Properties

Label 637.2.h.l.471.5
Level $637$
Weight $2$
Character 637.471
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - x^{11} + 7 x^{10} - 2 x^{9} + 33 x^{8} - 11 x^{7} + 55 x^{6} + 17 x^{5} + 47 x^{4} + x^{3} + 8 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 471.5
Root \(-1.02197 - 1.77010i\) of defining polynomial
Character \(\chi\) \(=\) 637.471
Dual form 637.2.h.l.165.5

$q$-expansion

\(f(q)\) \(=\) \(q+1.55469 q^{2} +(-0.244626 + 0.423704i) q^{3} +0.417051 q^{4} +(-0.595756 + 1.03188i) q^{5} +(-0.380316 + 0.658727i) q^{6} -2.46099 q^{8} +(1.38032 + 2.39078i) q^{9} +O(q^{10})\) \(q+1.55469 q^{2} +(-0.244626 + 0.423704i) q^{3} +0.417051 q^{4} +(-0.595756 + 1.03188i) q^{5} +(-0.380316 + 0.658727i) q^{6} -2.46099 q^{8} +(1.38032 + 2.39078i) q^{9} +(-0.926214 + 1.60425i) q^{10} +(-1.05807 + 1.83263i) q^{11} +(-0.102021 + 0.176706i) q^{12} +(-2.86133 + 2.19381i) q^{13} +(-0.291474 - 0.504848i) q^{15} -4.66017 q^{16} +0.906303 q^{17} +(2.14596 + 3.71691i) q^{18} +(3.34514 + 5.79395i) q^{19} +(-0.248461 + 0.430346i) q^{20} +(-1.64497 + 2.84917i) q^{22} +3.59733 q^{23} +(0.602021 - 1.04273i) q^{24} +(1.79015 + 3.10063i) q^{25} +(-4.44847 + 3.41068i) q^{26} -2.81840 q^{27} +(-4.25772 - 7.37459i) q^{29} +(-0.453151 - 0.784881i) q^{30} +(-2.64390 - 4.57937i) q^{31} -2.32313 q^{32} +(-0.517662 - 0.896617i) q^{33} +1.40902 q^{34} +(0.575663 + 0.997077i) q^{36} +4.99159 q^{37} +(5.20065 + 9.00778i) q^{38} +(-0.229570 - 1.74902i) q^{39} +(1.46615 - 2.53944i) q^{40} +(0.768181 + 1.33053i) q^{41} +(-2.71636 + 4.70488i) q^{43} +(-0.441269 + 0.764301i) q^{44} -3.28933 q^{45} +5.59272 q^{46} +(-1.59337 + 2.75979i) q^{47} +(1.14000 - 1.97453i) q^{48} +(2.78312 + 4.82051i) q^{50} +(-0.221705 + 0.384004i) q^{51} +(-1.19332 + 0.914930i) q^{52} +(1.41239 + 2.44632i) q^{53} -4.38173 q^{54} +(-1.26070 - 2.18360i) q^{55} -3.27323 q^{57} +(-6.61943 - 11.4652i) q^{58} +10.2460 q^{59} +(-0.121560 - 0.210548i) q^{60} +(-4.13423 - 7.16069i) q^{61} +(-4.11044 - 7.11949i) q^{62} +5.70861 q^{64} +(-0.559090 - 4.25952i) q^{65} +(-0.804802 - 1.39396i) q^{66} +(1.87182 - 3.24208i) q^{67} +0.377975 q^{68} +(-0.880000 + 1.52420i) q^{69} +(1.26510 - 2.19122i) q^{71} +(-3.39694 - 5.88368i) q^{72} +(-2.86522 - 4.96271i) q^{73} +7.76035 q^{74} -1.75167 q^{75} +(1.39510 + 2.41638i) q^{76} +(-0.356910 - 2.71918i) q^{78} +(-3.03620 + 5.25885i) q^{79} +(2.77632 - 4.80873i) q^{80} +(-3.45150 + 5.97817i) q^{81} +(1.19428 + 2.06856i) q^{82} +11.6309 q^{83} +(-0.539935 + 0.935195i) q^{85} +(-4.22310 + 7.31462i) q^{86} +4.16619 q^{87} +(2.60390 - 4.51008i) q^{88} +17.7511 q^{89} -5.11387 q^{90} +1.50027 q^{92} +2.58707 q^{93} +(-2.47719 + 4.29061i) q^{94} -7.97155 q^{95} +(0.568297 - 0.984319i) q^{96} +(3.10217 - 5.37312i) q^{97} -5.84188 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{2} - q^{3} + 8q^{4} - q^{5} + 9q^{6} - 6q^{8} + 3q^{9} + O(q^{10}) \) \( 12q - 4q^{2} - q^{3} + 8q^{4} - q^{5} + 9q^{6} - 6q^{8} + 3q^{9} - 4q^{10} + 4q^{11} - 5q^{12} + 2q^{13} - 2q^{15} - 16q^{16} + 10q^{17} + 3q^{18} + q^{19} + q^{20} - 5q^{22} + 2q^{23} + 11q^{24} + 7q^{25} + 16q^{26} + 8q^{27} + 3q^{29} - 5q^{30} - 16q^{31} - 16q^{32} - 16q^{33} - 32q^{34} - 21q^{36} + 26q^{37} + 17q^{38} - 20q^{39} + 5q^{40} + 8q^{41} - 11q^{43} + 21q^{44} - 14q^{45} - 32q^{46} + q^{47} - 21q^{48} + 6q^{50} - 20q^{51} - 41q^{52} - 2q^{53} - 36q^{54} - 9q^{55} + 42q^{57} - 8q^{58} + 26q^{59} + 20q^{60} + 5q^{61} - 5q^{62} - 30q^{64} - 5q^{65} - 18q^{66} - 11q^{67} + 58q^{68} - 23q^{69} + 6q^{71} + 25q^{72} + 30q^{73} + 6q^{74} - 6q^{75} + 9q^{76} + 16q^{78} + 7q^{79} + 7q^{80} - 6q^{81} - q^{82} + 54q^{83} - q^{85} - 7q^{86} + 32q^{87} + 8q^{89} + 16q^{90} + 54q^{92} + 14q^{93} - 45q^{94} + 12q^{95} - 19q^{96} + 35q^{97} - 20q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.55469 1.09933 0.549665 0.835385i \(-0.314755\pi\)
0.549665 + 0.835385i \(0.314755\pi\)
\(3\) −0.244626 + 0.423704i −0.141235 + 0.244626i −0.927962 0.372675i \(-0.878441\pi\)
0.786727 + 0.617301i \(0.211774\pi\)
\(4\) 0.417051 0.208526
\(5\) −0.595756 + 1.03188i −0.266430 + 0.461470i −0.967937 0.251192i \(-0.919177\pi\)
0.701507 + 0.712662i \(0.252511\pi\)
\(6\) −0.380316 + 0.658727i −0.155264 + 0.268924i
\(7\) 0 0
\(8\) −2.46099 −0.870091
\(9\) 1.38032 + 2.39078i 0.460105 + 0.796926i
\(10\) −0.926214 + 1.60425i −0.292894 + 0.507308i
\(11\) −1.05807 + 1.83263i −0.319020 + 0.552559i −0.980284 0.197595i \(-0.936687\pi\)
0.661264 + 0.750153i \(0.270020\pi\)
\(12\) −0.102021 + 0.176706i −0.0294511 + 0.0510107i
\(13\) −2.86133 + 2.19381i −0.793590 + 0.608453i
\(14\) 0 0
\(15\) −0.291474 0.504848i −0.0752584 0.130351i
\(16\) −4.66017 −1.16504
\(17\) 0.906303 0.219811 0.109905 0.993942i \(-0.464945\pi\)
0.109905 + 0.993942i \(0.464945\pi\)
\(18\) 2.14596 + 3.71691i 0.505808 + 0.876084i
\(19\) 3.34514 + 5.79395i 0.767428 + 1.32922i 0.938953 + 0.344045i \(0.111797\pi\)
−0.171525 + 0.985180i \(0.554870\pi\)
\(20\) −0.248461 + 0.430346i −0.0555575 + 0.0962284i
\(21\) 0 0
\(22\) −1.64497 + 2.84917i −0.350708 + 0.607444i
\(23\) 3.59733 0.750095 0.375048 0.927006i \(-0.377626\pi\)
0.375048 + 0.927006i \(0.377626\pi\)
\(24\) 0.602021 1.04273i 0.122887 0.212847i
\(25\) 1.79015 + 3.10063i 0.358030 + 0.620126i
\(26\) −4.44847 + 3.41068i −0.872417 + 0.668890i
\(27\) −2.81840 −0.542401
\(28\) 0 0
