Properties

Label 912.2.cc.c.401.1
Level $912$
Weight $2$
Character 912.401
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 401.1
Root \(-1.72388 - 0.168030i\) of defining polynomial
Character \(\chi\) \(=\) 912.401
Dual form 912.2.cc.c.257.1

$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

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

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 0.880802 + 0.473484i \(0.157004\pi\)
−0.370384 + 0.928879i \(0.620774\pi\)
\(6\) 0 0
\(7\) 1.07356 + 1.85947i 0.405769 + 0.702812i 0.994411 0.105582i \(-0.0336704\pi\)
−0.588642 + 0.808394i \(0.700337\pi\)
\(8\) 0 0
\(9\) 2.62726 + 1.44827i 0.875754 + 0.482758i
\(10\) 0 0
\(11\) 5.41799 + 3.12808i 1.63359 + 0.943151i 0.982975 + 0.183740i \(0.0588203\pi\)
0.650611 + 0.759412i \(0.274513\pi\)
\(12\) 0 0
\(13\) −2.56208 3.05336i −0.710592 0.846850i 0.283089 0.959094i \(-0.408641\pi\)
−0.993681 + 0.112243i \(0.964196\pi\)
\(14\) 0 0
\(15\) −0.560722 5.75264i −0.144778 1.48532i
\(16\) 0 0
\(17\) −0.403611 0.0711674i −0.0978899 0.0172606i 0.124489 0.992221i \(-0.460271\pi\)
−0.222379 + 0.974960i \(0.571382\pi\)
\(18\) 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 −0.907019 0.421090i \(-0.861647\pi\)
0.965488 + 0.260446i \(0.0838697\pi\)
\(24\) 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 0.963634 + 0.267226i \(0.0861071\pi\)
−0.814123 + 0.580693i \(0.802782\pi\)
\(30\) 0 0
\(31\) 2.02597 1.16970i 0.363875 0.210084i −0.306904 0.951740i \(-0.599293\pi\)
0.670779 + 0.741657i \(0.265960\pi\)
\(32\) 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 \(0.164577\pi\)
−0.869289 + 0.494303i \(0.835423\pi\)
\(38\) 0 0
\(39\) 2.97944 + 6.22774i 0.477093 + 0.997236i
\(40\) 0 0
\(41\) 0.926617 + 0.777524i 0.144713 + 0.121429i 0.712270 0.701905i \(-0.247667\pi\)
−0.567557 + 0.823334i \(0.692111\pi\)
\(42\) 0 0
\(43\) −5.87377 + 2.13788i −0.895741 + 0.326023i −0.748545 0.663084i \(-0.769247\pi\)
−0.147196 + 0.989107i \(0.547025\pi\)
\(44\) 0 0
\(45\) −1.54289 + 9.89147i −0.230001 + 1.47453i
\(46\) 0 0
\(47\) 7.59919 1.33994i 1.10846 0.195451i 0.410689 0.911776i \(-0.365288\pi\)
0.697767 + 0.716325i \(0.254177\pi\)
\(48\) 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 0.326831 0.945083i \(-0.394019\pi\)
−0.357121 + 0.934058i \(0.616242\pi\)
\(54\) 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 0.862410 + 0.506210i \(0.168954\pi\)
−0.983534 + 0.180721i \(0.942157\pi\)
\(60\) 0 0
\(61\) 7.30705 + 2.65955i 0.935572 + 0.340520i 0.764416 0.644723i \(-0.223027\pi\)
0.171156 + 0.985244i \(0.445250\pi\)
\(62\) 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 −0.382534 0.923942i \(-0.624948\pi\)
−0.0434574 + 0.999055i \(0.513837\pi\)
\(68\) 0 0
\(69\) −0.802953 + 1.17124i −0.0966642 + 0.141001i
\(70\) 0 0
\(71\) −4.19799 + 1.52794i −0.498210 + 0.181334i −0.578889 0.815407i \(-0.696513\pi\)
0.0806788 + 0.996740i \(0.474291\pi\)
\(72\) 0 0
\(73\) −4.33185 3.63485i −0.507005 0.425427i 0.353069 0.935597i \(-0.385138\pi\)
−0.860074 + 0.510170i \(0.829583\pi\)
\(74\) 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 −0.0903059 0.995914i \(-0.528784\pi\)
0.996465 0.0840047i \(-0.0267711\pi\)
\(80\) 0 0
