Properties

Label 2646.2.h.s.667.1
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.3317760000.3
Defining polynomial: \(x^{8} - 4 x^{6} + 7 x^{4} - 36 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 882)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(-1.01575 + 1.40294i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.s.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.44572 q^{5} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -3.44572 q^{5} -1.00000 q^{8} +(-1.72286 - 2.98408i) q^{10} -4.00000 q^{11} +(-2.12132 - 3.67423i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-0.707107 - 1.22474i) q^{17} +(-3.13707 + 5.43357i) q^{19} +(1.72286 - 2.98408i) q^{20} +(-2.00000 - 3.46410i) q^{22} +8.74597 q^{23} +6.87298 q^{25} +(2.12132 - 3.67423i) q^{26} +(0.563508 - 0.976025i) q^{29} +(2.73861 - 4.74342i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.707107 - 1.22474i) q^{34} +(-2.87298 + 4.97615i) q^{37} -6.27415 q^{38} +3.44572 q^{40} +(-2.82843 - 4.89898i) q^{41} +(-0.563508 + 0.976025i) q^{43} +(2.00000 - 3.46410i) q^{44} +(4.37298 + 7.57423i) q^{46} +(2.03151 + 3.51867i) q^{47} +(3.43649 + 5.95218i) q^{50} +4.24264 q^{52} +(6.30948 + 10.9283i) q^{53} +13.7829 q^{55} +1.12702 q^{58} +(4.15283 - 7.19291i) q^{59} +(3.13707 + 5.43357i) q^{61} +5.47723 q^{62} +1.00000 q^{64} +(7.30948 + 12.6604i) q^{65} +(3.43649 - 5.95218i) q^{67} +1.41421 q^{68} +9.87298 q^{71} +(2.21113 + 3.82980i) q^{73} -5.74597 q^{74} +(-3.13707 - 5.43357i) q^{76} +(0.936492 + 1.62205i) q^{79} +(1.72286 + 2.98408i) q^{80} +(2.82843 - 4.89898i) q^{82} +(1.32440 - 2.29393i) q^{83} +(2.43649 + 4.22013i) q^{85} -1.12702 q^{86} +4.00000 q^{88} +(-3.53553 + 6.12372i) q^{89} +(-4.37298 + 7.57423i) q^{92} +(-2.03151 + 3.51867i) q^{94} +(10.8095 - 18.7226i) q^{95} +(7.50873 - 13.0055i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} + O(q^{10}) \) \( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} - 32 q^{11} - 4 q^{16} - 16 q^{22} + 8 q^{23} + 24 q^{25} + 20 q^{29} + 4 q^{32} + 8 q^{37} - 20 q^{43} + 16 q^{44} + 4 q^{46} + 12 q^{50} + 4 q^{53} + 40 q^{58} + 8 q^{64} + 12 q^{65} + 12 q^{67} + 48 q^{71} + 16 q^{74} - 8 q^{79} + 4 q^{85} - 40 q^{86} + 32 q^{88} - 4 q^{92} + 40 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −3.44572 −1.54097 −0.770486 0.637457i \(-0.779987\pi\)
−0.770486 + 0.637457i \(0.779987\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) −1.72286 2.98408i −0.544816 0.943649i
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) 0 0
\(13\) −2.12132 3.67423i −0.588348 1.01905i −0.994449 0.105221i \(-0.966445\pi\)
0.406100 0.913828i \(-0.366888\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −0.707107 1.22474i −0.171499 0.297044i 0.767445 0.641114i \(-0.221528\pi\)
−0.938944 + 0.344070i \(0.888194\pi\)
\(18\) 0 0
\(19\) −3.13707 + 5.43357i −0.719694 + 1.24655i 0.241427 + 0.970419i \(0.422385\pi\)
−0.961121 + 0.276128i \(0.910949\pi\)
\(20\) 1.72286 2.98408i 0.385243 0.667261i
\(21\) 0 0
\(22\) −2.00000 3.46410i −0.426401 0.738549i
\(23\) 8.74597 1.82366 0.911830 0.410568i \(-0.134669\pi\)
0.911830 + 0.410568i \(0.134669\pi\)
\(24\) 0 0
\(25\) 6.87298 1.37460
\(26\) 2.12132 3.67423i 0.416025 0.720577i
\(27\) 0 0
\(28\) 0 0
\(29\) 0.563508 0.976025i 0.104641 0.181243i −0.808951 0.587877i \(-0.799964\pi\)
0.913591 + 0.406633i \(0.133297\pi\)
\(30\) 0 0
\(31\) 2.73861 4.74342i 0.491869 0.851943i −0.508087 0.861306i \(-0.669647\pi\)
0.999956 + 0.00936313i \(0.00298042\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 0.707107 1.22474i 0.121268 0.210042i
\(35\) 0 0
\(36\) 0 0
\(37\) −2.87298 + 4.97615i −0.472316 + 0.818075i −0.999498 0.0316775i \(-0.989915\pi\)
0.527183 + 0.849752i \(0.323248\pi\)
\(38\) −6.27415 −1.01780
\(39\) 0 0
\(40\) 3.44572 0.544816
\(41\) −2.82843 4.89898i −0.441726 0.765092i 0.556092 0.831121i \(-0.312300\pi\)
−0.997818 + 0.0660290i \(0.978967\pi\)
\(42\) 0 0
\(43\) −0.563508 + 0.976025i −0.0859342 + 0.148842i −0.905789 0.423729i \(-0.860721\pi\)
0.819855 + 0.572572i \(0.194054\pi\)
\(44\) 2.00000 3.46410i 0.301511 0.522233i
\(45\) 0 0
\(46\) 4.37298 + 7.57423i 0.644761 + 1.11676i
\(47\) 2.03151 + 3.51867i 0.296326 + 0.513251i 0.975292 0.220918i \(-0.0709053\pi\)
−0.678967 + 0.734169i \(0.737572\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 3.43649 + 5.95218i 0.485993 + 0.841765i
