Properties

Label 1078.2.c.b.1077.13
Level $1078$
Weight $2$
Character 1078.1077
Analytic conductor $8.608$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} - 102 x^{7} + 144 x^{6} - 432 x^{5} + 502 x^{4} + 288 x^{3} + 72 x^{2} + 12 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: no (minimal twist has level 154)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1077.13
Root \(1.60599 + 0.430324i\) of defining polynomial
Character \(\chi\) \(=\) 1078.1077
Dual form 1078.2.c.b.1077.4

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +1.02738i q^{3} -1.00000 q^{4} +1.25868i q^{5} -1.02738 q^{6} -1.00000i q^{8} +1.94448 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +1.02738i q^{3} -1.00000 q^{4} +1.25868i q^{5} -1.02738 q^{6} -1.00000i q^{8} +1.94448 q^{9} -1.25868 q^{10} +(-3.30824 + 0.235617i) q^{11} -1.02738i q^{12} -4.08338 q^{13} -1.29315 q^{15} +1.00000 q^{16} +3.20191 q^{17} +1.94448i q^{18} -7.62813 q^{19} -1.25868i q^{20} +(-0.235617 - 3.30824i) q^{22} -8.25273 q^{23} +1.02738 q^{24} +3.41572 q^{25} -4.08338i q^{26} +5.07988i q^{27} -3.54386i q^{29} -1.29315i q^{30} +9.18338i q^{31} +1.00000i q^{32} +(-0.242069 - 3.39883i) q^{33} +3.20191i q^{34} -1.94448 q^{36} -0.308245 q^{37} -7.62813i q^{38} -4.19520i q^{39} +1.25868 q^{40} -6.05276 q^{41} -7.57607i q^{43} +(3.30824 - 0.235617i) q^{44} +2.44749i q^{45} -8.25273i q^{46} +4.70267i q^{47} +1.02738i q^{48} +3.41572i q^{50} +3.28959i q^{51} +4.08338 q^{52} -4.79659 q^{53} -5.07988 q^{54} +(-0.296567 - 4.16403i) q^{55} -7.83701i q^{57} +3.54386 q^{58} -2.73329i q^{59} +1.29315 q^{60} +1.51010 q^{61} -9.18338 q^{62} -1.00000 q^{64} -5.13968i q^{65} +(3.39883 - 0.242069i) q^{66} +3.38087 q^{67} -3.20191 q^{68} -8.47871i q^{69} +3.50810 q^{71} -1.94448i q^{72} -0.966855 q^{73} -0.308245i q^{74} +3.50925i q^{75} +7.62813 q^{76} +4.19520 q^{78} -15.6129i q^{79} +1.25868i q^{80} +0.614474 q^{81} -6.05276i q^{82} -1.32998 q^{83} +4.03019i q^{85} +7.57607 q^{86} +3.64090 q^{87} +(0.235617 + 3.30824i) q^{88} +10.6498i q^{89} -2.44749 q^{90} +8.25273 q^{92} -9.43485 q^{93} -4.70267 q^{94} -9.60139i q^{95} -1.02738 q^{96} -10.6748i q^{97} +(-6.43283 + 0.458154i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4} - 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{4} - 32 q^{9} - 16 q^{11} - 8 q^{15} + 16 q^{16} - 8 q^{22} - 32 q^{23} + 32 q^{36} + 32 q^{37} + 16 q^{44} + 56 q^{53} + 24 q^{58} + 8 q^{60} - 16 q^{64} - 24 q^{67} + 8 q^{71} - 16 q^{78} + 16 q^{81} - 40 q^{86} + 8 q^{88} + 32 q^{92} + 88 q^{93} + 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(-1\) \(-1\)

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
\(3\) 1.02738i 0.593160i 0.955008 + 0.296580i \(0.0958461\pi\)
−0.955008 + 0.296580i \(0.904154\pi\)
\(4\) −1.00000 −0.500000
\(5\) 1.25868i 0.562900i 0.959576 + 0.281450i \(0.0908153\pi\)
−0.959576 + 0.281450i \(0.909185\pi\)
\(6\) −1.02738 −0.419427
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 1.94448 0.648162
\(10\) −1.25868 −0.398030
\(11\) −3.30824 + 0.235617i −0.997473 + 0.0710412i
\(12\) 1.02738i 0.296580i
\(13\) −4.08338 −1.13253 −0.566263 0.824224i \(-0.691612\pi\)
−0.566263 + 0.824224i \(0.691612\pi\)
\(14\) 0 0
\(15\) −1.29315 −0.333890
\(16\) 1.00000 0.250000
\(17\) 3.20191 0.776578 0.388289 0.921538i \(-0.373066\pi\)
0.388289 + 0.921538i \(0.373066\pi\)
\(18\) 1.94448i 0.458319i
\(19\) −7.62813 −1.75001 −0.875007 0.484111i \(-0.839143\pi\)
−0.875007 + 0.484111i \(0.839143\pi\)
\(20\) 1.25868i 0.281450i
\(21\) 0 0
\(22\) −0.235617 3.30824i −0.0502337 0.705320i
\(23\) −8.25273 −1.72081 −0.860407 0.509608i \(-0.829790\pi\)
−0.860407 + 0.509608i \(0.829790\pi\)
\(24\) 1.02738 0.209714
\(25\) 3.41572 0.683144
\(26\) 4.08338i 0.800817i
\(27\) 5.07988i 0.977623i
\(28\) 0 0
\(29\) 3.54386i 0.658079i −0.944316 0.329039i \(-0.893275\pi\)
0.944316 0.329039i \(-0.106725\pi\)
\(30\) 1.29315i 0.236096i
\(31\) 9.18338i 1.64938i 0.565582 + 0.824692i \(0.308651\pi\)
−0.565582 + 0.824692i \(0.691349\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −0.242069 3.39883i −0.0421388 0.591661i
\(34\) 3.20191i 0.549124i
\(35\) 0 0
\(36\) −1.94448 −0.324081
\(37\) −0.308245 −0.0506752 −0.0253376 0.999679i \(-0.508066\pi\)
