Properties

Label 400.2.l.g.301.6
Level $400$
Weight $2$
Character 400.301
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 301.6
Root \(1.35979 + 0.388551i\) of defining polynomial
Character \(\chi\) \(=\) 400.301
Dual form 400.2.l.g.101.6

$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(177\) \(351\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(1\)

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 0.940426 0.339999i \(-0.110427\pi\)
−0.339999 + 0.940426i \(0.610427\pi\)
\(4\) 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 \(-0.908721\pi\)
0.959165 0.282846i \(-0.0912786\pi\)
\(8\) 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 −0.640413 0.768031i \(-0.721237\pi\)
0.768031 + 0.640413i \(0.221237\pi\)
\(12\) 0.666995 + 2.86486i 0.192545 + 0.827014i
\(13\) 1.85704 + 1.85704i 0.515051 + 0.515051i 0.916070 0.401019i \(-0.131344\pi\)
−0.401019 + 0.916070i \(0.631344\pi\)
\(14\) 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 0.476198 0.879338i \(-0.342015\pi\)
−0.879338 + 0.476198i \(0.842015\pi\)
\(20\) 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 \(0.269906\pi\)
−0.661532 + 0.749917i \(0.730094\pi\)
\(24\) −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 −0.967036 0.254639i \(-0.918043\pi\)
−0.254639 0.967036i \(-0.581957\pi\)
\(30\) 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 −0.849178 0.528107i \(-0.822902\pi\)
0.528107 + 0.849178i \(0.322902\pi\)
\(38\) −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 \(-0.794430\pi\)
0.798609 0.601851i \(-0.205570\pi\)
\(42\) 2.72130 1.51174i 0.419906 0.233266i
\(43\) 6.13581 6.13581i 0.935702 0.935702i −0.0623522 0.998054i \(-0.519860\pi\)
0.998054 + 0.0623522i \(0.0198602\pi\)
\(44\) 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 −0.970056 0.242882i \(-0.921907\pi\)
0.242882 + 0.970056i \(0.421907\pi\)
\(54\) 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 −0.207685 0.978196i \(-0.566593\pi\)
0.978196 + 0.207685i \(0.0665929\pi\)
\(60\) 0 0
\(61\) −1.43686 1.43686i −0.183971 0.183971i 0.609113 0.793084i \(-0.291526\pi\)
−0.793084 + 0.609113i \(0.791526\pi\)
\(62\) −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 0.979238 0.202712i \(-0.0649756\pi\)
−0.202712 + 0.979238i \(0.564976\pi\)
\(68\) −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 \(0.0780188\pi\)
−0.970112 + 0.242657i \(0.921981\pi\)
\(72\) 1.75475 1.58883i 0.206799 0.187246i
\(73\) 2.43800i 0.285346i −0.989770 0.142673i \(-0.954430\pi\)
0.989770 0.142673i \(-0.0455698\pi\)
\(74\) −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 0.535571 0.844490i \(-0.320096\pi\)
−0.844490 + 0.535571i \(0.820096\pi\)
\(84\) 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 \(0.188960\pi\)
−0.828912 + 0.559379i \(0.811040\pi\)
\(90\) 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 −0.756970 0.653450i \(-0.773321\pi\)
0.653450 + 0.756970i \(0.273321\pi\)
\(102\) −6.57498 11.8357i −0.651020 1.17191i
\(103\) 0.955267i 0.0941253i 0.998892 + 0.0470626i \(0.0149860\pi\)
−0.998892 + 0.0470626i \(0.985014\pi\)
\(104\) −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 −0.963612 0.267305i \(-0.913867\pi\)
0.267305 + 0.963612i \(0.413867\pi\)
\(108\) 10.9922 2.55921i 1.05773 0.246260i
\(109\) −5.67807 5.67807i −0.543861 0.543861i 0.380798 0.924658i \(-0.375649\pi\)
−0.924658 + 0.380798i \(0.875649\pi\)
\(110\) 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 0.750680 0.660666i \(-0.229726\pi\)
−0.660666 + 0.750680i \(0.729726\pi\)
\(132\) 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 \(0.0512884\pi\)
