Properties

Label 2646.2.m.c.1763.7
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 1763.7
Character \(\chi\) \(=\) 2646.1763
Dual form 2646.2.m.c.881.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.995200 - 1.72374i) q^{5} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.995200 - 1.72374i) q^{5} -1.00000i q^{8} +1.99040i q^{10} +(-5.21285 - 3.00964i) q^{11} +(-3.43197 + 1.98145i) q^{13} +(-0.500000 + 0.866025i) q^{16} -1.56239 q^{17} -4.80549i q^{19} +(0.995200 - 1.72374i) q^{20} +(3.00964 + 5.21285i) q^{22} +(5.02324 - 2.90017i) q^{23} +(0.519152 - 0.899198i) q^{25} +3.96290 q^{26} +(-5.26041 - 3.03710i) q^{29} +(-1.11497 + 0.643725i) q^{31} +(0.866025 - 0.500000i) q^{32} +(1.35307 + 0.781195i) q^{34} +6.05245 q^{37} +(-2.40274 + 4.16168i) q^{38} +(-1.72374 + 0.995200i) q^{40} +(2.98046 + 5.16231i) q^{41} +(-4.53614 + 7.85683i) q^{43} -6.01929i q^{44} -5.80034 q^{46} +(-2.39381 + 4.14620i) q^{47} +(-0.899198 + 0.519152i) q^{50} +(-3.43197 - 1.98145i) q^{52} +8.39920i q^{53} +11.9808i q^{55} +(3.03710 + 5.26041i) q^{58} +(6.38986 + 11.0676i) q^{59} +(1.61609 + 0.933050i) q^{61} +1.28745 q^{62} -1.00000 q^{64} +(6.83100 + 3.94388i) q^{65} +(-3.79746 - 6.57739i) q^{67} +(-0.781195 - 1.35307i) q^{68} -5.48343i q^{71} +10.8252i q^{73} +(-5.24158 - 3.02623i) q^{74} +(4.16168 - 2.40274i) q^{76} +(6.94712 - 12.0328i) q^{79} +1.99040 q^{80} -5.96092i q^{82} +(3.35946 - 5.81876i) q^{83} +(1.55489 + 2.69315i) q^{85} +(7.85683 - 4.53614i) q^{86} +(-3.00964 + 5.21285i) q^{88} -4.11359 q^{89} +(5.02324 + 2.90017i) q^{92} +(4.14620 - 2.39381i) q^{94} +(-8.28340 + 4.78243i) q^{95} +(-14.1120 - 8.14755i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 24 q^{4} + O(q^{10}) \) \( 48 q + 24 q^{4} - 48 q^{11} - 24 q^{16} - 48 q^{23} - 24 q^{25} + 48 q^{50} - 48 q^{64} + 48 q^{79} + 48 q^{85} - 96 q^{86} - 48 q^{92} + 192 q^{95} + O(q^{100}) \)

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
\(5\) −0.995200 1.72374i −0.445067 0.770879i 0.552990 0.833188i \(-0.313487\pi\)
−0.998057 + 0.0623091i \(0.980154\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 1.99040i 0.629420i
\(11\) −5.21285 3.00964i −1.57173 0.907441i −0.995957 0.0898353i \(-0.971366\pi\)
−0.575778 0.817606i \(-0.695301\pi\)
\(12\) 0 0
\(13\) −3.43197 + 1.98145i −0.951857 + 0.549555i −0.893657 0.448750i \(-0.851869\pi\)
−0.0581999 + 0.998305i \(0.518536\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.56239 −0.378935 −0.189468 0.981887i \(-0.560676\pi\)
−0.189468 + 0.981887i \(0.560676\pi\)
\(18\) 0 0
\(19\) 4.80549i 1.10245i −0.834355 0.551227i \(-0.814160\pi\)
0.834355 0.551227i \(-0.185840\pi\)
\(20\) 0.995200 1.72374i 0.222534 0.385439i
\(21\) 0 0
\(22\) 3.00964 + 5.21285i 0.641658 + 1.11138i
\(23\) 5.02324 2.90017i 1.04742 0.604728i 0.125493 0.992094i \(-0.459949\pi\)
0.921926 + 0.387367i \(0.126615\pi\)
\(24\) 0 0
\(25\) 0.519152 0.899198i 0.103830 0.179840i
\(26\) 3.96290 0.777188
\(27\) 0 0
\(28\) 0 0
\(29\) −5.26041 3.03710i −0.976833 0.563975i −0.0755206 0.997144i \(-0.524062\pi\)
−0.901313 + 0.433169i \(0.857395\pi\)
\(30\) 0 0
\(31\) −1.11497 + 0.643725i −0.200254 + 0.115616i −0.596774 0.802410i \(-0.703551\pi\)
0.396520 + 0.918026i \(0.370218\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 1.35307 + 0.781195i 0.232050 + 0.133974i
\(35\) 0 0
\(36\) 0 0
\(37\) 6.05245 0.995017 0.497508 0.867459i \(-0.334248\pi\)
0.497508 + 0.867459i \(0.334248\pi\)
\(38\) −2.40274 + 4.16168i −0.389777 + 0.675113i
\(39\) 0 0
\(40\) −1.72374 + 0.995200i −0.272547 + 0.157355i
\(41\) 2.98046 + 5.16231i 0.465470 + 0.806218i 0.999223 0.0394230i \(-0.0125520\pi\)
−0.533753 + 0.845641i \(0.679219\pi\)
\(42\) 0 0
\(43\) −4.53614 + 7.85683i −0.691756 + 1.19816i 0.279507 + 0.960144i \(0.409829\pi\)
−0.971262 + 0.238012i \(0.923504\pi\)
\(44\) 6.01929i 0.907441i
\(45\) 0 0
\(46\) −5.80034 −0.855214
\(47\) −2.39381 + 4.14620i −0.349173 + 0.604786i −0.986103 0.166136i \(-0.946871\pi\)
0.636929 + 0.770922i \(0.280204\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −0.899198 + 0.519152i −0.127166 + 0.0734192i
\(51\) 0 0
\(52\) −3.43197 1.98145i −0.475929 0.274778i
\(53\) 8.39920i 1.15372i 0.816843 + 0.576860i \(0.195722\pi\)
−0.816843 + 0.576860i \(0.804278\pi\)
\(54\) 0 0
\(55\) 11.9808i 1.61549i
\(56\) 0 0
\(57\) 0 0
\(58\) 3.03710 + 5.26041i 0.398790 + 0.690725i
