Properties

Label 1050.2.b.d.251.12
Level $1050$
Weight $2$
Character 1050.251
Analytic conductor $8.384$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 4 x^{8} - 30 x^{6} + 36 x^{4} + 729\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 251.12
Root \(1.68439 + 0.403509i\) of defining polynomial
Character \(\chi\) \(=\) 1050.251
Dual form 1050.2.b.d.251.6

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(1.68439 - 0.403509i) q^{3} -1.00000 q^{4} +(0.403509 + 1.68439i) q^{6} +(-2.31502 - 1.28088i) q^{7} -1.00000i q^{8} +(2.67436 - 1.35934i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(1.68439 - 0.403509i) q^{3} -1.00000 q^{4} +(0.403509 + 1.68439i) q^{6} +(-2.31502 - 1.28088i) q^{7} -1.00000i q^{8} +(2.67436 - 1.35934i) q^{9} +5.34872i q^{11} +(-1.68439 + 0.403509i) q^{12} +3.95617i q^{13} +(1.28088 - 2.31502i) q^{14} +1.00000 q^{16} +7.32496 q^{17} +(1.35934 + 2.67436i) q^{18} -0.807019i q^{19} +(-4.41626 - 1.22338i) q^{21} -5.34872 q^{22} -0.281327i q^{23} +(-0.403509 - 1.68439i) q^{24} -3.95617 q^{26} +(3.95617 - 3.36879i) q^{27} +(2.31502 + 1.28088i) q^{28} -0.281327i q^{29} +9.07971i q^{31} +1.00000i q^{32} +(2.15826 + 9.00935i) q^{33} +7.32496i q^{34} +(-2.67436 + 1.35934i) q^{36} +6.06739 q^{37} +0.807019 q^{38} +(1.59635 + 6.66375i) q^{39} +6.15019 q^{41} +(1.22338 - 4.41626i) q^{42} +6.34872 q^{43} -5.34872i q^{44} +0.281327 q^{46} -5.78984 q^{47} +(1.68439 - 0.403509i) q^{48} +(3.71867 + 5.93055i) q^{49} +(12.3381 - 2.95569i) q^{51} -3.95617i q^{52} -10.9788i q^{53} +(3.36879 + 3.95617i) q^{54} +(-1.28088 + 2.31502i) q^{56} +(-0.325639 - 1.35934i) q^{57} +0.281327 q^{58} -4.90390 q^{59} +13.2555i q^{61} -9.07971 q^{62} +(-7.93236 - 0.278649i) q^{63} -1.00000 q^{64} +(-9.00935 + 2.15826i) q^{66} -6.71867 q^{67} -7.32496 q^{68} +(-0.113518 - 0.473865i) q^{69} -3.36995i q^{71} +(-1.35934 - 2.67436i) q^{72} -4.98282i q^{73} +6.06739i q^{74} +0.807019i q^{76} +(6.85109 - 12.3824i) q^{77} +(-6.66375 + 1.59635i) q^{78} -3.26010 q^{79} +(5.30441 - 7.27071i) q^{81} +6.15019i q^{82} -1.53511 q^{83} +(4.41626 + 1.22338i) q^{84} +6.34872i q^{86} +(-0.113518 - 0.473865i) q^{87} +5.34872 q^{88} -4.31652 q^{89} +(5.06739 - 9.15863i) q^{91} +0.281327i q^{92} +(3.66375 + 15.2938i) q^{93} -5.78984i q^{94} +(0.403509 + 1.68439i) q^{96} -15.0892i q^{97} +(-5.93055 + 3.71867i) q^{98} +(7.27071 + 14.3044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 12q^{4} - 4q^{7} + O(q^{10}) \) \( 12q - 12q^{4} - 4q^{7} + 12q^{16} + 8q^{18} + 14q^{21} + 4q^{28} - 8q^{37} + 12q^{39} + 14q^{42} + 12q^{43} + 20q^{46} + 28q^{49} + 28q^{51} - 36q^{57} + 20q^{58} - 22q^{63} - 12q^{64} - 64q^{67} - 8q^{72} + 8q^{78} + 56q^{79} - 16q^{81} - 14q^{84} - 20q^{91} - 44q^{93} + 48q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.68439 0.403509i 0.972485 0.232966i
\(4\) −1.00000 −0.500000
\(5\) 0 0
\(6\) 0.403509 + 1.68439i 0.164732 + 0.687651i
\(7\) −2.31502 1.28088i −0.874997 0.484129i
\(8\) 1.00000i 0.353553i
\(9\) 2.67436 1.35934i 0.891454 0.453112i
\(10\) 0 0
\(11\) 5.34872i 1.61270i 0.591439 + 0.806350i \(0.298560\pi\)
−0.591439 + 0.806350i \(0.701440\pi\)
\(12\) −1.68439 + 0.403509i −0.486242 + 0.116483i
\(13\) 3.95617i 1.09724i 0.836070 + 0.548622i \(0.184847\pi\)
−0.836070 + 0.548622i \(0.815153\pi\)
\(14\) 1.28088 2.31502i 0.342331 0.618716i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 7.32496 1.77656 0.888281 0.459300i \(-0.151900\pi\)
0.888281 + 0.459300i \(0.151900\pi\)
\(18\) 1.35934 + 2.67436i 0.320399 + 0.630353i
\(19\) 0.807019i 0.185143i −0.995706 0.0925714i \(-0.970491\pi\)
0.995706 0.0925714i \(-0.0295086\pi\)
\(20\) 0 0
\(21\) −4.41626 1.22338i −0.963707 0.266963i
\(22\) −5.34872 −1.14035
\(23\) 0.281327i 0.0586607i −0.999570 0.0293304i \(-0.990663\pi\)
0.999570 0.0293304i \(-0.00933749\pi\)
\(24\) −0.403509 1.68439i −0.0823660 0.343825i
\(25\) 0 0
\(26\) −3.95617 −0.775869
\(27\) 3.95617 3.36879i 0.761365 0.648323i
\(28\) 2.31502 + 1.28088i 0.437498 + 0.242064i
\(29\) 0.281327i 0.0522411i −0.999659 0.0261206i \(-0.991685\pi\)
0.999659 0.0261206i \(-0.00831538\pi\)
\(30\) 0 0
\(31\) 9.07971i 1.63076i 0.578924 + 0.815382i \(0.303473\pi\)
−0.578924 + 0.815382i \(0.696527\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.15826 + 9.00935i 0.375705 + 1.56833i
\(34\) 7.32496i 1.25622i
\(35\) 0 0
\(36\) −2.67436 + 1.35934i −0.445727 + 0.226556i
\(37\) 6.06739 0.997473 0.498737 0.866754i \(-0.333797\pi\)
0.498737 + 0.866754i \(0.333797\pi\)
\(38\) 0.807019 0.130916
\(39\) 1.59635 + 6.66375i 0.255621 + 1.06705i
\(40\) 0 0
\(41\) 6.15019 0.960498 0.480249 0.877132i \(-0.340546\pi\)
