Properties

Label 3150.2.bf.e.1601.2
Level 3150
Weight 2
Character 3150.1601
Analytic conductor 25.153
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.bf (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1601.2
Character \(\chi\) = 3150.1601
Dual form 3150.2.bf.e.1151.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.34325 + 1.22849i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-2.34325 + 1.22849i) q^{7} -1.00000i q^{8} +(2.03986 - 1.17771i) q^{11} -4.64698i q^{13} +(2.64356 + 0.107718i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.28109 + 3.95097i) q^{17} +(0.491268 + 0.283634i) q^{19} -2.35542 q^{22} +(-5.04588 - 2.91324i) q^{23} +(-2.32349 + 4.02440i) q^{26} +(-2.23553 - 1.41507i) q^{28} +2.55339i q^{29} +(-1.89659 + 1.09500i) q^{31} +(0.866025 - 0.500000i) q^{32} -4.56218i q^{34} +(4.63355 - 8.02554i) q^{37} +(-0.283634 - 0.491268i) q^{38} +8.68451 q^{41} -6.57695 q^{43} +(2.03986 + 1.17771i) q^{44} +(2.91324 + 5.04588i) q^{46} +(-3.15616 + 5.46663i) q^{47} +(3.98161 - 5.75732i) q^{49} +(4.02440 - 2.32349i) q^{52} +(-10.5228 + 6.07533i) q^{53} +(1.22849 + 2.34325i) q^{56} +(1.27670 - 2.21130i) q^{58} +(1.67739 + 2.90532i) q^{59} +(-6.85523 - 3.95787i) q^{61} +2.18999 q^{62} -1.00000 q^{64} +(2.00143 + 3.46657i) q^{67} +(-2.28109 + 3.95097i) q^{68} +2.02720i q^{71} +(7.11528 - 4.10801i) q^{73} +(-8.02554 + 4.63355i) q^{74} +0.567267i q^{76} +(-3.33308 + 5.26562i) q^{77} +(4.13212 - 7.15704i) q^{79} +(-7.52101 - 4.34226i) q^{82} +0.171637 q^{83} +(5.69581 + 3.28848i) q^{86} +(-1.17771 - 2.03986i) q^{88} +(-2.72938 + 4.72742i) q^{89} +(5.70878 + 10.8890i) q^{91} -5.82648i q^{92} +(5.46663 - 3.15616i) q^{94} -10.8564i q^{97} +(-6.32684 + 2.99518i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 12q^{4} + 4q^{7} + O(q^{10}) \) \( 24q + 12q^{4} + 4q^{7} - 12q^{16} + 12q^{19} - 4q^{28} - 28q^{37} - 96q^{43} - 8q^{46} - 52q^{49} + 12q^{52} - 8q^{58} - 12q^{61} - 24q^{64} + 4q^{67} + 12q^{73} + 4q^{79} + 68q^{91} - 24q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) −2.34325 + 1.22849i −0.885664 + 0.464326i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0 0
\(11\) 2.03986 1.17771i 0.615040 0.355093i −0.159896 0.987134i \(-0.551116\pi\)
0.774935 + 0.632041i \(0.217782\pi\)
\(12\) 0 0
\(13\) 4.64698i 1.28884i −0.764672 0.644420i \(-0.777099\pi\)
0.764672 0.644420i \(-0.222901\pi\)
\(14\) 2.64356 + 0.107718i 0.706520 + 0.0287888i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 2.28109 + 3.95097i 0.553246 + 0.958250i 0.998038 + 0.0626158i \(0.0199443\pi\)
−0.444792 + 0.895634i \(0.646722\pi\)
\(18\) 0 0
\(19\) 0.491268 + 0.283634i 0.112705 + 0.0650700i 0.555293 0.831655i \(-0.312606\pi\)
−0.442588 + 0.896725i \(0.645940\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −2.35542 −0.502178
\(23\) −5.04588 2.91324i −1.05214 0.607453i −0.128891 0.991659i \(-0.541142\pi\)
−0.923247 + 0.384206i \(0.874475\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −2.32349 + 4.02440i −0.455674 + 0.789250i
\(27\) 0 0
\(28\) −2.23553 1.41507i −0.422475 0.267422i
\(29\) 2.55339i 0.474153i 0.971491 + 0.237077i \(0.0761893\pi\)
−0.971491 + 0.237077i \(0.923811\pi\)
\(30\) 0 0
\(31\) −1.89659 + 1.09500i −0.340638 + 0.196667i −0.660554 0.750778i \(-0.729679\pi\)
0.319916 + 0.947446i \(0.396345\pi\)
\(32\) 0.866025 0.500000i 0.153093 0.0883883i
\(33\) 0 0
\(34\) 4.56218i 0.782408i
\(35\) 0 0
\(36\) 0 0
\(37\) 4.63355 8.02554i 0.761750 1.31939i −0.180197 0.983630i \(-0.557674\pi\)
0.941948 0.335760i \(-0.108993\pi\)
\(38\) −0.283634 0.491268i −0.0460114 0.0796942i
\(39\) 0 0
\(40\) 0 0
\(41\) 8.68451 1.35629 0.678147 0.734927i \(-0.262783\pi\)
0.678147 + 0.734927i \(0.262783\pi\)
\(42\) 0 0
\(43\) −6.57695 −1.00298 −0.501488 0.865165i \(-0.667214\pi\)
−0.501488 + 0.865165i \(0.667214\pi\)
\(44\) 2.03986 + 1.17771i 0.307520 + 0.177547i
\(45\) 0 0
\(46\) 2.91324 + 5.04588i 0.429534 + 0.743975i
\(47\) −3.15616 + 5.46663i −0.460374 + 0.797391i −0.998979 0.0451673i \(-0.985618\pi\)
0.538606 + 0.842558i \(0.318951\pi\)
\(48\) 0 0
\(49\) 3.98161 5.75732i 0.568802 0.822475i
\(50\) 0 0
\(51\) 0 0
\(52\) 4.02440 2.32349i 0.558084 0.322210i
\(53\) −10.5228 + 6.07533i −1.44542 + 0.834511i −0.998203 0.0599168i \(-0.980916\pi\)
