Properties

Label 810.3.j.e.269.4
Level $810$
Weight $3$
Character 810.269
Analytic conductor $22.071$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 810.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(22.0709014132\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 270)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 269.4
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 810.269
Dual form 810.3.j.e.539.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(4.82963 + 1.29410i) q^{5} +(4.33013 + 2.50000i) q^{7} -2.82843 q^{8} +O(q^{10})\) \(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(4.82963 + 1.29410i) q^{5} +(4.33013 + 2.50000i) q^{7} -2.82843 q^{8} +(5.00000 - 5.00000i) q^{10} +(1.22474 + 0.707107i) q^{11} +(-7.79423 + 4.50000i) q^{13} +(6.12372 - 3.53553i) q^{14} +(-2.00000 + 3.46410i) q^{16} +11.3137 q^{17} +21.0000 q^{19} +(-2.58819 - 9.65926i) q^{20} +(1.73205 - 1.00000i) q^{22} +(-0.707107 - 1.22474i) q^{23} +(21.6506 + 12.5000i) q^{25} +12.7279i q^{26} -10.0000i q^{28} +(33.0681 + 19.0919i) q^{29} +(-20.0000 - 34.6410i) q^{31} +(2.82843 + 4.89898i) q^{32} +(8.00000 - 13.8564i) q^{34} +(17.6777 + 17.6777i) q^{35} +25.0000i q^{37} +(14.8492 - 25.7196i) q^{38} +(-13.6603 - 3.66025i) q^{40} +(-45.3156 + 26.1630i) q^{41} +(55.4256 + 32.0000i) q^{43} -2.82843i q^{44} -2.00000 q^{46} +(-11.3137 + 19.5959i) q^{47} +(-12.0000 - 20.7846i) q^{49} +(30.6186 - 17.6777i) q^{50} +(15.5885 + 9.00000i) q^{52} +72.1249 q^{53} +(5.00000 + 5.00000i) q^{55} +(-12.2474 - 7.07107i) q^{56} +(46.7654 - 27.0000i) q^{58} +(-78.3837 + 45.2548i) q^{59} +(48.5000 - 84.0045i) q^{61} -56.5685 q^{62} +8.00000 q^{64} +(-43.4667 + 11.6469i) q^{65} +(113.449 - 65.5000i) q^{67} +(-11.3137 - 19.5959i) q^{68} +(34.1506 - 9.15064i) q^{70} +89.0955i q^{71} +17.0000i q^{73} +(30.6186 + 17.6777i) q^{74} +(-21.0000 - 36.3731i) q^{76} +(3.53553 + 6.12372i) q^{77} +(58.5000 - 101.325i) q^{79} +(-14.1421 + 14.1421i) q^{80} +74.0000i q^{82} +(28.9914 - 50.2145i) q^{83} +(54.6410 + 14.6410i) q^{85} +(78.3837 - 45.2548i) q^{86} +(-3.46410 - 2.00000i) q^{88} -147.078i q^{89} -45.0000 q^{91} +(-1.41421 + 2.44949i) q^{92} +(16.0000 + 27.7128i) q^{94} +(101.422 + 27.1760i) q^{95} +(-35.5070 - 20.5000i) q^{97} -33.9411 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{4} + 40 q^{10} - 16 q^{16} + 168 q^{19} - 160 q^{31} + 64 q^{34} - 40 q^{40} - 16 q^{46} - 96 q^{49} + 40 q^{55} + 388 q^{61} + 64 q^{64} + 100 q^{70} - 168 q^{76} + 468 q^{79} + 160 q^{85} - 360 q^{91} + 128 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 1.22474i 0.353553 0.612372i
\(3\) 0 0
\(4\) −1.00000 1.73205i −0.250000 0.433013i
\(5\) 4.82963 + 1.29410i 0.965926 + 0.258819i
\(6\) 0 0
\(7\) 4.33013 + 2.50000i 0.618590 + 0.357143i 0.776320 0.630339i \(-0.217084\pi\)
−0.157730 + 0.987482i \(0.550418\pi\)
\(8\) −2.82843 −0.353553
\(9\) 0 0
\(10\) 5.00000 5.00000i 0.500000 0.500000i
\(11\) 1.22474 + 0.707107i 0.111340 + 0.0642824i 0.554636 0.832093i \(-0.312857\pi\)
−0.443296 + 0.896375i \(0.646191\pi\)
\(12\) 0 0
\(13\) −7.79423 + 4.50000i −0.599556 + 0.346154i −0.768867 0.639409i \(-0.779179\pi\)
0.169311 + 0.985563i \(0.445846\pi\)
\(14\) 6.12372 3.53553i 0.437409 0.252538i
\(15\) 0 0
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) 11.3137 0.665512 0.332756 0.943013i \(-0.392021\pi\)
0.332756 + 0.943013i \(0.392021\pi\)
\(18\) 0 0
\(19\) 21.0000 1.10526 0.552632 0.833426i \(-0.313624\pi\)
0.552632 + 0.833426i \(0.313624\pi\)
\(20\) −2.58819 9.65926i −0.129410 0.482963i
\(21\) 0 0
\(22\) 1.73205 1.00000i 0.0787296 0.0454545i
\(23\) −0.707107 1.22474i −0.0307438 0.0532498i 0.850244 0.526389i \(-0.176454\pi\)
−0.880988 + 0.473139i \(0.843121\pi\)
\(24\) 0 0
\(25\) 21.6506 + 12.5000i 0.866025 + 0.500000i
\(26\) 12.7279i 0.489535i
\(27\) 0 0
\(28\) 10.0000i 0.357143i
\(29\) 33.0681 + 19.0919i 1.14028 + 0.658341i 0.946500 0.322704i \(-0.104592\pi\)
0.193780 + 0.981045i \(0.437925\pi\)
\(30\) 0 0
\(31\) −20.0000 34.6410i −0.645161 1.11745i −0.984264 0.176703i \(-0.943457\pi\)
0.339103 0.940749i \(-0.389876\pi\)
\(32\) 2.82843 + 4.89898i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) 8.00000 13.8564i 0.235294 0.407541i
\(35\) 17.6777 + 17.6777i 0.505076 + 0.505076i
\(36\) 0 0
\(37\) 25.0000i 0.675676i 0.941204 + 0.337838i \(0.109696\pi\)
−0.941204 + 0.337838i \(0.890304\pi\)
\(38\) 14.8492 25.7196i 0.390770 0.676833i
\(39\) 0 0
\(40\) −13.6603 3.66025i −0.341506 0.0915064i
\(41\) −45.3156 + 26.1630i −1.10526 + 0.638121i −0.937597 0.347724i \(-0.886955\pi\)
−0.167661 + 0.985845i \(0.553621\pi\)
\(42\) 0 0
\(43\) 55.4256 + 32.0000i 1.28897 + 0.744186i 0.978470 0.206388i \(-0.0661709\pi\)
