Properties

Label 855.2.c.d.514.4
Level $855$
Weight $2$
Character 855.514
Analytic conductor $6.827$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.16516096.1
Defining polynomial: \(x^{6} + 9 x^{4} + 13 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 514.4
Root \(0.285442i\) of defining polynomial
Character \(\chi\) \(=\) 855.514
Dual form 855.2.c.d.514.3

$q$-expansion

\(f(q)\) \(=\) \(q+0.906968i q^{2} +1.17741 q^{4} +(0.370556 - 2.20515i) q^{5} +2.59637i q^{7} +2.88181i q^{8} +O(q^{10})\) \(q+0.906968i q^{2} +1.17741 q^{4} +(0.370556 - 2.20515i) q^{5} +2.59637i q^{7} +2.88181i q^{8} +(2.00000 + 0.336083i) q^{10} -0.741113 q^{11} +3.78878i q^{13} -2.35482 q^{14} -0.258887 q^{16} +3.16725i q^{17} +1.00000 q^{19} +(0.436297 - 2.59637i) q^{20} -0.672165i q^{22} +0.570885i q^{23} +(-4.72538 - 1.63427i) q^{25} -3.43630 q^{26} +3.05699i q^{28} +6.00000 q^{29} +5.83705 q^{31} +5.52881i q^{32} -2.87259 q^{34} +(5.72538 + 0.962100i) q^{35} -1.40396i q^{37} +0.906968i q^{38} +(6.35482 + 1.06787i) q^{40} +3.83705 q^{41} +2.59637i q^{43} -0.872594 q^{44} -0.517774 q^{46} -5.08247i q^{47} +0.258887 q^{49} +(1.48223 - 4.28576i) q^{50} +4.46094i q^{52} -0.160905i q^{53} +(-0.274624 + 1.63427i) q^{55} -7.48223 q^{56} +5.44181i q^{58} +8.35482 q^{59} -8.57816 q^{61} +5.29401i q^{62} -5.53223 q^{64} +(8.35482 + 1.40396i) q^{65} -14.8464i q^{67} +3.72915i q^{68} +(-0.872594 + 5.19273i) q^{70} -3.64518 q^{71} +10.8461i q^{73} +1.27334 q^{74} +1.17741 q^{76} -1.92420i q^{77} -1.83705 q^{79} +(-0.0959323 + 0.570885i) q^{80} +3.48008i q^{82} -4.19876i q^{83} +(6.98426 + 1.17365i) q^{85} -2.35482 q^{86} -2.13574i q^{88} -16.9015 q^{89} -9.83705 q^{91} +0.672165i q^{92} +4.60963 q^{94} +(0.370556 - 2.20515i) q^{95} -3.78878i q^{97} +0.234802i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 8 q^{4} + q^{5} + O(q^{10}) \) \( 6 q - 8 q^{4} + q^{5} + 12 q^{10} - 2 q^{11} + 16 q^{14} - 4 q^{16} + 6 q^{19} - 10 q^{20} + 3 q^{25} - 8 q^{26} + 36 q^{29} + 8 q^{34} + 3 q^{35} + 8 q^{40} - 12 q^{41} + 20 q^{44} - 8 q^{46} + 4 q^{49} + 4 q^{50} - 33 q^{55} - 40 q^{56} + 20 q^{59} - 14 q^{61} + 12 q^{64} + 20 q^{65} + 20 q^{70} - 52 q^{71} - 40 q^{74} - 8 q^{76} + 24 q^{79} + 32 q^{80} + 13 q^{85} + 16 q^{86} + 24 q^{89} - 24 q^{91} + 48 q^{94} + q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.906968i 0.641323i 0.947194 + 0.320661i \(0.103905\pi\)
−0.947194 + 0.320661i \(0.896095\pi\)
\(3\) 0 0
\(4\) 1.17741 0.588705
\(5\) 0.370556 2.20515i 0.165718 0.986173i
\(6\) 0 0
\(7\) 2.59637i 0.981334i 0.871347 + 0.490667i \(0.163247\pi\)
−0.871347 + 0.490667i \(0.836753\pi\)
\(8\) 2.88181i 1.01887i
\(9\) 0 0
\(10\) 2.00000 + 0.336083i 0.632456 + 0.106279i
\(11\) −0.741113 −0.223454 −0.111727 0.993739i \(-0.535638\pi\)
−0.111727 + 0.993739i \(0.535638\pi\)
\(12\) 0 0
\(13\) 3.78878i 1.05082i 0.850850 + 0.525409i \(0.176088\pi\)
−0.850850 + 0.525409i \(0.823912\pi\)
\(14\) −2.35482 −0.629352
\(15\) 0 0
\(16\) −0.258887 −0.0647218
\(17\) 3.16725i 0.768171i 0.923298 + 0.384086i \(0.125483\pi\)
−0.923298 + 0.384086i \(0.874517\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0.436297 2.59637i 0.0975589 0.580565i
\(21\) 0 0
\(22\) 0.672165i 0.143306i
\(23\) 0.570885i 0.119038i 0.998227 + 0.0595189i \(0.0189566\pi\)
−0.998227 + 0.0595189i \(0.981043\pi\)
\(24\) 0 0
\(25\) −4.72538 1.63427i −0.945075 0.326853i
\(26\) −3.43630 −0.673913
\(27\) 0 0
\(28\) 3.05699i 0.577716i
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 5.83705 1.04836 0.524182 0.851606i \(-0.324371\pi\)
0.524182 + 0.851606i \(0.324371\pi\)
\(32\) 5.52881i 0.977365i
\(33\) 0 0
\(34\) −2.87259 −0.492646
\(35\) 5.72538 + 0.962100i 0.967765 + 0.162625i
\(36\) 0 0
\(37\) 1.40396i 0.230809i −0.993319 0.115404i \(-0.963184\pi\)
0.993319 0.115404i \(-0.0368164\pi\)
\(38\) 0.906968i 0.147130i
\(39\) 0 0
\(40\) 6.35482 + 1.06787i 1.00479 + 0.168845i
\(41\) 3.83705 0.599246 0.299623 0.954058i \(-0.403139\pi\)
0.299623 + 0.954058i \(0.403139\pi\)
