Properties

Label 570.2.f.d.341.5
Level $570$
Weight $2$
Character 570.341
Analytic conductor $4.551$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.7278137344.1
Defining polynomial: \(x^{8} - 2 x^{7} + x^{6} + 6 x^{5} - 20 x^{4} + 18 x^{3} + 9 x^{2} - 54 x + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 341.5
Root \(0.209196 + 1.71937i\) of defining polynomial
Character \(\chi\) \(=\) 570.341
Dual form 570.2.f.d.341.6

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-0.209196 - 1.71937i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(-0.209196 - 1.71937i) q^{6} +0.264536 q^{7} +1.00000 q^{8} +(-2.91247 + 0.719371i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(-0.209196 - 1.71937i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(-0.209196 - 1.71937i) q^{6} +0.264536 q^{7} +1.00000 q^{8} +(-2.91247 + 0.719371i) q^{9} -1.00000i q^{10} -2.00000i q^{11} +(-0.209196 - 1.71937i) q^{12} -5.43874i q^{13} +0.264536 q^{14} +(-1.71937 + 0.209196i) q^{15} +1.00000 q^{16} +3.28489i q^{17} +(-2.91247 + 0.719371i) q^{18} +(1.41839 - 4.12167i) q^{19} -1.00000i q^{20} +(-0.0553398 - 0.454835i) q^{21} -2.00000i q^{22} +3.96781i q^{23} +(-0.209196 - 1.71937i) q^{24} -1.00000 q^{25} -5.43874i q^{26} +(1.84614 + 4.85713i) q^{27} +0.264536 q^{28} -0.418392 q^{29} +(-1.71937 + 0.209196i) q^{30} -3.56041i q^{31} +1.00000 q^{32} +(-3.43874 + 0.418392i) q^{33} +3.28489i q^{34} -0.264536i q^{35} +(-2.91247 + 0.719371i) q^{36} -0.307712i q^{37} +(1.41839 - 4.12167i) q^{38} +(-9.35122 + 1.13776i) q^{39} -1.00000i q^{40} +2.15386 q^{41} +(-0.0553398 - 0.454835i) q^{42} +1.71427 q^{43} -2.00000i q^{44} +(0.719371 + 2.91247i) q^{45} +3.96781i q^{46} +5.71427i q^{47} +(-0.209196 - 1.71937i) q^{48} -6.93002 q^{49} -1.00000 q^{50} +(5.64794 - 0.687185i) q^{51} -5.43874i q^{52} -3.29588 q^{53} +(1.84614 + 4.85713i) q^{54} -2.00000 q^{55} +0.264536 q^{56} +(-7.38340 - 1.57651i) q^{57} -0.418392 q^{58} +12.5486 q^{59} +(-1.71937 + 0.209196i) q^{60} +9.18520 q^{61} -3.56041i q^{62} +(-0.770454 + 0.190299i) q^{63} +1.00000 q^{64} -5.43874 q^{65} +(-3.43874 + 0.418392i) q^{66} +0.666330i q^{67} +3.28489i q^{68} +(6.82214 - 0.830051i) q^{69} -0.264536i q^{70} +10.3484 q^{71} +(-2.91247 + 0.719371i) q^{72} +12.7024 q^{73} -0.307712i q^{74} +(0.209196 + 1.71937i) q^{75} +(1.41839 - 4.12167i) q^{76} -0.529072i q^{77} +(-9.35122 + 1.13776i) q^{78} +8.08948i q^{79} -1.00000i q^{80} +(7.96501 - 4.19030i) q^{81} +2.15386 q^{82} +16.7456i q^{83} +(-0.0553398 - 0.454835i) q^{84} +3.28489 q^{85} +1.71427 q^{86} +(0.0875259 + 0.719371i) q^{87} -2.00000i q^{88} -10.6829 q^{89} +(0.719371 + 2.91247i) q^{90} -1.43874i q^{91} +3.96781i q^{92} +(-6.12167 + 0.744824i) q^{93} +5.71427i q^{94} +(-4.12167 - 1.41839i) q^{95} +(-0.209196 - 1.71937i) q^{96} +1.47093i q^{97} -6.93002 q^{98} +(1.43874 + 5.82495i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{2} - 2q^{3} + 8q^{4} - 2q^{6} + 4q^{7} + 8q^{8} + 2q^{9} + O(q^{10}) \) \( 8q + 8q^{2} - 2q^{3} + 8q^{4} - 2q^{6} + 4q^{7} + 8q^{8} + 2q^{9} - 2q^{12} + 4q^{14} + 8q^{16} + 2q^{18} + 12q^{19} - 2q^{21} - 2q^{24} - 8q^{25} + 16q^{27} + 4q^{28} - 4q^{29} + 8q^{32} + 2q^{36} + 12q^{38} - 22q^{39} + 16q^{41} - 2q^{42} - 40q^{43} - 8q^{45} - 2q^{48} + 4q^{49} - 8q^{50} + 18q^{51} + 28q^{53} + 16q^{54} - 16q^{55} + 4q^{56} - 30q^{57} - 4q^{58} - 4q^{59} + 16q^{61} - 34q^{63} + 8q^{64} - 16q^{65} - 2q^{69} + 24q^{71} + 2q^{72} - 4q^{73} + 2q^{75} + 12q^{76} - 22q^{78} + 34q^{81} + 16q^{82} - 2q^{84} - 40q^{86} + 26q^{87} - 88q^{89} - 8q^{90} - 24q^{93} - 8q^{95} - 2q^{96} + 4q^{98} - 16q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −0.209196 1.71937i −0.120779 0.992679i
\(4\) 1.00000 0.500000
\(5\) 1.00000i 0.447214i
\(6\) −0.209196 1.71937i −0.0854039 0.701930i
\(7\) 0.264536 0.0999851 0.0499926 0.998750i \(-0.484080\pi\)
0.0499926 + 0.998750i \(0.484080\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.91247 + 0.719371i −0.970825 + 0.239790i
\(10\) 1.00000i 0.316228i
\(11\) 2.00000i 0.603023i −0.953463 0.301511i \(-0.902509\pi\)
0.953463 0.301511i \(-0.0974911\pi\)
\(12\) −0.209196 1.71937i −0.0603897 0.496340i
\(13\) 5.43874i 1.50844i −0.656624 0.754218i \(-0.728016\pi\)
0.656624 0.754218i \(-0.271984\pi\)
\(14\) 0.264536 0.0707002
\(15\) −1.71937 + 0.209196i −0.443940 + 0.0540142i
\(16\) 1.00000 0.250000
\(17\) 3.28489i 0.796702i 0.917233 + 0.398351i \(0.130417\pi\)
−0.917233 + 0.398351i \(0.869583\pi\)
\(18\) −2.91247 + 0.719371i −0.686477 + 0.169557i
\(19\) 1.41839 4.12167i 0.325401 0.945576i
\(20\) 1.00000i 0.223607i
\(21\) −0.0553398 0.454835i −0.0120761 0.0992532i
\(22\) 2.00000i 0.426401i
\(23\) 3.96781i 0.827346i 0.910425 + 0.413673i \(0.135754\pi\)
−0.910425 + 0.413673i \(0.864246\pi\)
\(24\) −0.209196 1.71937i −0.0427020 0.350965i
\(25\) −1.00000 −0.200000
\(26\) 5.43874i 1.06663i
\(27\) 1.84614 + 4.85713i 0.355291 + 0.934756i
\(28\) 0.264536 0.0499926
\(29\) −0.418392 −0.0776934 −0.0388467 0.999245i \(-0.512368\pi\)
−0.0388467 + 0.999245i \(0.512368\pi\)
\(30\) −1.71937 + 0.209196i −0.313913 + 0.0381938i
\(31\) 3.56041i 0.639469i −0.947507 0.319734i \(-0.896406\pi\)