0.480249 + 0.877132i \(0.340546\pi\)
\(42\) 1.22338 4.41626i 0.188771 0.681444i
\(43\) 6.34872 0.968171 0.484085 0.875021i \(-0.339152\pi\)
0.484085 + 0.875021i \(0.339152\pi\)
\(44\) 5.34872i 0.806350i
\(45\) 0 0
\(46\) 0.281327 0.0414794
\(47\) −5.78984 −0.844535 −0.422268 0.906471i \(-0.638766\pi\)
−0.422268 + 0.906471i \(0.638766\pi\)
\(48\) 1.68439 0.403509i 0.243121 0.0582415i
\(49\) 3.71867 + 5.93055i 0.531239 + 0.847222i
\(50\) 0 0
\(51\) 12.3381 2.95569i 1.72768 0.413879i
\(52\) 3.95617i 0.548622i
\(53\) 10.9788i 1.50805i −0.656846 0.754025i \(-0.728110\pi\)
0.656846 0.754025i \(-0.271890\pi\)
\(54\) 3.36879 + 3.95617i 0.458434 + 0.538367i
\(55\) 0 0
\(56\) −1.28088 + 2.31502i −0.171165 + 0.309358i
\(57\) −0.325639 1.35934i −0.0431320 0.180049i
\(58\) 0.281327 0.0369401
\(59\) −4.90390 −0.638433 −0.319217 0.947682i \(-0.603420\pi\)
−0.319217 + 0.947682i \(0.603420\pi\)
\(60\) 0 0
\(61\) 13.2555i 1.69719i 0.529040 + 0.848597i \(0.322552\pi\)
−0.529040 + 0.848597i \(0.677448\pi\)
\(62\) −9.07971 −1.15312
\(63\) −7.93236 0.278649i −0.999384 0.0351064i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −9.00935 + 2.15826i −1.10897 + 0.265663i
\(67\) −6.71867 −0.820817 −0.410408 0.911902i \(-0.634614\pi\)
−0.410408 + 0.911902i \(0.634614\pi\)
\(68\) −7.32496 −0.888281
\(69\) −0.113518 0.473865i −0.0136660 0.0570467i
\(70\) 0 0
\(71\) 3.36995i 0.399940i −0.979802 0.199970i \(-0.935916\pi\)
0.979802 0.199970i \(-0.0640844\pi\)
\(72\) −1.35934 2.67436i −0.160199 0.315176i
\(73\) 4.98282i 0.583195i −0.956541 0.291598i \(-0.905813\pi\)
0.956541 0.291598i \(-0.0941868\pi\)
\(74\) 6.06739i 0.705320i
\(75\) 0 0
\(76\) 0.807019i 0.0925714i
\(77\) 6.85109 12.3824i 0.780754 1.41111i
\(78\) −6.66375 + 1.59635i −0.754521 + 0.180751i
\(79\) −3.26010 −0.366789 −0.183395 0.983039i \(-0.558709\pi\)
−0.183395 + 0.983039i \(0.558709\pi\)
\(80\) 0 0
\(81\) 5.30441 7.27071i 0.589379 0.807857i
\(82\) 6.15019i 0.679175i
\(83\) −1.53511 −0.168501 −0.0842503 0.996445i \(-0.526850\pi\)
−0.0842503 + 0.996445i \(0.526850\pi\)
\(84\) 4.41626 + 1.22338i 0.481853 + 0.133482i
\(85\) 0 0
\(86\) 6.34872i 0.684600i
\(87\) −0.113518 0.473865i −0.0121704 0.0508037i
\(88\) 5.34872 0.570176
\(89\) −4.31652 −0.457550 −0.228775 0.973479i \(-0.573472\pi\)
−0.228775 + 0.973479i \(0.573472\pi\)
\(90\) 0 0
\(91\) 5.06739 9.15863i 0.531207 0.960085i
\(92\) 0.281327i 0.0293304i
\(93\) 3.66375 + 15.2938i 0.379913 + 1.58589i
\(94\) 5.78984i 0.597177i
\(95\) 0 0
\(96\) 0.403509 + 1.68439i 0.0411830 + 0.171913i
\(97\) 15.0892i 1.53207i −0.642796 0.766037i \(-0.722226\pi\)
0.642796 0.766037i \(-0.277774\pi\)
\(98\) −5.93055 + 3.71867i −0.599076 + 0.375643i
\(99\) 7.27071 + 14.3044i 0.730734 + 1.43765i
\(100\) 0 0
\(101\) −5.78984 −0.576111 −0.288055 0.957614i \(-0.593009\pi\)
−0.288055 + 0.957614i \(0.593009\pi\)
\(102\) 2.95569 + 12.3381i 0.292657 + 1.22165i
\(103\) 6.95721i 0.685514i 0.939424 + 0.342757i \(0.111361\pi\)
−0.939424 + 0.342757i \(0.888639\pi\)
\(104\) 3.95617 0.387934
\(105\) 0 0
\(106\) 10.9788 1.06635
\(107\) 10.6088i 1.02559i −0.858510 0.512797i \(-0.828610\pi\)
0.858510 0.512797i \(-0.171390\pi\)
\(108\) −3.95617 + 3.36879i −0.380683 + 0.324162i
\(109\) −18.1348 −1.73700 −0.868499 0.495691i \(-0.834915\pi\)
−0.868499 + 0.495691i \(0.834915\pi\)
\(110\) 0 0
\(111\) 10.2199 2.44825i 0.970028 0.232378i
\(112\) −2.31502 1.28088i −0.218749 0.121032i
\(113\) 8.54142i 0.803510i −0.915747 0.401755i \(-0.868400\pi\)
0.915747 0.401755i \(-0.131600\pi\)
\(114\) 1.35934 0.325639i 0.127314 0.0304989i
\(115\) 0 0
\(116\) 0.281327i 0.0261206i
\(117\) 5.37777 + 10.5802i 0.497175 + 0.978142i
\(118\) 4.90390i 0.451441i
\(119\) −16.9574 9.38242i −1.55449 0.860085i
\(120\) 0 0
\(121\) −17.6088 −1.60080
\(122\) −13.2555 −1.20010
\(123\) 10.3593 2.48166i 0.934070 0.223764i
\(124\) 9.07971i 0.815382i
\(125\) 0 0
\(126\) 0.278649 7.93236i 0.0248240 0.706671i
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 10.6937 2.56177i 0.941532 0.225551i
\(130\) 0 0
\(131\) 16.5454 1.44558 0.722788 0.691070i \(-0.242860\pi\)
0.722788 + 0.691070i \(0.242860\pi\)
\(132\) −2.15826 9.00935i −0.187852 0.784163i
\(133\) −1.03370 + 1.86827i −0.0896329 + 0.161999i
\(134\) 6.71867i 0.580405i
\(135\) 0 0
\(136\) 7.32496i 0.628110i
\(137\) 7.41612i 0.633601i 0.948492 + 0.316801i \(0.102609\pi\)
−0.948492 + 0.316801i \(0.897391\pi\)
\(138\) 0.473865 0.113518i 0.0403381 0.00966330i
\(139\) 6.36982i 0.540281i 0.962821 + 0.270141i \(0.0870702\pi\)
−0.962821 + 0.270141i \(0.912930\pi\)
\(140\) 0 0
\(141\) −9.75237 + 2.33625i −0.821298 + 0.196748i
\(142\) 3.36995 0.282800
\(143\) −21.1604 −1.76953
