Properties

Label 1456.2.cc.c.225.3
Level $1456$
Weight $2$
Character 1456.225
Analytic conductor $11.626$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.cc (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.6262185343\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.58891012706304.1
Defining polynomial: \( x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 225.3
Root \(1.34408 - 0.439820i\) of defining polynomial
Character \(\chi\) \(=\) 1456.225
Dual form 1456.2.cc.c.673.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.291146 + 0.504280i) q^{3} -1.68817i q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.33047 + 2.30444i) q^{9} +O(q^{10})\) \(q+(-0.291146 + 0.504280i) q^{3} -1.68817i q^{5} +(-0.866025 + 0.500000i) q^{7} +(1.33047 + 2.30444i) q^{9} +(0.315769 + 0.182309i) q^{11} +(1.80124 + 3.12338i) q^{13} +(0.851308 + 0.491503i) q^{15} +(-1.59277 - 2.75877i) q^{17} +(-1.25046 + 0.721954i) q^{19} -0.582292i q^{21} +(2.54161 - 4.40219i) q^{23} +2.15010 q^{25} -3.29632 q^{27} +(-4.09831 + 7.09848i) q^{29} +4.69775i q^{31} +(-0.183870 + 0.106157i) q^{33} +(0.844083 + 1.46199i) q^{35} +(5.46967 + 3.15792i) q^{37} +(-2.09948 - 0.00103020i) q^{39} +(-5.04661 - 2.91366i) q^{41} +(0.386561 + 0.669543i) q^{43} +(3.89027 - 2.24605i) q^{45} +12.7905i q^{47} +(0.500000 - 0.866025i) q^{49} +1.85492 q^{51} +1.37110 q^{53} +(0.307768 - 0.533070i) q^{55} -0.840776i q^{57} +(8.10770 - 4.68098i) q^{59} +(4.51242 + 7.81574i) q^{61} +(-2.30444 - 1.33047i) q^{63} +(5.27279 - 3.04080i) q^{65} +(11.6705 + 6.73797i) q^{67} +(1.47996 + 2.56336i) q^{69} +(6.13246 - 3.54058i) q^{71} +2.16083i q^{73} +(-0.625992 + 1.08425i) q^{75} -0.364618 q^{77} +6.88781 q^{79} +(-3.03169 + 5.25105i) q^{81} -0.567380i q^{83} +(-4.65725 + 2.68887i) q^{85} +(-2.38641 - 4.13339i) q^{87} +(-0.986346 - 0.569467i) q^{89} +(-3.12161 - 1.80431i) q^{91} +(-2.36898 - 1.36773i) q^{93} +(1.21878 + 2.11098i) q^{95} +(6.86572 - 3.96393i) q^{97} +0.970225i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 4 q^{9} - 6 q^{11} + 4 q^{13} - 6 q^{15} - 4 q^{17} + 12 q^{23} - 20 q^{25} - 12 q^{27} + 8 q^{29} - 30 q^{33} - 6 q^{35} - 42 q^{37} + 4 q^{39} + 30 q^{41} - 2 q^{43} + 6 q^{49} - 52 q^{51} - 44 q^{53} + 6 q^{55} - 18 q^{59} + 14 q^{61} - 12 q^{63} + 60 q^{65} + 24 q^{67} + 4 q^{69} + 24 q^{71} - 46 q^{75} + 8 q^{77} + 56 q^{79} + 2 q^{81} - 48 q^{85} + 2 q^{87} - 12 q^{89} - 14 q^{91} - 18 q^{93} + 22 q^{95} + 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times\).

\(n\) \(561\) \(911\) \(1093\) \(1249\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\) \(1\)

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
\(3\) −0.291146 + 0.504280i −0.168093 + 0.291146i −0.937749 0.347313i \(-0.887094\pi\)
0.769656 + 0.638459i \(0.220428\pi\)
\(4\) 0 0
\(5\) 1.68817i 0.754971i −0.926016 0.377485i \(-0.876789\pi\)
0.926016 0.377485i \(-0.123211\pi\)
\(6\) 0 0
\(7\) −0.866025 + 0.500000i −0.327327 + 0.188982i
\(8\) 0 0
\(9\) 1.33047 + 2.30444i 0.443489 + 0.768146i
\(10\) 0 0
\(11\) 0.315769 + 0.182309i 0.0952078 + 0.0549682i 0.546848 0.837232i \(-0.315828\pi\)
−0.451640 + 0.892200i \(0.649161\pi\)
\(12\) 0 0
\(13\) 1.80124 + 3.12338i 0.499575 + 0.866271i
\(14\) 0 0
\(15\) 0.851308 + 0.491503i 0.219807 + 0.126905i
\(16\) 0 0
\(17\) −1.59277 2.75877i −0.386304 0.669099i 0.605645 0.795735i \(-0.292915\pi\)
−0.991949 + 0.126636i \(0.959582\pi\)
\(18\) 0 0
\(19\) −1.25046 + 0.721954i −0.286875 + 0.165628i −0.636532 0.771250i \(-0.719632\pi\)
0.349657 + 0.936878i \(0.386298\pi\)
\(20\) 0 0
\(21\) 0.582292i 0.127067i
\(22\) 0 0
\(23\) 2.54161 4.40219i 0.529962 0.917920i −0.469428 0.882971i \(-0.655540\pi\)
0.999389 0.0349493i \(-0.0111270\pi\)
\(24\) 0 0
\(25\) 2.15010 0.430020
\(26\) 0 0
\(27\) −3.29632 −0.634377
\(28\) 0 0
\(29\) −4.09831 + 7.09848i −0.761037 + 1.31815i 0.181280 + 0.983432i \(0.441976\pi\)
−0.942317 + 0.334723i \(0.891357\pi\)
\(30\) 0 0
\(31\) 4.69775i 0.843742i 0.906656 + 0.421871i \(0.138626\pi\)
−0.906656 + 0.421871i \(0.861374\pi\)
\(32\) 0 0
\(33\) −0.183870 + 0.106157i −0.0320076 + 0.0184796i
\(34\) 0 0
\(35\) 0.844083 + 1.46199i 0.142676 + 0.247122i
\(36\) 0 0
\(37\) 5.46967 + 3.15792i 0.899209 + 0.519159i 0.876943 0.480594i \(-0.159579\pi\)
