Properties

Label 570.2.k.a.77.11
Level $570$
Weight $2$
Character 570.77
Analytic conductor $4.551$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 77.11
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.a.533.11

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-1.33397 + 1.10477i) q^{3} -1.00000i q^{4} +(2.20748 + 0.356413i) q^{5} +(-0.162066 + 1.72445i) q^{6} +(1.29452 + 1.29452i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.558949 - 2.94747i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-1.33397 + 1.10477i) q^{3} -1.00000i q^{4} +(2.20748 + 0.356413i) q^{5} +(-0.162066 + 1.72445i) q^{6} +(1.29452 + 1.29452i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.558949 - 2.94747i) q^{9} +(1.81295 - 1.30890i) q^{10} +4.05199i q^{11} +(1.10477 + 1.33397i) q^{12} +(0.882575 - 0.882575i) q^{13} +1.83072 q^{14} +(-3.33847 + 1.96332i) q^{15} -1.00000 q^{16} +(-1.10167 + 1.10167i) q^{17} +(-1.68894 - 2.47941i) q^{18} +1.00000i q^{19} +(0.356413 - 2.20748i) q^{20} +(-3.15700 - 0.296698i) q^{21} +(2.86519 + 2.86519i) q^{22} +(-0.877184 - 0.877184i) q^{23} +(1.72445 + 0.162066i) q^{24} +(4.74594 + 1.57355i) q^{25} -1.24815i q^{26} +(2.51067 + 4.54935i) q^{27} +(1.29452 - 1.29452i) q^{28} +5.03943 q^{29} +(-0.972374 + 3.74893i) q^{30} +9.76541 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-4.47654 - 5.40524i) q^{33} +1.55800i q^{34} +(2.39624 + 3.31901i) q^{35} +(-2.94747 - 0.558949i) q^{36} +(3.02131 + 3.02131i) q^{37} +(0.707107 + 0.707107i) q^{38} +(-0.202282 + 2.15237i) q^{39} +(-1.30890 - 1.81295i) q^{40} -1.87632i q^{41} +(-2.44213 + 2.02254i) q^{42} +(-0.199462 + 0.199462i) q^{43} +4.05199 q^{44} +(2.28439 - 6.30726i) q^{45} -1.24053 q^{46} +(-8.33748 + 8.33748i) q^{47} +(1.33397 - 1.10477i) q^{48} -3.64845i q^{49} +(4.46855 - 2.24322i) q^{50} +(0.252498 - 2.68669i) q^{51} +(-0.882575 - 0.882575i) q^{52} +(-6.34099 - 6.34099i) q^{53} +(4.99218 + 1.44156i) q^{54} +(-1.44418 + 8.94470i) q^{55} -1.83072i q^{56} +(-1.10477 - 1.33397i) q^{57} +(3.56341 - 3.56341i) q^{58} -1.21543 q^{59} +(1.96332 + 3.33847i) q^{60} +1.45771 q^{61} +(6.90519 - 6.90519i) q^{62} +(4.53912 - 3.09198i) q^{63} +1.00000i q^{64} +(2.26283 - 1.63371i) q^{65} +(-6.98747 - 0.656689i) q^{66} +(-2.25803 - 2.25803i) q^{67} +(1.10167 + 1.10167i) q^{68} +(2.13923 + 0.201047i) q^{69} +(4.04129 + 0.652495i) q^{70} -7.22853i q^{71} +(-2.47941 + 1.68894i) q^{72} +(-3.04969 + 3.04969i) q^{73} +4.27277 q^{74} +(-8.06936 + 3.14412i) q^{75} +1.00000 q^{76} +(-5.24538 + 5.24538i) q^{77} +(1.37892 + 1.66499i) q^{78} -13.1389i q^{79} +(-2.20748 - 0.356413i) q^{80} +(-8.37515 - 3.29497i) q^{81} +(-1.32676 - 1.32676i) q^{82} +(4.01176 + 4.01176i) q^{83} +(-0.296698 + 3.15700i) q^{84} +(-2.82457 + 2.03927i) q^{85} +0.282082i q^{86} +(-6.72244 + 5.56743i) q^{87} +(2.86519 - 2.86519i) q^{88} -15.5041 q^{89} +(-2.84460 - 6.07521i) q^{90} +2.28502 q^{91} +(-0.877184 + 0.877184i) q^{92} +(-13.0268 + 10.7886i) q^{93} +11.7910i q^{94} +(-0.356413 + 2.20748i) q^{95} +(0.162066 - 1.72445i) q^{96} +(-7.86520 - 7.86520i) q^{97} +(-2.57984 - 2.57984i) q^{98} +(11.9431 + 2.26486i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 4q^{3} + 4q^{6} - 12q^{7} + O(q^{10}) \) \( 36q + 4q^{3} + 4q^{6} - 12q^{7} - 4q^{10} - 4q^{12} + 8q^{13} + 4q^{15} - 36q^{16} - 32q^{21} - 4q^{22} + 32q^{25} + 28q^{27} - 12q^{28} - 8q^{30} + 8q^{31} + 36q^{33} + 4q^{36} - 32q^{37} - 8q^{40} + 12q^{42} - 24q^{43} - 28q^{45} - 16q^{46} - 4q^{48} - 40q^{51} - 8q^{52} - 4q^{55} + 4q^{57} - 4q^{58} - 24q^{60} + 200q^{61} + 28q^{63} + 12q^{70} - 68q^{73} - 36q^{75} + 36q^{76} + 24q^{78} - 92q^{81} + 24q^{82} + 24q^{85} + 28q^{87} - 4q^{88} - 68q^{90} + 64q^{91} + 16q^{93} - 4q^{96} - 148q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) −1.33397 + 1.10477i −0.770168 + 0.637842i
