Properties

Label 370.2.g.e.43.6
Level $370$
Weight $2$
Character 370.43
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.g (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: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.6
Root \(0.0477388 - 0.0477388i\) of defining polynomial
Character \(\chi\) \(=\) 370.43
Dual form 370.2.g.e.327.6

$q$-expansion

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

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −0.0477388 + 0.0477388i −0.0275620 + 0.0275620i −0.720753 0.693191i \(-0.756204\pi\)
0.693191 + 0.720753i \(0.256204\pi\)
\(4\) −1.00000 −0.500000
\(5\) 2.17208 + 0.531109i 0.971383 + 0.237519i
\(6\) −0.0477388 0.0477388i −0.0194893 0.0194893i
\(7\) −2.77997 + 2.77997i −1.05073 + 1.05073i −0.0520865 + 0.998643i \(0.516587\pi\)
−0.998643 + 0.0520865i \(0.983413\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 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
\(13\) 3.32010i 0.920831i 0.887703 + 0.460416i \(0.152300\pi\)
−0.887703 + 0.460416i \(0.847700\pi\)
\(14\) −2.77997 2.77997i −0.742978 0.742978i
\(15\) −0.129047 + 0.0783380i −0.0333198 + 0.0202268i
\(16\) 1.00000 0.250000
\(17\) 3.64900 0.885013 0.442507 0.896765i \(-0.354089\pi\)
0.442507 + 0.896765i \(0.354089\pi\)
\(18\) −2.99544 −0.706032
\(19\) −4.65117 + 4.65117i −1.06705 + 1.06705i −0.0694677 + 0.997584i \(0.522130\pi\)
−0.997584 + 0.0694677i \(0.977870\pi\)
\(20\) −2.17208 0.531109i −0.485691 0.118760i
\(21\) 0.265425i 0.0579205i
\(22\) 4.24241 0.904484
\(23\) 3.99058i 0.832094i 0.909343 + 0.416047i \(0.136585\pi\)
−0.909343 + 0.416047i \(0.863415\pi\)
\(24\) 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 0.575256 0.817973i \(-0.304902\pi\)
−0.817973 + 0.575256i \(0.804902\pi\)
\(30\) −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 \(0.0821411\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 0.202528 + 0.202528i 0.0352555 + 0.0352555i
\(34\) 3.64900i 0.625799i
\(35\) −7.51477 + 4.56184i −1.27023 + 0.771092i
\(36\) 2.99544i 0.499240i
\(37\) −4.65727 + 3.91278i −0.765650 + 0.643258i
\(38\) −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 \(-0.0676785\pi\)
\(42\) 0.265425 0.0409560
\(43\) 6.95570i 1.06073i −0.847768 0.530367i \(-0.822054\pi\)
0.847768 0.530367i \(-0.177946\pi\)
\(44\) 4.24241i 0.639567i
\(45\) −1.59091 + 6.50633i −0.237158 + 0.969907i
\(46\) −3.99058 −0.588380
\(47\) 1.34199 1.34199i 0.195749 0.195749i −0.602426 0.798175i \(-0.705799\pi\)
0.798175 + 0.602426i \(0.205799\pi\)
\(48\) −0.0477388 + 0.0477388i −0.00689051 + 0.00689051i
\(49\) 8.45644i 1.20806i
\(50\) −2.30722 + 4.43585i −0.326290 + 0.627324i
\(51\) −0.174199 + 0.174199i −0.0243928 + 0.0243928i
\(52\) 3.32010i 0.460416i
\(53\) 5.37378 + 5.37378i 0.738145 + 0.738145i 0.972219 0.234074i \(-0.0752057\pi\)
−0.234074 + 0.972219i \(0.575206\pi\)
\(54\) 0.286215 0.286215i 0.0389490 0.0389490i
\(55\) 2.25318 9.21484i 0.303819 1.24253i
\(56\) 2.77997 + 2.77997i 0.371489 + 0.371489i
\(57\) 0.444083i 0.0588202i
\(58\) 1.30707 1.30707i 0.171627 0.171627i
\(59\) 8.04404 8.04404i 1.04725 1.04725i 0.0484179 0.998827i \(-0.484582\pi\)
0.998827 0.0484179i \(-0.0154179\pi\)
\(60\) 0.129047 0.0783380i 0.0166599 0.0101134i
\(61\) 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 \(-0.127645\pi\)
−0.390348 + 0.920668i \(0.627645\pi\)
\(68\) −3.64900 −0.442507
\(69\) −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 \(0.393222\pi\)
\(72\) 2.99544 0.353016
\(73\) 11.1383 11.1383i 1.30364 1.30364i 0.377712 0.925923i \(-0.376711\pi\)
0.925923 0.377712i \(-0.123289\pi\)
\(74\) −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 −0.505436 0.862864i \(-0.668668\pi\)
0.862864 + 0.505436i \(0.168668\pi\)
\(80\) 2.17208 + 0.531109i 0.242846 + 0.0593798i
\(81\) −8.95900 −0.995444
\(82\) 2.70237 0.298427
\(83\) 7.08119 + 7.08119i 0.777261 + 0.777261i 0.979364 0.202103i \(-0.0647775\pi\)
