Properties

Label 77.2.e.b.67.1
Level $77$
Weight $2$
Character 77.67
Analytic conductor $0.615$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 77 = 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 77.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.614848095564\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.1783323.2
Defining polynomial: \(x^{6} - x^{5} + 5 x^{4} - 2 x^{3} + 19 x^{2} - 12 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(1.09935 - 1.90412i\) of defining polynomial
Character \(\chi\) \(=\) 77.67
Dual form 77.2.e.b.23.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.917122 - 1.58850i) q^{2} +(1.09935 - 1.90412i) q^{3} +(-0.682224 + 1.18165i) q^{4} +(0.317776 + 0.550404i) q^{5} -4.03293 q^{6} +(0.317776 + 2.62660i) q^{7} -1.16576 q^{8} +(-0.917122 - 1.58850i) q^{9} +O(q^{10})\) \(q+(-0.917122 - 1.58850i) q^{2} +(1.09935 - 1.90412i) q^{3} +(-0.682224 + 1.18165i) q^{4} +(0.317776 + 0.550404i) q^{5} -4.03293 q^{6} +(0.317776 + 2.62660i) q^{7} -1.16576 q^{8} +(-0.917122 - 1.58850i) q^{9} +(0.582878 - 1.00958i) q^{10} +(0.500000 - 0.866025i) q^{11} +(1.50000 + 2.59808i) q^{12} -1.80131 q^{13} +(3.88092 - 2.91370i) q^{14} +1.39738 q^{15} +(2.43359 + 4.21510i) q^{16} +(1.41712 - 2.45453i) q^{17} +(-1.68222 + 2.91370i) q^{18} +(2.78157 + 4.81782i) q^{19} -0.867178 q^{20} +(5.35071 + 2.28245i) q^{21} -1.83424 q^{22} +(-1.08288 - 1.87560i) q^{23} +(-1.28157 + 2.21974i) q^{24} +(2.29804 - 3.98032i) q^{25} +(1.65202 + 2.86138i) q^{26} +2.56314 q^{27} +(-3.32051 - 1.41643i) q^{28} -10.4303 q^{29} +(-1.28157 - 2.21974i) q^{30} +(-3.21516 + 5.56882i) q^{31} +(3.29804 - 5.71237i) q^{32} +(-1.09935 - 1.90412i) q^{33} -5.19869 q^{34} +(-1.34471 + 1.00958i) q^{35} +2.50273 q^{36} +(-3.03293 - 5.25320i) q^{37} +(5.10208 - 8.83705i) q^{38} +(-1.98026 + 3.42991i) q^{39} +(-0.370450 - 0.641637i) q^{40} +7.53566 q^{41} +(-1.28157 - 10.5929i) q^{42} -4.86718 q^{43} +(0.682224 + 1.18165i) q^{44} +(0.582878 - 1.00958i) q^{45} +(-1.98626 + 3.44031i) q^{46} +(1.41712 + 2.45453i) q^{47} +10.7014 q^{48} +(-6.79804 + 1.66934i) q^{49} -8.43032 q^{50} +(-3.11581 - 5.39675i) q^{51} +(1.22890 - 2.12851i) q^{52} +(-3.73490 + 6.46903i) q^{53} +(-2.35071 - 4.07155i) q^{54} +0.635552 q^{55} +(-0.370450 - 3.06197i) q^{56} +12.2316 q^{57} +(9.56587 + 16.5686i) q^{58} +(-5.90338 + 10.2250i) q^{59} +(-0.953328 + 1.65121i) q^{60} +(2.16576 + 3.75120i) q^{61} +11.7948 q^{62} +(3.88092 - 2.91370i) q^{63} -2.36445 q^{64} +(-0.572413 - 0.991448i) q^{65} +(-2.01647 + 3.49262i) q^{66} +(0.801309 - 1.38791i) q^{67} +(1.93359 + 3.34907i) q^{68} -4.76183 q^{69} +(2.83697 + 1.21017i) q^{70} +4.29204 q^{71} +(1.06914 + 1.85181i) q^{72} +(7.99673 - 13.8507i) q^{73} +(-5.56314 + 9.63564i) q^{74} +(-5.05267 - 8.75149i) q^{75} -7.59061 q^{76} +(2.43359 + 1.03810i) q^{77} +7.26456 q^{78} +(-2.38092 - 4.12387i) q^{79} +(-1.54667 + 2.67891i) q^{80} +(5.56914 - 9.64603i) q^{81} +(-6.91112 - 11.9704i) q^{82} -9.23163 q^{83} +(-6.34744 + 4.76550i) q^{84} +1.80131 q^{85} +(4.46379 + 7.73152i) q^{86} +(-11.4665 + 19.8606i) q^{87} +(-0.582878 + 1.00958i) q^{88} +(-0.182224 - 0.315621i) q^{89} -2.13828 q^{90} +(-0.572413 - 4.73131i) q^{91} +2.95506 q^{92} +(7.06914 + 12.2441i) q^{93} +(2.59935 - 4.50220i) q^{94} +(-1.76783 + 3.06197i) q^{95} +(-7.25136 - 12.5597i) q^{96} -2.59607 q^{97} +(8.88637 + 9.26770i) q^{98} -1.83424 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + q^{3} - 4q^{4} + 2q^{5} - 2q^{6} + 2q^{7} - 18q^{8} + O(q^{10}) \) \( 6q + q^{3} - 4q^{4} + 2q^{5} - 2q^{6} + 2q^{7} - 18q^{8} + 9q^{10} + 3q^{11} + 9q^{12} - 22q^{13} + 12q^{14} - 14q^{15} - 2q^{16} + 3q^{17} - 10q^{18} + 11q^{19} + 28q^{20} + 10q^{21} - 12q^{23} - 2q^{24} - 3q^{25} - q^{26} + 4q^{27} + 13q^{28} - 18q^{29} - 2q^{30} + 3q^{31} + 3q^{32} - q^{33} - 20q^{34} + 9q^{35} - 18q^{36} + 4q^{37} - 8q^{38} + 5q^{39} + 3q^{40} - 10q^{41} - 2q^{42} + 4q^{43} + 4q^{44} + 9q^{45} + 10q^{46} + 3q^{47} + 20q^{48} - 24q^{49} - 6q^{50} - 2q^{51} + 7q^{52} - 17q^{53} + 8q^{54} + 4q^{55} + 3q^{56} + 40q^{57} + 13q^{58} - 8q^{59} - 6q^{60} + 24q^{61} + 26q^{62} + 12q^{63} - 14q^{64} - 15q^{65} - q^{66} + 16q^{67} - 5q^{68} - 6q^{69} - 27q^{70} + 14q^{71} - 10q^{72} + 20q^{73} - 22q^{74} - 25q^{75} - 78q^{76} - 2q^{77} - 12q^{78} - 3q^{79} - 9q^{80} + 17q^{81} - 41q^{82} - 22q^{83} + 12q^{84} + 22q^{85} + 21q^{86} - 30q^{87} - 9q^{88} - q^{89} + 20q^{90} - 15q^{91} + 50q^{92} + 26q^{93} + 10q^{94} + 17q^{95} - 27q^{96} + 18q^{97} - 24q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/77\mathbb{Z}\right)^\times\).

