Properties

Label 441.2.h.b.373.2
Level $441$
Weight $2$
Character 441.373
Analytic conductor $3.521$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.2
Root \(0.500000 - 1.41036i\) of defining polynomial
Character \(\chi\) \(=\) 441.373
Dual form 441.2.h.b.214.2

$q$-expansion

\(f(q)\) \(=\) \(q-0.239123 q^{2} +(1.09097 - 1.34528i) q^{3} -1.94282 q^{4} +(0.590972 + 1.02359i) q^{5} +(-0.260877 + 0.321688i) q^{6} +0.942820 q^{8} +(-0.619562 - 2.93533i) q^{9} +O(q^{10})\) \(q-0.239123 q^{2} +(1.09097 - 1.34528i) q^{3} -1.94282 q^{4} +(0.590972 + 1.02359i) q^{5} +(-0.260877 + 0.321688i) q^{6} +0.942820 q^{8} +(-0.619562 - 2.93533i) q^{9} +(-0.141315 - 0.244765i) q^{10} +(1.85185 - 3.20750i) q^{11} +(-2.11956 + 2.61364i) q^{12} +(0.500000 - 0.866025i) q^{13} +(2.02175 + 0.321688i) q^{15} +3.66019 q^{16} +(-3.47141 - 6.01266i) q^{17} +(0.148152 + 0.701905i) q^{18} +(0.971410 - 1.68253i) q^{19} +(-1.14815 - 1.98866i) q^{20} +(-0.442820 + 0.766987i) q^{22} +(2.80150 + 4.85235i) q^{23} +(1.02859 - 1.26836i) q^{24} +(1.80150 - 3.12030i) q^{25} +(-0.119562 + 0.207087i) q^{26} +(-4.62476 - 2.36887i) q^{27} +(-0.119562 - 0.207087i) q^{29} +(-0.483448 - 0.0769231i) q^{30} -1.66019 q^{31} -2.76088 q^{32} +(-2.29467 - 5.99054i) q^{33} +(0.830095 + 1.43777i) q^{34} +(1.20370 + 5.70281i) q^{36} +(4.77292 - 8.26693i) q^{37} +(-0.232287 + 0.402332i) q^{38} +(-0.619562 - 1.61745i) q^{39} +(0.557180 + 0.965064i) q^{40} +(-5.09097 + 8.81782i) q^{41} +(-1.11273 - 1.92730i) q^{43} +(-3.59781 + 6.23159i) q^{44} +(2.63844 - 2.36887i) q^{45} +(-0.669905 - 1.16031i) q^{46} -5.82846 q^{47} +(3.99316 - 4.92398i) q^{48} +(-0.430782 + 0.746136i) q^{50} +(-11.8759 - 1.88962i) q^{51} +(-0.971410 + 1.68253i) q^{52} +(5.80150 + 10.0485i) q^{53} +(1.10589 + 0.566453i) q^{54} +4.37756 q^{55} +(-1.20370 - 3.14241i) q^{57} +(0.0285900 + 0.0495193i) q^{58} -2.60301 q^{59} +(-3.92790 - 0.624982i) q^{60} +7.60301 q^{61} +0.396990 q^{62} -6.66019 q^{64} +1.18194 q^{65} +(0.548709 + 1.43248i) q^{66} +3.50808 q^{67} +(6.74433 + 11.6815i) q^{68} +(9.58414 + 1.52496i) q^{69} +8.60301 q^{71} +(-0.584135 - 2.76748i) q^{72} +(7.57442 + 13.1193i) q^{73} +(-1.14132 + 1.97682i) q^{74} +(-2.23229 - 5.82769i) q^{75} +(-1.88727 + 3.26886i) q^{76} +(0.148152 + 0.386770i) q^{78} +7.37756 q^{79} +(2.16307 + 3.74654i) q^{80} +(-8.23229 + 3.63723i) q^{81} +(1.21737 - 2.10855i) q^{82} +(-3.47141 - 6.01266i) q^{83} +(4.10301 - 7.10662i) q^{85} +(0.266078 + 0.460861i) q^{86} +(-0.409028 - 0.0650819i) q^{87} +(1.74596 - 3.02409i) q^{88} +(1.37360 - 2.37915i) q^{89} +(-0.630912 + 0.566453i) q^{90} +(-5.44282 - 9.42724i) q^{92} +(-1.81122 + 2.23342i) q^{93} +1.39372 q^{94} +2.29630 q^{95} +(-3.01204 + 3.71415i) q^{96} +(3.58414 + 6.20790i) q^{97} +(-10.5624 - 3.44854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 2q^{2} - 2q^{3} + 6q^{4} - 5q^{5} - q^{6} - 12q^{8} - 4q^{9} + O(q^{10}) \) \( 6q - 2q^{2} - 2q^{3} + 6q^{4} - 5q^{5} - q^{6} - 12q^{8} - 4q^{9} + 2q^{11} - 13q^{12} + 3q^{13} + 11q^{15} + 6q^{16} - 12q^{17} + 10q^{18} - 3q^{19} - 16q^{20} + 15q^{22} + 15q^{24} - 6q^{25} - q^{26} + 7q^{27} - q^{29} + 31q^{30} + 6q^{31} - 16q^{32} + 13q^{33} - 3q^{34} - 11q^{36} + 3q^{37} + 8q^{38} - 4q^{39} + 21q^{40} - 22q^{41} + 3q^{43} - 23q^{44} + q^{45} - 12q^{46} + 18q^{47} + 14q^{48} - 10q^{50} - 12q^{51} + 3q^{52} + 18q^{53} - 13q^{54} + 12q^{55} + 11q^{57} + 9q^{58} + 18q^{59} - 17q^{60} + 12q^{61} + 36q^{62} - 24q^{64} - 10q^{65} - 34q^{66} + 6q^{68} + 39q^{69} + 18q^{71} + 15q^{72} + 3q^{73} - 6q^{74} - 4q^{75} - 21q^{76} + 10q^{78} + 30q^{79} + 11q^{80} - 40q^{81} + 9q^{82} - 12q^{83} - 9q^{85} - 34q^{86} - 11q^{87} + 21q^{88} - 2q^{89} - 73q^{90} - 15q^{92} - 18q^{93} - 48q^{94} + 32q^{95} + 7q^{96} + 3q^{97} - 46q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.239123 −0.169086 −0.0845428 0.996420i \(-0.526943\pi\)
−0.0845428 + 0.996420i \(0.526943\pi\)
\(3\) 1.09097 1.34528i 0.629873 0.776698i
\(4\) −1.94282 −0.971410
\(5\) 0.590972 + 1.02359i 0.264291 + 0.457765i 0.967378 0.253339i \(-0.0815289\pi\)
−0.703087 + 0.711104i \(0.748196\pi\)
\(6\) −0.260877 + 0.321688i −0.106502 + 0.131329i
\(7\) 0 0
\(8\) 0.942820 0.333337
\(9\) −0.619562 2.93533i −0.206521 0.978442i
\(10\) −0.141315 0.244765i −0.0446878 0.0774015i
\(11\) 1.85185 3.20750i 0.558353 0.967096i −0.439281 0.898350i \(-0.644767\pi\)
0.997634 0.0687465i \(-0.0219000\pi\)
\(12\) −2.11956 + 2.61364i −0.611865 + 0.754493i
\(13\) 0.500000 0.866025i 0.138675 0.240192i −0.788320 0.615265i \(-0.789049\pi\)
0.926995 + 0.375073i \(0.122382\pi\)
\(14\) 0 0
\(15\) 2.02175 + 0.321688i 0.522014 + 0.0830595i
\(16\) 3.66019 0.915047
\(17\) −3.47141 6.01266i −0.841941 1.45828i −0.888252 0.459357i \(-0.848080\pi\)
0.0463112 0.998927i \(-0.485253\pi\)
\(18\) 0.148152 + 0.701905i 0.0349197 + 0.165441i
\(19\) 0.971410 1.68253i 0.222857 0.385999i −0.732818 0.680425i \(-0.761795\pi\)
0.955674 + 0.294426i \(0.0951285\pi\)
\(20\) −1.14815 1.98866i −0.256735 0.444677i
\(21\) 0 0
\(22\) −0.442820 + 0.766987i −0.0944096 + 0.163522i
\(23\) 2.80150 + 4.85235i 0.584154 + 1.01178i 0.994980 + 0.100071i \(0.0319070\pi\)
−0.410826 + 0.911714i \(0.634760\pi\)
\(24\) 1.02859 1.26836i 0.209960 0.258902i
\(25\) 1.80150 3.12030i 0.360301 0.624060i
\(26\) −0.119562 + 0.207087i −0.0234480 + 0.0406131i
\(27\) −4.62476 2.36887i −0.890036 0.455890i
\(28\) 0 0
\(29\) −0.119562 0.207087i −0.0222020 0.0384551i 0.854711 0.519104i \(-0.173734\pi\)
−0.876913 + 0.480649i \(0.840401\pi\)
