Properties

Label 1456.2.r.p.625.3
Level $1456$
Weight $2$
Character 1456.625
Analytic conductor $11.626$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.6262185343\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - x^{9} + 8 x^{8} + 7 x^{7} + 41 x^{6} + 18 x^{5} + 58 x^{4} + 28 x^{3} + 64 x^{2} + 16 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 625.3
Root \(0.597828 - 1.03547i\) of defining polynomial
Character \(\chi\) \(=\) 1456.625
Dual form 1456.2.r.p.417.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.129894 - 0.224983i) q^{3} +(-1.96625 + 3.40565i) q^{5} +(-1.12324 + 2.39548i) q^{7} +(1.46625 - 2.53963i) q^{9} +O(q^{10})\) \(q+(-0.129894 - 0.224983i) q^{3} +(-1.96625 + 3.40565i) q^{5} +(-1.12324 + 2.39548i) q^{7} +(1.46625 - 2.53963i) q^{9} +(2.25314 + 3.90255i) q^{11} +1.00000 q^{13} +1.02162 q^{15} +(1.14070 + 1.97576i) q^{17} +(-0.893841 + 1.54818i) q^{19} +(0.684846 - 0.0584481i) q^{21} +(0.870106 - 1.50707i) q^{23} +(-5.23232 - 9.06264i) q^{25} -1.54120 q^{27} +1.65110 q^{29} +(2.80262 + 4.85427i) q^{31} +(0.585339 - 1.01384i) q^{33} +(-5.94959 - 8.53550i) q^{35} +(-3.57204 + 6.18695i) q^{37} +(-0.129894 - 0.224983i) q^{39} -8.11574 q^{41} -6.81353 q^{43} +(5.76606 + 9.98711i) q^{45} +(1.77271 - 3.07043i) q^{47} +(-4.47665 - 5.38141i) q^{49} +(0.296342 - 0.513279i) q^{51} +(-1.64483 - 2.84892i) q^{53} -17.7210 q^{55} +0.464419 q^{57} +(2.25314 + 3.90255i) q^{59} +(-3.77234 + 6.53388i) q^{61} +(4.43667 + 6.36500i) q^{63} +(-1.96625 + 3.40565i) q^{65} +(-6.33263 - 10.9684i) q^{67} -0.452087 q^{69} -9.54869 q^{71} +(-0.540019 - 0.935340i) q^{73} +(-1.35930 + 2.35437i) q^{75} +(-11.8793 + 1.01384i) q^{77} +(0.395849 - 0.685630i) q^{79} +(-4.19857 - 7.27214i) q^{81} +7.14643 q^{83} -8.97166 q^{85} +(-0.214468 - 0.371470i) q^{87} +(5.63281 - 9.75631i) q^{89} +(-1.12324 + 2.39548i) q^{91} +(0.728087 - 1.26108i) q^{93} +(-3.51504 - 6.08823i) q^{95} -8.81353 q^{97} +13.2147 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 2 q^{5} - q^{7} - 3 q^{9} + O(q^{10}) \) \( 10 q - 2 q^{5} - q^{7} - 3 q^{9} + 11 q^{11} + 10 q^{13} + 5 q^{17} + 9 q^{19} + 2 q^{21} + 10 q^{23} - 9 q^{25} - 6 q^{29} - 6 q^{31} - 8 q^{33} + 4 q^{35} - 4 q^{37} + 28 q^{41} - 4 q^{43} + 32 q^{45} + q^{47} - 11 q^{49} - 8 q^{51} - 17 q^{53} - 32 q^{57} + 11 q^{59} + 11 q^{61} - 5 q^{63} - 2 q^{65} + 13 q^{67} + 36 q^{69} - 30 q^{71} - 20 q^{75} - 46 q^{77} + 2 q^{79} + 19 q^{81} - 12 q^{83} - 44 q^{85} - 8 q^{87} + 4 q^{89} - q^{91} - 18 q^{93} - 12 q^{95} - 24 q^{97} - 22 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times\).

\(n\) \(561\) \(911\) \(1093\) \(1249\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.129894 0.224983i −0.0749945 0.129894i 0.826089 0.563539i \(-0.190561\pi\)
−0.901084 + 0.433645i \(0.857227\pi\)
\(4\) 0 0
\(5\) −1.96625 + 3.40565i −0.879336 + 1.52305i −0.0272650 + 0.999628i \(0.508680\pi\)
−0.852071 + 0.523426i \(0.824654\pi\)
\(6\) 0 0
\(7\) −1.12324 + 2.39548i −0.424546 + 0.905406i
\(8\) 0 0
\(9\) 1.46625 2.53963i 0.488752 0.846543i
\(10\) 0 0
\(11\) 2.25314 + 3.90255i 0.679346 + 1.17666i 0.975178 + 0.221422i \(0.0710699\pi\)
−0.295832 + 0.955240i \(0.595597\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 1.02162 0.263781
\(16\) 0 0
\(17\) 1.14070 + 1.97576i 0.276661 + 0.479192i 0.970553 0.240888i \(-0.0774386\pi\)
−0.693891 + 0.720080i \(0.744105\pi\)
\(18\) 0 0
\(19\) −0.893841 + 1.54818i −0.205061 + 0.355177i −0.950152 0.311786i \(-0.899073\pi\)
0.745091 + 0.666963i \(0.232406\pi\)
\(20\) 0 0
\(21\) 0.684846 0.0584481i 0.149446 0.0127544i
\(22\) 0 0
\(23\) 0.870106 1.50707i 0.181430 0.314245i −0.760938 0.648825i \(-0.775261\pi\)
0.942368 + 0.334579i \(0.108594\pi\)
\(24\) 0 0
\(25\) −5.23232 9.06264i −1.04646 1.81253i
\(26\) 0 0
\(27\) −1.54120 −0.296604
\(28\) 0 0
\(29\) 1.65110 0.306602 0.153301 0.988180i \(-0.451010\pi\)
0.153301 + 0.988180i \(0.451010\pi\)
\(30\) 0 0
\(31\) 2.80262 + 4.85427i 0.503365 + 0.871853i 0.999992 + 0.00388953i \(0.00123808\pi\)
−0.496628 + 0.867964i \(0.665429\pi\)
\(32\) 0 0
\(33\) 0.585339 1.01384i 0.101894 0.176486i
\(34\) 0 0
\(35\) −5.94959 8.53550i −1.00566 1.44276i
\(36\) 0 0
\(37\) −3.57204 + 6.18695i −0.587239 + 1.01713i 0.407353 + 0.913271i \(0.366452\pi\)