0.0222655 + 0.999752i \(0.492912\pi\)
\(38\) 0 0
\(39\) −2.09948 0.00103020i −0.336186 0.000164965i
\(40\) 0 0
\(41\) −5.04661 2.91366i −0.788148 0.455037i 0.0511624 0.998690i \(-0.483707\pi\)
−0.839310 + 0.543653i \(0.817041\pi\)
\(42\) 0 0
\(43\) 0.386561 + 0.669543i 0.0589500 + 0.102104i 0.893994 0.448078i \(-0.147891\pi\)
−0.835044 + 0.550183i \(0.814558\pi\)
\(44\) 0 0
\(45\) 3.89027 2.24605i 0.579928 0.334821i
\(46\) 0 0
\(47\) 12.7905i 1.86569i 0.360275 + 0.932846i \(0.382683\pi\)
−0.360275 + 0.932846i \(0.617317\pi\)
\(48\) 0 0
\(49\) 0.500000 0.866025i 0.0714286 0.123718i
\(50\) 0 0
\(51\) 1.85492 0.259741
\(52\) 0 0
\(53\) 1.37110 0.188334 0.0941672 0.995556i \(-0.469981\pi\)
0.0941672 + 0.995556i \(0.469981\pi\)
\(54\) 0 0
\(55\) 0.307768 0.533070i 0.0414994 0.0718791i
\(56\) 0 0
\(57\) 0.840776i 0.111363i
\(58\) 0 0
\(59\) 8.10770 4.68098i 1.05553 0.609412i 0.131340 0.991337i \(-0.458072\pi\)
0.924193 + 0.381925i \(0.124739\pi\)
\(60\) 0 0
\(61\) 4.51242 + 7.81574i 0.577756 + 1.00070i 0.995736 + 0.0922469i \(0.0294049\pi\)
−0.417980 + 0.908456i \(0.637262\pi\)
\(62\) 0 0
\(63\) −2.30444 1.33047i −0.290332 0.167623i
\(64\) 0 0
\(65\) 5.27279 3.04080i 0.654009 0.377164i
\(66\) 0 0
\(67\) 11.6705 + 6.73797i 1.42578 + 0.823174i 0.996784 0.0801330i \(-0.0255345\pi\)
0.428995 + 0.903307i \(0.358868\pi\)
\(68\) 0 0
\(69\) 1.47996 + 2.56336i 0.178166 + 0.308592i
\(70\) 0 0
\(71\) 6.13246 3.54058i 0.727789 0.420189i −0.0898239 0.995958i \(-0.528630\pi\)
0.817613 + 0.575769i \(0.195297\pi\)
\(72\) 0 0
\(73\) 2.16083i 0.252906i 0.991973 + 0.126453i \(0.0403592\pi\)
−0.991973 + 0.126453i \(0.959641\pi\)
\(74\) 0 0
\(75\) −0.625992 + 1.08425i −0.0722834 + 0.125198i
\(76\) 0 0
\(77\) −0.364618 −0.0415521
\(78\) 0 0
\(79\) 6.88781 0.774940 0.387470 0.921882i \(-0.373349\pi\)
0.387470 + 0.921882i \(0.373349\pi\)
\(80\) 0 0
\(81\) −3.03169 + 5.25105i −0.336855 + 0.583450i
\(82\) 0 0
\(83\) 0.567380i 0.0622780i −0.999515 0.0311390i \(-0.990087\pi\)
0.999515 0.0311390i \(-0.00991345\pi\)
\(84\) 0 0
\(85\) −4.65725 + 2.68887i −0.505150 + 0.291648i
\(86\) 0 0
\(87\) −2.38641 4.13339i −0.255850 0.443146i
\(88\) 0 0
\(89\) −0.986346 0.569467i −0.104553 0.0603634i 0.446812 0.894628i \(-0.352559\pi\)
−0.551364 + 0.834264i \(0.685893\pi\)
\(90\) 0 0
\(91\) −3.12161 1.80431i −0.327234 0.189143i
\(92\) 0 0
\(93\) −2.36898 1.36773i −0.245652 0.141827i
\(94\) 0 0
\(95\) 1.21878 + 2.11098i 0.125044 + 0.216582i
\(96\) 0 0
\(97\) 6.86572 3.96393i 0.697109 0.402476i −0.109161 0.994024i \(-0.534816\pi\)
0.806270 + 0.591548i \(0.201483\pi\)
\(98\) 0 0
\(99\) 0.970225i 0.0975113i
\(100\) 0 0
\(101\) −7.77322 + 13.4636i −0.773465 + 1.33968i 0.162189 + 0.986760i \(0.448145\pi\)
−0.935653 + 0.352920i \(0.885189\pi\)
\(102\) 0 0
\(103\) 10.2982 1.01471 0.507354 0.861738i \(-0.330624\pi\)
0.507354 + 0.861738i \(0.330624\pi\)
\(104\) 0 0
\(105\) −0.983005 −0.0959315
\(106\) 0 0
\(107\) −6.56220 + 11.3661i −0.634391 + 1.09880i 0.352252 + 0.935905i \(0.385416\pi\)
−0.986644 + 0.162893i \(0.947917\pi\)
\(108\) 0 0
\(109\) 10.4459i 1.00054i 0.865871 + 0.500268i \(0.166765\pi\)
−0.865871 + 0.500268i \(0.833235\pi\)
\(110\) 0 0
\(111\) −3.18495 + 1.83883i −0.302302 + 0.174534i
\(112\) 0 0
\(113\) −2.47631 4.28909i −0.232952 0.403484i 0.725724 0.687986i \(-0.241505\pi\)
−0.958675 + 0.284502i \(0.908172\pi\)
\(114\) 0 0
\(115\) −7.43163 4.29065i −0.693003 0.400105i
\(116\) 0 0
\(117\) −4.80115 + 8.30642i −0.443866 + 0.767928i
\(118\) 0 0
\(119\) 2.75877 + 1.59277i 0.252896 + 0.146009i
\(120\) 0 0
\(121\) −5.43353 9.41114i −0.493957 0.855559i
\(122\) 0 0
\(123\) 2.93860 1.69660i 0.264965 0.152977i
\(124\) 0 0
\(125\) 12.0705i 1.07962i
\(126\) 0 0
\(127\) −4.03366 + 6.98650i −0.357929 + 0.619951i −0.987615 0.156899i \(-0.949850\pi\)
0.629686 + 0.776850i \(0.283184\pi\)
\(128\) 0 0
\(129\) −0.450183 −0.0396364
\(130\) 0 0
\(131\) −18.9039 −1.65164 −0.825820 0.563934i \(-0.809287\pi\)
−0.825820 + 0.563934i \(0.809287\pi\)
\(132\) 0 0
\(133\) 0.721954 1.25046i 0.0626013 0.108429i
\(134\) 0 0
\(135\) 5.56473i 0.478936i
\(136\) 0 0
\(137\) 15.7837 9.11274i 1.34850 0.778554i 0.360459 0.932775i \(-0.382620\pi\)
0.988036 + 0.154221i \(0.0492867\pi\)
\(138\) 0 0
