Properties

Label 1183.2.e.f.508.2
Level $1183$
Weight $2$
Character 1183.508
Analytic conductor $9.446$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1183 = 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1183.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.44630255912\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 508.2
Root \(0.597828 + 1.03547i\) of defining polynomial
Character \(\chi\) \(=\) 1183.508
Dual form 1183.2.e.f.170.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0978281 - 0.169443i) q^{2} +(0.129894 - 0.224983i) q^{3} +(0.980859 - 1.69890i) q^{4} +(1.96625 + 3.40565i) q^{5} -0.0508292 q^{6} +(-1.12324 - 2.39548i) q^{7} -0.775135 q^{8} +(1.46625 + 2.53963i) q^{9} +O(q^{10})\) \(q+(-0.0978281 - 0.169443i) q^{2} +(0.129894 - 0.224983i) q^{3} +(0.980859 - 1.69890i) q^{4} +(1.96625 + 3.40565i) q^{5} -0.0508292 q^{6} +(-1.12324 - 2.39548i) q^{7} -0.775135 q^{8} +(1.46625 + 2.53963i) q^{9} +(0.384710 - 0.666337i) q^{10} +(2.25314 - 3.90255i) q^{11} +(-0.254816 - 0.441354i) q^{12} +(-0.296013 + 0.424671i) q^{14} +1.02162 q^{15} +(-1.88589 - 3.26645i) q^{16} +(1.14070 - 1.97576i) q^{17} +(0.286882 - 0.496894i) q^{18} +(-0.893841 - 1.54818i) q^{19} +7.71448 q^{20} +(-0.684846 - 0.0584481i) q^{21} -0.881681 q^{22} +(-0.870106 - 1.50707i) q^{23} +(-0.100686 + 0.174393i) q^{24} +(-5.23232 + 9.06264i) q^{25} +1.54120 q^{27} +(-5.17142 - 0.441354i) q^{28} +1.65110 q^{29} +(-0.0999432 - 0.173107i) q^{30} +(2.80262 - 4.85427i) q^{31} +(-1.14412 + 1.98168i) q^{32} +(-0.585339 - 1.01384i) q^{33} -0.446372 q^{34} +(5.94959 - 8.53550i) q^{35} +5.75276 q^{36} +(3.57204 + 6.18695i) q^{37} +(-0.174886 + 0.302911i) q^{38} +(-1.52411 - 2.63984i) q^{40} +8.11574 q^{41} +(0.0570936 + 0.121760i) q^{42} +6.81353 q^{43} +(-4.42002 - 7.65570i) q^{44} +(-5.76606 + 9.98711i) q^{45} +(-0.170242 + 0.294867i) q^{46} +(1.77271 + 3.07043i) q^{47} -0.979864 q^{48} +(-4.47665 + 5.38141i) q^{49} +2.04747 q^{50} +(-0.296342 - 0.513279i) q^{51} +(-1.64483 + 2.84892i) q^{53} +(-0.150772 - 0.261146i) q^{54} +17.7210 q^{55} +(0.870665 + 1.85682i) q^{56} -0.464419 q^{57} +(-0.161524 - 0.279768i) q^{58} +(2.25314 - 3.90255i) q^{59} +(1.00207 - 1.73563i) q^{60} +(-3.77234 - 6.53388i) q^{61} -1.09670 q^{62} +(4.43667 - 6.36500i) q^{63} -7.09585 q^{64} +(-0.114525 + 0.198364i) q^{66} +(-6.33263 + 10.9684i) q^{67} +(-2.23774 - 3.87588i) q^{68} -0.452087 q^{69} +(-2.02832 - 0.173107i) q^{70} -9.54869 q^{71} +(-1.13655 - 1.96855i) q^{72} +(0.540019 - 0.935340i) q^{73} +(0.698891 - 1.21052i) q^{74} +(1.35930 + 2.35437i) q^{75} -3.50693 q^{76} +(-11.8793 - 1.01384i) q^{77} +(-0.395849 - 0.685630i) q^{79} +(7.41628 - 12.8454i) q^{80} +(-4.19857 + 7.27214i) q^{81} +(-0.793947 - 1.37516i) q^{82} +7.14643 q^{83} +(-0.771035 + 1.10615i) q^{84} +8.97166 q^{85} +(-0.666555 - 1.15451i) q^{86} +(0.214468 - 0.371470i) q^{87} +(-1.74649 + 3.02500i) q^{88} +(-5.63281 - 9.75631i) q^{89} +2.25633 q^{90} -3.41381 q^{92} +(-0.728087 - 1.26108i) q^{93} +(0.346843 - 0.600749i) q^{94} +(3.51504 - 6.08823i) q^{95} +(0.297229 + 0.514816i) q^{96} +8.81353 q^{97} +(1.34979 + 0.232085i) q^{98} +13.2147 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 4q^{2} - 8q^{4} + 2q^{5} + 10q^{6} - q^{7} - 18q^{8} - 3q^{9} + O(q^{10}) \) \( 10q + 4q^{2} - 8q^{4} + 2q^{5} + 10q^{6} - q^{7} - 18q^{8} - 3q^{9} + 5q^{10} + 11q^{11} - 5q^{12} + 10q^{14} - 10q^{16} + 5q^{17} + 9q^{18} + 9q^{19} - 2q^{20} - 2q^{21} + 16q^{22} - 10q^{23} - 9q^{25} - 37q^{28} - 6q^{29} + 13q^{30} - 6q^{31} + 22q^{32} + 8q^{33} + 44q^{34} - 4q^{35} + 14q^{36} + 4q^{37} + 10q^{38} - 28q^{40} - 28q^{41} + 52q^{42} + 4q^{43} - 32q^{45} + 3q^{46} + q^{47} - 46q^{48} - 11q^{49} - 18q^{50} + 8q^{51} - 17q^{53} + 23q^{54} - 21q^{56} + 32q^{57} - 27q^{58} + 11q^{59} - 29q^{60} + 11q^{61} - 46q^{62} - 5q^{63} + 18q^{64} - 21q^{66} + 13q^{67} + 32q^{68} + 36q^{69} - 49q^{70} - 30q^{71} - 19q^{72} + 33q^{74} + 20q^{75} - 16q^{76} - 46q^{77} - 2q^{79} + 55q^{80} + 19q^{81} - 34q^{82} - 12q^{83} + 23q^{84} + 44q^{85} + 28q^{86} + 8q^{87} + 3q^{88} - 4q^{89} - 68q^{90} + 42q^{92} + 18q^{93} - 20q^{94} + 12q^{95} - 37q^{96} + 24q^{97} + 7q^{98} - 22q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).