\(59\) 6.38986 + 11.0676i 0.831888 + 1.44087i 0.896539 + 0.442965i \(0.146073\pi\)
−0.0646505 + 0.997908i \(0.520593\pi\)
\(60\) 0 0
\(61\) 1.61609 + 0.933050i 0.206919 + 0.119465i 0.599879 0.800091i \(-0.295215\pi\)
−0.392960 + 0.919556i \(0.628549\pi\)
\(62\) 1.28745 0.163506
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 6.83100 + 3.94388i 0.847281 + 0.489178i
\(66\) 0 0
\(67\) −3.79746 6.57739i −0.463933 0.803556i 0.535220 0.844713i \(-0.320229\pi\)
−0.999153 + 0.0411572i \(0.986896\pi\)
\(68\) −0.781195 1.35307i −0.0947338 0.164084i
\(69\) 0 0
\(70\) 0 0
\(71\) 5.48343i 0.650764i −0.945583 0.325382i \(-0.894507\pi\)
0.945583 0.325382i \(-0.105493\pi\)
\(72\) 0 0
\(73\) 10.8252i 1.26699i 0.773747 + 0.633494i \(0.218380\pi\)
−0.773747 + 0.633494i \(0.781620\pi\)
\(74\) −5.24158 3.02623i −0.609321 0.351792i
\(75\) 0 0
\(76\) 4.16168 2.40274i 0.477377 0.275614i
\(77\) 0 0
\(78\) 0 0
\(79\) 6.94712 12.0328i 0.781612 1.35379i −0.149391 0.988778i \(-0.547731\pi\)
0.931003 0.365013i \(-0.118935\pi\)
\(80\) 1.99040 0.222534
\(81\) 0 0
\(82\) 5.96092i 0.658274i
\(83\) 3.35946 5.81876i 0.368749 0.638692i −0.620621 0.784111i \(-0.713119\pi\)
0.989370 + 0.145418i \(0.0464528\pi\)
\(84\) 0 0
\(85\) 1.55489 + 2.69315i 0.168652 + 0.292113i
\(86\) 7.85683 4.53614i 0.847224 0.489145i
\(87\) 0 0
\(88\) −3.00964 + 5.21285i −0.320829 + 0.555692i
\(89\) −4.11359 −0.436040 −0.218020 0.975944i \(-0.569960\pi\)
−0.218020 + 0.975944i \(0.569960\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 5.02324 + 2.90017i 0.523709 + 0.302364i
\(93\) 0 0
\(94\) 4.14620 2.39381i 0.427648 0.246903i
\(95\) −8.28340 + 4.78243i −0.849859 + 0.490666i
\(96\) 0 0
\(97\) −14.1120 8.14755i −1.43285 0.827258i −0.435516 0.900181i \(-0.643434\pi\)
−0.997338 + 0.0729228i \(0.976767\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.03830 0.103830
\(101\) −3.16950 + 5.48974i −0.315377 + 0.546249i −0.979518 0.201359i \(-0.935464\pi\)
0.664141 + 0.747608i \(0.268798\pi\)
\(102\) 0 0
\(103\) −11.4058 + 6.58517i −1.12385 + 0.648856i −0.942381 0.334541i \(-0.891419\pi\)
−0.181470 + 0.983396i \(0.558086\pi\)
\(104\) 1.98145 + 3.43197i 0.194297 + 0.336532i
\(105\) 0 0
\(106\) 4.19960 7.27392i 0.407901 0.706506i
\(107\) 13.2248i 1.27849i 0.769003 + 0.639245i \(0.220753\pi\)
−0.769003 + 0.639245i \(0.779247\pi\)
\(108\) 0 0
\(109\) −2.29571 −0.219890 −0.109945 0.993938i \(-0.535067\pi\)
−0.109945 + 0.993938i \(0.535067\pi\)
\(110\) 5.99040 10.3757i 0.571162 0.989281i
\(111\) 0 0
\(112\) 0 0
\(113\) 12.0019 6.92933i 1.12905 0.651856i 0.185353 0.982672i \(-0.440657\pi\)
0.943695 + 0.330816i \(0.107324\pi\)
\(114\) 0 0
\(115\) −9.99827 5.77250i −0.932343 0.538289i
\(116\) 6.07420i 0.563975i
\(117\) 0 0
\(118\) 12.7797i 1.17647i
\(119\) 0 0
\(120\) 0 0
\(121\) 12.6159 + 21.8514i 1.14690 + 1.98649i
\(122\) −0.933050 1.61609i −0.0844744 0.146314i
\(123\) 0 0
\(124\) −1.11497 0.643725i −0.100127 0.0578082i
\(125\) −12.0186 −1.07498
\(126\) 0 0
\(127\) 10.1548 0.901094 0.450547 0.892753i \(-0.351229\pi\)
0.450547 + 0.892753i \(0.351229\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) −3.94388 6.83100i −0.345901 0.599118i
\(131\) −1.93767 3.35615i −0.169295 0.293228i 0.768877 0.639397i \(-0.220816\pi\)
−0.938172 + 0.346169i \(0.887482\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 7.59491i 0.656101i
\(135\) 0 0
\(136\) 1.56239i 0.133974i
\(137\) 3.50003 + 2.02074i 0.299028 + 0.172644i 0.642006 0.766700i \(-0.278102\pi\)
−0.342978 + 0.939343i \(0.611436\pi\)
\(138\) 0 0
\(139\) 1.11021 0.640978i 0.0941664 0.0543670i −0.452177 0.891928i \(-0.649353\pi\)
0.546344 + 0.837561i \(0.316019\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −2.74172 + 4.74879i −0.230080 + 0.398510i
\(143\) 23.8538 1.99476
\(144\) 0 0
\(145\) 12.0901i 1.00403i
\(146\) 5.41258 9.37486i 0.447948 0.775869i
\(147\) 0 0
\(148\) 3.02623 + 5.24158i 0.248754 + 0.430855i
\(149\) 11.9390 6.89299i 0.978082 0.564696i 0.0763911 0.997078i \(-0.475660\pi\)
0.901690 + 0.432382i \(0.142327\pi\)
\(150\) 0 0
\(151\) −1.85701 + 3.21644i −0.151122 + 0.261750i −0.931640 0.363383i \(-0.881622\pi\)
0.780519 + 0.625133i \(0.214955\pi\)
\(152\) −4.80549 −0.389777
\(153\) 0 0
\(154\) 0 0
\(155\) 2.21923 + 1.28127i 0.178253 + 0.102914i
\(156\) 0 0
