Properties

Label 441.2.p.c.215.8
Level $441$
Weight $2$
Character 441.215
Analytic conductor $3.521$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.p (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{48})\)
Defining polynomial: \(x^{16} - x^{8} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{6}\cdot 7^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 215.8
Root \(-0.991445 + 0.130526i\) of defining polynomial
Character \(\chi\) \(=\) 441.215
Dual form 441.2.p.c.80.8

$q$-expansion

\(f(q)\) \(=\) \(q+(2.09077 + 1.20711i) q^{2} +(1.91421 + 3.31552i) q^{4} +(1.68925 - 2.92586i) q^{5} +4.41421i q^{8} +O(q^{10})\) \(q+(2.09077 + 1.20711i) q^{2} +(1.91421 + 3.31552i) q^{4} +(1.68925 - 2.92586i) q^{5} +4.41421i q^{8} +(7.06365 - 4.07820i) q^{10} +(-0.717439 + 0.414214i) q^{11} +3.37849i q^{13} +(-1.50000 + 2.59808i) q^{16} +(0.699709 + 1.21193i) q^{17} +(-5.85172 - 3.37849i) q^{19} +12.9343 q^{20} -2.00000 q^{22} +(1.73205 + 1.00000i) q^{23} +(-3.20711 - 5.55487i) q^{25} +(-4.07820 + 7.06365i) q^{26} +4.82843i q^{29} +(-5.85172 + 3.37849i) q^{31} +(1.37333 - 0.792893i) q^{32} +3.37849i q^{34} +(1.29289 - 2.23936i) q^{37} +(-8.15640 - 14.1273i) q^{38} +(12.9154 + 7.45669i) q^{40} -8.15640 q^{41} -12.4853 q^{43} +(-2.74666 - 1.58579i) q^{44} +(2.41421 + 4.18154i) q^{46} +(3.37849 - 5.85172i) q^{47} -15.4853i q^{50} +(-11.2014 + 6.46716i) q^{52} +(6.12372 - 3.53553i) q^{53} +2.79884i q^{55} +(-5.82843 + 10.0951i) q^{58} +(3.37849 + 5.85172i) q^{59} +(7.06365 + 4.07820i) q^{61} -16.3128 q^{62} +9.82843 q^{64} +(9.88500 + 5.70711i) q^{65} +(-4.24264 - 7.34847i) q^{67} +(-2.67878 + 4.63979i) q^{68} -4.82843i q^{71} +(-1.21193 + 0.699709i) q^{73} +(5.40629 - 3.12132i) q^{74} -25.8686i q^{76} +(4.82843 - 8.36308i) q^{79} +(5.06774 + 8.77758i) q^{80} +(-17.0532 - 9.84565i) q^{82} +13.5140 q^{83} +4.72792 q^{85} +(-26.1039 - 15.0711i) q^{86} +(-1.82843 - 3.16693i) q^{88} +(3.08866 - 5.34972i) q^{89} +7.65685i q^{92} +(14.1273 - 8.15640i) q^{94} +(-19.7700 + 11.4142i) q^{95} +1.39942i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 8q^{4} + O(q^{10}) \) \( 16q + 8q^{4} - 24q^{16} - 32q^{22} - 40q^{25} + 32q^{37} - 64q^{43} + 16q^{46} - 48q^{58} + 112q^{64} + 32q^{79} - 128q^{85} + 16q^{88} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.09077 + 1.20711i 1.47840 + 0.853553i 0.999702 0.0244272i \(-0.00777619\pi\)
0.478696 + 0.877981i \(0.341110\pi\)
\(3\) 0 0
\(4\) 1.91421 + 3.31552i 0.957107 + 1.65776i
\(5\) 1.68925 2.92586i 0.755454 1.30848i −0.189694 0.981843i \(-0.560750\pi\)
0.945148 0.326641i \(-0.105917\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 4.41421i 1.56066i
\(9\) 0 0
\(10\) 7.06365 4.07820i 2.23372 1.28964i
\(11\) −0.717439 + 0.414214i −0.216316 + 0.124890i −0.604243 0.796800i \(-0.706524\pi\)
0.387927 + 0.921690i \(0.373191\pi\)
\(12\) 0 0
\(13\) 3.37849i 0.937025i 0.883457 + 0.468513i \(0.155210\pi\)
−0.883457 + 0.468513i \(0.844790\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.50000 + 2.59808i −0.375000 + 0.649519i
\(17\) 0.699709 + 1.21193i 0.169704 + 0.293936i 0.938316 0.345779i \(-0.112385\pi\)
−0.768612 + 0.639716i \(0.779052\pi\)
\(18\) 0 0
\(19\) −5.85172 3.37849i −1.34248 0.775079i −0.355307 0.934750i \(-0.615624\pi\)
−0.987170 + 0.159670i \(0.948957\pi\)
\(20\) 12.9343 2.89220
\(21\) 0 0
\(22\) −2.00000 −0.426401
\(23\) 1.73205 + 1.00000i 0.361158 + 0.208514i 0.669588 0.742732i \(-0.266471\pi\)
−0.308431 + 0.951247i \(0.599804\pi\)
\(24\) 0 0
\(25\) −3.20711 5.55487i −0.641421 1.11097i
\(26\) −4.07820 + 7.06365i −0.799801 + 1.38530i
\(27\) 0 0
\(28\) 0 0
\(29\) 4.82843i 0.896616i 0.893879 + 0.448308i \(0.147973\pi\)
−0.893879 + 0.448308i \(0.852027\pi\)
\(30\) 0 0
\(31\) −5.85172 + 3.37849i −1.05100 + 0.606795i −0.922929 0.384970i \(-0.874212\pi\)
−0.128071 + 0.991765i \(0.540879\pi\)
\(32\) 1.37333 0.792893i 0.242773 0.140165i
\(33\) 0 0
\(34\) 3.37849i 0.579407i
\(35\) 0 0
\(36\) 0 0
\(37\) 1.29289 2.23936i 0.212550 0.368148i −0.739962 0.672649i \(-0.765156\pi\)
0.952512 + 0.304501i \(0.0984897\pi\)
\(38\) −8.15640 14.1273i −1.32314 2.29175i
\(39\) 0 0
\(40\) 12.9154 + 7.45669i 2.04210 + 1.17901i
\(41\) −8.15640 −1.27382 −0.636908 0.770940i \(-0.719787\pi\)
−0.636908 + 0.770940i \(0.719787\pi\)
\(42\) 0 0
\(43\) −12.4853 −1.90399 −0.951994 0.306117i \(-0.900970\pi\)
−0.951994 + 0.306117i \(0.900970\pi\)
