.773204\pi\)
0.944509 + 0.328484i \(0.106538\pi\)
\(710\) 0 0
\(711\) −1.00000 1.73205i −0.0375029 0.0649570i
\(712\) 0 0
\(713\) −60.0000 −2.24702
\(714\) 0 0
\(715\) 36.0000 1.34632
\(716\) 0 0
\(717\) 13.5000 + 23.3827i 0.504167 + 0.873242i
\(718\) 0 0
\(719\) −1.50000 + 2.59808i −0.0559406 + 0.0968919i −0.892640 0.450771i \(-0.851149\pi\)
0.836699 + 0.547663i \(0.184482\pi\)
\(720\) 0 0
\(721\) 2.00000 10.3923i 0.0744839 0.387030i
\(722\) 0 0
\(723\) 11.0000 19.0526i 0.409094 0.708572i
\(724\) 0 0
\(725\) −12.0000 20.7846i −0.445669 0.771921i
\(726\) 0 0
\(727\) −40.0000 −1.48352 −0.741759 0.670667i \(-0.766008\pi\)
−0.741759 + 0.670667i \(0.766008\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 11.0000 19.0526i 0.406294 0.703722i −0.588177 0.808732i \(-0.700154\pi\)
0.994471 + 0.105010i \(0.0334875\pi\)
\(734\) 0 0
\(735\) −16.5000 + 12.9904i −0.608612 + 0.479157i
\(736\) 0 0
\(737\) 6.00000 10.3923i 0.221013 0.382805i
\(738\) 0 0
\(739\) 8.00000 + 13.8564i 0.294285 + 0.509716i 0.974818 0.223001i \(-0.0715853\pi\)
−0.680534 + 0.732717i \(0.738252\pi\)
\(740\) 0 0
\(741\) 28.0000 1.02861
\(742\) 0 0
\(743\) 6.00000 0.220119 0.110059 0.993925i \(-0.464896\pi\)
0.110059 + 0.993925i \(0.464896\pi\)
\(744\) 0 0
\(745\) 27.0000 + 46.7654i 0.989203 + 1.71335i
\(746\) 0 0
\(747\) 12.0000 20.7846i 0.439057 0.760469i
\(748\) 0 0
\(749\) −3.00000 + 15.5885i −0.109618 + 0.569590i
\(750\) 0 0
\(751\) 21.5000 37.2391i 0.784546 1.35887i −0.144724 0.989472i \(-0.546229\pi\)
0.929270 0.369402i \(-0.120437\pi\)
\(752\) 0 0
\(753\) −6.00000 10.3923i −0.218652 0.378717i
\(754\) 0 0
\(755\) 12.0000 0.436725
\(756\) 0 0
\(757\) −40.0000 −1.45382 −0.726912 0.686730i \(-0.759045\pi\)
−0.726912 + 0.686730i \(0.759045\pi\)
\(758\) 0 0
\(759\) −9.00000 15.5885i −0.326679 0.565825i
\(760\) 0 0
\(761\) −9.00000 + 15.5885i −0.326250 + 0.565081i −0.981764 0.190101i \(-0.939118\pi\)
0.655515 + 0.755182i \(0.272452\pi\)
\(762\) 0 0
\(763\) −16.0000 13.8564i −0.579239 0.501636i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 12.0000 + 20.7846i 0.433295 + 0.750489i
\(768\) 0 0
\(769\) 35.0000 1.26213 0.631066 0.775729i \(-0.282618\pi\)
0.631066 + 0.775729i \(0.282618\pi\)
\(770\) 0 0
\(771\) −6.00000 −0.216085
\(772\) 0 0
\(773\) −18.0000 31.1769i −0.647415 1.12136i −0.983738 0.179609i \(-0.942517\pi\)
0.336323 0.941747i \(-0.390817\pi\)
\(774\) 0 0
\(775\) 20.0000 34.6410i 0.718421 1.24434i
\(776\) 0 0
\(777\) 5.00000 1.73205i 0.179374 0.0621370i
\(778\) 0 0
\(779\) −3.50000 + 6.06218i −0.125401 + 0.217200i
\(780\) 0 0
\(781\) 13.5000 + 23.3827i 0.483068 + 0.836698i
\(782\) 0 0
\(783\) −30.0000 −1.07211
\(784\) 0 0
\(785\) −42.0000 −1.49904
\(786\) 0 0
\(787\) 14.0000 + 24.2487i 0.499046 + 0.864373i 0.999999 0.00110111i \(-0.000350496\pi\)
−0.500953 + 0.865474i \(0.667017\pi\)
\(788\) 0 0
\(789\) −6.00000 + 10.3923i −0.213606 + 0.369976i
\(790\) 0 0
\(791\) −7.50000 + 2.59808i −0.266669 + 0.0923770i
\(792\) 0 0
\(793\) −26.0000 + 45.0333i −0.923287 + 1.59918i
\(794\) 0 0
\(795\) −9.00000 15.5885i −0.319197 0.552866i
\(796\) 0 0
\(797\) −30.0000 −1.06265