Properties

Label 1040.2.dh.a.289.2
Level $1040$
Weight $2$
Character 1040.289
Analytic conductor $8.304$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1040.dh (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.30444181021\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 8 x^{10} + 54 x^{8} - 78 x^{6} + 92 x^{4} - 10 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 289.2
Root \(-2.20467 - 1.27287i\) of defining polynomial
Character \(\chi\) \(=\) 1040.289
Dual form 1040.2.dh.a.529.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.86449 + 1.07646i) q^{3} +(-0.817544 - 2.08125i) q^{5} +(-2.54486 - 1.46928i) q^{7} +(0.817544 - 1.41603i) q^{9} +O(q^{10})\) \(q+(-1.86449 + 1.07646i) q^{3} +(-0.817544 - 2.08125i) q^{5} +(-2.54486 - 1.46928i) q^{7} +(0.817544 - 1.41603i) q^{9} +(-0.317544 - 0.550003i) q^{11} +(-3.60484 - 0.0716710i) q^{13} +(3.76470 + 3.00042i) q^{15} +(1.05998 + 0.611979i) q^{17} +(-0.682456 + 1.18205i) q^{19} +6.32648 q^{21} +(1.86449 - 1.07646i) q^{23} +(-3.66324 + 3.40304i) q^{25} -2.93855i q^{27} +(1.50000 + 2.59808i) q^{29} +8.96157 q^{31} +(1.18412 + 0.683650i) q^{33} +(-0.977401 + 6.49770i) q^{35} +(1.05998 - 0.611979i) q^{37} +(6.79833 - 3.74685i) q^{39} +(4.98079 + 8.62698i) q^{41} +(1.18412 + 0.683650i) q^{43} +(-3.61549 - 0.543852i) q^{45} +6.16379i q^{47} +(0.817544 + 1.41603i) q^{49} -2.63509 q^{51} -0.642285i q^{53} +(-0.885090 + 1.11054i) q^{55} -2.93855i q^{57} +(-3.79833 + 6.57890i) q^{59} +(1.13509 - 1.96603i) q^{61} +(-4.16107 + 2.40240i) q^{63} +(2.79795 + 7.56118i) q^{65} +(-6.95421 + 4.01502i) q^{67} +(-2.31754 + 4.01410i) q^{69} +(1.31754 - 2.28205i) q^{71} +10.3263i q^{73} +(3.16683 - 10.2883i) q^{75} +1.86624i q^{77} +1.03843 q^{79} +(5.61588 + 9.72698i) q^{81} +11.8452i q^{83} +(0.407104 - 2.70640i) q^{85} +(-5.59346 - 3.22939i) q^{87} +(-6.27912 - 10.8758i) q^{89} +(9.06851 + 5.47890i) q^{91} +(-16.7087 + 9.64680i) q^{93} +(3.01808 + 0.453987i) q^{95} +(12.8031 + 7.39190i) q^{97} -1.03843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{5} + 6 q^{9} + O(q^{10}) \) \( 12 q - 6 q^{5} + 6 q^{9} + 4 q^{15} - 12 q^{19} - 8 q^{21} - 2 q^{25} + 18 q^{29} + 16 q^{31} - 10 q^{35} + 32 q^{39} + 14 q^{41} - 29 q^{45} + 6 q^{49} - 24 q^{51} + 26 q^{55} + 4 q^{59} + 6 q^{61} + 23 q^{65} - 24 q^{69} + 12 q^{71} - 2 q^{75} + 104 q^{79} + 14 q^{81} + 21 q^{85} + 20 q^{89} + 44 q^{91} - 20 q^{95} - 104 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(417\) \(561\) \(911\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) −1.86449 + 1.07646i −1.07646 + 0.621496i −0.929940 0.367711i \(-0.880142\pi\)
−0.146523 + 0.989207i \(0.546808\pi\)
\(4\) 0 0
\(5\) −0.817544 2.08125i −0.365617 0.930765i
\(6\) 0 0
\(7\) −2.54486 1.46928i −0.961867 0.555334i −0.0651198 0.997877i \(-0.520743\pi\)
−0.896747 + 0.442543i \(0.854076\pi\)
\(8\) 0 0
\(9\) 0.817544 1.41603i 0.272515 0.472010i
\(10\) 0 0
\(11\) −0.317544 0.550003i −0.0957433 0.165832i 0.814175 0.580619i \(-0.197189\pi\)
−0.909919 + 0.414787i \(0.863856\pi\)
\(12\) 0 0
\(13\) −3.60484 0.0716710i −0.999802 0.0198779i
\(14\) 0 0
\(15\) 3.76470 + 3.00042i 0.972040 + 0.774705i
\(16\) 0 0
\(17\) 1.05998 + 0.611979i 0.257082 + 0.148427i 0.623003 0.782220i \(-0.285912\pi\)
−0.365920 + 0.930646i \(0.619246\pi\)
\(18\) 0 0
\(19\) −0.682456 + 1.18205i −0.156566 + 0.271180i −0.933628 0.358244i \(-0.883376\pi\)
0.777062 + 0.629424i \(0.216709\pi\)
\(20\) 0 0
\(21\) 6.32648 1.38055
\(22\) 0 0
\(23\) 1.86449 1.07646i 0.388773 0.224458i −0.292856 0.956157i \(-0.594606\pi\)
0.681628 + 0.731699i \(0.261272\pi\)
\(24\) 0 0
\(25\) −3.66324 + 3.40304i −0.732648 + 0.680607i
\(26\) 0 0
\(27\) 2.93855i 0.565525i
\(28\) 0 0
\(29\) 1.50000 + 2.59808i 0.278543 + 0.482451i 0.971023 0.238987i \(-0.0768152\pi\)
−0.692480 + 0.721437i \(0.743482\pi\)
\(30\) 0 0
\(31\) 8.96157 1.60955 0.804773 0.593583i \(-0.202287\pi\)
0.804773 + 0.593583i \(0.202287\pi\)
\(32\) 0 0
\(33\) 1.18412 + 0.683650i 0.206128 + 0.119008i
\(34\) 0 0
\(35\) −0.977401 + 6.49770i −0.165211 + 1.09831i
\(36\) 0 0
\(37\) 1.05998 0.611979i 0.174259 0.100609i −0.410333 0.911936i \(-0.634588\pi\)
0.584593 + 0.811327i \(0.301254\pi\)
\(38\) 0 0
\(39\) 6.79833 3.74685i 1.08860 0.599975i
\(40\) 0 0
\(41\) 4.98079 + 8.62698i 0.777868 + 1.34731i 0.933168 + 0.359440i \(0.117032\pi\)
