Properties

Label 3150.2.bf.d.1151.2
Level 3150
Weight 2
Character 3150.1151
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 1151.2
Character \(\chi\) = 3150.1151
Dual form 3150.2.bf.d.1601.2

$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 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 \(-0.448884\pi\)
−0.774935 + 0.632041i \(0.782218\pi\)
\(12\) 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 −0.444792 0.895634i \(-0.646722\pi\)
0.998038 0.0626158i \(-0.0199443\pi\)
\(18\) 0 0
\(19\) 0.491268 0.283634i 0.112705 0.0650700i −0.442588 0.896725i \(-0.645940\pi\)
0.555293 + 0.831655i \(0.312606\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 2.35542 0.502178
\(23\) −5.04588 + 2.91324i −1.05214 + 0.607453i −0.923247 0.384206i \(-0.874475\pi\)
−0.128891 + 0.991659i \(0.541142\pi\)
\(24\) 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 0.319916 0.947446i \(-0.396345\pi\)
−0.660554 + 0.750778i \(0.729679\pi\)
\(32\) 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 −0.941948 0.335760i \(-0.891007\pi\)
0.180197 0.983630i \(-0.442326\pi\)
\(38\) −0.283634 + 0.491268i −0.0460114 + 0.0796942i
\(39\) 0 0
\(40\) 0 0
\(41\) −8.68451 −1.35629 −0.678147 0.734927i \(-0.737217\pi\)
−0.678147 + 0.734927i \(0.737217\pi\)
\(42\) 0 0
\(43\) 6.57695 1.00298 0.501488 0.865165i \(-0.332786\pi\)
0.501488 + 0.865165i \(0.332786\pi\)
\(44\) −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 0.538606 0.842558i \(-0.318951\pi\)
−0.998979 + 0.0451673i \(0.985618\pi\)
\(48\) 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 −0.447212 0.894428i \(-0.647583\pi\)
−0.998203 + 0.0599168i \(0.980916\pi\)
\(54\) 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 \(-0.903410\pi\)
0.735935 + 0.677053i \(0.236743\pi\)
\(60\) 0 0
\(61\) −6.85523 + 3.95787i −0.877722 + 0.506753i −0.869907 0.493216i \(-0.835821\pi\)
−0.00781543 + 0.999969i \(0.502488\pi\)
\(62\) 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 \(-0.911961\pi\)
0.717481 + 0.696578i \(0.245295\pi\)
\(68\) −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 \(-0.492989\pi\)
−0.854804 + 0.518952i \(0.826322\pi\)
\(74\) 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 0.999197 0.0400666i \(-0.0127570\pi\)
−0.534297 + 0.845297i \(0.679424\pi\)
\(80\) 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 \(-0.0732397\pi\)
−0.684333 + 0.729170i \(0.739906\pi\)
\(90\) 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 −0.424388 0.905480i \(-0.639511\pi\)
0.996363 0.0852090i \(-0.0271558\pi\)
\(102\) 0 0
\(103\) 16.7782 9.68690i 1.65320 0.954478i 0.677462 0.735558i \(-0.263080\pi\)
0.975743 0.218920i \(-0.0702535\pi\)
\(104\) 4.64698 0.455674
\(105\) 0 0
\(106\) 12.1507 1.18018
\(107\) −9.28430 + 5.36029i −0.897547 + 0.518199i −0.876404 0.481577i \(-0.840064\pi\)
−0.0211436 + 0.999776i \(0.506731\pi\)
\(108\) 0 0
\(109\) −5.41186 + 9.37362i −0.518363 + 0.897830i 0.481410 + 0.876496i \(0.340125\pi\)
−0.999772 + 0.0213347i \(0.993208\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.107718 2.64356i −0.0101784 0.249793i
\(113\) 18.4343i 1.73415i 0.498176 + 0.867076i \(0.334003\pi\)
−0.498176 + 0.867076i \(0.665997\pi\)
\(114\) 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 \(-0.557492\pi\)
−0.179637 + 0.983733i \(0.557492\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) −7.14129 12.3691i −0.623937 1.08069i −0.988745 0.149608i \(-0.952199\pi\)
0.364808 0.931083i \(-0.381134\pi\)
\(132\) 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 0.680794 0.732475i \(-0.261635\pi\)
−0.293945 + 0.955822i \(0.594968\pi\)
\(138\) 0 0
\(139\) 19.4726i 1.65164i 0.563933 + 0.825820i \(0.309288\pi\)
−0.563933 + 0.825820i \(0.690712\pi\)
\(140\) 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 \(-0.739540\pi\)
