Properties

Label 1008.2.r.k.673.2
Level 1008
Weight 2
Character 1008.673
Analytic conductor 8.049
Analytic rank 0
Dimension 6
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 673.2
Root \(0.500000 + 1.41036i\) of defining polynomial
Character \(\chi\) \(=\) 1008.673
Dual form 1008.2.r.k.337.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.619562 - 1.61745i) q^{3} +(-0.590972 - 1.02359i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-2.23229 - 2.00422i) q^{9} +O(q^{10})\) \(q+(0.619562 - 1.61745i) q^{3} +(-0.590972 - 1.02359i) q^{5} +(-0.500000 + 0.866025i) q^{7} +(-2.23229 - 2.00422i) q^{9} +(-1.85185 + 3.20750i) q^{11} +(-0.500000 - 0.866025i) q^{13} +(-2.02175 + 0.321688i) q^{15} -6.94282 q^{17} -1.94282 q^{19} +(1.09097 + 1.34528i) q^{21} +(-2.80150 - 4.85235i) q^{23} +(1.80150 - 3.12030i) q^{25} +(-4.62476 + 2.36887i) q^{27} +(-0.119562 + 0.207087i) q^{29} +(0.830095 + 1.43777i) q^{31} +(4.04063 + 4.98251i) q^{33} +1.18194 q^{35} -9.54583 q^{37} +(-1.71053 + 0.272169i) q^{39} +(5.09097 + 8.81782i) q^{41} +(1.11273 - 1.92730i) q^{43} +(-0.732287 + 3.46939i) q^{45} +(2.91423 - 5.04759i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-4.30150 + 11.2297i) q^{51} -11.6030 q^{53} +4.37756 q^{55} +(-1.20370 + 3.14241i) q^{57} +(1.30150 + 2.25427i) q^{59} +(3.80150 - 6.58440i) q^{61} +(2.85185 - 0.931107i) q^{63} +(-0.590972 + 1.02359i) q^{65} +(1.75404 + 3.03809i) q^{67} +(-9.58414 + 1.52496i) q^{69} -8.60301 q^{71} +15.1488 q^{73} +(-3.93078 - 4.84706i) q^{75} +(-1.85185 - 3.20750i) q^{77} +(3.68878 - 6.38915i) q^{79} +(0.966208 + 8.94799i) q^{81} +(-3.47141 + 6.01266i) q^{83} +(4.10301 + 7.10662i) q^{85} +(0.260877 + 0.321688i) q^{87} +2.74720 q^{89} +1.00000 q^{91} +(2.83981 - 0.451852i) q^{93} +(1.14815 + 1.98866i) q^{95} +(-3.58414 + 6.20790i) q^{97} +(10.5624 - 3.44854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 4q^{3} + 5q^{5} - 3q^{7} - 4q^{9} + O(q^{10}) \) \( 6q + 4q^{3} + 5q^{5} - 3q^{7} - 4q^{9} - 2q^{11} - 3q^{13} - 11q^{15} - 24q^{17} + 6q^{19} - 2q^{21} - 6q^{25} + 7q^{27} - q^{29} - 3q^{31} + 8q^{33} - 10q^{35} - 6q^{37} - 2q^{39} + 22q^{41} - 3q^{43} + 5q^{45} - 9q^{47} - 3q^{49} - 9q^{51} - 36q^{53} + 12q^{55} + 11q^{57} - 9q^{59} + 6q^{61} + 8q^{63} + 5q^{65} - 39q^{69} - 18q^{71} + 6q^{73} - 31q^{75} - 2q^{77} + 15q^{79} + 32q^{81} - 12q^{83} - 9q^{85} + q^{87} - 4q^{89} + 6q^{91} + 33q^{93} + 16q^{95} - 3q^{97} + 46q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.619562 1.61745i 0.357704 0.933835i
\(4\) 0 0
\(5\) −0.590972 1.02359i −0.264291 0.457765i 0.703087 0.711104i \(-0.251804\pi\)
−0.967378 + 0.253339i \(0.918471\pi\)
\(6\) 0 0
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) 0 0
\(9\) −2.23229 2.00422i −0.744096 0.668073i
\(10\) 0 0
\(11\) −1.85185 + 3.20750i −0.558353 + 0.967096i 0.439281 + 0.898350i \(0.355233\pi\)
−0.997634 + 0.0687465i \(0.978100\pi\)
\(12\) 0 0
\(13\) −0.500000 0.866025i −0.138675 0.240192i 0.788320 0.615265i \(-0.210951\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) 0 0
\(15\) −2.02175 + 0.321688i −0.522014 + 0.0830595i
\(16\) 0 0
\(17\) −6.94282 −1.68388 −0.841941 0.539570i \(-0.818587\pi\)
−0.841941 + 0.539570i \(0.818587\pi\)
\(18\) 0 0
\(19\) −1.94282 −0.445713 −0.222857 0.974851i \(-0.571538\pi\)
−0.222857 + 0.974851i \(0.571538\pi\)
\(20\) 0 0
\(21\) 1.09097 + 1.34528i 0.238070 + 0.293564i
\(22\) 0 0
\(23\) −2.80150 4.85235i −0.584154 1.01178i −0.994980 0.100071i \(-0.968093\pi\)
0.410826 0.911714i \(-0.365240\pi\)
\(24\) 0 0
\(25\) 1.80150 3.12030i 0.360301 0.624060i
\(26\) 0 0
\(27\) −4.62476 + 2.36887i −0.890036 + 0.455890i
\(28\) 0 0
\(29\) −0.119562 + 0.207087i −0.0222020 + 0.0384551i −0.876913 0.480649i \(-0.840401\pi\)
0.854711 + 0.519104i \(0.173734\pi\)
\(30\) 0 0
\(31\) 0.830095 + 1.43777i 0.149089 + 0.258231i 0.930891 0.365297i \(-0.119032\pi\)
−0.781802 + 0.623527i \(0.785699\pi\)
\(32\) 0 0
\(33\) 4.04063 + 4.98251i 0.703383 + 0.867344i
\(34\) 0 0
\(35\) 1.18194 0.199785
\(36\) 0 0
\(37\) −9.54583 −1.56932 −0.784662 0.619923i \(-0.787164\pi\)
−0.784662 + 0.619923i \(0.787164\pi\)
\(38\) 0 0
\(39\) −1.71053 + 0.272169i −0.273905 + 0.0435819i
\(40\) 0 0
\(41\) 5.09097 + 8.81782i 0.795076 + 1.37711i 0.922791 + 0.385301i \(0.125903\pi\)
−0.127715 + 0.991811i \(0.540764\pi\)
\(42\) 0 0