\(51\) 0 0
\(52\) 4.24264 0.588348
\(53\) 6.30948 + 10.9283i 0.866673 + 1.50112i 0.865376 + 0.501123i \(0.167079\pi\)
0.00129674 + 0.999999i \(0.499587\pi\)
\(54\) 0 0
\(55\) 13.7829 1.85848
\(56\) 0 0
\(57\) 0 0
\(58\) 1.12702 0.147985
\(59\) 4.15283 7.19291i 0.540652 0.936437i −0.458215 0.888842i \(-0.651511\pi\)
0.998867 0.0475951i \(-0.0151557\pi\)
\(60\) 0 0
\(61\) 3.13707 + 5.43357i 0.401661 + 0.695697i 0.993927 0.110045i \(-0.0350997\pi\)
−0.592265 + 0.805743i \(0.701766\pi\)
\(62\) 5.47723 0.695608
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 7.30948 + 12.6604i 0.906629 + 1.57033i
\(66\) 0 0
\(67\) 3.43649 5.95218i 0.419834 0.727174i −0.576088 0.817388i \(-0.695422\pi\)
0.995922 + 0.0902132i \(0.0287549\pi\)
\(68\) 1.41421 0.171499
\(69\) 0 0
\(70\) 0 0
\(71\) 9.87298 1.17171 0.585854 0.810417i \(-0.300759\pi\)
0.585854 + 0.810417i \(0.300759\pi\)
\(72\) 0 0
\(73\) 2.21113 + 3.82980i 0.258794 + 0.448244i 0.965919 0.258844i \(-0.0833417\pi\)
−0.707125 + 0.707088i \(0.750008\pi\)
\(74\) −5.74597 −0.667955
\(75\) 0 0
\(76\) −3.13707 5.43357i −0.359847 0.623273i
\(77\) 0 0
\(78\) 0 0
\(79\) 0.936492 + 1.62205i 0.105364 + 0.182495i 0.913887 0.405969i \(-0.133066\pi\)
−0.808523 + 0.588464i \(0.799733\pi\)
\(80\) 1.72286 + 2.98408i 0.192622 + 0.333630i
\(81\) 0 0
\(82\) 2.82843 4.89898i 0.312348 0.541002i
\(83\) 1.32440 2.29393i 0.145372 0.251791i −0.784140 0.620584i \(-0.786896\pi\)
0.929512 + 0.368793i \(0.120229\pi\)
\(84\) 0 0
\(85\) 2.43649 + 4.22013i 0.264275 + 0.457737i
\(86\) −1.12702 −0.121529
\(87\) 0 0
\(88\) 4.00000 0.426401
\(89\) −3.53553 + 6.12372i −0.374766 + 0.649113i −0.990292 0.139003i \(-0.955610\pi\)
0.615526 + 0.788116i \(0.288944\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −4.37298 + 7.57423i −0.455915 + 0.789668i
\(93\) 0 0
\(94\) −2.03151 + 3.51867i −0.209534 + 0.362923i
\(95\) 10.8095 18.7226i 1.10903 1.92089i
\(96\) 0 0
\(97\) 7.50873 13.0055i 0.762396 1.32051i −0.179216 0.983810i \(-0.557356\pi\)
0.941612 0.336699i \(-0.109311\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −3.43649 + 5.95218i −0.343649 + 0.595218i
\(101\) −13.3452 −1.32790 −0.663949 0.747778i \(-0.731121\pi\)
−0.663949 + 0.747778i \(0.731121\pi\)
\(102\) 0 0
\(103\) −3.88338 −0.382641 −0.191321 0.981528i \(-0.561277\pi\)
−0.191321 + 0.981528i \(0.561277\pi\)
\(104\) 2.12132 + 3.67423i 0.208013 + 0.360288i
\(105\) 0 0
\(106\) −6.30948 + 10.9283i −0.612830 + 1.06145i
\(107\) 0.127017 0.219999i 0.0122792 0.0212681i −0.859821 0.510596i \(-0.829425\pi\)
0.872100 + 0.489328i \(0.162758\pi\)
\(108\) 0 0
\(109\) −8.43649 14.6124i −0.808069 1.39962i −0.914199 0.405265i \(-0.867179\pi\)
0.106130 0.994352i \(-0.466154\pi\)
\(110\) 6.89144 + 11.9363i 0.657073 + 1.13808i
\(111\) 0 0
\(112\) 0 0
\(113\) 1.93649 + 3.35410i 0.182170 + 0.315527i 0.942619 0.333870i \(-0.108355\pi\)
−0.760449 + 0.649397i \(0.775021\pi\)
\(114\) 0 0
\(115\) −30.1361 −2.81021
\(116\) 0.563508 + 0.976025i 0.0523204 + 0.0906217i
\(117\) 0 0
\(118\) 8.30565 0.764597
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) −3.13707 + 5.43357i −0.284017 + 0.491932i
\(123\) 0 0
\(124\) 2.73861 + 4.74342i 0.245935 + 0.425971i
\(125\) −6.45378 −0.577243
\(126\) 0 0
\(127\) −0.745967 −0.0661938 −0.0330969 0.999452i \(-0.510537\pi\)
−0.0330969 + 0.999452i \(0.510537\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −7.30948 + 12.6604i −0.641083 + 1.11039i
\(131\) 13.3452 1.16598 0.582988 0.812480i \(-0.301883\pi\)
0.582988 + 0.812480i \(0.301883\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 6.87298 0.593735
\(135\) 0 0
\(136\) 0.707107 + 1.22474i 0.0606339 + 0.105021i
\(137\) 15.4919 1.32357 0.661783 0.749696i \(-0.269800\pi\)
0.661783 + 0.749696i \(0.269800\pi\)
\(138\) 0 0
\(139\) 9.93870 + 17.2143i 0.842989 + 1.46010i 0.887356 + 0.461085i \(0.152540\pi\)
−0.0443665 + 0.999015i \(0.514127\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 4.93649 + 8.55025i 0.414261 + 0.717521i
\(143\) 8.48528 + 14.6969i 0.709575 + 1.22902i
\(144\) 0 0
\(145\) −1.94169 + 3.36311i −0.161249 + 0.279291i
\(146\) −2.21113 + 3.82980i −0.182995 + 0.316956i
\(147\) 0 0
\(148\) −2.87298 4.97615i −0.236158 0.409037i
\(149\) 15.7460 1.28996 0.644980 0.764200i \(-0.276866\pi\)
0.644980 + 0.764200i \(0.276866\pi\)
\(150\) 0 0
\(151\) 11.0000 0.895167 0.447584 0.894242i \(-0.352285\pi\)
