Properties

Label 2646.2.h.r.667.2
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 667.2
Root \(0.306808 - 1.70466i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.r.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -0.613616 q^{5} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} -0.613616 q^{5} +1.00000 q^{8} +(0.306808 + 0.531407i) q^{10} +4.62348 q^{11} +(-3.25937 - 5.64539i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-1.01607 - 1.75988i) q^{17} +(-1.32288 + 2.29129i) q^{19} +(0.306808 - 0.531407i) q^{20} +(-2.31174 - 4.00405i) q^{22} +3.62348 q^{23} -4.62348 q^{25} +(-3.25937 + 5.64539i) q^{26} +(-2.00000 + 3.46410i) q^{29} +(3.25937 - 5.64539i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.01607 + 1.75988i) q^{34} +(-3.00000 + 5.19615i) q^{37} +2.64575 q^{38} -0.613616 q^{40} +(-1.01607 - 1.75988i) q^{41} +(1.31174 - 2.27200i) q^{43} +(-2.31174 + 4.00405i) q^{44} +(-1.81174 - 3.13802i) q^{46} +(5.29150 + 9.16515i) q^{47} +(2.31174 + 4.00405i) q^{50} +6.51873 q^{52} +(-2.00000 - 3.46410i) q^{53} -2.83704 q^{55} +4.00000 q^{58} +(6.11628 - 10.5937i) q^{59} +(-3.56618 - 6.17680i) q^{61} -6.51873 q^{62} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{65} +(-2.31174 + 4.00405i) q^{67} +2.03214 q^{68} +0.376525 q^{71} +(-3.66182 - 6.34246i) q^{73} +6.00000 q^{74} +(-1.32288 - 2.29129i) q^{76} +(-6.81174 - 11.7983i) q^{79} +(0.306808 + 0.531407i) q^{80} +(-1.01607 + 1.75988i) q^{82} +(3.87298 - 6.70820i) q^{83} +(0.623475 + 1.07989i) q^{85} -2.62348 q^{86} +4.62348 q^{88} +(-7.13235 + 12.3536i) q^{89} +(-1.81174 + 3.13802i) q^{92} +(5.29150 - 9.16515i) q^{94} +(0.811738 - 1.40597i) q^{95} +(8.14842 - 14.1135i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} + O(q^{10}) \) \( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 4 q^{11} - 4 q^{16} + 2 q^{22} - 12 q^{23} + 4 q^{25} - 16 q^{29} - 4 q^{32} - 24 q^{37} - 10 q^{43} + 2 q^{44} + 6 q^{46} - 2 q^{50} - 16 q^{53} + 32 q^{58} + 8 q^{64} + 16 q^{65} + 2 q^{67} + 44 q^{71} + 48 q^{74} - 34 q^{79} - 36 q^{85} + 20 q^{86} - 4 q^{88} + 6 q^{92} - 14 q^{95} + O(q^{100}) \)

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
\(5\) −0.613616 −0.274417 −0.137209 0.990542i \(-0.543813\pi\)
−0.137209 + 0.990542i \(0.543813\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0.306808 + 0.531407i 0.0970212 + 0.168046i
\(11\) 4.62348 1.39403 0.697015 0.717056i \(-0.254511\pi\)
0.697015 + 0.717056i \(0.254511\pi\)
\(12\) 0 0
\(13\) −3.25937 5.64539i −0.903986 1.56575i −0.822273 0.569094i \(-0.807294\pi\)
−0.0817130 0.996656i \(-0.526039\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.01607 1.75988i −0.246433 0.426834i 0.716101 0.697997i \(-0.245925\pi\)
−0.962533 + 0.271163i \(0.912592\pi\)
\(18\) 0 0
\(19\) −1.32288 + 2.29129i −0.303488 + 0.525657i −0.976924 0.213589i \(-0.931485\pi\)
0.673435 + 0.739246i \(0.264818\pi\)
\(20\) 0.306808 0.531407i 0.0686044 0.118826i
\(21\) 0 0
\(22\) −2.31174 4.00405i −0.492864 0.853666i
\(23\) 3.62348 0.755547 0.377773 0.925898i \(-0.376690\pi\)
0.377773 + 0.925898i \(0.376690\pi\)
\(24\) 0 0
\(25\) −4.62348 −0.924695
\(26\) −3.25937 + 5.64539i −0.639215 + 1.10715i
\(27\) 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
\(31\) 3.25937 5.64539i 0.585400 1.01394i −0.409426 0.912343i \(-0.634271\pi\)
0.994825 0.101599i \(-0.0323957\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −1.01607 + 1.75988i −0.174254 + 0.301817i
\(35\) 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
\(40\) −0.613616 −0.0970212
\(41\) −1.01607 1.75988i −0.158683 0.274847i 0.775711 0.631088i \(-0.217391\pi\)
−0.934394 + 0.356241i \(0.884058\pi\)
\(42\) 0 0
\(43\) 1.31174 2.27200i 0.200038 0.346476i −0.748502 0.663132i \(-0.769227\pi\)
0.948540 + 0.316656i \(0.102560\pi\)
\(44\) −2.31174 + 4.00405i −0.348508 + 0.603633i
\(45\) 0 0
\(46\) −1.81174 3.13802i −0.267126 0.462676i
\(47\) 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
\(50\) 2.31174 + 4.00405i 0.326929 + 0.566258i
\(51\) 0 0
\(52\) 6.51873 0.903986
\(53\) −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
\(55\) −2.83704 −0.382546
\(56\) 0 0
\(57\) 0 0
