Properties

Label 637.2.x.b.215.3
Level $637$
Weight $2$
Character 637.215
Analytic conductor $5.086$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.x (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 215.3
Character \(\chi\) \(=\) 637.215
Dual form 637.2.x.b.80.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0302180 - 0.112775i) q^{2} -2.59871i q^{3} +(1.72025 + 0.993184i) q^{4} +(0.456951 + 1.70537i) q^{5} +(-0.293070 - 0.0785278i) q^{6} +(0.329103 - 0.329103i) q^{8} -3.75328 q^{9} +O(q^{10})\) \(q+(0.0302180 - 0.112775i) q^{2} -2.59871i q^{3} +(1.72025 + 0.993184i) q^{4} +(0.456951 + 1.70537i) q^{5} +(-0.293070 - 0.0785278i) q^{6} +(0.329103 - 0.329103i) q^{8} -3.75328 q^{9} +0.206131 q^{10} +(-1.38433 + 1.38433i) q^{11} +(2.58100 - 4.47042i) q^{12} +(1.85749 - 3.09026i) q^{13} +(4.43175 - 1.18748i) q^{15} +(1.95920 + 3.39343i) q^{16} +(2.13907 - 3.70498i) q^{17} +(-0.113417 + 0.423277i) q^{18} +(3.01787 - 3.01787i) q^{19} +(-0.907674 + 3.38749i) q^{20} +(0.114286 + 0.197949i) q^{22} +(5.53927 - 3.19810i) q^{23} +(-0.855244 - 0.855244i) q^{24} +(1.63066 - 0.941462i) q^{25} +(-0.292376 - 0.302861i) q^{26} +1.95756i q^{27} +(-3.57954 + 6.19995i) q^{29} -0.535675i q^{30} +(-4.13397 - 1.10769i) q^{31} +(1.34103 - 0.359327i) q^{32} +(3.59746 + 3.59746i) q^{33} +(-0.353191 - 0.353191i) q^{34} +(-6.45657 - 3.72770i) q^{36} +(2.73261 + 0.732202i) q^{37} +(-0.249147 - 0.431534i) q^{38} +(-8.03069 - 4.82707i) q^{39} +(0.711626 + 0.410857i) q^{40} +(2.94901 + 11.0059i) q^{41} +(-1.55234 + 0.896243i) q^{43} +(-3.75627 + 1.00649i) q^{44} +(-1.71507 - 6.40072i) q^{45} +(-0.193281 - 0.721333i) q^{46} +(-6.40208 + 1.71543i) q^{47} +(8.81854 - 5.09139i) q^{48} +(-0.0568982 - 0.212347i) q^{50} +(-9.62816 - 5.55882i) q^{51} +(6.26454 - 3.47118i) q^{52} +(-2.13896 - 3.70479i) q^{53} +(0.220765 + 0.0591537i) q^{54} +(-2.99335 - 1.72821i) q^{55} +(-7.84255 - 7.84255i) q^{57} +(0.591034 + 0.591034i) q^{58} +(-1.62980 + 0.436704i) q^{59} +(8.80308 + 2.35878i) q^{60} -3.08259i q^{61} +(-0.249841 + 0.432737i) q^{62} +7.67470i q^{64} +(6.11881 + 1.75560i) q^{65} +(0.514413 - 0.296996i) q^{66} +(0.0139368 + 0.0139368i) q^{67} +(7.35945 - 4.24898i) q^{68} +(-8.31093 - 14.3949i) q^{69} +(1.23109 - 4.59449i) q^{71} +(-1.23522 + 1.23522i) q^{72} +(-0.255666 + 0.954158i) q^{73} +(0.165148 - 0.286046i) q^{74} +(-2.44658 - 4.23761i) q^{75} +(8.18877 - 2.19417i) q^{76} +(-0.787046 + 0.759799i) q^{78} +(2.96860 - 5.14176i) q^{79} +(-4.89178 + 4.89178i) q^{80} -6.17272 q^{81} +1.33030 q^{82} +(-9.87683 + 9.87683i) q^{83} +(7.29580 + 1.95490i) q^{85} +(0.0541654 + 0.202148i) q^{86} +(16.1119 + 9.30218i) q^{87} +0.911173i q^{88} +(-2.07993 + 7.76240i) q^{89} -0.773669 q^{90} +12.7052 q^{92} +(-2.87857 + 10.7430i) q^{93} +0.773833i q^{94} +(6.52558 + 3.76755i) q^{95} +(-0.933785 - 3.48493i) q^{96} +(-14.2676 - 3.82300i) q^{97} +(5.19577 - 5.19577i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 4q^{2} + 12q^{4} - 16q^{8} - 16q^{9} + O(q^{10}) \) \( 32q + 4q^{2} + 12q^{4} - 16q^{8} - 16q^{9} + 20q^{11} - 8q^{15} + 12q^{16} - 64q^{18} + 4q^{22} + 12q^{23} + 4q^{29} + 64q^{32} + 4q^{37} + 36q^{39} - 48q^{43} - 84q^{44} - 108q^{46} - 44q^{50} + 12q^{51} - 36q^{53} - 92q^{57} + 44q^{58} + 28q^{60} + 28q^{65} + 64q^{67} + 84q^{71} + 4q^{72} - 24q^{74} + 148q^{78} + 40q^{79} - 56q^{81} + 36q^{85} + 108q^{86} + 24q^{92} - 24q^{93} + 84q^{95} - 60q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{11}{12}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0302180 0.112775i 0.0213674 0.0797441i −0.954419 0.298471i \(-0.903524\pi\)
0.975786 + 0.218726i \(0.0701902\pi\)
\(3\) 2.59871i 1.50036i −0.661231 0.750182i \(-0.729966\pi\)
0.661231 0.750182i \(-0.270034\pi\)
\(4\) 1.72025 + 0.993184i 0.860123 + 0.496592i
\(5\) 0.456951 + 1.70537i 0.204355 + 0.762663i 0.989645 + 0.143535i \(0.0458470\pi\)
−0.785290 + 0.619128i \(0.787486\pi\)
\(6\) −0.293070 0.0785278i −0.119645 0.0320589i
\(7\) 0 0
\(8\) 0.329103 0.329103i 0.116356 0.116356i
\(9\) −3.75328 −1.25109
\(10\) 0.206131 0.0651844
\(11\) −1.38433 + 1.38433i −0.417390 + 0.417390i −0.884303 0.466913i \(-0.845366\pi\)
0.466913 + 0.884303i \(0.345366\pi\)
\(12\) 2.58100 4.47042i 0.745069 1.29050i
\(13\) 1.85749 3.09026i 0.515175 0.857085i
\(14\) 0 0
\(15\) 4.43175 1.18748i 1.14427 0.306607i
\(16\) 1.95920 + 3.39343i 0.489800 + 0.848358i
\(17\) 2.13907 3.70498i 0.518801 0.898589i −0.480960 0.876742i \(-0.659712\pi\)
0.999761 0.0218471i \(-0.00695471\pi\)
\(18\) −0.113417 + 0.423277i −0.0267326 + 0.0997674i
\(19\) 3.01787 3.01787i 0.692346 0.692346i −0.270402 0.962748i \(-0.587157\pi\)
0.962748 + 0.270402i \(0.0871566\pi\)
\(20\) −0.907674 + 3.38749i −0.202962 + 0.757465i
\(21\) 0 0
\(22\) 0.114286 + 0.197949i 0.0243659 + 0.0422030i
\(23\) 5.53927 3.19810i 1.15502 0.666850i 0.204913 0.978780i \(-0.434309\pi\)
0.950105 + 0.311930i \(0.100976\pi\)
\(24\) −0.855244 0.855244i −0.174576 0.174576i
\(25\) 1.63066 0.941462i 0.326132 0.188292i
\(26\) −0.292376 0.302861i −0.0573396 0.0593959i
\(27\) 1.95756i 0.376733i
\(28\) 0 0
\(29\) −3.57954 + 6.19995i −0.664704 + 1.15130i 0.314661 + 0.949204i \(0.398109\pi\)
−0.979365 + 0.202097i \(0.935224\pi\)
\(30\) 0.535675i 0.0978004i
\(31\) −4.13397 1.10769i −0.742483 0.198948i −0.132302 0.991210i \(-0.542237\pi\)
−0.610181 + 0.792262i \(0.708903\pi\)
\(32\) 1.34103 0.359327i 0.237062 0.0635206i
\(33\) 3.59746 + 3.59746i 0.626237 + 0.626237i
\(34\) −0.353191 0.353191i −0.0605718 0.0605718i
\(35\) 0 0
\(36\) −6.45657 3.72770i −1.07609 0.621284i
\(37\) 2.73261 + 0.732202i 0.449239 + 0.120373i 0.476343 0.879259i \(-0.341962\pi\)