\(144\) 2.67436 1.35934i 0.222863 0.113278i
\(145\) 0 0
\(146\) 4.98282 0.412381
\(147\) 8.65674 + 8.48887i 0.713996 + 0.700150i
\(148\) −6.06739 −0.498737
\(149\) 7.60882i 0.623339i −0.950191 0.311669i \(-0.899112\pi\)
0.950191 0.311669i \(-0.100888\pi\)
\(150\) 0 0
\(151\) −4.63005 −0.376788 −0.188394 0.982094i \(-0.560328\pi\)
−0.188394 + 0.982094i \(0.560328\pi\)
\(152\) −0.807019 −0.0654578
\(153\) 19.5896 9.95708i 1.58372 0.804982i
\(154\) 12.3824 + 6.85109i 0.997804 + 0.552077i
\(155\) 0 0
\(156\) −1.59635 6.66375i −0.127810 0.533527i
\(157\) 15.3162i 1.22237i 0.791489 + 0.611184i \(0.209306\pi\)
−0.791489 + 0.611184i \(0.790694\pi\)
\(158\) 3.26010i 0.259359i
\(159\) −4.43004 18.4926i −0.351325 1.46656i
\(160\) 0 0
\(161\) −0.360347 + 0.651279i −0.0283993 + 0.0513280i
\(162\) 7.27071 + 5.30441i 0.571241 + 0.416754i
\(163\) −3.06739 −0.240257 −0.120128 0.992758i \(-0.538331\pi\)
−0.120128 + 0.992758i \(0.538331\pi\)
\(164\) −6.15019 −0.480249
\(165\) 0 0
\(166\) 1.53511i 0.119148i
\(167\) −1.89546 −0.146675 −0.0733376 0.997307i \(-0.523365\pi\)
−0.0733376 + 0.997307i \(0.523365\pi\)
\(168\) −1.22338 + 4.41626i −0.0943857 + 0.340722i
\(169\) −2.65128 −0.203945
\(170\) 0 0
\(171\) −1.09701 2.15826i −0.0838904 0.165046i
\(172\) −6.34872 −0.484085
\(173\) 8.86007 0.673619 0.336809 0.941573i \(-0.390652\pi\)
0.336809 + 0.941573i \(0.390652\pi\)
\(174\) 0.473865 0.113518i 0.0359236 0.00860578i
\(175\) 0 0
\(176\) 5.34872i 0.403175i
\(177\) −8.26010 + 1.97877i −0.620867 + 0.148733i
\(178\) 4.31652i 0.323537i
\(179\) 11.3487i 0.848243i 0.905605 + 0.424122i \(0.139417\pi\)
−0.905605 + 0.424122i \(0.860583\pi\)
\(180\) 0 0
\(181\) 8.63303i 0.641688i −0.947132 0.320844i \(-0.896033\pi\)
0.947132 0.320844i \(-0.103967\pi\)
\(182\) 9.15863 + 5.06739i 0.678883 + 0.375620i
\(183\) 5.34872 + 22.3275i 0.395389 + 1.65050i
\(184\) −0.281327 −0.0207397
\(185\) 0 0
\(186\) −15.2938 + 3.66375i −1.12140 + 0.268639i
\(187\) 39.1791i 2.86506i
\(188\) 5.78984 0.422268
\(189\) −13.4737 + 2.73143i −0.980064 + 0.198682i
\(190\) 0 0
\(191\) 7.78607i 0.563380i −0.959505 0.281690i \(-0.909105\pi\)
0.959505 0.281690i \(-0.0908950\pi\)
\(192\) −1.68439 + 0.403509i −0.121561 + 0.0291208i
\(193\) −25.1715 −1.81188 −0.905941 0.423404i \(-0.860835\pi\)
−0.905941 + 0.423404i \(0.860835\pi\)
\(194\) 15.0892 1.08334
\(195\) 0 0
\(196\) −3.71867 5.93055i −0.265619 0.423611i
\(197\) 2.52597i 0.179968i 0.995943 + 0.0899840i \(0.0286816\pi\)
−0.995943 + 0.0899840i \(0.971318\pi\)
\(198\) −14.3044 + 7.27071i −1.01657 + 0.516707i
\(199\) 0.947731i 0.0671828i −0.999436 0.0335914i \(-0.989306\pi\)
0.999436 0.0335914i \(-0.0106945\pi\)
\(200\) 0 0
\(201\) −11.3169 + 2.71105i −0.798232 + 0.191222i
\(202\) 5.78984i 0.407372i
\(203\) −0.360347 + 0.651279i −0.0252914 + 0.0457108i
\(204\) −12.3381 + 2.95569i −0.863840 + 0.206940i
\(205\) 0 0
\(206\) −6.95721 −0.484732
\(207\) −0.382418 0.752370i −0.0265799 0.0522933i
\(208\) 3.95617i 0.274311i
\(209\) 4.31652 0.298580
\(210\) 0 0
\(211\) −12.8901 −0.887394 −0.443697 0.896177i \(-0.646333\pi\)
−0.443697 + 0.896177i \(0.646333\pi\)
\(212\) 10.9788i 0.754025i
\(213\) −1.35981 5.67632i −0.0931724 0.388935i
\(214\) 10.6088 0.725204
\(215\) 0 0
\(216\) −3.36879 3.95617i −0.229217 0.269183i
\(217\) 11.6300 21.0197i 0.789499 1.42691i
\(218\) 18.1348i 1.22824i
\(219\) −2.01062 8.39303i −0.135865 0.567149i
\(220\) 0 0
\(221\) 28.9788i 1.94932i
\(222\) 2.44825 + 10.2199i 0.164316 + 0.685913i
\(223\) 23.7296i 1.58905i −0.607230 0.794526i \(-0.707719\pi\)
0.607230 0.794526i \(-0.292281\pi\)
\(224\) 1.28088 2.31502i 0.0855827 0.154679i
\(225\) 0 0
\(226\) 8.54142 0.568167
\(227\) 10.4667 0.694700 0.347350 0.937736i \(-0.387082\pi\)
0.347350 + 0.937736i \(0.387082\pi\)
\(228\) 0.325639 + 1.35934i 0.0215660 + 0.0900243i
\(229\) 16.4762i 1.08878i −0.838833 0.544388i \(-0.816762\pi\)
0.838833 0.544388i \(-0.183238\pi\)
\(230\) 0 0
\(231\) 6.54351 23.6213i 0.430531 1.55417i
\(232\) −0.281327 −0.0184700
\(233\) 27.9575i 1.83156i −0.401681 0.915780i \(-0.631574\pi\)
0.401681 0.915780i \(-0.368426\pi\)
\(234\) −10.5802 + 5.37777i −0.691651 + 0.351556i
\(235\) 0 0
\(236\) 4.90390 0.319217
\(237\) −5.49128 + 1.31548i −0.356697 + 0.0854495i
\(238\) 9.38242 16.9574i 0.608172 1.09919i
\(239\) 17.2601i 1.11646i −0.829685 0.558231i \(-0.811480\pi\)
0.829685 0.558231i \(-0.188520\pi\)
\(240\) 0 0
\(241\) 19.1935i 1.23636i −0.786037 0.618180i \(-0.787870\pi\)
0.786037 0.618180i \(-0.212130\pi\)
\(242\) 17.6088i 1.13194i
\(243\) 6.00091 14.3871i 0.384959 0.922934i
\(244\) 13.2555i 0.848597i
\(245\) 0 0
\(246\) 2.48166 + 10.3593i 0.158225 + 0.660487i
