Properties

Label 370.2.h.e.117.5
Level $370$
Weight $2$
Character 370.117
Analytic conductor $2.954$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.h (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} - 7362 x^{11} + 13826 x^{10} + 4848 x^{9} + 13544 x^{8} - 44248 x^{7} + 76384 x^{6} + 24512 x^{5} + 28432 x^{4} - 61952 x^{3} + 61952 x^{2} - 5632 x + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 117.5
Root \(0.0477388 - 0.0477388i\) of defining polynomial
Character \(\chi\) \(=\) 370.117
Dual form 370.2.h.e.253.5

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(0.0477388 + 0.0477388i) q^{3} +1.00000 q^{4} +(0.531109 + 2.17208i) q^{5} +(-0.0477388 - 0.0477388i) q^{6} +(-2.77997 - 2.77997i) q^{7} -1.00000 q^{8} -2.99544i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(0.0477388 + 0.0477388i) q^{3} +1.00000 q^{4} +(0.531109 + 2.17208i) q^{5} +(-0.0477388 - 0.0477388i) q^{6} +(-2.77997 - 2.77997i) q^{7} -1.00000 q^{8} -2.99544i q^{9} +(-0.531109 - 2.17208i) q^{10} -4.24241i q^{11} +(0.0477388 + 0.0477388i) q^{12} +3.32010 q^{13} +(2.77997 + 2.77997i) q^{14} +(-0.0783380 + 0.129047i) q^{15} +1.00000 q^{16} +3.64900i q^{17} +2.99544i q^{18} +(4.65117 - 4.65117i) q^{19} +(0.531109 + 2.17208i) q^{20} -0.265425i q^{21} +4.24241i q^{22} +3.99058 q^{23} +(-0.0477388 - 0.0477388i) q^{24} +(-4.43585 + 2.30722i) q^{25} -3.32010 q^{26} +(0.286215 - 0.286215i) q^{27} +(-2.77997 - 2.77997i) q^{28} +(1.30707 + 1.30707i) q^{29} +(0.0783380 - 0.129047i) q^{30} +(3.96252 - 3.96252i) q^{31} -1.00000 q^{32} +(0.202528 - 0.202528i) q^{33} -3.64900i q^{34} +(4.56184 - 7.51477i) q^{35} -2.99544i q^{36} +(-3.91278 - 4.65727i) q^{37} +(-4.65117 + 4.65117i) q^{38} +(0.158498 + 0.158498i) q^{39} +(-0.531109 - 2.17208i) q^{40} -2.70237i q^{41} +0.265425i q^{42} -6.95570 q^{43} -4.24241i q^{44} +(6.50633 - 1.59091i) q^{45} -3.99058 q^{46} +(1.34199 + 1.34199i) q^{47} +(0.0477388 + 0.0477388i) q^{48} +8.45644i q^{49} +(4.43585 - 2.30722i) q^{50} +(-0.174199 + 0.174199i) q^{51} +3.32010 q^{52} +(5.37378 - 5.37378i) q^{53} +(-0.286215 + 0.286215i) q^{54} +(9.21484 - 2.25318i) q^{55} +(2.77997 + 2.77997i) q^{56} +0.444083 q^{57} +(-1.30707 - 1.30707i) q^{58} +(-8.04404 + 8.04404i) q^{59} +(-0.0783380 + 0.129047i) q^{60} +(1.55262 - 1.55262i) q^{61} +(-3.96252 + 3.96252i) q^{62} +(-8.32723 + 8.32723i) q^{63} +1.00000 q^{64} +(1.76334 + 7.21153i) q^{65} +(-0.202528 + 0.202528i) q^{66} +(-4.34085 + 4.34085i) q^{67} +3.64900i q^{68} +(0.190506 + 0.190506i) q^{69} +(-4.56184 + 7.51477i) q^{70} +5.54775 q^{71} +2.99544i q^{72} +(-11.1383 - 11.1383i) q^{73} +(3.91278 + 4.65727i) q^{74} +(-0.321906 - 0.101618i) q^{75} +(4.65117 - 4.65117i) q^{76} +(-11.7938 + 11.7938i) q^{77} +(-0.158498 - 0.158498i) q^{78} +(-3.17689 + 3.17689i) q^{79} +(0.531109 + 2.17208i) q^{80} -8.95900 q^{81} +2.70237i q^{82} +(7.08119 - 7.08119i) q^{83} -0.265425i q^{84} +(-7.92592 + 1.93802i) q^{85} +6.95570 q^{86} +0.124796i q^{87} +4.24241i q^{88} +(7.75651 + 7.75651i) q^{89} +(-6.50633 + 1.59091i) q^{90} +(-9.22978 - 9.22978i) q^{91} +3.99058 q^{92} +0.378332 q^{93} +(-1.34199 - 1.34199i) q^{94} +(12.5730 + 7.63243i) q^{95} +(-0.0477388 - 0.0477388i) q^{96} +10.0451i q^{97} -8.45644i q^{98} -12.7079 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 20q^{2} + 4q^{3} + 20q^{4} - 4q^{5} - 4q^{6} - 2q^{7} - 20q^{8} + O(q^{10}) \) \( 20q - 20q^{2} + 4q^{3} + 20q^{4} - 4q^{5} - 4q^{6} - 2q^{7} - 20q^{8} + 4q^{10} + 4q^{12} + 2q^{14} - 4q^{15} + 20q^{16} + 6q^{19} - 4q^{20} - 4q^{23} - 4q^{24} + 10q^{25} - 20q^{27} - 2q^{28} + 18q^{29} + 4q^{30} + 12q^{31} - 20q^{32} + 4q^{33} - 12q^{35} - 32q^{37} - 6q^{38} + 6q^{39} + 4q^{40} + 16q^{43} + 22q^{45} + 4q^{46} - 22q^{47} + 4q^{48} - 10q^{50} + 8q^{51} - 4q^{53} + 20q^{54} + 16q^{55} + 2q^{56} + 24q^{57} - 18q^{58} - 10q^{59} - 4q^{60} + 10q^{61} - 12q^{62} - 2q^{63} + 20q^{64} + 20q^{65} - 4q^{66} + 8q^{67} - 34q^{69} + 12q^{70} + 16q^{71} - 6q^{73} + 32q^{74} - 26q^{75} + 6q^{76} - 4q^{77} - 6q^{78} + 12q^{79} - 4q^{80} - 28q^{81} + 6q^{83} + 10q^{85} - 16q^{86} - 44q^{89} - 22q^{90} - 40q^{91} - 4q^{92} - 40q^{93} + 22q^{94} + 50q^{95} - 4q^{96} - 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.0477388 + 0.0477388i 0.0275620 + 0.0275620i 0.720753 0.693191i \(-0.243796\pi\)
−0.693191 + 0.720753i \(0.743796\pi\)
\(4\) 1.00000 0.500000
\(5\) 0.531109 + 2.17208i 0.237519 + 0.971383i
\(6\) −0.0477388 0.0477388i −0.0194893 0.0194893i
\(7\) −2.77997 2.77997i −1.05073 1.05073i −0.998643 0.0520865i \(-0.983413\pi\)
−0.0520865 0.998643i \(-0.516587\pi\)
\(8\) −1.00000 −0.353553
\(9\) 2.99544i 0.998481i
\(10\) −0.531109 2.17208i −0.167951 0.686871i
\(11\) 4.24241i 1.27913i −0.768735 0.639567i \(-0.779114\pi\)
0.768735 0.639567i \(-0.220886\pi\)
\(12\) 0.0477388 + 0.0477388i 0.0137810 + 0.0137810i
\(13\) 3.32010 0.920831 0.460416 0.887703i \(-0.347700\pi\)
0.460416 + 0.887703i \(0.347700\pi\)
\(14\) 2.77997 + 2.77997i 0.742978 + 0.742978i
\(15\) −0.0783380 + 0.129047i −0.0202268 + 0.0333198i
\(16\) 1.00000 0.250000
\(17\) 3.64900i 0.885013i 0.896765 + 0.442507i \(0.145911\pi\)
−0.896765 + 0.442507i \(0.854089\pi\)
\(18\) 2.99544i 0.706032i
\(19\) 4.65117 4.65117i 1.06705 1.06705i 0.0694677 0.997584i \(-0.477870\pi\)
0.997584 0.0694677i \(-0.0221301\pi\)
\(20\) 0.531109 + 2.17208i 0.118760 + 0.485691i
\(21\) 0.265425i 0.0579205i
\(22\) 4.24241i 0.904484i
\(23\) 3.99058 0.832094 0.416047 0.909343i \(-0.363415\pi\)
0.416047 + 0.909343i \(0.363415\pi\)
\(24\) −0.0477388 0.0477388i −0.00974465 0.00974465i
\(25\) −4.43585 + 2.30722i −0.887169 + 0.461444i
\(26\) −3.32010 −0.651126
\(27\) 0.286215 0.286215i 0.0550822 0.0550822i