\(n\) \(339\) \(1016\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0978281 0.169443i −0.0691749 0.119815i 0.829363 0.558710i \(-0.188703\pi\)
−0.898538 + 0.438895i \(0.855370\pi\)
\(3\) 0.129894 0.224983i 0.0749945 0.129894i −0.826089 0.563539i \(-0.809439\pi\)
0.901084 + 0.433645i \(0.142773\pi\)
\(4\) 0.980859 1.69890i 0.490430 0.849449i
\(5\) 1.96625 + 3.40565i 0.879336 + 1.52305i 0.852071 + 0.523426i \(0.175346\pi\)
0.0272650 + 0.999628i \(0.491320\pi\)
\(6\) −0.0508292 −0.0207509
\(7\) −1.12324 2.39548i −0.424546 0.905406i
\(8\) −0.775135 −0.274052
\(9\) 1.46625 + 2.53963i 0.488752 + 0.846543i
\(10\) 0.384710 0.666337i 0.121656 0.210714i
\(11\) 2.25314 3.90255i 0.679346 1.17666i −0.295832 0.955240i \(-0.595597\pi\)
0.975178 0.221422i \(-0.0710699\pi\)
\(12\) −0.254816 0.441354i −0.0735590 0.127408i
\(13\) 0 0
\(14\) −0.296013 + 0.424671i −0.0791129 + 0.113498i
\(15\) 1.02162 0.263781
\(16\) −1.88589 3.26645i −0.471472 0.816614i
\(17\) 1.14070 1.97576i 0.276661 0.479192i −0.693891 0.720080i \(-0.744105\pi\)
0.970553 + 0.240888i \(0.0774386\pi\)
\(18\) 0.286882 0.496894i 0.0676187 0.117119i
\(19\) −0.893841 1.54818i −0.205061 0.355177i 0.745091 0.666963i \(-0.232406\pi\)
−0.950152 + 0.311786i \(0.899073\pi\)
\(20\) 7.71448 1.72501
\(21\) −0.684846 0.0584481i −0.149446 0.0127544i
\(22\) −0.881681 −0.187975
\(23\) −0.870106 1.50707i −0.181430 0.314245i 0.760938 0.648825i \(-0.224739\pi\)
−0.942368 + 0.334579i \(0.891406\pi\)
\(24\) −0.100686 + 0.174393i −0.0205524 + 0.0355977i
\(25\) −5.23232 + 9.06264i −1.04646 + 1.81253i
\(26\) 0 0
\(27\) 1.54120 0.296604
\(28\) −5.17142 0.441354i −0.977307 0.0834081i
\(29\) 1.65110 0.306602 0.153301 0.988180i \(-0.451010\pi\)
0.153301 + 0.988180i \(0.451010\pi\)
\(30\) −0.0999432 0.173107i −0.0182471 0.0316048i
\(31\) 2.80262 4.85427i 0.503365 0.871853i −0.496628 0.867964i \(-0.665429\pi\)
0.999992 0.00388953i \(-0.00123808\pi\)
\(32\) −1.14412 + 1.98168i −0.202254 + 0.350314i
\(33\) −0.585339 1.01384i −0.101894 0.176486i
\(34\) −0.446372 −0.0765522
\(35\) 5.94959 8.53550i 1.00566 1.44276i
\(36\) 5.75276 0.958793
\(37\) 3.57204 + 6.18695i 0.587239 + 1.01713i 0.994592 + 0.103857i \(0.0331185\pi\)
−0.407353 + 0.913271i \(0.633548\pi\)
\(38\) −0.174886 + 0.302911i −0.0283702 + 0.0491386i
\(39\) 0 0
\(40\) −1.52411 2.63984i −0.240983 0.417396i
\(41\) 8.11574 1.26746 0.633732 0.773552i \(-0.281522\pi\)
0.633732 + 0.773552i \(0.281522\pi\)
\(42\) 0.0570936 + 0.121760i 0.00880973 + 0.0187880i
\(43\) 6.81353 1.03905 0.519527 0.854454i \(-0.326108\pi\)
0.519527 + 0.854454i \(0.326108\pi\)
\(44\) −4.42002 7.65570i −0.666343 1.15414i
\(45\) −5.76606 + 9.98711i −0.859554 + 1.48879i
\(46\) −0.170242 + 0.294867i −0.0251008 + 0.0434758i
\(47\) 1.77271 + 3.07043i 0.258577 + 0.447868i 0.965861 0.259061i \(-0.0834131\pi\)
−0.707284 + 0.706929i \(0.750080\pi\)
\(48\) −0.979864 −0.141431
\(49\) −4.47665 + 5.38141i −0.639522 + 0.768773i
\(50\) 2.04747 0.289556
\(51\) −0.296342 0.513279i −0.0414962 0.0718735i
\(52\) 0 0
\(53\) −1.64483 + 2.84892i −0.225934 + 0.391330i −0.956599 0.291406i \(-0.905877\pi\)
0.730665 + 0.682736i \(0.239210\pi\)
\(54\) −0.150772 0.261146i −0.0205175 0.0355374i
\(55\) 17.7210 2.38949
\(56\) 0.870665 + 1.85682i 0.116347 + 0.248128i
\(57\) −0.464419 −0.0615138
\(58\) −0.161524 0.279768i −0.0212092 0.0367353i
\(59\) 2.25314 3.90255i 0.293333 0.508068i −0.681262 0.732039i \(-0.738569\pi\)
0.974596 + 0.223971i \(0.0719021\pi\)
\(60\) 1.00207 1.73563i 0.129366 0.224069i
\(61\) −3.77234 6.53388i −0.482998 0.836577i 0.516811 0.856099i \(-0.327119\pi\)
−0.999809 + 0.0195220i \(0.993786\pi\)
\(62\) −1.09670 −0.139281
\(63\) 4.43667 6.36500i 0.558968 0.801915i
\(64\) −7.09585 −0.886981
\(65\) 0 0
\(66\) −0.114525 + 0.198364i −0.0140971 + 0.0244169i
\(67\) −6.33263 + 10.9684i −0.773653 + 1.34001i 0.161895 + 0.986808i \(0.448239\pi\)
−0.935548 + 0.353199i \(0.885094\pi\)
\(68\) −2.23774 3.87588i −0.271366 0.470020i
\(69\) −0.452087 −0.0544249
\(70\) −2.02832 0.173107i −0.242431 0.0206902i
\(71\) −9.54869 −1.13322 −0.566610 0.823986i \(-0.691746\pi\)
−0.566610 + 0.823986i \(0.691746\pi\)
\(72\) −1.13655 1.96855i −0.133943 0.231996i
\(73\) 0.540019 0.935340i 0.0632044 0.109473i −0.832692 0.553737i \(-0.813201\pi\)
0.895896 + 0.444264i \(0.146535\pi\)
\(74\) 0.698891 1.21052i 0.0812445 0.140720i
\(75\) 1.35930 + 2.35437i 0.156958 + 0.271859i
\(76\) −3.50693 −0.402273
\(77\) −11.8793 1.01384i −1.35377 0.115537i
\(78\) 0 0
\(79\) −0.395849 0.685630i −0.0445365 0.0771394i 0.842898 0.538074i \(-0.180848\pi\)
−0.887434 + 0.460934i \(0.847514\pi\)
\(80\) 7.41628 12.8454i 0.829165 1.43616i
\(81\) −4.19857 + 7.27214i −0.466508 + 0.808016i
\(82\) −0.793947 1.37516i −0.0876768 0.151861i
\(83\) 7.14643 0.784422 0.392211 0.919875i \(-0.371710\pi\)
0.392211 + 0.919875i \(0.371710\pi\)
\(84\) −0.771035 + 1.10615i −0.0841268 + 0.120691i
\(85\) 8.97166 0.973114
\(86\) −0.666555 1.15451i −0.0718765 0.124494i
\(87\) 0.214468 0.371470i 0.0229934 0.0398258i
\(88\) −1.74649 + 3.02500i −0.186176 + 0.322466i
\(89\) −5.63281 9.75631i −0.597077 1.03417i −0.993250 0.115992i \(-0.962995\pi\)
0.396174 0.918176i \(-0.370338\pi\)
\(90\) 2.25633 0.237838
\(91\) 0 0
\(92\) −3.41381 −0.355914
\(93\) −0.728087 1.26108i −0.0754991 0.130768i
\(94\) 0.346843 0.600749i 0.0357741 0.0619625i
\(95\) 3.51504 6.08823i 0.360636 0.624639i
\(96\) 0.297229 + 0.514816i 0.0303358 + 0.0525432i
\(97\) 8.81353 0.894879 0.447439 0.894314i \(-0.352336\pi\)
0.447439 + 0.894314i \(0.352336\pi\)
\(98\) 1.34979 + 0.232085i 0.136349 + 0.0234441i
\(99\) 13.2147 1.32813
\(100\) 10.2643 + 17.7783i 1.02643 + 1.77783i
\(101\) 7.15855 12.3990i 0.712303 1.23374i −0.251688 0.967808i \(-0.580986\pi\)
0.963991 0.265936i \(-0.0856810\pi\)
\(102\) −0.0579811 + 0.100426i −0.00574099 + 0.00994368i
