Properties

Label 1008.2.r.k.337.3
Level 1008
Weight 2
Character 1008.337
Analytic conductor 8.049
Analytic rank 0
Dimension 6
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 337.3
Root \(0.500000 + 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 1008.337
Dual form 1008.2.r.k.673.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.73025 + 0.0789082i) q^{3} +(1.29679 - 2.24611i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(2.98755 + 0.273062i) q^{9} +O(q^{10})\) \(q+(1.73025 + 0.0789082i) q^{3} +(1.29679 - 2.24611i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(2.98755 + 0.273062i) q^{9} +(2.25729 + 3.90975i) q^{11} +(-0.500000 + 0.866025i) q^{13} +(2.42101 - 3.78400i) q^{15} -0.945916 q^{17} +4.05408 q^{19} +(-0.796790 - 1.53790i) q^{21} +(-0.136673 + 0.236725i) q^{23} +(-0.863327 - 1.49533i) q^{25} +(5.14766 + 0.708209i) q^{27} +(-1.23025 - 2.13086i) q^{29} +(1.16372 - 2.01561i) q^{31} +(3.59718 + 6.94297i) q^{33} -2.59358 q^{35} +1.78074 q^{37} +(-0.933463 + 1.45899i) q^{39} +(3.20321 - 5.54812i) q^{41} +(-5.21780 - 9.03749i) q^{43} +(4.48755 - 6.35624i) q^{45} +(-6.08113 - 10.5328i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-1.63667 - 0.0746406i) q^{51} -6.27335 q^{53} +11.7089 q^{55} +(7.01459 + 0.319901i) q^{57} +(-1.36333 + 2.36135i) q^{59} +(1.13667 + 1.96878i) q^{61} +(-1.25729 - 2.72382i) q^{63} +(1.29679 + 2.24611i) q^{65} +(-7.90856 + 13.6980i) q^{67} +(-0.255158 + 0.398809i) q^{69} -3.27335 q^{71} -1.50739 q^{73} +(-1.37578 - 2.65542i) q^{75} +(2.25729 - 3.90975i) q^{77} +(7.35447 + 12.7383i) q^{79} +(8.85087 + 1.63157i) q^{81} +(-0.472958 - 0.819187i) q^{83} +(-1.22665 + 2.12463i) q^{85} +(-1.96050 - 3.78400i) q^{87} -14.3566 q^{89} +1.00000 q^{91} +(2.17257 - 3.39569i) q^{93} +(5.25729 - 9.10590i) q^{95} +(5.74484 + 9.95036i) q^{97} +(5.67617 + 12.2969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 4q^{3} + 5q^{5} - 3q^{7} - 4q^{9} + O(q^{10}) \) \( 6q + 4q^{3} + 5q^{5} - 3q^{7} - 4q^{9} - 2q^{11} - 3q^{13} - 11q^{15} - 24q^{17} + 6q^{19} - 2q^{21} - 6q^{25} + 7q^{27} - q^{29} - 3q^{31} + 8q^{33} - 10q^{35} - 6q^{37} - 2q^{39} + 22q^{41} - 3q^{43} + 5q^{45} - 9q^{47} - 3q^{49} - 9q^{51} - 36q^{53} + 12q^{55} + 11q^{57} - 9q^{59} + 6q^{61} + 8q^{63} + 5q^{65} - 39q^{69} - 18q^{71} + 6q^{73} - 31q^{75} - 2q^{77} + 15q^{79} + 32q^{81} - 12q^{83} - 9q^{85} + q^{87} - 4q^{89} + 6q^{91} + 33q^{93} + 16q^{95} - 3q^{97} + 46q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0
\(3\) 1.73025 + 0.0789082i 0.998962 + 0.0455577i
\(4\) 0 0
\(5\) 1.29679 2.24611i 0.579942 1.00449i −0.415543 0.909573i \(-0.636409\pi\)
0.995485 0.0949156i \(-0.0302581\pi\)
\(6\) 0 0
\(7\) −0.500000 0.866025i −0.188982 0.327327i
\(8\) 0 0
\(9\) 2.98755 + 0.273062i 0.995849 + 0.0910208i
\(10\) 0 0
\(11\) 2.25729 + 3.90975i 0.680600 + 1.17883i 0.974798 + 0.223089i \(0.0716141\pi\)
−0.294198 + 0.955744i \(0.595053\pi\)
\(12\) 0 0
\(13\) −0.500000 + 0.866025i −0.138675 + 0.240192i −0.926995 0.375073i \(-0.877618\pi\)
0.788320 + 0.615265i \(0.210951\pi\)
\(14\) 0 0
\(15\) 2.42101 3.78400i 0.625102 0.977025i
\(16\) 0 0
\(17\) −0.945916 −0.229418 −0.114709 0.993399i \(-0.536594\pi\)
−0.114709 + 0.993399i \(0.536594\pi\)
\(18\) 0 0
\(19\) 4.05408 0.930071 0.465035 0.885292i \(-0.346042\pi\)
0.465035 + 0.885292i \(0.346042\pi\)
\(20\) 0 0
\(21\) −0.796790 1.53790i −0.173874 0.335597i
\(22\) 0 0
\(23\) −0.136673 + 0.236725i −0.0284983 + 0.0493605i −0.879923 0.475117i \(-0.842406\pi\)
0.851425 + 0.524477i \(0.175739\pi\)
\(24\) 0 0
\(25\) −0.863327 1.49533i −0.172665 0.299065i
\(26\) 0 0
\(27\) 5.14766 + 0.708209i 0.990668 + 0.136295i
\(28\) 0 0
\(29\) −1.23025 2.13086i −0.228452 0.395691i 0.728897 0.684623i \(-0.240033\pi\)
−0.957350 + 0.288932i \(0.906700\pi\)
\(30\) 0 0
\(31\) 1.16372 2.01561i 0.209009 0.362015i −0.742393 0.669964i \(-0.766309\pi\)
0.951403 + 0.307949i \(0.0996427\pi\)
\(32\) 0 0
\(33\) 3.59718 + 6.94297i 0.626188 + 1.20862i
\(34\) 0 0
\(35\) −2.59358 −0.438395
\(36\) 0 0
\(37\) 1.78074 0.292752 0.146376 0.989229i \(-0.453239\pi\)
0.146376 + 0.989229i \(0.453239\pi\)
\(38\) 0 0
\(39\) −0.933463 + 1.45899i −0.149474 + 0.233625i
\(40\) 0 0
\(41\) 3.20321 5.54812i 0.500257 0.866471i −0.499743 0.866174i \(-0.666572\pi\)
1.00000 0.000297253i \(-9.46187e-5\pi\)
\(42\) 0 0