\(n\) \(45\) \(57\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.917122 1.58850i −0.648503 1.12324i −0.983481 0.181014i \(-0.942062\pi\)
0.334978 0.942226i \(-0.391271\pi\)
\(3\) 1.09935 1.90412i 0.634707 1.09935i −0.351870 0.936049i \(-0.614454\pi\)
0.986577 0.163297i \(-0.0522127\pi\)
\(4\) −0.682224 + 1.18165i −0.341112 + 0.590823i
\(5\) 0.317776 + 0.550404i 0.142114 + 0.246148i 0.928292 0.371851i \(-0.121277\pi\)
−0.786179 + 0.617999i \(0.787943\pi\)
\(6\) −4.03293 −1.64644
\(7\) 0.317776 + 2.62660i 0.120108 + 0.992761i
\(8\) −1.16576 −0.412157
\(9\) −0.917122 1.58850i −0.305707 0.529500i
\(10\) 0.582878 1.00958i 0.184322 0.319256i
\(11\) 0.500000 0.866025i 0.150756 0.261116i
\(12\) 1.50000 + 2.59808i 0.433013 + 0.750000i
\(13\) −1.80131 −0.499593 −0.249797 0.968298i \(-0.580364\pi\)
−0.249797 + 0.968298i \(0.580364\pi\)
\(14\) 3.88092 2.91370i 1.03722 0.778718i
\(15\) 1.39738 0.360803
\(16\) 2.43359 + 4.21510i 0.608397 + 1.05377i
\(17\) 1.41712 2.45453i 0.343702 0.595310i −0.641415 0.767194i \(-0.721652\pi\)
0.985117 + 0.171884i \(0.0549855\pi\)
\(18\) −1.68222 + 2.91370i −0.396504 + 0.686765i
\(19\) 2.78157 + 4.81782i 0.638136 + 1.10528i 0.985841 + 0.167680i \(0.0536275\pi\)
−0.347706 + 0.937604i \(0.613039\pi\)
\(20\) −0.867178 −0.193907
\(21\) 5.35071 + 2.28245i 1.16762 + 0.498073i
\(22\) −1.83424 −0.391062
\(23\) −1.08288 1.87560i −0.225796 0.391090i 0.730762 0.682632i \(-0.239165\pi\)
−0.956558 + 0.291542i \(0.905832\pi\)
\(24\) −1.28157 + 2.21974i −0.261599 + 0.453103i
\(25\) 2.29804 3.98032i 0.459607 0.796063i
\(26\) 1.65202 + 2.86138i 0.323988 + 0.561163i
\(27\) 2.56314 0.493276
\(28\) −3.32051 1.41643i −0.627517 0.267680i
\(29\) −10.4303 −1.93686 −0.968431 0.249283i \(-0.919805\pi\)
−0.968431 + 0.249283i \(0.919805\pi\)
\(30\) −1.28157 2.21974i −0.233982 0.405268i
\(31\) −3.21516 + 5.56882i −0.577460 + 1.00019i 0.418310 + 0.908304i \(0.362623\pi\)
−0.995770 + 0.0918849i \(0.970711\pi\)
\(32\) 3.29804 5.71237i 0.583016 1.00981i
\(33\) −1.09935 1.90412i −0.191372 0.331465i
\(34\) −5.19869 −0.891568
\(35\) −1.34471 + 1.00958i −0.227297 + 0.170649i
\(36\) 2.50273 0.417122
\(37\) −3.03293 5.25320i −0.498611 0.863620i 0.501387 0.865223i \(-0.332823\pi\)
−0.999999 + 0.00160274i \(0.999490\pi\)
\(38\) 5.10208 8.83705i 0.827666 1.43356i
\(39\) −1.98026 + 3.42991i −0.317096 + 0.549226i
\(40\) −0.370450 0.641637i −0.0585732 0.101452i
\(41\) 7.53566 1.17687 0.588436 0.808543i \(-0.299744\pi\)
0.588436 + 0.808543i \(0.299744\pi\)
\(42\) −1.28157 10.5929i −0.197750 1.63452i
\(43\) −4.86718 −0.742238 −0.371119 0.928585i \(-0.621026\pi\)
−0.371119 + 0.928585i \(0.621026\pi\)
\(44\) 0.682224 + 1.18165i 0.102849 + 0.178140i
\(45\) 0.582878 1.00958i 0.0868904 0.150499i
\(46\) −1.98626 + 3.44031i −0.292858 + 0.507246i
\(47\) 1.41712 + 2.45453i 0.206708 + 0.358030i 0.950676 0.310187i \(-0.100392\pi\)
−0.743967 + 0.668216i \(0.767058\pi\)
\(48\) 10.7014 1.54462
\(49\) −6.79804 + 1.66934i −0.971148 + 0.238477i
\(50\) −8.43032 −1.19223
\(51\) −3.11581 5.39675i −0.436301 0.755696i
\(52\) 1.22890 2.12851i 0.170417 0.295171i
\(53\) −3.73490 + 6.46903i −0.513028 + 0.888590i 0.486858 + 0.873481i \(0.338143\pi\)
−0.999886 + 0.0151089i \(0.995190\pi\)
\(54\) −2.35071 4.07155i −0.319891 0.554068i
\(55\) 0.635552 0.0856978
\(56\) −0.370450 3.06197i −0.0495034 0.409174i
\(57\) 12.2316 1.62012
\(58\) 9.56587 + 16.5686i 1.25606 + 2.17556i
\(59\) −5.90338 + 10.2250i −0.768555 + 1.33118i 0.169791 + 0.985480i \(0.445691\pi\)
−0.938346 + 0.345696i \(0.887643\pi\)
\(60\) −0.953328 + 1.65121i −0.123074 + 0.213171i
\(61\) 2.16576 + 3.75120i 0.277297 + 0.480292i 0.970712 0.240246i \(-0.0772282\pi\)
−0.693415 + 0.720538i \(0.743895\pi\)
\(62\) 11.7948 1.49794
\(63\) 3.88092 2.91370i 0.488949 0.367091i
\(64\) −2.36445 −0.295556
\(65\) −0.572413 0.991448i −0.0709990 0.122974i
\(66\) −2.01647 + 3.49262i −0.248210 + 0.429912i
\(67\) 0.801309 1.38791i 0.0978954 0.169560i −0.812918 0.582378i \(-0.802122\pi\)
0.910813 + 0.412818i \(0.135456\pi\)
\(68\) 1.93359 + 3.34907i 0.234482 + 0.406135i
\(69\) −4.76183 −0.573257
\(70\) 2.83697 + 1.21017i 0.339083 + 0.144643i
\(71\) 4.29204 0.509371 0.254685 0.967024i \(-0.418028\pi\)
0.254685 + 0.967024i \(0.418028\pi\)
\(72\) 1.06914 + 1.85181i 0.125999 + 0.218237i
\(73\) 7.99673 13.8507i 0.935946 1.62111i 0.163008 0.986625i \(-0.447880\pi\)
0.772938 0.634482i \(-0.218786\pi\)
\(74\) −5.56314 + 9.63564i −0.646702 + 1.12012i
\(75\) −5.05267 8.75149i −0.583432 1.01053i
\(76\) −7.59061 −0.870703
\(77\) 2.43359 + 1.03810i 0.277333 + 0.118302i
\(78\) 7.26456 0.822549
\(79\) −2.38092 4.12387i −0.267874 0.463971i 0.700439 0.713713i \(-0.252988\pi\)
−0.968313 + 0.249741i \(0.919654\pi\)
\(80\) −1.54667 + 2.67891i −0.172923 + 0.299512i
\(81\) 5.56914 9.64603i 0.618793 1.07178i
\(82\) −6.91112 11.9704i −0.763206 1.32191i
\(83\) −9.23163 −1.01330 −0.506651 0.862151i \(-0.669117\pi\)
−0.506651 + 0.862151i \(0.669117\pi\)
\(84\) −6.34744 + 4.76550i −0.692562 + 0.519959i
\(85\) 1.80131 0.195379
\(86\) 4.46379 + 7.73152i 0.481343 + 0.833711i
\(87\) −11.4665 + 19.8606i −1.22934 + 2.12928i
\(88\) −0.582878 + 1.00958i −0.0621350 + 0.107621i
\(89\) −0.182224 0.315621i −0.0193157 0.0334558i 0.856206 0.516635i \(-0.172815\pi\)
−0.875522 + 0.483179i \(0.839482\pi\)
\(90\) −2.13828 −0.225395
\(91\) −0.572413 4.73131i −0.0600051 0.495977i
\(92\) 2.95506 0.308087
\(93\) 7.06914 + 12.2441i 0.733036 + 1.26966i
\(94\) 2.59935 4.50220i 0.268102 0.464366i
\(95\) −1.76783 + 3.06197i −0.181376 + 0.314152i
\(96\) −7.25136 12.5597i −0.740089 1.28187i
\(97\) −2.59607 −0.263591 −0.131796 0.991277i \(-0.542074\pi\)
−0.131796 + 0.991277i \(0.542074\pi\)
\(98\) 8.88637 + 9.26770i 0.897659 + 0.936179i
\(99\) −1.83424 −0.184348
\(100\) 3.13555 + 5.43094i 0.313555 + 0.543094i
\(101\) 4.95006 8.57375i 0.492549 0.853120i −0.507414 0.861702i \(-0.669399\pi\)
0.999963 + 0.00858243i \(0.00273191\pi\)
\(102\) −5.71516 + 9.89894i −0.565885 + 0.980142i
\(103\) −3.11581 5.39675i −0.307010 0.531757i 0.670697 0.741732i \(-0.265995\pi\)