\(43\) 1.11273 1.92730i 0.169689 0.293910i −0.768622 0.639704i \(-0.779057\pi\)
0.938311 + 0.345794i \(0.112390\pi\)
\(44\) 0 0
\(45\) −0.732287 + 3.46939i −0.109163 + 0.517186i
\(46\) 0 0
\(47\) 2.91423 5.04759i 0.425084 0.736267i −0.571344 0.820711i \(-0.693578\pi\)
0.996428 + 0.0844432i \(0.0269112\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 0 0
\(51\) −4.30150 + 11.2297i −0.602331 + 1.57247i
\(52\) 0 0
\(53\) −11.6030 −1.59380 −0.796898 0.604114i \(-0.793527\pi\)
−0.796898 + 0.604114i \(0.793527\pi\)
\(54\) 0 0
\(55\) 4.37756 0.590270
\(56\) 0 0
\(57\) −1.20370 + 3.14241i −0.159434 + 0.416223i
\(58\) 0 0
\(59\) 1.30150 + 2.25427i 0.169442 + 0.293481i 0.938224 0.346029i \(-0.112470\pi\)
−0.768782 + 0.639511i \(0.779137\pi\)
\(60\) 0 0
\(61\) 3.80150 6.58440i 0.486733 0.843046i −0.513151 0.858298i \(-0.671522\pi\)
0.999884 + 0.0152524i \(0.00485519\pi\)
\(62\) 0 0
\(63\) 2.85185 0.931107i 0.359299 0.117308i
\(64\) 0 0
\(65\) −0.590972 + 1.02359i −0.0733010 + 0.126961i
\(66\) 0 0
\(67\) 1.75404 + 3.03809i 0.214290 + 0.371161i 0.953053 0.302804i \(-0.0979229\pi\)
−0.738763 + 0.673966i \(0.764590\pi\)
\(68\) 0 0
\(69\) −9.58414 + 1.52496i −1.15379 + 0.183584i
\(70\) 0 0
\(71\) −8.60301 −1.02099 −0.510495 0.859881i \(-0.670538\pi\)
−0.510495 + 0.859881i \(0.670538\pi\)
\(72\) 0 0
\(73\) 15.1488 1.77304 0.886519 0.462693i \(-0.153117\pi\)
0.886519 + 0.462693i \(0.153117\pi\)
\(74\) 0 0
\(75\) −3.93078 4.84706i −0.453888 0.559690i
\(76\) 0 0
\(77\) −1.85185 3.20750i −0.211038 0.365528i
\(78\) 0 0
\(79\) 3.68878 6.38915i 0.415020 0.718836i −0.580410 0.814324i \(-0.697108\pi\)
0.995431 + 0.0954881i \(0.0304412\pi\)
\(80\) 0 0
\(81\) 0.966208 + 8.94799i 0.107356 + 0.994221i
\(82\) 0 0
\(83\) −3.47141 + 6.01266i −0.381037 + 0.659975i −0.991211 0.132292i \(-0.957766\pi\)
0.610174 + 0.792267i \(0.291100\pi\)
\(84\) 0 0
\(85\) 4.10301 + 7.10662i 0.445034 + 0.770821i
\(86\) 0 0
\(87\) 0.260877 + 0.321688i 0.0279689 + 0.0344886i
\(88\) 0 0
\(89\) 2.74720 0.291203 0.145602 0.989343i \(-0.453488\pi\)
0.145602 + 0.989343i \(0.453488\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 2.83981 0.451852i 0.294475 0.0468548i
\(94\) 0 0
\(95\) 1.14815 + 1.98866i 0.117798 + 0.204032i
\(96\) 0 0
\(97\) −3.58414 + 6.20790i −0.363914 + 0.630317i −0.988601 0.150558i \(-0.951893\pi\)
0.624687 + 0.780875i \(0.285226\pi\)
\(98\) 0 0
\(99\) 10.5624 3.44854i 1.06156 0.346591i
\(100\) 0 0
\(101\) 6.39248 11.0721i 0.636075 1.10171i −0.350211 0.936671i \(-0.613890\pi\)
0.986286 0.165044i \(-0.0527765\pi\)
\(102\) 0 0
\(103\) −2.19850 3.80791i −0.216624 0.375204i 0.737150 0.675730i \(-0.236171\pi\)
−0.953774 + 0.300526i \(0.902838\pi\)
\(104\) 0 0
\(105\) 0.732287 1.91173i 0.0714639 0.186566i
\(106\) 0 0
\(107\) −13.7278 −1.32711 −0.663557 0.748126i \(-0.730954\pi\)
−0.663557 + 0.748126i \(0.730954\pi\)
\(108\) 0 0
\(109\) 1.26320 0.120993 0.0604963 0.998168i \(-0.480732\pi\)
0.0604963 + 0.998168i \(0.480732\pi\)
\(110\) 0 0
\(111\) −5.91423 + 15.4399i −0.561354 + 1.46549i
\(112\) 0 0
\(113\) −6.08126 10.5330i −0.572076 0.990866i −0.996353 0.0853326i \(-0.972805\pi\)
0.424276 0.905533i \(-0.360529\pi\)
\(114\) 0 0
\(115\) −3.31122 + 5.73520i −0.308773 + 0.534810i
\(116\) 0 0
\(117\) −0.619562 + 2.93533i −0.0572785 + 0.271371i
\(118\) 0 0
\(119\) 3.47141 6.01266i 0.318224 0.551180i
\(120\) 0 0
\(121\) −1.35868 2.35331i −0.123517 0.213937i
\(122\) 0 0
\(123\) 17.4166 2.77121i 1.57040 0.249871i
\(124\) 0 0
\(125\) −10.1683 −0.909478
\(126\) 0 0
\(127\) −1.33981 −0.118889 −0.0594445 0.998232i \(-0.518933\pi\)
−0.0594445 + 0.998232i \(0.518933\pi\)
\(128\) 0 0
\(129\) −2.42790 2.99386i −0.213765 0.263594i
\(130\) 0 0
\(131\) −2.48345 4.30146i −0.216980 0.375820i 0.736903 0.675998i \(-0.236287\pi\)
−0.953883 + 0.300178i \(0.902954\pi\)
\(132\) 0 0
\(133\) 0.971410 1.68253i 0.0842319 0.145894i
\(134\) 0 0
\(135\) 5.15787 + 3.33394i 0.443918 + 0.286940i
\(136\) 0 0
\(137\) 2.16991 3.75839i 0.185387 0.321101i −0.758320 0.651883i \(-0.773979\pi\)
0.943707 + 0.330782i \(0.107313\pi\)
\(138\) 0 0
\(139\) 1.97141 + 3.41458i 0.167213 + 0.289621i 0.937439 0.348150i \(-0.113190\pi\)
−0.770226 + 0.637771i \(0.779857\pi\)
\(140\) 0 0
\(141\) −6.35868 7.84092i −0.535498 0.660324i
\(142\) 0 0
\(143\) 3.70370 0.309719
\(144\) 0 0
\(145\) 0.282630 0.0234712
\(146\) 0 0