\(29\) −4.25772 7.37459i −0.790639 1.36943i −0.925572 0.378573i \(-0.876415\pi\)
0.134932 0.990855i \(-0.456918\pi\)
\(30\) −0.453151 0.784881i −0.0827337 0.143299i
\(31\) −2.64390 4.57937i −0.474859 0.822479i 0.524727 0.851271i \(-0.324168\pi\)
−0.999585 + 0.0287913i \(0.990834\pi\)
\(32\) −2.32313 −0.410675
\(33\) −0.517662 0.896617i −0.0901134 0.156081i
\(34\) 1.40902 0.241644
\(35\) 0 0
\(36\) 0.575663 + 0.997077i 0.0959438 + 0.166180i
\(37\) 4.99159 0.820612 0.410306 0.911948i \(-0.365422\pi\)
0.410306 + 0.911948i \(0.365422\pi\)
\(38\) 5.20065 + 9.00778i 0.843656 + 1.46126i
\(39\) −0.229570 1.74902i −0.0367606 0.280067i
\(40\) 1.46615 2.53944i 0.231818 0.401521i
\(41\) 0.768181 + 1.33053i 0.119970 + 0.207794i 0.919755 0.392492i \(-0.128387\pi\)
−0.799786 + 0.600286i \(0.795054\pi\)
\(42\) 0 0
\(43\) −2.71636 + 4.70488i −0.414242 + 0.717488i −0.995349 0.0963397i \(-0.969286\pi\)
0.581107 + 0.813827i \(0.302620\pi\)
\(44\) −0.441269 + 0.764301i −0.0665238 + 0.115223i
\(45\) −3.28933 −0.490344
\(46\) 5.59272 0.824602
\(47\) −1.59337 + 2.75979i −0.232416 + 0.402557i −0.958519 0.285030i \(-0.907997\pi\)
0.726102 + 0.687587i \(0.241330\pi\)
\(48\) 1.14000 1.97453i 0.164545 0.284999i
\(49\) 0 0
\(50\) 2.78312 + 4.82051i 0.393593 + 0.681723i
\(51\) −0.221705 + 0.384004i −0.0310449 + 0.0537714i
\(52\) −1.19332 + 0.914930i −0.165484 + 0.126878i
\(53\) 1.41239 + 2.44632i 0.194006 + 0.336029i 0.946574 0.322486i \(-0.104518\pi\)
−0.752568 + 0.658514i \(0.771185\pi\)
\(54\) −4.38173 −0.596278
\(55\) −1.26070 2.18360i −0.169993 0.294436i
\(56\) 0 0
\(57\) −3.27323 −0.433550
\(58\) −6.61943 11.4652i −0.869173 1.50545i
\(59\) 10.2460 1.33391 0.666956 0.745097i \(-0.267597\pi\)
0.666956 + 0.745097i \(0.267597\pi\)
\(60\) −0.121560 0.210548i −0.0156933 0.0271816i
\(61\) −4.13423 7.16069i −0.529333 0.916832i −0.999415 0.0342093i \(-0.989109\pi\)
0.470081 0.882623i \(-0.344225\pi\)
\(62\) −4.11044 7.11949i −0.522026 0.904176i
\(63\) 0 0
\(64\) 5.70861 0.713576
\(65\) −0.559090 4.25952i −0.0693465 0.528328i
\(66\) −0.804802 1.39396i −0.0990643 0.171584i
\(67\) 1.87182 3.24208i 0.228679 0.396083i −0.728738 0.684793i \(-0.759893\pi\)
0.957417 + 0.288709i \(0.0932261\pi\)
\(68\) 0.377975 0.0458362
\(69\) −0.880000 + 1.52420i −0.105939 + 0.183493i
\(70\) 0 0
\(71\) 1.26510 2.19122i 0.150140 0.260050i −0.781139 0.624357i \(-0.785361\pi\)
0.931279 + 0.364307i \(0.118694\pi\)
\(72\) −3.39694 5.88368i −0.400334 0.693398i
\(73\) −2.86522 4.96271i −0.335349 0.580841i 0.648203 0.761468i \(-0.275521\pi\)
−0.983552 + 0.180627i \(0.942187\pi\)
\(74\) 7.76035 0.902123
\(75\) −1.75167 −0.202265
\(76\) 1.39510 + 2.41638i 0.160028 + 0.277177i
\(77\) 0 0
\(78\) −0.356910 2.71918i −0.0404121 0.307886i
\(79\) −3.03620 + 5.25885i −0.341599 + 0.591667i −0.984730 0.174089i \(-0.944302\pi\)
0.643131 + 0.765756i \(0.277635\pi\)
\(80\) 2.77632 4.80873i 0.310402 0.537633i
\(81\) −3.45150 + 5.97817i −0.383500 + 0.664241i
\(82\) 1.19428 + 2.06856i 0.131886 + 0.228434i
\(83\) 11.6309 1.27665 0.638327 0.769766i \(-0.279627\pi\)
0.638327 + 0.769766i \(0.279627\pi\)
\(84\) 0 0
\(85\) −0.539935 + 0.935195i −0.0585642 + 0.101436i
\(86\) −4.22310 + 7.31462i −0.455388 + 0.788755i
\(87\) 4.16619 0.446663
\(88\) 2.60390 4.51008i 0.277576 0.480776i
\(89\) 17.7511 1.88162 0.940808 0.338939i \(-0.110068\pi\)
0.940808 + 0.338939i \(0.110068\pi\)
\(90\) −5.11387 −0.539049
\(91\) 0 0
\(92\) 1.50027 0.156414
\(93\) 2.58707 0.268266
\(94\) −2.47719 + 4.29061i −0.255502 + 0.442543i
\(95\) −7.97155 −0.817863
\(96\) 0.568297 0.984319i 0.0580015 0.100462i
\(97\) 3.10217 5.37312i 0.314978 0.545557i −0.664455 0.747328i \(-0.731336\pi\)
0.979433 + 0.201771i \(0.0646696\pi\)
\(98\) 0 0
\(99\) −5.84188 −0.587131
\(100\) 0.746584 + 1.29312i 0.0746584 + 0.129312i
\(101\) −3.61133 + 6.25501i −0.359341 + 0.622397i −0.987851 0.155405i \(-0.950332\pi\)
0.628510 + 0.777802i \(0.283665\pi\)
\(102\) −0.344682 + 0.597007i −0.0341286 + 0.0591125i
\(103\) 4.96322 8.59656i 0.489041 0.847044i −0.510879 0.859652i \(-0.670680\pi\)
0.999921 + 0.0126084i \(0.00401349\pi\)
\(104\) 7.04170 5.39894i 0.690496 0.529409i
\(105\) 0 0
\(106\) 2.19582 + 3.80327i 0.213277 + 0.369406i
\(107\) −2.20006 −0.212688 −0.106344 0.994329i \(-0.533915\pi\)
−0.106344 + 0.994329i \(0.533915\pi\)
\(108\) −1.17542 −0.113105
\(109\) −6.87291 11.9042i −0.658305 1.14022i −0.981054 0.193734i \(-0.937940\pi\)
0.322749 0.946485i \(-0.395393\pi\)
\(110\) −1.96000 3.39481i −0.186878 0.323683i
\(111\) −1.22107 + 2.11496i −0.115899 + 0.200743i
\(112\) 0 0
\(113\) 8.04736 13.9384i 0.757032 1.31122i −0.187326 0.982298i \(-0.559982\pi\)
0.944358 0.328920i \(-0.106685\pi\)
\(114\) −5.08885 −0.476614
\(115\) −2.14313 + 3.71201i −0.199848 + 0.346147i
\(116\) −1.77569 3.07558i −0.164869 0.285561i
\(117\) −9.19445 3.81266i −0.850027 0.352480i
\(118\) 15.9293 1.46641
\(119\) 0 0
\(120\) 0.717315 + 1.24243i 0.0654816 + 0.113418i
\(121\) 3.26098 + 5.64818i 0.296453 + 0.513471i
\(122\) −6.42743 11.1326i −0.581912 1.00790i
\(123\) −0.751668 −0.0677756
\(124\) −1.10264 1.90983i −0.0990202 0.171508i
\(125\) −10.2235 −0.914420
\(126\) 0 0
\(127\) 7.83921 + 13.5779i 0.695617 + 1.20484i 0.969972 + 0.243216i \(0.0782023\pi\)
−0.274355 + 0.961628i \(0.588464\pi\)
\(128\) 13.5213 1.19513
\(129\) −1.32899 2.30187i −0.117011 0.202668i
\(130\) −0.869209 6.62222i −0.0762347 0.580807i
