Properties

Label 91.2.f.c.22.1
Level $91$
Weight $2$
Character 91.22
Analytic conductor $0.727$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - x^{7} + 7 x^{6} + 38 x^{4} - 16 x^{3} + 15 x^{2} + 3 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 22.1
Root \(-1.11000 + 1.92258i\) of defining polynomial
Character \(\chi\) \(=\) 91.22
Dual form 91.2.f.c.29.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.11000 + 1.92258i) q^{2} +(-0.274776 + 0.475925i) q^{3} +(-1.46422 - 2.53610i) q^{4} -4.22001 q^{5} +(-0.610004 - 1.05656i) q^{6} +(0.500000 + 0.866025i) q^{7} +2.06113 q^{8} +(1.34900 + 2.33653i) q^{9} +O(q^{10})\) \(q+(-1.11000 + 1.92258i) q^{2} +(-0.274776 + 0.475925i) q^{3} +(-1.46422 - 2.53610i) q^{4} -4.22001 q^{5} +(-0.610004 - 1.05656i) q^{6} +(0.500000 + 0.866025i) q^{7} +2.06113 q^{8} +(1.34900 + 2.33653i) q^{9} +(4.68423 - 8.11332i) q^{10} +(0.274776 - 0.475925i) q^{11} +1.60932 q^{12} +(-2.95900 + 2.06017i) q^{13} -2.22001 q^{14} +(1.15956 - 2.00841i) q^{15} +(0.640570 - 1.10950i) q^{16} +(1.18944 + 2.06017i) q^{17} -5.98957 q^{18} +(1.80534 + 3.12694i) q^{19} +(6.17901 + 10.7024i) q^{20} -0.549551 q^{21} +(0.610004 + 1.05656i) q^{22} +(-2.90945 + 5.03931i) q^{23} +(-0.566349 + 0.980945i) q^{24} +12.8085 q^{25} +(-0.676353 - 7.97573i) q^{26} -3.13134 q^{27} +(1.46422 - 2.53610i) q^{28} +(1.79945 - 3.11673i) q^{29} +(2.57422 + 4.45868i) q^{30} -5.14844 q^{31} +(3.48320 + 6.03308i) q^{32} +(0.151003 + 0.261545i) q^{33} -5.28114 q^{34} +(-2.11000 - 3.65463i) q^{35} +(3.95045 - 6.84238i) q^{36} +(0.164772 - 0.285393i) q^{37} -8.01574 q^{38} +(-0.167428 - 1.97435i) q^{39} -8.69799 q^{40} +(3.14579 - 5.44866i) q^{41} +(0.610004 - 1.05656i) q^{42} +(-1.61000 - 2.78861i) q^{43} -1.60932 q^{44} +(-5.69278 - 9.86018i) q^{45} +(-6.45900 - 11.1873i) q^{46} +8.20957 q^{47} +(0.352026 + 0.609727i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-14.2174 + 24.6253i) q^{50} -1.30732 q^{51} +(9.55742 + 4.48778i) q^{52} +2.65866 q^{53} +(3.47580 - 6.02026i) q^{54} +(-1.15956 + 2.00841i) q^{55} +(1.03057 + 1.78499i) q^{56} -1.98426 q^{57} +(3.99478 + 6.91917i) q^{58} +(0.903765 + 1.56537i) q^{59} -6.79136 q^{60} +(-0.304662 - 0.527691i) q^{61} +(5.71479 - 9.89831i) q^{62} +(-1.34900 + 2.33653i) q^{63} -12.9032 q^{64} +(12.4870 - 8.69395i) q^{65} -0.670457 q^{66} +(-5.18490 + 8.98052i) q^{67} +(3.48320 - 6.03308i) q^{68} +(-1.59889 - 2.76936i) q^{69} +9.36845 q^{70} +(5.59889 + 9.69756i) q^{71} +(2.78046 + 4.81590i) q^{72} +4.90621 q^{73} +(0.365794 + 0.633574i) q^{74} +(-3.51945 + 6.09587i) q^{75} +(5.28682 - 9.15705i) q^{76} +0.549551 q^{77} +(3.98169 + 1.86964i) q^{78} -14.0171 q^{79} +(-2.70321 + 4.68210i) q^{80} +(-3.18657 + 5.51931i) q^{81} +(6.98367 + 12.0961i) q^{82} -5.73159 q^{83} +(0.804662 + 1.39372i) q^{84} +(-5.01945 - 8.69395i) q^{85} +7.14844 q^{86} +(0.988887 + 1.71280i) q^{87} +(0.566349 - 0.980945i) q^{88} +(3.73378 - 6.46709i) q^{89} +25.2760 q^{90} +(-3.26366 - 1.53248i) q^{91} +17.0403 q^{92} +(1.41467 - 2.45027i) q^{93} +(-9.11266 + 15.7836i) q^{94} +(-7.61856 - 13.1957i) q^{95} -3.82840 q^{96} +(3.42035 + 5.92422i) q^{97} +(-1.11000 - 1.92258i) q^{98} +1.48269 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + q^{2} - q^{3} - 5q^{4} - 14q^{5} + 5q^{6} + 4q^{7} - 12q^{8} - 7q^{9} + O(q^{10}) \) \( 8q + q^{2} - q^{3} - 5q^{4} - 14q^{5} + 5q^{6} + 4q^{7} - 12q^{8} - 7q^{9} + 11q^{10} + q^{11} + 24q^{12} + 4q^{13} + 2q^{14} - 3q^{15} - 19q^{16} + 4q^{17} - 6q^{18} - q^{19} + 2q^{20} - 2q^{21} - 5q^{22} + 2q^{23} + 3q^{24} + 10q^{25} + 12q^{26} - 52q^{27} + 5q^{28} - q^{29} + 4q^{30} - 8q^{31} + 33q^{32} + 19q^{33} + 6q^{34} - 7q^{35} + 34q^{36} + 10q^{37} - 46q^{38} + 20q^{39} - 34q^{40} + 22q^{41} - 5q^{42} - 3q^{43} - 24q^{44} + 11q^{45} - 24q^{46} + 4q^{47} - 11q^{48} - 4q^{49} - 43q^{50} + 14q^{51} + 65q^{52} + 4q^{53} - 5q^{54} + 3q^{55} - 6q^{56} - 34q^{57} + 11q^{58} + 8q^{59} - 22q^{60} - 8q^{61} + 5q^{62} + 7q^{63} + 28q^{64} + 7q^{65} + 12q^{66} + 6q^{67} + 33q^{68} + 18q^{69} + 22q^{70} + 14q^{71} - 5q^{72} - 16q^{73} - 20q^{74} + 7q^{75} - 32q^{76} + 2q^{77} - q^{78} - 52q^{79} - 7q^{80} - 24q^{81} + 14q^{82} + 12q^{84} - 5q^{85} + 24q^{86} - 13q^{87} - 3q^{88} + q^{89} + 52q^{90} - 4q^{91} + 24q^{92} + 7q^{93} - 33q^{94} - 21q^{95} - 116q^{96} - 3q^{97} + q^{98} + 46q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.11000 + 1.92258i −0.784891 + 1.35947i 0.144173 + 0.989553i \(0.453948\pi\)
−0.929064 + 0.369919i \(0.879385\pi\)
\(3\) −0.274776 + 0.475925i −0.158642 + 0.274776i −0.934379 0.356280i \(-0.884045\pi\)
0.775737 + 0.631056i \(0.217378\pi\)
\(4\) −1.46422 2.53610i −0.732109 1.26805i
\(5\) −4.22001 −1.88724 −0.943622 0.331024i \(-0.892606\pi\)
−0.943622 + 0.331024i \(0.892606\pi\)
\(6\) −0.610004 1.05656i −0.249033 0.431338i
\(7\) 0.500000 + 0.866025i 0.188982 + 0.327327i
\(8\) 2.06113 0.728720
\(9\) 1.34900 + 2.33653i 0.449666 + 0.778844i
\(10\) 4.68423 8.11332i 1.48128 2.56566i
\(11\) 0.274776 0.475925i 0.0828480 0.143497i −0.821624 0.570030i \(-0.806932\pi\)
0.904472 + 0.426533i \(0.140265\pi\)
\(12\) 1.60932 0.464572
\(13\) −2.95900 + 2.06017i −0.820679 + 0.571389i
\(14\) −2.22001 −0.593322
\(15\) 1.15956 2.00841i 0.299396 0.518569i
\(16\) 0.640570 1.10950i 0.160142 0.277375i
\(17\) 1.18944 + 2.06017i 0.288482 + 0.499665i 0.973448 0.228910i \(-0.0735161\pi\)
−0.684966 + 0.728575i \(0.740183\pi\)
\(18\) −5.98957 −1.41175
\(19\) 1.80534 + 3.12694i 0.414174 + 0.717370i 0.995341 0.0964139i \(-0.0307372\pi\)
−0.581168 + 0.813784i \(0.697404\pi\)
\(20\) 6.17901 + 10.7024i 1.38167 + 2.39312i
\(21\) −0.549551 −0.119922
\(22\) 0.610004 + 1.05656i 0.130053 + 0.225259i
\(23\) −2.90945 + 5.03931i −0.606662 + 1.05077i 0.385124 + 0.922865i \(0.374159\pi\)
−0.991786 + 0.127905i \(0.959175\pi\)