−0.994592 + 0.103857i \(0.966881\pi\)
\(38\) 0 0
\(39\) −0.129894 0.224983i −0.0207997 0.0360262i
\(40\) 0 0
\(41\) −8.11574 −1.26746 −0.633732 0.773552i \(-0.718478\pi\)
−0.633732 + 0.773552i \(0.718478\pi\)
\(42\) 0 0
\(43\) −6.81353 −1.03905 −0.519527 0.854454i \(-0.673892\pi\)
−0.519527 + 0.854454i \(0.673892\pi\)
\(44\) 0 0
\(45\) 5.76606 + 9.98711i 0.859554 + 1.48879i
\(46\) 0 0
\(47\) 1.77271 3.07043i 0.258577 0.447868i −0.707284 0.706929i \(-0.750080\pi\)
0.965861 + 0.259061i \(0.0834131\pi\)
\(48\) 0 0
\(49\) −4.47665 5.38141i −0.639522 0.768773i
\(50\) 0 0
\(51\) 0.296342 0.513279i 0.0414962 0.0718735i
\(52\) 0 0
\(53\) −1.64483 2.84892i −0.225934 0.391330i 0.730665 0.682736i \(-0.239210\pi\)
−0.956599 + 0.291406i \(0.905877\pi\)
\(54\) 0 0
\(55\) −17.7210 −2.38949
\(56\) 0 0
\(57\) 0.464419 0.0615138
\(58\) 0 0
\(59\) 2.25314 + 3.90255i 0.293333 + 0.508068i 0.974596 0.223971i \(-0.0719021\pi\)
−0.681262 + 0.732039i \(0.738569\pi\)
\(60\) 0 0
\(61\) −3.77234 + 6.53388i −0.482998 + 0.836577i −0.999809 0.0195220i \(-0.993786\pi\)
0.516811 + 0.856099i \(0.327119\pi\)
\(62\) 0 0
\(63\) 4.43667 + 6.36500i 0.558968 + 0.801915i
\(64\) 0 0
\(65\) −1.96625 + 3.40565i −0.243884 + 0.422419i
\(66\) 0 0
\(67\) −6.33263 10.9684i −0.773653 1.34001i −0.935548 0.353199i \(-0.885094\pi\)
0.161895 0.986808i \(-0.448239\pi\)
\(68\) 0 0
\(69\) −0.452087 −0.0544249
\(70\) 0 0
\(71\) −9.54869 −1.13322 −0.566610 0.823986i \(-0.691746\pi\)
−0.566610 + 0.823986i \(0.691746\pi\)
\(72\) 0 0
\(73\) −0.540019 0.935340i −0.0632044 0.109473i 0.832692 0.553737i \(-0.186799\pi\)
−0.895896 + 0.444264i \(0.853465\pi\)
\(74\) 0 0
\(75\) −1.35930 + 2.35437i −0.156958 + 0.271859i
\(76\) 0 0
\(77\) −11.8793 + 1.01384i −1.35377 + 0.115537i
\(78\) 0 0
\(79\) 0.395849 0.685630i 0.0445365 0.0771394i −0.842898 0.538074i \(-0.819152\pi\)
0.887434 + 0.460934i \(0.152486\pi\)
\(80\) 0 0
\(81\) −4.19857 7.27214i −0.466508 0.808016i
\(82\) 0 0
\(83\) 7.14643 0.784422 0.392211 0.919875i \(-0.371710\pi\)
0.392211 + 0.919875i \(0.371710\pi\)
\(84\) 0 0
\(85\) −8.97166 −0.973114
\(86\) 0 0
\(87\) −0.214468 0.371470i −0.0229934 0.0398258i
\(88\) 0 0
\(89\) 5.63281 9.75631i 0.597077 1.03417i −0.396174 0.918176i \(-0.629662\pi\)
0.993250 0.115992i \(-0.0370045\pi\)
\(90\) 0 0
\(91\) −1.12324 + 2.39548i −0.117748 + 0.251115i
\(92\) 0 0
\(93\) 0.728087 1.26108i 0.0754991 0.130768i
\(94\) 0 0
\(95\) −3.51504 6.08823i −0.360636 0.624639i
\(96\) 0 0
\(97\) −8.81353 −0.894879 −0.447439 0.894314i \(-0.647664\pi\)
−0.447439 + 0.894314i \(0.647664\pi\)
\(98\) 0 0
\(99\) 13.2147 1.32813
\(100\) 0 0
\(101\) 7.15855 + 12.3990i 0.712303 + 1.23374i 0.963991 + 0.265936i \(0.0856810\pi\)
−0.251688 + 0.967808i \(0.580986\pi\)
\(102\) 0 0
\(103\) −3.74607 + 6.48839i −0.369111 + 0.639320i −0.989427 0.145033i \(-0.953671\pi\)
0.620315 + 0.784352i \(0.287005\pi\)
\(104\) 0 0
\(105\) −1.14753 + 2.44727i −0.111987 + 0.238829i
\(106\) 0 0
\(107\) 5.48919 9.50756i 0.530660 0.919130i −0.468700 0.883357i \(-0.655277\pi\)
0.999360 0.0357726i \(-0.0113892\pi\)
\(108\) 0 0
\(109\) 6.22314 + 10.7788i 0.596068 + 1.03242i 0.993395 + 0.114744i \(0.0366046\pi\)
−0.397327 + 0.917677i \(0.630062\pi\)
\(110\) 0 0
\(111\) 1.85595 0.176159
\(112\) 0 0
\(113\) −1.65110 −0.155323 −0.0776613 0.996980i \(-0.524745\pi\)
−0.0776613 + 0.996980i \(0.524745\pi\)
\(114\) 0 0
\(115\) 3.42170 + 5.92656i 0.319075 + 0.552654i
\(116\) 0 0
\(117\) 1.46625 2.53963i 0.135555 0.234789i
\(118\) 0 0
\(119\) −6.01418 + 0.513279i −0.551319 + 0.0470522i
\(120\) 0 0
\(121\) −4.65325 + 8.05967i −0.423023 + 0.732697i
\(122\) 0 0
\(123\) 1.05419 + 1.82591i 0.0950528 + 0.164636i
\(124\) 0 0
\(125\) 21.4897 1.92210
\(126\) 0 0
\(127\) 4.49297 0.398687 0.199343 0.979930i \(-0.436119\pi\)
0.199343 + 0.979930i \(0.436119\pi\)
\(128\) 0 0
\(129\) 0.885039 + 1.53293i 0.0779233 + 0.134967i
\(130\) 0 0
\(131\) −6.32836 + 10.9610i −0.552911 + 0.957670i 0.445151 + 0.895455i \(0.353150\pi\)
−0.998063 + 0.0622152i \(0.980184\pi\)
\(132\) 0 0
\(133\) −2.70463 3.88016i −0.234521 0.336453i
\(134\) 0 0
\(135\) 3.03039 5.24878i 0.260814 0.451743i
\(136\) 0 0
\(137\) 4.64321 + 8.04227i 0.396696 + 0.687097i 0.993316 0.115426i \(-0.0368234\pi\)
