Properties

Label 1078.2.c.c.1077.4
Level $1078$
Weight $2$
Character 1078.1077
Analytic conductor $8.608$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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: \( x^{16} - 32x^{14} + 512x^{12} - 2272x^{10} - 1087x^{8} + 72448x^{6} + 819200x^{4} + 1310720x^{2} + 1048576 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1077.4
Root \(0.424903 + 1.02581i\) of defining polynomial
Character \(\chi\) \(=\) 1078.1077
Dual form 1078.2.c.c.1077.13

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -0.765367i q^{3} -1.00000 q^{4} +3.89937i q^{5} -0.765367 q^{6} +1.00000i q^{8} +2.41421 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} -0.765367i q^{3} -1.00000 q^{4} +3.89937i q^{5} -0.765367 q^{6} +1.00000i q^{8} +2.41421 q^{9} +3.89937 q^{10} +(0.214882 + 3.30966i) q^{11} +0.765367i q^{12} -1.81903 q^{13} +2.98445 q^{15} +1.00000 q^{16} -6.07606 q^{17} -2.41421i q^{18} -6.82952 q^{19} -3.89937i q^{20} +(3.30966 - 0.214882i) q^{22} -4.37667 q^{23} +0.765367 q^{24} -10.2051 q^{25} +1.81903i q^{26} -4.14386i q^{27} -9.36112i q^{29} -2.98445i q^{30} +7.88318i q^{31} -1.00000i q^{32} +(2.53310 - 0.164463i) q^{33} +6.07606i q^{34} -2.41421 q^{36} -4.60778 q^{37} +6.82952i q^{38} +1.39222i q^{39} -3.89937 q^{40} +3.58235 q^{41} +3.25819i q^{43} +(-0.214882 - 3.30966i) q^{44} +9.41392i q^{45} +4.37667i q^{46} +0.203854i q^{47} -0.765367i q^{48} +10.2051i q^{50} +4.65041i q^{51} +1.81903 q^{52} +4.98445 q^{53} -4.14386 q^{54} +(-12.9056 + 0.837904i) q^{55} +5.22709i q^{57} -9.36112 q^{58} +5.19752i q^{59} -2.98445 q^{60} +8.98372 q^{61} +7.88318 q^{62} -1.00000 q^{64} -7.09306i q^{65} +(-0.164463 - 2.53310i) q^{66} -8.03353 q^{67} +6.07606 q^{68} +3.34976i q^{69} +8.86195 q^{71} +2.41421i q^{72} +0.0557060 q^{73} +4.60778i q^{74} +7.81064i q^{75} +6.82952 q^{76} +1.39222 q^{78} +8.48528i q^{79} +3.89937i q^{80} +4.07107 q^{81} -3.58235i q^{82} -10.4676 q^{83} -23.6928i q^{85} +3.25819 q^{86} -7.16469 q^{87} +(-3.30966 + 0.214882i) q^{88} -1.68771i q^{89} +9.41392 q^{90} +4.37667 q^{92} +6.03353 q^{93} +0.203854 q^{94} -26.6308i q^{95} -0.765367 q^{96} +9.23880i q^{97} +(0.518771 + 7.99022i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{4} + 16 q^{9} + 16 q^{11} + 16 q^{16} - 8 q^{22} - 16 q^{23} - 64 q^{25} - 16 q^{36} - 80 q^{37} - 16 q^{44} + 32 q^{53} - 48 q^{58} - 16 q^{64} + 16 q^{67} - 48 q^{71} + 16 q^{78} - 48 q^{81} + 32 q^{86} + 8 q^{88} + 16 q^{92} - 48 q^{93} + 24 q^{99}+O(q^{100}) \) 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
\(3\) 0.765367i 0.441885i −0.975287 0.220942i \(-0.929087\pi\)
0.975287 0.220942i \(-0.0709133\pi\)
\(4\) −1.00000 −0.500000
\(5\) 3.89937i 1.74385i 0.489638 + 0.871926i \(0.337129\pi\)
−0.489638 + 0.871926i \(0.662871\pi\)
\(6\) −0.765367 −0.312460
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 2.41421 0.804738
\(10\) 3.89937 1.23309
\(11\) 0.214882 + 3.30966i 0.0647893 + 0.997899i
\(12\) 0.765367i 0.220942i
\(13\) −1.81903 −0.504507 −0.252254 0.967661i \(-0.581172\pi\)
−0.252254 + 0.967661i \(0.581172\pi\)
\(14\) 0 0
\(15\) 2.98445 0.770582
\(16\) 1.00000 0.250000
\(17\) −6.07606 −1.47366 −0.736830 0.676078i \(-0.763678\pi\)
−0.736830 + 0.676078i \(0.763678\pi\)
\(18\) 2.41421i 0.569036i
\(19\) −6.82952 −1.56680 −0.783400 0.621518i \(-0.786516\pi\)
−0.783400 + 0.621518i \(0.786516\pi\)
\(20\) 3.89937i 0.871926i
\(21\) 0 0
\(22\) 3.30966 0.214882i 0.705621 0.0458130i
\(23\) −4.37667 −0.912599 −0.456300 0.889826i \(-0.650825\pi\)
−0.456300 + 0.889826i \(0.650825\pi\)
\(24\) 0.765367 0.156230
\(25\) −10.2051 −2.04102
\(26\) 1.81903i 0.356740i
\(27\) 4.14386i 0.797486i
\(28\) 0 0
\(29\) 9.36112i 1.73832i −0.494534 0.869158i \(-0.664661\pi\)
0.494534 0.869158i \(-0.335339\pi\)
\(30\) 2.98445i 0.544884i
\(31\) 7.88318i 1.41586i 0.706282 + 0.707931i \(0.250371\pi\)
−0.706282 + 0.707931i \(0.749629\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.53310 0.164463i 0.440956 0.0286294i
\(34\) 6.07606i 1.04204i
\(35\) 0 0
\(36\) −2.41421 −0.402369
\(37\) −4.60778 −0.757514 −0.378757 0.925496i \(-0.623648\pi\)
−0.378757 + 0.925496i \(0.623648\pi\)
\(38\) 6.82952i 1.10789i
