Properties

Label 2100.2.bc.f.949.4
Level $2100$
Weight $2$
Character 2100.949
Analytic conductor $16.769$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2100.bc (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(16.7685844245\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 420)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 949.4
Root \(-0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 2100.949
Dual form 2100.2.bc.f.1549.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{3} +(2.09077 + 1.62132i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{3} +(2.09077 + 1.62132i) q^{7} +(0.500000 + 0.866025i) q^{9} +(2.12132 - 3.67423i) q^{11} -3.24264i q^{13} +(-3.67423 - 2.12132i) q^{17} +(-3.50000 - 6.06218i) q^{19} +(1.00000 + 2.44949i) q^{21} +(3.67423 - 2.12132i) q^{23} +1.00000i q^{27} +1.75736 q^{29} +(4.74264 - 8.21449i) q^{31} +(3.67423 - 2.12132i) q^{33} +(2.80821 - 1.62132i) q^{37} +(1.62132 - 2.80821i) q^{39} -4.24264 q^{41} -3.24264i q^{43} +(-5.19615 + 3.00000i) q^{47} +(1.74264 + 6.77962i) q^{49} +(-2.12132 - 3.67423i) q^{51} +(7.34847 + 4.24264i) q^{53} -7.00000i q^{57} +(-5.12132 + 8.87039i) q^{59} +(-2.24264 - 3.88437i) q^{61} +(-0.358719 + 2.62132i) q^{63} +(4.54026 + 2.62132i) q^{67} +4.24264 q^{69} -12.7279 q^{71} +(8.00436 + 4.62132i) q^{73} +(10.3923 - 4.24264i) q^{77} +(5.50000 + 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{81} +10.2426i q^{83} +(1.52192 + 0.878680i) q^{87} +(-5.12132 - 8.87039i) q^{89} +(5.25736 - 6.77962i) q^{91} +(8.21449 - 4.74264i) q^{93} -0.485281i q^{97} +4.24264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{9} - 28 q^{19} + 8 q^{21} + 48 q^{29} + 4 q^{31} - 4 q^{39} - 20 q^{49} - 24 q^{59} + 16 q^{61} + 44 q^{79} - 4 q^{81} - 24 q^{89} + 76 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).

\(n\) \(701\) \(1051\) \(1177\) \(1501\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 2.09077 + 1.62132i 0.790237 + 0.612801i
\(8\) 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
\(13\) 3.24264i 0.899347i −0.893193 0.449673i \(-0.851540\pi\)
0.893193 0.449673i \(-0.148460\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.67423 2.12132i −0.891133 0.514496i −0.0168199 0.999859i \(-0.505354\pi\)
−0.874313 + 0.485363i \(0.838688\pi\)
\(18\) 0 0
\(19\) −3.50000 6.06218i −0.802955 1.39076i −0.917663 0.397360i \(-0.869927\pi\)
0.114708 0.993399i \(-0.463407\pi\)
\(20\) 0 0
\(21\) 1.00000 + 2.44949i 0.218218 + 0.534522i
\(22\) 0 0
\(23\) 3.67423 2.12132i 0.766131 0.442326i −0.0653618 0.997862i \(-0.520820\pi\)
0.831493 + 0.555536i \(0.187487\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 1.75736 0.326333 0.163167 0.986599i \(-0.447829\pi\)
0.163167 + 0.986599i \(0.447829\pi\)
\(30\) 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
\(33\) 3.67423 2.12132i 0.639602 0.369274i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.80821 1.62132i 0.461667 0.266543i −0.251078 0.967967i \(-0.580785\pi\)
0.712745 + 0.701423i \(0.247452\pi\)
\(38\) 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
\(43\) 3.24264i 0.494498i −0.968952 0.247249i \(-0.920473\pi\)
0.968952 0.247249i \(-0.0795266\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.19615 + 3.00000i −0.757937 + 0.437595i −0.828554 0.559908i \(-0.810836\pi\)
0.0706177 + 0.997503i \(0.477503\pi\)