−0.202103 + 0.979364i \(0.564778\pi\)
\(84\) 0.265425i 0.0289602i
\(85\) 7.92592 + 1.93802i 0.859687 + 0.210208i
\(86\) 6.95570 0.750053
\(87\) 0.124796 0.0133795
\(88\) −4.24241 −0.452242
\(89\) −7.75651 7.75651i −0.822188 0.822188i 0.164233 0.986422i \(-0.447485\pi\)
−0.986422 + 0.164233i \(0.947485\pi\)
\(90\) −6.50633 1.59091i −0.685828 0.167696i
\(91\) −9.22978 9.22978i −0.967544 0.967544i
\(92\) 3.99058i 0.416047i
\(93\) 0.378332i 0.0392312i
\(94\) 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
\(97\) 10.0451 1.01992 0.509962 0.860197i \(-0.329660\pi\)
0.509962 + 0.860197i \(0.329660\pi\)
\(98\) 8.45644 0.854230
\(99\) 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
\(103\) −3.88757 −0.383054 −0.191527 0.981487i \(-0.561344\pi\)
−0.191527 + 0.981487i \(0.561344\pi\)
\(104\) 3.32010 0.325563
\(105\) 0.140969 0.576524i 0.0137572 0.0562629i
\(106\) −5.37378 + 5.37378i −0.521948 + 0.521948i
\(107\) 0.736249 0.736249i 0.0711758 0.0711758i −0.670623 0.741799i \(-0.733973\pi\)
0.741799 + 0.670623i \(0.233973\pi\)
\(108\) 0.286215 + 0.286215i 0.0275411 + 0.0275411i
\(109\) −1.72705 + 1.72705i −0.165422 + 0.165422i −0.784964 0.619542i \(-0.787318\pi\)
0.619542 + 0.784964i \(0.287318\pi\)
\(110\) 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
\(113\) −4.23008 −0.397933 −0.198966 0.980006i \(-0.563758\pi\)
−0.198966 + 0.980006i \(0.563758\pi\)
\(114\) 0.444083 0.0415922
\(115\) −2.11943 + 8.66786i −0.197638 + 0.808282i
\(116\) 1.30707 + 1.30707i 0.121358 + 0.121358i
\(117\) −9.94518 −0.919432
\(118\) 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
\(125\) 8.40962 + 7.36738i 0.752179 + 0.658958i
\(126\) 8.32723 8.32723i 0.741849 0.741849i
\(127\) 0.683408 0.683408i 0.0606426 0.0606426i −0.676135 0.736778i \(-0.736346\pi\)
0.736778 + 0.676135i \(0.236346\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0.332057 + 0.332057i 0.0292360 + 0.0292360i
\(130\) −7.21153 1.76334i −0.632493 0.154655i
\(131\) −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
\(133\) 25.8602i 2.24237i
\(134\) −4.34085 + 4.34085i −0.374993 + 0.374993i
\(135\) −0.469671 0.773694i −0.0404228 0.0665890i
\(136\) 3.64900i 0.312900i
\(137\) 15.4431 15.4431i 1.31939 1.31939i 0.405138 0.914256i \(-0.367223\pi\)
0.914256 0.405138i \(-0.132777\pi\)
\(138\) 0.190506 0.190506i 0.0162169 0.0162169i
\(139\) −17.8399 −1.51316 −0.756582 0.653899i \(-0.773132\pi\)
−0.756582 + 0.653899i \(0.773132\pi\)
\(140\) 7.51477 4.56184i 0.635114 0.385546i
\(141\) 0.128130i 0.0107905i
\(142\) 5.54775i 0.465557i
\(143\) 14.0852 1.17787
\(144\) 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
\(148\) 4.65727 3.91278i 0.382825 0.321629i
\(149\) 17.7144i 1.45122i −0.688106 0.725610i \(-0.741558\pi\)
0.688106 0.725610i \(-0.258442\pi\)
\(150\) −0.101618 0.321906i −0.00829709 0.0262835i
\(151\) 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
\(153\) 10.9304i 0.883669i
\(154\) −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 −0.832185 0.554498i \(-0.812910\pi\)
0.554498 + 0.832185i \(0.312910\pi\)
\(158\) 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
\(162\) 8.95900i 0.703885i
\(163\) −21.7952 −1.70713 −0.853566 0.520985i \(-0.825565\pi\)
−0.853566 + 0.520985i \(0.825565\pi\)
\(164\) 2.70237i 0.211020i
\(165\) 0.332342 + 0.547470i 0.0258728 + 0.0426205i
\(166\) −7.08119 + 7.08119i −0.549607 + 0.549607i
\(167\) −11.1575 −0.863394 −0.431697 0.902019i \(-0.642085\pi\)
−0.431697 + 0.902019i \(0.642085\pi\)
\(168\) −0.265425 −0.0204780
\(169\) 1.97691 0.152070
\(170\) −1.93802 + 7.92592i −0.148639 + 0.607890i
\(171\) −13.9323 13.9323i −1.06543 1.06543i
\(172\) 6.95570i 0.530367i
\(173\) −14.4965 + 14.4965i −1.10215 + 1.10215i −0.107994 + 0.994152i \(0.534443\pi\)
−0.994152 + 0.107994i \(0.965557\pi\)
\(174\) 0.124796i 0.00946076i