−0.596620 + 0.802524i \(0.703490\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) −0.921061 −0.0775673
\(142\) 0 0
\(143\) 2.25314 + 3.90255i 0.188417 + 0.326347i
\(144\) 0 0
\(145\) −3.24649 + 5.62308i −0.269606 + 0.466971i
\(146\) 0 0
\(147\) −0.629237 + 1.70619i −0.0518986 + 0.140724i
\(148\) 0 0
\(149\) 7.58243 13.1332i 0.621177 1.07591i −0.368090 0.929790i \(-0.619988\pi\)
0.989267 0.146120i \(-0.0466786\pi\)
\(150\) 0 0
\(151\) 2.57079 + 4.45274i 0.209208 + 0.362359i 0.951465 0.307756i \(-0.0995780\pi\)
−0.742257 + 0.670115i \(0.766245\pi\)
\(152\) 0 0
\(153\) 6.69025 0.540875
\(154\) 0 0
\(155\) −22.0426 −1.77051
\(156\) 0 0
\(157\) 5.36557 + 9.29344i 0.428219 + 0.741697i 0.996715 0.0809889i \(-0.0258078\pi\)
−0.568496 + 0.822686i \(0.692474\pi\)
\(158\) 0 0
\(159\) −0.427307 + 0.740117i −0.0338877 + 0.0586951i
\(160\) 0 0
\(161\) 2.63281 + 3.77712i 0.207495 + 0.297679i
\(162\) 0 0
\(163\) 1.18620 2.05455i 0.0929101 0.160925i −0.815824 0.578300i \(-0.803716\pi\)
0.908734 + 0.417375i \(0.137050\pi\)
\(164\) 0 0
\(165\) 2.30185 + 3.98692i 0.179199 + 0.310382i
\(166\) 0 0
\(167\) −12.0784 −0.934653 −0.467327 0.884085i \(-0.654783\pi\)
−0.467327 + 0.884085i \(0.654783\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 2.62120 + 4.54005i 0.200448 + 0.347186i
\(172\) 0 0
\(173\) 9.70485 16.8093i 0.737846 1.27799i −0.215618 0.976478i \(-0.569176\pi\)
0.953463 0.301509i \(-0.0974902\pi\)
\(174\) 0 0
\(175\) 27.5865 2.35437i 2.08535 0.177974i
\(176\) 0 0
\(177\) 0.585339 1.01384i 0.0439968 0.0762046i
\(178\) 0 0
\(179\) 7.32219 + 12.6824i 0.547286 + 0.947928i 0.998459 + 0.0554912i \(0.0176725\pi\)
−0.451173 + 0.892437i \(0.648994\pi\)
\(180\) 0 0
\(181\) −9.44627 −0.702136 −0.351068 0.936350i \(-0.614181\pi\)
−0.351068 + 0.936350i \(0.614181\pi\)
\(182\) 0 0
\(183\) 1.96002 0.144889
\(184\) 0 0
\(185\) −14.0471 24.3302i −1.03276 1.78879i
\(186\) 0 0
\(187\) −5.14033 + 8.90331i −0.375898 + 0.651074i
\(188\) 0 0
\(189\) 1.73114 3.69191i 0.125922 0.268547i
\(190\) 0 0
\(191\) 6.27687 10.8719i 0.454179 0.786660i −0.544462 0.838786i \(-0.683266\pi\)
0.998641 + 0.0521252i \(0.0165995\pi\)
\(192\) 0 0
\(193\) 4.68430 + 8.11344i 0.337183 + 0.584018i 0.983902 0.178710i \(-0.0571925\pi\)
−0.646719 + 0.762729i \(0.723859\pi\)
\(194\) 0 0
\(195\) 1.02162 0.0731598
\(196\) 0 0
\(197\) −7.62276 −0.543099 −0.271550 0.962424i \(-0.587536\pi\)
−0.271550 + 0.962424i \(0.587536\pi\)
\(198\) 0 0
\(199\) 6.76443 + 11.7163i 0.479518 + 0.830549i 0.999724 0.0234914i \(-0.00747822\pi\)
−0.520206 + 0.854041i \(0.674145\pi\)
\(200\) 0 0
\(201\) −1.64514 + 2.84947i −0.116039 + 0.200986i
\(202\) 0 0
\(203\) −1.85459 + 3.95518i −0.130167 + 0.277599i
\(204\) 0 0
\(205\) 15.9576 27.6394i 1.11453 1.93042i
\(206\) 0 0
\(207\) −2.55159 4.41949i −0.177348 0.307176i
\(208\) 0 0
\(209\) −8.05579 −0.557231
\(210\) 0 0
\(211\) 15.7995 1.08768 0.543840 0.839189i \(-0.316970\pi\)
0.543840 + 0.839189i \(0.316970\pi\)
\(212\) 0 0
\(213\) 1.24032 + 2.14830i 0.0849853 + 0.147199i
\(214\) 0 0
\(215\) 13.3971 23.2045i 0.913678 1.58254i
\(216\) 0 0
\(217\) −14.7763 + 1.26108i −1.00308 + 0.0856080i
\(218\) 0 0
\(219\) −0.140291 + 0.242991i −0.00947997 + 0.0164198i
\(220\) 0 0
\(221\) 1.14070 + 1.97576i 0.0767321 + 0.132904i
\(222\) 0 0
\(223\) −22.4737 −1.50495 −0.752474 0.658622i \(-0.771139\pi\)
−0.752474 + 0.658622i \(0.771139\pi\)
\(224\) 0 0
\(225\) −30.6876 −2.04584
\(226\) 0 0
\(227\) −4.60124 7.96959i −0.305395 0.528960i 0.671954 0.740593i \(-0.265455\pi\)
−0.977349 + 0.211633i \(0.932122\pi\)
\(228\) 0 0
\(229\) −7.64611 + 13.2435i −0.505269 + 0.875152i 0.494712 + 0.869057i \(0.335274\pi\)
−0.999981 + 0.00609528i \(0.998060\pi\)
\(230\) 0 0
\(231\) 1.77115 + 2.54095i 0.116533 + 0.167182i
\(232\) 0 0
\(233\) 4.02789 6.97652i 0.263876 0.457047i −0.703392 0.710802i \(-0.748332\pi\)
0.967269 + 0.253755i \(0.0816656\pi\)
\(234\) 0 0
\(235\) 6.97121 + 12.0745i 0.454752 + 0.787653i
\(236\) 0 0
\(237\) −0.205674 −0.0133600
\(238\) 0 0
\(239\) −21.7258 −1.40533 −0.702663 0.711523i \(-0.748006\pi\)
−0.702663 + 0.711523i \(0.748006\pi\)
\(240\) 0 0
\(241\) 10.2490 + 17.7518i 0.660195 + 1.14349i 0.980564 + 0.196199i \(0.0628598\pi\)
−0.320369 + 0.947293i \(0.603807\pi\)
\(242\) 0 0