\(39\) 1.39222i 0.222934i
\(40\) −3.89937 −0.616545
\(41\) 3.58235 0.559469 0.279734 0.960077i \(-0.409754\pi\)
0.279734 + 0.960077i \(0.409754\pi\)
\(42\) 0 0
\(43\) 3.25819i 0.496869i 0.968649 + 0.248435i \(0.0799161\pi\)
−0.968649 + 0.248435i \(0.920084\pi\)
\(44\) −0.214882 3.30966i −0.0323947 0.498949i
\(45\) 9.41392i 1.40334i
\(46\) 4.37667i 0.645305i
\(47\) 0.203854i 0.0297351i 0.999889 + 0.0148675i \(0.00473266\pi\)
−0.999889 + 0.0148675i \(0.995267\pi\)
\(48\) 0.765367i 0.110471i
\(49\) 0 0
\(50\) 10.2051i 1.44322i
\(51\) 4.65041i 0.651188i
\(52\) 1.81903 0.252254
\(53\) 4.98445 0.684667 0.342333 0.939579i \(-0.388783\pi\)
0.342333 + 0.939579i \(0.388783\pi\)
\(54\) −4.14386 −0.563908
\(55\) −12.9056 + 0.837904i −1.74019 + 0.112983i
\(56\) 0 0
\(57\) 5.22709i 0.692345i
\(58\) −9.36112 −1.22918
\(59\) 5.19752i 0.676659i 0.941028 + 0.338330i \(0.109862\pi\)
−0.941028 + 0.338330i \(0.890138\pi\)
\(60\) −2.98445 −0.385291
\(61\) 8.98372 1.15025 0.575124 0.818066i \(-0.304954\pi\)
0.575124 + 0.818066i \(0.304954\pi\)
\(62\) 7.88318 1.00117
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 7.09306i 0.879786i
\(66\) −0.164463 2.53310i −0.0202441 0.311803i
\(67\) −8.03353 −0.981451 −0.490726 0.871314i \(-0.663268\pi\)
−0.490726 + 0.871314i \(0.663268\pi\)
\(68\) 6.07606 0.736830
\(69\) 3.34976i 0.403264i
\(70\) 0 0
\(71\) 8.86195 1.05172 0.525860 0.850571i \(-0.323744\pi\)
0.525860 + 0.850571i \(0.323744\pi\)
\(72\) 2.41421i 0.284518i
\(73\) 0.0557060 0.00651989 0.00325995 0.999995i \(-0.498962\pi\)
0.00325995 + 0.999995i \(0.498962\pi\)
\(74\) 4.60778i 0.535643i
\(75\) 7.81064i 0.901896i
\(76\) 6.82952 0.783400
\(77\) 0 0
\(78\) 1.39222 0.157638
\(79\) 8.48528i 0.954669i 0.878722 + 0.477334i \(0.158397\pi\)
−0.878722 + 0.477334i \(0.841603\pi\)
\(80\) 3.89937i 0.435963i
\(81\) 4.07107 0.452341
\(82\) 3.58235i 0.395604i
\(83\) −10.4676 −1.14897 −0.574483 0.818517i \(-0.694797\pi\)
−0.574483 + 0.818517i \(0.694797\pi\)
\(84\) 0 0
\(85\) 23.6928i 2.56985i
\(86\) 3.25819 0.351340
\(87\) −7.16469 −0.768136
\(88\) −3.30966 + 0.214882i −0.352811 + 0.0229065i
\(89\) 1.68771i 0.178897i −0.995991 0.0894484i \(-0.971490\pi\)
0.995991 0.0894484i \(-0.0285104\pi\)
\(90\) 9.41392 0.992314
\(91\) 0 0
\(92\) 4.37667 0.456300
\(93\) 6.03353 0.625648
\(94\) 0.203854 0.0210259
\(95\) 26.6308i 2.73227i
\(96\) −0.765367 −0.0781149
\(97\) 9.23880i 0.938058i 0.883183 + 0.469029i \(0.155396\pi\)
−0.883183 + 0.469029i \(0.844604\pi\)
\(98\) 0 0
\(99\) 0.518771 + 7.99022i 0.0521384 + 0.803047i
\(100\) 10.2051 1.02051
\(101\) 5.34567 0.531914 0.265957 0.963985i \(-0.414312\pi\)
0.265957 + 0.963985i \(0.414312\pi\)
\(102\) 4.65041 0.460460
\(103\) 4.24513i 0.418285i 0.977885 + 0.209143i \(0.0670673\pi\)
−0.977885 + 0.209143i \(0.932933\pi\)
\(104\) 1.81903i 0.178370i
\(105\) 0 0
\(106\) 4.98445i 0.484133i
\(107\) 7.23863i 0.699784i 0.936790 + 0.349892i \(0.113782\pi\)
−0.936790 + 0.349892i \(0.886218\pi\)
\(108\) 4.14386i 0.398743i
\(109\) 6.00000i 0.574696i −0.957826 0.287348i \(-0.907226\pi\)
0.957826 0.287348i \(-0.0927736\pi\)
\(110\) 0.837904 + 12.9056i 0.0798910 + 1.23050i
\(111\) 3.52664i 0.334734i
\(112\) 0 0
\(113\) 16.8400 1.58417 0.792085 0.610411i \(-0.208996\pi\)
0.792085 + 0.610411i \(0.208996\pi\)
\(114\) 5.22709 0.489562
\(115\) 17.0663i 1.59144i
\(116\) 9.36112i 0.869158i
\(117\) −4.39152 −0.405996
\(118\) 5.19752 0.478470
\(119\) 0 0
\(120\) 2.98445i 0.272442i
\(121\) −10.9077 + 1.42237i −0.991605 + 0.129306i
\(122\) 8.98372i 0.813348i
\(123\) 2.74181i 0.247221i
\(124\) 7.88318i 0.707931i
\(125\) 20.2966i 1.81538i
\(126\) 0 0
\(127\) 17.3300i 1.53779i 0.639375 + 0.768895i \(0.279193\pi\)
−0.639375 + 0.768895i \(0.720807\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 2.49371 0.219559
\(130\) −7.09306 −0.622102
\(131\) −6.35552 −0.555284 −0.277642 0.960685i \(-0.589553\pi\)
−0.277642 + 0.960685i \(0.589553\pi\)
\(132\) −2.53310 + 0.164463i −0.220478 + 0.0143147i
\(133\) 0 0
\(134\) 8.03353i 0.693991i
\(135\) 16.1584 1.39070
\(136\) 6.07606i 0.521018i
\(137\) 1.34959 0.115303 0.0576515 0.998337i \(-0.481639\pi\)
0.0576515 + 0.998337i \(0.481639\pi\)
\(138\) 3.34976 0.285150
