Properties

Label 912.2.cc.c.257.1
Level $912$
Weight $2$
Character 912.257
Analytic conductor $7.282$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.cc (of order \(18\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(3\) over \(\Q(\zeta_{18})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Defining polynomial: \(x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + 162 x^{7} + 270 x^{6} + 2916 x^{5} - 4374 x^{4} - 729 x^{3} + 19683\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 114)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 257.1
Root \(-1.72388 + 0.168030i\) of defining polynomial
Character \(\chi\) \(=\) 912.257
Dual form 912.2.cc.c.401.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.67739 + 0.431705i) q^{3} +(1.14133 - 3.13578i) q^{5} +(1.07356 - 1.85947i) q^{7} +(2.62726 - 1.44827i) q^{9} +O(q^{10})\) \(q+(-1.67739 + 0.431705i) q^{3} +(1.14133 - 3.13578i) q^{5} +(1.07356 - 1.85947i) q^{7} +(2.62726 - 1.44827i) q^{9} +(5.41799 - 3.12808i) q^{11} +(-2.56208 + 3.05336i) q^{13} +(-0.560722 + 5.75264i) q^{15} +(-0.403611 + 0.0711674i) q^{17} +(-4.34640 - 0.329887i) q^{19} +(-0.998042 + 3.58251i) q^{21} +(0.280411 + 0.770422i) q^{23} +(-4.70025 - 3.94398i) q^{25} +(-3.78171 + 3.56352i) q^{27} +(0.805141 - 4.56618i) q^{29} +(2.02597 + 1.16970i) q^{31} +(-7.73767 + 7.58597i) q^{33} +(-4.60559 - 5.48872i) q^{35} -6.01346i q^{37} +(2.97944 - 6.22774i) q^{39} +(0.926617 - 0.777524i) q^{41} +(-5.87377 - 2.13788i) q^{43} +(-1.54289 - 9.89147i) q^{45} +(7.59919 + 1.33994i) q^{47} +(1.19492 + 2.06967i) q^{49} +(0.646288 - 0.293616i) q^{51} +(-0.220516 + 0.0802612i) q^{53} +(-3.62525 - 20.5598i) q^{55} +(7.43301 - 1.32301i) q^{57} +(-0.930375 - 5.27642i) q^{59} +(7.30705 - 2.65955i) q^{61} +(0.127515 - 6.44012i) q^{63} +(6.65050 + 11.5190i) q^{65} +(-3.48689 - 0.614832i) q^{67} +(-0.802953 - 1.17124i) q^{69} +(-4.19799 - 1.52794i) q^{71} +(-4.33185 + 3.63485i) q^{73} +(9.58679 + 4.58646i) q^{75} -13.4328i q^{77} +(8.05412 + 9.59853i) q^{79} +(4.80501 - 7.60999i) q^{81} +(-8.01579 - 4.62792i) q^{83} +(-0.237488 + 1.34686i) q^{85} +(0.620710 + 8.00685i) q^{87} +(-5.61888 - 4.71480i) q^{89} +(2.92708 + 8.04207i) q^{91} +(-3.90331 - 1.08741i) q^{93} +(-5.99513 + 13.2528i) q^{95} +(-16.0734 + 2.83418i) q^{97} +(9.70416 - 16.0650i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 3q^{3} - 3q^{9} + O(q^{10}) \) \( 18q - 3q^{3} - 3q^{9} - 12q^{13} - 18q^{15} + 6q^{17} + 6q^{19} - 18q^{25} + 6q^{27} - 6q^{29} - 24q^{33} + 24q^{35} - 6q^{39} + 3q^{41} + 6q^{43} - 54q^{45} - 30q^{47} + 21q^{49} - 42q^{51} - 60q^{53} - 30q^{55} + 12q^{57} - 3q^{59} + 54q^{61} + 18q^{63} + 24q^{65} + 15q^{67} + 30q^{69} - 36q^{71} - 42q^{73} + 6q^{79} - 3q^{81} - 36q^{83} - 60q^{89} + 18q^{91} - 66q^{93} - 6q^{95} + 9q^{97} + 102q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\) \(1\) \(-1\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.67739 + 0.431705i −0.968440 + 0.249245i
\(4\) 0 0
\(5\) 1.14133 3.13578i 0.510418 1.40236i −0.370384 0.928879i \(-0.620774\pi\)
0.880802 0.473484i \(-0.157004\pi\)
\(6\) 0 0
\(7\) 1.07356 1.85947i 0.405769 0.702812i −0.588642 0.808394i \(-0.700337\pi\)
0.994411 + 0.105582i \(0.0336704\pi\)
\(8\) 0 0
\(9\) 2.62726 1.44827i 0.875754 0.482758i
\(10\) 0 0
\(11\) 5.41799 3.12808i 1.63359 0.943151i 0.650611 0.759412i \(-0.274513\pi\)
0.982975 0.183740i \(-0.0588203\pi\)
\(12\) 0 0
\(13\) −2.56208 + 3.05336i −0.710592 + 0.846850i −0.993681 0.112243i \(-0.964196\pi\)
0.283089 + 0.959094i \(0.408641\pi\)
\(14\) 0 0
\(15\) −0.560722 + 5.75264i −0.144778 + 1.48532i
\(16\) 0 0
\(17\) −0.403611 + 0.0711674i −0.0978899 + 0.0172606i −0.222379 0.974960i \(-0.571382\pi\)
0.124489 + 0.992221i \(0.460271\pi\)
\(18\) 0 0
\(19\) −4.34640 0.329887i −0.997132 0.0756812i
\(20\) 0 0
\(21\) −0.998042 + 3.58251i −0.217791 + 0.781768i
\(22\) 0 0
\(23\) 0.280411 + 0.770422i 0.0584697 + 0.160644i 0.965488 0.260446i \(-0.0838697\pi\)
−0.907019 + 0.421090i \(0.861647\pi\)
\(24\) 0 0
\(25\) −4.70025 3.94398i −0.940051 0.788796i
\(26\) 0 0
\(27\) −3.78171 + 3.56352i −0.727790 + 0.685800i
\(28\) 0 0
\(29\) 0.805141 4.56618i 0.149511 0.847919i −0.814123 0.580693i \(-0.802782\pi\)
0.963634 0.267226i \(-0.0861071\pi\)
\(30\) 0 0
\(31\) 2.02597 + 1.16970i 0.363875 + 0.210084i 0.670779 0.741657i \(-0.265960\pi\)
−0.306904 + 0.951740i \(0.599293\pi\)
\(32\) 0 0
\(33\) −7.73767 + 7.58597i −1.34695 + 1.32055i
\(34\) 0 0
\(35\) −4.60559 5.48872i −0.778486 0.927764i
\(36\) 0 0
