Properties

Label 1152.2.i.a.769.1
Level $1152$
Weight $2$
Character 1152.769
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 769.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1152.769
Dual form 1152.2.i.a.385.1

$q$-expansion

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

Character values

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

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

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 −0.998203 0.0599153i \(-0.980917\pi\)
0.550990 + 0.834512i \(0.314250\pi\)
\(6\) 0 0
\(7\) 1.00000 + 1.73205i 0.377964 + 0.654654i 0.990766 0.135583i \(-0.0432908\pi\)
−0.612801 + 0.790237i \(0.709957\pi\)
\(8\) 0 0
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) 0 0
\(11\) −2.50000 4.33013i −0.753778 1.30558i −0.945979 0.324227i \(-0.894896\pi\)
0.192201 0.981356i \(-0.438437\pi\)
\(12\) 0 0
\(13\) 2.00000 3.46410i 0.554700 0.960769i −0.443227 0.896410i \(-0.646166\pi\)
0.997927 0.0643593i \(-0.0205004\pi\)
\(14\) 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 −0.578610 0.815604i \(-0.696405\pi\)
0.995639 + 0.0932891i \(0.0297381\pi\)
\(24\) 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 −0.997738 0.0672232i \(-0.978586\pi\)
0.440652 0.897678i \(-0.354747\pi\)
\(30\) 0 0
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) 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 −0.724797 0.688963i \(-0.758066\pi\)
0.959058 + 0.283211i \(0.0913998\pi\)
\(42\) 0 0
\(43\) 4.50000 + 7.79423i 0.686244 + 1.18861i 0.973044 + 0.230618i \(0.0740749\pi\)
−0.286801 + 0.957990i \(0.592592\pi\)
\(44\) 0 0
\(45\) 3.00000 + 5.19615i 0.447214 + 0.774597i
\(46\) 0 0
\(47\) −4.00000 6.92820i −0.583460 1.01058i −0.995066 0.0992202i \(-0.968365\pi\)
0.411606 0.911362i \(-0.364968\pi\)
\(48\) 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 −0.998726 0.0504625i \(-0.983930\pi\)
0.543065 + 0.839691i \(0.317264\pi\)
\(60\) 0 0
\(61\) 2.00000 + 3.46410i 0.256074 + 0.443533i 0.965187 0.261562i \(-0.0842377\pi\)
−0.709113 + 0.705095i \(0.750904\pi\)
\(62\) 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 −0.569066 0.822292i \(-0.692695\pi\)
0.996659 + 0.0816792i \(0.0260283\pi\)
\(68\) 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 0.804272 0.594261i \(-0.202555\pi\)
−0.916781 + 0.399390i \(0.869222\pi\)
\(80\) 0 0
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 0 0
\(83\) −6.00000 10.3923i −0.658586 1.14070i −0.980982 0.194099i \(-0.937822\pi\)
0.322396 0.946605i \(-0.395512\pi\)
\(84\) 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 −0.980622 0.195911i \(-0.937234\pi\)
0.320647 0.947199i \(-0.396100\pi\)
\(98\) 0 0
\(99\) −15.0000 −1.50756
\(100\) 0 0
\(101\) −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i \(-0.263157\pi\)
−0.975796 + 0.218685i \(0.929823\pi\)
\(102\) 0 0
\(103\) 4.00000 6.92820i 0.394132 0.682656i −0.598858 0.800855i \(-0.704379\pi\)
0.992990 + 0.118199i \(0.0377120\pi\)
\(104\) 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 0.322498 + 0.946570i \(0.395477\pi\)
−0.981003 + 0.193993i \(0.937856\pi\)
\(114\) 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 −0.475380 0.879781i \(-0.657689\pi\)
0.999602 0.0281993i \(-0.00897729\pi\)
\(132\) 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 0.843876 0.536538i \(-0.180268\pi\)