\(43\) −5.21780 9.03749i −0.795707 1.37820i −0.922389 0.386262i \(-0.873766\pi\)
0.126682 0.991943i \(-0.459567\pi\)
\(44\) 0 0
\(45\) 4.48755 6.35624i 0.668964 0.947533i
\(46\) 0 0
\(47\) −6.08113 10.5328i −0.887023 1.53637i −0.843377 0.537323i \(-0.819436\pi\)
−0.0436467 0.999047i \(-0.513898\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) 0 0
\(51\) −1.63667 0.0746406i −0.229180 0.0104518i
\(52\) 0 0
\(53\) −6.27335 −0.861710 −0.430855 0.902421i \(-0.641788\pi\)
−0.430855 + 0.902421i \(0.641788\pi\)
\(54\) 0 0
\(55\) 11.7089 1.57883
\(56\) 0 0
\(57\) 7.01459 + 0.319901i 0.929105 + 0.0423719i
\(58\) 0 0
\(59\) −1.36333 + 2.36135i −0.177490 + 0.307422i −0.941020 0.338350i \(-0.890131\pi\)
0.763530 + 0.645772i \(0.223464\pi\)
\(60\) 0 0
\(61\) 1.13667 + 1.96878i 0.145536 + 0.252076i 0.929573 0.368639i \(-0.120176\pi\)
−0.784037 + 0.620714i \(0.786843\pi\)
\(62\) 0 0
\(63\) −1.25729 2.72382i −0.158404 0.343169i
\(64\) 0 0
\(65\) 1.29679 + 2.24611i 0.160847 + 0.278595i
\(66\) 0 0
\(67\) −7.90856 + 13.6980i −0.966184 + 1.67348i −0.259784 + 0.965667i \(0.583651\pi\)
−0.706400 + 0.707813i \(0.749682\pi\)
\(68\) 0 0
\(69\) −0.255158 + 0.398809i −0.0307175 + 0.0480110i
\(70\) 0 0
\(71\) −3.27335 −0.388475 −0.194237 0.980955i \(-0.562223\pi\)
−0.194237 + 0.980955i \(0.562223\pi\)
\(72\) 0 0
\(73\) −1.50739 −0.176427 −0.0882134 0.996102i \(-0.528116\pi\)
−0.0882134 + 0.996102i \(0.528116\pi\)
\(74\) 0 0
\(75\) −1.37578 2.65542i −0.158861 0.306621i
\(76\) 0 0
\(77\) 2.25729 3.90975i 0.257243 0.445557i
\(78\) 0 0
\(79\) 7.35447 + 12.7383i 0.827443 + 1.43317i 0.900038 + 0.435811i \(0.143539\pi\)
−0.0725952 + 0.997361i \(0.523128\pi\)
\(80\) 0 0
\(81\) 8.85087 + 1.63157i 0.983430 + 0.181286i
\(82\) 0 0
\(83\) −0.472958 0.819187i −0.0519139 0.0899175i 0.838901 0.544285i \(-0.183199\pi\)
−0.890815 + 0.454367i \(0.849865\pi\)
\(84\) 0 0
\(85\) −1.22665 + 2.12463i −0.133049 + 0.230448i
\(86\) 0 0
\(87\) −1.96050 3.78400i −0.210188 0.405688i
\(88\) 0 0
\(89\) −14.3566 −1.52180 −0.760899 0.648871i \(-0.775242\pi\)
−0.760899 + 0.648871i \(0.775242\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 2.17257 3.39569i 0.225285 0.352117i
\(94\) 0 0
\(95\) 5.25729 9.10590i 0.539387 0.934246i
\(96\) 0 0
\(97\) 5.74484 + 9.95036i 0.583300 + 1.01031i 0.995085 + 0.0990246i \(0.0315722\pi\)
−0.411785 + 0.911281i \(0.635094\pi\)
\(98\) 0 0
\(99\) 5.67617 + 12.2969i 0.570476 + 1.23589i
\(100\) 0 0
\(101\) 1.83988 + 3.18677i 0.183075 + 0.317096i 0.942926 0.333002i \(-0.108061\pi\)
−0.759851 + 0.650097i \(0.774728\pi\)
\(102\) 0 0
\(103\) −4.86333 + 8.42353i −0.479198 + 0.829995i −0.999715 0.0238560i \(-0.992406\pi\)
0.520518 + 0.853851i \(0.325739\pi\)
\(104\) 0 0
\(105\) −4.48755 0.204655i −0.437940 0.0199723i
\(106\) 0 0
\(107\) 1.37432 0.132860 0.0664301 0.997791i \(-0.478839\pi\)
0.0664301 + 0.997791i \(0.478839\pi\)
\(108\) 0 0
\(109\) −3.39922 −0.325587 −0.162793 0.986660i \(-0.552050\pi\)
−0.162793 + 0.986660i \(0.552050\pi\)
\(110\) 0 0
\(111\) 3.08113 + 0.140515i 0.292448 + 0.0133371i
\(112\) 0 0
\(113\) −5.19436 + 8.99689i −0.488644 + 0.846356i −0.999915 0.0130636i \(-0.995842\pi\)
0.511271 + 0.859420i \(0.329175\pi\)
\(114\) 0 0
\(115\) 0.354473 + 0.613964i 0.0330547 + 0.0572525i
\(116\) 0 0
\(117\) −1.73025 + 2.45076i −0.159962 + 0.226573i
\(118\) 0 0
\(119\) 0.472958 + 0.819187i 0.0433560 + 0.0750948i
\(120\) 0 0
\(121\) −4.69076 + 8.12463i −0.426432 + 0.738603i
\(122\) 0 0
\(123\) 5.98016 9.34689i 0.539212 0.842781i
\(124\) 0 0
\(125\) 8.48968 0.759340
\(126\) 0 0
\(127\) −0.672570 −0.0596809 −0.0298405 0.999555i \(-0.509500\pi\)
−0.0298405 + 0.999555i \(0.509500\pi\)
\(128\) 0 0
\(129\) −8.31498 16.0489i −0.732093 1.41302i
\(130\) 0 0
\(131\) 3.95691 6.85356i 0.345717 0.598799i −0.639767 0.768569i \(-0.720969\pi\)
0.985484 + 0.169770i \(0.0543026\pi\)
\(132\) 0 0
\(133\) −2.02704 3.51094i −0.175767 0.304437i
\(134\) 0 0
\(135\) 8.26615 10.6438i 0.711437 0.916072i
\(136\) 0 0
\(137\) 1.83628 + 3.18054i 0.156884 + 0.271732i 0.933744 0.357943i \(-0.116522\pi\)
−0.776859 + 0.629674i \(0.783188\pi\)
\(138\) 0 0
\(139\) −1.02704 + 1.77889i −0.0871126 + 0.150883i −0.906289 0.422658i \(-0.861097\pi\)
0.819177 + 0.573541i \(0.194431\pi\)
\(140\) 0 0
\(141\) −9.69076 18.7043i −0.816109 1.57519i
\(142\) 0 0
\(143\) −4.51459 −0.377529
\(144\) 0 0