\(24\) −0.566349 + 0.980945i −0.115605 + 0.200235i
\(25\) 12.8085 2.56169
\(26\) −0.676353 7.97573i −0.132644 1.56417i
\(27\) −3.13134 −0.602626
\(28\) 1.46422 2.53610i 0.276711 0.479278i
\(29\) 1.79945 3.11673i 0.334149 0.578762i −0.649172 0.760641i \(-0.724885\pi\)
0.983321 + 0.181879i \(0.0582179\pi\)
\(30\) 2.57422 + 4.45868i 0.469986 + 0.814040i
\(31\) −5.14844 −0.924688 −0.462344 0.886701i \(-0.652991\pi\)
−0.462344 + 0.886701i \(0.652991\pi\)
\(32\) 3.48320 + 6.03308i 0.615749 + 1.06651i
\(33\) 0.151003 + 0.261545i 0.0262863 + 0.0455292i
\(34\) −5.28114 −0.905708
\(35\) −2.11000 3.65463i −0.356656 0.617746i
\(36\) 3.95045 6.84238i 0.658408 1.14040i
\(37\) 0.164772 0.285393i 0.0270883 0.0469183i −0.852163 0.523276i \(-0.824710\pi\)
0.879252 + 0.476357i \(0.158043\pi\)
\(38\) −8.01574 −1.30033
\(39\) −0.167428 1.97435i −0.0268099 0.316149i
\(40\) −8.69799 −1.37527
\(41\) 3.14579 5.44866i 0.491289 0.850938i −0.508660 0.860967i \(-0.669859\pi\)
0.999950 + 0.0100292i \(0.00319244\pi\)
\(42\) 0.610004 1.05656i 0.0941256 0.163030i
\(43\) −1.61000 2.78861i −0.245523 0.425259i 0.716755 0.697325i \(-0.245626\pi\)
−0.962279 + 0.272066i \(0.912293\pi\)
\(44\) −1.60932 −0.242615
\(45\) −5.69278 9.86018i −0.848629 1.46987i
\(46\) −6.45900 11.1873i −0.952328 1.64948i
\(47\) 8.20957 1.19749 0.598745 0.800940i \(-0.295666\pi\)
0.598745 + 0.800940i \(0.295666\pi\)
\(48\) 0.352026 + 0.609727i 0.0508106 + 0.0880065i
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) −14.2174 + 24.6253i −2.01065 + 3.48255i
\(51\) −1.30732 −0.183061
\(52\) 9.55742 + 4.48778i 1.32538 + 0.622343i
\(53\) 2.65866 0.365196 0.182598 0.983188i \(-0.441549\pi\)
0.182598 + 0.983188i \(0.441549\pi\)
\(54\) 3.47580 6.02026i 0.472996 0.819254i
\(55\) −1.15956 + 2.00841i −0.156354 + 0.270814i
\(56\) 1.03057 + 1.78499i 0.137715 + 0.238530i
\(57\) −1.98426 −0.262821
\(58\) 3.99478 + 6.91917i 0.524541 + 0.908531i
\(59\) 0.903765 + 1.56537i 0.117660 + 0.203793i 0.918840 0.394630i \(-0.129127\pi\)
−0.801180 + 0.598424i \(0.795794\pi\)
\(60\) −6.79136 −0.876761
\(61\) −0.304662 0.527691i −0.0390080 0.0675639i 0.845862 0.533401i \(-0.179086\pi\)
−0.884870 + 0.465838i \(0.845753\pi\)
\(62\) 5.71479 9.89831i 0.725779 1.25709i
\(63\) −1.34900 + 2.33653i −0.169958 + 0.294375i
\(64\) −12.9032 −1.61290
\(65\) 12.4870 8.69395i 1.54882 1.07835i
\(66\) −0.670457 −0.0825275
\(67\) −5.18490 + 8.98052i −0.633437 + 1.09714i 0.353407 + 0.935470i \(0.385023\pi\)
−0.986844 + 0.161675i \(0.948310\pi\)
\(68\) 3.48320 6.03308i 0.422400 0.731619i
\(69\) −1.59889 2.76936i −0.192484 0.333392i
\(70\) 9.36845 1.11974
\(71\) 5.59889 + 9.69756i 0.664466 + 1.15089i 0.979430 + 0.201785i \(0.0646743\pi\)
−0.314964 + 0.949104i \(0.601992\pi\)
\(72\) 2.78046 + 4.81590i 0.327680 + 0.567559i
\(73\) 4.90621 0.574228 0.287114 0.957896i \(-0.407304\pi\)
0.287114 + 0.957896i \(0.407304\pi\)
\(74\) 0.365794 + 0.633574i 0.0425227 + 0.0736515i
\(75\) −3.51945 + 6.09587i −0.406391 + 0.703891i
\(76\) 5.28682 9.15705i 0.606440 1.05039i
\(77\) 0.549551 0.0626272
\(78\) 3.98169 + 1.86964i 0.450838 + 0.211695i
\(79\) −14.0171 −1.57705 −0.788524 0.615004i \(-0.789154\pi\)
−0.788524 + 0.615004i \(0.789154\pi\)
\(80\) −2.70321 + 4.68210i −0.302228 + 0.523474i
\(81\) −3.18657 + 5.51931i −0.354064 + 0.613257i
\(82\) 6.98367 + 12.0961i 0.771217 + 1.33579i
\(83\) −5.73159 −0.629124 −0.314562 0.949237i \(-0.601858\pi\)
−0.314562 + 0.949237i \(0.601858\pi\)
\(84\) 0.804662 + 1.39372i 0.0877959 + 0.152067i
\(85\) −5.01945 8.69395i −0.544436 0.942991i
\(86\) 7.14844 0.770836
\(87\) 0.988887 + 1.71280i 0.106020 + 0.183632i
\(88\) 0.566349 0.980945i 0.0603730 0.104569i
\(89\) 3.73378 6.46709i 0.395779 0.685510i −0.597421 0.801928i \(-0.703808\pi\)
0.993200 + 0.116418i \(0.0371411\pi\)
\(90\) 25.2760 2.66433
\(91\) −3.26366 1.53248i −0.342125 0.160648i
\(92\) 17.0403 1.77657
\(93\) 1.41467 2.45027i 0.146694 0.254082i
\(94\) −9.11266 + 15.7836i −0.939899 + 1.62795i
\(95\) −7.61856 13.1957i −0.781647 1.35385i
\(96\) −3.82840 −0.390734
\(97\) 3.42035 + 5.92422i 0.347284 + 0.601514i 0.985766 0.168123i \(-0.0537706\pi\)
−0.638482 + 0.769637i \(0.720437\pi\)
\(98\) −1.11000 1.92258i −0.112127 0.194210i
\(99\) 1.48269 0.149015
\(100\) −18.7544 32.4835i −1.87544 3.24835i
\(101\) −2.87956 + 4.98755i −0.286527 + 0.496280i −0.972978 0.230896i \(-0.925834\pi\)
0.686451 + 0.727176i \(0.259168\pi\)
\(102\) 1.45113 2.51343i 0.143683 0.248866i
\(103\) 0.571776 0.0563388 0.0281694 0.999603i \(-0.491032\pi\)
0.0281694 + 0.999603i \(0.491032\pi\)
\(104\) −6.09889 + 4.24629i −0.598045 + 0.416383i
\(105\) 2.31911 0.226322
\(106\) −2.95113 + 5.11150i −0.286639 + 0.496473i
\(107\) −2.03578 + 3.52608i −0.196807 + 0.340879i −0.947491 0.319782i \(-0.896390\pi\)
0.750685 + 0.660661i \(0.229724\pi\)
\(108\) 4.58496 + 7.94138i 0.441188 + 0.764160i
\(109\) 15.3087 1.46631 0.733153 0.680064i \(-0.238048\pi\)
0.733153 + 0.680064i \(0.238048\pi\)
\(110\) −2.57422 4.45868i −0.245442 0.425119i
\(111\) 0.0905505 + 0.156838i 0.00859467 + 0.0148864i
\(112\) 1.28114 0.121056
\(113\) −6.08846 10.5455i −0.572754 0.992039i −0.996282 0.0861558i \(-0.972542\pi\)
0.423528 0.905883i \(-0.360792\pi\)
\(114\) 2.20253 3.81490i 0.206286 0.357298i
\(115\) 12.2779 21.2659i 1.14492 1.98306i
\(116\) −10.5391 −0.978533
\(117\) −8.80534 4.13463i −0.814054 0.382247i
\(118\) −4.01273 −0.369402
\(119\) −1.18944 + 2.06017i −0.109036 + 0.188856i
\(120\) 2.39000 4.13959i 0.218176 0.377892i
\(121\) 5.34900 + 9.26473i 0.486272 + 0.842249i
\(122\) 1.35271 0.122468
\(123\) 1.72877 + 2.99432i 0.155878 + 0.269989i
\(124\) 7.53844 + 13.0570i 0.676972 + 1.17255i
\(125\) −32.9518 −2.94730
\(126\) −2.99478 5.18712i −0.266797 0.462105i
\(127\) −0.980336 + 1.69799i −0.0869907 + 0.150672i −0.906238 0.422768i \(-0.861058\pi\)
