Properties

Label 441.2.h.f.373.3
Level $441$
Weight $2$
Character 441.373
Analytic conductor $3.521$
Analytic rank $0$
Dimension $10$
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: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
Defining polynomial: \(x^{10} - 2 x^{9} + 9 x^{8} - 8 x^{7} + 40 x^{6} - 36 x^{5} + 90 x^{4} - 3 x^{3} + 36 x^{2} - 9 x + 9\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.3
Root \(0.247934 + 0.429435i\) of defining polynomial
Character \(\chi\) \(=\) 441.373
Dual form 441.2.h.f.214.3

$q$-expansion

\(f(q)\) \(=\) \(q-0.495868 q^{2} +(0.221298 - 1.71786i) q^{3} -1.75411 q^{4} +(-1.84629 - 3.19787i) q^{5} +(-0.109735 + 0.851830i) q^{6} +1.86155 q^{8} +(-2.90205 - 0.760316i) q^{9} +O(q^{10})\) \(q-0.495868 q^{2} +(0.221298 - 1.71786i) q^{3} -1.75411 q^{4} +(-1.84629 - 3.19787i) q^{5} +(-0.109735 + 0.851830i) q^{6} +1.86155 q^{8} +(-2.90205 - 0.760316i) q^{9} +(0.915516 + 1.58572i) q^{10} +(0.446284 - 0.772987i) q^{11} +(-0.388182 + 3.01332i) q^{12} +(-0.598355 + 1.03638i) q^{13} +(-5.90205 + 2.46398i) q^{15} +2.58515 q^{16} +(0.124991 + 0.216492i) q^{17} +(1.43904 + 0.377017i) q^{18} +(-1.40414 + 2.43204i) q^{19} +(3.23860 + 5.60943i) q^{20} +(-0.221298 + 0.383300i) q^{22} +(-1.23886 - 2.14576i) q^{23} +(0.411957 - 3.19787i) q^{24} +(-4.31757 + 7.47825i) q^{25} +(0.296705 - 0.513909i) q^{26} +(-1.94833 + 4.81705i) q^{27} +(2.07128 + 3.58755i) q^{29} +(2.92664 - 1.22181i) q^{30} -3.58515 q^{31} -5.00499 q^{32} +(-1.22912 - 0.937712i) q^{33} +(-0.0619793 - 0.107351i) q^{34} +(5.09054 + 1.33368i) q^{36} +(-2.36568 + 4.09747i) q^{37} +(0.696267 - 1.20597i) q^{38} +(1.64794 + 1.25724i) q^{39} +(-3.43695 - 5.95298i) q^{40} +(2.39093 - 4.14121i) q^{41} +(-4.98928 - 8.64169i) q^{43} +(-0.782834 + 1.35591i) q^{44} +(2.92664 + 10.6841i) q^{45} +(0.614310 + 1.06402i) q^{46} +10.1731 q^{47} +(0.572088 - 4.44091i) q^{48} +(2.14095 - 3.70823i) q^{50} +(0.399562 - 0.166808i) q^{51} +(1.04958 - 1.81793i) q^{52} +(-4.94465 - 8.56438i) q^{53} +(0.966116 - 2.38862i) q^{54} -3.29588 q^{55} +(3.86715 + 2.95031i) q^{57} +(-1.02708 - 1.77895i) q^{58} -1.81237 q^{59} +(10.3529 - 4.32210i) q^{60} -10.8041 q^{61} +1.77776 q^{62} -2.68848 q^{64} +4.41895 q^{65} +(0.609480 + 0.464982i) q^{66} +1.02937 q^{67} +(-0.219249 - 0.379751i) q^{68} +(-3.96027 + 1.65332i) q^{69} -4.94533 q^{71} +(-5.40231 - 1.41536i) q^{72} +(0.915262 + 1.58528i) q^{73} +(1.17306 - 2.03181i) q^{74} +(11.8911 + 9.07189i) q^{75} +(2.46302 - 4.26607i) q^{76} +(-0.817161 - 0.623424i) q^{78} -1.79912 q^{79} +(-4.77293 - 8.26696i) q^{80} +(7.84384 + 4.41296i) q^{81} +(-1.18559 + 2.05350i) q^{82} +(-6.16156 - 10.6721i) q^{83} +(0.461541 - 0.799412i) q^{85} +(2.47403 + 4.28514i) q^{86} +(6.62127 - 2.76423i) q^{87} +(0.830779 - 1.43895i) q^{88} +(1.20370 - 2.08488i) q^{89} +(-1.45123 - 5.29793i) q^{90} +(2.17310 + 3.76392i) q^{92} +(-0.793387 + 6.15877i) q^{93} -5.04450 q^{94} +10.3698 q^{95} +(-1.10759 + 8.59784i) q^{96} +(-5.52210 - 9.56456i) q^{97} +(-1.88286 + 1.90393i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 4q^{2} + q^{3} + 8q^{4} - 4q^{5} + 2q^{6} - 6q^{8} + 11q^{9} + O(q^{10}) \) \( 10q - 4q^{2} + q^{3} + 8q^{4} - 4q^{5} + 2q^{6} - 6q^{8} + 11q^{9} + 7q^{10} + 4q^{11} + 20q^{12} + 8q^{13} - 19q^{15} - 4q^{16} - 12q^{17} + 4q^{18} - q^{19} - 5q^{20} - q^{22} + 3q^{23} - 6q^{24} - q^{25} - 11q^{26} + 7q^{27} + 7q^{29} + 16q^{30} - 6q^{31} + 4q^{32} - 14q^{33} - 3q^{34} + 34q^{36} - 20q^{38} + 2q^{39} + 3q^{40} - 5q^{41} - 7q^{43} - 10q^{44} + 16q^{45} + 3q^{46} + 54q^{47} + 5q^{48} + 19q^{50} - 9q^{51} + 10q^{52} - 21q^{53} - q^{54} - 4q^{55} - 4q^{57} - 10q^{58} + 60q^{59} + 10q^{60} - 28q^{61} + 12q^{62} - 50q^{64} + 22q^{65} - 19q^{66} + 4q^{67} - 27q^{68} - 15q^{69} - 6q^{71} - 36q^{72} - 15q^{73} - 36q^{74} + 14q^{75} - 5q^{76} - 20q^{78} + 8q^{79} - 20q^{80} + 23q^{81} + 5q^{82} - 9q^{83} - 6q^{85} - 8q^{86} - 2q^{87} - 18q^{88} - 28q^{89} - 28q^{90} + 27q^{92} - 6q^{93} - 6q^{94} + 28q^{95} - 59q^{96} + 12q^{97} + 35q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.495868 −0.350632 −0.175316 0.984512i \(-0.556095\pi\)
−0.175316 + 0.984512i \(0.556095\pi\)
\(3\) 0.221298 1.71786i 0.127767 0.991804i
\(4\) −1.75411 −0.877057
\(5\) −1.84629 3.19787i −0.825686 1.43013i −0.901394 0.433000i \(-0.857455\pi\)
0.0757082 0.997130i \(-0.475878\pi\)
\(6\) −0.109735 + 0.851830i −0.0447990 + 0.347758i
\(7\) 0 0
\(8\) 1.86155 0.658156
\(9\) −2.90205 0.760316i −0.967351 0.253439i
\(10\) 0.915516 + 1.58572i 0.289512 + 0.501449i
\(11\) 0.446284 0.772987i 0.134560 0.233064i −0.790869 0.611985i \(-0.790371\pi\)
0.925429 + 0.378921i \(0.123705\pi\)
\(12\) −0.388182 + 3.01332i −0.112059 + 0.869869i
\(13\) −0.598355 + 1.03638i −0.165954 + 0.287441i −0.936994 0.349346i \(-0.886404\pi\)
0.771040 + 0.636787i \(0.219737\pi\)
\(14\) 0 0
\(15\) −5.90205 + 2.46398i −1.52390 + 0.636196i
\(16\) 2.58515 0.646287
\(17\) 0.124991 + 0.216492i 0.0303149 + 0.0525069i 0.880785 0.473517i \(-0.157016\pi\)
−0.850470 + 0.526024i \(0.823682\pi\)
\(18\) 1.43904 + 0.377017i 0.339184 + 0.0888637i
\(19\) −1.40414 + 2.43204i −0.322131 + 0.557948i −0.980928 0.194374i \(-0.937733\pi\)
0.658796 + 0.752321i \(0.271066\pi\)
\(20\) 3.23860 + 5.60943i 0.724174 + 1.25431i
\(21\) 0 0
\(22\) −0.221298 + 0.383300i −0.0471809 + 0.0817198i
\(23\) −1.23886 2.14576i −0.258320 0.447423i 0.707472 0.706741i \(-0.249835\pi\)
−0.965792 + 0.259318i \(0.916502\pi\)
\(24\) 0.411957 3.19787i 0.0840903 0.652762i
\(25\) −4.31757 + 7.47825i −0.863514 + 1.49565i
