Properties

Label 91.2.f.c.29.4
Level $91$
Weight $2$
Character 91.29
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 29.4
Root \(1.37054 + 2.37385i\) of defining polynomial
Character \(\chi\) \(=\) 91.29
Dual form 91.2.f.c.22.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.37054 + 2.37385i) q^{2} +(-0.682410 - 1.18197i) q^{3} +(-2.75677 + 4.77486i) q^{4} +0.741082 q^{5} +(1.87054 - 3.23987i) q^{6} +(0.500000 - 0.866025i) q^{7} -9.63087 q^{8} +(0.568634 - 0.984903i) q^{9} +O(q^{10})\) \(q+(1.37054 + 2.37385i) q^{2} +(-0.682410 - 1.18197i) q^{3} +(-2.75677 + 4.77486i) q^{4} +0.741082 q^{5} +(1.87054 - 3.23987i) q^{6} +(0.500000 - 0.866025i) q^{7} -9.63087 q^{8} +(0.568634 - 0.984903i) q^{9} +(1.01568 + 1.75921i) q^{10} +(0.682410 + 1.18197i) q^{11} +7.52497 q^{12} +(0.301907 - 3.59289i) q^{13} +2.74108 q^{14} +(-0.505722 - 0.875935i) q^{15} +(-7.68598 - 13.3125i) q^{16} +(2.07436 - 3.59289i) q^{17} +3.11734 q^{18} +(-3.63303 + 6.29259i) q^{19} +(-2.04299 + 3.53856i) q^{20} -1.36482 q^{21} +(-1.87054 + 3.23987i) q^{22} +(1.16673 + 2.02083i) q^{23} +(6.57220 + 11.3834i) q^{24} -4.45080 q^{25} +(8.94274 - 4.20752i) q^{26} -5.64662 q^{27} +(2.75677 + 4.77486i) q^{28} +(0.203815 + 0.353017i) q^{29} +(1.38622 - 2.40101i) q^{30} -2.77245 q^{31} +(11.4370 - 19.8095i) q^{32} +(0.931366 - 1.61317i) q^{33} +11.3720 q^{34} +(0.370541 - 0.641796i) q^{35} +(3.13518 + 5.43029i) q^{36} +(3.05295 + 5.28787i) q^{37} -19.9169 q^{38} +(-4.45271 + 2.09498i) q^{39} -7.13727 q^{40} +(-0.627306 - 1.08653i) q^{41} +(-1.87054 - 3.23987i) q^{42} +(0.870541 - 1.50782i) q^{43} -7.52497 q^{44} +(0.421404 - 0.729894i) q^{45} +(-3.19809 + 5.53926i) q^{46} -5.85843 q^{47} +(-10.4900 + 18.1692i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-6.10000 - 10.5655i) q^{50} -5.66224 q^{51} +(16.3232 + 11.3463i) q^{52} +4.56778 q^{53} +(-7.73893 - 13.4042i) q^{54} +(0.505722 + 0.875935i) q^{55} +(-4.81544 + 8.34058i) q^{56} +9.91685 q^{57} +(-0.558672 + 0.967649i) q^{58} +(5.49213 - 9.51264i) q^{59} +5.57662 q^{60} +(-3.26249 + 5.65079i) q^{61} +(-3.79975 - 6.58137i) q^{62} +(-0.568634 - 0.984903i) q^{63} +31.9557 q^{64} +(0.223738 - 2.66263i) q^{65} +5.10590 q^{66} +(6.87983 + 11.9162i) q^{67} +(11.4370 + 19.8095i) q^{68} +(1.59237 - 2.75807i) q^{69} +2.03137 q^{70} +(2.40763 - 4.17014i) q^{71} +(-5.47644 + 9.48548i) q^{72} +6.06987 q^{73} +(-8.36839 + 14.4945i) q^{74} +(3.03727 + 5.26070i) q^{75} +(-20.0308 - 34.6944i) q^{76} +1.36482 q^{77} +(-11.0758 - 7.69879i) q^{78} -9.12582 q^{79} +(-5.69594 - 9.86566i) q^{80} +(2.14741 + 3.71942i) q^{81} +(1.71950 - 2.97826i) q^{82} +11.7368 q^{83} +(3.76249 - 6.51682i) q^{84} +(1.53727 - 2.66263i) q^{85} +4.77245 q^{86} +(0.278170 - 0.481805i) q^{87} +(-6.57220 - 11.3834i) q^{88} +(0.880503 + 1.52508i) q^{89} +2.31021 q^{90} +(-2.96058 - 2.05790i) q^{91} -12.8656 q^{92} +(1.89195 + 3.27695i) q^{93} +(-8.02921 - 13.9070i) q^{94} +(-2.69237 + 4.66332i) q^{95} -31.2189 q^{96} +(-4.76691 + 8.25652i) q^{97} +(1.37054 - 2.37385i) q^{98} +1.55217 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 \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.37054 + 2.37385i 0.969119 + 1.67856i 0.698116 + 0.715984i \(0.254022\pi\)
0.271003 + 0.962579i \(0.412645\pi\)
\(3\) −0.682410 1.18197i −0.393989 0.682410i 0.598982 0.800762i \(-0.295572\pi\)
−0.992972 + 0.118353i \(0.962239\pi\)
\(4\) −2.75677 + 4.77486i −1.37838 + 2.38743i
\(5\) 0.741082 0.331422 0.165711 0.986174i \(-0.447008\pi\)
0.165711 + 0.986174i \(0.447008\pi\)
\(6\) 1.87054 3.23987i 0.763645 1.32267i
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) −9.63087 −3.40503
\(9\) 0.568634 0.984903i 0.189545 0.328301i
\(10\) 1.01568 + 1.75921i 0.321187 + 0.556313i
\(11\) 0.682410 + 1.18197i 0.205754 + 0.356377i 0.950373 0.311113i \(-0.100702\pi\)
−0.744619 + 0.667490i \(0.767369\pi\)
\(12\) 7.52497 2.17227
\(13\) 0.301907 3.59289i 0.0837339 0.996488i
\(14\) 2.74108 0.732585
\(15\) −0.505722 0.875935i −0.130577 0.226166i
\(16\) −7.68598 13.3125i −1.92149 3.32813i
\(17\) 2.07436 3.59289i 0.503105 0.871404i −0.496888 0.867814i \(-0.665524\pi\)
0.999994 0.00358919i \(-0.00114248\pi\)
\(18\) 3.11734 0.734765
\(19\) −3.63303 + 6.29259i −0.833474 + 1.44362i 0.0617933 + 0.998089i \(0.480318\pi\)
−0.895267 + 0.445530i \(0.853015\pi\)
\(20\) −2.04299 + 3.53856i −0.456826 + 0.791246i
\(21\) −1.36482 −0.297828
\(22\) −1.87054 + 3.23987i −0.398801 + 0.690743i
\(23\) 1.16673 + 2.02083i 0.243279 + 0.421372i 0.961646 0.274292i \(-0.0884435\pi\)
−0.718367 + 0.695664i \(0.755110\pi\)
\(24\) 6.57220 + 11.3834i 1.34155 + 2.32362i
\(25\) −4.45080 −0.890159
\(26\) 8.94274 4.20752i 1.75382 0.825163i
\(27\) −5.64662 −1.08669
\(28\) 2.75677 + 4.77486i 0.520980 + 0.902363i
\(29\) 0.203815 + 0.353017i 0.0378474 + 0.0655536i 0.884329 0.466865i \(-0.154617\pi\)
−0.846481 + 0.532419i \(0.821283\pi\)
\(30\) 1.38622 2.40101i 0.253089 0.438363i
\(31\) −2.77245 −0.497946 −0.248973 0.968510i \(-0.580093\pi\)
−0.248973 + 0.968510i \(0.580093\pi\)
\(32\) 11.4370 19.8095i 2.02180 3.50186i
\(33\) 0.931366 1.61317i 0.162130 0.280817i
\(34\) 11.3720 1.95027
\(35\) 0.370541 0.641796i 0.0626329 0.108483i
\(36\) 3.13518 + 5.43029i 0.522530 + 0.905049i
\(37\) 3.05295 + 5.28787i 0.501902 + 0.869320i 0.999998 + 0.00219764i \(0.000699531\pi\)
−0.498096 + 0.867122i \(0.665967\pi\)
\(38\) −19.9169 −3.23094
\(39\) −4.45271 + 2.09498i −0.713003 + 0.335465i
\(40\) −7.13727 −1.12850
\(41\) −0.627306 1.08653i −0.0979688 0.169687i 0.812875 0.582438i \(-0.197901\pi\)
−0.910844 + 0.412751i \(0.864568\pi\)
\(42\) −1.87054 3.23987i −0.288631 0.499923i