\(4\) 1.00000i 0.500000i
\(5\) 2.20748 + 0.356413i 0.987215 + 0.159393i
\(6\) −0.162066 + 1.72445i −0.0661630 + 0.704005i
\(7\) 1.29452 + 1.29452i 0.489282 + 0.489282i 0.908080 0.418798i \(-0.137548\pi\)
−0.418798 + 0.908080i \(0.637548\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 0.558949 2.94747i 0.186316 0.982490i
\(10\) 1.81295 1.30890i 0.573304 0.413911i
\(11\) 4.05199i 1.22172i 0.791738 + 0.610861i \(0.209177\pi\)
−0.791738 + 0.610861i \(0.790823\pi\)
\(12\) 1.10477 + 1.33397i 0.318921 + 0.385084i
\(13\) 0.882575 0.882575i 0.244782 0.244782i −0.574043 0.818825i \(-0.694626\pi\)
0.818825 + 0.574043i \(0.194626\pi\)
\(14\) 1.83072 0.489282
\(15\) −3.33847 + 1.96332i −0.861989 + 0.506928i
\(16\) −1.00000 −0.250000
\(17\) −1.10167 + 1.10167i −0.267194 + 0.267194i −0.827969 0.560774i \(-0.810504\pi\)
0.560774 + 0.827969i \(0.310504\pi\)
\(18\) −1.68894 2.47941i −0.398087 0.584403i
\(19\) 1.00000i 0.229416i
\(20\) 0.356413 2.20748i 0.0796965 0.493608i
\(21\) −3.15700 0.296698i −0.688913 0.0647447i
\(22\) 2.86519 + 2.86519i 0.610861 + 0.610861i
\(23\) −0.877184 0.877184i −0.182905 0.182905i 0.609715 0.792621i \(-0.291284\pi\)
−0.792621 + 0.609715i \(0.791284\pi\)
\(24\) 1.72445 + 0.162066i 0.352002 + 0.0330815i
\(25\) 4.74594 + 1.57355i 0.949188 + 0.314710i
\(26\) 1.24815i 0.244782i
\(27\) 2.51067 + 4.54935i 0.483178 + 0.875522i
\(28\) 1.29452 1.29452i 0.244641 0.244641i
\(29\) 5.03943 0.935798 0.467899 0.883782i \(-0.345011\pi\)
0.467899 + 0.883782i \(0.345011\pi\)
\(30\) −0.972374 + 3.74893i −0.177530 + 0.684458i
\(31\) 9.76541 1.75392 0.876960 0.480564i \(-0.159568\pi\)
0.876960 + 0.480564i \(0.159568\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −4.47654 5.40524i −0.779265 0.940931i
\(34\) 1.55800i 0.267194i
\(35\) 2.39624 + 3.31901i 0.405038 + 0.561014i
\(36\) −2.94747 0.558949i −0.491245 0.0931581i
\(37\) 3.02131 + 3.02131i 0.496700 + 0.496700i 0.910409 0.413709i \(-0.135767\pi\)
−0.413709 + 0.910409i \(0.635767\pi\)
\(38\) 0.707107 + 0.707107i 0.114708 + 0.114708i
\(39\) −0.202282 + 2.15237i −0.0323911 + 0.344656i
\(40\) −1.30890 1.81295i −0.206956 0.286652i
\(41\) 1.87632i 0.293032i −0.989208 0.146516i \(-0.953194\pi\)
0.989208 0.146516i \(-0.0468060\pi\)
\(42\) −2.44213 + 2.02254i −0.376829 + 0.312084i
\(43\) −0.199462 + 0.199462i −0.0304177 + 0.0304177i −0.722152 0.691734i \(-0.756847\pi\)
0.691734 + 0.722152i \(0.256847\pi\)
\(44\) 4.05199 0.610861
\(45\) 2.28439 6.30726i 0.340536 0.940231i
\(46\) −1.24053 −0.182905
\(47\) −8.33748 + 8.33748i −1.21615 + 1.21615i −0.247176 + 0.968971i \(0.579503\pi\)
−0.968971 + 0.247176i \(0.920497\pi\)
\(48\) 1.33397 1.10477i 0.192542 0.159460i
\(49\) 3.64845i 0.521207i
\(50\) 4.46855 2.24322i 0.631949 0.317239i
\(51\) 0.252498 2.68669i 0.0353568 0.376212i
\(52\) −0.882575 0.882575i −0.122391 0.122391i
\(53\) −6.34099 6.34099i −0.871002 0.871002i 0.121580 0.992582i \(-0.461204\pi\)
−0.992582 + 0.121580i \(0.961204\pi\)
\(54\) 4.99218 + 1.44156i 0.679350 + 0.196172i
\(55\) −1.44418 + 8.94470i −0.194734 + 1.20610i
\(56\) 1.83072i 0.244641i
\(57\) −1.10477 1.33397i −0.146331 0.176689i
\(58\) 3.56341 3.56341i 0.467899 0.467899i
\(59\) −1.21543 −0.158236 −0.0791178 0.996865i \(-0.525210\pi\)
−0.0791178 + 0.996865i \(0.525210\pi\)
\(60\) 1.96332 + 3.33847i 0.253464 + 0.430994i
\(61\) 1.45771 0.186641 0.0933205 0.995636i \(-0.470252\pi\)
0.0933205 + 0.995636i \(0.470252\pi\)
\(62\) 6.90519 6.90519i 0.876960 0.876960i
\(63\) 4.53912 3.09198i 0.571875 0.389553i
\(64\) 1.00000i 0.125000i
\(65\) 2.26283 1.63371i 0.280669 0.202636i
\(66\) −6.98747 0.656689i −0.860098 0.0808328i
\(67\) −2.25803 2.25803i −0.275862 0.275862i 0.555593 0.831455i \(-0.312491\pi\)