\(44\) −2.74666 1.58579i −0.414075 0.239066i
\(45\) 0 0
\(46\) 2.41421 + 4.18154i 0.355956 + 0.616535i
\(47\) 3.37849 5.85172i 0.492804 0.853561i −0.507162 0.861851i \(-0.669305\pi\)
0.999966 + 0.00828959i \(0.00263869\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 15.4853i 2.18995i
\(51\) 0 0
\(52\) −11.2014 + 6.46716i −1.55336 + 0.896833i
\(53\) 6.12372 3.53553i 0.841158 0.485643i −0.0164995 0.999864i \(-0.505252\pi\)
0.857658 + 0.514221i \(0.171919\pi\)
\(54\) 0 0
\(55\) 2.79884i 0.377395i
\(56\) 0 0
\(57\) 0 0
\(58\) −5.82843 + 10.0951i −0.765310 + 1.32556i
\(59\) 3.37849 + 5.85172i 0.439842 + 0.761829i 0.997677 0.0681229i \(-0.0217010\pi\)
−0.557835 + 0.829952i \(0.688368\pi\)
\(60\) 0 0
\(61\) 7.06365 + 4.07820i 0.904408 + 0.522160i 0.878628 0.477507i \(-0.158460\pi\)
0.0257803 + 0.999668i \(0.491793\pi\)
\(62\) −16.3128 −2.07173
\(63\) 0 0
\(64\) 9.82843 1.22855
\(65\) 9.88500 + 5.70711i 1.22608 + 0.707879i
\(66\) 0 0
\(67\) −4.24264 7.34847i −0.518321 0.897758i −0.999773 0.0212861i \(-0.993224\pi\)
0.481452 0.876472i \(-0.340109\pi\)
\(68\) −2.67878 + 4.63979i −0.324850 + 0.562657i
\(69\) 0 0
\(70\) 0 0
\(71\) 4.82843i 0.573029i −0.958076 0.286514i \(-0.907503\pi\)
0.958076 0.286514i \(-0.0924966\pi\)
\(72\) 0 0
\(73\) −1.21193 + 0.699709i −0.141846 + 0.0818947i −0.569243 0.822169i \(-0.692764\pi\)
0.427398 + 0.904064i \(0.359430\pi\)
\(74\) 5.40629 3.12132i 0.628468 0.362846i
\(75\) 0 0
\(76\) 25.8686i 2.96734i
\(77\) 0 0
\(78\) 0 0
\(79\) 4.82843 8.36308i 0.543240 0.940920i −0.455475 0.890249i \(-0.650531\pi\)
0.998715 0.0506715i \(-0.0161361\pi\)
\(80\) 5.06774 + 8.77758i 0.566590 + 0.981363i
\(81\) 0 0
\(82\) −17.0532 9.84565i −1.88321 1.08727i
\(83\) 13.5140 1.48335 0.741676 0.670759i \(-0.234031\pi\)
0.741676 + 0.670759i \(0.234031\pi\)
\(84\) 0 0
\(85\) 4.72792 0.512815
\(86\) −26.1039 15.0711i −2.81485 1.62516i
\(87\) 0 0
\(88\) −1.82843 3.16693i −0.194911 0.337596i
\(89\) 3.08866 5.34972i 0.327398 0.567069i −0.654597 0.755978i \(-0.727162\pi\)
0.981995 + 0.188909i \(0.0604950\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 7.65685i 0.798282i
\(93\) 0 0
\(94\) 14.1273 8.15640i 1.45712 0.841269i
\(95\) −19.7700 + 11.4142i −2.02836 + 1.17107i
\(96\) 0 0
\(97\) 1.39942i 0.142089i 0.997473 + 0.0710447i \(0.0226333\pi\)
−0.997473 + 0.0710447i \(0.977367\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 12.2782 21.2664i 1.22782 2.12664i
\(101\) 6.46716 + 11.2014i 0.643506 + 1.11459i 0.984644 + 0.174572i \(0.0558542\pi\)
−0.341138 + 0.940013i \(0.610812\pi\)
\(102\) 0 0
\(103\) −2.42386 1.39942i −0.238830 0.137889i 0.375809 0.926697i \(-0.377365\pi\)
−0.614639 + 0.788809i \(0.710698\pi\)
\(104\) −14.9134 −1.46238
\(105\) 0 0
\(106\) 17.0711 1.65809
\(107\) −8.06591 4.65685i −0.779761 0.450195i 0.0565847 0.998398i \(-0.481979\pi\)
−0.836345 + 0.548203i \(0.815312\pi\)
\(108\) 0 0
\(109\) 1.29289 + 2.23936i 0.123837 + 0.214491i 0.921278 0.388906i \(-0.127147\pi\)
−0.797441 + 0.603397i \(0.793813\pi\)
\(110\) −3.37849 + 5.85172i −0.322127 + 0.557940i
\(111\) 0 0
\(112\) 0 0
\(113\) 5.89949i 0.554978i 0.960729 + 0.277489i \(0.0895022\pi\)
−0.960729 + 0.277489i \(0.910498\pi\)
\(114\) 0 0
\(115\) 5.85172 3.37849i 0.545676 0.315046i
\(116\) −16.0087 + 9.24264i −1.48637 + 0.858158i
\(117\) 0 0
\(118\) 16.3128i 1.50172i
\(119\) 0 0
\(120\) 0 0
\(121\) −5.15685 + 8.93193i −0.468805 + 0.811994i
\(122\) 9.84565 + 17.0532i 0.891383 + 1.54392i
\(123\) 0 0
\(124\) −22.4029 12.9343i −2.01184 1.16154i
\(125\) −4.77791 −0.427349
\(126\) 0 0
\(127\) −0.485281 −0.0430618 −0.0215309 0.999768i \(-0.506854\pi\)
−0.0215309 + 0.999768i \(0.506854\pi\)
\(128\) 17.8023 + 10.2782i 1.57352 + 0.908471i
\(129\) 0 0
\(130\) 13.7782 + 23.8645i 1.20843 + 2.09305i
\(131\) −4.77791 + 8.27558i −0.417448 + 0.723041i −0.995682 0.0928299i \(-0.970409\pi\)
0.578234 + 0.815871i \(0.303742\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 20.4853i 1.76966i
\(135\) 0 0
\(136\) −5.34972 + 3.08866i −0.458735 + 0.264851i
\(137\) 0.717439 0.414214i 0.0612949 0.0353887i −0.469039 0.883177i \(-0.655400\pi\)
0.530334 + 0.847789i \(0.322066\pi\)
\(138\) 0 0
\(139\) 9.55582i 0.810514i −0.914203 0.405257i \(-0.867182\pi\)
0.914203 0.405257i \(-0.132818\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 5.82843 10.0951i 0.489111 0.847165i
\(143\) −1.39942 2.42386i −0.117025 0.202694i
\(144\) 0 0
