Properties

Label 168.2.c.b.85.7
Level 168
Weight 2
Character 168.85
Analytic conductor 1.341
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 168.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.34148675396\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.386672896.3
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 85.7
Root \(-1.19503 - 0.756243i\) of \(x^{8} - x^{6} - 2 x^{5} + 2 x^{4} - 4 x^{3} - 4 x^{2} + 16\)
Character \(\chi\) \(=\) 168.85
Dual form 168.2.c.b.85.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.19503 - 0.756243i) q^{2} +1.00000i q^{3} +(0.856193 - 1.80747i) q^{4} +4.10245i q^{5} +(0.756243 + 1.19503i) q^{6} +1.00000 q^{7} +(-0.343707 - 2.80747i) q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(1.19503 - 0.756243i) q^{2} +1.00000i q^{3} +(0.856193 - 1.80747i) q^{4} +4.10245i q^{5} +(0.756243 + 1.19503i) q^{6} +1.00000 q^{7} +(-0.343707 - 2.80747i) q^{8} -1.00000 q^{9} +(3.10245 + 4.90255i) q^{10} -2.67767i q^{11} +(1.80747 + 0.856193i) q^{12} -3.02497i q^{13} +(1.19503 - 0.756243i) q^{14} -4.10245 q^{15} +(-2.53387 - 3.09508i) q^{16} -5.12742 q^{17} +(-1.19503 + 0.756243i) q^{18} -2.78012i q^{19} +(7.41503 + 3.51249i) q^{20} +1.00000i q^{21} +(-2.02497 - 3.19990i) q^{22} +7.12742 q^{23} +(2.80747 - 0.343707i) q^{24} -11.8301 q^{25} +(-2.28761 - 3.61493i) q^{26} -1.00000i q^{27} +(0.856193 - 1.80747i) q^{28} +8.83006i q^{29} +(-4.90255 + 3.10245i) q^{30} -1.42477 q^{31} +(-5.36868 - 1.78249i) q^{32} +2.67767 q^{33} +(-6.12742 + 3.87757i) q^{34} +4.10245i q^{35} +(-0.856193 + 1.80747i) q^{36} -1.42477i q^{37} +(-2.10245 - 3.32233i) q^{38} +3.02497 q^{39} +(11.5175 - 1.41004i) q^{40} +5.12742 q^{41} +(0.756243 + 1.19503i) q^{42} -2.39980i q^{43} +(-4.83980 - 2.29261i) q^{44} -4.10245i q^{45} +(8.51748 - 5.39006i) q^{46} -9.56024 q^{47} +(3.09508 - 2.53387i) q^{48} +1.00000 q^{49} +(-14.1373 + 8.94640i) q^{50} -5.12742i q^{51} +(-5.46753 - 2.58996i) q^{52} +2.78012i q^{53} +(-0.756243 - 1.19503i) q^{54} +10.9850 q^{55} +(-0.343707 - 2.80747i) q^{56} +2.78012 q^{57} +(6.67767 + 10.5522i) q^{58} -4.00000i q^{59} +(-3.51249 + 7.41503i) q^{60} +5.17992i q^{61} +(-1.70265 + 1.07747i) q^{62} -1.00000 q^{63} +(-7.76373 + 1.92989i) q^{64} +12.4098 q^{65} +(3.19990 - 2.02497i) q^{66} +0.244852i q^{67} +(-4.39006 + 9.26763i) q^{68} +7.12742i q^{69} +(3.10245 + 4.90255i) q^{70} -4.27787 q^{71} +(0.343707 + 2.80747i) q^{72} -4.15495 q^{73} +(-1.07747 - 1.70265i) q^{74} -11.8301i q^{75} +(-5.02497 - 2.38032i) q^{76} -2.67767i q^{77} +(3.61493 - 2.28761i) q^{78} +6.25484 q^{79} +(12.6974 - 10.3951i) q^{80} +1.00000 q^{81} +(6.12742 - 3.87757i) q^{82} +9.35535i q^{83} +(1.80747 + 0.856193i) q^{84} -21.0350i q^{85} +(-1.81483 - 2.86783i) q^{86} -8.83006 q^{87} +(-7.51748 + 0.920336i) q^{88} +11.2824 q^{89} +(-3.10245 - 4.90255i) q^{90} -3.02497i q^{91} +(6.10245 - 12.8826i) q^{92} -1.42477i q^{93} +(-11.4248 + 7.22986i) q^{94} +11.4053 q^{95} +(1.78249 - 5.36868i) q^{96} +6.69460 q^{97} +(1.19503 - 0.756243i) q^{98} +2.67767i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{4} + 2q^{6} + 8q^{7} - 6q^{8} - 8q^{9} + O(q^{10}) \) \( 8q + 2q^{4} + 2q^{6} + 8q^{7} - 6q^{8} - 8q^{9} - 4q^{10} - 4q^{12} - 4q^{15} - 6q^{16} + 4q^{17} + 24q^{20} + 12q^{23} + 4q^{24} - 24q^{25} - 28q^{26} + 2q^{28} - 12q^{30} + 8q^{31} - 30q^{32} + 12q^{33} - 4q^{34} - 2q^{36} + 12q^{38} + 8q^{39} + 28q^{40} - 4q^{41} + 2q^{42} + 16q^{44} + 4q^{46} + 16q^{48} + 8q^{49} - 20q^{50} - 12q^{52} - 2q^{54} - 8q^{55} - 6q^{56} - 16q^{57} + 44q^{58} - 20q^{60} + 12q^{62} - 8q^{63} + 26q^{64} - 16q^{65} + 24q^{66} - 16q^{68} - 4q^{70} - 28q^{71} + 6q^{72} - 8q^{73} + 4q^{74} - 24q^{76} - 8q^{78} - 40q^{79} - 4q^{80} + 8q^{81} + 4q^{82} - 4q^{84} + 24q^{86} + 4q^{88} + 20q^{89} + 4q^{90} + 20q^{92} - 72q^{94} + 40q^{95} + 12q^{96} + 40q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(85\) \(113\) \(127\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.19503 0.756243i 0.845014 0.534745i
\(3\) 1.00000i 0.577350i
\(4\) 0.856193 1.80747i 0.428097 0.903733i
\(5\) 4.10245i 1.83467i 0.398117 + 0.917335i \(0.369664\pi\)
−0.398117 + 0.917335i \(0.630336\pi\)
\(6\) 0.756243 + 1.19503i 0.308735 + 0.487869i
\(7\) 1.00000 0.377964
\(8\) −0.343707 2.80747i −0.121519 0.992589i
\(9\) −1.00000 −0.333333
\(10\) 3.10245 + 4.90255i 0.981080 + 1.55032i
\(11\) 2.67767i 0.807349i −0.914903 0.403674i \(-0.867733\pi\)
0.914903 0.403674i \(-0.132267\pi\)
\(12\) 1.80747 + 0.856193i 0.521770 + 0.247162i
\(13\) 3.02497i 0.838976i −0.907761 0.419488i \(-0.862210\pi\)
0.907761 0.419488i \(-0.137790\pi\)
\(14\) 1.19503 0.756243i 0.319385 0.202114i
\(15\) −4.10245 −1.05925
\(16\) −2.53387 3.09508i −0.633467 0.773770i
\(17\) −5.12742 −1.24358 −0.621791 0.783183i \(-0.713595\pi\)
−0.621791 + 0.783183i \(0.713595\pi\)
\(18\) −1.19503 + 0.756243i −0.281671 + 0.178248i
\(19\) 2.78012i 0.637803i −0.947788 0.318902i \(-0.896686\pi\)
0.947788 0.318902i \(-0.103314\pi\)
\(20\) 7.41503 + 3.51249i 1.65805 + 0.785416i
\(21\) 1.00000i 0.218218i
\(22\) −2.02497 3.19990i −0.431725 0.682221i
\(23\) 7.12742 1.48617 0.743085 0.669197i \(-0.233362\pi\)
0.743085 + 0.669197i \(0.233362\pi\)
\(24\) 2.80747 0.343707i 0.573072 0.0701589i
\(25\) −11.8301 −2.36601
\(26\) −2.28761 3.61493i −0.448638 0.708946i
\(27\) 1.00000i 0.192450i
\(28\) 0.856193 1.80747i 0.161805 0.341579i