\(58\) 4.00000 0.525226
\(59\) 6.11628 10.5937i 0.796272 1.37918i −0.125756 0.992061i \(-0.540136\pi\)
0.922028 0.387123i \(-0.126531\pi\)
\(60\) 0 0
\(61\) −3.56618 6.17680i −0.456602 0.790858i 0.542177 0.840264i \(-0.317600\pi\)
−0.998779 + 0.0494066i \(0.984267\pi\)
\(62\) −6.51873 −0.827880
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 2.00000 + 3.46410i 0.248069 + 0.429669i
\(66\) 0 0
\(67\) −2.31174 + 4.00405i −0.282424 + 0.489172i −0.971981 0.235059i \(-0.924472\pi\)
0.689557 + 0.724231i \(0.257805\pi\)
\(68\) 2.03214 0.246433
\(69\) 0 0
\(70\) 0 0
\(71\) 0.376525 0.0446853 0.0223426 0.999750i \(-0.492888\pi\)
0.0223426 + 0.999750i \(0.492888\pi\)
\(72\) 0 0
\(73\) −3.66182 6.34246i −0.428583 0.742328i 0.568164 0.822915i \(-0.307654\pi\)
−0.996748 + 0.0805869i \(0.974321\pi\)
\(74\) 6.00000 0.697486
\(75\) 0 0
\(76\) −1.32288 2.29129i −0.151744 0.262829i
\(77\) 0 0
\(78\) 0 0
\(79\) −6.81174 11.7983i −0.766380 1.32741i −0.939514 0.342511i \(-0.888722\pi\)
0.173133 0.984898i \(-0.444611\pi\)
\(80\) 0.306808 + 0.531407i 0.0343022 + 0.0594131i
\(81\) 0 0
\(82\) −1.01607 + 1.75988i −0.112206 + 0.194346i
\(83\) 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
\(85\) 0.623475 + 1.07989i 0.0676254 + 0.117131i
\(86\) −2.62348 −0.282897
\(87\) 0 0
\(88\) 4.62348 0.492864
\(89\) −7.13235 + 12.3536i −0.756028 + 1.30948i 0.188834 + 0.982009i \(0.439529\pi\)
−0.944862 + 0.327469i \(0.893804\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −1.81174 + 3.13802i −0.188887 + 0.327161i
\(93\) 0 0
\(94\) 5.29150 9.16515i 0.545777 0.945313i
\(95\) 0.811738 1.40597i 0.0832825 0.144250i
\(96\) 0 0
\(97\) 8.14842 14.1135i 0.827347 1.43301i −0.0727661 0.997349i \(-0.523183\pi\)
0.900113 0.435657i \(-0.143484\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 2.31174 4.00405i 0.231174 0.400405i
\(101\) −16.4881 −1.64063 −0.820315 0.571912i \(-0.806202\pi\)
−0.820315 + 0.571912i \(0.806202\pi\)
\(102\) 0 0
\(103\) −17.1017 −1.68508 −0.842542 0.538630i \(-0.818942\pi\)
−0.842542 + 0.538630i \(0.818942\pi\)
\(104\) −3.25937 5.64539i −0.319607 0.553576i
\(105\) 0 0
\(106\) −2.00000 + 3.46410i −0.194257 + 0.336463i
\(107\) 5.31174 9.20020i 0.513505 0.889417i −0.486372 0.873752i \(-0.661680\pi\)
0.999877 0.0156651i \(-0.00498658\pi\)
\(108\) 0 0
\(109\) 4.62348 + 8.00809i 0.442849 + 0.767036i 0.997900 0.0647800i \(-0.0206346\pi\)
−0.555051 + 0.831816i \(0.687301\pi\)
\(110\) 1.41852 + 2.45695i 0.135251 + 0.234261i
\(111\) 0 0
\(112\) 0 0
\(113\) −8.81174 15.2624i −0.828939 1.43576i −0.898872 0.438212i \(-0.855612\pi\)
0.0699331 0.997552i \(-0.477721\pi\)
\(114\) 0 0
\(115\) −2.22342 −0.207335
\(116\) −2.00000 3.46410i −0.185695 0.321634i
\(117\) 0 0
\(118\) −12.2326 −1.12610
\(119\) 0 0
\(120\) 0 0
\(121\) 10.3765 0.943320
\(122\) −3.56618 + 6.17680i −0.322866 + 0.559221i
\(123\) 0 0
\(124\) 3.25937 + 5.64539i 0.292700 + 0.506971i
\(125\) 5.90512 0.528170
\(126\) 0 0
\(127\) 11.6235 1.03142 0.515708 0.856764i \(-0.327529\pi\)
0.515708 + 0.856764i \(0.327529\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 2.00000 3.46410i 0.175412 0.303822i
\(131\) −13.6511 −1.19270 −0.596350 0.802724i \(-0.703383\pi\)
−0.596350 + 0.802724i \(0.703383\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 4.62348 0.399407
\(135\) 0 0
\(136\) −1.01607 1.75988i −0.0871271 0.150909i
\(137\) −9.87043 −0.843287 −0.421644 0.906762i \(-0.638547\pi\)
−0.421644 + 0.906762i \(0.638547\pi\)
\(138\) 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
\(142\) −0.188262 0.326080i −0.0157986 0.0273640i
\(143\) −15.0696 26.1013i −1.26018 2.18270i
\(144\) 0 0
\(145\) 1.22723 2.12563i 0.101916 0.176524i
\(146\) −3.66182 + 6.34246i −0.303054 + 0.524905i
\(147\) 0 0
\(148\) −3.00000 5.19615i −0.246598 0.427121i
\(149\) −15.2470 −1.24908 −0.624539 0.780993i \(-0.714713\pi\)
−0.624539 + 0.780993i \(0.714713\pi\)
\(150\) 0 0
\(151\) 1.62348 0.132117 0.0660583 0.997816i \(-0.478958\pi\)
0.0660583 + 0.997816i \(0.478958\pi\)
\(152\) −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
\(157\) 1.53404 2.65704i 0.122430 0.212055i −0.798296 0.602266i \(-0.794265\pi\)