\(26\) 0.296705 0.513909i 0.0581887 0.100786i
\(27\) −1.94833 + 4.81705i −0.374957 + 0.927042i
\(28\) 0 0
\(29\) 2.07128 + 3.58755i 0.384626 + 0.666192i 0.991717 0.128440i \(-0.0409970\pi\)
−0.607091 + 0.794632i \(0.707664\pi\)
\(30\) 2.92664 1.22181i 0.534329 0.223071i
\(31\) −3.58515 −0.643912 −0.321956 0.946755i \(-0.604340\pi\)
−0.321956 + 0.946755i \(0.604340\pi\)
\(32\) −5.00499 −0.884765
\(33\) −1.22912 0.937712i −0.213962 0.163235i
\(34\) −0.0619793 0.107351i −0.0106294 0.0184106i
\(35\) 0 0
\(36\) 5.09054 + 1.33368i 0.848423 + 0.222280i
\(37\) −2.36568 + 4.09747i −0.388915 + 0.673621i −0.992304 0.123826i \(-0.960483\pi\)
0.603389 + 0.797447i \(0.293817\pi\)
\(38\) 0.696267 1.20597i 0.112949 0.195634i
\(39\) 1.64794 + 1.25724i 0.263882 + 0.201319i
\(40\) −3.43695 5.95298i −0.543430 0.941249i
\(41\) 2.39093 4.14121i 0.373400 0.646748i −0.616686 0.787209i \(-0.711525\pi\)
0.990086 + 0.140461i \(0.0448584\pi\)
\(42\) 0 0
\(43\) −4.98928 8.64169i −0.760859 1.31785i −0.942408 0.334464i \(-0.891445\pi\)
0.181550 0.983382i \(-0.441889\pi\)
\(44\) −0.782834 + 1.35591i −0.118017 + 0.204411i
\(45\) 2.92664 + 10.6841i 0.436278 + 1.59270i
\(46\) 0.614310 + 1.06402i 0.0905751 + 0.156881i
\(47\) 10.1731 1.48389 0.741947 0.670459i \(-0.233903\pi\)
0.741947 + 0.670459i \(0.233903\pi\)
\(48\) 0.572088 4.44091i 0.0825738 0.640990i
\(49\) 0 0
\(50\) 2.14095 3.70823i 0.302776 0.524423i
\(51\) 0.399562 0.166808i 0.0559498 0.0233578i
\(52\) 1.04958 1.81793i 0.145551 0.252102i
\(53\) −4.94465 8.56438i −0.679199 1.17641i −0.975222 0.221227i \(-0.928994\pi\)
0.296023 0.955181i \(-0.404339\pi\)
\(54\) 0.966116 2.38862i 0.131472 0.325051i
\(55\) −3.29588 −0.444416
\(56\) 0 0
\(57\) 3.86715 + 2.95031i 0.512217 + 0.390778i
\(58\) −1.02708 1.77895i −0.134862 0.233588i
\(59\) −1.81237 −0.235951 −0.117975 0.993017i \(-0.537640\pi\)
−0.117975 + 0.993017i \(0.537640\pi\)
\(60\) 10.3529 4.32210i 1.33655 0.557980i
\(61\) −10.8041 −1.38332 −0.691662 0.722221i \(-0.743121\pi\)
−0.691662 + 0.722221i \(0.743121\pi\)
\(62\) 1.77776 0.225776
\(63\) 0 0
\(64\) −2.68848 −0.336060
\(65\) 4.41895 0.548103
\(66\) 0.609480 + 0.464982i 0.0750219 + 0.0572353i
\(67\) 1.02937 0.125757 0.0628787 0.998021i \(-0.479972\pi\)
0.0628787 + 0.998021i \(0.479972\pi\)
\(68\) −0.219249 0.379751i −0.0265879 0.0460516i
\(69\) −3.96027 + 1.65332i −0.476761 + 0.199037i
\(70\) 0 0
\(71\) −4.94533 −0.586903 −0.293451 0.955974i \(-0.594804\pi\)
−0.293451 + 0.955974i \(0.594804\pi\)
\(72\) −5.40231 1.41536i −0.636668 0.166802i
\(73\) 0.915262 + 1.58528i 0.107123 + 0.185543i 0.914604 0.404351i \(-0.132503\pi\)
−0.807480 + 0.589894i \(0.799169\pi\)
\(74\) 1.17306 2.03181i 0.136366 0.236193i
\(75\) 11.8911 + 9.07189i 1.37306 + 1.04753i
\(76\) 2.46302 4.26607i 0.282527 0.489352i
\(77\) 0 0
\(78\) −0.817161 0.623424i −0.0925253 0.0705889i
\(79\) −1.79912 −0.202417 −0.101209 0.994865i \(-0.532271\pi\)
−0.101209 + 0.994865i \(0.532271\pi\)
\(80\) −4.77293 8.26696i −0.533630 0.924274i
\(81\) 7.84384 + 4.41296i 0.871538 + 0.490329i
\(82\) −1.18559 + 2.05350i −0.130926 + 0.226771i
\(83\) −6.16156 10.6721i −0.676319 1.17142i −0.976082 0.217405i \(-0.930241\pi\)
0.299763 0.954014i \(-0.403092\pi\)
\(84\) 0 0
\(85\) 0.461541 0.799412i 0.0500611 0.0867084i
\(86\) 2.47403 + 4.28514i 0.266781 + 0.462079i
\(87\) 6.62127 2.76423i 0.709875 0.296357i
\(88\) 0.830779 1.43895i 0.0885613 0.153393i
\(89\) 1.20370 2.08488i 0.127592 0.220997i −0.795151 0.606412i \(-0.792608\pi\)
0.922743 + 0.385415i \(0.125942\pi\)
\(90\) −1.45123 5.29793i −0.152973 0.558451i
\(91\) 0 0
\(92\) 2.17310 + 3.76392i 0.226561 + 0.392416i
\(93\) −0.793387 + 6.15877i −0.0822704 + 0.638634i
\(94\) −5.04450 −0.520300
\(95\) 10.3698 1.06392
\(96\) −1.10759 + 8.59784i −0.113043 + 0.877513i
\(97\) −5.52210 9.56456i −0.560684 0.971134i −0.997437 0.0715522i \(-0.977205\pi\)
0.436752 0.899582i \(-0.356129\pi\)
\(98\) 0 0
\(99\) −1.88286 + 1.90393i −0.189234 + 0.191352i
\(100\) 7.57351 13.1177i 0.757351 1.31177i
\(101\) −1.29982 + 2.25136i −0.129337 + 0.224018i −0.923420 0.383791i \(-0.874618\pi\)
0.794083 + 0.607810i \(0.207952\pi\)
\(102\) −0.198130 + 0.0827148i −0.0196178 + 0.00818999i
\(103\) 4.85578 + 8.41045i 0.478454 + 0.828706i 0.999695 0.0247032i \(-0.00786408\pi\)
−0.521241 + 0.853409i \(0.674531\pi\)
\(104\) −1.11387 + 1.92927i −0.109224 + 0.189181i
\(105\) 0 0
\(106\) 2.45189 + 4.24680i 0.238149 + 0.412486i
\(107\) −5.45025 + 9.44012i −0.526896 + 0.912610i 0.472613 + 0.881270i \(0.343311\pi\)
−0.999509 + 0.0313403i \(0.990022\pi\)
\(108\) 3.41760 8.44966i 0.328859 0.813069i
\(109\) −1.06096 1.83764i −0.101622 0.176014i 0.810731 0.585419i \(-0.199070\pi\)
−0.912353 + 0.409404i \(0.865737\pi\)
\(110\) 1.63432 0.155826
\(111\) 6.51535 + 4.97066i 0.618410 + 0.471794i
\(112\) 0 0
\(113\) 7.91318 13.7060i 0.744409 1.28935i −0.206061 0.978539i \(-0.566065\pi\)
0.950470 0.310816i \(-0.100602\pi\)
\(114\) −1.91760 1.46297i −0.179600 0.137019i
\(115\) −4.57458 + 7.92341i −0.426582 + 0.738861i
\(116\) −3.63325 6.29298i −0.337339 0.584289i
\(117\) 2.52444 2.55270i 0.233384 0.235997i
\(118\) 0.898698 0.0827318
\(119\) 0 0
\(120\) −10.9869 + 4.58681i −1.00297 + 0.418716i
\(121\) 5.10166 + 8.83634i 0.463787 + 0.803303i
\(122\) 5.35741 0.485038
\(123\) −6.58489 5.02371i −0.593740 0.452973i
\(124\) 6.28876 0.564747
\(125\) 13.4230 1.20059
\(126\) 0 0
\(127\) −1.26946 −0.112647 −0.0563233 0.998413i \(-0.517938\pi\)
−0.0563233 + 0.998413i \(0.517938\pi\)
\(128\) 11.3431 1.00260