\(139\) 2.62542 + 4.54737i 0.222686 + 0.385703i 0.955623 0.294594i \(-0.0951843\pi\)
−0.732937 + 0.680297i \(0.761851\pi\)
\(140\) 0 0
\(141\) −6.45001 3.72392i −0.543189 0.313610i
\(142\) 0 0
\(143\) −0.000645091 1.31465i −5.39452e−5 0.109936i
\(144\) 0 0
\(145\) 11.9834 + 6.91862i 0.995167 + 0.574560i
\(146\) 0 0
\(147\) 0.291146 + 0.504280i 0.0240133 + 0.0415923i
\(148\) 0 0
\(149\) 8.03073 4.63654i 0.657903 0.379841i −0.133574 0.991039i \(-0.542646\pi\)
0.791478 + 0.611198i \(0.209312\pi\)
\(150\) 0 0
\(151\) 14.0132i 1.14038i −0.821513 0.570189i \(-0.806870\pi\)
0.821513 0.570189i \(-0.193130\pi\)
\(152\) 0 0
\(153\) 4.23827 7.34090i 0.342644 0.593476i
\(154\) 0 0
\(155\) 7.93059 0.637000
\(156\) 0 0
\(157\) −17.1825 −1.37131 −0.685656 0.727925i \(-0.740485\pi\)
−0.685656 + 0.727925i \(0.740485\pi\)
\(158\) 0 0
\(159\) −0.399189 + 0.691415i −0.0316577 + 0.0548328i
\(160\) 0 0
\(161\) 5.08321i 0.400613i
\(162\) 0 0
\(163\) −10.2128 + 5.89637i −0.799930 + 0.461840i −0.843447 0.537213i \(-0.819477\pi\)
0.0435169 + 0.999053i \(0.486144\pi\)
\(164\) 0 0
\(165\) 0.179211 + 0.310402i 0.0139515 + 0.0241648i
\(166\) 0 0
\(167\) −3.73852 2.15843i −0.289295 0.167025i 0.348329 0.937372i \(-0.386749\pi\)
−0.637624 + 0.770348i \(0.720083\pi\)
\(168\) 0 0
\(169\) −6.51105 + 11.2519i −0.500850 + 0.865534i
\(170\) 0 0
\(171\) −3.32739 1.92107i −0.254452 0.146908i
\(172\) 0 0
\(173\) 6.25985 + 10.8424i 0.475928 + 0.824331i 0.999620 0.0275769i \(-0.00877910\pi\)
−0.523692 + 0.851908i \(0.675446\pi\)
\(174\) 0 0
\(175\) −1.86204 + 1.07505i −0.140757 + 0.0812660i
\(176\) 0 0
\(177\) 5.45140i 0.409752i
\(178\) 0 0
\(179\) 3.29767 5.71173i 0.246479 0.426915i −0.716067 0.698031i \(-0.754060\pi\)
0.962547 + 0.271117i \(0.0873929\pi\)
\(180\) 0 0
\(181\) −11.0157 −0.818791 −0.409395 0.912357i \(-0.634260\pi\)
−0.409395 + 0.912357i \(0.634260\pi\)
\(182\) 0 0
\(183\) −5.25509 −0.388468
\(184\) 0 0
\(185\) 5.33109 9.23371i 0.391949 0.678876i
\(186\) 0 0
\(187\) 1.16151i 0.0849379i
\(188\) 0 0
\(189\) 2.85470 1.64816i 0.207649 0.119886i
\(190\) 0 0
\(191\) 2.96606 + 5.13737i 0.214617 + 0.371727i 0.953154 0.302486i \(-0.0978164\pi\)
−0.738537 + 0.674213i \(0.764483\pi\)
\(192\) 0 0
\(193\) 3.63380 + 2.09798i 0.261567 + 0.151016i 0.625049 0.780586i \(-0.285079\pi\)
−0.363482 + 0.931601i \(0.618412\pi\)
\(194\) 0 0
\(195\) −0.00173916 + 3.54428i −0.000124544 + 0.253811i
\(196\) 0 0
\(197\) 5.00990 + 2.89247i 0.356941 + 0.206080i 0.667738 0.744396i \(-0.267263\pi\)
−0.310797 + 0.950476i \(0.600596\pi\)
\(198\) 0 0
\(199\) −5.97988 10.3575i −0.423903 0.734221i 0.572415 0.819964i \(-0.306007\pi\)
−0.996317 + 0.0857435i \(0.972673\pi\)
\(200\) 0 0
\(201\) −6.79564 + 3.92347i −0.479328 + 0.276740i
\(202\) 0 0
\(203\) 8.19662i 0.575290i
\(204\) 0 0
\(205\) −4.91874 + 8.51951i −0.343540 + 0.595028i
\(206\) 0 0
\(207\) 13.5261 0.940129
\(208\) 0 0
\(209\) −0.526475 −0.0364170
\(210\) 0 0
\(211\) −4.11795 + 7.13251i −0.283492 + 0.491022i −0.972242 0.233976i \(-0.924826\pi\)
0.688751 + 0.724998i \(0.258160\pi\)
\(212\) 0 0
\(213\) 4.12330i 0.282524i
\(214\) 0 0
\(215\) 1.13030 0.652579i 0.0770858 0.0445055i
\(216\) 0 0
\(217\) −2.34888 4.06838i −0.159452 0.276179i
\(218\) 0 0
\(219\) −1.08966 0.629116i −0.0736325 0.0425117i
\(220\) 0 0
\(221\) 5.74771 9.94405i 0.386633 0.668909i
\(222\) 0 0
\(223\) −13.2515 7.65073i −0.887383 0.512331i −0.0142977 0.999898i \(-0.504551\pi\)
−0.873086 + 0.487567i \(0.837885\pi\)
\(224\) 0 0
\(225\) 2.86064 + 4.95477i 0.190709 + 0.330318i
\(226\) 0 0
\(227\) 6.02292 3.47733i 0.399755 0.230799i −0.286623 0.958043i \(-0.592533\pi\)
0.686378 + 0.727245i \(0.259199\pi\)
\(228\) 0 0
\(229\) 27.4219i 1.81209i −0.423180 0.906045i \(-0.639086\pi\)
0.423180 0.906045i \(-0.360914\pi\)
\(230\) 0 0
\(231\) 0.106157 0.183870i 0.00698463 0.0120977i
\(232\) 0 0
\(233\) 6.85333 0.448976 0.224488 0.974477i \(-0.427929\pi\)
0.224488 + 0.974477i \(0.427929\pi\)
\(234\) 0 0
\(235\) 21.5926 1.40854
\(236\) 0 0
\(237\) −2.00536 + 3.47338i −0.130262 + 0.225621i
\(238\) 0 0
\(239\) 22.0754i 1.42794i −0.700177 0.713970i \(-0.746895\pi\)
0.700177 0.713970i \(-0.253105\pi\)
\(240\) 0 0
\(241\) 13.6807 7.89855i 0.881251 0.508790i 0.0101802 0.999948i \(-0.496759\pi\)
0.871071 + 0.491158i \(0.163426\pi\)