\(243\) −3.40254 + 5.89337i −0.218273 + 0.378060i
\(244\) 0 0
\(245\) 27.1295 4.66470i 1.73324 0.298017i
\(246\) 0 0
\(247\) −0.893841 + 1.54818i −0.0568738 + 0.0985083i
\(248\) 0 0
\(249\) −0.928280 1.60783i −0.0588273 0.101892i
\(250\) 0 0
\(251\) −2.60871 −0.164660 −0.0823301 0.996605i \(-0.526236\pi\)
−0.0823301 + 0.996605i \(0.526236\pi\)
\(252\) 0 0
\(253\) 7.84187 0.493014
\(254\) 0 0
\(255\) 1.16537 + 2.01848i 0.0729781 + 0.126402i
\(256\) 0 0
\(257\) 4.49838 7.79142i 0.280601 0.486016i −0.690932 0.722920i \(-0.742799\pi\)
0.971533 + 0.236904i \(0.0761328\pi\)
\(258\) 0 0
\(259\) −10.8084 15.5062i −0.671604 0.963508i
\(260\) 0 0
\(261\) 2.42094 4.19318i 0.149852 0.259551i
\(262\) 0 0
\(263\) 0.716961 + 1.24181i 0.0442097 + 0.0765735i 0.887284 0.461224i \(-0.152590\pi\)
−0.843074 + 0.537798i \(0.819256\pi\)
\(264\) 0 0
\(265\) 12.9366 0.794689
\(266\) 0 0
\(267\) −2.92668 −0.179110
\(268\) 0 0
\(269\) 4.08416 + 7.07397i 0.249016 + 0.431308i 0.963253 0.268596i \(-0.0865596\pi\)
−0.714237 + 0.699904i \(0.753226\pi\)
\(270\) 0 0
\(271\) −0.106159 + 0.183872i −0.00644867 + 0.0111694i −0.869232 0.494405i \(-0.835386\pi\)
0.862783 + 0.505574i \(0.168719\pi\)
\(272\) 0 0
\(273\) 0.684846 0.0584481i 0.0414488 0.00353744i
\(274\) 0 0
\(275\) 23.5783 40.8387i 1.42182 2.46267i
\(276\) 0 0
\(277\) −11.4875 19.8969i −0.690215 1.19549i −0.971767 0.235942i \(-0.924182\pi\)
0.281552 0.959546i \(-0.409151\pi\)
\(278\) 0 0
\(279\) 16.4374 0.984081
\(280\) 0 0
\(281\) −0.345228 −0.0205946 −0.0102973 0.999947i \(-0.503278\pi\)
−0.0102973 + 0.999947i \(0.503278\pi\)
\(282\) 0 0
\(283\) −14.4857 25.0900i −0.861087 1.49145i −0.870880 0.491495i \(-0.836451\pi\)
0.00979277 0.999952i \(-0.496883\pi\)
\(284\) 0 0
\(285\) −0.913167 + 1.58165i −0.0540913 + 0.0936889i
\(286\) 0 0
\(287\) 9.11594 19.4411i 0.538097 1.14757i
\(288\) 0 0
\(289\) 5.89759 10.2149i 0.346917 0.600878i
\(290\) 0 0
\(291\) 1.14483 + 1.98290i 0.0671109 + 0.116240i
\(292\) 0 0
\(293\) 31.5427 1.84274 0.921372 0.388682i \(-0.127070\pi\)
0.921372 + 0.388682i \(0.127070\pi\)
\(294\) 0 0
\(295\) −17.7210 −1.03175
\(296\) 0 0
\(297\) −3.47253 6.01460i −0.201497 0.349002i
\(298\) 0 0
\(299\) 0.870106 1.50707i 0.0503195 0.0871560i
\(300\) 0 0
\(301\) 7.65325 16.3217i 0.441126 0.940766i
\(302\) 0 0
\(303\) 1.85971 3.22111i 0.106838 0.185048i
\(304\) 0 0
\(305\) −14.8348 25.6945i −0.849435 1.47127i
\(306\) 0 0
\(307\) 18.1941 1.03839 0.519197 0.854655i \(-0.326231\pi\)
0.519197 + 0.854655i \(0.326231\pi\)
\(308\) 0 0
\(309\) 1.94637 0.110725
\(310\) 0 0
\(311\) −0.188312 0.326165i −0.0106782 0.0184951i 0.860637 0.509219i \(-0.170066\pi\)
−0.871315 + 0.490724i \(0.836732\pi\)
\(312\) 0 0
\(313\) −5.49415 + 9.51615i −0.310548 + 0.537884i −0.978481 0.206337i \(-0.933846\pi\)
0.667933 + 0.744221i \(0.267179\pi\)
\(314\) 0 0
\(315\) −30.4006 + 2.59454i −1.71288 + 0.146186i
\(316\) 0 0
\(317\) −13.0903 + 22.6731i −0.735225 + 1.27345i 0.219400 + 0.975635i \(0.429590\pi\)
−0.954625 + 0.297812i \(0.903743\pi\)
\(318\) 0 0
\(319\) 3.72016 + 6.44350i 0.208289 + 0.360767i
\(320\) 0 0
\(321\) −2.85206 −0.159186
\(322\) 0 0
\(323\) −4.07844 −0.226930
\(324\) 0 0
\(325\) −5.23232 9.06264i −0.290237 0.502705i
\(326\) 0 0
\(327\) 1.61670 2.80020i 0.0894037 0.154852i
\(328\) 0 0
\(329\) 5.36397 + 7.69534i 0.295725 + 0.424258i
\(330\) 0 0
\(331\) −17.0466 + 29.5256i −0.936967 + 1.62287i −0.165878 + 0.986146i \(0.553046\pi\)
−0.771089 + 0.636728i \(0.780288\pi\)
\(332\) 0 0
\(333\) 10.4750 + 18.1433i 0.574028 + 0.994246i
\(334\) 0 0
\(335\) 49.8062 2.72120
\(336\) 0 0
\(337\) 14.7532 0.803657 0.401829 0.915715i \(-0.368375\pi\)
0.401829 + 0.915715i \(0.368375\pi\)
\(338\) 0 0
\(339\) 0.214468 + 0.371470i 0.0116483 + 0.0201755i
\(340\) 0 0
\(341\) −12.6294 + 21.8747i −0.683918 + 1.18458i
\(342\) 0 0
\(343\) 17.9194 4.67910i 0.967558 0.252648i
\(344\) 0 0
\(345\) 0.888918 1.53965i 0.0478577 0.0828920i
\(346\) 0 0
\(347\) 14.9733 + 25.9345i 0.803809 + 1.39224i 0.917092 + 0.398675i \(0.130530\pi\)
−0.113284 + 0.993563i \(0.536137\pi\)
\(348\) 0 0
\(349\) −13.4793 −0.721532 −0.360766 0.932656i \(-0.617485\pi\)
−0.360766 + 0.932656i \(0.617485\pi\)
\(350\) 0 0
\(351\) −1.54120 −0.0822630
\(352\) 0 0