0.447584 + 0.894242i \(0.352285\pi\)
\(152\) 3.13707 5.43357i 0.254450 0.440721i
\(153\) 0 0
\(154\) 0 0
\(155\) −9.43649 + 16.3445i −0.757957 + 1.31282i
\(156\) 0 0
\(157\) 5.96550 10.3325i 0.476099 0.824627i −0.523526 0.852010i \(-0.675384\pi\)
0.999625 + 0.0273823i \(0.00871714\pi\)
\(158\) −0.936492 + 1.62205i −0.0745033 + 0.129043i
\(159\) 0 0
\(160\) −1.72286 + 2.98408i −0.136204 + 0.235912i
\(161\) 0 0
\(162\) 0 0
\(163\) −5.00000 + 8.66025i −0.391630 + 0.678323i −0.992665 0.120900i \(-0.961422\pi\)
0.601035 + 0.799223i \(0.294755\pi\)
\(164\) 5.65685 0.441726
\(165\) 0 0
\(166\) 2.64880 0.205587
\(167\) −4.77012 8.26209i −0.369123 0.639340i 0.620306 0.784360i \(-0.287009\pi\)
−0.989429 + 0.145021i \(0.953675\pi\)
\(168\) 0 0
\(169\) −2.50000 + 4.33013i −0.192308 + 0.333087i
\(170\) −2.43649 + 4.22013i −0.186870 + 0.323669i
\(171\) 0 0
\(172\) −0.563508 0.976025i −0.0429671 0.0744212i
\(173\) −6.36396 11.0227i −0.483843 0.838041i 0.515985 0.856598i \(-0.327426\pi\)
−0.999828 + 0.0185571i \(0.994093\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.00000 + 3.46410i 0.150756 + 0.261116i
\(177\) 0 0
\(178\) −7.07107 −0.529999
\(179\) −3.43649 5.95218i −0.256855 0.444887i 0.708542 0.705668i \(-0.249353\pi\)
−0.965398 + 0.260782i \(0.916020\pi\)
\(180\) 0 0
\(181\) 13.3452 0.991942 0.495971 0.868339i \(-0.334812\pi\)
0.495971 + 0.868339i \(0.334812\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −8.74597 −0.644761
\(185\) 9.89949 17.1464i 0.727825 1.26063i
\(186\) 0 0
\(187\) 2.82843 + 4.89898i 0.206835 + 0.358249i
\(188\) −4.06301 −0.296326
\(189\) 0 0
\(190\) 21.6190 1.56840
\(191\) −3.06351 5.30615i −0.221668 0.383940i 0.733647 0.679531i \(-0.237817\pi\)
−0.955314 + 0.295591i \(0.904483\pi\)
\(192\) 0 0
\(193\) −11.9365 + 20.6746i −0.859207 + 1.48819i 0.0134785 + 0.999909i \(0.495710\pi\)
−0.872686 + 0.488282i \(0.837624\pi\)
\(194\) 15.0175 1.07819
\(195\) 0 0
\(196\) 0 0
\(197\) −16.6190 −1.18405 −0.592026 0.805919i \(-0.701672\pi\)
−0.592026 + 0.805919i \(0.701672\pi\)
\(198\) 0 0
\(199\) 6.09452 + 10.5560i 0.432029 + 0.748296i 0.997048 0.0767818i \(-0.0244645\pi\)
−0.565019 + 0.825078i \(0.691131\pi\)
\(200\) −6.87298 −0.485993
\(201\) 0 0
\(202\) −6.67261 11.5573i −0.469483 0.813168i
\(203\) 0 0
\(204\) 0 0
\(205\) 9.74597 + 16.8805i 0.680688 + 1.17899i
\(206\) −1.94169 3.36311i −0.135284 0.234319i
\(207\) 0 0
\(208\) −2.12132 + 3.67423i −0.147087 + 0.254762i
\(209\) 12.5483 21.7343i 0.867984 1.50339i
\(210\) 0 0
\(211\) −10.3095 17.8565i −0.709734 1.22929i −0.964956 0.262412i \(-0.915482\pi\)
0.255222 0.966882i \(-0.417851\pi\)
\(212\) −12.6190 −0.866673
\(213\) 0 0
\(214\) 0.254033 0.0173654
\(215\) 1.94169 3.36311i 0.132422 0.229362i
\(216\) 0 0
\(217\) 0 0
\(218\) 8.43649 14.6124i 0.571391 0.989679i
\(219\) 0 0
\(220\) −6.89144 + 11.9363i −0.464621 + 0.804747i
\(221\) −3.00000 + 5.19615i −0.201802 + 0.349531i
\(222\) 0 0
\(223\) −11.2239 + 19.4404i −0.751608 + 1.30182i 0.195436 + 0.980717i \(0.437388\pi\)
−0.947043 + 0.321106i \(0.895945\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −1.93649 + 3.35410i −0.128814 + 0.223112i
\(227\) 10.3372 0.686101 0.343051 0.939317i \(-0.388540\pi\)
0.343051 + 0.939317i \(0.388540\pi\)
\(228\) 0 0
\(229\) −13.3452 −0.881877 −0.440938 0.897537i \(-0.645354\pi\)
−0.440938 + 0.897537i \(0.645354\pi\)
\(230\) −15.0681 26.0987i −0.993559 1.72090i
\(231\) 0 0
\(232\) −0.563508 + 0.976025i −0.0369961 + 0.0640792i
\(233\) 3.62702 6.28218i 0.237614 0.411559i −0.722415 0.691459i \(-0.756968\pi\)
0.960029 + 0.279900i \(0.0903014\pi\)
\(234\) 0 0
\(235\) −7.00000 12.1244i −0.456630 0.790906i
\(236\) 4.15283 + 7.19291i 0.270326 + 0.468218i
\(237\) 0 0
\(238\) 0 0
\(239\) −7.50000 12.9904i −0.485135 0.840278i 0.514719 0.857359i \(-0.327896\pi\)
−0.999854 + 0.0170808i \(0.994563\pi\)
\(240\) 0 0
\(241\) 23.6824 1.52552 0.762758 0.646684i \(-0.223845\pi\)
0.762758 + 0.646684i \(0.223845\pi\)
\(242\) 2.50000 + 4.33013i 0.160706 + 0.278351i
\(243\) 0 0
\(244\) −6.27415 −0.401661
\(245\) 0 0
\(246\) 0 0
\(247\) 26.6190 1.69372
\(248\) −2.73861 + 4.74342i −0.173902 + 0.301207i
\(249\) 0 0
\(250\) −3.22689 5.58913i −0.204086 0.353488i
\(251\) 9.46183 0.597225 0.298613 0.954374i \(-0.403476\pi\)
0.298613 + 0.954374i \(0.403476\pi\)
\(252\) 0 0
\(253\) −34.9839 −2.19942
