Properties

Label 1008.2.r.k.673.3
Level $1008$
Weight $2$
Character 1008.673
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 673.3
Root \(0.500000 - 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 1008.673
Dual form 1008.2.r.k.337.3

$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0.995485 + 0.0949156i \(0.0302581\pi\)
−0.415543 + 0.909573i \(0.636409\pi\)
\(6\) 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 −0.294198 0.955744i \(-0.595053\pi\)
0.974798 0.223089i \(-0.0716141\pi\)
\(12\) 0 0
\(13\) −0.500000 0.866025i −0.138675 0.240192i 0.788320 0.615265i \(-0.210951\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) 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 0.851425 0.524477i \(-0.175739\pi\)
−0.879923 + 0.475117i \(0.842406\pi\)
\(24\) 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 −0.957350 0.288932i \(-0.906700\pi\)
0.728897 + 0.684623i \(0.240033\pi\)
\(30\) 0 0
\(31\) 1.16372 + 2.01561i 0.209009 + 0.362015i 0.951403 0.307949i \(-0.0996427\pi\)
−0.742393 + 0.669964i \(0.766309\pi\)
\(32\) 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 1.00000 0.000297253i \(9.46187e-5\pi\)
−0.499743 + 0.866174i \(0.666572\pi\)
\(42\) 0 0
\(43\) −5.21780 + 9.03749i −0.795707 + 1.37820i 0.126682 + 0.991943i \(0.459567\pi\)
−0.922389 + 0.386262i \(0.873766\pi\)
\(44\) 0 0
\(45\) 4.48755 + 6.35624i 0.668964 + 0.947533i
\(46\) 0 0
\(47\) −6.08113 + 10.5328i −0.887023 + 1.53637i −0.0436467 + 0.999047i \(0.513898\pi\)
−0.843377 + 0.537323i \(0.819436\pi\)
\(48\) 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 0.763530 0.645772i \(-0.223464\pi\)
−0.941020 + 0.338350i \(0.890131\pi\)
\(60\) 0 0
\(61\) 1.13667 1.96878i 0.145536 0.252076i −0.784037 0.620714i \(-0.786843\pi\)
0.929573 + 0.368639i \(0.120176\pi\)
\(62\) 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 −0.706400 0.707813i \(-0.749682\pi\)
−0.259784 0.965667i \(-0.583651\pi\)
\(68\) 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 −0.0725952 0.997361i \(-0.523128\pi\)
0.900038 0.435811i \(-0.143539\pi\)
\(80\) 0 0
\(81\) 8.85087 1.63157i 0.983430 0.181286i
\(82\) 0 0
\(83\) −0.472958 + 0.819187i −0.0519139 + 0.0899175i −0.890815 0.454367i \(-0.849865\pi\)
0.838901 + 0.544285i \(0.183199\pi\)
\(84\) 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 −0.411785 0.911281i \(-0.635094\pi\)
0.995085 0.0990246i \(-0.0315722\pi\)
\(98\) 0 0
\(99\) 5.67617 12.2969i 0.570476 1.23589i
\(100\) 0 0
\(101\) 1.83988 3.18677i 0.183075 0.317096i −0.759851 0.650097i \(-0.774728\pi\)
0.942926 + 0.333002i \(0.108061\pi\)
\(102\) 0 0
\(103\) −4.86333 8.42353i −0.479198 0.829995i 0.520518 0.853851i \(-0.325739\pi\)
−0.999715 + 0.0238560i \(0.992406\pi\)
\(104\) 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 0.511271 0.859420i \(-0.329175\pi\)
−0.999915 + 0.0130636i \(0.995842\pi\)
\(114\) 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 0.985484 0.169770i \(-0.0543026\pi\)
−0.639767 + 0.768569i \(0.720969\pi\)
\(132\) 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 −0.776859 0.629674i \(-0.783188\pi\)
0.933744 + 0.357943i \(0.116522\pi\)
\(138\) 0 0
\(139\) −1.02704 1.77889i −0.0871126 0.150883i 0.819177 0.573541i \(-0.194431\pi\)
−0.906289 + 0.422658i \(0.861097\pi\)
\(140\) 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 0.997921 + 0.0644482i \(0.0205287\pi\)