\(139\) 11.8957 1.00898 0.504491 0.863417i \(-0.331680\pi\)
0.504491 + 0.863417i \(0.331680\pi\)
\(140\) 0 0
\(141\) 0.156023 0.0131395
\(142\) 8.86195i 0.743679i
\(143\) −0.390876 6.02035i −0.0326867 0.503447i
\(144\) 2.41421 0.201184
\(145\) 36.5025 3.03137
\(146\) 0.0557060i 0.00461026i
\(147\) 0 0
\(148\) 4.60778 0.378757
\(149\) 6.57668i 0.538782i 0.963031 + 0.269391i \(0.0868225\pi\)
−0.963031 + 0.269391i \(0.913178\pi\)
\(150\) 7.81064 0.637736
\(151\) 8.63888i 0.703022i 0.936184 + 0.351511i \(0.114332\pi\)
−0.936184 + 0.351511i \(0.885668\pi\)
\(152\) 6.82952i 0.553947i
\(153\) −14.6689 −1.18591
\(154\) 0 0
\(155\) −30.7395 −2.46905
\(156\) 1.39222i 0.111467i
\(157\) 2.44991i 0.195524i 0.995210 + 0.0977619i \(0.0311684\pi\)
−0.995210 + 0.0977619i \(0.968832\pi\)
\(158\) 8.48528 0.675053
\(159\) 3.81493i 0.302544i
\(160\) 3.89937 0.308272
\(161\) 0 0
\(162\) 4.07107i 0.319853i
\(163\) 2.29005 0.179371 0.0896854 0.995970i \(-0.471414\pi\)
0.0896854 + 0.995970i \(0.471414\pi\)
\(164\) −3.58235 −0.279734
\(165\) 0.641304 + 9.87750i 0.0499255 + 0.768963i
\(166\) 10.4676i 0.812441i
\(167\) 8.51406 0.658838 0.329419 0.944184i \(-0.393147\pi\)
0.329419 + 0.944184i \(0.393147\pi\)
\(168\) 0 0
\(169\) −9.69114 −0.745473
\(170\) −23.6928 −1.81716
\(171\) −16.4879 −1.26086
\(172\) 3.25819i 0.248435i
\(173\) −23.9921 −1.82409 −0.912044 0.410092i \(-0.865497\pi\)
−0.912044 + 0.410092i \(0.865497\pi\)
\(174\) 7.16469i 0.543154i
\(175\) 0 0
\(176\) 0.214882 + 3.30966i 0.0161973 + 0.249475i
\(177\) 3.97801 0.299005
\(178\) −1.68771 −0.126499
\(179\) 20.1584 1.50671 0.753357 0.657612i \(-0.228433\pi\)
0.753357 + 0.657612i \(0.228433\pi\)
\(180\) 9.41392i 0.701672i
\(181\) 11.1135i 0.826062i 0.910717 + 0.413031i \(0.135530\pi\)
−0.910717 + 0.413031i \(0.864470\pi\)
\(182\) 0 0
\(183\) 6.87584i 0.508277i
\(184\) 4.37667i 0.322653i
\(185\) 17.9674i 1.32099i
\(186\) 6.03353i 0.442400i
\(187\) −1.30563 20.1097i −0.0954775 1.47056i
\(188\) 0.203854i 0.0148675i
\(189\) 0 0
\(190\) −26.6308 −1.93200
\(191\) −24.5084 −1.77336 −0.886681 0.462382i \(-0.846995\pi\)
−0.886681 + 0.462382i \(0.846995\pi\)
\(192\) 0.765367i 0.0552356i
\(193\) 12.6193i 0.908358i 0.890910 + 0.454179i \(0.150067\pi\)
−0.890910 + 0.454179i \(0.849933\pi\)
\(194\) 9.23880 0.663307
\(195\) −5.42879 −0.388764
\(196\) 0 0
\(197\) 17.2697i 1.23042i −0.788364 0.615209i \(-0.789072\pi\)
0.788364 0.615209i \(-0.210928\pi\)
\(198\) 7.99022 0.518771i 0.567840 0.0368674i
\(199\) 9.18309i 0.650972i 0.945547 + 0.325486i \(0.105528\pi\)
−0.945547 + 0.325486i \(0.894472\pi\)
\(200\) 10.2051i 0.721609i
\(201\) 6.14859i 0.433688i
\(202\) 5.34567i 0.376120i
\(203\) 0 0
\(204\) 4.65041i 0.325594i
\(205\) 13.9689i 0.975630i
\(206\) 4.24513 0.295772
\(207\) −10.5662 −0.734403
\(208\) −1.81903 −0.126127
\(209\) −1.46754 22.6034i −0.101512 1.56351i
\(210\) 0 0
\(211\) 2.12250i 0.146119i −0.997328 0.0730593i \(-0.976724\pi\)
0.997328 0.0730593i \(-0.0232762\pi\)
\(212\) −4.98445 −0.342333
\(213\) 6.78265i 0.464739i
\(214\) 7.23863 0.494822
\(215\) −12.7049 −0.866467
\(216\) 4.14386 0.281954
\(217\) 0 0
\(218\) −6.00000 −0.406371
\(219\) 0.0426355i 0.00288104i
\(220\) 12.9056 0.837904i 0.870094 0.0564915i
\(221\) 11.0525 0.743472
\(222\) 3.52664 0.236693
\(223\) 5.77586i 0.386780i −0.981122 0.193390i \(-0.938052\pi\)
0.981122 0.193390i \(-0.0619483\pi\)
\(224\) 0 0
\(225\) −24.6373 −1.64249
\(226\) 16.8400i 1.12018i
\(227\) 1.21054 0.0803463 0.0401731 0.999193i \(-0.487209\pi\)
0.0401731 + 0.999193i \(0.487209\pi\)
\(228\) 5.22709i 0.346173i
\(229\) 19.4012i 1.28207i −0.767511 0.641035i \(-0.778505\pi\)
0.767511 0.641035i \(-0.221495\pi\)
\(230\) −17.0663 −1.12532
\(231\) 0 0
\(232\) 9.36112 0.614588
\(233\) 19.7124i 1.29140i 0.763591 + 0.645700i \(0.223434\pi\)
−0.763591 + 0.645700i \(0.776566\pi\)
\(234\) 4.39152i 0.287082i
\(235\) −0.794901 −0.0518536
\(236\) 5.19752i 0.338330i
\(237\) 6.49435 0.421854
\(238\) 0 0
\(239\) 11.6292i 0.752229i 0.926573 + 0.376115i \(0.122740\pi\)
−0.926573 + 0.376115i \(0.877260\pi\)
\(240\) 2.98445 0.192645
\(241\) 27.3738 1.76330 0.881651 0.471903i \(-0.156433\pi\)
0.881651 + 0.471903i \(0.156433\pi\)
