Properties

Label 64.2.e.a.49.1
Level $64$
Weight $2$
Character 64.49
Analytic conductor $0.511$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 64 = 2^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 64.e (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.511042572936\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 16)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 49.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 64.49
Dual form 64.2.e.a.17.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{3} +(-1.00000 - 1.00000i) q^{5} +2.00000i q^{7} +1.00000i q^{9} +O(q^{10})\) \(q+(1.00000 - 1.00000i) q^{3} +(-1.00000 - 1.00000i) q^{5} +2.00000i q^{7} +1.00000i q^{9} +(-1.00000 - 1.00000i) q^{11} +(-1.00000 + 1.00000i) q^{13} -2.00000 q^{15} -2.00000 q^{17} +(-3.00000 + 3.00000i) q^{19} +(2.00000 + 2.00000i) q^{21} -6.00000i q^{23} -3.00000i q^{25} +(4.00000 + 4.00000i) q^{27} +(3.00000 - 3.00000i) q^{29} +8.00000 q^{31} -2.00000 q^{33} +(2.00000 - 2.00000i) q^{35} +(3.00000 + 3.00000i) q^{37} +2.00000i q^{39} +(-5.00000 - 5.00000i) q^{43} +(1.00000 - 1.00000i) q^{45} -8.00000 q^{47} +3.00000 q^{49} +(-2.00000 + 2.00000i) q^{51} +(-5.00000 - 5.00000i) q^{53} +2.00000i q^{55} +6.00000i q^{57} +(3.00000 + 3.00000i) q^{59} +(-9.00000 + 9.00000i) q^{61} -2.00000 q^{63} +2.00000 q^{65} +(5.00000 - 5.00000i) q^{67} +(-6.00000 - 6.00000i) q^{69} +10.0000i q^{71} -4.00000i q^{73} +(-3.00000 - 3.00000i) q^{75} +(2.00000 - 2.00000i) q^{77} +5.00000 q^{81} +(1.00000 - 1.00000i) q^{83} +(2.00000 + 2.00000i) q^{85} -6.00000i q^{87} +4.00000i q^{89} +(-2.00000 - 2.00000i) q^{91} +(8.00000 - 8.00000i) q^{93} +6.00000 q^{95} -2.00000 q^{97} +(1.00000 - 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{3} - 2q^{5} + O(q^{10}) \) \( 2q + 2q^{3} - 2q^{5} - 2q^{11} - 2q^{13} - 4q^{15} - 4q^{17} - 6q^{19} + 4q^{21} + 8q^{27} + 6q^{29} + 16q^{31} - 4q^{33} + 4q^{35} + 6q^{37} - 10q^{43} + 2q^{45} - 16q^{47} + 6q^{49} - 4q^{51} - 10q^{53} + 6q^{59} - 18q^{61} - 4q^{63} + 4q^{65} + 10q^{67} - 12q^{69} - 6q^{75} + 4q^{77} + 10q^{81} + 2q^{83} + 4q^{85} - 4q^{91} + 16q^{93} + 12q^{95} - 4q^{97} + 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/64\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(63\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

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
\(3\) 1.00000 1.00000i 0.577350 0.577350i −0.356822 0.934172i \(-0.616140\pi\)
0.934172 + 0.356822i \(0.116140\pi\)
\(4\) 0 0
\(5\) −1.00000 1.00000i −0.447214 0.447214i 0.447214 0.894427i \(-0.352416\pi\)
−0.894427 + 0.447214i \(0.852416\pi\)
\(6\) 0 0
\(7\) 2.00000i 0.755929i 0.925820 + 0.377964i \(0.123376\pi\)
−0.925820 + 0.377964i \(0.876624\pi\)
\(8\) 0 0
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) −1.00000 1.00000i −0.301511 0.301511i 0.540094 0.841605i \(-0.318389\pi\)
−0.841605 + 0.540094i \(0.818389\pi\)
\(12\) 0 0
\(13\) −1.00000 + 1.00000i −0.277350 + 0.277350i −0.832050 0.554700i \(-0.812833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 0 0
\(15\) −2.00000 −0.516398
\(16\) 0 0
\(17\) −2.00000 −0.485071 −0.242536 0.970143i \(-0.577979\pi\)
−0.242536 + 0.970143i \(0.577979\pi\)
\(18\) 0 0
\(19\) −3.00000 + 3.00000i −0.688247 + 0.688247i −0.961844 0.273597i \(-0.911786\pi\)
0.273597 + 0.961844i \(0.411786\pi\)
\(20\) 0 0
\(21\) 2.00000 + 2.00000i 0.436436 + 0.436436i
\(22\) 0 0
\(23\) 6.00000i 1.25109i −0.780189 0.625543i \(-0.784877\pi\)
0.780189 0.625543i \(-0.215123\pi\)
\(24\) 0 0
\(25\) 3.00000i 0.600000i
\(26\) 0 0
\(27\) 4.00000 + 4.00000i 0.769800 + 0.769800i
\(28\) 0 0
\(29\) 3.00000 3.00000i 0.557086 0.557086i −0.371391 0.928477i \(-0.621119\pi\)
0.928477 + 0.371391i \(0.121119\pi\)
\(30\) 0 0
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 0 0
\(33\) −2.00000 −0.348155
\(34\) 0 0