\(247\) 3.19270 0.203147
\(248\) 9.07971 0.576562
\(249\) −2.58574 + 0.619433i −0.163864 + 0.0392550i
\(250\) 0 0
\(251\) 21.0271 1.32722 0.663611 0.748078i \(-0.269023\pi\)
0.663611 + 0.748078i \(0.269023\pi\)
\(252\) 7.93236 + 0.278649i 0.499692 + 0.0175532i
\(253\) 1.50474 0.0946022
\(254\) 2.00000i 0.125491i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −14.5881 −0.909982 −0.454991 0.890496i \(-0.650358\pi\)
−0.454991 + 0.890496i \(0.650358\pi\)
\(258\) 2.56177 + 10.6937i 0.159489 + 0.665763i
\(259\) −14.0462 7.77163i −0.872786 0.482905i
\(260\) 0 0
\(261\) −0.382418 0.752370i −0.0236711 0.0465705i
\(262\) 16.5454i 1.02218i
\(263\) 8.91138i 0.549499i 0.961516 + 0.274749i \(0.0885949\pi\)
−0.961516 + 0.274749i \(0.911405\pi\)
\(264\) 9.00935 2.15826i 0.554487 0.132832i
\(265\) 0 0
\(266\) −1.86827 1.03370i −0.114551 0.0633800i
\(267\) −7.27071 + 1.74175i −0.444960 + 0.106594i
\(268\) 6.71867 0.410408
\(269\) 22.3352 1.36180 0.680901 0.732375i \(-0.261588\pi\)
0.680901 + 0.732375i \(0.261588\pi\)
\(270\) 0 0
\(271\) 7.17684i 0.435962i 0.975953 + 0.217981i \(0.0699471\pi\)
−0.975953 + 0.217981i \(0.930053\pi\)
\(272\) 7.32496 0.444141
\(273\) 4.83989 17.4715i 0.292924 1.05742i
\(274\) −7.41612 −0.448024
\(275\) 0 0
\(276\) 0.113518 + 0.473865i 0.00683298 + 0.0285233i
\(277\) 9.32749 0.560435 0.280217 0.959937i \(-0.409593\pi\)
0.280217 + 0.959937i \(0.409593\pi\)
\(278\) −6.36982 −0.382037
\(279\) 12.3424 + 24.2824i 0.738919 + 1.45375i
\(280\) 0 0
\(281\) 17.4373i 1.04022i −0.854098 0.520112i \(-0.825890\pi\)
0.854098 0.520112i \(-0.174110\pi\)
\(282\) −2.33625 9.75237i −0.139122 0.580745i
\(283\) 16.1776i 0.961660i 0.876814 + 0.480830i \(0.159665\pi\)
−0.876814 + 0.480830i \(0.840335\pi\)
\(284\) 3.36995i 0.199970i
\(285\) 0 0
\(286\) 21.1604i 1.25124i
\(287\) −14.2378 7.87768i −0.840433 0.465005i
\(288\) 1.35934 + 2.67436i 0.0800997 + 0.157588i
\(289\) 36.6550 2.15618
\(290\) 0 0
\(291\) −6.08862 25.4161i −0.356922 1.48992i
\(292\) 4.98282i 0.291598i
\(293\) 22.5623 1.31810 0.659050 0.752099i \(-0.270958\pi\)
0.659050 + 0.752099i \(0.270958\pi\)
\(294\) −8.48887 + 8.65674i −0.495081 + 0.504871i
\(295\) 0 0
\(296\) 6.06739i 0.352660i
\(297\) 18.0187 + 21.1604i 1.04555 + 1.22785i
\(298\) 7.60882 0.440767
\(299\) 1.11298 0.0643652
\(300\) 0 0
\(301\) −14.6974 8.13197i −0.847146 0.468719i
\(302\) 4.63005i 0.266429i
\(303\) −9.75237 + 2.33625i −0.560259 + 0.134214i
\(304\) 0.807019i 0.0462857i
\(305\) 0 0
\(306\) 9.95708 + 19.5896i 0.569208 + 1.11986i
\(307\) 19.4057i 1.10754i −0.832669 0.553771i \(-0.813188\pi\)
0.832669 0.553771i \(-0.186812\pi\)
\(308\) −6.85109 + 12.3824i −0.390377 + 0.705554i
\(309\) 2.80730 + 11.7187i 0.159702 + 0.666652i
\(310\) 0 0
\(311\) 6.73757 0.382053 0.191026 0.981585i \(-0.438818\pi\)
0.191026 + 0.981585i \(0.438818\pi\)
\(312\) 6.66375 1.59635i 0.377260 0.0903756i
\(313\) 21.3875i 1.20889i 0.796646 + 0.604446i \(0.206606\pi\)
−0.796646 + 0.604446i \(0.793394\pi\)
\(314\) −15.3162 −0.864344
\(315\) 0 0
\(316\) 3.26010 0.183395
\(317\) 3.47403i 0.195121i 0.995230 + 0.0975605i \(0.0311039\pi\)
−0.995230 + 0.0975605i \(0.968896\pi\)
\(318\) 18.4926 4.43004i 1.03701 0.248424i
\(319\) 1.50474 0.0842493
\(320\) 0 0
\(321\) −4.28076 17.8694i −0.238929 0.997374i
\(322\) −0.651279 0.360347i −0.0362944 0.0200814i
\(323\) 5.91138i 0.328918i
\(324\) −5.30441 + 7.27071i −0.294689 + 0.403928i
\(325\) 0 0
\(326\) 3.06739i 0.169887i
\(327\) −30.5461 + 7.31755i −1.68920 + 0.404662i
\(328\) 6.15019i 0.339587i
\(329\) 13.4036 + 7.41612i 0.738966 + 0.408864i
\(330\) 0 0
\(331\) −8.93261 −0.490980 −0.245490 0.969399i \(-0.578949\pi\)
−0.245490 + 0.969399i \(0.578949\pi\)
\(332\) 1.53511 0.0842503
\(333\) 16.2264 8.24763i 0.889201 0.451967i
\(334\) 1.89546i 0.103715i
\(335\) 0 0
\(336\) −4.41626 1.22338i −0.240927 0.0667408i
\(337\) 34.2176 1.86395 0.931977 0.362518i \(-0.118083\pi\)
0.931977 + 0.362518i \(0.118083\pi\)
\(338\) 2.65128i 0.144211i
\(339\) −3.44654 14.3871i −0.187191 0.781401i
\(340\) 0 0
\(341\) −48.5648 −2.62993
\(342\) 2.15826 1.09701i 0.116705 0.0593195i
\(343\) −1.01247 18.4926i −0.0546680 0.998505i
\(344\) 6.34872i 0.342300i
\(345\) 0 0
\(346\) 8.86007i 0.476320i
\(347\) 11.5260i 0.618747i −0.950941 0.309373i \(-0.899881\pi\)
0.950941 0.309373i \(-0.100119\pi\)
\(348\) 0.113518 + 0.473865i 0.00608521 + 0.0254018i
\(349\) 21.8342i 1.16876i 0.811482 + 0.584378i \(0.198661\pi\)
−0.811482 + 0.584378i \(0.801339\pi\)
\(350\) 0 0
\(351\) 13.3275 + 15.6513i 0.711369 + 0.835403i
\(352\) −5.34872 −0.285088
\(353\) −4.84211 −0.257720 −0.128860 0.991663i \(-0.541132\pi\)