−0.831455 + 0.555593i \(0.812491\pi\)
\(68\) 1.10167 + 1.10167i 0.133597 + 0.133597i
\(69\) 2.13923 + 0.201047i 0.257533 + 0.0242032i
\(70\) 4.04129 + 0.652495i 0.483026 + 0.0779880i
\(71\) 7.22853i 0.857869i −0.903336 0.428935i \(-0.858889\pi\)
0.903336 0.428935i \(-0.141111\pi\)
\(72\) −2.47941 + 1.68894i −0.292202 + 0.199043i
\(73\) −3.04969 + 3.04969i −0.356940 + 0.356940i −0.862684 0.505744i \(-0.831218\pi\)
0.505744 + 0.862684i \(0.331218\pi\)
\(74\) 4.27277 0.496700
\(75\) −8.06936 + 3.14412i −0.931769 + 0.363052i
\(76\) 1.00000 0.114708
\(77\) −5.24538 + 5.24538i −0.597766 + 0.597766i
\(78\) 1.37892 + 1.66499i 0.156132 + 0.188523i
\(79\) 13.1389i 1.47824i −0.673572 0.739122i \(-0.735241\pi\)
0.673572 0.739122i \(-0.264759\pi\)
\(80\) −2.20748 0.356413i −0.246804 0.0398482i
\(81\) −8.37515 3.29497i −0.930572 0.366108i
\(82\) −1.32676 1.32676i −0.146516 0.146516i
\(83\) 4.01176 + 4.01176i 0.440348 + 0.440348i 0.892129 0.451781i \(-0.149211\pi\)
−0.451781 + 0.892129i \(0.649211\pi\)
\(84\) −0.296698 + 3.15700i −0.0323724 + 0.344457i
\(85\) −2.82457 + 2.03927i −0.306367 + 0.221189i
\(86\) 0.282082i 0.0304177i
\(87\) −6.72244 + 5.56743i −0.720721 + 0.596891i
\(88\) 2.86519 2.86519i 0.305431 0.305431i
\(89\) −15.5041 −1.64343 −0.821715 0.569898i \(-0.806983\pi\)
−0.821715 + 0.569898i \(0.806983\pi\)
\(90\) −2.84460 6.07521i −0.299848 0.640384i
\(91\) 2.28502 0.239535
\(92\) −0.877184 + 0.877184i −0.0914527 + 0.0914527i
\(93\) −13.0268 + 10.7886i −1.35081 + 1.11872i
\(94\) 11.7910i 1.21615i
\(95\) −0.356413 + 2.20748i −0.0365672 + 0.226483i
\(96\) 0.162066 1.72445i 0.0165408 0.176001i
\(97\) −7.86520 7.86520i −0.798590 0.798590i 0.184283 0.982873i \(-0.441004\pi\)
−0.982873 + 0.184283i \(0.941004\pi\)
\(98\) −2.57984 2.57984i −0.260603 0.260603i
\(99\) 11.9431 + 2.26486i 1.20033 + 0.227627i
\(100\) 1.57355 4.74594i 0.157355 0.474594i
\(101\) 1.64156i 0.163341i 0.996659 + 0.0816705i \(0.0260255\pi\)
−0.996659 + 0.0816705i \(0.973974\pi\)
\(102\) −1.72123 2.07832i −0.170428 0.205784i
\(103\) 6.66370 6.66370i 0.656594 0.656594i −0.297979 0.954573i \(-0.596312\pi\)
0.954573 + 0.297979i \(0.0963124\pi\)
\(104\) −1.24815 −0.122391
\(105\) −6.86326 1.78015i −0.669786 0.173725i
\(106\) −8.96751 −0.871002
\(107\) −13.0841 + 13.0841i −1.26488 + 1.26488i −0.316188 + 0.948697i \(0.602403\pi\)
−0.948697 + 0.316188i \(0.897597\pi\)
\(108\) 4.54935 2.51067i 0.437761 0.241589i
\(109\) 13.1807i 1.26248i −0.775587 0.631241i \(-0.782546\pi\)
0.775587 0.631241i \(-0.217454\pi\)
\(110\) 5.30366 + 7.34605i 0.505684 + 0.700418i
\(111\) −7.36819 0.692470i −0.699358 0.0657263i
\(112\) −1.29452 1.29452i −0.122320 0.122320i
\(113\) −7.56560 7.56560i −0.711712 0.711712i 0.255181 0.966893i \(-0.417865\pi\)
−0.966893 + 0.255181i \(0.917865\pi\)
\(114\) −1.72445 0.162066i −0.161510 0.0151788i
\(115\) −1.62373 2.24901i −0.151413 0.209721i
\(116\) 5.03943i 0.467899i
\(117\) −2.10805 3.09468i −0.194889 0.286103i
\(118\) −0.859440 + 0.859440i −0.0791178 + 0.0791178i
\(119\) −2.85226 −0.261466
\(120\) 3.74893 + 0.972374i 0.342229 + 0.0887652i
\(121\) −5.41865 −0.492605
\(122\) 1.03076 1.03076i 0.0933205 0.0933205i
\(123\) 2.07291 + 2.50296i 0.186908 + 0.225684i
\(124\) 9.76541i 0.876960i
\(125\) 9.91573 + 5.16510i 0.886890 + 0.461981i
\(126\) 1.02328 5.39600i 0.0911611 0.480714i
\(127\) 1.08300 + 1.08300i 0.0961010 + 0.0961010i 0.753523 0.657422i \(-0.228353\pi\)
−0.657422 + 0.753523i \(0.728353\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) 0.0457158 0.486437i 0.00402505 0.0428284i
\(130\) 0.444857 2.75527i 0.0390166 0.241653i
\(131\) 6.00990i 0.525087i 0.964920 + 0.262544i \(0.0845613\pi\)
−0.964920 + 0.262544i \(0.915439\pi\)
