Properties

Label 322.2.e.a.277.4
Level $322$
Weight $2$
Character 322.277
Analytic conductor $2.571$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 322 = 2 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 322.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.57118294509\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.310217769.2
Defining polynomial: \(x^{8} + 4 x^{6} - 2 x^{5} + 15 x^{4} - 4 x^{3} + 5 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 277.4
Root \(-0.198169 + 0.343239i\) of defining polynomial
Character \(\chi\) \(=\) 322.277
Dual form 322.2.e.a.93.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.563379 - 0.975800i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.858079 - 1.48624i) q^{5} -1.12676 q^{6} +(0.779537 - 2.52830i) q^{7} +1.00000 q^{8} +(0.865209 + 1.49859i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(0.563379 - 0.975800i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.858079 - 1.48624i) q^{5} -1.12676 q^{6} +(0.779537 - 2.52830i) q^{7} +1.00000 q^{8} +(0.865209 + 1.49859i) q^{9} +(-0.858079 + 1.48624i) q^{10} +(1.82493 - 3.16087i) q^{11} +(0.563379 + 0.975800i) q^{12} -3.79833 q^{13} +(-2.57934 + 0.589053i) q^{14} -1.93369 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.08850 + 3.61738i) q^{17} +(0.865209 - 1.49859i) q^{18} +(-4.06135 - 7.03447i) q^{19} +1.71616 q^{20} +(-2.02795 - 2.18506i) q^{21} -3.64985 q^{22} +(0.500000 + 0.866025i) q^{23} +(0.563379 - 0.975800i) q^{24} +(1.02740 - 1.77951i) q^{25} +(1.89916 + 3.28945i) q^{26} +5.33003 q^{27} +(1.79981 + 1.93925i) q^{28} +2.80694 q^{29} +(0.966847 + 1.67463i) q^{30} +(-4.27150 + 7.39846i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.05625 - 3.56153i) q^{33} +4.17700 q^{34} +(-4.42656 + 1.01091i) q^{35} -1.73042 q^{36} +(-4.46765 - 7.73820i) q^{37} +(-4.06135 + 7.03447i) q^{38} +(-2.13990 + 3.70641i) q^{39} +(-0.858079 - 1.48624i) q^{40} +10.0518 q^{41} +(-0.878349 + 2.84878i) q^{42} +8.11069 q^{43} +(1.82493 + 3.16087i) q^{44} +(1.48484 - 2.57181i) q^{45} +(0.500000 - 0.866025i) q^{46} +(1.47568 + 2.55596i) q^{47} -1.12676 q^{48} +(-5.78464 - 3.94181i) q^{49} -2.05480 q^{50} +(2.35323 + 4.07591i) q^{51} +(1.89916 - 3.28945i) q^{52} +(-1.52740 + 2.64553i) q^{53} +(-2.66502 - 4.61594i) q^{54} -6.26373 q^{55} +(0.779537 - 2.52830i) q^{56} -9.15232 q^{57} +(-1.40347 - 2.43088i) q^{58} +(-2.09451 + 3.62779i) q^{59} +(0.966847 - 1.67463i) q^{60} +(5.65778 + 9.79957i) q^{61} +8.54301 q^{62} +(4.46335 - 1.01931i) q^{63} +1.00000 q^{64} +(3.25927 + 5.64522i) q^{65} +(-2.05625 + 3.56153i) q^{66} +(6.61841 - 11.4634i) q^{67} +(-2.08850 - 3.61738i) q^{68} +1.12676 q^{69} +(3.08875 + 3.32806i) q^{70} +14.3054 q^{71} +(0.865209 + 1.49859i) q^{72} +(2.13049 - 3.69011i) q^{73} +(-4.46765 + 7.73820i) q^{74} +(-1.15763 - 2.00507i) q^{75} +8.12271 q^{76} +(-6.56903 - 7.07798i) q^{77} +4.27979 q^{78} +(6.72409 + 11.6465i) q^{79} +(-0.858079 + 1.48624i) q^{80} +(0.407198 - 0.705288i) q^{81} +(-5.02592 - 8.70515i) q^{82} +9.43848 q^{83} +(2.90629 - 0.663720i) q^{84} +7.16839 q^{85} +(-4.05534 - 7.02406i) q^{86} +(1.58137 - 2.73901i) q^{87} +(1.82493 - 3.16087i) q^{88} +(-1.97918 - 3.42805i) q^{89} -2.96967 q^{90} +(-2.96094 + 9.60333i) q^{91} -1.00000 q^{92} +(4.81295 + 8.33627i) q^{93} +(1.47568 - 2.55596i) q^{94} +(-6.96993 + 12.0723i) q^{95} +(0.563379 + 0.975800i) q^{96} +0.121105 q^{97} +(-0.521390 + 6.98056i) q^{98} +6.31577 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{2} - 3q^{3} - 4q^{4} - 7q^{5} + 6q^{6} - q^{7} + 8q^{8} + q^{9} + O(q^{10}) \) \( 8q - 4q^{2} - 3q^{3} - 4q^{4} - 7q^{5} + 6q^{6} - q^{7} + 8q^{8} + q^{9} - 7q^{10} - 2q^{11} - 3q^{12} + 2q^{13} - q^{14} + 18q^{15} - 4q^{16} - 5q^{17} + q^{18} - 11q^{19} + 14q^{20} + q^{21} + 4q^{22} + 4q^{23} - 3q^{24} - 3q^{25} - q^{26} + 6q^{27} + 2q^{28} + 4q^{29} - 9q^{30} - 6q^{31} - 4q^{32} - 15q^{33} + 10q^{34} - 8q^{35} - 2q^{36} + 8q^{37} - 11q^{38} - 3q^{39} - 7q^{40} + 18q^{41} - 2q^{42} + 8q^{43} - 2q^{44} - 3q^{45} + 4q^{46} - 11q^{47} + 6q^{48} - 19q^{49} + 6q^{50} + 18q^{51} - q^{52} - q^{53} - 3q^{54} + 20q^{55} - q^{56} + 6q^{57} - 2q^{58} - 12q^{59} - 9q^{60} - 21q^{61} + 12q^{62} - 15q^{63} + 8q^{64} + 24q^{65} - 15q^{66} + 3q^{67} - 5q^{68} - 6q^{69} - 8q^{70} + 22q^{71} + q^{72} + 16q^{73} + 8q^{74} - 18q^{75} + 22q^{76} - 19q^{77} + 6q^{78} + 21q^{79} - 7q^{80} + 8q^{81} - 9q^{82} + 8q^{83} + q^{84} + 20q^{85} - 4q^{86} + 7q^{87} - 2q^{88} - 27q^{89} + 6q^{90} - 54q^{91} - 8q^{92} + 27q^{93} - 11q^{94} - 5q^{95} - 3q^{96} + 12q^{97} + 14q^{98} + 26q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/322\mathbb{Z}\right)^\times\).

