Properties

Label 1950.2.bc.g.751.3
Level $1950$
Weight $2$
Character 1950.751
Analytic conductor $15.571$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.bc (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.17284886784.1
Defining polynomial: \(x^{8} - 2 x^{7} + 2 x^{6} + 30 x^{5} + 185 x^{4} + 36 x^{3} + 8 x^{2} + 208 x + 2704\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 751.3
Root \(3.17270 + 3.17270i\) of defining polynomial
Character \(\chi\) \(=\) 1950.751
Dual form 1950.2.bc.g.901.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-1.14539 - 0.661290i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-1.14539 - 0.661290i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-3.99528 + 2.30668i) q^{11} +1.00000 q^{12} +(-3.20002 - 1.66129i) q^{13} -1.32258 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +1.00000i q^{18} +(1.98387 + 1.14539i) q^{19} -1.32258i q^{21} +(-2.30668 + 3.99528i) q^{22} +(-4.33399 - 7.50670i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-3.60194 + 0.161290i) q^{26} -1.00000 q^{27} +(-1.14539 + 0.661290i) q^{28} +(1.01141 + 1.75182i) q^{29} +10.1321i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-3.99528 - 2.30668i) q^{33} +4.00000i q^{34} +(0.500000 + 0.866025i) q^{36} +(-5.89721 + 3.40475i) q^{37} +2.29078 q^{38} +(-0.161290 - 3.60194i) q^{39} +(-4.02283 + 2.32258i) q^{41} +(-0.661290 - 1.14539i) q^{42} +(-4.30281 + 7.45269i) q^{43} +4.61335i q^{44} +(-7.50670 - 4.33399i) q^{46} -9.10926i q^{47} +(0.500000 - 0.866025i) q^{48} +(-2.62539 - 4.54731i) q^{49} -4.00000 q^{51} +(-3.03873 + 1.94065i) q^{52} -0.826674 q^{53} +(-0.866025 + 0.500000i) q^{54} +(-0.661290 + 1.14539i) q^{56} +2.29078i q^{57} +(1.75182 + 1.01141i) q^{58} +(2.72064 + 1.57076i) q^{59} +(-0.267949 + 0.464102i) q^{61} +(5.06604 + 8.77464i) q^{62} +(1.14539 - 0.661290i) q^{63} -1.00000 q^{64} -4.61335 q^{66} +(2.75488 - 1.59053i) q^{67} +(2.00000 + 3.46410i) q^{68} +(4.33399 - 7.50670i) q^{69} +(-9.81724 - 5.66799i) q^{71} +(0.866025 + 0.500000i) q^{72} -6.28304i q^{73} +(-3.40475 + 5.89721i) q^{74} +(1.98387 - 1.14539i) q^{76} +6.10153 q^{77} +(-1.94065 - 3.03873i) q^{78} +2.96774 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-2.32258 + 4.02283i) q^{82} +15.8719i q^{83} +(-1.14539 - 0.661290i) q^{84} +8.60562i q^{86} +(-1.01141 + 1.75182i) q^{87} +(2.30668 + 3.99528i) q^{88} +(10.2746 - 5.93207i) q^{89} +(2.56667 + 4.01896i) q^{91} -8.66799 q^{92} +(-8.77464 + 5.06604i) q^{93} +(-4.55463 - 7.88885i) q^{94} -1.00000i q^{96} +(7.63743 + 4.40947i) q^{97} +(-4.54731 - 2.62539i) q^{98} -4.61335i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{3} + 4q^{4} - 4q^{9} + O(q^{10}) \) \( 8q + 4q^{3} + 4q^{4} - 4q^{9} + 6q^{11} + 8q^{12} + 12q^{13} + 4q^{14} - 4q^{16} - 16q^{17} - 6q^{19} - 2q^{22} - 4q^{23} - 12q^{26} - 8q^{27} - 8q^{29} + 6q^{33} + 4q^{36} - 30q^{37} + 6q^{39} + 2q^{42} - 14q^{43} - 6q^{46} + 4q^{48} + 14q^{49} - 32q^{51} + 6q^{52} - 16q^{53} + 2q^{56} + 6q^{58} + 24q^{59} - 16q^{61} - 4q^{62} - 8q^{64} - 4q^{66} - 24q^{67} + 16q^{68} + 4q^{69} - 12q^{71} + 10q^{74} - 6q^{76} - 16q^{77} - 6q^{78} - 20q^{79} - 4q^{81} - 4q^{82} + 8q^{87} + 2q^{88} + 42q^{89} - 10q^{91} - 8q^{92} - 30q^{93} - 8q^{94} + 24q^{97} - 48q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) 0.866025 + 0.500000i 0.353553 + 0.204124i
\(7\) −1.14539 0.661290i −0.432916 0.249944i 0.267672 0.963510i \(-0.413746\pi\)
−0.700588 + 0.713566i \(0.747079\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −3.99528 + 2.30668i −1.20462 + 0.695489i −0.961580 0.274526i \(-0.911479\pi\)
−0.243043 + 0.970015i \(0.578146\pi\)
\(12\) 1.00000 0.288675
\(13\) −3.20002 1.66129i −0.887525 0.460759i
\(14\) −1.32258 −0.353474
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.00000 + 3.46410i −0.485071 + 0.840168i −0.999853 0.0171533i \(-0.994540\pi\)
0.514782 + 0.857321i \(0.327873\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 1.98387 + 1.14539i 0.455131 + 0.262770i 0.709995 0.704207i \(-0.248697\pi\)
−0.254864 + 0.966977i \(0.582031\pi\)
\(20\) 0 0
\(21\) 1.32258i 0.288611i
\(22\) −2.30668 + 3.99528i −0.491785 + 0.851797i
\(23\) −4.33399 7.50670i −0.903700 1.56525i −0.822653 0.568544i \(-0.807507\pi\)
−0.0810471 0.996710i \(-0.525826\pi\)
\(24\) 0.866025 0.500000i 0.176777 0.102062i
\(25\) 0 0
\(26\) −3.60194 + 0.161290i −0.706399 + 0.0316315i
\(27\) −1.00000 −0.192450
\(28\) −1.14539 + 0.661290i −0.216458 + 0.124972i
\(29\) 1.01141 + 1.75182i 0.187815 + 0.325305i 0.944521 0.328450i \(-0.106526\pi\)
−0.756707 + 0.653755i \(0.773193\pi\)
\(30\) 0 0
\(31\) 10.1321i 1.81978i 0.414853 + 0.909888i \(0.363833\pi\)
−0.414853 + 0.909888i \(0.636167\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) −3.99528 2.30668i −0.695489 0.401541i
\(34\) 4.00000i 0.685994i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) −5.89721 + 3.40475i −0.969495 + 0.559738i −0.899082 0.437780i \(-0.855765\pi\)
−0.0704126 + 0.997518i \(0.522432\pi\)
\(38\) 2.29078 0.371613
\(39\) −0.161290 3.60194i −0.0258270 0.576772i
\(40\) 0 0
