Properties

Label 420.2.q.d.361.2
Level $420$
Weight $2$
Character 420.361
Analytic conductor $3.354$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 420.q (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.35371688489\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 420.361
Dual form 420.2.q.d.121.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.62132 - 2.09077i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(1.62132 - 2.09077i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(2.12132 - 3.67423i) q^{11} +3.24264 q^{13} -1.00000 q^{15} +(-2.12132 + 3.67423i) q^{17} +(3.50000 + 6.06218i) q^{19} +(1.00000 + 2.44949i) q^{21} +(2.12132 + 3.67423i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{27} -1.75736 q^{29} +(4.74264 - 8.21449i) q^{31} +(2.12132 + 3.67423i) q^{33} +(2.62132 + 0.358719i) q^{35} +(-1.62132 - 2.80821i) q^{37} +(-1.62132 + 2.80821i) q^{39} -4.24264 q^{41} +3.24264 q^{43} +(0.500000 - 0.866025i) q^{45} +(3.00000 + 5.19615i) q^{47} +(-1.74264 - 6.77962i) q^{49} +(-2.12132 - 3.67423i) q^{51} +(-4.24264 + 7.34847i) q^{53} +4.24264 q^{55} -7.00000 q^{57} +(5.12132 - 8.87039i) q^{59} +(-2.24264 - 3.88437i) q^{61} +(-2.62132 - 0.358719i) q^{63} +(1.62132 + 2.80821i) q^{65} +(2.62132 - 4.54026i) q^{67} -4.24264 q^{69} -12.7279 q^{71} +(-4.62132 + 8.00436i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(-4.24264 - 10.3923i) q^{77} +(-5.50000 - 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{81} -10.2426 q^{83} -4.24264 q^{85} +(0.878680 - 1.52192i) q^{87} +(5.12132 + 8.87039i) q^{89} +(5.25736 - 6.77962i) q^{91} +(4.74264 + 8.21449i) q^{93} +(-3.50000 + 6.06218i) q^{95} -0.485281 q^{97} -4.24264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} + 2 q^{5} - 2 q^{7} - 2 q^{9} + O(q^{10}) \) \( 4 q - 2 q^{3} + 2 q^{5} - 2 q^{7} - 2 q^{9} - 4 q^{13} - 4 q^{15} + 14 q^{19} + 4 q^{21} - 2 q^{25} + 4 q^{27} - 24 q^{29} + 2 q^{31} + 2 q^{35} + 2 q^{37} + 2 q^{39} - 4 q^{43} + 2 q^{45} + 12 q^{47} + 10 q^{49} - 28 q^{57} + 12 q^{59} + 8 q^{61} - 2 q^{63} - 2 q^{65} + 2 q^{67} - 10 q^{73} - 2 q^{75} - 22 q^{79} - 2 q^{81} - 24 q^{83} + 12 q^{87} + 12 q^{89} + 38 q^{91} + 2 q^{93} - 14 q^{95} + 32 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/420\mathbb{Z}\right)^\times\).

\(n\) \(211\) \(241\) \(281\) \(337\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0 0
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) 1.62132 2.09077i 0.612801 0.790237i
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) 2.12132 3.67423i 0.639602 1.10782i −0.345918 0.938265i \(-0.612432\pi\)
0.985520 0.169559i \(-0.0542342\pi\)
\(12\) 0 0
\(13\) 3.24264 0.899347 0.449673 0.893193i \(-0.351540\pi\)
0.449673 + 0.893193i \(0.351540\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) −2.12132 + 3.67423i −0.514496 + 0.891133i 0.485363 + 0.874313i \(0.338688\pi\)
−0.999859 + 0.0168199i \(0.994646\pi\)
\(18\) 0 0
\(19\) 3.50000 + 6.06218i 0.802955 + 1.39076i 0.917663 + 0.397360i \(0.130073\pi\)
−0.114708 + 0.993399i \(0.536593\pi\)
\(20\) 0 0
\(21\) 1.00000 + 2.44949i 0.218218 + 0.534522i
\(22\) 0 0
\(23\) 2.12132 + 3.67423i 0.442326 + 0.766131i 0.997862 0.0653618i \(-0.0208201\pi\)
−0.555536 + 0.831493i \(0.687487\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.75736 −0.326333 −0.163167 0.986599i \(-0.552171\pi\)
−0.163167 + 0.986599i \(0.552171\pi\)
\(30\) 0 0
\(31\) 4.74264 8.21449i 0.851803 1.47537i −0.0277757 0.999614i \(-0.508842\pi\)
0.879579 0.475753i \(-0.157824\pi\)
\(32\) 0 0
\(33\) 2.12132 + 3.67423i 0.369274 + 0.639602i
\(34\) 0 0
\(35\) 2.62132 + 0.358719i 0.443084 + 0.0606347i
\(36\) 0 0
\(37\) −1.62132 2.80821i −0.266543 0.461667i 0.701423 0.712745i \(-0.252548\pi\)
−0.967967 + 0.251078i \(0.919215\pi\)
\(38\) 0 0
\(39\) −1.62132 + 2.80821i −0.259619 + 0.449673i
\(40\) 0 0
\(41\) −4.24264 −0.662589 −0.331295 0.943527i \(-0.607485\pi\)
−0.331295 + 0.943527i \(0.607485\pi\)
\(42\) 0 0
\(43\) 3.24264 0.494498 0.247249 0.968952i \(-0.420473\pi\)
0.247249 + 0.968952i \(0.420473\pi\)
\(44\) 0 0
\(45\) 0.500000 0.866025i 0.0745356 0.129099i
\(46\) 0 0