\(132\) −5.40524 + 4.47654i −0.470465 + 0.389633i
\(133\) −1.29452 + 1.29452i −0.112249 + 0.112249i
\(134\) −3.19333 −0.275862
\(135\) 3.92080 + 10.9374i 0.337449 + 0.941344i
\(136\) 1.55800 0.133597
\(137\) 1.40049 1.40049i 0.119652 0.119652i −0.644746 0.764397i \(-0.723037\pi\)
0.764397 + 0.644746i \(0.223037\pi\)
\(138\) 1.65482 1.37050i 0.140868 0.116665i
\(139\) 23.4290i 1.98722i −0.112872 0.993610i \(-0.536005\pi\)
0.112872 0.993610i \(-0.463995\pi\)
\(140\) 3.31901 2.39624i 0.280507 0.202519i
\(141\) 1.91091 20.3330i 0.160928 1.71235i
\(142\) −5.11134 5.11134i −0.428935 0.428935i
\(143\) 3.57619 + 3.57619i 0.299056 + 0.299056i
\(144\) −0.558949 + 2.94747i −0.0465791 + 0.245622i
\(145\) 11.1244 + 1.79612i 0.923834 + 0.149160i
\(146\) 4.31292i 0.356940i
\(147\) 4.03071 + 4.86692i 0.332447 + 0.401417i
\(148\) 3.02131 3.02131i 0.248350 0.248350i
\(149\) 4.36654 0.357721 0.178861 0.983874i \(-0.442759\pi\)
0.178861 + 0.983874i \(0.442759\pi\)
\(150\) −3.48267 + 7.92913i −0.284359 + 0.647410i
\(151\) −20.3330 −1.65468 −0.827340 0.561701i \(-0.810147\pi\)
−0.827340 + 0.561701i \(0.810147\pi\)
\(152\) 0.707107 0.707107i 0.0573539 0.0573539i
\(153\) 2.63136 + 3.86292i 0.212733 + 0.312298i
\(154\) 7.41808i 0.597766i
\(155\) 21.5569 + 3.48052i 1.73150 + 0.279562i
\(156\) 2.15237 + 0.202282i 0.172328 + 0.0161955i
\(157\) 8.36917 + 8.36917i 0.667932 + 0.667932i 0.957237 0.289305i \(-0.0934241\pi\)
−0.289305 + 0.957237i \(0.593424\pi\)
\(158\) −9.29061 9.29061i −0.739122 0.739122i
\(159\) 15.4640 + 1.45333i 1.22638 + 0.115256i
\(160\) −1.81295 + 1.30890i −0.143326 + 0.103478i
\(161\) 2.27106i 0.178985i
\(162\) −8.25202 + 3.59223i −0.648340 + 0.282232i
\(163\) −9.51819 + 9.51819i −0.745522 + 0.745522i −0.973635 0.228112i \(-0.926745\pi\)
0.228112 + 0.973635i \(0.426745\pi\)
\(164\) −1.87632 −0.146516
\(165\) −7.95537 13.5275i −0.619325 1.05311i
\(166\) 5.67349 0.440348
\(167\) 9.41306 9.41306i 0.728404 0.728404i −0.241897 0.970302i \(-0.577770\pi\)
0.970302 + 0.241897i \(0.0777698\pi\)
\(168\) 2.02254 + 2.44213i 0.156042 + 0.188414i
\(169\) 11.4421i 0.880163i
\(170\) −0.555291 + 3.43925i −0.0425889 + 0.263778i
\(171\) 2.94747 + 0.558949i 0.225399 + 0.0427439i
\(172\) 0.199462 + 0.199462i 0.0152088 + 0.0152088i
\(173\) −9.79289 9.79289i −0.744539 0.744539i 0.228909 0.973448i \(-0.426484\pi\)
−0.973448 + 0.228909i \(0.926484\pi\)
\(174\) −0.816718 + 8.69025i −0.0619152 + 0.658806i
\(175\) 4.10671 + 8.18069i 0.310438 + 0.618402i
\(176\) 4.05199i 0.305431i
\(177\) 1.62135 1.34278i 0.121868 0.100929i
\(178\) −10.9631 + 10.9631i −0.821715 + 0.821715i
\(179\) 2.70878 0.202464 0.101232 0.994863i \(-0.467722\pi\)
0.101232 + 0.994863i \(0.467722\pi\)
\(180\) −6.30726 2.28439i −0.470116 0.170268i
\(181\) 13.3331 0.991043 0.495522 0.868596i \(-0.334977\pi\)
0.495522 + 0.868596i \(0.334977\pi\)
\(182\) 1.61575 1.61575i 0.119767 0.119767i
\(183\) −1.94454 + 1.61044i −0.143745 + 0.119047i
\(184\) 1.24053i 0.0914527i
\(185\) 5.59264 + 7.74631i 0.411179 + 0.569520i
\(186\) −1.58264 + 16.8400i −0.116045 + 1.23477i
\(187\) −4.46396 4.46396i −0.326437 0.326437i
\(188\) 8.33748 + 8.33748i 0.608073 + 0.608073i
\(189\) −2.63911 + 9.13931i −0.191967 + 0.664787i
\(190\) 1.30890 + 1.81295i 0.0949577 + 0.131525i
\(191\) 15.6275i 1.13077i 0.824828 + 0.565383i \(0.191272\pi\)
−0.824828 + 0.565383i \(0.808728\pi\)
\(192\) −1.10477 1.33397i −0.0797302 0.0962710i
\(193\) −11.7380 + 11.7380i −0.844922 + 0.844922i −0.989494 0.144572i \(-0.953819\pi\)
0.144572 + 0.989494i \(0.453819\pi\)
\(194\) −11.1231 −0.798590
\(195\) −1.21367 + 4.67923i −0.0869126 + 0.335086i
\(196\) −3.64845 −0.260603
\(197\) 10.4406 10.4406i 0.743863 0.743863i −0.229456 0.973319i \(-0.573695\pi\)
0.973319 + 0.229456i \(0.0736946\pi\)
