Properties

Label 1050.2.d.g.1049.7
Level $1050$
Weight $2$
Character 1050.1049
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.d (of order \(2\), degree \(1\), not 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: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1049.7
Root \(1.68439 + 0.403509i\) of defining polynomial
Character \(\chi\) \(=\) 1050.1049
Dual form 1050.2.d.g.1049.8

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(0.403509 - 1.68439i) q^{3} +1.00000 q^{4} +(-0.403509 + 1.68439i) q^{6} +(-1.28088 + 2.31502i) q^{7} -1.00000 q^{8} +(-2.67436 - 1.35934i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(0.403509 - 1.68439i) q^{3} +1.00000 q^{4} +(-0.403509 + 1.68439i) q^{6} +(-1.28088 + 2.31502i) q^{7} -1.00000 q^{8} +(-2.67436 - 1.35934i) q^{9} -5.34872i q^{11} +(0.403509 - 1.68439i) q^{12} -3.95617 q^{13} +(1.28088 - 2.31502i) q^{14} +1.00000 q^{16} +7.32496i q^{17} +(2.67436 + 1.35934i) q^{18} +0.807019i q^{19} +(3.38256 + 3.09165i) q^{21} +5.34872i q^{22} -0.281327 q^{23} +(-0.403509 + 1.68439i) q^{24} +3.95617 q^{26} +(-3.36879 + 3.95617i) q^{27} +(-1.28088 + 2.31502i) q^{28} -0.281327i q^{29} +9.07971i q^{31} -1.00000 q^{32} +(-9.00935 - 2.15826i) q^{33} -7.32496i q^{34} +(-2.67436 - 1.35934i) q^{36} -6.06739i q^{37} -0.807019i q^{38} +(-1.59635 + 6.66375i) q^{39} -6.15019 q^{41} +(-3.38256 - 3.09165i) q^{42} +6.34872i q^{43} -5.34872i q^{44} +0.281327 q^{46} -5.78984i q^{47} +(0.403509 - 1.68439i) q^{48} +(-3.71867 - 5.93055i) q^{49} +(12.3381 + 2.95569i) q^{51} -3.95617 q^{52} -10.9788 q^{53} +(3.36879 - 3.95617i) q^{54} +(1.28088 - 2.31502i) q^{56} +(1.35934 + 0.325639i) q^{57} +0.281327i q^{58} -4.90390 q^{59} +13.2555i q^{61} -9.07971i q^{62} +(6.57244 - 4.45006i) q^{63} +1.00000 q^{64} +(9.00935 + 2.15826i) q^{66} +6.71867i q^{67} +7.32496i q^{68} +(-0.113518 + 0.473865i) q^{69} +3.36995i q^{71} +(2.67436 + 1.35934i) q^{72} +4.98282 q^{73} +6.06739i q^{74} +0.807019i q^{76} +(12.3824 + 6.85109i) q^{77} +(1.59635 - 6.66375i) q^{78} +3.26010 q^{79} +(5.30441 + 7.27071i) q^{81} +6.15019 q^{82} +1.53511i q^{83} +(3.38256 + 3.09165i) q^{84} -6.34872i q^{86} +(-0.473865 - 0.113518i) q^{87} +5.34872i q^{88} -4.31652 q^{89} +(5.06739 - 9.15863i) q^{91} -0.281327 q^{92} +(15.2938 + 3.66375i) q^{93} +5.78984i q^{94} +(-0.403509 + 1.68439i) q^{96} -15.0892 q^{97} +(3.71867 + 5.93055i) q^{98} +(-7.27071 + 14.3044i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 12q^{2} + 12q^{4} - 12q^{8} + O(q^{10}) \) \( 12q - 12q^{2} + 12q^{4} - 12q^{8} + 12q^{16} + 14q^{21} - 20q^{23} - 12q^{32} - 12q^{39} - 14q^{42} + 20q^{46} - 28q^{49} + 28q^{51} - 20q^{53} + 8q^{57} - 30q^{63} + 12q^{64} + 44q^{77} + 12q^{78} - 56q^{79} - 16q^{81} + 14q^{84} - 20q^{91} - 20q^{92} + 48q^{93} + 28q^{98} - 48q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0.403509 1.68439i 0.232966 0.972485i
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) −0.403509 + 1.68439i −0.164732 + 0.687651i
\(7\) −1.28088 + 2.31502i −0.484129 + 0.874997i
\(8\) −1.00000 −0.353553
\(9\) −2.67436 1.35934i −0.891454 0.453112i
\(10\) 0 0
\(11\) 5.34872i 1.61270i −0.591439 0.806350i \(-0.701440\pi\)
0.591439 0.806350i \(-0.298560\pi\)
\(12\) 0.403509 1.68439i 0.116483 0.486242i
\(13\) −3.95617 −1.09724 −0.548622 0.836070i \(-0.684847\pi\)
−0.548622 + 0.836070i \(0.684847\pi\)
\(14\) 1.28088 2.31502i 0.342331 0.618716i
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 7.32496i 1.77656i 0.459300 + 0.888281i \(0.348100\pi\)
−0.459300 + 0.888281i \(0.651900\pi\)
\(18\) 2.67436 + 1.35934i 0.630353 + 0.320399i
\(19\) 0.807019i 0.185143i 0.995706 + 0.0925714i \(0.0295086\pi\)
−0.995706 + 0.0925714i \(0.970491\pi\)
\(20\) 0 0
\(21\) 3.38256 + 3.09165i 0.738136 + 0.674652i
\(22\) 5.34872i 1.14035i
\(23\) −0.281327 −0.0586607 −0.0293304 0.999570i \(-0.509337\pi\)
−0.0293304 + 0.999570i \(0.509337\pi\)
\(24\) −0.403509 + 1.68439i −0.0823660 + 0.343825i
\(25\) 0 0
\(26\) 3.95617 0.775869
\(27\) −3.36879 + 3.95617i −0.648323 + 0.761365i
\(28\) −1.28088 + 2.31502i −0.242064 + 0.437498i
\(29\) 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 \(0.696527\pi\)
\(32\) −1.00000 −0.176777
\(33\) −9.00935 2.15826i −1.56833 0.375705i
\(34\) 7.32496i 1.25622i
\(35\) 0 0
\(36\) −2.67436 1.35934i −0.445727 0.226556i
\(37\) 6.06739i 0.997473i −0.866754 0.498737i \(-0.833797\pi\)