\(n\) \(185\) \(281\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0.563379 0.975800i 0.325267 0.563379i −0.656300 0.754500i \(-0.727879\pi\)
0.981566 + 0.191122i \(0.0612126\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.858079 1.48624i −0.383745 0.664665i 0.607849 0.794052i \(-0.292032\pi\)
−0.991594 + 0.129387i \(0.958699\pi\)
\(6\) −1.12676 −0.459997
\(7\) 0.779537 2.52830i 0.294637 0.955609i
\(8\) 1.00000 0.353553
\(9\) 0.865209 + 1.49859i 0.288403 + 0.499529i
\(10\) −0.858079 + 1.48624i −0.271349 + 0.469989i
\(11\) 1.82493 3.16087i 0.550236 0.953037i −0.448021 0.894023i \(-0.647871\pi\)
0.998257 0.0590137i \(-0.0187956\pi\)
\(12\) 0.563379 + 0.975800i 0.162633 + 0.281689i
\(13\) −3.79833 −1.05347 −0.526733 0.850031i \(-0.676583\pi\)
−0.526733 + 0.850031i \(0.676583\pi\)
\(14\) −2.57934 + 0.589053i −0.689359 + 0.157431i
\(15\) −1.93369 −0.499278
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.08850 + 3.61738i −0.506535 + 0.877345i 0.493436 + 0.869782i \(0.335741\pi\)
−0.999971 + 0.00756264i \(0.997593\pi\)
\(18\) 0.865209 1.49859i 0.203932 0.353220i
\(19\) −4.06135 7.03447i −0.931739 1.61382i −0.780349 0.625345i \(-0.784958\pi\)
−0.151390 0.988474i \(-0.548375\pi\)
\(20\) 1.71616 0.383745
\(21\) −2.02795 2.18506i −0.442534 0.476820i
\(22\) −3.64985 −0.778151
\(23\) 0.500000 + 0.866025i 0.104257 + 0.180579i
\(24\) 0.563379 0.975800i 0.114999 0.199184i
\(25\) 1.02740 1.77951i 0.205480 0.355902i
\(26\) 1.89916 + 3.28945i 0.372457 + 0.645114i
\(27\) 5.33003 1.02577
\(28\) 1.79981 + 1.93925i 0.340132 + 0.366484i
\(29\) 2.80694 0.521235 0.260618 0.965442i \(-0.416074\pi\)
0.260618 + 0.965442i \(0.416074\pi\)
\(30\) 0.966847 + 1.67463i 0.176521 + 0.305744i
\(31\) −4.27150 + 7.39846i −0.767185 + 1.32880i 0.171899 + 0.985115i \(0.445010\pi\)
−0.939084 + 0.343688i \(0.888324\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −2.05625 3.56153i −0.357947 0.619982i
\(34\) 4.17700 0.716349
\(35\) −4.42656 + 1.01091i −0.748226 + 0.170875i
\(36\) −1.73042 −0.288403
\(37\) −4.46765 7.73820i −0.734477 1.27215i −0.954952 0.296759i \(-0.904094\pi\)
0.220475 0.975393i \(-0.429239\pi\)
\(38\) −4.06135 + 7.03447i −0.658839 + 1.14114i
\(39\) −2.13990 + 3.70641i −0.342658 + 0.593501i
\(40\) −0.858079 1.48624i −0.135674 0.234995i
\(41\) 10.0518 1.56983 0.784917 0.619601i \(-0.212706\pi\)
0.784917 + 0.619601i \(0.212706\pi\)
\(42\) −0.878349 + 2.84878i −0.135532 + 0.439577i
\(43\) 8.11069 1.23687 0.618434 0.785837i \(-0.287767\pi\)
0.618434 + 0.785837i \(0.287767\pi\)
\(44\) 1.82493 + 3.16087i 0.275118 + 0.476518i
\(45\) 1.48484 2.57181i 0.221346 0.383383i
\(46\) 0.500000 0.866025i 0.0737210 0.127688i
\(47\) 1.47568 + 2.55596i 0.215250 + 0.372825i 0.953350 0.301867i \(-0.0976099\pi\)
−0.738100 + 0.674692i \(0.764277\pi\)
\(48\) −1.12676 −0.162633
\(49\) −5.78464 3.94181i −0.826378 0.563116i
\(50\) −2.05480 −0.290593
\(51\) 2.35323 + 4.07591i 0.329518 + 0.570742i
\(52\) 1.89916 3.28945i 0.263367 0.456165i
\(53\) −1.52740 + 2.64553i −0.209804 + 0.363392i −0.951653 0.307176i \(-0.900616\pi\)
0.741848 + 0.670568i \(0.233949\pi\)
\(54\) −2.66502 4.61594i −0.362663 0.628150i
\(55\) −6.26373 −0.844601
\(56\) 0.779537 2.52830i 0.104170 0.337859i
\(57\) −9.15232 −1.21225
\(58\) −1.40347 2.43088i −0.184284 0.319190i
\(59\) −2.09451 + 3.62779i −0.272682 + 0.472299i −0.969548 0.244903i \(-0.921244\pi\)
0.696866 + 0.717201i \(0.254577\pi\)
\(60\) 0.966847 1.67463i 0.124819 0.216194i
\(61\) 5.65778 + 9.79957i 0.724405 + 1.25471i 0.959218 + 0.282666i \(0.0912188\pi\)
−0.234813 + 0.972040i \(0.575448\pi\)
\(62\) 8.54301 1.08496
\(63\) 4.46335 1.01931i 0.562329 0.128421i
\(64\) 1.00000 0.125000
\(65\) 3.25927 + 5.64522i 0.404262 + 0.700203i
\(66\) −2.05625 + 3.56153i −0.253107 + 0.438394i
\(67\) 6.61841 11.4634i 0.808567 1.40048i −0.105290 0.994442i \(-0.533577\pi\)
0.913856 0.406037i \(-0.133090\pi\)
\(68\) −2.08850 3.61738i −0.253268 0.438672i
\(69\) 1.12676 0.135646
\(70\) 3.08875 + 3.32806i 0.369177 + 0.397780i
\(71\) 14.3054 1.69773 0.848867 0.528607i \(-0.177285\pi\)
0.848867 + 0.528607i \(0.177285\pi\)
\(72\) 0.865209 + 1.49859i 0.101966 + 0.176610i
\(73\) 2.13049 3.69011i 0.249355 0.431895i −0.713992 0.700154i \(-0.753115\pi\)
0.963347 + 0.268259i \(0.0864482\pi\)
\(74\) −4.46765 + 7.73820i −0.519354 + 0.899547i
\(75\) −1.15763 2.00507i −0.133672 0.231526i
\(76\) 8.12271 0.931739
\(77\) −6.56903 7.07798i −0.748610 0.806611i
\(78\) 4.27979 0.484591
\(79\) 6.72409 + 11.6465i 0.756519 + 1.31033i 0.944615 + 0.328179i \(0.106435\pi\)
−0.188096 + 0.982151i \(0.560232\pi\)
\(80\) −0.858079 + 1.48624i −0.0959362 + 0.166166i
\(81\) 0.407198 0.705288i 0.0452442 0.0783653i
\(82\) −5.02592 8.70515i −0.555020 0.961323i
\(83\) 9.43848 1.03601 0.518004 0.855378i \(-0.326675\pi\)
0.518004 + 0.855378i \(0.326675\pi\)
\(84\) 2.90629 0.663720i 0.317103 0.0724177i
\(85\) 7.16839 0.777521
\(86\) −4.05534 7.02406i −0.437299 0.757424i
\(87\) 1.58137 2.73901i 0.169540 0.293653i
\(88\) 1.82493 3.16087i 0.194538 0.336949i
\(89\) −1.97918 3.42805i −0.209793 0.363372i 0.741856 0.670559i \(-0.233946\pi\)
−0.951649 + 0.307187i \(0.900612\pi\)
\(90\) −2.96967 −0.313031
\(91\) −2.96094 + 9.60333i −0.310391 + 1.00670i
\(92\) −1.00000 −0.104257
\(93\) 4.81295 + 8.33627i 0.499079 + 0.864431i
\(94\) 1.47568 2.55596i 0.152205 0.263627i
\(95\) −6.96993 + 12.0723i −0.715100 + 1.23859i
\(96\) 0.563379 + 0.975800i 0.0574996 + 0.0995922i
\(97\) 0.121105 0.0122964 0.00614819 0.999981i \(-0.498043\pi\)
0.00614819 + 0.999981i \(0.498043\pi\)
\(98\) −0.521390 + 6.98056i −0.0526683 + 0.705143i
\(99\) 6.31577 0.634759
\(100\) 1.02740 + 1.77951i 0.102740 + 0.177951i
\(101\) 1.86148 3.22418i 0.185224 0.320818i −0.758428 0.651757i \(-0.774032\pi\)
0.943652 + 0.330939i \(0.107366\pi\)
\(102\) 2.35323 4.07591i 0.233004 0.403576i
\(103\) −7.56418 13.1015i −0.745321 1.29093i −0.950045 0.312114i \(-0.898963\pi\)
0.204724 0.978820i \(-0.434370\pi\)
\(104\) −3.79833 −0.372457
\(105\) −1.50739 + 4.88897i −0.147106 + 0.477114i