\(35\) 2.00000 2.00000i 0.338062 0.338062i
\(36\) 0 0
\(37\) 3.00000 + 3.00000i 0.493197 + 0.493197i 0.909312 0.416115i \(-0.136609\pi\)
−0.416115 + 0.909312i \(0.636609\pi\)
\(38\) 0 0
\(39\) 2.00000i 0.320256i
\(40\) 0 0
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) −5.00000 5.00000i −0.762493 0.762493i 0.214280 0.976772i \(-0.431260\pi\)
−0.976772 + 0.214280i \(0.931260\pi\)
\(44\) 0 0
\(45\) 1.00000 1.00000i 0.149071 0.149071i
\(46\) 0 0
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 0 0
\(49\) 3.00000 0.428571
\(50\) 0 0
\(51\) −2.00000 + 2.00000i −0.280056 + 0.280056i
\(52\) 0 0
\(53\) −5.00000 5.00000i −0.686803 0.686803i 0.274721 0.961524i \(-0.411414\pi\)
−0.961524 + 0.274721i \(0.911414\pi\)
\(54\) 0 0
\(55\) 2.00000i 0.269680i
\(56\) 0 0
\(57\) 6.00000i 0.794719i
\(58\) 0 0
\(59\) 3.00000 + 3.00000i 0.390567 + 0.390567i 0.874889 0.484323i \(-0.160934\pi\)
−0.484323 + 0.874889i \(0.660934\pi\)
\(60\) 0 0
\(61\) −9.00000 + 9.00000i −1.15233 + 1.15233i −0.166248 + 0.986084i \(0.553165\pi\)
−0.986084 + 0.166248i \(0.946835\pi\)
\(62\) 0 0
\(63\) −2.00000 −0.251976
\(64\) 0 0
\(65\) 2.00000 0.248069
\(66\) 0 0
\(67\) 5.00000 5.00000i 0.610847 0.610847i −0.332320 0.943167i \(-0.607831\pi\)
0.943167 + 0.332320i \(0.107831\pi\)
\(68\) 0 0
\(69\) −6.00000 6.00000i −0.722315 0.722315i
\(70\) 0 0
\(71\) 10.0000i 1.18678i 0.804914 + 0.593391i \(0.202211\pi\)
−0.804914 + 0.593391i \(0.797789\pi\)
\(72\) 0 0
\(73\) 4.00000i 0.468165i −0.972217 0.234082i \(-0.924791\pi\)
0.972217 0.234082i \(-0.0752085\pi\)
\(74\) 0 0
\(75\) −3.00000 3.00000i −0.346410 0.346410i
\(76\) 0 0
\(77\) 2.00000 2.00000i 0.227921 0.227921i
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 5.00000 0.555556
\(82\) 0 0
\(83\) 1.00000 1.00000i 0.109764 0.109764i −0.650092 0.759856i \(-0.725269\pi\)
0.759856 + 0.650092i \(0.225269\pi\)
\(84\) 0 0
\(85\) 2.00000 + 2.00000i 0.216930 + 0.216930i
\(86\) 0 0
\(87\) 6.00000i 0.643268i
\(88\) 0 0
\(89\) 4.00000i 0.423999i 0.977270 + 0.212000i \(0.0679975\pi\)
−0.977270 + 0.212000i \(0.932002\pi\)
\(90\) 0 0
\(91\) −2.00000 2.00000i −0.209657 0.209657i
\(92\) 0 0
\(93\) 8.00000 8.00000i 0.829561 0.829561i
\(94\) 0 0
\(95\) 6.00000 0.615587
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) 1.00000 1.00000i 0.100504 0.100504i
\(100\) 0 0
\(101\) 11.0000 + 11.0000i 1.09454 + 1.09454i 0.995037 + 0.0995037i \(0.0317255\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 0 0
\(103\) 6.00000i 0.591198i −0.955312 0.295599i \(-0.904481\pi\)
0.955312 0.295599i \(-0.0955191\pi\)
\(104\) 0 0
\(105\) 4.00000i 0.390360i
\(106\) 0 0
\(107\) 7.00000 + 7.00000i 0.676716 + 0.676716i 0.959256 0.282540i \(-0.0911770\pi\)
−0.282540 + 0.959256i \(0.591177\pi\)
\(108\) 0 0
\(109\) 3.00000 3.00000i 0.287348 0.287348i −0.548683 0.836031i \(-0.684871\pi\)
0.836031 + 0.548683i \(0.184871\pi\)
\(110\) 0 0
\(111\) 6.00000 0.569495
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) −6.00000 + 6.00000i −0.559503 + 0.559503i
\(116\) 0 0
\(117\) −1.00000 1.00000i −0.0924500 0.0924500i
\(118\) 0 0
\(119\) 4.00000i 0.366679i
\(120\) 0 0
\(121\) 9.00000i 0.818182i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −8.00000 + 8.00000i −0.715542 + 0.715542i
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 0 0
\(129\) −10.0000 −0.880451
\(130\) 0 0
\(131\) −11.0000 + 11.0000i −0.961074 + 0.961074i −0.999270 0.0381958i \(-0.987839\pi\)
0.0381958 + 0.999270i \(0.487839\pi\)
\(132\) 0 0
\(133\) −6.00000 6.00000i −0.520266 0.520266i
\(134\) 0 0
\(135\) 8.00000i 0.688530i
\(136\) 0 0
\(137\) 8.00000i 0.683486i 0.939793 + 0.341743i \(0.111017\pi\)
−0.939793 + 0.341743i \(0.888983\pi\)
\(138\) 0 0
\(139\) 3.00000 + 3.00000i 0.254457 + 0.254457i 0.822795 0.568338i \(-0.192414\pi\)
−0.568338 + 0.822795i \(0.692414\pi\)
\(140\) 0 0
\(141\) −8.00000 + 8.00000i −0.673722 + 0.673722i
