Properties

Label 260.2.z.a.49.5
Level $260$
Weight $2$
Character 260.49
Analytic conductor $2.076$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.z (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 7x^{14} + 21x^{12} - 22x^{10} - 26x^{8} - 198x^{6} + 1701x^{4} - 5103x^{2} + 6561 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.5
Root \(-1.72890 + 0.104392i\) of defining polynomial
Character \(\chi\) \(=\) 260.49
Dual form 260.2.z.a.69.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.180812 - 0.104392i) q^{3} +(-1.60081 + 1.56122i) q^{5} +(-1.72890 + 2.99455i) q^{7} +(-1.47820 + 2.56033i) q^{9} +O(q^{10})\) \(q+(0.180812 - 0.104392i) q^{3} +(-1.60081 + 1.56122i) q^{5} +(-1.72890 + 2.99455i) q^{7} +(-1.47820 + 2.56033i) q^{9} +(0.625212 - 0.360966i) q^{11} +(-3.18457 - 1.69071i) q^{13} +(-0.126468 + 0.449398i) q^{15} +(3.10921 + 1.79510i) q^{17} +(6.51351 + 3.76057i) q^{19} +0.721933i q^{21} +(-2.05486 + 1.18637i) q^{23} +(0.125212 - 4.99843i) q^{25} +1.24360i q^{27} +(-3.68231 - 6.37795i) q^{29} +0.668447i q^{31} +(0.0753639 - 0.130534i) q^{33} +(-1.90748 - 7.49290i) q^{35} +(3.36538 + 5.82902i) q^{37} +(-0.752305 + 0.0267426i) q^{39} +(-6.32932 + 3.65423i) q^{41} +(7.06075 + 4.07653i) q^{43} +(-1.63089 - 6.40640i) q^{45} +6.40326 q^{47} +(-2.47820 - 4.29238i) q^{49} +0.749576 q^{51} -11.7433i q^{53} +(-0.437302 + 1.55393i) q^{55} +1.57029 q^{57} +(-4.20410 - 2.42724i) q^{59} +(2.68231 - 4.64590i) q^{61} +(-5.11134 - 8.85310i) q^{63} +(7.73747 - 2.26529i) q^{65} +(7.80620 + 13.5207i) q^{67} +(-0.247695 + 0.429021i) q^{69} +(-4.10530 - 2.37019i) q^{71} -6.36914 q^{73} +(-0.499155 - 0.916847i) q^{75} +2.49630i q^{77} +5.20683 q^{79} +(-4.30479 - 7.45612i) q^{81} +13.3902 q^{83} +(-7.77981 + 1.98052i) q^{85} +(-1.33161 - 0.768806i) q^{87} +(4.20410 - 2.42724i) q^{89} +(10.5687 - 6.61328i) q^{91} +(0.0697804 + 0.120863i) q^{93} +(-16.2980 + 4.14901i) q^{95} +(1.83435 - 3.17719i) q^{97} +2.13433i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 10 q^{9} - 6 q^{11} + 6 q^{15} - 18 q^{19} - 14 q^{25} + 12 q^{29} + 18 q^{39} - 48 q^{41} + 45 q^{45} - 6 q^{49} + 44 q^{51} + 2 q^{55} - 30 q^{59} - 28 q^{61} - 15 q^{65} - 34 q^{69} - 18 q^{71} - 42 q^{75} - 16 q^{79} - 44 q^{81} - 45 q^{85} + 30 q^{89} - 10 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).

\(n\) \(41\) \(131\) \(157\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

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
\(3\) 0.180812 0.104392i 0.104392 0.0602706i −0.446895 0.894586i \(-0.647470\pi\)
0.551287 + 0.834316i \(0.314137\pi\)
\(4\) 0 0
\(5\) −1.60081 + 1.56122i −0.715906 + 0.698197i
\(6\) 0 0
\(7\) −1.72890 + 2.99455i −0.653464 + 1.13183i 0.328813 + 0.944395i \(0.393351\pi\)
−0.982277 + 0.187437i \(0.939982\pi\)
\(8\) 0 0
\(9\) −1.47820 + 2.56033i −0.492735 + 0.853442i
\(10\) 0 0
\(11\) 0.625212 0.360966i 0.188509 0.108835i −0.402776 0.915299i \(-0.631955\pi\)
0.591284 + 0.806463i \(0.298621\pi\)
\(12\) 0 0
\(13\) −3.18457 1.69071i −0.883241 0.468919i
\(14\) 0 0
\(15\) −0.126468 + 0.449398i −0.0326539 + 0.116034i
\(16\) 0 0
\(17\) 3.10921 + 1.79510i 0.754094 + 0.435376i 0.827171 0.561950i \(-0.189949\pi\)
−0.0730774 + 0.997326i \(0.523282\pi\)
\(18\) 0 0
\(19\) 6.51351 + 3.76057i 1.49430 + 0.862735i 0.999979 0.00654367i \(-0.00208293\pi\)
0.494322 + 0.869279i \(0.335416\pi\)
\(20\) 0 0
\(21\) 0.721933i 0.157539i
\(22\) 0 0
\(23\) −2.05486 + 1.18637i −0.428468 + 0.247376i −0.698694 0.715421i \(-0.746235\pi\)
0.270226 + 0.962797i \(0.412902\pi\)
\(24\) 0 0
\(25\) 0.125212 4.99843i 0.0250424 0.999686i
\(26\) 0 0
\(27\) 1.24360i 0.239331i
\(28\) 0 0
\(29\) −3.68231 6.37795i −0.683788 1.18435i −0.973816 0.227337i \(-0.926998\pi\)
0.290028 0.957018i \(-0.406335\pi\)
\(30\) 0 0
\(31\) 0.668447i 0.120057i 0.998197 + 0.0600284i \(0.0191191\pi\)
−0.998197 + 0.0600284i \(0.980881\pi\)
\(32\) 0 0
\(33\) 0.0753639 0.130534i 0.0131192 0.0227231i
\(34\) 0 0
\(35\) −1.90748 7.49290i −0.322423 1.26653i
\(36\) 0 0
\(37\) 3.36538 + 5.82902i 0.553266 + 0.958284i 0.998036 + 0.0626397i \(0.0199519\pi\)
−0.444771 + 0.895645i \(0.646715\pi\)
\(38\) 0 0
\(39\) −0.752305 + 0.0267426i −0.120465 + 0.00428225i
\(40\) 0 0
\(41\) −6.32932 + 3.65423i −0.988473 + 0.570695i −0.904818 0.425799i \(-0.859993\pi\)