\(145\) 14.1273 + 8.15640i 1.17321 + 0.677352i
\(146\) −3.37849 −0.279606
\(147\) 0 0
\(148\) 9.89949 0.813733
\(149\) 3.67423 + 2.12132i 0.301005 + 0.173785i 0.642894 0.765955i \(-0.277733\pi\)
−0.341889 + 0.939740i \(0.611067\pi\)
\(150\) 0 0
\(151\) 6.24264 + 10.8126i 0.508019 + 0.879915i 0.999957 + 0.00928431i \(0.00295533\pi\)
−0.491938 + 0.870630i \(0.663711\pi\)
\(152\) 14.9134 25.8307i 1.20964 2.09515i
\(153\) 0 0
\(154\) 0 0
\(155\) 22.8284i 1.83362i
\(156\) 0 0
\(157\) −6.35372 + 3.66832i −0.507082 + 0.292764i −0.731633 0.681698i \(-0.761242\pi\)
0.224551 + 0.974462i \(0.427908\pi\)
\(158\) 20.1903 11.6569i 1.60625 0.927370i
\(159\) 0 0
\(160\) 5.35757i 0.423553i
\(161\) 0 0
\(162\) 0 0
\(163\) −7.41421 + 12.8418i −0.580726 + 1.00585i 0.414667 + 0.909973i \(0.363898\pi\)
−0.995393 + 0.0958740i \(0.969435\pi\)
\(164\) −15.6131 27.0427i −1.21918 2.11168i
\(165\) 0 0
\(166\) 28.2546 + 16.3128i 2.19298 + 1.26612i
\(167\) −2.79884 −0.216580 −0.108290 0.994119i \(-0.534538\pi\)
−0.108290 + 0.994119i \(0.534538\pi\)
\(168\) 0 0
\(169\) 1.58579 0.121984
\(170\) 9.88500 + 5.70711i 0.758145 + 0.437715i
\(171\) 0 0
\(172\) −23.8995 41.3951i −1.82232 3.15635i
\(173\) 4.07820 7.06365i 0.310060 0.537040i −0.668315 0.743878i \(-0.732984\pi\)
0.978375 + 0.206839i \(0.0663175\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.48528i 0.187335i
\(177\) 0 0
\(178\) 12.9154 7.45669i 0.968048 0.558903i
\(179\) 8.23999 4.75736i 0.615886 0.355582i −0.159380 0.987217i \(-0.550949\pi\)
0.775265 + 0.631636i \(0.217616\pi\)
\(180\) 0 0
\(181\) 17.7122i 1.31654i −0.752782 0.658270i \(-0.771289\pi\)
0.752782 0.658270i \(-0.228711\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −4.41421 + 7.64564i −0.325420 + 0.563644i
\(185\) −4.36803 7.56565i −0.321144 0.556238i
\(186\) 0 0
\(187\) −1.00400 0.579658i −0.0734195 0.0423888i
\(188\) 25.8686 1.88666
\(189\) 0 0
\(190\) −55.1127 −3.99830
\(191\) −18.0379 10.4142i −1.30518 0.753546i −0.323892 0.946094i \(-0.604992\pi\)
−0.981288 + 0.192548i \(0.938325\pi\)
\(192\) 0 0
\(193\) 8.82843 + 15.2913i 0.635484 + 1.10069i 0.986412 + 0.164288i \(0.0525328\pi\)
−0.350928 + 0.936402i \(0.614134\pi\)
\(194\) −1.68925 + 2.92586i −0.121281 + 0.210065i
\(195\) 0 0
\(196\) 0 0
\(197\) 16.2426i 1.15724i −0.815597 0.578620i \(-0.803591\pi\)
0.815597 0.578620i \(-0.196409\pi\)
\(198\) 0 0
\(199\) −16.5512 + 9.55582i −1.17328 + 0.677394i −0.954451 0.298369i \(-0.903557\pi\)
−0.218830 + 0.975763i \(0.570224\pi\)
\(200\) 24.5204 14.1569i 1.73385 1.00104i
\(201\) 0 0
\(202\) 31.2262i 2.19707i
\(203\) 0 0
\(204\) 0 0
\(205\) −13.7782 + 23.8645i −0.962309 + 1.66677i
\(206\) −3.37849 5.85172i −0.235391 0.407709i
\(207\) 0 0
\(208\) −8.77758 5.06774i −0.608616 0.351384i
\(209\) 5.59767 0.387199
\(210\) 0 0
\(211\) 7.31371 0.503496 0.251748 0.967793i \(-0.418995\pi\)
0.251748 + 0.967793i \(0.418995\pi\)
\(212\) 23.4442 + 13.5355i 1.61016 + 0.929624i
\(213\) 0 0
\(214\) −11.2426 19.4728i −0.768531 1.33113i
\(215\) −21.0907 + 36.5302i −1.43837 + 2.49134i
\(216\) 0 0
\(217\) 0 0
\(218\) 6.24264i 0.422805i
\(219\) 0 0
\(220\) −9.27958 + 5.35757i −0.625629 + 0.361207i
\(221\) −4.09450 + 2.36396i −0.275426 + 0.159017i
\(222\) 0 0
\(223\) 23.0698i 1.54487i 0.635095 + 0.772434i \(0.280961\pi\)
−0.635095 + 0.772434i \(0.719039\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −7.12132 + 12.3345i −0.473703 + 0.820478i
\(227\) 1.39942 + 2.42386i 0.0928826 + 0.160877i 0.908723 0.417400i \(-0.137059\pi\)
−0.815840 + 0.578277i \(0.803725\pi\)
\(228\) 0 0
\(229\) 10.4915 + 6.05728i 0.693299 + 0.400276i 0.804847 0.593483i \(-0.202248\pi\)
−0.111548 + 0.993759i \(0.535581\pi\)
\(230\) 16.3128 1.07563
\(231\) 0 0
\(232\) −21.3137 −1.39931
\(233\) −9.37769 5.41421i −0.614353 0.354697i 0.160314 0.987066i \(-0.448749\pi\)
−0.774667 + 0.632369i \(0.782083\pi\)
\(234\) 0 0
\(235\) −11.4142 19.7700i −0.744581 1.28965i
\(236\) −12.9343 + 22.4029i −0.841952 + 1.45830i
\(237\) 0 0
\(238\) 0 0
\(239\) 0.343146i 0.0221963i 0.999938 + 0.0110981i \(0.00353272\pi\)
−0.999938 + 0.0110981i \(0.996467\pi\)
\(240\) 0 0
\(241\) 7.77359 4.48808i 0.500741 0.289103i −0.228279 0.973596i \(-0.573310\pi\)
0.729019 + 0.684493i \(0.239976\pi\)
\(242\) −21.5636 + 12.4497i −1.38616 + 0.800300i
\(243\) 0 0
\(244\) 31.2262i 1.99905i
\(245\) 0 0
\(246\) 0 0
\(247\) 11.4142 19.7700i 0.726269 1.25793i