\(48\) 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
\(53\) 7.34847 + 4.24264i 1.00939 + 0.582772i 0.911013 0.412378i \(-0.135302\pi\)
0.0983769 + 0.995149i \(0.468635\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 7.00000i 0.927173i
\(58\) 0 0
\(59\) −5.12132 + 8.87039i −0.666739 + 1.15483i 0.312072 + 0.950059i \(0.398977\pi\)
−0.978811 + 0.204767i \(0.934356\pi\)
\(60\) 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
\(63\) −0.358719 + 2.62132i −0.0451944 + 0.330255i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 4.54026 + 2.62132i 0.554681 + 0.320245i 0.751008 0.660293i \(-0.229568\pi\)
−0.196327 + 0.980539i \(0.562901\pi\)
\(68\) 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
\(73\) 8.00436 + 4.62132i 0.936840 + 0.540885i 0.888968 0.457969i \(-0.151423\pi\)
0.0478714 + 0.998854i \(0.484756\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 10.3923 4.24264i 1.18431 0.483494i
\(78\) 0 0
\(79\) 5.50000 + 9.52628i 0.618798 + 1.07179i 0.989705 + 0.143120i \(0.0457135\pi\)
−0.370907 + 0.928670i \(0.620953\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 10.2426i 1.12428i 0.827043 + 0.562138i \(0.190021\pi\)
−0.827043 + 0.562138i \(0.809979\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 1.52192 + 0.878680i 0.163167 + 0.0942043i
\(88\) 0 0
\(89\) −5.12132 8.87039i −0.542859 0.940259i −0.998738 0.0502176i \(-0.984009\pi\)
0.455879 0.890042i \(-0.349325\pi\)
\(90\) 0 0
\(91\) 5.25736 6.77962i 0.551121 0.710697i
\(92\) 0 0
\(93\) 8.21449 4.74264i 0.851803 0.491789i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0.485281i 0.0492729i −0.999696 0.0246364i \(-0.992157\pi\)
0.999696 0.0246364i \(-0.00784281\pi\)
\(98\) 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
\(103\) 14.9326 8.62132i 1.47135 0.849484i 0.471867 0.881670i \(-0.343580\pi\)
0.999482 + 0.0321856i \(0.0102468\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 11.0227 6.36396i 1.06561 0.615227i 0.138628 0.990345i \(-0.455731\pi\)
0.926977 + 0.375117i \(0.122398\pi\)
\(108\) 0 0
\(109\) −4.74264 + 8.21449i −0.454263 + 0.786806i −0.998645 0.0520310i \(-0.983431\pi\)
0.544383 + 0.838837i \(0.316764\pi\)
\(110\) 0 0
\(111\) 3.24264 0.307778
\(112\) 0 0
\(113\) 18.0000i 1.69330i 0.532152 + 0.846649i \(0.321383\pi\)
−0.532152 + 0.846649i \(0.678617\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 2.80821 1.62132i 0.259619 0.149891i
\(118\) 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
\(123\) −3.67423 2.12132i −0.331295 0.191273i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 2.75736i 0.244676i −0.992488 0.122338i \(-0.960961\pi\)
0.992488 0.122338i \(-0.0390392\pi\)
\(128\) 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
\(133\) 2.51104 18.3492i 0.217734 1.59108i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −3.67423 2.12132i −0.313911 0.181237i 0.334764 0.942302i \(-0.391343\pi\)
−0.648675 + 0.761065i \(0.724677\pi\)
\(138\) 0 0
\(139\) 15.4853 1.31344 0.656722 0.754133i \(-0.271942\pi\)
0.656722 + 0.754133i \(0.271942\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) −11.9142 6.87868i −0.996317 0.575224i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −1.88064 + 6.74264i −0.155112 + 0.556124i
\(148\) 0 0
\(149\) −6.00000 10.3923i −0.491539 0.851371i 0.508413 0.861113i \(-0.330232\pi\)