\(157\) −19.3727 + 11.1848i −1.54611 + 0.892645i −0.547673 + 0.836693i \(0.684486\pi\)
−0.998433 + 0.0559519i \(0.982181\pi\)
\(158\) −12.0328 + 6.94712i −0.957275 + 0.552683i
\(159\) 0 0
\(160\) −1.72374 0.995200i −0.136273 0.0786775i
\(161\) 0 0
\(162\) 0 0
\(163\) −7.44762 −0.583343 −0.291671 0.956519i \(-0.594211\pi\)
−0.291671 + 0.956519i \(0.594211\pi\)
\(164\) −2.98046 + 5.16231i −0.232735 + 0.403109i
\(165\) 0 0
\(166\) −5.81876 + 3.35946i −0.451624 + 0.260745i
\(167\) 4.77750 + 8.27487i 0.369694 + 0.640329i 0.989518 0.144413i \(-0.0461292\pi\)
−0.619824 + 0.784741i \(0.712796\pi\)
\(168\) 0 0
\(169\) 1.35228 2.34222i 0.104021 0.180170i
\(170\) 3.10978i 0.238509i
\(171\) 0 0
\(172\) −9.07229 −0.691756
\(173\) −1.09522 + 1.89697i −0.0832677 + 0.144224i −0.904652 0.426152i \(-0.859869\pi\)
0.821384 + 0.570376i \(0.193202\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 5.21285 3.00964i 0.392934 0.226860i
\(177\) 0 0
\(178\) 3.56248 + 2.05680i 0.267019 + 0.154163i
\(179\) 20.2676i 1.51487i 0.652911 + 0.757435i \(0.273548\pi\)
−0.652911 + 0.757435i \(0.726452\pi\)
\(180\) 0 0
\(181\) 13.4363i 0.998712i 0.866397 + 0.499356i \(0.166430\pi\)
−0.866397 + 0.499356i \(0.833570\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −2.90017 5.02324i −0.213803 0.370318i
\(185\) −6.02340 10.4328i −0.442849 0.767038i
\(186\) 0 0
\(187\) 8.14451 + 4.70224i 0.595586 + 0.343862i
\(188\) −4.78762 −0.349173
\(189\) 0 0
\(190\) 9.56485 0.693907
\(191\) 5.73219 + 3.30948i 0.414767 + 0.239466i 0.692836 0.721095i \(-0.256361\pi\)
−0.278069 + 0.960561i \(0.589694\pi\)
\(192\) 0 0
\(193\) −1.80171 3.12066i −0.129690 0.224630i 0.793866 0.608092i \(-0.208065\pi\)
−0.923557 + 0.383462i \(0.874732\pi\)
\(194\) 8.14755 + 14.1120i 0.584960 + 1.01318i
\(195\) 0 0
\(196\) 0 0
\(197\) 7.20722i 0.513493i 0.966479 + 0.256747i \(0.0826506\pi\)
−0.966479 + 0.256747i \(0.917349\pi\)
\(198\) 0 0
\(199\) 23.6397i 1.67577i 0.545846 + 0.837886i \(0.316208\pi\)
−0.545846 + 0.837886i \(0.683792\pi\)
\(200\) −0.899198 0.519152i −0.0635829 0.0367096i
\(201\) 0 0
\(202\) 5.48974 3.16950i 0.386256 0.223005i
\(203\) 0 0
\(204\) 0 0
\(205\) 5.93231 10.2751i 0.414331 0.717642i
\(206\) 13.1703 0.917621
\(207\) 0 0
\(208\) 3.96290i 0.274778i
\(209\) −14.4628 + 25.0503i −1.00041 + 1.73277i
\(210\) 0 0
\(211\) −8.63157 14.9503i −0.594222 1.02922i −0.993656 0.112461i \(-0.964127\pi\)
0.399434 0.916762i \(-0.369207\pi\)
\(212\) −7.27392 + 4.19960i −0.499575 + 0.288430i
\(213\) 0 0
\(214\) 6.61241 11.4530i 0.452015 0.782913i
\(215\) 18.0575 1.23151
\(216\) 0 0
\(217\) 0 0
\(218\) 1.98815 + 1.14786i 0.134654 + 0.0777427i
\(219\) 0 0
\(220\) −10.3757 + 5.99040i −0.699527 + 0.403872i
\(221\) 5.36208 3.09580i 0.360692 0.208246i
\(222\) 0 0
\(223\) 20.6001 + 11.8934i 1.37948 + 0.796444i 0.992097 0.125474i \(-0.0400451\pi\)
0.387385 + 0.921918i \(0.373378\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −13.8587 −0.921864
\(227\) −7.20788 + 12.4844i −0.478404 + 0.828620i −0.999693 0.0247599i \(-0.992118\pi\)
0.521289 + 0.853380i \(0.325451\pi\)
\(228\) 0 0
\(229\) 6.42951 3.71208i 0.424874 0.245301i −0.272287 0.962216i \(-0.587780\pi\)
0.697160 + 0.716915i \(0.254447\pi\)
\(230\) 5.77250 + 9.99827i 0.380628 + 0.659266i
\(231\) 0 0
\(232\) −3.03710 + 5.26041i −0.199395 + 0.345363i
\(233\) 4.51809i 0.295990i −0.988988 0.147995i \(-0.952718\pi\)
0.988988 0.147995i \(-0.0472819\pi\)
\(234\) 0 0
\(235\) 9.52929 0.621622
\(236\) −6.38986 + 11.0676i −0.415944 + 0.720436i
\(237\) 0 0
\(238\) 0 0
\(239\) 6.10620 3.52542i 0.394977 0.228040i −0.289337 0.957227i \(-0.593435\pi\)
0.684315 + 0.729187i \(0.260102\pi\)
\(240\) 0 0
\(241\) −6.12881 3.53847i −0.394791 0.227933i 0.289443 0.957195i \(-0.406530\pi\)
−0.684234 + 0.729262i \(0.739863\pi\)
\(242\) 25.2318i 1.62196i
\(243\) 0 0
\(244\) 1.86610i 0.119465i
\(245\) 0 0
\(246\) 0 0
\(247\) 9.52183 + 16.4923i 0.605860 + 1.04938i
\(248\) 0.643725 + 1.11497i 0.0408766 + 0.0708004i
\(249\) 0 0
\(250\) 10.4085 + 6.00932i 0.658288 + 0.380063i
\(251\) −11.9661 −0.755291 −0.377645 0.925950i \(-0.623266\pi\)
−0.377645 + 0.925950i \(0.623266\pi\)
\(252\) 0 0
\(253\) −34.9139 −2.19502
\(254\) −8.79432 5.07740i −0.551805 0.318585i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −1.79537 3.10968i −0.111992 0.193976i 0.804581 0.593843i \(-0.202390\pi\)