−0.128860 + 0.991663i \(0.541132\pi\)
\(354\) −1.97877 8.26010i −0.105170 0.439019i
\(355\) 0 0
\(356\) 4.31652 0.228775
\(357\) −32.3489 8.96119i −1.71209 0.474277i
\(358\) −11.3487 −0.599799
\(359\) 30.3063i 1.59950i 0.600331 + 0.799752i \(0.295035\pi\)
−0.600331 + 0.799752i \(0.704965\pi\)
\(360\) 0 0
\(361\) 18.3487 0.965722
\(362\) 8.63303 0.453742
\(363\) −29.6602 + 7.10532i −1.55676 + 0.372933i
\(364\) −5.06739 + 9.15863i −0.265604 + 0.480043i
\(365\) 0 0
\(366\) −22.3275 + 5.34872i −1.16708 + 0.279582i
\(367\) 13.9910i 0.730325i −0.930944 0.365162i \(-0.881013\pi\)
0.930944 0.365162i \(-0.118987\pi\)
\(368\) 0.281327i 0.0146652i
\(369\) 16.4478 8.36018i 0.856239 0.435213i
\(370\) 0 0
\(371\) −14.0625 + 25.4161i −0.730090 + 1.31954i
\(372\) −3.66375 15.2938i −0.189956 0.792946i
\(373\) 4.24464 0.219779 0.109890 0.993944i \(-0.464950\pi\)
0.109890 + 0.993944i \(0.464950\pi\)
\(374\) −39.1791 −2.02591
\(375\) 0 0
\(376\) 5.78984i 0.298588i
\(377\) 1.11298 0.0573213
\(378\) −2.73143 13.4737i −0.140489 0.693010i
\(379\) −1.63005 −0.0837299 −0.0418650 0.999123i \(-0.513330\pi\)
−0.0418650 + 0.999123i \(0.513330\pi\)
\(380\) 0 0
\(381\) 3.36879 0.807019i 0.172588 0.0413448i
\(382\) 7.78607 0.398370
\(383\) −16.9994 −0.868631 −0.434316 0.900761i \(-0.643010\pi\)
−0.434316 + 0.900761i \(0.643010\pi\)
\(384\) −0.403509 1.68439i −0.0205915 0.0859563i
\(385\) 0 0
\(386\) 25.1715i 1.28119i
\(387\) 16.9788 8.63005i 0.863079 0.438690i
\(388\) 15.0892i 0.766037i
\(389\) 29.4623i 1.49380i −0.664938 0.746898i \(-0.731542\pi\)
0.664938 0.746898i \(-0.268458\pi\)
\(390\) 0 0
\(391\) 2.06071i 0.104214i
\(392\) 5.93055 3.71867i 0.299538 0.187821i
\(393\) 27.8689 6.67621i 1.40580 0.336770i
\(394\) −2.52597 −0.127257
\(395\) 0 0
\(396\) −7.27071 14.3044i −0.365367 0.718824i
\(397\) 17.8706i 0.896899i 0.893808 + 0.448449i \(0.148024\pi\)
−0.893808 + 0.448449i \(0.851976\pi\)
\(398\) 0.947731 0.0475054
\(399\) −0.987289 + 3.56400i −0.0494263 + 0.178423i
\(400\) 0 0
\(401\) 12.6762i 0.633020i 0.948589 + 0.316510i \(0.102511\pi\)
−0.948589 + 0.316510i \(0.897489\pi\)
\(402\) −2.71105 11.3169i −0.135215 0.564435i
\(403\) −35.9209 −1.78935
\(404\) 5.78984 0.288055
\(405\) 0 0
\(406\) −0.651279 0.360347i −0.0323224 0.0178837i
\(407\) 32.4528i 1.60863i
\(408\) −2.95569 12.3381i −0.146328 0.610827i
\(409\) 5.26425i 0.260300i −0.991494 0.130150i \(-0.958454\pi\)
0.991494 0.130150i \(-0.0415459\pi\)
\(410\) 0 0
\(411\) 2.99247 + 12.4917i 0.147608 + 0.616168i
\(412\) 6.95721i 0.342757i
\(413\) 11.3526 + 6.28133i 0.558627 + 0.309084i
\(414\) 0.752370 0.382418i 0.0369770 0.0187948i
\(415\) 0 0
\(416\) −3.95617 −0.193967
\(417\) 2.57028 + 10.7293i 0.125867 + 0.525416i
\(418\) 4.31652i 0.211128i
\(419\) −13.1148 −0.640700 −0.320350 0.947299i \(-0.603800\pi\)
−0.320350 + 0.947299i \(0.603800\pi\)
\(420\) 0 0
\(421\) 3.86521 0.188379 0.0941895 0.995554i \(-0.469974\pi\)
0.0941895 + 0.995554i \(0.469974\pi\)
\(422\) 12.8901i 0.627482i
\(423\) −15.4841 + 7.87034i −0.752864 + 0.382669i
\(424\) −10.9788 −0.533176
\(425\) 0 0
\(426\) 5.67632 1.35981i 0.275019 0.0658829i
\(427\) 16.9788 30.6868i 0.821660 1.48504i
\(428\) 10.6088i 0.512797i
\(429\) −35.6425 + 8.53844i −1.72084 + 0.412240i
\(430\) 0 0
\(431\) 10.2389i 0.493189i −0.969119 0.246594i \(-0.920688\pi\)
0.969119 0.246594i \(-0.0793115\pi\)
\(432\) 3.95617 3.36879i 0.190341 0.162081i
\(433\) 22.7030i 1.09103i 0.838099 + 0.545517i \(0.183667\pi\)
−0.838099 + 0.545517i \(0.816333\pi\)
\(434\) 21.0197 + 11.6300i 1.00898 + 0.558260i
\(435\) 0 0
\(436\) 18.1348 0.868499
\(437\) −0.227036 −0.0108606
\(438\) 8.39303 2.01062i 0.401035 0.0960709i
\(439\) 26.4492i 1.26235i −0.775639 0.631176i \(-0.782572\pi\)
0.775639 0.631176i \(-0.217428\pi\)
\(440\) 0 0
\(441\) 18.0067 + 10.8055i 0.857461 + 0.514548i
\(442\) −28.9788 −1.37838
\(443\) 27.8689i 1.32409i 0.749463 + 0.662046i \(0.230312\pi\)
−0.749463 + 0.662046i \(0.769688\pi\)
\(444\) −10.2199 + 2.44825i −0.485014 + 0.116189i
\(445\) 0 0
\(446\) 23.7296 1.12363
\(447\) −3.07023 12.8162i −0.145217 0.606187i
\(448\) 2.31502 + 1.28088i 0.109375 + 0.0605161i
\(449\) 9.45858i 0.446378i −0.974775 0.223189i \(-0.928353\pi\)
0.974775 0.223189i \(-0.0716467\pi\)
\(450\) 0 0
\(451\) 32.8956i 1.54900i
\(452\) 8.54142i 0.401755i
\(453\) −7.79882 + 1.86827i −0.366421 + 0.0877789i
\(454\) 10.4667i 0.491227i
\(455\) 0 0
\(456\) −1.35934 + 0.325639i −0.0636568 + 0.0152495i
\(457\) −31.8322 −1.48905 −0.744524 0.667595i \(-0.767324\pi\)
−0.744524 + 0.667595i \(0.767324\pi\)
\(458\) 16.4762 0.769881
\(459\) 28.9788 24.6762i 1.35261 1.15179i
\(460\) 0 0