\(254\) −0.372983 0.646026i −0.0234031 0.0405353i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 3.00806 0.187637 0.0938187 0.995589i \(-0.470093\pi\)
0.0938187 + 0.995589i \(0.470093\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −14.6190 −0.906629
\(261\) 0 0
\(262\) 6.67261 + 11.5573i 0.412235 + 0.714012i
\(263\) 17.6190 1.08643 0.543216 0.839593i \(-0.317207\pi\)
0.543216 + 0.839593i \(0.317207\pi\)
\(264\) 0 0
\(265\) −21.7407 37.6560i −1.33552 2.31319i
\(266\) 0 0
\(267\) 0 0
\(268\) 3.43649 + 5.95218i 0.209917 + 0.363587i
\(269\) 1.01575 + 1.75934i 0.0619316 + 0.107269i 0.895329 0.445406i \(-0.146941\pi\)
−0.833397 + 0.552674i \(0.813607\pi\)
\(270\) 0 0
\(271\) 3.53553 6.12372i 0.214768 0.371990i −0.738433 0.674327i \(-0.764434\pi\)
0.953201 + 0.302338i \(0.0977670\pi\)
\(272\) −0.707107 + 1.22474i −0.0428746 + 0.0742611i
\(273\) 0 0
\(274\) 7.74597 + 13.4164i 0.467951 + 0.810515i
\(275\) −27.4919 −1.65783
\(276\) 0 0
\(277\) 14.3649 0.863104 0.431552 0.902088i \(-0.357966\pi\)
0.431552 + 0.902088i \(0.357966\pi\)
\(278\) −9.93870 + 17.2143i −0.596084 + 1.03245i
\(279\) 0 0
\(280\) 0 0
\(281\) 4.37298 7.57423i 0.260870 0.451841i −0.705603 0.708607i \(-0.749324\pi\)
0.966473 + 0.256767i \(0.0826572\pi\)
\(282\) 0 0
\(283\) 2.51978 4.36439i 0.149785 0.259436i −0.781363 0.624077i \(-0.785475\pi\)
0.931148 + 0.364641i \(0.118808\pi\)
\(284\) −4.93649 + 8.55025i −0.292927 + 0.507364i
\(285\) 0 0
\(286\) −8.48528 + 14.6969i −0.501745 + 0.869048i
\(287\) 0 0
\(288\) 0 0
\(289\) 7.50000 12.9904i 0.441176 0.764140i
\(290\) −3.88338 −0.228040
\(291\) 0 0
\(292\) −4.42227 −0.258794
\(293\) 0.398461 + 0.690154i 0.0232783 + 0.0403192i 0.877430 0.479705i \(-0.159256\pi\)
−0.854152 + 0.520024i \(0.825923\pi\)
\(294\) 0 0
\(295\) −14.3095 + 24.7847i −0.833130 + 1.44302i
\(296\) 2.87298 4.97615i 0.166989 0.289233i
\(297\) 0 0
\(298\) 7.87298 + 13.6364i 0.456070 + 0.789936i
\(299\) −18.5530 32.1347i −1.07295 1.85840i
\(300\) 0 0
\(301\) 0 0
\(302\) 5.50000 + 9.52628i 0.316489 + 0.548176i
\(303\) 0 0
\(304\) 6.27415 0.359847
\(305\) −10.8095 18.7226i −0.618949 1.07205i
\(306\) 0 0
\(307\) −14.2205 −0.811609 −0.405805 0.913960i \(-0.633009\pi\)
−0.405805 + 0.913960i \(0.633009\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −18.8730 −1.07191
\(311\) 0.707107 1.22474i 0.0400963 0.0694489i −0.845281 0.534322i \(-0.820567\pi\)
0.885377 + 0.464873i \(0.153900\pi\)
\(312\) 0 0
\(313\) 7.86799 + 13.6278i 0.444725 + 0.770286i 0.998033 0.0626904i \(-0.0199681\pi\)
−0.553308 + 0.832977i \(0.686635\pi\)
\(314\) 11.9310 0.673305
\(315\) 0 0
\(316\) −1.87298 −0.105364
\(317\) 12.3095 + 21.3206i 0.691369 + 1.19749i 0.971389 + 0.237492i \(0.0763254\pi\)
−0.280020 + 0.959994i \(0.590341\pi\)
\(318\) 0 0
\(319\) −2.25403 + 3.90410i −0.126202 + 0.218588i
\(320\) −3.44572 −0.192622
\(321\) 0 0
\(322\) 0 0
\(323\) 8.87298 0.493706
\(324\) 0 0
\(325\) −14.5798 25.2530i −0.808742 1.40078i
\(326\) −10.0000 −0.553849
\(327\) 0 0
\(328\) 2.82843 + 4.89898i 0.156174 + 0.270501i
\(329\) 0 0
\(330\) 0 0
\(331\) −10.1825 17.6365i −0.559679 0.969392i −0.997523 0.0703409i \(-0.977591\pi\)
0.437844 0.899051i \(-0.355742\pi\)
\(332\) 1.32440 + 2.29393i 0.0726859 + 0.125896i
\(333\) 0 0
\(334\) 4.77012 8.26209i 0.261009 0.452081i
\(335\) −11.8412 + 20.5095i −0.646953 + 1.12056i
\(336\) 0 0
\(337\) −7.87298 13.6364i −0.428869 0.742822i 0.567904 0.823095i \(-0.307754\pi\)
−0.996773 + 0.0802722i \(0.974421\pi\)
\(338\) −5.00000 −0.271964
\(339\) 0 0
\(340\) −4.87298 −0.264275
\(341\) −10.9545 + 18.9737i −0.593217 + 1.02748i
\(342\) 0 0
\(343\) 0 0
\(344\) 0.563508 0.976025i 0.0303823 0.0526237i
\(345\) 0 0
\(346\) 6.36396 11.0227i 0.342129 0.592584i
\(347\) 3.87298 6.70820i 0.207913 0.360115i −0.743144 0.669131i \(-0.766666\pi\)
0.951057 + 0.309016i \(0.0999997\pi\)
\(348\) 0 0
\(349\) −8.21584 + 14.2302i −0.439784 + 0.761728i −0.997672 0.0681880i \(-0.978278\pi\)
0.557889 + 0.829916i \(0.311612\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −2.00000 + 3.46410i −0.106600 + 0.184637i
\(353\) 3.88338 0.206692 0.103346 0.994645i \(-0.467045\pi\)
0.103346 + 0.994645i \(0.467045\pi\)
\(354\) 0 0
\(355\) −34.0195 −1.80557
\(356\) −3.53553 6.12372i −0.187383 0.324557i
\(357\) 0 0
\(358\) 3.43649 5.95218i 0.181624 0.314582i
\(359\) 9.11895 15.7945i 0.481280 0.833601i −0.518489 0.855084i \(-0.673505\pi\)