\(353\) −0.0817659 0.141623i −0.00435196 0.00753781i 0.863841 0.503764i \(-0.168052\pi\)
−0.868193 + 0.496226i \(0.834719\pi\)
\(354\) 0 0
\(355\) 18.7752 32.5195i 0.996482 1.72596i
\(356\) 0 0
\(357\) 0.896686 + 1.28642i 0.0474577 + 0.0680845i
\(358\) 0 0
\(359\) 4.46065 7.72607i 0.235424 0.407766i −0.723972 0.689830i \(-0.757685\pi\)
0.959396 + 0.282063i \(0.0910188\pi\)
\(360\) 0 0
\(361\) 7.90209 + 13.6868i 0.415900 + 0.720359i
\(362\) 0 0
\(363\) 2.41772 0.126898
\(364\) 0 0
\(365\) 4.24726 0.222312
\(366\) 0 0
\(367\) 18.3276 + 31.7443i 0.956693 + 1.65704i 0.730445 + 0.682971i \(0.239313\pi\)
0.226248 + 0.974070i \(0.427354\pi\)
\(368\) 0 0
\(369\) −11.8997 + 20.6110i −0.619476 + 1.07296i
\(370\) 0 0
\(371\) 8.67208 0.740117i 0.450232 0.0384250i
\(372\) 0 0
\(373\) −13.5637 + 23.4930i −0.702302 + 1.21642i 0.265355 + 0.964151i \(0.414511\pi\)
−0.967656 + 0.252271i \(0.918822\pi\)
\(374\) 0 0
\(375\) −2.79139 4.83483i −0.144147 0.249670i
\(376\) 0 0
\(377\) 1.65110 0.0850360
\(378\) 0 0
\(379\) 15.8943 0.816434 0.408217 0.912885i \(-0.366151\pi\)
0.408217 + 0.912885i \(0.366151\pi\)
\(380\) 0 0
\(381\) −0.583611 1.01084i −0.0298993 0.0517871i
\(382\) 0 0
\(383\) 0.575394 0.996611i 0.0294013 0.0509245i −0.850950 0.525246i \(-0.823973\pi\)
0.880352 + 0.474322i \(0.157307\pi\)
\(384\) 0 0
\(385\) 19.9049 42.4502i 1.01445 2.16346i
\(386\) 0 0
\(387\) −9.99038 + 17.3038i −0.507839 + 0.879604i
\(388\) 0 0
\(389\) 7.15651 + 12.3954i 0.362850 + 0.628474i 0.988429 0.151687i \(-0.0484705\pi\)
−0.625579 + 0.780161i \(0.715137\pi\)
\(390\) 0 0
\(391\) 3.97013 0.200778
\(392\) 0 0
\(393\) 3.28807 0.165861
\(394\) 0 0
\(395\) 1.55668 + 2.69625i 0.0783251 + 0.135663i
\(396\) 0 0
\(397\) 12.9588 22.4453i 0.650383 1.12650i −0.332647 0.943051i \(-0.607942\pi\)
0.983030 0.183445i \(-0.0587248\pi\)
\(398\) 0 0
\(399\) −0.521656 + 1.11251i −0.0261154 + 0.0556950i
\(400\) 0 0
\(401\) 2.14816 3.72072i 0.107274 0.185804i −0.807391 0.590017i \(-0.799121\pi\)
0.914665 + 0.404213i \(0.132455\pi\)
\(402\) 0 0
\(403\) 2.80262 + 4.85427i 0.139608 + 0.241809i
\(404\) 0 0
\(405\) 33.0219 1.64087
\(406\) 0 0
\(407\) −32.1931 −1.59575
\(408\) 0 0
\(409\) 12.3536 + 21.3970i 0.610844 + 1.05801i 0.991098 + 0.133131i \(0.0425030\pi\)
−0.380255 + 0.924882i \(0.624164\pi\)
\(410\) 0 0
\(411\) 1.20625 2.08929i 0.0595000 0.103057i
\(412\) 0 0
\(413\) −11.8793 + 1.01384i −0.584542 + 0.0498876i
\(414\) 0 0
\(415\) −14.0517 + 24.3383i −0.689771 + 1.19472i
\(416\) 0 0
\(417\) −0.519577 0.899934i −0.0254438 0.0440699i
\(418\) 0 0
\(419\) 24.9293 1.21787 0.608937 0.793218i \(-0.291596\pi\)
0.608937 + 0.793218i \(0.291596\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) 0 0
\(423\) −5.19850 9.00407i −0.252760 0.437793i
\(424\) 0 0
\(425\) 11.9371 20.6756i 0.579032 1.00291i
\(426\) 0 0
\(427\) −11.4145 16.3757i −0.552388 0.792475i
\(428\) 0 0
\(429\) 0.585339 1.01384i 0.0282604 0.0489485i
\(430\) 0 0
\(431\) −2.84426 4.92639i −0.137003 0.237296i 0.789358 0.613933i \(-0.210414\pi\)
−0.926361 + 0.376637i \(0.877080\pi\)
\(432\) 0 0
\(433\) 12.2598 0.589169 0.294584 0.955625i \(-0.404819\pi\)
0.294584 + 0.955625i \(0.404819\pi\)
\(434\) 0 0
\(435\) 1.68680 0.0808758
\(436\) 0 0
\(437\) 1.55547 + 2.69416i 0.0744084 + 0.128879i
\(438\) 0 0
\(439\) 2.51158 4.35019i 0.119871 0.207623i −0.799845 0.600206i \(-0.795085\pi\)
0.919717 + 0.392583i \(0.128418\pi\)
\(440\) 0 0
\(441\) −20.2307 + 3.47851i −0.963367 + 0.165643i
\(442\) 0 0
\(443\) 0.289401 0.501258i 0.0137499 0.0238155i −0.859069 0.511860i \(-0.828956\pi\)
0.872818 + 0.488045i \(0.162290\pi\)
\(444\) 0 0
\(445\) 22.1511 + 38.3668i 1.05006 + 1.81876i
\(446\) 0 0
\(447\) −3.93966 −0.186339
\(448\) 0 0
\(449\) −7.36359 −0.347509 −0.173755 0.984789i \(-0.555590\pi\)
−0.173755 + 0.984789i \(0.555590\pi\)
\(450\) 0 0
\(451\) −18.2859 31.6720i −0.861048 1.49138i
\(452\) 0 0
\(453\) 0.667862 1.15677i 0.0313789 0.0543499i
\(454\) 0 0
\(455\) −5.94959 8.53550i −0.278921 0.400150i
\(456\) 0 0
\(457\) −3.95912 + 6.85739i −0.185200 + 0.320775i −0.943644 0.330963i \(-0.892627\pi\)
0.758444 + 0.651738i \(0.225960\pi\)
\(458\) 0 0
\(459\) −1.75805 3.04503i −0.0820588 0.142130i
\(460\) 0 0
\(461\) −9.53600 −0.444136 −0.222068 0.975031i \(-0.571281\pi\)