\(47\) 3.00000 + 5.19615i 0.437595 + 0.757937i 0.997503 0.0706177i \(-0.0224970\pi\)
−0.559908 + 0.828554i \(0.689164\pi\)
\(48\) 0 0
\(49\) −1.74264 6.77962i −0.248949 0.968517i
\(50\) 0 0
\(51\) −2.12132 3.67423i −0.297044 0.514496i
\(52\) 0 0
\(53\) −4.24264 + 7.34847i −0.582772 + 1.00939i 0.412378 + 0.911013i \(0.364698\pi\)
−0.995149 + 0.0983769i \(0.968635\pi\)
\(54\) 0 0
\(55\) 4.24264 0.572078
\(56\) 0 0
\(57\) −7.00000 −0.927173
\(58\) 0 0
\(59\) 5.12132 8.87039i 0.666739 1.15483i −0.312072 0.950059i \(-0.601023\pi\)
0.978811 0.204767i \(-0.0656438\pi\)
\(60\) 0 0
\(61\) −2.24264 3.88437i −0.287141 0.497342i 0.685985 0.727615i \(-0.259371\pi\)
−0.973126 + 0.230273i \(0.926038\pi\)
\(62\) 0 0
\(63\) −2.62132 0.358719i −0.330255 0.0451944i
\(64\) 0 0
\(65\) 1.62132 + 2.80821i 0.201100 + 0.348315i
\(66\) 0 0
\(67\) 2.62132 4.54026i 0.320245 0.554681i −0.660293 0.751008i \(-0.729568\pi\)
0.980539 + 0.196327i \(0.0629013\pi\)
\(68\) 0 0
\(69\) −4.24264 −0.510754
\(70\) 0 0
\(71\) −12.7279 −1.51053 −0.755263 0.655422i \(-0.772491\pi\)
−0.755263 + 0.655422i \(0.772491\pi\)
\(72\) 0 0
\(73\) −4.62132 + 8.00436i −0.540885 + 0.936840i 0.457969 + 0.888968i \(0.348577\pi\)
−0.998854 + 0.0478714i \(0.984756\pi\)
\(74\) 0 0
\(75\) −0.500000 0.866025i −0.0577350 0.100000i
\(76\) 0 0
\(77\) −4.24264 10.3923i −0.483494 1.18431i
\(78\) 0 0
\(79\) −5.50000 9.52628i −0.618798 1.07179i −0.989705 0.143120i \(-0.954286\pi\)
0.370907 0.928670i \(-0.379047\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −10.2426 −1.12428 −0.562138 0.827043i \(-0.690021\pi\)
−0.562138 + 0.827043i \(0.690021\pi\)
\(84\) 0 0
\(85\) −4.24264 −0.460179
\(86\) 0 0
\(87\) 0.878680 1.52192i 0.0942043 0.163167i
\(88\) 0 0
\(89\) 5.12132 + 8.87039i 0.542859 + 0.940259i 0.998738 + 0.0502176i \(0.0159915\pi\)
−0.455879 + 0.890042i \(0.650675\pi\)
\(90\) 0 0
\(91\) 5.25736 6.77962i 0.551121 0.710697i
\(92\) 0 0
\(93\) 4.74264 + 8.21449i 0.491789 + 0.851803i
\(94\) 0 0
\(95\) −3.50000 + 6.06218i −0.359092 + 0.621966i
\(96\) 0 0
\(97\) −0.485281 −0.0492729 −0.0246364 0.999696i \(-0.507843\pi\)
−0.0246364 + 0.999696i \(0.507843\pi\)
\(98\) 0 0
\(99\) −4.24264 −0.426401
\(100\) 0 0
\(101\) 3.87868 6.71807i 0.385943 0.668473i −0.605956 0.795498i \(-0.707209\pi\)
0.991900 + 0.127025i \(0.0405428\pi\)
\(102\) 0 0
\(103\) 8.62132 + 14.9326i 0.849484 + 1.47135i 0.881670 + 0.471867i \(0.156420\pi\)
−0.0321856 + 0.999482i \(0.510247\pi\)
\(104\) 0 0
\(105\) −1.62132 + 2.09077i −0.158225 + 0.204038i
\(106\) 0 0
\(107\) −6.36396 11.0227i −0.615227 1.06561i −0.990345 0.138628i \(-0.955731\pi\)
0.375117 0.926977i \(-0.377602\pi\)
\(108\) 0 0
\(109\) 4.74264 8.21449i 0.454263 0.786806i −0.544383 0.838837i \(-0.683236\pi\)
0.998645 + 0.0520310i \(0.0165695\pi\)
\(110\) 0 0
\(111\) 3.24264 0.307778
\(112\) 0 0
\(113\) −18.0000 −1.69330 −0.846649 0.532152i \(-0.821383\pi\)
−0.846649 + 0.532152i \(0.821383\pi\)
\(114\) 0 0
\(115\) −2.12132 + 3.67423i −0.197814 + 0.342624i
\(116\) 0 0
\(117\) −1.62132 2.80821i −0.149891 0.259619i
\(118\) 0 0
\(119\) 4.24264 + 10.3923i 0.388922 + 0.952661i
\(120\) 0 0
\(121\) −3.50000 6.06218i −0.318182 0.551107i
\(122\) 0 0
\(123\) 2.12132 3.67423i 0.191273 0.331295i
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −2.75736 −0.244676 −0.122338 0.992488i \(-0.539039\pi\)
−0.122338 + 0.992488i \(0.539039\pi\)
\(128\) 0 0
\(129\) −1.62132 + 2.80821i −0.142749 + 0.247249i
\(130\) 0 0
\(131\) −7.24264 12.5446i −0.632792 1.09603i −0.986978 0.160854i \(-0.948575\pi\)
0.354186 0.935175i \(-0.384758\pi\)
\(132\) 0 0
\(133\) 18.3492 + 2.51104i 1.59108 + 0.217734i
\(134\) 0 0
\(135\) 0.500000 + 0.866025i 0.0430331 + 0.0745356i
\(136\) 0 0
\(137\) −2.12132 + 3.67423i −0.181237 + 0.313911i −0.942302 0.334764i \(-0.891343\pi\)
0.761065 + 0.648675i \(0.224677\pi\)
\(138\) 0 0
\(139\) −15.4853 −1.31344 −0.656722 0.754133i \(-0.728058\pi\)
−0.656722 + 0.754133i \(0.728058\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) 6.87868 11.9142i 0.575224 0.996317i
\(144\) 0 0
\(145\) −0.878680 1.52192i −0.0729704 0.126388i
\(146\) 0 0
\(147\) 6.74264 + 1.88064i 0.556124 + 0.155112i
\(148\) 0 0
