Properties

Label 260.2.x.a.101.2
Level $260$
Weight $2$
Character 260.101
Analytic conductor $2.076$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.x (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.22581504.2
Defining polynomial: \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 101.2
Root \(-1.27597 + 0.609843i\) of defining polynomial
Character \(\chi\) \(=\) 260.101
Dual form 260.2.x.a.121.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.800098 - 1.38581i) q^{3} +1.00000i q^{5} +(3.75184 + 2.16612i) q^{7} +(0.219687 - 0.380509i) q^{9} +O(q^{10})\) \(q+(-0.800098 - 1.38581i) q^{3} +1.00000i q^{5} +(3.75184 + 2.16612i) q^{7} +(0.219687 - 0.380509i) q^{9} +(1.50000 - 0.866025i) q^{11} +(-3.11256 - 1.81988i) q^{13} +(1.38581 - 0.800098i) q^{15} +(3.75184 - 6.49837i) q^{17} +(4.65213 + 2.68591i) q^{19} -6.93244i q^{21} +(-0.580411 - 1.00530i) q^{23} -1.00000 q^{25} -5.50367 q^{27} +(1.01236 + 1.75347i) q^{29} +7.86488i q^{31} +(-2.40029 - 1.38581i) q^{33} +(-2.16612 + 3.75184i) q^{35} +(-8.25551 + 4.76632i) q^{37} +(-0.0316594 + 5.76950i) q^{39} +(6.69615 - 3.86603i) q^{41} +(2.09277 - 3.62479i) q^{43} +(0.380509 + 0.219687i) q^{45} +3.46410i q^{47} +(5.88418 + 10.1917i) q^{49} -12.0073 q^{51} -12.6471 q^{53} +(0.866025 + 1.50000i) q^{55} -8.59596i q^{57} +(5.49674 + 3.17354i) q^{59} +(-1.85154 + 3.20696i) q^{61} +(1.64846 - 0.951738i) q^{63} +(1.81988 - 3.11256i) q^{65} +(-4.55568 + 2.63022i) q^{67} +(-0.928771 + 1.60868i) q^{69} +(-10.8377 - 6.25714i) q^{71} -5.23898i q^{73} +(0.800098 + 1.38581i) q^{75} +7.50367 q^{77} -8.16719 q^{79} +(3.74441 + 6.48552i) q^{81} -0.456760i q^{83} +(6.49837 + 3.75184i) q^{85} +(1.61998 - 2.80589i) q^{87} +(-11.4967 + 6.63765i) q^{89} +(-7.73572 - 13.5701i) q^{91} +(10.8992 - 6.29268i) q^{93} +(-2.68591 + 4.65213i) q^{95} +(-2.43371 - 1.40511i) q^{97} -0.761018i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{3} + 6 q^{7} - 4 q^{9} + 12 q^{11} - 8 q^{13} - 6 q^{15} + 6 q^{17} - 6 q^{23} - 8 q^{25} + 4 q^{27} - 6 q^{33} - 6 q^{35} + 6 q^{37} - 4 q^{39} + 12 q^{41} + 10 q^{43} - 4 q^{49} + 24 q^{53} - 24 q^{59} - 4 q^{61} + 24 q^{63} - 54 q^{67} - 24 q^{69} - 36 q^{71} + 2 q^{75} + 12 q^{77} - 16 q^{79} + 8 q^{81} + 18 q^{85} - 6 q^{87} - 24 q^{89} + 24 q^{93} - 30 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

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 0
\(3\) −0.800098 1.38581i −0.461937 0.800098i 0.537121 0.843505i \(-0.319512\pi\)
−0.999057 + 0.0434075i \(0.986179\pi\)
\(4\) 0 0
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 3.75184 + 2.16612i 1.41806 + 0.818718i 0.996128 0.0879098i \(-0.0280187\pi\)
0.421932 + 0.906627i \(0.361352\pi\)
\(8\) 0 0
\(9\) 0.219687 0.380509i 0.0732290 0.126836i
\(10\) 0 0
\(11\) 1.50000 0.866025i 0.452267 0.261116i −0.256520 0.966539i \(-0.582576\pi\)
0.708787 + 0.705422i \(0.249243\pi\)
\(12\) 0 0
\(13\) −3.11256 1.81988i −0.863269 0.504745i
\(14\) 0 0
\(15\) 1.38581 0.800098i 0.357815 0.206584i
\(16\) 0 0
\(17\) 3.75184 6.49837i 0.909954 1.57609i 0.0958278 0.995398i \(-0.469450\pi\)
0.814126 0.580688i \(-0.197216\pi\)
\(18\) 0 0
\(19\) 4.65213 + 2.68591i 1.06727 + 0.616190i 0.927435 0.373985i \(-0.122009\pi\)
0.139837 + 0.990175i \(0.455342\pi\)
\(20\) 0 0
\(21\) 6.93244i 1.51278i
\(22\) 0 0
\(23\) −0.580411 1.00530i −0.121024 0.209620i 0.799148 0.601135i \(-0.205284\pi\)
−0.920172 + 0.391515i \(0.871951\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 0 0
\(27\) −5.50367 −1.05918
\(28\) 0 0
\(29\) 1.01236 + 1.75347i 0.187991 + 0.325610i 0.944580 0.328280i \(-0.106469\pi\)
−0.756589 + 0.653891i \(0.773136\pi\)
\(30\) 0 0
\(31\) 7.86488i 1.41257i 0.707925 + 0.706287i \(0.249631\pi\)
−0.707925 + 0.706287i \(0.750369\pi\)
\(32\) 0 0
\(33\) −2.40029 1.38581i −0.417837 0.241239i
\(34\) 0 0
\(35\) −2.16612 + 3.75184i −0.366142 + 0.634176i
\(36\) 0 0
\(37\) −8.25551 + 4.76632i −1.35720 + 0.783578i −0.989245 0.146267i \(-0.953274\pi\)
−0.367952 + 0.929845i \(0.619941\pi\)
\(38\) 0 0
\(39\) −0.0316594 + 5.76950i −0.00506956 + 0.923860i
\(40\) 0 0
\(41\) 6.69615 3.86603i 1.04576 0.603772i 0.124303 0.992244i \(-0.460331\pi\)
0.921460 + 0.388473i \(0.126997\pi\)
\(42\) 0 0