\(30\) −0.483448 0.0769231i −0.0882652 0.0140442i
\(31\) −1.66019 −0.298179 −0.149089 0.988824i \(-0.547634\pi\)
−0.149089 + 0.988824i \(0.547634\pi\)
\(32\) −2.76088 −0.488059
\(33\) −2.29467 5.99054i −0.399451 1.04282i
\(34\) 0.830095 + 1.43777i 0.142360 + 0.246575i
\(35\) 0 0
\(36\) 1.20370 + 5.70281i 0.200616 + 0.950469i
\(37\) 4.77292 8.26693i 0.784662 1.35908i −0.144538 0.989499i \(-0.546170\pi\)
0.929201 0.369576i \(-0.120497\pi\)
\(38\) −0.232287 + 0.402332i −0.0376819 + 0.0652669i
\(39\) −0.619562 1.61745i −0.0992093 0.258999i
\(40\) 0.557180 + 0.965064i 0.0880979 + 0.152590i
\(41\) −5.09097 + 8.81782i −0.795076 + 1.37711i 0.127715 + 0.991811i \(0.459236\pi\)
−0.922791 + 0.385301i \(0.874097\pi\)
\(42\) 0 0
\(43\) −1.11273 1.92730i −0.169689 0.293910i 0.768622 0.639704i \(-0.220943\pi\)
−0.938311 + 0.345794i \(0.887610\pi\)
\(44\) −3.59781 + 6.23159i −0.542390 + 0.939447i
\(45\) 2.63844 2.36887i 0.393315 0.353131i
\(46\) −0.669905 1.16031i −0.0987721 0.171078i
\(47\) −5.82846 −0.850168 −0.425084 0.905154i \(-0.639755\pi\)
−0.425084 + 0.905154i \(0.639755\pi\)
\(48\) 3.99316 4.92398i 0.576364 0.710716i
\(49\) 0 0
\(50\) −0.430782 + 0.746136i −0.0609217 + 0.105520i
\(51\) −11.8759 1.88962i −1.66296 0.264599i
\(52\) −0.971410 + 1.68253i −0.134710 + 0.233325i
\(53\) 5.80150 + 10.0485i 0.796898 + 1.38027i 0.921627 + 0.388077i \(0.126861\pi\)
−0.124729 + 0.992191i \(0.539806\pi\)
\(54\) 1.10589 + 0.566453i 0.150492 + 0.0770845i
\(55\) 4.37756 0.590270
\(56\) 0 0
\(57\) −1.20370 3.14241i −0.159434 0.416223i
\(58\) 0.0285900 + 0.0495193i 0.00375405 + 0.00650220i
\(59\) −2.60301 −0.338883 −0.169442 0.985540i \(-0.554196\pi\)
−0.169442 + 0.985540i \(0.554196\pi\)
\(60\) −3.92790 0.624982i −0.507090 0.0806848i
\(61\) 7.60301 0.973466 0.486733 0.873551i \(-0.338189\pi\)
0.486733 + 0.873551i \(0.338189\pi\)
\(62\) 0.396990 0.0504178
\(63\) 0 0
\(64\) −6.66019 −0.832524
\(65\) 1.18194 0.146602
\(66\) 0.548709 + 1.43248i 0.0675414 + 0.176326i
\(67\) 3.50808 0.428580 0.214290 0.976770i \(-0.431256\pi\)
0.214290 + 0.976770i \(0.431256\pi\)
\(68\) 6.74433 + 11.6815i 0.817870 + 1.41659i
\(69\) 9.58414 + 1.52496i 1.15379 + 0.183584i
\(70\) 0 0
\(71\) 8.60301 1.02099 0.510495 0.859881i \(-0.329462\pi\)
0.510495 + 0.859881i \(0.329462\pi\)
\(72\) −0.584135 2.76748i −0.0688410 0.326151i
\(73\) 7.57442 + 13.1193i 0.886519 + 1.53550i 0.843963 + 0.536402i \(0.180217\pi\)
0.0425559 + 0.999094i \(0.486450\pi\)
\(74\) −1.14132 + 1.97682i −0.132675 + 0.229800i
\(75\) −2.23229 5.82769i −0.257762 0.672923i
\(76\) −1.88727 + 3.26886i −0.216485 + 0.374963i
\(77\) 0 0
\(78\) 0.148152 + 0.386770i 0.0167749 + 0.0437931i
\(79\) 7.37756 0.830040 0.415020 0.909812i \(-0.363775\pi\)
0.415020 + 0.909812i \(0.363775\pi\)
\(80\) 2.16307 + 3.74654i 0.241838 + 0.418876i
\(81\) −8.23229 + 3.63723i −0.914699 + 0.404137i
\(82\) 1.21737 2.10855i 0.134436 0.232850i
\(83\) −3.47141 6.01266i −0.381037 0.659975i 0.610174 0.792267i \(-0.291100\pi\)
−0.991211 + 0.132292i \(0.957766\pi\)
\(84\) 0 0
\(85\) 4.10301 7.10662i 0.445034 0.770821i
\(86\) 0.266078 + 0.460861i 0.0286920 + 0.0496960i
\(87\) −0.409028 0.0650819i −0.0438524 0.00697751i
\(88\) 1.74596 3.02409i 0.186120 0.322369i
\(89\) 1.37360 2.37915i 0.145602 0.252189i −0.783996 0.620766i \(-0.786822\pi\)
0.929597 + 0.368577i \(0.120155\pi\)
\(90\) −0.630912 + 0.566453i −0.0665039 + 0.0597094i
\(91\) 0 0
\(92\) −5.44282 9.42724i −0.567453 0.982858i
\(93\) −1.81122 + 2.23342i −0.187815 + 0.231595i
\(94\) 1.39372 0.143751
\(95\) 2.29630 0.235596
\(96\) −3.01204 + 3.71415i −0.307415 + 0.379074i
\(97\) 3.58414 + 6.20790i 0.363914 + 0.630317i 0.988601 0.150558i \(-0.0481069\pi\)
−0.624687 + 0.780875i \(0.714774\pi\)
\(98\) 0 0
\(99\) −10.5624 3.44854i −1.06156 0.346591i
\(100\) −3.50000 + 6.06218i −0.350000 + 0.606218i
\(101\) −6.39248 + 11.0721i −0.636075 + 1.10171i 0.350211 + 0.936671i \(0.386110\pi\)
−0.986286 + 0.165044i \(0.947223\pi\)
\(102\) 2.83981 + 0.451852i 0.281183 + 0.0447400i
\(103\) −2.19850 3.80791i −0.216624 0.375204i 0.737150 0.675730i \(-0.236171\pi\)
−0.953774 + 0.300526i \(0.902838\pi\)
\(104\) 0.471410 0.816506i 0.0462256 0.0800650i
\(105\) 0 0
\(106\) −1.38727 2.40283i −0.134744 0.233384i
\(107\) −6.86389 + 11.8886i −0.663557 + 1.14931i 0.316117 + 0.948720i \(0.397621\pi\)
−0.979674 + 0.200594i \(0.935713\pi\)
\(108\) 8.98508 + 4.60230i 0.864590 + 0.442856i
\(109\) −0.631600 1.09396i −0.0604963 0.104783i 0.834191 0.551476i \(-0.185935\pi\)
−0.894687 + 0.446693i \(0.852602\pi\)
\(110\) −1.04678 −0.0998062
\(111\) −5.91423 15.4399i −0.561354 1.46549i
\(112\) 0 0
\(113\) −6.08126 + 10.5330i −0.572076 + 0.990866i 0.424276 + 0.905533i \(0.360529\pi\)
−0.996353 + 0.0853326i \(0.972805\pi\)
\(114\) 0.287832 + 0.751424i 0.0269579 + 0.0703773i
\(115\) −3.31122 + 5.73520i −0.308773 + 0.534810i
\(116\) 0.232287 + 0.402332i 0.0215673 + 0.0373556i
\(117\) −2.85185 0.931107i −0.263653 0.0860809i
\(118\) 0.622440 0.0573003
\(119\) 0 0
\(120\) 1.90615 + 0.303294i 0.174007 + 0.0276868i
\(121\) −1.35868 2.35331i −0.123517 0.213937i
\(122\) −1.81806 −0.164599
\(123\) 6.30834 + 16.4688i 0.568804 + 1.48494i
\(124\) 3.22545 0.289654
\(125\) 10.1683 0.909478
\(126\) 0 0
\(127\) 1.33981 0.118889 0.0594445 0.998232i \(-0.481067\pi\)
0.0594445 + 0.998232i \(0.481067\pi\)
\(128\) 7.11436 0.628827
\(129\) −3.80671 0.605698i −0.335162 0.0533287i
\(130\) −0.282630 −0.0247883
\(131\) −2.48345 4.30146i −0.216980 0.375820i 0.736903 0.675998i \(-0.236287\pi\)
−0.953883 + 0.300178i \(0.902954\pi\)