\(147\) −1.71053 + 0.272169i −0.141082 + 0.0224481i
\(148\) 0 0
\(149\) −5.55555 9.62249i −0.455128 0.788305i 0.543568 0.839365i \(-0.317073\pi\)
−0.998696 + 0.0510606i \(0.983740\pi\)
\(150\) 0 0
\(151\) 6.96169 12.0580i 0.566535 0.981267i −0.430370 0.902652i \(-0.641617\pi\)
0.996905 0.0786145i \(-0.0250496\pi\)
\(152\) 0 0
\(153\) 15.4984 + 13.9149i 1.25297 + 1.12496i
\(154\) 0 0
\(155\) 0.981125 1.69936i 0.0788059 0.136496i
\(156\) 0 0
\(157\) −0.0285900 0.0495193i −0.00228173 0.00395207i 0.864882 0.501975i \(-0.167393\pi\)
−0.867164 + 0.498023i \(0.834060\pi\)
\(158\) 0 0
\(159\) −7.18878 + 18.7673i −0.570107 + 1.48834i
\(160\) 0 0
\(161\) 5.60301 0.441579
\(162\) 0 0
\(163\) 1.50808 0.118122 0.0590610 0.998254i \(-0.481189\pi\)
0.0590610 + 0.998254i \(0.481189\pi\)
\(164\) 0 0
\(165\) 2.71217 7.08048i 0.211142 0.551215i
\(166\) 0 0
\(167\) −7.34213 12.7169i −0.568151 0.984067i −0.996749 0.0805714i \(-0.974325\pi\)
0.428598 0.903496i \(-0.359008\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) 0 0
\(171\) 4.33693 + 3.89384i 0.331653 + 0.297769i
\(172\) 0 0
\(173\) −0.126398 + 0.218928i −0.00960987 + 0.0166448i −0.870790 0.491655i \(-0.836392\pi\)
0.861180 + 0.508299i \(0.169726\pi\)
\(174\) 0 0
\(175\) 1.80150 + 3.12030i 0.136181 + 0.235872i
\(176\) 0 0
\(177\) 4.45254 0.708458i 0.334673 0.0532510i
\(178\) 0 0
\(179\) −14.1923 −1.06079 −0.530393 0.847752i \(-0.677956\pi\)
−0.530393 + 0.847752i \(0.677956\pi\)
\(180\) 0 0
\(181\) −1.43147 −0.106400 −0.0532002 0.998584i \(-0.516942\pi\)
−0.0532002 + 0.998584i \(0.516942\pi\)
\(182\) 0 0
\(183\) −8.29467 10.2282i −0.613160 0.756089i
\(184\) 0 0
\(185\) 5.64132 + 9.77104i 0.414758 + 0.718381i
\(186\) 0 0
\(187\) 12.8571 22.2691i 0.940201 1.62848i
\(188\) 0 0
\(189\) 0.260877 5.18960i 0.0189760 0.377488i
\(190\) 0 0
\(191\) 7.53379 13.0489i 0.545126 0.944186i −0.453473 0.891270i \(-0.649815\pi\)
0.998599 0.0529159i \(-0.0168515\pi\)
\(192\) 0 0
\(193\) 3.92395 + 6.79647i 0.282452 + 0.489221i 0.971988 0.235030i \(-0.0755190\pi\)
−0.689536 + 0.724251i \(0.742186\pi\)
\(194\) 0 0
\(195\) 1.28947 + 1.59005i 0.0923406 + 0.113866i
\(196\) 0 0
\(197\) 6.69002 0.476644 0.238322 0.971186i \(-0.423403\pi\)
0.238322 + 0.971186i \(0.423403\pi\)
\(198\) 0 0
\(199\) 19.9396 1.41348 0.706739 0.707475i \(-0.250166\pi\)
0.706739 + 0.707475i \(0.250166\pi\)
\(200\) 0 0
\(201\) 6.00069 0.954790i 0.423256 0.0673457i
\(202\) 0 0
\(203\) −0.119562 0.207087i −0.00839158 0.0145346i
\(204\) 0 0
\(205\) 6.01724 10.4222i 0.420262 0.727916i
\(206\) 0 0
\(207\) −3.47141 + 16.4467i −0.241280 + 1.14312i
\(208\) 0 0
\(209\) 3.59781 6.23159i 0.248866 0.431048i
\(210\) 0 0
\(211\) −9.04583 15.6678i −0.622741 1.07862i −0.988973 0.148095i \(-0.952686\pi\)
0.366233 0.930523i \(-0.380647\pi\)
\(212\) 0 0
\(213\) −5.33009 + 13.9149i −0.365212 + 0.953436i
\(214\) 0 0
\(215\) −2.63036 −0.179389
\(216\) 0 0
\(217\) −1.66019 −0.112701
\(218\) 0 0
\(219\) 9.38564 24.5025i 0.634223 1.65572i
\(220\) 0 0
\(221\) 3.47141 + 6.01266i 0.233512 + 0.404455i
\(222\) 0 0
\(223\) −11.3285 + 19.6215i −0.758610 + 1.31395i 0.184950 + 0.982748i \(0.440788\pi\)
−0.943560 + 0.331203i \(0.892546\pi\)
\(224\) 0 0
\(225\) −10.2752 + 3.35479i −0.685016 + 0.223653i
\(226\) 0 0
\(227\) −2.64132 + 4.57489i −0.175310 + 0.303646i −0.940269 0.340433i \(-0.889426\pi\)
0.764958 + 0.644080i \(0.222760\pi\)
\(228\) 0 0
\(229\) −9.66827 16.7459i −0.638897 1.10660i −0.985675 0.168655i \(-0.946058\pi\)
0.346778 0.937947i \(-0.387276\pi\)
\(230\) 0 0
\(231\) −6.33530 + 1.00803i −0.416832 + 0.0663235i
\(232\) 0 0
\(233\) −16.9806 −1.11243 −0.556217 0.831037i \(-0.687748\pi\)
−0.556217 + 0.831037i \(0.687748\pi\)
\(234\) 0 0
\(235\) −6.88891 −0.449383
\(236\) 0 0
\(237\) −8.04871 9.92489i −0.522820 0.644691i
\(238\) 0 0
\(239\) 8.44282 + 14.6234i 0.546121 + 0.945909i 0.998535 + 0.0541011i \(0.0172293\pi\)
−0.452415 + 0.891808i \(0.649437\pi\)
\(240\) 0 0
\(241\) −13.5728 + 23.5088i −0.874300 + 1.51433i −0.0167933 + 0.999859i \(0.505346\pi\)
−0.857507 + 0.514473i \(0.827988\pi\)
\(242\) 0 0
\(243\) 15.0715 + 3.98104i 0.966840 + 0.255384i
\(244\) 0 0
\(245\) −0.590972 + 1.02359i −0.0377558 + 0.0653950i
\(246\) 0 0
\(247\) 0.971410 + 1.68253i 0.0618093 + 0.107057i
\(248\) 0 0
\(249\) 7.57442 + 9.34004i 0.480009 + 0.591901i
\(250\) 0 0