\(43\) 2.09277 3.62479i 0.319145 0.552776i −0.661165 0.750241i \(-0.729938\pi\)
0.980310 + 0.197465i \(0.0632709\pi\)
\(44\) 0 0
\(45\) 0.380509 + 0.219687i 0.0567229 + 0.0327490i
\(46\) 0 0
\(47\) 3.46410i 0.505291i 0.967559 + 0.252646i \(0.0813007\pi\)
−0.967559 + 0.252646i \(0.918699\pi\)
\(48\) 0 0
\(49\) 5.88418 + 10.1917i 0.840597 + 1.45596i
\(50\) 0 0
\(51\) −12.0073 −1.68136
\(52\) 0 0
\(53\) −12.6471 −1.73721 −0.868607 0.495502i \(-0.834984\pi\)
−0.868607 + 0.495502i \(0.834984\pi\)
\(54\) 0 0
\(55\) 0.866025 + 1.50000i 0.116775 + 0.202260i
\(56\) 0 0
\(57\) 8.59596i 1.13856i
\(58\) 0 0
\(59\) 5.49674 + 3.17354i 0.715615 + 0.413160i 0.813136 0.582073i \(-0.197758\pi\)
−0.0975219 + 0.995233i \(0.531092\pi\)
\(60\) 0 0
\(61\) −1.85154 + 3.20696i −0.237066 + 0.410610i −0.959871 0.280442i \(-0.909519\pi\)
0.722805 + 0.691052i \(0.242852\pi\)
\(62\) 0 0
\(63\) 1.64846 0.951738i 0.207686 0.119908i
\(64\) 0 0
\(65\) 1.81988 3.11256i 0.225729 0.386066i
\(66\) 0 0
\(67\) −4.55568 + 2.63022i −0.556565 + 0.321333i −0.751766 0.659430i \(-0.770798\pi\)
0.195200 + 0.980763i \(0.437464\pi\)
\(68\) 0 0
\(69\) −0.928771 + 1.60868i −0.111811 + 0.193662i
\(70\) 0 0
\(71\) −10.8377 6.25714i −1.28620 0.742586i −0.308222 0.951314i \(-0.599734\pi\)
−0.977974 + 0.208729i \(0.933067\pi\)
\(72\) 0 0
\(73\) 5.23898i 0.613177i −0.951842 0.306588i \(-0.900813\pi\)
0.951842 0.306588i \(-0.0991875\pi\)
\(74\) 0 0
\(75\) 0.800098 + 1.38581i 0.0923873 + 0.160020i
\(76\) 0 0
\(77\) 7.50367 0.855123
\(78\) 0 0
\(79\) −8.16719 −0.918880 −0.459440 0.888209i \(-0.651950\pi\)
−0.459440 + 0.888209i \(0.651950\pi\)
\(80\) 0 0
\(81\) 3.74441 + 6.48552i 0.416046 + 0.720613i
\(82\) 0 0
\(83\) 0.456760i 0.0501359i −0.999686 0.0250679i \(-0.992020\pi\)
0.999686 0.0250679i \(-0.00798021\pi\)
\(84\) 0 0
\(85\) 6.49837 + 3.75184i 0.704847 + 0.406944i
\(86\) 0 0
\(87\) 1.61998 2.80589i 0.173680 0.300823i
\(88\) 0 0
\(89\) −11.4967 + 6.63765i −1.21865 + 0.703589i −0.964630 0.263609i \(-0.915087\pi\)
−0.254022 + 0.967198i \(0.581754\pi\)
\(90\) 0 0
\(91\) −7.73572 13.5701i −0.810924 1.42253i
\(92\) 0 0
\(93\) 10.8992 6.29268i 1.13020 0.652520i
\(94\) 0 0
\(95\) −2.68591 + 4.65213i −0.275568 + 0.477298i
\(96\) 0 0
\(97\) −2.43371 1.40511i −0.247106 0.142667i 0.371332 0.928500i \(-0.378901\pi\)
−0.618439 + 0.785833i \(0.712234\pi\)
\(98\) 0 0
\(99\) 0.761018i 0.0764852i
\(100\) 0 0
\(101\) −3.31988 5.75021i −0.330341 0.572167i 0.652238 0.758014i \(-0.273830\pi\)
−0.982579 + 0.185847i \(0.940497\pi\)
\(102\) 0 0
\(103\) 7.37605 0.726784 0.363392 0.931636i \(-0.381619\pi\)
0.363392 + 0.931636i \(0.381619\pi\)
\(104\) 0 0
\(105\) 6.93244 0.676537
\(106\) 0 0
\(107\) 3.95668 + 6.85317i 0.382507 + 0.662521i 0.991420 0.130716i \(-0.0417275\pi\)
−0.608913 + 0.793237i \(0.708394\pi\)
\(108\) 0 0
\(109\) 9.18301i 0.879572i −0.898102 0.439786i \(-0.855054\pi\)
0.898102 0.439786i \(-0.144946\pi\)
\(110\) 0 0
\(111\) 13.2104 + 7.62704i 1.25388 + 0.723927i
\(112\) 0 0
\(113\) 2.88793 5.00204i 0.271674 0.470552i −0.697617 0.716471i \(-0.745756\pi\)
0.969291 + 0.245919i \(0.0790896\pi\)
\(114\) 0 0
\(115\) 1.00530 0.580411i 0.0937448 0.0541236i
\(116\) 0 0
\(117\) −1.37627 + 0.784552i −0.127236 + 0.0725319i
\(118\) 0 0
\(119\) 28.1525 16.2539i 2.58074 1.48999i
\(120\) 0 0
\(121\) −4.00000 + 6.92820i −0.363636 + 0.629837i
\(122\) 0 0
\(123\) −10.7152 6.18640i −0.966153 0.557809i
\(124\) 0 0
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 9.48389 + 16.4266i 0.841559 + 1.45762i 0.888576 + 0.458729i \(0.151695\pi\)
−0.0470176 + 0.998894i \(0.514972\pi\)
\(128\) 0 0
\(129\) −6.69770 −0.589699
\(130\) 0 0
\(131\) −1.34637 −0.117633 −0.0588165 0.998269i \(-0.518733\pi\)
−0.0588165 + 0.998269i \(0.518733\pi\)
\(132\) 0 0
\(133\) 11.6360 + 20.1542i 1.00897 + 1.74759i
\(134\) 0 0
\(135\) 5.50367i 0.473681i
\(136\) 0 0
\(137\) −10.7152 6.18640i −0.915457 0.528540i −0.0332744 0.999446i \(-0.510594\pi\)
−0.882183 + 0.470907i \(0.843927\pi\)
\(138\) 0 0
\(139\) −4.38418 + 7.59362i −0.371861 + 0.644083i −0.989852 0.142103i \(-0.954614\pi\)
0.617991 + 0.786185i \(0.287947\pi\)
\(140\) 0 0
\(141\) 4.80059 2.77162i 0.404282 0.233413i
\(142\) 0 0