−0.0253376 + 0.999679i \(0.508066\pi\)
\(38\) 7.62813i 1.23745i
\(39\) 4.19520i 0.671769i
\(40\) 1.25868 0.199015
\(41\) −6.05276 −0.945283 −0.472641 0.881255i \(-0.656699\pi\)
−0.472641 + 0.881255i \(0.656699\pi\)
\(42\) 0 0
\(43\) 7.57607i 1.15534i −0.816270 0.577670i \(-0.803962\pi\)
0.816270 0.577670i \(-0.196038\pi\)
\(44\) 3.30824 0.235617i 0.498737 0.0355206i
\(45\) 2.44749i 0.364850i
\(46\) 8.25273i 1.21680i
\(47\) 4.70267i 0.685954i 0.939344 + 0.342977i \(0.111435\pi\)
−0.939344 + 0.342977i \(0.888565\pi\)
\(48\) 1.02738i 0.148290i
\(49\) 0 0
\(50\) 3.41572i 0.483056i
\(51\) 3.28959i 0.460635i
\(52\) 4.08338 0.566263
\(53\) −4.79659 −0.658863 −0.329431 0.944180i \(-0.606857\pi\)
−0.329431 + 0.944180i \(0.606857\pi\)
\(54\) −5.07988 −0.691284
\(55\) −0.296567 4.16403i −0.0399891 0.561478i
\(56\) 0 0
\(57\) 7.83701i 1.03804i
\(58\) 3.54386 0.465332
\(59\) 2.73329i 0.355844i −0.984045 0.177922i \(-0.943063\pi\)
0.984045 0.177922i \(-0.0569374\pi\)
\(60\) 1.29315 0.166945
\(61\) 1.51010 0.193349 0.0966743 0.995316i \(-0.469179\pi\)
0.0966743 + 0.995316i \(0.469179\pi\)
\(62\) −9.18338 −1.16629
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 5.13968i 0.637499i
\(66\) 3.39883 0.242069i 0.418368 0.0297966i
\(67\) 3.38087 0.413039 0.206520 0.978442i \(-0.433786\pi\)
0.206520 + 0.978442i \(0.433786\pi\)
\(68\) −3.20191 −0.388289
\(69\) 8.47871i 1.02072i
\(70\) 0 0
\(71\) 3.50810 0.416334 0.208167 0.978093i \(-0.433250\pi\)
0.208167 + 0.978093i \(0.433250\pi\)
\(72\) 1.94448i 0.229160i
\(73\) −0.966855 −0.113162 −0.0565809 0.998398i \(-0.518020\pi\)
−0.0565809 + 0.998398i \(0.518020\pi\)
\(74\) 0.308245i 0.0358327i
\(75\) 3.50925i 0.405213i
\(76\) 7.62813 0.875007
\(77\) 0 0
\(78\) 4.19520 0.475013
\(79\) 15.6129i 1.75659i −0.478117 0.878296i \(-0.658681\pi\)
0.478117 0.878296i \(-0.341319\pi\)
\(80\) 1.25868i 0.140725i
\(81\) 0.614474 0.0682749
\(82\) 6.05276i 0.668416i
\(83\) −1.32998 −0.145984 −0.0729921 0.997333i \(-0.523255\pi\)
−0.0729921 + 0.997333i \(0.523255\pi\)
\(84\) 0 0
\(85\) 4.03019i 0.437136i
\(86\) 7.57607 0.816949
\(87\) 3.64090 0.390346
\(88\) 0.235617 + 3.30824i 0.0251169 + 0.352660i
\(89\) 10.6498i 1.12887i 0.825477 + 0.564436i \(0.190906\pi\)
−0.825477 + 0.564436i \(0.809094\pi\)
\(90\) −2.44749 −0.257988
\(91\) 0 0
\(92\) 8.25273 0.860407
\(93\) −9.43485 −0.978348
\(94\) −4.70267 −0.485043
\(95\) 9.60139i 0.985082i
\(96\) −1.02738 −0.104857
\(97\) 10.6748i 1.08386i −0.840424 0.541930i \(-0.817694\pi\)
0.840424 0.541930i \(-0.182306\pi\)
\(98\) 0 0
\(99\) −6.43283 + 0.458154i −0.646524 + 0.0460462i
\(100\) −3.41572 −0.341572
\(101\) −10.0648 −1.00149 −0.500745 0.865595i \(-0.666941\pi\)
−0.500745 + 0.865595i \(0.666941\pi\)
\(102\) −3.28959 −0.325718
\(103\) 2.88523i 0.284290i 0.989846 + 0.142145i \(0.0453999\pi\)
−0.989846 + 0.142145i \(0.954600\pi\)
\(104\) 4.08338i 0.400409i
\(105\) 0 0
\(106\) 4.79659i 0.465886i
\(107\) 16.3000i 1.57578i 0.615814 + 0.787892i \(0.288827\pi\)
−0.615814 + 0.787892i \(0.711173\pi\)
\(108\) 5.07988i 0.488812i
\(109\) 11.5034i 1.10183i 0.834561 + 0.550915i \(0.185721\pi\)
−0.834561 + 0.550915i \(0.814279\pi\)
\(110\) 4.16403 0.296567i 0.397025 0.0282766i
\(111\) 0.316686i 0.0300585i
\(112\) 0 0
\(113\) 0.558958 0.0525824 0.0262912 0.999654i \(-0.491630\pi\)
0.0262912 + 0.999654i \(0.491630\pi\)
\(114\) 7.83701 0.734003
\(115\) 10.3876i 0.968645i
\(116\) 3.54386i 0.329039i
\(117\) −7.94008 −0.734060
\(118\) 2.73329 0.251619
\(119\) 0 0
\(120\) 1.29315i 0.118048i
\(121\) 10.8890 1.55896i 0.989906 0.141723i
\(122\) 1.51010i 0.136718i
\(123\) 6.21850i 0.560704i
\(124\) 9.18338i 0.824692i
\(125\) 10.5927i 0.947441i
\(126\) 0 0
\(127\) 11.2829i 1.00120i 0.865679 + 0.500599i \(0.166887\pi\)
−0.865679 + 0.500599i \(0.833113\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 7.78352 0.685301
\(130\) 5.13968 0.450780
\(131\) 7.03388 0.614553 0.307276 0.951620i \(-0.400582\pi\)
0.307276 + 0.951620i \(0.400582\pi\)
\(132\) 0.242069 + 3.39883i 0.0210694 + 0.295831i
\(133\) 0 0
\(134\) 3.38087i 0.292063i
\(135\) −6.39395 −0.550304
\(136\) 3.20191i 0.274562i
\(137\) 9.08974 0.776589 0.388294 0.921535i \(-0.373064\pi\)