0.920725 + 0.390211i \(0.127598\pi\)
\(158\) −6.81174 + 11.7983i −0.541913 + 0.938620i
\(159\) 0 0
\(160\) 0.306808 0.531407i 0.0242553 0.0420114i
\(161\) 0 0
\(162\) 0 0
\(163\) −9.62348 + 16.6683i −0.753769 + 1.30557i 0.192215 + 0.981353i \(0.438433\pi\)
−0.945984 + 0.324213i \(0.894901\pi\)
\(164\) 2.03214 0.158683
\(165\) 0 0
\(166\) −7.74597 −0.601204
\(167\) 0.613616 + 1.06281i 0.0474830 + 0.0822430i 0.888790 0.458315i \(-0.151547\pi\)
−0.841307 + 0.540558i \(0.818213\pi\)
\(168\) 0 0
\(169\) −14.7470 + 25.5425i −1.13438 + 1.96481i
\(170\) 0.623475 1.07989i 0.0478184 0.0828239i
\(171\) 0 0
\(172\) 1.31174 + 2.27200i 0.100019 + 0.173238i
\(173\) −3.25937 5.64539i −0.247805 0.429211i 0.715111 0.699010i \(-0.246376\pi\)
−0.962917 + 0.269799i \(0.913043\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −2.31174 4.00405i −0.174254 0.301816i
\(177\) 0 0
\(178\) 14.2647 1.06918
\(179\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(180\) 0 0
\(181\) 7.13235 0.530143 0.265072 0.964229i \(-0.414604\pi\)
0.265072 + 0.964229i \(0.414604\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 3.62348 0.267126
\(185\) 1.84085 3.18844i 0.135342 0.234419i
\(186\) 0 0
\(187\) −4.69776 8.13677i −0.343535 0.595019i
\(188\) −10.5830 −0.771845
\(189\) 0 0
\(190\) −1.62348 −0.117779
\(191\) 7.81174 + 13.5303i 0.565238 + 0.979020i 0.997028 + 0.0770459i \(0.0245488\pi\)
−0.431790 + 0.901974i \(0.642118\pi\)
\(192\) 0 0
\(193\) 13.7470 23.8104i 0.989527 1.71391i 0.369756 0.929129i \(-0.379441\pi\)
0.619772 0.784782i \(-0.287225\pi\)
\(194\) −16.2968 −1.17004
\(195\) 0 0
\(196\) 0 0
\(197\) 13.2470 0.943806 0.471903 0.881650i \(-0.343567\pi\)
0.471903 + 0.881650i \(0.343567\pi\)
\(198\) 0 0
\(199\) −10.3917 17.9990i −0.736649 1.27591i −0.953996 0.299820i \(-0.903074\pi\)
0.217347 0.976095i \(-0.430260\pi\)
\(200\) −4.62348 −0.326929
\(201\) 0 0
\(202\) 8.24406 + 14.2791i 0.580050 + 1.00468i
\(203\) 0 0
\(204\) 0 0
\(205\) 0.623475 + 1.07989i 0.0435454 + 0.0754229i
\(206\) 8.55087 + 14.8105i 0.595767 + 1.03190i
\(207\) 0 0
\(208\) −3.25937 + 5.64539i −0.225996 + 0.391437i
\(209\) −6.11628 + 10.5937i −0.423072 + 0.732782i
\(210\) 0 0
\(211\) −7.62348 13.2042i −0.524822 0.909018i −0.999582 0.0289028i \(-0.990799\pi\)
0.474761 0.880115i \(-0.342535\pi\)
\(212\) 4.00000 0.274721
\(213\) 0 0
\(214\) −10.6235 −0.726206
\(215\) −0.804903 + 1.39413i −0.0548939 + 0.0950791i
\(216\) 0 0
\(217\) 0 0
\(218\) 4.62348 8.00809i 0.313141 0.542377i
\(219\) 0 0
\(220\) 1.41852 2.45695i 0.0956366 0.165647i
\(221\) −6.62348 + 11.4722i −0.445543 + 0.771703i
\(222\) 0 0
\(223\) −0.613616 + 1.06281i −0.0410908 + 0.0711713i −0.885839 0.463992i \(-0.846417\pi\)
0.844749 + 0.535163i \(0.179750\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −8.81174 + 15.2624i −0.586148 + 1.01524i
\(227\) 2.26318 0.150212 0.0751062 0.997176i \(-0.476070\pi\)
0.0751062 + 0.997176i \(0.476070\pi\)
\(228\) 0 0
\(229\) −7.51493 −0.496600 −0.248300 0.968683i \(-0.579872\pi\)
−0.248300 + 0.968683i \(0.579872\pi\)
\(230\) 1.11171 + 1.92554i 0.0733041 + 0.126966i
\(231\) 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
\(235\) −3.24695 5.62388i −0.211808 0.366862i
\(236\) 6.11628 + 10.5937i 0.398136 + 0.689592i
\(237\) 0 0
\(238\) 0 0
\(239\) 1.18826 + 2.05813i 0.0768623 + 0.133129i 0.901895 0.431956i \(-0.142176\pi\)
−0.825032 + 0.565086i \(0.808843\pi\)
\(240\) 0 0
\(241\) −8.16830 −0.526166 −0.263083 0.964773i \(-0.584739\pi\)
−0.263083 + 0.964773i \(0.584739\pi\)
\(242\) −5.18826 8.98633i −0.333514 0.577663i
\(243\) 0 0
\(244\) 7.13235 0.456602
\(245\) 0 0
\(246\) 0 0
\(247\) 17.2470 1.09740
\(248\) 3.25937 5.64539i 0.206970 0.358483i
\(249\) 0 0
\(250\) −2.95256 5.11398i −0.186736 0.323437i
\(251\) −10.3917 −0.655919 −0.327960 0.944692i \(-0.606361\pi\)
−0.327960 + 0.944692i \(0.606361\pi\)
\(252\) 0 0
\(253\) 16.7530 1.05326
\(254\) −5.81174 10.0662i −0.364661 0.631611i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 28.1071 1.75327 0.876636 0.481155i \(-0.159783\pi\)
0.876636 + 0.481155i \(0.159783\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −4.00000 −0.248069
\(261\) 0 0