\(143\) −6.24490 0.0342681i −0.522225 0.00286565i
\(144\) 0 0
\(145\) −1.75347 + 1.01236i −0.145617 + 0.0840722i
\(146\) 0 0
\(147\) 9.41584 16.3087i 0.776605 1.34512i
\(148\) 0 0
\(149\) 4.10443 + 2.36970i 0.336248 + 0.194133i 0.658612 0.752483i \(-0.271144\pi\)
−0.322363 + 0.946616i \(0.604477\pi\)
\(150\) 0 0
\(151\) 1.56063i 0.127002i −0.997982 0.0635010i \(-0.979773\pi\)
0.997982 0.0635010i \(-0.0202266\pi\)
\(152\) 0 0
\(153\) −1.64846 2.85521i −0.133270 0.230830i
\(154\) 0 0
\(155\) −7.86488 −0.631723
\(156\) 0 0
\(157\) −9.15332 −0.730515 −0.365257 0.930907i \(-0.619019\pi\)
−0.365257 + 0.930907i \(0.619019\pi\)
\(158\) 0 0
\(159\) 10.1189 + 17.5265i 0.802483 + 1.38994i
\(160\) 0 0
\(161\) 5.02897i 0.396338i
\(162\) 0 0
\(163\) 2.28893 + 1.32151i 0.179283 + 0.103509i 0.586956 0.809619i \(-0.300326\pi\)
−0.407673 + 0.913128i \(0.633660\pi\)
\(164\) 0 0
\(165\) 1.38581 2.40029i 0.107885 0.186863i
\(166\) 0 0
\(167\) 7.71515 4.45435i 0.597017 0.344688i −0.170850 0.985297i \(-0.554651\pi\)
0.767867 + 0.640609i \(0.221318\pi\)
\(168\) 0 0
\(169\) 6.37605 + 11.3290i 0.490466 + 0.871460i
\(170\) 0 0
\(171\) 2.04402 1.18012i 0.156310 0.0902458i
\(172\) 0 0
\(173\) 6.90396 11.9580i 0.524899 0.909151i −0.474681 0.880158i \(-0.657437\pi\)
0.999580 0.0289933i \(-0.00923014\pi\)
\(174\) 0 0
\(175\) −3.75184 2.16612i −0.283612 0.163744i
\(176\) 0 0
\(177\) 10.1566i 0.763416i
\(178\) 0 0
\(179\) −12.1751 21.0879i −0.910009 1.57618i −0.814048 0.580797i \(-0.802741\pi\)
−0.0959612 0.995385i \(-0.530592\pi\)
\(180\) 0 0
\(181\) 24.8336 1.84587 0.922935 0.384956i \(-0.125783\pi\)
0.922935 + 0.384956i \(0.125783\pi\)
\(182\) 0 0
\(183\) 5.92566 0.438037
\(184\) 0 0
\(185\) −4.76632 8.25551i −0.350427 0.606957i
\(186\) 0 0
\(187\) 12.9967i 0.950416i
\(188\) 0 0
\(189\) −20.6489 11.9216i −1.50198 0.867171i
\(190\) 0 0
\(191\) −2.98438 + 5.16909i −0.215942 + 0.374022i −0.953564 0.301192i \(-0.902615\pi\)
0.737622 + 0.675214i \(0.235949\pi\)
\(192\) 0 0
\(193\) −7.83988 + 4.52636i −0.564327 + 0.325814i −0.754880 0.655862i \(-0.772305\pi\)
0.190553 + 0.981677i \(0.438972\pi\)
\(194\) 0 0
\(195\) −5.76950 0.0316594i −0.413163 0.00226718i
\(196\) 0 0
\(197\) −9.86320 + 5.69452i −0.702724 + 0.405718i −0.808361 0.588687i \(-0.799645\pi\)
0.105637 + 0.994405i \(0.466312\pi\)
\(198\) 0 0
\(199\) 5.38863 9.33339i 0.381990 0.661626i −0.609357 0.792896i \(-0.708572\pi\)
0.991347 + 0.131270i \(0.0419055\pi\)
\(200\) 0 0
\(201\) 7.28998 + 4.20887i 0.514196 + 0.296871i
\(202\) 0 0
\(203\) 8.77162i 0.615647i
\(204\) 0 0
\(205\) 3.86603 + 6.69615i 0.270015 + 0.467680i
\(206\) 0 0
\(207\) −0.510035 −0.0354499
\(208\) 0 0
\(209\) 9.30426 0.643589
\(210\) 0 0
\(211\) 1.61256 + 2.79304i 0.111013 + 0.192280i 0.916179 0.400769i \(-0.131257\pi\)
−0.805166 + 0.593050i \(0.797924\pi\)
\(212\) 0 0
\(213\) 20.0253i 1.37211i
\(214\) 0 0
\(215\) 3.62479 + 2.09277i 0.247209 + 0.142726i
\(216\) 0 0
\(217\) −17.0363 + 29.5078i −1.15650 + 2.00312i
\(218\) 0 0
\(219\) −7.26023 + 4.19170i −0.490601 + 0.283249i
\(220\) 0 0
\(221\) −23.5041 + 13.3987i −1.58106 + 0.901292i
\(222\) 0 0
\(223\) −14.7046 + 8.48968i −0.984690 + 0.568511i −0.903683 0.428203i \(-0.859147\pi\)
−0.0810069 + 0.996714i \(0.525814\pi\)
\(224\) 0 0
\(225\) −0.219687 + 0.380509i −0.0146458 + 0.0253673i
\(226\) 0 0
\(227\) 2.07891 + 1.20026i 0.137982 + 0.0796641i 0.567402 0.823441i \(-0.307949\pi\)
−0.429420 + 0.903105i \(0.641282\pi\)
\(228\) 0 0
\(229\) 7.35671i 0.486145i −0.970008 0.243073i \(-0.921845\pi\)
0.970008 0.243073i \(-0.0781553\pi\)
\(230\) 0 0
\(231\) −6.00367 10.3987i −0.395013 0.684182i
\(232\) 0 0
\(233\) −3.37410 −0.221045 −0.110522 0.993874i \(-0.535252\pi\)
−0.110522 + 0.993874i \(0.535252\pi\)
\(234\) 0 0
\(235\) −3.46410 −0.225973
\(236\) 0 0
\(237\) 6.53455 + 11.3182i 0.424464 + 0.735194i
\(238\) 0 0
\(239\) 23.7807i 1.53824i −0.639103 0.769121i \(-0.720694\pi\)
0.639103 0.769121i \(-0.279306\pi\)
\(240\) 0 0
\(241\) 19.3307 + 11.1606i 1.24520 + 0.718918i 0.970149 0.242511i \(-0.0779709\pi\)
0.275054 + 0.961429i \(0.411304\pi\)
\(242\) 0 0
\(243\) −2.26371 + 3.92086i −0.145217 + 0.251523i
\(244\) 0 0
\(245\) −10.1917 + 5.88418i −0.651124 + 0.375926i
\(246\) 0 0
