Properties

Label 448.3.s.d.129.1
Level $448$
Weight $3$
Character 448.129
Analytic conductor $12.207$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 448 = 2^{6} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 448.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.2071158433\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 129.1
Root \(-0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 448.129
Dual form 448.3.s.d.257.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.621320 - 0.358719i) q^{3} +(5.74264 - 3.31552i) q^{5} +(6.24264 - 3.16693i) q^{7} +(-4.24264 - 7.34847i) q^{9} +O(q^{10})\) \(q+(-0.621320 - 0.358719i) q^{3} +(5.74264 - 3.31552i) q^{5} +(6.24264 - 3.16693i) q^{7} +(-4.24264 - 7.34847i) q^{9} +(-2.37868 + 4.11999i) q^{11} -15.2913i q^{13} -4.75736 q^{15} +(-3.25736 - 1.88064i) q^{17} +(-3.62132 + 2.09077i) q^{19} +(-5.01472 - 0.271680i) q^{21} +(13.8640 + 24.0131i) q^{23} +(9.48528 - 16.4290i) q^{25} +12.5446i q^{27} -3.51472 q^{29} +(-42.3198 - 24.4334i) q^{31} +(2.95584 - 1.70656i) q^{33} +(25.3492 - 38.8841i) q^{35} +(-1.47056 - 2.54709i) q^{37} +(-5.48528 + 9.50079i) q^{39} -27.9590i q^{41} +10.4853 q^{43} +(-48.7279 - 28.1331i) q^{45} +(45.6213 - 26.3395i) q^{47} +(28.9411 - 39.5400i) q^{49} +(1.34924 + 2.33696i) q^{51} +(27.9853 - 48.4719i) q^{53} +31.5462i q^{55} +3.00000 q^{57} +(-33.5330 - 19.3603i) q^{59} +(78.3823 - 45.2540i) q^{61} +(-49.7574 - 32.4377i) q^{63} +(-50.6985 - 87.8124i) q^{65} +(-17.3198 + 29.9988i) q^{67} -19.8931i q^{69} +36.4264 q^{71} +(45.5589 + 26.3034i) q^{73} +(-11.7868 + 6.80511i) q^{75} +(-1.80152 + 33.2528i) q^{77} +(16.8934 + 29.2602i) q^{79} +(-33.6838 + 58.3420i) q^{81} +127.577i q^{83} -24.9411 q^{85} +(2.18377 + 1.26080i) q^{87} +(-43.5883 + 25.1657i) q^{89} +(-48.4264 - 95.4580i) q^{91} +(17.5294 + 30.3619i) q^{93} +(-13.8640 + 24.0131i) q^{95} +101.792i q^{97} +40.3675 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 6 q^{3} + 6 q^{5} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 6 q^{3} + 6 q^{5} + 8 q^{7} - 18 q^{11} - 36 q^{15} - 30 q^{17} - 6 q^{19} - 54 q^{21} + 30 q^{23} + 4 q^{25} - 48 q^{29} - 42 q^{31} - 90 q^{33} + 42 q^{35} + 62 q^{37} + 12 q^{39} + 8 q^{43} - 144 q^{45} + 174 q^{47} - 20 q^{49} - 54 q^{51} + 78 q^{53} + 12 q^{57} + 78 q^{59} + 42 q^{61} - 216 q^{63} - 84 q^{65} + 58 q^{67} - 24 q^{71} + 318 q^{73} - 132 q^{75} - 126 q^{77} + 110 q^{79} + 18 q^{81} + 36 q^{85} - 144 q^{87} - 378 q^{89} - 24 q^{91} + 138 q^{93} - 30 q^{95} - 144 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\)

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
\(3\) −0.621320 0.358719i −0.207107 0.119573i 0.392859 0.919599i \(-0.371486\pi\)
−0.599966 + 0.800025i \(0.704819\pi\)
\(4\) 0 0
\(5\) 5.74264 3.31552i 1.14853 0.663103i 0.200000 0.979796i \(-0.435906\pi\)
0.948528 + 0.316693i \(0.102572\pi\)
\(6\) 0 0
\(7\) 6.24264 3.16693i 0.891806 0.452418i
\(8\) 0 0
\(9\) −4.24264 7.34847i −0.471405 0.816497i
\(10\) 0 0
\(11\) −2.37868 + 4.11999i −0.216244 + 0.374545i −0.953657 0.300897i \(-0.902714\pi\)
0.737413 + 0.675442i \(0.236047\pi\)
\(12\) 0 0
\(13\) 15.2913i 1.17625i −0.808769 0.588126i \(-0.799866\pi\)
0.808769 0.588126i \(-0.200134\pi\)
\(14\) 0 0
\(15\) −4.75736 −0.317157
\(16\) 0 0
\(17\) −3.25736 1.88064i −0.191609 0.110626i 0.401126 0.916023i \(-0.368619\pi\)
−0.592736 + 0.805397i \(0.701952\pi\)
\(18\) 0 0
\(19\) −3.62132 + 2.09077i −0.190596 + 0.110041i −0.592261 0.805746i \(-0.701765\pi\)
0.401666 + 0.915786i \(0.368431\pi\)
\(20\) 0 0
\(21\) −5.01472 0.271680i −0.238796 0.0129371i
\(22\) 0 0
\(23\) 13.8640 + 24.0131i 0.602781 + 1.04405i 0.992398 + 0.123070i \(0.0392740\pi\)
−0.389617 + 0.920977i \(0.627393\pi\)
\(24\) 0 0
\(25\) 9.48528 16.4290i 0.379411 0.657160i
\(26\) 0 0
\(27\) 12.5446i 0.464616i
\(28\) 0 0
\(29\) −3.51472 −0.121197 −0.0605986 0.998162i \(-0.519301\pi\)
−0.0605986 + 0.998162i \(0.519301\pi\)
\(30\) 0 0
\(31\) −42.3198 24.4334i −1.36516 0.788173i −0.374850 0.927085i \(-0.622306\pi\)
−0.990305 + 0.138913i \(0.955639\pi\)
\(32\) 0 0
\(33\) 2.95584 1.70656i 0.0895710 0.0517139i
\(34\) 0 0
\(35\) 25.3492 38.8841i 0.724264 1.11097i
\(36\) 0 0
\(37\) −1.47056 2.54709i −0.0397449 0.0688403i 0.845469 0.534025i \(-0.179321\pi\)