0.388294 + 0.921535i \(0.373064\pi\)
\(138\) 8.47871 0.721756
\(139\) 7.86546 0.667140 0.333570 0.942725i \(-0.391747\pi\)
0.333570 + 0.942725i \(0.391747\pi\)
\(140\) 0 0
\(141\) −4.83144 −0.406880
\(142\) 3.50810i 0.294393i
\(143\) 13.5088 0.962115i 1.12967 0.0804561i
\(144\) 1.94448 0.162040
\(145\) 4.46060 0.370432
\(146\) 0.966855i 0.0800175i
\(147\) 0 0
\(148\) 0.308245 0.0253376
\(149\) 6.23096i 0.510460i 0.966880 + 0.255230i \(0.0821513\pi\)
−0.966880 + 0.255230i \(0.917849\pi\)
\(150\) −3.50925 −0.286529
\(151\) 17.5101i 1.42495i 0.701696 + 0.712476i \(0.252426\pi\)
−0.701696 + 0.712476i \(0.747574\pi\)
\(152\) 7.62813i 0.618723i
\(153\) 6.22607 0.503348
\(154\) 0 0
\(155\) −11.5590 −0.928438
\(156\) 4.19520i 0.335885i
\(157\) 7.77404i 0.620436i 0.950665 + 0.310218i \(0.100402\pi\)
−0.950665 + 0.310218i \(0.899598\pi\)
\(158\) 15.6129 1.24210
\(159\) 4.92794i 0.390811i
\(160\) −1.25868 −0.0995076
\(161\) 0 0
\(162\) 0.614474i 0.0482776i
\(163\) −18.2123 −1.42650 −0.713249 0.700911i \(-0.752777\pi\)
−0.713249 + 0.700911i \(0.752777\pi\)
\(164\) 6.05276 0.472641
\(165\) 4.27805 0.304688i 0.333046 0.0237199i
\(166\) 1.32998i 0.103226i
\(167\) −14.3653 −1.11162 −0.555809 0.831310i \(-0.687591\pi\)
−0.555809 + 0.831310i \(0.687591\pi\)
\(168\) 0 0
\(169\) 3.67402 0.282617
\(170\) −4.03019 −0.309102
\(171\) −14.8328 −1.13429
\(172\) 7.57607i 0.577670i
\(173\) 4.76319 0.362139 0.181069 0.983470i \(-0.442044\pi\)
0.181069 + 0.983470i \(0.442044\pi\)
\(174\) 3.64090i 0.276016i
\(175\) 0 0
\(176\) −3.30824 + 0.235617i −0.249368 + 0.0177603i
\(177\) 2.80813 0.211072
\(178\) −10.6498 −0.798233
\(179\) −3.89051 −0.290790 −0.145395 0.989374i \(-0.546445\pi\)
−0.145395 + 0.989374i \(0.546445\pi\)
\(180\) 2.44749i 0.182425i
\(181\) 13.0698i 0.971474i −0.874105 0.485737i \(-0.838551\pi\)
0.874105 0.485737i \(-0.161449\pi\)
\(182\) 0 0
\(183\) 1.55145i 0.114687i
\(184\) 8.25273i 0.608399i
\(185\) 0.387982i 0.0285250i
\(186\) 9.43485i 0.691797i
\(187\) −10.5927 + 0.754426i −0.774616 + 0.0551691i
\(188\) 4.70267i 0.342977i
\(189\) 0 0
\(190\) 9.60139 0.696558
\(191\) 6.00000 0.434145 0.217072 0.976156i \(-0.430349\pi\)
0.217072 + 0.976156i \(0.430349\pi\)
\(192\) 1.02738i 0.0741450i
\(193\) 9.38289i 0.675395i −0.941255 0.337698i \(-0.890352\pi\)
0.941255 0.337698i \(-0.109648\pi\)
\(194\) 10.6748 0.766405
\(195\) 5.28042 0.378139
\(196\) 0 0
\(197\) 17.3471i 1.23593i 0.786205 + 0.617966i \(0.212043\pi\)
−0.786205 + 0.617966i \(0.787957\pi\)
\(198\) −0.458154 6.43283i −0.0325596 0.457161i
\(199\) 2.92547i 0.207381i −0.994610 0.103690i \(-0.966935\pi\)
0.994610 0.103690i \(-0.0330651\pi\)
\(200\) 3.41572i 0.241528i
\(201\) 3.47345i 0.244998i
\(202\) 10.0648i 0.708160i
\(203\) 0 0
\(204\) 3.28959i 0.230317i
\(205\) 7.61851i 0.532100i
\(206\) −2.88523 −0.201023
\(207\) −16.0473 −1.11536
\(208\) −4.08338 −0.283132
\(209\) 25.2357 1.79732i 1.74559 0.124323i
\(210\) 0 0
\(211\) 0.252729i 0.0173986i 0.999962 + 0.00869931i \(0.00276911\pi\)
−0.999962 + 0.00869931i \(0.997231\pi\)
\(212\) 4.79659 0.329431
\(213\) 3.60416i 0.246953i
\(214\) −16.3000 −1.11425
\(215\) 9.53587 0.650341
\(216\) 5.07988 0.345642
\(217\) 0 0
\(218\) −11.5034 −0.779111
\(219\) 0.993331i 0.0671231i
\(220\) 0.296567 + 4.16403i 0.0199946 + 0.280739i
\(221\) −13.0746 −0.879496
\(222\) 0.316686 0.0212545
\(223\) 19.0370i 1.27482i 0.770527 + 0.637408i \(0.219993\pi\)
−0.770527 + 0.637408i \(0.780007\pi\)
\(224\) 0 0
\(225\) 6.64181 0.442788
\(226\) 0.558958i 0.0371814i
\(227\) −18.4070 −1.22172 −0.610858 0.791740i \(-0.709175\pi\)
−0.610858 + 0.791740i \(0.709175\pi\)
\(228\) 7.83701i 0.519019i
\(229\) 5.30786i 0.350753i −0.984501 0.175377i \(-0.943886\pi\)
0.984501 0.175377i \(-0.0561143\pi\)
\(230\) 10.3876 0.684936
\(231\) 0 0
\(232\) −3.54386 −0.232666
\(233\) 21.3192i 1.39666i 0.715774 + 0.698332i \(0.246074\pi\)
−0.715774 + 0.698332i \(0.753926\pi\)
\(234\) 7.94008i 0.519059i
\(235\) −5.91916 −0.386124
\(236\) 2.73329i 0.177922i
\(237\) 16.0405 1.04194
\(238\) 0 0
\(239\) 7.25163i 0.469069i 0.972108 + 0.234535i \(0.0753566\pi\)
−0.972108 + 0.234535i \(0.924643\pi\)
\(240\) −1.29315 −0.0834724
\(241\) 3.55410 0.228939 0.114470 0.993427i \(-0.463483\pi\)