−0.916573 + 0.399866i \(0.869057\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 7.88775i 0.489178i
\(261\) 0 0
\(262\) 3.87534i 0.239420i
\(263\) 6.45370 + 3.72604i 0.397952 + 0.229758i 0.685600 0.727979i \(-0.259540\pi\)
−0.287648 + 0.957736i \(0.592873\pi\)
\(264\) 0 0
\(265\) 14.4780 8.35889i 0.889378 0.513483i
\(266\) 0 0
\(267\) 0 0
\(268\) 3.79746 6.57739i 0.231967 0.401778i
\(269\) −17.8443 −1.08799 −0.543994 0.839089i \(-0.683089\pi\)
−0.543994 + 0.839089i \(0.683089\pi\)
\(270\) 0 0
\(271\) 24.9811i 1.51749i −0.651385 0.758747i \(-0.725812\pi\)
0.651385 0.758747i \(-0.274188\pi\)
\(272\) 0.781195 1.35307i 0.0473669 0.0820419i
\(273\) 0 0
\(274\) −2.02074 3.50003i −0.122078 0.211445i
\(275\) −5.41253 + 3.12493i −0.326388 + 0.188440i
\(276\) 0 0
\(277\) 10.8175 18.7364i 0.649960 1.12576i −0.333172 0.942866i \(-0.608119\pi\)
0.983132 0.182898i \(-0.0585477\pi\)
\(278\) −1.28196 −0.0768866
\(279\) 0 0
\(280\) 0 0
\(281\) −0.931426 0.537759i −0.0555642 0.0320800i 0.471961 0.881620i \(-0.343546\pi\)
−0.527525 + 0.849540i \(0.676880\pi\)
\(282\) 0 0
\(283\) 25.3901 14.6590i 1.50929 0.871387i 0.509345 0.860562i \(-0.329888\pi\)
0.999941 0.0108247i \(-0.00344569\pi\)
\(284\) 4.74879 2.74172i 0.281789 0.162691i
\(285\) 0 0
\(286\) −20.6580 11.9269i −1.22153 0.705253i
\(287\) 0 0
\(288\) 0 0
\(289\) −14.5589 −0.856408
\(290\) 6.04504 10.4703i 0.354977 0.614838i
\(291\) 0 0
\(292\) −9.37486 + 5.41258i −0.548622 + 0.316747i
\(293\) −12.8648 22.2826i −0.751572 1.30176i −0.947061 0.321055i \(-0.895963\pi\)
0.195489 0.980706i \(-0.437371\pi\)
\(294\) 0 0
\(295\) 12.7184 22.0289i 0.740492 1.28257i
\(296\) 6.05245i 0.351792i
\(297\) 0 0
\(298\) −13.7860 −0.798600
\(299\) −11.4931 + 19.9066i −0.664662 + 1.15123i
\(300\) 0 0
\(301\) 0 0
\(302\) 3.21644 1.85701i 0.185085 0.106859i
\(303\) 0 0
\(304\) 4.16168 + 2.40274i 0.238688 + 0.137807i
\(305\) 3.71429i 0.212679i
\(306\) 0 0
\(307\) 15.0090i 0.856607i 0.903635 + 0.428304i \(0.140889\pi\)
−0.903635 + 0.428304i \(0.859111\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −1.28127 2.21923i −0.0727713 0.126044i
\(311\) 10.5961 + 18.3531i 0.600852 + 1.04071i 0.992692 + 0.120673i \(0.0385053\pi\)
−0.391840 + 0.920033i \(0.628161\pi\)
\(312\) 0 0
\(313\) 13.2023 + 7.62233i 0.746236 + 0.430839i 0.824332 0.566106i \(-0.191551\pi\)
−0.0780965 + 0.996946i \(0.524884\pi\)
\(314\) 22.3696 1.26239
\(315\) 0 0
\(316\) 13.8942 0.781612
\(317\) −13.8197 7.97880i −0.776191 0.448134i 0.0588876 0.998265i \(-0.481245\pi\)
−0.835079 + 0.550130i \(0.814578\pi\)
\(318\) 0 0
\(319\) 18.2812 + 31.6639i 1.02355 + 1.77284i
\(320\) 0.995200 + 1.72374i 0.0556334 + 0.0963599i
\(321\) 0 0
\(322\) 0 0
\(323\) 7.50805i 0.417759i
\(324\) 0 0
\(325\) 4.11469i 0.228242i
\(326\) 6.44983 + 3.72381i 0.357223 + 0.206243i
\(327\) 0 0
\(328\) 5.16231 2.98046i 0.285041 0.164569i
\(329\) 0 0
\(330\) 0 0
\(331\) −2.96229 + 5.13083i −0.162822 + 0.282016i −0.935880 0.352320i \(-0.885393\pi\)
0.773058 + 0.634336i \(0.218726\pi\)
\(332\) 6.71893 0.368749
\(333\) 0 0
\(334\) 9.55499i 0.522826i
\(335\) −7.55846 + 13.0916i −0.412963 + 0.715273i
\(336\) 0 0
\(337\) 12.2615 + 21.2376i 0.667928 + 1.15689i 0.978483 + 0.206330i \(0.0661519\pi\)
−0.310555 + 0.950556i \(0.600515\pi\)
\(338\) −2.34222 + 1.35228i −0.127400 + 0.0735543i
\(339\) 0 0
\(340\) −1.55489 + 2.69315i −0.0843258 + 0.146057i
\(341\) 7.74953 0.419661
\(342\) 0 0
\(343\) 0 0
\(344\) 7.85683 + 4.53614i 0.423612 + 0.244573i
\(345\) 0 0
\(346\) 1.89697 1.09522i 0.101982 0.0588792i
\(347\) 12.6506 7.30380i 0.679117 0.392088i −0.120405 0.992725i \(-0.538419\pi\)
0.799522 + 0.600636i \(0.205086\pi\)
\(348\) 0 0
\(349\) −15.5532 8.97965i −0.832545 0.480670i 0.0221785 0.999754i \(-0.492940\pi\)
−0.854723 + 0.519084i \(0.826273\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −6.01929 −0.320829
\(353\) 1.62784 2.81950i 0.0866410 0.150067i −0.819448 0.573153i \(-0.805720\pi\)
0.906089 + 0.423086i \(0.139053\pi\)
\(354\) 0 0
\(355\) −9.45200 + 5.45711i −0.501660 + 0.289633i
\(356\) −2.05680 3.56248i −0.109010 0.188811i
\(357\) 0 0
\(358\) 10.1338 17.5522i 0.535587 0.927664i
\(359\) 20.3428i 1.07365i −0.843694 0.536825i \(-0.819624\pi\)
0.843694 0.536825i \(-0.180376\pi\)
\(360\) 0 0
\(361\) −4.09273 −0.215407
\(362\) 6.71815 11.6362i 0.353098 0.611584i
\(363\) 0 0
\(364\) 0 0