0.947507 0.319734i \(-0.103594\pi\)
\(32\) 1.00000 0.176777
\(33\) −3.43874 + 0.418392i −0.598608 + 0.0728327i
\(34\) 3.28489i 0.563353i
\(35\) 0.264536i 0.0447147i
\(36\) −2.91247 + 0.719371i −0.485412 + 0.119895i
\(37\) 0.307712i 0.0505876i −0.999680 0.0252938i \(-0.991948\pi\)
0.999680 0.0252938i \(-0.00805212\pi\)
\(38\) 1.41839 4.12167i 0.230094 0.668623i
\(39\) −9.35122 + 1.13776i −1.49739 + 0.182188i
\(40\) 1.00000i 0.158114i
\(41\) 2.15386 0.336376 0.168188 0.985755i \(-0.446208\pi\)
0.168188 + 0.985755i \(0.446208\pi\)
\(42\) −0.0553398 0.454835i −0.00853912 0.0701826i
\(43\) 1.71427 0.261423 0.130712 0.991420i \(-0.458274\pi\)
0.130712 + 0.991420i \(0.458274\pi\)
\(44\) 2.00000i 0.301511i
\(45\) 0.719371 + 2.91247i 0.107238 + 0.434166i
\(46\) 3.96781i 0.585022i
\(47\) 5.71427i 0.833512i 0.909018 + 0.416756i \(0.136833\pi\)
−0.909018 + 0.416756i \(0.863167\pi\)
\(48\) −0.209196 1.71937i −0.0301948 0.248170i
\(49\) −6.93002 −0.990003
\(50\) −1.00000 −0.141421
\(51\) 5.64794 0.687185i 0.790870 0.0962252i
\(52\) 5.43874i 0.754218i
\(53\) −3.29588 −0.452723 −0.226362 0.974043i \(-0.572683\pi\)
−0.226362 + 0.974043i \(0.572683\pi\)
\(54\) 1.84614 + 4.85713i 0.251228 + 0.660972i
\(55\) −2.00000 −0.269680
\(56\) 0.264536 0.0353501
\(57\) −7.38340 1.57651i −0.977956 0.208813i
\(58\) −0.418392 −0.0549376
\(59\) 12.5486 1.63369 0.816843 0.576860i \(-0.195722\pi\)
0.816843 + 0.576860i \(0.195722\pi\)
\(60\) −1.71937 + 0.209196i −0.221970 + 0.0270071i
\(61\) 9.18520 1.17604 0.588022 0.808845i \(-0.299907\pi\)
0.588022 + 0.808845i \(0.299907\pi\)
\(62\) 3.56041i 0.452173i
\(63\) −0.770454 + 0.190299i −0.0970681 + 0.0239755i
\(64\) 1.00000 0.125000
\(65\) −5.43874 −0.674593
\(66\) −3.43874 + 0.418392i −0.423280 + 0.0515005i
\(67\) 0.666330i 0.0814052i 0.999171 + 0.0407026i \(0.0129596\pi\)
−0.999171 + 0.0407026i \(0.987040\pi\)
\(68\) 3.28489i 0.398351i
\(69\) 6.82214 0.830051i 0.821290 0.0999264i
\(70\) 0.264536i 0.0316181i
\(71\) 10.3484 1.22813 0.614065 0.789255i \(-0.289533\pi\)
0.614065 + 0.789255i \(0.289533\pi\)
\(72\) −2.91247 + 0.719371i −0.343238 + 0.0847787i
\(73\) 12.7024 1.48671 0.743354 0.668899i \(-0.233234\pi\)
0.743354 + 0.668899i \(0.233234\pi\)
\(74\) 0.307712i 0.0357708i
\(75\) 0.209196 + 1.71937i 0.0241559 + 0.198536i
\(76\) 1.41839 4.12167i 0.162701 0.472788i
\(77\) 0.529072i 0.0602933i
\(78\) −9.35122 + 1.13776i −1.05882 + 0.128826i
\(79\) 8.08948i 0.910138i 0.890456 + 0.455069i \(0.150385\pi\)
−0.890456 + 0.455069i \(0.849615\pi\)
\(80\) 1.00000i 0.111803i
\(81\) 7.96501 4.19030i 0.885001 0.465589i
\(82\) 2.15386 0.237854
\(83\) 16.7456i 1.83807i 0.394177 + 0.919035i \(0.371030\pi\)
−0.394177 + 0.919035i \(0.628970\pi\)
\(84\) −0.0553398 0.454835i −0.00603807 0.0496266i
\(85\) 3.28489 0.356296
\(86\) 1.71427 0.184854
\(87\) 0.0875259 + 0.719371i 0.00938376 + 0.0771247i
\(88\) 2.00000i 0.213201i
\(89\) −10.6829 −1.13239 −0.566194 0.824272i \(-0.691585\pi\)
−0.566194 + 0.824272i \(0.691585\pi\)
\(90\) 0.719371 + 2.91247i 0.0758284 + 0.307002i
\(91\) 1.43874i 0.150821i
\(92\) 3.96781i 0.413673i
\(93\) −6.12167 + 0.744824i −0.634788 + 0.0772347i
\(94\) 5.71427i 0.589382i
\(95\) −4.12167 1.41839i −0.422874 0.145524i
\(96\) −0.209196 1.71937i −0.0213510 0.175483i
\(97\) 1.47093i 0.149350i 0.997208 + 0.0746751i \(0.0237920\pi\)
−0.997208 + 0.0746751i \(0.976208\pi\)
\(98\) −6.93002 −0.700038
\(99\) 1.43874 + 5.82495i 0.144599 + 0.585429i
\(100\) −1.00000 −0.100000
\(101\) 6.28404i 0.625285i −0.949871 0.312643i \(-0.898786\pi\)
0.949871 0.312643i \(-0.101214\pi\)
\(102\) 5.64794 0.687185i 0.559229 0.0680415i
\(103\) 9.42854i 0.929021i 0.885568 + 0.464511i \(0.153770\pi\)
−0.885568 + 0.464511i \(0.846230\pi\)
\(104\) 5.43874i 0.533313i
\(105\) −0.454835 + 0.0553398i −0.0443874 + 0.00540062i
\(106\) −3.29588 −0.320124
\(107\) 10.1734 0.983496 0.491748 0.870738i \(-0.336358\pi\)
0.491748 + 0.870738i \(0.336358\pi\)
\(108\) 1.84614 + 4.85713i 0.177645 + 0.467378i
\(109\) 4.99915i 0.478832i 0.970917 + 0.239416i \(0.0769560\pi\)
−0.970917 + 0.239416i \(0.923044\pi\)
\(110\) −2.00000 −0.190693
\(111\) −0.529072 + 0.0643722i −0.0502173 + 0.00610994i
\(112\) 0.264536 0.0249963
\(113\) −18.6325 −1.75279 −0.876397 0.481590i \(-0.840060\pi\)
−0.876397 + 0.481590i \(0.840060\pi\)
\(114\) −7.38340 1.57651i −0.691519 0.147653i
\(115\) 3.96781 0.370001
\(116\) −0.418392 −0.0388467
\(117\) 3.91247 + 15.8402i 0.361708 + 1.46443i
\(118\) 12.5486 1.15519
\(119\) 0.868970i 0.0796584i
\(120\) −1.71937 + 0.209196i −0.156956 + 0.0190969i
\(121\) 7.00000 0.636364
\(122\) 9.18520 0.831589
\(123\) −0.450578 3.70328i −0.0406273 0.333913i
\(124\) 3.56041i 0.319734i
\(125\) 1.00000i 0.0894427i
\(126\) −0.770454 + 0.190299i −0.0686375 + 0.0169532i
\(127\) 2.83678i 0.251724i −0.992048 0.125862i \(-0.959830\pi\)
0.992048 0.125862i \(-0.0401696\pi\)
\(128\) 1.00000 0.0883883
\(129\) −0.358618 2.94746i −0.0315746 0.259510i
\(130\) −5.43874 −0.477009
\(131\) 3.08012i 0.269112i −0.990906 0.134556i \(-0.957039\pi\)
0.990906 0.134556i \(-0.0429608\pi\)
\(132\) −3.43874 + 0.418392i −0.299304 + 0.0364163i