\(132\) 4.45813 + 11.6385i 0.388030 + 1.01301i
\(133\) 0 0
\(134\) −0.838864 −0.0724668
\(135\) −0.308342 6.13381i −0.0265378 0.527915i
\(136\) −3.27292 5.66886i −0.280650 0.486100i
\(137\) 2.16991 3.75839i 0.185387 0.321101i −0.758320 0.651883i \(-0.773979\pi\)
0.943707 + 0.330782i \(0.107313\pi\)
\(138\) −2.29179 0.364654i −0.195090 0.0310414i
\(139\) 1.97141 3.41458i 0.167213 0.289621i −0.770226 0.637771i \(-0.779857\pi\)
0.937439 + 0.348150i \(0.113190\pi\)
\(140\) 0 0
\(141\) −6.35868 + 7.84092i −0.535498 + 0.660324i
\(142\) −2.05718 −0.172635
\(143\) −1.85185 3.20750i −0.154859 0.268224i
\(144\) −2.26771 10.7439i −0.188976 0.895321i
\(145\) 0.141315 0.244765i 0.0117356 0.0203266i
\(146\) −1.81122 3.13713i −0.149898 0.259630i
\(147\) 0 0
\(148\) −9.27292 + 16.0612i −0.762229 + 1.32022i
\(149\) −5.55555 9.62249i −0.455128 0.788305i 0.543568 0.839365i \(-0.317073\pi\)
−0.998696 + 0.0510606i \(0.983740\pi\)
\(150\) 0.533792 + 1.39354i 0.0435839 + 0.113782i
\(151\) −6.96169 + 12.0580i −0.566535 + 0.981267i 0.430370 + 0.902652i \(0.358383\pi\)
−0.996905 + 0.0786145i \(0.974950\pi\)
\(152\) 0.915865 1.58632i 0.0742864 0.128668i
\(153\) −15.4984 + 13.9149i −1.25297 + 1.12496i
\(154\) 0 0
\(155\) −0.981125 1.69936i −0.0788059 0.136496i
\(156\) 1.20370 + 3.14241i 0.0963729 + 0.251594i
\(157\) −0.0571799 −0.00456346 −0.00228173 0.999997i \(-0.500726\pi\)
−0.00228173 + 0.999997i \(0.500726\pi\)
\(158\) −1.76415 −0.140348
\(159\) 19.8473 + 3.15798i 1.57400 + 0.250444i
\(160\) −1.63160 2.82601i −0.128989 0.223416i
\(161\) 0 0
\(162\) 1.96853 0.869747i 0.154662 0.0683338i
\(163\) 0.754040 1.30604i 0.0590610 0.102297i −0.834983 0.550276i \(-0.814523\pi\)
0.894044 + 0.447979i \(0.147856\pi\)
\(164\) 9.89084 17.1314i 0.772345 1.33774i
\(165\) 4.77579 5.88905i 0.371795 0.458462i
\(166\) 0.830095 + 1.43777i 0.0644279 + 0.111592i
\(167\) −7.34213 + 12.7169i −0.568151 + 0.984067i 0.428598 + 0.903496i \(0.359008\pi\)
−0.996749 + 0.0805714i \(0.974325\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) −0.981125 + 1.69936i −0.0752489 + 0.130335i
\(171\) −5.54063 1.80897i −0.423702 0.138336i
\(172\) 2.16182 + 3.74439i 0.164838 + 0.285507i
\(173\) −0.252796 −0.0192197 −0.00960987 0.999954i \(-0.503059\pi\)
−0.00960987 + 0.999954i \(0.503059\pi\)
\(174\) 0.0978082 + 0.0155626i 0.00741482 + 0.00117980i
\(175\) 0 0
\(176\) 6.77812 11.7400i 0.510920 0.884939i
\(177\) −2.83981 + 3.50178i −0.213453 + 0.263210i
\(178\) −0.328460 + 0.568910i −0.0246191 + 0.0426416i
\(179\) −7.09617 12.2909i −0.530393 0.918667i −0.999371 0.0354578i \(-0.988711\pi\)
0.468978 0.883210i \(-0.344622\pi\)
\(180\) −5.12601 + 4.60230i −0.382070 + 0.343035i
\(181\) 1.43147 0.106400 0.0532002 0.998584i \(-0.483058\pi\)
0.0532002 + 0.998584i \(0.483058\pi\)
\(182\) 0 0
\(183\) 8.29467 10.2282i 0.613160 0.756089i
\(184\) 2.64132 + 4.57489i 0.194720 + 0.337266i
\(185\) 11.2826 0.829515
\(186\) 0.433105 0.534063i 0.0317568 0.0391594i
\(187\) −25.7141 −1.88040
\(188\) 11.3236 0.825862
\(189\) 0 0
\(190\) −0.549100 −0.0398359
\(191\) 15.0676 1.09025 0.545126 0.838354i \(-0.316482\pi\)
0.545126 + 0.838354i \(0.316482\pi\)
\(192\) −7.26608 + 8.95983i −0.524384 + 0.646620i
\(193\) −7.84789 −0.564904 −0.282452 0.959282i \(-0.591148\pi\)
−0.282452 + 0.959282i \(0.591148\pi\)
\(194\) −0.857050 1.48445i −0.0615326 0.106578i
\(195\) 1.28947 1.59005i 0.0923406 0.113866i
\(196\) 0 0
\(197\) 6.69002 0.476644 0.238322 0.971186i \(-0.423403\pi\)
0.238322 + 0.971186i \(0.423403\pi\)
\(198\) 2.52571 + 0.824626i 0.179494 + 0.0586036i
\(199\) −9.96978 17.2682i −0.706739 1.22411i −0.966060 0.258316i \(-0.916832\pi\)
0.259322 0.965791i \(-0.416501\pi\)
\(200\) 1.69850 2.94188i 0.120102 0.208022i
\(201\) 3.82722 4.71935i 0.269951 0.332878i
\(202\) 1.52859 2.64760i 0.107551 0.186284i
\(203\) 0 0
\(204\) 23.0728 + 3.67119i 1.61542 + 0.257035i
\(205\) −12.0345 −0.840525
\(206\) 0.525711 + 0.910559i 0.0366280 + 0.0634416i
\(207\) 12.5075 11.2297i 0.869333 0.780515i
\(208\) 1.83009 3.16982i 0.126894 0.219787i
\(209\) −3.59781 6.23159i −0.248866 0.431048i
\(210\) 0 0
\(211\) 9.04583 15.6678i 0.622741 1.07862i −0.366233 0.930523i \(-0.619353\pi\)
0.988973 0.148095i \(-0.0473141\pi\)
\(212\) −11.2713 19.5224i −0.774115 1.34081i
\(213\) 9.38564 11.5735i 0.643093 0.793001i
\(214\) 1.64132 2.84284i 0.112198 0.194333i
\(215\) 1.31518 2.27796i 0.0896944 0.155355i
\(216\) −4.36032 2.23342i −0.296682 0.151965i
\(217\) 0 0
\(218\) 0.151030 + 0.261592i 0.0102291 + 0.0177172i
\(219\) 25.9126 + 4.12304i 1.75101 + 0.278609i
\(220\) −8.50481 −0.573394
\(221\) −6.94282 −0.467025
\(222\) 1.41423 + 3.69204i 0.0949169 + 0.247793i
\(223\) −11.3285 19.6215i −0.758610 1.31395i −0.943560 0.331203i \(-0.892546\pi\)
0.184950 0.982748i \(-0.440788\pi\)
\(224\) 0 0
\(225\) −10.2752 3.35479i −0.685016 0.223653i
\(226\) 1.45417 2.51870i 0.0967299 0.167541i
\(227\) −2.64132 + 4.57489i −0.175310 + 0.303646i −0.940269 0.340433i \(-0.889426\pi\)
0.764958 + 0.644080i \(0.222760\pi\)
\(228\) 2.33857 + 6.10514i 0.154875 + 0.404323i
\(229\) 9.66827 + 16.7459i 0.638897 + 1.10660i 0.985675 + 0.168655i \(0.0539425\pi\)
−0.346778 + 0.937947i \(0.612724\pi\)
\(230\) 0.791790 1.37142i 0.0522091 0.0904288i
\(231\) 0 0
\(232\) −0.112725 0.195246i −0.00740077 0.0128185i
\(233\) 8.49028 14.7056i 0.556217 0.963396i −0.441591 0.897217i \(-0.645586\pi\)
0.997808 0.0661796i \(-0.0210810\pi\)
\(234\) 0.681943 + 0.222649i 0.0445800 + 0.0145550i
\(235\) −3.44445 5.96597i −0.224691 0.389177i