0.114470 + 0.993427i \(0.463483\pi\)
\(242\) 1.55896 + 10.8890i 0.100214 + 0.699969i
\(243\) 15.8709i 1.01812i
\(244\) −1.51010 −0.0966743
\(245\) 0 0
\(246\) 6.21850 0.396477
\(247\) 31.1486 1.98194
\(248\) 9.18338 0.583145
\(249\) 1.36640i 0.0865919i
\(250\) −10.5927 −0.669942
\(251\) 0.735728i 0.0464387i 0.999730 + 0.0232194i \(0.00739162\pi\)
−0.999730 + 0.0232194i \(0.992608\pi\)
\(252\) 0 0
\(253\) 27.3021 1.94448i 1.71647 0.122249i
\(254\) −11.2829 −0.707954
\(255\) −4.14055 −0.259291
\(256\) 1.00000 0.0625000
\(257\) 16.2065i 1.01093i −0.862846 0.505467i \(-0.831320\pi\)
0.862846 0.505467i \(-0.168680\pi\)
\(258\) 7.78352i 0.484581i
\(259\) 0 0
\(260\) 5.13968i 0.318750i
\(261\) 6.89099i 0.426541i
\(262\) 7.03388i 0.434555i
\(263\) 24.3021i 1.49853i 0.662271 + 0.749264i \(0.269593\pi\)
−0.662271 + 0.749264i \(0.730407\pi\)
\(264\) −3.39883 + 0.242069i −0.209184 + 0.0148983i
\(265\) 6.03738i 0.370874i
\(266\) 0 0
\(267\) −10.9414 −0.669601
\(268\) −3.38087 −0.206520
\(269\) 27.0484i 1.64917i 0.565737 + 0.824586i \(0.308592\pi\)
−0.565737 + 0.824586i \(0.691408\pi\)
\(270\) 6.39395i 0.389124i
\(271\) 10.4433 0.634386 0.317193 0.948361i \(-0.397260\pi\)
0.317193 + 0.948361i \(0.397260\pi\)
\(272\) 3.20191 0.194145
\(273\) 0 0
\(274\) 9.08974i 0.549131i
\(275\) −11.3000 + 0.804802i −0.681418 + 0.0485314i
\(276\) 8.47871i 0.510359i
\(277\) 20.4006i 1.22575i −0.790178 0.612877i \(-0.790012\pi\)
0.790178 0.612877i \(-0.209988\pi\)
\(278\) 7.86546i 0.471739i
\(279\) 17.8569i 1.06907i
\(280\) 0 0
\(281\) 9.99535i 0.596272i 0.954523 + 0.298136i \(0.0963650\pi\)
−0.954523 + 0.298136i \(0.903635\pi\)
\(282\) 4.83144i 0.287708i
\(283\) 3.48896 0.207397 0.103699 0.994609i \(-0.466932\pi\)
0.103699 + 0.994609i \(0.466932\pi\)
\(284\) −3.50810 −0.208167
\(285\) 9.86431 0.584311
\(286\) 0.962115 + 13.5088i 0.0568911 + 0.798794i
\(287\) 0 0
\(288\) 1.94448i 0.114580i
\(289\) −6.74775 −0.396926
\(290\) 4.46060i 0.261935i
\(291\) 10.9671 0.642902
\(292\) 0.966855 0.0565809
\(293\) −17.3549 −1.01388 −0.506942 0.861980i \(-0.669224\pi\)
−0.506942 + 0.861980i \(0.669224\pi\)
\(294\) 0 0
\(295\) 3.44034 0.200304
\(296\) 0.308245i 0.0179164i
\(297\) −1.19691 16.8055i −0.0694516 0.975153i
\(298\) −6.23096 −0.360950
\(299\) 33.6991 1.94887
\(300\) 3.50925i 0.202607i
\(301\) 0 0
\(302\) −17.5101 −1.00759
\(303\) 10.3405i 0.594044i
\(304\) −7.62813 −0.437503
\(305\) 1.90074i 0.108836i
\(306\) 6.22607i 0.355921i
\(307\) 22.6829 1.29458 0.647290 0.762244i \(-0.275902\pi\)
0.647290 + 0.762244i \(0.275902\pi\)
\(308\) 0 0
\(309\) −2.96423 −0.168629
\(310\) 11.5590i 0.656505i
\(311\) 6.64116i 0.376585i −0.982113 0.188293i \(-0.939705\pi\)
0.982113 0.188293i \(-0.0602954\pi\)
\(312\) −4.19520 −0.237506
\(313\) 0.502967i 0.0284294i −0.999899 0.0142147i \(-0.995475\pi\)
0.999899 0.0142147i \(-0.00452483\pi\)
\(314\) −7.77404 −0.438715
\(315\) 0 0
\(316\) 15.6129i 0.878296i
\(317\) −10.5487 −0.592476 −0.296238 0.955114i \(-0.595732\pi\)
−0.296238 + 0.955114i \(0.595732\pi\)
\(318\) 4.92794 0.276345
\(319\) 0.834995 + 11.7240i 0.0467507 + 0.656416i
\(320\) 1.25868i 0.0703625i
\(321\) −16.7464 −0.934692
\(322\) 0 0
\(323\) −24.4246 −1.35902
\(324\) −0.614474 −0.0341374
\(325\) −13.9477 −0.773679
\(326\) 18.2123i 1.00869i
\(327\) −11.8184 −0.653561
\(328\) 6.05276i 0.334208i
\(329\) 0 0
\(330\) 0.304688 + 4.27805i 0.0167725 + 0.235499i
\(331\) −5.78058 −0.317729 −0.158865 0.987300i \(-0.550783\pi\)
−0.158865 + 0.987300i \(0.550783\pi\)
\(332\) 1.32998 0.0729921
\(333\) −0.599378 −0.0328457
\(334\) 14.3653i 0.786033i
\(335\) 4.25544i 0.232500i
\(336\) 0 0
\(337\) 11.1226i 0.605885i 0.953009 + 0.302943i \(0.0979690\pi\)
−0.953009 + 0.302943i \(0.902031\pi\)
\(338\) 3.67402i 0.199840i
\(339\) 0.574264i 0.0311898i
\(340\) 4.03019i 0.218568i
\(341\) −2.16376 30.3809i −0.117174 1.64522i
\(342\) 14.8328i 0.802065i
\(343\) 0 0
\(344\) −7.57607 −0.408474
\(345\) 10.6720 0.574561
\(346\) 4.76319i 0.256071i
\(347\) 14.6714i 0.787601i 0.919196 + 0.393801i \(0.128840\pi\)
−0.919196 + 0.393801i \(0.871160\pi\)
\(348\) −3.64090 −0.195173
\(349\) 24.6769 1.32093 0.660463 0.750859i \(-0.270360\pi\)
0.660463 + 0.750859i \(0.270360\pi\)