−0.0836556 + 0.996495i \(0.526660\pi\)
\(42\) 0 0
\(43\) 7.06075 + 4.07653i 1.07675 + 0.621665i 0.930019 0.367511i \(-0.119790\pi\)
0.146736 + 0.989176i \(0.453123\pi\)
\(44\) 0 0
\(45\) −1.63089 6.40640i −0.243119 0.955010i
\(46\) 0 0
\(47\) 6.40326 0.934011 0.467005 0.884254i \(-0.345333\pi\)
0.467005 + 0.884254i \(0.345333\pi\)
\(48\) 0 0
\(49\) −2.47820 4.29238i −0.354029 0.613197i
\(50\) 0 0
\(51\) 0.749576 0.104962
\(52\) 0 0
\(53\) 11.7433i 1.61306i −0.591193 0.806530i \(-0.701343\pi\)
0.591193 0.806530i \(-0.298657\pi\)
\(54\) 0 0
\(55\) −0.437302 + 1.55393i −0.0589658 + 0.209532i
\(56\) 0 0
\(57\) 1.57029 0.207990
\(58\) 0 0
\(59\) −4.20410 2.42724i −0.547328 0.316000i 0.200716 0.979650i \(-0.435673\pi\)
−0.748044 + 0.663650i \(0.769007\pi\)
\(60\) 0 0
\(61\) 2.68231 4.64590i 0.343435 0.594846i −0.641634 0.767011i \(-0.721743\pi\)
0.985068 + 0.172165i \(0.0550763\pi\)
\(62\) 0 0
\(63\) −5.11134 8.85310i −0.643969 1.11539i
\(64\) 0 0
\(65\) 7.73747 2.26529i 0.959715 0.280975i
\(66\) 0 0
\(67\) 7.80620 + 13.5207i 0.953679 + 1.65182i 0.737362 + 0.675498i \(0.236071\pi\)
0.216318 + 0.976323i \(0.430595\pi\)
\(68\) 0 0
\(69\) −0.247695 + 0.429021i −0.0298190 + 0.0516480i
\(70\) 0 0
\(71\) −4.10530 2.37019i −0.487209 0.281290i 0.236207 0.971703i \(-0.424096\pi\)
−0.723416 + 0.690412i \(0.757429\pi\)
\(72\) 0 0
\(73\) −6.36914 −0.745452 −0.372726 0.927941i \(-0.621577\pi\)
−0.372726 + 0.927941i \(0.621577\pi\)
\(74\) 0 0
\(75\) −0.499155 0.916847i −0.0576375 0.105868i
\(76\) 0 0
\(77\) 2.49630i 0.284480i
\(78\) 0 0
\(79\) 5.20683 0.585815 0.292907 0.956141i \(-0.405377\pi\)
0.292907 + 0.956141i \(0.405377\pi\)
\(80\) 0 0
\(81\) −4.30479 7.45612i −0.478310 0.828458i
\(82\) 0 0
\(83\) 13.3902 1.46977 0.734883 0.678194i \(-0.237237\pi\)
0.734883 + 0.678194i \(0.237237\pi\)
\(84\) 0 0
\(85\) −7.77981 + 1.98052i −0.843838 + 0.214817i
\(86\) 0 0
\(87\) −1.33161 0.768806i −0.142764 0.0824246i
\(88\) 0 0
\(89\) 4.20410 2.42724i 0.445634 0.257287i −0.260350 0.965514i \(-0.583838\pi\)
0.705985 + 0.708227i \(0.250505\pi\)
\(90\) 0 0
\(91\) 10.5687 6.61328i 1.10790 0.693260i
\(92\) 0 0
\(93\) 0.0697804 + 0.120863i 0.00723589 + 0.0125329i
\(94\) 0 0
\(95\) −16.2980 + 4.14901i −1.67214 + 0.425679i
\(96\) 0 0
\(97\) 1.83435 3.17719i 0.186250 0.322595i −0.757747 0.652548i \(-0.773700\pi\)
0.943997 + 0.329954i \(0.107033\pi\)
\(98\) 0 0
\(99\) 2.13433i 0.214508i
\(100\) 0 0
\(101\) 4.85299 + 8.40563i 0.482891 + 0.836391i 0.999807 0.0196446i \(-0.00625347\pi\)
−0.516916 + 0.856036i \(0.672920\pi\)
\(102\) 0 0
\(103\) 5.36274i 0.528407i 0.964467 + 0.264203i \(0.0851090\pi\)
−0.964467 + 0.264203i \(0.914891\pi\)
\(104\) 0 0
\(105\) −1.12709 1.15568i −0.109993 0.112783i
\(106\) 0 0
\(107\) −13.6408 + 7.87552i −1.31871 + 0.761355i −0.983520 0.180798i \(-0.942132\pi\)
−0.335185 + 0.942152i \(0.608799\pi\)
\(108\) 0 0
\(109\) 14.4879i 1.38769i 0.720123 + 0.693847i \(0.244085\pi\)
−0.720123 + 0.693847i \(0.755915\pi\)
\(110\) 0 0
\(111\) 1.21700 + 0.702637i 0.115513 + 0.0666913i
\(112\) 0 0
\(113\) −2.74758 1.58632i −0.258471 0.149228i 0.365166 0.930942i \(-0.381012\pi\)
−0.623637 + 0.781714i \(0.714346\pi\)
\(114\) 0 0
\(115\) 1.43726 5.10724i 0.134025 0.476253i
\(116\) 0 0
\(117\) 9.03622 5.65433i 0.835399 0.522743i
\(118\) 0 0
\(119\) −10.7510 + 6.20711i −0.985546 + 0.569005i
\(120\) 0 0
\(121\) −5.23941 + 9.07492i −0.476310 + 0.824993i
\(122\) 0 0
\(123\) −0.762944 + 1.32146i −0.0687923 + 0.119152i
\(124\) 0 0
\(125\) 7.60319 + 8.19704i 0.680050 + 0.733166i
\(126\) 0 0
\(127\) −1.33161 + 0.768806i −0.118161 + 0.0682205i −0.557916 0.829898i \(-0.688399\pi\)
0.439754 + 0.898118i \(0.355065\pi\)
\(128\) 0 0
\(129\) 1.70222 0.149872
\(130\) 0 0
\(131\) 6.45180 0.563696 0.281848 0.959459i \(-0.409053\pi\)
0.281848 + 0.959459i \(0.409053\pi\)
\(132\) 0 0
\(133\) −22.5224 + 13.0033i −1.95294 + 1.12753i
\(134\) 0 0
\(135\) −1.94153 1.99077i −0.167100 0.171338i
\(136\) 0 0
\(137\) −4.62163 + 8.00490i −0.394853 + 0.683905i −0.993082 0.117420i \(-0.962538\pi\)
0.598230 + 0.801325i \(0.295871\pi\)
\(138\) 0 0
\(139\) 8.38641 14.5257i 0.711326 1.23205i −0.253033 0.967458i \(-0.581428\pi\)
0.964359 0.264596i \(-0.0852385\pi\)
\(140\) 0 0
\(141\) 1.15778 0.668447i 0.0975031 0.0562934i