−0.447212 + 0.894428i \(0.647583\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.22849 + 2.34325i 0.164164 + 0.313130i
\(57\) 0 0
\(58\) 1.27670 2.21130i 0.167639 0.290359i
\(59\) 1.67739 + 2.90532i 0.218377 + 0.378241i 0.954312 0.298812i \(-0.0965903\pi\)
−0.735935 + 0.677053i \(0.763257\pi\)
\(60\) 0 0
\(61\) −6.85523 3.95787i −0.877722 0.506753i −0.00781543 0.999969i \(-0.502488\pi\)
−0.869907 + 0.493216i \(0.835821\pi\)
\(62\) 2.18999 0.278130
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 2.00143 + 3.46657i 0.244513 + 0.423509i 0.961995 0.273068i \(-0.0880385\pi\)
−0.717481 + 0.696578i \(0.754705\pi\)
\(68\) −2.28109 + 3.95097i −0.276623 + 0.479125i
\(69\) 0 0
\(70\) 0 0
\(71\) 2.02720i 0.240585i 0.992738 + 0.120292i \(0.0383832\pi\)
−0.992738 + 0.120292i \(0.961617\pi\)
\(72\) 0 0
\(73\) 7.11528 4.10801i 0.832780 0.480806i −0.0220235 0.999757i \(-0.507011\pi\)
0.854804 + 0.518952i \(0.173678\pi\)
\(74\) −8.02554 + 4.63355i −0.932950 + 0.538639i
\(75\) 0 0
\(76\) 0.567267i 0.0650700i
\(77\) −3.33308 + 5.26562i −0.379839 + 0.600073i
\(78\) 0 0
\(79\) 4.13212 7.15704i 0.464900 0.805230i −0.534297 0.845297i \(-0.679424\pi\)
0.999197 + 0.0400666i \(0.0127570\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −7.52101 4.34226i −0.830556 0.479522i
\(83\) 0.171637 0.0188396 0.00941978 0.999956i \(-0.497002\pi\)
0.00941978 + 0.999956i \(0.497002\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 5.69581 + 3.28848i 0.614195 + 0.354606i
\(87\) 0 0
\(88\) −1.17771 2.03986i −0.125544 0.217449i
\(89\) −2.72938 + 4.72742i −0.289313 + 0.501105i −0.973646 0.228065i \(-0.926760\pi\)
0.684333 + 0.729170i \(0.260094\pi\)
\(90\) 0 0
\(91\) 5.70878 + 10.8890i 0.598443 + 1.14148i
\(92\) 5.82648i 0.607453i
\(93\) 0 0
\(94\) 5.46663 3.15616i 0.563840 0.325533i
\(95\) 0 0
\(96\) 0 0
\(97\) 10.8564i 1.10230i −0.834406 0.551151i \(-0.814189\pi\)
0.834406 0.551151i \(-0.185811\pi\)
\(98\) −6.32684 + 2.99518i −0.639107 + 0.302559i
\(99\) 0 0
\(100\) 0 0
\(101\) −5.74827 9.95630i −0.571975 0.990689i −0.996363 0.0852090i \(-0.972844\pi\)
0.424388 0.905480i \(-0.360489\pi\)
\(102\) 0 0
\(103\) −16.7782 9.68690i −1.65320 0.954478i −0.975743 0.218920i \(-0.929747\pi\)
−0.677462 0.735558i \(-0.736920\pi\)
\(104\) −4.64698 −0.455674
\(105\) 0 0
\(106\) 12.1507 1.18018
\(107\) −9.28430 5.36029i −0.897547 0.518199i −0.0211436 0.999776i \(-0.506731\pi\)
−0.876404 + 0.481577i \(0.840064\pi\)
\(108\) 0 0
\(109\) −5.41186 9.37362i −0.518363 0.897830i −0.999772 0.0213347i \(-0.993208\pi\)
0.481410 0.876496i \(-0.340125\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.107718 2.64356i 0.0101784 0.249793i
\(113\) 18.4343i 1.73415i −0.498176 0.867076i \(-0.665997\pi\)
0.498176 0.867076i \(-0.334003\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −2.21130 + 1.27670i −0.205314 + 0.118538i
\(117\) 0 0
\(118\) 3.35478i 0.308832i
\(119\) −10.1989 6.45578i −0.934931 0.591801i
\(120\) 0 0
\(121\) −2.72599 + 4.72156i −0.247817 + 0.429232i
\(122\) 3.95787 + 6.85523i 0.358329 + 0.620643i
\(123\) 0 0
\(124\) −1.89659 1.09500i −0.170319 0.0983337i
\(125\) 0 0
\(126\) 0 0
\(127\) 4.04880 0.359273 0.179637 0.983733i \(-0.442508\pi\)
0.179637 + 0.983733i \(0.442508\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) 7.14129 12.3691i 0.623937 1.08069i −0.364808 0.931083i \(-0.618866\pi\)
0.988745 0.149608i \(-0.0478012\pi\)
\(132\) 0 0
\(133\) −1.49960 0.0611049i −0.130032 0.00529846i
\(134\) 4.00285i 0.345794i
\(135\) 0 0
\(136\) 3.95097 2.28109i 0.338792 0.195602i
\(137\) 4.52794 2.61421i 0.386848 0.223347i −0.293945 0.955822i \(-0.594968\pi\)
0.680794 + 0.732475i \(0.261635\pi\)
\(138\) 0 0
\(139\) 19.4726i 1.65164i −0.563933 0.825820i \(-0.690712\pi\)
0.563933 0.825820i \(-0.309288\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.01360 1.75561i 0.0850596 0.147328i
\(143\) −5.47280 9.47917i −0.457659 0.792688i
\(144\) 0 0
\(145\) 0 0
\(146\) −8.21601 −0.679962
\(147\) 0 0
\(148\) 9.26709 0.761750
\(149\) 4.79814 + 2.77021i 0.393079 + 0.226944i 0.683493 0.729957i \(-0.260460\pi\)
−0.290414 + 0.956901i \(0.593793\pi\)
\(150\) 0 0
\(151\) 4.23984 + 7.34362i 0.345033 + 0.597615i 0.985360 0.170488i \(-0.0545343\pi\)
−0.640327 + 0.768103i \(0.721201\pi\)
\(152\) 0.283634 0.491268i 0.0230057 0.0398471i
\(153\) 0 0
\(154\) 5.51934 2.89362i 0.444761 0.233174i