\(29\) 8.83006i 1.63970i 0.572577 + 0.819851i \(0.305944\pi\)
−0.572577 + 0.819851i \(0.694056\pi\)
\(30\) −4.90255 + 3.10245i −0.895078 + 0.566427i
\(31\) −1.42477 −0.255897 −0.127948 0.991781i \(-0.540839\pi\)
−0.127948 + 0.991781i \(0.540839\pi\)
\(32\) −5.36868 1.78249i −0.949057 0.315103i
\(33\) 2.67767 0.466123
\(34\) −6.12742 + 3.87757i −1.05084 + 0.664998i
\(35\) 4.10245i 0.693440i
\(36\) −0.856193 + 1.80747i −0.142699 + 0.301244i
\(37\) 1.42477i 0.234231i −0.993118 0.117116i \(-0.962635\pi\)
0.993118 0.117116i \(-0.0373648\pi\)
\(38\) −2.10245 3.32233i −0.341062 0.538952i
\(39\) 3.02497 0.484383
\(40\) 11.5175 1.41004i 1.82107 0.222947i
\(41\) 5.12742 0.800768 0.400384 0.916347i \(-0.368877\pi\)
0.400384 + 0.916347i \(0.368877\pi\)
\(42\) 0.756243 + 1.19503i 0.116691 + 0.184397i
\(43\) 2.39980i 0.365966i −0.983116 0.182983i \(-0.941425\pi\)
0.983116 0.182983i \(-0.0585754\pi\)
\(44\) −4.83980 2.29261i −0.729628 0.345623i
\(45\) 4.10245i 0.611557i
\(46\) 8.51748 5.39006i 1.25583 0.794721i
\(47\) −9.56024 −1.39450 −0.697252 0.716826i \(-0.745594\pi\)
−0.697252 + 0.716826i \(0.745594\pi\)
\(48\) 3.09508 2.53387i 0.446736 0.365732i
\(49\) 1.00000 0.142857
\(50\) −14.1373 + 8.94640i −1.99931 + 1.26521i
\(51\) 5.12742i 0.717982i
\(52\) −5.46753 2.58996i −0.758211 0.359163i
\(53\) 2.78012i 0.381879i 0.981602 + 0.190939i \(0.0611534\pi\)
−0.981602 + 0.190939i \(0.938847\pi\)
\(54\) −0.756243 1.19503i −0.102912 0.162623i
\(55\) 10.9850 1.48122
\(56\) −0.343707 2.80747i −0.0459298 0.375163i
\(57\) 2.78012 0.368236
\(58\) 6.67767 + 10.5522i 0.876822 + 1.38557i
\(59\) 4.00000i 0.520756i −0.965507 0.260378i \(-0.916153\pi\)
0.965507 0.260378i \(-0.0838471\pi\)
\(60\) −3.51249 + 7.41503i −0.453460 + 0.957276i
\(61\) 5.17992i 0.663221i 0.943416 + 0.331610i \(0.107592\pi\)
−0.943416 + 0.331610i \(0.892408\pi\)
\(62\) −1.70265 + 1.07747i −0.216236 + 0.136839i
\(63\) −1.00000 −0.125988
\(64\) −7.76373 + 1.92989i −0.970466 + 0.241237i
\(65\) 12.4098 1.53924
\(66\) 3.19990 2.02497i 0.393880 0.249257i
\(67\) 0.244852i 0.0299135i 0.999888 + 0.0149567i \(0.00476105\pi\)
−0.999888 + 0.0149567i \(0.995239\pi\)
\(68\) −4.39006 + 9.26763i −0.532373 + 1.12387i
\(69\) 7.12742i 0.858040i
\(70\) 3.10245 + 4.90255i 0.370813 + 0.585966i
\(71\) −4.27787 −0.507690 −0.253845 0.967245i \(-0.581695\pi\)
−0.253845 + 0.967245i \(0.581695\pi\)
\(72\) 0.343707 + 2.80747i 0.0405063 + 0.330863i
\(73\) −4.15495 −0.486300 −0.243150 0.969989i \(-0.578181\pi\)
−0.243150 + 0.969989i \(0.578181\pi\)
\(74\) −1.07747 1.70265i −0.125254 0.197929i
\(75\) 11.8301i 1.36602i
\(76\) −5.02497 2.38032i −0.576404 0.273041i
\(77\) 2.67767i 0.305149i
\(78\) 3.61493 2.28761i 0.409310 0.259021i
\(79\) 6.25484 0.703724 0.351862 0.936052i \(-0.385549\pi\)
0.351862 + 0.936052i \(0.385549\pi\)
\(80\) 12.6974 10.3951i 1.41961 1.16220i
\(81\) 1.00000 0.111111
\(82\) 6.12742 3.87757i 0.676660 0.428206i
\(83\) 9.35535i 1.02688i 0.858125 + 0.513441i \(0.171630\pi\)
−0.858125 + 0.513441i \(0.828370\pi\)
\(84\) 1.80747 + 0.856193i 0.197211 + 0.0934183i
\(85\) 21.0350i 2.28156i
\(86\) −1.81483 2.86783i −0.195698 0.309246i
\(87\) −8.83006 −0.946682
\(88\) −7.51748 + 0.920336i −0.801366 + 0.0981081i
\(89\) 11.2824 1.19593 0.597964 0.801523i \(-0.295976\pi\)
0.597964 + 0.801523i \(0.295976\pi\)
\(90\) −3.10245 4.90255i −0.327027 0.516774i
\(91\) 3.02497i 0.317103i
\(92\) 6.10245 12.8826i 0.636224 1.34310i
\(93\) 1.42477i 0.147742i
\(94\) −11.4248 + 7.22986i −1.17838 + 0.745704i
\(95\) 11.4053 1.17016
\(96\) 1.78249 5.36868i 0.181925 0.547939i
\(97\) 6.69460 0.679733 0.339867 0.940474i \(-0.389618\pi\)
0.339867 + 0.940474i \(0.389618\pi\)
\(98\) 1.19503 0.756243i 0.120716 0.0763921i
\(99\) 2.67767i 0.269116i
\(100\) −10.1288 + 21.3824i −1.01288 + 2.13824i
\(101\) 1.45779i 0.145056i −0.997366 0.0725279i \(-0.976893\pi\)
0.997366 0.0725279i \(-0.0231066\pi\)
\(102\) −3.87757 6.12742i −0.383937 0.606705i
\(103\) 8.13547 0.801611 0.400806 0.916163i \(-0.368730\pi\)
0.400806 + 0.916163i \(0.368730\pi\)
\(104\) −8.49251 + 1.03970i −0.832759 + 0.101951i
\(105\) −4.10245 −0.400358
\(106\) 2.10245 + 3.32233i 0.204208 + 0.322693i
\(107\) 5.32233i 0.514529i −0.966341 0.257264i \(-0.917179\pi\)
0.966341 0.257264i \(-0.0828211\pi\)
\(108\) −1.80747 0.856193i −0.173923 0.0823872i
\(109\) 13.5602i 1.29884i 0.760432 + 0.649418i \(0.224987\pi\)
−0.760432 + 0.649418i \(0.775013\pi\)
\(110\) 13.1274 8.30734i 1.25165 0.792074i
\(111\) 1.42477 0.135233
\(112\) −2.53387 3.09508i −0.239428 0.292458i
\(113\) −4.15495 −0.390865 −0.195432 0.980717i \(-0.562611\pi\)
−0.195432 + 0.980717i \(0.562611\pi\)
\(114\) 3.32233 2.10245i 0.311164 0.196912i
\(115\) 29.2398i 2.72663i
\(116\) 15.9600 + 7.56024i 1.48185 + 0.701951i
\(117\) 3.02497i 0.279659i
\(118\) −3.02497 4.78012i −0.278471 0.440046i
\(119\) −5.12742 −0.470030
\(120\) 1.41004 + 11.5175i 0.128718 + 1.05140i
\(121\) 3.83006 0.348188
\(122\) 3.91728 + 6.19016i 0.354654 + 0.560431i
\(123\) 5.12742i 0.462324i
\(124\) −1.21988 + 2.57523i −0.109548 + 0.231262i
\(125\) 28.0200i 2.50618i
\(126\) −1.19503 + 0.756243i −0.106462 + 0.0673715i
\(127\) −0.694597 −0.0616355 −0.0308177 0.999525i \(-0.509811\pi\)
−0.0308177 + 0.999525i \(0.509811\pi\)
\(128\) −7.81842 + 8.17755i −0.691058 + 0.722800i
\(129\) 2.39980 0.211291
