Properties

Label 2646.2.m.c.1763.14
Level $2646$
Weight $2$
Character 2646.1763
Analytic conductor $21.128$
Analytic rank $0$
Dimension $48$
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.m (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 882)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1763.14
Character \(\chi\) \(=\) 2646.1763
Dual form 2646.2.m.c.881.14

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.35026 + 2.33872i) q^{5} +1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(1.35026 + 2.33872i) q^{5} +1.00000i q^{8} +2.70053i q^{10} +(0.205998 + 0.118933i) q^{11} +(-2.31418 + 1.33609i) q^{13} +(-0.500000 + 0.866025i) q^{16} -5.86724 q^{17} +1.15274i q^{19} +(-1.35026 + 2.33872i) q^{20} +(0.118933 + 0.205998i) q^{22} +(-7.02271 + 4.05456i) q^{23} +(-1.14642 + 1.98566i) q^{25} -2.67219 q^{26} +(-8.88796 - 5.13146i) q^{29} +(-5.21902 + 3.01320i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-5.08118 - 2.93362i) q^{34} +9.68488 q^{37} +(-0.576368 + 0.998299i) q^{38} +(-2.33872 + 1.35026i) q^{40} +(3.81891 + 6.61455i) q^{41} +(2.69219 - 4.66301i) q^{43} +0.237866i q^{44} -8.10913 q^{46} +(-0.221142 + 0.383029i) q^{47} +(-1.98566 + 1.14642i) q^{50} +(-2.31418 - 1.33609i) q^{52} -0.219155i q^{53} +0.642362i q^{55} +(-5.13146 - 8.88796i) q^{58} +(0.983559 + 1.70357i) q^{59} +(10.8615 + 6.27087i) q^{61} -6.02640 q^{62} -1.00000 q^{64} +(-6.24951 - 3.60816i) q^{65} +(4.48336 + 7.76541i) q^{67} +(-2.93362 - 5.08118i) q^{68} -2.24510i q^{71} +7.25634i q^{73} +(8.38735 + 4.84244i) q^{74} +(-0.998299 + 0.576368i) q^{76} +(5.43592 - 9.41528i) q^{79} -2.70053 q^{80} +7.63782i q^{82} +(0.762403 - 1.32052i) q^{83} +(-7.92232 - 13.7219i) q^{85} +(4.66301 - 2.69219i) q^{86} +(-0.118933 + 0.205998i) q^{88} -13.5277 q^{89} +(-7.02271 - 4.05456i) q^{92} +(-0.383029 + 0.221142i) q^{94} +(-2.69593 + 1.55650i) q^{95} +(1.37708 + 0.795057i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 24 q^{4} + O(q^{10}) \) \( 48 q + 24 q^{4} - 48 q^{11} - 24 q^{16} - 48 q^{23} - 24 q^{25} + 48 q^{50} - 48 q^{64} + 48 q^{79} + 48 q^{85} - 96 q^{86} - 48 q^{92} + 192 q^{95} + O(q^{100}) \)

Character values

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

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.35026 + 2.33872i 0.603856 + 1.04591i 0.992231 + 0.124408i \(0.0397032\pi\)
−0.388375 + 0.921501i \(0.626963\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 2.70053i 0.853982i
\(11\) 0.205998 + 0.118933i 0.0621106 + 0.0358596i 0.530734 0.847539i \(-0.321916\pi\)
−0.468623 + 0.883398i \(0.655250\pi\)
\(12\) 0 0
\(13\) −2.31418 + 1.33609i −0.641839 + 0.370566i −0.785322 0.619087i \(-0.787503\pi\)
0.143484 + 0.989653i \(0.454169\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −5.86724 −1.42301 −0.711507 0.702679i \(-0.751987\pi\)
−0.711507 + 0.702679i \(0.751987\pi\)
\(18\) 0 0
\(19\) 1.15274i 0.264456i 0.991219 + 0.132228i \(0.0422131\pi\)
−0.991219 + 0.132228i \(0.957787\pi\)
\(20\) −1.35026 + 2.33872i −0.301928 + 0.522955i
\(21\) 0 0
\(22\) 0.118933 + 0.205998i 0.0253566 + 0.0439188i
\(23\) −7.02271 + 4.05456i −1.46434 + 0.845435i −0.999207 0.0398080i \(-0.987325\pi\)
−0.465129 + 0.885243i \(0.653992\pi\)
\(24\) 0 0
\(25\) −1.14642 + 1.98566i −0.229284 + 0.397132i
\(26\) −2.67219 −0.524059
\(27\) 0 0
\(28\) 0 0
\(29\) −8.88796 5.13146i −1.65045 0.952889i −0.976886 0.213762i \(-0.931428\pi\)
−0.673566 0.739127i \(-0.735238\pi\)
\(30\) 0 0
\(31\) −5.21902 + 3.01320i −0.937364 + 0.541187i −0.889133 0.457649i \(-0.848692\pi\)
−0.0482307 + 0.998836i \(0.515358\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) −5.08118 2.93362i −0.871415 0.503112i
\(35\) 0 0
\(36\) 0 0
\(37\) 9.68488 1.59218 0.796092 0.605175i \(-0.206897\pi\)
0.796092 + 0.605175i \(0.206897\pi\)
\(38\) −0.576368 + 0.998299i −0.0934993 + 0.161945i
\(39\) 0 0
\(40\) −2.33872 + 1.35026i −0.369785 + 0.213495i
\(41\) 3.81891 + 6.61455i 0.596414 + 1.03302i 0.993346 + 0.115171i \(0.0367416\pi\)
−0.396932 + 0.917848i \(0.629925\pi\)
\(42\) 0 0
\(43\) 2.69219 4.66301i 0.410555 0.711103i −0.584395 0.811469i \(-0.698668\pi\)
0.994951 + 0.100366i \(0.0320015\pi\)
\(44\) 0.237866i 0.0358596i
\(45\) 0 0
\(46\) −8.10913 −1.19563
\(47\) −0.221142 + 0.383029i −0.0322568 + 0.0558705i −0.881703 0.471805i \(-0.843603\pi\)
0.849446 + 0.527675i \(0.176936\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −1.98566 + 1.14642i −0.280815 + 0.162129i