\(198\) 10.0466 6.84357i 0.713978 0.486351i
\(199\) 7.28579i 0.516476i 0.966081 + 0.258238i \(0.0831419\pi\)
−0.966081 + 0.258238i \(0.916858\pi\)
\(200\) −2.24322 4.46855i −0.158619 0.315975i
\(201\) 5.50674 + 0.517529i 0.388416 + 0.0365037i
\(202\) 1.16076 + 1.16076i 0.0816705 + 0.0816705i
\(203\) 6.52363 + 6.52363i 0.457869 + 0.457869i
\(204\) −2.68669 0.252498i −0.188106 0.0176784i
\(205\) 0.668746 4.14194i 0.0467073 0.289286i
\(206\) 9.42390i 0.656594i
\(207\) −3.07577 + 2.09517i −0.213781 + 0.145624i
\(208\) −0.882575 + 0.882575i −0.0611956 + 0.0611956i
\(209\) −4.05199 −0.280282
\(210\) −6.11181 + 3.59430i −0.421755 + 0.248030i
\(211\) 1.27863 0.0880248 0.0440124 0.999031i \(-0.485986\pi\)
0.0440124 + 0.999031i \(0.485986\pi\)
\(212\) −6.34099 + 6.34099i −0.435501 + 0.435501i
\(213\) 7.98589 + 9.64264i 0.547185 + 0.660703i
\(214\) 18.5037i 1.26488i
\(215\) −0.511400 + 0.369218i −0.0348772 + 0.0251804i
\(216\) 1.44156 4.99218i 0.0980860 0.339675i
\(217\) 12.6415 + 12.6415i 0.858161 + 0.858161i
\(218\) −9.32016 9.32016i −0.631241 0.631241i
\(219\) 0.698976 7.43742i 0.0472324 0.502574i
\(220\) 8.94470 + 1.44418i 0.603051 + 0.0973669i
\(221\) 1.94461i 0.130809i
\(222\) −5.69975 + 4.72045i −0.382542 + 0.316816i
\(223\) 19.5872 19.5872i 1.31166 1.31166i 0.391462 0.920194i \(-0.371970\pi\)
0.920194 0.391462i \(-0.128030\pi\)
\(224\) −1.83072 −0.122320
\(225\) 7.29073 13.1090i 0.486049 0.873932i
\(226\) −10.6994 −0.711712
\(227\) −2.14570 + 2.14570i −0.142415 + 0.142415i −0.774720 0.632305i \(-0.782109\pi\)
0.632305 + 0.774720i \(0.282109\pi\)
\(228\) −1.33397 + 1.10477i −0.0883443 + 0.0731654i
\(229\) 18.1839i 1.20163i −0.799389 0.600813i \(-0.794844\pi\)
0.799389 0.600813i \(-0.205156\pi\)
\(230\) −2.73844 0.442140i −0.180567 0.0291538i
\(231\) 1.20222 12.7921i 0.0791000 0.841660i
\(232\) −3.56341 3.56341i −0.233950 0.233950i
\(233\) −5.13824 5.13824i −0.336617 0.336617i 0.518475 0.855092i \(-0.326500\pi\)
−0.855092 + 0.518475i \(0.826500\pi\)
\(234\) −3.67888 0.697652i −0.240496 0.0456069i
\(235\) −21.3764 + 15.4332i −1.39444 + 1.00675i
\(236\) 1.21543i 0.0791178i
\(237\) 14.5155 + 17.5269i 0.942885 + 1.13849i
\(238\) −2.01685 + 2.01685i −0.130733 + 0.130733i
\(239\) −25.9094 −1.67594 −0.837970 0.545716i \(-0.816258\pi\)
−0.837970 + 0.545716i \(0.816258\pi\)
\(240\) 3.33847 1.96332i 0.215497 0.126732i
\(241\) 23.3453 1.50380 0.751902 0.659275i \(-0.229137\pi\)
0.751902 + 0.659275i \(0.229137\pi\)
\(242\) −3.83157 + 3.83157i −0.246302 + 0.246302i
\(243\) 14.8124 4.85726i 0.950215 0.311594i
\(244\) 1.45771i 0.0933205i
\(245\) 1.30036 8.05388i 0.0830767 0.514543i
\(246\) 3.23563 + 0.304087i 0.206296 + 0.0193879i
\(247\) 0.882575 + 0.882575i 0.0561569 + 0.0561569i
\(248\) −6.90519 6.90519i −0.438480 0.438480i
\(249\) −9.78366 0.919478i −0.620014 0.0582695i
\(250\) 10.6638 3.35921i 0.674435 0.212455i
\(251\) 26.5769i 1.67752i −0.544504 0.838758i \(-0.683282\pi\)
0.544504 0.838758i \(-0.316718\pi\)
\(252\) −3.09198 4.53912i −0.194777 0.285938i
\(253\) 3.55434 3.55434i 0.223460 0.223460i
\(254\) 1.53160 0.0961010
\(255\) 1.51496 5.84082i 0.0948702 0.365767i
\(256\) 1.00000 0.0625000
\(257\) 3.31338 3.31338i 0.206683 0.206683i −0.596173 0.802856i \(-0.703313\pi\)
0.802856 + 0.596173i \(0.203313\pi\)
\(258\) −0.311637 0.376289i −0.0194017 0.0234267i
\(259\) 7.82227i 0.486052i
\(260\) −1.63371 2.26283i −0.101318 0.140335i
\(261\) 2.81678 14.8536i 0.174354 0.919412i
\(262\) 4.24964 + 4.24964i 0.262544 + 0.262544i
\(263\) −8.50623 8.50623i −0.524517 0.524517i 0.394416 0.918932i \(-0.370947\pi\)
−0.918932 + 0.394416i \(0.870947\pi\)
\(264\) −0.656689 + 6.98747i −0.0404164 + 0.430049i
\(265\) −11.7376 16.2576i −0.721035 0.998698i
\(266\) 1.83072i 0.112249i
