Properties

Label 1134.2.d.a.1133.16
Level $1134$
Weight $2$
Character 1134.1133
Analytic conductor $9.055$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1134.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.05503558921\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} + 9 x^{12} + 54 x^{10} - 288 x^{8} + 486 x^{6} + 729 x^{4} - 4374 x^{2} + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{6} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1133.16
Root \(-1.62181 - 0.608059i\) of defining polynomial
Character \(\chi\) \(=\) 1134.1133
Dual form 1134.2.d.a.1133.8

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000 q^{4} +3.89111 q^{5} +(-2.44383 - 1.01375i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000 q^{4} +3.89111 q^{5} +(-2.44383 - 1.01375i) q^{7} -1.00000i q^{8} +3.89111i q^{10} -3.94462i q^{11} -2.84849i q^{13} +(1.01375 - 2.44383i) q^{14} +1.00000 q^{16} -0.742117 q^{17} -1.78474i q^{19} -3.89111 q^{20} +3.94462 q^{22} -6.25311i q^{23} +10.1408 q^{25} +2.84849 q^{26} +(2.44383 + 1.01375i) q^{28} +2.88766i q^{29} -3.51174i q^{31} +1.00000i q^{32} -0.742117i q^{34} +(-9.50923 - 3.94462i) q^{35} +3.00158 q^{37} +1.78474 q^{38} -3.89111i q^{40} -10.4941 q^{41} -0.943042 q^{43} +3.94462i q^{44} +6.25311 q^{46} +2.18525 q^{47} +(4.94462 + 4.95487i) q^{49} +10.1408i q^{50} +2.84849i q^{52} -15.3490i q^{55} +(-1.01375 + 2.44383i) q^{56} -2.88766 q^{58} +0.0211346 q^{59} -2.46911i q^{61} +3.51174 q^{62} -1.00000 q^{64} -11.0838i q^{65} +13.4493 q^{67} +0.742117 q^{68} +(3.94462 - 9.50923i) q^{70} +1.94304i q^{71} +4.85486i q^{73} +3.00158i q^{74} +1.78474i q^{76} +(-3.99886 + 9.63998i) q^{77} +3.63613 q^{79} +3.89111 q^{80} -10.4941i q^{82} -8.05995 q^{83} -2.88766 q^{85} -0.943042i q^{86} -3.94462 q^{88} +9.26646 q^{89} +(-2.88766 + 6.96124i) q^{91} +6.25311i q^{92} +2.18525i q^{94} -6.94462i q^{95} +18.8196i q^{97} +(-4.95487 + 4.94462i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4} - 4 q^{7} + O(q^{10}) \) \( 16 q - 16 q^{4} - 4 q^{7} + 16 q^{16} + 16 q^{25} + 4 q^{28} - 8 q^{37} - 8 q^{43} + 24 q^{46} + 16 q^{49} + 24 q^{58} - 16 q^{64} + 56 q^{67} + 8 q^{79} + 24 q^{85} + 24 q^{91} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(-1\) \(-1\)

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 0
\(4\) −1.00000 −0.500000
\(5\) 3.89111 1.74016 0.870080 0.492911i \(-0.164067\pi\)
0.870080 + 0.492911i \(0.164067\pi\)
\(6\) 0 0
\(7\) −2.44383 1.01375i −0.923681 0.383162i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 3.89111i 1.23048i
\(11\) 3.94462i 1.18935i −0.803967 0.594674i \(-0.797281\pi\)
0.803967 0.594674i \(-0.202719\pi\)
\(12\) 0 0
\(13\) 2.84849i 0.790030i −0.918675 0.395015i \(-0.870739\pi\)
0.918675 0.395015i \(-0.129261\pi\)
\(14\) 1.01375 2.44383i 0.270936 0.653141i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −0.742117 −0.179990 −0.0899949 0.995942i \(-0.528685\pi\)
−0.0899949 + 0.995942i \(0.528685\pi\)
\(18\) 0 0
\(19\) 1.78474i 0.409447i −0.978820 0.204723i \(-0.934370\pi\)
0.978820 0.204723i \(-0.0656295\pi\)
\(20\) −3.89111 −0.870080
\(21\) 0 0
\(22\) 3.94462 0.840996
\(23\) 6.25311i 1.30386i −0.758278 0.651932i \(-0.773959\pi\)
0.758278 0.651932i \(-0.226041\pi\)
\(24\) 0 0
\(25\) 10.1408 2.02815
\(26\) 2.84849 0.558636
\(27\) 0 0
\(28\) 2.44383 + 1.01375i 0.461841 + 0.191581i
\(29\) 2.88766i 0.536225i 0.963388 + 0.268113i \(0.0864000\pi\)
−0.963388 + 0.268113i \(0.913600\pi\)
\(30\) 0 0
\(31\) 3.51174i 0.630726i −0.948971 0.315363i \(-0.897874\pi\)
0.948971 0.315363i \(-0.102126\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) 0.742117i 0.127272i
\(35\) −9.50923 3.94462i −1.60735 0.666762i
\(36\) 0 0
\(37\) 3.00158 0.493456 0.246728 0.969085i \(-0.420645\pi\)
0.246728 + 0.969085i \(0.420645\pi\)
\(38\) 1.78474 0.289523
\(39\) 0 0
\(40\) 3.89111i 0.615239i
\(41\) −10.4941 −1.63890 −0.819452 0.573148i \(-0.805722\pi\)