\(42\) 0 0
\(43\) 2.59637i 0.395942i 0.980208 + 0.197971i \(0.0634352\pi\)
−0.980208 + 0.197971i \(0.936565\pi\)
\(44\) −0.872594 −0.131548
\(45\) 0 0
\(46\) −0.517774 −0.0763416
\(47\) 5.08247i 0.741354i −0.928762 0.370677i \(-0.879126\pi\)
0.928762 0.370677i \(-0.120874\pi\)
\(48\) 0 0
\(49\) 0.258887 0.0369839
\(50\) 1.48223 4.28576i 0.209618 0.606098i
\(51\) 0 0
\(52\) 4.46094i 0.618621i
\(53\) 0.160905i 0.0221020i −0.999939 0.0110510i \(-0.996482\pi\)
0.999939 0.0110510i \(-0.00351771\pi\)
\(54\) 0 0
\(55\) −0.274624 + 1.63427i −0.0370303 + 0.220364i
\(56\) −7.48223 −0.999854
\(57\) 0 0
\(58\) 5.44181i 0.714544i
\(59\) 8.35482 1.08770 0.543852 0.839181i \(-0.316965\pi\)
0.543852 + 0.839181i \(0.316965\pi\)
\(60\) 0 0
\(61\) −8.57816 −1.09832 −0.549160 0.835717i \(-0.685052\pi\)
−0.549160 + 0.835717i \(0.685052\pi\)
\(62\) 5.29401i 0.672340i
\(63\) 0 0
\(64\) −5.53223 −0.691529
\(65\) 8.35482 + 1.40396i 1.03629 + 0.174139i
\(66\) 0 0
\(67\) 14.8464i 1.81378i −0.421371 0.906888i \(-0.638451\pi\)
0.421371 0.906888i \(-0.361549\pi\)
\(68\) 3.72915i 0.452226i
\(69\) 0 0
\(70\) −0.872594 + 5.19273i −0.104295 + 0.620650i
\(71\) −3.64518 −0.432603 −0.216302 0.976327i \(-0.569399\pi\)
−0.216302 + 0.976327i \(0.569399\pi\)
\(72\) 0 0
\(73\) 10.8461i 1.26944i 0.772743 + 0.634719i \(0.218884\pi\)
−0.772743 + 0.634719i \(0.781116\pi\)
\(74\) 1.27334 0.148023
\(75\) 0 0
\(76\) 1.17741 0.135058
\(77\) 1.92420i 0.219283i
\(78\) 0 0
\(79\) −1.83705 −0.206684 −0.103342 0.994646i \(-0.532954\pi\)
−0.103342 + 0.994646i \(0.532954\pi\)
\(80\) −0.0959323 + 0.570885i −0.0107256 + 0.0638269i
\(81\) 0 0
\(82\) 3.48008i 0.384310i
\(83\) 4.19876i 0.460873i −0.973087 0.230437i \(-0.925985\pi\)
0.973087 0.230437i \(-0.0740154\pi\)
\(84\) 0 0
\(85\) 6.98426 + 1.17365i 0.757550 + 0.127300i
\(86\) −2.35482 −0.253927
\(87\) 0 0
\(88\) 2.13574i 0.227671i
\(89\) −16.9015 −1.79156 −0.895778 0.444502i \(-0.853381\pi\)
−0.895778 + 0.444502i \(0.853381\pi\)
\(90\) 0 0
\(91\) −9.83705 −1.03120
\(92\) 0.672165i 0.0700781i
\(93\) 0 0
\(94\) 4.60963 0.475447
\(95\) 0.370556 2.20515i 0.0380183 0.226244i
\(96\) 0 0
\(97\) 3.78878i 0.384692i −0.981327 0.192346i \(-0.938390\pi\)
0.981327 0.192346i \(-0.0616096\pi\)
\(98\) 0.234802i 0.0237186i
\(99\) 0 0
\(100\) −5.56370 1.92420i −0.556370 0.192420i
\(101\) −8.35482 −0.831336 −0.415668 0.909517i \(-0.636452\pi\)
−0.415668 + 0.909517i \(0.636452\pi\)
\(102\) 0 0
\(103\) 2.07612i 0.204566i −0.994755 0.102283i \(-0.967385\pi\)
0.994755 0.102283i \(-0.0326148\pi\)
\(104\) −10.9185 −1.07065
\(105\) 0 0
\(106\) 0.145935 0.0141745
\(107\) 5.70399i 0.551426i 0.961240 + 0.275713i \(0.0889139\pi\)
−0.961240 + 0.275713i \(0.911086\pi\)
\(108\) 0 0
\(109\) −1.64518 −0.157580 −0.0787899 0.996891i \(-0.525106\pi\)
−0.0787899 + 0.996891i \(0.525106\pi\)
\(110\) −1.48223 0.249075i −0.141325 0.0237484i
\(111\) 0 0
\(112\) 0.672165i 0.0635137i
\(113\) 3.89006i 0.365946i −0.983118 0.182973i \(-0.941428\pi\)
0.983118 0.182973i \(-0.0585720\pi\)
\(114\) 0 0
\(115\) 1.25889 + 0.211545i 0.117392 + 0.0197267i
\(116\) 7.06446 0.655918
\(117\) 0 0
\(118\) 7.57755i 0.697570i
\(119\) −8.22334 −0.753832
\(120\) 0 0
\(121\) −10.4508 −0.950068
\(122\) 7.78011i 0.704378i
\(123\) 0 0
\(124\) 6.87259 0.617177
\(125\) −5.35482 + 9.81458i −0.478950 + 0.877842i
\(126\) 0 0
\(127\) 14.4233i 1.27986i −0.768432 0.639931i \(-0.778963\pi\)
0.768432 0.639931i \(-0.221037\pi\)
\(128\) 6.04007i 0.533872i
\(129\) 0 0
\(130\) −1.27334 + 7.57755i −0.111679 + 0.664595i
\(131\) −9.96853 −0.870954 −0.435477 0.900200i \(-0.643420\pi\)
−0.435477 + 0.900200i \(0.643420\pi\)
\(132\) 0 0
\(133\) 2.59637i 0.225133i
\(134\) 13.4652 1.16322
\(135\) 0 0
\(136\) −9.12741 −0.782669
\(137\) 9.70431i 0.829095i 0.910028 + 0.414548i \(0.136060\pi\)
−0.910028 + 0.414548i \(0.863940\pi\)
\(138\) 0 0
\(139\) 13.4508 1.14088 0.570439 0.821340i \(-0.306773\pi\)
0.570439 + 0.821340i \(0.306773\pi\)
\(140\) 6.74111 + 1.13279i 0.569728 + 0.0957379i
\(141\) 0 0