−0.885214 + 0.465185i \(0.845988\pi\)
\(38\) 0 0
\(39\) −5.48528 + 9.50079i −0.140648 + 0.243610i
\(40\) 0 0
\(41\) 27.9590i 0.681927i −0.940077 0.340963i \(-0.889247\pi\)
0.940077 0.340963i \(-0.110753\pi\)
\(42\) 0 0
\(43\) 10.4853 0.243844 0.121922 0.992540i \(-0.461094\pi\)
0.121922 + 0.992540i \(0.461094\pi\)
\(44\) 0 0
\(45\) −48.7279 28.1331i −1.08284 0.625180i
\(46\) 0 0
\(47\) 45.6213 26.3395i 0.970666 0.560415i 0.0712271 0.997460i \(-0.477309\pi\)
0.899439 + 0.437046i \(0.143975\pi\)
\(48\) 0 0
\(49\) 28.9411 39.5400i 0.590635 0.806939i
\(50\) 0 0
\(51\) 1.34924 + 2.33696i 0.0264557 + 0.0458227i
\(52\) 0 0
\(53\) 27.9853 48.4719i 0.528024 0.914565i −0.471442 0.881897i \(-0.656266\pi\)
0.999466 0.0326677i \(-0.0104003\pi\)
\(54\) 0 0
\(55\) 31.5462i 0.573567i
\(56\) 0 0
\(57\) 3.00000 0.0526316
\(58\) 0 0
\(59\) −33.5330 19.3603i −0.568356 0.328141i 0.188136 0.982143i \(-0.439755\pi\)
−0.756492 + 0.654002i \(0.773089\pi\)
\(60\) 0 0
\(61\) 78.3823 45.2540i 1.28495 0.741869i 0.307205 0.951643i \(-0.400606\pi\)
0.977750 + 0.209774i \(0.0672729\pi\)
\(62\) 0 0
\(63\) −49.7574 32.4377i −0.789799 0.514884i
\(64\) 0 0
\(65\) −50.6985 87.8124i −0.779977 1.35096i
\(66\) 0 0
\(67\) −17.3198 + 29.9988i −0.258505 + 0.447743i −0.965842 0.259134i \(-0.916563\pi\)
0.707337 + 0.706877i \(0.249896\pi\)
\(68\) 0 0
\(69\) 19.8931i 0.288306i
\(70\) 0 0
\(71\) 36.4264 0.513048 0.256524 0.966538i \(-0.417423\pi\)
0.256524 + 0.966538i \(0.417423\pi\)
\(72\) 0 0
\(73\) 45.5589 + 26.3034i 0.624094 + 0.360321i 0.778461 0.627693i \(-0.216001\pi\)
−0.154367 + 0.988014i \(0.549334\pi\)
\(74\) 0 0
\(75\) −11.7868 + 6.80511i −0.157157 + 0.0907348i
\(76\) 0 0
\(77\) −1.80152 + 33.2528i −0.0233963 + 0.431854i
\(78\) 0 0
\(79\) 16.8934 + 29.2602i 0.213840 + 0.370383i 0.952913 0.303243i \(-0.0980694\pi\)
−0.739073 + 0.673626i \(0.764736\pi\)
\(80\) 0 0
\(81\) −33.6838 + 58.3420i −0.415849 + 0.720272i
\(82\) 0 0
\(83\) 127.577i 1.53708i 0.639803 + 0.768539i \(0.279016\pi\)
−0.639803 + 0.768539i \(0.720984\pi\)
\(84\) 0 0
\(85\) −24.9411 −0.293425
\(86\) 0 0
\(87\) 2.18377 + 1.26080i 0.0251008 + 0.0144919i
\(88\) 0 0
\(89\) −43.5883 + 25.1657i −0.489756 + 0.282761i −0.724473 0.689303i \(-0.757917\pi\)
0.234717 + 0.972064i \(0.424584\pi\)
\(90\) 0 0
\(91\) −48.4264 95.4580i −0.532158 1.04899i
\(92\) 0 0
\(93\) 17.5294 + 30.3619i 0.188489 + 0.326472i
\(94\) 0 0
\(95\) −13.8640 + 24.0131i −0.145936 + 0.252769i
\(96\) 0 0
\(97\) 101.792i 1.04940i 0.851287 + 0.524700i \(0.175823\pi\)
−0.851287 + 0.524700i \(0.824177\pi\)
\(98\) 0 0
\(99\) 40.3675 0.407753
\(100\) 0 0
\(101\) 51.6838 + 29.8396i 0.511720 + 0.295442i 0.733541 0.679646i \(-0.237866\pi\)
−0.221820 + 0.975088i \(0.571200\pi\)
\(102\) 0 0
\(103\) 104.077 60.0890i 1.01046 0.583388i 0.0991322 0.995074i \(-0.468393\pi\)
0.911326 + 0.411686i \(0.135060\pi\)
\(104\) 0 0
\(105\) −29.6985 + 15.0662i −0.282843 + 0.143488i
\(106\) 0 0
\(107\) −56.8051 98.3893i −0.530889 0.919526i −0.999350 0.0360423i \(-0.988525\pi\)
0.468462 0.883484i \(-0.344808\pi\)
\(108\) 0 0
\(109\) −72.6543 + 125.841i −0.666553 + 1.15450i 0.312308 + 0.949981i \(0.398898\pi\)
−0.978862 + 0.204524i \(0.934435\pi\)
\(110\) 0 0
\(111\) 2.11008i 0.0190097i
\(112\) 0 0
\(113\) 34.5442 0.305700 0.152850 0.988249i \(-0.451155\pi\)
0.152850 + 0.988249i \(0.451155\pi\)
\(114\) 0 0
\(115\) 159.231 + 91.9323i 1.38462 + 0.799412i
\(116\) 0 0
\(117\) −112.368 + 64.8754i −0.960406 + 0.554491i
\(118\) 0 0
\(119\) −26.2904 1.42432i −0.220927 0.0119691i
\(120\) 0 0
\(121\) 49.1838 + 85.1888i 0.406477 + 0.704040i
\(122\) 0 0
\(123\) −10.0294 + 17.3715i −0.0815401 + 0.141232i
\(124\) 0 0
\(125\) 39.9814i 0.319851i
\(126\) 0 0
\(127\) −247.338 −1.94754 −0.973772 0.227526i \(-0.926936\pi\)
−0.973772 + 0.227526i \(0.926936\pi\)
\(128\) 0 0
\(129\) −6.51472 3.76127i −0.0505017 0.0291572i
\(130\) 0 0
\(131\) 127.864 73.8223i 0.976061 0.563529i 0.0749822 0.997185i \(-0.476110\pi\)
0.901079 + 0.433656i \(0.142777\pi\)
\(132\) 0 0
\(133\) −15.9853 + 24.5204i −0.120190 + 0.184364i
\(134\) 0 0
\(135\) 41.5919 + 72.0393i 0.308088 + 0.533624i
\(136\) 0 0
\(137\) 16.2868 28.2096i 0.118882 0.205909i −0.800443 0.599409i \(-0.795402\pi\)
0.919325 + 0.393500i \(0.128736\pi\)
