Properties

Label 2646.2.h.r.667.4
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.31116960000.2
Defining polynomial: \(x^{8} + x^{6} - 8 x^{4} + 9 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 882)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.4
Root \(-1.62968 - 0.586627i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.r.361.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.25937 q^{5} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.25937 q^{5} +1.00000 q^{8} +(-1.62968 - 2.82269i) q^{10} -5.62348 q^{11} +(0.613616 + 1.06281i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-2.95256 - 5.11398i) q^{17} +(-1.32288 + 2.29129i) q^{19} +(-1.62968 + 2.82269i) q^{20} +(2.81174 + 4.87007i) q^{22} -6.62348 q^{23} +5.62348 q^{25} +(0.613616 - 1.06281i) q^{26} +(-2.00000 + 3.46410i) q^{29} +(-0.613616 + 1.06281i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.95256 + 5.11398i) q^{34} +(-3.00000 + 5.19615i) q^{37} +2.64575 q^{38} +3.25937 q^{40} +(-2.95256 - 5.11398i) q^{41} +(-3.81174 + 6.60212i) q^{43} +(2.81174 - 4.87007i) q^{44} +(3.31174 + 5.73610i) q^{46} +(5.29150 + 9.16515i) q^{47} +(-2.81174 - 4.87007i) q^{50} -1.22723 q^{52} +(-2.00000 - 3.46410i) q^{53} -18.3290 q^{55} +4.00000 q^{58} +(-7.43916 + 12.8850i) q^{59} +(2.24330 + 3.88551i) q^{61} +1.22723 q^{62} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{65} +(2.81174 - 4.87007i) q^{67} +5.90512 q^{68} +10.6235 q^{71} +(-5.59831 - 9.69656i) q^{73} +6.00000 q^{74} +(-1.32288 - 2.29129i) q^{76} +(-1.68826 - 2.92416i) q^{79} +(-1.62968 - 2.82269i) q^{80} +(-2.95256 + 5.11398i) q^{82} +(-3.87298 + 6.70820i) q^{83} +(-9.62348 - 16.6683i) q^{85} +7.62348 q^{86} -5.62348 q^{88} +(4.48660 - 7.77102i) q^{89} +(3.31174 - 5.73610i) q^{92} +(5.29150 - 9.16515i) q^{94} +(-4.31174 + 7.46815i) q^{95} +(-1.53404 + 2.65704i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} + O(q^{10}) \) \( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 4 q^{11} - 4 q^{16} + 2 q^{22} - 12 q^{23} + 4 q^{25} - 16 q^{29} - 4 q^{32} - 24 q^{37} - 10 q^{43} + 2 q^{44} + 6 q^{46} - 2 q^{50} - 16 q^{53} + 32 q^{58} + 8 q^{64} + 16 q^{65} + 2 q^{67} + 44 q^{71} + 48 q^{74} - 34 q^{79} - 36 q^{85} + 20 q^{86} - 4 q^{88} + 6 q^{92} - 14 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 3.25937 1.45763 0.728817 0.684709i \(-0.240071\pi\)
0.728817 + 0.684709i \(0.240071\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −1.62968 2.82269i −0.515351 0.892615i
\(11\) −5.62348 −1.69554 −0.847771 0.530363i \(-0.822056\pi\)
−0.847771 + 0.530363i \(0.822056\pi\)
\(12\) 0 0
\(13\) 0.613616 + 1.06281i 0.170186 + 0.294772i 0.938485 0.345320i \(-0.112230\pi\)
−0.768298 + 0.640092i \(0.778896\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.95256 5.11398i −0.716101 1.24032i −0.962533 0.271163i \(-0.912592\pi\)
0.246433 0.969160i \(-0.420742\pi\)
\(18\) 0 0
\(19\) −1.32288 + 2.29129i −0.303488 + 0.525657i −0.976924 0.213589i \(-0.931485\pi\)
0.673435 + 0.739246i \(0.264818\pi\)
\(20\) −1.62968 + 2.82269i −0.364408 + 0.631174i
\(21\) 0 0
\(22\) 2.81174 + 4.87007i 0.599464 + 1.03830i
\(23\) −6.62348 −1.38109 −0.690545 0.723289i \(-0.742629\pi\)
−0.690545 + 0.723289i \(0.742629\pi\)
\(24\) 0 0
\(25\) 5.62348 1.12470
\(26\) 0.613616 1.06281i 0.120340 0.208435i
\(27\) 0 0
\(28\) 0 0
\(29\) −2.00000 + 3.46410i −0.371391 + 0.643268i −0.989780 0.142605i \(-0.954452\pi\)
0.618389 + 0.785872i \(0.287786\pi\)
\(30\) 0 0
\(31\) −0.613616 + 1.06281i −0.110209 + 0.190887i −0.915854 0.401511i \(-0.868485\pi\)
0.805646 + 0.592398i \(0.201819\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −2.95256 + 5.11398i −0.506360 + 0.877041i
\(35\) 0 0
\(36\) 0 0
\(37\) −3.00000 + 5.19615i −0.493197 + 0.854242i −0.999969 0.00783774i \(-0.997505\pi\)
0.506772 + 0.862080i \(0.330838\pi\)
\(38\) 2.64575 0.429198
\(39\) 0 0
\(40\) 3.25937 0.515351
\(41\) −2.95256 5.11398i −0.461112 0.798670i 0.537904 0.843006i \(-0.319216\pi\)
−0.999017 + 0.0443359i \(0.985883\pi\)
\(42\) 0 0
\(43\) −3.81174 + 6.60212i −0.581285 + 1.00681i 0.414043 + 0.910257i \(0.364116\pi\)
−0.995327 + 0.0965570i \(0.969217\pi\)
\(44\) 2.81174 4.87007i 0.423885 0.734191i
\(45\) 0 0
\(46\) 3.31174 + 5.73610i 0.488289 + 0.845742i
\(47\) 5.29150 + 9.16515i 0.771845 + 1.33687i 0.936551 + 0.350532i \(0.113999\pi\)