\(142\) 3.30606i 0.277438i
\(143\) 2.80791i 0.234809i
\(144\) 0 0
\(145\) 2.22334 13.2309i 0.184638 1.09877i
\(146\) −9.83705 −0.814120
\(147\) 0 0
\(148\) 1.65303i 0.135878i
\(149\) 15.0959 1.23671 0.618353 0.785900i \(-0.287800\pi\)
0.618353 + 0.785900i \(0.287800\pi\)
\(150\) 0 0
\(151\) 14.1919 1.15492 0.577459 0.816420i \(-0.304044\pi\)
0.577459 + 0.816420i \(0.304044\pi\)
\(152\) 2.88181i 0.233745i
\(153\) 0 0
\(154\) 1.74519 0.140631
\(155\) 2.16295 12.8716i 0.173733 1.03387i
\(156\) 0 0
\(157\) 7.57755i 0.604754i −0.953188 0.302377i \(-0.902220\pi\)
0.953188 0.302377i \(-0.0977802\pi\)
\(158\) 1.66614i 0.132551i
\(159\) 0 0
\(160\) 12.1919 + 2.04874i 0.963852 + 0.161967i
\(161\) −1.48223 −0.116816
\(162\) 0 0
\(163\) 19.6757i 1.54112i −0.637369 0.770559i \(-0.719977\pi\)
0.637369 0.770559i \(-0.280023\pi\)
\(164\) 4.51777 0.352779
\(165\) 0 0
\(166\) 3.80814 0.295569
\(167\) 10.7954i 0.835376i −0.908590 0.417688i \(-0.862840\pi\)
0.908590 0.417688i \(-0.137160\pi\)
\(168\) 0 0
\(169\) −1.35482 −0.104217
\(170\) −1.06446 + 6.33450i −0.0816402 + 0.485834i
\(171\) 0 0
\(172\) 3.05699i 0.233093i
\(173\) 20.3895i 1.55018i −0.631848 0.775092i \(-0.717703\pi\)
0.631848 0.775092i \(-0.282297\pi\)
\(174\) 0 0
\(175\) 4.24315 12.2688i 0.320752 0.927434i
\(176\) 0.191865 0.0144623
\(177\) 0 0
\(178\) 15.3291i 1.14897i
\(179\) 25.0645 1.87341 0.936703 0.350126i \(-0.113861\pi\)
0.936703 + 0.350126i \(0.113861\pi\)
\(180\) 0 0
\(181\) −19.4193 −1.44342 −0.721712 0.692194i \(-0.756644\pi\)
−0.721712 + 0.692194i \(0.756644\pi\)
\(182\) 8.92188i 0.661334i
\(183\) 0 0
\(184\) −1.64518 −0.121284
\(185\) −3.09593 0.520245i −0.227617 0.0382491i
\(186\) 0 0
\(187\) 2.34729i 0.171651i
\(188\) 5.98414i 0.436439i
\(189\) 0 0
\(190\) 2.00000 + 0.336083i 0.145095 + 0.0243820i
\(191\) −11.4508 −0.828547 −0.414274 0.910152i \(-0.635964\pi\)
−0.414274 + 0.910152i \(0.635964\pi\)
\(192\) 0 0
\(193\) 3.78878i 0.272722i 0.990659 + 0.136361i \(0.0435407\pi\)
−0.990659 + 0.136361i \(0.956459\pi\)
\(194\) 3.43630 0.246712
\(195\) 0 0
\(196\) 0.304816 0.0217726
\(197\) 2.28354i 0.162695i 0.996686 + 0.0813477i \(0.0259224\pi\)
−0.996686 + 0.0813477i \(0.974078\pi\)
\(198\) 0 0
\(199\) 19.4508 1.37883 0.689414 0.724368i \(-0.257868\pi\)
0.689414 + 0.724368i \(0.257868\pi\)
\(200\) 4.70964 13.6176i 0.333022 0.962911i
\(201\) 0 0
\(202\) 7.57755i 0.533155i
\(203\) 15.5782i 1.09337i
\(204\) 0 0
\(205\) 1.42184 8.46126i 0.0993057 0.590960i
\(206\) 1.88297 0.131193
\(207\) 0 0
\(208\) 0.980865i 0.0680108i
\(209\) −0.741113 −0.0512639
\(210\) 0 0
\(211\) 11.2274 0.772927 0.386463 0.922305i \(-0.373697\pi\)
0.386463 + 0.922305i \(0.373697\pi\)
\(212\) 0.189451i 0.0130115i
\(213\) 0 0
\(214\) −5.17334 −0.353642
\(215\) 5.72538 + 0.962100i 0.390467 + 0.0656147i
\(216\) 0 0
\(217\) 15.1551i 1.02880i
\(218\) 1.49213i 0.101059i
\(219\) 0 0
\(220\) −0.323345 + 1.92420i −0.0217999 + 0.129730i
\(221\) −12.0000 −0.807207
\(222\) 0 0
\(223\) 4.03785i 0.270394i −0.990819 0.135197i \(-0.956833\pi\)
0.990819 0.135197i \(-0.0431668\pi\)
\(224\) −14.3548 −0.959122
\(225\) 0 0
\(226\) 3.52815 0.234689
\(227\) 11.2185i 0.744600i −0.928112 0.372300i \(-0.878569\pi\)
0.928112 0.372300i \(-0.121431\pi\)
\(228\) 0 0
\(229\) −16.1315 −1.06600 −0.532999 0.846116i \(-0.678935\pi\)
−0.532999 + 0.846116i \(0.678935\pi\)
\(230\) −0.191865 + 1.14177i −0.0126512 + 0.0752861i
\(231\) 0 0
\(232\) 17.2908i 1.13520i
\(233\) 2.12676i 0.139329i 0.997570 + 0.0696644i \(0.0221928\pi\)
−0.997570 + 0.0696644i \(0.977807\pi\)
\(234\) 0 0
\(235\) −11.2076 1.88334i −0.731103 0.122856i
\(236\) 9.83705 0.640337
\(237\) 0 0
\(238\) 7.45830i 0.483450i
\(239\) −14.4152 −0.932442 −0.466221 0.884668i \(-0.654385\pi\)
−0.466221 + 0.884668i \(0.654385\pi\)
\(240\) 0 0
\(241\) −0.162955 −0.0104968 −0.00524842 0.999986i \(-0.501671\pi\)
−0.00524842 + 0.999986i \(0.501671\pi\)
\(242\) 9.47849i 0.609301i
\(243\) 0 0
\(244\) −10.1000 −0.646587
\(245\) 0.0959323 0.570885i 0.00612889 0.0364725i