\(142\) 0 0
\(143\) 2.00000 0.167248
\(144\) 0 0
\(145\) −6.00000 −0.498273
\(146\) 0 0
\(147\) 3.00000 3.00000i 0.247436 0.247436i
\(148\) 0 0
\(149\) 7.00000 + 7.00000i 0.573462 + 0.573462i 0.933094 0.359632i \(-0.117098\pi\)
−0.359632 + 0.933094i \(0.617098\pi\)
\(150\) 0 0
\(151\) 10.0000i 0.813788i 0.913475 + 0.406894i \(0.133388\pi\)
−0.913475 + 0.406894i \(0.866612\pi\)
\(152\) 0 0
\(153\) 2.00000i 0.161690i
\(154\) 0 0
\(155\) −8.00000 8.00000i −0.642575 0.642575i
\(156\) 0 0
\(157\) 15.0000 15.0000i 1.19713 1.19713i 0.222108 0.975022i \(-0.428706\pi\)
0.975022 0.222108i \(-0.0712939\pi\)
\(158\) 0 0
\(159\) −10.0000 −0.793052
\(160\) 0 0
\(161\) 12.0000 0.945732
\(162\) 0 0
\(163\) 1.00000 1.00000i 0.0783260 0.0783260i −0.666858 0.745184i \(-0.732361\pi\)
0.745184 + 0.666858i \(0.232361\pi\)
\(164\) 0 0
\(165\) 2.00000 + 2.00000i 0.155700 + 0.155700i
\(166\) 0 0
\(167\) 2.00000i 0.154765i 0.997001 + 0.0773823i \(0.0246562\pi\)
−0.997001 + 0.0773823i \(0.975344\pi\)
\(168\) 0 0
\(169\) 11.0000i 0.846154i
\(170\) 0 0
\(171\) −3.00000 3.00000i −0.229416 0.229416i
\(172\) 0 0
\(173\) −1.00000 + 1.00000i −0.0760286 + 0.0760286i −0.744099 0.668070i \(-0.767121\pi\)
0.668070 + 0.744099i \(0.267121\pi\)
\(174\) 0 0
\(175\) 6.00000 0.453557
\(176\) 0 0
\(177\) 6.00000 0.450988
\(178\) 0 0
\(179\) 17.0000 17.0000i 1.27064 1.27064i 0.324887 0.945753i \(-0.394674\pi\)
0.945753 0.324887i \(-0.105326\pi\)
\(180\) 0 0
\(181\) −9.00000 9.00000i −0.668965 0.668965i 0.288512 0.957476i \(-0.406840\pi\)
−0.957476 + 0.288512i \(0.906840\pi\)
\(182\) 0 0
\(183\) 18.0000i 1.33060i
\(184\) 0 0
\(185\) 6.00000i 0.441129i
\(186\) 0 0
\(187\) 2.00000 + 2.00000i 0.146254 + 0.146254i
\(188\) 0 0
\(189\) −8.00000 + 8.00000i −0.581914 + 0.581914i
\(190\) 0 0
\(191\) 8.00000 0.578860 0.289430 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 0 0
\(193\) 14.0000 1.00774 0.503871 0.863779i \(-0.331909\pi\)
0.503871 + 0.863779i \(0.331909\pi\)
\(194\) 0 0
\(195\) 2.00000 2.00000i 0.143223 0.143223i
\(196\) 0 0
\(197\) −17.0000 17.0000i −1.21120 1.21120i −0.970632 0.240567i \(-0.922666\pi\)
−0.240567 0.970632i \(-0.577334\pi\)
\(198\) 0 0
\(199\) 14.0000i 0.992434i −0.868199 0.496217i \(-0.834722\pi\)
0.868199 0.496217i \(-0.165278\pi\)
\(200\) 0 0
\(201\) 10.0000i 0.705346i
\(202\) 0 0
\(203\) 6.00000 + 6.00000i 0.421117 + 0.421117i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 6.00000 0.417029
\(208\) 0 0
\(209\) 6.00000 0.415029
\(210\) 0 0
\(211\) 9.00000 9.00000i 0.619586 0.619586i −0.325840 0.945425i \(-0.605647\pi\)
0.945425 + 0.325840i \(0.105647\pi\)
\(212\) 0 0
\(213\) 10.0000 + 10.0000i 0.685189 + 0.685189i
\(214\) 0 0
\(215\) 10.0000i 0.681994i
\(216\) 0 0
\(217\) 16.0000i 1.08615i
\(218\) 0 0
\(219\) −4.00000 4.00000i −0.270295 0.270295i
\(220\) 0 0
\(221\) 2.00000 2.00000i 0.134535 0.134535i
\(222\) 0 0
\(223\) −24.0000 −1.60716 −0.803579 0.595198i \(-0.797074\pi\)
−0.803579 + 0.595198i \(0.797074\pi\)
\(224\) 0 0
\(225\) 3.00000 0.200000
\(226\) 0 0
\(227\) −15.0000 + 15.0000i −0.995585 + 0.995585i −0.999990 0.00440533i \(-0.998598\pi\)
0.00440533 + 0.999990i \(0.498598\pi\)
\(228\) 0 0
\(229\) 7.00000 + 7.00000i 0.462573 + 0.462573i 0.899498 0.436925i \(-0.143932\pi\)
−0.436925 + 0.899498i \(0.643932\pi\)
\(230\) 0 0
\(231\) 4.00000i 0.263181i
\(232\) 0 0
\(233\) 4.00000i 0.262049i −0.991379 0.131024i \(-0.958173\pi\)
0.991379 0.131024i \(-0.0418266\pi\)
\(234\) 0 0
\(235\) 8.00000 + 8.00000i 0.521862 + 0.521862i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −18.0000 −1.15948 −0.579741 0.814801i \(-0.696846\pi\)
−0.579741 + 0.814801i \(0.696846\pi\)
\(242\) 0 0
\(243\) −7.00000 + 7.00000i −0.449050 + 0.449050i
\(244\) 0 0
\(245\) −3.00000 3.00000i −0.191663 0.191663i
\(246\) 0 0
\(247\) 6.00000i 0.381771i
\(248\) 0 0
\(249\) 2.00000i 0.126745i
\(250\) 0 0