\(133\) 0.375216 1.09033i 0.0325353 0.0945436i
\(134\) 0.666330i 0.0575622i
\(135\) 4.85713 1.84614i 0.418036 0.158891i
\(136\) 3.28489i 0.281677i
\(137\) 4.79651i 0.409794i −0.978784 0.204897i \(-0.934314\pi\)
0.978784 0.204897i \(-0.0656859\pi\)
\(138\) 6.82214 0.830051i 0.580740 0.0706586i
\(139\) 11.7550 0.997043 0.498522 0.866877i \(-0.333876\pi\)
0.498522 + 0.866877i \(0.333876\pi\)
\(140\) 0.264536i 0.0223574i
\(141\) 9.82495 1.19540i 0.827410 0.100671i
\(142\) 10.3484 0.868420
\(143\) −10.8775 −0.909621
\(144\) −2.91247 + 0.719371i −0.242706 + 0.0599476i
\(145\) 0.418392i 0.0347456i
\(146\) 12.7024 1.05126
\(147\) 1.44973 + 11.9153i 0.119572 + 0.982756i
\(148\) 0.307712i 0.0252938i
\(149\) 17.4473i 1.42933i −0.699464 0.714667i \(-0.746578\pi\)
0.699464 0.714667i \(-0.253422\pi\)
\(150\) 0.209196 + 1.71937i 0.0170808 + 0.140386i
\(151\) 13.2934i 1.08180i 0.841086 + 0.540901i \(0.181917\pi\)
−0.841086 + 0.540901i \(0.818083\pi\)
\(152\) 1.41839 4.12167i 0.115047 0.334312i
\(153\) −2.36305 9.56715i −0.191041 0.773458i
\(154\) 0.529072i 0.0426338i
\(155\) −3.56041 −0.285979
\(156\) −9.35122 + 1.13776i −0.748697 + 0.0910940i
\(157\) −4.39720 −0.350934 −0.175467 0.984485i \(-0.556144\pi\)
−0.175467 + 0.984485i \(0.556144\pi\)
\(158\) 8.08948i 0.643565i
\(159\) 0.689484 + 5.66683i 0.0546797 + 0.449409i
\(160\) 1.00000i 0.0790569i
\(161\) 1.04963i 0.0827224i
\(162\) 7.96501 4.19030i 0.625790 0.329221i
\(163\) −11.7330 −0.918999 −0.459499 0.888178i \(-0.651971\pi\)
−0.459499 + 0.888178i \(0.651971\pi\)
\(164\) 2.15386 0.168188
\(165\) 0.418392 + 3.43874i 0.0325718 + 0.267706i
\(166\) 16.7456i 1.29971i
\(167\) 6.24334 0.483124 0.241562 0.970385i \(-0.422340\pi\)
0.241562 + 0.970385i \(0.422340\pi\)
\(168\) −0.0553398 0.454835i −0.00426956 0.0350913i
\(169\) −16.5799 −1.27538
\(170\) 3.28489 0.251939
\(171\) −1.16602 + 13.0246i −0.0891677 + 0.996017i
\(172\) 1.71427 0.130712
\(173\) −15.3422 −1.16644 −0.583222 0.812313i \(-0.698208\pi\)
−0.583222 + 0.812313i \(0.698208\pi\)
\(174\) 0.0875259 + 0.719371i 0.00663532 + 0.0545354i
\(175\) −0.264536 −0.0199970
\(176\) 2.00000i 0.150756i
\(177\) −2.62511 21.5757i −0.197315 1.62173i
\(178\) −10.6829 −0.800719
\(179\) −20.6812 −1.54579 −0.772894 0.634535i \(-0.781192\pi\)
−0.772894 + 0.634535i \(0.781192\pi\)
\(180\) 0.719371 + 2.91247i 0.0536188 + 0.217083i
\(181\) 9.76305i 0.725682i −0.931851 0.362841i \(-0.881807\pi\)
0.931851 0.362841i \(-0.118193\pi\)
\(182\) 1.43874i 0.106647i
\(183\) −1.92151 15.7928i −0.142042 1.16743i
\(184\) 3.96781i 0.292511i
\(185\) −0.307712 −0.0226235
\(186\) −6.12167 + 0.744824i −0.448863 + 0.0546131i
\(187\) 6.56977 0.480429
\(188\) 5.71427i 0.416756i
\(189\) 0.488371 + 1.28489i 0.0355238 + 0.0934617i
\(190\) −4.12167 1.41839i −0.299017 0.102901i
\(191\) 19.3100i 1.39722i 0.715501 + 0.698611i \(0.246198\pi\)
−0.715501 + 0.698611i \(0.753802\pi\)
\(192\) −0.209196 1.71937i −0.0150974 0.124085i
\(193\) 15.0565i 1.08379i 0.840447 + 0.541894i \(0.182292\pi\)
−0.840447 + 0.541894i \(0.817708\pi\)
\(194\) 1.47093i 0.105606i
\(195\) 1.13776 + 9.35122i 0.0814769 + 0.669655i
\(196\) −6.93002 −0.495001
\(197\) 15.5116i 1.10516i −0.833461 0.552579i \(-0.813644\pi\)
0.833461 0.552579i \(-0.186356\pi\)
\(198\) 1.43874 + 5.82495i 0.102247 + 0.413961i
\(199\) 15.8469 1.12336 0.561680 0.827355i \(-0.310155\pi\)
0.561680 + 0.827355i \(0.310155\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 1.14567 0.139394i 0.0808093 0.00983207i
\(202\) 6.28404i 0.442144i
\(203\) −0.110680 −0.00776819
\(204\) 5.64794 0.687185i 0.395435 0.0481126i
\(205\) 2.15386i 0.150432i
\(206\) 9.42854i 0.656917i
\(207\) −2.85433 11.5562i −0.198390 0.803208i
\(208\) 5.43874i 0.377109i
\(209\) −8.24334 2.83678i −0.570204 0.196224i
\(210\) −0.454835 + 0.0553398i −0.0313866 + 0.00381881i
\(211\) 6.88600i 0.474052i −0.971503 0.237026i \(-0.923827\pi\)
0.971503 0.237026i \(-0.0761726\pi\)
\(212\) −3.29588 −0.226362
\(213\) −2.16485 17.7928i −0.148333 1.21914i
\(214\) 10.1734 0.695437
\(215\) 1.71427i 0.116912i
\(216\) 1.84614 + 4.85713i 0.125614 + 0.330486i
\(217\) 0.941857i 0.0639374i
\(218\) 4.99915i 0.338585i
\(219\) −2.65730 21.8402i −0.179564 1.47582i
\(220\) −2.00000 −0.134840
\(221\) 17.8656 1.20177
\(222\) −0.529072 + 0.0643722i −0.0355090 + 0.00432038i
\(223\) 6.67484i 0.446981i −0.974706 0.223490i \(-0.928255\pi\)
0.974706 0.223490i \(-0.0717451\pi\)
\(224\) 0.264536 0.0176750
\(225\) 2.91247 0.719371i 0.194165 0.0479581i
\(226\) −18.6325 −1.23941
\(227\) −13.8656 −0.920295 −0.460148 0.887842i \(-0.652204\pi\)
−0.460148 + 0.887842i \(0.652204\pi\)
\(228\) −7.38340 1.57651i −0.488978 0.104407i
\(229\) −9.64990 −0.637683 −0.318842 0.947808i \(-0.603294\pi\)
−0.318842 + 0.947808i \(0.603294\pi\)
\(230\) 3.96781 0.261630
\(231\) −0.909671 + 0.110680i −0.0598519 + 0.00728219i
\(232\) −0.418392 −0.0274688
\(233\) 26.3548i 1.72656i 0.504725 + 0.863280i \(0.331594\pi\)
−0.504725 + 0.863280i \(0.668406\pi\)
\(234\) 3.91247 + 15.8402i 0.255766 + 1.03551i
\(235\) 5.71427 0.372758
\(236\) 12.5486 0.816843
\(237\) 13.9088 1.69229i 0.903475 0.109926i