\(130\) 14.8301 9.38481i 1.30068 0.823102i
\(131\) 12.2049i 1.06635i 0.846006 + 0.533173i \(0.179001\pi\)
−0.846006 + 0.533173i \(0.820999\pi\)
\(132\) 2.29261 4.83980i 0.199546 0.421251i
\(133\) 2.78012i 0.241067i
\(134\) 0.185168 + 0.292606i 0.0159961 + 0.0252773i
\(135\) 4.10245 0.353082
\(136\) 1.76233 + 14.3951i 0.151119 + 1.23437i
\(137\) −15.1044 −1.29045 −0.645227 0.763991i \(-0.723237\pi\)
−0.645227 + 0.763991i \(0.723237\pi\)
\(138\) 5.39006 + 8.51748i 0.458832 + 0.725056i
\(139\) 7.61018i 0.645487i 0.946486 + 0.322744i \(0.104605\pi\)
−0.946486 + 0.322744i \(0.895395\pi\)
\(140\) 7.41503 + 3.51249i 0.626685 + 0.296859i
\(141\) 9.56024i 0.805117i
\(142\) −5.11219 + 3.23511i −0.429005 + 0.271485i
\(143\) −8.09989 −0.677347
\(144\) 2.53387 + 3.09508i 0.211156 + 0.257923i
\(145\) −36.2249 −3.00831
\(146\) −4.96529 + 3.14215i −0.410930 + 0.260046i
\(147\) 1.00000i 0.0824786i
\(148\) −2.57523 1.21988i −0.211682 0.100274i
\(149\) 5.21988i 0.427629i −0.976874 0.213815i \(-0.931411\pi\)
0.976874 0.213815i \(-0.0685889\pi\)
\(150\) −8.94640 14.1373i −0.730471 1.15430i
\(151\) −5.56024 −0.452486 −0.226243 0.974071i \(-0.572644\pi\)
−0.226243 + 0.974071i \(0.572644\pi\)
\(152\) −7.80509 + 0.955547i −0.633077 + 0.0775051i
\(153\) 5.12742 0.414527
\(154\) −2.02497 3.19990i −0.163177 0.257855i
\(155\) 5.84505i 0.469486i
\(156\) 2.58996 5.46753i 0.207363 0.437753i
\(157\) 0.519169i 0.0414342i 0.999785 + 0.0207171i \(0.00659493\pi\)
−0.999785 + 0.0207171i \(0.993405\pi\)
\(158\) 7.47472 4.73018i 0.594656 0.376313i
\(159\) −2.78012 −0.220478
\(160\) 7.31259 22.0247i 0.578111 1.74121i
\(161\) 7.12742 0.561719
\(162\) 1.19503 0.756243i 0.0938904 0.0594161i
\(163\) 8.65464i 0.677883i −0.940807 0.338942i \(-0.889931\pi\)
0.940807 0.338942i \(-0.110069\pi\)
\(164\) 4.39006 9.26763i 0.342806 0.723681i
\(165\) 10.9850i 0.855182i
\(166\) 7.07492 + 11.1799i 0.549120 + 0.867730i
\(167\) −25.1044 −1.94264 −0.971318 0.237786i \(-0.923578\pi\)
−0.971318 + 0.237786i \(0.923578\pi\)
\(168\) 2.80747 0.343707i 0.216601 0.0265176i
\(169\) 3.84954 0.296119
\(170\) −15.9075 25.1374i −1.22005 1.92795i
\(171\) 2.78012i 0.212601i
\(172\) −4.33756 2.05469i −0.330736 0.156669i
\(173\) 1.94750i 0.148066i 0.997256 + 0.0740328i \(0.0235869\pi\)
−0.997256 + 0.0740328i \(0.976413\pi\)
\(174\) −10.5522 + 6.67767i −0.799959 + 0.506233i
\(175\) −11.8301 −0.894269
\(176\) −8.28761 + 6.78487i −0.624702 + 0.511429i
\(177\) 4.00000 0.300658
\(178\) 13.4828 8.53221i 1.01058 0.639516i
\(179\) 22.6976i 1.69650i −0.529595 0.848251i \(-0.677656\pi\)
0.529595 0.848251i \(-0.322344\pi\)
\(180\) −7.41503 3.51249i −0.552684 0.261805i
\(181\) 10.5353i 0.783080i −0.920161 0.391540i \(-0.871942\pi\)
0.920161 0.391540i \(-0.128058\pi\)
\(182\) −2.28761 3.61493i −0.169569 0.267957i
\(183\) −5.17992 −0.382911
\(184\) −2.44974 20.0100i −0.180598 1.47516i
\(185\) 5.84505 0.429737
\(186\) −1.07747 1.70265i −0.0790042 0.124844i
\(187\) 13.7296i 1.00400i
\(188\) −8.18541 + 17.2798i −0.596982 + 1.26026i
\(189\) 1.00000i 0.0727393i
\(190\) 13.6297 8.62517i 0.988800 0.625736i
\(191\) −4.27787 −0.309536 −0.154768 0.987951i \(-0.549463\pi\)
−0.154768 + 0.987951i \(0.549463\pi\)
\(192\) −1.92989 7.76373i −0.139278 0.560299i
\(193\) 23.1400 1.66565 0.832825 0.553536i \(-0.186722\pi\)
0.832825 + 0.553536i \(0.186722\pi\)
\(194\) 8.00024 5.06274i 0.574384 0.363484i
\(195\) 12.4098i 0.888683i
\(196\) 0.856193 1.80747i 0.0611566 0.129105i
\(197\) 19.4747i 1.38752i 0.720208 + 0.693758i \(0.244046\pi\)
−0.720208 + 0.693758i \(0.755954\pi\)
\(198\) 2.02497 + 3.19990i 0.143908 + 0.227407i
\(199\) −17.5602 −1.24481 −0.622406 0.782694i \(-0.713845\pi\)
−0.622406 + 0.782694i \(0.713845\pi\)
\(200\) 4.06608 + 33.2125i 0.287515 + 2.34848i
\(201\) −0.244852 −0.0172705
\(202\) −1.10245 1.74211i −0.0775678 0.122574i
\(203\) 8.83006i 0.619749i
\(204\) −9.26763 4.39006i −0.648864 0.307366i
\(205\) 21.0350i 1.46915i
\(206\) 9.72213 6.15239i 0.677373 0.428657i
\(207\) −7.12742 −0.495390
\(208\) −9.36253 + 7.66488i −0.649175 + 0.531464i
\(209\) −7.44425 −0.514930
\(210\) −4.90255 + 3.10245i −0.338308 + 0.214089i
\(211\) 23.9600i 1.64948i 0.565514 + 0.824739i \(0.308678\pi\)
−0.565514 + 0.824739i \(0.691322\pi\)
\(212\) 5.02497 + 2.38032i 0.345116 + 0.163481i
\(213\) 4.27787i 0.293115i
\(214\) −4.02497 6.36034i −0.275141 0.434784i
\(215\) 9.84505 0.671427
\(216\) −2.80747 + 0.343707i −0.191024 + 0.0233863i
\(217\) −1.42477 −0.0967199
\(218\) 10.2548 + 16.2049i 0.694545 + 1.09753i
\(219\) 4.15495i 0.280765i
\(220\) 9.40529 19.8550i 0.634105 1.33863i
\(221\) 15.5103i 1.04334i
\(222\) 1.70265 1.07747i 0.114274 0.0723153i
\(223\) 2.74966 0.184131 0.0920653 0.995753i \(-0.470653\pi\)
0.0920653 + 0.995753i \(0.470653\pi\)
\(224\) −5.36868 1.78249i −0.358710 0.119098i
\(225\) 11.8301 0.788671
\(226\) −4.96529 + 3.14215i −0.330286 + 0.209013i
\(227\) 8.30478i 0.551208i −0.961271 0.275604i \(-0.911122\pi\)
0.961271 0.275604i \(-0.0888778\pi\)
\(228\) 2.38032 5.02497i 0.157640 0.332787i
\(229\) 11.9245i 0.787991i −0.919112 0.393995i \(-0.871093\pi\)
0.919112 0.393995i \(-0.128907\pi\)
\(230\) 22.1124 + 34.9425i 1.45805 + 2.30404i
\(231\) 2.67767 0.176178
\(232\) 24.7901 3.03496i 1.62755 0.199255i
\(233\) −3.56024 −0.233239 −0.116620 0.993177i \(-0.537206\pi\)
−0.116620 + 0.993177i \(0.537206\pi\)
\(234\) 2.28761 + 3.61493i 0.149546 + 0.236315i
