Properties

Label 1134.2.d.a.1133.7
Level $1134$
Weight $2$
Character 1134.1133
Analytic conductor $9.055$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} + 9 x^{12} + 54 x^{10} - 288 x^{8} + 486 x^{6} + 729 x^{4} - 4374 x^{2} + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{6} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1133.7
Root \(1.40917 + 1.00709i\) of defining polynomial
Character \(\chi\) \(=\) 1134.1133
Dual form 1134.2.d.a.1133.15

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{4} +2.34936 q^{5} +(1.07781 - 2.41626i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{4} +2.34936 q^{5} +(1.07781 - 2.41626i) q^{7} +1.00000i q^{8} -2.34936i q^{10} -5.67667i q^{11} +1.71985i q^{13} +(-2.41626 - 1.07781i) q^{14} +1.00000 q^{16} +1.76883 q^{17} -1.13932i q^{19} -2.34936 q^{20} -5.67667 q^{22} +3.67509i q^{23} +0.519482 q^{25} +1.71985 q^{26} +(-1.07781 + 2.41626i) q^{28} +4.15561i q^{29} -8.37019i q^{31} -1.00000i q^{32} -1.76883i q^{34} +(2.53215 - 5.67667i) q^{35} -9.19773 q^{37} -1.13932 q^{38} +2.34936i q^{40} +7.99419 q^{41} -3.52106 q^{43} +5.67667i q^{44} +3.67509 q^{46} +11.8099 q^{47} +(-4.67667 - 5.20853i) q^{49} -0.519482i q^{50} -1.71985i q^{52} -13.3365i q^{55} +(2.41626 + 1.07781i) q^{56} +4.15561 q^{58} +2.22966 q^{59} -8.99970i q^{61} -8.37019 q^{62} -1.00000 q^{64} +4.04054i q^{65} +10.8712 q^{67} -1.76883 q^{68} +(-5.67667 - 2.53215i) q^{70} -4.52106i q^{71} +5.34234i q^{73} +9.19773i q^{74} +1.13932i q^{76} +(-13.7163 - 6.11835i) q^{77} -13.0284 q^{79} +2.34936 q^{80} -7.99419i q^{82} -12.5460 q^{83} +4.15561 q^{85} +3.52106i q^{86} +5.67667 q^{88} +1.16106 q^{89} +(4.15561 + 1.85366i) q^{91} -3.67509i q^{92} -11.8099i q^{94} -2.67667i q^{95} +4.59035i q^{97} +(-5.20853 + 4.67667i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4} - 4 q^{7} + O(q^{10}) \) \( 16 q - 16 q^{4} - 4 q^{7} + 16 q^{16} + 16 q^{25} + 4 q^{28} - 8 q^{37} - 8 q^{43} + 24 q^{46} + 16 q^{49} + 24 q^{58} - 16 q^{64} + 56 q^{67} + 8 q^{79} + 24 q^{85} + 24 q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) 2.34936 1.05066 0.525332 0.850897i \(-0.323941\pi\)
0.525332 + 0.850897i \(0.323941\pi\)
\(6\) 0 0
\(7\) 1.07781 2.41626i 0.407372 0.913262i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 2.34936i 0.742932i
\(11\) 5.67667i 1.71158i −0.517323 0.855790i \(-0.673071\pi\)
0.517323 0.855790i \(-0.326929\pi\)
\(12\) 0 0
\(13\) 1.71985i 0.477000i 0.971142 + 0.238500i \(0.0766558\pi\)
−0.971142 + 0.238500i \(0.923344\pi\)
\(14\) −2.41626 1.07781i −0.645774 0.288056i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 1.76883 0.429004 0.214502 0.976724i \(-0.431187\pi\)
0.214502 + 0.976724i \(0.431187\pi\)
\(18\) 0 0
\(19\) 1.13932i 0.261378i −0.991423 0.130689i \(-0.958281\pi\)
0.991423 0.130689i \(-0.0417189\pi\)
\(20\) −2.34936 −0.525332
\(21\) 0 0
\(22\) −5.67667 −1.21027
\(23\) 3.67509i 0.766310i 0.923684 + 0.383155i \(0.125162\pi\)
−0.923684 + 0.383155i \(0.874838\pi\)
\(24\) 0 0
\(25\) 0.519482 0.103896
\(26\) 1.71985 0.337290
\(27\) 0 0
\(28\) −1.07781 + 2.41626i −0.203686 + 0.456631i
\(29\) 4.15561i 0.771678i 0.922566 + 0.385839i \(0.126088\pi\)
−0.922566 + 0.385839i \(0.873912\pi\)
\(30\) 0 0
\(31\) 8.37019i 1.50333i −0.659545 0.751665i \(-0.729251\pi\)
0.659545 0.751665i \(-0.270749\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 1.76883i 0.303352i
\(35\) 2.53215 5.67667i 0.428012 0.959532i
\(36\) 0 0
\(37\) −9.19773 −1.51210 −0.756049 0.654515i \(-0.772873\pi\)
−0.756049 + 0.654515i \(0.772873\pi\)
\(38\) −1.13932 −0.184822
\(39\) 0 0
\(40\) 2.34936i 0.371466i
\(41\) 7.99419 1.24848 0.624241 0.781232i \(-0.285408\pi\)
0.624241 + 0.781232i \(0.285408\pi\)
\(42\) 0 0
\(43\) −3.52106 −0.536956 −0.268478 0.963286i \(-0.586521\pi\)
−0.268478 + 0.963286i \(0.586521\pi\)
\(44\) 5.67667i 0.855790i
\(45\) 0 0
\(46\) 3.67509 0.541863