\(145\) −6.38151 −0.529956
\(146\) 0 0
\(147\) −0.933463 + 1.45899i −0.0769907 + 0.120335i
\(148\) 0 0
\(149\) 6.77188 11.7292i 0.554774 0.960897i −0.443147 0.896449i \(-0.646138\pi\)
0.997921 0.0644482i \(-0.0205287\pi\)
\(150\) 0 0
\(151\) 4.96410 + 8.59808i 0.403973 + 0.699702i 0.994201 0.107535i \(-0.0342956\pi\)
−0.590228 + 0.807236i \(0.700962\pi\)
\(152\) 0 0
\(153\) −2.82597 0.258294i −0.228466 0.0208818i
\(154\) 0 0
\(155\) −3.01819 5.22765i −0.242427 0.419895i
\(156\) 0 0
\(157\) −3.02704 + 5.24299i −0.241584 + 0.418436i −0.961166 0.275972i \(-0.911000\pi\)
0.719581 + 0.694408i \(0.244334\pi\)
\(158\) 0 0
\(159\) −10.8545 0.495019i −0.860816 0.0392575i
\(160\) 0 0
\(161\) 0.273346 0.0215427
\(162\) 0 0
\(163\) −17.8171 −1.39554 −0.697772 0.716320i \(-0.745825\pi\)
−0.697772 + 0.716320i \(0.745825\pi\)
\(164\) 0 0
\(165\) 20.2594 + 0.923932i 1.57719 + 0.0719280i
\(166\) 0 0
\(167\) −4.23385 + 7.33325i −0.327625 + 0.567464i −0.982040 0.188672i \(-0.939582\pi\)
0.654415 + 0.756136i \(0.272915\pi\)
\(168\) 0 0
\(169\) 6.00000 + 10.3923i 0.461538 + 0.799408i
\(170\) 0 0
\(171\) 12.1118 + 1.10702i 0.926210 + 0.0846558i
\(172\) 0 0
\(173\) −8.67830 15.0313i −0.659799 1.14281i −0.980667 0.195682i \(-0.937308\pi\)
0.320868 0.947124i \(-0.396025\pi\)
\(174\) 0 0
\(175\) −0.863327 + 1.49533i −0.0652614 + 0.113036i
\(176\) 0 0
\(177\) −2.54523 + 3.97816i −0.191311 + 0.299017i
\(178\) 0 0
\(179\) 11.3494 0.848295 0.424147 0.905593i \(-0.360574\pi\)
0.424147 + 0.905593i \(0.360574\pi\)
\(180\) 0 0
\(181\) 21.8889 1.62699 0.813495 0.581572i \(-0.197562\pi\)
0.813495 + 0.581572i \(0.197562\pi\)
\(182\) 0 0
\(183\) 1.81138 + 3.49617i 0.133901 + 0.258444i
\(184\) 0 0
\(185\) 2.30924 3.99973i 0.169779 0.294066i
\(186\) 0 0
\(187\) −2.13521 3.69829i −0.156142 0.270446i
\(188\) 0 0
\(189\) −1.96050 4.81211i −0.142606 0.350030i
\(190\) 0 0
\(191\) −0.350874 0.607731i −0.0253883 0.0439739i 0.853052 0.521826i \(-0.174749\pi\)
−0.878440 + 0.477852i \(0.841416\pi\)
\(192\) 0 0
\(193\) −6.07227 + 10.5175i −0.437092 + 0.757065i −0.997464 0.0711760i \(-0.977325\pi\)
0.560372 + 0.828241i \(0.310658\pi\)
\(194\) 0 0
\(195\) 2.06654 + 3.98866i 0.147988 + 0.285634i
\(196\) 0 0
\(197\) −16.4107 −1.16921 −0.584607 0.811317i \(-0.698751\pi\)
−0.584607 + 0.811317i \(0.698751\pi\)
\(198\) 0 0
\(199\) −22.7060 −1.60959 −0.804794 0.593555i \(-0.797724\pi\)
−0.804794 + 0.593555i \(0.797724\pi\)
\(200\) 0 0
\(201\) −14.7647 + 23.0770i −1.04142 + 1.62773i
\(202\) 0 0
\(203\) −1.23025 + 2.13086i −0.0863468 + 0.149557i
\(204\) 0 0
\(205\) −8.30778 14.3895i −0.580241 1.00501i
\(206\) 0 0
\(207\) −0.472958 + 0.669906i −0.0328728 + 0.0465617i
\(208\) 0 0
\(209\) 9.15126 + 15.8505i 0.633006 + 1.09640i
\(210\) 0 0
\(211\) 2.28074 3.95035i 0.157012 0.271954i −0.776778 0.629775i \(-0.783147\pi\)
0.933790 + 0.357822i \(0.116480\pi\)
\(212\) 0 0
\(213\) −5.66372 0.258294i −0.388071 0.0176980i
\(214\) 0 0
\(215\) −27.0656 −1.84586
\(216\) 0 0
\(217\) −2.32743 −0.157996
\(218\) 0 0
\(219\) −2.60817 0.118946i −0.176244 0.00803760i
\(220\) 0 0
\(221\) 0.472958 0.819187i 0.0318146 0.0551045i
\(222\) 0 0
\(223\) 6.66225 + 11.5394i 0.446137 + 0.772733i 0.998131 0.0611159i \(-0.0194659\pi\)
−0.551993 + 0.833849i \(0.686133\pi\)
\(224\) 0 0
\(225\) −2.17091 4.70310i −0.144727 0.313540i
\(226\) 0 0
\(227\) 0.690757 + 1.19643i 0.0458472 + 0.0794096i 0.888038 0.459769i \(-0.152068\pi\)
−0.842191 + 0.539179i \(0.818735\pi\)
\(228\) 0 0
\(229\) 8.98968 15.5706i 0.594055 1.02893i −0.399625 0.916679i \(-0.630859\pi\)
0.993679 0.112254i \(-0.0358072\pi\)
\(230\) 0 0
\(231\) 4.21420 6.58673i 0.277274 0.433375i
\(232\) 0 0
\(233\) −18.9823 −1.24357 −0.621786 0.783187i \(-0.713592\pi\)
−0.621786 + 0.783187i \(0.713592\pi\)
\(234\) 0 0
\(235\) −31.5438 −2.05769
\(236\) 0 0
\(237\) 11.7199 + 22.6208i 0.761292 + 1.46938i
\(238\) 0 0
\(239\) 2.44592 4.23645i 0.158213 0.274033i −0.776011 0.630719i \(-0.782760\pi\)
0.934224 + 0.356686i \(0.116093\pi\)
\(240\) 0 0
\(241\) 13.0797 + 22.6546i 0.842535 + 1.45931i 0.887745 + 0.460336i \(0.152271\pi\)
−0.0452094 + 0.998978i \(0.514396\pi\)
\(242\) 0 0
\(243\) 15.1855 + 3.52144i 0.974150 + 0.225901i
\(244\) 0 0
\(245\) 1.29679 + 2.24611i 0.0828489 + 0.143498i
\(246\) 0 0
\(247\) −2.02704 + 3.51094i −0.128978 + 0.223396i
\(248\) 0 0