0.866754 0.498737i \(-0.166203\pi\)
\(38\) 0.807019i 0.130916i
\(39\) −1.59635 + 6.66375i −0.255621 + 1.06705i
\(40\) 0 0
\(41\) −6.15019 −0.960498 −0.480249 0.877132i \(-0.659454\pi\)
−0.480249 + 0.877132i \(0.659454\pi\)
\(42\) −3.38256 3.09165i −0.521941 0.477051i
\(43\) 6.34872i 0.968171i 0.875021 + 0.484085i \(0.160848\pi\)
−0.875021 + 0.484085i \(0.839152\pi\)
\(44\) 5.34872i 0.806350i
\(45\) 0 0
\(46\) 0.281327 0.0414794
\(47\) 5.78984i 0.844535i −0.906471 0.422268i \(-0.861234\pi\)
0.906471 0.422268i \(-0.138766\pi\)
\(48\) 0.403509 1.68439i 0.0582415 0.243121i
\(49\) −3.71867 5.93055i −0.531239 0.847222i
\(50\) 0 0
\(51\) 12.3381 + 2.95569i 1.72768 + 0.413879i
\(52\) −3.95617 −0.548622
\(53\) −10.9788 −1.50805 −0.754025 0.656846i \(-0.771890\pi\)
−0.754025 + 0.656846i \(0.771890\pi\)
\(54\) 3.36879 3.95617i 0.458434 0.538367i
\(55\) 0 0
\(56\) 1.28088 2.31502i 0.171165 0.309358i
\(57\) 1.35934 + 0.325639i 0.180049 + 0.0431320i
\(58\) 0.281327i 0.0369401i
\(59\) −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 \(0.677448\pi\)
\(62\) 9.07971i 1.15312i
\(63\) 6.57244 4.45006i 0.828050 0.560654i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 9.00935 + 2.15826i 1.10897 + 0.265663i
\(67\) 6.71867i 0.820817i 0.911902 + 0.410408i \(0.134614\pi\)
−0.911902 + 0.410408i \(0.865386\pi\)
\(68\) 7.32496i 0.888281i
\(69\) −0.113518 + 0.473865i −0.0136660 + 0.0570467i
\(70\) 0 0
\(71\) 3.36995i 0.399940i 0.979802 + 0.199970i \(0.0640844\pi\)
−0.979802 + 0.199970i \(0.935916\pi\)
\(72\) 2.67436 + 1.35934i 0.315176 + 0.160199i
\(73\) 4.98282 0.583195 0.291598 0.956541i \(-0.405813\pi\)
0.291598 + 0.956541i \(0.405813\pi\)
\(74\) 6.06739i 0.705320i
\(75\) 0 0
\(76\) 0.807019i 0.0925714i
\(77\) 12.3824 + 6.85109i 1.41111 + 0.780754i
\(78\) 1.59635 6.66375i 0.180751 0.754521i
\(79\) 3.26010 0.366789 0.183395 0.983039i \(-0.441291\pi\)
0.183395 + 0.983039i \(0.441291\pi\)
\(80\) 0 0
\(81\) 5.30441 + 7.27071i 0.589379 + 0.807857i
\(82\) 6.15019 0.679175
\(83\) 1.53511i 0.168501i 0.996445 + 0.0842503i \(0.0268495\pi\)
−0.996445 + 0.0842503i \(0.973150\pi\)
\(84\) 3.38256 + 3.09165i 0.369068 + 0.337326i
\(85\) 0 0
\(86\) 6.34872i 0.684600i
\(87\) −0.473865 0.113518i −0.0508037 0.0121704i
\(88\) 5.34872i 0.570176i
\(89\) −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
\(92\) −0.281327 −0.0293304
\(93\) 15.2938 + 3.66375i 1.58589 + 0.379913i
\(94\) 5.78984i 0.597177i
\(95\) 0 0
\(96\) −0.403509 + 1.68439i −0.0411830 + 0.171913i
\(97\) −15.0892 −1.53207 −0.766037 0.642796i \(-0.777774\pi\)
−0.766037 + 0.642796i \(0.777774\pi\)
\(98\) 3.71867 + 5.93055i 0.375643 + 0.599076i
\(99\) −7.27071 + 14.3044i −0.730734 + 1.43765i
\(100\) 0 0
\(101\) 5.78984 0.576111 0.288055 0.957614i \(-0.406991\pi\)
0.288055 + 0.957614i \(0.406991\pi\)
\(102\) −12.3381 2.95569i −1.22165 0.292657i
\(103\) −6.95721 −0.685514 −0.342757 0.939424i \(-0.611361\pi\)
−0.342757 + 0.939424i \(0.611361\pi\)
\(104\) 3.95617 0.387934
\(105\) 0 0
\(106\) 10.9788 1.06635
\(107\) 10.6088 1.02559 0.512797 0.858510i \(-0.328610\pi\)
0.512797 + 0.858510i \(0.328610\pi\)
\(108\) −3.36879 + 3.95617i −0.324162 + 0.380683i
\(109\) 18.1348 1.73700 0.868499 0.495691i \(-0.165085\pi\)
0.868499 + 0.495691i \(0.165085\pi\)
\(110\) 0 0
\(111\) −10.2199 2.44825i −0.970028 0.232378i
\(112\) −1.28088 + 2.31502i −0.121032 + 0.218749i
\(113\) −8.54142 −0.803510 −0.401755 0.915747i \(-0.631600\pi\)
−0.401755 + 0.915747i \(0.631600\pi\)
\(114\) −1.35934 0.325639i −0.127314 0.0304989i
\(115\) 0 0
\(116\) 0.281327i 0.0261206i
\(117\) 10.5802 + 5.37777i 0.978142 + 0.497175i
\(118\) 4.90390 0.451441
\(119\) −16.9574 9.38242i −1.55449 0.860085i
\(120\) 0 0
\(121\) −17.6088 −1.60080
\(122\) 13.2555i 1.20010i
\(123\) −2.48166 + 10.3593i −0.223764 + 0.934070i
\(124\) 9.07971i 0.815382i
\(125\) 0 0
\(126\) −6.57244 + 4.45006i −0.585520 + 0.396443i
\(127\) 2.00000i 0.177471i −0.996055 0.0887357i \(-0.971717\pi\)
0.996055 0.0887357i \(-0.0282826\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 10.6937 + 2.56177i 0.941532 + 0.225551i
\(130\) 0 0
\(131\) −16.5454 −1.44558 −0.722788 0.691070i \(-0.757140\pi\)
−0.722788 + 0.691070i \(0.757140\pi\)
\(132\) −9.00935 2.15826i −0.784163 0.187852i
\(133\) −1.86827 1.03370i −0.161999 0.0896329i
\(134\) 6.71867i 0.580405i
\(135\) 0 0
\(136\) 7.32496i 0.628110i
\(137\) −7.41612 −0.633601 −0.316801 0.948492i \(-0.602609\pi\)