\(47\) 11.8099 1.72265 0.861324 0.508055i \(-0.169635\pi\)
0.861324 + 0.508055i \(0.169635\pi\)
\(48\) 0 0
\(49\) −4.67667 5.20853i −0.668096 0.744075i
\(50\) 0.519482i 0.0734659i
\(51\) 0 0
\(52\) 1.71985i 0.238500i
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 13.3365i 1.79830i
\(56\) 2.41626 + 1.07781i 0.322887 + 0.144028i
\(57\) 0 0
\(58\) 4.15561 0.545658
\(59\) 2.22966 0.290277 0.145139 0.989411i \(-0.453637\pi\)
0.145139 + 0.989411i \(0.453637\pi\)
\(60\) 0 0
\(61\) 8.99970i 1.15229i −0.817346 0.576146i \(-0.804556\pi\)
0.817346 0.576146i \(-0.195444\pi\)
\(62\) −8.37019 −1.06301
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 4.04054i 0.501167i
\(66\) 0 0
\(67\) 10.8712 1.32813 0.664067 0.747673i \(-0.268829\pi\)
0.664067 + 0.747673i \(0.268829\pi\)
\(68\) −1.76883 −0.214502
\(69\) 0 0
\(70\) −5.67667 2.53215i −0.678492 0.302650i
\(71\) 4.52106i 0.536551i −0.963342 0.268276i \(-0.913546\pi\)
0.963342 0.268276i \(-0.0864538\pi\)
\(72\) 0 0
\(73\) 5.34234i 0.625274i 0.949873 + 0.312637i \(0.101212\pi\)
−0.949873 + 0.312637i \(0.898788\pi\)
\(74\) 9.19773i 1.06921i
\(75\) 0 0
\(76\) 1.13932i 0.130689i
\(77\) −13.7163 6.11835i −1.56312 0.697250i
\(78\) 0 0
\(79\) −13.0284 −1.46581 −0.732907 0.680329i \(-0.761837\pi\)
−0.732907 + 0.680329i \(0.761837\pi\)
\(80\) 2.34936 0.262666
\(81\) 0 0
\(82\) 7.99419i 0.882810i
\(83\) −12.5460 −1.37710 −0.688549 0.725189i \(-0.741752\pi\)
−0.688549 + 0.725189i \(0.741752\pi\)
\(84\) 0 0
\(85\) 4.15561 0.450739
\(86\) 3.52106i 0.379686i
\(87\) 0 0
\(88\) 5.67667 0.605135
\(89\) 1.16106 0.123072 0.0615360 0.998105i \(-0.480400\pi\)
0.0615360 + 0.998105i \(0.480400\pi\)
\(90\) 0 0
\(91\) 4.15561 + 1.85366i 0.435626 + 0.194317i
\(92\) 3.67509i 0.383155i
\(93\) 0 0
\(94\) 11.8099i 1.21810i
\(95\) 2.67667i 0.274621i
\(96\) 0 0
\(97\) 4.59035i 0.466079i 0.972467 + 0.233039i \(0.0748671\pi\)
−0.972467 + 0.233039i \(0.925133\pi\)
\(98\) −5.20853 + 4.67667i −0.526141 + 0.472415i
\(99\) 0 0
\(100\) −0.519482 −0.0519482
\(101\) 6.62310 0.659023 0.329511 0.944152i \(-0.393116\pi\)
0.329511 + 0.944152i \(0.393116\pi\)
\(102\) 0 0
\(103\) 5.85977i 0.577381i −0.957423 0.288690i \(-0.906780\pi\)
0.957423 0.288690i \(-0.0932198\pi\)
\(104\) −1.71985 −0.168645
\(105\) 0 0
\(106\) 0 0
\(107\) 4.71563i 0.455878i 0.973675 + 0.227939i \(0.0731986\pi\)
−0.973675 + 0.227939i \(0.926801\pi\)
\(108\) 0 0
\(109\) 4.23669 0.405802 0.202901 0.979199i \(-0.434963\pi\)
0.202901 + 0.979199i \(0.434963\pi\)
\(110\) −13.3365 −1.27159
\(111\) 0 0
\(112\) 1.07781 2.41626i 0.101843 0.228316i
\(113\) 6.83228i 0.642727i −0.946956 0.321363i \(-0.895859\pi\)
0.946956 0.321363i \(-0.104141\pi\)
\(114\) 0 0
\(115\) 8.63411i 0.805135i
\(116\) 4.15561i 0.385839i
\(117\) 0 0
\(118\) 2.22966i 0.205257i
\(119\) 1.90645 4.27396i 0.174764 0.391793i
\(120\) 0 0
\(121\) −21.2246 −1.92951
\(122\) −8.99970 −0.814794
\(123\) 0 0
\(124\) 8.37019i 0.751665i
\(125\) −10.5263 −0.941504
\(126\) 0 0
\(127\) −6.67667 −0.592459 −0.296229 0.955117i \(-0.595729\pi\)
−0.296229 + 0.955117i \(0.595729\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 4.04054 0.354379
\(131\) 7.47305 0.652923 0.326462 0.945210i \(-0.394144\pi\)
0.326462 + 0.945210i \(0.394144\pi\)
\(132\) 0 0
\(133\) −2.75290 1.22797i −0.238707 0.106478i
\(134\) 10.8712i 0.939133i
\(135\) 0 0
\(136\) 1.76883i 0.151676i
\(137\) 7.98789i 0.682452i 0.939981 + 0.341226i \(0.110842\pi\)
−0.939981 + 0.341226i \(0.889158\pi\)
\(138\) 0 0
\(139\) 20.7606i 1.76089i 0.474147 + 0.880446i \(0.342756\pi\)
−0.474147 + 0.880446i \(0.657244\pi\)
\(140\) −2.53215 + 5.67667i −0.214006 + 0.479766i
\(141\) 0 0
\(142\) −4.52106 −0.379399
\(143\) 9.76302 0.816425
\(144\) 0 0
\(145\) 9.76302i 0.810774i
\(146\) 5.34234 0.442135
\(147\) 0 0
\(148\) 9.19773 0.756049
\(149\) 1.19773i 0.0981218i 0.998796 + 0.0490609i \(0.0156228\pi\)