\(51\) 0 0
\(52\) −2.31418 1.33609i −0.320919 0.185283i
\(53\) 0.219155i 0.0301032i −0.999887 0.0150516i \(-0.995209\pi\)
0.999887 0.0150516i \(-0.00479126\pi\)
\(54\) 0 0
\(55\) 0.642362i 0.0866161i
\(56\) 0 0
\(57\) 0 0
\(58\) −5.13146 8.88796i −0.673794 1.16705i
\(59\) 0.983559 + 1.70357i 0.128048 + 0.221786i 0.922920 0.384991i \(-0.125795\pi\)
−0.794872 + 0.606777i \(0.792462\pi\)
\(60\) 0 0
\(61\) 10.8615 + 6.27087i 1.39067 + 0.802902i 0.993389 0.114796i \(-0.0366214\pi\)
0.397278 + 0.917698i \(0.369955\pi\)
\(62\) −6.02640 −0.765354
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −6.24951 3.60816i −0.775156 0.447537i
\(66\) 0 0
\(67\) 4.48336 + 7.76541i 0.547730 + 0.948696i 0.998430 + 0.0560206i \(0.0178412\pi\)
−0.450700 + 0.892676i \(0.648825\pi\)
\(68\) −2.93362 5.08118i −0.355754 0.616183i
\(69\) 0 0
\(70\) 0 0
\(71\) 2.24510i 0.266445i −0.991086 0.133222i \(-0.957468\pi\)
0.991086 0.133222i \(-0.0425324\pi\)
\(72\) 0 0
\(73\) 7.25634i 0.849291i 0.905360 + 0.424645i \(0.139601\pi\)
−0.905360 + 0.424645i \(0.860399\pi\)
\(74\) 8.38735 + 4.84244i 0.975010 + 0.562922i
\(75\) 0 0
\(76\) −0.998299 + 0.576368i −0.114513 + 0.0661140i
\(77\) 0 0
\(78\) 0 0
\(79\) 5.43592 9.41528i 0.611588 1.05930i −0.379385 0.925239i \(-0.623864\pi\)
0.990973 0.134063i \(-0.0428024\pi\)
\(80\) −2.70053 −0.301928
\(81\) 0 0
\(82\) 7.63782i 0.843456i
\(83\) 0.762403 1.32052i 0.0836846 0.144946i −0.821145 0.570719i \(-0.806665\pi\)
0.904830 + 0.425773i \(0.139998\pi\)
\(84\) 0 0
\(85\) −7.92232 13.7219i −0.859296 1.48834i
\(86\) 4.66301 2.69219i 0.502826 0.290307i
\(87\) 0 0
\(88\) −0.118933 + 0.205998i −0.0126783 + 0.0219594i
\(89\) −13.5277 −1.43393 −0.716967 0.697107i \(-0.754470\pi\)
−0.716967 + 0.697107i \(0.754470\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −7.02271 4.05456i −0.732168 0.422717i
\(93\) 0 0
\(94\) −0.383029 + 0.221142i −0.0395064 + 0.0228090i
\(95\) −2.69593 + 1.55650i −0.276597 + 0.159693i
\(96\) 0 0
\(97\) 1.37708 + 0.795057i 0.139821 + 0.0807258i 0.568279 0.822836i \(-0.307610\pi\)
−0.428458 + 0.903562i \(0.640943\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.29284 −0.229284
\(101\) −6.48353 + 11.2298i −0.645135 + 1.11741i 0.339135 + 0.940738i \(0.389866\pi\)
−0.984270 + 0.176670i \(0.943468\pi\)
\(102\) 0 0
\(103\) −15.9765 + 9.22402i −1.57421 + 0.908870i −0.578564 + 0.815637i \(0.696387\pi\)
−0.995644 + 0.0932327i \(0.970280\pi\)
\(104\) −1.33609 2.31418i −0.131015 0.226924i
\(105\) 0 0
\(106\) 0.109577 0.189794i 0.0106431 0.0184344i
\(107\) 4.65158i 0.449686i −0.974395 0.224843i \(-0.927813\pi\)
0.974395 0.224843i \(-0.0721868\pi\)
\(108\) 0 0
\(109\) 10.0651 0.964066 0.482033 0.876153i \(-0.339898\pi\)
0.482033 + 0.876153i \(0.339898\pi\)
\(110\) −0.321181 + 0.556302i −0.0306234 + 0.0530413i
\(111\) 0 0
\(112\) 0 0
\(113\) 8.33618 4.81290i 0.784202 0.452759i −0.0537156 0.998556i \(-0.517106\pi\)
0.837917 + 0.545797i \(0.183773\pi\)
\(114\) 0 0
\(115\) −18.9650 10.9495i −1.76850 1.02104i
\(116\) 10.2629i 0.952889i
\(117\) 0 0
\(118\) 1.96712i 0.181088i
\(119\) 0 0
\(120\) 0 0
\(121\) −5.47171 9.47728i −0.497428 0.861571i
\(122\) 6.27087 + 10.8615i 0.567738 + 0.983350i
\(123\) 0 0
\(124\) −5.21902 3.01320i −0.468682 0.270594i
\(125\) 7.31075 0.653893
\(126\) 0 0
\(127\) −4.69657 −0.416753 −0.208377 0.978049i \(-0.566818\pi\)
−0.208377 + 0.978049i \(0.566818\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) −3.60816 6.24951i −0.316456 0.548118i
\(131\) 7.02151 + 12.1616i 0.613472 + 1.06257i 0.990650 + 0.136424i \(0.0435611\pi\)
−0.377178 + 0.926141i \(0.623106\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 8.96673i 0.774607i
\(135\) 0 0
\(136\) 5.86724i 0.503112i
\(137\) 9.39626 + 5.42494i 0.802777 + 0.463483i 0.844441 0.535648i \(-0.179933\pi\)
−0.0416643 + 0.999132i \(0.513266\pi\)
\(138\) 0 0
\(139\) 19.5606 11.2933i 1.65911 0.957886i 0.685980 0.727620i \(-0.259374\pi\)
0.973128 0.230266i \(-0.0739597\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.12255 1.94432i 0.0942024 0.163163i
\(143\) −0.635621 −0.0531533
\(144\) 0 0
\(145\) 27.7153i 2.30163i
\(146\) −3.62817 + 6.28418i −0.300270 + 0.520082i
\(147\) 0 0
\(148\) 4.84244 + 8.38735i 0.398046 + 0.689436i
\(149\) −0.236156 + 0.136345i −0.0193467 + 0.0111698i −0.509642 0.860386i \(-0.670222\pi\)
0.490295 + 0.871556i \(0.336889\pi\)
\(150\) 0 0