0.310498 + 0.950574i \(0.399504\pi\)
\(44\) 2.82843i 0.0642824i
\(45\) 0 0
\(46\) −2.00000 −0.0434783
\(47\) −11.3137 + 19.5959i −0.240717 + 0.416934i −0.960919 0.276830i \(-0.910716\pi\)
0.720202 + 0.693765i \(0.244049\pi\)
\(48\) 0 0
\(49\) −12.0000 20.7846i −0.244898 0.424176i
\(50\) 30.6186 17.6777i 0.612372 0.353553i
\(51\) 0 0
\(52\) 15.5885 + 9.00000i 0.299778 + 0.173077i
\(53\) 72.1249 1.36085 0.680424 0.732819i \(-0.261796\pi\)
0.680424 + 0.732819i \(0.261796\pi\)
\(54\) 0 0
\(55\) 5.00000 + 5.00000i 0.0909091 + 0.0909091i
\(56\) −12.2474 7.07107i −0.218704 0.126269i
\(57\) 0 0
\(58\) 46.7654 27.0000i 0.806300 0.465517i
\(59\) −78.3837 + 45.2548i −1.32854 + 0.767031i −0.985073 0.172135i \(-0.944933\pi\)
−0.343463 + 0.939166i \(0.611600\pi\)
\(60\) 0 0
\(61\) 48.5000 84.0045i 0.795082 1.37712i −0.127705 0.991812i \(-0.540761\pi\)
0.922787 0.385310i \(-0.125906\pi\)
\(62\) −56.5685 −0.912396
\(63\) 0 0
\(64\) 8.00000 0.125000
\(65\) −43.4667 + 11.6469i −0.668718 + 0.179182i
\(66\) 0 0
\(67\) 113.449 65.5000i 1.69327 0.977612i 0.741429 0.671032i \(-0.234149\pi\)
0.951845 0.306580i \(-0.0991848\pi\)
\(68\) −11.3137 19.5959i −0.166378 0.288175i
\(69\) 0 0
\(70\) 34.1506 9.15064i 0.487866 0.130723i
\(71\) 89.0955i 1.25487i 0.778671 + 0.627433i \(0.215894\pi\)
−0.778671 + 0.627433i \(0.784106\pi\)
\(72\) 0 0
\(73\) 17.0000i 0.232877i 0.993198 + 0.116438i \(0.0371477\pi\)
−0.993198 + 0.116438i \(0.962852\pi\)
\(74\) 30.6186 + 17.6777i 0.413765 + 0.238887i
\(75\) 0 0
\(76\) −21.0000 36.3731i −0.276316 0.478593i
\(77\) 3.53553 + 6.12372i 0.0459160 + 0.0795289i
\(78\) 0 0
\(79\) 58.5000 101.325i 0.740506 1.28259i −0.211759 0.977322i \(-0.567919\pi\)
0.952265 0.305273i \(-0.0987476\pi\)
\(80\) −14.1421 + 14.1421i −0.176777 + 0.176777i
\(81\) 0 0
\(82\) 74.0000i 0.902439i
\(83\) 28.9914 50.2145i 0.349294 0.604994i −0.636830 0.771004i \(-0.719755\pi\)
0.986124 + 0.166009i \(0.0530882\pi\)
\(84\) 0 0
\(85\) 54.6410 + 14.6410i 0.642835 + 0.172247i
\(86\) 78.3837 45.2548i 0.911438 0.526219i
\(87\) 0 0
\(88\) −3.46410 2.00000i −0.0393648 0.0227273i
\(89\) 147.078i 1.65256i −0.563257 0.826282i \(-0.690452\pi\)
0.563257 0.826282i \(-0.309548\pi\)
\(90\) 0 0
\(91\) −45.0000 −0.494505
\(92\) −1.41421 + 2.44949i −0.0153719 + 0.0266249i
\(93\) 0 0
\(94\) 16.0000 + 27.7128i 0.170213 + 0.294817i
\(95\) 101.422 + 27.1760i 1.06760 + 0.286063i
\(96\) 0 0
\(97\) −35.5070 20.5000i −0.366052 0.211340i 0.305680 0.952134i \(-0.401116\pi\)
−0.671732 + 0.740794i \(0.734449\pi\)
\(98\) −33.9411 −0.346338
\(99\) 0 0
\(100\) 50.0000i 0.500000i
\(101\) −78.3837 45.2548i −0.776076 0.448068i 0.0589618 0.998260i \(-0.481221\pi\)
−0.835038 + 0.550193i \(0.814554\pi\)
\(102\) 0 0
\(103\) 11.2583 6.50000i 0.109304 0.0631068i −0.444351 0.895853i \(-0.646566\pi\)
0.553655 + 0.832746i \(0.313232\pi\)
\(104\) 22.0454 12.7279i 0.211975 0.122384i
\(105\) 0 0
\(106\) 51.0000 88.3346i 0.481132 0.833345i
\(107\) −123.037 −1.14987 −0.574937 0.818197i \(-0.694974\pi\)
−0.574937 + 0.818197i \(0.694974\pi\)
\(108\) 0 0
\(109\) 8.00000 0.0733945 0.0366972 0.999326i \(-0.488316\pi\)
0.0366972 + 0.999326i \(0.488316\pi\)
\(110\) 9.65926 2.58819i 0.0878114 0.0235290i
\(111\) 0 0
\(112\) −17.3205 + 10.0000i −0.154647 + 0.0892857i
\(113\) 19.0919 + 33.0681i 0.168955 + 0.292638i 0.938053 0.346493i \(-0.112628\pi\)
−0.769098 + 0.639131i \(0.779294\pi\)
\(114\) 0 0
\(115\) −1.83013 6.83013i −0.0159141 0.0593924i
\(116\) 76.3675i 0.658341i
\(117\) 0 0
\(118\) 128.000i 1.08475i
\(119\) 48.9898 + 28.2843i 0.411679 + 0.237683i
\(120\) 0 0
\(121\) −59.5000 103.057i −0.491736 0.851711i
\(122\) −68.5894 118.800i −0.562208 0.973773i
\(123\) 0 0
\(124\) −40.0000 + 69.2820i −0.322581 + 0.558726i
\(125\) 88.3883 + 88.3883i 0.707107 + 0.707107i
\(126\) 0 0
\(127\) 8.00000i 0.0629921i −0.999504 0.0314961i \(-0.989973\pi\)
0.999504 0.0314961i \(-0.0100272\pi\)
\(128\) 5.65685 9.79796i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) −16.4711 + 61.4711i −0.126701 + 0.472855i
\(131\) 117.576 67.8823i 0.897523 0.518185i 0.0211272 0.999777i \(-0.493274\pi\)
0.876396 + 0.481592i \(0.159941\pi\)
\(132\) 0 0
\(133\) 90.9327 + 52.5000i 0.683704 + 0.394737i
\(134\) 185.262i 1.38255i
\(135\) 0 0
\(136\) −32.0000 −0.235294
\(137\) −133.643 + 231.477i −0.975498 + 1.68961i −0.297215 + 0.954811i \(0.596058\pi\)
−0.678283 + 0.734801i \(0.737276\pi\)
\(138\) 0 0
\(139\) 18.5000 + 32.0429i 0.133094 + 0.230525i 0.924868 0.380289i \(-0.124176\pi\)
−0.791774 + 0.610814i \(0.790842\pi\)
\(140\) 12.9410 48.2963i 0.0924354 0.344974i
\(141\) 0 0
\(142\) 109.119 + 63.0000i 0.768445 + 0.443662i
\(143\) −12.7279 −0.0890064
\(144\) 0 0
\(145\) 135.000 + 135.000i 0.931034 + 0.931034i