\(251\) −21.0000 21.0000i −1.32551 1.32551i −0.909243 0.416265i \(-0.863339\pi\)
−0.416265 0.909243i \(-0.636661\pi\)
\(252\) 0 0
\(253\) −6.00000 + 6.00000i −0.377217 + 0.377217i
\(254\) 0 0
\(255\) 4.00000 0.250490
\(256\) 0 0
\(257\) −22.0000 −1.37232 −0.686161 0.727450i \(-0.740706\pi\)
−0.686161 + 0.727450i \(0.740706\pi\)
\(258\) 0 0
\(259\) −6.00000 + 6.00000i −0.372822 + 0.372822i
\(260\) 0 0
\(261\) 3.00000 + 3.00000i 0.185695 + 0.185695i
\(262\) 0 0
\(263\) 6.00000i 0.369976i −0.982741 0.184988i \(-0.940775\pi\)
0.982741 0.184988i \(-0.0592246\pi\)
\(264\) 0 0
\(265\) 10.0000i 0.614295i
\(266\) 0 0
\(267\) 4.00000 + 4.00000i 0.244796 + 0.244796i
\(268\) 0 0
\(269\) 3.00000 3.00000i 0.182913 0.182913i −0.609711 0.792624i \(-0.708714\pi\)
0.792624 + 0.609711i \(0.208714\pi\)
\(270\) 0 0
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) 0 0
\(273\) −4.00000 −0.242091
\(274\) 0 0
\(275\) −3.00000 + 3.00000i −0.180907 + 0.180907i
\(276\) 0 0
\(277\) 3.00000 + 3.00000i 0.180253 + 0.180253i 0.791466 0.611213i \(-0.209318\pi\)
−0.611213 + 0.791466i \(0.709318\pi\)
\(278\) 0 0
\(279\) 8.00000i 0.478947i
\(280\) 0 0
\(281\) 20.0000i 1.19310i −0.802576 0.596550i \(-0.796538\pi\)
0.802576 0.596550i \(-0.203462\pi\)
\(282\) 0 0
\(283\) 15.0000 + 15.0000i 0.891657 + 0.891657i 0.994679 0.103022i \(-0.0328511\pi\)
−0.103022 + 0.994679i \(0.532851\pi\)
\(284\) 0 0
\(285\) 6.00000 6.00000i 0.355409 0.355409i
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) −2.00000 + 2.00000i −0.117242 + 0.117242i
\(292\) 0 0
\(293\) 15.0000 + 15.0000i 0.876309 + 0.876309i 0.993151 0.116841i \(-0.0372769\pi\)
−0.116841 + 0.993151i \(0.537277\pi\)
\(294\) 0 0
\(295\) 6.00000i 0.349334i
\(296\) 0 0
\(297\) 8.00000i 0.464207i
\(298\) 0 0
\(299\) 6.00000 + 6.00000i 0.346989 + 0.346989i
\(300\) 0 0
\(301\) 10.0000 10.0000i 0.576390 0.576390i
\(302\) 0 0
\(303\) 22.0000 1.26387
\(304\) 0 0
\(305\) 18.0000 1.03068
\(306\) 0 0
\(307\) 5.00000 5.00000i 0.285365 0.285365i −0.549879 0.835244i \(-0.685326\pi\)
0.835244 + 0.549879i \(0.185326\pi\)
\(308\) 0 0
\(309\) −6.00000 6.00000i −0.341328 0.341328i
\(310\) 0 0
\(311\) 30.0000i 1.70114i −0.525859 0.850572i \(-0.676256\pi\)
0.525859 0.850572i \(-0.323744\pi\)
\(312\) 0 0
\(313\) 16.0000i 0.904373i 0.891923 + 0.452187i \(0.149356\pi\)
−0.891923 + 0.452187i \(0.850644\pi\)
\(314\) 0 0
\(315\) 2.00000 + 2.00000i 0.112687 + 0.112687i
\(316\) 0 0
\(317\) −5.00000 + 5.00000i −0.280828 + 0.280828i −0.833439 0.552611i \(-0.813631\pi\)
0.552611 + 0.833439i \(0.313631\pi\)
\(318\) 0 0
\(319\) −6.00000 −0.335936
\(320\) 0 0
\(321\) 14.0000 0.781404
\(322\) 0 0
\(323\) 6.00000 6.00000i 0.333849 0.333849i
\(324\) 0 0
\(325\) 3.00000 + 3.00000i 0.166410 + 0.166410i
\(326\) 0 0
\(327\) 6.00000i 0.331801i
\(328\) 0 0
\(329\) 16.0000i 0.882109i
\(330\) 0 0
\(331\) −1.00000 1.00000i −0.0549650 0.0549650i 0.679090 0.734055i \(-0.262375\pi\)
−0.734055 + 0.679090i \(0.762375\pi\)
\(332\) 0 0
\(333\) −3.00000 + 3.00000i −0.164399 + 0.164399i
\(334\) 0 0
\(335\) −10.0000 −0.546358
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 0 0
\(339\) −6.00000 + 6.00000i −0.325875 + 0.325875i
\(340\) 0 0
\(341\) −8.00000 8.00000i −0.433224 0.433224i
\(342\) 0 0
\(343\) 20.0000i 1.07990i
\(344\) 0 0
\(345\) 12.0000i 0.646058i
\(346\) 0 0
\(347\) −13.0000 13.0000i −0.697877 0.697877i 0.266076 0.963952i \(-0.414273\pi\)
−0.963952 + 0.266076i \(0.914273\pi\)
\(348\) 0 0
\(349\) 3.00000 3.00000i 0.160586 0.160586i −0.622240 0.782826i \(-0.713777\pi\)
0.782826 + 0.622240i \(0.213777\pi\)
\(350\) 0 0
\(351\) −8.00000 −0.427008
\(352\) 0 0
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 0 0
\(355\) 10.0000 10.0000i 0.530745 0.530745i
\(356\) 0 0
\(357\) −4.00000 4.00000i −0.211702 0.211702i
\(358\) 0 0
\(359\) 26.0000i 1.37223i 0.727494 + 0.686114i \(0.240685\pi\)