−0.998796 + 0.0490609i \(0.984377\pi\)
\(150\) 0 0
\(151\) 15.2246 1.23896 0.619480 0.785013i \(-0.287344\pi\)
0.619480 + 0.785013i \(0.287344\pi\)
\(152\) 1.13932 0.0924111
\(153\) 0 0
\(154\) −6.11835 + 13.7163i −0.493030 + 1.10529i
\(155\) 19.6646i 1.57950i
\(156\) 0 0
\(157\) 10.0269i 0.800237i 0.916463 + 0.400118i \(0.131031\pi\)
−0.916463 + 0.400118i \(0.868969\pi\)
\(158\) 13.0284i 1.03649i
\(159\) 0 0
\(160\) 2.34936i 0.185733i
\(161\) 8.88000 + 3.96104i 0.699842 + 0.312173i
\(162\) 0 0
\(163\) 12.0032 0.940160 0.470080 0.882624i \(-0.344225\pi\)
0.470080 + 0.882624i \(0.344225\pi\)
\(164\) −7.99419 −0.624241
\(165\) 0 0
\(166\) 12.5460i 0.973756i
\(167\) 17.1494 1.32706 0.663532 0.748148i \(-0.269057\pi\)
0.663532 + 0.748148i \(0.269057\pi\)
\(168\) 0 0
\(169\) 10.0421 0.772471
\(170\) 4.15561i 0.318721i
\(171\) 0 0
\(172\) 3.52106 0.268478
\(173\) 1.98748 0.151105 0.0755525 0.997142i \(-0.475928\pi\)
0.0755525 + 0.997142i \(0.475928\pi\)
\(174\) 0 0
\(175\) 0.559901 1.25521i 0.0423245 0.0948847i
\(176\) 5.67667i 0.427895i
\(177\) 0 0
\(178\) 1.16106i 0.0870250i
\(179\) 8.31122i 0.621210i 0.950539 + 0.310605i \(0.100532\pi\)
−0.950539 + 0.310605i \(0.899468\pi\)
\(180\) 0 0
\(181\) 15.4541i 1.14870i −0.818611 0.574348i \(-0.805256\pi\)
0.818611 0.574348i \(-0.194744\pi\)
\(182\) 1.85366 4.15561i 0.137403 0.308034i
\(183\) 0 0
\(184\) −3.67509 −0.270931
\(185\) −21.6088 −1.58871
\(186\) 0 0
\(187\) 10.0411i 0.734275i
\(188\) −11.8099 −0.861324
\(189\) 0 0
\(190\) −2.67667 −0.194186
\(191\) 12.3381i 0.892752i 0.894845 + 0.446376i \(0.147286\pi\)
−0.894845 + 0.446376i \(0.852714\pi\)
\(192\) 0 0
\(193\) 4.39388 0.316279 0.158139 0.987417i \(-0.449451\pi\)
0.158139 + 0.987417i \(0.449451\pi\)
\(194\) 4.59035 0.329568
\(195\) 0 0
\(196\) 4.67667 + 5.20853i 0.334048 + 0.372038i
\(197\) 10.8865i 0.775632i 0.921737 + 0.387816i \(0.126770\pi\)
−0.921737 + 0.387816i \(0.873230\pi\)
\(198\) 0 0
\(199\) 27.5665i 1.95414i 0.212926 + 0.977068i \(0.431701\pi\)
−0.212926 + 0.977068i \(0.568299\pi\)
\(200\) 0.519482i 0.0367329i
\(201\) 0 0
\(202\) 6.62310i 0.465999i
\(203\) 10.0411 + 4.47894i 0.704744 + 0.314360i
\(204\) 0 0
\(205\) 18.7812 1.31174
\(206\) −5.85977 −0.408270
\(207\) 0 0
\(208\) 1.71985i 0.119250i
\(209\) −6.46754 −0.447369
\(210\) 0 0
\(211\) −10.3112 −0.709854 −0.354927 0.934894i \(-0.615494\pi\)
−0.354927 + 0.934894i \(0.615494\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 4.71563 0.322354
\(215\) −8.27223 −0.564161
\(216\) 0 0
\(217\) −20.2246 9.02143i −1.37293 0.612415i
\(218\) 4.23669i 0.286945i
\(219\) 0 0
\(220\) 13.3365i 0.899149i
\(221\) 3.04212i 0.204635i
\(222\) 0 0
\(223\) 7.20913i 0.482759i 0.970431 + 0.241379i \(0.0775998\pi\)
−0.970431 + 0.241379i \(0.922400\pi\)
\(224\) −2.41626 1.07781i −0.161443 0.0720139i
\(225\) 0 0
\(226\) −6.83228 −0.454477
\(227\) 12.7560 0.846645 0.423323 0.905979i \(-0.360864\pi\)
0.423323 + 0.905979i \(0.360864\pi\)
\(228\) 0 0
\(229\) 4.49418i 0.296984i 0.988914 + 0.148492i \(0.0474419\pi\)
−0.988914 + 0.148492i \(0.952558\pi\)
\(230\) 8.63411 0.569316
\(231\) 0 0
\(232\) −4.15561 −0.272829
\(233\) 2.15403i 0.141115i 0.997508 + 0.0705577i \(0.0224779\pi\)
−0.997508 + 0.0705577i \(0.977522\pi\)
\(234\) 0 0
\(235\) 27.7456 1.80993
\(236\) −2.22966 −0.145139
\(237\) 0 0
\(238\) −4.27396 1.90645i −0.277040 0.123577i
\(239\) 10.1419i 0.656027i 0.944673 + 0.328013i \(0.106379\pi\)
−0.944673 + 0.328013i \(0.893621\pi\)
\(240\) 0 0
\(241\) 10.5481i 0.679461i −0.940523 0.339731i \(-0.889664\pi\)
0.940523 0.339731i \(-0.110336\pi\)
\(242\) 21.2246i 1.36437i
\(243\) 0 0
\(244\) 8.99970i 0.576146i
\(245\) −10.9872 12.2367i −0.701945 0.781774i
\(246\) 0 0
\(247\) 1.95946 0.124677
\(248\) 8.37019 0.531507
\(249\) 0 0
\(250\) 10.5263i 0.665744i
\(251\) 29.3005 1.84943 0.924714 0.380662i \(-0.124304\pi\)