\(103\) 3.74607 + 6.48839i 0.369111 + 0.639320i 0.989427 0.145033i \(-0.0463287\pi\)
−0.620315 + 0.784352i \(0.712995\pi\)
\(104\) 0 0
\(105\) −1.14753 2.44727i −0.111987 0.238829i
\(106\) 0.643641 0.0625160
\(107\) −5.48919 9.50756i −0.530660 0.919130i −0.999360 0.0357726i \(-0.988611\pi\)
0.468700 0.883357i \(-0.344723\pi\)
\(108\) 1.51170 2.61834i 0.145463 0.251950i
\(109\) −6.22314 + 10.7788i −0.596068 + 1.03242i 0.397327 + 0.917677i \(0.369938\pi\)
−0.993395 + 0.114744i \(0.963395\pi\)
\(110\) −1.73361 3.00270i −0.165293 0.286296i
\(111\) 1.85595 0.176159
\(112\) −5.70642 + 8.18663i −0.539206 + 0.773564i
\(113\) −1.65110 −0.155323 −0.0776613 0.996980i \(-0.524745\pi\)
−0.0776613 + 0.996980i \(0.524745\pi\)
\(114\) 0.0454333 + 0.0786927i 0.00425522 + 0.00737025i
\(115\) 3.42170 5.92656i 0.319075 0.552654i
\(116\) 1.61950 2.80505i 0.150367 0.260443i
\(117\) 0 0
\(118\) −0.881681 −0.0811653
\(119\) −6.01418 0.513279i −0.551319 0.0470522i
\(120\) −0.791894 −0.0722897
\(121\) −4.65325 8.05967i −0.423023 0.732697i
\(122\) −0.738081 + 1.27839i −0.0668227 + 0.115740i
\(123\) 1.05419 1.82591i 0.0950528 0.164636i
\(124\) −5.49794 9.52272i −0.493730 0.855165i
\(125\) −21.4897 −1.92210
\(126\) −1.51254 0.129087i −0.134748 0.0115000i
\(127\) −4.49297 −0.398687 −0.199343 0.979930i \(-0.563881\pi\)
−0.199343 + 0.979930i \(0.563881\pi\)
\(128\) 2.98242 + 5.16569i 0.263611 + 0.456587i
\(129\) 0.885039 1.53293i 0.0779233 0.134967i
\(130\) 0 0
\(131\) 6.32836 + 10.9610i 0.552911 + 0.957670i 0.998063 + 0.0622152i \(0.0198165\pi\)
−0.445151 + 0.895455i \(0.646850\pi\)
\(132\) −2.29654 −0.199888
\(133\) −2.70463 + 3.88016i −0.234521 + 0.336453i
\(134\) 2.47804 0.214070
\(135\) 3.03039 + 5.24878i 0.260814 + 0.451743i
\(136\) −0.884200 + 1.53148i −0.0758195 + 0.131323i
\(137\) −4.64321 + 8.04227i −0.396696 + 0.687097i −0.993316 0.115426i \(-0.963177\pi\)
0.596620 + 0.802524i \(0.296510\pi\)
\(138\) 0.0442268 + 0.0766031i 0.00376484 + 0.00652089i
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) −8.66523 18.4799i −0.732346 1.56183i
\(141\) 0.921061 0.0775673
\(142\) 0.934130 + 1.61796i 0.0783905 + 0.135776i
\(143\) 0 0
\(144\) 5.53039 9.57891i 0.460866 0.798243i
\(145\) 3.24649 + 5.62308i 0.269606 + 0.466971i
\(146\) −0.211316 −0.0174887
\(147\) 0.629237 + 1.70619i 0.0518986 + 0.140724i
\(148\) 14.0147 1.15200
\(149\) −7.58243 13.1332i −0.621177 1.07591i −0.989267 0.146120i \(-0.953321\pi\)
0.368090 0.929790i \(-0.380012\pi\)
\(150\) 0.265955 0.460647i 0.0217151 0.0376117i
\(151\) 2.57079 4.45274i 0.209208 0.362359i −0.742257 0.670115i \(-0.766245\pi\)
0.951465 + 0.307756i \(0.0995780\pi\)
\(152\) 0.692848 + 1.20005i 0.0561974 + 0.0973367i
\(153\) 6.69025 0.540875
\(154\) 0.990341 + 2.11205i 0.0798040 + 0.170194i
\(155\) 22.0426 1.77051
\(156\) 0 0
\(157\) 5.36557 9.29344i 0.428219 0.741697i −0.568496 0.822686i \(-0.692474\pi\)
0.996715 + 0.0809889i \(0.0258078\pi\)
\(158\) −0.0774503 + 0.134148i −0.00616162 + 0.0106722i
\(159\) 0.427307 + 0.740117i 0.0338877 + 0.0586951i
\(160\) −8.99853 −0.711397
\(161\) −2.63281 + 3.77712i −0.207495 + 0.297679i
\(162\) 1.64295 0.129083
\(163\) 1.18620 + 2.05455i 0.0929101 + 0.160925i 0.908734 0.417375i \(-0.137050\pi\)
−0.815824 + 0.578300i \(0.803716\pi\)
\(164\) 7.96039 13.7878i 0.621602 1.07665i
\(165\) 2.30185 3.98692i 0.179199 0.310382i
\(166\) −0.699122 1.21091i −0.0542624 0.0939852i
\(167\) −12.0784 −0.934653 −0.467327 0.884085i \(-0.654783\pi\)
−0.467327 + 0.884085i \(0.654783\pi\)
\(168\) 0.530848 + 0.0453052i 0.0409558 + 0.00349537i
\(169\) 0 0
\(170\) −0.877681 1.52019i −0.0673151 0.116593i
\(171\) 2.62120 4.54005i 0.200448 0.347186i
\(172\) 6.68312 11.5755i 0.509583 0.882624i
\(173\) 9.70485 + 16.8093i 0.737846 + 1.27799i 0.953463 + 0.301509i \(0.0974902\pi\)
−0.215618 + 0.976478i \(0.569176\pi\)
\(174\) −0.0839242 −0.00636228
\(175\) 27.5865 + 2.35437i 2.08535 + 0.177974i
\(176\) −16.9967 −1.28117
\(177\) −0.585339 1.01384i −0.0439968 0.0762046i
\(178\) −1.10209 + 1.90888i −0.0826055 + 0.143077i
\(179\) −7.32219 + 12.6824i −0.547286 + 0.947928i 0.451173 + 0.892437i \(0.351006\pi\)
−0.998459 + 0.0554912i \(0.982328\pi\)
\(180\) 11.3114 + 19.5919i 0.843101 + 1.46029i
\(181\) −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
\(184\) 0.674450 + 1.16818i 0.0497211 + 0.0861194i
\(185\) −14.0471 + 24.3302i −1.03276 + 1.78879i
\(186\) −0.142455 + 0.246739i −0.0104453 + 0.0180918i
\(187\) −5.14033 8.90331i −0.375898 0.651074i
\(188\) 6.95513 0.507255
\(189\) −1.73114 3.69191i −0.125922 0.268547i
\(190\) −1.37548 −0.0997878
\(191\) −6.27687 10.8719i −0.454179 0.786660i 0.544462 0.838786i \(-0.316734\pi\)
−0.998641 + 0.0521252i \(0.983401\pi\)
\(192\) −0.921709 + 1.59645i −0.0665186 + 0.115214i
\(193\) −4.68430 + 8.11344i −0.337183 + 0.584018i −0.983902 0.178710i \(-0.942807\pi\)
0.646719 + 0.762729i \(0.276141\pi\)
\(194\) −0.862212 1.49339i −0.0619032 0.107219i
\(195\) 0 0
\(196\) 4.75151 + 12.8838i 0.339393 + 0.920270i
\(197\) 7.62276 0.543099 0.271550 0.962424i \(-0.412464\pi\)
0.271550 + 0.962424i \(0.412464\pi\)
\(198\) −1.29277 2.23914i −0.0918731 0.159129i
\(199\) −6.76443 + 11.7163i −0.479518 + 0.830549i −0.999724 0.0234914i \(-0.992522\pi\)
0.520206 + 0.854041i \(0.325855\pi\)
\(200\) 4.05575 7.02477i 0.286785 0.496726i
\(201\) 1.64514 + 2.84947i 0.116039 + 0.200986i
\(202\) −2.80123 −0.197094
\(203\) −1.85459 3.95518i −0.130167 0.277599i
\(204\) −1.16268 −0.0814038
\(205\) 15.9576 + 27.6394i 1.11453 + 1.93042i
\(206\) 0.732942 1.26949i 0.0510665 0.0884498i
\(207\) 2.55159 4.41949i 0.177348 0.307176i
\(208\) 0 0
\(209\) −8.05579 −0.557231
\(210\) −0.302413 + 0.433853i −0.0208685 + 0.0299387i
\(211\) −15.7995 −1.08768 −0.543840 0.839189i \(-0.683030\pi\)
−0.543840 + 0.839189i \(0.683030\pi\)
\(212\) 3.22669 + 5.58879i 0.221610 + 0.383839i