\(129\) −15.9493 + 6.65848i −1.40426 + 0.586246i
\(130\) −2.19122 −0.192182
\(131\) −7.51444 13.0154i −0.656540 1.13716i −0.981505 0.191435i \(-0.938686\pi\)
0.324965 0.945726i \(-0.394647\pi\)
\(132\) 2.15601 + 1.64485i 0.187657 + 0.143166i
\(133\) 0 0
\(134\) −0.510432 −0.0440946
\(135\) 19.0015 2.66316i 1.63539 0.229209i
\(136\) 0.232677 + 0.403009i 0.0199519 + 0.0345577i
\(137\) 0.244246 0.423047i 0.0208674 0.0361433i −0.855403 0.517963i \(-0.826691\pi\)
0.876271 + 0.481819i \(0.160024\pi\)
\(138\) 1.96377 0.819831i 0.167167 0.0697887i
\(139\) 4.93487 8.54745i 0.418570 0.724985i −0.577226 0.816585i \(-0.695865\pi\)
0.995796 + 0.0915997i \(0.0291980\pi\)
\(140\) 0 0
\(141\) 2.25128 17.4759i 0.189592 1.47173i
\(142\) 2.45223 0.205787
\(143\) 0.534073 + 0.925042i 0.0446614 + 0.0773559i
\(144\) −7.50224 1.96553i −0.625187 0.163794i
\(145\) 7.64835 13.2473i 0.635161 1.10013i
\(146\) −0.453849 0.786090i −0.0375609 0.0650573i
\(147\) 0 0
\(148\) 4.14967 7.18744i 0.341101 0.590804i
\(149\) −10.5120 18.2073i −0.861175 1.49160i −0.870796 0.491645i \(-0.836396\pi\)
0.00962096 0.999954i \(-0.496938\pi\)
\(150\) −5.89641 4.49846i −0.481440 0.367298i
\(151\) −0.749191 + 1.29764i −0.0609683 + 0.105600i −0.894898 0.446270i \(-0.852752\pi\)
0.833930 + 0.551870i \(0.186086\pi\)
\(152\) −2.61387 + 4.52735i −0.212013 + 0.367217i
\(153\) −0.198130 0.723303i −0.0160179 0.0584756i
\(154\) 0 0
\(155\) 6.61922 + 11.4648i 0.531669 + 0.920877i
\(156\) −2.89068 2.20534i −0.231439 0.176568i
\(157\) 16.6796 1.33118 0.665590 0.746317i \(-0.268180\pi\)
0.665590 + 0.746317i \(0.268180\pi\)
\(158\) 0.892128 0.0709739
\(159\) −15.8066 + 6.59890i −1.25355 + 0.523327i
\(160\) 9.24065 + 16.0053i 0.730538 + 1.26533i
\(161\) 0 0
\(162\) −3.88951 2.18825i −0.305589 0.171925i
\(163\) −3.34135 + 5.78738i −0.261714 + 0.453303i −0.966698 0.255921i \(-0.917621\pi\)
0.704983 + 0.709224i \(0.250954\pi\)
\(164\) −4.19396 + 7.26416i −0.327494 + 0.567236i
\(165\) −0.729372 + 5.66184i −0.0567815 + 0.440774i
\(166\) 3.05532 + 5.29197i 0.237139 + 0.410737i
\(167\) −8.81549 + 15.2689i −0.682163 + 1.18154i 0.292156 + 0.956371i \(0.405627\pi\)
−0.974319 + 0.225170i \(0.927706\pi\)
\(168\) 0 0
\(169\) 5.78394 + 10.0181i 0.444919 + 0.770622i
\(170\) −0.228863 + 0.396403i −0.0175530 + 0.0304027i
\(171\) 5.92400 5.99031i 0.453020 0.458091i
\(172\) 8.75178 + 15.1585i 0.667317 + 1.15583i
\(173\) 3.88685 0.295511 0.147756 0.989024i \(-0.452795\pi\)
0.147756 + 0.989024i \(0.452795\pi\)
\(174\) −3.28328 + 1.37070i −0.248905 + 0.103912i
\(175\) 0 0
\(176\) 1.15371 1.99829i 0.0869642 0.150626i
\(177\) −0.401075 + 3.11339i −0.0301466 + 0.234017i
\(178\) −0.596879 + 1.03382i −0.0447380 + 0.0774884i
\(179\) 3.66758 + 6.35244i 0.274128 + 0.474804i 0.969915 0.243445i \(-0.0782775\pi\)
−0.695787 + 0.718248i \(0.744944\pi\)
\(180\) −5.13366 18.7412i −0.382641 1.39689i
\(181\) −11.2566 −0.836693 −0.418346 0.908288i \(-0.637390\pi\)
−0.418346 + 0.908288i \(0.637390\pi\)
\(182\) 0 0
\(183\) −2.39093 + 18.5599i −0.176743 + 1.37199i
\(184\) −2.30619 3.99444i −0.170015 0.294474i
\(185\) 17.4709 1.28449
\(186\) 0.393415 3.05394i 0.0288466 0.223925i
\(187\) 0.223127 0.0163167
\(188\) −17.8447 −1.30146
\(189\) 0 0
\(190\) −5.14204 −0.373043
\(191\) −23.8459 −1.72543 −0.862715 0.505690i \(-0.831238\pi\)
−0.862715 + 0.505690i \(0.831238\pi\)
\(192\) −0.594956 + 4.61842i −0.0429373 + 0.333306i
\(193\) 5.93456 0.427179 0.213589 0.976924i \(-0.431485\pi\)
0.213589 + 0.976924i \(0.431485\pi\)
\(194\) 2.73823 + 4.74276i 0.196594 + 0.340510i
\(195\) 0.977905 7.59112i 0.0700293 0.543611i
\(196\) 0 0
\(197\) −15.4682 −1.10206 −0.551032 0.834484i \(-0.685766\pi\)
−0.551032 + 0.834484i \(0.685766\pi\)
\(198\) 0.933648 0.944100i 0.0663515 0.0670942i
\(199\) −7.74818 13.4202i −0.549254 0.951336i −0.998326 0.0578402i \(-0.981579\pi\)
0.449072 0.893496i \(-0.351755\pi\)
\(200\) −8.03736 + 13.9211i −0.568327 + 0.984371i
\(201\) 0.227798 1.76831i 0.0160676 0.124727i
\(202\) 0.644540 1.11638i 0.0453497 0.0785480i
\(203\) 0 0
\(204\) −0.700877 + 0.292600i −0.0490712 + 0.0204861i
\(205\) −17.6574 −1.23325
\(206\) −2.40783 4.17048i −0.167761 0.290571i
\(207\) 1.96377 + 7.16905i 0.136492 + 0.498283i
\(208\) −1.54684 + 2.67920i −0.107254 + 0.185769i
\(209\) 1.25329 + 2.17076i 0.0866918 + 0.150155i
\(210\) 0 0
\(211\) 0.771898 1.33697i 0.0531397 0.0920406i −0.838232 0.545314i \(-0.816410\pi\)
0.891372 + 0.453273i \(0.149744\pi\)
\(212\) 8.67347 + 15.0229i 0.595697 + 1.03178i
\(213\) −1.09439 + 8.49536i −0.0749866 + 0.582093i
\(214\) 2.70261 4.68105i 0.184746 0.319990i
\(215\) −18.4233 + 31.9101i −1.25646 + 2.17625i
\(216\) −3.62691 + 8.96717i −0.246780 + 0.610138i
\(217\) 0 0
\(218\) 0.526098 + 0.911229i 0.0356319 + 0.0617162i
\(219\) 2.92583 1.22147i 0.197709 0.0825392i
\(220\) 5.78135 0.389779
\(221\) −0.299157 −0.0201235
\(222\) −3.23075 2.46479i −0.216834 0.165426i
\(223\) 2.72171 + 4.71414i 0.182259 + 0.315682i 0.942649 0.333784i \(-0.108326\pi\)
−0.760390 + 0.649466i \(0.774992\pi\)
\(224\) 0 0
\(225\) 18.2157 18.4196i 1.21438 1.22797i
\(226\) −3.92389 + 6.79638i −0.261014 + 0.452089i
\(227\) −8.03818 + 13.9225i −0.533513 + 0.924072i 0.465721 + 0.884932i \(0.345795\pi\)
−0.999234 + 0.0391399i \(0.987538\pi\)
\(228\) −6.78343 5.17518i −0.449244 0.342735i
\(229\) −4.98420 8.63289i −0.329365 0.570477i 0.653021 0.757340i \(-0.273501\pi\)
−0.982386 + 0.186863i \(0.940168\pi\)
\(230\) 2.26839 3.92897i 0.149573 0.259068i
\(231\) 0 0
\(232\) 3.85578 + 6.67840i 0.253144 + 0.438458i