\(238\) 0.868970i 0.0563270i
\(239\) 13.3149i 0.861273i −0.902526 0.430636i \(-0.858289\pi\)
0.902526 0.430636i \(-0.141711\pi\)
\(240\) −1.71937 + 0.209196i −0.110985 + 0.0135035i
\(241\) 22.0627i 1.42118i −0.703605 0.710591i \(-0.748428\pi\)
0.703605 0.710591i \(-0.251572\pi\)
\(242\) 7.00000 0.449977
\(243\) −8.87093 12.8182i −0.569070 0.822289i
\(244\) 9.18520 0.588022
\(245\) 6.93002i 0.442743i
\(246\) −0.450578 3.70328i −0.0287278 0.236112i
\(247\) −22.4167 7.71427i −1.42634 0.490847i
\(248\) 3.56041i 0.226086i
\(249\) 28.7919 3.50311i 1.82461 0.222001i
\(250\) 1.00000i 0.0632456i
\(251\) 20.6137i 1.30113i 0.759452 + 0.650564i \(0.225467\pi\)
−0.759452 + 0.650564i \(0.774533\pi\)
\(252\) −0.770454 + 0.190299i −0.0485340 + 0.0119877i
\(253\) 7.93563 0.498909
\(254\) 2.83678i 0.177996i
\(255\) −0.687185 5.64794i −0.0430332 0.353688i
\(256\) 1.00000 0.0625000
\(257\) −13.4066 −0.836278 −0.418139 0.908383i \(-0.637318\pi\)
−0.418139 + 0.908383i \(0.637318\pi\)
\(258\) −0.358618 2.94746i −0.0223266 0.183501i
\(259\) 0.0814009i 0.00505801i
\(260\) −5.43874 −0.337296
\(261\) 1.21856 0.300979i 0.0754267 0.0186301i
\(262\) 3.08012i 0.190291i
\(263\) 14.6748i 0.904890i −0.891792 0.452445i \(-0.850552\pi\)
0.891792 0.452445i \(-0.149448\pi\)
\(264\) −3.43874 + 0.418392i −0.211640 + 0.0257502i
\(265\) 3.29588i 0.202464i
\(266\) 0.375216 1.09033i 0.0230059 0.0668524i
\(267\) 2.23483 + 18.3679i 0.136769 + 1.12410i
\(268\) 0.666330i 0.0407026i
\(269\) −13.3235 −0.812346 −0.406173 0.913796i \(-0.633137\pi\)
−0.406173 + 0.913796i \(0.633137\pi\)
\(270\) 4.85713 1.84614i 0.295596 0.112353i
\(271\) 21.5579 1.30955 0.654776 0.755823i \(-0.272763\pi\)
0.654776 + 0.755823i \(0.272763\pi\)
\(272\) 3.28489i 0.199175i
\(273\) −2.47373 + 0.300979i −0.149717 + 0.0182161i
\(274\) 4.79651i 0.289768i
\(275\) 2.00000i 0.120605i
\(276\) 6.82214 0.830051i 0.410645 0.0499632i
\(277\) −20.0471 −1.20451 −0.602257 0.798303i \(-0.705732\pi\)
−0.602257 + 0.798303i \(0.705732\pi\)
\(278\) 11.7550 0.705016
\(279\) 2.56126 + 10.3696i 0.153338 + 0.620812i
\(280\) 0.264536i 0.0158090i
\(281\) −6.33282 −0.377785 −0.188892 0.981998i \(-0.560490\pi\)
−0.188892 + 0.981998i \(0.560490\pi\)
\(282\) 9.82495 1.19540i 0.585067 0.0711852i
\(283\) −33.2022 −1.97367 −0.986834 0.161738i \(-0.948290\pi\)
−0.986834 + 0.161738i \(0.948290\pi\)
\(284\) 10.3484 0.614065
\(285\) −1.57651 + 7.38340i −0.0933841 + 0.437355i
\(286\) −10.8775 −0.643199
\(287\) 0.569772 0.0336326
\(288\) −2.91247 + 0.719371i −0.171619 + 0.0423893i
\(289\) 6.20952 0.365266
\(290\) 0.418392i 0.0245688i
\(291\) 2.52907 0.307712i 0.148257 0.0180384i
\(292\) 12.7024 0.743354
\(293\) 29.4748 1.72194 0.860969 0.508657i \(-0.169858\pi\)
0.860969 + 0.508657i \(0.169858\pi\)
\(294\) 1.44973 + 11.9153i 0.0845501 + 0.694913i
\(295\) 12.5486i 0.730606i
\(296\) 0.307712i 0.0178854i
\(297\) 9.71427 3.69229i 0.563679 0.214248i
\(298\) 17.4473i 1.01069i
\(299\) 21.5799 1.24800
\(300\) 0.209196 + 1.71937i 0.0120779 + 0.0992679i
\(301\) 0.453485 0.0261385
\(302\) 13.2934i 0.764949i
\(303\) −10.8046 + 1.31460i −0.620708 + 0.0755216i
\(304\) 1.41839 4.12167i 0.0813504 0.236394i
\(305\) 9.18520i 0.525943i
\(306\) −2.36305 9.56715i −0.135087 0.546917i
\(307\) 1.81934i 0.103835i 0.998651 + 0.0519176i \(0.0165333\pi\)
−0.998651 + 0.0519176i \(0.983467\pi\)
\(308\) 0.529072i 0.0301467i
\(309\) 16.2112 1.97241i 0.922220 0.112207i
\(310\) −3.56041 −0.202218
\(311\) 15.9898i 0.906698i −0.891333 0.453349i \(-0.850229\pi\)
0.891333 0.453349i \(-0.149771\pi\)
\(312\) −9.35122 + 1.13776i −0.529408 + 0.0644132i
\(313\) 21.4416 1.21195 0.605977 0.795482i \(-0.292782\pi\)
0.605977 + 0.795482i \(0.292782\pi\)
\(314\) −4.39720 −0.248148
\(315\) 0.190299 + 0.770454i 0.0107222 + 0.0434102i
\(316\) 8.08948i 0.455069i
\(317\) −6.44037 −0.361727 −0.180864 0.983508i \(-0.557889\pi\)
−0.180864 + 0.983508i \(0.557889\pi\)
\(318\) 0.689484 + 5.66683i 0.0386644 + 0.317780i
\(319\) 0.836784i 0.0468509i
\(320\) 1.00000i 0.0559017i
\(321\) −2.12823 17.4918i −0.118786 0.976296i
\(322\) 1.04963i 0.0584935i
\(323\) 13.5392 + 4.65926i 0.753342 + 0.259248i
\(324\) 7.96501 4.19030i 0.442501 0.232794i
\(325\) 5.43874i 0.301687i
\(326\) −11.7330 −0.649830
\(327\) 8.59540 1.04580i 0.475327 0.0578330i
\(328\) 2.15386 0.118927
\(329\) 1.51163i 0.0833388i
\(330\) 0.418392 + 3.43874i 0.0230317 + 0.189297i
\(331\) 24.6239i 1.35345i 0.736234 + 0.676727i \(0.236602\pi\)
−0.736234 + 0.676727i \(0.763398\pi\)
\(332\) 16.7456i 0.919035i
\(333\) 0.221359 + 0.896204i 0.0121304 + 0.0491117i
\(334\) 6.24334 0.341620
\(335\) 0.666330 0.0364055
\(336\) −0.0553398 0.454835i −0.00301904 0.0248133i
\(337\) 25.6686i 1.39826i −0.714995 0.699129i \(-0.753571\pi\)
0.714995 0.699129i \(-0.246429\pi\)
\(338\) −16.5799 −0.901829
\(339\) 3.89783 + 32.0361i 0.211701 + 1.73996i
\(340\) 3.28489 0.178148
\(341\) −7.12082 −0.385614
\(342\) −1.16602 + 13.0246i −0.0630511 + 0.704290i
\(343\) −3.68499 −0.198971
\(344\) 1.71427 0.0924272
\(345\) −0.830051 6.82214i −0.0446884 0.367292i
\(346\) −15.3422 −0.824801
\(347\) 3.23398i 0.173609i 0.996225 + 0.0868046i \(0.0276656\pi\)