\(246\) 0 0
\(247\) 3.78878i 0.241074i
\(248\) 16.8212i 1.06815i
\(249\) 0 0
\(250\) −8.90150 4.85665i −0.562980 0.307161i
\(251\) −12.9330 −0.816322 −0.408161 0.912910i \(-0.633830\pi\)
−0.408161 + 0.912910i \(0.633830\pi\)
\(252\) 0 0
\(253\) 0.423090i 0.0265995i
\(254\) 13.0815 0.820805
\(255\) 0 0
\(256\) −16.5426 −1.03391
\(257\) 11.0445i 0.688938i −0.938798 0.344469i \(-0.888059\pi\)
0.938798 0.344469i \(-0.111941\pi\)
\(258\) 0 0
\(259\) 3.64518 0.226501
\(260\) 9.83705 + 1.65303i 0.610068 + 0.102517i
\(261\) 0 0
\(262\) 9.04113i 0.558563i
\(263\) 17.8527i 1.10085i −0.834885 0.550424i \(-0.814466\pi\)
0.834885 0.550424i \(-0.185534\pi\)
\(264\) 0 0
\(265\) −0.354819 0.0596243i −0.0217964 0.00366269i
\(266\) −2.35482 −0.144383
\(267\) 0 0
\(268\) 17.4803i 1.06778i
\(269\) 24.9934 1.52387 0.761936 0.647652i \(-0.224249\pi\)
0.761936 + 0.647652i \(0.224249\pi\)
\(270\) 0 0
\(271\) −23.8660 −1.44975 −0.724877 0.688879i \(-0.758103\pi\)
−0.724877 + 0.688879i \(0.758103\pi\)
\(272\) 0.819960i 0.0497174i
\(273\) 0 0
\(274\) −8.80150 −0.531718
\(275\) 3.50204 + 1.21118i 0.211181 + 0.0730366i
\(276\) 0 0
\(277\) 21.2315i 1.27568i 0.770169 + 0.637840i \(0.220172\pi\)
−0.770169 + 0.637840i \(0.779828\pi\)
\(278\) 12.1994i 0.731671i
\(279\) 0 0
\(280\) −2.77259 + 16.4994i −0.165694 + 0.986030i
\(281\) −3.83705 −0.228899 −0.114449 0.993429i \(-0.536510\pi\)
−0.114449 + 0.993429i \(0.536510\pi\)
\(282\) 0 0
\(283\) 0.211545i 0.0125751i 0.999980 + 0.00628753i \(0.00200139\pi\)
−0.999980 + 0.00628753i \(0.997999\pi\)
\(284\) −4.29187 −0.254676
\(285\) 0 0
\(286\) 2.54668 0.150589
\(287\) 9.96237i 0.588060i
\(288\) 0 0
\(289\) 6.96853 0.409913
\(290\) 12.0000 + 2.01650i 0.704664 + 0.118413i
\(291\) 0 0
\(292\) 12.7703i 0.747324i
\(293\) 14.9942i 0.875970i 0.898982 + 0.437985i \(0.144308\pi\)
−0.898982 + 0.437985i \(0.855692\pi\)
\(294\) 0 0
\(295\) 3.09593 18.4236i 0.180252 1.07267i
\(296\) 4.04593 0.235165
\(297\) 0 0
\(298\) 13.6915i 0.793129i
\(299\) −2.16295 −0.125087
\(300\) 0 0
\(301\) −6.74111 −0.388551
\(302\) 12.8716i 0.740675i
\(303\) 0 0
\(304\) −0.258887 −0.0148482
\(305\) −3.17869 + 18.9161i −0.182011 + 1.08313i
\(306\) 0 0
\(307\) 1.65303i 0.0943434i −0.998887 0.0471717i \(-0.984979\pi\)
0.998887 0.0471717i \(-0.0150208\pi\)
\(308\) 2.26557i 0.129093i
\(309\) 0 0
\(310\) 11.6741 + 1.96173i 0.663044 + 0.111419i
\(311\) 0.741113 0.0420247 0.0210123 0.999779i \(-0.493311\pi\)
0.0210123 + 0.999779i \(0.493311\pi\)
\(312\) 0 0
\(313\) 26.8849i 1.51962i −0.650143 0.759812i \(-0.725291\pi\)
0.650143 0.759812i \(-0.274709\pi\)
\(314\) 6.87259 0.387843
\(315\) 0 0
\(316\) −2.16295 −0.121676
\(317\) 8.16155i 0.458398i −0.973380 0.229199i \(-0.926389\pi\)
0.973380 0.229199i \(-0.0736107\pi\)
\(318\) 0 0
\(319\) −4.44668 −0.248966
\(320\) −2.05000 + 12.1994i −0.114599 + 0.681967i
\(321\) 0 0
\(322\) 1.34433i 0.0749166i
\(323\) 3.16725i 0.176231i
\(324\) 0 0
\(325\) 6.19186 17.9034i 0.343463 0.993101i
\(326\) 17.8452 0.988354
\(327\) 0 0
\(328\) 11.0576i 0.610555i
\(329\) 13.1959 0.727516
\(330\) 0 0
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 4.94366i 0.271318i
\(333\) 0 0
\(334\) 9.79112 0.535746
\(335\) −32.7385 5.50143i −1.78870 0.300575i
\(336\) 0 0
\(337\) 9.90275i 0.539437i 0.962939 + 0.269718i \(0.0869306\pi\)
−0.962939 + 0.269718i \(0.913069\pi\)
\(338\) 1.22878i 0.0668367i
\(339\) 0 0
\(340\) 8.22334 + 1.38186i 0.445973 + 0.0749419i
\(341\) −4.32591 −0.234261
\(342\) 0 0
\(343\) 18.8467i 1.01763i
\(344\) −7.48223 −0.403415
\(345\) 0 0
\(346\) 18.4926 0.994169
\(347\) 21.2781i 1.14227i −0.820858 0.571133i \(-0.806504\pi\)
0.820858 0.571133i \(-0.193496\pi\)
\(348\) 0 0
\(349\) 16.4152 0.878686 0.439343 0.898319i \(-0.355211\pi\)
0.439343 + 0.898319i \(0.355211\pi\)
\(350\) 11.1274 + 3.84840i 0.594785 + 0.205706i
\(351\) 0 0
\(352\) 4.09748i 0.218396i
\(353\) 23.8744i 1.27071i −0.772221 0.635354i \(-0.780854\pi\)
0.772221 0.635354i \(-0.219146\pi\)
\(354\) 0 0