−0.987047 + 0.160431i \(0.948712\pi\)
\(138\) −13.0784 + 7.26530i −1.11331 + 0.618463i
\(139\) 12.9485 12.9485i 1.09828 1.09828i 0.103669 0.994612i \(-0.466942\pi\)
0.994612 0.103669i \(-0.0330584\pi\)
\(140\) 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 −0.368709 + 0.929545i \(0.620200\pi\)
−0.929545 + 0.368709i \(0.879800\pi\)
\(150\) 0 0
\(151\) 11.5316i 0.938424i 0.883085 + 0.469212i \(0.155462\pi\)
−0.883085 + 0.469212i \(0.844538\pi\)
\(152\) 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 0.889470 0.456994i \(-0.151074\pi\)
−0.456994 + 0.889470i \(0.651074\pi\)
\(158\) 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 0.406608 0.913603i \(-0.366711\pi\)
−0.913603 + 0.406608i \(0.866711\pi\)
\(164\) 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 \(0.104030\pi\)
−0.947068 + 0.321034i \(0.895970\pi\)
\(168\) 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 0.0881700 0.996105i \(-0.471898\pi\)
−0.996105 + 0.0881700i \(0.971898\pi\)
\(174\) 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 0.172524 0.985005i \(-0.444808\pi\)
−0.985005 + 0.172524i \(0.944808\pi\)
\(180\) 0 0
\(181\) −4.09403 + 4.09403i −0.304307 + 0.304307i −0.842696 0.538389i \(-0.819033\pi\)
0.538389 + 0.842696i \(0.319033\pi\)
\(182\) 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 −0.599751 0.800186i \(-0.704734\pi\)
0.800186 + 0.599751i \(0.204734\pi\)
\(198\) −0.344048 0.619327i −0.0244505 0.0440136i
\(199\) 21.2194i 1.50420i 0.659048 + 0.752101i \(0.270959\pi\)
−0.659048 + 0.752101i \(0.729041\pi\)
\(200\) 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 0.997200 + 0.0747872i \(0.0238278\pi\)
0.0747872 + 0.997200i \(0.476172\pi\)
\(212\) −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 0.877337 0.479874i \(-0.159318\pi\)
−0.479874 + 0.877337i \(0.659318\pi\)
\(228\) 3.86220 6.20635i 0.255780 0.411026i
\(229\) 19.4584 19.4584i 1.28585 1.28585i 0.348563 0.937286i \(-0.386670\pi\)
0.937286 0.348563i \(-0.113330\pi\)
\(230\) 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 \(0.0280543\pi\)
−0.996119 + 0.0880212i \(0.971946\pi\)
\(234\) 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 −0.947683 0.319213i \(-0.896581\pi\)
0.319213 + 0.947683i \(0.396581\pi\)
\(252\) −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 \(0.214162\pi\)
−0.782075 + 0.623185i \(0.785838\pi\)
\(264\) 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 0.999435 + 0.0335999i \(0.0106972\pi\)
0.0335999 + 0.999435i \(0.489303\pi\)
\(270\) 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 −0.0374115 0.999300i \(-0.511911\pi\)
0.999300 + 0.0374115i \(0.0119112\pi\)
\(278\) 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 \(-0.947365\pi\)
0.986360 0.164605i \(-0.0526350\pi\)
\(282\) 6.72170 + 12.0998i 0.400271 + 0.720535i
\(283\) −2.36694 + 2.36694i −0.140700 + 0.140700i −0.773949 0.633249i \(-0.781721\pi\)
0.633249 + 0.773949i \(0.281721\pi\)
\(284\) −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 0.128922 0.991655i \(-0.458848\pi\)
0.991655 0.128922i \(-0.0411517\pi\)
\(294\) 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 −0.988911 0.148507i \(-0.952553\pi\)
−0.148507 0.988911i \(-0.547447\pi\)
\(308\) −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 \(0.0519713\pi\)
−0.986701 + 0.162548i \(0.948029\pi\)
\(312\) −8.09845 + 7.33271i −0.458484 + 0.415133i
\(313\) 0.212621i 0.0120180i 0.999982 + 0.00600902i \(0.00191274\pi\)
−0.999982 + 0.00600902i \(0.998087\pi\)
\(314\) 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 0.791625 0.611007i \(-0.209235\pi\)