\(28\) −2.77997 2.77997i −0.525365 0.525365i
\(29\) 1.30707 + 1.30707i 0.242717 + 0.242717i 0.817973 0.575256i \(-0.195098\pi\)
−0.575256 + 0.817973i \(0.695098\pi\)
\(30\) 0.0783380 0.129047i 0.0143025 0.0235607i
\(31\) 3.96252 3.96252i 0.711689 0.711689i −0.255199 0.966888i \(-0.582141\pi\)
0.966888 + 0.255199i \(0.0821411\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0.202528 0.202528i 0.0352555 0.0352555i
\(34\) 3.64900i 0.625799i
\(35\) 4.56184 7.51477i 0.771092 1.27023i
\(36\) 2.99544i 0.499240i
\(37\) −3.91278 4.65727i −0.643258 0.765650i
\(38\) −4.65117 + 4.65117i −0.754520 + 0.754520i
\(39\) 0.158498 + 0.158498i 0.0253800 + 0.0253800i
\(40\) −0.531109 2.17208i −0.0839757 0.343436i
\(41\) 2.70237i 0.422040i −0.977482 0.211020i \(-0.932321\pi\)
0.977482 0.211020i \(-0.0676785\pi\)
\(42\) 0.265425i 0.0409560i
\(43\) −6.95570 −1.06073 −0.530367 0.847768i \(-0.677946\pi\)
−0.530367 + 0.847768i \(0.677946\pi\)
\(44\) 4.24241i 0.639567i
\(45\) 6.50633 1.59091i 0.969907 0.237158i
\(46\) −3.99058 −0.588380
\(47\) 1.34199 + 1.34199i 0.195749 + 0.195749i 0.798175 0.602426i \(-0.205799\pi\)
−0.602426 + 0.798175i \(0.705799\pi\)
\(48\) 0.0477388 + 0.0477388i 0.00689051 + 0.00689051i
\(49\) 8.45644i 1.20806i
\(50\) 4.43585 2.30722i 0.627324 0.326290i
\(51\) −0.174199 + 0.174199i −0.0243928 + 0.0243928i
\(52\) 3.32010 0.460416
\(53\) 5.37378 5.37378i 0.738145 0.738145i −0.234074 0.972219i \(-0.575206\pi\)
0.972219 + 0.234074i \(0.0752057\pi\)
\(54\) −0.286215 + 0.286215i −0.0389490 + 0.0389490i
\(55\) 9.21484 2.25318i 1.24253 0.303819i
\(56\) 2.77997 + 2.77997i 0.371489 + 0.371489i
\(57\) 0.444083 0.0588202
\(58\) −1.30707 1.30707i −0.171627 0.171627i
\(59\) −8.04404 + 8.04404i −1.04725 + 1.04725i −0.0484179 + 0.998827i \(0.515418\pi\)
−0.998827 + 0.0484179i \(0.984582\pi\)
\(60\) −0.0783380 + 0.129047i −0.0101134 + 0.0166599i
\(61\) 1.55262 1.55262i 0.198793 0.198793i −0.600690 0.799482i \(-0.705107\pi\)
0.799482 + 0.600690i \(0.205107\pi\)
\(62\) −3.96252 + 3.96252i −0.503240 + 0.503240i
\(63\) −8.32723 + 8.32723i −1.04913 + 1.04913i
\(64\) 1.00000 0.125000
\(65\) 1.76334 + 7.21153i 0.218715 + 0.894480i
\(66\) −0.202528 + 0.202528i −0.0249294 + 0.0249294i
\(67\) −4.34085 + 4.34085i −0.530320 + 0.530320i −0.920668 0.390348i \(-0.872355\pi\)
0.390348 + 0.920668i \(0.372355\pi\)
\(68\) 3.64900i 0.442507i
\(69\) 0.190506 + 0.190506i 0.0229342 + 0.0229342i
\(70\) −4.56184 + 7.51477i −0.545244 + 0.898187i
\(71\) 5.54775 0.658397 0.329198 0.944261i \(-0.393222\pi\)
0.329198 + 0.944261i \(0.393222\pi\)
\(72\) 2.99544i 0.353016i
\(73\) −11.1383 11.1383i −1.30364 1.30364i −0.925923 0.377712i \(-0.876711\pi\)
−0.377712 0.925923i \(-0.623289\pi\)
\(74\) 3.91278 + 4.65727i 0.454852 + 0.541396i
\(75\) −0.321906 0.101618i −0.0371705 0.0117339i
\(76\) 4.65117 4.65117i 0.533526 0.533526i
\(77\) −11.7938 + 11.7938i −1.34402 + 1.34402i
\(78\) −0.158498 0.158498i −0.0179464 0.0179464i
\(79\) −3.17689 + 3.17689i −0.357428 + 0.357428i −0.862864 0.505436i \(-0.831332\pi\)
0.505436 + 0.862864i \(0.331332\pi\)
\(80\) 0.531109 + 2.17208i 0.0593798 + 0.242846i
\(81\) −8.95900 −0.995444
\(82\) 2.70237i 0.298427i
\(83\) 7.08119 7.08119i 0.777261 0.777261i −0.202103 0.979364i \(-0.564778\pi\)
0.979364 + 0.202103i \(0.0647775\pi\)
\(84\) 0.265425i 0.0289602i
\(85\) −7.92592 + 1.93802i −0.859687 + 0.210208i
\(86\) 6.95570 0.750053
\(87\) 0.124796i 0.0133795i
\(88\) 4.24241i 0.452242i
\(89\) 7.75651 + 7.75651i 0.822188 + 0.822188i 0.986422 0.164233i \(-0.0525149\pi\)
−0.164233 + 0.986422i \(0.552515\pi\)
\(90\) −6.50633 + 1.59091i −0.685828 + 0.167696i
\(91\) −9.22978 9.22978i −0.967544 0.967544i
\(92\) 3.99058 0.416047
\(93\) 0.378332 0.0392312
\(94\) −1.34199 1.34199i −0.138416 0.138416i
\(95\) 12.5730 + 7.63243i 1.28996 + 0.783071i
\(96\) −0.0477388 0.0477388i −0.00487233 0.00487233i
\(97\) 10.0451i 1.01992i 0.860197 + 0.509962i \(0.170340\pi\)
−0.860197 + 0.509962i \(0.829660\pi\)
\(98\) 8.45644i 0.854230i
\(99\) −12.7079 −1.27719
\(100\) −4.43585 + 2.30722i −0.443585 + 0.230722i
\(101\) 1.51442i 0.150691i 0.997157 + 0.0753454i \(0.0240059\pi\)
−0.997157 + 0.0753454i \(0.975994\pi\)
\(102\) 0.174199 0.174199i 0.0172483 0.0172483i
\(103\) 3.88757i 0.383054i 0.981487 + 0.191527i \(0.0613439\pi\)
−0.981487 + 0.191527i \(0.938656\pi\)
\(104\) −3.32010 −0.325563
\(105\) 0.576524 0.140969i 0.0562629 0.0137572i
\(106\) −5.37378 + 5.37378i −0.521948 + 0.521948i
\(107\) 0.736249 + 0.736249i 0.0711758 + 0.0711758i 0.741799 0.670623i \(-0.233973\pi\)
−0.670623 + 0.741799i \(0.733973\pi\)
\(108\) 0.286215 0.286215i 0.0275411 0.0275411i
\(109\) 1.72705 1.72705i 0.165422 0.165422i −0.619542 0.784964i \(-0.712682\pi\)
0.784964 + 0.619542i \(0.212682\pi\)
\(110\) −9.21484 + 2.25318i −0.878600 + 0.214832i
\(111\) 0.0355407 0.409124i 0.00337337 0.0388324i
\(112\) −2.77997 2.77997i −0.262682 0.262682i
\(113\) 4.23008i 0.397933i 0.980006 + 0.198966i \(0.0637585\pi\)
−0.980006 + 0.198966i \(0.936242\pi\)
\(114\) −0.444083 −0.0415922
\(115\) 2.11943 + 8.66786i 0.197638 + 0.808282i
\(116\) 1.30707 + 1.30707i 0.121358 + 0.121358i
\(117\) 9.94518i 0.919432i
\(118\) 8.04404 8.04404i 0.740514 0.740514i
\(119\) 10.1441 10.1441i 0.929909 0.929909i
\(120\) 0.0783380 0.129047i 0.00715125 0.0117803i
\(121\) −6.99802 −0.636183
\(122\) −1.55262 + 1.55262i −0.140568 + 0.140568i
\(123\) 0.129008 0.129008i 0.0116323 0.0116323i
\(124\) 3.96252 3.96252i 0.355845 0.355845i
\(125\) −7.36738 8.40962i −0.658958 0.752179i
\(126\) 8.32723 8.32723i 0.741849 0.741849i
\(127\) 0.683408 + 0.683408i 0.0606426 + 0.0606426i 0.736778 0.676135i \(-0.236346\pi\)