\(43\) 0.870541 1.50782i 0.132756 0.229941i −0.791982 0.610545i \(-0.790951\pi\)
0.924738 + 0.380604i \(0.124284\pi\)
\(44\) −7.52497 −1.13443
\(45\) 0.421404 0.729894i 0.0628193 0.108806i
\(46\) −3.19809 + 5.53926i −0.471533 + 0.816719i
\(47\) −5.85843 −0.854539 −0.427270 0.904124i \(-0.640525\pi\)
−0.427270 + 0.904124i \(0.640525\pi\)
\(48\) −10.4900 + 18.1692i −1.51410 + 2.62249i
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) −6.10000 10.5655i −0.862670 1.49419i
\(51\) −5.66224 −0.792872
\(52\) 16.3232 + 11.3463i 2.26363 + 1.57345i
\(53\) 4.56778 0.627433 0.313717 0.949517i \(-0.398426\pi\)
0.313717 + 0.949517i \(0.398426\pi\)
\(54\) −7.73893 13.4042i −1.05313 1.82408i
\(55\) 0.505722 + 0.875935i 0.0681915 + 0.118111i
\(56\) −4.81544 + 8.34058i −0.643490 + 1.11456i
\(57\) 9.91685 1.31352
\(58\) −0.558672 + 0.967649i −0.0733573 + 0.127059i
\(59\) 5.49213 9.51264i 0.715014 1.23844i −0.247940 0.968775i \(-0.579754\pi\)
0.962954 0.269665i \(-0.0869130\pi\)
\(60\) 5.57662 0.719939
\(61\) −3.26249 + 5.65079i −0.417719 + 0.723510i −0.995710 0.0925333i \(-0.970504\pi\)
0.577991 + 0.816043i \(0.303837\pi\)
\(62\) −3.79975 6.58137i −0.482569 0.835834i
\(63\) −0.568634 0.984903i −0.0716411 0.124086i
\(64\) 31.9557 3.99446
\(65\) 0.223738 2.66263i 0.0277513 0.330258i
\(66\) 5.10590 0.628493
\(67\) 6.87983 + 11.9162i 0.840505 + 1.45580i 0.889468 + 0.456997i \(0.151075\pi\)
−0.0489630 + 0.998801i \(0.515592\pi\)
\(68\) 11.4370 + 19.8095i 1.38694 + 2.40226i
\(69\) 1.59237 2.75807i 0.191699 0.332032i
\(70\) 2.03137 0.242795
\(71\) 2.40763 4.17014i 0.285733 0.494904i −0.687054 0.726607i \(-0.741096\pi\)
0.972787 + 0.231703i \(0.0744296\pi\)
\(72\) −5.47644 + 9.48548i −0.645405 + 1.11787i
\(73\) 6.06987 0.710425 0.355212 0.934786i \(-0.384409\pi\)
0.355212 + 0.934786i \(0.384409\pi\)
\(74\) −8.36839 + 14.4945i −0.972805 + 1.68495i
\(75\) 3.03727 + 5.26070i 0.350713 + 0.607453i
\(76\) −20.0308 34.6944i −2.29769 3.97972i
\(77\) 1.36482 0.155536
\(78\) −11.0758 7.69879i −1.25408 0.871716i
\(79\) −9.12582 −1.02674 −0.513368 0.858169i \(-0.671602\pi\)
−0.513368 + 0.858169i \(0.671602\pi\)
\(80\) −5.69594 9.86566i −0.636825 1.10301i
\(81\) 2.14741 + 3.71942i 0.238601 + 0.413269i
\(82\) 1.71950 2.97826i 0.189887 0.328894i
\(83\) 11.7368 1.28828 0.644139 0.764908i \(-0.277216\pi\)
0.644139 + 0.764908i \(0.277216\pi\)
\(84\) 3.76249 6.51682i 0.410521 0.711043i
\(85\) 1.53727 2.66263i 0.166740 0.288802i
\(86\) 4.77245 0.514626
\(87\) 0.278170 0.481805i 0.0298230 0.0516549i
\(88\) −6.57220 11.3834i −0.700599 1.21347i
\(89\) 0.880503 + 1.52508i 0.0933331 + 0.161658i 0.908912 0.416989i \(-0.136915\pi\)
−0.815579 + 0.578646i \(0.803581\pi\)
\(90\) 2.31021 0.243517
\(91\) −2.96058 2.05790i −0.310353 0.215727i
\(92\) −12.8656 −1.34133
\(93\) 1.89195 + 3.27695i 0.196186 + 0.339803i
\(94\) −8.02921 13.9070i −0.828150 1.43440i
\(95\) −2.69237 + 4.66332i −0.276231 + 0.478447i
\(96\) −31.2189 −3.18627
\(97\) −4.76691 + 8.25652i −0.484006 + 0.838323i −0.999831 0.0183708i \(-0.994152\pi\)
0.515825 + 0.856694i \(0.327485\pi\)
\(98\) 1.37054 2.37385i 0.138446 0.239795i
\(99\) 1.55217 0.155998
\(100\) 12.2698 21.2519i 1.22698 2.12519i
\(101\) 3.74680 + 6.48965i 0.372821 + 0.645745i 0.989998 0.141079i \(-0.0450573\pi\)
−0.617177 + 0.786824i \(0.711724\pi\)
\(102\) −7.76033 13.4413i −0.768388 1.33089i
\(103\) 2.80848 0.276728 0.138364 0.990381i \(-0.455816\pi\)
0.138364 + 0.990381i \(0.455816\pi\)
\(104\) −2.90763 + 34.6027i −0.285116 + 3.39307i
\(105\) −1.01144 −0.0987067
\(106\) 6.26033 + 10.8432i 0.608057 + 1.05319i
\(107\) −0.743235 1.28732i −0.0718512 0.124450i 0.827861 0.560933i \(-0.189557\pi\)
−0.899713 + 0.436483i \(0.856224\pi\)
\(108\) 15.5664 26.9618i 1.49788 2.59440i
\(109\) 2.87121 0.275012 0.137506 0.990501i \(-0.456091\pi\)
0.137506 + 0.990501i \(0.456091\pi\)
\(110\) −1.38622 + 2.40101i −0.132171 + 0.228927i
\(111\) 4.16673 7.21698i 0.395488 0.685006i
\(112\) −15.3720 −1.45251
\(113\) 6.20972 10.7555i 0.584161 1.01180i −0.410819 0.911717i \(-0.634757\pi\)
0.994979 0.100079i \(-0.0319096\pi\)
\(114\) 13.5915 + 23.5411i 1.27296 + 2.20483i
\(115\) 0.864640 + 1.49760i 0.0806281 + 0.139652i
\(116\) −2.24747 −0.208673
\(117\) −3.36697 2.34039i −0.311277 0.216369i
\(118\) 30.1087 2.77173
\(119\) −2.07436 3.59289i −0.190156 0.329360i
\(120\) 4.87054 + 8.43602i 0.444618 + 0.770100i
\(121\) 4.56863 7.91311i 0.415330 0.719373i
\(122\) −17.8855 −1.61928
\(123\) −0.856160 + 1.48291i −0.0771973 + 0.133710i
\(124\) 7.64299 13.2380i 0.686361 1.18881i
\(125\) −7.00382 −0.626440
\(126\) 1.55867 2.69970i 0.138858 0.240508i
\(127\) −2.71526 4.70296i −0.240940 0.417321i 0.720042 0.693930i \(-0.244122\pi\)
−0.960982 + 0.276610i \(0.910789\pi\)
\(128\) 20.9226 + 36.2390i 1.84931 + 3.20310i
\(129\) −2.37626 −0.209218
\(130\) 6.62731 3.11812i 0.581253 0.273477i
\(131\) −11.3220 −0.989209 −0.494604 0.869118i \(-0.664687\pi\)
−0.494604 + 0.869118i \(0.664687\pi\)
\(132\) 5.13512 + 8.89428i 0.446954 + 0.774148i
\(133\) 3.63303 + 6.29259i 0.315023 + 0.545637i
\(134\) −18.8582 + 32.6633i −1.62910 + 2.82168i
\(135\) −4.18461 −0.360154
\(136\) −19.9779 + 34.6027i −1.71309 + 2.96715i
\(137\) 6.98771 12.1031i 0.597000 1.03403i −0.396261 0.918138i \(-0.629693\pi\)
0.993261 0.115897i \(-0.0369741\pi\)
\(138\) 8.72964 0.743116
\(139\) −5.21544 + 9.03340i −0.442368 + 0.766203i −0.997865 0.0653153i \(-0.979195\pi\)
0.555497 + 0.831518i \(0.312528\pi\)
\(140\) 2.04299 + 3.53856i 0.172664 + 0.299063i
\(141\) 3.99785 + 6.92447i 0.336679 + 0.583146i
\(142\) 13.1990 1.10764