\(251\) 19.0780 1.20419 0.602096 0.798424i \(-0.294332\pi\)
0.602096 + 0.798424i \(0.294332\pi\)
\(252\) 0 0
\(253\) 20.7518 1.30466
\(254\) 0 0
\(255\) 14.0367 2.23342i 0.879010 0.139862i
\(256\) 0 0
\(257\) 7.42107 + 12.8537i 0.462913 + 0.801790i 0.999105 0.0423070i \(-0.0134707\pi\)
−0.536191 + 0.844097i \(0.680137\pi\)
\(258\) 0 0
\(259\) 4.77292 8.26693i 0.296575 0.513682i
\(260\) 0 0
\(261\) 0.681943 0.222649i 0.0422112 0.0137817i
\(262\) 0 0
\(263\) −3.87072 + 6.70429i −0.238679 + 0.413404i −0.960335 0.278847i \(-0.910048\pi\)
0.721656 + 0.692251i \(0.243381\pi\)
\(264\) 0 0
\(265\) 6.85705 + 11.8768i 0.421225 + 0.729584i
\(266\) 0 0
\(267\) 1.70206 4.44346i 0.104165 0.271936i
\(268\) 0 0
\(269\) −1.51135 −0.0921486 −0.0460743 0.998938i \(-0.514671\pi\)
−0.0460743 + 0.998938i \(0.514671\pi\)
\(270\) 0 0
\(271\) 21.9806 1.33522 0.667612 0.744509i \(-0.267316\pi\)
0.667612 + 0.744509i \(0.267316\pi\)
\(272\) 0 0
\(273\) 0.619562 1.61745i 0.0374976 0.0978925i
\(274\) 0 0
\(275\) 6.67223 + 11.5566i 0.402350 + 0.696892i
\(276\) 0 0
\(277\) 5.41423 9.37772i 0.325310 0.563453i −0.656265 0.754530i \(-0.727865\pi\)
0.981575 + 0.191077i \(0.0611982\pi\)
\(278\) 0 0
\(279\) 1.02859 4.87320i 0.0615801 0.291751i
\(280\) 0 0
\(281\) 8.43831 14.6156i 0.503387 0.871892i −0.496605 0.867977i \(-0.665420\pi\)
0.999992 0.00391559i \(-0.00124638\pi\)
\(282\) 0 0
\(283\) −7.65856 13.2650i −0.455254 0.788523i 0.543449 0.839442i \(-0.317118\pi\)
−0.998703 + 0.0509194i \(0.983785\pi\)
\(284\) 0 0
\(285\) 3.92790 0.624982i 0.232669 0.0370207i
\(286\) 0 0
\(287\) −10.1819 −0.601021
\(288\) 0 0
\(289\) 31.2028 1.83546
\(290\) 0 0
\(291\) 7.82038 + 9.64334i 0.458439 + 0.565302i
\(292\) 0 0
\(293\) 4.68482 + 8.11435i 0.273690 + 0.474045i 0.969804 0.243886i \(-0.0784224\pi\)
−0.696114 + 0.717932i \(0.745089\pi\)
\(294\) 0 0
\(295\) 1.53831 2.66442i 0.0895636 0.155129i
\(296\) 0 0
\(297\) 0.966208 19.2207i 0.0560651 1.11530i
\(298\) 0 0
\(299\) −2.80150 + 4.85235i −0.162015 + 0.280619i
\(300\) 0 0
\(301\) 1.11273 + 1.92730i 0.0641364 + 0.111088i
\(302\) 0 0
\(303\) −13.9480 17.1994i −0.801293 0.988077i
\(304\) 0 0
\(305\) −8.98633 −0.514556
\(306\) 0 0
\(307\) −2.71410 −0.154902 −0.0774509 0.996996i \(-0.524678\pi\)
−0.0774509 + 0.996996i \(0.524678\pi\)
\(308\) 0 0
\(309\) −7.52120 + 1.19672i −0.427866 + 0.0680792i
\(310\) 0 0
\(311\) −6.99028 12.1075i −0.396383 0.686555i 0.596894 0.802320i \(-0.296401\pi\)
−0.993277 + 0.115765i \(0.963068\pi\)
\(312\) 0 0
\(313\) 9.52696 16.5012i 0.538495 0.932701i −0.460490 0.887665i \(-0.652326\pi\)
0.998985 0.0450364i \(-0.0143404\pi\)
\(314\) 0 0
\(315\) −2.63844 2.36887i −0.148659 0.133471i
\(316\) 0 0
\(317\) 2.00972 3.48093i 0.112877 0.195508i −0.804052 0.594559i \(-0.797327\pi\)
0.916929 + 0.399050i \(0.130660\pi\)
\(318\) 0 0
\(319\) −0.442820 0.766987i −0.0247932 0.0429430i
\(320\) 0 0
\(321\) −8.50520 + 22.2040i −0.474714 + 1.23931i
\(322\) 0 0
\(323\) 13.4887 0.750529
\(324\) 0 0
\(325\) −3.60301 −0.199859
\(326\) 0 0
\(327\) 0.782630 2.04316i 0.0432795 0.112987i
\(328\) 0 0
\(329\) 2.91423 + 5.04759i 0.160667 + 0.278283i
\(330\) 0 0
\(331\) −6.18878 + 10.7193i −0.340166 + 0.589185i −0.984463 0.175590i \(-0.943817\pi\)
0.644297 + 0.764775i \(0.277150\pi\)
\(332\) 0 0
\(333\) 21.3090 + 19.1319i 1.16773 + 1.04842i
\(334\) 0 0
\(335\) 2.07318 3.59085i 0.113270 0.196189i
\(336\) 0 0
\(337\) −6.12997 10.6174i −0.333920 0.578367i 0.649356 0.760484i \(-0.275038\pi\)
−0.983277 + 0.182117i \(0.941705\pi\)
\(338\) 0 0
\(339\) −20.8044 + 3.31026i −1.12994 + 0.179788i
\(340\) 0 0
\(341\) −6.14884 −0.332978
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 7.22489 + 8.90904i 0.388975 + 0.479647i
\(346\) 0 0
\(347\) 3.32489 + 5.75888i 0.178490 + 0.309153i 0.941363 0.337394i \(-0.109546\pi\)
−0.762874 + 0.646547i \(0.776212\pi\)
\(348\) 0 0
\(349\) −5.71737 + 9.90278i −0.306044 + 0.530083i −0.977493 0.210967i \(-0.932339\pi\)
0.671449 + 0.741050i \(0.265672\pi\)
\(350\) 0 0
\(351\) 4.36389 + 2.82073i 0.232927 + 0.150559i
\(352\) 0 0
\(353\) 11.0978 19.2220i 0.590677 1.02308i −0.403465 0.914995i \(-0.632194\pi\)
0.994141 0.108087i \(-0.0344725\pi\)
\(354\) 0 0
\(355\) 5.08414 + 8.80598i 0.269838 + 0.467373i
\(356\) 0 0
\(357\) −7.57442 9.34004i −0.400881 0.494328i
\(358\) 0 0