−0.977707 + 0.209975i \(0.932662\pi\)
\(104\) 2.09989 0.205911
\(105\) 0.444055 + 3.67036i 0.0433353 + 0.358191i
\(106\) 13.7014 1.33080
\(107\) −5.54940 9.61185i −0.536481 0.929212i −0.999090 0.0426499i \(-0.986420\pi\)
0.462609 0.886562i \(-0.346913\pi\)
\(108\) −1.74864 + 3.02873i −0.168263 + 0.291439i
\(109\) 7.15202 12.3877i 0.685039 1.18652i −0.288385 0.957514i \(-0.593118\pi\)
0.973424 0.229008i \(-0.0735483\pi\)
\(110\) −0.582878 1.00958i −0.0555753 0.0962592i
\(111\) −13.3370 −1.26589
\(112\) −10.2980 + 7.73152i −0.973073 + 0.730560i
\(113\) −8.68942 −0.817432 −0.408716 0.912662i \(-0.634023\pi\)
−0.408716 + 0.912662i \(0.634023\pi\)
\(114\) −11.2179 19.4300i −1.05065 1.81978i
\(115\) 0.688225 1.19204i 0.0641774 0.111158i
\(116\) 7.11581 12.3249i 0.660687 1.14434i
\(117\) 1.65202 + 2.86138i 0.152729 + 0.264535i
\(118\) 21.6565 1.99364
\(119\) 6.89738 + 2.94222i 0.632282 + 0.269713i
\(120\) −1.62901 −0.148707
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) 3.97252 6.88061i 0.359655 0.622942i
\(123\) 8.28430 14.3488i 0.746970 1.29379i
\(124\) −4.38692 7.59836i −0.393957 0.682353i
\(125\) 6.09880 0.545494
\(126\) −8.18768 3.49262i −0.729417 0.311148i
\(127\) 20.9989 1.86335 0.931676 0.363290i \(-0.118346\pi\)
0.931676 + 0.363290i \(0.118346\pi\)
\(128\) −4.42759 7.66881i −0.391347 0.677833i
\(129\) −5.35071 + 9.26770i −0.471104 + 0.815976i
\(130\) −1.04994 + 1.81856i −0.0920862 + 0.159498i
\(131\) 6.85071 + 11.8658i 0.598549 + 1.03672i 0.993035 + 0.117816i \(0.0375893\pi\)
−0.394486 + 0.918902i \(0.629077\pi\)
\(132\) 3.00000 0.261116
\(133\) −11.7706 + 8.83705i −1.02064 + 0.766270i
\(134\) −2.93959 −0.253942
\(135\) 0.814504 + 1.41076i 0.0701013 + 0.121419i
\(136\) −1.65202 + 2.86138i −0.141659 + 0.245361i
\(137\) −3.63228 + 6.29129i −0.310327 + 0.537501i −0.978433 0.206564i \(-0.933772\pi\)
0.668106 + 0.744066i \(0.267105\pi\)
\(138\) 4.36718 + 7.56417i 0.371759 + 0.643905i
\(139\) −2.60262 −0.220751 −0.110376 0.993890i \(-0.535205\pi\)
−0.110376 + 0.993890i \(0.535205\pi\)
\(140\) −0.275568 2.27773i −0.0232898 0.192503i
\(141\) 6.23163 0.524798
\(142\) −3.93632 6.81790i −0.330328 0.572146i
\(143\) −0.900654 + 1.55998i −0.0753165 + 0.130452i
\(144\) 4.46379 7.73152i 0.371983 0.644293i
\(145\) −3.31450 5.74089i −0.275255 0.476755i
\(146\) −29.3359 −2.42786
\(147\) −4.29476 + 14.7795i −0.354226 + 1.21899i
\(148\) 8.27656 0.680329
\(149\) 0.500000 + 0.866025i 0.0409616 + 0.0709476i 0.885779 0.464107i \(-0.153625\pi\)
−0.844818 + 0.535054i \(0.820291\pi\)
\(150\) −9.26783 + 16.0524i −0.756715 + 1.31067i
\(151\) −0.867720 + 1.50294i −0.0706140 + 0.122307i −0.899171 0.437598i \(-0.855829\pi\)
0.828557 + 0.559905i \(0.189163\pi\)
\(152\) −3.24263 5.61641i −0.263012 0.455551i
\(153\) −5.19869 −0.420289
\(154\) −0.582878 4.81782i −0.0469697 0.388231i
\(155\) −4.08680 −0.328260
\(156\) −2.70196 4.67994i −0.216330 0.374695i
\(157\) 3.96980 6.87589i 0.316824 0.548756i −0.662999 0.748620i \(-0.730717\pi\)
0.979824 + 0.199864i \(0.0640502\pi\)
\(158\) −4.36718 + 7.56417i −0.347434 + 0.601773i
\(159\) 8.21189 + 14.2234i 0.651245 + 1.12799i
\(160\) 4.19215 0.331418
\(161\) 4.58234 3.44031i 0.361139 0.271134i
\(162\) −20.4303 −1.60516
\(163\) 8.00273 + 13.8611i 0.626822 + 1.08569i 0.988185 + 0.153263i \(0.0489781\pi\)
−0.361363 + 0.932425i \(0.617689\pi\)
\(164\) −5.14101 + 8.90449i −0.401446 + 0.695324i
\(165\) 0.698691 1.21017i 0.0543930 0.0942115i
\(166\) 8.46652 + 14.6644i 0.657130 + 1.13818i
\(167\) 1.15921 0.0897026 0.0448513 0.998994i \(-0.485719\pi\)
0.0448513 + 0.998994i \(0.485719\pi\)
\(168\) −6.23763 2.66079i −0.481243 0.205284i
\(169\) −9.75529 −0.750407
\(170\) −1.65202 2.86138i −0.126704 0.219458i
\(171\) 5.10208 8.83705i 0.390165 0.675786i
\(172\) 3.32051 5.75128i 0.253186 0.438531i
\(173\) 0.496728 + 0.860358i 0.0377655 + 0.0654118i 0.884290 0.466937i \(-0.154643\pi\)
−0.846525 + 0.532349i \(0.821309\pi\)
\(174\) 42.0648 3.18892
\(175\) 11.1850 + 4.77117i 0.845503 + 0.360667i
\(176\) 4.86718 0.366877
\(177\) 12.9797 + 22.4815i 0.975615 + 1.68982i
\(178\) −0.334243 + 0.578926i −0.0250526 + 0.0433924i
\(179\) 9.83097 17.0277i 0.734801 1.27271i −0.220009 0.975498i \(-0.570609\pi\)
0.954810 0.297215i \(-0.0960579\pi\)
\(180\) 0.795307 + 1.37751i 0.0592787 + 0.102674i
\(181\) −23.8726 −1.77444 −0.887220 0.461347i \(-0.847366\pi\)
−0.887220 + 0.461347i \(0.847366\pi\)
\(182\) −6.99073 + 5.24847i −0.518187 + 0.389042i
\(183\) 9.52366 0.704009
\(184\) 1.26237 + 2.18649i 0.0930634 + 0.161190i
\(185\) 1.92759 3.33868i 0.141719 0.245465i
\(186\) 12.9665 22.4587i 0.950752 1.64675i
\(187\) −1.41712 2.45453i −0.103630 0.179493i
\(188\) −3.86718 −0.282043
\(189\) 0.814504 + 6.73234i 0.0592465 + 0.489705i
\(190\) 6.48527 0.470491
\(191\) 5.56587 + 9.64037i 0.402732 + 0.697553i 0.994055 0.108883i \(-0.0347273\pi\)
−0.591322 + 0.806435i \(0.701394\pi\)
\(192\) −2.59935 + 4.50220i −0.187592 + 0.324918i
\(193\) −1.80731 + 3.13035i −0.130093 + 0.225328i −0.923712 0.383087i \(-0.874861\pi\)
0.793619 + 0.608415i \(0.208194\pi\)
\(194\) 2.38092 + 4.12387i 0.170940 + 0.296076i
\(195\) −2.51712 −0.180255
\(196\) 2.66521 9.17174i 0.190372 0.655124i
\(197\) 2.41831 0.172298 0.0861489 0.996282i \(-0.472544\pi\)
0.0861489 + 0.996282i \(0.472544\pi\)
\(198\) 1.68222 + 2.91370i 0.119550 + 0.207067i
\(199\) 9.24809 16.0182i 0.655580 1.13550i −0.326168 0.945312i \(-0.605758\pi\)
0.981748 0.190186i \(-0.0609091\pi\)
\(200\) −2.67895 + 4.64008i −0.189431 + 0.328103i
\(201\) −1.76183 3.05158i −0.124270 0.215242i
\(202\) −18.1592 −1.27768
\(203\) −3.31450 27.3963i −0.232633 1.92284i
\(204\) 8.50273 0.595310
\(205\) 2.39465 + 4.14766i 0.167250 + 0.289685i
\(206\) −5.71516 + 9.89894i −0.398194 + 0.689692i
\(207\) −1.98626 + 3.44031i −0.138055 + 0.239118i
\(208\) −4.38364 7.59270i −0.303951 0.526459i
\(209\) 5.56314 0.384810
\(210\) 5.42312 4.07155i 0.374231 0.280964i
\(211\) −7.85517 −0.540773 −0.270386 0.962752i \(-0.587151\pi\)
−0.270386 + 0.962752i \(0.587151\pi\)