\(143\) 4.45271 2.09498i 0.372354 0.175191i
\(144\) −17.4820 −1.45684
\(145\) 0.151043 + 0.261615i 0.0125435 + 0.0217259i
\(146\) 8.31901 + 14.4089i 0.688486 + 1.19249i
\(147\) −0.682410 + 1.18197i −0.0562842 + 0.0974871i
\(148\) −33.6651 −2.76725
\(149\) −4.08216 + 7.07052i −0.334424 + 0.579239i −0.983374 0.181592i \(-0.941875\pi\)
0.648950 + 0.760831i \(0.275208\pi\)
\(150\) −8.32540 + 14.4200i −0.679766 + 1.17739i
\(151\) −2.46188 −0.200345 −0.100173 0.994970i \(-0.531939\pi\)
−0.100173 + 0.994970i \(0.531939\pi\)
\(152\) 34.9892 60.6031i 2.83800 4.91556i
\(153\) −2.35910 4.08608i −0.190722 0.330340i
\(154\) 1.87054 + 3.23987i 0.150732 + 0.261076i
\(155\) −2.05461 −0.165030
\(156\) 2.27184 27.0364i 0.181893 2.16464i
\(157\) −12.9198 −1.03111 −0.515557 0.856855i \(-0.672415\pi\)
−0.515557 + 0.856855i \(0.672415\pi\)
\(158\) −12.5073 21.6633i −0.995029 1.72344i
\(159\) −3.11710 5.39897i −0.247202 0.428167i
\(160\) 8.47577 14.6805i 0.670069 1.16059i
\(161\) 2.33345 0.183902
\(162\) −5.88622 + 10.1952i −0.462465 + 0.801014i
\(163\) 3.01371 5.21990i 0.236052 0.408854i −0.723526 0.690297i \(-0.757480\pi\)
0.959578 + 0.281443i \(0.0908131\pi\)
\(164\) 6.91734 0.540154
\(165\) 0.690219 1.19549i 0.0537334 0.0930691i
\(166\) 16.0857 + 27.8613i 1.24850 + 2.16246i
\(167\) −3.82558 6.62610i −0.296032 0.512743i 0.679192 0.733960i \(-0.262330\pi\)
−0.975224 + 0.221218i \(0.928997\pi\)
\(168\) 13.1444 1.01411
\(169\) −12.8177 2.16944i −0.985977 0.166880i
\(170\) 8.42755 0.646364
\(171\) 4.13173 + 7.15636i 0.315961 + 0.547260i
\(172\) 4.79975 + 8.31342i 0.365978 + 0.633892i
\(173\) 0.0822298 0.142426i 0.00625182 0.0108285i −0.862883 0.505404i \(-0.831343\pi\)
0.869134 + 0.494576i \(0.164677\pi\)
\(174\) 1.52497 0.115608
\(175\) −2.22540 + 3.85450i −0.168224 + 0.291373i
\(176\) 10.4900 18.1692i 0.790711 1.36955i
\(177\) −14.9915 −1.12683
\(178\) −2.41353 + 4.18036i −0.180902 + 0.313331i
\(179\) −0.384316 0.665655i −0.0287252 0.0497534i 0.851305 0.524670i \(-0.175811\pi\)
−0.880031 + 0.474917i \(0.842478\pi\)
\(180\) 2.32343 + 4.02429i 0.173178 + 0.299953i
\(181\) −9.92152 −0.737461 −0.368730 0.929536i \(-0.620207\pi\)
−0.368730 + 0.929536i \(0.620207\pi\)
\(182\) 0.827552 9.84840i 0.0613422 0.730012i
\(183\) 8.90541 0.658307
\(184\) −11.2366 19.4624i −0.828373 1.43478i
\(185\) 2.26249 + 3.91874i 0.166341 + 0.288112i
\(186\) −5.18598 + 8.98238i −0.380254 + 0.658620i
\(187\) 5.66224 0.414064
\(188\) 16.1503 27.9732i 1.17788 2.04015i
\(189\) −2.82331 + 4.89012i −0.205366 + 0.355704i
\(190\) −14.7600 −1.07080
\(191\) −4.94847 + 8.57099i −0.358058 + 0.620175i −0.987636 0.156762i \(-0.949894\pi\)
0.629578 + 0.776937i \(0.283228\pi\)
\(192\) −21.8069 37.7706i −1.57378 2.72586i
\(193\) −4.35037 7.53507i −0.313147 0.542386i 0.665895 0.746045i \(-0.268050\pi\)
−0.979042 + 0.203659i \(0.934716\pi\)
\(194\) −26.1330 −1.87624
\(195\) −3.29982 + 1.55255i −0.236305 + 0.111180i
\(196\) 5.51353 0.393824
\(197\) 13.0093 + 22.5328i 0.926874 + 1.60539i 0.788520 + 0.615009i \(0.210848\pi\)
0.138354 + 0.990383i \(0.455819\pi\)
\(198\) 2.12731 + 3.68460i 0.151181 + 0.261853i
\(199\) −5.06648 + 8.77540i −0.359153 + 0.622072i −0.987820 0.155603i \(-0.950268\pi\)
0.628666 + 0.777675i \(0.283601\pi\)
\(200\) 42.8651 3.03102
\(201\) 9.38973 16.2635i 0.662300 1.14714i
\(202\) −10.2703 + 17.7887i −0.722615 + 1.25161i
\(203\) 0.407629 0.0286099
\(204\) 15.6095 27.0364i 1.09288 1.89293i
\(205\) −0.464885 0.805205i −0.0324690 0.0562380i
\(206\) 3.84914 + 6.66690i 0.268182 + 0.464505i
\(207\) 2.65376 0.184449
\(208\) −50.1508 + 23.5957i −3.47733 + 1.63607i
\(209\) −9.91685 −0.685963
\(210\) −1.38622 2.40101i −0.0956586 0.165685i
\(211\) −8.33911 14.4438i −0.574088 0.994349i −0.996140 0.0877779i \(-0.972023\pi\)
0.422052 0.906572i \(-0.361310\pi\)
\(212\) −12.5923 + 21.8105i −0.864843 + 1.49795i
\(213\) −6.57196 −0.450303
\(214\) 2.03727 3.52865i 0.139265 0.241214i
\(215\) 0.645142 1.11742i 0.0439983 0.0762074i
\(216\) 54.3819 3.70022
\(217\) −1.38622 + 2.40101i −0.0941030 + 0.162991i
\(218\) 3.93511 + 6.81582i 0.266520 + 0.461625i
\(219\) −4.14214 7.17439i −0.279900 0.484801i
\(220\) −5.57662 −0.375976
\(221\) −12.2826 8.53765i −0.826216 0.574304i
\(222\) 22.8427 1.53310
\(223\) −0.535180 0.926959i −0.0358383 0.0620738i 0.847550 0.530716i \(-0.178077\pi\)
−0.883388 + 0.468642i \(0.844743\pi\)
\(224\) −11.4370 19.8095i −0.764168 1.32358i
\(225\) −2.53087 + 4.38360i −0.168725 + 0.292240i
\(226\) 34.0427 2.26449
\(227\) 12.2332 21.1885i 0.811947 1.40633i −0.0995534 0.995032i \(-0.531741\pi\)
0.911500 0.411300i \(-0.134925\pi\)
\(228\) −27.3384 + 47.3516i −1.81053 + 3.13593i
\(229\) 4.72964 0.312543 0.156272 0.987714i \(-0.450052\pi\)
0.156272 + 0.987714i \(0.450052\pi\)
\(230\) −2.37005 + 4.10505i −0.156276 + 0.270679i
\(231\) −0.931366 1.61317i −0.0612794 0.106139i
\(232\) −1.96291 3.39986i −0.128871 0.223212i
\(233\) 20.5507 1.34632 0.673160 0.739497i \(-0.264936\pi\)
0.673160 + 0.739497i \(0.264936\pi\)
\(234\) 0.941148 11.2003i 0.0615248 0.732185i
\(235\) −4.34157 −0.283213
\(236\) 30.2810 + 52.4482i 1.97113 + 3.41409i
\(237\) 6.22755 + 10.7864i 0.404523 + 0.700654i
\(238\) 5.68598 9.84840i 0.368567 0.638377i
\(239\) 6.25461 0.404577 0.202289 0.979326i \(-0.435162\pi\)
0.202289 + 0.979326i \(0.435162\pi\)
\(240\) −7.77393 + 13.4648i −0.501805 + 0.869152i
\(241\) 6.07220 10.5174i 0.391145 0.677483i −0.601456 0.798906i \(-0.705412\pi\)
0.992601 + 0.121423i \(0.0387458\pi\)
\(242\) 25.0460 1.61002
\(243\) −5.53911 + 9.59402i −0.355334 + 0.615457i
\(244\) −17.9878 31.1558i −1.15155 1.99455i