\(359\) 7.55623 0.398803 0.199401 0.979918i \(-0.436100\pi\)
0.199401 + 0.979918i \(0.436100\pi\)
\(360\) 0 0
\(361\) −15.2255 −0.801339
\(362\) 0 0
\(363\) −4.64815 + 0.739583i −0.243965 + 0.0388180i
\(364\) 0 0
\(365\) −8.95254 15.5062i −0.468597 0.811634i
\(366\) 0 0
\(367\) −9.26157 + 16.0415i −0.483450 + 0.837360i −0.999819 0.0190063i \(-0.993950\pi\)
0.516370 + 0.856366i \(0.327283\pi\)
\(368\) 0 0
\(369\) 6.30834 29.8873i 0.328399 1.55587i
\(370\) 0 0
\(371\) 5.80150 10.0485i 0.301199 0.521692i
\(372\) 0 0
\(373\) −7.83009 13.5621i −0.405427 0.702220i 0.588944 0.808174i \(-0.299544\pi\)
−0.994371 + 0.105954i \(0.966210\pi\)
\(374\) 0 0
\(375\) −6.29987 + 16.4467i −0.325324 + 0.849302i
\(376\) 0 0
\(377\) 0.239123 0.0123155
\(378\) 0 0
\(379\) −4.03775 −0.207405 −0.103703 0.994608i \(-0.533069\pi\)
−0.103703 + 0.994608i \(0.533069\pi\)
\(380\) 0 0
\(381\) −0.830095 + 2.16708i −0.0425271 + 0.111023i
\(382\) 0 0
\(383\) 0.112725 + 0.195246i 0.00575998 + 0.00997659i 0.868891 0.495003i \(-0.164833\pi\)
−0.863131 + 0.504980i \(0.831500\pi\)
\(384\) 0 0
\(385\) −2.18878 + 3.79108i −0.111551 + 0.193211i
\(386\) 0 0
\(387\) −6.34665 + 2.07213i −0.322618 + 0.105332i
\(388\) 0 0
\(389\) −12.6316 + 21.8786i −0.640448 + 1.10929i 0.344885 + 0.938645i \(0.387918\pi\)
−0.985333 + 0.170643i \(0.945416\pi\)
\(390\) 0 0
\(391\) 19.4503 + 33.6890i 0.983646 + 1.70373i
\(392\) 0 0
\(393\) −8.49604 + 1.35183i −0.428569 + 0.0681910i
\(394\) 0 0
\(395\) −8.71986 −0.438744
\(396\) 0 0
\(397\) −20.3009 −1.01888 −0.509438 0.860508i \(-0.670147\pi\)
−0.509438 + 0.860508i \(0.670147\pi\)
\(398\) 0 0
\(399\) −2.11956 2.61364i −0.106111 0.130846i
\(400\) 0 0
\(401\) 7.61273 + 13.1856i 0.380161 + 0.658459i 0.991085 0.133231i \(-0.0425351\pi\)
−0.610924 + 0.791689i \(0.709202\pi\)
\(402\) 0 0
\(403\) 0.830095 1.43777i 0.0413500 0.0716203i
\(404\) 0 0
\(405\) 8.58809 6.27701i 0.426746 0.311907i
\(406\) 0 0
\(407\) 17.6774 30.6182i 0.876238 1.51769i
\(408\) 0 0
\(409\) −0.828460 1.43494i −0.0409647 0.0709530i 0.844816 0.535057i \(-0.179710\pi\)
−0.885781 + 0.464104i \(0.846376\pi\)
\(410\) 0 0
\(411\) −4.73461 5.83826i −0.233541 0.287980i
\(412\) 0 0
\(413\) −2.60301 −0.128086
\(414\) 0 0
\(415\) 8.20602 0.402818
\(416\) 0 0
\(417\) 6.74433 1.07311i 0.330271 0.0525505i
\(418\) 0 0
\(419\) 16.6871 + 28.9030i 0.815220 + 1.41200i 0.909170 + 0.416426i \(0.136718\pi\)
−0.0939492 + 0.995577i \(0.529949\pi\)
\(420\) 0 0
\(421\) −9.12025 + 15.7967i −0.444494 + 0.769886i −0.998017 0.0629481i \(-0.979950\pi\)
0.553523 + 0.832834i \(0.313283\pi\)
\(422\) 0 0
\(423\) −16.6219 + 5.42692i −0.808184 + 0.263866i
\(424\) 0 0
\(425\) −12.5075 + 21.6637i −0.606704 + 1.05084i
\(426\) 0 0
\(427\) 3.80150 + 6.58440i 0.183968 + 0.318641i
\(428\) 0 0
\(429\) 2.29467 5.99054i 0.110788 0.289226i
\(430\) 0 0
\(431\) −29.2826 −1.41049 −0.705247 0.708961i \(-0.749164\pi\)
−0.705247 + 0.708961i \(0.749164\pi\)
\(432\) 0 0
\(433\) −12.2449 −0.588451 −0.294226 0.955736i \(-0.595062\pi\)
−0.294226 + 0.955736i \(0.595062\pi\)
\(434\) 0 0
\(435\) 0.175107 0.457140i 0.00839573 0.0219182i
\(436\) 0 0
\(437\) 5.44282 + 9.42724i 0.260365 + 0.450966i
\(438\) 0 0
\(439\) −2.41586 + 4.18440i −0.115303 + 0.199711i −0.917901 0.396810i \(-0.870117\pi\)
0.802598 + 0.596520i \(0.203451\pi\)
\(440\) 0 0
\(441\) −0.619562 + 2.93533i −0.0295029 + 0.139777i
\(442\) 0 0
\(443\) 0.622440 1.07810i 0.0295730 0.0512220i −0.850860 0.525392i \(-0.823919\pi\)
0.880433 + 0.474170i \(0.157252\pi\)
\(444\) 0 0
\(445\) −1.62352 2.81202i −0.0769622 0.133302i
\(446\) 0 0
\(447\) −19.0059 + 3.02409i −0.898948 + 0.143035i
\(448\) 0 0
\(449\) 8.82846 0.416641 0.208320 0.978061i \(-0.433200\pi\)
0.208320 + 0.978061i \(0.433200\pi\)
\(450\) 0 0
\(451\) −37.7108 −1.77573
\(452\) 0 0
\(453\) −15.1900 18.7309i −0.713690 0.880053i
\(454\) 0 0
\(455\) −0.590972 1.02359i −0.0277052 0.0479868i
\(456\) 0 0
\(457\) 5.25404 9.10026i 0.245774 0.425692i −0.716575 0.697510i \(-0.754291\pi\)
0.962349 + 0.271817i \(0.0876247\pi\)
\(458\) 0 0
\(459\) 32.1089 16.4467i 1.49872 0.767665i
\(460\) 0 0
\(461\) −11.2758 + 19.5302i −0.525166 + 0.909614i 0.474404 + 0.880307i \(0.342663\pi\)
−0.999570 + 0.0293073i \(0.990670\pi\)
\(462\) 0 0
\(463\) 5.19850 + 9.00406i 0.241595 + 0.418454i 0.961169 0.275962i \(-0.0889963\pi\)
−0.719574 + 0.694416i \(0.755663\pi\)