\(81\) 4.80501 + 7.60999i 0.533889 + 0.845554i
\(82\) 0 0
\(83\) −8.01579 + 4.62792i −0.879848 + 0.507980i −0.870608 0.491977i \(-0.836274\pi\)
−0.00923947 + 0.999957i \(0.502941\pi\)
\(84\) 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 −0.890028 0.455906i \(-0.849315\pi\)
0.294428 + 0.955674i \(0.404871\pi\)
\(90\) 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 −0.718786 0.695231i \(-0.755302\pi\)
−0.913221 + 0.407464i \(0.866413\pi\)
\(98\) 0 0
\(99\) 9.70416 + 16.0650i 0.975305 + 1.61459i
\(100\) 0 0
\(101\) −3.69207 4.40004i −0.367375 0.437820i 0.550412 0.834893i \(-0.314471\pi\)
−0.917787 + 0.397073i \(0.870026\pi\)
\(102\) 0 0
\(103\) 0.957127 + 0.552597i 0.0943085 + 0.0544490i 0.546413 0.837516i \(-0.315993\pi\)
−0.452104 + 0.891965i \(0.649326\pi\)
\(104\) 0 0
\(105\) 10.0949 7.21847i 0.985158 0.704450i
\(106\) 0 0
\(107\) 3.47626 + 6.02105i 0.336062 + 0.582077i 0.983688 0.179881i \(-0.0575713\pi\)
−0.647626 + 0.761958i \(0.724238\pi\)
\(108\) 0 0
\(109\) 2.42887 + 6.67327i 0.232644 + 0.639183i 0.999998 0.00204008i \(-0.000649379\pi\)
−0.767354 + 0.641223i \(0.778427\pi\)
\(110\) 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 0.729752 0.683712i \(-0.239635\pi\)
−0.800045 + 0.599941i \(0.795191\pi\)
\(128\) 0 0
\(129\) 10.7755 1.05031i 0.948732 0.0924749i
\(130\) 0 0
\(131\) −6.34320 1.11848i −0.554208 0.0977218i −0.110472 0.993879i \(-0.535236\pi\)
−0.443736 + 0.896157i \(0.646347\pi\)
\(132\) 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 −0.676882 0.736091i \(-0.736669\pi\)
0.991672 0.128787i \(-0.0411084\pi\)
\(138\) 0 0
\(139\) −6.45972 + 5.42035i −0.547906 + 0.459748i −0.874231 0.485510i \(-0.838634\pi\)
0.326325 + 0.945258i \(0.394190\pi\)
\(140\) 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 −0.887500 0.460808i \(-0.847560\pi\)
0.607920 + 0.793998i \(0.292004\pi\)
\(150\) 0 0
\(151\) 2.55987i 0.208319i 0.994561 + 0.104160i \(0.0332153\pi\)
−0.994561 + 0.104160i \(0.966785\pi\)
\(152\) 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 0.374573 0.927197i \(-0.377789\pi\)
0.882931 + 0.469503i \(0.155567\pi\)
\(158\) 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 −0.995318 0.0966559i \(-0.969185\pi\)
0.581365 + 0.813643i \(0.302519\pi\)
\(164\) 0 0
\(165\) 14.9567 32.9217i 1.16438 2.56295i
\(166\) 0 0
\(167\) 10.5199 + 3.82893i 0.814054 + 0.296292i 0.715298 0.698820i \(-0.246291\pi\)
0.0987568 + 0.995112i \(0.468513\pi\)
\(168\) 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 −0.400051 0.916493i \(-0.631007\pi\)
0.689384 0.724396i \(-0.257881\pi\)
\(174\) 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 −0.120833 0.992673i \(-0.538557\pi\)
0.920097 0.391692i \(-0.128110\pi\)
\(180\) 0 0
\(181\) −18.0057 + 3.17489i −1.33835 + 0.235988i −0.796578 0.604536i \(-0.793359\pi\)
−0.541775 + 0.840523i \(0.682248\pi\)
\(182\) 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 \(-0.960036\pi\)
0.992129 0.125220i \(-0.0399638\pi\)
\(192\) 0 0
\(193\) 6.64414 7.91818i 0.478256 0.569963i −0.471934 0.881634i \(-0.656444\pi\)
0.950190 + 0.311671i \(0.100889\pi\)
\(194\) 0 0
\(195\) −16.1283 + 16.4508i −1.15497 + 1.17806i
\(196\) 0 0
\(197\) 10.2877 5.93959i 0.732966 0.423178i −0.0865400 0.996248i \(-0.527581\pi\)