0.290414 + 0.956901i \(0.406207\pi\)
\(150\) 0 0
\(151\) 4.23984 7.34362i 0.345033 0.597615i −0.640327 0.768103i \(-0.721201\pi\)
0.985360 + 0.170488i \(0.0545343\pi\)
\(152\) 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 \(-0.319090\pi\)
−0.460762 + 0.887524i \(0.652424\pi\)
\(158\) −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 \(-0.251372\pi\)
−0.967032 + 0.254654i \(0.918038\pi\)
\(164\) −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 −0.999589 0.0286558i \(-0.990877\pi\)
0.474978 0.879998i \(-0.342456\pi\)
\(174\) 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 \(-0.365252\pi\)
−0.584183 + 0.811622i \(0.698585\pi\)
\(180\) 0 0
\(181\) 6.88082i 0.511447i −0.966750 0.255724i \(-0.917686\pi\)
0.966750 0.255724i \(-0.0823137\pi\)
\(182\) 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 \(-0.784405\pi\)
0.153110 + 0.988209i \(0.451071\pi\)
\(192\) 0 0
\(193\) 12.5643 21.7620i 0.904398 1.56646i 0.0826753 0.996577i \(-0.473654\pi\)
0.821723 0.569887i \(-0.193013\pi\)
\(194\) 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 \(-0.746263\pi\)
0.698757 0.715359i \(-0.253737\pi\)
\(198\) 0 0
\(199\) −10.3028 5.94834i −0.730348 0.421667i 0.0882014 0.996103i \(-0.471888\pi\)
−0.818550 + 0.574436i \(0.805221\pi\)
\(200\) 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 −0.898819 0.438319i \(-0.855574\pi\)
0.829005 + 0.559241i \(0.188907\pi\)
\(228\) 0 0
\(229\) −14.0269 + 8.09841i −0.926920 + 0.535158i −0.885836 0.463998i \(-0.846415\pi\)
−0.0410842 + 0.999156i \(0.513081\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −2.55339 −0.167639
\(233\) 6.93805 4.00569i 0.454527 0.262421i −0.255213 0.966885i \(-0.582146\pi\)
0.709740 + 0.704464i \(0.248812\pi\)
\(234\) 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 0.381462 0.924385i \(-0.375421\pi\)
−0.609809 + 0.792548i \(0.708754\pi\)
\(242\) 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 \(-0.283324\pi\)
0.629343 + 0.777128i \(0.283324\pi\)
\(252\) 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 0.986615 + 0.163067i \(0.0521385\pi\)
−0.352088 + 0.935967i \(0.614528\pi\)
\(258\) 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 0.593433 0.804883i \(-0.297772\pi\)
−0.400333 + 0.916370i \(0.631105\pi\)
\(264\) 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 −0.336410 0.941716i \(-0.609213\pi\)
0.983755 0.179518i \(-0.0574539\pi\)
\(270\) 0 0
\(271\) −18.9957 + 10.9672i −1.15390 + 0.666207i −0.949836 0.312749i \(-0.898750\pi\)
−0.204069 + 0.978956i \(0.565417\pi\)
\(272\) −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 \(-0.929749\pi\)
0.677456 + 0.735564i \(0.263083\pi\)
\(278\) −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 \(-0.568765\pi\)
−0.953072 + 0.302742i \(0.902098\pi\)
\(284\) 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 −0.198236 0.980154i \(-0.563521\pi\)
0.947956 0.318400i \(-0.103146\pi\)
\(312\) 0 0
\(313\) −14.3180 + 8.26650i −0.809301 + 0.467250i −0.846713 0.532050i \(-0.821422\pi\)
0.0374122 + 0.999300i \(0.488089\pi\)
\(314\) −1.12094 −0.0632583
\(315\) 0 0
\(316\) 8.26424 0.464900
\(317\) 10.6181 6.13038i 0.596374 0.344317i −0.171240 0.985229i \(-0.554777\pi\)
0.767614 + 0.640913i \(0.221444\pi\)
\(318\) 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 −0.755598 0.655036i \(-0.772654\pi\)
−0.189479 0.981885i \(-0.560680\pi\)
\(332\) 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 \(-0.273755\pi\)
0.652418 + 0.757860i \(0.273755\pi\)
\(338\) 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 −0.348340 0.937368i \(-0.613254\pi\)
−0.985955 + 0.167013i \(0.946588\pi\)
\(348\) 0 0
\(349\) 3.57176i 0.191192i 0.995420 + 0.0955960i \(0.0304757\pi\)
−0.995420 + 0.0955960i \(0.969524\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.17771 2.03986i −0.0627722 0.108725i