\(233\) 8.27045 14.3248i 0.541815 0.938451i −0.456985 0.889474i \(-0.651071\pi\)
0.998800 0.0489765i \(-0.0155959\pi\)
\(234\) −1.25179 + 1.26580i −0.0818320 + 0.0827480i
\(235\) −18.7824 32.5321i −1.22523 2.12216i
\(236\) 3.17911 0.206942
\(237\) −0.398143 + 3.09063i −0.0258621 + 0.200758i
\(238\) 0 0
\(239\) −11.0119 + 19.0732i −0.712303 + 1.23375i 0.251687 + 0.967809i \(0.419015\pi\)
−0.963990 + 0.265937i \(0.914319\pi\)
\(240\) −15.2577 + 6.36974i −0.984879 + 0.411165i
\(241\) 8.36004 14.4800i 0.538517 0.932739i −0.460467 0.887677i \(-0.652318\pi\)
0.998984 0.0450623i \(-0.0143486\pi\)
\(242\) −2.52975 4.38166i −0.162619 0.281664i
\(243\) 9.31665 12.4980i 0.597664 0.801747i
\(244\) 18.9516 1.21325
\(245\) 0 0
\(246\) 3.26524 + 2.49110i 0.208184 + 0.158827i
\(247\) −1.68035 2.91045i −0.106918 0.185187i
\(248\) −6.67392 −0.423794
\(249\) −19.6967 + 8.22294i −1.24823 + 0.521108i
\(250\) −6.65606 −0.420966
\(251\) 8.53099 0.538471 0.269236 0.963074i \(-0.413229\pi\)
0.269236 + 0.963074i \(0.413229\pi\)
\(252\) 0 0
\(253\) −2.21153 −0.139038
\(254\) 0.629487 0.0394975
\(255\) −1.27114 0.969769i −0.0796017 0.0607293i
\(256\) −0.247722 −0.0154826
\(257\) −8.55986 14.8261i −0.533950 0.924828i −0.999213 0.0396557i \(-0.987374\pi\)
0.465264 0.885172i \(-0.345959\pi\)
\(258\) 7.90875 3.30173i 0.492377 0.205557i
\(259\) 0 0
\(260\) −7.75135 −0.480718
\(261\) −3.28328 11.9861i −0.203230 0.741921i
\(262\) 3.72617 + 6.45392i 0.230204 + 0.398725i
\(263\) −10.2763 + 17.7991i −0.633666 + 1.09754i 0.353130 + 0.935574i \(0.385117\pi\)
−0.986796 + 0.161967i \(0.948216\pi\)
\(264\) −2.28806 1.74559i −0.140820 0.107434i
\(265\) −18.2585 + 31.6246i −1.12161 + 1.94269i
\(266\) 0 0
\(267\) −3.31514 2.52917i −0.202883 0.154783i
\(268\) −1.80563 −0.110297
\(269\) −9.92267 17.1866i −0.604996 1.04788i −0.992052 0.125827i \(-0.959842\pi\)
0.387057 0.922056i \(-0.373492\pi\)
\(270\) −9.42223 + 1.32058i −0.573419 + 0.0803679i
\(271\) −5.32056 + 9.21548i −0.323201 + 0.559801i −0.981147 0.193265i \(-0.938092\pi\)
0.657946 + 0.753065i \(0.271426\pi\)
\(272\) 0.323121 + 0.559663i 0.0195921 + 0.0339345i
\(273\) 0 0
\(274\) −0.121114 + 0.209776i −0.00731676 + 0.0126730i
\(275\) 3.85373 + 6.67485i 0.232388 + 0.402509i
\(276\) 6.94677 2.90012i 0.418146 0.174567i
\(277\) 12.4407 21.5479i 0.747487 1.29469i −0.201536 0.979481i \(-0.564593\pi\)
0.949024 0.315205i \(-0.102073\pi\)
\(278\) −2.44705 + 4.23841i −0.146764 + 0.254203i
\(279\) 10.4043 + 2.72585i 0.622889 + 0.163192i
\(280\) 0 0
\(281\) −6.83733 11.8426i −0.407881 0.706470i 0.586771 0.809753i \(-0.300399\pi\)
−0.994652 + 0.103282i \(0.967065\pi\)
\(282\) −1.11634 + 8.66572i −0.0664770 + 0.516036i
\(283\) −6.32179 −0.375791 −0.187896 0.982189i \(-0.560167\pi\)
−0.187896 + 0.982189i \(0.560167\pi\)
\(284\) 8.67468 0.514747
\(285\) 2.29481 17.8138i 0.135933 1.05520i
\(286\) −0.264830 0.458699i −0.0156597 0.0271234i
\(287\) 0 0
\(288\) 14.5247 + 3.80537i 0.855878 + 0.224234i
\(289\) 8.46875 14.6683i 0.498162 0.862842i
\(290\) −3.79257 + 6.56893i −0.222708 + 0.385741i
\(291\) −17.6526 + 7.36955i −1.03481 + 0.432011i
\(292\) −1.60547 2.78076i −0.0939533 0.162732i
\(293\) 1.31508 2.27778i 0.0768277 0.133069i −0.825052 0.565057i \(-0.808854\pi\)
0.901880 + 0.431987i \(0.142188\pi\)
\(294\) 0 0
\(295\) 3.34616 + 5.79573i 0.194821 + 0.337440i
\(296\) −4.40382 + 7.62764i −0.255967 + 0.443348i
\(297\) 2.85401 + 3.65581i 0.165606 + 0.212132i
\(298\) 5.21256 + 9.02841i 0.301955 + 0.523002i
\(299\) 2.96511 0.171477
\(300\) −20.8583 15.9131i −1.20426 0.918745i
\(301\) 0 0
\(302\) 0.371500 0.643457i 0.0213774 0.0370268i
\(303\) 3.57986 + 2.73113i 0.205657 + 0.156899i
\(304\) −3.62990 + 6.28717i −0.208189 + 0.360594i
\(305\) 19.9475 + 34.5501i 1.14219 + 1.97833i
\(306\) 0.0982463 + 0.358663i 0.00561637 + 0.0205034i
\(307\) 2.79496 0.159517 0.0797583 0.996814i \(-0.474585\pi\)
0.0797583 + 0.996814i \(0.474585\pi\)
\(308\) 0 0
\(309\) 15.5225 6.48030i 0.883045 0.368652i
\(310\) −3.28226 5.68504i −0.186420 0.322889i
\(311\) 15.1003 0.856258 0.428129 0.903718i \(-0.359173\pi\)
0.428129 + 0.903718i \(0.359173\pi\)
\(312\) 3.06772 + 2.34041i 0.173675 + 0.132499i
\(313\) 25.4785 1.44013 0.720064 0.693908i \(-0.244112\pi\)
0.720064 + 0.693908i \(0.244112\pi\)
\(314\) −8.27090 −0.466754
\(315\) 0 0
\(316\) 3.15587 0.177531
\(317\) 32.5209 1.82656 0.913278 0.407337i \(-0.133543\pi\)
0.913278 + 0.407337i \(0.133543\pi\)
\(318\) 7.83799 3.27219i 0.439533 0.183495i
\(319\) 3.69751 0.207021
\(320\) 4.96372 + 8.59741i 0.277480 + 0.480610i
\(321\) 15.0106 + 11.4518i 0.837811 + 0.639179i
\(322\) 0 0
\(323\) −0.702021 −0.0390615
\(324\) −13.7590 7.74084i −0.764388 0.430046i
\(325\) −5.16688 8.94931i −0.286607 0.496418i
\(326\) 1.65687 2.86978i 0.0917654 0.158942i
\(327\) −3.39159 + 1.41591i −0.187556 + 0.0783003i
\(328\) 4.45083 7.70906i 0.245756 0.425661i
\(329\) 0 0
\(330\) 0.361672 2.80753i 0.0199094 0.154549i
\(331\) 18.0948 0.994582 0.497291 0.867584i \(-0.334328\pi\)
0.497291 + 0.867584i \(0.334328\pi\)
\(332\) 10.8081 + 18.7201i 0.593170 + 1.02740i
\(333\) 9.98070 10.0924i 0.546939 0.553062i
\(334\) 4.37132 7.57135i 0.239188 0.414286i
\(335\) −1.90051 3.29179i −0.103836 0.179850i
\(336\) 0 0
\(337\) −12.5086 + 21.6656i −0.681389 + 1.18020i 0.293168 + 0.956061i \(0.405290\pi\)
−0.974557 + 0.224139i \(0.928043\pi\)
\(338\) −2.86807 4.96765i −0.156003 0.270204i
\(339\) −21.7938 16.6268i −1.18368 0.903045i
\(340\) −0.809596 + 1.40226i −0.0439065 + 0.0760483i
\(341\) −1.59999 + 2.77127i −0.0866446 + 0.150073i