\(355\) −1.35075 + 8.03817i −0.0716901 + 0.426622i
\(356\) −19.9000 −1.05470
\(357\) 0 0
\(358\) 22.7327i 1.20146i
\(359\) 2.22334 0.117343 0.0586717 0.998277i \(-0.481313\pi\)
0.0586717 + 0.998277i \(0.481313\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 17.6127i 0.925701i
\(363\) 0 0
\(364\) −11.5822 −0.607074
\(365\) 23.9172 + 4.01909i 1.25189 + 0.210369i
\(366\) 0 0
\(367\) 4.52057i 0.235972i 0.993015 + 0.117986i \(0.0376437\pi\)
−0.993015 + 0.117986i \(0.962356\pi\)
\(368\) 0.147795i 0.00770433i
\(369\) 0 0
\(370\) 0.471845 2.80791i 0.0245301 0.145976i
\(371\) 0.417768 0.0216894
\(372\) 0 0
\(373\) 15.5186i 0.803521i 0.915745 + 0.401760i \(0.131602\pi\)
−0.915745 + 0.401760i \(0.868398\pi\)
\(374\) 2.12892 0.110084
\(375\) 0 0
\(376\) 14.6467 0.755345
\(377\) 22.7327i 1.17079i
\(378\) 0 0
\(379\) 18.9015 0.970905 0.485453 0.874263i \(-0.338655\pi\)
0.485453 + 0.874263i \(0.338655\pi\)
\(380\) 0.436297 2.59637i 0.0223816 0.133191i
\(381\) 0 0
\(382\) 10.3855i 0.531366i
\(383\) 13.7046i 0.700274i 0.936699 + 0.350137i \(0.113865\pi\)
−0.936699 + 0.350137i \(0.886135\pi\)
\(384\) 0 0
\(385\) −4.24315 0.713025i −0.216251 0.0363391i
\(386\) −3.43630 −0.174903
\(387\) 0 0
\(388\) 4.46094i 0.226470i
\(389\) 12.7411 0.646000 0.323000 0.946399i \(-0.395309\pi\)
0.323000 + 0.946399i \(0.395309\pi\)
\(390\) 0 0
\(391\) −1.80814 −0.0914413
\(392\) 0.746063i 0.0376819i
\(393\) 0 0
\(394\) −2.07110 −0.104340
\(395\) −0.680729 + 4.05096i −0.0342512 + 0.203826i
\(396\) 0 0
\(397\) 38.6522i 1.93990i 0.243306 + 0.969950i \(0.421768\pi\)
−0.243306 + 0.969950i \(0.578232\pi\)
\(398\) 17.6412i 0.884274i
\(399\) 0 0
\(400\) 1.22334 + 0.423090i 0.0611669 + 0.0211545i
\(401\) −31.8660 −1.59131 −0.795655 0.605750i \(-0.792873\pi\)
−0.795655 + 0.605750i \(0.792873\pi\)
\(402\) 0 0
\(403\) 22.1153i 1.10164i
\(404\) −9.83705 −0.489411
\(405\) 0 0
\(406\) −14.1289 −0.701206
\(407\) 1.04049i 0.0515751i
\(408\) 0 0
\(409\) −11.0645 −0.547102 −0.273551 0.961857i \(-0.588198\pi\)
−0.273551 + 0.961857i \(0.588198\pi\)
\(410\) 7.67409 + 1.28956i 0.378996 + 0.0636871i
\(411\) 0 0
\(412\) 2.44444i 0.120429i
\(413\) 21.6922i 1.06740i
\(414\) 0 0
\(415\) −9.25889 1.55588i −0.454501 0.0763749i
\(416\) −20.9474 −1.02703
\(417\) 0 0
\(418\) 0.672165i 0.0328767i
\(419\) −25.7452 −1.25773 −0.628867 0.777513i \(-0.716481\pi\)
−0.628867 + 0.777513i \(0.716481\pi\)
\(420\) 0 0
\(421\) 27.4482 1.33774 0.668871 0.743378i \(-0.266778\pi\)
0.668871 + 0.743378i \(0.266778\pi\)
\(422\) 10.1829i 0.495696i
\(423\) 0 0
\(424\) 0.463697 0.0225191
\(425\) 5.17613 14.9664i 0.251079 0.725979i
\(426\) 0 0
\(427\) 22.2720i 1.07782i
\(428\) 6.71593i 0.324627i
\(429\) 0 0
\(430\) −0.872594 + 5.19273i −0.0420802 + 0.250416i
\(431\) −1.74519 −0.0840627 −0.0420314 0.999116i \(-0.513383\pi\)
−0.0420314 + 0.999116i \(0.513383\pi\)
\(432\) 0 0
\(433\) 18.5208i 0.890052i −0.895518 0.445026i \(-0.853194\pi\)
0.895518 0.445026i \(-0.146806\pi\)
\(434\) −13.7452 −0.659790
\(435\) 0 0
\(436\) −1.93705 −0.0927679
\(437\) 0.570885i 0.0273091i
\(438\) 0 0
\(439\) −29.4482 −1.40549 −0.702743 0.711444i \(-0.748041\pi\)
−0.702743 + 0.711444i \(0.748041\pi\)
\(440\) −4.70964 0.791414i −0.224523 0.0377292i
\(441\) 0 0
\(442\) 10.8836i 0.517681i
\(443\) 11.7388i 0.557726i −0.960331 0.278863i \(-0.910042\pi\)
0.960331 0.278863i \(-0.0899576\pi\)
\(444\) 0 0
\(445\) −6.26296 + 37.2704i −0.296893 + 1.76678i
\(446\) 3.66220 0.173410
\(447\) 0 0
\(448\) 14.3637i 0.678620i
\(449\) −7.06446 −0.333392 −0.166696 0.986008i \(-0.553310\pi\)
−0.166696 + 0.986008i \(0.553310\pi\)
\(450\) 0 0
\(451\) −2.84368 −0.133904
\(452\) 4.58019i 0.215434i
\(453\) 0 0
\(454\) 10.1748 0.477529
\(455\) −3.64518 + 21.6922i −0.170889 + 1.01694i
\(456\) 0 0
\(457\) 34.5000i 1.61384i 0.590660 + 0.806920i \(0.298867\pi\)
−0.590660 + 0.806920i \(0.701133\pi\)
\(458\) 14.6307i 0.683649i
\(459\) 0 0
\(460\) 1.48223 + 0.249075i 0.0691091 + 0.0116132i
\(461\) −8.03147 −0.374063 −0.187032 0.982354i \(-0.559887\pi\)