0.924714 + 0.380662i \(0.124304\pi\)
\(252\) 0 0
\(253\) 20.8623 1.31160
\(254\) 6.67667i 0.418932i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −7.62860 −0.475859 −0.237930 0.971282i \(-0.576469\pi\)
−0.237930 + 0.971282i \(0.576469\pi\)
\(258\) 0 0
\(259\) −9.91336 + 22.2241i −0.615986 + 1.38094i
\(260\) 4.04054i 0.250584i
\(261\) 0 0
\(262\) 7.47305i 0.461687i
\(263\) 12.1856i 0.751398i −0.926742 0.375699i \(-0.877403\pi\)
0.926742 0.375699i \(-0.122597\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −1.22797 + 2.75290i −0.0752914 + 0.168791i
\(267\) 0 0
\(268\) −10.8712 −0.664067
\(269\) −2.77433 −0.169154 −0.0845771 0.996417i \(-0.526954\pi\)
−0.0845771 + 0.996417i \(0.526954\pi\)
\(270\) 0 0
\(271\) 3.20793i 0.194868i −0.995242 0.0974338i \(-0.968937\pi\)
0.995242 0.0974338i \(-0.0310634\pi\)
\(272\) 1.76883 0.107251
\(273\) 0 0
\(274\) 7.98789 0.482566
\(275\) 2.94893i 0.177827i
\(276\) 0 0
\(277\) 10.0811 0.605714 0.302857 0.953036i \(-0.402060\pi\)
0.302857 + 0.953036i \(0.402060\pi\)
\(278\) 20.7606 1.24514
\(279\) 0 0
\(280\) 5.67667 + 2.53215i 0.339246 + 0.151325i
\(281\) 4.87282i 0.290688i 0.989381 + 0.145344i \(0.0464289\pi\)
−0.989381 + 0.145344i \(0.953571\pi\)
\(282\) 0 0
\(283\) 2.81781i 0.167502i −0.996487 0.0837508i \(-0.973310\pi\)
0.996487 0.0837508i \(-0.0266900\pi\)
\(284\) 4.52106i 0.268276i
\(285\) 0 0
\(286\) 9.76302i 0.577299i
\(287\) 8.61618 19.3161i 0.508597 1.14019i
\(288\) 0 0
\(289\) −13.8712 −0.815956
\(290\) 9.76302 0.573304
\(291\) 0 0
\(292\) 5.34234i 0.312637i
\(293\) −8.11389 −0.474018 −0.237009 0.971507i \(-0.576167\pi\)
−0.237009 + 0.971507i \(0.576167\pi\)
\(294\) 0 0
\(295\) 5.23827 0.304984
\(296\) 9.19773i 0.534607i
\(297\) 0 0
\(298\) 1.19773 0.0693826
\(299\) −6.32061 −0.365530
\(300\) 0 0
\(301\) −3.79502 + 8.50781i −0.218741 + 0.490382i
\(302\) 15.2246i 0.876076i
\(303\) 0 0
\(304\) 1.13932i 0.0653445i
\(305\) 21.1435i 1.21067i
\(306\) 0 0
\(307\) 10.8996i 0.622074i 0.950398 + 0.311037i \(0.100676\pi\)
−0.950398 + 0.311037i \(0.899324\pi\)
\(308\) 13.7163 + 6.11835i 0.781561 + 0.348625i
\(309\) 0 0
\(310\) −19.6646 −1.11687
\(311\) 8.23637 0.467042 0.233521 0.972352i \(-0.424975\pi\)
0.233521 + 0.972352i \(0.424975\pi\)
\(312\) 0 0
\(313\) 33.8023i 1.91062i 0.295611 + 0.955308i \(0.404477\pi\)
−0.295611 + 0.955308i \(0.595523\pi\)
\(314\) 10.0269 0.565853
\(315\) 0 0
\(316\) 13.0284 0.732907
\(317\) 6.73090i 0.378045i 0.981973 + 0.189022i \(0.0605319\pi\)
−0.981973 + 0.189022i \(0.939468\pi\)
\(318\) 0 0
\(319\) 23.5900 1.32079
\(320\) −2.34936 −0.131333
\(321\) 0 0
\(322\) 3.96104 8.88000i 0.220740 0.494863i
\(323\) 2.01526i 0.112132i
\(324\) 0 0
\(325\) 0.893431i 0.0495586i
\(326\) 12.0032i 0.664793i
\(327\) 0 0
\(328\) 7.99419i 0.441405i
\(329\) 12.7288 28.5358i 0.701759 1.57323i
\(330\) 0 0
\(331\) −32.0569 −1.76200 −0.881002 0.473112i \(-0.843131\pi\)
−0.881002 + 0.473112i \(0.843131\pi\)
\(332\) 12.5460 0.688549
\(333\) 0 0
\(334\) 17.1494i 0.938375i
\(335\) 25.5404 1.39542
\(336\) 0 0
\(337\) 24.2246 1.31960 0.659799 0.751442i \(-0.270642\pi\)
0.659799 + 0.751442i \(0.270642\pi\)
\(338\) 10.0421i 0.546219i
\(339\) 0 0
\(340\) −4.15561 −0.225370
\(341\) −47.5148 −2.57307
\(342\) 0 0
\(343\) −17.6257 + 5.68629i −0.951700 + 0.307031i
\(344\) 3.52106i 0.189843i
\(345\) 0 0
\(346\) 1.98748i 0.106847i
\(347\) 22.7999i 1.22396i −0.790873 0.611981i \(-0.790373\pi\)
0.790873 0.611981i \(-0.209627\pi\)
\(348\) 0 0
\(349\) 2.84505i 0.152292i 0.997097 + 0.0761461i \(0.0242615\pi\)
−0.997097 + 0.0761461i \(0.975738\pi\)
\(350\) −1.25521 0.559901i −0.0670936 0.0299279i
\(351\) 0 0
\(352\) −5.67667 −0.302568
\(353\) −7.14424 −0.380249 −0.190125 0.981760i \(-0.560889\pi\)
−0.190125 + 0.981760i \(0.560889\pi\)
\(354\) 0 0
\(355\) 10.6216i 0.563735i
\(356\) −1.16106 −0.0615360
\(357\) 0 0
\(358\) 8.31122 0.439262