\(245\) −0.370541 0.641796i −0.0236730 0.0410028i
\(246\) −4.69361 −0.299254
\(247\) 21.5117 + 14.9528i 1.36876 + 0.951427i
\(248\) 26.7011 1.69552
\(249\) −8.00929 13.8725i −0.507568 0.879134i
\(250\) −9.59902 16.6260i −0.607095 1.05152i
\(251\) 3.15719 5.46842i 0.199280 0.345163i −0.749015 0.662553i \(-0.769473\pi\)
0.948295 + 0.317390i \(0.102806\pi\)
\(252\) 6.27036 0.394996
\(253\) −1.59237 + 2.75807i −0.100112 + 0.173398i
\(254\) 7.44274 12.8912i 0.466999 0.808866i
\(255\) −4.19619 −0.262775
\(256\) −25.3948 + 43.9850i −1.58717 + 2.74907i
\(257\) −12.1781 21.0931i −0.759649 1.31575i −0.943030 0.332709i \(-0.892037\pi\)
0.183380 0.983042i \(-0.441296\pi\)
\(258\) −3.25677 5.64088i −0.202757 0.351186i
\(259\) 6.10590 0.379402
\(260\) 12.0969 + 8.40855i 0.750216 + 0.521476i
\(261\) 0.463583 0.0286951
\(262\) −15.5173 26.8767i −0.958661 1.66045i
\(263\) 4.78955 + 8.29574i 0.295336 + 0.511537i 0.975063 0.221928i \(-0.0712350\pi\)
−0.679727 + 0.733465i \(0.737902\pi\)
\(264\) −8.96987 + 15.5363i −0.552057 + 0.956191i
\(265\) 3.38510 0.207945
\(266\) −9.95843 + 17.2485i −0.610590 + 1.05757i
\(267\) 1.20173 2.08145i 0.0735445 0.127383i
\(268\) −75.8643 −4.63415
\(269\) −14.6995 + 25.4603i −0.896245 + 1.55234i −0.0639886 + 0.997951i \(0.520382\pi\)
−0.832256 + 0.554391i \(0.812951\pi\)
\(270\) −5.73518 9.93362i −0.349032 0.604541i
\(271\) 0.150192 + 0.260141i 0.00912354 + 0.0158024i 0.870551 0.492078i \(-0.163763\pi\)
−0.861428 + 0.507880i \(0.830429\pi\)
\(272\) −63.7738 −3.86686
\(273\) −0.412049 + 4.90364i −0.0249383 + 0.296782i
\(274\) 38.3078 2.31426
\(275\) −3.03727 5.26070i −0.183154 0.317232i
\(276\) 8.77959 + 15.2067i 0.528469 + 0.915335i
\(277\) 16.3855 28.3805i 0.984509 1.70522i 0.340408 0.940278i \(-0.389435\pi\)
0.644100 0.764941i \(-0.277232\pi\)
\(278\) −28.5919 −1.71483
\(279\) −1.57651 + 2.73059i −0.0943831 + 0.163476i
\(280\) −3.56863 + 6.18106i −0.213267 + 0.369389i
\(281\) 4.29482 0.256207 0.128104 0.991761i \(-0.459111\pi\)
0.128104 + 0.991761i \(0.459111\pi\)
\(282\) −10.9584 + 18.9806i −0.652565 + 1.13028i
\(283\) 10.5501 + 18.2734i 0.627140 + 1.08624i 0.988123 + 0.153666i \(0.0491079\pi\)
−0.360983 + 0.932572i \(0.617559\pi\)
\(284\) 13.2745 + 22.9922i 0.787699 + 1.36433i
\(285\) 7.34920 0.435329
\(286\) 11.0758 + 7.69879i 0.654924 + 0.455239i
\(287\) −1.25461 −0.0740574
\(288\) −13.0070 22.5287i −0.766442 1.32752i
\(289\) −0.105901 0.183427i −0.00622950 0.0107898i
\(290\) −0.414022 + 0.717107i −0.0243122 + 0.0421100i
\(291\) 13.0119 0.762773
\(292\) −16.7332 + 28.9828i −0.979237 + 1.69609i
\(293\) −8.88192 + 15.3839i −0.518887 + 0.898739i 0.480872 + 0.876791i \(0.340320\pi\)
−0.999759 + 0.0219482i \(0.993013\pi\)
\(294\) −3.74108 −0.218184
\(295\) 4.07012 7.04965i 0.236971 0.410446i
\(296\) −29.4026 50.9268i −1.70899 2.96006i
\(297\) −3.85331 6.67413i −0.223592 0.387272i
\(298\) −22.3791 −1.29639
\(299\) 7.61286 3.58182i 0.440263 0.207142i
\(300\) −33.4921 −1.93367
\(301\) −0.870541 1.50782i −0.0501771 0.0869094i
\(302\) −3.37411 5.84413i −0.194158 0.336292i
\(303\) 5.11371 8.85721i 0.293775 0.508833i
\(304\) 111.693 6.40606
\(305\) −2.41777 + 4.18770i −0.138441 + 0.239787i
\(306\) 6.46648 11.2003i 0.369664 0.640277i
\(307\) 18.0156 1.02821 0.514103 0.857729i \(-0.328125\pi\)
0.514103 + 0.857729i \(0.328125\pi\)
\(308\) −3.76249 + 6.51682i −0.214388 + 0.371330i
\(309\) −1.91653 3.31953i −0.109028 0.188842i
\(310\) −2.81593 4.87733i −0.159934 0.277014i
\(311\) 17.2545 0.978412 0.489206 0.872168i \(-0.337287\pi\)
0.489206 + 0.872168i \(0.337287\pi\)
\(312\) 42.8834 20.1765i 2.42780 1.14227i
\(313\) 6.81526 0.385221 0.192611 0.981275i \(-0.438305\pi\)
0.192611 + 0.981275i \(0.438305\pi\)
\(314\) −17.7071 30.6697i −0.999272 1.73079i
\(315\) −0.421404 0.729894i −0.0237434 0.0411249i
\(316\) 25.1578 43.5745i 1.41523 2.45126i
\(317\) −25.0770 −1.40847 −0.704233 0.709969i \(-0.748709\pi\)
−0.704233 + 0.709969i \(0.748709\pi\)
\(318\) 8.54423 14.7990i 0.479136 0.829889i
\(319\) −0.278170 + 0.481805i −0.0155745 + 0.0269759i
\(320\) 23.6818 1.32385
\(321\) −1.01438 + 1.75696i −0.0566172 + 0.0980639i
\(322\) 3.19809 + 5.53926i 0.178223 + 0.308691i
\(323\) 15.0724 + 26.1061i 0.838650 + 1.45258i
\(324\) −23.6796 −1.31553
\(325\) −1.34373 + 15.9912i −0.0745366 + 0.887033i
\(326\) 16.5217 0.915050
\(327\) −1.95934 3.39368i −0.108352 0.187671i
\(328\) 6.04151 + 10.4642i 0.333586 + 0.577789i
\(329\) −2.92921 + 5.07355i −0.161493 + 0.279714i
\(330\) 3.78389 0.208296
\(331\) 1.49767 2.59404i 0.0823193 0.142581i −0.821926 0.569594i \(-0.807101\pi\)
0.904246 + 0.427012i \(0.140434\pi\)
\(332\) −32.3555 + 56.0414i −1.77574 + 3.07567i
\(333\) 6.94405 0.380531
\(334\) 10.4862 18.1627i 0.573781 0.993817i
\(335\) 5.09852 + 8.83089i 0.278562 + 0.482483i
\(336\) 10.4900 + 18.1692i 0.572275 + 0.991209i
\(337\) −29.4888 −1.60636 −0.803179 0.595738i \(-0.796860\pi\)
−0.803179 + 0.595738i \(0.796860\pi\)
\(338\) −12.4173 33.4006i −0.675411 1.81675i
\(339\) −16.9503 −0.920613
\(340\) 8.47577 + 14.6805i 0.459663 + 0.796160i
\(341\) −1.89195 3.27695i −0.102455 0.177457i
\(342\) −11.3254 + 19.6162i −0.612407 + 1.06072i
\(343\) −1.00000 −0.0539949
\(344\) −8.38407 + 14.5216i −0.452039 + 0.782954i
\(345\) 1.18008 2.04395i 0.0635332 0.110043i
\(346\) 0.450797 0.0242350
\(347\) 2.99343 5.18477i 0.160696 0.278333i −0.774423 0.632668i \(-0.781960\pi\)
0.935118 + 0.354336i \(0.115293\pi\)
\(348\) 1.53370 + 2.65644i 0.0822149 + 0.142400i
\(349\) 15.1681 + 26.2719i 0.811929 + 1.40630i 0.911513 + 0.411272i \(0.134915\pi\)
−0.0995840 + 0.995029i \(0.531751\pi\)
\(350\) −12.2000 −0.652117