\(249\) −0.753696 1.45472i −0.0477635 0.0921892i
\(250\) 0 0
\(251\) −18.4576 −1.16503 −0.582516 0.812819i \(-0.697932\pi\)
−0.582516 + 0.812819i \(0.697932\pi\)
\(252\) 0 0
\(253\) −1.23405 −0.0775838
\(254\) 0 0
\(255\) −2.29007 + 3.57935i −0.143410 + 0.224147i
\(256\) 0 0
\(257\) 5.86693 10.1618i 0.365969 0.633876i −0.622962 0.782252i \(-0.714071\pi\)
0.988931 + 0.148375i \(0.0474044\pi\)
\(258\) 0 0
\(259\) −0.890369 1.54216i −0.0553248 0.0958254i
\(260\) 0 0
\(261\) −3.09358 6.70198i −0.191488 0.414842i
\(262\) 0 0
\(263\) −3.76089 6.51406i −0.231907 0.401674i 0.726463 0.687206i \(-0.241163\pi\)
−0.958369 + 0.285532i \(0.907830\pi\)
\(264\) 0 0
\(265\) −8.13521 + 14.0906i −0.499742 + 0.865579i
\(266\) 0 0
\(267\) −24.8406 1.13285i −1.52022 0.0693296i
\(268\) 0 0
\(269\) −18.8348 −1.14838 −0.574190 0.818722i \(-0.694683\pi\)
−0.574190 + 0.818722i \(0.694683\pi\)
\(270\) 0 0
\(271\) 23.9823 1.45682 0.728410 0.685141i \(-0.240260\pi\)
0.728410 + 0.685141i \(0.240260\pi\)
\(272\) 0 0
\(273\) 1.73025 + 0.0789082i 0.104720 + 0.00477574i
\(274\) 0 0
\(275\) 3.89757 6.75078i 0.235032 0.407088i
\(276\) 0 0
\(277\) −3.58113 6.20269i −0.215169 0.372684i 0.738156 0.674630i \(-0.235697\pi\)
−0.953325 + 0.301947i \(0.902364\pi\)
\(278\) 0 0
\(279\) 4.02704 5.70397i 0.241093 0.341488i
\(280\) 0 0
\(281\) −7.44085 12.8879i −0.443884 0.768830i 0.554090 0.832457i \(-0.313067\pi\)
−0.997974 + 0.0636271i \(0.979733\pi\)
\(282\) 0 0
\(283\) 9.99854 17.3180i 0.594351 1.02945i −0.399287 0.916826i \(-0.630742\pi\)
0.993638 0.112621i \(-0.0359245\pi\)
\(284\) 0 0
\(285\) 9.81498 15.3407i 0.581389 0.908703i
\(286\) 0 0
\(287\) −6.40642 −0.378159
\(288\) 0 0
\(289\) −16.1052 −0.947367
\(290\) 0 0
\(291\) 9.15486 + 17.6699i 0.536667 + 1.03583i
\(292\) 0 0
\(293\) −7.53278 + 13.0472i −0.440070 + 0.762223i −0.997694 0.0678705i \(-0.978380\pi\)
0.557625 + 0.830093i \(0.311713\pi\)
\(294\) 0 0
\(295\) 3.53590 + 6.12435i 0.205868 + 0.356574i
\(296\) 0 0
\(297\) 8.85087 + 21.7247i 0.513580 + 1.26060i
\(298\) 0 0
\(299\) −0.136673 0.236725i −0.00790401 0.0136901i
\(300\) 0 0
\(301\) −5.21780 + 9.03749i −0.300749 + 0.520912i
\(302\) 0 0
\(303\) 2.93200 + 5.65910i 0.168439 + 0.325107i
\(304\) 0 0
\(305\) 5.89610 0.337610
\(306\) 0 0
\(307\) 27.2704 1.55641 0.778203 0.628013i \(-0.216132\pi\)
0.778203 + 0.628013i \(0.216132\pi\)
\(308\) 0 0
\(309\) −9.07947 + 14.1911i −0.516513 + 0.807302i
\(310\) 0 0
\(311\) −7.99115 + 13.8411i −0.453136 + 0.784855i −0.998579 0.0532931i \(-0.983028\pi\)
0.545443 + 0.838148i \(0.316362\pi\)
\(312\) 0 0
\(313\) −5.79893 10.0440i −0.327775 0.567722i 0.654295 0.756239i \(-0.272965\pi\)
−0.982070 + 0.188517i \(0.939632\pi\)
\(314\) 0 0
\(315\) −7.74844 0.708209i −0.436575 0.0399031i
\(316\) 0 0
\(317\) 1.00885 + 1.74739i 0.0566629 + 0.0981430i 0.892965 0.450125i \(-0.148621\pi\)
−0.836303 + 0.548268i \(0.815287\pi\)
\(318\) 0 0
\(319\) 5.55408 9.61996i 0.310969 0.538614i
\(320\) 0 0
\(321\) 2.37792 + 0.108445i 0.132722 + 0.00605281i
\(322\) 0 0
\(323\) −3.83482 −0.213375
\(324\) 0 0
\(325\) 1.72665 0.0957775
\(326\) 0 0
\(327\) −5.88151 0.268227i −0.325249 0.0148330i
\(328\) 0 0
\(329\) −6.08113 + 10.5328i −0.335263 + 0.580693i
\(330\) 0 0
\(331\) −9.85447 17.0684i −0.541651 0.938167i −0.998809 0.0487815i \(-0.984466\pi\)
0.457159 0.889385i \(-0.348867\pi\)
\(332\) 0 0
\(333\) 5.32004 + 0.486253i 0.291536 + 0.0266465i
\(334\) 0 0
\(335\) 20.5115 + 35.5269i 1.12066 + 1.94104i
\(336\) 0 0
\(337\) 14.5256 25.1590i 0.791259 1.37050i −0.133929 0.990991i \(-0.542759\pi\)
0.925188 0.379509i \(-0.123907\pi\)
\(338\) 0 0
\(339\) −9.69748 + 15.1570i −0.526695 + 0.823216i
\(340\) 0 0
\(341\) 10.5074 0.569007
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0.564880 + 1.09028i 0.0304121 + 0.0586989i
\(346\) 0 0
\(347\) 14.5416 25.1868i 0.780636 1.35210i −0.150936 0.988544i \(-0.548229\pi\)
0.931572 0.363557i \(-0.118438\pi\)
\(348\) 0 0
\(349\) −12.3815 21.4454i −0.662767 1.14795i −0.979885 0.199561i \(-0.936049\pi\)
0.317118 0.948386i \(-0.397285\pi\)
\(350\) 0 0
\(351\) −3.18716 + 4.10390i −0.170118 + 0.219050i
\(352\) 0 0
\(353\) 16.6513 + 28.8408i 0.886257 + 1.53504i 0.844266 + 0.535925i \(0.180037\pi\)
0.0419914 + 0.999118i \(0.486630\pi\)
\(354\) 0 0
\(355\) −4.24484 + 7.35228i −0.225293 + 0.390219i
\(356\) 0 0