\(267\) 20.6820 17.1285i 1.26572 1.04825i
\(268\) −2.25803 + 2.25803i −0.137931 + 0.137931i
\(269\) 19.1132 1.16535 0.582676 0.812704i \(-0.302006\pi\)
0.582676 + 0.812704i \(0.302006\pi\)
\(270\) 10.5064 + 4.96151i 0.639396 + 0.301948i
\(271\) 16.0634 0.975780 0.487890 0.872905i \(-0.337767\pi\)
0.487890 + 0.872905i \(0.337767\pi\)
\(272\) 1.10167 1.10167i 0.0667986 0.0667986i
\(273\) −3.04814 + 2.52443i −0.184482 + 0.152785i
\(274\) 1.98059i 0.119652i
\(275\) −6.37602 + 19.2305i −0.384488 + 1.15964i
\(276\) 0.201047 2.13923i 0.0121016 0.128766i
\(277\) −10.2934 10.2934i −0.618473 0.618473i 0.326667 0.945140i \(-0.394075\pi\)
−0.945140 + 0.326667i \(0.894075\pi\)
\(278\) −16.5668 16.5668i −0.993610 0.993610i
\(279\) 5.45836 28.7832i 0.326784 1.72321i
\(280\) 0.652495 4.04129i 0.0389940 0.241513i
\(281\) 22.3640i 1.33413i −0.745001 0.667063i \(-0.767551\pi\)
0.745001 0.667063i \(-0.232449\pi\)
\(282\) −13.0264 15.7288i −0.775709 0.936637i
\(283\) −22.8633 + 22.8633i −1.35908 + 1.35908i −0.484030 + 0.875052i \(0.660827\pi\)
−0.875052 + 0.484030i \(0.839173\pi\)
\(284\) −7.22853 −0.428935
\(285\) −1.96332 3.33847i −0.116297 0.197754i
\(286\) 5.05750 0.299056
\(287\) 2.42893 2.42893i 0.143375 0.143375i
\(288\) 1.68894 + 2.47941i 0.0995217 + 0.146101i
\(289\) 14.5726i 0.857214i
\(290\) 9.13621 6.59612i 0.536497 0.387337i
\(291\) 19.1812 + 1.80267i 1.12442 + 0.105674i
\(292\) 3.04969 + 3.04969i 0.178470 + 0.178470i
\(293\) 16.7421 + 16.7421i 0.978084 + 0.978084i 0.999765 0.0216809i \(-0.00690179\pi\)
−0.0216809 + 0.999765i \(0.506902\pi\)
\(294\) 6.29157 + 0.591288i 0.366932 + 0.0344846i
\(295\) −2.68304 0.433196i −0.156213 0.0252216i
\(296\) 4.27277i 0.248350i
\(297\) −18.4339 + 10.1732i −1.06964 + 0.590309i
\(298\) 3.08761 3.08761i 0.178861 0.178861i
\(299\) −1.54836 −0.0895440
\(300\) 3.14412 + 8.06936i 0.181526 + 0.465884i
\(301\) −0.516414 −0.0297656
\(302\) −14.3776 + 14.3776i −0.827340 + 0.827340i
\(303\) −1.81355 2.18979i −0.104186 0.125800i
\(304\) 1.00000i 0.0573539i
\(305\) 3.21787 + 0.519548i 0.184255 + 0.0297493i
\(306\) 4.59215 + 0.870840i 0.262516 + 0.0497826i
\(307\) 0.385994 + 0.385994i 0.0220298 + 0.0220298i 0.718036 0.696006i \(-0.245041\pi\)
−0.696006 + 0.718036i \(0.745041\pi\)
\(308\) 5.24538 + 5.24538i 0.298883 + 0.298883i
\(309\) −1.52729 + 16.2511i −0.0868845 + 0.924490i
\(310\) 17.7042 12.7820i 1.00553 0.725967i
\(311\) 29.7986i 1.68972i 0.534984 + 0.844862i \(0.320318\pi\)
−0.534984 + 0.844862i \(0.679682\pi\)
\(312\) 1.66499 1.37892i 0.0942617 0.0780662i
\(313\) −14.6220 + 14.6220i −0.826486 + 0.826486i −0.987029 0.160543i \(-0.948675\pi\)
0.160543 + 0.987029i \(0.448675\pi\)
\(314\) 11.8358 0.667932
\(315\) 11.1220 5.20769i 0.626656 0.293420i
\(316\) −13.1389 −0.739122
\(317\) 2.69314 2.69314i 0.151262 0.151262i −0.627420 0.778681i \(-0.715889\pi\)
0.778681 + 0.627420i \(0.215889\pi\)
\(318\) 11.9624 9.90707i 0.670817 0.555561i
\(319\) 20.4197i 1.14329i
\(320\) −0.356413 + 2.20748i −0.0199241 + 0.123402i
\(321\) 2.99881 31.9087i 0.167377 1.78097i
\(322\) −1.60588 1.60588i −0.0894923 0.0894923i
\(323\) −1.10167 1.10167i −0.0612986 0.0612986i
\(324\) −3.29497 + 8.37515i −0.183054 + 0.465286i
\(325\) 5.57742 2.79987i 0.309380 0.155309i
\(326\) 13.4608i 0.745522i
\(327\) 14.5617 + 17.5826i 0.805263 + 0.972323i
\(328\) −1.32676 + 1.32676i −0.0732581 + 0.0732581i
\(329\) −21.5860 −1.19008
\(330\) −15.1906 3.94006i −0.836218 0.216893i
\(331\) −3.14392 −0.172805 −0.0864027 0.996260i \(-0.527537\pi\)
−0.0864027 + 0.996260i \(0.527537\pi\)
\(332\) 4.01176 4.01176i 0.220174 0.220174i
\(333\) 10.5940 7.21645i 0.580546 0.395459i
\(334\) 13.3121i 0.728404i
\(335\) −4.17976 5.78934i −0.228364 0.316305i
\(336\) 3.15700 + 0.296698i 0.172228 + 0.0161862i