\(262\) 6.82554 + 11.8222i 0.421683 + 0.730377i
\(263\) 13.6235 0.840059 0.420030 0.907510i \(-0.362020\pi\)
0.420030 + 0.907510i \(0.362020\pi\)
\(264\) 0 0
\(265\) 1.22723 + 2.12563i 0.0753883 + 0.130576i
\(266\) 0 0
\(267\) 0 0
\(268\) −2.31174 4.00405i −0.141212 0.244586i
\(269\) −5.40702 9.36524i −0.329672 0.571009i 0.652775 0.757552i \(-0.273605\pi\)
−0.982447 + 0.186543i \(0.940272\pi\)
\(270\) 0 0
\(271\) −9.16449 + 15.8734i −0.556703 + 0.964238i 0.441066 + 0.897475i \(0.354600\pi\)
−0.997769 + 0.0667630i \(0.978733\pi\)
\(272\) −1.01607 + 1.75988i −0.0616082 + 0.106708i
\(273\) 0 0
\(274\) 4.93521 + 8.54804i 0.298147 + 0.516406i
\(275\) −21.3765 −1.28905
\(276\) 0 0
\(277\) 12.4939 0.750686 0.375343 0.926886i \(-0.377525\pi\)
0.375343 + 0.926886i \(0.377525\pi\)
\(278\) −3.96863 + 6.87386i −0.238022 + 0.412267i
\(279\) 0 0
\(280\) 0 0
\(281\) 2.43521 4.21791i 0.145273 0.251620i −0.784202 0.620506i \(-0.786927\pi\)
0.929475 + 0.368886i \(0.120261\pi\)
\(282\) 0 0
\(283\) −5.59831 + 9.69656i −0.332785 + 0.576401i −0.983057 0.183301i \(-0.941322\pi\)
0.650272 + 0.759702i \(0.274655\pi\)
\(284\) −0.188262 + 0.326080i −0.0111713 + 0.0193493i
\(285\) 0 0
\(286\) −15.0696 + 26.1013i −0.891084 + 1.54340i
\(287\) 0 0
\(288\) 0 0
\(289\) 6.43521 11.1461i 0.378542 0.655654i
\(290\) −2.45446 −0.144131
\(291\) 0 0
\(292\) 7.32364 0.428583
\(293\) 7.01683 + 12.1535i 0.409928 + 0.710015i 0.994881 0.101051i \(-0.0322206\pi\)
−0.584954 + 0.811067i \(0.698887\pi\)
\(294\) 0 0
\(295\) −3.75305 + 6.50047i −0.218511 + 0.378472i
\(296\) −3.00000 + 5.19615i −0.174371 + 0.302020i
\(297\) 0 0
\(298\) 7.62348 + 13.2042i 0.441616 + 0.764901i
\(299\) −11.8102 20.4559i −0.683004 1.18300i
\(300\) 0 0
\(301\) 0 0
\(302\) −0.811738 1.40597i −0.0467103 0.0809045i
\(303\) 0 0
\(304\) 2.64575 0.151744
\(305\) 2.18826 + 3.79018i 0.125300 + 0.217025i
\(306\) 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
\(311\) −5.10022 + 8.83383i −0.289207 + 0.500921i −0.973621 0.228173i \(-0.926725\pi\)
0.684414 + 0.729094i \(0.260058\pi\)
\(312\) 0 0
\(313\) −8.95332 15.5076i −0.506072 0.876542i −0.999975 0.00702519i \(-0.997764\pi\)
0.493904 0.869517i \(-0.335570\pi\)
\(314\) −3.06808 −0.173142
\(315\) 0 0
\(316\) 13.6235 0.766380
\(317\) −6.62348 11.4722i −0.372011 0.644343i 0.617863 0.786285i \(-0.287998\pi\)
−0.989875 + 0.141943i \(0.954665\pi\)
\(318\) 0 0
\(319\) −9.24695 + 16.0162i −0.517730 + 0.896734i
\(320\) −0.613616 −0.0343022
\(321\) 0 0
\(322\) 0 0
\(323\) 5.37652 0.299158
\(324\) 0 0
\(325\) 15.0696 + 26.1013i 0.835911 + 1.44784i
\(326\) 19.2470 1.06599
\(327\) 0 0
\(328\) −1.01607 1.75988i −0.0561030 0.0971732i
\(329\) 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
\(334\) 0.613616 1.06281i 0.0335756 0.0581546i
\(335\) 1.41852 2.45695i 0.0775020 0.134237i
\(336\) 0 0
\(337\) −16.9352 29.3326i −0.922520 1.59785i −0.795502 0.605951i \(-0.792793\pi\)
−0.127018 0.991900i \(-0.540541\pi\)
\(338\) 29.4939 1.60426
\(339\) 0 0
\(340\) −1.24695 −0.0676254
\(341\) 15.0696 26.1013i 0.816065 1.41347i
\(342\) 0 0
\(343\) 0 0
\(344\) 1.31174 2.27200i 0.0707242 0.122498i
\(345\) 0 0
\(346\) −3.25937 + 5.64539i −0.175225 + 0.303498i
\(347\) 3.31174 5.73610i 0.177783 0.307930i −0.763338 0.646000i \(-0.776441\pi\)
0.941121 + 0.338070i \(0.109774\pi\)
\(348\) 0 0
\(349\) −5.71383 + 9.89665i −0.305854 + 0.529755i −0.977451 0.211161i \(-0.932275\pi\)
0.671597 + 0.740917i \(0.265609\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −2.31174 + 4.00405i −0.123216 + 0.213416i
\(353\) 2.03214 0.108160 0.0540798 0.998537i \(-0.482777\pi\)
0.0540798 + 0.998537i \(0.482777\pi\)
\(354\) 0 0
\(355\) −0.231042 −0.0122624
\(356\) −7.13235 12.3536i −0.378014 0.654739i
\(357\) 0 0
\(358\) 0 0
\(359\) −10.0587 + 17.4222i −0.530877 + 0.919506i 0.468473 + 0.883478i \(0.344804\pi\)
−0.999351 + 0.0360288i \(0.988529\pi\)
\(360\) 0 0
\(361\) 6.00000 + 10.3923i 0.315789 + 0.546963i
\(362\) −3.56618 6.17680i −0.187434 0.324645i
\(363\) 0 0
\(364\) 0 0
\(365\) 2.24695 + 3.89183i 0.117611 + 0.203708i
\(366\) 0 0
\(367\) −30.1392 −1.57325 −0.786627 0.617429i \(-0.788174\pi\)
−0.786627 + 0.617429i \(0.788174\pi\)