\(142\) 0 0
\(143\) −2.60132 + 0.0924708i −0.217534 + 0.00773280i
\(144\) 0 0
\(145\) 15.8520 + 4.46103i 1.31644 + 0.370468i
\(146\) 0 0
\(147\) −0.896178 0.517408i −0.0739155 0.0426751i
\(148\) 0 0
\(149\) 2.17153 + 1.25373i 0.177899 + 0.102710i 0.586305 0.810090i \(-0.300582\pi\)
−0.408406 + 0.912800i \(0.633915\pi\)
\(150\) 0 0
\(151\) 11.0238i 0.897108i 0.893756 + 0.448554i \(0.148061\pi\)
−0.893756 + 0.448554i \(0.851939\pi\)
\(152\) 0 0
\(153\) −9.19209 + 5.30706i −0.743137 + 0.429050i
\(154\) 0 0
\(155\) −1.04359 1.07006i −0.0838232 0.0859493i
\(156\) 0 0
\(157\) 0.946504i 0.0755392i 0.999286 + 0.0377696i \(0.0120253\pi\)
−0.999286 + 0.0377696i \(0.987975\pi\)
\(158\) 0 0
\(159\) −1.22590 2.12332i −0.0972202 0.168390i
\(160\) 0 0
\(161\) 8.20449i 0.646604i
\(162\) 0 0
\(163\) 7.20187 12.4740i 0.564094 0.977039i −0.433039 0.901375i \(-0.642559\pi\)
0.997133 0.0756643i \(-0.0241077\pi\)
\(164\) 0 0
\(165\) 0.0831482 + 0.326620i 0.00647308 + 0.0254273i
\(166\) 0 0
\(167\) −9.35429 16.2021i −0.723857 1.25376i −0.959443 0.281903i \(-0.909034\pi\)
0.235586 0.971854i \(-0.424299\pi\)
\(168\) 0 0
\(169\) 7.28300 + 10.7684i 0.560231 + 0.828337i
\(170\) 0 0
\(171\) −19.2566 + 11.1178i −1.47259 + 0.850199i
\(172\) 0 0
\(173\) 15.3261 + 8.84855i 1.16523 + 0.672743i 0.952551 0.304380i \(-0.0984493\pi\)
0.212675 + 0.977123i \(0.431783\pi\)
\(174\) 0 0
\(175\) 14.7516 + 9.01675i 1.11511 + 0.681602i
\(176\) 0 0
\(177\) −1.01354 −0.0761820
\(178\) 0 0
\(179\) −4.20410 7.28172i −0.314230 0.544262i 0.665044 0.746804i \(-0.268413\pi\)
−0.979273 + 0.202543i \(0.935079\pi\)
\(180\) 0 0
\(181\) 16.6150 1.23499 0.617493 0.786576i \(-0.288148\pi\)
0.617493 + 0.786576i \(0.288148\pi\)
\(182\) 0 0
\(183\) 1.12004i 0.0827961i
\(184\) 0 0
\(185\) −14.4877 4.07708i −1.06516 0.299753i
\(186\) 0 0
\(187\) 2.59189 0.189537
\(188\) 0 0
\(189\) −3.72402 2.15006i −0.270883 0.156394i
\(190\) 0 0
\(191\) −8.93461 + 15.4752i −0.646486 + 1.11975i 0.337470 + 0.941336i \(0.390429\pi\)
−0.983956 + 0.178410i \(0.942905\pi\)
\(192\) 0 0
\(193\) −3.62156 6.27273i −0.260686 0.451521i 0.705739 0.708472i \(-0.250615\pi\)
−0.966424 + 0.256952i \(0.917282\pi\)
\(194\) 0 0
\(195\) 1.16255 1.21732i 0.0832519 0.0871741i
\(196\) 0 0
\(197\) −5.36349 9.28984i −0.382133 0.661873i 0.609234 0.792990i \(-0.291477\pi\)
−0.991367 + 0.131117i \(0.958144\pi\)
\(198\) 0 0
\(199\) −1.62521 + 2.81495i −0.115208 + 0.199547i −0.917863 0.396897i \(-0.870087\pi\)
0.802655 + 0.596444i \(0.203420\pi\)
\(200\) 0 0
\(201\) 2.82291 + 1.62981i 0.199113 + 0.114958i
\(202\) 0 0
\(203\) 25.4654 1.78732
\(204\) 0 0
\(205\) 4.42702 15.7312i 0.309196 1.09871i
\(206\) 0 0
\(207\) 7.01481i 0.487563i
\(208\) 0 0
\(209\) 5.42976 0.375585
\(210\) 0 0
\(211\) −11.7639 20.3757i −0.809862 1.40272i −0.912959 0.408051i \(-0.866208\pi\)
0.103097 0.994671i \(-0.467125\pi\)
\(212\) 0 0
\(213\) −0.989715 −0.0678142
\(214\) 0 0
\(215\) −17.6673 + 4.49759i −1.20490 + 0.306733i
\(216\) 0 0
\(217\) −2.00170 1.15568i −0.135884 0.0784527i
\(218\) 0 0
\(219\) −1.15162 + 0.664886i −0.0778191 + 0.0449289i
\(220\) 0 0
\(221\) −6.86650 10.9734i −0.461891 0.738151i
\(222\) 0 0
\(223\) 6.29378 + 10.9011i 0.421463 + 0.729995i 0.996083 0.0884255i \(-0.0281835\pi\)
−0.574620 + 0.818420i \(0.694850\pi\)
\(224\) 0 0
\(225\) 12.6125 + 7.70929i 0.840835 + 0.513953i
\(226\) 0 0
\(227\) 4.22075 7.31055i 0.280141 0.485218i −0.691278 0.722589i \(-0.742952\pi\)
0.971419 + 0.237370i \(0.0762855\pi\)
\(228\) 0 0
\(229\) 8.26510i 0.546173i −0.961989 0.273087i \(-0.911955\pi\)
0.961989 0.273087i \(-0.0880445\pi\)
\(230\) 0 0
\(231\) 0.260593 + 0.451361i 0.0171458 + 0.0296974i
\(232\) 0 0
\(233\) 5.31046i 0.347900i −0.984755 0.173950i \(-0.944347\pi\)
0.984755 0.173950i \(-0.0556531\pi\)
\(234\) 0 0
\(235\) −10.2504 + 9.99686i −0.668664 + 0.652123i
\(236\) 0 0
\(237\) 0.941457 0.543551i 0.0611542 0.0353074i
\(238\) 0 0
\(239\) 4.14744i 0.268276i 0.990963 + 0.134138i \(0.0428265\pi\)
−0.990963 + 0.134138i \(0.957173\pi\)
\(240\) 0 0
\(241\) −1.46804 0.847571i −0.0945645 0.0545968i 0.451972 0.892032i \(-0.350721\pi\)
−0.546536 + 0.837435i \(0.684054\pi\)
\(242\) 0 0
\(243\) −4.78768 2.76417i −0.307130 0.177322i
\(244\) 0 0
\(245\) 10.6685 + 3.00229i 0.681584 + 0.191809i
\(246\) 0 0