\(235\) 39.2204i 2.55845i
\(236\) −7.22986 3.42477i −0.470624 0.222934i
\(237\) 6.25484i 0.406295i
\(238\) −6.12742 + 3.87757i −0.397182 + 0.251346i
\(239\) 26.9425 1.74277 0.871383 0.490604i \(-0.163224\pi\)
0.871383 + 0.490604i \(0.163224\pi\)
\(240\) 10.3951 + 12.6974i 0.670998 + 0.819614i
\(241\) 25.8151 1.66290 0.831448 0.555603i \(-0.187513\pi\)
0.831448 + 0.555603i \(0.187513\pi\)
\(242\) 4.57704 2.89646i 0.294223 0.186191i
\(243\) 1.00000i 0.0641500i
\(244\) 9.36253 + 4.43501i 0.599375 + 0.283923i
\(245\) 4.10245i 0.262096i
\(246\) 3.87757 + 6.12742i 0.247225 + 0.390670i
\(247\) −8.40978 −0.535102
\(248\) 0.489704 + 4.00000i 0.0310963 + 0.254000i
\(249\) −9.35535 −0.592871
\(250\) −21.1899 33.4847i −1.34017 2.11776i
\(251\) 27.1543i 1.71397i −0.515345 0.856983i \(-0.672336\pi\)
0.515345 0.856983i \(-0.327664\pi\)
\(252\) −0.856193 + 1.80747i −0.0539351 + 0.113860i
\(253\) 19.0849i 1.19986i
\(254\) −0.830064 + 0.525284i −0.0520828 + 0.0329592i
\(255\) 21.0350 1.31726
\(256\) −3.15904 + 15.6850i −0.197440 + 0.980315i
\(257\) −31.3823 −1.95757 −0.978786 0.204887i \(-0.934317\pi\)
−0.978786 + 0.204887i \(0.934317\pi\)
\(258\) 2.86783 1.81483i 0.178544 0.112987i
\(259\) 1.42477i 0.0885310i
\(260\) 10.6252 22.4303i 0.658945 1.39107i
\(261\) 8.83006i 0.546567i
\(262\) 9.22986 + 14.5852i 0.570223 + 0.901077i
\(263\) −11.0275 −0.679987 −0.339993 0.940428i \(-0.610425\pi\)
−0.339993 + 0.940428i \(0.610425\pi\)
\(264\) −0.920336 7.51748i −0.0566427 0.462669i
\(265\) −11.4053 −0.700621
\(266\) −2.10245 3.32233i −0.128909 0.203705i
\(267\) 11.2824i 0.690470i
\(268\) 0.442562 + 0.209641i 0.0270338 + 0.0128058i
\(269\) 21.0019i 1.28051i −0.768162 0.640255i \(-0.778829\pi\)
0.768162 0.640255i \(-0.221171\pi\)
\(270\) 4.90255 3.10245i 0.298359 0.188809i
\(271\) 28.6451 1.74007 0.870034 0.492991i \(-0.164097\pi\)
0.870034 + 0.492991i \(0.164097\pi\)
\(272\) 12.9922 + 15.8698i 0.787767 + 0.962246i
\(273\) 3.02497 0.183080
\(274\) −18.0502 + 11.4226i −1.09045 + 0.690063i
\(275\) 31.6771i 1.91020i
\(276\) 12.8826 + 6.10245i 0.775439 + 0.367324i
\(277\) 2.96504i 0.178152i −0.996025 0.0890761i \(-0.971609\pi\)
0.996025 0.0890761i \(-0.0283914\pi\)
\(278\) 5.75515 + 9.09440i 0.345171 + 0.545446i
\(279\) 1.42477 0.0852989
\(280\) 11.5175 1.41004i 0.688301 0.0842660i
\(281\) 26.4098 1.57548 0.787738 0.616011i \(-0.211252\pi\)
0.787738 + 0.616011i \(0.211252\pi\)
\(282\) −7.22986 11.4248i −0.430532 0.680335i
\(283\) 11.2698i 0.669922i −0.942232 0.334961i \(-0.891277\pi\)
0.942232 0.334961i \(-0.108723\pi\)
\(284\) −3.66269 + 7.73211i −0.217340 + 0.458816i
\(285\) 11.4053i 0.675591i
\(286\) −9.67961 + 6.12548i −0.572367 + 0.362207i
\(287\) 5.12742 0.302662
\(288\) 5.36868 + 1.78249i 0.316352 + 0.105034i
\(289\) 9.29042 0.546495
\(290\) −43.2898 + 27.3948i −2.54206 + 1.60868i
\(291\) 6.69460i 0.392444i
\(292\) −3.55744 + 7.50993i −0.208183 + 0.439485i
\(293\) 10.5622i 0.617049i −0.951216 0.308524i \(-0.900165\pi\)
0.951216 0.308524i \(-0.0998351\pi\)
\(294\) 0.756243 + 1.19503i 0.0441050 + 0.0696956i
\(295\) 16.4098 0.955415
\(296\) −4.00000 + 0.489704i −0.232495 + 0.0284635i
\(297\) −2.67767 −0.155374
\(298\) −3.94750 6.23791i −0.228672 0.361353i
\(299\) 21.5602i 1.24686i
\(300\) −21.3824 10.1288i −1.23452 0.584788i
\(301\) 2.39980i 0.138322i
\(302\) −6.64465 + 4.20489i −0.382357 + 0.241964i
\(303\) 1.45779 0.0837480
\(304\) −8.60469 + 7.04445i −0.493513 + 0.404027i
\(305\) −21.2503 −1.21679
\(306\) 6.12742 3.87757i 0.350281 0.221666i
\(307\) 10.7801i 0.615254i 0.951507 + 0.307627i \(0.0995349\pi\)
−0.951507 + 0.307627i \(0.900465\pi\)
\(308\) −4.83980 2.29261i −0.275773 0.130633i
\(309\) 8.13547i 0.462811i
\(310\) −4.42028 6.98501i −0.251055 0.396722i
\(311\) 9.56024 0.542111 0.271056 0.962564i \(-0.412627\pi\)
0.271056 + 0.962564i \(0.412627\pi\)
\(312\) −1.03970 8.49251i −0.0588617 0.480793i
\(313\) 7.69909 0.435178 0.217589 0.976040i \(-0.430181\pi\)
0.217589 + 0.976040i \(0.430181\pi\)
\(314\) 0.392618 + 0.620423i 0.0221567 + 0.0350125i
\(315\) 4.10245i 0.231147i
\(316\) 5.35535 11.3054i 0.301262 0.635979i
\(317\) 10.7801i 0.605472i 0.953074 + 0.302736i \(0.0979000\pi\)
−0.953074 + 0.302736i \(0.902100\pi\)
\(318\) −3.32233 + 2.10245i −0.186307 + 0.117899i
\(319\) 23.6440 1.32381
\(320\) −7.91728 31.8503i −0.442589 1.78049i
\(321\) 5.32233 0.297063
\(322\) 8.51748 5.39006i 0.474660 0.300376i
\(323\) 14.2548i 0.793160i
\(324\) 0.856193 1.80747i 0.0475663 0.100415i
\(325\) 35.7856i 1.98503i
\(326\) −6.54501 10.3425i −0.362494 0.572821i
\(327\) −13.5602 −0.749883
\(328\) −1.76233 14.3951i −0.0973084 0.794834i
\(329\) −9.56024 −0.527073
\(330\) 8.30734 + 13.1274i 0.457304 + 0.722641i
\(331\) 25.2104i 1.38569i −0.721088 0.692844i \(-0.756357\pi\)
0.721088 0.692844i \(-0.243643\pi\)
\(332\) 16.9095 + 8.00998i 0.928028 + 0.439605i
\(333\) 1.42477i 0.0780770i
\(334\) −30.0005 + 18.9850i −1.64155 + 1.03881i
\(335\) −1.00449 −0.0548813
\(336\) 3.09508 2.53387i 0.168850 0.138234i
\(337\) −23.9700 −1.30573 −0.652865 0.757474i \(-0.726433\pi\)
−0.652865 + 0.757474i \(0.726433\pi\)
\(338\) 4.60032 2.91119i 0.250224 0.158348i
\(339\) 4.15495i 0.225666i
\(340\) −38.0200 18.0100i −2.06192 0.976729i
\(341\) 3.81508i 0.206598i
\(342\) 2.10245 + 3.32233i 0.113687 + 0.179651i
\(343\) 1.00000 0.0539949