\(464\) 0 0
\(465\) −2.14076 2.63978i −0.0992753 0.122417i
\(466\) 0 0
\(467\) −13.3171 −0.616242 −0.308121 0.951347i \(-0.599700\pi\)
−0.308121 + 0.951347i \(0.599700\pi\)
\(468\) 0 0
\(469\) −3.50808 −0.161988
\(470\) 0 0
\(471\) −0.0978082 + 0.0155626i −0.00450676 + 0.000717086i
\(472\) 0 0
\(473\) 4.12120 + 7.13812i 0.189493 + 0.328211i
\(474\) 0 0
\(475\) −3.50000 + 6.06218i −0.160591 + 0.278152i
\(476\) 0 0
\(477\) 25.9012 + 23.2550i 1.18594 + 1.06477i
\(478\) 0 0
\(479\) 7.26771 12.5880i 0.332070 0.575163i −0.650847 0.759209i \(-0.725586\pi\)
0.982918 + 0.184046i \(0.0589195\pi\)
\(480\) 0 0
\(481\) 4.77292 + 8.26693i 0.217626 + 0.376940i
\(482\) 0 0
\(483\) 3.47141 9.06259i 0.157955 0.412362i
\(484\) 0 0
\(485\) 8.47249 0.384716
\(486\) 0 0
\(487\) −13.0539 −0.591529 −0.295765 0.955261i \(-0.595574\pi\)
−0.295765 + 0.955261i \(0.595574\pi\)
\(488\) 0 0
\(489\) 0.934349 2.43924i 0.0422527 0.110306i
\(490\) 0 0
\(491\) 9.67223 + 16.7528i 0.436502 + 0.756043i 0.997417 0.0718303i \(-0.0228840\pi\)
−0.560915 + 0.827873i \(0.689551\pi\)
\(492\) 0 0
\(493\) 0.830095 1.43777i 0.0373856 0.0647538i
\(494\) 0 0
\(495\) −9.77197 8.77359i −0.439217 0.394344i
\(496\) 0 0
\(497\) 4.30150 7.45043i 0.192949 0.334197i
\(498\) 0 0
\(499\) −18.1111 31.3693i −0.810764 1.40428i −0.912330 0.409455i \(-0.865719\pi\)
0.101566 0.994829i \(-0.467615\pi\)
\(500\) 0 0
\(501\) −25.1179 + 3.99660i −1.12219 + 0.178555i
\(502\) 0 0
\(503\) −15.6764 −0.698974 −0.349487 0.936941i \(-0.613644\pi\)
−0.349487 + 0.936941i \(0.613644\pi\)
\(504\) 0 0
\(505\) −15.1111 −0.672435
\(506\) 0 0
\(507\) −13.0917 16.1434i −0.581421 0.716952i
\(508\) 0 0
\(509\) −17.1517 29.7076i −0.760237 1.31677i −0.942729 0.333561i \(-0.891750\pi\)
0.182492 0.983207i \(-0.441584\pi\)
\(510\) 0 0
\(511\) −7.57442 + 13.1193i −0.335073 + 0.580363i
\(512\) 0 0
\(513\) 8.98508 4.60230i 0.396701 0.203196i
\(514\) 0 0
\(515\) −2.59850 + 4.50073i −0.114503 + 0.198326i
\(516\) 0 0
\(517\) 10.7934 + 18.6948i 0.474694 + 0.822195i
\(518\) 0 0
\(519\) 0.275794 + 0.340082i 0.0121060 + 0.0149279i
\(520\) 0 0
\(521\) −10.2449 −0.448836 −0.224418 0.974493i \(-0.572048\pi\)
−0.224418 + 0.974493i \(0.572048\pi\)
\(522\) 0 0
\(523\) −30.6030 −1.33818 −0.669088 0.743183i \(-0.733315\pi\)
−0.669088 + 0.743183i \(0.733315\pi\)
\(524\) 0 0
\(525\) 6.16307 0.980627i 0.268978 0.0427981i
\(526\) 0 0
\(527\) −5.76320 9.98215i −0.251049 0.434829i
\(528\) 0 0
\(529\) −4.19686 + 7.26918i −0.182472 + 0.316051i
\(530\) 0 0
\(531\) 1.61273 7.64068i 0.0699863 0.331577i
\(532\) 0 0
\(533\) 5.09097 8.81782i 0.220514 0.381942i
\(534\) 0 0
\(535\) 8.11273 + 14.0517i 0.350744 + 0.607506i
\(536\) 0 0
\(537\) −8.79303 + 22.9554i −0.379447 + 0.990599i
\(538\) 0 0
\(539\) 3.70370 0.159530
\(540\) 0 0
\(541\) −26.0917 −1.12177 −0.560884 0.827894i \(-0.689539\pi\)
−0.560884 + 0.827894i \(0.689539\pi\)
\(542\) 0 0
\(543\) −0.886884 + 2.31533i −0.0380598 + 0.0993604i
\(544\) 0 0
\(545\) −0.746515 1.29300i −0.0319772 0.0553861i
\(546\) 0 0
\(547\) −5.46169 + 9.45993i −0.233525 + 0.404478i −0.958843 0.283937i \(-0.908359\pi\)
0.725318 + 0.688414i \(0.241693\pi\)
\(548\) 0 0
\(549\) −21.6826 + 7.07922i −0.925392 + 0.302134i
\(550\) 0 0
\(551\) 0.232287 0.402332i 0.00989575 0.0171399i
\(552\) 0 0
\(553\) 3.68878 + 6.38915i 0.156863 + 0.271694i
\(554\) 0 0
\(555\) 19.2993 3.07078i 0.819210 0.130347i
\(556\) 0 0
\(557\) −13.9442 −0.590835 −0.295417 0.955368i \(-0.595459\pi\)
−0.295417 + 0.955368i \(0.595459\pi\)
\(558\) 0 0
\(559\) −2.22545 −0.0941265
\(560\) 0 0
\(561\) −28.0534 34.5927i −1.18441 1.46050i
\(562\) 0 0
\(563\) 15.1287 + 26.2037i 0.637600 + 1.10435i 0.985958 + 0.166993i \(0.0534059\pi\)
−0.348358 + 0.937361i \(0.613261\pi\)
\(564\) 0 0
\(565\) −7.18770 + 12.4495i −0.302389 + 0.523753i
\(566\) 0 0
\(567\) −8.23229 3.63723i −0.345724 0.152749i
\(568\) 0 0
\(569\) 10.5676 18.3036i 0.443016 0.767326i −0.554896 0.831920i \(-0.687242\pi\)
0.997912 + 0.0645936i \(0.0205751\pi\)
\(570\) 0 0
\(571\) −16.3932 28.3938i −0.686033 1.18824i −0.973111 0.230336i \(-0.926017\pi\)
0.287078 0.957907i \(-0.407316\pi\)
\(572\) 0 0
\(573\) −16.4383 20.2701i −0.686720 0.846797i
\(574\) 0 0
\(575\) −20.1877 −0.841885
\(576\) 0 0
\(577\) −17.3743 −0.723301 −0.361651 0.932314i \(-0.617787\pi\)
−0.361651 + 0.932314i \(0.617787\pi\)