\(236\) 5.05718 0.329194
\(237\) 8.04871 9.92489i 0.522820 0.644691i
\(238\) 0 0
\(239\) −8.44282 + 14.6234i −0.546121 + 0.945909i 0.452415 + 0.891808i \(0.350563\pi\)
−0.998535 + 0.0541011i \(0.982771\pi\)
\(240\) 7.40000 + 1.17744i 0.477668 + 0.0760034i
\(241\) 13.5728 23.5088i 0.874300 1.51433i 0.0167933 0.999859i \(-0.494654\pi\)
0.857507 0.514473i \(-0.172012\pi\)
\(242\) 0.324893 + 0.562732i 0.0208849 + 0.0361738i
\(243\) −4.08809 + 15.0429i −0.262251 + 0.965000i
\(244\) −14.7713 −0.945634
\(245\) 0 0
\(246\) −1.50847 3.93807i −0.0961766 0.251082i
\(247\) −0.971410 1.68253i −0.0618093 0.107057i
\(248\) −1.56526 −0.0993941
\(249\) −11.8759 1.88962i −0.752606 0.119750i
\(250\) −2.43147 −0.153780
\(251\) 19.0780 1.20419 0.602096 0.798424i \(-0.294332\pi\)
0.602096 + 0.798424i \(0.294332\pi\)
\(252\) 0 0
\(253\) 20.7518 1.30466
\(254\) −0.320380 −0.0201024
\(255\) −5.08414 13.2728i −0.318381 0.831176i
\(256\) 11.6192 0.726198
\(257\) −7.42107 12.8537i −0.462913 0.801790i 0.536191 0.844097i \(-0.319863\pi\)
−0.999105 + 0.0423070i \(0.986529\pi\)
\(258\) 0.910272 + 0.144836i 0.0566711 + 0.00901712i
\(259\) 0 0
\(260\) −2.29630 −0.142411
\(261\) −0.533792 + 0.479256i −0.0330409 + 0.0296652i
\(262\) 0.593850 + 1.02858i 0.0366882 + 0.0635458i
\(263\) 3.87072 6.70429i 0.238679 0.413404i −0.721656 0.692251i \(-0.756619\pi\)
0.960335 + 0.278847i \(0.0899523\pi\)
\(264\) −2.16346 5.64800i −0.133152 0.347611i
\(265\) −6.85705 + 11.8768i −0.421225 + 0.729584i
\(266\) 0 0
\(267\) −1.70206 4.44346i −0.104165 0.271936i
\(268\) −6.81557 −0.416327
\(269\) −0.755675 1.30887i −0.0460743 0.0798031i 0.842069 0.539371i \(-0.181338\pi\)
−0.888143 + 0.459567i \(0.848004\pi\)
\(270\) 0.0737316 + 1.46674i 0.00448716 + 0.0892628i
\(271\) −10.9903 + 19.0357i −0.667612 + 1.15634i 0.310958 + 0.950424i \(0.399350\pi\)
−0.978570 + 0.205915i \(0.933983\pi\)
\(272\) −12.7060 22.0075i −0.770416 1.33440i
\(273\) 0 0
\(274\) −0.518875 + 0.898718i −0.0313464 + 0.0542935i
\(275\) −6.67223 11.5566i −0.402350 0.696892i
\(276\) −18.6202 2.96273i −1.12081 0.178335i
\(277\) 5.41423 9.37772i 0.325310 0.563453i −0.656265 0.754530i \(-0.727865\pi\)
0.981575 + 0.191077i \(0.0611982\pi\)
\(278\) −0.471410 + 0.816506i −0.0282733 + 0.0489708i
\(279\) 1.02859 + 4.87320i 0.0615801 + 0.291751i
\(280\) 0 0
\(281\) 8.43831 + 14.6156i 0.503387 + 0.871892i 0.999992 + 0.00391559i \(0.00124638\pi\)
−0.496605 + 0.867977i \(0.665420\pi\)
\(282\) 1.52051 1.87495i 0.0905450 0.111651i
\(283\) 15.3171 0.910508 0.455254 0.890362i \(-0.349549\pi\)
0.455254 + 0.890362i \(0.349549\pi\)
\(284\) −16.7141 −0.991799
\(285\) 2.50520 3.08917i 0.148395 0.182987i
\(286\) 0.442820 + 0.766987i 0.0261845 + 0.0453529i
\(287\) 0 0
\(288\) 1.71053 + 8.10408i 0.100794 + 0.477537i
\(289\) −15.6014 + 27.0224i −0.917728 + 1.58955i
\(290\) −0.0337917 + 0.0585290i −0.00198432 + 0.00343694i
\(291\) 12.2616 + 1.95098i 0.718786 + 0.114368i
\(292\) −14.7157 25.4884i −0.861173 1.49160i
\(293\) −4.68482 + 8.11435i −0.273690 + 0.474045i −0.969804 0.243886i \(-0.921578\pi\)
0.696114 + 0.717932i \(0.254911\pi\)
\(294\) 0 0
\(295\) −1.53831 2.66442i −0.0895636 0.155129i
\(296\) 4.50000 7.79423i 0.261557 0.453030i
\(297\) −16.1625 + 10.4471i −0.937844 + 0.606203i
\(298\) 1.32846 + 2.30096i 0.0769556 + 0.133291i
\(299\) 5.60301 0.324030
\(300\) 4.33693 + 11.3221i 0.250393 + 0.653684i
\(301\) 0 0
\(302\) 1.66470 2.88335i 0.0957929 0.165918i
\(303\) 7.92107 + 20.6790i 0.455053 + 1.18798i
\(304\) 3.55555 6.15838i 0.203925 0.353208i
\(305\) 4.49316 + 7.78239i 0.257278 + 0.445618i
\(306\) 3.70602 3.32738i 0.211859 0.190214i
\(307\) −2.71410 −0.154902 −0.0774509 0.996996i \(-0.524678\pi\)
−0.0774509 + 0.996996i \(0.524678\pi\)
\(308\) 0 0
\(309\) −7.52120 1.19672i −0.427866 0.0680792i
\(310\) 0.234610 + 0.406356i 0.0133249 + 0.0230795i
\(311\) 13.9806 0.792765 0.396383 0.918085i \(-0.370265\pi\)
0.396383 + 0.918085i \(0.370265\pi\)
\(312\) −0.584135 1.52496i −0.0330701 0.0863341i
\(313\) 19.0539 1.07699 0.538495 0.842628i \(-0.318993\pi\)
0.538495 + 0.842628i \(0.318993\pi\)
\(314\) 0.0136731 0.000771615
\(315\) 0 0
\(316\) −14.3333 −0.806309
\(317\) −4.01943 −0.225754 −0.112877 0.993609i \(-0.536007\pi\)
−0.112877 + 0.993609i \(0.536007\pi\)
\(318\) −4.74596 0.755146i −0.266140 0.0423465i
\(319\) −0.885640 −0.0495863
\(320\) −3.93598 6.81732i −0.220028 0.381100i
\(321\) 8.50520 + 22.2040i 0.474714 + 1.23931i
\(322\) 0 0
\(323\) −13.4887 −0.750529
\(324\) 15.9939 7.06649i 0.888547 0.392583i
\(325\) −1.80150 3.12030i −0.0999295 0.173083i
\(326\) −0.180309 + 0.312304i −0.00998637 + 0.0172969i
\(327\) −2.16075 0.343803i −0.119489 0.0190124i
\(328\) −4.79987 + 8.31362i −0.265028 + 0.459043i
\(329\) 0 0
\(330\) −1.14200 + 1.40821i −0.0628652 + 0.0775193i
\(331\) −12.3776 −0.680332 −0.340166 0.940365i \(-0.610483\pi\)
−0.340166 + 0.940365i \(0.610483\pi\)
\(332\) 6.74433 + 11.6815i 0.370143 + 0.641106i
\(333\) −27.2233 8.88819i −1.49183 0.487070i
\(334\) 1.75567 3.04092i 0.0960663 0.166392i
\(335\) 2.07318 + 3.59085i 0.113270 + 0.196189i
\(336\) 0 0
\(337\) −6.12997 + 10.6174i −0.333920 + 0.578367i −0.983277 0.182117i \(-0.941705\pi\)
0.649356 + 0.760484i \(0.275038\pi\)
\(338\) −1.43474 2.48504i −0.0780395 0.135168i
\(339\) 7.53543 + 19.6723i 0.409268 + 1.06845i
\(340\) −7.97141 + 13.8069i −0.432310 + 0.748784i
\(341\) −3.07442 + 5.32505i −0.166489 + 0.288368i
\(342\) 1.32489 + 0.432568i 0.0716420 + 0.0233906i
\(343\) 0 0
\(344\) −1.04910 1.81709i −0.0565637 0.0979711i
