Properties

Label 637.2.x.b.80.4
Level $637$
Weight $2$
Character 637.80
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 80.4
Character \(\chi\) \(=\) 637.80
Dual form 637.2.x.b.215.3

$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

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 0.975786 0.218726i \(-0.0701902\pi\)
−0.954419 + 0.298471i \(0.903524\pi\)
\(3\) 2.59871i 1.50036i 0.661231 + 0.750182i \(0.270034\pi\)
−0.661231 + 0.750182i \(0.729966\pi\)
\(4\) 1.72025 0.993184i 0.860123 0.496592i
\(5\) 0.456951 1.70537i 0.204355 0.762663i −0.785290 0.619128i \(-0.787486\pi\)
0.989645 0.143535i \(-0.0458470\pi\)
\(6\) −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 0.466913 0.884303i \(-0.345366\pi\)
−0.884303 + 0.466913i \(0.845366\pi\)
\(12\) 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 0.999761 + 0.0218471i \(0.00695471\pi\)
−0.480960 + 0.876742i \(0.659712\pi\)
\(18\) −0.113417 0.423277i −0.0267326 0.0997674i
\(19\) 3.01787 + 3.01787i 0.692346 + 0.692346i 0.962748 0.270402i \(-0.0871566\pi\)
−0.270402 + 0.962748i \(0.587157\pi\)
\(20\) −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 0.950105 0.311930i \(-0.100976\pi\)
0.204913 + 0.978780i \(0.434309\pi\)
\(24\) −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 −0.979365 0.202097i \(-0.935224\pi\)
0.314661 0.949204i \(-0.398109\pi\)
\(30\) 0.535675i 0.0978004i
\(31\) −4.13397 + 1.10769i −0.742483 + 0.198948i −0.610181 0.792262i \(-0.708903\pi\)
−0.132302 + 0.991210i \(0.542237\pi\)
\(32\) 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 −0.0271042 0.999633i \(-0.508629\pi\)
0.476343 + 0.879259i \(0.341962\pi\)
\(38\) −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 −0.210654 0.977561i \(-0.567559\pi\)
0.671212 0.741266i \(-0.265774\pi\)
\(42\) 0 0
\(43\) −1.55234 0.896243i −0.236730 0.136676i 0.376943 0.926236i \(-0.376975\pi\)
−0.613673 + 0.789561i \(0.710309\pi\)
\(44\) −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 −0.240348 0.970687i \(-0.577262\pi\)
−0.693491 + 0.720465i \(0.743928\pi\)
\(48\) 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 −0.974707 0.223486i \(-0.928256\pi\)
0.680898 + 0.732378i \(0.261590\pi\)
\(54\) 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 0.151162 0.988509i \(-0.451698\pi\)
−0.363344 + 0.931655i \(0.618365\pi\)
\(60\) 8.80308 2.35878i 1.13647 0.304517i
\(61\) 3.08259i 0.394685i 0.980335 + 0.197342i \(0.0632311\pi\)
−0.980335 + 0.197342i \(0.936769\pi\)
\(62\) −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 −0.706255 0.707958i \(-0.749617\pi\)
0.707958 + 0.706255i \(0.249617\pi\)
\(68\) 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 0.999704 + 0.0243373i \(0.00774758\pi\)
−0.853600 + 0.520929i \(0.825586\pi\)
\(72\) −1.23522 1.23522i −0.145572 0.145572i
\(73\) −0.255666 0.954158i −0.0299234 0.111676i 0.949349 0.314224i \(-0.101744\pi\)
−0.979272 + 0.202548i \(0.935078\pi\)
\(74\) 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 0.983291 0.182041i \(-0.0582704\pi\)
−0.649298 + 0.760534i \(0.724937\pi\)
\(80\) −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 −0.996120 0.0880033i \(-0.971951\pi\)
−0.0880033 0.996120i \(-0.528049\pi\)
\(84\) 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 −0.984168 0.177237i \(-0.943284\pi\)
0.763696 0.645576i \(-0.223383\pi\)
\(90\) −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 −0.895557 0.444946i \(-0.853223\pi\)
−0.553102 + 0.833113i \(0.686556\pi\)
\(98\) 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 −0.995232 0.0975405i \(-0.968902\pi\)