−0.222068 + 0.975031i \(0.571281\pi\)
\(462\) 0 0
\(463\) −2.16049 −0.100406 −0.0502032 0.998739i \(-0.515987\pi\)
−0.0502032 + 0.998739i \(0.515987\pi\)
\(464\) 0 0
\(465\) 2.86321 + 4.95923i 0.132778 + 0.229979i
\(466\) 0 0
\(467\) −4.05950 + 7.03126i −0.187851 + 0.325368i −0.944534 0.328415i \(-0.893486\pi\)
0.756682 + 0.653783i \(0.226819\pi\)
\(468\) 0 0
\(469\) 33.3877 2.84947i 1.54170 0.131576i
\(470\) 0 0
\(471\) 1.39391 2.41433i 0.0642281 0.111246i
\(472\) 0 0
\(473\) −15.3518 26.5901i −0.705878 1.22262i
\(474\) 0 0
\(475\) 18.7074 0.858357
\(476\) 0 0
\(477\) −9.64694 −0.441703
\(478\) 0 0
\(479\) 7.27663 + 12.6035i 0.332478 + 0.575868i 0.982997 0.183621i \(-0.0587820\pi\)
−0.650519 + 0.759490i \(0.725449\pi\)
\(480\) 0 0
\(481\) −3.57204 + 6.18695i −0.162871 + 0.282101i
\(482\) 0 0
\(483\) 0.507803 1.08297i 0.0231058 0.0492766i
\(484\) 0 0
\(485\) 17.3297 30.0158i 0.786899 1.36295i
\(486\) 0 0
\(487\) −16.6295 28.8031i −0.753554 1.30519i −0.946090 0.323904i \(-0.895005\pi\)
0.192536 0.981290i \(-0.438329\pi\)
\(488\) 0 0
\(489\) −0.616320 −0.0278710
\(490\) 0 0
\(491\) 22.5563 1.01795 0.508977 0.860780i \(-0.330024\pi\)
0.508977 + 0.860780i \(0.330024\pi\)
\(492\) 0 0
\(493\) 1.88342 + 3.26218i 0.0848249 + 0.146921i
\(494\) 0 0
\(495\) −25.9835 + 45.0047i −1.16787 + 2.02281i
\(496\) 0 0
\(497\) 10.7255 22.8737i 0.481104 1.02603i
\(498\) 0 0
\(499\) −5.69271 + 9.86007i −0.254841 + 0.441397i −0.964852 0.262793i \(-0.915356\pi\)
0.710011 + 0.704190i \(0.248690\pi\)
\(500\) 0 0
\(501\) 1.56891 + 2.71743i 0.0700938 + 0.121406i
\(502\) 0 0
\(503\) 8.81825 0.393186 0.196593 0.980485i \(-0.437012\pi\)
0.196593 + 0.980485i \(0.437012\pi\)
\(504\) 0 0
\(505\) −56.3022 −2.50541
\(506\) 0 0
\(507\) −0.129894 0.224983i −0.00576880 0.00999186i
\(508\) 0 0
\(509\) −9.64188 + 16.7002i −0.427369 + 0.740225i −0.996638 0.0819263i \(-0.973893\pi\)
0.569269 + 0.822151i \(0.307226\pi\)
\(510\) 0 0
\(511\) 2.84716 0.242991i 0.125951 0.0107493i
\(512\) 0 0
\(513\) 1.37759 2.38605i 0.0608219 0.105347i
\(514\) 0 0
\(515\) −14.7315 25.5156i −0.649146 1.12435i
\(516\) 0 0
\(517\) 15.9767 0.702653
\(518\) 0 0
\(519\) −5.04241 −0.221337
\(520\) 0 0
\(521\) −12.5584 21.7518i −0.550193 0.952963i −0.998260 0.0589629i \(-0.981221\pi\)
0.448067 0.894000i \(-0.352113\pi\)
\(522\) 0 0
\(523\) −14.9824 + 25.9503i −0.655134 + 1.13473i 0.326726 + 0.945119i \(0.394054\pi\)
−0.981860 + 0.189606i \(0.939279\pi\)
\(524\) 0 0
\(525\) −4.11303 5.90069i −0.179507 0.257527i
\(526\) 0 0
\(527\) −6.39391 + 11.0746i −0.278523 + 0.482416i
\(528\) 0 0
\(529\) 9.98583 + 17.2960i 0.434167 + 0.751999i
\(530\) 0 0
\(531\) 13.2147 0.573469
\(532\) 0 0
\(533\) −8.11574 −0.351532
\(534\) 0 0
\(535\) 21.5863 + 37.3886i 0.933257 + 1.61645i
\(536\) 0 0
\(537\) 1.90222 3.29474i 0.0820869 0.142179i
\(538\) 0 0
\(539\) 10.9147 29.5954i 0.470130 1.27476i
\(540\) 0 0
\(541\) −2.54987 + 4.41650i −0.109627 + 0.189880i −0.915619 0.402046i \(-0.868299\pi\)
0.805992 + 0.591926i \(0.201632\pi\)
\(542\) 0 0
\(543\) 1.22702 + 2.12525i 0.0526563 + 0.0912034i
\(544\) 0 0
\(545\) −48.9451 −2.09658
\(546\) 0 0
\(547\) −2.92025 −0.124861 −0.0624305 0.998049i \(-0.519885\pi\)
−0.0624305 + 0.998049i \(0.519885\pi\)
\(548\) 0 0
\(549\) 11.0624 + 19.1607i 0.472132 + 0.817757i
\(550\) 0 0
\(551\) −1.47582 + 2.55620i −0.0628722 + 0.108898i
\(552\) 0 0
\(553\) 1.19778 + 1.71838i 0.0509348 + 0.0730728i
\(554\) 0 0
\(555\) −3.64927 + 6.32071i −0.154903 + 0.268299i
\(556\) 0 0
\(557\) −12.9937 22.5058i −0.550561 0.953600i −0.998234 0.0594024i \(-0.981080\pi\)
0.447673 0.894197i \(-0.352253\pi\)
\(558\) 0 0
\(559\) −6.81353 −0.288182
\(560\) 0 0
\(561\) 2.67079 0.112761
\(562\) 0 0
\(563\) 1.82534 + 3.16159i 0.0769291 + 0.133245i 0.901924 0.431896i \(-0.142155\pi\)
−0.824994 + 0.565141i \(0.808822\pi\)
\(564\) 0 0
\(565\) 3.24649 5.62308i 0.136581 0.236565i
\(566\) 0 0
\(567\) 22.1363 1.88922i 0.929637 0.0793397i
\(568\) 0 0
\(569\) 12.6766 21.9566i 0.531432 0.920468i −0.467895 0.883784i \(-0.654987\pi\)
0.999327 0.0366835i \(-0.0116793\pi\)
\(570\) 0 0
\(571\) 13.8626 + 24.0108i 0.580133 + 1.00482i 0.995463 + 0.0951493i \(0.0303329\pi\)
−0.415330 + 0.909671i \(0.636334\pi\)
\(572\) 0 0
\(573\) −3.26132 −0.136244