\(106\) 3.05480 0.296708
\(107\) 6.86772 + 11.8952i 0.663927 + 1.14996i 0.979575 + 0.201079i \(0.0644449\pi\)
−0.315648 + 0.948876i \(0.602222\pi\)
\(108\) −2.66502 + 4.61594i −0.256441 + 0.444169i
\(109\) −4.69467 + 8.13140i −0.449668 + 0.778847i −0.998364 0.0571745i \(-0.981791\pi\)
0.548697 + 0.836022i \(0.315124\pi\)
\(110\) 3.13186 + 5.42455i 0.298611 + 0.517210i
\(111\) −10.0679 −0.955604
\(112\) −2.57934 + 0.589053i −0.243725 + 0.0556603i
\(113\) −9.39338 −0.883655 −0.441828 0.897100i \(-0.645670\pi\)
−0.441828 + 0.897100i \(0.645670\pi\)
\(114\) 4.57616 + 7.92614i 0.428597 + 0.742351i
\(115\) 0.858079 1.48624i 0.0800163 0.138592i
\(116\) −1.40347 + 2.43088i −0.130309 + 0.225701i
\(117\) −3.28635 5.69212i −0.303823 0.526237i
\(118\) 4.18902 0.385630
\(119\) 7.51779 + 8.10024i 0.689154 + 0.742548i
\(120\) −1.93369 −0.176521
\(121\) −1.16071 2.01041i −0.105519 0.182765i
\(122\) 5.65778 9.79957i 0.512232 0.887211i
\(123\) 5.66299 9.80859i 0.510615 0.884411i
\(124\) −4.27150 7.39846i −0.383592 0.664401i
\(125\) −12.1072 −1.08290
\(126\) −3.11442 3.35572i −0.277455 0.298951i
\(127\) 2.53575 0.225012 0.112506 0.993651i \(-0.464112\pi\)
0.112506 + 0.993651i \(0.464112\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 4.56939 7.91441i 0.402312 0.696825i
\(130\) 3.25927 5.64522i 0.285857 0.495118i
\(131\) 2.63129 + 4.55753i 0.229897 + 0.398193i 0.957777 0.287511i \(-0.0928278\pi\)
−0.727881 + 0.685704i \(0.759494\pi\)
\(132\) 4.11250 0.357947
\(133\) −20.9513 + 4.78471i −1.81670 + 0.414887i
\(134\) −13.2368 −1.14349
\(135\) −4.57359 7.92169i −0.393632 0.681791i
\(136\) −2.08850 + 3.61738i −0.179087 + 0.310188i
\(137\) 6.92566 11.9956i 0.591699 1.02485i −0.402305 0.915506i \(-0.631791\pi\)
0.994004 0.109347i \(-0.0348760\pi\)
\(138\) −0.563379 0.975800i −0.0479580 0.0830656i
\(139\) −9.65665 −0.819067 −0.409533 0.912295i \(-0.634308\pi\)
−0.409533 + 0.912295i \(0.634308\pi\)
\(140\) 1.33781 4.33897i 0.113066 0.366710i
\(141\) 3.32547 0.280055
\(142\) −7.15268 12.3888i −0.600239 1.03965i
\(143\) −6.93167 + 12.0060i −0.579655 + 1.00399i
\(144\) 0.865209 1.49859i 0.0721008 0.124882i
\(145\) −2.40857 4.17177i −0.200021 0.346447i
\(146\) −4.26097 −0.352641
\(147\) −7.10537 + 3.42392i −0.586041 + 0.282400i
\(148\) 8.93530 0.734477
\(149\) 4.78066 + 8.28034i 0.391647 + 0.678352i 0.992667 0.120882i \(-0.0385722\pi\)
−0.601020 + 0.799234i \(0.705239\pi\)
\(150\) −1.15763 + 2.00507i −0.0945201 + 0.163714i
\(151\) −3.62836 + 6.28451i −0.295272 + 0.511426i −0.975048 0.221994i \(-0.928744\pi\)
0.679776 + 0.733420i \(0.262077\pi\)
\(152\) −4.06135 7.03447i −0.329419 0.570571i
\(153\) −7.22795 −0.584345
\(154\) −2.84520 + 9.22794i −0.229272 + 0.743608i
\(155\) 14.6612 1.17761
\(156\) −2.13990 3.70641i −0.171329 0.296750i
\(157\) 1.37755 2.38598i 0.109940 0.190422i −0.805806 0.592180i \(-0.798267\pi\)
0.915746 + 0.401758i \(0.131601\pi\)
\(158\) 6.72409 11.6465i 0.534940 0.926543i
\(159\) 1.72101 + 2.98087i 0.136485 + 0.236399i
\(160\) 1.71616 0.135674
\(161\) 2.57934 0.589053i 0.203281 0.0464239i
\(162\) −0.814396 −0.0639850
\(163\) −10.1420 17.5665i −0.794386 1.37592i −0.923228 0.384252i \(-0.874459\pi\)
0.128842 0.991665i \(-0.458874\pi\)
\(164\) −5.02592 + 8.70515i −0.392459 + 0.679758i
\(165\) −3.52885 + 6.11215i −0.274721 + 0.475830i
\(166\) −4.71924 8.17397i −0.366284 0.634423i
\(167\) −0.325472 −0.0251858 −0.0125929 0.999921i \(-0.504009\pi\)
−0.0125929 + 0.999921i \(0.504009\pi\)
\(168\) −2.02795 2.18506i −0.156459 0.168581i
\(169\) 1.42730 0.109792
\(170\) −3.58419 6.20801i −0.274895 0.476132i
\(171\) 7.02784 12.1726i 0.537433 0.930861i
\(172\) −4.05534 + 7.02406i −0.309217 + 0.535580i
\(173\) −6.70089 11.6063i −0.509459 0.882410i −0.999940 0.0109575i \(-0.996512\pi\)
0.490480 0.871452i \(-0.336821\pi\)
\(174\) −3.16274 −0.239766
\(175\) −3.69824 3.98477i −0.279561 0.301220i
\(176\) −3.64985 −0.275118
\(177\) 2.36000 + 4.08764i 0.177389 + 0.307246i
\(178\) −1.97918 + 3.42805i −0.148346 + 0.256943i
\(179\) −10.4273 + 18.0606i −0.779370 + 1.34991i 0.152935 + 0.988236i \(0.451128\pi\)
−0.932305 + 0.361673i \(0.882206\pi\)
\(180\) 1.48484 + 2.57181i 0.110673 + 0.191692i
\(181\) 1.57738 0.117246 0.0586229 0.998280i \(-0.481329\pi\)
0.0586229 + 0.998280i \(0.481329\pi\)
\(182\) 9.79720 2.23742i 0.726217 0.165848i
\(183\) 12.7499 0.942500
\(184\) 0.500000 + 0.866025i 0.0368605 + 0.0638442i
\(185\) −7.66719 + 13.2800i −0.563703 + 0.976363i
\(186\) 4.81295 8.33627i 0.352902 0.611245i
\(187\) 7.62271 + 13.2029i 0.557428 + 0.965493i
\(188\) −2.95137 −0.215250
\(189\) 4.15496 13.4759i 0.302229 0.980231i
\(190\) 13.9399 1.01130
\(191\) −3.13049 5.42216i −0.226514 0.392334i 0.730259 0.683171i \(-0.239400\pi\)
−0.956773 + 0.290837i \(0.906066\pi\)
\(192\) 0.563379 0.975800i 0.0406583 0.0704223i
\(193\) −6.51789 + 11.2893i −0.469168 + 0.812623i −0.999379 0.0352433i \(-0.988779\pi\)
0.530211 + 0.847866i \(0.322113\pi\)
\(194\) −0.0605527 0.104880i −0.00434743 0.00752997i
\(195\) 7.34481 0.525972
\(196\) 6.30603 3.03874i 0.450431 0.217053i
\(197\) −21.2551 −1.51436 −0.757182 0.653204i \(-0.773425\pi\)
−0.757182 + 0.653204i \(0.773425\pi\)
\(198\) −3.15789 5.46962i −0.224421 0.388709i
\(199\) −2.36862 + 4.10257i −0.167907 + 0.290824i −0.937684 0.347490i \(-0.887034\pi\)
0.769777 + 0.638313i \(0.220368\pi\)
\(200\) 1.02740 1.77951i 0.0726481 0.125830i
\(201\) −7.45734 12.9165i −0.526000 0.911058i
\(202\) −3.72296 −0.261947
\(203\) 2.18811 7.09679i 0.153575 0.498097i
\(204\) −4.70646 −0.329518
\(205\) −8.62528 14.9394i −0.602416 1.04341i
\(206\) −7.56418 + 13.1015i −0.527021 + 0.912828i
\(207\) −0.865209 + 1.49859i −0.0601362 + 0.104159i
\(208\) 1.89916 + 3.28945i 0.131683 + 0.228082i
\(209\) −29.6467 −2.05070
\(210\) 4.98766 1.13905i 0.344181 0.0786018i
\(211\) 16.7617 1.15392 0.576962 0.816771i \(-0.304238\pi\)
0.576962 + 0.816771i \(0.304238\pi\)
\(212\) −1.52740 2.64553i −0.104902 0.181696i
\(213\) 8.05933 13.9592i 0.552216 0.956467i
\(214\) 6.86772 11.8952i 0.469467 0.813142i