\(131\) −4.76884 + 8.25988i −0.416656 + 0.721669i −0.995601 0.0936976i \(-0.970131\pi\)
0.578945 + 0.815367i \(0.303465\pi\)
\(132\) −0.215892 0.373935i −0.0187910 0.0325469i
\(133\) 0 0
\(134\) 2.91009 5.04042i 0.251393 0.435426i
\(135\) 1.67908 2.90825i 0.144512 0.250302i
\(136\) −2.23040 −0.191255
\(137\) −2.76461 −0.236197 −0.118098 0.993002i \(-0.537680\pi\)
−0.118098 + 0.993002i \(0.537680\pi\)
\(138\) −1.36812 + 2.36966i −0.116462 + 0.201719i
\(139\) −11.3983 + 19.7425i −0.966795 + 1.67454i −0.262081 + 0.965046i \(0.584409\pi\)
−0.704714 + 0.709492i \(0.748925\pi\)
\(140\) 0 0
\(141\) −0.779557 1.35023i −0.0656505 0.113710i
\(142\) 1.96684 3.40666i 0.165053 0.285881i
\(143\) −0.992950 7.56496i −0.0830346 0.632614i
\(144\) −6.43251 11.1414i −0.536043 0.928453i
\(145\) 10.1462 0.842600
\(146\) −4.45452 7.71546i −0.368659 0.638536i
\(147\) 0 0
\(148\) 2.08175 0.171119
\(149\) 7.20581 + 12.4808i 0.590323 + 1.02247i 0.994189 + 0.107651i \(0.0343329\pi\)
−0.403866 + 0.914818i \(0.632334\pi\)
\(150\) −2.72329 −0.222356
\(151\) −7.62901 13.2138i −0.620840 1.07533i −0.989330 0.145695i \(-0.953458\pi\)
0.368489 0.929632i \(-0.379875\pi\)
\(152\) −8.23236 14.2589i −0.667732 1.15655i
\(153\) 1.25098 + 2.16677i 0.101136 + 0.175173i
\(154\) 0 0
\(155\) 6.30048 0.506067
\(156\) −0.0957425 0.729431i −0.00766554 0.0584012i
\(157\) −5.70745 9.88559i −0.455504 0.788956i 0.543213 0.839595i \(-0.317208\pi\)
−0.998717 + 0.0506387i \(0.983874\pi\)
\(158\) −4.72034 + 8.17587i −0.375530 + 0.650437i
\(159\) −1.38202 −0.109602
\(160\) 1.38402 2.39719i 0.109416 0.189514i
\(161\) 0 0
\(162\) −5.36600 + 9.29418i −0.421592 + 0.730220i
\(163\) 7.20385 + 12.4774i 0.564249 + 0.977308i 0.997119 + 0.0758514i \(0.0241675\pi\)
−0.432870 + 0.901456i \(0.642499\pi\)
\(164\) 0.320371 + 0.554899i 0.0250168 + 0.0433303i
\(165\) 1.23360 0.0960357
\(166\) 18.0824 1.40346
\(167\) 3.88595 + 6.73066i 0.300704 + 0.520834i 0.976296 0.216442i \(-0.0694452\pi\)
−0.675592 + 0.737276i \(0.736112\pi\)
\(168\) 0 0
\(169\) 3.37442 12.5544i 0.259571 0.965724i
\(170\) −0.839430 + 1.45394i −0.0643813 + 0.111512i
\(171\) −9.23471 + 15.9950i −0.706196 + 1.22317i
\(172\) −1.13286 + 1.96218i −0.0863800 + 0.149615i
\(173\) 3.04731 + 5.27809i 0.231682 + 0.401286i 0.958303 0.285753i \(-0.0922436\pi\)
−0.726621 + 0.687039i \(0.758910\pi\)
\(174\) 6.47713 0.491030
\(175\) 0 0
\(176\) 4.93078 8.54037i 0.371672 0.643754i
\(177\) −2.50643 + 4.34126i −0.188395 + 0.326309i
\(178\) 27.5975 2.06852
\(179\) −9.26488 + 16.0472i −0.692490 + 1.19943i 0.278530 + 0.960428i \(0.410153\pi\)
−0.971020 + 0.239000i \(0.923181\pi\)
\(180\) −1.37182 −0.102249
\(181\) 5.60520 0.416631 0.208316 0.978062i \(-0.433202\pi\)
0.208316 + 0.978062i \(0.433202\pi\)
\(182\) 0 0
\(183\) 4.04535 0.299041
\(184\) −8.85299 −0.652651
\(185\) −2.97377 + 5.15071i −0.218636 + 0.378688i
\(186\) 4.02208 0.294913
\(187\) −0.958931 + 1.66092i −0.0701240 + 0.121458i
\(188\) −0.664516 + 1.15097i −0.0484648 + 0.0839435i
\(189\) 0 0
\(190\) −12.3933 −0.899102
\(191\) −0.251851 0.436219i −0.0182233 0.0315637i 0.856770 0.515699i \(-0.172468\pi\)
−0.874993 + 0.484135i \(0.839134\pi\)
\(192\) −1.39647 + 2.41876i −0.100782 + 0.174559i
\(193\) 1.85622 3.21507i 0.133614 0.231426i −0.791453 0.611230i \(-0.790675\pi\)
0.925067 + 0.379804i \(0.124009\pi\)
\(194\) 4.82290 8.35351i 0.346264 0.599747i
\(195\) 1.94154 + 0.805100i 0.139037 + 0.0576544i
\(196\) 0 0
\(197\) 3.72225 + 6.44713i 0.265200 + 0.459339i 0.967616 0.252427i \(-0.0812288\pi\)
−0.702416 + 0.711766i \(0.747895\pi\)
\(198\) −9.08230 −0.645451
\(199\) −7.50556 −0.532055 −0.266028 0.963965i \(-0.585711\pi\)
−0.266028 + 0.963965i \(0.585711\pi\)
\(200\) −4.40554 7.63062i −0.311519 0.539566i
\(201\) 0.915789 + 1.58619i 0.0645948 + 0.111881i
\(202\) −5.61449 + 9.72458i −0.395034 + 0.684219i
\(203\) 0 0
\(204\) −0.0924624 + 0.160149i −0.00647366 + 0.0112127i
\(205\) −1.83059 −0.127854
\(206\) 7.71626 13.3650i 0.537617 0.931181i
\(207\) 4.96545 + 8.60042i 0.345123 + 0.597770i
\(208\) 13.3343 10.2235i 0.924567 0.708873i
\(209\) −14.1576 −0.979299
\(210\) 0 0
\(211\) −1.89531 3.28278i −0.130479 0.225996i 0.793383 0.608723i \(-0.208318\pi\)
−0.923861 + 0.382728i \(0.874985\pi\)
\(212\) 0.589037 + 1.02024i 0.0404553 + 0.0700706i
\(213\) 0.618953 + 1.07206i 0.0424100 + 0.0734562i
\(214\) −3.42041 −0.233814
\(215\) −3.23658 5.60592i −0.220733 0.382320i
\(216\) 6.93605 0.471938
\(217\) 0 0
\(218\) −10.6852 18.5073i −0.723695 1.25348i
\(219\) 2.80363 0.189452
\(220\) −0.525777 0.910673i −0.0354479 0.0613975i
\(221\) −2.59323 + 1.98825i −0.174440 + 0.133744i
\(222\) −1.89838 + 3.28809i −0.127411 + 0.220682i
\(223\) 2.43440 + 4.21650i 0.163019 + 0.282358i 0.935950 0.352133i \(-0.114543\pi\)
−0.772931 + 0.634490i \(0.781210\pi\)
\(224\) 0 0
\(225\) −4.94195 + 8.55971i −0.329463 + 0.570647i
\(226\) 12.5111 21.6699i 0.832228 1.44146i
\(227\) −24.1767 −1.60466 −0.802332 0.596877i \(-0.796408\pi\)
−0.802332 + 0.596877i \(0.796408\pi\)
\(228\) −1.36510 −0.0904063
\(229\) −10.8561 + 18.8034i −0.717394 + 1.24256i 0.244635 + 0.969615i \(0.421332\pi\)
−0.962029 + 0.272947i \(0.912002\pi\)
\(230\) −3.33190 + 5.77101i −0.219699 + 0.380529i
\(231\) 0 0
\(232\) 10.4782 + 18.1488i 0.687928 + 1.19153i
\(233\) −1.89842 + 3.28816i −0.124370 + 0.215414i −0.921486 0.388411i \(-0.873024\pi\)
0.797117 + 0.603825i \(0.206358\pi\)