−0.187032 + 0.982354i \(0.559887\pi\)
\(462\) 0 0
\(463\) 25.3290i 1.17714i −0.808447 0.588570i \(-0.799691\pi\)
0.808447 0.588570i \(-0.200309\pi\)
\(464\) −1.55332 −0.0721112
\(465\) 0 0
\(466\) −1.92890 −0.0893547
\(467\) 26.8759i 1.24367i 0.783149 + 0.621834i \(0.213612\pi\)
−0.783149 + 0.621834i \(0.786388\pi\)
\(468\) 0 0
\(469\) 38.5467 1.77992
\(470\) 1.70813 10.1649i 0.0787901 0.468873i
\(471\) 0 0
\(472\) 24.0770i 1.10823i
\(473\) 1.92420i 0.0884748i
\(474\) 0 0
\(475\) −4.72538 1.63427i −0.216815 0.0749852i
\(476\) −9.68224 −0.443785
\(477\) 0 0
\(478\) 13.0741i 0.597996i
\(479\) −28.9015 −1.32054 −0.660272 0.751027i \(-0.729559\pi\)
−0.660272 + 0.751027i \(0.729559\pi\)
\(480\) 0 0
\(481\) 5.31927 0.242538
\(482\) 0.147795i 0.00673187i
\(483\) 0 0
\(484\) −12.3048 −0.559310
\(485\) −8.35482 1.40396i −0.379373 0.0637503i
\(486\) 0 0
\(487\) 17.7294i 0.803395i 0.915773 + 0.401697i \(0.131580\pi\)
−0.915773 + 0.401697i \(0.868420\pi\)
\(488\) 24.7206i 1.11905i
\(489\) 0 0
\(490\) 0.517774 + 0.0870075i 0.0233907 + 0.00393060i
\(491\) 35.1645 1.58695 0.793475 0.608603i \(-0.208270\pi\)
0.793475 + 0.608603i \(0.208270\pi\)
\(492\) 0 0
\(493\) 19.0035i 0.855875i
\(494\) −3.43630 −0.154606
\(495\) 0 0
\(496\) −1.51114 −0.0678520
\(497\) 9.46422i 0.424528i
\(498\) 0 0
\(499\) −21.4508 −0.960268 −0.480134 0.877195i \(-0.659412\pi\)
−0.480134 + 0.877195i \(0.659412\pi\)
\(500\) −6.30482 + 11.5558i −0.281960 + 0.516790i
\(501\) 0 0
\(502\) 11.7298i 0.523526i
\(503\) 5.34053i 0.238122i 0.992887 + 0.119061i \(0.0379884\pi\)
−0.992887 + 0.119061i \(0.962012\pi\)
\(504\) 0 0
\(505\) −3.09593 + 18.4236i −0.137767 + 0.819841i
\(506\) 0.383729 0.0170588
\(507\) 0 0
\(508\) 16.9821i 0.753461i
\(509\) 36.1919 1.60418 0.802088 0.597206i \(-0.203722\pi\)
0.802088 + 0.597206i \(0.203722\pi\)
\(510\) 0 0
\(511\) −28.1604 −1.24574
\(512\) 2.92346i 0.129200i
\(513\) 0 0
\(514\) 10.0170 0.441832
\(515\) −4.57816 0.769320i −0.201738 0.0339003i
\(516\) 0 0
\(517\) 3.76668i 0.165658i
\(518\) 3.30606i 0.145260i
\(519\) 0 0
\(520\) −4.04593 + 24.0770i −0.177426 + 1.05585i
\(521\) 2.77259 0.121469 0.0607346 0.998154i \(-0.480656\pi\)
0.0607346 + 0.998154i \(0.480656\pi\)
\(522\) 0 0
\(523\) 20.5373i 0.898033i −0.893524 0.449016i \(-0.851774\pi\)
0.893524 0.449016i \(-0.148226\pi\)
\(524\) −11.7370 −0.512735
\(525\) 0 0
\(526\) 16.1919 0.705999
\(527\) 18.4874i 0.805323i
\(528\) 0 0
\(529\) 22.6741 0.985830
\(530\) 0.0540773 0.321810i 0.00234897 0.0139785i
\(531\) 0 0
\(532\) 3.05699i 0.132537i
\(533\) 14.5377i 0.629698i
\(534\) 0 0
\(535\) 12.5782 + 2.11365i 0.543801 + 0.0913811i
\(536\) 42.7845 1.84801
\(537\) 0 0
\(538\) 22.6682i 0.977294i
\(539\) −0.191865 −0.00826419
\(540\) 0 0
\(541\) 35.4797 1.52539 0.762695 0.646758i \(-0.223876\pi\)
0.762695 + 0.646758i \(0.223876\pi\)
\(542\) 21.6456i 0.929760i
\(543\) 0 0
\(544\) −17.5111 −0.750784
\(545\) −0.609632 + 3.62787i −0.0261138 + 0.155401i
\(546\) 0 0
\(547\) 43.0756i 1.84178i −0.389822 0.920890i \(-0.627463\pi\)
0.389822 0.920890i \(-0.372537\pi\)
\(548\) 11.4260i 0.488092i
\(549\) 0 0
\(550\) −1.09850 + 3.17623i −0.0468401 + 0.135435i
\(551\) 6.00000 0.255609
\(552\) 0 0
\(553\) 4.76964i 0.202826i
\(554\) −19.2563 −0.818123
\(555\) 0 0
\(556\) 15.8370 0.671640
\(557\) 40.4376i 1.71340i 0.515818 + 0.856698i \(0.327488\pi\)
−0.515818 + 0.856698i \(0.672512\pi\)
\(558\) 0 0
\(559\) −9.83705 −0.416063
\(560\) −1.48223 0.249075i −0.0626355 0.0105254i
\(561\) 0 0
\(562\) 3.48008i 0.146798i
\(563\) 19.7173i 0.830986i −0.909596 0.415493i \(-0.863609\pi\)
0.909596 0.415493i \(-0.136391\pi\)
\(564\) 0 0
\(565\) −8.57816 1.44149i −0.360886 0.0606437i
\(566\) −0.191865 −0.00806467
\(567\) 0 0
\(568\) 10.5047i 0.440768i
\(569\) 18.6807 0.783137 0.391568 0.920149i \(-0.371933\pi\)
0.391568 + 0.920149i \(0.371933\pi\)
\(570\) 0 0
\(571\) −29.9371 −1.25283 −0.626413 0.779491i \(-0.715478\pi\)
−0.626413 + 0.779491i \(0.715478\pi\)
\(572\) 3.30606i 0.138233i
\(573\) 0 0