−0.999953 + 0.00974235i \(0.996899\pi\)
\(150\) 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
\(153\) 4.24264i 0.342997i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 5.61642 + 3.24264i 0.448239 + 0.258791i 0.707086 0.707127i \(-0.250009\pi\)
−0.258847 + 0.965918i \(0.583343\pi\)
\(158\) 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
\(163\) −6.92820 + 4.00000i −0.542659 + 0.313304i −0.746156 0.665771i \(-0.768103\pi\)
0.203497 + 0.979076i \(0.434769\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 18.7279i 1.44921i 0.689164 + 0.724605i \(0.257978\pi\)
−0.689164 + 0.724605i \(0.742022\pi\)
\(168\) 0 0
\(169\) 2.48528 0.191175
\(170\) 0 0
\(171\) 3.50000 6.06218i 0.267652 0.463586i
\(172\) 0 0
\(173\) 17.7408 10.2426i 1.34881 0.778734i 0.360726 0.932672i \(-0.382529\pi\)
0.988080 + 0.153938i \(0.0491957\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −8.87039 + 5.12132i −0.666739 + 0.384942i
\(178\) 0 0
\(179\) −3.00000 + 5.19615i −0.224231 + 0.388379i −0.956088 0.293079i \(-0.905320\pi\)
0.731858 + 0.681457i \(0.238654\pi\)
\(180\) 0 0
\(181\) −13.0000 −0.966282 −0.483141 0.875542i \(-0.660504\pi\)
−0.483141 + 0.875542i \(0.660504\pi\)
\(182\) 0 0
\(183\) 4.48528i 0.331562i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −15.5885 + 9.00000i −1.13994 + 0.658145i
\(188\) 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
\(193\) 5.85204 + 3.37868i 0.421239 + 0.243203i 0.695607 0.718422i \(-0.255135\pi\)
−0.274368 + 0.961625i \(0.588469\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 16.2426i 1.15724i −0.815597 0.578620i \(-0.803591\pi\)
0.815597 0.578620i \(-0.196409\pi\)
\(198\) 0 0
\(199\) 5.24264 9.08052i 0.371641 0.643701i −0.618177 0.786039i \(-0.712129\pi\)
0.989818 + 0.142338i \(0.0454619\pi\)
\(200\) 0 0
\(201\) 2.62132 + 4.54026i 0.184894 + 0.320245i
\(202\) 0 0
\(203\) 3.67423 + 2.84924i 0.257881 + 0.199978i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 3.67423 + 2.12132i 0.255377 + 0.147442i
\(208\) 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
\(213\) −11.0227 6.36396i −0.755263 0.436051i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 23.2341 9.48528i 1.57723 0.643903i
\(218\) 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
\(223\) 7.51472i 0.503223i 0.967828 + 0.251611i \(0.0809605\pi\)
−0.967828 + 0.251611i \(0.919040\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 13.1750 + 7.60660i 0.874457 + 0.504868i 0.868827 0.495116i \(-0.164875\pi\)
0.00563010 + 0.999984i \(0.498208\pi\)
\(228\) 0 0
\(229\) −3.50000 6.06218i −0.231287 0.400600i 0.726900 0.686743i \(-0.240960\pi\)
−0.958187 + 0.286143i \(0.907627\pi\)
\(230\) 0 0
\(231\) 11.1213 + 1.52192i 0.731729 + 0.100135i
\(232\) 0 0
\(233\) −12.5446 + 7.24264i −0.821825 + 0.474481i −0.851046 0.525092i \(-0.824031\pi\)
0.0292201 + 0.999573i \(0.490698\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 11.0000i 0.714527i
\(238\) 0 0
\(239\) −10.9706 −0.709627 −0.354813 0.934937i \(-0.615456\pi\)
−0.354813 + 0.934937i \(0.615456\pi\)
\(240\) 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
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −19.6575 + 11.3492i −1.25077 + 0.722135i
\(248\) 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