−0.316801 + 0.948492i \(0.602609\pi\)
\(138\) 0.113518 0.473865i 0.00966330 0.0403381i
\(139\) 6.36982i 0.540281i −0.962821 0.270141i \(-0.912930\pi\)
0.962821 0.270141i \(-0.0870702\pi\)
\(140\) 0 0
\(141\) −9.75237 2.33625i −0.821298 0.196748i
\(142\) 3.36995i 0.282800i
\(143\) 21.1604i 1.76953i
\(144\) −2.67436 1.35934i −0.222863 0.113278i
\(145\) 0 0
\(146\) −4.98282 −0.412381
\(147\) −11.4899 + 3.87067i −0.947671 + 0.319248i
\(148\) 6.06739i 0.498737i
\(149\) 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 \(0.560328\pi\)
\(152\) 0.807019i 0.0654578i
\(153\) 9.95708 19.5896i 0.804982 1.58372i
\(154\) −12.3824 6.85109i −0.997804 0.552077i
\(155\) 0 0
\(156\) −1.59635 + 6.66375i −0.127810 + 0.533527i
\(157\) 15.3162 1.22237 0.611184 0.791489i \(-0.290694\pi\)
0.611184 + 0.791489i \(0.290694\pi\)
\(158\) −3.26010 −0.259359
\(159\) −4.43004 + 18.4926i −0.351325 + 1.46656i
\(160\) 0 0
\(161\) 0.360347 0.651279i 0.0283993 0.0513280i
\(162\) −5.30441 7.27071i −0.416754 0.571241i
\(163\) 3.06739i 0.240257i −0.992758 0.120128i \(-0.961669\pi\)
0.992758 0.120128i \(-0.0383306\pi\)
\(164\) −6.15019 −0.480249
\(165\) 0 0
\(166\) 1.53511i 0.119148i
\(167\) 1.89546i 0.146675i −0.997307 0.0733376i \(-0.976635\pi\)
0.997307 0.0733376i \(-0.0233651\pi\)
\(168\) −3.38256 3.09165i −0.260970 0.238526i
\(169\) 2.65128 0.203945
\(170\) 0 0
\(171\) 1.09701 2.15826i 0.0838904 0.165046i
\(172\) 6.34872i 0.484085i
\(173\) 8.86007i 0.673619i −0.941573 0.336809i \(-0.890652\pi\)
0.941573 0.336809i \(-0.109348\pi\)
\(174\) 0.473865 + 0.113518i 0.0359236 + 0.00860578i
\(175\) 0 0
\(176\) 5.34872i 0.403175i
\(177\) −1.97877 + 8.26010i −0.148733 + 0.620867i
\(178\) 4.31652 0.323537
\(179\) 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 \(-0.103967\pi\)
\(182\) −5.06739 + 9.15863i −0.375620 + 0.678883i
\(183\) 22.3275 + 5.34872i 1.65050 + 0.395389i
\(184\) 0.281327 0.0207397
\(185\) 0 0
\(186\) −15.2938 3.66375i −1.12140 0.268639i
\(187\) 39.1791 2.86506
\(188\) 5.78984i 0.422268i
\(189\) −4.84360 12.8662i −0.352320 0.935879i
\(190\) 0 0
\(191\) 7.78607i 0.563380i 0.959505 + 0.281690i \(0.0908950\pi\)
−0.959505 + 0.281690i \(0.909105\pi\)
\(192\) 0.403509 1.68439i 0.0291208 0.121561i
\(193\) 25.1715i 1.81188i −0.423404 0.905941i \(-0.639165\pi\)
0.423404 0.905941i \(-0.360835\pi\)
\(194\) 15.0892 1.08334
\(195\) 0 0
\(196\) −3.71867 5.93055i −0.265619 0.423611i
\(197\) −2.52597 −0.179968 −0.0899840 0.995943i \(-0.528682\pi\)
−0.0899840 + 0.995943i \(0.528682\pi\)
\(198\) 7.27071 14.3044i 0.516707 1.01657i
\(199\) 0.947731i 0.0671828i 0.999436 + 0.0335914i \(0.0106945\pi\)
−0.999436 + 0.0335914i \(0.989306\pi\)
\(200\) 0 0
\(201\) 11.3169 + 2.71105i 0.798232 + 0.191222i
\(202\) −5.78984 −0.407372
\(203\) 0.651279 + 0.360347i 0.0457108 + 0.0252914i
\(204\) 12.3381 + 2.95569i 0.863840 + 0.206940i
\(205\) 0 0
\(206\) 6.95721 0.484732
\(207\) 0.752370 + 0.382418i 0.0522933 + 0.0265799i
\(208\) −3.95617 −0.274311
\(209\) 4.31652 0.298580
\(210\) 0 0
\(211\) −12.8901 −0.887394 −0.443697 0.896177i \(-0.646333\pi\)
−0.443697 + 0.896177i \(0.646333\pi\)
\(212\) −10.9788 −0.754025
\(213\) 5.67632 + 1.35981i 0.388935 + 0.0931724i
\(214\) −10.6088 −0.725204
\(215\) 0 0
\(216\) 3.36879 3.95617i 0.229217 0.269183i
\(217\) −21.0197 11.6300i −1.42691 0.789499i
\(218\) −18.1348 −1.22824
\(219\) 2.01062 8.39303i 0.135865 0.567149i
\(220\) 0 0
\(221\) 28.9788i 1.94932i
\(222\) 10.2199 + 2.44825i 0.685913 + 0.164316i
\(223\) 23.7296 1.58905 0.794526 0.607230i \(-0.207719\pi\)
0.794526 + 0.607230i \(0.207719\pi\)
\(224\) 1.28088 2.31502i 0.0855827 0.154679i
\(225\) 0 0
\(226\) 8.54142 0.568167
\(227\) 10.4667i 0.694700i 0.937736 + 0.347350i \(0.112918\pi\)
−0.937736 + 0.347350i \(0.887082\pi\)
\(228\) 1.35934 + 0.325639i 0.0900243 + 0.0215660i
\(229\) 16.4762i 1.08878i 0.838833 + 0.544388i \(0.183238\pi\)
−0.838833 + 0.544388i \(0.816762\pi\)
\(230\) 0 0
\(231\) 16.5364 18.0924i 1.08801 1.19039i
\(232\) 0.281327i 0.0184700i
\(233\) −27.9575 −1.83156 −0.915780 0.401681i \(-0.868426\pi\)
−0.915780 + 0.401681i \(0.868426\pi\)
\(234\) −10.5802 5.37777i −0.691651 0.351556i
\(235\) 0 0
\(236\) −4.90390 −0.319217
\(237\) 1.31548 5.49128i 0.0854495 0.356697i
\(238\) 16.9574 + 9.38242i 1.09919 + 0.608172i
\(239\) 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 \(-0.212130\pi\)