\(151\) −9.42148 + 16.3185i −0.766709 + 1.32798i 0.172629 + 0.984987i \(0.444774\pi\)
−0.939338 + 0.342992i \(0.888560\pi\)
\(152\) −1.15274 −0.0934993
\(153\) 0 0
\(154\) 0 0
\(155\) −14.0941 8.13723i −1.13207 0.653598i
\(156\) 0 0
\(157\) 2.82310 1.62992i 0.225308 0.130082i −0.383098 0.923708i \(-0.625143\pi\)
0.608406 + 0.793626i \(0.291809\pi\)
\(158\) 9.41528 5.43592i 0.749040 0.432458i
\(159\) 0 0
\(160\) −2.33872 1.35026i −0.184892 0.106748i
\(161\) 0 0
\(162\) 0 0
\(163\) −3.13675 −0.245689 −0.122844 0.992426i \(-0.539202\pi\)
−0.122844 + 0.992426i \(0.539202\pi\)
\(164\) −3.81891 + 6.61455i −0.298207 + 0.516509i
\(165\) 0 0
\(166\) 1.32052 0.762403i 0.102492 0.0591739i
\(167\) −3.19575 5.53520i −0.247295 0.428327i 0.715480 0.698634i \(-0.246208\pi\)
−0.962774 + 0.270307i \(0.912875\pi\)
\(168\) 0 0
\(169\) −2.92971 + 5.07440i −0.225362 + 0.390339i
\(170\) 15.8446i 1.21523i
\(171\) 0 0
\(172\) 5.38438 0.410555
\(173\) 0.146767 0.254207i 0.0111585 0.0193270i −0.860392 0.509632i \(-0.829781\pi\)
0.871551 + 0.490305i \(0.163115\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.205998 + 0.118933i −0.0155277 + 0.00896490i
\(177\) 0 0
\(178\) −11.7153 6.76386i −0.878102 0.506972i
\(179\) 23.0747i 1.72468i 0.506326 + 0.862342i \(0.331003\pi\)
−0.506326 + 0.862342i \(0.668997\pi\)
\(180\) 0 0
\(181\) 10.9176i 0.811500i 0.913984 + 0.405750i \(0.132990\pi\)
−0.913984 + 0.405750i \(0.867010\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −4.05456 7.02271i −0.298906 0.517721i
\(185\) 13.0771 + 22.6503i 0.961451 + 1.66528i
\(186\) 0 0
\(187\) −1.20864 0.697807i −0.0883843 0.0510287i
\(188\) −0.442283 −0.0322568
\(189\) 0 0
\(190\) −3.11300 −0.225840
\(191\) −11.1456 6.43490i −0.806465 0.465613i 0.0392616 0.999229i \(-0.487499\pi\)
−0.845727 + 0.533616i \(0.820833\pi\)
\(192\) 0 0
\(193\) 5.11771 + 8.86414i 0.368381 + 0.638054i 0.989313 0.145810i \(-0.0465789\pi\)
−0.620932 + 0.783865i \(0.713246\pi\)
\(194\) 0.795057 + 1.37708i 0.0570818 + 0.0988686i
\(195\) 0 0
\(196\) 0 0
\(197\) 3.89068i 0.277200i 0.990348 + 0.138600i \(0.0442602\pi\)
−0.990348 + 0.138600i \(0.955740\pi\)
\(198\) 0 0
\(199\) 2.33150i 0.165276i 0.996580 + 0.0826378i \(0.0263345\pi\)
−0.996580 + 0.0826378i \(0.973666\pi\)
\(200\) −1.98566 1.14642i −0.140407 0.0810643i
\(201\) 0 0
\(202\) −11.2298 + 6.48353i −0.790126 + 0.456180i
\(203\) 0 0
\(204\) 0 0
\(205\) −10.3131 + 17.8628i −0.720296 + 1.24759i
\(206\) −18.4480 −1.28534
\(207\) 0 0
\(208\) 2.67219i 0.185283i
\(209\) −0.137098 + 0.237461i −0.00948328 + 0.0164255i
\(210\) 0 0
\(211\) −7.48854 12.9705i −0.515532 0.892928i −0.999837 0.0180288i \(-0.994261\pi\)
0.484305 0.874899i \(-0.339072\pi\)
\(212\) 0.189794 0.109577i 0.0130351 0.00752581i
\(213\) 0 0
\(214\) 2.32579 4.02839i 0.158988 0.275375i
\(215\) 14.5407 0.991666
\(216\) 0 0
\(217\) 0 0
\(218\) 8.71667 + 5.03257i 0.590368 + 0.340849i
\(219\) 0 0
\(220\) −0.556302 + 0.321181i −0.0375059 + 0.0216540i
\(221\) 13.5779 7.83918i 0.913345 0.527320i
\(222\) 0 0
\(223\) −17.5517 10.1335i −1.17535 0.678590i −0.220417 0.975406i \(-0.570742\pi\)
−0.954935 + 0.296816i \(0.904075\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 9.62579 0.640298
\(227\) 5.15484 8.92845i 0.342139 0.592602i −0.642691 0.766126i \(-0.722182\pi\)
0.984830 + 0.173524i \(0.0555153\pi\)
\(228\) 0 0
\(229\) 7.57314 4.37235i 0.500447 0.288933i −0.228451 0.973555i \(-0.573366\pi\)
0.728898 + 0.684622i \(0.240033\pi\)
\(230\) −10.9495 18.9650i −0.721986 1.25052i
\(231\) 0 0
\(232\) 5.13146 8.88796i 0.336897 0.583523i
\(233\) 15.6014i 1.02208i 0.859557 + 0.511039i \(0.170739\pi\)
−0.859557 + 0.511039i \(0.829261\pi\)
\(234\) 0 0
\(235\) −1.19440 −0.0779139
\(236\) −0.983559 + 1.70357i −0.0640242 + 0.110893i
\(237\) 0 0
\(238\) 0 0
\(239\) 19.2977 11.1415i 1.24827 0.720686i 0.277502 0.960725i \(-0.410494\pi\)
0.970763 + 0.240039i \(0.0771602\pi\)
\(240\) 0 0
\(241\) 0.568566 + 0.328262i 0.0366245 + 0.0211452i 0.518200 0.855259i \(-0.326602\pi\)
−0.481576 + 0.876404i \(0.659935\pi\)
\(242\) 10.9434i 0.703470i
\(243\) 0 0
\(244\) 12.5417i 0.802902i
\(245\) 0 0
\(246\) 0 0
\(247\) −1.54016 2.66764i −0.0979983 0.169738i
\(248\) −3.01320 5.21902i −0.191339 0.331408i
\(249\) 0 0
\(250\) 6.33129 + 3.65537i 0.400426 + 0.231186i
\(251\) −3.48276 −0.219830 −0.109915 0.993941i \(-0.535058\pi\)
−0.109915 + 0.993941i \(0.535058\pi\)
\(252\) 0 0
\(253\) −1.92888 −0.121268