\(253\) 18.0000i 1.13165i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 8.87039 5.12132i 0.553320 0.319459i −0.197140 0.980375i \(-0.563165\pi\)
0.750460 + 0.660916i \(0.229832\pi\)
\(258\) 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
\(263\) −7.34847 4.24264i −0.453126 0.261612i 0.256023 0.966671i \(-0.417588\pi\)
−0.709150 + 0.705058i \(0.750921\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 10.2426i 0.626839i
\(268\) 0 0
\(269\) −1.24264 + 2.15232i −0.0757651 + 0.131229i −0.901419 0.432948i \(-0.857473\pi\)
0.825654 + 0.564177i \(0.190807\pi\)
\(270\) 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
\(273\) 7.94282 3.24264i 0.480721 0.196254i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −15.3528 8.86396i −0.922462 0.532584i −0.0380425 0.999276i \(-0.512112\pi\)
−0.884420 + 0.466692i \(0.845446\pi\)
\(278\) 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
\(283\) 20.5490 + 11.8640i 1.22151 + 0.705239i 0.965240 0.261366i \(-0.0841729\pi\)
0.256270 + 0.966605i \(0.417506\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8.87039 6.87868i −0.523602 0.406036i
\(288\) 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
\(293\) 4.97056i 0.290383i 0.989404 + 0.145192i \(0.0463799\pi\)
−0.989404 + 0.145192i \(0.953620\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 3.67423 + 2.12132i 0.213201 + 0.123091i
\(298\) 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
\(303\) 6.71807 3.87868i 0.385943 0.222824i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 3.24264i 0.185067i 0.995710 + 0.0925336i \(0.0294966\pi\)
−0.995710 + 0.0925336i \(0.970503\pi\)
\(308\) 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
\(313\) −20.5490 + 11.8640i −1.16150 + 0.670591i −0.951662 0.307146i \(-0.900626\pi\)
−0.209835 + 0.977737i \(0.567293\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −21.4150 + 12.3640i −1.20279 + 0.694429i −0.961174 0.275943i \(-0.911010\pi\)
−0.241613 + 0.970373i \(0.577676\pi\)
\(318\) 0 0
\(319\) 3.72792 6.45695i 0.208724 0.361520i
\(320\) 0 0
\(321\) 12.7279 0.710403
\(322\) 0 0
\(323\) 29.6985i 1.65247i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −8.21449 + 4.74264i −0.454263 + 0.262269i
\(328\) 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
\(333\) 2.80821 + 1.62132i 0.153889 + 0.0888478i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 13.7279i 0.747808i −0.927467 0.373904i \(-0.878019\pi\)
0.927467 0.373904i \(-0.121981\pi\)
\(338\) 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
\(343\) −7.34847 + 17.0000i −0.396780 + 0.917914i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 20.7846 + 12.0000i 1.11578 + 0.644194i 0.940319 0.340293i \(-0.110526\pi\)
0.175457 + 0.984487i \(0.443860\pi\)
\(348\) 0 0
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 0 0
\(351\) 3.24264 0.173079
\(352\) 0 0
\(353\) −8.87039 5.12132i −0.472123 0.272580i 0.245005 0.969522i \(-0.421210\pi\)
−0.717128 + 0.696941i \(0.754544\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 1.52192 11.1213i 0.0805484 0.588603i
\(358\) 0 0
\(359\) 0.878680 + 1.52192i 0.0463749 + 0.0803237i 0.888281 0.459300i \(-0.151900\pi\)
−0.841906 + 0.539624i \(0.818566\pi\)
\(360\) 0 0
\(361\) −15.0000 + 25.9808i −0.789474 + 1.36741i
\(362\) 0 0
\(363\) 7.00000i 0.367405i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −30.9413 17.8640i −1.61512 0.932491i −0.988157 0.153443i \(-0.950964\pi\)