\(461\) 10.6320 0.495179 0.247590 0.968865i \(-0.420362\pi\)
0.247590 + 0.968865i \(0.420362\pi\)
\(462\) 23.6213 + 6.54351i 1.09896 + 0.304432i
\(463\) −12.8322 −0.596364 −0.298182 0.954509i \(-0.596380\pi\)
−0.298182 + 0.954509i \(0.596380\pi\)
\(464\) 0.281327i 0.0130603i
\(465\) 0 0
\(466\) 27.9575 1.29511
\(467\) −20.8716 −0.965824 −0.482912 0.875669i \(-0.660421\pi\)
−0.482912 + 0.875669i \(0.660421\pi\)
\(468\) −5.37777 10.5802i −0.248587 0.489071i
\(469\) 15.5539 + 8.60584i 0.718212 + 0.397381i
\(470\) 0 0
\(471\) 6.18024 + 25.7985i 0.284770 + 1.18873i
\(472\) 4.90390i 0.225720i
\(473\) 33.9575i 1.56137i
\(474\) −1.31548 5.49128i −0.0604220 0.252223i
\(475\) 0 0
\(476\) 16.9574 + 9.38242i 0.777243 + 0.430042i
\(477\) −14.9238 29.3612i −0.683316 1.34436i
\(478\) 17.2601 0.789458
\(479\) 33.6879 1.53924 0.769619 0.638504i \(-0.220446\pi\)
0.769619 + 0.638504i \(0.220446\pi\)
\(480\) 0 0
\(481\) 24.0036i 1.09447i
\(482\) 19.1935 0.874238
\(483\) −0.344169 + 1.24241i −0.0156603 + 0.0565318i
\(484\) 17.6088 0.800401
\(485\) 0 0
\(486\) 14.3871 + 6.00091i 0.652613 + 0.272207i
\(487\) −33.3524 −1.51134 −0.755671 0.654951i \(-0.772689\pi\)
−0.755671 + 0.654951i \(0.772689\pi\)
\(488\) 13.2555 0.600049
\(489\) −5.16670 + 1.23772i −0.233646 + 0.0559717i
\(490\) 0 0
\(491\) 30.0000i 1.35388i −0.736038 0.676941i \(-0.763305\pi\)
0.736038 0.676941i \(-0.236695\pi\)
\(492\) −10.3593 + 2.48166i −0.467035 + 0.111882i
\(493\) 2.06071i 0.0928096i
\(494\) 3.19270i 0.143646i
\(495\) 0 0
\(496\) 9.07971i 0.407691i
\(497\) −4.31652 + 7.80152i −0.193622 + 0.349946i
\(498\) −0.619433 2.58574i −0.0277574 0.115870i
\(499\) −19.1810 −0.858657 −0.429329 0.903148i \(-0.641250\pi\)
−0.429329 + 0.903148i \(0.641250\pi\)
\(500\) 0 0
\(501\) −3.19270 + 0.764836i −0.142639 + 0.0341704i
\(502\) 21.0271i 0.938487i
\(503\) −36.9851 −1.64909 −0.824543 0.565800i \(-0.808568\pi\)
−0.824543 + 0.565800i \(0.808568\pi\)
\(504\) −0.278649 + 7.93236i −0.0124120 + 0.353335i
\(505\) 0 0
\(506\) 1.50474i 0.0668938i
\(507\) −4.46580 + 1.06982i −0.198333 + 0.0475122i
\(508\) −2.00000 −0.0887357
\(509\) −36.0374 −1.59733 −0.798665 0.601776i \(-0.794460\pi\)
−0.798665 + 0.601776i \(0.794460\pi\)
\(510\) 0 0
\(511\) −6.38242 + 11.5354i −0.282342 + 0.510294i
\(512\) 1.00000i 0.0441942i
\(513\) −2.71867 3.19270i −0.120032 0.140961i
\(514\) 14.5881i 0.643455i
\(515\) 0 0
\(516\) −10.6937 + 2.56177i −0.470766 + 0.112776i
\(517\) 30.9682i 1.36198i
\(518\) 7.77163 14.0462i 0.341466 0.617153i
\(519\) 14.9238 3.57512i 0.655084 0.156930i
\(520\) 0 0
\(521\) −3.65761 −0.160243 −0.0801214 0.996785i \(-0.525531\pi\)
−0.0801214 + 0.996785i \(0.525531\pi\)
\(522\) 0.752370 0.382418i 0.0329303 0.0167380i
\(523\) 2.26321i 0.0989633i −0.998775 0.0494816i \(-0.984243\pi\)
0.998775 0.0494816i \(-0.0157569\pi\)
\(524\) −16.5454 −0.722788
\(525\) 0 0
\(526\) −8.91138 −0.388554
\(527\) 66.5084i 2.89715i
\(528\) 2.15826 + 9.00935i 0.0939261 + 0.392082i
\(529\) 22.9209 0.996559
\(530\) 0 0
\(531\) −13.1148 + 6.66605i −0.569134 + 0.289282i
\(532\) 1.03370 1.86827i 0.0448164 0.0809997i
\(533\) 24.3312i 1.05390i
\(534\) −1.74175 7.27071i −0.0753731 0.314634i
\(535\) 0 0
\(536\) 6.71867i 0.290202i
\(537\) 4.57931 + 19.1157i 0.197612 + 0.824904i
\(538\) 22.3352i 0.962940i
\(539\) −31.7209 + 19.8901i −1.36632 + 0.856729i
\(540\) 0 0
\(541\) 15.1502 0.651360 0.325680 0.945480i \(-0.394407\pi\)
0.325680 + 0.945480i \(0.394407\pi\)
\(542\) −7.17684 −0.308272
\(543\) −3.48351 14.5414i −0.149492 0.624032i
\(544\) 7.32496i 0.314055i
\(545\) 0 0
\(546\) 17.4715 + 4.83989i 0.747710 + 0.207128i
\(547\) −2.89014 −0.123574 −0.0617868 0.998089i \(-0.519680\pi\)
−0.0617868 + 0.998089i \(0.519680\pi\)
\(548\) 7.41612i 0.316801i
\(549\) 18.0187 + 35.4500i 0.769019 + 1.51297i
\(550\) 0 0
\(551\) −0.227036 −0.00967206
\(552\) −0.473865 + 0.113518i −0.0201690 + 0.00483165i
\(553\) 7.54720 + 4.17580i 0.320940 + 0.177573i
\(554\) 9.32749i 0.396287i
\(555\) 0 0
\(556\) 6.36982i 0.270141i
\(557\) 32.4777i 1.37613i −0.725651 0.688063i \(-0.758461\pi\)
0.725651 0.688063i \(-0.241539\pi\)
\(558\) −24.2824 + 12.3424i −1.02796 + 0.522494i
\(559\) 25.1166i 1.06232i
\(560\) 0 0
\(561\) 15.8091 + 65.9931i 0.667463 + 2.78623i
\(562\) 17.4373 0.735550
\(563\) −10.9208 −0.460256 −0.230128 0.973160i \(-0.573914\pi\)
−0.230128 + 0.973160i \(0.573914\pi\)
\(564\) 9.75237 2.33625i 0.410649 0.0983741i
\(565\) 0 0
\(566\) −16.1776 −0.679996
\(567\) −21.5928 + 10.0375i −0.906811 + 0.421537i
\(568\) −3.36995 −0.141400
\(569\) 4.58388i 0.192166i −0.995373 0.0960832i \(-0.969369\pi\)
0.995373 0.0960832i \(-0.0306315\pi\)
\(570\) 0 0