\(213\) −1.24032 + 2.14830i −0.0849853 + 0.147199i
\(214\) −1.07399 + 1.86021i −0.0734167 + 0.127162i
\(215\) 13.3971 + 23.2045i 0.913678 + 1.58254i
\(216\) −1.19464 −0.0812847
\(217\) −14.7763 1.26108i −1.00308 0.0856080i
\(218\) 2.43519 0.164932
\(219\) −0.140291 0.242991i −0.00947997 0.0164198i
\(220\) 17.3818 30.1061i 1.17188 2.02975i
\(221\) 0 0
\(222\) −0.181564 0.314478i −0.0121858 0.0211064i
\(223\) −22.4737 −1.50495 −0.752474 0.658622i \(-0.771139\pi\)
−0.752474 + 0.658622i \(0.771139\pi\)
\(224\) 6.03219 + 0.514816i 0.403043 + 0.0343976i
\(225\) −30.6876 −2.04584
\(226\) 0.161524 + 0.279768i 0.0107444 + 0.0186099i
\(227\) −4.60124 + 7.96959i −0.305395 + 0.528960i −0.977349 0.211633i \(-0.932122\pi\)
0.671954 + 0.740593i \(0.265455\pi\)
\(228\) −0.455530 + 0.789001i −0.0301682 + 0.0522529i
\(229\) 7.64611 + 13.2435i 0.505269 + 0.875152i 0.999981 + 0.00609528i \(0.00194020\pi\)
−0.494712 + 0.869057i \(0.664726\pi\)
\(230\) −1.33895 −0.0882880
\(231\) −1.77115 + 2.54095i −0.116533 + 0.167182i
\(232\) −1.27983 −0.0840247
\(233\) 4.02789 + 6.97652i 0.263876 + 0.457047i 0.967269 0.253755i \(-0.0816656\pi\)
−0.703392 + 0.710802i \(0.748332\pi\)
\(234\) 0 0
\(235\) −6.97121 + 12.0745i −0.454752 + 0.787653i
\(236\) −4.42002 7.65570i −0.287719 0.498344i
\(237\) −0.205674 −0.0133600
\(238\) 0.501384 + 1.06928i 0.0324999 + 0.0693108i
\(239\) −21.7258 −1.40533 −0.702663 0.711523i \(-0.748006\pi\)
−0.702663 + 0.711523i \(0.748006\pi\)
\(240\) −1.92666 3.33708i −0.124366 0.215407i
\(241\) −10.2490 + 17.7518i −0.660195 + 1.14349i 0.320369 + 0.947293i \(0.396193\pi\)
−0.980564 + 0.196199i \(0.937140\pi\)
\(242\) −0.910438 + 1.57692i −0.0585252 + 0.101369i
\(243\) 3.40254 + 5.89337i 0.218273 + 0.378060i
\(244\) −14.8005 −0.947507
\(245\) −27.1295 4.66470i −1.73324 0.298017i
\(246\) −0.412517 −0.0263011
\(247\) 0 0
\(248\) −2.17241 + 3.76272i −0.137948 + 0.238933i
\(249\) 0.928280 1.60783i 0.0588273 0.101892i
\(250\) 2.10230 + 3.64129i 0.132961 + 0.230295i
\(251\) 2.60871 0.164660 0.0823301 0.996605i \(-0.473764\pi\)
0.0823301 + 0.996605i \(0.473764\pi\)
\(252\) −6.46175 13.7806i −0.407052 0.868098i
\(253\) −7.84187 −0.493014
\(254\) 0.439539 + 0.761304i 0.0275791 + 0.0477685i
\(255\) 1.16537 2.01848i 0.0729781 0.126402i
\(256\) −6.51232 + 11.2797i −0.407020 + 0.704979i
\(257\) 4.49838 + 7.79142i 0.280601 + 0.486016i 0.971533 0.236904i \(-0.0761328\pi\)
−0.690932 + 0.722920i \(0.742799\pi\)
\(258\) −0.346327 −0.0215614
\(259\) 10.8084 15.5062i 0.671604 0.963508i
\(260\) 0 0
\(261\) 2.42094 + 4.19318i 0.149852 + 0.259551i
\(262\) 1.23818 2.14460i 0.0764952 0.132494i
\(263\) −0.716961 + 1.24181i −0.0442097 + 0.0765735i −0.887284 0.461224i \(-0.847410\pi\)
0.843074 + 0.537798i \(0.180744\pi\)
\(264\) 0.453717 + 0.785860i 0.0279243 + 0.0483664i
\(265\) −12.9366 −0.794689
\(266\) 0.922056 + 0.0786927i 0.0565349 + 0.00482496i
\(267\) −2.92668 −0.179110
\(268\) 12.4228 + 21.5170i 0.758845 + 1.31436i
\(269\) 4.08416 7.07397i 0.249016 0.431308i −0.714237 0.699904i \(-0.753226\pi\)
0.963253 + 0.268596i \(0.0865596\pi\)
\(270\) 0.592914 1.02696i 0.0360836 0.0624986i
\(271\) −0.106159 0.183872i −0.00644867 0.0111694i 0.862783 0.505574i \(-0.168719\pi\)
−0.869232 + 0.494405i \(0.835386\pi\)
\(272\) −8.60497 −0.521753
\(273\) 0 0
\(274\) 1.81695 0.109766
\(275\) 23.5783 + 40.8387i 1.42182 + 2.46267i
\(276\) −0.443434 + 0.768049i −0.0266916 + 0.0462311i
\(277\) −11.4875 + 19.8969i −0.690215 + 1.19549i 0.281552 + 0.959546i \(0.409151\pi\)
−0.971767 + 0.235942i \(0.924182\pi\)
\(278\) 0.391313 + 0.677773i 0.0234694 + 0.0406501i
\(279\) 16.4374 0.984081
\(280\) −4.61174 + 6.61617i −0.275604 + 0.395392i
\(281\) 0.345228 0.0205946 0.0102973 0.999947i \(-0.496722\pi\)
0.0102973 + 0.999947i \(0.496722\pi\)
\(282\) −0.0901057 0.156068i −0.00536572 0.00929369i
\(283\) 14.4857 25.0900i 0.861087 1.49145i −0.00979277 0.999952i \(-0.503117\pi\)
0.870880 0.491495i \(-0.163549\pi\)
\(284\) −9.36592 + 16.2222i −0.555765 + 0.962613i
\(285\) −0.913167 1.58165i −0.0540913 0.0936889i
\(286\) 0 0
\(287\) −9.11594 19.4411i −0.538097 1.14757i
\(288\) −6.71029 −0.395408
\(289\) 5.89759 + 10.2149i 0.346917 + 0.600878i
\(290\) 0.635195 1.10019i 0.0372999 0.0646054i
\(291\) 1.14483 1.98290i 0.0671109 0.116240i
\(292\) −1.05937 1.83487i −0.0619947 0.107378i
\(293\) −31.5427 −1.84274 −0.921372 0.388682i \(-0.872930\pi\)
−0.921372 + 0.388682i \(0.872930\pi\)
\(294\) 0.227545 0.273533i 0.0132707 0.0159528i
\(295\) 17.7210 1.03175
\(296\) −2.76881 4.79572i −0.160934 0.278746i
\(297\) 3.47253 6.01460i 0.201497 0.349002i
\(298\) −1.48355 + 2.56958i −0.0859398 + 0.148852i
\(299\) 0 0
\(300\) 5.33311 0.307907
\(301\) −7.65325 16.3217i −0.441126 0.940766i
\(302\) −1.00598 −0.0578879
\(303\) −1.85971 3.22111i −0.106838 0.185048i
\(304\) −3.37137 + 5.83939i −0.193361 + 0.334912i
\(305\) 14.8348 25.6945i 0.849435 1.47127i
\(306\) −0.654495 1.13362i −0.0374150 0.0648047i
\(307\) 18.1941 1.03839 0.519197 0.854655i \(-0.326231\pi\)
0.519197 + 0.854655i \(0.326231\pi\)
\(308\) −13.3743 + 19.1873i −0.762073 + 1.09330i
\(309\) 1.94637 0.110725
\(310\) −2.15639 3.73498i −0.122475 0.212132i
\(311\) 0.188312 0.326165i 0.0106782 0.0184951i −0.860637 0.509219i \(-0.829934\pi\)
0.871315 + 0.490724i \(0.163268\pi\)
\(312\) 0 0
\(313\) −5.49415 9.51615i −0.310548 0.537884i 0.667933 0.744221i \(-0.267179\pi\)
−0.978481 + 0.206337i \(0.933846\pi\)
\(314\) −2.09961 −0.118488
\(315\) 30.4006 + 2.59454i 1.71288 + 0.146186i
\(316\) −1.55309 −0.0873680
\(317\) 13.0903 + 22.6731i 0.735225 + 1.27345i 0.954625 + 0.297812i \(0.0962568\pi\)
−0.219400 + 0.975635i \(0.570410\pi\)
\(318\) 0.0836053 0.144809i 0.00468835 0.00812046i
\(319\) 3.72016 6.44350i 0.208289 0.360767i
\(320\) −13.9522 24.1660i −0.779954 1.35092i
\(321\) −2.85206 −0.159186