\(149\) 6.00000 + 10.3923i 0.491539 + 0.851371i 0.999953 0.00974235i \(-0.00310113\pi\)
−0.508413 + 0.861113i \(0.669768\pi\)
\(150\) 0 0
\(151\) −11.2426 + 19.4728i −0.914913 + 1.58468i −0.107885 + 0.994163i \(0.534408\pi\)
−0.807028 + 0.590513i \(0.798926\pi\)
\(152\) 0 0
\(153\) 4.24264 0.342997
\(154\) 0 0
\(155\) 9.48528 0.761876
\(156\) 0 0
\(157\) 3.24264 5.61642i 0.258791 0.448239i −0.707127 0.707086i \(-0.750009\pi\)
0.965918 + 0.258847i \(0.0833426\pi\)
\(158\) 0 0
\(159\) −4.24264 7.34847i −0.336463 0.582772i
\(160\) 0 0
\(161\) 11.1213 + 1.52192i 0.876483 + 0.119944i
\(162\) 0 0
\(163\) −4.00000 6.92820i −0.313304 0.542659i 0.665771 0.746156i \(-0.268103\pi\)
−0.979076 + 0.203497i \(0.934769\pi\)
\(164\) 0 0
\(165\) −2.12132 + 3.67423i −0.165145 + 0.286039i
\(166\) 0 0
\(167\) 18.7279 1.44921 0.724605 0.689164i \(-0.242022\pi\)
0.724605 + 0.689164i \(0.242022\pi\)
\(168\) 0 0
\(169\) −2.48528 −0.191175
\(170\) 0 0
\(171\) 3.50000 6.06218i 0.267652 0.463586i
\(172\) 0 0
\(173\) 10.2426 + 17.7408i 0.778734 + 1.34881i 0.932672 + 0.360726i \(0.117471\pi\)
−0.153938 + 0.988080i \(0.549196\pi\)
\(174\) 0 0
\(175\) 1.00000 + 2.44949i 0.0755929 + 0.185164i
\(176\) 0 0
\(177\) 5.12132 + 8.87039i 0.384942 + 0.666739i
\(178\) 0 0
\(179\) 3.00000 5.19615i 0.224231 0.388379i −0.731858 0.681457i \(-0.761346\pi\)
0.956088 + 0.293079i \(0.0946798\pi\)
\(180\) 0 0
\(181\) −13.0000 −0.966282 −0.483141 0.875542i \(-0.660504\pi\)
−0.483141 + 0.875542i \(0.660504\pi\)
\(182\) 0 0
\(183\) 4.48528 0.331562
\(184\) 0 0
\(185\) 1.62132 2.80821i 0.119202 0.206464i
\(186\) 0 0
\(187\) 9.00000 + 15.5885i 0.658145 + 1.13994i
\(188\) 0 0
\(189\) 1.62132 2.09077i 0.117934 0.152081i
\(190\) 0 0
\(191\) −3.00000 5.19615i −0.217072 0.375980i 0.736839 0.676068i \(-0.236317\pi\)
−0.953912 + 0.300088i \(0.902984\pi\)
\(192\) 0 0
\(193\) −3.37868 + 5.85204i −0.243203 + 0.421239i −0.961625 0.274368i \(-0.911531\pi\)
0.718422 + 0.695607i \(0.244865\pi\)
\(194\) 0 0
\(195\) −3.24264 −0.232210
\(196\) 0 0
\(197\) −16.2426 −1.15724 −0.578620 0.815597i \(-0.696409\pi\)
−0.578620 + 0.815597i \(0.696409\pi\)
\(198\) 0 0
\(199\) −5.24264 + 9.08052i −0.371641 + 0.643701i −0.989818 0.142338i \(-0.954538\pi\)
0.618177 + 0.786039i \(0.287871\pi\)
\(200\) 0 0
\(201\) 2.62132 + 4.54026i 0.184894 + 0.320245i
\(202\) 0 0
\(203\) −2.84924 + 3.67423i −0.199978 + 0.257881i
\(204\) 0 0
\(205\) −2.12132 3.67423i −0.148159 0.256620i
\(206\) 0 0
\(207\) 2.12132 3.67423i 0.147442 0.255377i
\(208\) 0 0
\(209\) 29.6985 2.05429
\(210\) 0 0
\(211\) 22.4853 1.54795 0.773975 0.633216i \(-0.218265\pi\)
0.773975 + 0.633216i \(0.218265\pi\)
\(212\) 0 0
\(213\) 6.36396 11.0227i 0.436051 0.755263i
\(214\) 0 0
\(215\) 1.62132 + 2.80821i 0.110573 + 0.191518i
\(216\) 0 0
\(217\) −9.48528 23.2341i −0.643903 1.57723i
\(218\) 0 0
\(219\) −4.62132 8.00436i −0.312280 0.540885i
\(220\) 0 0
\(221\) −6.87868 + 11.9142i −0.462710 + 0.801437i
\(222\) 0 0
\(223\) −7.51472 −0.503223 −0.251611 0.967828i \(-0.580960\pi\)
−0.251611 + 0.967828i \(0.580960\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) 7.60660 13.1750i 0.504868 0.874457i −0.495116 0.868827i \(-0.664875\pi\)
0.999984 0.00563010i \(-0.00179213\pi\)
\(228\) 0 0
\(229\) 3.50000 + 6.06218i 0.231287 + 0.400600i 0.958187 0.286143i \(-0.0923732\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) 0 0
\(231\) 11.1213 + 1.52192i 0.731729 + 0.100135i
\(232\) 0 0
\(233\) −7.24264 12.5446i −0.474481 0.821825i 0.525092 0.851046i \(-0.324031\pi\)
−0.999573 + 0.0292201i \(0.990698\pi\)
\(234\) 0 0
\(235\) −3.00000 + 5.19615i −0.195698 + 0.338960i
\(236\) 0 0
\(237\) 11.0000 0.714527
\(238\) 0 0
\(239\) 10.9706 0.709627 0.354813 0.934937i \(-0.384544\pi\)
0.354813 + 0.934937i \(0.384544\pi\)
\(240\) 0 0
\(241\) 2.00000 3.46410i 0.128831 0.223142i −0.794393 0.607404i \(-0.792211\pi\)
0.923224 + 0.384262i \(0.125544\pi\)
\(242\) 0 0
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) 0 0
\(245\) 5.00000 4.89898i 0.319438 0.312984i
\(246\) 0 0
\(247\) 11.3492 + 19.6575i 0.722135 + 1.25077i
\(248\) 0 0
\(249\) 5.12132 8.87039i 0.324550 0.562138i
\(250\) 0 0