\(242\) 0 0
\(243\) −6.70981 11.6217i −0.430434 0.745534i
\(244\) 0 0
\(245\) −1.46199 0.844083i −0.0934034 0.0539265i
\(246\) 0 0
\(247\) −4.50732 2.60525i −0.286794 0.165768i
\(248\) 0 0
\(249\) 0.286118 + 0.165190i 0.0181320 + 0.0104685i
\(250\) 0 0
\(251\) −11.2783 19.5346i −0.711882 1.23302i −0.964150 0.265359i \(-0.914510\pi\)
0.252268 0.967658i \(-0.418824\pi\)
\(252\) 0 0
\(253\) 1.60512 0.926716i 0.100913 0.0582621i
\(254\) 0 0
\(255\) 3.13141i 0.196097i
\(256\) 0 0
\(257\) 10.2064 17.6781i 0.636660 1.10273i −0.349501 0.936936i \(-0.613649\pi\)
0.986161 0.165791i \(-0.0530179\pi\)
\(258\) 0 0
\(259\) −6.31584 −0.392447
\(260\) 0 0
\(261\) −21.8107 −1.35005
\(262\) 0 0
\(263\) −14.7701 + 25.5826i −0.910764 + 1.57749i −0.0977768 + 0.995208i \(0.531173\pi\)
−0.812987 + 0.582281i \(0.802160\pi\)
\(264\) 0 0
\(265\) 2.31464i 0.142187i
\(266\) 0 0
\(267\) 0.574342 0.331596i 0.0351491 0.0202934i
\(268\) 0 0
\(269\) −13.9581 24.1762i −0.851043 1.47405i −0.880268 0.474477i \(-0.842637\pi\)
0.0292252 0.999573i \(-0.490696\pi\)
\(270\) 0 0
\(271\) 25.5036 + 14.7245i 1.54924 + 0.894451i 0.998200 + 0.0599690i \(0.0191002\pi\)
0.551035 + 0.834482i \(0.314233\pi\)
\(272\) 0 0
\(273\) 1.81872 1.04885i 0.110074 0.0634793i
\(274\) 0 0
\(275\) 0.678933 + 0.391982i 0.0409412 + 0.0236374i
\(276\) 0 0
\(277\) 3.42927 + 5.93967i 0.206045 + 0.356880i 0.950465 0.310831i \(-0.100607\pi\)
−0.744420 + 0.667711i \(0.767274\pi\)
\(278\) 0 0
\(279\) −10.8257 + 6.25021i −0.648117 + 0.374190i
\(280\) 0 0
\(281\) 29.0940i 1.73561i −0.496909 0.867803i \(-0.665532\pi\)
0.496909 0.867803i \(-0.334468\pi\)
\(282\) 0 0
\(283\) −5.80511 + 10.0547i −0.345078 + 0.597692i −0.985368 0.170441i \(-0.945481\pi\)
0.640290 + 0.768133i \(0.278814\pi\)
\(284\) 0 0
\(285\) −1.41937 −0.0840761
\(286\) 0 0
\(287\) 5.82732 0.343976
\(288\) 0 0
\(289\) 3.42614 5.93425i 0.201538 0.349074i
\(290\) 0 0
\(291\) 4.61633i 0.270614i
\(292\) 0 0
\(293\) −15.4054 + 8.89430i −0.899992 + 0.519610i −0.877197 0.480130i \(-0.840590\pi\)
−0.0227942 + 0.999740i \(0.507256\pi\)
\(294\) 0 0
\(295\) −7.90228 13.6871i −0.460088 0.796896i
\(296\) 0 0
\(297\) −1.04087 0.600949i −0.0603976 0.0348706i
\(298\) 0 0
\(299\) 18.3278 + 0.00899334i 1.05992 + 0.000520098i
\(300\) 0 0
\(301\) −0.669543 0.386561i −0.0385918 0.0222810i
\(302\) 0 0
\(303\) −4.52629 7.83976i −0.260028 0.450382i
\(304\) 0 0
\(305\) 13.1943 7.61771i 0.755501 0.436189i
\(306\) 0 0
\(307\) 9.07966i 0.518204i −0.965850 0.259102i \(-0.916573\pi\)
0.965850 0.259102i \(-0.0834265\pi\)
\(308\) 0 0
\(309\) −2.99827 + 5.19315i −0.170566 + 0.295428i
\(310\) 0 0
\(311\) 1.57073 0.0890677 0.0445338 0.999008i \(-0.485820\pi\)
0.0445338 + 0.999008i \(0.485820\pi\)
\(312\) 0 0
\(313\) 20.6232 1.16569 0.582846 0.812582i \(-0.301939\pi\)
0.582846 + 0.812582i \(0.301939\pi\)
\(314\) 0 0
\(315\) −2.24605 + 3.89027i −0.126551 + 0.219192i
\(316\) 0 0
\(317\) 30.5435i 1.71549i 0.514072 + 0.857747i \(0.328137\pi\)
−0.514072 + 0.857747i \(0.671863\pi\)
\(318\) 0 0
\(319\) −2.58823 + 1.49432i −0.144913 + 0.0836657i
\(320\) 0 0
\(321\) −3.82111 6.61836i −0.213274 0.369401i
\(322\) 0 0
\(323\) 3.98340 + 2.29982i 0.221642 + 0.127965i
\(324\) 0 0
\(325\) 3.87285 + 6.71558i 0.214827 + 0.372513i
\(326\) 0 0
\(327\) −5.26765 3.04128i −0.291302 0.168183i
\(328\) 0 0
\(329\) −6.39527 11.0769i −0.352583 0.610691i
\(330\) 0 0
\(331\) 22.3894 12.9265i 1.23063 0.710507i 0.263472 0.964667i \(-0.415132\pi\)
0.967162 + 0.254161i \(0.0817992\pi\)
\(332\) 0 0
\(333\) 16.8060i 0.920965i
\(334\) 0 0
\(335\) 11.3748 19.7017i 0.621472 1.07642i
\(336\) 0 0
\(337\) −21.3954 −1.16548 −0.582742 0.812657i \(-0.698020\pi\)
−0.582742 + 0.812657i \(0.698020\pi\)
\(338\) 0 0
\(339\) 2.88387 0.156630
\(340\) 0 0
\(341\) −0.856443 + 1.48340i −0.0463790 + 0.0803308i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) 4.32738 2.49841i 0.232978 0.134510i
\(346\) 0 0
\(347\) 1.10442 + 1.91291i 0.0592882 + 0.102690i 0.894146 0.447775i \(-0.147784\pi\)
−0.834858 + 0.550466i \(0.814450\pi\)
\(348\) 0 0
\(349\) −9.77843 5.64558i −0.523427 0.302201i 0.214908 0.976634i \(-0.431055\pi\)
−0.738336 + 0.674433i \(0.764388\pi\)
\(350\) 0 0
\(351\) −5.93747 10.2957i −0.316919 0.549542i
\(352\) 0 0