0.819247 + 0.573441i \(0.194392\pi\)
\(128\) 7.35619 12.7413i 0.650201 1.12618i
\(129\) 1.76956 0.155801
\(130\) 2.85421 + 33.6576i 0.250331 + 2.95197i
\(131\) −6.50021 −0.567926 −0.283963 0.958835i \(-0.591649\pi\)
−0.283963 + 0.958835i \(0.591649\pi\)
\(132\) 0.442203 0.765918i 0.0384888 0.0666646i
\(133\) −1.80534 + 3.12694i −0.156543 + 0.271140i
\(134\) −11.5105 19.9368i −0.994358 1.72228i
\(135\) 13.2143 1.13730
\(136\) 2.45160 + 4.24629i 0.210223 + 0.364116i
\(137\) 7.62878 + 13.2134i 0.651770 + 1.12890i 0.982693 + 0.185242i \(0.0593068\pi\)
−0.330923 + 0.943658i \(0.607360\pi\)
\(138\) 7.09910 0.604316
\(139\) 8.74801 + 15.1520i 0.741997 + 1.28518i 0.951585 + 0.307386i \(0.0994544\pi\)
−0.209588 + 0.977790i \(0.567212\pi\)
\(140\) −6.17901 + 10.7024i −0.522222 + 0.904514i
\(141\) −2.25579 + 3.90714i −0.189972 + 0.329041i
\(142\) −24.8592 −2.08613
\(143\) 0.167428 + 1.97435i 0.0140010 + 0.165103i
\(144\) 3.45651 0.288042
\(145\) −7.59367 + 13.1526i −0.630620 + 1.09227i
\(146\) −5.44591 + 9.43260i −0.450707 + 0.780647i
\(147\) −0.274776 0.475925i −0.0226631 0.0392537i
\(148\) −0.965046 −0.0793263
\(149\) −2.27743 3.94463i −0.186574 0.323156i 0.757531 0.652799i \(-0.226405\pi\)
−0.944106 + 0.329642i \(0.893072\pi\)
\(150\) −7.81321 13.5329i −0.637946 1.10496i
\(151\) −6.32912 −0.515057 −0.257528 0.966271i \(-0.582908\pi\)
−0.257528 + 0.966271i \(0.582908\pi\)
\(152\) 3.72105 + 6.44504i 0.301817 + 0.522762i
\(153\) −3.20911 + 5.55833i −0.259441 + 0.449365i
\(154\) −0.610004 + 1.05656i −0.0491555 + 0.0851398i
\(155\) 21.7265 1.74511
\(156\) −4.76199 + 3.31549i −0.381265 + 0.265451i
\(157\) 16.3100 1.30168 0.650841 0.759214i \(-0.274416\pi\)
0.650841 + 0.759214i \(0.274416\pi\)
\(158\) 15.5590 26.9490i 1.23781 2.14395i
\(159\) −0.730536 + 1.26533i −0.0579353 + 0.100347i
\(160\) −14.6991 25.4597i −1.16207 2.01276i
\(161\) −5.81890 −0.458593
\(162\) −7.07422 12.2529i −0.555803 0.962680i
\(163\) −11.7999 20.4381i −0.924241 1.60083i −0.792778 0.609511i \(-0.791366\pi\)
−0.131463 0.991321i \(-0.541967\pi\)
\(164\) −18.4245 −1.43871
\(165\) −0.637235 1.10372i −0.0496087 0.0859247i
\(166\) 6.36209 11.0195i 0.493794 0.855276i
\(167\) 8.91513 15.4415i 0.689874 1.19490i −0.282005 0.959413i \(-0.590999\pi\)
0.971878 0.235483i \(-0.0756673\pi\)
\(168\) −1.13270 −0.0873895
\(169\) 4.51137 12.1921i 0.347028 0.937855i
\(170\) 22.2865 1.70929
\(171\) −4.87080 + 8.43647i −0.372479 + 0.645153i
\(172\) −4.71479 + 8.16626i −0.359499 + 0.622671i
\(173\) 3.78568 + 6.55699i 0.287820 + 0.498518i 0.973289 0.229583i \(-0.0737363\pi\)
−0.685469 + 0.728101i \(0.740403\pi\)
\(174\) −4.39068 −0.332856
\(175\) 6.40423 + 11.0925i 0.484115 + 0.838511i
\(176\) −0.352026 0.609727i −0.0265350 0.0459599i
\(177\) −0.993330 −0.0746632
\(178\) 8.28901 + 14.3570i 0.621288 + 1.07610i
\(179\) 11.4017 19.7483i 0.852201 1.47606i −0.0270166 0.999635i \(-0.508601\pi\)
0.879218 0.476420i \(-0.158066\pi\)
\(180\) −16.6709 + 28.8749i −1.24258 + 2.15221i
\(181\) 13.9294 1.03536 0.517681 0.855574i \(-0.326795\pi\)
0.517681 + 0.855574i \(0.326795\pi\)
\(182\) 6.56900 4.57360i 0.486927 0.339018i
\(183\) 0.334855 0.0247532
\(184\) −5.99676 + 10.3867i −0.442087 + 0.765717i
\(185\) −0.695338 + 1.20436i −0.0511222 + 0.0885463i
\(186\) 3.14057 + 5.43963i 0.230278 + 0.398853i
\(187\) 1.30732 0.0956006
\(188\) −12.0206 20.8203i −0.876692 1.51848i
\(189\) −1.56567 2.71182i −0.113886 0.197256i
\(190\) 33.8265 2.45403
\(191\) 6.33591 + 10.9741i 0.458450 + 0.794059i 0.998879 0.0473305i \(-0.0150714\pi\)
−0.540429 + 0.841390i \(0.681738\pi\)
\(192\) 3.54548 6.14096i 0.255873 0.443185i
\(193\) 2.07746 3.59827i 0.149539 0.259009i −0.781518 0.623882i \(-0.785554\pi\)
0.931057 + 0.364873i \(0.118888\pi\)
\(194\) −15.1864 −1.09032
\(195\) 0.706545 + 8.33177i 0.0505968 + 0.596650i
\(196\) 2.92843 0.209174
\(197\) 3.42510 5.93245i 0.244028 0.422669i −0.717830 0.696219i \(-0.754864\pi\)
0.961858 + 0.273549i \(0.0881977\pi\)
\(198\) −1.64579 + 2.85059i −0.116961 + 0.202582i
\(199\) 0.406794 + 0.704587i 0.0288368 + 0.0499469i 0.880084 0.474819i \(-0.157486\pi\)
−0.851247 + 0.524766i \(0.824153\pi\)
\(200\) 26.3999 1.86676
\(201\) −2.84937 4.93525i −0.200979 0.348106i
\(202\) −6.39265 11.0724i −0.449785 0.779051i
\(203\) 3.59889 0.252593
\(204\) 1.91420 + 3.31549i 0.134021 + 0.232131i
\(205\) −13.2752 + 22.9934i −0.927183 + 1.60593i
\(206\) −0.634674 + 1.09929i −0.0442198 + 0.0765910i
\(207\) −15.6994 −1.09118
\(208\) 0.390315 + 4.60270i 0.0270635 + 0.319140i
\(209\) 1.98426 0.137254
\(210\) −2.57422 + 4.45868i −0.177638 + 0.307678i
\(211\) 6.98670 12.1013i 0.480984 0.833089i −0.518778 0.854909i \(-0.673613\pi\)
0.999762 + 0.0218200i \(0.00694608\pi\)
\(212\) −3.89286 6.74264i −0.267363 0.463086i
\(213\) −6.15375 −0.421648
\(214\) −4.51945 7.82792i −0.308943 0.535106i
\(215\) 6.79423 + 11.7679i 0.463363 + 0.802568i
\(216\) −6.45410 −0.439146
\(217\) −2.57422 4.45868i −0.174750 0.302675i
\(218\) −16.9927 + 29.4322i −1.15089 + 1.99340i
\(219\) −1.34811 + 2.33499i −0.0910966 + 0.157784i
\(220\) 6.79136 0.457874
\(221\) −7.76387 3.64560i −0.522255 0.245229i
\(222\) −0.402045 −0.0269835
\(223\) 6.76700 11.7208i 0.453152 0.784882i −0.545428 0.838158i \(-0.683633\pi\)
0.998580 + 0.0532758i \(0.0169662\pi\)
\(224\) −3.48320 + 6.03308i −0.232731 + 0.403102i
\(225\) 17.2786 + 29.9274i 1.15191 + 1.99516i
\(226\) 27.0328 1.79820
\(227\) 2.68376 + 4.64840i 0.178127 + 0.308525i 0.941239 0.337741i \(-0.109663\pi\)
−0.763112 + 0.646266i \(0.776329\pi\)
\(228\) 2.90538 + 5.03227i 0.192414 + 0.333270i
\(229\) 3.09910 0.204794 0.102397 0.994744i \(-0.467349\pi\)
0.102397 + 0.994744i \(0.467349\pi\)
\(230\) 27.2570 + 47.2106i 1.79728 + 3.11297i
\(231\) −0.151003 + 0.261545i −0.00993528 + 0.0172084i