\(322\) 0.897571 + 0.0766031i 0.0500197 + 0.00426892i
\(323\) −4.07844 −0.226930
\(324\) 8.23642 + 14.2659i 0.457579 + 0.792550i
\(325\) 0 0
\(326\) 0.232087 0.401986i 0.0128541 0.0222639i
\(327\) 1.61670 + 2.80020i 0.0894037 + 0.154852i
\(328\) −6.29079 −0.347351
\(329\) 5.36397 7.69534i 0.295725 0.424258i
\(330\) −0.900743 −0.0495843
\(331\) −17.0466 29.5256i −0.936967 1.62287i −0.771089 0.636728i \(-0.780288\pi\)
−0.165878 0.986146i \(-0.553046\pi\)
\(332\) 7.00964 12.1411i 0.384704 0.666327i
\(333\) −10.4750 + 18.1433i −0.574028 + 0.994246i
\(334\) 1.18161 + 2.04660i 0.0646546 + 0.111985i
\(335\) −49.8062 −2.72120
\(336\) 1.10063 + 2.34725i 0.0600440 + 0.128053i
\(337\) 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
\(340\) 8.79994 15.2419i 0.477244 0.826610i
\(341\) −12.6294 21.8747i −0.683918 1.18458i
\(342\) −1.02571 −0.0554639
\(343\) 17.9194 + 4.67910i 0.967558 + 0.252648i
\(344\) −5.28141 −0.284754
\(345\) −0.888918 1.53965i −0.0478577 0.0828920i
\(346\) 1.89881 3.28884i 0.102081 0.176809i
\(347\) −14.9733 + 25.9345i −0.803809 + 1.39224i 0.113284 + 0.993563i \(0.463863\pi\)
−0.917092 + 0.398675i \(0.869470\pi\)
\(348\) −0.420727 0.728720i −0.0225533 0.0390635i
\(349\) 13.4793 0.721532 0.360766 0.932656i \(-0.382515\pi\)
0.360766 + 0.932656i \(0.382515\pi\)
\(350\) −2.29981 4.90468i −0.122930 0.262166i
\(351\) 0 0
\(352\) 5.15572 + 8.92997i 0.274801 + 0.475969i
\(353\) 0.0817659 0.141623i 0.00435196 0.00753781i −0.863841 0.503764i \(-0.831948\pi\)
0.868193 + 0.496226i \(0.165281\pi\)
\(354\) −0.114525 + 0.198364i −0.00608695 + 0.0105429i
\(355\) −18.7752 32.5195i −0.996482 1.72596i
\(356\) −22.1000 −1.17130
\(357\) −0.896686 + 1.28642i −0.0474577 + 0.0680845i
\(358\) 2.86527 0.151434
\(359\) 4.46065 + 7.72607i 0.235424 + 0.407766i 0.959396 0.282063i \(-0.0910188\pi\)
−0.723972 + 0.689830i \(0.757685\pi\)
\(360\) 4.46948 7.74136i 0.235562 0.408006i
\(361\) 7.90209 13.6868i 0.415900 0.720359i
\(362\) 0.924111 + 1.60061i 0.0485702 + 0.0841261i
\(363\) −2.41772 −0.126898
\(364\) 0 0
\(365\) 4.24726 0.222312
\(366\) 0.191745 + 0.332112i 0.0100227 + 0.0173598i
\(367\) −18.3276 + 31.7443i −0.956693 + 1.65704i −0.226248 + 0.974070i \(0.572646\pi\)
−0.730445 + 0.682971i \(0.760687\pi\)
\(368\) −3.28185 + 5.68432i −0.171078 + 0.296316i
\(369\) 11.8997 + 20.6110i 0.619476 + 1.07296i
\(370\) 5.49679 0.285765
\(371\) 8.67208 + 0.740117i 0.450232 + 0.0384250i
\(372\) −2.85660 −0.148108
\(373\) −13.5637 23.4930i −0.702302 1.21642i −0.967656 0.252271i \(-0.918822\pi\)
0.265355 0.964151i \(-0.414511\pi\)
\(374\) −1.00574 + 1.74199i −0.0520054 + 0.0900761i
\(375\) −2.79139 + 4.83483i −0.144147 + 0.249670i
\(376\) −1.37409 2.38000i −0.0708634 0.122739i
\(377\) 0 0
\(378\) −0.456215 + 0.654502i −0.0234652 + 0.0336640i
\(379\) 15.8943 0.816434 0.408217 0.912885i \(-0.366151\pi\)
0.408217 + 0.912885i \(0.366151\pi\)
\(380\) −6.89552 11.9434i −0.353733 0.612683i
\(381\) −0.583611 + 1.01084i −0.0298993 + 0.0517871i
\(382\) −1.22811 + 2.12715i −0.0628355 + 0.108834i
\(383\) 0.575394 + 0.996611i 0.0294013 + 0.0509245i 0.880352 0.474322i \(-0.157307\pi\)
−0.850950 + 0.525246i \(0.823973\pi\)
\(384\) 1.54959 0.0790774
\(385\) −19.9049 42.4502i −1.01445 2.16346i
\(386\) 1.83302 0.0932985
\(387\) 9.99038 + 17.3038i 0.507839 + 0.879604i
\(388\) 8.64484 14.9733i 0.438875 0.760154i
\(389\) 7.15651 12.3954i 0.362850 0.628474i −0.625579 0.780161i \(-0.715137\pi\)
0.988429 + 0.151687i \(0.0484705\pi\)
\(390\) 0 0
\(391\) −3.97013 −0.200778
\(392\) 3.47001 4.17132i 0.175262 0.210684i
\(393\) 3.28807 0.165861
\(394\) −0.745721 1.29163i −0.0375689 0.0650712i
\(395\) 1.55668 2.69625i 0.0783251 0.135663i
\(396\) 12.9618 22.4504i 0.651353 1.12818i
\(397\) −12.9588 22.4453i −0.650383 1.12650i −0.983030 0.183445i \(-0.941275\pi\)
0.332647 0.943051i \(-0.392058\pi\)
\(398\) 2.64701 0.132682
\(399\) 0.521656 + 1.11251i 0.0261154 + 0.0556950i
\(400\) 39.4703 1.97351
\(401\) −2.14816 3.72072i −0.107274 0.185804i 0.807391 0.590017i \(-0.200879\pi\)
−0.914665 + 0.404213i \(0.867545\pi\)
\(402\) 0.321882 0.557517i 0.0160540 0.0278064i
\(403\) 0 0
\(404\) −14.0431 24.3233i −0.698669 1.21013i
\(405\) −33.0219 −1.64087
\(406\) −0.488748 + 0.701175i −0.0242562 + 0.0347987i
\(407\) 32.1931 1.59575
\(408\) 0.229705 + 0.397861i 0.0113721 + 0.0196970i
\(409\) −12.3536 + 21.3970i −0.610844 + 1.05801i 0.380255 + 0.924882i \(0.375836\pi\)
−0.991098 + 0.133131i \(0.957497\pi\)
\(410\) 3.12221 5.40782i 0.154195 0.267073i
\(411\) 1.20625 + 2.08929i 0.0595000 + 0.103057i
\(412\) 14.6975 0.724093
\(413\) −11.8793 1.01384i −0.584542 0.0498876i
\(414\) −0.998471 −0.0490722
\(415\) 14.0517 + 24.3383i 0.689771 + 1.19472i
\(416\) 0 0
\(417\) −0.519577 + 0.899934i −0.0254438 + 0.0440699i
\(418\) 0.788083 + 1.36500i 0.0385464 + 0.0667643i
\(419\) −24.9293 −1.21787 −0.608937 0.793218i \(-0.708404\pi\)
−0.608937 + 0.793218i \(0.708404\pi\)
\(420\) −5.28323 0.450896i −0.257795 0.0220015i
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 1.54563 + 2.67712i 0.0752402 + 0.130320i
\(423\) −5.19850 + 9.00407i −0.252760 + 0.437793i
\(424\) 1.27496 2.20830i 0.0619177 0.107245i
\(425\) 11.9371 + 20.6756i 0.579032 + 1.00291i
\(426\) 0.485352 0.0235154
\(427\) −11.4145 + 16.3757i −0.552388 + 0.792475i
\(428\) −21.5365 −1.04101
\(429\) 0 0
\(430\) 2.62124 4.54011i 0.126407 0.218944i
\(431\) −2.84426 + 4.92639i −0.137003 + 0.237296i −0.926361 0.376637i \(-0.877080\pi\)
0.789358 + 0.613933i \(0.210414\pi\)
\(432\) −2.90653 5.03425i −0.139840 0.242211i
\(433\) 12.2598 0.589169 0.294584 0.955625i \(-0.404819\pi\)
0.294584 + 0.955625i \(0.404819\pi\)
\(434\) 1.23186 + 2.62712i 0.0591311 + 0.126106i
\(435\) 1.68680 0.0808758
\(436\) 12.2080 + 21.1450i 0.584659 + 1.01266i
\(437\) −1.55547 + 2.69416i −0.0744084 + 0.128879i
