Properties

Label 810.3.j.e.539.3
Level $810$
Weight $3$
Character 810.539
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 539.3
Root \(0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 810.539
Dual form 810.3.j.e.269.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.29410 - 4.82963i) q^{5} +(-4.33013 + 2.50000i) q^{7} -2.82843 q^{8} +O(q^{10})\) \(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.29410 - 4.82963i) q^{5} +(-4.33013 + 2.50000i) q^{7} -2.82843 q^{8} +(5.00000 - 5.00000i) q^{10} +(-1.22474 + 0.707107i) q^{11} +(7.79423 + 4.50000i) q^{13} +(-6.12372 - 3.53553i) q^{14} +(-2.00000 - 3.46410i) q^{16} +11.3137 q^{17} +21.0000 q^{19} +(9.65926 + 2.58819i) q^{20} +(-1.73205 - 1.00000i) q^{22} +(-0.707107 + 1.22474i) q^{23} +(-21.6506 + 12.5000i) q^{25} +12.7279i q^{26} -10.0000i q^{28} +(-33.0681 + 19.0919i) q^{29} +(-20.0000 + 34.6410i) q^{31} +(2.82843 - 4.89898i) q^{32} +(8.00000 + 13.8564i) q^{34} +(17.6777 + 17.6777i) q^{35} +25.0000i q^{37} +(14.8492 + 25.7196i) q^{38} +(3.66025 + 13.6603i) q^{40} +(45.3156 + 26.1630i) q^{41} +(-55.4256 + 32.0000i) q^{43} -2.82843i q^{44} -2.00000 q^{46} +(-11.3137 - 19.5959i) q^{47} +(-12.0000 + 20.7846i) q^{49} +(-30.6186 - 17.6777i) q^{50} +(-15.5885 + 9.00000i) q^{52} +72.1249 q^{53} +(5.00000 + 5.00000i) q^{55} +(12.2474 - 7.07107i) q^{56} +(-46.7654 - 27.0000i) q^{58} +(78.3837 + 45.2548i) q^{59} +(48.5000 + 84.0045i) q^{61} -56.5685 q^{62} +8.00000 q^{64} +(11.6469 - 43.4667i) q^{65} +(-113.449 - 65.5000i) q^{67} +(-11.3137 + 19.5959i) q^{68} +(-9.15064 + 34.1506i) q^{70} +89.0955i q^{71} +17.0000i q^{73} +(-30.6186 + 17.6777i) q^{74} +(-21.0000 + 36.3731i) q^{76} +(3.53553 - 6.12372i) q^{77} +(58.5000 + 101.325i) q^{79} +(-14.1421 + 14.1421i) q^{80} +74.0000i q^{82} +(28.9914 + 50.2145i) q^{83} +(-14.6410 - 54.6410i) q^{85} +(-78.3837 - 45.2548i) q^{86} +(3.46410 - 2.00000i) q^{88} -147.078i q^{89} -45.0000 q^{91} +(-1.41421 - 2.44949i) q^{92} +(16.0000 - 27.7128i) q^{94} +(-27.1760 - 101.422i) q^{95} +(35.5070 - 20.5000i) q^{97} -33.9411 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{4}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).