\(234\) −14.2945 5.92749i −0.934460 0.387492i
\(235\) −1.89851 3.28832i −0.123845 0.214507i
\(236\) 4.27309 0.278155
\(237\) −1.48547 2.57290i −0.0964914 0.167128i
\(238\) 0 0
\(239\) 21.9100 1.41724 0.708619 0.705592i \(-0.249319\pi\)
0.708619 + 0.705592i \(0.249319\pi\)
\(240\) 1.35832 + 2.35268i 0.0876792 + 0.151865i
\(241\) 20.7488 1.33655 0.668273 0.743916i \(-0.267034\pi\)
0.668273 + 0.743916i \(0.267034\pi\)
\(242\) 5.06980 + 8.78115i 0.325899 + 0.564474i
\(243\) −5.91625 10.2472i −0.379527 0.657361i
\(244\) −1.72418 2.98637i −0.110380 0.191183i
\(245\) 0 0
\(246\) −1.16861 −0.0745077
\(247\) −22.2824 9.23982i −1.41779 0.587916i
\(248\) 6.50661 + 11.2698i 0.413170 + 0.715632i
\(249\) −2.84521 + 4.92805i −0.180308 + 0.312302i
\(250\) −15.8944 −1.00525
\(251\) 6.62891 11.4816i 0.418413 0.724713i −0.577367 0.816485i \(-0.695920\pi\)
0.995780 + 0.0917718i \(0.0292530\pi\)
\(252\) 0 0
\(253\) −3.80622 + 6.59257i −0.239295 + 0.414472i
\(254\) 12.1875 + 21.1094i 0.764713 + 1.32452i
\(255\) −0.264164 0.457546i −0.0165426 0.0286526i
\(256\) 9.60425 0.600266
\(257\) 13.1711 0.821590 0.410795 0.911728i \(-0.365251\pi\)
0.410795 + 0.911728i \(0.365251\pi\)
\(258\) −2.06616 3.57869i −0.128633 0.222799i
\(259\) 0 0
\(260\) −0.233169 1.77644i −0.0144605 0.110170i
\(261\) 11.7540 20.3585i 0.727555 1.26016i
\(262\) −7.41406 + 12.8415i −0.458042 + 0.793352i
\(263\) 9.57028 16.5762i 0.590129 1.02213i −0.404086 0.914721i \(-0.632410\pi\)
0.994215 0.107412i \(-0.0342564\pi\)
\(264\) 1.27396 + 2.20657i 0.0784069 + 0.135805i
\(265\) −3.36575 −0.206756
\(266\) 0 0
\(267\) −4.34239 + 7.52123i −0.265750 + 0.460292i
\(268\) 0.780643 1.35211i 0.0476854 0.0825935i
\(269\) 28.4822 1.73659 0.868296 0.496047i \(-0.165216\pi\)
0.868296 + 0.496047i \(0.165216\pi\)
\(270\) 2.61044 4.52141i 0.158866 0.275164i
\(271\) −17.9474 −1.09023 −0.545114 0.838362i \(-0.683514\pi\)
−0.545114 + 0.838362i \(0.683514\pi\)
\(272\) −4.22353 −0.256089
\(273\) 0 0
\(274\) −4.29811 −0.259658
\(275\) −7.57641 −0.456875
\(276\) −0.367005 + 0.635671i −0.0220911 + 0.0382629i
\(277\) 13.4389 0.807463 0.403732 0.914877i \(-0.367713\pi\)
0.403732 + 0.914877i \(0.367713\pi\)
\(278\) −17.7209 + 30.6934i −1.06283 + 1.84087i
\(279\) 7.29884 12.6420i 0.436970 0.756855i
\(280\) 0 0
\(281\) −29.9530 −1.78685 −0.893424 0.449214i \(-0.851704\pi\)
−0.893424 + 0.449214i \(0.851704\pi\)
\(282\) −1.21197 2.09919i −0.0721716 0.125005i
\(283\) −4.94561 + 8.56604i −0.293986 + 0.509199i −0.974748 0.223306i \(-0.928315\pi\)
0.680763 + 0.732504i \(0.261649\pi\)
\(284\) 0.527613 0.913852i 0.0313080 0.0542271i
\(285\) 1.95005 3.37758i 0.115511 0.200070i
\(286\) −1.54373 11.7611i −0.0912824 0.695451i
\(287\) 0 0
\(288\) −3.20665 5.55408i −0.188954 0.327277i
\(289\) −16.1786 −0.951683
\(290\) 15.7742 0.926295
\(291\) 1.51774 + 2.62881i 0.0889716 + 0.154103i
\(292\) −1.19494 2.06970i −0.0699288 0.121120i
\(293\) 3.95529 6.85076i 0.231071 0.400226i −0.727053 0.686581i \(-0.759111\pi\)
0.958123 + 0.286356i \(0.0924438\pi\)
\(294\) 0 0
\(295\) −6.10409 + 10.5726i −0.355394 + 0.615561i
\(296\) −12.2842 −0.714007
\(297\) 2.98206 5.16508i 0.173037 0.299708i
\(298\) 11.2028 + 19.4038i 0.648959 + 1.12403i
\(299\) −10.2931 + 7.89185i −0.595268 + 0.456397i
\(300\) −0.730535 −0.0421775
\(301\) 0 0
\(302\) −11.8607 20.5434i −0.682508 1.18214i
\(303\) −1.76685 3.06027i −0.101503 0.175808i
\(304\) −15.5889 27.0008i −0.894086 1.54860i
\(305\) 9.85196 0.564121
\(306\) 1.94489 + 3.36865i 0.111182 + 0.192573i
\(307\) −1.27238 −0.0726187 −0.0363094 0.999341i \(-0.511560\pi\)
−0.0363094 + 0.999341i \(0.511560\pi\)
\(308\) 0 0
\(309\) 2.42827 + 4.20588i 0.138139 + 0.239264i
\(310\) 9.79527 0.556334
\(311\) 12.3817 + 21.4458i 0.702103 + 1.21608i 0.967727 + 0.252002i \(0.0810888\pi\)
−0.265624 + 0.964077i \(0.585578\pi\)
\(312\) 0.564970 + 4.30432i 0.0319851 + 0.243684i
\(313\) 1.18826 2.05812i 0.0671642 0.116332i −0.830488 0.557037i \(-0.811938\pi\)
0.897652 + 0.440705i \(0.145272\pi\)
\(314\) −8.87330 15.3690i −0.500749 0.867323i
\(315\) 0 0
\(316\) −1.26625 + 2.19321i −0.0712322 + 0.123378i
\(317\) 9.88979 17.1296i 0.555466 0.962096i −0.442401 0.896817i \(-0.645873\pi\)
0.997867 0.0652782i \(-0.0207935\pi\)
\(318\) −2.14862 −0.120488
\(319\) 18.0199 1.00892
\(320\) −3.40093 + 5.89059i −0.190118 + 0.329294i
\(321\) 0.538192 0.932176i 0.0300390 0.0520290i
\(322\) 0 0
\(323\) 3.03171 + 5.25108i 0.168689 + 0.292178i
\(324\) −1.43945 + 2.49320i −0.0799695 + 0.138511i
\(325\) −11.9244 4.94469i −0.661447 0.274282i
\(326\) 11.1997 + 19.3985i 0.620295 + 1.07438i
\(327\) 6.72516 0.371902
\(328\) −1.89049 3.27442i −0.104385 0.180799i
\(329\) 0 0
\(330\) 1.91786 0.105575
\(331\) −1.96386 3.40151i −0.107944 0.186964i 0.806993 0.590561i \(-0.201093\pi\)
−0.914937 + 0.403596i \(0.867760\pi\)
\(332\) 4.85067 0.266215
\(333\) 6.88997 + 11.9338i 0.377568 + 0.653967i
\(334\) 6.04143 + 10.4641i 0.330572 + 0.572568i
\(335\) 2.23029 + 3.86298i 0.121854 + 0.211057i
\(336\) 0 0
\(337\) −7.14099 −0.388995 −0.194497 0.980903i \(-0.562308\pi\)
−0.194497 + 0.980903i \(0.562308\pi\)
\(338\) 5.24617 19.5182i 0.285354 1.06165i
\(339\) 3.93718 + 6.81940i 0.213838 + 0.370379i
\(340\) −0.225181 + 0.390024i −0.0122121 + 0.0211520i
\(341\) 11.1897 0.605958
\(342\) −14.3571 + 24.8672i −0.776342 + 1.34466i
\(343\) 0 0
\(344\) 6.68494 11.5787i 0.360428 0.624280i