−0.155300 + 0.987867i \(0.549634\pi\)
\(42\) 0 0
\(43\) 1.18412 + 0.683650i 0.180576 + 0.104256i 0.587563 0.809178i \(-0.300087\pi\)
−0.406987 + 0.913434i \(0.633421\pi\)
\(44\) 0 0
\(45\) −3.61549 0.543852i −0.538966 0.0810727i
\(46\) 0 0
\(47\) 6.16379i 0.899081i 0.893260 + 0.449540i \(0.148412\pi\)
−0.893260 + 0.449540i \(0.851588\pi\)
\(48\) 0 0
\(49\) 0.817544 + 1.41603i 0.116792 + 0.202290i
\(50\) 0 0
\(51\) −2.63509 −0.368986
\(52\) 0 0
\(53\) 0.642285i 0.0882246i −0.999027 0.0441123i \(-0.985954\pi\)
0.999027 0.0441123i \(-0.0140459\pi\)
\(54\) 0 0
\(55\) −0.885090 + 1.11054i −0.119345 + 0.149746i
\(56\) 0 0
\(57\) 2.93855i 0.389221i
\(58\) 0 0
\(59\) −3.79833 + 6.57890i −0.494501 + 0.856500i −0.999980 0.00633858i \(-0.997982\pi\)
0.505479 + 0.862839i \(0.331316\pi\)
\(60\) 0 0
\(61\) 1.13509 1.96603i 0.145333 0.251725i −0.784164 0.620554i \(-0.786908\pi\)
0.929497 + 0.368829i \(0.120241\pi\)
\(62\) 0 0
\(63\) −4.16107 + 2.40240i −0.524246 + 0.302674i
\(64\) 0 0
\(65\) 2.79795 + 7.56118i 0.347043 + 0.937849i
\(66\) 0 0
\(67\) −6.95421 + 4.01502i −0.849592 + 0.490512i −0.860513 0.509428i \(-0.829857\pi\)
0.0109212 + 0.999940i \(0.496524\pi\)
\(68\) 0 0
\(69\) −2.31754 + 4.01410i −0.279000 + 0.483241i
\(70\) 0 0
\(71\) 1.31754 2.28205i 0.156364 0.270830i −0.777191 0.629265i \(-0.783356\pi\)
0.933555 + 0.358435i \(0.116689\pi\)
\(72\) 0 0
\(73\) 10.3263i 1.20860i 0.796756 + 0.604301i \(0.206547\pi\)
−0.796756 + 0.604301i \(0.793453\pi\)
\(74\) 0 0
\(75\) 3.16683 10.2883i 0.365674 1.18799i
\(76\) 0 0
\(77\) 1.86624i 0.212678i
\(78\) 0 0
\(79\) 1.03843 0.116832 0.0584161 0.998292i \(-0.481395\pi\)
0.0584161 + 0.998292i \(0.481395\pi\)
\(80\) 0 0
\(81\) 5.61588 + 9.72698i 0.623986 + 1.08078i
\(82\) 0 0
\(83\) 11.8452i 1.30018i 0.759855 + 0.650092i \(0.225270\pi\)
−0.759855 + 0.650092i \(0.774730\pi\)
\(84\) 0 0
\(85\) 0.407104 2.70640i 0.0441566 0.293551i
\(86\) 0 0
\(87\) −5.59346 3.22939i −0.599682 0.346227i
\(88\) 0 0
\(89\) −6.27912 10.8758i −0.665585 1.15283i −0.979126 0.203253i \(-0.934849\pi\)
0.313541 0.949575i \(-0.398485\pi\)
\(90\) 0 0
\(91\) 9.06851 + 5.47890i 0.950638 + 0.574344i
\(92\) 0 0
\(93\) −16.7087 + 9.64680i −1.73262 + 1.00033i
\(94\) 0 0
\(95\) 3.01808 + 0.453987i 0.309648 + 0.0465781i
\(96\) 0 0
\(97\) 12.8031 + 7.39190i 1.29996 + 0.750534i 0.980397 0.197031i \(-0.0631299\pi\)
0.319565 + 0.947564i \(0.396463\pi\)
\(98\) 0 0
\(99\) −1.03843 −0.104366
\(100\) 0 0
\(101\) −6.61588 11.4590i −0.658304 1.14022i −0.981054 0.193732i \(-0.937941\pi\)
0.322750 0.946484i \(-0.395393\pi\)
\(102\) 0 0
\(103\) 10.9686i 1.08077i 0.841419 + 0.540383i \(0.181721\pi\)
−0.841419 + 0.540383i \(0.818279\pi\)
\(104\) 0 0
\(105\) −5.17218 13.1670i −0.504753 1.28497i
\(106\) 0 0
\(107\) 9.24360 5.33680i 0.893613 0.515928i 0.0184903 0.999829i \(-0.494114\pi\)
0.875123 + 0.483901i \(0.160781\pi\)
\(108\) 0 0
\(109\) 3.27018 0.313226 0.156613 0.987660i \(-0.449942\pi\)
0.156613 + 0.987660i \(0.449942\pi\)
\(110\) 0 0
\(111\) −1.31754 + 2.28205i −0.125056 + 0.216603i
\(112\) 0 0
\(113\) −4.78895 2.76490i −0.450507 0.260100i 0.257537 0.966268i \(-0.417089\pi\)
−0.708044 + 0.706168i \(0.750422\pi\)
\(114\) 0 0
\(115\) −3.76470 3.00042i −0.351060 0.279790i
\(116\) 0 0
\(117\) −3.04860 + 5.04596i −0.281844 + 0.466499i
\(118\) 0 0
\(119\) −1.79833 3.11480i −0.164853 0.285533i
\(120\) 0 0
\(121\) 5.29833 9.17698i 0.481666 0.834271i
\(122\) 0 0
\(123\) −18.5732 10.7233i −1.67469 0.966884i
\(124\) 0 0
\(125\) 10.0774 + 4.84201i 0.901354 + 0.433082i
\(126\) 0 0
\(127\) 14.9231 8.61586i 1.32421 0.764534i 0.339813 0.940493i \(-0.389636\pi\)
0.984397 + 0.175959i \(0.0563027\pi\)
\(128\) 0 0
\(129\) −2.94369 −0.259178
\(130\) 0 0
\(131\) −10.0000 −0.873704 −0.436852 0.899533i \(-0.643907\pi\)
−0.436852 + 0.899533i \(0.643907\pi\)
\(132\) 0 0
\(133\) 3.47351 2.00543i 0.301191 0.173893i
\(134\) 0 0
\(135\) −6.11588 + 2.40240i −0.526371 + 0.206765i
\(136\) 0 0
\(137\) 7.51044 + 4.33616i 0.641661 + 0.370463i 0.785254 0.619174i \(-0.212532\pi\)
−0.143593 + 0.989637i \(0.545866\pi\)
\(138\) 0 0
\(139\) −7.16324 + 12.4071i −0.607578 + 1.05236i 0.384060 + 0.923308i \(0.374526\pi\)
−0.991638 + 0.129048i \(0.958808\pi\)
\(140\) 0 0
\(141\) −6.63509 11.4923i −0.558775 0.967827i
