Properties

Label 260.2.x.a.121.2
Level $260$
Weight $2$
Character 260.121
Analytic conductor $2.076$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 121.2
Root \(-1.27597 - 0.609843i\) of defining polynomial
Character \(\chi\) \(=\) 260.121
Dual form 260.2.x.a.101.2

$q$-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 \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

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

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 −0.999057 0.0434075i \(-0.986179\pi\)
0.537121 + 0.843505i \(0.319512\pi\)
\(4\) 0 0
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) 3.75184 2.16612i 1.41806 0.818718i 0.421932 0.906627i \(-0.361352\pi\)
0.996128 + 0.0879098i \(0.0280187\pi\)
\(8\) 0 0
\(9\) 0.219687 + 0.380509i 0.0732290 + 0.126836i
\(10\) 0 0
\(11\) 1.50000 + 0.866025i 0.452267 + 0.261116i 0.708787 0.705422i \(-0.249243\pi\)
−0.256520 + 0.966539i \(0.582576\pi\)
\(12\) 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 0.814126 + 0.580688i \(0.197216\pi\)
0.0958278 + 0.995398i \(0.469450\pi\)
\(18\) 0 0
\(19\) 4.65213 2.68591i 1.06727 0.616190i 0.139837 0.990175i \(-0.455342\pi\)
0.927435 + 0.373985i \(0.122009\pi\)
\(20\) 0 0
\(21\) 6.93244i 1.51278i
\(22\) 0 0
\(23\) −0.580411 + 1.00530i −0.121024 + 0.209620i −0.920172 0.391515i \(-0.871951\pi\)
0.799148 + 0.601135i \(0.205284\pi\)
\(24\) 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 −0.756589 0.653891i \(-0.773136\pi\)
0.944580 + 0.328280i \(0.106469\pi\)
\(30\) 0 0
\(31\) 7.86488i 1.41257i −0.707925 0.706287i \(-0.750369\pi\)
0.707925 0.706287i \(-0.249631\pi\)
\(32\) 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 −0.367952 0.929845i \(-0.619941\pi\)
−0.989245 + 0.146267i \(0.953274\pi\)
\(38\) 0 0
\(39\) −0.0316594 5.76950i −0.00506956 0.923860i
\(40\) 0 0
\(41\) 6.69615 + 3.86603i 1.04576 + 0.603772i 0.921460 0.388473i \(-0.126997\pi\)
0.124303 + 0.992244i \(0.460331\pi\)
\(42\) 0 0
\(43\) 2.09277 + 3.62479i 0.319145 + 0.552776i 0.980310 0.197465i \(-0.0632709\pi\)
−0.661165 + 0.750241i \(0.729938\pi\)
\(44\) 0 0
\(45\) 0.380509 0.219687i 0.0567229 0.0327490i
\(46\) 0 0
\(47\) 3.46410i 0.505291i −0.967559 0.252646i \(-0.918699\pi\)
0.967559 0.252646i \(-0.0813007\pi\)
\(48\) 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 −0.0975219 0.995233i \(-0.531092\pi\)
0.813136 + 0.582073i \(0.197758\pi\)
\(60\) 0 0
\(61\) −1.85154 3.20696i −0.237066 0.410610i 0.722805 0.691052i \(-0.242852\pi\)
−0.959871 + 0.280442i \(0.909519\pi\)
\(62\) 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 0.195200 0.980763i \(-0.437464\pi\)
−0.751766 + 0.659430i \(0.770798\pi\)
\(68\) 0 0
\(69\) −0.928771 1.60868i −0.111811 0.193662i
\(70\) 0 0
\(71\) −10.8377 + 6.25714i −1.28620 + 0.742586i −0.977974 0.208729i \(-0.933067\pi\)
−0.308222 + 0.951314i \(0.599734\pi\)
\(72\) 0 0
\(73\) 5.23898i 0.613177i 0.951842 + 0.306588i \(0.0991875\pi\)
−0.951842 + 0.306588i \(0.900813\pi\)
\(74\) 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 \(0.00798021\pi\)
−0.999686 + 0.0250679i \(0.992020\pi\)
\(84\) 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 −0.254022 0.967198i \(-0.581754\pi\)
−0.964630 + 0.263609i \(0.915087\pi\)
\(90\) 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 −0.618439 0.785833i \(-0.712234\pi\)
0.371332 + 0.928500i \(0.378901\pi\)
\(98\) 0 0
\(99\) 0.761018i 0.0764852i