\(345\) 4.10301 + 10.7115i 0.220899 + 0.576686i
\(346\) 0.0604495 0.00324978
\(347\) 6.64979 0.356979 0.178490 0.983942i \(-0.442879\pi\)
0.178490 + 0.983942i \(0.442879\pi\)
\(348\) 0.794668 + 0.126442i 0.0425987 + 0.00677802i
\(349\) 5.71737 + 9.90278i 0.306044 + 0.530083i 0.977493 0.210967i \(-0.0676613\pi\)
−0.671449 + 0.741050i \(0.734328\pi\)
\(350\) 0 0
\(351\) −4.36389 + 2.82073i −0.232927 + 0.150559i
\(352\) −5.11273 + 8.85550i −0.272509 + 0.472000i
\(353\) −11.0978 + 19.2220i −0.590677 + 1.02308i 0.403465 + 0.914995i \(0.367806\pi\)
−0.994141 + 0.108087i \(0.965528\pi\)
\(354\) 0.679065 0.837357i 0.0360919 0.0445050i
\(355\) 5.08414 + 8.80598i 0.269838 + 0.467373i
\(356\) −2.66866 + 4.62226i −0.141439 + 0.244979i
\(357\) 0 0
\(358\) 1.69686 + 2.93905i 0.0896819 + 0.155334i
\(359\) 3.77812 6.54389i 0.199401 0.345373i −0.748933 0.662646i \(-0.769434\pi\)
0.948334 + 0.317272i \(0.102767\pi\)
\(360\) 2.48757 2.23342i 0.131106 0.117712i
\(361\) 7.61273 + 13.1856i 0.400670 + 0.693980i
\(362\) −0.342298 −0.0179908
\(363\) −4.64815 0.739583i −0.243965 0.0388180i
\(364\) 0 0
\(365\) −8.95254 + 15.5062i −0.468597 + 0.811634i
\(366\) −1.98345 + 2.44580i −0.103677 + 0.127844i
\(367\) −9.26157 + 16.0415i −0.483450 + 0.837360i −0.999819 0.0190063i \(-0.993950\pi\)
0.516370 + 0.856366i \(0.327283\pi\)
\(368\) 10.2540 + 17.7605i 0.534529 + 0.925831i
\(369\) 29.0374 + 9.48048i 1.51162 + 0.493534i
\(370\) −2.69794 −0.140259
\(371\) 0 0
\(372\) 3.51887 4.33914i 0.182445 0.224974i
\(373\) −7.83009 13.5621i −0.405427 0.702220i 0.588944 0.808174i \(-0.299544\pi\)
−0.994371 + 0.105954i \(0.966210\pi\)
\(374\) 6.14884 0.317949
\(375\) 11.0933 13.6792i 0.572855 0.706390i
\(376\) −5.49519 −0.283393
\(377\) −0.239123 −0.0123155
\(378\) 0 0
\(379\) 4.03775 0.207405 0.103703 0.994608i \(-0.466931\pi\)
0.103703 + 0.994608i \(0.466931\pi\)
\(380\) −4.46130 −0.228860
\(381\) 1.46169 1.80242i 0.0748849 0.0923408i
\(382\) −3.60301 −0.184346
\(383\) 0.112725 + 0.195246i 0.00575998 + 0.00997659i 0.868891 0.495003i \(-0.164833\pi\)
−0.863131 + 0.504980i \(0.831500\pi\)
\(384\) 7.76157 9.57081i 0.396081 0.488408i
\(385\) 0 0
\(386\) 1.87661 0.0955171
\(387\) −4.96784 + 4.46029i −0.252530 + 0.226729i
\(388\) −6.96333 12.0608i −0.353510 0.612296i
\(389\) −12.6316 + 21.8786i −0.640448 + 1.10929i 0.344885 + 0.938645i \(0.387918\pi\)
−0.985333 + 0.170643i \(0.945416\pi\)
\(390\) −0.308342 + 0.380217i −0.0156135 + 0.0192530i
\(391\) 19.4503 33.6890i 0.983646 1.70373i
\(392\) 0 0
\(393\) −8.49604 1.35183i −0.428569 0.0681910i
\(394\) −1.59974 −0.0805938
\(395\) 4.35993 + 7.55162i 0.219372 + 0.379963i
\(396\) 20.5208 + 6.69989i 1.03121 + 0.336682i
\(397\) −10.1505 + 17.5811i −0.509438 + 0.882372i 0.490503 + 0.871440i \(0.336813\pi\)
−0.999940 + 0.0109322i \(0.996520\pi\)
\(398\) 2.38401 + 4.12922i 0.119499 + 0.206979i
\(399\) 0 0
\(400\) 6.59385 11.4209i 0.329693 0.571044i
\(401\) 7.61273 + 13.1856i 0.380161 + 0.658459i 0.991085 0.133231i \(-0.0425351\pi\)
−0.610924 + 0.791689i \(0.709202\pi\)
\(402\) −0.915177 + 1.12851i −0.0456449 + 0.0562848i
\(403\) −0.830095 + 1.43777i −0.0413500 + 0.0716203i
\(404\) 12.4194 21.5111i 0.617890 1.07022i
\(405\) −8.58809 6.27701i −0.426746 0.311907i
\(406\) 0 0
\(407\) −17.6774 30.6182i −0.876238 1.51769i
\(408\) −11.1969 1.78157i −0.554327 0.0882009i
\(409\) −1.65692 −0.0819294 −0.0409647 0.999161i \(-0.513043\pi\)
−0.0409647 + 0.999161i \(0.513043\pi\)
\(410\) 2.87772 0.142121
\(411\) −2.68878 7.01942i −0.132628 0.346243i
\(412\) 4.27128 + 7.39807i 0.210431 + 0.364477i
\(413\) 0 0
\(414\) −2.99084 + 2.68527i −0.146992 + 0.131974i
\(415\) 4.10301 7.10662i 0.201409 0.348850i
\(416\) −1.38044 + 2.39099i −0.0676816 + 0.117228i
\(417\) −2.44282 6.37731i −0.119625 0.312298i
\(418\) 0.860320 + 1.49012i 0.0420796 + 0.0728840i
\(419\) 16.6871 28.9030i 0.815220 1.41200i −0.0939492 0.995577i \(-0.529949\pi\)
0.909170 0.416426i \(-0.136718\pi\)
\(420\) 0 0
\(421\) −9.12025 15.7967i −0.444494 0.769886i 0.553523 0.832834i \(-0.313283\pi\)
−0.998017 + 0.0629481i \(0.979950\pi\)
\(422\) −2.16307 + 3.74654i −0.105297 + 0.182379i
\(423\) 3.61109 + 17.1084i 0.175577 + 0.831841i
\(424\) 5.46978 + 9.47393i 0.265636 + 0.460095i
\(425\) −25.0150 −1.21341
\(426\) −2.24433 + 2.76748i −0.108738 + 0.134085i
\(427\) 0 0
\(428\) 13.3353 23.0974i 0.644586 1.11646i
\(429\) −6.33530 1.00803i −0.305871 0.0486682i
\(430\) −0.314490 + 0.544712i −0.0151660 + 0.0262684i
\(431\) −14.6413 25.3595i −0.705247 1.22152i −0.966602 0.256281i \(-0.917503\pi\)
0.261355 0.965243i \(-0.415831\pi\)
\(432\) −16.9275 8.67053i −0.814425 0.417161i
\(433\) 12.2449 0.588451 0.294226 0.955736i \(-0.404938\pi\)
0.294226 + 0.955736i \(0.404938\pi\)
\(434\) 0 0
\(435\) −0.175107 0.457140i −0.00839573 0.0219182i
\(436\) 1.22708 + 2.12537i 0.0587667 + 0.101787i
\(437\) 10.8856 0.520731
\(438\) −6.19630 0.985915i −0.296071 0.0471088i
\(439\) 4.83173 0.230606 0.115303 0.993330i \(-0.463216\pi\)
0.115303 + 0.993330i \(0.463216\pi\)
\(440\) 4.12725 0.196759
\(441\) 0 0
\(442\) 1.66019 0.0789672
\(443\) 1.24488 0.0591461 0.0295730 0.999563i \(-0.490585\pi\)
0.0295730 + 0.999563i \(0.490585\pi\)
\(444\) 11.4903 + 29.9969i 0.545305 + 1.42359i
\(445\) 3.24704 0.153924
\(446\) 2.70890 + 4.69195i 0.128270 + 0.222170i
\(447\) −19.0059 3.02409i −0.898948 0.143035i
\(448\) 0 0
\(449\) 8.82846 0.416641 0.208320 0.978061i \(-0.433200\pi\)
0.208320 + 0.978061i \(0.433200\pi\)
\(450\) 2.45705 + 0.802208i 0.115826 + 0.0378165i