\(350\) 0 0
\(351\) 20.7431i 1.10718i
\(352\) −0.235617 3.30824i −0.0125584 0.176330i
\(353\) 19.2447i 1.02429i 0.858898 + 0.512147i \(0.171150\pi\)
−0.858898 + 0.512147i \(0.828850\pi\)
\(354\) 2.80813i 0.149250i
\(355\) 4.41558i 0.234355i
\(356\) 10.6498i 0.564436i
\(357\) 0 0
\(358\) 3.89051i 0.205620i
\(359\) 3.29407i 0.173854i 0.996215 + 0.0869271i \(0.0277047\pi\)
−0.996215 + 0.0869271i \(0.972295\pi\)
\(360\) 2.44749 0.128994
\(361\) 39.1884 2.06255
\(362\) 13.0698 0.686936
\(363\) 1.60165 + 11.1871i 0.0840647 + 0.587173i
\(364\) 0 0
\(365\) 1.21696i 0.0636988i
\(366\) −1.55145 −0.0810956
\(367\) 30.9410i 1.61511i −0.589793 0.807555i \(-0.700791\pi\)
0.589793 0.807555i \(-0.299209\pi\)
\(368\) −8.25273 −0.430203
\(369\) −11.7695 −0.612696
\(370\) 0.387982 0.0201702
\(371\) 0 0
\(372\) 9.43485 0.489174
\(373\) 0.961597i 0.0497896i 0.999690 + 0.0248948i \(0.00792508\pi\)
−0.999690 + 0.0248948i \(0.992075\pi\)
\(374\) −0.754426 10.5927i −0.0390104 0.547736i
\(375\) −10.8828 −0.561984
\(376\) 4.70267 0.242521
\(377\) 14.4709i 0.745292i
\(378\) 0 0
\(379\) −1.41216 −0.0725379 −0.0362689 0.999342i \(-0.511547\pi\)
−0.0362689 + 0.999342i \(0.511547\pi\)
\(380\) 9.60139i 0.492541i
\(381\) −11.5919 −0.593870
\(382\) 6.00000i 0.306987i
\(383\) 3.78079i 0.193189i 0.995324 + 0.0965946i \(0.0307950\pi\)
−0.995324 + 0.0965946i \(0.969205\pi\)
\(384\) 1.02738 0.0524284
\(385\) 0 0
\(386\) 9.38289 0.477576
\(387\) 14.7316i 0.748847i
\(388\) 10.6748i 0.541930i
\(389\) −3.37886 −0.171315 −0.0856574 0.996325i \(-0.527299\pi\)
−0.0856574 + 0.996325i \(0.527299\pi\)
\(390\) 5.28042i 0.267385i
\(391\) −26.4245 −1.33635
\(392\) 0 0
\(393\) 7.22649i 0.364528i
\(394\) −17.3471 −0.873935
\(395\) 19.6517 0.988785
\(396\) 6.43283 0.458154i 0.323262 0.0230231i
\(397\) 11.5300i 0.578673i −0.957227 0.289336i \(-0.906565\pi\)
0.957227 0.289336i \(-0.0934346\pi\)
\(398\) 2.92547 0.146640
\(399\) 0 0
\(400\) 3.41572 0.170786
\(401\) 26.0523 1.30099 0.650494 0.759512i \(-0.274562\pi\)
0.650494 + 0.759512i \(0.274562\pi\)
\(402\) −3.47345 −0.173240
\(403\) 37.4993i 1.86797i
\(404\) 10.0648 0.500745
\(405\) 0.773427i 0.0384319i
\(406\) 0 0
\(407\) 1.01975 0.0726278i 0.0505471 0.00360003i
\(408\) 3.28959 0.162859
\(409\) −35.0217 −1.73171 −0.865856 0.500293i \(-0.833226\pi\)
−0.865856 + 0.500293i \(0.833226\pi\)
\(410\) 7.61851 0.376251
\(411\) 9.33864i 0.460641i
\(412\) 2.88523i 0.142145i
\(413\) 0 0
\(414\) 16.0473i 0.788682i
\(415\) 1.67402i 0.0821745i
\(416\) 4.08338i 0.200204i
\(417\) 8.08084i 0.395720i
\(418\) 1.79732 + 25.2357i 0.0879097 + 1.23432i
\(419\) 12.1242i 0.592307i −0.955140 0.296154i \(-0.904296\pi\)
0.955140 0.296154i \(-0.0957040\pi\)
\(420\) 0 0
\(421\) 18.6940 0.911089 0.455545 0.890213i \(-0.349445\pi\)
0.455545 + 0.890213i \(0.349445\pi\)
\(422\) −0.252729 −0.0123027
\(423\) 9.14426i 0.444609i
\(424\) 4.79659i 0.232943i
\(425\) 10.9368 0.530515
\(426\) −3.60416 −0.174622
\(427\) 0 0
\(428\) 16.3000i 0.787892i
\(429\) 0.988461 + 13.8787i 0.0477233 + 0.670072i
\(430\) 9.53587i 0.459860i
\(431\) 33.9418i 1.63492i −0.575984 0.817461i \(-0.695381\pi\)
0.575984 0.817461i \(-0.304619\pi\)
\(432\) 5.07988i 0.244406i
\(433\) 27.0949i 1.30210i −0.759037 0.651048i \(-0.774330\pi\)
0.759037 0.651048i \(-0.225670\pi\)
\(434\) 0 0
\(435\) 4.58274i 0.219726i
\(436\) 11.5034i 0.550915i
\(437\) 62.9529 3.01145
\(438\) 0.993331 0.0474632
\(439\) −20.4538 −0.976208 −0.488104 0.872785i \(-0.662311\pi\)
−0.488104 + 0.872785i \(0.662311\pi\)
\(440\) −4.16403 + 0.296567i −0.198512 + 0.0141383i
\(441\) 0 0
\(442\) 13.0746i 0.621897i
\(443\) −3.59736 −0.170916 −0.0854579 0.996342i \(-0.527235\pi\)
−0.0854579 + 0.996342i \(0.527235\pi\)
\(444\) 0.316686i 0.0150292i
\(445\) −13.4047 −0.635442
\(446\) −19.0370 −0.901430
\(447\) −6.40159 −0.302785
\(448\) 0 0
\(449\) 37.0664 1.74927 0.874637 0.484779i \(-0.161100\pi\)
0.874637 + 0.484779i \(0.161100\pi\)
\(450\) 6.64181i 0.313098i
\(451\) 20.0240 1.42613i 0.942894 0.0671541i
\(452\) −0.558958 −0.0262912
\(453\) −17.9896 −0.845225
\(454\) 18.4070i 0.863883i
\(455\) 0 0
\(456\) −7.83701 −0.367002
\(457\) 18.1512i 0.849078i 0.905410 + 0.424539i \(0.139564\pi\)