\(353\) −6.26984 + 10.8597i −0.333710 + 0.578003i −0.983236 0.182337i \(-0.941634\pi\)
0.649526 + 0.760339i \(0.274967\pi\)
\(354\) 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 \(-0.529652\pi\)
0.815761 + 0.578389i \(0.196318\pi\)
\(360\) 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 0.988857 + 0.148867i \(0.0475627\pi\)
0.623351 + 0.781942i \(0.285771\pi\)
\(368\) 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 0.993256 + 0.115939i \(0.0369876\pi\)
−0.396222 + 0.918155i \(0.629679\pi\)
\(374\) 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 0.919118 0.393982i \(-0.128903\pi\)
−0.800757 + 0.598989i \(0.795569\pi\)
\(384\) 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 \(-0.656417\pi\)
−0.999482 + 0.0321938i \(0.989751\pi\)
\(390\) 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 \(-0.820897\pi\)
0.0390613 + 0.999237i \(0.487563\pi\)
\(398\) 11.8967 0.596327
\(399\) 0 0
\(400\) 0 0
\(401\) −12.1377 + 7.00770i −0.606128 + 0.349948i −0.771448 0.636292i \(-0.780467\pi\)
0.165321 + 0.986240i \(0.447134\pi\)
\(402\) 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 0.913932 0.405868i \(-0.133031\pi\)
0.105474 + 0.994422i \(0.466364\pi\)
\(410\) 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 \(-0.353902\pi\)
0.443034 + 0.896505i \(0.353902\pi\)
\(420\) 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 \(-0.0611488\pi\)
0.325456 + 0.945557i \(0.394482\pi\)
\(432\) 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 −0.697502 0.716583i \(-0.745705\pi\)
0.271828 + 0.962346i \(0.412372\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 21.2004 1.00840
\(443\) 35.9968 20.7828i 1.71026 0.987419i 0.776067 0.630651i \(-0.217212\pi\)
0.934193 0.356768i \(-0.116121\pi\)
\(444\) 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 \(-0.311379\pi\)
−0.997622 + 0.0689182i \(0.978045\pi\)
\(458\) 8.09841 14.0269i 0.378414 0.655432i
\(459\) 0 0
\(460\) 0 0
\(461\) 17.4662 0.813484 0.406742 0.913543i \(-0.366665\pi\)
0.406742 + 0.913543i \(0.366665\pi\)
\(462\) 0 0
\(463\) 2.99345 0.139117 0.0695586 0.997578i \(-0.477841\pi\)
0.0695586 + 0.997578i \(0.477841\pi\)
\(464\) 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 −0.994505 0.104694i \(-0.966614\pi\)
0.406585 0.913613i \(-0.366720\pi\)
\(468\) 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 0.457304 + 0.889311i \(0.348815\pi\)
−0.998817 + 0.0486188i \(0.984518\pi\)
\(480\) 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 \(-0.907681\pi\)
0.726783 + 0.686867i \(0.241015\pi\)
\(488\) −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 −0.925028 0.379900i \(-0.875958\pi\)
0.133511 0.991047i \(-0.457375\pi\)
\(500\) 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 \(-0.151999\pi\)
−0.842074 + 0.539362i \(0.818666\pi\)
\(510\) 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 \(-0.765010\pi\)
0.952652 + 0.304062i \(0.0983431\pi\)
\(522\) 0 0
\(523\) −1.20378 + 0.695001i −0.0526375 + 0.0303903i −0.526088 0.850430i \(-0.676342\pi\)
0.473450 + 0.880821i \(0.343008\pi\)
\(524\) −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 −0.696884 0.717184i \(-0.745431\pi\)
−0.272658 0.962111i \(-0.587903\pi\)
\(542\) 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 \(-0.423477\pi\)
0.238096 + 0.971242i \(0.423477\pi\)
\(548\) 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 −0.0966925 0.995314i \(-0.530826\pi\)
−0.910314 + 0.413919i \(0.864160\pi\)
\(558\) 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 −0.266640 0.963796i \(-0.585914\pi\)
0.967992 0.250981i \(-0.0807531\pi\)
\(564\) 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 \(-0.869884\pi\)
−0.114575 + 0.993415i \(0.536551\pi\)
\(570\) 0 0
