Properties

Label 1152.2.i.d.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.d.385.1

$q$-expansion

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

Character values

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

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

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 −0.550990 0.834512i \(-0.685750\pi\)
0.998203 + 0.0599153i \(0.0190830\pi\)
\(6\) 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 \(0.105104\pi\)
−0.192201 + 0.981356i \(0.561563\pi\)
\(12\) 0 0
\(13\) −2.00000 + 3.46410i −0.554700 + 0.960769i 0.443227 + 0.896410i \(0.353834\pi\)
−0.997927 + 0.0643593i \(0.979500\pi\)
\(14\) 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 \(-0.305570\pi\)
0.573539 + 0.819178i \(0.305570\pi\)
\(20\) 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 \(0.0214140\pi\)
−0.440652 + 0.897678i \(0.645253\pi\)
\(30\) 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 \(-0.807139\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 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 \(-0.925925\pi\)
0.286801 0.957990i \(-0.407408\pi\)
\(44\) 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 \(-0.808354\pi\)
−0.824163 + 0.566352i \(0.808354\pi\)
\(54\) 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 \(-0.682736\pi\)
0.998726 + 0.0504625i \(0.0160695\pi\)
\(60\) 0 0
\(61\) −2.00000 3.46410i −0.256074 0.443533i 0.709113 0.705095i \(-0.249096\pi\)
−0.965187 + 0.261562i \(0.915762\pi\)
\(62\) 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 \(-0.973972\pi\)
0.569066 + 0.822292i \(0.307305\pi\)
\(68\) 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 \(0.0621783\pi\)
−0.322396 + 0.946605i \(0.604488\pi\)
\(84\) 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 0.975796 0.218685i \(-0.0701767\pi\)
−0.677284 + 0.735721i \(0.736843\pi\)
\(102\) 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 \(-0.678449\pi\)
−0.531705 + 0.846930i \(0.678449\pi\)
\(108\) 0 0
\(109\) −12.0000 −1.14939 −0.574696 0.818367i \(-0.694880\pi\)
−0.574696 + 0.818367i \(0.694880\pi\)
\(110\) 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 \(0.342311\pi\)
−0.999602 + 0.0281993i \(0.991023\pi\)
\(132\) 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 −0.844042 0.536278i \(-0.819830\pi\)
0.886451 + 0.462822i \(0.153163\pi\)
\(140\) 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 \(-0.426242\pi\)
0.728055 0.685519i \(-0.240425\pi\)
\(158\) 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 \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 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 \(0.0732068\pi\)
−0.289412 + 0.957205i \(0.593460\pi\)
\(174\) 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 \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) −20.0000 −1.48659 −0.743294 0.668965i \(-0.766738\pi\)
−0.743294 + 0.668965i \(0.766738\pi\)
\(182\) 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 \(-0.247576\pi\)
0.712470 + 0.701702i \(0.247576\pi\)
\(198\) 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 \(0.408366\pi\)
−0.972346 + 0.233544i \(0.924968\pi\)
\(212\) 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 0.811943 0.583736i \(-0.198410\pi\)
−0.911502 + 0.411296i \(0.865076\pi\)
\(228\) 0 0
\(229\) −7.00000 + 12.1244i −0.462573 + 0.801200i −0.999088 0.0426906i \(-0.986407\pi\)
0.536515 + 0.843891i \(0.319740\pi\)
\(230\) 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 \(-0.469817\pi\)
0.0946792 + 0.995508i \(0.469817\pi\)
\(252\) 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 \(-0.538912\pi\)
−0.121942 + 0.992537i \(0.538912\pi\)
\(270\) 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 \(0.419479\pi\)
−0.963602 + 0.267342i \(0.913855\pi\)
\(284\) 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 \(-0.738978\pi\)
0.974307 + 0.225225i \(0.0723116\pi\)
\(294\) 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 \(-0.472716\pi\)
0.0856095 + 0.996329i \(0.472716\pi\)
\(308\) 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 0.983866 0.178908i \(-0.0572566\pi\)
−0.646872 + 0.762598i \(0.723923\pi\)
\(318\) 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 \(-0.981428\pi\)
0.448649 0.893708i \(-0.351905\pi\)
\(332\) 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 −0.903475 0.428640i \(-0.858993\pi\)
0.822951 + 0.568112i \(0.192326\pi\)
\(348\) 0 0
\(349\) 8.00000 + 13.8564i 0.428230 + 0.741716i 0.996716 0.0809766i \(-0.0258039\pi\)