\(353\) −30.8680 17.8217i −1.64294 0.948552i −0.979781 0.200072i \(-0.935882\pi\)
−0.663158 0.748479i \(-0.730784\pi\)
\(354\) 0 0
\(355\) −5.97708 10.3526i −0.317230 0.549459i
\(356\) 0 0
\(357\) −1.60641 + 0.927459i −0.0850201 + 0.0490864i
\(358\) 0 0
\(359\) 19.3218i 1.01976i −0.860244 0.509882i \(-0.829689\pi\)
0.860244 0.509882i \(-0.170311\pi\)
\(360\) 0 0
\(361\) −8.45757 + 14.6489i −0.445135 + 0.770997i
\(362\) 0 0
\(363\) 6.32780 0.332123
\(364\) 0 0
\(365\) 3.64783 0.190936
\(366\) 0 0
\(367\) −1.86032 + 3.22218i −0.0971082 + 0.168196i −0.910487 0.413539i \(-0.864293\pi\)
0.813378 + 0.581735i \(0.197626\pi\)
\(368\) 0 0
\(369\) 15.5061i 0.807217i
\(370\) 0 0
\(371\) −1.18740 + 0.685548i −0.0616469 + 0.0355919i
\(372\) 0 0
\(373\) 1.75638 + 3.04214i 0.0909420 + 0.157516i 0.907908 0.419170i \(-0.137679\pi\)
−0.816966 + 0.576686i \(0.804346\pi\)
\(374\) 0 0
\(375\) 6.08693 + 3.51429i 0.314328 + 0.181477i
\(376\) 0 0
\(377\) −29.5533 0.0145016i −1.52207 0.000746873i
\(378\) 0 0
\(379\) −21.6647 12.5081i −1.11284 0.642500i −0.173279 0.984873i \(-0.555436\pi\)
−0.939564 + 0.342373i \(0.888770\pi\)
\(380\) 0 0
\(381\) −2.34877 4.06818i −0.120331 0.208419i
\(382\) 0 0
\(383\) 19.4556 11.2327i 0.994134 0.573964i 0.0876266 0.996153i \(-0.472072\pi\)
0.906507 + 0.422190i \(0.138738\pi\)
\(384\) 0 0
\(385\) 0.615536i 0.0313706i
\(386\) 0 0
\(387\) −1.02861 + 1.78161i −0.0522874 + 0.0905644i
\(388\) 0 0
\(389\) 13.3364 0.676184 0.338092 0.941113i \(-0.390219\pi\)
0.338092 + 0.941113i \(0.390219\pi\)
\(390\) 0 0
\(391\) −16.1928 −0.818906
\(392\) 0 0
\(393\) 5.50379 9.53284i 0.277629 0.480868i
\(394\) 0 0
\(395\) 11.6278i 0.585057i
\(396\) 0 0
\(397\) −22.3723 + 12.9166i −1.12283 + 0.648268i −0.942123 0.335268i \(-0.891173\pi\)
−0.180710 + 0.983536i \(0.557840\pi\)
\(398\) 0 0
\(399\) 0.420388 + 0.728133i 0.0210457 + 0.0364522i
\(400\) 0 0
\(401\) 15.2078 + 8.78025i 0.759443 + 0.438465i 0.829096 0.559106i \(-0.188856\pi\)
−0.0696524 + 0.997571i \(0.522189\pi\)
\(402\) 0 0
\(403\) −14.6729 + 8.46180i −0.730909 + 0.421512i
\(404\) 0 0
\(405\) 8.86464 + 5.11800i 0.440487 + 0.254316i
\(406\) 0 0
\(407\) 1.15143 + 1.99434i 0.0570745 + 0.0988559i
\(408\) 0 0
\(409\) 12.5818 7.26410i 0.622129 0.359186i −0.155568 0.987825i \(-0.549721\pi\)
0.777698 + 0.628639i \(0.216388\pi\)
\(410\) 0 0
\(411\) 10.6126i 0.523479i
\(412\) 0 0
\(413\) −4.68098 + 8.10770i −0.230336 + 0.398954i
\(414\) 0 0
\(415\) −0.957831 −0.0470181
\(416\) 0 0
\(417\) −3.05753 −0.149728
\(418\) 0 0
\(419\) −2.30096 + 3.98538i −0.112409 + 0.194699i −0.916741 0.399482i \(-0.869190\pi\)
0.804332 + 0.594180i \(0.202523\pi\)
\(420\) 0 0
\(421\) 19.2645i 0.938895i −0.882960 0.469447i \(-0.844453\pi\)
0.882960 0.469447i \(-0.155547\pi\)
\(422\) 0 0
\(423\) −29.4750 + 17.0174i −1.43312 + 0.827415i
\(424\) 0 0
\(425\) −3.42462 5.93161i −0.166118 0.287726i
\(426\) 0 0
\(427\) −7.81574 4.51242i −0.378230 0.218371i
\(428\) 0 0
\(429\) −0.662763 0.383080i −0.0319985 0.0184953i
\(430\) 0 0
\(431\) 24.5649 + 14.1825i 1.18325 + 0.683149i 0.956764 0.290865i \(-0.0939432\pi\)
0.226485 + 0.974015i \(0.427277\pi\)
\(432\) 0 0
\(433\) −6.26014 10.8429i −0.300843 0.521076i 0.675484 0.737375i \(-0.263935\pi\)
−0.976327 + 0.216299i \(0.930601\pi\)
\(434\) 0 0
\(435\) −6.97784 + 4.02866i −0.334562 + 0.193159i
\(436\) 0 0
\(437\) 7.33969i 0.351105i
\(438\) 0 0
\(439\) −15.8637 + 27.4767i −0.757132 + 1.31139i 0.187176 + 0.982326i \(0.440067\pi\)
−0.944307 + 0.329064i \(0.893267\pi\)
\(440\) 0 0
\(441\) 2.66094 0.126711
\(442\) 0 0
\(443\) −1.73048 −0.0822177 −0.0411088 0.999155i \(-0.513089\pi\)
−0.0411088 + 0.999155i \(0.513089\pi\)
\(444\) 0 0
\(445\) −0.961355 + 1.66512i −0.0455726 + 0.0789341i
\(446\) 0 0
\(447\) 5.39965i 0.255394i
\(448\) 0 0
\(449\) −9.14208 + 5.27818i −0.431442 + 0.249093i −0.699961 0.714181i \(-0.746799\pi\)
0.268519 + 0.963274i \(0.413466\pi\)
\(450\) 0 0
\(451\) −1.06237 1.84008i −0.0500252 0.0866462i
\(452\) 0 0
\(453\) 7.06658 + 4.07989i 0.332017 + 0.191690i
\(454\) 0 0
\(455\) −3.04597 + 5.26980i −0.142797 + 0.247052i
\(456\) 0 0
\(457\) −6.88399 3.97447i −0.322019 0.185918i 0.330273 0.943885i \(-0.392859\pi\)
−0.652292 + 0.757968i \(0.726193\pi\)
\(458\) 0 0
\(459\) 5.25029 + 9.09377i 0.245062 + 0.424461i
