Properties

Label 420.2.q.d.121.2
Level $420$
Weight $2$
Character 420.121
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: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
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 121.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 420.121
Dual form 420.2.q.d.361.2

$q$-expansion

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

Character values

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

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

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 0.985520 + 0.169559i \(0.0542342\pi\)
−0.345918 + 0.938265i \(0.612432\pi\)
\(12\) 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 −0.999859 0.0168199i \(-0.994646\pi\)
0.485363 0.874313i \(-0.338688\pi\)
\(18\) 0 0
\(19\) 3.50000 6.06218i 0.802955 1.39076i −0.114708 0.993399i \(-0.536593\pi\)
0.917663 0.397360i \(-0.130073\pi\)
\(20\) 0 0
\(21\) 1.00000 2.44949i 0.218218 0.534522i
\(22\) 0 0
\(23\) 2.12132 3.67423i 0.442326 0.766131i −0.555536 0.831493i \(-0.687487\pi\)
0.997862 + 0.0653618i \(0.0208201\pi\)
\(24\) 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 0.879579 + 0.475753i \(0.157824\pi\)
−0.0277757 + 0.999614i \(0.508842\pi\)
\(32\) 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 −0.967967 0.251078i \(-0.919215\pi\)
0.701423 + 0.712745i \(0.252548\pi\)
\(38\) 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 −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 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 −0.995149 0.0983769i \(-0.968635\pi\)
0.412378 0.911013i \(-0.364698\pi\)
\(54\) 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 0.978811 + 0.204767i \(0.0656438\pi\)
−0.312072 + 0.950059i \(0.601023\pi\)
\(60\) 0 0
\(61\) −2.24264 + 3.88437i −0.287141 + 0.497342i −0.973126 0.230273i \(-0.926038\pi\)
0.685985 + 0.727615i \(0.259371\pi\)
\(62\) 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 0.980539 0.196327i \(-0.0629013\pi\)
−0.660293 + 0.751008i \(0.729568\pi\)
\(68\) 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 −0.998854 0.0478714i \(-0.984756\pi\)
0.457969 0.888968i \(-0.348577\pi\)
\(74\) 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 0.370907 + 0.928670i \(0.379047\pi\)
−0.989705 + 0.143120i \(0.954286\pi\)
\(80\) 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 −0.455879 0.890042i \(-0.650675\pi\)
0.998738 0.0502176i \(-0.0159915\pi\)
\(90\) 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 0.991900 0.127025i \(-0.0405428\pi\)
−0.605956 + 0.795498i \(0.707209\pi\)
\(102\) 0 0
\(103\) 8.62132 14.9326i 0.849484 1.47135i −0.0321856 0.999482i \(-0.510247\pi\)
0.881670 0.471867i \(-0.156420\pi\)
\(104\) 0 0
\(105\) −1.62132 2.09077i −0.158225 0.204038i
\(106\) 0 0
\(107\) −6.36396 + 11.0227i −0.615227 + 1.06561i 0.375117 + 0.926977i \(0.377602\pi\)
−0.990345 + 0.138628i \(0.955731\pi\)
\(108\) 0 0
\(109\) 4.74264 + 8.21449i 0.454263 + 0.786806i 0.998645 0.0520310i \(-0.0165695\pi\)
−0.544383 + 0.838837i \(0.683236\pi\)
\(110\) 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 0.354186 + 0.935175i \(0.384758\pi\)
−0.986978 + 0.160854i \(0.948575\pi\)
\(132\) 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 0.761065 0.648675i \(-0.224677\pi\)
−0.942302 + 0.334764i \(0.891343\pi\)
\(138\) 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 −0.508413 0.861113i \(-0.669768\pi\)
0.999953 + 0.00974235i \(0.00310113\pi\)
\(150\) 0 0
\(151\) −11.2426 19.4728i −0.914913 1.58468i −0.807028 0.590513i \(-0.798926\pi\)
−0.107885 0.994163i \(-0.534408\pi\)
\(152\) 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 0.965918 0.258847i \(-0.0833426\pi\)
−0.707127 + 0.707086i \(0.750009\pi\)
\(158\) 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 −0.979076 0.203497i \(-0.934769\pi\)
0.665771 + 0.746156i \(0.268103\pi\)
\(164\) 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 −0.153938 0.988080i \(-0.549196\pi\)
0.932672 0.360726i \(-0.117471\pi\)
\(174\) 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 0.956088 0.293079i \(-0.0946798\pi\)
−0.731858 + 0.681457i \(0.761346\pi\)
\(180\) 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 −0.953912 0.300088i \(-0.902984\pi\)
0.736839 + 0.676068i \(0.236317\pi\)
\(192\) 0 0
\(193\) −3.37868 5.85204i −0.243203 0.421239i 0.718422 0.695607i \(-0.244865\pi\)
−0.961625 + 0.274368i \(0.911531\pi\)