0.413143 0.910666i \(-0.364431\pi\)
\(104\) −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 −0.991944 0.126678i \(-0.959568\pi\)
0.605679 + 0.795709i \(0.292902\pi\)
\(108\) −1.94422 3.36749i −0.187083 0.324037i
\(109\) −3.20509 11.9616i −0.306992 1.14571i −0.931217 0.364465i \(-0.881252\pi\)
0.624225 0.781245i \(-0.285415\pi\)
\(110\) −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 −0.592063 0.805892i \(-0.701686\pi\)
0.993954 + 0.109795i \(0.0350195\pi\)
\(114\) −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 −0.716173 0.697923i \(-0.754108\pi\)
0.246333 + 0.969185i \(0.420774\pi\)
\(128\) 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 −0.265808 0.964026i \(-0.585639\pi\)
0.701967 + 0.712209i \(0.252305\pi\)
\(132\) 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 −0.861183 0.508296i \(-0.830276\pi\)
0.999954 0.00960548i \(-0.00305757\pi\)
\(138\) −1.87453 0.502280i −0.159571 0.0427569i
\(139\) 18.1314 + 10.4682i 1.53789 + 0.887900i 0.998962 + 0.0455477i \(0.0145033\pi\)
0.538927 + 0.842353i \(0.318830\pi\)
\(140\) 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 −0.0995972 0.995028i \(-0.531755\pi\)
0.995028 + 0.0995972i \(0.0317554\pi\)
\(150\) −0.551828 0.147862i −0.0450566 0.0120729i
\(151\) −4.27019 + 1.14419i −0.347503 + 0.0931131i −0.428349 0.903614i \(-0.640905\pi\)
0.0808459 + 0.996727i \(0.474238\pi\)
\(152\) 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 0.240988 0.970528i \(-0.422529\pi\)
−0.720008 + 0.693966i \(0.755862\pi\)
\(158\) −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 0.967868 0.251458i \(-0.0809101\pi\)
−0.251458 + 0.967868i \(0.580910\pi\)
\(164\) −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 0.293492 0.955962i \(-0.405183\pi\)
−0.223810 + 0.974633i \(0.571849\pi\)
\(168\) 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 \(0.100016\pi\)
−0.951041 + 0.309066i \(0.899984\pi\)
\(180\) 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 0.999994 0.00351052i \(-0.00111744\pi\)
−0.00351052 + 0.999994i \(0.501117\pi\)
\(194\) −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 −0.585196 0.810892i \(-0.698982\pi\)
−0.912240 + 0.409655i \(0.865649\pi\)
\(198\) −0.428948 + 0.742960i −0.0304840 + 0.0527999i
\(199\) 9.64065 + 16.6981i 0.683408 + 1.18370i 0.973934 + 0.226830i \(0.0728362\pi\)
−0.290527 + 0.956867i \(0.593830\pi\)
\(200\) 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 0.913346 0.407184i \(-0.133489\pi\)
−0.809304 + 0.587389i \(0.800156\pi\)
\(212\) 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 −0.993514 0.113712i \(-0.963726\pi\)
0.917264 + 0.398279i \(0.130392\pi\)
\(224\) 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 −0.992154 0.125024i \(-0.960099\pi\)
0.921742 + 0.387803i \(0.126766\pi\)
\(228\) −5.70202 + 21.2802i −0.377625 + 1.40932i
\(229\) 13.1144 + 3.51399i 0.866623 + 0.232211i 0.664627 0.747176i \(-0.268591\pi\)
0.201996 + 0.979386i \(0.435257\pi\)
\(230\) 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 0.0415633 0.999136i \(-0.486766\pi\)
0.886059 + 0.463573i \(0.153433\pi\)
\(234\) 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 −0.481115 0.876658i \(-0.659768\pi\)
0.876658 + 0.481115i \(0.159768\pi\)
\(240\) 12.7123 12.7123i 0.820577 0.820577i
\(241\) 12.9736 + 3.47625i 0.835700 + 0.223925i 0.651199 0.758907i \(-0.274266\pi\)
0.184501 + 0.982832i \(0.440933\pi\)
\(242\) 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 −0.805759 0.592243i \(-0.798242\pi\)
0.915777 + 0.401686i \(0.131576\pi\)