\(212\) −5.09607 8.82666i −0.350000 0.606217i
\(213\) 4.71843 8.17256i 0.323302 0.559975i
\(214\) −10.1790 + 17.6305i −0.695819 + 1.20519i
\(215\) −1.54667 2.67891i −0.105482 0.182700i
\(216\) −2.98800 −0.203307
\(217\) −15.6487 6.67529i −1.06231 0.453148i
\(218\) −26.2371 −1.77700
\(219\) −17.5823 30.4535i −1.18810 2.05786i
\(220\) −0.433589 + 0.750998i −0.0292326 + 0.0506323i
\(221\) −2.55267 + 4.42136i −0.171711 + 0.297413i
\(222\) 12.2316 + 21.1858i 0.820933 + 1.42190i
\(223\) 20.3370 1.36186 0.680932 0.732346i \(-0.261575\pi\)
0.680932 + 0.732346i \(0.261575\pi\)
\(224\) 16.0521 + 6.84736i 1.07253 + 0.457509i
\(225\) −8.43032 −0.562021
\(226\) 7.96925 + 13.8032i 0.530107 + 0.918172i
\(227\) −3.60981 + 6.25238i −0.239592 + 0.414985i −0.960597 0.277944i \(-0.910347\pi\)
0.721006 + 0.692929i \(0.243680\pi\)
\(228\) −8.34471 + 14.4535i −0.552642 + 0.957204i
\(229\) −6.03566 10.4541i −0.398848 0.690825i 0.594736 0.803921i \(-0.297257\pi\)
−0.993584 + 0.113096i \(0.963923\pi\)
\(230\) −2.52475 −0.166477
\(231\) 4.65202 3.49262i 0.306080 0.229798i
\(232\) 12.1592 0.798291
\(233\) 3.77110 + 6.53174i 0.247053 + 0.427909i 0.962707 0.270547i \(-0.0872044\pi\)
−0.715654 + 0.698455i \(0.753871\pi\)
\(234\) 3.03020 5.24847i 0.198091 0.343103i
\(235\) −0.900654 + 1.55998i −0.0587522 + 0.101762i
\(236\) −8.05486 13.9514i −0.524327 0.908161i
\(237\) −10.4698 −0.680086
\(238\) −1.65202 13.6549i −0.107084 0.885114i
\(239\) −9.84625 −0.636901 −0.318450 0.947940i \(-0.603162\pi\)
−0.318450 + 0.947940i \(0.603162\pi\)
\(240\) 3.40065 + 5.89011i 0.219511 + 0.380205i
\(241\) 0.837515 1.45062i 0.0539491 0.0934426i −0.837790 0.545993i \(-0.816152\pi\)
0.891739 + 0.452551i \(0.149486\pi\)
\(242\) −0.917122 + 1.58850i −0.0589548 + 0.102113i
\(243\) −8.40011 14.5494i −0.538867 0.933346i
\(244\) −5.91013 −0.378357
\(245\) −3.07906 3.21119i −0.196714 0.205156i
\(246\) −30.3908 −1.93765
\(247\) −5.01047 8.67838i −0.318808 0.552192i
\(248\) 3.74809 6.49189i 0.238004 0.412235i
\(249\) −10.1487 + 17.5781i −0.643151 + 1.11397i
\(250\) −5.59334 9.68796i −0.353754 0.612720i
\(251\) 19.7738 1.24811 0.624057 0.781379i \(-0.285483\pi\)
0.624057 + 0.781379i \(0.285483\pi\)
\(252\) 0.795307 + 6.57367i 0.0500997 + 0.414102i
\(253\) −2.16576 −0.136160
\(254\) −19.2586 33.3568i −1.20839 2.09299i
\(255\) 1.98026 3.42991i 0.124009 0.214789i
\(256\) −10.4857 + 18.1618i −0.655358 + 1.13511i
\(257\) −1.35998 2.35556i −0.0848335 0.146936i 0.820487 0.571665i \(-0.193702\pi\)
−0.905320 + 0.424730i \(0.860369\pi\)
\(258\) 19.6290 1.22205
\(259\) 12.8342 9.63564i 0.797481 0.598730i
\(260\) 1.56205 0.0968745
\(261\) 9.56587 + 16.5686i 0.592112 + 1.02557i
\(262\) 12.5659 21.7647i 0.776322 1.34463i
\(263\) −6.34744 + 10.9941i −0.391400 + 0.677924i −0.992634 0.121148i \(-0.961342\pi\)
0.601235 + 0.799073i \(0.294676\pi\)
\(264\) 1.28157 + 2.21974i 0.0788752 + 0.136616i
\(265\) −4.74744 −0.291633
\(266\) 24.8327 + 10.5929i 1.52259 + 0.649492i
\(267\) −0.801309 −0.0490393
\(268\) 1.09334 + 1.89373i 0.0667866 + 0.115678i
\(269\) 3.54667 6.14302i 0.216244 0.374546i −0.737412 0.675443i \(-0.763953\pi\)
0.953657 + 0.300896i \(0.0972859\pi\)
\(270\) 1.49400 2.58768i 0.0909219 0.157481i
\(271\) 9.10808 + 15.7757i 0.553276 + 0.958303i 0.998035 + 0.0626524i \(0.0199559\pi\)
−0.444759 + 0.895650i \(0.646711\pi\)
\(272\) 13.7948 0.836430
\(273\) −9.63828 4.11141i −0.583335 0.248834i
\(274\) 13.3250 0.804991
\(275\) −2.29804 3.98032i −0.138577 0.240022i
\(276\) 3.24864 5.62680i 0.195545 0.338694i
\(277\) −6.92432 + 11.9933i −0.416042 + 0.720606i −0.995537 0.0943700i \(-0.969916\pi\)
0.579495 + 0.814976i \(0.303250\pi\)
\(278\) 2.38692 + 4.13426i 0.143158 + 0.247956i
\(279\) 11.7948 0.706134
\(280\) 1.56760 1.17692i 0.0936822 0.0703344i
\(281\) 21.0329 1.25472 0.627360 0.778730i \(-0.284136\pi\)
0.627360 + 0.778730i \(0.284136\pi\)
\(282\) −5.71516 9.89894i −0.340333 0.589474i
\(283\) −0.176223 + 0.305226i −0.0104753 + 0.0181438i −0.871216 0.490901i \(-0.836668\pi\)
0.860740 + 0.509044i \(0.170001\pi\)
\(284\) −2.92813 + 5.07167i −0.173753 + 0.300948i
\(285\) 3.88692 + 6.73234i 0.230241 + 0.398789i
\(286\) 3.30404 0.195372
\(287\) 2.39465 + 19.7932i 0.141352 + 1.16835i
\(288\) −12.0988 −0.712929
\(289\) 4.48353 + 7.76571i 0.263737 + 0.456806i
\(290\) −6.07961 + 10.5302i −0.357007 + 0.618354i
\(291\) −2.85398 + 4.94324i −0.167303 + 0.289778i
\(292\) 10.9111 + 18.8986i 0.638525 + 1.10596i
\(293\) −3.46325 −0.202325 −0.101163 0.994870i \(-0.532256\pi\)
−0.101163 + 0.994870i \(0.532256\pi\)
\(294\) 27.4160 6.73234i 1.59894 0.392638i
\(295\) −7.50381 −0.436889
\(296\) 3.53566 + 6.12395i 0.205506 + 0.355947i
\(297\) 1.28157 2.21974i 0.0743642 0.128803i
\(298\) 0.917122 1.58850i 0.0531274 0.0920194i
\(299\) 1.95060 + 3.37854i 0.112806 + 0.195386i
\(300\) 13.7882 0.796063
\(301\) −1.54667 12.7841i −0.0891487 0.736864i
\(302\) 3.18322 0.183174
\(303\) −10.8836 18.8510i −0.625249 1.08296i
\(304\) −13.5384 + 23.4492i −0.776480 + 1.34490i
\(305\) −1.37645 + 2.38408i −0.0788154 + 0.136512i
\(306\) 4.76783 + 8.25813i 0.272559 + 0.472086i
\(307\) −6.51473 −0.371815 −0.185908 0.982567i \(-0.559523\pi\)
−0.185908 + 0.982567i \(0.559523\pi\)
\(308\) −2.88692 + 2.16743i −0.164497 + 0.123501i
\(309\) −13.7014 −0.779447
\(310\) 3.74809 + 6.49189i 0.212877 + 0.368714i
\(311\) −5.81505 + 10.0720i −0.329741 + 0.571128i −0.982460 0.186472i \(-0.940295\pi\)
0.652719 + 0.757600i \(0.273628\pi\)
\(312\) 2.30850 3.99844i 0.130693 0.226367i
\(313\) 13.5489 + 23.4673i 0.765827 + 1.32645i 0.939808 + 0.341702i \(0.111003\pi\)
−0.173982 + 0.984749i \(0.555663\pi\)
\(314\) −14.5631 −0.821845
\(315\) 2.83697 + 1.21017i 0.159845 + 0.0681853i
\(316\) 6.49727 0.365500
\(317\) −1.93086 3.34435i −0.108448 0.187837i 0.806694 0.590970i \(-0.201255\pi\)
−0.915142 + 0.403132i \(0.867921\pi\)
\(318\) 15.0626 26.0892i 0.844668 1.46301i
\(319\) −5.21516 + 9.03292i −0.291993 + 0.505746i
\(320\) −0.751365 1.30140i −0.0420026 0.0727506i
\(321\) −24.4028 −1.36203
\(322\) −9.66749 4.12387i −0.538748 0.229814i