\(155\) 0 0
\(156\) 0 0
\(157\) −0.970763 + 0.560470i −0.0774753 + 0.0447304i −0.538237 0.842793i \(-0.680910\pi\)
0.460762 + 0.887524i \(0.347576\pi\)
\(158\) −7.15704 + 4.13212i −0.569384 + 0.328734i
\(159\) 0 0
\(160\) 0 0
\(161\) 15.4026 + 0.627617i 1.21390 + 0.0494631i
\(162\) 0 0
\(163\) 3.35749 5.81534i 0.262979 0.455493i −0.704053 0.710147i \(-0.748628\pi\)
0.967032 + 0.254654i \(0.0819617\pi\)
\(164\) 4.34226 + 7.52101i 0.339073 + 0.587292i
\(165\) 0 0
\(166\) −0.148642 0.0858183i −0.0115368 0.00666079i
\(167\) −2.80110 −0.216756 −0.108378 0.994110i \(-0.534566\pi\)
−0.108378 + 0.994110i \(0.534566\pi\)
\(168\) 0 0
\(169\) −8.59442 −0.661109
\(170\) 0 0
\(171\) 0 0
\(172\) −3.28848 5.69581i −0.250744 0.434301i
\(173\) −6.90018 + 11.9515i −0.524611 + 0.908653i 0.474978 + 0.879998i \(0.342456\pi\)
−0.999589 + 0.0286558i \(0.990877\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.35542i 0.177547i
\(177\) 0 0
\(178\) 4.72742 2.72938i 0.354335 0.204575i
\(179\) 2.31980 1.33933i 0.173390 0.100107i −0.410794 0.911728i \(-0.634748\pi\)
0.584183 + 0.811622i \(0.301415\pi\)
\(180\) 0 0
\(181\) 6.88082i 0.511447i 0.966750 + 0.255724i \(0.0823137\pi\)
−0.966750 + 0.255724i \(0.917686\pi\)
\(182\) 0.500563 12.2846i 0.0371042 0.910592i
\(183\) 0 0
\(184\) −2.91324 + 5.04588i −0.214767 + 0.371987i
\(185\) 0 0
\(186\) 0 0
\(187\) 9.30619 + 5.37293i 0.680536 + 0.392908i
\(188\) −6.31233 −0.460374
\(189\) 0 0
\(190\) 0 0
\(191\) 8.65356 + 4.99614i 0.626150 + 0.361508i 0.779260 0.626701i \(-0.215595\pi\)
−0.153110 + 0.988209i \(0.548929\pi\)
\(192\) 0 0
\(193\) −12.5643 21.7620i −0.904398 1.56646i −0.821723 0.569887i \(-0.806987\pi\)
−0.0826753 0.996577i \(-0.526346\pi\)
\(194\) −5.42821 + 9.40193i −0.389723 + 0.675019i
\(195\) 0 0
\(196\) 6.97679 + 0.569517i 0.498342 + 0.0406798i
\(197\) 20.0811i 1.43072i 0.698757 + 0.715359i \(0.253737\pi\)
−0.698757 + 0.715359i \(0.746263\pi\)
\(198\) 0 0
\(199\) −10.3028 + 5.94834i −0.730348 + 0.421667i −0.818550 0.574436i \(-0.805221\pi\)
0.0882014 + 0.996103i \(0.471888\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 11.4965i 0.808894i
\(203\) −3.13683 5.98323i −0.220162 0.419941i
\(204\) 0 0
\(205\) 0 0
\(206\) 9.68690 + 16.7782i 0.674918 + 1.16899i
\(207\) 0 0
\(208\) 4.02440 + 2.32349i 0.279042 + 0.161105i
\(209\) 1.33615 0.0924237
\(210\) 0 0
\(211\) −6.78640 −0.467195 −0.233597 0.972333i \(-0.575050\pi\)
−0.233597 + 0.972333i \(0.575050\pi\)
\(212\) −10.5228 6.07533i −0.722708 0.417256i
\(213\) 0 0
\(214\) 5.36029 + 9.28430i 0.366422 + 0.634662i
\(215\) 0 0
\(216\) 0 0
\(217\) 3.09899 4.89580i 0.210373 0.332348i
\(218\) 10.8237i 0.733075i
\(219\) 0 0
\(220\) 0 0
\(221\) 18.3601 10.6002i 1.23503 0.713045i
\(222\) 0 0
\(223\) 28.7684i 1.92648i −0.268646 0.963239i \(-0.586576\pi\)
0.268646 0.963239i \(-0.413424\pi\)
\(224\) −1.41507 + 2.23553i −0.0945480 + 0.149368i
\(225\) 0 0
\(226\) −9.21714 + 15.9646i −0.613115 + 1.06195i
\(227\) −1.05185 1.82186i −0.0698140 0.120921i 0.829005 0.559241i \(-0.188907\pi\)
−0.898819 + 0.438319i \(0.855574\pi\)
\(228\) 0 0
\(229\) −14.0269 8.09841i −0.926920 0.535158i −0.0410842 0.999156i \(-0.513081\pi\)
−0.885836 + 0.463998i \(0.846415\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 2.55339 0.167639
\(233\) 6.93805 + 4.00569i 0.454527 + 0.262421i 0.709740 0.704464i \(-0.248812\pi\)
−0.255213 + 0.966885i \(0.582146\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −1.67739 + 2.90532i −0.109189 + 0.189120i
\(237\) 0 0
\(238\) 5.60460 + 10.6903i 0.363293 + 0.692950i
\(239\) 15.6233i 1.01059i −0.862947 0.505294i \(-0.831384\pi\)
0.862947 0.505294i \(-0.168616\pi\)
\(240\) 0 0
\(241\) −3.54491 + 2.04665i −0.228348 + 0.131837i −0.609809 0.792548i \(-0.708754\pi\)
0.381462 + 0.924385i \(0.375421\pi\)
\(242\) 4.72156 2.72599i 0.303513 0.175233i
\(243\) 0 0
\(244\) 7.91574i 0.506753i
\(245\) 0 0
\(246\) 0 0
\(247\) 1.31804 2.28291i 0.0838648 0.145258i
\(248\) 1.09500 + 1.89659i 0.0695324 + 0.120434i
\(249\) 0 0
\(250\) 0 0
\(251\) −19.9413 −1.25869 −0.629343 0.777128i \(-0.716676\pi\)
−0.629343 + 0.777128i \(0.716676\pi\)
\(252\) 0 0
\(253\) −13.7238 −0.862810
\(254\) −3.50637 2.02440i −0.220009 0.127022i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 10.1722 17.6188i 0.634527 1.09903i −0.352088 0.935967i \(-0.614528\pi\)