\(254\) −4.06735 2.34829i −0.255208 0.147345i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 1.02515 + 1.77562i 0.0639474 + 0.110760i 0.896227 0.443597i \(-0.146298\pi\)
−0.832279 + 0.554357i \(0.812964\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 7.21631i 0.447537i
\(261\) 0 0
\(262\) 14.0430i 0.867581i
\(263\) −8.81710 5.09055i −0.543686 0.313897i 0.202886 0.979202i \(-0.434968\pi\)
−0.746571 + 0.665305i \(0.768301\pi\)
\(264\) 0 0
\(265\) 0.512543 0.295917i 0.0314853 0.0181780i
\(266\) 0 0
\(267\) 0 0
\(268\) −4.48336 + 7.76541i −0.273865 + 0.474348i
\(269\) 0.349999 0.0213398 0.0106699 0.999943i \(-0.496604\pi\)
0.0106699 + 0.999943i \(0.496604\pi\)
\(270\) 0 0
\(271\) 13.9073i 0.844807i −0.906408 0.422403i \(-0.861187\pi\)
0.906408 0.422403i \(-0.138813\pi\)
\(272\) 2.93362 5.08118i 0.177877 0.308092i
\(273\) 0 0
\(274\) 5.42494 + 9.39626i 0.327732 + 0.567649i
\(275\) −0.472321 + 0.272694i −0.0284820 + 0.0164441i
\(276\) 0 0
\(277\) −7.90100 + 13.6849i −0.474725 + 0.822248i −0.999581 0.0289428i \(-0.990786\pi\)
0.524856 + 0.851191i \(0.324119\pi\)
\(278\) 22.5866 1.35466
\(279\) 0 0
\(280\) 0 0
\(281\) 22.2334 + 12.8365i 1.32633 + 0.765759i 0.984731 0.174086i \(-0.0556970\pi\)
0.341603 + 0.939844i \(0.389030\pi\)
\(282\) 0 0
\(283\) 5.73018 3.30832i 0.340624 0.196659i −0.319924 0.947443i \(-0.603657\pi\)
0.660548 + 0.750784i \(0.270324\pi\)
\(284\) 1.94432 1.12255i 0.115374 0.0666112i
\(285\) 0 0
\(286\) −0.550464 0.317811i −0.0325496 0.0187925i
\(287\) 0 0
\(288\) 0 0
\(289\) 17.4245 1.02497
\(290\) 13.8577 24.0022i 0.813750 1.40946i
\(291\) 0 0
\(292\) −6.28418 + 3.62817i −0.367754 + 0.212323i
\(293\) 8.68306 + 15.0395i 0.507270 + 0.878617i 0.999965 + 0.00841456i \(0.00267847\pi\)
−0.492695 + 0.870202i \(0.663988\pi\)
\(294\) 0 0
\(295\) −2.65613 + 4.60055i −0.154646 + 0.267854i
\(296\) 9.68488i 0.562922i
\(297\) 0 0
\(298\) −0.272690 −0.0157965
\(299\) 10.8346 18.7660i 0.626578 1.08527i
\(300\) 0 0
\(301\) 0 0
\(302\) −16.3185 + 9.42148i −0.939023 + 0.542145i
\(303\) 0 0
\(304\) −0.998299 0.576368i −0.0572564 0.0330570i
\(305\) 33.8693i 1.93935i
\(306\) 0 0
\(307\) 1.18328i 0.0675336i 0.999430 + 0.0337668i \(0.0107504\pi\)
−0.999430 + 0.0337668i \(0.989250\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −8.13723 14.0941i −0.462164 0.800491i
\(311\) −12.6616 21.9306i −0.717975 1.24357i −0.961801 0.273751i \(-0.911736\pi\)
0.243825 0.969819i \(-0.421598\pi\)
\(312\) 0 0
\(313\) −1.58789 0.916770i −0.0897530 0.0518189i 0.454452 0.890771i \(-0.349835\pi\)
−0.544205 + 0.838952i \(0.683169\pi\)
\(314\) 3.25984 0.183963
\(315\) 0 0
\(316\) 10.8718 0.611588
\(317\) −8.23307 4.75337i −0.462415 0.266976i 0.250644 0.968079i \(-0.419358\pi\)
−0.713059 + 0.701104i \(0.752691\pi\)
\(318\) 0 0
\(319\) −1.22060 2.11414i −0.0683404 0.118369i
\(320\) −1.35026 2.33872i −0.0754820 0.130739i
\(321\) 0 0
\(322\) 0 0
\(323\) 6.76338i 0.376324i
\(324\) 0 0
\(325\) 6.12691i 0.339860i
\(326\) −2.71650 1.56837i −0.150453 0.0868642i
\(327\) 0 0
\(328\) −6.61455 + 3.81891i −0.365227 + 0.210864i
\(329\) 0 0
\(330\) 0 0
\(331\) −9.26852 + 16.0535i −0.509444 + 0.882382i 0.490496 + 0.871443i \(0.336815\pi\)
−0.999940 + 0.0109393i \(0.996518\pi\)
\(332\) 1.52481 0.0836846
\(333\) 0 0
\(334\) 6.39150i 0.349727i
\(335\) −12.1074 + 20.9707i −0.661500 + 1.14575i
\(336\) 0 0
\(337\) 4.70730 + 8.15329i 0.256423 + 0.444138i 0.965281 0.261213i \(-0.0841226\pi\)
−0.708858 + 0.705351i \(0.750789\pi\)
\(338\) −5.07440 + 2.92971i −0.276011 + 0.159355i
\(339\) 0 0
\(340\) 7.92232 13.7219i 0.429648 0.744172i
\(341\) −1.43347 −0.0776270
\(342\) 0 0
\(343\) 0 0
\(344\) 4.66301 + 2.69219i 0.251413 + 0.145153i
\(345\) 0 0
\(346\) 0.254207 0.146767i 0.0136663 0.00789022i
\(347\) −9.73647 + 5.62136i −0.522681 + 0.301770i −0.738031 0.674767i \(-0.764244\pi\)
0.215350 + 0.976537i \(0.430911\pi\)
\(348\) 0 0
\(349\) −0.889499 0.513552i −0.0476138 0.0274898i 0.476004 0.879443i \(-0.342085\pi\)
−0.523618 + 0.851953i \(0.675418\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −0.237866 −0.0126783
\(353\) −12.3144 + 21.3291i −0.655429 + 1.13524i 0.326357 + 0.945246i \(0.394179\pi\)
−0.981786 + 0.189990i \(0.939155\pi\)
\(354\) 0 0
\(355\) 5.25068 3.03148i 0.278677 0.160894i
\(356\) −6.76386 11.7153i −0.358484 0.620912i
\(357\) 0 0
\(358\) −11.5374 + 19.9833i −0.609768 + 1.05615i