−0.626965 0.779048i \(-0.715703\pi\)
\(368\) 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
\(373\) −15.3528 + 8.86396i −0.794939 + 0.458959i −0.841699 0.539948i \(-0.818444\pi\)
0.0467591 + 0.998906i \(0.485111\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 5.69848i 0.293487i
\(378\) 0 0
\(379\) 20.4558 1.05075 0.525373 0.850872i \(-0.323926\pi\)
0.525373 + 0.850872i \(0.323926\pi\)
\(380\) 0 0
\(381\) 1.37868 2.38794i 0.0706319 0.122338i
\(382\) 0 0
\(383\) −22.0454 + 12.7279i −1.12647 + 0.650366i −0.943044 0.332668i \(-0.892051\pi\)
−0.183424 + 0.983034i \(0.558718\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2.80821 1.62132i 0.142749 0.0824163i
\(388\) 0 0
\(389\) −10.6066 + 18.3712i −0.537776 + 0.931455i 0.461247 + 0.887272i \(0.347402\pi\)
−0.999023 + 0.0441839i \(0.985931\pi\)
\(390\) 0 0
\(391\) −18.0000 −0.910299
\(392\) 0 0
\(393\) 14.4853i 0.730686i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −7.58410 + 4.37868i −0.380635 + 0.219760i −0.678094 0.734975i \(-0.737194\pi\)
0.297460 + 0.954734i \(0.403861\pi\)
\(398\) 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
\(403\) −26.6367 15.3787i −1.32687 0.766067i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 13.7574i 0.681927i
\(408\) 0 0
\(409\) 8.50000 14.7224i 0.420298 0.727977i −0.575670 0.817682i \(-0.695259\pi\)
0.995968 + 0.0897044i \(0.0285922\pi\)
\(410\) 0 0
\(411\) −2.12132 3.67423i −0.104637 0.181237i
\(412\) 0 0
\(413\) −25.0892 + 10.2426i −1.23456 + 0.504007i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 13.4106 + 7.74264i 0.656722 + 0.379159i
\(418\) 0 0
\(419\) 14.4853 0.707652 0.353826 0.935311i \(-0.384880\pi\)
0.353826 + 0.935311i \(0.384880\pi\)
\(420\) 0 0
\(421\) 31.4853 1.53450 0.767249 0.641349i \(-0.221625\pi\)
0.767249 + 0.641349i \(0.221625\pi\)
\(422\) 0 0
\(423\) −5.19615 3.00000i −0.252646 0.145865i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 1.60896 11.7574i 0.0778629 0.568978i
\(428\) 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
\(433\) 33.2426i 1.59754i −0.601637 0.798770i \(-0.705485\pi\)
0.601637 0.798770i \(-0.294515\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −25.7196 14.8492i −1.23034 0.710336i
\(438\) 0 0
\(439\) −5.00000 8.66025i −0.238637 0.413331i 0.721686 0.692220i \(-0.243367\pi\)
−0.960323 + 0.278889i \(0.910034\pi\)
\(440\) 0 0
\(441\) −5.00000 + 4.89898i −0.238095 + 0.233285i
\(442\) 0 0
\(443\) −17.7408 + 10.2426i −0.842890 + 0.486643i −0.858245 0.513240i \(-0.828445\pi\)
0.0153558 + 0.999882i \(0.495112\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 12.0000i 0.567581i
\(448\) 0 0
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 0 0
\(451\) −9.00000 + 15.5885i −0.423793 + 0.734032i
\(452\) 0 0
\(453\) −19.4728 + 11.2426i −0.914913 + 0.528225i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 27.8975 16.1066i 1.30499 0.753435i 0.323733 0.946149i \(-0.395062\pi\)
0.981255 + 0.192714i \(0.0617288\pi\)
\(458\) 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
\(463\) 10.2721i 0.477384i −0.971095 0.238692i \(-0.923281\pi\)
0.971095 0.238692i \(-0.0767186\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −9.50079 + 5.48528i −0.439644 + 0.253829i −0.703447 0.710748i \(-0.748357\pi\)
