Properties

Label 400.2.l.g.101.6
Level $400$
Weight $2$
Character 400.101
Analytic conductor $3.194$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 400.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.19401608085\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.4767670494822400.1
Defining polynomial: \(x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + 112 x^{2} - 128 x + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 101.6
Root \(1.35979 - 0.388551i\) of defining polynomial
Character \(\chi\) \(=\) 400.101
Dual form 400.2.l.g.301.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.35979 - 0.388551i) q^{2} +(1.03997 - 1.03997i) q^{3} +(1.69806 - 1.05670i) q^{4} +(1.01006 - 1.81822i) q^{6} +1.49668i q^{7} +(1.89842 - 2.09667i) q^{8} +0.836925i q^{9} +O(q^{10})\) \(q+(1.35979 - 0.388551i) q^{2} +(1.03997 - 1.03997i) q^{3} +(1.69806 - 1.05670i) q^{4} +(1.01006 - 1.81822i) q^{6} +1.49668i q^{7} +(1.89842 - 2.09667i) q^{8} +0.836925i q^{9} +(0.423260 + 0.423260i) q^{11} +(0.666995 - 2.86486i) q^{12} +(1.85704 - 1.85704i) q^{13} +(0.581538 + 2.03517i) q^{14} +(1.76679 - 3.58866i) q^{16} -6.50950 q^{17} +(0.325188 + 1.13804i) q^{18} +(-1.75725 + 1.75725i) q^{19} +(1.55650 + 1.55650i) q^{21} +(0.740003 + 0.411086i) q^{22} -7.19295i q^{23} +(-0.206172 - 4.15477i) q^{24} +(1.80363 - 3.24674i) q^{26} +(3.99029 + 3.99029i) q^{27} +(1.58154 + 2.54145i) q^{28} +(-6.57892 + 6.57892i) q^{29} -6.75252 q^{31} +(1.00808 - 5.56631i) q^{32} +0.880355 q^{33} +(-8.85156 + 2.52928i) q^{34} +(0.884375 + 1.42115i) q^{36} +(-1.95300 - 1.95300i) q^{37} +(-1.70671 + 3.07227i) q^{38} -3.86254i q^{39} +7.70745i q^{41} +(2.72130 + 1.51174i) q^{42} +(6.13581 + 6.13581i) q^{43} +(1.16598 + 0.271462i) q^{44} +(-2.79483 - 9.78090i) q^{46} +6.65476 q^{47} +(-1.89469 - 5.56950i) q^{48} +4.75994 q^{49} +(-6.76969 + 6.76969i) q^{51} +(1.19103 - 5.11569i) q^{52} +(-5.29390 - 5.29390i) q^{53} +(6.97638 + 3.87552i) q^{54} +(3.13804 + 2.84133i) q^{56} +3.65497i q^{57} +(-6.38970 + 11.5022i) q^{58} +(5.91841 + 5.91841i) q^{59} +(-1.43686 + 1.43686i) q^{61} +(-9.18201 + 2.62370i) q^{62} -1.25261 q^{63} +(-0.792016 - 7.96070i) q^{64} +(1.19710 - 0.342063i) q^{66} +(6.35614 - 6.35614i) q^{67} +(-11.0535 + 6.87857i) q^{68} +(-7.48045 - 7.48045i) q^{69} -4.08932i q^{71} +(1.75475 + 1.58883i) q^{72} +2.43800i q^{73} +(-3.41451 - 1.89683i) q^{74} +(-1.12703 + 4.84079i) q^{76} +(-0.633485 + 0.633485i) q^{77} +(-1.50079 - 5.25224i) q^{78} +11.6722 q^{79} +5.78878 q^{81} +(2.99474 + 10.4805i) q^{82} +(-2.81439 + 2.81439i) q^{83} +(4.28778 + 0.998279i) q^{84} +(10.7275 + 5.95933i) q^{86} +13.6838i q^{87} +(1.69096 - 0.0839103i) q^{88} -10.5543i q^{89} +(2.77940 + 2.77940i) q^{91} +(-7.60076 - 12.2140i) q^{92} +(-7.02242 + 7.02242i) q^{93} +(9.04907 - 2.58572i) q^{94} +(-4.74042 - 6.83717i) q^{96} -18.1512 q^{97} +(6.47252 - 1.84948i) q^{98} +(-0.354237 + 0.354237i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 4q^{2} + 2q^{3} + 2q^{4} + 6q^{6} - 8q^{8} + O(q^{10}) \) \( 12q + 4q^{2} + 2q^{3} + 2q^{4} + 6q^{6} - 8q^{8} - 2q^{11} + 8q^{12} - 4q^{13} + 14q^{14} + 2q^{16} - 8q^{17} + 18q^{18} - 14q^{19} - 20q^{21} + 2q^{22} - 14q^{24} - 16q^{26} - 10q^{27} + 26q^{28} - 4q^{31} - 16q^{32} + 28q^{33} - 6q^{34} + 2q^{36} + 8q^{37} + 10q^{38} + 10q^{42} - 44q^{44} - 10q^{46} + 8q^{47} - 28q^{48} + 4q^{49} + 10q^{51} - 12q^{52} - 16q^{53} + 10q^{54} + 6q^{56} - 60q^{58} + 20q^{59} + 4q^{61} - 18q^{62} - 8q^{63} + 38q^{64} + 32q^{66} + 50q^{67} - 60q^{68} - 14q^{72} + 10q^{74} + 60q^{76} - 8q^{77} + 4q^{78} + 12q^{79} - 8q^{81} + 42q^{82} - 2q^{83} + 34q^{84} + 6q^{86} + 30q^{88} - 2q^{92} - 44q^{93} + 32q^{94} - 34q^{96} + 64q^{98} + 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(177\) \(351\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.35979 0.388551i 0.961516 0.274747i
\(3\) 1.03997 1.03997i 0.600427 0.600427i −0.339999 0.940426i \(-0.610427\pi\)
0.940426 + 0.339999i \(0.110427\pi\)
\(4\) 1.69806 1.05670i 0.849028 0.528348i
\(5\) 0 0
\(6\) 1.01006 1.81822i 0.412355 0.742286i
\(7\) 1.49668i 0.565693i 0.959165 + 0.282846i \(0.0912786\pi\)
−0.959165 + 0.282846i \(0.908721\pi\)
\(8\) 1.89842 2.09667i 0.671192 0.741283i
\(9\) 0.836925i 0.278975i
\(10\) 0 0
\(11\) 0.423260 + 0.423260i 0.127618 + 0.127618i 0.768031 0.640413i \(-0.221237\pi\)
−0.640413 + 0.768031i \(0.721237\pi\)
\(12\) 0.666995 2.86486i 0.192545 0.827014i
\(13\) 1.85704 1.85704i 0.515051 0.515051i −0.401019 0.916070i \(-0.631344\pi\)
0.916070 + 0.401019i \(0.131344\pi\)
\(14\) 0.581538 + 2.03517i 0.155422 + 0.543923i
\(15\) 0 0
\(16\) 1.76679 3.58866i 0.441697 0.897164i
\(17\) −6.50950 −1.57879 −0.789393 0.613888i \(-0.789605\pi\)
−0.789393 + 0.613888i \(0.789605\pi\)
\(18\) 0.325188 + 1.13804i 0.0766476 + 0.268239i
\(19\) −1.75725 + 1.75725i −0.403141 + 0.403141i −0.879338 0.476198i \(-0.842015\pi\)
0.476198 + 0.879338i \(0.342015\pi\)
\(20\) 0 0
\(21\) 1.55650 + 1.55650i 0.339657 + 0.339657i
\(22\) 0.740003 + 0.411086i 0.157769 + 0.0876439i
\(23\) 7.19295i 1.49983i −0.661532 0.749917i \(-0.730094\pi\)
0.661532 0.749917i \(-0.269906\pi\)
\(24\) −0.206172 4.15477i −0.0420846 0.848088i
\(25\) 0 0
\(26\) 1.80363 3.24674i 0.353721 0.636739i
\(27\) 3.99029 + 3.99029i 0.767931 + 0.767931i