\(368\) −1.81174 3.13802i −0.0944434 0.163581i
\(369\) 0 0
\(370\) −3.68170 −0.191402
\(371\) 0 0
\(372\) 0 0
\(373\) −9.24695 −0.478789 −0.239394 0.970922i \(-0.576949\pi\)
−0.239394 + 0.970922i \(0.576949\pi\)
\(374\) −4.69776 + 8.13677i −0.242916 + 0.420742i
\(375\) 0 0
\(376\) 5.29150 + 9.16515i 0.272888 + 0.472657i
\(377\) 26.0749 1.34293
\(378\) 0 0
\(379\) 5.37652 0.276174 0.138087 0.990420i \(-0.455905\pi\)
0.138087 + 0.990420i \(0.455905\pi\)
\(380\) 0.811738 + 1.40597i 0.0416413 + 0.0721248i
\(381\) 0 0
\(382\) 7.81174 13.5303i 0.399683 0.692272i
\(383\) −19.9388 −1.01882 −0.509412 0.860523i \(-0.670137\pi\)
−0.509412 + 0.860523i \(0.670137\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −27.4939 −1.39940
\(387\) 0 0
\(388\) 8.14842 + 14.1135i 0.413673 + 0.716503i
\(389\) −16.7530 −0.849413 −0.424707 0.905331i \(-0.639623\pi\)
−0.424707 + 0.905331i \(0.639623\pi\)
\(390\) 0 0
\(391\) −3.68170 6.37688i −0.186191 0.322493i
\(392\) 0 0
\(393\) 0 0
\(394\) −6.62348 11.4722i −0.333686 0.577961i
\(395\) 4.17979 + 7.23961i 0.210308 + 0.364264i
\(396\) 0 0
\(397\) 8.55087 14.8105i 0.429156 0.743320i −0.567643 0.823275i \(-0.692144\pi\)
0.996798 + 0.0799553i \(0.0254778\pi\)
\(398\) −10.3917 + 17.9990i −0.520890 + 0.902208i
\(399\) 0 0
\(400\) 2.31174 + 4.00405i 0.115587 + 0.200202i
\(401\) 15.0000 0.749064 0.374532 0.927214i \(-0.377803\pi\)
0.374532 + 0.927214i \(0.377803\pi\)
\(402\) 0 0
\(403\) −42.4939 −2.11677
\(404\) 8.24406 14.2791i 0.410157 0.710413i
\(405\) 0 0
\(406\) 0 0
\(407\) −13.8704 + 24.0243i −0.687531 + 1.19084i
\(408\) 0 0
\(409\) −10.7942 + 18.6961i −0.533737 + 0.924460i 0.465486 + 0.885055i \(0.345880\pi\)
−0.999223 + 0.0394049i \(0.987454\pi\)
\(410\) 0.623475 1.07989i 0.0307913 0.0533320i
\(411\) 0 0
\(412\) 8.55087 14.8105i 0.421271 0.729663i
\(413\) 0 0
\(414\) 0 0
\(415\) −2.37652 + 4.11626i −0.116659 + 0.202059i
\(416\) 6.51873 0.319607
\(417\) 0 0
\(418\) 12.2326 0.598314
\(419\) 6.21193 + 10.7594i 0.303472 + 0.525630i 0.976920 0.213605i \(-0.0685206\pi\)
−0.673448 + 0.739235i \(0.735187\pi\)
\(420\) 0 0
\(421\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(422\) −7.62348 + 13.2042i −0.371105 + 0.642773i
\(423\) 0 0
\(424\) −2.00000 3.46410i −0.0971286 0.168232i
\(425\) 4.69776 + 8.13677i 0.227875 + 0.394691i
\(426\) 0 0
\(427\) 0 0
\(428\) 5.31174 + 9.20020i 0.256753 + 0.444708i
\(429\) 0 0
\(430\) 1.60981 0.0776318
\(431\) −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
\(433\) 4.48660 0.215612 0.107806 0.994172i \(-0.465617\pi\)
0.107806 + 0.994172i \(0.465617\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −9.24695 −0.442849
\(437\) −4.79341 + 8.30243i −0.229300 + 0.397159i
\(438\) 0 0
\(439\) 15.4919 + 26.8328i 0.739390 + 1.28066i 0.952770 + 0.303691i \(0.0982192\pi\)
−0.213381 + 0.976969i \(0.568448\pi\)
\(440\) −2.83704 −0.135251
\(441\) 0 0
\(442\) 13.2470 0.630093
\(443\) 15.3117 + 26.5207i 0.727483 + 1.26004i 0.957944 + 0.286955i \(0.0926431\pi\)
−0.230461 + 0.973081i \(0.574024\pi\)
\(444\) 0 0
\(445\) 4.37652 7.58036i 0.207467 0.359344i
\(446\) 1.22723 0.0581111
\(447\) 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
\(451\) −4.69776 8.13677i −0.221209 0.383145i
\(452\) 17.6235 0.828939
\(453\) 0 0
\(454\) −1.13159 1.95997i −0.0531081 0.0919859i
\(455\) 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 \(0.916159\pi\)
\(458\) 3.75746 + 6.50812i 0.175575 + 0.304104i
\(459\) 0 0
\(460\) 1.11171 1.92554i 0.0518338 0.0897788i
\(461\) −0.920424 + 1.59422i −0.0428684 + 0.0742503i −0.886664 0.462415i \(-0.846983\pi\)
0.843795 + 0.536666i \(0.180316\pi\)
\(462\) 0 0
\(463\) −17.8117 30.8508i −0.827782 1.43376i −0.899775 0.436355i \(-0.856269\pi\)
0.0719931 0.997405i \(-0.477064\pi\)
\(464\) 4.00000 0.185695
\(465\) 0 0
\(466\) −17.0000 −0.787510
\(467\) 3.66182 6.34246i 0.169449 0.293494i −0.768777 0.639516i \(-0.779135\pi\)
0.938226 + 0.346023i \(0.112468\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −3.24695 + 5.62388i −0.149771 + 0.259410i
\(471\) 0 0
\(472\) 6.11628 10.5937i 0.281525 0.487615i
\(473\) 6.06479 10.5045i 0.278859 0.482998i
\(474\) 0 0