−0.0271042 + 0.999633i \(0.508629\pi\)
\(38\) −0.249147 0.431534i −0.0404169 0.0700041i
\(39\) −8.03069 4.82707i −1.28594 0.772951i
\(40\) 0.711626 + 0.410857i 0.112518 + 0.0649623i
\(41\) 2.94901 + 11.0059i 0.460558 + 1.71883i 0.671212 + 0.741266i \(0.265774\pi\)
−0.210654 + 0.977561i \(0.567559\pi\)
\(42\) 0 0
\(43\) −1.55234 + 0.896243i −0.236730 + 0.136676i −0.613673 0.789561i \(-0.710309\pi\)
0.376943 + 0.926236i \(0.376975\pi\)
\(44\) −3.75627 + 1.00649i −0.566279 + 0.151734i
\(45\) −1.71507 6.40072i −0.255667 0.954163i
\(46\) −0.193281 0.721333i −0.0284977 0.106355i
\(47\) −6.40208 + 1.71543i −0.933839 + 0.250222i −0.693491 0.720465i \(-0.743928\pi\)
−0.240348 + 0.970687i \(0.577262\pi\)
\(48\) 8.81854 5.09139i 1.27285 0.734878i
\(49\) 0 0
\(50\) −0.0568982 0.212347i −0.00804663 0.0300304i
\(51\) −9.62816 5.55882i −1.34821 0.778390i
\(52\) 6.26454 3.47118i 0.868736 0.481366i
\(53\) −2.13896 3.70479i −0.293809 0.508893i 0.680898 0.732378i \(-0.261590\pi\)
−0.974707 + 0.223486i \(0.928256\pi\)
\(54\) 0.220765 + 0.0591537i 0.0300423 + 0.00804980i
\(55\) −2.99335 1.72821i −0.403624 0.233032i
\(56\) 0 0
\(57\) −7.84255 7.84255i −1.03877 1.03877i
\(58\) 0.591034 + 0.591034i 0.0776066 + 0.0776066i
\(59\) −1.62980 + 0.436704i −0.212182 + 0.0568541i −0.363344 0.931655i \(-0.618365\pi\)
0.151162 + 0.988509i \(0.451698\pi\)
\(60\) 8.80308 + 2.35878i 1.13647 + 0.304517i
\(61\) 3.08259i 0.394685i −0.980335 0.197342i \(-0.936769\pi\)
0.980335 0.197342i \(-0.0632311\pi\)
\(62\) −0.249841 + 0.432737i −0.0317298 + 0.0549577i
\(63\) 0 0
\(64\) 7.67470i 0.959338i
\(65\) 6.11881 + 1.75560i 0.758945 + 0.217755i
\(66\) 0.514413 0.296996i 0.0633198 0.0365577i
\(67\) 0.0139368 + 0.0139368i 0.00170265 + 0.00170265i 0.707958 0.706255i \(-0.249617\pi\)
−0.706255 + 0.707958i \(0.749617\pi\)
\(68\) 7.35945 4.24898i 0.892465 0.515265i
\(69\) −8.31093 14.3949i −1.00052 1.73295i
\(70\) 0 0
\(71\) 1.23109 4.59449i 0.146104 0.545266i −0.853600 0.520929i \(-0.825586\pi\)
0.999704 0.0243373i \(-0.00774758\pi\)
\(72\) −1.23522 + 1.23522i −0.145572 + 0.145572i
\(73\) −0.255666 + 0.954158i −0.0299234 + 0.111676i −0.979272 0.202548i \(-0.935078\pi\)
0.949349 + 0.314224i \(0.101744\pi\)
\(74\) 0.165148 0.286046i 0.0191981 0.0332521i
\(75\) −2.44658 4.23761i −0.282507 0.489317i
\(76\) 8.18877 2.19417i 0.939316 0.251689i
\(77\) 0 0
\(78\) −0.787046 + 0.759799i −0.0891154 + 0.0860303i
\(79\) 2.96860 5.14176i 0.333993 0.578493i −0.649298 0.760534i \(-0.724937\pi\)
0.983291 + 0.182041i \(0.0582704\pi\)
\(80\) −4.89178 + 4.89178i −0.546918 + 0.546918i
\(81\) −6.17272 −0.685857
\(82\) 1.33030 0.146907
\(83\) −9.87683 + 9.87683i −1.08412 + 1.08412i −0.0880033 + 0.996120i \(0.528049\pi\)
−0.996120 + 0.0880033i \(0.971951\pi\)
\(84\) 0 0
\(85\) 7.29580 + 1.95490i 0.791340 + 0.212039i
\(86\) 0.0541654 + 0.202148i 0.00584081 + 0.0217982i
\(87\) 16.1119 + 9.30218i 1.72737 + 0.997299i
\(88\) 0.911173i 0.0971314i
\(89\) −2.07993 + 7.76240i −0.220472 + 0.822813i 0.763696 + 0.645576i \(0.223383\pi\)
−0.984168 + 0.177237i \(0.943284\pi\)
\(90\) −0.773669 −0.0815519
\(91\) 0 0
\(92\) 12.7052 1.32461
\(93\) −2.87857 + 10.7430i −0.298494 + 1.11400i
\(94\) 0.773833i 0.0798148i
\(95\) 6.52558 + 3.76755i 0.669511 + 0.386542i
\(96\) −0.933785 3.48493i −0.0953041 0.355680i
\(97\) −14.2676 3.82300i −1.44866 0.388167i −0.553102 0.833113i \(-0.686556\pi\)
−0.895557 + 0.444946i \(0.853223\pi\)
\(98\) 0 0
\(99\) 5.19577 5.19577i 0.522194 0.522194i
\(100\) 3.74018 0.374018
\(101\) −16.0096 −1.59301 −0.796506 0.604630i \(-0.793321\pi\)
−0.796506 + 0.604630i \(0.793321\pi\)
\(102\) −0.917841 + 0.917841i −0.0908798 + 0.0908798i
\(103\) −5.90755 + 10.2322i −0.582088 + 1.00821i 0.413143 + 0.910666i \(0.364431\pi\)
−0.995232 + 0.0975405i \(0.968902\pi\)
\(104\) −0.405710 1.62832i −0.0397831 0.159670i
\(105\) 0 0
\(106\) −0.482444 + 0.129271i −0.0468591 + 0.0125559i
\(107\) −3.99556 6.92051i −0.386265 0.669031i 0.605679 0.795709i \(-0.292902\pi\)
−0.991944 + 0.126678i \(0.959568\pi\)
\(108\) −1.94422 + 3.36749i −0.187083 + 0.324037i
\(109\) −3.20509 + 11.9616i −0.306992 + 1.14571i 0.624225 + 0.781245i \(0.285415\pi\)
−0.931217 + 0.364465i \(0.881252\pi\)
\(110\) −0.285353 + 0.285353i −0.0272073 + 0.0272073i
\(111\) 1.90278 7.10127i 0.180604 0.674022i
\(112\) 0 0
\(113\) 4.27217 + 7.39961i 0.401892 + 0.696097i 0.993954 0.109795i \(-0.0350195\pi\)
−0.592063 + 0.805892i \(0.701686\pi\)
\(114\) −1.12143 + 0.647459i −0.105032 + 0.0606401i
\(115\) 7.98511 + 7.98511i 0.744615 + 0.744615i
\(116\) −12.3154 + 7.11029i −1.14345 + 0.660174i
\(117\) −6.97169 + 11.5986i −0.644533 + 1.07229i
\(118\) 0.196998i 0.0181351i
\(119\) 0 0
\(120\) 1.06770 1.84931i 0.0974671 0.168818i
\(121\) 7.16728i 0.651571i
\(122\) −0.347640 0.0931497i −0.0314738 0.00843338i
\(123\) 28.6010 7.66362i 2.57887 0.691005i
\(124\) −6.01130 6.01130i −0.539831 0.539831i
\(125\) 8.59274 + 8.59274i 0.768558 + 0.768558i
\(126\) 0 0
\(127\) −5.29483 3.05697i −0.469840 0.271262i 0.246333 0.969185i \(-0.420774\pi\)
−0.716173 + 0.697923i \(0.754108\pi\)
\(128\) 3.54757 + 0.950568i 0.313564 + 0.0840191i
\(129\) 2.32907 + 4.03408i 0.205064 + 0.355181i
\(130\) 0.382887 0.637000i 0.0335814 0.0558686i
\(131\) 4.99207 + 2.88218i 0.436159 + 0.251817i 0.701967 0.712209i \(-0.252305\pi\)
−0.265808 + 0.964026i \(0.585639\pi\)
\(132\) 2.61557 + 9.76146i 0.227657 + 0.849626i
\(133\) 0 0
\(134\) 0.00199287 0.00115058i 0.000172157 9.93951e-5i
\(135\) −3.33836 + 0.894511i −0.287320 + 0.0769872i
\(136\) −0.515346 1.92330i −0.0441905 0.164921i
\(137\) 1.62427 + 6.06188i 0.138771 + 0.517901i 0.999954 + 0.00960548i \(0.00305757\pi\)