\(194\) 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 0.618177 0.786039i \(-0.287871\pi\)
−0.989818 + 0.142338i \(0.954538\pi\)
\(200\) 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 0.999984 + 0.00563010i \(0.00179213\pi\)
−0.495116 + 0.868827i \(0.664875\pi\)
\(228\) 0 0
\(229\) 3.50000 6.06218i 0.231287 0.400600i −0.726900 0.686743i \(-0.759040\pi\)
0.958187 + 0.286143i \(0.0923732\pi\)
\(230\) 0 0
\(231\) 11.1213 1.52192i 0.731729 0.100135i
\(232\) 0 0
\(233\) −7.24264 + 12.5446i −0.474481 + 0.821825i −0.999573 0.0292201i \(-0.990698\pi\)
0.525092 + 0.851046i \(0.324031\pi\)
\(234\) 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 0.923224 0.384262i \(-0.125544\pi\)
−0.794393 + 0.607404i \(0.792211\pi\)
\(242\) 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 −0.980375 0.197140i \(-0.936835\pi\)
0.660916 + 0.750460i \(0.270168\pi\)
\(258\) 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 0.966671 0.256023i \(-0.0824124\pi\)
−0.705058 + 0.709150i \(0.749079\pi\)
\(264\) 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 0.901419 0.432948i \(-0.142527\pi\)
−0.825654 + 0.564177i \(0.809193\pi\)
\(270\) 0 0
\(271\) 11.7279 20.3134i 0.712421 1.23395i −0.251525 0.967851i \(-0.580932\pi\)
0.963946 0.266098i \(-0.0857344\pi\)
\(272\) 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 −0.999276 0.0380425i \(-0.987888\pi\)
0.466692 0.884420i \(-0.345446\pi\)
\(278\) 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 −0.966605 0.256270i \(-0.917506\pi\)
0.261366 0.965240i \(-0.415827\pi\)
\(284\) 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 −0.992602 0.121410i \(-0.961258\pi\)
0.391157 0.920324i \(-0.372075\pi\)
\(312\) 0 0
\(313\) −11.8640 + 20.5490i −0.670591 + 1.16150i 0.307146 + 0.951662i \(0.400626\pi\)
−0.977737 + 0.209835i \(0.932707\pi\)
\(314\) 0 0
\(315\) −1.00000 + 2.44949i −0.0563436 + 0.138013i
\(316\) 0 0
\(317\) 12.3640 21.4150i 0.694429 1.20279i −0.275943 0.961174i \(-0.588990\pi\)
0.970373 0.241613i \(-0.0776764\pi\)
\(318\) 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 −0.999298 0.0374662i \(-0.988071\pi\)
0.532096 + 0.846684i \(0.321405\pi\)
\(332\) 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 0.984487 + 0.175457i \(0.0561403\pi\)
−0.340293 + 0.940319i \(0.610526\pi\)
\(348\) 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 0.969522 0.245005i \(-0.0787896\pi\)
−0.696941 + 0.717128i \(0.745456\pi\)
\(354\) 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 −0.888281 0.459300i \(-0.848100\pi\)
0.841906 + 0.539624i \(0.181434\pi\)
\(360\) 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 −0.779048 0.626965i \(-0.784297\pi\)
−0.153443 0.988157i \(-0.549036\pi\)
\(368\) 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 −0.998906 0.0467591i \(-0.985111\pi\)
0.539948 + 0.841699i \(0.318444\pi\)
\(374\) 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 0.332668 + 0.943044i \(0.392051\pi\)
−0.983034 + 0.183424i \(0.941282\pi\)
\(384\) 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 0.999023 + 0.0441839i \(0.0140687\pi\)
−0.461247 + 0.887272i \(0.652598\pi\)
\(390\) 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 −0.734975 0.678094i \(-0.762806\pi\)
0.954734 + 0.297460i \(0.0961394\pi\)
\(398\) 0 0
\(399\) −11.3492 14.6354i −0.568173 0.732686i
\(400\) 0 0
\(401\) 1.75736 3.04384i 0.0877583 0.152002i −0.818805 0.574072i \(-0.805363\pi\)
0.906563 + 0.422070i \(0.138696\pi\)
\(402\) 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 0.575670 0.817682i \(-0.304741\pi\)
−0.995968 + 0.0897044i \(0.971408\pi\)
\(410\) 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 0.530777 0.847511i \(-0.321900\pi\)
−0.999355 + 0.0359112i \(0.988567\pi\)
\(432\) 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 −0.721686 0.692220i \(-0.756633\pi\)
0.960323 + 0.278889i \(0.0899661\pi\)
\(440\) 0 0
\(441\) −5.00000 4.89898i −0.238095 0.233285i
\(442\) 0 0
\(443\) −10.2426 + 17.7408i −0.486643 + 0.842890i −0.999882 0.0153558i \(-0.995112\pi\)
0.513240 + 0.858245i \(0.328445\pi\)
\(444\) 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 0.192714 + 0.981255i \(0.438271\pi\)
−0.946149 + 0.323733i \(0.895062\pi\)
\(458\) 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 −0.710748 0.703447i \(-0.751643\pi\)
0.964577 + 0.263803i \(0.0849768\pi\)
\(468\) 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 0.695773 0.718262i \(-0.255062\pi\)