\(247\) −14.3847 22.9883i −0.915276 1.46271i
\(248\) 0 0
\(249\) 2.42111 1.39783i 0.153431 0.0885837i
\(250\) 0 0
\(251\) 9.86650 17.0893i 0.622768 1.07867i −0.366200 0.930536i \(-0.619341\pi\)
0.988968 0.148130i \(-0.0473252\pi\)
\(252\) 0 0
\(253\) −0.856482 + 1.48347i −0.0538465 + 0.0932649i
\(254\) 0 0
\(255\) −1.19993 + 1.17025i −0.0751426 + 0.0732839i
\(256\) 0 0
\(257\) 10.2231 5.90232i 0.637701 0.368177i −0.146027 0.989281i \(-0.546649\pi\)
0.783728 + 0.621104i \(0.213315\pi\)
\(258\) 0 0
\(259\) −23.2737 −1.44616
\(260\) 0 0
\(261\) 21.7728 1.34770
\(262\) 0 0
\(263\) 12.3013 7.10216i 0.758531 0.437938i −0.0702373 0.997530i \(-0.522376\pi\)
0.828768 + 0.559592i \(0.189042\pi\)
\(264\) 0 0
\(265\) 18.3338 + 18.7988i 1.12623 + 1.15480i
\(266\) 0 0
\(267\) 0.506768 0.877748i 0.0310137 0.0537173i
\(268\) 0 0
\(269\) 4.33120 7.50185i 0.264078 0.457396i −0.703244 0.710949i \(-0.748266\pi\)
0.967322 + 0.253553i \(0.0815991\pi\)
\(270\) 0 0
\(271\) 3.51351 2.02852i 0.213430 0.123224i −0.389474 0.921037i \(-0.627343\pi\)
0.602905 + 0.797813i \(0.294010\pi\)
\(272\) 0 0
\(273\) 1.22058 2.29905i 0.0738728 0.139145i
\(274\) 0 0
\(275\) −1.72598 3.17028i −0.104081 0.191175i
\(276\) 0 0
\(277\) −1.17344 0.677485i −0.0705051 0.0407061i 0.464333 0.885661i \(-0.346294\pi\)
−0.534838 + 0.844955i \(0.679627\pi\)
\(278\) 0 0
\(279\) −1.71144 0.988102i −0.102461 0.0591561i
\(280\) 0 0
\(281\) 20.3840i 1.21601i −0.793934 0.608004i \(-0.791970\pi\)
0.793934 0.608004i \(-0.208030\pi\)
\(282\) 0 0
\(283\) 2.22779 1.28621i 0.132428 0.0764575i −0.432322 0.901719i \(-0.642306\pi\)
0.564751 + 0.825262i \(0.308972\pi\)
\(284\) 0 0
\(285\) −2.51375 + 2.45157i −0.148902 + 0.145218i
\(286\) 0 0
\(287\) 25.2712i 1.49171i
\(288\) 0 0
\(289\) −2.05522 3.55974i −0.120895 0.209396i
\(290\) 0 0
\(291\) 0.765964i 0.0449016i
\(292\) 0 0
\(293\) −9.38481 + 16.2550i −0.548267 + 0.949626i 0.450127 + 0.892965i \(0.351379\pi\)
−0.998393 + 0.0566611i \(0.981955\pi\)
\(294\) 0 0
\(295\) 10.5194 2.67795i 0.612465 0.155916i
\(296\) 0 0
\(297\) 0.448898 + 0.777514i 0.0260477 + 0.0451159i
\(298\) 0 0
\(299\) 8.54966 0.303920i 0.494439 0.0175761i
\(300\) 0 0
\(301\) −24.4147 + 14.0958i −1.40724 + 0.812470i
\(302\) 0 0
\(303\) 1.75496 + 1.01323i 0.100820 + 0.0582083i
\(304\) 0 0
\(305\) 2.95937 + 11.6249i 0.169453 + 0.665639i
\(306\) 0 0
\(307\) −2.93740 −0.167646 −0.0838230 0.996481i \(-0.526713\pi\)
−0.0838230 + 0.996481i \(0.526713\pi\)
\(308\) 0 0
\(309\) 0.559826 + 0.969647i 0.0318474 + 0.0551613i
\(310\) 0 0
\(311\) 4.13623 0.234544 0.117272 0.993100i \(-0.462585\pi\)
0.117272 + 0.993100i \(0.462585\pi\)
\(312\) 0 0
\(313\) 12.2199i 0.690710i 0.938472 + 0.345355i \(0.112242\pi\)
−0.938472 + 0.345355i \(0.887758\pi\)
\(314\) 0 0
\(315\) 22.0039 + 6.19227i 1.23978 + 0.348895i
\(316\) 0 0
\(317\) −11.6351 −0.653490 −0.326745 0.945112i \(-0.605952\pi\)
−0.326745 + 0.945112i \(0.605952\pi\)
\(318\) 0 0
\(319\) −4.60445 2.65838i −0.257800 0.148841i
\(320\) 0 0
\(321\) −1.64428 + 2.84797i −0.0917747 + 0.158958i
\(322\) 0 0
\(323\) 13.5012 + 23.3848i 0.751229 + 1.30117i
\(324\) 0 0
\(325\) −8.84965 + 15.7062i −0.490890 + 0.871221i
\(326\) 0 0
\(327\) 1.51242 + 2.61959i 0.0836372 + 0.144864i
\(328\) 0 0
\(329\) −11.0706 + 19.1748i −0.610342 + 1.05714i
\(330\) 0 0
\(331\) −11.9346 6.89045i −0.655986 0.378734i 0.134760 0.990878i \(-0.456974\pi\)
−0.790746 + 0.612145i \(0.790307\pi\)
\(332\) 0 0
\(333\) −19.8989 −1.09045
\(334\) 0 0
\(335\) −33.6051 9.45703i −1.83604 0.516693i
\(336\) 0 0
\(337\) 17.6710i 0.962599i −0.876556 0.481299i \(-0.840165\pi\)
0.876556 0.481299i \(-0.159835\pi\)
\(338\) 0 0
\(339\) −0.662395 −0.0359763
\(340\) 0 0
\(341\) 0.241287 + 0.417921i 0.0130664 + 0.0226317i
\(342\) 0 0
\(343\) −7.06634 −0.381546
\(344\) 0 0
\(345\) −0.273280 1.07349i −0.0147129 0.0577947i
\(346\) 0 0
\(347\) −27.3190 15.7726i −1.46656 0.846719i −0.467260 0.884120i \(-0.654759\pi\)
−0.999300 + 0.0374015i \(0.988092\pi\)
\(348\) 0 0
\(349\) 1.19794 0.691629i 0.0641241 0.0370221i −0.467595 0.883943i \(-0.654879\pi\)
0.531719 + 0.846921i \(0.321546\pi\)
\(350\) 0 0
\(351\) 2.10257 3.96034i 0.112227 0.211387i
\(352\) 0 0
\(353\) 4.84369 + 8.38952i 0.257804 + 0.446529i 0.965653 0.259834i \(-0.0836678\pi\)
−0.707849 + 0.706363i \(0.750335\pi\)