0.986615 0.163067i \(-0.0521385\pi\)
\(258\) 0 0
\(259\) −0.998233 + 24.4981i −0.0620272 + 1.52224i
\(260\) 0 0
\(261\) 0 0
\(262\) −12.3691 + 7.14129i −0.764164 + 0.441190i
\(263\) 3.13156 1.80801i 0.193100 0.111487i −0.400333 0.916370i \(-0.631105\pi\)
0.593433 + 0.804883i \(0.297772\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 1.26814 + 0.802720i 0.0777548 + 0.0492179i
\(267\) 0 0
\(268\) −2.00143 + 3.46657i −0.122257 + 0.211755i
\(269\) −10.6172 18.3896i −0.647345 1.12123i −0.983755 0.179518i \(-0.942546\pi\)
0.336410 0.941716i \(-0.390787\pi\)
\(270\) 0 0
\(271\) −18.9957 10.9672i −1.15390 0.666207i −0.204069 0.978956i \(-0.565417\pi\)
−0.949836 + 0.312749i \(0.898750\pi\)
\(272\) −4.56218 −0.276623
\(273\) 0 0
\(274\) −5.22842 −0.315860
\(275\) 0 0
\(276\) 0 0
\(277\) 4.96452 + 8.59880i 0.298289 + 0.516652i 0.975745 0.218912i \(-0.0702508\pi\)
−0.677456 + 0.735564i \(0.736917\pi\)
\(278\) −9.73628 + 16.8637i −0.583943 + 1.01142i
\(279\) 0 0
\(280\) 0 0
\(281\) 11.0696i 0.660358i −0.943918 0.330179i \(-0.892891\pi\)
0.943918 0.330179i \(-0.107109\pi\)
\(282\) 0 0
\(283\) 19.6392 11.3387i 1.16743 0.674014i 0.214354 0.976756i \(-0.431235\pi\)
0.953072 + 0.302742i \(0.0979021\pi\)
\(284\) −1.75561 + 1.01360i −0.104176 + 0.0601462i
\(285\) 0 0
\(286\) 10.9456i 0.647227i
\(287\) −20.3500 + 10.6689i −1.20122 + 0.629763i
\(288\) 0 0
\(289\) −1.90675 + 3.30259i −0.112162 + 0.194270i
\(290\) 0 0
\(291\) 0 0
\(292\) 7.11528 + 4.10801i 0.416390 + 0.240403i
\(293\) 12.3248 0.720020 0.360010 0.932949i \(-0.382773\pi\)
0.360010 + 0.932949i \(0.382773\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −8.02554 4.63355i −0.466475 0.269319i
\(297\) 0 0
\(298\) −2.77021 4.79814i −0.160474 0.277949i
\(299\) −13.5378 + 23.4481i −0.782909 + 1.35604i
\(300\) 0 0
\(301\) 15.4114 8.07974i 0.888300 0.465708i
\(302\) 8.47968i 0.487951i
\(303\) 0 0
\(304\) −0.491268 + 0.283634i −0.0281761 + 0.0162675i
\(305\) 0 0
\(306\) 0 0
\(307\) 8.06274i 0.460165i −0.973171 0.230082i \(-0.926100\pi\)
0.973171 0.230082i \(-0.0738996\pi\)
\(308\) −6.22670 0.253721i −0.354799 0.0144571i
\(309\) 0 0
\(310\) 0 0
\(311\) −13.2215 22.9003i −0.749721 1.29855i −0.947956 0.318400i \(-0.896854\pi\)
0.198236 0.980154i \(-0.436479\pi\)
\(312\) 0 0
\(313\) 14.3180 + 8.26650i 0.809301 + 0.467250i 0.846713 0.532050i \(-0.178578\pi\)
−0.0374122 + 0.999300i \(0.511911\pi\)
\(314\) 1.12094 0.0632583
\(315\) 0 0
\(316\) 8.26424 0.464900
\(317\) 10.6181 + 6.13038i 0.596374 + 0.344317i 0.767614 0.640913i \(-0.221444\pi\)
−0.171240 + 0.985229i \(0.554777\pi\)
\(318\) 0 0
\(319\) 3.00716 + 5.20856i 0.168369 + 0.291623i
\(320\) 0 0
\(321\) 0 0
\(322\) −13.0253 8.24485i −0.725870 0.459468i
\(323\) 2.58798i 0.143999i
\(324\) 0 0
\(325\) 0 0
\(326\) −5.81534 + 3.35749i −0.322082 + 0.185954i
\(327\) 0 0
\(328\) 8.68451i 0.479522i
\(329\) 0.679951 16.6870i 0.0374869 0.919984i
\(330\) 0 0
\(331\) −17.1942 + 29.7812i −0.945077 + 1.63692i −0.189479 + 0.981885i \(0.560680\pi\)
−0.755598 + 0.655036i \(0.772654\pi\)
\(332\) 0.0858183 + 0.148642i 0.00470989 + 0.00815777i
\(333\) 0 0
\(334\) 2.42583 + 1.40055i 0.132735 + 0.0766348i
\(335\) 0 0
\(336\) 0 0
\(337\) −23.9536 −1.30484 −0.652418 0.757860i \(-0.726245\pi\)
−0.652418 + 0.757860i \(0.726245\pi\)
\(338\) 7.44298 + 4.29721i 0.404845 + 0.233737i
\(339\) 0 0
\(340\) 0 0
\(341\) −2.57918 + 4.46727i −0.139671 + 0.241916i
\(342\) 0 0
\(343\) −2.25708 + 18.3822i −0.121871 + 0.992546i
\(344\) 6.57695i 0.354606i
\(345\) 0 0
\(346\) 11.9515 6.90018i 0.642515 0.370956i
\(347\) −24.8552 + 14.3501i −1.33429 + 0.770355i −0.985955 0.167013i \(-0.946588\pi\)
−0.348340 + 0.937368i \(0.613254\pi\)
\(348\) 0 0
\(349\) 3.57176i 0.191192i −0.995420 0.0955960i \(-0.969524\pi\)
0.995420 0.0955960i \(-0.0304757\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.17771 2.03986i 0.0627722 0.108725i
\(353\) −6.26984 10.8597i −0.333710 0.578003i 0.649526 0.760339i \(-0.274967\pi\)
−0.983236 + 0.182337i \(0.941634\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −5.45875 −0.289313
\(357\) 0 0
\(358\) −2.67867 −0.141572
\(359\) −13.6940 7.90624i −0.722742 0.417275i 0.0930190 0.995664i \(-0.470348\pi\)
−0.815761 + 0.578389i \(0.803682\pi\)
\(360\) 0 0