\(359\) 10.5234i 0.555402i 0.960668 + 0.277701i \(0.0895725\pi\)
−0.960668 + 0.277701i \(0.910428\pi\)
\(360\) 0 0
\(361\) 17.6712 0.930063
\(362\) −5.45881 + 9.45493i −0.286908 + 0.496940i
\(363\) 0 0
\(364\) 0 0
\(365\) −16.9706 + 9.79797i −0.888281 + 0.512849i
\(366\) 0 0
\(367\) −6.00271 3.46567i −0.313339 0.180906i 0.335081 0.942189i \(-0.391236\pi\)
−0.648420 + 0.761283i \(0.724570\pi\)
\(368\) 8.10913i 0.422717i
\(369\) 0 0
\(370\) 26.1543i 1.35970i
\(371\) 0 0
\(372\) 0 0
\(373\) −0.950237 1.64586i −0.0492014 0.0852193i 0.840376 0.542004i \(-0.182334\pi\)
−0.889577 + 0.456785i \(0.849001\pi\)
\(374\) −0.697807 1.20864i −0.0360827 0.0624971i
\(375\) 0 0
\(376\) −0.383029 0.221142i −0.0197532 0.0114045i
\(377\) 27.4245 1.41243
\(378\) 0 0
\(379\) 37.4655 1.92447 0.962236 0.272217i \(-0.0877569\pi\)
0.962236 + 0.272217i \(0.0877569\pi\)
\(380\) −2.69593 1.55650i −0.138298 0.0798467i
\(381\) 0 0
\(382\) −6.43490 11.1456i −0.329238 0.570257i
\(383\) 0.740653 + 1.28285i 0.0378456 + 0.0655505i 0.884328 0.466867i \(-0.154617\pi\)
−0.846482 + 0.532417i \(0.821284\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 10.2354i 0.520969i
\(387\) 0 0
\(388\) 1.59011i 0.0807258i
\(389\) −11.0008 6.35131i −0.557763 0.322024i 0.194484 0.980906i \(-0.437697\pi\)
−0.752247 + 0.658881i \(0.771030\pi\)
\(390\) 0 0
\(391\) 41.2039 23.7891i 2.08377 1.20307i
\(392\) 0 0
\(393\) 0 0
\(394\) −1.94534 + 3.36943i −0.0980049 + 0.169749i
\(395\) 29.3597 1.47725
\(396\) 0 0
\(397\) 19.3486i 0.971080i 0.874215 + 0.485540i \(0.161377\pi\)
−0.874215 + 0.485540i \(0.838623\pi\)
\(398\) −1.16575 + 2.01914i −0.0584338 + 0.101210i
\(399\) 0 0
\(400\) −1.14642 1.98566i −0.0573211 0.0992831i
\(401\) 9.43887 5.44954i 0.471355 0.272137i −0.245452 0.969409i \(-0.578936\pi\)
0.716807 + 0.697272i \(0.245603\pi\)
\(402\) 0 0
\(403\) 8.05184 13.9462i 0.401091 0.694709i
\(404\) −12.9671 −0.645135
\(405\) 0 0
\(406\) 0 0
\(407\) 1.99506 + 1.15185i 0.0988916 + 0.0570951i
\(408\) 0 0
\(409\) 17.7691 10.2590i 0.878627 0.507275i 0.00842142 0.999965i \(-0.497319\pi\)
0.870205 + 0.492689i \(0.163986\pi\)
\(410\) −17.8628 + 10.3131i −0.882179 + 0.509326i
\(411\) 0 0
\(412\) −15.9765 9.22402i −0.787104 0.454435i
\(413\) 0 0
\(414\) 0 0
\(415\) 4.11778 0.202134
\(416\) 1.33609 2.31418i 0.0655074 0.113462i
\(417\) 0 0
\(418\) −0.237461 + 0.137098i −0.0116146 + 0.00670569i
\(419\) −2.73087 4.73000i −0.133412 0.231076i 0.791578 0.611068i \(-0.209260\pi\)
−0.924990 + 0.379993i \(0.875927\pi\)
\(420\) 0 0
\(421\) 14.2759 24.7265i 0.695763 1.20510i −0.274160 0.961684i \(-0.588400\pi\)
0.969923 0.243412i \(-0.0782669\pi\)
\(422\) 14.9771i 0.729073i
\(423\) 0 0
\(424\) 0.219155 0.0106431
\(425\) 6.72633 11.6504i 0.326275 0.565125i
\(426\) 0 0
\(427\) 0 0
\(428\) 4.02839 2.32579i 0.194720 0.112421i
\(429\) 0 0
\(430\) 12.5926 + 7.27034i 0.607269 + 0.350607i
\(431\) 9.55639i 0.460315i −0.973153 0.230157i \(-0.926076\pi\)
0.973153 0.230157i \(-0.0739241\pi\)
\(432\) 0 0
\(433\) 19.7122i 0.947309i −0.880711 0.473654i \(-0.842935\pi\)
0.880711 0.473654i \(-0.157065\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 5.03257 + 8.71667i 0.241017 + 0.417453i
\(437\) −4.67384 8.09533i −0.223580 0.387252i
\(438\) 0 0
\(439\) 21.1001 + 12.1822i 1.00706 + 0.581424i 0.910328 0.413887i \(-0.135829\pi\)
0.0967271 + 0.995311i \(0.469163\pi\)
\(440\) −0.642362 −0.0306234
\(441\) 0 0
\(442\) 15.6784 0.745743
\(443\) 32.4731 + 18.7483i 1.54284 + 0.890760i 0.998658 + 0.0517947i \(0.0164941\pi\)
0.544184 + 0.838966i \(0.316839\pi\)
\(444\) 0 0
\(445\) −18.2660 31.6376i −0.865890 1.49977i
\(446\) −10.1335 17.5517i −0.479835 0.831099i
\(447\) 0 0
\(448\) 0 0
\(449\) 22.6997i 1.07127i 0.844451 + 0.535633i \(0.179927\pi\)
−0.844451 + 0.535633i \(0.820073\pi\)
\(450\) 0 0
\(451\) 1.81678i 0.0855486i
\(452\) 8.33618 + 4.81290i 0.392101 + 0.226380i
\(453\) 0 0
\(454\) 8.92845 5.15484i 0.419033 0.241929i
\(455\) 0 0
\(456\) 0 0
\(457\) −19.9116 + 34.4878i −0.931424 + 1.61327i −0.150533 + 0.988605i \(0.548099\pi\)
−0.780890 + 0.624668i \(0.785234\pi\)
\(458\) 8.74471 0.408613
\(459\) 0 0
\(460\) 21.8989i 1.02104i
\(461\) 4.33763 7.51299i 0.202024 0.349915i −0.747157 0.664648i \(-0.768582\pi\)
0.949180 + 0.314733i \(0.101915\pi\)
\(462\) 0 0
\(463\) 7.06605 + 12.2388i 0.328387 + 0.568783i 0.982192 0.187880i \(-0.0601616\pi\)
−0.653805 + 0.756663i \(0.726828\pi\)
\(464\) 8.88796 5.13146i 0.412613 0.238222i