\(365\) 18.6597 10.7732i 0.976695 0.563895i
\(366\) 0 0
\(367\) 3.04871 + 1.76018i 0.159142 + 0.0918804i 0.577456 0.816422i \(-0.304046\pi\)
−0.418314 + 0.908302i \(0.637379\pi\)
\(368\) 5.80034i 0.302364i
\(369\) 0 0
\(370\) 12.0468i 0.626283i
\(371\) 0 0
\(372\) 0 0
\(373\) 2.92210 + 5.06122i 0.151300 + 0.262060i 0.931706 0.363214i \(-0.118321\pi\)
−0.780405 + 0.625274i \(0.784987\pi\)
\(374\) −4.70224 8.14451i −0.243147 0.421143i
\(375\) 0 0
\(376\) 4.14620 + 2.39381i 0.213824 + 0.123451i
\(377\) 24.0714 1.23974
\(378\) 0 0
\(379\) −1.11033 −0.0570337 −0.0285168 0.999593i \(-0.509078\pi\)
−0.0285168 + 0.999593i \(0.509078\pi\)
\(380\) −8.28340 4.78243i −0.424930 0.245333i
\(381\) 0 0
\(382\) −3.30948 5.73219i −0.169328 0.293284i
\(383\) −4.01664 6.95702i −0.205241 0.355487i 0.744969 0.667099i \(-0.232464\pi\)
−0.950209 + 0.311612i \(0.899131\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 3.60343i 0.183410i
\(387\) 0 0
\(388\) 16.2951i 0.827258i
\(389\) −19.4971 11.2566i −0.988541 0.570734i −0.0837030 0.996491i \(-0.526675\pi\)
−0.904838 + 0.425756i \(0.860008\pi\)
\(390\) 0 0
\(391\) −7.84827 + 4.53120i −0.396904 + 0.229153i
\(392\) 0 0
\(393\) 0 0
\(394\) 3.60361 6.24164i 0.181547 0.314449i
\(395\) −27.6551 −1.39148
\(396\) 0 0
\(397\) 29.9426i 1.50278i 0.659860 + 0.751388i \(0.270615\pi\)
−0.659860 + 0.751388i \(0.729385\pi\)
\(398\) 11.8198 20.4725i 0.592475 1.02620i
\(399\) 0 0
\(400\) 0.519152 + 0.899198i 0.0259576 + 0.0449599i
\(401\) −23.9666 + 13.8371i −1.19684 + 0.690994i −0.959848 0.280519i \(-0.909493\pi\)
−0.236988 + 0.971513i \(0.576160\pi\)
\(402\) 0 0
\(403\) 2.55102 4.41849i 0.127075 0.220101i
\(404\) −6.33900 −0.315377
\(405\) 0 0
\(406\) 0 0
\(407\) −31.5505 18.2157i −1.56390 0.902919i
\(408\) 0 0
\(409\) 31.8350 18.3800i 1.57414 0.908830i 0.578487 0.815692i \(-0.303644\pi\)
0.995653 0.0931382i \(-0.0296898\pi\)
\(410\) −10.2751 + 5.93231i −0.507450 + 0.292976i
\(411\) 0 0
\(412\) −11.4058 6.58517i −0.561926 0.324428i
\(413\) 0 0
\(414\) 0 0
\(415\) −13.3734 −0.656472
\(416\) −1.98145 + 3.43197i −0.0971485 + 0.168266i
\(417\) 0 0
\(418\) 25.0503 14.4628i 1.22525 0.707399i
\(419\) −7.82990 13.5618i −0.382516 0.662537i 0.608905 0.793243i \(-0.291609\pi\)
−0.991421 + 0.130706i \(0.958276\pi\)
\(420\) 0 0
\(421\) −12.8725 + 22.2959i −0.627368 + 1.08663i 0.360710 + 0.932678i \(0.382535\pi\)
−0.988078 + 0.153955i \(0.950799\pi\)
\(422\) 17.2631i 0.840357i
\(423\) 0 0
\(424\) 8.39920 0.407901
\(425\) −0.811118 + 1.40490i −0.0393450 + 0.0681476i
\(426\) 0 0
\(427\) 0 0
\(428\) −11.4530 + 6.61241i −0.553603 + 0.319623i
\(429\) 0 0
\(430\) −15.6382 9.02875i −0.754143 0.435405i
\(431\) 21.3314i 1.02750i 0.857941 + 0.513748i \(0.171743\pi\)
−0.857941 + 0.513748i \(0.828257\pi\)
\(432\) 0 0
\(433\) 32.5613i 1.56480i 0.622778 + 0.782399i \(0.286004\pi\)
−0.622778 + 0.782399i \(0.713996\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.14786 1.98815i −0.0549724 0.0952150i
\(437\) −13.9367 24.1391i −0.666685 1.15473i
\(438\) 0 0
\(439\) 5.81892 + 3.35955i 0.277722 + 0.160343i 0.632392 0.774649i \(-0.282073\pi\)
−0.354670 + 0.934992i \(0.615407\pi\)
\(440\) 11.9808 0.571162
\(441\) 0 0
\(442\) −6.19159 −0.294504
\(443\) 1.39735 + 0.806761i 0.0663902 + 0.0383304i 0.532828 0.846224i \(-0.321129\pi\)
−0.466437 + 0.884554i \(0.654463\pi\)
\(444\) 0 0
\(445\) 4.09385 + 7.09076i 0.194067 + 0.336134i
\(446\) −11.8934 20.6001i −0.563171 0.975441i
\(447\) 0 0
\(448\) 0 0
\(449\) 7.27512i 0.343334i −0.985155 0.171667i \(-0.945085\pi\)
0.985155 0.171667i \(-0.0549154\pi\)
\(450\) 0 0
\(451\) 35.8805i 1.68955i
\(452\) 12.0019 + 6.92933i 0.564524 + 0.325928i
\(453\) 0 0
\(454\) 12.4844 7.20788i 0.585923 0.338283i
\(455\) 0 0
\(456\) 0 0
\(457\) 0.138131 0.239249i 0.00646148 0.0111916i −0.862777 0.505585i \(-0.831277\pi\)
0.869238 + 0.494394i \(0.164610\pi\)
\(458\) −7.42416 −0.346908
\(459\) 0 0
\(460\) 11.5450i 0.538289i
\(461\) 8.30512 14.3849i 0.386808 0.669971i −0.605210 0.796066i \(-0.706911\pi\)
0.992018 + 0.126094i \(0.0402442\pi\)
\(462\) 0 0
\(463\) −3.19859 5.54011i −0.148651 0.257471i 0.782078 0.623180i \(-0.214160\pi\)
−0.930729 + 0.365709i \(0.880826\pi\)
\(464\) 5.26041 3.03710i 0.244208 0.140994i
\(465\) 0 0
\(466\) −2.25905 + 3.91278i −0.104648 + 0.181256i
\(467\) 6.79198 0.314295 0.157148 0.987575i \(-0.449770\pi\)
