Properties

Label 1386.2.g.a.881.4
Level $1386$
Weight $2$
Character 1386.881
Analytic conductor $11.067$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.0672657201\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{14} + 8 x^{12} + 80 x^{10} + 1189 x^{8} - 2028 x^{6} + 1800 x^{4} + 1080 x^{2} + 324\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{9}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 881.4
Root \(1.12256 - 0.464978i\) of defining polynomial
Character \(\chi\) \(=\) 1386.881
Dual form 1386.2.g.a.881.12

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{4} -0.929956 q^{5} +(-2.07739 - 1.63843i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{4} -0.929956 q^{5} +(-2.07739 - 1.63843i) q^{7} +1.00000i q^{8} +0.929956i q^{10} +1.00000i q^{11} +(-1.63843 + 2.07739i) q^{14} +1.00000 q^{16} +2.34690 q^{17} +6.87928i q^{19} +0.929956 q^{20} +1.00000 q^{22} +3.04733i q^{23} -4.13518 q^{25} +(2.07739 + 1.63843i) q^{28} +6.39743i q^{29} -10.0122i q^{31} -1.00000i q^{32} -2.34690i q^{34} +(1.93188 + 1.52366i) q^{35} -5.04733 q^{37} +6.87928 q^{38} -0.929956i q^{40} +10.1561 q^{41} +6.15479 q^{43} -1.00000i q^{44} +3.04733 q^{46} +12.0160 q^{47} +(1.63112 + 6.80731i) q^{49} +4.13518i q^{50} +11.2021i q^{53} -0.929956i q^{55} +(1.63843 - 2.07739i) q^{56} +6.39743 q^{58} -1.85991 q^{59} -10.2735i q^{61} -10.0122 q^{62} -1.00000 q^{64} -0.0878550 q^{67} -2.34690 q^{68} +(1.52366 - 1.93188i) q^{70} +11.5326i q^{71} +12.0160i q^{73} +5.04733i q^{74} -6.87928i q^{76} +(1.63843 - 2.07739i) q^{77} +13.5995 q^{79} -0.929956 q^{80} -10.1561i q^{82} -4.06286 q^{83} -2.18251 q^{85} -6.15479i q^{86} -1.00000 q^{88} +17.0354 q^{89} -3.04733i q^{92} -12.0160i q^{94} -6.39743i q^{95} +15.6185i q^{97} +(6.80731 - 1.63112i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{4} - 8q^{7} + O(q^{10}) \) \( 16q - 16q^{4} - 8q^{7} + 16q^{16} + 16q^{22} + 16q^{25} + 8q^{28} - 16q^{37} + 48q^{43} - 16q^{46} + 8q^{49} - 16q^{58} - 16q^{64} + 16q^{67} - 8q^{70} - 16q^{79} + 112q^{85} - 16q^{88} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(1135\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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
\(5\) −0.929956 −0.415889 −0.207944 0.978141i \(-0.566677\pi\)
−0.207944 + 0.978141i \(0.566677\pi\)
\(6\) 0 0
\(7\) −2.07739 1.63843i −0.785181 0.619267i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0.929956i 0.294078i
\(11\) 1.00000i 0.301511i
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) −1.63843 + 2.07739i −0.437888 + 0.555207i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 2.34690 0.569206 0.284603 0.958645i \(-0.408138\pi\)
0.284603 + 0.958645i \(0.408138\pi\)
\(18\) 0 0
\(19\) 6.87928i 1.57822i 0.614255 + 0.789108i \(0.289457\pi\)
−0.614255 + 0.789108i \(0.710543\pi\)
\(20\) 0.929956 0.207944
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) 3.04733i 0.635412i 0.948189 + 0.317706i \(0.102912\pi\)
−0.948189 + 0.317706i \(0.897088\pi\)
\(24\) 0 0
\(25\) −4.13518 −0.827036
\(26\) 0 0
\(27\) 0 0
\(28\) 2.07739 + 1.63843i 0.392590 + 0.309633i
\(29\) 6.39743i 1.18797i 0.804475 + 0.593986i \(0.202447\pi\)
−0.804475 + 0.593986i \(0.797553\pi\)
\(30\) 0 0
\(31\) 10.0122i 1.79824i −0.437700 0.899121i \(-0.644207\pi\)
0.437700 0.899121i \(-0.355793\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 2.34690i 0.402489i
\(35\) 1.93188 + 1.52366i 0.326548 + 0.257546i
\(36\) 0 0
\(37\) −5.04733 −0.829775 −0.414888 0.909873i \(-0.636179\pi\)
−0.414888 + 0.909873i \(0.636179\pi\)
\(38\) 6.87928 1.11597
\(39\) 0 0
\(40\) 0.929956i 0.147039i
\(41\) 10.1561 1.58612 0.793061 0.609143i \(-0.208486\pi\)
0.793061 + 0.609143i \(0.208486\pi\)
\(42\) 0 0
\(43\) 6.15479 0.938596 0.469298 0.883040i \(-0.344507\pi\)
0.469298 + 0.883040i \(0.344507\pi\)
\(44\) 1.00000i 0.150756i