\(342\) −2.93752 + 2.97041i −0.158843 + 0.160621i
\(343\) 0 0
\(344\) −9.28778 16.0869i −0.500764 0.867348i
\(345\) 12.5989 + 9.61190i 0.678303 + 0.517488i
\(346\) −1.92736 −0.103616
\(347\) 10.7489 0.577030 0.288515 0.957475i \(-0.406838\pi\)
0.288515 + 0.957475i \(0.406838\pi\)
\(348\) −11.6145 + 4.84878i −0.622601 + 0.259922i
\(349\) 1.64301 + 2.84577i 0.0879482 + 0.152331i 0.906644 0.421897i \(-0.138636\pi\)
−0.818695 + 0.574228i \(0.805302\pi\)
\(350\) 0 0
\(351\) −3.82651 4.90153i −0.204244 0.261624i
\(352\) −2.23365 + 3.86879i −0.119054 + 0.206207i
\(353\) 8.40960 14.5658i 0.447598 0.775262i −0.550631 0.834748i \(-0.685613\pi\)
0.998229 + 0.0594866i \(0.0189463\pi\)
\(354\) 0.198880 1.54383i 0.0105704 0.0820538i
\(355\) 9.13051 + 15.8145i 0.484597 + 0.839347i
\(356\) −2.11144 + 3.65711i −0.111906 + 0.193827i
\(357\) 0 0
\(358\) −1.81864 3.14997i −0.0961180 0.166481i
\(359\) 11.8921 20.5978i 0.627642 1.08711i −0.360382 0.932805i \(-0.617354\pi\)
0.988024 0.154303i \(-0.0493131\pi\)
\(360\) 5.44808 + 19.8890i 0.287139 + 1.04824i
\(361\) 5.55680 + 9.62466i 0.292463 + 0.506561i
\(362\) 5.58177 0.293371
\(363\) 16.3085 6.80845i 0.855976 0.357351i
\(364\) 0 0
\(365\) 3.37968 5.85377i 0.176900 0.306401i
\(366\) 1.18559 9.20326i 0.0619716 0.481062i
\(367\) −0.344992 + 0.597544i −0.0180084 + 0.0311915i −0.874889 0.484323i \(-0.839066\pi\)
0.856881 + 0.515515i \(0.172399\pi\)
\(368\) −3.20263 5.54712i −0.166949 0.289164i
\(369\) −10.0872 + 10.2002i −0.525121 + 0.530999i
\(370\) −8.66327 −0.450382
\(371\) 0 0
\(372\) 1.39169 10.8032i 0.0721558 0.560119i
\(373\) 1.88006 + 3.25636i 0.0973457 + 0.168608i 0.910585 0.413321i \(-0.135631\pi\)
−0.813239 + 0.581929i \(0.802298\pi\)
\(374\) −0.110642 −0.00572114
\(375\) 2.97050 23.0589i 0.153396 1.19075i
\(376\) 18.9376 0.976634
\(377\) −4.95744 −0.255321
\(378\) 0 0
\(379\) 32.8735 1.68860 0.844300 0.535872i \(-0.180017\pi\)
0.844300 + 0.535872i \(0.180017\pi\)
\(380\) −18.1898 −0.933116
\(381\) −0.280930 + 2.18075i −0.0143925 + 0.111723i
\(382\) 11.8244 0.604991
\(383\) −0.536335 0.928960i −0.0274055 0.0474676i 0.851997 0.523546i \(-0.175391\pi\)
−0.879403 + 0.476078i \(0.842058\pi\)
\(384\) 2.51021 19.4858i 0.128099 0.994381i
\(385\) 0 0
\(386\) −2.94276 −0.149782
\(387\) 7.90875 + 28.8721i 0.402024 + 1.46765i
\(388\) 9.68640 + 16.7773i 0.491752 + 0.851740i
\(389\) 11.8718 20.5626i 0.601925 1.04256i −0.390605 0.920559i \(-0.627734\pi\)
0.992529 0.122006i \(-0.0389326\pi\)
\(390\) −0.484912 + 3.76419i −0.0245545 + 0.190607i
\(391\) 0.309693 0.536405i 0.0156619 0.0271271i
\(392\) 0 0
\(393\) −24.0215 + 10.0284i −1.21172 + 0.505868i
\(394\) 7.67019 0.386419
\(395\) 3.32170 + 5.75336i 0.167133 + 0.289483i
\(396\) 3.30274 3.33972i 0.165969 0.167827i
\(397\) 0.0160489 0.0277975i 0.000805471 0.00139512i −0.865622 0.500697i \(-0.833077\pi\)
0.866428 + 0.499302i \(0.166410\pi\)
\(398\) 3.84208 + 6.65467i 0.192586 + 0.333569i
\(399\) 0 0
\(400\) −11.1616 + 19.3324i −0.558078 + 0.966619i
\(401\) −12.2628 21.2398i −0.612374 1.06066i −0.990839 0.135048i \(-0.956881\pi\)
0.378465 0.925616i \(-0.376452\pi\)
\(402\) −0.112958 + 0.876848i −0.00563381 + 0.0437332i
\(403\) 2.14519 3.71558i 0.106860 0.185086i
\(404\) 2.28004 3.94914i 0.113436 0.196477i
\(405\) −0.369938 33.2312i −0.0183824 1.65127i
\(406\) 0 0
\(407\) 2.11153 + 3.65728i 0.104665 + 0.181284i
\(408\) 0.743802 0.310521i 0.0368237 0.0153731i
\(409\) −26.7897 −1.32467 −0.662333 0.749210i \(-0.730433\pi\)
−0.662333 + 0.749210i \(0.730433\pi\)
\(410\) 8.75574 0.432415
\(411\) −0.672682 0.513199i −0.0331810 0.0253143i
\(412\) −8.51759 14.7529i −0.419631 0.726823i
\(413\) 0 0
\(414\) −0.973773 3.55490i −0.0478583 0.174714i
\(415\) −22.7520 + 39.4077i −1.11685 + 1.93445i
\(416\) 2.99476 5.18708i 0.146830 0.254317i
\(417\) −13.5912 10.3689i −0.665564 0.507769i
\(418\) −0.621466 1.07641i −0.0303969 0.0526490i
\(419\) 10.5262 18.2320i 0.514240 0.890689i −0.485624 0.874168i \(-0.661407\pi\)
0.999864 0.0165215i \(-0.00525920\pi\)
\(420\) 0 0
\(421\) −7.44533 12.8957i −0.362863 0.628498i 0.625568 0.780170i \(-0.284867\pi\)
−0.988431 + 0.151672i \(0.951534\pi\)
\(422\) −0.382760 + 0.662959i −0.0186325 + 0.0322724i
\(423\) −29.5228 7.73475i −1.43545 0.376076i
\(424\) −9.20469 15.9430i −0.447019 0.774260i
\(425\) −2.15864 −0.104709
\(426\) 0.542675 4.21258i 0.0262927 0.204100i
\(427\) 0 0
\(428\) 9.56037 16.5590i 0.462118 0.800412i
\(429\) 1.70728 0.712750i 0.0824281 0.0344119i
\(430\) 9.13554 15.8232i 0.440555 0.763064i
\(431\) −7.95192 13.7731i −0.383031 0.663428i 0.608463 0.793582i \(-0.291786\pi\)
−0.991494 + 0.130154i \(0.958453\pi\)
\(432\) −5.03673 + 12.4528i −0.242330 + 0.599135i
\(433\) 16.3658 0.786490 0.393245 0.919434i \(-0.371352\pi\)
0.393245 + 0.919434i \(0.371352\pi\)
\(434\) 0 0
\(435\) −21.0644 16.0704i −1.00996 0.770515i
\(436\) 1.86105 + 3.22344i 0.0891282 + 0.154375i
\(437\) 6.95811 0.332851
\(438\) −1.45083 + 0.605687i −0.0693231 + 0.0289409i
\(439\) 15.5447 0.741909 0.370954 0.928651i \(-0.379031\pi\)
0.370954 + 0.928651i \(0.379031\pi\)
\(440\) −6.13543 −0.292495
\(441\) 0 0
\(442\) 0.148343 0.00705594
\(443\) 1.79005 0.0850480 0.0425240 0.999095i \(-0.486460\pi\)
0.0425240 + 0.999095i \(0.486460\pi\)
\(444\) −11.4287 8.71910i −0.542381 0.413790i
\(445\) −8.88955 −0.421405
\(446\) −1.34961 2.33759i −0.0639058 0.110688i
\(447\) −33.6038 + 14.0288i −1.58940 + 0.663540i
\(448\) 0 0
\(449\) 13.5666 0.640250 0.320125 0.947375i \(-0.396275\pi\)
0.320125 + 0.947375i \(0.396275\pi\)