\(28\) 1.58154 + 2.54145i 0.298883 + 0.480289i
\(29\) −6.57892 + 6.57892i −1.22167 + 1.22167i −0.254639 + 0.967036i \(0.581957\pi\)
−0.967036 + 0.254639i \(0.918043\pi\)
\(30\) 0 0
\(31\) −6.75252 −1.21279 −0.606394 0.795164i \(-0.707385\pi\)
−0.606394 + 0.795164i \(0.707385\pi\)
\(32\) 1.00808 5.56631i 0.178205 0.983993i
\(33\) 0.880355 0.153250
\(34\) −8.85156 + 2.52928i −1.51803 + 0.433767i
\(35\) 0 0
\(36\) 0.884375 + 1.42115i 0.147396 + 0.236858i
\(37\) −1.95300 1.95300i −0.321071 0.321071i 0.528107 0.849178i \(-0.322902\pi\)
−0.849178 + 0.528107i \(0.822902\pi\)
\(38\) −1.70671 + 3.07227i −0.276865 + 0.498388i
\(39\) 3.86254i 0.618501i
\(40\) 0 0
\(41\) 7.70745i 1.20370i 0.798609 + 0.601851i \(0.205570\pi\)
−0.798609 + 0.601851i \(0.794430\pi\)
\(42\) 2.72130 + 1.51174i 0.419906 + 0.233266i
\(43\) 6.13581 + 6.13581i 0.935702 + 0.935702i 0.998054 0.0623522i \(-0.0198602\pi\)
−0.0623522 + 0.998054i \(0.519860\pi\)
\(44\) 1.16598 + 0.271462i 0.175778 + 0.0409244i
\(45\) 0 0
\(46\) −2.79483 9.78090i −0.412075 1.44211i
\(47\) 6.65476 0.970697 0.485348 0.874321i \(-0.338693\pi\)
0.485348 + 0.874321i \(0.338693\pi\)
\(48\) −1.89469 5.56950i −0.273475 0.803888i
\(49\) 4.75994 0.679992
\(50\) 0 0
\(51\) −6.76969 + 6.76969i −0.947946 + 0.947946i
\(52\) 1.19103 5.11569i 0.165167 0.709419i
\(53\) −5.29390 5.29390i −0.727173 0.727173i 0.242882 0.970056i \(-0.421907\pi\)
−0.970056 + 0.242882i \(0.921907\pi\)
\(54\) 6.97638 + 3.87552i 0.949365 + 0.527391i
\(55\) 0 0
\(56\) 3.13804 + 2.84133i 0.419338 + 0.379688i
\(57\) 3.65497i 0.484113i
\(58\) −6.38970 + 11.5022i −0.839009 + 1.51031i
\(59\) 5.91841 + 5.91841i 0.770511 + 0.770511i 0.978196 0.207685i \(-0.0665929\pi\)
−0.207685 + 0.978196i \(0.566593\pi\)
\(60\) 0 0
\(61\) −1.43686 + 1.43686i −0.183971 + 0.183971i −0.793084 0.609113i \(-0.791526\pi\)
0.609113 + 0.793084i \(0.291526\pi\)
\(62\) −9.18201 + 2.62370i −1.16612 + 0.333210i
\(63\) −1.25261 −0.157814
\(64\) −0.792016 7.96070i −0.0990020 0.995087i
\(65\) 0 0
\(66\) 1.19710 0.342063i 0.147353 0.0421051i
\(67\) 6.35614 6.35614i 0.776526 0.776526i −0.202712 0.979238i \(-0.564976\pi\)
0.979238 + 0.202712i \(0.0649756\pi\)
\(68\) −11.0535 + 6.87857i −1.34043 + 0.834149i
\(69\) −7.48045 7.48045i −0.900540 0.900540i
\(70\) 0 0
\(71\) 4.08932i 0.485313i −0.970112 0.242657i \(-0.921981\pi\)
0.970112 0.242657i \(-0.0780188\pi\)
\(72\) 1.75475 + 1.58883i 0.206799 + 0.187246i
\(73\) 2.43800i 0.285346i 0.989770 + 0.142673i \(0.0455698\pi\)
−0.989770 + 0.142673i \(0.954430\pi\)
\(74\) −3.41451 1.89683i −0.396929 0.220502i
\(75\) 0 0
\(76\) −1.12703 + 4.84079i −0.129279 + 0.555276i
\(77\) −0.633485 + 0.633485i −0.0721924 + 0.0721924i
\(78\) −1.50079 5.25224i −0.169931 0.594699i
\(79\) 11.6722 1.31323 0.656615 0.754226i \(-0.271988\pi\)
0.656615 + 0.754226i \(0.271988\pi\)
\(80\) 0 0
\(81\) 5.78878 0.643198
\(82\) 2.99474 + 10.4805i 0.330714 + 1.15738i
\(83\) −2.81439 + 2.81439i −0.308919 + 0.308919i −0.844490 0.535571i \(-0.820096\pi\)
0.535571 + 0.844490i \(0.320096\pi\)
\(84\) 4.28778 + 0.998279i 0.467835 + 0.108921i
\(85\) 0 0
\(86\) 10.7275 + 5.95933i 1.15677 + 0.642611i
\(87\) 13.6838i 1.46705i
\(88\) 1.69096 0.0839103i 0.180257 0.00894487i
\(89\) 10.5543i 1.11876i −0.828912 0.559379i \(-0.811040\pi\)
0.828912 0.559379i \(-0.188960\pi\)
\(90\) 0 0
\(91\) 2.77940 + 2.77940i 0.291360 + 0.291360i
\(92\) −7.60076 12.2140i −0.792434 1.27340i
\(93\) −7.02242 + 7.02242i −0.728191 + 0.728191i
\(94\) 9.04907 2.58572i 0.933341 0.266696i
\(95\) 0 0
\(96\) −4.74042 6.83717i −0.483817 0.697815i
\(97\) −18.1512 −1.84298 −0.921488 0.388407i \(-0.873025\pi\)
−0.921488 + 0.388407i \(0.873025\pi\)
\(98\) 6.47252 1.84948i 0.653823 0.186826i
\(99\) −0.354237 + 0.354237i −0.0356021 + 0.0356021i
\(100\) 0 0
\(101\) −1.04036 1.04036i −0.103520 0.103520i 0.653450 0.756970i \(-0.273321\pi\)
−0.756970 + 0.653450i \(0.773321\pi\)
\(102\) −6.57498 + 11.8357i −0.651020 + 1.17191i
\(103\) 0.955267i 0.0941253i −0.998892 0.0470626i \(-0.985014\pi\)
0.998892 0.0470626i \(-0.0149860\pi\)
\(104\) −0.368154 7.41904i −0.0361005 0.727497i
\(105\) 0 0
\(106\) −9.25555 5.14164i −0.898978 0.499400i
\(107\) −7.20266 7.20266i −0.696308 0.696308i 0.267305 0.963612i \(-0.413867\pi\)
−0.963612 + 0.267305i \(0.913867\pi\)
\(108\) 10.9922 + 2.55921i 1.05773 + 0.246260i
\(109\) −5.67807 + 5.67807i −0.543861 + 0.543861i −0.924658 0.380798i \(-0.875649\pi\)
0.380798 + 0.924658i \(0.375649\pi\)
\(110\) 0 0
\(111\) −4.06212 −0.385560
\(112\) 5.37108 + 2.64432i 0.507519 + 0.249865i
\(113\) −1.94751 −0.183206 −0.0916029 0.995796i \(-0.529199\pi\)
−0.0916029 + 0.995796i \(0.529199\pi\)
\(114\) 1.42014 + 4.97000i 0.133009 + 0.465483i
\(115\) 0 0
\(116\) −4.21946 + 18.1233i −0.391767 + 1.68271i
\(117\) 1.55420 + 1.55420i 0.143686 + 0.143686i
\(118\) 10.3474 + 5.74818i 0.952555 + 0.529163i
\(119\) 9.74266i 0.893108i
\(120\) 0 0
\(121\) 10.6417i 0.967427i
\(122\) −1.39553 + 2.51212i −0.126346 + 0.227437i
\(123\) 8.01552 + 8.01552i 0.722735 + 0.722735i
\(124\) −11.4662 + 7.13536i −1.02969 + 0.640774i
\(125\) 0 0
\(126\) −1.70329 + 0.486703i −0.151741 + 0.0433590i
\(127\) 1.31796 0.116950 0.0584750 0.998289i \(-0.481376\pi\)
0.0584750 + 0.998289i \(0.481376\pi\)
\(128\) −4.17011 10.5171i −0.368589 0.929592i
