Properties

Label 1152.2.i.a.385.1
Level $1152$
Weight $2$
Character 1152.385
Analytic conductor $9.199$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
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 385.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1152.385
Dual form 1152.2.i.a.769.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(1.00000 - 1.73205i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(1.00000 - 1.73205i) q^{7} +(1.50000 + 2.59808i) q^{9} +(-2.50000 + 4.33013i) q^{11} +(2.00000 + 3.46410i) q^{13} +3.46410i q^{15} +1.00000 q^{17} -5.00000 q^{19} +(-3.00000 + 1.73205i) q^{21} +(2.00000 + 3.46410i) q^{23} +(0.500000 - 0.866025i) q^{25} -5.19615i q^{27} +(-3.00000 + 5.19615i) q^{29} +(7.50000 - 4.33013i) q^{33} -4.00000 q^{35} +10.0000 q^{37} -6.92820i q^{39} +(1.50000 + 2.59808i) q^{41} +(4.50000 - 7.79423i) q^{43} +(3.00000 - 5.19615i) q^{45} +(-4.00000 + 6.92820i) q^{47} +(1.50000 + 2.59808i) q^{49} +(-1.50000 - 0.866025i) q^{51} +12.0000 q^{53} +10.0000 q^{55} +(7.50000 + 4.33013i) q^{57} +(-3.50000 - 6.06218i) q^{59} +(2.00000 - 3.46410i) q^{61} +6.00000 q^{63} +(4.00000 - 6.92820i) q^{65} +(3.50000 + 6.06218i) q^{67} -6.92820i q^{69} +6.00000 q^{71} -13.0000 q^{73} +(-1.50000 + 0.866025i) q^{75} +(5.00000 + 8.66025i) q^{77} +(-1.00000 + 1.73205i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-6.00000 + 10.3923i) q^{83} +(-1.00000 - 1.73205i) q^{85} +(9.00000 - 5.19615i) q^{87} +10.0000 q^{89} +8.00000 q^{91} +(5.00000 + 8.66025i) q^{95} +(-6.50000 + 11.2583i) q^{97} -15.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 3q^{3} - 2q^{5} + 2q^{7} + 3q^{9} + O(q^{10}) \) \( 2q - 3q^{3} - 2q^{5} + 2q^{7} + 3q^{9} - 5q^{11} + 4q^{13} + 2q^{17} - 10q^{19} - 6q^{21} + 4q^{23} + q^{25} - 6q^{29} + 15q^{33} - 8q^{35} + 20q^{37} + 3q^{41} + 9q^{43} + 6q^{45} - 8q^{47} + 3q^{49} - 3q^{51} + 24q^{53} + 20q^{55} + 15q^{57} - 7q^{59} + 4q^{61} + 12q^{63} + 8q^{65} + 7q^{67} + 12q^{71} - 26q^{73} - 3q^{75} + 10q^{77} - 2q^{79} - 9q^{81} - 12q^{83} - 2q^{85} + 18q^{87} + 20q^{89} + 16q^{91} + 10q^{95} - 13q^{97} - 30q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) −1.50000 0.866025i −0.866025 0.500000i
\(4\) 0 0
\(5\) −1.00000 1.73205i −0.447214 0.774597i 0.550990 0.834512i \(-0.314250\pi\)
−0.998203 + 0.0599153i \(0.980917\pi\)
\(6\) 0 0
\(7\) 1.00000 1.73205i 0.377964 0.654654i −0.612801 0.790237i \(-0.709957\pi\)
0.990766 + 0.135583i \(0.0432908\pi\)
\(8\) 0 0
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 0 0
\(11\) −2.50000 + 4.33013i −0.753778 + 1.30558i 0.192201 + 0.981356i \(0.438437\pi\)
−0.945979 + 0.324227i \(0.894896\pi\)
\(12\) 0 0
\(13\) 2.00000 + 3.46410i 0.554700 + 0.960769i 0.997927 + 0.0643593i \(0.0205004\pi\)
−0.443227 + 0.896410i \(0.646166\pi\)
\(14\) 0 0
\(15\) 3.46410i 0.894427i
\(16\) 0 0
\(17\) 1.00000 0.242536 0.121268 0.992620i \(-0.461304\pi\)
0.121268 + 0.992620i \(0.461304\pi\)
\(18\) 0 0
\(19\) −5.00000 −1.14708 −0.573539 0.819178i \(-0.694430\pi\)
−0.573539 + 0.819178i \(0.694430\pi\)
\(20\) 0 0
\(21\) −3.00000 + 1.73205i −0.654654 + 0.377964i
\(22\) 0 0
\(23\) 2.00000 + 3.46410i 0.417029 + 0.722315i 0.995639 0.0932891i \(-0.0297381\pi\)
−0.578610 + 0.815604i \(0.696405\pi\)
\(24\) 0 0
\(25\) 0.500000 0.866025i 0.100000 0.173205i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) −3.00000 + 5.19615i −0.557086 + 0.964901i 0.440652 + 0.897678i \(0.354747\pi\)
−0.997738 + 0.0672232i \(0.978586\pi\)
\(30\) 0 0
\(31\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(32\) 0 0
\(33\) 7.50000 4.33013i 1.30558 0.753778i
\(34\) 0 0
\(35\) −4.00000 −0.676123
\(36\) 0 0
\(37\) 10.0000 1.64399 0.821995 0.569495i \(-0.192861\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) 0 0
\(39\) 6.92820i 1.10940i
\(40\) 0 0
\(41\) 1.50000 + 2.59808i 0.234261 + 0.405751i 0.959058 0.283211i \(-0.0913998\pi\)
−0.724797 + 0.688963i \(0.758066\pi\)
\(42\) 0 0
\(43\) 4.50000 7.79423i 0.686244 1.18861i −0.286801 0.957990i \(-0.592592\pi\)