\(345\) −1.04853 1.81611i −0.0564509 0.0977759i
\(346\) 4.73761 + 8.20578i 0.254695 + 0.441145i
\(347\) 10.0700 0.540584 0.270292 0.962778i \(-0.412880\pi\)
0.270292 + 0.962778i \(0.412880\pi\)
\(348\) 1.73752 0.0931407
\(349\) −3.14418 5.44588i −0.168304 0.291512i 0.769520 0.638623i \(-0.220496\pi\)
−0.937824 + 0.347112i \(0.887162\pi\)
\(350\) 0 0
\(351\) 8.06437 6.18302i 0.430444 0.330025i
\(352\) 2.45803 4.25743i 0.131013 0.226922i
\(353\) 17.0836 29.5897i 0.909269 1.57490i 0.0941861 0.995555i \(-0.469975\pi\)
0.815083 0.579345i \(-0.196692\pi\)
\(354\) −3.89671 + 6.74930i −0.207108 + 0.358721i
\(355\) 1.50738 + 2.61087i 0.0800036 + 0.138570i
\(356\) 7.40313 0.392365
\(357\) 0 0
\(358\) −14.4040 + 24.9484i −0.761274 + 1.31857i
\(359\) −9.34327 + 16.1830i −0.493119 + 0.854107i −0.999969 0.00792750i \(-0.997477\pi\)
0.506850 + 0.862034i \(0.330810\pi\)
\(360\) 8.09500 0.426644
\(361\) −12.8799 + 22.3087i −0.677891 + 1.17414i
\(362\) 8.71433 0.458015
\(363\) −3.19088 −0.167478
\(364\) 0 0
\(365\) 6.82788 0.357388
\(366\) 6.28926 0.328745
\(367\) −15.5305 + 26.8997i −0.810687 + 1.40415i 0.101696 + 0.994816i \(0.467573\pi\)
−0.912384 + 0.409336i \(0.865760\pi\)
\(368\) −16.7642 −0.873893
\(369\) −2.12067 + 3.67310i −0.110397 + 0.191214i
\(370\) −4.62327 + 8.00775i −0.240353 + 0.416303i
\(371\) 0 0
\(372\) 1.07894 0.0559404
\(373\) 1.46852 + 2.54355i 0.0760371 + 0.131700i 0.901537 0.432702i \(-0.142440\pi\)
−0.825500 + 0.564403i \(0.809107\pi\)
\(374\) −1.49084 + 2.58221i −0.0770894 + 0.133523i
\(375\) 2.50094 4.33175i 0.129148 0.223691i
\(376\) 3.92126 6.79182i 0.202223 0.350261i
\(377\) 28.3612 + 11.7605i 1.46068 + 0.605698i
\(378\) 0 0
\(379\) −5.04254 8.73394i −0.259018 0.448632i 0.706961 0.707252i \(-0.250066\pi\)
−0.965979 + 0.258620i \(0.916732\pi\)
\(380\) −3.32454 −0.170545
\(381\) −7.67069 −0.392981
\(382\) −0.391550 0.678184i −0.0200334 0.0346989i
\(383\) 1.84466 + 3.19504i 0.0942576 + 0.163259i 0.909299 0.416144i \(-0.136619\pi\)
−0.815041 + 0.579403i \(0.803286\pi\)
\(384\) −3.30767 + 5.72905i −0.168794 + 0.292360i
\(385\) 0 0
\(386\) 2.88584 4.99842i 0.146885 0.254413i
\(387\) −14.9978 −0.762379
\(388\) 1.29376 2.24086i 0.0656809 0.113763i
\(389\) −11.3333 19.6299i −0.574623 0.995277i −0.996082 0.0884295i \(-0.971815\pi\)
0.421459 0.906847i \(-0.361518\pi\)
\(390\) 3.01849 + 1.25168i 0.152847 + 0.0633812i
\(391\) 3.26027 0.164879
\(392\) 0 0
\(393\) −2.33316 4.04116i −0.117693 0.203849i
\(394\) 5.78694 + 10.0233i 0.291542 + 0.504965i
\(395\) −3.61767 6.26598i −0.182025 0.315276i
\(396\) −2.43636 −0.122432
\(397\) −14.5680 25.2325i −0.731146 1.26638i −0.956394 0.292080i \(-0.905652\pi\)
0.225248 0.974302i \(-0.427681\pi\)
\(398\) −11.6688 −0.584904
\(399\) 0 0
\(400\) −8.34241 14.4495i −0.417120 0.722474i
\(401\) 8.12052 0.405519 0.202760 0.979229i \(-0.435009\pi\)
0.202760 + 0.979229i \(0.435009\pi\)
\(402\) 1.42377 + 2.46603i 0.0710110 + 0.122995i
\(403\) 17.6113 + 7.30289i 0.877283 + 0.363783i
\(404\) −1.50611 + 2.60866i −0.0749318 + 0.129786i
\(405\) −4.11250 7.12305i −0.204352 0.353947i
\(406\) 0 0
\(407\) −5.28144 + 9.14773i −0.261791 + 0.453436i
\(408\) 0.545614 0.945031i 0.0270119 0.0467860i
\(409\) 8.32261 0.411527 0.205763 0.978602i \(-0.434032\pi\)
0.205763 + 0.978602i \(0.434032\pi\)
\(410\) −2.84600 −0.140554
\(411\) 0.676295 1.17138i 0.0333592 0.0577798i
\(412\) 2.06992 3.58520i 0.101978 0.176630i
\(413\) 0 0
\(414\) 7.71973 + 13.3710i 0.379404 + 0.657147i
\(415\) −6.92915 + 12.0016i −0.340139 + 0.589138i
\(416\) 6.64723 5.09649i 0.325907 0.249876i
\(417\) −5.57666 9.65905i −0.273090 0.473006i
\(418\) −22.0106 −1.07657
\(419\) −6.50832 11.2727i −0.317952 0.550710i 0.662108 0.749408i \(-0.269662\pi\)
−0.980061 + 0.198699i \(0.936329\pi\)
\(420\) 0 0
\(421\) −8.89681 −0.433604 −0.216802 0.976216i \(-0.569563\pi\)
−0.216802 + 0.976216i \(0.569563\pi\)
\(422\) −2.94662 5.10369i −0.143439 0.248444i
\(423\) −8.79740 −0.427744
\(424\) −3.47587 6.02038i −0.168803 0.292376i
\(425\) 1.62242 + 2.81011i 0.0786988 + 0.136310i
\(426\) 0.962279 + 1.66672i 0.0466225 + 0.0807526i
\(427\) 0 0
\(428\) −0.917539 −0.0443509
\(429\) 3.44821 + 1.42987i 0.166481 + 0.0690346i
\(430\) −5.03187 8.71545i −0.242658 0.420296i
\(431\) 4.47872 7.75736i 0.215732 0.373659i −0.737767 0.675056i \(-0.764120\pi\)
0.953499 + 0.301397i \(0.0974529\pi\)
\(432\) 13.1342 0.631920
\(433\) −0.0864547 + 0.149744i −0.00415475 + 0.00719624i −0.868095 0.496398i \(-0.834656\pi\)
0.863941 + 0.503594i \(0.167989\pi\)
\(434\) 0 0
\(435\) −2.48203 + 4.29901i −0.119004 + 0.206122i
\(436\) −2.86636 4.96467i −0.137274 0.237765i
\(437\) 12.0336 + 20.8428i 0.575644 + 0.997045i
\(438\) 4.35876 0.208270
\(439\) −9.54160 −0.455396 −0.227698 0.973732i \(-0.573120\pi\)
−0.227698 + 0.973732i \(0.573120\pi\)
\(440\) 3.10257 + 5.37382i 0.147909 + 0.256187i
\(441\) 0 0
\(442\) −4.03166 + 3.09111i −0.191767 + 0.147029i
\(443\) 6.93676 12.0148i 0.329576 0.570842i −0.652852 0.757485i \(-0.726428\pi\)
0.982428 + 0.186644i \(0.0597610\pi\)
\(444\) −0.509249 + 0.882045i −0.0241679 + 0.0418600i
\(445\) −10.5753 + 18.3170i −0.501319 + 0.868310i
\(446\) 3.78473 + 6.55534i 0.179212 + 0.310404i
\(447\) −7.05091 −0.333496
\(448\) 0 0
\(449\) 10.6456 18.4388i 0.502398 0.870180i −0.497598 0.867408i \(-0.665784\pi\)
0.999996 0.00277167i \(-0.000882252\pi\)