0.157148 + 0.987575i \(0.449770\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −8.25261 4.76465i −0.380664 0.219777i
\(471\) 0 0
\(472\) 11.0676 6.38986i 0.509426 0.294117i
\(473\) 47.2925 27.3043i 2.17451 1.25546i
\(474\) 0 0
\(475\) −4.32109 2.49478i −0.198265 0.114468i
\(476\) 0 0
\(477\) 0 0
\(478\) −7.05083 −0.322498
\(479\) 12.4257 21.5219i 0.567743 0.983360i −0.429045 0.903283i \(-0.641150\pi\)
0.996789 0.0800774i \(-0.0255167\pi\)
\(480\) 0 0
\(481\) −20.7718 + 11.9926i −0.947114 + 0.546817i
\(482\) 3.53847 + 6.12881i 0.161173 + 0.279160i
\(483\) 0 0
\(484\) −12.6159 + 21.8514i −0.573450 + 0.993244i
\(485\) 32.4338i 1.47274i
\(486\) 0 0
\(487\) 13.3168 0.603442 0.301721 0.953396i \(-0.402439\pi\)
0.301721 + 0.953396i \(0.402439\pi\)
\(488\) 0.933050 1.61609i 0.0422372 0.0731570i
\(489\) 0 0
\(490\) 0 0
\(491\) −24.2581 + 14.0054i −1.09475 + 0.632057i −0.934838 0.355074i \(-0.884456\pi\)
−0.159916 + 0.987131i \(0.551122\pi\)
\(492\) 0 0
\(493\) 8.21881 + 4.74513i 0.370157 + 0.213710i
\(494\) 19.0437i 0.856815i
\(495\) 0 0
\(496\) 1.28745i 0.0578082i
\(497\) 0 0
\(498\) 0 0
\(499\) −5.94998 10.3057i −0.266357 0.461345i 0.701561 0.712609i \(-0.252487\pi\)
−0.967918 + 0.251265i \(0.919153\pi\)
\(500\) −6.00932 10.4085i −0.268745 0.465480i
\(501\) 0 0
\(502\) 10.3629 + 5.98303i 0.462519 + 0.267036i
\(503\) −5.08019 −0.226514 −0.113257 0.993566i \(-0.536128\pi\)
−0.113257 + 0.993566i \(0.536128\pi\)
\(504\) 0 0
\(505\) 12.6172 0.561456
\(506\) 30.2363 + 17.4570i 1.34417 + 0.776057i
\(507\) 0 0
\(508\) 5.07740 + 8.79432i 0.225273 + 0.390185i
\(509\) −0.500521 0.866928i −0.0221852 0.0384259i 0.854720 0.519090i \(-0.173729\pi\)
−0.876905 + 0.480664i \(0.840396\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 3.59074i 0.158381i
\(515\) 22.7022 + 13.1071i 1.00038 + 0.577569i
\(516\) 0 0
\(517\) 24.9572 14.4090i 1.09762 0.633709i
\(518\) 0 0
\(519\) 0 0
\(520\) 3.94388 6.83100i 0.172950 0.299559i
\(521\) −23.8750 −1.04598 −0.522991 0.852338i \(-0.675184\pi\)
−0.522991 + 0.852338i \(0.675184\pi\)
\(522\) 0 0
\(523\) 8.04399i 0.351739i −0.984413 0.175870i \(-0.943726\pi\)
0.984413 0.175870i \(-0.0562737\pi\)
\(524\) 1.93767 3.35615i 0.0846476 0.146614i
\(525\) 0 0
\(526\) −3.72604 6.45370i −0.162463 0.281395i
\(527\) 1.74201 1.00575i 0.0758832 0.0438112i
\(528\) 0 0
\(529\) 5.32199 9.21796i 0.231391 0.400781i
\(530\) −16.7178 −0.726174
\(531\) 0 0
\(532\) 0 0
\(533\) −20.4577 11.8113i −0.886122 0.511603i
\(534\) 0 0
\(535\) 22.7961 13.1613i 0.985562 0.569014i
\(536\) −6.57739 + 3.79746i −0.284100 + 0.164025i
\(537\) 0 0
\(538\) 15.4536 + 8.92216i 0.666254 + 0.384662i
\(539\) 0 0
\(540\) 0 0
\(541\) 0.125869 0.00541152 0.00270576 0.999996i \(-0.499139\pi\)
0.00270576 + 0.999996i \(0.499139\pi\)
\(542\) −12.4906 + 21.6343i −0.536515 + 0.929272i
\(543\) 0 0
\(544\) −1.35307 + 0.781195i −0.0580124 + 0.0334935i
\(545\) 2.28470 + 3.95721i 0.0978656 + 0.169508i
\(546\) 0 0
\(547\) 6.59217 11.4180i 0.281861 0.488197i −0.689982 0.723826i \(-0.742382\pi\)
0.971843 + 0.235629i \(0.0757150\pi\)
\(548\) 4.04149i 0.172644i
\(549\) 0 0
\(550\) 6.24985 0.266495
\(551\) −14.5947 + 25.2788i −0.621757 + 1.07691i
\(552\) 0 0
\(553\) 0 0
\(554\) −18.7364 + 10.8175i −0.796035 + 0.459591i
\(555\) 0 0
\(556\) 1.11021 + 0.640978i 0.0470832 + 0.0271835i
\(557\) 27.2846i 1.15609i −0.816006 0.578043i \(-0.803817\pi\)
0.816006 0.578043i \(-0.196183\pi\)
\(558\) 0 0
\(559\) 35.9526i 1.52063i
\(560\) 0 0
\(561\) 0 0
\(562\) 0.537759 + 0.931426i 0.0226840 + 0.0392898i
\(563\) 3.46343 + 5.99884i 0.145966 + 0.252821i 0.929733 0.368234i \(-0.120038\pi\)
−0.783767 + 0.621055i \(0.786704\pi\)
\(564\) 0 0
\(565\) −23.8887 13.7921i −1.00500 0.580240i
\(566\) −29.3180 −1.23233
\(567\) 0 0
\(568\) −5.48343 −0.230080
\(569\) −15.4829 8.93906i −0.649077 0.374745i 0.139025 0.990289i \(-0.455603\pi\)
−0.788103 + 0.615544i \(0.788936\pi\)
\(570\) 0 0
\(571\) 13.6121 + 23.5769i 0.569649 + 0.986661i 0.996600 + 0.0823863i \(0.0262541\pi\)
−0.426952 + 0.904274i \(0.640413\pi\)
\(572\) 11.9269 + 20.6580i 0.498689 + 0.863755i
\(573\) 0 0
\(574\) 0 0
\(575\) 6.02252i 0.251157i
\(576\) 0 0
\(577\) 2.56165i 0.106643i −0.998577 0.0533215i \(-0.983019\pi\)
0.998577 0.0533215i \(-0.0169808\pi\)
\(578\) 12.6084 + 7.27947i 0.524441 + 0.302786i
\(579\) 0 0