\(45\) 0 0
\(46\) 3.04733 0.449304
\(47\) 12.0160 1.75272 0.876360 0.481657i \(-0.159965\pi\)
0.876360 + 0.481657i \(0.159965\pi\)
\(48\) 0 0
\(49\) 1.63112 + 6.80731i 0.233017 + 0.972473i
\(50\) 4.13518i 0.584803i
\(51\) 0 0
\(52\) 0 0
\(53\) 11.2021i 1.53873i 0.638810 + 0.769364i \(0.279427\pi\)
−0.638810 + 0.769364i \(0.720573\pi\)
\(54\) 0 0
\(55\) 0.929956i 0.125395i
\(56\) 1.63843 2.07739i 0.218944 0.277603i
\(57\) 0 0
\(58\) 6.39743 0.840023
\(59\) −1.85991 −0.242140 −0.121070 0.992644i \(-0.538633\pi\)
−0.121070 + 0.992644i \(0.538633\pi\)
\(60\) 0 0
\(61\) 10.2735i 1.31539i −0.753284 0.657695i \(-0.771532\pi\)
0.753284 0.657695i \(-0.228468\pi\)
\(62\) −10.0122 −1.27155
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −0.0878550 −0.0107332 −0.00536660 0.999986i \(-0.501708\pi\)
−0.00536660 + 0.999986i \(0.501708\pi\)
\(68\) −2.34690 −0.284603
\(69\) 0 0
\(70\) 1.52366 1.93188i 0.182113 0.230904i
\(71\) 11.5326i 1.36867i 0.729168 + 0.684334i \(0.239907\pi\)
−0.729168 + 0.684334i \(0.760093\pi\)
\(72\) 0 0
\(73\) 12.0160i 1.40637i 0.711006 + 0.703186i \(0.248240\pi\)
−0.711006 + 0.703186i \(0.751760\pi\)
\(74\) 5.04733i 0.586740i
\(75\) 0 0
\(76\) 6.87928i 0.789108i
\(77\) 1.63843 2.07739i 0.186716 0.236741i
\(78\) 0 0
\(79\) 13.5995 1.53007 0.765034 0.643990i \(-0.222722\pi\)
0.765034 + 0.643990i \(0.222722\pi\)
\(80\) −0.929956 −0.103972
\(81\) 0 0
\(82\) 10.1561i 1.12156i
\(83\) −4.06286 −0.445957 −0.222979 0.974823i \(-0.571578\pi\)
−0.222979 + 0.974823i \(0.571578\pi\)
\(84\) 0 0
\(85\) −2.18251 −0.236726
\(86\) 6.15479i 0.663688i
\(87\) 0 0
\(88\) −1.00000 −0.106600
\(89\) 17.0354 1.80575 0.902875 0.429903i \(-0.141452\pi\)
0.902875 + 0.429903i \(0.141452\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 3.04733i 0.317706i
\(93\) 0 0
\(94\) 12.0160i 1.23936i
\(95\) 6.39743i 0.656362i
\(96\) 0 0
\(97\) 15.6185i 1.58582i 0.609342 + 0.792908i \(0.291434\pi\)
−0.609342 + 0.792908i \(0.708566\pi\)
\(98\) 6.80731 1.63112i 0.687642 0.164768i
\(99\) 0 0
\(100\) 4.13518 0.413518
\(101\) −4.54985 −0.452727 −0.226363 0.974043i \(-0.572684\pi\)
−0.226363 + 0.974043i \(0.572684\pi\)
\(102\) 0 0
\(103\) 4.06286i 0.400326i 0.979763 + 0.200163i \(0.0641471\pi\)
−0.979763 + 0.200163i \(0.935853\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 11.2021 1.08805
\(107\) 5.57182i 0.538648i 0.963050 + 0.269324i \(0.0868002\pi\)
−0.963050 + 0.269324i \(0.913200\pi\)
\(108\) 0 0
\(109\) −15.6597 −1.49992 −0.749962 0.661481i \(-0.769928\pi\)
−0.749962 + 0.661481i \(0.769928\pi\)
\(110\) −0.929956 −0.0886678
\(111\) 0 0
\(112\) −2.07739 1.63843i −0.196295 0.154817i
\(113\) 13.6874i 1.28760i 0.765193 + 0.643801i \(0.222643\pi\)
−0.765193 + 0.643801i \(0.777357\pi\)
\(114\) 0 0
\(115\) 2.83388i 0.264261i
\(116\) 6.39743i 0.593986i
\(117\) 0 0
\(118\) 1.85991i 0.171219i
\(119\) −4.87542 3.84521i −0.446929 0.352490i
\(120\) 0 0
\(121\) −1.00000 −0.0909091
\(122\) −10.2735 −0.930121
\(123\) 0 0
\(124\) 10.0122i 0.899121i
\(125\) 8.49532 0.759844
\(126\) 0 0
\(127\) 4.98040 0.441939 0.220969 0.975281i \(-0.429078\pi\)
0.220969 + 0.975281i \(0.429078\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 0 0
\(131\) −20.7992 −1.81724 −0.908619 0.417625i \(-0.862862\pi\)
−0.908619 + 0.417625i \(0.862862\pi\)
\(132\) 0 0
\(133\) 11.2712 14.2910i 0.977336 1.23918i
\(134\) 0.0878550i 0.00758951i
\(135\) 0 0
\(136\) 2.34690i 0.201245i
\(137\) 0.330496i 0.0282362i −0.999900 0.0141181i \(-0.995506\pi\)
0.999900 0.0141181i \(-0.00449407\pi\)
\(138\) 0 0
\(139\) 19.0944i 1.61957i −0.586728 0.809784i \(-0.699584\pi\)
0.586728 0.809784i \(-0.300416\pi\)
\(140\) −1.93188 1.52366i −0.163274 0.128773i
\(141\) 0 0
\(142\) 11.5326 0.967795
\(143\) 0 0
\(144\) 0 0
\(145\) 5.94932i 0.494064i
\(146\) 12.0160 0.994455
\(147\) 0 0
\(148\) 5.04733 0.414888