\(41\) −4.02283 + 2.32258i −0.628260 + 0.362726i −0.780078 0.625682i \(-0.784821\pi\)
0.151818 + 0.988408i \(0.451487\pi\)
\(42\) −0.661290 1.14539i −0.102039 0.176737i
\(43\) −4.30281 + 7.45269i −0.656173 + 1.13652i 0.325426 + 0.945568i \(0.394492\pi\)
−0.981598 + 0.190957i \(0.938841\pi\)
\(44\) 4.61335i 0.695489i
\(45\) 0 0
\(46\) −7.50670 4.33399i −1.10680 0.639012i
\(47\) 9.10926i 1.32872i −0.747412 0.664361i \(-0.768704\pi\)
0.747412 0.664361i \(-0.231296\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) −2.62539 4.54731i −0.375056 0.649616i
\(50\) 0 0
\(51\) −4.00000 −0.560112
\(52\) −3.03873 + 1.94065i −0.421396 + 0.269120i
\(53\) −0.826674 −0.113552 −0.0567762 0.998387i \(-0.518082\pi\)
−0.0567762 + 0.998387i \(0.518082\pi\)
\(54\) −0.866025 + 0.500000i −0.117851 + 0.0680414i
\(55\) 0 0
\(56\) −0.661290 + 1.14539i −0.0883686 + 0.153059i
\(57\) 2.29078i 0.303421i
\(58\) 1.75182 + 1.01141i 0.230025 + 0.132805i
\(59\) 2.72064 + 1.57076i 0.354197 + 0.204496i 0.666532 0.745476i \(-0.267778\pi\)
−0.312335 + 0.949972i \(0.601111\pi\)
\(60\) 0 0
\(61\) −0.267949 + 0.464102i −0.0343074 + 0.0594221i −0.882669 0.469995i \(-0.844256\pi\)
0.848362 + 0.529417i \(0.177589\pi\)
\(62\) 5.06604 + 8.77464i 0.643388 + 1.11438i
\(63\) 1.14539 0.661290i 0.144305 0.0833147i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −4.61335 −0.567865
\(67\) 2.75488 1.59053i 0.336562 0.194314i −0.322189 0.946675i \(-0.604419\pi\)
0.658751 + 0.752361i \(0.271085\pi\)
\(68\) 2.00000 + 3.46410i 0.242536 + 0.420084i
\(69\) 4.33399 7.50670i 0.521751 0.903700i
\(70\) 0 0
\(71\) −9.81724 5.66799i −1.16509 0.672666i −0.212573 0.977145i \(-0.568184\pi\)
−0.952519 + 0.304479i \(0.901518\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) 6.28304i 0.735375i −0.929949 0.367687i \(-0.880150\pi\)
0.929949 0.367687i \(-0.119850\pi\)
\(74\) −3.40475 + 5.89721i −0.395795 + 0.685536i
\(75\) 0 0
\(76\) 1.98387 1.14539i 0.227565 0.131385i
\(77\) 6.10153 0.695334
\(78\) −1.94065 3.03873i −0.219736 0.344068i
\(79\) 2.96774 0.333897 0.166948 0.985966i \(-0.446609\pi\)
0.166948 + 0.985966i \(0.446609\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.32258 + 4.02283i −0.256486 + 0.444247i
\(83\) 15.8719i 1.74216i 0.491138 + 0.871082i \(0.336581\pi\)
−0.491138 + 0.871082i \(0.663419\pi\)
\(84\) −1.14539 0.661290i −0.124972 0.0721526i
\(85\) 0 0
\(86\) 8.60562i 0.927968i
\(87\) −1.01141 + 1.75182i −0.108435 + 0.187815i
\(88\) 2.30668 + 3.99528i 0.245893 + 0.425899i
\(89\) 10.2746 5.93207i 1.08911 0.628798i 0.155771 0.987793i \(-0.450214\pi\)
0.933339 + 0.358995i \(0.116881\pi\)
\(90\) 0 0
\(91\) 2.56667 + 4.01896i 0.269060 + 0.421302i
\(92\) −8.66799 −0.903700
\(93\) −8.77464 + 5.06604i −0.909888 + 0.525324i
\(94\) −4.55463 7.88885i −0.469774 0.813673i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) 7.63743 + 4.40947i 0.775463 + 0.447714i 0.834820 0.550523i \(-0.185572\pi\)
−0.0593568 + 0.998237i \(0.518905\pi\)
\(98\) −4.54731 2.62539i −0.459348 0.265205i
\(99\) 4.61335i 0.463660i
\(100\) 0 0
\(101\) −3.61335 6.25851i −0.359542 0.622745i 0.628342 0.777937i \(-0.283734\pi\)
−0.987884 + 0.155192i \(0.950400\pi\)
\(102\) −3.46410 + 2.00000i −0.342997 + 0.198030i
\(103\) 18.4000 1.81301 0.906505 0.422196i \(-0.138740\pi\)
0.906505 + 0.422196i \(0.138740\pi\)
\(104\) −1.66129 + 3.20002i −0.162903 + 0.313788i
\(105\) 0 0
\(106\) −0.715920 + 0.413337i −0.0695363 + 0.0401468i
\(107\) 1.53590 + 2.66025i 0.148481 + 0.257176i 0.930666 0.365869i \(-0.119228\pi\)
−0.782185 + 0.623046i \(0.785895\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 13.2267i 1.26689i −0.773788 0.633445i \(-0.781640\pi\)
0.773788 0.633445i \(-0.218360\pi\)
\(110\) 0 0
\(111\) −5.89721 3.40475i −0.559738 0.323165i
\(112\) 1.32258i 0.124972i
\(113\) −4.04322 + 7.00306i −0.380354 + 0.658792i −0.991113 0.133024i \(-0.957531\pi\)
0.610759 + 0.791817i \(0.290864\pi\)
\(114\) 1.14539 + 1.98387i 0.107275 + 0.185806i
\(115\) 0 0
\(116\) 2.02283 0.187815
\(117\) 3.03873 1.94065i 0.280931 0.179413i
\(118\) 3.14152 0.289201
\(119\) 4.58155 2.64516i 0.419990 0.242481i
\(120\) 0 0
\(121\) 5.14152 8.90538i 0.467411 0.809580i
\(122\) 0.535898i 0.0485180i
\(123\) −4.02283 2.32258i −0.362726 0.209420i
\(124\) 8.77464 + 5.06604i 0.787986 + 0.454944i
\(125\) 0 0
\(126\) 0.661290 1.14539i 0.0589124 0.102039i
\(127\) −5.73592 9.93490i −0.508980 0.881580i −0.999946 0.0104008i \(-0.996689\pi\)
0.490966 0.871179i \(-0.336644\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) −8.60562 −0.757683
\(130\) 0 0
\(131\) −15.9906 −1.39710 −0.698551 0.715560i \(-0.746172\pi\)
−0.698551 + 0.715560i \(0.746172\pi\)
\(132\) −3.99528 + 2.30668i −0.347745 + 0.200771i
\(133\) −1.51487 2.62383i −0.131356 0.227515i
\(134\) 1.59053 2.75488i 0.137401 0.237985i
\(135\) 0 0
\(136\) 3.46410 + 2.00000i 0.297044 + 0.171499i
\(137\) −13.9168 8.03486i −1.18899 0.686465i −0.230914 0.972974i \(-0.574172\pi\)
−0.958077 + 0.286509i \(0.907505\pi\)
\(138\) 8.66799i 0.737868i
\(139\) −4.66129 + 8.07359i −0.395365 + 0.684793i −0.993148 0.116865i \(-0.962715\pi\)
0.597782 + 0.801658i \(0.296049\pi\)
\(140\) 0 0