0.819506 + 0.573070i \(0.194248\pi\)
\(198\) 0 0
\(199\) −4.24330 24.0650i −0.300800 1.70592i −0.642645 0.766164i \(-0.722163\pi\)
0.341845 0.939756i \(-0.388948\pi\)
\(200\) 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 0.704303 0.709900i \(-0.251260\pi\)
0.419028 + 0.907973i \(0.362371\pi\)
\(212\) 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 0.998275 + 0.0587091i \(0.0186984\pi\)
−0.726986 + 0.686653i \(0.759079\pi\)
\(224\) 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 −0.860792 0.508958i \(-0.830031\pi\)
0.332253 0.943190i \(-0.392191\pi\)
\(234\) 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 0.999497 + 0.0317050i \(0.0100937\pi\)
0.527206 + 0.849738i \(0.323240\pi\)
\(240\) 0 0
\(241\) 13.6728 + 16.2946i 0.880739 + 1.04962i 0.998399 + 0.0565704i \(0.0180165\pi\)
−0.117659 + 0.993054i \(0.537539\pi\)
\(242\) 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 −0.963598 0.267355i \(-0.913850\pi\)
0.910012 + 0.414583i \(0.136072\pi\)
\(252\) 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 0.983085 + 0.183149i \(0.0586291\pi\)
−0.861157 + 0.508339i \(0.830260\pi\)
\(258\) 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 −0.947252 0.320490i \(-0.896153\pi\)
0.480109 + 0.877209i \(0.340597\pi\)
\(264\) 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 0.873794 0.486296i \(-0.161652\pi\)
−0.327175 + 0.944964i \(0.606097\pi\)
\(270\) 0 0
\(271\) 29.1999 10.6279i 1.77377 0.645598i 0.773841 0.633380i \(-0.218333\pi\)
0.999925 0.0122180i \(-0.00388921\pi\)
\(272\) 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 −0.802575 0.596551i \(-0.796537\pi\)
0.917916 + 0.396775i \(0.129871\pi\)
\(278\) 0 0
\(279\) 7.01680 0.138933i 0.420085 0.00831773i
\(280\) 0 0
\(281\) 23.0658 + 8.39528i 1.37599 + 0.500820i 0.920961 0.389655i \(-0.127406\pi\)
0.455031 + 0.890475i \(0.349628\pi\)
\(282\) 0 0
\(283\) 4.03563 22.8872i 0.239894 1.36050i −0.592165 0.805817i \(-0.701727\pi\)
0.832059 0.554688i \(-0.187162\pi\)
\(284\) 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 −0.660066 0.751207i \(-0.729472\pi\)
0.980598 + 0.196031i \(0.0628052\pi\)
\(294\) 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 −0.755919 0.654665i \(-0.772810\pi\)
0.775983 + 0.630754i \(0.217254\pi\)
\(308\) 0 0
\(309\) −1.36691 1.34012i −0.0777610 0.0762366i
\(310\) 0 0
\(311\) −12.1908 + 7.03836i −0.691277 + 0.399109i −0.804090 0.594507i \(-0.797347\pi\)
0.112813 + 0.993616i \(0.464014\pi\)
\(312\) 0 0
\(313\) −3.23018 18.3193i −0.182580 1.03547i −0.929025 0.370018i \(-0.879352\pi\)
0.746444 0.665448i \(-0.231759\pi\)
\(314\) 0 0
\(315\) −20.0493 + 7.75016i −1.12965 + 0.436672i
\(316\) 0 0
\(317\) −20.8301 + 17.4785i −1.16993 + 0.981690i −0.999993 0.00376423i \(-0.998802\pi\)
−0.169940 + 0.985454i \(0.554357\pi\)
\(318\) 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 −0.403214 0.915106i \(-0.632107\pi\)
−0.994112 + 0.108360i \(0.965440\pi\)
\(332\) 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 0.999643 + 0.0267031i \(0.00850087\pi\)
−0.748607 + 0.663014i \(0.769277\pi\)
\(338\) 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 0.872033 0.489447i \(-0.162801\pi\)