0.999769 + 0.0214830i \(0.00683878\pi\)
\(360\) 0 0
\(361\) −10.1825 17.6365i −0.535919 0.928239i
\(362\) 6.67261 + 11.5573i 0.350704 + 0.607438i
\(363\) 0 0
\(364\) 0 0
\(365\) −7.61895 13.1964i −0.398794 0.690732i
\(366\) 0 0
\(367\) −6.89144 −0.359730 −0.179865 0.983691i \(-0.557566\pi\)
−0.179865 + 0.983691i \(0.557566\pi\)
\(368\) −4.37298 7.57423i −0.227958 0.394834i
\(369\) 0 0
\(370\) 19.7990 1.02930
\(371\) 0 0
\(372\) 0 0
\(373\) −1.12702 −0.0583547 −0.0291774 0.999574i \(-0.509289\pi\)
−0.0291774 + 0.999574i \(0.509289\pi\)
\(374\) −2.82843 + 4.89898i −0.146254 + 0.253320i
\(375\) 0 0
\(376\) −2.03151 3.51867i −0.104767 0.181462i
\(377\) −4.78153 −0.246261
\(378\) 0 0
\(379\) 26.3649 1.35427 0.677137 0.735857i \(-0.263220\pi\)
0.677137 + 0.735857i \(0.263220\pi\)
\(380\) 10.8095 + 18.7226i 0.554514 + 0.960447i
\(381\) 0 0
\(382\) 3.06351 5.30615i 0.156743 0.271486i
\(383\) −12.9076 −0.659545 −0.329773 0.944060i \(-0.606972\pi\)
−0.329773 + 0.944060i \(0.606972\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −23.8730 −1.21510
\(387\) 0 0
\(388\) 7.50873 + 13.0055i 0.381198 + 0.660254i
\(389\) −13.1270 −0.665566 −0.332783 0.943003i \(-0.607988\pi\)
−0.332783 + 0.943003i \(0.607988\pi\)
\(390\) 0 0
\(391\) −6.18433 10.7116i −0.312755 0.541708i
\(392\) 0 0
\(393\) 0 0
\(394\) −8.30948 14.3924i −0.418625 0.725080i
\(395\) −3.22689 5.58913i −0.162362 0.281220i
\(396\) 0 0
\(397\) 3.53553 6.12372i 0.177443 0.307341i −0.763561 0.645736i \(-0.776551\pi\)
0.941004 + 0.338395i \(0.109884\pi\)
\(398\) −6.09452 + 10.5560i −0.305491 + 0.529125i
\(399\) 0 0
\(400\) −3.43649 5.95218i −0.171825 0.297609i
\(401\) 3.87298 0.193408 0.0967038 0.995313i \(-0.469170\pi\)
0.0967038 + 0.995313i \(0.469170\pi\)
\(402\) 0 0
\(403\) −23.2379 −1.15756
\(404\) 6.67261 11.5573i 0.331975 0.574997i
\(405\) 0 0
\(406\) 0 0
\(407\) 11.4919 19.9046i 0.569634 0.986635i
\(408\) 0 0
\(409\) 11.5717 20.0428i 0.572186 0.991055i −0.424155 0.905589i \(-0.639429\pi\)
0.996341 0.0854655i \(-0.0272378\pi\)
\(410\) −9.74597 + 16.8805i −0.481319 + 0.833669i
\(411\) 0 0
\(412\) 1.94169 3.36311i 0.0956603 0.165688i
\(413\) 0 0
\(414\) 0 0
\(415\) −4.56351 + 7.90423i −0.224014 + 0.388003i
\(416\) −4.24264 −0.208013
\(417\) 0 0
\(418\) 25.0966 1.22751
\(419\) 15.6854 + 27.1679i 0.766280 + 1.32724i 0.939567 + 0.342365i \(0.111228\pi\)
−0.173287 + 0.984871i \(0.555439\pi\)
\(420\) 0 0
\(421\) 6.43649 11.1483i 0.313695 0.543336i −0.665464 0.746430i \(-0.731766\pi\)
0.979159 + 0.203094i \(0.0650996\pi\)
\(422\) 10.3095 17.8565i 0.501857 0.869243i
\(423\) 0 0
\(424\) −6.30948 10.9283i −0.306415 0.530727i
\(425\) −4.85993 8.41765i −0.235741 0.408316i
\(426\) 0 0
\(427\) 0 0
\(428\) 0.127017 + 0.219999i 0.00613958 + 0.0106341i
\(429\) 0 0
\(430\) 3.88338 0.187273
\(431\) −10.7460 18.6126i −0.517615 0.896535i −0.999791 0.0204609i \(-0.993487\pi\)
0.482176 0.876075i \(-0.339847\pi\)
\(432\) 0 0
\(433\) 29.6985 1.42722 0.713609 0.700544i \(-0.247059\pi\)
0.713609 + 0.700544i \(0.247059\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 16.8730 0.808069
\(437\) −27.4367 + 47.5218i −1.31248 + 2.27328i
\(438\) 0 0
\(439\) −5.47723 9.48683i −0.261414 0.452782i 0.705204 0.709004i \(-0.250855\pi\)
−0.966618 + 0.256223i \(0.917522\pi\)
\(440\) −13.7829 −0.657073
\(441\) 0 0
\(442\) −6.00000 −0.285391
\(443\) −7.18246 12.4404i −0.341249 0.591060i 0.643416 0.765517i \(-0.277517\pi\)
−0.984665 + 0.174456i \(0.944183\pi\)
\(444\) 0 0
\(445\) 12.1825 21.1006i 0.577504 1.00027i
\(446\) −22.4478 −1.06293
\(447\) 0 0
\(448\) 0 0
\(449\) −9.00000 −0.424736 −0.212368 0.977190i \(-0.568118\pi\)
−0.212368 + 0.977190i \(0.568118\pi\)
\(450\) 0 0
\(451\) 11.3137 + 19.5959i 0.532742 + 0.922736i
\(452\) −3.87298 −0.182170
\(453\) 0 0
\(454\) 5.16858 + 8.95224i 0.242573 + 0.420150i
\(455\) 0 0
\(456\) 0 0
\(457\) −13.0635 22.6267i −0.611085 1.05843i −0.991058 0.133433i \(-0.957400\pi\)
0.379973 0.924998i \(-0.375933\pi\)
\(458\) −6.67261 11.5573i −0.311790 0.540037i
\(459\) 0 0
\(460\) 15.0681 26.0987i 0.702553 1.21686i
\(461\) −14.1813 + 24.5628i −0.660491 + 1.14400i 0.319996 + 0.947419i \(0.396318\pi\)
−0.980487 + 0.196585i \(0.937015\pi\)
\(462\) 0 0
\(463\) 0.809475 + 1.40205i 0.0376195 + 0.0651589i 0.884222 0.467067i \(-0.154689\pi\)
−0.846603 + 0.532226i \(0.821356\pi\)