\(129\) 12.7621 1.12364
\(130\) 0 0
\(131\) 1.03026 1.03026i 0.0900139 0.0900139i −0.660666 0.750680i \(-0.729726\pi\)
0.750680 + 0.660666i \(0.229726\pi\)
\(132\) 1.49489 0.930268i 0.130114 0.0809694i
\(133\) −2.63004 2.63004i −0.228054 0.228054i
\(134\) 6.17333 11.1127i 0.533294 0.959991i
\(135\) 0 0
\(136\) −12.3578 + 13.6483i −1.05967 + 1.17033i
\(137\) 3.75559i 0.320862i −0.987047 0.160431i \(-0.948712\pi\)
0.987047 0.160431i \(-0.0512884\pi\)
\(138\) −13.0784 7.26530i −1.11331 0.618463i
\(139\) 12.9485 + 12.9485i 1.09828 + 1.09828i 0.994612 + 0.103669i \(0.0330584\pi\)
0.103669 + 0.994612i \(0.466942\pi\)
\(140\) 0 0
\(141\) 6.92075 6.92075i 0.582832 0.582832i
\(142\) −1.58891 5.56062i −0.133338 0.466637i
\(143\) 1.57202 0.131459
\(144\) 3.00344 + 1.47867i 0.250286 + 0.123222i
\(145\) 0 0
\(146\) 0.947288 + 3.31517i 0.0783982 + 0.274365i
\(147\) 4.95020 4.95020i 0.408285 0.408285i
\(148\) −5.38003 1.25258i −0.442236 0.102961i
\(149\) −15.8472 15.8472i −1.29825 1.29825i −0.929545 0.368709i \(-0.879800\pi\)
−0.368709 0.929545i \(-0.620200\pi\)
\(150\) 0 0
\(151\) 11.5316i 0.938424i −0.883085 0.469212i \(-0.844538\pi\)
0.883085 0.469212i \(-0.155462\pi\)
\(152\) 0.348371 + 7.02036i 0.0282566 + 0.569427i
\(153\) 5.44797i 0.440442i
\(154\) −0.615265 + 1.10755i −0.0495795 + 0.0892488i
\(155\) 0 0
\(156\) −4.08153 6.55880i −0.326784 0.525125i
\(157\) 5.41891 5.41891i 0.432476 0.432476i −0.456994 0.889470i \(-0.651074\pi\)
0.889470 + 0.456994i \(0.151074\pi\)
\(158\) 15.8718 4.53526i 1.26269 0.360806i
\(159\) −11.0110 −0.873229
\(160\) 0 0
\(161\) 10.7656 0.848445
\(162\) 7.87153 2.24924i 0.618446 0.176717i
\(163\) −6.47288 + 6.47288i −0.506995 + 0.506995i −0.913603 0.406608i \(-0.866711\pi\)
0.406608 + 0.913603i \(0.366711\pi\)
\(164\) 8.14443 + 13.0877i 0.635973 + 1.02198i
\(165\) 0 0
\(166\) −2.73344 + 4.92051i −0.212156 + 0.381906i
\(167\) 8.29734i 0.642068i −0.947068 0.321034i \(-0.895970\pi\)
0.947068 0.321034i \(-0.104030\pi\)
\(168\) 6.21837 0.308573i 0.479757 0.0238069i
\(169\) 6.10279i 0.469445i
\(170\) 0 0
\(171\) −1.47069 1.47069i −0.112466 0.112466i
\(172\) 16.9026 + 3.93526i 1.28881 + 0.300061i
\(173\) −11.9420 + 11.9420i −0.907935 + 0.907935i −0.996105 0.0881700i \(-0.971898\pi\)
0.0881700 + 0.996105i \(0.471898\pi\)
\(174\) 5.31684 + 18.6070i 0.403069 + 1.41060i
\(175\) 0 0
\(176\) 2.26675 0.771125i 0.170862 0.0581257i
\(177\) 12.3099 0.925271
\(178\) −4.10090 14.3517i −0.307376 1.07570i
\(179\) −10.8703 + 10.8703i −0.812481 + 0.812481i −0.985005 0.172524i \(-0.944808\pi\)
0.172524 + 0.985005i \(0.444808\pi\)
\(180\) 0 0
\(181\) −4.09403 4.09403i −0.304307 0.304307i 0.538389 0.842696i \(-0.319033\pi\)
−0.842696 + 0.538389i \(0.819033\pi\)
\(182\) 4.85934 + 2.69946i 0.360198 + 0.200097i
\(183\) 2.98858i 0.220922i
\(184\) −15.0812 13.6552i −1.11180 1.00668i
\(185\) 0 0
\(186\) −6.82044 + 12.2776i −0.500099 + 0.900236i
\(187\) −2.75521 2.75521i −0.201481 0.201481i
\(188\) 11.3002 7.03206i 0.824148 0.512866i
\(189\) −5.97219 + 5.97219i −0.434413 + 0.434413i
\(190\) 0 0
\(191\) 19.2542 1.39319 0.696594 0.717466i \(-0.254698\pi\)
0.696594 + 0.717466i \(0.254698\pi\)
\(192\) −9.10256 7.45521i −0.656921 0.538034i
\(193\) 24.8152 1.78624 0.893119 0.449820i \(-0.148512\pi\)
0.893119 + 0.449820i \(0.148512\pi\)
\(194\) −24.6818 + 7.05267i −1.77205 + 0.506352i
\(195\) 0 0
\(196\) 8.08265 5.02981i 0.577332 0.359272i
\(197\) 2.81324 + 2.81324i 0.200435 + 0.200435i 0.800186 0.599751i \(-0.204734\pi\)
−0.599751 + 0.800186i \(0.704734\pi\)
\(198\) −0.344048 + 0.619327i −0.0244505 + 0.0440136i
\(199\) 21.2194i 1.50420i −0.659048 0.752101i \(-0.729041\pi\)
0.659048 0.752101i \(-0.270959\pi\)
\(200\) 0 0
\(201\) 13.2204i 0.932495i
\(202\) −1.81891 1.01044i −0.127978 0.0710944i
\(203\) −9.84655 9.84655i −0.691092 0.691092i
\(204\) −4.34181 + 18.6488i −0.303987 + 1.30568i
\(205\) 0 0
\(206\) −0.371170 1.29896i −0.0258607 0.0905030i
\(207\) 6.01996 0.418416
\(208\) −3.38329 9.94529i −0.234589 0.689582i
\(209\) −1.48755 −0.102896
\(210\) 0 0
\(211\) 15.5715 15.5715i 1.07199 1.07199i 0.0747872 0.997200i \(-0.476172\pi\)
0.997200 0.0747872i \(-0.0238278\pi\)
\(212\) −14.5834 3.39530i −1.00159 0.233190i
\(213\) −4.25277 4.25277i −0.291395 0.291395i
\(214\) −12.5927 6.99550i −0.860820 0.478203i
\(215\) 0 0
\(216\) 15.9415 0.791065i 1.08468 0.0538251i
\(217\) 10.1064i 0.686065i
\(218\) −5.51476 + 9.92721i −0.373507 + 0.672355i
\(219\) 2.53545 + 2.53545i 0.171330 + 0.171330i
\(220\) 0 0
\(221\) −12.0884 + 12.0884i −0.813155 + 0.813155i
\(222\) −5.52363 + 1.57834i −0.370722 + 0.105931i
\(223\) 7.88779 0.528205 0.264103 0.964495i \(-0.414924\pi\)
0.264103 + 0.964495i \(0.414924\pi\)
\(224\) 8.33099 + 1.50878i 0.556638 + 0.100809i
\(225\) 0 0
\(226\) −2.64820 + 0.756705i −0.176155 + 0.0503353i
\(227\) 5.98838 5.98838i 0.397463 0.397463i −0.479874 0.877337i \(-0.659318\pi\)
0.877337 + 0.479874i \(0.159318\pi\)
\(228\) 3.86220 + 6.20635i 0.255780 + 0.411026i
\(229\) 19.4584 + 19.4584i 1.28585 + 1.28585i 0.937286 + 0.348563i \(0.113330\pi\)
0.348563 + 0.937286i \(0.386670\pi\)
\(230\) 0 0
\(231\) 1.31761i 0.0866925i
\(232\) 1.30426 + 26.2833i 0.0856286 + 1.72559i
\(233\) 2.68717i 0.176042i −0.996119 0.0880212i \(-0.971946\pi\)
0.996119 0.0880212i \(-0.0280543\pi\)