\(344\) −6.73736 + 0.824828i −0.363254 + 0.0444718i
\(345\) −29.2398 −1.57422
\(346\) 1.47278 + 2.32732i 0.0791772 + 0.125117i
\(347\) 6.98757i 0.375112i −0.982254 0.187556i \(-0.939943\pi\)
0.982254 0.187556i \(-0.0600567\pi\)
\(348\) −7.56024 + 15.9600i −0.405271 + 0.855548i
\(349\) 20.8900i 1.11822i 0.829095 + 0.559108i \(0.188856\pi\)
−0.829095 + 0.559108i \(0.811144\pi\)
\(350\) −14.1373 + 8.94640i −0.755669 + 0.478205i
\(351\) −3.02497 −0.161461
\(352\) −4.77294 + 14.3756i −0.254398 + 0.766220i
\(353\) 3.38225 0.180019 0.0900096 0.995941i \(-0.471310\pi\)
0.0900096 + 0.995941i \(0.471310\pi\)
\(354\) 4.78012 3.02497i 0.254060 0.160775i
\(355\) 17.5497i 0.931444i
\(356\) 9.65988 20.3925i 0.511973 1.08080i
\(357\) 5.12742i 0.271372i
\(358\) −17.1649 27.1244i −0.907195 1.43357i
\(359\) 20.6877 1.09185 0.545926 0.837833i \(-0.316178\pi\)
0.545926 + 0.837833i \(0.316178\pi\)
\(360\) −11.5175 + 1.41004i −0.607024 + 0.0743156i
\(361\) 11.2709 0.593207
\(362\) −7.96722 12.5900i −0.418748 0.661714i
\(363\) 3.83006i 0.201026i
\(364\) −5.46753 2.58996i −0.286577 0.135751i
\(365\) 17.0455i 0.892200i
\(366\) −6.19016 + 3.91728i −0.323565 + 0.204759i
\(367\) −9.56024 −0.499040 −0.249520 0.968370i \(-0.580273\pi\)
−0.249520 + 0.968370i \(0.580273\pi\)
\(368\) −18.0599 22.0599i −0.941439 1.14995i
\(369\) −5.12742 −0.266923
\(370\) 6.98501 4.42028i 0.363133 0.229799i
\(371\) 2.78012i 0.144337i
\(372\) −2.57523 1.21988i −0.133519 0.0632478i
\(373\) 1.95006i 0.100970i −0.998725 0.0504850i \(-0.983923\pi\)
0.998725 0.0504850i \(-0.0160767\pi\)
\(374\) 10.3829 + 16.4072i 0.536886 + 0.848397i
\(375\) 28.0200 1.44694
\(376\) 3.28592 + 26.8400i 0.169459 + 1.38417i
\(377\) 26.7107 1.37567
\(378\) −0.756243 1.19503i −0.0388969 0.0614657i
\(379\) 32.3698i 1.66273i −0.555730 0.831363i \(-0.687561\pi\)
0.555730 0.831363i \(-0.312439\pi\)
\(380\) 9.76513 20.6147i 0.500941 1.05751i
\(381\) 0.694597i 0.0355853i
\(382\) −5.11219 + 3.23511i −0.261562 + 0.165523i
\(383\) −17.8451 −0.911840 −0.455920 0.890021i \(-0.650690\pi\)
−0.455920 + 0.890021i \(0.650690\pi\)
\(384\) −8.17755 7.81842i −0.417309 0.398982i
\(385\) 10.9850 0.559848
\(386\) 27.6529 17.4994i 1.40750 0.890698i
\(387\) 2.39980i 0.121989i
\(388\) 5.73187 12.1003i 0.290991 0.614297i
\(389\) 6.11937i 0.310264i −0.987894 0.155132i \(-0.950420\pi\)
0.987894 0.155132i \(-0.0495803\pi\)
\(390\) 9.38481 + 14.8301i 0.475218 + 0.750949i
\(391\) −36.5453 −1.84817
\(392\) −0.343707 2.80747i −0.0173598 0.141798i
\(393\) −12.2049 −0.615655
\(394\) 14.7276 + 23.2729i 0.741967 + 1.17247i
\(395\) 25.6601i 1.29110i
\(396\) 4.83980 + 2.29261i 0.243209 + 0.115208i
\(397\) 3.71957i 0.186680i −0.995634 0.0933399i \(-0.970246\pi\)
0.995634 0.0933399i \(-0.0297543\pi\)
\(398\) −20.9850 + 13.2798i −1.05188 + 0.665657i
\(399\) 2.78012 0.139180
\(400\) 29.9758 + 36.6150i 1.49879 + 1.83075i
\(401\) −32.5258 −1.62426 −0.812130 0.583477i \(-0.801692\pi\)
−0.812130 + 0.583477i \(0.801692\pi\)
\(402\) −0.292606 + 0.185168i −0.0145938 + 0.00923533i
\(403\) 4.30990i 0.214691i
\(404\) −2.63491 1.24815i −0.131092 0.0620979i
\(405\) 4.10245i 0.203852i
\(406\) 6.67767 + 10.5522i 0.331407 + 0.523696i
\(407\) −3.81508 −0.189106
\(408\) −14.3951 + 1.76233i −0.712661 + 0.0872483i
\(409\) −1.13436 −0.0560903 −0.0280452 0.999607i \(-0.508928\pi\)
−0.0280452 + 0.999607i \(0.508928\pi\)
\(410\) 15.9075 + 25.1374i 0.785617 + 1.24145i
\(411\) 15.1044i 0.745044i
\(412\) 6.96553 14.7046i 0.343167 0.724443i
\(413\) 4.00000i 0.196827i
\(414\) −8.51748 + 5.39006i −0.418611 + 0.264907i
\(415\) −38.3798 −1.88399
\(416\) −5.39199 + 16.2401i −0.264364 + 0.796237i
\(417\) −7.61018 −0.372672
\(418\) −8.89611 + 5.62966i −0.435123 + 0.275356i
\(419\) 1.56024i 0.0762227i −0.999273 0.0381113i \(-0.987866\pi\)
0.999273 0.0381113i \(-0.0121342\pi\)
\(420\) −3.51249 + 7.41503i −0.171392 + 0.361817i
\(421\) 31.8845i 1.55396i 0.629528 + 0.776978i \(0.283248\pi\)
−0.629528 + 0.776978i \(0.716752\pi\)
\(422\) 18.1196 + 28.6330i 0.882049 + 1.39383i
\(423\) 9.56024 0.464835
\(424\) 7.80509 0.955547i 0.379049 0.0464055i
\(425\) 60.6577 2.94233
\(426\) −3.23511 5.11219i −0.156742 0.247686i
\(427\) 5.17992i 0.250674i
\(428\) −9.61992 4.55694i −0.464997 0.220268i
\(429\) 8.09989i 0.391066i
\(430\) 11.7651 7.44525i 0.567365 0.359042i
\(431\) 8.87258 0.427377 0.213689 0.976902i \(-0.431452\pi\)
0.213689 + 0.976902i \(0.431452\pi\)
\(432\) −3.09508 + 2.53387i −0.148912 + 0.121911i
\(433\) 11.5602 0.555550 0.277775 0.960646i \(-0.410403\pi\)
0.277775 + 0.960646i \(0.410403\pi\)
\(434\) −1.70265 + 1.07747i −0.0817296 + 0.0517204i
\(435\) 36.2249i 1.73685i
\(436\) 24.5097 + 11.6102i 1.17380 + 0.556027i
\(437\) 19.8151i 0.947884i
\(438\) −3.14215 4.96529i −0.150138 0.237251i
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) −3.77563 30.8400i −0.179996 1.47024i
\(441\) −1.00000 −0.0476190
\(442\) 11.7296 + 18.5353i 0.557918 + 0.881633i
\(443\) 5.87807i 0.279276i −0.990203 0.139638i \(-0.955406\pi\)
0.990203 0.139638i \(-0.0445938\pi\)
\(444\) 1.21988 2.57523i 0.0578930 0.122215i
\(445\) 46.2853i 2.19413i
\(446\) 3.28592 2.07941i 0.155593 0.0984629i
\(447\) 5.21988 0.246892
\(448\) −7.76373 + 1.92989i −0.366802 + 0.0911788i
\(449\) −11.8451 −0.559003 −0.279501 0.960145i \(-0.590169\pi\)
−0.279501 + 0.960145i \(0.590169\pi\)
\(450\) 14.1373 8.94640i 0.666438 0.421737i