\(464\) −1.12702 −0.0523204
\(465\) 0 0
\(466\) 7.25403 0.336037
\(467\) −3.09787 + 5.36567i −0.143352 + 0.248294i −0.928757 0.370689i \(-0.879122\pi\)
0.785405 + 0.618983i \(0.212455\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 7.00000 12.1244i 0.322886 0.559255i
\(471\) 0 0
\(472\) −4.15283 + 7.19291i −0.191149 + 0.331080i
\(473\) 2.25403 3.90410i 0.103641 0.179511i
\(474\) 0 0
\(475\) −21.5611 + 37.3448i −0.989289 + 1.71350i
\(476\) 0 0
\(477\) 0 0
\(478\) 7.50000 12.9904i 0.343042 0.594166i
\(479\) 3.88338 0.177436 0.0887182 0.996057i \(-0.471723\pi\)
0.0887182 + 0.996057i \(0.471723\pi\)
\(480\) 0 0
\(481\) 24.3781 1.11154
\(482\) 11.8412 + 20.5095i 0.539351 + 0.934184i
\(483\) 0 0
\(484\) −2.50000 + 4.33013i −0.113636 + 0.196824i
\(485\) −25.8730 + 44.8133i −1.17483 + 2.03487i
\(486\) 0 0
\(487\) 0.245967 + 0.426027i 0.0111458 + 0.0193051i 0.871545 0.490316i \(-0.163119\pi\)
−0.860399 + 0.509622i \(0.829785\pi\)
\(488\) −3.13707 5.43357i −0.142009 0.245966i
\(489\) 0 0
\(490\) 0 0
\(491\) 0.872983 + 1.51205i 0.0393972 + 0.0682379i 0.885052 0.465493i \(-0.154123\pi\)
−0.845654 + 0.533731i \(0.820790\pi\)
\(492\) 0 0
\(493\) −1.59384 −0.0717830
\(494\) 13.3095 + 23.0527i 0.598822 + 1.03719i
\(495\) 0 0
\(496\) −5.47723 −0.245935
\(497\) 0 0
\(498\) 0 0
\(499\) −29.7460 −1.33161 −0.665806 0.746125i \(-0.731912\pi\)
−0.665806 + 0.746125i \(0.731912\pi\)
\(500\) 3.22689 5.58913i 0.144311 0.249954i
\(501\) 0 0
\(502\) 4.73092 + 8.19419i 0.211151 + 0.365724i
\(503\) −3.88338 −0.173152 −0.0865758 0.996245i \(-0.527592\pi\)
−0.0865758 + 0.996245i \(0.527592\pi\)
\(504\) 0 0
\(505\) 45.9839 2.04626
\(506\) −17.4919 30.2969i −0.777611 1.34686i
\(507\) 0 0
\(508\) 0.372983 0.646026i 0.0165485 0.0286628i
\(509\) 22.8070 1.01090 0.505452 0.862855i \(-0.331326\pi\)
0.505452 + 0.862855i \(0.331326\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 1.50403 + 2.60505i 0.0663398 + 0.114904i
\(515\) 13.3810 0.589640
\(516\) 0 0
\(517\) −8.12602 14.0747i −0.357382 0.619004i
\(518\) 0 0
\(519\) 0 0
\(520\) −7.30948 12.6604i −0.320542 0.555194i
\(521\) −0.707107 1.22474i −0.0309789 0.0536570i 0.850120 0.526589i \(-0.176529\pi\)
−0.881099 + 0.472931i \(0.843196\pi\)
\(522\) 0 0
\(523\) 9.14178 15.8340i 0.399742 0.692373i −0.593952 0.804501i \(-0.702433\pi\)
0.993694 + 0.112127i \(0.0357664\pi\)
\(524\) −6.67261 + 11.5573i −0.291494 + 0.504883i
\(525\) 0 0
\(526\) 8.80948 + 15.2585i 0.384111 + 0.665300i
\(527\) −7.74597 −0.337420
\(528\) 0 0
\(529\) 53.4919 2.32574
\(530\) 21.7407 37.6560i 0.944355 1.63567i
\(531\) 0 0
\(532\) 0 0
\(533\) −12.0000 + 20.7846i −0.519778 + 0.900281i
\(534\) 0 0
\(535\) −0.437664 + 0.758056i −0.0189219 + 0.0327736i
\(536\) −3.43649 + 5.95218i −0.148434 + 0.257095i
\(537\) 0 0
\(538\) −1.01575 + 1.75934i −0.0437922 + 0.0758504i
\(539\) 0 0
\(540\) 0 0
\(541\) 19.0554 33.0050i 0.819257 1.41900i −0.0869727 0.996211i \(-0.527719\pi\)
0.906230 0.422785i \(-0.138947\pi\)
\(542\) 7.07107 0.303728
\(543\) 0 0
\(544\) −1.41421 −0.0606339
\(545\) 29.0698 + 50.3503i 1.24521 + 2.15677i
\(546\) 0 0
\(547\) 16.4919 28.5649i 0.705144 1.22135i −0.261495 0.965205i \(-0.584216\pi\)
0.966639 0.256141i \(-0.0824511\pi\)
\(548\) −7.74597 + 13.4164i −0.330891 + 0.573121i
\(549\) 0 0
\(550\) −13.7460 23.8087i −0.586130 1.01521i
\(551\) 3.53553 + 6.12372i 0.150619 + 0.260879i
\(552\) 0 0
\(553\) 0 0
\(554\) 7.18246 + 12.4404i 0.305153 + 0.528541i
\(555\) 0 0
\(556\) −19.8774 −0.842989
\(557\) 13.3095 + 23.0527i 0.563941 + 0.976774i 0.997147 + 0.0754792i \(0.0240486\pi\)
−0.433207 + 0.901295i \(0.642618\pi\)
\(558\) 0 0
\(559\) 4.78153 0.202237
\(560\) 0 0
\(561\) 0 0
\(562\) 8.74597 0.368926
\(563\) 10.8254 18.7502i 0.456238 0.790227i −0.542521 0.840042i \(-0.682530\pi\)
0.998758 + 0.0498156i \(0.0158634\pi\)
\(564\) 0 0
\(565\) −6.67261 11.5573i −0.280719 0.486219i
\(566\) 5.03956 0.211829
\(567\) 0 0
\(568\) −9.87298 −0.414261
\(569\) −11.7460 20.3446i −0.492417 0.852890i 0.507545 0.861625i \(-0.330553\pi\)
−0.999962 + 0.00873460i \(0.997220\pi\)
\(570\) 0 0
\(571\) −15.7460 + 27.2728i −0.658948 + 1.14133i 0.321940 + 0.946760i \(0.395665\pi\)
−0.980888 + 0.194572i \(0.937668\pi\)
\(572\) −16.9706 −0.709575
\(573\) 0 0
\(574\) 0 0
\(575\) 60.1109 2.50680
\(576\) 0 0
\(577\) 12.1106 + 20.9762i 0.504172 + 0.873252i 0.999988 + 0.00482425i \(0.00153561\pi\)