\(234\) 2.71728 + 1.50950i 0.177634 + 0.0986793i
\(235\) 0 0
\(236\) 16.3037 + 3.79583i 1.06128 + 0.247087i
\(237\) 12.1388 12.1388i 0.788499 0.788499i
\(238\) −3.78552 13.2480i −0.245379 0.858738i
\(239\) −12.6359 −0.817346 −0.408673 0.912681i \(-0.634008\pi\)
−0.408673 + 0.912681i \(0.634008\pi\)
\(240\) 0 0
\(241\) 7.53314 0.485252 0.242626 0.970120i \(-0.421991\pi\)
0.242626 + 0.970120i \(0.421991\pi\)
\(242\) −4.13485 14.4705i −0.265798 0.930197i
\(243\) −5.95070 + 5.95070i −0.381738 + 0.381738i
\(244\) −0.921544 + 3.95819i −0.0589958 + 0.253397i
\(245\) 0 0
\(246\) 14.0139 + 7.78498i 0.893491 + 0.496352i
\(247\) 6.52658i 0.415276i
\(248\) −12.8191 + 14.1578i −0.814014 + 0.899020i
\(249\) 5.85376i 0.370967i
\(250\) 0 0
\(251\) −9.95683 9.95683i −0.628470 0.628470i 0.319213 0.947683i \(-0.396581\pi\)
−0.947683 + 0.319213i \(0.896581\pi\)
\(252\) −2.12700 + 1.32363i −0.133989 + 0.0833807i
\(253\) 3.04449 3.04449i 0.191405 0.191405i
\(254\) 1.79215 0.512094i 0.112449 0.0321317i
\(255\) 0 0
\(256\) −9.75692 12.6808i −0.609808 0.792549i
\(257\) −4.51630 −0.281719 −0.140860 0.990030i \(-0.544987\pi\)
−0.140860 + 0.990030i \(0.544987\pi\)
\(258\) 17.3538 4.95874i 1.08040 0.308717i
\(259\) 2.92302 2.92302i 0.181628 0.181628i
\(260\) 0 0
\(261\) −5.50606 5.50606i −0.340817 0.340817i
\(262\) 1.00062 1.80124i 0.0618188 0.111281i
\(263\) 20.2127i 1.24637i −0.782075 0.623185i \(-0.785838\pi\)
0.782075 0.623185i \(-0.214162\pi\)
\(264\) 1.67128 1.84581i 0.102860 0.113602i
\(265\) 0 0
\(266\) −4.59821 2.55440i −0.281935 0.156620i
\(267\) −10.9762 10.9762i −0.671732 0.671732i
\(268\) 4.07657 17.5096i 0.249016 1.06957i
\(269\) 16.9430 16.9430i 1.03304 1.03304i 0.0335999 0.999435i \(-0.489303\pi\)
0.999435 0.0335999i \(-0.0106972\pi\)
\(270\) 0 0
\(271\) −3.64054 −0.221147 −0.110573 0.993868i \(-0.535269\pi\)
−0.110573 + 0.993868i \(0.535269\pi\)
\(272\) −11.5009 + 23.3604i −0.697345 + 1.41643i
\(273\) 5.78099 0.349881
\(274\) −1.45924 5.10681i −0.0881559 0.308514i
\(275\) 0 0
\(276\) −20.6068 4.79766i −1.24038 0.288785i
\(277\) 16.0090 + 16.0090i 0.961888 + 0.961888i 0.999300 0.0374115i \(-0.0119112\pi\)
−0.0374115 + 0.999300i \(0.511911\pi\)
\(278\) 22.6385 + 12.5761i 1.35777 + 0.754266i
\(279\) 5.65135i 0.338338i
\(280\) 0 0
\(281\) 5.51857i 0.329210i 0.986360 + 0.164605i \(0.0526350\pi\)
−0.986360 + 0.164605i \(0.947365\pi\)
\(282\) 6.72170 12.0998i 0.400271 0.720535i
\(283\) −2.36694 2.36694i −0.140700 0.140700i 0.633249 0.773949i \(-0.281721\pi\)
−0.773949 + 0.633249i \(0.781721\pi\)
\(284\) −4.32117 6.94389i −0.256414 0.412044i
\(285\) 0 0
\(286\) 2.13762 0.610812i 0.126400 0.0361180i
\(287\) −11.5356 −0.680925
\(288\) 4.65858 + 0.843689i 0.274509 + 0.0497148i
\(289\) 25.3736 1.49257
\(290\) 0 0
\(291\) −18.8767 + 18.8767i −1.10657 + 1.10657i
\(292\) 2.57623 + 4.13986i 0.150762 + 0.242267i
\(293\) 19.1812 + 19.1812i 1.12058 + 1.12058i 0.991655 + 0.128922i \(0.0411517\pi\)
0.128922 + 0.991655i \(0.458848\pi\)
\(294\) 4.80782 8.65463i 0.280398 0.504749i
\(295\) 0 0
\(296\) −7.80240 + 0.387177i −0.453505 + 0.0225042i
\(297\) 3.37786i 0.196003i
\(298\) −27.7063 15.3914i −1.60498 0.891601i
\(299\) −13.3576 13.3576i −0.772491 0.772491i
\(300\) 0 0
\(301\) −9.18335 + 9.18335i −0.529320 + 0.529320i
\(302\) −4.48060 15.6805i −0.257829 0.902311i
\(303\) −2.16390 −0.124313
\(304\) 3.20148 + 9.41086i 0.183618 + 0.539750i
\(305\) 0 0
\(306\) −2.11681 7.40809i −0.121010 0.423492i
\(307\) −19.9292 + 19.9292i −1.13742 + 1.13742i −0.148507 + 0.988911i \(0.547447\pi\)
−0.988911 + 0.148507i \(0.952553\pi\)
\(308\) −0.406292 + 1.74510i −0.0231506 + 0.0994360i
\(309\) −0.993449 0.993449i −0.0565153 0.0565153i
\(310\) 0 0
\(311\) 5.73314i 0.325096i −0.986701 0.162548i \(-0.948029\pi\)
0.986701 0.162548i \(-0.0519713\pi\)
\(312\) −8.09845 7.33271i −0.458484 0.415133i
\(313\) 0.212621i 0.0120180i −0.999982 0.00600902i \(-0.998087\pi\)
0.999982 0.00600902i \(-0.00191274\pi\)
\(314\) 5.26306 9.47411i 0.297011 0.534655i
\(315\) 0 0
\(316\) 19.8201 12.3340i 1.11497 0.693842i
\(317\) 3.21582 3.21582i 0.180618 0.180618i −0.611007 0.791625i \(-0.709235\pi\)
0.791625 + 0.611007i \(0.209235\pi\)
\(318\) −14.9726 + 4.27834i −0.839624 + 0.239917i
\(319\) −5.56919 −0.311815
\(320\) 0 0
\(321\) −14.9811 −0.836164
\(322\) 14.6389 4.18297i 0.815793 0.233108i
\(323\) 11.4388 11.4388i 0.636473 0.636473i
\(324\) 9.82968 6.11698i 0.546093 0.339832i
\(325\) 0 0
\(326\) −6.28671 + 11.3168i −0.348188 + 0.626779i
\(327\) 11.8101i 0.653097i
\(328\) 16.1599 + 14.6320i 0.892284 + 0.807915i
\(329\) 9.96006i 0.549116i
\(330\) 0 0
\(331\) 22.0295 + 22.0295i 1.21085 + 1.21085i 0.970747 + 0.240106i \(0.0771824\pi\)
0.240106 + 0.970747i \(0.422818\pi\)
\(332\) −1.80504 + 7.75295i −0.0990643 + 0.425498i
\(333\) 1.63451 1.63451i 0.0895708 0.0895708i
\(334\) −3.22394 11.2826i −0.176406 0.617359i
\(335\) 0 0
\(336\) 8.33577 2.83575i 0.454754 0.154703i
\(337\) 11.2122 0.610767 0.305384 0.952229i \(-0.401215\pi\)
0.305384 + 0.952229i \(0.401215\pi\)
\(338\) 2.37125 + 8.29851i 0.128979 + 0.451379i
\(339\) −2.02535 + 2.02535i −0.110002 + 0.110002i
\(340\) 0 0
\(341\) −2.85807 2.85807i −0.154773 0.154773i
\(342\) −2.57126 1.42839i −0.139038 0.0772383i
\(343\) 17.6009i 0.950359i