−0.996225 + 0.0868046i \(0.972334\pi\)
\(348\) 0.0875259 + 0.719371i 0.00469188 + 0.0385623i
\(349\) −17.9576 −0.961249 −0.480624 0.876927i \(-0.659590\pi\)
−0.480624 + 0.876927i \(0.659590\pi\)
\(350\) −0.264536 −0.0141400
\(351\) 26.4167 10.0407i 1.41002 0.535933i
\(352\) 2.00000i 0.106600i
\(353\) 7.59260i 0.404113i −0.979374 0.202057i \(-0.935237\pi\)
0.979374 0.202057i \(-0.0647625\pi\)
\(354\) −2.62511 21.5757i −0.139523 1.14673i
\(355\) 10.3484i 0.549237i
\(356\) −10.6829 −0.566194
\(357\) 1.49408 0.181785i 0.0790752 0.00962109i
\(358\) −20.6812 −1.09304
\(359\) 36.7605i 1.94015i −0.242814 0.970073i \(-0.578070\pi\)
0.242814 0.970073i \(-0.421930\pi\)
\(360\) 0.719371 + 2.91247i 0.0379142 + 0.153501i
\(361\) −14.9763 11.6923i −0.788228 0.615384i
\(362\) 9.76305i 0.513135i
\(363\) −1.46437 12.0356i −0.0768596 0.631705i
\(364\) 1.43874i 0.0754106i
\(365\) 12.7024i 0.664876i
\(366\) −1.92151 15.7928i −0.100439 0.825501i
\(367\) −35.2917 −1.84221 −0.921106 0.389312i \(-0.872713\pi\)
−0.921106 + 0.389312i \(0.872713\pi\)
\(368\) 3.96781i 0.206837i
\(369\) −6.27305 + 1.54942i −0.326562 + 0.0806597i
\(370\) −0.307712 −0.0159972
\(371\) −0.871877 −0.0452656
\(372\) −6.12167 + 0.744824i −0.317394 + 0.0386173i
\(373\) 21.6821i 1.12266i 0.827594 + 0.561328i \(0.189709\pi\)
−0.827594 + 0.561328i \(0.810291\pi\)
\(374\) 6.56977 0.339715
\(375\) 1.71937 0.209196i 0.0887879 0.0108028i
\(376\) 5.71427i 0.294691i
\(377\) 2.27553i 0.117196i
\(378\) 0.488371 + 1.28489i 0.0251191 + 0.0660874i
\(379\) 13.1750i 0.676754i −0.941011 0.338377i \(-0.890122\pi\)
0.941011 0.338377i \(-0.109878\pi\)
\(380\) −4.12167 1.41839i −0.211437 0.0727620i
\(381\) −4.87748 + 0.593444i −0.249881 + 0.0304031i
\(382\) 19.3100i 0.987985i
\(383\) 27.2354 1.39166 0.695832 0.718204i \(-0.255036\pi\)
0.695832 + 0.718204i \(0.255036\pi\)
\(384\) −0.209196 1.71937i −0.0106755 0.0877413i
\(385\) −0.529072 −0.0269640
\(386\) 15.0565i 0.766353i
\(387\) −4.99276 + 1.23320i −0.253796 + 0.0626868i
\(388\) 1.47093i 0.0746751i
\(389\) 27.4236i 1.39043i −0.718801 0.695215i \(-0.755309\pi\)
0.718801 0.695215i \(-0.244691\pi\)
\(390\) 1.13776 + 9.35122i 0.0576129 + 0.473517i
\(391\) −13.0338 −0.659148
\(392\) −6.93002 −0.350019
\(393\) −5.29588 + 0.644350i −0.267142 + 0.0325031i
\(394\) 15.5116i 0.781465i
\(395\) 8.08948 0.407026
\(396\) 1.43874 + 5.82495i 0.0722995 + 0.292715i
\(397\) 4.00313 0.200911 0.100456 0.994942i \(-0.467970\pi\)
0.100456 + 0.994942i \(0.467970\pi\)
\(398\) 15.8469 0.794335
\(399\) −1.95317 0.417042i −0.0977810 0.0208782i
\(400\) −1.00000 −0.0500000
\(401\) −6.98569 −0.348849 −0.174424 0.984671i \(-0.555806\pi\)
−0.174424 + 0.984671i \(0.555806\pi\)
\(402\) 1.14567 0.139394i 0.0571408 0.00695232i
\(403\) −19.3642 −0.964598
\(404\) 6.28404i 0.312643i
\(405\) −4.19030 7.96501i −0.208218 0.395785i
\(406\) −0.110680 −0.00549294
\(407\) −0.615425 −0.0305055
\(408\) 5.64794 0.687185i 0.279615 0.0340207i
\(409\) 25.9763i 1.28445i 0.766518 + 0.642223i \(0.221988\pi\)
−0.766518 + 0.642223i \(0.778012\pi\)
\(410\) 2.15386i 0.106371i
\(411\) −8.24699 + 1.00341i −0.406794 + 0.0494947i
\(412\) 9.42854i 0.464511i
\(413\) 3.31955 0.163344
\(414\) −2.85433 11.5562i −0.140283 0.567954i
\(415\) 16.7456 0.822010
\(416\) 5.43874i 0.266656i
\(417\) −2.45909 20.2112i −0.120422 0.989744i
\(418\) −8.24334 2.83678i −0.403195 0.138752i
\(419\) 15.1395i 0.739615i 0.929108 + 0.369808i \(0.120576\pi\)
−0.929108 + 0.369808i \(0.879424\pi\)
\(420\) −0.454835 + 0.0553398i −0.0221937 + 0.00270031i
\(421\) 28.7728i 1.40230i −0.713013 0.701151i \(-0.752670\pi\)
0.713013 0.701151i \(-0.247330\pi\)
\(422\) 6.88600i 0.335205i
\(423\) −4.11068 16.6427i −0.199868 0.809194i
\(424\) −3.29588 −0.160062
\(425\) 3.28489i 0.159340i
\(426\) −2.16485 17.7928i −0.104887 0.862062i
\(427\) 2.42981 0.117587
\(428\) 10.1734 0.491748
\(429\) 2.27553 + 18.7024i 0.109863 + 0.902962i
\(430\) 1.71427i 0.0826694i
\(431\) −20.4485 −0.984971 −0.492486 0.870321i \(-0.663912\pi\)
−0.492486 + 0.870321i \(0.663912\pi\)
\(432\) 1.84614 + 4.85713i 0.0888226 + 0.233689i
\(433\) 35.3422i 1.69844i 0.528042 + 0.849218i \(0.322926\pi\)
−0.528042 + 0.849218i \(0.677074\pi\)
\(434\) 0.941857i 0.0452106i
\(435\) 0.719371 0.0875259i 0.0344912 0.00419655i
\(436\) 4.99915i 0.239416i
\(437\) 16.3540 + 5.62792i 0.782319 + 0.269220i
\(438\) −2.65730 21.8402i −0.126971 1.04356i
\(439\) 22.1741i 1.05831i 0.848524 + 0.529157i \(0.177492\pi\)
−0.848524 + 0.529157i \(0.822508\pi\)
\(440\) −2.00000 −0.0953463
\(441\) 20.1835 4.98526i 0.961119 0.237393i
\(442\) 17.8656 0.849782
\(443\) 21.4205i 1.01772i 0.860850 + 0.508858i \(0.169932\pi\)
−0.860850 + 0.508858i \(0.830068\pi\)
\(444\) −0.529072 + 0.0643722i −0.0251086 + 0.00305497i
\(445\) 10.6829i 0.506419i
\(446\) 6.67484i 0.316063i
\(447\) −29.9983 + 3.64990i −1.41887 + 0.172634i
\(448\) 0.264536 0.0124981
\(449\) −9.43662 −0.445342 −0.222671 0.974894i \(-0.571478\pi\)
−0.222671 + 0.974894i \(0.571478\pi\)
\(450\) 2.91247 0.719371i 0.137295 0.0339115i
\(451\) 4.30771i 0.202842i
\(452\) −18.6325 −0.876397