−0.495816 + 0.868427i \(0.665131\pi\)
\(578\) 15.0000 0.623918
\(579\) 0 0
\(580\) −1.94169 3.36311i −0.0806244 0.139645i
\(581\) 0 0
\(582\) 0 0
\(583\) −25.2379 43.7133i −1.04525 1.81042i
\(584\) −2.21113 3.82980i −0.0914974 0.158478i
\(585\) 0 0
\(586\) −0.398461 + 0.690154i −0.0164603 + 0.0285100i
\(587\) −4.28184 + 7.41637i −0.176731 + 0.306106i −0.940759 0.339076i \(-0.889885\pi\)
0.764028 + 0.645183i \(0.223219\pi\)
\(588\) 0 0
\(589\) 17.1825 + 29.7609i 0.707991 + 1.22628i
\(590\) −28.6190 −1.17822
\(591\) 0 0
\(592\) 5.74597 0.236158
\(593\) −16.8807 + 29.2383i −0.693209 + 1.20067i 0.277571 + 0.960705i \(0.410470\pi\)
−0.970781 + 0.239969i \(0.922863\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −7.87298 + 13.6364i −0.322490 + 0.558569i
\(597\) 0 0
\(598\) 18.5530 32.1347i 0.758688 1.31409i
\(599\) −22.6190 + 39.1772i −0.924185 + 1.60074i −0.131319 + 0.991340i \(0.541921\pi\)
−0.792866 + 0.609396i \(0.791412\pi\)
\(600\) 0 0
\(601\) −2.39076 + 4.14092i −0.0975213 + 0.168912i −0.910658 0.413161i \(-0.864425\pi\)
0.813137 + 0.582073i \(0.197758\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −5.50000 + 9.52628i −0.223792 + 0.387619i
\(605\) −17.2286 −0.700442
\(606\) 0 0
\(607\) −26.6904 −1.08333 −0.541666 0.840594i \(-0.682206\pi\)
−0.541666 + 0.840594i \(0.682206\pi\)
\(608\) 3.13707 + 5.43357i 0.127225 + 0.220360i
\(609\) 0 0
\(610\) 10.8095 18.7226i 0.437663 0.758054i
\(611\) 8.61895 14.9285i 0.348685 0.603941i
\(612\) 0 0
\(613\) −13.3095 23.0527i −0.537565 0.931089i −0.999034 0.0439334i \(-0.986011\pi\)
0.461470 0.887156i \(-0.347322\pi\)
\(614\) −7.11027 12.3154i −0.286947 0.497007i
\(615\) 0 0
\(616\) 0 0
\(617\) −6.12702 10.6123i −0.246664 0.427235i 0.715934 0.698168i \(-0.246001\pi\)
−0.962598 + 0.270933i \(0.912668\pi\)
\(618\) 0 0
\(619\) 37.9029 1.52345 0.761723 0.647902i \(-0.224354\pi\)
0.761723 + 0.647902i \(0.224354\pi\)
\(620\) −9.43649 16.3445i −0.378979 0.656410i
\(621\) 0 0
\(622\) 1.41421 0.0567048
\(623\) 0 0
\(624\) 0 0
\(625\) −12.1270 −0.485081
\(626\) −7.86799 + 13.6278i −0.314468 + 0.544675i
\(627\) 0 0
\(628\) 5.96550 + 10.3325i 0.238049 + 0.412314i
\(629\) 8.12602 0.324006
\(630\) 0 0
\(631\) −4.38105 −0.174407 −0.0872034 0.996191i \(-0.527793\pi\)
−0.0872034 + 0.996191i \(0.527793\pi\)
\(632\) −0.936492 1.62205i −0.0372516 0.0645217i
\(633\) 0 0
\(634\) −12.3095 + 21.3206i −0.488872 + 0.846751i
\(635\) 2.57039 0.102003
\(636\) 0 0
\(637\) 0 0
\(638\) −4.50807 −0.178476
\(639\) 0 0
\(640\) −1.72286 2.98408i −0.0681020 0.117956i
\(641\) −17.1109 −0.675839 −0.337920 0.941175i \(-0.609723\pi\)
−0.337920 + 0.941175i \(0.609723\pi\)
\(642\) 0 0
\(643\) 1.76206 + 3.05198i 0.0694890 + 0.120358i 0.898676 0.438612i \(-0.144530\pi\)
−0.829187 + 0.558971i \(0.811196\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 4.43649 + 7.68423i 0.174551 + 0.302332i
\(647\) 2.73861 + 4.74342i 0.107666 + 0.186483i 0.914824 0.403852i \(-0.132329\pi\)
−0.807158 + 0.590335i \(0.798996\pi\)
\(648\) 0 0
\(649\) −16.6113 + 28.7716i −0.652051 + 1.12939i
\(650\) 14.5798 25.2530i 0.571867 0.990502i
\(651\) 0 0
\(652\) −5.00000 8.66025i −0.195815 0.339162i
\(653\) 14.5081 0.567745 0.283872 0.958862i \(-0.408381\pi\)
0.283872 + 0.958862i \(0.408381\pi\)
\(654\) 0 0
\(655\) −45.9839 −1.79674
\(656\) −2.82843 + 4.89898i −0.110432 + 0.191273i
\(657\) 0 0
\(658\) 0 0
\(659\) 14.5635 25.2247i 0.567314 0.982616i −0.429517 0.903059i \(-0.641316\pi\)
0.996830 0.0795572i \(-0.0253506\pi\)
\(660\) 0 0
\(661\) −23.1043 + 40.0178i −0.898652 + 1.55651i −0.0694345 + 0.997587i \(0.522119\pi\)
−0.829218 + 0.558925i \(0.811214\pi\)
\(662\) 10.1825 17.6365i 0.395752 0.685463i
\(663\) 0 0
\(664\) −1.32440 + 2.29393i −0.0513967 + 0.0890216i
\(665\) 0 0
\(666\) 0 0
\(667\) 4.92843 8.53628i 0.190829 0.330526i
\(668\) 9.54024 0.369123
\(669\) 0 0
\(670\) −23.6824 −0.914930
\(671\) −12.5483 21.7343i −0.484421 0.839043i
\(672\) 0 0
\(673\) −7.11895 + 12.3304i −0.274415 + 0.475301i −0.969987 0.243155i \(-0.921818\pi\)
0.695572 + 0.718456i \(0.255151\pi\)
\(674\) 7.87298 13.6364i 0.303256 0.525255i
\(675\) 0 0
\(676\) −2.50000 4.33013i −0.0961538 0.166543i
\(677\) −6.36396 11.0227i −0.244587 0.423637i 0.717428 0.696632i \(-0.245319\pi\)
−0.962015 + 0.272995i \(0.911986\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −2.43649 4.22013i −0.0934352 0.161834i