\(351\) −1.70476 + 20.2877i −0.0909931 + 1.08288i
\(352\) 31.2189 1.66398
\(353\) 14.3031 + 24.7738i 0.761280 + 1.31857i 0.942191 + 0.335075i \(0.108762\pi\)
−0.180912 + 0.983499i \(0.557905\pi\)
\(354\) −20.5465 35.5876i −1.09203 1.89146i
\(355\) 1.78425 3.09041i 0.0946982 0.164022i
\(356\) −9.70936 −0.514595
\(357\) −2.83112 + 4.90364i −0.149839 + 0.259528i
\(358\) 1.05344 1.82462i 0.0556762 0.0964340i
\(359\) 23.4618 1.23826 0.619132 0.785287i \(-0.287485\pi\)
0.619132 + 0.785287i \(0.287485\pi\)
\(360\) −4.05849 + 7.02952i −0.213901 + 0.370488i
\(361\) −16.8978 29.2678i −0.889357 1.54041i
\(362\) −13.5978 23.5522i −0.714687 1.23787i
\(363\) −12.4707 −0.654543
\(364\) 17.9878 8.46319i 0.942818 0.443592i
\(365\) 4.49827 0.235450
\(366\) 12.2052 + 21.1401i 0.637978 + 1.10501i
\(367\) −18.2598 31.6270i −0.953156 1.65091i −0.738533 0.674218i \(-0.764481\pi\)
−0.214623 0.976697i \(-0.568852\pi\)
\(368\) 17.9349 31.0641i 0.934920 1.61933i
\(369\) −1.42683 −0.0742778
\(370\) −6.20166 + 10.7416i −0.322409 + 0.558429i
\(371\) 2.28389 3.95582i 0.118574 0.205376i
\(372\) −20.8626 −1.08168
\(373\) 6.52491 11.3015i 0.337847 0.585168i −0.646181 0.763185i \(-0.723635\pi\)
0.984028 + 0.178017i \(0.0569680\pi\)
\(374\) 7.76033 + 13.4413i 0.401277 + 0.695033i
\(375\) 4.77947 + 8.27829i 0.246811 + 0.427489i
\(376\) 56.4218 2.90973
\(377\) 1.32988 0.625705i 0.0684925 0.0322254i
\(378\) −15.4779 −0.796095
\(379\) −15.3018 26.5036i −0.786003 1.36140i −0.928398 0.371587i \(-0.878814\pi\)
0.142395 0.989810i \(-0.454520\pi\)
\(380\) −14.8445 25.7114i −0.761505 1.31897i
\(381\) −3.70584 + 6.41870i −0.189856 + 0.328840i
\(382\) −27.1283 −1.38800
\(383\) 2.44299 4.23138i 0.124831 0.216213i −0.796836 0.604196i \(-0.793495\pi\)
0.921667 + 0.387982i \(0.126828\pi\)
\(384\) 28.5555 49.4596i 1.45722 2.52398i
\(385\) 1.01144 0.0515479
\(386\) 11.9247 20.6542i 0.606953 1.05127i
\(387\) −0.990038 1.71480i −0.0503265 0.0871680i
\(388\) −26.2825 45.5226i −1.33429 2.31106i
\(389\) −1.85425 −0.0940143 −0.0470072 0.998895i \(-0.514968\pi\)
−0.0470072 + 0.998895i \(0.514968\pi\)
\(390\) −8.20805 5.70543i −0.415631 0.288906i
\(391\) 9.68082 0.489580
\(392\) 4.81544 + 8.34058i 0.243216 + 0.421263i
\(393\) 7.72625 + 13.3823i 0.389738 + 0.675046i
\(394\) −35.6595 + 61.7641i −1.79650 + 3.11163i
\(395\) −6.76298 −0.340283
\(396\) −4.27896 + 7.41137i −0.215026 + 0.372435i
\(397\) −10.7567 + 18.6312i −0.539863 + 0.935071i 0.459048 + 0.888412i \(0.348191\pi\)
−0.998911 + 0.0466590i \(0.985143\pi\)
\(398\) −27.7753 −1.39225
\(399\) 4.95843 8.58825i 0.248232 0.429950i
\(400\) 34.2087 + 59.2513i 1.71044 + 2.96256i
\(401\) 7.28266 + 12.6139i 0.363678 + 0.629910i 0.988563 0.150808i \(-0.0481874\pi\)
−0.624885 + 0.780717i \(0.714854\pi\)
\(402\) 51.4760 2.56739
\(403\) −0.837022 + 9.96110i −0.0416950 + 0.496198i
\(404\) −41.3162 −2.05556
\(405\) 1.59141 + 2.75640i 0.0790776 + 0.136966i
\(406\) 0.558672 + 0.967649i 0.0277264 + 0.0480236i
\(407\) −4.16673 + 7.21698i −0.206537 + 0.357733i
\(408\) 54.5323 2.69975
\(409\) 11.0645 19.1643i 0.547105 0.947613i −0.451366 0.892339i \(-0.649063\pi\)
0.998471 0.0552745i \(-0.0176034\pi\)
\(410\) 1.27429 2.20713i 0.0629326 0.109003i
\(411\) −19.0739 −0.940847
\(412\) −7.74232 + 13.4101i −0.381437 + 0.660668i
\(413\) −5.49213 9.51264i −0.270250 0.468086i
\(414\) 3.63709 + 6.29962i 0.178753 + 0.309610i
\(415\) 8.69791 0.426964
\(416\) −67.7204 47.0726i −3.32027 2.30792i
\(417\) 14.2363 0.697153
\(418\) −13.5915 23.5411i −0.664780 1.15143i
\(419\) −1.68795 2.92362i −0.0824618 0.142828i 0.821845 0.569711i \(-0.192945\pi\)
−0.904307 + 0.426883i \(0.859612\pi\)
\(420\) 2.78831 4.82950i 0.136056 0.235655i
\(421\) −25.1101 −1.22379 −0.611895 0.790939i \(-0.709593\pi\)
−0.611895 + 0.790939i \(0.709593\pi\)
\(422\) 22.8582 39.5915i 1.11272 1.92729i
\(423\) −3.33130 + 5.76998i −0.161973 + 0.280546i
\(424\) −43.9917 −2.13643
\(425\) −9.23254 + 15.9912i −0.447844 + 0.775688i
\(426\) −9.00714 15.6008i −0.436397 0.755862i
\(427\) 3.26249 + 5.65079i 0.157883 + 0.273461i
\(428\) 8.19570 0.396154
\(429\) −5.51477 3.83332i −0.266255 0.185075i
\(430\) 3.53678 0.170558
\(431\) −5.39742 9.34861i −0.259985 0.450307i 0.706253 0.707960i \(-0.250384\pi\)
−0.966238 + 0.257653i \(0.917051\pi\)
\(432\) 43.3998 + 75.1707i 2.08808 + 3.61665i
\(433\) 7.25910 12.5731i 0.348850 0.604226i −0.637195 0.770702i \(-0.719906\pi\)
0.986045 + 0.166476i \(0.0532389\pi\)
\(434\) −7.59951 −0.364788
\(435\) 0.206147 0.357057i 0.00988398 0.0171196i
\(436\) −7.91526 + 13.7096i −0.379072 + 0.656572i
\(437\) −16.9550 −0.811068
\(438\) 11.3539 19.6656i 0.542512 0.939659i
\(439\) 7.21544 + 12.4975i 0.344374 + 0.596473i 0.985240 0.171180i \(-0.0547578\pi\)
−0.640866 + 0.767653i \(0.721425\pi\)
\(440\) −4.87054 8.43602i −0.232194 0.402172i
\(441\) −1.13727 −0.0541556
\(442\) 3.43327 40.8582i 0.163304 1.94343i
\(443\) −30.2430 −1.43689 −0.718445 0.695584i \(-0.755146\pi\)
−0.718445 + 0.695584i \(0.755146\pi\)
\(444\) 22.9734 + 39.7910i 1.09027 + 1.88840i
\(445\) 0.652525 + 1.13021i 0.0309326 + 0.0535769i
\(446\) 1.46697 2.54087i 0.0694632 0.120314i
\(447\) 11.1428 0.527038
\(448\) 15.9779 27.6745i 0.754883 1.30750i
\(449\) −15.6380 + 27.0858i −0.738003 + 1.27826i 0.215390 + 0.976528i \(0.430898\pi\)
−0.953393 + 0.301731i \(0.902435\pi\)
\(450\) −13.8747 −0.654058
\(451\) 0.856160 1.48291i 0.0403150 0.0698276i
\(452\) 34.2375 + 59.3010i 1.61039 + 2.78928i
\(453\) 1.68001 + 2.90987i 0.0789338 + 0.136717i
\(454\) 67.0645 3.14749
\(455\) −2.19403 1.52508i −0.102858 0.0714966i
\(456\) −95.5080 −4.47257