\(357\) 0.753696 + 1.45472i 0.0398898 + 0.0769920i
\(358\) 0 0
\(359\) −25.5366 −1.34777 −0.673884 0.738837i \(-0.735375\pi\)
−0.673884 + 0.738837i \(0.735375\pi\)
\(360\) 0 0
\(361\) −2.56440 −0.134968
\(362\) 0 0
\(363\) −8.75729 + 13.6875i −0.459639 + 0.718409i
\(364\) 0 0
\(365\) −1.95477 + 3.38576i −0.102317 + 0.177219i
\(366\) 0 0
\(367\) 13.7252 + 23.7727i 0.716449 + 1.24093i 0.962398 + 0.271644i \(0.0875672\pi\)
−0.245949 + 0.969283i \(0.579100\pi\)
\(368\) 0 0
\(369\) 11.0847 15.7006i 0.577048 0.817341i
\(370\) 0 0
\(371\) 3.13667 + 5.43288i 0.162848 + 0.282061i
\(372\) 0 0
\(373\) −8.16372 + 14.1400i −0.422701 + 0.732140i −0.996203 0.0870646i \(-0.972251\pi\)
0.573502 + 0.819204i \(0.305585\pi\)
\(374\) 0 0
\(375\) 14.6893 + 0.669906i 0.758552 + 0.0345938i
\(376\) 0 0
\(377\) 2.46050 0.126722
\(378\) 0 0
\(379\) −12.0364 −0.618267 −0.309134 0.951019i \(-0.600039\pi\)
−0.309134 + 0.951019i \(0.600039\pi\)
\(380\) 0 0
\(381\) −1.16372 0.0530713i −0.0596189 0.00271892i
\(382\) 0 0
\(383\) −6.21780 + 10.7695i −0.317715 + 0.550298i −0.980011 0.198944i \(-0.936249\pi\)
0.662296 + 0.749242i \(0.269582\pi\)
\(384\) 0 0
\(385\) −5.85447 10.1402i −0.298372 0.516795i
\(386\) 0 0
\(387\) −13.1206 28.4247i −0.666959 1.44491i
\(388\) 0 0
\(389\) −10.3004 17.8408i −0.522250 0.904564i −0.999665 0.0258860i \(-0.991759\pi\)
0.477414 0.878678i \(-0.341574\pi\)
\(390\) 0 0
\(391\) 0.129281 0.223922i 0.00653803 0.0113242i
\(392\) 0 0
\(393\) 7.38725 11.5462i 0.372637 0.582427i
\(394\) 0 0
\(395\) 38.1488 1.91948
\(396\) 0 0
\(397\) −23.6372 −1.18631 −0.593157 0.805087i \(-0.702119\pi\)
−0.593157 + 0.805087i \(0.702119\pi\)
\(398\) 0 0
\(399\) −3.23025 6.23476i −0.161715 0.312129i
\(400\) 0 0
\(401\) 1.28220 2.22084i 0.0640300 0.110903i −0.832233 0.554426i \(-0.812938\pi\)
0.896263 + 0.443522i \(0.146271\pi\)
\(402\) 0 0
\(403\) 1.16372 + 2.01561i 0.0579688 + 0.100405i
\(404\) 0 0
\(405\) 15.1424 17.7642i 0.752432 0.882710i
\(406\) 0 0
\(407\) 4.01965 + 6.96224i 0.199247 + 0.345105i
\(408\) 0 0
\(409\) 17.1623 29.7259i 0.848619 1.46985i −0.0338223 0.999428i \(-0.510768\pi\)
0.882441 0.470423i \(-0.155899\pi\)
\(410\) 0 0
\(411\) 2.92627 + 5.64803i 0.144342 + 0.278597i
\(412\) 0 0
\(413\) 2.72665 0.134170
\(414\) 0 0
\(415\) −2.45331 −0.120428
\(416\) 0 0
\(417\) −1.91741 + 2.99689i −0.0938960 + 0.146758i
\(418\) 0 0
\(419\) 2.02850 3.51347i 0.0990989 0.171644i −0.812213 0.583361i \(-0.801737\pi\)
0.911312 + 0.411717i \(0.135071\pi\)
\(420\) 0 0
\(421\) 10.5344 + 18.2462i 0.513417 + 0.889264i 0.999879 + 0.0155624i \(0.00495387\pi\)
−0.486462 + 0.873702i \(0.661713\pi\)
\(422\) 0 0
\(423\) −15.2915 33.1278i −0.743500 1.61073i
\(424\) 0 0
\(425\) 0.816635 + 1.41445i 0.0396126 + 0.0686110i
\(426\) 0 0
\(427\) 1.13667 1.96878i 0.0550075 0.0952757i
\(428\) 0 0
\(429\) −7.81138 0.356238i −0.377137 0.0171993i
\(430\) 0 0
\(431\) −22.6185 −1.08949 −0.544747 0.838600i \(-0.683374\pi\)
−0.544747 + 0.838600i \(0.683374\pi\)
\(432\) 0 0
\(433\) 2.41789 0.116196 0.0580982 0.998311i \(-0.481496\pi\)
0.0580982 + 0.998311i \(0.481496\pi\)
\(434\) 0 0
\(435\) −11.0416 0.503554i −0.529406 0.0241436i
\(436\) 0 0
\(437\) −0.554084 + 0.959702i −0.0265054 + 0.0459088i
\(438\) 0 0
\(439\) −11.7448 20.3427i −0.560551 0.970902i −0.997448 0.0713911i \(-0.977256\pi\)
0.436898 0.899511i \(-0.356077\pi\)
\(440\) 0 0
\(441\) −1.73025 + 2.45076i −0.0823930 + 0.116703i
\(442\) 0 0
\(443\) −6.70895 11.6202i −0.318752 0.552094i 0.661476 0.749966i \(-0.269930\pi\)
−0.980228 + 0.197872i \(0.936597\pi\)
\(444\) 0 0
\(445\) −18.6175 + 32.2465i −0.882554 + 1.52863i
\(446\) 0 0
\(447\) 12.6426 19.7602i 0.597975 0.934625i
\(448\) 0 0
\(449\) −9.16225 −0.432393 −0.216197 0.976350i \(-0.569365\pi\)
−0.216197 + 0.976350i \(0.569365\pi\)
\(450\) 0 0
\(451\) 28.9224 1.36190
\(452\) 0 0
\(453\) 7.91069 + 15.2686i 0.371677 + 0.717379i
\(454\) 0 0
\(455\) 1.29679 2.24611i 0.0607944 0.105299i
\(456\) 0 0
\(457\) −4.40856 7.63584i −0.206224 0.357190i 0.744298 0.667847i \(-0.232784\pi\)
−0.950522 + 0.310658i \(0.899451\pi\)
\(458\) 0 0
\(459\) −4.86926 0.669906i −0.227277 0.0312685i
\(460\) 0 0
\(461\) 2.82957 + 4.90095i 0.131786 + 0.228260i 0.924365 0.381509i \(-0.124595\pi\)
−0.792579 + 0.609769i \(0.791262\pi\)
\(462\) 0 0
\(463\) 7.86333 13.6197i 0.365440 0.632960i −0.623407 0.781898i \(-0.714252\pi\)