\(450\) −7.68318 + 13.3077i −0.362189 + 0.627329i
\(451\) −3.25116 −0.153091
\(452\) 3.35616 5.81304i 0.157861 0.273423i
\(453\) 7.46501 0.350737
\(454\) −37.5872 −1.76406
\(455\) 0 0
\(456\) 8.05539 0.377228
\(457\) 9.68564 0.453075 0.226538 0.974002i \(-0.427259\pi\)
0.226538 + 0.974002i \(0.427259\pi\)
\(458\) −16.8779 + 29.2334i −0.788652 + 1.36599i
\(459\) −2.55432 −0.119226
\(460\) −0.893795 + 1.54810i −0.0416734 + 0.0721804i
\(461\) −0.687178 + 1.19023i −0.0320051 + 0.0554344i −0.881584 0.472027i \(-0.843523\pi\)
0.849579 + 0.527461i \(0.176856\pi\)
\(462\) 0 0
\(463\) 31.7710 1.47653 0.738263 0.674513i \(-0.235646\pi\)
0.738263 + 0.674513i \(0.235646\pi\)
\(464\) 19.8417 + 34.3669i 0.921128 + 1.59544i
\(465\) −1.54126 + 2.66954i −0.0714742 + 0.123797i
\(466\) −2.95145 + 5.11206i −0.136723 + 0.236812i
\(467\) −14.5605 + 25.2195i −0.673778 + 1.16702i 0.303046 + 0.952976i \(0.401996\pi\)
−0.976824 + 0.214042i \(0.931337\pi\)
\(468\) −3.83456 1.59007i −0.177252 0.0735012i
\(469\) 0 0
\(470\) −2.95160 5.11231i −0.136147 0.235813i
\(471\) 5.58476 0.257332
\(472\) −25.2152 −1.16062
\(473\) −5.74820 9.95618i −0.264303 0.457786i
\(474\) −2.30943 4.00006i −0.106076 0.183729i
\(475\) −11.9766 + 20.7441i −0.549525 + 0.951804i
\(476\) 0 0
\(477\) −3.89908 + 6.75341i −0.178527 + 0.309217i
\(478\) 34.0631 1.55801
\(479\) 4.86092 8.41936i 0.222101 0.384690i −0.733345 0.679857i \(-0.762042\pi\)
0.955446 + 0.295167i \(0.0953752\pi\)
\(480\) 0.677132 + 1.17283i 0.0309067 + 0.0535320i
\(481\) −14.2826 + 10.9506i −0.651229 + 0.499303i
\(482\) 32.2578 1.46930
\(483\) 0 0
\(484\) 1.36000 + 2.35558i 0.0618180 + 0.107072i
\(485\) 3.69627 + 6.40213i 0.167839 + 0.290706i
\(486\) −9.19791 15.9313i −0.417226 0.722656i
\(487\) −17.1133 −0.775478 −0.387739 0.921769i \(-0.626744\pi\)
−0.387739 + 0.921769i \(0.626744\pi\)
\(488\) 10.1743 + 17.6224i 0.460568 + 0.797728i
\(489\) −7.04899 −0.318766
\(490\) 0 0
\(491\) 12.8607 + 22.2753i 0.580394 + 1.00527i 0.995432 + 0.0954681i \(0.0304348\pi\)
−0.415038 + 0.909804i \(0.636232\pi\)
\(492\) −0.313484 −0.0141329
\(493\) −3.85879 6.68361i −0.173791 0.301015i
\(494\) −34.6421 14.3650i −1.55862 0.646313i
\(495\) 3.48033 6.02812i 0.156429 0.270944i
\(496\) 12.3210 + 21.3407i 0.553231 + 0.958224i
\(497\) 0 0
\(498\) −4.42341 + 7.66157i −0.198218 + 0.343323i
\(499\) −2.70198 + 4.67996i −0.120957 + 0.209504i −0.920145 0.391577i \(-0.871930\pi\)
0.799188 + 0.601081i \(0.205263\pi\)
\(500\) −4.26373 −0.190680
\(501\) −3.80241 −0.169879
\(502\) 10.3059 17.8503i 0.459974 0.796699i
\(503\) −6.30847 + 10.9266i −0.281281 + 0.487193i −0.971700 0.236216i \(-0.924093\pi\)
0.690420 + 0.723409i \(0.257426\pi\)
\(504\) 0 0
\(505\) −4.30294 7.45292i −0.191478 0.331650i
\(506\) −5.91749 + 10.2494i −0.263064 + 0.455641i
\(507\) 4.49389 + 4.50089i 0.199581 + 0.199892i
\(508\) 3.26935 + 5.66268i 0.145054 + 0.251241i
\(509\) 1.95876 0.0868204 0.0434102 0.999057i \(-0.486178\pi\)
0.0434102 + 0.999057i \(0.486178\pi\)
\(510\) −0.410692 0.711340i −0.0181858 0.0314987i
\(511\) 0 0
\(512\) −12.1111 −0.535240
\(513\) −9.42794 16.3297i −0.416254 0.720973i
\(514\) 20.4769 0.903198
\(515\) 5.91374 + 10.2429i 0.260590 + 0.451356i
\(516\) −0.554255 0.959998i −0.0243997 0.0422615i
\(517\) −3.37178 5.84010i −0.148291 0.256847i
\(518\) 0 0
\(519\) −2.98180 −0.130886
\(520\) 1.37591 + 10.4826i 0.0603378 + 0.459694i
\(521\) −19.5477 33.8576i −0.856401 1.48333i −0.875339 0.483509i \(-0.839362\pi\)
0.0189387 0.999821i \(-0.493971\pi\)
\(522\) 18.2738 31.6512i 0.799823 1.38533i
\(523\) 8.71268 0.380979 0.190489 0.981689i \(-0.438993\pi\)
0.190489 + 0.981689i \(0.438993\pi\)
\(524\) −1.98885 + 3.44479i −0.0868834 + 0.150486i
\(525\) 0 0
\(526\) 14.8788 25.7708i 0.648746 1.12366i
\(527\) −2.39618 4.15030i −0.104379 0.180790i
\(528\) 2.41239 + 4.17839i 0.104986 + 0.181841i
\(529\) −10.0592 −0.437357
\(530\) −5.23269 −0.227293
\(531\) 14.1427 + 24.4958i 0.613740 + 1.06303i
\(532\) 0 0
\(533\) −5.11694 2.12184i −0.221639 0.0919072i
\(534\) −6.75105 + 11.6932i −0.292147 + 0.506013i
\(535\) 1.31070 2.27020i 0.0566665 0.0981493i
\(536\) −4.60652 + 7.97873i −0.198971 + 0.344629i
\(537\) −4.53286 7.85114i −0.195607 0.338802i
\(538\) 44.2809 1.90909
\(539\) 0 0
\(540\) 0.700261 1.21289i 0.0301344 0.0521944i
\(541\) 10.7497 18.6190i 0.462165 0.800493i −0.536904 0.843644i \(-0.680406\pi\)
0.999069 + 0.0431505i \(0.0137395\pi\)
\(542\) −27.9026 −1.19852
\(543\) −1.37118 + 2.37495i −0.0588428 + 0.101919i
\(544\) −2.10546 −0.0902707
\(545\) 16.3783 0.701569
\(546\) 0 0
\(547\) −30.2968 −1.29540 −0.647699 0.761896i \(-0.724269\pi\)
−0.647699 + 0.761896i \(0.724269\pi\)
\(548\) −1.15299 −0.0492531
\(549\) 11.4131 19.7680i 0.487098 0.843679i
\(550\) −11.7789 −0.502256
\(551\) 28.4854 49.3381i 1.21352 2.10187i
\(552\) 2.16567 3.75105i 0.0921770 0.159655i
\(553\) 0 0
\(554\) 20.8932 0.887668
\(555\) −1.45492 2.51999i −0.0617579 0.106968i
\(556\) −4.75369 + 8.23364i −0.201601 + 0.349184i
\(557\) 8.84201 15.3148i 0.374648 0.648909i −0.615626 0.788038i \(-0.711097\pi\)
0.990274 + 0.139129i \(0.0444302\pi\)
\(558\) 11.3474 19.6543i 0.480374 0.832033i
\(559\) −2.54918 19.4214i −0.107819 0.821437i
\(560\) 0 0
\(561\) −0.469159 0.812606i −0.0198079 0.0343083i
\(562\) −46.5676 −1.96433
\(563\) 41.7390 1.75909 0.879545 0.475816i \(-0.157847\pi\)
0.879545 + 0.475816i \(0.157847\pi\)