\(149\) 1.26224i 0.103407i −0.998662 0.0517035i \(-0.983535\pi\)
0.998662 0.0517035i \(-0.0164651\pi\)
\(150\) 0 0
\(151\) −17.3778 −1.41419 −0.707094 0.707120i \(-0.749994\pi\)
−0.707094 + 0.707120i \(0.749994\pi\)
\(152\) −6.87928 −0.557983
\(153\) 0 0
\(154\) −2.07739 1.63843i −0.167401 0.132028i
\(155\) 9.31089i 0.747869i
\(156\) 0 0
\(157\) 14.0199i 1.11891i 0.828861 + 0.559455i \(0.188989\pi\)
−0.828861 + 0.559455i \(0.811011\pi\)
\(158\) 13.5995i 1.08192i
\(159\) 0 0
\(160\) 0.929956i 0.0735195i
\(161\) 4.99282 6.33050i 0.393489 0.498913i
\(162\) 0 0
\(163\) −13.8422 −1.08420 −0.542102 0.840313i \(-0.682371\pi\)
−0.542102 + 0.840313i \(0.682371\pi\)
\(164\) −10.1561 −0.793061
\(165\) 0 0
\(166\) 4.06286i 0.315339i
\(167\) −6.69765 −0.518279 −0.259140 0.965840i \(-0.583439\pi\)
−0.259140 + 0.965840i \(0.583439\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 2.18251i 0.167391i
\(171\) 0 0
\(172\) −6.15479 −0.469298
\(173\) −5.20100 −0.395425 −0.197712 0.980260i \(-0.563351\pi\)
−0.197712 + 0.980260i \(0.563351\pi\)
\(174\) 0 0
\(175\) 8.59040 + 6.77519i 0.649373 + 0.512156i
\(176\) 1.00000i 0.0753778i
\(177\) 0 0
\(178\) 17.0354i 1.27686i
\(179\) 3.91215i 0.292407i 0.989255 + 0.146204i \(0.0467055\pi\)
−0.989255 + 0.146204i \(0.953294\pi\)
\(180\) 0 0
\(181\) 0.768549i 0.0571258i −0.999592 0.0285629i \(-0.990907\pi\)
0.999592 0.0285629i \(-0.00909309\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −3.04733 −0.224652
\(185\) 4.69379 0.345094
\(186\) 0 0
\(187\) 2.34690i 0.171622i
\(188\) −12.0160 −0.876360
\(189\) 0 0
\(190\) −6.39743 −0.464118
\(191\) 20.1518i 1.45813i −0.684445 0.729065i \(-0.739955\pi\)
0.684445 0.729065i \(-0.260045\pi\)
\(192\) 0 0
\(193\) −6.17571 −0.444537 −0.222269 0.974985i \(-0.571346\pi\)
−0.222269 + 0.974985i \(0.571346\pi\)
\(194\) 15.6185 1.12134
\(195\) 0 0
\(196\) −1.63112 6.80731i −0.116509 0.486236i
\(197\) 14.2772i 1.01721i −0.861001 0.508603i \(-0.830162\pi\)
0.861001 0.508603i \(-0.169838\pi\)
\(198\) 0 0
\(199\) 7.46620i 0.529265i −0.964349 0.264632i \(-0.914749\pi\)
0.964349 0.264632i \(-0.0852506\pi\)
\(200\) 4.13518i 0.292402i
\(201\) 0 0
\(202\) 4.54985i 0.320126i
\(203\) 10.4817 13.2900i 0.735672 0.932773i
\(204\) 0 0
\(205\) −9.44475 −0.659650
\(206\) 4.06286 0.283073
\(207\) 0 0
\(208\) 0 0
\(209\) −6.87928 −0.475850
\(210\) 0 0
\(211\) 16.4252 1.13075 0.565377 0.824833i \(-0.308731\pi\)
0.565377 + 0.824833i \(0.308731\pi\)
\(212\) 11.2021i 0.769364i
\(213\) 0 0
\(214\) 5.57182 0.380881
\(215\) −5.72368 −0.390352
\(216\) 0 0
\(217\) −16.4042 + 20.7992i −1.11359 + 1.41194i
\(218\) 15.6597i 1.06061i
\(219\) 0 0
\(220\) 0.929956i 0.0626976i
\(221\) 0 0
\(222\) 0 0
\(223\) 6.81504i 0.456369i −0.973618 0.228184i \(-0.926721\pi\)
0.973618 0.228184i \(-0.0732789\pi\)
\(224\) −1.63843 + 2.07739i −0.109472 + 0.138802i
\(225\) 0 0
\(226\) 13.6874 0.910472
\(227\) −0.0265489 −0.00176211 −0.000881055 1.00000i \(-0.500280\pi\)
−0.000881055 1.00000i \(0.500280\pi\)
\(228\) 0 0
\(229\) 9.69570i 0.640710i 0.947298 + 0.320355i \(0.103802\pi\)
−0.947298 + 0.320355i \(0.896198\pi\)
\(230\) −2.83388 −0.186860
\(231\) 0 0
\(232\) −6.39743 −0.420012
\(233\) 2.48528i 0.162816i 0.996681 + 0.0814081i \(0.0259417\pi\)
−0.996681 + 0.0814081i \(0.974058\pi\)
\(234\) 0 0
\(235\) −11.1744 −0.728937
\(236\) 1.85991 0.121070
\(237\) 0 0
\(238\) −3.84521 + 4.87542i −0.249248 + 0.316027i
\(239\) 11.4380i 0.739860i 0.929060 + 0.369930i \(0.120618\pi\)
−0.929060 + 0.369930i \(0.879382\pi\)
\(240\) 0 0
\(241\) 7.69184i 0.495475i −0.968827 0.247738i \(-0.920313\pi\)
0.968827 0.247738i \(-0.0796871\pi\)
\(242\) 1.00000i 0.0642824i
\(243\) 0 0
\(244\) 10.2735i 0.657695i
\(245\) −1.51687 6.33050i −0.0969094 0.404441i
\(246\) 0 0
\(247\) 0 0
\(248\) 10.0122 0.635775
\(249\) 0 0
\(250\) 8.49532i 0.537291i