0.263803 + 0.964577i \(0.415023\pi\)
\(468\) 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
\(473\) −11.9142 6.87868i −0.547817 0.316282i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 8.48528i 0.388514i
\(478\) 0 0
\(479\) 6.00000 10.3923i 0.274147 0.474837i −0.695773 0.718262i \(-0.744938\pi\)
0.969920 + 0.243426i \(0.0782712\pi\)
\(480\) 0 0
\(481\) −5.25736 9.10601i −0.239715 0.415198i
\(482\) 0 0
\(483\) 8.87039 + 6.87868i 0.403617 + 0.312991i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 32.6733 + 18.8640i 1.48057 + 0.854808i 0.999758 0.0220157i \(-0.00700837\pi\)
0.480813 + 0.876823i \(0.340342\pi\)
\(488\) 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
\(493\) −6.45695 3.72792i −0.290806 0.167897i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −26.6112 20.6360i −1.19367 0.925653i
\(498\) 0 0
\(499\) 9.74264 + 16.8747i 0.436140 + 0.755417i 0.997388 0.0722305i \(-0.0230117\pi\)
−0.561247 + 0.827648i \(0.689678\pi\)
\(500\) 0 0
\(501\) −9.36396 + 16.2189i −0.418351 + 0.724605i
\(502\) 0 0
\(503\) 26.4853i 1.18092i 0.807067 + 0.590460i \(0.201054\pi\)
−0.807067 + 0.590460i \(0.798946\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 2.15232 + 1.24264i 0.0955877 + 0.0551876i
\(508\) 0 0
\(509\) −9.72792 16.8493i −0.431183 0.746830i 0.565793 0.824547i \(-0.308570\pi\)
−0.996975 + 0.0777173i \(0.975237\pi\)
\(510\) 0 0
\(511\) 9.24264 + 22.6398i 0.408870 + 1.00152i
\(512\) 0 0
\(513\) 6.06218 3.50000i 0.267652 0.154529i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 25.4558i 1.11955i
\(518\) 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
\(523\) 4.54026 2.62132i 0.198532 0.114622i −0.397439 0.917629i \(-0.630101\pi\)
0.595970 + 0.803006i \(0.296768\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −34.8511 + 20.1213i −1.51814 + 0.876498i
\(528\) 0 0
\(529\) −2.50000 + 4.33013i −0.108696 + 0.188266i
\(530\) 0 0
\(531\) −10.2426 −0.444493
\(532\) 0 0
\(533\) 13.7574i 0.595897i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −5.19615 + 3.00000i −0.224231 + 0.129460i
\(538\) 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
\(543\) −11.2583 6.50000i −0.483141 0.278942i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 33.4558i 1.43047i 0.698885 + 0.715234i \(0.253680\pi\)
−0.698885 + 0.715234i \(0.746320\pi\)
\(548\) 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
\(553\) −3.94591 + 28.8345i −0.167797 + 1.22617i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 25.9808 + 15.0000i 1.10084 + 0.635570i 0.936442 0.350824i \(-0.114098\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(558\) 0 0
\(559\) −10.5147 −0.444725
\(560\) 0 0
\(561\) −18.0000 −0.759961
\(562\) 0 0
\(563\) −5.19615 3.00000i −0.218992 0.126435i 0.386492 0.922293i \(-0.373687\pi\)
−0.605483 + 0.795858i \(0.707020\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −2.44949 + 1.00000i −0.102869 + 0.0419961i
\(568\) 0 0
\(569\) −20.8492 36.1119i −0.874046 1.51389i −0.857776 0.514024i \(-0.828154\pi\)
−0.0162699 0.999868i \(-0.505179\pi\)
\(570\) 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
\(573\) 6.00000i 0.250654i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −11.0482 6.37868i −0.459942 0.265548i 0.252078 0.967707i \(-0.418886\pi\)
−0.712020 + 0.702159i \(0.752220\pi\)