\(175\) −18.7455 + 5.91752i −1.41703 + 0.447322i
\(176\) 4.24241i 0.319783i
\(177\) 0.768026i 0.0577284i
\(178\) 7.75651 7.75651i 0.581375 0.581375i
\(179\) 12.6119 + 12.6119i 0.942658 + 0.942658i 0.998443 0.0557848i \(-0.0177661\pi\)
−0.0557848 + 0.998443i \(0.517766\pi\)
\(180\) 1.59091 6.50633i 0.118579 0.484954i
\(181\) 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
\(183\) 0.148241i 0.0109583i
\(184\) 3.99058 0.294190
\(185\) −12.1941 + 6.02536i −0.896525 + 0.442993i
\(186\) −0.378332 −0.0277406
\(187\) 15.4806i 1.13205i
\(188\) −1.34199 + 1.34199i −0.0978746 + 0.0978746i
\(189\) 1.59134 0.115753
\(190\) −7.63243 12.5730i −0.553715 0.912140i
\(191\) 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
\(193\) 7.58052i 0.545658i 0.962063 + 0.272829i \(0.0879593\pi\)
−0.962063 + 0.272829i \(0.912041\pi\)
\(194\) 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 −0.230649 + 0.973037i \(0.574085\pi\)
−0.973037 + 0.230649i \(0.925915\pi\)
\(198\) 12.7079i 0.903110i
\(199\) −0.576031 0.576031i −0.0408338 0.0408338i 0.686395 0.727229i \(-0.259192\pi\)
−0.727229 + 0.686395i \(0.759192\pi\)
\(200\) 2.30722 4.43585i 0.163145 0.313662i
\(201\) −0.414455 −0.0292334
\(202\) −1.51442 −0.106554
\(203\) 7.26722 0.510059
\(204\) 0.174199 0.174199i 0.0121964 0.0121964i
\(205\) 1.43525 5.86977i 0.100243 0.409962i
\(206\) 3.88757i 0.270860i
\(207\) −11.9536 −0.830830
\(208\) 3.32010i 0.230208i
\(209\) 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
\(217\) 22.0313i 1.49559i
\(218\) −1.72705 1.72705i −0.116971 0.116971i
\(219\) 1.06346i 0.0718617i
\(220\) −2.25318 + 9.21484i −0.151909 + 0.621264i
\(221\) 12.1151i 0.814948i
\(222\) 0.409124 + 0.0355407i 0.0274586 + 0.00238534i
\(223\) 14.0320 + 14.0320i 0.939655 + 0.939655i 0.998280 0.0586249i \(-0.0186716\pi\)
−0.0586249 + 0.998280i \(0.518672\pi\)
\(224\) −2.77997 2.77997i −0.185744 0.185744i
\(225\) −6.91114 + 13.2873i −0.460743 + 0.885822i
\(226\) 4.23008i 0.281381i
\(227\) −17.0093 −1.12895 −0.564475 0.825450i \(-0.690921\pi\)
−0.564475 + 0.825450i \(0.690921\pi\)
\(228\) 0.444083i 0.0294101i
\(229\) 8.49131i 0.561121i 0.959836 + 0.280561i \(0.0905204\pi\)
−0.959836 + 0.280561i \(0.909480\pi\)
\(230\) −8.66786 2.11943i −0.571542 0.139751i
\(231\) −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 \(-0.922263\pi\)
0.241797 + 0.970327i \(0.422263\pi\)
\(234\) 9.94518i 0.650137i
\(235\) 3.62765 2.20216i 0.236642 0.143653i
\(236\) −8.04404 + 8.04404i −0.523623 + 0.523623i
\(237\) 0.303322i 0.0197029i
\(238\) −10.1441 10.1441i −0.657545 0.657545i
\(239\) 14.6371 14.6371i 0.946797 0.946797i −0.0518580 0.998654i \(-0.516514\pi\)
0.998654 + 0.0518580i \(0.0165143\pi\)
\(240\) −0.129047 + 0.0783380i −0.00832995 + 0.00505669i
\(241\) 10.5430 + 10.5430i 0.679137 + 0.679137i 0.959805 0.280668i \(-0.0905560\pi\)
−0.280668 + 0.959805i \(0.590556\pi\)
\(242\) 6.99802i 0.449850i
\(243\) 1.28634 1.28634i 0.0825187 0.0825187i
\(244\) −1.55262 + 1.55262i −0.0993963 + 0.0993963i
\(245\) 4.49129 18.3681i 0.286938 1.17349i
\(246\) −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
\(253\) 16.9297 1.06436
\(254\) 0.683408 + 0.683408i 0.0428808 + 0.0428808i
\(255\) −0.470893 + 0.285856i −0.0294885 + 0.0179010i
\(256\) 1.00000 0.0625000
\(257\) 5.00407 0.312145 0.156073 0.987746i \(-0.450117\pi\)
0.156073 + 0.987746i \(0.450117\pi\)
\(258\) −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 \(-0.567748\pi\)
0.977436 + 0.211233i \(0.0677477\pi\)
\(264\) 0.202528 0.202528i 0.0124647 0.0124647i
\(265\) 8.81821 + 14.5263i 0.541698 + 0.892345i
\(266\) 25.8602 1.58559
\(267\) 0.740574 0.0453224
\(268\) −4.34085 4.34085i −0.265160 0.265160i
\(269\) 22.6019i 1.37806i −0.724732 0.689030i \(-0.758037\pi\)
0.724732 0.689030i \(-0.241963\pi\)
\(270\) 0.773694 0.469671i 0.0470855 0.0285833i
\(271\) 18.1930 1.10514 0.552572 0.833465i \(-0.313647\pi\)