\(354\) 0 0
\(355\) 10.2722 2.61501i 0.545192 0.138790i
\(356\) 0 0
\(357\) −1.29594 + 2.24464i −0.0685886 + 0.118799i
\(358\) 0 0
\(359\) 33.1233i 1.74818i 0.485762 + 0.874091i \(0.338542\pi\)
−0.485762 + 0.874091i \(0.661458\pi\)
\(360\) 0 0
\(361\) 18.7838 + 32.5346i 0.988623 + 1.71235i
\(362\) 0 0
\(363\) 2.18780i 0.114830i
\(364\) 0 0
\(365\) 10.1958 9.94361i 0.533673 0.520472i
\(366\) 0 0
\(367\) −1.20396 + 0.695107i −0.0628462 + 0.0362843i −0.531094 0.847313i \(-0.678219\pi\)
0.468248 + 0.883597i \(0.344886\pi\)
\(368\) 0 0
\(369\) 21.6068i 1.12481i
\(370\) 0 0
\(371\) 35.1657 + 20.3029i 1.82571 + 1.05408i
\(372\) 0 0
\(373\) −9.67280 5.58460i −0.500839 0.289159i 0.228221 0.973609i \(-0.426709\pi\)
−0.729060 + 0.684450i \(0.760042\pi\)
\(374\) 0 0
\(375\) 2.23045 + 0.688413i 0.115180 + 0.0355495i
\(376\) 0 0
\(377\) 0.943318 + 26.5367i 0.0485834 + 1.36671i
\(378\) 0 0
\(379\) 30.3827 17.5415i 1.56066 0.901045i 0.563466 0.826139i \(-0.309468\pi\)
0.997191 0.0749058i \(-0.0238656\pi\)
\(380\) 0 0
\(381\) −0.160514 + 0.278018i −0.00822338 + 0.0142433i
\(382\) 0 0
\(383\) 8.27327 14.3297i 0.422745 0.732215i −0.573462 0.819232i \(-0.694400\pi\)
0.996207 + 0.0870169i \(0.0277334\pi\)
\(384\) 0 0
\(385\) −3.89727 3.99612i −0.198623 0.203661i
\(386\) 0 0
\(387\) −20.8745 + 12.0519i −1.06111 + 0.612632i
\(388\) 0 0
\(389\) 25.6856 1.30231 0.651157 0.758943i \(-0.274284\pi\)
0.651157 + 0.758943i \(0.274284\pi\)
\(390\) 0 0
\(391\) −8.51864 −0.430806
\(392\) 0 0
\(393\) 1.16656 0.673515i 0.0588453 0.0339743i
\(394\) 0 0
\(395\) −8.33517 + 8.12899i −0.419388 + 0.409014i
\(396\) 0 0
\(397\) 9.90231 17.1513i 0.496983 0.860799i −0.503011 0.864280i \(-0.667775\pi\)
0.999994 + 0.00348048i \(0.00110787\pi\)
\(398\) 0 0
\(399\) −2.71488 + 4.70231i −0.135914 + 0.235410i
\(400\) 0 0
\(401\) −25.8364 + 14.9167i −1.29021 + 0.744903i −0.978691 0.205338i \(-0.934171\pi\)
−0.311518 + 0.950240i \(0.600837\pi\)
\(402\) 0 0
\(403\) 1.13015 2.12872i 0.0562968 0.106039i
\(404\) 0 0
\(405\) 18.5318 + 5.21515i 0.920852 + 0.259143i
\(406\) 0 0
\(407\) 4.20816 + 2.42958i 0.208591 + 0.120430i
\(408\) 0 0
\(409\) −1.36923 0.790524i −0.0677040 0.0390889i 0.465766 0.884908i \(-0.345779\pi\)
−0.533470 + 0.845819i \(0.679112\pi\)
\(410\) 0 0
\(411\) 1.92984i 0.0951921i
\(412\) 0 0
\(413\) 14.5370 8.39292i 0.715318 0.412989i
\(414\) 0 0
\(415\) −21.4352 + 20.9050i −1.05221 + 1.02619i
\(416\) 0 0
\(417\) 3.50189i 0.171488i
\(418\) 0 0
\(419\) 10.8627 + 18.8148i 0.530679 + 0.919164i 0.999359 + 0.0357956i \(0.0113965\pi\)
−0.468680 + 0.883368i \(0.655270\pi\)
\(420\) 0 0
\(421\) 0.356564i 0.0173779i −0.999962 0.00868894i \(-0.997234\pi\)
0.999962 0.00868894i \(-0.00276581\pi\)
\(422\) 0 0
\(423\) −9.46532 + 16.3944i −0.460220 + 0.797124i
\(424\) 0 0
\(425\) 9.36201 15.3164i 0.454124 0.742954i
\(426\) 0 0
\(427\) 9.27490 + 16.0646i 0.448844 + 0.777420i
\(428\) 0 0
\(429\) −0.460697 + 0.288277i −0.0222427 + 0.0139181i
\(430\) 0 0
\(431\) −19.7959 + 11.4292i −0.953535 + 0.550524i −0.894177 0.447713i \(-0.852239\pi\)
−0.0593575 + 0.998237i \(0.518905\pi\)
\(432\) 0 0
\(433\) −32.0555 18.5073i −1.54049 0.889402i −0.998808 0.0488177i \(-0.984455\pi\)
−0.541681 0.840584i \(-0.682212\pi\)
\(434\) 0 0
\(435\) 3.33193 0.848216i 0.159754 0.0406688i
\(436\) 0 0
\(437\) −17.8458 −0.853679
\(438\) 0 0
\(439\) −1.04632 1.81228i −0.0499381 0.0864953i 0.839976 0.542624i \(-0.182569\pi\)
−0.889914 + 0.456128i \(0.849236\pi\)
\(440\) 0 0
\(441\) 14.6532 0.697770
\(442\) 0 0
\(443\) 3.10367i 0.147460i 0.997278 + 0.0737298i \(0.0234902\pi\)
−0.997278 + 0.0737298i \(0.976510\pi\)
\(444\) 0 0
\(445\) −2.94054 + 10.4491i −0.139395 + 0.495334i
\(446\) 0 0
\(447\) 0.523518 0.0247616
\(448\) 0 0
\(449\) −16.0733 9.27994i −0.758547 0.437948i 0.0702265 0.997531i \(-0.477628\pi\)
−0.828774 + 0.559583i \(0.810961\pi\)
\(450\) 0 0
\(451\) −2.63811 + 4.56934i −0.124224 + 0.215162i
\(452\) 0 0
\(453\) 1.15080 + 1.99324i 0.0540692 + 0.0936507i
\(454\) 0 0
\(455\) −6.59381 + 27.0867i −0.309123 + 1.26984i
\(456\) 0 0
\(457\) −15.2853 26.4750i −0.715018 1.23845i −0.962953 0.269670i \(-0.913085\pi\)
0.247935 0.968777i \(-0.420248\pi\)
\(458\) 0 0
\(459\) −2.23239 + 3.86661i −0.104199 + 0.180478i
\(460\) 0 0