−0.568486 + 0.822693i \(0.692471\pi\)
\(350\) 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 \(0.477443\pi\)
−0.899255 + 0.437425i \(0.855891\pi\)
\(374\) 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 \(-0.278071\pi\)
0.642082 + 0.766636i \(0.278071\pi\)
\(380\) 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 \(-0.753125\pi\)
−0.249323 0.968420i \(-0.580208\pi\)
\(390\) 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 \(-0.649181\pi\)
−0.451697 + 0.892171i \(0.649181\pi\)
\(398\) 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 −0.999913 0.0131919i \(-0.995801\pi\)
0.511381 + 0.859354i \(0.329134\pi\)
\(420\) 0 0
\(421\) −1.00000 1.73205i −0.0487370 0.0844150i 0.840628 0.541613i \(-0.182186\pi\)
−0.889365 + 0.457198i \(0.848853\pi\)
\(422\) 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 0.987346 0.158583i \(-0.0506926\pi\)
−0.631010 + 0.775775i \(0.717359\pi\)
\(444\) 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 0.533488 0.845807i \(-0.320881\pi\)
−0.999235 + 0.0391109i \(0.987547\pi\)
\(462\) 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 \(-0.734126\pi\)
−0.670980 + 0.741475i \(0.734126\pi\)
\(468\) 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 \(-0.642550\pi\)
0.997131 0.0756923i \(-0.0241167\pi\)
\(492\) 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 \(-0.869032\pi\)
0.804627 + 0.593780i \(0.202365\pi\)
\(500\) 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 \(-0.620247\pi\)
0.989385 0.145315i \(-0.0464195\pi\)
\(510\) 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 \(-0.0880406\pi\)
0.961993 + 0.273075i \(0.0880406\pi\)
\(524\) 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 \(-0.486311\pi\)
0.0429934 + 0.999075i \(0.486311\pi\)
\(542\) 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 \(-0.173472\pi\)
−0.876517 + 0.481371i \(0.840139\pi\)
\(548\) 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 \(-0.685688\pi\)
−0.550828 + 0.834619i \(0.685688\pi\)
\(558\) 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 \(-0.588564\pi\)
0.970048 0.242912i \(-0.0781026\pi\)
\(564\) 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 −0.595862 0.803087i \(-0.703189\pi\)
0.993425 + 0.114488i \(0.0365228\pi\)
\(572\) 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 \(-0.199570\pi\)
−0.912996 + 0.407969i \(0.866237\pi\)
\(588\) 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 \(-0.324041\pi\)
0.525065 + 0.851062i \(0.324041\pi\)
\(614\) 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 \(0.0816620\pi\)
−0.263887 + 0.964554i \(0.585005\pi\)
\(620\) 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 −0.995331 0.0965169i \(-0.969230\pi\)
0.581252 + 0.813724i \(0.302563\pi\)
\(644\) 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 \(-0.947899\pi\)
0.634437 + 0.772975i \(0.281232\pi\)
\(654\) 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 \(-0.321495\pi\)
−0.999309 + 0.0371821i \(0.988162\pi\)
\(660\) 0 0
\(661\) −1.00000 + 1.73205i −0.0388955 + 0.0673690i −0.884818 0.465937i \(-0.845717\pi\)
0.845922 + 0.533306i \(0.179051\pi\)
\(662\) 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 \(-0.985823\pi\)
0.460945 0.887429i \(-0.347511\pi\)
\(678\) 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 \(-0.592651\pi\)
−0.286980 + 0.957937i \(0.592651\pi\)
\(684\) 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 \(-0.239967\pi\)
−0.957290 + 0.289130i \(0.906634\pi\)
\(692\) 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 \(-0.402294\pi\)
0.302156 + 0.953259i \(0.402294\pi\)
\(702\) 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 \(-0.0441178\pi\)
−0.614852 + 0.788642i \(0.710784\pi\)
\(710\) 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 −0.650564 0.759452i \(-0.725467\pi\)
0.982986 + 0.183679i \(0.0588007\pi\)
\(734\) 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 \(-0.373771\pi\)
0.386249 + 0.922395i \(0.373771\pi\)
\(740\) 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 \(-0.581884\pi\)
−0.254419 + 0.967094i \(0.581884\pi\)
\(758\) 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 \(-0.357946\pi\)
0.431610 + 0.902060i \(0.357946\pi\)
\(774\) 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 \(-0.667017\pi\)
0.999999 + 0.00110111i \(0.000350496\pi\)
\(788\) 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 25.9808i 0.531327 0.920286i −0.468004 0.883726i \(-0.655027\pi\)
0.999331 0.0365596i