\(564\) −0.325115 0.563116i −0.0136898 0.0237115i
\(565\) 9.58852 + 16.6078i 0.403392 + 0.698696i
\(566\) −7.68887 + 13.3175i −0.323187 + 0.559777i
\(567\) 0 0
\(568\) −3.11340 + 5.39257i −0.130636 + 0.226267i
\(569\) 5.46775 0.229220 0.114610 0.993411i \(-0.463438\pi\)
0.114610 + 0.993411i \(0.463438\pi\)
\(570\) 3.03171 5.25108i 0.126984 0.219943i
\(571\) −4.67621 8.09944i −0.195693 0.338951i 0.751434 0.659808i \(-0.229362\pi\)
−0.947128 + 0.320857i \(0.896029\pi\)
\(572\) −0.414111 3.15498i −0.0173149 0.131916i
\(573\) 0.246437 0.0102951
\(574\) 0 0
\(575\) 6.43976 + 11.1540i 0.268557 + 0.465154i
\(576\) 7.87968 + 13.6480i 0.328320 + 0.568667i
\(577\) −1.68462 2.91786i −0.0701318 0.121472i 0.828827 0.559505i \(-0.189009\pi\)
−0.898959 + 0.438033i \(0.855675\pi\)
\(578\) −25.1527 −1.04621
\(579\) 0.908159 + 1.57298i 0.0377418 + 0.0653707i
\(580\) 4.23151 0.175704
\(581\) 0 0
\(582\) 2.35961 + 4.08697i 0.0978091 + 0.169410i
\(583\) −5.97761 −0.247567
\(584\) 7.05128 + 12.2132i 0.291784 + 0.505385i
\(585\) 9.41185 7.21614i 0.389132 0.298351i
\(586\) 6.14924 10.6508i 0.254023 0.439980i
\(587\) −6.57639 11.3906i −0.271437 0.470142i 0.697793 0.716299i \(-0.254165\pi\)
−0.969230 + 0.246157i \(0.920832\pi\)
\(588\) 0 0
\(589\) 17.6884 30.6373i 0.728840 1.26239i
\(590\) −9.48995 + 16.4371i −0.390695 + 0.676704i
\(591\) −3.64224 −0.149822
\(592\) −23.2616 −0.956048
\(593\) 19.2958 33.4213i 0.792384 1.37245i −0.132102 0.991236i \(-0.542173\pi\)
0.924487 0.381214i \(-0.124494\pi\)
\(594\) 4.63617 8.03008i 0.190224 0.329478i
\(595\) 0 0
\(596\) 3.00519 + 5.20515i 0.123097 + 0.213211i
\(597\) 1.83605 3.18014i 0.0751447 0.130154i
\(598\) −16.0026 + 12.2694i −0.654396 + 0.501731i
\(599\) −9.20762 15.9481i −0.376213 0.651620i 0.614295 0.789077i \(-0.289441\pi\)
−0.990508 + 0.137457i \(0.956107\pi\)
\(600\) 4.31084 0.175989
\(601\) −20.7018 35.8566i −0.844445 1.46262i −0.886102 0.463490i \(-0.846597\pi\)
0.0416571 0.999132i \(-0.486736\pi\)
\(602\) 0 0
\(603\) 10.3348 0.420865
\(604\) −3.18169 5.51085i −0.129461 0.224233i
\(605\) −7.77099 −0.315936
\(606\) −2.74690 4.75777i −0.111585 0.193271i
\(607\) 6.15255 + 10.6565i 0.249724 + 0.432535i 0.963449 0.267891i \(-0.0863266\pi\)
−0.713725 + 0.700426i \(0.752993\pi\)
\(608\) −7.77119 13.4601i −0.315163 0.545879i
\(609\) 0 0
\(610\) 15.3167 0.620155
\(611\) −1.49530 11.3922i −0.0604934 0.460880i
\(612\) 0.521725 + 0.903654i 0.0210895 + 0.0365280i
\(613\) −13.1112 + 22.7093i −0.529556 + 0.917219i 0.469849 + 0.882747i \(0.344308\pi\)
−0.999406 + 0.0344720i \(0.989025\pi\)
\(614\) −1.97816 −0.0798319
\(615\) 0.447810 0.775630i 0.0180575 0.0312764i
\(616\) 0 0
\(617\) 9.41259 16.3031i 0.378936 0.656337i −0.611971 0.790880i \(-0.709623\pi\)
0.990908 + 0.134543i \(0.0429565\pi\)
\(618\) 3.77519 + 6.53882i 0.151860 + 0.263030i
\(619\) −7.90415 13.6904i −0.317695 0.550263i 0.662312 0.749228i \(-0.269575\pi\)
−0.980007 + 0.198965i \(0.936242\pi\)
\(620\) 2.62762 0.105528
\(621\) −10.1387 −0.406852
\(622\) 19.2497 + 33.3415i 0.771843 + 1.33687i
\(623\) 0 0
\(624\) 1.06984 + 8.15073i 0.0428277 + 0.326290i
\(625\) −2.86003 + 4.95371i −0.114401 + 0.198149i
\(626\) 1.84737 3.19973i 0.0738356 0.127887i
\(627\) 3.46331 5.99862i 0.138311 0.239562i
\(628\) −2.38030 4.12280i −0.0949843 0.164518i
\(629\) 4.52389 0.180379
\(630\) 0 0
\(631\) 8.33817 14.4421i 0.331937 0.574933i −0.650954 0.759117i \(-0.725631\pi\)
0.982892 + 0.184184i \(0.0589644\pi\)
\(632\) 7.47206 12.9420i 0.297222 0.514804i
\(633\) 1.85457 0.0737125
\(634\) 15.3755 26.6312i 0.610640 1.05766i
\(635\) −18.6810 −0.741333
\(636\) −0.576375 −0.0228548
\(637\) 0 0
\(638\) 28.0152 1.10913
\(639\) 6.98497 0.276321
\(640\) −8.05542 + 13.9524i −0.318418 + 0.551517i
\(641\) 49.2464 1.94512 0.972559 0.232658i \(-0.0747422\pi\)
0.972559 + 0.232658i \(0.0747422\pi\)
\(642\) 0.836720 1.44924i 0.0330227 0.0571970i
\(643\) 21.4355 37.1275i 0.845335 1.46416i −0.0399940 0.999200i \(-0.512734\pi\)
0.885330 0.464964i \(-0.153933\pi\)
\(644\) 0 0
\(645\) 3.16700 0.124701
\(646\) 4.71336 + 8.16378i 0.185445 + 0.321200i
\(647\) 2.12929 3.68804i 0.0837112 0.144992i −0.821130 0.570741i \(-0.806656\pi\)
0.904841 + 0.425749i \(0.139989\pi\)
\(648\) 8.49410 14.7122i 0.333680 0.577950i
\(649\) −10.8409 + 18.7771i −0.425544 + 0.737064i
\(650\) −18.5387 7.68744i −0.727148 0.301526i
\(651\) 0 0
\(652\) 3.00437 + 5.20373i 0.117660 + 0.203794i
\(653\) −2.09552 −0.0820040 −0.0410020 0.999159i \(-0.513055\pi\)
−0.0410020 + 0.999159i \(0.513055\pi\)
\(654\) 10.4555 0.408843
\(655\) −5.68213 9.84174i −0.222019 0.384549i
\(656\) −3.57986 6.20049i −0.139770 0.242089i
\(657\) 7.90982 13.7002i 0.308592 0.534496i
\(658\) 0 0
\(659\) −12.7259 + 22.0419i −0.495732 + 0.858632i −0.999988 0.00492170i \(-0.998433\pi\)
0.504256 + 0.863554i \(0.331767\pi\)
\(660\) 0.514475 0.0200259
\(661\) 13.9054 24.0848i 0.540857 0.936792i −0.457998 0.888953i \(-0.651433\pi\)
0.998855 0.0478387i \(-0.0152333\pi\)
\(662\) −3.05319 5.28829i −0.118666 0.205535i
\(663\) −0.208060 1.58514i −0.00808038 0.0615618i
\(664\) −28.6234 −1.11080
\(665\) 0 0
\(666\) 10.7117 + 18.5533i 0.415072 + 0.718925i
\(667\) −15.3164 26.5288i −0.593055 1.02720i
\(668\) 1.62064 + 2.80703i 0.0627044 + 0.108607i
\(669\) −2.38207 −0.0920960
\(670\) 3.46740 + 6.00572i 0.133957 + 0.232021i
\(671\) 17.4972 0.675472
\(672\) 0 0