\(141\) 7.88885 4.55463i 0.664361 0.383569i
\(142\) −11.3360 −0.951294
\(143\) 16.6170 0.744087i 1.38959 0.0622237i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) −3.14152 5.44128i −0.259994 0.450323i
\(147\) 2.62539 4.54731i 0.216539 0.375056i
\(148\) 6.80951i 0.559738i
\(149\) 3.53788 + 2.04259i 0.289834 + 0.167336i 0.637867 0.770146i \(-0.279817\pi\)
−0.348033 + 0.937482i \(0.613150\pi\)
\(150\) 0 0
\(151\) 19.9811i 1.62604i 0.582235 + 0.813021i \(0.302178\pi\)
−0.582235 + 0.813021i \(0.697822\pi\)
\(152\) 1.14539 1.98387i 0.0929032 0.160913i
\(153\) −2.00000 3.46410i −0.161690 0.280056i
\(154\) 5.28408 3.05076i 0.425803 0.245838i
\(155\) 0 0
\(156\) −3.20002 1.66129i −0.256206 0.133010i
\(157\) −7.13379 −0.569338 −0.284669 0.958626i \(-0.591884\pi\)
−0.284669 + 0.958626i \(0.591884\pi\)
\(158\) 2.57014 1.48387i 0.204469 0.118050i
\(159\) −0.413337 0.715920i −0.0327797 0.0567762i
\(160\) 0 0
\(161\) 11.4641i 0.903498i
\(162\) −0.866025 0.500000i −0.0680414 0.0392837i
\(163\) 8.56906 + 4.94735i 0.671180 + 0.387506i 0.796524 0.604607i \(-0.206670\pi\)
−0.125343 + 0.992113i \(0.540003\pi\)
\(164\) 4.64516i 0.362726i
\(165\) 0 0
\(166\) 7.93593 + 13.7454i 0.615948 + 1.06685i
\(167\) −20.8171 + 12.0187i −1.61087 + 0.930037i −0.621704 + 0.783253i \(0.713559\pi\)
−0.989168 + 0.146785i \(0.953108\pi\)
\(168\) −1.32258 −0.102039
\(169\) 7.48023 + 10.6323i 0.575402 + 0.817870i
\(170\) 0 0
\(171\) −1.98387 + 1.14539i −0.151710 + 0.0875900i
\(172\) 4.30281 + 7.45269i 0.328086 + 0.568262i
\(173\) −1.26408 + 2.18946i −0.0961065 + 0.166461i −0.910070 0.414455i \(-0.863972\pi\)
0.813963 + 0.580916i \(0.197306\pi\)
\(174\) 2.02283i 0.153350i
\(175\) 0 0
\(176\) 3.99528 + 2.30668i 0.301156 + 0.173872i
\(177\) 3.14152i 0.236131i
\(178\) 5.93207 10.2746i 0.444627 0.770117i
\(179\) −3.13784 5.43490i −0.234533 0.406223i 0.724604 0.689166i \(-0.242023\pi\)
−0.959137 + 0.282942i \(0.908689\pi\)
\(180\) 0 0
\(181\) −12.2830 −0.912991 −0.456496 0.889726i \(-0.650896\pi\)
−0.456496 + 0.889726i \(0.650896\pi\)
\(182\) 4.23228 + 2.19719i 0.313717 + 0.162866i
\(183\) −0.535898 −0.0396147
\(184\) −7.50670 + 4.33399i −0.553401 + 0.319506i
\(185\) 0 0
\(186\) −5.06604 + 8.77464i −0.371460 + 0.643388i
\(187\) 18.4534i 1.34945i
\(188\) −7.88885 4.55463i −0.575354 0.332181i
\(189\) 1.14539 + 0.661290i 0.0833147 + 0.0481018i
\(190\) 0 0
\(191\) 4.87357 8.44128i 0.352639 0.610789i −0.634072 0.773274i \(-0.718618\pi\)
0.986711 + 0.162485i \(0.0519509\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 11.9188 6.88130i 0.857932 0.495327i −0.00538741 0.999985i \(-0.501715\pi\)
0.863319 + 0.504658i \(0.168382\pi\)
\(194\) 8.81894 0.633163
\(195\) 0 0
\(196\) −5.25078 −0.375056
\(197\) 8.78282 5.07076i 0.625750 0.361277i −0.153354 0.988171i \(-0.549008\pi\)
0.779104 + 0.626894i \(0.215674\pi\)
\(198\) −2.30668 3.99528i −0.163928 0.283932i
\(199\) 4.78668 8.29078i 0.339319 0.587717i −0.644986 0.764194i \(-0.723137\pi\)
0.984305 + 0.176477i \(0.0564701\pi\)
\(200\) 0 0
\(201\) 2.75488 + 1.59053i 0.194314 + 0.112187i
\(202\) −6.25851 3.61335i −0.440348 0.254235i
\(203\) 2.67535i 0.187773i
\(204\) −2.00000 + 3.46410i −0.140028 + 0.242536i
\(205\) 0 0
\(206\) 15.9349 9.20002i 1.11024 0.640996i
\(207\) 8.66799 0.602467
\(208\) 0.161290 + 3.60194i 0.0111834 + 0.249750i
\(209\) −10.5682 −0.731015
\(210\) 0 0
\(211\) 0.542594 + 0.939800i 0.0373537 + 0.0646985i 0.884098 0.467302i \(-0.154774\pi\)
−0.846744 + 0.532000i \(0.821441\pi\)
\(212\) −0.413337 + 0.715920i −0.0283881 + 0.0491696i
\(213\) 11.3360i 0.776728i
\(214\) 2.66025 + 1.53590i 0.181851 + 0.104992i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 6.70025 11.6052i 0.454842 0.787810i
\(218\) −6.61335 11.4547i −0.447913 0.775808i
\(219\) 5.44128 3.14152i 0.367687 0.212284i
\(220\) 0 0
\(221\) 12.1549 7.76261i 0.817628 0.522170i
\(222\) −6.80951 −0.457024
\(223\) −21.6001 + 12.4708i −1.44645 + 0.835106i −0.998268 0.0588375i \(-0.981261\pi\)
−0.448179 + 0.893944i \(0.647927\pi\)
\(224\) 0.661290 + 1.14539i 0.0441843 + 0.0765294i
\(225\) 0 0
\(226\) 8.08643i 0.537902i
\(227\) 16.7321 + 9.66025i 1.11055 + 0.641174i 0.938971 0.343998i \(-0.111781\pi\)
0.171575 + 0.985171i \(0.445115\pi\)
\(228\) 1.98387 + 1.14539i 0.131385 + 0.0758551i
\(229\) 4.15491i 0.274564i −0.990532 0.137282i \(-0.956163\pi\)
0.990532 0.137282i \(-0.0438367\pi\)
\(230\) 0 0
\(231\) 3.05076 + 5.28408i 0.200726 + 0.347667i
\(232\) 1.75182 1.01141i 0.115013 0.0664025i
\(233\) −16.9665 −1.11151 −0.555756 0.831346i \(-0.687571\pi\)
−0.555756 + 0.831346i \(0.687571\pi\)
\(234\) 1.66129 3.20002i 0.108602 0.209192i
\(235\) 0 0
\(236\) 2.72064 1.57076i 0.177098 0.102248i
\(237\) 1.48387 + 2.57014i 0.0963877 + 0.166948i
\(238\) 2.64516 4.58155i 0.171460 0.296978i
\(239\) 6.34416i 0.410370i 0.978723 + 0.205185i \(0.0657795\pi\)
−0.978723 + 0.205185i \(0.934220\pi\)
\(240\) 0 0
\(241\) 20.9452 + 12.0927i 1.34920 + 0.778962i 0.988136 0.153579i \(-0.0490800\pi\)
0.361065 + 0.932541i \(0.382413\pi\)
\(242\) 10.2830i 0.661019i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0.267949 + 0.464102i 0.0171537 + 0.0297111i