\(n\) \(487\) \(731\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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
\(5\) −1.29410 4.82963i −0.258819 0.965926i
\(6\) 0 0
\(7\) −4.33013 + 2.50000i −0.618590 + 0.357143i −0.776320 0.630339i \(-0.782916\pi\)
0.157730 + 0.987482i \(0.449582\pi\)
\(8\) −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 \(-0.687143\pi\)
0.443296 + 0.896375i \(0.353809\pi\)
\(12\) 0 0
\(13\) 7.79423 + 4.50000i 0.599556 + 0.346154i 0.768867 0.639409i \(-0.220821\pi\)
−0.169311 + 0.985563i \(0.554154\pi\)
\(14\) −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 \(0.313624\pi\)
\(20\) 9.65926 + 2.58819i 0.482963 + 0.129410i
\(21\) 0 0
\(22\) −1.73205 1.00000i −0.0787296 0.0454545i
\(23\) −0.707107 + 1.22474i −0.0307438 + 0.0532498i −0.880988 0.473139i \(-0.843121\pi\)
0.850244 + 0.526389i \(0.176454\pi\)
\(24\) 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 \(-0.895408\pi\)
−0.193780 + 0.981045i \(0.562075\pi\)
\(30\) 0 0
\(31\) −20.0000 + 34.6410i −0.645161 + 1.11745i 0.339103 + 0.940749i \(0.389876\pi\)
−0.984264 + 0.176703i \(0.943457\pi\)
\(32\) 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
\(40\) 3.66025 + 13.6603i 0.0915064 + 0.341506i
\(41\) 45.3156 + 26.1630i 1.10526 + 0.638121i 0.937597 0.347724i \(-0.113045\pi\)
0.167661 + 0.985845i \(0.446379\pi\)
\(42\) 0 0
\(43\) −55.4256 + 32.0000i −1.28897 + 0.744186i −0.978470 0.206388i \(-0.933829\pi\)
−0.310498 + 0.950574i \(0.600496\pi\)
\(44\) 2.82843i 0.0642824i
\(45\) 0 0
\(46\) −2.00000 −0.0434783
\(47\) −11.3137 19.5959i −0.240717 0.416934i 0.720202 0.693765i \(-0.244049\pi\)
−0.960919 + 0.276830i \(0.910716\pi\)
\(48\) 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 \(-0.0550665\pi\)
0.343463 + 0.939166i \(0.388400\pi\)
\(60\) 0 0
\(61\) 48.5000 + 84.0045i 0.795082 + 1.37712i 0.922787 + 0.385310i \(0.125906\pi\)
−0.127705 + 0.991812i \(0.540761\pi\)
\(62\) −56.5685 −0.912396
\(63\) 0 0
\(64\) 8.00000 0.125000
\(65\) 11.6469 43.4667i 0.179182 0.668718i
\(66\) 0 0
\(67\) −113.449 65.5000i −1.69327 0.977612i −0.951845 0.306580i \(-0.900815\pi\)
−0.741429 0.671032i \(-0.765851\pi\)
\(68\) −11.3137 + 19.5959i −0.166378 + 0.288175i
\(69\) 0 0
\(70\) −9.15064 + 34.1506i −0.130723 + 0.487866i
\(71\) 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 0.952265 + 0.305273i \(0.0987476\pi\)
−0.211759 + 0.977322i \(0.567919\pi\)
\(80\) −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 0.986124 0.166009i \(-0.0530882\pi\)
−0.636830 + 0.771004i \(0.719755\pi\)
\(84\) 0 0
\(85\) −14.6410 54.6410i −0.172247 0.642835i
\(86\) −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
\(95\) −27.1760 101.422i −0.286063 1.06760i
\(96\) 0 0
\(97\) 35.5070 20.5000i 0.366052 0.211340i −0.305680 0.952134i \(-0.598884\pi\)
0.671732 + 0.740794i \(0.265551\pi\)
\(98\) −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 \(-0.518779\pi\)
0.835038 + 0.550193i \(0.185446\pi\)
\(102\) 0 0
\(103\) −11.2583 6.50000i −0.109304 0.0631068i 0.444351 0.895853i \(-0.353434\pi\)