−0.164706 + 0.986343i \(0.552667\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −2.81174 4.87007i −0.397640 0.688732i
\(51\) 0 0
\(52\) −1.22723 −0.170186
\(53\) −2.00000 3.46410i −0.274721 0.475831i 0.695344 0.718677i \(-0.255252\pi\)
−0.970065 + 0.242846i \(0.921919\pi\)
\(54\) 0 0
\(55\) −18.3290 −2.47148
\(56\) 0 0
\(57\) 0 0
\(58\) 4.00000 0.525226
\(59\) −7.43916 + 12.8850i −0.968496 + 1.67748i −0.268582 + 0.963257i \(0.586555\pi\)
−0.699914 + 0.714227i \(0.746778\pi\)
\(60\) 0 0
\(61\) 2.24330 + 3.88551i 0.287225 + 0.497488i 0.973146 0.230187i \(-0.0739339\pi\)
−0.685921 + 0.727676i \(0.740601\pi\)
\(62\) 1.22723 0.155859
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 2.00000 + 3.46410i 0.248069 + 0.429669i
\(66\) 0 0
\(67\) 2.81174 4.87007i 0.343508 0.594974i −0.641573 0.767062i \(-0.721718\pi\)
0.985082 + 0.172088i \(0.0550513\pi\)
\(68\) 5.90512 0.716101
\(69\) 0 0
\(70\) 0 0
\(71\) 10.6235 1.26077 0.630387 0.776281i \(-0.282896\pi\)
0.630387 + 0.776281i \(0.282896\pi\)
\(72\) 0 0
\(73\) −5.59831 9.69656i −0.655233 1.13490i −0.981835 0.189735i \(-0.939237\pi\)
0.326603 0.945162i \(-0.394096\pi\)
\(74\) 6.00000 0.697486
\(75\) 0 0
\(76\) −1.32288 2.29129i −0.151744 0.262829i
\(77\) 0 0
\(78\) 0 0
\(79\) −1.68826 2.92416i −0.189944 0.328993i 0.755287 0.655394i \(-0.227497\pi\)
−0.945231 + 0.326401i \(0.894164\pi\)
\(80\) −1.62968 2.82269i −0.182204 0.315587i
\(81\) 0 0
\(82\) −2.95256 + 5.11398i −0.326056 + 0.564745i
\(83\) −3.87298 + 6.70820i −0.425115 + 0.736321i −0.996431 0.0844091i \(-0.973100\pi\)
0.571316 + 0.820730i \(0.306433\pi\)
\(84\) 0 0
\(85\) −9.62348 16.6683i −1.04381 1.80794i
\(86\) 7.62348 0.822060
\(87\) 0 0
\(88\) −5.62348 −0.599464
\(89\) 4.48660 7.77102i 0.475579 0.823726i −0.524030 0.851700i \(-0.675572\pi\)
0.999609 + 0.0279735i \(0.00890540\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 3.31174 5.73610i 0.345273 0.598030i
\(93\) 0 0
\(94\) 5.29150 9.16515i 0.545777 0.945313i
\(95\) −4.31174 + 7.46815i −0.442375 + 0.766216i
\(96\) 0 0
\(97\) −1.53404 + 2.65704i −0.155758 + 0.269781i −0.933335 0.359007i \(-0.883115\pi\)
0.777577 + 0.628788i \(0.216449\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.81174 + 4.87007i −0.281174 + 0.487007i
\(101\) −12.6151 −1.25525 −0.627627 0.778514i \(-0.715974\pi\)
−0.627627 + 0.778514i \(0.715974\pi\)
\(102\) 0 0
\(103\) −9.35577 −0.921852 −0.460926 0.887439i \(-0.652483\pi\)
−0.460926 + 0.887439i \(0.652483\pi\)
\(104\) 0.613616 + 1.06281i 0.0601700 + 0.104217i
\(105\) 0 0
\(106\) −2.00000 + 3.46410i −0.194257 + 0.336463i
\(107\) 0.188262 0.326080i 0.0182000 0.0315233i −0.856782 0.515679i \(-0.827540\pi\)
0.874982 + 0.484156i \(0.160873\pi\)
\(108\) 0 0
\(109\) −5.62348 9.74015i −0.538631 0.932937i −0.998978 0.0451975i \(-0.985608\pi\)
0.460347 0.887739i \(-0.347725\pi\)
\(110\) 9.16449 + 15.8734i 0.873799 + 1.51347i
\(111\) 0 0
\(112\) 0 0
\(113\) −3.68826 6.38826i −0.346963 0.600957i 0.638746 0.769418i \(-0.279454\pi\)
−0.985708 + 0.168461i \(0.946120\pi\)
\(114\) 0 0
\(115\) −21.5883 −2.01312
\(116\) −2.00000 3.46410i −0.185695 0.321634i
\(117\) 0 0
\(118\) 14.8783 1.36966
\(119\) 0 0
\(120\) 0 0
\(121\) 20.6235 1.87486
\(122\) 2.24330 3.88551i 0.203099 0.351777i
\(123\) 0 0
\(124\) −0.613616 1.06281i −0.0551043 0.0954435i
\(125\) 2.03214 0.181760
\(126\) 0 0
\(127\) 1.37652 0.122147 0.0610734 0.998133i \(-0.480548\pi\)
0.0610734 + 0.998133i \(0.480548\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 2.00000 3.46410i 0.175412 0.303822i
\(131\) 5.71383 0.499220 0.249610 0.968346i \(-0.419698\pi\)
0.249610 + 0.968346i \(0.419698\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −5.62348 −0.485794
\(135\) 0 0
\(136\) −2.95256 5.11398i −0.253180 0.438520i
\(137\) 20.8704 1.78308 0.891540 0.452941i \(-0.149625\pi\)
0.891540 + 0.452941i \(0.149625\pi\)
\(138\) 0 0
\(139\) −3.96863 6.87386i −0.336615 0.583033i 0.647179 0.762338i \(-0.275949\pi\)
−0.983794 + 0.179305i \(0.942615\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −5.31174 9.20020i −0.445751 0.772064i
\(143\) −3.45065 5.97671i −0.288558 0.499798i
\(144\) 0 0
\(145\) −6.51873 + 11.2908i −0.541351 + 0.937648i
\(146\) −5.59831 + 9.69656i −0.463319 + 0.802493i
\(147\) 0 0
\(148\) −3.00000 5.19615i −0.246598 0.427121i
\(149\) 5.24695 0.429847 0.214923 0.976631i \(-0.431050\pi\)