\(215\) −6.95962 12.0544i −0.474642 0.822104i
\(216\) 5.33003 0.362663
\(217\) 15.3758 + 16.5670i 1.04377 + 1.12464i
\(218\) 9.38933 0.635926
\(219\) −2.40054 4.15786i −0.162214 0.280962i
\(220\) 3.13186 5.42455i 0.211150 0.365723i
\(221\) 7.93280 13.7400i 0.533618 0.924253i
\(222\) 5.03396 + 8.71907i 0.337857 + 0.585185i
\(223\) 1.23469 0.0826812 0.0413406 0.999145i \(-0.486837\pi\)
0.0413406 + 0.999145i \(0.486837\pi\)
\(224\) 1.79981 + 1.93925i 0.120255 + 0.129572i
\(225\) 3.55566 0.237044
\(226\) 4.69669 + 8.13491i 0.312419 + 0.541126i
\(227\) −11.5210 + 19.9550i −0.764678 + 1.32446i 0.175739 + 0.984437i \(0.443768\pi\)
−0.940417 + 0.340024i \(0.889565\pi\)
\(228\) 4.57616 7.92614i 0.303064 0.524922i
\(229\) 2.41831 + 4.18864i 0.159807 + 0.276793i 0.934799 0.355178i \(-0.115580\pi\)
−0.774992 + 0.631971i \(0.782246\pi\)
\(230\) −1.71616 −0.113160
\(231\) −10.6075 + 2.42248i −0.697925 + 0.159387i
\(232\) 2.80694 0.184284
\(233\) 6.62724 + 11.4787i 0.434165 + 0.751996i 0.997227 0.0744188i \(-0.0237101\pi\)
−0.563062 + 0.826415i \(0.690377\pi\)
\(234\) −3.28635 + 5.69212i −0.214835 + 0.372106i
\(235\) 2.53251 4.38643i 0.165202 0.286139i
\(236\) −2.09451 3.62779i −0.136341 0.236149i
\(237\) 15.1528 0.984282
\(238\) 3.25612 10.5607i 0.211063 0.684550i
\(239\) −5.40250 −0.349459 −0.174729 0.984616i \(-0.555905\pi\)
−0.174729 + 0.984616i \(0.555905\pi\)
\(240\) 0.966847 + 1.67463i 0.0624097 + 0.108097i
\(241\) 8.61037 14.9136i 0.554643 0.960670i −0.443288 0.896379i \(-0.646188\pi\)
0.997931 0.0642905i \(-0.0204784\pi\)
\(242\) −1.16071 + 2.01041i −0.0746134 + 0.129234i
\(243\) 7.53624 + 13.0531i 0.483450 + 0.837359i
\(244\) −11.3156 −0.724405
\(245\) −0.894788 + 11.9797i −0.0571659 + 0.765358i
\(246\) −11.3260 −0.722118
\(247\) 15.4264 + 26.7192i 0.981556 + 1.70010i
\(248\) −4.27150 + 7.39846i −0.271241 + 0.469803i
\(249\) 5.31744 9.21007i 0.336979 0.583665i
\(250\) 6.05358 + 10.4851i 0.382862 + 0.663136i
\(251\) 16.9165 1.06776 0.533879 0.845561i \(-0.320734\pi\)
0.533879 + 0.845561i \(0.320734\pi\)
\(252\) −1.34893 + 4.37502i −0.0849743 + 0.275601i
\(253\) 3.64985 0.229464
\(254\) −1.26788 2.19602i −0.0795536 0.137791i
\(255\) 4.03852 6.99491i 0.252902 0.438039i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 6.13308 + 10.6228i 0.382571 + 0.662633i 0.991429 0.130646i \(-0.0417053\pi\)
−0.608858 + 0.793279i \(0.708372\pi\)
\(258\) −9.13878 −0.568955
\(259\) −23.0472 + 5.26336i −1.43208 + 0.327050i
\(260\) −6.51854 −0.404262
\(261\) 2.42859 + 4.20644i 0.150326 + 0.260372i
\(262\) 2.63129 4.55753i 0.162562 0.281565i
\(263\) −6.52900 + 11.3086i −0.402596 + 0.697316i −0.994038 0.109031i \(-0.965225\pi\)
0.591443 + 0.806347i \(0.298559\pi\)
\(264\) −2.05625 3.56153i −0.126553 0.219197i
\(265\) 5.24252 0.322045
\(266\) 14.6193 + 15.7520i 0.896367 + 0.965815i
\(267\) −4.46012 −0.272955
\(268\) 6.61841 + 11.4634i 0.404283 + 0.700239i
\(269\) −1.78352 + 3.08915i −0.108743 + 0.188349i −0.915261 0.402860i \(-0.868016\pi\)
0.806518 + 0.591209i \(0.201349\pi\)
\(270\) −4.57359 + 7.92169i −0.278340 + 0.482099i
\(271\) −0.988595 1.71230i −0.0600529 0.104015i 0.834436 0.551105i \(-0.185794\pi\)
−0.894489 + 0.447090i \(0.852460\pi\)
\(272\) 4.17700 0.253268
\(273\) 7.70280 + 8.29959i 0.466195 + 0.502314i
\(274\) −13.8513 −0.836789
\(275\) −3.74986 6.49494i −0.226125 0.391660i
\(276\) −0.563379 + 0.975800i −0.0339114 + 0.0587363i
\(277\) 5.46819 9.47119i 0.328552 0.569069i −0.653673 0.756777i \(-0.726773\pi\)
0.982225 + 0.187709i \(0.0601061\pi\)
\(278\) 4.82833 + 8.36291i 0.289584 + 0.501574i
\(279\) −14.7830 −0.885034
\(280\) −4.42656 + 1.01091i −0.264538 + 0.0604133i
\(281\) −4.58034 −0.273240 −0.136620 0.990624i \(-0.543624\pi\)
−0.136620 + 0.990624i \(0.543624\pi\)
\(282\) −1.66274 2.87994i −0.0990145 0.171498i
\(283\) 7.54044 13.0604i 0.448233 0.776361i −0.550039 0.835139i \(-0.685387\pi\)
0.998271 + 0.0587778i \(0.0187203\pi\)
\(284\) −7.15268 + 12.3888i −0.424433 + 0.735140i
\(285\) 7.85342 + 13.6025i 0.465196 + 0.805744i
\(286\) 13.8633 0.819757
\(287\) 7.83579 25.4141i 0.462532 1.50015i
\(288\) −1.73042 −0.101966
\(289\) −0.223647 0.387368i −0.0131557 0.0227863i
\(290\) −2.40857 + 4.17177i −0.141436 + 0.244975i
\(291\) 0.0682282 0.118175i 0.00399961 0.00692752i
\(292\) 2.13049 + 3.69011i 0.124677 + 0.215947i
\(293\) 14.5555 0.850344 0.425172 0.905113i \(-0.360214\pi\)
0.425172 + 0.905113i \(0.360214\pi\)
\(294\) 6.51789 + 4.44147i 0.380131 + 0.259032i
\(295\) 7.18902 0.418561
\(296\) −4.46765 7.73820i −0.259677 0.449773i
\(297\) 9.72692 16.8475i 0.564413 0.977592i
\(298\) 4.78066 8.28034i 0.276936 0.479667i
\(299\) −1.89916 3.28945i −0.109832 0.190234i
\(300\) 2.31526 0.133672
\(301\) 6.32258 20.5063i 0.364428 1.18196i
\(302\) 7.25672 0.417577
\(303\) −2.09744 3.63286i −0.120495 0.208703i
\(304\) −4.06135 + 7.03447i −0.232935 + 0.403455i
\(305\) 9.70966 16.8176i 0.555973 0.962974i
\(306\) 3.61398 + 6.25959i 0.206597 + 0.357837i
\(307\) −12.7024 −0.724965 −0.362482 0.931991i \(-0.618071\pi\)
−0.362482 + 0.931991i \(0.618071\pi\)
\(308\) 9.41423 2.14996i 0.536425 0.122505i
\(309\) −17.0460 −0.969712
\(310\) −7.33058 12.6969i −0.416349 0.721137i
\(311\) 4.60947 7.98383i 0.261379 0.452722i −0.705230 0.708979i \(-0.749156\pi\)
0.966609 + 0.256257i \(0.0824894\pi\)
\(312\) −2.13990 + 3.70641i −0.121148 + 0.209834i
\(313\) 7.82833 + 13.5591i 0.442483 + 0.766403i 0.997873 0.0651867i \(-0.0207643\pi\)
−0.555390 + 0.831590i \(0.687431\pi\)
\(314\) −2.75509 −0.155479
\(315\) −5.34484 5.75894i −0.301147 0.324480i
\(316\) −13.4482 −0.756519
\(317\) −5.51911 9.55938i −0.309984 0.536908i 0.668374 0.743825i \(-0.266990\pi\)
−0.978359 + 0.206917i \(0.933657\pi\)
\(318\) 1.72101 2.98087i 0.0965094 0.167159i
\(319\) 5.12245 8.87235i 0.286802 0.496756i
\(320\) −0.858079 1.48624i −0.0479681 0.0830832i
\(321\) 15.4765 0.863814
\(322\) −1.79981 1.93925i −0.100299 0.108070i
\(323\) 33.9285 1.88783
\(324\) 0.407198 + 0.705288i 0.0226221 + 0.0391827i
\(325\) −3.90240 + 6.75916i −0.216466 + 0.374931i