−0.676135 + 0.736778i \(0.736346\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −0.332057 0.332057i −0.0292360 0.0292360i
\(130\) −1.76334 7.21153i −0.154655 0.632493i
\(131\) −3.35210 + 3.35210i −0.292875 + 0.292875i −0.838215 0.545340i \(-0.816400\pi\)
0.545340 + 0.838215i \(0.316400\pi\)
\(132\) 0.202528 0.202528i 0.0176278 0.0176278i
\(133\) −25.8602 −2.24237
\(134\) 4.34085 4.34085i 0.374993 0.374993i
\(135\) 0.773694 + 0.469671i 0.0665890 + 0.0404228i
\(136\) 3.64900i 0.312900i
\(137\) 15.4431 + 15.4431i 1.31939 + 1.31939i 0.914256 + 0.405138i \(0.132777\pi\)
0.405138 + 0.914256i \(0.367223\pi\)
\(138\) −0.190506 0.190506i −0.0162169 0.0162169i
\(139\) 17.8399 1.51316 0.756582 0.653899i \(-0.226868\pi\)
0.756582 + 0.653899i \(0.226868\pi\)
\(140\) 4.56184 7.51477i 0.385546 0.635114i
\(141\) 0.128130i 0.0107905i
\(142\) −5.54775 −0.465557
\(143\) 14.0852i 1.17787i
\(144\) 2.99544i 0.249620i
\(145\) −2.14486 + 3.53325i −0.178121 + 0.293421i
\(146\) 11.1383 + 11.1383i 0.921809 + 0.921809i
\(147\) −0.403701 + 0.403701i −0.0332967 + 0.0332967i
\(148\) −3.91278 4.65727i −0.321629 0.382825i
\(149\) 17.7144i 1.45122i 0.688106 + 0.725610i \(0.258442\pi\)
−0.688106 + 0.725610i \(0.741558\pi\)
\(150\) 0.321906 + 0.101618i 0.0262835 + 0.00829709i
\(151\) 5.53031i 0.450050i −0.974353 0.225025i \(-0.927754\pi\)
0.974353 0.225025i \(-0.0722464\pi\)
\(152\) −4.65117 + 4.65117i −0.377260 + 0.377260i
\(153\) 10.9304 0.883669
\(154\) 11.7938 11.7938i 0.950368 0.950368i
\(155\) 10.7114 + 6.50237i 0.860362 + 0.522283i
\(156\) 0.158498 + 0.158498i 0.0126900 + 0.0126900i
\(157\) −3.47940 3.47940i −0.277687 0.277687i 0.554498 0.832185i \(-0.312910\pi\)
−0.832185 + 0.554498i \(0.812910\pi\)
\(158\) 3.17689 3.17689i 0.252740 0.252740i
\(159\) 0.513076 0.0406896
\(160\) −0.531109 2.17208i −0.0419878 0.171718i
\(161\) −11.0937 11.0937i −0.874306 0.874306i
\(162\) 8.95900 0.703885
\(163\) 21.7952i 1.70713i 0.520985 + 0.853566i \(0.325565\pi\)
−0.520985 + 0.853566i \(0.674435\pi\)
\(164\) 2.70237i 0.211020i
\(165\) 0.547470 + 0.332342i 0.0426205 + 0.0258728i
\(166\) −7.08119 + 7.08119i −0.549607 + 0.549607i
\(167\) 11.1575i 0.863394i −0.902019 0.431697i \(-0.857915\pi\)
0.902019 0.431697i \(-0.142085\pi\)
\(168\) 0.265425i 0.0204780i
\(169\) −1.97691 −0.152070
\(170\) 7.92592 1.93802i 0.607890 0.148639i
\(171\) −13.9323 13.9323i −1.06543 1.06543i
\(172\) −6.95570 −0.530367
\(173\) 14.4965 + 14.4965i 1.10215 + 1.10215i 0.994152 + 0.107994i \(0.0344428\pi\)
0.107994 + 0.994152i \(0.465557\pi\)
\(174\) 0.124796i 0.00946076i
\(175\) 18.7455 + 5.91752i 1.41703 + 0.447322i
\(176\) 4.24241i 0.319783i
\(177\) −0.768026 −0.0577284
\(178\) −7.75651 7.75651i −0.581375 0.581375i
\(179\) −12.6119 12.6119i −0.942658 0.942658i 0.0557848 0.998443i \(-0.482234\pi\)
−0.998443 + 0.0557848i \(0.982234\pi\)
\(180\) 6.50633 1.59091i 0.484954 0.118579i
\(181\) 12.8145 0.952494 0.476247 0.879312i \(-0.341997\pi\)
0.476247 + 0.879312i \(0.341997\pi\)
\(182\) 9.22978 + 9.22978i 0.684157 + 0.684157i
\(183\) 0.148241 0.0109583
\(184\) −3.99058 −0.294190
\(185\) 8.03783 10.9724i 0.590953 0.806706i
\(186\) −0.378332 −0.0277406
\(187\) 15.4806 1.13205
\(188\) 1.34199 + 1.34199i 0.0978746 + 0.0978746i
\(189\) −1.59134 −0.115753
\(190\) −12.5730 7.63243i −0.912140 0.553715i
\(191\) 10.0822 + 10.0822i 0.729521 + 0.729521i 0.970524 0.241003i \(-0.0774763\pi\)
−0.241003 + 0.970524i \(0.577476\pi\)
\(192\) 0.0477388 + 0.0477388i 0.00344525 + 0.00344525i
\(193\) 7.58052 0.545658 0.272829 0.962063i \(-0.412041\pi\)
0.272829 + 0.962063i \(0.412041\pi\)
\(194\) 10.0451i 0.721195i
\(195\) −0.260090 + 0.428450i −0.0186255 + 0.0306819i
\(196\) 8.45644i 0.604032i
\(197\) −16.8945 16.8945i −1.20369 1.20369i −0.973037 0.230649i \(-0.925915\pi\)
−0.230649 0.973037i \(-0.574085\pi\)
\(198\) 12.7079 0.903110
\(199\) 0.576031 + 0.576031i 0.0408338 + 0.0408338i 0.727229 0.686395i \(-0.240808\pi\)
−0.686395 + 0.727229i \(0.740808\pi\)
\(200\) 4.43585 2.30722i 0.313662 0.163145i
\(201\) −0.414455 −0.0292334
\(202\) 1.51442i 0.106554i
\(203\) 7.26722i 0.510059i
\(204\) −0.174199 + 0.174199i −0.0121964 + 0.0121964i
\(205\) 5.86977 1.43525i 0.409962 0.100243i
\(206\) 3.88757i 0.270860i
\(207\) 11.9536i 0.830830i
\(208\) 3.32010 0.230208
\(209\) −19.7322 19.7322i −1.36490 1.36490i
\(210\) −0.576524 + 0.140969i −0.0397839 + 0.00972782i
\(211\) −21.1449 −1.45568 −0.727838 0.685749i \(-0.759475\pi\)
−0.727838 + 0.685749i \(0.759475\pi\)
\(212\) 5.37378 5.37378i 0.369073 0.369073i
\(213\) 0.264843 + 0.264843i 0.0181467 + 0.0181467i
\(214\) −0.736249 0.736249i −0.0503289 0.0503289i
\(215\) −3.69423 15.1083i −0.251945 1.03038i
\(216\) −0.286215 + 0.286215i −0.0194745 + 0.0194745i
\(217\) −22.0313 −1.49559
\(218\) −1.72705 + 1.72705i −0.116971 + 0.116971i
\(219\) 1.06346i 0.0718617i
\(220\) 9.21484 2.25318i 0.621264 0.151909i
\(221\) 12.1151i 0.814948i
\(222\) −0.0355407 + 0.409124i −0.00238534 + 0.0274586i
\(223\) 14.0320 14.0320i 0.939655 0.939655i −0.0586249 0.998280i \(-0.518672\pi\)
0.998280 + 0.0586249i \(0.0186716\pi\)
\(224\) 2.77997 + 2.77997i 0.185744 + 0.185744i
\(225\) 6.91114 + 13.2873i 0.460743 + 0.885822i
\(226\) 4.23008i 0.281381i
\(227\) 17.0093i 1.12895i −0.825450 0.564475i \(-0.809079\pi\)
0.825450 0.564475i \(-0.190921\pi\)
\(228\) 0.444083 0.0294101
\(229\) 8.49131i 0.561121i −0.959836 0.280561i \(-0.909480\pi\)
0.959836 0.280561i \(-0.0905204\pi\)
\(230\) −2.11943 8.66786i −0.139751 0.571542i
\(231\) −1.12604 −0.0740880
\(232\) −1.30707 1.30707i −0.0858133 0.0858133i
\(233\) 11.1205 + 11.1205i 0.728530 + 0.728530i 0.970327 0.241797i \(-0.0777367\pi\)
−0.241797 + 0.970327i \(0.577737\pi\)