\(248\) −14.9134 25.8307i −0.947001 1.64025i
\(249\) 0 0
\(250\) −9.98951 5.76745i −0.631792 0.364765i
\(251\) 25.8686 1.63281 0.816407 0.577477i \(-0.195963\pi\)
0.816407 + 0.577477i \(0.195963\pi\)
\(252\) 0 0
\(253\) −1.65685 −0.104166
\(254\) −1.01461 0.585786i −0.0636624 0.0367555i
\(255\) 0 0
\(256\) 14.9853 + 25.9553i 0.936580 + 1.62220i
\(257\) 10.8352 18.7671i 0.675880 1.17066i −0.300330 0.953835i \(-0.597097\pi\)
0.976211 0.216824i \(-0.0695698\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 43.6985i 2.71006i
\(261\) 0 0
\(262\) −19.9790 + 11.5349i −1.23431 + 0.712628i
\(263\) −20.9077 + 12.0711i −1.28922 + 0.744334i −0.978516 0.206171i \(-0.933900\pi\)
−0.310708 + 0.950505i \(0.600566\pi\)
\(264\) 0 0
\(265\) 23.8896i 1.46752i
\(266\) 0 0
\(267\) 0 0
\(268\) 16.2426 28.1331i 0.992177 1.71850i
\(269\) −15.6131 27.0427i −0.951947 1.64882i −0.741204 0.671280i \(-0.765745\pi\)
−0.210743 0.977541i \(-0.567588\pi\)
\(270\) 0 0
\(271\) 5.85172 + 3.37849i 0.355467 + 0.205229i 0.667090 0.744977i \(-0.267539\pi\)
−0.311624 + 0.950206i \(0.600873\pi\)
\(272\) −4.19825 −0.254556
\(273\) 0 0
\(274\) 2.00000 0.120824
\(275\) 4.60181 + 2.65685i 0.277499 + 0.160214i
\(276\) 0 0
\(277\) 10.4853 + 18.1610i 0.630000 + 1.09119i 0.987551 + 0.157298i \(0.0502783\pi\)
−0.357552 + 0.933893i \(0.616388\pi\)
\(278\) 11.5349 19.9790i 0.691817 1.19826i
\(279\) 0 0
\(280\) 0 0
\(281\) 18.8284i 1.12321i −0.827406 0.561605i \(-0.810184\pi\)
0.827406 0.561605i \(-0.189816\pi\)
\(282\) 0 0
\(283\) 25.8307 14.9134i 1.53548 0.886509i 0.536384 0.843974i \(-0.319790\pi\)
0.999095 0.0425346i \(-0.0135433\pi\)
\(284\) 16.0087 9.24264i 0.949943 0.548450i
\(285\) 0 0
\(286\) 6.75699i 0.399549i
\(287\) 0 0
\(288\) 0 0
\(289\) 7.52082 13.0264i 0.442401 0.766261i
\(290\) 19.6913 + 34.1063i 1.15631 + 2.00279i
\(291\) 0 0
\(292\) −4.63979 2.67878i −0.271523 0.156764i
\(293\) −7.33664 −0.428611 −0.214306 0.976767i \(-0.568749\pi\)
−0.214306 + 0.976767i \(0.568749\pi\)
\(294\) 0 0
\(295\) 22.8284 1.32912
\(296\) 9.88500 + 5.70711i 0.574554 + 0.331719i
\(297\) 0 0
\(298\) 5.12132 + 8.87039i 0.296670 + 0.513848i
\(299\) −3.37849 + 5.85172i −0.195383 + 0.338414i
\(300\) 0 0
\(301\) 0 0
\(302\) 30.1421i 1.73448i
\(303\) 0 0
\(304\) 17.5552 10.1355i 1.00686 0.581310i
\(305\) 23.8645 13.7782i 1.36648 0.788936i
\(306\) 0 0
\(307\) 12.3547i 0.705117i 0.935790 + 0.352559i \(0.114688\pi\)
−0.935790 + 0.352559i \(0.885312\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −27.5563 + 47.7290i −1.56510 + 2.71082i
\(311\) 5.35757 + 9.27958i 0.303800 + 0.526197i 0.976993 0.213270i \(-0.0684113\pi\)
−0.673194 + 0.739466i \(0.735078\pi\)
\(312\) 0 0
\(313\) −11.2014 6.46716i −0.633143 0.365545i 0.148825 0.988864i \(-0.452451\pi\)
−0.781968 + 0.623318i \(0.785784\pi\)
\(314\) −17.7122 −0.999559
\(315\) 0 0
\(316\) 36.9706 2.07976
\(317\) 20.5745 + 11.8787i 1.15558 + 0.667173i 0.950240 0.311518i \(-0.100837\pi\)
0.205338 + 0.978691i \(0.434171\pi\)
\(318\) 0 0
\(319\) −2.00000 3.46410i −0.111979 0.193952i
\(320\) 16.6026 28.7566i 0.928116 1.60754i
\(321\) 0 0
\(322\) 0 0
\(323\) 9.45584i 0.526137i
\(324\) 0 0
\(325\) 18.7671 10.8352i 1.04101 0.601028i
\(326\) −31.0028 + 17.8995i −1.71709 + 0.991361i
\(327\) 0 0
\(328\) 36.0041i 1.98799i
\(329\) 0 0
\(330\) 0 0
\(331\) −5.17157 + 8.95743i −0.284255 + 0.492345i −0.972428 0.233202i \(-0.925080\pi\)
0.688173 + 0.725547i \(0.258413\pi\)
\(332\) 25.8686 + 44.8058i 1.41973 + 2.45904i
\(333\) 0 0
\(334\) −5.85172 3.37849i −0.320192 0.184863i
\(335\) −28.6675 −1.56627
\(336\) 0 0
\(337\) −12.9289 −0.704284 −0.352142 0.935947i \(-0.614547\pi\)
−0.352142 + 0.935947i \(0.614547\pi\)
\(338\) 3.31552 + 1.91421i 0.180340 + 0.104119i
\(339\) 0 0
\(340\) 9.05025 + 15.6755i 0.490819 + 0.850123i
\(341\) 2.79884 4.84772i 0.151565 0.262519i
\(342\) 0 0
\(343\) 0 0
\(344\) 55.1127i 2.97148i
\(345\) 0 0
\(346\) 17.0532 9.84565i 0.916784 0.529305i
\(347\) 16.4290 9.48528i 0.881954 0.509197i 0.0106521 0.999943i \(-0.496609\pi\)
0.871302 + 0.490747i \(0.163276\pi\)
\(348\) 0 0
\(349\) 6.17733i 0.330665i −0.986238 0.165332i \(-0.947130\pi\)
0.986238 0.165332i \(-0.0528697\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.656854 + 1.13770i −0.0350104 + 0.0606399i
\(353\) 11.8247 + 20.4810i 0.629367 + 1.09009i 0.987679 + 0.156493i \(0.0500189\pi\)
−0.358312 + 0.933602i \(0.616648\pi\)
\(354\) 0 0