\(580\) −10.4703 + 6.04504i −0.434756 + 0.251007i
\(581\) 0 0
\(582\) 0 0
\(583\) 25.2786 43.7838i 1.04693 1.81334i
\(584\) 10.8252 0.447948
\(585\) 0 0
\(586\) 25.7297i 1.06288i
\(587\) −1.52947 + 2.64912i −0.0631280 + 0.109341i −0.895862 0.444332i \(-0.853441\pi\)
0.832734 + 0.553673i \(0.186774\pi\)
\(588\) 0 0
\(589\) 3.09342 + 5.35795i 0.127462 + 0.220771i
\(590\) −22.0289 + 12.7184i −0.906914 + 0.523607i
\(591\) 0 0
\(592\) −3.02623 + 5.24158i −0.124377 + 0.215427i
\(593\) −18.2944 −0.751261 −0.375631 0.926769i \(-0.622574\pi\)
−0.375631 + 0.926769i \(0.622574\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 11.9390 + 6.89299i 0.489041 + 0.282348i
\(597\) 0 0
\(598\) 19.9066 11.4931i 0.814042 0.469987i
\(599\) −34.2837 + 19.7937i −1.40079 + 0.808749i −0.994474 0.104981i \(-0.966522\pi\)
−0.406321 + 0.913731i \(0.633188\pi\)
\(600\) 0 0
\(601\) −20.8019 12.0100i −0.848526 0.489897i 0.0116274 0.999932i \(-0.496299\pi\)
−0.860153 + 0.510036i \(0.829632\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −3.71402 −0.151122
\(605\) 25.1107 43.4930i 1.02089 1.76824i
\(606\) 0 0
\(607\) 18.5544 10.7124i 0.753099 0.434802i −0.0737135 0.997279i \(-0.523485\pi\)
0.826813 + 0.562477i \(0.190152\pi\)
\(608\) −2.40274 4.16168i −0.0974442 0.168778i
\(609\) 0 0
\(610\) −1.85714 + 3.21667i −0.0751936 + 0.130239i
\(611\) 18.9729i 0.767560i
\(612\) 0 0
\(613\) −4.35620 −0.175945 −0.0879726 0.996123i \(-0.528039\pi\)
−0.0879726 + 0.996123i \(0.528039\pi\)
\(614\) 7.50448 12.9981i 0.302856 0.524563i
\(615\) 0 0
\(616\) 0 0
\(617\) −28.4809 + 16.4434i −1.14660 + 0.661988i −0.948056 0.318105i \(-0.896954\pi\)
−0.198541 + 0.980093i \(0.563620\pi\)
\(618\) 0 0
\(619\) 3.59040 + 2.07292i 0.144310 + 0.0833176i 0.570417 0.821355i \(-0.306782\pi\)
−0.426106 + 0.904673i \(0.640115\pi\)
\(620\) 2.56254i 0.102914i
\(621\) 0 0
\(622\) 21.1923i 0.849733i
\(623\) 0 0
\(624\) 0 0
\(625\) 9.36520 + 16.2210i 0.374608 + 0.648840i
\(626\) −7.62233 13.2023i −0.304649 0.527668i
\(627\) 0 0
\(628\) −19.3727 11.1848i −0.773053 0.446322i
\(629\) −9.45629 −0.377047
\(630\) 0 0
\(631\) −18.7414 −0.746084 −0.373042 0.927815i \(-0.621685\pi\)
−0.373042 + 0.927815i \(0.621685\pi\)
\(632\) −12.0328 6.94712i −0.478637 0.276341i
\(633\) 0 0
\(634\) 7.97880 + 13.8197i 0.316879 + 0.548850i
\(635\) −10.1061 17.5042i −0.401047 0.694634i
\(636\) 0 0
\(637\) 0 0
\(638\) 36.5623i 1.44752i
\(639\) 0 0
\(640\) 1.99040i 0.0786775i
\(641\) −5.81323 3.35627i −0.229609 0.132565i 0.380783 0.924665i \(-0.375655\pi\)
−0.610392 + 0.792100i \(0.708988\pi\)
\(642\) 0 0
\(643\) 7.11267 4.10650i 0.280496 0.161945i −0.353152 0.935566i \(-0.614890\pi\)
0.633648 + 0.773621i \(0.281557\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 3.75402 6.50216i 0.147700 0.255824i
\(647\) 16.8049 0.660670 0.330335 0.943864i \(-0.392838\pi\)
0.330335 + 0.943864i \(0.392838\pi\)
\(648\) 0 0
\(649\) 76.9247i 3.01956i
\(650\) 2.05735 3.56343i 0.0806958 0.139769i
\(651\) 0 0
\(652\) −3.72381 6.44983i −0.145836 0.252595i
\(653\) −20.2758 + 11.7062i −0.793452 + 0.458100i −0.841177 0.540761i \(-0.818137\pi\)
0.0477241 + 0.998861i \(0.484803\pi\)
\(654\) 0 0
\(655\) −3.85674 + 6.68008i −0.150695 + 0.261012i
\(656\) −5.96092 −0.232735
\(657\) 0 0
\(658\) 0 0
\(659\) 14.5941 + 8.42589i 0.568504 + 0.328226i 0.756552 0.653934i \(-0.226883\pi\)
−0.188047 + 0.982160i \(0.560216\pi\)
\(660\) 0 0
\(661\) −33.1759 + 19.1541i −1.29039 + 0.745009i −0.978724 0.205181i \(-0.934222\pi\)
−0.311670 + 0.950191i \(0.600888\pi\)
\(662\) 5.13083 2.96229i 0.199415 0.115132i
\(663\) 0 0
\(664\) −5.81876 3.35946i −0.225812 0.130372i
\(665\) 0 0
\(666\) 0 0
\(667\) −35.2324 −1.36420
\(668\) −4.77750 + 8.27487i −0.184847 + 0.320164i
\(669\) 0 0
\(670\) 13.0916 7.55846i 0.505774 0.292009i
\(671\) −5.61629 9.72771i −0.216815 0.375534i
\(672\) 0 0
\(673\) −3.52300 + 6.10201i −0.135802 + 0.235215i −0.925903 0.377760i \(-0.876694\pi\)
0.790102 + 0.612976i \(0.210028\pi\)
\(674\) 24.5231i 0.944593i
\(675\) 0 0
\(676\) 2.70456 0.104021
\(677\) 21.9550 38.0272i 0.843801 1.46151i −0.0428578 0.999081i \(-0.513646\pi\)
0.886659 0.462425i \(-0.153020\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 2.69315 1.55489i 0.103278 0.0596274i
\(681\) 0 0
\(682\) −6.71129 3.87477i −0.256989 0.148372i
\(683\) 11.3888i 0.435781i −0.975973 0.217891i \(-0.930082\pi\)