−0.861183 + 0.508296i \(0.830276\pi\)
\(138\) −1.87453 + 0.502280i −0.159571 + 0.0427569i
\(139\) 18.1314 10.4682i 1.53789 0.887900i 0.538927 0.842353i \(-0.318830\pi\)
0.998962 0.0455477i \(-0.0145033\pi\)
\(140\) 0 0
\(141\) 4.45791 + 16.6371i 0.375424 + 1.40110i
\(142\) −0.480944 0.277673i −0.0403599 0.0233018i
\(143\) 1.70656 + 6.84931i 0.142710 + 0.572768i
\(144\) −7.35343 12.7365i −0.612786 1.06138i
\(145\) −12.2089 3.27135i −1.01389 0.271671i
\(146\) 0.0998797 + 0.0576656i 0.00826610 + 0.00477244i
\(147\) 0 0
\(148\) 3.97356 + 3.97356i 0.326624 + 0.326624i
\(149\) 10.9301 + 10.9301i 0.895431 + 0.895431i 0.995028 0.0995972i \(-0.0317554\pi\)
−0.0995972 + 0.995028i \(0.531755\pi\)
\(150\) −0.551828 + 0.147862i −0.0450566 + 0.0120729i
\(151\) −4.27019 1.14419i −0.347503 0.0931131i 0.0808459 0.996727i \(-0.474238\pi\)
−0.428349 + 0.903614i \(0.640905\pi\)
\(152\) 1.98638i 0.161117i
\(153\) −8.02854 + 13.9058i −0.649069 + 1.12422i
\(154\) 0 0
\(155\) 7.55609i 0.606920i
\(156\) −9.02059 16.2797i −0.722225 1.30342i
\(157\) −6.00211 + 3.46532i −0.479020 + 0.276563i −0.720008 0.693966i \(-0.755862\pi\)
0.240988 + 0.970528i \(0.422529\pi\)
\(158\) −0.490158 0.490158i −0.0389949 0.0389949i
\(159\) −9.62768 + 5.55854i −0.763525 + 0.440821i
\(160\) 1.22557 + 2.12274i 0.0968896 + 0.167818i
\(161\) 0 0
\(162\) −0.186527 + 0.696129i −0.0146550 + 0.0546931i
\(163\) 9.14651 9.14651i 0.716410 0.716410i −0.251458 0.967868i \(-0.580910\pi\)
0.967868 + 0.251458i \(0.0809101\pi\)
\(164\) −5.85782 + 21.8617i −0.457419 + 1.70711i
\(165\) −4.49112 + 7.77885i −0.349633 + 0.605583i
\(166\) 0.815404 + 1.41232i 0.0632876 + 0.109617i
\(167\) 0.900490 0.241286i 0.0696820 0.0186712i −0.223810 0.974633i \(-0.571849\pi\)
0.293492 + 0.955962i \(0.405183\pi\)
\(168\) 0 0
\(169\) −6.09946 11.4803i −0.469189 0.883098i
\(170\) 0.440929 0.763712i 0.0338177 0.0585740i
\(171\) −11.3269 + 11.3269i −0.866190 + 0.866190i
\(172\) −3.56054 −0.271489
\(173\) −0.527560 −0.0401096 −0.0200548 0.999799i \(-0.506384\pi\)
−0.0200548 + 0.999799i \(0.506384\pi\)
\(174\) 1.53592 1.53592i 0.116438 0.116438i
\(175\) 0 0
\(176\) −7.40979 1.98545i −0.558534 0.149659i
\(177\) 1.13487 + 4.23538i 0.0853018 + 0.318351i
\(178\) 0.812555 + 0.469129i 0.0609036 + 0.0351627i
\(179\) 8.27003i 0.618131i −0.951041 0.309066i \(-0.899984\pi\)
0.951041 0.309066i \(-0.100016\pi\)
\(180\) 3.40676 12.7142i 0.253925 0.947660i
\(181\) −14.9785 −1.11334 −0.556672 0.830732i \(-0.687922\pi\)
−0.556672 + 0.830732i \(0.687922\pi\)
\(182\) 0 0
\(183\) −8.01075 −0.592171
\(184\) 0.770488 2.87550i 0.0568011 0.211985i
\(185\) 4.99469i 0.367217i
\(186\) 1.12456 + 0.649263i 0.0824565 + 0.0476063i
\(187\) 2.16773 + 8.09007i 0.158520 + 0.591605i
\(188\) −12.7169 3.40748i −0.927475 0.248516i
\(189\) 0 0
\(190\) 0.622076 0.622076i 0.0451301 0.0451301i
\(191\) −14.5292 −1.05130 −0.525649 0.850702i \(-0.676177\pi\)
−0.525649 + 0.850702i \(0.676177\pi\)
\(192\) 19.9443 1.43936
\(193\) 13.8436 13.8436i 0.996483 0.996483i −0.00351052 0.999994i \(-0.501117\pi\)
0.999994 + 0.00351052i \(0.00111744\pi\)
\(194\) −0.862280 + 1.49351i −0.0619081 + 0.107228i
\(195\) 4.56229 15.9010i 0.326712 1.13869i
\(196\) 0 0
\(197\) −21.0175 + 5.63163i −1.49744 + 0.401237i −0.912240 0.409655i \(-0.865649\pi\)
−0.585196 + 0.810892i \(0.698982\pi\)
\(198\) −0.428948 0.742960i −0.0304840 0.0527999i
\(199\) 9.64065 16.6981i 0.683408 1.18370i −0.290527 0.956867i \(-0.593830\pi\)
0.973934 0.226830i \(-0.0728362\pi\)
\(200\) 0.226817 0.846494i 0.0160384 0.0598562i
\(201\) 0.0362176 0.0362176i 0.00255459 0.00255459i
\(202\) −0.483778 + 1.80548i −0.0340385 + 0.127033i
\(203\) 0 0
\(204\) −11.0419 19.1251i −0.773085 1.33902i
\(205\) −17.4215 + 10.0583i −1.21677 + 0.702501i
\(206\) 0.975422 + 0.975422i 0.0679609 + 0.0679609i
\(207\) −20.7905 + 12.0034i −1.44504 + 0.834292i
\(208\) 14.1258 + 0.248825i 0.979447 + 0.0172529i
\(209\) 8.35542i 0.577957i
\(210\) 0 0
\(211\) 1.51130 2.61764i 0.104042 0.180206i −0.809304 0.587389i \(-0.800156\pi\)
0.913346 + 0.407184i \(0.133489\pi\)
\(212\) 8.49754i 0.583614i
\(213\) −11.9397 3.19925i −0.818098 0.219209i
\(214\) −0.901200 + 0.241476i −0.0616048 + 0.0165070i
\(215\) −2.23777 2.23777i −0.152614 0.152614i
\(216\) 0.644241 + 0.644241i 0.0438350 + 0.0438350i
\(217\) 0 0
\(218\) 1.25212 + 0.722910i 0.0848040 + 0.0489616i
\(219\) 2.47958 + 0.664401i 0.167554 + 0.0448961i
\(220\) −3.43287 5.94590i −0.231444 0.400873i
\(221\) −7.47606 13.4923i −0.502894 0.907587i
\(222\) −0.743349 0.429173i −0.0498903 0.0288042i
\(223\) −1.13865 4.24949i −0.0762495 0.284567i 0.917264 0.398279i \(-0.130392\pi\)
−0.993514 + 0.113712i \(0.963726\pi\)
\(224\) 0 0
\(225\) −6.12033 + 3.53357i −0.408022 + 0.235571i
\(226\) 0.963589 0.258193i 0.0640970 0.0171747i
\(227\) −1.06086 3.95917i −0.0704116 0.262780i 0.921742 0.387803i \(-0.126766\pi\)
−0.992154 + 0.125024i \(0.960099\pi\)
\(228\) −5.70202 21.2802i −0.377625 1.40932i
\(229\) 13.1144 3.51399i 0.866623 0.232211i 0.201996 0.979386i \(-0.435257\pi\)
0.664627 + 0.747176i \(0.268591\pi\)
\(230\) 1.14182 0.659228i 0.0752892 0.0434682i
\(231\) 0 0
\(232\) 0.862385 + 3.21846i 0.0566183 + 0.211303i
\(233\) 14.1595 + 8.17501i 0.927622 + 0.535563i 0.886059 0.463573i \(-0.153433\pi\)
0.0415633 + 0.999136i \(0.486766\pi\)
\(234\) 1.09737 + 1.13672i 0.0717372 + 0.0743098i
\(235\) −5.85088 10.1340i −0.381669 0.661071i
\(236\) −3.23739 0.867456i −0.210736 0.0564666i
\(237\) −13.3619 7.71452i −0.867951 0.501112i
\(238\) 0 0
\(239\) 6.11495 + 6.11495i 0.395543 + 0.395543i 0.876658 0.481115i \(-0.159768\pi\)
−0.481115 + 0.876658i \(0.659768\pi\)
\(240\) 12.7123 + 12.7123i 0.820577 + 0.820577i