\(451\) 13.7296i 0.646499i
\(452\) −3.55744 + 7.50993i −0.167328 + 0.353237i
\(453\) 5.56024i 0.261243i
\(454\) −6.28043 9.92446i −0.294755 0.465778i
\(455\) 12.4098 0.581780
\(456\) −0.955547 7.80509i −0.0447476 0.365507i
\(457\) −28.2088 −1.31955 −0.659775 0.751463i \(-0.729348\pi\)
−0.659775 + 0.751463i \(0.729348\pi\)
\(458\) −9.01779 14.2501i −0.421374 0.665863i
\(459\) 5.12742i 0.239327i
\(460\) 52.8500 + 25.0350i 2.46415 + 1.16726i
\(461\) 11.0519i 0.514737i 0.966313 + 0.257369i \(0.0828555\pi\)
−0.966313 + 0.257369i \(0.917145\pi\)
\(462\) 3.19990 2.02497i 0.148873 0.0942102i
\(463\) −22.2548 −1.03427 −0.517135 0.855904i \(-0.673001\pi\)
−0.517135 + 0.855904i \(0.673001\pi\)
\(464\) 27.3298 22.3742i 1.26875 1.03870i
\(465\) 5.84505 0.271058
\(466\) −4.25459 + 2.69241i −0.197090 + 0.124723i
\(467\) 21.4552i 0.992830i −0.868085 0.496415i \(-0.834649\pi\)
0.868085 0.496415i \(-0.165351\pi\)
\(468\) 5.46753 + 2.58996i 0.252737 + 0.119721i
\(469\) 0.244852i 0.0113062i
\(470\) −29.6601 46.8695i −1.36812 2.16193i
\(471\) −0.519169 −0.0239221
\(472\) −11.2299 + 1.37483i −0.516896 + 0.0632816i
\(473\) −6.42588 −0.295462
\(474\) 4.73018 + 7.47472i 0.217264 + 0.343325i
\(475\) 32.8890i 1.50905i
\(476\) −4.39006 + 9.26763i −0.201218 + 0.424781i
\(477\) 2.78012i 0.127293i
\(478\) 32.1971 20.3751i 1.47266 0.931934i
\(479\) 8.09989 0.370093 0.185047 0.982730i \(-0.440756\pi\)
0.185047 + 0.982730i \(0.440756\pi\)
\(480\) 22.0247 + 7.31259i 1.00529 + 0.333772i
\(481\) −4.30990 −0.196514
\(482\) 30.8498 19.5225i 1.40517 0.889224i
\(483\) 7.12742i 0.324309i
\(484\) 3.27927 6.92271i 0.149058 0.314669i
\(485\) 27.4642i 1.24709i
\(486\) 0.756243 + 1.19503i 0.0343039 + 0.0542077i
\(487\) −16.4098 −0.743598 −0.371799 0.928313i \(-0.621259\pi\)
−0.371799 + 0.928313i \(0.621259\pi\)
\(488\) 14.5424 1.78038i 0.658306 0.0805938i
\(489\) 8.65464 0.391376
\(490\) 3.10245 + 4.90255i 0.140154 + 0.221474i
\(491\) 39.5971i 1.78699i 0.449070 + 0.893497i \(0.351755\pi\)
−0.449070 + 0.893497i \(0.648245\pi\)
\(492\) 9.26763 + 4.39006i 0.417817 + 0.197919i
\(493\) 45.2754i 2.03910i
\(494\) −10.0499 + 6.35984i −0.452168 + 0.286143i
\(495\) −10.9850 −0.493740
\(496\) 3.61018 + 4.40978i 0.162102 + 0.198005i
\(497\) −4.27787 −0.191889
\(498\) −11.1799 + 7.07492i −0.500984 + 0.317035i
\(499\) 1.14946i 0.0514568i 0.999669 + 0.0257284i \(0.00819050\pi\)
−0.999669 + 0.0257284i \(0.991809\pi\)
\(500\) −50.6451 23.9905i −2.26492 1.07289i
\(501\) 25.1044i 1.12158i
\(502\) −20.5353 32.4502i −0.916534 1.44832i
\(503\) 9.00449 0.401490 0.200745 0.979643i \(-0.435664\pi\)
0.200745 + 0.979643i \(0.435664\pi\)
\(504\) 0.343707 + 2.80747i 0.0153099 + 0.125054i
\(505\) 5.98052 0.266130
\(506\) −14.4328 22.8070i −0.641617 1.01390i
\(507\) 3.84954i 0.170964i
\(508\) −0.594709 + 1.25546i −0.0263859 + 0.0557020i
\(509\) 36.5122i 1.61838i 0.587550 + 0.809188i \(0.300093\pi\)
−0.587550 + 0.809188i \(0.699907\pi\)
\(510\) 25.1374 15.9075i 1.11310 0.704398i
\(511\) −4.15495 −0.183804
\(512\) 8.08656 + 21.1331i 0.357379 + 0.933960i
\(513\) −2.78012 −0.122745
\(514\) −37.5027 + 23.7326i −1.65417 + 1.04680i
\(515\) 33.3753i 1.47069i
\(516\) 2.05469 4.33756i 0.0904528 0.190950i
\(517\) 25.5992i 1.12585i
\(518\) −1.07747 1.70265i −0.0473415 0.0748100i
\(519\) −1.94750 −0.0854857
\(520\) −4.26533 34.8400i −0.187047 1.52784i
\(521\) −18.0929 −0.792666 −0.396333 0.918107i \(-0.629718\pi\)
−0.396333 + 0.918107i \(0.629718\pi\)
\(522\) −6.67767 10.5522i −0.292274 0.461857i
\(523\) 14.7107i 0.643254i 0.946866 + 0.321627i \(0.104230\pi\)
−0.946866 + 0.321627i \(0.895770\pi\)
\(524\) 22.0599 + 10.4497i 0.963692 + 0.456499i
\(525\) 11.8301i 0.516306i
\(526\) −13.1782 + 8.33949i −0.574598 + 0.363619i
\(527\) 7.30540 0.318228
\(528\) −6.78487 8.28761i −0.295273 0.360672i
\(529\) 27.8001 1.20870
\(530\) −13.6297 + 8.62517i −0.592035 + 0.374654i
\(531\) 4.00000i 0.173585i
\(532\) −5.02497 2.38032i −0.217860 0.103200i
\(533\) 15.5103i 0.671825i
\(534\) 8.53221 + 13.4828i 0.369225 + 0.583456i
\(535\) 21.8346 0.943990
\(536\) 0.687414 0.0841574i 0.0296918 0.00363505i
\(537\) 22.6976 0.979476
\(538\) −15.8826 25.0979i −0.684746 1.08205i
\(539\) 2.67767i 0.115336i
\(540\) 3.51249 7.41503i 0.151153 0.319092i
\(541\) 37.7157i 1.62152i −0.585376 0.810762i \(-0.699053\pi\)
0.585376 0.810762i \(-0.300947\pi\)
\(542\) 34.2318 21.6627i 1.47038 0.930492i
\(543\) 10.5353 0.452112
\(544\) 27.5275 + 9.13959i 1.18023 + 0.391857i
\(545\) −55.6302 −2.38293
\(546\) 3.61493 2.28761i 0.154705 0.0979008i
\(547\) 23.1144i 0.988299i 0.869377 + 0.494149i \(0.164520\pi\)
−0.869377 + 0.494149i \(0.835480\pi\)
\(548\) −12.9323 + 27.3007i −0.552439 + 1.16623i
\(549\) 5.17992i 0.221074i
\(550\) 23.9555 + 37.8550i 1.02147 + 1.61414i
\(551\) 24.5486 1.04581
\(552\) 20.0100 2.44974i 0.851681 0.104268i
\(553\) 6.25484 0.265983
\(554\) −2.24229 3.54332i −0.0952659 0.150541i
\(555\) 5.84505i 0.248109i
\(556\) 13.7551 + 6.51579i 0.583348 + 0.276331i
\(557\) 11.1899i 0.474131i −0.971494 0.237066i \(-0.923814\pi\)
0.971494 0.237066i \(-0.0761857\pi\)
\(558\) 1.70265 1.07747i 0.0720787 0.0456131i
\(559\) −7.25933 −0.307037
\(560\) 12.6974 10.3951i 0.536563 0.439271i
\(561\) −13.7296 −0.579662
\(562\) 31.5605 19.9722i 1.33130 0.842477i
\(563\) 2.81058i 0.118452i 0.998245 + 0.0592260i \(0.0188632\pi\)
−0.998245 + 0.0592260i \(0.981137\pi\)