−0.727494 + 0.686114i \(0.759315\pi\)
\(360\) 0 0
\(361\) 1.00000i 0.0526316i
\(362\) 0 0
\(363\) −9.00000 9.00000i −0.472377 0.472377i
\(364\) 0 0
\(365\) −4.00000 + 4.00000i −0.209370 + 0.209370i
\(366\) 0 0
\(367\) −8.00000 −0.417597 −0.208798 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 10.0000 10.0000i 0.519174 0.519174i
\(372\) 0 0
\(373\) −5.00000 5.00000i −0.258890 0.258890i 0.565712 0.824603i \(-0.308601\pi\)
−0.824603 + 0.565712i \(0.808601\pi\)
\(374\) 0 0
\(375\) 16.0000i 0.826236i
\(376\) 0 0
\(377\) 6.00000i 0.309016i
\(378\) 0 0
\(379\) 3.00000 + 3.00000i 0.154100 + 0.154100i 0.779946 0.625847i \(-0.215246\pi\)
−0.625847 + 0.779946i \(0.715246\pi\)
\(380\) 0 0
\(381\) −8.00000 + 8.00000i −0.409852 + 0.409852i
\(382\) 0 0
\(383\) 16.0000 0.817562 0.408781 0.912633i \(-0.365954\pi\)
0.408781 + 0.912633i \(0.365954\pi\)
\(384\) 0 0
\(385\) −4.00000 −0.203859
\(386\) 0 0
\(387\) 5.00000 5.00000i 0.254164 0.254164i
\(388\) 0 0
\(389\) −13.0000 13.0000i −0.659126 0.659126i 0.296047 0.955173i \(-0.404331\pi\)
−0.955173 + 0.296047i \(0.904331\pi\)
\(390\) 0 0
\(391\) 12.0000i 0.606866i
\(392\) 0 0
\(393\) 22.0000i 1.10975i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −5.00000 + 5.00000i −0.250943 + 0.250943i −0.821357 0.570414i \(-0.806783\pi\)
0.570414 + 0.821357i \(0.306783\pi\)
\(398\) 0 0
\(399\) −12.0000 −0.600751
\(400\) 0 0
\(401\) −18.0000 −0.898877 −0.449439 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) 0 0
\(403\) −8.00000 + 8.00000i −0.398508 + 0.398508i
\(404\) 0 0
\(405\) −5.00000 5.00000i −0.248452 0.248452i
\(406\) 0 0
\(407\) 6.00000i 0.297409i
\(408\) 0 0
\(409\) 16.0000i 0.791149i −0.918434 0.395575i \(-0.870545\pi\)
0.918434 0.395575i \(-0.129455\pi\)
\(410\) 0 0
\(411\) 8.00000 + 8.00000i 0.394611 + 0.394611i
\(412\) 0 0
\(413\) −6.00000 + 6.00000i −0.295241 + 0.295241i
\(414\) 0 0
\(415\) −2.00000 −0.0981761
\(416\) 0 0
\(417\) 6.00000 0.293821
\(418\) 0 0
\(419\) −3.00000 + 3.00000i −0.146560 + 0.146560i −0.776579 0.630020i \(-0.783047\pi\)
0.630020 + 0.776579i \(0.283047\pi\)
\(420\) 0 0
\(421\) −9.00000 9.00000i −0.438633 0.438633i 0.452919 0.891552i \(-0.350383\pi\)
−0.891552 + 0.452919i \(0.850383\pi\)
\(422\) 0 0
\(423\) 8.00000i 0.388973i
\(424\) 0 0
\(425\) 6.00000i 0.291043i
\(426\) 0 0
\(427\) −18.0000 18.0000i −0.871081 0.871081i
\(428\) 0 0
\(429\) 2.00000 2.00000i 0.0965609 0.0965609i
\(430\) 0 0
\(431\) −32.0000 −1.54139 −0.770693 0.637207i \(-0.780090\pi\)
−0.770693 + 0.637207i \(0.780090\pi\)
\(432\) 0 0
\(433\) 14.0000 0.672797 0.336399 0.941720i \(-0.390791\pi\)
0.336399 + 0.941720i \(0.390791\pi\)
\(434\) 0 0
\(435\) −6.00000 + 6.00000i −0.287678 + 0.287678i
\(436\) 0 0
\(437\) 18.0000 + 18.0000i 0.861057 + 0.861057i
\(438\) 0 0
\(439\) 14.0000i 0.668184i −0.942541 0.334092i \(-0.891570\pi\)
0.942541 0.334092i \(-0.108430\pi\)
\(440\) 0 0
\(441\) 3.00000i 0.142857i
\(442\) 0 0
\(443\) 15.0000 + 15.0000i 0.712672 + 0.712672i 0.967093 0.254422i \(-0.0818852\pi\)
−0.254422 + 0.967093i \(0.581885\pi\)
\(444\) 0 0
\(445\) 4.00000 4.00000i 0.189618 0.189618i
\(446\) 0 0
\(447\) 14.0000 0.662177
\(448\) 0 0
\(449\) 30.0000 1.41579 0.707894 0.706319i \(-0.249646\pi\)
0.707894 + 0.706319i \(0.249646\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 10.0000 + 10.0000i 0.469841 + 0.469841i
\(454\) 0 0
\(455\) 4.00000i 0.187523i
\(456\) 0 0
\(457\) 32.0000i 1.49690i −0.663193 0.748448i \(-0.730799\pi\)
0.663193 0.748448i \(-0.269201\pi\)
\(458\) 0 0
\(459\) −8.00000 8.00000i −0.373408 0.373408i
\(460\) 0 0
\(461\) 11.0000 11.0000i 0.512321 0.512321i −0.402916 0.915237i \(-0.632003\pi\)
0.915237 + 0.402916i \(0.132003\pi\)
\(462\) 0 0
\(463\) 16.0000 0.743583 0.371792 0.928316i \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 0 0
\(465\) −16.0000 −0.741982
\(466\) 0 0