\(138\) 0 0
\(139\) 68.5857i 0.493422i −0.969089 0.246711i \(-0.920650\pi\)
0.969089 0.246711i \(-0.0793499\pi\)
\(140\) 0 0
\(141\) −37.7939 −0.268042
\(142\) 0 0
\(143\) 63.0000 + 36.3731i 0.440559 + 0.254357i
\(144\) 0 0
\(145\) −20.1838 + 11.6531i −0.139198 + 0.0803662i
\(146\) 0 0
\(147\) −32.1655 + 14.1853i −0.218813 + 0.0964984i
\(148\) 0 0
\(149\) 46.1985 + 80.0181i 0.310057 + 0.537034i 0.978374 0.206842i \(-0.0663185\pi\)
−0.668317 + 0.743876i \(0.732985\pi\)
\(150\) 0 0
\(151\) 45.8934 79.4897i 0.303930 0.526422i −0.673093 0.739558i \(-0.735035\pi\)
0.977022 + 0.213136i \(0.0683678\pi\)
\(152\) 0 0
\(153\) 31.9155i 0.208598i
\(154\) 0 0
\(155\) −324.037 −2.09056
\(156\) 0 0
\(157\) −7.32338 4.22815i −0.0466457 0.0269309i 0.476496 0.879177i \(-0.341907\pi\)
−0.523142 + 0.852246i \(0.675240\pi\)
\(158\) 0 0
\(159\) −34.7756 + 20.0777i −0.218715 + 0.126275i
\(160\) 0 0
\(161\) 162.595 + 105.999i 1.00991 + 0.658378i
\(162\) 0 0
\(163\) 110.989 + 192.238i 0.680913 + 1.17938i 0.974703 + 0.223506i \(0.0717503\pi\)
−0.293789 + 0.955870i \(0.594916\pi\)
\(164\) 0 0
\(165\) 11.3162 19.6003i 0.0685832 0.118790i
\(166\) 0 0
\(167\) 168.841i 1.01102i 0.862820 + 0.505511i \(0.168696\pi\)
−0.862820 + 0.505511i \(0.831304\pi\)
\(168\) 0 0
\(169\) −64.8234 −0.383570
\(170\) 0 0
\(171\) 30.7279 + 17.7408i 0.179695 + 0.103747i
\(172\) 0 0
\(173\) 142.323 82.1704i 0.822678 0.474974i −0.0286608 0.999589i \(-0.509124\pi\)
0.851339 + 0.524616i \(0.175791\pi\)
\(174\) 0 0
\(175\) 7.18377 132.599i 0.0410501 0.757711i
\(176\) 0 0
\(177\) 13.8898 + 24.0579i 0.0784736 + 0.135920i
\(178\) 0 0
\(179\) 92.5919 160.374i 0.517273 0.895943i −0.482526 0.875882i \(-0.660280\pi\)
0.999799 0.0200614i \(-0.00638618\pi\)
\(180\) 0 0
\(181\) 155.086i 0.856830i 0.903582 + 0.428415i \(0.140928\pi\)
−0.903582 + 0.428415i \(0.859072\pi\)
\(182\) 0 0
\(183\) −64.9340 −0.354831
\(184\) 0 0
\(185\) −16.8898 9.75135i −0.0912964 0.0527100i
\(186\) 0 0
\(187\) 15.4964 8.94687i 0.0828686 0.0478442i
\(188\) 0 0
\(189\) 39.7279 + 78.3116i 0.210201 + 0.414347i
\(190\) 0 0
\(191\) −124.048 214.857i −0.649465 1.12491i −0.983251 0.182257i \(-0.941660\pi\)
0.333786 0.942649i \(-0.391674\pi\)
\(192\) 0 0
\(193\) −77.1690 + 133.661i −0.399840 + 0.692543i −0.993706 0.112021i \(-0.964268\pi\)
0.593866 + 0.804564i \(0.297601\pi\)
\(194\) 0 0
\(195\) 72.7461i 0.373057i
\(196\) 0 0
\(197\) 181.103 0.919303 0.459651 0.888099i \(-0.347974\pi\)
0.459651 + 0.888099i \(0.347974\pi\)
\(198\) 0 0
\(199\) 301.989 + 174.353i 1.51753 + 0.876147i 0.999788 + 0.0206121i \(0.00656150\pi\)
0.517744 + 0.855535i \(0.326772\pi\)
\(200\) 0 0
\(201\) 21.5223 12.4259i 0.107076 0.0618204i
\(202\) 0 0
\(203\) −21.9411 + 11.1309i −0.108084 + 0.0548318i
\(204\) 0 0
\(205\) −92.6985 160.558i −0.452188 0.783212i
\(206\) 0 0
\(207\) 117.640 203.758i 0.568307 0.984337i
\(208\) 0 0
\(209\) 19.8931i 0.0951823i
\(210\) 0 0
\(211\) −364.073 −1.72547 −0.862733 0.505660i \(-0.831249\pi\)
−0.862733 + 0.505660i \(0.831249\pi\)
\(212\) 0 0
\(213\) −22.6325 13.0669i −0.106256 0.0613468i
\(214\) 0 0
\(215\) 60.2132 34.7641i 0.280061 0.161694i
\(216\) 0 0
\(217\) −341.566 18.5048i −1.57404 0.0852757i
\(218\) 0 0
\(219\) −18.8711 32.6857i −0.0861694 0.149250i
\(220\) 0 0
\(221\) −28.7574 + 49.8092i −0.130124 + 0.225381i
\(222\) 0 0
\(223\) 123.231i 0.552603i 0.961071 + 0.276302i \(0.0891089\pi\)
−0.961071 + 0.276302i \(0.910891\pi\)
\(224\) 0 0
\(225\) −160.971 −0.715425
\(226\) 0 0
\(227\) 66.1432 + 38.1878i 0.291380 + 0.168228i 0.638564 0.769569i \(-0.279529\pi\)
−0.347184 + 0.937797i \(0.612862\pi\)
\(228\) 0 0
\(229\) −309.419 + 178.643i −1.35117 + 0.780101i −0.988414 0.151782i \(-0.951499\pi\)
−0.362760 + 0.931883i \(0.618166\pi\)
\(230\) 0 0
\(231\) 13.0477 20.0144i 0.0564837 0.0866423i
\(232\) 0 0
\(233\) 136.537 + 236.488i 0.585994 + 1.01497i 0.994751 + 0.102328i \(0.0326291\pi\)
−0.408757 + 0.912643i \(0.634038\pi\)
\(234\) 0 0
\(235\) 174.658 302.516i 0.743225 1.28730i
\(236\) 0 0
\(237\) 24.2400i 0.102278i
\(238\) 0 0
\(239\) −265.103 −1.10922 −0.554608 0.832112i \(-0.687132\pi\)
−0.554608 + 0.832112i \(0.687132\pi\)
\(240\) 0 0
\(241\) −75.8970 43.8191i −0.314925 0.181822i 0.334203 0.942501i \(-0.391533\pi\)