\(241\) 12.9736 3.47625i 0.835700 0.223925i 0.184501 0.982832i \(-0.440933\pi\)
0.651199 + 0.758907i \(0.274266\pi\)
\(242\) 0.808292 + 0.216581i 0.0519590 + 0.0139224i
\(243\) 21.9138i 1.40577i
\(244\) 3.06158 5.30281i 0.195997 0.339478i
\(245\) 0 0
\(246\) 3.45707i 0.220414i
\(247\) −3.72034 14.9317i −0.236720 0.950078i
\(248\) −1.72505 + 0.995958i −0.109541 + 0.0632434i
\(249\) 25.6670 + 25.6670i 1.62658 + 1.62658i
\(250\) 1.22870 0.709393i 0.0777101 0.0448659i
\(251\) 1.74301 + 3.01899i 0.110018 + 0.190557i 0.915777 0.401686i \(-0.131576\pi\)
−0.805759 + 0.592243i \(0.798242\pi\)
\(252\) 0 0
\(253\) −3.24095 + 12.0954i −0.203756 + 0.760430i
\(254\) −0.504750 + 0.504750i −0.0316708 + 0.0316708i
\(255\) 5.08022 18.9596i 0.318136 1.18730i
\(256\) −7.46030 + 12.9216i −0.466269 + 0.807601i
\(257\) −6.72396 11.6462i −0.419429 0.726472i 0.576453 0.817130i \(-0.304436\pi\)
−0.995882 + 0.0906578i \(0.971103\pi\)
\(258\) 0.525324 0.140760i 0.0327052 0.00876334i
\(259\) 0 0
\(260\) 8.78223 + 9.09717i 0.544651 + 0.564183i
\(261\) 13.4350 23.2702i 0.831608 1.44039i
\(262\) 0.475889 0.475889i 0.0294005 0.0294005i
\(263\) 20.5358 1.26629 0.633147 0.774032i \(-0.281763\pi\)
0.633147 + 0.774032i \(0.281763\pi\)
\(264\) 2.36787 0.145733
\(265\) 5.34063 5.34063i 0.328072 0.328072i
\(266\) 0 0
\(267\) 20.1722 + 5.40513i 1.23452 + 0.330788i
\(268\) 0.0101329 + 0.0378165i 0.000618965 + 0.00231001i
\(269\) −9.29875 5.36864i −0.566955 0.327332i 0.188977 0.981981i \(-0.439483\pi\)
−0.755932 + 0.654650i \(0.772816\pi\)
\(270\) 0.403515i 0.0245571i
\(271\) −0.387901 + 1.44767i −0.0235633 + 0.0879396i −0.976706 0.214581i \(-0.931161\pi\)
0.953143 + 0.302521i \(0.0978281\pi\)
\(272\) 16.7635 1.01643
\(273\) 0 0
\(274\) 0.732712 0.0442647
\(275\) −0.954075 + 3.56065i −0.0575329 + 0.214716i
\(276\) 33.0171i 1.98740i
\(277\) −4.07919 2.35512i −0.245095 0.141506i 0.372421 0.928064i \(-0.378528\pi\)
−0.617516 + 0.786558i \(0.711861\pi\)
\(278\) −0.632656 2.36111i −0.0379442 0.141610i
\(279\) 15.5160 + 4.15749i 0.928916 + 0.248902i
\(280\) 0 0
\(281\) 8.01227 8.01227i 0.477972 0.477972i −0.426511 0.904483i \(-0.640257\pi\)
0.904483 + 0.426511i \(0.140257\pi\)
\(282\) 2.01097 0.119751
\(283\) −7.87867 −0.468338 −0.234169 0.972196i \(-0.575237\pi\)
−0.234169 + 0.972196i \(0.575237\pi\)
\(284\) 6.68096 6.68096i 0.396442 0.396442i
\(285\) 9.79075 16.9581i 0.579954 1.00451i
\(286\) 0.824001 + 0.0145147i 0.0487242 + 0.000858275i
\(287\) 0 0
\(288\) −5.03325 + 1.34865i −0.296587 + 0.0794703i
\(289\) −0.651246 1.12799i −0.0383086 0.0663525i
\(290\) −0.737855 + 1.27800i −0.0433284 + 0.0750469i
\(291\) −9.93487 + 37.0774i −0.582392 + 2.17352i
\(292\) −1.38746 + 1.38746i −0.0811951 + 0.0811951i
\(293\) −3.16216 + 11.8013i −0.184735 + 0.689442i 0.809952 + 0.586497i \(0.199493\pi\)
−0.994687 + 0.102945i \(0.967173\pi\)
\(294\) 0 0
\(295\) −1.48948 2.57986i −0.0867210 0.150205i
\(296\) 1.14028 0.658343i 0.0662776 0.0382654i
\(297\) −2.70991 2.70991i −0.157245 0.157245i
\(298\) 1.56293 0.902360i 0.0905383 0.0522723i
\(299\) 0.406170 23.0582i 0.0234894 1.33349i
\(300\) 9.71963i 0.561163i
\(301\) 0 0
\(302\) −0.258073 + 0.446996i −0.0148504 + 0.0257217i
\(303\) 41.6042i 2.39010i
\(304\) 16.1535 + 4.32832i 0.926468 + 0.248246i
\(305\) 5.25694 1.40859i 0.301011 0.0806558i
\(306\) 1.32563 + 1.32563i 0.0757811 + 0.0757811i
\(307\) 7.97207 + 7.97207i 0.454990 + 0.454990i 0.897007 0.442017i \(-0.145737\pi\)
−0.442017 + 0.897007i \(0.645737\pi\)
\(308\) 0 0
\(309\) 26.5904 + 15.3520i 1.51268 + 0.873345i
\(310\) −0.852140 0.228330i −0.0483983 0.0129683i
\(311\) −6.52139 11.2954i −0.369794 0.640502i 0.619739 0.784808i \(-0.287238\pi\)
−0.989533 + 0.144306i \(0.953905\pi\)
\(312\) −4.23154 + 1.05432i −0.239564 + 0.0596892i
\(313\) −3.09510 1.78696i −0.174945 0.101005i 0.409970 0.912099i \(-0.365539\pi\)
−0.584916 + 0.811094i \(0.698872\pi\)
\(314\) 0.209430 + 0.781604i 0.0118188 + 0.0441085i
\(315\) 0 0
\(316\) 10.2134 5.89673i 0.574551 0.331717i
\(317\) −32.0422 + 8.58569i −1.79967 + 0.482220i −0.993927 0.110045i \(-0.964901\pi\)
−0.805743 + 0.592265i \(0.798234\pi\)
\(318\) 0.335936 + 1.25373i 0.0188384 + 0.0703058i
\(319\) −3.62750 13.5380i −0.203101 0.757983i
\(320\) −13.0882 + 3.50697i −0.731651 + 0.196045i
\(321\) −17.9844 + 10.3833i −1.00379 + 0.579539i
\(322\) 0 0
\(323\) −4.72570 17.6366i −0.262945 0.981324i
\(324\) −10.6186 6.13064i −0.589921 0.340591i
\(325\) 0.119569 6.78792i 0.00663249 0.376526i
\(326\) −0.755110 1.30789i −0.0418217 0.0724373i
\(327\) 31.0846 + 8.32910i 1.71898 + 0.460600i
\(328\) 4.59260 + 2.65154i 0.253584 + 0.146407i
\(329\) 0 0
\(330\) 0.741549 + 0.741549i 0.0408209 + 0.0408209i
\(331\) −0.670431 0.670431i −0.0368502 0.0368502i 0.688442 0.725292i \(-0.258295\pi\)
−0.725292 + 0.688442i \(0.758295\pi\)
\(332\) −26.8001 + 7.18106i −1.47085 + 0.394112i
\(333\) −10.2563 2.74816i −0.562040 0.150598i
\(334\) 0.108844i 0.00595569i
\(335\) −0.0173989 + 0.0301357i −0.000950602 + 0.00164649i
\(336\) 0 0
\(337\) 14.1901i 0.772982i −0.922293 0.386491i \(-0.873687\pi\)
0.922293 0.386491i \(-0.126313\pi\)
\(338\) −1.47900 + 0.340957i −0.0804472 + 0.0185456i
\(339\) 19.2294 11.1021i 1.04440 0.602984i
\(340\) 10.6090 + 10.6090i 0.575353 + 0.575353i
\(341\) 7.25617 4.18935i 0.392944 0.226866i
\(342\) 0.935117 + 1.61967i 0.0505654 + 0.0875818i
\(343\) 0 0
\(344\) −0.215923 + 0.805837i −0.0116418 + 0.0434478i
\(345\) 20.7510 20.7510i 1.11719 1.11719i
\(346\) −0.0159418 + 0.0594957i −0.000857038 + 0.00319851i
\(347\) −6.92103 + 11.9876i −0.371540 + 0.643527i −0.989803 0.142445i \(-0.954504\pi\)
0.618262 + 0.785972i \(0.287837\pi\)