−0.905410 + 0.424539i \(0.860436\pi\)
\(458\) 5.30786 0.248020
\(459\) 16.2653i 0.759201i
\(460\) 10.3876i 0.484323i
\(461\) −22.4278 −1.04457 −0.522284 0.852772i \(-0.674920\pi\)
−0.522284 + 0.852772i \(0.674920\pi\)
\(462\) 0 0
\(463\) −15.6274 −0.726267 −0.363134 0.931737i \(-0.618293\pi\)
−0.363134 + 0.931737i \(0.618293\pi\)
\(464\) 3.54386i 0.164520i
\(465\) 11.8755i 0.550712i
\(466\) −21.3192 −0.987591
\(467\) 6.09520i 0.282052i −0.990006 0.141026i \(-0.954960\pi\)
0.990006 0.141026i \(-0.0450402\pi\)
\(468\) 7.94008 0.367030
\(469\) 0 0
\(470\) 5.91916i 0.273031i
\(471\) −7.98692 −0.368018
\(472\) −2.73329 −0.125810
\(473\) 1.78505 + 25.0635i 0.0820768 + 1.15242i
\(474\) 16.0405i 0.736763i
\(475\) −26.0556 −1.19551
\(476\) 0 0
\(477\) −9.32690 −0.427049
\(478\) −7.25163 −0.331682
\(479\) 30.6275 1.39941 0.699704 0.714433i \(-0.253315\pi\)
0.699704 + 0.714433i \(0.253315\pi\)
\(480\) 1.29315i 0.0590239i
\(481\) 1.25868 0.0573910
\(482\) 3.55410i 0.161885i
\(483\) 0 0
\(484\) −10.8890 + 1.55896i −0.494953 + 0.0708617i
\(485\) 13.4362 0.610105
\(486\) −15.8709 −0.719920
\(487\) −3.17453 −0.143852 −0.0719258 0.997410i \(-0.522914\pi\)
−0.0719258 + 0.997410i \(0.522914\pi\)
\(488\) 1.51010i 0.0683590i
\(489\) 18.7110i 0.846141i
\(490\) 0 0
\(491\) 32.6507i 1.47351i −0.676162 0.736753i \(-0.736358\pi\)
0.676162 0.736753i \(-0.263642\pi\)
\(492\) 6.21850i 0.280352i
\(493\) 11.3471i 0.511050i
\(494\) 31.1486i 1.40144i
\(495\) −0.576670 8.09689i −0.0259194 0.363928i
\(496\) 9.18338i 0.412346i
\(497\) 0 0
\(498\) 1.36640 0.0612297
\(499\) 28.4548 1.27381 0.636906 0.770941i \(-0.280214\pi\)
0.636906 + 0.770941i \(0.280214\pi\)
\(500\) 10.5927i 0.473721i
\(501\) 14.7586i 0.659367i
\(502\) −0.735728 −0.0328372
\(503\) 22.5058 1.00348 0.501741 0.865018i \(-0.332693\pi\)
0.501741 + 0.865018i \(0.332693\pi\)
\(504\) 0 0
\(505\) 12.6684i 0.563739i
\(506\) 1.94448 + 27.3021i 0.0864429 + 1.21372i
\(507\) 3.77463i 0.167637i
\(508\) 11.2829i 0.500599i
\(509\) 13.4450i 0.595939i −0.954575 0.297969i \(-0.903691\pi\)
0.954575 0.297969i \(-0.0963093\pi\)
\(510\) 4.14055i 0.183347i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 38.7500i 1.71085i
\(514\) 16.2065 0.714838
\(515\) −3.63159 −0.160027
\(516\) −7.78352 −0.342651
\(517\) −1.10803 15.5576i −0.0487310 0.684221i
\(518\) 0 0
\(519\) 4.89362i 0.214806i
\(520\) −5.13968 −0.225390
\(521\) 39.5299i 1.73184i −0.500187 0.865918i \(-0.666735\pi\)
0.500187 0.865918i \(-0.333265\pi\)
\(522\) 6.89099 0.301610
\(523\) −29.6122 −1.29485 −0.647425 0.762129i \(-0.724154\pi\)
−0.647425 + 0.762129i \(0.724154\pi\)
\(524\) −7.03388 −0.307276
\(525\) 0 0
\(526\) −24.3021 −1.05962
\(527\) 29.4044i 1.28088i
\(528\) −0.242069 3.39883i −0.0105347 0.147915i
\(529\) 45.1075 1.96120
\(530\) 6.03738 0.262247
\(531\) 5.31483i 0.230644i
\(532\) 0 0
\(533\) 24.7158 1.07056
\(534\) 10.9414i 0.473479i
\(535\) −20.5166 −0.887008
\(536\) 3.38087i 0.146031i
\(537\) 3.99704i 0.172485i
\(538\) −27.0484 −1.16614
\(539\) 0 0
\(540\) 6.39395 0.275152
\(541\) 17.4488i 0.750185i −0.926987 0.375092i \(-0.877611\pi\)
0.926987 0.375092i \(-0.122389\pi\)
\(542\) 10.4433i 0.448579i
\(543\) 13.4277 0.576239
\(544\) 3.20191i 0.137281i
\(545\) −14.4792 −0.620220
\(546\) 0 0
\(547\) 1.16878i 0.0499734i −0.999688 0.0249867i \(-0.992046\pi\)
0.999688 0.0249867i \(-0.00795434\pi\)
\(548\) −9.08974 −0.388294
\(549\) 2.93637 0.125321
\(550\) −0.804802 11.3000i −0.0343169 0.481835i
\(551\) 27.0330i 1.15165i
\(552\) −8.47871 −0.360878
\(553\) 0 0
\(554\) 20.4006 0.866739
\(555\) 0.398606 0.0169199
\(556\) −7.86546 −0.333570
\(557\) 4.85149i 0.205564i 0.994704 + 0.102782i \(0.0327744\pi\)
−0.994704 + 0.102782i \(0.967226\pi\)
\(558\) −17.8569 −0.755945
\(559\) 30.9360i 1.30845i
\(560\) 0 0
\(561\) −0.775084 10.8828i −0.0327241 0.459471i
\(562\) −9.99535 −0.421628
\(563\) −26.1145 −1.10059 −0.550297 0.834969i \(-0.685486\pi\)
−0.550297 + 0.834969i \(0.685486\pi\)
\(564\) 4.83144 0.203440
\(565\) 0.703551i 0.0295986i
\(566\) 3.48896i 0.146652i
\(567\) 0 0
\(568\) 3.50810i 0.147196i
\(569\) 7.48146i 0.313639i 0.987627 + 0.156820i \(0.0501241\pi\)
−0.987627 + 0.156820i \(0.949876\pi\)
\(570\) 9.86431i 0.413170i