−0.649128 + 0.760679i \(0.724866\pi\)
\(242\) 0 0
\(243\) 139.632 80.6168i 0.574619 0.331757i
\(244\) 0 0
\(245\) 35.1030 323.019i 0.143278 1.31844i
\(246\) 0 0
\(247\) 31.9706 + 55.3746i 0.129435 + 0.224189i
\(248\) 0 0
\(249\) 45.7645 79.2664i 0.183793 0.318339i
\(250\) 0 0
\(251\) 495.655i 1.97472i 0.158491 + 0.987360i \(0.449337\pi\)
−0.158491 + 0.987360i \(0.550663\pi\)
\(252\) 0 0
\(253\) −131.912 −0.521390
\(254\) 0 0
\(255\) 15.4964 + 8.94687i 0.0607703 + 0.0350858i
\(256\) 0 0
\(257\) 346.875 200.268i 1.34971 0.779254i 0.361499 0.932372i \(-0.382265\pi\)
0.988208 + 0.153119i \(0.0489317\pi\)
\(258\) 0 0
\(259\) −17.2466 11.2434i −0.0665894 0.0434108i
\(260\) 0 0
\(261\) 14.9117 + 25.8278i 0.0571329 + 0.0989571i
\(262\) 0 0
\(263\) 16.1726 28.0118i 0.0614928 0.106509i −0.833640 0.552308i \(-0.813747\pi\)
0.895133 + 0.445799i \(0.147081\pi\)
\(264\) 0 0
\(265\) 371.142i 1.40054i
\(266\) 0 0
\(267\) 36.1097 0.135242
\(268\) 0 0
\(269\) 265.838 + 153.482i 0.988246 + 0.570564i 0.904749 0.425944i \(-0.140058\pi\)
0.0834963 + 0.996508i \(0.473391\pi\)
\(270\) 0 0
\(271\) −65.8051 + 37.9926i −0.242823 + 0.140194i −0.616474 0.787376i \(-0.711439\pi\)
0.373650 + 0.927570i \(0.378106\pi\)
\(272\) 0 0
\(273\) −4.15433 + 76.6815i −0.0152173 + 0.280885i
\(274\) 0 0
\(275\) 45.1249 + 78.1586i 0.164091 + 0.284213i
\(276\) 0 0
\(277\) 139.206 241.111i 0.502547 0.870438i −0.497448 0.867494i \(-0.665730\pi\)
0.999996 0.00294398i \(-0.000937098\pi\)
\(278\) 0 0
\(279\) 414.648i 1.48619i
\(280\) 0 0
\(281\) 394.690 1.40459 0.702296 0.711885i \(-0.252158\pi\)
0.702296 + 0.711885i \(0.252158\pi\)
\(282\) 0 0
\(283\) −126.783 73.1981i −0.447996 0.258650i 0.258988 0.965881i \(-0.416611\pi\)
−0.706983 + 0.707230i \(0.749944\pi\)
\(284\) 0 0
\(285\) 17.2279 9.94655i 0.0604488 0.0349002i
\(286\) 0 0
\(287\) −88.5442 174.538i −0.308516 0.608146i
\(288\) 0 0
\(289\) −137.426 238.030i −0.475524 0.823632i
\(290\) 0 0
\(291\) 36.5147 63.2453i 0.125480 0.217338i
\(292\) 0 0
\(293\) 299.678i 1.02279i −0.859345 0.511396i \(-0.829128\pi\)
0.859345 0.511396i \(-0.170872\pi\)
\(294\) 0 0
\(295\) −256.757 −0.870364
\(296\) 0 0
\(297\) −51.6838 29.8396i −0.174019 0.100470i
\(298\) 0 0
\(299\) 367.191 211.998i 1.22806 0.709023i
\(300\) 0 0
\(301\) 65.4558 33.2061i 0.217461 0.110319i
\(302\) 0 0
\(303\) −21.4081 37.0799i −0.0706539 0.122376i
\(304\) 0 0
\(305\) 300.081 519.755i 0.983871 1.70412i
\(306\) 0 0
\(307\) 20.9886i 0.0683666i 0.999416 + 0.0341833i \(0.0108830\pi\)
−0.999416 + 0.0341833i \(0.989117\pi\)
\(308\) 0 0
\(309\) −86.2203 −0.279030
\(310\) 0 0
\(311\) 157.651 + 91.0197i 0.506916 + 0.292668i 0.731565 0.681772i \(-0.238790\pi\)
−0.224649 + 0.974440i \(0.572124\pi\)
\(312\) 0 0
\(313\) −84.8087 + 48.9643i −0.270954 + 0.156435i −0.629321 0.777145i \(-0.716667\pi\)
0.358367 + 0.933581i \(0.383334\pi\)
\(314\) 0 0
\(315\) −393.286 21.3068i −1.24853 0.0676408i
\(316\) 0 0
\(317\) −240.985 417.399i −0.760206 1.31672i −0.942744 0.333517i \(-0.891765\pi\)
0.182538 0.983199i \(-0.441569\pi\)
\(318\) 0 0
\(319\) 8.36039 14.4806i 0.0262081 0.0453938i
\(320\) 0 0
\(321\) 81.5084i 0.253920i
\(322\) 0 0
\(323\) 15.7279 0.0486933
\(324\) 0 0
\(325\) −251.220 145.042i −0.772986 0.446283i
\(326\) 0 0
\(327\) 90.2832 52.1250i 0.276095 0.159404i
\(328\) 0 0
\(329\) 201.382 308.907i 0.612104 0.938928i
\(330\) 0 0
\(331\) 112.504 + 194.862i 0.339890 + 0.588707i 0.984412 0.175879i \(-0.0562768\pi\)
−0.644522 + 0.764586i \(0.722944\pi\)
\(332\) 0 0
\(333\) −12.4781 + 21.6128i −0.0374719 + 0.0649032i
\(334\) 0 0
\(335\) 229.696i 0.685661i
\(336\) 0 0
\(337\) −264.368 −0.784473 −0.392237 0.919864i \(-0.628299\pi\)
−0.392237 + 0.919864i \(0.628299\pi\)
\(338\) 0 0
\(339\) −21.4630 12.3917i −0.0633126 0.0365536i
\(340\) 0 0
\(341\) 201.331 116.238i 0.590412 0.340875i
\(342\) 0 0
\(343\) 55.4487 338.488i 0.161658 0.986847i
\(344\) 0 0
\(345\) −65.9558 114.239i −0.191176 0.331127i
\(346\) 0 0
\(347\) −95.6285 + 165.633i −0.275586 + 0.477330i −0.970283 0.241973i \(-0.922205\pi\)
0.694697 + 0.719303i \(0.255539\pi\)
\(348\) 0 0
\(349\) 135.448i 0.388104i −0.980991 0.194052i \(-0.937837\pi\)
0.980991 0.194052i \(-0.0621630\pi\)
\(350\) 0 0
\(351\) 191.823 0.546505
\(352\) 0 0