\(451\) 18.8554 + 32.6585i 0.887867 + 1.53783i
\(452\) 11.8148 20.4638i 0.555721 0.962537i
\(453\) 8.62640 + 22.5204i 0.405304 + 1.05810i
\(454\) 0.631600 1.09396i 0.0296425 0.0513422i
\(455\) 0 0
\(456\) −1.13487 2.96273i −0.0531451 0.138743i
\(457\) −10.5081 −0.491547 −0.245774 0.969327i \(-0.579042\pi\)
−0.245774 + 0.969327i \(0.579042\pi\)
\(458\) −2.31191 4.00434i −0.108028 0.187111i
\(459\) 1.81122 + 36.0305i 0.0845405 + 1.68176i
\(460\) 6.43310 11.1425i 0.299945 0.519520i
\(461\) 11.2758 + 19.5302i 0.525166 + 0.909614i 0.999570 + 0.0293073i \(0.00933013\pi\)
−0.474404 + 0.880307i \(0.657337\pi\)
\(462\) 0 0
\(463\) −5.19850 + 9.00406i −0.241595 + 0.418454i −0.961169 0.275962i \(-0.911004\pi\)
0.719574 + 0.694416i \(0.244337\pi\)
\(464\) −0.437618 0.757977i −0.0203159 0.0351882i
\(465\) −3.35649 0.534063i −0.155654 0.0247666i
\(466\) −2.03022 + 3.51645i −0.0940483 + 0.162897i
\(467\) 6.65856 11.5330i 0.308121 0.533682i −0.669830 0.742514i \(-0.733633\pi\)
0.977951 + 0.208833i \(0.0669664\pi\)
\(468\) 5.54063 + 1.80897i 0.256116 + 0.0836198i
\(469\) 0 0
\(470\) 0.823649 + 1.42660i 0.0379921 + 0.0658043i
\(471\) −0.0623817 + 0.0769231i −0.00287440 + 0.00354443i
\(472\) −2.45417 −0.112962
\(473\) −8.24239 −0.378986
\(474\) −1.92463 + 2.37327i −0.0884013 + 0.109008i
\(475\) −3.50000 6.06218i −0.160591 0.278152i
\(476\) 0 0
\(477\) 25.9012 23.2550i 1.18594 1.06477i
\(478\) 2.01887 3.49679i 0.0923412 0.159940i
\(479\) 7.26771 12.5880i 0.332070 0.575163i −0.650847 0.759209i \(-0.725586\pi\)
0.982918 + 0.184046i \(0.0589195\pi\)
\(480\) −5.58181 0.888141i −0.254774 0.0405379i
\(481\) −4.77292 8.26693i −0.217626 0.376940i
\(482\) −3.24557 + 5.62149i −0.147832 + 0.256052i
\(483\) 0 0
\(484\) 2.63968 + 4.57206i 0.119985 + 0.207821i
\(485\) −4.23624 + 7.33739i −0.192358 + 0.333174i
\(486\) 0.977558 3.59710i 0.0443429 0.163168i
\(487\) −6.52696 11.3050i −0.295765 0.512279i 0.679398 0.733770i \(-0.262241\pi\)
−0.975162 + 0.221491i \(0.928908\pi\)
\(488\) 7.16827 0.324492
\(489\) −0.934349 2.43924i −0.0422527 0.110306i
\(490\) 0 0
\(491\) −9.67223 + 16.7528i −0.436502 + 0.756043i −0.997417 0.0718303i \(-0.977116\pi\)
0.560915 + 0.827873i \(0.310449\pi\)
\(492\) −12.2560 31.9959i −0.552542 1.44249i
\(493\) −0.830095 + 1.43777i −0.0373856 + 0.0647538i
\(494\) 0.232287 + 0.402332i 0.0104511 + 0.0181018i
\(495\) −2.71217 12.8496i −0.121903 0.577545i
\(496\) −6.07661 −0.272848
\(497\) 0 0
\(498\) 2.83981 + 0.451852i 0.127255 + 0.0202480i
\(499\) 18.1111 + 31.3693i 0.810764 + 1.40428i 0.912330 + 0.409455i \(0.134281\pi\)
−0.101566 + 0.994829i \(0.532385\pi\)
\(500\) −19.7551 −0.883476
\(501\) 9.09781 + 23.7511i 0.406460 + 1.06112i
\(502\) −4.56199 −0.203612
\(503\) −15.6764 −0.698974 −0.349487 0.936941i \(-0.613644\pi\)
−0.349487 + 0.936941i \(0.613644\pi\)
\(504\) 0 0
\(505\) −15.1111 −0.672435
\(506\) −4.96225 −0.220599
\(507\) 20.5264 + 3.26602i 0.911609 + 0.145049i
\(508\) −2.60301 −0.115490
\(509\) 17.1517 + 29.7076i 0.760237 + 1.31677i 0.942729 + 0.333561i \(0.108250\pi\)
−0.182492 + 0.983207i \(0.558416\pi\)
\(510\) 1.21574 + 3.17384i 0.0538337 + 0.140540i
\(511\) 0 0
\(512\) −17.0071 −0.751616
\(513\) −8.47825 + 5.48016i −0.374324 + 0.241955i
\(514\) 1.77455 + 3.07361i 0.0782720 + 0.135571i
\(515\) 2.59850 4.50073i 0.114503 0.198326i
\(516\) 7.39575 + 1.17676i 0.325580 + 0.0518041i
\(517\) −10.7934 + 18.6948i −0.474694 + 0.822195i
\(518\) 0 0
\(519\) −0.275794 + 0.340082i −0.0121060 + 0.0149279i
\(520\) 1.11436 0.0488679
\(521\) −5.12244 8.87233i −0.224418 0.388704i 0.731727 0.681598i \(-0.238715\pi\)
−0.956145 + 0.292895i \(0.905381\pi\)
\(522\) 0.127642 0.114601i 0.00558674 0.00501596i
\(523\) 15.3015 26.5030i 0.669088 1.15889i −0.309071 0.951039i \(-0.600018\pi\)
0.978159 0.207856i \(-0.0666485\pi\)
\(524\) 4.82489 + 8.35696i 0.210776 + 0.365075i
\(525\) 0 0
\(526\) −0.925580 + 1.60315i −0.0403572 + 0.0699007i
\(527\) 5.76320 + 9.98215i 0.251049 + 0.434829i
\(528\) −8.39892 21.9265i −0.365516 0.954230i
\(529\) −4.19686 + 7.26918i −0.182472 + 0.316051i
\(530\) 1.63968 2.84001i 0.0712232 0.123362i
\(531\) 1.61273 + 7.64068i 0.0699863 + 0.331577i
\(532\) 0 0
\(533\) 5.09097 + 8.81782i 0.220514 + 0.381942i
\(534\) 0.407003 + 1.06254i 0.0176127 + 0.0459804i
\(535\) −16.2255 −0.701487
\(536\) 3.30749 0.142862
\(537\) −24.2765 3.86271i −1.04761 0.166688i
\(538\) 0.180699 + 0.312981i 0.00779051 + 0.0134936i
\(539\) 0 0
\(540\) 0.599052 + 11.9169i 0.0257791 + 0.512821i
\(541\) 13.0458 22.5960i 0.560884 0.971480i −0.436536 0.899687i \(-0.643795\pi\)
0.997420 0.0717926i \(-0.0228720\pi\)
\(542\) 2.62803 4.55189i 0.112884 0.195520i
\(543\) 1.56169 1.92573i 0.0670187 0.0826410i
\(544\) 9.58414 + 16.6002i 0.410916 + 0.711728i
\(545\) 0.746515 1.29300i 0.0319772 0.0553861i
\(546\) 0 0
\(547\) 5.46169 + 9.45993i 0.233525 + 0.404478i 0.958843 0.283937i \(-0.0916405\pi\)
−0.725318 + 0.688414i \(0.758307\pi\)
\(548\) −4.21574 + 7.30187i −0.180087 + 0.311920i
\(549\) −4.71053 22.3173i −0.201041 0.952480i
\(550\) 1.59549 + 2.76346i 0.0680317 + 0.117834i
\(551\) −0.464574 −0.0197915
\(552\) 9.03611 + 1.43777i 0.384603 + 0.0611954i
\(553\) 0 0
\(554\) −1.29467 + 2.24243i −0.0550052 + 0.0952718i
\(555\) 12.3090 15.1783i 0.522489 0.644283i
\(556\) −3.83009 + 6.63392i −0.162432 + 0.281341i
\(557\) 6.97210 + 12.0760i 0.295417 + 0.511678i 0.975082 0.221845i \(-0.0712080\pi\)
−0.679665 + 0.733523i \(0.737875\pi\)
\(558\) −0.245960 1.16530i −0.0104123 0.0493309i
\(559\) −2.22545 −0.0941265
\(560\) 0 0