0.214923 + 0.976631i \(0.431050\pi\)
\(150\) 0 0
\(151\) −8.62348 −0.701768 −0.350884 0.936419i \(-0.614119\pi\)
−0.350884 + 0.936419i \(0.614119\pi\)
\(152\) −1.32288 + 2.29129i −0.107299 + 0.185848i
\(153\) 0 0
\(154\) 0 0
\(155\) −2.00000 + 3.46410i −0.160644 + 0.278243i
\(156\) 0 0
\(157\) −8.14842 + 14.1135i −0.650315 + 1.12638i 0.332732 + 0.943021i \(0.392030\pi\)
−0.983046 + 0.183356i \(0.941304\pi\)
\(158\) −1.68826 + 2.92416i −0.134311 + 0.232633i
\(159\) 0 0
\(160\) −1.62968 + 2.82269i −0.128838 + 0.223154i
\(161\) 0 0
\(162\) 0 0
\(163\) 0.623475 1.07989i 0.0488344 0.0845836i −0.840575 0.541695i \(-0.817783\pi\)
0.889409 + 0.457112i \(0.151116\pi\)
\(164\) 5.90512 0.461112
\(165\) 0 0
\(166\) 7.74597 0.601204
\(167\) −3.25937 5.64539i −0.252217 0.436853i 0.711919 0.702262i \(-0.247826\pi\)
−0.964136 + 0.265409i \(0.914493\pi\)
\(168\) 0 0
\(169\) 5.74695 9.95401i 0.442073 0.765693i
\(170\) −9.62348 + 16.6683i −0.738087 + 1.27840i
\(171\) 0 0
\(172\) −3.81174 6.60212i −0.290642 0.503407i
\(173\) 0.613616 + 1.06281i 0.0466524 + 0.0808043i 0.888409 0.459053i \(-0.151811\pi\)
−0.841756 + 0.539858i \(0.818478\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.81174 + 4.87007i 0.211943 + 0.367096i
\(177\) 0 0
\(178\) −8.97320 −0.672570
\(179\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(180\) 0 0
\(181\) −4.48660 −0.333486 −0.166743 0.986000i \(-0.553325\pi\)
−0.166743 + 0.986000i \(0.553325\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −6.62348 −0.488289
\(185\) −9.77810 + 16.9362i −0.718900 + 1.24517i
\(186\) 0 0
\(187\) 16.6036 + 28.7584i 1.21418 + 2.10302i
\(188\) −10.5830 −0.771845
\(189\) 0 0
\(190\) 8.62348 0.625613
\(191\) 2.68826 + 4.65621i 0.194516 + 0.336911i 0.946742 0.321994i \(-0.104353\pi\)
−0.752226 + 0.658905i \(0.771020\pi\)
\(192\) 0 0
\(193\) −6.74695 + 11.6861i −0.485656 + 0.841181i −0.999864 0.0164844i \(-0.994753\pi\)
0.514208 + 0.857666i \(0.328086\pi\)
\(194\) 3.06808 0.220275
\(195\) 0 0
\(196\) 0 0
\(197\) −7.24695 −0.516324 −0.258162 0.966102i \(-0.583117\pi\)
−0.258162 + 0.966102i \(0.583117\pi\)
\(198\) 0 0
\(199\) 5.10022 + 8.83383i 0.361545 + 0.626214i 0.988215 0.153071i \(-0.0489162\pi\)
−0.626671 + 0.779284i \(0.715583\pi\)
\(200\) 5.62348 0.397640
\(201\) 0 0
\(202\) 6.30757 + 10.9250i 0.443799 + 0.768683i
\(203\) 0 0
\(204\) 0 0
\(205\) −9.62348 16.6683i −0.672133 1.16417i
\(206\) 4.67789 + 8.10234i 0.325924 + 0.564517i
\(207\) 0 0
\(208\) 0.613616 1.06281i 0.0425466 0.0736929i
\(209\) 7.43916 12.8850i 0.514577 0.891274i
\(210\) 0 0
\(211\) 2.62348 + 4.54399i 0.180607 + 0.312821i 0.942088 0.335367i \(-0.108860\pi\)
−0.761480 + 0.648188i \(0.775527\pi\)
\(212\) 4.00000 0.274721
\(213\) 0 0
\(214\) −0.376525 −0.0257387
\(215\) −12.4239 + 21.5187i −0.847300 + 1.46757i
\(216\) 0 0
\(217\) 0 0
\(218\) −5.62348 + 9.74015i −0.380870 + 0.659686i
\(219\) 0 0
\(220\) 9.16449 15.8734i 0.617870 1.07018i
\(221\) 3.62348 6.27604i 0.243741 0.422172i
\(222\) 0 0
\(223\) 3.25937 5.64539i 0.218263 0.378043i −0.736014 0.676967i \(-0.763294\pi\)
0.954277 + 0.298923i \(0.0966275\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −3.68826 + 6.38826i −0.245340 + 0.424941i
\(227\) −28.7207 −1.90626 −0.953130 0.302562i \(-0.902158\pi\)
−0.953130 + 0.302562i \(0.902158\pi\)
\(228\) 0 0
\(229\) −26.8798 −1.77627 −0.888135 0.459583i \(-0.847999\pi\)
−0.888135 + 0.459583i \(0.847999\pi\)
\(230\) 10.7942 + 18.6961i 0.711746 + 1.23278i
\(231\) 0 0
\(232\) −2.00000 + 3.46410i −0.131306 + 0.227429i
\(233\) 8.50000 14.7224i 0.556854 0.964499i −0.440903 0.897555i \(-0.645342\pi\)
0.997757 0.0669439i \(-0.0213249\pi\)
\(234\) 0 0
\(235\) 17.2470 + 29.8726i 1.12507 + 1.94867i
\(236\) −7.43916 12.8850i −0.484248 0.838742i
\(237\) 0 0
\(238\) 0 0
\(239\) 6.31174 + 10.9323i 0.408272 + 0.707148i 0.994696 0.102856i \(-0.0327980\pi\)
−0.586424 + 0.810004i \(0.699465\pi\)
\(240\) 0 0
\(241\) 26.6886 1.71916 0.859580 0.511000i \(-0.170725\pi\)
0.859580 + 0.511000i \(0.170725\pi\)
\(242\) −10.3117 17.8605i −0.662864 1.14811i
\(243\) 0 0
\(244\) −4.48660 −0.287225
\(245\) 0 0
\(246\) 0 0
\(247\) −3.24695 −0.206599
\(248\) −0.613616 + 1.06281i −0.0389647 + 0.0674888i
\(249\) 0 0
\(250\) −1.01607 1.75988i −0.0642618 0.111305i
\(251\) 5.10022 0.321923 0.160961 0.986961i \(-0.448541\pi\)
0.160961 + 0.986961i \(0.448541\pi\)