\(453\) 22.8563 2.78093i 1.07388 0.130659i
\(454\) −13.8656 −0.650747
\(455\) −1.43874 −0.0674493
\(456\) −7.38340 1.57651i −0.345759 0.0738266i
\(457\) −26.1921 −1.22521 −0.612607 0.790388i \(-0.709879\pi\)
−0.612607 + 0.790388i \(0.709879\pi\)
\(458\) −9.64990 −0.450910
\(459\) −15.9551 + 6.06437i −0.744722 + 0.283061i
\(460\) 3.96781 0.185000
\(461\) 17.2828i 0.804939i 0.915433 + 0.402469i \(0.131848\pi\)
−0.915433 + 0.402469i \(0.868152\pi\)
\(462\) −0.909671 + 0.110680i −0.0423217 + 0.00514928i
\(463\) 1.17880 0.0547837 0.0273918 0.999625i \(-0.491280\pi\)
0.0273918 + 0.999625i \(0.491280\pi\)
\(464\) −0.418392 −0.0194234
\(465\) 0.744824 + 6.12167i 0.0345404 + 0.283886i
\(466\) 26.3548i 1.22086i
\(467\) 2.25142i 0.104183i −0.998642 0.0520917i \(-0.983411\pi\)
0.998642 0.0520917i \(-0.0165888\pi\)
\(468\) 3.91247 + 15.8402i 0.180854 + 0.732213i
\(469\) 0.176268i 0.00813931i
\(470\) 5.71427 0.263580
\(471\) 0.919876 + 7.56041i 0.0423856 + 0.348365i
\(472\) 12.5486 0.577595
\(473\) 3.42854i 0.157644i
\(474\) 13.9088 1.69229i 0.638853 0.0777293i
\(475\) −1.41839 + 4.12167i −0.0650803 + 0.189115i
\(476\) 0.868970i 0.0398292i
\(477\) 9.59915 2.37096i 0.439515 0.108559i
\(478\) 13.3149i 0.609012i
\(479\) 16.0407i 0.732918i 0.930434 + 0.366459i \(0.119430\pi\)
−0.930434 + 0.366459i \(0.880570\pi\)
\(480\) −1.71937 + 0.209196i −0.0784782 + 0.00954845i
\(481\) −1.67357 −0.0763081
\(482\) 22.0627i 1.00493i
\(483\) 1.80470 0.219578i 0.0821168 0.00999115i
\(484\) 7.00000 0.318182
\(485\) 1.47093 0.0667914
\(486\) −8.87093 12.8182i −0.402393 0.581446i
\(487\) 2.59344i 0.117520i −0.998272 0.0587601i \(-0.981285\pi\)
0.998272 0.0587601i \(-0.0187147\pi\)
\(488\) 9.18520 0.415794
\(489\) 2.45449 + 20.1734i 0.110996 + 0.912271i
\(490\) 6.93002i 0.313066i
\(491\) 6.94017i 0.313205i 0.987662 + 0.156603i \(0.0500542\pi\)
−0.987662 + 0.156603i \(0.949946\pi\)
\(492\) −0.450578 3.70328i −0.0203136 0.166957i
\(493\) 1.37437i 0.0618985i
\(494\) −22.4167 7.71427i −1.00858 0.347081i
\(495\) 5.82495 1.43874i 0.261812 0.0646667i
\(496\) 3.56041i 0.159867i
\(497\) 2.73753 0.122795
\(498\) 28.7919 3.50311i 1.29020 0.156978i
\(499\) 22.4111 1.00326 0.501629 0.865083i \(-0.332734\pi\)
0.501629 + 0.865083i \(0.332734\pi\)
\(500\) 1.00000i 0.0447214i
\(501\) −1.30608 10.7346i −0.0583514 0.479587i
\(502\) 20.6137i 0.920036i
\(503\) 6.44002i 0.287146i −0.989640 0.143573i \(-0.954141\pi\)
0.989640 0.143573i \(-0.0458592\pi\)
\(504\) −0.770454 + 0.190299i −0.0343187 + 0.00847661i
\(505\) −6.28404 −0.279636
\(506\) 7.93563 0.352782
\(507\) 3.46845 + 28.5070i 0.154039 + 1.26604i
\(508\) 2.83678i 0.125862i
\(509\) 31.2574 1.38546 0.692730 0.721197i \(-0.256408\pi\)
0.692730 + 0.721197i \(0.256408\pi\)
\(510\) −0.687185 5.64794i −0.0304291 0.250095i
\(511\) 3.36025 0.148649
\(512\) 1.00000 0.0441942
\(513\) 22.6381 0.719875i 0.999495 0.0317833i
\(514\) −13.4066 −0.591338
\(515\) 9.42854 0.415471
\(516\) −0.358618 2.94746i −0.0157873 0.129755i
\(517\) 11.4285 0.502626
\(518\) 0.0814009i 0.00357655i
\(519\) 3.20952 + 26.3789i 0.140882 + 1.15791i
\(520\) −5.43874 −0.238505
\(521\) 1.11769 0.0489670 0.0244835 0.999700i \(-0.492206\pi\)
0.0244835 + 0.999700i \(0.492206\pi\)
\(522\) 1.21856 0.300979i 0.0533347 0.0131735i
\(523\) 15.4794i 0.676869i 0.940990 + 0.338434i \(0.109897\pi\)
−0.940990 + 0.338434i \(0.890103\pi\)
\(524\) 3.08012i 0.134556i
\(525\) 0.0553398 + 0.454835i 0.00241523 + 0.0198506i
\(526\) 14.6748i 0.639854i
\(527\) 11.6955 0.509466
\(528\) −3.43874 + 0.418392i −0.149652 + 0.0182082i
\(529\) 7.25645 0.315498
\(530\) 3.29588i 0.143164i
\(531\) −36.5474 + 9.02708i −1.58602 + 0.391742i
\(532\) 0.375216 1.09033i 0.0162677 0.0472718i
\(533\) 11.7143i 0.507401i
\(534\) 2.23483 + 18.3679i 0.0967104 + 0.794858i
\(535\) 10.1734i 0.439833i
\(536\) 0.666330i 0.0287811i
\(537\) 4.32643 + 35.5587i 0.186699 + 1.53447i
\(538\) −13.3235 −0.574415
\(539\) 13.8600i 0.596994i
\(540\) 4.85713 1.84614i 0.209018 0.0794454i
\(541\) 25.4032 1.09217 0.546084 0.837731i \(-0.316118\pi\)
0.546084 + 0.837731i \(0.316118\pi\)
\(542\) 21.5579 0.925993
\(543\) −16.7863 + 2.04239i −0.720369 + 0.0876474i
\(544\) 3.28489i 0.140838i
\(545\) 4.99915 0.214140
\(546\) −2.47373 + 0.300979i −0.105866 + 0.0128807i
\(547\) 8.46965i 0.362136i 0.983471 + 0.181068i \(0.0579554\pi\)
−0.983471 + 0.181068i \(0.942045\pi\)
\(548\) 4.79651i 0.204897i
\(549\) −26.7516 + 6.60757i −1.14173 + 0.282004i
\(550\) 2.00000i 0.0852803i
\(551\) −0.593444 + 1.72447i −0.0252816 + 0.0734651i
\(552\) 6.82214 0.830051i 0.290370 0.0353293i
\(553\) 2.13996i 0.0910003i
\(554\) −20.0471 −0.851719
\(555\) 0.0643722 + 0.529072i 0.00273245 + 0.0224578i
\(556\) 11.7550 0.498522
\(557\) 1.89324i 0.0802190i −0.999195 0.0401095i \(-0.987229\pi\)
0.999195 0.0401095i \(-0.0127707\pi\)
\(558\) 2.56126 + 10.3696i 0.108427 + 0.438981i
\(559\) 9.32346i 0.394341i
\(560\) 0.264536i 0.0111787i
\(561\) −1.37437 11.2959i −0.0580259 0.476912i
\(562\) −6.33282 −0.267134
\(563\) 24.2229 1.02087 0.510437 0.859915i \(-0.329484\pi\)
0.510437 + 0.859915i \(0.329484\pi\)
\(564\) 9.82495 1.19540i 0.413705 0.0503355i