\(561\) −28.0534 + 34.5927i −1.18441 + 1.46050i
\(562\) −2.01780 3.49492i −0.0851156 0.147424i
\(563\) −30.2574 −1.27520 −0.637600 0.770368i \(-0.720073\pi\)
−0.637600 + 0.770368i \(0.720073\pi\)
\(564\) 12.3538 15.2335i 0.520188 0.641446i
\(565\) −14.3754 −0.604778
\(566\) −3.66268 −0.153954
\(567\) 0 0
\(568\) 8.11109 0.340334
\(569\) −21.1352 −0.886032 −0.443016 0.896514i \(-0.646092\pi\)
−0.443016 + 0.896514i \(0.646092\pi\)
\(570\) −0.599052 + 0.738693i −0.0250915 + 0.0309405i
\(571\) −32.7863 −1.37207 −0.686033 0.727571i \(-0.740649\pi\)
−0.686033 + 0.727571i \(0.740649\pi\)
\(572\) 3.59781 + 6.23159i 0.150432 + 0.260556i
\(573\) 16.4383 20.2701i 0.686720 0.846797i
\(574\) 0 0
\(575\) 20.1877 0.841885
\(576\) 4.12640 + 19.5498i 0.171933 + 0.814576i
\(577\) −8.68715 15.0466i −0.361651 0.626397i 0.626582 0.779355i \(-0.284453\pi\)
−0.988233 + 0.152958i \(0.951120\pi\)
\(578\) 3.73065 6.46168i 0.155175 0.268770i
\(579\) −8.56183 + 10.5576i −0.355817 + 0.438760i
\(580\) −0.274550 + 0.475534i −0.0114001 + 0.0197455i
\(581\) 0 0
\(582\) −2.93203 0.466524i −0.121536 0.0193381i
\(583\) 42.9740 1.77980
\(584\) 7.14132 + 12.3691i 0.295510 + 0.511838i
\(585\) −0.732287 3.46939i −0.0302763 0.143442i
\(586\) 1.12025 1.94033i 0.0462771 0.0801543i
\(587\) 8.48796 + 14.7016i 0.350336 + 0.606799i 0.986308 0.164913i \(-0.0527342\pi\)
−0.635973 + 0.771712i \(0.719401\pi\)
\(588\) 0 0
\(589\) −1.61273 + 2.79332i −0.0664512 + 0.115097i
\(590\) 0.367845 + 0.637125i 0.0151439 + 0.0262300i
\(591\) 7.29863 8.99996i 0.300225 0.370209i
\(592\) 17.4698 30.2585i 0.718003 1.24362i
\(593\) −6.53667 + 11.3218i −0.268429 + 0.464932i −0.968456 0.249184i \(-0.919838\pi\)
0.700027 + 0.714116i \(0.253171\pi\)
\(594\) 3.86483 2.49815i 0.158576 0.102500i
\(595\) 0 0
\(596\) 10.7934 + 18.6948i 0.442116 + 0.765767i
\(597\) −34.1073 5.42692i −1.39592 0.222109i
\(598\) −1.33981 −0.0547889
\(599\) 29.2060 1.19333 0.596663 0.802492i \(-0.296493\pi\)
0.596663 + 0.802492i \(0.296493\pi\)
\(600\) −2.10464 5.49446i −0.0859218 0.224310i
\(601\) 3.89536 + 6.74695i 0.158895 + 0.275214i 0.934470 0.356041i \(-0.115874\pi\)
−0.775576 + 0.631255i \(0.782540\pi\)
\(602\) 0 0
\(603\) −2.17347 10.2974i −0.0885106 0.419341i
\(604\) 13.5253 23.4265i 0.550337 0.953212i
\(605\) 1.60589 2.78148i 0.0652887 0.113083i
\(606\) −1.89411 4.94483i −0.0769430 0.200870i
\(607\) −9.82038 17.0094i −0.398597 0.690390i 0.594956 0.803758i \(-0.297169\pi\)
−0.993553 + 0.113368i \(0.963836\pi\)
\(608\) −2.68194 + 4.64526i −0.108767 + 0.188390i
\(609\) 0 0
\(610\) −1.07442 1.86095i −0.0435020 0.0753477i
\(611\) −2.91423 + 5.04759i −0.117897 + 0.204204i
\(612\) 30.1105 27.0342i 1.21715 1.09279i
\(613\) −11.7826 20.4081i −0.475896 0.824276i 0.523723 0.851889i \(-0.324543\pi\)
−0.999619 + 0.0276128i \(0.991209\pi\)
\(614\) 0.649005 0.0261917
\(615\) −13.1293 + 16.1898i −0.529424 + 0.652834i
\(616\) 0 0
\(617\) 5.33009 9.23200i 0.214582 0.371666i −0.738562 0.674186i \(-0.764495\pi\)
0.953143 + 0.302520i \(0.0978279\pi\)
\(618\) 1.79849 + 0.286164i 0.0723460 + 0.0115112i
\(619\) −9.00752 + 15.6015i −0.362043 + 0.627077i −0.988297 0.152542i \(-0.951254\pi\)
0.626254 + 0.779619i \(0.284587\pi\)
\(620\) 1.90615 + 3.30155i 0.0765528 + 0.132593i
\(621\) −1.46169 29.0774i −0.0586558 1.16683i
\(622\) −3.34308 −0.134045
\(623\) 0 0
\(624\) −2.26771 5.92017i −0.0907812 0.236997i
\(625\) −2.99837 5.19332i −0.119935 0.207733i
\(626\) −4.55623 −0.182104
\(627\) −12.3083 1.95842i −0.491548 0.0782118i
\(628\) 0.111090 0.00443299
\(629\) −66.2750 −2.64256
\(630\) 0 0
\(631\) 12.4703 0.496436 0.248218 0.968704i \(-0.420155\pi\)
0.248218 + 0.968704i \(0.420155\pi\)
\(632\) 6.95571 0.276683
\(633\) −11.2089 29.2623i −0.445514 1.16307i
\(634\) 0.961139 0.0381717
\(635\) 0.791790 + 1.37142i 0.0314212 + 0.0544232i
\(636\) −38.5598 6.13538i −1.52900 0.243284i
\(637\) 0 0
\(638\) 0.211777 0.00838434
\(639\) −5.33009 25.2526i −0.210855 0.998979i
\(640\) 4.20439 + 7.28221i 0.166193 + 0.287855i
\(641\) −9.57279 + 16.5806i −0.378102 + 0.654892i −0.990786 0.135436i \(-0.956757\pi\)
0.612684 + 0.790328i \(0.290090\pi\)
\(642\) −2.03379 5.30949i −0.0802674 0.209549i
\(643\) 3.24433 5.61934i 0.127944 0.221605i −0.794936 0.606693i \(-0.792496\pi\)
0.922880 + 0.385088i \(0.125829\pi\)
\(644\) 0 0
\(645\) −1.62967 4.25447i −0.0641681 0.167520i
\(646\) 3.22545 0.126904
\(647\) −24.0494 41.6548i −0.945479 1.63762i −0.754789 0.655968i \(-0.772261\pi\)
−0.190691 0.981650i \(-0.561073\pi\)
\(648\) −7.76157 + 3.42926i −0.304903 + 0.134714i
\(649\) −4.82038 + 8.34914i −0.189216 + 0.327733i
\(650\) 0.430782 + 0.746136i 0.0168967 + 0.0292659i
\(651\) 0 0
\(652\) −1.46496 + 2.53739i −0.0573724 + 0.0993720i
\(653\) 21.6202 + 37.4474i 0.846066 + 1.46543i 0.884692 + 0.466175i \(0.154368\pi\)
−0.0386267 + 0.999254i \(0.512298\pi\)
\(654\) 0.516685 + 0.0822114i 0.0202040 + 0.00321472i
\(655\) 2.93530 5.08408i 0.114691 0.198651i
\(656\) −18.6339 + 32.2749i −0.727532 + 1.26012i
\(657\) 33.8166 30.3616i 1.31931 1.18452i
\(658\) 0 0
\(659\) 1.25404 + 2.17206i 0.0488505 + 0.0846115i 0.889417 0.457097i \(-0.151111\pi\)
−0.840566 + 0.541709i \(0.817778\pi\)
\(660\) −9.27851 + 11.4414i −0.361165 + 0.445354i
\(661\) 42.3354 1.64666 0.823329 0.567565i \(-0.192114\pi\)
0.823329 + 0.567565i \(0.192114\pi\)
\(662\) 2.95976 0.115034
\(663\) −7.57442 + 9.34004i −0.294166 + 0.362737i
\(664\) −3.27292 5.66886i −0.127014 0.219994i
\(665\) 0 0
\(666\) 6.50972 + 2.12537i 0.252246 + 0.0823566i
\(667\) 0.669905 1.16031i 0.0259388 0.0449274i