−0.443147 + 0.896449i \(0.646138\pi\)
\(150\) 0 0
\(151\) 4.96410 8.59808i 0.403973 0.699702i −0.590228 0.807236i \(-0.700962\pi\)
0.994201 + 0.107535i \(0.0342956\pi\)
\(152\) 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 0.719581 0.694408i \(-0.244334\pi\)
−0.961166 + 0.275972i \(0.911000\pi\)
\(158\) 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 0.654415 0.756136i \(-0.272915\pi\)
−0.982040 + 0.188672i \(0.939582\pi\)
\(168\) 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 0.320868 + 0.947124i \(0.396025\pi\)
−0.980667 + 0.195682i \(0.937308\pi\)
\(174\) 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 −0.878440 0.477852i \(-0.841416\pi\)
0.853052 + 0.521826i \(0.174749\pi\)
\(192\) 0 0
\(193\) −6.07227 10.5175i −0.437092 0.757065i 0.560372 0.828241i \(-0.310658\pi\)
−0.997464 + 0.0711760i \(0.977325\pi\)
\(194\) 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 0.933790 0.357822i \(-0.116480\pi\)
−0.776778 + 0.629775i \(0.783147\pi\)
\(212\) 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 −0.551993 0.833849i \(-0.686133\pi\)
0.998131 + 0.0611159i \(0.0194659\pi\)
\(224\) 0 0
\(225\) −2.17091 + 4.70310i −0.144727 + 0.313540i
\(226\) 0 0
\(227\) 0.690757 1.19643i 0.0458472 0.0794096i −0.842191 0.539179i \(-0.818735\pi\)
0.888038 + 0.459769i \(0.152068\pi\)
\(228\) 0 0
\(229\) 8.98968 + 15.5706i 0.594055 + 1.02893i 0.993679 + 0.112254i \(0.0358072\pi\)
−0.399625 + 0.916679i \(0.630859\pi\)
\(230\) 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 0.934224 0.356686i \(-0.116093\pi\)
−0.776011 + 0.630719i \(0.782760\pi\)
\(240\) 0 0
\(241\) 13.0797 22.6546i 0.842535 1.45931i −0.0452094 0.998978i \(-0.514396\pi\)
0.887745 0.460336i \(-0.152271\pi\)
\(242\) 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 0.988931 0.148375i \(-0.0474044\pi\)
−0.622962 + 0.782252i \(0.714071\pi\)
\(258\) 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 −0.958369 0.285532i \(-0.907830\pi\)
0.726463 + 0.687206i \(0.241163\pi\)
\(264\) 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 −0.953325 0.301947i \(-0.902364\pi\)
0.738156 + 0.674630i \(0.235697\pi\)
\(278\) 0 0
\(279\) 4.02704 + 5.70397i 0.241093 + 0.341488i
\(280\) 0 0
\(281\) −7.44085 + 12.8879i −0.443884 + 0.768830i −0.997974 0.0636271i \(-0.979733\pi\)
0.554090 + 0.832457i \(0.313067\pi\)
\(282\) 0 0
\(283\) 9.99854 + 17.3180i 0.594351 + 1.02945i 0.993638 + 0.112621i \(0.0359245\pi\)
−0.399287 + 0.916826i \(0.630742\pi\)
\(284\) 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 0.557625 0.830093i \(-0.311713\pi\)
−0.997694 + 0.0678705i \(0.978380\pi\)
\(294\) 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 0.545443 0.838148i \(-0.316362\pi\)
−0.998579 + 0.0532931i \(0.983028\pi\)
\(312\) 0 0
\(313\) −5.79893 + 10.0440i −0.327775 + 0.567722i −0.982070 0.188517i \(-0.939632\pi\)
0.654295 + 0.756239i \(0.272965\pi\)
\(314\) 0 0
\(315\) −7.74844 + 0.708209i −0.436575 + 0.0399031i
\(316\) 0 0
\(317\) 1.00885 1.74739i 0.0566629 0.0981430i −0.836303 0.548268i \(-0.815287\pi\)
0.892965 + 0.450125i \(0.148621\pi\)
\(318\) 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 0.457159 + 0.889385i \(0.348867\pi\)
−0.998809 + 0.0487815i \(0.984466\pi\)
\(332\) 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 0.925188 + 0.379509i \(0.123907\pi\)
−0.133929 + 0.990991i \(0.542759\pi\)