\(355\) −14.1273 8.15640i −0.749799 0.432897i
\(356\) 23.6494 1.25342
\(357\) 0 0
\(358\) 22.9706 1.21403
\(359\) −0.891519 0.514719i −0.0470526 0.0271658i 0.476289 0.879289i \(-0.341982\pi\)
−0.523342 + 0.852123i \(0.675315\pi\)
\(360\) 0 0
\(361\) 13.3284 + 23.0855i 0.701496 + 1.21503i
\(362\) 21.3805 37.0322i 1.12374 1.94637i
\(363\) 0 0
\(364\) 0 0
\(365\) 4.72792i 0.247471i
\(366\) 0 0
\(367\) 3.42786 1.97908i 0.178933 0.103307i −0.407858 0.913045i \(-0.633724\pi\)
0.586791 + 0.809738i \(0.300391\pi\)
\(368\) −5.19615 + 3.00000i −0.270868 + 0.156386i
\(369\) 0 0
\(370\) 21.0907i 1.09645i
\(371\) 0 0
\(372\) 0 0
\(373\) 11.3137 19.5959i 0.585802 1.01464i −0.408973 0.912546i \(-0.634113\pi\)
0.994775 0.102092i \(-0.0325536\pi\)
\(374\) −1.39942 2.42386i −0.0723622 0.125335i
\(375\) 0 0
\(376\) 25.8307 + 14.9134i 1.33212 + 0.769099i
\(377\) −16.3128 −0.840152
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) −75.6880 43.6985i −3.88271 2.24168i
\(381\) 0 0
\(382\) −25.1421 43.5475i −1.28638 2.22808i
\(383\) −13.5140 + 23.4069i −0.690532 + 1.19604i 0.281132 + 0.959669i \(0.409290\pi\)
−0.971664 + 0.236367i \(0.924043\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 42.6274i 2.16968i
\(387\) 0 0
\(388\) −4.63979 + 2.67878i −0.235550 + 0.135995i
\(389\) 11.9503 6.89949i 0.605903 0.349818i −0.165457 0.986217i \(-0.552910\pi\)
0.771360 + 0.636399i \(0.219577\pi\)
\(390\) 0 0
\(391\) 2.79884i 0.141543i
\(392\) 0 0
\(393\) 0 0
\(394\) 19.6066 33.9596i 0.987766 1.71086i
\(395\) −16.3128 28.2546i −0.820786 1.42164i
\(396\) 0 0
\(397\) −23.6148 13.6340i −1.18519 0.684272i −0.227983 0.973665i \(-0.573213\pi\)
−0.957210 + 0.289393i \(0.906547\pi\)
\(398\) −46.1396 −2.31277
\(399\) 0 0
\(400\) 19.2426 0.962132
\(401\) 9.37769 + 5.41421i 0.468300 + 0.270373i 0.715528 0.698584i \(-0.246186\pi\)
−0.247228 + 0.968957i \(0.579520\pi\)
\(402\) 0 0
\(403\) −11.4142 19.7700i −0.568582 0.984814i
\(404\) −24.7590 + 42.8839i −1.23181 + 2.13355i
\(405\) 0 0
\(406\) 0 0
\(407\) 2.14214i 0.106182i
\(408\) 0 0
\(409\) −15.3392 + 8.85611i −0.758476 + 0.437907i −0.828748 0.559621i \(-0.810947\pi\)
0.0702721 + 0.997528i \(0.477613\pi\)
\(410\) −57.6140 + 33.2635i −2.84535 + 1.64276i
\(411\) 0 0
\(412\) 10.7151i 0.527897i
\(413\) 0 0
\(414\) 0 0
\(415\) 22.8284 39.5400i 1.12060 1.94094i
\(416\) 2.67878 + 4.63979i 0.131338 + 0.227484i
\(417\) 0 0
\(418\) 11.7034 + 6.75699i 0.572434 + 0.330495i
\(419\) 35.4244 1.73060 0.865299 0.501256i \(-0.167129\pi\)
0.865299 + 0.501256i \(0.167129\pi\)
\(420\) 0 0
\(421\) −23.3137 −1.13624 −0.568120 0.822946i \(-0.692329\pi\)
−0.568120 + 0.822946i \(0.692329\pi\)
\(422\) 15.2913 + 8.82843i 0.744368 + 0.429761i
\(423\) 0 0
\(424\) 15.6066 + 27.0314i 0.757924 + 1.31276i
\(425\) 4.48808 7.77359i 0.217704 0.377074i
\(426\) 0 0
\(427\) 0 0
\(428\) 35.6569i 1.72354i
\(429\) 0 0
\(430\) −88.1917 + 50.9175i −4.25298 + 2.45546i
\(431\) 13.3852 7.72792i 0.644740 0.372241i −0.141698 0.989910i \(-0.545256\pi\)
0.786438 + 0.617669i \(0.211923\pi\)
\(432\) 0 0
\(433\) 8.15640i 0.391972i 0.980607 + 0.195986i \(0.0627907\pi\)
−0.980607 + 0.195986i \(0.937209\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −4.94975 + 8.57321i −0.237050 + 0.410582i
\(437\) −6.75699 11.7034i −0.323230 0.559852i
\(438\) 0 0
\(439\) −24.8268 14.3337i −1.18492 0.684112i −0.227769 0.973715i \(-0.573143\pi\)
−0.957147 + 0.289603i \(0.906477\pi\)
\(440\) −12.3547 −0.588985
\(441\) 0 0
\(442\) −11.4142 −0.542919
\(443\) −21.5020 12.4142i −1.02159 0.589817i −0.107028 0.994256i \(-0.534133\pi\)
−0.914565 + 0.404439i \(0.867467\pi\)
\(444\) 0 0
\(445\) −10.4350 18.0740i −0.494668 0.856790i
\(446\) −27.8477 + 48.2336i −1.31863 + 2.28393i
\(447\) 0 0
\(448\) 0 0
\(449\) 24.2426i 1.14408i −0.820225 0.572040i \(-0.806152\pi\)
0.820225 0.572040i \(-0.193848\pi\)
\(450\) 0 0
\(451\) 5.85172 3.37849i 0.275547 0.159087i
\(452\) −19.5599 + 11.2929i −0.920019 + 0.531173i
\(453\) 0 0
\(454\) 6.75699i 0.317121i
\(455\) 0 0
\(456\) 0 0
\(457\) −14.3137 + 24.7921i −0.669567 + 1.15972i 0.308458 + 0.951238i \(0.400187\pi\)
−0.978025 + 0.208486i \(0.933146\pi\)
\(458\) 14.6236 + 25.3287i 0.683314 + 1.18353i
\(459\) 0 0
\(460\) 22.4029 + 12.9343i 1.04454 + 0.603065i
\(461\) −21.6704 −1.00929 −0.504645 0.863327i \(-0.668377\pi\)
−0.504645 + 0.863327i \(0.668377\pi\)
\(462\) 0 0
\(463\) 3.51472 0.163343 0.0816714 0.996659i \(-0.473974\pi\)