\(252\) 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 −0.995882 0.0906578i \(-0.971103\pi\)
0.576453 + 0.817130i \(0.304436\pi\)
\(258\) 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 −0.755932 0.654650i \(-0.772816\pi\)
0.188977 + 0.981981i \(0.439483\pi\)
\(270\) 0.403515i 0.0245571i
\(271\) −0.387901 1.44767i −0.0235633 0.0879396i 0.953143 0.302521i \(-0.0978281\pi\)
−0.976706 + 0.214581i \(0.931161\pi\)
\(272\) 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 −0.617516 0.786558i \(-0.711861\pi\)
0.372421 + 0.928064i \(0.378528\pi\)
\(278\) −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 0.904483 0.426511i \(-0.140257\pi\)
−0.426511 + 0.904483i \(0.640257\pi\)
\(282\) 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 −0.994687 0.102945i \(-0.967173\pi\)
0.809952 0.586497i \(-0.199493\pi\)
\(294\) 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 −0.442017 0.897007i \(-0.645737\pi\)
0.897007 + 0.442017i \(0.145737\pi\)
\(308\) 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 −0.989533 0.144306i \(-0.953905\pi\)
0.619739 + 0.784808i \(0.287238\pi\)
\(312\) −4.23154 1.05432i −0.239564 0.0596892i
\(313\) −3.09510 + 1.78696i −0.174945 + 0.101005i −0.584916 0.811094i \(-0.698872\pi\)
0.409970 + 0.912099i \(0.365539\pi\)
\(314\) 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 −0.805743 0.592265i \(-0.798234\pi\)
−0.993927 + 0.110045i \(0.964901\pi\)
\(318\) 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 −0.725292 0.688442i \(-0.758295\pi\)
0.688442 + 0.725292i \(0.258295\pi\)
\(332\) −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 \(0.126313\pi\)
−0.922293 + 0.386491i \(0.873687\pi\)
\(338\) −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 0.618262 0.785972i \(-0.287837\pi\)
−0.989803 + 0.142445i \(0.954504\pi\)
\(348\) 18.4776 32.0041i 0.990502 1.71560i
\(349\) −14.7875 3.96231i −0.791559 0.212098i −0.159684 0.987168i \(-0.551048\pi\)
−0.631875 + 0.775071i \(0.717714\pi\)
\(350\) 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 0.938379 0.345607i \(-0.112327\pi\)
−0.345607 + 0.938379i \(0.612327\pi\)
\(354\) 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 −0.996309 0.0858388i \(-0.972643\pi\)
0.905748 + 0.423816i \(0.139310\pi\)
\(360\) −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 \(-0.671984\pi\)
0.514396 0.857553i \(-0.328016\pi\)
\(368\) 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 0.525521 0.850781i \(-0.323870\pi\)
0.0297243 + 0.999558i \(0.490537\pi\)
\(380\) 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 0.749313 0.662216i \(-0.230384\pi\)
−0.662216 + 0.749313i \(0.730384\pi\)
\(384\) 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 0.0829624 0.996553i \(-0.473562\pi\)
−0.821559 + 0.570124i \(0.806895\pi\)
\(390\) −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 −0.153306 0.988179i \(-0.548992\pi\)
0.988179 + 0.153306i \(0.0489921\pi\)
\(398\) −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 −0.460840 0.887483i \(-0.652452\pi\)
0.0446427 + 0.999003i \(0.485785\pi\)
\(402\) −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 0.825103 + 0.564982i \(0.191117\pi\)
−0.997051 + 0.0767375i \(0.975550\pi\)
\(410\) 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 −0.0850532 0.996376i \(-0.527106\pi\)
0.820361 + 0.571846i \(0.193773\pi\)
\(420\) 0 0
\(421\) −21.2490 + 21.2490i −1.03561 + 1.03561i −0.0362722 + 0.999342i \(0.511548\pi\)
−0.999342 + 0.0362722i \(0.988452\pi\)
\(422\) −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 −0.986381 0.164479i \(-0.947406\pi\)
0.164479 + 0.986381i \(0.447406\pi\)