\(37\) 6.01346i 0.988607i −0.869289 0.494303i \(-0.835423\pi\)
0.869289 0.494303i \(-0.164577\pi\)
\(38\) 0 0
\(39\) 2.97944 6.22774i 0.477093 0.997236i
\(40\) 0 0
\(41\) 0.926617 0.777524i 0.144713 0.121429i −0.567557 0.823334i \(-0.692111\pi\)
0.712270 + 0.701905i \(0.247667\pi\)
\(42\) 0 0
\(43\) −5.87377 2.13788i −0.895741 0.326023i −0.147196 0.989107i \(-0.547025\pi\)
−0.748545 + 0.663084i \(0.769247\pi\)
\(44\) 0 0
\(45\) −1.54289 9.89147i −0.230001 1.47453i
\(46\) 0 0
\(47\) 7.59919 + 1.33994i 1.10846 + 0.195451i 0.697767 0.716325i \(-0.254177\pi\)
0.410689 + 0.911776i \(0.365288\pi\)
\(48\) 0 0
\(49\) 1.19492 + 2.06967i 0.170703 + 0.295666i
\(50\) 0 0
\(51\) 0.646288 0.293616i 0.0904984 0.0411145i
\(52\) 0 0
\(53\) −0.220516 + 0.0802612i −0.0302902 + 0.0110247i −0.357121 0.934058i \(-0.616242\pi\)
0.326831 + 0.945083i \(0.394019\pi\)
\(54\) 0 0
\(55\) −3.62525 20.5598i −0.488828 2.77228i
\(56\) 0 0
\(57\) 7.43301 1.32301i 0.984526 0.175237i
\(58\) 0 0
\(59\) −0.930375 5.27642i −0.121124 0.686931i −0.983534 0.180721i \(-0.942157\pi\)
0.862410 0.506210i \(-0.168954\pi\)
\(60\) 0 0
\(61\) 7.30705 2.65955i 0.935572 0.340520i 0.171156 0.985244i \(-0.445250\pi\)
0.764416 + 0.644723i \(0.223027\pi\)
\(62\) 0 0
\(63\) 0.127515 6.44012i 0.0160654 0.811379i
\(64\) 0 0
\(65\) 6.65050 + 11.5190i 0.824893 + 1.42876i
\(66\) 0 0
\(67\) −3.48689 0.614832i −0.425991 0.0751137i −0.0434574 0.999055i \(-0.513837\pi\)
−0.382534 + 0.923942i \(0.624948\pi\)
\(68\) 0 0
\(69\) −0.802953 1.17124i −0.0966642 0.141001i
\(70\) 0 0
\(71\) −4.19799 1.52794i −0.498210 0.181334i 0.0806788 0.996740i \(-0.474291\pi\)
−0.578889 + 0.815407i \(0.696513\pi\)
\(72\) 0 0
\(73\) −4.33185 + 3.63485i −0.507005 + 0.425427i −0.860074 0.510170i \(-0.829583\pi\)
0.353069 + 0.935597i \(0.385138\pi\)
\(74\) 0 0
\(75\) 9.58679 + 4.58646i 1.10699 + 0.529599i
\(76\) 0 0
\(77\) 13.4328i 1.53081i
\(78\) 0 0
\(79\) 8.05412 + 9.59853i 0.906159 + 1.07992i 0.996465 + 0.0840047i \(0.0267711\pi\)
−0.0903059 + 0.995914i \(0.528784\pi\)
\(80\) 0 0
\(81\) 4.80501 7.60999i 0.533889 0.845554i
\(82\) 0 0
\(83\) −8.01579 4.62792i −0.879848 0.507980i −0.00923947 0.999957i \(-0.502941\pi\)
−0.870608 + 0.491977i \(0.836274\pi\)
\(84\) 0 0
\(85\) −0.237488 + 1.34686i −0.0257591 + 0.146087i
\(86\) 0 0
\(87\) 0.620710 + 8.00685i 0.0665471 + 0.858424i
\(88\) 0 0
\(89\) −5.61888 4.71480i −0.595600 0.499767i 0.294428 0.955674i \(-0.404871\pi\)
−0.890028 + 0.455906i \(0.849315\pi\)
\(90\) 0 0
\(91\) 2.92708 + 8.04207i 0.306841 + 0.843038i
\(92\) 0 0
\(93\) −3.90331 1.08741i −0.404754 0.112759i
\(94\) 0 0
\(95\) −5.99513 + 13.2528i −0.615087 + 1.35971i
\(96\) 0 0
\(97\) −16.0734 + 2.83418i −1.63201 + 0.287767i −0.913221 0.407464i \(-0.866413\pi\)
−0.718786 + 0.695231i \(0.755302\pi\)
\(98\) 0 0
\(99\) 9.70416 16.0650i 0.975305 1.61459i
\(100\) 0 0
\(101\) −3.69207 + 4.40004i −0.367375 + 0.437820i −0.917787 0.397073i \(-0.870026\pi\)
0.550412 + 0.834893i \(0.314471\pi\)
\(102\) 0 0
\(103\) 0.957127 0.552597i 0.0943085 0.0544490i −0.452104 0.891965i \(-0.649326\pi\)
0.546413 + 0.837516i \(0.315993\pi\)
\(104\) 0 0
\(105\) 10.0949 + 7.21847i 0.985158 + 0.704450i
\(106\) 0 0
\(107\) 3.47626 6.02105i 0.336062 0.582077i −0.647626 0.761958i \(-0.724238\pi\)
0.983688 + 0.179881i \(0.0575713\pi\)
\(108\) 0 0
\(109\) 2.42887 6.67327i 0.232644 0.639183i −0.767354 0.641223i \(-0.778427\pi\)
0.999998 + 0.00204008i \(0.000649379\pi\)
\(110\) 0 0
\(111\) 2.59604 + 10.0869i 0.246405 + 0.957407i
\(112\) 0 0
\(113\) 2.33000 0.219188 0.109594 0.993976i \(-0.465045\pi\)
0.109594 + 0.993976i \(0.465045\pi\)
\(114\) 0 0
\(115\) 2.73592 0.255125
\(116\) 0 0
\(117\) −2.30914 + 11.7326i −0.213480 + 1.08468i
\(118\) 0 0
\(119\) −0.300968 + 0.826903i −0.0275897 + 0.0758021i
\(120\) 0 0
\(121\) 14.0697 24.3695i 1.27907 2.21541i
\(122\) 0 0
\(123\) −1.21863 + 1.70423i −0.109881 + 0.153666i
\(124\) 0 0
\(125\) −3.28225 + 1.89501i −0.293573 + 0.169495i
\(126\) 0 0
\(127\) −0.792153 + 0.944052i −0.0702922 + 0.0837710i −0.800045 0.599941i \(-0.795191\pi\)
0.729752 + 0.683712i \(0.239635\pi\)
\(128\) 0 0
\(129\) 10.7755 + 1.05031i 0.948732 + 0.0924749i
\(130\) 0 0
\(131\) −6.34320 + 1.11848i −0.554208 + 0.0977218i −0.443736 0.896157i \(-0.646347\pi\)
−0.110472 + 0.993879i \(0.535236\pi\)
\(132\) 0 0
\(133\) −5.27955 + 7.72783i −0.457795 + 0.670088i
\(134\) 0 0
\(135\) 6.85823 + 15.9258i 0.590262 + 1.37067i
\(136\) 0 0
\(137\) 3.68452 + 10.1231i 0.314790 + 0.864878i 0.991672 + 0.128787i \(0.0411084\pi\)