\(252\) 0 0
\(253\) 37.2470 2.34170
\(254\) −0.688262 1.19211i −0.0431854 0.0747993i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 0.996190 0.0621407 0.0310703 0.999517i \(-0.490108\pi\)
0.0310703 + 0.999517i \(0.490108\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −4.00000 −0.248069
\(261\) 0 0
\(262\) −2.85692 4.94832i −0.176501 0.305708i
\(263\) 3.37652 0.208205 0.104103 0.994567i \(-0.466803\pi\)
0.104103 + 0.994567i \(0.466803\pi\)
\(264\) 0 0
\(265\) −6.51873 11.2908i −0.400443 0.693587i
\(266\) 0 0
\(267\) 0 0
\(268\) 2.81174 + 4.87007i 0.171754 + 0.297487i
\(269\) 12.0214 + 20.8217i 0.732958 + 1.26952i 0.955614 + 0.294623i \(0.0951941\pi\)
−0.222656 + 0.974897i \(0.571473\pi\)
\(270\) 0 0
\(271\) −1.41852 + 2.45695i −0.0861689 + 0.149249i −0.905889 0.423516i \(-0.860796\pi\)
0.819720 + 0.572765i \(0.194129\pi\)
\(272\) −2.95256 + 5.11398i −0.179025 + 0.310081i
\(273\) 0 0
\(274\) −10.4352 18.0743i −0.630414 1.09191i
\(275\) −31.6235 −1.90697
\(276\) 0 0
\(277\) −28.4939 −1.71203 −0.856016 0.516949i \(-0.827068\pi\)
−0.856016 + 0.516949i \(0.827068\pi\)
\(278\) −3.96863 + 6.87386i −0.238022 + 0.412267i
\(279\) 0 0
\(280\) 0 0
\(281\) −12.9352 + 22.4044i −0.771650 + 1.33654i 0.165008 + 0.986292i \(0.447235\pi\)
−0.936658 + 0.350245i \(0.886098\pi\)
\(282\) 0 0
\(283\) −3.66182 + 6.34246i −0.217673 + 0.377020i −0.954096 0.299501i \(-0.903180\pi\)
0.736423 + 0.676521i \(0.236513\pi\)
\(284\) −5.31174 + 9.20020i −0.315194 + 0.545931i
\(285\) 0 0
\(286\) −3.45065 + 5.97671i −0.204041 + 0.353410i
\(287\) 0 0
\(288\) 0 0
\(289\) −8.93521 + 15.4762i −0.525601 + 0.910367i
\(290\) 13.0375 0.765587
\(291\) 0 0
\(292\) 11.1966 0.655233
\(293\) 12.8263 + 22.2158i 0.749321 + 1.29786i 0.948149 + 0.317827i \(0.102953\pi\)
−0.198828 + 0.980034i \(0.563713\pi\)
\(294\) 0 0
\(295\) −24.2470 + 41.9970i −1.41171 + 2.44516i
\(296\) −3.00000 + 5.19615i −0.174371 + 0.302020i
\(297\) 0 0
\(298\) −2.62348 4.54399i −0.151974 0.263226i
\(299\) −4.06427 7.03952i −0.235043 0.407106i
\(300\) 0 0
\(301\) 0 0
\(302\) 4.31174 + 7.46815i 0.248113 + 0.429744i
\(303\) 0 0
\(304\) 2.64575 0.151744
\(305\) 7.31174 + 12.6643i 0.418669 + 0.725156i
\(306\) 0 0
\(307\) 13.2288 0.755005 0.377503 0.926009i \(-0.376783\pi\)
0.377503 + 0.926009i \(0.376783\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 4.00000 0.227185
\(311\) 10.3917 17.9990i 0.589260 1.02063i −0.405069 0.914286i \(-0.632753\pi\)
0.994330 0.106343i \(-0.0339141\pi\)
\(312\) 0 0
\(313\) −10.8898 18.8617i −0.615529 1.06613i −0.990292 0.139006i \(-0.955609\pi\)
0.374763 0.927121i \(-0.377724\pi\)
\(314\) 16.2968 0.919684
\(315\) 0 0
\(316\) 3.37652 0.189944
\(317\) 3.62348 + 6.27604i 0.203515 + 0.352498i 0.949658 0.313287i \(-0.101430\pi\)
−0.746144 + 0.665785i \(0.768097\pi\)
\(318\) 0 0
\(319\) 11.2470 19.4803i 0.629708 1.09069i
\(320\) 3.25937 0.182204
\(321\) 0 0
\(322\) 0 0
\(323\) 15.6235 0.869313
\(324\) 0 0
\(325\) 3.45065 + 5.97671i 0.191408 + 0.331528i
\(326\) −1.24695 −0.0690622
\(327\) 0 0
\(328\) −2.95256 5.11398i −0.163028 0.282372i
\(329\) 0 0
\(330\) 0 0
\(331\) −4.00000 6.92820i −0.219860 0.380808i 0.734905 0.678170i \(-0.237227\pi\)
−0.954765 + 0.297361i \(0.903893\pi\)
\(332\) −3.87298 6.70820i −0.212558 0.368161i
\(333\) 0 0
\(334\) −3.25937 + 5.64539i −0.178345 + 0.308902i
\(335\) 9.16449 15.8734i 0.500709 0.867254i
\(336\) 0 0
\(337\) −1.56479 2.71029i −0.0852394 0.147639i 0.820254 0.572000i \(-0.193832\pi\)
−0.905493 + 0.424361i \(0.860499\pi\)
\(338\) −11.4939 −0.625186
\(339\) 0 0
\(340\) 19.2470 1.04381
\(341\) 3.45065 5.97671i 0.186863 0.323657i
\(342\) 0 0
\(343\) 0 0
\(344\) −3.81174 + 6.60212i −0.205515 + 0.355963i
\(345\) 0 0
\(346\) 0.613616 1.06281i 0.0329882 0.0571372i
\(347\) −1.81174 + 3.13802i −0.0972592 + 0.168458i −0.910549 0.413401i \(-0.864341\pi\)
0.813290 + 0.581858i \(0.197674\pi\)
\(348\) 0 0
\(349\) 13.6511 23.6444i 0.730726 1.26565i −0.225848 0.974163i \(-0.572515\pi\)
0.956573 0.291492i \(-0.0941515\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 2.81174 4.87007i 0.149866 0.259576i
\(353\) 5.90512 0.314298 0.157149 0.987575i \(-0.449770\pi\)
0.157149 + 0.987575i \(0.449770\pi\)
\(354\) 0 0
\(355\) 34.6258 1.83775
\(356\) 4.48660 + 7.77102i 0.237789 + 0.411863i
\(357\) 0 0
\(358\) 0 0