−0.819452 + 0.573148i \(0.805722\pi\)
\(42\) 0 0
\(43\) −0.943042 −0.143813 −0.0719063 0.997411i \(-0.522908\pi\)
−0.0719063 + 0.997411i \(0.522908\pi\)
\(44\) 3.94462i 0.594674i
\(45\) 0 0
\(46\) 6.25311 0.921971
\(47\) 2.18525 0.318752 0.159376 0.987218i \(-0.449052\pi\)
0.159376 + 0.987218i \(0.449052\pi\)
\(48\) 0 0
\(49\) 4.94462 + 4.95487i 0.706374 + 0.707839i
\(50\) 10.1408i 1.43412i
\(51\) 0 0
\(52\) 2.84849i 0.395015i
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 15.3490i 2.06965i
\(56\) −1.01375 + 2.44383i −0.135468 + 0.326571i
\(57\) 0 0
\(58\) −2.88766 −0.379169
\(59\) 0.0211346 0.00275149 0.00137575 0.999999i \(-0.499562\pi\)
0.00137575 + 0.999999i \(0.499562\pi\)
\(60\) 0 0
\(61\) 2.46911i 0.316138i −0.987428 0.158069i \(-0.949473\pi\)
0.987428 0.158069i \(-0.0505268\pi\)
\(62\) 3.51174 0.445991
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 11.0838i 1.37478i
\(66\) 0 0
\(67\) 13.4493 1.64309 0.821544 0.570144i \(-0.193113\pi\)
0.821544 + 0.570144i \(0.193113\pi\)
\(68\) 0.742117 0.0899949
\(69\) 0 0
\(70\) 3.94462 9.50923i 0.471472 1.13657i
\(71\) 1.94304i 0.230597i 0.993331 + 0.115298i \(0.0367824\pi\)
−0.993331 + 0.115298i \(0.963218\pi\)
\(72\) 0 0
\(73\) 4.85486i 0.568218i 0.958792 + 0.284109i \(0.0916978\pi\)
−0.958792 + 0.284109i \(0.908302\pi\)
\(74\) 3.00158i 0.348926i
\(75\) 0 0
\(76\) 1.78474i 0.204723i
\(77\) −3.99886 + 9.63998i −0.455712 + 1.09858i
\(78\) 0 0
\(79\) 3.63613 0.409096 0.204548 0.978856i \(-0.434427\pi\)
0.204548 + 0.978856i \(0.434427\pi\)
\(80\) 3.89111 0.435040
\(81\) 0 0
\(82\) 10.4941i 1.15888i
\(83\) −8.05995 −0.884695 −0.442347 0.896844i \(-0.645854\pi\)
−0.442347 + 0.896844i \(0.645854\pi\)
\(84\) 0 0
\(85\) −2.88766 −0.313211
\(86\) 0.943042i 0.101691i
\(87\) 0 0
\(88\) −3.94462 −0.420498
\(89\) 9.26646 0.982243 0.491122 0.871091i \(-0.336587\pi\)
0.491122 + 0.871091i \(0.336587\pi\)
\(90\) 0 0
\(91\) −2.88766 + 6.96124i −0.302709 + 0.729736i
\(92\) 6.25311i 0.651932i
\(93\) 0 0
\(94\) 2.18525i 0.225392i
\(95\) 6.94462i 0.712503i
\(96\) 0 0
\(97\) 18.8196i 1.91084i 0.295248 + 0.955421i \(0.404598\pi\)
−0.295248 + 0.955421i \(0.595402\pi\)
\(98\) −4.95487 + 4.94462i −0.500517 + 0.499482i
\(99\) 0 0
\(100\) −10.1408 −1.01408
\(101\) 8.28158 0.824048 0.412024 0.911173i \(-0.364822\pi\)
0.412024 + 0.911173i \(0.364822\pi\)
\(102\) 0 0
\(103\) 17.0487i 1.67986i 0.542697 + 0.839929i \(0.317403\pi\)
−0.542697 + 0.839929i \(0.682597\pi\)
\(104\) −2.84849 −0.279318
\(105\) 0 0
\(106\) 0 0
\(107\) 14.3369i 1.38600i −0.720936 0.693001i \(-0.756288\pi\)
0.720936 0.693001i \(-0.243712\pi\)
\(108\) 0 0
\(109\) 11.2800 1.08042 0.540212 0.841529i \(-0.318344\pi\)
0.540212 + 0.841529i \(0.318344\pi\)
\(110\) 15.3490 1.46347
\(111\) 0 0
\(112\) −2.44383 1.01375i −0.230920 0.0957904i
\(113\) 9.83228i 0.924943i −0.886634 0.462472i \(-0.846963\pi\)
0.886634 0.462472i \(-0.153037\pi\)
\(114\) 0 0
\(115\) 24.3316i 2.26893i
\(116\) 2.88766i 0.268113i
\(117\) 0 0
\(118\) 0.0211346i 0.00194560i
\(119\) 1.81361 + 0.752321i 0.166253 + 0.0689652i
\(120\) 0 0
\(121\) −4.56002 −0.414548
\(122\) 2.46911 0.223543
\(123\) 0 0
\(124\) 3.51174i 0.315363i
\(125\) 20.0033 1.78915
\(126\) 0 0
\(127\) 2.94462 0.261293 0.130646 0.991429i \(-0.458295\pi\)
0.130646 + 0.991429i \(0.458295\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 11.0838 0.972115
\(131\) 15.0651 1.31624 0.658122 0.752911i \(-0.271351\pi\)
0.658122 + 0.752911i \(0.271351\pi\)
\(132\) 0 0
\(133\) −1.80928 + 4.36160i −0.156884 + 0.378198i
\(134\) 13.4493i 1.16184i
\(135\) 0 0
\(136\) 0.742117i 0.0636360i
\(137\) 15.7199i 1.34305i 0.740984 + 0.671523i \(0.234359\pi\)
−0.740984 + 0.671523i \(0.765641\pi\)
\(138\) 0 0
\(139\) 3.30675i 0.280475i −0.990118 0.140237i \(-0.955213\pi\)
0.990118 0.140237i \(-0.0447866\pi\)
\(140\) 9.50923 + 3.94462i 0.803676 + 0.333381i
\(141\) 0 0