\(245\) 0 0
\(246\) −4.64516 −0.296165
\(247\) −4.44560 6.96104i −0.282867 0.442921i
\(248\) 10.1321 0.643388
\(249\) −13.7454 + 7.93593i −0.871082 + 0.502919i
\(250\) 0 0
\(251\) 4.41249 7.64265i 0.278514 0.482400i −0.692502 0.721416i \(-0.743492\pi\)
0.971016 + 0.239016i \(0.0768249\pi\)
\(252\) 1.32258i 0.0833147i
\(253\) 34.6311 + 19.9942i 2.17724 + 1.25703i
\(254\) −9.93490 5.73592i −0.623371 0.359903i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −4.19247 7.26157i −0.261519 0.452964i 0.705127 0.709081i \(-0.250890\pi\)
−0.966646 + 0.256117i \(0.917557\pi\)
\(258\) −7.45269 + 4.30281i −0.463984 + 0.267881i
\(259\) 9.00612 0.559613
\(260\) 0 0
\(261\) −2.02283 −0.125210
\(262\) −13.8482 + 7.99528i −0.855547 + 0.493950i
\(263\) 0.960648 + 1.66389i 0.0592361 + 0.102600i 0.894123 0.447822i \(-0.147800\pi\)
−0.834887 + 0.550422i \(0.814467\pi\)
\(264\) −2.30668 + 3.99528i −0.141966 + 0.245893i
\(265\) 0 0
\(266\) −2.62383 1.51487i −0.160877 0.0928824i
\(267\) 10.2746 + 5.93207i 0.628798 + 0.363037i
\(268\) 3.18106i 0.194314i
\(269\) 16.1549 27.9811i 0.984982 1.70604i 0.342968 0.939347i \(-0.388568\pi\)
0.642014 0.766693i \(-0.278099\pi\)
\(270\) 0 0
\(271\) 20.3105 11.7263i 1.23378 0.712322i 0.265962 0.963983i \(-0.414310\pi\)
0.967815 + 0.251662i \(0.0809770\pi\)
\(272\) 4.00000 0.242536
\(273\) −2.19719 + 4.23228i −0.132980 + 0.256149i
\(274\) −16.0697 −0.970808
\(275\) 0 0
\(276\) −4.33399 7.50670i −0.260876 0.451850i
\(277\) 4.50283 7.79913i 0.270549 0.468604i −0.698454 0.715655i \(-0.746128\pi\)
0.969002 + 0.247051i \(0.0794615\pi\)
\(278\) 9.32258i 0.559131i
\(279\) −8.77464 5.06604i −0.525324 0.303296i
\(280\) 0 0
\(281\) 1.71696i 0.102425i −0.998688 0.0512125i \(-0.983691\pi\)
0.998688 0.0512125i \(-0.0163086\pi\)
\(282\) 4.55463 7.88885i 0.271224 0.469774i
\(283\) 0.774645 + 1.34172i 0.0460479 + 0.0797572i 0.888131 0.459591i \(-0.152004\pi\)
−0.842083 + 0.539348i \(0.818671\pi\)
\(284\) −9.81724 + 5.66799i −0.582546 + 0.336333i
\(285\) 0 0
\(286\) 14.0187 8.95292i 0.828945 0.529397i
\(287\) 6.14359 0.362645
\(288\) 0.866025 0.500000i 0.0510310 0.0294628i
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) 8.81894i 0.516976i
\(292\) −5.44128 3.14152i −0.318427 0.183844i
\(293\) −26.3321 15.2028i −1.53834 0.888160i −0.998936 0.0461113i \(-0.985317\pi\)
−0.539402 0.842049i \(-0.681350\pi\)
\(294\) 5.25078i 0.306232i
\(295\) 0 0
\(296\) 3.40475 + 5.89721i 0.197897 + 0.342768i
\(297\) 3.99528 2.30668i 0.231830 0.133847i
\(298\) 4.08519 0.236649
\(299\) 1.39806 + 31.2216i 0.0808518 + 1.80559i
\(300\) 0 0
\(301\) 9.85677 5.69081i 0.568135 0.328013i
\(302\) 9.99057 + 17.3042i 0.574892 + 0.995743i
\(303\) 3.61335 6.25851i 0.207582 0.359542i
\(304\) 2.29078i 0.131385i
\(305\) 0 0
\(306\) −3.46410 2.00000i −0.198030 0.114332i
\(307\) 9.82622i 0.560812i 0.959882 + 0.280406i \(0.0904691\pi\)
−0.959882 + 0.280406i \(0.909531\pi\)
\(308\) 3.05076 5.28408i 0.173833 0.301088i
\(309\) 9.20002 + 15.9349i 0.523371 + 0.906505i
\(310\) 0 0
\(311\) −3.40049 −0.192824 −0.0964121 0.995342i \(-0.530737\pi\)
−0.0964121 + 0.995342i \(0.530737\pi\)
\(312\) −3.60194 + 0.161290i −0.203920 + 0.00913124i
\(313\) 16.2340 0.917599 0.458800 0.888540i \(-0.348280\pi\)
0.458800 + 0.888540i \(0.348280\pi\)
\(314\) −6.17804 + 3.56690i −0.348647 + 0.201292i
\(315\) 0 0
\(316\) 1.48387 2.57014i 0.0834742 0.144582i
\(317\) 23.5231i 1.32119i 0.750742 + 0.660596i \(0.229696\pi\)
−0.750742 + 0.660596i \(0.770304\pi\)
\(318\) −0.715920 0.413337i −0.0401468 0.0231788i
\(319\) −8.08176 4.66601i −0.452492 0.261246i
\(320\) 0 0
\(321\) −1.53590 + 2.66025i −0.0857255 + 0.148481i
\(322\) 5.73205 + 9.92820i 0.319435 + 0.553277i
\(323\) −7.93548 + 4.58155i −0.441542 + 0.254924i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) 9.89470 0.548016
\(327\) 11.4547 6.61335i 0.633445 0.365719i
\(328\) 2.32258 + 4.02283i 0.128243 + 0.222123i
\(329\) −6.02386 + 10.4336i −0.332106 + 0.575225i
\(330\) 0 0
\(331\) 15.6667 + 9.04520i 0.861122 + 0.497169i 0.864388 0.502826i \(-0.167706\pi\)
−0.00326597 + 0.999995i \(0.501040\pi\)
\(332\) 13.7454 + 7.93593i 0.754379 + 0.435541i
\(333\) 6.80951i 0.373159i
\(334\) −12.0187 + 20.8171i −0.657636 + 1.13906i
\(335\) 0 0
\(336\) −1.14539 + 0.661290i −0.0624860 + 0.0360763i
\(337\) 5.69900 0.310444 0.155222 0.987880i \(-0.450391\pi\)
0.155222 + 0.987880i \(0.450391\pi\)
\(338\) 11.7942 + 5.46774i 0.641521 + 0.297406i
\(339\) −8.08643 −0.439195
\(340\) 0 0
\(341\) −23.3715 40.4806i −1.26564 2.19214i
\(342\) −1.14539 + 1.98387i −0.0619355 + 0.107275i
\(343\) 16.2026i 0.874860i
\(344\) 7.45269 + 4.30281i 0.401822 + 0.231992i
\(345\) 0 0
\(346\) 2.52817i 0.135915i
\(347\) −7.87357 + 13.6374i −0.422676 + 0.732095i −0.996200 0.0870928i \(-0.972242\pi\)
0.573525 + 0.819188i \(0.305576\pi\)
\(348\) 1.01141 + 1.75182i 0.0542174 + 0.0939073i
\(349\) 13.2679 7.66025i 0.710217 0.410044i −0.100924 0.994894i \(-0.532180\pi\)
0.811141 + 0.584850i \(0.198847\pi\)
\(350\) 0 0
\(351\) 3.20002 + 1.66129i 0.170804 + 0.0886731i
\(352\) 4.61335 0.245893