0.552572 + 0.833465i \(0.313647\pi\)
\(272\) 3.64900 0.221253
\(273\) 0.881238 0.0533350
\(274\) 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
\(277\) 23.4453i 1.40869i −0.709857 0.704346i \(-0.751241\pi\)
0.709857 0.704346i \(-0.248759\pi\)
\(278\) 17.8399i 1.06997i
\(279\) 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 \(0.705253\pi\)
\(282\) −0.128130 −0.00763003
\(283\) 12.1785 0.723935 0.361968 0.932191i \(-0.382105\pi\)
0.361968 + 0.932191i \(0.382105\pi\)
\(284\) −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
\(288\) −2.99544 −0.176508
\(289\) −3.68477 −0.216751
\(290\) 3.53325 2.14486i 0.207480 0.125951i
\(291\) −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 0.737529 0.675315i \(-0.235992\pi\)
−0.675315 + 0.737529i \(0.735992\pi\)
\(294\) −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
\(298\) 17.7144 1.02617
\(299\) −13.2492 −0.766219
\(300\) 0.321906 0.101618i 0.0185853 0.00586693i
\(301\) 19.3366 + 19.3366i 1.11454 + 1.11454i
\(302\) 5.53031 0.318233
\(303\) −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 \(-0.475133\pi\)
−0.996950 + 0.0780426i \(0.975133\pi\)
\(308\) −11.7938 11.7938i −0.672012 0.672012i
\(309\) 0.185588 0.185588i 0.0105577 0.0105577i
\(310\) 6.50237 + 10.7114i 0.369310 + 0.608368i
\(311\) −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
\(313\) 21.7608i 1.22999i −0.788531 0.614995i \(-0.789158\pi\)
0.788531 0.614995i \(-0.210842\pi\)
\(314\) −3.47940 3.47940i −0.196354 0.196354i
\(315\) −13.6647 22.5101i −0.769921 1.26830i
\(316\) −3.17689 + 3.17689i −0.178714 + 0.178714i
\(317\) 22.3061 + 22.3061i 1.25284 + 1.25284i 0.954443 + 0.298392i \(0.0964504\pi\)
0.298392 + 0.954443i \(0.403550\pi\)
\(318\) 0.513076i 0.0287719i
\(319\) −5.54512 + 5.54512i −0.310467 + 0.310467i
\(320\) −2.17208 0.531109i −0.121423 0.0296899i
\(321\) 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
\(325\) −7.66021 + 14.7275i −0.424912 + 0.816933i
\(326\) 21.7952i 1.20712i
\(327\) 0.164895i 0.00911871i
\(328\) −2.70237 −0.149214
\(329\) 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
\(333\) −11.7205 13.9506i −0.642280 0.764486i
\(334\) 11.1575i 0.610512i
\(335\) 7.12321 + 11.7341i 0.389183 + 0.641105i
\(336\) 0.265425i 0.0144801i
\(337\) −17.5570 17.5570i −0.956390 0.956390i 0.0426980 0.999088i \(-0.486405\pi\)
−0.999088 + 0.0426980i \(0.986405\pi\)
\(338\) 1.97691i 0.107530i
\(339\) 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
\(347\) 11.0678i 0.594151i −0.954854 0.297075i \(-0.903989\pi\)
0.954854 0.297075i \(-0.0960112\pi\)
\(348\) −0.124796 −0.00668977
\(349\) 31.6855i 1.69609i −0.529926 0.848044i \(-0.677780\pi\)
0.529926 0.848044i \(-0.322220\pi\)
\(350\) −5.91752 18.7455i −0.316305 1.00199i
\(351\) 0.950265 0.950265i 0.0507214 0.0507214i
\(352\) 4.24241 0.226121
\(353\) −15.6047 −0.830555 −0.415278 0.909695i \(-0.636316\pi\)
−0.415278 + 0.909695i \(0.636316\pi\)
\(354\) −0.768026 −0.0408201
\(355\) 12.0501 + 2.94646i 0.639555 + 0.156382i
\(356\) 7.75651 + 7.75651i 0.411094 + 0.411094i
\(357\) 0.968537i 0.0512604i
\(358\) −12.6119 + 12.6119i −0.666560 + 0.666560i
\(359\) 34.4499i 1.81820i 0.416580 + 0.909099i \(0.363229\pi\)
−0.416580 + 0.909099i \(0.636771\pi\)
\(360\) 6.50633 + 1.59091i 0.342914 + 0.0838481i
\(361\) 24.2668i 1.27720i
\(362\) 12.8145i 0.673515i
\(363\) 0.334077 0.334077i 0.0175345 0.0175345i
\(364\) 9.22978 + 9.22978i 0.483772 + 0.483772i
\(365\) 30.1088 18.2775i 1.57597 0.956691i
\(366\) −0.148241 −0.00774866
\(367\) −4.61443 + 4.61443i −0.240871 + 0.240871i −0.817211 0.576339i \(-0.804481\pi\)
0.576339 + 0.817211i \(0.304481\pi\)
\(368\) 3.99058i 0.208024i
\(369\) 8.09481 0.421399
\(370\) −6.02536 12.1941i −0.313243 0.633939i
\(371\) −29.8779 −1.55118
\(372\) 0.378332i 0.0196156i
\(373\) −15.3464 + 15.3464i −0.794607 + 0.794607i −0.982239 0.187632i \(-0.939919\pi\)