\(142\) −1.94304 −0.163056
\(143\) −11.2362 −0.939620
\(144\) 0 0
\(145\) 11.2362i 0.933118i
\(146\) −4.85486 −0.401791
\(147\) 0 0
\(148\) −3.00158 −0.246728
\(149\) 11.0016i 0.901284i 0.892705 + 0.450642i \(0.148805\pi\)
−0.892705 + 0.450642i \(0.851195\pi\)
\(150\) 0 0
\(151\) −1.43998 −0.117184 −0.0585918 0.998282i \(-0.518661\pi\)
−0.0585918 + 0.998282i \(0.518661\pi\)
\(152\) −1.78474 −0.144761
\(153\) 0 0
\(154\) −9.63998 3.99886i −0.776812 0.322237i
\(155\) 13.6646i 1.09756i
\(156\) 0 0
\(157\) 16.6071i 1.32539i −0.748890 0.662695i \(-0.769413\pi\)
0.748890 0.662695i \(-0.230587\pi\)
\(158\) 3.63613i 0.289275i
\(159\) 0 0
\(160\) 3.89111i 0.307620i
\(161\) −6.33909 + 15.2815i −0.499591 + 1.20435i
\(162\) 0 0
\(163\) −12.3955 −0.970887 −0.485444 0.874268i \(-0.661342\pi\)
−0.485444 + 0.874268i \(0.661342\pi\)
\(164\) 10.4941 0.819452
\(165\) 0 0
\(166\) 8.05995i 0.625574i
\(167\) −11.7217 −0.907056 −0.453528 0.891242i \(-0.649835\pi\)
−0.453528 + 0.891242i \(0.649835\pi\)
\(168\) 0 0
\(169\) 4.88608 0.375853
\(170\) 2.88766i 0.221474i
\(171\) 0 0
\(172\) 0.943042 0.0719063
\(173\) −16.7710 −1.27507 −0.637536 0.770420i \(-0.720046\pi\)
−0.637536 + 0.770420i \(0.720046\pi\)
\(174\) 0 0
\(175\) −24.7823 10.2802i −1.87337 0.777111i
\(176\) 3.94462i 0.297337i
\(177\) 0 0
\(178\) 9.26646i 0.694551i
\(179\) 5.77532i 0.431668i 0.976430 + 0.215834i \(0.0692470\pi\)
−0.976430 + 0.215834i \(0.930753\pi\)
\(180\) 0 0
\(181\) 5.53310i 0.411272i 0.978629 + 0.205636i \(0.0659263\pi\)
−0.978629 + 0.205636i \(0.934074\pi\)
\(182\) −6.96124 2.88766i −0.516001 0.214048i
\(183\) 0 0
\(184\) −6.25311 −0.460985
\(185\) 11.6795 0.858692
\(186\) 0 0
\(187\) 2.92737i 0.214070i
\(188\) −2.18525 −0.159376
\(189\) 0 0
\(190\) 6.94462 0.503816
\(191\) 6.21372i 0.449609i 0.974404 + 0.224805i \(0.0721744\pi\)
−0.974404 + 0.224805i \(0.927826\pi\)
\(192\) 0 0
\(193\) −7.80542 −0.561847 −0.280923 0.959730i \(-0.590641\pi\)
−0.280923 + 0.959730i \(0.590641\pi\)
\(194\) −18.8196 −1.35117
\(195\) 0 0
\(196\) −4.94462 4.95487i −0.353187 0.353919i
\(197\) 12.7737i 0.910092i −0.890468 0.455046i \(-0.849623\pi\)
0.890468 0.455046i \(-0.150377\pi\)
\(198\) 0 0
\(199\) 1.81201i 0.128450i 0.997935 + 0.0642250i \(0.0204575\pi\)
−0.997935 + 0.0642250i \(0.979542\pi\)
\(200\) 10.1408i 0.717061i
\(201\) 0 0
\(202\) 8.28158i 0.582690i
\(203\) 2.92737 7.05696i 0.205461 0.495301i
\(204\) 0 0
\(205\) −40.8338 −2.85195
\(206\) −17.0487 −1.18784
\(207\) 0 0
\(208\) 2.84849i 0.197507i
\(209\) −7.04011 −0.486975
\(210\) 0 0
\(211\) 3.77532 0.259904 0.129952 0.991520i \(-0.458518\pi\)
0.129952 + 0.991520i \(0.458518\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 14.3369 0.980052
\(215\) −3.66949 −0.250257
\(216\) 0 0
\(217\) −3.56002 + 8.58209i −0.241670 + 0.582590i
\(218\) 11.2800i 0.763976i
\(219\) 0 0
\(220\) 15.3490i 1.03483i
\(221\) 2.11392i 0.142197i
\(222\) 0 0
\(223\) 12.7782i 0.855691i 0.903852 + 0.427846i \(0.140727\pi\)
−0.903852 + 0.427846i \(0.859273\pi\)
\(224\) 1.01375 2.44383i 0.0677341 0.163285i
\(225\) 0 0
\(226\) 9.83228 0.654034
\(227\) −19.9822 −1.32627 −0.663133 0.748502i \(-0.730773\pi\)
−0.663133 + 0.748502i \(0.730773\pi\)
\(228\) 0 0
\(229\) 10.1314i 0.669500i −0.942307 0.334750i \(-0.891348\pi\)
0.942307 0.334750i \(-0.108652\pi\)
\(230\) 24.3316 1.60438
\(231\) 0 0
\(232\) 2.88766 0.189584
\(233\) 7.31007i 0.478898i −0.970909 0.239449i \(-0.923033\pi\)
0.970909 0.239449i \(-0.0769669\pi\)
\(234\) 0 0
\(235\) 8.50307 0.554679
\(236\) −0.0211346 −0.00137575
\(237\) 0 0
\(238\) −0.752321 + 1.81361i −0.0487658 + 0.117559i
\(239\) 8.40988i 0.543990i 0.962299 + 0.271995i \(0.0876834\pi\)
−0.962299 + 0.271995i \(0.912317\pi\)
\(240\) 0 0
\(241\) 8.95213i 0.576657i −0.957531 0.288329i \(-0.906900\pi\)
0.957531 0.288329i \(-0.0930996\pi\)
\(242\) 4.56002i 0.293129i
\(243\) 0 0
\(244\) 2.46911i 0.158069i