−0.553655 + 0.832746i \(0.686768\pi\)
\(104\) −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 \(0.488316\pi\)
\(110\) −2.58819 + 9.65926i −0.0235290 + 0.0878114i
\(111\) 0 0
\(112\) 17.3205 + 10.0000i 0.154647 + 0.0892857i
\(113\) 19.0919 33.0681i 0.168955 0.292638i −0.769098 0.639131i \(-0.779294\pi\)
0.938053 + 0.346493i \(0.112628\pi\)
\(114\) 0 0
\(115\) 6.83013 + 1.83013i 0.0593924 + 0.0159141i
\(116\) 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
\(130\) 61.4711 16.4711i 0.472855 0.126701i
\(131\) −117.576 67.8823i −0.897523 0.518185i −0.0211272 0.999777i \(-0.506726\pi\)
−0.876396 + 0.481592i \(0.840059\pi\)
\(132\) 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 −0.678283 0.734801i \(-0.737276\pi\)
−0.297215 0.954811i \(-0.596058\pi\)
\(138\) 0 0
\(139\) 18.5000 32.0429i 0.133094 0.230525i −0.791774 0.610814i \(-0.790842\pi\)
0.924868 + 0.380289i \(0.124176\pi\)
\(140\) −48.2963 + 12.9410i −0.344974 + 0.0924354i
\(141\) 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 0.999894 + 0.0145438i \(0.00462959\pi\)
0.512542 + 0.858662i \(0.328704\pi\)
\(150\) 0 0
\(151\) −54.5000 94.3968i −0.360927 0.625144i 0.627187 0.778869i \(-0.284206\pi\)
−0.988114 + 0.153725i \(0.950873\pi\)
\(152\) −59.3970 −0.390770
\(153\) 0 0
\(154\) 10.0000 0.0649351
\(155\) 193.185 + 51.7638i 1.24636 + 0.333960i
\(156\) 0 0
\(157\) 102.191 + 59.0000i 0.650898 + 0.375796i 0.788800 0.614650i \(-0.210703\pi\)
−0.137902 + 0.990446i \(0.544036\pi\)
\(158\) −82.7315 + 143.295i −0.523617 + 0.906931i
\(159\) 0 0
\(160\) −27.3205 7.32051i −0.170753 0.0457532i
\(161\) 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 −0.672370 0.740215i \(-0.734724\pi\)
0.977230 + 0.212182i \(0.0680569\pi\)
\(168\) 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 0.849213 0.528050i \(-0.177077\pi\)
−0.881912 + 0.471415i \(0.843743\pi\)
\(174\) 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
\(185\) 120.741 32.3524i 0.652653 0.174878i
\(186\) 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 \(-0.580782\pi\)
0.712752 + 0.701416i \(0.247448\pi\)
\(192\) 0 0
\(193\) 234.693 + 135.500i 1.21603 + 0.702073i 0.964065 0.265665i \(-0.0855915\pi\)
0.251960 + 0.967738i \(0.418925\pi\)
\(194\) 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
\(205\) 67.7147 252.715i 0.330316 1.23275i
\(206\) 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 −0.983316 0.181906i \(-0.941774\pi\)
0.649193 + 0.760624i \(0.275107\pi\)
\(212\) −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
\(220\) −13.6603 + 3.66025i −0.0620921 + 0.0166375i
\(221\) 88.1816 + 50.9117i 0.399012 + 0.230370i
\(222\) 0 0
\(223\) 6.92820 4.00000i 0.0310682 0.0179372i −0.484385 0.874855i \(-0.660957\pi\)
0.515454 + 0.856917i \(0.327623\pi\)
\(224\) 28.2843i 0.126269i
\(225\) 0 0
\(226\) 54.0000 0.238938
\(227\) 34.6482 + 60.0125i 0.152635 + 0.264372i 0.932196 0.361955i \(-0.117891\pi\)
−0.779560 + 0.626327i \(0.784557\pi\)
\(228\) 0 0
\(229\) 4.00000 6.92820i 0.0174672 0.0302542i −0.857160 0.515051i \(-0.827773\pi\)