\(242\) 1.42237 + 10.9077i 0.0914334 + 0.701170i
\(243\) 15.5474i 0.997369i
\(244\) −8.98372 −0.575124
\(245\) 0 0
\(246\) −2.74181 −0.174811
\(247\) 12.4231 0.790462
\(248\) −7.88318 −0.500583
\(249\) 8.01154i 0.507710i
\(250\) −20.2966 −1.28367
\(251\) 13.5021i 0.852243i 0.904666 + 0.426122i \(0.140120\pi\)
−0.904666 + 0.426122i \(0.859880\pi\)
\(252\) 0 0
\(253\) −0.940467 14.4853i −0.0591267 0.910682i
\(254\) 17.3300 1.08738
\(255\) −18.1337 −1.13558
\(256\) 1.00000 0.0625000
\(257\) 2.80639i 0.175058i −0.996162 0.0875289i \(-0.972103\pi\)
0.996162 0.0875289i \(-0.0278970\pi\)
\(258\) 2.49371i 0.155252i
\(259\) 0 0
\(260\) 7.09306i 0.439893i
\(261\) 22.5997i 1.39889i
\(262\) 6.35552i 0.392645i
\(263\) 8.48528i 0.523225i 0.965173 + 0.261612i \(0.0842542\pi\)
−0.965173 + 0.261612i \(0.915746\pi\)
\(264\) 0.164463 + 2.53310i 0.0101220 + 0.155902i
\(265\) 19.4362i 1.19396i
\(266\) 0 0
\(267\) −1.29172 −0.0790518
\(268\) 8.03353 0.490726
\(269\) 20.9576i 1.27781i −0.769286 0.638905i \(-0.779388\pi\)
0.769286 0.638905i \(-0.220612\pi\)
\(270\) 16.1584i 0.983372i
\(271\) 14.6132 0.887688 0.443844 0.896104i \(-0.353614\pi\)
0.443844 + 0.896104i \(0.353614\pi\)
\(272\) −6.07606 −0.368415
\(273\) 0 0
\(274\) 1.34959i 0.0815315i
\(275\) −2.19289 33.7754i −0.132236 2.03673i
\(276\) 3.34976i 0.201632i
\(277\) 11.1242i 0.668386i −0.942505 0.334193i \(-0.891536\pi\)
0.942505 0.334193i \(-0.108464\pi\)
\(278\) 11.8957i 0.713458i
\(279\) 19.0317i 1.13940i
\(280\) 0 0
\(281\) 7.28929i 0.434843i 0.976078 + 0.217421i \(0.0697646\pi\)
−0.976078 + 0.217421i \(0.930235\pi\)
\(282\) 0.156023i 0.00929102i
\(283\) −16.0139 −0.951929 −0.475965 0.879464i \(-0.657901\pi\)
−0.475965 + 0.879464i \(0.657901\pi\)
\(284\) −8.86195 −0.525860
\(285\) −20.3824 −1.20735
\(286\) −6.02035 + 0.390876i −0.355991 + 0.0231130i
\(287\) 0 0
\(288\) 2.41421i 0.142259i
\(289\) 19.9185 1.17168
\(290\) 36.5025i 2.14350i
\(291\) 7.07107 0.414513
\(292\) −0.0557060 −0.00325995
\(293\) 14.2550 0.832783 0.416392 0.909185i \(-0.363295\pi\)
0.416392 + 0.909185i \(0.363295\pi\)
\(294\) 0 0
\(295\) −20.2671 −1.17999
\(296\) 4.60778i 0.267822i
\(297\) 13.7148 0.890440i 0.795811 0.0516686i
\(298\) 6.57668 0.380977
\(299\) 7.96128 0.460413
\(300\) 7.81064i 0.450948i
\(301\) 0 0
\(302\) 8.63888 0.497112
\(303\) 4.09140i 0.235045i
\(304\) −6.82952 −0.391700
\(305\) 35.0309i 2.00586i
\(306\) 14.6689i 0.838565i
\(307\) −6.75074 −0.385285 −0.192643 0.981269i \(-0.561706\pi\)
−0.192643 + 0.981269i \(0.561706\pi\)
\(308\) 0 0
\(309\) 3.24908 0.184834
\(310\) 30.7395i 1.74588i
\(311\) 17.8705i 1.01334i −0.862139 0.506672i \(-0.830876\pi\)
0.862139 0.506672i \(-0.169124\pi\)
\(312\) −1.39222 −0.0788191
\(313\) 15.0328i 0.849704i 0.905263 + 0.424852i \(0.139674\pi\)
−0.905263 + 0.424852i \(0.860326\pi\)
\(314\) 2.44991 0.138256
\(315\) 0 0
\(316\) 8.48528i 0.477334i
\(317\) 9.73194 0.546600 0.273300 0.961929i \(-0.411885\pi\)
0.273300 + 0.961929i \(0.411885\pi\)
\(318\) −3.81493 −0.213931
\(319\) 30.9821 2.01154i 1.73466 0.112624i
\(320\) 3.89937i 0.217982i
\(321\) 5.54020 0.309224
\(322\) 0 0
\(323\) 41.4966 2.30893
\(324\) −4.07107 −0.226170
\(325\) 18.5633 1.02971
\(326\) 2.29005i 0.126834i
\(327\) −4.59220 −0.253949
\(328\) 3.58235i 0.197802i
\(329\) 0 0
\(330\) 9.87750 0.641304i 0.543739 0.0353026i
\(331\) 18.2599 1.00365 0.501826 0.864968i \(-0.332662\pi\)
0.501826 + 0.864968i \(0.332662\pi\)
\(332\) 10.4676 0.574483
\(333\) −11.1242 −0.609600
\(334\) 8.51406i 0.465869i
\(335\) 31.3257i 1.71151i
\(336\) 0 0
\(337\) 29.6928i 1.61747i 0.588173 + 0.808735i \(0.299847\pi\)
−0.588173 + 0.808735i \(0.700153\pi\)
\(338\) 9.69114i 0.527129i
\(339\) 12.8887i 0.700021i
\(340\) 23.6928i 1.28492i
\(341\) −26.0906 + 1.69395i −1.41289 + 0.0917327i
\(342\) 16.4879i 0.891565i
\(343\) 0 0
\(344\) −3.25819 −0.175670
\(345\) −13.0620 −0.703232
\(346\) 23.9921i 1.28983i
\(347\) 19.2813i 1.03507i −0.855661 0.517536i \(-0.826849\pi\)
0.855661 0.517536i \(-0.173151\pi\)
\(348\) 7.16469 0.384068
\(349\) −23.9921 −1.28427 −0.642135 0.766592i \(-0.721951\pi\)
−0.642135 + 0.766592i \(0.721951\pi\)
\(350\) 0 0
\(351\) 7.53779i 0.402337i
\(352\) 3.30966 0.214882i 0.176405 0.0114532i