\(245\) 19.2401 + 19.2800i 1.22920 + 1.23175i
\(246\) 0 0
\(247\) −5.08381 −0.323475
\(248\) −3.51174 −0.222995
\(249\) 0 0
\(250\) 20.0033i 1.26512i
\(251\) −12.6432 −0.798033 −0.399017 0.916944i \(-0.630648\pi\)
−0.399017 + 0.916944i \(0.630648\pi\)
\(252\) 0 0
\(253\) −24.6661 −1.55075
\(254\) 2.94462i 0.184762i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −16.3066 −1.01718 −0.508588 0.861010i \(-0.669832\pi\)
−0.508588 + 0.861010i \(0.669832\pi\)
\(258\) 0 0
\(259\) −7.33535 3.04285i −0.455796 0.189074i
\(260\) 11.0838i 0.687389i
\(261\) 0 0
\(262\) 15.0651i 0.930725i
\(263\) 23.7215i 1.46273i −0.681985 0.731366i \(-0.738883\pi\)
0.681985 0.731366i \(-0.261117\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −4.36160 1.80928i −0.267427 0.110934i
\(267\) 0 0
\(268\) −13.4493 −0.821544
\(269\) −7.28288 −0.444045 −0.222022 0.975042i \(-0.571266\pi\)
−0.222022 + 0.975042i \(0.571266\pi\)
\(270\) 0 0
\(271\) 22.6879i 1.37819i 0.724669 + 0.689097i \(0.241993\pi\)
−0.724669 + 0.689097i \(0.758007\pi\)
\(272\) −0.742117 −0.0449974
\(273\) 0 0
\(274\) −15.7199 −0.949677
\(275\) 40.0015i 2.41218i
\(276\) 0 0
\(277\) 24.1676 1.45209 0.726046 0.687646i \(-0.241356\pi\)
0.726046 + 0.687646i \(0.241356\pi\)
\(278\) 3.30675 0.198326
\(279\) 0 0
\(280\) −3.94462 + 9.50923i −0.235736 + 0.568285i
\(281\) 4.74847i 0.283270i 0.989919 + 0.141635i \(0.0452359\pi\)
−0.989919 + 0.141635i \(0.954764\pi\)
\(282\) 0 0
\(283\) 29.3853i 1.74677i 0.487027 + 0.873387i \(0.338081\pi\)
−0.487027 + 0.873387i \(0.661919\pi\)
\(284\) 1.94304i 0.115298i
\(285\) 0 0
\(286\) 11.2362i 0.664412i
\(287\) 25.6458 + 10.6384i 1.51382 + 0.627965i
\(288\) 0 0
\(289\) −16.4493 −0.967604
\(290\) −11.2362 −0.659814
\(291\) 0 0
\(292\) 4.85486i 0.284109i
\(293\) 6.62413 0.386986 0.193493 0.981102i \(-0.438018\pi\)
0.193493 + 0.981102i \(0.438018\pi\)
\(294\) 0 0
\(295\) 0.0822372 0.00478803
\(296\) 3.00158i 0.174463i
\(297\) 0 0
\(298\) −11.0016 −0.637304
\(299\) −17.8119 −1.03009
\(300\) 0 0
\(301\) 2.30464 + 0.956010i 0.132837 + 0.0551035i
\(302\) 1.43998i 0.0828613i
\(303\) 0 0
\(304\) 1.78474i 0.102362i
\(305\) 9.60761i 0.550130i
\(306\) 0 0
\(307\) 21.7242i 1.23987i −0.784655 0.619933i \(-0.787160\pi\)
0.784655 0.619933i \(-0.212840\pi\)
\(308\) 3.99886 9.63998i 0.227856 0.549289i
\(309\) 0 0
\(310\) 13.6646 0.776095
\(311\) 6.29800 0.357127 0.178563 0.983928i \(-0.442855\pi\)
0.178563 + 0.983928i \(0.442855\pi\)
\(312\) 0 0
\(313\) 22.2191i 1.25590i −0.778256 0.627948i \(-0.783895\pi\)
0.778256 0.627948i \(-0.216105\pi\)
\(314\) 16.6071 0.937192
\(315\) 0 0
\(316\) −3.63613 −0.204548
\(317\) 15.6614i 0.879632i −0.898088 0.439816i \(-0.855044\pi\)
0.898088 0.439816i \(-0.144956\pi\)
\(318\) 0 0
\(319\) 11.3907 0.637758
\(320\) −3.89111 −0.217520
\(321\) 0 0
\(322\) −15.2815 6.33909i −0.851607 0.353264i
\(323\) 1.32448i 0.0736963i
\(324\) 0 0
\(325\) 28.8859i 1.60230i
\(326\) 12.3955i 0.686521i
\(327\) 0 0
\(328\) 10.4941i 0.579440i
\(329\) −5.34039 2.21530i −0.294425 0.122133i
\(330\) 0 0
\(331\) 1.27226 0.0699296 0.0349648 0.999389i \(-0.488868\pi\)
0.0349648 + 0.999389i \(0.488868\pi\)
\(332\) 8.05995 0.442347
\(333\) 0 0
\(334\) 11.7217i 0.641386i
\(335\) 52.3326 2.85924
\(336\) 0 0
\(337\) 7.56002 0.411821 0.205910 0.978571i \(-0.433984\pi\)
0.205910 + 0.978571i \(0.433984\pi\)
\(338\) 4.88608i 0.265768i
\(339\) 0 0
\(340\) 2.88766 0.156605
\(341\) −13.8525 −0.750153
\(342\) 0 0
\(343\) −7.06081 17.1215i −0.381248 0.924473i
\(344\) 0.943042i 0.0508454i
\(345\) 0 0
\(346\) 16.7710i 0.901613i
\(347\) 22.1091i 1.18688i 0.804879 + 0.593439i \(0.202230\pi\)
−0.804879 + 0.593439i \(0.797770\pi\)
\(348\) 0 0
\(349\) 14.7435i 0.789200i −0.918853 0.394600i \(-0.870883\pi\)
0.918853 0.394600i \(-0.129117\pi\)
\(350\) 10.2802 24.7823i 0.549501 1.32467i
\(351\) 0 0
\(352\) 3.94462 0.210249
\(353\) 17.2776 0.919595 0.459798 0.888024i \(-0.347922\pi\)
