Properties

Label 1078.2.c.b.1077.5
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 1077.5
Root \(0.430324 - 1.60599i\) of defining polynomial
Character \(\chi\) \(=\) 1078.1077
Dual form 1078.2.c.b.1077.12

$q$-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 \(-0.308388\pi\)
0.566263 + 0.824224i \(0.308388\pi\)
\(14\) 0 0
\(15\) −1.29315 −0.333890
\(16\) 1.00000 0.250000
\(17\) −3.20191 −0.776578 −0.388289 0.921538i \(-0.626934\pi\)
−0.388289 + 0.921538i \(0.626934\pi\)
\(18\) 1.94448i 0.458319i
\(19\) 7.62813 1.75001 0.875007 0.484111i \(-0.160857\pi\)
0.875007 + 0.484111i \(0.160857\pi\)
\(20\) 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 \(0.106725\pi\)
−0.944316 + 0.329039i \(0.893275\pi\)
\(30\) 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 \(-0.343301\pi\)
0.472641 + 0.881255i \(0.343301\pi\)
\(42\) 0 0
\(43\) 7.57607i 1.15534i 0.816270 + 0.577670i \(0.196038\pi\)
−0.816270 + 0.577670i \(0.803962\pi\)
\(44\) 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 \(-0.530821\pi\)
−0.0966743 + 0.995316i \(0.530821\pi\)
\(62\) 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 \(-0.481980\pi\)
0.0565809 + 0.998398i \(0.481980\pi\)
\(74\) 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 \(0.341319\pi\)
−0.478117 + 0.878296i \(0.658681\pi\)
\(80\) 1.25868i 0.140725i
\(81\) 0.614474 0.0682749
\(82\) 6.05276i 0.668416i
\(83\) 1.32998 0.145984 0.0729921 0.997333i \(-0.476745\pi\)
0.0729921 + 0.997333i \(0.476745\pi\)
\(84\) 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 \(-0.333059\pi\)
0.500745 + 0.865595i \(0.333059\pi\)
\(102\) −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 \(-0.711173\pi\)
0.615814 0.787892i \(-0.288827\pi\)
\(108\) 5.07988i 0.488812i
\(109\) 11.5034i 1.10183i −0.834561 0.550915i \(-0.814279\pi\)
0.834561 0.550915i \(-0.185721\pi\)
\(110\) −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 \(-0.833113\pi\)
0.865679 0.500599i \(-0.166887\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −7.78352 −0.685301
\(130\) 5.13968 0.450780
\(131\) −7.03388 −0.614553 −0.307276 0.951620i \(-0.599418\pi\)
−0.307276 + 0.951620i \(0.599418\pi\)
\(132\) −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 \(-0.608253\pi\)
−0.333570 + 0.942725i \(0.608253\pi\)
\(140\) 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 \(-0.917849\pi\)
0.966880 0.255230i \(-0.0821513\pi\)
\(150\) 3.50925 0.286529
\(151\) 17.5101i 1.42495i −0.701696 0.712476i \(-0.747574\pi\)
0.701696 0.712476i \(-0.252426\pi\)
\(152\) 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 \(-0.312409\pi\)
0.555809 + 0.831310i \(0.312409\pi\)
\(168\) 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 \(-0.557956\pi\)
−0.181069 + 0.983470i \(0.557956\pi\)
\(174\) 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 \(0.109648\pi\)
−0.941255 + 0.337698i \(0.890352\pi\)
\(194\) −10.6748 −0.766405
\(195\) −5.28042 −0.378139
\(196\) 0 0
\(197\) 17.3471i 1.23593i −0.786205 0.617966i \(-0.787957\pi\)
0.786205 0.617966i \(-0.212043\pi\)
\(198\) −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 \(-0.997231\pi\)
0.999962 0.00869931i \(-0.00276911\pi\)
\(212\) 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 \(-0.290825\pi\)
0.610858 + 0.791740i \(0.290825\pi\)
\(228\) 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 \(-0.753926\pi\)
0.715774 0.698332i \(-0.246074\pi\)
\(234\) 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 \(-0.924643\pi\)
0.972108 0.234535i \(-0.0753566\pi\)
\(240\) −1.29315 −0.0834724
\(241\) −3.55410 −0.228939 −0.114470 0.993427i \(-0.536517\pi\)
−0.114470 + 0.993427i \(0.536517\pi\)
\(242\) 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 \(-0.730407\pi\)
0.662271 0.749264i \(-0.269593\pi\)
\(264\) 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 \(-0.602740\pi\)
−0.317193 + 0.948361i \(0.602740\pi\)
\(272\) −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 \(0.209988\pi\)
−0.790178 + 0.612877i \(0.790012\pi\)
\(278\) 7.86546i 0.471739i
\(279\) 17.8569i 1.06907i
\(280\) 0 0
\(281\) 9.99535i 0.596272i −0.954523 0.298136i \(-0.903635\pi\)
0.954523 0.298136i \(-0.0963650\pi\)
\(282\) 4.83144i 0.287708i
\(283\) −3.48896 −0.207397 −0.103699 0.994609i \(-0.533068\pi\)
−0.103699 + 0.994609i \(0.533068\pi\)
\(284\) −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 \(-0.330776\pi\)
0.506942 + 0.861980i \(0.330776\pi\)