0.988847 + 0.148937i \(0.0475853\pi\)
\(464\) 0 0
\(465\) −4.80972 9.28332i −0.223045 0.430504i
\(466\) 0 0
\(467\) 21.9971 1.01790 0.508952 0.860795i \(-0.330033\pi\)
0.508952 + 0.860795i \(0.330033\pi\)
\(468\) 0 0
\(469\) 15.8171 0.730366
\(470\) 0 0
\(471\) −5.65126 + 8.83284i −0.260396 + 0.406996i
\(472\) 0 0
\(473\) 23.5562 40.8006i 1.08312 1.87601i
\(474\) 0 0
\(475\) −3.50000 6.06218i −0.160591 0.278152i
\(476\) 0 0
\(477\) −18.7419 1.71301i −0.858133 0.0784336i
\(478\) 0 0
\(479\) 12.4875 + 21.6291i 0.570571 + 0.988257i 0.996507 + 0.0835043i \(0.0266112\pi\)
−0.425937 + 0.904753i \(0.640055\pi\)
\(480\) 0 0
\(481\) −0.890369 + 1.54216i −0.0405973 + 0.0703166i
\(482\) 0 0
\(483\) 0.472958 + 0.0215693i 0.0215203 + 0.000981436i
\(484\) 0 0
\(485\) 29.7994 1.35312
\(486\) 0 0
\(487\) 17.5979 0.797435 0.398717 0.917074i \(-0.369455\pi\)
0.398717 + 0.917074i \(0.369455\pi\)
\(488\) 0 0
\(489\) −30.8281 1.40592i −1.39410 0.0635778i
\(490\) 0 0
\(491\) 6.89757 11.9469i 0.311283 0.539158i −0.667358 0.744737i \(-0.732575\pi\)
0.978640 + 0.205580i \(0.0659080\pi\)
\(492\) 0 0
\(493\) 1.16372 + 2.01561i 0.0524111 + 0.0907787i
\(494\) 0 0
\(495\) 34.9810 + 3.19727i 1.57228 + 0.143707i
\(496\) 0 0
\(497\) 1.63667 + 2.83480i 0.0734148 + 0.127158i
\(498\) 0 0
\(499\) 6.54377 11.3341i 0.292939 0.507386i −0.681564 0.731758i \(-0.738700\pi\)
0.974503 + 0.224373i \(0.0720333\pi\)
\(500\) 0 0
\(501\) −7.90428 + 12.3543i −0.353137 + 0.551949i
\(502\) 0 0
\(503\) 22.3068 0.994611 0.497305 0.867576i \(-0.334323\pi\)
0.497305 + 0.867576i \(0.334323\pi\)
\(504\) 0 0
\(505\) 9.54377 0.424692
\(506\) 0 0
\(507\) 9.56148 + 18.4548i 0.424640 + 0.819605i
\(508\) 0 0
\(509\) 7.94659 13.7639i 0.352226 0.610074i −0.634413 0.772994i \(-0.718758\pi\)
0.986639 + 0.162920i \(0.0520914\pi\)
\(510\) 0 0
\(511\) 0.753696 + 1.30544i 0.0333415 + 0.0577492i
\(512\) 0 0
\(513\) 20.8691 + 2.87114i 0.921392 + 0.126764i
\(514\) 0 0
\(515\) 12.6134 + 21.8471i 0.555814 + 0.962698i
\(516\) 0 0
\(517\) 27.4538 47.5514i 1.20742 2.09131i
\(518\) 0 0
\(519\) −13.8296 26.6927i −0.607051 1.17168i
\(520\) 0 0
\(521\) 4.41789 0.193551 0.0967756 0.995306i \(-0.469147\pi\)
0.0967756 + 0.995306i \(0.469147\pi\)
\(522\) 0 0
\(523\) −25.2733 −1.10513 −0.552563 0.833471i \(-0.686350\pi\)
−0.552563 + 0.833471i \(0.686350\pi\)
\(524\) 0 0
\(525\) −1.61177 + 2.51917i −0.0703433 + 0.109946i
\(526\) 0 0
\(527\) −1.10078 + 1.90660i −0.0479506 + 0.0830528i
\(528\) 0 0
\(529\) 11.4626 + 19.8539i 0.498376 + 0.863212i
\(530\) 0 0
\(531\) −4.71780 + 6.68238i −0.204735 + 0.289990i
\(532\) 0 0
\(533\) 3.20321 + 5.54812i 0.138746 + 0.240316i
\(534\) 0 0
\(535\) 1.78220 3.08686i 0.0770513 0.133457i
\(536\) 0 0
\(537\) 19.6373 + 0.895562i 0.847414 + 0.0386464i
\(538\) 0 0
\(539\) −4.51459 −0.194457
\(540\) 0 0
\(541\) −3.43852 −0.147834 −0.0739168 0.997264i \(-0.523550\pi\)
−0.0739168 + 0.997264i \(0.523550\pi\)
\(542\) 0 0
\(543\) 37.8733 + 1.72722i 1.62530 + 0.0741219i
\(544\) 0 0
\(545\) −4.40808 + 7.63501i −0.188821 + 0.327048i
\(546\) 0 0
\(547\) −3.46410 6.00000i −0.148114 0.256542i 0.782416 0.622756i \(-0.213987\pi\)
−0.930531 + 0.366214i \(0.880654\pi\)
\(548\) 0 0
\(549\) 2.85827 + 6.19219i 0.121988 + 0.264276i
\(550\) 0 0
\(551\) −4.98755 8.63868i −0.212477 0.368020i
\(552\) 0 0
\(553\) 7.35447 12.7383i 0.312744 0.541688i
\(554\) 0 0
\(555\) 4.31118 6.73832i 0.183000 0.286026i
\(556\) 0 0
\(557\) 33.5835 1.42298 0.711488 0.702698i \(-0.248021\pi\)
0.711488 + 0.702698i \(0.248021\pi\)
\(558\) 0 0
\(559\) 10.4356 0.441379
\(560\) 0 0
\(561\) −3.40263 6.56747i −0.143659 0.277279i
\(562\) 0 0
\(563\) 21.2396 36.7880i 0.895142 1.55043i 0.0615128 0.998106i \(-0.480407\pi\)
0.833629 0.552325i \(-0.186259\pi\)
\(564\) 0 0
\(565\) 13.4720 + 23.3341i 0.566770 + 0.981675i
\(566\) 0 0
\(567\) −3.01245 8.48087i −0.126511 0.356163i
\(568\) 0 0
\(569\) −5.20175 9.00969i −0.218069 0.377706i 0.736149 0.676820i \(-0.236642\pi\)
−0.954217 + 0.299114i \(0.903309\pi\)
\(570\) 0 0
\(571\) 8.92480 15.4582i 0.373491 0.646906i −0.616609 0.787270i \(-0.711494\pi\)
0.990100 + 0.140364i \(0.0448272\pi\)
\(572\) 0 0
\(573\) −0.559145 1.07922i −0.0233586 0.0450849i
\(574\) 0 0
\(575\) 0.471974 0.0196827
\(576\) 0 0
\(577\) 11.9430 0.497193 0.248597 0.968607i \(-0.420031\pi\)