\(353\) 16.1478i 0.859462i 0.902957 + 0.429731i \(0.141392\pi\)
−0.902957 + 0.429731i \(0.858608\pi\)
\(354\) 3.97801i 0.211429i
\(355\) 34.5561i 1.83404i
\(356\) 1.68771i 0.0894484i
\(357\) 0 0
\(358\) 20.1584i 1.06541i
\(359\) 18.1456i 0.957686i −0.877900 0.478843i \(-0.841056\pi\)
0.877900 0.478843i \(-0.158944\pi\)
\(360\) −9.41392 −0.496157
\(361\) 27.6424 1.45486
\(362\) 11.1135 0.584114
\(363\) 1.08864 + 8.34836i 0.0571385 + 0.438175i
\(364\) 0 0
\(365\) 0.217218i 0.0113697i
\(366\) −6.87584 −0.359406
\(367\) 4.91547i 0.256585i 0.991736 + 0.128293i \(0.0409497\pi\)
−0.991736 + 0.128293i \(0.959050\pi\)
\(368\) −4.37667 −0.228150
\(369\) 8.64855 0.450225
\(370\) −17.9674 −0.934083
\(371\) 0 0
\(372\) −6.03353 −0.312824
\(373\) 2.26806i 0.117436i 0.998275 + 0.0587179i \(0.0187013\pi\)
−0.998275 + 0.0587179i \(0.981299\pi\)
\(374\) −20.1097 + 1.30563i −1.03985 + 0.0675128i
\(375\) −15.5344 −0.802191
\(376\) −0.203854 −0.0105129
\(377\) 17.0281i 0.876993i
\(378\) 0 0
\(379\) 14.7984 0.760143 0.380072 0.924957i \(-0.375899\pi\)
0.380072 + 0.924957i \(0.375899\pi\)
\(380\) 26.6308i 1.36613i
\(381\) 13.2638 0.679526
\(382\) 24.5084i 1.25396i
\(383\) 7.27031i 0.371495i −0.982597 0.185748i \(-0.940529\pi\)
0.982597 0.185748i \(-0.0594707\pi\)
\(384\) 0.765367 0.0390575
\(385\) 0 0
\(386\) 12.6193 0.642306
\(387\) 7.86597i 0.399850i
\(388\) 9.23880i 0.469029i
\(389\) −35.1936 −1.78439 −0.892194 0.451652i \(-0.850835\pi\)
−0.892194 + 0.451652i \(0.850835\pi\)
\(390\) 5.42879i 0.274898i
\(391\) 26.5929 1.34486
\(392\) 0 0
\(393\) 4.86431i 0.245372i
\(394\) −17.2697 −0.870036
\(395\) −33.0873 −1.66480
\(396\) −0.518771 7.99022i −0.0260692 0.401524i
\(397\) 18.8310i 0.945101i −0.881304 0.472550i \(-0.843333\pi\)
0.881304 0.472550i \(-0.156667\pi\)
\(398\) 9.18309 0.460307
\(399\) 0 0
\(400\) −10.2051 −0.510255
\(401\) −7.10695 −0.354904 −0.177452 0.984129i \(-0.556785\pi\)
−0.177452 + 0.984129i \(0.556785\pi\)
\(402\) 6.14859 0.306664
\(403\) 14.3397i 0.714312i
\(404\) −5.34567 −0.265957
\(405\) 15.8746i 0.788816i
\(406\) 0 0
\(407\) −0.990128 15.2502i −0.0490788 0.755922i
\(408\) −4.65041 −0.230230
\(409\) 9.71411 0.480332 0.240166 0.970732i \(-0.422798\pi\)
0.240166 + 0.970732i \(0.422798\pi\)
\(410\) 13.9689 0.689875
\(411\) 1.03293i 0.0509506i
\(412\) 4.24513i 0.209143i
\(413\) 0 0
\(414\) 10.5662i 0.519301i
\(415\) 40.8170i 2.00363i
\(416\) 1.81903i 0.0891851i
\(417\) 9.10459i 0.445854i
\(418\) −22.6034 + 1.46754i −1.10557 + 0.0717798i
\(419\) 23.0474i 1.12594i −0.826478 0.562970i \(-0.809659\pi\)
0.826478 0.562970i \(-0.190341\pi\)
\(420\) 0 0
\(421\) −1.67074 −0.0814270 −0.0407135 0.999171i \(-0.512963\pi\)
−0.0407135 + 0.999171i \(0.512963\pi\)
\(422\) −2.12250 −0.103322
\(423\) 0.492146i 0.0239290i
\(424\) 4.98445i 0.242066i
\(425\) 62.0068 3.00777
\(426\) −6.78265 −0.328620
\(427\) 0 0
\(428\) 7.23863i 0.349892i
\(429\) −4.60778 + 0.299163i −0.222466 + 0.0144437i
\(430\) 12.7049i 0.612685i
\(431\) 38.8481i 1.87125i −0.353001 0.935623i \(-0.614839\pi\)
0.353001 0.935623i \(-0.385161\pi\)
\(432\) 4.14386i 0.199372i
\(433\) 31.8479i 1.53051i −0.643726 0.765256i \(-0.722612\pi\)
0.643726 0.765256i \(-0.277388\pi\)
\(434\) 0 0
\(435\) 27.9378i 1.33951i
\(436\) 6.00000i 0.287348i
\(437\) 29.8906 1.42986
\(438\) −0.0426355 −0.00203720
\(439\) −12.0407 −0.574671 −0.287336 0.957830i \(-0.592770\pi\)
−0.287336 + 0.957830i \(0.592770\pi\)
\(440\) −0.837904 12.9056i −0.0399455 0.615249i
\(441\) 0 0
\(442\) 11.0525i 0.525714i
\(443\) −30.5523 −1.45159 −0.725793 0.687914i \(-0.758527\pi\)
−0.725793 + 0.687914i \(0.758527\pi\)
\(444\) 3.52664i 0.167367i
\(445\) 6.58101 0.311970
\(446\) −5.77586 −0.273495
\(447\) 5.03357 0.238080
\(448\) 0 0
\(449\) 15.7378 0.742712 0.371356 0.928490i \(-0.378893\pi\)
0.371356 + 0.928490i \(0.378893\pi\)
\(450\) 24.6373i 1.16141i
\(451\) 0.769781 + 11.8563i 0.0362476 + 0.558293i
\(452\) −16.8400 −0.792085
\(453\) 6.61191 0.310655
\(454\) 1.21054i 0.0568134i
\(455\) 0 0
\(456\) −5.22709 −0.244781
\(457\) 17.1668i 0.803029i 0.915853 + 0.401514i \(0.131516\pi\)
−0.915853 + 0.401514i \(0.868484\pi\)
\(458\) −19.4012 −0.906561
\(459\) 25.1783i 1.17522i