\(326\) −10.1420 + 17.5665i −0.561716 + 0.972921i
\(327\) 5.28975 + 9.16211i 0.292524 + 0.506666i
\(328\) 10.0518 0.555020
\(329\) 7.61259 1.73851i 0.419696 0.0958472i
\(330\) 7.05770 0.388513
\(331\) 7.84574 + 13.5892i 0.431241 + 0.746931i 0.996980 0.0776528i \(-0.0247426\pi\)
−0.565740 + 0.824584i \(0.691409\pi\)
\(332\) −4.71924 + 8.17397i −0.259002 + 0.448605i
\(333\) 7.73090 13.3903i 0.423651 0.733785i
\(334\) 0.162736 + 0.281867i 0.00890451 + 0.0154231i
\(335\) −22.7165 −1.24113
\(336\) −0.878349 + 2.84878i −0.0479179 + 0.155414i
\(337\) 5.18787 0.282601 0.141301 0.989967i \(-0.454872\pi\)
0.141301 + 0.989967i \(0.454872\pi\)
\(338\) −0.713651 1.23608i −0.0388175 0.0672339i
\(339\) −5.29203 + 9.16606i −0.287424 + 0.497832i
\(340\) −3.58419 + 6.20801i −0.194380 + 0.336676i
\(341\) 15.5904 + 27.0033i 0.844265 + 1.46231i
\(342\) −14.0557 −0.760045
\(343\) −14.4755 + 11.5525i −0.781601 + 0.623779i
\(344\) 8.11069 0.437299
\(345\) −0.966847 1.67463i −0.0520533 0.0901589i
\(346\) −6.70089 + 11.6063i −0.360242 + 0.623958i
\(347\) 8.87970 15.3801i 0.476687 0.825646i −0.522956 0.852360i \(-0.675171\pi\)
0.999643 + 0.0267134i \(0.00850415\pi\)
\(348\) 1.58137 + 2.73901i 0.0847702 + 0.146826i
\(349\) −15.3654 −0.822488 −0.411244 0.911525i \(-0.634906\pi\)
−0.411244 + 0.911525i \(0.634906\pi\)
\(350\) −1.60179 + 5.19516i −0.0856194 + 0.277693i
\(351\) −20.2452 −1.08061
\(352\) 1.82493 + 3.16087i 0.0972689 + 0.168475i
\(353\) 13.2323 22.9190i 0.704283 1.21985i −0.262666 0.964887i \(-0.584602\pi\)
0.966950 0.254968i \(-0.0820648\pi\)
\(354\) 2.36000 4.08764i 0.125433 0.217256i
\(355\) −12.2751 21.2612i −0.651496 1.12842i
\(356\) 3.95837 0.209793
\(357\) 12.1396 2.77235i 0.642495 0.146729i
\(358\) 20.8545 1.10220
\(359\) −3.75001 6.49521i −0.197918 0.342804i 0.749935 0.661511i \(-0.230085\pi\)
−0.947853 + 0.318707i \(0.896751\pi\)
\(360\) 1.48484 2.57181i 0.0782578 0.135546i
\(361\) −23.4892 + 40.6845i −1.23627 + 2.14129i
\(362\) −0.788691 1.36605i −0.0414527 0.0717981i
\(363\) −2.61568 −0.137288
\(364\) −6.83626 7.36591i −0.358317 0.386079i
\(365\) −7.31251 −0.382754
\(366\) −6.37495 11.0417i −0.333224 0.577161i
\(367\) 0.805459 1.39510i 0.0420446 0.0728234i −0.844237 0.535970i \(-0.819946\pi\)
0.886282 + 0.463146i \(0.153280\pi\)
\(368\) 0.500000 0.866025i 0.0260643 0.0451447i
\(369\) 8.69695 + 15.0636i 0.452745 + 0.784177i
\(370\) 15.3344 0.797197
\(371\) 5.49805 + 5.92402i 0.285444 + 0.307560i
\(372\) −9.62589 −0.499079
\(373\) −9.05039 15.6757i −0.468612 0.811659i 0.530745 0.847532i \(-0.321912\pi\)
−0.999356 + 0.0358726i \(0.988579\pi\)
\(374\) 7.62271 13.2029i 0.394161 0.682707i
\(375\) −6.82091 + 11.8142i −0.352230 + 0.610081i
\(376\) 1.47568 + 2.55596i 0.0761025 + 0.131813i
\(377\) −10.6617 −0.549104
\(378\) −13.7480 + 3.13967i −0.707120 + 0.161487i
\(379\) −10.3909 −0.533747 −0.266873 0.963732i \(-0.585991\pi\)
−0.266873 + 0.963732i \(0.585991\pi\)
\(380\) −6.96993 12.0723i −0.357550 0.619294i
\(381\) 1.42859 2.47439i 0.0731888 0.126767i
\(382\) −3.13049 + 5.42216i −0.160170 + 0.277422i
\(383\) 3.69781 + 6.40480i 0.188949 + 0.327270i 0.944900 0.327359i \(-0.106158\pi\)
−0.755951 + 0.654628i \(0.772825\pi\)
\(384\) −1.12676 −0.0574996
\(385\) −4.88281 + 15.8366i −0.248851 + 0.807108i
\(386\) 13.0358 0.663504
\(387\) 7.01744 + 12.1546i 0.356717 + 0.617851i
\(388\) −0.0605527 + 0.104880i −0.00307410 + 0.00532449i
\(389\) −2.03971 + 3.53288i −0.103417 + 0.179124i −0.913090 0.407757i \(-0.866311\pi\)
0.809673 + 0.586881i \(0.199644\pi\)
\(390\) −3.67240 6.36079i −0.185959 0.322091i
\(391\) −4.17700 −0.211240
\(392\) −5.78464 3.94181i −0.292169 0.199092i
\(393\) 5.92965 0.299111
\(394\) 10.6276 + 18.4075i 0.535409 + 0.927355i
\(395\) 11.5396 19.9872i 0.580621 1.00566i
\(396\) −3.15789 + 5.46962i −0.158690 + 0.274859i
\(397\) −4.43055 7.67394i −0.222363 0.385144i 0.733162 0.680054i \(-0.238044\pi\)
−0.955525 + 0.294910i \(0.904710\pi\)
\(398\) 4.73724 0.237456
\(399\) −7.13457 + 23.1398i −0.357175 + 1.15844i
\(400\) −2.05480 −0.102740
\(401\) −8.30173 14.3790i −0.414569 0.718054i 0.580814 0.814036i \(-0.302734\pi\)
−0.995383 + 0.0959821i \(0.969401\pi\)
\(402\) −7.45734 + 12.9165i −0.371938 + 0.644216i
\(403\) 16.2246 28.1018i 0.808204 1.39985i
\(404\) 1.86148 + 3.22418i 0.0926121 + 0.160409i
\(405\) −1.39763 −0.0694489
\(406\) −7.24006 + 1.65343i −0.359318 + 0.0820586i
\(407\) −32.6125 −1.61654
\(408\) 2.35323 + 4.07591i 0.116502 + 0.201788i
\(409\) −16.8717 + 29.2227i −0.834253 + 1.44497i 0.0603848 + 0.998175i \(0.480767\pi\)
−0.894637 + 0.446793i \(0.852566\pi\)
\(410\) −8.62528 + 14.9394i −0.425972 + 0.737805i
\(411\) −7.80354 13.5161i −0.384920 0.666701i
\(412\) 15.1284 0.745321
\(413\) 7.53942 + 8.12355i 0.370991 + 0.399734i
\(414\) 1.73042 0.0850454
\(415\) −8.09897 14.0278i −0.397563 0.688599i
\(416\) 1.89916 3.28945i 0.0931142 0.161279i
\(417\) −5.44035 + 9.42296i −0.266415 + 0.461445i
\(418\) 14.8233 + 25.6748i 0.725034 + 1.25579i
\(419\) 36.5806 1.78708 0.893539 0.448985i \(-0.148214\pi\)
0.893539 + 0.448985i \(0.148214\pi\)
\(420\) −3.48028 3.74992i −0.169820 0.182977i
\(421\) −32.7603 −1.59664 −0.798321 0.602233i \(-0.794278\pi\)
−0.798321 + 0.602233i \(0.794278\pi\)
\(422\) −8.38086 14.5161i −0.407974 0.706631i
\(423\) −2.55355 + 4.42288i −0.124158 + 0.215048i
\(424\) −1.52740 + 2.64553i −0.0741771 + 0.128478i
\(425\) 4.29144 + 7.43300i 0.208166 + 0.360553i
\(426\) −16.1187 −0.780952
\(427\) 29.1867 6.66547i 1.41245 0.322565i
\(428\) −13.7354 −0.663927
\(429\) 7.81031 + 13.5279i 0.377085 + 0.653131i
\(430\) −6.95962 + 12.0544i −0.335622 + 0.581315i
\(431\) 8.85968 15.3454i 0.426756 0.739163i −0.569827 0.821765i \(-0.692990\pi\)
0.996583 + 0.0826019i \(0.0263230\pi\)
\(432\) −2.66502 4.61594i −0.128221 0.222085i
\(433\) −4.51989 −0.217212 −0.108606 0.994085i \(-0.534639\pi\)
−0.108606 + 0.994085i \(0.534639\pi\)
\(434\) 6.65959 21.5993i 0.319671 1.03680i
\(435\) −5.42776 −0.260241
\(436\) −4.69467 8.13140i −0.224834 0.389424i
\(437\) 4.06135 7.03447i 0.194281 0.336504i