\(323\) 15.7673 0.877315
\(324\) 7.59880 + 13.1615i 0.422156 + 0.731195i
\(325\) −4.13947 + 7.16978i −0.229617 + 0.397708i
\(326\) 14.6790 25.4247i 0.812992 1.40814i
\(327\) −15.7251 27.2366i −0.869599 1.50619i
\(328\) −8.78475 −0.485057
\(329\) −5.99673 + 4.50220i −0.330610 + 0.248214i
\(330\) −2.56314 −0.141096
\(331\) −3.07514 5.32630i −0.169025 0.292760i 0.769052 0.639186i \(-0.220729\pi\)
−0.938077 + 0.346426i \(0.887395\pi\)
\(332\) 6.29804 10.9085i 0.345650 0.598683i
\(333\) −5.56314 + 9.63564i −0.304858 + 0.528030i
\(334\) −1.06314 1.84141i −0.0581724 0.100758i
\(335\) 1.01855 0.0556491
\(336\) 3.40065 + 28.1083i 0.185521 + 1.53344i
\(337\) −11.7607 −0.640649 −0.320324 0.947308i \(-0.603792\pi\)
−0.320324 + 0.947308i \(0.603792\pi\)
\(338\) 8.94678 + 15.4963i 0.486641 + 0.842887i
\(339\) −9.55267 + 16.5457i −0.518830 + 0.898640i
\(340\) −1.22890 + 2.12851i −0.0666462 + 0.115435i
\(341\) 3.21516 + 5.56882i 0.174111 + 0.301568i
\(342\) −18.7169 −1.01209
\(343\) −6.54494 17.3252i −0.353393 0.935475i
\(344\) 5.67395 0.305919
\(345\) −1.51320 2.62093i −0.0814677 0.141106i
\(346\) 0.911120 1.57811i 0.0489821 0.0848395i
\(347\) 0.420393 0.728143i 0.0225679 0.0390888i −0.854521 0.519417i \(-0.826149\pi\)
0.877089 + 0.480328i \(0.159482\pi\)
\(348\) −15.6455 27.0988i −0.838686 1.45265i
\(349\) 9.13174 0.488811 0.244405 0.969673i \(-0.421407\pi\)
0.244405 + 0.969673i \(0.421407\pi\)
\(350\) −2.67895 22.1431i −0.143196 1.18360i
\(351\) −4.61701 −0.246438
\(352\) −3.29804 5.71237i −0.175786 0.304470i
\(353\) −11.3639 + 19.6829i −0.604840 + 1.04761i 0.387237 + 0.921980i \(0.373429\pi\)
−0.992077 + 0.125633i \(0.959904\pi\)
\(354\) 23.8080 41.2366i 1.26538 2.19170i
\(355\) 1.36391 + 2.36235i 0.0723886 + 0.125381i
\(356\) 0.497270 0.0263553
\(357\) 13.1850 9.89894i 0.697822 0.523908i
\(358\) −36.0648 −1.90608
\(359\) 13.1093 + 22.7059i 0.691881 + 1.19837i 0.971221 + 0.238180i \(0.0765510\pi\)
−0.279340 + 0.960192i \(0.590116\pi\)
\(360\) −0.679494 + 1.17692i −0.0358125 + 0.0620291i
\(361\) −5.97426 + 10.3477i −0.314435 + 0.544617i
\(362\) 21.8941 + 37.9217i 1.15073 + 1.99312i
\(363\) −2.19869 −0.115401
\(364\) 5.98126 + 2.55143i 0.313503 + 0.133731i
\(365\) 10.1647 0.532043
\(366\) −8.73436 15.1283i −0.456552 0.790771i
\(367\) 1.91112 3.31016i 0.0997597 0.172789i −0.811825 0.583900i \(-0.801526\pi\)
0.911585 + 0.411111i \(0.134859\pi\)
\(368\) 5.27056 9.12888i 0.274747 0.475876i
\(369\) −6.91112 11.9704i −0.359779 0.623155i
\(370\) −7.07133 −0.367621
\(371\) −18.1784 7.75437i −0.943776 0.402587i
\(372\) −19.2910 −1.00019
\(373\) −7.55387 13.0837i −0.391124 0.677447i 0.601474 0.798893i \(-0.294580\pi\)
−0.992598 + 0.121445i \(0.961247\pi\)
\(374\) −2.59935 + 4.50220i −0.134409 + 0.232803i
\(375\) 6.70469 11.6129i 0.346229 0.599686i
\(376\) −1.65202 2.86138i −0.0851964 0.147564i
\(377\) 18.7882 0.967643
\(378\) 9.94733 7.46821i 0.511635 0.384123i
\(379\) −11.3765 −0.584369 −0.292185 0.956362i \(-0.594382\pi\)
−0.292185 + 0.956362i \(0.594382\pi\)
\(380\) −2.41211 4.17791i −0.123739 0.214322i
\(381\) 23.0851 39.9845i 1.18268 2.04847i
\(382\) 10.2092 17.6828i 0.522346 0.904730i
\(383\) −4.44286 7.69526i −0.227020 0.393210i 0.729904 0.683550i \(-0.239565\pi\)
−0.956923 + 0.290340i \(0.906231\pi\)
\(384\) −19.4698 −0.993564
\(385\) 0.201963 + 1.66934i 0.0102930 + 0.0850774i
\(386\) 6.63009 0.337463
\(387\) 4.46379 + 7.73152i 0.226907 + 0.393015i
\(388\) 1.77110 3.06764i 0.0899142 0.155736i
\(389\) 9.94951 17.2331i 0.504460 0.873751i −0.495526 0.868593i \(-0.665025\pi\)
0.999987 0.00515807i \(-0.00164187\pi\)
\(390\) 2.30850 + 3.99844i 0.116896 + 0.202469i
\(391\) −6.13828 −0.310426
\(392\) 7.92486 1.94604i 0.400266 0.0982901i
\(393\) 30.1252 1.51962
\(394\) −2.21789 3.84149i −0.111736 0.193532i
\(395\) 1.51320 2.62093i 0.0761371 0.131873i
\(396\) 1.25136 2.16743i 0.0628834 0.108917i
\(397\) 17.4303 + 30.1902i 0.874803 + 1.51520i 0.856973 + 0.515361i \(0.172342\pi\)
0.0178296 + 0.999841i \(0.494324\pi\)
\(398\) −33.9265 −1.70058
\(399\) 3.88692 + 32.1276i 0.194589 + 1.60839i
\(400\) 22.3699 1.11850
\(401\) −5.69815 9.86948i −0.284552 0.492858i 0.687948 0.725760i \(-0.258511\pi\)
−0.972500 + 0.232901i \(0.925178\pi\)
\(402\) −3.23163 + 5.59734i −0.161179 + 0.279170i
\(403\) 5.79149 10.0312i 0.288495 0.499688i
\(404\) 6.75409 + 11.6984i 0.336029 + 0.582019i
\(405\) 7.07896 0.351756
\(406\) −40.4792 + 30.3908i −2.00895 + 1.50827i
\(407\) −6.06587 −0.300674
\(408\) 3.63228 + 6.29129i 0.179825 + 0.311465i
\(409\) 2.04394 3.54021i 0.101066 0.175052i −0.811058 0.584966i \(-0.801108\pi\)
0.912124 + 0.409914i \(0.134441\pi\)
\(410\) 4.39238 7.60782i 0.216924 0.375723i
\(411\) 7.98626 + 13.8326i 0.393933 + 0.682312i
\(412\) 8.50273 0.418899
\(413\) −28.7328 12.2566i −1.41385 0.603106i
\(414\) 7.28658 0.358116
\(415\) −2.93359 5.08112i −0.144004 0.249423i
\(416\) −5.94078 + 10.2897i −0.291271 + 0.504496i
\(417\) −2.86118 + 4.95570i −0.140112 + 0.242682i
\(418\) −5.10208 8.83705i −0.249551 0.432234i
\(419\) 32.8002 1.60240 0.801198 0.598399i \(-0.204196\pi\)
0.801198 + 0.598399i \(0.204196\pi\)
\(420\) −4.64002 1.97929i −0.226410 0.0965796i
\(421\) −8.52128 −0.415302 −0.207651 0.978203i \(-0.566582\pi\)
−0.207651 + 0.978203i \(0.566582\pi\)
\(422\) 7.20415 + 12.4780i 0.350693 + 0.607417i
\(423\) 2.59935 4.50220i 0.126385 0.218904i
\(424\) 4.35398 7.54132i 0.211448 0.366239i
\(425\) −6.51320 11.2812i −0.315936 0.547218i
\(426\) −17.3095 −0.838648
\(427\) −9.16467 + 6.88061i −0.443510 + 0.332976i
\(428\) 15.1437 0.732000
\(429\) 1.98026 + 3.42991i 0.0956079 + 0.165598i
\(430\) −2.83697 + 4.91378i −0.136811 + 0.236964i
\(431\) 8.36718 14.4924i 0.403033 0.698073i −0.591058 0.806629i \(-0.701289\pi\)
0.994090 + 0.108556i \(0.0346227\pi\)
\(432\) 6.23763 + 10.8039i 0.300108 + 0.519802i
\(433\) −25.8661 −1.24305 −0.621523 0.783396i \(-0.713486\pi\)
−0.621523 + 0.783396i \(0.713486\pi\)
\(434\) 3.74809 + 30.9801i 0.179914 + 1.48709i
\(435\) −14.5751 −0.698825
\(436\) 9.75856 + 16.9023i 0.467350 + 0.809474i