\(571\) 5.82853 0.243916 0.121958 0.992535i \(-0.461083\pi\)
0.121958 + 0.992535i \(0.461083\pi\)
\(572\) 21.1604 0.884763
\(573\) −3.14175 13.1148i −0.131248 0.547879i
\(574\) 7.87768 14.2378i 0.328808 0.594276i
\(575\) 0 0
\(576\) −2.67436 + 1.35934i −0.111432 + 0.0566390i
\(577\) 9.82493i 0.409017i 0.978865 + 0.204509i \(0.0655597\pi\)
−0.978865 + 0.204509i \(0.934440\pi\)
\(578\) 36.6550i 1.52465i
\(579\) −42.3987 + 10.1569i −1.76203 + 0.422107i
\(580\) 0 0
\(581\) 3.55383 + 1.96630i 0.147438 + 0.0815760i
\(582\) 25.4161 6.08862i 1.05353 0.252382i
\(583\) 58.7224 2.43203
\(584\) −4.98282 −0.206191
\(585\) 0 0
\(586\) 22.5623i 0.932038i
\(587\) 27.3106 1.12723 0.563615 0.826037i \(-0.309410\pi\)
0.563615 + 0.826037i \(0.309410\pi\)
\(588\) −8.65674 8.48887i −0.356998 0.350075i
\(589\) 7.32749 0.301924
\(590\) 0 0
\(591\) 1.01925 + 4.25473i 0.0419264 + 0.175016i
\(592\) 6.06739 0.249368
\(593\) 26.8788 1.10378 0.551889 0.833917i \(-0.313907\pi\)
0.551889 + 0.833917i \(0.313907\pi\)
\(594\) −21.1604 + 18.0187i −0.868224 + 0.739316i
\(595\) 0 0
\(596\) 7.60882i 0.311669i
\(597\) −0.382418 1.59635i −0.0156513 0.0653343i
\(598\) 1.11298i 0.0455130i
\(599\) 6.45858i 0.263890i 0.991257 + 0.131945i \(0.0421223\pi\)
−0.991257 + 0.131945i \(0.957878\pi\)
\(600\) 0 0
\(601\) 1.31548i 0.0536595i 0.999640 + 0.0268298i \(0.00854120\pi\)
−0.999640 + 0.0268298i \(0.991459\pi\)
\(602\) 8.13197 14.6974i 0.331435 0.599023i
\(603\) −17.9682 + 9.13294i −0.731720 + 0.371922i
\(604\) 4.63005 0.188394
\(605\) 0 0
\(606\) −2.33625 9.75237i −0.0949039 0.396163i
\(607\) 26.9651i 1.09448i −0.836976 0.547240i \(-0.815679\pi\)
0.836976 0.547240i \(-0.184321\pi\)
\(608\) 0.807019 0.0327289
\(609\) −0.344169 + 1.24241i −0.0139464 + 0.0503451i
\(610\) 0 0
\(611\) 22.9056i 0.926661i
\(612\) −19.5896 + 9.95708i −0.791862 + 0.402491i
\(613\) 33.9151 1.36982 0.684909 0.728629i \(-0.259842\pi\)
0.684909 + 0.728629i \(0.259842\pi\)
\(614\) 19.4057 0.783150
\(615\) 0 0
\(616\) −12.3824 6.85109i −0.498902 0.276038i
\(617\) 13.1253i 0.528405i 0.964467 + 0.264203i \(0.0851087\pi\)
−0.964467 + 0.264203i \(0.914891\pi\)
\(618\) −11.7187 + 2.80730i −0.471394 + 0.112926i
\(619\) 38.0907i 1.53099i 0.643439 + 0.765497i \(0.277507\pi\)
−0.643439 + 0.765497i \(0.722493\pi\)
\(620\) 0 0
\(621\) −0.947731 1.11298i −0.0380311 0.0446623i
\(622\) 6.73757i 0.270152i
\(623\) 9.99284 + 5.52896i 0.400355 + 0.221513i
\(624\) 1.59635 + 6.66375i 0.0639052 + 0.266763i
\(625\) 0 0
\(626\) −21.3875 −0.854816
\(627\) 7.27071 1.74175i 0.290364 0.0695590i
\(628\) 15.3162i 0.611184i
\(629\) 44.4434 1.77207
\(630\) 0 0
\(631\) −12.0674 −0.480395 −0.240198 0.970724i \(-0.577212\pi\)
−0.240198 + 0.970724i \(0.577212\pi\)
\(632\) 3.26010i 0.129680i
\(633\) −21.7121 + 5.20129i −0.862977 + 0.206733i
\(634\) −3.47403 −0.137971
\(635\) 0 0
\(636\) 4.43004 + 18.4926i 0.175662 + 0.733278i
\(637\) −23.4623 + 14.7117i −0.929609 + 0.582899i
\(638\) 1.50474i 0.0595732i
\(639\) −4.58090 9.01247i −0.181218 0.356528i
\(640\) 0 0
\(641\) 17.4373i 0.688734i 0.938835 + 0.344367i \(0.111906\pi\)
−0.938835 + 0.344367i \(0.888094\pi\)
\(642\) 17.8694 4.28076i 0.705250 0.168948i
\(643\) 6.01688i 0.237283i −0.992937 0.118641i \(-0.962146\pi\)
0.992937 0.118641i \(-0.0378538\pi\)
\(644\) 0.360347 0.651279i 0.0141997 0.0256640i
\(645\) 0 0
\(646\) 5.91138 0.232580
\(647\) −36.7581 −1.44511 −0.722555 0.691314i \(-0.757032\pi\)
−0.722555 + 0.691314i \(0.757032\pi\)
\(648\) −7.27071 5.30441i −0.285621 0.208377i
\(649\) 26.2296i 1.02960i
\(650\) 0 0
\(651\) 11.1079 40.0983i 0.435354 1.57158i
\(652\) 3.06739 0.120128
\(653\) 14.8073i 0.579454i −0.957109 0.289727i \(-0.906435\pi\)
0.957109 0.289727i \(-0.0935646\pi\)
\(654\) −7.31755 30.5461i −0.286139 1.19445i
\(655\) 0 0
\(656\) 6.15019 0.240125
\(657\) −6.77333 13.3259i −0.264253 0.519892i
\(658\) −7.41612 + 13.4036i −0.289110 + 0.522528i
\(659\) 11.3487i 0.442083i 0.975264 + 0.221042i \(0.0709457\pi\)
−0.975264 + 0.221042i \(0.929054\pi\)
\(660\) 0 0
\(661\) 19.7043i 0.766407i 0.923664 + 0.383203i \(0.125179\pi\)
−0.923664 + 0.383203i \(0.874821\pi\)
\(662\) 8.93261i 0.347176i
\(663\) 11.6932 + 48.8116i 0.454126 + 1.89569i
\(664\) 1.53511i 0.0595740i
\(665\) 0 0
\(666\) 8.24763 + 16.2264i 0.319589 + 0.628760i
\(667\) −0.0791449 −0.00306450
\(668\) 1.89546 0.0733376
\(669\) −9.57512 39.9700i −0.370196 1.54533i
\(670\) 0 0
\(671\) −70.9000 −2.73707
\(672\) 1.22338 4.41626i 0.0471928 0.170361i
\(673\) −21.7861 −0.839791 −0.419896 0.907572i \(-0.637933\pi\)
−0.419896 + 0.907572i \(0.637933\pi\)
\(674\) 34.2176i 1.31801i
\(675\) 0 0
\(676\) 2.65128 0.101972