\(251\) 8.41361 0.531063 0.265531 0.964102i \(-0.414453\pi\)
0.265531 + 0.964102i \(0.414453\pi\)
\(252\) 0 0
\(253\) −3.04733 −0.191584
\(254\) 4.98040i 0.312498i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −17.0354 −1.06264 −0.531320 0.847171i \(-0.678304\pi\)
−0.531320 + 0.847171i \(0.678304\pi\)
\(258\) 0 0
\(259\) 10.4853 + 8.26967i 0.651524 + 0.513852i
\(260\) 0 0
\(261\) 0 0
\(262\) 20.7992i 1.28498i
\(263\) 31.2869i 1.92923i −0.263653 0.964617i \(-0.584928\pi\)
0.263653 0.964617i \(-0.415072\pi\)
\(264\) 0 0
\(265\) 10.4175i 0.639940i
\(266\) −14.2910 11.2712i −0.876235 0.691081i
\(267\) 0 0
\(268\) 0.0878550 0.00536660
\(269\) 3.68213 0.224504 0.112252 0.993680i \(-0.464194\pi\)
0.112252 + 0.993680i \(0.464194\pi\)
\(270\) 0 0
\(271\) 18.2442i 1.10825i 0.832432 + 0.554127i \(0.186948\pi\)
−0.832432 + 0.554127i \(0.813052\pi\)
\(272\) 2.34690 0.142301
\(273\) 0 0
\(274\) −0.330496 −0.0199660
\(275\) 4.13518i 0.249361i
\(276\) 0 0
\(277\) −15.8354 −0.951456 −0.475728 0.879592i \(-0.657815\pi\)
−0.475728 + 0.879592i \(0.657815\pi\)
\(278\) −19.0944 −1.14521
\(279\) 0 0
\(280\) −1.52366 + 1.93188i −0.0910563 + 0.115452i
\(281\) 10.9706i 0.654449i 0.944947 + 0.327224i \(0.106113\pi\)
−0.944947 + 0.327224i \(0.893887\pi\)
\(282\) 0 0
\(283\) 15.6625i 0.931038i 0.885038 + 0.465519i \(0.154132\pi\)
−0.885038 + 0.465519i \(0.845868\pi\)
\(284\) 11.5326i 0.684334i
\(285\) 0 0
\(286\) 0 0
\(287\) −21.0983 16.6401i −1.24539 0.982232i
\(288\) 0 0
\(289\) −11.4921 −0.676005
\(290\) −5.94932 −0.349356
\(291\) 0 0
\(292\) 12.0160i 0.703186i
\(293\) −11.7547 −0.686717 −0.343359 0.939204i \(-0.611565\pi\)
−0.343359 + 0.939204i \(0.611565\pi\)
\(294\) 0 0
\(295\) 1.72964 0.100703
\(296\) 5.04733i 0.293370i
\(297\) 0 0
\(298\) −1.26224 −0.0731198
\(299\) 0 0
\(300\) 0 0
\(301\) −12.7859 10.0842i −0.736967 0.581241i
\(302\) 17.3778i 0.999981i
\(303\) 0 0
\(304\) 6.87928i 0.394554i
\(305\) 9.55393i 0.547056i
\(306\) 0 0
\(307\) 22.5327i 1.28601i 0.765863 + 0.643004i \(0.222312\pi\)
−0.765863 + 0.643004i \(0.777688\pi\)
\(308\) −1.63843 + 2.07739i −0.0933580 + 0.118370i
\(309\) 0 0
\(310\) 9.31089 0.528823
\(311\) −6.06672 −0.344012 −0.172006 0.985096i \(-0.555025\pi\)
−0.172006 + 0.985096i \(0.555025\pi\)
\(312\) 0 0
\(313\) 5.48889i 0.310250i 0.987895 + 0.155125i \(0.0495781\pi\)
−0.987895 + 0.155125i \(0.950422\pi\)
\(314\) 14.0199 0.791189
\(315\) 0 0
\(316\) −13.5995 −0.765034
\(317\) 34.2119i 1.92153i 0.277362 + 0.960765i \(0.410540\pi\)
−0.277362 + 0.960765i \(0.589460\pi\)
\(318\) 0 0
\(319\) −6.39743 −0.358187
\(320\) 0.929956 0.0519861
\(321\) 0 0
\(322\) −6.33050 4.99282i −0.352785 0.278239i
\(323\) 16.1450i 0.898329i
\(324\) 0 0
\(325\) 0 0
\(326\) 13.8422i 0.766647i
\(327\) 0 0
\(328\) 10.1561i 0.560779i
\(329\) −24.9620 19.6874i −1.37620 1.08540i
\(330\) 0 0
\(331\) 14.8017 0.813572 0.406786 0.913523i \(-0.366649\pi\)
0.406786 + 0.913523i \(0.366649\pi\)
\(332\) 4.06286 0.222979
\(333\) 0 0
\(334\) 6.69765i 0.366479i
\(335\) 0.0817013 0.00446382
\(336\) 0 0
\(337\) −12.4042 −0.675701 −0.337851 0.941200i \(-0.609700\pi\)
−0.337851 + 0.941200i \(0.609700\pi\)
\(338\) 13.0000i 0.707107i
\(339\) 0 0
\(340\) 2.18251 0.118363
\(341\) 10.0122 0.542190
\(342\) 0 0
\(343\) 7.76479 16.8139i 0.419259 0.907867i
\(344\) 6.15479i 0.331844i
\(345\) 0 0
\(346\) 5.20100i 0.279608i
\(347\) 20.0179i 1.07462i −0.843386 0.537308i \(-0.819441\pi\)
0.843386 0.537308i \(-0.180559\pi\)
\(348\) 0 0
\(349\) 14.0464i 0.751889i 0.926642 + 0.375945i \(0.122682\pi\)
−0.926642 + 0.375945i \(0.877318\pi\)
\(350\) 6.77519 8.59040i 0.362149 0.459176i
\(351\) 0 0
\(352\) 1.00000 0.0533002
\(353\) 24.4751 1.30268 0.651338 0.758788i \(-0.274208\pi\)
0.651338 + 0.758788i \(0.274208\pi\)
\(354\) 0 0
\(355\) 10.7248i 0.569214i
\(356\) −17.0354 −0.902875
\(357\) 0 0
\(358\) 3.91215 0.206763