\(437\) 6.02420 10.4342i 0.288177 0.499137i
\(438\) −32.2503 + 55.8591i −1.54098 + 2.66905i
\(439\) 4.78430 + 8.28665i 0.228342 + 0.395500i 0.957317 0.289040i \(-0.0933362\pi\)
−0.728975 + 0.684541i \(0.760003\pi\)
\(440\) −0.740899 −0.0353210
\(441\) 8.88637 + 9.26770i 0.423161 + 0.441319i
\(442\) 9.36445 0.445421
\(443\) −9.51647 16.4830i −0.452141 0.783131i 0.546378 0.837539i \(-0.316006\pi\)
−0.998519 + 0.0544076i \(0.982673\pi\)
\(444\) 9.09880 15.7596i 0.431810 0.747917i
\(445\) 0.115813 0.200594i 0.00549005 0.00950905i
\(446\) −18.6515 32.3053i −0.883173 1.52970i
\(447\) 2.19869 0.103995
\(448\) −0.751365 6.21046i −0.0354986 0.293416i
\(449\) 33.3424 1.57353 0.786763 0.617255i \(-0.211755\pi\)
0.786763 + 0.617255i \(0.211755\pi\)
\(450\) 7.73163 + 13.3916i 0.364472 + 0.631285i
\(451\) 3.76783 6.52608i 0.177420 0.307301i
\(452\) 5.92813 10.2678i 0.278836 0.482958i
\(453\) 1.90785 + 3.30449i 0.0896385 + 0.155258i
\(454\) 13.2425 0.621503
\(455\) 2.42224 1.81856i 0.113556 0.0852552i
\(456\) −14.2591 −0.667744
\(457\) −5.98026 10.3581i −0.279745 0.484532i 0.691576 0.722303i \(-0.256917\pi\)
−0.971321 + 0.237771i \(0.923583\pi\)
\(458\) −11.0709 + 19.1753i −0.517308 + 0.896004i
\(459\) 3.63228 6.29129i 0.169540 0.293652i
\(460\) 0.939048 + 1.62648i 0.0437833 + 0.0758350i
\(461\) 12.4896 0.581701 0.290850 0.956769i \(-0.406062\pi\)
0.290850 + 0.956769i \(0.406062\pi\)
\(462\) −9.81450 4.18658i −0.456612 0.194777i
\(463\) 12.3095 0.572071 0.286035 0.958219i \(-0.407662\pi\)
0.286035 + 0.958219i \(0.407662\pi\)
\(464\) −25.3831 43.9648i −1.17838 2.04102i
\(465\) −4.49281 + 7.78177i −0.208349 + 0.360871i
\(466\) 6.91712 11.9808i 0.320429 0.555000i
\(467\) −16.3804 28.3716i −0.757993 1.31288i −0.943872 0.330310i \(-0.892847\pi\)
0.185879 0.982573i \(-0.440487\pi\)
\(468\) −4.50819 −0.208391
\(469\) 3.90011 + 1.66367i 0.180090 + 0.0768213i
\(470\) 3.30404 0.152404
\(471\) −8.72835 15.1180i −0.402181 0.696598i
\(472\) 6.88191 11.9198i 0.316766 0.548654i
\(473\) −2.43359 + 4.21510i −0.111897 + 0.193810i
\(474\) 9.60208 + 16.6313i 0.441038 + 0.763900i
\(475\) 25.5686 1.17317
\(476\) −8.18222 + 6.14302i −0.375032 + 0.281565i
\(477\) 13.7014 0.627345
\(478\) 9.03020 + 15.6408i 0.413032 + 0.715392i
\(479\) −12.9890 + 22.4976i −0.593482 + 1.02794i 0.400277 + 0.916394i \(0.368914\pi\)
−0.993759 + 0.111547i \(0.964419\pi\)
\(480\) 4.60862 7.98236i 0.210354 0.364343i
\(481\) 5.46325 + 9.46263i 0.249103 + 0.431459i
\(482\) −3.07241 −0.139945
\(483\) −1.51320 12.5074i −0.0688528 0.569107i
\(484\) 1.36445 0.0620204
\(485\) −0.824970 1.42889i −0.0374600 0.0648825i
\(486\) −15.4078 + 26.6872i −0.698914 + 1.21055i
\(487\) −7.26783 + 12.5883i −0.329337 + 0.570428i −0.982380 0.186892i \(-0.940159\pi\)
0.653044 + 0.757320i \(0.273492\pi\)
\(488\) −2.52475 4.37299i −0.114290 0.197956i
\(489\) 35.1911 1.59139
\(490\) −2.27711 + 7.83615i −0.102869 + 0.354001i
\(491\) −39.3952 −1.77788 −0.888941 0.458023i \(-0.848558\pi\)
−0.888941 + 0.458023i \(0.848558\pi\)
\(492\) 11.3035 + 19.5782i 0.509601 + 0.882655i
\(493\) −14.7810 + 25.6015i −0.665704 + 1.15303i
\(494\) −9.19041 + 15.9183i −0.413496 + 0.716196i
\(495\) −0.582878 1.00958i −0.0261984 0.0453770i
\(496\) −31.2975 −1.40530
\(497\) 1.36391 + 11.2735i 0.0611795 + 0.505683i
\(498\) 37.2305 1.66834
\(499\) 13.1153 + 22.7163i 0.587120 + 1.01692i 0.994607 + 0.103711i \(0.0330717\pi\)
−0.407487 + 0.913211i \(0.633595\pi\)
\(500\) −4.16075 + 7.20663i −0.186074 + 0.322290i
\(501\) 1.27438 2.20728i 0.0569349 0.0986142i
\(502\) −18.1350 31.4108i −0.809405 1.40193i
\(503\) 3.94613 0.175949 0.0879747 0.996123i \(-0.471961\pi\)
0.0879747 + 0.996123i \(0.471961\pi\)
\(504\) −4.52420 + 3.39666i −0.201524 + 0.151299i
\(505\) 6.29204 0.279992
\(506\) 1.98626 + 3.44031i 0.0883001 + 0.152940i
\(507\) −10.7244 + 18.5753i −0.476289 + 0.824956i
\(508\) −14.3260 + 24.8133i −0.635612 + 1.10091i
\(509\) −8.45279 14.6407i −0.374663 0.648936i 0.615613 0.788048i \(-0.288908\pi\)
−0.990277 + 0.139113i \(0.955575\pi\)
\(510\) −7.26456 −0.321680
\(511\) 38.9215 + 16.6028i 1.72179 + 0.734463i
\(512\) 20.7564 0.917311
\(513\) 7.12955 + 12.3487i 0.314777 + 0.545210i
\(514\) −2.49454 + 4.32067i −0.110029 + 0.190577i
\(515\) 1.98026 3.42991i 0.0872607 0.151140i
\(516\) −7.30077 12.6453i −0.321398 0.556678i
\(517\) 2.83424 0.124650
\(518\) −27.0768 11.5502i −1.18969 0.507485i
\(519\) 2.18430 0.0958803
\(520\) 0.667294 + 1.15579i 0.0292628 + 0.0506846i
\(521\) −0.778840 + 1.34899i −0.0341216 + 0.0591004i −0.882582 0.470159i \(-0.844197\pi\)
0.848460 + 0.529259i \(0.177530\pi\)
\(522\) 17.5461 30.3908i 0.767973 1.33017i
\(523\) 6.25136 + 10.8277i 0.273353 + 0.473461i 0.969718 0.244226i \(-0.0785339\pi\)
−0.696365 + 0.717688i \(0.745201\pi\)
\(524\) −18.6949 −0.816689
\(525\) 21.3810 16.0524i 0.933144 0.700582i
\(526\) 23.2855 1.01530
\(527\) 9.11254 + 15.7834i 0.396949 + 0.687535i
\(528\) 5.35071 9.26770i 0.232860 0.403325i
\(529\) 9.15475 15.8565i 0.398033 0.689413i
\(530\) 4.35398 + 7.54132i 0.189125 + 0.327574i
\(531\) 21.6565 0.939811
\(532\) −2.41211 19.9375i −0.104578 0.864400i
\(533\) −13.5741 −0.587958
\(534\) 0.734898 + 1.27288i 0.0318021 + 0.0550829i
\(535\) 3.52693 6.10883i 0.152483 0.264108i
\(536\) −0.934131 + 1.61796i −0.0403483 + 0.0698853i
\(537\) −21.6153 37.4387i −0.932768 1.61560i
\(538\) −13.0109 −0.560941
\(539\) −1.95333 + 6.72194i −0.0841358 + 0.289535i
\(540\) −2.22270 −0.0956497
\(541\) 8.28103 + 14.3432i 0.356029 + 0.616661i 0.987294 0.158907i \(-0.0507970\pi\)
−0.631264 + 0.775568i \(0.717464\pi\)
\(542\) 16.7064 28.9364i 0.717603 1.24292i
\(543\) −26.2443 + 45.4564i −1.12625 + 1.95072i
\(544\) −9.34744 16.1902i −0.400768 0.694151i
\(545\) 9.09096 0.389414
\(546\) 2.30850 + 19.0811i 0.0987948 + 0.816595i
\(547\) −6.64448 −0.284097 −0.142049 0.989860i \(-0.545369\pi\)
−0.142049 + 0.989860i \(0.545369\pi\)
\(548\) −4.95606 8.58414i −0.211712 0.366696i
\(549\) 3.97252 6.88061i 0.169543 0.293657i
\(550\) −4.21516 + 7.30087i −0.179735 + 0.311310i