\(353\) −301.802 174.245i −0.854962 0.493612i 0.00736010 0.999973i \(-0.497657\pi\)
−0.862322 + 0.506360i \(0.830991\pi\)
\(354\) 0 0
\(355\) 209.184 120.772i 0.589250 0.340204i
\(356\) 0 0
\(357\) 15.8238 + 10.3158i 0.0443244 + 0.0288959i
\(358\) 0 0
\(359\) −152.415 263.991i −0.424555 0.735351i 0.571824 0.820377i \(-0.306236\pi\)
−0.996379 + 0.0850256i \(0.972903\pi\)
\(360\) 0 0
\(361\) −171.757 + 297.492i −0.475782 + 0.824079i
\(362\) 0 0
\(363\) 70.5727i 0.194415i
\(364\) 0 0
\(365\) 348.838 0.955720
\(366\) 0 0
\(367\) −82.2761 47.5021i −0.224186 0.129434i 0.383701 0.923457i \(-0.374649\pi\)
−0.607887 + 0.794024i \(0.707983\pi\)
\(368\) 0 0
\(369\) −205.456 + 118.620i −0.556791 + 0.321463i
\(370\) 0 0
\(371\) 21.1949 391.220i 0.0571291 1.05450i
\(372\) 0 0
\(373\) 126.779 + 219.588i 0.339891 + 0.588708i 0.984412 0.175879i \(-0.0562766\pi\)
−0.644521 + 0.764586i \(0.722943\pi\)
\(374\) 0 0
\(375\) 14.3421 24.8412i 0.0382456 0.0662433i
\(376\) 0 0
\(377\) 53.7446i 0.142559i
\(378\) 0 0
\(379\) −508.250 −1.34103 −0.670514 0.741897i \(-0.733926\pi\)
−0.670514 + 0.741897i \(0.733926\pi\)
\(380\) 0 0
\(381\) 153.676 + 88.7250i 0.403350 + 0.232874i
\(382\) 0 0
\(383\) 413.753 238.881i 1.08030 0.623709i 0.149320 0.988789i \(-0.452292\pi\)
0.930976 + 0.365080i \(0.118958\pi\)
\(384\) 0 0
\(385\) 99.9045 + 196.932i 0.259492 + 0.511511i
\(386\) 0 0
\(387\) −44.4853 77.0508i −0.114949 0.199098i
\(388\) 0 0
\(389\) 85.1102 147.415i 0.218792 0.378959i −0.735647 0.677365i \(-0.763122\pi\)
0.954439 + 0.298406i \(0.0964550\pi\)
\(390\) 0 0
\(391\) 104.292i 0.266732i
\(392\) 0 0
\(393\) −105.926 −0.269532
\(394\) 0 0
\(395\) 194.025 + 112.021i 0.491204 + 0.283597i
\(396\) 0 0
\(397\) −211.786 + 122.275i −0.533467 + 0.307997i −0.742427 0.669927i \(-0.766325\pi\)
0.208960 + 0.977924i \(0.432992\pi\)
\(398\) 0 0
\(399\) 18.7279 9.50079i 0.0469371 0.0238115i
\(400\) 0 0
\(401\) 208.786 + 361.629i 0.520664 + 0.901817i 0.999711 + 0.0240277i \(0.00764899\pi\)
−0.479047 + 0.877789i \(0.659018\pi\)
\(402\) 0 0
\(403\) −373.617 + 647.124i −0.927090 + 1.60577i
\(404\) 0 0
\(405\) 446.716i 1.10300i
\(406\) 0 0
\(407\) 13.9920 0.0343784
\(408\) 0 0
\(409\) 266.919 + 154.106i 0.652614 + 0.376787i 0.789457 0.613806i \(-0.210362\pi\)
−0.136843 + 0.990593i \(0.543696\pi\)
\(410\) 0 0
\(411\) −20.2386 + 11.6848i −0.0492424 + 0.0284301i
\(412\) 0 0
\(413\) −270.647 14.6627i −0.655320 0.0355029i
\(414\) 0 0
\(415\) 422.985 + 732.631i 1.01924 + 1.76538i
\(416\) 0 0
\(417\) −24.6030 + 42.6137i −0.0590001 + 0.102191i
\(418\) 0 0
\(419\) 103.142i 0.246163i 0.992397 + 0.123081i \(0.0392776\pi\)
−0.992397 + 0.123081i \(0.960722\pi\)
\(420\) 0 0
\(421\) 165.220 0.392447 0.196224 0.980559i \(-0.437132\pi\)
0.196224 + 0.980559i \(0.437132\pi\)
\(422\) 0 0
\(423\) −387.110 223.498i −0.915153 0.528364i
\(424\) 0 0
\(425\) −61.7939 + 35.6767i −0.145398 + 0.0839453i
\(426\) 0 0
\(427\) 345.996 530.736i 0.810295 1.24294i
\(428\) 0 0
\(429\) −26.0955 45.1987i −0.0608286 0.105358i
\(430\) 0 0
\(431\) −297.268 + 514.883i −0.689717 + 1.19463i 0.282212 + 0.959352i \(0.408932\pi\)
−0.971929 + 0.235273i \(0.924402\pi\)
\(432\) 0 0
\(433\) 40.6267i 0.0938261i −0.998899 0.0469131i \(-0.985062\pi\)
0.998899 0.0469131i \(-0.0149384\pi\)
\(434\) 0 0
\(435\) 16.7208 0.0384386
\(436\) 0 0
\(437\) −100.412 57.9727i −0.229775 0.132661i
\(438\) 0 0
\(439\) 126.959 73.3001i 0.289201 0.166971i −0.348380 0.937353i \(-0.613268\pi\)
0.637582 + 0.770383i \(0.279935\pi\)
\(440\) 0 0
\(441\) −413.345 44.9190i −0.937291 0.101857i
\(442\) 0 0
\(443\) 53.6802 + 92.9768i 0.121174 + 0.209880i 0.920231 0.391376i \(-0.128001\pi\)
−0.799057 + 0.601256i \(0.794667\pi\)
\(444\) 0 0
\(445\) −166.875 + 289.035i −0.374999 + 0.649518i
\(446\) 0 0
\(447\) 66.2892i 0.148298i
\(448\) 0 0
\(449\) 135.161 0.301028 0.150514 0.988608i \(-0.451907\pi\)
0.150514 + 0.988608i \(0.451907\pi\)
\(450\) 0 0
\(451\) 115.191 + 66.5055i 0.255412 + 0.147462i
\(452\) 0 0
\(453\) −57.0290 + 32.9257i −0.125892 + 0.0726837i
\(454\) 0 0
\(455\) −594.588 387.622i −1.30679 0.851918i
\(456\) 0 0
\(457\) −79.8675 138.335i −0.174765 0.302702i 0.765315 0.643656i \(-0.222583\pi\)
−0.940080 + 0.340954i \(0.889250\pi\)
\(458\) 0 0