0.248597 + 0.968607i \(0.420031\pi\)
\(578\) 0 0
\(579\) −11.3365 + 17.7187i −0.471128 + 0.736366i
\(580\) 0 0
\(581\) −0.472958 + 0.819187i −0.0196216 + 0.0339856i
\(582\) 0 0
\(583\) −14.1608 24.5272i −0.586480 1.01581i
\(584\) 0 0
\(585\) 3.26089 + 7.06445i 0.134821 + 0.292079i
\(586\) 0 0
\(587\) 11.9299 + 20.6631i 0.492398 + 0.852859i 0.999962 0.00875568i \(-0.00278706\pi\)
−0.507563 + 0.861614i \(0.669454\pi\)
\(588\) 0 0
\(589\) 4.71780 8.17147i 0.194394 0.336699i
\(590\) 0 0
\(591\) −28.3946 1.29494i −1.16800 0.0532667i
\(592\) 0 0
\(593\) 19.5801 0.804060 0.402030 0.915626i \(-0.368305\pi\)
0.402030 + 0.915626i \(0.368305\pi\)
\(594\) 0 0
\(595\) 2.45331 0.100576
\(596\) 0 0
\(597\) −39.2871 1.79169i −1.60792 0.0733291i
\(598\) 0 0
\(599\) 9.27335 16.0619i 0.378899 0.656272i −0.612004 0.790855i \(-0.709636\pi\)
0.990902 + 0.134583i \(0.0429696\pi\)
\(600\) 0 0
\(601\) 9.09931 + 15.7605i 0.371169 + 0.642883i 0.989746 0.142841i \(-0.0456238\pi\)
−0.618577 + 0.785724i \(0.712290\pi\)
\(602\) 0 0
\(603\) −27.3676 + 38.7640i −1.11449 + 1.57859i
\(604\) 0 0
\(605\) 12.1659 + 21.0719i 0.494612 + 0.856693i
\(606\) 0 0
\(607\) −11.1549 + 19.3208i −0.452762 + 0.784206i −0.998556 0.0537125i \(-0.982895\pi\)
0.545795 + 0.837919i \(0.316228\pi\)
\(608\) 0 0
\(609\) −2.29679 + 3.58985i −0.0930706 + 0.145468i
\(610\) 0 0
\(611\) 12.1623 0.492032
\(612\) 0 0
\(613\) 10.2370 0.413467 0.206734 0.978397i \(-0.433717\pi\)
0.206734 + 0.978397i \(0.433717\pi\)
\(614\) 0 0
\(615\) −13.2391 25.5530i −0.533852 1.03040i
\(616\) 0 0
\(617\) 5.66372 9.80984i 0.228013 0.394929i −0.729206 0.684294i \(-0.760111\pi\)
0.957219 + 0.289364i \(0.0934439\pi\)
\(618\) 0 0
\(619\) 4.31663 + 7.47663i 0.173500 + 0.300511i 0.939641 0.342161i \(-0.111159\pi\)
−0.766141 + 0.642672i \(0.777826\pi\)
\(620\) 0 0
\(621\) −0.871198 + 1.12179i −0.0349600 + 0.0450157i
\(622\) 0 0
\(623\) 7.17830 + 12.4332i 0.287593 + 0.498125i
\(624\) 0 0
\(625\) 15.3260 26.5454i 0.613039 1.06181i
\(626\) 0 0
\(627\) 14.5833 + 28.1474i 0.582399 + 1.12410i
\(628\) 0 0
\(629\) −1.68443 −0.0671626
\(630\) 0 0
\(631\) 14.8535 0.591308 0.295654 0.955295i \(-0.404462\pi\)
0.295654 + 0.955295i \(0.404462\pi\)
\(632\) 0 0
\(633\) 4.25797 6.65514i 0.169239 0.264518i
\(634\) 0 0
\(635\) −0.872181 + 1.51066i −0.0346115 + 0.0599488i
\(636\) 0 0
\(637\) −0.500000 0.866025i −0.0198107 0.0343132i
\(638\) 0 0
\(639\) −9.77928 0.893828i −0.386862 0.0353593i
\(640\) 0 0
\(641\) 17.0797 + 29.5828i 0.674606 + 1.16845i 0.976584 + 0.215137i \(0.0690199\pi\)
−0.301978 + 0.953315i \(0.597647\pi\)
\(642\) 0 0
\(643\) −5.41741 + 9.38323i −0.213642 + 0.370039i −0.952852 0.303437i \(-0.901866\pi\)
0.739210 + 0.673475i \(0.235199\pi\)
\(644\) 0 0
\(645\) −46.8302 2.13570i −1.84394 0.0840929i
\(646\) 0 0
\(647\) −32.9692 −1.29615 −0.648077 0.761575i \(-0.724427\pi\)
−0.648077 + 0.761575i \(0.724427\pi\)
\(648\) 0 0
\(649\) −12.3097 −0.483199
\(650\) 0 0
\(651\) −4.02704 0.183653i −0.157832 0.00719795i
\(652\) 0 0
\(653\) 1.96557 3.40446i 0.0769185 0.133227i −0.825000 0.565132i \(-0.808825\pi\)
0.901919 + 0.431905i \(0.142159\pi\)
\(654\) 0 0
\(655\) −10.2626 17.7753i −0.400991 0.694537i
\(656\) 0 0
\(657\) −4.50340 0.411612i −0.175695 0.0160585i
\(658\) 0 0
\(659\) 8.40856 + 14.5640i 0.327551 + 0.567335i 0.982025 0.188749i \(-0.0604434\pi\)
−0.654474 + 0.756084i \(0.727110\pi\)
\(660\) 0 0
\(661\) 8.51080 14.7411i 0.331032 0.573364i −0.651683 0.758492i \(-0.725937\pi\)
0.982714 + 0.185128i \(0.0592700\pi\)
\(662\) 0 0
\(663\) 0.882977 1.38008i 0.0342920 0.0535979i
\(664\) 0 0
\(665\) −10.5146 −0.407738
\(666\) 0 0
\(667\) 0.672570 0.0260420
\(668\) 0 0
\(669\) 10.6168 + 20.4917i 0.410470 + 0.792255i
\(670\) 0 0
\(671\) −5.13161 + 8.88821i −0.198104 + 0.343126i
\(672\) 0 0
\(673\) −14.3727 24.8942i −0.554025 0.959600i −0.997979 0.0635501i \(-0.979758\pi\)
0.443953 0.896050i \(-0.353576\pi\)
\(674\) 0 0
\(675\) −3.38511 8.30885i −0.130293 0.319808i
\(676\) 0 0
\(677\) 3.01819 + 5.22765i 0.115998 + 0.200915i 0.918178 0.396167i \(-0.129660\pi\)
−0.802180 + 0.597082i \(0.796327\pi\)
\(678\) 0 0
\(679\) 5.74484 9.95036i 0.220467 0.381860i
\(680\) 0 0
\(681\) 1.10078 + 2.12463i 0.0421818 + 0.0814159i
\(682\) 0 0
\(683\) −20.5113 −0.784842 −0.392421 0.919786i \(-0.628362\pi\)
−0.392421 + 0.919786i \(0.628362\pi\)