\(146\) 20.8207 + 12.0208i 0.142607 + 0.0823344i
\(147\) 0 0
\(148\) 43.3013 25.0000i 0.292576 0.168919i
\(149\) −225.353 + 130.108i −1.51244 + 0.873206i −0.512542 + 0.858662i \(0.671296\pi\)
−0.999894 + 0.0145438i \(0.995370\pi\)
\(150\) 0 0
\(151\) −54.5000 + 94.3968i −0.360927 + 0.625144i −0.988114 0.153725i \(-0.950873\pi\)
0.627187 + 0.778869i \(0.284206\pi\)
\(152\) −59.3970 −0.390770
\(153\) 0 0
\(154\) 10.0000 0.0649351
\(155\) −51.7638 193.185i −0.333960 1.24636i
\(156\) 0 0
\(157\) −102.191 + 59.0000i −0.650898 + 0.375796i −0.788800 0.614650i \(-0.789297\pi\)
0.137902 + 0.990446i \(0.455964\pi\)
\(158\) −82.7315 143.295i −0.523617 0.906931i
\(159\) 0 0
\(160\) 7.32051 + 27.3205i 0.0457532 + 0.170753i
\(161\) 7.07107i 0.0439197i
\(162\) 0 0
\(163\) 203.000i 1.24540i −0.782461 0.622699i \(-0.786036\pi\)
0.782461 0.622699i \(-0.213964\pi\)
\(164\) 90.6311 + 52.3259i 0.552629 + 0.319060i
\(165\) 0 0
\(166\) −41.0000 71.0141i −0.246988 0.427796i
\(167\) 50.9117 + 88.1816i 0.304860 + 0.528034i 0.977230 0.212182i \(-0.0680569\pi\)
−0.672370 + 0.740215i \(0.734724\pi\)
\(168\) 0 0
\(169\) −44.0000 + 76.2102i −0.260355 + 0.450948i
\(170\) 56.5685 56.5685i 0.332756 0.332756i
\(171\) 0 0
\(172\) 128.000i 0.744186i
\(173\) −5.65685 + 9.79796i −0.0326986 + 0.0566356i −0.881912 0.471415i \(-0.843743\pi\)
0.849213 + 0.528050i \(0.177077\pi\)
\(174\) 0 0
\(175\) 62.5000 + 108.253i 0.357143 + 0.618590i
\(176\) −4.89898 + 2.82843i −0.0278351 + 0.0160706i
\(177\) 0 0
\(178\) −180.133 104.000i −1.01198 0.584270i
\(179\) 125.865i 0.703156i 0.936159 + 0.351578i \(0.114355\pi\)
−0.936159 + 0.351578i \(0.885645\pi\)
\(180\) 0 0
\(181\) −127.000 −0.701657 −0.350829 0.936440i \(-0.614100\pi\)
−0.350829 + 0.936440i \(0.614100\pi\)
\(182\) −31.8198 + 55.1135i −0.174834 + 0.302822i
\(183\) 0 0
\(184\) 2.00000 + 3.46410i 0.0108696 + 0.0188266i
\(185\) −32.3524 + 120.741i −0.174878 + 0.652653i
\(186\) 0 0
\(187\) 13.8564 + 8.00000i 0.0740984 + 0.0427807i
\(188\) 45.2548 0.240717
\(189\) 0 0
\(190\) 105.000 105.000i 0.552632 0.552632i
\(191\) −88.1816 50.9117i −0.461684 0.266553i 0.251068 0.967969i \(-0.419218\pi\)
−0.712752 + 0.701416i \(0.752552\pi\)
\(192\) 0 0
\(193\) −234.693 + 135.500i −1.21603 + 0.702073i −0.964065 0.265665i \(-0.914408\pi\)
−0.251960 + 0.967738i \(0.581075\pi\)
\(194\) −50.2145 + 28.9914i −0.258838 + 0.149440i
\(195\) 0 0
\(196\) −24.0000 + 41.5692i −0.122449 + 0.212088i
\(197\) −316.784 −1.60804 −0.804020 0.594602i \(-0.797309\pi\)
−0.804020 + 0.594602i \(0.797309\pi\)
\(198\) 0 0
\(199\) 147.000 0.738693 0.369347 0.929292i \(-0.379581\pi\)
0.369347 + 0.929292i \(0.379581\pi\)
\(200\) −61.2372 35.3553i −0.306186 0.176777i
\(201\) 0 0
\(202\) −110.851 + 64.0000i −0.548769 + 0.316832i
\(203\) 95.4594 + 165.341i 0.470243 + 0.814486i
\(204\) 0 0
\(205\) −252.715 + 67.7147i −1.23275 + 0.330316i
\(206\) 18.3848i 0.0892465i
\(207\) 0 0
\(208\) 36.0000i 0.173077i
\(209\) 25.7196 + 14.8492i 0.123060 + 0.0710490i
\(210\) 0 0
\(211\) −70.5000 122.110i −0.334123 0.578718i 0.649193 0.760624i \(-0.275107\pi\)
−0.983316 + 0.181906i \(0.941774\pi\)
\(212\) −72.1249 124.924i −0.340212 0.589264i
\(213\) 0 0
\(214\) −87.0000 + 150.688i −0.406542 + 0.704151i
\(215\) 226.274 + 226.274i 1.05244 + 1.05244i
\(216\) 0 0
\(217\) 200.000i 0.921659i
\(218\) 5.65685 9.79796i 0.0259489 0.0449448i
\(219\) 0 0
\(220\) 3.66025 13.6603i 0.0166375 0.0620921i
\(221\) −88.1816 + 50.9117i −0.399012 + 0.230370i
\(222\) 0 0
\(223\) −6.92820 4.00000i −0.0310682 0.0179372i 0.484385 0.874855i \(-0.339043\pi\)
−0.515454 + 0.856917i \(0.672377\pi\)
\(224\) 28.2843i 0.126269i
\(225\) 0 0
\(226\) 54.0000 0.238938
\(227\) 34.6482 60.0125i 0.152635 0.264372i −0.779560 0.626327i \(-0.784557\pi\)
0.932196 + 0.361955i \(0.117891\pi\)
\(228\) 0 0
\(229\) 4.00000 + 6.92820i 0.0174672 + 0.0302542i 0.874627 0.484797i \(-0.161106\pi\)
−0.857160 + 0.515051i \(0.827773\pi\)
\(230\) −9.65926 2.58819i −0.0419968 0.0112530i
\(231\) 0 0
\(232\) −93.5307 54.0000i −0.403150 0.232759i
\(233\) 316.784 1.35959 0.679794 0.733403i \(-0.262069\pi\)
0.679794 + 0.733403i \(0.262069\pi\)
\(234\) 0 0
\(235\) −80.0000 + 80.0000i −0.340426 + 0.340426i
\(236\) 156.767 + 90.5097i 0.664268 + 0.383516i
\(237\) 0 0
\(238\) 69.2820 40.0000i 0.291101 0.168067i
\(239\) 177.588 102.530i 0.743046 0.428998i −0.0801297 0.996784i \(-0.525533\pi\)
0.823176 + 0.567787i \(0.192200\pi\)
\(240\) 0 0
\(241\) −39.5000 + 68.4160i −0.163900 + 0.283884i −0.936264 0.351297i \(-0.885741\pi\)
0.772364 + 0.635180i \(0.219074\pi\)
\(242\) −168.291 −0.695419
\(243\) 0 0
\(244\) −194.000 −0.795082
\(245\) −31.0583 115.911i −0.126769 0.473107i
\(246\) 0 0
\(247\) −163.679 + 94.5000i −0.662667 + 0.382591i