\(251\) −18.7279 −1.18210 −0.591048 0.806636i \(-0.701286\pi\)
−0.591048 + 0.806636i \(0.701286\pi\)
\(252\) 0 0
\(253\) 18.0000 1.13165
\(254\) 0 0
\(255\) 2.12132 3.67423i 0.132842 0.230089i
\(256\) 0 0
\(257\) −5.12132 8.87039i −0.319459 0.553320i 0.660916 0.750460i \(-0.270168\pi\)
−0.980375 + 0.197140i \(0.936835\pi\)
\(258\) 0 0
\(259\) −8.50000 1.16320i −0.528164 0.0722776i
\(260\) 0 0
\(261\) 0.878680 + 1.52192i 0.0543889 + 0.0942043i
\(262\) 0 0
\(263\) 4.24264 7.34847i 0.261612 0.453126i −0.705058 0.709150i \(-0.749079\pi\)
0.966671 + 0.256023i \(0.0824124\pi\)
\(264\) 0 0
\(265\) −8.48528 −0.521247
\(266\) 0 0
\(267\) −10.2426 −0.626839
\(268\) 0 0
\(269\) 1.24264 2.15232i 0.0757651 0.131229i −0.825654 0.564177i \(-0.809193\pi\)
0.901419 + 0.432948i \(0.142527\pi\)
\(270\) 0 0
\(271\) 11.7279 + 20.3134i 0.712421 + 1.23395i 0.963946 + 0.266098i \(0.0857344\pi\)
−0.251525 + 0.967851i \(0.580932\pi\)
\(272\) 0 0
\(273\) 3.24264 + 7.94282i 0.196254 + 0.480721i
\(274\) 0 0
\(275\) 2.12132 + 3.67423i 0.127920 + 0.221565i
\(276\) 0 0
\(277\) −8.86396 + 15.3528i −0.532584 + 0.922462i 0.466692 + 0.884420i \(0.345446\pi\)
−0.999276 + 0.0380425i \(0.987888\pi\)
\(278\) 0 0
\(279\) −9.48528 −0.567869
\(280\) 0 0
\(281\) 28.9706 1.72824 0.864119 0.503287i \(-0.167876\pi\)
0.864119 + 0.503287i \(0.167876\pi\)
\(282\) 0 0
\(283\) −11.8640 + 20.5490i −0.705239 + 1.22151i 0.261366 + 0.965240i \(0.415827\pi\)
−0.966605 + 0.256270i \(0.917506\pi\)
\(284\) 0 0
\(285\) −3.50000 6.06218i −0.207322 0.359092i
\(286\) 0 0
\(287\) −6.87868 + 8.87039i −0.406036 + 0.523602i
\(288\) 0 0
\(289\) −0.500000 0.866025i −0.0294118 0.0509427i
\(290\) 0 0
\(291\) 0.242641 0.420266i 0.0142238 0.0246364i
\(292\) 0 0
\(293\) −4.97056 −0.290383 −0.145192 0.989404i \(-0.546380\pi\)
−0.145192 + 0.989404i \(0.546380\pi\)
\(294\) 0 0
\(295\) 10.2426 0.596350
\(296\) 0 0
\(297\) 2.12132 3.67423i 0.123091 0.213201i
\(298\) 0 0
\(299\) 6.87868 + 11.9142i 0.397804 + 0.689017i
\(300\) 0 0
\(301\) 5.25736 6.77962i 0.303029 0.390771i
\(302\) 0 0
\(303\) 3.87868 + 6.71807i 0.222824 + 0.385943i
\(304\) 0 0
\(305\) 2.24264 3.88437i 0.128413 0.222418i
\(306\) 0 0
\(307\) 3.24264 0.185067 0.0925336 0.995710i \(-0.470503\pi\)
0.0925336 + 0.995710i \(0.470503\pi\)
\(308\) 0 0
\(309\) −17.2426 −0.980900
\(310\) 0 0
\(311\) −10.6066 + 18.3712i −0.601445 + 1.04173i 0.391157 + 0.920324i \(0.372075\pi\)
−0.992602 + 0.121410i \(0.961258\pi\)
\(312\) 0 0
\(313\) −11.8640 20.5490i −0.670591 1.16150i −0.977737 0.209835i \(-0.932707\pi\)
0.307146 0.951662i \(-0.400626\pi\)
\(314\) 0 0
\(315\) −1.00000 2.44949i −0.0563436 0.138013i
\(316\) 0 0
\(317\) 12.3640 + 21.4150i 0.694429 + 1.20279i 0.970373 + 0.241613i \(0.0776764\pi\)
−0.275943 + 0.961174i \(0.588990\pi\)
\(318\) 0 0
\(319\) −3.72792 + 6.45695i −0.208724 + 0.361520i
\(320\) 0 0
\(321\) 12.7279 0.710403
\(322\) 0 0
\(323\) −29.6985 −1.65247
\(324\) 0 0
\(325\) −1.62132 + 2.80821i −0.0899347 + 0.155771i
\(326\) 0 0
\(327\) 4.74264 + 8.21449i 0.262269 + 0.454263i
\(328\) 0 0
\(329\) 15.7279 + 2.15232i 0.867108 + 0.118661i
\(330\) 0 0
\(331\) −8.50000 14.7224i −0.467202 0.809218i 0.532096 0.846684i \(-0.321405\pi\)
−0.999298 + 0.0374662i \(0.988071\pi\)
\(332\) 0 0
\(333\) −1.62132 + 2.80821i −0.0888478 + 0.153889i
\(334\) 0 0
\(335\) 5.24264 0.286436
\(336\) 0 0
\(337\) −13.7279 −0.747808 −0.373904 0.927467i \(-0.621981\pi\)
−0.373904 + 0.927467i \(0.621981\pi\)
\(338\) 0 0
\(339\) 9.00000 15.5885i 0.488813 0.846649i
\(340\) 0 0
\(341\) −20.1213 34.8511i −1.08963 1.88730i
\(342\) 0 0
\(343\) −17.0000 7.34847i −0.917914 0.396780i
\(344\) 0 0
\(345\) −2.12132 3.67423i −0.114208 0.197814i
\(346\) 0 0
\(347\) 12.0000 20.7846i 0.644194 1.11578i −0.340293 0.940319i \(-0.610526\pi\)
0.984487 0.175457i \(-0.0561403\pi\)
\(348\) 0 0
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 0 0
\(351\) 3.24264 0.173079
\(352\) 0 0
\(353\) 5.12132 8.87039i 0.272580 0.472123i −0.696941 0.717128i \(-0.745456\pi\)
0.969522 + 0.245005i \(0.0787896\pi\)
\(354\) 0 0
\(355\) −6.36396 11.0227i −0.337764 0.585024i
\(356\) 0 0
\(357\) −11.1213 1.52192i −0.588603 0.0805484i