\(359\) 5.04053i 0.266029i 0.991114 + 0.133014i \(0.0424657\pi\)
−0.991114 + 0.133014i \(0.957534\pi\)
\(360\) 0 0
\(361\) −28.3245 −1.49076
\(362\) −0.768549 −0.0403940
\(363\) 0 0
\(364\) 0 0
\(365\) 11.1744i 0.584894i
\(366\) 0 0
\(367\) 6.21066i 0.324194i −0.986775 0.162097i \(-0.948174\pi\)
0.986775 0.162097i \(-0.0518257\pi\)
\(368\) 3.04733i 0.158853i
\(369\) 0 0
\(370\) 4.69379i 0.244019i
\(371\) 18.3538 23.2712i 0.952883 1.20818i
\(372\) 0 0
\(373\) 9.78508 0.506652 0.253326 0.967381i \(-0.418475\pi\)
0.253326 + 0.967381i \(0.418475\pi\)
\(374\) 2.34690 0.121355
\(375\) 0 0
\(376\) 12.0160i 0.619680i
\(377\) 0 0
\(378\) 0 0
\(379\) −17.8422 −0.916491 −0.458246 0.888826i \(-0.651522\pi\)
−0.458246 + 0.888826i \(0.651522\pi\)
\(380\) 6.39743i 0.328181i
\(381\) 0 0
\(382\) −20.1518 −1.03105
\(383\) 34.2699 1.75111 0.875556 0.483118i \(-0.160496\pi\)
0.875556 + 0.483118i \(0.160496\pi\)
\(384\) 0 0
\(385\) −1.52366 + 1.93188i −0.0776531 + 0.0984579i
\(386\) 6.17571i 0.314335i
\(387\) 0 0
\(388\) 15.6185i 0.792908i
\(389\) 13.5927i 0.689179i −0.938753 0.344590i \(-0.888018\pi\)
0.938753 0.344590i \(-0.111982\pi\)
\(390\) 0 0
\(391\) 7.15176i 0.361680i
\(392\) −6.80731 + 1.63112i −0.343821 + 0.0823841i
\(393\) 0 0
\(394\) −14.2772 −0.719273
\(395\) −12.6470 −0.636338
\(396\) 0 0
\(397\) 19.1741i 0.962322i 0.876632 + 0.481161i \(0.159785\pi\)
−0.876632 + 0.481161i \(0.840215\pi\)
\(398\) −7.46620 −0.374247
\(399\) 0 0
\(400\) −4.13518 −0.206759
\(401\) 14.8550i 0.741823i 0.928668 + 0.370911i \(0.120955\pi\)
−0.928668 + 0.370911i \(0.879045\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 4.54985 0.226363
\(405\) 0 0
\(406\) −13.2900 10.4817i −0.659570 0.520198i
\(407\) 5.04733i 0.250187i
\(408\) 0 0
\(409\) 7.40395i 0.366102i 0.983103 + 0.183051i \(0.0585973\pi\)
−0.983103 + 0.183051i \(0.941403\pi\)
\(410\) 9.44475i 0.466443i
\(411\) 0 0
\(412\) 4.06286i 0.200163i
\(413\) 3.86377 + 3.04733i 0.190124 + 0.149949i
\(414\) 0 0
\(415\) 3.77828 0.185469
\(416\) 0 0
\(417\) 0 0
\(418\) 6.87928i 0.336477i
\(419\) 19.3383 0.944738 0.472369 0.881401i \(-0.343399\pi\)
0.472369 + 0.881401i \(0.343399\pi\)
\(420\) 0 0
\(421\) 34.0179 1.65793 0.828965 0.559300i \(-0.188930\pi\)
0.828965 + 0.559300i \(0.188930\pi\)
\(422\) 16.4252i 0.799564i
\(423\) 0 0
\(424\) −11.2021 −0.544023
\(425\) −9.70484 −0.470754
\(426\) 0 0
\(427\) −16.8324 + 21.3422i −0.814577 + 1.03282i
\(428\) 5.57182i 0.269324i
\(429\) 0 0
\(430\) 5.72368i 0.276020i
\(431\) 2.92191i 0.140744i −0.997521 0.0703718i \(-0.977581\pi\)
0.997521 0.0703718i \(-0.0224186\pi\)
\(432\) 0 0
\(433\) 9.60690i 0.461678i −0.972992 0.230839i \(-0.925853\pi\)
0.972992 0.230839i \(-0.0741471\pi\)
\(434\) 20.7992 + 16.4042i 0.998396 + 0.787428i
\(435\) 0 0
\(436\) 15.6597 0.749962
\(437\) −20.9634 −1.00282
\(438\) 0 0
\(439\) 36.6616i 1.74976i −0.484338 0.874881i \(-0.660939\pi\)
0.484338 0.874881i \(-0.339061\pi\)
\(440\) 0.929956 0.0443339
\(441\) 0 0
\(442\) 0 0
\(443\) 28.7624i 1.36655i 0.730163 + 0.683273i \(0.239444\pi\)
−0.730163 + 0.683273i \(0.760556\pi\)
\(444\) 0 0
\(445\) −15.8422 −0.750991
\(446\) −6.81504 −0.322702
\(447\) 0 0
\(448\) 2.07739 + 1.63843i 0.0981476 + 0.0774083i
\(449\) 24.0916i 1.13695i 0.822699 + 0.568477i \(0.192467\pi\)
−0.822699 + 0.568477i \(0.807533\pi\)
\(450\) 0 0
\(451\) 10.1561i 0.478234i
\(452\) 13.6874i 0.643801i
\(453\) 0 0
\(454\) 0.0265489i 0.00124600i
\(455\) 0 0
\(456\) 0 0
\(457\) −10.4853 −0.490481 −0.245240 0.969462i \(-0.578867\pi\)
−0.245240 + 0.969462i \(0.578867\pi\)
\(458\) 9.69570 0.453050
\(459\) 0 0
\(460\) 2.83388i 0.132130i
\(461\) −20.4562 −0.952741 −0.476370 0.879245i \(-0.658048\pi\)
−0.476370 + 0.879245i \(0.658048\pi\)
\(462\) 0 0
\(463\) 36.4989 1.69625 0.848123 0.529799i \(-0.177733\pi\)
0.848123 + 0.529799i \(0.177733\pi\)