\(475\) 6.11628 10.5937i 0.280634 0.486073i
\(476\) 0 0
\(477\) 0 0
\(478\) 1.18826 2.05813i 0.0543499 0.0941367i
\(479\) 15.4919 0.707845 0.353922 0.935275i \(-0.384848\pi\)
0.353922 + 0.935275i \(0.384848\pi\)
\(480\) 0 0
\(481\) 39.1124 1.78337
\(482\) 4.08415 + 7.07395i 0.186028 + 0.322210i
\(483\) 0 0
\(484\) −5.18826 + 8.98633i −0.235830 + 0.408470i
\(485\) −5.00000 + 8.66025i −0.227038 + 0.393242i
\(486\) 0 0
\(487\) 2.81174 + 4.87007i 0.127412 + 0.220684i 0.922673 0.385583i \(-0.126000\pi\)
−0.795261 + 0.606267i \(0.792666\pi\)
\(488\) −3.56618 6.17680i −0.161433 0.279610i
\(489\) 0 0
\(490\) 0 0
\(491\) 7.55869 + 13.0920i 0.341119 + 0.590835i 0.984641 0.174593i \(-0.0558608\pi\)
−0.643522 + 0.765428i \(0.722527\pi\)
\(492\) 0 0
\(493\) 8.12854 0.366091
\(494\) −8.62348 14.9363i −0.387989 0.672016i
\(495\) 0 0
\(496\) −6.51873 −0.292700
\(497\) 0 0
\(498\) 0 0
\(499\) 18.6235 0.833701 0.416851 0.908975i \(-0.363134\pi\)
0.416851 + 0.908975i \(0.363134\pi\)
\(500\) −2.95256 + 5.11398i −0.132042 + 0.228704i
\(501\) 0 0
\(502\) 5.19586 + 8.99949i 0.231903 + 0.401667i
\(503\) 10.2004 0.454815 0.227407 0.973800i \(-0.426975\pi\)
0.227407 + 0.973800i \(0.426975\pi\)
\(504\) 0 0
\(505\) 10.1174 0.450217
\(506\) −8.37652 14.5086i −0.372382 0.644984i
\(507\) 0 0
\(508\) −5.81174 + 10.0662i −0.257854 + 0.446617i
\(509\) 22.0107 0.975606 0.487803 0.872954i \(-0.337798\pi\)
0.487803 + 0.872954i \(0.337798\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −14.0535 24.3414i −0.619875 1.07365i
\(515\) 10.4939 0.462417
\(516\) 0 0
\(517\) 24.4651 + 42.3749i 1.07598 + 1.86364i
\(518\) 0 0
\(519\) 0 0
\(520\) 2.00000 + 3.46410i 0.0877058 + 0.151911i
\(521\) 17.5042 + 30.3181i 0.766873 + 1.32826i 0.939251 + 0.343231i \(0.111522\pi\)
−0.172378 + 0.985031i \(0.555145\pi\)
\(522\) 0 0
\(523\) 7.43916 12.8850i 0.325292 0.563422i −0.656280 0.754518i \(-0.727871\pi\)
0.981571 + 0.191096i \(0.0612042\pi\)
\(524\) 6.82554 11.8222i 0.298175 0.516455i
\(525\) 0 0
\(526\) −6.81174 11.7983i −0.297006 0.514429i
\(527\) −13.2470 −0.577046
\(528\) 0 0
\(529\) −9.87043 −0.429149
\(530\) 1.22723 2.12563i 0.0533076 0.0923314i
\(531\) 0 0
\(532\) 0 0
\(533\) −6.62348 + 11.4722i −0.286895 + 0.496916i
\(534\) 0 0
\(535\) −3.25937 + 5.64539i −0.140915 + 0.244071i
\(536\) −2.31174 + 4.00405i −0.0998519 + 0.172948i
\(537\) 0 0
\(538\) −5.40702 + 9.36524i −0.233113 + 0.403764i
\(539\) 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 \(0.194071\pi\)
\(542\) 18.3290 0.787297
\(543\) 0 0
\(544\) 2.03214 0.0871271
\(545\) −2.83704 4.91389i −0.121525 0.210488i
\(546\) 0 0
\(547\) −4.68826 + 8.12031i −0.200456 + 0.347199i −0.948675 0.316252i \(-0.897576\pi\)
0.748220 + 0.663451i \(0.230909\pi\)
\(548\) 4.93521 8.54804i 0.210822 0.365154i
\(549\) 0 0
\(550\) 10.6883 + 18.5126i 0.455749 + 0.789380i
\(551\) −5.29150 9.16515i −0.225426 0.390449i
\(552\) 0 0
\(553\) 0 0
\(554\) −6.24695 10.8200i −0.265408 0.459699i
\(555\) 0 0
\(556\) 7.93725 0.336615
\(557\) 21.6235 + 37.4530i 0.916216 + 1.58693i 0.805111 + 0.593124i \(0.202106\pi\)
0.111105 + 0.993809i \(0.464561\pi\)
\(558\) 0 0
\(559\) −17.1017 −0.723327
\(560\) 0 0
\(561\) 0 0
\(562\) −4.87043 −0.205447
\(563\) 10.4874 18.1646i 0.441990 0.765548i −0.555847 0.831284i \(-0.687606\pi\)
0.997837 + 0.0657359i \(0.0209395\pi\)
\(564\) 0 0
\(565\) 5.40702 + 9.36524i 0.227475 + 0.393999i
\(566\) 11.1966 0.470629
\(567\) 0 0
\(568\) 0.376525 0.0157986
\(569\) −0.935213 1.61984i −0.0392062 0.0679071i 0.845756 0.533569i \(-0.179150\pi\)
−0.884963 + 0.465662i \(0.845816\pi\)
\(570\) 0 0
\(571\) 9.31174 16.1284i 0.389684 0.674953i −0.602723 0.797951i \(-0.705918\pi\)
0.992407 + 0.122998i \(0.0392509\pi\)
\(572\) 30.1392 1.26018
\(573\) 0 0
\(574\) 0 0
\(575\) −16.7530 −0.698650
\(576\) 0 0
\(577\) 6.30757 + 10.9250i 0.262588 + 0.454815i 0.966929 0.255047i \(-0.0820908\pi\)
−0.704341 + 0.709862i \(0.748757\pi\)
\(578\) −12.8704 −0.535339
\(579\) 0 0
\(580\) 1.22723 + 2.12563i 0.0509580 + 0.0882619i
\(581\) 0 0
\(582\) 0 0
\(583\) −9.24695 16.0162i −0.382970 0.663323i
\(584\) −3.66182 6.34246i −0.151527 0.262453i
\(585\) 0 0