\(359\) 11.6037i 0.612421i 0.951964 + 0.306210i \(0.0990611\pi\)
−0.951964 + 0.306210i \(0.900939\pi\)
\(360\) 0 0
\(361\) 17.7019 0.931682
\(362\) −15.4541 −0.812250
\(363\) 0 0
\(364\) −4.15561 1.85366i −0.217813 0.0971583i
\(365\) 12.5511i 0.656953i
\(366\) 0 0
\(367\) 7.83493i 0.408980i −0.978869 0.204490i \(-0.934446\pi\)
0.978869 0.204490i \(-0.0655536\pi\)
\(368\) 3.67509i 0.191577i
\(369\) 0 0
\(370\) 21.6088i 1.12339i
\(371\) 0 0
\(372\) 0 0
\(373\) 25.6677 1.32902 0.664512 0.747278i \(-0.268639\pi\)
0.664512 + 0.747278i \(0.268639\pi\)
\(374\) −10.0411 −0.519211
\(375\) 0 0
\(376\) 11.8099i 0.609048i
\(377\) −7.14702 −0.368091
\(378\) 0 0
\(379\) −15.1045 −0.775868 −0.387934 0.921687i \(-0.626811\pi\)
−0.387934 + 0.921687i \(0.626811\pi\)
\(380\) 2.67667i 0.137310i
\(381\) 0 0
\(382\) 12.3381 0.631271
\(383\) 1.52664 0.0780079 0.0390040 0.999239i \(-0.487582\pi\)
0.0390040 + 0.999239i \(0.487582\pi\)
\(384\) 0 0
\(385\) −32.2246 14.3742i −1.64232 0.732576i
\(386\) 4.39388i 0.223643i
\(387\) 0 0
\(388\) 4.59035i 0.233039i
\(389\) 14.8897i 0.754936i 0.926023 + 0.377468i \(0.123205\pi\)
−0.926023 + 0.377468i \(0.876795\pi\)
\(390\) 0 0
\(391\) 6.50061i 0.328750i
\(392\) 5.20853 4.67667i 0.263070 0.236208i
\(393\) 0 0
\(394\) 10.8865 0.548454
\(395\) −30.6085 −1.54008
\(396\) 0 0
\(397\) 28.7869i 1.44478i 0.691488 + 0.722388i \(0.256955\pi\)
−0.691488 + 0.722388i \(0.743045\pi\)
\(398\) 27.5665 1.38178
\(399\) 0 0
\(400\) 0.519482 0.0259741
\(401\) 38.1735i 1.90629i 0.302507 + 0.953147i \(0.402176\pi\)
−0.302507 + 0.953147i \(0.597824\pi\)
\(402\) 0 0
\(403\) 14.3955 0.717089
\(404\) −6.62310 −0.329511
\(405\) 0 0
\(406\) 4.47894 10.0411i 0.222286 0.498329i
\(407\) 52.2125i 2.58808i
\(408\) 0 0
\(409\) 6.96694i 0.344493i 0.985054 + 0.172247i \(0.0551026\pi\)
−0.985054 + 0.172247i \(0.944897\pi\)
\(410\) 18.7812i 0.927538i
\(411\) 0 0
\(412\) 5.85977i 0.288690i
\(413\) 2.40314 5.38745i 0.118251 0.265099i
\(414\) 0 0
\(415\) −29.4750 −1.44687
\(416\) 1.71985 0.0843225
\(417\) 0 0
\(418\) 6.46754i 0.316338i
\(419\) −34.8463 −1.70235 −0.851177 0.524878i \(-0.824111\pi\)
−0.851177 + 0.524878i \(0.824111\pi\)
\(420\) 0 0
\(421\) −5.69193 −0.277408 −0.138704 0.990334i \(-0.544294\pi\)
−0.138704 + 0.990334i \(0.544294\pi\)
\(422\) 10.3112i 0.501942i
\(423\) 0 0
\(424\) 0 0
\(425\) 0.918875 0.0445720
\(426\) 0 0
\(427\) −21.7456 9.69992i −1.05235 0.469412i
\(428\) 4.71563i 0.227939i
\(429\) 0 0
\(430\) 8.27223i 0.398922i
\(431\) 30.2936i 1.45919i −0.683880 0.729595i \(-0.739709\pi\)
0.683880 0.729595i \(-0.260291\pi\)
\(432\) 0 0
\(433\) 23.6094i 1.13459i 0.823513 + 0.567297i \(0.192011\pi\)
−0.823513 + 0.567297i \(0.807989\pi\)
\(434\) −9.02143 + 20.2246i −0.433043 + 0.970811i
\(435\) 0 0
\(436\) −4.23669 −0.202901
\(437\) 4.18711 0.200297
\(438\) 0 0
\(439\) 25.0202i 1.19415i −0.802185 0.597075i \(-0.796329\pi\)
0.802185 0.597075i \(-0.203671\pi\)
\(440\) 13.3365 0.635794
\(441\) 0 0
\(442\) 3.04212 0.144699
\(443\) 23.0300i 1.09419i −0.837071 0.547094i \(-0.815734\pi\)
0.837071 0.547094i \(-0.184266\pi\)
\(444\) 0 0
\(445\) 2.72774 0.129307
\(446\) 7.20913 0.341362
\(447\) 0 0
\(448\) −1.07781 + 2.41626i −0.0509215 + 0.114158i
\(449\) 15.9028i 0.750501i 0.926923 + 0.375251i \(0.122443\pi\)
−0.926923 + 0.375251i \(0.877557\pi\)
\(450\) 0 0
\(451\) 45.3804i 2.13688i
\(452\) 6.83228i 0.321363i
\(453\) 0 0
\(454\) 12.7560i 0.598669i
\(455\) 9.76302 + 4.35492i 0.457697 + 0.204162i
\(456\) 0 0
\(457\) −5.66614 −0.265051 −0.132525 0.991180i \(-0.542309\pi\)
−0.132525 + 0.991180i \(0.542309\pi\)
\(458\) 4.49418 0.209999
\(459\) 0 0
\(460\) 8.63411i 0.402567i
\(461\) −31.4584 −1.46516 −0.732582 0.680679i \(-0.761685\pi\)
−0.732582 + 0.680679i \(0.761685\pi\)
\(462\) 0 0
\(463\) −9.10296 −0.423051 −0.211525 0.977373i \(-0.567843\pi\)
−0.211525 + 0.977373i \(0.567843\pi\)