\(438\) −0.0274487 + 0.0475426i −0.00131155 + 0.00227167i
\(439\) −2.51158 4.35019i −0.119871 0.207623i 0.799845 0.600206i \(-0.204915\pi\)
−0.919717 + 0.392583i \(0.871582\pi\)
\(440\) −13.7361 −0.654845
\(441\) −20.2307 3.47851i −0.963367 0.165643i
\(442\) 0 0
\(443\) −0.289401 0.501258i −0.0137499 0.0238155i 0.859069 0.511860i \(-0.171044\pi\)
−0.872818 + 0.488045i \(0.837710\pi\)
\(444\) 1.82042 3.15307i 0.0863935 0.149638i
\(445\) 22.1511 38.3668i 1.05006 1.81876i
\(446\) 2.19856 + 3.80801i 0.104105 + 0.180315i
\(447\) −3.93966 −0.186339
\(448\) 7.97036 + 16.9980i 0.376564 + 0.803078i
\(449\) 7.36359 0.347509 0.173755 0.984789i \(-0.444410\pi\)
0.173755 + 0.984789i \(0.444410\pi\)
\(450\) 3.00212 + 5.19982i 0.141521 + 0.245122i
\(451\) 18.2859 31.6720i 0.861048 1.49138i
\(452\) −1.61950 + 2.80505i −0.0761748 + 0.131939i
\(453\) −0.667862 1.15677i −0.0313789 0.0543499i
\(454\) 1.80052 0.0845028
\(455\) 0 0
\(456\) 0.359988 0.0168580
\(457\) 3.95912 + 6.85739i 0.185200 + 0.320775i 0.943644 0.330963i \(-0.107373\pi\)
−0.758444 + 0.651738i \(0.774040\pi\)
\(458\) 1.49601 2.59117i 0.0699040 0.121077i
\(459\) 1.75805 3.04503i 0.0820588 0.142130i
\(460\) −6.71241 11.6262i −0.312968 0.542076i
\(461\) 9.53600 0.444136 0.222068 0.975031i \(-0.428719\pi\)
0.222068 + 0.975031i \(0.428719\pi\)
\(462\) 0.603816 + 0.0515325i 0.0280920 + 0.00239751i
\(463\) −2.16049 −0.100406 −0.0502032 0.998739i \(-0.515987\pi\)
−0.0502032 + 0.998739i \(0.515987\pi\)
\(464\) −3.11379 5.39325i −0.144554 0.250375i
\(465\) 2.86321 4.95923i 0.132778 0.229979i
\(466\) 0.788083 1.36500i 0.0365072 0.0632324i
\(467\) 4.05950 + 7.03126i 0.187851 + 0.325368i 0.944534 0.328415i \(-0.106514\pi\)
−0.756682 + 0.653783i \(0.773181\pi\)
\(468\) 0 0
\(469\) 33.3877 + 2.84947i 1.54170 + 0.131576i
\(470\) 2.72792 0.125830
\(471\) −1.39391 2.41433i −0.0642281 0.111246i
\(472\) −1.74649 + 3.02500i −0.0803885 + 0.139237i
\(473\) 15.3518 26.5901i 0.705878 1.22262i
\(474\) 0.0201207 + 0.0348501i 0.000924174 + 0.00160072i
\(475\) 18.7074 0.858357
\(476\) −6.77107 + 9.71402i −0.310352 + 0.445241i
\(477\) −9.64694 −0.441703
\(478\) 2.12540 + 3.68129i 0.0972133 + 0.168378i
\(479\) 7.27663 12.6035i 0.332478 0.575868i −0.650519 0.759490i \(-0.725449\pi\)
0.982997 + 0.183621i \(0.0587820\pi\)
\(480\) −1.16886 + 2.02452i −0.0533508 + 0.0924063i
\(481\) 0 0
\(482\) 4.01056 0.182676
\(483\) 0.507803 + 1.08297i 0.0231058 + 0.0492766i
\(484\) −18.2567 −0.829852
\(485\) 17.3297 + 30.0158i 0.786899 + 1.36295i
\(486\) 0.665728 1.15307i 0.0301980 0.0523045i
\(487\) −16.6295 + 28.8031i −0.753554 + 1.30519i 0.192536 + 0.981290i \(0.438329\pi\)
−0.946090 + 0.323904i \(0.895005\pi\)
\(488\) 2.92407 + 5.06464i 0.132366 + 0.229265i
\(489\) 0.616320 0.0278710
\(490\) 1.86362 + 5.05324i 0.0841899 + 0.228282i
\(491\) −22.5563 −1.01795 −0.508977 0.860780i \(-0.669976\pi\)
−0.508977 + 0.860780i \(0.669976\pi\)
\(492\) −2.06802 3.58191i −0.0932335 0.161485i
\(493\) 1.88342 3.26218i 0.0848249 0.146921i
\(494\) 0 0
\(495\) 25.9835 + 45.0047i 1.16787 + 2.02281i
\(496\) −21.1417 −0.949290
\(497\) 10.7255 + 22.8737i 0.481104 + 1.02603i
\(498\) −0.363248 −0.0162775
\(499\) −5.69271 9.86007i −0.254841 0.441397i 0.710011 0.704190i \(-0.248690\pi\)
−0.964852 + 0.262793i \(0.915356\pi\)
\(500\) −21.0784 + 36.5089i −0.942655 + 1.63273i
\(501\) −1.56891 + 2.71743i −0.0700938 + 0.121406i
\(502\) −0.255205 0.442028i −0.0113904 0.0197287i
\(503\) −8.81825 −0.393186 −0.196593 0.980485i \(-0.562988\pi\)
−0.196593 + 0.980485i \(0.562988\pi\)
\(504\) −3.43902 + 4.93374i −0.153186 + 0.219766i
\(505\) 56.3022 2.50541
\(506\) 0.767156 + 1.32875i 0.0341042 + 0.0590702i
\(507\) 0 0
\(508\) −4.40697 + 7.63310i −0.195528 + 0.338664i
\(509\) 9.64188 + 16.7002i 0.427369 + 0.740225i 0.996638 0.0819263i \(-0.0261072\pi\)
−0.569269 + 0.822151i \(0.692774\pi\)
\(510\) −0.456023 −0.0201930
\(511\) −2.84716 0.242991i −0.125951 0.0107493i
\(512\) 14.4780 0.639844
\(513\) −1.37759 2.38605i −0.0608219 0.105347i
\(514\) 0.880136 1.52444i 0.0388211 0.0672402i
\(515\) −14.7315 + 25.5156i −0.649146 + 1.12435i
\(516\) −1.73620 3.00718i −0.0764318 0.132384i
\(517\) 15.9767 0.702653
\(518\) −3.68479 0.314478i −0.161900 0.0138174i
\(519\) 5.04241 0.221337
\(520\) 0 0
\(521\) −12.5584 + 21.7518i −0.550193 + 0.952963i 0.448067 + 0.894000i \(0.352113\pi\)
−0.998260 + 0.0589629i \(0.981221\pi\)
\(522\) 0.473671 0.820422i 0.0207320 0.0359089i
\(523\) 14.9824 + 25.9503i 0.655134 + 1.13473i 0.981860 + 0.189606i \(0.0607212\pi\)
−0.326726 + 0.945119i \(0.605946\pi\)
\(524\) 24.8289 1.08466
\(525\) 4.11303 5.90069i 0.179507 0.257527i
\(526\) 0.280556 0.0122328
\(527\) −6.39391 11.0746i −0.278523 0.482416i
\(528\) −2.20777 + 3.82397i −0.0960808 + 0.166417i
\(529\) 9.98583 17.2960i 0.434167 0.751999i
\(530\) 1.26556 + 2.19202i 0.0549726 + 0.0952153i
\(531\) 13.2147 0.573469
\(532\) 3.93913 + 8.40078i 0.170783 + 0.364220i
\(533\) 0 0
\(534\) 0.286311 + 0.495906i 0.0123899 + 0.0214599i
\(535\) 21.5863 37.3886i 0.933257 1.61645i
\(536\) 4.90864 8.50201i 0.212021 0.367231i
\(537\) 1.90222 + 3.29474i 0.0820869 + 0.142179i
\(538\) −1.59818 −0.0689026
\(539\) 10.9147 + 29.5954i 0.470130 + 1.27476i
\(540\) 11.8895 0.511644
\(541\) 2.54987 + 4.41650i 0.109627 + 0.189880i 0.915619 0.402046i \(-0.131701\pi\)
−0.805992 + 0.591926i \(0.798368\pi\)
\(542\) −0.0207706 + 0.0359757i −0.000892173 + 0.00154529i
\(543\) −1.22702 + 2.12525i −0.0526563 + 0.0912034i
\(544\) 2.61021 + 4.52101i 0.111912 + 0.193837i
\(545\) −48.9451 −2.09658
\(546\) 0 0
\(547\) 2.92025 0.124861 0.0624305 0.998049i \(-0.480115\pi\)
0.0624305 + 0.998049i \(0.480115\pi\)
\(548\) 9.10867 + 15.7767i 0.389103 + 0.673946i
\(549\) 11.0624 19.1607i 0.472132 0.817757i
\(550\) 4.61323 7.99035i 0.196709 0.340710i
\(551\) −1.47582 2.55620i −0.0628722 0.108898i
\(552\) 0.350428 0.0149152