\(464\) 6.39743i 0.296993i
\(465\) 0 0
\(466\) 2.48528 0.115128
\(467\) −16.9557 −0.784616 −0.392308 0.919834i \(-0.628323\pi\)
−0.392308 + 0.919834i \(0.628323\pi\)
\(468\) 0 0
\(469\) 0.182509 + 0.143944i 0.00842750 + 0.00664671i
\(470\) 11.1744i 0.515436i
\(471\) 0 0
\(472\) 1.85991i 0.0856094i
\(473\) 6.15479i 0.282997i
\(474\) 0 0
\(475\) 28.4471i 1.30524i
\(476\) 4.87542 + 3.84521i 0.223465 + 0.176245i
\(477\) 0 0
\(478\) 11.4380 0.523160
\(479\) −31.9385 −1.45931 −0.729653 0.683817i \(-0.760319\pi\)
−0.729653 + 0.683817i \(0.760319\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −7.69184 −0.350354
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 14.5245i 0.659523i
\(486\) 0 0
\(487\) 6.57994 0.298165 0.149083 0.988825i \(-0.452368\pi\)
0.149083 + 0.988825i \(0.452368\pi\)
\(488\) 10.2735 0.465061
\(489\) 0 0
\(490\) −6.33050 + 1.51687i −0.285983 + 0.0685253i
\(491\) 9.14198i 0.412572i −0.978492 0.206286i \(-0.933862\pi\)
0.978492 0.206286i \(-0.0661377\pi\)
\(492\) 0 0
\(493\) 15.0141i 0.676201i
\(494\) 0 0
\(495\) 0 0
\(496\) 10.0122i 0.449560i
\(497\) 18.8953 23.9578i 0.847571 1.07465i
\(498\) 0 0
\(499\) −6.47848 −0.290017 −0.145008 0.989430i \(-0.546321\pi\)
−0.145008 + 0.989430i \(0.546321\pi\)
\(500\) −8.49532 −0.379922
\(501\) 0 0
\(502\) 8.41361i 0.375518i
\(503\) 2.97782 0.132775 0.0663873 0.997794i \(-0.478853\pi\)
0.0663873 + 0.997794i \(0.478853\pi\)
\(504\) 0 0
\(505\) 4.23116 0.188284
\(506\) 3.04733i 0.135470i
\(507\) 0 0
\(508\) −4.98040 −0.220969
\(509\) 7.40196 0.328086 0.164043 0.986453i \(-0.447546\pi\)
0.164043 + 0.986453i \(0.447546\pi\)
\(510\) 0 0
\(511\) 19.6874 24.9620i 0.870919 1.10426i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 17.0354i 0.751400i
\(515\) 3.77828i 0.166491i
\(516\) 0 0
\(517\) 12.0160i 0.528465i
\(518\) 8.26967 10.4853i 0.363348 0.460697i
\(519\) 0 0
\(520\) 0 0
\(521\) 6.02271 0.263860 0.131930 0.991259i \(-0.457883\pi\)
0.131930 + 0.991259i \(0.457883\pi\)
\(522\) 0 0
\(523\) 21.2422i 0.928857i −0.885611 0.464429i \(-0.846260\pi\)
0.885611 0.464429i \(-0.153740\pi\)
\(524\) 20.7992 0.908619
\(525\) 0 0
\(526\) −31.2869 −1.36418
\(527\) 23.4976i 1.02357i
\(528\) 0 0
\(529\) 13.7138 0.596252
\(530\) −10.4175 −0.452506
\(531\) 0 0
\(532\) −11.2712 + 14.2910i −0.488668 + 0.619592i
\(533\) 0 0
\(534\) 0 0
\(535\) 5.18154i 0.224018i
\(536\) 0.0878550i 0.00379476i
\(537\) 0 0
\(538\) 3.68213i 0.158748i
\(539\) −6.80731 + 1.63112i −0.293212 + 0.0702574i
\(540\) 0 0
\(541\) 26.0947 1.12190 0.560948 0.827851i \(-0.310437\pi\)
0.560948 + 0.827851i \(0.310437\pi\)
\(542\) 18.2442 0.783654
\(543\) 0 0
\(544\) 2.34690i 0.100622i
\(545\) 14.5628 0.623802
\(546\) 0 0
\(547\) −4.42515 −0.189206 −0.0946029 0.995515i \(-0.530158\pi\)
−0.0946029 + 0.995515i \(0.530158\pi\)
\(548\) 0.330496i 0.0141181i
\(549\) 0 0
\(550\) −4.13518 −0.176325
\(551\) −44.0097 −1.87488
\(552\) 0 0
\(553\) −28.2516 22.2818i −1.20138 0.947520i
\(554\) 15.8354i 0.672781i
\(555\) 0 0
\(556\) 19.0944i 0.809784i
\(557\) 14.2772i 0.604943i −0.953158 0.302471i \(-0.902188\pi\)
0.953158 0.302471i \(-0.0978117\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 1.93188 + 1.52366i 0.0816370 + 0.0643865i
\(561\) 0 0
\(562\) 10.9706 0.462765
\(563\) 7.08746 0.298701 0.149350 0.988784i \(-0.452282\pi\)
0.149350 + 0.988784i \(0.452282\pi\)
\(564\) 0 0
\(565\) 12.7287i 0.535499i
\(566\) 15.6625 0.658343
\(567\) 0 0
\(568\) −11.5326 −0.483898
\(569\) 14.4853i 0.607255i 0.952791 + 0.303627i \(0.0981978\pi\)
−0.952791 + 0.303627i \(0.901802\pi\)
\(570\) 0 0
\(571\) 40.1095 1.67853 0.839265 0.543722i \(-0.182985\pi\)
0.839265 + 0.543722i \(0.182985\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −16.6401 + 21.0983i −0.694543 + 0.880625i
\(575\) 12.6013i 0.525509i
\(576\) 0 0
\(577\) 4.98168i 0.207390i 0.994609 + 0.103695i \(0.0330666\pi\)