0.874627 + 0.484797i \(0.161106\pi\)
\(230\) 2.58819 + 9.65926i 0.0112530 + 0.0419968i
\(231\) 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 \(-0.474467\pi\)
−0.823176 + 0.567787i \(0.807800\pi\)
\(240\) 0 0
\(241\) −39.5000 68.4160i −0.163900 0.283884i 0.772364 0.635180i \(-0.219074\pi\)
−0.936264 + 0.351297i \(0.885741\pi\)
\(242\) −168.291 −0.695419
\(243\) 0 0
\(244\) −194.000 −0.795082
\(245\) 115.911 + 31.0583i 0.473107 + 0.126769i
\(246\) 0 0
\(247\) 163.679 + 94.5000i 0.662667 + 0.382591i
\(248\) 56.5685 97.9796i 0.228099 0.395079i
\(249\) 0 0
\(250\) −45.7532 + 170.753i −0.183013 + 0.683013i
\(251\) 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 −0.982544 0.186029i \(-0.940438\pi\)
0.652378 + 0.757894i \(0.273772\pi\)
\(258\) 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 0.999026 + 0.0441219i \(0.0140490\pi\)
−0.461302 + 0.887243i \(0.652618\pi\)
\(264\) 0 0
\(265\) −93.3365 348.336i −0.352213 1.31448i
\(266\) −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 \(-0.615890\pi\)
0.631215 + 0.775608i \(0.282556\pi\)
\(278\) 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 \(-0.784696\pi\)
0.152205 + 0.988349i \(0.451362\pi\)
\(282\) 0 0
\(283\) 27.7128 + 16.0000i 0.0979251 + 0.0565371i 0.548163 0.836372i \(-0.315327\pi\)
−0.450238 + 0.892909i \(0.648661\pi\)
\(284\) −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
\(290\) −69.8811 + 260.800i −0.240969 + 0.899310i
\(291\) 0 0
\(292\) −29.4449 17.0000i −0.100839 0.0582192i
\(293\) 86.9741 150.644i 0.296840 0.514142i −0.678571 0.734535i \(-0.737401\pi\)
0.975411 + 0.220393i \(0.0707338\pi\)
\(294\) 0 0
\(295\) 117.128 437.128i 0.397045 1.48179i
\(296\) 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
\(310\) 73.2051 + 273.205i 0.236145 + 0.881307i
\(311\) 58.7878 + 33.9411i 0.189028 + 0.109135i 0.591528 0.806285i \(-0.298525\pi\)
−0.402499 + 0.915420i \(0.631858\pi\)
\(312\) 0 0
\(313\) 243.353 140.500i 0.777486 0.448882i −0.0580525 0.998314i \(-0.518489\pi\)
0.835539 + 0.549432i \(0.185156\pi\)
\(314\) 166.877i 0.531456i
\(315\) 0 0
\(316\) −234.000 −0.740506
\(317\) −260.215 450.706i −0.820868 1.42179i −0.905036 0.425334i \(-0.860157\pi\)
0.0841679 0.996452i \(-0.473177\pi\)
\(318\) 0 0
\(319\) 27.0000 46.7654i 0.0846395 0.146600i
\(320\) −10.3528 38.6370i −0.0323524 0.120741i
\(321\) 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 0.907141 0.420827i \(-0.138260\pi\)
−0.818017 + 0.575194i \(0.804927\pi\)
\(332\) −115.966 −0.349294
\(333\) 0 0
\(334\) 144.000 0.431138
\(335\) −169.526 + 632.681i −0.506049 + 1.88860i
\(336\) 0 0
\(337\) −47.6314 27.5000i −0.141339 0.0816024i 0.427663 0.903938i \(-0.359337\pi\)
−0.569002 + 0.822336i \(0.692670\pi\)
\(338\) 62.2254 107.778i 0.184099 0.318868i
\(339\) 0 0
\(340\) 109.282 + 29.2820i 0.321418 + 0.0861236i
\(341\) 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 0.00803996 + 0.999968i \(0.497441\pi\)
−0.870017 + 0.493021i \(0.835893\pi\)
\(348\) 0 0
\(349\) 219.500 + 380.185i 0.628940 + 1.08936i 0.987765 + 0.155951i \(0.0498442\pi\)