\(681\) 0 0
\(682\) −21.9089 −0.838935
\(683\) 3.87298 + 6.70820i 0.148196 + 0.256682i 0.930561 0.366138i \(-0.119320\pi\)
−0.782365 + 0.622820i \(0.785987\pi\)
\(684\) 0 0
\(685\) −53.3809 −2.03958
\(686\) 0 0
\(687\) 0 0
\(688\) 1.12702 0.0429671
\(689\) 26.7688 46.3650i 1.01981 1.76637i
\(690\) 0 0
\(691\) 8.52448 + 14.7648i 0.324287 + 0.561681i 0.981368 0.192139i \(-0.0615424\pi\)
−0.657081 + 0.753820i \(0.728209\pi\)
\(692\) 12.7279 0.483843
\(693\) 0 0
\(694\) 7.74597 0.294033
\(695\) −34.2460 59.3158i −1.29902 2.24997i
\(696\) 0 0
\(697\) −4.00000 + 6.92820i −0.151511 + 0.262424i
\(698\) −16.4317 −0.621948
\(699\) 0 0
\(700\) 0 0
\(701\) 16.2540 0.613906 0.306953 0.951725i \(-0.400690\pi\)
0.306953 + 0.951725i \(0.400690\pi\)
\(702\) 0 0
\(703\) −18.0255 31.2211i −0.679845 1.17753i
\(704\) −4.00000 −0.150756
\(705\) 0 0
\(706\) 1.94169 + 3.36311i 0.0730765 + 0.126572i
\(707\) 0 0
\(708\) 0 0
\(709\) 26.3649 + 45.6654i 0.990155 + 1.71500i 0.616298 + 0.787513i \(0.288632\pi\)
0.373857 + 0.927486i \(0.378035\pi\)
\(710\) −17.0098 29.4618i −0.638365 1.10568i
\(711\) 0 0
\(712\) 3.53553 6.12372i 0.132500 0.229496i
\(713\) 23.9518 41.4858i 0.897003 1.55365i
\(714\) 0 0
\(715\) −29.2379 50.6415i −1.09344 1.89389i
\(716\) 6.87298 0.256855
\(717\) 0 0
\(718\) 18.2379 0.680632
\(719\) 11.7514 20.3540i 0.438252 0.759075i −0.559303 0.828964i \(-0.688931\pi\)
0.997555 + 0.0698884i \(0.0222643\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 10.1825 17.6365i 0.378952 0.656364i
\(723\) 0 0
\(724\) −6.67261 + 11.5573i −0.247985 + 0.429523i
\(725\) 3.87298 6.70820i 0.143839 0.249136i
\(726\) 0 0
\(727\) 1.68366 2.91618i 0.0624434 0.108155i −0.833114 0.553102i \(-0.813444\pi\)
0.895557 + 0.444947i \(0.146777\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 7.61895 13.1964i 0.281990 0.488421i
\(731\) 1.59384 0.0589504
\(732\) 0 0
\(733\) 37.0276 1.36765 0.683823 0.729648i \(-0.260316\pi\)
0.683823 + 0.729648i \(0.260316\pi\)
\(734\) −3.44572 5.96816i −0.127184 0.220289i
\(735\) 0 0
\(736\) 4.37298 7.57423i 0.161190 0.279190i
\(737\) −13.7460 + 23.8087i −0.506339 + 0.877005i
\(738\) 0 0
\(739\) 15.0000 + 25.9808i 0.551784 + 0.955718i 0.998146 + 0.0608653i \(0.0193860\pi\)
−0.446362 + 0.894852i \(0.647281\pi\)
\(740\) 9.89949 + 17.1464i 0.363913 + 0.630315i
\(741\) 0 0
\(742\) 0 0
\(743\) −6.12702 10.6123i −0.224778 0.389328i 0.731475 0.681869i \(-0.238833\pi\)
−0.956253 + 0.292541i \(0.905499\pi\)
\(744\) 0 0
\(745\) −54.2562 −1.98779
\(746\) −0.563508 0.976025i −0.0206315 0.0357348i
\(747\) 0 0
\(748\) −5.65685 −0.206835
\(749\) 0 0
\(750\) 0 0
\(751\) −13.0000 −0.474377 −0.237188 0.971464i \(-0.576226\pi\)
−0.237188 + 0.971464i \(0.576226\pi\)
\(752\) 2.03151 3.51867i 0.0740814 0.128313i
\(753\) 0 0
\(754\) −2.39076 4.14092i −0.0870665 0.150804i
\(755\) −37.9029 −1.37943
\(756\) 0 0
\(757\) 31.2379 1.13536 0.567680 0.823249i \(-0.307841\pi\)
0.567680 + 0.823249i \(0.307841\pi\)
\(758\) 13.1825 + 22.8327i 0.478808 + 0.829321i
\(759\) 0 0
\(760\) −10.8095 + 18.7226i −0.392101 + 0.679139i
\(761\) −30.5738 −1.10830 −0.554150 0.832417i \(-0.686957\pi\)
−0.554150 + 0.832417i \(0.686957\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 6.12702 0.221668
\(765\) 0 0
\(766\) −6.45378 11.1783i −0.233184 0.403887i
\(767\) −35.2379 −1.27237
\(768\) 0 0
\(769\) −0.617292 1.06918i −0.0222601 0.0385557i 0.854681 0.519154i \(-0.173753\pi\)
−0.876941 + 0.480598i \(0.840420\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −11.9365 20.6746i −0.429604 0.744095i
\(773\) 1.01575 + 1.75934i 0.0365341 + 0.0632789i 0.883714 0.468027i \(-0.155035\pi\)
−0.847180 + 0.531306i \(0.821702\pi\)
\(774\) 0 0
\(775\) 18.8224 32.6014i 0.676122 1.17108i
\(776\) −7.50873 + 13.0055i −0.269548 + 0.466870i
\(777\) 0 0
\(778\) −6.56351 11.3683i −0.235313 0.407574i
\(779\) 35.4919 1.27163
\(780\) 0 0
\(781\) −39.4919 −1.41313
\(782\) 6.18433 10.7116i 0.221151 0.383045i
\(783\) 0 0
\(784\) 0 0
\(785\) −20.5554 + 35.6031i −0.733655 + 1.27073i
\(786\) 0 0
\(787\) 6.18433 10.7116i 0.220448 0.381827i −0.734496 0.678613i \(-0.762582\pi\)
0.954944 + 0.296786i \(0.0959149\pi\)
\(788\) 8.30948 14.3924i 0.296013 0.512709i
\(789\) 0 0
\(790\) 3.22689 5.58913i 0.114808 0.198852i
\(791\) 0 0
\(792\) 0 0
\(793\) 13.3095 23.0527i 0.472633 0.818625i
\(794\) 7.07107