\(673\) −7.76033 13.4413i −0.299139 0.518124i 0.676800 0.736167i \(-0.263366\pi\)
−0.975939 + 0.218043i \(0.930033\pi\)
\(674\) −11.1020 −0.427633
\(675\) −5.04536 8.73881i −0.194196 0.336357i
\(676\) 1.40731 5.23583i 0.0541272 0.201378i
\(677\) 17.2813 29.9321i 0.664175 1.15038i −0.315334 0.948981i \(-0.602116\pi\)
0.979508 0.201403i \(-0.0645502\pi\)
\(678\) 6.12109 + 10.6020i 0.235079 + 0.407169i
\(679\) 0 0
\(680\) 1.32877 2.30150i 0.0509562 0.0882587i
\(681\) 5.91425 10.2438i 0.226634 0.392542i
\(682\) 17.3965 0.666147
\(683\) 47.0064 1.79865 0.899325 0.437281i \(-0.144058\pi\)
0.899325 + 0.437281i \(0.144058\pi\)
\(684\) −3.85135 + 6.67073i −0.147260 + 0.255062i
\(685\) 1.64703 2.85275i 0.0629299 0.108998i
\(686\) 0 0
\(687\) −5.31138 9.19958i −0.202642 0.350986i
\(688\) 12.6587 21.9255i 0.482609 0.835904i
\(689\) −9.40807 3.90124i −0.358419 0.148625i
\(690\) −1.63013 2.82348i −0.0620582 0.107488i
\(691\) −19.0060 −0.723023 −0.361512 0.932368i \(-0.617739\pi\)
−0.361512 + 0.932368i \(0.617739\pi\)
\(692\) 1.27088 + 2.20123i 0.0483117 + 0.0836784i
\(693\) 0 0
\(694\) 15.6556 0.594280
\(695\) −13.5813 23.5234i −0.515166 0.892294i
\(696\) −10.2530 −0.388638
\(697\) 0.696205 + 1.20586i 0.0263706 + 0.0456753i
\(698\) −4.88822 8.46665i −0.185022 0.320467i
\(699\) −0.928805 1.60874i −0.0351306 0.0608480i
\(700\) 0 0
\(701\) −45.4648 −1.71718 −0.858591 0.512662i \(-0.828659\pi\)
−0.858591 + 0.512662i \(0.828659\pi\)
\(702\) 12.5376 9.61266i 0.473200 0.362807i
\(703\) 16.6976 + 28.9210i 0.629760 + 1.09078i
\(704\) −6.04010 + 10.4618i −0.227645 + 0.394293i
\(705\) 1.85770 0.0699651
\(706\) 26.5597 46.0027i 0.999586 1.73133i
\(707\) 0 0
\(708\) −1.04531 + 1.81053i −0.0392851 + 0.0680438i
\(709\) 4.89390 + 8.47648i 0.183794 + 0.318341i 0.943170 0.332312i \(-0.107829\pi\)
−0.759375 + 0.650653i \(0.774495\pi\)
\(710\) 2.34351 + 4.05908i 0.0879504 + 0.152334i
\(711\) −16.7637 −0.628687
\(712\) −43.6854 −1.63718
\(713\) −9.51099 16.4735i −0.356189 0.616938i
\(714\) 0 0
\(715\) 8.39768 + 3.48226i 0.314055 + 0.130229i
\(716\) −3.86393 + 6.69252i −0.144402 + 0.250111i
\(717\) −5.35974 + 9.28334i −0.200163 + 0.346693i
\(718\) −14.5259 + 25.1595i −0.542100 + 0.938945i
\(719\) −13.9201 24.1104i −0.519133 0.899165i −0.999753 0.0222358i \(-0.992922\pi\)
0.480620 0.876929i \(-0.340412\pi\)
\(720\) 15.3288 0.571271
\(721\) 0 0
\(722\) −20.0243 + 34.6830i −0.745226 + 1.29077i
\(723\) −5.07568 + 8.79134i −0.188767 + 0.326953i
\(724\) 2.33766 0.0868783
\(725\) 15.2439 26.4033i 0.566145 0.980592i
\(726\) −4.96082 −0.184113
\(727\) 14.5650 0.540186 0.270093 0.962834i \(-0.412945\pi\)
0.270093 + 0.962834i \(0.412945\pi\)
\(728\) 0 0
\(729\) −14.9199 −0.552589
\(730\) 10.6152 0.392887
\(731\) −2.46185 + 4.26405i −0.0910547 + 0.157711i
\(732\) 1.68712 0.0623577
\(733\) 8.83030 15.2945i 0.326155 0.564916i −0.655591 0.755116i \(-0.727580\pi\)
0.981745 + 0.190200i \(0.0609136\pi\)
\(734\) −24.1451 + 41.8206i −0.891213 + 1.54363i
\(735\) 0 0
\(736\) −8.35705 −0.308045
\(737\) 3.96102 + 6.86069i 0.145906 + 0.252717i
\(738\) −3.29697 + 5.71052i −0.121363 + 0.210207i
\(739\) −4.48279 + 7.76443i −0.164902 + 0.285619i −0.936621 0.350345i \(-0.886064\pi\)
0.771718 + 0.635964i \(0.219398\pi\)
\(740\) −1.24021 + 2.14811i −0.0455911 + 0.0789661i
\(741\) 9.36579 7.18084i 0.344061 0.263795i
\(742\) 0 0
\(743\) 13.1839 + 22.8352i 0.483671 + 0.837743i 0.999824 0.0187532i \(-0.00596968\pi\)
−0.516153 + 0.856497i \(0.672636\pi\)
\(744\) −6.36674 −0.233416
\(745\) −17.1716 −0.629119
\(746\) 2.28309 + 3.95442i 0.0835898 + 0.144782i
\(747\) 16.0543 + 27.8068i 0.587395 + 1.01740i
\(748\) −0.399923 + 0.692688i −0.0146226 + 0.0253272i
\(749\) 0 0
\(750\) 3.88818 6.73452i 0.141976 0.245910i
\(751\) −20.2876 −0.740305 −0.370152 0.928971i \(-0.620695\pi\)
−0.370152 + 0.928971i \(0.620695\pi\)
\(752\) 7.42536 12.8611i 0.270775 0.468996i
\(753\) 3.24321 + 5.61740i 0.118189 + 0.204709i
\(754\) 44.0928 + 18.2839i 1.60576 + 0.665861i
\(755\) 18.1801 0.661642
\(756\) 0 0
\(757\) −12.4992 21.6493i −0.454292 0.786857i 0.544355 0.838855i \(-0.316774\pi\)
−0.998647 + 0.0519981i \(0.983441\pi\)
\(758\) −7.83957 13.5785i −0.284746 0.493195i
\(759\) −1.86220 3.22543i −0.0675936 0.117076i
\(760\) 19.6179 0.711616
\(761\) 10.0711 + 17.4436i 0.365077 + 0.632332i 0.988789 0.149323i \(-0.0477094\pi\)
−0.623712 + 0.781655i \(0.714376\pi\)
\(762\) −11.9255 −0.432016
\(763\) 0 0
\(764\) −0.105035 0.181926i −0.00380003 0.00658184i
\(765\) −2.98112 −0.107783
\(766\) 2.86786 + 4.96729i 0.103620 + 0.179475i
\(767\) −29.3171 + 22.4777i −1.05858 + 0.811622i
\(768\) −2.34945 + 4.06936i −0.0847784 + 0.146840i
\(769\) 4.33610 + 7.51034i 0.156364 + 0.270830i 0.933555 0.358435i \(-0.116689\pi\)
−0.777191 + 0.629265i \(0.783356\pi\)
\(770\) 0 0
\(771\) −3.22199 + 5.58065i −0.116037 + 0.200982i
\(772\) 0.774139 1.34085i 0.0278619 0.0482582i
\(773\) −2.34567 −0.0843679 −0.0421839 0.999110i \(-0.513432\pi\)
−0.0421839 + 0.999110i \(0.513432\pi\)
\(774\) −23.3168 −0.838106
\(775\) 9.46596 16.3955i 0.340027 0.588945i
\(776\) −7.63441 + 13.2232i −0.274059 + 0.474685i
\(777\) 0 0
\(778\) −17.6198 30.5184i −0.631701 1.09414i
\(779\) −5.13935 + 8.90161i −0.184136 + 0.318933i
\(780\) 0.809724 + 0.335768i 0.0289928 + 0.0120224i
\(781\) 2.67713 + 4.63693i 0.0957953 + 0.165922i
\(782\) 5.06870 0.181256
\(783\) 12.0000