−0.358825 + 0.933405i \(0.616823\pi\)
\(350\) 176.777 0.505076
\(351\) 0 0
\(352\) 8.00000i 0.0227273i
\(353\) −260.215 450.706i −0.737154 1.27679i −0.953772 0.300531i \(-0.902836\pi\)
0.216618 0.976256i \(-0.430497\pi\)
\(354\) 0 0
\(355\) 430.298 115.298i 1.21211 0.324783i
\(356\) 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
\(365\) 82.1037 21.9996i 0.224942 0.0602729i
\(366\) 0 0
\(367\) 510.089 294.500i 1.38989 0.802452i 0.396586 0.917998i \(-0.370195\pi\)
0.993302 + 0.115545i \(0.0368615\pi\)
\(368\) 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 \(-0.329493\pi\)
−0.489516 + 0.871995i \(0.662826\pi\)
\(374\) −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 \(0.433590\pi\)
\(380\) 202.844 + 54.3520i 0.533801 + 0.143032i
\(381\) 0 0
\(382\) 124.708 + 72.0000i 0.326460 + 0.188482i
\(383\) −141.421 + 244.949i −0.369246 + 0.639553i −0.989448 0.144889i \(-0.953717\pi\)
0.620202 + 0.784443i \(0.287051\pi\)
\(384\) 0 0
\(385\) −34.1506 9.15064i −0.0887029 0.0237679i
\(386\) 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 \(-0.386559\pi\)
0.986052 + 0.166436i \(0.0532260\pi\)
\(390\) 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 \(-0.172181\pi\)
−0.0173221 + 0.999850i \(0.505514\pi\)
\(402\) 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 −0.940942 0.338569i \(-0.890057\pi\)
0.763680 + 0.645595i \(0.223391\pi\)
\(410\) 357.393 95.7630i 0.871689 0.233568i
\(411\) 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 \(-0.649056\pi\)
−0.998470 + 0.0552959i \(0.982390\pi\)
\(420\) 0 0
\(421\) −252.500 437.343i −0.599762 1.03882i −0.992856 0.119320i \(-0.961928\pi\)
0.393093 0.919499i \(-0.371405\pi\)
\(422\) −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
\(430\) −117.128 + 437.128i −0.272391 + 1.01658i
\(431\) 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 0.996146 + 0.0877097i \(0.0279548\pi\)
−0.422114 + 0.906543i \(0.638712\pi\)
\(440\) −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 0.968386 0.249456i \(-0.0802518\pi\)
−0.700228 + 0.713919i \(0.746918\pi\)
\(444\) 0 0
\(445\) −710.333 + 190.333i −1.59625 + 0.427715i
\(446\) 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
\(455\) 58.2343 + 217.333i 0.127987 + 0.477656i
\(456\) 0 0
\(457\) −651.251 + 376.000i −1.42506 + 0.822757i −0.996725 0.0808643i \(-0.974232\pi\)
−0.428332 + 0.903621i \(0.640899\pi\)
\(458\) 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 \(-0.436109\pi\)
0.948326 + 0.317298i \(0.102776\pi\)
\(462\) 0 0
\(463\) 517.017 + 298.500i 1.11667 + 0.644708i 0.940548 0.339660i \(-0.110312\pi\)
0.176120 + 0.984369i \(0.443645\pi\)
\(464\) 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
\(470\) −154.548 41.4110i −0.328826 0.0881086i
\(471\) 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 \(-0.722876\pi\)
0.340090 + 0.940393i \(0.389542\pi\)
\(480\) 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
\(490\) 43.9230 + 163.923i 0.0896389 + 0.334537i
\(491\) −371.098 214.253i −0.755800 0.436361i 0.0719859 0.997406i \(-0.477066\pi\)