\(232\) 3.70890 6.42399i 0.243501 0.421756i
\(233\) −20.3712 −1.33456 −0.667280 0.744807i \(-0.732541\pi\)
−0.667280 + 0.744807i \(0.732541\pi\)
\(234\) 17.7231 12.3395i 1.15860 0.806661i
\(235\) −34.6445 −2.25996
\(236\) 2.64662 4.58407i 0.172280 0.298398i
\(237\) 3.85156 6.67109i 0.250186 0.433334i
\(238\) −2.64057 4.57360i −0.171163 0.296463i
\(239\) −1.29157 −0.0835449 −0.0417725 0.999127i \(-0.513300\pi\)
−0.0417725 + 0.999127i \(0.513300\pi\)
\(240\) −1.48555 2.57305i −0.0958920 0.166090i
\(241\) −1.06635 1.84697i −0.0686896 0.118974i 0.829635 0.558306i \(-0.188548\pi\)
−0.898325 + 0.439332i \(0.855215\pi\)
\(242\) −23.7496 −1.52668
\(243\) −6.44819 11.1686i −0.413652 0.716466i
\(244\) −0.892184 + 1.54531i −0.0571162 + 0.0989282i
\(245\) 2.11000 3.65463i 0.134803 0.233486i
\(246\) −7.67577 −0.489389
\(247\) −11.7841 5.53331i −0.749801 0.352076i
\(248\) −10.6116 −0.673839
\(249\) 1.57490 2.72781i 0.0998053 0.172868i
\(250\) 36.5766 63.3525i 2.31331 4.00677i
\(251\) 15.3856 + 26.6486i 0.971128 + 1.68204i 0.692164 + 0.721741i \(0.256658\pi\)
0.278964 + 0.960302i \(0.410009\pi\)
\(252\) 7.90090 0.497710
\(253\) 1.59889 + 2.76936i 0.100521 + 0.174108i
\(254\) −2.17635 3.76955i −0.136557 0.236523i
\(255\) 5.51689 0.345481
\(256\) 3.42761 + 5.93679i 0.214225 + 0.371049i
\(257\) 0.736805 1.27618i 0.0459607 0.0796062i −0.842130 0.539275i \(-0.818698\pi\)
0.888091 + 0.459669i \(0.152032\pi\)
\(258\) −1.96422 + 3.40212i −0.122287 + 0.211807i
\(259\) 0.329543 0.0204768
\(260\) −40.3324 18.9385i −2.50131 1.17451i
\(261\) 9.70979 0.601021
\(262\) 7.21526 12.4972i 0.445760 0.772079i
\(263\) −3.33847 + 5.78240i −0.205859 + 0.356558i −0.950406 0.311012i \(-0.899332\pi\)
0.744547 + 0.667570i \(0.232665\pi\)
\(264\) 0.311238 + 0.539079i 0.0191553 + 0.0331780i
\(265\) −11.2196 −0.689214
\(266\) −4.00787 6.94184i −0.245738 0.425631i
\(267\) 2.05190 + 3.55400i 0.125574 + 0.217501i
\(268\) 30.3673 1.85498
\(269\) −3.78786 6.56077i −0.230950 0.400017i 0.727138 0.686492i \(-0.240850\pi\)
−0.958088 + 0.286474i \(0.907517\pi\)
\(270\) −14.6679 + 25.4055i −0.892660 + 1.54613i
\(271\) −10.2840 + 17.8124i −0.624709 + 1.08203i 0.363888 + 0.931443i \(0.381449\pi\)
−0.988597 + 0.150585i \(0.951884\pi\)
\(272\) 3.04768 0.184793
\(273\) 1.62612 1.13217i 0.0984174 0.0685221i
\(274\) −33.8719 −2.04628
\(275\) 3.51945 6.09587i 0.212231 0.367595i
\(276\) −4.68225 + 8.10989i −0.281838 + 0.488158i
\(277\) −2.85271 4.94103i −0.171402 0.296878i 0.767508 0.641039i \(-0.221497\pi\)
−0.938910 + 0.344162i \(0.888163\pi\)
\(278\) −38.8413 −2.32955
\(279\) −6.94523 12.0295i −0.415800 0.720187i
\(280\) −4.34900 7.53268i −0.259902 0.450164i
\(281\) −6.37315 −0.380190 −0.190095 0.981766i \(-0.560880\pi\)
−0.190095 + 0.981766i \(0.560880\pi\)
\(282\) −5.00787 8.67389i −0.298214 0.516523i
\(283\) −13.5097 + 23.3995i −0.803068 + 1.39096i 0.114519 + 0.993421i \(0.463467\pi\)
−0.917587 + 0.397534i \(0.869866\pi\)
\(284\) 16.3960 28.3987i 0.972923 1.68515i
\(285\) 8.37357 0.496008
\(286\) −3.98169 1.86964i −0.235443 0.110554i
\(287\) 6.29157 0.371380
\(288\) −9.39766 + 16.2772i −0.553762 + 0.959144i
\(289\) 5.67046 9.82152i 0.333556 0.577736i
\(290\) −16.8580 29.1989i −0.989937 1.71462i
\(291\) −3.75932 −0.220375
\(292\) −7.18376 12.4426i −0.420398 0.728150i
\(293\) 2.43736 + 4.22163i 0.142392 + 0.246630i 0.928397 0.371590i \(-0.121187\pi\)
−0.786005 + 0.618220i \(0.787854\pi\)
\(294\) 1.22001 0.0711523
\(295\) −3.81389 6.60586i −0.222053 0.384608i
\(296\) 0.339616 0.588232i 0.0197398 0.0341903i
\(297\) −0.860415 + 1.49028i −0.0499264 + 0.0864750i
\(298\) 10.1118 0.585763
\(299\) −1.77280 20.9053i −0.102524 1.20899i
\(300\) 20.6130 1.19009
\(301\) 1.61000 2.78861i 0.0927991 0.160733i
\(302\) 7.02535 12.1683i 0.404263 0.700205i
\(303\) −1.58247 2.74091i −0.0909104 0.157461i
\(304\) 4.62579 0.265307
\(305\) 1.28568 + 2.22686i 0.0736177 + 0.127510i
\(306\) −7.12424 12.3395i −0.407266 0.705405i
\(307\) 16.1760 0.923212 0.461606 0.887085i \(-0.347273\pi\)
0.461606 + 0.887085i \(0.347273\pi\)
\(308\) −0.804662 1.39372i −0.0458499 0.0794143i
\(309\) −0.157110 + 0.272123i −0.00893769 + 0.0154805i
\(310\) −24.1165 + 41.7709i −1.36972 + 2.37243i
\(311\) −1.30806 −0.0741735 −0.0370868 0.999312i \(-0.511808\pi\)
−0.0370868 + 0.999312i \(0.511808\pi\)
\(312\) −0.345090 4.06939i −0.0195369 0.230384i
\(313\) 13.1978 0.745983 0.372991 0.927835i \(-0.378332\pi\)
0.372991 + 0.927835i \(0.378332\pi\)
\(314\) −18.1042 + 31.3574i −1.02168 + 1.76960i
\(315\) 5.69278 9.86018i 0.320752 0.555558i
\(316\) 20.5241 + 35.5488i 1.15457 + 1.99977i
\(317\) −8.07552 −0.453566 −0.226783 0.973945i \(-0.572821\pi\)
−0.226783 + 0.973945i \(0.572821\pi\)
\(318\) −1.62180 2.80903i −0.0909458 0.157523i
\(319\) −0.988887 1.71280i −0.0553671 0.0958986i
\(320\) 54.4516 3.04394
\(321\) −1.11877 1.93776i −0.0624435 0.108155i
\(322\) 6.45900 11.1873i 0.359946 0.623445i
\(323\) −4.29470 + 7.43863i −0.238963 + 0.413897i
\(324\) 18.6634 1.03685
\(325\) −37.9003 + 26.3877i −2.10233 + 1.46372i
\(326\) 52.3918 2.90171
\(327\) −4.20645 + 7.28579i −0.232617 + 0.402905i
\(328\) 6.48388 11.2304i 0.358012 0.620096i
\(329\) 4.10479 + 7.10970i 0.226304 + 0.391970i
\(330\) 2.82933 0.155750
\(331\) 7.47256 + 12.9429i 0.410729 + 0.711403i 0.994970 0.100177i \(-0.0319409\pi\)
−0.584241 + 0.811580i \(0.698608\pi\)
\(332\) 8.39229 + 14.5359i 0.460587 + 0.797760i
\(333\) 0.889106 0.0487227
\(334\) 19.7917 + 34.2802i 1.08295 + 1.87573i
\(335\) 21.8803 37.8979i 1.19545 2.07058i
\(336\) −0.352026 + 0.609727i −0.0192046 + 0.0332633i
\(337\) −17.1695 −0.935282 −0.467641 0.883918i \(-0.654896\pi\)
−0.467641 + 0.883918i \(0.654896\pi\)
\(338\) 18.4327 + 22.2068i 1.00261 + 1.20789i
\(339\) 6.69184 0.363451