\(361\) −9.33910 16.1758i −0.491532 0.851358i
\(362\) 3.44041 5.95896i 0.180824 0.313196i
\(363\) 0 0
\(364\) −6.57578 + 10.3885i −0.344664 + 0.544503i
\(365\) 0 0
\(366\) 0 0
\(367\) −30.8855 + 17.8317i −1.61221 + 0.930809i −0.623351 + 0.781942i \(0.714229\pi\)
−0.988857 + 0.148867i \(0.952437\pi\)
\(368\) 5.04588 2.91324i 0.263035 0.151863i
\(369\) 0 0
\(370\) 0 0
\(371\) 17.1940 27.1632i 0.892667 1.41024i
\(372\) 0 0
\(373\) −11.5306 + 19.9717i −0.597034 + 1.03409i 0.396222 + 0.918155i \(0.370321\pi\)
−0.993256 + 0.115939i \(0.963012\pi\)
\(374\) −5.37293 9.30619i −0.277828 0.481212i
\(375\) 0 0
\(376\) 5.46663 + 3.15616i 0.281920 + 0.162767i
\(377\) 11.8656 0.611108
\(378\) 0 0
\(379\) 8.20110 0.421262 0.210631 0.977566i \(-0.432448\pi\)
0.210631 + 0.977566i \(0.432448\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −4.99614 8.65356i −0.255625 0.442755i
\(383\) 2.31637 4.01207i 0.118361 0.205007i −0.800757 0.598989i \(-0.795569\pi\)
0.919118 + 0.393982i \(0.128903\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 25.1286i 1.27901i
\(387\) 0 0
\(388\) 9.40193 5.42821i 0.477311 0.275575i
\(389\) 29.0194 16.7544i 1.47134 0.849480i 0.471860 0.881673i \(-0.343583\pi\)
0.999482 + 0.0321938i \(0.0102494\pi\)
\(390\) 0 0
\(391\) 26.5815i 1.34428i
\(392\) −5.75732 3.98161i −0.290789 0.201102i
\(393\) 0 0
\(394\) 10.0405 17.3907i 0.505835 0.876132i
\(395\) 0 0
\(396\) 0 0
\(397\) 16.0748 + 9.28081i 0.806772 + 0.465790i 0.845834 0.533447i \(-0.179103\pi\)
−0.0390613 + 0.999237i \(0.512437\pi\)
\(398\) 11.8967 0.596327
\(399\) 0 0
\(400\) 0 0
\(401\) 12.1377 + 7.00770i 0.606128 + 0.349948i 0.771448 0.636292i \(-0.219533\pi\)
−0.165321 + 0.986240i \(0.552866\pi\)
\(402\) 0 0
\(403\) 5.08843 + 8.81342i 0.253473 + 0.439028i
\(404\) 5.74827 9.95630i 0.285987 0.495345i
\(405\) 0 0
\(406\) −0.275047 + 6.75005i −0.0136503 + 0.334999i
\(407\) 21.8279i 1.08197i
\(408\) 0 0
\(409\) 20.6162 11.9028i 1.01941 0.588555i 0.105474 0.994422i \(-0.466364\pi\)
0.913932 + 0.405868i \(0.133031\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 19.3738i 0.954478i
\(413\) −7.49970 4.74723i −0.369036 0.233596i
\(414\) 0 0
\(415\) 0 0
\(416\) −2.32349 4.02440i −0.113918 0.197313i
\(417\) 0 0
\(418\) −1.15714 0.668077i −0.0565977 0.0326767i
\(419\) −18.1374 −0.886068 −0.443034 0.896505i \(-0.646098\pi\)
−0.443034 + 0.896505i \(0.646098\pi\)
\(420\) 0 0
\(421\) 7.98092 0.388966 0.194483 0.980906i \(-0.437697\pi\)
0.194483 + 0.980906i \(0.437697\pi\)
\(422\) 5.87719 + 3.39320i 0.286097 + 0.165178i
\(423\) 0 0
\(424\) 6.07533 + 10.5228i 0.295044 + 0.511032i
\(425\) 0 0
\(426\) 0 0
\(427\) 20.9257 + 0.852667i 1.01267 + 0.0412635i
\(428\) 10.7206i 0.518199i
\(429\) 0 0
\(430\) 0 0
\(431\) −27.1353 + 15.6666i −1.30706 + 0.754632i −0.981605 0.190925i \(-0.938851\pi\)
−0.325456 + 0.945557i \(0.605518\pi\)
\(432\) 0 0
\(433\) 5.21564i 0.250648i 0.992116 + 0.125324i \(0.0399970\pi\)
−0.992116 + 0.125324i \(0.960003\pi\)
\(434\) −5.13170 + 2.69039i −0.246329 + 0.129143i
\(435\) 0 0
\(436\) 5.41186 9.37362i 0.259181 0.448915i
\(437\) −1.65259 2.86236i −0.0790539 0.136925i
\(438\) 0 0
\(439\) −8.91887 5.14931i −0.425675 0.245763i 0.271828 0.962346i \(-0.412372\pi\)
−0.697502 + 0.716583i \(0.745705\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −21.2004 −1.00840
\(443\) 35.9968 + 20.7828i 1.71026 + 0.987419i 0.934193 + 0.356768i \(0.116121\pi\)
0.776067 + 0.630651i \(0.217212\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −14.3842 + 24.9142i −0.681113 + 1.17972i
\(447\) 0 0
\(448\) 2.34325 1.22849i 0.110708 0.0580408i
\(449\) 23.7838i 1.12242i −0.827672 0.561212i \(-0.810335\pi\)
0.827672 0.561212i \(-0.189665\pi\)
\(450\) 0 0
\(451\) 17.7152 10.2279i 0.834174 0.481611i
\(452\) 15.9646 9.21714i 0.750910 0.433538i
\(453\) 0 0
\(454\) 2.10371i 0.0987319i
\(455\) 0 0
\(456\) 0 0
\(457\) 9.38745 16.2595i 0.439126 0.760589i −0.558496 0.829507i \(-0.688621\pi\)
0.997622 + 0.0689182i \(0.0219547\pi\)
\(458\) 8.09841 + 14.0269i 0.378414 + 0.655432i
\(459\) 0 0
\(460\) 0 0
\(461\) −17.4662 −0.813484 −0.406742 0.913543i \(-0.633335\pi\)
−0.406742 + 0.913543i \(0.633335\pi\)
\(462\) 0 0
\(463\) −2.99345 −0.139117 −0.0695586 0.997578i \(-0.522159\pi\)
−0.0695586 + 0.997578i \(0.522159\pi\)