\(247\) −9.59199 16.8264i −0.610324 1.07064i
\(248\) 0 0
\(249\) −0.632982 + 0.365452i −0.0401136 + 0.0231596i
\(250\) 0 0
\(251\) −2.31119 + 4.00310i −0.145881 + 0.252673i −0.929701 0.368314i \(-0.879935\pi\)
0.783820 + 0.620988i \(0.213268\pi\)
\(252\) 0 0
\(253\) −1.74123 1.00530i −0.109470 0.0632028i
\(254\) 0 0
\(255\) 12.0073i 0.751929i
\(256\) 0 0
\(257\) 10.9320 + 18.9347i 0.681916 + 1.18111i 0.974395 + 0.224842i \(0.0721866\pi\)
−0.292479 + 0.956272i \(0.594480\pi\)
\(258\) 0 0
\(259\) −41.2977 −2.56612
\(260\) 0 0
\(261\) 0.889612 0.0550656
\(262\) 0 0
\(263\) 10.0895 + 17.4756i 0.622146 + 1.07759i 0.989085 + 0.147344i \(0.0470724\pi\)
−0.366939 + 0.930245i \(0.619594\pi\)
\(264\) 0 0
\(265\) 12.6471i 0.776906i
\(266\) 0 0
\(267\) 18.3970 + 10.6215i 1.12588 + 0.650027i
\(268\) 0 0
\(269\) −3.64344 + 6.31062i −0.222144 + 0.384765i −0.955459 0.295124i \(-0.904639\pi\)
0.733315 + 0.679889i \(0.237972\pi\)
\(270\) 0 0
\(271\) −4.23650 + 2.44595i −0.257349 + 0.148581i −0.623125 0.782122i \(-0.714137\pi\)
0.365775 + 0.930703i \(0.380804\pi\)
\(272\) 0 0
\(273\) −12.6162 + 21.5776i −0.763569 + 1.30594i
\(274\) 0 0
\(275\) −1.50000 + 0.866025i −0.0904534 + 0.0522233i
\(276\) 0 0
\(277\) 4.40029 7.62153i 0.264388 0.457933i −0.703015 0.711175i \(-0.748163\pi\)
0.967403 + 0.253241i \(0.0814967\pi\)
\(278\) 0 0
\(279\) 2.99266 + 1.72781i 0.179166 + 0.103441i
\(280\) 0 0
\(281\) 12.6085i 0.752161i 0.926587 + 0.376081i \(0.122728\pi\)
−0.926587 + 0.376081i \(0.877272\pi\)
\(282\) 0 0
\(283\) −10.4505 18.1007i −0.621216 1.07598i −0.989260 0.146169i \(-0.953306\pi\)
0.368044 0.929808i \(-0.380028\pi\)
\(284\) 0 0
\(285\) 8.59596 0.509181
\(286\) 0 0
\(287\) 33.4972 1.97727
\(288\) 0 0
\(289\) −19.6525 34.0392i −1.15603 2.00231i
\(290\) 0 0
\(291\) 4.49689i 0.263612i
\(292\) 0 0
\(293\) −0.599706 0.346241i −0.0350352 0.0202276i 0.482380 0.875962i \(-0.339772\pi\)
−0.517415 + 0.855734i \(0.673106\pi\)
\(294\) 0 0
\(295\) −3.17354 + 5.49674i −0.184771 + 0.320033i
\(296\) 0 0
\(297\) −8.25551 + 4.76632i −0.479033 + 0.276570i
\(298\) 0 0
\(299\) −0.0229665 + 4.18534i −0.00132819 + 0.242044i
\(300\) 0 0
\(301\) 15.7035 9.06642i 0.905134 0.522580i
\(302\) 0 0
\(303\) −5.31246 + 9.20145i −0.305193 + 0.528610i
\(304\) 0 0
\(305\) −3.20696 1.85154i −0.183630 0.106019i
\(306\) 0 0
\(307\) 8.83168i 0.504051i −0.967721 0.252025i \(-0.918903\pi\)
0.967721 0.252025i \(-0.0810966\pi\)
\(308\) 0 0
\(309\) −5.90157 10.2218i −0.335728 0.581499i
\(310\) 0 0
\(311\) −11.3958 −0.646198 −0.323099 0.946365i \(-0.604725\pi\)
−0.323099 + 0.946365i \(0.604725\pi\)
\(312\) 0 0
\(313\) −3.38496 −0.191329 −0.0956647 0.995414i \(-0.530498\pi\)
−0.0956647 + 0.995414i \(0.530498\pi\)
\(314\) 0 0
\(315\) 0.951738 + 1.64846i 0.0536243 + 0.0928801i
\(316\) 0 0
\(317\) 0.557104i 0.0312901i 0.999878 + 0.0156450i \(0.00498017\pi\)
−0.999878 + 0.0156450i \(0.995020\pi\)
\(318\) 0 0
\(319\) 3.03709 + 1.75347i 0.170044 + 0.0981752i
\(320\) 0 0
\(321\) 6.33146 10.9664i 0.353388 0.612086i
\(322\) 0 0
\(323\) 34.9080 20.1542i 1.94234 1.12141i
\(324\) 0 0
\(325\) 3.11256 + 1.81988i 0.172654 + 0.100949i
\(326\) 0 0
\(327\) −12.7259 + 7.34730i −0.703744 + 0.406307i
\(328\) 0 0
\(329\) −7.50367 + 12.9967i −0.413691 + 0.716533i
\(330\) 0 0
\(331\) 3.43266 + 1.98185i 0.188676 + 0.108932i 0.591363 0.806406i \(-0.298590\pi\)
−0.402687 + 0.915338i \(0.631924\pi\)
\(332\) 0 0
\(333\) 4.18839i 0.229522i
\(334\) 0 0
\(335\) −2.63022 4.55568i −0.143705 0.248904i
\(336\) 0 0
\(337\) 16.7243 0.911030 0.455515 0.890228i \(-0.349455\pi\)
0.455515 + 0.890228i \(0.349455\pi\)
\(338\) 0 0
\(339\) −9.24251 −0.501984
\(340\) 0 0
\(341\) 6.81119 + 11.7973i 0.368847 + 0.638861i
\(342\) 0 0
\(343\) 20.6577i 1.11541i
\(344\) 0 0
\(345\) −1.60868 0.928771i −0.0866084 0.0500034i
\(346\) 0 0
\(347\) −3.79043 + 6.56521i −0.203481 + 0.352439i −0.949648 0.313320i \(-0.898559\pi\)
0.746167 + 0.665759i \(0.231892\pi\)
\(348\) 0 0
\(349\) 23.6733 13.6678i 1.26720 0.731621i 0.292746 0.956190i \(-0.405431\pi\)
0.974458 + 0.224569i \(0.0720975\pi\)
\(350\) 0 0
\(351\) 17.1305 + 10.0160i 0.914359 + 0.534616i
\(352\) 0 0
\(353\) 22.5964 13.0461i 1.20269 0.694372i 0.241536 0.970392i \(-0.422349\pi\)