\(450\) −9.03257 + 9.13368i −0.425799 + 0.430566i
\(451\) −2.13407 3.69631i −0.100489 0.174053i
\(452\) −13.8806 + 24.0419i −0.652890 + 1.13084i
\(453\) 2.06336 + 1.57417i 0.0969450 + 0.0739608i
\(454\) 3.98588 6.90375i 0.187067 0.324009i
\(455\) 0 0
\(456\) 7.19889 + 5.49214i 0.337119 + 0.257193i
\(457\) 2.56917 0.120181 0.0600905 0.998193i \(-0.480861\pi\)
0.0600905 + 0.998193i \(0.480861\pi\)
\(458\) 2.47151 + 4.28078i 0.115486 + 0.200028i
\(459\) −1.28638 + 0.180293i −0.0600429 + 0.00841535i
\(460\) 8.02434 13.8986i 0.374137 0.648024i
\(461\) −18.0934 31.3388i −0.842695 1.45959i −0.887608 0.460600i \(-0.847634\pi\)
0.0449122 0.998991i \(-0.485699\pi\)
\(462\) 0 0
\(463\) 8.19224 14.1894i 0.380726 0.659436i −0.610440 0.792062i \(-0.709008\pi\)
0.991166 + 0.132626i \(0.0423409\pi\)
\(464\) 5.35455 + 9.27436i 0.248579 + 0.430551i
\(465\) 21.1597 8.83372i 0.981259 0.409654i
\(466\) −4.10105 + 7.10323i −0.189978 + 0.329051i
\(467\) 4.35022 7.53480i 0.201304 0.348669i −0.747645 0.664099i \(-0.768815\pi\)
0.948949 + 0.315430i \(0.102149\pi\)
\(468\) −4.42815 + 4.47772i −0.204692 + 0.206983i
\(469\) 0 0
\(470\) 9.31361 + 16.1316i 0.429605 + 0.744097i
\(471\) 3.69117 28.6532i 0.170080 1.32027i
\(472\) −3.37381 −0.155292
\(473\) −8.90655 −0.409524
\(474\) 0.197426 1.53255i 0.00906809 0.0703922i
\(475\) −12.1249 21.0010i −0.556330 0.963591i
\(476\) 0 0
\(477\) 7.83799 + 28.6138i 0.358877 + 1.31014i
\(478\) 5.46047 9.45782i 0.249756 0.432591i
\(479\) −8.88370 + 15.3870i −0.405907 + 0.703051i −0.994427 0.105432i \(-0.966378\pi\)
0.588520 + 0.808483i \(0.299711\pi\)
\(480\) 29.5397 12.3322i 1.34830 0.562884i
\(481\) −2.83103 4.90349i −0.129084 0.223580i
\(482\) −4.14548 + 7.18018i −0.188821 + 0.327048i
\(483\) 0 0
\(484\) −8.94890 15.4999i −0.406768 0.704543i
\(485\) −20.3908 + 35.3179i −0.925898 + 1.60370i
\(486\) −4.61983 + 6.19736i −0.209560 + 0.281118i
\(487\) 8.32763 + 14.4239i 0.377361 + 0.653608i 0.990677 0.136229i \(-0.0434983\pi\)
−0.613316 + 0.789837i \(0.710165\pi\)
\(488\) −20.1123 −0.910443
\(489\) 9.20245 + 7.02068i 0.416149 + 0.317486i
\(490\) 0 0
\(491\) −3.21021 + 5.56025i −0.144875 + 0.250930i −0.929326 0.369260i \(-0.879611\pi\)
0.784451 + 0.620190i \(0.212945\pi\)
\(492\) 11.5507 + 8.81217i 0.520744 + 0.397283i
\(493\) −0.517784 + 0.896827i −0.0233198 + 0.0403911i
\(494\) 0.833230 + 1.44320i 0.0374888 + 0.0649325i
\(495\) 9.56482 + 2.50591i 0.429907 + 0.112632i
\(496\) −9.26814 −0.416152
\(497\) 0 0
\(498\) 9.76698 4.07750i 0.437669 0.182717i
\(499\) −5.57296 9.65264i −0.249480 0.432112i 0.713902 0.700246i \(-0.246926\pi\)
−0.963382 + 0.268134i \(0.913593\pi\)
\(500\) −23.5456 −1.05299
\(501\) 24.2789 + 18.5227i 1.08470 + 0.827533i
\(502\) −4.23025 −0.188805
\(503\) 17.7223 0.790200 0.395100 0.918638i \(-0.370710\pi\)
0.395100 + 0.918638i \(0.370710\pi\)
\(504\) 0 0
\(505\) 9.59939 0.427167
\(506\) 1.09663 0.0487511
\(507\) 18.4896 7.71899i 0.821151 0.342812i
\(508\) 2.22678 0.0987976
\(509\) 15.5411 + 26.9180i 0.688848 + 1.19312i 0.972211 + 0.234107i \(0.0752167\pi\)
−0.283362 + 0.959013i \(0.591450\pi\)
\(510\) 0.630316 + 0.480878i 0.0279109 + 0.0212936i
\(511\) 0 0
\(512\) −22.5634 −0.997169
\(513\) −8.97952 11.5022i −0.396456 0.507835i
\(514\) 4.24456 + 7.35180i 0.187220 + 0.324274i
\(515\) 17.9303 31.0563i 0.790105 1.36850i
\(516\) 27.9769 11.6797i 1.23161 0.514172i
\(517\) 4.54008 7.86365i 0.199672 0.345843i
\(518\) 0 0
\(519\) 0.860152 6.67704i 0.0377565 0.293089i
\(520\) 8.22608 0.360737
\(521\) 2.37986 + 4.12203i 0.104263 + 0.180590i 0.913437 0.406980i \(-0.133418\pi\)
−0.809174 + 0.587570i \(0.800085\pi\)
\(522\) 1.62807 + 5.94353i 0.0712588 + 0.260141i
\(523\) −20.1258 + 34.8588i −0.880038 + 1.52427i −0.0287402 + 0.999587i \(0.509150\pi\)
−0.851298 + 0.524683i \(0.824184\pi\)
\(524\) 13.1812 + 22.8305i 0.575823 + 0.997355i
\(525\) 0 0
\(526\) 5.09571 8.82602i 0.222183 0.384833i
\(527\) −0.448113 0.776154i −0.0195201 0.0338098i
\(528\) −3.17745 2.42412i −0.138281 0.105496i
\(529\) 8.43046 14.6020i 0.366542 0.634869i
\(530\) 9.05381 15.6817i 0.393272 0.681168i
\(531\) 5.25960 + 1.37798i 0.228247 + 0.0597991i
\(532\) 0 0
\(533\) 2.86125 + 4.95583i 0.123935 + 0.214661i
\(534\) 1.64387 + 1.25413i 0.0711373 + 0.0542717i
\(535\) 40.2510 1.74020
\(536\) 1.91622 0.0827680
\(537\) 11.7242 4.89459i 0.505937 0.211217i
\(538\) 4.92033 + 8.52227i 0.212131 + 0.367421i
\(539\) 0 0
\(540\) −33.3308 + 4.67150i −1.43433 + 0.201029i
\(541\) 12.0547 20.8794i 0.518273 0.897675i −0.481502 0.876445i \(-0.659908\pi\)
0.999775 0.0212301i \(-0.00675826\pi\)
\(542\) 2.63830 4.56966i 0.113325 0.196284i
\(543\) −2.49105 + 19.3371i −0.106901 + 0.829836i
\(544\) −0.625580 1.08354i −0.0268215 0.0464563i
\(545\) −3.91769 + 6.78564i −0.167815 + 0.290665i
\(546\) 0 0
\(547\) −6.17751 10.6998i −0.264131 0.457489i 0.703204 0.710988i \(-0.251752\pi\)
−0.967336 + 0.253499i \(0.918419\pi\)
\(548\) −0.428436 + 0.742073i −0.0183019 + 0.0316998i
\(549\) 31.3541 + 8.21454i 1.33816 + 0.350588i
\(550\) −1.91094 3.30985i −0.0814828 0.141132i
\(551\) −11.6334 −0.495600
\(552\) −7.37223 + 3.07774i −0.313783 + 0.130997i
\(553\) 0 0
\(554\) −6.16893 + 10.6849i −0.262093 + 0.453958i
\(555\) 3.86628 30.0125i 0.164114 1.27396i
\(556\) −8.65633 + 14.9932i −0.367110 + 0.635853i
\(557\) 4.03845 + 6.99479i 0.171114 + 0.296379i 0.938810 0.344436i \(-0.111930\pi\)
−0.767695 + 0.640815i \(0.778597\pi\)
\(558\) −5.15916 1.35166i −0.218405 0.0572204i
\(559\) 11.9415 0.505070
\(560\) 0 0
\(561\) 0.0493776 0.383300i 0.00208472 0.0161829i