\(142\) 0 0
\(143\) 1.10528 + 2.00543i 0.0924279 + 0.167703i
\(144\) 0 0
\(145\) 4.18094 5.24592i 0.347208 0.435650i
\(146\) 0 0
\(147\) −3.04860 1.76011i −0.251445 0.145172i
\(148\) 0 0
\(149\) −8.57745 + 14.8566i −0.702692 + 1.21710i 0.264826 + 0.964296i \(0.414685\pi\)
−0.967518 + 0.252802i \(0.918648\pi\)
\(150\) 0 0
\(151\) 21.3828 1.74011 0.870053 0.492957i \(-0.164084\pi\)
0.870053 + 0.492957i \(0.164084\pi\)
\(152\) 0 0
\(153\) 1.73316 1.00064i 0.140118 0.0808969i
\(154\) 0 0
\(155\) −7.32648 18.6513i −0.588477 1.49811i
\(156\) 0 0
\(157\) 18.3646i 1.46566i −0.680413 0.732829i \(-0.738200\pi\)
0.680413 0.732829i \(-0.261800\pi\)
\(158\) 0 0
\(159\) 0.691395 + 1.19753i 0.0548312 + 0.0949705i
\(160\) 0 0
\(161\) −6.32648 −0.498597
\(162\) 0 0
\(163\) 3.47351 + 2.00543i 0.272066 + 0.157078i 0.629826 0.776736i \(-0.283126\pi\)
−0.357760 + 0.933814i \(0.616459\pi\)
\(164\) 0 0
\(165\) 0.454782 3.02336i 0.0354047 0.235368i
\(166\) 0 0
\(167\) −2.54486 + 1.46928i −0.196927 + 0.113696i −0.595221 0.803562i \(-0.702936\pi\)
0.398294 + 0.917258i \(0.369602\pi\)
\(168\) 0 0
\(169\) 12.9897 + 0.516725i 0.999210 + 0.0397480i
\(170\) 0 0
\(171\) 1.11588 + 1.93275i 0.0853331 + 0.147801i
\(172\) 0 0
\(173\) 1.18412 + 0.683650i 0.0900267 + 0.0519769i 0.544337 0.838866i \(-0.316781\pi\)
−0.454311 + 0.890843i \(0.650114\pi\)
\(174\) 0 0
\(175\) 14.3224 3.27794i 1.08267 0.247789i
\(176\) 0 0
\(177\) 16.3550i 1.22932i
\(178\) 0 0
\(179\) −3.89306 6.74299i −0.290981 0.503994i 0.683061 0.730362i \(-0.260648\pi\)
−0.974042 + 0.226367i \(0.927315\pi\)
\(180\) 0 0
\(181\) −3.86684 −0.287420 −0.143710 0.989620i \(-0.545903\pi\)
−0.143710 + 0.989620i \(0.545903\pi\)
\(182\) 0 0
\(183\) 4.88752i 0.361296i
\(184\) 0 0
\(185\) −2.14026 1.70576i −0.157355 0.125410i
\(186\) 0 0
\(187\) 0.777322i 0.0568434i
\(188\) 0 0
\(189\) −4.31754 + 7.47821i −0.314055 + 0.543959i
\(190\) 0 0
\(191\) 2.47185 4.28136i 0.178857 0.309789i −0.762633 0.646832i \(-0.776094\pi\)
0.941489 + 0.337043i \(0.109427\pi\)
\(192\) 0 0
\(193\) −4.29240 + 2.47822i −0.308974 + 0.178386i −0.646467 0.762942i \(-0.723754\pi\)
0.337493 + 0.941328i \(0.390421\pi\)
\(194\) 0 0
\(195\) −13.3561 11.0858i −0.956449 0.793874i
\(196\) 0 0
\(197\) 5.84174 3.37273i 0.416207 0.240297i −0.277246 0.960799i \(-0.589422\pi\)
0.693453 + 0.720502i \(0.256088\pi\)
\(198\) 0 0
\(199\) −2.58772 + 4.48207i −0.183439 + 0.317725i −0.943049 0.332653i \(-0.892056\pi\)
0.759611 + 0.650378i \(0.225390\pi\)
\(200\) 0 0
\(201\) 8.64403 14.9719i 0.609703 1.05604i
\(202\) 0 0
\(203\) 8.81566i 0.618738i
\(204\) 0 0
\(205\) 13.8829 17.4192i 0.969625 1.21661i
\(206\) 0 0
\(207\) 3.52022i 0.244673i
\(208\) 0 0
\(209\) 0.866840 0.0599606
\(210\) 0 0
\(211\) −7.00894 12.1398i −0.482515 0.835741i 0.517283 0.855814i \(-0.326943\pi\)
−0.999799 + 0.0200732i \(0.993610\pi\)
\(212\) 0 0
\(213\) 5.67315i 0.388718i
\(214\) 0 0
\(215\) 0.454782 3.02336i 0.0310158 0.206191i
\(216\) 0 0
\(217\) −22.8060 13.1670i −1.54817 0.893836i
\(218\) 0 0
\(219\) −11.1159 19.2533i −0.751141 1.30101i
\(220\) 0 0
\(221\) −3.77719 2.28205i −0.254081 0.153508i
\(222\) 0 0
\(223\) −0.00719226 + 0.00415245i −0.000481629 + 0.000278069i −0.500241 0.865886i \(-0.666755\pi\)
0.499759 + 0.866164i \(0.333422\pi\)
\(224\) 0 0
\(225\) 1.82393 + 7.96939i 0.121596 + 0.531293i
\(226\) 0 0
\(227\) 9.75454 + 5.63179i 0.647431 + 0.373795i 0.787471 0.616351i \(-0.211390\pi\)
−0.140040 + 0.990146i \(0.544723\pi\)
\(228\) 0 0
\(229\) 16.5404 1.09302 0.546509 0.837453i \(-0.315957\pi\)
0.546509 + 0.837453i \(0.315957\pi\)
\(230\) 0 0
\(231\) −2.00894 3.47959i −0.132179 0.228940i
\(232\) 0 0
\(233\) 6.94941i 0.455271i −0.973746 0.227636i \(-0.926900\pi\)
0.973746 0.227636i \(-0.0730995\pi\)
\(234\) 0 0
\(235\) 12.8284 5.03917i 0.836833 0.328719i
\(236\) 0 0
\(237\) −1.93613 + 1.11783i −0.125765 + 0.0726107i
\(238\) 0 0
\(239\) 4.00000 0.258738 0.129369 0.991596i \(-0.458705\pi\)
0.129369 + 0.991596i \(0.458705\pi\)
\(240\) 0 0
\(241\) −9.88605 + 17.1231i −0.636817 + 1.10300i 0.349310 + 0.937007i \(0.386416\pi\)
−0.986127 + 0.165992i \(0.946917\pi\)
\(242\) 0 0
\(243\) −13.3069 7.68273i −0.853637 0.492848i
\(244\) 0 0
\(245\) 2.27874 2.85918i 0.145583 0.182667i
\(246\) 0 0
\(247\) 2.54486 4.21218i 0.161926 0.268015i