0.187632 + 0.982239i \(0.439919\pi\)
\(374\) 15.4806 0.800481
\(375\) −0.753176 + 0.0497555i −0.0388938 + 0.00256937i
\(376\) −1.34199 1.34199i −0.0692078 0.0692078i
\(377\) 4.33961 4.33961i 0.223501 0.223501i
\(378\) 1.59134i 0.0818497i
\(379\) 23.4892i 1.20656i −0.797531 0.603278i \(-0.793861\pi\)
0.797531 0.603278i \(-0.206139\pi\)
\(380\) 12.5730 7.63243i 0.644981 0.391535i
\(381\) 0.0652502i 0.00334287i
\(382\) −10.0822 + 10.0822i −0.515850 + 0.515850i
\(383\) 0.480522i 0.0245535i 0.999925 + 0.0122768i \(0.00390791\pi\)
−0.999925 + 0.0122768i \(0.996092\pi\)
\(384\) 0.0477388 + 0.0477388i 0.00243616 + 0.00243616i
\(385\) 19.3532 + 31.8807i 0.986330 + 1.62479i
\(386\) −7.58052 −0.385838
\(387\) 20.8354 1.05912
\(388\) −10.0451 −0.509962
\(389\) 11.0293 11.0293i 0.559208 0.559208i −0.369874 0.929082i \(-0.620599\pi\)
0.929082 + 0.369874i \(0.120599\pi\)
\(390\) 0.428450 0.260090i 0.0216954 0.0131702i
\(391\) 14.5617i 0.736415i
\(392\) −8.45644 −0.427115
\(393\) 0.320051i 0.0161444i
\(394\) −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 \(-0.480027\pi\)
−0.998032 + 0.0627054i \(0.980027\pi\)
\(398\) 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 \(-0.0606980\pi\)
\(402\) 0.414455i 0.0206711i
\(403\) 13.1560 + 13.1560i 0.655346 + 0.655346i
\(404\) 1.51442i 0.0753454i
\(405\) −19.4596 4.75820i −0.966958 0.236437i
\(406\) 7.26722i 0.360666i
\(407\) 16.5996 + 19.7580i 0.822813 + 0.979369i
\(408\) 0.174199 + 0.174199i 0.00862415 + 0.00862415i
\(409\) 20.5642 + 20.5642i 1.01684 + 1.01684i 0.999856 + 0.0169803i \(0.00540527\pi\)
0.0169803 + 0.999856i \(0.494595\pi\)
\(410\) 5.86977 + 1.43525i 0.289887 + 0.0708822i
\(411\) 1.47447i 0.0727303i
\(412\) 3.88757 0.191527
\(413\) 44.7244i 2.20074i
\(414\) 11.9536i 0.587486i
\(415\) 11.6200 + 19.1418i 0.570404 + 0.939633i
\(416\) −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 \(-0.623329\pi\)
0.377827 0.925876i \(-0.376671\pi\)
\(420\) −0.140969 + 0.576524i −0.00687861 + 0.0281315i
\(421\) 24.4985 24.4985i 1.19398 1.19398i 0.218043 0.975939i \(-0.430033\pi\)
0.975939 0.218043i \(-0.0699674\pi\)
\(422\) 21.1449i 1.02932i
\(423\) 4.01985 + 4.01985i 0.195452 + 0.195452i
\(424\) 5.37378 5.37378i 0.260974 0.260974i
\(425\) 16.1864 + 8.41905i 0.785157 + 0.408384i
\(426\) −0.264843 0.264843i −0.0128317 0.0128317i
\(427\) 8.63247i 0.417754i
\(428\) −0.736249 + 0.736249i −0.0355879 + 0.0355879i
\(429\) −0.672413 + 0.672413i −0.0324644 + 0.0324644i
\(430\) 15.1083 + 3.69423i 0.728588 + 0.178152i
\(431\) 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 0.189341 0.981911i \(-0.439365\pi\)
−0.981911 + 0.189341i \(0.939365\pi\)
\(434\) −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
\(438\) −1.06346 −0.0508139
\(439\) 17.5768 + 17.5768i 0.838896 + 0.838896i 0.988714 0.149817i \(-0.0478686\pi\)
−0.149817 + 0.988714i \(0.547869\pi\)
\(440\) −9.21484 2.25318i −0.439300 0.107416i
\(441\) 25.3308 1.20623
\(442\) −12.1151 −0.576255
\(443\) 14.2624 14.2624i 0.677629 0.677629i −0.281834 0.959463i \(-0.590943\pi\)
0.959463 + 0.281834i \(0.0909427\pi\)
\(444\) −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 −0.987604 0.156965i \(-0.949829\pi\)
0.156965 + 0.987604i \(0.449829\pi\)
\(450\) −13.2873 6.91114i −0.626370 0.325794i
\(451\) −11.4646 −0.539846
\(452\) 4.23008 0.198966
\(453\) 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
\(457\) −8.32533 −0.389443 −0.194721 0.980859i \(-0.562380\pi\)
−0.194721 + 0.980859i \(0.562380\pi\)
\(458\) −8.49131 −0.396773
\(459\) −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 \(0.747616\pi\)
\(462\) 1.12604i 0.0523881i
\(463\) 0.781658i 0.0363267i 0.999835 + 0.0181634i \(0.00578189\pi\)
−0.999835 + 0.0181634i \(0.994218\pi\)
\(464\) −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
\(467\) −2.66280 −0.123220 −0.0616098 0.998100i \(-0.519623\pi\)
−0.0616098 + 0.998100i \(0.519623\pi\)