\(248\) 56.5685 + 97.9796i 0.228099 + 0.395079i
\(249\) 0 0
\(250\) 170.753 45.7532i 0.683013 0.183013i
\(251\) 46.6690i 0.185932i 0.995669 + 0.0929662i \(0.0296349\pi\)
−0.995669 + 0.0929662i \(0.970365\pi\)
\(252\) 0 0
\(253\) 2.00000i 0.00790514i
\(254\) −9.79796 5.65685i −0.0385746 0.0222711i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) −84.8528 146.969i −0.330167 0.571865i 0.652378 0.757894i \(-0.273772\pi\)
−0.982544 + 0.186029i \(0.940438\pi\)
\(258\) 0 0
\(259\) −62.5000 + 108.253i −0.241313 + 0.417966i
\(260\) 63.6396 + 63.6396i 0.244768 + 0.244768i
\(261\) 0 0
\(262\) 192.000i 0.732824i
\(263\) 141.421 244.949i 0.537724 0.931365i −0.461302 0.887243i \(-0.652618\pi\)
0.999026 0.0441219i \(-0.0140490\pi\)
\(264\) 0 0
\(265\) 348.336 + 93.3365i 1.31448 + 0.352213i
\(266\) 128.598 74.2462i 0.483452 0.279121i
\(267\) 0 0
\(268\) −226.899 131.000i −0.846637 0.488806i
\(269\) 101.823i 0.378526i 0.981926 + 0.189263i \(0.0606098\pi\)
−0.981926 + 0.189263i \(0.939390\pi\)
\(270\) 0 0
\(271\) −221.000 −0.815498 −0.407749 0.913094i \(-0.633686\pi\)
−0.407749 + 0.913094i \(0.633686\pi\)
\(272\) −22.6274 + 39.1918i −0.0831890 + 0.144088i
\(273\) 0 0
\(274\) 189.000 + 327.358i 0.689781 + 1.19474i
\(275\) 17.6777 + 30.6186i 0.0642824 + 0.111340i
\(276\) 0 0
\(277\) −76.2102 44.0000i −0.275127 0.158845i 0.356088 0.934452i \(-0.384110\pi\)
−0.631215 + 0.775608i \(0.717444\pi\)
\(278\) 52.3259 0.188223
\(279\) 0 0
\(280\) −50.0000 50.0000i −0.178571 0.178571i
\(281\) 176.363 + 101.823i 0.627627 + 0.362361i 0.779833 0.625988i \(-0.215304\pi\)
−0.152205 + 0.988349i \(0.548638\pi\)
\(282\) 0 0
\(283\) −27.7128 + 16.0000i −0.0979251 + 0.0565371i −0.548163 0.836372i \(-0.684673\pi\)
0.450238 + 0.892909i \(0.351339\pi\)
\(284\) 154.318 89.0955i 0.543373 0.313716i
\(285\) 0 0
\(286\) −9.00000 + 15.5885i −0.0314685 + 0.0545051i
\(287\) −261.630 −0.911601
\(288\) 0 0
\(289\) −161.000 −0.557093
\(290\) 260.800 69.8811i 0.899310 0.240969i
\(291\) 0 0
\(292\) 29.4449 17.0000i 0.100839 0.0582192i
\(293\) 86.9741 + 150.644i 0.296840 + 0.514142i 0.975411 0.220393i \(-0.0707338\pi\)
−0.678571 + 0.734535i \(0.737401\pi\)
\(294\) 0 0
\(295\) −437.128 + 117.128i −1.48179 + 0.397045i
\(296\) 70.7107i 0.238887i
\(297\) 0 0
\(298\) 368.000i 1.23490i
\(299\) 11.0227 + 6.36396i 0.0368652 + 0.0212842i
\(300\) 0 0
\(301\) 160.000 + 277.128i 0.531561 + 0.920691i
\(302\) 77.0746 + 133.497i 0.255214 + 0.442044i
\(303\) 0 0
\(304\) −42.0000 + 72.7461i −0.138158 + 0.239296i
\(305\) 342.947 342.947i 1.12442 1.12442i
\(306\) 0 0
\(307\) 486.000i 1.58306i 0.611129 + 0.791531i \(0.290716\pi\)
−0.611129 + 0.791531i \(0.709284\pi\)
\(308\) 7.07107 12.2474i 0.0229580 0.0397644i
\(309\) 0 0
\(310\) −273.205 73.2051i −0.881307 0.236145i
\(311\) −58.7878 + 33.9411i −0.189028 + 0.109135i −0.591528 0.806285i \(-0.701475\pi\)
0.402499 + 0.915420i \(0.368142\pi\)
\(312\) 0 0
\(313\) −243.353 140.500i −0.777486 0.448882i 0.0580525 0.998314i \(-0.481511\pi\)
−0.835539 + 0.549432i \(0.814844\pi\)
\(314\) 166.877i 0.531456i
\(315\) 0 0
\(316\) −234.000 −0.740506
\(317\) −260.215 + 450.706i −0.820868 + 1.42179i 0.0841679 + 0.996452i \(0.473177\pi\)
−0.905036 + 0.425334i \(0.860157\pi\)
\(318\) 0 0
\(319\) 27.0000 + 46.7654i 0.0846395 + 0.146600i
\(320\) 38.6370 + 10.3528i 0.120741 + 0.0323524i
\(321\) 0 0
\(322\) −8.66025 5.00000i −0.0268952 0.0155280i
\(323\) 237.588 0.735566
\(324\) 0 0
\(325\) −225.000 −0.692308
\(326\) −248.623 143.543i −0.762648 0.440315i
\(327\) 0 0
\(328\) 128.172 74.0000i 0.390768 0.225610i
\(329\) −97.9796 + 56.5685i −0.297810 + 0.171941i
\(330\) 0 0
\(331\) 29.5000 51.0955i 0.0891239 0.154367i −0.818017 0.575194i \(-0.804927\pi\)
0.907141 + 0.420827i \(0.138260\pi\)
\(332\) −115.966 −0.349294
\(333\) 0 0
\(334\) 144.000 0.431138
\(335\) 632.681 169.526i 1.88860 0.506049i
\(336\) 0 0
\(337\) 47.6314 27.5000i 0.141339 0.0816024i −0.427663 0.903938i \(-0.640663\pi\)
0.569002 + 0.822336i \(0.307330\pi\)
\(338\) 62.2254 + 107.778i 0.184099 + 0.318868i
\(339\) 0 0
\(340\) −29.2820 109.282i −0.0861236 0.321418i
\(341\) 56.5685i 0.165890i
\(342\) 0 0
\(343\) 365.000i 1.06414i
\(344\) −156.767 90.5097i −0.455719 0.263109i
\(345\) 0 0
\(346\) 8.00000 + 13.8564i 0.0231214 + 0.0400474i
\(347\) −299.106 518.067i −0.861977 1.49299i −0.870017 0.493021i \(-0.835893\pi\)
0.00803996 0.999968i \(-0.497441\pi\)
\(348\) 0 0
\(349\) 219.500 380.185i 0.628940 1.08936i −0.358825 0.933405i \(-0.616823\pi\)
0.987765 0.155951i \(-0.0498442\pi\)
\(350\) 176.777 0.505076
\(351\) 0 0
\(352\) 8.00000i 0.0227273i
\(353\) −260.215 + 450.706i −0.737154 + 1.27679i 0.216618 + 0.976256i \(0.430497\pi\)