\(248\) 0 0
\(249\) −12.7510 22.0853i −0.808060 1.39960i
\(250\) 0 0
\(251\) 1.83676 3.18136i 0.115935 0.200806i −0.802218 0.597031i \(-0.796347\pi\)
0.918153 + 0.396226i \(0.129680\pi\)
\(252\) 0 0
\(253\) −1.18412 0.683650i −0.0744447 0.0429807i
\(254\) 0 0
\(255\) 2.15430 + 5.48429i 0.134908 + 0.343440i
\(256\) 0 0
\(257\) −11.4877 + 6.63242i −0.716583 + 0.413719i −0.813494 0.581574i \(-0.802437\pi\)
0.0969108 + 0.995293i \(0.469104\pi\)
\(258\) 0 0
\(259\) −3.59666 −0.223486
\(260\) 0 0
\(261\) 4.90527 0.303628
\(262\) 0 0
\(263\) −26.2150 + 15.1352i −1.61649 + 0.933279i −0.628667 + 0.777674i \(0.716399\pi\)
−0.987819 + 0.155605i \(0.950267\pi\)
\(264\) 0 0
\(265\) −1.33676 + 0.525096i −0.0821164 + 0.0322564i
\(266\) 0 0
\(267\) 23.4147 + 13.5185i 1.43296 + 0.827317i
\(268\) 0 0
\(269\) −11.1248 + 19.2687i −0.678292 + 1.17484i 0.297203 + 0.954814i \(0.403946\pi\)
−0.975495 + 0.220022i \(0.929387\pi\)
\(270\) 0 0
\(271\) −5.91421 10.2437i −0.359262 0.622261i 0.628575 0.777749i \(-0.283638\pi\)
−0.987838 + 0.155488i \(0.950305\pi\)
\(272\) 0 0
\(273\) −22.8060 0.453425i −1.38028 0.0274425i
\(274\) 0 0
\(275\) 3.03492 + 0.934179i 0.183013 + 0.0563331i
\(276\) 0 0
\(277\) 14.5363 + 8.39254i 0.873402 + 0.504259i 0.868477 0.495729i \(-0.165099\pi\)
0.00492452 + 0.999988i \(0.498432\pi\)
\(278\) 0 0
\(279\) 7.32648 12.6898i 0.438625 0.759721i
\(280\) 0 0
\(281\) −10.5967 −0.632144 −0.316072 0.948735i \(-0.602364\pi\)
−0.316072 + 0.948735i \(0.602364\pi\)
\(282\) 0 0
\(283\) 7.63458 4.40783i 0.453829 0.262018i −0.255617 0.966778i \(-0.582279\pi\)
0.709446 + 0.704760i \(0.248945\pi\)
\(284\) 0 0
\(285\) −6.11588 + 2.40240i −0.362273 + 0.142306i
\(286\) 0 0
\(287\) 29.2726i 1.72791i
\(288\) 0 0
\(289\) −7.75096 13.4251i −0.455939 0.789710i
\(290\) 0 0
\(291\) −31.8284 −1.86581
\(292\) 0 0
\(293\) 24.4675 + 14.1263i 1.42940 + 0.825267i 0.997074 0.0764476i \(-0.0243578\pi\)
0.432331 + 0.901715i \(0.357691\pi\)
\(294\) 0 0
\(295\) 16.7977 + 2.52675i 0.977999 + 0.147113i
\(296\) 0 0
\(297\) −1.61621 + 0.933121i −0.0937822 + 0.0541452i
\(298\) 0 0
\(299\) −6.79833 + 3.74685i −0.393158 + 0.216686i
\(300\) 0 0
\(301\) −2.00894 3.47959i −0.115793 0.200560i
\(302\) 0 0
\(303\) 24.6704 + 14.2435i 1.41728 + 0.818267i
\(304\) 0 0
\(305\) −5.01980 0.755091i −0.287433 0.0432364i
\(306\) 0 0
\(307\) 12.7219i 0.726077i 0.931774 + 0.363039i \(0.118261\pi\)
−0.931774 + 0.363039i \(0.881739\pi\)
\(308\) 0 0
\(309\) −11.8073 20.4508i −0.671692 1.16340i
\(310\) 0 0
\(311\) −27.9231 −1.58338 −0.791688 0.610925i \(-0.790798\pi\)
−0.791688 + 0.610925i \(0.790798\pi\)
\(312\) 0 0
\(313\) 24.5807i 1.38938i 0.719307 + 0.694692i \(0.244460\pi\)
−0.719307 + 0.694692i \(0.755540\pi\)
\(314\) 0 0
\(315\) 8.40186 + 6.69619i 0.473391 + 0.377287i
\(316\) 0 0
\(317\) 0.234377i 0.0131639i 0.999978 + 0.00658196i \(0.00209512\pi\)
−0.999978 + 0.00658196i \(0.997905\pi\)
\(318\) 0 0
\(319\) 0.952633 1.65001i 0.0533372 0.0923828i
\(320\) 0 0
\(321\) −11.4897 + 19.9008i −0.641294 + 1.11075i
\(322\) 0 0
\(323\) −1.44678 + 0.835296i −0.0805008 + 0.0464771i
\(324\) 0 0
\(325\) 13.4493 12.0048i 0.746033 0.665909i
\(326\) 0 0
\(327\) −6.09721 + 3.52022i −0.337176 + 0.194669i
\(328\) 0 0
\(329\) 9.05631 15.6860i 0.499290 0.864796i
\(330\) 0 0
\(331\) −9.16324 + 15.8712i −0.503657 + 0.872360i 0.496334 + 0.868132i \(0.334679\pi\)
−0.999991 + 0.00422829i \(0.998654\pi\)
\(332\) 0 0
\(333\) 2.00128i 0.109669i
\(334\) 0 0
\(335\) 14.0416 + 11.1910i 0.767177 + 0.611431i
\(336\) 0 0
\(337\) 21.2949i 1.16001i 0.814614 + 0.580003i \(0.196949\pi\)
−0.814614 + 0.580003i \(0.803051\pi\)
\(338\) 0 0
\(339\) 11.9053 0.646605
\(340\) 0 0
\(341\) −2.84570 4.92889i −0.154103 0.266915i
\(342\) 0 0
\(343\) 15.7651i 0.851234i
\(344\) 0 0
\(345\) 10.2491 + 1.54169i 0.551791 + 0.0830019i
\(346\) 0 0
\(347\) 3.30407 + 1.90761i 0.177372 + 0.102406i 0.586057 0.810270i \(-0.300679\pi\)
−0.408685 + 0.912675i \(0.634013\pi\)
\(348\) 0 0
\(349\) 12.1632 + 21.0674i 0.651083 + 1.12771i 0.982860 + 0.184352i \(0.0590185\pi\)
−0.331777 + 0.943358i \(0.607648\pi\)
\(350\) 0 0
\(351\) −0.210609 + 10.5930i −0.0112415 + 0.565413i
\(352\) 0 0
\(353\) −23.4338 + 13.5295i −1.24726 + 0.720104i −0.970562 0.240853i \(-0.922573\pi\)
−0.276696 + 0.960958i \(0.589239\pi\)