\(348\) 18.4776 + 32.0041i 0.990502 + 1.71560i
\(349\) −14.7875 + 3.96231i −0.791559 + 0.212098i −0.631875 0.775071i \(-0.717714\pi\)
−0.159684 + 0.987168i \(0.551048\pi\)
\(350\) 0 0
\(351\) 6.04939 + 3.63615i 0.322892 + 0.194084i
\(352\) −1.35899 + 2.35384i −0.0724345 + 0.125460i
\(353\) 11.1372 11.1372i 0.592773 0.592773i −0.345607 0.938379i \(-0.612327\pi\)
0.938379 + 0.345607i \(0.112327\pi\)
\(354\) 0.511940 0.0272093
\(355\) 8.39784 0.445711
\(356\) −11.2875 + 11.2875i −0.598235 + 0.598235i
\(357\) 0 0
\(358\) −0.932655 0.249904i −0.0492924 0.0132078i
\(359\) −1.71588 6.40375i −0.0905607 0.337977i 0.905748 0.423816i \(-0.139310\pi\)
−0.996309 + 0.0858388i \(0.972643\pi\)
\(360\) −2.67093 1.54206i −0.140771 0.0812739i
\(361\) 0.784981i 0.0413148i
\(362\) −0.452621 + 1.68920i −0.0237892 + 0.0887826i
\(363\) 18.6257 0.977594
\(364\) 0 0
\(365\) −1.74402 −0.0912859
\(366\) −0.242069 + 0.903414i −0.0126531 + 0.0472222i
\(367\) 32.8567i 1.71511i 0.514396 + 0.857553i \(0.328016\pi\)
−0.514396 + 0.857553i \(0.671984\pi\)
\(368\) 21.7051 + 12.5314i 1.13145 + 0.653246i
\(369\) −11.0685 41.3081i −0.576202 2.15041i
\(370\) 0.563277 + 0.150930i 0.0292834 + 0.00784646i
\(371\) 0 0
\(372\) −15.6216 + 15.6216i −0.809943 + 0.809943i
\(373\) 7.87973 0.407997 0.203998 0.978971i \(-0.434606\pi\)
0.203998 + 0.978971i \(0.434606\pi\)
\(374\) 0.977864 0.0505642
\(375\) 22.3300 22.3300i 1.15312 1.15312i
\(376\) −1.54239 + 2.67150i −0.0795428 + 0.137772i
\(377\) 12.5105 + 22.5781i 0.644324 + 1.16283i
\(378\) 0 0
\(379\) 10.8095 2.89639i 0.555245 0.148778i 0.0297243 0.999558i \(-0.490537\pi\)
0.525521 + 0.850781i \(0.323870\pi\)
\(380\) 7.48374 + 12.9622i 0.383908 + 0.664947i
\(381\) −7.94417 + 13.7597i −0.406992 + 0.704931i
\(382\) −0.439044 + 1.63854i −0.0224635 + 0.0838348i
\(383\) 1.70452 1.70452i 0.0870968 0.0870968i −0.662216 0.749313i \(-0.730384\pi\)
0.749313 + 0.662216i \(0.230384\pi\)
\(384\) 2.47025 9.21909i 0.126059 0.470460i
\(385\) 0 0
\(386\) −1.14289 1.97954i −0.0581715 0.100756i
\(387\) 5.82637 3.36386i 0.296171 0.170994i
\(388\) −20.7469 20.7469i −1.05326 1.05326i
\(389\) −14.5674 + 8.41049i −0.738596 + 0.426429i −0.821559 0.570124i \(-0.806895\pi\)
0.0829624 + 0.996553i \(0.473562\pi\)
\(390\) −1.65538 0.995011i −0.0838232 0.0503843i
\(391\) 27.3638i 1.38385i
\(392\) 0 0
\(393\) 7.48993 12.9729i 0.377817 0.654398i
\(394\) 2.54043i 0.127985i
\(395\) 10.1251 + 2.71301i 0.509448 + 0.136506i
\(396\) 14.0984 3.77764i 0.708469 0.189834i
\(397\) 16.6347 + 16.6347i 0.834873 + 0.834873i 0.988179 0.153306i \(-0.0489921\pi\)
−0.153306 + 0.988179i \(0.548992\pi\)
\(398\) −1.59181 1.59181i −0.0797903 0.0797903i
\(399\) 0 0
\(400\) 6.38957 + 3.68902i 0.319479 + 0.184451i
\(401\) −8.33434 2.23318i −0.416197 0.111520i 0.0446427 0.999003i \(-0.485785\pi\)
−0.460840 + 0.887483i \(0.652452\pi\)
\(402\) −0.00299003 0.00517888i −0.000149129 0.000258299i
\(403\) −11.1019 + 10.7175i −0.553024 + 0.533878i
\(404\) −27.5404 15.9005i −1.37019 0.791078i
\(405\) −2.82063 10.5267i −0.140158 0.523078i
\(406\) 0 0
\(407\) −4.79644 + 2.76922i −0.237751 + 0.137265i
\(408\) −4.99809 + 1.33923i −0.247442 + 0.0663019i
\(409\) −3.47744 12.9780i −0.171948 0.641720i −0.997051 0.0767375i \(-0.975550\pi\)
0.825103 0.564982i \(-0.191117\pi\)
\(410\) 0.607883 + 2.26865i 0.0300212 + 0.112041i
\(411\) 15.7530 4.22102i 0.777040 0.208207i
\(412\) −20.3249 + 11.7346i −1.00133 + 0.578121i
\(413\) 0 0
\(414\) 0.725437 + 2.70737i 0.0356533 + 0.133060i
\(415\) −21.3568 12.3304i −1.04837 0.605275i
\(416\) 1.38053 4.81157i 0.0676859 0.235907i
\(417\) −27.2038 47.1183i −1.33217 2.30739i
\(418\) 0.942285 + 0.252484i 0.0460886 + 0.0123494i
\(419\) 15.0514 + 8.68991i 0.735308 + 0.424530i 0.820361 0.571846i \(-0.193773\pi\)
−0.0850532 + 0.996376i \(0.527106\pi\)
\(420\) 0 0
\(421\) −21.2490 21.2490i −1.03561 1.03561i −0.999342 0.0362722i \(-0.988452\pi\)
−0.0362722 0.999342i \(-0.511548\pi\)
\(422\) −0.249537 0.249537i −0.0121473 0.0121473i
\(423\) 24.0288 6.43850i 1.16832 0.313051i
\(424\) −1.92320 0.515320i −0.0933989 0.0250262i
\(425\) 8.05541i 0.390745i
\(426\) −0.721591 + 1.24983i −0.0349612 + 0.0605546i
\(427\) 0 0
\(428\) 15.8733i 0.767265i
\(429\) 17.7993 4.43485i 0.859361 0.214117i
\(430\) −0.319986 + 0.184744i −0.0154311 + 0.00890913i
\(431\) −17.0631 17.0631i −0.821902 0.821902i 0.164479 0.986381i \(-0.447406\pi\)
−0.986381 + 0.164479i \(0.947406\pi\)
\(432\) −6.64286 + 3.83525i −0.319605 + 0.184524i
\(433\) 2.27124 + 3.93391i 0.109149 + 0.189051i 0.915426 0.402487i \(-0.131854\pi\)
−0.806277 + 0.591538i \(0.798521\pi\)
\(434\) 0 0
\(435\) −8.50129 + 31.7273i −0.407606 + 1.52121i
\(436\) −17.3936 + 17.3936i −0.833001 + 0.833001i
\(437\) 7.06534 26.3682i 0.337981 1.26136i
\(438\) 0.149856 0.259558i 0.00716039 0.0124022i
\(439\) −8.50036 14.7231i −0.405700 0.702693i 0.588703 0.808350i \(-0.299639\pi\)
−0.994403 + 0.105657i \(0.966306\pi\)
\(440\) −1.55388 + 0.416362i −0.0740785 + 0.0198493i
\(441\) 0 0
\(442\) −1.74750 + 0.435405i −0.0831203 + 0.0207101i
\(443\) 18.3082 31.7108i 0.869851 1.50663i 0.00770183 0.999970i \(-0.497548\pi\)
0.862149 0.506655i \(-0.169118\pi\)
\(444\) 10.3261 10.3261i 0.490056 0.490056i
\(445\) −14.1882 −0.672583
\(446\) −0.513645 −0.0243218
\(447\) 28.4042 28.4042i 1.34347 1.34347i
\(448\) 0 0
\(449\) −32.7480 8.77481i −1.54547 0.414109i −0.617445 0.786614i \(-0.711832\pi\)
−0.928030 + 0.372505i \(0.878499\pi\)
\(450\) 0.213555 + 0.796999i 0.0100671 + 0.0375709i
\(451\) −19.3181 11.1533i −0.909654 0.525189i
\(452\) 16.9722i 0.798305i
\(453\) −2.97342 + 11.0970i −0.139704 + 0.521381i
\(454\) −0.478554 −0.0224596