\(337\) −0.402927 0.402927i −0.0219488 0.0219488i 0.696047 0.717996i \(-0.254940\pi\)
−0.717996 + 0.696047i \(0.754940\pi\)
\(338\) 8.09080 + 8.09080i 0.440082 + 0.440082i
\(339\) 18.4506 + 1.73400i 1.00210 + 0.0941780i
\(340\) 2.03927 + 2.82457i 0.110595 + 0.153184i
\(341\) 39.5694i 2.14280i
\(342\) 2.47941 1.68894i 0.134071 0.0913274i
\(343\) 13.7846 13.7846i 0.744299 0.744299i
\(344\) 0.282082 0.0152088
\(345\) 4.65064 + 1.20626i 0.250382 + 0.0649426i
\(346\) −13.8492 −0.744539
\(347\) 14.5943 14.5943i 0.783464 0.783464i −0.196950 0.980414i \(-0.563104\pi\)
0.980414 + 0.196950i \(0.0631035\pi\)
\(348\) 5.56743 + 6.72244i 0.298445 + 0.360361i
\(349\) 6.25742i 0.334952i 0.985876 + 0.167476i \(0.0535617\pi\)
−0.985876 + 0.167476i \(0.946438\pi\)
\(350\) 8.68851 + 2.88074i 0.464420 + 0.153982i
\(351\) 6.23099 + 1.79929i 0.332586 + 0.0960389i
\(352\) −2.86519 2.86519i −0.152715 0.152715i
\(353\) 0.898203 + 0.898203i 0.0478065 + 0.0478065i 0.730606 0.682799i \(-0.239238\pi\)
−0.682799 + 0.730606i \(0.739238\pi\)
\(354\) 0.196980 2.09595i 0.0104694 0.111399i
\(355\) 2.57635 15.9568i 0.136738 0.846901i
\(356\) 15.5041i 0.821715i
\(357\) 3.80483 3.15111i 0.201373 0.166774i
\(358\) 1.91540 1.91540i 0.101232 0.101232i
\(359\) −0.967026 −0.0510377 −0.0255188 0.999674i \(-0.508124\pi\)
−0.0255188 + 0.999674i \(0.508124\pi\)
\(360\) −6.07521 + 2.84460i −0.320192 + 0.149924i
\(361\) −1.00000 −0.0526316
\(362\) 9.42794 9.42794i 0.495522 0.495522i
\(363\) 7.22832 5.98639i 0.379388 0.314204i
\(364\) 2.28502i 0.119767i
\(365\) −7.81909 + 5.64519i −0.409270 + 0.295483i
\(366\) −0.236245 + 2.51376i −0.0123487 + 0.131396i
\(367\) −19.7540 19.7540i −1.03115 1.03115i −0.999499 0.0316528i \(-0.989923\pi\)
−0.0316528 0.999499i \(-0.510077\pi\)
\(368\) 0.877184 + 0.877184i 0.0457264 + 0.0457264i
\(369\) −5.53040 1.04877i −0.287901 0.0545967i
\(370\) 9.43206 + 1.52287i 0.490350 + 0.0791704i
\(371\) 16.4170i 0.852330i
\(372\) 10.7886 + 13.0268i 0.559361 + 0.675406i
\(373\) −9.91796 + 9.91796i −0.513532 + 0.513532i −0.915607 0.402075i \(-0.868289\pi\)
0.402075 + 0.915607i \(0.368289\pi\)
\(374\) −6.31299 −0.326437
\(375\) −18.9336 + 4.06456i −0.977724 + 0.209893i
\(376\) 11.7910 0.608073
\(377\) 4.44767 4.44767i 0.229067 0.229067i
\(378\) 4.59634 + 8.32860i 0.236410 + 0.428377i
\(379\) 21.6057i 1.10981i 0.831913 + 0.554906i \(0.187246\pi\)
−0.831913 + 0.554906i \(0.812754\pi\)
\(380\) 2.20748 + 0.356413i 0.113241 + 0.0182836i
\(381\) −2.64117 0.248220i −0.135311 0.0127167i
\(382\) 11.0503 + 11.0503i 0.565383 + 0.565383i
\(383\) −21.2148 21.2148i −1.08403 1.08403i −0.996129 0.0878986i \(-0.971985\pi\)
−0.0878986 0.996129i \(-0.528015\pi\)
\(384\) −1.72445 0.162066i −0.0880006 0.00827038i
\(385\) −13.4486 + 9.70955i −0.685404 + 0.494844i
\(386\) 16.6001i 0.844922i
\(387\) 0.476419 + 0.699397i 0.0242178 + 0.0355524i
\(388\) −7.86520 + 7.86520i −0.399295 + 0.399295i
\(389\) 27.1443 1.37627 0.688136 0.725581i \(-0.258429\pi\)
0.688136 + 0.725581i \(0.258429\pi\)
\(390\) 2.45052 + 4.16691i 0.124087 + 0.211000i
\(391\) 1.93273 0.0977426
\(392\) −2.57984 + 2.57984i −0.130302 + 0.130302i
\(393\) −6.63958 8.01702i −0.334922 0.404405i
\(394\) 14.7653i 0.743863i
\(395\) 4.68288 29.0039i 0.235621 1.45934i
\(396\) 2.26486 11.9431i 0.113813 0.600165i
\(397\) 6.88529 + 6.88529i 0.345563 + 0.345563i 0.858454 0.512891i \(-0.171426\pi\)
−0.512891 + 0.858454i \(0.671426\pi\)
\(398\) 5.15183 + 5.15183i 0.258238 + 0.258238i
\(399\) 0.296698 3.15700i 0.0148535 0.158048i
\(400\) −4.74594 1.57355i −0.237297 0.0786776i
\(401\) 23.1091i 1.15401i 0.816740 + 0.577006i \(0.195779\pi\)
−0.816740 + 0.577006i \(0.804221\pi\)
\(402\) 4.25980 3.52791i 0.212460 0.175956i
\(403\) 8.61871 8.61871i 0.429328 0.429328i