\(354\) 0 0
\(355\) −5.82669 0.876465i −0.309248 0.0465179i
\(356\) 0 0
\(357\) 6.70593 + 3.87167i 0.354916 + 0.204911i
\(358\) 0 0
\(359\) 27.0039 1.42521 0.712605 0.701566i \(-0.247515\pi\)
0.712605 + 0.701566i \(0.247515\pi\)
\(360\) 0 0
\(361\) 8.56851 + 14.8411i 0.450974 + 0.781110i
\(362\) 0 0
\(363\) 22.8138i 1.19742i
\(364\) 0 0
\(365\) 21.4917 8.44221i 1.12492 0.441885i
\(366\) 0 0
\(367\) −6.01118 + 3.47055i −0.313781 + 0.181161i −0.648617 0.761115i \(-0.724652\pi\)
0.334836 + 0.942276i \(0.391319\pi\)
\(368\) 0 0
\(369\) 16.2881 0.847922
\(370\) 0 0
\(371\) −0.943693 + 1.63452i −0.0489941 + 0.0848603i
\(372\) 0 0
\(373\) −2.00301 1.15644i −0.103712 0.0598781i 0.447247 0.894411i \(-0.352405\pi\)
−0.550959 + 0.834532i \(0.685738\pi\)
\(374\) 0 0
\(375\) −24.0015 + 1.82013i −1.23943 + 0.0939913i
\(376\) 0 0
\(377\) −5.22105 9.47315i −0.268898 0.487892i
\(378\) 0 0
\(379\) −2.58772 4.48207i −0.132922 0.230228i 0.791880 0.610677i \(-0.209103\pi\)
−0.924802 + 0.380449i \(0.875769\pi\)
\(380\) 0 0
\(381\) −18.5493 + 32.1283i −0.950309 + 1.64598i
\(382\) 0 0
\(383\) −17.8929 10.3305i −0.914283 0.527861i −0.0324760 0.999473i \(-0.510339\pi\)
−0.881807 + 0.471611i \(0.843673\pi\)
\(384\) 0 0
\(385\) 3.88412 1.52574i 0.197953 0.0777587i
\(386\) 0 0
\(387\) 1.93613 1.11783i 0.0984193 0.0568224i
\(388\) 0 0
\(389\) −19.7477 −1.00125 −0.500624 0.865665i \(-0.666896\pi\)
−0.500624 + 0.865665i \(0.666896\pi\)
\(390\) 0 0
\(391\) 2.63509 0.133262
\(392\) 0 0
\(393\) 18.6449 10.7646i 0.940510 0.543004i
\(394\) 0 0
\(395\) −0.848960 2.16123i −0.0427158 0.108743i
\(396\) 0 0
\(397\) −8.13113 4.69451i −0.408090 0.235611i 0.281879 0.959450i \(-0.409042\pi\)
−0.689969 + 0.723839i \(0.742376\pi\)
\(398\) 0 0
\(399\) −4.31754 + 7.47821i −0.216148 + 0.374379i
\(400\) 0 0
\(401\) −12.2510 21.2193i −0.611784 1.05964i −0.990940 0.134308i \(-0.957119\pi\)
0.379156 0.925333i \(-0.376214\pi\)
\(402\) 0 0
\(403\) −32.3050 0.642285i −1.60923 0.0319945i
\(404\) 0 0
\(405\) 15.6531 19.6403i 0.777809 0.975935i
\(406\) 0 0
\(407\) −0.673180 0.388661i −0.0333683 0.0192652i
\(408\) 0 0
\(409\) 18.0582 31.2778i 0.892922 1.54659i 0.0565671 0.998399i \(-0.481985\pi\)
0.836355 0.548188i \(-0.184682\pi\)
\(410\) 0 0
\(411\) −18.6708 −0.920965
\(412\) 0 0
\(413\) 19.3324 11.1616i 0.951288 0.549226i
\(414\) 0 0
\(415\) 24.6530 9.68401i 1.21017 0.475370i
\(416\) 0 0
\(417\) 30.8439i 1.51043i
\(418\) 0 0
\(419\) 3.43342 + 5.94686i 0.167734 + 0.290523i 0.937623 0.347655i \(-0.113022\pi\)
−0.769889 + 0.638178i \(0.779689\pi\)
\(420\) 0 0
\(421\) 33.9795 1.65606 0.828029 0.560686i \(-0.189462\pi\)
0.828029 + 0.560686i \(0.189462\pi\)
\(422\) 0 0
\(423\) 8.72810 + 5.03917i 0.424375 + 0.245013i
\(424\) 0 0
\(425\) −5.96554 + 1.36532i −0.289371 + 0.0662277i
\(426\) 0 0
\(427\) −5.77729 + 3.33552i −0.279582 + 0.161417i
\(428\) 0 0
\(429\) −4.21955 2.54931i −0.203722 0.123082i
\(430\) 0 0
\(431\) −8.12482 14.0726i −0.391359 0.677853i 0.601270 0.799046i \(-0.294661\pi\)
−0.992629 + 0.121193i \(0.961328\pi\)
\(432\) 0 0
\(433\) −0.221929 0.128130i −0.0106652 0.00615756i 0.494658 0.869088i \(-0.335293\pi\)
−0.505323 + 0.862930i \(0.668627\pi\)
\(434\) 0 0
\(435\) −2.14827 + 14.2816i −0.103002 + 0.684750i
\(436\) 0 0
\(437\) 2.93855i 0.140570i
\(438\) 0 0
\(439\) 3.79833 + 6.57890i 0.181284 + 0.313994i 0.942318 0.334718i \(-0.108641\pi\)
−0.761034 + 0.648712i \(0.775308\pi\)
\(440\) 0 0
\(441\) 2.67352 0.127310
\(442\) 0 0
\(443\) 4.32246i 0.205366i −0.994714 0.102683i \(-0.967257\pi\)
0.994714 0.102683i \(-0.0327428\pi\)
\(444\) 0 0
\(445\) −17.5017 + 21.9599i −0.829663 + 1.04100i
\(446\) 0 0
\(447\) 36.9332i 1.74688i
\(448\) 0 0
\(449\) 1.64403 2.84754i 0.0775865 0.134384i −0.824622 0.565685i \(-0.808612\pi\)
0.902208 + 0.431301i \(0.141945\pi\)
\(450\) 0 0
\(451\) 3.16324 5.47890i 0.148951 0.257991i
\(452\) 0 0
\(453\) −39.8680 + 23.0178i −1.87316 + 1.08147i
\(454\) 0 0
\(455\) 3.98907 23.3531i 0.187010 1.09481i
\(456\) 0 0
\(457\) 13.3594 7.71304i 0.624925 0.360801i −0.153859 0.988093i \(-0.549170\pi\)
0.778784 + 0.627292i \(0.215837\pi\)
\(458\) 0 0
\(459\) 1.79833 3.11480i 0.0839389 0.145386i
\(460\) 0 0
\(461\) −12.9424 + 22.4168i −0.602786 + 1.04406i 0.389611 + 0.920979i \(0.372609\pi\)
−0.992397 + 0.123076i \(0.960724\pi\)