\(459\) 23.5919 40.8623i 0.0513984 0.0890247i
\(460\) 0 0
\(461\) 310.250i 0.672993i −0.941685 0.336497i \(-0.890758\pi\)
0.941685 0.336497i \(-0.109242\pi\)
\(462\) 0 0
\(463\) −326.014 −0.704135 −0.352067 0.935975i \(-0.614521\pi\)
−0.352067 + 0.935975i \(0.614521\pi\)
\(464\) 0 0
\(465\) 201.331 + 116.238i 0.432969 + 0.249975i
\(466\) 0 0
\(467\) −515.769 + 297.779i −1.10443 + 0.637643i −0.937381 0.348306i \(-0.886757\pi\)
−0.167048 + 0.985949i \(0.553424\pi\)
\(468\) 0 0
\(469\) −13.1173 + 242.122i −0.0279687 + 0.516252i
\(470\) 0 0
\(471\) 3.03344 + 5.25408i 0.00644043 + 0.0111551i
\(472\) 0 0
\(473\) −24.9411 + 43.1993i −0.0527297 + 0.0913304i
\(474\) 0 0
\(475\) 79.3262i 0.167002i
\(476\) 0 0
\(477\) −474.926 −0.995652
\(478\) 0 0
\(479\) 438.798 + 253.340i 0.916071 + 0.528894i 0.882379 0.470539i \(-0.155940\pi\)
0.0336914 + 0.999432i \(0.489274\pi\)
\(480\) 0 0
\(481\) −38.9483 + 22.4868i −0.0809735 + 0.0467501i
\(482\) 0 0
\(483\) −63.0000 124.185i −0.130435 0.257113i
\(484\) 0 0
\(485\) 337.492 + 584.554i 0.695861 + 1.20527i
\(486\) 0 0
\(487\) −105.651 + 182.992i −0.216942 + 0.375755i −0.953872 0.300215i \(-0.902942\pi\)
0.736930 + 0.675970i \(0.236275\pi\)
\(488\) 0 0
\(489\) 159.255i 0.325676i
\(490\) 0 0
\(491\) 784.161 1.59707 0.798534 0.601949i \(-0.205609\pi\)
0.798534 + 0.601949i \(0.205609\pi\)
\(492\) 0 0
\(493\) 11.4487 + 6.60991i 0.0232225 + 0.0134075i
\(494\) 0 0
\(495\) 231.816 133.839i 0.468316 0.270382i
\(496\) 0 0
\(497\) 227.397 115.360i 0.457539 0.232112i
\(498\) 0 0
\(499\) −85.7462 148.517i −0.171836 0.297629i 0.767226 0.641377i \(-0.221637\pi\)
−0.939062 + 0.343748i \(0.888303\pi\)
\(500\) 0 0
\(501\) 60.5665 104.904i 0.120891 0.209390i
\(502\) 0 0
\(503\) 20.0883i 0.0399370i −0.999801 0.0199685i \(-0.993643\pi\)
0.999801 0.0199685i \(-0.00635659\pi\)
\(504\) 0 0
\(505\) 395.735 0.783634
\(506\) 0 0
\(507\) 40.2761 + 23.2534i 0.0794400 + 0.0458647i
\(508\) 0 0
\(509\) 412.890 238.382i 0.811178 0.468334i −0.0361865 0.999345i \(-0.511521\pi\)
0.847365 + 0.531011i \(0.178188\pi\)
\(510\) 0 0
\(511\) 367.709 + 19.9211i 0.719587 + 0.0389846i
\(512\) 0 0
\(513\) −26.2279 45.4281i −0.0511266 0.0885538i
\(514\) 0 0
\(515\) 398.452 690.139i 0.773693 1.34008i
\(516\) 0 0
\(517\) 250.613i 0.484744i
\(518\) 0 0
\(519\) −117.905 −0.227176
\(520\) 0 0
\(521\) 739.823 + 427.137i 1.42001 + 0.819841i 0.996299 0.0859587i \(-0.0273953\pi\)
0.423707 + 0.905799i \(0.360729\pi\)
\(522\) 0 0
\(523\) 513.554 296.501i 0.981940 0.566923i 0.0790845 0.996868i \(-0.474800\pi\)
0.902855 + 0.429945i \(0.141467\pi\)
\(524\) 0 0
\(525\) −52.0294 + 79.8098i −0.0991037 + 0.152019i
\(526\) 0 0
\(527\) 91.9005 + 159.176i 0.174384 + 0.302043i
\(528\) 0 0
\(529\) −119.919 + 207.706i −0.226690 + 0.392638i
\(530\) 0 0
\(531\) 328.555i 0.618748i
\(532\) 0 0
\(533\) −427.529 −0.802118
\(534\) 0 0
\(535\) −652.422 376.676i −1.21948 0.704068i
\(536\) 0 0
\(537\) −115.058 + 66.4290i −0.214262 + 0.123704i
\(538\) 0 0
\(539\) 94.0629 + 213.290i 0.174514 + 0.395715i
\(540\) 0 0
\(541\) 427.595 + 740.617i 0.790380 + 1.36898i 0.925732 + 0.378180i \(0.123450\pi\)
−0.135352 + 0.990798i \(0.543217\pi\)
\(542\) 0 0
\(543\) 55.6325 96.3583i 0.102454 0.177455i
\(544\) 0 0
\(545\) 963.546i 1.76797i
\(546\) 0 0
\(547\) −415.897 −0.760323 −0.380161 0.924920i \(-0.624132\pi\)
−0.380161 + 0.924920i \(0.624132\pi\)
\(548\) 0 0
\(549\) −665.095 383.993i −1.21147 0.699441i
\(550\) 0 0
\(551\) 12.7279 7.34847i 0.0230997 0.0133366i
\(552\) 0 0
\(553\) 198.124 + 129.161i 0.358272 + 0.233564i
\(554\) 0 0
\(555\) 6.99600 + 12.1174i 0.0126054 + 0.0218332i
\(556\) 0 0
\(557\) −292.110 + 505.950i −0.524435 + 0.908348i 0.475160 + 0.879899i \(0.342390\pi\)
−0.999595 + 0.0284485i \(0.990943\pi\)
\(558\) 0 0
\(559\) 160.333i 0.286822i
\(560\) 0 0
\(561\) −12.8377 −0.0228835
\(562\) 0 0
\(563\) −789.076 455.573i −1.40156 0.809189i −0.407004 0.913426i \(-0.633427\pi\)
−0.994552 + 0.104237i \(0.966760\pi\)
\(564\) 0 0
\(565\) 198.375 114.532i 0.351106 0.202711i
\(566\) 0 0
\(567\) −25.5107 + 470.882i −0.0449924 + 0.830480i
\(568\) 0 0
\(569\) −350.000 606.217i −0.615113 1.06541i −0.990365 0.138485i \(-0.955777\pi\)
0.375251 0.926923i \(-0.377556\pi\)
\(570\) 0 0