\(344\) 24.5131 1.21641i 1.32166 0.0655844i
\(345\) 0 0
\(346\) −11.5986 + 20.8787i −0.623542 + 1.12245i
\(347\) −1.23653 1.23653i −0.0663803 0.0663803i 0.673137 0.739518i \(-0.264946\pi\)
−0.739518 + 0.673137i \(0.764946\pi\)
\(348\) 14.4596 + 23.2358i 0.775115 + 1.24557i
\(349\) −5.61778 + 5.61778i −0.300713 + 0.300713i −0.841293 0.540580i \(-0.818205\pi\)
0.540580 + 0.841293i \(0.318205\pi\)
\(350\) 0 0
\(351\) 14.8203 0.791047
\(352\) 2.78268 1.92931i 0.148317 0.102833i
\(353\) −0.748709 −0.0398497 −0.0199249 0.999801i \(-0.506343\pi\)
−0.0199249 + 0.999801i \(0.506343\pi\)
\(354\) 16.7389 4.78304i 0.889663 0.254216i
\(355\) 0 0
\(356\) −11.1527 17.9219i −0.591093 0.949856i
\(357\) −10.1321 10.1321i −0.536246 0.536246i
\(358\) −10.5576 + 19.0049i −0.557987 + 1.00444i
\(359\) 2.69883i 0.142439i −0.997461 0.0712195i \(-0.977311\pi\)
0.997461 0.0712195i \(-0.0226891\pi\)
\(360\) 0 0
\(361\) 12.8241i 0.674955i
\(362\) −7.15776 3.97628i −0.376204 0.208989i
\(363\) −11.0671 11.0671i −0.580870 0.580870i
\(364\) 7.65656 + 1.78260i 0.401313 + 0.0934335i
\(365\) 0 0
\(366\) 1.16122 + 4.06384i 0.0606978 + 0.212420i
\(367\) −20.6101 −1.07584 −0.537920 0.842996i \(-0.680790\pi\)
−0.537920 + 0.842996i \(0.680790\pi\)
\(368\) −25.8130 12.7084i −1.34560 0.662472i
\(369\) −6.45056 −0.335802
\(370\) 0 0
\(371\) 7.92329 7.92329i 0.411357 0.411357i
\(372\) −4.50390 + 19.3450i −0.233516 + 1.00299i
\(373\) −5.24143 5.24143i −0.271391 0.271391i 0.558269 0.829660i \(-0.311466\pi\)
−0.829660 + 0.558269i \(0.811466\pi\)
\(374\) −4.81705 2.67597i −0.249084 0.138371i
\(375\) 0 0
\(376\) 12.6335 13.9528i 0.651524 0.719561i
\(377\) 24.4347i 1.25845i
\(378\) −5.80042 + 10.4414i −0.298341 + 0.537049i
\(379\) 5.41344 + 5.41344i 0.278070 + 0.278070i 0.832338 0.554268i \(-0.187002\pi\)
−0.554268 + 0.832338i \(0.687002\pi\)
\(380\) 0 0
\(381\) 1.37064 1.37064i 0.0702199 0.0702199i
\(382\) 26.1817 7.48125i 1.33957 0.382774i
\(383\) −29.5087 −1.50782 −0.753912 0.656975i \(-0.771836\pi\)
−0.753912 + 0.656975i \(0.771836\pi\)
\(384\) −15.2743 6.60071i −0.779463 0.336841i
\(385\) 0 0
\(386\) 33.7435 9.64199i 1.71750 0.490764i
\(387\) −5.13521 + 5.13521i −0.261037 + 0.261037i
\(388\) −30.8218 + 19.1803i −1.56474 + 0.973732i
\(389\) 1.37884 + 1.37884i 0.0699099 + 0.0699099i 0.741197 0.671287i \(-0.234258\pi\)
−0.671287 + 0.741197i \(0.734258\pi\)
\(390\) 0 0
\(391\) 46.8225i 2.36792i
\(392\) 9.03636 9.98001i 0.456405 0.504067i
\(393\) 2.14287i 0.108094i
\(394\) 4.91850 + 2.73232i 0.247790 + 0.137652i
\(395\) 0 0
\(396\) −0.227193 + 0.975834i −0.0114169 + 0.0490375i
\(397\) −21.9750 + 21.9750i −1.10289 + 1.10289i −0.108832 + 0.994060i \(0.534711\pi\)
−0.994060 + 0.108832i \(0.965289\pi\)
\(398\) −8.24482 28.8539i −0.413275 1.44632i
\(399\) −5.47033 −0.273859
\(400\) 0 0
\(401\) −31.4584 −1.57096 −0.785479 0.618889i \(-0.787583\pi\)
−0.785479 + 0.618889i \(0.787583\pi\)
\(402\) −5.13680 17.9770i −0.256200 0.896609i
\(403\) −12.5397 + 12.5397i −0.624648 + 0.624648i
\(404\) −2.86595 0.667248i −0.142586 0.0331968i
\(405\) 0 0
\(406\) −17.2151 9.56335i −0.854372 0.474621i
\(407\) 1.65325i 0.0819487i
\(408\) 1.34207 + 27.0455i 0.0664426 + 1.33895i
\(409\) 12.8017i 0.633003i −0.948592 0.316502i \(-0.897492\pi\)
0.948592 0.316502i \(-0.102508\pi\)
\(410\) 0 0
\(411\) −3.90570 3.90570i −0.192654 0.192654i
\(412\) −1.00943 1.62210i −0.0497309 0.0799150i
\(413\) −8.85797 + 8.85797i −0.435872 + 0.435872i
\(414\) 8.18588 2.33906i 0.402314 0.114959i
\(415\) 0 0
\(416\) −8.46482 12.2089i −0.415022 0.598592i
\(417\) 26.9322 1.31888
\(418\) −2.02275 + 0.577988i −0.0989360 + 0.0282703i
\(419\) −11.4979 + 11.4979i −0.561709 + 0.561709i −0.929793 0.368084i \(-0.880014\pi\)
0.368084 + 0.929793i \(0.380014\pi\)
\(420\) 0 0
\(421\) 12.5714 + 12.5714i 0.612690 + 0.612690i 0.943646 0.330956i \(-0.107371\pi\)
−0.330956 + 0.943646i \(0.607371\pi\)
\(422\) 15.1236 27.2243i 0.736208 1.32526i
\(423\) 5.56953i 0.270800i
\(424\) −21.1496 + 1.04950i −1.02711 + 0.0509684i
\(425\) 0 0
\(426\) −7.43529 4.13045i −0.360241 0.200121i
\(427\) −2.15052 2.15052i −0.104071 0.104071i
\(428\) −19.8415 4.61950i −0.959077 0.223292i
\(429\) 1.63486 1.63486i 0.0789316 0.0789316i
\(430\) 0 0
\(431\) −15.2579 −0.734946 −0.367473 0.930034i \(-0.619777\pi\)
−0.367473 + 0.930034i \(0.619777\pi\)
\(432\) 21.3698 7.26978i 1.02815 0.349768i
\(433\) −12.1705 −0.584877 −0.292439 0.956284i \(-0.594467\pi\)
−0.292439 + 0.956284i \(0.594467\pi\)
\(434\) −3.92684 13.7425i −0.188495 0.659663i
\(435\) 0 0
\(436\) −3.64169 + 15.6417i −0.174405 + 0.749101i
\(437\) 12.6398 + 12.6398i 0.604644 + 0.604644i
\(438\) 4.43283 + 2.46252i 0.211809 + 0.117664i
\(439\) 39.7535i 1.89733i 0.316283 + 0.948665i \(0.397565\pi\)
−0.316283 + 0.948665i \(0.602435\pi\)
\(440\) 0 0
\(441\) 3.98371i 0.189701i
\(442\) −11.7407 + 21.1347i −0.558450 + 1.00527i
\(443\) 3.62318 + 3.62318i 0.172142 + 0.172142i 0.787920 0.615778i \(-0.211158\pi\)
−0.615778 + 0.787920i \(0.711158\pi\)
\(444\) −6.89771 + 4.29243i −0.327351 + 0.203710i
\(445\) 0 0
\(446\) 10.7257 3.06481i 0.507878 0.145123i
\(447\) −32.9612 −1.55901
\(448\) 11.9146 1.18540i 0.562913 0.0560047i
\(449\) −5.38425 −0.254098 −0.127049 0.991896i \(-0.540551\pi\)
−0.127049 + 0.991896i \(0.540551\pi\)
\(450\) 0 0