\(553\) −1.19778 + 1.71838i −0.0509348 + 0.0730728i
\(554\) 4.49519 0.190982
\(555\) 3.64927 + 6.32071i 0.154903 + 0.268299i
\(556\) −3.92344 + 6.79559i −0.166391 + 0.288197i
\(557\) 12.9937 22.5058i 0.550561 0.953600i −0.447673 0.894197i \(-0.647747\pi\)
0.998234 0.0594024i \(-0.0189195\pi\)
\(558\) −1.60804 2.78521i −0.0680738 0.117907i
\(559\) 0 0
\(560\) −39.1011 3.33708i −1.65232 0.141017i
\(561\) −2.67079 −0.112761
\(562\) −0.0337730 0.0584965i −0.00142463 0.00246753i
\(563\) −1.82534 + 3.16159i −0.0769291 + 0.133245i −0.901924 0.431896i \(-0.857845\pi\)
0.824994 + 0.565141i \(0.191178\pi\)
\(564\) 0.903431 1.56479i 0.0380413 0.0658895i
\(565\) −3.24649 5.62308i −0.136581 0.236565i
\(566\) −5.66845 −0.238263
\(567\) 22.1363 + 1.88922i 0.929637 + 0.0793397i
\(568\) 7.40152 0.310561
\(569\) 12.6766 + 21.9566i 0.531432 + 0.920468i 0.999327 + 0.0366835i \(0.0116793\pi\)
−0.467895 + 0.883784i \(0.654987\pi\)
\(570\) −0.178667 + 0.309460i −0.00748353 + 0.0129619i
\(571\) −13.8626 + 24.0108i −0.580133 + 1.00482i 0.415330 + 0.909671i \(0.363666\pi\)
−0.995463 + 0.0951493i \(0.969667\pi\)
\(572\) 0 0
\(573\) −3.26132 −0.136244
\(574\) −2.40237 + 3.44652i −0.100273 + 0.143855i
\(575\) 18.2107 0.759438
\(576\) −10.4043 18.0208i −0.433513 0.750867i
\(577\) 19.7877 34.2733i 0.823773 1.42682i −0.0790809 0.996868i \(-0.525199\pi\)
0.902854 0.429948i \(-0.141468\pi\)
\(578\) 1.15390 1.99861i 0.0479959 0.0831313i
\(579\) 1.21693 + 2.10778i 0.0505737 + 0.0875963i
\(580\) 12.7374 0.528891
\(581\) −8.02717 17.1191i −0.333023 0.710221i
\(582\) −0.447985 −0.0185696
\(583\) 7.41204 + 12.8380i 0.306975 + 0.531697i
\(584\) −0.418588 + 0.725015i −0.0173213 + 0.0300013i
\(585\) 0 0
\(586\) 3.08576 + 5.34470i 0.127472 + 0.220787i
\(587\) 8.24177 0.340174 0.170087 0.985429i \(-0.445595\pi\)
0.170087 + 0.985429i \(0.445595\pi\)
\(588\) 3.51583 + 0.604519i 0.144990 + 0.0249299i
\(589\) −10.0204 −0.412882
\(590\) −1.73361 3.00270i −0.0713716 0.123619i
\(591\) 0.990153 1.71500i 0.0407295 0.0705455i
\(592\) 13.4729 23.3358i 0.553734 0.959095i
\(593\) −5.96149 10.3256i −0.244809 0.424021i 0.717269 0.696796i \(-0.245392\pi\)
−0.962078 + 0.272775i \(0.912059\pi\)
\(594\) −1.35884 −0.0557540
\(595\) −10.0774 21.4914i −0.413131 0.881063i
\(596\) −29.7492 −1.21857
\(597\) 1.75732 + 3.04377i 0.0719224 + 0.124573i
\(598\) 0 0
\(599\) 17.8079 30.8442i 0.727611 1.26026i −0.230279 0.973125i \(-0.573964\pi\)
0.957890 0.287135i \(-0.0927027\pi\)
\(600\) −1.05364 1.82495i −0.0430146 0.0745034i
\(601\) 38.9252 1.58779 0.793896 0.608054i \(-0.208050\pi\)
0.793896 + 0.608054i \(0.208050\pi\)
\(602\) −2.01690 + 2.89351i −0.0822026 + 0.117931i
\(603\) −37.1410 −1.51250
\(604\) −5.04317 8.73503i −0.205204 0.355423i
\(605\) 18.2990 31.6947i 0.743959 1.28857i
\(606\) −0.363864 + 0.630231i −0.0147810 + 0.0256014i
\(607\) 6.84828 + 11.8616i 0.277963 + 0.481446i 0.970878 0.239573i \(-0.0770074\pi\)
−0.692915 + 0.721019i \(0.743674\pi\)
\(608\) 4.09065 0.165898
\(609\) −1.13075 0.0965037i −0.0458203 0.00391053i
\(610\) −5.80502 −0.235039
\(611\) 0 0
\(612\) 6.56220 11.3661i 0.265261 0.459446i
\(613\) 1.58056 2.73761i 0.0638382 0.110571i −0.832340 0.554266i \(-0.812999\pi\)
0.896178 + 0.443695i \(0.146333\pi\)
\(614\) −1.77990 3.08287i −0.0718308 0.124415i
\(615\) 8.29120 0.334334
\(616\) 9.20806 + 0.785860i 0.371003 + 0.0316632i
\(617\) −20.9297 −0.842597 −0.421299 0.906922i \(-0.638426\pi\)
−0.421299 + 0.906922i \(0.638426\pi\)
\(618\) −0.190410 0.329800i −0.00765941 0.0132665i
\(619\) 15.4772 26.8073i 0.622082 1.07748i −0.367016 0.930215i \(-0.619621\pi\)
0.989097 0.147262i \(-0.0470461\pi\)
\(620\) 21.6207 37.4482i 0.868309 1.50396i
\(621\) −1.34100 2.32269i −0.0538127 0.0932063i
\(622\) −0.0736887 −0.00295465
\(623\) −17.0440 + 24.4520i −0.682855 + 0.979648i
\(624\) 0 0
\(625\) −16.0927 27.8734i −0.643708 1.11494i
\(626\) −1.07496 + 1.86189i −0.0429642 + 0.0744162i
\(627\) −1.04640 + 1.81242i −0.0417892 + 0.0723810i
\(628\) −10.5257 18.2311i −0.420023 0.727501i
\(629\) 16.2986 0.649866
\(630\) −2.53441 5.40500i −0.100973 0.215340i
\(631\) 15.1218 0.601988 0.300994 0.953626i \(-0.402682\pi\)
0.300994 + 0.953626i \(0.402682\pi\)
\(632\) 0.306836 + 0.531456i 0.0122053 + 0.0211402i
\(633\) −2.05226 + 3.55462i −0.0815700 + 0.141283i
\(634\) 2.56120 4.43613i 0.101718 0.176181i
\(635\) −8.83433 15.3015i −0.350580 0.607222i
\(636\) 1.67651 0.0664780
\(637\) 0 0
\(638\) −1.45574 −0.0576335
\(639\) −14.0008 24.2501i −0.553864 0.959320i
\(640\) −11.7284 + 20.3141i −0.463605 + 0.802987i
\(641\) 23.6207 40.9123i 0.932962 1.61594i 0.154733 0.987956i \(-0.450548\pi\)
0.778229 0.627981i \(-0.216118\pi\)
\(642\) 0.279011 + 0.483262i 0.0110117 + 0.0190728i
\(643\) −39.9249 −1.57448 −0.787241 0.616645i \(-0.788491\pi\)
−0.787241 + 0.616645i \(0.788491\pi\)
\(644\) 3.83453 + 8.17770i 0.151102 + 0.322247i
\(645\) 6.96085 0.274083
\(646\) 0.398986 + 0.691064i 0.0156979 + 0.0271895i
\(647\) 14.9139 25.8317i 0.586327 1.01555i −0.408382 0.912811i \(-0.633907\pi\)
0.994709 0.102736i \(-0.0327598\pi\)
\(648\) 3.25446 5.63689i 0.127847 0.221438i
\(649\) −10.1533 17.5859i −0.398550 0.690309i
\(650\) 0 0
\(651\) −2.20308 + 3.16062i −0.0863456 + 0.123875i
\(652\) 4.65397 0.182263
\(653\) −12.5774 21.7848i −0.492194 0.852504i 0.507766 0.861495i \(-0.330471\pi\)
−0.999960 + 0.00899079i \(0.997138\pi\)
\(654\) 0.316317 0.547878i 0.0123690 0.0214237i
\(655\) −24.8863 + 43.1044i −0.972390 + 1.68423i
\(656\) −15.3054 26.5097i −0.597574 1.03503i
\(657\) 3.16722 0.123565
\(658\) −1.82867 0.156068i −0.0712890 0.00608415i
\(659\) 17.3155 0.674517 0.337258 0.941412i \(-0.390500\pi\)
0.337258 + 0.941412i \(0.390500\pi\)
\(660\) −4.51558 7.82122i −0.175769 0.304441i
\(661\) −4.60037 + 7.96808i −0.178934 + 0.309922i −0.941516 0.336969i \(-0.890598\pi\)