\(353\) −1.03917 + 0.599964i −0.0553093 + 0.0319328i −0.527400 0.849617i \(-0.676833\pi\)
0.472090 + 0.881550i \(0.343500\pi\)
\(354\) 1.57076 + 2.72064i 0.0834850 + 0.144600i
\(355\) 0 0
\(356\) 11.8641i 0.628798i
\(357\) 4.58155 + 2.64516i 0.242481 + 0.139997i
\(358\) −5.43490 3.13784i −0.287243 0.165840i
\(359\) 16.2830i 0.859386i −0.902975 0.429693i \(-0.858622\pi\)
0.902975 0.429693i \(-0.141378\pi\)
\(360\) 0 0
\(361\) −6.87617 11.9099i −0.361904 0.626836i
\(362\) −10.6374 + 6.14152i −0.559091 + 0.322791i
\(363\) 10.2830 0.539720
\(364\) 4.76386 0.213319i 0.249694 0.0111809i
\(365\) 0 0
\(366\) −0.464102 + 0.267949i −0.0242590 + 0.0140059i
\(367\) −9.81724 17.0040i −0.512456 0.887599i −0.999896 0.0144428i \(-0.995403\pi\)
0.487440 0.873156i \(-0.337931\pi\)
\(368\) −4.33399 + 7.50670i −0.225925 + 0.391314i
\(369\) 4.64516i 0.241817i
\(370\) 0 0
\(371\) 0.946862 + 0.546671i 0.0491586 + 0.0283817i
\(372\) 10.1321i 0.525324i
\(373\) −1.27874 + 2.21484i −0.0662106 + 0.114680i −0.897230 0.441563i \(-0.854424\pi\)
0.831020 + 0.556243i \(0.187758\pi\)
\(374\) −9.22671 15.9811i −0.477102 0.826365i
\(375\) 0 0
\(376\) −9.10926 −0.469774
\(377\) −0.326261 7.28610i −0.0168033 0.375253i
\(378\) 1.32258 0.0680262
\(379\) −13.0846 + 7.55440i −0.672111 + 0.388044i −0.796876 0.604143i \(-0.793516\pi\)
0.124765 + 0.992186i \(0.460182\pi\)
\(380\) 0 0
\(381\) 5.73592 9.93490i 0.293860 0.508980i
\(382\) 9.74715i 0.498707i
\(383\) 16.2210 + 9.36517i 0.828852 + 0.478538i 0.853459 0.521159i \(-0.174500\pi\)
−0.0246073 + 0.999697i \(0.507834\pi\)
\(384\) −0.866025 0.500000i −0.0441942 0.0255155i
\(385\) 0 0
\(386\) 6.88130 11.9188i 0.350249 0.606649i
\(387\) −4.30281 7.45269i −0.218724 0.378841i
\(388\) 7.63743 4.40947i 0.387732 0.223857i
\(389\) 6.96899 0.353342 0.176671 0.984270i \(-0.443467\pi\)
0.176671 + 0.984270i \(0.443467\pi\)
\(390\) 0 0
\(391\) 34.6719 1.75344
\(392\) −4.54731 + 2.62539i −0.229674 + 0.132602i
\(393\) −7.99528 13.8482i −0.403309 0.698551i
\(394\) 5.07076 8.78282i 0.255461 0.442472i
\(395\) 0 0
\(396\) −3.99528 2.30668i −0.200771 0.115915i
\(397\) 16.0839 + 9.28606i 0.807229 + 0.466054i 0.845993 0.533195i \(-0.179009\pi\)
−0.0387637 + 0.999248i \(0.512342\pi\)
\(398\) 9.57336i 0.479869i
\(399\) 1.51487 2.62383i 0.0758382 0.131356i
\(400\) 0 0
\(401\) −25.7126 + 14.8452i −1.28403 + 0.741333i −0.977582 0.210556i \(-0.932473\pi\)
−0.306444 + 0.951889i \(0.599139\pi\)
\(402\) 3.18106 0.158657
\(403\) 16.8323 32.4229i 0.838478 1.61510i
\(404\) −7.22671 −0.359542
\(405\) 0 0
\(406\) −1.33767 2.31692i −0.0663877 0.114987i
\(407\) 15.7073 27.2059i 0.778584 1.34855i
\(408\) 4.00000i 0.198030i
\(409\) −21.0752 12.1678i −1.04210 0.601657i −0.121673 0.992570i \(-0.538826\pi\)
−0.920427 + 0.390913i \(0.872159\pi\)
\(410\) 0 0
\(411\) 16.0697i 0.792661i
\(412\) 9.20002 15.9349i 0.453252 0.785056i
\(413\) −2.07746 3.59826i −0.102225 0.177059i
\(414\) 7.50670 4.33399i 0.368934 0.213004i
\(415\) 0 0
\(416\) 1.94065 + 3.03873i 0.0951483 + 0.148986i
\(417\) −9.32258 −0.456529
\(418\) −9.15229 + 5.28408i −0.447653 + 0.258453i
\(419\) 1.44128 + 2.49636i 0.0704109 + 0.121955i 0.899081 0.437781i \(-0.144236\pi\)
−0.828671 + 0.559737i \(0.810902\pi\)
\(420\) 0 0
\(421\) 4.94707i 0.241106i 0.992707 + 0.120553i \(0.0384667\pi\)
−0.992707 + 0.120553i \(0.961533\pi\)
\(422\) 0.939800 + 0.542594i 0.0457488 + 0.0264131i
\(423\) 7.88885 + 4.55463i 0.383569 + 0.221454i
\(424\) 0.826674i 0.0401468i
\(425\) 0 0
\(426\) −5.66799 9.81724i −0.274615 0.475647i
\(427\) 0.613811 0.354384i 0.0297044 0.0171499i
\(428\) 3.07180 0.148481
\(429\) 8.95292 + 14.0187i 0.432251 + 0.676831i
\(430\) 0 0
\(431\) −15.3829 + 8.88130i −0.740967 + 0.427797i −0.822421 0.568880i \(-0.807377\pi\)
0.0814539 + 0.996677i \(0.474044\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) −17.9188 + 31.0362i −0.861121 + 1.49151i 0.00972676 + 0.999953i \(0.496904\pi\)
−0.870848 + 0.491553i \(0.836430\pi\)
\(434\) 13.4005i 0.643244i
\(435\) 0 0
\(436\) −11.4547 6.61335i −0.548579 0.316722i
\(437\) 19.8564i 0.949861i
\(438\) 3.14152 5.44128i 0.150108 0.259994i
\(439\) 5.04520 + 8.73854i 0.240794 + 0.417068i 0.960941 0.276754i \(-0.0892588\pi\)
−0.720147 + 0.693822i \(0.755925\pi\)
\(440\) 0 0
\(441\) 5.25078 0.250037
\(442\) 6.64516 12.8001i 0.316078 0.608837i
\(443\) −13.6981 −0.650816 −0.325408 0.945574i \(-0.605502\pi\)
−0.325408 + 0.945574i \(0.605502\pi\)
\(444\) −5.89721 + 3.40475i −0.279869 + 0.161582i
\(445\) 0 0
\(446\) −12.4708 + 21.6001i −0.590509 + 1.02279i
\(447\) 4.08519i 0.193223i
\(448\) 1.14539 + 0.661290i 0.0541145 + 0.0312430i
\(449\) 13.2613 + 7.65639i 0.625837 + 0.361327i 0.779138 0.626852i \(-0.215657\pi\)
−0.153301 + 0.988180i \(0.548990\pi\)
\(450\) 0 0
\(451\) 10.7149 18.5587i 0.504544 0.873896i
\(452\) 4.04322 + 7.00306i 0.190177 + 0.329396i
\(453\) −17.3042 + 9.99057i −0.813021 + 0.469398i
\(454\) 19.3205 0.906756
\(455\) 0 0
\(456\) 2.29078 0.107275
\(457\) 13.4714 7.77770i 0.630164 0.363826i −0.150651 0.988587i \(-0.548137\pi\)
0.780816 + 0.624761i \(0.214804\pi\)