0.961152 + 0.276020i \(0.0890156\pi\)
\(354\) 0 0
\(355\) 6.25714 10.8377i 0.332094 0.575204i
\(356\) 0 0
\(357\) −45.0496 26.0094i −2.38428 1.37656i
\(358\) 0 0
\(359\) 0.694176i 0.0366372i −0.999832 0.0183186i \(-0.994169\pi\)
0.999832 0.0183186i \(-0.00583132\pi\)
\(360\) 0 0
\(361\) 4.92820 + 8.53590i 0.259379 + 0.449258i
\(362\) 0 0
\(363\) 12.8016 0.671908
\(364\) 0 0
\(365\) 5.23898 0.274221
\(366\) 0 0
\(367\) −11.4109 19.7643i −0.595644 1.03169i −0.993456 0.114218i \(-0.963564\pi\)
0.397812 0.917467i \(-0.369770\pi\)
\(368\) 0 0
\(369\) 3.39726i 0.176854i
\(370\) 0 0
\(371\) −47.4499 27.3952i −2.46347 1.42229i
\(372\) 0 0
\(373\) 3.94065 6.82540i 0.204039 0.353406i −0.745787 0.666184i \(-0.767926\pi\)
0.949826 + 0.312779i \(0.101260\pi\)
\(374\) 0 0
\(375\) −1.38581 + 0.800098i −0.0715629 + 0.0413169i
\(376\) 0 0
\(377\) 0.0400587 7.30015i 0.00206313 0.375977i
\(378\) 0 0
\(379\) 26.9703 15.5713i 1.38537 0.799843i 0.392580 0.919718i \(-0.371583\pi\)
0.992789 + 0.119875i \(0.0382494\pi\)
\(380\) 0 0
\(381\) 15.1761 26.2857i 0.777494 1.34666i
\(382\) 0 0
\(383\) 29.8885 + 17.2561i 1.52723 + 0.881747i 0.999477 + 0.0323495i \(0.0102990\pi\)
0.527754 + 0.849397i \(0.323034\pi\)
\(384\) 0 0
\(385\) 7.50367i 0.382422i
\(386\) 0 0
\(387\) −0.919510 1.59264i −0.0467413 0.0809584i
\(388\) 0 0
\(389\) −6.18414 −0.313548 −0.156774 0.987634i \(-0.550109\pi\)
−0.156774 + 0.987634i \(0.550109\pi\)
\(390\) 0 0
\(391\) −8.71043 −0.440505
\(392\) 0 0
\(393\) 1.07723 + 1.86582i 0.0543390 + 0.0941179i
\(394\) 0 0
\(395\) 8.16719i 0.410936i
\(396\) 0 0
\(397\) 19.6209 + 11.3281i 0.984745 + 0.568543i 0.903699 0.428167i \(-0.140841\pi\)
0.0810459 + 0.996710i \(0.474174\pi\)
\(398\) 0 0
\(399\) 18.6199 32.2506i 0.932161 1.61455i
\(400\) 0 0
\(401\) 3.35847 1.93902i 0.167714 0.0968298i −0.413793 0.910371i \(-0.635796\pi\)
0.581508 + 0.813541i \(0.302463\pi\)
\(402\) 0 0
\(403\) 14.3132 24.4799i 0.712990 1.21943i
\(404\) 0 0
\(405\) −6.48552 + 3.74441i −0.322268 + 0.186061i
\(406\) 0 0
\(407\) −8.25551 + 14.2990i −0.409210 + 0.708773i
\(408\) 0 0
\(409\) 12.0037 + 6.93032i 0.593543 + 0.342682i 0.766497 0.642248i \(-0.221998\pi\)
−0.172954 + 0.984930i \(0.555331\pi\)
\(410\) 0 0
\(411\) 19.7989i 0.976607i
\(412\) 0 0
\(413\) 13.7486 + 23.8132i 0.676523 + 1.17177i
\(414\) 0 0
\(415\) 0.456760 0.0224214
\(416\) 0 0
\(417\) 14.0311 0.687106
\(418\) 0 0
\(419\) 15.1751 + 26.2840i 0.741352 + 1.28406i 0.951880 + 0.306471i \(0.0991484\pi\)
−0.210528 + 0.977588i \(0.567518\pi\)
\(420\) 0 0
\(421\) 0.608516i 0.0296573i −0.999890 0.0148286i \(-0.995280\pi\)
0.999890 0.0148286i \(-0.00472027\pi\)
\(422\) 0 0
\(423\) 1.31812 + 0.761018i 0.0640892 + 0.0370019i
\(424\) 0 0
\(425\) −3.75184 + 6.49837i −0.181991 + 0.315217i
\(426\) 0 0
\(427\) −13.8934 + 8.02134i −0.672347 + 0.388180i
\(428\) 0 0
\(429\) 4.94905 + 8.68167i 0.238942 + 0.419155i
\(430\) 0 0
\(431\) −34.0819 + 19.6772i −1.64167 + 0.947818i −0.661429 + 0.750008i \(0.730050\pi\)
−0.980240 + 0.197810i \(0.936617\pi\)
\(432\) 0 0
\(433\) 3.21474 5.56810i 0.154491 0.267586i −0.778383 0.627790i \(-0.783960\pi\)
0.932873 + 0.360204i \(0.117293\pi\)
\(434\) 0 0
\(435\) 2.80589 + 1.61998i 0.134532 + 0.0776721i
\(436\) 0 0
\(437\) 6.23572i 0.298295i
\(438\) 0 0
\(439\) 0.735722 + 1.27431i 0.0351141 + 0.0608194i 0.883048 0.469282i \(-0.155487\pi\)
−0.847934 + 0.530101i \(0.822154\pi\)
\(440\) 0 0
\(441\) 5.17071 0.246224
\(442\) 0 0
\(443\) −16.9193 −0.803860 −0.401930 0.915670i \(-0.631660\pi\)
−0.401930 + 0.915670i \(0.631660\pi\)
\(444\) 0 0
\(445\) −6.63765 11.4967i −0.314655 0.544998i
\(446\) 0 0
\(447\) 7.58396i 0.358709i
\(448\) 0 0
\(449\) −7.89557 4.55851i −0.372615 0.215129i 0.301985 0.953313i \(-0.402351\pi\)
−0.674600 + 0.738183i \(0.735684\pi\)
\(450\) 0 0
\(451\) 6.69615 11.5981i 0.315310 0.546132i
\(452\) 0 0
\(453\) −2.16273 + 1.24865i −0.101614 + 0.0586669i
\(454\) 0 0
\(455\) 13.5701 7.73572i 0.636176 0.362656i
\(456\) 0 0
\(457\) −15.2041 + 8.77811i −0.711220 + 0.410623i −0.811512 0.584335i \(-0.801355\pi\)
0.100293 + 0.994958i \(0.468022\pi\)
\(458\) 0 0
\(459\) −20.6489 + 35.7649i −0.963807 + 1.66936i
\(460\) 0 0