\(571\) −281.231 + 487.107i −0.492525 + 0.853077i −0.999963 0.00861055i \(-0.997259\pi\)
0.507438 + 0.861688i \(0.330592\pi\)
\(572\) 0 0
\(573\) 177.993i 0.310634i
\(574\) 0 0
\(575\) 526.014 0.914807
\(576\) 0 0
\(577\) −573.014 330.830i −0.993092 0.573362i −0.0868946 0.996218i \(-0.527694\pi\)
−0.906197 + 0.422856i \(0.861028\pi\)
\(578\) 0 0
\(579\) 95.8934 55.3641i 0.165619 0.0956202i
\(580\) 0 0
\(581\) 404.029 + 796.420i 0.695402 + 1.37077i
\(582\) 0 0
\(583\) 133.136 + 230.598i 0.228364 + 0.395538i
\(584\) 0 0
\(585\) −430.191 + 745.113i −0.735369 + 1.27370i
\(586\) 0 0
\(587\) 823.029i 1.40209i 0.713116 + 0.701046i \(0.247283\pi\)
−0.713116 + 0.701046i \(0.752717\pi\)
\(588\) 0 0
\(589\) 204.338 0.346924
\(590\) 0 0
\(591\) −112.523 64.9650i −0.190394 0.109924i
\(592\) 0 0
\(593\) −538.890 + 311.128i −0.908752 + 0.524668i −0.880029 0.474919i \(-0.842477\pi\)
−0.0287225 + 0.999587i \(0.509144\pi\)
\(594\) 0 0
\(595\) −155.698 + 78.9868i −0.261678 + 0.132751i
\(596\) 0 0
\(597\) −125.088 216.659i −0.209527 0.362912i
\(598\) 0 0
\(599\) 256.422 444.137i 0.428084 0.741463i −0.568619 0.822601i \(-0.692522\pi\)
0.996703 + 0.0811377i \(0.0258554\pi\)
\(600\) 0 0
\(601\) 680.160i 1.13171i 0.824504 + 0.565857i \(0.191454\pi\)
−0.824504 + 0.565857i \(0.808546\pi\)
\(602\) 0 0
\(603\) 293.927 0.487441
\(604\) 0 0
\(605\) 564.889 + 326.139i 0.933701 + 0.539073i
\(606\) 0 0
\(607\) 33.5482 19.3690i 0.0552688 0.0319095i −0.472111 0.881539i \(-0.656508\pi\)
0.527380 + 0.849630i \(0.323175\pi\)
\(608\) 0 0
\(609\) 17.6253 + 0.954877i 0.0289414 + 0.00156794i
\(610\) 0 0
\(611\) −402.765 697.609i −0.659189 1.14175i
\(612\) 0 0
\(613\) 200.552 347.366i 0.327164 0.566665i −0.654784 0.755816i \(-0.727240\pi\)
0.981948 + 0.189151i \(0.0605736\pi\)
\(614\) 0 0
\(615\) 133.011i 0.216278i
\(616\) 0 0
\(617\) −959.044 −1.55437 −0.777183 0.629275i \(-0.783352\pi\)
−0.777183 + 0.629275i \(0.783352\pi\)
\(618\) 0 0
\(619\) 869.951 + 502.267i 1.40541 + 0.811416i 0.994941 0.100457i \(-0.0320303\pi\)
0.410473 + 0.911873i \(0.365364\pi\)
\(620\) 0 0
\(621\) −301.235 + 173.918i −0.485081 + 0.280061i
\(622\) 0 0
\(623\) −192.408 + 295.142i −0.308841 + 0.473743i
\(624\) 0 0
\(625\) 369.691 + 640.323i 0.591505 + 1.02452i
\(626\) 0 0
\(627\) −7.13604 + 12.3600i −0.0113812 + 0.0197129i
\(628\) 0 0
\(629\) 11.0624i 0.0175873i
\(630\) 0 0
\(631\) −386.514 −0.612542 −0.306271 0.951944i \(-0.599081\pi\)
−0.306271 + 0.951944i \(0.599081\pi\)
\(632\) 0 0
\(633\) 226.206 + 130.600i 0.357356 + 0.206319i
\(634\) 0 0
\(635\) −1420.37 + 820.053i −2.23681 + 1.29142i
\(636\) 0 0
\(637\) −604.617 442.547i −0.949164 0.694736i
\(638\) 0 0
\(639\) −154.544 267.678i −0.241853 0.418902i
\(640\) 0 0
\(641\) 496.074 859.225i 0.773906 1.34044i −0.161502 0.986872i \(-0.551634\pi\)
0.935407 0.353572i \(-0.115033\pi\)
\(642\) 0 0
\(643\) 944.986i 1.46965i −0.678256 0.734826i \(-0.737264\pi\)
0.678256 0.734826i \(-0.262736\pi\)
\(644\) 0 0
\(645\) −49.8823 −0.0773368
\(646\) 0 0
\(647\) 2.50357 + 1.44544i 0.00386951 + 0.00223406i 0.501934 0.864906i \(-0.332622\pi\)
−0.498064 + 0.867140i \(0.665956\pi\)
\(648\) 0 0
\(649\) 159.529 92.1039i 0.245807 0.141917i
\(650\) 0 0
\(651\) 205.584 + 134.024i 0.315797 + 0.205874i
\(652\) 0 0
\(653\) −161.529 279.777i −0.247365 0.428449i 0.715429 0.698686i \(-0.246231\pi\)
−0.962794 + 0.270237i \(0.912898\pi\)
\(654\) 0 0
\(655\) 489.518 847.870i 0.747356 1.29446i
\(656\) 0 0
\(657\) 446.384i 0.679428i
\(658\) 0 0
\(659\) −295.955 −0.449098 −0.224549 0.974463i \(-0.572091\pi\)
−0.224549 + 0.974463i \(0.572091\pi\)
\(660\) 0 0
\(661\) −17.9710 10.3756i −0.0271876 0.0156968i 0.486345 0.873767i \(-0.338330\pi\)
−0.513532 + 0.858070i \(0.671663\pi\)
\(662\) 0 0
\(663\) 35.7351 20.6316i 0.0538990 0.0311186i
\(664\) 0 0
\(665\) −10.5000 + 193.811i −0.0157895 + 0.291445i
\(666\) 0 0
\(667\) −48.7279 84.3992i −0.0730554 0.126536i
\(668\) 0 0
\(669\) 44.2052 76.5656i 0.0660765 0.114448i
\(670\) 0 0
\(671\) 430.579i 0.641698i
\(672\) 0 0
\(673\) 627.044 0.931714 0.465857 0.884860i \(-0.345746\pi\)
0.465857 + 0.884860i \(0.345746\pi\)
\(674\) 0 0
\(675\) 206.095 + 118.989i 0.305327 + 0.176280i
\(676\) 0 0
\(677\) 94.6097 54.6230i 0.139749 0.0806838i −0.428496 0.903544i \(-0.640956\pi\)