\(465\) 0 0
\(466\) −7.80068 + 13.5112i −0.361359 + 0.625893i
\(467\) −24.6082 −1.13873 −0.569366 0.822084i \(-0.692811\pi\)
−0.569366 + 0.822084i \(0.692811\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −1.03438 0.597199i −0.0477124 0.0275467i
\(471\) 0 0
\(472\) −1.70357 + 0.983559i −0.0784133 + 0.0452720i
\(473\) 1.10917 0.640380i 0.0509997 0.0294447i
\(474\) 0 0
\(475\) −2.28894 1.32152i −0.105024 0.0606356i
\(476\) 0 0
\(477\) 0 0
\(478\) 22.2831 1.01920
\(479\) 14.7674 25.5779i 0.674741 1.16869i −0.301804 0.953370i \(-0.597589\pi\)
0.976545 0.215315i \(-0.0690779\pi\)
\(480\) 0 0
\(481\) −22.4126 + 12.9399i −1.02193 + 0.590009i
\(482\) 0.328262 + 0.568566i 0.0149519 + 0.0258975i
\(483\) 0 0
\(484\) 5.47171 9.47728i 0.248714 0.430785i
\(485\) 4.29415i 0.194987i
\(486\) 0 0
\(487\) 1.08694 0.0492538 0.0246269 0.999697i \(-0.492160\pi\)
0.0246269 + 0.999697i \(0.492160\pi\)
\(488\) −6.27087 + 10.8615i −0.283869 + 0.491675i
\(489\) 0 0
\(490\) 0 0
\(491\) 9.43373 5.44657i 0.425738 0.245800i −0.271791 0.962356i \(-0.587616\pi\)
0.697529 + 0.716556i \(0.254283\pi\)
\(492\) 0 0
\(493\) 52.1478 + 30.1075i 2.34862 + 1.35597i
\(494\) 3.08033i 0.138590i
\(495\) 0 0
\(496\) 6.02640i 0.270594i
\(497\) 0 0
\(498\) 0 0
\(499\) −20.0342 34.7002i −0.896853 1.55340i −0.831494 0.555534i \(-0.812514\pi\)
−0.0653593 0.997862i \(-0.520819\pi\)
\(500\) 3.65537 + 6.33129i 0.163473 + 0.283144i
\(501\) 0 0
\(502\) −3.01616 1.74138i −0.134618 0.0777216i
\(503\) 27.5061 1.22644 0.613219 0.789913i \(-0.289874\pi\)
0.613219 + 0.789913i \(0.289874\pi\)
\(504\) 0 0
\(505\) −35.0179 −1.55828
\(506\) −1.67046 0.964441i −0.0742610 0.0428746i
\(507\) 0 0
\(508\) −2.34829 4.06735i −0.104188 0.180459i
\(509\) −4.17535 7.23192i −0.185069 0.320549i 0.758531 0.651637i \(-0.225918\pi\)
−0.943600 + 0.331088i \(0.892584\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 2.05031i 0.0904353i
\(515\) −43.1449 24.9097i −1.90119 1.09765i
\(516\) 0 0
\(517\) −0.0911093 + 0.0526020i −0.00400698 + 0.00231343i
\(518\) 0 0
\(519\) 0 0
\(520\) 3.60816 6.24951i 0.158228 0.274059i
\(521\) 8.33273 0.365064 0.182532 0.983200i \(-0.441571\pi\)
0.182532 + 0.983200i \(0.441571\pi\)
\(522\) 0 0
\(523\) 15.4297i 0.674694i 0.941380 + 0.337347i \(0.109530\pi\)
−0.941380 + 0.337347i \(0.890470\pi\)
\(524\) −7.02151 + 12.1616i −0.306736 + 0.531283i
\(525\) 0 0
\(526\) −5.09055 8.81710i −0.221959 0.384444i
\(527\) 30.6212 17.6792i 1.33388 0.770117i
\(528\) 0 0
\(529\) 21.3790 37.0295i 0.929521 1.60998i
\(530\) 0.591834 0.0257076
\(531\) 0 0
\(532\) 0 0
\(533\) −17.6753 10.2048i −0.765603 0.442021i
\(534\) 0 0
\(535\) 10.8788 6.28086i 0.470330 0.271545i
\(536\) −7.76541 + 4.48336i −0.335415 + 0.193652i
\(537\) 0 0
\(538\) 0.303108 + 0.174999i 0.0130679 + 0.00754476i
\(539\) 0 0
\(540\) 0 0
\(541\) −6.27007 −0.269571 −0.134786 0.990875i \(-0.543035\pi\)
−0.134786 + 0.990875i \(0.543035\pi\)
\(542\) 6.95364 12.0441i 0.298684 0.517336i
\(543\) 0 0
\(544\) 5.08118 2.93362i 0.217854 0.125778i
\(545\) 13.5906 + 23.5396i 0.582157 + 1.00833i
\(546\) 0 0
\(547\) −14.8501 + 25.7211i −0.634945 + 1.09976i 0.351582 + 0.936157i \(0.385644\pi\)
−0.986527 + 0.163600i \(0.947690\pi\)
\(548\) 10.8499i 0.463483i
\(549\) 0 0
\(550\) −0.545389 −0.0232555
\(551\) 5.91523 10.2455i 0.251997 0.436472i
\(552\) 0 0
\(553\) 0 0
\(554\) −13.6849 + 7.90100i −0.581417 + 0.335682i
\(555\) 0 0
\(556\) 19.5606 + 11.2933i 0.829554 + 0.478943i
\(557\) 17.9103i 0.758883i −0.925216 0.379442i \(-0.876116\pi\)
0.925216 0.379442i \(-0.123884\pi\)
\(558\) 0 0
\(559\) 14.3881i 0.608551i
\(560\) 0 0
\(561\) 0 0
\(562\) 12.8365 + 22.2334i 0.541473 + 0.937859i
\(563\) −21.7205 37.6210i −0.915409 1.58553i −0.806302 0.591504i \(-0.798534\pi\)
−0.109107 0.994030i \(-0.534799\pi\)
\(564\) 0 0
\(565\) 22.5121 + 12.9974i 0.947090 + 0.546803i
\(566\) 6.61664 0.278118
\(567\) 0 0
\(568\) 2.24510 0.0942024
\(569\) 4.14890 + 2.39537i 0.173931 + 0.100419i 0.584438 0.811438i \(-0.301315\pi\)
−0.410507 + 0.911857i \(0.634648\pi\)
\(570\) 0 0
\(571\) 6.69405 + 11.5944i 0.280137 + 0.485212i 0.971418 0.237374i \(-0.0762867\pi\)
−0.691281 + 0.722586i \(0.742953\pi\)
\(572\) −0.317811 0.550464i −0.0132883 0.0230161i
\(573\) 0 0
\(574\) 0 0
\(575\) 18.5930i 0.775380i
\(576\) 0 0
\(577\) 10.7792i 0.448746i 0.974503 + 0.224373i \(0.0720334\pi\)
−0.974503 + 0.224373i \(0.927967\pi\)