\(242\) 17.6088 1.13194
\(243\) 14.3871 6.00091i 0.922934 0.384959i
\(244\) 13.2555i 0.848597i
\(245\) 0 0
\(246\) 2.48166 10.3593i 0.158225 0.660487i
\(247\) 3.19270i 0.203147i
\(248\) 9.07971i 0.576562i
\(249\) 2.58574 + 0.619433i 0.163864 + 0.0392550i
\(250\) 0 0
\(251\) −21.0271 −1.32722 −0.663611 0.748078i \(-0.730977\pi\)
−0.663611 + 0.748078i \(0.730977\pi\)
\(252\) 6.57244 4.45006i 0.414025 0.280327i
\(253\) 1.50474i 0.0946022i
\(254\) 2.00000i 0.125491i
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 14.5881i 0.909982i −0.890496 0.454991i \(-0.849642\pi\)
0.890496 0.454991i \(-0.150358\pi\)
\(258\) −10.6937 2.56177i −0.665763 0.159489i
\(259\) 14.0462 + 7.77163i 0.872786 + 0.482905i
\(260\) 0 0
\(261\) −0.382418 + 0.752370i −0.0236711 + 0.0465705i
\(262\) 16.5454 1.02218
\(263\) 8.91138 0.549499 0.274749 0.961516i \(-0.411405\pi\)
0.274749 + 0.961516i \(0.411405\pi\)
\(264\) 9.00935 + 2.15826i 0.554487 + 0.132832i
\(265\) 0 0
\(266\) 1.86827 + 1.03370i 0.114551 + 0.0633800i
\(267\) −1.74175 + 7.27071i −0.106594 + 0.444960i
\(268\) 6.71867i 0.410408i
\(269\) 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 \(0.930053\pi\)
\(272\) 7.32496i 0.444141i
\(273\) −13.3820 12.2311i −0.809915 0.740258i
\(274\) 7.41612 0.448024
\(275\) 0 0
\(276\) −0.113518 + 0.473865i −0.00683298 + 0.0285233i
\(277\) 9.32749i 0.560435i −0.959937 0.280217i \(-0.909593\pi\)
0.959937 0.280217i \(-0.0904065\pi\)
\(278\) 6.36982i 0.382037i
\(279\) 12.3424 24.2824i 0.738919 1.45375i
\(280\) 0 0
\(281\) 17.4373i 1.04022i 0.854098 + 0.520112i \(0.174110\pi\)
−0.854098 + 0.520112i \(0.825890\pi\)
\(282\) 9.75237 + 2.33625i 0.580745 + 0.139122i
\(283\) −16.1776 −0.961660 −0.480830 0.876814i \(-0.659665\pi\)
−0.480830 + 0.876814i \(0.659665\pi\)
\(284\) 3.36995i 0.199970i
\(285\) 0 0
\(286\) 21.1604i 1.25124i
\(287\) 7.87768 14.2378i 0.465005 0.840433i
\(288\) 2.67436 + 1.35934i 0.157588 + 0.0800997i
\(289\) −36.6550 −2.15618
\(290\) 0 0
\(291\) −6.08862 + 25.4161i −0.356922 + 1.48992i
\(292\) 4.98282 0.291598
\(293\) 22.5623i 1.31810i −0.752099 0.659050i \(-0.770958\pi\)
0.752099 0.659050i \(-0.229042\pi\)
\(294\) 11.4899 3.87067i 0.670105 0.225742i
\(295\) 0 0
\(296\) 6.06739i 0.352660i
\(297\) 21.1604 + 18.0187i 1.22785 + 1.04555i
\(298\) 7.60882i 0.440767i
\(299\) 1.11298 0.0643652
\(300\) 0 0
\(301\) −14.6974 8.13197i −0.847146 0.468719i
\(302\) 4.63005 0.266429
\(303\) 2.33625 9.75237i 0.134214 0.560259i
\(304\) 0.807019i 0.0462857i
\(305\) 0 0
\(306\) −9.95708 + 19.5896i −0.569208 + 1.11986i
\(307\) −19.4057 −1.10754 −0.553771 0.832669i \(-0.686812\pi\)
−0.553771 + 0.832669i \(0.686812\pi\)
\(308\) 12.3824 + 6.85109i 0.705554 + 0.390377i
\(309\) −2.80730 + 11.7187i −0.159702 + 0.666652i
\(310\) 0 0
\(311\) −6.73757 −0.382053 −0.191026 0.981585i \(-0.561182\pi\)
−0.191026 + 0.981585i \(0.561182\pi\)
\(312\) 1.59635 6.66375i 0.0903756 0.377260i
\(313\) −21.3875 −1.20889 −0.604446 0.796646i \(-0.706606\pi\)
−0.604446 + 0.796646i \(0.706606\pi\)
\(314\) −15.3162 −0.864344
\(315\) 0 0
\(316\) 3.26010 0.183395
\(317\) −3.47403 −0.195121 −0.0975605 0.995230i \(-0.531104\pi\)
−0.0975605 + 0.995230i \(0.531104\pi\)
\(318\) 4.43004 18.4926i 0.248424 1.03701i
\(319\) −1.50474 −0.0842493
\(320\) 0 0
\(321\) 4.28076 17.8694i 0.238929 0.997374i
\(322\) −0.360347 + 0.651279i −0.0200814 + 0.0362944i
\(323\) −5.91138 −0.328918
\(324\) 5.30441 + 7.27071i 0.294689 + 0.403928i
\(325\) 0 0
\(326\) 3.06739i 0.169887i
\(327\) 7.31755 30.5461i 0.404662 1.68920i
\(328\) 6.15019 0.339587
\(329\) 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 \(0.578949\pi\)
\(332\) 1.53511i 0.0842503i
\(333\) −8.24763 + 16.2264i −0.451967 + 0.889201i
\(334\) 1.89546i 0.103715i
\(335\) 0 0
\(336\) 3.38256 + 3.09165i 0.184534 + 0.168663i
\(337\) 34.2176i 1.86395i −0.362518 0.931977i \(-0.618083\pi\)
0.362518 0.931977i \(-0.381917\pi\)
\(338\) −2.65128 −0.144211
\(339\) −3.44654 + 14.3871i −0.187191 + 0.781401i
\(340\) 0 0
\(341\) 48.5648 2.62993
\(342\) −1.09701 + 2.15826i −0.0593195 + 0.116705i
\(343\) 18.4926 1.01247i 0.998505 0.0546680i
\(344\) 6.34872i 0.342300i
\(345\) 0 0
\(346\) 8.86007i 0.476320i
\(347\) 11.5260 0.618747 0.309373 0.950941i \(-0.399881\pi\)
0.309373 + 0.950941i \(0.399881\pi\)
\(348\) −0.473865 0.113518i −0.0254018 0.00608521i
\(349\) 21.8342i 1.16876i −0.811482 0.584378i \(-0.801339\pi\)