\(457\) −10.3233 17.8805i −0.482904 0.836415i 0.516903 0.856044i \(-0.327085\pi\)
−0.999807 + 0.0196293i \(0.993751\pi\)
\(458\) 6.48216 + 11.2274i 0.302892 + 0.524624i
\(459\) −11.7131 + 20.2877i −0.546721 + 0.946948i
\(460\) −9.53444 −0.444545
\(461\) −13.6480 + 23.6391i −0.635653 + 1.10098i 0.350724 + 0.936479i \(0.385936\pi\)
−0.986376 + 0.164504i \(0.947398\pi\)
\(462\) 2.55295 4.42184i 0.118774 0.205723i
\(463\) 5.65977 0.263032 0.131516 0.991314i \(-0.458016\pi\)
0.131516 + 0.991314i \(0.458016\pi\)
\(464\) 3.13303 5.42656i 0.145447 0.251922i
\(465\) 1.40209 + 2.42849i 0.0650202 + 0.112618i
\(466\) 28.1656 + 48.7842i 1.30474 + 2.25988i
\(467\) 42.2145 1.95345 0.976727 0.214486i \(-0.0688075\pi\)
0.976727 + 0.214486i \(0.0688075\pi\)
\(468\) 20.4570 9.62491i 0.945624 0.444912i
\(469\) 13.7597 0.635362
\(470\) −5.95031 10.3062i −0.274467 0.475391i
\(471\) 8.81661 + 15.2708i 0.406248 + 0.703642i
\(472\) −52.8940 + 91.6151i −2.43464 + 4.21692i
\(473\) 2.37626 0.109261
\(474\) −17.0702 + 29.5665i −0.784062 + 1.35803i
\(475\) 16.1699 28.0070i 0.741925 1.28505i
\(476\) 22.8740 1.04843
\(477\) 2.59740 4.49882i 0.118927 0.205987i
\(478\) 8.57220 + 14.8475i 0.392083 + 0.679108i
\(479\) −16.2658 28.1732i −0.743204 1.28727i −0.951029 0.309101i \(-0.899972\pi\)
0.207825 0.978166i \(-0.433361\pi\)
\(480\) −23.1358 −1.05600
\(481\) 19.9204 9.37247i 0.908293 0.427348i
\(482\) 33.2888 1.51626
\(483\) −1.59237 2.75807i −0.0724554 0.125496i
\(484\) 25.1893 + 43.6292i 1.14497 + 1.98314i
\(485\) −3.53267 + 6.11876i −0.160410 + 0.277839i
\(486\) −30.3663 −1.37744
\(487\) −13.4291 + 23.2600i −0.608533 + 1.05401i 0.382950 + 0.923769i \(0.374908\pi\)
−0.991482 + 0.130240i \(0.958425\pi\)
\(488\) 31.4206 54.4221i 1.42234 2.46357i
\(489\) −8.22634 −0.372008
\(490\) 1.01568 1.75921i 0.0458839 0.0794732i
\(491\) −21.8439 37.8348i −0.985802 1.70746i −0.638317 0.769774i \(-0.720369\pi\)
−0.347485 0.937685i \(-0.612964\pi\)
\(492\) −4.72046 8.17608i −0.212815 0.368606i
\(493\) 1.69113 0.0761649
\(494\) −6.01304 + 71.5590i −0.270539 + 3.21959i
\(495\) 1.15028 0.0517013
\(496\) 21.3090 + 36.9082i 0.956801 + 1.65723i
\(497\) −2.40763 4.17014i −0.107997 0.187056i
\(498\) 21.9541 38.0257i 0.983788 1.70397i
\(499\) −18.1020 −0.810355 −0.405177 0.914238i \(-0.632790\pi\)
−0.405177 + 0.914238i \(0.632790\pi\)
\(500\) 19.3079 33.4422i 0.863474 1.49558i
\(501\) −5.22122 + 9.04343i −0.233267 + 0.404030i
\(502\) 17.3082 0.772505
\(503\) 14.2077 24.6085i 0.633492 1.09724i −0.353341 0.935495i \(-0.614954\pi\)
0.986833 0.161745i \(-0.0517123\pi\)
\(504\) 5.47644 + 9.48548i 0.243940 + 0.422517i
\(505\) 2.77669 + 4.80937i 0.123561 + 0.214014i
\(506\) −8.72964 −0.388080
\(507\) 6.18272 + 16.6306i 0.274584 + 0.738589i
\(508\) 29.9413 1.32843
\(509\) −8.73956 15.1374i −0.387374 0.670952i 0.604721 0.796437i \(-0.293285\pi\)
−0.992095 + 0.125485i \(0.959951\pi\)
\(510\) −5.75104 9.96110i −0.254660 0.441085i
\(511\) 3.03494 5.25666i 0.134258 0.232541i
\(512\) −55.5280 −2.45402
\(513\) 20.5143 35.5319i 0.905730 1.56877i
\(514\) 33.3812 57.8179i 1.47238 2.55024i
\(515\) 2.08131 0.0917136
\(516\) 6.55080 11.3463i 0.288383 0.499494i
\(517\) −3.99785 6.92447i −0.175825 0.304538i
\(518\) 8.36839 + 14.4945i 0.367686 + 0.636851i
\(519\) −0.224458 −0.00985260
\(520\) −2.15479 + 25.6434i −0.0944939 + 1.12454i
\(521\) 19.3087 0.845931 0.422966 0.906146i \(-0.360989\pi\)
0.422966 + 0.906146i \(0.360989\pi\)
\(522\) 0.635360 + 1.10048i 0.0278090 + 0.0481665i
\(523\) 5.01144 + 8.68007i 0.219135 + 0.379553i 0.954544 0.298071i \(-0.0963431\pi\)
−0.735409 + 0.677624i \(0.763010\pi\)
\(524\) 31.2121 54.0610i 1.36351 2.36167i
\(525\) 6.07453 0.265114
\(526\) −13.1285 + 22.7393i −0.572432 + 0.991481i
\(527\) −5.75104 + 9.96110i −0.250519 + 0.433912i
\(528\) −28.6338 −1.24613
\(529\) 8.77750 15.2031i 0.381630 0.661003i
\(530\) 4.63942 + 8.03571i 0.201524 + 0.349049i
\(531\) −6.24602 10.8184i −0.271054 0.469479i
\(532\) −40.0616 −1.73689
\(533\) −4.09316 + 1.92581i −0.177294 + 0.0834162i
\(534\) 6.58807 0.285093
\(535\) −0.550798 0.954010i −0.0238131 0.0412454i
\(536\) −66.2588 114.764i −2.86194 4.95703i
\(537\) −0.524522 + 0.908500i −0.0226348 + 0.0392046i
\(538\) −80.5851 −3.47427
\(539\) 0.682410 1.18197i 0.0293935 0.0509110i
\(540\) 11.5360 19.9809i 0.496430 0.859842i
\(541\) 17.6153 0.757339 0.378670 0.925532i \(-0.376382\pi\)
0.378670 + 0.925532i \(0.376382\pi\)
\(542\) −0.411690 + 0.713067i −0.0176836 + 0.0306289i
\(543\) 6.77054 + 11.7269i 0.290552 + 0.503250i
\(544\) −47.4489 82.1839i −2.03435 3.52361i
\(545\) 2.12780 0.0911451
\(546\) −12.2052 + 5.74251i −0.522336 + 0.245757i
\(547\) 2.98425 0.127597 0.0637987 0.997963i \(-0.479678\pi\)
0.0637987 + 0.997963i \(0.479678\pi\)
\(548\) 38.5269 + 66.7306i 1.64579 + 2.85059i
\(549\) 3.71032 + 6.42647i 0.158353 + 0.274275i
\(550\) 8.32540 14.4200i 0.354996 0.614871i
\(551\) −2.96185 −0.126179
\(552\) −15.3359 + 26.5626i −0.652740 + 1.13058i
\(553\) −4.56291 + 7.90320i −0.194035 + 0.336078i
\(554\) 89.8279 3.81642
\(555\) 3.08789 5.34838i 0.131073 0.227026i
\(556\) −28.7555 49.8059i −1.21950 2.11224i
\(557\) −3.62798 6.28384i −0.153722 0.266255i 0.778871 0.627184i \(-0.215793\pi\)
−0.932593 + 0.360930i \(0.882459\pi\)
\(558\) −8.64268 −0.365874
\(559\) −5.15461 3.58298i −0.218017 0.151544i
\(560\) −11.3919 −0.481395
\(561\) −3.86397 6.69259i −0.163137 0.282561i
\(562\) 5.88622 + 10.1952i 0.248295 + 0.430060i
\(563\) −2.13967 + 3.70601i −0.0901762 + 0.156190i −0.907585 0.419868i \(-0.862076\pi\)
0.817409 + 0.576058i \(0.195410\pi\)
\(564\) −44.0845 −1.85629
\(565\) 4.60191 7.97074i 0.193604 0.335332i