\(564\) −17.2798 8.18541i −0.727611 0.344668i
\(565\) 17.0455i 0.717108i
\(566\) −8.52273 13.4678i −0.358237 0.566093i
\(567\) 1.00000 0.0419961
\(568\) 1.47034 + 12.0100i 0.0616939 + 0.503928i
\(569\) −20.0699 −0.841374 −0.420687 0.907206i \(-0.638211\pi\)
−0.420687 + 0.907206i \(0.638211\pi\)
\(570\) 8.62517 + 13.6297i 0.361269 + 0.570884i
\(571\) 2.46584i 0.103192i 0.998668 + 0.0515961i \(0.0164309\pi\)
−0.998668 + 0.0515961i \(0.983569\pi\)
\(572\) −6.93507 + 14.6403i −0.289970 + 0.612141i
\(573\) 4.27787i 0.178711i
\(574\) 6.12742 3.87757i 0.255753 0.161847i
\(575\) −84.3178 −3.51630
\(576\) 7.76373 1.92989i 0.323489 0.0804122i
\(577\) 4.84954 0.201889 0.100945 0.994892i \(-0.467814\pi\)
0.100945 + 0.994892i \(0.467814\pi\)
\(578\) 11.1023 7.02581i 0.461796 0.292235i
\(579\) 23.1400i 0.961664i
\(580\) −31.0155 + 65.4752i −1.28785 + 2.71871i
\(581\) 9.35535i 0.388125i
\(582\) 5.06274 + 8.00024i 0.209857 + 0.331621i
\(583\) 7.44425 0.308309
\(584\) 1.42809 + 11.6649i 0.0590946 + 0.482696i
\(585\) −12.4098 −0.513081
\(586\) −7.98757 12.6221i −0.329963 0.521415i
\(587\) 19.0155i 0.784853i −0.919783 0.392426i \(-0.871636\pi\)
0.919783 0.392426i \(-0.128364\pi\)
\(588\) 1.80747 + 0.856193i 0.0745386 + 0.0353088i
\(589\) 3.96104i 0.163212i
\(590\) 19.6102 12.4098i 0.807338 0.510903i
\(591\) −19.4747 −0.801083
\(592\) −4.40978 + 3.61018i −0.181241 + 0.148378i
\(593\) 24.0379 0.987118 0.493559 0.869712i \(-0.335696\pi\)
0.493559 + 0.869712i \(0.335696\pi\)
\(594\) −3.19990 + 2.02497i −0.131293 + 0.0830856i
\(595\) 21.0350i 0.862349i
\(596\) −9.43476 4.46923i −0.386463 0.183067i
\(597\) 17.5602i 0.718693i
\(598\) −16.3048 25.7651i −0.666752 1.05361i
\(599\) 33.9631 1.38769 0.693847 0.720122i \(-0.255914\pi\)
0.693847 + 0.720122i \(0.255914\pi\)
\(600\) −33.2125 + 4.06608i −1.35589 + 0.165997i
\(601\) 10.0999 0.411983 0.205992 0.978554i \(-0.433958\pi\)
0.205992 + 0.978554i \(0.433958\pi\)
\(602\) −1.81483 2.86783i −0.0739670 0.116884i
\(603\) 0.244852i 0.00997115i
\(604\) −4.76064 + 10.0499i −0.193708 + 0.408926i
\(605\) 15.7126i 0.638809i
\(606\) 1.74211 1.10245i 0.0707683 0.0447838i
\(607\) 8.17105 0.331653 0.165826 0.986155i \(-0.446971\pi\)
0.165826 + 0.986155i \(0.446971\pi\)
\(608\) −4.95555 + 14.9256i −0.200974 + 0.605312i
\(609\) −8.83006 −0.357812
\(610\) −25.3948 + 16.0704i −1.02821 + 0.650672i
\(611\) 28.9195i 1.16996i
\(612\) 4.39006 9.26763i 0.177458 0.374622i
\(613\) 23.0206i 0.929793i −0.885365 0.464896i \(-0.846092\pi\)
0.885365 0.464896i \(-0.153908\pi\)
\(614\) 8.15239 + 12.8826i 0.329004 + 0.519898i
\(615\) −21.0350 −0.848211
\(616\) −7.51748 + 0.920336i −0.302888 + 0.0370814i
\(617\) 31.1044 1.25222 0.626108 0.779737i \(-0.284647\pi\)
0.626108 + 0.779737i \(0.284647\pi\)
\(618\) 6.15239 + 9.72213i 0.247485 + 0.391081i
\(619\) 40.9195i 1.64469i −0.568988 0.822346i \(-0.692665\pi\)
0.568988 0.822346i \(-0.307335\pi\)
\(620\) −10.5647 5.00449i −0.424290 0.200985i
\(621\) 7.12742i 0.286013i
\(622\) 11.4248 7.22986i 0.458092 0.289891i
\(623\) 11.2824 0.452018
\(624\) −7.66488 9.36253i −0.306841 0.374801i
\(625\) 55.8001 2.23200
\(626\) 9.20064 5.82238i 0.367732 0.232709i
\(627\) 7.44425i 0.297295i
\(628\) 0.938381 + 0.444509i 0.0374455 + 0.0177378i
\(629\) 7.30540i 0.291286i
\(630\) −3.10245 4.90255i −0.123604 0.195322i
\(631\) −2.29380 −0.0913147 −0.0456573 0.998957i \(-0.514538\pi\)
−0.0456573 + 0.998957i \(0.514538\pi\)
\(632\) −2.14983 17.5602i −0.0855157 0.698509i
\(633\) −23.9600 −0.952326
\(634\) 8.15239 + 12.8826i 0.323773 + 0.511632i
\(635\) 2.84954i 0.113081i
\(636\) −2.38032 + 5.02497i −0.0943858 + 0.199253i
\(637\) 3.02497i 0.119854i
\(638\) 28.2553 17.8806i 1.11864 0.707901i
\(639\) 4.27787 0.169230
\(640\) −33.5479 32.0747i −1.32610 1.26786i
\(641\) 27.0654 1.06902 0.534510 0.845162i \(-0.320496\pi\)
0.534510 + 0.845162i \(0.320496\pi\)
\(642\) 6.36034 4.02497i 0.251023 0.158853i
\(643\) 31.9895i 1.26154i −0.775969 0.630771i \(-0.782739\pi\)
0.775969 0.630771i \(-0.217261\pi\)
\(644\) 6.10245 12.8826i 0.240470 0.507644i
\(645\) 9.84505i 0.387649i
\(646\) 10.7801 + 17.0350i 0.424138 + 0.670231i
\(647\) −12.5947 −0.495149 −0.247575 0.968869i \(-0.579634\pi\)
−0.247575 + 0.968869i \(0.579634\pi\)
\(648\) −0.343707 2.80747i −0.0135021 0.110288i
\(649\) −10.7107 −0.420432
\(650\) 27.0626 + 42.7649i 1.06148 + 1.67738i
\(651\) 1.42477i 0.0558412i
\(652\) −15.6430 7.41004i −0.612626 0.290200i
\(653\) 21.8346i 0.854452i 0.904145 + 0.427226i \(0.140509\pi\)
−0.904145 + 0.427226i \(0.859491\pi\)
\(654\) −16.2049 + 10.2548i −0.633661 + 0.400996i
\(655\) −50.0699 −1.95639
\(656\) −12.9922 15.8698i −0.507260 0.619610i
\(657\) 4.15495 0.162100
\(658\) −11.4248 + 7.22986i −0.445384 + 0.281849i
\(659\) 24.7865i 0.965547i −0.875745 0.482773i \(-0.839629\pi\)
0.875745 0.482773i \(-0.160371\pi\)
\(660\) 19.8550 + 9.40529i 0.772856 + 0.366100i
\(661\) 3.09101i 0.120227i 0.998192 + 0.0601133i \(0.0191462\pi\)
−0.998192 + 0.0601133i \(0.980854\pi\)
\(662\) −19.0652 30.1272i −0.740989 1.17093i
\(663\) −15.5103 −0.602370
\(664\) 26.2648 3.21550i 1.01927 0.124786i
\(665\) 11.4053 0.442278
\(666\) 1.07747 + 1.70265i 0.0417513 + 0.0659762i
\(667\) 62.9356i 2.43687i
\(668\) −21.4942 + 45.3753i −0.831635 + 1.75562i
\(669\) 2.74966i 0.106308i
\(670\) −1.20040 + 0.759641i −0.0463755 + 0.0293475i