0.975973 0.217891i \(-0.0699176\pi\)
\(684\) 0 0
\(685\) 8.04418i 0.307352i
\(686\) 0 0
\(687\) 0 0
\(688\) −4.53614 7.85683i −0.172939 0.299539i
\(689\) −16.6426 28.8258i −0.634032 1.09818i
\(690\) 0 0
\(691\) −1.81342 1.04698i −0.0689856 0.0398288i 0.465110 0.885253i \(-0.346015\pi\)
−0.534096 + 0.845424i \(0.679348\pi\)
\(692\) −2.19043 −0.0832677
\(693\) 0 0
\(694\) −14.6076 −0.554497
\(695\) −2.20975 1.27580i −0.0838208 0.0483939i
\(696\) 0 0
\(697\) −4.65665 8.06555i −0.176383 0.305504i
\(698\) 8.97965 + 15.5532i 0.339885 + 0.588698i
\(699\) 0 0
\(700\) 0 0
\(701\) 7.35719i 0.277877i 0.990301 + 0.138939i \(0.0443690\pi\)
−0.990301 + 0.138939i \(0.955631\pi\)
\(702\) 0 0
\(703\) 29.0850i 1.09696i
\(704\) 5.21285 + 3.00964i 0.196467 + 0.113430i
\(705\) 0 0
\(706\) −2.81950 + 1.62784i −0.106113 + 0.0612645i
\(707\) 0 0
\(708\) 0 0
\(709\) −11.4937 + 19.9077i −0.431656 + 0.747649i −0.997016 0.0771946i \(-0.975404\pi\)
0.565361 + 0.824844i \(0.308737\pi\)
\(710\) 10.9142 0.409604
\(711\) 0 0
\(712\) 4.11359i 0.154163i
\(713\) −3.73383 + 6.46718i −0.139833 + 0.242198i
\(714\) 0 0
\(715\) −23.7393 41.1177i −0.887800 1.53772i
\(716\) −17.5522 + 10.1338i −0.655958 + 0.378717i
\(717\) 0 0
\(718\) −10.1714 + 17.6173i −0.379592 + 0.657473i
\(719\) −0.669842 −0.0249809 −0.0124905 0.999922i \(-0.503976\pi\)
−0.0124905 + 0.999922i \(0.503976\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 3.54441 + 2.04636i 0.131909 + 0.0761578i
\(723\) 0 0
\(724\) −11.6362 + 6.71815i −0.432455 + 0.249678i
\(725\) −5.46190 + 3.15343i −0.202850 + 0.117116i
\(726\) 0 0
\(727\) −10.8032 6.23723i −0.400669 0.231326i 0.286104 0.958199i \(-0.407640\pi\)
−0.686772 + 0.726873i \(0.740973\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −21.5464 −0.797468
\(731\) 7.08723 12.2754i 0.262131 0.454024i
\(732\) 0 0
\(733\) −18.5364 + 10.7020i −0.684659 + 0.395288i −0.801608 0.597850i \(-0.796022\pi\)
0.116949 + 0.993138i \(0.462689\pi\)
\(734\) −1.76018 3.04871i −0.0649693 0.112530i
\(735\) 0 0
\(736\) 2.90017 5.02324i 0.106902 0.185159i
\(737\) 45.7159i 1.68397i
\(738\) 0 0
\(739\) −23.2840 −0.856517 −0.428258 0.903656i \(-0.640873\pi\)
−0.428258 + 0.903656i \(0.640873\pi\)
\(740\) 6.02340 10.4328i 0.221425 0.383519i
\(741\) 0 0
\(742\) 0 0
\(743\) 5.94043 3.42971i 0.217933 0.125824i −0.387060 0.922055i \(-0.626509\pi\)
0.604993 + 0.796231i \(0.293176\pi\)
\(744\) 0 0
\(745\) −23.7634 13.7198i −0.870624 0.502655i
\(746\) 5.84420i 0.213971i
\(747\) 0 0
\(748\) 9.40447i 0.343862i
\(749\) 0 0
\(750\) 0 0
\(751\) −22.5956 39.1367i −0.824524 1.42812i −0.902282 0.431146i \(-0.858109\pi\)
0.0777577 0.996972i \(-0.475224\pi\)
\(752\) −2.39381 4.14620i −0.0872933 0.151197i
\(753\) 0 0
\(754\) −20.8465 12.0357i −0.759183 0.438315i
\(755\) 7.39240 0.269037
\(756\) 0 0
\(757\) −17.8760 −0.649716 −0.324858 0.945763i \(-0.605316\pi\)
−0.324858 + 0.945763i \(0.605316\pi\)
\(758\) 0.961571 + 0.555163i 0.0349258 + 0.0201644i
\(759\) 0 0
\(760\) 4.78243 + 8.28340i 0.173477 + 0.300471i
\(761\) −5.70198 9.87613i −0.206697 0.358009i 0.743975 0.668207i \(-0.232938\pi\)
−0.950672 + 0.310198i \(0.899605\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 6.61896i 0.239466i
\(765\) 0 0
\(766\) 8.03327i 0.290254i
\(767\) −43.8596 25.3223i −1.58368 0.914337i
\(768\) 0 0
\(769\) 0.332429 0.191928i 0.0119877 0.00692109i −0.493994 0.869465i \(-0.664464\pi\)
0.505982 + 0.862544i \(0.331130\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1.80171 3.12066i 0.0648451 0.112315i
\(773\) −27.8659 −1.00227 −0.501134 0.865370i \(-0.667084\pi\)
−0.501134 + 0.865370i \(0.667084\pi\)
\(774\) 0 0
\(775\) 1.33677i 0.0480181i
\(776\) −8.14755 + 14.1120i −0.292480 + 0.506590i
\(777\) 0 0
\(778\) 11.2566 + 19.4971i 0.403570 + 0.699004i
\(779\) 24.8074 14.3226i 0.888819 0.513160i
\(780\) 0 0
\(781\) −16.5032 + 28.5843i −0.590530 + 1.02283i
\(782\) 9.06240 0.324071
\(783\) 0 0
\(784\) 0 0
\(785\) 38.5593 + 22.2622i 1.37624 + 0.794574i
\(786\) 0 0
\(787\) 27.3935 15.8156i 0.976473 0.563767i 0.0752696 0.997163i \(-0.476018\pi\)
0.901203 + 0.433396i \(0.142685\pi\)
\(788\) −6.24164 + 3.60361i −0.222349 + 0.128373i
\(789\) 0 0
\(790\) 23.9500 + 13.8275i 0.852103 + 0.491962i
\(791\) 0 0
\(792\) 0 0
\(793\) −7.39516 −0.262610
\(794\) 14.9713 25.9311i 0.531312 0.920259i
\(795\) 0 0