\(451\) −3.26225 + 3.26225i −0.153614 + 0.153614i
\(452\) −3.30697 + 2.05792i −0.155547 + 0.0967964i
\(453\) −11.9925 11.9925i −0.563455 0.563455i
\(454\) 5.81615 10.4697i 0.272965 0.491369i
\(455\) 0 0
\(456\) 7.66326 + 6.93867i 0.358865 + 0.324933i
\(457\) 14.3039i 0.669108i −0.942377 0.334554i \(-0.891414\pi\)
0.942377 0.334554i \(-0.108586\pi\)
\(458\) 34.0199 + 18.8988i 1.58965 + 0.883081i
\(459\) −25.9748 25.9748i −1.21240 1.21240i
\(460\) 0 0
\(461\) −4.50363 + 4.50363i −0.209755 + 0.209755i −0.804163 0.594408i \(-0.797386\pi\)
0.594408 + 0.804163i \(0.297386\pi\)
\(462\) 0.511960 + 1.79167i 0.0238185 + 0.0833563i
\(463\) 19.3500 0.899271 0.449636 0.893212i \(-0.351554\pi\)
0.449636 + 0.893212i \(0.351554\pi\)
\(464\) 11.9859 + 35.2330i 0.556433 + 1.63565i
\(465\) 0 0
\(466\) −1.04410 3.65399i −0.0483672 0.169268i
\(467\) −17.1773 + 17.1773i −0.794871 + 0.794871i −0.982282 0.187410i \(-0.939991\pi\)
0.187410 + 0.982282i \(0.439991\pi\)
\(468\) 4.28145 + 0.996805i 0.197910 + 0.0460773i
\(469\) 9.51312 + 9.51312i 0.439275 + 0.439275i
\(470\) 0 0
\(471\) 11.2710i 0.519341i
\(472\) 23.6445 1.17331i 1.08833 0.0540060i
\(473\) 5.19408i 0.238824i
\(474\) 11.7897 21.2227i 0.541517 0.974792i
\(475\) 0 0
\(476\) −10.2950 16.5436i −0.471872 0.758273i
\(477\) 4.43060 4.43060i 0.202863 0.202863i
\(478\) −17.1821 + 4.90968i −0.785892 + 0.224564i
\(479\) 5.54474 0.253346 0.126673 0.991945i \(-0.459570\pi\)
0.126673 + 0.991945i \(0.459570\pi\)
\(480\) 0 0
\(481\) −7.25361 −0.330736
\(482\) 10.2435 2.92701i 0.466578 0.133322i
\(483\) 11.1959 11.1959i 0.509429 0.509429i
\(484\) −11.2450 18.0702i −0.511138 0.821373i
\(485\) 0 0
\(486\) −5.77955 + 10.4039i −0.262166 + 0.471928i
\(487\) 31.7138i 1.43709i −0.695480 0.718546i \(-0.744808\pi\)
0.695480 0.718546i \(-0.255192\pi\)
\(488\) 0.284854 + 5.74037i 0.0128947 + 0.259855i
\(489\) 13.4632i 0.608827i
\(490\) 0 0
\(491\) 7.39419 + 7.39419i 0.333695 + 0.333695i 0.853988 0.520293i \(-0.174177\pi\)
−0.520293 + 0.853988i \(0.674177\pi\)
\(492\) 22.0808 + 5.14083i 0.995477 + 0.231767i
\(493\) 42.8255 42.8255i 1.92876 1.92876i
\(494\) 2.53591 + 8.87477i 0.114096 + 0.399295i
\(495\) 0 0
\(496\) −11.9303 + 24.2325i −0.535685 + 1.08807i
\(497\) 6.12041 0.274538
\(498\) 2.27449 + 7.95988i 0.101922 + 0.356691i
\(499\) 14.0103 14.0103i 0.627189 0.627189i −0.320171 0.947360i \(-0.603740\pi\)
0.947360 + 0.320171i \(0.103740\pi\)
\(500\) 0 0
\(501\) −8.62899 8.62899i −0.385515 0.385515i
\(502\) −17.4079 9.67046i −0.776954 0.431614i
\(503\) 8.43795i 0.376230i −0.982147 0.188115i \(-0.939762\pi\)
0.982147 0.188115i \(-0.0602377\pi\)
\(504\) −2.37798 + 2.62631i −0.105924 + 0.116985i
\(505\) 0 0
\(506\) 2.95692 5.32280i 0.131451 0.236627i
\(507\) 6.34671 + 6.34671i 0.281868 + 0.281868i
\(508\) 2.23797 1.39268i 0.0992937 0.0617902i
\(509\) 2.09367 2.09367i 0.0928004 0.0928004i −0.659183 0.751983i \(-0.729098\pi\)
0.751983 + 0.659183i \(0.229098\pi\)
\(510\) 0 0
\(511\) −3.64891 −0.161418
\(512\) −18.1945 13.4521i −0.804091 0.594506i
\(513\) −14.0239 −0.619169
\(514\) −6.14122 + 1.75481i −0.270878 + 0.0774016i
\(515\) 0 0
\(516\) 21.6708 13.4857i 0.954003 0.593674i
\(517\) 2.81669 + 2.81669i 0.123878 + 0.123878i
\(518\) 2.83895 5.11043i 0.124736 0.224540i
\(519\) 24.8387i 1.09030i
\(520\) 0 0
\(521\) 28.2558i 1.23791i 0.785428 + 0.618954i \(0.212443\pi\)
−0.785428 + 0.618954i \(0.787557\pi\)
\(522\) −9.62647 5.34770i −0.421339 0.234062i
\(523\) 10.1929 + 10.1929i 0.445703 + 0.445703i 0.893923 0.448220i \(-0.147942\pi\)
−0.448220 + 0.893923i \(0.647942\pi\)
\(524\) 0.660765 2.83810i 0.0288657 0.123983i
\(525\) 0 0
\(526\) −7.85368 27.4851i −0.342437 1.19841i
\(527\) 43.9555 1.91473
\(528\) 1.55540 3.15929i 0.0676901 0.137491i
\(529\) −28.7385 −1.24950
\(530\) 0 0
\(531\) −4.95326 + 4.95326i −0.214953 + 0.214953i
\(532\) −7.24512 1.68681i −0.314116 0.0731323i
\(533\) 14.3131 + 14.3131i 0.619967 + 0.619967i
\(534\) −19.1901 10.6605i −0.830438 0.461325i
\(535\) 0 0
\(536\) −1.26009 25.3933i −0.0544276 1.09682i
\(537\) 22.6095i 0.975671i
\(538\) 16.4557 29.6222i 0.709457 1.27710i
\(539\) 2.01469 + 2.01469i 0.0867790 + 0.0867790i
\(540\) 0 0
\(541\) 3.86053 3.86053i 0.165977 0.165977i −0.619231 0.785209i \(-0.712556\pi\)
0.785209 + 0.619231i \(0.212556\pi\)
\(542\) −4.95036 + 1.41453i −0.212636 + 0.0607595i
\(543\) −8.51534 −0.365428
\(544\) −6.56211 + 36.2339i −0.281348 + 1.55352i
\(545\) 0 0
\(546\) 7.86093 2.24621i 0.336417 0.0961289i
\(547\) 20.6231 20.6231i 0.881781 0.881781i −0.111935 0.993716i \(-0.535705\pi\)
0.993716 + 0.111935i \(0.0357048\pi\)
\(548\) −3.96852 6.37720i −0.169527 0.272421i
\(549\) −1.20254 1.20254i −0.0513233 0.0513233i
\(550\) 0 0
\(551\) 23.1216i 0.985014i
\(552\) −29.8850 + 1.48298i −1.27199 + 0.0631199i
\(553\) 17.4696i 0.742884i
\(554\) 27.9892 + 15.5486i 1.18915 + 0.660595i
\(555\) 0 0
\(556\) 35.6700 + 8.30468i 1.51275 + 0.352197i
\(557\) −1.28512 + 1.28512i −0.0544523 + 0.0544523i −0.733809 0.679356i \(-0.762259\pi\)
0.679356 + 0.733809i \(0.262259\pi\)
\(558\) −2.19584 7.68465i −0.0929573 0.325317i
\(559\) 22.7889 0.963868
\(560\) 0 0
\(561\) −5.73068 −0.241949
\(562\) 2.14425 + 7.50409i 0.0904496 + 0.316541i
\(563\) 21.9152 21.9152i 0.923615 0.923615i −0.0736677 0.997283i \(-0.523470\pi\)