\(340\) −14.6991 + 25.4597i −0.797173 + 1.38074i
\(341\) −1.41467 + 2.45027i −0.0766085 + 0.132690i
\(342\) −10.8132 18.7290i −0.584712 1.01275i
\(343\) −1.00000 −0.0539949
\(344\) −3.31843 5.74769i −0.178918 0.309895i
\(345\) 6.74733 + 11.6867i 0.363264 + 0.629192i
\(346\) −16.8085 −0.903629
\(347\) 1.96922 + 3.41079i 0.105713 + 0.183101i 0.914029 0.405648i \(-0.132954\pi\)
−0.808316 + 0.588749i \(0.799621\pi\)
\(348\) 2.89589 5.01583i 0.155236 0.268877i
\(349\) −8.58883 + 14.8763i −0.459750 + 0.796310i −0.998947 0.0458695i \(-0.985394\pi\)
0.539198 + 0.842179i \(0.318728\pi\)
\(350\) −28.4349 −1.51991
\(351\) 9.26563 6.45110i 0.494563 0.344334i
\(352\) 3.82840 0.204054
\(353\) 9.09821 15.7586i 0.484249 0.838744i −0.515587 0.856837i \(-0.672426\pi\)
0.999836 + 0.0180932i \(0.00575957\pi\)
\(354\) 1.10260 1.90976i 0.0586025 0.101503i
\(355\) −23.6274 40.9238i −1.25401 2.17201i
\(356\) −21.8682 −1.15901
\(357\) −0.653659 1.13217i −0.0345953 0.0599208i
\(358\) 25.3118 + 43.8413i 1.33777 + 2.31709i
\(359\) 16.3126 0.860948 0.430474 0.902603i \(-0.358346\pi\)
0.430474 + 0.902603i \(0.358346\pi\)
\(360\) −11.7336 20.3231i −0.618413 1.07112i
\(361\) 2.98148 5.16408i 0.156920 0.271794i
\(362\) −15.4617 + 26.7804i −0.812647 + 1.40755i
\(363\) −5.87909 −0.308572
\(364\) 0.892184 + 10.5209i 0.0467631 + 0.551443i
\(365\) −20.7042 −1.08371
\(366\) −0.371690 + 0.643787i −0.0194286 + 0.0336513i
\(367\) 18.0982 31.3469i 0.944716 1.63630i 0.188398 0.982093i \(-0.439671\pi\)
0.756319 0.654203i \(-0.226996\pi\)
\(368\) 3.72741 + 6.45607i 0.194305 + 0.336546i
\(369\) 16.9746 0.883664
\(370\) −1.54366 2.67369i −0.0802508 0.138998i
\(371\) 1.32933 + 2.30247i 0.0690155 + 0.119538i
\(372\) −8.28551 −0.429584
\(373\) −4.89892 8.48518i −0.253657 0.439346i 0.710873 0.703320i \(-0.248300\pi\)
−0.964530 + 0.263974i \(0.914967\pi\)
\(374\) −1.45113 + 2.51343i −0.0750361 + 0.129966i
\(375\) 9.05435 15.6826i 0.467564 0.809845i
\(376\) 16.9210 0.872635
\(377\) 1.09645 + 12.9296i 0.0564699 + 0.665907i
\(378\) 6.95160 0.357552
\(379\) −6.53275 + 11.3151i −0.335565 + 0.581216i −0.983593 0.180401i \(-0.942261\pi\)
0.648028 + 0.761616i \(0.275594\pi\)
\(380\) −22.3104 + 38.6428i −1.14450 + 1.98233i
\(381\) −0.538745 0.933133i −0.0276007 0.0478058i
\(382\) −28.1315 −1.43933
\(383\) −13.8965 24.0694i −0.710076 1.22989i −0.964828 0.262881i \(-0.915327\pi\)
0.254753 0.967006i \(-0.418006\pi\)
\(384\) 4.04260 + 7.00199i 0.206298 + 0.357319i
\(385\) −2.31911 −0.118193
\(386\) 4.61198 + 7.98818i 0.234744 + 0.406588i
\(387\) 4.34378 7.52365i 0.220807 0.382449i
\(388\) 10.0163 17.3487i 0.508499 0.880747i
\(389\) 13.7047 0.694854 0.347427 0.937707i \(-0.387055\pi\)
0.347427 + 0.937707i \(0.387055\pi\)
\(390\) −16.8028 7.88990i −0.850842 0.399521i
\(391\) −13.8425 −0.700044
\(392\) −1.03057 + 1.78499i −0.0520514 + 0.0901557i
\(393\) 1.78610 3.09361i 0.0900968 0.156052i
\(394\) 7.60375 + 13.1701i 0.383071 + 0.663499i
\(395\) 59.1523 2.97627
\(396\) −2.17097 3.76024i −0.109096 0.188959i
\(397\) −3.95597 6.85194i −0.198545 0.343889i 0.749512 0.661991i \(-0.230288\pi\)
−0.948057 + 0.318101i \(0.896955\pi\)
\(398\) −1.80617 −0.0905351
\(399\) −0.992128 1.71842i −0.0496685 0.0860284i
\(400\) 8.20472 14.2110i 0.410236 0.710549i
\(401\) 8.27212 14.3277i 0.413090 0.715493i −0.582136 0.813092i \(-0.697783\pi\)
0.995226 + 0.0975987i \(0.0311162\pi\)
\(402\) 12.6512 0.630987
\(403\) 15.2342 10.6067i 0.758872 0.528357i
\(404\) 16.8652 0.839076
\(405\) 13.4474 23.2915i 0.668205 1.15737i
\(406\) −3.99478 + 6.91917i −0.198258 + 0.343393i
\(407\) −0.0905505 0.156838i −0.00448842 0.00777417i
\(408\) −2.69456 −0.133400
\(409\) −12.8909 22.3278i −0.637416 1.10404i −0.985998 0.166758i \(-0.946670\pi\)
0.348582 0.937278i \(-0.386663\pi\)
\(410\) −29.4711 51.0455i −1.45548 2.52096i
\(411\) −8.38481 −0.413592
\(412\) −0.837205 1.45008i −0.0412461 0.0714404i
\(413\) −0.903765 + 1.56537i −0.0444713 + 0.0770266i
\(414\) 17.4263 30.1833i 0.856458 1.48343i
\(415\) 24.1873 1.18731
\(416\) −22.7360 10.6759i −1.11472 0.523429i
\(417\) −9.61496 −0.470847
\(418\) −2.20253 + 3.81490i −0.107729 + 0.186593i
\(419\) −11.8436 + 20.5137i −0.578596 + 1.00216i 0.417044 + 0.908886i \(0.363066\pi\)
−0.995641 + 0.0932720i \(0.970267\pi\)
\(420\) −3.39568 5.88149i −0.165692 0.286987i
\(421\) −20.8246 −1.01493 −0.507465 0.861672i \(-0.669417\pi\)
−0.507465 + 0.861672i \(0.669417\pi\)
\(422\) 15.5105 + 26.8650i 0.755041 + 1.30777i
\(423\) 11.0747 + 19.1819i 0.538470 + 0.932657i
\(424\) 5.47986 0.266125
\(425\) 15.2349 + 26.3877i 0.739002 + 1.27999i
\(426\) 6.83069 11.8311i 0.330948 0.573219i
\(427\) 0.304662 0.527691i 0.0147436 0.0255367i
\(428\) 11.9233 0.576335
\(429\) −0.985647 0.462820i −0.0475875 0.0223451i
\(430\) −30.1665 −1.45476
\(431\) −9.97521 + 17.2776i −0.480489 + 0.832232i −0.999749 0.0223845i \(-0.992874\pi\)
0.519260 + 0.854616i \(0.326208\pi\)
\(432\) −2.00584 + 3.47422i −0.0965061 + 0.167153i
\(433\) −0.00834083 0.0144467i −0.000400835 0.000694266i 0.865825 0.500347i \(-0.166794\pi\)
−0.866226 + 0.499653i \(0.833461\pi\)
\(434\) 11.4296 0.548638
\(435\) −4.17311 7.22804i −0.200085 0.346558i
\(436\) −22.4152 38.8243i −1.07349 1.85935i
\(437\) −21.0102 −1.00505
\(438\) −2.99281 5.18369i −0.143002 0.247686i
\(439\) −6.74801 + 11.6879i −0.322065 + 0.557833i −0.980914 0.194442i \(-0.937710\pi\)
0.658849 + 0.752275i \(0.271044\pi\)
\(440\) −2.39000 + 4.13959i −0.113939 + 0.197347i
\(441\) −2.69799 −0.128476
\(442\) 15.6269 10.8801i 0.743296 0.517512i
\(443\) −15.0110 −0.713196 −0.356598 0.934258i \(-0.616063\pi\)
−0.356598 + 0.934258i \(0.616063\pi\)
\(444\) 0.265171 0.459290i 0.0125845 0.0217969i
\(445\) −15.7566 + 27.2912i −0.746933 + 1.29373i
\(446\) 15.0228 + 26.0202i 0.711350 + 1.23209i
\(447\) 2.50313 0.118394