\(461\) −24.8953 14.3733i −1.15949 0.669432i −0.208308 0.978063i \(-0.566796\pi\)
−0.951182 + 0.308631i \(0.900129\pi\)
\(462\) 0 0
\(463\) −8.47784 −0.393999 −0.196999 0.980404i \(-0.563120\pi\)
−0.196999 + 0.980404i \(0.563120\pi\)
\(464\) 0 0
\(465\) −0.300399 0.0845373i −0.0139307 0.00392032i
\(466\) 0 0
\(467\) 37.8996i 1.75379i 0.480686 + 0.876893i \(0.340388\pi\)
−0.480686 + 0.876893i \(0.659612\pi\)
\(468\) 0 0
\(469\) −53.9846 −2.49278
\(470\) 0 0
\(471\) 0.0988073 + 0.171139i 0.00455280 + 0.00788568i
\(472\) 0 0
\(473\) 5.88596 0.270637
\(474\) 0 0
\(475\) 19.6125 32.0864i 0.899885 1.47223i
\(476\) 0 0
\(477\) 30.0666 + 17.3589i 1.37665 + 0.794811i
\(478\) 0 0
\(479\) 16.6522 9.61417i 0.760860 0.439282i −0.0687447 0.997634i \(-0.521899\pi\)
0.829604 + 0.558352i \(0.188566\pi\)
\(480\) 0 0
\(481\) −0.862130 24.2528i −0.0393097 1.10583i
\(482\) 0 0
\(483\) −0.856482 1.48347i −0.0389713 0.0675002i
\(484\) 0 0
\(485\) 2.02382 + 7.94990i 0.0918970 + 0.360986i
\(486\) 0 0
\(487\) 7.32952 12.6951i 0.332132 0.575270i −0.650798 0.759251i \(-0.725565\pi\)
0.982930 + 0.183982i \(0.0588987\pi\)
\(488\) 0 0
\(489\) 3.00726i 0.135993i
\(490\) 0 0
\(491\) 15.2876 + 26.4789i 0.689920 + 1.19498i 0.971863 + 0.235545i \(0.0756877\pi\)
−0.281943 + 0.959431i \(0.590979\pi\)
\(492\) 0 0
\(493\) 26.4405i 1.19082i
\(494\) 0 0
\(495\) −3.33215 3.41666i −0.149769 0.153568i
\(496\) 0 0
\(497\) 14.1953 8.19567i 0.636747 0.367626i
\(498\) 0 0
\(499\) 0.440262i 0.0197088i −0.999951 0.00985441i \(-0.996863\pi\)
0.999951 0.00985441i \(-0.00313681\pi\)
\(500\) 0 0
\(501\) −3.38273 1.95302i −0.151129 0.0872546i
\(502\) 0 0
\(503\) 35.6208 + 20.5657i 1.58825 + 0.916978i 0.993595 + 0.112999i \(0.0360456\pi\)
0.594657 + 0.803979i \(0.297288\pi\)
\(504\) 0 0
\(505\) −20.8917 5.87928i −0.929670 0.261625i
\(506\) 0 0
\(507\) 2.44098 + 1.18677i 0.108408 + 0.0527061i
\(508\) 0 0
\(509\) 22.3434 12.9000i 0.990355 0.571782i 0.0849747 0.996383i \(-0.472919\pi\)
0.905380 + 0.424601i \(0.139586\pi\)
\(510\) 0 0
\(511\) 11.0116 19.0727i 0.487126 0.843726i
\(512\) 0 0
\(513\) −4.67665 + 8.10020i −0.206479 + 0.357633i
\(514\) 0 0
\(515\) −8.37240 8.58475i −0.368932 0.378289i
\(516\) 0 0
\(517\) 4.00339 2.31136i 0.176069 0.101654i
\(518\) 0 0
\(519\) 3.69487 0.162187
\(520\) 0 0
\(521\) 26.1632 1.14623 0.573116 0.819474i \(-0.305734\pi\)
0.573116 + 0.819474i \(0.305734\pi\)
\(522\) 0 0
\(523\) 18.3510 10.5949i 0.802433 0.463285i −0.0418883 0.999122i \(-0.513337\pi\)
0.844321 + 0.535838i \(0.180004\pi\)
\(524\) 0 0
\(525\) 3.60853 + 0.0903947i 0.157489 + 0.00394515i
\(526\) 0 0
\(527\) −1.19993 + 2.07834i −0.0522698 + 0.0905340i
\(528\) 0 0
\(529\) −8.68504 + 15.0429i −0.377610 + 0.654040i
\(530\) 0 0
\(531\) 12.4291 7.17592i 0.539375 0.311408i
\(532\) 0 0
\(533\) 26.3344 0.936126i 1.14067 0.0405481i
\(534\) 0 0
\(535\) 9.54100 33.9035i 0.412493 1.46577i
\(536\) 0 0
\(537\) −1.52030 0.877748i −0.0656060 0.0378776i
\(538\) 0 0
\(539\) −3.09881 1.78910i −0.133475 0.0770619i
\(540\) 0 0
\(541\) 25.1921i 1.08309i −0.840670 0.541547i \(-0.817839\pi\)
0.840670 0.541547i \(-0.182161\pi\)
\(542\) 0 0
\(543\) 3.00420 1.73447i 0.128922 0.0744334i
\(544\) 0 0
\(545\) −22.6188 23.1925i −0.968883 0.993458i
\(546\) 0 0
\(547\) 22.4525i 0.959999i 0.877269 + 0.479999i \(0.159363\pi\)
−0.877269 + 0.479999i \(0.840637\pi\)
\(548\) 0 0
\(549\) 7.93000 + 13.7352i 0.338444 + 0.586203i
\(550\) 0 0
\(551\) 55.3904i 2.35971i
\(552\) 0 0
\(553\) −9.00211 + 15.5921i −0.382808 + 0.663044i
\(554\) 0 0
\(555\) −3.04516 + 0.775213i −0.129260 + 0.0329059i
\(556\) 0 0
\(557\) −6.72965 11.6561i −0.285144 0.493885i 0.687500 0.726185i \(-0.258708\pi\)
−0.972644 + 0.232300i \(0.925375\pi\)
\(558\) 0 0
\(559\) −15.5932 24.9197i −0.659524 1.05399i
\(560\) 0 0
\(561\) 0.468644 0.270572i 0.0197862 0.0114235i
\(562\) 0 0
\(563\) −38.8796 22.4472i −1.63858 0.946035i −0.981323 0.192368i \(-0.938383\pi\)
−0.657257 0.753666i \(-0.728283\pi\)
\(564\) 0 0
\(565\) 6.87496 1.75017i 0.289232 0.0736302i
\(566\) 0 0
\(567\) 29.7703 1.25023
\(568\) 0 0
\(569\) −9.39931 16.2801i −0.394040 0.682497i 0.598938 0.800795i \(-0.295589\pi\)
−0.992978 + 0.118298i \(0.962256\pi\)
\(570\) 0 0
\(571\) −8.79062 −0.367876 −0.183938 0.982938i \(-0.558885\pi\)
−0.183938 + 0.982938i \(0.558885\pi\)