\(455\) 0 0
\(456\) −5.16202 −0.241734
\(457\) 0.585644 2.18565i 0.0273953 0.102241i −0.950874 0.309577i \(-0.899813\pi\)
0.978270 + 0.207336i \(0.0664793\pi\)
\(458\) 1.58516i 0.0740698i
\(459\) 7.25273 + 4.18737i 0.338528 + 0.195449i
\(460\) 5.80566 + 21.6670i 0.270690 + 1.01023i
\(461\) 24.5455 + 6.57694i 1.14320 + 0.306319i 0.780235 0.625486i \(-0.215099\pi\)
0.362961 + 0.931804i \(0.381766\pi\)
\(462\) 0 0
\(463\) −22.6265 + 22.6265i −1.05154 + 1.05154i −0.0529442 + 0.998597i \(0.516861\pi\)
−0.998597 + 0.0529442i \(0.983139\pi\)
\(464\) −28.0521 −1.30229
\(465\) −19.6361 −0.910601
\(466\) 1.34981 1.34981i 0.0625288 0.0625288i
\(467\) −5.64704 + 9.78095i −0.261314 + 0.452609i −0.966591 0.256323i \(-0.917489\pi\)
0.705278 + 0.708931i \(0.250822\pi\)
\(468\) −23.5126 + 13.0283i −1.08687 + 0.602235i
\(469\) 0 0
\(470\) −1.31967 + 0.353604i −0.0608718 + 0.0163105i
\(471\) 9.00535 + 15.5977i 0.414945 + 0.718705i
\(472\) −0.392653 + 0.680095i −0.0180733 + 0.0313039i
\(473\) 0.908251 3.38964i 0.0417614 0.155856i
\(474\) −1.27378 + 1.27378i −0.0585066 + 0.0585066i
\(475\) 2.07991 7.76231i 0.0954326 0.356159i
\(476\) 0 0
\(477\) 8.02814 + 13.9051i 0.367583 + 0.636673i
\(478\) 0.874396 0.504833i 0.0399939 0.0230905i
\(479\) 14.1810 + 14.1810i 0.647945 + 0.647945i 0.952496 0.304551i \(-0.0985064\pi\)
−0.304551 + 0.952496i \(0.598506\pi\)
\(480\) 5.51639 3.18489i 0.251788 0.145370i
\(481\) 7.33850 7.08444i 0.334607 0.323023i
\(482\) 1.56814i 0.0714269i
\(483\) 0 0
\(484\) −7.11843 + 12.3295i −0.323565 + 0.560431i
\(485\) 26.0785i 1.18416i
\(486\) 2.47133 + 0.662191i 0.112102 + 0.0300376i
\(487\) 30.3456 8.13109i 1.37509 0.368455i 0.505756 0.862676i \(-0.331213\pi\)
0.869336 + 0.494221i \(0.164547\pi\)
\(488\) −1.01449 1.01449i −0.0459238 0.0459238i
\(489\) −23.7691 23.7691i −1.07488 1.07488i
\(490\) 0 0
\(491\) −16.8341 9.71919i −0.759714 0.438621i 0.0694792 0.997583i \(-0.477866\pi\)
−0.829193 + 0.558962i \(0.811200\pi\)
\(492\) 56.8122 + 15.2228i 2.56129 + 0.686296i
\(493\) 15.3138 + 26.5243i 0.689698 + 1.19459i
\(494\) −1.79634 0.0316425i −0.0808213 0.00142366i
\(495\) 11.2349 + 6.48647i 0.504971 + 0.291545i
\(496\) −4.34038 16.1985i −0.194889 0.727336i
\(497\) 0 0
\(498\) 3.67021 2.11900i 0.164466 0.0949545i
\(499\) −16.1261 + 4.32098i −0.721904 + 0.193434i −0.601021 0.799233i \(-0.705239\pi\)
−0.120883 + 0.992667i \(0.538573\pi\)
\(500\) 6.24745 + 23.3158i 0.279394 + 1.04271i
\(501\) −0.627031 2.34011i −0.0280137 0.104548i
\(502\) 0.393138 0.105341i 0.0175466 0.00470160i
\(503\) −25.9585 + 14.9871i −1.15743 + 0.668243i −0.950687 0.310153i \(-0.899620\pi\)
−0.206743 + 0.978395i \(0.566287\pi\)
\(504\) 0 0
\(505\) −7.31560 27.3022i −0.325540 1.21493i
\(506\) 1.26612 + 0.730997i 0.0562861 + 0.0324968i
\(507\) −29.8339 + 15.8507i −1.32497 + 0.703955i
\(508\) −6.07227 10.5175i −0.269413 0.466638i
\(509\) −13.5446 3.62928i −0.600356 0.160865i −0.0541739 0.998532i \(-0.517253\pi\)
−0.546182 + 0.837667i \(0.683919\pi\)
\(510\) −1.98466 1.14585i −0.0878824 0.0507389i
\(511\) 0 0
\(512\) 6.42580 + 6.42580i 0.283983 + 0.283983i
\(513\) 5.90766 + 5.90766i 0.260830 + 0.260830i
\(514\) −1.51659 + 0.406370i −0.0668940 + 0.0179242i
\(515\) −20.1491 5.39893i −0.887874 0.237905i
\(516\) 9.25280i 0.407332i
\(517\) 6.48785 11.2373i 0.285335 0.494215i
\(518\) 0 0
\(519\) 1.37097i 0.0601791i
\(520\) 2.59150 1.43595i 0.113645 0.0629705i
\(521\) −0.757986 + 0.437623i −0.0332080 + 0.0191726i −0.516512 0.856280i \(-0.672770\pi\)
0.483304 + 0.875453i \(0.339437\pi\)
\(522\) −2.21832 2.21832i −0.0970931 0.0970931i
\(523\) −11.7198 + 6.76640i −0.512469 + 0.295874i −0.733848 0.679314i \(-0.762278\pi\)
0.221379 + 0.975188i \(0.428944\pi\)
\(524\) 5.72506 + 9.91610i 0.250100 + 0.433187i
\(525\) 0 0
\(526\) 0.620553 2.31593i 0.0270574 0.100980i
\(527\) −12.9468 + 12.9468i −0.563973 + 0.563973i
\(528\) −5.15960 + 19.2559i −0.224543 + 0.838004i
\(529\) 8.95568 15.5117i 0.389377 0.674421i
\(530\) −0.440907 0.763674i −0.0191518 0.0331719i
\(531\) 6.11711 1.63908i 0.265460 0.0711298i
\(532\) 0 0
\(533\) 39.4888 + 11.3301i 1.71045 + 0.490759i
\(534\) 1.21913 2.11159i 0.0527569 0.0913776i
\(535\) 9.97623 9.97623i 0.431310 0.431310i
\(536\) 0.00917329 0.000396226
\(537\) −21.4914 −0.927423
\(538\) −0.886440 + 0.886440i −0.0382171 + 0.0382171i
\(539\) 0 0
\(540\) −6.63121 1.77683i −0.285362 0.0764625i
\(541\) 3.18000 + 11.8679i 0.136719 + 0.510241i 0.999985 + 0.00549222i \(0.00174824\pi\)
−0.863266 + 0.504749i \(0.831585\pi\)
\(542\) 0.151539 + 0.0874914i 0.00650918 + 0.00375808i
\(543\) 38.9248i 1.67042i
\(544\) 1.53725 5.73710i 0.0659091 0.245976i
\(545\) −21.8634 −0.936526
\(546\) 0 0
\(547\) 16.2786 0.696022 0.348011 0.937490i \(-0.386857\pi\)
0.348011 + 0.937490i \(0.386857\pi\)
\(548\) −3.22641 + 12.0411i −0.137825 + 0.514371i
\(549\) 11.5698i 0.493788i
\(550\) 0.372723 + 0.215192i 0.0158930 + 0.00917582i
\(551\) 7.90803 + 29.5132i 0.336894 + 1.25730i
\(552\) −7.47258 2.00227i −0.318054 0.0852224i
\(553\) 0 0
\(554\) −0.388865 + 0.388865i −0.0165213 + 0.0165213i
\(555\) 12.9797 0.550959
\(556\) 41.5874 1.76370
\(557\) 5.84312 5.84312i 0.247581 0.247581i −0.572396 0.819977i \(-0.693986\pi\)
0.819977 + 0.572396i \(0.193986\pi\)
\(558\) 0.937724 1.62418i 0.0396970 0.0687572i
\(559\) −0.113826 + 6.46190i −0.00481433 + 0.273309i
\(560\) 0 0
\(561\) 21.0237 5.63329i 0.887623 0.237838i
\(562\) −0.661470 1.14570i −0.0279024 0.0483285i
\(563\) −14.0767 + 24.3815i −0.593261 + 1.02756i 0.400528 + 0.916284i \(0.368827\pi\)
−0.993790 + 0.111274i \(0.964507\pi\)
\(564\) −8.85505 + 33.0475i −0.372865 + 1.39155i
\(565\) −10.6669 + 10.6669i −0.448759 + 0.448759i