0.811482 0.584378i \(-0.198661\pi\)
\(350\) 0 0
\(351\) 13.3275 15.6513i 0.711369 0.835403i
\(352\) 5.34872i 0.285088i
\(353\) 4.84211i 0.257720i 0.991663 + 0.128860i \(0.0411317\pi\)
−0.991663 + 0.128860i \(0.958868\pi\)
\(354\) 1.97877 8.26010i 0.105170 0.439019i
\(355\) 0 0
\(356\) −4.31652 −0.228775
\(357\) −22.6462 + 24.7771i −1.19856 + 1.31134i
\(358\) 11.3487i 0.599799i
\(359\) 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
\(362\) 8.63303i 0.453742i
\(363\) −7.10532 + 29.6602i −0.372933 + 1.55676i
\(364\) 5.06739 9.15863i 0.265604 0.480043i
\(365\) 0 0
\(366\) −22.3275 5.34872i −1.16708 0.279582i
\(367\) −13.9910 −0.730325 −0.365162 0.930944i \(-0.618987\pi\)
−0.365162 + 0.930944i \(0.618987\pi\)
\(368\) −0.281327 −0.0146652
\(369\) 16.4478 + 8.36018i 0.856239 + 0.435213i
\(370\) 0 0
\(371\) 14.0625 25.4161i 0.730090 1.31954i
\(372\) 15.2938 + 3.66375i 0.792946 + 0.189956i
\(373\) 4.24464i 0.219779i 0.993944 + 0.109890i \(0.0350497\pi\)
−0.993944 + 0.109890i \(0.964950\pi\)
\(374\) −39.1791 −2.02591
\(375\) 0 0
\(376\) 5.78984i 0.298588i
\(377\) 1.11298i 0.0573213i
\(378\) 4.84360 + 12.8662i 0.249128 + 0.661767i
\(379\) 1.63005 0.0837299 0.0418650 0.999123i \(-0.486670\pi\)
0.0418650 + 0.999123i \(0.486670\pi\)
\(380\) 0 0
\(381\) −3.36879 0.807019i −0.172588 0.0413448i
\(382\) 7.78607i 0.398370i
\(383\) 16.9994i 0.868631i 0.900761 + 0.434316i \(0.143010\pi\)
−0.900761 + 0.434316i \(0.856990\pi\)
\(384\) −0.403509 + 1.68439i −0.0205915 + 0.0859563i
\(385\) 0 0
\(386\) 25.1715i 1.28119i
\(387\) 8.63005 16.9788i 0.438690 0.863079i
\(388\) −15.0892 −0.766037
\(389\) 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
\(392\) 3.71867 + 5.93055i 0.187821 + 0.299538i
\(393\) −6.67621 + 27.8689i −0.336770 + 1.40580i
\(394\) 2.52597 0.127257
\(395\) 0 0
\(396\) −7.27071 + 14.3044i −0.365367 + 0.718824i
\(397\) 17.8706 0.896899 0.448449 0.893808i \(-0.351976\pi\)
0.448449 + 0.893808i \(0.351976\pi\)
\(398\) 0.947731i 0.0475054i
\(399\) −2.49502 + 2.72979i −0.124907 + 0.136660i
\(400\) 0 0
\(401\) 12.6762i 0.633020i −0.948589 0.316510i \(-0.897489\pi\)
0.948589 0.316510i \(-0.102511\pi\)
\(402\) −11.3169 2.71105i −0.564435 0.135215i
\(403\) 35.9209i 1.78935i
\(404\) 5.78984 0.288055
\(405\) 0 0
\(406\) −0.651279 0.360347i −0.0323224 0.0178837i
\(407\) −32.4528 −1.60863
\(408\) −12.3381 2.95569i −0.610827 0.146328i
\(409\) 5.26425i 0.260300i 0.991494 + 0.130150i \(0.0415459\pi\)
−0.991494 + 0.130150i \(0.958454\pi\)
\(410\) 0 0
\(411\) −2.99247 + 12.4917i −0.147608 + 0.616168i
\(412\) −6.95721 −0.342757
\(413\) 6.28133 11.3526i 0.309084 0.558627i
\(414\) −0.752370 0.382418i −0.0369770 0.0187948i
\(415\) 0 0
\(416\) 3.95617 0.193967
\(417\) −10.7293 2.57028i −0.525416 0.125867i
\(418\) −4.31652 −0.211128
\(419\) −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 \(0.469974\pi\)
\(422\) 12.8901 0.627482
\(423\) −7.87034 + 15.4841i −0.382669 + 0.752864i
\(424\) 10.9788 0.533176
\(425\) 0 0
\(426\) −5.67632 1.35981i −0.275019 0.0658829i
\(427\) −30.6868 16.9788i −1.48504 0.821660i
\(428\) 10.6088 0.512797
\(429\) 35.6425 + 8.53844i 1.72084 + 0.412240i
\(430\) 0 0
\(431\) 10.2389i 0.493189i 0.969119 + 0.246594i \(0.0793115\pi\)
−0.969119 + 0.246594i \(0.920688\pi\)
\(432\) −3.36879 + 3.95617i −0.162081 + 0.190341i
\(433\) −22.7030 −1.09103 −0.545517 0.838099i \(-0.683667\pi\)
−0.545517 + 0.838099i \(0.683667\pi\)
\(434\) 21.0197 + 11.6300i 1.00898 + 0.558260i
\(435\) 0 0
\(436\) 18.1348 0.868499
\(437\) 0.227036i 0.0108606i
\(438\) −2.01062 + 8.39303i −0.0960709 + 0.401035i
\(439\) 26.4492i 1.26235i 0.775639 + 0.631176i \(0.217428\pi\)
−0.775639 + 0.631176i \(0.782572\pi\)
\(440\) 0 0
\(441\) 1.88345 + 20.9154i 0.0896883 + 0.995970i
\(442\) 28.9788i 1.37838i
\(443\) 27.8689 1.32409 0.662046 0.749463i \(-0.269688\pi\)
0.662046 + 0.749463i \(0.269688\pi\)
\(444\) −10.2199 2.44825i −0.485014 0.116189i
\(445\) 0 0
\(446\) −23.7296 −1.12363
\(447\) −12.8162 3.07023i −0.606187 0.145217i
\(448\) −1.28088 + 2.31502i −0.0605161 + 0.109375i
\(449\) 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
\(452\) −8.54142 −0.401755
\(453\) −1.86827 + 7.79882i −0.0877789 + 0.366421i
\(454\) 10.4667i 0.491227i
\(455\) 0 0
\(456\) −1.35934 0.325639i −0.0636568 0.0152495i
\(457\) 31.8322i 1.48905i 0.667595 + 0.744524i \(0.267324\pi\)
−0.667595 + 0.744524i \(0.732676\pi\)
\(458\) 16.4762i 0.769881i