\(464\) −2.21130 1.27670i −0.102657 0.0592692i
\(465\) 0 0
\(466\) −4.00569 6.93805i −0.185560 0.321399i
\(467\) −12.7050 + 22.0058i −0.587920 + 1.01831i 0.406585 + 0.913613i \(0.366720\pi\)
−0.994505 + 0.104694i \(0.966614\pi\)
\(468\) 0 0
\(469\) −8.94849 5.66430i −0.413203 0.261553i
\(470\) 0 0
\(471\) 0 0
\(472\) 2.90532 1.67739i 0.133728 0.0772081i
\(473\) −13.4160 + 7.74575i −0.616870 + 0.356150i
\(474\) 0 0
\(475\) 0 0
\(476\) 0.491429 12.0604i 0.0225246 0.552787i
\(477\) 0 0
\(478\) −7.81165 + 13.5302i −0.357297 + 0.618856i
\(479\) 11.8516 + 20.5276i 0.541514 + 0.937929i 0.998817 + 0.0486188i \(0.0154819\pi\)
−0.457304 + 0.889311i \(0.651185\pi\)
\(480\) 0 0
\(481\) −37.2945 21.5320i −1.70048 0.981774i
\(482\) 4.09331 0.186445
\(483\) 0 0
\(484\) −5.45198 −0.247817
\(485\) 0 0
\(486\) 0 0
\(487\) 5.10772 + 8.84683i 0.231453 + 0.400888i 0.958236 0.285979i \(-0.0923188\pi\)
−0.726783 + 0.686867i \(0.758985\pi\)
\(488\) −3.95787 + 6.85523i −0.179164 + 0.310322i
\(489\) 0 0
\(490\) 0 0
\(491\) 2.25910i 0.101952i −0.998700 0.0509758i \(-0.983767\pi\)
0.998700 0.0509758i \(-0.0162331\pi\)
\(492\) 0 0
\(493\) −10.0884 + 5.82452i −0.454357 + 0.262323i
\(494\) −2.28291 + 1.31804i −0.102713 + 0.0593014i
\(495\) 0 0
\(496\) 2.18999i 0.0983337i
\(497\) −2.49041 4.75024i −0.111710 0.213077i
\(498\) 0 0
\(499\) −17.6811 + 30.6246i −0.791517 + 1.37095i 0.133511 + 0.991047i \(0.457375\pi\)
−0.925028 + 0.379900i \(0.875958\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 17.2697 + 9.97066i 0.770784 + 0.445012i
\(503\) 30.7297 1.37017 0.685084 0.728464i \(-0.259766\pi\)
0.685084 + 0.728464i \(0.259766\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 11.8852 + 6.86191i 0.528361 + 0.305049i
\(507\) 0 0
\(508\) 2.02440 + 3.50637i 0.0898183 + 0.155570i
\(509\) −1.03925 + 1.80003i −0.0460637 + 0.0797847i −0.888138 0.459577i \(-0.848001\pi\)
0.842074 + 0.539362i \(0.181334\pi\)
\(510\) 0 0
\(511\) −11.6262 + 18.3671i −0.514313 + 0.812514i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −17.6188 + 10.1722i −0.777134 + 0.448679i
\(515\) 0 0
\(516\) 0 0
\(517\) 14.8682i 0.653903i
\(518\) 13.1135 20.7169i 0.576176 0.910246i
\(519\) 0 0
\(520\) 0 0
\(521\) −4.86182 8.42093i −0.213000 0.368927i 0.739652 0.672990i \(-0.234990\pi\)
−0.952652 + 0.304062i \(0.901657\pi\)
\(522\) 0 0
\(523\) 1.20378 + 0.695001i 0.0526375 + 0.0303903i 0.526088 0.850430i \(-0.323658\pi\)
−0.473450 + 0.880821i \(0.656992\pi\)
\(524\) 14.2826 0.623937
\(525\) 0 0
\(526\) −3.61602 −0.157666
\(527\) −8.65259 4.99558i −0.376913 0.217611i
\(528\) 0 0
\(529\) 5.47394 + 9.48114i 0.237997 + 0.412224i
\(530\) 0 0
\(531\) 0 0
\(532\) −0.696883 1.32925i −0.0302137 0.0576302i
\(533\) 40.3568i 1.74805i
\(534\) 0 0
\(535\) 0 0
\(536\) 3.46657 2.00143i 0.149733 0.0864485i
\(537\) 0 0
\(538\) 21.2345i 0.915484i
\(539\) 1.34145 16.4333i 0.0577805 0.707832i
\(540\) 0 0
\(541\) −22.5510 + 39.0594i −0.969541 + 1.67930i −0.272658 + 0.962111i \(0.587903\pi\)
−0.696884 + 0.717184i \(0.745431\pi\)
\(542\) 10.9672 + 18.9957i 0.471080 + 0.815934i
\(543\) 0 0
\(544\) 3.95097 + 2.28109i 0.169396 + 0.0978010i
\(545\) 0 0
\(546\) 0 0
\(547\) −11.1372 −0.476193 −0.238096 0.971242i \(-0.576523\pi\)
−0.238096 + 0.971242i \(0.576523\pi\)
\(548\) 4.52794 + 2.61421i 0.193424 + 0.111673i
\(549\) 0 0
\(550\) 0 0
\(551\) −0.724228 + 1.25440i −0.0308532 + 0.0534393i
\(552\) 0 0
\(553\) −0.890207 + 21.8470i −0.0378555 + 0.929029i
\(554\) 9.92903i 0.421844i
\(555\) 0 0
\(556\) 16.8637 9.73628i 0.715181 0.412910i
\(557\) −23.7662 + 13.7214i −1.00701 + 0.581395i −0.910314 0.413919i \(-0.864160\pi\)
−0.0966925 + 0.995314i \(0.530826\pi\)
\(558\) 0 0
\(559\) 30.5630i 1.29268i
\(560\) 0 0
\(561\) 0 0
\(562\) −5.53481 + 9.58656i −0.233472 + 0.404385i
\(563\) 16.6414 + 28.8238i 0.701352 + 1.21478i 0.967992 + 0.250981i \(0.0807531\pi\)
−0.266640 + 0.963796i \(0.585914\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −22.6773 −0.953200
\(567\) 0 0
\(568\) 2.02720 0.0850596
\(569\) 24.6215 + 14.2152i 1.03219 + 0.595932i 0.917610 0.397482i \(-0.130116\pi\)
0.114575 + 0.993415i \(0.463449\pi\)
\(570\) 0 0
\(571\) −14.0784 24.3845i −0.589162 1.02046i −0.994343 0.106221i \(-0.966125\pi\)
0.405181 0.914237i \(-0.367209\pi\)
\(572\) 5.47280 9.47917i 0.228829 0.396344i
\(573\) 0 0