\(234\) 9.94518i 0.650137i
\(235\) −2.20216 + 3.62765i −0.143653 + 0.236642i
\(236\) −8.04404 + 8.04404i −0.523623 + 0.523623i
\(237\) −0.303322 −0.0197029
\(238\) −10.1441 + 10.1441i −0.657545 + 0.657545i
\(239\) −14.6371 + 14.6371i −0.946797 + 0.946797i −0.998654 0.0518580i \(-0.983486\pi\)
0.0518580 + 0.998654i \(0.483486\pi\)
\(240\) −0.0783380 + 0.129047i −0.00505669 + 0.00832995i
\(241\) 10.5430 + 10.5430i 0.679137 + 0.679137i 0.959805 0.280668i \(-0.0905560\pi\)
−0.280668 + 0.959805i \(0.590556\pi\)
\(242\) 6.99802 0.449850
\(243\) −1.28634 1.28634i −0.0825187 0.0825187i
\(244\) 1.55262 1.55262i 0.0993963 0.0993963i
\(245\) −18.3681 + 4.49129i −1.17349 + 0.286938i
\(246\) −0.129008 + 0.129008i −0.00822526 + 0.00822526i
\(247\) 15.4424 15.4424i 0.982575 0.982575i
\(248\) −3.96252 + 3.96252i −0.251620 + 0.251620i
\(249\) 0.676095 0.0428458
\(250\) 7.36738 + 8.40962i 0.465954 + 0.531871i
\(251\) −16.2391 + 16.2391i −1.02500 + 1.02500i −0.0253206 + 0.999679i \(0.508061\pi\)
−0.999679 + 0.0253206i \(0.991939\pi\)
\(252\) −8.32723 + 8.32723i −0.524566 + 0.524566i
\(253\) 16.9297i 1.06436i
\(254\) −0.683408 0.683408i −0.0428808 0.0428808i
\(255\) −0.470893 0.285856i −0.0294885 0.0179010i
\(256\) 1.00000 0.0625000
\(257\) 5.00407i 0.312145i 0.987746 + 0.156073i \(0.0498834\pi\)
−0.987746 + 0.156073i \(0.950117\pi\)
\(258\) 0.332057 + 0.332057i 0.0206730 + 0.0206730i
\(259\) −2.06964 + 23.8245i −0.128601 + 1.48038i
\(260\) 1.76334 + 7.21153i 0.109357 + 0.447240i
\(261\) 3.91525 3.91525i 0.242348 0.242348i
\(262\) 3.35210 3.35210i 0.207094 0.207094i
\(263\) −12.4257 12.4257i −0.766203 0.766203i 0.211233 0.977436i \(-0.432252\pi\)
−0.977436 + 0.211233i \(0.932252\pi\)
\(264\) −0.202528 + 0.202528i −0.0124647 + 0.0124647i
\(265\) 14.5263 + 8.81821i 0.892345 + 0.541698i
\(266\) 25.8602 1.58559
\(267\) 0.740574i 0.0453224i
\(268\) −4.34085 + 4.34085i −0.265160 + 0.265160i
\(269\) 22.6019i 1.37806i 0.724732 + 0.689030i \(0.241963\pi\)
−0.724732 + 0.689030i \(0.758037\pi\)
\(270\) −0.773694 0.469671i −0.0470855 0.0285833i
\(271\) 18.1930 1.10514 0.552572 0.833465i \(-0.313647\pi\)
0.552572 + 0.833465i \(0.313647\pi\)
\(272\) 3.64900i 0.221253i
\(273\) 0.881238i 0.0533350i
\(274\) −15.4431 15.4431i −0.932952 0.932952i
\(275\) 9.78816 + 18.8187i 0.590248 + 1.13481i
\(276\) 0.190506 + 0.190506i 0.0114671 + 0.0114671i
\(277\) 23.4453 1.40869 0.704346 0.709857i \(-0.251241\pi\)
0.704346 + 0.709857i \(0.251241\pi\)
\(278\) −17.8399 −1.06997
\(279\) −11.8695 11.8695i −0.710608 0.710608i
\(280\) −4.56184 + 7.51477i −0.272622 + 0.449094i
\(281\) 3.32166 + 3.32166i 0.198154 + 0.198154i 0.799208 0.601054i \(-0.205253\pi\)
−0.601054 + 0.799208i \(0.705253\pi\)
\(282\) 0.128130i 0.00763003i
\(283\) 12.1785i 0.723935i −0.932191 0.361968i \(-0.882105\pi\)
0.932191 0.361968i \(-0.117895\pi\)
\(284\) 5.54775 0.329198
\(285\) 0.235856 + 0.964583i 0.0139709 + 0.0571370i
\(286\) 14.0852i 0.832877i
\(287\) −7.51251 + 7.51251i −0.443450 + 0.443450i
\(288\) 2.99544i 0.176508i
\(289\) 3.68477 0.216751
\(290\) 2.14486 3.53325i 0.125951 0.207480i
\(291\) −0.479541 + 0.479541i −0.0281112 + 0.0281112i
\(292\) −11.1383 11.1383i −0.651818 0.651818i
\(293\) 1.06493 1.06493i 0.0622140 0.0622140i −0.675315 0.737529i \(-0.735992\pi\)
0.737529 + 0.675315i \(0.235992\pi\)
\(294\) 0.403701 0.403701i 0.0235443 0.0235443i
\(295\) −21.7445 13.2000i −1.26602 0.768535i
\(296\) 3.91278 + 4.65727i 0.227426 + 0.270698i
\(297\) −1.21424 1.21424i −0.0704575 0.0704575i
\(298\) 17.7144i 1.02617i
\(299\) 13.2492 0.766219
\(300\) −0.321906 0.101618i −0.0185853 0.00586693i
\(301\) 19.3366 + 19.3366i 1.11454 + 1.11454i
\(302\) 5.53031i 0.318233i
\(303\) −0.0722968 + 0.0722968i −0.00415334 + 0.00415334i
\(304\) 4.65117 4.65117i 0.266763 0.266763i
\(305\) 4.19702 + 2.54780i 0.240321 + 0.145887i
\(306\) −10.9304 −0.624848
\(307\) 16.1006 16.1006i 0.918907 0.918907i −0.0780426 0.996950i \(-0.524867\pi\)
0.996950 + 0.0780426i \(0.0248670\pi\)
\(308\) −11.7938 + 11.7938i −0.672012 + 0.672012i
\(309\) −0.185588 + 0.185588i −0.0105577 + 0.0105577i
\(310\) −10.7114 6.50237i −0.608368 0.369310i
\(311\) −18.5878 + 18.5878i −1.05402 + 1.05402i −0.0555639 + 0.998455i \(0.517696\pi\)
−0.998455 + 0.0555639i \(0.982304\pi\)
\(312\) −0.158498 0.158498i −0.00897318 0.00897318i
\(313\) −21.7608 −1.22999 −0.614995 0.788531i \(-0.710842\pi\)
−0.614995 + 0.788531i \(0.710842\pi\)
\(314\) 3.47940 + 3.47940i 0.196354 + 0.196354i
\(315\) −22.5101 13.6647i −1.26830 0.769921i
\(316\) −3.17689 + 3.17689i −0.178714 + 0.178714i
\(317\) −22.3061 + 22.3061i −1.25284 + 1.25284i −0.298392 + 0.954443i \(0.596450\pi\)
−0.954443 + 0.298392i \(0.903550\pi\)
\(318\) −0.513076 −0.0287719
\(319\) 5.54512 5.54512i 0.310467 0.310467i
\(320\) 0.531109 + 2.17208i 0.0296899 + 0.121423i
\(321\) 0.0702953i 0.00392350i
\(322\) 11.0937 + 11.0937i 0.618228 + 0.618228i
\(323\) 16.9721 + 16.9721i 0.944355 + 0.944355i
\(324\) −8.95900 −0.497722
\(325\) −14.7275 + 7.66021i −0.816933 + 0.424912i
\(326\) 21.7952i 1.20712i
\(327\) 0.164895 0.00911871
\(328\) 2.70237i 0.149214i
\(329\) 7.46137i 0.411359i
\(330\) −0.547470 0.332342i −0.0301372 0.0182948i
\(331\) 23.9871 + 23.9871i 1.31845 + 1.31845i 0.915003 + 0.403447i \(0.132188\pi\)
0.403447 + 0.915003i \(0.367812\pi\)
\(332\) 7.08119 7.08119i 0.388631 0.388631i
\(333\) −13.9506 + 11.7205i −0.764486 + 0.642280i
\(334\) 11.1575i 0.610512i
\(335\) −11.7341 7.12321i −0.641105 0.389183i
\(336\) 0.265425i 0.0144801i
\(337\) 17.5570 17.5570i 0.956390 0.956390i −0.0426980 0.999088i \(-0.513595\pi\)
0.999088 + 0.0426980i \(0.0135953\pi\)
\(338\) 1.97691 0.107530
\(339\) −0.201939 + 0.201939i −0.0109678 + 0.0109678i