−0.827786 + 0.561044i \(0.810400\pi\)
\(492\) 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 −0.0115517 + 0.999933i \(0.503677\pi\)
−0.860192 + 0.509971i \(0.829656\pi\)
\(500\) −241.481 + 64.7048i −0.482963 + 0.129410i
\(501\) 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 \(-0.630820\pi\)
−0.993666 + 0.112377i \(0.964154\pi\)
\(510\) 0 0
\(511\) −42.5000 73.6122i −0.0831703 0.144055i
\(512\) −22.6274 −0.0441942
\(513\) 0 0
\(514\) −240.000 −0.466926
\(515\) −16.8232 + 62.7852i −0.0326665 + 0.121913i
\(516\) 0 0
\(517\) 27.7128 + 16.0000i 0.0536031 + 0.0309478i
\(518\) 88.3883 153.093i 0.170634 0.295547i
\(519\) 0 0
\(520\) −32.9423 + 122.942i −0.0633506 + 0.236427i
\(521\) 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
\(535\) 159.221 + 594.221i 0.297609 + 1.11069i
\(536\) 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
\(545\) −10.3528 38.6370i −0.0189959 0.0708936i
\(546\) 0 0
\(547\) −336.884 + 194.500i −0.615875 + 0.355576i −0.775261 0.631640i \(-0.782382\pi\)
0.159386 + 0.987216i \(0.449049\pi\)
\(548\) 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
\(560\) 25.8819 96.5926i 0.0462177 0.172487i
\(561\) 0 0
\(562\) −249.415 144.000i −0.443799 0.256228i
\(563\) −311.127 + 538.888i −0.552623 + 0.957172i 0.445461 + 0.895301i \(0.353040\pi\)
−0.998084 + 0.0618704i \(0.980293\pi\)
\(564\) 0 0
\(565\) −184.413 49.4134i −0.326395 0.0874574i
\(566\) 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 \(-0.533028\pi\)
0.809580 + 0.587010i \(0.199695\pi\)
\(570\) 0 0
\(571\) 461.500 799.341i 0.808231 1.39990i −0.105857 0.994381i \(-0.533758\pi\)
0.914088 0.405516i \(-0.132908\pi\)
\(572\) 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
\(580\) −368.827 + 98.8269i −0.635908 + 0.170391i
\(581\) −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 0.605321 0.795982i \(-0.293045\pi\)
−0.992001 + 0.126232i \(0.959712\pi\)
\(588\) 0 0
\(589\) −420.000 + 727.461i −0.713073 + 1.23508i
\(590\) 618.193 165.644i 1.04778 0.280753i
\(591\) 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 \(-0.393435\pi\)
−0.653663 + 0.756786i \(0.726769\pi\)
\(600\) 0 0
\(601\) 368.000 + 637.395i 0.612313 + 1.06056i 0.990850 + 0.134971i \(0.0430940\pi\)
−0.378537 + 0.925586i \(0.623573\pi\)
\(602\) 452.548 0.751741
\(603\) 0 0
\(604\) 218.000 0.360927
\(605\) 574.726 + 153.997i 0.949960 + 0.254541i
\(606\) 0 0
\(607\) −378.453 218.500i −0.623481 0.359967i 0.154742 0.987955i \(-0.450545\pi\)
−0.778223 + 0.627988i \(0.783879\pi\)
\(608\) 59.3970 102.879i 0.0976924 0.169208i
\(609\) 0 0
\(610\) 662.522 + 177.522i 1.08610 + 0.291020i
\(611\) 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 −0.743472 0.668767i \(-0.766822\pi\)
0.950905 + 0.309482i \(0.100156\pi\)
\(618\) 0 0
\(619\) 482.500 + 835.715i 0.779483 + 1.35010i 0.932240 + 0.361840i \(0.117851\pi\)
−0.152757 + 0.988264i \(0.548815\pi\)
\(620\) −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
\(635\) −38.6370 + 10.3528i −0.0608457 + 0.0163036i