\(468\) 9.94518 0.459716
\(469\) −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
\(473\) −29.5089 −1.35682
\(474\) −0.303322 −0.0139320
\(475\) −31.3632 + 9.90061i −1.43904 + 0.454271i
\(476\) 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 −0.974522 0.224294i \(-0.927993\pi\)
0.224294 + 0.974522i \(0.427993\pi\)
\(480\) −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
\(483\) 1.05920 0.0481953
\(484\) 6.99802 0.318092
\(485\) 21.8187 + 5.33503i 0.990736 + 0.242251i
\(486\) 1.28634 + 1.28634i 0.0583495 + 0.0583495i
\(487\) 9.02775 0.409087 0.204543 0.978858i \(-0.434429\pi\)
0.204543 + 0.978858i \(0.434429\pi\)
\(488\) −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
\(495\) 27.6025 + 6.74927i 1.24064 + 0.303357i
\(496\) 3.96252 3.96252i 0.177922 0.177922i
\(497\) −15.4226 + 15.4226i −0.691796 + 0.691796i
\(498\) 0.676095i 0.0302966i
\(499\) 11.5866 + 11.5866i 0.518686 + 0.518686i 0.917174 0.398487i \(-0.130465\pi\)
−0.398487 + 0.917174i \(0.630465\pi\)
\(500\) −8.40962 7.36738i −0.376090 0.329479i
\(501\) 0.532647 0.532647i 0.0237969 0.0237969i
\(502\) −16.2391 16.2391i −0.724784 0.724784i
\(503\) 19.3861i 0.864382i 0.901782 + 0.432191i \(0.142259\pi\)
−0.901782 + 0.432191i \(0.857741\pi\)
\(504\) −8.32723 + 8.32723i −0.370924 + 0.370924i
\(505\) −0.804324 + 3.28945i −0.0357919 + 0.146378i
\(506\) 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 \(-0.554566\pi\)
−0.170585 + 0.985343i \(0.554566\pi\)
\(510\) −0.285856 0.470893i −0.0126579 0.0208515i
\(511\) 61.9280i 2.73953i
\(512\) 1.00000i 0.0441942i
\(513\) 2.66247 0.117551
\(514\) 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
\(518\) 23.8245 + 2.06964i 1.04679 + 0.0909346i
\(519\) 1.38409i 0.0607548i
\(520\) 7.21153 + 1.76334i 0.316246 + 0.0773274i
\(521\) 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
\(523\) 8.67427i 0.379299i 0.981852 + 0.189650i \(0.0607352\pi\)
−0.981852 + 0.189650i \(0.939265\pi\)
\(524\) 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
\(532\) 25.8602i 1.12118i
\(533\) 8.97216 0.388628
\(534\) 0.740574i 0.0320478i
\(535\) 1.99022 1.20816i 0.0860446 0.0522334i
\(536\) 4.34085 4.34085i 0.187496 0.187496i
\(537\) −1.20416 −0.0519631
\(538\) 22.6019 0.974436
\(539\) −35.8757 −1.54527
\(540\) 0.469671 + 0.773694i 0.0202114 + 0.0332945i
\(541\) 19.2216 + 19.2216i 0.826402 + 0.826402i 0.987017 0.160615i \(-0.0513477\pi\)
−0.160615 + 0.987017i \(0.551348\pi\)
\(542\) 18.1930i 0.781454i
\(543\) −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
\(547\) 0.0420593i 0.00179833i −1.00000 0.000899163i \(-0.999714\pi\)
1.00000 0.000899163i \(-0.000286213\pi\)
\(548\) −15.4431 + 15.4431i −0.659697 + 0.659697i
\(549\) 4.65078 + 4.65078i 0.198491 + 0.198491i
\(550\) 18.8187 + 9.78816i 0.802431 + 0.417369i
\(551\) 12.1588 0.517983
\(552\) −0.190506 + 0.190506i −0.00810847 + 0.00810847i
\(553\) 17.6633i 0.751120i
\(554\) 23.4453 0.996095
\(555\) 0.294487 0.869774i 0.0125003 0.0369198i
\(556\) 17.8399 0.756582
\(557\) 12.8111i 0.542823i 0.962463 + 0.271412i \(0.0874905\pi\)
−0.962463 + 0.271412i \(0.912509\pi\)
\(558\) −11.8695 + 11.8695i −0.502476 + 0.502476i
\(559\) 23.0937 0.976758
\(560\) −7.51477 + 4.56184i −0.317557 + 0.192773i
\(561\) 0.739024 + 0.739024i 0.0312016 + 0.0312016i
\(562\) −3.32166 + 3.32166i −0.140116 + 0.140116i
\(563\) 29.4317i 1.24040i −0.784444 0.620200i \(-0.787051\pi\)
0.784444 0.620200i \(-0.212949\pi\)
\(564\) 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
\(568\) 5.54775i 0.232778i
\(569\) −1.25554 1.25554i −0.0526351 0.0526351i 0.680299 0.732934i \(-0.261850\pi\)
−0.732934 + 0.680299i \(0.761850\pi\)
\(570\) 0.964583 + 0.235856i 0.0404019 + 0.00987894i
\(571\) −40.9624 −1.71422 −0.857111 0.515132i \(-0.827743\pi\)
−0.857111 + 0.515132i \(0.827743\pi\)
\(572\) −14.0852 −0.588933
\(573\) −0.962624 −0.0402142