\(340\) −7.92592 + 1.93802i −0.429843 + 0.105104i
\(341\) −16.8106 16.8106i −0.910346 0.910346i
\(342\) 13.9323 + 13.9323i 0.753373 + 0.753373i
\(343\) 4.04887 4.04887i 0.218618 0.218618i
\(344\) 6.95570 0.375026
\(345\) −0.312614 + 0.514973i −0.0168306 + 0.0277252i
\(346\) −14.4965 14.4965i −0.779335 0.779335i
\(347\) 11.0678 0.594151 0.297075 0.954854i \(-0.403989\pi\)
0.297075 + 0.954854i \(0.403989\pi\)
\(348\) 0.124796i 0.00668977i
\(349\) 31.6855i 1.69609i 0.529926 + 0.848044i \(0.322220\pi\)
−0.529926 + 0.848044i \(0.677780\pi\)
\(350\) −18.7455 5.91752i −1.00199 0.316305i
\(351\) 0.950265 0.950265i 0.0507214 0.0507214i
\(352\) 4.24241i 0.226121i
\(353\) 15.6047i 0.830555i 0.909695 + 0.415278i \(0.136316\pi\)
−0.909695 + 0.415278i \(0.863684\pi\)
\(354\) 0.768026 0.0408201
\(355\) 2.94646 + 12.0501i 0.156382 + 0.639555i
\(356\) 7.75651 + 7.75651i 0.411094 + 0.411094i
\(357\) 0.968537 0.0512604
\(358\) 12.6119 + 12.6119i 0.666560 + 0.666560i
\(359\) 34.4499i 1.81820i −0.416580 0.909099i \(-0.636771\pi\)
0.416580 0.909099i \(-0.363229\pi\)
\(360\) −6.50633 + 1.59091i −0.342914 + 0.0838481i
\(361\) 24.2668i 1.27720i
\(362\) −12.8145 −0.673515
\(363\) −0.334077 0.334077i −0.0175345 0.0175345i
\(364\) −9.22978 9.22978i −0.483772 0.483772i
\(365\) 18.2775 30.1088i 0.956691 1.57597i
\(366\) −0.148241 −0.00774866
\(367\) −4.61443 4.61443i −0.240871 0.240871i 0.576339 0.817211i \(-0.304481\pi\)
−0.817211 + 0.576339i \(0.804481\pi\)
\(368\) 3.99058 0.208024
\(369\) −8.09481 −0.421399
\(370\) −8.03783 + 10.9724i −0.417867 + 0.570427i
\(371\) −29.8779 −1.55118
\(372\) 0.378332 0.0196156
\(373\) 15.3464 + 15.3464i 0.794607 + 0.794607i 0.982239 0.187632i \(-0.0600813\pi\)
−0.187632 + 0.982239i \(0.560081\pi\)
\(374\) −15.4806 −0.800481
\(375\) 0.0497555 0.753176i 0.00256937 0.0388938i
\(376\) −1.34199 1.34199i −0.0692078 0.0692078i
\(377\) 4.33961 + 4.33961i 0.223501 + 0.223501i
\(378\) 1.59134 0.0818497
\(379\) 23.4892i 1.20656i 0.797531 + 0.603278i \(0.206139\pi\)
−0.797531 + 0.603278i \(0.793861\pi\)
\(380\) 12.5730 + 7.63243i 0.644981 + 0.391535i
\(381\) 0.0652502i 0.00334287i
\(382\) −10.0822 10.0822i −0.515850 0.515850i
\(383\) 0.480522 0.0245535 0.0122768 0.999925i \(-0.496092\pi\)
0.0122768 + 0.999925i \(0.496092\pi\)
\(384\) −0.0477388 0.0477388i −0.00243616 0.00243616i
\(385\) −31.8807 19.3532i −1.62479 0.986330i
\(386\) −7.58052 −0.385838
\(387\) 20.8354i 1.05912i
\(388\) 10.0451i 0.509962i
\(389\) −11.0293 + 11.0293i −0.559208 + 0.559208i −0.929082 0.369874i \(-0.879401\pi\)
0.369874 + 0.929082i \(0.379401\pi\)
\(390\) 0.260090 0.428450i 0.0131702 0.0216954i
\(391\) 14.5617i 0.736415i
\(392\) 8.45644i 0.427115i
\(393\) −0.320051 −0.0161444
\(394\) 16.8945 + 16.8945i 0.851134 + 0.851134i
\(395\) −8.58772 5.21318i −0.432095 0.262303i
\(396\) −12.7079 −0.638595
\(397\) 18.6363 18.6363i 0.935327 0.935327i −0.0627054 0.998032i \(-0.519973\pi\)
0.998032 + 0.0627054i \(0.0199729\pi\)
\(398\) −0.576031 0.576031i −0.0288738 0.0288738i
\(399\) −1.23454 1.23454i −0.0618041 0.0618041i
\(400\) −4.43585 + 2.30722i −0.221792 + 0.115361i
\(401\) 23.4574 23.4574i 1.17141 1.17141i 0.189535 0.981874i \(-0.439302\pi\)
0.981874 0.189535i \(-0.0606980\pi\)
\(402\) 0.414455 0.0206711
\(403\) 13.1560 13.1560i 0.655346 0.655346i
\(404\) 1.51442i 0.0753454i
\(405\) −4.75820 19.4596i −0.236437 0.966958i
\(406\) 7.26722i 0.360666i
\(407\) −19.7580 + 16.5996i −0.979369 + 0.822813i
\(408\) 0.174199 0.174199i 0.00862415 0.00862415i
\(409\) −20.5642 20.5642i −1.01684 1.01684i −0.999856 0.0169803i \(-0.994595\pi\)
−0.0169803 0.999856i \(-0.505405\pi\)
\(410\) −5.86977 + 1.43525i −0.289887 + 0.0708822i
\(411\) 1.47447i 0.0727303i
\(412\) 3.88757i 0.191527i
\(413\) 44.7244 2.20074
\(414\) 11.9536i 0.587486i
\(415\) 19.1418 + 11.6200i 0.939633 + 0.570404i
\(416\) −3.32010 −0.162782
\(417\) 0.851658 + 0.851658i 0.0417059 + 0.0417059i
\(418\) 19.7322 + 19.7322i 0.965132 + 0.965132i
\(419\) 37.9044i 1.85175i 0.377827 + 0.925876i \(0.376671\pi\)
−0.377827 + 0.925876i \(0.623329\pi\)
\(420\) 0.576524 0.140969i 0.0281315 0.00687861i
\(421\) 24.4985 24.4985i 1.19398 1.19398i 0.218043 0.975939i \(-0.430033\pi\)
0.975939 0.218043i \(-0.0699674\pi\)
\(422\) 21.1449 1.02932
\(423\) 4.01985 4.01985i 0.195452 0.195452i
\(424\) −5.37378 + 5.37378i −0.260974 + 0.260974i
\(425\) −8.41905 16.1864i −0.408384 0.785157i
\(426\) −0.264843 0.264843i −0.0128317 0.0128317i
\(427\) −8.63247 −0.417754
\(428\) 0.736249 + 0.736249i 0.0355879 + 0.0355879i
\(429\) 0.672413 0.672413i 0.0324644 0.0324644i
\(430\) 3.69423 + 15.1083i 0.178152 + 0.728588i
\(431\) 15.3753 15.3753i 0.740601 0.740601i −0.232092 0.972694i \(-0.574557\pi\)
0.972694 + 0.232092i \(0.0745571\pi\)
\(432\) 0.286215 0.286215i 0.0137705 0.0137705i
\(433\) −16.4923 + 16.4923i −0.792570 + 0.792570i −0.981911 0.189341i \(-0.939365\pi\)
0.189341 + 0.981911i \(0.439365\pi\)
\(434\) 22.0313 1.05754
\(435\) −0.271067 + 0.0662802i −0.0129966 + 0.00317789i
\(436\) 1.72705 1.72705i 0.0827108 0.0827108i
\(437\) 18.5609 18.5609i 0.887888 0.887888i
\(438\) 1.06346i 0.0508139i
\(439\) −17.5768 17.5768i −0.838896 0.838896i 0.149817 0.988714i \(-0.452131\pi\)
−0.988714 + 0.149817i \(0.952131\pi\)
\(440\) −9.21484 + 2.25318i −0.439300 + 0.107416i
\(441\) 25.3308 1.20623
\(442\) 12.1151i 0.576255i
\(443\) −14.2624 14.2624i −0.677629 0.677629i 0.281834 0.959463i \(-0.409057\pi\)
−0.959463 + 0.281834i \(0.909057\pi\)
\(444\) 0.0355407 0.409124i 0.00168669 0.0194162i
\(445\) −12.7282 + 20.9673i −0.603374 + 0.993945i
\(446\) −14.0320 + 14.0320i −0.664437 + 0.664437i
\(447\) −0.845665 + 0.845665i −0.0399986 + 0.0399986i