0.459798 + 0.888024i \(0.347922\pi\)
\(354\) 0 0
\(355\) 7.56060i 0.401275i
\(356\) −9.26646 −0.491122
\(357\) 0 0
\(358\) −5.77532 −0.305235
\(359\) 10.9129i 0.575963i −0.957636 0.287982i \(-0.907016\pi\)
0.957636 0.287982i \(-0.0929842\pi\)
\(360\) 0 0
\(361\) 15.8147 0.832353
\(362\) −5.53310 −0.290813
\(363\) 0 0
\(364\) 2.88766 6.96124i 0.151355 0.364868i
\(365\) 18.8908i 0.988791i
\(366\) 0 0
\(367\) 35.7272i 1.86494i 0.361242 + 0.932472i \(0.382353\pi\)
−0.361242 + 0.932472i \(0.617647\pi\)
\(368\) 6.25311i 0.325966i
\(369\) 0 0
\(370\) 11.6795i 0.607187i
\(371\) 0 0
\(372\) 0 0
\(373\) −32.0600 −1.66001 −0.830003 0.557760i \(-0.811661\pi\)
−0.830003 + 0.557760i \(0.811661\pi\)
\(374\) −2.92737 −0.151371
\(375\) 0 0
\(376\) 2.18525i 0.112696i
\(377\) 8.22549 0.423634
\(378\) 0 0
\(379\) 34.8891 1.79214 0.896068 0.443918i \(-0.146412\pi\)
0.896068 + 0.443918i \(0.146412\pi\)
\(380\) 6.94462i 0.356251i
\(381\) 0 0
\(382\) −6.21372 −0.317922
\(383\) −17.5342 −0.895957 −0.447978 0.894044i \(-0.647856\pi\)
−0.447978 + 0.894044i \(0.647856\pi\)
\(384\) 0 0
\(385\) −15.5600 + 37.5103i −0.793012 + 1.91170i
\(386\) 7.80542i 0.397286i
\(387\) 0 0
\(388\) 18.8196i 0.955421i
\(389\) 7.62171i 0.386436i 0.981156 + 0.193218i \(0.0618925\pi\)
−0.981156 + 0.193218i \(0.938108\pi\)
\(390\) 0 0
\(391\) 4.64054i 0.234682i
\(392\) 4.95487 4.94462i 0.250259 0.249741i
\(393\) 0 0
\(394\) 12.7737 0.643532
\(395\) 14.1486 0.711893
\(396\) 0 0
\(397\) 37.6469i 1.88944i −0.327873 0.944722i \(-0.606332\pi\)
0.327873 0.944722i \(-0.393668\pi\)
\(398\) −1.81201 −0.0908278
\(399\) 0 0
\(400\) 10.1408 0.507039
\(401\) 21.4415i 1.07074i 0.844619 + 0.535368i \(0.179827\pi\)
−0.844619 + 0.535368i \(0.820173\pi\)
\(402\) 0 0
\(403\) −10.0032 −0.498293
\(404\) −8.28158 −0.412024
\(405\) 0 0
\(406\) 7.05696 + 2.92737i 0.350231 + 0.145283i
\(407\) 11.8401i 0.586891i
\(408\) 0 0
\(409\) 29.5703i 1.46216i 0.682293 + 0.731079i \(0.260983\pi\)
−0.682293 + 0.731079i \(0.739017\pi\)
\(410\) 40.8338i 2.01664i
\(411\) 0 0
\(412\) 17.0487i 0.839929i
\(413\) −0.0516494 0.0214252i −0.00254150 0.00105427i
\(414\) 0 0
\(415\) −31.3622 −1.53951
\(416\) 2.84849 0.139659
\(417\) 0 0
\(418\) 7.04011i 0.344343i
\(419\) 7.12962 0.348305 0.174152 0.984719i \(-0.444281\pi\)
0.174152 + 0.984719i \(0.444281\pi\)
\(420\) 0 0
\(421\) 4.62014 0.225172 0.112586 0.993642i \(-0.464087\pi\)
0.112586 + 0.993642i \(0.464087\pi\)
\(422\) 3.77532i 0.183780i
\(423\) 0 0
\(424\) 0 0
\(425\) −7.52564 −0.365047
\(426\) 0 0
\(427\) −2.50307 + 6.03410i −0.121132 + 0.292010i
\(428\) 14.3369i 0.693001i
\(429\) 0 0
\(430\) 3.66949i 0.176958i
\(431\) 4.00771i 0.193045i 0.995331 + 0.0965223i \(0.0307719\pi\)
−0.995331 + 0.0965223i \(0.969228\pi\)
\(432\) 0 0
\(433\) 29.4125i 1.41348i 0.707475 + 0.706738i \(0.249834\pi\)
−0.707475 + 0.706738i \(0.750166\pi\)
\(434\) −8.58209 3.56002i −0.411953 0.170887i
\(435\) 0 0
\(436\) −11.2800 −0.540212
\(437\) −11.1602 −0.533863
\(438\) 0 0
\(439\) 21.3769i 1.02027i 0.860096 + 0.510133i \(0.170404\pi\)
−0.860096 + 0.510133i \(0.829596\pi\)
\(440\) −15.3490 −0.731733
\(441\) 0 0
\(442\) −2.11392 −0.100549
\(443\) 5.83386i 0.277175i −0.990350 0.138587i \(-0.955744\pi\)
0.990350 0.138587i \(-0.0442562\pi\)
\(444\) 0 0
\(445\) 36.0569 1.70926
\(446\) −12.7782 −0.605065
\(447\) 0 0
\(448\) 2.44383 + 1.01375i 0.115460 + 0.0478952i
\(449\) 22.5823i 1.06573i 0.846202 + 0.532863i \(0.178884\pi\)
−0.846202 + 0.532863i \(0.821116\pi\)
\(450\) 0 0
\(451\) 41.3953i 1.94923i
\(452\) 9.83228i 0.462472i
\(453\) 0 0
\(454\) 19.9822i 0.937811i
\(455\) −11.2362 + 27.0870i −0.526762 + 1.26986i
\(456\) 0 0
\(457\) 39.8623 1.86468 0.932340 0.361584i \(-0.117764\pi\)
0.932340 + 0.361584i \(0.117764\pi\)
\(458\) 10.1314 0.473408
\(459\) 0 0
\(460\) 24.3316i 1.13447i
\(461\) 7.36507 0.343026 0.171513 0.985182i \(-0.445135\pi\)
0.171513 + 0.985182i \(0.445135\pi\)