\(458\) −2.07746 3.59826i −0.0970732 0.168136i
\(459\) 2.00000 3.46410i 0.0933520 0.161690i
\(460\) 0 0
\(461\) 13.5473 + 7.82154i 0.630961 + 0.364286i 0.781124 0.624376i \(-0.214647\pi\)
−0.150163 + 0.988661i \(0.547980\pi\)
\(462\) 5.28408 + 3.05076i 0.245838 + 0.141934i
\(463\) 13.7170i 0.637481i 0.947842 + 0.318741i \(0.103260\pi\)
−0.947842 + 0.318741i \(0.896740\pi\)
\(464\) 1.01141 1.75182i 0.0469537 0.0813261i
\(465\) 0 0
\(466\) −14.6934 + 8.48325i −0.680659 + 0.392979i
\(467\) 0.943666 0.0436677 0.0218338 0.999762i \(-0.493050\pi\)
0.0218338 + 0.999762i \(0.493050\pi\)
\(468\) −0.161290 3.60194i −0.00745563 0.166500i
\(469\) −4.20720 −0.194271
\(470\) 0 0
\(471\) −3.56690 6.17804i −0.164354 0.284669i
\(472\) 1.57076 2.72064i 0.0723001 0.125228i
\(473\) 39.7008i 1.82544i
\(474\) 2.57014 + 1.48387i 0.118050 + 0.0681564i
\(475\) 0 0
\(476\) 5.29032i 0.242481i
\(477\) 0.413337 0.715920i 0.0189254 0.0327797i
\(478\) 3.17208 + 5.49420i 0.145088 + 0.251299i
\(479\) −9.61460 + 5.55099i −0.439302 + 0.253631i −0.703302 0.710892i \(-0.748292\pi\)
0.263999 + 0.964523i \(0.414958\pi\)
\(480\) 0 0
\(481\) 24.5275 1.09830i 1.11836 0.0500784i
\(482\) 24.1855 1.10162
\(483\) −9.92820 + 5.73205i −0.451749 + 0.260817i
\(484\) −5.14152 8.90538i −0.233706 0.404790i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 28.5283 + 16.4708i 1.29274 + 0.746363i 0.979139 0.203192i \(-0.0651316\pi\)
0.313600 + 0.949555i \(0.398465\pi\)
\(488\) 0.464102 + 0.267949i 0.0210089 + 0.0121295i
\(489\) 9.89470i 0.447454i
\(490\) 0 0
\(491\) 14.2257 + 24.6396i 0.641996 + 1.11197i 0.984987 + 0.172630i \(0.0552266\pi\)
−0.342991 + 0.939339i \(0.611440\pi\)
\(492\) −4.02283 + 2.32258i −0.181363 + 0.104710i
\(493\) −8.09130 −0.364414
\(494\) −7.33052 3.80564i −0.329816 0.171224i
\(495\) 0 0
\(496\) 8.77464 5.06604i 0.393993 0.227472i
\(497\) 7.49636 + 12.9841i 0.336258 + 0.582416i
\(498\) −7.93593 + 13.7454i −0.355618 + 0.615948i
\(499\) 4.10926i 0.183956i 0.995761 + 0.0919779i \(0.0293189\pi\)
−0.995761 + 0.0919779i \(0.970681\pi\)
\(500\) 0 0
\(501\) −20.8171 12.0187i −0.930037 0.536957i
\(502\) 8.82497i 0.393878i
\(503\) 2.86800 4.96753i 0.127878 0.221491i −0.794976 0.606641i \(-0.792517\pi\)
0.922854 + 0.385149i \(0.125850\pi\)
\(504\) −0.661290 1.14539i −0.0294562 0.0510196i
\(505\) 0 0
\(506\) 39.9885 1.77771
\(507\) −5.46774 + 11.7942i −0.242831 + 0.523800i
\(508\) −11.4718 −0.508980
\(509\) −13.1129 + 7.57076i −0.581221 + 0.335568i −0.761618 0.648026i \(-0.775595\pi\)
0.180397 + 0.983594i \(0.442262\pi\)
\(510\) 0 0
\(511\) −4.15491 + 7.19652i −0.183803 + 0.318355i
\(512\) 1.00000i 0.0441942i
\(513\) −1.98387 1.14539i −0.0875900 0.0505701i
\(514\) −7.26157 4.19247i −0.320294 0.184922i
\(515\) 0 0
\(516\) −4.30281 + 7.45269i −0.189421 + 0.328086i
\(517\) 21.0121 + 36.3941i 0.924112 + 1.60061i
\(518\) 7.79953 4.50306i 0.342691 0.197853i
\(519\) −2.52817 −0.110974
\(520\) 0 0
\(521\) 8.93027 0.391242 0.195621 0.980680i \(-0.437328\pi\)
0.195621 + 0.980680i \(0.437328\pi\)
\(522\) −1.75182 + 1.01141i −0.0766750 + 0.0442683i
\(523\) −4.90844 8.50166i −0.214631 0.371752i 0.738527 0.674223i \(-0.235522\pi\)
−0.953158 + 0.302472i \(0.902188\pi\)
\(524\) −7.99528 + 13.8482i −0.349276 + 0.604963i
\(525\) 0 0
\(526\) 1.66389 + 0.960648i 0.0725491 + 0.0418863i
\(527\) −35.0986 20.2642i −1.52892 0.882721i
\(528\) 4.61335i 0.200771i
\(529\) −26.0670 + 45.1493i −1.13335 + 1.96301i
\(530\) 0 0
\(531\) −2.72064 + 1.57076i −0.118066 + 0.0681652i
\(532\) −3.02973 −0.131356
\(533\) 16.7316 0.749217i 0.724726 0.0324522i
\(534\) 11.8641 0.513411
\(535\) 0 0
\(536\) −1.59053 2.75488i −0.0687004 0.118993i
\(537\) 3.13784 5.43490i 0.135408 0.234533i
\(538\) 32.3098i 1.39298i
\(539\) 20.9784 + 12.1119i 0.903602 + 0.521695i
\(540\) 0 0
\(541\) 3.80826i 0.163730i −0.996643 0.0818650i \(-0.973912\pi\)
0.996643 0.0818650i \(-0.0260876\pi\)
\(542\) 11.7263 20.3105i 0.503688 0.872413i
\(543\) −6.14152 10.6374i −0.263558 0.456496i
\(544\) 3.46410 2.00000i 0.148522 0.0857493i
\(545\) 0 0
\(546\) 0.213319 + 4.76386i 0.00912920 + 0.203874i
\(547\) −45.5847 −1.94906 −0.974530 0.224257i \(-0.928005\pi\)
−0.974530 + 0.224257i \(0.928005\pi\)
\(548\) −13.9168 + 8.03486i −0.594496 + 0.343232i
\(549\) −0.267949 0.464102i −0.0114358 0.0198074i
\(550\) 0 0
\(551\) 4.63384i 0.197408i
\(552\) −7.50670 4.33399i −0.319506 0.184467i
\(553\) −3.39921 1.96254i −0.144549 0.0834555i
\(554\) 9.00566i 0.382614i
\(555\) 0 0
\(556\) 4.66129 + 8.07359i 0.197683 + 0.342397i
\(557\) 31.9209 18.4296i 1.35253 0.780885i 0.363929 0.931427i \(-0.381435\pi\)
0.988604 + 0.150541i \(0.0481016\pi\)
\(558\) −10.1321 −0.428925
\(559\) 26.1502 16.7005i 1.10603 0.706357i
\(560\) 0 0
\(561\) 15.9811 9.22671i 0.674724 0.389552i
\(562\) −0.858478 1.48693i −0.0362127 0.0627223i
\(563\) −16.8870 + 29.2491i −0.711701 + 1.23270i 0.252518 + 0.967592i \(0.418741\pi\)
−0.964218 + 0.265109i \(0.914592\pi\)
\(564\) 9.10926i 0.383569i
\(565\) 0 0
\(566\) 1.34172 + 0.774645i 0.0563969 + 0.0325607i
\(567\) 1.32258i 0.0555431i
\(568\) −5.66799 + 9.81724i −0.237823 + 0.411922i