−0.676882 + 0.736091i \(0.736669\pi\)
\(138\) 0 0
\(139\) −6.45972 5.42035i −0.547906 0.459748i 0.326325 0.945258i \(-0.394190\pi\)
−0.874231 + 0.485510i \(0.838634\pi\)
\(140\) 0 0
\(141\) −13.3253 + 1.03301i −1.12219 + 0.0869948i
\(142\) 0 0
\(143\) −4.33014 + 24.5575i −0.362105 + 2.05360i
\(144\) 0 0
\(145\) −13.3996 7.73627i −1.11278 0.642462i
\(146\) 0 0
\(147\) −2.89783 2.95578i −0.239009 0.243788i
\(148\) 0 0
\(149\) −3.41271 4.06711i −0.279580 0.333190i 0.607920 0.793998i \(-0.292004\pi\)
−0.887500 + 0.460808i \(0.847560\pi\)
\(150\) 0 0
\(151\) 2.55987i 0.208319i −0.994561 0.104160i \(-0.966785\pi\)
0.994561 0.104160i \(-0.0332153\pi\)
\(152\) 0 0
\(153\) −0.957320 + 0.771514i −0.0773948 + 0.0623732i
\(154\) 0 0
\(155\) 5.98021 5.01799i 0.480342 0.403055i
\(156\) 0 0
\(157\) 15.7565 + 5.73489i 1.25750 + 0.457694i 0.882931 0.469503i \(-0.155567\pi\)
0.374573 + 0.927197i \(0.377789\pi\)
\(158\) 0 0
\(159\) 0.335241 0.229827i 0.0265864 0.0182265i
\(160\) 0 0
\(161\) 1.73361 + 0.305683i 0.136628 + 0.0240912i
\(162\) 0 0
\(163\) −5.28499 9.15387i −0.413952 0.716987i 0.581365 0.813643i \(-0.302519\pi\)
−0.995318 + 0.0966559i \(0.969185\pi\)
\(164\) 0 0
\(165\) 14.9567 + 32.9217i 1.16438 + 2.56295i
\(166\) 0 0
\(167\) 10.5199 3.82893i 0.814054 0.296292i 0.0987568 0.995112i \(-0.468513\pi\)
0.715298 + 0.698820i \(0.246291\pi\)
\(168\) 0 0
\(169\) −0.501366 2.84339i −0.0385666 0.218722i
\(170\) 0 0
\(171\) −11.8969 + 5.42808i −0.909778 + 0.415095i
\(172\) 0 0
\(173\) 3.80558 + 21.5825i 0.289333 + 1.64089i 0.689384 + 0.724396i \(0.257881\pi\)
−0.400051 + 0.916493i \(0.631007\pi\)
\(174\) 0 0
\(175\) −12.3797 + 4.50585i −0.935819 + 0.340610i
\(176\) 0 0
\(177\) 3.83846 + 8.44895i 0.288516 + 0.635062i
\(178\) 0 0
\(179\) 10.6934 + 18.5215i 0.799263 + 1.38436i 0.920097 + 0.391692i \(0.128110\pi\)
−0.120833 + 0.992673i \(0.538557\pi\)
\(180\) 0 0
\(181\) −18.0057 3.17489i −1.33835 0.235988i −0.541775 0.840523i \(-0.682248\pi\)
−0.796578 + 0.604536i \(0.793359\pi\)
\(182\) 0 0
\(183\) −11.1086 + 7.61559i −0.821173 + 0.562961i
\(184\) 0 0
\(185\) −18.8569 6.86334i −1.38639 0.504603i
\(186\) 0 0
\(187\) −1.96414 + 1.64811i −0.143632 + 0.120522i
\(188\) 0 0
\(189\) 2.56634 + 10.8576i 0.186674 + 0.789776i
\(190\) 0 0
\(191\) 3.46116i 0.250441i 0.992129 + 0.125220i \(0.0399638\pi\)
−0.992129 + 0.125220i \(0.960036\pi\)
\(192\) 0 0
\(193\) 6.64414 + 7.91818i 0.478256 + 0.569963i 0.950190 0.311671i \(-0.100889\pi\)
−0.471934 + 0.881634i \(0.656444\pi\)
\(194\) 0 0
\(195\) −16.1283 16.4508i −1.15497 1.17806i
\(196\) 0 0
\(197\) 10.2877 + 5.93959i 0.732966 + 0.423178i 0.819506 0.573070i \(-0.194248\pi\)
−0.0865400 + 0.996248i \(0.527581\pi\)
\(198\) 0 0
\(199\) −4.24330 + 24.0650i −0.300800 + 1.70592i 0.341845 + 0.939756i \(0.388948\pi\)
−0.642645 + 0.766164i \(0.722163\pi\)
\(200\) 0 0
\(201\) 6.11429 0.473995i 0.431269 0.0334330i
\(202\) 0 0
\(203\) −7.62630 6.39922i −0.535261 0.449137i
\(204\) 0 0
\(205\) −1.38057 3.79308i −0.0964230 0.264920i
\(206\) 0 0
\(207\) 1.85249 + 1.61799i 0.128757 + 0.112458i
\(208\) 0 0
\(209\) −24.5807 + 11.8085i −1.70028 + 0.816814i
\(210\) 0 0
\(211\) 16.3173 2.87718i 1.12333 0.198074i 0.419028 0.907973i \(-0.362371\pi\)
0.704303 + 0.709900i \(0.251260\pi\)
\(212\) 0 0
\(213\) 7.70128 + 0.750660i 0.527683 + 0.0514344i
\(214\) 0 0
\(215\) −13.4078 + 15.9788i −0.914405 + 1.08975i
\(216\) 0 0
\(217\) 4.35002 2.51149i 0.295299 0.170491i
\(218\) 0 0
\(219\) 5.69701 7.96714i 0.384968 0.538370i
\(220\) 0 0
\(221\) 0.816781 1.41471i 0.0549426 0.0951634i
\(222\) 0 0
\(223\) 4.05122 11.1306i 0.271290 0.745362i −0.726986 0.686653i \(-0.759079\pi\)
0.998275 0.0587091i \(-0.0186984\pi\)
\(224\) 0 0
\(225\) −18.0608 3.55461i −1.20405 0.236974i
\(226\) 0 0
\(227\) 23.0722 1.53135 0.765676 0.643226i \(-0.222405\pi\)
0.765676 + 0.643226i \(0.222405\pi\)
\(228\) 0 0
\(229\) 14.0461 0.928192 0.464096 0.885785i \(-0.346379\pi\)
0.464096 + 0.885785i \(0.346379\pi\)
\(230\) 0 0
\(231\) 5.79899 + 22.5320i 0.381546 + 1.48249i
\(232\) 0 0
\(233\) −8.06779 + 22.1661i −0.528539 + 1.45215i 0.332253 + 0.943190i \(0.392191\pi\)
−0.860792 + 0.508958i \(0.830031\pi\)
\(234\) 0 0
\(235\) 12.8749 22.3001i 0.839869 1.45470i
\(236\) 0 0
\(237\) −17.6536 12.6235i −1.14673 0.819981i
\(238\) 0 0
\(239\) 23.6023 13.6268i 1.52670 0.881443i 0.527206 0.849738i \(-0.323240\pi\)
0.999497 0.0317050i \(-0.0100937\pi\)
\(240\) 0 0
\(241\) 13.6728 16.2946i 0.880739 1.04962i −0.117659 0.993054i \(-0.537539\pi\)