\(100\) 0 0
\(101\) −3.31988 + 5.75021i −0.330341 + 0.572167i −0.982579 0.185847i \(-0.940497\pi\)
0.652238 + 0.758014i \(0.273830\pi\)
\(102\) 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 −0.608913 0.793237i \(-0.708394\pi\)
0.991420 + 0.130716i \(0.0417275\pi\)
\(108\) 0 0
\(109\) 9.18301i 0.879572i 0.898102 + 0.439786i \(0.144946\pi\)
−0.898102 + 0.439786i \(0.855054\pi\)
\(110\) 0 0
\(111\) 13.2104 7.62704i 1.25388 0.723927i
\(112\) 0 0
\(113\) 2.88793 + 5.00204i 0.271674 + 0.470552i 0.969291 0.245919i \(-0.0790896\pi\)
−0.697617 + 0.716471i \(0.745756\pi\)
\(114\) 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 −0.0470176 0.998894i \(-0.514972\pi\)
0.888576 0.458729i \(-0.151695\pi\)
\(128\) 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 −0.882183 0.470907i \(-0.843927\pi\)
−0.0332744 + 0.999446i \(0.510594\pi\)
\(138\) 0 0
\(139\) −4.38418 7.59362i −0.371861 0.644083i 0.617991 0.786185i \(-0.287947\pi\)
−0.989852 + 0.142103i \(0.954614\pi\)
\(140\) 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 −0.322363 0.946616i \(-0.604477\pi\)
0.658612 + 0.752483i \(0.271144\pi\)
\(150\) 0 0
\(151\) 1.56063i 0.127002i 0.997982 + 0.0635010i \(0.0202266\pi\)
−0.997982 + 0.0635010i \(0.979773\pi\)
\(152\) 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 −0.407673 0.913128i \(-0.633660\pi\)
0.586956 + 0.809619i \(0.300326\pi\)
\(164\) 0 0
\(165\) 1.38581 + 2.40029i 0.107885 + 0.186863i
\(166\) 0 0
\(167\) 7.71515 + 4.45435i 0.597017 + 0.344688i 0.767867 0.640609i \(-0.221318\pi\)
−0.170850 + 0.985297i \(0.554651\pi\)
\(168\) 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 0.999580 + 0.0289933i \(0.00923014\pi\)
−0.474681 + 0.880158i \(0.657437\pi\)
\(174\) 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 −0.0959612 + 0.995385i \(0.530592\pi\)
−0.814048 + 0.580797i \(0.802741\pi\)
\(180\) 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 0.737622 0.675214i \(-0.235949\pi\)
−0.953564 + 0.301192i \(0.902615\pi\)
\(192\) 0 0
\(193\) −7.83988 4.52636i −0.564327 0.325814i 0.190553 0.981677i \(-0.438972\pi\)
−0.754880 + 0.655862i \(0.772305\pi\)
\(194\) 0 0
\(195\) −5.76950 + 0.0316594i −0.413163 + 0.00226718i
\(196\) 0 0
\(197\) −9.86320 5.69452i −0.702724 0.405718i 0.105637 0.994405i \(-0.466312\pi\)
−0.808361 + 0.588687i \(0.799645\pi\)
\(198\) 0 0
\(199\) 5.38863 + 9.33339i 0.381990 + 0.661626i 0.991347 0.131270i \(-0.0419055\pi\)
−0.609357 + 0.792896i \(0.708572\pi\)
\(200\) 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 −0.805166 0.593050i \(-0.797924\pi\)
0.916179 + 0.400769i \(0.131257\pi\)
\(212\) 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 −0.0810069 0.996714i \(-0.525814\pi\)
−0.903683 + 0.428203i \(0.859147\pi\)
\(224\) 0 0
\(225\) −0.219687 0.380509i −0.0146458 0.0253673i
\(226\) 0 0
\(227\) 2.07891 1.20026i 0.137982 0.0796641i −0.429420 0.903105i \(-0.641282\pi\)
0.567402 + 0.823441i \(0.307949\pi\)
\(228\) 0 0
\(229\) 7.35671i 0.486145i 0.970008 + 0.243073i \(0.0781553\pi\)
−0.970008 + 0.243073i \(0.921845\pi\)
\(230\) 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 \(0.279306\pi\)
−0.639103 + 0.769121i \(0.720694\pi\)
\(240\) 0 0
\(241\) 19.3307 11.1606i 1.24520 0.718918i 0.275054 0.961429i \(-0.411304\pi\)
0.970149 + 0.242511i \(0.0779709\pi\)
\(242\) 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 0.783820 0.620988i \(-0.213268\pi\)