\(464\) 4.15561i 0.192919i
\(465\) 0 0
\(466\) 2.15403 0.0997837
\(467\) 30.3032 1.40226 0.701132 0.713032i \(-0.252678\pi\)
0.701132 + 0.713032i \(0.252678\pi\)
\(468\) 0 0
\(469\) 11.7171 26.2678i 0.541045 1.21293i
\(470\) 27.7456i 1.27981i
\(471\) 0 0
\(472\) 2.22966i 0.102628i
\(473\) 19.9879i 0.919044i
\(474\) 0 0
\(475\) 0.591856i 0.0271562i
\(476\) −1.90645 + 4.27396i −0.0873821 + 0.195897i
\(477\) 0 0
\(478\) 10.1419 0.463881
\(479\) −4.66286 −0.213052 −0.106526 0.994310i \(-0.533973\pi\)
−0.106526 + 0.994310i \(0.533973\pi\)
\(480\) 0 0
\(481\) 15.8187i 0.721271i
\(482\) −10.5481 −0.480452
\(483\) 0 0
\(484\) 21.2246 0.964754
\(485\) 10.7844i 0.489693i
\(486\) 0 0
\(487\) −19.4821 −0.882818 −0.441409 0.897306i \(-0.645521\pi\)
−0.441409 + 0.897306i \(0.645521\pi\)
\(488\) 8.99970 0.407397
\(489\) 0 0
\(490\) −12.2367 + 10.9872i −0.552797 + 0.496350i
\(491\) 20.4886i 0.924640i 0.886713 + 0.462320i \(0.152983\pi\)
−0.886713 + 0.462320i \(0.847017\pi\)
\(492\) 0 0
\(493\) 7.35056i 0.331053i
\(494\) 1.95946i 0.0881602i
\(495\) 0 0
\(496\) 8.37019i 0.375832i
\(497\) −10.9241 4.87282i −0.490012 0.218576i
\(498\) 0 0
\(499\) −10.2520 −0.458941 −0.229470 0.973316i \(-0.573699\pi\)
−0.229470 + 0.973316i \(0.573699\pi\)
\(500\) 10.5263 0.470752
\(501\) 0 0
\(502\) 29.3005i 1.30774i
\(503\) 14.5521 0.648845 0.324422 0.945912i \(-0.394830\pi\)
0.324422 + 0.945912i \(0.394830\pi\)
\(504\) 0 0
\(505\) 15.5600 0.692412
\(506\) 20.8623i 0.927442i
\(507\) 0 0
\(508\) 6.67667 0.296229
\(509\) −33.3234 −1.47703 −0.738517 0.674235i \(-0.764473\pi\)
−0.738517 + 0.674235i \(0.764473\pi\)
\(510\) 0 0
\(511\) 12.9085 + 5.75800i 0.571039 + 0.254719i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 7.62860i 0.336483i
\(515\) 13.7667i 0.606634i
\(516\) 0 0
\(517\) 67.0408i 2.94845i
\(518\) 22.2241 + 9.91336i 0.976473 + 0.435568i
\(519\) 0 0
\(520\) −4.04054 −0.177189
\(521\) 6.53925 0.286490 0.143245 0.989687i \(-0.454246\pi\)
0.143245 + 0.989687i \(0.454246\pi\)
\(522\) 0 0
\(523\) 0.786858i 0.0344069i −0.999852 0.0172034i \(-0.994524\pi\)
0.999852 0.0172034i \(-0.00547630\pi\)
\(524\) −7.47305 −0.326462
\(525\) 0 0
\(526\) −12.1856 −0.531318
\(527\) 14.8054i 0.644934i
\(528\) 0 0
\(529\) 9.49369 0.412769
\(530\) 0 0
\(531\) 0 0
\(532\) 2.75290 + 1.22797i 0.119353 + 0.0532391i
\(533\) 13.7488i 0.595527i
\(534\) 0 0
\(535\) 11.0787i 0.478975i
\(536\) 10.8712i 0.469566i
\(537\) 0 0
\(538\) 2.77433i 0.119610i
\(539\) −29.5671 + 26.5479i −1.27354 + 1.14350i
\(540\) 0 0
\(541\) 5.60454 0.240958 0.120479 0.992716i \(-0.461557\pi\)
0.120479 + 0.992716i \(0.461557\pi\)
\(542\) −3.20793 −0.137792
\(543\) 0 0
\(544\) 1.76883i 0.0758379i
\(545\) 9.95351 0.426362
\(546\) 0 0
\(547\) 13.8291 0.591291 0.295645 0.955298i \(-0.404465\pi\)
0.295645 + 0.955298i \(0.404465\pi\)
\(548\) 7.98789i 0.341226i
\(549\) 0 0
\(550\) −2.94893 −0.125743
\(551\) 4.73457 0.201700
\(552\) 0 0
\(553\) −14.0421 + 31.4801i −0.597132 + 1.33867i
\(554\) 10.0811i 0.428304i
\(555\) 0 0
\(556\) 20.7606i 0.880446i
\(557\) 27.8233i 1.17891i 0.807800 + 0.589456i \(0.200658\pi\)
−0.807800 + 0.589456i \(0.799342\pi\)
\(558\) 0 0
\(559\) 6.05569i 0.256128i
\(560\) 2.53215 5.67667i 0.107003 0.239883i
\(561\) 0 0
\(562\) 4.87282 0.205548
\(563\) 24.5300 1.03382 0.516909 0.856040i \(-0.327083\pi\)
0.516909 + 0.856040i \(0.327083\pi\)
\(564\) 0 0
\(565\) 16.0515i 0.675291i
\(566\) −2.81781 −0.118441
\(567\) 0 0
\(568\) 4.52106 0.189699
\(569\) 27.1079i 1.13642i −0.822882 0.568212i \(-0.807635\pi\)
0.822882 0.568212i \(-0.192365\pi\)
\(570\) 0 0
\(571\) −29.8354 −1.24857 −0.624287 0.781195i \(-0.714610\pi\)
−0.624287 + 0.781195i \(0.714610\pi\)
\(572\) −9.76302 −0.408212
\(573\) 0 0
\(574\) −19.3161 8.61618i −0.806237 0.359632i
\(575\) 1.90915i 0.0796169i
\(576\) 0 0
\(577\) 28.1666i 1.17259i −0.810097 0.586296i \(-0.800585\pi\)
