Properties

Label 2646.2.h.r.667.1
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: \( x^{8} + x^{6} - 8x^{4} + 9x^{2} + 81 \) Copy content Toggle raw display
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 667.1
Root \(1.62968 + 0.586627i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.r.361.1

$q$-expansion

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

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 \(-0.759929\pi\)
−0.728817 + 0.684709i \(0.759929\pi\)
\(6\) 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 0.768298 0.640092i \(-0.221104\pi\)
−0.938485 + 0.345320i \(0.887770\pi\)
\(14\) 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 \(0.0874083\pi\)
−0.246433 + 0.969160i \(0.579258\pi\)
\(18\) 0 0
\(19\) 1.32288 2.29129i 0.303488 0.525657i −0.673435 0.739246i \(-0.735182\pi\)
0.976924 + 0.213589i \(0.0685153\pi\)
\(20\) 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 −0.805646 0.592398i \(-0.798181\pi\)
0.915854 + 0.401511i \(0.131515\pi\)
\(32\) −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 0.999017 0.0443359i \(-0.0141172\pi\)
−0.537904 + 0.843006i \(0.680784\pi\)
\(42\) 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 \(-0.886001\pi\)
0.164706 0.986343i \(-0.447333\pi\)
\(48\) 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 \(-0.413445\pi\)
0.699914 0.714227i \(-0.253222\pi\)
\(60\) 0 0
\(61\) −2.24330 3.88551i −0.287225 0.497488i 0.685921 0.727676i \(-0.259399\pi\)
−0.973146 + 0.230187i \(0.926066\pi\)
\(62\) −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 \(0.0607628\pi\)
−0.326603 + 0.945162i \(0.605904\pi\)
\(74\) 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 −0.571316 0.820730i \(-0.693567\pi\)
0.996431 + 0.0844091i \(0.0269003\pi\)
\(84\) 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 −0.999609 0.0279735i \(-0.991095\pi\)
0.524030 + 0.851700i \(0.324428\pi\)
\(90\) 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 −0.777577 0.628788i \(-0.783551\pi\)
0.933335 + 0.359007i \(0.116885\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.81174 + 4.87007i −0.281174 + 0.487007i
\(101\) 12.6151 1.25525 0.627627 0.778514i \(-0.284026\pi\)
0.627627 + 0.778514i \(0.284026\pi\)
\(102\) 0 0
\(103\) 9.35577 0.921852 0.460926 0.887439i \(-0.347517\pi\)
0.460926 + 0.887439i \(0.347517\pi\)
\(104\) −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 \(-0.580302\pi\)
−0.249610 + 0.968346i \(0.580302\pi\)
\(132\) 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 0.983794 0.179305i \(-0.0573847\pi\)
−0.647179 + 0.762338i \(0.724051\pi\)
\(140\) 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 \(-0.607970\pi\)
0.983046 0.183356i \(-0.0586962\pi\)
\(158\) −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 0.964136 0.265409i \(-0.0855069\pi\)
−0.711919 + 0.702262i \(0.752174\pi\)
\(168\) 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 0.841756 0.539858i \(-0.181522\pi\)
−0.888409 + 0.459053i \(0.848189\pi\)
\(174\) 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 \(-0.446675\pi\)
0.166743 + 0.986000i \(0.446675\pi\)
\(182\) 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 0.626671 0.779284i \(-0.284417\pi\)
−0.988215 + 0.153071i \(0.951084\pi\)
\(200\) 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 −0.954277 0.298923i \(-0.903373\pi\)
0.736014 + 0.676967i \(0.236706\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −3.68826 + 6.38826i −0.245340 + 0.424941i
\(227\) 28.7207 1.90626 0.953130 0.302562i \(-0.0978421\pi\)
0.953130 + 0.302562i \(0.0978421\pi\)
\(228\) 0 0
\(229\) 26.8798 1.77627 0.888135 0.459583i \(-0.152001\pi\)
0.888135 + 0.459583i \(0.152001\pi\)
\(230\) −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 \(-0.829275\pi\)
−0.859580 + 0.511000i \(0.829275\pi\)
\(242\) −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 \(-0.551459\pi\)
−0.160961 + 0.986961i \(0.551459\pi\)
\(252\) 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 \(-0.509892\pi\)
−0.0310703 + 0.999517i \(0.509892\pi\)
\(258\) 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 \(-0.904806\pi\)
0.222656 0.974897i \(-0.428527\pi\)
\(270\) 0 0
\(271\) 1.41852 2.45695i 0.0861689 0.149249i −0.819720 0.572765i \(-0.805871\pi\)
0.905889 + 0.423516i \(0.139204\pi\)
\(272\) 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 −0.736423 0.676521i \(-0.763487\pi\)
0.954096 + 0.299501i \(0.0968202\pi\)
\(284\) −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 \(-0.897047\pi\)
0.198828 0.980034i \(-0.436287\pi\)
\(294\) 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 \(-0.623217\pi\)
−0.377503 + 0.926009i \(0.623217\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 4.00000 0.227185
\(311\) −10.3917 + 17.9990i −0.589260 + 1.02063i 0.405069 + 0.914286i \(0.367247\pi\)