−0.953772 + 0.300531i \(0.902836\pi\)
\(354\) 0 0
\(355\) −115.298 + 430.298i −0.324783 + 1.21211i
\(356\) −254.747 + 147.078i −0.715581 + 0.413141i
\(357\) 0 0
\(358\) 154.153 + 89.0000i 0.430594 + 0.248603i
\(359\) 55.1543i 0.153633i 0.997045 + 0.0768166i \(0.0244756\pi\)
−0.997045 + 0.0768166i \(0.975524\pi\)
\(360\) 0 0
\(361\) 80.0000 0.221607
\(362\) −89.8026 + 155.543i −0.248073 + 0.429676i
\(363\) 0 0
\(364\) 45.0000 + 77.9423i 0.123626 + 0.214127i
\(365\) −21.9996 + 82.1037i −0.0602729 + 0.224942i
\(366\) 0 0
\(367\) −510.089 294.500i −1.38989 0.802452i −0.396586 0.917998i \(-0.629805\pi\)
−0.993302 + 0.115545i \(0.963138\pi\)
\(368\) 5.65685 0.0153719
\(369\) 0 0
\(370\) 125.000 + 125.000i 0.337838 + 0.337838i
\(371\) 312.310 + 180.312i 0.841806 + 0.486017i
\(372\) 0 0
\(373\) −7.79423 + 4.50000i −0.0208961 + 0.0120643i −0.510412 0.859930i \(-0.670507\pi\)
0.489516 + 0.871995i \(0.337174\pi\)
\(374\) 19.5959 11.3137i 0.0523955 0.0302506i
\(375\) 0 0
\(376\) 32.0000 55.4256i 0.0851064 0.147409i
\(377\) −343.654 −0.911549
\(378\) 0 0
\(379\) 157.000 0.414248 0.207124 0.978315i \(-0.433590\pi\)
0.207124 + 0.978315i \(0.433590\pi\)
\(380\) −54.3520 202.844i −0.143032 0.533801i
\(381\) 0 0
\(382\) −124.708 + 72.0000i −0.326460 + 0.188482i
\(383\) −141.421 244.949i −0.369246 0.639553i 0.620202 0.784443i \(-0.287051\pi\)
−0.989448 + 0.144889i \(0.953717\pi\)
\(384\) 0 0
\(385\) 9.15064 + 34.1506i 0.0237679 + 0.0887029i
\(386\) 383.252i 0.992881i
\(387\) 0 0
\(388\) 82.0000i 0.211340i
\(389\) −519.292 299.813i −1.33494 0.770728i −0.348888 0.937164i \(-0.613441\pi\)
−0.986052 + 0.166436i \(0.946774\pi\)
\(390\) 0 0
\(391\) −8.00000 13.8564i −0.0204604 0.0354384i
\(392\) 33.9411 + 58.7878i 0.0865845 + 0.149969i
\(393\) 0 0
\(394\) −224.000 + 387.979i −0.568528 + 0.984719i
\(395\) 413.657 413.657i 1.04723 1.04723i
\(396\) 0 0
\(397\) 296.000i 0.745592i −0.927913 0.372796i \(-0.878399\pi\)
0.927913 0.372796i \(-0.121601\pi\)
\(398\) 103.945 180.037i 0.261168 0.452356i
\(399\) 0 0
\(400\) −86.6025 + 50.0000i −0.216506 + 0.125000i
\(401\) −336.805 + 194.454i −0.839912 + 0.484924i −0.857234 0.514926i \(-0.827819\pi\)
0.0173221 + 0.999850i \(0.494486\pi\)
\(402\) 0 0
\(403\) 311.769 + 180.000i 0.773621 + 0.446650i
\(404\) 181.019i 0.448068i
\(405\) 0 0
\(406\) 270.000 0.665025
\(407\) −17.6777 + 30.6186i −0.0434341 + 0.0752300i
\(408\) 0 0
\(409\) −72.5000 125.574i −0.177262 0.307026i 0.763680 0.645595i \(-0.223391\pi\)
−0.940942 + 0.338569i \(0.890057\pi\)
\(410\) −95.7630 + 357.393i −0.233568 + 0.871689i
\(411\) 0 0
\(412\) −22.5167 13.0000i −0.0546521 0.0315534i
\(413\) −452.548 −1.09576
\(414\) 0 0
\(415\) 205.000 205.000i 0.493976 0.493976i
\(416\) −44.0908 25.4558i −0.105988 0.0611919i
\(417\) 0 0
\(418\) 36.3731 21.0000i 0.0870169 0.0502392i
\(419\) 607.473 350.725i 1.44982 0.837052i 0.451347 0.892348i \(-0.350944\pi\)
0.998470 + 0.0552959i \(0.0176102\pi\)
\(420\) 0 0
\(421\) −252.500 + 437.343i −0.599762 + 1.03882i 0.393093 + 0.919499i \(0.371405\pi\)
−0.992856 + 0.119320i \(0.961928\pi\)
\(422\) −199.404 −0.472522
\(423\) 0 0
\(424\) −204.000 −0.481132
\(425\) 244.949 + 141.421i 0.576351 + 0.332756i
\(426\) 0 0
\(427\) 420.022 242.500i 0.983659 0.567916i
\(428\) 123.037 + 213.106i 0.287469 + 0.497910i
\(429\) 0 0
\(430\) 437.128 117.128i 1.01658 0.272391i
\(431\) 43.8406i 0.101718i −0.998706 0.0508592i \(-0.983804\pi\)
0.998706 0.0508592i \(-0.0161960\pi\)
\(432\) 0 0
\(433\) 32.0000i 0.0739030i 0.999317 + 0.0369515i \(0.0117647\pi\)
−0.999317 + 0.0369515i \(0.988235\pi\)
\(434\) −244.949 141.421i −0.564399 0.325856i
\(435\) 0 0
\(436\) −8.00000 13.8564i −0.0183486 0.0317807i
\(437\) −14.8492 25.7196i −0.0339800 0.0588550i
\(438\) 0 0
\(439\) 252.000 436.477i 0.574032 0.994252i −0.422114 0.906543i \(-0.638712\pi\)
0.996146 0.0877097i \(-0.0279548\pi\)
\(440\) −14.1421 14.1421i −0.0321412 0.0321412i
\(441\) 0 0
\(442\) 144.000i 0.325792i
\(443\) 118.794 205.757i 0.268158 0.464463i −0.700228 0.713919i \(-0.746918\pi\)
0.968386 + 0.249456i \(0.0802518\pi\)
\(444\) 0 0
\(445\) 190.333 710.333i 0.427715 1.59625i
\(446\) −9.79796 + 5.65685i −0.0219685 + 0.0126835i
\(447\) 0 0
\(448\) 34.6410 + 20.0000i 0.0773237 + 0.0446429i
\(449\) 67.8823i 0.151185i 0.997139 + 0.0755927i \(0.0240849\pi\)
−0.997139 + 0.0755927i \(0.975915\pi\)
\(450\) 0 0
\(451\) −74.0000 −0.164080
\(452\) 38.1838 66.1362i 0.0844774 0.146319i
\(453\) 0 0
\(454\) −49.0000 84.8705i −0.107930 0.186939i
\(455\) −217.333 58.2343i −0.477656 0.127987i
\(456\) 0 0
\(457\) 651.251 + 376.000i 1.42506 + 0.822757i 0.996725 0.0808643i \(-0.0257680\pi\)
0.428332 + 0.903621i \(0.359101\pi\)
\(458\) 11.3137 0.0247024
\(459\) 0 0