0.973044 0.230618i \(-0.0740749\pi\)
\(44\) 0 0
\(45\) 3.00000 5.19615i 0.447214 0.774597i
\(46\) 0 0
\(47\) −4.00000 + 6.92820i −0.583460 + 1.01058i 0.411606 + 0.911362i \(0.364968\pi\)
−0.995066 + 0.0992202i \(0.968365\pi\)
\(48\) 0 0
\(49\) 1.50000 + 2.59808i 0.214286 + 0.371154i
\(50\) 0 0
\(51\) −1.50000 0.866025i −0.210042 0.121268i
\(52\) 0 0
\(53\) 12.0000 1.64833 0.824163 0.566352i \(-0.191646\pi\)
0.824163 + 0.566352i \(0.191646\pi\)
\(54\) 0 0
\(55\) 10.0000 1.34840
\(56\) 0 0
\(57\) 7.50000 + 4.33013i 0.993399 + 0.573539i
\(58\) 0 0
\(59\) −3.50000 6.06218i −0.455661 0.789228i 0.543065 0.839691i \(-0.317264\pi\)
−0.998726 + 0.0504625i \(0.983930\pi\)
\(60\) 0 0
\(61\) 2.00000 3.46410i 0.256074 0.443533i −0.709113 0.705095i \(-0.750904\pi\)
0.965187 + 0.261562i \(0.0842377\pi\)
\(62\) 0 0
\(63\) 6.00000 0.755929
\(64\) 0 0
\(65\) 4.00000 6.92820i 0.496139 0.859338i
\(66\) 0 0
\(67\) 3.50000 + 6.06218i 0.427593 + 0.740613i 0.996659 0.0816792i \(-0.0260283\pi\)
−0.569066 + 0.822292i \(0.692695\pi\)
\(68\) 0 0
\(69\) 6.92820i 0.834058i
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) −13.0000 −1.52153 −0.760767 0.649025i \(-0.775177\pi\)
−0.760767 + 0.649025i \(0.775177\pi\)
\(74\) 0 0
\(75\) −1.50000 + 0.866025i −0.173205 + 0.100000i
\(76\) 0 0
\(77\) 5.00000 + 8.66025i 0.569803 + 0.986928i
\(78\) 0 0
\(79\) −1.00000 + 1.73205i −0.112509 + 0.194871i −0.916781 0.399390i \(-0.869222\pi\)
0.804272 + 0.594261i \(0.202555\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 0 0
\(83\) −6.00000 + 10.3923i −0.658586 + 1.14070i 0.322396 + 0.946605i \(0.395512\pi\)
−0.980982 + 0.194099i \(0.937822\pi\)
\(84\) 0 0
\(85\) −1.00000 1.73205i −0.108465 0.187867i
\(86\) 0 0
\(87\) 9.00000 5.19615i 0.964901 0.557086i
\(88\) 0 0
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) 0 0
\(91\) 8.00000 0.838628
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 5.00000 + 8.66025i 0.512989 + 0.888523i
\(96\) 0 0
\(97\) −6.50000 + 11.2583i −0.659975 + 1.14311i 0.320647 + 0.947199i \(0.396100\pi\)
−0.980622 + 0.195911i \(0.937234\pi\)
\(98\) 0 0
\(99\) −15.0000 −1.50756
\(100\) 0 0
\(101\) −3.00000 + 5.19615i −0.298511 + 0.517036i −0.975796 0.218685i \(-0.929823\pi\)
0.677284 + 0.735721i \(0.263157\pi\)
\(102\) 0 0
\(103\) 4.00000 + 6.92820i 0.394132 + 0.682656i 0.992990 0.118199i \(-0.0377120\pi\)
−0.598858 + 0.800855i \(0.704379\pi\)
\(104\) 0 0
\(105\) 6.00000 + 3.46410i 0.585540 + 0.338062i
\(106\) 0 0
\(107\) 11.0000 1.06341 0.531705 0.846930i \(-0.321551\pi\)
0.531705 + 0.846930i \(0.321551\pi\)
\(108\) 0 0
\(109\) 12.0000 1.14939 0.574696 0.818367i \(-0.305120\pi\)
0.574696 + 0.818367i \(0.305120\pi\)
\(110\) 0 0
\(111\) −15.0000 8.66025i −1.42374 0.821995i
\(112\) 0 0
\(113\) −7.00000 12.1244i −0.658505 1.14056i −0.981003 0.193993i \(-0.937856\pi\)
0.322498 0.946570i \(-0.395477\pi\)
\(114\) 0 0
\(115\) 4.00000 6.92820i 0.373002 0.646058i
\(116\) 0 0
\(117\) −6.00000 + 10.3923i −0.554700 + 0.960769i
\(118\) 0 0
\(119\) 1.00000 1.73205i 0.0916698 0.158777i
\(120\) 0 0
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) 0 0
\(123\) 5.19615i 0.468521i
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) 20.0000 1.77471 0.887357 0.461084i \(-0.152539\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) 0 0
\(129\) −13.5000 + 7.79423i −1.18861 + 0.686244i
\(130\) 0 0
\(131\) 6.00000 + 10.3923i 0.524222 + 0.907980i 0.999602 + 0.0281993i \(0.00897729\pi\)
−0.475380 + 0.879781i \(0.657689\pi\)
\(132\) 0 0
\(133\) −5.00000 + 8.66025i −0.433555 + 0.750939i
\(134\) 0 0
\(135\) −9.00000 + 5.19615i −0.774597 + 0.447214i
\(136\) 0 0
\(137\) −0.500000 + 0.866025i −0.0427179 + 0.0739895i −0.886594 0.462549i \(-0.846935\pi\)
0.843876 + 0.536538i \(0.180268\pi\)
\(138\) 0 0
\(139\) −0.500000 0.866025i −0.0424094 0.0734553i 0.844042 0.536278i \(-0.180170\pi\)
−0.886451 + 0.462822i \(0.846837\pi\)
\(140\) 0 0
\(141\) 12.0000 6.92820i 1.01058 0.583460i
\(142\) 0 0
\(143\) −20.0000 −1.67248
\(144\) 0 0
\(145\) 12.0000 0.996546