\(438\) −2.40054 + 4.15786i −0.114702 + 0.198670i
\(439\) −3.19897 5.54078i −0.152679 0.264447i 0.779533 0.626361i \(-0.215457\pi\)
−0.932211 + 0.361914i \(0.882123\pi\)
\(440\) −6.26373 −0.298611
\(441\) 0.902222 12.0793i 0.0429630 0.575204i
\(442\) −15.8656 −0.754650
\(443\) 8.56844 + 14.8410i 0.407099 + 0.705116i 0.994563 0.104134i \(-0.0332070\pi\)
−0.587464 + 0.809250i \(0.699874\pi\)
\(444\) 5.03396 8.71907i 0.238901 0.413789i
\(445\) −3.39660 + 5.88308i −0.161014 + 0.278885i
\(446\) −0.617347 1.06928i −0.0292322 0.0506317i
\(447\) 10.7733 0.509559
\(448\) 0.779537 2.52830i 0.0368297 0.119451i
\(449\) −13.2695 −0.626226 −0.313113 0.949716i \(-0.601372\pi\)
−0.313113 + 0.949716i \(0.601372\pi\)
\(450\) −1.77783 3.07929i −0.0838078 0.145159i
\(451\) 18.3439 31.7725i 0.863779 1.49611i
\(452\) 4.69669 8.13491i 0.220914 0.382634i
\(453\) 4.08828 + 7.08111i 0.192084 + 0.332700i
\(454\) 23.0421 1.08142
\(455\) 16.8135 3.83976i 0.788231 0.180011i
\(456\) −9.15232 −0.428597
\(457\) 15.2314 + 26.3815i 0.712494 + 1.23408i 0.963918 + 0.266199i \(0.0857679\pi\)
−0.251424 + 0.967877i \(0.580899\pi\)
\(458\) 2.41831 4.18864i 0.113000 0.195722i
\(459\) −11.1318 + 19.2808i −0.519586 + 0.899950i
\(460\) 0.858079 + 1.48624i 0.0400082 + 0.0692962i
\(461\) 13.1239 0.611239 0.305620 0.952154i \(-0.401136\pi\)
0.305620 + 0.952154i \(0.401136\pi\)
\(462\) 7.40170 + 7.97516i 0.344358 + 0.371038i
\(463\) −21.3453 −0.991998 −0.495999 0.868323i \(-0.665198\pi\)
−0.495999 + 0.868323i \(0.665198\pi\)
\(464\) −1.40347 2.43088i −0.0651544 0.112851i
\(465\) 8.25978 14.3064i 0.383038 0.663442i
\(466\) 6.62724 11.4787i 0.307001 0.531741i
\(467\) −11.1802 19.3647i −0.517358 0.896091i −0.999797 0.0201608i \(-0.993582\pi\)
0.482439 0.875930i \(-0.339751\pi\)
\(468\) 6.57270 0.303823
\(469\) −23.8237 25.6695i −1.10008 1.18531i
\(470\) −5.06501 −0.233632
\(471\) −1.55216 2.68842i −0.0715198 0.123876i
\(472\) −2.09451 + 3.62779i −0.0964075 + 0.166983i
\(473\) 14.8014 25.6368i 0.680570 1.17878i
\(474\) −7.57642 13.1227i −0.347996 0.602747i
\(475\) −16.6905 −0.765814
\(476\) −10.7739 + 2.46047i −0.493821 + 0.112776i
\(477\) −5.28608 −0.242033
\(478\) 2.70125 + 4.67871i 0.123552 + 0.213999i
\(479\) 8.73350 15.1269i 0.399044 0.691164i −0.594564 0.804048i \(-0.702675\pi\)
0.993608 + 0.112884i \(0.0360088\pi\)
\(480\) 0.966847 1.67463i 0.0441303 0.0764360i
\(481\) 16.9696 + 29.3922i 0.773747 + 1.34017i
\(482\) −17.2207 −0.784383
\(483\) 0.878349 2.84878i 0.0399663 0.129624i
\(484\) 2.32142 0.105519
\(485\) −0.103918 0.179991i −0.00471867 0.00817298i
\(486\) 7.53624 13.0531i 0.341851 0.592103i
\(487\) 2.89533 5.01486i 0.131200 0.227245i −0.792939 0.609301i \(-0.791450\pi\)
0.924139 + 0.382055i \(0.124784\pi\)
\(488\) 5.65778 + 9.79957i 0.256116 + 0.443606i
\(489\) −22.8552 −1.03355
\(490\) 10.8222 5.21496i 0.488895 0.235588i
\(491\) −8.47054 −0.382270 −0.191135 0.981564i \(-0.561217\pi\)
−0.191135 + 0.981564i \(0.561217\pi\)
\(492\) 5.66299 + 9.80859i 0.255307 + 0.442205i
\(493\) −5.86228 + 10.1538i −0.264024 + 0.457303i
\(494\) 15.4264 26.7192i 0.694065 1.20216i
\(495\) −5.41943 9.38674i −0.243585 0.421902i
\(496\) 8.54301 0.383592
\(497\) 11.1516 36.1683i 0.500216 1.62237i
\(498\) −10.6349 −0.476560
\(499\) 1.26100 + 2.18412i 0.0564502 + 0.0977746i 0.892870 0.450315i \(-0.148688\pi\)
−0.836419 + 0.548090i \(0.815355\pi\)
\(500\) 6.05358 10.4851i 0.270724 0.468908i
\(501\) −0.183364 + 0.317596i −0.00819209 + 0.0141891i
\(502\) −8.45824 14.6501i −0.377510 0.653866i
\(503\) 8.34455 0.372065 0.186033 0.982544i \(-0.440437\pi\)
0.186033 + 0.982544i \(0.440437\pi\)
\(504\) 4.46335 1.01931i 0.198813 0.0454036i
\(505\) −6.38919 −0.284315
\(506\) −1.82493 3.16087i −0.0811279 0.140518i
\(507\) 0.804111 1.39276i 0.0357118 0.0618547i
\(508\) −1.26788 + 2.19602i −0.0562529 + 0.0974329i
\(509\) 8.43774 + 14.6146i 0.373996 + 0.647781i 0.990176 0.139825i \(-0.0446539\pi\)
−0.616180 + 0.787605i \(0.711321\pi\)
\(510\) −8.07703 −0.357657
\(511\) −7.66893 8.26310i −0.339253 0.365538i
\(512\) 1.00000 0.0441942
\(513\) −21.6472 37.4940i −0.955745 1.65540i
\(514\) 6.13308 10.6228i 0.270519 0.468552i
\(515\) −12.9813 + 22.4843i −0.572026 + 0.990778i
\(516\) 4.56939 + 7.91441i 0.201156 + 0.348413i
\(517\) 10.7720 0.473754
\(518\) 16.0818 + 17.3278i 0.706594 + 0.761339i
\(519\) −15.1006 −0.662841
\(520\) 3.25927 + 5.64522i 0.142928 + 0.247559i
\(521\) −3.43970 + 5.95774i −0.150696 + 0.261013i −0.931484 0.363783i \(-0.881485\pi\)
0.780787 + 0.624797i \(0.214818\pi\)
\(522\) 2.42859 4.20644i 0.106296 0.184111i
\(523\) −10.6428 18.4338i −0.465375 0.806053i 0.533843 0.845583i \(-0.320747\pi\)
−0.999218 + 0.0395302i \(0.987414\pi\)
\(524\) −5.26258 −0.229897
\(525\) −5.97185 + 1.36381i −0.260633 + 0.0595216i
\(526\) 13.0580 0.569356
\(527\) −17.8421 30.9033i −0.777212 1.34617i
\(528\) −2.05625 + 3.56153i −0.0894867 + 0.154996i
\(529\) −0.500000 + 0.866025i −0.0217391 + 0.0376533i
\(530\) −2.62126 4.54016i −0.113860 0.197212i
\(531\) −7.24875 −0.314569
\(532\) 6.33195 20.5367i 0.274525 0.890378i
\(533\) −38.1802 −1.65377
\(534\) 2.23006 + 3.86258i 0.0965041 + 0.167150i
\(535\) 11.7861 20.4141i 0.509557 0.882579i
\(536\) 6.61841 11.4634i 0.285872 0.495144i
\(537\) 11.7490 + 20.3499i 0.507007 + 0.878161i
\(538\) 3.56705 0.153786
\(539\) −23.0161 + 11.0910i −0.991373 + 0.477721i
\(540\) 9.14718 0.393632
\(541\) 22.2528 + 38.5429i 0.956721 + 1.65709i 0.730379 + 0.683042i \(0.239343\pi\)
0.226342 + 0.974048i \(0.427323\pi\)
\(542\) −0.988595 + 1.71230i −0.0424638 + 0.0735494i
\(543\) 0.888663 1.53921i 0.0381362 0.0660538i
\(544\) −2.08850 3.61738i −0.0895436 0.155094i
\(545\) 16.1136 0.690230
\(546\) 3.33626 10.8206i 0.142779 0.463080i
\(547\) 4.70118 0.201008 0.100504 0.994937i \(-0.467954\pi\)
0.100504 + 0.994937i \(0.467954\pi\)
\(548\) 6.92566 + 11.9956i 0.295850 + 0.512426i
\(549\) −9.79034 + 16.9574i −0.417841 + 0.723722i
\(550\) −3.74986 + 6.49494i −0.159894 + 0.276945i
\(551\) −11.4000 19.7453i −0.485655 0.841179i