\(569\) −12.7159 22.0246i −0.533079 0.923320i −0.999254 0.0386274i \(-0.987701\pi\)
0.466175 0.884693i \(-0.345632\pi\)
\(570\) 0 0
\(571\) 13.3682 0.559443 0.279722 0.960081i \(-0.409758\pi\)
0.279722 + 0.960081i \(0.409758\pi\)
\(572\) 7.66412 14.7628i 0.320453 0.617264i
\(573\) 9.74715 0.407193
\(574\) 5.32051 3.07180i 0.222074 0.128214i
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 9.57428i 0.398582i −0.979940 0.199291i \(-0.936136\pi\)
0.979940 0.199291i \(-0.0638639\pi\)
\(578\) 0.866025 + 0.500000i 0.0360219 + 0.0207973i
\(579\) 11.9188 + 6.88130i 0.495327 + 0.285977i
\(580\) 0 0
\(581\) 10.4959 18.1794i 0.435444 0.754210i
\(582\) 4.40947 + 7.63743i 0.182778 + 0.316582i
\(583\) 3.30279 1.90687i 0.136788 0.0789745i
\(584\) −6.28304 −0.259994
\(585\) 0 0
\(586\) −30.4057 −1.25605
\(587\) −1.21286 + 0.700246i −0.0500602 + 0.0289023i −0.524821 0.851212i \(-0.675868\pi\)
0.474761 + 0.880115i \(0.342534\pi\)
\(588\) −2.62539 4.54731i −0.108269 0.187528i
\(589\) −11.6052 + 20.1007i −0.478183 + 0.828237i
\(590\) 0 0
\(591\) 8.78282 + 5.07076i 0.361277 + 0.208583i
\(592\) 5.89721 + 3.40475i 0.242374 + 0.139935i
\(593\) 10.7303i 0.440643i −0.975427 0.220321i \(-0.929289\pi\)
0.975427 0.220321i \(-0.0707106\pi\)
\(594\) 2.30668 3.99528i 0.0946441 0.163928i
\(595\) 0 0
\(596\) 3.53788 2.04259i 0.144917 0.0836679i
\(597\) 9.57336 0.391812
\(598\) 16.8215 + 26.3397i 0.687884 + 1.07711i
\(599\) −40.7967 −1.66691 −0.833453 0.552590i \(-0.813640\pi\)
−0.833453 + 0.552590i \(0.813640\pi\)
\(600\) 0 0
\(601\) −21.4416 37.1379i −0.874621 1.51489i −0.857166 0.515040i \(-0.827777\pi\)
−0.0174548 0.999848i \(-0.505556\pi\)
\(602\) 5.69081 9.85677i 0.231940 0.401732i
\(603\) 3.18106i 0.129543i
\(604\) 17.3042 + 9.99057i 0.704097 + 0.406510i
\(605\) 0 0
\(606\) 7.22671i 0.293565i
\(607\) −3.43616 + 5.95161i −0.139470 + 0.241568i −0.927296 0.374329i \(-0.877873\pi\)
0.787826 + 0.615897i \(0.211206\pi\)
\(608\) −1.14539 1.98387i −0.0464516 0.0804565i
\(609\) 2.31692 1.33767i 0.0938863 0.0542053i
\(610\) 0 0
\(611\) −15.1331 + 29.1498i −0.612221 + 1.17927i
\(612\) −4.00000 −0.161690
\(613\) 0.659358 0.380681i 0.0266312 0.0153755i −0.486625 0.873611i \(-0.661772\pi\)
0.513257 + 0.858235i \(0.328439\pi\)
\(614\) 4.91311 + 8.50975i 0.198277 + 0.343426i
\(615\) 0 0
\(616\) 6.10153i 0.245838i
\(617\) −21.3061 12.3011i −0.857753 0.495224i 0.00550613 0.999985i \(-0.498247\pi\)
−0.863259 + 0.504761i \(0.831581\pi\)
\(618\) 15.9349 + 9.20002i 0.640996 + 0.370079i
\(619\) 17.2035i 0.691468i −0.938333 0.345734i \(-0.887630\pi\)
0.938333 0.345734i \(-0.112370\pi\)
\(620\) 0 0
\(621\) 4.33399 + 7.50670i 0.173917 + 0.301233i
\(622\) −2.94491 + 1.70025i −0.118080 + 0.0681737i
\(623\) −15.6913 −0.628657
\(624\) −3.03873 + 1.94065i −0.121646 + 0.0776883i
\(625\) 0 0
\(626\) 14.0590 8.11699i 0.561912 0.324420i
\(627\) −5.28408 9.15229i −0.211026 0.365507i
\(628\) −3.56690 + 6.17804i −0.142335 + 0.246531i
\(629\) 27.2380i 1.08605i
\(630\) 0 0
\(631\) 2.08519 + 1.20388i 0.0830100 + 0.0479259i 0.540930 0.841067i \(-0.318072\pi\)
−0.457920 + 0.888993i \(0.651406\pi\)
\(632\) 2.96774i 0.118050i
\(633\) −0.542594 + 0.939800i −0.0215662 + 0.0373537i
\(634\) 11.7616 + 20.3716i 0.467112 + 0.809061i
\(635\) 0 0
\(636\) −0.826674 −0.0327797
\(637\) 0.846898 + 18.9130i 0.0335553 + 0.749361i
\(638\) −9.33201 −0.369458
\(639\) 9.81724 5.66799i 0.388364 0.224222i
\(640\) 0 0
\(641\) −9.73875 + 16.8680i −0.384657 + 0.666246i −0.991722 0.128407i \(-0.959014\pi\)
0.607064 + 0.794653i \(0.292347\pi\)
\(642\) 3.07180i 0.121234i
\(643\) 20.7451 + 11.9772i 0.818106 + 0.472334i 0.849763 0.527165i \(-0.176745\pi\)
−0.0316570 + 0.999499i \(0.510078\pi\)
\(644\) 9.92820 + 5.73205i 0.391226 + 0.225874i
\(645\) 0 0
\(646\) −4.58155 + 7.93548i −0.180259 + 0.312217i
\(647\) −9.10540 15.7710i −0.357970 0.620022i 0.629652 0.776878i \(-0.283198\pi\)
−0.987622 + 0.156855i \(0.949864\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) −14.4930 −0.568898
\(650\) 0 0
\(651\) 13.4005 0.525207
\(652\) 8.56906 4.94735i 0.335590 0.193753i
\(653\) −24.0793 41.7065i −0.942294 1.63210i −0.761081 0.648657i \(-0.775331\pi\)
−0.181213 0.983444i \(-0.558002\pi\)
\(654\) 6.61335 11.4547i 0.258603 0.447913i
\(655\) 0 0
\(656\) 4.02283 + 2.32258i 0.157065 + 0.0906815i
\(657\) 5.44128 + 3.14152i 0.212284 + 0.122562i
\(658\) 12.0477i 0.469669i
\(659\) 18.4127 31.8917i 0.717257 1.24233i −0.244826 0.969567i \(-0.578731\pi\)
0.962083 0.272758i \(-0.0879359\pi\)
\(660\) 0 0
\(661\) −19.5131 + 11.2659i −0.758971 + 0.438192i −0.828926 0.559358i \(-0.811048\pi\)
0.0699555 + 0.997550i \(0.477714\pi\)
\(662\) 18.0904 0.703103
\(663\) 12.8001 + 6.64516i 0.497114 + 0.258077i
\(664\) 15.8719 0.615948
\(665\) 0 0
\(666\) −3.40475 5.89721i −0.131932 0.228512i
\(667\) 8.76691 15.1847i 0.339456 0.587955i
\(668\) 24.0375i 0.930037i
\(669\) −21.6001 12.4708i −0.835106 0.482149i
\(670\) 0 0
\(671\) 2.47229i 0.0954417i
\(672\) −0.661290 + 1.14539i −0.0255098 + 0.0441843i
\(673\) −11.8719 20.5627i −0.457627 0.792633i 0.541208 0.840889i \(-0.317967\pi\)