\(566\) −0.238078 + 0.888519i −0.0100072 + 0.0373472i
\(567\) 0 0
\(568\) −1.10691 1.91722i −0.0464448 0.0804447i
\(569\) 8.62645 4.98048i 0.361640 0.208793i −0.308160 0.951335i \(-0.599713\pi\)
0.669800 + 0.742542i \(0.266380\pi\)
\(570\) −1.61659 1.61659i −0.0677117 0.0677117i
\(571\) −4.46188 + 2.57607i −0.186724 + 0.107805i −0.590448 0.807076i \(-0.701049\pi\)
0.403724 + 0.914881i \(0.367716\pi\)
\(572\) −3.86692 + 13.4774i −0.161684 + 0.563519i
\(573\) 37.7572i 1.57733i
\(574\) 0 0
\(575\) 6.02177 10.4300i 0.251125 0.434962i
\(576\) 28.8053i 1.20022i
\(577\) −12.9819 3.47849i −0.540444 0.144812i −0.0217373 0.999764i \(-0.506920\pi\)
−0.518707 + 0.854952i \(0.673586\pi\)
\(578\) −0.146889 + 0.0393588i −0.00610978 + 0.00163711i
\(579\) −35.9754 35.9754i −1.49509 1.49509i
\(580\) −17.7532 17.7532i −0.737161 0.737161i
\(581\) 0 0
\(582\) 3.88120 + 2.24081i 0.160881 + 0.0928847i
\(583\) 8.08967 + 2.16762i 0.335040 + 0.0897737i
\(584\) 0.229876 + 0.398157i 0.00951234 + 0.0164759i
\(585\) −22.9656 6.58926i −0.949512 0.272433i
\(586\) 1.23535 + 0.713227i 0.0510317 + 0.0294631i
\(587\) −9.73498 36.3314i −0.401806 1.49956i −0.809872 0.586607i \(-0.800463\pi\)
0.408066 0.912952i \(-0.366203\pi\)
\(588\) 0 0
\(589\) −15.8186 + 9.13289i −0.651795 + 0.376314i
\(590\) −0.335953 + 0.0900184i −0.0138310 + 0.00370600i
\(591\) 14.6350 + 54.6184i 0.602001 + 2.24670i
\(592\) 2.86906 + 10.7075i 0.117918 + 0.440074i
\(593\) 35.2975 9.45795i 1.44950 0.388391i 0.553648 0.832751i \(-0.313235\pi\)
0.895848 + 0.444360i \(0.146569\pi\)
\(594\) −0.387498 + 0.223722i −0.0158992 + 0.00917944i
\(595\) 0 0
\(596\) 7.94687 + 29.6581i 0.325517 + 1.21484i
\(597\) −43.3935 25.0532i −1.77598 1.02536i
\(598\) −2.58813 0.742581i −0.105836 0.0303664i
\(599\) −2.66014 4.60749i −0.108690 0.188257i 0.806550 0.591166i \(-0.201332\pi\)
−0.915240 + 0.402909i \(0.867999\pi\)
\(600\) −2.19979 0.589432i −0.0898061 0.0240635i
\(601\) 21.4564 + 12.3879i 0.875225 + 0.505312i 0.869081 0.494669i \(-0.164711\pi\)
0.00614424 + 0.999981i \(0.498044\pi\)
\(602\) 0 0
\(603\) −0.0523087 0.0523087i −0.00213017 0.00213017i
\(604\) −6.20937 6.20937i −0.252656 0.252656i
\(605\) −12.2228 + 3.27510i −0.496929 + 0.133152i
\(606\) 4.69193 + 1.25720i 0.190596 + 0.0510702i
\(607\) 22.5591i 0.915644i −0.889044 0.457822i \(-0.848630\pi\)
0.889044 0.457822i \(-0.151370\pi\)
\(608\) 2.96263 5.13143i 0.120151 0.208107i
\(609\) 0 0
\(610\) 0.635418i 0.0257273i
\(611\) −6.59066 + 22.9705i −0.266630 + 0.929288i
\(612\) −27.6221 + 15.9476i −1.11656 + 0.644645i
\(613\) 16.2662 + 16.2662i 0.656986 + 0.656986i 0.954666 0.297680i \(-0.0962128\pi\)
−0.297680 + 0.954666i \(0.596213\pi\)
\(614\) 1.13995 0.658151i 0.0460047 0.0265608i
\(615\) 26.1385 + 45.2733i 1.05401 + 1.82560i
\(616\) 0 0
\(617\) 7.79350 29.0858i 0.313755 1.17095i −0.611389 0.791330i \(-0.709389\pi\)
0.925143 0.379618i \(-0.123945\pi\)
\(618\) 2.53484 2.53484i 0.101966 0.101966i
\(619\) −2.76561 + 10.3214i −0.111159 + 0.414852i −0.998971 0.0453549i \(-0.985558\pi\)
0.887812 + 0.460207i \(0.152225\pi\)
\(620\) 7.50459 12.9983i 0.301392 0.522026i
\(621\) 6.26048 + 10.8435i 0.251224 + 0.435133i
\(622\) −1.47090 + 0.394127i −0.0589778 + 0.0158031i
\(623\) 0 0
\(624\) 0.646624 36.7088i 0.0258857 1.46953i
\(625\) −6.01999 + 10.4269i −0.240800 + 0.417077i
\(626\) −0.295052 + 0.295052i −0.0117927 + 0.0117927i
\(627\) 21.7133 0.867146
\(628\) −13.7668 −0.549355
\(629\) 8.55805 8.55805i 0.341232 0.341232i
\(630\) 0 0
\(631\) 13.6759 + 3.66444i 0.544428 + 0.145879i 0.520543 0.853836i \(-0.325730\pi\)
0.0238855 + 0.999715i \(0.492396\pi\)
\(632\) −0.715196 2.66915i −0.0284490 0.106173i
\(633\) −6.80249 3.92742i −0.270375 0.156101i
\(634\) 3.87301i 0.153817i
\(635\) 2.79377 10.4265i 0.110867 0.413763i
\(636\) −22.0826 −0.875633
\(637\) 0 0
\(638\) −1.63637 −0.0647844
\(639\) −4.62063 + 17.2444i −0.182789 + 0.682179i
\(640\) 6.48426i 0.256313i
\(641\) 32.0667 + 18.5137i 1.26656 + 0.731248i 0.974335 0.225102i \(-0.0722714\pi\)
0.292224 + 0.956350i \(0.405605\pi\)
\(642\) 0.627525 + 2.34196i 0.0247664 + 0.0924296i
\(643\) 33.2886 + 8.91965i 1.31277 + 0.351757i 0.846266 0.532761i \(-0.178845\pi\)
0.466507 + 0.884517i \(0.345512\pi\)
\(644\) 0 0
\(645\) −5.81530 + 5.81530i −0.228977 + 0.228977i
\(646\) −2.13177 −0.0838733
\(647\) 6.06726 0.238529 0.119264 0.992863i \(-0.461946\pi\)
0.119264 + 0.992863i \(0.461946\pi\)
\(648\) −2.03146 + 2.03146i −0.0798034 + 0.0798034i
\(649\) 1.65164 2.86072i 0.0648325 0.112293i
\(650\) −0.761896 0.218602i −0.0298840 0.00857428i
\(651\) 0 0
\(652\) 24.8184 6.65007i 0.971964 0.260437i
\(653\) −15.1009 26.1555i −0.590943 1.02354i −0.994106 0.108416i \(-0.965422\pi\)
0.403162 0.915129i \(-0.367911\pi\)
\(654\) 1.87863 3.25389i 0.0734603 0.127237i
\(655\) −2.63403 + 9.83033i −0.102920 + 0.384103i
\(656\) −31.5699 + 31.5699i −1.23260 + 1.23260i
\(657\) 0.959586 3.58123i 0.0374370 0.139717i
\(658\) 0 0
\(659\) 4.37179 + 7.57216i 0.170301 + 0.294969i 0.938525 0.345211i \(-0.112193\pi\)
−0.768224 + 0.640181i \(0.778859\pi\)
\(660\) −15.4517 + 8.92102i −0.601455 + 0.347250i
\(661\) 12.7006 + 12.7006i 0.493996 + 0.493996i 0.909563 0.415566i \(-0.136417\pi\)
−0.415566 + 0.909563i \(0.636417\pi\)
\(662\) −0.0958671 + 0.0553489i −0.00372598 + 0.00215120i
\(663\) −35.0624 + 19.4281i −1.36171 + 0.754525i
\(664\) 6.50100i 0.252288i
\(665\) 0 0
\(666\) −0.619849 + 1.07361i −0.0240187 + 0.0416015i
\(667\) 45.7909i 1.77303i
\(668\) 1.78870 + 0.479282i 0.0692071 + 0.0185440i
\(669\) −11.0432 + 2.95901i −0.426954 + 0.114402i
\(670\) 0.00287281 + 0.00287281i 0.000110986 + 0.000110986i