\(586\) 7.01683 12.1535i 0.289863 0.502057i
\(587\) 17.0061 29.4554i 0.701917 1.21576i −0.265876 0.964007i \(-0.585661\pi\)
0.967793 0.251748i \(-0.0810055\pi\)
\(588\) 0 0
\(589\) 8.62348 + 14.9363i 0.355324 + 0.615439i
\(590\) 7.50610 0.309021
\(591\) 0 0
\(592\) 6.00000 0.246598
\(593\) 17.7154 30.6839i 0.727482 1.26004i −0.230462 0.973081i \(-0.574024\pi\)
0.957944 0.286955i \(-0.0926431\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 7.62348 13.2042i 0.312270 0.540867i
\(597\) 0 0
\(598\) −11.8102 + 20.4559i −0.482957 + 0.836505i
\(599\) 19.2470 33.3367i 0.786409 1.36210i −0.141745 0.989903i \(-0.545271\pi\)
0.928154 0.372197i \(-0.121396\pi\)
\(600\) 0 0
\(601\) 5.31138 9.19958i 0.216656 0.375259i −0.737128 0.675753i \(-0.763818\pi\)
0.953783 + 0.300495i \(0.0971518\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −0.811738 + 1.40597i −0.0330291 + 0.0572081i
\(605\) −6.36720 −0.258864
\(606\) 0 0
\(607\) 19.9388 0.809290 0.404645 0.914474i \(-0.367395\pi\)
0.404645 + 0.914474i \(0.367395\pi\)
\(608\) −1.32288 2.29129i −0.0536497 0.0929240i
\(609\) 0 0
\(610\) 2.18826 3.79018i 0.0886002 0.153460i
\(611\) 34.4939 59.7452i 1.39547 2.41703i
\(612\) 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
\(617\) −5.55869 9.62793i −0.223784 0.387606i 0.732170 0.681122i \(-0.238508\pi\)
−0.955954 + 0.293516i \(0.905174\pi\)
\(618\) 0 0
\(619\) −3.02833 −0.121719 −0.0608593 0.998146i \(-0.519384\pi\)
−0.0608593 + 0.998146i \(0.519384\pi\)
\(620\) −2.00000 3.46410i −0.0803219 0.139122i
\(621\) 0 0
\(622\) 10.2004 0.409000
\(623\) 0 0
\(624\) 0 0
\(625\) 19.4939 0.779756
\(626\) −8.95332 + 15.5076i −0.357847 + 0.619809i
\(627\) 0 0
\(628\) 1.53404 + 2.65704i 0.0612149 + 0.106027i
\(629\) 12.1928 0.486159
\(630\) 0 0
\(631\) 20.3765 0.811177 0.405588 0.914056i \(-0.367067\pi\)
0.405588 + 0.914056i \(0.367067\pi\)
\(632\) −6.81174 11.7983i −0.270956 0.469310i
\(633\) 0 0
\(634\) −6.62348 + 11.4722i −0.263052 + 0.455619i
\(635\) −7.13235 −0.283039
\(636\) 0 0
\(637\) 0 0
\(638\) 18.4939 0.732181
\(639\) 0 0
\(640\) 0.306808 + 0.531407i 0.0121277 + 0.0210057i
\(641\) −15.4939 −0.611972 −0.305986 0.952036i \(-0.598986\pi\)
−0.305986 + 0.952036i \(0.598986\pi\)
\(642\) 0 0
\(643\) −2.85692 4.94832i −0.112666 0.195143i 0.804178 0.594388i \(-0.202606\pi\)
−0.916844 + 0.399245i \(0.869272\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −2.68826 4.65621i −0.105768 0.183196i
\(647\) 9.58681 + 16.6049i 0.376897 + 0.652804i 0.990609 0.136726i \(-0.0436579\pi\)
−0.613712 + 0.789530i \(0.710325\pi\)
\(648\) 0 0
\(649\) 28.2785 48.9798i 1.11003 1.92262i
\(650\) 15.0696 26.1013i 0.591079 1.02378i
\(651\) 0 0
\(652\) −9.62348 16.6683i −0.376884 0.652783i
\(653\) −18.7530 −0.733864 −0.366932 0.930248i \(-0.619592\pi\)
−0.366932 + 0.930248i \(0.619592\pi\)
\(654\) 0 0
\(655\) 8.37652 0.327298
\(656\) −1.01607 + 1.75988i −0.0396708 + 0.0687118i
\(657\) 0 0
\(658\) 0 0
\(659\) 15.2470 26.4085i 0.593937 1.02873i −0.399759 0.916620i \(-0.630906\pi\)
0.993696 0.112109i \(-0.0357605\pi\)
\(660\) 0 0
\(661\) −15.9900 + 27.6955i −0.621940 + 1.07723i 0.367184 + 0.930148i \(0.380322\pi\)
−0.989124 + 0.147083i \(0.953011\pi\)
\(662\) −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
\(667\) −7.24695 + 12.5521i −0.280603 + 0.486019i
\(668\) −1.22723 −0.0474830
\(669\) 0 0
\(670\) −2.83704 −0.109604
\(671\) −16.4881 28.5583i −0.636517 1.10248i
\(672\) 0 0
\(673\) −14.8117 + 25.6547i −0.570951 + 0.988915i 0.425518 + 0.904950i \(0.360092\pi\)
−0.996469 + 0.0839654i \(0.973241\pi\)
\(674\) −16.9352 + 29.3326i −0.652320 + 1.12985i
\(675\) 0 0
\(676\) −14.7470 25.5425i −0.567190 0.982403i
\(677\) 13.4598 + 23.3131i 0.517302 + 0.895993i 0.999798 + 0.0200953i \(0.00639696\pi\)
−0.482496 + 0.875898i \(0.660270\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0.623475 + 1.07989i 0.0239092 + 0.0414119i
\(681\) 0 0
\(682\) −30.1392 −1.15409
\(683\) 22.1822 + 38.4206i 0.848777 + 1.47012i 0.882300 + 0.470687i \(0.155994\pi\)
−0.0335235 + 0.999438i \(0.510673\pi\)
\(684\) 0 0
\(685\) 6.05665 0.231413
\(686\) 0 0
\(687\) 0 0
\(688\) −2.62348 −0.100019
\(689\) −13.0375 + 22.5816i −0.496688 + 0.860289i