\(461\) −13.2973 7.67722i −0.619318 0.357564i 0.157285 0.987553i \(-0.449726\pi\)
−0.776604 + 0.629990i \(0.783059\pi\)
\(462\) 0 0
\(463\) 18.8614i 0.876562i 0.898838 + 0.438281i \(0.144412\pi\)
−0.898838 + 0.438281i \(0.855588\pi\)
\(464\) 0 0
\(465\) 6.29268 + 10.8992i 0.291816 + 0.505440i
\(466\) 0 0
\(467\) 32.9302 1.52383 0.761913 0.647679i \(-0.224260\pi\)
0.761913 + 0.647679i \(0.224260\pi\)
\(468\) 0 0
\(469\) −22.7896 −1.05232
\(470\) 0 0
\(471\) 7.32355 + 12.6848i 0.337452 + 0.584483i
\(472\) 0 0
\(473\) 7.24958i 0.333336i
\(474\) 0 0
\(475\) −4.65213 2.68591i −0.213454 0.123238i
\(476\) 0 0
\(477\) −2.77840 + 4.81234i −0.127214 + 0.220342i
\(478\) 0 0
\(479\) −14.9368 + 8.62378i −0.682481 + 0.394031i −0.800789 0.598946i \(-0.795586\pi\)
0.118308 + 0.992977i \(0.462253\pi\)
\(480\) 0 0
\(481\) 34.3699 + 0.188601i 1.56713 + 0.00859944i
\(482\) 0 0
\(483\) −6.96919 + 4.02367i −0.317109 + 0.183083i
\(484\) 0 0
\(485\) 1.40511 2.43371i 0.0638026 0.110509i
\(486\) 0 0
\(487\) −15.5663 8.98720i −0.705376 0.407249i 0.103971 0.994580i \(-0.466845\pi\)
−0.809346 + 0.587331i \(0.800178\pi\)
\(488\) 0 0
\(489\) 4.22936i 0.191258i
\(490\) 0 0
\(491\) 13.0977 + 22.6858i 0.591089 + 1.02380i 0.994086 + 0.108595i \(0.0346350\pi\)
−0.402997 + 0.915201i \(0.632032\pi\)
\(492\) 0 0
\(493\) 15.1929 0.684253
\(494\) 0 0
\(495\) 0.761018 0.0342052
\(496\) 0 0
\(497\) −27.1075 46.9515i −1.21594 2.10606i
\(498\) 0 0
\(499\) 18.3428i 0.821139i 0.911829 + 0.410569i \(0.134670\pi\)
−0.911829 + 0.410569i \(0.865330\pi\)
\(500\) 0 0
\(501\) −12.3458 7.12783i −0.551568 0.318448i
\(502\) 0 0
\(503\) 7.12811 12.3462i 0.317827 0.550492i −0.662208 0.749320i \(-0.730380\pi\)
0.980034 + 0.198829i \(0.0637137\pi\)
\(504\) 0 0
\(505\) 5.75021 3.31988i 0.255881 0.147733i
\(506\) 0 0
\(507\) 10.5984 17.9003i 0.470690 0.794980i
\(508\) 0 0
\(509\) 27.5380 15.8991i 1.22060 0.704714i 0.255555 0.966795i \(-0.417742\pi\)
0.965046 + 0.262081i \(0.0844086\pi\)
\(510\) 0 0
\(511\) 11.3483 19.6558i 0.502018 0.869521i
\(512\) 0 0
\(513\) −25.6038 14.7824i −1.13043 0.652657i
\(514\) 0 0
\(515\) 7.37605i 0.325028i
\(516\) 0 0
\(517\) 3.00000 + 5.19615i 0.131940 + 0.228527i
\(518\) 0 0
\(519\) −22.0954 −0.969880
\(520\) 0 0
\(521\) −45.1676 −1.97883 −0.989414 0.145122i \(-0.953642\pi\)
−0.989414 + 0.145122i \(0.953642\pi\)
\(522\) 0 0
\(523\) −13.0573 22.6159i −0.570955 0.988924i −0.996468 0.0839712i \(-0.973240\pi\)
0.425513 0.904952i \(-0.360094\pi\)
\(524\) 0 0
\(525\) 6.93244i 0.302557i
\(526\) 0 0
\(527\) 51.1089 + 29.5078i 2.22634 + 1.28538i
\(528\) 0 0
\(529\) 10.8262 18.7516i 0.470706 0.815287i
\(530\) 0 0
\(531\) 2.41512 1.39437i 0.104807 0.0605106i
\(532\) 0 0
\(533\) −27.8779 0.152976i −1.20753 0.00662615i
\(534\) 0 0
\(535\) −6.85317 + 3.95668i −0.296288 + 0.171062i
\(536\) 0 0
\(537\) −19.4825 + 33.7447i −0.840733 + 1.45619i
\(538\) 0 0
\(539\) 17.6525 + 10.1917i 0.760349 + 0.438988i
\(540\) 0 0
\(541\) 31.4750i 1.35321i −0.736344 0.676607i \(-0.763450\pi\)
0.736344 0.676607i \(-0.236550\pi\)
\(542\) 0 0
\(543\) −19.8693 34.4147i −0.852675 1.47688i
\(544\) 0 0
\(545\) 9.18301 0.393357
\(546\) 0 0
\(547\) −5.70391 −0.243881 −0.121941 0.992537i \(-0.538912\pi\)
−0.121941 + 0.992537i \(0.538912\pi\)
\(548\) 0 0
\(549\) 0.813519 + 1.40906i 0.0347201 + 0.0601370i
\(550\) 0 0
\(551\) 10.8765i 0.463353i
\(552\) 0 0
\(553\) −30.6419 17.6911i −1.30303 0.752303i
\(554\) 0 0
\(555\) −7.62704 + 13.2104i −0.323750 + 0.560751i
\(556\) 0 0
\(557\) 18.0757 10.4360i 0.765890 0.442187i −0.0655165 0.997851i \(-0.520870\pi\)
0.831406 + 0.555665i \(0.187536\pi\)
\(558\) 0 0
\(559\) −13.1106 + 7.47378i −0.554519 + 0.316107i
\(560\) 0 0
\(561\) −18.0110 + 10.3987i −0.760426 + 0.439032i
\(562\) 0 0
\(563\) −16.6157 + 28.7793i −0.700270 + 1.21290i 0.268102 + 0.963391i \(0.413604\pi\)
−0.968372 + 0.249513i \(0.919730\pi\)
\(564\) 0 0
\(565\) 5.00204 + 2.88793i 0.210437 + 0.121496i
\(566\) 0 0
\(567\) 32.4435i 1.36250i
\(568\) 0 0
\(569\) −20.0336 34.6992i −0.839851 1.45466i −0.890019 0.455924i \(-0.849309\pi\)
0.0501680 0.998741i \(-0.484024\pi\)
\(570\) 0 0
\(571\) −4.53590 −0.189821 −0.0949107 0.995486i \(-0.530257\pi\)
−0.0949107 + 0.995486i \(0.530257\pi\)