\(448\) −6.45160 11.1745i −0.304809 0.527945i
\(449\) 11.8918 + 20.5972i 0.561210 + 0.972044i 0.997391 + 0.0721852i \(0.0229973\pi\)
−0.436181 + 0.899859i \(0.643669\pi\)
\(450\) −76.7172 −3.61648
\(451\) −1.72877 2.99432i −0.0814046 0.140997i
\(452\) −17.8297 + 30.8819i −0.838636 + 1.45256i
\(453\) 1.73909 3.01219i 0.0817095 0.141525i
\(454\) −11.9159 −0.559242
\(455\) 13.7727 + 6.46709i 0.645673 + 0.303182i
\(456\) −4.08981 −0.191523
\(457\) −9.06567 + 15.7022i −0.424074 + 0.734518i −0.996333 0.0855548i \(-0.972734\pi\)
0.572259 + 0.820073i \(0.306067\pi\)
\(458\) −3.44002 + 5.95828i −0.160741 + 0.278412i
\(459\) −3.72455 6.45110i −0.173847 0.301112i
\(460\) −71.9101 −3.35282
\(461\) 3.03980 + 5.26508i 0.141577 + 0.245219i 0.928091 0.372354i \(-0.121449\pi\)
−0.786513 + 0.617573i \(0.788116\pi\)
\(462\) −0.335228 0.580633i −0.0155962 0.0270135i
\(463\) 5.19289 0.241334 0.120667 0.992693i \(-0.461497\pi\)
0.120667 + 0.992693i \(0.461497\pi\)
\(464\) −2.30534 3.99297i −0.107023 0.185369i
\(465\) −5.96990 + 10.3402i −0.276848 + 0.479514i
\(466\) 22.6121 39.1653i 1.04748 1.81430i
\(467\) −8.69968 −0.402573 −0.201287 0.979532i \(-0.564512\pi\)
−0.201287 + 0.979532i \(0.564512\pi\)
\(468\) 2.40711 + 28.3852i 0.111268 + 1.31211i
\(469\) −10.3698 −0.478833
\(470\) 38.4555 66.6069i 1.77382 3.07235i
\(471\) −4.48160 + 7.76236i −0.206501 + 0.357671i
\(472\) 1.86278 + 3.22643i 0.0857413 + 0.148508i
\(473\) −1.76956 −0.0813644
\(474\) 8.55049 + 14.8099i 0.392737 + 0.680240i
\(475\) 23.1237 + 40.0513i 1.06099 + 1.83768i
\(476\) 6.96640 0.319305
\(477\) 3.58653 + 6.21205i 0.164216 + 0.284430i
\(478\) 1.43365 2.48316i 0.0655737 0.113577i
\(479\) −12.1094 + 20.9741i −0.553294 + 0.958332i 0.444741 + 0.895659i \(0.353296\pi\)
−0.998034 + 0.0626730i \(0.980037\pi\)
\(480\) 16.1559 0.737411
\(481\) 0.100399 + 1.18394i 0.00457782 + 0.0539828i
\(482\) 4.73461 0.215655
\(483\) 1.59889 2.76936i 0.0727521 0.126010i
\(484\) 15.6642 27.1312i 0.712009 1.23323i
\(485\) −14.4339 25.0003i −0.655410 1.13520i
\(486\) 28.6301 1.29869
\(487\) −0.886967 1.53627i −0.0401923 0.0696151i 0.845229 0.534404i \(-0.179464\pi\)
−0.885422 + 0.464788i \(0.846130\pi\)
\(488\) −0.627949 1.08764i −0.0284259 0.0492351i
\(489\) 12.9693 0.586493
\(490\) 4.68423 + 8.11332i 0.211612 + 0.366522i
\(491\) 3.34483 5.79342i 0.150950 0.261453i −0.780627 0.624997i \(-0.785100\pi\)
0.931577 + 0.363544i \(0.118433\pi\)
\(492\) 5.06259 8.76867i 0.228239 0.395322i
\(493\) 8.56134 0.385584
\(494\) 23.7186 16.5138i 1.06715 0.742992i
\(495\) −6.25694 −0.281229
\(496\) −3.29794 + 5.71220i −0.148082 + 0.256485i
\(497\) −5.59889 + 9.69756i −0.251145 + 0.434995i
\(498\) 3.49629 + 6.05575i 0.156673 + 0.271365i
\(499\) 24.6387 1.10298 0.551491 0.834181i \(-0.314059\pi\)
0.551491 + 0.834181i \(0.314059\pi\)
\(500\) 48.2486 + 83.5690i 2.15774 + 3.73732i
\(501\) 4.89932 + 8.48588i 0.218886 + 0.379121i
\(502\) −68.3121 −3.04892
\(503\) −16.5726 28.7046i −0.738936 1.27987i −0.952975 0.303049i \(-0.901995\pi\)
0.214039 0.976825i \(-0.431338\pi\)
\(504\) −2.78046 + 4.81590i −0.123852 + 0.214517i
\(505\) 12.1518 21.0475i 0.540747 0.936601i
\(506\) −7.09910 −0.315594
\(507\) 4.56292 + 5.49717i 0.202646 + 0.244138i
\(508\) 5.74170 0.254747
\(509\) 13.8290 23.9526i 0.612961 1.06168i −0.377778 0.925896i \(-0.623312\pi\)
0.990739 0.135783i \(-0.0433549\pi\)
\(510\) −6.12377 + 10.6067i −0.271165 + 0.469672i
\(511\) 2.45310 + 4.24890i 0.108519 + 0.187960i
\(512\) 14.2061 0.627828
\(513\) −5.65314 9.79152i −0.249592 0.432306i
\(514\) 1.63571 + 2.83314i 0.0721482 + 0.124964i
\(515\) −2.41290 −0.106325
\(516\) −2.59102 4.48778i −0.114063 0.197563i
\(517\) 2.25579 3.90714i 0.0992096 0.171836i
\(518\) −0.365794 + 0.633574i −0.0160721 + 0.0278377i
\(519\) −4.16085 −0.182641
\(520\) 25.7374 17.9194i 1.12866 0.785817i
\(521\) 1.42217 0.0623062 0.0311531 0.999515i \(-0.490082\pi\)
0.0311531 + 0.999515i \(0.490082\pi\)
\(522\) −10.7779 + 18.6679i −0.471736 + 0.817070i
\(523\) 1.68089 2.91139i 0.0735002 0.127306i −0.826933 0.562301i \(-0.809916\pi\)
0.900433 + 0.434995i \(0.143250\pi\)
\(524\) 9.51772 + 16.4852i 0.415784 + 0.720158i
\(525\) −7.03891 −0.307203
\(526\) −7.41143 12.8370i −0.323154 0.559718i
\(527\) −6.12377 10.6067i −0.266756 0.462034i
\(528\) 0.386913 0.0168382
\(529\) −5.42979 9.40468i −0.236078 0.408899i
\(530\) 12.4538 21.5706i 0.540958 0.936966i
\(531\) −2.43835 + 4.22335i −0.105815 + 0.183278i
\(532\) 10.5736 0.458426
\(533\) 1.91681 + 22.6035i 0.0830260 + 0.979065i
\(534\) −9.11047 −0.394249
\(535\) 8.59102 14.8801i 0.371422 0.643322i
\(536\) −10.6868 + 18.5100i −0.461598 + 0.799512i
\(537\) 6.26580 + 10.8527i 0.270389 + 0.468328i
\(538\) 16.8182 0.725083
\(539\) 0.274776 + 0.475925i 0.0118354 + 0.0204996i
\(540\) −19.3486 33.5127i −0.832630 1.44216i
\(541\) 7.76289 0.333753 0.166876 0.985978i \(-0.446632\pi\)
0.166876 + 0.985978i \(0.446632\pi\)
\(542\) −22.8306 39.5437i −0.980657 1.69855i
\(543\) −3.82745 + 6.62934i −0.164252 + 0.284492i
\(544\) −8.28613 + 14.3520i −0.355265 + 0.615337i
\(545\) −64.6027 −2.76728
\(546\) 0.371690 + 4.38307i 0.0159069 + 0.187578i
\(547\) −6.19247 −0.264771 −0.132385 0.991198i \(-0.542264\pi\)
−0.132385 + 0.991198i \(0.542264\pi\)
\(548\) 22.3404 38.6947i 0.954334 1.65295i
\(549\) 0.821977 1.42371i 0.0350811 0.0607623i
\(550\) 7.81321 + 13.5329i 0.333157 + 0.577044i
\(551\) 12.9945 0.553582
\(552\) −3.29553 5.70802i −0.140267 0.242949i
\(553\) −7.00855 12.1392i −0.298034 0.516210i
\(554\) 12.6661 0.538129
\(555\) −0.382124 0.661858i −0.0162202 0.0280943i
\(556\) 25.6180 44.3717i 1.08644 1.88178i
\(557\) −14.7729 + 25.5874i −0.625948 + 1.08417i 0.362409 + 0.932019i \(0.381954\pi\)
−0.988357 + 0.152154i \(0.951379\pi\)
\(558\) 30.8369 1.30543
\(559\) 10.5090 + 4.93461i 0.444484 + 0.208712i