\(578\) 0 0
\(579\) 13.4241 2.13595i 0.557886 0.0887671i
\(580\) 0 0
\(581\) −3.47141 6.01266i −0.144018 0.249447i
\(582\) 0 0
\(583\) 21.4870 37.2166i 0.889901 1.54135i
\(584\) 0 0
\(585\) 3.37072 1.10052i 0.139362 0.0455007i
\(586\) 0 0
\(587\) 8.48796 14.7016i 0.350336 0.606799i −0.635973 0.771712i \(-0.719401\pi\)
0.986308 + 0.164913i \(0.0527342\pi\)
\(588\) 0 0
\(589\) −1.61273 2.79332i −0.0664512 0.115097i
\(590\) 0 0
\(591\) 4.14488 10.8208i 0.170498 0.445107i
\(592\) 0 0
\(593\) −13.0733 −0.536858 −0.268429 0.963300i \(-0.586504\pi\)
−0.268429 + 0.963300i \(0.586504\pi\)
\(594\) 0 0
\(595\) −8.20602 −0.336414
\(596\) 0 0
\(597\) 12.3538 32.2512i 0.505607 1.31995i
\(598\) 0 0
\(599\) 14.6030 + 25.2932i 0.596663 + 1.03345i 0.993310 + 0.115479i \(0.0368403\pi\)
−0.396647 + 0.917971i \(0.629826\pi\)
\(600\) 0 0
\(601\) −3.89536 + 6.74695i −0.158895 + 0.275214i −0.934470 0.356041i \(-0.884126\pi\)
0.775576 + 0.631255i \(0.217460\pi\)
\(602\) 0 0
\(603\) 2.17347 10.2974i 0.0885106 0.419341i
\(604\) 0 0
\(605\) −1.60589 + 2.78148i −0.0652887 + 0.113083i
\(606\) 0 0
\(607\) −9.82038 17.0094i −0.398597 0.690390i 0.594956 0.803758i \(-0.297169\pi\)
−0.993553 + 0.113368i \(0.963836\pi\)
\(608\) 0 0
\(609\) −0.409028 + 0.0650819i −0.0165747 + 0.00263725i
\(610\) 0 0
\(611\) −5.82846 −0.235794
\(612\) 0 0
\(613\) 23.5653 0.951792 0.475896 0.879502i \(-0.342124\pi\)
0.475896 + 0.879502i \(0.342124\pi\)
\(614\) 0 0
\(615\) −13.1293 16.1898i −0.529424 0.652834i
\(616\) 0 0
\(617\) 5.33009 + 9.23200i 0.214582 + 0.371666i 0.953143 0.302520i \(-0.0978279\pi\)
−0.738562 + 0.674186i \(0.764495\pi\)
\(618\) 0 0
\(619\) −9.00752 + 15.6015i −0.362043 + 0.627077i −0.988297 0.152542i \(-0.951254\pi\)
0.626254 + 0.779619i \(0.284587\pi\)
\(620\) 0 0
\(621\) 24.4509 + 15.8046i 0.981181 + 0.634215i
\(622\) 0 0
\(623\) −1.37360 + 2.37915i −0.0550322 + 0.0953186i
\(624\) 0 0
\(625\) −2.99837 5.19332i −0.119935 0.207733i
\(626\) 0 0
\(627\) −7.85021 9.68013i −0.313507 0.386587i
\(628\) 0 0
\(629\) 66.2750 2.64256
\(630\) 0 0
\(631\) −12.4703 −0.496436 −0.248218 0.968704i \(-0.579845\pi\)
−0.248218 + 0.968704i \(0.579845\pi\)
\(632\) 0 0
\(633\) −30.9464 + 4.92398i −1.23001 + 0.195711i
\(634\) 0 0
\(635\) 0.791790 + 1.37142i 0.0314212 + 0.0544232i
\(636\) 0 0
\(637\) −0.500000 + 0.866025i −0.0198107 + 0.0343132i
\(638\) 0 0
\(639\) 19.2044 + 17.2423i 0.759714 + 0.682096i
\(640\) 0 0
\(641\) −9.57279 + 16.5806i −0.378102 + 0.654892i −0.990786 0.135436i \(-0.956757\pi\)
0.612684 + 0.790328i \(0.290090\pi\)
\(642\) 0 0
\(643\) 3.24433 + 5.61934i 0.127944 + 0.221605i 0.922880 0.385088i \(-0.125829\pi\)
−0.794936 + 0.606693i \(0.792496\pi\)
\(644\) 0 0
\(645\) −1.62967 + 4.25447i −0.0641681 + 0.167520i
\(646\) 0 0
\(647\) 48.0988 1.89096 0.945479 0.325682i \(-0.105594\pi\)
0.945479 + 0.325682i \(0.105594\pi\)
\(648\) 0 0
\(649\) −9.64076 −0.378433
\(650\) 0 0
\(651\) −1.02859 + 2.68527i −0.0403136 + 0.105244i
\(652\) 0 0
\(653\) 21.6202 + 37.4474i 0.846066 + 1.46543i 0.884692 + 0.466175i \(0.154368\pi\)
−0.0386267 + 0.999254i \(0.512298\pi\)
\(654\) 0 0
\(655\) −2.93530 + 5.08408i −0.114691 + 0.198651i
\(656\) 0 0
\(657\) −33.8166 30.3616i −1.31931 1.18452i
\(658\) 0 0
\(659\) −1.25404 + 2.17206i −0.0488505 + 0.0846115i −0.889417 0.457097i \(-0.848889\pi\)
0.840566 + 0.541709i \(0.182222\pi\)
\(660\) 0 0
\(661\) 21.1677 + 36.6636i 0.823329 + 1.42605i 0.903190 + 0.429241i \(0.141219\pi\)
−0.0798613 + 0.996806i \(0.525448\pi\)
\(662\) 0 0
\(663\) 11.8759 1.88962i 0.461223 0.0733867i
\(664\) 0 0
\(665\) −2.29630 −0.0890468
\(666\) 0 0
\(667\) 1.33981 0.0518777
\(668\) 0 0
\(669\) 24.7181 + 30.4799i 0.955655 + 1.17842i
\(670\) 0 0
\(671\) 14.0796 + 24.3866i 0.543538 + 0.941435i
\(672\) 0 0
\(673\) −6.70765 + 11.6180i −0.258561 + 0.447841i −0.965857 0.259077i \(-0.916582\pi\)
0.707296 + 0.706918i \(0.249915\pi\)
\(674\) 0 0
\(675\) −0.939941 + 18.6982i −0.0361784 + 0.719693i
\(676\) 0 0
\(677\) −0.981125 + 1.69936i −0.0377077 + 0.0653117i −0.884263 0.466989i \(-0.845339\pi\)
0.846556 + 0.532300i \(0.178672\pi\)
\(678\) 0 0
\(679\) −3.58414 6.20790i −0.137546 0.238237i
\(680\) 0 0
\(681\) 5.76320 + 7.10662i 0.220846 + 0.272326i
\(682\) 0 0
\(683\) −27.1672 −1.03952 −0.519761 0.854312i \(-0.673979\pi\)
−0.519761 + 0.854312i \(0.673979\pi\)