−0.982627 + 0.185594i \(0.940579\pi\)
\(348\) 0 0
\(349\) −14.3065 24.7795i −0.765808 1.32642i −0.939818 0.341675i \(-0.889006\pi\)
0.174010 0.984744i \(-0.444328\pi\)
\(350\) 0 0
\(351\) −1.19169 + 20.6769i −0.0636078 + 1.10365i
\(352\) 0 0
\(353\) 14.6066 + 8.43315i 0.777433 + 0.448851i 0.835520 0.549460i \(-0.185167\pi\)
−0.0580867 + 0.998312i \(0.518500\pi\)
\(354\) 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 0.585898 0.810385i \(-0.300742\pi\)
0.273397 + 0.961901i \(0.411853\pi\)
\(360\) 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 −0.431290 0.902213i \(-0.641941\pi\)
0.813614 + 0.581405i \(0.197497\pi\)
\(368\) 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 −0.399710 0.916642i \(-0.630889\pi\)
0.593980 + 0.804480i \(0.297556\pi\)
\(374\) 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 \(0.0489844\pi\)
−0.988182 + 0.153282i \(0.951016\pi\)
\(380\) 0 0
\(381\) 0.921197 + 1.92552i 0.0471943 + 0.0986472i
\(382\) 0 0
\(383\) −3.37004 2.82780i −0.172201 0.144494i 0.552614 0.833437i \(-0.313630\pi\)
−0.724815 + 0.688944i \(0.758075\pi\)
\(384\) 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 −0.528708 0.848804i \(-0.677323\pi\)
−0.206515 + 0.978443i \(0.566212\pi\)
\(390\) 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 −0.909035 0.416719i \(-0.863180\pi\)
0.996740 0.0806794i \(-0.0257090\pi\)
\(398\) 0 0
\(399\) 5.51971 + 15.2418i 0.276331 + 0.763043i
\(400\) 0 0
\(401\) −2.58090 + 14.6370i −0.128884 + 0.730937i 0.850041 + 0.526717i \(0.176577\pi\)
−0.978925 + 0.204221i \(0.934534\pi\)
\(402\) 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 −0.410874 0.911692i \(-0.634777\pi\)
−0.0742787 + 0.997238i \(0.523665\pi\)
\(410\) 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 \(-0.934630\pi\)
0.978987 0.203925i \(-0.0653698\pi\)
\(420\) 0 0
\(421\) 23.4446 27.9402i 1.14262 1.36172i 0.220234 0.975447i \(-0.429318\pi\)
0.922384 0.386273i \(-0.126238\pi\)
\(422\) 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 −0.815879 0.578223i \(-0.803746\pi\)
0.427762 + 0.903891i \(0.359302\pi\)
\(432\) 0 0
\(433\) −12.6127 + 34.6530i −0.606126 + 1.66532i 0.132485 + 0.991185i \(0.457704\pi\)
−0.738611 + 0.674132i \(0.764518\pi\)
\(434\) 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 −0.148218 0.988955i \(-0.547354\pi\)
−0.477522 + 0.878620i \(0.658465\pi\)
\(440\) 0 0
\(441\) 6.13681 3.70698i 0.292229 0.176523i
\(442\) 0 0
\(443\) −4.79891 5.71912i −0.228003 0.271724i 0.639899 0.768459i \(-0.278976\pi\)
−0.867902 + 0.496736i \(0.834532\pi\)
\(444\) 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 0.996072 + 0.0885490i \(0.0282230\pi\)
−0.421350 + 0.906898i \(0.638444\pi\)
\(450\) 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 0.956232 0.292608i \(-0.0945232\pi\)
−0.920601 + 0.390503i \(0.872301\pi\)
\(462\) 0 0
\(463\) −1.84091 3.18854i −0.0855541 0.148184i 0.820073 0.572259i \(-0.193933\pi\)
−0.905627 + 0.424075i \(0.860599\pi\)
\(464\) 0 0
\(465\) −7.86484 10.9988i −0.364723 0.510058i
\(466\) 0 0
\(467\) 11.3948 + 6.57879i 0.527288 + 0.304430i 0.739911 0.672704i \(-0.234867\pi\)
−0.212623 + 0.977134i \(0.568201\pi\)