\(574\) −9.03555 −0.377137
\(575\) 0.932977 2.69765i 0.0389079 0.112500i
\(576\) 0 0
\(577\) 0.156779i 0.00652679i 0.999995 + 0.00326339i \(0.00103877\pi\)
−0.999995 + 0.00326339i \(0.998961\pi\)
\(578\) 6.32023i 0.262887i
\(579\) 0 0
\(580\) 2.61778 15.5782i 0.108697 0.646849i
\(581\) 10.9015 0.452271
\(582\) 0 0
\(583\) 0.119249i 0.00493877i
\(584\) −31.2563 −1.29340
\(585\) 0 0
\(586\) −13.5993 −0.561780
\(587\) 31.1474i 1.28559i 0.766038 + 0.642795i \(0.222225\pi\)
−0.766038 + 0.642795i \(0.777775\pi\)
\(588\) 0 0
\(589\) 5.83705 0.240511
\(590\) 16.7096 + 2.80791i 0.687925 + 0.115600i
\(591\) 0 0
\(592\) 0.363466i 0.0149384i
\(593\) 28.8728i 1.18567i −0.805326 0.592833i \(-0.798009\pi\)
0.805326 0.592833i \(-0.201991\pi\)
\(594\) 0 0
\(595\) −3.04721 + 18.1337i −0.124923 + 0.743409i
\(596\) 17.7741 0.728055
\(597\) 0 0
\(598\) 1.96173i 0.0802211i
\(599\) 25.3274 1.03485 0.517425 0.855728i \(-0.326891\pi\)
0.517425 + 0.855728i \(0.326891\pi\)
\(600\) 0 0
\(601\) −19.8370 −0.809170 −0.404585 0.914500i \(-0.632584\pi\)
−0.404585 + 0.914500i \(0.632584\pi\)
\(602\) 6.11397i 0.249187i
\(603\) 0 0
\(604\) 16.7096 0.679906
\(605\) −3.87259 + 23.0455i −0.157443 + 0.936932i
\(606\) 0 0
\(607\) 2.49921i 0.101440i 0.998713 + 0.0507199i \(0.0161516\pi\)
−0.998713 + 0.0507199i \(0.983848\pi\)
\(608\) 5.52881i 0.224223i
\(609\) 0 0
\(610\) −17.1563 2.88297i −0.694639 0.116728i
\(611\) 19.2563 0.779027
\(612\) 0 0
\(613\) 0.883711i 0.0356927i −0.999841 0.0178464i \(-0.994319\pi\)
0.999841 0.0178464i \(-0.00568098\pi\)
\(614\) 1.49925 0.0605046
\(615\) 0 0
\(616\) 5.54517 0.223421
\(617\) 29.4085i 1.18394i −0.805959 0.591971i \(-0.798350\pi\)
0.805959 0.591971i \(-0.201650\pi\)
\(618\) 0 0
\(619\) −30.3208 −1.21870 −0.609348 0.792903i \(-0.708569\pi\)
−0.609348 + 0.792903i \(0.708569\pi\)
\(620\) 2.54668 15.1551i 0.102277 0.608644i
\(621\) 0 0
\(622\) 0.672165i 0.0269514i
\(623\) 43.8825i 1.75811i
\(624\) 0 0
\(625\) 19.6584 + 15.4450i 0.786334 + 0.617801i
\(626\) 24.3837 0.974570
\(627\) 0 0
\(628\) 8.92188i 0.356022i
\(629\) 4.44668 0.177301
\(630\) 0 0
\(631\) 17.7767 0.707678 0.353839 0.935306i \(-0.384876\pi\)
0.353839 + 0.935306i \(0.384876\pi\)
\(632\) 5.29401i 0.210584i
\(633\) 0 0
\(634\) 7.40226 0.293981
\(635\) −31.8056 5.34465i −1.26217 0.212096i
\(636\) 0 0
\(637\) 0.980865i 0.0388633i
\(638\) 4.03299i 0.159668i
\(639\) 0 0
\(640\) 13.3193 + 2.23819i 0.526490 + 0.0884722i
\(641\) 32.6675 1.29029 0.645143 0.764062i \(-0.276798\pi\)
0.645143 + 0.764062i \(0.276798\pi\)
\(642\) 0 0
\(643\) 31.8661i 1.25668i 0.777941 + 0.628338i \(0.216264\pi\)
−0.777941 + 0.628338i \(0.783736\pi\)
\(644\) −1.74519 −0.0687700
\(645\) 0 0
\(646\) −2.87259 −0.113021
\(647\) 21.2601i 0.835820i 0.908488 + 0.417910i \(0.137237\pi\)
−0.908488 + 0.417910i \(0.862763\pi\)
\(648\) 0 0
\(649\) −6.19186 −0.243052
\(650\) 16.2378 + 5.61582i 0.636899 + 0.220271i
\(651\) 0 0
\(652\) 23.1663i 0.907263i
\(653\) 12.8340i 0.502234i −0.967957 0.251117i \(-0.919202\pi\)
0.967957 0.251117i \(-0.0807980\pi\)
\(654\) 0 0
\(655\) −3.69390 + 21.9821i −0.144333 + 0.858912i
\(656\) −0.993361 −0.0387842
\(657\) 0 0
\(658\) 11.9683i 0.466573i
\(659\) 20.3548 0.792911 0.396456 0.918054i \(-0.370240\pi\)
0.396456 + 0.918054i \(0.370240\pi\)
\(660\) 0 0
\(661\) −30.7385 −1.19559 −0.597795 0.801649i \(-0.703957\pi\)
−0.597795 + 0.801649i \(0.703957\pi\)
\(662\) 7.25574i 0.282002i
\(663\) 0 0
\(664\) 12.1000 0.469571
\(665\) 5.72538 + 0.962100i 0.222021 + 0.0373086i
\(666\) 0 0
\(667\) 3.42531i 0.132629i
\(668\) 12.7107i 0.491790i
\(669\) 0 0
\(670\) 4.98962 29.6928i 0.192766 1.14713i
\(671\) 6.35738 0.245424
\(672\) 0 0
\(673\) 21.2094i 0.817564i 0.912632 + 0.408782i \(0.134046\pi\)
−0.912632 + 0.408782i \(0.865954\pi\)
\(674\) −8.98147 −0.345953
\(675\) 0 0
\(676\) −1.59518 −0.0613530
\(677\) 11.2650i 0.432951i 0.976288 + 0.216475i \(0.0694561\pi\)
−0.976288 + 0.216475i \(0.930544\pi\)
\(678\) 0 0
\(679\) 9.83705 0.377511