−0.994609 + 0.103695i \(0.966933\pi\)
\(578\) 11.4921i 0.478008i
\(579\) 0 0
\(580\) 5.94932i 0.247032i
\(581\) 8.44016 + 6.65670i 0.350157 + 0.276166i
\(582\) 0 0
\(583\) −11.2021 −0.463944
\(584\) −12.0160 −0.497227
\(585\) 0 0
\(586\) 11.7547i 0.485582i
\(587\) −39.6855 −1.63800 −0.818998 0.573797i \(-0.805470\pi\)
−0.818998 + 0.573797i \(0.805470\pi\)
\(588\) 0 0
\(589\) 68.8766 2.83801
\(590\) 1.72964i 0.0712080i
\(591\) 0 0
\(592\) −5.04733 −0.207444
\(593\) 10.5194 0.431980 0.215990 0.976396i \(-0.430702\pi\)
0.215990 + 0.976396i \(0.430702\pi\)
\(594\) 0 0
\(595\) 4.53393 + 3.57588i 0.185873 + 0.146597i
\(596\) 1.26224i 0.0517035i
\(597\) 0 0
\(598\) 0 0
\(599\) 2.85802i 0.116775i −0.998294 0.0583877i \(-0.981404\pi\)
0.998294 0.0583877i \(-0.0185960\pi\)
\(600\) 0 0
\(601\) 33.5307i 1.36775i 0.729600 + 0.683874i \(0.239706\pi\)
−0.729600 + 0.683874i \(0.760294\pi\)
\(602\) −10.0842 + 12.7859i −0.411000 + 0.521115i
\(603\) 0 0
\(604\) 17.3778 0.707094
\(605\) 0.929956 0.0378081
\(606\) 0 0
\(607\) 22.9030i 0.929605i −0.885414 0.464803i \(-0.846125\pi\)
0.885414 0.464803i \(-0.153875\pi\)
\(608\) 6.87928 0.278992
\(609\) 0 0
\(610\) 9.55393 0.386827
\(611\) 0 0
\(612\) 0 0
\(613\) −46.9885 −1.89785 −0.948923 0.315508i \(-0.897825\pi\)
−0.948923 + 0.315508i \(0.897825\pi\)
\(614\) 22.5327 0.909345
\(615\) 0 0
\(616\) 2.07739 + 1.63843i 0.0837005 + 0.0660141i
\(617\) 33.3471i 1.34250i 0.741230 + 0.671251i \(0.234243\pi\)
−0.741230 + 0.671251i \(0.765757\pi\)
\(618\) 0 0
\(619\) 28.7259i 1.15459i −0.816535 0.577295i \(-0.804108\pi\)
0.816535 0.577295i \(-0.195892\pi\)
\(620\) 9.31089i 0.373934i
\(621\) 0 0
\(622\) 6.06672i 0.243253i
\(623\) −35.3892 27.9113i −1.41784 1.11824i
\(624\) 0 0
\(625\) 12.7756 0.511026
\(626\) 5.48889 0.219380
\(627\) 0 0
\(628\) 14.0199i 0.559455i
\(629\) −11.8456 −0.472313
\(630\) 0 0
\(631\) 37.1599 1.47931 0.739656 0.672986i \(-0.234988\pi\)
0.739656 + 0.672986i \(0.234988\pi\)
\(632\) 13.5995i 0.540961i
\(633\) 0 0
\(634\) 34.2119 1.35873
\(635\) −4.63155 −0.183797
\(636\) 0 0
\(637\) 0 0
\(638\) 6.39743i 0.253277i
\(639\) 0 0
\(640\) 0.929956i 0.0367597i
\(641\) 24.8618i 0.981981i −0.871165 0.490991i \(-0.836635\pi\)
0.871165 0.490991i \(-0.163365\pi\)
\(642\) 0 0
\(643\) 22.8233i 0.900064i 0.893012 + 0.450032i \(0.148587\pi\)
−0.893012 + 0.450032i \(0.851413\pi\)
\(644\) −4.99282 + 6.33050i −0.196745 + 0.249456i
\(645\) 0 0
\(646\) 16.1450 0.635215
\(647\) 38.9637 1.53182 0.765911 0.642947i \(-0.222288\pi\)
0.765911 + 0.642947i \(0.222288\pi\)
\(648\) 0 0
\(649\) 1.85991i 0.0730079i
\(650\) 0 0
\(651\) 0 0
\(652\) 13.8422 0.542102
\(653\) 29.4306i 1.15171i 0.817552 + 0.575855i \(0.195331\pi\)
−0.817552 + 0.575855i \(0.804669\pi\)
\(654\) 0 0
\(655\) 19.3424 0.755769
\(656\) 10.1561 0.396530
\(657\) 0 0
\(658\) −19.6874 + 24.9620i −0.767495 + 0.973122i
\(659\) 7.74588i 0.301736i 0.988554 + 0.150868i \(0.0482069\pi\)
−0.988554 + 0.150868i \(0.951793\pi\)
\(660\) 0 0
\(661\) 31.2167i 1.21419i −0.794629 0.607095i \(-0.792335\pi\)
0.794629 0.607095i \(-0.207665\pi\)
\(662\) 14.8017i 0.575283i
\(663\) 0 0
\(664\) 4.06286i 0.157670i
\(665\) −10.4817 + 13.2900i −0.406463 + 0.515363i
\(666\) 0 0
\(667\) −19.4951 −0.754851
\(668\) 6.69765 0.259140
\(669\) 0 0
\(670\) 0.0817013i 0.00315639i
\(671\) 10.2735 0.396605
\(672\) 0 0
\(673\) 40.5603 1.56348 0.781742 0.623602i \(-0.214332\pi\)
0.781742 + 0.623602i \(0.214332\pi\)
\(674\) 12.4042i 0.477793i
\(675\) 0 0
\(676\) −13.0000 −0.500000
\(677\) 42.7038 1.64124 0.820619 0.571475i \(-0.193629\pi\)
0.820619 + 0.571475i \(0.193629\pi\)
\(678\) 0 0
\(679\) 25.5897 32.4457i 0.982043 1.24515i
\(680\) 2.18251i 0.0836954i
\(681\) 0 0
\(682\) 10.0122i 0.383386i
\(683\) 24.4529i 0.935663i 0.883818 + 0.467832i \(0.154965\pi\)