\(560\) −5.40642 −0.228463
\(561\) −0.359219 + 0.622186i −0.0151662 + 0.0262687i
\(562\) 7.07422 12.2529i 0.298408 0.516858i
\(563\) −3.23368 5.60090i −0.136283 0.236050i 0.789804 0.613360i \(-0.210182\pi\)
−0.926087 + 0.377310i \(0.876849\pi\)
\(564\) 13.2119 0.556320
\(565\) 25.6933 + 44.5022i 1.08093 + 1.87222i
\(566\) −29.9916 51.9470i −1.26064 2.18350i
\(567\) −6.37315 −0.267647
\(568\) 11.5401 + 19.9880i 0.484210 + 0.838676i
\(569\) −10.8478 + 18.7889i −0.454763 + 0.787673i −0.998675 0.0514697i \(-0.983609\pi\)
0.543911 + 0.839143i \(0.316943\pi\)
\(570\) −9.29470 + 16.0989i −0.389312 + 0.674308i
\(571\) −16.6418 −0.696436 −0.348218 0.937414i \(-0.613213\pi\)
−0.348218 + 0.937414i \(0.613213\pi\)
\(572\) 4.76199 3.31549i 0.199109 0.138628i
\(573\) −6.96381 −0.290917
\(574\) −6.98367 + 12.0961i −0.291493 + 0.504880i
\(575\) −37.2656 + 64.5459i −1.55408 + 2.69175i
\(576\) −17.4064 30.1487i −0.725265 1.25620i
\(577\) −2.64240 −0.110005 −0.0550024 0.998486i \(-0.517517\pi\)
−0.0550024 + 0.998486i \(0.517517\pi\)
\(578\) 12.5885 + 21.8038i 0.523611 + 0.906921i
\(579\) 1.14167 + 1.97743i 0.0474462 + 0.0821793i
\(580\) 44.4752 1.84673
\(581\) −2.86579 4.96370i −0.118893 0.205929i
\(582\) 4.17286 7.22760i 0.172970 0.299594i
\(583\) 0.730536 1.26533i 0.0302557 0.0524044i
\(584\) 10.1123 0.418452
\(585\) 37.1586 + 17.4482i 1.53632 + 0.721393i
\(586\) −10.8219 −0.447049
\(587\) −3.69407 + 6.39832i −0.152471 + 0.264087i −0.932135 0.362110i \(-0.882056\pi\)
0.779664 + 0.626198i \(0.215390\pi\)
\(588\) −0.804662 + 1.39372i −0.0331837 + 0.0574759i
\(589\) −9.29470 16.0989i −0.382981 0.663343i
\(590\) 16.9337 0.697151
\(591\) 1.88227 + 3.26018i 0.0774261 + 0.134106i
\(592\) −0.211096 0.365628i −0.00867597 0.0150272i
\(593\) 46.9030 1.92607 0.963037 0.269370i \(-0.0868153\pi\)
0.963037 + 0.269370i \(0.0868153\pi\)
\(594\) −1.91013 3.30844i −0.0783735 0.135747i
\(595\) 5.01945 8.69395i 0.205778 0.356417i
\(596\) −6.66931 + 11.5516i −0.273186 + 0.473171i
\(597\) −0.447108 −0.0182989
\(598\) 42.1600 + 19.7966i 1.72405 + 0.809544i
\(599\) 1.62290 0.0663098 0.0331549 0.999450i \(-0.489445\pi\)
0.0331549 + 0.999450i \(0.489445\pi\)
\(600\) −7.25406 + 12.5644i −0.296146 + 0.512939i
\(601\) 23.5174 40.7333i 0.959293 1.66154i 0.235070 0.971978i \(-0.424468\pi\)
0.724223 0.689566i \(-0.242199\pi\)
\(602\) 3.57422 + 6.19073i 0.145674 + 0.252315i
\(603\) −27.9777 −1.13934
\(604\) 9.26721 + 16.0513i 0.377077 + 0.653117i
\(605\) −22.5728 39.0973i −0.917715 1.58953i
\(606\) 7.02618 0.285419
\(607\) 14.1935 + 24.5838i 0.576095 + 0.997825i 0.995922 + 0.0902211i \(0.0287574\pi\)
−0.419827 + 0.907604i \(0.637909\pi\)
\(608\) −12.5767 + 21.7836i −0.510054 + 0.883440i
\(609\) −0.988887 + 1.71280i −0.0400717 + 0.0694063i
\(610\) −5.70843 −0.231127
\(611\) −24.2921 + 16.9131i −0.982755 + 0.684233i
\(612\) 18.7953 0.759756
\(613\) 23.7782 41.1851i 0.960393 1.66345i 0.238878 0.971050i \(-0.423220\pi\)
0.721514 0.692399i \(-0.243446\pi\)
\(614\) −17.9554 + 31.0997i −0.724621 + 1.25508i
\(615\) −7.29543 12.6360i −0.294180 0.509535i
\(616\) 1.13270 0.0456377
\(617\) 8.24338 + 14.2780i 0.331866 + 0.574809i 0.982878 0.184259i \(-0.0589885\pi\)
−0.651012 + 0.759068i \(0.725655\pi\)
\(618\) −0.348786 0.604115i −0.0140302 0.0243011i
\(619\) −31.9412 −1.28382 −0.641912 0.766778i \(-0.721859\pi\)
−0.641912 + 0.766778i \(0.721859\pi\)
\(620\) −31.8123 55.1005i −1.27761 2.21289i
\(621\) 9.11047 15.7798i 0.365591 0.633222i
\(622\) 1.45196 2.51486i 0.0582182 0.100837i
\(623\) 7.46755 0.299181
\(624\) −2.29779 1.07895i −0.0919851 0.0431925i
\(625\) 75.0145 3.00058
\(626\) −14.6496 + 25.3738i −0.585515 + 1.01414i
\(627\) −0.545225 + 0.944357i −0.0217742 + 0.0377140i
\(628\) −23.8814 41.3639i −0.952973 1.65060i
\(629\) 0.783945 0.0312579
\(630\) 12.6380 + 21.8897i 0.503510 + 0.872105i
\(631\) −6.59577 11.4242i −0.262573 0.454790i 0.704352 0.709851i \(-0.251238\pi\)
−0.966925 + 0.255061i \(0.917905\pi\)
\(632\) −28.8911 −1.14923
\(633\) 3.83955 + 6.65029i 0.152608 + 0.264325i
\(634\) 8.96386 15.5259i 0.356000 0.616610i
\(635\) 4.13702 7.16554i 0.164173 0.284356i
\(636\) 4.27865 0.169660
\(637\) −0.304662 3.59266i −0.0120712 0.142346i
\(638\) 4.39068 0.173829
\(639\) −15.1058 + 26.1640i −0.597575 + 1.03503i
\(640\) −31.0432 + 53.7684i −1.22709 + 2.12538i
\(641\) 23.5814 + 40.8441i 0.931408 + 1.61325i 0.780918 + 0.624634i \(0.214752\pi\)
0.150490 + 0.988612i \(0.451915\pi\)
\(642\) 4.96734 0.196045
\(643\) 1.40679 + 2.43664i 0.0554785 + 0.0960916i 0.892431 0.451184i \(-0.148998\pi\)
−0.836952 + 0.547276i \(0.815665\pi\)
\(644\) 8.52013 + 14.7573i 0.335740 + 0.581519i
\(645\) −7.46755 −0.294035
\(646\) −9.53426 16.5138i −0.375121 0.649728i
\(647\) −12.9891 + 22.4979i −0.510656 + 0.884482i 0.489268 + 0.872134i \(0.337264\pi\)
−0.999924 + 0.0123485i \(0.996069\pi\)
\(648\) −6.56795 + 11.3760i −0.258014 + 0.446893i
\(649\) 0.993330 0.0389916
\(650\) −8.66304 102.157i −0.339792 4.00692i
\(651\) 2.82933 0.110890
\(652\) −34.5553 + 59.8515i −1.35329 + 2.34397i
\(653\) 13.4213 23.2464i 0.525216 0.909700i −0.474353 0.880335i \(-0.657318\pi\)
0.999569 0.0293654i \(-0.00934865\pi\)
\(654\) −9.33835 16.1745i −0.365158 0.632473i
\(655\) 27.4309 1.07182
\(656\) −4.03019 6.98050i −0.157353 0.272543i
\(657\) 6.61846 + 11.4635i 0.258211 + 0.447234i
\(658\) −18.2253 −0.710497
\(659\) −7.78666 13.4869i −0.303325 0.525375i 0.673562 0.739131i \(-0.264764\pi\)
−0.976887 + 0.213756i \(0.931430\pi\)
\(660\) −1.86610 + 3.23218i −0.0726379 + 0.125812i
\(661\) −16.6902 + 28.9083i −0.649174 + 1.12440i 0.334146 + 0.942521i \(0.391552\pi\)
−0.983320 + 0.181881i \(0.941781\pi\)
\(662\) −33.1783 −1.28951
\(663\) 3.86836 2.69330i 0.150234 0.104599i
\(664\) −11.8136 −0.458455