\(551\) −29.0127 50.2514i −1.23598 2.14078i
\(552\) 5.55114 0.236272
\(553\) 10.0751 7.56417i 0.428439 0.321661i
\(554\) 25.4018 1.07922
\(555\) −4.23817 7.34072i −0.179900 0.311596i
\(556\) 1.77557 3.07537i 0.0753009 0.130425i
\(557\) −6.55595 + 11.3552i −0.277784 + 0.481137i −0.970834 0.239753i \(-0.922933\pi\)
0.693049 + 0.720890i \(0.256267\pi\)
\(558\) −10.8172 18.7360i −0.457930 0.793158i
\(559\) 8.76729 0.370817
\(560\) −7.52793 3.21119i −0.318113 0.135698i
\(561\) −6.23163 −0.263099
\(562\) −19.2898 33.4108i −0.813689 1.40935i
\(563\) −15.2443 + 26.4039i −0.642470 + 1.11279i 0.342410 + 0.939551i \(0.388757\pi\)
−0.984880 + 0.173240i \(0.944577\pi\)
\(564\) −4.25136 + 7.36358i −0.179015 + 0.310063i
\(565\) −2.76129 4.78269i −0.116168 0.201209i
\(566\) 0.646470 0.0271732
\(567\) 27.1060 + 11.5626i 1.13834 + 0.485584i
\(568\) −5.00347 −0.209941
\(569\) 17.6790 + 30.6208i 0.741140 + 1.28369i 0.951976 + 0.306171i \(0.0990480\pi\)
−0.210836 + 0.977521i \(0.567619\pi\)
\(570\) 7.12955 12.3487i 0.298624 0.517232i
\(571\) 20.6422 35.7533i 0.863849 1.49623i −0.00433587 0.999991i \(-0.501380\pi\)
0.868185 0.496240i \(-0.165287\pi\)
\(572\) −1.22890 2.12851i −0.0513827 0.0889975i
\(573\) 24.4753 1.02247
\(574\) 29.2453 21.9566i 1.22067 0.916453i
\(575\) −9.95398 −0.415110
\(576\) 2.16849 + 3.75593i 0.0903536 + 0.156497i
\(577\) −4.35125 + 7.53659i −0.181145 + 0.313752i −0.942271 0.334852i \(-0.891314\pi\)
0.761126 + 0.648604i \(0.224647\pi\)
\(578\) 8.22389 14.2442i 0.342069 0.592480i
\(579\) 3.97372 + 6.88268i 0.165142 + 0.286034i
\(580\) 9.04494 0.375571
\(581\) −2.93359 24.2478i −0.121706 1.00597i
\(582\) 10.4698 0.433987
\(583\) 3.73490 + 6.46903i 0.154684 + 0.267920i
\(584\) −9.32224 + 16.1466i −0.385757 + 0.668151i
\(585\) −1.04994 + 1.81856i −0.0434098 + 0.0751881i
\(586\) 3.17622 + 5.50138i 0.131209 + 0.227260i
\(587\) −23.0539 −0.951535 −0.475767 0.879571i \(-0.657830\pi\)
−0.475767 + 0.879571i \(0.657830\pi\)
\(588\) −14.5341 15.1578i −0.599377 0.625097i
\(589\) −35.7727 −1.47399
\(590\) 6.88191 + 11.9198i 0.283324 + 0.490731i
\(591\) 2.65856 4.60477i 0.109359 0.189415i
\(592\) 14.7618 25.5682i 0.606707 1.05085i
\(593\) −15.0494 26.0663i −0.618005 1.07042i −0.989849 0.142121i \(-0.954608\pi\)
0.371844 0.928295i \(-0.378725\pi\)
\(594\) −4.70142 −0.192902
\(595\) 0.572413 + 4.73131i 0.0234666 + 0.193965i
\(596\) −1.36445 −0.0558900
\(597\) −20.3337 35.2190i −0.832203 1.44142i
\(598\) 3.57787 6.19706i 0.146310 0.253416i
\(599\) −14.6257 + 25.3325i −0.597591 + 1.03506i 0.395584 + 0.918430i \(0.370542\pi\)
−0.993176 + 0.116629i \(0.962791\pi\)
\(600\) 5.89019 + 10.2021i 0.240466 + 0.416499i
\(601\) −26.8222 −1.09410 −0.547051 0.837099i \(-0.684250\pi\)
−0.547051 + 0.837099i \(0.684250\pi\)
\(602\) −18.8891 + 14.1815i −0.769862 + 0.577994i
\(603\) −2.93959 −0.119709
\(604\) −1.18396 2.05068i −0.0481746 0.0834409i
\(605\) 0.317776 0.550404i 0.0129194 0.0223771i
\(606\) −19.9633 + 34.5774i −0.810952 + 1.40461i
\(607\) −16.1048 27.8943i −0.653674 1.13220i −0.982224 0.187710i \(-0.939893\pi\)
0.328551 0.944486i \(-0.393440\pi\)
\(608\) 36.6949 1.48817
\(609\) −55.8096 23.8067i −2.26152 0.964697i
\(610\) 5.04949 0.204448
\(611\) −2.55267 4.42136i −0.103270 0.178869i
\(612\) 3.54667 6.14302i 0.143366 0.248317i
\(613\) −22.2975 + 38.6204i −0.900587 + 1.55986i −0.0738539 + 0.997269i \(0.523530\pi\)
−0.826733 + 0.562594i \(0.809803\pi\)
\(614\) 5.97480 + 10.3487i 0.241123 + 0.417638i
\(615\) 10.5302 0.424619
\(616\) −2.83697 1.21017i −0.114305 0.0487591i
\(617\) −0.531290 −0.0213889 −0.0106945 0.999943i \(-0.503404\pi\)
−0.0106945 + 0.999943i \(0.503404\pi\)
\(618\) 12.5659 + 21.7647i 0.505473 + 0.875506i
\(619\) −20.8726 + 36.1525i −0.838942 + 1.45309i 0.0518379 + 0.998656i \(0.483492\pi\)
−0.890780 + 0.454435i \(0.849841\pi\)
\(620\) 2.78811 4.82915i 0.111973 0.193943i
\(621\) −2.77557 4.80743i −0.111380 0.192915i
\(622\) 21.3324 0.855352
\(623\) 0.771104 0.578926i 0.0308936 0.0231942i
\(624\) −19.2766 −0.771680
\(625\) −9.55213 16.5448i −0.382085 0.661791i
\(626\) 24.8519 43.0448i 0.993282 1.72041i
\(627\) 6.11581 10.5929i 0.244242 0.423040i
\(628\) 5.41658 + 9.38179i 0.216145 + 0.374374i
\(629\) −17.1921 −0.685496
\(630\) −0.679494 5.61641i −0.0270717 0.223763i
\(631\) −0.217238 −0.00864810 −0.00432405 0.999991i \(-0.501376\pi\)
−0.00432405 + 0.999991i \(0.501376\pi\)
\(632\) 2.77557 + 4.80743i 0.110406 + 0.191229i
\(633\) −8.63555 + 14.9572i −0.343232 + 0.594496i
\(634\) −3.54167 + 6.13434i −0.140658 + 0.243626i
\(635\) 6.67295 + 11.5579i 0.264808 + 0.458661i
\(636\) −22.4094 −0.888590
\(637\) 12.2454 3.00700i 0.485179 0.119142i
\(638\) 19.1317 0.757433
\(639\) −3.93632 6.81790i −0.155718 0.269712i
\(640\) 2.81396 4.87392i 0.111232 0.192659i
\(641\) 4.84525 8.39222i 0.191376 0.331473i −0.754331 0.656495i \(-0.772038\pi\)
0.945706 + 0.325022i \(0.105372\pi\)
\(642\) 22.3804 + 38.7639i 0.883283 + 1.52989i
\(643\) 16.4633 0.649247 0.324624 0.945843i \(-0.394762\pi\)
0.324624 + 0.945843i \(0.394762\pi\)
\(644\) 0.939048 + 7.76176i 0.0370037 + 0.305856i
\(645\) −6.80131 −0.267801
\(646\) −14.4605 25.0464i −0.568942 0.985436i
\(647\) −0.436861 + 0.756665i −0.0171748 + 0.0297476i −0.874485 0.485052i \(-0.838801\pi\)
0.857310 + 0.514800i \(0.172134\pi\)
\(648\) −6.49226 + 11.2449i −0.255040 + 0.441743i
\(649\) 5.90338 + 10.2250i 0.231728 + 0.401365i
\(650\) 15.1856 0.595628
\(651\) −29.9140 + 22.4587i −1.17242 + 0.880225i
\(652\) −21.8386 −0.855266
\(653\) 19.9665 + 34.5830i 0.781350 + 1.35334i 0.931155 + 0.364623i \(0.118802\pi\)
−0.149805 + 0.988716i \(0.547865\pi\)
\(654\) −28.8436 + 49.9586i −1.12787 + 1.95354i
\(655\) −4.35398 + 7.54132i −0.170124 + 0.294664i
\(656\) 18.3387 + 31.7636i 0.716006 + 1.24016i
\(657\) −29.3359 −1.14450
\(658\) 12.6515 + 5.39675i 0.493206 + 0.210387i
\(659\) −6.89465 −0.268578 −0.134289 0.990942i \(-0.542875\pi\)
−0.134289 + 0.990942i \(0.542875\pi\)
\(660\) 0.953328 + 1.65121i 0.0371082 + 0.0642734i
\(661\) 20.0072 34.6535i 0.778190 1.34786i −0.154795 0.987947i \(-0.549472\pi\)