\(571\) 32.9377i 1.37840i −0.724572 0.689199i \(-0.757962\pi\)
0.724572 0.689199i \(-0.242038\pi\)
\(572\) −13.5088 + 0.962115i −0.564833 + 0.0402281i
\(573\) 6.16430i 0.257517i
\(574\) 0 0
\(575\) −28.1890 −1.17556
\(576\) −1.94448 −0.0810202
\(577\) 1.55542i 0.0647530i −0.999476 0.0323765i \(-0.989692\pi\)
0.999476 0.0323765i \(-0.0103076\pi\)
\(578\) 6.74775i 0.280669i
\(579\) 9.63982 0.400617
\(580\) −4.46060 −0.185216
\(581\) 0 0
\(582\) 10.9671i 0.454600i
\(583\) 15.8683 1.13016i 0.657198 0.0468064i
\(584\) 0.966855i 0.0400088i
\(585\) 9.99403i 0.413202i
\(586\) 17.3549i 0.716924i
\(587\) 42.8124i 1.76706i 0.468376 + 0.883529i \(0.344839\pi\)
−0.468376 + 0.883529i \(0.655161\pi\)
\(588\) 0 0
\(589\) 70.0520i 2.88644i
\(590\) 3.44034i 0.141637i
\(591\) −17.8221 −0.733105
\(592\) −0.308245 −0.0126688
\(593\) −33.5422 −1.37741 −0.688707 0.725039i \(-0.741822\pi\)
−0.688707 + 0.725039i \(0.741822\pi\)
\(594\) 16.8055 1.19691i 0.689537 0.0491097i
\(595\) 0 0
\(596\) 6.23096i 0.255230i
\(597\) 3.00557 0.123010
\(598\) 33.6991i 1.37806i
\(599\) 14.0171 0.572724 0.286362 0.958122i \(-0.407554\pi\)
0.286362 + 0.958122i \(0.407554\pi\)
\(600\) 3.50925 0.143265
\(601\) −36.1513 −1.47464 −0.737322 0.675542i \(-0.763910\pi\)
−0.737322 + 0.675542i \(0.763910\pi\)
\(602\) 0 0
\(603\) 6.57405 0.267716
\(604\) 17.5101i 0.712476i
\(605\) 1.96223 + 13.7058i 0.0797761 + 0.557218i
\(606\) 10.3405 0.420052
\(607\) −29.6393 −1.20302 −0.601511 0.798865i \(-0.705434\pi\)
−0.601511 + 0.798865i \(0.705434\pi\)
\(608\) 7.62813i 0.309362i
\(609\) 0 0
\(610\) −1.90074 −0.0769586
\(611\) 19.2028i 0.776862i
\(612\) −6.22607 −0.251674
\(613\) 33.4822i 1.35233i 0.736750 + 0.676166i \(0.236360\pi\)
−0.736750 + 0.676166i \(0.763640\pi\)
\(614\) 22.6829i 0.915406i
\(615\) 7.82712 0.315620
\(616\) 0 0
\(617\) 8.79395 0.354031 0.177016 0.984208i \(-0.443356\pi\)
0.177016 + 0.984208i \(0.443356\pi\)
\(618\) 2.96423i 0.119239i
\(619\) 27.9952i 1.12522i −0.826722 0.562610i \(-0.809797\pi\)
0.826722 0.562610i \(-0.190203\pi\)
\(620\) 11.5590 0.464219
\(621\) 41.9229i 1.68231i
\(622\) 6.64116 0.266286
\(623\) 0 0
\(624\) 4.19520i 0.167942i
\(625\) 3.74573 0.149829
\(626\) 0.502967 0.0201026
\(627\) 1.84653 + 25.9268i 0.0737435 + 1.03541i
\(628\) 7.77404i 0.310218i
\(629\) −0.986974 −0.0393532
\(630\) 0 0
\(631\) −0.154087 −0.00613412 −0.00306706 0.999995i \(-0.500976\pi\)
−0.00306706 + 0.999995i \(0.500976\pi\)
\(632\) −15.6129 −0.621049
\(633\) −0.259650 −0.0103202
\(634\) 10.5487i 0.418944i
\(635\) −14.2016 −0.563574
\(636\) 4.92794i 0.195405i
\(637\) 0 0
\(638\) −11.7240 + 0.834995i −0.464156 + 0.0330578i
\(639\) 6.82144 0.269852
\(640\) 1.25868 0.0497538
\(641\) −19.8403 −0.783646 −0.391823 0.920041i \(-0.628155\pi\)
−0.391823 + 0.920041i \(0.628155\pi\)
\(642\) 16.7464i 0.660927i
\(643\) 25.2948i 0.997529i −0.866737 0.498765i \(-0.833787\pi\)
0.866737 0.498765i \(-0.166213\pi\)
\(644\) 0 0
\(645\) 9.79699i 0.385756i
\(646\) 24.4246i 0.960974i
\(647\) 0.939459i 0.0369340i −0.999829 0.0184670i \(-0.994121\pi\)
0.999829 0.0184670i \(-0.00587856\pi\)
\(648\) 0.614474i 0.0241388i
\(649\) 0.644009 + 9.04238i 0.0252796 + 0.354944i
\(650\) 13.9477i 0.547073i
\(651\) 0 0
\(652\) 18.2123 0.713249
\(653\) −11.0075 −0.430757 −0.215379 0.976531i \(-0.569099\pi\)
−0.215379 + 0.976531i \(0.569099\pi\)
\(654\) 11.8184i 0.462138i
\(655\) 8.85342i 0.345932i
\(656\) −6.05276 −0.236321
\(657\) −1.88004 −0.0733472
\(658\) 0 0
\(659\) 29.9068i 1.16500i 0.812830 + 0.582501i \(0.197926\pi\)
−0.812830 + 0.582501i \(0.802074\pi\)
\(660\) −4.27805 + 0.304688i −0.166523 + 0.0118600i
\(661\) 2.68925i 0.104600i −0.998631 0.0522999i \(-0.983345\pi\)
0.998631 0.0522999i \(-0.0166552\pi\)
\(662\) 5.78058i 0.224668i
\(663\) 13.4327i 0.521681i
\(664\) 1.32998i 0.0516132i
\(665\) 0 0
\(666\) 0.599378i 0.0232254i
\(667\) 29.2465i 1.13243i
\(668\) 14.3653 0.555809
\(669\) −19.5583 −0.756169
\(670\) −4.25544 −0.164402
\(671\) −4.99578 + 0.355806i −0.192860 + 0.0137357i
\(672\) 0 0
\(673\) 3.56361i 0.137367i −0.997638 0.0686836i \(-0.978120\pi\)
0.997638 0.0686836i \(-0.0218799\pi\)
\(674\) −11.1226 −0.428425
\(675\) 17.3514i 0.667857i
\(676\) −3.67402 −0.141309