\(460\) −10.0000 + 10.0000i −0.0217391 + 0.0217391i
\(461\) −529.090 305.470i −1.14770 0.662625i −0.199374 0.979923i \(-0.563891\pi\)
−0.948326 + 0.317298i \(0.897224\pi\)
\(462\) 0 0
\(463\) −517.017 + 298.500i −1.11667 + 0.644708i −0.940548 0.339660i \(-0.889688\pi\)
−0.176120 + 0.984369i \(0.556355\pi\)
\(464\) −132.272 + 76.3675i −0.285070 + 0.164585i
\(465\) 0 0
\(466\) 224.000 387.979i 0.480687 0.832574i
\(467\) −848.528 −1.81698 −0.908488 0.417910i \(-0.862763\pi\)
−0.908488 + 0.417910i \(0.862763\pi\)
\(468\) 0 0
\(469\) 655.000 1.39659
\(470\) 41.4110 + 154.548i 0.0881086 + 0.328826i
\(471\) 0 0
\(472\) 221.703 128.000i 0.469709 0.271186i
\(473\) 45.2548 + 78.3837i 0.0956762 + 0.165716i
\(474\) 0 0
\(475\) 454.663 + 262.500i 0.957186 + 0.552632i
\(476\) 113.137i 0.237683i
\(477\) 0 0
\(478\) 290.000i 0.606695i
\(479\) 145.745 + 84.1457i 0.304269 + 0.175670i 0.644359 0.764723i \(-0.277124\pi\)
−0.340090 + 0.940393i \(0.610458\pi\)
\(480\) 0 0
\(481\) −112.500 194.856i −0.233888 0.405105i
\(482\) 55.8614 + 96.7548i 0.115895 + 0.200736i
\(483\) 0 0
\(484\) −119.000 + 206.114i −0.245868 + 0.425855i
\(485\) −144.957 144.957i −0.298880 0.298880i
\(486\) 0 0
\(487\) 507.000i 1.04107i 0.853841 + 0.520534i \(0.174267\pi\)
−0.853841 + 0.520534i \(0.825733\pi\)
\(488\) −137.179 + 237.601i −0.281104 + 0.486886i
\(489\) 0 0
\(490\) −163.923 43.9230i −0.334537 0.0896389i
\(491\) 371.098 214.253i 0.755800 0.436361i −0.0719859 0.997406i \(-0.522934\pi\)
0.827786 + 0.561044i \(0.189600\pi\)
\(492\) 0 0
\(493\) 374.123 + 216.000i 0.758870 + 0.438134i
\(494\) 267.286i 0.541066i
\(495\) 0 0
\(496\) 160.000 0.322581
\(497\) −222.739 + 385.795i −0.448166 + 0.776247i
\(498\) 0 0
\(499\) −435.000 753.442i −0.871743 1.50990i −0.860192 0.509971i \(-0.829656\pi\)
−0.0115517 0.999933i \(-0.503677\pi\)
\(500\) 64.7048 241.481i 0.129410 0.482963i
\(501\) 0 0
\(502\) 57.1577 + 33.0000i 0.113860 + 0.0657371i
\(503\) 462.448 0.919379 0.459690 0.888080i \(-0.347961\pi\)
0.459690 + 0.888080i \(0.347961\pi\)
\(504\) 0 0
\(505\) −320.000 320.000i −0.633663 0.633663i
\(506\) −2.44949 1.41421i −0.00484089 0.00279489i
\(507\) 0 0
\(508\) −13.8564 + 8.00000i −0.0272764 + 0.0157480i
\(509\) 709.127 409.415i 1.39318 0.804351i 0.399512 0.916728i \(-0.369180\pi\)
0.993666 + 0.112377i \(0.0358464\pi\)
\(510\) 0 0
\(511\) −42.5000 + 73.6122i −0.0831703 + 0.144055i
\(512\) −22.6274 −0.0441942
\(513\) 0 0
\(514\) −240.000 −0.466926
\(515\) 62.7852 16.8232i 0.121913 0.0326665i
\(516\) 0 0
\(517\) −27.7128 + 16.0000i −0.0536031 + 0.0309478i
\(518\) 88.3883 + 153.093i 0.170634 + 0.295547i
\(519\) 0 0
\(520\) 122.942 32.9423i 0.236427 0.0633506i
\(521\) 864.084i 1.65851i −0.558869 0.829256i \(-0.688765\pi\)
0.558869 0.829256i \(-0.311235\pi\)
\(522\) 0 0
\(523\) 163.000i 0.311663i 0.987784 + 0.155832i \(0.0498058\pi\)
−0.987784 + 0.155832i \(0.950194\pi\)
\(524\) −235.151 135.765i −0.448761 0.259093i
\(525\) 0 0
\(526\) −200.000 346.410i −0.380228 0.658574i
\(527\) −226.274 391.918i −0.429363 0.743678i
\(528\) 0 0
\(529\) 263.500 456.395i 0.498110 0.862751i
\(530\) 360.624 360.624i 0.680424 0.680424i
\(531\) 0 0
\(532\) 210.000i 0.394737i
\(533\) 235.467 407.840i 0.441776 0.765178i
\(534\) 0 0
\(535\) −594.221 159.221i −1.11069 0.297609i
\(536\) −320.883 + 185.262i −0.598663 + 0.345638i
\(537\) 0 0
\(538\) 124.708 + 72.0000i 0.231799 + 0.133829i
\(539\) 33.9411i 0.0629705i
\(540\) 0 0
\(541\) 697.000 1.28835 0.644177 0.764876i \(-0.277200\pi\)
0.644177 + 0.764876i \(0.277200\pi\)
\(542\) −156.271 + 270.669i −0.288322 + 0.499389i
\(543\) 0 0
\(544\) 32.0000 + 55.4256i 0.0588235 + 0.101885i
\(545\) 38.6370 + 10.3528i 0.0708936 + 0.0189959i
\(546\) 0 0
\(547\) 336.884 + 194.500i 0.615875 + 0.355576i 0.775261 0.631640i \(-0.217618\pi\)
−0.159386 + 0.987216i \(0.550951\pi\)
\(548\) 534.573 0.975498
\(549\) 0 0
\(550\) 50.0000 0.0909091
\(551\) 694.430 + 400.930i 1.26031 + 0.727640i
\(552\) 0 0
\(553\) 506.625 292.500i 0.916139 0.528933i
\(554\) −107.778 + 62.2254i −0.194544 + 0.112320i
\(555\) 0 0
\(556\) 37.0000 64.0859i 0.0665468 0.115262i
\(557\) −1086.12 −1.94994 −0.974969 0.222339i \(-0.928631\pi\)
−0.974969 + 0.222339i \(0.928631\pi\)
\(558\) 0 0
\(559\) −576.000 −1.03041
\(560\) −96.5926 + 25.8819i −0.172487 + 0.0462177i
\(561\) 0 0
\(562\) 249.415 144.000i 0.443799 0.256228i
\(563\) −311.127 538.888i −0.552623 0.957172i −0.998084 0.0618704i \(-0.980293\pi\)
0.445461 0.895301i \(-0.353040\pi\)
\(564\) 0 0
\(565\) 49.4134 + 184.413i 0.0874574 + 0.326395i
\(566\) 45.2548i 0.0799555i
\(567\) 0 0
\(568\) 252.000i 0.443662i
\(569\) −401.716 231.931i −0.706004 0.407612i 0.103576 0.994622i \(-0.466972\pi\)
−0.809580 + 0.587010i \(0.800305\pi\)