\(460\) 17.0663i 0.795719i
\(461\) 0.312096 0.0145357 0.00726787 0.999974i \(-0.497687\pi\)
0.00726787 + 0.999974i \(0.497687\pi\)
\(462\) 0 0
\(463\) −31.9402 −1.48439 −0.742194 0.670185i \(-0.766215\pi\)
−0.742194 + 0.670185i \(0.766215\pi\)
\(464\) 9.36112i 0.434579i
\(465\) 23.5270i 1.09104i
\(466\) 19.7124 0.913158
\(467\) 18.8521i 0.872370i −0.899857 0.436185i \(-0.856329\pi\)
0.899857 0.436185i \(-0.143671\pi\)
\(468\) 4.39152 0.202998
\(469\) 0 0
\(470\) 0.794901i 0.0366660i
\(471\) 1.87508 0.0863990
\(472\) −5.19752 −0.239235
\(473\) −10.7835 + 0.700126i −0.495826 + 0.0321918i
\(474\) 6.49435i 0.298296i
\(475\) 69.6960 3.19787
\(476\) 0 0
\(477\) 12.0335 0.550977
\(478\) 11.6292 0.531907
\(479\) 29.0540 1.32751 0.663755 0.747950i \(-0.268962\pi\)
0.663755 + 0.747950i \(0.268962\pi\)
\(480\) 2.98445i 0.136221i
\(481\) 8.38167 0.382171
\(482\) 27.3738i 1.24684i
\(483\) 0 0
\(484\) 10.9077 1.42237i 0.495802 0.0646532i
\(485\) −36.0255 −1.63583
\(486\) −15.5474 −0.705246
\(487\) −33.1349 −1.50148 −0.750742 0.660595i \(-0.770304\pi\)
−0.750742 + 0.660595i \(0.770304\pi\)
\(488\) 8.98372i 0.406674i
\(489\) 1.75273i 0.0792613i
\(490\) 0 0
\(491\) 42.4151i 1.91416i 0.289817 + 0.957082i \(0.406406\pi\)
−0.289817 + 0.957082i \(0.593594\pi\)
\(492\) 2.74181i 0.123610i
\(493\) 56.8787i 2.56169i
\(494\) 12.4231i 0.558941i
\(495\) −31.1568 + 2.02288i −1.40040 + 0.0909217i
\(496\) 7.88318i 0.353965i
\(497\) 0 0
\(498\) 8.01154 0.359005
\(499\) 15.4421 0.691282 0.345641 0.938367i \(-0.387662\pi\)
0.345641 + 0.938367i \(0.387662\pi\)
\(500\) 20.2966i 0.907692i
\(501\) 6.51638i 0.291130i
\(502\) 13.5021 0.602627
\(503\) −39.5816 −1.76486 −0.882429 0.470446i \(-0.844093\pi\)
−0.882429 + 0.470446i \(0.844093\pi\)
\(504\) 0 0
\(505\) 20.8447i 0.927579i
\(506\) −14.4853 + 0.940467i −0.643949 + 0.0418089i
\(507\) 7.41728i 0.329413i
\(508\) 17.3300i 0.768895i
\(509\) 5.27888i 0.233982i −0.993133 0.116991i \(-0.962675\pi\)
0.993133 0.116991i \(-0.0373249\pi\)
\(510\) 18.1337i 0.802973i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 28.3006i 1.24950i
\(514\) −2.80639 −0.123785
\(515\) −16.5533 −0.729427
\(516\) −2.49371 −0.109780
\(517\) −0.674685 + 0.0438044i −0.0296726 + 0.00192652i
\(518\) 0 0
\(519\) 18.3628i 0.806037i
\(520\) 7.09306 0.311051
\(521\) 27.3087i 1.19641i 0.801341 + 0.598207i \(0.204120\pi\)
−0.801341 + 0.598207i \(0.795880\pi\)
\(522\) −22.5997 −0.989164
\(523\) 8.65289 0.378365 0.189182 0.981942i \(-0.439416\pi\)
0.189182 + 0.981942i \(0.439416\pi\)
\(524\) 6.35552 0.277642
\(525\) 0 0
\(526\) 8.48528 0.369976
\(527\) 47.8987i 2.08650i
\(528\) 2.53310 0.164463i 0.110239 0.00715735i
\(529\) −3.84474 −0.167163
\(530\) 19.4362 0.844256
\(531\) 12.5479i 0.544533i
\(532\) 0 0
\(533\) −6.51638 −0.282256
\(534\) 1.29172i 0.0558981i
\(535\) −28.2261 −1.22032
\(536\) 8.03353i 0.346995i
\(537\) 15.4286i 0.665794i
\(538\) −20.9576 −0.903548
\(539\) 0 0
\(540\) −16.1584 −0.695349
\(541\) 0.516382i 0.0222010i 0.999938 + 0.0111005i \(0.00353347\pi\)
−0.999938 + 0.0111005i \(0.996467\pi\)
\(542\) 14.6132i 0.627690i
\(543\) 8.50593 0.365024
\(544\) 6.07606i 0.260509i
\(545\) 23.3962 1.00218
\(546\) 0 0
\(547\) 28.0407i 1.19894i 0.800399 + 0.599468i \(0.204621\pi\)
−0.800399 + 0.599468i \(0.795379\pi\)
\(548\) −1.34959 −0.0576515
\(549\) 21.6886 0.925648
\(550\) −33.7754 + 2.19289i −1.44019 + 0.0935052i
\(551\) 63.9320i 2.72359i
\(552\) −3.34976 −0.142575
\(553\) 0 0
\(554\) −11.1242 −0.472620
\(555\) −13.7517 −0.583726
\(556\) −11.8957 −0.504491
\(557\) 28.7453i 1.21798i 0.793179 + 0.608989i \(0.208425\pi\)
−0.793179 + 0.608989i \(0.791575\pi\)
\(558\) 19.0317 0.805675
\(559\) 5.92673i 0.250674i
\(560\) 0 0
\(561\) −15.3913 + 0.999289i −0.649820 + 0.0421900i
\(562\) 7.28929 0.307480
\(563\) −6.75074 −0.284510 −0.142255 0.989830i \(-0.545435\pi\)
−0.142255 + 0.989830i \(0.545435\pi\)
\(564\) −0.156023 −0.00656974
\(565\) 65.6653i 2.76256i
\(566\) 16.0139i 0.673115i
\(567\) 0 0
\(568\) 8.86195i 0.371839i
\(569\) 9.72058i 0.407508i 0.979022 + 0.203754i \(0.0653143\pi\)
−0.979022 + 0.203754i \(0.934686\pi\)
\(570\) 20.3824i 0.853723i
\(571\) 20.3824i 0.852975i 0.904494 + 0.426487i \(0.140249\pi\)