−0.969920 + 0.243426i \(0.921729\pi\)
\(480\) 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 0.876823 + 0.480813i \(0.159658\pi\)
−0.0220157 + 0.999758i \(0.507008\pi\)
\(488\) 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 −0.997388 0.0722305i \(-0.976988\pi\)
0.561247 + 0.827648i \(0.310322\pi\)
\(500\) 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 −0.565793 0.824547i \(-0.691430\pi\)
0.996975 + 0.0777173i \(0.0247632\pi\)
\(510\) 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 0.974928 0.222520i \(-0.0714284\pi\)
−0.680172 + 0.733052i \(0.738095\pi\)
\(522\) 0 0
\(523\) 2.62132 4.54026i 0.114622 0.198532i −0.803006 0.595970i \(-0.796768\pi\)
0.917629 + 0.397439i \(0.130101\pi\)
\(524\) 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 0.0288675 0.999583i \(-0.490810\pi\)
0.851231 0.524792i \(-0.175857\pi\)
\(542\) 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 0.986394 + 0.164399i \(0.0525683\pi\)
−0.350824 + 0.936442i \(0.614098\pi\)
\(558\) 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 0.922293 0.386492i \(-0.126313\pi\)
−0.795858 + 0.605483i \(0.792980\pi\)
\(564\) 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 0.0162699 0.999868i \(-0.494821\pi\)
0.857776 0.514024i \(-0.171846\pi\)
\(570\) 0 0
\(571\) 14.4706 + 25.0637i 0.605574 + 1.04889i 0.991960 + 0.126548i \(0.0403898\pi\)
−0.386386 + 0.922337i \(0.626277\pi\)
\(572\) 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 0.702159 0.712020i \(-0.252220\pi\)
−0.967707 + 0.252078i \(0.918886\pi\)
\(578\) 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 −0.897126 0.441774i \(-0.854349\pi\)
0.831151 + 0.556047i \(0.187682\pi\)
\(594\) 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 0.979648 + 0.200724i \(0.0643296\pi\)
−0.315991 + 0.948762i \(0.602337\pi\)
\(600\) 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 −0.400301 0.916384i \(-0.631094\pi\)
0.993762 0.111521i \(-0.0355722\pi\)
\(608\) 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 0.915843 0.401537i \(-0.131524\pi\)
−0.805663 + 0.592374i \(0.798191\pi\)
\(614\) 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 0.960876 0.276977i \(-0.0893327\pi\)
−0.720308 + 0.693655i \(0.755999\pi\)
\(620\) 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 −0.976101 0.217316i \(-0.930270\pi\)
0.299850 0.953986i \(-0.403063\pi\)
\(642\) 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 0.747621 0.664126i \(-0.231196\pi\)
−0.948960 + 0.315395i \(0.897863\pi\)
\(648\) 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 −0.948661 0.316293i \(-0.897562\pi\)
0.748249 + 0.663418i \(0.230895\pi\)
\(654\) 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 0.885085 0.465430i \(-0.154100\pi\)
−0.845617 + 0.533791i \(0.820767\pi\)
\(662\) 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 −0.962015 0.272995i \(-0.911986\pi\)
0.717428 + 0.696632i \(0.245319\pi\)
\(678\) 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 −0.986423 0.164224i \(-0.947488\pi\)
0.350989 0.936380i \(-0.385845\pi\)
\(684\) 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 0.487452 + 0.873150i \(0.337927\pi\)
−0.999896 + 0.0144296i \(0.995407\pi\)
\(692\) 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 −0.288283 0.957545i \(-0.593085\pi\)
0.973400 0.229112i \(-0.0735822\pi\)
\(710\) 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 −0.999975 0.00706717i \(-0.997750\pi\)
0.506108 + 0.862470i \(0.331084\pi\)
\(720\) 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 −0.882053 0.471150i \(-0.843839\pi\)
0.849055 + 0.528305i \(0.177172\pi\)
\(734\) 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 0.972565 0.232632i \(-0.0747336\pi\)
−0.687747 + 0.725950i \(0.741400\pi\)
\(740\) 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 0.0857467 + 0.996317i \(0.472672\pi\)
−0.905709 + 0.423900i \(0.860661\pi\)
\(752\) 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 0.0532948 + 0.998579i \(0.483028\pi\)
−0.891442 + 0.453135i \(0.850306\pi\)
\(762\) 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 0.741452 0.671006i \(-0.234138\pi\)
−0.951834 + 0.306613i \(0.900804\pi\)
\(774\) 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 −0.999960 0.00890869i \(-0.997164\pi\)
0.492265 0.870445i \(-0.336169\pi\)
\(788\) 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