\(570\) 0 0
\(571\) 461.500 + 799.341i 0.808231 + 1.39990i 0.914088 + 0.405516i \(0.132908\pi\)
−0.105857 + 0.994381i \(0.533758\pi\)
\(572\) 12.7279 + 22.0454i 0.0222516 + 0.0385409i
\(573\) 0 0
\(574\) −185.000 + 320.429i −0.322300 + 0.558239i
\(575\) 35.3553i 0.0614875i
\(576\) 0 0
\(577\) 247.000i 0.428076i 0.976825 + 0.214038i \(0.0686617\pi\)
−0.976825 + 0.214038i \(0.931338\pi\)
\(578\) −113.844 + 197.184i −0.196962 + 0.341149i
\(579\) 0 0
\(580\) 98.8269 368.827i 0.170391 0.635908i
\(581\) 251.073 144.957i 0.432139 0.249496i
\(582\) 0 0
\(583\) 88.3346 + 51.0000i 0.151517 + 0.0874786i
\(584\) 48.0833i 0.0823344i
\(585\) 0 0
\(586\) 246.000 0.419795
\(587\) −226.981 + 393.143i −0.386680 + 0.669750i −0.992001 0.126232i \(-0.959712\pi\)
0.605321 + 0.795982i \(0.293045\pi\)
\(588\) 0 0
\(589\) −420.000 727.461i −0.713073 1.23508i
\(590\) −165.644 + 618.193i −0.280753 + 1.04778i
\(591\) 0 0
\(592\) −86.6025 50.0000i −0.146288 0.0844595i
\(593\) 4.24264 0.00715454 0.00357727 0.999994i \(-0.498861\pi\)
0.00357727 + 0.999994i \(0.498861\pi\)
\(594\) 0 0
\(595\) 200.000 + 200.000i 0.336134 + 0.336134i
\(596\) 450.706 + 260.215i 0.756218 + 0.436603i
\(597\) 0 0
\(598\) 15.5885 9.00000i 0.0260677 0.0150502i
\(599\) 194.734 112.430i 0.325099 0.187696i −0.328564 0.944482i \(-0.606565\pi\)
0.653663 + 0.756786i \(0.273231\pi\)
\(600\) 0 0
\(601\) 368.000 637.395i 0.612313 1.06056i −0.378537 0.925586i \(-0.623573\pi\)
0.990850 0.134971i \(-0.0430940\pi\)
\(602\) 452.548 0.751741
\(603\) 0 0
\(604\) 218.000 0.360927
\(605\) −153.997 574.726i −0.254541 0.949960i
\(606\) 0 0
\(607\) 378.453 218.500i 0.623481 0.359967i −0.154742 0.987955i \(-0.549455\pi\)
0.778223 + 0.627988i \(0.216121\pi\)
\(608\) 59.3970 + 102.879i 0.0976924 + 0.169208i
\(609\) 0 0
\(610\) −177.522 662.522i −0.291020 1.08610i
\(611\) 203.647i 0.333301i
\(612\) 0 0
\(613\) 335.000i 0.546493i 0.961944 + 0.273246i \(0.0880974\pi\)
−0.961944 + 0.273246i \(0.911903\pi\)
\(614\) 595.226 + 343.654i 0.969423 + 0.559697i
\(615\) 0 0
\(616\) −10.0000 17.3205i −0.0162338 0.0281177i
\(617\) 127.986 + 221.679i 0.207433 + 0.359285i 0.950905 0.309482i \(-0.100156\pi\)
−0.743472 + 0.668767i \(0.766822\pi\)
\(618\) 0 0
\(619\) 482.500 835.715i 0.779483 1.35010i −0.152757 0.988264i \(-0.548815\pi\)
0.932240 0.361840i \(-0.117851\pi\)
\(620\) −282.843 + 282.843i −0.456198 + 0.456198i
\(621\) 0 0
\(622\) 96.0000i 0.154341i
\(623\) 367.696 636.867i 0.590201 1.02226i
\(624\) 0 0
\(625\) 312.500 + 541.266i 0.500000 + 0.866025i
\(626\) −344.153 + 198.697i −0.549766 + 0.317407i
\(627\) 0 0
\(628\) 204.382 + 118.000i 0.325449 + 0.187898i
\(629\) 282.843i 0.449670i
\(630\) 0 0
\(631\) 275.000 0.435816 0.217908 0.975969i \(-0.430077\pi\)
0.217908 + 0.975969i \(0.430077\pi\)
\(632\) −165.463 + 286.590i −0.261809 + 0.453466i
\(633\) 0 0
\(634\) 368.000 + 637.395i 0.580442 + 1.00535i
\(635\) 10.3528 38.6370i 0.0163036 0.0608457i
\(636\) 0 0
\(637\) 187.061 + 108.000i 0.293660 + 0.169545i
\(638\) 76.3675 0.119698
\(639\) 0 0
\(640\) 40.0000 40.0000i 0.0625000 0.0625000i
\(641\) −421.312 243.245i −0.657273 0.379477i 0.133964 0.990986i \(-0.457229\pi\)
−0.791237 + 0.611509i \(0.790563\pi\)
\(642\) 0 0
\(643\) 997.661 576.000i 1.55157 0.895801i 0.553559 0.832810i \(-0.313269\pi\)
0.998014 0.0629907i \(-0.0200639\pi\)
\(644\) −12.2474 + 7.07107i −0.0190178 + 0.0109799i
\(645\) 0 0
\(646\) 168.000 290.985i 0.260062 0.450440i
\(647\) 691.550 1.06886 0.534428 0.845214i \(-0.320527\pi\)
0.534428 + 0.845214i \(0.320527\pi\)
\(648\) 0 0
\(649\) −128.000 −0.197227
\(650\) −159.099 + 275.568i −0.244768 + 0.423950i
\(651\) 0 0
\(652\) −351.606 + 203.000i −0.539273 + 0.311350i
\(653\) 175.362 + 303.737i 0.268549 + 0.465140i 0.968487 0.249063i \(-0.0801226\pi\)
−0.699938 + 0.714203i \(0.746789\pi\)
\(654\) 0 0
\(655\) 655.692 175.692i 1.00106 0.268232i
\(656\) 209.304i 0.319060i
\(657\) 0 0
\(658\) 160.000i 0.243161i
\(659\) 431.110 + 248.902i 0.654188 + 0.377696i 0.790059 0.613031i \(-0.210050\pi\)
−0.135871 + 0.990727i \(0.543383\pi\)
\(660\) 0 0
\(661\) 288.500 + 499.697i 0.436460 + 0.755971i 0.997414 0.0718765i \(-0.0228987\pi\)
−0.560954 + 0.827847i \(0.689565\pi\)
\(662\) −41.7193 72.2599i −0.0630201 0.109154i
\(663\) 0 0
\(664\) −82.0000 + 142.028i −0.123494 + 0.213898i
\(665\) 371.231 + 371.231i 0.558242 + 0.558242i
\(666\) 0 0
\(667\) 54.0000i 0.0809595i
\(668\) 101.823 176.363i 0.152430 0.264017i
\(669\) 0 0
\(670\) 239.747 894.747i 0.357831 1.33544i
\(671\) 118.800 68.5894i 0.177050 0.102220i
\(672\) 0 0
\(673\) −423.486 244.500i −0.629252 0.363299i 0.151210 0.988502i \(-0.451683\pi\)
−0.780462 + 0.625203i \(0.785016\pi\)
\(674\) 77.7817i 0.115403i