\(146\) 0 0
\(147\) 5.19615i 0.428571i
\(148\) 0 0
\(149\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(150\) 0 0
\(151\) 8.00000 13.8564i 0.651031 1.12762i −0.331842 0.943335i \(-0.607670\pi\)
0.982873 0.184284i \(-0.0589965\pi\)
\(152\) 0 0
\(153\) 1.50000 + 2.59808i 0.121268 + 0.210042i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −12.0000 20.7846i −0.957704 1.65879i −0.728055 0.685519i \(-0.759575\pi\)
−0.229650 0.973273i \(-0.573758\pi\)
\(158\) 0 0
\(159\) −18.0000 10.3923i −1.42749 0.824163i
\(160\) 0 0
\(161\) 8.00000 0.630488
\(162\) 0 0
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) 0 0
\(165\) −15.0000 8.66025i −1.16775 0.674200i
\(166\) 0 0
\(167\) −1.00000 1.73205i −0.0773823 0.134030i 0.824737 0.565516i \(-0.191323\pi\)
−0.902120 + 0.431486i \(0.857990\pi\)
\(168\) 0 0
\(169\) −1.50000 + 2.59808i −0.115385 + 0.199852i
\(170\) 0 0
\(171\) −7.50000 12.9904i −0.573539 0.993399i
\(172\) 0 0
\(173\) −9.00000 + 15.5885i −0.684257 + 1.18517i 0.289412 + 0.957205i \(0.406540\pi\)
−0.973670 + 0.227964i \(0.926793\pi\)
\(174\) 0 0
\(175\) −1.00000 1.73205i −0.0755929 0.130931i
\(176\) 0 0
\(177\) 12.1244i 0.911322i
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) 20.0000 1.48659 0.743294 0.668965i \(-0.233262\pi\)
0.743294 + 0.668965i \(0.233262\pi\)
\(182\) 0 0
\(183\) −6.00000 + 3.46410i −0.443533 + 0.256074i
\(184\) 0 0
\(185\) −10.0000 17.3205i −0.735215 1.27343i
\(186\) 0 0
\(187\) −2.50000 + 4.33013i −0.182818 + 0.316650i
\(188\) 0 0
\(189\) −9.00000 5.19615i −0.654654 0.377964i
\(190\) 0 0
\(191\) 1.00000 1.73205i 0.0723575 0.125327i −0.827577 0.561353i \(-0.810281\pi\)
0.899934 + 0.436026i \(0.143614\pi\)
\(192\) 0 0
\(193\) −0.500000 0.866025i −0.0359908 0.0623379i 0.847469 0.530845i \(-0.178125\pi\)
−0.883460 + 0.468507i \(0.844792\pi\)
\(194\) 0 0
\(195\) −12.0000 + 6.92820i −0.859338 + 0.496139i
\(196\) 0 0
\(197\) −20.0000 −1.42494 −0.712470 0.701702i \(-0.752424\pi\)
−0.712470 + 0.701702i \(0.752424\pi\)
\(198\) 0 0
\(199\) −2.00000 −0.141776 −0.0708881 0.997484i \(-0.522583\pi\)
−0.0708881 + 0.997484i \(0.522583\pi\)
\(200\) 0 0
\(201\) 12.1244i 0.855186i
\(202\) 0 0
\(203\) 6.00000 + 10.3923i 0.421117 + 0.729397i
\(204\) 0 0
\(205\) 3.00000 5.19615i 0.209529 0.362915i
\(206\) 0 0
\(207\) −6.00000 + 10.3923i −0.417029 + 0.722315i
\(208\) 0 0
\(209\) 12.5000 21.6506i 0.864643 1.49761i
\(210\) 0 0
\(211\) 10.0000 + 17.3205i 0.688428 + 1.19239i 0.972346 + 0.233544i \(0.0750324\pi\)
−0.283918 + 0.958849i \(0.591634\pi\)
\(212\) 0 0
\(213\) −9.00000 5.19615i −0.616670 0.356034i
\(214\) 0 0
\(215\) −18.0000 −1.22759
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 19.5000 + 11.2583i 1.31769 + 0.760767i
\(220\) 0 0
\(221\) 2.00000 + 3.46410i 0.134535 + 0.233021i
\(222\) 0 0
\(223\) −12.0000 + 20.7846i −0.803579 + 1.39184i 0.113666 + 0.993519i \(0.463740\pi\)
−0.917246 + 0.398321i \(0.869593\pi\)
\(224\) 0 0
\(225\) 3.00000 0.200000
\(226\) 0 0
\(227\) 1.50000 2.59808i 0.0995585 0.172440i −0.811943 0.583736i \(-0.801590\pi\)
0.911502 + 0.411296i \(0.134924\pi\)
\(228\) 0 0
\(229\) 7.00000 + 12.1244i 0.462573 + 0.801200i 0.999088 0.0426906i \(-0.0135930\pi\)
−0.536515 + 0.843891i \(0.680260\pi\)
\(230\) 0 0
\(231\) 17.3205i 1.13961i
\(232\) 0 0
\(233\) −9.00000 −0.589610 −0.294805 0.955557i \(-0.595255\pi\)
−0.294805 + 0.955557i \(0.595255\pi\)
\(234\) 0 0
\(235\) 16.0000 1.04372
\(236\) 0 0
\(237\) 3.00000 1.73205i 0.194871 0.112509i
\(238\) 0 0
\(239\) 6.00000 + 10.3923i 0.388108 + 0.672222i 0.992195 0.124696i \(-0.0397955\pi\)
−0.604087 + 0.796918i \(0.706462\pi\)
\(240\) 0 0
\(241\) −12.5000 + 21.6506i −0.805196 + 1.39464i 0.110963 + 0.993825i \(0.464606\pi\)
−0.916159 + 0.400815i \(0.868727\pi\)
\(242\) 0 0
\(243\) 13.5000 7.79423i 0.866025 0.500000i
\(244\) 0 0
\(245\) 3.00000 5.19615i 0.191663 0.331970i
\(246\) 0 0
\(247\) −10.0000 17.3205i −0.636285 1.10208i
\(248\) 0 0
\(249\) 18.0000 10.3923i 1.14070 0.658586i
\(250\) 0 0