\(432\) −6.64286 3.83525i −0.319605 0.184524i
\(433\) 2.27124 3.93391i 0.109149 0.189051i −0.806277 0.591538i \(-0.798521\pi\)
0.915426 + 0.402487i \(0.131854\pi\)
\(434\) 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 −0.994403 0.105657i \(-0.966306\pi\)
0.588703 + 0.808350i \(0.299639\pi\)
\(440\) −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 0.862149 + 0.506655i \(0.169118\pi\)
0.00770183 + 0.999970i \(0.497548\pi\)
\(444\) 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 −0.928030 0.372505i \(-0.878499\pi\)
−0.617445 + 0.786614i \(0.711832\pi\)
\(450\) 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 0.978270 0.207336i \(-0.0664793\pi\)
−0.950874 + 0.309577i \(0.899813\pi\)
\(458\) 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 0.362961 0.931804i \(-0.381766\pi\)
0.780235 + 0.625486i \(0.215099\pi\)
\(462\) 0 0
\(463\) −22.6265 22.6265i −1.05154 1.05154i −0.998597 0.0529442i \(-0.983139\pi\)
−0.0529442 0.998597i \(-0.516861\pi\)
\(464\) −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 0.705278 0.708931i \(-0.250822\pi\)
−0.966591 + 0.256323i \(0.917489\pi\)
\(468\) −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 −0.304551 0.952496i \(-0.598506\pi\)
0.952496 + 0.304551i \(0.0985064\pi\)
\(480\) 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 0.869336 0.494221i \(-0.164547\pi\)
0.505756 + 0.862676i \(0.331213\pi\)
\(488\) −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 −0.829193 0.558962i \(-0.811200\pi\)
0.0694792 + 0.997583i \(0.477866\pi\)
\(492\) 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 −0.120883 0.992667i \(-0.538573\pi\)
−0.601021 + 0.799233i \(0.705239\pi\)
\(500\) 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 −0.206743 0.978395i \(-0.566287\pi\)
−0.950687 + 0.310153i \(0.899620\pi\)
\(504\) 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 −0.546182 0.837667i \(-0.683919\pi\)
−0.0541739 + 0.998532i \(0.517253\pi\)
\(510\) −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 0.483304 0.875453i \(-0.339437\pi\)
−0.516512 + 0.856280i \(0.672770\pi\)
\(522\) −2.21832 + 2.21832i −0.0970931 + 0.0970931i
\(523\) −11.7198 6.76640i −0.512469 0.295874i 0.221379 0.975188i \(-0.428944\pi\)
−0.733848 + 0.679314i \(0.762278\pi\)
\(524\) 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 −0.863266 0.504749i \(-0.831585\pi\)
0.999985 0.00549222i \(-0.00174824\pi\)
\(542\) 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 0.819977 0.572396i \(-0.193986\pi\)
−0.572396 + 0.819977i \(0.693986\pi\)
\(558\) 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 −0.993790 0.111274i \(-0.964507\pi\)
0.400528 0.916284i \(-0.368827\pi\)
\(564\) −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 0.669800 0.742542i \(-0.266380\pi\)
−0.308160 + 0.951335i \(0.599713\pi\)
\(570\) −1.61659 + 1.61659i −0.0677117 + 0.0677117i
\(571\) −4.46188 2.57607i −0.186724 0.107805i 0.403724 0.914881i \(-0.367716\pi\)
−0.590448 + 0.807076i \(0.701049\pi\)
\(572\) −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 −0.518707 0.854952i \(-0.673586\pi\)
−0.0217373 + 0.999764i \(0.506920\pi\)
\(578\) −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 0.408066 + 0.912952i \(0.366203\pi\)
−0.809872 + 0.586607i \(0.800463\pi\)
\(588\) 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 0.895848 0.444360i \(-0.146569\pi\)
0.553648 + 0.832751i \(0.313235\pi\)
\(594\) −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 −0.915240 0.402909i \(-0.867999\pi\)
0.806550 + 0.591166i \(0.201332\pi\)
\(600\) −2.19979 + 0.589432i −0.0898061 + 0.0240635i