0.998399 0.0565704i \(-0.0180165\pi\)
\(242\) 0 0
\(243\) −4.77459 + 14.8392i −0.306290 + 0.951938i
\(244\) 0 0
\(245\) 7.85381 1.38484i 0.501762 0.0884741i
\(246\) 0 0
\(247\) 12.1431 12.4259i 0.772645 0.790643i
\(248\) 0 0
\(249\) 15.4435 + 4.30236i 0.978692 + 0.272651i
\(250\) 0 0
\(251\) −0.848967 2.33252i −0.0535863 0.147227i 0.910012 0.414583i \(-0.136072\pi\)
−0.963598 + 0.267355i \(0.913850\pi\)
\(252\) 0 0
\(253\) 3.92920 + 3.29699i 0.247027 + 0.207280i
\(254\) 0 0
\(255\) −0.183087 2.36173i −0.0114654 0.147897i
\(256\) 0 0
\(257\) 1.95465 11.0854i 0.121928 0.691488i −0.861157 0.508339i \(-0.830260\pi\)
0.983085 0.183149i \(-0.0586291\pi\)
\(258\) 0 0
\(259\) −11.1818 6.45583i −0.694805 0.401146i
\(260\) 0 0
\(261\) −4.49777 13.1626i −0.278405 0.814746i
\(262\) 0 0
\(263\) −7.57578 9.02847i −0.467143 0.556719i 0.480109 0.877209i \(-0.340597\pi\)
−0.947252 + 0.320490i \(0.896153\pi\)
\(264\) 0 0
\(265\) 0.783093i 0.0481050i
\(266\) 0 0
\(267\) 11.4604 + 5.48285i 0.701367 + 0.335545i
\(268\) 0 0
\(269\) 8.96522 7.52271i 0.546619 0.458668i −0.327175 0.944964i \(-0.606097\pi\)
0.873794 + 0.486296i \(0.161652\pi\)
\(270\) 0 0
\(271\) 29.1999 + 10.6279i 1.77377 + 0.645598i 0.999925 + 0.0122180i \(0.00388921\pi\)
0.773841 + 0.633380i \(0.218333\pi\)
\(272\) 0 0
\(273\) −8.38165 12.2260i −0.507280 0.739954i
\(274\) 0 0
\(275\) −37.8030 6.66569i −2.27961 0.401956i
\(276\) 0 0
\(277\) 1.91965 + 3.32494i 0.115341 + 0.199776i 0.917916 0.396775i \(-0.129871\pi\)
−0.802575 + 0.596551i \(0.796537\pi\)
\(278\) 0 0
\(279\) 7.01680 + 0.138933i 0.420085 + 0.00831773i
\(280\) 0 0
\(281\) 23.0658 8.39528i 1.37599 0.500820i 0.455031 0.890475i \(-0.349628\pi\)
0.920961 + 0.389655i \(0.127406\pi\)
\(282\) 0 0
\(283\) 4.03563 + 22.8872i 0.239894 + 1.36050i 0.832059 + 0.554688i \(0.187162\pi\)
−0.592165 + 0.805817i \(0.701727\pi\)
\(284\) 0 0
\(285\) 4.33484 24.8183i 0.256774 1.47011i
\(286\) 0 0
\(287\) −0.450998 2.55773i −0.0266215 0.150978i
\(288\) 0 0
\(289\) −15.8169 + 5.75689i −0.930408 + 0.338641i
\(290\) 0 0
\(291\) 25.7378 11.6930i 1.50878 0.685455i
\(292\) 0 0
\(293\) 5.48661 + 9.50309i 0.320531 + 0.555177i 0.980598 0.196031i \(-0.0628052\pi\)
−0.660066 + 0.751207i \(0.729472\pi\)
\(294\) 0 0
\(295\) −17.6075 3.10468i −1.02515 0.180762i
\(296\) 0 0
\(297\) −9.34230 + 31.1366i −0.542095 + 1.80673i
\(298\) 0 0
\(299\) −3.07081 1.11768i −0.177590 0.0646374i
\(300\) 0 0
\(301\) −10.2812 + 8.62693i −0.592597 + 0.497248i
\(302\) 0 0
\(303\) 4.29352 8.97446i 0.246656 0.515569i
\(304\) 0 0
\(305\) 25.9487i 1.48582i
\(306\) 0 0
\(307\) 0.351542 + 0.418952i 0.0200636 + 0.0239108i 0.775983 0.630754i \(-0.217254\pi\)
−0.755919 + 0.654665i \(0.772810\pi\)
\(308\) 0 0
\(309\) −1.36691 + 1.34012i −0.0777610 + 0.0762366i
\(310\) 0 0
\(311\) −12.1908 7.03836i −0.691277 0.399109i 0.112813 0.993616i \(-0.464014\pi\)
−0.804090 + 0.594507i \(0.797347\pi\)
\(312\) 0 0
\(313\) −3.23018 + 18.3193i −0.182580 + 1.03547i 0.746444 + 0.665448i \(0.231759\pi\)
−0.929025 + 0.370018i \(0.879352\pi\)
\(314\) 0 0
\(315\) −20.0493 7.75016i −1.12965 0.436672i
\(316\) 0 0
\(317\) −20.8301 17.4785i −1.16993 0.981690i −0.169940 0.985454i \(-0.554357\pi\)
−0.999993 + 0.00376423i \(0.998802\pi\)
\(318\) 0 0
\(319\) −9.92113 27.2581i −0.555477 1.52616i
\(320\) 0 0
\(321\) −3.23171 + 11.6004i −0.180377 + 0.647469i
\(322\) 0 0
\(323\) 1.77773 0.176176i 0.0989155 0.00980270i
\(324\) 0 0
\(325\) 24.0848 4.24680i 1.33598 0.235570i
\(326\) 0 0
\(327\) −1.19328 + 12.2422i −0.0659883 + 0.676996i
\(328\) 0 0
\(329\) 10.6498 12.6919i 0.587142 0.699729i
\(330\) 0 0
\(331\) −25.4221 + 14.6775i −1.39733 + 0.806746i −0.994112 0.108360i \(-0.965440\pi\)
−0.403214 + 0.915106i \(0.632107\pi\)
\(332\) 0 0
\(333\) −8.70914 15.7989i −0.477258 0.865776i
\(334\) 0 0
\(335\) −5.90767 + 10.2324i −0.322770 + 0.559055i
\(336\) 0 0
\(337\) 4.60842 12.6615i 0.251037 0.689717i −0.748607 0.663014i \(-0.769277\pi\)
0.999643 0.0267031i \(-0.00850087\pi\)
\(338\) 0 0
\(339\) −3.90832 + 1.00587i −0.212271 + 0.0546316i
\(340\) 0 0
\(341\) 14.6356 0.792562
\(342\) 0 0
\(343\) 20.1612 1.08860
\(344\) 0 0
\(345\) −4.58919 + 1.18111i −0.247074 + 0.0635888i
\(346\) 0 0
\(347\) −2.06013 + 5.66016i −0.110594 + 0.303854i −0.982627 0.185594i \(-0.940579\pi\)
0.872033 + 0.489447i \(0.162801\pi\)
\(348\) 0 0
\(349\) −14.3065 + 24.7795i −0.765808 + 1.32642i 0.174010 + 0.984744i \(0.444328\pi\)
−0.939818 + 0.341675i \(0.889006\pi\)
\(350\) 0 0
\(351\) −1.19169 20.6769i −0.0636078 1.10365i