−0.611007 + 0.791625i \(0.709235\pi\)
\(318\) −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 0.240106 0.970747i \(-0.422818\pi\)
0.970747 0.240106i \(-0.0771824\pi\)
\(332\) −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 −0.739518 0.673137i \(-0.764946\pi\)
0.673137 + 0.739518i \(0.264946\pi\)
\(348\) 14.4596 23.2358i 0.775115 1.24557i
\(349\) −5.61778 5.61778i −0.300713 0.300713i 0.540580 0.841293i \(-0.318205\pi\)
−0.841293 + 0.540580i \(0.818205\pi\)
\(350\) 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 \(0.0226891\pi\)
−0.997461 + 0.0712195i \(0.977311\pi\)
\(360\) 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 −0.829660 0.558269i \(-0.811466\pi\)
0.558269 + 0.829660i \(0.311466\pi\)
\(374\) −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 −0.554268 0.832338i \(-0.687002\pi\)
0.832338 + 0.554268i \(0.187002\pi\)
\(380\) 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 −0.671287 0.741197i \(-0.734258\pi\)
0.741197 + 0.671287i \(0.234258\pi\)
\(390\) 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 −0.994060 0.108832i \(-0.965289\pi\)
−0.108832 0.994060i \(-0.534711\pi\)
\(398\) −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 \(0.102508\pi\)
−0.948592 + 0.316502i \(0.897492\pi\)
\(410\) 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 0.368084 0.929793i \(-0.380014\pi\)
−0.929793 + 0.368084i \(0.880014\pi\)
\(420\) 0 0
\(421\) 12.5714 12.5714i 0.612690 0.612690i −0.330956 0.943646i \(-0.607371\pi\)
0.943646 + 0.330956i \(0.107371\pi\)
\(422\) 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 \(-0.602435\pi\)
0.316283 0.948665i \(-0.397565\pi\)
\(440\) 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 −0.615778 0.787920i \(-0.711158\pi\)
0.787920 + 0.615778i \(0.211158\pi\)
\(444\) −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 \(0.108586\pi\)
−0.942377 + 0.334554i \(0.891414\pi\)
\(458\) 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 0.594408 0.804163i \(-0.297386\pi\)
−0.804163 + 0.594408i \(0.797386\pi\)
\(462\) 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 0.187410 0.982282i \(-0.439991\pi\)
−0.982282 + 0.187410i \(0.939991\pi\)
\(468\) 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 \(0.255192\pi\)
−0.695480 + 0.718546i \(0.744808\pi\)
\(488\) 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 −0.520293 0.853988i \(-0.674177\pi\)
0.853988 + 0.520293i \(0.174177\pi\)
\(492\) 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 0.947360 0.320171i \(-0.103740\pi\)
−0.320171 + 0.947360i \(0.603740\pi\)
\(500\) 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 \(0.0602377\pi\)
−0.982147 + 0.188115i \(0.939762\pi\)
\(504\) −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 0.751983 0.659183i \(-0.229098\pi\)
−0.659183 + 0.751983i \(0.729098\pi\)
\(510\) 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 \(-0.787557\pi\)
0.785428 0.618954i \(-0.212443\pi\)
\(522\) −9.62647 + 5.34770i −0.421339 + 0.234062i
\(523\) 10.1929 10.1929i 0.445703 0.445703i −0.448220 0.893923i \(-0.647942\pi\)
0.893923 + 0.448220i \(0.147942\pi\)
\(524\) 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 0.785209 0.619231i \(-0.212556\pi\)
−0.619231 + 0.785209i \(0.712556\pi\)
\(542\) −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 0.993716 0.111935i \(-0.0357048\pi\)
−0.111935 + 0.993716i \(0.535705\pi\)
\(548\) −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 0.679356 0.733809i \(-0.262259\pi\)
−0.733809 + 0.679356i \(0.762259\pi\)