\(677\) 31.1803 1.19836 0.599178 0.800616i \(-0.295494\pi\)
0.599178 + 0.800616i \(0.295494\pi\)
\(678\) −0.574264 −0.0220545
\(679\) 0 0
\(680\) 4.03019 0.154551
\(681\) 18.9110i 0.724672i
\(682\) 30.3809 2.16376i 1.16334 0.0828547i
\(683\) −15.5999 −0.596912 −0.298456 0.954423i \(-0.596472\pi\)
−0.298456 + 0.954423i \(0.596472\pi\)
\(684\) 14.8328 0.567146
\(685\) 11.4411i 0.437142i
\(686\) 0 0
\(687\) 5.45320 0.208053
\(688\) 7.57607i 0.288835i
\(689\) 19.5863 0.746179
\(690\) 10.6720i 0.406276i
\(691\) 36.8236i 1.40084i −0.713732 0.700419i \(-0.752997\pi\)
0.713732 0.700419i \(-0.247003\pi\)
\(692\) −4.76319 −0.181069
\(693\) 0 0
\(694\) −14.6714 −0.556918
\(695\) 9.90012i 0.375533i
\(696\) 3.64090i 0.138008i
\(697\) −19.3804 −0.734086
\(698\) 24.6769i 0.934036i
\(699\) −21.9029 −0.828445
\(700\) 0 0
\(701\) 15.6940i 0.592754i −0.955071 0.296377i \(-0.904222\pi\)
0.955071 0.296377i \(-0.0957784\pi\)
\(702\) 20.7431 0.782898
\(703\) 2.35133 0.0886822
\(704\) 3.30824 0.235617i 0.124684 0.00888016i
\(705\) 6.08125i 0.229033i
\(706\) −19.2447 −0.724285
\(707\) 0 0
\(708\) −2.80813 −0.105536
\(709\) −24.3465 −0.914352 −0.457176 0.889376i \(-0.651139\pi\)
−0.457176 + 0.889376i \(0.651139\pi\)
\(710\) −4.41558 −0.165714
\(711\) 30.3591i 1.13856i
\(712\) 10.6498 0.399116
\(713\) 75.7880i 2.83828i
\(714\) 0 0
\(715\) 1.21100 + 17.0033i 0.0452887 + 0.635888i
\(716\) 3.89051 0.145395
\(717\) −7.45020 −0.278233
\(718\) −3.29407 −0.122934
\(719\) 42.6166i 1.58933i 0.607048 + 0.794665i \(0.292354\pi\)
−0.607048 + 0.794665i \(0.707646\pi\)
\(720\) 2.44749i 0.0912125i
\(721\) 0 0
\(722\) 39.1884i 1.45844i
\(723\) 3.65142i 0.135798i
\(724\) 13.0698i 0.485737i
\(725\) 12.1048i 0.449562i
\(726\) −11.1871 + 1.60165i −0.415194 + 0.0594427i
\(727\) 23.2698i 0.863031i 0.902106 + 0.431515i \(0.142021\pi\)
−0.902106 + 0.431515i \(0.857979\pi\)
\(728\) 0 0
\(729\) −14.4621 −0.535633
\(730\) 1.21696 0.0450419
\(731\) 24.2579i 0.897212i
\(732\) 1.55145i 0.0573433i
\(733\) 37.6757 1.39158 0.695791 0.718244i \(-0.255054\pi\)
0.695791 + 0.718244i \(0.255054\pi\)
\(734\) 30.9410 1.14205
\(735\) 0 0
\(736\) 8.25273i 0.304200i
\(737\) −11.1848 + 0.796592i −0.411996 + 0.0293428i
\(738\) 11.7695i 0.433241i
\(739\) 0.554007i 0.0203795i −0.999948 0.0101897i \(-0.996756\pi\)
0.999948 0.0101897i \(-0.00324355\pi\)
\(740\) 0.387982i 0.0142625i
\(741\) 32.0015i 1.17561i
\(742\) 0 0
\(743\) 20.1974i 0.740972i −0.928838 0.370486i \(-0.879191\pi\)
0.928838 0.370486i \(-0.120809\pi\)
\(744\) 9.43485i 0.345898i
\(745\) −7.84280 −0.287338
\(746\) −0.961597 −0.0352066
\(747\) −2.58612 −0.0946213
\(748\) 10.5927 0.754426i 0.387308 0.0275845i
\(749\) 0 0
\(750\) 10.8828i 0.397383i
\(751\) 7.40062 0.270053 0.135026 0.990842i \(-0.456888\pi\)
0.135026 + 0.990842i \(0.456888\pi\)
\(752\) 4.70267i 0.171489i
\(753\) −0.755874 −0.0275456
\(754\) −14.4709 −0.527001
\(755\) −22.0397 −0.802106
\(756\) 0 0
\(757\) −29.1994 −1.06127 −0.530636 0.847600i \(-0.678047\pi\)
−0.530636 + 0.847600i \(0.678047\pi\)
\(758\) 1.41216i 0.0512920i
\(759\) 1.99773 + 28.0497i 0.0725130 + 1.01814i
\(760\) −9.60139 −0.348279
\(761\) 50.9662 1.84752 0.923761 0.382968i \(-0.125098\pi\)
0.923761 + 0.382968i \(0.125098\pi\)
\(762\) 11.5919i 0.419930i
\(763\) 0 0
\(764\) −6.00000 −0.217072
\(765\) 7.83665i 0.283335i
\(766\) −3.78079 −0.136605
\(767\) 11.1611i 0.403002i
\(768\) 1.02738i 0.0370725i
\(769\) 32.9963 1.18988 0.594938 0.803771i \(-0.297176\pi\)
0.594938 + 0.803771i \(0.297176\pi\)
\(770\) 0 0
\(771\) 16.6503 0.599645
\(772\) 9.38289i 0.337698i
\(773\) 32.5391i 1.17035i 0.810907 + 0.585175i \(0.198974\pi\)
−0.810907 + 0.585175i \(0.801026\pi\)
\(774\) 14.7316 0.529515
\(775\) 31.3678i 1.12677i
\(776\) −10.6748 −0.383202
\(777\) 0 0
\(778\) 3.37886i 0.121138i
\(779\) 46.1713 1.65426
\(780\) −5.28042 −0.189069
\(781\) −11.6056 + 0.826568i −0.415283 + 0.0295769i
\(782\) 26.4245i 0.944939i
\(783\) 18.0024 0.643353
\(784\) 0 0
\(785\) −9.78505 −0.349243
\(786\) −7.22649 −0.257760
\(787\) 20.1154 0.717038 0.358519 0.933522i \(-0.383282\pi\)
0.358519 + 0.933522i \(0.383282\pi\)
\(788\) 17.3471i 0.617966i
\(789\) −24.9675 −0.888867
\(790\) 19.6517i 0.699177i
\(791\) 0 0
\(792\) 0.458154