\(460\) 0 0
\(461\) 9.43262 5.44592i 0.439321 0.253642i −0.263989 0.964526i \(-0.585038\pi\)
0.703309 + 0.710884i \(0.251705\pi\)
\(462\) 0 0
\(463\) 35.8227i 1.66482i 0.554158 + 0.832411i \(0.313040\pi\)
−0.554158 + 0.832411i \(0.686960\pi\)
\(464\) 0 0
\(465\) −2.30896 + 3.99923i −0.107075 + 0.185460i
\(466\) 0 0
\(467\) 19.8983 0.920785 0.460393 0.887715i \(-0.347709\pi\)
0.460393 + 0.887715i \(0.347709\pi\)
\(468\) 0 0
\(469\) −13.4759 −0.622261
\(470\) 0 0
\(471\) 5.00262 8.66479i 0.230508 0.399252i
\(472\) 0 0
\(473\) 0.281894i 0.0129615i
\(474\) 0 0
\(475\) −2.68861 + 1.55227i −0.123362 + 0.0712231i
\(476\) 0 0
\(477\) 1.82420 + 3.15960i 0.0835243 + 0.144668i
\(478\) 0 0
\(479\) −22.7680 13.1451i −1.04030 0.600615i −0.120379 0.992728i \(-0.538411\pi\)
−0.919917 + 0.392113i \(0.871744\pi\)
\(480\) 0 0
\(481\) −0.0111741 + 22.7721i −0.000509496 + 1.03832i
\(482\) 0 0
\(483\) −2.56336 1.47996i −0.116637 0.0673404i
\(484\) 0 0
\(485\) −6.69177 11.5905i −0.303857 0.526296i
\(486\) 0 0
\(487\) −5.52491 + 3.18981i −0.250358 + 0.144544i −0.619928 0.784659i \(-0.712838\pi\)
0.369570 + 0.929203i \(0.379505\pi\)
\(488\) 0 0
\(489\) 6.86682i 0.310528i
\(490\) 0 0
\(491\) 1.48384 2.57008i 0.0669647 0.115986i −0.830599 0.556871i \(-0.812002\pi\)
0.897564 + 0.440885i \(0.145335\pi\)
\(492\) 0 0
\(493\) 26.1107 1.17597
\(494\) 0 0
\(495\) 1.63790 0.0736182
\(496\) 0 0
\(497\) −3.54058 + 6.13246i −0.158817 + 0.275078i
\(498\) 0 0
\(499\) 28.1331i 1.25941i 0.776835 + 0.629704i \(0.216824\pi\)
−0.776835 + 0.629704i \(0.783176\pi\)
\(500\) 0 0
\(501\) 2.17691 1.25684i 0.0972571 0.0561514i
\(502\) 0 0
\(503\) −15.7688 27.3124i −0.703097 1.21780i −0.967374 0.253353i \(-0.918467\pi\)
0.264277 0.964447i \(-0.414867\pi\)
\(504\) 0 0
\(505\) 22.7288 + 13.1225i 1.01142 + 0.583943i
\(506\) 0 0
\(507\) −3.77846 6.55935i −0.167807 0.291311i
\(508\) 0 0
\(509\) 11.7731 + 6.79719i 0.521832 + 0.301280i 0.737684 0.675146i \(-0.235919\pi\)
−0.215852 + 0.976426i \(0.569253\pi\)
\(510\) 0 0
\(511\) −1.08041 1.87133i −0.0477947 0.0827828i
\(512\) 0 0
\(513\) 4.12191 2.37979i 0.181987 0.105070i
\(514\) 0 0
\(515\) 17.3850i 0.766074i
\(516\) 0 0
\(517\) −2.33183 + 4.03885i −0.102554 + 0.177628i
\(518\) 0 0
\(519\) −7.29012 −0.320001
\(520\) 0 0
\(521\) 8.78344 0.384810 0.192405 0.981316i \(-0.438371\pi\)
0.192405 + 0.981316i \(0.438371\pi\)
\(522\) 0 0
\(523\) 16.2849 28.2063i 0.712088 1.23337i −0.251983 0.967732i \(-0.581083\pi\)
0.964072 0.265642i \(-0.0855839\pi\)
\(524\) 0 0
\(525\) 1.25198i 0.0546411i
\(526\) 0 0
\(527\) 12.9600 7.48246i 0.564547 0.325941i
\(528\) 0 0
\(529\) −1.41953 2.45869i −0.0617185 0.106900i
\(530\) 0 0
\(531\) 21.5741 + 12.4558i 0.936235 + 0.540536i
\(532\) 0 0
\(533\) 0.0103098 21.0107i 0.000446568 0.910074i
\(534\) 0 0
\(535\) 19.1878 + 11.0781i 0.829560 + 0.478947i
\(536\) 0 0
\(537\) 1.92021 + 3.32590i 0.0828631 + 0.143523i
\(538\) 0 0
\(539\) 0.315769 0.182309i 0.0136011 0.00785261i
\(540\) 0 0
\(541\) 6.94870i 0.298748i −0.988781 0.149374i \(-0.952274\pi\)
0.988781 0.149374i \(-0.0477258\pi\)
\(542\) 0 0
\(543\) 3.20718 5.55500i 0.137633 0.238388i
\(544\) 0 0
\(545\) 17.6344 0.755375
\(546\) 0 0
\(547\) −10.9095 −0.466457 −0.233229 0.972422i \(-0.574929\pi\)
−0.233229 + 0.972422i \(0.574929\pi\)
\(548\) 0 0
\(549\) −12.0073 + 20.7972i −0.512457 + 0.887602i
\(550\) 0 0
\(551\) 11.8352i 0.504194i
\(552\) 0 0
\(553\) −5.96502 + 3.44391i −0.253659 + 0.146450i
\(554\) 0 0
\(555\) 3.10425 + 5.37672i 0.131768 + 0.228229i
\(556\) 0 0
\(557\) 29.9901 + 17.3148i 1.27072 + 0.733650i 0.975123 0.221662i \(-0.0711483\pi\)
0.295596 + 0.955313i \(0.404482\pi\)
\(558\) 0 0
\(559\) −1.39495 + 2.41339i −0.0590001 + 0.102075i
\(560\) 0 0
\(561\) 0.585725 + 0.338169i 0.0247293 + 0.0142775i
\(562\) 0 0
\(563\) −4.56839 7.91269i −0.192535 0.333480i 0.753555 0.657385i \(-0.228338\pi\)
−0.946090 + 0.323905i \(0.895004\pi\)
\(564\) 0 0
\(565\) −7.24070 + 4.18042i −0.304618 + 0.175872i
\(566\) 0 0
\(567\) 6.06339i 0.254638i
\(568\) 0 0
\(569\) 9.15000 15.8483i 0.383588 0.664394i −0.607984 0.793949i \(-0.708022\pi\)
0.991572 + 0.129555i \(0.0413549\pi\)
\(570\) 0 0
\(571\) 10.1791 0.425981 0.212990 0.977054i \(-0.431680\pi\)