\(680\) −3.38222 + 20.1273i −0.129702 + 0.771847i
\(681\) 0 0
\(682\) 3.92346i 0.150237i
\(683\) 12.3603i 0.472954i 0.971637 + 0.236477i \(0.0759928\pi\)
−0.971637 + 0.236477i \(0.924007\pi\)
\(684\) 0 0
\(685\) 21.3995 + 3.59600i 0.817632 + 0.137396i
\(686\) −17.0934 −0.652628
\(687\) 0 0
\(688\) 0.672165i 0.0256261i
\(689\) 0.609632 0.0232251
\(690\) 0 0
\(691\) 22.7493 0.865423 0.432711 0.901533i \(-0.357557\pi\)
0.432711 + 0.901533i \(0.357557\pi\)
\(692\) 24.0068i 0.912601i
\(693\) 0 0
\(694\) 19.2985 0.732561
\(695\) 4.98426 29.6609i 0.189064 1.12510i
\(696\) 0 0
\(697\) 12.1529i 0.460323i
\(698\) 14.8881i 0.563521i
\(699\) 0 0
\(700\) 4.99593 14.4454i 0.188828 0.545985i
\(701\) 16.0289 0.605404 0.302702 0.953085i \(-0.402111\pi\)
0.302702 + 0.953085i \(0.402111\pi\)
\(702\) 0 0
\(703\) 1.40396i 0.0529512i
\(704\) 4.10001 0.154525
\(705\) 0 0
\(706\) 21.6533 0.814934
\(707\) 21.6922i 0.815818i
\(708\) 0 0
\(709\) −31.4193 −1.17998 −0.589988 0.807412i \(-0.700867\pi\)
−0.589988 + 0.807412i \(0.700867\pi\)
\(710\) −7.29036 1.22508i −0.273602 0.0459765i
\(711\) 0 0
\(712\) 48.7069i 1.82537i
\(713\) 3.33228i 0.124795i
\(714\) 0 0
\(715\) −6.19186 1.04049i −0.231563 0.0389121i
\(716\) 29.5111 1.10288
\(717\) 0 0
\(718\) 2.01650i 0.0752550i
\(719\) 11.2589 0.419886 0.209943 0.977714i \(-0.432672\pi\)
0.209943 + 0.977714i \(0.432672\pi\)
\(720\) 0 0
\(721\) 5.39037 0.200748
\(722\) 0.906968i 0.0337538i
\(723\) 0 0
\(724\) −22.8644 −0.849750
\(725\) −28.3523 9.80559i −1.05298 0.364171i
\(726\) 0 0
\(727\) 48.9829i 1.81668i −0.418237 0.908338i \(-0.637352\pi\)
0.418237 0.908338i \(-0.362648\pi\)
\(728\) 28.3485i 1.05066i
\(729\) 0 0
\(730\) −3.64518 + 21.6922i −0.134914 + 0.802863i
\(731\) −8.22334 −0.304151
\(732\) 0 0
\(733\) 35.9260i 1.32696i −0.748195 0.663479i \(-0.769079\pi\)
0.748195 0.663479i \(-0.230921\pi\)
\(734\) −4.10001 −0.151334
\(735\) 0 0
\(736\) −3.15632 −0.116343
\(737\) 11.0029i 0.405296i
\(738\) 0 0
\(739\) −14.3523 −0.527956 −0.263978 0.964529i \(-0.585035\pi\)
−0.263978 + 0.964529i \(0.585035\pi\)
\(740\) −3.64518 0.612541i −0.134000 0.0225175i
\(741\) 0 0
\(742\) 0.378902i 0.0139099i
\(743\) 12.5629i 0.460887i −0.973086 0.230443i \(-0.925982\pi\)
0.973086 0.230443i \(-0.0740176\pi\)
\(744\) 0 0
\(745\) 5.59390 33.2888i 0.204944 1.21961i
\(746\) −14.0748 −0.515316
\(747\) 0 0
\(748\) 2.76372i 0.101052i
\(749\) −14.8096 −0.541133
\(750\) 0 0
\(751\) 26.4548 0.965350 0.482675 0.875799i \(-0.339665\pi\)
0.482675 + 0.875799i \(0.339665\pi\)
\(752\) 1.31578i 0.0479817i
\(753\) 0 0
\(754\) −20.6178 −0.750855
\(755\) 5.25889 31.2952i 0.191390 1.13895i
\(756\) 0 0
\(757\) 15.7350i 0.571897i 0.958245 + 0.285949i \(0.0923087\pi\)
−0.958245 + 0.285949i \(0.907691\pi\)
\(758\) 17.1431i 0.622664i
\(759\) 0 0
\(760\) 6.35482 + 1.06787i 0.230514 + 0.0387358i
\(761\) −16.9619 −0.614868 −0.307434 0.951569i \(-0.599470\pi\)
−0.307434 + 0.951569i \(0.599470\pi\)
\(762\) 0 0
\(763\) 4.27149i 0.154638i
\(764\) −13.4822 −0.487770
\(765\) 0 0
\(766\) −12.4297 −0.449102
\(767\) 31.6545i 1.14298i
\(768\) 0 0
\(769\) −41.9974 −1.51447 −0.757233 0.653145i \(-0.773449\pi\)
−0.757233 + 0.653145i \(0.773449\pi\)
\(770\) 0.646690 3.84840i 0.0233051 0.138687i
\(771\) 0 0
\(772\) 4.46094i 0.160553i
\(773\) 40.9579i 1.47315i 0.676355 + 0.736576i \(0.263559\pi\)
−0.676355 + 0.736576i \(0.736441\pi\)
\(774\) 0 0
\(775\) −27.5822 9.53928i −0.990783 0.342661i
\(776\) 10.9185 0.391952
\(777\) 0 0
\(778\) 11.5558i 0.414295i
\(779\) 3.83705 0.137476
\(780\) 0 0
\(781\) 2.70149 0.0966669
\(782\) 1.63992i 0.0586434i
\(783\) 0 0
\(784\) −0.0670225 −0.00239366
\(785\) −16.7096 2.80791i −0.596393 0.100219i
\(786\) 0 0
\(787\) 28.5379i 1.01727i 0.860983 + 0.508634i \(0.169849\pi\)
−0.860983 + 0.508634i \(0.830151\pi\)
\(788\) 2.68866i 0.0957796i
\(789\) 0 0
\(790\) −3.67409 0.617399i −0.130718 0.0219661i
\(791\) 10.1000 0.359115
\(792\) 0 0
\(793\) 32.5007i 1.15413i
\(794\) −35.0563 −1.24410
\(795\) 0 0
\(796\) 22.9015 0.811722
\(797\)