\(574\) 22.9580 + 0.935478i 0.958249 + 0.0390461i
\(575\) 0 0
\(576\) 0 0
\(577\) −1.77604 + 1.02540i −0.0739377 + 0.0426879i −0.536513 0.843892i \(-0.680259\pi\)
0.462575 + 0.886580i \(0.346925\pi\)
\(578\) 3.30259 1.90675i 0.137370 0.0793103i
\(579\) 0 0
\(580\) 0 0
\(581\) −0.402187 + 0.210854i −0.0166855 + 0.00874771i
\(582\) 0 0
\(583\) −14.3100 + 24.7856i −0.592659 + 1.02652i
\(584\) −4.10801 7.11528i −0.169991 0.294432i
\(585\) 0 0
\(586\) −10.6735 6.16238i −0.440920 0.254565i
\(587\) 36.2336 1.49552 0.747761 0.663968i \(-0.231129\pi\)
0.747761 + 0.663968i \(0.231129\pi\)
\(588\) 0 0
\(589\) −1.24231 −0.0511886
\(590\) 0 0
\(591\) 0 0
\(592\) 4.63355 + 8.02554i 0.190438 + 0.329848i
\(593\) −17.3920 + 30.1239i −0.714205 + 1.23704i 0.249061 + 0.968488i \(0.419878\pi\)
−0.963265 + 0.268551i \(0.913455\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 5.54041i 0.226944i
\(597\) 0 0
\(598\) 23.4481 13.5378i 0.958864 0.553601i
\(599\) −31.6459 + 18.2708i −1.29302 + 0.746524i −0.979188 0.202956i \(-0.934945\pi\)
−0.313829 + 0.949479i \(0.601612\pi\)
\(600\) 0 0
\(601\) 45.5137i 1.85654i −0.371902 0.928272i \(-0.621294\pi\)
0.371902 0.928272i \(-0.378706\pi\)
\(602\) −17.3866 0.708456i −0.708623 0.0288745i
\(603\) 0 0
\(604\) −4.23984 + 7.34362i −0.172517 + 0.298807i
\(605\) 0 0
\(606\) 0 0
\(607\) 31.8414 + 18.3836i 1.29240 + 0.746169i 0.979080 0.203478i \(-0.0652245\pi\)
0.313323 + 0.949647i \(0.398558\pi\)
\(608\) 0.567267 0.0230057
\(609\) 0 0
\(610\) 0 0
\(611\) 25.4033 + 14.6666i 1.02771 + 0.593348i
\(612\) 0 0
\(613\) 16.3557 + 28.3288i 0.660599 + 1.14419i 0.980459 + 0.196726i \(0.0630309\pi\)
−0.319860 + 0.947465i \(0.603636\pi\)
\(614\) −4.03137 + 6.98254i −0.162693 + 0.281792i
\(615\) 0 0
\(616\) 5.26562 + 3.33308i 0.212158 + 0.134294i
\(617\) 20.5530i 0.827435i −0.910405 0.413717i \(-0.864230\pi\)
0.910405 0.413717i \(-0.135770\pi\)
\(618\) 0 0
\(619\) 14.9593 8.63675i 0.601265 0.347140i −0.168274 0.985740i \(-0.553819\pi\)
0.769539 + 0.638600i \(0.220486\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 26.4429i 1.06027i
\(623\) 0.588006 14.4305i 0.0235580 0.578147i
\(624\) 0 0
\(625\) 0 0
\(626\) −8.26650 14.3180i −0.330396 0.572262i
\(627\) 0 0
\(628\) −0.970763 0.560470i −0.0387377 0.0223652i
\(629\) 42.2782 1.68574
\(630\) 0 0
\(631\) 32.7501 1.30376 0.651880 0.758322i \(-0.273981\pi\)
0.651880 + 0.758322i \(0.273981\pi\)
\(632\) −7.15704 4.13212i −0.284692 0.164367i
\(633\) 0 0
\(634\) −6.13038 10.6181i −0.243469 0.421700i
\(635\) 0 0
\(636\) 0 0
\(637\) −26.7542 18.5025i −1.06004 0.733095i
\(638\) 6.01432i 0.238109i
\(639\) 0 0
\(640\) 0 0
\(641\) 18.9300 10.9292i 0.747688 0.431678i −0.0771698 0.997018i \(-0.524588\pi\)
0.824858 + 0.565340i \(0.191255\pi\)
\(642\) 0 0
\(643\) 4.13643i 0.163125i −0.996668 0.0815624i \(-0.974009\pi\)
0.996668 0.0815624i \(-0.0259910\pi\)
\(644\) 7.15779 + 13.6529i 0.282056 + 0.537999i
\(645\) 0 0
\(646\) 1.29399 2.24125i 0.0509113 0.0881809i
\(647\) 15.4046 + 26.6816i 0.605618 + 1.04896i 0.991953 + 0.126603i \(0.0404075\pi\)
−0.386335 + 0.922358i \(0.626259\pi\)
\(648\) 0 0
\(649\) 6.84327 + 3.95096i 0.268622 + 0.155089i
\(650\) 0 0
\(651\) 0 0
\(652\) 6.71498 0.262979
\(653\) −5.97747 3.45110i −0.233917 0.135052i 0.378461 0.925617i \(-0.376453\pi\)
−0.612378 + 0.790565i \(0.709787\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −4.34226 + 7.52101i −0.169537 + 0.293646i
\(657\) 0 0
\(658\) −8.93235 + 14.1114i −0.348219 + 0.550119i
\(659\) 11.0895i 0.431985i 0.976395 + 0.215992i \(0.0692986\pi\)
−0.976395 + 0.215992i \(0.930701\pi\)
\(660\) 0 0
\(661\) 13.7077 7.91416i 0.533169 0.307825i −0.209137 0.977886i \(-0.567065\pi\)
0.742306 + 0.670061i \(0.233732\pi\)
\(662\) 29.7812 17.1942i 1.15748 0.668270i
\(663\) 0 0
\(664\) 0.171637i 0.00666079i
\(665\) 0 0
\(666\) 0 0
\(667\) 7.43865 12.8841i 0.288026 0.498875i
\(668\) −1.40055 2.42583i −0.0541890 0.0938581i
\(669\) 0 0
\(670\) 0 0
\(671\) −18.6449 −0.719779
\(672\) 0 0
\(673\) 27.8980 1.07539 0.537695 0.843139i \(-0.319295\pi\)
0.537695 + 0.843139i \(0.319295\pi\)
\(674\) 20.7444 + 11.9768i 0.799045 + 0.461329i
\(675\) 0 0
\(676\) −4.29721 7.44298i −0.165277 0.286269i
\(677\) 15.5739 26.9749i 0.598555 1.03673i −0.394479 0.918905i \(-0.629075\pi\)
0.993035 0.117823i \(-0.0375916\pi\)