\(468\) 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 −0.342424 0.939546i \(-0.611248\pi\)
0.866240 0.499628i \(-0.166530\pi\)
\(480\) 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 −0.114228 0.993455i \(-0.536439\pi\)
0.803243 + 0.595651i \(0.203106\pi\)
\(488\) 0 0
\(489\) 12.8168 13.0730i 0.579594 0.591183i
\(490\) 0 0
\(491\) −15.8204 + 18.8540i −0.713964 + 0.850869i −0.994030 0.109112i \(-0.965199\pi\)
0.280065 + 0.959981i \(0.409644\pi\)
\(492\) 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 −0.631902 0.775048i \(-0.717726\pi\)
0.0141259 + 0.999900i \(0.495503\pi\)
\(500\) 0 0
\(501\) −15.9930 10.9641i −0.714514 0.489840i
\(502\) 0 0
\(503\) 4.24201 0.747980i 0.189142 0.0333508i −0.0782748 0.996932i \(-0.524941\pi\)
0.267417 + 0.963581i \(0.413830\pi\)
\(504\) 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 0.243637 0.969867i \(-0.421660\pi\)
−0.436782 + 0.899567i \(0.643882\pi\)
\(510\) 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 −0.870502 0.492165i \(-0.836206\pi\)
0.861478 + 0.507794i \(0.169539\pi\)
\(522\) 0 0
\(523\) 19.2248 3.38986i 0.840643 0.148228i 0.263284 0.964718i \(-0.415194\pi\)
0.577359 + 0.816490i \(0.304083\pi\)
\(524\) 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 −0.974369 0.224957i \(-0.927776\pi\)
0.838667 0.544644i \(-0.183335\pi\)
\(542\) 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 −0.966412 0.256999i \(-0.917266\pi\)
0.905510 + 0.424324i \(0.139488\pi\)
\(548\) 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 0.924386 0.381459i \(-0.124578\pi\)
−0.536181 + 0.844103i \(0.680134\pi\)
\(558\) 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 0.926878 0.375363i \(-0.122482\pi\)
−0.788513 + 0.615018i \(0.789149\pi\)
\(564\) 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 −0.949276 0.314446i \(-0.898181\pi\)
0.202320 0.979319i \(-0.435152\pi\)
\(578\) 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 −0.474118 0.880461i \(-0.657233\pi\)
−0.746661 + 0.665205i \(0.768344\pi\)
\(588\) 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 −0.945082 0.326832i \(-0.894019\pi\)
0.934059 + 0.357119i \(0.116241\pi\)
\(594\) 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 0.994308 + 0.106548i \(0.0339798\pi\)
−0.897902 + 0.440196i \(0.854909\pi\)
\(600\) 0 0
\(601\) 1.41283 0.815696i 0.0576304 0.0332729i −0.470908 0.882182i \(-0.656074\pi\)
0.528538 + 0.848909i \(0.322740\pi\)
\(602\) 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 \(-0.840525\pi\)
0.877100 0.480308i \(-0.159475\pi\)
\(608\) 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 −0.0273321 0.999626i \(-0.508701\pi\)
0.621610 + 0.783327i \(0.286479\pi\)
\(614\) 0 0
\(615\) 3.95324 5.76646i 0.159410 0.232526i
\(616\) 0 0
\(617\) 19.6258 3.46056i 0.790105 0.139317i 0.235988 0.971756i \(-0.424167\pi\)
0.554117 + 0.832439i \(0.313056\pi\)
\(618\) 0 0
\(619\) 3.55524 6.15786i 0.142897 0.247505i −0.785689 0.618621i \(-0.787691\pi\)
0.928587 + 0.371116i \(0.121025\pi\)
\(620\) 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 0.365139 0.930953i \(-0.381021\pi\)
−0.318692 + 0.947858i \(0.603244\pi\)
\(632\) 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 −0.477750 0.878496i \(-0.658548\pi\)