0.762582 + 0.646892i \(0.223931\pi\)
\(662\) −3.33528 + 5.77687i −0.129629 + 0.224524i
\(663\) 0 0
\(664\) −5.53945 −0.214972
\(665\) −18.5325 1.58165i −0.718659 0.0613338i
\(666\) 4.09901 0.158833
\(667\) −1.43663 2.48832i −0.0556266 0.0963482i
\(668\) −11.8472 + 20.5199i −0.458382 + 0.793940i
\(669\) −2.91920 + 5.05620i −0.112863 + 0.195484i
\(670\) 4.87245 + 8.43933i 0.188239 + 0.326040i
\(671\) −33.9984 −1.31249
\(672\) 0.899372 1.29027i 0.0346940 0.0497733i
\(673\) 17.3609 0.669212 0.334606 0.942358i \(-0.391397\pi\)
0.334606 + 0.942358i \(0.391397\pi\)
\(674\) −1.44328 2.49983i −0.0555930 0.0962898i
\(675\) −8.06403 + 13.9673i −0.310385 + 0.537602i
\(676\) 0 0
\(677\) −24.9913 43.2861i −0.960492 1.66362i −0.721267 0.692657i \(-0.756440\pi\)
−0.239225 0.970964i \(-0.576893\pi\)
\(678\) 0.0839242 0.00322309
\(679\) −9.89974 21.1126i −0.379917 0.810229i
\(680\) −6.95425 −0.266683
\(681\) 1.19535 + 2.07041i 0.0458059 + 0.0793382i
\(682\) −2.47101 + 4.27992i −0.0946200 + 0.163887i
\(683\) 16.8077 29.1117i 0.643128 1.11393i −0.341603 0.939844i \(-0.610970\pi\)
0.984731 0.174086i \(-0.0556969\pi\)
\(684\) −5.14205 8.90630i −0.196611 0.340541i
\(685\) −36.5189 −1.39532
\(686\) −0.960183 3.49408i −0.0366599 0.133404i
\(687\) 3.97274 0.151570
\(688\) −12.8496 22.2561i −0.489885 0.848506i
\(689\) 0 0
\(690\) −0.173922 + 0.301242i −0.00662111 + 0.0114681i
\(691\) −7.56545 13.1038i −0.287803 0.498490i 0.685482 0.728090i \(-0.259592\pi\)
−0.973285 + 0.229600i \(0.926258\pi\)
\(692\) 38.0764 1.44745
\(693\) −14.8433 31.6555i −0.563851 1.20249i
\(694\) 5.85924 0.222414
\(695\) −7.86502 13.6226i −0.298337 0.516735i
\(696\) −0.166242 + 0.287940i −0.00630139 + 0.0109143i
\(697\) 9.25766 16.0347i 0.350659 0.607359i
\(698\) −1.31866 2.28398i −0.0499119 0.0864500i
\(699\) 2.09280 0.0791570
\(700\) 31.0583 44.5574i 1.17390 1.68411i
\(701\) 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
\(704\) −15.9879 + 27.6919i −0.602567 + 1.04368i
\(705\) 1.81104 + 3.13681i 0.0682077 + 0.118139i
\(706\) −0.0319960 −0.00120419
\(707\) −37.7423 3.22111i −1.41945 0.121142i
\(708\) −2.29654 −0.0863093
\(709\) −15.2276 26.3751i −0.571886 0.990536i −0.996372 0.0851015i \(-0.972879\pi\)
0.424486 0.905434i \(-0.360455\pi\)
\(710\) −3.67348 + 6.36265i −0.137863 + 0.238786i
\(711\) 1.16083 2.01062i 0.0435346 0.0754041i
\(712\) 4.36619 + 7.56246i 0.163630 + 0.283415i
\(713\) −9.75429 −0.365301
\(714\) 0.305696 + 0.0260896i 0.0114404 + 0.000976378i
\(715\) 0 0
\(716\) 14.3641 + 24.8793i 0.536811 + 0.929784i
\(717\) −2.82206 + 4.88795i −0.105392 + 0.182544i
\(718\) 0.872754 1.51165i 0.0325709 0.0564144i
\(719\) 12.2123 + 21.1523i 0.455442 + 0.788848i 0.998713 0.0507089i \(-0.0161481\pi\)
−0.543272 + 0.839557i \(0.682815\pi\)
\(720\) 43.4966 1.62102
\(721\) 11.3351 16.2617i 0.422139 0.605616i
\(722\) −3.09219 −0.115079
\(723\) 2.66257 + 4.61170i 0.0990220 + 0.171511i
\(724\) −9.26547 + 16.0483i −0.344348 + 0.596429i
\(725\) −8.63908 + 14.9633i −0.320848 + 0.555724i
\(726\) 0.236521 + 0.409667i 0.00877813 + 0.0152042i
\(727\) −3.09307 −0.114716 −0.0573578 0.998354i \(-0.518268\pi\)
−0.0573578 + 0.998354i \(0.518268\pi\)
\(728\) 0 0
\(729\) −23.4236 −0.867539
\(730\) −0.415501 0.719670i −0.0153784 0.0266362i
\(731\) 7.77223 13.4619i 0.287466 0.497906i
\(732\) −1.92250 + 3.32987i −0.0710577 + 0.123076i
\(733\) −4.20713 7.28697i −0.155394 0.269150i 0.777808 0.628501i \(-0.216331\pi\)
−0.933202 + 0.359351i \(0.882998\pi\)
\(734\) 7.17182 0.264717
\(735\) −4.57344 + 5.49776i −0.168694 + 0.202788i
\(736\) 3.98203 0.146779
\(737\) 28.5365 + 49.4267i 1.05116 + 1.82066i
\(738\) 2.32826 4.03266i 0.0857044 0.148444i
\(739\) −3.61379 + 6.25927i −0.132936 + 0.230251i −0.924807 0.380437i \(-0.875774\pi\)
0.791871 + 0.610688i \(0.209107\pi\)
\(740\) 27.5564 + 47.7291i 1.01299 + 1.75456i
\(741\) 0 0
\(742\) −0.722966 1.54183i −0.0265409 0.0566024i
\(743\) 53.9092 1.97774 0.988869 0.148791i \(-0.0475383\pi\)
0.988869 + 0.148791i \(0.0475383\pi\)
\(744\) 0.564366 + 0.977510i 0.0206907 + 0.0358373i
\(745\) 29.8180 51.6463i 1.09245 1.89217i
\(746\) −2.65382 + 4.59656i −0.0971634 + 0.168292i
\(747\) 10.4785 + 18.1493i 0.383388 + 0.664047i
\(748\) −20.1678 −0.737406
\(749\) −16.6095 + 23.8285i −0.606897 + 0.870676i
\(750\) 1.09231 0.0398854
\(751\) −14.6221 25.3262i −0.533568 0.924168i −0.999231 0.0392053i \(-0.987517\pi\)
0.465663 0.884962i \(-0.345816\pi\)
\(752\) 6.68628 11.5810i 0.243824 0.422315i
\(753\) 0.338856 0.586916i 0.0123486 0.0213884i
\(754\) 0 0
\(755\) 20.2193 0.735857
\(756\) −7.97018 0.680214i −0.289873 0.0247391i
\(757\) −22.0597 −0.801773 −0.400887 0.916128i \(-0.631298\pi\)
−0.400887 + 0.916128i \(0.631298\pi\)
\(758\) −1.55491 2.69318i −0.0564768 0.0978206i
\(759\) −1.01861 + 1.76429i −0.0369733 + 0.0640397i
\(760\) −2.72463 + 4.71920i −0.0988328 + 0.171183i
\(761\) 8.90805 + 15.4292i 0.322917 + 0.559308i 0.981089 0.193560i \(-0.0620033\pi\)
−0.658172 + 0.752868i \(0.728670\pi\)
\(762\) 0.228374 0.00827313
\(763\) 32.8105 + 2.80020i 1.18782 + 0.101374i
\(764\) −24.6269 −0.890971
\(765\) 13.1547 + 22.7847i 0.475611 + 0.823782i
\(766\) 0.112579 0.194993i 0.00406766 0.00704539i
\(767\) 0 0
\(768\) 1.69182 + 2.93033i 0.0610485 + 0.105739i
\(769\) 11.3069 0.407738 0.203869 0.978998i \(-0.434648\pi\)
0.203869 + 0.978998i \(0.434648\pi\)
\(770\) −5.24564 + 7.52559i −0.189040 + 0.271203i
\(771\) 2.33725 0.0841741
\(772\) 9.18927 + 15.9163i 0.330729 + 0.572840i
\(773\) −0.964104 + 1.66988i −0.0346764 + 0.0600613i −0.882843 0.469669i \(-0.844373\pi\)
0.848166 + 0.529730i \(0.177707\pi\)
\(774\) 1.95468 3.38561i 0.0702595 0.121693i
\(775\) 29.3284 + 50.7982i 1.05351 + 1.82472i
\(776\) −6.83168 −0.245243
\(777\) −2.08468 4.44588i −0.0747875 0.159495i
\(778\) −2.80043 −0.100400
\(779\) −7.25418 12.5646i −0.259908 0