\(566\) −28.9188 + 50.0888i −1.21555 + 2.10539i
\(567\) 4.29482 0.180365
\(568\) −23.1876 + 40.1621i −0.972929 + 1.68516i
\(569\) 9.88131 + 17.1149i 0.414246 + 0.717495i 0.995349 0.0963347i \(-0.0307119\pi\)
−0.581103 + 0.813830i \(0.697379\pi\)
\(570\) 10.0724 + 17.4459i 0.421886 + 0.730727i
\(571\) −19.9236 −0.833778 −0.416889 0.908957i \(-0.636880\pi\)
−0.416889 + 0.908957i \(0.636880\pi\)
\(572\) −2.27184 + 27.0364i −0.0949905 + 1.13045i
\(573\) 13.5075 0.564285
\(574\) −1.71950 2.97826i −0.0717704 0.124310i
\(575\) −5.19286 8.99430i −0.216557 0.375088i
\(576\) 18.1711 31.4733i 0.757129 1.31139i
\(577\) −28.7300 −1.19605 −0.598023 0.801479i \(-0.704047\pi\)
−0.598023 + 0.801479i \(0.704047\pi\)
\(578\) 0.290284 0.502787i 0.0120742 0.0209132i
\(579\) −5.93747 + 10.2840i −0.246753 + 0.427389i
\(580\) −1.66556 −0.0691587
\(581\) 5.86839 10.1643i 0.243462 0.421688i
\(582\) 17.8334 + 30.8883i 0.739218 + 1.28036i
\(583\) 3.11710 + 5.39897i 0.129097 + 0.223603i
\(584\) −58.4582 −2.41902
\(585\) −2.49520 1.73442i −0.103164 0.0717094i
\(586\) −48.6921 −2.01145
\(587\) −15.7694 27.3134i −0.650872 1.12734i −0.982912 0.184078i \(-0.941070\pi\)
0.332040 0.943265i \(-0.392263\pi\)
\(588\) −3.76249 6.51682i −0.155162 0.268749i
\(589\) 10.0724 17.4459i 0.415025 0.718845i
\(590\) 22.3130 0.918613
\(591\) 17.7553 30.7531i 0.730357 1.26502i
\(592\) 46.9298 81.2848i 1.92880 3.34079i
\(593\) −11.1181 −0.456564 −0.228282 0.973595i \(-0.573311\pi\)
−0.228282 + 0.973595i \(0.573311\pi\)
\(594\) 10.5622 18.2943i 0.433374 0.750626i
\(595\) −1.53727 2.66263i −0.0630218 0.109157i
\(596\) −22.5071 38.9835i −0.921928 1.59683i
\(597\) 13.8297 0.566010
\(598\) 18.9364 + 13.1627i 0.774368 + 0.538264i
\(599\) −7.29572 −0.298095 −0.149048 0.988830i \(-0.547621\pi\)
−0.149048 + 0.988830i \(0.547621\pi\)
\(600\) −29.2515 50.6652i −1.19419 2.06840i
\(601\) 0.586291 + 1.01548i 0.0239153 + 0.0414225i 0.877735 0.479146i \(-0.159053\pi\)
−0.853820 + 0.520568i \(0.825720\pi\)
\(602\) 2.38622 4.13306i 0.0972552 0.168451i
\(603\) 15.6484 0.637253
\(604\) 6.78683 11.7551i 0.276152 0.478310i
\(605\) 3.38573 5.86426i 0.137650 0.238416i
\(606\) 28.0342 1.13881
\(607\) −0.316919 + 0.548920i −0.0128633 + 0.0222800i −0.872385 0.488819i \(-0.837428\pi\)
0.859522 + 0.511099i \(0.170761\pi\)
\(608\) 83.1020 + 143.937i 3.37023 + 5.83741i
\(609\) −0.278170 0.481805i −0.0112720 0.0195237i
\(610\) −13.2546 −0.536664
\(611\) −1.76870 + 21.0487i −0.0715540 + 0.851538i
\(612\) 26.0139 1.05155
\(613\) 15.4275 + 26.7212i 0.623110 + 1.07926i 0.988903 + 0.148562i \(0.0474646\pi\)
−0.365793 + 0.930696i \(0.619202\pi\)
\(614\) 24.6911 + 42.7663i 0.996453 + 1.72591i
\(615\) −0.634485 + 1.09896i −0.0255849 + 0.0443143i
\(616\) −13.1444 −0.529603
\(617\) −16.9105 + 29.2898i −0.680790 + 1.17916i 0.293951 + 0.955821i \(0.405030\pi\)
−0.974740 + 0.223341i \(0.928304\pi\)
\(618\) 5.25338 9.09911i 0.211322 0.366020i
\(619\) −0.404797 −0.0162702 −0.00813509 0.999967i \(-0.502590\pi\)
−0.00813509 + 0.999967i \(0.502590\pi\)
\(620\) 5.66408 9.81048i 0.227475 0.393998i
\(621\) −6.58807 11.4109i −0.264370 0.457902i
\(622\) 23.6480 + 40.9595i 0.948197 + 1.64233i
\(623\) 1.76101 0.0705532
\(624\) 62.1128 + 43.1747i 2.48650 + 1.72837i
\(625\) 17.0636 0.682543
\(626\) 9.34059 + 16.1784i 0.373325 + 0.646618i
\(627\) 6.76736 + 11.7214i 0.270262 + 0.468108i
\(628\) 35.6169 61.6903i 1.42127 2.46171i
\(629\) 25.3316 1.01004
\(630\) 1.15510 2.00070i 0.0460204 0.0797097i
\(631\) −15.2254 + 26.3712i −0.606114 + 1.04982i 0.385761 + 0.922599i \(0.373939\pi\)
−0.991874 + 0.127221i \(0.959394\pi\)
\(632\) 87.8897 3.49606
\(633\) −11.3814 + 19.7131i −0.452369 + 0.783526i
\(634\) −34.3691 59.5290i −1.36497 2.36420i
\(635\) −2.01223 3.48528i −0.0798529 0.138309i
\(636\) 34.3724 1.36296
\(637\) −3.26249 + 1.53499i −0.129264 + 0.0608183i
\(638\) −1.52497 −0.0603743
\(639\) −2.73812 4.74256i −0.108318 0.187613i
\(640\) 15.5053 + 26.8560i 0.612903 + 1.06158i
\(641\) −4.82282 + 8.35337i −0.190490 + 0.329938i −0.945413 0.325875i \(-0.894341\pi\)
0.754923 + 0.655814i \(0.227674\pi\)
\(642\) −5.56100 −0.219475
\(643\) −4.06648 + 7.04335i −0.160366 + 0.277763i −0.935000 0.354647i \(-0.884601\pi\)
0.774634 + 0.632410i \(0.217934\pi\)
\(644\) −6.43278 + 11.1419i −0.253487 + 0.439053i
\(645\) −1.76101 −0.0693395
\(646\) −41.3146 + 71.5590i −1.62550 + 2.81545i
\(647\) 5.76136 + 9.97898i 0.226503 + 0.392314i 0.956769 0.290848i \(-0.0939375\pi\)
−0.730267 + 0.683162i \(0.760604\pi\)
\(648\) −20.6814 35.8213i −0.812443 1.40719i
\(649\) 14.9915 0.588469
\(650\) −39.8023 + 18.7268i −1.56118 + 0.734526i
\(651\) 3.78389 0.148302
\(652\) 16.6162 + 28.7801i 0.650740 + 1.12711i
\(653\) −21.2020 36.7229i −0.829697 1.43708i −0.898276 0.439431i \(-0.855180\pi\)
0.0685797 0.997646i \(-0.478153\pi\)
\(654\) 5.37072 9.30236i 0.210012 0.363751i
\(655\) −8.39054 −0.327845
\(656\) −9.64292 + 16.7020i −0.376493 + 0.652105i
\(657\) 3.45153 5.97823i 0.134657 0.233233i
\(658\) −16.0584 −0.626023
\(659\) 1.25044 2.16582i 0.0487101 0.0843684i −0.840642 0.541591i \(-0.817822\pi\)
0.889352 + 0.457222i \(0.151156\pi\)
\(660\) 3.80554 + 6.59139i 0.148130 + 0.256570i
\(661\) −7.41968 12.8513i −0.288592 0.499856i 0.684882 0.728654i \(-0.259854\pi\)
−0.973474 + 0.228798i \(0.926520\pi\)
\(662\) 8.21046 0.319109
\(663\) −1.70947 + 20.3438i −0.0663903 + 0.790088i
\(664\) −113.035 −4.38663
\(665\) 2.69237 + 4.66332i 0.104406 + 0.180836i
\(666\) 9.51710 + 16.4841i 0.368780 + 0.638746i
\(667\) −0.475592 + 0.823749i −0.0184150 + 0.0318957i
\(668\) 42.1849 1.63218