\(352\) 0 0
\(353\) 14.6066 8.43315i 0.777433 0.448851i −0.0580867 0.998312i \(-0.518500\pi\)
0.835520 + 0.549460i \(0.185167\pi\)
\(354\) 0 0
\(355\) −9.58259 + 11.4201i −0.508591 + 0.606115i
\(356\) 0 0
\(357\) 0.147862 1.51697i 0.00782569 0.0802864i
\(358\) 0 0
\(359\) 16.2813 2.87084i 0.859295 0.151517i 0.273397 0.961901i \(-0.411853\pi\)
0.585898 + 0.810385i \(0.300742\pi\)
\(360\) 0 0
\(361\) 18.7823 + 2.86764i 0.988545 + 0.150928i
\(362\) 0 0
\(363\) −13.0800 + 46.9511i −0.686521 + 2.46429i
\(364\) 0 0
\(365\) 6.45403 + 17.7323i 0.337819 + 0.928151i
\(366\) 0 0
\(367\) 7.32428 + 6.14580i 0.382324 + 0.320808i 0.813614 0.581405i \(-0.197497\pi\)
−0.431290 + 0.902213i \(0.641941\pi\)
\(368\) 0 0
\(369\) 1.30840 3.38475i 0.0681124 0.176203i
\(370\) 0 0
\(371\) −0.0874947 + 0.496207i −0.00454250 + 0.0257618i
\(372\) 0 0
\(373\) 3.75197 + 2.16620i 0.194270 + 0.112162i 0.593980 0.804480i \(-0.297556\pi\)
−0.399710 + 0.916642i \(0.630889\pi\)
\(374\) 0 0
\(375\) 4.68752 4.59562i 0.242062 0.237317i
\(376\) 0 0
\(377\) 11.8794 + 14.1573i 0.611819 + 0.729138i
\(378\) 0 0
\(379\) 5.96818i 0.306565i −0.988182 0.153282i \(-0.951016\pi\)
0.988182 0.153282i \(-0.0489844\pi\)
\(380\) 0 0
\(381\) 0.921197 1.92552i 0.0471943 0.0986472i
\(382\) 0 0
\(383\) −3.37004 + 2.82780i −0.172201 + 0.144494i −0.724815 0.688944i \(-0.758075\pi\)
0.552614 + 0.833437i \(0.313630\pi\)
\(384\) 0 0
\(385\) −42.1222 15.3312i −2.14675 0.781351i
\(386\) 0 0
\(387\) −18.5282 + 2.89006i −0.941839 + 0.146910i
\(388\) 0 0
\(389\) −14.5009 2.55689i −0.735223 0.129640i −0.206515 0.978443i \(-0.566212\pi\)
−0.528708 + 0.848804i \(0.677323\pi\)
\(390\) 0 0
\(391\) −0.168006 0.290994i −0.00849641 0.0147162i
\(392\) 0 0
\(393\) 10.1572 4.61451i 0.512361 0.232771i
\(394\) 0 0
\(395\) 39.2913 14.3009i 1.97696 0.719554i
\(396\) 0 0
\(397\) 1.74751 + 9.91059i 0.0877048 + 0.497398i 0.996740 + 0.0806794i \(0.0257090\pi\)
−0.909035 + 0.416719i \(0.863180\pi\)
\(398\) 0 0
\(399\) 5.51971 15.2418i 0.276331 0.763043i
\(400\) 0 0
\(401\) −2.58090 14.6370i −0.128884 0.730937i −0.978925 0.204221i \(-0.934534\pi\)
0.850041 0.526717i \(-0.176577\pi\)
\(402\) 0 0
\(403\) −8.76220 + 3.18918i −0.436476 + 0.158864i
\(404\) 0 0
\(405\) −18.3791 23.7529i −0.913267 1.18029i
\(406\) 0 0
\(407\) −18.8106 32.5809i −0.932405 1.61497i
\(408\) 0 0
\(409\) −9.81162 1.73005i −0.485153 0.0855456i −0.0742787 0.997238i \(-0.523665\pi\)
−0.410874 + 0.911692i \(0.634777\pi\)
\(410\) 0 0
\(411\) −10.5506 15.3898i −0.520422 0.759123i
\(412\) 0 0
\(413\) −10.8101 3.93457i −0.531932 0.193607i
\(414\) 0 0
\(415\) −23.6608 + 19.8538i −1.16146 + 0.974583i
\(416\) 0 0
\(417\) 13.1754 + 6.30333i 0.645204 + 0.308676i
\(418\) 0 0
\(419\) 8.34847i 0.407849i 0.978987 + 0.203925i \(0.0653698\pi\)
−0.978987 + 0.203925i \(0.934630\pi\)
\(420\) 0 0
\(421\) 23.4446 + 27.9402i 1.14262 + 1.36172i 0.922384 + 0.386273i \(0.126238\pi\)
0.220234 + 0.975447i \(0.429318\pi\)
\(422\) 0 0
\(423\) 21.9057 7.48533i 1.06509 0.363949i
\(424\) 0 0
\(425\) 2.17775 + 1.25733i 0.105637 + 0.0609893i
\(426\) 0 0
\(427\) 2.89924 16.4424i 0.140304 0.795705i
\(428\) 0 0
\(429\) −3.33825 43.0617i −0.161172 2.07904i
\(430\) 0 0
\(431\) −8.05751 6.76105i −0.388116 0.325668i 0.427762 0.903891i \(-0.359302\pi\)
−0.815879 + 0.578223i \(0.803746\pi\)
\(432\) 0 0
\(433\) −12.6127 34.6530i −0.606126 1.66532i −0.738611 0.674132i \(-0.764518\pi\)
0.132485 0.991185i \(-0.457704\pi\)
\(434\) 0 0
\(435\) 25.8161 + 7.19205i 1.23779 + 0.344832i
\(436\) 0 0
\(437\) −0.964625 3.44107i −0.0461443 0.164608i
\(438\) 0 0
\(439\) −13.1107 + 2.31177i −0.625739 + 0.110335i −0.477522 0.878620i \(-0.658465\pi\)
−0.148218 + 0.988955i \(0.547354\pi\)
\(440\) 0 0
\(441\) 6.13681 + 3.70698i 0.292229 + 0.176523i
\(442\) 0 0
\(443\) −4.79891 + 5.71912i −0.228003 + 0.271724i −0.867902 0.496736i \(-0.834532\pi\)
0.639899 + 0.768459i \(0.278976\pi\)
\(444\) 0 0
\(445\) −21.1976 + 12.2384i −1.00486 + 0.580156i
\(446\) 0 0
\(447\) 7.48023 + 5.34883i 0.353803 + 0.252991i
\(448\) 0 0
\(449\) 12.1781 21.0931i 0.574722 0.995447i −0.421350 0.906898i \(-0.638444\pi\)
0.996072 0.0885490i \(-0.0282230\pi\)
\(450\) 0 0
\(451\) 2.58825 7.11115i 0.121876 0.334851i
\(452\) 0 0
\(453\) 1.10511 + 4.29390i 0.0519226 + 0.201745i
\(454\) 0 0
\(455\) 28.5589 1.33886
\(456\) 0 0
\(457\) −34.8127 −1.62847 −0.814236 0.580534i \(-0.802844\pi\)
−0.814236 + 0.580534i \(0.802844\pi\)
\(458\) 0 0
\(459\) 1.27273 1.70741i 0.0594060 0.0796950i
\(460\) 0 0