0.568244 + 0.822860i \(0.307623\pi\)
\(678\) 0 0
\(679\) 322.368 + 635.450i 0.474768 + 0.935861i
\(680\) 0 0
\(681\) −27.3974 47.4537i −0.0402311 0.0696824i
\(682\) 0 0
\(683\) 396.783 687.248i 0.580941 1.00622i −0.414427 0.910083i \(-0.636018\pi\)
0.995368 0.0961370i \(-0.0306487\pi\)
\(684\) 0 0
\(685\) 215.996i 0.315323i
\(686\) 0 0
\(687\) 256.331 0.373116
\(688\) 0 0
\(689\) −741.198 427.931i −1.07576 0.621090i
\(690\) 0 0
\(691\) −159.253 + 91.9447i −0.230467 + 0.133060i −0.610788 0.791794i \(-0.709147\pi\)
0.380320 + 0.924855i \(0.375814\pi\)
\(692\) 0 0
\(693\) 252.000 127.841i 0.363636 0.184475i
\(694\) 0 0
\(695\) −227.397 393.863i −0.327190 0.566710i
\(696\) 0 0
\(697\) −52.5807 + 91.0725i −0.0754386 + 0.130664i
\(698\) 0 0
\(699\) 195.913i 0.280277i
\(700\) 0 0
\(701\) 1043.82 1.48905 0.744525 0.667595i \(-0.232676\pi\)
0.744525 + 0.667595i \(0.232676\pi\)
\(702\) 0 0
\(703\) 10.6508 + 6.14922i 0.0151504 + 0.00874711i
\(704\) 0 0
\(705\) −217.037 + 125.306i −0.307854 + 0.177740i
\(706\) 0 0
\(707\) 417.143 + 22.5993i 0.590019 + 0.0319651i
\(708\) 0 0
\(709\) −490.279 849.188i −0.691507 1.19773i −0.971344 0.237678i \(-0.923614\pi\)
0.279836 0.960048i \(-0.409720\pi\)
\(710\) 0 0
\(711\) 143.345 248.281i 0.201611 0.349200i
\(712\) 0 0
\(713\) 1354.97i 1.90038i
\(714\) 0 0
\(715\) 482.382 0.674660
\(716\) 0 0
\(717\) 164.714 + 95.0975i 0.229726 + 0.132632i
\(718\) 0 0
\(719\) −674.187 + 389.242i −0.937673 + 0.541366i −0.889230 0.457460i \(-0.848759\pi\)
−0.0484429 + 0.998826i \(0.515426\pi\)
\(720\) 0 0
\(721\) 459.419 704.719i 0.637197 0.977419i
\(722\) 0 0
\(723\) 31.4376 + 54.4514i 0.0434821 + 0.0753132i
\(724\) 0 0
\(725\) −33.3381 + 57.7433i −0.0459836 + 0.0796459i
\(726\) 0 0
\(727\) 735.255i 1.01135i −0.862723 0.505677i \(-0.831243\pi\)
0.862723 0.505677i \(-0.168757\pi\)
\(728\) 0 0
\(729\) 490.632 0.673021
\(730\) 0 0
\(731\) −34.1543 19.7190i −0.0467227 0.0269754i
\(732\) 0 0
\(733\) 414.705 239.430i 0.565764 0.326644i −0.189692 0.981844i \(-0.560749\pi\)
0.755456 + 0.655200i \(0.227415\pi\)
\(734\) 0 0
\(735\) −137.683 + 188.106i −0.187324 + 0.255926i
\(736\) 0 0
\(737\) −82.3965 142.715i −0.111800 0.193643i
\(738\) 0 0
\(739\) −9.95227 + 17.2378i −0.0134672 + 0.0233259i −0.872680 0.488292i \(-0.837620\pi\)
0.859213 + 0.511618i \(0.170954\pi\)
\(740\) 0 0
\(741\) 45.8739i 0.0619080i
\(742\) 0 0
\(743\) 43.3095 0.0582901 0.0291450 0.999575i \(-0.490722\pi\)
0.0291450 + 0.999575i \(0.490722\pi\)
\(744\) 0 0
\(745\) 530.603 + 306.344i 0.712218 + 0.411199i
\(746\) 0 0
\(747\) 937.499 541.265i 1.25502 0.724585i
\(748\) 0 0
\(749\) −666.206 434.311i −0.889460 0.579855i
\(750\) 0 0
\(751\) −112.665 195.142i −0.150020 0.259842i 0.781215 0.624263i \(-0.214600\pi\)
−0.931235 + 0.364420i \(0.881267\pi\)
\(752\) 0 0
\(753\) 177.801 307.961i 0.236124 0.408978i
\(754\) 0 0
\(755\) 608.641i 0.806147i
\(756\) 0 0
\(757\) −935.779 −1.23617 −0.618084 0.786112i \(-0.712091\pi\)
−0.618084 + 0.786112i \(0.712091\pi\)
\(758\) 0 0
\(759\) 81.9594 + 47.3193i 0.107983 + 0.0623443i
\(760\) 0 0
\(761\) 1214.79 701.357i 1.59630 0.921625i 0.604110 0.796901i \(-0.293529\pi\)
0.992191 0.124724i \(-0.0398046\pi\)
\(762\) 0 0
\(763\) −55.0254 + 1015.67i −0.0721172 + 1.33115i
\(764\) 0 0
\(765\) 105.816 + 183.279i 0.138322 + 0.239581i
\(766\) 0 0
\(767\) −296.044 + 512.763i −0.385976 + 0.668530i
\(768\) 0 0
\(769\) 1.72330i 0.00224097i 0.999999 + 0.00112048i \(0.000356661\pi\)
−0.999999 + 0.00112048i \(0.999643\pi\)
\(770\) 0 0
\(771\) −287.360 −0.372711
\(772\) 0 0
\(773\) −194.213 112.129i −0.251245 0.145057i 0.369089 0.929394i \(-0.379670\pi\)
−0.620334 + 0.784337i \(0.713003\pi\)
\(774\) 0 0
\(775\) −802.831 + 463.514i −1.03591 + 0.598083i
\(776\) 0 0
\(777\) 6.68247 + 13.1725i 0.00860034 + 0.0169530i
\(778\) 0 0
\(779\) 58.4558 + 101.248i 0.0750396 + 0.129972i
\(780\) 0 0
\(781\) −86.6468 + 150.077i −0.110943 + 0.192160i
\(782\) 0 0
\(783\) 44.0908i 0.0563101i
\(784\) 0 0
\(785\) −56.0740 −0.0714319
\(786\) 0 0
\(787\) −60.7979 35.1017i −0.0772528 0.0446019i 0.460876 0.887465i \(-0.347535\pi\)
−0.538129 + 0.842863i \(0.680869\pi\)
\(788\) 0 0
\(789\) −20.0968 + 11.6029i −0.0254712 + 0.0147058i
\(790\) 0 0
\(791\) 215.647 109.399i 0.272625 0.138305i
\(792\) 0 0