\(675\) 0 0
\(676\) 176.000 0.260355
\(677\) 299.813 519.292i 0.442856 0.767048i −0.555044 0.831821i \(-0.687299\pi\)
0.997900 + 0.0647722i \(0.0206321\pi\)
\(678\) 0 0
\(679\) −102.500 177.535i −0.150957 0.261466i
\(680\) −154.548 41.4110i −0.227277 0.0608986i
\(681\) 0 0
\(682\) −69.2820 40.0000i −0.101587 0.0586510i
\(683\) −236.174 −0.345789 −0.172894 0.984940i \(-0.555312\pi\)
−0.172894 + 0.984940i \(0.555312\pi\)
\(684\) 0 0
\(685\) −945.000 + 945.000i −1.37956 + 1.37956i
\(686\) −447.032 258.094i −0.651650 0.376230i
\(687\) 0 0
\(688\) −221.703 + 128.000i −0.322242 + 0.186047i
\(689\) −562.158 + 324.562i −0.815904 + 0.471062i
\(690\) 0 0
\(691\) −320.000 + 554.256i −0.463097 + 0.802107i −0.999113 0.0421001i \(-0.986595\pi\)
0.536016 + 0.844208i \(0.319928\pi\)
\(692\) 22.6274 0.0326986
\(693\) 0 0
\(694\) −846.000 −1.21902
\(695\) 47.8815 + 178.696i 0.0688943 + 0.257117i
\(696\) 0 0
\(697\) −512.687 + 296.000i −0.735562 + 0.424677i
\(698\) −310.420 537.663i −0.444728 0.770291i
\(699\) 0 0
\(700\) 125.000 216.506i 0.178571 0.309295i
\(701\) 1093.19i 1.55947i 0.626111 + 0.779734i \(0.284646\pi\)
−0.626111 + 0.779734i \(0.715354\pi\)
\(702\) 0 0
\(703\) 525.000i 0.746799i
\(704\) 9.79796 + 5.65685i 0.0139176 + 0.00803530i
\(705\) 0 0
\(706\) 368.000 + 637.395i 0.521246 + 0.902825i
\(707\) −226.274 391.918i −0.320048 0.554340i
\(708\) 0 0
\(709\) 244.500 423.486i 0.344852 0.597301i −0.640475 0.767979i \(-0.721262\pi\)
0.985327 + 0.170678i \(0.0545958\pi\)
\(710\) 445.477 + 445.477i 0.627433 + 0.627433i
\(711\) 0 0
\(712\) 416.000i 0.584270i
\(713\) −28.2843 + 48.9898i −0.0396694 + 0.0687094i
\(714\) 0 0
\(715\) −61.4711 16.4711i −0.0859736 0.0230366i
\(716\) 218.005 125.865i 0.304476 0.175789i
\(717\) 0 0
\(718\) 67.5500 + 39.0000i 0.0940808 + 0.0543175i
\(719\) 620.840i 0.863477i 0.901999 + 0.431738i \(0.142100\pi\)
−0.901999 + 0.431738i \(0.857900\pi\)
\(720\) 0 0
\(721\) 65.0000 0.0901526
\(722\) 56.5685 97.9796i 0.0783498 0.135706i
\(723\) 0 0
\(724\) 127.000 + 219.970i 0.175414 + 0.303827i
\(725\) 477.297 + 826.703i 0.658341 + 1.14028i
\(726\) 0 0
\(727\) −935.307 540.000i −1.28653 0.742779i −0.308496 0.951225i \(-0.599826\pi\)
−0.978034 + 0.208447i \(0.933159\pi\)
\(728\) 127.279 0.174834
\(729\) 0 0
\(730\) 85.0000 + 85.0000i 0.116438 + 0.116438i
\(731\) 627.069 + 362.039i 0.857824 + 0.495265i
\(732\) 0 0
\(733\) −214.774 + 124.000i −0.293007 + 0.169168i −0.639297 0.768960i \(-0.720775\pi\)
0.346290 + 0.938128i \(0.387441\pi\)
\(734\) −721.375 + 416.486i −0.982799 + 0.567419i
\(735\) 0 0
\(736\) 4.00000 6.92820i 0.00543478 0.00941332i
\(737\) 185.262 0.251373
\(738\) 0 0
\(739\) 848.000 1.14750 0.573748 0.819032i \(-0.305489\pi\)
0.573748 + 0.819032i \(0.305489\pi\)
\(740\) 241.481 64.7048i 0.326326 0.0874389i
\(741\) 0 0
\(742\) 441.673 255.000i 0.595247 0.343666i
\(743\) 16.9706 + 29.3939i 0.0228406 + 0.0395611i 0.877220 0.480089i \(-0.159396\pi\)
−0.854379 + 0.519650i \(0.826062\pi\)
\(744\) 0 0
\(745\) −1256.74 + 336.743i −1.68690 + 0.452005i
\(746\) 12.7279i 0.0170616i
\(747\) 0 0
\(748\) 32.0000i 0.0427807i
\(749\) −532.764 307.591i −0.711300 0.410669i
\(750\) 0 0
\(751\) 66.5000 + 115.181i 0.0885486 + 0.153371i 0.906898 0.421351i \(-0.138444\pi\)
−0.818349 + 0.574721i \(0.805110\pi\)
\(752\) −45.2548 78.3837i −0.0601793 0.104234i
\(753\) 0 0
\(754\) −243.000 + 420.888i −0.322281 + 0.558207i
\(755\) −385.373 + 385.373i −0.510428 + 0.510428i
\(756\) 0 0
\(757\) 1271.00i 1.67900i −0.543363 0.839498i \(-0.682849\pi\)
0.543363 0.839498i \(-0.317151\pi\)
\(758\) 111.016 192.285i 0.146459 0.253674i
\(759\) 0 0
\(760\) −286.865 76.8653i −0.377454 0.101139i
\(761\) 466.628 269.408i 0.613177 0.354018i −0.161031 0.986949i \(-0.551482\pi\)
0.774208 + 0.632931i \(0.218148\pi\)
\(762\) 0 0
\(763\) 34.6410 + 20.0000i 0.0454011 + 0.0262123i
\(764\) 203.647i 0.266553i
\(765\) 0 0
\(766\) −400.000 −0.522193
\(767\) 407.294 705.453i 0.531022 0.919756i
\(768\) 0 0
\(769\) 40.5000 + 70.1481i 0.0526658 + 0.0912198i 0.891156 0.453696i \(-0.149895\pi\)
−0.838491 + 0.544916i \(0.816562\pi\)
\(770\) 48.2963 + 12.9410i 0.0627225 + 0.0168064i
\(771\) 0 0
\(772\) 469.386 + 271.000i 0.608013 + 0.351036i
\(773\) −445.477 −0.576297 −0.288148 0.957586i \(-0.593040\pi\)
−0.288148 + 0.957586i \(0.593040\pi\)
\(774\) 0 0
\(775\) 1000.00i 1.29032i
\(776\) 100.429 + 57.9828i 0.129419 + 0.0747200i
\(777\) 0 0
\(778\) −734.390 + 424.000i −0.943945 + 0.544987i
\(779\) −951.627 + 549.422i −1.22160 + 0.705291i
\(780\) 0 0
\(781\) −63.0000 + 109.119i −0.0806658 + 0.139717i
\(782\) −22.6274 −0.0289353
\(783\) 0 0
\(784\) 96.0000 0.122449
\(785\) −569.896 + 152.703i −0.725982 + 0.194526i
\(786\) 0 0