\(574\) −7.51251 + 7.51251i −0.313566 + 0.313566i
\(575\) −9.20715 + 17.7016i −0.383965 + 0.738209i
\(576\) 2.99544i 0.124810i
\(577\) −7.71924 −0.321356 −0.160678 0.987007i \(-0.551368\pi\)
−0.160678 + 0.987007i \(0.551368\pi\)
\(578\) 3.68477i 0.153266i
\(579\) −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
\(587\) 5.39311i 0.222597i 0.993787 + 0.111299i \(0.0355010\pi\)
−0.993787 + 0.111299i \(0.964499\pi\)
\(588\) −0.403701 0.403701i −0.0166483 0.0166483i
\(589\) 36.8607i 1.51882i
\(590\) 13.2000 + 21.7445i 0.543437 + 0.895209i
\(591\) 1.61305i 0.0663521i
\(592\) −4.65727 + 3.91278i −0.191412 + 0.160814i
\(593\) −10.4329 10.4329i −0.428427 0.428427i 0.459665 0.888092i \(-0.347969\pi\)
−0.888092 + 0.459665i \(0.847969\pi\)
\(594\) −1.21424 1.21424i −0.0498210 0.0498210i
\(595\) −27.4214 + 16.6462i −1.12417 + 0.682427i
\(596\) 17.7144i 0.725610i
\(597\) 0.0549981 0.00225092
\(598\) 13.2492i 0.541798i
\(599\) 19.3788i 0.791798i −0.918294 0.395899i \(-0.870433\pi\)
0.918294 0.395899i \(-0.129567\pi\)
\(600\) 0.101618 + 0.321906i 0.00414855 + 0.0131418i
\(601\) −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
\(605\) −15.2002 3.71671i −0.617978 0.151106i
\(606\) 0.0722968 0.0722968i 0.00293686 0.00293686i
\(607\) 29.8434i 1.21131i −0.795729 0.605653i \(-0.792912\pi\)
0.795729 0.605653i \(-0.207088\pi\)
\(608\) −4.65117 4.65117i −0.188630 0.188630i
\(609\) −0.346929 + 0.346929i −0.0140583 + 0.0140583i
\(610\) 2.54780 + 4.19702i 0.103158 + 0.169932i
\(611\) 4.45554 + 4.45554i 0.180252 + 0.180252i
\(612\) 10.9304i 0.441834i
\(613\) −7.97850 + 7.97850i −0.322248 + 0.322248i −0.849629 0.527381i \(-0.823174\pi\)
0.527381 + 0.849629i \(0.323174\pi\)
\(614\) 16.1006 16.1006i 0.649766 0.649766i
\(615\) 0.211699 + 0.348733i 0.00853651 + 0.0140623i
\(616\) 11.7938 11.7938i 0.475184 0.475184i
\(617\) −21.2579 21.2579i −0.855812 0.855812i 0.135030 0.990842i \(-0.456887\pi\)
−0.990842 + 0.135030i \(0.956887\pi\)
\(618\) 0.185588 + 0.185588i 0.00746545 + 0.00746545i
\(619\) 7.54167 0.303125 0.151563 0.988448i \(-0.451569\pi\)
0.151563 + 0.988448i \(0.451569\pi\)
\(620\) −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
\(623\) 43.1257 1.72779
\(624\) −0.158498 0.158498i −0.00634500 0.00634500i
\(625\) 14.3535 + 20.4689i 0.574139 + 0.818758i
\(626\) 21.7608 0.869735
\(627\) −1.88398 −0.0752390
\(628\) 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
\(635\) 1.84738 1.12145i 0.0733110 0.0445034i
\(636\) 0.513076 0.0203448
\(637\) 28.0763 1.11242
\(638\) −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 \(0.577475\pi\)
\(642\) −0.0702953 −0.00277433
\(643\) −26.4268 −1.04217 −0.521085 0.853505i \(-0.674472\pi\)
−0.521085 + 0.853505i \(0.674472\pi\)
\(644\) 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
\(647\) 23.6177i 0.928509i 0.885702 + 0.464255i \(0.153678\pi\)
−0.885702 + 0.464255i \(0.846322\pi\)
\(648\) 8.95900i 0.351943i
\(649\) −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
\(652\) 21.7952 0.853566
\(653\) −11.5143 −0.450588 −0.225294 0.974291i \(-0.572334\pi\)
−0.225294 + 0.974291i \(0.572334\pi\)
\(654\) 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
\(658\) −7.46137 −0.290875
\(659\) 45.6299 1.77749 0.888744 0.458404i \(-0.151579\pi\)
0.888744 + 0.458404i \(0.151579\pi\)
\(660\) −0.332342 0.547470i −0.0129364 0.0213102i
\(661\) −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
\(668\) 11.1575 0.431697
\(669\) −1.33975 −0.0517976
\(670\) −11.7341 + 7.12321i −0.453329 + 0.275194i
\(671\) −6.58685 6.58685i −0.254282 0.254282i
\(672\) 0.265425 0.0102390
\(673\) −25.0377 25.0377i −0.965134 0.965134i 0.0342781 0.999412i \(-0.489087\pi\)
−0.999412 + 0.0342781i \(0.989087\pi\)
\(674\) 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 \(-0.319967\pi\)
−0.844273 + 0.535914i \(0.819967\pi\)
\(678\) 0.201939 + 0.201939i 0.00775543 + 0.00775543i