\(572\) 0 0
\(573\) 9.55117 0.399006
\(574\) 0 0
\(575\) 0.580411 + 1.00530i 0.0242048 + 0.0419240i
\(576\) 0 0
\(577\) 35.2706i 1.46834i 0.678968 + 0.734168i \(0.262427\pi\)
−0.678968 + 0.734168i \(0.737573\pi\)
\(578\) 0 0
\(579\) 12.5453 + 7.24306i 0.521367 + 0.301011i
\(580\) 0 0
\(581\) 0.989397 1.71369i 0.0410471 0.0710957i
\(582\) 0 0
\(583\) −18.9707 + 10.9527i −0.785684 + 0.453615i
\(584\) 0 0
\(585\) −0.784552 1.37627i −0.0324372 0.0569018i
\(586\) 0 0
\(587\) −35.6511 + 20.5832i −1.47148 + 0.849558i −0.999486 0.0320457i \(-0.989798\pi\)
−0.471991 + 0.881603i \(0.656464\pi\)
\(588\) 0 0
\(589\) −21.1244 + 36.5885i −0.870414 + 1.50760i
\(590\) 0 0
\(591\) 15.7831 + 9.11235i 0.649228 + 0.374832i
\(592\) 0 0
\(593\) 9.39726i 0.385899i −0.981209 0.192950i \(-0.938195\pi\)
0.981209 0.192950i \(-0.0618054\pi\)
\(594\) 0 0
\(595\) 16.2539 + 28.1525i 0.666344 + 1.15414i
\(596\) 0 0
\(597\) −17.2457 −0.705821
\(598\) 0 0
\(599\) 21.7881 0.890239 0.445119 0.895471i \(-0.353161\pi\)
0.445119 + 0.895471i \(0.353161\pi\)
\(600\) 0 0
\(601\) −12.5481 21.7340i −0.511848 0.886547i −0.999906 0.0137352i \(-0.995628\pi\)
0.488058 0.872811i \(-0.337706\pi\)
\(602\) 0 0
\(603\) 2.31130i 0.0941236i
\(604\) 0 0
\(605\) −6.92820 4.00000i −0.281672 0.162623i
\(606\) 0 0
\(607\) 16.9888 29.4254i 0.689552 1.19434i −0.282431 0.959288i \(-0.591141\pi\)
0.971983 0.235052i \(-0.0755259\pi\)
\(608\) 0 0
\(609\) 12.1558 7.01815i 0.492578 0.284390i
\(610\) 0 0
\(611\) 6.30426 10.7822i 0.255043 0.436202i
\(612\) 0 0
\(613\) 18.5736 10.7235i 0.750182 0.433118i −0.0755778 0.997140i \(-0.524080\pi\)
0.825760 + 0.564022i \(0.190747\pi\)
\(614\) 0 0
\(615\) 6.18640 10.7152i 0.249460 0.432077i
\(616\) 0 0
\(617\) 29.5092 + 17.0372i 1.18800 + 0.685890i 0.957851 0.287266i \(-0.0927464\pi\)
0.230146 + 0.973156i \(0.426080\pi\)
\(618\) 0 0
\(619\) 26.9791i 1.08438i 0.840256 + 0.542191i \(0.182405\pi\)
−0.840256 + 0.542191i \(0.817595\pi\)
\(620\) 0 0
\(621\) 3.19439 + 5.53285i 0.128186 + 0.222026i
\(622\) 0 0
\(623\) −57.5118 −2.30416
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −7.44432 12.8939i −0.297297 0.514934i
\(628\) 0 0
\(629\) 71.5298i 2.85208i
\(630\) 0 0
\(631\) −32.8863 18.9869i −1.30918 0.755857i −0.327223 0.944947i \(-0.606113\pi\)
−0.981960 + 0.189090i \(0.939446\pi\)
\(632\) 0 0
\(633\) 2.58041 4.46940i 0.102562 0.177643i
\(634\) 0 0
\(635\) −16.4266 + 9.48389i −0.651869 + 0.376357i
\(636\) 0 0
\(637\) 0.232834 42.4308i 0.00922521 1.68117i
\(638\) 0 0
\(639\) −4.76179 + 2.74922i −0.188374 + 0.108758i
\(640\) 0 0
\(641\) −4.12590 + 7.14627i −0.162963 + 0.282261i −0.935930 0.352186i \(-0.885439\pi\)
0.772967 + 0.634446i \(0.218772\pi\)
\(642\) 0 0
\(643\) 41.6992 + 24.0750i 1.64446 + 0.949427i 0.979222 + 0.202791i \(0.0650011\pi\)
0.665233 + 0.746636i \(0.268332\pi\)
\(644\) 0 0
\(645\) 6.69770i 0.263722i
\(646\) 0 0
\(647\) −1.08951 1.88709i −0.0428332 0.0741893i 0.843814 0.536636i \(-0.180305\pi\)
−0.886647 + 0.462446i \(0.846972\pi\)
\(648\) 0 0
\(649\) 10.9935 0.431532
\(650\) 0 0
\(651\) 54.5229 2.13692
\(652\) 0 0
\(653\) −16.9341 29.3308i −0.662684 1.14780i −0.979908 0.199451i \(-0.936084\pi\)
0.317224 0.948351i \(-0.397249\pi\)
\(654\) 0 0
\(655\) 1.34637i 0.0526071i
\(656\) 0 0
\(657\) −1.99348 1.15094i −0.0777730 0.0449023i
\(658\) 0 0
\(659\) −13.2246 + 22.9056i −0.515155 + 0.892275i 0.484690 + 0.874686i \(0.338932\pi\)
−0.999845 + 0.0175892i \(0.994401\pi\)
\(660\) 0 0
\(661\) −26.3259 + 15.1993i −1.02396 + 0.591182i −0.915248 0.402891i \(-0.868005\pi\)
−0.108710 + 0.994074i \(0.534672\pi\)
\(662\) 0 0
\(663\) 37.3736 + 21.8520i 1.45147 + 0.848660i
\(664\) 0 0
\(665\) −20.1542 + 11.6360i −0.781545 + 0.451225i
\(666\) 0 0
\(667\) 1.17517 2.03546i 0.0455029 0.0788134i
\(668\) 0 0
\(669\) 23.5302 + 13.5851i 0.909729 + 0.525232i
\(670\) 0 0
\(671\) 6.41393i 0.247607i
\(672\) 0 0
\(673\) −18.1976 31.5192i −0.701467 1.21498i −0.967952 0.251137i \(-0.919196\pi\)
0.266485 0.963839i \(-0.414138\pi\)
\(674\) 0 0
\(675\) 5.50367 0.211836
\(676\) 0 0
\(677\) 36.0043 1.38376 0.691880 0.722013i \(-0.256783\pi\)
0.691880 + 0.722013i \(0.256783\pi\)
\(678\) 0 0
\(679\) −6.08726 10.5435i −0.233608 0.404620i