\(462\) 0 0
\(463\) 7.04045i 0.327197i −0.986527 0.163599i \(-0.947690\pi\)
0.986527 0.163599i \(-0.0523102\pi\)
\(464\) 0 0
\(465\) 33.7376 + 26.8885i 1.56454 + 1.24692i
\(466\) 0 0
\(467\) 18.8113i 0.870482i 0.900314 + 0.435241i \(0.143337\pi\)
−0.900314 + 0.435241i \(0.856663\pi\)
\(468\) 0 0
\(469\) 23.5967 1.08959
\(470\) 0 0
\(471\) 19.7688 + 34.2406i 0.910900 + 1.57773i
\(472\) 0 0
\(473\) 0.868356i 0.0399271i
\(474\) 0 0
\(475\) −1.52255 6.65255i −0.0698594 0.305240i
\(476\) 0 0
\(477\) −0.909493 0.525096i −0.0416428 0.0240425i
\(478\) 0 0
\(479\) 9.73876 + 16.8680i 0.444975 + 0.770720i 0.998051 0.0624114i \(-0.0198791\pi\)
−0.553075 + 0.833131i \(0.686546\pi\)
\(480\) 0 0
\(481\) −3.86491 + 2.13011i −0.176225 + 0.0971249i
\(482\) 0 0
\(483\) 11.7957 6.81023i 0.536721 0.309876i
\(484\) 0 0
\(485\) 4.91728 32.6898i 0.223282 1.48437i
\(486\) 0 0
\(487\) 27.9935 + 16.1620i 1.26851 + 0.732372i 0.974705 0.223495i \(-0.0717467\pi\)
0.293800 + 0.955867i \(0.405080\pi\)
\(488\) 0 0
\(489\) −8.63509 −0.390492
\(490\) 0 0
\(491\) 14.3354 + 24.8297i 0.646949 + 1.12055i 0.983848 + 0.179007i \(0.0572885\pi\)
−0.336899 + 0.941541i \(0.609378\pi\)
\(492\) 0 0
\(493\) 3.67187i 0.165373i
\(494\) 0 0
\(495\) 0.848960 + 2.16123i 0.0381579 + 0.0971401i
\(496\) 0 0
\(497\) −6.70593 + 3.87167i −0.300802 + 0.173668i
\(498\) 0 0
\(499\) 28.9616 1.29650 0.648249 0.761428i \(-0.275502\pi\)
0.648249 + 0.761428i \(0.275502\pi\)
\(500\) 0 0
\(501\) 3.16324 5.47890i 0.141323 0.244779i
\(502\) 0 0
\(503\) −24.3433 14.0546i −1.08542 0.626665i −0.153063 0.988216i \(-0.548914\pi\)
−0.932352 + 0.361551i \(0.882247\pi\)
\(504\) 0 0
\(505\) −18.4404 + 23.1376i −0.820587 + 1.02961i
\(506\) 0 0
\(507\) −24.7754 + 13.0195i −1.10032 + 0.578218i
\(508\) 0 0
\(509\) 10.5563 + 18.2841i 0.467900 + 0.810427i 0.999327 0.0366773i \(-0.0116774\pi\)
−0.531427 + 0.847104i \(0.678344\pi\)
\(510\) 0 0
\(511\) 15.1722 26.2790i 0.671178 1.16251i
\(512\) 0 0
\(513\) 3.47351 + 2.00543i 0.153359 + 0.0885420i
\(514\) 0 0
\(515\) 22.8284 8.96730i 1.00594 0.395147i
\(516\) 0 0
\(517\) 3.39010 1.95728i 0.149097 0.0860809i
\(518\) 0 0
\(519\) −2.94369 −0.129214
\(520\) 0 0
\(521\) 0.673516 0.0295073 0.0147536 0.999891i \(-0.495304\pi\)
0.0147536 + 0.999891i \(0.495304\pi\)
\(522\) 0 0
\(523\) 25.8618 14.9313i 1.13086 0.652900i 0.186706 0.982416i \(-0.440219\pi\)
0.944150 + 0.329516i \(0.106886\pi\)
\(524\) 0 0
\(525\) −23.1754 + 21.5293i −1.01146 + 0.939614i
\(526\) 0 0
\(527\) 9.49907 + 5.48429i 0.413786 + 0.238899i
\(528\) 0 0
\(529\) −9.18246 + 15.9045i −0.399237 + 0.691499i
\(530\) 0 0
\(531\) 6.21061 + 10.7571i 0.269517 + 0.466818i
\(532\) 0 0
\(533\) −17.3366 31.4558i −0.750933 1.36250i
\(534\) 0 0
\(535\) −18.6643 14.8752i −0.806928 0.643112i
\(536\) 0 0
\(537\) 14.5171 + 8.38148i 0.626461 + 0.361687i
\(538\) 0 0
\(539\) 0.519213 0.899304i 0.0223641 0.0387358i
\(540\) 0 0
\(541\) 6.28806 0.270345 0.135172 0.990822i \(-0.456841\pi\)
0.135172 + 0.990822i \(0.456841\pi\)
\(542\) 0 0
\(543\) 7.20968 4.16251i 0.309397 0.178630i
\(544\) 0 0
\(545\) −2.67352 6.80607i −0.114521 0.291540i
\(546\) 0 0
\(547\) 3.03789i 0.129891i −0.997889 0.0649454i \(-0.979313\pi\)
0.997889 0.0649454i \(-0.0206873\pi\)
\(548\) 0 0
\(549\) −1.85597 3.21464i −0.0792109 0.137197i
\(550\) 0 0
\(551\) −4.09473 −0.174442
\(552\) 0 0
\(553\) −2.64265 1.52574i −0.112377 0.0648809i
\(554\) 0 0
\(555\) 5.82669 + 0.876465i 0.247329 + 0.0372039i
\(556\) 0 0
\(557\) −17.9264 + 10.3498i −0.759566 + 0.438536i −0.829140 0.559041i \(-0.811169\pi\)
0.0695738 + 0.997577i \(0.477836\pi\)
\(558\) 0 0
\(559\) −4.21955 2.54931i −0.178468 0.107824i
\(560\) 0 0
\(561\) 0.836758 + 1.44931i 0.0353279 + 0.0611898i
\(562\) 0 0
\(563\) 9.49188 + 5.48014i 0.400035 + 0.230960i 0.686499 0.727131i \(-0.259147\pi\)
−0.286464 + 0.958091i \(0.592480\pi\)
\(564\) 0 0
\(565\) −1.83929 + 12.2275i −0.0773794 + 0.514413i
\(566\) 0 0
\(567\) 33.0051i 1.38608i
\(568\) 0 0
\(569\) 21.3566 + 36.9907i 0.895314 + 1.55073i 0.833416 + 0.552647i \(0.186382\pi\)
0.0618981 + 0.998082i \(0.480285\pi\)
\(570\) 0 0
\(571\) 23.6145 0.988238 0.494119 0.869394i \(-0.335491\pi\)
0.494119 + 0.869394i \(0.335491\pi\)
\(572\) 0 0
\(573\) 10.6434i 0.444635i
\(574\) 0 0
\(575\) −3.16683 + 10.2883i −0.132066 + 0.429050i