\(636\) 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 \(-0.542771\pi\)
0.791237 + 0.611509i \(0.209437\pi\)
\(642\) 0 0
\(643\) −997.661 576.000i −1.55157 0.895801i −0.998014 0.0629907i \(-0.979936\pi\)
−0.553559 0.832810i \(-0.686731\pi\)
\(644\) 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 −0.699938 0.714203i \(-0.746789\pi\)
0.968487 + 0.249063i \(0.0801226\pi\)
\(654\) 0 0
\(655\) −175.692 + 655.692i −0.268232 + 1.00106i
\(656\) 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 \(-0.789950\pi\)
0.135871 + 0.990727i \(0.456617\pi\)
\(660\) 0 0
\(661\) 288.500 499.697i 0.436460 0.755971i −0.560954 0.827847i \(-0.689565\pi\)
0.997414 + 0.0718765i \(0.0228987\pi\)
\(662\) −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
\(670\) −894.747 + 239.747i −1.33544 + 0.357831i
\(671\) −118.800 68.5894i −0.177050 0.102220i
\(672\) 0 0
\(673\) 423.486 244.500i 0.629252 0.363299i −0.151210 0.988502i \(-0.548317\pi\)
0.780462 + 0.625203i \(0.214984\pi\)
\(674\) 77.7817i 0.115403i
\(675\) 0 0
\(676\) 176.000 0.260355
\(677\) 299.813 + 519.292i 0.442856 + 0.767048i 0.997900 0.0647722i \(-0.0206321\pi\)
−0.555044 + 0.831821i \(0.687299\pi\)
\(678\) 0 0
\(679\) −102.500 + 177.535i −0.150957 + 0.261466i
\(680\) 41.4110 + 154.548i 0.0608986 + 0.227277i
\(681\) 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 0.536016 0.844208i \(-0.319928\pi\)
−0.999113 + 0.0421001i \(0.986595\pi\)
\(692\) 22.6274 0.0326986
\(693\) 0 0
\(694\) −846.000 −1.21902
\(695\) −178.696 47.8815i −0.257117 0.0688943i
\(696\) 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 0.985327 0.170678i \(-0.0545958\pi\)
−0.640475 + 0.767979i \(0.721262\pi\)
\(710\) 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
\(715\) 16.4711 + 61.4711i 0.0230366 + 0.0859736i
\(716\) −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 \(-0.400174\pi\)
0.978034 + 0.208447i \(0.0668409\pi\)
\(728\) 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 \(-0.279225\pi\)
−0.346290 + 0.938128i \(0.612559\pi\)
\(734\) 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 \(0.305489\pi\)
\(740\) −64.7048 + 241.481i −0.0874389 + 0.326326i
\(741\) 0 0
\(742\) −441.673 255.000i −0.595247 0.343666i
\(743\) 16.9706 29.3939i 0.0228406 0.0395611i −0.854379 0.519650i \(-0.826062\pi\)
0.877220 + 0.480089i \(0.159396\pi\)
\(744\) 0 0
\(745\) 336.743 1256.74i 0.452005 1.68690i
\(746\) 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 −0.818349 0.574721i \(-0.805110\pi\)
0.906898 + 0.421351i \(0.138444\pi\)
\(752\) −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
\(760\) 76.8653 + 286.865i 0.101139 + 0.377454i
\(761\) −466.628 269.408i −0.613177 0.354018i 0.161031 0.986949i \(-0.448518\pi\)
−0.774208 + 0.632931i \(0.781852\pi\)
\(762\) 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 −0.838491 0.544916i \(-0.816562\pi\)
0.891156 + 0.453696i \(0.149895\pi\)
\(770\) −12.9410 48.2963i −0.0168064 0.0627225i
\(771\) 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
\(785\) 152.703 569.896i 0.194526 0.725982i
\(786\) 0 0