\(562\) 3.39041 + 5.87237i 0.143016 + 0.247711i
\(563\) −45.2127 −1.90549 −0.952744 0.303774i \(-0.901753\pi\)
−0.952744 + 0.303774i \(0.901753\pi\)
\(564\) −3.94900 + 30.6547i −0.166283 + 1.29079i
\(565\) −58.4401 −2.45859
\(566\) 3.13477 0.131764
\(567\) 0 0
\(568\) −9.20596 −0.386274
\(569\) 22.4299 0.940309 0.470155 0.882584i \(-0.344198\pi\)
0.470155 + 0.882584i \(0.344198\pi\)
\(570\) −1.13792 + 8.83329i −0.0476624 + 0.369986i
\(571\) −21.8269 −0.913426 −0.456713 0.889614i \(-0.650973\pi\)
−0.456713 + 0.889614i \(0.650973\pi\)
\(572\) −0.936826 1.62263i −0.0391706 0.0678455i
\(573\) −5.27706 + 40.9638i −0.220452 + 1.71129i
\(574\) 0 0
\(575\) 21.3954 0.892251
\(576\) 7.80212 + 2.04410i 0.325088 + 0.0851707i
\(577\) 16.1022 + 27.8898i 0.670342 + 1.16107i 0.977807 + 0.209508i \(0.0671861\pi\)
−0.307465 + 0.951559i \(0.599481\pi\)
\(578\) −4.19939 + 7.27355i −0.174671 + 0.302540i
\(579\) 1.31331 10.1947i 0.0545791 0.423678i
\(580\) −13.4161 + 23.2373i −0.557072 + 0.964878i
\(581\) 0 0
\(582\) 8.75335 3.65433i 0.362838 0.151477i
\(583\) −8.82687 −0.365571
\(584\) 1.70380 + 2.95107i 0.0705039 + 0.122116i
\(585\) −12.8240 3.35980i −0.530209 0.138911i
\(586\) −0.652105 + 1.12948i −0.0269382 + 0.0466584i
\(587\) 9.72304 + 16.8408i 0.401313 + 0.695094i 0.993885 0.110424i \(-0.0352208\pi\)
−0.592572 + 0.805518i \(0.701887\pi\)
\(588\) 0 0
\(589\) 5.03404 8.71921i 0.207424 0.359269i
\(590\) −1.65926 2.87392i −0.0683105 0.118317i
\(591\) −3.42309 + 26.5721i −0.140807 + 1.09303i
\(592\) −6.11563 + 10.5926i −0.251351 + 0.435352i
\(593\) 14.4202 24.9766i 0.592168 1.02566i −0.401772 0.915740i \(-0.631606\pi\)
0.993940 0.109925i \(-0.0350611\pi\)
\(594\) −1.41521 1.81280i −0.0580669 0.0743801i
\(595\) 0 0
\(596\) 18.4392 + 31.9377i 0.755300 + 1.30822i
\(597\) −24.7687 + 10.3404i −1.01372 + 0.423204i
\(598\) −1.47030 −0.0601252
\(599\) −46.9989 −1.92032 −0.960161 0.279447i \(-0.909849\pi\)
−0.960161 + 0.279447i \(0.909849\pi\)
\(600\) 22.1358 + 16.8877i 0.903690 + 0.689439i
\(601\) 7.80843 + 13.5246i 0.318512 + 0.551680i 0.980178 0.198119i \(-0.0634834\pi\)
−0.661665 + 0.749799i \(0.730150\pi\)
\(602\) 0 0
\(603\) −2.98729 0.782646i −0.121652 0.0318718i
\(604\) 1.31417 2.27620i 0.0534727 0.0926174i
\(605\) 18.8383 32.6289i 0.765885 1.32655i
\(606\) −1.77514 1.35428i −0.0721100 0.0550138i
\(607\) −14.3266 24.8144i −0.581500 1.00719i −0.995302 0.0968200i \(-0.969133\pi\)
0.413802 0.910367i \(-0.364200\pi\)
\(608\) 7.02769 12.1723i 0.285010 0.493652i
\(609\) 0 0
\(610\) −9.89134 17.1323i −0.400489 0.693667i
\(611\) −6.08711 + 10.5432i −0.246258 + 0.426531i
\(612\) 0.347543 + 1.26876i 0.0140486 + 0.0512865i
\(613\) 14.6734 + 25.4151i 0.592653 + 1.02651i 0.993873 + 0.110524i \(0.0352529\pi\)
−0.401220 + 0.915982i \(0.631414\pi\)
\(614\) −1.38593 −0.0559316
\(615\) −3.90755 + 30.3328i −0.157568 + 1.22314i
\(616\) 0 0
\(617\) 2.06401 3.57497i 0.0830938 0.143923i −0.821484 0.570232i \(-0.806853\pi\)
0.904577 + 0.426310i \(0.140187\pi\)
\(618\) −7.69712 + 3.21338i −0.309624 + 0.129261i
\(619\) 11.3565 19.6700i 0.456456 0.790605i −0.542315 0.840175i \(-0.682452\pi\)
0.998771 + 0.0495708i \(0.0157853\pi\)
\(620\) −11.6109 20.1106i −0.466304 0.807662i
\(621\) 12.7500 1.78698i 0.511639 0.0717090i
\(622\) −7.48774 −0.300231
\(623\) 0 0
\(624\) 4.26017 + 3.25014i 0.170543 + 0.130110i
\(625\) −3.19498 5.53387i −0.127799 0.221355i
\(626\) −12.6340 −0.504955
\(627\) 4.00640 1.67258i 0.160000 0.0667965i
\(628\) −29.2580 −1.16752
\(629\) −1.18276 −0.0471597
\(630\) 0 0
\(631\) −38.6411 −1.53828 −0.769138 0.639082i \(-0.779314\pi\)
−0.769138 + 0.639082i \(0.779314\pi\)
\(632\) −3.34915 −0.133222
\(633\) −2.12590 1.62188i −0.0844968 0.0644639i
\(634\) −16.1261 −0.640449
\(635\) 2.34380 + 4.05958i 0.0930107 + 0.161099i
\(636\) 27.7266 11.5752i 1.09943 0.458988i
\(637\) 0 0
\(638\) −1.83348 −0.0725881
\(639\) 14.3516 + 3.76002i 0.567741 + 0.148744i
\(640\) −20.9427 36.2737i −0.827831 1.43385i
\(641\) 14.2363 24.6580i 0.562301 0.973933i −0.434995 0.900433i \(-0.643250\pi\)
0.997295 0.0735002i \(-0.0234169\pi\)
\(642\) −7.44329 5.67860i −0.293763 0.224116i
\(643\) 8.52125 14.7592i 0.336045 0.582048i −0.647640 0.761947i \(-0.724244\pi\)
0.983685 + 0.179899i \(0.0575771\pi\)
\(644\) 0 0
\(645\) 50.7400 + 38.7103i 1.99788 + 1.52422i
\(646\) 0.348110 0.0136962
\(647\) −1.68809 2.92386i −0.0663657 0.114949i 0.830933 0.556372i \(-0.187807\pi\)
−0.897299 + 0.441423i \(0.854474\pi\)
\(648\) 14.6017 + 8.21493i 0.573608 + 0.322713i
\(649\) −0.808833 + 1.40094i −0.0317495 + 0.0549917i
\(650\) 2.56209 + 4.43768i 0.100494 + 0.174060i
\(651\) 0 0
\(652\) 5.86110 10.1517i 0.229538 0.397572i
\(653\) 9.17255 + 15.8873i 0.358950 + 0.621719i 0.987786 0.155819i \(-0.0498017\pi\)
−0.628836 + 0.777538i \(0.716468\pi\)
\(654\) 1.68178 0.702107i 0.0657629 0.0274546i
\(655\) −27.7477 + 48.0604i −1.08419 + 1.87787i
\(656\) 6.18090 10.7056i 0.241324 0.417985i
\(657\) −1.45083 5.29646i −0.0566021 0.206635i
\(658\) 0 0
\(659\) −13.9248 24.1184i −0.542432 0.939519i −0.998764 0.0497098i \(-0.984170\pi\)
0.456332 0.889810i \(-0.349163\pi\)
\(660\) 1.27940 9.93152i 0.0498007 0.386584i
\(661\) −39.0141 −1.51747 −0.758737 0.651397i \(-0.774183\pi\)
−0.758737 + 0.651397i \(0.774183\pi\)
\(662\) −8.97265 −0.348732
\(663\) −0.0662030 + 0.513909i −0.00257111 + 0.0199586i
\(664\) −11.4700 19.8667i −0.445123 0.770976i
\(665\) 0 0
\(666\) −4.94911 + 5.00452i −0.191774 + 0.193921i
\(667\) 5.13203 8.88894i 0.198713 0.344181i
\(668\) 15.4634 26.7834i 0.598296 1.03628i