−0.929701 + 0.368314i \(0.879935\pi\)
\(252\) 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 −0.292479 0.956272i \(-0.594480\pi\)
0.974395 0.224842i \(-0.0721866\pi\)
\(258\) 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 −0.366939 0.930245i \(-0.619594\pi\)
0.989085 0.147344i \(-0.0470724\pi\)
\(264\) 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 0.733315 0.679889i \(-0.237972\pi\)
−0.955459 + 0.295124i \(0.904639\pi\)
\(270\) 0 0
\(271\) −4.23650 2.44595i −0.257349 0.148581i 0.365775 0.930703i \(-0.380804\pi\)
−0.623125 + 0.782122i \(0.714137\pi\)
\(272\) 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 0.967403 0.253241i \(-0.0814967\pi\)
−0.703015 + 0.711175i \(0.748163\pi\)
\(278\) 0 0
\(279\) 2.99266 1.72781i 0.179166 0.103441i
\(280\) 0 0
\(281\) 12.6085i 0.752161i −0.926587 0.376081i \(-0.877272\pi\)
0.926587 0.376081i \(-0.122728\pi\)
\(282\) 0 0
\(283\) −10.4505 + 18.1007i −0.621216 + 1.07598i 0.368044 + 0.929808i \(0.380028\pi\)
−0.989260 + 0.146169i \(0.953306\pi\)
\(284\) 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 −0.517415 0.855734i \(-0.673106\pi\)
0.482380 + 0.875962i \(0.339772\pi\)
\(294\) 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 \(0.0810966\pi\)
−0.967721 + 0.252025i \(0.918903\pi\)
\(308\) 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 \(-0.995020\pi\)
0.999878 0.0156450i \(-0.00498017\pi\)
\(318\) 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 −0.402687 0.915338i \(-0.631924\pi\)
0.591363 + 0.806406i \(0.298590\pi\)
\(332\) 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 0.746167 0.665759i \(-0.231892\pi\)
−0.949648 + 0.313320i \(0.898559\pi\)
\(348\) 0 0
\(349\) 23.6733 + 13.6678i 1.26720 + 0.731621i 0.974458 0.224569i \(-0.0720975\pi\)
0.292746 + 0.956190i \(0.405431\pi\)
\(350\) 0 0
\(351\) 17.1305 10.0160i 0.914359 0.534616i
\(352\) 0 0
\(353\) 22.5964 + 13.0461i 1.20269 + 0.694372i 0.961152 0.276020i \(-0.0890156\pi\)
0.241536 + 0.970392i \(0.422349\pi\)
\(354\) 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 \(0.00583132\pi\)
−0.999832 + 0.0183186i \(0.994169\pi\)
\(360\) 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 0.397812 + 0.917467i \(0.369770\pi\)
−0.993456 + 0.114218i \(0.963564\pi\)
\(368\) 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 0.949826 0.312779i \(-0.101260\pi\)
−0.745787 + 0.666184i \(0.767926\pi\)
\(374\) 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 0.992789 0.119875i \(-0.0382494\pi\)
0.392580 + 0.919718i \(0.371583\pi\)
\(380\) 0 0
\(381\) 15.1761 + 26.2857i 0.777494 + 1.34666i
\(382\) 0 0
\(383\) 29.8885 17.2561i 1.52723 0.881747i 0.527754 0.849397i \(-0.323034\pi\)
0.999477 0.0323495i \(-0.0102990\pi\)
\(384\) 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 0.0810459 0.996710i \(-0.474174\pi\)
0.903699 + 0.428167i \(0.140841\pi\)
\(398\) 0 0
\(399\) 18.6199 + 32.2506i 0.932161 + 1.61455i
\(400\) 0 0
\(401\) 3.35847 + 1.93902i 0.167714 + 0.0968298i 0.581508 0.813541i \(-0.302463\pi\)
−0.413793 + 0.910371i \(0.635796\pi\)
\(402\) 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 −0.172954 0.984930i \(-0.555331\pi\)
0.766497 + 0.642248i \(0.221998\pi\)
\(410\) 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 −0.210528 0.977588i \(-0.567518\pi\)
0.951880 0.306471i \(-0.0991484\pi\)
\(420\) 0 0
\(421\) 0.608516i 0.0296573i 0.999890 + 0.0148286i \(0.00472027\pi\)