\(571\) −14.0784 + 24.3845i −0.589162 + 1.02046i 0.405181 + 0.914237i \(0.367209\pi\)
−0.994343 + 0.106221i \(0.966125\pi\)
\(572\) 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 \(-0.319741\pi\)
−0.462575 + 0.886580i \(0.653075\pi\)
\(578\) 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 −0.963265 0.268551i \(-0.913455\pi\)
0.249061 0.968488i \(-0.419878\pi\)
\(594\) 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 \(-0.0650547\pi\)
0.313829 + 0.949479i \(0.398388\pi\)
\(600\) 0 0
\(601\) 45.5137i 1.85654i 0.371902 + 0.928272i \(0.378706\pi\)
−0.371902 + 0.928272i \(0.621294\pi\)
\(602\) −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 \(-0.934776\pi\)
−0.313323 + 0.949647i \(0.601442\pi\)
\(608\) 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 0.319860 + 0.947465i \(0.396364\pi\)
−0.980459 + 0.196726i \(0.936969\pi\)
\(614\) 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 \(0.135770\pi\)
−0.910405 + 0.413717i \(0.864230\pi\)
\(618\) 0 0
\(619\) 14.9593 + 8.63675i 0.601265 + 0.347140i 0.769539 0.638600i \(-0.220486\pi\)
−0.168274 + 0.985740i \(0.553819\pi\)
\(620\) 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 \(-0.475412\pi\)
−0.824858 + 0.565340i \(0.808745\pi\)
\(642\) 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 −0.386335 0.922358i \(-0.626259\pi\)
0.991953 0.126603i \(-0.0404075\pi\)
\(648\) 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 −0.612378 0.790565i \(-0.709787\pi\)
0.378461 + 0.925617i \(0.376453\pi\)
\(654\) 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 0.742306 0.670061i \(-0.233732\pi\)
−0.209137 + 0.977886i \(0.567065\pi\)
\(662\) 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 \(-0.680705\pi\)
−0.537695 + 0.843139i \(0.680705\pi\)
\(674\) −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 0.993035 + 0.117823i \(0.0375916\pi\)
−0.394479 + 0.918905i \(0.629075\pi\)
\(678\) 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 0.855493 0.517815i \(-0.173254\pi\)
−0.0206948 + 0.999786i \(0.506588\pi\)
\(684\) 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 −0.918933 0.394414i \(-0.870948\pi\)
−0.117894 + 0.993026i \(0.537614\pi\)
\(692\) −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 −0.976788 0.214207i \(-0.931283\pi\)
0.302885 0.953027i \(-0.402050\pi\)
\(710\) 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 \(-0.328525\pi\)
−0.999886 + 0.0151058i \(0.995191\pi\)
\(720\) 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 \(-0.614468\pi\)
0.634674 + 0.772780i \(0.281134\pi\)
\(734\) −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 −0.674711 0.738082i \(-0.735732\pi\)
0.976553 + 0.215276i \(0.0690650\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 28.4720 + 14.9270i 1.04524 + 0.547987i
\(743\) 47.4829i 1.74198i 0.491302 + 0.870989i \(0.336521\pi\)
−0.491302 + 0.870989i \(0.663479\pi\)
\(744\) 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 0.986492 + 0.163809i \(0.0523781\pi\)
−0.351383 + 0.936232i \(0.614289\pi\)
\(752\) −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 \(-0.556322\pi\)
−0.176018 + 0.984387i \(0.556322\pi\)
\(758\) −7.10236 + 4.10055i −0.257969 + 0.148939i
\(759\) 0 0
\(760\) 0 0
\(761\) 22.2236 + 38.4924i 0.805605 + 1.39535i 0.915882 + 0.401448i \(0.131493\pi\)
−0.110277 + 0.993901i \(0.535174\pi\)
\(762\) 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 \(0.265066\pi\)
−0.672858 + 0.739771i \(0.734934\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −12.5643 21.7620i −0.452199 0.783232i
\(773\) −17.4971 + 30.3059i −0.629327 + 1.09003i 0.358360 + 0.933583i \(0.383336\pi\)
−0.987687 + 0.156443i \(0.949997\pi\)
\(774\) 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 \(-0.203216\pi\)
−0.114572 + 0.993415i \(0.536550\pi\)
\(788\) −17.3907