−0.904494 + 0.426487i \(0.859751\pi\)
\(572\) 0.390876 + 6.02035i 0.0163433 + 0.251724i
\(573\) 18.7579i 0.783622i
\(574\) 0 0
\(575\) 44.6644 1.86263
\(576\) −2.41421 −0.100592
\(577\) 12.2145i 0.508497i −0.967139 0.254248i \(-0.918172\pi\)
0.967139 0.254248i \(-0.0818281\pi\)
\(578\) 19.9185i 0.828499i
\(579\) 9.65840 0.401390
\(580\) −36.5025 −1.51568
\(581\) 0 0
\(582\) 7.07107i 0.293105i
\(583\) 1.07107 + 16.4968i 0.0443591 + 0.683228i
\(584\) 0.0557060i 0.00230513i
\(585\) 17.1242i 0.707997i
\(586\) 14.2550i 0.588867i
\(587\) 22.5689i 0.931519i −0.884911 0.465759i \(-0.845781\pi\)
0.884911 0.465759i \(-0.154219\pi\)
\(588\) 0 0
\(589\) 53.8384i 2.21837i
\(590\) 20.2671i 0.834382i
\(591\) −13.2177 −0.543703
\(592\) −4.60778 −0.189378
\(593\) 36.6696 1.50584 0.752920 0.658112i \(-0.228645\pi\)
0.752920 + 0.658112i \(0.228645\pi\)
\(594\) −0.890440 13.7148i −0.0365352 0.562723i
\(595\) 0 0
\(596\) 6.57668i 0.269391i
\(597\) 7.02843 0.287655
\(598\) 7.96128i 0.325561i
\(599\) 6.34557 0.259273 0.129637 0.991562i \(-0.458619\pi\)
0.129637 + 0.991562i \(0.458619\pi\)
\(600\) −7.81064 −0.318868
\(601\) −1.60141 −0.0653230 −0.0326615 0.999466i \(-0.510398\pi\)
−0.0326615 + 0.999466i \(0.510398\pi\)
\(602\) 0 0
\(603\) −19.3946 −0.789811
\(604\) 8.63888i 0.351511i
\(605\) −5.54635 42.5330i −0.225491 1.72921i
\(606\) −4.09140 −0.166202
\(607\) 16.7443 0.679631 0.339815 0.940492i \(-0.389635\pi\)
0.339815 + 0.940492i \(0.389635\pi\)
\(608\) 6.82952i 0.276974i
\(609\) 0 0
\(610\) 35.0309 1.41836
\(611\) 0.370815i 0.0150016i
\(612\) 14.6689 0.592955
\(613\) 1.82333i 0.0736437i −0.999322 0.0368219i \(-0.988277\pi\)
0.999322 0.0368219i \(-0.0117234\pi\)
\(614\) 6.75074i 0.272438i
\(615\) 10.6913 0.431116
\(616\) 0 0
\(617\) 46.7616 1.88255 0.941276 0.337638i \(-0.109628\pi\)
0.941276 + 0.337638i \(0.109628\pi\)
\(618\) 3.24908i 0.130697i
\(619\) 40.4744i 1.62680i 0.581702 + 0.813402i \(0.302387\pi\)
−0.581702 + 0.813402i \(0.697613\pi\)
\(620\) 30.7395 1.23453
\(621\) 18.1363i 0.727785i
\(622\) −17.8705 −0.716542
\(623\) 0 0
\(624\) 1.39222i 0.0557335i
\(625\) 28.1186 1.12474
\(626\) 15.0328 0.600832
\(627\) −17.2999 + 1.12321i −0.690890 + 0.0448566i
\(628\) 2.44991i 0.0977619i
\(629\) 27.9971 1.11632
\(630\) 0 0
\(631\) 12.6619 0.504064 0.252032 0.967719i \(-0.418901\pi\)
0.252032 + 0.967719i \(0.418901\pi\)
\(632\) −8.48528 −0.337526
\(633\) −1.62449 −0.0645676
\(634\) 9.73194i 0.386505i
\(635\) −67.5762 −2.68168
\(636\) 3.81493i 0.151272i
\(637\) 0 0
\(638\) −2.01154 30.9821i −0.0796374 1.22659i
\(639\) 21.3946 0.846359
\(640\) −3.89937 −0.154136
\(641\) −1.30695 −0.0516215 −0.0258107 0.999667i \(-0.508217\pi\)
−0.0258107 + 0.999667i \(0.508217\pi\)
\(642\) 5.54020i 0.218654i
\(643\) 39.1745i 1.54489i 0.635081 + 0.772446i \(0.280967\pi\)
−0.635081 + 0.772446i \(0.719033\pi\)
\(644\) 0 0
\(645\) 9.72391i 0.382878i
\(646\) 41.4966i 1.63266i
\(647\) 16.5405i 0.650273i −0.945667 0.325136i \(-0.894590\pi\)
0.945667 0.325136i \(-0.105410\pi\)
\(648\) 4.07107i 0.159927i
\(649\) −17.2020 + 1.11685i −0.675238 + 0.0438403i
\(650\) 18.5633i 0.728114i
\(651\) 0 0
\(652\) −2.29005 −0.0896854
\(653\) 34.7706 1.36068 0.680339 0.732898i \(-0.261833\pi\)
0.680339 + 0.732898i \(0.261833\pi\)
\(654\) 4.59220i 0.179569i
\(655\) 24.7825i 0.968334i
\(656\) 3.58235 0.139867
\(657\) 0.134486 0.00524680
\(658\) 0 0
\(659\) 22.4888i 0.876039i −0.898966 0.438019i \(-0.855680\pi\)
0.898966 0.438019i \(-0.144320\pi\)
\(660\) −0.641304 9.87750i −0.0249627 0.384481i
\(661\) 26.2795i 1.02215i −0.859535 0.511077i \(-0.829247\pi\)
0.859535 0.511077i \(-0.170753\pi\)
\(662\) 18.2599i 0.709689i
\(663\) 8.45922i 0.328529i
\(664\) 10.4676i 0.406221i
\(665\) 0 0
\(666\) 11.1242i 0.431052i
\(667\) 40.9706i 1.58639i
\(668\) −8.51406 −0.329419
\(669\) −4.42065 −0.170912
\(670\) −31.3257 −1.21022
\(671\) 1.93044 + 29.7330i 0.0745237 + 1.14783i
\(672\) 0 0
\(673\) 3.77457i 0.145499i 0.997350 + 0.0727495i \(0.0231774\pi\)
−0.997350 + 0.0727495i \(0.976823\pi\)
\(674\) 29.6928 1.14372
\(675\) 42.2885i 1.62769i
\(676\) 9.69114 0.372736
\(677\) −31.4258 −1.20779 −0.603896 0.797063i \(-0.706386\pi\)