0.997283 + 0.0736677i \(0.0234704\pi\)
\(564\) 4.43869 19.0650i 0.186903 0.802779i
\(565\) 0 0
\(566\) −4.13822 2.29886i −0.173942 0.0966284i
\(567\) 8.66397i 0.363852i
\(568\) −8.57394 7.76324i −0.359754 0.325738i
\(569\) 35.6668i 1.49523i −0.664132 0.747615i \(-0.731199\pi\)
0.664132 0.747615i \(-0.268801\pi\)
\(570\) 0 0
\(571\) 5.60524 + 5.60524i 0.234572 + 0.234572i 0.814598 0.580026i \(-0.196958\pi\)
−0.580026 + 0.814598i \(0.696958\pi\)
\(572\) 2.66938 1.66115i 0.111613 0.0694562i
\(573\) 20.0238 20.0238i 0.836507 0.836507i
\(574\) −15.6860 + 4.48217i −0.654720 + 0.187082i
\(575\) 0 0
\(576\) 6.66251 0.662858i 0.277604 0.0276191i
\(577\) −2.43681 −0.101446 −0.0507230 0.998713i \(-0.516153\pi\)
−0.0507230 + 0.998713i \(0.516153\pi\)
\(578\) 34.5028 9.85896i 1.43513 0.410079i
\(579\) 25.8071 25.8071i 1.07251 1.07251i
\(580\) 0 0
\(581\) −4.21225 4.21225i −0.174753 0.174753i
\(582\) −18.3338 + 33.0029i −0.759960 + 1.36802i
\(583\) 4.48139i 0.185600i
\(584\) 5.11167 + 4.62835i 0.211523 + 0.191522i
\(585\) 0 0
\(586\) 33.5353 + 18.6295i 1.38533 + 0.769578i
\(587\) 0.415982 + 0.415982i 0.0171694 + 0.0171694i 0.715639 0.698470i \(-0.246135\pi\)
−0.698470 + 0.715639i \(0.746135\pi\)
\(588\) 3.17486 13.6366i 0.130929 0.562363i
\(589\) 11.8659 11.8659i 0.488924 0.488924i
\(590\) 0 0
\(591\) 5.85136 0.240693
\(592\) −10.4592 + 3.55811i −0.429870 + 0.146237i
\(593\) −15.3439 −0.630098 −0.315049 0.949075i \(-0.602021\pi\)
−0.315049 + 0.949075i \(0.602021\pi\)
\(594\) 1.31247 + 4.59318i 0.0538513 + 0.188460i
\(595\) 0 0
\(596\) −43.6551 10.1638i −1.78818 0.416324i
\(597\) −22.0675 22.0675i −0.903163 0.903163i
\(598\) −23.3537 12.9734i −0.955002 0.530523i
\(599\) 43.3487i 1.77118i 0.464468 + 0.885590i \(0.346246\pi\)
−0.464468 + 0.885590i \(0.653754\pi\)
\(600\) 0 0
\(601\) 38.7291i 1.57979i −0.613239 0.789897i \(-0.710134\pi\)
0.613239 0.789897i \(-0.289866\pi\)
\(602\) −8.91923 + 16.0556i −0.363520 + 0.654379i
\(603\) 5.31961 + 5.31961i 0.216631 + 0.216631i
\(604\) −12.1853 19.5812i −0.495815 0.796748i
\(605\) 0 0
\(606\) −2.94244 + 0.840784i −0.119529 + 0.0341545i
\(607\) −34.9068 −1.41682 −0.708412 0.705800i \(-0.750588\pi\)
−0.708412 + 0.705800i \(0.750588\pi\)
\(608\) 8.00994 + 11.5528i 0.324846 + 0.468530i
\(609\) −20.4802 −0.829901
\(610\) 0 0
\(611\) 12.3582 12.3582i 0.499958 0.499958i
\(612\) −5.75684 9.25095i −0.232707 0.373947i
\(613\) −0.151779 0.151779i −0.00613031 0.00613031i 0.704035 0.710165i \(-0.251380\pi\)
−0.710165 + 0.704035i \(0.751380\pi\)
\(614\) −19.3560 + 34.8430i −0.781144 + 1.40615i
\(615\) 0 0
\(616\) 0.125587 + 2.53083i 0.00506004 + 0.101970i
\(617\) 0.288199i 0.0116025i 0.999983 + 0.00580123i \(0.00184660\pi\)
−0.999983 + 0.00580123i \(0.998153\pi\)
\(618\) −1.73689 0.964876i −0.0698679 0.0388130i
\(619\) −11.5307 11.5307i −0.463460 0.463460i 0.436328 0.899788i \(-0.356279\pi\)
−0.899788 + 0.436328i \(0.856279\pi\)
\(620\) 0 0
\(621\) 28.7019 28.7019i 1.15177 1.15177i
\(622\) −2.22762 7.79586i −0.0893193 0.312585i
\(623\) 15.7965 0.632873
\(624\) −13.8613 6.82428i −0.554897 0.273190i
\(625\) 0 0
\(626\) −0.0826141 0.289120i −0.00330192 0.0115555i
\(627\) −1.54700 + 1.54700i −0.0617814 + 0.0617814i
\(628\) 3.47547 14.9278i 0.138686 0.595682i
\(629\) 12.7131 + 12.7131i 0.506903 + 0.506903i
\(630\) 0 0
\(631\) 14.2062i 0.565541i 0.959188 + 0.282771i \(0.0912536\pi\)
−0.959188 + 0.282771i \(0.908746\pi\)
\(632\) 22.1588 24.4728i 0.881430 0.973475i
\(633\) 32.3878i 1.28730i
\(634\) 3.12332 5.62234i 0.124043 0.223292i
\(635\) 0 0
\(636\) −18.6973 + 11.6353i −0.741396 + 0.461369i
\(637\) 8.83942 8.83942i 0.350230 0.350230i
\(638\) −7.57292 + 2.16391i −0.299815 + 0.0856702i
\(639\) 3.42245 0.135390
\(640\) 0 0
\(641\) 19.7372 0.779572 0.389786 0.920905i \(-0.372549\pi\)
0.389786 + 0.920905i \(0.372549\pi\)
\(642\) −20.3712 + 5.82093i −0.803985 + 0.229734i
\(643\) −5.80043 + 5.80043i −0.228747 + 0.228747i −0.812169 0.583422i \(-0.801713\pi\)
0.583422 + 0.812169i \(0.301713\pi\)
\(644\) 18.2805 11.3759i 0.720353 0.448274i
\(645\) 0 0
\(646\) 11.1098 19.9990i 0.437110 0.786849i
\(647\) 46.3186i 1.82097i −0.413541 0.910485i \(-0.635708\pi\)
0.413541 0.910485i \(-0.364292\pi\)
\(648\) 10.9895 12.1371i 0.431710 0.476792i
\(649\) 5.01005i 0.196662i
\(650\) 0 0
\(651\) −10.5103 10.5103i −0.411932 0.411932i
\(652\) −4.15144 + 17.8312i −0.162583 + 0.698322i
\(653\) −4.42354 + 4.42354i −0.173106 + 0.173106i −0.788343 0.615236i \(-0.789061\pi\)
0.615236 + 0.788343i \(0.289061\pi\)
\(654\) 4.58881 + 16.0592i 0.179437 + 0.627964i
\(655\) 0 0
\(656\) 27.6594 + 13.6174i 1.07992 + 0.531671i
\(657\) −2.04042 −0.0796045
\(658\) 3.86999 + 13.5436i 0.150868 + 0.527984i
\(659\) −15.2461 + 15.2461i −0.593905 + 0.593905i −0.938684 0.344779i \(-0.887954\pi\)
0.344779 + 0.938684i \(0.387954\pi\)
\(660\) 0 0
\(661\) 19.1271 + 19.1271i 0.743958 + 0.743958i 0.973337 0.229379i \(-0.0736696\pi\)
−0.229379 + 0.973337i \(0.573670\pi\)
\(662\) 38.5151 + 21.3959i 1.49693 + 0.831577i
\(663\) 25.1432i 0.976481i
\(664\) 0.557946 + 11.2437i 0.0216525 + 0.436341i
\(665\) 0 0
\(666\) 1.58750 2.85769i 0.0615145 0.110733i
\(667\) 47.3218 + 47.3218i 1.83231 + 1.83231i
\(668\) −8.76777 14.0894i −0.339235 0.545133i
\(669\) 8.20306 8.20306i 0.317149 0.317149i
\(670\) 0 0