\(665\) 7.61856 13.1957i 0.295435 0.511708i
\(666\) −0.986911 + 1.70938i −0.0382420 + 0.0662371i
\(667\) 10.4708 + 18.1359i 0.405431 + 0.702227i
\(668\) −52.2148 −2.02025
\(669\) 3.71881 + 6.44117i 0.143778 + 0.249030i
\(670\) 48.5745 + 84.1335i 1.87660 + 3.25036i
\(671\) −0.334855 −0.0129269
\(672\) −1.91420 3.31549i −0.0738418 0.127898i
\(673\) −0.427076 + 0.739717i −0.0164626 + 0.0285140i −0.874139 0.485675i \(-0.838574\pi\)
0.857677 + 0.514189i \(0.171907\pi\)
\(674\) 19.0582 33.0098i 0.734095 1.27149i
\(675\) −40.1076 −1.54374
\(676\) −37.5260 + 6.41062i −1.44331 + 0.246562i
\(677\) −24.5449 −0.943339 −0.471669 0.881775i \(-0.656348\pi\)
−0.471669 + 0.881775i \(0.656348\pi\)
\(678\) −7.42797 + 12.8656i −0.285269 + 0.494101i
\(679\) −3.42035 + 5.92422i −0.131261 + 0.227351i
\(680\) −10.3458 17.9194i −0.396742 0.687177i
\(681\) −2.94972 −0.113034
\(682\) −3.14057 5.43963i −0.120259 0.208294i
\(683\) 21.5186 + 37.2714i 0.823387 + 1.42615i 0.903146 + 0.429334i \(0.141252\pi\)
−0.0797583 + 0.996814i \(0.525415\pi\)
\(684\) 28.5276 1.09078
\(685\) −32.1935 55.7608i −1.23005 2.13051i
\(686\) 1.11000 1.92258i 0.0423801 0.0734046i
\(687\) −0.851558 + 1.47494i −0.0324889 + 0.0562725i
\(688\) −4.12528 −0.157275
\(689\) −7.86699 + 5.47731i −0.299708 + 0.208669i
\(690\) −29.9583 −1.14049
\(691\) 12.9098 22.3604i 0.491110 0.850628i −0.508837 0.860863i \(-0.669925\pi\)
0.999948 + 0.0102348i \(0.00325788\pi\)
\(692\) 11.0861 19.2017i 0.421431 0.729939i
\(693\) 0.741343 + 1.28404i 0.0281613 + 0.0487768i
\(694\) −8.74338 −0.331894
\(695\) −36.9167 63.9416i −1.40033 2.42544i
\(696\) 2.03823 + 3.53031i 0.0772588 + 0.133816i
\(697\) 14.9669 0.566913
\(698\) −19.0673 33.0255i −0.721707 1.25003i
\(699\) 5.59750 9.69515i 0.211717 0.366704i
\(700\) 18.7544 32.4835i 0.708849 1.22776i
\(701\) 16.3178 0.616313 0.308156 0.951336i \(-0.400288\pi\)
0.308156 + 0.951336i \(0.400288\pi\)
\(702\) 2.11789 + 24.9747i 0.0799346 + 0.942609i
\(703\) 1.18988 0.0448770
\(704\) −3.54548 + 6.14096i −0.133625 + 0.231446i
\(705\) 9.51945 16.4882i 0.358523 0.620981i
\(706\) 20.1981 + 34.9841i 0.760166 + 1.31665i
\(707\) −5.75913 −0.216594
\(708\) 1.45445 + 2.51918i 0.0546616 + 0.0946767i
\(709\) 11.1897 + 19.3811i 0.420238 + 0.727874i 0.995963 0.0897702i \(-0.0286133\pi\)
−0.575725 + 0.817644i \(0.695280\pi\)
\(710\) 104.906 3.93705
\(711\) −18.9090 32.7514i −0.709144 1.22827i
\(712\) 7.69581 13.3295i 0.288413 0.499545i
\(713\) 14.9791 25.9446i 0.560973 0.971634i
\(714\) 2.90226 0.108614
\(715\) −0.706545 8.33177i −0.0264233 0.311590i
\(716\) −66.7781 −2.49561
\(717\) 0.354893 0.614692i 0.0132537 0.0229561i
\(718\) −18.1071 + 31.3624i −0.675750 + 1.17043i
\(719\) 11.3723 + 19.6973i 0.424113 + 0.734586i 0.996337 0.0855115i \(-0.0272524\pi\)
−0.572224 + 0.820098i \(0.693919\pi\)
\(720\) −14.5865 −0.543606
\(721\) 0.285888 + 0.495173i 0.0106470 + 0.0184412i
\(722\) 6.61892 + 11.4643i 0.246331 + 0.426657i
\(723\) 1.17203 0.0435881
\(724\) −20.3956 35.3263i −0.757997 1.31289i
\(725\) 23.0481 39.9205i 0.855986 1.48261i
\(726\) 6.52582 11.3030i 0.242196 0.419495i
\(727\) 18.7274 0.694561 0.347280 0.937761i \(-0.387105\pi\)
0.347280 + 0.937761i \(0.387105\pi\)
\(728\) −6.72684 3.15865i −0.249313 0.117067i
\(729\) −12.0322 −0.445638
\(730\) 22.9818 39.8056i 0.850594 1.47327i
\(731\) 3.83001 6.63377i 0.141658 0.245359i
\(732\) −0.490300 0.849225i −0.0181220 0.0313883i
\(733\) −1.69268 −0.0625206 −0.0312603 0.999511i \(-0.509952\pi\)
−0.0312603 + 0.999511i \(0.509952\pi\)
\(734\) 40.1781 + 69.5904i 1.48300 + 2.56863i
\(735\) 1.15956 + 2.00841i 0.0427708 + 0.0740813i
\(736\) −40.5368 −1.49421
\(737\) 2.84937 + 4.93525i 0.104958 + 0.181792i
\(738\) −18.8419 + 32.6351i −0.693580 + 1.20132i
\(739\) −23.4581 + 40.6305i −0.862919 + 1.49462i 0.00618065 + 0.999981i \(0.498033\pi\)
−0.869099 + 0.494638i \(0.835301\pi\)
\(740\) 4.07250 0.149708
\(741\) 5.87141 4.08791i 0.215692 0.150173i
\(742\) −5.90226 −0.216679
\(743\) −6.44831 + 11.1688i −0.236566 + 0.409744i −0.959727 0.280936i \(-0.909355\pi\)
0.723161 + 0.690680i \(0.242688\pi\)
\(744\) 2.91581 5.05034i 0.106899 0.185154i
\(745\) 9.61078 + 16.6464i 0.352112 + 0.609875i
\(746\) 21.7513 0.796371
\(747\) −7.73189 13.3920i −0.282895 0.489989i
\(748\) −1.91420 3.31549i −0.0699900 0.121226i
\(749\) −4.07157 −0.148772
\(750\) 20.1007 + 34.8155i 0.733974 + 1.27128i
\(751\) 22.8166 39.5196i 0.832591 1.44209i −0.0633855 0.997989i \(-0.520190\pi\)
0.895977 0.444101i \(-0.146477\pi\)
\(752\) 5.25881 9.10852i 0.191769 0.332154i
\(753\) −16.9103 −0.616245
\(754\) −26.0753 12.2439i −0.949605 0.445896i
\(755\) 26.7089 0.972038
\(756\) −4.58496 + 7.94138i −0.166753 + 0.288825i
\(757\) 19.0782 33.0445i 0.693410 1.20102i −0.277303 0.960782i \(-0.589441\pi\)
0.970714 0.240239i \(-0.0772260\pi\)
\(758\) −14.5028 25.1195i −0.526764 0.912382i
\(759\) −1.75735 −0.0637876
\(760\) −15.7028 27.1981i −0.569602 0.986580i
\(761\) −21.3672 37.0092i −0.774562 1.34158i −0.935040 0.354542i \(-0.884637\pi\)
0.160478 0.987039i \(-0.448696\pi\)
\(762\) 2.39203 0.0866543
\(763\) 7.65434 + 13.2577i 0.277106 + 0.479961i
\(764\) 18.5543 32.1370i 0.671271 1.16267i
\(765\) 13.5425 23.4562i 0.489628 0.848061i
\(766\) 61.7005 2.22933
\(767\) −5.89917 2.77001i −0.213007 0.100019i
\(768\) −3.76729 −0.135940
\(769\) −10.8088 + 18.7215i −0.389777 + 0.675113i −0.992419 0.122898i \(-0.960781\pi\)
0.602643 + 0.798011i \(0.294114\pi\)
\(770\) 2.57422 4.45868i 0.0927685 0.160680i
\(771\) 0.404912 + 0.701329i 0.0145826 + 0.0252577i
\(772\) −12.1674 −0.437915
\(773\) −5.00056 8.66123i −0.179858 0.311523i 0.761974 0.647608i \(-0.224230\pi\)
−0.941832 + 0.336085i \(0.890897\pi\)
\(774\) 9.64323 + 16.7026i 0.346619 + 0.600361i
\(775\) −65.9436 −2.36877
\(776\) 7.04980 + 12.2106i 0.253073 + 0.438335i