\(461\) 0.765028 2.10190i 0.0356309 0.0978951i −0.920601 0.390503i \(-0.872301\pi\)
0.956232 + 0.292608i \(0.0945232\pi\)
\(462\) 0 0
\(463\) −1.84091 + 3.18854i −0.0855541 + 0.148184i −0.905627 0.424075i \(-0.860599\pi\)
0.820073 + 0.572259i \(0.193933\pi\)
\(464\) 0 0
\(465\) −7.86484 + 10.9988i −0.364723 + 0.510058i
\(466\) 0 0
\(467\) 11.3948 6.57879i 0.527288 0.304430i −0.212623 0.977134i \(-0.568201\pi\)
0.739911 + 0.672704i \(0.234867\pi\)
\(468\) 0 0
\(469\) −4.88666 + 5.82369i −0.225645 + 0.268913i
\(470\) 0 0
\(471\) −28.9055 2.81748i −1.33190 0.129823i
\(472\) 0 0
\(473\) −38.5115 + 6.79061i −1.77076 + 0.312233i
\(474\) 0 0
\(475\) 19.1281 + 18.6927i 0.877658 + 0.857678i
\(476\) 0 0
\(477\) −0.463112 + 0.530234i −0.0212045 + 0.0242778i
\(478\) 0 0
\(479\) 11.4643 + 31.4978i 0.523816 + 1.43917i 0.866240 + 0.499628i \(0.166530\pi\)
−0.342424 + 0.939546i \(0.611248\pi\)
\(480\) 0 0
\(481\) 18.3613 + 15.4069i 0.837202 + 0.702496i
\(482\) 0 0
\(483\) −3.03991 + 0.235661i −0.138321 + 0.0107229i
\(484\) 0 0
\(485\) −9.45772 + 53.6374i −0.429453 + 2.43555i
\(486\) 0 0
\(487\) 15.2052 + 8.77875i 0.689015 + 0.397803i 0.803243 0.595651i \(-0.203106\pi\)
−0.114228 + 0.993455i \(0.536439\pi\)
\(488\) 0 0
\(489\) 12.8168 + 13.0730i 0.579594 + 0.591183i
\(490\) 0 0
\(491\) −15.8204 18.8540i −0.713964 0.850869i 0.280065 0.959981i \(-0.409644\pi\)
−0.994030 + 0.109112i \(0.965199\pi\)
\(492\) 0 0
\(493\) 1.90026i 0.0855834i
\(494\) 0 0
\(495\) −39.3007 48.7656i −1.76643 2.19185i
\(496\) 0 0
\(497\) −7.34797 + 6.16568i −0.329602 + 0.276569i
\(498\) 0 0
\(499\) −13.8001 5.02282i −0.617777 0.224852i 0.0141259 0.999900i \(-0.495503\pi\)
−0.631902 + 0.775048i \(0.717726\pi\)
\(500\) 0 0
\(501\) −15.9930 + 10.9641i −0.714514 + 0.489840i
\(502\) 0 0
\(503\) 4.24201 + 0.747980i 0.189142 + 0.0333508i 0.267417 0.963581i \(-0.413830\pi\)
−0.0782748 + 0.996932i \(0.524941\pi\)
\(504\) 0 0
\(505\) 9.58368 + 16.5994i 0.426468 + 0.738665i
\(506\) 0 0
\(507\) 2.06849 + 4.55303i 0.0918650 + 0.202207i
\(508\) 0 0
\(509\) −4.35756 + 1.58602i −0.193145 + 0.0702991i −0.436782 0.899567i \(-0.643882\pi\)
0.243637 + 0.969867i \(0.421660\pi\)
\(510\) 0 0
\(511\) 2.10837 + 11.9572i 0.0932690 + 0.528955i
\(512\) 0 0
\(513\) 17.6124 14.2409i 0.777605 0.628753i
\(514\) 0 0
\(515\) −0.640425 3.63203i −0.0282205 0.160047i
\(516\) 0 0
\(517\) 45.3638 16.5111i 1.99510 0.726156i
\(518\) 0 0
\(519\) −15.7007 34.5594i −0.689185 1.51699i
\(520\) 0 0
\(521\) −0.205968 0.356747i −0.00902363 0.0156294i 0.861478 0.507794i \(-0.169539\pi\)
−0.870502 + 0.492165i \(0.836206\pi\)
\(522\) 0 0
\(523\) 19.2248 + 3.38986i 0.840643 + 0.148228i 0.577359 0.816490i \(-0.304083\pi\)
0.263284 + 0.964718i \(0.415194\pi\)
\(524\) 0 0
\(525\) 18.8204 12.9025i 0.821390 0.563109i
\(526\) 0 0
\(527\) −0.900948 0.327918i −0.0392459 0.0142843i
\(528\) 0 0
\(529\) 17.1041 14.3520i 0.743657 0.624002i
\(530\) 0 0
\(531\) −10.0860 12.5151i −0.437697 0.543109i
\(532\) 0 0
\(533\) 4.82137i 0.208837i
\(534\) 0 0
\(535\) −14.9131 17.7728i −0.644751 0.768385i
\(536\) 0 0
\(537\) −25.9328 26.4514i −1.11908 1.14146i
\(538\) 0 0
\(539\) 12.9481 + 7.47562i 0.557716 + 0.321998i
\(540\) 0 0
\(541\) −3.15633 + 17.9005i −0.135701 + 0.769601i 0.838667 + 0.544644i \(0.183335\pi\)
−0.974369 + 0.224957i \(0.927776\pi\)
\(542\) 0 0
\(543\) 31.5732 2.44763i 1.35493 0.105038i
\(544\) 0 0
\(545\) −18.1538 15.2328i −0.777622 0.652502i
\(546\) 0 0
\(547\) −1.42436 3.91340i −0.0609014 0.167325i 0.905510 0.424324i \(-0.139488\pi\)
−0.966412 + 0.256999i \(0.917266\pi\)
\(548\) 0 0
\(549\) 15.3458 17.5699i 0.654942 0.749867i
\(550\) 0 0
\(551\) −5.00579 + 19.5808i −0.213254 + 0.834172i
\(552\) 0 0
\(553\) 26.4948 4.67174i 1.12667 0.198663i
\(554\) 0 0
\(555\) 34.5932 + 3.37188i 1.46840 + 0.143128i
\(556\) 0 0
\(557\) 9.16196 10.9188i 0.388205 0.462644i −0.536181 0.844103i \(-0.680134\pi\)
0.924386 + 0.381459i \(0.124578\pi\)
\(558\) 0 0
\(559\) 21.5767 12.4573i 0.912599 0.526889i
\(560\) 0 0
\(561\) 2.58313 3.61245i 0.109060 0.152518i
\(562\) 0 0
\(563\) 3.28307 5.68645i 0.138365 0.239655i −0.788513 0.615018i \(-0.789149\pi\)
0.926878 + 0.375363i \(0.122482\pi\)
\(564\) 0 0
\(565\) 2.65930 7.30637i 0.111878 0.307381i
\(566\) 0 0
\(567\) −8.99204 17.1046i −0.377630 0.718324i
\(568\) 0 0
\(569\) 45.7506 1.91797 0.958983 0.283465i \(-0.0914840\pi\)
0.958983 + 0.283465i \(0.0914840\pi\)
\(570\) 0 0
\(571\) −5.82547 −0.243788 −0.121894 0.992543i \(-0.538897\pi\)
−0.121894 + 0.992543i \(0.538897\pi\)