0.0816714 + 0.996659i \(0.473974\pi\)
\(464\) −12.5446 7.24264i −0.582369 0.336231i
\(465\) 0 0
\(466\) −13.0711 22.6398i −0.605506 1.04877i
\(467\) −1.39942 + 2.42386i −0.0647573 + 0.112163i −0.896586 0.442869i \(-0.853961\pi\)
0.831829 + 0.555032i \(0.187294\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 55.1127i 2.54216i
\(471\) 0 0
\(472\) −25.8307 + 14.9134i −1.18896 + 0.686444i
\(473\) 8.95743 5.17157i 0.411863 0.237789i
\(474\) 0 0
\(475\) 43.3407i 1.98861i
\(476\) 0 0
\(477\) 0 0
\(478\) −0.414214 + 0.717439i −0.0189457 + 0.0328149i
\(479\) −4.19825 7.27159i −0.191823 0.332247i 0.754031 0.656838i \(-0.228107\pi\)
−0.945854 + 0.324591i \(0.894773\pi\)
\(480\) 0 0
\(481\) 7.56565 + 4.36803i 0.344964 + 0.199165i
\(482\) 21.6704 0.987059
\(483\) 0 0
\(484\) −39.4853 −1.79479
\(485\) 4.09450 + 2.36396i 0.185922 + 0.107342i
\(486\) 0 0
\(487\) −4.72792 8.18900i −0.214243 0.371079i 0.738795 0.673930i \(-0.235395\pi\)
−0.953038 + 0.302851i \(0.902062\pi\)
\(488\) −18.0021 + 31.1805i −0.814915 + 1.41147i
\(489\) 0 0
\(490\) 0 0
\(491\) 2.68629i 0.121231i 0.998161 + 0.0606153i \(0.0193063\pi\)
−0.998161 + 0.0606153i \(0.980694\pi\)
\(492\) 0 0
\(493\) −5.85172 + 3.37849i −0.263548 + 0.152160i
\(494\) 47.7290 27.5563i 2.14743 1.23982i
\(495\) 0 0
\(496\) 20.2710i 0.910193i
\(497\) 0 0
\(498\) 0 0
\(499\) 1.07107 1.85514i 0.0479476 0.0830476i −0.841056 0.540949i \(-0.818065\pi\)
0.889003 + 0.457901i \(0.151399\pi\)
\(500\) −9.14594 15.8412i −0.409019 0.708442i
\(501\) 0 0
\(502\) 54.0854 + 31.2262i 2.41395 + 1.39369i
\(503\) −32.6256 −1.45470 −0.727352 0.686264i \(-0.759249\pi\)
−0.727352 + 0.686264i \(0.759249\pi\)
\(504\) 0 0
\(505\) 43.6985 1.94456
\(506\) −3.46410 2.00000i −0.153998 0.0889108i
\(507\) 0 0
\(508\) −0.928932 1.60896i −0.0412147 0.0713860i
\(509\) 18.4119 31.8904i 0.816095 1.41352i −0.0924447 0.995718i \(-0.529468\pi\)
0.908539 0.417799i \(-0.137199\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 31.2426i 1.38074i
\(513\) 0 0
\(514\) 45.3078 26.1585i 1.99844 1.15380i
\(515\) −8.18900 + 4.72792i −0.360851 + 0.208337i
\(516\) 0 0
\(517\) 5.59767i 0.246185i
\(518\) 0 0
\(519\) 0 0
\(520\) −25.1924 + 43.6345i −1.10476 + 1.91350i
\(521\) −21.3805 37.0322i −0.936699 1.62241i −0.771576 0.636137i \(-0.780531\pi\)
−0.165122 0.986273i \(-0.552802\pi\)
\(522\) 0 0
\(523\) −15.1313 8.73606i −0.661646 0.382001i 0.131258 0.991348i \(-0.458098\pi\)
−0.792904 + 0.609347i \(0.791432\pi\)
\(524\) −36.5838 −1.59817
\(525\) 0 0
\(526\) −58.2843 −2.54131
\(527\) −8.18900 4.72792i −0.356718 0.205952i
\(528\) 0 0
\(529\) −9.50000 16.4545i −0.413043 0.715412i
\(530\) 28.8372 49.9476i 1.25261 2.16958i
\(531\) 0 0
\(532\) 0 0
\(533\) 27.5563i 1.19360i
\(534\) 0 0
\(535\) −27.2506 + 15.7331i −1.17815 + 0.680203i
\(536\) 32.4377 18.7279i 1.40110 0.808923i
\(537\) 0 0
\(538\) 75.3867i 3.25015i
\(539\) 0 0
\(540\) 0 0
\(541\) −9.48528 + 16.4290i −0.407804 + 0.706337i −0.994643 0.103366i \(-0.967039\pi\)
0.586839 + 0.809703i \(0.300372\pi\)
\(542\) 8.15640 + 14.1273i 0.350348 + 0.606820i
\(543\) 0 0
\(544\) 1.92186 + 1.10959i 0.0823992 + 0.0475732i
\(545\) 8.73606 0.374212
\(546\) 0 0
\(547\) −26.6274 −1.13851 −0.569253 0.822162i \(-0.692768\pi\)
−0.569253 + 0.822162i \(0.692768\pi\)
\(548\) 2.74666 + 1.58579i 0.117332 + 0.0677414i
\(549\) 0 0
\(550\) 6.41421 + 11.1097i 0.273503 + 0.473721i
\(551\) 16.3128 28.2546i 0.694949 1.20369i
\(552\) 0 0
\(553\) 0 0
\(554\) 50.6274i 2.15095i
\(555\) 0 0
\(556\) 31.6825 18.2919i 1.34364 0.775749i
\(557\) 9.16756 5.29289i 0.388442 0.224267i −0.293043 0.956099i \(-0.594668\pi\)
0.681485 + 0.731832i \(0.261335\pi\)
\(558\) 0 0
\(559\) 42.1814i 1.78408i
\(560\) 0 0
\(561\) 0 0
\(562\) 22.7279 39.3659i 0.958720 1.66055i
\(563\) 1.39942 + 2.42386i 0.0589784 + 0.102154i 0.894007 0.448053i \(-0.147882\pi\)
−0.835029 + 0.550206i \(0.814549\pi\)
\(564\) 0 0
\(565\) 17.2611 + 9.96570i 0.726180 + 0.419260i
\(566\) 72.0082 3.02673
\(567\) 0 0
\(568\) 21.3137 0.894303
\(569\) 21.7482 + 12.5563i 0.911733 + 0.526390i 0.880988 0.473138i \(-0.156879\pi\)
0.0307450 + 0.999527i \(0.490212\pi\)
\(570\) 0 0
\(571\) 5.65685 + 9.79796i 0.236732 + 0.410032i 0.959775 0.280772i \(-0.0905903\pi\)
−0.723043 + 0.690803i \(0.757257\pi\)
\(572\) 5.35757 9.27958i 0.224011 0.387999i
\(573\) 0 0
\(574\) 0 0
\(575\) 12.8284i 0.534982i
\(576\) 0 0