\(565\) 18.6325i 0.783873i
\(566\) −33.2022 −1.39559
\(567\) 2.10703 1.10848i 0.0884870 0.0465520i
\(568\) 10.3484 0.434210
\(569\) −37.1991 −1.55947 −0.779734 0.626111i \(-0.784645\pi\)
−0.779734 + 0.626111i \(0.784645\pi\)
\(570\) −1.57651 + 7.38340i −0.0660325 + 0.309257i
\(571\) −34.0847 −1.42640 −0.713199 0.700961i \(-0.752755\pi\)
−0.713199 + 0.700961i \(0.752755\pi\)
\(572\) −10.8775 −0.454810
\(573\) 33.2011 4.03957i 1.38699 0.168756i
\(574\) 0.569772 0.0237818
\(575\) 3.96781i 0.165469i
\(576\) −2.91247 + 0.719371i −0.121353 + 0.0299738i
\(577\) 34.2522 1.42594 0.712969 0.701196i \(-0.247350\pi\)
0.712969 + 0.701196i \(0.247350\pi\)
\(578\) 6.20952 0.258282
\(579\) 25.8876 3.14975i 1.07585 0.130899i
\(580\) 0.418392i 0.0173728i
\(581\) 4.42981i 0.183780i
\(582\) 2.52907 0.307712i 0.104833 0.0127551i
\(583\) 6.59175i 0.273003i
\(584\) 12.7024 0.525630
\(585\) 15.8402 3.91247i 0.654911 0.161761i
\(586\) 29.4748 1.21759
\(587\) 46.9321i 1.93709i 0.248830 + 0.968547i \(0.419954\pi\)
−0.248830 + 0.968547i \(0.580046\pi\)
\(588\) 1.44973 + 11.9153i 0.0597860 + 0.491378i
\(589\) −14.6748 5.05006i −0.604666 0.208084i
\(590\) 12.5486i 0.516617i
\(591\) −26.6702 + 3.24497i −1.09707 + 0.133480i
\(592\) 0.307712i 0.0126469i
\(593\) 19.4977i 0.800676i 0.916368 + 0.400338i \(0.131107\pi\)
−0.916368 + 0.400338i \(0.868893\pi\)
\(594\) 9.71427 3.69229i 0.398581 0.151496i
\(595\) 0.868970 0.0356243
\(596\) 17.4473i 0.714667i
\(597\) −3.31511 27.2468i −0.135679 1.11514i
\(598\) 21.5799 0.882468
\(599\) −12.8538 −0.525193 −0.262596 0.964906i \(-0.584579\pi\)
−0.262596 + 0.964906i \(0.584579\pi\)
\(600\) 0.209196 + 1.71937i 0.00854039 + 0.0701930i
\(601\) 38.3280i 1.56343i 0.623635 + 0.781716i \(0.285655\pi\)
−0.623635 + 0.781716i \(0.714345\pi\)
\(602\) 0.453485 0.0184827
\(603\) −0.479339 1.94067i −0.0195202 0.0790302i
\(604\) 13.2934i 0.540901i
\(605\) 7.00000i 0.284590i
\(606\) −10.8046 + 1.31460i −0.438907 + 0.0534018i
\(607\) 9.26078i 0.375884i −0.982180 0.187942i \(-0.939818\pi\)
0.982180 0.187942i \(-0.0601816\pi\)
\(608\) 1.41839 4.12167i 0.0575234 0.167156i
\(609\) 0.0231537 + 0.190299i 0.000938237 + 0.00771132i
\(610\) 9.18520i 0.371898i
\(611\) 31.0784 1.25730
\(612\) −2.36305 9.56715i −0.0955207 0.386729i
\(613\) 36.0691 1.45682 0.728408 0.685144i \(-0.240261\pi\)
0.728408 + 0.685144i \(0.240261\pi\)
\(614\) 1.81934i 0.0734226i
\(615\) −3.70328 + 0.450578i −0.149331 + 0.0181691i
\(616\) 0.529072i 0.0213169i
\(617\) 33.9935i 1.36853i 0.729235 + 0.684263i \(0.239876\pi\)
−0.729235 + 0.684263i \(0.760124\pi\)
\(618\) 16.2112 1.97241i 0.652108 0.0793421i
\(619\) 0.772412 0.0310459 0.0155229 0.999880i \(-0.495059\pi\)
0.0155229 + 0.999880i \(0.495059\pi\)
\(620\) −3.56041 −0.142990
\(621\) −19.2722 + 7.32516i −0.773367 + 0.293948i
\(622\) 15.9898i 0.641132i
\(623\) −2.82602 −0.113222
\(624\) −9.35122 + 1.13776i −0.374348 + 0.0455470i
\(625\) 1.00000 0.0400000
\(626\) 21.4416 0.856981
\(627\) −3.15301 + 14.7668i −0.125919 + 0.589729i
\(628\) −4.39720 −0.175467
\(629\) 1.01080 0.0403032
\(630\) 0.190299 + 0.770454i 0.00758171 + 0.0306956i
\(631\) 25.9339 1.03241 0.516207 0.856464i \(-0.327344\pi\)
0.516207 + 0.856464i \(0.327344\pi\)
\(632\) 8.08948i 0.321782i
\(633\) −11.8396 + 1.44052i −0.470581 + 0.0572557i
\(634\) −6.44037 −0.255780
\(635\) −2.83678 −0.112574
\(636\) 0.689484 + 5.66683i 0.0273398 + 0.224705i
\(637\) 37.6906i 1.49336i
\(638\) 0.836784i 0.0331286i
\(639\) −30.1395 + 7.44435i −1.19230 + 0.294494i
\(640\) 1.00000i 0.0395285i
\(641\) −43.6027 −1.72220 −0.861101 0.508434i \(-0.830225\pi\)
−0.861101 + 0.508434i \(0.830225\pi\)
\(642\) −2.12823 17.4918i −0.0839944 0.690346i
\(643\) 15.6312 0.616433 0.308217 0.951316i \(-0.400268\pi\)
0.308217 + 0.951316i \(0.400268\pi\)
\(644\) 1.04963i 0.0413612i
\(645\) −2.94746 + 0.358618i −0.116056 + 0.0141206i
\(646\) 13.5392 + 4.65926i 0.532693 + 0.183316i
\(647\) 26.9740i 1.06046i −0.847854 0.530230i \(-0.822106\pi\)
0.847854 0.530230i \(-0.177894\pi\)
\(648\) 7.96501 4.19030i 0.312895 0.164611i
\(649\) 25.0972i 0.985149i
\(650\) 5.43874i 0.213325i
\(651\) −1.61940 + 0.197033i −0.0634693 + 0.00772232i
\(652\) −11.7330 −0.459499
\(653\) 39.3405i 1.53951i 0.638338 + 0.769756i \(0.279622\pi\)
−0.638338 + 0.769756i \(0.720378\pi\)
\(654\) 8.59540 1.04580i 0.336107 0.0408941i
\(655\) −3.08012 −0.120350
\(656\) 2.15386 0.0840940
\(657\) −36.9955 + 9.13776i −1.44333 + 0.356498i
\(658\) 1.51163i 0.0589294i
\(659\) 28.4622 1.10873 0.554365 0.832273i \(-0.312961\pi\)
0.554365 + 0.832273i \(0.312961\pi\)
\(660\) 0.418392 + 3.43874i 0.0162859 + 0.133853i
\(661\) 8.93478i 0.347523i −0.984788 0.173761i \(-0.944408\pi\)
0.984788 0.173761i \(-0.0555921\pi\)
\(662\) 24.6239i 0.957037i
\(663\) −3.73742 30.7177i −0.145149 1.19298i
\(664\) 16.7456i 0.649856i
\(665\) −1.09033 0.375216i −0.0422812 0.0145502i
\(666\) 0.221359 + 0.896204i 0.00857750 + 0.0347272i
\(667\) 1.66010i 0.0642794i
\(668\) 6.24334 0.241562
\(669\) −11.4765 + 1.39635i −0.443708 + 0.0539860i
\(670\) 0.666330 0.0257426
\(671\) 18.3704i 0.709181i
\(672\) −0.0553398 0.454835i −0.00213478 0.0175457i
