Properties

Label 637.2.x.b.80.3
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 80.3
Character \(\chi\) \(=\) 637.80
Dual form 637.2.x.b.215.4

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

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

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 \(-0.729966\pi\)
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 0.785290 + 0.619128i \(0.212514\pi\)
−0.989645 + 0.143535i \(0.954153\pi\)
\(6\) 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 \(-0.993045\pi\)
0.480960 0.876742i \(-0.340288\pi\)
\(18\) −0.113417 0.423277i −0.0267326 0.0997674i
\(19\) −3.01787 3.01787i −0.692346 0.692346i 0.270402 0.962748i \(-0.412843\pi\)
−0.962748 + 0.270402i \(0.912843\pi\)
\(20\) 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 0.132302 0.991210i \(-0.457763\pi\)
0.610181 + 0.792262i \(0.291097\pi\)
\(32\) 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 \(0.432441\pi\)
−0.671212 + 0.741266i \(0.734226\pi\)
\(42\) 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 0.693491 0.720465i \(-0.256072\pi\)
0.240348 + 0.970687i \(0.422738\pi\)
\(48\) −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 0.363344 0.931655i \(-0.381635\pi\)
−0.151162 + 0.988509i \(0.548302\pi\)
\(60\) 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 −0.706255 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 0.979272 0.202548i \(-0.0649223\pi\)
−0.949349 + 0.314224i \(0.898256\pi\)
\(74\) 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 \(0.0280486\pi\)
0.0880033 + 0.996120i \(0.471951\pi\)
\(84\) 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 \(0.0567159\pi\)
−0.763696 + 0.645576i \(0.776617\pi\)
\(90\) 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 \(-0.313444\pi\)
0.895557 + 0.444946i \(0.146777\pi\)
\(98\) 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 \(-0.206679\pi\)
0.796506 + 0.604630i \(0.206679\pi\)
\(102\) −0.917841 0.917841i −0.0908798 0.0908798i
\(103\) 5.90755 + 10.2322i 0.582088 + 1.00821i 0.995232 + 0.0975405i \(0.0310976\pi\)
−0.413143 + 0.910666i \(0.635569\pi\)
\(104\) 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 −0.701967 0.712209i \(-0.747695\pi\)
0.265808 + 0.964026i \(0.414361\pi\)
\(132\) −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 \(-0.985497\pi\)
−0.538927 0.842353i \(-0.681170\pi\)
\(140\) 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 0.720008 0.693966i \(-0.244138\pi\)
−0.240988 + 0.970528i \(0.577471\pi\)
\(158\) −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 0.223810 0.974633i \(-0.428151\pi\)
−0.293492 + 0.955962i \(0.594817\pi\)
\(168\) 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 \(-0.493616\pi\)
0.0200548 + 0.999799i \(0.493616\pi\)
\(174\) −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 \(-0.312078\pi\)
0.556672 + 0.830732i \(0.312078\pi\)
\(182\) 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 \(-0.927164\pi\)
0.290527 0.956867i \(-0.406170\pi\)
\(200\) 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 −0.917264 0.398279i \(-0.869608\pi\)
0.993514 + 0.113712i \(0.0362742\pi\)
\(224\) 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 \(-0.873234\pi\)
0.992154 + 0.125024i \(0.0399007\pi\)
\(228\) −5.70202 + 21.2802i −0.377625 + 1.40932i
\(229\) −13.1144 3.51399i −0.866623 0.232211i −0.201996 0.979386i \(-0.564743\pi\)
−0.664627 + 0.747176i \(0.731409\pi\)
\(230\) −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 −0.184501 0.982832i \(-0.559067\pi\)
−0.651199 + 0.758907i \(0.725734\pi\)
\(242\) 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 \(-0.868424\pi\)
0.805759 + 0.592243i \(0.201758\pi\)
\(252\) 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 \(-0.695564\pi\)
0.995882 + 0.0906578i \(0.0288970\pi\)
\(258\) −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 \(-0.560517\pi\)
0.755932 + 0.654650i \(0.227184\pi\)
\(270\) 0.403515i 0.0245571i
\(271\) 0.387901 + 1.44767i 0.0235633 + 0.0879396i 0.976706 0.214581i \(-0.0688386\pi\)
−0.953143 + 0.302521i \(0.902172\pi\)
\(272\) −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 \(-0.424763\pi\)
0.234169 + 0.972196i \(0.424763\pi\)
\(284\) 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 \(0.0328267\pi\)
−0.809952 + 0.586497i \(0.800507\pi\)
\(294\) 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 \(-0.854263\pi\)
0.442017 + 0.897007i \(0.354263\pi\)
\(308\) 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 \(-0.712762\pi\)
0.989533 + 0.144306i \(0.0460949\pi\)