\(462\) 0 0
\(463\) 28.6914 1.33340 0.666702 0.745325i \(-0.267706\pi\)
0.666702 + 0.745325i \(0.267706\pi\)
\(464\) 2.88766i 0.134056i
\(465\) 0 0
\(466\) 7.31007 0.338632
\(467\) −13.6704 −0.632590 −0.316295 0.948661i \(-0.602439\pi\)
−0.316295 + 0.948661i \(0.602439\pi\)
\(468\) 0 0
\(469\) −32.8677 13.6342i −1.51769 0.629569i
\(470\) 8.50307i 0.392217i
\(471\) 0 0
\(472\) 0.0211346i 0.000972799i
\(473\) 3.71994i 0.171043i
\(474\) 0 0
\(475\) 18.0986i 0.830422i
\(476\) −1.81361 0.752321i −0.0831266 0.0344826i
\(477\) 0 0
\(478\) −8.40988 −0.384659
\(479\) −10.4107 −0.475679 −0.237839 0.971304i \(-0.576439\pi\)
−0.237839 + 0.971304i \(0.576439\pi\)
\(480\) 0 0
\(481\) 8.54997i 0.389845i
\(482\) 8.95213 0.407758
\(483\) 0 0
\(484\) 4.56002 0.207274
\(485\) 73.2292i 3.32517i
\(486\) 0 0
\(487\) 2.33850 0.105968 0.0529838 0.998595i \(-0.483127\pi\)
0.0529838 + 0.998595i \(0.483127\pi\)
\(488\) −2.46911 −0.111772
\(489\) 0 0
\(490\) −19.2800 + 19.2401i −0.870980 + 0.869178i
\(491\) 33.8844i 1.52918i −0.644516 0.764591i \(-0.722941\pi\)
0.644516 0.764591i \(-0.277059\pi\)
\(492\) 0 0
\(493\) 2.14298i 0.0965151i
\(494\) 5.08381i 0.228732i
\(495\) 0 0
\(496\) 3.51174i 0.157682i
\(497\) 1.96976 4.74847i 0.0883558 0.212998i
\(498\) 0 0
\(499\) −16.6045 −0.743317 −0.371659 0.928369i \(-0.621211\pi\)
−0.371659 + 0.928369i \(0.621211\pi\)
\(500\) −20.0033 −0.894576
\(501\) 0 0
\(502\) 12.6432i 0.564295i
\(503\) −35.3661 −1.57690 −0.788449 0.615100i \(-0.789115\pi\)
−0.788449 + 0.615100i \(0.789115\pi\)
\(504\) 0 0
\(505\) 32.2246 1.43398
\(506\) 24.6661i 1.09654i
\(507\) 0 0
\(508\) −2.94462 −0.130646
\(509\) 37.0582 1.64257 0.821287 0.570515i \(-0.193256\pi\)
0.821287 + 0.570515i \(0.193256\pi\)
\(510\) 0 0
\(511\) 4.92162 11.8645i 0.217720 0.524853i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 16.3066i 0.719252i
\(515\) 66.3384i 2.92322i
\(516\) 0 0
\(517\) 8.61999i 0.379107i
\(518\) 3.04285 7.33535i 0.133695 0.322297i
\(519\) 0 0
\(520\) −11.0838 −0.486057
\(521\) 1.78309 0.0781187 0.0390594 0.999237i \(-0.487564\pi\)
0.0390594 + 0.999237i \(0.487564\pi\)
\(522\) 0 0
\(523\) 24.0538i 1.05180i 0.850546 + 0.525901i \(0.176272\pi\)
−0.850546 + 0.525901i \(0.823728\pi\)
\(524\) −15.0651 −0.658122
\(525\) 0 0
\(526\) 23.7215 1.03431
\(527\) 2.60612i 0.113524i
\(528\) 0 0
\(529\) −16.1014 −0.700060
\(530\) 0 0
\(531\) 0 0
\(532\) 1.80928 4.36160i 0.0784422 0.189099i
\(533\) 29.8924i 1.29478i
\(534\) 0 0
\(535\) 55.7866i 2.41187i
\(536\) 13.4493i 0.580920i
\(537\) 0 0
\(538\) 7.28288i 0.313987i
\(539\) 19.5451 19.5046i 0.841866 0.840124i
\(540\) 0 0
\(541\) 30.0032 1.28994 0.644968 0.764209i \(-0.276871\pi\)
0.644968 + 0.764209i \(0.276871\pi\)
\(542\) −22.6879 −0.974530
\(543\) 0 0
\(544\) 0.742117i 0.0318180i
\(545\) 43.8916 1.88011
\(546\) 0 0
\(547\) 21.5632 0.921975 0.460987 0.887407i \(-0.347495\pi\)
0.460987 + 0.887407i \(0.347495\pi\)
\(548\) 15.7199i 0.671523i
\(549\) 0 0
\(550\) 40.0015 1.70567
\(551\) 5.15372 0.219556
\(552\) 0 0
\(553\) −8.88608 3.68613i −0.377875 0.156750i
\(554\) 24.1676i 1.02678i
\(555\) 0 0
\(556\) 3.30675i 0.140237i
\(557\) 36.9477i 1.56552i 0.622321 + 0.782762i \(0.286190\pi\)
−0.622321 + 0.782762i \(0.713810\pi\)
\(558\) 0 0
\(559\) 2.68625i 0.113616i
\(560\) −9.50923 3.94462i −0.401838 0.166691i
\(561\) 0 0
\(562\) −4.74847 −0.200302
\(563\) −15.1684 −0.639273 −0.319637 0.947540i \(-0.603561\pi\)
−0.319637 + 0.947540i \(0.603561\pi\)
\(564\) 0 0
\(565\) 38.2585i 1.60955i
\(566\) −29.3853 −1.23516
\(567\) 0 0
\(568\) 1.94304 0.0815282
\(569\) 36.7292i 1.53977i 0.638183 + 0.769885i \(0.279686\pi\)
−0.638183 + 0.769885i \(0.720314\pi\)
\(570\) 0 0
\(571\) 11.2277 0.469866 0.234933 0.972012i \(-0.424513\pi\)
0.234933 + 0.972012i \(0.424513\pi\)
\(572\) 11.2362 0.469810
\(573\) 0 0
\(574\) −10.6384 + 25.6458i −0.444038 + 1.07044i
\(575\) 63.4114i 2.64444i
\(576\) 0 0