\(459\) −28.9788 24.6762i −1.35261 1.15179i
\(460\) 0 0
\(461\) −10.6320 −0.495179 −0.247590 0.968865i \(-0.579638\pi\)
−0.247590 + 0.968865i \(0.579638\pi\)
\(462\) −16.5364 + 18.0924i −0.769341 + 0.841734i
\(463\) 12.8322i 0.596364i −0.954509 0.298182i \(-0.903620\pi\)
0.954509 0.298182i \(-0.0963803\pi\)
\(464\) 0.281327i 0.0130603i
\(465\) 0 0
\(466\) 27.9575 1.29511
\(467\) 20.8716i 0.965824i −0.875669 0.482912i \(-0.839579\pi\)
0.875669 0.482912i \(-0.160421\pi\)
\(468\) 10.5802 + 5.37777i 0.489071 + 0.248587i
\(469\) −15.5539 8.60584i −0.718212 0.397381i
\(470\) 0 0
\(471\) 6.18024 25.7985i 0.284770 1.18873i
\(472\) 4.90390 0.225720
\(473\) 33.9575 1.56137
\(474\) −1.31548 + 5.49128i −0.0604220 + 0.252223i
\(475\) 0 0
\(476\) −16.9574 9.38242i −0.777243 0.430042i
\(477\) 29.3612 + 14.9238i 1.34436 + 0.683316i
\(478\) 17.2601i 0.789458i
\(479\) 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
\(482\) 19.1935i 0.874238i
\(483\) −0.951606 0.869764i −0.0432996 0.0395756i
\(484\) −17.6088 −0.800401
\(485\) 0 0
\(486\) −14.3871 + 6.00091i −0.652613 + 0.272207i
\(487\) 33.3524i 1.51134i 0.654951 + 0.755671i \(0.272689\pi\)
−0.654951 + 0.755671i \(0.727311\pi\)
\(488\) 13.2555i 0.600049i
\(489\) −5.16670 1.23772i −0.233646 0.0559717i
\(490\) 0 0
\(491\) 30.0000i 1.35388i 0.736038 + 0.676941i \(0.236695\pi\)
−0.736038 + 0.676941i \(0.763305\pi\)
\(492\) −2.48166 + 10.3593i −0.111882 + 0.467035i
\(493\) 2.06071 0.0928096
\(494\) 3.19270i 0.143646i
\(495\) 0 0
\(496\) 9.07971i 0.407691i
\(497\) −7.80152 4.31652i −0.349946 0.193622i
\(498\) −2.58574 0.619433i −0.115870 0.0277574i
\(499\) 19.1810 0.858657 0.429329 0.903148i \(-0.358750\pi\)
0.429329 + 0.903148i \(0.358750\pi\)
\(500\) 0 0
\(501\) −3.19270 0.764836i −0.142639 0.0341704i
\(502\) 21.0271 0.938487
\(503\) 36.9851i 1.64909i 0.565800 + 0.824543i \(0.308568\pi\)
−0.565800 + 0.824543i \(0.691432\pi\)
\(504\) −6.57244 + 4.45006i −0.292760 + 0.198221i
\(505\) 0 0
\(506\) 1.50474i 0.0668938i
\(507\) 1.06982 4.46580i 0.0475122 0.198333i
\(508\) 2.00000i 0.0887357i
\(509\) −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
\(512\) −1.00000 −0.0441942
\(513\) −3.19270 2.71867i −0.140961 0.120032i
\(514\) 14.5881i 0.643455i
\(515\) 0 0
\(516\) 10.6937 + 2.56177i 0.470766 + 0.112776i
\(517\) −30.9682 −1.36198
\(518\) −14.0462 7.77163i −0.617153 0.341466i
\(519\) −14.9238 3.57512i −0.655084 0.156930i
\(520\) 0 0
\(521\) 3.65761 0.160243 0.0801214 0.996785i \(-0.474469\pi\)
0.0801214 + 0.996785i \(0.474469\pi\)
\(522\) 0.382418 0.752370i 0.0167380 0.0329303i
\(523\) 2.26321 0.0989633 0.0494816 0.998775i \(-0.484243\pi\)
0.0494816 + 0.998775i \(0.484243\pi\)
\(524\) −16.5454 −0.722788
\(525\) 0 0
\(526\) −8.91138 −0.388554
\(527\) −66.5084 −2.89715
\(528\) −9.00935 2.15826i −0.392082 0.0939261i
\(529\) −22.9209 −0.996559
\(530\) 0 0
\(531\) 13.1148 + 6.66605i 0.569134 + 0.289282i
\(532\) −1.86827 1.03370i −0.0809997 0.0448164i
\(533\) 24.3312 1.05390
\(534\) 1.74175 7.27071i 0.0753731 0.314634i
\(535\) 0 0
\(536\) 6.71867i 0.290202i
\(537\) 19.1157 + 4.57931i 0.824904 + 0.197612i
\(538\) −22.3352 −0.962940
\(539\) −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 \(0.394407\pi\)
\(542\) 7.17684i 0.308272i
\(543\) −14.5414 3.48351i −0.624032 0.149492i
\(544\) 7.32496i 0.314055i
\(545\) 0 0
\(546\) 13.3820 + 12.2311i 0.572696 + 0.523442i
\(547\) 2.89014i 0.123574i 0.998089 + 0.0617868i \(0.0196799\pi\)
−0.998089 + 0.0617868i \(0.980320\pi\)
\(548\) −7.41612 −0.316801
\(549\) 18.0187 35.4500i 0.769019 1.51297i
\(550\) 0 0
\(551\) 0.227036 0.00967206
\(552\) 0.113518 0.473865i 0.00483165 0.0201690i
\(553\) −4.17580 + 7.54720i −0.177573 + 0.320940i
\(554\) 9.32749i 0.396287i
\(555\) 0 0
\(556\) 6.36982i 0.270141i
\(557\) 32.4777 1.37613 0.688063 0.725651i \(-0.258461\pi\)
0.688063 + 0.725651i \(0.258461\pi\)
\(558\) −12.3424 + 24.2824i −0.522494 + 1.02796i
\(559\) 25.1166i 1.06232i
\(560\) 0 0
\(561\) 15.8091 65.9931i 0.667463 2.78623i
\(562\) 17.4373i 0.735550i
\(563\) 10.9208i 0.460256i 0.973160 + 0.230128i \(0.0739145\pi\)
−0.973160 + 0.230128i \(0.926086\pi\)
\(564\) −9.75237 2.33625i −0.410649 0.0983741i
\(565\) 0 0
\(566\) 16.1776 0.679996
\(567\) −23.6262 + 2.96690i −0.992207 + 0.124598i
\(568\) 3.36995i 0.141400i
\(569\) 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 \(0.461083\pi\)