\(467\) 5.00000 5.00000i 0.231372 0.231372i −0.581893 0.813265i \(-0.697688\pi\)
0.813265 + 0.581893i \(0.197688\pi\)
\(468\) 0 0
\(469\) 10.0000 + 10.0000i 0.461757 + 0.461757i
\(470\) 0 0
\(471\) 30.0000i 1.38233i
\(472\) 0 0
\(473\) 10.0000i 0.459800i
\(474\) 0 0
\(475\) 9.00000 + 9.00000i 0.412948 + 0.412948i
\(476\) 0 0
\(477\) 5.00000 5.00000i 0.228934 0.228934i
\(478\) 0 0
\(479\) 40.0000 1.82765 0.913823 0.406112i \(-0.133116\pi\)
0.913823 + 0.406112i \(0.133116\pi\)
\(480\) 0 0
\(481\) −6.00000 −0.273576
\(482\) 0 0
\(483\) 12.0000 12.0000i 0.546019 0.546019i
\(484\) 0 0
\(485\) 2.00000 + 2.00000i 0.0908153 + 0.0908153i
\(486\) 0 0
\(487\) 2.00000i 0.0906287i 0.998973 + 0.0453143i \(0.0144289\pi\)
−0.998973 + 0.0453143i \(0.985571\pi\)
\(488\) 0 0
\(489\) 2.00000i 0.0904431i
\(490\) 0 0
\(491\) 19.0000 + 19.0000i 0.857458 + 0.857458i 0.991038 0.133580i \(-0.0426473\pi\)
−0.133580 + 0.991038i \(0.542647\pi\)
\(492\) 0 0
\(493\) −6.00000 + 6.00000i −0.270226 + 0.270226i
\(494\) 0 0
\(495\) −2.00000 −0.0898933
\(496\) 0 0
\(497\) −20.0000 −0.897123
\(498\) 0 0
\(499\) −23.0000 + 23.0000i −1.02962 + 1.02962i −0.0300737 + 0.999548i \(0.509574\pi\)
−0.999548 + 0.0300737i \(0.990426\pi\)
\(500\) 0 0
\(501\) 2.00000 + 2.00000i 0.0893534 + 0.0893534i
\(502\) 0 0
\(503\) 6.00000i 0.267527i −0.991013 0.133763i \(-0.957294\pi\)
0.991013 0.133763i \(-0.0427062\pi\)
\(504\) 0 0
\(505\) 22.0000i 0.978987i
\(506\) 0 0
\(507\) 11.0000 + 11.0000i 0.488527 + 0.488527i
\(508\) 0 0
\(509\) 23.0000 23.0000i 1.01946 1.01946i 0.0196502 0.999807i \(-0.493745\pi\)
0.999807 0.0196502i \(-0.00625524\pi\)
\(510\) 0 0
\(511\) 8.00000 0.353899
\(512\) 0 0
\(513\) −24.0000 −1.05963
\(514\) 0 0
\(515\) −6.00000 + 6.00000i −0.264392 + 0.264392i
\(516\) 0 0
\(517\) 8.00000 + 8.00000i 0.351840 + 0.351840i
\(518\) 0 0
\(519\) 2.00000i 0.0877903i
\(520\) 0 0
\(521\) 40.0000i 1.75243i 0.481919 + 0.876216i \(0.339940\pi\)
−0.481919 + 0.876216i \(0.660060\pi\)
\(522\) 0 0
\(523\) −25.0000 25.0000i −1.09317 1.09317i −0.995188 0.0979859i \(-0.968760\pi\)
−0.0979859 0.995188i \(-0.531240\pi\)
\(524\) 0 0
\(525\) 6.00000 6.00000i 0.261861 0.261861i
\(526\) 0 0
\(527\) −16.0000 −0.696971
\(528\) 0 0
\(529\) −13.0000 −0.565217
\(530\) 0 0
\(531\) −3.00000 + 3.00000i −0.130189 + 0.130189i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 14.0000i 0.605273i
\(536\) 0 0
\(537\) 34.0000i 1.46721i
\(538\) 0 0
\(539\) −3.00000 3.00000i −0.129219 0.129219i
\(540\) 0 0
\(541\) −9.00000 + 9.00000i −0.386940 + 0.386940i −0.873595 0.486654i \(-0.838217\pi\)
0.486654 + 0.873595i \(0.338217\pi\)
\(542\) 0 0
\(543\) −18.0000 −0.772454
\(544\) 0 0
\(545\) −6.00000 −0.257012
\(546\) 0 0
\(547\) 5.00000 5.00000i 0.213785 0.213785i −0.592088 0.805873i \(-0.701696\pi\)
0.805873 + 0.592088i \(0.201696\pi\)
\(548\) 0 0
\(549\) −9.00000 9.00000i −0.384111 0.384111i
\(550\) 0 0
\(551\) 18.0000i 0.766826i
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −6.00000 6.00000i −0.254686 0.254686i
\(556\) 0 0
\(557\) −25.0000 + 25.0000i −1.05928 + 1.05928i −0.0611558 + 0.998128i \(0.519479\pi\)
−0.998128 + 0.0611558i \(0.980521\pi\)
\(558\) 0 0
\(559\) 10.0000 0.422955
\(560\) 0 0
\(561\) 4.00000 0.168880
\(562\) 0 0
\(563\) −19.0000 + 19.0000i −0.800755 + 0.800755i −0.983213 0.182459i \(-0.941594\pi\)
0.182459 + 0.983213i \(0.441594\pi\)
\(564\) 0 0
\(565\) 6.00000 + 6.00000i 0.252422 + 0.252422i
\(566\) 0 0
\(567\) 10.0000i 0.419961i
\(568\) 0 0
\(569\) 24.0000i 1.00613i 0.864248 + 0.503066i \(0.167795\pi\)
−0.864248 + 0.503066i \(0.832205\pi\)
\(570\) 0 0
\(571\) −1.00000 1.00000i −0.0418487 0.0418487i 0.685873 0.727721i \(-0.259421\pi\)
−0.727721 + 0.685873i \(0.759421\pi\)
\(572\) 0 0
\(573\) 8.00000 8.00000i 0.334205 0.334205i
\(574\) 0 0
\(575\) −18.0000 −0.750652
\(576\) 0 0
\(577\) 18.0000 0.749350 0.374675 0.927156i \(-0.377754\pi\)