−0.994330 + 0.106343i \(0.966086\pi\)
\(312\) 0 0
\(313\) 10.8898 + 18.8617i 0.615529 + 1.06613i 0.990292 + 0.139006i \(0.0443908\pi\)
−0.374763 + 0.927121i \(0.622276\pi\)
\(314\) −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 \(0.427485\pi\)
−0.956573 + 0.291492i \(0.905848\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 2.81174 4.87007i 0.149866 0.259576i
\(353\) −5.90512 −0.314298 −0.157149 0.987575i \(-0.550230\pi\)
−0.157149 + 0.987575i \(0.550230\pi\)
\(354\) 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 \(-0.442351\pi\)
0.180123 + 0.983644i \(0.442351\pi\)
\(368\) 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 \(-0.249908\pi\)
0.707312 + 0.706901i \(0.249908\pi\)
\(384\) 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 −0.959208 0.282702i \(-0.908769\pi\)
0.724431 + 0.689347i \(0.242102\pi\)
\(398\) −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 −0.837231 0.546850i \(-0.815827\pi\)
0.892201 + 0.451638i \(0.149160\pi\)
\(410\) −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 0.856027 0.516930i \(-0.172925\pi\)
−0.875689 + 0.482876i \(0.839592\pi\)
\(420\) 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 \(-0.445178\pi\)
0.171379 + 0.985205i \(0.445178\pi\)
\(434\) 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 \(0.0982192\pi\)
−0.213381 + 0.976969i \(0.568448\pi\)
\(440\) 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 −0.957128 0.289666i \(-0.906456\pi\)
0.729422 + 0.684064i \(0.239789\pi\)
\(462\) 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 −0.965990 0.258579i \(-0.916746\pi\)
0.706931 + 0.707282i \(0.250079\pi\)
\(468\) 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 \(-0.384848\pi\)
0.353922 + 0.935275i \(0.384848\pi\)
\(480\) 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 \(-0.346650\pi\)
0.463344 + 0.886179i \(0.346650\pi\)
\(504\) 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 \(-0.379175\pi\)
0.370532 + 0.928820i \(0.379175\pi\)
\(510\) 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 \(-0.927763\pi\)
0.292326 0.956319i \(-0.405571\pi\)
\(522\) 0 0
\(523\) 6.11628 10.5937i 0.267446 0.463231i −0.700755 0.713402i \(-0.747154\pi\)
0.968202 + 0.250171i \(0.0804868\pi\)
\(524\) 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 −0.917994 0.396595i \(-0.870192\pi\)
0.802458 + 0.596709i \(0.203525\pi\)
\(564\) 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 0.641821 0.766854i \(-0.278179\pi\)
−0.985026 + 0.172406i \(0.944846\pi\)
\(578\) 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 −0.895581 0.444899i \(-0.853239\pi\)
0.833084 + 0.553146i \(0.186573\pi\)
\(588\) 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 −0.963622 0.267269i \(-0.913879\pi\)
0.713273 + 0.700887i \(0.247212\pi\)
\(594\) 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 \(-0.532676\pi\)
0.912704 0.408622i \(-0.133991\pi\)
\(602\) 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 \(-0.689908\pi\)
−0.561845 + 0.827243i \(0.689908\pi\)
\(608\) 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 \(-0.260443\pi\)
0.683533 + 0.729920i \(0.260443\pi\)
\(620\) −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 0.699475 0.714657i \(-0.253417\pi\)
−0.968649 + 0.248435i \(0.920084\pi\)
\(644\) 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 \(0.0752580\pi\)
−0.283238 + 0.959050i \(0.591409\pi\)
\(648\) 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 −0.892643 0.450765i \(-0.851151\pi\)
0.836695 + 0.547669i \(0.184484\pi\)
\(662\) −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 \(0.140674\pi\)
−0.0815682 + 0.996668i \(0.525993\pi\)
\(678\) 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 0.971226 0.238160i \(-0.0765442\pi\)
−0.691865 + 0.722026i \(0.743211\pi\)
\(692\) 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 −0.734652 0.678444i \(-0.762655\pi\)
0.954876 + 0.297005i \(0.0959879\pi\)
\(720\) 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 \(0.474606\pi\)
−0.903117 + 0.429394i \(0.858727\pi\)
\(728\) 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 \(-0.451798\pi\)
0.150851 + 0.988556i \(0.451798\pi\)
\(734\) −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 \(-0.532794\pi\)
−0.102843 + 0.994698i \(0.532794\pi\)
\(762\) 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 0.858310 0.513131i \(-0.171515\pi\)
−0.873540 + 0.486753i \(0.838181\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −6.74695 11.6861i −0.242828 0.420591i
\(773\) 6.72990 + 11.6565i 0.242058 + 0.419256i 0.961300 0.275503i \(-0.0888444\pi\)
−0.719243 + 0.694759i \(0.755511\pi\)
\(774\) 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 −0.999470 0.0325406i \(-0.989640\pi\)
0.527916 + 0.849296i \(0.322974\pi\)
\(788\) 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