\(558\) −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 0.997283 0.0736677i \(-0.0234704\pi\)
−0.0736677 + 0.997283i \(0.523470\pi\)
\(564\) 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 \(0.268801\pi\)
−0.664132 + 0.747615i \(0.731199\pi\)
\(570\) 0 0
\(571\) 5.60524 5.60524i 0.234572 0.234572i −0.580026 0.814598i \(-0.696958\pi\)
0.814598 + 0.580026i \(0.196958\pi\)
\(572\) 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 −0.698470 0.715639i \(-0.746135\pi\)
0.715639 + 0.698470i \(0.246135\pi\)
\(588\) 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 \(-0.653754\pi\)
0.464468 0.885590i \(-0.346246\pi\)
\(600\) 0 0
\(601\) 38.7291i 1.57979i 0.613239 + 0.789897i \(0.289866\pi\)
−0.613239 + 0.789897i \(0.710134\pi\)
\(602\) −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 −0.710165 0.704035i \(-0.751380\pi\)
0.704035 + 0.710165i \(0.251380\pi\)
\(614\) −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 \(-0.998153\pi\)
0.999983 0.00580123i \(-0.00184660\pi\)
\(618\) −1.73689 + 0.964876i −0.0698679 + 0.0388130i
\(619\) −11.5307 + 11.5307i −0.463460 + 0.463460i −0.899788 0.436328i \(-0.856279\pi\)
0.436328 + 0.899788i \(0.356279\pi\)
\(620\) 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 \(-0.908746\pi\)
0.959188 0.282771i \(-0.0912536\pi\)
\(632\) 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 0.583422 0.812169i \(-0.301713\pi\)
−0.812169 + 0.583422i \(0.801713\pi\)
\(644\) 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 \(0.364292\pi\)
−0.413541 + 0.910485i \(0.635708\pi\)
\(648\) 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 0.615236 0.788343i \(-0.289061\pi\)
−0.788343 + 0.615236i \(0.789061\pi\)
\(654\) 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 0.344779 0.938684i \(-0.387954\pi\)
−0.938684 + 0.344779i \(0.887954\pi\)
\(660\) 0 0
\(661\) 19.1271 19.1271i 0.743958 0.743958i −0.229379 0.973337i \(-0.573670\pi\)
0.973337 + 0.229379i \(0.0736696\pi\)
\(662\) 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 −0.757414 0.652935i \(-0.773537\pi\)
0.652935 + 0.757414i \(0.273537\pi\)
\(678\) −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 −0.906596 0.421999i \(-0.861329\pi\)
0.421999 + 0.906596i \(0.361329\pi\)
\(684\) −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 0.999731 + 0.0231826i \(0.00737991\pi\)
0.0231826 + 0.999731i \(0.492620\pi\)
\(692\) −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 0.999165 0.0408602i \(-0.0130098\pi\)
−0.0408602 + 0.999165i \(0.513010\pi\)
\(702\) 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 −0.336570 0.941659i \(-0.609267\pi\)
0.941659 + 0.336570i \(0.109267\pi\)
\(710\) 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 \(-0.975570\pi\)
0.997056 0.0766724i \(-0.0244296\pi\)
\(728\) 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 0.251817 0.967775i \(-0.418972\pi\)
−0.967775 + 0.251817i \(0.918972\pi\)
\(734\) −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 0.993757 0.111564i \(-0.0355859\pi\)
−0.111564 + 0.993757i \(0.535586\pi\)
\(740\) 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 \(-0.939215\pi\)
0.981822 0.189802i \(-0.0607846\pi\)
\(744\) 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 −0.112345 + 0.993669i \(0.535836\pi\)
−0.993669 + 0.112345i \(0.964164\pi\)
\(758\) 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 \(-0.714564\pi\)
0.624174 0.781285i \(-0.285436\pi\)
\(762\) 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 −0.115527 0.993304i \(-0.536856\pi\)
0.993304 + 0.115527i \(0.0368556\pi\)
\(774\) −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