\(448\) −2.77997 2.77997i −0.131341 0.131341i
\(449\) 17.6009 17.6009i 0.830639 0.830639i −0.156965 0.987604i \(-0.550171\pi\)
0.987604 + 0.156965i \(0.0501709\pi\)
\(450\) −6.91114 13.2873i −0.325794 0.626370i
\(451\) −11.4646 −0.539846
\(452\) 4.23008i 0.198966i
\(453\) 0.264010 0.264010i 0.0124043 0.0124043i
\(454\) 17.0093i 0.798288i
\(455\) 15.1458 24.9498i 0.710046 1.16967i
\(456\) −0.444083 −0.0207961
\(457\) 8.32533i 0.389443i −0.980859 0.194721i \(-0.937620\pi\)
0.980859 0.194721i \(-0.0623802\pi\)
\(458\) 8.49131i 0.396773i
\(459\) 1.04440 + 1.04440i 0.0487485 + 0.0487485i
\(460\) 2.11943 + 8.66786i 0.0988191 + 0.404141i
\(461\) 0.227378 + 0.227378i 0.0105900 + 0.0105900i 0.712382 0.701792i \(-0.247616\pi\)
−0.701792 + 0.712382i \(0.747616\pi\)
\(462\) 1.12604 0.0523881
\(463\) 0.781658 0.0363267 0.0181634 0.999835i \(-0.494218\pi\)
0.0181634 + 0.999835i \(0.494218\pi\)
\(464\) 1.30707 + 1.30707i 0.0606792 + 0.0606792i
\(465\) 0.200935 + 0.821767i 0.00931816 + 0.0381085i
\(466\) −11.1205 11.1205i −0.515149 0.515149i
\(467\) 2.66280i 0.123220i −0.998100 0.0616098i \(-0.980377\pi\)
0.998100 0.0616098i \(-0.0196235\pi\)
\(468\) 9.94518i 0.459716i
\(469\) 24.1349 1.11444
\(470\) 2.20216 3.62765i 0.101578 0.167331i
\(471\) 0.332205i 0.0153072i
\(472\) 8.04404 8.04404i 0.370257 0.370257i
\(473\) 29.5089i 1.35682i
\(474\) 0.303322 0.0139320
\(475\) −9.90061 + 31.3632i −0.454271 + 1.43904i
\(476\) 10.1441 10.1441i 0.464955 0.464955i
\(477\) −16.0968 16.0968i −0.737024 0.737024i
\(478\) 14.6371 14.6371i 0.669486 0.669486i
\(479\) 16.4195 16.4195i 0.750228 0.750228i −0.224294 0.974522i \(-0.572007\pi\)
0.974522 + 0.224294i \(0.0720075\pi\)
\(480\) 0.0783380 0.129047i 0.00357562 0.00589016i
\(481\) −12.9909 15.4626i −0.592332 0.705034i
\(482\) −10.5430 10.5430i −0.480222 0.480222i
\(483\) 1.05920i 0.0481953i
\(484\) −6.99802 −0.318092
\(485\) −21.8187 + 5.33503i −0.990736 + 0.242251i
\(486\) 1.28634 + 1.28634i 0.0583495 + 0.0583495i
\(487\) 9.02775i 0.409087i 0.978858 + 0.204543i \(0.0655709\pi\)
−0.978858 + 0.204543i \(0.934429\pi\)
\(488\) −1.55262 + 1.55262i −0.0702838 + 0.0702838i
\(489\) −1.04048 + 1.04048i −0.0470520 + 0.0470520i
\(490\) 18.3681 4.49129i 0.829784 0.202896i
\(491\) −2.91238 −0.131434 −0.0657169 0.997838i \(-0.520933\pi\)
−0.0657169 + 0.997838i \(0.520933\pi\)
\(492\) 0.129008 0.129008i 0.00581614 0.00581614i
\(493\) −4.76950 + 4.76950i −0.214808 + 0.214808i
\(494\) −15.4424 + 15.4424i −0.694785 + 0.694785i
\(495\) −6.74927 27.6025i −0.303357 1.24064i
\(496\) 3.96252 3.96252i 0.177922 0.177922i
\(497\) −15.4226 15.4226i −0.691796 0.691796i
\(498\) −0.676095 −0.0302966
\(499\) −11.5866 11.5866i −0.518686 0.518686i 0.398487 0.917174i \(-0.369535\pi\)
−0.917174 + 0.398487i \(0.869535\pi\)
\(500\) −7.36738 8.40962i −0.329479 0.376090i
\(501\) 0.532647 0.532647i 0.0237969 0.0237969i
\(502\) 16.2391 16.2391i 0.724784 0.724784i
\(503\) 19.3861 0.864382 0.432191 0.901782i \(-0.357741\pi\)
0.432191 + 0.901782i \(0.357741\pi\)
\(504\) 8.32723 8.32723i 0.370924 0.370924i
\(505\) −3.28945 + 0.804324i −0.146378 + 0.0357919i
\(506\) 16.9297i 0.752616i
\(507\) −0.0943752 0.0943752i −0.00419135 0.00419135i
\(508\) 0.683408 + 0.683408i 0.0303213 + 0.0303213i
\(509\) 7.69714 0.341170 0.170585 0.985343i \(-0.445434\pi\)
0.170585 + 0.985343i \(0.445434\pi\)
\(510\) 0.470893 + 0.285856i 0.0208515 + 0.0126579i
\(511\) 61.9280i 2.73953i
\(512\) −1.00000 −0.0441942
\(513\) 2.66247i 0.117551i
\(514\) 5.00407i 0.220720i
\(515\) −8.44410 + 2.06472i −0.372092 + 0.0909825i
\(516\) −0.332057 0.332057i −0.0146180 0.0146180i
\(517\) 5.69326 5.69326i 0.250389 0.250389i
\(518\) 2.06964 23.8245i 0.0909346 1.04679i
\(519\) 1.38409i 0.0607548i
\(520\) −1.76334 7.21153i −0.0773274 0.316246i
\(521\) 15.1959i 0.665746i −0.942972 0.332873i \(-0.891982\pi\)
0.942972 0.332873i \(-0.108018\pi\)
\(522\) −3.91525 + 3.91525i −0.171366 + 0.171366i
\(523\) 8.67427 0.379299 0.189650 0.981852i \(-0.439265\pi\)
0.189650 + 0.981852i \(0.439265\pi\)
\(524\) −3.35210 + 3.35210i −0.146437 + 0.146437i
\(525\) 0.612393 + 1.17738i 0.0267270 + 0.0513853i
\(526\) 12.4257 + 12.4257i 0.541788 + 0.541788i
\(527\) 14.4592 + 14.4592i 0.629855 + 0.629855i
\(528\) 0.202528 0.202528i 0.00881388 0.00881388i
\(529\) −7.07523 −0.307619
\(530\) −14.5263 8.81821i −0.630983 0.383038i
\(531\) 24.0955 + 24.0955i 1.04565 + 1.04565i
\(532\) −25.8602 −1.12118
\(533\) 8.97216i 0.388628i
\(534\) 0.740574i 0.0320478i
\(535\) −1.20816 + 1.99022i −0.0522334 + 0.0860446i
\(536\) 4.34085 4.34085i 0.187496 0.187496i
\(537\) 1.20416i 0.0519631i
\(538\) 22.6019i 0.974436i
\(539\) 35.8757 1.54527
\(540\) 0.773694 + 0.469671i 0.0332945 + 0.0202114i
\(541\) 19.2216 + 19.2216i 0.826402 + 0.826402i 0.987017 0.160615i \(-0.0513477\pi\)
−0.160615 + 0.987017i \(0.551348\pi\)
\(542\) −18.1930 −0.781454
\(543\) 0.611749 + 0.611749i 0.0262527 + 0.0262527i
\(544\) 3.64900i 0.156450i
\(545\) 4.66854 + 2.83404i 0.199978 + 0.121397i
\(546\) 0.881238i 0.0377135i
\(547\) 0.0420593 0.00179833 0.000899163 1.00000i \(-0.499714\pi\)
0.000899163 1.00000i \(0.499714\pi\)
\(548\) 15.4431 + 15.4431i 0.659697 + 0.659697i
\(549\) −4.65078 4.65078i −0.198491 0.198491i
\(550\) −9.78816 18.8187i −0.417369 0.802431i
\(551\) 12.1588 0.517983
\(552\) −0.190506 0.190506i −0.00810847 0.00810847i
\(553\) 17.6633 0.751120
\(554\) −23.4453 −0.996095
\(555\) 0.907526 0.140092i 0.0385223 0.00594659i
\(556\) 17.8399 0.756582
\(557\) −12.8111 −0.542823 −0.271412 0.962463i \(-0.587491\pi\)
−0.271412 + 0.962463i \(0.587491\pi\)
\(558\) 11.8695 + 11.8695i 0.502476 + 0.502476i
\(559\) −23.0937 −0.976758
\(560\) 4.56184 7.51477i 0.192773 0.317557i