\(577\) 11.9114 6.87704i 0.495877 0.286295i −0.231132 0.972922i \(-0.574243\pi\)
0.727009 + 0.686628i \(0.240910\pi\)
\(578\) 31.4486 18.1569i 1.30809 0.755226i
\(579\) 0 0
\(580\) 62.4524i 2.59319i
\(581\) 0 0
\(582\) 0 0
\(583\) −2.92893 + 5.07306i −0.121304 + 0.210105i
\(584\) −3.08866 5.34972i −0.127810 0.221373i
\(585\) 0 0
\(586\) −15.3392 8.85611i −0.633658 0.365843i
\(587\) 20.2710 0.836672 0.418336 0.908292i \(-0.362613\pi\)
0.418336 + 0.908292i \(0.362613\pi\)
\(588\) 0 0
\(589\) 45.6569 1.88126
\(590\) 47.7290 + 27.5563i 1.96497 + 1.13448i
\(591\) 0 0
\(592\) 3.87868 + 6.71807i 0.159413 + 0.276111i
\(593\) −10.2555 + 17.7631i −0.421144 + 0.729443i −0.996052 0.0887754i \(-0.971705\pi\)
0.574908 + 0.818218i \(0.305038\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 16.2426i 0.665324i
\(597\) 0 0
\(598\) −14.1273 + 8.15640i −0.577708 + 0.333540i
\(599\) −5.61642 + 3.24264i −0.229481 + 0.132491i −0.610332 0.792145i \(-0.708964\pi\)
0.380852 + 0.924636i \(0.375631\pi\)
\(600\) 0 0
\(601\) 27.6076i 1.12614i 0.826410 + 0.563069i \(0.190379\pi\)
−0.826410 + 0.563069i \(0.809621\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −23.8995 + 41.3951i −0.972457 + 1.68434i
\(605\) 17.4224 + 30.1765i 0.708321 + 1.22685i
\(606\) 0 0
\(607\) −19.9790 11.5349i −0.810924 0.468187i 0.0363529 0.999339i \(-0.488426\pi\)
−0.847277 + 0.531152i \(0.821759\pi\)
\(608\) −10.7151 −0.434556
\(609\) 0 0
\(610\) 66.5269 2.69360
\(611\) 19.7700 + 11.4142i 0.799809 + 0.461770i
\(612\) 0 0
\(613\) 5.43503 + 9.41375i 0.219519 + 0.380218i 0.954661 0.297695i \(-0.0962180\pi\)
−0.735142 + 0.677913i \(0.762885\pi\)
\(614\) −14.9134 + 25.8307i −0.601855 + 1.04244i
\(615\) 0 0
\(616\) 0 0
\(617\) 30.4853i 1.22729i 0.789582 + 0.613646i \(0.210298\pi\)
−0.789582 + 0.613646i \(0.789702\pi\)
\(618\) 0 0
\(619\) 21.3989 12.3547i 0.860094 0.496576i −0.00394972 0.999992i \(-0.501257\pi\)
0.864044 + 0.503417i \(0.167924\pi\)
\(620\) −75.6880 + 43.6985i −3.03970 + 1.75497i
\(621\) 0 0
\(622\) 25.8686i 1.03724i
\(623\) 0 0
\(624\) 0 0
\(625\) 7.96447 13.7949i 0.318579 0.551794i
\(626\) −15.6131 27.0427i −0.624025 1.08084i
\(627\) 0 0
\(628\) −24.3248 14.0439i −0.970663 0.560413i
\(629\) 3.61859 0.144283
\(630\) 0 0
\(631\) −21.1716 −0.842827 −0.421414 0.906869i \(-0.638466\pi\)
−0.421414 + 0.906869i \(0.638466\pi\)
\(632\) 36.9164 + 21.3137i 1.46846 + 0.847814i
\(633\) 0 0
\(634\) 28.6777 + 49.6712i 1.13894 + 1.97269i
\(635\) −0.819760 + 1.41987i −0.0325312 + 0.0563456i
\(636\) 0 0
\(637\) 0 0
\(638\) 9.65685i 0.382319i
\(639\) 0 0
\(640\) 60.1450 34.7247i 2.37744 1.37262i
\(641\) −6.50794 + 3.75736i −0.257048 + 0.148407i −0.622987 0.782232i \(-0.714081\pi\)
0.365939 + 0.930639i \(0.380748\pi\)
\(642\) 0 0
\(643\) 6.75699i 0.266469i 0.991085 + 0.133235i \(0.0425364\pi\)
−0.991085 + 0.133235i \(0.957464\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 11.4142 19.7700i 0.449086 0.777840i
\(647\) 12.9343 + 22.4029i 0.508500 + 0.880748i 0.999952 + 0.00984331i \(0.00313327\pi\)
−0.491451 + 0.870905i \(0.663533\pi\)
\(648\) 0 0
\(649\) −4.84772 2.79884i −0.190290 0.109864i
\(650\) 52.3169 2.05204
\(651\) 0 0
\(652\) −56.7696 −2.22327
\(653\) −33.3292 19.2426i −1.30427 0.753023i −0.323140 0.946351i \(-0.604738\pi\)
−0.981134 + 0.193329i \(0.938072\pi\)
\(654\) 0 0
\(655\) 16.1421 + 27.9590i 0.630725 + 1.09245i
\(656\) 12.2346 21.1910i 0.477681 0.827368i
\(657\) 0 0
\(658\) 0 0
\(659\) 47.4558i 1.84862i 0.381646 + 0.924309i \(0.375357\pi\)
−0.381646 + 0.924309i \(0.624643\pi\)
\(660\) 0 0
\(661\) 6.35372 3.66832i 0.247131 0.142681i −0.371319 0.928505i \(-0.621094\pi\)
0.618450 + 0.785824i \(0.287761\pi\)
\(662\) −21.6251 + 12.4853i −0.840485 + 0.485254i
\(663\) 0 0
\(664\) 59.6536i 2.31501i
\(665\) 0 0
\(666\) 0 0
\(667\) −4.82843 + 8.36308i −0.186957 + 0.323820i
\(668\) −5.35757 9.27958i −0.207291 0.359038i
\(669\) 0 0
\(670\) −59.9371 34.6047i −2.31557 1.33690i
\(671\) −6.75699 −0.260851
\(672\) 0 0
\(673\) −37.8995 −1.46092 −0.730459 0.682956i \(-0.760694\pi\)
−0.730459 + 0.682956i \(0.760694\pi\)
\(674\) −27.0314 15.6066i −1.04121 0.601144i
\(675\) 0 0
\(676\) 3.03553 + 5.25770i 0.116751 + 0.202219i
\(677\) −16.4329 + 28.4625i −0.631566 + 1.09390i 0.355666 + 0.934613i \(0.384254\pi\)
−0.987232 + 0.159291i \(0.949079\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 20.8701i 0.800330i
\(681\) 0 0