−0.998835 + 0.0482556i \(0.984634\pi\)
\(674\) 4.93548 2.84950i 0.190108 0.109759i
\(675\) 0 0
\(676\) 12.9480 1.16191i 0.497999 0.0446890i
\(677\) −1.16559 −0.0447975 −0.0223987 0.999749i \(-0.507130\pi\)
−0.0223987 + 0.999749i \(0.507130\pi\)
\(678\) −7.00306 + 4.04322i −0.268951 + 0.155279i
\(679\) −5.83188 10.1011i −0.223807 0.387645i
\(680\) 0 0
\(681\) 19.3205i 0.740363i
\(682\) −40.4806 23.3715i −1.55008 0.894939i
\(683\) −12.0134 6.93593i −0.459680 0.265396i 0.252230 0.967667i \(-0.418836\pi\)
−0.711910 + 0.702271i \(0.752169\pi\)
\(684\) 2.29078i 0.0875900i
\(685\) 0 0
\(686\) 8.10132 + 14.0319i 0.309310 + 0.535740i
\(687\) 3.59826 2.07746i 0.137282 0.0792599i
\(688\) 8.60562 0.328086
\(689\) 2.64537 + 1.37334i 0.100781 + 0.0523203i
\(690\) 0 0
\(691\) −35.6967 + 20.6095i −1.35797 + 0.784022i −0.989349 0.145560i \(-0.953502\pi\)
−0.368616 + 0.929582i \(0.620168\pi\)
\(692\) 1.26408 + 2.18946i 0.0480532 + 0.0832307i
\(693\) −3.05076 + 5.28408i −0.115889 + 0.200726i
\(694\) 15.7471i 0.597753i
\(695\) 0 0
\(696\) 1.75182 + 1.01141i 0.0664025 + 0.0383375i
\(697\) 18.5806i 0.703792i
\(698\) 7.66025 13.2679i 0.289945 0.502199i
\(699\) −8.48325 14.6934i −0.320866 0.555756i
\(700\) 0 0
\(701\) −23.0112 −0.869122 −0.434561 0.900642i \(-0.643096\pi\)
−0.434561 + 0.900642i \(0.643096\pi\)
\(702\) 3.60194 0.161290i 0.135947 0.00608749i
\(703\) −15.5991 −0.588329
\(704\) 3.99528 2.30668i 0.150578 0.0869362i
\(705\) 0 0
\(706\) −0.599964 + 1.03917i −0.0225799 + 0.0391096i
\(707\) 9.55790i 0.359462i
\(708\) 2.72064 + 1.57076i 0.102248 + 0.0590328i
\(709\) −14.7944 8.54156i −0.555616 0.320785i 0.195768 0.980650i \(-0.437280\pi\)
−0.751384 + 0.659865i \(0.770613\pi\)
\(710\) 0 0
\(711\) −1.48387 + 2.57014i −0.0556495 + 0.0963877i
\(712\) −5.93207 10.2746i −0.222314 0.385059i
\(713\) 76.0585 43.9124i 2.84841 1.64453i
\(714\) 5.29032 0.197985
\(715\) 0 0
\(716\) −6.27568 −0.234533
\(717\) −5.49420 + 3.17208i −0.205185 + 0.118463i
\(718\) −8.14152 14.1015i −0.303839 0.526264i
\(719\) −21.8564 + 37.8564i −0.815106 + 1.41181i 0.0941451 + 0.995558i \(0.469988\pi\)
−0.909251 + 0.416247i \(0.863345\pi\)
\(720\) 0 0
\(721\) −21.0752 12.1678i −0.784880 0.453151i
\(722\) −11.9099 6.87617i −0.443240 0.255905i
\(723\) 24.1855i 0.899467i
\(724\) −6.14152 + 10.6374i −0.228248 + 0.395337i
\(725\) 0 0
\(726\) 8.90538 5.14152i 0.330510 0.190820i
\(727\) −31.8453 −1.18108 −0.590538 0.807010i \(-0.701084\pi\)
−0.590538 + 0.807010i \(0.701084\pi\)
\(728\) 4.01896 2.56667i 0.148953 0.0951270i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −17.2112 29.8108i −0.636581 1.10259i
\(732\) −0.267949 + 0.464102i −0.00990369 + 0.0171537i
\(733\) 5.96774i 0.220423i −0.993908 0.110212i \(-0.964847\pi\)
0.993908 0.110212i \(-0.0351529\pi\)
\(734\) −17.0040 9.81724i −0.627627 0.362361i
\(735\) 0 0
\(736\) 8.66799i 0.319506i
\(737\) −7.33767 + 12.7092i −0.270287 + 0.468150i
\(738\) −2.32258 4.02283i −0.0854953 0.148082i
\(739\) 9.37833 5.41458i 0.344988 0.199179i −0.317488 0.948262i \(-0.602839\pi\)
0.662475 + 0.749084i \(0.269506\pi\)
\(740\) 0 0
\(741\) 3.80564 7.33052i 0.139804 0.269293i
\(742\) 1.09334 0.0401378
\(743\) −17.1909 + 9.92515i −0.630671 + 0.364118i −0.781012 0.624516i \(-0.785296\pi\)
0.150341 + 0.988634i \(0.451963\pi\)
\(744\) 5.06604 + 8.77464i 0.185730 + 0.321694i
\(745\) 0 0
\(746\) 2.55748i 0.0936359i
\(747\) −13.7454 7.93593i −0.502919 0.290361i
\(748\) −15.9811 9.22671i −0.584328 0.337362i
\(749\) 4.06270i 0.148448i
\(750\) 0 0
\(751\) −7.66538 13.2768i −0.279714 0.484479i 0.691600 0.722281i \(-0.256906\pi\)
−0.971314 + 0.237802i \(0.923573\pi\)
\(752\) −7.88885 + 4.55463i −0.287677 + 0.166090i
\(753\) 8.82497 0.321600
\(754\) −3.92560 6.14682i −0.142962 0.223854i
\(755\) 0 0
\(756\) 1.14539 0.661290i 0.0416573 0.0240509i
\(757\) 22.5816 + 39.1125i 0.820744 + 1.42157i 0.905129 + 0.425137i \(0.139774\pi\)
−0.0843855 + 0.996433i \(0.526893\pi\)
\(758\) −7.55440 + 13.0846i −0.274388 + 0.475254i
\(759\) 39.9885i 1.45149i
\(760\) 0 0
\(761\) −18.7978 10.8529i −0.681419 0.393418i 0.118970 0.992898i \(-0.462041\pi\)
−0.800390 + 0.599480i \(0.795374\pi\)
\(762\) 11.4718i 0.415581i
\(763\) −8.74669 + 15.1497i −0.316651 + 0.548456i
\(764\) −4.87357 8.44128i −0.176320 0.305395i
\(765\) 0 0
\(766\) 18.7303 0.676755
\(767\) −6.09660 9.54623i −0.220136 0.344694i
\(768\) −1.00000 −0.0360844
\(769\) 36.4711 21.0566i 1.31518 0.759321i 0.332233 0.943197i \(-0.392198\pi\)
0.982949 + 0.183877i \(0.0588647\pi\)
\(770\) 0 0
\(771\) 4.19247 7.26157i 0.150988 0.261519i
\(772\) 13.7626i 0.495327i
\(773\) −25.7734 14.8803i −0.927004 0.535206i −0.0411413 0.999153i \(-0.513099\pi\)
−0.885863 + 0.463947i \(0.846433\pi\)
\(774\) −7.45269 4.30281i −0.267881 0.154661i
\(775\) 0 0
\(776\) 4.40947 7.63743i 0.158291 0.274168i
\(777\) 4.50306 + 7.79953i 0.161546 + 0.279806i
\(778\) 6.03532 3.48449i 0.216377 0.124925i
\(779\) −10.6410 −0.381254
\(780\) 0 0
\(781\) 52.2969 1.87133
\(782\) 30.0268 17.3360i 1.07376 0.619933i
\(783\) −1.01141 1.75182i −0.0361450 0.0626049i
\(784\) −2.62539 + 4.54731i −0.0937640 + 0.162404i