\(690\) 0 0
\(691\) 13.9579 + 24.1758i 0.530983 + 0.919690i 0.999346 + 0.0361539i \(0.0115106\pi\)
−0.468363 + 0.883536i \(0.655156\pi\)
\(692\) 6.51873 0.247805
\(693\) 0 0
\(694\) −6.62348 −0.251424
\(695\) 2.43521 + 4.21791i 0.0923729 + 0.159995i
\(696\) 0 0
\(697\) −2.06479 + 3.57632i −0.0782094 + 0.135463i
\(698\) 11.4277 0.432543
\(699\) 0 0
\(700\) 0 0
\(701\) 0.753049 0.0284423 0.0142211 0.999899i \(-0.495473\pi\)
0.0142211 + 0.999899i \(0.495473\pi\)
\(702\) 0 0
\(703\) −7.93725 13.7477i −0.299359 0.518505i
\(704\) 4.62348 0.174254
\(705\) 0 0
\(706\) −1.01607 1.75988i −0.0382402 0.0662340i
\(707\) 0 0
\(708\) 0 0
\(709\) 11.2470 + 19.4803i 0.422388 + 0.731598i 0.996173 0.0874087i \(-0.0278586\pi\)
−0.573784 + 0.819006i \(0.694525\pi\)
\(710\) 0.115521 + 0.200088i 0.00433542 + 0.00750916i
\(711\) 0 0
\(712\) −7.13235 + 12.3536i −0.267296 + 0.462970i
\(713\) 11.8102 20.4559i 0.442297 0.766081i
\(714\) 0 0
\(715\) 9.24695 + 16.0162i 0.345816 + 0.598971i
\(716\) 0 0
\(717\) 0 0
\(718\) 20.1174 0.750774
\(719\) −2.03214 + 3.51976i −0.0757859 + 0.131265i −0.901428 0.432930i \(-0.857480\pi\)
0.825642 + 0.564195i \(0.190813\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 6.00000 10.3923i 0.223297 0.386762i
\(723\) 0 0
\(724\) −3.56618 + 6.17680i −0.132536 + 0.229559i
\(725\) 9.24695 16.0162i 0.343423 0.594826i
\(726\) 0 0
\(727\) −1.03594 + 1.79431i −0.0384211 + 0.0665472i −0.884596 0.466357i \(-0.845566\pi\)
0.846175 + 0.532904i \(0.178899\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 2.24695 3.89183i 0.0831634 0.144043i
\(731\) −5.33126 −0.197184
\(732\) 0 0
\(733\) 26.6886 0.985764 0.492882 0.870096i \(-0.335943\pi\)
0.492882 + 0.870096i \(0.335943\pi\)
\(734\) 15.0696 + 26.1013i 0.556229 + 0.963417i
\(735\) 0 0
\(736\) −1.81174 + 3.13802i −0.0667815 + 0.115669i
\(737\) −10.6883 + 18.5126i −0.393707 + 0.681921i
\(738\) 0 0
\(739\) 4.93521 + 8.54804i 0.181545 + 0.314445i 0.942407 0.334469i \(-0.108557\pi\)
−0.760862 + 0.648914i \(0.775224\pi\)
\(740\) 1.84085 + 3.18844i 0.0676709 + 0.117209i
\(741\) 0 0
\(742\) 0 0
\(743\) 5.37652 + 9.31241i 0.197246 + 0.341639i 0.947634 0.319357i \(-0.103467\pi\)
−0.750389 + 0.660997i \(0.770134\pi\)
\(744\) 0 0
\(745\) 9.35577 0.342769
\(746\) 4.62348 + 8.00809i 0.169277 + 0.293197i
\(747\) 0 0
\(748\) 9.39553 0.343535
\(749\) 0 0
\(750\) 0 0
\(751\) −21.6235 −0.789052 −0.394526 0.918885i \(-0.629091\pi\)
−0.394526 + 0.918885i \(0.629091\pi\)
\(752\) 5.29150 9.16515i 0.192961 0.334219i
\(753\) 0 0
\(754\) −13.0375 22.5816i −0.474797 0.822372i
\(755\) −0.996190 −0.0362551
\(756\) 0 0
\(757\) −17.7409 −0.644802 −0.322401 0.946603i \(-0.604490\pi\)
−0.322401 + 0.946603i \(0.604490\pi\)
\(758\) −2.68826 4.65621i −0.0976421 0.169121i
\(759\) 0 0
\(760\) 0.811738 1.40597i 0.0294448 0.0509999i
\(761\) 36.6579 1.32885 0.664425 0.747355i \(-0.268677\pi\)
0.664425 + 0.747355i \(0.268677\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −15.6235 −0.565238
\(765\) 0 0
\(766\) 9.96939 + 17.2675i 0.360209 + 0.623900i
\(767\) −79.7409 −2.87928
\(768\) 0 0
\(769\) −18.9426 32.8095i −0.683087 1.18314i −0.974034 0.226402i \(-0.927304\pi\)
0.290947 0.956739i \(-0.406030\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 13.7470 + 23.8104i 0.494764 + 0.856956i
\(773\) 10.6985 + 18.5304i 0.384799 + 0.666492i 0.991741 0.128254i \(-0.0409373\pi\)
−0.606942 + 0.794746i \(0.707604\pi\)
\(774\) 0 0
\(775\) −15.0696 + 26.1013i −0.541316 + 0.937587i
\(776\) 8.14842 14.1135i 0.292511 0.506644i
\(777\) 0 0
\(778\) 8.37652 + 14.5086i 0.300313 + 0.520157i
\(779\) 5.37652 0.192634
\(780\) 0 0
\(781\) 1.74085 0.0622926
\(782\) −3.68170 + 6.37688i −0.131657 + 0.228037i
\(783\) 0 0
\(784\) 0 0
\(785\) −0.941312 + 1.63040i −0.0335968 + 0.0581915i
\(786\) 0 0
\(787\) 13.2288 22.9129i 0.471554 0.816756i −0.527916 0.849296i \(-0.677026\pi\)
0.999470 + 0.0325406i \(0.0103598\pi\)
\(788\) −6.62348 + 11.4722i −0.235952 + 0.408680i
\(789\) 0 0
\(790\) 4.17979 7.23961i 0.148710 0.257574i
\(791\) 0 0
\(792\) 0 0
\(793\) −23.2470 + 40.2649i −0.825523 + 1.42985i
\(794\) −17.1017 −0.606918
\(795\) 0 0
\(796\)