\(572\) 0 0
\(573\) 3.73080i 0.155856i
\(574\) 0 0
\(575\) 5.67271 + 10.4196i 0.236568 + 0.434528i
\(576\) 0 0
\(577\) 24.2751 1.01059 0.505293 0.862948i \(-0.331385\pi\)
0.505293 + 0.862948i \(0.331385\pi\)
\(578\) 0 0
\(579\) −1.30964 0.756122i −0.0544269 0.0314234i
\(580\) 0 0
\(581\) −23.1503 + 40.0976i −0.960438 + 1.66353i
\(582\) 0 0
\(583\) −4.23892 7.34203i −0.175558 0.304076i
\(584\) 0 0
\(585\) −5.63769 + 23.1590i −0.233090 + 0.957507i
\(586\) 0 0
\(587\) 11.5202 + 19.9535i 0.475489 + 0.823571i 0.999606 0.0280755i \(-0.00893788\pi\)
−0.524117 + 0.851646i \(0.675605\pi\)
\(588\) 0 0
\(589\) −2.51375 + 4.35394i −0.103577 + 0.179401i
\(590\) 0 0
\(591\) −1.93957 1.11981i −0.0797831 0.0460628i
\(592\) 0 0
\(593\) 27.4174 1.12590 0.562949 0.826491i \(-0.309667\pi\)
0.562949 + 0.826491i \(0.309667\pi\)
\(594\) 0 0
\(595\) 7.51977 26.7211i 0.308280 1.09546i
\(596\) 0 0
\(597\) 0.678635i 0.0277747i
\(598\) 0 0
\(599\) −8.02325 −0.327821 −0.163911 0.986475i \(-0.552411\pi\)
−0.163911 + 0.986475i \(0.552411\pi\)
\(600\) 0 0
\(601\) −5.18146 8.97455i −0.211356 0.366080i 0.740783 0.671744i \(-0.234455\pi\)
−0.952139 + 0.305665i \(0.901121\pi\)
\(602\) 0 0
\(603\) −46.1567 −1.87964
\(604\) 0 0
\(605\) −5.78059 22.7071i −0.235014 0.923175i
\(606\) 0 0
\(607\) 28.1239 + 16.2374i 1.14151 + 0.659054i 0.946805 0.321807i \(-0.104290\pi\)
0.194710 + 0.980861i \(0.437624\pi\)
\(608\) 0 0
\(609\) 4.60445 2.65838i 0.186582 0.107723i
\(610\) 0 0
\(611\) −20.3916 10.8261i −0.824957 0.437975i
\(612\) 0 0
\(613\) −17.8135 30.8539i −0.719482 1.24618i −0.961205 0.275833i \(-0.911046\pi\)
0.241724 0.970345i \(-0.422287\pi\)
\(614\) 0 0
\(615\) −0.841749 3.30653i −0.0339426 0.133332i
\(616\) 0 0
\(617\) −21.3902 + 37.0490i −0.861139 + 1.49154i 0.00969198 + 0.999953i \(0.496915\pi\)
−0.870831 + 0.491583i \(0.836418\pi\)
\(618\) 0 0
\(619\) 6.85102i 0.275366i 0.990476 + 0.137683i \(0.0439655\pi\)
−0.990476 + 0.137683i \(0.956035\pi\)
\(620\) 0 0
\(621\) −1.47537 2.55542i −0.0592047 0.102546i
\(622\) 0 0
\(623\) 16.7858i 0.672511i
\(624\) 0 0
\(625\) −24.9686 1.25173i −0.998746 0.0500691i
\(626\) 0 0
\(627\) 0.981766 0.566823i 0.0392080 0.0226367i
\(628\) 0 0
\(629\) 24.1648i 0.963515i
\(630\) 0 0
\(631\) 38.3170 + 22.1223i 1.52538 + 0.880677i 0.999547 + 0.0300867i \(0.00957833\pi\)
0.525829 + 0.850590i \(0.323755\pi\)
\(632\) 0 0
\(633\) −4.25412 2.45612i −0.169086 0.0976218i
\(634\) 0 0
\(635\) 0.931390 3.30965i 0.0369611 0.131339i
\(636\) 0 0
\(637\) 0.634856 + 17.8593i 0.0251539 + 0.707612i
\(638\) 0 0
\(639\) 12.1369 7.00727i 0.480130 0.277203i
\(640\) 0 0
\(641\) 15.5706 26.9691i 0.615002 1.06521i −0.375382 0.926870i \(-0.622489\pi\)
0.990384 0.138344i \(-0.0441781\pi\)
\(642\) 0 0
\(643\) 4.83855 8.38061i 0.190814 0.330499i −0.754706 0.656063i \(-0.772221\pi\)
0.945520 + 0.325564i \(0.105554\pi\)
\(644\) 0 0
\(645\) −2.72494 + 2.65754i −0.107295 + 0.104640i
\(646\) 0 0
\(647\) 19.6951 11.3710i 0.774296 0.447040i −0.0601089 0.998192i \(-0.519145\pi\)
0.834405 + 0.551152i \(0.185811\pi\)
\(648\) 0 0
\(649\) −3.50461 −0.137568
\(650\) 0 0
\(651\) −0.482574 −0.0189136
\(652\) 0 0
\(653\) 15.5155 8.95789i 0.607169 0.350549i −0.164688 0.986346i \(-0.552662\pi\)
0.771857 + 0.635796i \(0.219328\pi\)
\(654\) 0 0
\(655\) −10.3281 + 10.0727i −0.403554 + 0.393571i
\(656\) 0 0
\(657\) 9.41490 16.3071i 0.367310 0.636200i
\(658\) 0 0
\(659\) 10.2041 17.6740i 0.397495 0.688482i −0.595921 0.803043i \(-0.703213\pi\)
0.993416 + 0.114561i \(0.0365461\pi\)
\(660\) 0 0
\(661\) −35.0818 + 20.2545i −1.36452 + 0.787808i −0.990222 0.139499i \(-0.955451\pi\)
−0.374302 + 0.927307i \(0.622118\pi\)
\(662\) 0 0
\(663\) −2.38708 1.26732i −0.0927064 0.0492185i
\(664\) 0 0
\(665\) 15.7532 55.9783i 0.610884 2.17074i
\(666\) 0 0
\(667\) 15.1332 + 8.73718i 0.585962 + 0.338305i
\(668\) 0 0
\(669\) 2.27598 + 1.31404i 0.0879945 + 0.0508036i
\(670\) 0 0
\(671\) 3.87289i 0.149511i
\(672\) 0 0
\(673\) 18.6979 10.7952i 0.720749 0.416125i −0.0942791 0.995546i \(-0.530055\pi\)
0.815028 + 0.579421i \(0.196721\pi\)
\(674\) 0 0
\(675\) 6.21605 + 0.155714i 0.239256 + 0.00599343i
\(676\) 0 0
\(677\) 36.7466i 1.41229i 0.708068 + 0.706144i \(0.249567\pi\)
−0.708068 + 0.706144i \(0.750433\pi\)
\(678\) 0 0