\(680\) 0 0
\(681\) 3.84130i 0.147199i
\(682\) 0 0
\(683\) −11.1107 6.41478i −0.425140 0.245455i 0.272134 0.962259i \(-0.412271\pi\)
−0.697274 + 0.716805i \(0.745604\pi\)
\(684\) 0 0
\(685\) 6.18640 10.7152i 0.236370 0.409405i
\(686\) 0 0
\(687\) −10.1950 + 5.88609i −0.388964 + 0.224568i
\(688\) 0 0
\(689\) 39.3649 + 23.0162i 1.49968 + 0.876849i
\(690\) 0 0
\(691\) 28.5608 16.4896i 1.08650 0.627294i 0.153861 0.988092i \(-0.450829\pi\)
0.932644 + 0.360799i \(0.117496\pi\)
\(692\) 0 0
\(693\) 1.64846 2.85521i 0.0626197 0.108461i
\(694\) 0 0
\(695\) −7.59362 4.38418i −0.288043 0.166301i
\(696\) 0 0
\(697\) 58.0188i 2.19762i
\(698\) 0 0
\(699\) 2.69961 + 4.67586i 0.102109 + 0.176857i
\(700\) 0 0
\(701\) 40.7352 1.53855 0.769273 0.638921i \(-0.220619\pi\)
0.769273 + 0.638921i \(0.220619\pi\)
\(702\) 0 0
\(703\) −51.2076 −1.93133
\(704\) 0 0
\(705\) 2.77162 + 4.80059i 0.104385 + 0.180801i
\(706\) 0 0
\(707\) 28.7651i 1.08182i
\(708\) 0 0
\(709\) −15.2932 8.82956i −0.574350 0.331601i 0.184535 0.982826i \(-0.440922\pi\)
−0.758885 + 0.651225i \(0.774255\pi\)
\(710\) 0 0
\(711\) −1.79422 + 3.10769i −0.0672886 + 0.116547i
\(712\) 0 0
\(713\) 7.90658 4.56487i 0.296104 0.170956i
\(714\) 0 0
\(715\) 0.0342681 6.24490i 0.00128156 0.233546i
\(716\) 0 0
\(717\) −32.9555 + 19.0269i −1.23074 + 0.710571i
\(718\) 0 0
\(719\) 24.7836 42.9265i 0.924273 1.60089i 0.131546 0.991310i \(-0.458006\pi\)
0.792727 0.609577i \(-0.208661\pi\)
\(720\) 0 0
\(721\) 27.6737 + 15.9774i 1.03062 + 0.595031i
\(722\) 0 0
\(723\) 35.7183i 1.32838i
\(724\) 0 0
\(725\) −1.01236 1.75347i −0.0375983 0.0651221i
\(726\) 0 0
\(727\) −36.4738 −1.35274 −0.676370 0.736562i \(-0.736448\pi\)
−0.676370 + 0.736562i \(0.736448\pi\)
\(728\) 0 0
\(729\) 29.7112 1.10042
\(730\) 0 0
\(731\) −15.7035 27.1993i −0.580815 1.00600i
\(732\) 0 0
\(733\) 28.8491i 1.06556i 0.846252 + 0.532782i \(0.178854\pi\)
−0.846252 + 0.532782i \(0.821146\pi\)
\(734\) 0 0
\(735\) 16.3087 + 9.41584i 0.601556 + 0.347308i
\(736\) 0 0
\(737\) −4.55568 + 7.89067i −0.167811 + 0.290657i
\(738\) 0 0
\(739\) 17.1330 9.89173i 0.630247 0.363873i −0.150601 0.988595i \(-0.548121\pi\)
0.780848 + 0.624721i \(0.214787\pi\)
\(740\) 0 0
\(741\) −15.6436 + 26.7554i −0.574683 + 0.982885i
\(742\) 0 0
\(743\) −22.8635 + 13.2003i −0.838781 + 0.484271i −0.856850 0.515566i \(-0.827582\pi\)
0.0180685 + 0.999837i \(0.494248\pi\)
\(744\) 0 0
\(745\) −2.36970 + 4.10443i −0.0868190 + 0.150375i
\(746\) 0 0
\(747\) −0.173801 0.100344i −0.00635905 0.00367140i
\(748\) 0 0
\(749\) 34.2826i 1.25266i
\(750\) 0 0
\(751\) −6.90171 11.9541i −0.251847 0.436212i 0.712187 0.701990i \(-0.247705\pi\)
−0.964034 + 0.265778i \(0.914371\pi\)
\(752\) 0 0
\(753\) 7.39671 0.269551
\(754\) 0 0
\(755\) 1.56063 0.0567970
\(756\) 0 0
\(757\) 2.59080 + 4.48739i 0.0941642 + 0.163097i 0.909259 0.416230i \(-0.136649\pi\)
−0.815095 + 0.579327i \(0.803315\pi\)
\(758\) 0 0
\(759\) 3.21736i 0.116783i
\(760\) 0 0
\(761\) 0.00743288 + 0.00429137i 0.000269442 + 0.000155562i 0.500135 0.865948i \(-0.333284\pi\)
−0.499865 + 0.866103i \(0.666617\pi\)
\(762\) 0 0
\(763\) 19.8915 34.4531i 0.720121 1.24729i
\(764\) 0 0
\(765\) 2.85521 1.64846i 0.103230 0.0596001i
\(766\) 0 0
\(767\) −11.3335 19.8813i −0.409227 0.717871i
\(768\) 0 0
\(769\) 10.2610 5.92417i 0.370020 0.213631i −0.303447 0.952848i \(-0.598138\pi\)
0.673467 + 0.739217i \(0.264804\pi\)
\(770\) 0 0
\(771\) 17.4933 30.2992i 0.630005 1.09120i
\(772\) 0 0
\(773\) −18.2262 10.5229i −0.655550 0.378482i 0.135030 0.990842i \(-0.456887\pi\)
−0.790579 + 0.612360i \(0.790220\pi\)
\(774\) 0 0
\(775\) 7.86488i 0.282515i
\(776\) 0 0
\(777\) 33.0422 + 57.2308i 1.18538 + 2.05314i
\(778\) 0 0
\(779\) 41.5352 1.48815
\(780\) 0 0
\(781\) −21.6754 −0.775605
\(782\) 0 0
\(783\) −5.57172 9.65050i −0.199117 0.344881i
\(784\) 0 0
\(785\) 9.15332i 0.326696i
\(786\) 0 0
\(787\) −4.34029 2.50587i −0.154715 0.0893246i 0.420644 0.907226i \(-0.361804\pi\)
−0.575359 + 0.817901i \(0.695138\pi\)
\(788\) 0 0
\(789\) 16.1452 27.9643i 0.574784 0.995556i
\(790\) 0 0
\(791\) 21.6701 12.5112i 0.770499 0.444848i
\(792\) 0 0
\(793\) 11.5993 6.61228i 0.411904 0.234809i
\(794\) 0 0
\(795\) −17.5265 + 10.1189i