−0.999890 + 0.0148286i \(0.995280\pi\)
\(422\) 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 −0.980240 0.197810i \(-0.936617\pi\)
−0.661429 0.750008i \(-0.730050\pi\)
\(432\) 0 0
\(433\) 3.21474 + 5.56810i 0.154491 + 0.267586i 0.932873 0.360204i \(-0.117293\pi\)
−0.778383 + 0.627790i \(0.783960\pi\)
\(434\) 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 −0.847934 0.530101i \(-0.822154\pi\)
0.883048 + 0.469282i \(0.155487\pi\)
\(440\) 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 −0.674600 0.738183i \(-0.735684\pi\)
0.301985 + 0.953313i \(0.402351\pi\)
\(450\) 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 0.100293 0.994958i \(-0.468022\pi\)
−0.811512 + 0.584335i \(0.801355\pi\)
\(458\) 0 0
\(459\) −20.6489 35.7649i −0.963807 1.66936i
\(460\) 0 0
\(461\) −13.2973 + 7.67722i −0.619318 + 0.357564i −0.776604 0.629990i \(-0.783059\pi\)
0.157285 + 0.987553i \(0.449726\pi\)
\(462\) 0 0
\(463\) 18.8614i 0.876562i −0.898838 0.438281i \(-0.855588\pi\)
0.898838 0.438281i \(-0.144412\pi\)
\(464\) 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 0.118308 0.992977i \(-0.462253\pi\)
−0.800789 + 0.598946i \(0.795586\pi\)
\(480\) 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 −0.809346 0.587331i \(-0.800178\pi\)
0.103971 + 0.994580i \(0.466845\pi\)
\(488\) 0 0
\(489\) 4.22936i 0.191258i
\(490\) 0 0
\(491\) 13.0977 22.6858i 0.591089 1.02380i −0.402997 0.915201i \(-0.632032\pi\)
0.994086 0.108595i \(-0.0346350\pi\)
\(492\) 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 \(-0.865330\pi\)
0.911829 0.410569i \(-0.134670\pi\)
\(500\) 0 0
\(501\) −12.3458 + 7.12783i −0.551568 + 0.318448i
\(502\) 0 0
\(503\) 7.12811 + 12.3462i 0.317827 + 0.550492i 0.980034 0.198829i \(-0.0637137\pi\)
−0.662208 + 0.749320i \(0.730380\pi\)
\(504\) 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 0.965046 0.262081i \(-0.0844086\pi\)
0.255555 + 0.966795i \(0.417742\pi\)
\(510\) 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 0.425513 + 0.904952i \(0.360094\pi\)
−0.996468 + 0.0839712i \(0.973240\pi\)
\(524\) 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 \(0.236550\pi\)
−0.736344 + 0.676607i \(0.763450\pi\)
\(542\) 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 0.831406 0.555665i \(-0.187536\pi\)
−0.0655165 + 0.997851i \(0.520870\pi\)
\(558\) 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 −0.968372 0.249513i \(-0.919730\pi\)
0.268102 0.963391i \(-0.413604\pi\)
\(564\) 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 0.0501680 + 0.998741i \(0.484024\pi\)
−0.890019 + 0.455924i \(0.849309\pi\)
\(570\) 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 \(-0.737573\pi\)
0.678968 0.734168i \(-0.262427\pi\)
\(578\) 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 −0.471991 0.881603i \(-0.656464\pi\)
−0.999486 + 0.0320457i \(0.989798\pi\)
\(588\) 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 \(0.0618054\pi\)
−0.981209 + 0.192950i \(0.938195\pi\)
\(594\) 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 0.488058 + 0.872811i \(0.337706\pi\)
−0.999906 + 0.0137352i \(0.995628\pi\)
\(602\) 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 0.971983 + 0.235052i \(0.0755259\pi\)
−0.282431 + 0.959288i \(0.591141\pi\)
\(608\) 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 0.825760 0.564022i \(-0.190747\pi\)
−0.0755778 + 0.997140i \(0.524080\pi\)
\(614\) 0 0