\(574\) 0 0
\(575\) −18.2107 −0.759438
\(576\) 0 0
\(577\) −19.7877 34.2733i −0.823773 1.42682i −0.902854 0.429948i \(-0.858532\pi\)
0.0790809 0.996868i \(-0.474801\pi\)
\(578\) 0 0
\(579\) 1.21693 2.10778i 0.0505737 0.0875963i
\(580\) 0 0
\(581\) −8.02717 + 17.1191i −0.333023 + 0.710221i
\(582\) 0 0
\(583\) 7.41204 12.8380i 0.306975 0.531697i
\(584\) 0 0
\(585\) 5.76606 + 9.98711i 0.238397 + 0.412916i
\(586\) 0 0
\(587\) 8.24177 0.340174 0.170087 0.985429i \(-0.445595\pi\)
0.170087 + 0.985429i \(0.445595\pi\)
\(588\) 0 0
\(589\) −10.0204 −0.412882
\(590\) 0 0
\(591\) 0.990153 + 1.71500i 0.0407295 + 0.0705455i
\(592\) 0 0
\(593\) 5.96149 10.3256i 0.244809 0.424021i −0.717269 0.696796i \(-0.754608\pi\)
0.962078 + 0.272775i \(0.0879415\pi\)
\(594\) 0 0
\(595\) 10.0774 21.4914i 0.413131 0.881063i
\(596\) 0 0
\(597\) 1.75732 3.04377i 0.0719224 0.124573i
\(598\) 0 0
\(599\) −17.8079 30.8442i −0.727611 1.26026i −0.957890 0.287135i \(-0.907297\pi\)
0.230279 0.973125i \(-0.426036\pi\)
\(600\) 0 0
\(601\) 38.9252 1.58779 0.793896 0.608054i \(-0.208050\pi\)
0.793896 + 0.608054i \(0.208050\pi\)
\(602\) 0 0
\(603\) −37.1410 −1.51250
\(604\) 0 0
\(605\) −18.2990 31.6947i −0.743959 1.28857i
\(606\) 0 0
\(607\) −6.84828 + 11.8616i −0.277963 + 0.481446i −0.970878 0.239573i \(-0.922993\pi\)
0.692915 + 0.721019i \(0.256326\pi\)
\(608\) 0 0
\(609\) 1.13075 0.0965037i 0.0458203 0.00391053i
\(610\) 0 0
\(611\) 1.77271 3.07043i 0.0717163 0.124216i
\(612\) 0 0
\(613\) −1.58056 2.73761i −0.0638382 0.110571i 0.832340 0.554266i \(-0.187001\pi\)
−0.896178 + 0.443695i \(0.853667\pi\)
\(614\) 0 0
\(615\) −8.29120 −0.334334
\(616\) 0 0
\(617\) 20.9297 0.842597 0.421299 0.906922i \(-0.361574\pi\)
0.421299 + 0.906922i \(0.361574\pi\)
\(618\) 0 0
\(619\) 15.4772 + 26.8073i 0.622082 + 1.07748i 0.989097 + 0.147262i \(0.0470461\pi\)
−0.367016 + 0.930215i \(0.619621\pi\)
\(620\) 0 0
\(621\) −1.34100 + 2.32269i −0.0538127 + 0.0932063i
\(622\) 0 0
\(623\) 17.0440 + 24.4520i 0.682855 + 0.979648i
\(624\) 0 0
\(625\) −16.0927 + 27.8734i −0.643708 + 1.11494i
\(626\) 0 0
\(627\) 1.04640 + 1.81242i 0.0417892 + 0.0723810i
\(628\) 0 0
\(629\) −16.2986 −0.649866
\(630\) 0 0
\(631\) 15.1218 0.601988 0.300994 0.953626i \(-0.402682\pi\)
0.300994 + 0.953626i \(0.402682\pi\)
\(632\) 0 0
\(633\) −2.05226 3.55462i −0.0815700 0.141283i
\(634\) 0 0
\(635\) −8.83433 + 15.3015i −0.350580 + 0.607222i
\(636\) 0 0
\(637\) −4.47665 5.38141i −0.177371 0.213219i
\(638\) 0 0
\(639\) −14.0008 + 24.2501i −0.553864 + 0.959320i
\(640\) 0 0
\(641\) 23.6207 + 40.9123i 0.932962 + 1.61594i 0.778229 + 0.627981i \(0.216118\pi\)
0.154733 + 0.987956i \(0.450548\pi\)
\(642\) 0 0
\(643\) −39.9249 −1.57448 −0.787241 0.616645i \(-0.788491\pi\)
−0.787241 + 0.616645i \(0.788491\pi\)
\(644\) 0 0
\(645\) −6.96085 −0.274083
\(646\) 0 0
\(647\) −14.9139 25.8317i −0.586327 1.01555i −0.994709 0.102736i \(-0.967240\pi\)
0.408382 0.912811i \(-0.366093\pi\)
\(648\) 0 0
\(649\) −10.1533 + 17.5859i −0.398550 + 0.690309i
\(650\) 0 0
\(651\) 2.20308 + 3.16062i 0.0863456 + 0.123875i
\(652\) 0 0
\(653\) −12.5774 + 21.7848i −0.492194 + 0.852504i −0.999960 0.00899079i \(-0.997138\pi\)
0.507766 + 0.861495i \(0.330471\pi\)
\(654\) 0 0
\(655\) −24.8863 43.1044i −0.972390 1.68423i
\(656\) 0 0
\(657\) −3.16722 −0.123565
\(658\) 0 0
\(659\) −17.3155 −0.674517 −0.337258 0.941412i \(-0.609500\pi\)
−0.337258 + 0.941412i \(0.609500\pi\)
\(660\) 0 0
\(661\) 4.60037 + 7.96808i 0.178934 + 0.309922i 0.941516 0.336969i \(-0.109402\pi\)
−0.762582 + 0.646892i \(0.776069\pi\)
\(662\) 0 0
\(663\) 0.296342 0.513279i 0.0115090 0.0199341i
\(664\) 0 0
\(665\) 18.5325 1.58165i 0.718659 0.0613338i
\(666\) 0 0
\(667\) 1.43663 2.48832i 0.0556266 0.0963482i
\(668\) 0 0
\(669\) 2.91920 + 5.05620i 0.112863 + 0.195484i
\(670\) 0 0
\(671\) −33.9984 −1.31249
\(672\) 0 0
\(673\) 17.3609 0.669212 0.334606 0.942358i \(-0.391397\pi\)
0.334606 + 0.942358i \(0.391397\pi\)
\(674\) 0 0
\(675\) 8.06403 + 13.9673i 0.310385 + 0.537602i
\(676\) 0 0
\(677\) −24.9913 + 43.2861i −0.960492 + 1.66362i −0.239225 + 0.970964i \(0.576893\pi\)
−0.721267 + 0.692657i \(0.756440\pi\)
\(678\) 0 0
\(679\) 9.89974 21.1126i 0.379917 0.810229i
\(680\) 0 0
\(681\) −1.19535 + 2.07041i −0.0458059 + 0.0793382i