\(572\) 0 0
\(573\) −1.49420 5.80571i −0.0624212 0.242537i
\(574\) 0 0
\(575\) 1.72053 4.72712i 0.0717510 0.197134i
\(576\) 0 0
\(577\) −17.9425 + 31.0773i −0.746956 + 1.29377i 0.202320 + 0.979319i \(0.435152\pi\)
−0.949276 + 0.314446i \(0.898181\pi\)
\(578\) 0 0
\(579\) −14.5631 10.4135i −0.605223 0.432772i
\(580\) 0 0
\(581\) −17.2109 + 9.93674i −0.714030 + 0.412245i
\(582\) 0 0
\(583\) −0.943689 + 1.12464i −0.0390836 + 0.0465780i
\(584\) 0 0
\(585\) 34.1553 + 20.6317i 1.41215 + 0.853015i
\(586\) 0 0
\(587\) −29.5771 + 5.21525i −1.22078 + 0.215256i −0.746661 0.665205i \(-0.768344\pi\)
−0.474118 + 0.880461i \(0.657233\pi\)
\(588\) 0 0
\(589\) −8.41982 5.75231i −0.346932 0.237020i
\(590\) 0 0
\(591\) −19.8206 5.52176i −0.815309 0.227135i
\(592\) 0 0
\(593\) −0.268437 0.737526i −0.0110234 0.0302866i 0.934059 0.357119i \(-0.116241\pi\)
−0.945082 + 0.326832i \(0.894019\pi\)
\(594\) 0 0
\(595\) 2.24948 + 1.88754i 0.0922198 + 0.0773816i
\(596\) 0 0
\(597\) −3.27130 42.1981i −0.133886 1.72706i
\(598\) 0 0
\(599\) 2.35948 13.3813i 0.0964057 0.546744i −0.897902 0.440196i \(-0.854909\pi\)
0.994308 0.106548i \(-0.0339798\pi\)
\(600\) 0 0
\(601\) 1.41283 + 0.815696i 0.0576304 + 0.0332729i 0.528538 0.848909i \(-0.322740\pi\)
−0.470908 + 0.882182i \(0.656074\pi\)
\(602\) 0 0
\(603\) −10.0514 + 3.43464i −0.409325 + 0.139869i
\(604\) 0 0
\(605\) −60.3592 71.9333i −2.45395 2.92450i
\(606\) 0 0
\(607\) 23.6670i 0.960615i 0.877100 + 0.480308i \(0.159475\pi\)
−0.877100 + 0.480308i \(0.840525\pi\)
\(608\) 0 0
\(609\) 15.5548 + 7.44167i 0.630314 + 0.301552i
\(610\) 0 0
\(611\) −23.5610 + 19.7700i −0.953177 + 0.799811i
\(612\) 0 0
\(613\) 14.7136 + 5.35532i 0.594278 + 0.216299i 0.621610 0.783327i \(-0.286479\pi\)
−0.0273321 + 0.999626i \(0.508701\pi\)
\(614\) 0 0
\(615\) 3.95324 + 5.76646i 0.159410 + 0.232526i
\(616\) 0 0
\(617\) 19.6258 + 3.46056i 0.790105 + 0.139317i 0.554117 0.832439i \(-0.313056\pi\)
0.235988 + 0.971756i \(0.424167\pi\)
\(618\) 0 0
\(619\) 3.55524 + 6.15786i 0.142897 + 0.247505i 0.928587 0.371116i \(-0.121025\pi\)
−0.785689 + 0.618621i \(0.787691\pi\)
\(620\) 0 0
\(621\) −3.80585 1.91426i −0.152723 0.0768168i
\(622\) 0 0
\(623\) −14.7992 + 5.38648i −0.592919 + 0.215805i
\(624\) 0 0
\(625\) −3.13111 17.7574i −0.125244 0.710297i
\(626\) 0 0
\(627\) 36.1335 30.4191i 1.44303 1.21482i
\(628\) 0 0
\(629\) 0.427962 + 2.42710i 0.0170640 + 0.0967746i
\(630\) 0 0
\(631\) 1.16675 0.424661i 0.0464474 0.0169055i −0.318692 0.947858i \(-0.603244\pi\)
0.365139 + 0.930953i \(0.381021\pi\)
\(632\) 0 0
\(633\) −26.1284 + 11.8704i −1.03851 + 0.471807i
\(634\) 0 0
\(635\) 2.05623 + 3.56149i 0.0815989 + 0.141334i
\(636\) 0 0
\(637\) −9.38092 1.65411i −0.371685 0.0655382i
\(638\) 0 0
\(639\) −13.2421 + 2.06553i −0.523849 + 0.0817112i
\(640\) 0 0
\(641\) −7.06477 2.57137i −0.279042 0.101563i 0.198708 0.980059i \(-0.436325\pi\)
−0.477750 + 0.878496i \(0.658548\pi\)
\(642\) 0 0
\(643\) 9.31005 7.81206i 0.367153 0.308078i −0.440481 0.897762i \(-0.645192\pi\)
0.807634 + 0.589684i \(0.200748\pi\)
\(644\) 0 0
\(645\) 15.5920 32.5909i 0.613933 1.28327i
\(646\) 0 0
\(647\) 38.1298i 1.49904i −0.661983 0.749519i \(-0.730285\pi\)
0.661983 0.749519i \(-0.269715\pi\)
\(648\) 0 0
\(649\) −21.5458 25.6773i −0.845747 1.00792i
\(650\) 0 0
\(651\) −6.21245 + 6.09066i −0.243485 + 0.238712i
\(652\) 0 0
\(653\) 39.7547 + 22.9524i 1.55572 + 0.898196i 0.997658 + 0.0683980i \(0.0217888\pi\)
0.558063 + 0.829798i \(0.311545\pi\)
\(654\) 0 0
\(655\) −3.73239 + 21.1674i −0.145836 + 0.827080i
\(656\) 0 0
\(657\) −6.11664 + 15.8234i −0.238633 + 0.617330i
\(658\) 0 0
\(659\) 14.3577 + 12.0475i 0.559295 + 0.469304i 0.878074 0.478525i \(-0.158828\pi\)
−0.318779 + 0.947829i \(0.603273\pi\)
\(660\) 0 0
\(661\) 4.05073 + 11.1293i 0.157555 + 0.432879i 0.993204 0.116385i \(-0.0371306\pi\)
−0.835649 + 0.549263i \(0.814908\pi\)
\(662\) 0 0
\(663\) −0.759323 + 2.72562i −0.0294896 + 0.105854i
\(664\) 0 0
\(665\) 18.2071 + 25.3755i 0.706039 + 0.984020i
\(666\) 0 0
\(667\) 3.74366 0.660108i 0.144955 0.0255595i
\(668\) 0 0
\(669\) −1.99031 + 20.4193i −0.0769500 + 0.789456i
\(670\) 0 0
\(671\) 31.2703 37.2665i 1.20718 1.43866i
\(672\) 0 0
\(673\) −9.02264 + 5.20922i −0.347797 + 0.200801i −0.663715 0.747986i \(-0.731021\pi\)
0.315917 + 0.948787i \(0.397688\pi\)
\(674\) 0 0
\(675\) 31.8294 1.83445i 1.22512 0.0706082i
\(676\) 0 0
\(677\) 10.3670 17.9562i 0.398437 0.690112i −0.595097 0.803654i \(-0.702886\pi\)
0.993533 + 0.113542i \(0.0362196\pi\)
\(678\) 0 0