\(251\) −3.00000 −0.189358 −0.0946792 0.995508i \(-0.530183\pi\)
−0.0946792 + 0.995508i \(0.530183\pi\)
\(252\) 0 0
\(253\) −20.0000 −1.25739
\(254\) 0 0
\(255\) 3.46410i 0.216930i
\(256\) 0 0
\(257\) −1.50000 2.59808i −0.0935674 0.162064i 0.815442 0.578838i \(-0.196494\pi\)
−0.909010 + 0.416775i \(0.863160\pi\)
\(258\) 0 0
\(259\) 10.0000 17.3205i 0.621370 1.07624i
\(260\) 0 0
\(261\) −18.0000 −1.11417
\(262\) 0 0
\(263\) −9.00000 + 15.5885i −0.554964 + 0.961225i 0.442943 + 0.896550i \(0.353935\pi\)
−0.997906 + 0.0646755i \(0.979399\pi\)
\(264\) 0 0
\(265\) −12.0000 20.7846i −0.737154 1.27679i
\(266\) 0 0
\(267\) −15.0000 8.66025i −0.917985 0.529999i
\(268\) 0 0
\(269\) 4.00000 0.243884 0.121942 0.992537i \(-0.461088\pi\)
0.121942 + 0.992537i \(0.461088\pi\)
\(270\) 0 0
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 0 0
\(273\) −12.0000 6.92820i −0.726273 0.419314i
\(274\) 0 0
\(275\) 2.50000 + 4.33013i 0.150756 + 0.261116i
\(276\) 0 0
\(277\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −15.0000 + 25.9808i −0.894825 + 1.54988i −0.0608039 + 0.998150i \(0.519366\pi\)
−0.834021 + 0.551733i \(0.813967\pi\)
\(282\) 0 0
\(283\) 12.0000 + 20.7846i 0.713326 + 1.23552i 0.963602 + 0.267342i \(0.0861454\pi\)
−0.250276 + 0.968175i \(0.580521\pi\)
\(284\) 0 0
\(285\) 17.3205i 1.02598i
\(286\) 0 0
\(287\) 6.00000 0.354169
\(288\) 0 0
\(289\) −16.0000 −0.941176
\(290\) 0 0
\(291\) 19.5000 11.2583i 1.14311 0.659975i
\(292\) 0 0
\(293\) −5.00000 8.66025i −0.292103 0.505937i 0.682204 0.731162i \(-0.261022\pi\)
−0.974307 + 0.225225i \(0.927688\pi\)
\(294\) 0 0
\(295\) −7.00000 + 12.1244i −0.407556 + 0.705907i
\(296\) 0 0
\(297\) 22.5000 + 12.9904i 1.30558 + 0.753778i
\(298\) 0 0
\(299\) −8.00000 + 13.8564i −0.462652 + 0.801337i
\(300\) 0 0
\(301\) −9.00000 15.5885i −0.518751 0.898504i
\(302\) 0 0
\(303\) 9.00000 5.19615i 0.517036 0.298511i
\(304\) 0 0
\(305\) −8.00000 −0.458079
\(306\) 0 0
\(307\) −3.00000 −0.171219 −0.0856095 0.996329i \(-0.527284\pi\)
−0.0856095 + 0.996329i \(0.527284\pi\)
\(308\) 0 0
\(309\) 13.8564i 0.788263i
\(310\) 0 0
\(311\) −5.00000 8.66025i −0.283524 0.491078i 0.688726 0.725022i \(-0.258170\pi\)
−0.972250 + 0.233944i \(0.924837\pi\)
\(312\) 0 0
\(313\) −12.5000 + 21.6506i −0.706542 + 1.22377i 0.259590 + 0.965719i \(0.416412\pi\)
−0.966132 + 0.258047i \(0.916921\pi\)
\(314\) 0 0
\(315\) −6.00000 10.3923i −0.338062 0.585540i
\(316\) 0 0
\(317\) −6.00000 + 10.3923i −0.336994 + 0.583690i −0.983866 0.178908i \(-0.942743\pi\)
0.646872 + 0.762598i \(0.276077\pi\)
\(318\) 0 0
\(319\) −15.0000 25.9808i −0.839839 1.45464i
\(320\) 0 0
\(321\) −16.5000 9.52628i −0.920940 0.531705i
\(322\) 0 0
\(323\) −5.00000 −0.278207
\(324\) 0 0
\(325\) 4.00000 0.221880
\(326\) 0 0
\(327\) −18.0000 10.3923i −0.995402 0.574696i
\(328\) 0 0
\(329\) 8.00000 + 13.8564i 0.441054 + 0.763928i
\(330\) 0 0
\(331\) 10.0000 17.3205i 0.549650 0.952021i −0.448649 0.893708i \(-0.648095\pi\)
0.998298 0.0583130i \(-0.0185721\pi\)
\(332\) 0 0
\(333\) 15.0000 + 25.9808i 0.821995 + 1.42374i
\(334\) 0 0
\(335\) 7.00000 12.1244i 0.382451 0.662424i
\(336\) 0 0
\(337\) −9.50000 16.4545i −0.517498 0.896333i −0.999793 0.0203242i \(-0.993530\pi\)
0.482295 0.876009i \(-0.339803\pi\)
\(338\) 0 0
\(339\) 24.2487i 1.31701i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 20.0000 1.07990
\(344\) 0 0
\(345\) −12.0000 + 6.92820i −0.646058 + 0.373002i
\(346\) 0 0
\(347\) 1.50000 + 2.59808i 0.0805242 + 0.139472i 0.903475 0.428640i \(-0.141007\pi\)
−0.822951 + 0.568112i \(0.807674\pi\)
\(348\) 0 0
\(349\) −8.00000 + 13.8564i −0.428230 + 0.741716i −0.996716 0.0809766i \(-0.974196\pi\)
0.568486 + 0.822693i \(0.307529\pi\)
\(350\) 0 0
\(351\) 18.0000 10.3923i 0.960769 0.554700i
\(352\) 0 0
\(353\) 4.50000 7.79423i 0.239511 0.414845i −0.721063 0.692869i \(-0.756346\pi\)
0.960574 + 0.278024i \(0.0896796\pi\)
\(354\) 0 0
\(355\) −6.00000 10.3923i −0.318447 0.551566i
\(356\) 0 0
\(357\) −3.00000 + 1.73205i −0.158777 + 0.0916698i
\(358\) 0 0