\(673\) 19.1411i 0.737836i −0.929462 0.368918i \(-0.879728\pi\)
0.929462 0.368918i \(-0.120272\pi\)
\(674\) 25.6686i 0.988718i
\(675\) −1.84614 4.85713i −0.0710581 0.186951i
\(676\) −16.5799 −0.637689
\(677\) −20.0114 −0.769101 −0.384551 0.923104i \(-0.625644\pi\)
−0.384551 + 0.923104i \(0.625644\pi\)
\(678\) 3.89783 + 32.0361i 0.149695 + 1.23034i
\(679\) 0.389113i 0.0149328i
\(680\) 3.28489 0.125970
\(681\) 2.90064 + 23.8402i 0.111153 + 0.913558i
\(682\) −7.12082 −0.272670
\(683\) 35.9527 1.37569 0.687845 0.725858i \(-0.258557\pi\)
0.687845 + 0.725858i \(0.258557\pi\)
\(684\) −1.16602 + 13.0246i −0.0445839 + 0.498008i
\(685\) −4.79651 −0.183265
\(686\) −3.68499 −0.140694
\(687\) 2.01872 + 16.5918i 0.0770190 + 0.633015i
\(688\) 1.71427 0.0653559
\(689\) 17.9254i 0.682904i
\(690\) −0.830051 6.82214i −0.0315995 0.259715i
\(691\) −14.9419 −0.568415 −0.284208 0.958763i \(-0.591730\pi\)
−0.284208 + 0.958763i \(0.591730\pi\)
\(692\) −15.3422 −0.583222
\(693\) 0.380599 + 1.54091i 0.0144578 + 0.0585342i
\(694\) 3.23398i 0.122760i
\(695\) 11.7550i 0.445891i
\(696\) 0.0875259 + 0.719371i 0.00331766 + 0.0272677i
\(697\) 7.07517i 0.267991i
\(698\) −17.9576 −0.679706
\(699\) 45.3137 5.51332i 1.71392 0.208533i
\(700\) −0.264536 −0.00999851
\(701\) 26.7894i 1.01182i 0.862585 + 0.505912i \(0.168844\pi\)
−0.862585 + 0.505912i \(0.831156\pi\)
\(702\) 26.4167 10.0407i 0.997034 0.378962i
\(703\) −1.26829 0.436457i −0.0478344 0.0164613i
\(704\) 2.00000i 0.0753778i
\(705\) −1.19540 9.82495i −0.0450214 0.370029i
\(706\) 7.59260i 0.285751i
\(707\) 1.66235i 0.0625193i
\(708\) −2.62511 21.5757i −0.0986577 0.810863i
\(709\) −41.3861 −1.55429 −0.777145 0.629322i \(-0.783333\pi\)
−0.777145 + 0.629322i \(0.783333\pi\)
\(710\) 10.3484i 0.388369i
\(711\) −5.81934 23.5604i −0.218242 0.883584i
\(712\) −10.6829 −0.400360
\(713\) 14.1271 0.529062
\(714\) 1.49408 0.181785i 0.0559146 0.00680314i
\(715\) 10.8775i 0.406795i
\(716\) −20.6812 −0.772894
\(717\) −22.8933 + 2.78543i −0.854967 + 0.104024i
\(718\) 36.7605i 1.37189i
\(719\) 37.3320i 1.39225i −0.717922 0.696124i \(-0.754906\pi\)
0.717922 0.696124i \(-0.245094\pi\)
\(720\) 0.719371 + 2.91247i 0.0268094 + 0.108541i
\(721\) 2.49419i 0.0928883i
\(722\) −14.9763 11.6923i −0.557361 0.435142i
\(723\) −37.9339 + 4.61542i −1.41078 + 0.171649i
\(724\) 9.76305i 0.362841i
\(725\) 0.418392 0.0155387
\(726\) −1.46437 12.0356i −0.0543479 0.446683i
\(727\) 38.4900 1.42752 0.713758 0.700393i \(-0.246992\pi\)
0.713758 + 0.700393i \(0.246992\pi\)
\(728\) 1.43874i 0.0533233i
\(729\) −20.1835 + 17.9339i −0.747537 + 0.664220i
\(730\) 12.7024i 0.470138i
\(731\) 5.63118i 0.208277i
\(732\) −1.92151 15.7928i −0.0710209 0.583717i
\(733\) 3.30004 0.121890 0.0609449 0.998141i \(-0.480589\pi\)
0.0609449 + 0.998141i \(0.480589\pi\)
\(734\) −35.2917 −1.30264
\(735\) 11.9153 1.44973i 0.439502 0.0534742i
\(736\) 3.96781i 0.146256i
\(737\) 1.33266 0.0490892
\(738\) −6.27305 + 1.54942i −0.230914 + 0.0570350i
\(739\) 0.119548 0.00439764 0.00219882 0.999998i \(-0.499300\pi\)
0.00219882 + 0.999998i \(0.499300\pi\)
\(740\) −0.307712 −0.0113117
\(741\) −8.57421 + 40.1564i −0.314981 + 1.47518i
\(742\) −0.871877 −0.0320076
\(743\) 35.7330 1.31092 0.655458 0.755232i \(-0.272476\pi\)
0.655458 + 0.755232i \(0.272476\pi\)
\(744\) −6.12167 + 0.744824i −0.224431 + 0.0273066i
\(745\) −17.4473 −0.639218
\(746\) 21.6821i 0.793837i
\(747\) −12.0463 48.7712i −0.440751 1.78444i
\(748\) 6.56977 0.240215
\(749\) 2.69122 0.0983350
\(750\) 1.71937 0.209196i 0.0627826 0.00763876i
\(751\) 24.9370i 0.909965i −0.890500 0.454983i \(-0.849645\pi\)
0.890500 0.454983i \(-0.150355\pi\)
\(752\) 5.71427i 0.208378i
\(753\) 35.4427 4.31231i 1.29160 0.157149i
\(754\) 2.27553i 0.0828698i
\(755\) 13.2934 0.483796
\(756\) 0.488371 + 1.28489i 0.0177619 + 0.0467309i
\(757\) 5.45534 0.198278 0.0991388 0.995074i \(-0.468391\pi\)
0.0991388 + 0.995074i \(0.468391\pi\)
\(758\) 13.1750i 0.478537i
\(759\) −1.66010 13.6443i −0.0602579 0.495256i
\(760\) −4.12167 1.41839i −0.149509 0.0514505i
\(761\) 12.3494i 0.447666i −0.974627 0.223833i \(-0.928143\pi\)
0.974627 0.223833i \(-0.0718571\pi\)
\(762\) −4.87748 + 0.593444i −0.176693 + 0.0214982i
\(763\) 1.32246i 0.0478761i
\(764\) 19.3100i 0.698611i
\(765\) −9.56715 + 2.36305i −0.345901 + 0.0854363i
\(766\) 27.2354 0.984056
\(767\) 68.2485i 2.46431i
\(768\) −0.209196 1.71937i −0.00754871 0.0620425i
\(769\) −13.0932 −0.472154 −0.236077 0.971734i \(-0.575862\pi\)
−0.236077 + 0.971734i \(0.575862\pi\)
\(770\) −0.529072 −0.0190664
\(771\) 2.80460 + 23.0508i 0.101005 + 0.830156i
\(772\) 15.0565i 0.541894i
\(773\) −36.5720 −1.31540 −0.657702 0.753279i \(-0.728471\pi\)
−0.657702 + 0.753279i \(0.728471\pi\)
\(774\) −4.99276 + 1.23320i −0.179461 + 0.0443263i
\(775\) 3.56041i 0.127894i
\(776\) 1.47093i 0.0528032i
\(777\) −0.139958 + 0.0170288i −0.00502098 + 0.000610903i
\(778\) 27.4236i 0.983183i
\(779\) 3.05501 8.87748i 0.109457 0.318069i
\(780\) 1.13776 + 9.35122i 0.0407385 + 0.334827i
\(781\) 20.6968i 0.740591i
\(782\) −13.0338 −0.466088
\(783\) −0.772412 2.03219i −0.0276037 0.0726244i
\(784\) −6.93002