\(359\) 15.5587 26.9484i 0.821156 1.42228i −0.0836657 0.996494i \(-0.526663\pi\)
0.904822 0.425790i \(-0.140004\pi\)
\(360\) 0 0
\(361\) 6.00000 + 10.3923i 0.315789 + 0.546963i
\(362\) 2.24330 + 3.88551i 0.117905 + 0.204218i
\(363\) 0 0
\(364\) 0 0
\(365\) −18.2470 31.6046i −0.955089 1.65426i
\(366\) 0 0
\(367\) −6.90131 −0.360245 −0.180123 0.983644i \(-0.557649\pi\)
−0.180123 + 0.983644i \(0.557649\pi\)
\(368\) 3.31174 + 5.73610i 0.172636 + 0.299015i
\(369\) 0 0
\(370\) 19.5562 1.01668
\(371\) 0 0
\(372\) 0 0
\(373\) 11.2470 0.582345 0.291173 0.956671i \(-0.405955\pi\)
0.291173 + 0.956671i \(0.405955\pi\)
\(374\) 16.6036 28.7584i 0.858554 1.48706i
\(375\) 0 0
\(376\) 5.29150 + 9.16515i 0.272888 + 0.472657i
\(377\) −4.90893 −0.252823
\(378\) 0 0
\(379\) 15.6235 0.802524 0.401262 0.915963i \(-0.368572\pi\)
0.401262 + 0.915963i \(0.368572\pi\)
\(380\) −4.31174 7.46815i −0.221187 0.383108i
\(381\) 0 0
\(382\) 2.68826 4.65621i 0.137543 0.238232i
\(383\) −27.6847 −1.41462 −0.707312 0.706901i \(-0.750092\pi\)
−0.707312 + 0.706901i \(0.750092\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 13.4939 0.686822
\(387\) 0 0
\(388\) −1.53404 2.65704i −0.0778791 0.134891i
\(389\) −37.2470 −1.88850 −0.944248 0.329236i \(-0.893209\pi\)
−0.944248 + 0.329236i \(0.893209\pi\)
\(390\) 0 0
\(391\) 19.5562 + 33.8723i 0.989000 + 1.71300i
\(392\) 0 0
\(393\) 0 0
\(394\) 3.62348 + 6.27604i 0.182548 + 0.316183i
\(395\) −5.50267 9.53090i −0.276869 0.479552i
\(396\) 0 0
\(397\) 4.67789 8.10234i 0.234776 0.406645i −0.724431 0.689347i \(-0.757898\pi\)
0.959208 + 0.282702i \(0.0912309\pi\)
\(398\) 5.10022 8.83383i 0.255651 0.442800i
\(399\) 0 0
\(400\) −2.81174 4.87007i −0.140587 0.243504i
\(401\) 15.0000 0.749064 0.374532 0.927214i \(-0.377803\pi\)
0.374532 + 0.927214i \(0.377803\pi\)
\(402\) 0 0
\(403\) −1.50610 −0.0750241
\(404\) 6.30757 10.9250i 0.313813 0.543541i
\(405\) 0 0
\(406\) 0 0
\(407\) 16.8704 29.2204i 0.836236 1.44840i
\(408\) 0 0
\(409\) −1.11171 + 1.92554i −0.0549706 + 0.0952118i −0.892201 0.451638i \(-0.850840\pi\)
0.837231 + 0.546850i \(0.184173\pi\)
\(410\) −9.62348 + 16.6683i −0.475270 + 0.823191i
\(411\) 0 0
\(412\) 4.67789 8.10234i 0.230463 0.399174i
\(413\) 0 0
\(414\) 0 0
\(415\) −12.6235 + 21.8645i −0.619662 + 1.07329i
\(416\) −1.22723 −0.0601700
\(417\) 0 0
\(418\) −14.8783 −0.727722
\(419\) 0.402452 + 0.697067i 0.0196610 + 0.0340539i 0.875689 0.482876i \(-0.160408\pi\)
−0.856027 + 0.516930i \(0.827075\pi\)
\(420\) 0 0
\(421\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(422\) 2.62348 4.54399i 0.127709 0.221198i
\(423\) 0 0
\(424\) −2.00000 3.46410i −0.0971286 0.168232i
\(425\) −16.6036 28.7584i −0.805395 1.39499i
\(426\) 0 0
\(427\) 0 0
\(428\) 0.188262 + 0.326080i 0.00910000 + 0.0157617i
\(429\) 0 0
\(430\) 24.8477 1.19826
\(431\) −4.00000 6.92820i −0.192673 0.333720i 0.753462 0.657491i \(-0.228382\pi\)
−0.946135 + 0.323772i \(0.895049\pi\)
\(432\) 0 0
\(433\) −7.13235 −0.342759 −0.171379 0.985205i \(-0.554822\pi\)
−0.171379 + 0.985205i \(0.554822\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 11.2470 0.538631
\(437\) 8.76203 15.1763i 0.419145 0.725980i
\(438\) 0 0
\(439\) −15.4919 26.8328i −0.739390 1.28066i −0.952770 0.303691i \(-0.901781\pi\)
0.213381 0.976969i \(-0.431552\pi\)
\(440\) −18.3290 −0.873799
\(441\) 0 0
\(442\) −7.24695 −0.344702
\(443\) 10.1883 + 17.6466i 0.484059 + 0.838415i 0.999832 0.0183103i \(-0.00582869\pi\)
−0.515773 + 0.856725i \(0.672495\pi\)
\(444\) 0 0
\(445\) 14.6235 25.3286i 0.693219 1.20069i
\(446\) −6.51873 −0.308671
\(447\) 0 0
\(448\) 0 0
\(449\) 15.0000 0.707894 0.353947 0.935266i \(-0.384839\pi\)
0.353947 + 0.935266i \(0.384839\pi\)
\(450\) 0 0
\(451\) 16.6036 + 28.7584i 0.781835 + 1.35418i
\(452\) 7.37652 0.346963
\(453\) 0 0
\(454\) 14.3603 + 24.8728i 0.673964 + 1.16734i
\(455\) 0 0
\(456\) 0 0
\(457\) −5.50000 9.52628i −0.257279 0.445621i 0.708233 0.705979i \(-0.249493\pi\)
−0.965512 + 0.260358i \(0.916159\pi\)
\(458\) 13.4399 + 23.2786i 0.628006 + 1.08774i
\(459\) 0 0
\(460\) 10.7942 18.6961i 0.503281 0.871708i
\(461\) 4.88905 8.46808i 0.227706 0.394398i −0.729422 0.684064i \(-0.760211\pi\)
0.957128 + 0.289666i \(0.0935442\pi\)
\(462\) 0 0
\(463\) −12.6883 21.9767i −0.589674 1.02134i −0.994275 0.106851i \(-0.965923\pi\)
0.404601 0.914493i \(-0.367410\pi\)
\(464\) 4.00000 0.185695
\(465\) 0 0