0.374675 + 0.927156i \(0.377754\pi\)
\(578\) 0 0
\(579\) 14.0000 14.0000i 0.581820 0.581820i
\(580\) 0 0
\(581\) 2.00000 + 2.00000i 0.0829740 + 0.0829740i
\(582\) 0 0
\(583\) 10.0000i 0.414158i
\(584\) 0 0
\(585\) 2.00000i 0.0826898i
\(586\) 0 0
\(587\) 7.00000 + 7.00000i 0.288921 + 0.288921i 0.836653 0.547733i \(-0.184509\pi\)
−0.547733 + 0.836653i \(0.684509\pi\)
\(588\) 0 0
\(589\) −24.0000 + 24.0000i −0.988903 + 0.988903i
\(590\) 0 0
\(591\) −34.0000 −1.39857
\(592\) 0 0
\(593\) 34.0000 1.39621 0.698106 0.715994i \(-0.254026\pi\)
0.698106 + 0.715994i \(0.254026\pi\)
\(594\) 0 0
\(595\) −4.00000 + 4.00000i −0.163984 + 0.163984i
\(596\) 0 0
\(597\) −14.0000 14.0000i −0.572982 0.572982i
\(598\) 0 0
\(599\) 14.0000i 0.572024i −0.958226 0.286012i \(-0.907670\pi\)
0.958226 0.286012i \(-0.0923298\pi\)
\(600\) 0 0
\(601\) 20.0000i 0.815817i 0.913023 + 0.407909i \(0.133742\pi\)
−0.913023 + 0.407909i \(0.866258\pi\)
\(602\) 0 0
\(603\) 5.00000 + 5.00000i 0.203616 + 0.203616i
\(604\) 0 0
\(605\) −9.00000 + 9.00000i −0.365902 + 0.365902i
\(606\) 0 0
\(607\) 32.0000 1.29884 0.649420 0.760430i \(-0.275012\pi\)
0.649420 + 0.760430i \(0.275012\pi\)
\(608\) 0 0
\(609\) 12.0000 0.486265
\(610\) 0 0
\(611\) 8.00000 8.00000i 0.323645 0.323645i
\(612\) 0 0
\(613\) −25.0000 25.0000i −1.00974 1.00974i −0.999952 0.00978840i \(-0.996884\pi\)
−0.00978840 0.999952i \(-0.503116\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 12.0000i 0.483102i −0.970388 0.241551i \(-0.922344\pi\)
0.970388 0.241551i \(-0.0776561\pi\)
\(618\) 0 0
\(619\) −17.0000 17.0000i −0.683288 0.683288i 0.277452 0.960740i \(-0.410510\pi\)
−0.960740 + 0.277452i \(0.910510\pi\)
\(620\) 0 0
\(621\) 24.0000 24.0000i 0.963087 0.963087i
\(622\) 0 0
\(623\) −8.00000 −0.320513
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 6.00000 6.00000i 0.239617 0.239617i
\(628\) 0 0
\(629\) −6.00000 6.00000i −0.239236 0.239236i
\(630\) 0 0
\(631\) 10.0000i 0.398094i 0.979990 + 0.199047i \(0.0637846\pi\)
−0.979990 + 0.199047i \(0.936215\pi\)
\(632\) 0 0
\(633\) 18.0000i 0.715436i
\(634\) 0 0
\(635\) 8.00000 + 8.00000i 0.317470 + 0.317470i
\(636\) 0 0
\(637\) −3.00000 + 3.00000i −0.118864 + 0.118864i
\(638\) 0 0
\(639\) −10.0000 −0.395594
\(640\) 0 0
\(641\) −18.0000 −0.710957 −0.355479 0.934684i \(-0.615682\pi\)
−0.355479 + 0.934684i \(0.615682\pi\)
\(642\) 0 0
\(643\) 21.0000 21.0000i 0.828159 0.828159i −0.159103 0.987262i \(-0.550860\pi\)
0.987262 + 0.159103i \(0.0508601\pi\)
\(644\) 0 0
\(645\) 10.0000 + 10.0000i 0.393750 + 0.393750i
\(646\) 0 0
\(647\) 42.0000i 1.65119i 0.564263 + 0.825595i \(0.309160\pi\)
−0.564263 + 0.825595i \(0.690840\pi\)
\(648\) 0 0
\(649\) 6.00000i 0.235521i
\(650\) 0 0
\(651\) 16.0000 + 16.0000i 0.627089 + 0.627089i
\(652\) 0 0
\(653\) 19.0000 19.0000i 0.743527 0.743527i −0.229728 0.973255i \(-0.573784\pi\)
0.973255 + 0.229728i \(0.0737835\pi\)
\(654\) 0 0
\(655\) 22.0000 0.859611
\(656\) 0 0
\(657\) 4.00000 0.156055
\(658\) 0 0
\(659\) 17.0000 17.0000i 0.662226 0.662226i −0.293678 0.955904i \(-0.594879\pi\)
0.955904 + 0.293678i \(0.0948794\pi\)
\(660\) 0 0
\(661\) −9.00000 9.00000i −0.350059 0.350059i 0.510072 0.860132i \(-0.329619\pi\)
−0.860132 + 0.510072i \(0.829619\pi\)
\(662\) 0 0
\(663\) 4.00000i 0.155347i
\(664\) 0 0
\(665\) 12.0000i 0.465340i
\(666\) 0 0
\(667\) −18.0000 18.0000i −0.696963 0.696963i
\(668\) 0 0
\(669\) −24.0000 + 24.0000i −0.927894 + 0.927894i
\(670\) 0 0
\(671\) 18.0000 0.694882
\(672\) 0 0
\(673\) 14.0000 0.539660 0.269830 0.962908i \(-0.413032\pi\)
0.269830 + 0.962908i \(0.413032\pi\)
\(674\) 0 0
\(675\) 12.0000 12.0000i 0.461880 0.461880i
\(676\) 0 0
\(677\) 3.00000 + 3.00000i 0.115299 + 0.115299i 0.762402 0.647103i \(-0.224020\pi\)
−0.647103 + 0.762402i \(0.724020\pi\)
\(678\) 0 0
\(679\) 4.00000i 0.153506i
\(680\) 0 0
\(681\) 30.0000i 1.14960i
\(682\) 0 0