\(679\) −27.9250 + 27.9250i −1.07166 + 1.07166i
\(680\) 1.93802 7.92592i 0.0743196 0.303945i
\(681\) 0.812006 0.812006i 0.0311161 0.0311161i
\(682\) 16.8106 16.8106i 0.643712 0.643712i
\(683\) 14.7249i 0.563434i −0.959498 0.281717i \(-0.909096\pi\)
0.959498 0.281717i \(-0.0909039\pi\)
\(684\) 13.9323 + 13.9323i 0.532715 + 0.532715i
\(685\) 41.7456 25.3417i 1.59502 0.968255i
\(686\) −4.04887 + 4.04887i −0.154586 + 0.154586i
\(687\) −0.405365 0.405365i −0.0154656 0.0154656i
\(688\) 6.95570i 0.265184i
\(689\) −17.8415 + 17.8415i −0.679707 + 0.679707i
\(690\) 0.514973 0.312614i 0.0196047 0.0119010i
\(691\) 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
\(695\) −38.7497 9.47495i −1.46986 0.359405i
\(696\) 0.124796i 0.00473038i
\(697\) 9.86097i 0.373511i
\(698\) 31.6855 1.19931
\(699\) 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
\(703\) 3.46271 39.8608i 0.130599 1.50338i
\(704\) 4.24241i 0.159892i
\(705\) −0.0680510 + 0.278308i −0.00256295 + 0.0104817i
\(706\) 15.6047i 0.587291i
\(707\) −4.21005 4.21005i −0.158335 0.158335i
\(708\) 0.768026i 0.0288642i
\(709\) −24.5474 + 24.5474i −0.921895 + 0.921895i −0.997163 0.0752682i \(-0.976019\pi\)
0.0752682 + 0.997163i \(0.476019\pi\)
\(710\) −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
\(717\) 1.39752i 0.0521913i
\(718\) −34.4499 −1.28566
\(719\) 12.2897i 0.458329i −0.973388 0.229164i \(-0.926401\pi\)
0.973388 0.229164i \(-0.0735993\pi\)
\(720\) −1.59091 + 6.50633i −0.0592895 + 0.242477i
\(721\) 10.8073 10.8073i 0.402486 0.402486i
\(722\) 24.2668 0.903116
\(723\) −1.00663 −0.0374368
\(724\) −12.8145 −0.476247
\(725\) −2.78226 8.81366i −0.103331 0.327331i
\(726\) 0.334077 + 0.334077i 0.0123988 + 0.0123988i
\(727\) 12.2686i 0.455016i −0.973776 0.227508i \(-0.926942\pi\)
0.973776 0.227508i \(-0.0730579\pi\)
\(728\) −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
\(732\) 0.148241i 0.00547913i
\(733\) 26.4738 26.4738i 0.977831 0.977831i −0.0219285 0.999760i \(-0.506981\pi\)
0.999760 + 0.0219285i \(0.00698063\pi\)
\(734\) −4.61443 4.61443i −0.170322 0.170322i
\(735\) 0.662461 + 1.09128i 0.0244352 + 0.0402524i
\(736\) −3.99058 −0.147095
\(737\) 18.4157 18.4157i 0.678350 0.678350i
\(738\) 8.09481i 0.297974i
\(739\) 23.9200 0.879912 0.439956 0.898019i \(-0.354994\pi\)
0.439956 + 0.898019i \(0.354994\pi\)
\(740\) 12.1941 6.02536i 0.448263 0.221497i
\(741\) 1.47440 0.0541635
\(742\) 29.8779i 1.09685i
\(743\) 8.98938 8.98938i 0.329788 0.329788i −0.522718 0.852506i \(-0.675082\pi\)
0.852506 + 0.522718i \(0.175082\pi\)
\(744\) 0.378332 0.0138703
\(745\) 9.40827 38.4771i 0.344692 1.40969i
\(746\) −15.3464 15.3464i −0.561872 0.561872i
\(747\) −21.2113 + 21.2113i −0.776080 + 0.776080i
\(748\) 15.4806i 0.566025i
\(749\) 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
\(753\) 1.55047i 0.0565022i
\(754\) 4.33961 + 4.33961i 0.158039 + 0.158039i
\(755\) 2.93719 12.0123i 0.106895 0.437171i
\(756\) −1.59134 −0.0578765
\(757\) 2.66868 0.0969950 0.0484975 0.998823i \(-0.484557\pi\)
0.0484975 + 0.998823i \(0.484557\pi\)
\(758\) 23.4892 0.853164
\(759\) −0.808204 + 0.808204i −0.0293359 + 0.0293359i
\(760\) 7.63243 + 12.5730i 0.276857 + 0.456070i
\(761\) 50.1338i 1.81735i 0.417507 + 0.908674i \(0.362904\pi\)
−0.417507 + 0.908674i \(0.637096\pi\)
\(762\) −0.0652502 −0.00236376
\(763\) 9.60230i 0.347626i
\(764\) −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 \(-0.895654\pi\)
−0.321974 0.946748i \(-0.604346\pi\)
\(770\) −31.8807 + 19.3532i −1.14890 + 0.697441i
\(771\) −0.238888 + 0.238888i −0.00860335 + 0.00860335i
\(772\) 7.58052i 0.272829i
\(773\) −5.35033 5.35033i −0.192438 0.192438i 0.604311 0.796749i \(-0.293449\pi\)
−0.796749 + 0.604311i \(0.793449\pi\)
\(774\) 20.8354i 0.748913i
\(775\) 26.7195 8.43473i 0.959793 0.302984i
\(776\) 10.0451i 0.360597i
\(777\) 1.03855 + 1.23615i 0.0372578 +