\(338\) 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 0.931572 + 0.363557i \(0.118438\pi\)
−0.150936 + 0.988544i \(0.548229\pi\)
\(348\) 0 0
\(349\) −12.3815 + 21.4454i −0.662767 + 1.14795i 0.317118 + 0.948386i \(0.397285\pi\)
−0.979885 + 0.199561i \(0.936049\pi\)
\(350\) 0 0
\(351\) −3.18716 4.10390i −0.170118 0.219050i
\(352\) 0 0
\(353\) 16.6513 28.8408i 0.886257 1.53504i 0.0419914 0.999118i \(-0.486630\pi\)
0.844266 0.535925i \(-0.180037\pi\)
\(354\) 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 −0.245949 0.969283i \(-0.579100\pi\)
0.962398 0.271644i \(-0.0875672\pi\)
\(368\) 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 0.573502 0.819204i \(-0.305585\pi\)
−0.996203 + 0.0870646i \(0.972251\pi\)
\(374\) 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 0.662296 0.749242i \(-0.269582\pi\)
−0.980011 + 0.198944i \(0.936249\pi\)
\(384\) 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 0.477414 + 0.878678i \(0.341574\pi\)
−0.999665 + 0.0258860i \(0.991759\pi\)
\(390\) 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 0.896263 0.443522i \(-0.146271\pi\)
−0.832233 + 0.554426i \(0.812938\pi\)
\(402\) 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 0.882441 + 0.470423i \(0.155899\pi\)
−0.0338223 + 0.999428i \(0.510768\pi\)
\(410\) 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 0.911312 0.411717i \(-0.135071\pi\)
−0.812213 + 0.583361i \(0.801737\pi\)
\(420\) 0 0
\(421\) 10.5344 18.2462i 0.513417 0.889264i −0.486462 0.873702i \(-0.661713\pi\)
0.999879 0.0155624i \(-0.00495387\pi\)
\(422\) 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 0.436898 + 0.899511i \(0.356077\pi\)
−0.997448 + 0.0713911i \(0.977256\pi\)
\(440\) 0 0
\(441\) −1.73025 2.45076i −0.0823930 0.116703i
\(442\) 0 0
\(443\) −6.70895 + 11.6202i −0.318752 + 0.552094i −0.980228 0.197872i \(-0.936597\pi\)
0.661476 + 0.749966i \(0.269930\pi\)
\(444\) 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 −0.950522 0.310658i \(-0.899451\pi\)
0.744298 + 0.667847i \(0.232784\pi\)
\(458\) 0 0
\(459\) −4.86926 + 0.669906i −0.227277 + 0.0312685i
\(460\) 0 0
\(461\) 2.82957 4.90095i 0.131786 0.228260i −0.792579 0.609769i \(-0.791262\pi\)
0.924365 + 0.381509i \(0.124595\pi\)
\(462\) 0 0
\(463\) 7.86333 + 13.6197i 0.365440 + 0.632960i 0.988847 0.148937i \(-0.0475853\pi\)
−0.623407 + 0.781898i \(0.714252\pi\)
\(464\) 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 −0.425937 0.904753i \(-0.640055\pi\)
0.996507 0.0835043i \(-0.0266112\pi\)
\(480\) 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 0.978640 0.205580i \(-0.0659080\pi\)
−0.667358 + 0.744737i \(0.732575\pi\)
\(492\) 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 0.974503 0.224373i \(-0.0720333\pi\)
−0.681564 + 0.731758i \(0.738700\pi\)
\(500\) 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 0.986639 0.162920i \(-0.0520914\pi\)
−0.634413 + 0.772994i \(0.718758\pi\)
\(510\) 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 −0.930531 0.366214i \(-0.880654\pi\)
0.782416 + 0.622756i \(0.213987\pi\)
\(548\) 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 0.833629 + 0.552325i \(0.186259\pi\)
0.0615128 + 0.998106i \(0.480407\pi\)
\(564\) 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 −0.954217 0.299114i \(-0.903309\pi\)
0.736149 + 0.676820i \(0.236642\pi\)
\(570\) 0 0