\(572\) 21.1604i 0.884763i
\(573\) 13.1148 + 3.14175i 0.547879 + 0.131248i
\(574\) −7.87768 + 14.2378i −0.328808 + 0.594276i
\(575\) 0 0
\(576\) −2.67436 1.35934i −0.111432 0.0566390i
\(577\) 9.82493 0.409017 0.204509 0.978865i \(-0.434440\pi\)
0.204509 + 0.978865i \(0.434440\pi\)
\(578\) 36.6550 1.52465
\(579\) −42.3987 10.1569i −1.76203 0.422107i
\(580\) 0 0
\(581\) −3.55383 1.96630i −0.147438 0.0815760i
\(582\) 6.08862 25.4161i 0.252382 1.05353i
\(583\) 58.7224i 2.43203i
\(584\) −4.98282 −0.206191
\(585\) 0 0
\(586\) 22.5623i 0.932038i
\(587\) 27.3106i 1.12723i 0.826037 + 0.563615i \(0.190590\pi\)
−0.826037 + 0.563615i \(0.809410\pi\)
\(588\) −11.4899 + 3.87067i −0.473836 + 0.159624i
\(589\) −7.32749 −0.301924
\(590\) 0 0
\(591\) −1.01925 + 4.25473i −0.0419264 + 0.175016i
\(592\) 6.06739i 0.249368i
\(593\) 26.8788i 1.10378i −0.833917 0.551889i \(-0.813907\pi\)
0.833917 0.551889i \(-0.186093\pi\)
\(594\) −21.1604 18.0187i −0.868224 0.739316i
\(595\) 0 0
\(596\) 7.60882i 0.311669i
\(597\) 1.59635 + 0.382418i 0.0653343 + 0.0156513i
\(598\) −1.11298 −0.0455130
\(599\) 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 \(0.991459\pi\)
\(602\) 14.6974 + 8.13197i 0.599023 + 0.331435i
\(603\) 9.13294 17.9682i 0.371922 0.731720i
\(604\) −4.63005 −0.188394
\(605\) 0 0
\(606\) −2.33625 + 9.75237i −0.0949039 + 0.396163i
\(607\) −26.9651 −1.09448 −0.547240 0.836976i \(-0.684321\pi\)
−0.547240 + 0.836976i \(0.684321\pi\)
\(608\) 0.807019i 0.0327289i
\(609\) 0.869764 0.951606i 0.0352446 0.0385610i
\(610\) 0 0
\(611\) 22.9056i 0.926661i
\(612\) 9.95708 19.5896i 0.402491 0.791862i
\(613\) 33.9151i 1.36982i 0.728629 + 0.684909i \(0.240158\pi\)
−0.728629 + 0.684909i \(0.759842\pi\)
\(614\) 19.4057 0.783150
\(615\) 0 0
\(616\) −12.3824 6.85109i −0.498902 0.276038i
\(617\) −13.1253 −0.528405 −0.264203 0.964467i \(-0.585109\pi\)
−0.264203 + 0.964467i \(0.585109\pi\)
\(618\) 2.80730 11.7187i 0.112926 0.471394i
\(619\) 38.0907i 1.53099i −0.643439 0.765497i \(-0.722493\pi\)
0.643439 0.765497i \(-0.277507\pi\)
\(620\) 0 0
\(621\) 0.947731 1.11298i 0.0380311 0.0446623i
\(622\) 6.73757 0.270152
\(623\) 5.52896 9.99284i 0.221513 0.400355i
\(624\) −1.59635 + 6.66375i −0.0639052 + 0.266763i
\(625\) 0 0
\(626\) 21.3875 0.854816
\(627\) 1.74175 7.27071i 0.0695590 0.290364i
\(628\) 15.3162 0.611184
\(629\) 44.4434 1.77207
\(630\) 0 0
\(631\) −12.0674 −0.480395 −0.240198 0.970724i \(-0.577212\pi\)
−0.240198 + 0.970724i \(0.577212\pi\)
\(632\) −3.26010 −0.129680
\(633\) −5.20129 + 21.7121i −0.206733 + 0.862977i
\(634\) 3.47403 0.137971
\(635\) 0 0
\(636\) −4.43004 + 18.4926i −0.175662 + 0.733278i
\(637\) 14.7117 + 23.4623i 0.582899 + 0.929609i
\(638\) 1.50474 0.0595732
\(639\) 4.58090 9.01247i 0.181218 0.356528i
\(640\) 0 0
\(641\) 17.4373i 0.688734i −0.938835 0.344367i \(-0.888094\pi\)
0.938835 0.344367i \(-0.111906\pi\)
\(642\) −4.28076 + 17.8694i −0.168948 + 0.705250i
\(643\) 6.01688 0.237283 0.118641 0.992937i \(-0.462146\pi\)
0.118641 + 0.992937i \(0.462146\pi\)
\(644\) 0.360347 0.651279i 0.0141997 0.0256640i
\(645\) 0 0
\(646\) 5.91138 0.232580
\(647\) 36.7581i 1.44511i −0.691314 0.722555i \(-0.742968\pi\)
0.691314 0.722555i \(-0.257032\pi\)
\(648\) −5.30441 7.27071i −0.208377 0.285621i
\(649\) 26.2296i 1.02960i
\(650\) 0 0
\(651\) −28.0712 + 30.7127i −1.10020 + 1.20372i
\(652\) 3.06739i 0.120128i
\(653\) −14.8073 −0.579454 −0.289727 0.957109i \(-0.593565\pi\)
−0.289727 + 0.957109i \(0.593565\pi\)
\(654\) −7.31755 + 30.5461i −0.286139 + 1.19445i
\(655\) 0 0
\(656\) −6.15019 −0.240125
\(657\) −13.3259 6.77333i −0.519892 0.264253i
\(658\) −13.4036 7.41612i −0.522528 0.289110i
\(659\) 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 \(0.874821\pi\)
\(662\) 8.93261 0.347176
\(663\) −48.8116 11.6932i −1.89569 0.454126i
\(664\) 1.53511i 0.0595740i
\(665\) 0 0
\(666\) 8.24763 16.2264i 0.319589 0.628760i
\(667\) 0.0791449i 0.00306450i
\(668\) 1.89546i 0.0733376i
\(669\) 9.57512 39.9700i 0.370196 1.54533i
\(670\) 0 0
\(671\) 70.9000 2.73707
\(672\) −3.38256 3.09165i −0.130485 0.119263i
\(673\) 21.7861i 0.839791i −0.907572 0.419896i \(-0.862067\pi\)
0.907572 0.419896i \(-0.137933\pi\)
\(674\) 34.2176i 1.31801i
\(675\) 0 0
\(676\) 2.65128 0.101972
\(677\) 15.3706i 0.590740i 0.955383 + 0.295370i \(0.0954430\pi\)
−0.955383 + 0.295370i \(0.904557\pi\)
\(678\) 3.44654 14.3871i 0.132364 0.552534i