\(358\) 0 0
\(359\) −0.878680 1.52192i −0.0463749 0.0803237i 0.841906 0.539624i \(-0.181434\pi\)
−0.888281 + 0.459300i \(0.848100\pi\)
\(360\) 0 0
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) 0 0
\(363\) 7.00000 0.367405
\(364\) 0 0
\(365\) −9.24264 −0.483782
\(366\) 0 0
\(367\) −17.8640 + 30.9413i −0.932491 + 1.61512i −0.153443 + 0.988157i \(0.549036\pi\)
−0.779048 + 0.626965i \(0.784297\pi\)
\(368\) 0 0
\(369\) 2.12132 + 3.67423i 0.110432 + 0.191273i
\(370\) 0 0
\(371\) 8.48528 + 20.7846i 0.440534 + 1.07908i
\(372\) 0 0
\(373\) −8.86396 15.3528i −0.458959 0.794939i 0.539948 0.841699i \(-0.318444\pi\)
−0.998906 + 0.0467591i \(0.985111\pi\)
\(374\) 0 0
\(375\) 0.500000 0.866025i 0.0258199 0.0447214i
\(376\) 0 0
\(377\) −5.69848 −0.293487
\(378\) 0 0
\(379\) −20.4558 −1.05075 −0.525373 0.850872i \(-0.676074\pi\)
−0.525373 + 0.850872i \(0.676074\pi\)
\(380\) 0 0
\(381\) 1.37868 2.38794i 0.0706319 0.122338i
\(382\) 0 0
\(383\) −12.7279 22.0454i −0.650366 1.12647i −0.983034 0.183424i \(-0.941282\pi\)
0.332668 0.943044i \(-0.392051\pi\)
\(384\) 0 0
\(385\) 6.87868 8.87039i 0.350570 0.452077i
\(386\) 0 0
\(387\) −1.62132 2.80821i −0.0824163 0.142749i
\(388\) 0 0
\(389\) 10.6066 18.3712i 0.537776 0.931455i −0.461247 0.887272i \(-0.652598\pi\)
0.999023 0.0441839i \(-0.0140687\pi\)
\(390\) 0 0
\(391\) −18.0000 −0.910299
\(392\) 0 0
\(393\) 14.4853 0.730686
\(394\) 0 0
\(395\) 5.50000 9.52628i 0.276735 0.479319i
\(396\) 0 0
\(397\) 4.37868 + 7.58410i 0.219760 + 0.380635i 0.954734 0.297460i \(-0.0961394\pi\)
−0.734975 + 0.678094i \(0.762806\pi\)
\(398\) 0 0
\(399\) −11.3492 + 14.6354i −0.568173 + 0.732686i
\(400\) 0 0
\(401\) 1.75736 + 3.04384i 0.0877583 + 0.152002i 0.906563 0.422070i \(-0.138696\pi\)
−0.818805 + 0.574072i \(0.805363\pi\)
\(402\) 0 0
\(403\) 15.3787 26.6367i 0.766067 1.32687i
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) −13.7574 −0.681927
\(408\) 0 0
\(409\) −8.50000 + 14.7224i −0.420298 + 0.727977i −0.995968 0.0897044i \(-0.971408\pi\)
0.575670 + 0.817682i \(0.304741\pi\)
\(410\) 0 0
\(411\) −2.12132 3.67423i −0.104637 0.181237i
\(412\) 0 0
\(413\) −10.2426 25.0892i −0.504007 1.23456i
\(414\) 0 0
\(415\) −5.12132 8.87039i −0.251396 0.435430i
\(416\) 0 0
\(417\) 7.74264 13.4106i 0.379159 0.656722i
\(418\) 0 0
\(419\) −14.4853 −0.707652 −0.353826 0.935311i \(-0.615120\pi\)
−0.353826 + 0.935311i \(0.615120\pi\)
\(420\) 0 0
\(421\) 31.4853 1.53450 0.767249 0.641349i \(-0.221625\pi\)
0.767249 + 0.641349i \(0.221625\pi\)
\(422\) 0 0
\(423\) 3.00000 5.19615i 0.145865 0.252646i
\(424\) 0 0
\(425\) −2.12132 3.67423i −0.102899 0.178227i
\(426\) 0 0
\(427\) −11.7574 1.60896i −0.568978 0.0778629i
\(428\) 0 0
\(429\) 6.87868 + 11.9142i 0.332106 + 0.575224i
\(430\) 0 0
\(431\) −9.72792 + 16.8493i −0.468578 + 0.811600i −0.999355 0.0359112i \(-0.988567\pi\)
0.530777 + 0.847511i \(0.321900\pi\)
\(432\) 0 0
\(433\) 33.2426 1.59754 0.798770 0.601637i \(-0.205485\pi\)
0.798770 + 0.601637i \(0.205485\pi\)
\(434\) 0 0
\(435\) 1.75736 0.0842589
\(436\) 0 0
\(437\) −14.8492 + 25.7196i −0.710336 + 1.23034i
\(438\) 0 0
\(439\) 5.00000 + 8.66025i 0.238637 + 0.413331i 0.960323 0.278889i \(-0.0899661\pi\)
−0.721686 + 0.692220i \(0.756633\pi\)
\(440\) 0 0
\(441\) −5.00000 + 4.89898i −0.238095 + 0.233285i
\(442\) 0 0
\(443\) −10.2426 17.7408i −0.486643 0.842890i 0.513240 0.858245i \(-0.328445\pi\)
−0.999882 + 0.0153558i \(0.995112\pi\)
\(444\) 0 0
\(445\) −5.12132 + 8.87039i −0.242774 + 0.420497i
\(446\) 0 0
\(447\) −12.0000 −0.567581
\(448\) 0 0
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 0 0
\(451\) −9.00000 + 15.5885i −0.423793 + 0.734032i
\(452\) 0 0
\(453\) −11.2426 19.4728i −0.528225 0.914913i
\(454\) 0 0
\(455\) 8.50000 + 1.16320i 0.398486 + 0.0545316i
\(456\) 0 0
\(457\) −16.1066 27.8975i −0.753435 1.30499i −0.946149 0.323733i \(-0.895062\pi\)
0.192714 0.981255i \(-0.438271\pi\)
\(458\) 0 0
\(459\) −2.12132 + 3.67423i −0.0990148 + 0.171499i
\(460\) 0 0
\(461\) 18.7279 0.872246 0.436123 0.899887i \(-0.356351\pi\)
0.436123 + 0.899887i \(0.356351\pi\)
\(462\) 0 0
\(463\) 10.2721 0.477384 0.238692 0.971095i \(-0.423281\pi\)