\(571\) 8.92480 + 15.4582i 0.373491 + 0.646906i 0.990100 0.140364i \(-0.0448272\pi\)
−0.616609 + 0.787270i \(0.711494\pi\)
\(572\) 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 −0.507563 0.861614i \(-0.669454\pi\)
0.999962 + 0.00875568i \(0.00278706\pi\)
\(588\) 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 0.990902 0.134583i \(-0.0429696\pi\)
−0.612004 + 0.790855i \(0.709636\pi\)
\(600\) 0 0
\(601\) 9.09931 15.7605i 0.371169 0.642883i −0.618577 0.785724i \(-0.712290\pi\)
0.989746 + 0.142841i \(0.0456238\pi\)
\(602\) 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 0.545795 0.837919i \(-0.316228\pi\)
−0.998556 + 0.0537125i \(0.982895\pi\)
\(608\) 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 0.957219 0.289364i \(-0.0934439\pi\)
−0.729206 + 0.684294i \(0.760111\pi\)
\(618\) 0 0
\(619\) 4.31663 7.47663i 0.173500 0.300511i −0.766141 0.642672i \(-0.777826\pi\)
0.939641 + 0.342161i \(0.111159\pi\)
\(620\) 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 −0.301978 0.953315i \(-0.597647\pi\)
0.976584 0.215137i \(-0.0690199\pi\)
\(642\) 0 0
\(643\) −5.41741 9.38323i −0.213642 0.370039i 0.739210 0.673475i \(-0.235199\pi\)
−0.952852 + 0.303437i \(0.901866\pi\)
\(644\) 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 0.901919 0.431905i \(-0.142159\pi\)
−0.825000 + 0.565132i \(0.808825\pi\)
\(654\) 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 −0.654474 0.756084i \(-0.727110\pi\)
0.982025 + 0.188749i \(0.0604434\pi\)
\(660\) 0 0
\(661\) 8.51080 + 14.7411i 0.331032 + 0.573364i 0.982714 0.185128i \(-0.0592700\pi\)
−0.651683 + 0.758492i \(0.725937\pi\)
\(662\) 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 0.443953 + 0.896050i \(0.353576\pi\)
−0.997979 + 0.0635501i \(0.979758\pi\)
\(674\) 0 0
\(675\) −3.38511 + 8.30885i −0.130293 + 0.319808i
\(676\) 0 0
\(677\) 3.01819 5.22765i 0.115998 0.200915i −0.802180 0.597082i \(-0.796327\pi\)
0.918178 + 0.396167i \(0.129660\pi\)
\(678\) 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 −0.972699 0.232072i \(-0.925450\pi\)
0.687330 + 0.726346i \(0.258783\pi\)
\(692\) 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 −0.928799 0.370584i \(-0.879158\pi\)
0.785334 + 0.619072i \(0.212491\pi\)
\(710\) 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 −0.832199 0.554478i \(-0.812918\pi\)
0.896291 + 0.443466i \(0.146251\pi\)
\(728\) 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 −0.964295 0.264829i \(-0.914685\pi\)
0.252799 0.967519i \(-0.418649\pi\)
\(734\) 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 0.939821 0.341668i \(-0.110992\pi\)
−0.765803 + 0.643075i \(0.777658\pi\)
\(744\) 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 0.762285 0.647242i \(-0.224078\pi\)
−0.941670 + 0.336537i \(0.890744\pi\)
\(752\) 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 0.579084 0.815268i \(-0.303410\pi\)
−0.995585 + 0.0938675i \(0.970077\pi\)
\(762\) 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 0.805923 0.592021i \(-0.201670\pi\)
−0.915666 + 0.401939i \(0.868336\pi\)
\(770\) 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 0.995982 + 0.0895491i \(0.0285426\pi\)
−0.420439 + 0.907321i \(0.638124\pi\)
\(788\) 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 −0.902132 0.431461i \(-0.857998\pi\)
0.0774101 0.996999i \(-0.475335\pi\)
\(798\) 0 0
\(799\) 5.75223 9.96316i 0.203499 0.352471i
\(800\)