\(577\) 36.5515i 1.52166i −0.648952 0.760829i \(-0.724792\pi\)
0.648952 0.760829i \(-0.275208\pi\)
\(578\) 16.4493i 0.684199i
\(579\) 0 0
\(580\) 11.2362i 0.466559i
\(581\) 19.6972 + 8.17078i 0.817176 + 0.338981i
\(582\) 0 0
\(583\) 0 0
\(584\) 4.85486 0.200896
\(585\) 0 0
\(586\) 6.62413i 0.273640i
\(587\) −9.99475 −0.412528 −0.206264 0.978496i \(-0.566131\pi\)
−0.206264 + 0.978496i \(0.566131\pi\)
\(588\) 0 0
\(589\) −6.26753 −0.258249
\(590\) 0.0822372i 0.00338565i
\(591\) 0 0
\(592\) 3.00158 0.123364
\(593\) 7.78223 0.319578 0.159789 0.987151i \(-0.448919\pi\)
0.159789 + 0.987151i \(0.448919\pi\)
\(594\) 0 0
\(595\) 7.05696 + 2.92737i 0.289307 + 0.120010i
\(596\) 11.0016i 0.450642i
\(597\) 0 0
\(598\) 17.8119i 0.728385i
\(599\) 25.0124i 1.02198i 0.859586 + 0.510990i \(0.170721\pi\)
−0.859586 + 0.510990i \(0.829279\pi\)
\(600\) 0 0
\(601\) 30.0136i 1.22428i −0.790750 0.612139i \(-0.790309\pi\)
0.790750 0.612139i \(-0.209691\pi\)
\(602\) −0.956010 + 2.30464i −0.0389640 + 0.0939300i
\(603\) 0 0
\(604\) 1.43998 0.0585918
\(605\) −17.7436 −0.721379
\(606\) 0 0
\(607\) 4.58280i 0.186010i 0.995666 + 0.0930050i \(0.0296473\pi\)
−0.995666 + 0.0930050i \(0.970353\pi\)
\(608\) 1.78474 0.0723807
\(609\) 0 0
\(610\) 9.60761 0.389001
\(611\) 6.22468i 0.251823i
\(612\) 0 0
\(613\) 30.5522 1.23399 0.616996 0.786966i \(-0.288349\pi\)
0.616996 + 0.786966i \(0.288349\pi\)
\(614\) 21.7242 0.876717
\(615\) 0 0
\(616\) 9.63998 + 3.99886i 0.388406 + 0.161119i
\(617\) 32.6185i 1.31317i −0.754252 0.656585i \(-0.772000\pi\)
0.754252 0.656585i \(-0.228000\pi\)
\(618\) 0 0
\(619\) 20.0045i 0.804049i 0.915629 + 0.402024i \(0.131693\pi\)
−0.915629 + 0.402024i \(0.868307\pi\)
\(620\) 13.6646i 0.548782i
\(621\) 0 0
\(622\) 6.29800i 0.252527i
\(623\) −22.6457 9.39388i −0.907280 0.376358i
\(624\) 0 0
\(625\) 27.1314 1.08526
\(626\) 22.2191 0.888052
\(627\) 0 0
\(628\) 16.6071i 0.662695i
\(629\) −2.22752 −0.0888171
\(630\) 0 0
\(631\) 6.09634 0.242692 0.121346 0.992610i \(-0.461279\pi\)
0.121346 + 0.992610i \(0.461279\pi\)
\(632\) 3.63613i 0.144637i
\(633\) 0 0
\(634\) 15.6614 0.621994
\(635\) 11.4579 0.454691
\(636\) 0 0
\(637\) 14.1139 14.0847i 0.559214 0.558057i
\(638\) 11.3907i 0.450963i
\(639\) 0 0
\(640\) 3.89111i 0.153810i
\(641\) 33.4415i 1.32086i −0.750888 0.660429i \(-0.770374\pi\)
0.750888 0.660429i \(-0.229626\pi\)
\(642\) 0 0
\(643\) 19.1705i 0.756012i −0.925803 0.378006i \(-0.876610\pi\)
0.925803 0.378006i \(-0.123390\pi\)
\(644\) 6.33909 15.2815i 0.249795 0.602177i
\(645\) 0 0
\(646\) −1.32448 −0.0521111
\(647\) 44.6049 1.75360 0.876800 0.480854i \(-0.159673\pi\)
0.876800 + 0.480854i \(0.159673\pi\)
\(648\) 0 0
\(649\) 0.0833680i 0.00327248i
\(650\) 28.8859 1.13300
\(651\) 0 0
\(652\) 12.3955 0.485444
\(653\) 0.652123i 0.0255195i −0.999919 0.0127598i \(-0.995938\pi\)
0.999919 0.0127598i \(-0.00406167\pi\)
\(654\) 0 0
\(655\) 58.6200 2.29047
\(656\) −10.4941 −0.409726
\(657\) 0 0
\(658\) 2.21530 5.34039i 0.0863614 0.208190i
\(659\) 30.3384i 1.18182i −0.806739 0.590908i \(-0.798769\pi\)
0.806739 0.590908i \(-0.201231\pi\)
\(660\) 0 0
\(661\) 12.8176i 0.498548i 0.968433 + 0.249274i \(0.0801919\pi\)
−0.968433 + 0.249274i \(0.919808\pi\)
\(662\) 1.27226i 0.0494477i
\(663\) 0 0
\(664\) 8.05995i 0.312787i
\(665\) −7.04011 + 16.9715i −0.273004 + 0.658126i
\(666\) 0 0
\(667\) 18.0569 0.699165
\(668\) 11.7217 0.453528
\(669\) 0 0
\(670\) 52.3326i 2.02179i
\(671\) −9.73972 −0.375998
\(672\) 0 0
\(673\) −22.4493 −0.865355 −0.432678 0.901549i \(-0.642431\pi\)
−0.432678 + 0.901549i \(0.642431\pi\)
\(674\) 7.56002i 0.291201i
\(675\) 0 0
\(676\) −4.88608 −0.187926
\(677\) 51.1807 1.96703 0.983516 0.180820i \(-0.0578752\pi\)
0.983516 + 0.180820i \(0.0578752\pi\)
\(678\) 0 0
\(679\) 19.0784 45.9919i 0.732161 1.76501i
\(680\) 2.88766i 0.110737i
\(681\) 0 0
\(682\) 13.8525i 0.530438i
\(683\) 14.5616i 0.557184i 0.960410 + 0.278592i \(0.0898677\pi\)