\(312\) −4.23154 1.05432i −0.239564 0.0596892i
\(313\) 3.09510 1.78696i 0.174945 0.101005i −0.409970 0.912099i \(-0.634461\pi\)
0.584916 + 0.811094i \(0.301128\pi\)
\(314\) −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 0.631875 0.775071i \(-0.282286\pi\)
0.159684 + 0.987168i \(0.448952\pi\)
\(350\) 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 \(-0.387673\pi\)
−0.938379 + 0.345607i \(0.887673\pi\)
\(354\) 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 \(0.328016\pi\)
−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 0.525521 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 0.662216 0.749313i \(-0.269616\pi\)
−0.749313 + 0.662216i \(0.769616\pi\)
\(384\) −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 −0.988179 0.153306i \(-0.951008\pi\)
0.153306 + 0.988179i \(0.451008\pi\)
\(398\) 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 \(-0.808883\pi\)
0.997051 0.0767375i \(-0.0244503\pi\)
\(410\) 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 \(-0.806227\pi\)
0.0850532 + 0.996376i \(0.472894\pi\)
\(420\) 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 −0.915426 0.402487i \(-0.868146\pi\)
0.806277 + 0.591538i \(0.201479\pi\)
\(434\) 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 \(-0.700361\pi\)
0.994403 + 0.105657i \(0.0336944\pi\)
\(440\) 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 −0.780235 0.625486i \(-0.784901\pi\)
−0.362961 + 0.931804i \(0.618234\pi\)
\(462\) 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 0.966591 0.256323i \(-0.0825110\pi\)
−0.705278 + 0.708931i \(0.749178\pi\)
\(468\) 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 \(-0.901494\pi\)
0.304551 + 0.952496i \(0.401494\pi\)
\(480\) 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 0.950687 0.310153i \(-0.100380\pi\)
0.206743 + 0.978395i \(0.433713\pi\)
\(504\) 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 \(-0.482747\pi\)
0.546182 + 0.837667i \(0.316081\pi\)
\(510\) 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 \(-0.327230\pi\)
−0.483304 + 0.875453i \(0.660563\pi\)
\(522\) −2.21832 + 2.21832i −0.0970931 + 0.0970931i
\(523\) 11.7198 + 6.76640i 0.512469 + 0.295874i 0.733848 0.679314i \(-0.237722\pi\)
−0.221379 + 0.975188i \(0.571056\pi\)
\(524\) −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 \(0.0354932\pi\)
−0.400528 + 0.916284i \(0.631173\pi\)
\(564\) −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 0.0217373 0.999764i \(-0.493080\pi\)
0.518707 + 0.854952i \(0.326414\pi\)
\(578\) −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 \(-0.633797\pi\)
0.809872 0.586607i \(-0.199537\pi\)
\(588\) 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 \(-0.686765\pi\)
−0.895848 + 0.444360i \(0.853431\pi\)
\(594\) 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 −0.869081 0.494669i \(-0.835289\pi\)
−0.00614424 + 0.999981i \(0.501956\pi\)
\(602\) 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 −0.297680 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 0.998971 0.0453549i \(-0.0144419\pi\)
−0.887812 + 0.460207i \(0.847775\pi\)
\(620\) 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 −0.846266 0.532761i \(-0.821155\pi\)
−0.466507 + 0.884517i \(0.654488\pi\)
\(644\) 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 \(-0.538054\pi\)
−0.119264 + 0.992863i \(0.538054\pi\)
\(648\) −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 −0.909563 0.415566i \(-0.863583\pi\)
0.415566 + 0.909563i \(0.363583\pi\)
\(662\) −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 −0.817476 0.575963i \(-0.804627\pi\)
0.0900609 + 0.995936i \(0.471294\pi\)
\(678\) 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 0.298010 0.954563i \(-0.403677\pi\)
0.735365 + 0.677671i \(0.237011\pi\)
\(692\) 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 \(-0.685360\pi\)
−0.549968 + 0.835186i \(0.685360\pi\)
\(720\) −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 \(-0.517977\pi\)
−0.0564455 + 0.998406i \(0.517977\pi\)
\(728\) 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 \(-0.908948\pi\)
0.971917 + 0.235323i \(0.0756148\pi\)
\(734\) −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 −0.998167 0.0605137i \(-0.980726\pi\)
0.0605137 + 0.998167i \(0.480726\pi\)
\(762\) −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 \(-0.732238\pi\)
0.949987 0.312288i \(-0.101096\pi\)
\(770\) 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 \(-0.800561\pi\)
0.994705 0.102776i \(-0.0327724\pi\)
\(774\) −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 −0.846480