−0.886594 + 0.462549i \(0.846935\pi\)
\(138\) 0 0
\(139\) −0.500000 + 0.866025i −0.0424094 + 0.0734553i −0.886451 0.462822i \(-0.846837\pi\)
0.844042 + 0.536278i \(0.180170\pi\)
\(140\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(150\) 0 0
\(151\) 8.00000 + 13.8564i 0.651031 + 1.12762i 0.982873 + 0.184284i \(0.0589965\pi\)
−0.331842 + 0.943335i \(0.607670\pi\)
\(152\) 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 −0.229650 + 0.973273i \(0.573758\pi\)
−0.728055 + 0.685519i \(0.759575\pi\)
\(158\) 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 −0.902120 0.431486i \(-0.857990\pi\)
0.824737 + 0.565516i \(0.191323\pi\)
\(168\) 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 −0.973670 0.227964i \(-0.926793\pi\)
0.289412 0.957205i \(-0.406540\pi\)
\(174\) 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 0.899934 0.436026i \(-0.143614\pi\)
−0.827577 + 0.561353i \(0.810281\pi\)
\(192\) 0 0
\(193\) −0.500000 + 0.866025i −0.0359908 + 0.0623379i −0.883460 0.468507i \(-0.844792\pi\)
0.847469 + 0.530845i \(0.178125\pi\)
\(194\) 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 −0.283918 0.958849i \(-0.591634\pi\)
0.972346 0.233544i \(-0.0750324\pi\)
\(212\) 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 −0.917246 0.398321i \(-0.869593\pi\)
0.113666 0.993519i \(-0.463740\pi\)
\(224\) 0 0
\(225\) 3.00000 0.200000
\(226\) 0 0
\(227\) 1.50000 + 2.59808i 0.0995585 + 0.172440i 0.911502 0.411296i \(-0.134924\pi\)
−0.811943 + 0.583736i \(0.801590\pi\)
\(228\) 0 0
\(229\) 7.00000 12.1244i 0.462573 0.801200i −0.536515 0.843891i \(-0.680260\pi\)
0.999088 + 0.0426906i \(0.0135930\pi\)
\(230\) 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 −0.604087 0.796918i \(-0.706462\pi\)
0.992195 + 0.124696i \(0.0397955\pi\)
\(240\) 0 0
\(241\) −12.5000 21.6506i −0.805196 1.39464i −0.916159 0.400815i \(-0.868727\pi\)
0.110963 0.993825i \(-0.464606\pi\)
\(242\) 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 −0.909010 0.416775i \(-0.863160\pi\)
0.815442 + 0.578838i \(0.196494\pi\)
\(258\) 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 −0.997906 0.0646755i \(-0.979399\pi\)
0.442943 0.896550i \(-0.353935\pi\)
\(264\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −15.0000 25.9808i −0.894825 1.54988i −0.834021 0.551733i \(-0.813967\pi\)
−0.0608039 0.998150i \(-0.519366\pi\)
\(282\) 0 0
\(283\) 12.0000 20.7846i 0.713326 1.23552i −0.250276 0.968175i \(-0.580521\pi\)
0.963602 0.267342i \(-0.0861454\pi\)
\(284\) 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 −0.974307 0.225225i \(-0.927688\pi\)
0.682204 + 0.731162i \(0.261022\pi\)
\(294\) 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 −0.972250 0.233944i \(-0.924837\pi\)
0.688726 + 0.725022i \(0.258170\pi\)
\(312\) 0 0
\(313\) −12.5000 21.6506i −0.706542 1.22377i −0.966132 0.258047i \(-0.916921\pi\)
0.259590 0.965719i \(-0.416412\pi\)
\(314\) 0 0
\(315\) −6.00000 + 10.3923i −0.338062 + 0.585540i
\(316\) 0 0
\(317\) −6.00000 10.3923i −0.336994 0.583690i 0.646872 0.762598i \(-0.276077\pi\)
−0.983866 + 0.178908i \(0.942743\pi\)
\(318\) 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 0.998298 + 0.0583130i \(0.0185721\pi\)
−0.448649 + 0.893708i \(0.648095\pi\)
\(332\) 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 0.482295 + 0.876009i \(0.339803\pi\)