\(466\) −17.0000 −0.787510
\(467\) 5.59831 9.69656i 0.259059 0.448703i −0.706931 0.707282i \(-0.749921\pi\)
0.965990 + 0.258579i \(0.0832543\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 17.2470 29.8726i 0.795543 1.37792i
\(471\) 0 0
\(472\) −7.43916 + 12.8850i −0.342415 + 0.593080i
\(473\) 21.4352 37.1269i 0.985592 1.70710i
\(474\) 0 0
\(475\) −7.43916 + 12.8850i −0.341332 + 0.591204i
\(476\) 0 0
\(477\) 0 0
\(478\) 6.31174 10.9323i 0.288692 0.500029i
\(479\) −15.4919 −0.707845 −0.353922 0.935275i \(-0.615152\pi\)
−0.353922 + 0.935275i \(0.615152\pi\)
\(480\) 0 0
\(481\) −7.36339 −0.335742
\(482\) −13.3443 23.1130i −0.607815 1.05277i
\(483\) 0 0
\(484\) −10.3117 + 17.8605i −0.468715 + 0.811839i
\(485\) −5.00000 + 8.66025i −0.227038 + 0.393242i
\(486\) 0 0
\(487\) −2.31174 4.00405i −0.104755 0.181441i 0.808883 0.587969i \(-0.200072\pi\)
−0.913638 + 0.406529i \(0.866739\pi\)
\(488\) 2.24330 + 3.88551i 0.101549 + 0.175889i
\(489\) 0 0
\(490\) 0 0
\(491\) −18.0587 31.2786i −0.814977 1.41158i −0.909344 0.416044i \(-0.863416\pi\)
0.0943671 0.995537i \(-0.469917\pi\)
\(492\) 0 0
\(493\) 23.6205 1.06381
\(494\) 1.62348 + 2.81194i 0.0730436 + 0.126515i
\(495\) 0 0
\(496\) 1.22723 0.0551043
\(497\) 0 0
\(498\) 0 0
\(499\) 8.37652 0.374985 0.187492 0.982266i \(-0.439964\pi\)
0.187492 + 0.982266i \(0.439964\pi\)
\(500\) −1.01607 + 1.75988i −0.0454399 + 0.0787043i
\(501\) 0 0
\(502\) −2.55011 4.41692i −0.113817 0.197137i
\(503\) −20.7834 −0.926688 −0.463344 0.886179i \(-0.653350\pi\)
−0.463344 + 0.886179i \(0.653350\pi\)
\(504\) 0 0
\(505\) −41.1174 −1.82970
\(506\) −18.6235 32.2568i −0.827914 1.43399i
\(507\) 0 0
\(508\) −0.688262 + 1.19211i −0.0305367 + 0.0528911i
\(509\) −16.7192 −0.741064 −0.370532 0.928820i \(-0.620825\pi\)
−0.370532 + 0.928820i \(0.620825\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −0.498095 0.862726i −0.0219700 0.0380532i
\(515\) −30.4939 −1.34372
\(516\) 0 0
\(517\) −29.7566 51.5400i −1.30870 2.26673i
\(518\) 0 0
\(519\) 0 0
\(520\) 2.00000 + 3.46410i 0.0877058 + 0.151911i
\(521\) 15.5677 + 26.9640i 0.682033 + 1.18132i 0.974359 + 0.224998i \(0.0722374\pi\)
−0.292326 + 0.956319i \(0.594429\pi\)
\(522\) 0 0
\(523\) −6.11628 + 10.5937i −0.267446 + 0.463231i −0.968202 0.250171i \(-0.919513\pi\)
0.700755 + 0.713402i \(0.252846\pi\)
\(524\) −2.85692 + 4.94832i −0.124805 + 0.216169i
\(525\) 0 0
\(526\) −1.68826 2.92416i −0.0736117 0.127499i
\(527\) 7.24695 0.315682
\(528\) 0 0
\(529\) 20.8704 0.907410
\(530\) −6.51873 + 11.2908i −0.283156 + 0.490440i
\(531\) 0 0
\(532\) 0 0
\(533\) 3.62348 6.27604i 0.156950 0.271846i
\(534\) 0 0
\(535\) 0.613616 1.06281i 0.0265289 0.0459495i
\(536\) 2.81174 4.87007i 0.121449 0.210355i
\(537\) 0 0
\(538\) 12.0214 20.8217i 0.518279 0.897686i
\(539\) 0 0
\(540\) 0 0
\(541\) −2.00000 + 3.46410i −0.0859867 + 0.148933i −0.905811 0.423681i \(-0.860738\pi\)
0.819825 + 0.572615i \(0.194071\pi\)
\(542\) 2.83704 0.121861
\(543\) 0 0
\(544\) 5.90512 0.253180
\(545\) −18.3290 31.7467i −0.785127 1.35988i
\(546\) 0 0
\(547\) −9.81174 + 16.9944i −0.419520 + 0.726629i −0.995891 0.0905585i \(-0.971135\pi\)
0.576372 + 0.817188i \(0.304468\pi\)
\(548\) −10.4352 + 18.0743i −0.445770 + 0.772097i
\(549\) 0 0
\(550\) 15.8117 + 27.3867i 0.674215 + 1.16777i
\(551\) −5.29150 9.16515i −0.225426 0.390449i
\(552\) 0 0
\(553\) 0 0
\(554\) 14.2470 + 24.6764i 0.605295 + 1.04840i
\(555\) 0 0
\(556\) 7.93725 0.336615
\(557\) 11.3765 + 19.7047i 0.482039 + 0.834916i 0.999787 0.0206171i \(-0.00656308\pi\)
−0.517749 + 0.855533i \(0.673230\pi\)
\(558\) 0 0
\(559\) −9.35577 −0.395707
\(560\) 0 0
\(561\) 0 0
\(562\) 25.8704 1.09128
\(563\) 2.74139 4.74824i 0.115536 0.200114i −0.802458 0.596709i \(-0.796475\pi\)
0.917994 + 0.396595i \(0.129808\pi\)
\(564\) 0 0
\(565\) −12.0214 20.8217i −0.505744 0.875975i
\(566\) 7.32364 0.307835
\(567\) 0 0
\(568\) 10.6235 0.445751
\(569\) 14.4352 + 25.0025i 0.605156 + 1.04816i 0.992027 + 0.126027i \(0.0402224\pi\)
−0.386871 + 0.922134i \(0.626444\pi\)
\(570\) 0 0
\(571\) 4.18826 7.25428i 0.175273 0.303582i −0.764983 0.644051i \(-0.777252\pi\)
0.940256 + 0.340469i \(0.110586\pi\)
\(572\) 6.90131 0.288558
\(573\) 0 0
\(574\) 0 0
\(575\) −37.2470 −1.55331
\(576\) 0 0
\(577\) 8.24406 + 14.2791i 0.343205 + 0.594448i 0.985026 0.172406i \(-0.0551542\pi\)
−0.641821 + 0.766854i \(0.721821\pi\)