\(683\) −5.00000 5.00000i −0.191320 0.191320i 0.604946 0.796266i \(-0.293195\pi\)
−0.796266 + 0.604946i \(0.793195\pi\)
\(684\) 0 0
\(685\) 8.00000 8.00000i 0.305664 0.305664i
\(686\) 0 0
\(687\) 14.0000 0.534133
\(688\) 0 0
\(689\) 10.0000 0.380970
\(690\) 0 0
\(691\) 9.00000 9.00000i 0.342376 0.342376i −0.514884 0.857260i \(-0.672165\pi\)
0.857260 + 0.514884i \(0.172165\pi\)
\(692\) 0 0
\(693\) 2.00000 + 2.00000i 0.0759737 + 0.0759737i
\(694\) 0 0
\(695\) 6.00000i 0.227593i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −4.00000 4.00000i −0.151294 0.151294i
\(700\) 0 0
\(701\) 31.0000 31.0000i 1.17085 1.17085i 0.188847 0.982006i \(-0.439525\pi\)
0.982006 0.188847i \(-0.0604752\pi\)
\(702\) 0 0
\(703\) −18.0000 −0.678883
\(704\) 0 0
\(705\) 16.0000 0.602595
\(706\) 0 0
\(707\) −22.0000 + 22.0000i −0.827395 + 0.827395i
\(708\) 0 0
\(709\) 27.0000 + 27.0000i 1.01401 + 1.01401i 0.999901 + 0.0141058i \(0.00449016\pi\)
0.0141058 + 0.999901i \(0.495510\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 48.0000i 1.79761i
\(714\) 0 0
\(715\) −2.00000 2.00000i −0.0747958 0.0747958i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 12.0000 0.446903
\(722\) 0 0
\(723\) −18.0000 + 18.0000i −0.669427 + 0.669427i
\(724\) 0 0
\(725\) −9.00000 9.00000i −0.334252 0.334252i
\(726\) 0 0
\(727\) 2.00000i 0.0741759i 0.999312 + 0.0370879i \(0.0118082\pi\)
−0.999312 + 0.0370879i \(0.988192\pi\)
\(728\) 0 0
\(729\) 29.0000i 1.07407i
\(730\) 0 0
\(731\) 10.0000 + 10.0000i 0.369863 + 0.369863i
\(732\) 0 0
\(733\) −21.0000 + 21.0000i −0.775653 + 0.775653i −0.979088 0.203436i \(-0.934789\pi\)
0.203436 + 0.979088i \(0.434789\pi\)
\(734\) 0 0
\(735\) −6.00000 −0.221313
\(736\) 0 0
\(737\) −10.0000 −0.368355
\(738\) 0 0
\(739\) −23.0000 + 23.0000i −0.846069 + 0.846069i −0.989640 0.143571i \(-0.954141\pi\)
0.143571 + 0.989640i \(0.454141\pi\)
\(740\) 0 0
\(741\) −6.00000 6.00000i −0.220416 0.220416i
\(742\) 0 0
\(743\) 46.0000i 1.68758i −0.536676 0.843788i \(-0.680320\pi\)
0.536676 0.843788i \(-0.319680\pi\)
\(744\) 0 0
\(745\) 14.0000i 0.512920i
\(746\) 0 0
\(747\) 1.00000 + 1.00000i 0.0365881 + 0.0365881i
\(748\) 0 0
\(749\) −14.0000 + 14.0000i −0.511549 + 0.511549i
\(750\) 0 0
\(751\) −32.0000 −1.16770 −0.583848 0.811863i \(-0.698454\pi\)
−0.583848 + 0.811863i \(0.698454\pi\)
\(752\) 0 0
\(753\) −42.0000 −1.53057
\(754\) 0 0
\(755\) 10.0000 10.0000i 0.363937 0.363937i
\(756\) 0 0
\(757\) 23.0000 + 23.0000i 0.835949 + 0.835949i 0.988323 0.152374i \(-0.0486917\pi\)
−0.152374 + 0.988323i \(0.548692\pi\)
\(758\) 0 0
\(759\) 12.0000i 0.435572i
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) 0 0
\(763\) 6.00000 + 6.00000i 0.217215 + 0.217215i
\(764\) 0 0
\(765\) −2.00000 + 2.00000i −0.0723102 + 0.0723102i
\(766\) 0 0
\(767\) −6.00000 −0.216647
\(768\) 0 0
\(769\) −50.0000 −1.80305 −0.901523 0.432731i \(-0.857550\pi\)
−0.901523 + 0.432731i \(0.857550\pi\)
\(770\) 0 0
\(771\) −22.0000 + 22.0000i −0.792311 + 0.792311i
\(772\) 0 0
\(773\) −5.00000 5.00000i −0.179838 0.179838i 0.611448 0.791285i \(-0.290588\pi\)
−0.791285 + 0.611448i \(0.790588\pi\)
\(774\) 0 0
\(775\) 24.0000i 0.862105i
\(776\) 0 0
\(777\) 12.0000i 0.430498i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 10.0000 10.0000i 0.357828 0.357828i
\(782\) 0 0
\(783\) 24.0000 0.857690
\(784\) 0 0
\(785\) −30.0000 −1.07075
\(786\) 0 0
\(787\) −15.0000 + 15.0000i −0.534692 + 0.534692i −0.921965 0.387273i \(-0.873417\pi\)
0.387273 + 0.921965i \(0.373417\pi\)
\(788\) 0 0
\(789\) −6.00000 6.00000i −0.213606 0.213606i
\(790\) 0 0
\(791\) 12.0000i 0.426671i
\(792\) 0 0
\(793\) 18.0000i 0.639199i
\(794\) 0 0
\(795\) 10.0000 + 10.0000i 0.354663 + 0.354663i
\(796\) 0 0
\(797\) −25.0000 + 25.0000i −0.885545 + 0.885545i −0.994091 0.108546i \(-0.965381\pi\)
0.108546 + 0.994091i \(0.465381\pi\)
\(798\) 0 0
\(799\) 16.0000 0.566039