−0.999793 + 0.0203242i \(0.993530\pi\)
\(338\) 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 −0.822951 0.568112i \(-0.807674\pi\)
0.903475 + 0.428640i \(0.141007\pi\)
\(348\) 0 0
\(349\) −8.00000 13.8564i −0.428230 0.741716i 0.568486 0.822693i \(-0.307529\pi\)
−0.996716 + 0.0809766i \(0.974196\pi\)
\(350\) 0 0
\(351\) 18.0000 + 10.3923i 0.960769 + 0.554700i
\(352\) 0 0
\(353\) 4.50000 + 7.79423i 0.239511 + 0.414845i 0.960574 0.278024i \(-0.0896796\pi\)
−0.721063 + 0.692869i \(0.756346\pi\)
\(354\) 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 0.996129 + 0.0879086i \(0.0280183\pi\)
−0.421933 + 0.906627i \(0.638648\pi\)
\(368\) 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 −0.0708063 0.997490i \(-0.522557\pi\)
0.899255 0.437425i \(-0.144109\pi\)
\(374\) 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 −0.932436 0.361335i \(-0.882321\pi\)
0.779143 + 0.626846i \(0.215654\pi\)
\(384\) 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 0.714015 + 0.700130i \(0.246875\pi\)
0.249323 + 0.968420i \(0.419792\pi\)
\(390\) 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 −0.826139 0.563466i \(-0.809468\pi\)
0.901046 + 0.433724i \(0.142801\pi\)
\(402\) 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 0.371750 + 0.928333i \(0.378758\pi\)
−0.989835 + 0.142222i \(0.954575\pi\)
\(410\) 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 −0.511381 0.859354i \(-0.670866\pi\)
0.999913 + 0.0131919i \(0.00419923\pi\)
\(420\) 0 0
\(421\) 1.00000 + 1.73205i 0.0487370 + 0.0844150i 0.889365 0.457198i \(-0.151147\pi\)
−0.840628 + 0.541613i \(0.817814\pi\)
\(422\) 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 −0.996284 0.0861252i \(-0.972552\pi\)
0.423556 0.905870i \(-0.360782\pi\)
\(440\) 0 0
\(441\) −4.50000 7.79423i −0.214286 0.371154i
\(442\) 0 0
\(443\) −7.50000 12.9904i −0.356336 0.617192i 0.631010 0.775775i \(-0.282641\pi\)
−0.987346 + 0.158583i \(0.949307\pi\)
\(444\) 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 0.898974 0.438001i \(-0.144313\pi\)
−0.828807 + 0.559534i \(0.810980\pi\)
\(458\) 0 0
\(459\) 5.19615i 0.242536i
\(460\) 0 0
\(461\) 10.0000 + 17.3205i 0.465746 + 0.806696i 0.999235 0.0391109i \(-0.0124526\pi\)
−0.533488 + 0.845807i \(0.679119\pi\)
\(462\) 0 0
\(463\) −1.00000 + 1.73205i −0.0464739 + 0.0804952i −0.888327 0.459212i \(-0.848132\pi\)
0.841853 + 0.539707i \(0.181465\pi\)
\(464\) 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 0.995023 0.0996406i \(-0.0317693\pi\)
−0.583803 + 0.811895i \(0.698436\pi\)
\(480\) 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 0.433014 + 0.901387i \(0.357450\pi\)
−0.997131 + 0.0756923i \(0.975883\pi\)
\(492\) 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 −0.804627 0.593780i \(-0.797635\pi\)
0.916542 + 0.399937i \(0.130968\pi\)
\(500\) 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 0.368846 + 0.929490i \(0.379753\pi\)
−0.989385 + 0.145315i \(0.953580\pi\)
\(510\) 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 0.876517 0.481371i \(-0.159861\pi\)
−0.855138 + 0.518400i \(0.826528\pi\)
\(548\) 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 0.274656 + 0.961542i \(0.411436\pi\)
−0.970048 + 0.242912i \(0.921897\pi\)
\(564\) 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 0.993511 0.113732i \(-0.0362806\pi\)