\(679\) 6.34282 + 10.9861i 0.243415 + 0.421608i
\(680\) 0 0
\(681\) 1.76245i 0.0675371i
\(682\) 0 0
\(683\) 16.9494 29.3573i 0.648552 1.12332i −0.334917 0.942248i \(-0.608708\pi\)
0.983469 0.181077i \(-0.0579583\pi\)
\(684\) 0 0
\(685\) −5.09900 20.0297i −0.194823 0.765296i
\(686\) 0 0
\(687\) −0.862808 1.49443i −0.0329182 0.0570160i
\(688\) 0 0
\(689\) −19.8544 + 37.3973i −0.756394 + 1.42472i
\(690\) 0 0
\(691\) −40.6461 + 23.4670i −1.54625 + 0.892727i −0.547826 + 0.836593i \(0.684544\pi\)
−0.998423 + 0.0561347i \(0.982122\pi\)
\(692\) 0 0
\(693\) −6.39135 3.69005i −0.242787 0.140173i
\(694\) 0 0
\(695\) 9.25265 + 36.3459i 0.350973 + 1.37868i
\(696\) 0 0
\(697\) −26.2389 −0.993869
\(698\) 0 0
\(699\) −0.554368 0.960194i −0.0209681 0.0363179i
\(700\) 0 0
\(701\) 28.1412 1.06288 0.531439 0.847096i \(-0.321651\pi\)
0.531439 + 0.847096i \(0.321651\pi\)
\(702\) 0 0
\(703\) 50.6231i 1.90929i
\(704\) 0 0
\(705\) −0.809808 + 2.87761i −0.0304991 + 0.108377i
\(706\) 0 0
\(707\) −33.5614 −1.26221
\(708\) 0 0
\(709\) 26.5939 + 15.3540i 0.998753 + 0.576630i 0.907879 0.419232i \(-0.137701\pi\)
0.0908741 + 0.995862i \(0.471034\pi\)
\(710\) 0 0
\(711\) −7.69677 + 13.3312i −0.288651 + 0.499959i
\(712\) 0 0
\(713\) −0.793028 1.37356i −0.0296991 0.0514404i
\(714\) 0 0
\(715\) 4.01987 4.20925i 0.150335 0.157417i
\(716\) 0 0
\(717\) 0.432959 + 0.749907i 0.0161692 + 0.0280058i
\(718\) 0 0
\(719\) 24.4815 42.4033i 0.913007 1.58138i 0.103215 0.994659i \(-0.467087\pi\)
0.809793 0.586716i \(-0.199580\pi\)
\(720\) 0 0
\(721\) −16.0590 9.27166i −0.598068 0.345294i
\(722\) 0 0
\(723\) −0.353918 −0.0131623
\(724\) 0 0
\(725\) −32.3408 + 17.6072i −1.20111 + 0.653914i
\(726\) 0 0
\(727\) 17.7593i 0.658655i 0.944216 + 0.329328i \(0.106822\pi\)
−0.944216 + 0.329328i \(0.893178\pi\)
\(728\) 0 0
\(729\) 24.6745 0.913871
\(730\) 0 0
\(731\) 14.6356 + 25.3495i 0.541316 + 0.937587i
\(732\) 0 0
\(733\) 11.4924 0.424481 0.212241 0.977217i \(-0.431924\pi\)
0.212241 + 0.977217i \(0.431924\pi\)
\(734\) 0 0
\(735\) 2.24240 0.570852i 0.0827122 0.0210562i
\(736\) 0 0
\(737\) 9.76107 + 5.63555i 0.359553 + 0.207588i
\(738\) 0 0
\(739\) −44.6663 + 25.7881i −1.64308 + 0.948631i −0.663347 + 0.748312i \(0.730865\pi\)
−0.979731 + 0.200320i \(0.935802\pi\)
\(740\) 0 0
\(741\) −5.00071 2.65491i −0.183706 0.0975306i
\(742\) 0 0
\(743\) −6.69913 11.6032i −0.245767 0.425681i 0.716580 0.697505i \(-0.245707\pi\)
−0.962347 + 0.271824i \(0.912373\pi\)
\(744\) 0 0
\(745\) −5.43357 + 1.38323i −0.199071 + 0.0506777i
\(746\) 0 0
\(747\) −19.7935 + 34.2833i −0.724205 + 1.25436i
\(748\) 0 0
\(749\) 54.4640i 1.99007i
\(750\) 0 0
\(751\) 23.7548 + 41.1445i 0.866825 + 1.50138i 0.865224 + 0.501386i \(0.167176\pi\)
0.00160088 + 0.999999i \(0.499490\pi\)
\(752\) 0 0
\(753\) 4.11993i 0.150138i
\(754\) 0 0
\(755\) −17.2106 17.6471i −0.626358 0.642245i
\(756\) 0 0
\(757\) 9.27646 5.35576i 0.337158 0.194659i −0.321856 0.946789i \(-0.604307\pi\)
0.659015 + 0.752130i \(0.270973\pi\)
\(758\) 0 0
\(759\) 0.357639i 0.0129815i
\(760\) 0 0
\(761\) 27.4754 + 15.8629i 0.995982 + 0.575030i 0.907057 0.421008i \(-0.138324\pi\)
0.0889247 + 0.996038i \(0.471657\pi\)
\(762\) 0 0
\(763\) −43.3848 25.0482i −1.57064 0.906807i
\(764\) 0 0
\(765\) 6.42937 22.8464i 0.232454 0.826015i
\(766\) 0 0
\(767\) 9.28451 + 14.8376i 0.335244 + 0.535756i
\(768\) 0 0
\(769\) 10.0143 5.78174i 0.361124 0.208495i −0.308450 0.951241i \(-0.599810\pi\)
0.669574 + 0.742746i \(0.266477\pi\)
\(770\) 0 0
\(771\) 1.23231 2.13442i 0.0443805 0.0768693i
\(772\) 0 0
\(773\) −13.5093 + 23.3988i −0.485895 + 0.841595i −0.999869 0.0162108i \(-0.994840\pi\)
0.513973 + 0.857806i \(0.328173\pi\)
\(774\) 0 0
\(775\) 3.34119 + 0.0836977i 0.120019 + 0.00300651i
\(776\) 0 0
\(777\) −4.20816 + 2.42958i −0.150967 + 0.0871607i
\(778\) 0 0
\(779\) −54.9681 −1.96944
\(780\) 0 0
\(781\) −3.42224 −0.122457
\(782\) 0 0
\(783\) 7.93162 4.57932i 0.283453 0.163652i
\(784\) 0 0
\(785\) −1.47770 1.51518i −0.0527413 0.0540790i
\(786\) 0 0
\(787\) 4.20573 7.28453i 0.149918 0.259666i −0.781279 0.624182i \(-0.785432\pi\)
0.931197 + 0.364516i \(0.118766\pi\)
\(788\) 0 0
\(789\) 1.48281 2.56831i 0.0527896 0.0914342i
\(790\) 0 0
\(791\) 9.50061 5.48518i 0.337803 0.195031i
\(792\) 0 0
\(793\) −16.3969 + 10.2602i −0.582270 + 0.364350i
\(794\) 0 0