\(359\) 34.0000 1.79445 0.897226 0.441572i \(-0.145579\pi\)
0.897226 + 0.441572i \(0.145579\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) 0 0
\(363\) 24.2487i 1.27273i
\(364\) 0 0
\(365\) 13.0000 + 22.5167i 0.680451 + 1.17858i
\(366\) 0 0
\(367\) 11.0000 19.0526i 0.574195 0.994535i −0.421933 0.906627i \(-0.638648\pi\)
0.996129 0.0879086i \(-0.0280183\pi\)
\(368\) 0 0
\(369\) −4.50000 + 7.79423i −0.234261 + 0.405751i
\(370\) 0 0
\(371\) 12.0000 20.7846i 0.623009 1.07908i
\(372\) 0 0
\(373\) 16.0000 + 27.7128i 0.828449 + 1.43492i 0.899255 + 0.437425i \(0.144109\pi\)
−0.0708063 + 0.997490i \(0.522557\pi\)
\(374\) 0 0
\(375\) 18.0000 + 10.3923i 0.929516 + 0.536656i
\(376\) 0 0
\(377\) −24.0000 −1.23606
\(378\) 0 0
\(379\) −25.0000 −1.28416 −0.642082 0.766636i \(-0.721929\pi\)
−0.642082 + 0.766636i \(0.721929\pi\)
\(380\) 0 0
\(381\) −30.0000 17.3205i −1.53695 0.887357i
\(382\) 0 0
\(383\) −3.00000 5.19615i −0.153293 0.265511i 0.779143 0.626846i \(-0.215654\pi\)
−0.932436 + 0.361335i \(0.882321\pi\)
\(384\) 0 0
\(385\) 10.0000 17.3205i 0.509647 0.882735i
\(386\) 0 0
\(387\) 27.0000 1.37249
\(388\) 0 0
\(389\) 19.0000 32.9090i 0.963338 1.66855i 0.249323 0.968420i \(-0.419792\pi\)
0.714015 0.700130i \(-0.246875\pi\)
\(390\) 0 0
\(391\) 2.00000 + 3.46410i 0.101144 + 0.175187i
\(392\) 0 0
\(393\) 20.7846i 1.04844i
\(394\) 0 0
\(395\) 4.00000 0.201262
\(396\) 0 0
\(397\) 18.0000 0.903394 0.451697 0.892171i \(-0.350819\pi\)
0.451697 + 0.892171i \(0.350819\pi\)
\(398\) 0 0
\(399\) 15.0000 8.66025i 0.750939 0.433555i
\(400\) 0 0
\(401\) 1.50000 + 2.59808i 0.0749064 + 0.129742i 0.901046 0.433724i \(-0.142801\pi\)
−0.826139 + 0.563466i \(0.809468\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 18.0000 0.894427
\(406\) 0 0
\(407\) −25.0000 + 43.3013i −1.23920 + 2.14636i
\(408\) 0 0
\(409\) −12.5000 21.6506i −0.618085 1.07056i −0.989835 0.142222i \(-0.954575\pi\)
0.371750 0.928333i \(-0.378758\pi\)
\(410\) 0 0
\(411\) 1.50000 0.866025i 0.0739895 0.0427179i
\(412\) 0 0
\(413\) −14.0000 −0.688895
\(414\) 0 0
\(415\) 24.0000 1.17811
\(416\) 0 0
\(417\) 1.73205i 0.0848189i
\(418\) 0 0
\(419\) 10.0000 + 17.3205i 0.488532 + 0.846162i 0.999913 0.0131919i \(-0.00419923\pi\)
−0.511381 + 0.859354i \(0.670866\pi\)
\(420\) 0 0
\(421\) 1.00000 1.73205i 0.0487370 0.0844150i −0.840628 0.541613i \(-0.817814\pi\)
0.889365 + 0.457198i \(0.151147\pi\)
\(422\) 0 0
\(423\) −24.0000 −1.16692
\(424\) 0 0
\(425\) 0.500000 0.866025i 0.0242536 0.0420084i
\(426\) 0 0
\(427\) −4.00000 6.92820i −0.193574 0.335279i
\(428\) 0 0
\(429\) 30.0000 + 17.3205i 1.44841 + 0.836242i
\(430\) 0 0
\(431\) −10.0000 −0.481683 −0.240842 0.970564i \(-0.577423\pi\)
−0.240842 + 0.970564i \(0.577423\pi\)
\(432\) 0 0
\(433\) 33.0000 1.58588 0.792939 0.609301i \(-0.208550\pi\)
0.792939 + 0.609301i \(0.208550\pi\)
\(434\) 0 0
\(435\) −18.0000 10.3923i −0.863034 0.498273i
\(436\) 0 0
\(437\) −10.0000 17.3205i −0.478365 0.828552i
\(438\) 0 0
\(439\) −12.0000 + 20.7846i −0.572729 + 0.991995i 0.423556 + 0.905870i \(0.360782\pi\)
−0.996284 + 0.0861252i \(0.972552\pi\)
\(440\) 0 0
\(441\) −4.50000 + 7.79423i −0.214286 + 0.371154i
\(442\) 0 0
\(443\) −7.50000 + 12.9904i −0.356336 + 0.617192i −0.987346 0.158583i \(-0.949307\pi\)
0.631010 + 0.775775i \(0.282641\pi\)
\(444\) 0 0
\(445\) −10.0000 17.3205i −0.474045 0.821071i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 17.0000 0.802280 0.401140 0.916017i \(-0.368614\pi\)
0.401140 + 0.916017i \(0.368614\pi\)
\(450\) 0 0
\(451\) −15.0000 −0.706322
\(452\) 0 0
\(453\) −24.0000 + 13.8564i −1.12762 + 0.651031i
\(454\) 0 0
\(455\) −8.00000 13.8564i −0.375046 0.649598i
\(456\) 0 0
\(457\) 1.50000 2.59808i 0.0701670 0.121533i −0.828807 0.559534i \(-0.810980\pi\)
0.898974 + 0.438001i \(0.144313\pi\)
\(458\) 0 0
\(459\) 5.19615i 0.242536i
\(460\) 0 0
\(461\) 10.0000 17.3205i 0.465746 0.806696i −0.533488 0.845807i \(-0.679119\pi\)
0.999235 + 0.0391109i \(0.0124526\pi\)
\(462\) 0 0
\(463\) −1.00000 1.73205i −0.0464739 0.0804952i 0.841853 0.539707i \(-0.181465\pi\)