\(671\) 13.8701 0.535451
\(672\) 1.78249 5.36868i 0.0687612 0.207101i
\(673\) −27.6496 −1.06581 −0.532907 0.846174i \(-0.678901\pi\)
−0.532907 + 0.846174i \(0.678901\pi\)
\(674\) −28.6449 + 18.1272i −1.10336 + 0.698232i
\(675\) 11.8301i 0.455339i
\(676\) 3.29595 6.95792i 0.126767 0.267612i
\(677\) 5.84249i 0.224545i 0.993677 + 0.112273i \(0.0358130\pi\)
−0.993677 + 0.112273i \(0.964187\pi\)
\(678\) −3.14215 4.96529i −0.120674 0.190691i
\(679\) 6.69460 0.256915
\(680\) −59.0549 + 7.22986i −2.26465 + 0.277253i
\(681\) 8.30478 0.318240
\(682\) 2.88512 + 4.55913i 0.110477 + 0.174578i
\(683\) 15.5433i 0.594748i 0.954761 + 0.297374i \(0.0961109\pi\)
−0.954761 + 0.297374i \(0.903889\pi\)
\(684\) 5.02497 + 2.38032i 0.192135 + 0.0910138i
\(685\) 61.9649i 2.36756i
\(686\) 1.19503 0.756243i 0.0456265 0.0288735i
\(687\) 11.9245 0.454947
\(688\) −7.42757 + 6.08077i −0.283174 + 0.231827i
\(689\) 8.40978 0.320387
\(690\) −34.9425 + 22.1124i −1.33024 + 0.841806i
\(691\) 42.9304i 1.63315i 0.577239 + 0.816575i \(0.304130\pi\)
−0.577239 + 0.816575i \(0.695870\pi\)
\(692\) 3.52004 + 1.66743i 0.133812 + 0.0633863i
\(693\) 2.67767i 0.101716i
\(694\) −5.28430 8.35036i −0.200589 0.316975i
\(695\) −31.2204 −1.18426
\(696\) 3.03496 + 24.7901i 0.115040 + 0.939666i
\(697\) −26.2904 −0.995820
\(698\) 15.7979 + 24.9642i 0.597960 + 0.944908i
\(699\) 3.56024i 0.134661i
\(700\) −10.1288 + 21.3824i −0.382833 + 0.808180i
\(701\) 5.21476i 0.196959i 0.995139 + 0.0984795i \(0.0313979\pi\)
−0.995139 + 0.0984795i \(0.968602\pi\)
\(702\) −3.61493 + 2.28761i −0.136437 + 0.0863404i
\(703\) −3.96104 −0.149393
\(704\) 5.16762 + 20.7887i 0.194762 + 0.783505i
\(705\) 39.2204 1.47712
\(706\) 4.04189 2.55781i 0.152119 0.0962643i
\(707\) 1.45779i 0.0548260i
\(708\) 3.42477 7.22986i 0.128711 0.271715i
\(709\) 41.6601i 1.56458i 0.622915 + 0.782289i \(0.285948\pi\)
−0.622915 + 0.782289i \(0.714052\pi\)
\(710\) −13.2719 20.9725i −0.498084 0.787083i
\(711\) −6.25484 −0.234575
\(712\) −3.87783 31.6749i −0.145328 1.18707i
\(713\) −10.1549 −0.380306
\(714\) −3.87757 6.12742i −0.145115 0.229313i
\(715\) 33.2294i 1.24271i
\(716\) −41.0252 19.4336i −1.53318 0.726266i
\(717\) 26.9425i 1.00619i
\(718\) 24.7224 15.6449i 0.922631 0.583862i
\(719\) 14.3547 0.535341 0.267670 0.963511i \(-0.413746\pi\)
0.267670 + 0.963511i \(0.413746\pi\)
\(720\) −12.6974 + 10.3951i −0.473204 + 0.387401i
\(721\) 8.13547 0.302981
\(722\) 13.4691 8.52356i 0.501268 0.317214i
\(723\) 25.8151i 0.960073i
\(724\) −19.0421 9.02022i −0.707695 0.335234i
\(725\) 104.460i 3.87955i
\(726\) 2.89646 + 4.57704i 0.107498 + 0.169870i
\(727\) 53.4647 1.98290 0.991448 0.130501i \(-0.0416587\pi\)
0.991448 + 0.130501i \(0.0416587\pi\)
\(728\) −8.49251 + 1.03970i −0.314753 + 0.0385340i
\(729\) −1.00000 −0.0370370
\(730\) −12.8905 20.3698i −0.477099 0.753921i
\(731\) 12.3048i 0.455109i
\(732\) −4.43501 + 9.36253i −0.163923 + 0.346049i
\(733\) 49.1149i 1.81410i −0.421025 0.907049i \(-0.638329\pi\)
0.421025 0.907049i \(-0.361671\pi\)
\(734\) −11.4248 + 7.22986i −0.421696 + 0.266859i
\(735\) −4.10245 −0.151321
\(736\) −38.2648 12.7046i −1.41046 0.468297i
\(737\) 0.655634 0.0241506
\(738\) −6.12742 + 3.87757i −0.225553 + 0.142735i
\(739\) 7.75515i 0.285278i 0.989775 + 0.142639i \(0.0455587\pi\)
−0.989775 + 0.142639i \(0.954441\pi\)
\(740\) 5.00449 10.5647i 0.183969 0.388367i
\(741\) 8.40978i 0.308941i
\(742\) 2.10245 + 3.32233i 0.0771832 + 0.121966i
\(743\) 30.9886 1.13686 0.568430 0.822732i \(-0.307551\pi\)
0.568430 + 0.822732i \(0.307551\pi\)
\(744\) −4.00000 + 0.489704i −0.146647 + 0.0179534i
\(745\) 21.4143 0.784558
\(746\) −1.47472 2.33038i −0.0539932 0.0853211i
\(747\) 9.35535i 0.342294i
\(748\) 24.8157 + 11.7551i 0.907352 + 0.429811i
\(749\) 5.32233i 0.194474i
\(750\) 33.4847 21.1899i 1.22269 0.773746i
\(751\) −34.9105 −1.27390 −0.636951 0.770905i \(-0.719804\pi\)
−0.636951 + 0.770905i \(0.719804\pi\)
\(752\) 24.2244 + 29.5897i 0.883372 + 1.07903i
\(753\) 27.1543 0.989559
\(754\) 31.9201 20.1998i 1.16246 0.735632i
\(755\) 22.8106i 0.830162i
\(756\) −1.80747 0.856193i −0.0657369 0.0311394i
\(757\) 9.25034i 0.336209i −0.985769 0.168105i \(-0.946235\pi\)
0.985769 0.168105i \(-0.0537647\pi\)
\(758\) −24.4795 38.6829i −0.889134 1.40503i
\(759\) 19.0849 0.692738
\(760\) −3.92008 32.0200i −0.142196 1.16149i
\(761\) −11.8381 −0.429131 −0.214566 0.976710i \(-0.568834\pi\)
−0.214566 + 0.976710i \(0.568834\pi\)
\(762\) −0.525284 0.830064i −0.0190290 0.0300700i
\(763\) 13.5602i 0.490914i
\(764\) −3.66269 + 7.73211i −0.132511 + 0.279738i
\(765\) 21.0350i 0.760520i
\(766\) −21.3254 + 13.4952i −0.770517 + 0.487601i
\(767\) −12.0999 −0.436902
\(768\) −15.6850 3.15904i −0.565985 0.113992i
\(769\) −20.0699 −0.723740 −0.361870 0.932229i \(-0.617861\pi\)
−0.361870 + 0.932229i \(0.617861\pi\)
\(770\) 13.1274 8.30734i 0.473079 0.299376i
\(771\) 31.3823i 1.13020i
\(772\) 19.8123 41.8247i 0.713059 1.50530i
\(773\) 18.8521i 0.678063i 0.940775 + 0.339032i \(0.110099\pi\)
−0.940775 + 0.339032i \(0.889901\pi\)
\(774\) 1.81483 + 2.86783i 0.0652328 + 0.103082i
\(775\) 16.8551 0.605455
\(776\) −2.30098 18.7949i −0.0826004 0.674696i
\(777\) 1.42477 0.0511134
\(778\) −4.62773 7.31283i −0.165912 0.262178i
\(779\) 14.2548i 0.510733i
\(780\) 22.4303 + 10.6252i 0.803132 + 0.380442i
\(781\) 11.4547i 0.409883i
\(782\) −43.6727 + 27.6371i −1.56173 + 0.988300i