\(294\) 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 \(-0.724098\pi\)
−0.647290 + 0.762244i \(0.724098\pi\)
\(308\) 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 \(-0.902031\pi\)
0.953009 0.302943i \(-0.0979690\pi\)
\(338\) 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 \(-0.871160\pi\)
0.919196 0.393801i \(-0.128840\pi\)
\(348\) 3.64090 0.195173
\(349\) −24.6769 −1.32093 −0.660463 0.750859i \(-0.729640\pi\)
−0.660463 + 0.750859i \(0.729640\pi\)
\(350\) 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 \(-0.972295\pi\)
0.996215 0.0869271i \(-0.0277047\pi\)
\(360\) −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 \(-0.992075\pi\)
0.999690 0.0248948i \(-0.00792508\pi\)
\(374\) 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 \(-0.166774\pi\)
0.865856 + 0.500293i \(0.166774\pi\)
\(410\) 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 \(0.304619\pi\)
−0.575984 + 0.817461i \(0.695381\pi\)
\(432\) 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 \(-0.337689\pi\)
0.488104 + 0.872785i \(0.337689\pi\)
\(440\) 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 \(-0.860436\pi\)
0.905410 0.424539i \(-0.139564\pi\)
\(458\) −5.30786 −0.248020
\(459\) 16.2653i 0.759201i
\(460\) 10.3876i 0.484323i
\(461\) 22.4278 1.04457 0.522284 0.852772i \(-0.325080\pi\)
0.522284 + 0.852772i \(0.325080\pi\)
\(462\) 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 \(-0.746685\pi\)
−0.699704 + 0.714433i \(0.746685\pi\)
\(480\) 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 \(0.263642\pi\)
−0.676162 + 0.736753i \(0.736358\pi\)
\(492\) 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 \(-0.667307\pi\)
−0.501741 + 0.865018i \(0.667307\pi\)
\(504\) 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 \(-0.275846\pi\)
0.647425 + 0.762129i \(0.275846\pi\)
\(524\) 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 \(0.122389\pi\)
−0.926987 + 0.375092i \(0.877611\pi\)
\(542\) 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 \(0.00795434\pi\)
−0.999688 + 0.0249867i \(0.992046\pi\)
\(548\) −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 \(-0.967226\pi\)
0.994704 0.102782i \(-0.0327744\pi\)
\(558\) 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 \(-0.314514\pi\)
0.550297 + 0.834969i \(0.314514\pi\)
\(564\) 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 \(-0.949876\pi\)
0.987627 0.156820i \(-0.0501241\pi\)
\(570\) 9.86431i 0.413170i
\(571\) 32.9377i 1.37840i 0.724572 + 0.689199i \(0.242038\pi\)
−0.724572 + 0.689199i \(0.757962\pi\)
\(572\) 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 \(-0.258178\pi\)
0.688707 + 0.725039i \(0.258178\pi\)
\(594\) −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 \(-0.236090\pi\)
0.737322 + 0.675542i \(0.236090\pi\)
\(602\) 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 \(-0.294566\pi\)
0.601511 + 0.798865i \(0.294566\pi\)
\(608\) 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 \(-0.763640\pi\)
0.736750 0.676166i \(-0.236360\pi\)
\(614\) 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 \(-0.802074\pi\)
0.812830 0.582501i \(-0.197926\pi\)
\(660\) −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 \(0.0218799\pi\)
−0.997638 + 0.0686836i \(0.978120\pi\)
\(674\) −11.1226 −0.428425
\(675\) 17.3514i 0.667857i
\(676\) −3.67402 −0.141309
\(677\) −31.1803 −1.19836 −0.599178 0.800616i \(-0.704506\pi\)
−0.599178 + 0.800616i \(0.704506\pi\)
\(678\) 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 \(0.0957784\pi\)
−0.955071 + 0.296377i \(0.904222\pi\)
\(702\) 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 \(-0.744946\pi\)
−0.695791 + 0.718244i \(0.744946\pi\)
\(734\) −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 \(0.00324355\pi\)
−0.999948 + 0.0101897i \(0.996756\pi\)
\(740\) 0.387982i 0.0142625i
\(741\) 32.0015i 1.17561i
\(742\) 0 0
\(743\) 20.1974i 0.740972i 0.928838 + 0.370486i \(0.120809\pi\)
−0.928838 + 0.370486i \(0.879191\pi\)
\(744\) 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 \(-0.874902\pi\)
−0.923761 + 0.382968i \(0.874902\pi\)
\(762\) 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 \(-0.702824\pi\)
−0.594938 + 0.803771i \(0.702824\pi\)
\(770\) 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 \(-0.616718\pi\)
−0.358519 + 0.933522i \(0.616718\pi\)
\(788\) 17.3471i 0.617966i
\(789\) 24.9675 0.888867
\(790\) 19.6517i 0.699177i
\(791\) 0 0
\(792\) 0.458154 6.43283