\(578\) 17.8704 0.743312
\(579\) 0 0
\(580\) −6.51873 11.2908i −0.270676 0.468824i
\(581\) 0 0
\(582\) 0 0
\(583\) 11.2470 + 19.4803i 0.465801 + 0.806791i
\(584\) −5.59831 9.69656i −0.231660 0.401246i
\(585\) 0 0
\(586\) 12.8263 22.2158i 0.529850 0.917727i
\(587\) 1.51416 2.62261i 0.0624962 0.108247i −0.833084 0.553146i \(-0.813427\pi\)
0.895581 + 0.444899i \(0.146761\pi\)
\(588\) 0 0
\(589\) −1.62348 2.81194i −0.0668941 0.115864i
\(590\) 48.4939 1.99646
\(591\) 0 0
\(592\) 6.00000 0.246598
\(593\) 6.09641 10.5593i 0.250349 0.433618i −0.713273 0.700887i \(-0.752788\pi\)
0.963622 + 0.267269i \(0.0861212\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −2.62348 + 4.54399i −0.107462 + 0.186129i
\(597\) 0 0
\(598\) −4.06427 + 7.03952i −0.166200 + 0.287868i
\(599\) −1.24695 + 2.15978i −0.0509490 + 0.0882463i −0.890375 0.455227i \(-0.849558\pi\)
0.839426 + 0.543474i \(0.182891\pi\)
\(600\) 0 0
\(601\) −19.8630 + 34.4037i −0.810229 + 1.40336i 0.102474 + 0.994736i \(0.467324\pi\)
−0.912704 + 0.408622i \(0.866009\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 4.31174 7.46815i 0.175442 0.303875i
\(605\) 67.2195 2.73286
\(606\) 0 0
\(607\) 27.6847 1.12369 0.561845 0.827243i \(-0.310092\pi\)
0.561845 + 0.827243i \(0.310092\pi\)
\(608\) −1.32288 2.29129i −0.0536497 0.0929240i
\(609\) 0 0
\(610\) 7.31174 12.6643i 0.296044 0.512763i
\(611\) −6.49390 + 11.2478i −0.262715 + 0.455036i
\(612\) 0 0
\(613\) −1.00000 1.73205i −0.0403896 0.0699569i 0.845124 0.534570i \(-0.179527\pi\)
−0.885514 + 0.464614i \(0.846193\pi\)
\(614\) −6.61438 11.4564i −0.266935 0.462344i
\(615\) 0 0
\(616\) 0 0
\(617\) 20.0587 + 34.7427i 0.807532 + 1.39869i 0.914568 + 0.404432i \(0.132531\pi\)
−0.107036 + 0.994255i \(0.534136\pi\)
\(618\) 0 0
\(619\) −34.0122 −1.36707 −0.683533 0.729920i \(-0.739557\pi\)
−0.683533 + 0.729920i \(0.739557\pi\)
\(620\) −2.00000 3.46410i −0.0803219 0.139122i
\(621\) 0 0
\(622\) −20.7834 −0.833340
\(623\) 0 0
\(624\) 0 0
\(625\) −21.4939 −0.859756
\(626\) −10.8898 + 18.8617i −0.435244 + 0.753866i
\(627\) 0 0
\(628\) −8.14842 14.1135i −0.325157 0.563189i
\(629\) 35.4307 1.41271
\(630\) 0 0
\(631\) 30.6235 1.21910 0.609551 0.792747i \(-0.291350\pi\)
0.609551 + 0.792747i \(0.291350\pi\)
\(632\) −1.68826 2.92416i −0.0671555 0.116317i
\(633\) 0 0
\(634\) 3.62348 6.27604i 0.143907 0.249254i
\(635\) 4.48660 0.178045
\(636\) 0 0
\(637\) 0 0
\(638\) −22.4939 −0.890542
\(639\) 0 0
\(640\) −1.62968 2.82269i −0.0644189 0.111577i
\(641\) 25.4939 1.00695 0.503474 0.864010i \(-0.332055\pi\)
0.503474 + 0.864010i \(0.332055\pi\)
\(642\) 0 0
\(643\) 6.82554 + 11.8222i 0.269173 + 0.466222i 0.968649 0.248435i \(-0.0799163\pi\)
−0.699475 + 0.714657i \(0.746583\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −7.81174 13.5303i −0.307349 0.532344i
\(647\) −17.5241 30.3526i −0.688942 1.19328i −0.972180 0.234233i \(-0.924742\pi\)
0.283238 0.959050i \(-0.408591\pi\)
\(648\) 0 0
\(649\) 41.8339 72.4585i 1.64213 2.84424i
\(650\) 3.45065 5.97671i 0.135346 0.234426i
\(651\) 0 0
\(652\) 0.623475 + 1.07989i 0.0244172 + 0.0422918i
\(653\) −39.2470 −1.53585 −0.767926 0.640539i \(-0.778711\pi\)
−0.767926 + 0.640539i \(0.778711\pi\)
\(654\) 0 0
\(655\) 18.6235 0.727679
\(656\) −2.95256 + 5.11398i −0.115278 + 0.199667i
\(657\) 0 0
\(658\) 0 0
\(659\) −5.24695 + 9.08799i −0.204392 + 0.354018i −0.949939 0.312436i \(-0.898855\pi\)
0.745547 + 0.666453i \(0.232188\pi\)
\(660\) 0 0
\(661\) 1.43840 2.49138i 0.0559471 0.0969033i −0.836695 0.547669i \(-0.815516\pi\)
0.892643 + 0.450765i \(0.148849\pi\)
\(662\) −4.00000 + 6.92820i −0.155464 + 0.269272i
\(663\) 0 0
\(664\) −3.87298 + 6.70820i −0.150301 + 0.260329i
\(665\) 0 0
\(666\) 0 0
\(667\) 13.2470 22.9444i 0.512924 0.888410i
\(668\) 6.51873 0.252217
\(669\) 0 0
\(670\) −18.3290 −0.708110
\(671\) −12.6151 21.8501i −0.487002 0.843512i
\(672\) 0 0
\(673\) −9.68826 + 16.7806i −0.373455 + 0.646843i −0.990095 0.140403i \(-0.955160\pi\)
0.616639 + 0.787246i \(0.288494\pi\)
\(674\) −1.56479 + 2.71029i −0.0602733 + 0.104396i
\(675\) 0 0
\(676\) 5.74695 + 9.95401i 0.221037 + 0.382847i
\(677\) −21.3971 37.0608i −0.822356 1.42436i −0.903924 0.427694i \(-0.859326\pi\)
0.0815682 0.996668i \(-0.474007\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −9.62348 16.6683i −0.369043 0.639202i
\(681\) 0 0