0.238692 + 0.971095i \(0.423281\pi\)
\(464\) 0 0
\(465\) −4.74264 + 8.21449i −0.219935 + 0.380938i
\(466\) 0 0
\(467\) 5.48528 + 9.50079i 0.253829 + 0.439644i 0.964577 0.263803i \(-0.0849768\pi\)
−0.710748 + 0.703447i \(0.751643\pi\)
\(468\) 0 0
\(469\) −5.24264 12.8418i −0.242083 0.592979i
\(470\) 0 0
\(471\) 3.24264 + 5.61642i 0.149413 + 0.258791i
\(472\) 0 0
\(473\) 6.87868 11.9142i 0.316282 0.547817i
\(474\) 0 0
\(475\) −7.00000 −0.321182
\(476\) 0 0
\(477\) 8.48528 0.388514
\(478\) 0 0
\(479\) −6.00000 + 10.3923i −0.274147 + 0.474837i −0.969920 0.243426i \(-0.921729\pi\)
0.695773 + 0.718262i \(0.255062\pi\)
\(480\) 0 0
\(481\) −5.25736 9.10601i −0.239715 0.415198i
\(482\) 0 0
\(483\) −6.87868 + 8.87039i −0.312991 + 0.403617i
\(484\) 0 0
\(485\) −0.242641 0.420266i −0.0110177 0.0190833i
\(486\) 0 0
\(487\) 18.8640 32.6733i 0.854808 1.48057i −0.0220157 0.999758i \(-0.507008\pi\)
0.876823 0.480813i \(-0.159658\pi\)
\(488\) 0 0
\(489\) 8.00000 0.361773
\(490\) 0 0
\(491\) 15.5147 0.700169 0.350085 0.936718i \(-0.386153\pi\)
0.350085 + 0.936718i \(0.386153\pi\)
\(492\) 0 0
\(493\) 3.72792 6.45695i 0.167897 0.290806i
\(494\) 0 0
\(495\) −2.12132 3.67423i −0.0953463 0.165145i
\(496\) 0 0
\(497\) −20.6360 + 26.6112i −0.925653 + 1.19367i
\(498\) 0 0
\(499\) −9.74264 16.8747i −0.436140 0.755417i 0.561247 0.827648i \(-0.310322\pi\)
−0.997388 + 0.0722305i \(0.976988\pi\)
\(500\) 0 0
\(501\) −9.36396 + 16.2189i −0.418351 + 0.724605i
\(502\) 0 0
\(503\) −26.4853 −1.18092 −0.590460 0.807067i \(-0.701054\pi\)
−0.590460 + 0.807067i \(0.701054\pi\)
\(504\) 0 0
\(505\) 7.75736 0.345198
\(506\) 0 0
\(507\) 1.24264 2.15232i 0.0551876 0.0955877i
\(508\) 0 0
\(509\) 9.72792 + 16.8493i 0.431183 + 0.746830i 0.996975 0.0777173i \(-0.0247632\pi\)
−0.565793 + 0.824547i \(0.691430\pi\)
\(510\) 0 0
\(511\) 9.24264 + 22.6398i 0.408870 + 1.00152i
\(512\) 0 0
\(513\) 3.50000 + 6.06218i 0.154529 + 0.267652i
\(514\) 0 0
\(515\) −8.62132 + 14.9326i −0.379901 + 0.658007i
\(516\) 0 0
\(517\) 25.4558 1.11955
\(518\) 0 0
\(519\) −20.4853 −0.899204
\(520\) 0 0
\(521\) 6.72792 11.6531i 0.294756 0.510532i −0.680172 0.733052i \(-0.738095\pi\)
0.974928 + 0.222520i \(0.0714284\pi\)
\(522\) 0 0
\(523\) 2.62132 + 4.54026i 0.114622 + 0.198532i 0.917629 0.397439i \(-0.130101\pi\)
−0.803006 + 0.595970i \(0.796768\pi\)
\(524\) 0 0
\(525\) −2.62132 0.358719i −0.114404 0.0156558i
\(526\) 0 0
\(527\) 20.1213 + 34.8511i 0.876498 + 1.51814i
\(528\) 0 0
\(529\) 2.50000 4.33013i 0.108696 0.188266i
\(530\) 0 0
\(531\) −10.2426 −0.444493
\(532\) 0 0
\(533\) −13.7574 −0.595897
\(534\) 0 0
\(535\) 6.36396 11.0227i 0.275138 0.476553i
\(536\) 0 0
\(537\) 3.00000 + 5.19615i 0.129460 + 0.224231i
\(538\) 0 0
\(539\) −28.6066 7.97887i −1.23217 0.343674i
\(540\) 0 0
\(541\) 20.4706 + 35.4561i 0.880098 + 1.52437i 0.851231 + 0.524792i \(0.175857\pi\)
0.0288675 + 0.999583i \(0.490810\pi\)
\(542\) 0 0
\(543\) 6.50000 11.2583i 0.278942 0.483141i
\(544\) 0 0
\(545\) 9.48528 0.406305
\(546\) 0 0
\(547\) 33.4558 1.43047 0.715234 0.698885i \(-0.246320\pi\)
0.715234 + 0.698885i \(0.246320\pi\)
\(548\) 0 0
\(549\) −2.24264 + 3.88437i −0.0957136 + 0.165781i
\(550\) 0 0
\(551\) −6.15076 10.6534i −0.262031 0.453851i
\(552\) 0 0
\(553\) −28.8345 3.94591i −1.22617 0.167797i
\(554\) 0 0
\(555\) 1.62132 + 2.80821i 0.0688212 + 0.119202i
\(556\) 0 0
\(557\) 15.0000 25.9808i 0.635570 1.10084i −0.350824 0.936442i \(-0.614098\pi\)
0.986394 0.164399i \(-0.0525683\pi\)
\(558\) 0 0
\(559\) 10.5147 0.444725
\(560\) 0 0
\(561\) −18.0000 −0.759961
\(562\) 0 0
\(563\) 3.00000 5.19615i 0.126435 0.218992i −0.795858 0.605483i \(-0.792980\pi\)
0.922293 + 0.386492i \(0.126313\pi\)
\(564\) 0 0
\(565\) −9.00000 15.5885i −0.378633 0.655811i
\(566\) 0 0
\(567\) 1.00000 + 2.44949i 0.0419961 + 0.102869i
\(568\) 0 0
\(569\) 20.8492 + 36.1119i 0.874046 + 1.51389i 0.857776 + 0.514024i \(0.171846\pi\)
0.0162699 + 0.999868i \(0.494821\pi\)
\(570\) 0 0
\(571\) 14.4706 25.0637i 0.605574 1.04889i −0.386386 0.922337i \(-0.626277\pi\)
0.991960 0.126548i \(-0.0403898\pi\)
\(572\) 0 0
\(573\) 6.00000 0.250654
\(574\) 0 0
\(575\) −4.24264 −0.176930
\(576\) 0 0