\(561\) 0.739024 + 0.739024i 0.0312016 + 0.0312016i
\(562\) −3.32166 3.32166i −0.140116 0.140116i
\(563\) −29.4317 −1.24040 −0.620200 0.784444i \(-0.712949\pi\)
−0.620200 + 0.784444i \(0.712949\pi\)
\(564\) 0.128130i 0.00539525i
\(565\) −9.18807 + 2.24663i −0.386545 + 0.0945166i
\(566\) 12.1785i 0.511900i
\(567\) 24.9057 + 24.9057i 1.04594 + 1.04594i
\(568\) −5.54775 −0.232778
\(569\) 1.25554 + 1.25554i 0.0526351 + 0.0526351i 0.732934 0.680299i \(-0.238150\pi\)
−0.680299 + 0.732934i \(0.738150\pi\)
\(570\) −0.235856 0.964583i −0.00987894 0.0404019i
\(571\) −40.9624 −1.71422 −0.857111 0.515132i \(-0.827743\pi\)
−0.857111 + 0.515132i \(0.827743\pi\)
\(572\) 14.0852i 0.588933i
\(573\) 0.962624i 0.0402142i
\(574\) 7.51251 7.51251i 0.313566 0.313566i
\(575\) −17.7016 + 9.20715i −0.738209 + 0.383965i
\(576\) 2.99544i 0.124810i
\(577\) 7.71924i 0.321356i −0.987007 0.160678i \(-0.948632\pi\)
0.987007 0.160678i \(-0.0513681\pi\)
\(578\) −3.68477 −0.153266
\(579\) 0.361885 + 0.361885i 0.0150394 + 0.0150394i
\(580\) −2.14486 + 3.53325i −0.0890605 + 0.146710i
\(581\) −39.3710 −1.63338
\(582\) 0.479541 0.479541i 0.0198776 0.0198776i
\(583\) −22.7978 22.7978i −0.944187 0.944187i
\(584\) 11.1383 + 11.1383i 0.460905 + 0.460905i
\(585\) 21.6017 5.28197i 0.893121 0.218383i
\(586\) −1.06493 + 1.06493i −0.0439919 + 0.0439919i
\(587\) −5.39311 −0.222597 −0.111299 0.993787i \(-0.535501\pi\)
−0.111299 + 0.993787i \(0.535501\pi\)
\(588\) −0.403701 + 0.403701i −0.0166483 + 0.0166483i
\(589\) 36.8607i 1.51882i
\(590\) 21.7445 + 13.2000i 0.895209 + 0.543437i
\(591\) 1.61305i 0.0663521i
\(592\) −3.91278 4.65727i −0.160814 0.191412i
\(593\) −10.4329 + 10.4329i −0.428427 + 0.428427i −0.888092 0.459665i \(-0.847969\pi\)
0.459665 + 0.888092i \(0.347969\pi\)
\(594\) 1.21424 + 1.21424i 0.0498210 + 0.0498210i
\(595\) 27.4214 + 16.6462i 1.12417 + 0.682427i
\(596\) 17.7144i 0.725610i
\(597\) 0.0549981i 0.00225092i
\(598\) −13.2492 −0.541798
\(599\) 19.3788i 0.791798i 0.918294 + 0.395899i \(0.129567\pi\)
−0.918294 + 0.395899i \(0.870433\pi\)
\(600\) 0.321906 + 0.101618i 0.0131418 + 0.00414855i
\(601\) −4.17046 −0.170117 −0.0850583 0.996376i \(-0.527108\pi\)
−0.0850583 + 0.996376i \(0.527108\pi\)
\(602\) −19.3366 19.3366i −0.788102 0.788102i
\(603\) 13.0028 + 13.0028i 0.529514 + 0.529514i
\(604\) 5.53031i 0.225025i
\(605\) −3.71671 15.2002i −0.151106 0.617978i
\(606\) 0.0722968 0.0722968i 0.00293686 0.00293686i
\(607\) 29.8434 1.21131 0.605653 0.795729i \(-0.292912\pi\)
0.605653 + 0.795729i \(0.292912\pi\)
\(608\) −4.65117 + 4.65117i −0.188630 + 0.188630i
\(609\) 0.346929 0.346929i 0.0140583 0.0140583i
\(610\) −4.19702 2.54780i −0.169932 0.103158i
\(611\) 4.45554 + 4.45554i 0.180252 + 0.180252i
\(612\) 10.9304 0.441834
\(613\) 7.97850 + 7.97850i 0.322248 + 0.322248i 0.849629 0.527381i \(-0.176826\pi\)
−0.527381 + 0.849629i \(0.676826\pi\)
\(614\) −16.1006 + 16.1006i −0.649766 + 0.649766i
\(615\) 0.348733 + 0.211699i 0.0140623 + 0.00853651i
\(616\) 11.7938 11.7938i 0.475184 0.475184i
\(617\) 21.2579 21.2579i 0.855812 0.855812i −0.135030 0.990842i \(-0.543113\pi\)
0.990842 + 0.135030i \(0.0431130\pi\)
\(618\) 0.185588 0.185588i 0.00746545 0.00746545i
\(619\) −7.54167 −0.303125 −0.151563 0.988448i \(-0.548431\pi\)
−0.151563 + 0.988448i \(0.548431\pi\)
\(620\) 10.7114 + 6.50237i 0.430181 + 0.261141i
\(621\) 1.14217 1.14217i 0.0458336 0.0458336i
\(622\) 18.5878 18.5878i 0.745304 0.745304i
\(623\) 43.1257i 1.72779i
\(624\) 0.158498 + 0.158498i 0.00634500 + 0.00634500i
\(625\) 14.3535 20.4689i 0.574139 0.818758i
\(626\) 21.7608 0.869735
\(627\) 1.88398i 0.0752390i
\(628\) −3.47940 3.47940i −0.138843 0.138843i
\(629\) 16.9944 14.2778i 0.677610 0.569292i
\(630\) 22.5101 + 13.6647i 0.896822 + 0.544416i
\(631\) 23.1881 23.1881i 0.923103 0.923103i −0.0741448 0.997247i \(-0.523623\pi\)
0.997247 + 0.0741448i \(0.0236227\pi\)
\(632\) 3.17689 3.17689i 0.126370 0.126370i
\(633\) −1.00943 1.00943i −0.0401214 0.0401214i
\(634\) 22.3061 22.3061i 0.885889 0.885889i
\(635\) −1.12145 + 1.84738i −0.0445034 + 0.0733110i
\(636\) 0.513076 0.0203448
\(637\) 28.0763i 1.11242i
\(638\) −5.54512 + 5.54512i −0.219533 + 0.219533i
\(639\) 16.6180i 0.657396i
\(640\) −0.531109 2.17208i −0.0209939 0.0858589i
\(641\) −12.2032 −0.481999 −0.240999 0.970525i \(-0.577475\pi\)
−0.240999 + 0.970525i \(0.577475\pi\)
\(642\) 0.0702953i 0.00277433i
\(643\) 26.4268i 1.04217i 0.853505 + 0.521085i \(0.174472\pi\)
−0.853505 + 0.521085i \(0.825528\pi\)
\(644\) −11.0937 11.0937i −0.437153 0.437153i
\(645\) 0.544896 0.897613i 0.0214552 0.0353435i
\(646\) −16.9721 16.9721i −0.667760 0.667760i
\(647\) −23.6177 −0.928509 −0.464255 0.885702i \(-0.653678\pi\)
−0.464255 + 0.885702i \(0.653678\pi\)
\(648\) 8.95900 0.351943
\(649\) 34.1261 + 34.1261i 1.33957 + 1.33957i
\(650\) 14.7275 7.66021i 0.577659 0.300458i
\(651\) −1.05175 1.05175i −0.0412214 0.0412214i
\(652\) 21.7952i 0.853566i
\(653\) 11.5143i 0.450588i 0.974291 + 0.225294i \(0.0723342\pi\)
−0.974291 + 0.225294i \(0.927666\pi\)
\(654\) −0.164895 −0.00644790
\(655\) −9.06136 5.50070i −0.354057 0.214930i
\(656\) 2.70237i 0.105510i
\(657\) −33.3640 + 33.3640i −1.30165 + 1.30165i
\(658\) 7.46137i 0.290875i
\(659\) −45.6299 −1.77749 −0.888744 0.458404i \(-0.848421\pi\)
−0.888744 + 0.458404i \(0.848421\pi\)
\(660\) 0.547470 + 0.332342i 0.0213102 + 0.0129364i
\(661\) −8.90268 + 8.90268i −0.346274 + 0.346274i −0.858720 0.512446i \(-0.828740\pi\)
0.512446 + 0.858720i \(0.328740\pi\)
\(662\) −23.9871 23.9871i −0.932285 0.932285i
\(663\) −0.578360 + 0.578360i −0.0224616 + 0.0224616i
\(664\) −7.08119 + 7.08119i −0.274803 + 0.274803i