\(576\) 0 0
\(577\) 18.3646i 0.764530i 0.924053 + 0.382265i \(0.124856\pi\)
−0.924053 + 0.382265i \(0.875144\pi\)
\(578\) 0 0
\(579\) 5.33542 9.24123i 0.221733 0.384052i
\(580\) 0 0
\(581\) 17.4039 30.1445i 0.722037 1.25060i
\(582\) 0 0
\(583\) −0.353259 + 0.203954i −0.0146305 + 0.00844691i
\(584\) 0 0
\(585\) 12.9943 + 2.21962i 0.537248 + 0.0917702i
\(586\) 0 0
\(587\) −0.608726 + 0.351448i −0.0251248 + 0.0145058i −0.512510 0.858681i \(-0.671284\pi\)
0.487385 + 0.873187i \(0.337951\pi\)
\(588\) 0 0
\(589\) −6.11588 + 10.5930i −0.252000 + 0.436477i
\(590\) 0 0
\(591\) −7.26124 + 12.5768i −0.298687 + 0.517342i
\(592\) 0 0
\(593\) 37.1593i 1.52595i −0.646428 0.762975i \(-0.723738\pi\)
0.646428 0.762975i \(-0.276262\pi\)
\(594\) 0 0
\(595\) −5.01248 + 6.28927i −0.205492 + 0.257835i
\(596\) 0 0
\(597\) 11.1423i 0.456026i
\(598\) 0 0
\(599\) −15.6914 −0.641133 −0.320567 0.947226i \(-0.603873\pi\)
−0.320567 + 0.947226i \(0.603873\pi\)
\(600\) 0 0
\(601\) −6.00193 10.3956i −0.244824 0.424047i 0.717258 0.696807i \(-0.245397\pi\)
−0.962082 + 0.272760i \(0.912063\pi\)
\(602\) 0 0
\(603\) 13.1298i 0.534687i
\(604\) 0 0
\(605\) −23.4313 3.52459i −0.952616 0.143295i
\(606\) 0 0
\(607\) −33.5035 19.3433i −1.35987 0.785119i −0.370261 0.928928i \(-0.620732\pi\)
−0.989606 + 0.143809i \(0.954065\pi\)
\(608\) 0 0
\(609\) 9.48973 + 16.4367i 0.384543 + 0.666048i
\(610\) 0 0
\(611\) 0.441765 22.2195i 0.0178719 0.898903i
\(612\) 0 0
\(613\) −14.9684 + 8.64201i −0.604568 + 0.349047i −0.770836 0.637033i \(-0.780161\pi\)
0.166269 + 0.986081i \(0.446828\pi\)
\(614\) 0 0
\(615\) −7.13340 + 47.4224i −0.287646 + 1.91225i
\(616\) 0 0
\(617\) 22.9229 + 13.2345i 0.922841 + 0.532803i 0.884540 0.466464i \(-0.154472\pi\)
0.0383009 + 0.999266i \(0.487805\pi\)
\(618\) 0 0
\(619\) −31.0039 −1.24615 −0.623075 0.782162i \(-0.714117\pi\)
−0.623075 + 0.782162i \(0.714117\pi\)
\(620\) 0 0
\(621\) −3.16324 5.47890i −0.126937 0.219861i
\(622\) 0 0
\(623\) 36.9030i 1.47849i
\(624\) 0 0
\(625\) 1.83869 24.9323i 0.0735475 0.997292i
\(626\) 0 0
\(627\) −1.61621 + 0.933121i −0.0645453 + 0.0372653i
\(628\) 0 0
\(629\) 1.49807 0.0597320
\(630\) 0 0
\(631\) −10.3566 + 17.9381i −0.412288 + 0.714104i −0.995140 0.0984745i \(-0.968604\pi\)
0.582851 + 0.812579i \(0.301937\pi\)
\(632\) 0 0
\(633\) 26.1362 + 15.0897i 1.03882 + 0.599763i
\(634\) 0 0
\(635\) −30.1321 24.0149i −1.19576 0.953003i
\(636\) 0 0
\(637\) −2.84563 5.16315i −0.112748 0.204571i
\(638\) 0 0
\(639\) −2.15430 3.73136i −0.0852229 0.147610i
\(640\) 0 0
\(641\) −10.5947 + 18.3506i −0.418467 + 0.724806i −0.995785 0.0917132i \(-0.970766\pi\)
0.577319 + 0.816519i \(0.304099\pi\)
\(642\) 0 0
\(643\) −9.98843 5.76682i −0.393905 0.227421i 0.289946 0.957043i \(-0.406363\pi\)
−0.683851 + 0.729622i \(0.739696\pi\)
\(644\) 0 0
\(645\) 2.40660 + 6.12658i 0.0947598 + 0.241234i
\(646\) 0 0
\(647\) −30.1779 + 17.4232i −1.18641 + 0.684977i −0.957490 0.288467i \(-0.906854\pi\)
−0.228925 + 0.973444i \(0.573521\pi\)
\(648\) 0 0
\(649\) 4.82456 0.189380
\(650\) 0 0
\(651\) 56.6953 2.22206
\(652\) 0 0
\(653\) 19.3324 11.1616i 0.756537 0.436787i −0.0715139 0.997440i \(-0.522783\pi\)
0.828051 + 0.560653i \(0.189450\pi\)
\(654\) 0 0
\(655\) 8.17544 + 20.8125i 0.319441 + 0.813214i
\(656\) 0 0
\(657\) 14.6223 + 8.44221i 0.570471 + 0.329362i
\(658\) 0 0
\(659\) 0.433420 0.750705i 0.0168836 0.0292433i −0.857460 0.514550i \(-0.827959\pi\)
0.874344 + 0.485307i \(0.161292\pi\)
\(660\) 0 0
\(661\) −6.65430 11.5256i −0.258822 0.448293i 0.707104 0.707109i \(-0.250001\pi\)
−0.965927 + 0.258816i \(0.916668\pi\)
\(662\) 0 0
\(663\) 9.49907 + 0.188859i 0.368913 + 0.00733469i
\(664\) 0 0
\(665\) −7.01356 5.58973i −0.271974 0.216760i
\(666\) 0 0
\(667\) 5.59346 + 3.22939i 0.216580 + 0.125042i
\(668\) 0 0
\(669\) 0.00893993 0.0154844i 0.000345637 0.000598662i
\(670\) 0 0
\(671\) −1.44176 −0.0556587
\(672\) 0 0
\(673\) −4.77457 + 2.75660i −0.184046 + 0.106259i −0.589192 0.807993i \(-0.700554\pi\)
0.405146 + 0.914252i \(0.367221\pi\)
\(674\) 0 0
\(675\) 10.0000 + 10.7646i 0.384900 + 0.414331i
\(676\) 0 0
\(677\) 4.80479i 0.184663i 0.995728 + 0.0923316i \(0.0294320\pi\)
−0.995728 + 0.0923316i \(0.970568\pi\)
\(678\) 0 0
\(679\) −21.7215 37.6227i −0.833594 1.44383i
\(680\) 0 0
\(681\) −24.2496 −0.929248