\(679\) 19.3275 34.9318i 0.741721 1.34056i
\(680\) 0 0
\(681\) 17.6300 + 4.22341i 0.675585 + 0.161842i
\(682\) −48.5648 −1.85964
\(683\) 22.0462 0.843573 0.421786 0.906695i \(-0.361403\pi\)
0.421786 + 0.906695i \(0.361403\pi\)
\(684\) 1.09701 2.15826i 0.0419452 0.0825231i
\(685\) 0 0
\(686\) −18.4926 + 1.01247i −0.706049 + 0.0386561i
\(687\) 27.7524 + 6.64829i 1.05882 + 0.253648i
\(688\) 6.34872i 0.242043i
\(689\) 43.4339 1.65470
\(690\) 0 0
\(691\) 31.7209i 1.20672i 0.797469 + 0.603360i \(0.206172\pi\)
−0.797469 + 0.603360i \(0.793828\pi\)
\(692\) 8.86007i 0.336809i
\(693\) −23.8021 35.1542i −0.904168 1.33540i
\(694\) −11.5260 −0.437520
\(695\) 0 0
\(696\) 0.473865 + 0.113518i 0.0179618 + 0.00430289i
\(697\) 45.0499i 1.70639i
\(698\) 21.8342i 0.826435i
\(699\) −11.2811 + 47.0915i −0.426691 + 1.78116i
\(700\) 0 0
\(701\) 49.4316i 1.86700i 0.358571 + 0.933502i \(0.383264\pi\)
−0.358571 + 0.933502i \(0.616736\pi\)
\(702\) −13.3275 + 15.6513i −0.503014 + 0.590719i
\(703\) 4.89650 0.184675
\(704\) 5.34872i 0.201588i
\(705\) 0 0
\(706\) 4.84211i 0.182235i
\(707\) −7.41612 + 13.4036i −0.278912 + 0.504095i
\(708\) −1.97877 + 8.26010i −0.0743667 + 0.310433i
\(709\) 0.697442 0.0261930 0.0130965 0.999914i \(-0.495831\pi\)
0.0130965 + 0.999914i \(0.495831\pi\)
\(710\) 0 0
\(711\) −8.71867 4.43157i −0.326976 0.166197i
\(712\) 4.31652 0.161768
\(713\) 2.55437i 0.0956618i
\(714\) 22.6462 24.7771i 0.847512 0.927260i
\(715\) 0 0
\(716\) 11.3487i 0.424122i
\(717\) −29.0728 6.96461i −1.08574 0.260098i
\(718\) 30.3063i 1.13102i
\(719\) 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
\(722\) −18.3487 −0.682869
\(723\) −32.3293 7.74474i −1.20234 0.288030i
\(724\) 8.63303i 0.320844i
\(725\) 0 0
\(726\) 7.10532 29.6602i 0.263703 1.10079i
\(727\) 27.3970 1.01610 0.508049 0.861328i \(-0.330367\pi\)
0.508049 + 0.861328i \(0.330367\pi\)
\(728\) −5.06739 + 9.15863i −0.187810 + 0.339441i
\(729\) −4.30256 26.6550i −0.159354 0.987222i
\(730\) 0 0
\(731\) −46.5041 −1.72002
\(732\) 22.3275 + 5.34872i 0.825248 + 0.197694i
\(733\) −0.0617893 −0.00228224 −0.00114112 0.999999i \(-0.500363\pi\)
−0.00114112 + 0.999999i \(0.500363\pi\)
\(734\) 13.9910 0.516417
\(735\) 0 0
\(736\) 0.281327 0.0103699
\(737\) 35.9363 1.32373
\(738\) −16.4478 8.36018i −0.605453 0.307742i
\(739\) 45.0037 1.65549 0.827744 0.561106i \(-0.189624\pi\)
0.827744 + 0.561106i \(0.189624\pi\)
\(740\) 0 0
\(741\) −5.37777 1.28828i −0.197557 0.0473263i
\(742\) −14.0625 + 25.4161i −0.516252 + 0.933055i
\(743\) −38.1655 −1.40016 −0.700078 0.714066i \(-0.746852\pi\)
−0.700078 + 0.714066i \(0.746852\pi\)
\(744\) −15.2938 3.66375i −0.560698 0.134319i
\(745\) 0 0
\(746\) 4.24464i 0.155407i
\(747\) 2.08674 4.10545i 0.0763497 0.150211i
\(748\) 39.1791 1.43253
\(749\) −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 \(0.669934\pi\)
\(752\) 5.78984i 0.211134i
\(753\) −8.48464 + 35.4180i −0.309198 + 1.29070i
\(754\) 1.11298i 0.0405323i
\(755\) 0 0
\(756\) −4.84360 12.8662i −0.176160 0.467940i
\(757\) 38.5876i 1.40249i 0.712921 + 0.701245i \(0.247372\pi\)
−0.712921 + 0.701245i \(0.752628\pi\)
\(758\) −1.63005 −0.0592060
\(759\) 2.53457 + 0.607177i 0.0919992 + 0.0220391i
\(760\) 0 0
\(761\) 28.9173 1.04825 0.524125 0.851641i \(-0.324392\pi\)
0.524125 + 0.851641i \(0.324392\pi\)
\(762\) 3.36879 + 0.807019i 0.122038 + 0.0292352i
\(763\) −23.2286 + 41.9825i −0.840930 + 1.51987i
\(764\) 7.78607i 0.281690i
\(765\) 0 0
\(766\) 16.9994i 0.614215i
\(767\) 19.4007 0.700517
\(768\) 0.403509 1.68439i 0.0145604 0.0607803i
\(769\) 30.3191i 1.09333i 0.837350 + 0.546667i \(0.184104\pi\)
−0.837350 + 0.546667i \(0.815896\pi\)
\(770\) 0 0
\(771\) −24.5721 5.88644i −0.884944 0.211995i
\(772\) 25.1715i 0.905941i
\(773\) 23.7370i 0.853761i −0.904308 0.426881i \(-0.859612\pi\)
0.904308 0.426881i \(-0.140388\pi\)
\(774\) −8.63005 + 16.9788i −0.310201 + 0.610289i
\(775\) 0 0
\(776\) 15.0892 0.541670
\(777\) 18.7582 20.5233i 0.672948 0.736271i
\(778\) 29.4623i 1.05627i
\(779\) 4.96332i 0.177829i
\(780\) 0 0
\(781\) 18.0249 0.644983
\(782\) 2.06071i 0.0736908i
\(783\) 1.11298 + 0.947731i 0.0397746 + 0.0338691i
\(784\) −3.71867 5.93055i −0.132810 0.211806i
\(785\) 0 0
\(786\) 6.67621 27.8689i 0.238133 0.994051i
\(787\) 30.7560 1.09633 0.548167 0.836369i \(-0.315326\pi\)
0.548167 + 0.836369i \(0.315326\pi\)
\(788\) −2.52597 −0.0899840
\(789\) 3.59582 15.0103i 0.128015 0.534379i