\(682\) 0 0
\(683\) 16.8077 + 29.1117i 0.643128 + 1.11393i 0.984731 + 0.174086i \(0.0556969\pi\)
−0.341603 + 0.939844i \(0.610970\pi\)
\(684\) 0 0
\(685\) −36.5189 −1.39532
\(686\) 0 0
\(687\) 3.97274 0.151570
\(688\) 0 0
\(689\) −1.64483 2.84892i −0.0626629 0.108535i
\(690\) 0 0
\(691\) −7.56545 + 13.1038i −0.287803 + 0.498490i −0.973285 0.229600i \(-0.926258\pi\)
0.685482 + 0.728090i \(0.259592\pi\)
\(692\) 0 0
\(693\) −14.8433 + 31.6555i −0.563851 + 1.20249i
\(694\) 0 0
\(695\) −7.86502 + 13.6226i −0.298337 + 0.516735i
\(696\) 0 0
\(697\) −9.25766 16.0347i −0.350659 0.607359i
\(698\) 0 0
\(699\) −2.09280 −0.0791570
\(700\) 0 0
\(701\) 2.02467 0.0764705 0.0382353 0.999269i \(-0.487826\pi\)
0.0382353 + 0.999269i \(0.487826\pi\)
\(702\) 0 0
\(703\) −6.38567 11.0603i −0.240840 0.417147i
\(704\) 0 0
\(705\) 1.81104 3.13681i 0.0682077 0.118139i
\(706\) 0 0
\(707\) −37.7423 + 3.22111i −1.41945 + 0.121142i
\(708\) 0 0
\(709\) 15.2276 26.3751i 0.571886 0.990536i −0.424486 0.905434i \(-0.639545\pi\)
0.996372 0.0851015i \(-0.0271215\pi\)
\(710\) 0 0
\(711\) −1.16083 2.01062i −0.0435346 0.0754041i
\(712\) 0 0
\(713\) 9.75429 0.365301
\(714\) 0 0
\(715\) −17.7210 −0.662727
\(716\) 0 0
\(717\) 2.82206 + 4.88795i 0.105392 + 0.182544i
\(718\) 0 0
\(719\) −12.2123 + 21.1523i −0.455442 + 0.788848i −0.998713 0.0507089i \(-0.983852\pi\)
0.543272 + 0.839557i \(0.317185\pi\)
\(720\) 0 0
\(721\) −11.3351 16.2617i −0.422139 0.605616i
\(722\) 0 0
\(723\) 2.66257 4.61170i 0.0990220 0.171511i
\(724\) 0 0
\(725\) −8.63908 14.9633i −0.320848 0.555724i
\(726\) 0 0
\(727\) 3.09307 0.114716 0.0573578 0.998354i \(-0.481732\pi\)
0.0573578 + 0.998354i \(0.481732\pi\)
\(728\) 0 0
\(729\) −23.4236 −0.867539
\(730\) 0 0
\(731\) −7.77223 13.4619i −0.287466 0.497906i
\(732\) 0 0
\(733\) 4.20713 7.28697i 0.155394 0.269150i −0.777808 0.628501i \(-0.783669\pi\)
0.933202 + 0.359351i \(0.117002\pi\)
\(734\) 0 0
\(735\) −4.57344 5.49776i −0.168694 0.202788i
\(736\) 0 0
\(737\) 28.5365 49.4267i 1.05116 1.82066i
\(738\) 0 0
\(739\) −3.61379 6.25927i −0.132936 0.230251i 0.791871 0.610688i \(-0.209107\pi\)
−0.924807 + 0.380437i \(0.875774\pi\)
\(740\) 0 0
\(741\) 0.464419 0.0170609
\(742\) 0 0
\(743\) 53.9092 1.97774 0.988869 0.148791i \(-0.0475383\pi\)
0.988869 + 0.148791i \(0.0475383\pi\)
\(744\) 0 0
\(745\) 29.8180 + 51.6463i 1.09245 + 1.89217i
\(746\) 0 0
\(747\) 10.4785 18.1493i 0.383388 0.664047i
\(748\) 0 0
\(749\) 16.6095 + 23.8285i 0.606897 + 0.870676i
\(750\) 0 0
\(751\) 14.6221 25.3262i 0.533568 0.924168i −0.465663 0.884962i \(-0.654184\pi\)
0.999231 0.0392053i \(-0.0124826\pi\)
\(752\) 0 0
\(753\) 0.338856 + 0.586916i 0.0123486 + 0.0213884i
\(754\) 0 0
\(755\) −20.2193 −0.735857
\(756\) 0 0
\(757\) −22.0597 −0.801773 −0.400887 0.916128i \(-0.631298\pi\)
−0.400887 + 0.916128i \(0.631298\pi\)
\(758\) 0 0
\(759\) −1.01861 1.76429i −0.0369733 0.0640397i
\(760\) 0 0
\(761\) −8.90805 + 15.4292i −0.322917 + 0.559308i −0.981089 0.193560i \(-0.937997\pi\)
0.658172 + 0.752868i \(0.271330\pi\)
\(762\) 0 0
\(763\) −32.8105 + 2.80020i −1.18782 + 0.101374i
\(764\) 0 0
\(765\) −13.1547 + 22.7847i −0.475611 + 0.823782i
\(766\) 0 0
\(767\) 2.25314 + 3.90255i 0.0813561 + 0.140913i
\(768\) 0 0
\(769\) −11.3069 −0.407738 −0.203869 0.978998i \(-0.565352\pi\)
−0.203869 + 0.978998i \(0.565352\pi\)
\(770\) 0 0
\(771\) −2.33725 −0.0841741
\(772\) 0 0
\(773\) 0.964104 + 1.66988i 0.0346764 + 0.0600613i 0.882843 0.469669i \(-0.155627\pi\)
−0.848166 + 0.529730i \(0.822293\pi\)
\(774\) 0 0
\(775\) 29.3284 50.7982i 1.05351 1.82472i
\(776\) 0 0
\(777\) −2.08468 + 4.44588i −0.0747875 + 0.159495i
\(778\) 0 0
\(779\) 7.25418 12.5646i 0.259908 0.450174i
\(780\) 0 0
\(781\) −21.5145 37.2642i −0.769849 1.33342i
\(782\) 0 0
\(783\) −2.54467 −0.0909392
\(784\) 0 0
\(785\) −42.2003 −1.50619
\(786\) 0 0
\(787\) 2.76577 + 4.79046i 0.0985892 + 0.170761i 0.911101 0.412183i \(-0.135234\pi\)
−0.812512 + 0.582945i \(0.801900\pi\)
\(788\) 0 0
\(789\) 0.186258 0.322609i 0.00663097 0.0114852i
\(790\) 0 0
\(791\) 1.85459 3.95518i 0.0659415 0.140630i
\(792\) 0 0
\(793\) −3.77234 + 6.53388i −0.133960 + 0.232025i
\(794\) 0 0
\(795\) −1.68039 2.91052i −0.0595973 0.103225i
\(796\) 0 0
\(797\) −13.8038