−0.888327 + 0.459212i \(0.848132\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 29.0000 1.34196 0.670980 0.741475i \(-0.265874\pi\)
0.670980 + 0.741475i \(0.265874\pi\)
\(468\) 0 0
\(469\) 14.0000 0.646460
\(470\) 0 0
\(471\) 41.5692i 1.91541i
\(472\) 0 0
\(473\) 22.5000 + 38.9711i 1.03455 + 1.79190i
\(474\) 0 0
\(475\) −2.50000 + 4.33013i −0.114708 + 0.198680i
\(476\) 0 0
\(477\) 18.0000 + 31.1769i 0.824163 + 1.42749i
\(478\) 0 0
\(479\) 9.00000 15.5885i 0.411220 0.712255i −0.583803 0.811895i \(-0.698436\pi\)
0.995023 + 0.0996406i \(0.0317693\pi\)
\(480\) 0 0
\(481\) 20.0000 + 34.6410i 0.911922 + 1.57949i
\(482\) 0 0
\(483\) −12.0000 6.92820i −0.546019 0.315244i
\(484\) 0 0
\(485\) 26.0000 1.18060
\(486\) 0 0
\(487\) −10.0000 −0.453143 −0.226572 0.973995i \(-0.572752\pi\)
−0.226572 + 0.973995i \(0.572752\pi\)
\(488\) 0 0
\(489\) −6.00000 3.46410i −0.271329 0.156652i
\(490\) 0 0
\(491\) −12.5000 21.6506i −0.564117 0.977079i −0.997131 0.0756923i \(-0.975883\pi\)
0.433014 0.901387i \(-0.357450\pi\)
\(492\) 0 0
\(493\) −3.00000 + 5.19615i −0.135113 + 0.234023i
\(494\) 0 0
\(495\) 15.0000 + 25.9808i 0.674200 + 1.16775i
\(496\) 0 0
\(497\) 6.00000 10.3923i 0.269137 0.466159i
\(498\) 0 0
\(499\) 2.50000 + 4.33013i 0.111915 + 0.193843i 0.916542 0.399937i \(-0.130968\pi\)
−0.804627 + 0.593780i \(0.797635\pi\)
\(500\) 0 0
\(501\) 3.46410i 0.154765i
\(502\) 0 0
\(503\) 4.00000 0.178351 0.0891756 0.996016i \(-0.471577\pi\)
0.0891756 + 0.996016i \(0.471577\pi\)
\(504\) 0 0
\(505\) 12.0000 0.533993
\(506\) 0 0
\(507\) 4.50000 2.59808i 0.199852 0.115385i
\(508\) 0 0
\(509\) −14.0000 24.2487i −0.620539 1.07481i −0.989385 0.145315i \(-0.953580\pi\)
0.368846 0.929490i \(-0.379753\pi\)
\(510\) 0 0
\(511\) −13.0000 + 22.5167i −0.575086 + 0.996078i
\(512\) 0 0
\(513\) 25.9808i 1.14708i
\(514\) 0 0
\(515\) 8.00000 13.8564i 0.352522 0.610586i
\(516\) 0 0
\(517\) −20.0000 34.6410i −0.879599 1.52351i
\(518\) 0 0
\(519\) 27.0000 15.5885i 1.18517 0.684257i
\(520\) 0 0
\(521\) −7.00000 −0.306676 −0.153338 0.988174i \(-0.549002\pi\)
−0.153338 + 0.988174i \(0.549002\pi\)
\(522\) 0 0
\(523\) −44.0000 −1.92399 −0.961993 0.273075i \(-0.911959\pi\)
−0.961993 + 0.273075i \(0.911959\pi\)
\(524\) 0 0
\(525\) 3.46410i 0.151186i
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 3.50000 6.06218i 0.152174 0.263573i
\(530\) 0 0
\(531\) 10.5000 18.1865i 0.455661 0.789228i
\(532\) 0 0
\(533\) −6.00000 + 10.3923i −0.259889 + 0.450141i
\(534\) 0 0
\(535\) −11.0000 19.0526i −0.475571 0.823714i
\(536\) 0 0
\(537\) 18.0000 + 10.3923i 0.776757 + 0.448461i
\(538\) 0 0
\(539\) −15.0000 −0.646096
\(540\) 0 0
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) 0 0
\(543\) −30.0000 17.3205i −1.28742 0.743294i
\(544\) 0 0
\(545\) −12.0000 20.7846i −0.514024 0.890315i
\(546\) 0 0
\(547\) 0.500000 0.866025i 0.0213785 0.0370286i −0.855138 0.518400i \(-0.826528\pi\)
0.876517 + 0.481371i \(0.159861\pi\)
\(548\) 0 0
\(549\) 12.0000 0.512148
\(550\) 0 0
\(551\) 15.0000 25.9808i 0.639021 1.10682i
\(552\) 0 0
\(553\) 2.00000 + 3.46410i 0.0850487 + 0.147309i
\(554\) 0 0
\(555\) 34.6410i 1.47043i
\(556\) 0 0
\(557\) 26.0000 1.10166 0.550828 0.834619i \(-0.314312\pi\)
0.550828 + 0.834619i \(0.314312\pi\)
\(558\) 0 0
\(559\) 36.0000 1.52264
\(560\) 0 0
\(561\) 7.50000 4.33013i 0.316650 0.182818i
\(562\) 0 0
\(563\) −16.5000 28.5788i −0.695392 1.20445i −0.970048 0.242912i \(-0.921897\pi\)
0.274656 0.961542i \(-0.411436\pi\)
\(564\) 0 0
\(565\) −14.0000 + 24.2487i −0.588984 + 1.02015i
\(566\) 0 0
\(567\) 9.00000 + 15.5885i 0.377964 + 0.654654i
\(568\) 0 0
\(569\) 9.50000 16.4545i 0.398261 0.689808i −0.595251 0.803540i \(-0.702947\pi\)
0.993511 + 0.113732i \(0.0362806\pi\)
\(570\) 0 0
\(571\) −9.50000 16.4545i −0.397563 0.688599i 0.595862 0.803087i \(-0.296811\pi\)
−0.993425 + 0.114488i \(0.963477\pi\)
\(572\) 0 0
\(573\) −3.00000 + 1.73205i −0.125327 + 0.0723575i
\(574\) 0 0
\(575\) 4.00000 0.166812
\(576\) 0 0