\(669\) −0.730424 + 1.26513i −0.0282398 + 0.0489128i
\(670\) −13.9755 + 24.2062i −0.539919 + 0.935167i
\(671\) −8.90541 −0.343790
\(672\) −15.6095 + 27.0364i −0.602148 + 1.04295i
\(673\) −19.8046 34.3025i −0.763410 1.32226i −0.941083 0.338175i \(-0.890190\pi\)
0.177674 0.984089i \(-0.443143\pi\)
\(674\) −40.4156 70.0019i −1.55675 2.69637i
\(675\) 25.1320 0.967330
\(676\) 45.6942 55.2221i 1.75747 2.12393i
\(677\) 17.0321 0.654596 0.327298 0.944921i \(-0.393862\pi\)
0.327298 + 0.944921i \(0.393862\pi\)
\(678\) −23.2311 40.2374i −0.892183 1.54531i
\(679\) 4.76691 + 8.25652i 0.182937 + 0.316856i
\(680\) −14.8052 + 25.6434i −0.567755 + 0.983380i
\(681\) −33.3922 −1.27959
\(682\) 5.18598 8.98238i 0.198581 0.343953i
\(683\) −16.4456 + 28.4846i −0.629272 + 1.08993i 0.358426 + 0.933558i \(0.383314\pi\)
−0.987698 + 0.156374i \(0.950020\pi\)
\(684\) −45.5608 −1.74206
\(685\) 5.17846 8.96936i 0.197859 0.342702i
\(686\) −1.37054 2.37385i −0.0523275 0.0906339i
\(687\) −3.22755 5.59028i −0.123139 0.213283i
\(688\) −26.7638 −1.02036
\(689\) 1.37905 16.4115i 0.0525375 0.625230i
\(690\) 6.46938 0.246285
\(691\) 11.8961 + 20.6047i 0.452550 + 0.783839i 0.998544 0.0539500i \(-0.0171812\pi\)
−0.545994 + 0.837789i \(0.683848\pi\)
\(692\) 0.453377 + 0.785272i 0.0172348 + 0.0298515i
\(693\) 0.776083 1.34421i 0.0294809 0.0510625i
\(694\) 16.4105 0.622933
\(695\) −3.86507 + 6.69449i −0.146610 + 0.253937i
\(696\) −2.67902 + 4.64020i −0.101548 + 0.175886i
\(697\) −5.20502 −0.197154
\(698\) −41.5769 + 72.0134i −1.57371 + 2.72575i
\(699\) −14.0240 24.2903i −0.530436 0.918742i
\(700\) −12.2698 21.2519i −0.463755 0.803247i
\(701\) 29.7796 1.12476 0.562380 0.826879i \(-0.309886\pi\)
0.562380 + 0.826879i \(0.309886\pi\)
\(702\) −50.4963 + 23.7583i −1.90586 + 0.896699i
\(703\) −44.3658 −1.67329
\(704\) 21.8069 + 37.7706i 0.821878 + 1.42353i
\(705\) 2.96273 + 5.13160i 0.111583 + 0.193267i
\(706\) −39.2061 + 67.9069i −1.47554 + 2.55571i
\(707\) 7.49361 0.281826
\(708\) 41.3281 71.5824i 1.55321 2.69023i
\(709\) −5.96518 + 10.3320i −0.224027 + 0.388026i −0.956027 0.293278i \(-0.905254\pi\)
0.732000 + 0.681305i \(0.238587\pi\)
\(710\) 9.78155 0.367095
\(711\) −5.18925 + 8.98805i −0.194612 + 0.337078i
\(712\) −8.48001 14.6878i −0.317802 0.550449i
\(713\) −3.23469 5.60265i −0.121140 0.209821i
\(714\) −15.5207 −0.580846
\(715\) 3.29982 1.55255i 0.123406 0.0580621i
\(716\) 4.23788 0.158377
\(717\) −4.26821 7.39275i −0.159399 0.276087i
\(718\) 32.1553 + 55.6946i 1.20002 + 2.07850i
\(719\) −16.1819 + 28.0279i −0.603484 + 1.04526i 0.388805 + 0.921320i \(0.372888\pi\)
−0.992289 + 0.123945i \(0.960446\pi\)
\(720\) −12.9556 −0.482827
\(721\) 1.40424 2.43221i 0.0522966 0.0905804i
\(722\) 46.3182 80.2255i 1.72379 2.98568i
\(723\) −16.5749 −0.616428
\(724\) 27.3513 47.3738i 1.01650 1.76063i
\(725\) −0.907137 1.57121i −0.0336902 0.0583532i
\(726\) −17.0916 29.6036i −0.634330 1.09869i
\(727\) −31.4897 −1.16789 −0.583943 0.811794i \(-0.698491\pi\)
−0.583943 + 0.811794i \(0.698491\pi\)
\(728\) 28.5130 + 19.8194i 1.05676 + 0.734556i
\(729\) 28.0042 1.03719
\(730\) 6.16507 + 10.6782i 0.228179 + 0.395218i
\(731\) −3.61162 6.25551i −0.133581 0.231369i
\(732\) −24.5501 + 42.5221i −0.907399 + 1.57166i
\(733\) 2.66224 0.0983321 0.0491661 0.998791i \(-0.484344\pi\)
0.0491661 + 0.998791i \(0.484344\pi\)
\(734\) 50.0517 86.6921i 1.84744 3.19986i
\(735\) −0.505722 + 0.875935i −0.0186538 + 0.0323094i
\(736\) 53.3755 1.96745
\(737\) −9.38973 + 16.2635i −0.345875 + 0.599073i
\(738\) −1.95553 3.38708i −0.0719840 0.124680i
\(739\) 17.7914 + 30.8156i 0.654467 + 1.13357i 0.982027 + 0.188739i \(0.0604402\pi\)
−0.327560 + 0.944830i \(0.606226\pi\)
\(740\) −24.9486 −0.917128
\(741\) 2.99397 35.6302i 0.109986 1.30891i
\(742\) 12.5207 0.459648
\(743\) −12.1203 20.9929i −0.444650 0.770156i 0.553378 0.832930i \(-0.313339\pi\)
−0.998028 + 0.0627740i \(0.980005\pi\)
\(744\) −18.2211 31.5599i −0.668018 1.15704i
\(745\) −3.02522 + 5.23983i −0.110835 + 0.191973i
\(746\) 35.7706 1.30966
\(747\) 6.67393 11.5596i 0.244186 0.422943i
\(748\) −15.6095 + 27.0364i −0.570739 + 0.988549i
\(749\) −1.48647 −0.0543144
\(750\) −13.1009 + 22.6915i −0.478378 + 0.828575i
\(751\) 14.5705 + 25.2368i 0.531684 + 0.920904i 0.999316 + 0.0369807i \(0.0117740\pi\)
−0.467632 + 0.883923i \(0.654893\pi\)
\(752\) 45.0277 + 77.9903i 1.64199 + 2.84401i
\(753\) −8.61799 −0.314057
\(754\) 3.30799 + 2.29939i 0.120470 + 0.0837388i
\(755\) −1.82446 −0.0663988
\(756\) −15.5664 26.9618i −0.566145 0.980592i
\(757\) 2.49495 + 4.32138i 0.0906805 + 0.157063i 0.907798 0.419408i \(-0.137762\pi\)
−0.817117 + 0.576472i \(0.804429\pi\)
\(758\) 41.9436 72.6485i 1.52346 2.63871i
\(759\) 4.34660 0.157772
\(760\) 25.9299 44.9119i 0.940576 1.62913i
\(761\) 5.91858 10.2513i 0.214548 0.371609i −0.738584 0.674161i \(-0.764505\pi\)
0.953133 + 0.302552i \(0.0978387\pi\)
\(762\) −20.3160 −0.735971
\(763\) 1.43561 2.48654i 0.0519724 0.0900189i
\(764\) −27.2835 47.2564i −0.987083 1.70968i
\(765\) −1.74828 3.02812i −0.0632094 0.109482i
\(766\) 13.3929 0.483904
\(767\) −32.5198 22.6045i −1.17422 0.816202i
\(768\) 69.3186 2.50132
\(769\) 17.9092 + 31.0196i 0.645821 + 1.11859i 0.984111 + 0.177553i \(0.0568180\pi\)
−0.338291 + 0.941042i \(0.609849\pi\)
\(770\) 1.38622 + 2.40101i 0.0499561 + 0.0865264i
\(771\) −16.6209 + 28.7883i −0.598588 + 1.03678i
\(772\) 47.9718 1.72654
\(773\) 9.97669 17.2801i 0.358837 0.621523i −0.628930 0.777462i \(-0.716507\pi\)
0.987767 + 0.155939i \(0.0498402\pi\)
\(774\) 2.71378 4.70040i 0.0975447 0.168952i
\(775\) 12.3396 0.443252
\(776\) 45.9095 79.5176i 1.64805 2.85451i