\(678\) 0 0
\(679\) 13.3370 + 25.4393i 0.511828 + 0.976269i
\(680\) 0 0
\(681\) 0 0
\(682\) 4.46727 2.57918i 0.171061 0.0987620i
\(683\) 21.8168 12.5960i 0.834798 0.481971i −0.0206948 0.999786i \(-0.506588\pi\)
0.855493 + 0.517815i \(0.173254\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 11.1458 14.7909i 0.425548 0.564720i
\(687\) 0 0
\(688\) 3.28848 5.69581i 0.125372 0.217151i
\(689\) 28.2319 + 48.8992i 1.07555 + 1.86291i
\(690\) 0 0
\(691\) −27.2549 15.7356i −1.03683 0.598612i −0.117894 0.993026i \(-0.537614\pi\)
−0.918933 + 0.394414i \(0.870948\pi\)
\(692\) −13.8004 −0.524611
\(693\) 0 0
\(694\) 28.7003 1.08945
\(695\) 0 0
\(696\) 0 0
\(697\) 19.8102 + 34.3122i 0.750363 + 1.29967i
\(698\) −1.78588 + 3.09324i −0.0675966 + 0.117081i
\(699\) 0 0
\(700\) 0 0
\(701\) 5.19395i 0.196173i −0.995178 0.0980864i \(-0.968728\pi\)
0.995178 0.0980864i \(-0.0312721\pi\)
\(702\) 0 0
\(703\) 4.55262 2.62846i 0.171705 0.0991342i
\(704\) −2.03986 + 1.17771i −0.0768800 + 0.0443867i
\(705\) 0 0
\(706\) 12.5397i 0.471937i
\(707\) 25.7009 + 16.2684i 0.966581 + 0.611835i
\(708\) 0 0
\(709\) −17.9440 + 31.0800i −0.673903 + 1.16723i 0.302885 + 0.953027i \(0.402050\pi\)
−0.976788 + 0.214207i \(0.931283\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 4.72742 + 2.72938i 0.177167 + 0.102288i
\(713\) 12.7600 0.477864
\(714\) 0 0
\(715\) 0 0
\(716\) 2.31980 + 1.33933i 0.0866948 + 0.0500533i
\(717\) 0 0
\(718\) 7.90624 + 13.6940i 0.295058 + 0.511056i
\(719\) 13.0548 22.6115i 0.486861 0.843268i −0.513025 0.858374i \(-0.671475\pi\)
0.999886 + 0.0151058i \(0.00480851\pi\)
\(720\) 0 0
\(721\) 51.2157 + 2.08691i 1.90737 + 0.0777204i
\(722\) 18.6782i 0.695131i
\(723\) 0 0
\(724\) −5.95896 + 3.44041i −0.221463 + 0.127862i
\(725\) 0 0
\(726\) 0 0
\(727\) 19.0193i 0.705386i 0.935739 + 0.352693i \(0.114734\pi\)
−0.935739 + 0.352693i \(0.885266\pi\)
\(728\) 10.8890 5.70878i 0.403574 0.211581i
\(729\) 0 0
\(730\) 0 0
\(731\) −15.0026 25.9853i −0.554892 0.961101i
\(732\) 0 0
\(733\) −7.65553 4.41992i −0.282763 0.163254i 0.351910 0.936034i \(-0.385532\pi\)
−0.634674 + 0.772780i \(0.718866\pi\)
\(734\) 35.6635 1.31636
\(735\) 0 0
\(736\) −5.82648 −0.214767
\(737\) 8.16524 + 4.71421i 0.300771 + 0.173650i
\(738\) 0 0
\(739\) 8.20546 + 14.2123i 0.301843 + 0.522807i 0.976553 0.215276i \(-0.0690650\pi\)
−0.674711 + 0.738082i \(0.735732\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −28.4720 + 14.9270i −1.04524 + 0.547987i
\(743\) 47.4829i 1.74198i −0.491302 0.870989i \(-0.663479\pi\)
0.491302 0.870989i \(-0.336521\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 19.9717 11.5306i 0.731214 0.422167i
\(747\) 0 0
\(748\) 10.7459i 0.392908i
\(749\) 28.3405 + 1.15480i 1.03554 + 0.0421955i
\(750\) 0 0
\(751\) 17.4048 30.1459i 0.635109 1.10004i −0.351383 0.936232i \(-0.614289\pi\)
0.986492 0.163809i \(-0.0523781\pi\)
\(752\) −3.15616 5.46663i −0.115093 0.199348i
\(753\) 0 0
\(754\) −10.2759 5.93279i −0.374226 0.216059i
\(755\) 0 0
\(756\) 0 0
\(757\) 9.68581 0.352037 0.176018 0.984387i \(-0.443678\pi\)
0.176018 + 0.984387i \(0.443678\pi\)
\(758\) −7.10236 4.10055i −0.257969 0.148939i
\(759\) 0 0
\(760\) 0 0
\(761\) −22.2236 + 38.4924i −0.805605 + 1.39535i 0.110277 + 0.993901i \(0.464826\pi\)
−0.915882 + 0.401448i \(0.868507\pi\)
\(762\) 0 0
\(763\) 24.1968 + 15.3163i 0.875982 + 0.554487i
\(764\) 9.99228i 0.361508i
\(765\) 0 0
\(766\) −4.01207 + 2.31637i −0.144962 + 0.0836939i
\(767\) 13.5010 7.79479i 0.487492 0.281454i
\(768\) 0 0
\(769\) 41.0290i 1.47954i −0.672858 0.739771i \(-0.734934\pi\)
0.672858 0.739771i \(-0.265066\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 12.5643 21.7620i 0.452199 0.783232i
\(773\) −17.4971 30.3059i −0.629327 1.09003i −0.987687 0.156443i \(-0.949997\pi\)
0.358360 0.933583i \(-0.383336\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −10.8564 −0.389723
\(777\) 0 0
\(778\) −33.5087 −1.20135
\(779\) 4.26642 + 2.46322i 0.152860 + 0.0882540i
\(780\) 0 0
\(781\) 2.38746 + 4.13521i 0.0854301 + 0.147969i
\(782\) −13.2907 + 23.0202i −0.475276 + 0.823201i
\(783\) 0 0
\(784\) 2.99518 + 6.32684i 0.106971 + 0.225959i
\(785\) 0 0
\(786\) 0 0
\(787\) −19.3139 + 11.1509i −0.688465 + 0.397485i −0.803037 0.595930i \(-0.796784\pi\)
0.114572 + 0.993415i \(0.463450\pi\)