\(682\) 11.7034 6.75699i 0.448148 0.258738i
\(683\) −33.5754 + 19.3848i −1.28473 + 0.741738i −0.977709 0.209966i \(-0.932665\pi\)
−0.307019 + 0.951703i \(0.599331\pi\)
\(684\) 0 0
\(685\) 2.79884i 0.106938i
\(686\) 0 0
\(687\) 0 0
\(688\) 18.7279 32.4377i 0.713995 1.23668i
\(689\) 11.9448 + 20.6890i 0.455060 + 0.788187i
\(690\) 0 0
\(691\) 8.27558 + 4.77791i 0.314818 + 0.181760i 0.649080 0.760720i \(-0.275154\pi\)
−0.334262 + 0.942480i \(0.608487\pi\)
\(692\) 31.2262 1.18704
\(693\) 0 0
\(694\) 45.7990 1.73851
\(695\) −27.9590 16.1421i −1.06055 0.612306i
\(696\) 0 0
\(697\) −5.70711 9.88500i −0.216172 0.374421i
\(698\) 7.45669 12.9154i 0.282240 0.488854i
\(699\) 0 0
\(700\) 0 0
\(701\) 40.7696i 1.53984i 0.638138 + 0.769922i \(0.279705\pi\)
−0.638138 + 0.769922i \(0.720295\pi\)
\(702\) 0 0
\(703\) −15.1313 + 8.73606i −0.570688 + 0.329487i
\(704\) −7.05130 + 4.07107i −0.265756 + 0.153434i
\(705\) 0 0
\(706\) 57.0948i 2.14879i
\(707\) 0 0
\(708\) 0 0
\(709\) 16.3640 28.3432i 0.614561 1.06445i −0.375900 0.926660i \(-0.622666\pi\)
0.990461 0.137791i \(-0.0440003\pi\)
\(710\) −19.6913 34.1063i −0.739001 1.27999i
\(711\) 0 0
\(712\) 23.6148 + 13.6340i 0.885003 + 0.510957i
\(713\) −13.5140 −0.506102
\(714\) 0 0
\(715\) −9.45584 −0.353629
\(716\) 31.5462 + 18.2132i 1.17894 + 0.680659i
\(717\) 0 0
\(718\) −1.24264 2.15232i −0.0463749 0.0803237i
\(719\) −6.75699 + 11.7034i −0.251993 + 0.436465i −0.964074 0.265632i \(-0.914419\pi\)
0.712081 + 0.702097i \(0.247753\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 64.3553i 2.39506i
\(723\) 0 0
\(724\) 58.7251 33.9050i 2.18250 1.26007i
\(725\) 26.8213 15.4853i 0.996118 0.575109i
\(726\) 0 0
\(727\) 43.3407i 1.60742i −0.595022 0.803710i \(-0.702857\pi\)
0.595022 0.803710i \(-0.297143\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −5.70711 + 9.88500i −0.211229 + 0.365860i
\(731\) −8.73606 15.1313i −0.323115 0.559651i
\(732\) 0 0
\(733\) 20.1870 + 11.6549i 0.745622 + 0.430485i 0.824110 0.566430i \(-0.191676\pi\)
−0.0784876 + 0.996915i \(0.525009\pi\)
\(734\) 9.55582 0.352712
\(735\) 0 0
\(736\) 3.17157 0.116906
\(737\) 6.08767 + 3.51472i 0.224242 + 0.129466i
\(738\) 0 0
\(739\) 9.41421 + 16.3059i 0.346307 + 0.599822i 0.985590 0.169149i \(-0.0541021\pi\)
−0.639283 + 0.768972i \(0.720769\pi\)
\(740\) 16.7227 28.9645i 0.614738 1.06476i
\(741\) 0 0
\(742\) 0 0
\(743\) 52.4264i 1.92334i −0.274212 0.961669i \(-0.588417\pi\)
0.274212 0.961669i \(-0.411583\pi\)
\(744\) 0 0
\(745\) 12.4134 7.16687i 0.454791 0.262574i
\(746\) 47.3087 27.3137i 1.73210 1.00003i
\(747\) 0 0
\(748\) 4.43835i 0.162282i
\(749\) 0 0
\(750\) 0 0
\(751\) −10.3431 + 17.9149i −0.377427 + 0.653722i −0.990687 0.136159i \(-0.956524\pi\)
0.613260 + 0.789881i \(0.289858\pi\)
\(752\) 10.1355 + 17.5552i 0.369603 + 0.640171i
\(753\) 0 0
\(754\) −34.1063 19.6913i −1.24208 0.717115i
\(755\) 42.1814 1.53514
\(756\) 0 0
\(757\) 6.87006 0.249696 0.124848 0.992176i \(-0.460156\pi\)
0.124848 + 0.992176i \(0.460156\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) −50.3848 87.2690i −1.82765 3.16558i
\(761\) −0.289829 + 0.501998i −0.0105063 + 0.0181974i −0.871231 0.490874i \(-0.836678\pi\)
0.860724 + 0.509071i \(0.170011\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 79.7401i 2.88490i
\(765\) 0 0
\(766\) −56.5092 + 32.6256i −2.04176 + 1.17881i
\(767\) −19.7700 + 11.4142i −0.713853 + 0.412143i
\(768\) 0 0
\(769\) 45.8995i 1.65518i −0.561335 0.827589i \(-0.689712\pi\)
0.561335 0.827589i \(-0.310288\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −33.7990 + 58.5416i −1.21645 + 2.10696i
\(773\) 9.43577 + 16.3432i 0.339381 + 0.587825i 0.984316 0.176412i \(-0.0564491\pi\)
−0.644935 + 0.764237i \(0.723116\pi\)
\(774\) 0 0
\(775\) 37.5342 + 21.6704i 1.34827 + 0.778423i
\(776\) −6.17733 −0.221753
\(777\) 0 0
\(778\) 33.3137 1.19435
\(779\) 47.7290 + 27.5563i 1.71007 + 0.987309i
\(780\) 0 0
\(781\) 2.00000 + 3.46410i 0.0715656 + 0.123955i
\(782\) −3.37849 + 5.85172i −0.120815 + 0.209257i
\(783\) 0 0
\(784\) 0 0
\(785\) 24.7868i 0.884679i
\(786\) 0 0
\(787\) −11.7034 + 6.75699i −0.417183 + 0.240861i −0.693871 0.720099i \(-0.744096\pi\)
0.276689 + 0.960960i \(0.410763\pi\)
\(788\) 53.8527 31.0919i 1.91842 1.10760i
\(789\) 0 0
\(790\) 78.7652i 2.80234i
\(791\) 0 0
\(792\) 0 0
\(793\) −13.7782 + 23.8645i −0.489277 + 0.847453i
\(794\) −32.9154 57.0112i −1.16813 2.02325i
\(795\) 0