\(577\) 23.0000 0.957503 0.478751 0.877951i \(-0.341090\pi\)
0.478751 + 0.877951i \(0.341090\pi\)
\(578\) 0 0
\(579\) 1.73205i 0.0719816i
\(580\) 0 0
\(581\) 12.0000 + 20.7846i 0.497844 + 0.862291i
\(582\) 0 0
\(583\) −30.0000 + 51.9615i −1.24247 + 2.15203i
\(584\) 0 0
\(585\) 24.0000 0.992278
\(586\) 0 0
\(587\) 2.50000 4.33013i 0.103186 0.178723i −0.809810 0.586693i \(-0.800430\pi\)
0.912996 + 0.407969i \(0.133763\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 30.0000 + 17.3205i 1.23404 + 0.712470i
\(592\) 0 0
\(593\) 6.00000 0.246390 0.123195 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) 0 0
\(595\) −4.00000 −0.163984
\(596\) 0 0
\(597\) 3.00000 + 1.73205i 0.122782 + 0.0708881i
\(598\) 0 0
\(599\) −21.0000 36.3731i −0.858037 1.48616i −0.873799 0.486287i \(-0.838351\pi\)
0.0157622 0.999876i \(-0.494983\pi\)
\(600\) 0 0
\(601\) 4.50000 7.79423i 0.183559 0.317933i −0.759531 0.650471i \(-0.774572\pi\)
0.943090 + 0.332538i \(0.107905\pi\)
\(602\) 0 0
\(603\) −10.5000 + 18.1865i −0.427593 + 0.740613i
\(604\) 0 0
\(605\) −14.0000 + 24.2487i −0.569181 + 0.985850i
\(606\) 0 0
\(607\) 4.00000 + 6.92820i 0.162355 + 0.281207i 0.935713 0.352763i \(-0.114758\pi\)
−0.773358 + 0.633970i \(0.781424\pi\)
\(608\) 0 0
\(609\) 20.7846i 0.842235i
\(610\) 0 0
\(611\) −32.0000 −1.29458
\(612\) 0 0
\(613\) −26.0000 −1.05013 −0.525065 0.851062i \(-0.675959\pi\)
−0.525065 + 0.851062i \(0.675959\pi\)
\(614\) 0 0
\(615\) −9.00000 + 5.19615i −0.362915 + 0.209529i
\(616\) 0 0
\(617\) 8.50000 + 14.7224i 0.342197 + 0.592703i 0.984840 0.173463i \(-0.0554956\pi\)
−0.642643 + 0.766165i \(0.722162\pi\)
\(618\) 0 0
\(619\) −17.5000 + 30.3109i −0.703384 + 1.21830i 0.263887 + 0.964554i \(0.414995\pi\)
−0.967271 + 0.253744i \(0.918338\pi\)
\(620\) 0 0
\(621\) 18.0000 10.3923i 0.722315 0.417029i
\(622\) 0 0
\(623\) 10.0000 17.3205i 0.400642 0.693932i
\(624\) 0 0
\(625\) 9.50000 + 16.4545i 0.380000 + 0.658179i
\(626\) 0 0
\(627\) −37.5000 + 21.6506i −1.49761 + 0.864643i
\(628\) 0 0
\(629\) 10.0000 0.398726
\(630\) 0 0
\(631\) −22.0000 −0.875806 −0.437903 0.899022i \(-0.644279\pi\)
−0.437903 + 0.899022i \(0.644279\pi\)
\(632\) 0 0
\(633\) 34.6410i 1.37686i
\(634\) 0 0
\(635\) −20.0000 34.6410i −0.793676 1.37469i
\(636\) 0 0
\(637\) −6.00000 + 10.3923i −0.237729 + 0.411758i
\(638\) 0 0
\(639\) 9.00000 + 15.5885i 0.356034 + 0.616670i
\(640\) 0 0
\(641\) −16.5000 + 28.5788i −0.651711 + 1.12880i 0.330997 + 0.943632i \(0.392615\pi\)
−0.982708 + 0.185164i \(0.940718\pi\)
\(642\) 0 0
\(643\) 10.5000 + 18.1865i 0.414080 + 0.717207i 0.995331 0.0965169i \(-0.0307702\pi\)
−0.581252 + 0.813724i \(0.697437\pi\)
\(644\) 0 0
\(645\) 27.0000 + 15.5885i 1.06312 + 0.613795i
\(646\) 0 0
\(647\) 42.0000 1.65119 0.825595 0.564263i \(-0.190840\pi\)
0.825595 + 0.564263i \(0.190840\pi\)
\(648\) 0 0
\(649\) 35.0000 1.37387
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 9.00000 + 15.5885i 0.352197 + 0.610023i 0.986634 0.162951i \(-0.0521013\pi\)
−0.634437 + 0.772975i \(0.718768\pi\)
\(654\) 0 0
\(655\) 12.0000 20.7846i 0.468879 0.812122i
\(656\) 0 0
\(657\) −19.5000 33.7750i −0.760767 1.31769i
\(658\) 0 0
\(659\) 12.0000 20.7846i 0.467454 0.809653i −0.531855 0.846836i \(-0.678505\pi\)
0.999309 + 0.0371821i \(0.0118382\pi\)
\(660\) 0 0
\(661\) 1.00000 + 1.73205i 0.0388955 + 0.0673690i 0.884818 0.465937i \(-0.154283\pi\)
−0.845922 + 0.533306i \(0.820949\pi\)
\(662\) 0 0
\(663\) 6.92820i 0.269069i
\(664\) 0 0
\(665\) 20.0000 0.775567
\(666\) 0 0
\(667\) −24.0000 −0.929284
\(668\) 0 0
\(669\) 36.0000 20.7846i 1.39184 0.803579i
\(670\) 0 0
\(671\) 10.0000 + 17.3205i 0.386046 + 0.668651i
\(672\) 0 0
\(673\) −5.00000 + 8.66025i −0.192736 + 0.333828i −0.946156 0.323711i \(-0.895069\pi\)
0.753420 + 0.657539i \(0.228403\pi\)
\(674\) 0 0
\(675\) −4.50000 2.59808i −0.173205 0.100000i
\(676\) 0 0
\(677\) 14.0000 24.2487i 0.538064 0.931954i −0.460945 0.887429i \(-0.652489\pi\)
0.999008 0.0445248i \(-0.0141774\pi\)
\(678\) 0 0
\(679\) 13.0000 + 22.5167i 0.498894 + 0.864110i
\(680\) 0 0