−0.960410 + 0.278592i \(0.910132\pi\)
\(684\) 0 0
\(685\) 61.1681i 2.33711i
\(686\) 17.1215 7.06081i 0.653701 0.269583i
\(687\) 0 0
\(688\) −0.943042 −0.0359532
\(689\) 0 0
\(690\) 0 0
\(691\) 24.4515i 0.930180i −0.885263 0.465090i \(-0.846022\pi\)
0.885263 0.465090i \(-0.153978\pi\)
\(692\) 16.7710 0.637536
\(693\) 0 0
\(694\) −22.1091 −0.839250
\(695\) 12.8669i 0.488071i
\(696\) 0 0
\(697\) 7.78785 0.294986
\(698\) 14.7435 0.558048
\(699\) 0 0
\(700\) 24.7823 + 10.2802i 0.936684 + 0.388556i
\(701\) 2.21697i 0.0837337i 0.999123 + 0.0418669i \(0.0133305\pi\)
−0.999123 + 0.0418669i \(0.986669\pi\)
\(702\) 0 0
\(703\) 5.35703i 0.202044i
\(704\) 3.94462i 0.148668i
\(705\) 0 0
\(706\) 17.2776i 0.650252i
\(707\) −20.2388 8.39546i −0.761158 0.315744i
\(708\) 0 0
\(709\) −24.3923 −0.916072 −0.458036 0.888934i \(-0.651447\pi\)
−0.458036 + 0.888934i \(0.651447\pi\)
\(710\) −7.56060 −0.283744
\(711\) 0 0
\(712\) 9.26646i 0.347275i
\(713\) −21.9593 −0.822381
\(714\) 0 0
\(715\) −43.7214 −1.63509
\(716\) 5.77532i 0.215834i
\(717\) 0 0
\(718\) 10.9129 0.407267
\(719\) 2.22752 0.0830725 0.0415363 0.999137i \(-0.486775\pi\)
0.0415363 + 0.999137i \(0.486775\pi\)
\(720\) 0 0
\(721\) 17.2831 41.6641i 0.643657 1.55165i
\(722\) 15.8147i 0.588563i
\(723\) 0 0
\(724\) 5.53310i 0.205636i
\(725\) 29.2831i 1.08755i
\(726\) 0 0
\(727\) 12.1105i 0.449152i 0.974457 + 0.224576i \(0.0720997\pi\)
−0.974457 + 0.224576i \(0.927900\pi\)
\(728\) 6.96124 + 2.88766i 0.258001 + 0.107024i
\(729\) 0 0
\(730\) −18.8908 −0.699180
\(731\) 0.699848 0.0258848
\(732\) 0 0
\(733\) 15.6661i 0.578641i −0.957232 0.289321i \(-0.906571\pi\)
0.957232 0.289321i \(-0.0934293\pi\)
\(734\) −35.7272 −1.31871
\(735\) 0 0
\(736\) 6.25311 0.230493
\(737\) 53.0522i 1.95420i
\(738\) 0 0
\(739\) −8.10454 −0.298130 −0.149065 0.988827i \(-0.547626\pi\)
−0.149065 + 0.988827i \(0.547626\pi\)
\(740\) −11.6795 −0.429346
\(741\) 0 0
\(742\) 0 0
\(743\) 12.1739i 0.446618i −0.974748 0.223309i \(-0.928314\pi\)
0.974748 0.223309i \(-0.0716860\pi\)
\(744\) 0 0
\(745\) 42.8084i 1.56838i
\(746\) 32.0600i 1.17380i
\(747\) 0 0
\(748\) 2.92737i 0.107035i
\(749\) −14.5341 + 35.0370i −0.531063 + 1.28022i
\(750\) 0 0
\(751\) 34.6123 1.26302 0.631511 0.775367i \(-0.282435\pi\)
0.631511 + 0.775367i \(0.282435\pi\)
\(752\) 2.18525 0.0796879
\(753\) 0 0
\(754\) 8.22549i 0.299555i
\(755\) −5.60311 −0.203918
\(756\) 0 0
\(757\) −39.0553 −1.41949 −0.709744 0.704459i \(-0.751190\pi\)
−0.709744 + 0.704459i \(0.751190\pi\)
\(758\) 34.8891i 1.26723i
\(759\) 0 0
\(760\) −6.94462 −0.251908
\(761\) 10.2252 0.370665 0.185332 0.982676i \(-0.440664\pi\)
0.185332 + 0.982676i \(0.440664\pi\)
\(762\) 0 0
\(763\) −27.5663 11.4351i −0.997968 0.413977i
\(764\) 6.21372i 0.224805i
\(765\) 0 0
\(766\) 17.5342i 0.633537i
\(767\) 0.0602018i 0.00217376i
\(768\) 0 0
\(769\) 30.8011i 1.11072i 0.831611 + 0.555359i \(0.187419\pi\)
−0.831611 + 0.555359i \(0.812581\pi\)
\(770\) −37.5103 15.5600i −1.35178 0.560744i
\(771\) 0 0
\(772\) 7.80542 0.280923
\(773\) 35.7833 1.28704 0.643518 0.765431i \(-0.277474\pi\)
0.643518 + 0.765431i \(0.277474\pi\)
\(774\) 0 0
\(775\) 35.6117i 1.27921i
\(776\) 18.8196 0.675584
\(777\) 0 0
\(778\) −7.62171 −0.273252
\(779\) 18.7292i 0.671044i
\(780\) 0 0
\(781\) 7.66456 0.274260
\(782\) −4.64054 −0.165945
\(783\) 0 0
\(784\) 4.94462 + 4.95487i 0.176594 + 0.176960i
\(785\) 64.6200i 2.30639i
\(786\) 0 0
\(787\) 15.3413i 0.546857i −0.961892 0.273429i \(-0.911842\pi\)
0.961892 0.273429i \(-0.0881578\pi\)
\(788\) 12.7737i 0.455046i
\(789\) 0 0
\(790\) 14.1486i 0.503384i
\(791\) −9.96748 + 24.0284i −0.354403 + 0.854353i
\(792\) 0 0
\(793\) −7.03326 −0.249758
\(794\) 37.6469 1.33604
\(795\) 0 0
\(796\) 1.81201i 0.0642250i
\(797\) −35.0400 −1.24118 −0.620590 0.784135i \(-0.713107\pi\)
−0.620590 + 0.784135i \(0.713107\pi\)
\(798\) 0 0
\(799\) −1.62171 −0.0573721 <