0.932984 0.359917i \(-0.117195\pi\)
\(662\) −5.64056 + 9.76973i −0.219227 + 0.379711i
\(663\) 5.61254 + 9.72121i 0.217973 + 0.377540i
\(664\) 10.7618 0.417640
\(665\) −8.60435 3.67036i −0.333662 0.142331i
\(666\) 20.4083 0.790806
\(667\) 11.2948 + 19.5631i 0.437335 + 0.757487i
\(668\) −0.790843 + 1.36978i −0.0305986 + 0.0529984i
\(669\) 22.3574 38.7241i 0.864386 1.49716i
\(670\) −0.934131 1.61796i −0.0360886 0.0625073i
\(671\) 4.33151 0.167216
\(672\) 30.6851 23.0376i 1.18370 0.888695i
\(673\) 31.3788 1.20957 0.604783 0.796391i \(-0.293260\pi\)
0.604783 + 0.796391i \(0.293260\pi\)
\(674\) 10.7860 + 18.6820i 0.415463 + 0.719602i
\(675\) 5.89019 10.2021i 0.226713 0.392679i
\(676\) 6.65529 11.5273i 0.255973 0.443358i
\(677\) 18.2658 + 31.6372i 0.702010 + 1.21592i 0.967760 + 0.251875i \(0.0810471\pi\)
−0.265750 + 0.964042i \(0.585620\pi\)
\(678\) 35.0439 1.34585
\(679\) −0.824970 6.81884i −0.0316594 0.261683i
\(680\) −2.09989 −0.0805270
\(681\) 7.93686 + 13.7470i 0.304141 + 0.526788i
\(682\) 5.89738 10.2146i 0.225822 0.391136i
\(683\) 7.63501 13.2242i 0.292146 0.506011i −0.682171 0.731192i \(-0.738964\pi\)
0.974317 + 0.225181i \(0.0722975\pi\)
\(684\) 6.96152 + 12.0577i 0.266180 + 0.461038i
\(685\) −4.61701 −0.176407
\(686\) −21.5187 + 26.2860i −0.821586 + 1.00360i
\(687\) −26.5411 −1.01261
\(688\) −11.8447 20.5156i −0.451575 0.782151i
\(689\) 6.72770 11.6527i 0.256305 0.443933i
\(690\) −2.77557 + 4.80743i −0.105664 + 0.183016i
\(691\) 19.1921 + 33.2418i 0.730104 + 1.26458i 0.956839 + 0.290620i \(0.0938616\pi\)
−0.226735 + 0.973957i \(0.572805\pi\)
\(692\) −1.35552 −0.0515291
\(693\) −0.582878 4.81782i −0.0221417 0.183014i
\(694\) −1.54221 −0.0585414
\(695\) −0.827049 1.43249i −0.0313718 0.0543375i
\(696\) 13.3672 23.1526i 0.506682 0.877598i
\(697\) 10.6790 18.4965i 0.404494 0.700604i
\(698\) −8.37491 14.5058i −0.316995 0.549052i
\(699\) 16.5830 0.627226
\(700\) −13.2685 + 9.96166i −0.501501 + 0.376515i
\(701\) 17.9056 0.676284 0.338142 0.941095i \(-0.390202\pi\)
0.338142 + 0.941095i \(0.390202\pi\)
\(702\) 4.23436 + 7.33412i 0.159815 + 0.276808i
\(703\) 16.8726 29.2243i 0.636364 1.10221i
\(704\) −1.18222 + 2.04767i −0.0445567 + 0.0771745i
\(705\) 1.98026 + 3.42991i 0.0745809 + 0.129178i
\(706\) 41.6883 1.56896
\(707\) 24.0928 + 10.2773i 0.906103 + 0.386517i
\(708\) −35.4203 −1.33118
\(709\) −17.1997 29.7907i −0.645948 1.11881i −0.984082 0.177716i \(-0.943129\pi\)
0.338134 0.941098i \(-0.390204\pi\)
\(710\) 2.50173 4.33313i 0.0938884 0.162620i
\(711\) −4.36718 + 7.56417i −0.163782 + 0.283679i
\(712\) 0.212429 + 0.367938i 0.00796111 + 0.0137890i
\(713\) 13.9265 0.521552
\(714\) −27.8167 11.8658i −1.04101 0.444066i
\(715\) −1.14483 −0.0428140
\(716\) 13.4138 + 23.2335i 0.501299 + 0.868276i
\(717\) −10.8244 + 18.7485i −0.404246 + 0.700174i
\(718\) 24.0456 41.6482i 0.897373 1.55430i
\(719\) −24.7086 42.7966i −0.921476 1.59604i −0.797133 0.603804i \(-0.793651\pi\)
−0.124343 0.992239i \(-0.539682\pi\)
\(720\) 5.67395 0.211455
\(721\) 13.1850 9.89894i 0.491033 0.368656i
\(722\) 21.9165 0.815647
\(723\) −1.84144 3.18946i −0.0684838 0.118617i
\(724\) 16.2865 28.2090i 0.605283 1.04838i
\(725\) −23.9693 + 41.5160i −0.890196 + 1.54186i
\(726\) 2.01647 + 3.49262i 0.0748381 + 0.129623i
\(727\) −19.8201 −0.735086 −0.367543 0.930007i \(-0.619801\pi\)
−0.367543 + 0.930007i \(0.619801\pi\)
\(728\) 0.667294 + 5.51556i 0.0247316 + 0.204420i
\(729\) −3.52366 −0.130506
\(730\) −9.32224 16.1466i −0.345032 0.597612i
\(731\) −6.89738 + 11.9466i −0.255109 + 0.441862i
\(732\) −6.49727 + 11.2536i −0.240146 + 0.415945i
\(733\) 15.3238 + 26.5416i 0.565997 + 0.980335i 0.996956 + 0.0779637i \(0.0248418\pi\)
−0.430960 + 0.902371i \(0.641825\pi\)
\(734\) −7.01092 −0.258778
\(735\) −9.49946 + 2.33271i −0.350393 + 0.0860432i
\(736\) −14.2855 −0.526570
\(737\) −0.801309 1.38791i −0.0295166 0.0511242i
\(738\) −12.6767 + 21.9566i −0.466635 + 0.808235i
\(739\) −8.55094 + 14.8107i −0.314551 + 0.544819i −0.979342 0.202211i \(-0.935187\pi\)
0.664791 + 0.747030i \(0.268521\pi\)
\(740\) 2.63009 + 4.55545i 0.0966841 + 0.167462i
\(741\) −22.0329 −0.809400
\(742\) 4.35398 + 35.9881i 0.159840 + 1.32117i
\(743\) −6.97252 −0.255797 −0.127899 0.991787i \(-0.540823\pi\)
−0.127899 + 0.991787i \(0.540823\pi\)
\(744\) −8.24090 14.2737i −0.302126 0.523298i
\(745\) −0.317776 + 0.550404i −0.0116424 + 0.0201652i
\(746\) −13.8556 + 23.9987i −0.507291 + 0.878653i
\(747\) 8.46652 + 14.6644i 0.309774 + 0.536544i
\(748\) 3.86718 0.141398
\(749\) 23.4830 17.6305i 0.858050 0.644203i
\(750\) −24.5961 −0.898122
\(751\) −7.61636 13.1919i −0.277925 0.481380i 0.692944 0.720991i \(-0.256313\pi\)
−0.970869 + 0.239612i \(0.922980\pi\)
\(752\) −6.89738 + 11.9466i −0.251522 + 0.435648i
\(753\) 21.7383 37.6518i 0.792187 1.37211i
\(754\) −17.2311 29.8451i −0.627519 1.08689i
\(755\) −1.10296 −0.0401409
\(756\) −8.51092 3.63051i −0.309539 0.132040i
\(757\) −14.5326 −0.528196 −0.264098 0.964496i \(-0.585074\pi\)
−0.264098 + 0.964496i \(0.585074\pi\)
\(758\) 10.4336 + 18.0715i 0.378965 + 0.656387i
\(759\) −2.38092 + 4.12387i −0.0864217 + 0.149687i
\(760\) 2.06086 3.56952i 0.0747553 0.129480i
\(761\) 0.856712 + 1.48387i 0.0310558 + 0.0537902i 0.881136 0.472864i \(-0.156780\pi\)
−0.850080 + 0.526654i \(0.823446\pi\)
\(762\) −84.6872 −3.06790
\(763\) 34.8101 + 14.8490i 1.26021 + 0.537569i
\(764\) −15.1887 −0.549507
\(765\) −1.65202 2.86138i −0.0597289 0.103453i
\(766\) −8.14929 + 14.1150i −0.294446 + 0.509995i
\(767\) 10.6338 18.4183i 0.383965 0.665047i
\(768\) 23.0549 + 39.9322i 0.831921 + 1.44093i
\(769\) −36.5874 −1.31937 −0.659687 0.751540i \(-0.729311\pi\)
−0.659687 + 0.751540i \(0.729311\pi\)
\(770\) 2.46652 1.85181i 0.0888873 0.0667345i
\(771\) −5.98037 −0.215378
\(772\) −2.46598 4.27120i −0.0887526 0.153724i
\(773\) −13.4106 + 23.2278i −0.482345 + 0.835446i −0.999795 0.0202677i \(-0.993548\pi\)
0.517450 + 0.855714i \(0.326881\pi\)
\(774\) 8.18768 14.1815i 0.294300 0.509743i
\(775\) 14.7771 + 25.5947i 0.530809 + 0.919389i
\(776\) 3.02639 0.108641