\(577\) −6.37868 + 11.0482i −0.265548 + 0.459942i −0.967707 0.252078i \(-0.918886\pi\)
0.702159 + 0.712020i \(0.252220\pi\)
\(578\) 0 0
\(579\) −3.37868 5.85204i −0.140413 0.243203i
\(580\) 0 0
\(581\) −16.6066 + 21.4150i −0.688958 + 0.888444i
\(582\) 0 0
\(583\) 18.0000 + 31.1769i 0.745484 + 1.29122i
\(584\) 0 0
\(585\) 1.62132 2.80821i 0.0670333 0.116105i
\(586\) 0 0
\(587\) 45.2132 1.86615 0.933074 0.359684i \(-0.117115\pi\)
0.933074 + 0.359684i \(0.117115\pi\)
\(588\) 0 0
\(589\) 66.3970 2.73584
\(590\) 0 0
\(591\) 8.12132 14.0665i 0.334066 0.578620i
\(592\) 0 0
\(593\) −1.60660 2.78272i −0.0659752 0.114272i 0.831151 0.556047i \(-0.187682\pi\)
−0.897126 + 0.441774i \(0.854349\pi\)
\(594\) 0 0
\(595\) −6.87868 + 8.87039i −0.281998 + 0.363650i
\(596\) 0 0
\(597\) −5.24264 9.08052i −0.214567 0.371641i
\(598\) 0 0
\(599\) 16.2426 28.1331i 0.663656 1.14949i −0.315991 0.948762i \(-0.602337\pi\)
0.979648 0.200724i \(-0.0643296\pi\)
\(600\) 0 0
\(601\) −3.48528 −0.142168 −0.0710838 0.997470i \(-0.522646\pi\)
−0.0710838 + 0.997470i \(0.522646\pi\)
\(602\) 0 0
\(603\) −5.24264 −0.213497
\(604\) 0 0
\(605\) 3.50000 6.06218i 0.142295 0.246463i
\(606\) 0 0
\(607\) 14.6213 + 25.3249i 0.593461 + 1.02790i 0.993762 + 0.111521i \(0.0355722\pi\)
−0.400301 + 0.916384i \(0.631094\pi\)
\(608\) 0 0
\(609\) −1.75736 4.30463i −0.0712118 0.174433i
\(610\) 0 0
\(611\) 9.72792 + 16.8493i 0.393550 + 0.681648i
\(612\) 0 0
\(613\) 2.72792 4.72490i 0.110180 0.190837i −0.805663 0.592374i \(-0.798191\pi\)
0.915843 + 0.401537i \(0.131524\pi\)
\(614\) 0 0
\(615\) 4.24264 0.171080
\(616\) 0 0
\(617\) −26.4853 −1.06626 −0.533129 0.846034i \(-0.678984\pi\)
−0.533129 + 0.846034i \(0.678984\pi\)
\(618\) 0 0
\(619\) 5.98528 10.3668i 0.240569 0.416677i −0.720308 0.693655i \(-0.755999\pi\)
0.960876 + 0.276977i \(0.0893327\pi\)
\(620\) 0 0
\(621\) 2.12132 + 3.67423i 0.0851257 + 0.147442i
\(622\) 0 0
\(623\) 26.8492 + 3.67423i 1.07569 + 0.147205i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) −14.8492 + 25.7196i −0.593022 + 1.02714i
\(628\) 0 0
\(629\) 13.7574 0.548542
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 0 0
\(633\) −11.2426 + 19.4728i −0.446855 + 0.773975i
\(634\) 0 0
\(635\) −1.37868 2.38794i −0.0547112 0.0947626i
\(636\) 0 0
\(637\) −5.65076 21.9839i −0.223891 0.871032i
\(638\) 0 0
\(639\) 6.36396 + 11.0227i 0.251754 + 0.436051i
\(640\) 0 0
\(641\) −17.1213 + 29.6550i −0.676251 + 1.17130i 0.299850 + 0.953986i \(0.403063\pi\)
−0.976101 + 0.217316i \(0.930270\pi\)
\(642\) 0 0
\(643\) −19.7279 −0.777993 −0.388997 0.921239i \(-0.627178\pi\)
−0.388997 + 0.921239i \(0.627178\pi\)
\(644\) 0 0
\(645\) −3.24264 −0.127679
\(646\) 0 0
\(647\) −5.12132 + 8.87039i −0.201340 + 0.348731i −0.948960 0.315395i \(-0.897863\pi\)
0.747621 + 0.664126i \(0.231196\pi\)
\(648\) 0 0
\(649\) −21.7279 37.6339i −0.852896 1.47726i
\(650\) 0 0
\(651\) 24.8640 + 3.40256i 0.974495 + 0.133357i
\(652\) 0 0
\(653\) −5.12132 8.87039i −0.200413 0.347125i 0.748249 0.663418i \(-0.230895\pi\)
−0.948661 + 0.316293i \(0.897562\pi\)
\(654\) 0 0
\(655\) 7.24264 12.5446i 0.282993 0.490159i
\(656\) 0 0
\(657\) 9.24264 0.360590
\(658\) 0 0
\(659\) 40.9706 1.59599 0.797993 0.602666i \(-0.205895\pi\)
0.797993 + 0.602666i \(0.205895\pi\)
\(660\) 0 0
\(661\) 1.01472 1.75754i 0.0394680 0.0683605i −0.845617 0.533791i \(-0.820767\pi\)
0.885085 + 0.465430i \(0.154100\pi\)
\(662\) 0 0
\(663\) −6.87868 11.9142i −0.267146 0.462710i
\(664\) 0 0
\(665\) 7.00000 + 17.1464i 0.271448 + 0.664910i
\(666\) 0 0
\(667\) −3.72792 6.45695i −0.144346 0.250014i
\(668\) 0 0
\(669\) 3.75736 6.50794i 0.145268 0.251611i
\(670\) 0 0
\(671\) −19.0294 −0.734623
\(672\) 0 0
\(673\) 29.7279 1.14593 0.572964 0.819581i \(-0.305794\pi\)
0.572964 + 0.819581i \(0.305794\pi\)
\(674\) 0 0
\(675\) −0.500000 + 0.866025i −0.0192450 + 0.0333333i
\(676\) 0 0
\(677\) −6.36396 11.0227i −0.244587 0.423637i 0.717428 0.696632i \(-0.245319\pi\)
−0.962015 + 0.272995i \(0.911986\pi\)
\(678\) 0 0
\(679\) −0.786797 + 1.01461i −0.0301945 + 0.0389372i
\(680\) 0 0
\(681\) 7.60660 + 13.1750i 0.291486 + 0.504868i
\(682\) 0 0