\(671\) 4.26731 + 4.26731i 0.164738 + 0.164738i
\(672\) 0 0
\(673\) 22.0524 + 12.7319i 0.850057 + 0.490780i 0.860670 0.509163i \(-0.170045\pi\)
−0.0106133 + 0.999944i \(0.503378\pi\)
\(674\) −1.60029 0.428796i −0.0616408 0.0165166i
\(675\) 1.84297 + 3.19212i 0.0709359 + 0.122865i
\(676\) 0.909453 25.8068i 0.0349790 0.992568i
\(677\) 18.9268 + 10.9274i 0.727415 + 0.419973i 0.817476 0.575963i \(-0.195373\pi\)
−0.0900609 + 0.995936i \(0.528706\pi\)
\(678\) −0.670968 2.50409i −0.0257684 0.0961689i
\(679\) 0 0
\(680\) 3.04444 1.75771i 0.116749 0.0674050i
\(681\) −10.2887 + 2.75686i −0.394265 + 0.105643i
\(682\) −0.253188 0.944911i −0.00969507 0.0361825i
\(683\) −8.29515 30.9579i −0.317405 1.18457i −0.921729 0.387833i \(-0.873224\pi\)
0.604324 0.796738i \(-0.293443\pi\)
\(684\) −30.7348 + 8.23535i −1.17517 + 0.314887i
\(685\) −9.59550 + 5.53997i −0.366625 + 0.211671i
\(686\) 0 0
\(687\) −9.13183 34.0804i −0.348401 1.30025i
\(688\) −6.08268 3.51184i −0.231900 0.133888i
\(689\) −15.4219 0.271656i −0.587527 0.0103493i
\(690\) −1.71314 2.96725i −0.0652182 0.112961i
\(691\) −27.1642 7.27863i −1.03337 0.276892i −0.298010 0.954563i \(-0.596323\pi\)
−0.735365 + 0.677671i \(0.762989\pi\)
\(692\) −0.907533 0.523964i −0.0344992 0.0199181i
\(693\) 0 0
\(694\) 1.14276 + 1.14276i 0.0433786 + 0.0433786i
\(695\) 26.1373 + 26.1373i 0.991444 + 0.991444i
\(696\) 8.36385 2.24109i 0.317031 0.0849482i
\(697\) 47.0846 + 12.6163i 1.78346 + 0.477876i
\(698\) 1.78740i 0.0676542i
\(699\) 21.2445 36.7965i 0.803540 1.39177i
\(700\) 0 0
\(701\) 41.8411i 1.58032i 0.612904 + 0.790158i \(0.290001\pi\)
−0.612904 + 0.790158i \(0.709999\pi\)
\(702\) 0.592869 0.572343i 0.0223764 0.0216017i
\(703\) 10.4563 6.03698i 0.394369 0.227689i
\(704\) −10.6243 10.6243i −0.400418 0.400418i
\(705\) −26.3354 + 15.2047i −0.991847 + 0.572643i
\(706\) −0.919455 1.59254i −0.0346041 0.0599361i
\(707\) 0 0
\(708\) −2.25426 + 8.41303i −0.0847204 + 0.316181i
\(709\) 26.4279 26.4279i 0.992520 0.992520i −0.00745226 0.999972i \(-0.502372\pi\)
0.999972 + 0.00745226i \(0.00237215\pi\)
\(710\) 0.253766 0.947068i 0.00952368 0.0355428i
\(711\) −11.1420 + 19.2985i −0.417857 + 0.723750i
\(712\) 1.87012 + 3.23914i 0.0700857 + 0.121392i
\(713\) −26.4417 + 7.08503i −0.990249 + 0.265336i
\(714\) 0 0
\(715\) −10.9008 + 6.04011i −0.407665 + 0.225887i
\(716\) 8.21367 14.2265i 0.306959 0.531669i
\(717\) 15.8910 15.8910i 0.593459 0.593459i
\(718\) −0.774035 −0.0288867
\(719\) 29.4939 1.09994 0.549968 0.835186i \(-0.314640\pi\)
0.549968 + 0.835186i \(0.314640\pi\)
\(720\) 18.3602 18.3602i 0.684246 0.684246i
\(721\) 0 0
\(722\) 0.0885265 + 0.0237206i 0.00329461 + 0.000882789i
\(723\) −9.03377 33.7145i −0.335969 1.25386i
\(724\) −25.7667 14.8764i −0.957612 0.552878i
\(725\) 13.4800i 0.500635i
\(726\) 0.562831 2.10051i 0.0208886 0.0779574i
\(727\) 3.04387 0.112891 0.0564455 0.998406i \(-0.482023\pi\)
0.0564455 + 0.998406i \(0.482023\pi\)
\(728\) 0 0
\(729\) 38.4293 1.42331
\(730\) −0.0527007 + 0.196682i −0.00195054 + 0.00727952i
\(731\) 7.66851i 0.283630i
\(732\) −13.7805 7.95615i −0.509340 0.294068i
\(733\) −0.339796 1.26813i −0.0125506 0.0468396i 0.959367 0.282163i \(-0.0910518\pi\)
−0.971917 + 0.235323i \(0.924385\pi\)
\(734\) 3.70542 + 0.992865i 0.136770 + 0.0366473i
\(735\) 0 0
\(736\) 6.27914 6.27914i 0.231452 0.231452i
\(737\) −0.0385861 −0.00142134
\(738\) −4.99300 −0.183795
\(739\) −21.2184 + 21.2184i −0.780533 + 0.780533i −0.979921 0.199388i \(-0.936105\pi\)
0.199388 + 0.979921i \(0.436105\pi\)
\(740\) −4.96065 + 8.59209i −0.182357 + 0.315852i
\(741\) −38.8030 + 9.66809i −1.42546 + 0.355166i
\(742\) 0 0
\(743\) −39.4397 + 10.5678i −1.44690 + 0.387697i −0.894946 0.446175i \(-0.852786\pi\)
−0.551958 + 0.833872i \(0.686119\pi\)
\(744\) 2.58820 + 4.48290i 0.0948881 + 0.164351i
\(745\) −13.6453 + 23.6344i −0.499926 + 0.865897i
\(746\) 0.238110 0.888638i 0.00871782 0.0325354i
\(747\) 37.0706 37.0706i 1.35634 1.35634i
\(748\) −4.30591 + 16.0699i −0.157440 + 0.587573i
\(749\) 0 0
\(750\) −1.84350 3.19304i −0.0673153 0.116593i
\(751\) 31.0690 17.9377i 1.13372 0.654556i 0.188856 0.982005i \(-0.439522\pi\)
0.944869 + 0.327448i \(0.106189\pi\)
\(752\) −18.3642 18.3642i −0.669672 0.669672i
\(753\) 7.84547 4.52958i 0.285905 0.165067i
\(754\) 2.92429 0.728611i 0.106496 0.0265345i
\(755\) 7.80507i 0.284056i
\(756\) 0 0
\(757\) −0.439138 + 0.760610i −0.0159607 + 0.0276448i −0.873895 0.486114i \(-0.838414\pi\)
0.857935 + 0.513759i \(0.171747\pi\)
\(758\) 1.30656i 0.0474566i
\(759\) 31.4323 + 8.42227i 1.14092 + 0.305709i
\(760\) 3.38750 0.907679i 0.122878 0.0329250i
\(761\) 25.8663 + 25.8663i 0.937654 + 0.937654i 0.998167 0.0605137i \(-0.0192739\pi\)
−0.0605137 + 0.998167i \(0.519274\pi\)
\(762\) 1.31170 + 1.31170i 0.0475178 + 0.0475178i
\(763\) 0 0
\(764\) −24.9938 14.4302i −0.904245 0.522066i
\(765\) −27.3832 7.33730i −0.990041 0.265281i
\(766\) −0.140720 0.243735i −0.00508443 0.00880649i
\(767\) −1.67781 + 5.84769i −0.0605822 + 0.211148i
\(768\) 33.5795 + 19.3871i 1.21170 + 0.699573i
\(769\) −7.85943 29.3318i −0.283418 1.05773i −0.949987 0.312288i \(-0.898904\pi\)
0.666569 0.745443i \(-0.267762\pi\)
\(770\) 0 0
\(771\) −30.2652 + 17.4736i −1.08997 + 0.629297i
\(772\) 37.5636 10.0651i 1.35194 0.362252i
\(773\) −5.13389 19.1599i −0.184653 0.689134i −0.994705 0.102776i \(-0.967228\pi\)
0.810052 0.586359i \(-0.199439\pi\)
\(774\) −0.203298 0.758719i −0.00730740 0.0272716i
\(775\) −7.78395 + 2.08570i −0.279608 + 0.0749206i
\(776\) −5.95369 + 3.43737i −0.213725 + 0.123394i
\(777\) 0 0
\(778\) 0.508297 + 1.89699i 0.0182233 + 0.0680104i
\(779\) 42.1139 + 24.3145i 1.50889 + 0.871157i
\(780\) 23.6409 22.8224i