\(601\) 21.4564 12.3879i 0.875225 0.505312i 0.00614424 0.999981i \(-0.498044\pi\)
0.869081 + 0.494669i \(0.164711\pi\)
\(602\) 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 \(0.151370\pi\)
−0.889044 + 0.457822i \(0.848630\pi\)
\(608\) 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 −0.297680 0.954666i \(-0.596213\pi\)
0.954666 + 0.297680i \(0.0962128\pi\)
\(614\) 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 0.925143 + 0.379618i \(0.123945\pi\)
−0.611389 + 0.791330i \(0.709389\pi\)
\(618\) 2.53484 + 2.53484i 0.101966 + 0.101966i
\(619\) −2.76561 10.3214i −0.111159 0.414852i 0.887812 0.460207i \(-0.152225\pi\)
−0.998971 + 0.0453549i \(0.985558\pi\)
\(620\) 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 0.0238855 0.999715i \(-0.492396\pi\)
0.520543 + 0.853836i \(0.325730\pi\)
\(632\) −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 0.292224 0.956350i \(-0.405605\pi\)
0.974335 + 0.225102i \(0.0722714\pi\)
\(642\) 0.627525 2.34196i 0.0247664 0.0924296i
\(643\) 33.2886 8.91965i 1.31277 0.351757i 0.466507 0.884517i \(-0.345512\pi\)
0.846266 + 0.532761i \(0.178845\pi\)
\(644\) 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 0.403162 + 0.915129i \(0.367911\pi\)
−0.994106 + 0.108416i \(0.965422\pi\)
\(654\) 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 −0.768224 0.640181i \(-0.778859\pi\)
0.938525 + 0.345211i \(0.112193\pi\)
\(660\) −15.4517 8.92102i −0.601455 0.347250i
\(661\) 12.7006 12.7006i 0.493996 0.493996i −0.415566 0.909563i \(-0.636417\pi\)
0.909563 + 0.415566i \(0.136417\pi\)
\(662\) −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 −0.0106133 0.999944i \(-0.503378\pi\)
0.860670 + 0.509163i \(0.170045\pi\)
\(674\) −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 −0.0900609 0.995936i \(-0.528706\pi\)
0.817476 + 0.575963i \(0.195373\pi\)
\(678\) −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 0.604324 + 0.796738i \(0.293443\pi\)
−0.921729 + 0.387833i \(0.873224\pi\)
\(684\) −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 −0.735365 0.677671i \(-0.762989\pi\)
−0.298010 + 0.954563i \(0.596323\pi\)
\(692\) −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 \(-0.709999\pi\)
0.612904 0.790158i \(-0.290001\pi\)
\(702\) 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 0.999972 0.00745226i \(-0.00237215\pi\)
−0.00745226 + 0.999972i \(0.502372\pi\)
\(710\) 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 −0.971917 0.235323i \(-0.924385\pi\)
0.959367 + 0.282163i \(0.0910518\pi\)
\(734\) 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 0.199388 0.979921i \(-0.436105\pi\)
−0.979921 + 0.199388i \(0.936105\pi\)
\(740\) −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 −0.551958 0.833872i \(-0.686119\pi\)
−0.894946 + 0.446175i \(0.852786\pi\)
\(744\) 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 0.944869 0.327448i \(-0.106189\pi\)
0.188856 + 0.982005i \(0.439522\pi\)
\(752\) −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 0.857935 0.513759i \(-0.171747\pi\)
−0.873895 + 0.486114i \(0.838414\pi\)
\(758\) 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 −0.0605137 0.998167i \(-0.519274\pi\)
0.998167 + 0.0605137i \(0.0192739\pi\)
\(762\) 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 0.666569 + 0.745443i \(0.267762\pi\)
−0.949987 + 0.312288i \(0.898904\pi\)
\(770\) 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 0.810052 + 0.586359i \(0.199439\pi\)
−0.994705 + 0.102776i \(0.967228\pi\)
\(774\) −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 +