\(671\) −1.21633 −0.0469559
\(672\) 10.2331 7.09490i 0.394749 0.273692i
\(673\) −18.5586 −0.715382 −0.357691 0.933840i \(-0.616436\pi\)
−0.357691 + 0.933840i \(0.616436\pi\)
\(674\) 15.2462 4.35651i 0.587263 0.167807i
\(675\) 0 0
\(676\) 6.44879 + 10.3629i 0.248030 + 0.398572i
\(677\) −2.71844 2.71844i −0.104478 0.104478i 0.652935 0.757414i \(-0.273537\pi\)
−0.757414 + 0.652935i \(0.773537\pi\)
\(678\) −1.96709 + 3.54100i −0.0755458 + 0.135991i
\(679\) 27.1666i 1.04256i
\(680\) 0 0
\(681\) 12.4555i 0.477295i
\(682\) −4.99688 2.77587i −0.191340 0.106293i
\(683\) −12.6646 12.6646i −0.484598 0.484598i 0.421999 0.906596i \(-0.361329\pi\)
−0.906596 + 0.421999i \(0.861329\pi\)
\(684\) −4.05138 0.943239i −0.154908 0.0360657i
\(685\) 0 0
\(686\) 6.83885 + 23.9335i 0.261108 + 0.913786i
\(687\) 40.4723 1.54412
\(688\) 32.8600 11.1786i 1.25278 0.426182i
\(689\) −19.6620 −0.749063
\(690\) 0 0
\(691\) 26.8892 26.8892i 1.02291 1.02291i 0.0231826 0.999731i \(-0.492620\pi\)
0.999731 0.0231826i \(-0.00737991\pi\)
\(692\) −7.65914 + 32.8973i −0.291157 + 1.25057i
\(693\) −0.530180 0.530180i −0.0201399 0.0201399i
\(694\) −2.16187 1.20096i −0.0820636 0.0455880i
\(695\) 0 0
\(696\) 28.6903 + 25.9775i 1.08750 + 0.984675i
\(697\) 50.1717i 1.90039i
\(698\) −5.45621 + 9.82180i −0.206521 + 0.371761i
\(699\) −2.79458 2.79458i −0.105701 0.105701i
\(700\) 0 0
\(701\) 25.3725 25.3725i 0.958305 0.958305i −0.0408602 0.999165i \(-0.513010\pi\)
0.999165 + 0.0408602i \(0.0130098\pi\)
\(702\) 20.1524 5.75843i 0.760605 0.217338i
\(703\) 6.86382 0.258874
\(704\) 3.03422 3.70467i 0.114356 0.139625i
\(705\) 0 0
\(706\) −1.01809 + 0.290912i −0.0383162 + 0.0109486i
\(707\) 1.55709 1.55709i 0.0585606 0.0585606i
\(708\) 20.9029 13.0079i 0.785581 0.488865i
\(709\) 16.1117 + 16.1117i 0.605089 + 0.605089i 0.941659 0.336570i \(-0.109267\pi\)
−0.336570 + 0.941659i \(0.609267\pi\)
\(710\) 0 0
\(711\) 9.76879i 0.366358i
\(712\) −22.1289 20.0365i −0.829316 0.750901i
\(713\) 48.5705i 1.81898i
\(714\) −17.7143 9.84066i −0.662941 0.368277i
\(715\) 0 0
\(716\) −6.97175 + 29.9449i −0.260546 + 1.11909i
\(717\) −13.1409 + 13.1409i −0.490757 + 0.490757i
\(718\) −1.04864 3.66985i −0.0391347 0.136958i
\(719\) 29.1676 1.08777 0.543884 0.839160i \(-0.316953\pi\)
0.543884 + 0.839160i \(0.316953\pi\)
\(720\) 0 0
\(721\) 1.42973 0.0532460
\(722\) 4.98284 + 17.4381i 0.185442 + 0.648980i
\(723\) 7.83424 7.83424i 0.291358 0.291358i
\(724\) −11.2780 2.62575i −0.419145 0.0975852i
\(725\) 0 0
\(726\) −19.3490 10.7487i −0.718108 0.398923i
\(727\) 4.13463i 0.153345i 0.997056 + 0.0766724i \(0.0244296\pi\)
−0.997056 + 0.0766724i \(0.975570\pi\)
\(728\) 11.1039 0.551010i 0.411540 0.0204218i
\(729\) 29.7434i 1.10161i
\(730\) 0 0
\(731\) −39.9411 39.9411i −1.47727 1.47727i
\(732\) 3.15802 + 5.07478i 0.116724 + 0.187569i
\(733\) −19.3838 + 19.3838i −0.715957 + 0.715957i −0.967775 0.251817i \(-0.918972\pi\)
0.251817 + 0.967775i \(0.418972\pi\)
\(734\) −28.0255 + 8.00809i −1.03444 + 0.295584i
\(735\) 0 0
\(736\) −40.0382 7.25108i −1.47583 0.267278i
\(737\) 5.38060 0.198197
\(738\) −8.77140 + 2.50637i −0.322880 + 0.0922608i
\(739\) 23.9820 23.9820i 0.882194 0.882194i −0.111564 0.993757i \(-0.535586\pi\)
0.993757 + 0.111564i \(0.0355859\pi\)
\(740\) 0 0
\(741\) 6.78744 + 6.78744i 0.249343 + 0.249343i
\(742\) 7.69540 13.8526i 0.282507 0.508545i
\(743\) 10.3473i 0.379604i 0.981822 + 0.189802i \(0.0607846\pi\)
−0.981822 + 0.189802i \(0.939215\pi\)
\(744\) 1.39218 + 28.0551i 0.0510397 + 1.02855i
\(745\) 0 0
\(746\) −9.16380 5.09068i −0.335511 0.186383i
\(747\) −2.35543 2.35543i −0.0861808 0.0861808i
\(748\) −7.58993 1.76708i −0.277515 0.0646109i
\(749\) 10.7801 10.7801i 0.393896 0.393896i
\(750\) 0 0
\(751\) −37.0217 −1.35094 −0.675470 0.737387i \(-0.736059\pi\)
−0.675470 + 0.737387i \(0.736059\pi\)
\(752\) 11.7575 23.8817i 0.428754 0.870874i
\(753\) −20.7096 −0.754700
\(754\) 9.49412 + 33.2260i 0.345756 + 1.21002i
\(755\) 0 0
\(756\) −3.83032 + 16.4519i −0.139308 + 0.598350i
\(757\) −30.4305 30.4305i −1.10601 1.10601i −0.993669 0.112345i \(-0.964164\pi\)
−0.112345 0.993669i \(-0.535836\pi\)
\(758\) 9.46454 + 5.25774i 0.343768 + 0.190970i
\(759\) 6.33235i 0.229850i
\(760\) 0 0
\(761\) 43.1054i 1.56257i 0.624174 + 0.781285i \(0.285436\pi\)
−0.624174 + 0.781285i \(0.714564\pi\)
\(762\) 1.33122 2.39634i 0.0482249 0.0868103i
\(763\) −8.49827 8.49827i −0.307658 0.307658i
\(764\) 32.6948 20.3459i 1.18285 0.736088i
\(765\) 0 0
\(766\) −40.1256 + 11.4656i −1.44980 + 0.414271i
\(767\) 21.9815 0.793705
\(768\) −23.3345 3.04073i −0.842013 0.109723i
\(769\) −31.2507 −1.12693 −0.563465 0.826140i \(-0.690532\pi\)
−0.563465 + 0.826140i \(0.690532\pi\)
\(770\) 0 0
\(771\) −4.69682 + 4.69682i −0.169152 + 0.169152i
\(772\) 42.1376 26.2221i 1.51657 0.943756i
\(773\) 24.4047 + 24.4047i 0.877778 + 0.877778i 0.993304 0.115527i \(-0.0368556\pi\)
−0.115527 + 0.993304i \(0.536856\pi\)
\(774\) −4.98751 + 8.97810i −0.179272 + 0.322711i
\(775\) 0 0
\(776\) −34.4586 + 38.0570i −1.23699 + 1.36617i
\(777\) 6.07970i 0.218108i
\(778\) 2.41068 + 1.33918i 0.0864271 + 0.0480120i
\(779\) −13.5439 13.5439i −0.485261 0.485261i
\(780\) 0 0
\(781\) 1.73085 1.73085i 0.0619345 0.0619345i
\(782\) 18.1929 + 63.6688i 0.650579 + 2.27679i
\(783\) −52.5036 −1.87632