0.810097 0.586296i \(-0.199415\pi\)
\(578\) 13.8712i 0.576968i
\(579\) 0 0
\(580\) 9.76302i 0.405387i
\(581\) −13.5221 + 30.3144i −0.560992 + 1.25765i
\(582\) 0 0
\(583\) 0 0
\(584\) −5.34234 −0.221068
\(585\) 0 0
\(586\) 8.11389i 0.335182i
\(587\) 9.91857 0.409383 0.204692 0.978827i \(-0.434381\pi\)
0.204692 + 0.978827i \(0.434381\pi\)
\(588\) 0 0
\(589\) −9.53632 −0.392937
\(590\) 5.23827i 0.215656i
\(591\) 0 0
\(592\) −9.19773 −0.378024
\(593\) 4.69872 0.192953 0.0964766 0.995335i \(-0.469243\pi\)
0.0964766 + 0.995335i \(0.469243\pi\)
\(594\) 0 0
\(595\) 4.47894 10.0411i 0.183619 0.411643i
\(596\) 1.19773i 0.0490609i
\(597\) 0 0
\(598\) 6.32061i 0.258469i
\(599\) 14.7004i 0.600641i −0.953838 0.300320i \(-0.902906\pi\)
0.953838 0.300320i \(-0.0970936\pi\)
\(600\) 0 0
\(601\) 18.8127i 0.767385i −0.923461 0.383693i \(-0.874652\pi\)
0.923461 0.383693i \(-0.125348\pi\)
\(602\) 8.50781 + 3.79502i 0.346752 + 0.154673i
\(603\) 0 0
\(604\) −15.2246 −0.619480
\(605\) −49.8641 −2.02727
\(606\) 0 0
\(607\) 12.5922i 0.511100i 0.966796 + 0.255550i \(0.0822565\pi\)
−0.966796 + 0.255550i \(0.917743\pi\)
\(608\) −1.13932 −0.0462055
\(609\) 0 0
\(610\) −21.1435 −0.856075
\(611\) 20.3112i 0.821704i
\(612\) 0 0
\(613\) −9.82017 −0.396633 −0.198317 0.980138i \(-0.563547\pi\)
−0.198317 + 0.980138i \(0.563547\pi\)
\(614\) 10.8996 0.439873
\(615\) 0 0
\(616\) 6.11835 13.7163i 0.246515 0.552647i
\(617\) 3.75460i 0.151154i 0.997140 + 0.0755772i \(0.0240799\pi\)
−0.997140 + 0.0755772i \(0.975920\pi\)
\(618\) 0 0
\(619\) 11.0494i 0.444111i −0.975034 0.222055i \(-0.928723\pi\)
0.975034 0.222055i \(-0.0712766\pi\)
\(620\) 19.6646i 0.789748i
\(621\) 0 0
\(622\) 8.23637i 0.330248i
\(623\) 1.25140 2.80542i 0.0501361 0.112397i
\(624\) 0 0
\(625\) −27.3275 −1.09310
\(626\) 33.8023 1.35101
\(627\) 0 0
\(628\) 10.0269i 0.400118i
\(629\) −16.2692 −0.648696
\(630\) 0 0
\(631\) 19.4921 0.775969 0.387984 0.921666i \(-0.373171\pi\)
0.387984 + 0.921666i \(0.373171\pi\)
\(632\) 13.0284i 0.518243i
\(633\) 0 0
\(634\) 6.73090 0.267318
\(635\) −15.6859 −0.622475
\(636\) 0 0
\(637\) 8.95788 8.04317i 0.354924 0.318682i
\(638\) 23.5900i 0.933938i
\(639\) 0 0
\(640\) 2.34936i 0.0928665i
\(641\) 26.1735i 1.03379i −0.856048 0.516896i \(-0.827087\pi\)
0.856048 0.516896i \(-0.172913\pi\)
\(642\) 0 0
\(643\) 10.9807i 0.433036i 0.976279 + 0.216518i \(0.0694699\pi\)
−0.976279 + 0.216518i \(0.930530\pi\)
\(644\) −8.88000 3.96104i −0.349921 0.156087i
\(645\) 0 0
\(646\) −2.01526 −0.0792894
\(647\) −32.0126 −1.25855 −0.629273 0.777185i \(-0.716647\pi\)
−0.629273 + 0.777185i \(0.716647\pi\)
\(648\) 0 0
\(649\) 12.6570i 0.496833i
\(650\) 0.893431 0.0350432
\(651\) 0 0
\(652\) −12.0032 −0.470080
\(653\) 22.3649i 0.875208i −0.899168 0.437604i \(-0.855827\pi\)
0.899168 0.437604i \(-0.144173\pi\)
\(654\) 0 0
\(655\) 17.5569 0.686004
\(656\) 7.99419 0.312121
\(657\) 0 0
\(658\) −28.5358 12.7288i −1.11244 0.496219i
\(659\) 22.2333i 0.866086i −0.901373 0.433043i \(-0.857440\pi\)
0.901373 0.433043i \(-0.142560\pi\)
\(660\) 0 0
\(661\) 10.5499i 0.410343i −0.978726 0.205171i \(-0.934225\pi\)
0.978726 0.205171i \(-0.0657751\pi\)
\(662\) 32.0569i 1.24593i
\(663\) 0 0
\(664\) 12.5460i 0.486878i
\(665\) −6.46754 2.88493i −0.250801 0.111873i
\(666\) 0 0
\(667\) −15.2723 −0.591344
\(668\) −17.1494 −0.663532
\(669\) 0 0
\(670\) 25.5404i 0.986713i
\(671\) −51.0883 −1.97224
\(672\) 0 0
\(673\) −19.8712 −0.765980 −0.382990 0.923752i \(-0.625106\pi\)
−0.382990 + 0.923752i \(0.625106\pi\)
\(674\) 24.2246i 0.933096i
\(675\) 0 0
\(676\) −10.0421 −0.386235
\(677\) −15.9290 −0.612201 −0.306100 0.951999i \(-0.599024\pi\)
−0.306100 + 0.951999i \(0.599024\pi\)
\(678\) 0 0
\(679\) 11.0915 + 4.94750i 0.425652 + 0.189868i
\(680\) 4.15561i 0.159360i
\(681\) 0 0
\(682\) 47.5148i 1.81944i
\(683\) 19.0269i 0.728042i −0.931391 0.364021i \(-0.881404\pi\)