\(681\) −4.50000 + 2.59808i −0.172440 + 0.0995585i
\(682\) 0 0
\(683\) 15.0000 0.573959 0.286980 0.957937i \(-0.407349\pi\)
0.286980 + 0.957937i \(0.407349\pi\)
\(684\) 0 0
\(685\) 2.00000 0.0764161
\(686\) 0 0
\(687\) 24.2487i 0.925146i
\(688\) 0 0
\(689\) 24.0000 + 41.5692i 0.914327 + 1.58366i
\(690\) 0 0
\(691\) 6.00000 10.3923i 0.228251 0.395342i −0.729039 0.684472i \(-0.760033\pi\)
0.957290 + 0.289130i \(0.0933661\pi\)
\(692\) 0 0
\(693\) −15.0000 + 25.9808i −0.569803 + 0.986928i
\(694\) 0 0
\(695\) −1.00000 + 1.73205i −0.0379322 + 0.0657004i
\(696\) 0 0
\(697\) 1.50000 + 2.59808i 0.0568166 + 0.0984092i
\(698\) 0 0
\(699\) 13.5000 + 7.79423i 0.510617 + 0.294805i
\(700\) 0 0
\(701\) −16.0000 −0.604312 −0.302156 0.953259i \(-0.597706\pi\)
−0.302156 + 0.953259i \(0.597706\pi\)
\(702\) 0 0
\(703\) −50.0000 −1.88579
\(704\) 0 0
\(705\) −24.0000 13.8564i −0.903892 0.521862i
\(706\) 0 0
\(707\) 6.00000 + 10.3923i 0.225653 + 0.390843i
\(708\) 0 0
\(709\) −10.0000 + 17.3205i −0.375558 + 0.650485i −0.990410 0.138157i \(-0.955882\pi\)
0.614852 + 0.788642i \(0.289216\pi\)
\(710\) 0 0
\(711\) −6.00000 −0.225018
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 20.0000 + 34.6410i 0.747958 + 1.29550i
\(716\) 0 0
\(717\) 20.7846i 0.776215i
\(718\) 0 0
\(719\) 30.0000 1.11881 0.559406 0.828894i \(-0.311029\pi\)
0.559406 + 0.828894i \(0.311029\pi\)
\(720\) 0 0
\(721\) 16.0000 0.595871
\(722\) 0 0
\(723\) 37.5000 21.6506i 1.39464 0.805196i
\(724\) 0 0
\(725\) 3.00000 + 5.19615i 0.111417 + 0.192980i
\(726\) 0 0
\(727\) 24.0000 41.5692i 0.890111 1.54172i 0.0503692 0.998731i \(-0.483960\pi\)
0.839742 0.542986i \(-0.182706\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 4.50000 7.79423i 0.166439 0.288280i
\(732\) 0 0
\(733\) −9.00000 15.5885i −0.332423 0.575773i 0.650564 0.759452i \(-0.274533\pi\)
−0.982986 + 0.183679i \(0.941199\pi\)
\(734\) 0 0
\(735\) −9.00000 + 5.19615i −0.331970 + 0.191663i
\(736\) 0 0
\(737\) −35.0000 −1.28924
\(738\) 0 0
\(739\) −21.0000 −0.772497 −0.386249 0.922395i \(-0.626229\pi\)
−0.386249 + 0.922395i \(0.626229\pi\)
\(740\) 0 0
\(741\) 34.6410i 1.27257i
\(742\) 0 0
\(743\) 19.0000 + 32.9090i 0.697042 + 1.20731i 0.969487 + 0.245141i \(0.0788344\pi\)
−0.272445 + 0.962171i \(0.587832\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −36.0000 −1.31717
\(748\) 0 0
\(749\) 11.0000 19.0526i 0.401931 0.696165i
\(750\) 0 0
\(751\) 1.00000 + 1.73205i 0.0364905 + 0.0632034i 0.883694 0.468065i \(-0.155049\pi\)
−0.847203 + 0.531269i \(0.821715\pi\)
\(752\) 0 0
\(753\) 4.50000 + 2.59808i 0.163989 + 0.0946792i
\(754\) 0 0
\(755\) −32.0000 −1.16460
\(756\) 0 0
\(757\) 14.0000 0.508839 0.254419 0.967094i \(-0.418116\pi\)
0.254419 + 0.967094i \(0.418116\pi\)
\(758\) 0 0
\(759\) 30.0000 + 17.3205i 1.08893 + 0.628695i
\(760\) 0 0
\(761\) −5.00000 8.66025i −0.181250 0.313934i 0.761057 0.648686i \(-0.224681\pi\)
−0.942306 + 0.334752i \(0.891348\pi\)
\(762\) 0 0
\(763\) 12.0000 20.7846i 0.434429 0.752453i
\(764\) 0 0
\(765\) 3.00000 5.19615i 0.108465 0.187867i
\(766\) 0 0
\(767\) 14.0000 24.2487i 0.505511 0.875570i
\(768\) 0 0
\(769\) −1.00000 1.73205i −0.0360609 0.0624593i 0.847432 0.530904i \(-0.178148\pi\)
−0.883493 + 0.468445i \(0.844814\pi\)
\(770\) 0 0
\(771\) 5.19615i 0.187135i
\(772\) 0 0
\(773\) −24.0000 −0.863220 −0.431610 0.902060i \(-0.642054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −30.0000 + 17.3205i −1.07624 + 0.621370i
\(778\) 0 0
\(779\) −7.50000 12.9904i −0.268715 0.465429i
\(780\) 0 0
\(781\) −15.0000 + 25.9808i −0.536742 + 0.929665i
\(782\) 0 0
\(783\) 27.0000 + 15.5885i 0.964901 + 0.557086i
\(784\) 0 0
\(785\) −24.0000 + 41.5692i −0.856597 + 1.48367i
\(786\) 0 0
\(787\) −14.0000 24.2487i −0.499046 0.864373i 0.500953 0.865474i \(-0.332983\pi\)
−0.999999 + 0.00110111i \(0.999650\pi\)
\(788\) 0 0
\(789\) 27.0000 15.5885i 0.961225 0.554964i
\(790\) 0 0
\(791\) −28.0000 −0.995565
\(792\) 0 0
\(793\) 16.0000 0.568177
\(794\) 0 0
\(795\) 41.5692i 1.47431i
\(796\) 0 0
\(797\) −15.0000