\(679\) −11.9858 + 32.9306i −0.459972 + 1.26376i
\(680\) 0 0
\(681\) −38.7009 + 9.96036i −1.48302 + 0.381682i
\(682\) 0 0
\(683\) 2.79983 0.107132 0.0535662 0.998564i \(-0.482941\pi\)
0.0535662 + 0.998564i \(0.482941\pi\)
\(684\) 0 0
\(685\) 35.9492 1.37355
\(686\) 0 0
\(687\) −23.5608 + 6.06377i −0.898899 + 0.231347i
\(688\) 0 0
\(689\) 0.319912 0.878950i 0.0121877 0.0334853i
\(690\) 0 0
\(691\) 4.20182 7.27776i 0.159845 0.276859i −0.774968 0.632001i \(-0.782234\pi\)
0.934813 + 0.355142i \(0.115567\pi\)
\(692\) 0 0
\(693\) −19.4543 35.2914i −0.739009 1.34061i
\(694\) 0 0
\(695\) −24.3697 + 14.0698i −0.924395 + 0.533700i
\(696\) 0 0
\(697\) −0.318658 + 0.379762i −0.0120700 + 0.0143845i
\(698\) 0 0
\(699\) 3.96361 40.6640i 0.149918 1.53805i
\(700\) 0 0
\(701\) 14.9472 2.63560i 0.564549 0.0995451i 0.115912 0.993259i \(-0.463021\pi\)
0.448636 + 0.893714i \(0.351910\pi\)
\(702\) 0 0
\(703\) −1.98376 + 26.1369i −0.0748190 + 0.985771i
\(704\) 0 0
\(705\) −11.9692 + 42.9640i −0.450787 + 1.61812i
\(706\) 0 0
\(707\) 4.21806 + 11.5890i 0.158636 + 0.435850i
\(708\) 0 0
\(709\) −29.3000 24.5857i −1.10039 0.923334i −0.102935 0.994688i \(-0.532823\pi\)
−0.997451 + 0.0713544i \(0.977268\pi\)
\(710\) 0 0
\(711\) 35.0616 + 13.5533i 1.31491 + 0.508287i
\(712\) 0 0
\(713\) −0.333055 + 1.88885i −0.0124730 + 0.0707380i
\(714\) 0 0
\(715\) 72.0647 + 41.6065i 2.69507 + 1.55600i
\(716\) 0 0
\(717\) −33.7074 + 33.0466i −1.25883 + 1.23415i
\(718\) 0 0
\(719\) −24.9620 29.7485i −0.930924 1.10943i −0.993775 0.111410i \(-0.964463\pi\)
0.0628501 0.998023i \(-0.479981\pi\)
\(720\) 0 0
\(721\) 2.37299i 0.0883749i
\(722\) 0 0
\(723\) −15.9001 + 33.2349i −0.591330 + 1.23602i
\(724\) 0 0
\(725\) −21.7933 + 18.2868i −0.809383 + 0.679153i
\(726\) 0 0
\(727\) −35.9582 13.0877i −1.33361 0.485396i −0.425818 0.904809i \(-0.640014\pi\)
−0.907796 + 0.419413i \(0.862236\pi\)
\(728\) 0 0
\(729\) 1.60266 26.9524i 0.0593577 0.998237i
\(730\) 0 0
\(731\) 2.52286 + 0.444849i 0.0933114 + 0.0164533i
\(732\) 0 0
\(733\) −7.71039 13.3548i −0.284790 0.493270i 0.687768 0.725930i \(-0.258590\pi\)
−0.972558 + 0.232660i \(0.925257\pi\)
\(734\) 0 0
\(735\) −12.5761 + 5.71344i −0.463875 + 0.210744i
\(736\) 0 0
\(737\) −20.8152 + 7.57610i −0.766736 + 0.279069i
\(738\) 0 0
\(739\) 4.98207 + 28.2547i 0.183268 + 1.03937i 0.928160 + 0.372181i \(0.121390\pi\)
−0.744892 + 0.667185i \(0.767499\pi\)
\(740\) 0 0
\(741\) −15.0043 + 26.0853i −0.551196 + 0.958269i
\(742\) 0 0
\(743\) 4.95784 + 28.1173i 0.181886 + 1.03152i 0.929892 + 0.367833i \(0.119900\pi\)
−0.748006 + 0.663691i \(0.768989\pi\)
\(744\) 0 0
\(745\) −16.6486 + 6.05959i −0.609957 + 0.222006i
\(746\) 0 0
\(747\) −27.7621 0.549693i −1.01576 0.0201122i
\(748\) 0 0
\(749\) −7.46397 12.9280i −0.272727 0.472378i
\(750\) 0 0
\(751\) −12.4716 2.19908i −0.455096 0.0802457i −0.0585987 0.998282i \(-0.518663\pi\)
−0.396497 + 0.918036i \(0.629774\pi\)
\(752\) 0 0
\(753\) 2.43101 + 3.54603i 0.0885908 + 0.129225i
\(754\) 0 0
\(755\) −8.02719 2.92166i −0.292139 0.106330i
\(756\) 0 0
\(757\) 38.4432 32.2577i 1.39724 1.17243i 0.434934 0.900462i \(-0.356772\pi\)
0.962308 0.271963i \(-0.0876729\pi\)
\(758\) 0 0
\(759\) −8.01413 3.83408i −0.290894 0.139168i
\(760\) 0 0
\(761\) 26.6803i 0.967159i 0.875300 + 0.483580i \(0.160664\pi\)
−0.875300 + 0.483580i \(0.839336\pi\)
\(762\) 0 0
\(763\) −9.80118 11.6806i −0.354826 0.422866i
\(764\) 0 0
\(765\) 1.32668 + 3.88250i 0.0479662 + 0.140372i
\(766\) 0 0
\(767\) 18.4945 + 10.6778i 0.667798 + 0.385553i
\(768\) 0 0
\(769\) −6.83201 + 38.7463i −0.246369 + 1.39723i 0.570924 + 0.821003i \(0.306585\pi\)
−0.817292 + 0.576223i \(0.804526\pi\)
\(770\) 0 0
\(771\) 1.50691 + 19.4383i 0.0542699 + 0.700054i
\(772\) 0 0
\(773\) −2.48012 2.08107i −0.0892039 0.0748509i 0.597095 0.802170i \(-0.296321\pi\)
−0.686299 + 0.727319i \(0.740766\pi\)
\(774\) 0 0
\(775\) −4.90933 13.4883i −0.176348 0.484513i
\(776\) 0 0
\(777\) 21.5433 + 6.00168i 0.772861 + 0.215309i
\(778\) 0 0
\(779\) −4.28394 + 3.07375i −0.153488 + 0.110128i
\(780\) 0 0
\(781\) −27.5242 + 4.85326i −0.984893 + 0.173663i
\(782\) 0 0
\(783\) 13.2269 + 20.1371i 0.472690 + 0.719642i
\(784\) 0 0
\(785\) 35.9667 42.8634i 1.28371 1.52986i
\(786\) 0 0
\(787\) 22.8624 13.1996i 0.814956 0.470515i −0.0337179 0.999431i \(-0.510735\pi\)
0.848674 + 0.528916i \(0.177401\pi\)
\(788\) 0 0
\(789\) 16.6052 + 11.8737i 0.591160 + 0.422716i
\(790\) 0 0
\(791\) 2.50141 4.33256i 0.0889397 0.154048i
\(792\) 0 0
\(793\) −10.6007 + 29.1251i −0.376440 + 1.03426i