0.931391 0.364021i \(-0.118596\pi\)
\(684\) 0 0
\(685\) 18.7664i 0.717028i
\(686\) 5.68629 + 17.6257i 0.217104 + 0.672953i
\(687\) 0 0
\(688\) −3.52106 −0.134239
\(689\) 0 0
\(690\) 0 0
\(691\) 0.161055i 0.00612681i −0.999995 0.00306340i \(-0.999025\pi\)
0.999995 0.00306340i \(-0.000975113\pi\)
\(692\) −1.98748 −0.0755525
\(693\) 0 0
\(694\) −22.7999 −0.865471
\(695\) 48.7741i 1.85011i
\(696\) 0 0
\(697\) 14.1403 0.535604
\(698\) 2.84505 0.107687
\(699\) 0 0
\(700\) −0.559901 + 1.25521i −0.0211623 + 0.0474423i
\(701\) 9.98234i 0.377028i 0.982071 + 0.188514i \(0.0603670\pi\)
−0.982071 + 0.188514i \(0.939633\pi\)
\(702\) 0 0
\(703\) 10.4792i 0.395229i
\(704\) 5.67667i 0.213948i
\(705\) 0 0
\(706\) 7.14424i 0.268877i
\(707\) 7.13841 16.0032i 0.268468 0.601861i
\(708\) 0 0
\(709\) −24.3923 −0.916072 −0.458036 0.888934i \(-0.651447\pi\)
−0.458036 + 0.888934i \(0.651447\pi\)
\(710\) −10.6216 −0.398621
\(711\) 0 0
\(712\) 1.16106i 0.0435125i
\(713\) 30.7612 1.15202
\(714\) 0 0
\(715\) 22.9368 0.857788
\(716\) 8.31122i 0.310605i
\(717\) 0 0
\(718\) 11.6037 0.433047
\(719\) 16.2692 0.606739 0.303370 0.952873i \(-0.401888\pi\)
0.303370 + 0.952873i \(0.401888\pi\)
\(720\) 0 0
\(721\) −14.1588 6.31570i −0.527300 0.235209i
\(722\) 17.7019i 0.658798i
\(723\) 0 0
\(724\) 15.4541i 0.574348i
\(725\) 2.15877i 0.0801745i
\(726\) 0 0
\(727\) 23.8592i 0.884887i −0.896796 0.442444i \(-0.854112\pi\)
0.896796 0.442444i \(-0.145888\pi\)
\(728\) −1.85366 + 4.15561i −0.0687013 + 0.154017i
\(729\) 0 0
\(730\) 12.5511 0.464536
\(731\) −6.22815 −0.230356
\(732\) 0 0
\(733\) 12.2697i 0.453193i 0.973989 + 0.226596i \(0.0727598\pi\)
−0.973989 + 0.226596i \(0.927240\pi\)
\(734\) −7.83493 −0.289193
\(735\) 0 0
\(736\) 3.67509 0.135466
\(737\) 61.7125i 2.27321i
\(738\) 0 0
\(739\) 41.8891 1.54092 0.770459 0.637490i \(-0.220027\pi\)
0.770459 + 0.637490i \(0.220027\pi\)
\(740\) 21.6088 0.794354
\(741\) 0 0
\(742\) 0 0
\(743\) 50.7098i 1.86036i −0.367099 0.930182i \(-0.619649\pi\)
0.367099 0.930182i \(-0.380351\pi\)
\(744\) 0 0
\(745\) 2.81390i 0.103093i
\(746\) 25.6677i 0.939762i
\(747\) 0 0
\(748\) 10.0411i 0.367137i
\(749\) 11.3942 + 5.08254i 0.416336 + 0.185712i
\(750\) 0 0
\(751\) −32.7367 −1.19458 −0.597289 0.802026i \(-0.703756\pi\)
−0.597289 + 0.802026i \(0.703756\pi\)
\(752\) 11.8099 0.430662
\(753\) 0 0
\(754\) 7.14702i 0.260279i
\(755\) 35.7680 1.30173
\(756\) 0 0
\(757\) −17.9255 −0.651512 −0.325756 0.945454i \(-0.605619\pi\)
−0.325756 + 0.945454i \(0.605619\pi\)
\(758\) 15.1045i 0.548622i
\(759\) 0 0
\(760\) 2.67667 0.0970930
\(761\) 43.7019 1.58419 0.792096 0.610397i \(-0.208990\pi\)
0.792096 + 0.610397i \(0.208990\pi\)
\(762\) 0 0
\(763\) 4.56633 10.2370i 0.165312 0.370603i
\(764\) 12.3381i 0.446376i
\(765\) 0 0
\(766\) 1.52664i 0.0551599i
\(767\) 3.83468i 0.138462i
\(768\) 0 0
\(769\) 42.8237i 1.54426i −0.635463 0.772131i \(-0.719191\pi\)
0.635463 0.772131i \(-0.280809\pi\)
\(770\) −14.3742 + 32.2246i −0.518010 + 1.16129i
\(771\) 0 0
\(772\) −4.39388 −0.158139
\(773\) 21.6051 0.777080 0.388540 0.921432i \(-0.372980\pi\)
0.388540 + 0.921432i \(0.372980\pi\)
\(774\) 0 0
\(775\) 4.34816i 0.156191i
\(776\) −4.59035 −0.164784
\(777\) 0 0
\(778\) 14.8897 0.533820
\(779\) 9.10794i 0.326326i
\(780\) 0 0
\(781\) −25.6646 −0.918350
\(782\) 6.50061 0.232461
\(783\) 0 0
\(784\) −4.67667 5.20853i −0.167024 0.186019i
\(785\) 23.5569i 0.840781i
\(786\) 0 0
\(787\) 51.3042i 1.82880i −0.404817 0.914398i \(-0.632665\pi\)
0.404817 0.914398i \(-0.367335\pi\)
\(788\) 10.8865i 0.387816i
\(789\) 0 0
\(790\) 30.6085i 1.08900i
\(791\) −16.5086 7.36387i −0.586978 0.261829i
\(792\) 0 0
\(793\) 15.4781 0.549644
\(794\) 28.7869 1.02161
\(795\) 0 0
\(796\) 27.5665i 0.977068i
\(797\) −1.79819 −0.0636951 −0.0318476 0.999493i \(-0.510139\pi\)
−0.0318476 + 0.999493i \(0.510139\pi\)
\(798\) 0 0
\(799\) 20.8897 0.739023