\(683\) −16.6066 + 28.7635i −0.635434 + 1.10060i 0.350989 + 0.936380i \(0.385845\pi\)
−0.986423 + 0.164224i \(0.947488\pi\)
\(684\) 0 0
\(685\) −4.24264 −0.162103
\(686\) 0 0
\(687\) −7.00000 −0.267067
\(688\) 0 0
\(689\) −13.7574 + 23.8284i −0.524114 + 0.907791i
\(690\) 0 0
\(691\) −13.4706 23.3317i −0.512444 0.887580i −0.999896 0.0144296i \(-0.995407\pi\)
0.487452 0.873150i \(-0.337927\pi\)
\(692\) 0 0
\(693\) −6.87868 + 8.87039i −0.261299 + 0.336958i
\(694\) 0 0
\(695\) −7.74264 13.4106i −0.293695 0.508695i
\(696\) 0 0
\(697\) 9.00000 15.5885i 0.340899 0.590455i
\(698\) 0 0
\(699\) 14.4853 0.547884
\(700\) 0 0
\(701\) 8.78680 0.331873 0.165936 0.986136i \(-0.446935\pi\)
0.165936 + 0.986136i \(0.446935\pi\)
\(702\) 0 0
\(703\) 11.3492 19.6575i 0.428045 0.741395i
\(704\) 0 0
\(705\) −3.00000 5.19615i −0.112987 0.195698i
\(706\) 0 0
\(707\) −7.75736 19.0016i −0.291746 0.714628i
\(708\) 0 0
\(709\) 18.2426 + 31.5972i 0.685117 + 1.18666i 0.973400 + 0.229112i \(0.0735822\pi\)
−0.288283 + 0.957545i \(0.593085\pi\)
\(710\) 0 0
\(711\) −5.50000 + 9.52628i −0.206266 + 0.357263i
\(712\) 0 0
\(713\) 40.2426 1.50710
\(714\) 0 0
\(715\) 13.7574 0.514496
\(716\) 0 0
\(717\) −5.48528 + 9.50079i −0.204852 + 0.354813i
\(718\) 0 0
\(719\) −13.2426 22.9369i −0.493867 0.855403i 0.506108 0.862470i \(-0.331084\pi\)
−0.999975 + 0.00706717i \(0.997750\pi\)
\(720\) 0 0
\(721\) 45.1985 + 6.18527i 1.68328 + 0.230352i
\(722\) 0 0
\(723\) 2.00000 + 3.46410i 0.0743808 + 0.128831i
\(724\) 0 0
\(725\) 0.878680 1.52192i 0.0326333 0.0565226i
\(726\) 0 0
\(727\) 0.757359 0.0280889 0.0140445 0.999901i \(-0.495529\pi\)
0.0140445 + 0.999901i \(0.495529\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −6.87868 + 11.9142i −0.254417 + 0.440663i
\(732\) 0 0
\(733\) −0.893398 1.54741i −0.0329984 0.0571549i 0.849055 0.528305i \(-0.177172\pi\)
−0.882053 + 0.471150i \(0.843839\pi\)
\(734\) 0 0
\(735\) 1.74264 + 6.77962i 0.0642783 + 0.250070i
\(736\) 0 0
\(737\) −11.1213 19.2627i −0.409659 0.709550i
\(738\) 0 0
\(739\) 7.74264 13.4106i 0.284818 0.493319i −0.687747 0.725950i \(-0.741400\pi\)
0.972565 + 0.232632i \(0.0747336\pi\)
\(740\) 0 0
\(741\) −22.6985 −0.833850
\(742\) 0 0
\(743\) 15.2132 0.558118 0.279059 0.960274i \(-0.409977\pi\)
0.279059 + 0.960274i \(0.409977\pi\)
\(744\) 0 0
\(745\) −6.00000 + 10.3923i −0.219823 + 0.380745i
\(746\) 0 0
\(747\) 5.12132 + 8.87039i 0.187379 + 0.324550i
\(748\) 0 0
\(749\) −33.3640 4.56575i −1.21909 0.166829i
\(750\) 0 0
\(751\) −22.4706 38.9202i −0.819962 1.42022i −0.905709 0.423900i \(-0.860661\pi\)
0.0857467 0.996317i \(-0.472672\pi\)
\(752\) 0 0
\(753\) 9.36396 16.2189i 0.341242 0.591048i
\(754\) 0 0
\(755\) −22.4853 −0.818323
\(756\) 0 0
\(757\) 9.02944 0.328180 0.164090 0.986445i \(-0.447531\pi\)
0.164090 + 0.986445i \(0.447531\pi\)
\(758\) 0 0
\(759\) −9.00000 + 15.5885i −0.326679 + 0.565825i
\(760\) 0 0
\(761\) −23.1213 40.0473i −0.838147 1.45171i −0.891442 0.453135i \(-0.850306\pi\)
0.0532948 0.998579i \(-0.483028\pi\)
\(762\) 0 0
\(763\) −9.48528 23.2341i −0.343390 0.841131i
\(764\) 0 0
\(765\) 2.12132 + 3.67423i 0.0766965 + 0.132842i
\(766\) 0 0
\(767\) 16.6066 28.7635i 0.599630 1.03859i
\(768\) 0 0
\(769\) 5.00000 0.180305 0.0901523 0.995928i \(-0.471265\pi\)
0.0901523 + 0.995928i \(0.471265\pi\)
\(770\) 0 0
\(771\) 10.2426 0.368880
\(772\) 0 0
\(773\) −5.84924 + 10.1312i −0.210383 + 0.364393i −0.951834 0.306613i \(-0.900804\pi\)
0.741452 + 0.671006i \(0.234138\pi\)
\(774\) 0 0
\(775\) 4.74264 + 8.21449i 0.170361 + 0.295073i
\(776\) 0 0
\(777\) 5.25736 6.77962i 0.188607 0.243217i
\(778\) 0 0
\(779\) −14.8492 25.7196i −0.532029 0.921502i
\(780\) 0 0
\(781\) −27.0000 + 46.7654i −0.966136 + 1.67340i
\(782\) 0 0
\(783\) −1.75736 −0.0628029
\(784\) 0 0
\(785\) 6.48528 0.231470
\(786\) 0 0
\(787\) −14.2426 + 24.6690i −0.507695 + 0.879354i 0.492265 + 0.870445i \(0.336169\pi\)
−0.999960 + 0.00890869i \(0.997164\pi\)
\(788\) 0 0
\(789\) 4.24264 + 7.34847i 0.151042 + 0.261612i
\(790\) 0 0
\(791\) −29.1838 + 37.6339i −1.03766 + 1.33811i
\(792\) 0 0
\(793\) −7.27208 12.5956i −0.258239 0.447283i
\(794\) 0 0
\(795\) 4.24264 7.34847i 0.150471 0.260623i
\(796\) 0 0