\(665\) −13.7346 56.1704i −0.532604 2.17819i
\(666\) 13.9506 11.7205i 0.540574 0.454161i
\(667\) 5.21597 + 5.21597i 0.201963 + 0.201963i
\(668\) 11.1575i 0.431697i
\(669\) 1.33975 0.0517976
\(670\) 11.7341 + 7.12321i 0.453329 + 0.275194i
\(671\) −6.58685 6.58685i −0.254282 0.254282i
\(672\) 0.265425i 0.0102390i
\(673\) −25.0377 + 25.0377i −0.965134 + 0.965134i −0.999412 0.0342781i \(-0.989087\pi\)
0.0342781 + 0.999412i \(0.489087\pi\)
\(674\) −17.5570 + 17.5570i −0.676270 + 0.676270i
\(675\) −0.609246 + 1.92997i −0.0234499 + 0.0742846i
\(676\) −1.97691 −0.0760348
\(677\) 8.02326 8.02326i 0.308359 0.308359i −0.535914 0.844273i \(-0.680033\pi\)
0.844273 + 0.535914i \(0.180033\pi\)
\(678\) 0.201939 0.201939i 0.00775543 0.00775543i
\(679\) 27.9250 27.9250i 1.07166 1.07166i
\(680\) 7.92592 1.93802i 0.303945 0.0743196i
\(681\) 0.812006 0.812006i 0.0311161 0.0311161i
\(682\) 16.8106 + 16.8106i 0.643712 + 0.643712i
\(683\) −14.7249 −0.563434 −0.281717 0.959498i \(-0.590904\pi\)
−0.281717 + 0.959498i \(0.590904\pi\)
\(684\) −13.9323 13.9323i −0.532715 0.532715i
\(685\) −25.3417 + 41.7456i −0.968255 + 1.59502i
\(686\) −4.04887 + 4.04887i −0.154586 + 0.154586i
\(687\) 0.405365 0.405365i 0.0154656 0.0154656i
\(688\) −6.95570 −0.265184
\(689\) 17.8415 17.8415i 0.679707 0.679707i
\(690\) 0.312614 0.514973i 0.0119010 0.0196047i
\(691\) 7.03274i 0.267538i 0.991013 + 0.133769i \(0.0427080\pi\)
−0.991013 + 0.133769i \(0.957292\pi\)
\(692\) 14.4965 + 14.4965i 0.551073 + 0.551073i
\(693\) 35.3275 + 35.3275i 1.34198 + 1.34198i
\(694\) −11.0678 −0.420128
\(695\) 9.47495 + 38.7497i 0.359405 + 1.46986i
\(696\) 0.124796i 0.00473038i
\(697\) 9.86097 0.373511
\(698\) 31.6855i 1.19931i
\(699\) 1.06176i 0.0401595i
\(700\) 18.7455 + 5.91752i 0.708514 + 0.223661i
\(701\) −18.7062 18.7062i −0.706523 0.706523i 0.259279 0.965802i \(-0.416515\pi\)
−0.965802 + 0.259279i \(0.916515\pi\)
\(702\) −0.950265 + 0.950265i −0.0358654 + 0.0358654i
\(703\) −39.8608 3.46271i −1.50338 0.130599i
\(704\) 4.24241i 0.159892i
\(705\) −0.278308 + 0.0680510i −0.0104817 + 0.00256295i
\(706\) 15.6047i 0.587291i
\(707\) 4.21005 4.21005i 0.158335 0.158335i
\(708\) −0.768026 −0.0288642
\(709\) 24.5474 24.5474i 0.921895 0.921895i −0.0752682 0.997163i \(-0.523981\pi\)
0.997163 + 0.0752682i \(0.0239813\pi\)
\(710\) −2.94646 12.0501i −0.110579 0.452234i
\(711\) 9.51618 + 9.51618i 0.356885 + 0.356885i
\(712\) −7.75651 7.75651i −0.290688 0.290688i
\(713\) 15.8128 15.8128i 0.592193 0.592193i
\(714\) −0.968537 −0.0362466
\(715\) 30.5942 7.48079i 1.14416 0.279766i
\(716\) −12.6119 12.6119i −0.471329 0.471329i
\(717\) −1.39752 −0.0521913
\(718\) 34.4499i 1.28566i
\(719\) 12.2897i 0.458329i 0.973388 + 0.229164i \(0.0735993\pi\)
−0.973388 + 0.229164i \(0.926401\pi\)
\(720\) 6.50633 1.59091i 0.242477 0.0592895i
\(721\) 10.8073 10.8073i 0.402486 0.402486i
\(722\) 24.2668i 0.903116i
\(723\) 1.00663i 0.0374368i
\(724\) 12.8145 0.476247
\(725\) −8.81366 2.78226i −0.327331 0.103331i
\(726\) 0.334077 + 0.334077i 0.0123988 + 0.0123988i
\(727\) 12.2686 0.455016 0.227508 0.973776i \(-0.426942\pi\)
0.227508 + 0.973776i \(0.426942\pi\)
\(728\) 9.22978 + 9.22978i 0.342079 + 0.342079i
\(729\) 26.7542i 0.990896i
\(730\) −18.2775 + 30.1088i −0.676482 + 1.11438i
\(731\) 25.3814i 0.938765i
\(732\) 0.148241 0.00547913
\(733\) −26.4738 26.4738i −0.977831 0.977831i 0.0219285 0.999760i \(-0.493019\pi\)
−0.999760 + 0.0219285i \(0.993019\pi\)
\(734\) 4.61443 + 4.61443i 0.170322 + 0.170322i
\(735\) −1.09128 0.662461i −0.0402524 0.0244352i
\(736\) −3.99058 −0.147095
\(737\) 18.4157 + 18.4157i 0.678350 + 0.678350i
\(738\) 8.09481 0.297974
\(739\) −23.9200 −0.879912 −0.439956 0.898019i \(-0.645006\pi\)
−0.439956 + 0.898019i \(0.645006\pi\)
\(740\) 8.03783 10.9724i 0.295477 0.403353i
\(741\) 1.47440 0.0541635
\(742\) 29.8779 1.09685
\(743\) −8.98938 8.98938i −0.329788 0.329788i 0.522718 0.852506i \(-0.324918\pi\)
−0.852506 + 0.522718i \(0.824918\pi\)
\(744\) −0.378332 −0.0138703
\(745\) −38.4771 + 9.40827i −1.40969 + 0.344692i
\(746\) −15.3464 15.3464i −0.561872 0.561872i
\(747\) −21.2113 21.2113i −0.776080 0.776080i
\(748\) 15.4806 0.566025
\(749\) 4.09349i 0.149573i
\(750\) −0.0497555 + 0.753176i −0.00181682 + 0.0275021i
\(751\) 34.7552i 1.26824i 0.773236 + 0.634118i \(0.218637\pi\)
−0.773236 + 0.634118i \(0.781363\pi\)
\(752\) 1.34199 + 1.34199i 0.0489373 + 0.0489373i
\(753\) −1.55047 −0.0565022
\(754\) −4.33961 4.33961i −0.158039 0.158039i
\(755\) 12.0123 2.93719i 0.437171 0.106895i
\(756\) −1.59134 −0.0578765
\(757\) 2.66868i 0.0969950i 0.998823 + 0.0484975i \(0.0154433\pi\)
−0.998823 + 0.0484975i \(0.984557\pi\)
\(758\) 23.4892i 0.853164i
\(759\) 0.808204 0.808204i 0.0293359 0.0293359i
\(760\) −12.5730 7.63243i −0.456070 0.276857i
\(761\) 50.1338i 1.81735i 0.417507 + 0.908674i \(0.362904\pi\)
−0.417507 + 0.908674i \(0.637096\pi\)
\(762\) 0.0652502i 0.00236376i
\(763\) −9.60230 −0.347626
\(764\) 10.0822 + 10.0822i 0.364761 + 0.364761i
\(765\) 5.80522 + 23.7416i 0.209888 + 0.858381i
\(766\) −0.480522 −0.0173620
\(767\) −26.7071 + 26.7071i −0.964336 + 0.964336i
\(768\) 0.0477388 + 0.0477388i 0.00172263 + 0.00172263i
\(769\) 35.1828 + 35.1828i 1.26872 + 1.26872i 0.946748 + 0.321974i \(0.104346\pi\)
0.321974 + 0.946748i \(0.395654\pi\)
\(770\) 31.8807 + 19.3532i 1.14890 + 0.697441i
\(771\) −0.238888 + 0.238888i −0.00860335 + 0.00860335i
\(772\) 7.58052 0.272829
\(773\) −5.35033 + 5.35033i −0.192438 + 0.192438i −0.796749 0.604311i \(-0.793449\pi\)
0.604311 + 0.796749i \(0.293449\pi\)
\(774\) 20.8354i 0.748913i
\(775\) −8.43473 + 26.7195i −0.302984 + 0.959793i
\(776\) 10.0451i 0.360597i
\(777\) −1.23615 + 1.03855i −0.0443468 + 0.0372578i