\(684\) 0 0
\(685\) −5.12941 −0.195985
\(686\) 0 0
\(687\) −33.0758 + 5.26280i −1.26192 + 0.200788i
\(688\) 0 0
\(689\) 5.80150 + 10.0485i 0.221020 + 0.382817i
\(690\) 0 0
\(691\) −25.1586 + 43.5759i −0.957077 + 1.65771i −0.227534 + 0.973770i \(0.573066\pi\)
−0.729543 + 0.683935i \(0.760267\pi\)
\(692\) 0 0
\(693\) −2.29467 + 10.8716i −0.0871672 + 0.412976i
\(694\) 0 0
\(695\) 2.33009 4.03584i 0.0883855 0.153088i
\(696\) 0 0
\(697\) −35.3457 61.2205i −1.33881 2.31889i
\(698\) 0 0
\(699\) −10.5205 + 27.4652i −0.397922 + 1.03883i
\(700\) 0 0
\(701\) 45.1672 1.70594 0.852970 0.521960i \(-0.174799\pi\)
0.852970 + 0.521960i \(0.174799\pi\)
\(702\) 0 0
\(703\) 18.5458 0.699469
\(704\) 0 0
\(705\) −4.26810 + 11.1425i −0.160746 + 0.419649i
\(706\) 0 0
\(707\) 6.39248 + 11.0721i 0.240414 + 0.416409i
\(708\) 0 0
\(709\) −19.8090 + 34.3102i −0.743944 + 1.28855i 0.206743 + 0.978395i \(0.433714\pi\)
−0.950687 + 0.310153i \(0.899620\pi\)
\(710\) 0 0
\(711\) −21.0397 + 6.86930i −0.789050 + 0.257619i
\(712\) 0 0
\(713\) 4.65103 8.05582i 0.174182 0.301693i
\(714\) 0 0
\(715\) −2.18878 3.79108i −0.0818557 0.141778i
\(716\) 0 0
\(717\) 28.8834 4.59574i 1.07867 0.171631i
\(718\) 0 0
\(719\) 22.0377 0.821869 0.410935 0.911665i \(-0.365202\pi\)
0.410935 + 0.911665i \(0.365202\pi\)
\(720\) 0 0
\(721\) 4.39699 0.163752
\(722\) 0 0
\(723\) 29.6150 + 36.5184i 1.10140 + 1.35813i
\(724\) 0 0
\(725\) 0.430782 + 0.746136i 0.0159988 + 0.0277108i
\(726\) 0 0
\(727\) 14.0555 24.3449i 0.521291 0.902903i −0.478402 0.878141i \(-0.658784\pi\)
0.999693 0.0247621i \(-0.00788284\pi\)
\(728\) 0 0
\(729\) 15.7769 21.9110i 0.584329 0.811517i
\(730\) 0 0
\(731\) −7.72545 + 13.3809i −0.285736 + 0.494909i
\(732\) 0 0
\(733\) −5.93474 10.2793i −0.219205 0.379674i 0.735360 0.677676i \(-0.237013\pi\)
−0.954565 + 0.298003i \(0.903680\pi\)
\(734\) 0 0
\(735\) 1.28947 + 1.59005i 0.0475627 + 0.0586497i
\(736\) 0 0
\(737\) −12.9929 −0.478598
\(738\) 0 0
\(739\) 12.1844 0.448212 0.224106 0.974565i \(-0.428054\pi\)
0.224106 + 0.974565i \(0.428054\pi\)
\(740\) 0 0
\(741\) 3.32326 0.528775i 0.122083 0.0194250i
\(742\) 0 0
\(743\) −22.2427 38.5255i −0.816005 1.41336i −0.908604 0.417659i \(-0.862851\pi\)
0.0925987 0.995704i \(-0.470483\pi\)
\(744\) 0 0
\(745\) −6.56634 + 11.3732i −0.240572 + 0.416683i
\(746\) 0 0
\(747\) 19.7999 6.46451i 0.724439 0.236524i
\(748\) 0 0
\(749\) 6.86389 11.8886i 0.250801 0.434400i
\(750\) 0 0
\(751\) 21.4029 + 37.0709i 0.781002 + 1.35274i 0.931358 + 0.364104i \(0.118625\pi\)
−0.150356 + 0.988632i \(0.548042\pi\)
\(752\) 0 0
\(753\) 11.8200 30.8577i 0.430744 1.12452i
\(754\) 0 0
\(755\) −16.4567 −0.598919
\(756\) 0 0
\(757\) −22.4919 −0.817483 −0.408741 0.912650i \(-0.634032\pi\)
−0.408741 + 0.912650i \(0.634032\pi\)
\(758\) 0 0
\(759\) 12.8571 33.5651i 0.466681 1.21833i
\(760\) 0 0
\(761\) 7.16827 + 12.4158i 0.259850 + 0.450073i 0.966201 0.257788i \(-0.0829937\pi\)
−0.706352 + 0.707861i \(0.749660\pi\)
\(762\) 0 0
\(763\) −0.631600 + 1.09396i −0.0228655 + 0.0396041i
\(764\) 0 0
\(765\) 5.08414 24.0874i 0.183817 0.870880i
\(766\) 0 0
\(767\) 1.30150 2.25427i 0.0469946 0.0813971i
\(768\) 0 0
\(769\) 15.6105 + 27.0382i 0.562930 + 0.975024i 0.997239 + 0.0742597i \(0.0236594\pi\)
−0.434309 + 0.900764i \(0.643007\pi\)
\(770\) 0 0
\(771\) 25.3880 4.03956i 0.914325 0.145481i
\(772\) 0 0
\(773\) 4.38005 0.157539 0.0787697 0.996893i \(-0.474901\pi\)
0.0787697 + 0.996893i \(0.474901\pi\)
\(774\) 0 0
\(775\) 5.98168 0.214868
\(776\) 0 0
\(777\) −10.4142 12.8418i −0.373608 0.460698i
\(778\) 0 0
\(779\) −9.89084 17.1314i −0.354376 0.613798i
\(780\) 0 0
\(781\) 15.9315 27.5941i 0.570073 0.987395i
\(782\) 0 0
\(783\) 0.0623817 1.24095i 0.00222934 0.0443481i
\(784\) 0 0
\(785\) −0.0337917 + 0.0585290i −0.00120608 + 0.00208899i
\(786\) 0 0
\(787\) 13.8107 + 23.9208i 0.492297 + 0.852683i 0.999961 0.00887191i \(-0.00282405\pi\)
−0.507664 + 0.861555i \(0.669491\pi\)
\(788\) 0 0
\(789\) 8.44570 + 10.4144i 0.300675 + 0.370763i
\(790\) 0 0
\(791\) 12.1625 0.432449
\(792\) 0 0
\(793\) −7.60301 −0.269991
\(794\) 0 0
\(795\) 23.4584 3.73255i 0.831985 0.132380i
\(796\) 0 0
\(797\) 1.48181 + 2.56658i 0.0524885 + 0.0909128i 0.891076 0.453854i \(-0.149951\pi\)
−0.838587 + 0.544767i \(0.816618\pi\)
\(798\) 0 0
\(799\) −20.2330 + 35.0445i −0.715791 + 1.23979i
\(800\)