0.198708 + 0.980059i \(0.436325\pi\)
\(642\) 0 0
\(643\) 9.31005 + 7.81206i 0.367153 + 0.308078i 0.807634 0.589684i \(-0.200748\pi\)
−0.440481 + 0.897762i \(0.645192\pi\)
\(644\) 0 0
\(645\) 15.5920 + 32.5909i 0.613933 + 1.28327i
\(646\) 0 0
\(647\) 38.1298i 1.49904i 0.661983 + 0.749519i \(0.269715\pi\)
−0.661983 + 0.749519i \(0.730285\pi\)
\(648\) 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 0.558063 0.829798i \(-0.311545\pi\)
0.997658 0.0683980i \(-0.0217888\pi\)
\(654\) 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 −0.318779 0.947829i \(-0.603273\pi\)
0.878074 + 0.478525i \(0.158828\pi\)
\(660\) 0 0
\(661\) 4.05073 11.1293i 0.157555 0.432879i −0.835649 0.549263i \(-0.814908\pi\)
0.993204 + 0.116385i \(0.0371306\pi\)
\(662\) 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 0.315917 0.948787i \(-0.397688\pi\)
−0.663715 + 0.747986i \(0.731021\pi\)
\(674\) 0 0
\(675\) 31.8294 + 1.83445i 1.22512 + 0.0706082i
\(676\) 0 0
\(677\) 10.3670 + 17.9562i 0.398437 + 0.690112i 0.993533 0.113542i \(-0.0362196\pi\)
−0.595097 + 0.803654i \(0.702886\pi\)
\(678\) 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 0.934813 0.355142i \(-0.115567\pi\)
−0.774968 + 0.632001i \(0.782234\pi\)
\(692\) 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 0.448636 0.893714i \(-0.351910\pi\)
0.115912 + 0.993259i \(0.463021\pi\)
\(702\) 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 −0.997451 0.0713544i \(-0.977268\pi\)
−0.102935 + 0.994688i \(0.532823\pi\)
\(710\) 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 0.0628501 + 0.998023i \(0.479981\pi\)
−0.993775 + 0.111410i \(0.964463\pi\)
\(720\) 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 −0.907796 0.419413i \(-0.862236\pi\)
−0.425818 + 0.904809i \(0.640014\pi\)
\(728\) 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 −0.972558 0.232660i \(-0.925257\pi\)
0.687768 + 0.725930i \(0.258590\pi\)
\(734\) 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 −0.744892 0.667185i \(-0.767499\pi\)
0.928160 0.372181i \(-0.121390\pi\)
\(740\) 0 0
\(741\) −15.0043 26.0853i −0.551196 0.958269i
\(742\) 0 0
\(743\) 4.95784 28.1173i 0.181886 1.03152i −0.748006 0.663691i \(-0.768989\pi\)
0.929892 0.367833i \(-0.119900\pi\)
\(744\) 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 −0.396497 0.918036i \(-0.629774\pi\)
−0.0585987 + 0.998282i \(0.518663\pi\)
\(752\) 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 0.962308 + 0.271963i \(0.0876729\pi\)
0.434934 + 0.900462i \(0.356772\pi\)
\(758\) 0 0
\(759\) −8.01413 + 3.83408i −0.290894 + 0.139168i
\(760\) 0 0
\(761\) 26.6803i 0.967159i −0.875300 0.483580i \(-0.839336\pi\)
0.875300 0.483580i \(-0.160664\pi\)
\(762\) 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 −0.817292 0.576223i \(-0.804526\pi\)
0.570924 0.821003i \(-0.306585\pi\)
\(770\) 0 0
\(771\) 1.50691 19.4383i 0.0542699 0.700054i
\(772\) 0 0
\(773\) −2.48012 + 2.08107i −0.0892039 + 0.0748509i −0.686299 0.727319i \(-0.740766\pi\)
0.597095 + 0.802170i \(0.296321\pi\)
\(774\) 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 0.848674 0.528916i \(-0.177401\pi\)
−0.0337179 + 0.999431i \(0.510735\pi\)
\(788\) 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