\(684\) 0 0
\(685\) 9.52510 0.363935
\(686\) 0 0
\(687\) 16.7831 26.2317i 0.640314 1.00080i
\(688\) 0 0
\(689\) 3.13667 5.43288i 0.119498 0.206976i
\(690\) 0 0
\(691\) −7.50146 12.9929i −0.285369 0.494274i 0.687330 0.726346i \(-0.258783\pi\)
−0.972699 + 0.232072i \(0.925450\pi\)
\(692\) 0 0
\(693\) 7.81138 11.0642i 0.296730 0.420293i
\(694\) 0 0
\(695\) 2.66372 + 4.61369i 0.101040 + 0.175007i
\(696\) 0 0
\(697\) −3.02997 + 5.24806i −0.114768 + 0.198784i
\(698\) 0 0
\(699\) −32.8442 1.49786i −1.24228 0.0566542i
\(700\) 0 0
\(701\) 38.5113 1.45455 0.727275 0.686346i \(-0.240786\pi\)
0.727275 + 0.686346i \(0.240786\pi\)
\(702\) 0 0
\(703\) 7.21926 0.272280
\(704\) 0 0
\(705\) −54.5787 2.48906i −2.05555 0.0937435i
\(706\) 0 0
\(707\) 1.83988 3.18677i 0.0691959 0.119851i
\(708\) 0 0
\(709\) −3.82004 6.61650i −0.143465 0.248488i 0.785334 0.619072i \(-0.212491\pi\)
−0.928799 + 0.370584i \(0.879158\pi\)
\(710\) 0 0
\(711\) 18.4935 + 40.0646i 0.693560 + 1.50254i
\(712\) 0 0
\(713\) 0.318097 + 0.550960i 0.0119128 + 0.0206336i
\(714\) 0 0
\(715\) −5.85447 + 10.1402i −0.218945 + 0.379224i
\(716\) 0 0
\(717\) 4.56634 7.13713i 0.170533 0.266541i
\(718\) 0 0
\(719\) 30.0364 1.12017 0.560084 0.828436i \(-0.310769\pi\)
0.560084 + 0.828436i \(0.310769\pi\)
\(720\) 0 0
\(721\) 9.72665 0.362240
\(722\) 0 0
\(723\) 20.8435 + 40.2303i 0.775177 + 1.49618i
\(724\) 0 0
\(725\) −2.12422 + 3.67926i −0.0788916 + 0.136644i
\(726\) 0 0
\(727\) 1.72812 + 2.99319i 0.0640923 + 0.111011i 0.896291 0.443466i \(-0.146251\pi\)
−0.832199 + 0.554478i \(0.812918\pi\)
\(728\) 0 0
\(729\) 25.9969 + 7.29124i 0.962847 + 0.270046i
\(730\) 0 0
\(731\) 4.93560 + 8.54871i 0.182550 + 0.316185i
\(732\) 0 0
\(733\) −19.2630 + 33.3645i −0.711496 + 1.23235i 0.252799 + 0.967519i \(0.418649\pi\)
−0.964295 + 0.264829i \(0.914685\pi\)
\(734\) 0 0
\(735\) 2.06654 + 3.98866i 0.0762254 + 0.147124i
\(736\) 0 0
\(737\) −71.4078 −2.63034
\(738\) 0 0
\(739\) −45.1239 −1.65991 −0.829955 0.557830i \(-0.811634\pi\)
−0.829955 + 0.557830i \(0.811634\pi\)
\(740\) 0 0
\(741\) −3.78434 + 5.91486i −0.139021 + 0.217288i
\(742\) 0 0
\(743\) 4.74338 8.21577i 0.174018 0.301407i −0.765803 0.643075i \(-0.777658\pi\)
0.939821 + 0.341668i \(0.110992\pi\)
\(744\) 0 0
\(745\) −17.5634 30.4207i −0.643474 1.11453i
\(746\) 0 0
\(747\) −1.18929 2.57651i −0.0435140 0.0942695i
\(748\) 0 0
\(749\) −0.687159 1.19019i −0.0251082 0.0434887i
\(750\) 0 0
\(751\) −4.91595 + 8.51467i −0.179386 + 0.310705i −0.941670 0.336537i \(-0.890744\pi\)
0.762285 + 0.647242i \(0.224078\pi\)
\(752\) 0 0
\(753\) −31.9363 1.45646i −1.16382 0.0530762i
\(754\) 0 0
\(755\) 25.7496 0.937124
\(756\) 0 0
\(757\) −41.8171 −1.51987 −0.759934 0.650000i \(-0.774769\pi\)
−0.759934 + 0.650000i \(0.774769\pi\)
\(758\) 0 0
\(759\) −2.13521 0.0973764i −0.0775032 0.00353454i
\(760\) 0 0
\(761\) −11.4897 + 19.9007i −0.416501 + 0.721400i −0.995585 0.0938675i \(-0.970077\pi\)
0.579084 + 0.815268i \(0.303410\pi\)
\(762\) 0 0
\(763\) 1.69961 + 2.94381i 0.0615301 + 0.106573i
\(764\) 0 0
\(765\) −4.24484 + 6.01247i −0.153473 + 0.217381i
\(766\) 0 0
\(767\) −1.36333 2.36135i −0.0492269 0.0852635i
\(768\) 0 0
\(769\) −3.04329 + 5.27113i −0.109744 + 0.190082i −0.915666 0.401939i \(-0.868336\pi\)
0.805923 + 0.592021i \(0.201670\pi\)
\(770\) 0 0
\(771\) 10.9531 17.1196i 0.394467 0.616546i
\(772\) 0 0
\(773\) −41.8214 −1.50421 −0.752105 0.659043i \(-0.770962\pi\)
−0.752105 + 0.659043i \(0.770962\pi\)
\(774\) 0 0
\(775\) −4.01867 −0.144355
\(776\) 0 0
\(777\) −1.41887 2.73859i −0.0509018 0.0982464i
\(778\) 0 0
\(779\) 12.9861 22.4926i 0.465275 0.805880i
\(780\) 0 0
\(781\) −7.38891 12.7980i −0.264396 0.457947i
\(782\) 0 0
\(783\) −4.82383 11.8402i −0.172390 0.423135i
\(784\) 0 0
\(785\) 7.85087 + 13.5981i 0.280210 + 0.485337i
\(786\) 0 0
\(787\) 16.1460 27.9657i 0.575543 0.996870i −0.420439 0.907321i \(-0.638124\pi\)
0.995982 0.0895491i \(-0.0285426\pi\)
\(788\) 0 0
\(789\) −5.99328 11.5677i −0.213366 0.411822i
\(790\) 0 0
\(791\) 10.3887 0.369380
\(792\) 0 0
\(793\) −2.27335 −0.0807289
\(794\) 0 0
\(795\) −15.1878 + 23.7384i −0.538657 + 0.841913i
\(796\) 0 0
\(797\) −23.2829 + 40.3271i −0.824722 + 1.42846i 0.0774101 + 0.996999i \(0.475335\pi\)
−0.902132 + 0.431461i \(0.857998\pi\)
\(798\) 0 0
\(799\) 5.75223 + 9.96316i 0.203499 + 0.352471i
\(800\)