\(578\) 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
\(583\) 31.1769 18.0000i 1.29122 0.745484i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 45.2132i 1.86615i 0.359684 + 0.933074i \(0.382885\pi\)
−0.359684 + 0.933074i \(0.617115\pi\)
\(588\) 0 0
\(589\) −66.3970 −2.73584
\(590\) 0 0
\(591\) 8.12132 14.0665i 0.334066 0.578620i
\(592\) 0 0
\(593\) −2.78272 + 1.60660i −0.114272 + 0.0659752i −0.556047 0.831151i \(-0.687682\pi\)
0.441774 + 0.897126i \(0.354349\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 9.08052 5.24264i 0.371641 0.214567i
\(598\) 0 0
\(599\) −16.2426 + 28.1331i −0.663656 + 1.14949i 0.315991 + 0.948762i \(0.397663\pi\)
−0.979648 + 0.200724i \(0.935670\pi\)
\(600\) 0 0
\(601\) −3.48528 −0.142168 −0.0710838 0.997470i \(-0.522646\pi\)
−0.0710838 + 0.997470i \(0.522646\pi\)
\(602\) 0 0
\(603\) 5.24264i 0.213497i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −25.3249 + 14.6213i −1.02790 + 0.593461i −0.916384 0.400301i \(-0.868906\pi\)
−0.111521 + 0.993762i \(0.535572\pi\)
\(608\) 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
\(613\) −4.72490 2.72792i −0.190837 0.110180i 0.401537 0.915843i \(-0.368476\pi\)
−0.592374 + 0.805663i \(0.701809\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 26.4853i 1.06626i −0.846034 0.533129i \(-0.821016\pi\)
0.846034 0.533129i \(-0.178984\pi\)
\(618\) 0 0
\(619\) −5.98528 + 10.3668i −0.240569 + 0.416677i −0.960876 0.276977i \(-0.910667\pi\)
0.720308 + 0.693655i \(0.244001\pi\)
\(620\) 0 0
\(621\) 2.12132 + 3.67423i 0.0851257 + 0.147442i
\(622\) 0 0
\(623\) 3.67423 26.8492i 0.147205 1.07569i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −25.7196 14.8492i −1.02714 0.593022i
\(628\) 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
\(633\) 19.4728 + 11.2426i 0.773975 + 0.446855i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 21.9839 5.65076i 0.871032 0.223891i
\(638\) 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
\(643\) 19.7279i 0.777993i 0.921239 + 0.388997i \(0.127178\pi\)
−0.921239 + 0.388997i \(0.872822\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −8.87039 5.12132i −0.348731 0.201340i 0.315395 0.948960i \(-0.397863\pi\)
−0.664126 + 0.747621i \(0.731196\pi\)
\(648\) 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
\(653\) −8.87039 + 5.12132i −0.347125 + 0.200413i −0.663418 0.748249i \(-0.730895\pi\)
0.316293 + 0.948661i \(0.397562\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 9.24264i 0.360590i
\(658\) 0 0
\(659\) −40.9706 −1.59599 −0.797993 0.602666i \(-0.794105\pi\)
−0.797993 + 0.602666i \(0.794105\pi\)
\(660\) 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
\(663\) −11.9142 + 6.87868i −0.462710 + 0.267146i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 6.45695 3.72792i 0.250014 0.144346i
\(668\) 0 0
\(669\) −3.75736 + 6.50794i −0.145268 + 0.251611i
\(670\) 0 0
\(671\) −19.0294 −0.734623
\(672\) 0 0
\(673\) 29.7279i 1.14593i −0.819581 0.572964i \(-0.805794\pi\)
0.819581 0.572964i \(-0.194206\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 11.0227 6.36396i 0.423637 0.244587i −0.272995 0.962015i \(-0.588014\pi\)
0.696632 + 0.717428i \(0.254681\pi\)
\(678\) 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
\(683\) 28.7635 + 16.6066i 1.10060 + 0.635434i 0.936380 0.350989i \(-0.114155\pi\)