\(669\) 8.70051 3.63227i 0.336381 0.140432i
\(670\) 0.942405 + 1.63229i 0.0364083 + 0.0630610i
\(671\) −4.82170 + 8.35143i −0.186140 + 0.322404i
\(672\) 0 0
\(673\) 24.6154 + 42.6352i 0.948856 + 1.64347i 0.747841 + 0.663878i \(0.231090\pi\)
0.201014 + 0.979588i \(0.435576\pi\)
\(674\) 6.20264 10.7433i 0.238917 0.413816i
\(675\) −27.6111 35.3681i −1.06275 1.36132i
\(676\) −10.1457 17.5729i −0.390219 0.675879i
\(677\) 23.3915 0.899010 0.449505 0.893278i \(-0.351600\pi\)
0.449505 + 0.893278i \(0.351600\pi\)
\(678\) 10.8069 + 8.24471i 0.415035 + 0.316636i
\(679\) 0 0
\(680\) 0.859180 1.48814i 0.0329480 0.0570677i
\(681\) 22.1381 + 16.8895i 0.848333 + 0.647206i
\(682\) 0.793387 1.37419i 0.0303803 0.0526203i
\(683\) −15.1632 26.2634i −0.580204 1.00494i −0.995455 0.0952356i \(-0.969640\pi\)
0.415251 0.909707i \(-0.363694\pi\)
\(684\) −10.3914 + 10.5077i −0.397324 + 0.401772i
\(685\) −1.80380 −0.0689196
\(686\) 0 0
\(687\) −15.9330 + 6.65169i −0.607884 + 0.253778i
\(688\) −12.8980 22.3401i −0.491733 0.851707i
\(689\) 11.8346 0.450863
\(690\) −6.24741 4.76624i −0.237835 0.181448i
\(691\) 4.11330 0.156477 0.0782387 0.996935i \(-0.475070\pi\)
0.0782387 + 0.996935i \(0.475070\pi\)
\(692\) −6.81797 −0.259180
\(693\) 0 0
\(694\) −5.33003 −0.202325
\(695\) −36.4448 −1.38243
\(696\) 12.3258 5.14575i 0.467208 0.195049i
\(697\) 1.19538 0.0452784
\(698\) −0.814716 1.41113i −0.0308375 0.0534120i
\(699\) −22.7778 17.3775i −0.861534 0.657277i
\(700\) 0 0
\(701\) 29.1835 1.10225 0.551123 0.834424i \(-0.314200\pi\)
0.551123 + 0.834424i \(0.314200\pi\)
\(702\) 1.89745 + 2.43051i 0.0716145 + 0.0917338i
\(703\) −6.64347 11.5068i −0.250563 0.433988i
\(704\) −1.19983 + 2.07816i −0.0452202 + 0.0783236i
\(705\) −60.0420 + 25.0662i −2.26131 + 0.944047i
\(706\) −4.17005 + 7.22274i −0.156942 + 0.271831i
\(707\) 0 0
\(708\) 0.703531 5.46125i 0.0264403 0.205246i
\(709\) −42.4617 −1.59468 −0.797342 0.603528i \(-0.793761\pi\)
−0.797342 + 0.603528i \(0.793761\pi\)
\(710\) −4.52753 7.84192i −0.169915 0.294302i
\(711\) 5.22115 + 1.36790i 0.195809 + 0.0513004i
\(712\) 2.24075 3.88109i 0.0839757 0.145450i
\(713\) 4.44149 + 7.69288i 0.166335 + 0.288101i
\(714\) 0 0
\(715\) 1.97211 3.41579i 0.0737526 0.127743i
\(716\) −6.43336 11.1429i −0.240426 0.416430i
\(717\) 30.3282 + 23.1378i 1.13263 + 0.864097i
\(718\) −5.89692 + 10.2138i −0.220071 + 0.381175i
\(719\) 5.57126 9.64970i 0.207773 0.359873i −0.743240 0.669025i \(-0.766712\pi\)
0.951013 + 0.309152i \(0.100045\pi\)
\(720\) 7.56580 + 27.6201i 0.281961 + 1.02934i
\(721\) 0 0
\(722\) −2.75544 4.77256i −0.102547 0.177616i
\(723\) −23.0245 17.5657i −0.856290 0.653277i
\(724\) 19.7453 0.733828
\(725\) −35.7715 −1.32852
\(726\) −8.08689 + 3.37609i −0.300132 + 0.125299i
\(727\) 14.3410 + 24.8393i 0.531878 + 0.921239i 0.999308 + 0.0372089i \(0.0118467\pi\)
−0.467430 + 0.884030i \(0.654820\pi\)
\(728\) 0 0
\(729\) −19.4080 18.7704i −0.718815 0.695202i
\(730\) −1.67588 + 2.90270i −0.0620269 + 0.107434i
\(731\) 1.24724 2.16028i 0.0461307 0.0799007i
\(732\) 4.19396 32.5562i 0.155013 1.20331i
\(733\) −12.5264 21.6964i −0.462674 0.801375i 0.536419 0.843952i \(-0.319777\pi\)
−0.999093 + 0.0425768i \(0.986443\pi\)
\(734\) 0.171071 0.296303i 0.00631433 0.0109367i
\(735\) 0 0
\(736\) 6.20047 + 10.7395i 0.228552 + 0.395864i
\(737\) 0.459391 0.795689i 0.0169219 0.0293096i
\(738\) 5.00194 5.05793i 0.184124 0.186185i
\(739\) 13.7608 + 23.8344i 0.506198 + 0.876761i 0.999974 + 0.00717223i \(0.00228301\pi\)
−0.493776 + 0.869589i \(0.664384\pi\)
\(740\) −30.6460 −1.12657
\(741\) −5.37158 + 2.24252i −0.197330 + 0.0823809i
\(742\) 0 0
\(743\) −7.00608 + 12.1349i −0.257028 + 0.445186i −0.965444 0.260609i \(-0.916077\pi\)
0.708416 + 0.705795i \(0.249410\pi\)
\(744\) −1.47693 + 11.4648i −0.0541467 + 0.420321i
\(745\) −38.8163 + 67.2318i −1.42212 + 2.46318i
\(746\) −0.932261 1.61472i −0.0341325 0.0591192i
\(747\) 9.76698 + 35.6558i 0.357355 + 1.30458i
\(748\) −0.391390 −0.0143106
\(749\) 0 0
\(750\) −1.47297 + 11.4342i −0.0537854 + 0.417516i
\(751\) 26.1297 + 45.2580i 0.953486 + 1.65149i 0.737795 + 0.675025i \(0.235867\pi\)
0.215692 + 0.976461i \(0.430799\pi\)
\(752\) 26.2989 0.959021
\(753\) 1.88789 14.6550i 0.0687986 0.534058i
\(754\) 2.45824 0.0895237
\(755\) 5.53289 0.201363
\(756\) 0 0
\(757\) −43.3447 −1.57539 −0.787694 0.616066i \(-0.788725\pi\)
−0.787694 + 0.616066i \(0.788725\pi\)
\(758\) −16.3009 −0.592077
\(759\) −0.489408 + 3.79909i −0.0177644 + 0.137898i
\(760\) 19.3038 0.700223
\(761\) −8.62550 14.9398i −0.312674 0.541568i 0.666266 0.745714i \(-0.267891\pi\)
−0.978940 + 0.204146i \(0.934558\pi\)
\(762\) 0.139304 1.08137i 0.00504646 0.0391738i
\(763\) 0 0
\(764\) 41.8285 1.51330
\(765\) −1.94722 + 1.96902i −0.0704020 + 0.0711901i
\(766\) 0.265952 + 0.460642i 0.00960922 + 0.0166437i
\(767\) 1.08444 1.87831i 0.0391570 0.0678218i
\(768\) −0.0548204 + 0.425550i −0.00197816 + 0.0153557i
\(769\) 10.6727 18.4856i 0.384867 0.666609i −0.606884 0.794790i \(-0.707581\pi\)
0.991751 + 0.128182i \(0.0409141\pi\)
\(770\) 0 0
\(771\) −27.3634 + 11.4236i −0.985469 + 0.411411i
\(772\) −10.4099 −0.374660
\(773\) 6.57357 + 11.3858i 0.236435 + 0.409517i 0.959689 0.281065i \(-0.0906877\pi\)
−0.723254 + 0.690582i \(0.757354\pi\)
\(774\) −3.92170 14.3168i −0.140963 0.514605i
\(775\) 15.4791 26.8106i 0.556027 0.963066i
\(776\) −10.2796 17.8049i −0.369018 0.639158i
\(777\) 0 0
\(778\) −5.88685 + 10.1963i −0.211054 + 0.365556i
\(779\) 6.71439 + 11.6297i 0.240568 + 0.416676i
\(780\) −1.71536 + 13.3157i −0.0614197 + 0.476778i