\(615\) 6.18640 + 10.7152i 0.249460 + 0.432077i
\(616\) 0 0
\(617\) 29.5092 17.0372i 1.18800 0.685890i 0.230146 0.973156i \(-0.426080\pi\)
0.957851 + 0.287266i \(0.0927464\pi\)
\(618\) 0 0
\(619\) 26.9791i 1.08438i −0.840256 0.542191i \(-0.817595\pi\)
0.840256 0.542191i \(-0.182405\pi\)
\(620\) 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 −0.981960 0.189090i \(-0.939446\pi\)
−0.327223 + 0.944947i \(0.606113\pi\)
\(632\) 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 0.772967 0.634446i \(-0.218772\pi\)
−0.935930 + 0.352186i \(0.885439\pi\)
\(642\) 0 0
\(643\) 41.6992 24.0750i 1.64446 0.949427i 0.665233 0.746636i \(-0.268332\pi\)
0.979222 0.202791i \(-0.0650011\pi\)
\(644\) 0 0
\(645\) 6.69770i 0.263722i
\(646\) 0 0
\(647\) −1.08951 + 1.88709i −0.0428332 + 0.0741893i −0.886647 0.462446i \(-0.846972\pi\)
0.843814 + 0.536636i \(0.180305\pi\)
\(648\) 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 0.317224 + 0.948351i \(0.397249\pi\)
−0.979908 + 0.199451i \(0.936084\pi\)
\(654\) 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 −0.999845 0.0175892i \(-0.994401\pi\)
0.484690 0.874686i \(-0.338932\pi\)
\(660\) 0 0
\(661\) −26.3259 15.1993i −1.02396 0.591182i −0.108710 0.994074i \(-0.534672\pi\)
−0.915248 + 0.402891i \(0.868005\pi\)
\(662\) 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 0.266485 + 0.963839i \(0.414138\pi\)
−0.967952 + 0.251137i \(0.919196\pi\)
\(674\) 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 −0.697274 0.716805i \(-0.745604\pi\)
0.272134 + 0.962259i \(0.412271\pi\)
\(684\) 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 0.932644 0.360799i \(-0.117496\pi\)
0.153861 + 0.988092i \(0.450829\pi\)
\(692\) 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 −0.758885 0.651225i \(-0.774255\pi\)
0.184535 + 0.982826i \(0.440922\pi\)
\(710\) 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 0.792727 + 0.609577i \(0.208661\pi\)
0.131546 + 0.991310i \(0.458006\pi\)
\(720\) 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 \(-0.821146\pi\)
0.846252 0.532782i \(-0.178854\pi\)
\(734\) 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 0.780848 0.624721i \(-0.214787\pi\)
−0.150601 + 0.988595i \(0.548121\pi\)
\(740\) 0 0
\(741\) −15.6436 26.7554i −0.574683 0.982885i
\(742\) 0 0
\(743\) −22.8635 13.2003i −0.838781 0.484271i 0.0180685 0.999837i \(-0.494248\pi\)
−0.856850 + 0.515566i \(0.827582\pi\)
\(744\) 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 −0.964034 0.265778i \(-0.914371\pi\)
0.712187 + 0.701990i \(0.247705\pi\)
\(752\) 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 −0.815095 0.579327i \(-0.803315\pi\)
0.909259 + 0.416230i \(0.136649\pi\)
\(758\) 0 0
\(759\) 3.21736i 0.116783i
\(760\) 0 0
\(761\) 0.00743288 0.00429137i 0.000269442 0.000155562i −0.499865 0.866103i \(-0.666617\pi\)
0.500135 + 0.865948i \(0.333284\pi\)
\(762\) 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 0.673467 0.739217i \(-0.264804\pi\)
−0.303447 + 0.952848i \(0.598138\pi\)
\(770\) 0 0
\(771\) 17.4933 + 30.2992i 0.630005 + 1.09120i
\(772\) 0 0
\(773\) −18.2262 + 10.5229i −0.655550 + 0.378482i −0.790579 0.612360i \(-0.790220\pi\)
0.135030 + 0.990842i \(0.456887\pi\)
\(774\) 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 −0.575359 0.817901i \(-0.695138\pi\)
0.420644 + 0.907226i \(0.361804\pi\)
\(788\) 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