0.164224 + 0.986423i \(0.447488\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 7.00000i 0.267067i
\(688\) 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
\(693\) 8.87039 + 6.87868i 0.336958 + 0.261299i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 15.5885 + 9.00000i 0.590455 + 0.340899i
\(698\) 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
\(703\) −19.6575 11.3492i −0.741395 0.428045i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 19.0016 7.75736i 0.714628 0.291746i
\(708\) 0 0
\(709\) −18.2426 31.5972i −0.685117 1.18666i −0.973400 0.229112i \(-0.926418\pi\)
0.288283 0.957545i \(-0.406915\pi\)
\(710\) 0 0
\(711\) −5.50000 + 9.52628i −0.206266 + 0.357263i
\(712\) 0 0
\(713\) 40.2426i 1.50710i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −9.50079 5.48528i −0.354813 0.204852i
\(718\) 0 0
\(719\) 13.2426 + 22.9369i 0.493867 + 0.855403i 0.999975 0.00706717i \(-0.00224957\pi\)
−0.506108 + 0.862470i \(0.668916\pi\)
\(720\) 0 0
\(721\) 45.1985 + 6.18527i 1.68328 + 0.230352i
\(722\) 0 0
\(723\) 3.46410 2.00000i 0.128831 0.0743808i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0.757359i 0.0280889i 0.999901 + 0.0140445i \(0.00447063\pi\)
−0.999901 + 0.0140445i \(0.995529\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −6.87868 + 11.9142i −0.254417 + 0.440663i
\(732\) 0 0
\(733\) −1.54741 + 0.893398i −0.0571549 + 0.0329984i −0.528305 0.849055i \(-0.677172\pi\)
0.471150 + 0.882053i \(0.343839\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 19.2627 11.1213i 0.709550 0.409659i
\(738\) 0 0
\(739\) −7.74264 + 13.4106i −0.284818 + 0.493319i −0.972565 0.232632i \(-0.925266\pi\)
0.687747 + 0.725950i \(0.258600\pi\)
\(740\) 0 0
\(741\) −22.6985 −0.833850
\(742\) 0 0
\(743\) 15.2132i 0.558118i −0.960274 0.279059i \(-0.909977\pi\)
0.960274 0.279059i \(-0.0900226\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −8.87039 + 5.12132i −0.324550 + 0.187379i
\(748\) 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
\(753\) −16.2189 9.36396i −0.591048 0.341242i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 9.02944i 0.328180i 0.986445 + 0.164090i \(0.0524688\pi\)
−0.986445 + 0.164090i \(0.947531\pi\)
\(758\) 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
\(763\) −23.2341 + 9.48528i −0.841131 + 0.343390i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 28.7635 + 16.6066i 1.03859 + 0.599630i
\(768\) 0 0
\(769\) −5.00000 −0.180305 −0.0901523 0.995928i \(-0.528735\pi\)
−0.0901523 + 0.995928i \(0.528735\pi\)
\(770\) 0 0
\(771\) 10.2426 0.368880
\(772\) 0 0
\(773\) 10.1312 + 5.84924i 0.364393 + 0.210383i 0.671006 0.741452i \(-0.265862\pi\)
−0.306613 + 0.951834i \(0.599196\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 6.77962 + 5.25736i 0.243217 + 0.188607i
\(778\) 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
\(783\) 1.75736i 0.0628029i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −24.6690 14.2426i −0.879354 0.507695i −0.00890869 0.999960i \(-0.502836\pi\)
−0.870445 + 0.492265i \(0.836169\pi\)
\(788\) 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
\(793\) −12.5956 + 7.27208i −0.447283 + 0.258239i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 31.7574i 1.12490i −0.826830 0.562452i \(-0.809858\pi\)
0.826830 0.562452i \(-0.190142\pi\)
\(798\) 0 0
\(799\) 25.4558