\(677\) 15.3706 0.590740 0.295370 0.955383i \(-0.404557\pi\)
0.295370 + 0.955383i \(0.404557\pi\)
\(678\) 14.3871 3.44654i 0.552534 0.132364i
\(679\) −19.3275 + 34.9318i −0.741721 + 1.34056i
\(680\) 0 0
\(681\) 17.6300 4.22341i 0.675585 0.161842i
\(682\) 48.5648i 1.85964i
\(683\) 22.0462i 0.843573i 0.906695 + 0.421786i \(0.138597\pi\)
−0.906695 + 0.421786i \(0.861403\pi\)
\(684\) 1.09701 + 2.15826i 0.0419452 + 0.0825231i
\(685\) 0 0
\(686\) 18.4926 1.01247i 0.706049 0.0386561i
\(687\) −6.64829 27.7524i −0.253648 1.05882i
\(688\) 6.34872 0.242043
\(689\) 43.4339 1.65470
\(690\) 0 0
\(691\) 31.7209i 1.20672i 0.797469 + 0.603360i \(0.206172\pi\)
−0.797469 + 0.603360i \(0.793828\pi\)
\(692\) −8.86007 −0.336809
\(693\) 1.49041 42.4280i 0.0566161 1.61171i
\(694\) 11.5260 0.437520
\(695\) 0 0
\(696\) −0.473865 + 0.113518i −0.0179618 + 0.00430289i
\(697\) 45.0499 1.70639
\(698\) −21.8342 −0.826435
\(699\) −11.2811 47.0915i −0.426691 1.78116i
\(700\) 0 0
\(701\) 49.4316i 1.86700i −0.358571 0.933502i \(-0.616736\pi\)
0.358571 0.933502i \(-0.383264\pi\)
\(702\) −15.6513 + 13.3275i −0.590719 + 0.503014i
\(703\) 4.89650i 0.184675i
\(704\) 5.34872i 0.201588i
\(705\) 0 0
\(706\) 4.84211i 0.182235i
\(707\) 13.4036 + 7.41612i 0.504095 + 0.278912i
\(708\) 8.26010 1.97877i 0.310433 0.0743667i
\(709\) −0.697442 −0.0261930 −0.0130965 0.999914i \(-0.504169\pi\)
−0.0130965 + 0.999914i \(0.504169\pi\)
\(710\) 0 0
\(711\) −8.71867 + 4.43157i −0.326976 + 0.166197i
\(712\) 4.31652i 0.161768i
\(713\) 2.55437 0.0956618
\(714\) 8.96119 32.3489i 0.335364 1.21063i
\(715\) 0 0
\(716\) 11.3487i 0.424122i
\(717\) −6.96461 29.0728i −0.260098 1.08574i
\(718\) −30.3063 −1.13102
\(719\) 32.1430 1.19873 0.599366 0.800475i \(-0.295419\pi\)
0.599366 + 0.800475i \(0.295419\pi\)
\(720\) 0 0
\(721\) 8.91138 16.1061i 0.331877 0.599823i
\(722\) 18.3487i 0.682869i
\(723\) −7.74474 32.3293i −0.288030 1.20234i
\(724\) 8.63303i 0.320844i
\(725\) 0 0
\(726\) −7.10532 29.6602i −0.263703 1.10079i
\(727\) 27.3970i 1.01610i 0.861328 + 0.508049i \(0.169633\pi\)
−0.861328 + 0.508049i \(0.830367\pi\)
\(728\) −9.15863 5.06739i −0.339441 0.187810i
\(729\) 4.30256 26.6550i 0.159354 0.987222i
\(730\) 0 0
\(731\) 46.5041 1.72002
\(732\) −5.34872 22.3275i −0.197694 0.825248i
\(733\) 0.0617893i 0.00228224i 0.999999 + 0.00114112i \(0.000363230\pi\)
−0.999999 + 0.00114112i \(0.999637\pi\)
\(734\) 13.9910 0.516417
\(735\) 0 0
\(736\) 0.281327 0.0103699
\(737\) 35.9363i 1.32373i
\(738\) 8.36018 + 16.4478i 0.307742 + 0.605453i
\(739\) −45.0037 −1.65549 −0.827744 0.561106i \(-0.810376\pi\)
−0.827744 + 0.561106i \(0.810376\pi\)
\(740\) 0 0
\(741\) 5.37777 1.28828i 0.197557 0.0473263i
\(742\) −25.4161 14.0625i −0.933055 0.516252i
\(743\) 38.1655i 1.40016i −0.714066 0.700078i \(-0.753148\pi\)
0.714066 0.700078i \(-0.246852\pi\)
\(744\) 15.2938 3.66375i 0.560698 0.134319i
\(745\) 0 0
\(746\) 4.24464i 0.155407i
\(747\) −4.10545 + 2.08674i −0.150211 + 0.0763497i
\(748\) 39.1791i 1.43253i
\(749\) −13.5887 + 24.5597i −0.496519 + 0.897391i
\(750\) 0 0
\(751\) −27.8901 −1.01773 −0.508863 0.860848i \(-0.669934\pi\)
−0.508863 + 0.860848i \(0.669934\pi\)
\(752\) −5.78984 −0.211134
\(753\) 35.4180 8.48464i 1.29070 0.309198i
\(754\) 1.11298i 0.0405323i
\(755\) 0 0
\(756\) 13.4737 2.73143i 0.490032 0.0993411i
\(757\) −38.5876 −1.40249 −0.701245 0.712921i \(-0.747372\pi\)
−0.701245 + 0.712921i \(0.747372\pi\)
\(758\) 1.63005i 0.0592060i
\(759\) 2.53457 0.607177i 0.0919992 0.0220391i
\(760\) 0 0
\(761\) −28.9173 −1.04825 −0.524125 0.851641i \(-0.675608\pi\)
−0.524125 + 0.851641i \(0.675608\pi\)
\(762\) 0.807019 + 3.36879i 0.0292352 + 0.122038i
\(763\) 41.9825 + 23.2286i 1.51987 + 0.840930i
\(764\) 7.78607i 0.281690i
\(765\) 0 0
\(766\) 16.9994i 0.614215i
\(767\) 19.4007i 0.700517i
\(768\) 1.68439 0.403509i 0.0607803 0.0145604i
\(769\) 30.3191i 1.09333i −0.837350 0.546667i \(-0.815896\pi\)
0.837350 0.546667i \(-0.184104\pi\)
\(770\) 0 0
\(771\) −24.5721 + 5.88644i −0.884944 + 0.211995i
\(772\) 25.1715 0.905941
\(773\) 23.7370 0.853761 0.426881 0.904308i \(-0.359612\pi\)
0.426881 + 0.904308i \(0.359612\pi\)
\(774\) 8.63005 + 16.9788i 0.310201 + 0.610289i
\(775\) 0 0
\(776\) −15.0892 −0.541670
\(777\) −26.7952 7.42272i −0.961272 0.266289i
\(778\) 29.4623 1.05627
\(779\) 4.96332i 0.177829i
\(780\) 0 0
\(781\) 18.0249 0.644983
\(782\) 2.06071 0.0736908
\(783\) −0.947731 1.11298i −0.0338691 0.0397746i
\(784\) 3.71867 + 5.93055i 0.132810 + 0.211806i
\(785\) 0 0
\(786\) 6.67621 + 27.8689i 0.238133 + 0.994051i
\(787\) 30.7560i 1.09633i 0.836369 + 0.548167i \(0.184674\pi\)
−0.836369 + 0.548167i \(0.815326\pi\)
\(788\)