\(578\) 15.0900 + 8.71224i 0.627663 + 0.362381i
\(579\) 0 0
\(580\) 24.0022 13.8577i 0.996636 0.575408i
\(581\) 0 0
\(582\) 0 0
\(583\) 0.0260647 0.0451454i 0.00107949 0.00186973i
\(584\) −7.25634 −0.300270
\(585\) 0 0
\(586\) 17.3661i 0.717387i
\(587\) 10.0173 17.3504i 0.413458 0.716130i −0.581808 0.813326i \(-0.697654\pi\)
0.995265 + 0.0971969i \(0.0309877\pi\)
\(588\) 0 0
\(589\) −3.47343 6.01615i −0.143120 0.247891i
\(590\) −4.60055 + 2.65613i −0.189402 + 0.109351i
\(591\) 0 0
\(592\) −4.84244 + 8.38735i −0.199023 + 0.344718i
\(593\) 22.7549 0.934433 0.467217 0.884143i \(-0.345257\pi\)
0.467217 + 0.884143i \(0.345257\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −0.236156 0.136345i −0.00967333 0.00558490i
\(597\) 0 0
\(598\) 18.7660 10.8346i 0.767399 0.443058i
\(599\) 22.0525 12.7320i 0.901040 0.520216i 0.0235025 0.999724i \(-0.492518\pi\)
0.877537 + 0.479508i \(0.159185\pi\)
\(600\) 0 0
\(601\) 8.94631 + 5.16515i 0.364928 + 0.210691i 0.671240 0.741240i \(-0.265762\pi\)
−0.306313 + 0.951931i \(0.599095\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −18.8430 −0.766709
\(605\) 14.7765 25.5936i 0.600750 1.04053i
\(606\) 0 0
\(607\) −6.05553 + 3.49616i −0.245786 + 0.141905i −0.617833 0.786309i \(-0.711989\pi\)
0.372047 + 0.928214i \(0.378656\pi\)
\(608\) −0.576368 0.998299i −0.0233748 0.0404864i
\(609\) 0 0
\(610\) −16.9346 + 29.3317i −0.685664 + 1.18760i
\(611\) 1.18186i 0.0478131i
\(612\) 0 0
\(613\) 10.3097 0.416405 0.208203 0.978086i \(-0.433239\pi\)
0.208203 + 0.978086i \(0.433239\pi\)
\(614\) −0.591642 + 1.02475i −0.0238767 + 0.0413557i
\(615\) 0 0
\(616\) 0 0
\(617\) −3.11226 + 1.79686i −0.125295 + 0.0723389i −0.561337 0.827587i \(-0.689713\pi\)
0.436043 + 0.899926i \(0.356380\pi\)
\(618\) 0 0
\(619\) −27.4694 15.8594i −1.10409 0.637445i −0.166796 0.985991i \(-0.553342\pi\)
−0.937291 + 0.348547i \(0.886675\pi\)
\(620\) 16.2745i 0.653598i
\(621\) 0 0
\(622\) 25.3233i 1.01537i
\(623\) 0 0
\(624\) 0 0
\(625\) 15.6035 + 27.0261i 0.624142 + 1.08105i
\(626\) −0.916770 1.58789i −0.0366415 0.0634649i
\(627\) 0 0
\(628\) 2.82310 + 1.62992i 0.112654 + 0.0650408i
\(629\) −56.8235 −2.26570
\(630\) 0 0
\(631\) 4.92443 0.196038 0.0980192 0.995185i \(-0.468749\pi\)
0.0980192 + 0.995185i \(0.468749\pi\)
\(632\) 9.41528 + 5.43592i 0.374520 + 0.216229i
\(633\) 0 0
\(634\) −4.75337 8.23307i −0.188780 0.326977i
\(635\) −6.34161 10.9840i −0.251659 0.435886i
\(636\) 0 0
\(637\) 0 0
\(638\) 2.44120i 0.0966479i
\(639\) 0 0
\(640\) 2.70053i 0.106748i
\(641\) −7.27479 4.20010i −0.287337 0.165894i 0.349403 0.936972i \(-0.386384\pi\)
−0.636740 + 0.771078i \(0.719718\pi\)
\(642\) 0 0
\(643\) −6.34290 + 3.66208i −0.250140 + 0.144418i −0.619828 0.784738i \(-0.712798\pi\)
0.369689 + 0.929156i \(0.379464\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 3.38169 5.85726i 0.133051 0.230451i
\(647\) −3.89938 −0.153301 −0.0766503 0.997058i \(-0.524422\pi\)
−0.0766503 + 0.997058i \(0.524422\pi\)
\(648\) 0 0
\(649\) 0.467910i 0.0183671i
\(650\) 3.06345 5.30606i 0.120159 0.208121i
\(651\) 0 0
\(652\) −1.56837 2.71650i −0.0614222 0.106386i
\(653\) −20.0302 + 11.5644i −0.783843 + 0.452552i −0.837790 0.545992i \(-0.816153\pi\)
0.0539477 + 0.998544i \(0.482820\pi\)
\(654\) 0 0
\(655\) −18.9618 + 32.8428i −0.740898 + 1.28327i
\(656\) −7.63782 −0.298207
\(657\) 0 0
\(658\) 0 0
\(659\) 28.2312 + 16.2993i 1.09973 + 0.634930i 0.936150 0.351600i \(-0.114362\pi\)
0.163580 + 0.986530i \(0.447696\pi\)
\(660\) 0 0
\(661\) 43.4612 25.0924i 1.69045 0.975979i 0.736292 0.676664i \(-0.236575\pi\)
0.954154 0.299315i \(-0.0967583\pi\)
\(662\) −16.0535 + 9.26852i −0.623939 + 0.360231i
\(663\) 0 0
\(664\) 1.32052 + 0.762403i 0.0512461 + 0.0295870i
\(665\) 0 0
\(666\) 0 0
\(667\) 83.2234 3.22242
\(668\) 3.19575 5.53520i 0.123647 0.214163i
\(669\) 0 0
\(670\) −20.9707 + 12.1074i −0.810169 + 0.467751i
\(671\) 1.49162 + 2.58357i 0.0575835 + 0.0997375i
\(672\) 0 0
\(673\) −9.02645 + 15.6343i −0.347944 + 0.602657i −0.985884 0.167429i \(-0.946453\pi\)
0.637940 + 0.770086i \(0.279787\pi\)
\(674\) 9.41461i 0.362637i
\(675\) 0 0
\(676\) −5.85942 −0.225362
\(677\) −10.1509 + 17.5819i −0.390131 + 0.675726i −0.992466 0.122517i \(-0.960903\pi\)
0.602336 + 0.798243i \(0.294237\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 13.7219 7.92232i 0.526209 0.303807i
\(681\) 0 0
\(682\) −1.24142 0.716737i −0.0475366 0.0274453i