\(552\) 1.12676 0.0479580
\(553\) 34.6875 7.92169i 1.47506 0.336865i
\(554\) −10.9364 −0.464643
\(555\) 8.63907 + 14.9633i 0.366708 + 0.635157i
\(556\) 4.82833 8.36291i 0.204767 0.354666i
\(557\) −11.6577 + 20.1917i −0.493951 + 0.855548i −0.999976 0.00697093i \(-0.997781\pi\)
0.506025 + 0.862519i \(0.331114\pi\)
\(558\) 7.39149 + 12.8024i 0.312907 + 0.541970i
\(559\) −30.8071 −1.30300
\(560\) 3.08875 + 3.32806i 0.130524 + 0.140636i
\(561\) 17.1779 0.725251
\(562\) 2.29017 + 3.96669i 0.0966050 + 0.167325i
\(563\) −19.6307 + 34.0014i −0.827335 + 1.43299i 0.0727857 + 0.997348i \(0.476811\pi\)
−0.900121 + 0.435639i \(0.856522\pi\)
\(564\) −1.66274 + 2.87994i −0.0700138 + 0.121267i
\(565\) 8.06027 + 13.9608i 0.339098 + 0.587335i
\(566\) −15.0809 −0.633896
\(567\) −1.46576 1.57932i −0.0615560 0.0663251i
\(568\) 14.3054 0.600239
\(569\) −14.2620 24.7026i −0.597895 1.03559i −0.993131 0.117006i \(-0.962670\pi\)
0.395236 0.918580i \(-0.370663\pi\)
\(570\) 7.85342 13.6025i 0.328943 0.569747i
\(571\) −5.73892 + 9.94011i −0.240167 + 0.415981i −0.960762 0.277376i \(-0.910535\pi\)
0.720595 + 0.693356i \(0.243869\pi\)
\(572\) −6.93167 12.0060i −0.289828 0.501996i
\(573\) −7.05460 −0.294710
\(574\) −25.9272 + 5.92107i −1.08218 + 0.247141i
\(575\) 2.05480 0.0856911
\(576\) 0.865209 + 1.49859i 0.0360504 + 0.0624411i
\(577\) −11.4092 + 19.7613i −0.474970 + 0.822672i −0.999589 0.0286648i \(-0.990874\pi\)
0.524619 + 0.851337i \(0.324208\pi\)
\(578\) −0.223647 + 0.387368i −0.00930248 + 0.0161124i
\(579\) 7.34408 + 12.7203i 0.305209 + 0.528638i
\(580\) 4.81715 0.200021
\(581\) 7.35765 23.8634i 0.305247 0.990019i
\(582\) −0.136456 −0.00565630
\(583\) 5.57478 + 9.65581i 0.230884 + 0.399903i
\(584\) 2.13049 3.69011i 0.0881602 0.152698i
\(585\) −5.63990 + 9.76859i −0.233181 + 0.403881i
\(586\) −7.27777 12.6055i −0.300642 0.520727i
\(587\) 20.6525 0.852422 0.426211 0.904624i \(-0.359848\pi\)
0.426211 + 0.904624i \(0.359848\pi\)
\(588\) 0.587480 7.86539i 0.0242272 0.324363i
\(589\) 69.3924 2.85926
\(590\) −3.59451 6.22587i −0.147984 0.256315i
\(591\) −11.9747 + 20.7407i −0.492572 + 0.853160i
\(592\) −4.46765 + 7.73820i −0.183619 + 0.318038i
\(593\) 3.83376 + 6.64027i 0.157434 + 0.272683i 0.933943 0.357423i \(-0.116345\pi\)
−0.776509 + 0.630106i \(0.783011\pi\)
\(594\) −19.4538 −0.798200
\(595\) 5.58803 18.1239i 0.229087 0.743006i
\(596\) −9.56131 −0.391647
\(597\) 2.66886 + 4.62260i 0.109229 + 0.189190i
\(598\) −1.89916 + 3.28945i −0.0776626 + 0.134516i
\(599\) −18.7730 + 32.5158i −0.767043 + 1.32856i 0.172117 + 0.985077i \(0.444939\pi\)
−0.939160 + 0.343481i \(0.888394\pi\)
\(600\) −1.15763 2.00507i −0.0472600 0.0818568i
\(601\) −16.2537 −0.663003 −0.331501 0.943455i \(-0.607555\pi\)
−0.331501 + 0.943455i \(0.607555\pi\)
\(602\) −20.9203 + 4.77763i −0.852646 + 0.194722i
\(603\) 22.9052 0.932773
\(604\) −3.62836 6.28451i −0.147636 0.255713i
\(605\) −1.99197 + 3.45019i −0.0809849 + 0.140270i
\(606\) −2.09744 + 3.63286i −0.0852025 + 0.147575i
\(607\) −2.16135 3.74356i −0.0877264 0.151947i 0.818823 0.574046i \(-0.194627\pi\)
−0.906550 + 0.422099i \(0.861293\pi\)
\(608\) 8.12271 0.329419
\(609\) −5.69231 6.13334i −0.230664 0.248535i
\(610\) −19.4193 −0.786265
\(611\) −5.60513 9.70837i −0.226759 0.392758i
\(612\) 3.61398 6.25959i 0.146086 0.253029i
\(613\) −20.0725 + 34.7666i −0.810720 + 1.40421i 0.101640 + 0.994821i \(0.467591\pi\)
−0.912360 + 0.409388i \(0.865742\pi\)
\(614\) 6.35121 + 11.0006i 0.256314 + 0.443949i
\(615\) −19.4372 −0.783783
\(616\) −6.56903 7.07798i −0.264674 0.285180i
\(617\) −27.7668 −1.11785 −0.558925 0.829218i \(-0.688786\pi\)
−0.558925 + 0.829218i \(0.688786\pi\)
\(618\) 8.52299 + 14.7623i 0.342845 + 0.593825i
\(619\) 8.36648 14.4912i 0.336277 0.582450i −0.647452 0.762106i \(-0.724165\pi\)
0.983729 + 0.179657i \(0.0574987\pi\)
\(620\) −7.33058 + 12.6969i −0.294403 + 0.509921i
\(621\) 2.66502 + 4.61594i 0.106943 + 0.185231i
\(622\) −9.21894 −0.369646
\(623\) −10.2100 + 2.33169i −0.409055 + 0.0934172i
\(624\) 4.27979 0.171329
\(625\) 5.25190 + 9.09656i 0.210076 + 0.363862i
\(626\) 7.82833 13.5591i 0.312883 0.541929i
\(627\) −16.7023 + 28.9292i −0.667026 + 1.15532i
\(628\) 1.37755 + 2.38598i 0.0549701 + 0.0952110i
\(629\) 37.3227 1.48815
\(630\) −2.31497 + 7.50824i −0.0922306 + 0.299135i
\(631\) 16.4804 0.656073 0.328037 0.944665i \(-0.393613\pi\)
0.328037 + 0.944665i \(0.393613\pi\)
\(632\) 6.72409 + 11.6465i 0.267470 + 0.463272i
\(633\) 9.44319 16.3561i 0.375333 0.650096i
\(634\) −5.51911 + 9.55938i −0.219192 + 0.379651i
\(635\) −2.17588 3.76873i −0.0863470 0.149557i
\(636\) −3.44202 −0.136485
\(637\) 21.9720 + 14.9723i 0.870561 + 0.593224i
\(638\) −10.2449 −0.405600
\(639\) 12.3771 + 21.4378i 0.489632 + 0.848067i
\(640\) −0.858079 + 1.48624i −0.0339186 + 0.0587487i
\(641\) −0.882551 + 1.52862i −0.0348587 + 0.0603770i −0.882928 0.469508i \(-0.844431\pi\)
0.848070 + 0.529885i \(0.177765\pi\)
\(642\) −7.73825 13.4030i −0.305404 0.528976i
\(643\) −8.26706 −0.326021 −0.163010 0.986624i \(-0.552120\pi\)
−0.163010 + 0.986624i \(0.552120\pi\)
\(644\) −0.779537 + 2.52830i −0.0307181 + 0.0996291i
\(645\) −15.6836 −0.617541
\(646\) −16.9643 29.3830i −0.667450 1.15606i
\(647\) 7.76187 13.4439i 0.305150 0.528536i −0.672144 0.740420i \(-0.734627\pi\)
0.977295 + 0.211884i \(0.0679599\pi\)
\(648\) 0.407198 0.705288i 0.0159963 0.0277063i
\(649\) 7.64464 + 13.2409i 0.300079 + 0.519751i
\(650\) 7.80480 0.306130
\(651\) 24.8285 5.67016i 0.973105 0.222231i
\(652\) 20.2841 0.794386
\(653\) −9.92962 17.1986i −0.388576 0.673033i 0.603682 0.797225i \(-0.293700\pi\)
−0.992258 + 0.124192i \(0.960366\pi\)
\(654\) 5.28975 9.16211i 0.206846 0.358267i
\(655\) 4.51571 7.82144i 0.176443 0.305609i
\(656\) −5.02592 8.70515i −0.196229 0.339879i
\(657\) 7.37327 0.287659
\(658\) −5.31189 5.72344i −0.207079 0.223123i
\(659\) −1.62164 −0.0631702 −0.0315851 0.999501i \(-0.510056\pi\)
−0.0315851 + 0.999501i \(0.510056\pi\)
\(660\) −3.52885 6.11215i −0.137360 0.237915i
\(661\) 4.53150 7.84879i 0.176255 0.305283i −0.764340 0.644814i \(-0.776935\pi\)