\(682\) −6.90131 −0.264265
\(683\) −13.6822 23.6982i −0.523533 0.906787i −0.999625 0.0273907i \(-0.991280\pi\)
0.476091 0.879396i \(-0.342053\pi\)
\(684\) 0 0
\(685\) 68.0244 2.59908
\(686\) 0 0
\(687\) 0 0
\(688\) 7.62348 0.290642
\(689\) 2.45446 4.25126i 0.0935076 0.161960i
\(690\) 0 0
\(691\) −7.34352 12.7193i −0.279360 0.483867i 0.691865 0.722026i \(-0.256789\pi\)
−0.971226 + 0.238160i \(0.923456\pi\)
\(692\) −1.22723 −0.0466524
\(693\) 0 0
\(694\) 3.62348 0.137545
\(695\) −12.9352 22.4044i −0.490661 0.849849i
\(696\) 0 0
\(697\) −17.4352 + 30.1987i −0.660406 + 1.14386i
\(698\) −27.3022 −1.03340
\(699\) 0 0
\(700\) 0 0
\(701\) 21.2470 0.802486 0.401243 0.915972i \(-0.368578\pi\)
0.401243 + 0.915972i \(0.368578\pi\)
\(702\) 0 0
\(703\) −7.93725 13.7477i −0.299359 0.518505i
\(704\) −5.62348 −0.211943
\(705\) 0 0
\(706\) −2.95256 5.11398i −0.111121 0.192467i
\(707\) 0 0
\(708\) 0 0
\(709\) −9.24695 16.0162i −0.347277 0.601501i 0.638488 0.769632i \(-0.279560\pi\)
−0.985765 + 0.168131i \(0.946227\pi\)
\(710\) −17.3129 29.9868i −0.649742 1.12539i
\(711\) 0 0
\(712\) 4.48660 7.77102i 0.168142 0.291231i
\(713\) 4.06427 7.03952i 0.152208 0.263632i
\(714\) 0 0
\(715\) −11.2470 19.4803i −0.420612 0.728522i
\(716\) 0 0
\(717\) 0 0
\(718\) −31.1174 −1.16129
\(719\) −5.90512 + 10.2280i −0.220224 + 0.381439i −0.954876 0.297005i \(-0.904012\pi\)
0.734652 + 0.678444i \(0.237345\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 6.00000 10.3923i 0.223297 0.386762i
\(723\) 0 0
\(724\) 2.24330 3.88551i 0.0833716 0.144404i
\(725\) −11.2470 + 19.4803i −0.417701 + 0.723480i
\(726\) 0 0
\(727\) 22.2020 38.4549i 0.823425 1.42621i −0.0796922 0.996820i \(-0.525394\pi\)
0.903117 0.429394i \(-0.141273\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −18.2470 + 31.6046i −0.675350 + 1.16974i
\(731\) 45.0175 1.66503
\(732\) 0 0
\(733\) −8.16830 −0.301703 −0.150851 0.988556i \(-0.548202\pi\)
−0.150851 + 0.988556i \(0.548202\pi\)
\(734\) 3.45065 + 5.97671i 0.127366 + 0.220604i
\(735\) 0 0
\(736\) 3.31174 5.73610i 0.122072 0.211435i
\(737\) −15.8117 + 27.3867i −0.582433 + 1.00880i
\(738\) 0 0
\(739\) −10.4352 18.0743i −0.383866 0.664875i 0.607746 0.794132i \(-0.292074\pi\)
−0.991611 + 0.129257i \(0.958741\pi\)
\(740\) −9.77810 16.9362i −0.359450 0.622586i
\(741\) 0 0
\(742\) 0 0
\(743\) 15.6235 + 27.0607i 0.573170 + 0.992759i 0.996238 + 0.0866612i \(0.0276198\pi\)
−0.423068 + 0.906098i \(0.639047\pi\)
\(744\) 0 0
\(745\) 17.1017 0.626559
\(746\) −5.62348 9.74015i −0.205890 0.356612i
\(747\) 0 0
\(748\) −33.2073 −1.21418
\(749\) 0 0
\(750\) 0 0
\(751\) −11.3765 −0.415135 −0.207568 0.978221i \(-0.566555\pi\)
−0.207568 + 0.978221i \(0.566555\pi\)
\(752\) 5.29150 9.16515i 0.192961 0.334219i
\(753\) 0 0
\(754\) 2.45446 + 4.25126i 0.0893863 + 0.154822i
\(755\) −28.1071 −1.02292
\(756\) 0 0
\(757\) 43.7409 1.58979 0.794894 0.606748i \(-0.207526\pi\)
0.794894 + 0.606748i \(0.207526\pi\)
\(758\) −7.81174 13.5303i −0.283735 0.491444i
\(759\) 0 0
\(760\) −4.31174 + 7.46815i −0.156403 + 0.270898i
\(761\) 5.67408 0.205685 0.102843 0.994698i \(-0.467206\pi\)
0.102843 + 0.994698i \(0.467206\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −5.37652 −0.194516
\(765\) 0 0
\(766\) 13.8424 + 23.9757i 0.500145 + 0.866277i
\(767\) −18.2591 −0.659300
\(768\) 0 0
\(769\) 0.422329 + 0.731495i 0.0152296 + 0.0263784i 0.873540 0.486753i \(-0.161819\pi\)
−0.858310 + 0.513131i \(0.828485\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −6.74695 11.6861i −0.242828 0.420591i
\(773\) −6.72990 11.6565i −0.242058 0.419256i 0.719243 0.694759i \(-0.244489\pi\)
−0.961300 + 0.275503i \(0.911156\pi\)
\(774\) 0 0
\(775\) −3.45065 + 5.97671i −0.123951 + 0.214690i
\(776\) −1.53404 + 2.65704i −0.0550688 + 0.0953820i
\(777\) 0 0
\(778\) 18.6235 + 32.2568i 0.667684 + 1.15646i
\(779\) 15.6235 0.559769
\(780\) 0 0
\(781\) −59.7409 −2.13770
\(782\) 19.5562 33.8723i 0.699328 1.21127i
\(783\) 0 0
\(784\) 0 0
\(785\) −26.5587 + 46.0010i −0.947920 + 1.64185i
\(786\) 0 0
\(787\) 13.2288 22.9129i 0.471554 0.816756i −0.527916 0.849296i \(-0.677026\pi\)
0.999470 + 0.0325406i \(0.0103598\pi\)
\(788\) 3.62348 6.27604i 0.129081 0.223575i
\(789\) 0 0
\(790\) −5.50267 + 9.53090i −0.195776 + 0.339094i
\(791\) 0 0
\(792\) 0 0
\(793\) −2.75305 + 4.76842i −0.0977636 + 0.169332i
\(794\) −9.35577 −0.332024
\(795\) 0 0