−0.603896 + 0.797063i \(0.706386\pi\)
\(678\) −12.8887 −0.494989
\(679\) 0 0
\(680\) 23.6928 0.908578
\(681\) 0.926506i 0.0355038i
\(682\) 1.69395 + 26.0906i 0.0648648 + 0.999062i
\(683\) −19.9006 −0.761474 −0.380737 0.924683i \(-0.624330\pi\)
−0.380737 + 0.924683i \(0.624330\pi\)
\(684\) 16.4879 0.630432
\(685\) 5.26254i 0.201071i
\(686\) 0 0
\(687\) −14.8491 −0.566527
\(688\) 3.25819i 0.124217i
\(689\) −9.06684 −0.345419
\(690\) 13.0620i 0.497260i
\(691\) 28.6007i 1.08802i 0.839078 + 0.544011i \(0.183095\pi\)
−0.839078 + 0.544011i \(0.816905\pi\)
\(692\) 23.9921 0.912044
\(693\) 0 0
\(694\) −19.2813 −0.731907
\(695\) 46.3859i 1.75952i
\(696\) 7.16469i 0.271577i
\(697\) −21.7665 −0.824467
\(698\) 23.9921i 0.908116i
\(699\) 15.0872 0.570650
\(700\) 0 0
\(701\) 21.2928i 0.804218i 0.915592 + 0.402109i \(0.131723\pi\)
−0.915592 + 0.402109i \(0.868277\pi\)
\(702\) 7.53779 0.284496
\(703\) 31.4689 1.18687
\(704\) −0.214882 3.30966i −0.00809866 0.124737i
\(705\) 0.608391i 0.0229133i
\(706\) 16.1478 0.607731
\(707\) 0 0
\(708\) −3.97801 −0.149503
\(709\) −16.8783 −0.633877 −0.316938 0.948446i \(-0.602655\pi\)
−0.316938 + 0.948446i \(0.602655\pi\)
\(710\) 34.5561 1.29687
\(711\) 20.4853i 0.768258i
\(712\) 1.68771 0.0632496
\(713\) 34.5021i 1.29211i
\(714\) 0 0
\(715\) 23.4756 1.52417i 0.877937 0.0570007i
\(716\) −20.1584 −0.753357
\(717\) 8.90059 0.332399
\(718\) −18.1456 −0.677187
\(719\) 36.1474i 1.34807i −0.738699 0.674036i \(-0.764559\pi\)
0.738699 0.674036i \(-0.235441\pi\)
\(720\) 9.41392i 0.350836i
\(721\) 0 0
\(722\) 27.6424i 1.02874i
\(723\) 20.9510i 0.779176i
\(724\) 11.1135i 0.413031i
\(725\) 95.5312i 3.54794i
\(726\) 8.34836 1.08864i 0.309837 0.0404030i
\(727\) 8.74172i 0.324212i −0.986773 0.162106i \(-0.948171\pi\)
0.986773 0.162106i \(-0.0518287\pi\)
\(728\) 0 0
\(729\) 0.313708 0.0116188
\(730\) 0.217218 0.00803961
\(731\) 19.7970i 0.732217i
\(732\) 6.87584i 0.254138i
\(733\) 13.4645 0.497323 0.248661 0.968590i \(-0.420009\pi\)
0.248661 + 0.968590i \(0.420009\pi\)
\(734\) 4.91547 0.181433
\(735\) 0 0
\(736\) 4.37667i 0.161326i
\(737\) −1.72626 26.5882i −0.0635876 0.979389i
\(738\) 8.64855i 0.318357i
\(739\) 37.3416i 1.37363i −0.726832 0.686816i \(-0.759008\pi\)
0.726832 0.686816i \(-0.240992\pi\)
\(740\) 17.9674i 0.660496i
\(741\) 9.50821i 0.349293i
\(742\) 0 0
\(743\) 17.5472i 0.643746i 0.946783 + 0.321873i \(0.104312\pi\)
−0.946783 + 0.321873i \(0.895688\pi\)
\(744\) 6.03353i 0.221200i
\(745\) −25.6449 −0.939557
\(746\) 2.26806 0.0830397
\(747\) −25.2710 −0.924616
\(748\) 1.30563 + 20.1097i 0.0477387 + 0.735282i
\(749\) 0 0
\(750\) 15.5344i 0.567235i
\(751\) −34.7247 −1.26712 −0.633561 0.773693i \(-0.718407\pi\)
−0.633561 + 0.773693i \(0.718407\pi\)
\(752\) 0.203854i 0.00743377i
\(753\) 10.3340 0.376593
\(754\) 17.0281 0.620128
\(755\) −33.6862 −1.22597
\(756\) 0 0
\(757\) 28.0627 1.01996 0.509978 0.860187i \(-0.329653\pi\)
0.509978 + 0.860187i \(0.329653\pi\)
\(758\) 14.7984i 0.537502i
\(759\) −11.0866 + 0.719803i −0.402416 + 0.0261272i
\(760\) 26.6308 0.966002
\(761\) 7.58299 0.274883 0.137442 0.990510i \(-0.456112\pi\)
0.137442 + 0.990510i \(0.456112\pi\)
\(762\) 13.2638i 0.480498i
\(763\) 0 0
\(764\) 24.5084 0.886681
\(765\) 57.1995i 2.06805i
\(766\) −7.27031 −0.262687
\(767\) 9.45442i 0.341379i
\(768\) 0.765367i 0.0276178i
\(769\) −1.95786 −0.0706022 −0.0353011 0.999377i \(-0.511239\pi\)
−0.0353011 + 0.999377i \(0.511239\pi\)
\(770\) 0 0
\(771\) −2.14792 −0.0773554
\(772\) 12.6193i 0.454179i
\(773\) 9.44572i 0.339739i 0.985467 + 0.169869i \(0.0543346\pi\)
−0.985467 + 0.169869i \(0.945665\pi\)
\(774\) 7.86597 0.282736
\(775\) 80.4487i 2.88980i
\(776\) −9.23880 −0.331653
\(777\) 0 0
\(778\) 35.1936i 1.26175i
\(779\) −24.4657 −0.876575
\(780\) 5.42879 0.194382
\(781\) 1.90427 + 29.3300i 0.0681402 + 1.04951i
\(782\) 26.5929i 0.950961i
\(783\) −38.7912 −1.38628
\(784\) 0 0
\(785\) −9.55310 −0.340965
\(786\) 4.86431 0.173504
\(787\) −20.0872 −0.716031 −0.358016 0.933716i \(-0.616547\pi\)
−0.358016 + 0.933716i \(0.616547\pi\)
\(788\) 17.2697i 0.615209i
\(789\) 6.49435 0.231205
\(790\) 33.0873i 1.17719i
\(791\) 0 0
\(792\) −7.99022 + 0.518771i −0.283920 + 0.0184337i
\(793\) −16.3416