\(682\) 0 0
\(683\) 10.1866 + 5.88126i 0.389781 + 0.225040i 0.682065 0.731291i \(-0.261082\pi\)
−0.292284 + 0.956331i \(0.594415\pi\)
\(684\) 0 0
\(685\) 2.88453 19.1761i 0.110212 0.732683i
\(686\) 0 0
\(687\) −30.8393 + 17.8051i −1.17659 + 0.679306i
\(688\) 0 0
\(689\) −0.0460332 + 2.31533i −0.00175372 + 0.0882071i
\(690\) 0 0
\(691\) 2.43342 + 4.21481i 0.0925717 + 0.160339i 0.908593 0.417684i \(-0.137158\pi\)
−0.816021 + 0.578022i \(0.803825\pi\)
\(692\) 0 0
\(693\) 2.64265 + 1.52574i 0.100386 + 0.0579579i
\(694\) 0 0
\(695\) 31.6786 + 4.76518i 1.20164 + 0.180753i
\(696\) 0 0
\(697\) 12.1925i 0.461825i
\(698\) 0 0
\(699\) 7.48079 + 12.9571i 0.282949 + 0.490083i
\(700\) 0 0
\(701\) 21.3828 0.807617 0.403808 0.914844i \(-0.367686\pi\)
0.403808 + 0.914844i \(0.367686\pi\)
\(702\) 0 0
\(703\) 1.67059i 0.0630076i
\(704\) 0 0
\(705\) −18.4939 + 23.2048i −0.696522 + 0.873943i
\(706\) 0 0
\(707\) 38.8822i 1.46232i
\(708\) 0 0
\(709\) −13.0582 + 22.6175i −0.490412 + 0.849419i −0.999939 0.0110357i \(-0.996487\pi\)
0.509527 + 0.860455i \(0.329820\pi\)
\(710\) 0 0
\(711\) 0.848960 1.47044i 0.0318385 0.0551459i
\(712\) 0 0
\(713\) 16.7087 9.64680i 0.625748 0.361276i
\(714\) 0 0
\(715\) 3.27020 3.93989i 0.122299 0.147344i
\(716\) 0 0
\(717\) −7.45795 + 4.30585i −0.278522 + 0.160805i
\(718\) 0 0
\(719\) −18.3387 + 31.7635i −0.683918 + 1.18458i 0.289858 + 0.957070i \(0.406392\pi\)
−0.973776 + 0.227510i \(0.926941\pi\)
\(720\) 0 0
\(721\) 16.1159 27.9135i 0.600187 1.03955i
\(722\) 0 0
\(723\) 42.5679i 1.58312i
\(724\) 0 0
\(725\) −14.3362 4.41283i −0.532434 0.163888i
\(726\) 0 0
\(727\) 26.2596i 0.973916i −0.873425 0.486958i \(-0.838107\pi\)
0.873425 0.486958i \(-0.161893\pi\)
\(728\) 0 0
\(729\) −0.614542 −0.0227608
\(730\) 0 0
\(731\) 0.836758 + 1.44931i 0.0309486 + 0.0536046i
\(732\) 0 0
\(733\) 31.7811i 1.17386i 0.809637 + 0.586931i \(0.199664\pi\)
−0.809637 + 0.586931i \(0.800336\pi\)
\(734\) 0 0
\(735\) −1.17087 + 7.78389i −0.0431883 + 0.287113i
\(736\) 0 0
\(737\) 4.41654 + 2.54989i 0.162685 + 0.0939265i
\(738\) 0 0
\(739\) 17.0685 + 29.5635i 0.627875 + 1.08751i 0.987977 + 0.154599i \(0.0494085\pi\)
−0.360102 + 0.932913i \(0.617258\pi\)
\(740\) 0 0
\(741\) −0.210609 + 10.5930i −0.00773691 + 0.389144i
\(742\) 0 0
\(743\) −2.70254 + 1.56031i −0.0991465 + 0.0572423i −0.548753 0.835984i \(-0.684897\pi\)
0.449607 + 0.893227i \(0.351564\pi\)
\(744\) 0 0
\(745\) 37.9328 + 5.70594i 1.38975 + 0.209050i
\(746\) 0 0
\(747\) 16.7732 + 9.68401i 0.613699 + 0.354320i
\(748\) 0 0
\(749\) −31.3649 −1.14605
\(750\) 0 0
\(751\) 0.742024 + 1.28522i 0.0270769 + 0.0468985i 0.879246 0.476367i \(-0.158047\pi\)
−0.852169 + 0.523266i \(0.824713\pi\)
\(752\) 0 0
\(753\) 7.90881i 0.288213i
\(754\) 0 0
\(755\) −17.4814 44.5030i −0.636213 1.61963i
\(756\) 0 0
\(757\) −4.41654 + 2.54989i −0.160522 + 0.0926774i −0.578109 0.815960i \(-0.696209\pi\)
0.417587 + 0.908637i \(0.362876\pi\)
\(758\) 0 0
\(759\) 2.94369 0.106849
\(760\) 0 0
\(761\) 14.8931 25.7955i 0.539873 0.935088i −0.459037 0.888417i \(-0.651806\pi\)
0.998910 0.0466707i \(-0.0148611\pi\)
\(762\) 0 0
\(763\) −8.32215 4.80479i −0.301282 0.173945i
\(764\) 0 0
\(765\) −3.49952 2.78908i −0.126525 0.100839i
\(766\) 0 0
\(767\) 14.1639 23.4437i 0.511428 0.846501i
\(768\) 0 0
\(769\) 9.54930 + 16.5399i 0.344356 + 0.596443i 0.985237 0.171198i \(-0.0547638\pi\)
−0.640880 + 0.767641i \(0.721430\pi\)
\(770\) 0 0
\(771\) 14.2791 24.7322i 0.514250 0.890707i
\(772\) 0 0
\(773\) −42.6350 24.6153i −1.53347 0.885351i −0.999198 0.0400400i \(-0.987251\pi\)
−0.534275 0.845311i \(-0.679415\pi\)
\(774\) 0 0
\(775\) −32.8284 + 30.4966i −1.17923 + 1.09547i
\(776\) 0 0
\(777\) 6.70593 3.87167i 0.240574 0.138895i
\(778\) 0 0
\(779\) −13.5967 −0.487151
\(780\) 0 0
\(781\) −1.67352 −0.0598831
\(782\) 0 0
\(783\) 7.63458 4.40783i 0.272838 0.157523i
\(784\) 0 0
\(785\) −38.2215 + 15.0139i −1.36418 + 0.535869i
\(786\) 0 0
\(787\) 8.47263 + 4.89168i 0.302017 + 0.174369i 0.643349 0.765573i \(-0.277545\pi\)
−0.341332 + 0.939943i \(0.610878\pi\)
\(788\) 0 0
\(789\) 32.5851 56.4390i 1.16006 2.00928i
\(790\) 0 0
\(791\) 8.12482 + 14.0726i 0.288885 + 0.500364i
\(792\) 0 0
\(793\) −4.23272 + 7.00587i −0.150308 + 0.248786i
\(794\) 0 0
\(795\) 1.92712 2.41801i 0.0683480 0.0857578i
\(796\) 0 0