0.212990 + 0.977054i \(0.431680\pi\)
\(572\) 0 0
\(573\) −3.45423 −0.144303
\(574\) 0 0
\(575\) 5.46470 9.46514i 0.227894 0.394724i
\(576\) 0 0
\(577\) 19.5165i 0.812482i 0.913766 + 0.406241i \(0.133161\pi\)
−0.913766 + 0.406241i \(0.866839\pi\)
\(578\) 0 0
\(579\) −2.11593 + 1.22163i −0.0879352 + 0.0507694i
\(580\) 0 0
\(581\) 0.283690 + 0.491365i 0.0117694 + 0.0203853i
\(582\) 0 0
\(583\) 0.432949 + 0.249963i 0.0179309 + 0.0103524i
\(584\) 0 0
\(585\) 14.0226 + 8.10513i 0.579763 + 0.335106i
\(586\) 0 0
\(587\) 30.6486 + 17.6950i 1.26501 + 0.730351i 0.974039 0.226382i \(-0.0726898\pi\)
0.290967 + 0.956733i \(0.406023\pi\)
\(588\) 0 0
\(589\) −3.39156 5.87436i −0.139747 0.242049i
\(590\) 0 0
\(591\) −2.91723 + 1.68426i −0.119999 + 0.0692812i
\(592\) 0 0
\(593\) 18.0881i 0.742790i −0.928475 0.371395i \(-0.878880\pi\)
0.928475 0.371395i \(-0.121120\pi\)
\(594\) 0 0
\(595\) 2.68887 4.65725i 0.110233 0.190929i
\(596\) 0 0
\(597\) 6.96407 0.285021
\(598\) 0 0
\(599\) −9.05992 −0.370178 −0.185089 0.982722i \(-0.559257\pi\)
−0.185089 + 0.982722i \(0.559257\pi\)
\(600\) 0 0
\(601\) −14.6440 + 25.3642i −0.597343 + 1.03463i 0.395869 + 0.918307i \(0.370444\pi\)
−0.993212 + 0.116321i \(0.962890\pi\)
\(602\) 0 0
\(603\) 35.8586i 1.46028i
\(604\) 0 0
\(605\) −15.8876 + 9.17269i −0.645922 + 0.372923i
\(606\) 0 0
\(607\) −19.6825 34.0911i −0.798887 1.38371i −0.920341 0.391116i \(-0.872089\pi\)
0.121454 0.992597i \(-0.461244\pi\)
\(608\) 0 0
\(609\) 4.13339 + 2.38641i 0.167493 + 0.0967023i
\(610\) 0 0
\(611\) −39.9498 + 23.0389i −1.61619 + 0.932053i
\(612\) 0 0
\(613\) 4.79186 + 2.76658i 0.193541 + 0.111741i 0.593639 0.804731i \(-0.297691\pi\)
−0.400098 + 0.916472i \(0.631024\pi\)
\(614\) 0 0
\(615\) −2.86414 4.96084i −0.115493 0.200040i
\(616\) 0 0
\(617\) 10.8959 6.29077i 0.438654 0.253257i −0.264373 0.964421i \(-0.585165\pi\)
0.703026 + 0.711164i \(0.251832\pi\)
\(618\) 0 0
\(619\) 22.3955i 0.900149i −0.892991 0.450075i \(-0.851397\pi\)
0.892991 0.450075i \(-0.148603\pi\)
\(620\) 0 0
\(621\) −8.37794 + 14.5110i −0.336195 + 0.582307i
\(622\) 0 0
\(623\) 1.13893 0.0456305
\(624\) 0 0
\(625\) −9.62659 −0.385064
\(626\) 0 0
\(627\) 0.153281 0.265491i 0.00612145 0.0106027i
\(628\) 0 0
\(629\) 20.1194i 0.802213i
\(630\) 0 0
\(631\) −1.68778 + 0.974439i −0.0671894 + 0.0387918i −0.533218 0.845978i \(-0.679018\pi\)
0.466029 + 0.884769i \(0.345684\pi\)
\(632\) 0 0
\(633\) −2.39785 4.15320i −0.0953061 0.165075i
\(634\) 0 0
\(635\) 11.7944 + 6.80948i 0.468045 + 0.270226i
\(636\) 0 0
\(637\) 3.60555 + 0.00176922i 0.142857 + 7.00992e-5i
\(638\) 0 0
\(639\) 16.3181 + 9.42125i 0.645533 + 0.372699i
\(640\) 0 0
\(641\) 5.21051 + 9.02487i 0.205803 + 0.356461i 0.950388 0.311066i \(-0.100686\pi\)
−0.744585 + 0.667527i \(0.767353\pi\)
\(642\) 0 0
\(643\) −13.2247 + 7.63531i −0.521533 + 0.301107i −0.737562 0.675280i \(-0.764023\pi\)
0.216029 + 0.976387i \(0.430690\pi\)
\(644\) 0 0
\(645\) 0.759983i 0.0299243i
\(646\) 0 0
\(647\) −8.75328 + 15.1611i −0.344127 + 0.596045i −0.985195 0.171439i \(-0.945158\pi\)
0.641068 + 0.767484i \(0.278492\pi\)
\(648\) 0 0
\(649\) 3.41354 0.133993
\(650\) 0 0
\(651\) 2.73547 0.107211
\(652\) 0 0
\(653\) 5.09169 8.81906i 0.199253 0.345117i −0.749033 0.662532i \(-0.769482\pi\)
0.948287 + 0.317416i \(0.102815\pi\)
\(654\) 0 0
\(655\) 31.9129i 1.24694i
\(656\) 0 0
\(657\) −4.97949 + 2.87491i −0.194268 + 0.112161i
\(658\) 0 0
\(659\) −21.9294 37.9828i −0.854247 1.47960i −0.877342 0.479866i \(-0.840685\pi\)
0.0230945 0.999733i \(-0.492648\pi\)
\(660\) 0 0
\(661\) −28.5156 16.4635i −1.10913 0.640356i −0.170526 0.985353i \(-0.554547\pi\)
−0.938604 + 0.344997i \(0.887880\pi\)
\(662\) 0 0
\(663\) 3.34116 + 5.79362i 0.129760 + 0.225006i
\(664\) 0 0
\(665\) −2.11098 1.21878i −0.0818604 0.0472621i
\(666\) 0 0
\(667\) 20.8326 + 36.0831i 0.806640 + 1.39714i
\(668\) 0 0
\(669\) 7.71622 4.45496i 0.298326 0.172239i
\(670\) 0 0
\(671\) 3.29062i 0.127033i
\(672\) 0 0
\(673\) 13.3423 23.1095i 0.514307 0.890806i −0.485555 0.874206i \(-0.661383\pi\)
0.999862 0.0165997i \(-0.00528409\pi\)
\(674\) 0 0
\(675\) −7.08740 −0.272794
\(676\) 0 0
\(677\) 29.5328 1.13504 0.567519 0.823361i \(-0.307904\pi\)
0.567519 + 0.823361i \(0.307904\pi\)
\(678\) 0 0
\(679\) −3.96393 + 6.86572i −0.152122 + 0.263482i