0.940595 + 0.339531i \(0.110268\pi\)
\(662\) 7.84574 13.5892i 0.304933 0.528160i
\(663\) −8.93834 15.4817i −0.347136 0.601258i
\(664\) 9.43848 0.366284
\(665\) 25.0891 + 27.0329i 0.972912 + 1.04829i
\(666\) −15.4618 −0.599133
\(667\) 1.40347 + 2.43088i 0.0543425 + 0.0941240i
\(668\) 0.162736 0.281867i 0.00629644 0.0109058i
\(669\) 0.695600 1.20481i 0.0268934 0.0465808i
\(670\) 11.3582 + 19.6730i 0.438807 + 0.760036i
\(671\) 41.3002 1.59438
\(672\) 2.90629 0.663720i 0.112113 0.0256035i
\(673\) 8.45539 0.325931 0.162966 0.986632i \(-0.447894\pi\)
0.162966 + 0.986632i \(0.447894\pi\)
\(674\) −2.59393 4.49282i −0.0999146 0.173057i
\(675\) 5.47607 9.48484i 0.210774 0.365072i
\(676\) −0.713651 + 1.23608i −0.0274481 + 0.0475415i
\(677\) 15.3193 + 26.5338i 0.588767 + 1.01978i 0.994394 + 0.105736i \(0.0337199\pi\)
−0.405627 + 0.914039i \(0.632947\pi\)
\(678\) 10.5841 0.406478
\(679\) 0.0944061 0.306191i 0.00362297 0.0117505i
\(680\) 7.16839 0.274895
\(681\) 12.9814 + 22.4845i 0.497448 + 0.861606i
\(682\) 15.5904 27.0033i 0.596986 1.03401i
\(683\) 14.5152 25.1411i 0.555410 0.961998i −0.442462 0.896787i \(-0.645895\pi\)
0.997872 0.0652106i \(-0.0207719\pi\)
\(684\) 7.02784 + 12.1726i 0.268716 + 0.465430i
\(685\) −23.7711 −0.908246
\(686\) 17.2425 + 6.75983i 0.658323 + 0.258092i
\(687\) 5.44971 0.207919
\(688\) −4.05534 7.02406i −0.154609 0.267790i
\(689\) 5.80157 10.0486i 0.221022 0.382821i
\(690\) −0.966847 + 1.67463i −0.0368072 + 0.0637520i
\(691\) −11.1056 19.2355i −0.422477 0.731751i 0.573704 0.819062i \(-0.305506\pi\)
−0.996181 + 0.0873113i \(0.972173\pi\)
\(692\) 13.4018 0.509459
\(693\) 4.92338 15.9682i 0.187024 0.606582i
\(694\) −17.7594 −0.674137
\(695\) 8.28617 + 14.3521i 0.314313 + 0.544405i
\(696\) 1.58137 2.73901i 0.0599416 0.103822i
\(697\) −20.9933 + 36.3614i −0.795176 + 1.37729i
\(698\) 7.68268 + 13.3068i 0.290794 + 0.503669i
\(699\) 14.9346 0.564878
\(700\) 5.30003 1.21039i 0.200322 0.0457483i
\(701\) −2.49593 −0.0942699 −0.0471350 0.998889i \(-0.515009\pi\)
−0.0471350 + 0.998889i \(0.515009\pi\)
\(702\) 10.1226 + 17.5329i 0.382053 + 0.661736i
\(703\) −36.2894 + 62.8551i −1.36868 + 2.37063i
\(704\) 1.82493 3.16087i 0.0687795 0.119130i
\(705\) −2.85352 4.94244i −0.107470 0.186143i
\(706\) −26.4646 −0.996007
\(707\) −6.70061 7.21975i −0.252002 0.271527i
\(708\) −4.72000 −0.177389
\(709\) 20.0638 + 34.7515i 0.753510 + 1.30512i 0.946111 + 0.323841i \(0.104974\pi\)
−0.192601 + 0.981277i \(0.561692\pi\)
\(710\) −12.2751 + 21.2612i −0.460677 + 0.797917i
\(711\) −11.6355 + 20.1533i −0.436365 + 0.755806i
\(712\) −1.97918 3.42805i −0.0741731 0.128472i
\(713\) −8.54301 −0.319938
\(714\) −8.47072 9.12701i −0.317009 0.341570i
\(715\) 23.7917 0.889759
\(716\) −10.4273 18.0606i −0.389685 0.674955i
\(717\) −3.04365 + 5.27176i −0.113667 + 0.196878i
\(718\) −3.75001 + 6.49521i −0.139949 + 0.242399i
\(719\) −5.69592 9.86562i −0.212422 0.367926i 0.740050 0.672552i \(-0.234802\pi\)
−0.952472 + 0.304626i \(0.901468\pi\)
\(720\) −2.96967 −0.110673
\(721\) −39.0213 + 8.91141i −1.45323 + 0.331878i
\(722\) 46.9784 1.74836
\(723\) −9.70180 16.8040i −0.360814 0.624948i
\(724\) −0.788691 + 1.36605i −0.0293115 + 0.0507689i
\(725\) 2.88385 4.99497i 0.107103 0.185508i
\(726\) 1.30784 + 2.26525i 0.0485385 + 0.0840712i
\(727\) −22.5154 −0.835051 −0.417526 0.908665i \(-0.637103\pi\)
−0.417526 + 0.908665i \(0.637103\pi\)
\(728\) −2.96094 + 9.60333i −0.109740 + 0.355923i
\(729\) 19.4262 0.719489
\(730\) 3.65625 + 6.33282i 0.135324 + 0.234388i
\(731\) −16.9392 + 29.3395i −0.626517 + 1.08516i
\(732\) −6.37495 + 11.0417i −0.235625 + 0.408114i
\(733\) 6.17468 + 10.6949i 0.228067 + 0.395024i 0.957235 0.289311i \(-0.0934261\pi\)
−0.729168 + 0.684335i \(0.760093\pi\)
\(734\) −1.61092 −0.0594600
\(735\) 11.1857 + 7.62226i 0.412592 + 0.281151i
\(736\) −1.00000 −0.0368605
\(737\) −24.1562 41.8398i −0.889805 1.54119i
\(738\) 8.69695 15.0636i 0.320139 0.554497i
\(739\) 4.74812 8.22398i 0.174662 0.302524i −0.765382 0.643576i \(-0.777450\pi\)
0.940044 + 0.341052i \(0.110783\pi\)
\(740\) −7.66719 13.2800i −0.281852 0.488181i
\(741\) 34.7635 1.27707
\(742\) 2.38133 7.72346i 0.0874214 0.283537i
\(743\) −31.7348 −1.16424 −0.582118 0.813104i \(-0.697776\pi\)
−0.582118 + 0.813104i \(0.697776\pi\)
\(744\) 4.81295 + 8.33627i 0.176451 + 0.305622i
\(745\) 8.20437 14.2104i 0.300585 0.520628i
\(746\) −9.05039 + 15.6757i −0.331358 + 0.573930i
\(747\) 8.16626 + 14.1444i 0.298788 + 0.517516i
\(748\) −15.2454 −0.557428
\(749\) 35.4284 8.09090i 1.29453 0.295635i
\(750\) 13.6418 0.498129
\(751\) 0.729462 + 1.26346i 0.0266184 + 0.0461045i 0.879028 0.476771i \(-0.158193\pi\)
−0.852409 + 0.522875i \(0.824859\pi\)
\(752\) 1.47568 2.55596i 0.0538126 0.0932062i
\(753\) 9.53038 16.5071i 0.347306 0.601552i
\(754\) 5.33083 + 9.23328i 0.194138 + 0.336256i
\(755\) 12.4537 0.453236
\(756\) 9.59303 + 10.3363i 0.348895 + 0.375927i
\(757\) 13.7895 0.501186 0.250593 0.968092i \(-0.419374\pi\)
0.250593 + 0.968092i \(0.419374\pi\)
\(758\) 5.19547 + 8.99882i 0.188708 + 0.326852i
\(759\) 2.05625 3.56153i 0.0746371 0.129275i
\(760\) −6.96993 + 12.0723i −0.252826 + 0.437907i
\(761\) 2.63708 + 4.56756i 0.0955942 + 0.165574i 0.909856 0.414923i \(-0.136192\pi\)
−0.814262 + 0.580497i \(0.802858\pi\)
\(762\) −2.85718 −0.103505
\(763\) 16.8990 + 18.2083i 0.611785 + 0.659184i
\(764\) 6.26097 0.226514
\(765\) 6.20216 + 10.7424i 0.224239 + 0.388394i
\(766\) 3.69781 6.40480i 0.133607 0.231415i
\(767\) 7.95563 13.7796i 0.287261 0.497551i
\(768\) 0.563379 + 0.975800i 0.0203292 + 0.0352112i
\(769\) −4.68371 −0.168899 −0.0844495 0.996428i \(-0.526913\pi\)
−0.0844495 + 0.996428i \(0.526913\pi\)
\(770\) 16.1563 3.68967i 0.582233 0.132966i
\(771\) 13.8210 0.497751
\(772\) −6.51789 11.2893i −0.234584 0.406311i
\(773\) 4.20158 7.27735i 0.151120 0.261748i −0.780519 0.625132i \(-0.785045\pi\)
0.931640 + 0.363384i \(0.118379\pi\)
\(774\) 7.01744 12.1546i 0.252237 0.436887i
\(775\) 8.77708 + 15.2024i 0.315282 + 0.546085i
\(776\) 0.121105 0.00434743