\(668\) 14.2644 24.7067i 0.551908 0.955933i
\(669\) −38.7554 6.16650i −1.49837 0.238411i
\(670\) −0.495745 0.858655i −0.0191523 0.0331727i
\(671\) 14.0796 24.3866i 0.543538 0.941435i
\(672\) 0 0
\(673\) −6.70765 11.6180i −0.258561 0.447841i 0.707296 0.706918i \(-0.249915\pi\)
−0.965857 + 0.259077i \(0.916582\pi\)
\(674\) 1.46582 2.53887i 0.0564612 0.0977936i
\(675\) −15.7231 + 10.1631i −0.605183 + 0.391178i
\(676\) −11.6569 20.1904i −0.448343 0.776553i
\(677\) −1.96225 −0.0754154 −0.0377077 0.999289i \(-0.512006\pi\)
−0.0377077 + 0.999289i \(0.512006\pi\)
\(678\) −1.80190 4.70409i −0.0692014 0.180660i
\(679\) 0 0
\(680\) 3.86840 6.70027i 0.148346 0.256943i
\(681\) 3.27292 + 8.54439i 0.125418 + 0.327422i
\(682\) 0.735165 1.27334i 0.0281509 0.0487589i
\(683\) −13.5836 23.5275i −0.519761 0.900253i −0.999736 0.0229706i \(-0.992688\pi\)
0.479975 0.877282i \(-0.340646\pi\)
\(684\) 10.7644 + 3.51451i 0.411589 + 0.134381i
\(685\) 5.12941 0.195985
\(686\) 0 0
\(687\) 33.0758 + 5.26280i 1.26192 + 0.200788i
\(688\) −4.07279 7.05427i −0.155273 0.268942i
\(689\) 11.6030 0.442039
\(690\) −0.981125 2.56136i −0.0373508 0.0975093i
\(691\) 50.3171 1.91415 0.957077 0.289835i \(-0.0936005\pi\)
0.957077 + 0.289835i \(0.0936005\pi\)
\(692\) 0.491138 0.0186703
\(693\) 0 0
\(694\) −1.59012 −0.0603601
\(695\) 4.66019 0.176771
\(696\) −0.385640 0.0613605i −0.0146177 0.00232586i
\(697\) 70.6914 2.67763
\(698\) −1.36716 2.36798i −0.0517476 0.0896295i
\(699\) −10.5205 27.4652i −0.397922 1.03883i
\(700\) 0 0
\(701\) 45.1672 1.70594 0.852970 0.521960i \(-0.174799\pi\)
0.852970 + 0.521960i \(0.174799\pi\)
\(702\) 1.04351 0.674501i 0.0393846 0.0254574i
\(703\) −9.27292 16.0612i −0.349735 0.605758i
\(704\) −12.3337 + 21.3625i −0.464842 + 0.805131i
\(705\) −11.7837 1.87495i −0.443800 0.0706145i
\(706\) 2.65374 4.59642i 0.0998750 0.172989i
\(707\) 0 0
\(708\) 5.51724 6.80333i 0.207351 0.255685i
\(709\) 39.6181 1.48789 0.743944 0.668242i \(-0.232953\pi\)
0.743944 + 0.668242i \(0.232953\pi\)
\(710\) −1.21574 2.10571i −0.0456257 0.0790261i
\(711\) −4.57085 21.6555i −0.171420 0.812147i
\(712\) 1.29506 2.24311i 0.0485344 0.0840640i
\(713\) −4.65103 8.05582i −0.174182 0.301693i
\(714\) 0 0
\(715\) 2.18878 3.79108i 0.0818557 0.141778i
\(716\) 13.7866 + 23.8791i 0.515229 + 0.892403i
\(717\) 10.4617 + 27.3117i 0.390699 + 1.01997i
\(718\) −0.903436 + 1.56480i −0.0337159 + 0.0583977i
\(719\) −11.0189 + 19.0853i −0.410935 + 0.711760i −0.994992 0.0999525i \(-0.968131\pi\)
0.584058 + 0.811712i \(0.301464\pi\)
\(720\) 9.65718 8.67053i 0.359902 0.323132i
\(721\) 0 0
\(722\) −1.82038 3.15299i −0.0677475 0.117342i
\(723\) −16.8184 43.9066i −0.625481 1.63290i
\(724\) −2.78109 −0.103358
\(725\) −0.861564 −0.0319977
\(726\) 1.11148 + 0.176852i 0.0412509 + 0.00656358i
\(727\) 14.0555 + 24.3449i 0.521291 + 0.902903i 0.999693 + 0.0247621i \(0.00788284\pi\)
−0.478402 + 0.878141i \(0.658784\pi\)
\(728\) 0 0
\(729\) 15.7769 + 21.9110i 0.584329 + 0.811517i
\(730\) 2.14076 3.70790i 0.0792331 0.137236i
\(731\) −7.72545 + 13.3809i −0.285736 + 0.494909i
\(732\) −16.1150 + 19.8715i −0.595629 + 0.734473i
\(733\) 5.93474 + 10.2793i 0.219205 + 0.379674i 0.954565 0.298003i \(-0.0963204\pi\)
−0.735360 + 0.677676i \(0.762987\pi\)
\(734\) 2.21466 3.83590i 0.0817444 0.141586i
\(735\) 0 0
\(736\) −7.73461 13.3967i −0.285102 0.493810i
\(737\) 6.49643 11.2522i 0.239299 0.414478i
\(738\) −6.94351 2.26700i −0.255594 0.0834496i
\(739\) 6.09222 + 10.5520i 0.224106 + 0.388163i 0.956051 0.293201i \(-0.0947206\pi\)
−0.731945 + 0.681364i \(0.761387\pi\)
\(740\) −21.9201 −0.805800
\(741\) −3.32326 0.528775i −0.122083 0.0194250i
\(742\) 0 0
\(743\) 22.2427 38.5255i 0.816005 1.41336i −0.0925987 0.995704i \(-0.529517\pi\)
0.908604 0.417659i \(-0.137149\pi\)
\(744\) −1.70765 + 2.10571i −0.0626057 + 0.0771993i
\(745\) 6.56634 11.3732i 0.240572 0.416683i
\(746\) 1.87236 + 3.24302i 0.0685519 + 0.118735i
\(747\) −15.4984 + 13.9149i −0.567056 + 0.509121i
\(748\) 49.9579 1.82664
\(749\) 0 0
\(750\) −2.65267 + 3.27101i −0.0968616 + 0.119440i
\(751\) −21.4029 37.0709i −0.781002 1.35274i −0.931358 0.364104i \(-0.881375\pi\)
0.150356 0.988632i \(-0.451958\pi\)
\(752\) −21.3333 −0.777944
\(753\) 20.8135 25.6653i 0.758488 0.935294i
\(754\) 0.0571799 0.00208237
\(755\) −16.4567 −0.598919
\(756\) 0 0
\(757\) −22.4919 −0.817483 −0.408741 0.912650i \(-0.634032\pi\)
−0.408741 + 0.912650i \(0.634032\pi\)
\(758\) −0.965520 −0.0350693
\(759\) 22.6397 27.9171i 0.821768 1.01333i
\(760\) 2.16500 0.0785328
\(761\) −7.16827 12.4158i −0.259850 0.450073i 0.706352 0.707861i \(-0.250340\pi\)
−0.966201 + 0.257788i \(0.917006\pi\)
\(762\) −0.349525 + 0.431001i −0.0126620 + 0.0156135i
\(763\) 0 0
\(764\) −29.2736 −1.05908
\(765\) −23.4023 7.64068i −0.846113 0.276250i
\(766\) −0.0269552 0.0466878i −0.000973931 0.00168690i
\(767\) −1.30150 + 2.25427i −0.0469946 + 0.0813971i
\(768\) 12.6762 15.6310i 0.457412 0.564037i
\(769\) −15.6105 + 27.0382i −0.562930 + 0.975024i 0.434309 + 0.900764i \(0.356993\pi\)
−0.997239 + 0.0742597i \(0.976341\pi\)
\(770\) 0 0
\(771\) −25.3880 4.03956i −0.914325 0.145481i
\(772\) 15.2470 0.548753
\(773\) 2.19002 + 3.79323i 0.0787697 + 0.136433i 0.902719 0.430230i \(-0.141567\pi\)
−0.823950 + 0.566663i \(0.808234\pi\)
\(774\) 1.18793 1.06656i 0.0426992 0.0383367i
\(775\) −2.99084 + 5.18029i −0.107434 + 0.186081i
\(776\) 3.37919 + 5.85294i 0.121306 + 0.210108i
\(777\) 0 0
\(778\) 3.02051 5.23168i 0.108291 0.187565i
\(779\) 9.89084 + 17.1314i 0.354376 +