\(683\) 20.0741i 0.768113i −0.923310 0.384056i \(-0.874527\pi\)
0.923310 0.384056i \(-0.125473\pi\)
\(684\) 0 0
\(685\) 29.3004i 1.11951i
\(686\) 0 0
\(687\) 0 0
\(688\) 2.69219 + 4.66301i 0.102639 + 0.177776i
\(689\) 0.292811 + 0.507164i 0.0111552 + 0.0193214i
\(690\) 0 0
\(691\) −21.3874 12.3480i −0.813616 0.469742i 0.0345939 0.999401i \(-0.488986\pi\)
−0.848210 + 0.529660i \(0.822320\pi\)
\(692\) 0.293533 0.0111585
\(693\) 0 0
\(694\) −11.2427 −0.426767
\(695\) 52.8239 + 30.4979i 2.00372 + 1.15685i
\(696\) 0 0
\(697\) −22.4065 38.8091i −0.848705 1.47000i
\(698\) −0.513552 0.889499i −0.0194382 0.0336680i
\(699\) 0 0
\(700\) 0 0
\(701\) 21.1616i 0.799263i −0.916676 0.399632i \(-0.869138\pi\)
0.916676 0.399632i \(-0.130862\pi\)
\(702\) 0 0
\(703\) 11.1641i 0.421063i
\(704\) −0.205998 0.118933i −0.00776383 0.00448245i
\(705\) 0 0
\(706\) −21.3291 + 12.3144i −0.802733 + 0.463458i
\(707\) 0 0
\(708\) 0 0
\(709\) −10.4861 + 18.1624i −0.393812 + 0.682103i −0.992949 0.118544i \(-0.962177\pi\)
0.599137 + 0.800647i \(0.295511\pi\)
\(710\) 6.06296 0.227539
\(711\) 0 0
\(712\) 13.5277i 0.506972i
\(713\) 24.4344 42.3217i 0.915077 1.58496i
\(714\) 0 0
\(715\) −0.858256 1.48654i −0.0320970 0.0555936i
\(716\) −19.9833 + 11.5374i −0.746810 + 0.431171i
\(717\) 0 0
\(718\) −5.26168 + 9.11350i −0.196364 + 0.340113i
\(719\) −22.7726 −0.849273 −0.424637 0.905364i \(-0.639598\pi\)
−0.424637 + 0.905364i \(0.639598\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 15.3037 + 8.83560i 0.569545 + 0.328827i
\(723\) 0 0
\(724\) −9.45493 + 5.45881i −0.351390 + 0.202875i
\(725\) 20.3787 11.7657i 0.756846 0.436965i
\(726\) 0 0
\(727\) −15.4847 8.94010i −0.574296 0.331570i 0.184567 0.982820i \(-0.440912\pi\)
−0.758863 + 0.651250i \(0.774245\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −19.5959 −0.725279
\(731\) −15.7957 + 27.3590i −0.584226 + 1.01191i
\(732\) 0 0
\(733\) 18.8378 10.8760i 0.695790 0.401715i −0.109987 0.993933i \(-0.535081\pi\)
0.805778 + 0.592218i \(0.201748\pi\)
\(734\) −3.46567 6.00271i −0.127920 0.221564i
\(735\) 0 0
\(736\) 4.05456 7.02271i 0.149453 0.258861i
\(737\) 2.13288i 0.0785655i
\(738\) 0 0
\(739\) −26.5207 −0.975578 −0.487789 0.872961i \(-0.662197\pi\)
−0.487789 + 0.872961i \(0.662197\pi\)
\(740\) −13.0771 + 22.6503i −0.480725 + 0.832641i
\(741\) 0 0
\(742\) 0 0
\(743\) 1.53406 0.885688i 0.0562791 0.0324927i −0.471596 0.881814i \(-0.656322\pi\)
0.527876 + 0.849322i \(0.322989\pi\)
\(744\) 0 0
\(745\) −0.637746 0.368203i −0.0233652 0.0134899i
\(746\) 1.90047i 0.0695813i
\(747\) 0 0
\(748\) 1.39561i 0.0510287i
\(749\) 0 0
\(750\) 0 0
\(751\) 19.9293 + 34.5186i 0.727231 + 1.25960i 0.958049 + 0.286605i \(0.0925266\pi\)
−0.230818 + 0.972997i \(0.574140\pi\)
\(752\) −0.221142 0.383029i −0.00806421 0.0139676i
\(753\) 0 0
\(754\) 23.7503 + 13.7122i 0.864934 + 0.499370i
\(755\) −50.8859 −1.85193
\(756\) 0 0
\(757\) −37.2462 −1.35374 −0.676869 0.736104i \(-0.736663\pi\)
−0.676869 + 0.736104i \(0.736663\pi\)
\(758\) 32.4460 + 18.7327i 1.17849 + 0.680403i
\(759\) 0 0
\(760\) −1.55650 2.69593i −0.0564601 0.0977918i
\(761\) 21.6642 + 37.5235i 0.785327 + 1.36023i 0.928804 + 0.370573i \(0.120839\pi\)
−0.143477 + 0.989654i \(0.545828\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 12.8698i 0.465613i
\(765\) 0 0
\(766\) 1.48131i 0.0535218i
\(767\) −4.55227 2.62825i −0.164373 0.0949007i
\(768\) 0 0
\(769\) 18.2010 10.5084i 0.656345 0.378941i −0.134538 0.990908i \(-0.542955\pi\)
0.790883 + 0.611967i \(0.209622\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −5.11771 + 8.86414i −0.184190 + 0.319027i
\(773\) −3.08047 −0.110797 −0.0553984 0.998464i \(-0.517643\pi\)
−0.0553984 + 0.998464i \(0.517643\pi\)
\(774\) 0 0
\(775\) 13.8176i 0.496343i
\(776\) −0.795057 + 1.37708i −0.0285409 + 0.0494343i
\(777\) 0 0
\(778\) −6.35131 11.0008i −0.227706 0.394398i
\(779\) −7.62483 + 4.40220i −0.273188 + 0.157725i
\(780\) 0 0
\(781\) 0.267016 0.462486i 0.00955459 0.0165490i
\(782\) 47.5782 1.70139
\(783\) 0 0
\(784\) 0 0
\(785\) 7.62386 + 4.40164i 0.272107 + 0.157101i
\(786\) 0 0
\(787\) −31.0182 + 17.9083i −1.10568 + 0.638363i −0.937707 0.347428i \(-0.887055\pi\)
−0.167971 + 0.985792i \(0.553722\pi\)
\(788\) −3.36943 + 1.94534i −0.120031 + 0.0692999i
\(789\) 0 0
\(790\) 25.4262 + 14.6798i 0.904624 + 0.522285i
\(791\) 0 0
\(792\) 0 0
\(793\) −33.5139 −1.19011
\(794\) −9.67431 + 16.7564i −0.343328 + 0.594662i
\(795\) 0 0