\(680\) 0 0
\(681\) 4.04965i 0.155183i
\(682\) 0 0
\(683\) 15.8379 9.14400i 0.606019 0.349885i −0.165387 0.986229i \(-0.552887\pi\)
0.771406 + 0.636343i \(0.219554\pi\)
\(684\) 0 0
\(685\) −15.3838 26.6456i −0.587786 1.01807i
\(686\) 0 0
\(687\) 13.8283 + 7.98378i 0.527583 + 0.304600i
\(688\) 0 0
\(689\) 2.46968 + 4.28246i 0.0940872 + 0.163149i
\(690\) 0 0
\(691\) 8.95525 + 5.17031i 0.340674 + 0.196688i 0.660570 0.750765i \(-0.270315\pi\)
−0.319896 + 0.947453i \(0.603648\pi\)
\(692\) 0 0
\(693\) −0.485113 0.840240i −0.0184279 0.0319181i
\(694\) 0 0
\(695\) 7.67671 4.43215i 0.291194 0.168121i
\(696\) 0 0
\(697\) 18.5632i 0.703131i
\(698\) 0 0
\(699\) −1.99532 + 3.45599i −0.0754699 + 0.130718i
\(700\) 0 0
\(701\) 41.6959 1.57483 0.787415 0.616423i \(-0.211419\pi\)
0.787415 + 0.616423i \(0.211419\pi\)
\(702\) 0 0
\(703\) −9.11948 −0.343948
\(704\) 0 0
\(705\) −6.28659 + 10.8887i −0.236766 + 0.410092i
\(706\) 0 0
\(707\) 15.5464i 0.584684i
\(708\) 0 0
\(709\) 0.00947974 0.00547313i 0.000356019 0.000205548i −0.499822 0.866128i \(-0.666601\pi\)
0.500178 + 0.865923i \(0.333268\pi\)
\(710\) 0 0
\(711\) 9.16402 + 15.8725i 0.343677 + 0.595267i
\(712\) 0 0
\(713\) 20.6804 + 11.9398i 0.774488 + 0.447151i
\(714\) 0 0
\(715\) 2.21935 + 0.00108902i 0.0829988 + 4.07271e-5i
\(716\) 0 0
\(717\) 11.1322 + 6.42717i 0.415739 + 0.240027i
\(718\) 0 0
\(719\) 12.7330 + 22.0542i 0.474861 + 0.822484i 0.999586 0.0287885i \(-0.00916494\pi\)
−0.524724 + 0.851272i \(0.675832\pi\)
\(720\) 0 0
\(721\) −8.91847 + 5.14908i −0.332141 + 0.191762i
\(722\) 0 0
\(723\) 9.19853i 0.342097i
\(724\) 0 0
\(725\) −8.81176 + 15.2624i −0.327261 + 0.566832i
\(726\) 0 0
\(727\) 23.5565 0.873663 0.436831 0.899543i \(-0.356101\pi\)
0.436831 + 0.899543i \(0.356101\pi\)
\(728\) 0 0
\(729\) −10.3760 −0.384297
\(730\) 0 0
\(731\) 1.23141 2.13286i 0.0455453 0.0788867i
\(732\) 0 0
\(733\) 6.23249i 0.230202i 0.993354 + 0.115101i \(0.0367192\pi\)
−0.993354 + 0.115101i \(0.963281\pi\)
\(734\) 0 0
\(735\) 0.851308 0.491503i 0.0314010 0.0181293i
\(736\) 0 0
\(737\) 2.45679 + 4.25528i 0.0904969 + 0.156745i
\(738\) 0 0
\(739\) −1.12339 0.648588i −0.0413244 0.0238587i 0.479195 0.877708i \(-0.340929\pi\)
−0.520520 + 0.853850i \(0.674262\pi\)
\(740\) 0 0
\(741\) 2.62606 1.51444i 0.0964709 0.0556344i
\(742\) 0 0
\(743\) −5.25627 3.03471i −0.192834 0.111333i 0.400475 0.916308i \(-0.368845\pi\)
−0.593309 + 0.804975i \(0.702179\pi\)
\(744\) 0 0
\(745\) −7.82725 13.5572i −0.286768 0.496697i
\(746\) 0 0
\(747\) 1.30749 0.754880i 0.0478386 0.0276196i
\(748\) 0 0
\(749\) 13.1244i 0.479555i
\(750\) 0 0
\(751\) 18.3023 31.7005i 0.667860 1.15677i −0.310641 0.950527i \(-0.600544\pi\)
0.978501 0.206241i \(-0.0661230\pi\)
\(752\) 0 0
\(753\) 13.1346 0.478650
\(754\) 0 0
\(755\) −23.6566 −0.860952
\(756\) 0 0
\(757\) −5.83991 + 10.1150i −0.212255 + 0.367636i −0.952420 0.304789i \(-0.901414\pi\)
0.740165 + 0.672425i \(0.234747\pi\)
\(758\) 0 0
\(759\) 1.07924i 0.0391739i
\(760\) 0 0
\(761\) −34.4408 + 19.8844i −1.24848 + 0.720810i −0.970806 0.239866i \(-0.922896\pi\)
−0.277673 + 0.960676i \(0.589563\pi\)
\(762\) 0 0
\(763\) −5.22295 9.04641i −0.189083 0.327502i
\(764\) 0 0
\(765\) −12.3926 7.15490i −0.448057 0.258686i
\(766\) 0 0
\(767\) 29.2245 + 16.8919i 1.05523 + 0.609930i
\(768\) 0 0
\(769\) −8.62507 4.97969i −0.311028 0.179572i 0.336358 0.941734i \(-0.390805\pi\)
−0.647386 + 0.762162i \(0.724138\pi\)
\(770\) 0 0
\(771\) 5.94313 + 10.2938i 0.214036 + 0.370722i
\(772\) 0 0
\(773\) 11.0433 6.37588i 0.397201 0.229324i −0.288074 0.957608i \(-0.593015\pi\)
0.685276 + 0.728284i \(0.259682\pi\)
\(774\) 0 0
\(775\) 10.1006i 0.362825i
\(776\) 0 0
\(777\) 1.83883 3.18495i 0.0659677 0.114259i
\(778\) 0 0
\(779\) 8.41411 0.301467
\(780\) 0 0
\(781\) 2.58192 0.0923882
\(782\) 0 0
\(783\) 13.5093 23.3988i 0.482784 0.836206i
\(784\) 0 0
\(785\) 29.0069i 1.03530i
\(786\) 0 0
\(787\) −7.52380 + 4.34387i −0.268194 + 0.154842i −0.628067 0.778159i \(-0.716154\pi\)
0.359872 + 0.933002i \(0.382820\pi\)
\(788\) 0 0
\(789\) −8.60052 14.8965i −0.306187 0.530331i
\(790\) 0 0
\(791\) 4.28909 + 2.47631i 0.152503 + 0.0880474i
\(792\) 0 0
\(793\) −16.2836 + 28.1721i −0.578247 + 1.00042i
\(794\) 0 0
\(795\) 1.16722 + 0.673897i 0.0413972