−0.883818 + 0.467832i \(0.845035\pi\)
\(684\) 0 0
\(685\) 0.307346i 0.0117431i
\(686\) −16.8139 7.76479i −0.641959 0.296461i
\(687\) 0 0
\(688\) 6.15479 0.234649
\(689\) 0 0
\(690\) 0 0
\(691\) 3.95461i 0.150441i −0.997167 0.0752203i \(-0.976034\pi\)
0.997167 0.0752203i \(-0.0239660\pi\)
\(692\) 5.20100 0.197712
\(693\) 0 0
\(694\) −20.0179 −0.759869
\(695\) 17.7570i 0.673560i
\(696\) 0 0
\(697\) 23.8354 0.902829
\(698\) 14.0464 0.531666
\(699\) 0 0
\(700\) −8.59040 6.77519i −0.324687 0.256078i
\(701\) 9.37479i 0.354081i 0.984204 + 0.177040i \(0.0566523\pi\)
−0.984204 + 0.177040i \(0.943348\pi\)
\(702\) 0 0
\(703\) 34.7220i 1.30956i
\(704\) 1.00000i 0.0376889i
\(705\) 0 0
\(706\) 24.4751i 0.921131i
\(707\) 9.45182 + 7.45459i 0.355472 + 0.280359i
\(708\) 0 0
\(709\) −16.4461 −0.617645 −0.308823 0.951120i \(-0.599935\pi\)
−0.308823 + 0.951120i \(0.599935\pi\)
\(710\) −10.7248 −0.402495
\(711\) 0 0
\(712\) 17.0354i 0.638429i
\(713\) 30.5104 1.14262
\(714\) 0 0
\(715\) 0 0
\(716\) 3.91215i 0.146204i
\(717\) 0 0
\(718\) 5.04053 0.188111
\(719\) 3.80861 0.142037 0.0710187 0.997475i \(-0.477375\pi\)
0.0710187 + 0.997475i \(0.477375\pi\)
\(720\) 0 0
\(721\) 6.65670 8.44016i 0.247908 0.314328i
\(722\) 28.3245i 1.05413i
\(723\) 0 0
\(724\) 0.768549i 0.0285629i
\(725\) 26.4545i 0.982496i
\(726\) 0 0
\(727\) 44.3709i 1.64563i −0.568313 0.822813i \(-0.692404\pi\)
0.568313 0.822813i \(-0.307596\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −11.1744 −0.413583
\(731\) 14.4446 0.534254
\(732\) 0 0
\(733\) 16.8272i 0.621528i −0.950487 0.310764i \(-0.899415\pi\)
0.950487 0.310764i \(-0.100585\pi\)
\(734\) −6.21066 −0.229240
\(735\) 0 0
\(736\) 3.04733 0.112326
\(737\) 0.0878550i 0.00323618i
\(738\) 0 0
\(739\) 5.97908 0.219944 0.109972 0.993935i \(-0.464924\pi\)
0.109972 + 0.993935i \(0.464924\pi\)
\(740\) −4.69379 −0.172547
\(741\) 0 0
\(742\) −23.2712 18.3538i −0.854312 0.673790i
\(743\) 2.38634i 0.0875462i −0.999041 0.0437731i \(-0.986062\pi\)
0.999041 0.0437731i \(-0.0139379\pi\)
\(744\) 0 0
\(745\) 1.17383i 0.0430059i
\(746\) 9.78508i 0.358257i
\(747\) 0 0
\(748\) 2.34690i 0.0858110i
\(749\) 9.12901 11.5748i 0.333567 0.422936i
\(750\) 0 0
\(751\) 11.2187 0.409378 0.204689 0.978827i \(-0.434382\pi\)
0.204689 + 0.978827i \(0.434382\pi\)
\(752\) 12.0160 0.438180
\(753\) 0 0
\(754\) 0 0
\(755\) 16.1606 0.588145
\(756\) 0 0
\(757\) −30.0315 −1.09151 −0.545757 0.837944i \(-0.683758\pi\)
−0.545757 + 0.837944i \(0.683758\pi\)
\(758\) 17.8422i 0.648057i
\(759\) 0 0
\(760\) 6.39743 0.232059
\(761\) 2.71648 0.0984725 0.0492362 0.998787i \(-0.484321\pi\)
0.0492362 + 0.998787i \(0.484321\pi\)
\(762\) 0 0
\(763\) 32.5313 + 25.6572i 1.17771 + 0.928853i
\(764\) 20.1518i 0.729065i
\(765\) 0 0
\(766\) 34.2699i 1.23822i
\(767\) 0 0
\(768\) 0 0
\(769\) 31.4424i 1.13384i −0.823773 0.566920i \(-0.808135\pi\)
0.823773 0.566920i \(-0.191865\pi\)
\(770\) 1.93188 + 1.52366i 0.0696203 + 0.0549090i
\(771\) 0 0
\(772\) 6.17571 0.222269
\(773\) −9.42527 −0.339003 −0.169502 0.985530i \(-0.554216\pi\)
−0.169502 + 0.985530i \(0.554216\pi\)
\(774\) 0 0
\(775\) 41.4022i 1.48721i
\(776\) −15.6185 −0.560670
\(777\) 0 0
\(778\) −13.5927 −0.487323
\(779\) 69.8669i 2.50324i
\(780\) 0 0
\(781\) −11.5326 −0.412669
\(782\) 7.15176 0.255746
\(783\) 0 0
\(784\) 1.63112 + 6.80731i 0.0582544 + 0.243118i
\(785\) 13.0379i 0.465342i
\(786\) 0 0
\(787\) 16.6301i 0.592800i −0.955064 0.296400i \(-0.904214\pi\)
0.955064 0.296400i \(-0.0957862\pi\)
\(788\) 14.2772i 0.508603i
\(789\) 0 0
\(790\) 12.6470i 0.449959i
\(791\) 22.4258 28.4341i 0.797369 1.01100i
\(792\) 0 0
\(793\) 0 0
\(794\) 19.1741 0.680464
\(795\) 0 0
\(796\) 7.46620i 0.264632i
\(797\) 20.5847 0.729149 0.364574 0.931174i \(-0.381214\pi\)
0.364574 + 0.931174i \(0.381214\pi\)
\(798\) 0 0
\(799\) 28.2004 0.997658
\(800\) 4.13518i 0.146201i
\(801\) 0 0