−0.595251 + 0.803540i \(0.702947\pi\)
\(570\) 0 0
\(571\) −9.50000 + 16.4545i −0.397563 + 0.688599i −0.993425 0.114488i \(-0.963477\pi\)
0.595862 + 0.803087i \(0.296811\pi\)
\(572\) 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 0.912996 0.407969i \(-0.133763\pi\)
−0.809810 + 0.586693i \(0.800430\pi\)
\(588\) 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 0.0157622 + 0.999876i \(0.494983\pi\)
−0.873799 + 0.486287i \(0.838351\pi\)
\(600\) 0 0
\(601\) 4.50000 + 7.79423i 0.183559 + 0.317933i 0.943090 0.332538i \(-0.107905\pi\)
−0.759531 + 0.650471i \(0.774572\pi\)
\(602\) 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 −0.773358 0.633970i \(-0.781424\pi\)
0.935713 + 0.352763i \(0.114758\pi\)
\(608\) 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 −0.642643 0.766165i \(-0.722162\pi\)
0.984840 + 0.173463i \(0.0554956\pi\)
\(618\) 0 0
\(619\) −17.5000 30.3109i −0.703384 1.21830i −0.967271 0.253744i \(-0.918338\pi\)
0.263887 0.964554i \(-0.414995\pi\)
\(620\) 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 −0.982708 0.185164i \(-0.940718\pi\)
0.330997 0.943632i \(-0.392615\pi\)
\(642\) 0 0
\(643\) 10.5000 18.1865i 0.414080 0.717207i −0.581252 0.813724i \(-0.697437\pi\)
0.995331 + 0.0965169i \(0.0307702\pi\)
\(644\) 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 −0.634437 0.772975i \(-0.718768\pi\)
0.986634 + 0.162951i \(0.0521013\pi\)
\(654\) 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 0.999309 0.0371821i \(-0.0118382\pi\)
−0.531855 + 0.846836i \(0.678505\pi\)
\(660\) 0 0
\(661\) 1.00000 1.73205i 0.0388955 0.0673690i −0.845922 0.533306i \(-0.820949\pi\)
0.884818 + 0.465937i \(0.154283\pi\)
\(662\) 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 0.753420 0.657539i \(-0.228403\pi\)
−0.946156 + 0.323711i \(0.895069\pi\)
\(674\) 0 0
\(675\) −4.50000 + 2.59808i −0.173205 + 0.100000i
\(676\) 0 0
\(677\) 14.0000 + 24.2487i 0.538064 + 0.931954i 0.999008 + 0.0445248i \(0.0141774\pi\)
−0.460945 + 0.887429i \(0.652489\pi\)
\(678\) 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 0.957290 0.289130i \(-0.0933661\pi\)
−0.729039 + 0.684472i \(0.760033\pi\)
\(692\) 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 0.614852 0.788642i \(-0.289216\pi\)
−0.990410 + 0.138157i \(0.955882\pi\)
\(710\) 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 0.839742 + 0.542986i \(0.182706\pi\)
0.0503692 + 0.998731i \(0.483960\pi\)
\(728\) 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 −0.982986 0.183679i \(-0.941199\pi\)
0.650564 + 0.759452i \(0.274533\pi\)
\(734\) 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 −0.272445 0.962171i \(-0.587832\pi\)
0.969487 0.245141i \(-0.0788344\pi\)
\(744\) 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 −0.847203 0.531269i \(-0.821715\pi\)
0.883694 + 0.468065i \(0.155049\pi\)
\(752\) 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 −0.942306 0.334752i \(-0.891348\pi\)
0.761057 + 0.648686i \(0.224681\pi\)
\(762\) 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 −0.883493 0.468445i \(-0.844814\pi\)
0.847432 + 0.530904i \(0.178148\pi\)
\(770\) 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 −0.999999 0.00110111i \(-0.999650\pi\)
0.500953 + 0.865474i \(0.332983\pi\)
\(788\) 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