\(404\) 1.64156 0.0816705
\(405\) −17.3136 10.2586i −0.860320 0.509754i
\(406\) 9.22580 0.457869
\(407\) −12.2423 + 12.2423i −0.606829 + 0.606829i
\(408\) −2.07832 + 1.72123i −0.102892 + 0.0852138i
\(409\) 23.2391i 1.14910i −0.818469 0.574550i \(-0.805177\pi\)
0.818469 0.574550i \(-0.194823\pi\)
\(410\) −2.45592 3.40167i −0.121289 0.167997i
\(411\) −0.320985 + 3.41543i −0.0158330 + 0.168471i
\(412\) −6.66370 6.66370i −0.328297 0.328297i
\(413\) −1.57340 1.57340i −0.0774218 0.0774218i
\(414\) −0.693390 + 3.65641i −0.0340783 + 0.179703i
\(415\) 7.42604 + 10.2857i 0.364530 + 0.504907i
\(416\) 1.24815i 0.0611956i
\(417\) 25.8837 + 31.2535i 1.26753 + 1.53049i
\(418\) −2.86519 + 2.86519i −0.140141 + 0.140141i
\(419\) 18.0505 0.881827 0.440913 0.897550i \(-0.354655\pi\)
0.440913 + 0.897550i \(0.354655\pi\)
\(420\) −1.78015 + 6.86326i −0.0868624 + 0.334893i
\(421\) 16.0363 0.781559 0.390780 0.920484i \(-0.372205\pi\)
0.390780 + 0.920484i \(0.372205\pi\)
\(422\) 0.904131 0.904131i 0.0440124 0.0440124i
\(423\) 19.9142 + 29.2347i 0.968264 + 1.42144i
\(424\) 8.96751i 0.435501i
\(425\) −6.96199 + 3.49492i −0.337706 + 0.169529i
\(426\) 12.4653 + 1.17150i 0.603944 + 0.0567592i
\(427\) 1.88703 + 1.88703i 0.0913200 + 0.0913200i
\(428\) 13.0841 + 13.0841i 0.632442 + 0.632442i
\(429\) −8.72141 0.819646i −0.421074 0.0395729i
\(430\) −0.100538 + 0.622690i −0.00484836 + 0.0300288i
\(431\) 26.9716i 1.29918i 0.760285 + 0.649589i \(0.225059\pi\)
−0.760285 + 0.649589i \(0.774941\pi\)
\(432\) −2.51067 4.54935i −0.120795 0.218881i
\(433\) −24.4001 + 24.4001i −1.17259 + 1.17259i −0.191004 + 0.981589i \(0.561175\pi\)
−0.981589 + 0.191004i \(0.938825\pi\)
\(434\) 17.8778 0.858161
\(435\) −16.8240 + 9.89402i −0.806647 + 0.474382i
\(436\) −13.1807 −0.631241
\(437\) 0.877184 0.877184i 0.0419614 0.0419614i
\(438\) −4.76480 5.75330i −0.227671 0.274903i
\(439\) 30.0037i 1.43200i 0.698102 + 0.715999i \(0.254028\pi\)
−0.698102 + 0.715999i \(0.745972\pi\)
\(440\) 7.34605 5.30366i 0.350209 0.252842i
\(441\) −10.7537 2.03930i −0.512080 0.0971093i
\(442\) 1.37505 + 1.37505i 0.0654044 + 0.0654044i
\(443\) −15.2430 15.2430i −0.724218 0.724218i 0.245244 0.969461i \(-0.421132\pi\)
−0.969461 + 0.245244i \(0.921132\pi\)
\(444\) −0.692470 + 7.36819i −0.0328632 + 0.349679i
\(445\) −34.2250 5.52587i −1.62242 0.261951i
\(446\) 27.7005i 1.31166i
\(447\) −5.82483 + 4.82404i −0.275505 + 0.228169i
\(448\) −1.29452 + 1.29452i −0.0611602 + 0.0611602i
\(449\) 31.8336 1.50232 0.751159 0.660121i \(-0.229495\pi\)
0.751159 + 0.660121i \(0.229495\pi\)
\(450\) −4.11412 14.4248i −0.193941 0.679990i
\(451\) 7.60285 0.358004
\(452\) −7.56560 + 7.56560i −0.355856 + 0.355856i
\(453\) 27.1237 22.4634i 1.27438 1.05542i
\(454\) 3.03448i 0.142415i
\(455\) 5.04413 + 0.814411i 0.236473 + 0.0381802i
\(456\) −0.162066 + 1.72445i −0.00758942 + 0.0807549i
\(457\) −14.6130 14.6130i −0.683567 0.683567i 0.277235 0.960802i \(-0.410582\pi\)
−0.960802 + 0.277235i \(0.910582\pi\)
\(458\) −12.8580 12.8580i −0.600813 0.600813i
\(459\) −7.77781 2.24595i −0.363037 0.104832i
\(460\) −2.24901 + 1.62373i −0.104860 + 0.0757066i
\(461\) 23.6296i 1.10054i 0.834987 + 0.550270i \(0.185475\pi\)
−0.834987 + 0.550270i \(0.814525\pi\)
\(462\) −8.19531 9.89550i −0.381280 0.460380i
\(463\) −4.82963 + 4.82963i −0.224452 + 0.224452i −0.810370 0.585918i \(-0.800734\pi\)
0.585918 + 0.810370i \(0.300734\pi\)
\(464\) −5.03943 −0.233950
\(465\) −32.6015 + 19.1726i −1.51186 + 0.889110i
\(466\) −7.26656 −0.336617
\(467\) 14.3607 14.3607i 0.664534 0.664534i −0.291911 0.956445i \(-0.594291\pi\)
0.956445 + 0.291911i \(0.0942912\pi\)
\(468\) −3.09468 + 2.10805i −0.143052 + 0.0974446i
\(469\) 5.84611i 0.269948i
\(470\) −4.20246 + 26.0284i −0.193845 + 1.20060i
\(471\) −20.4103 1.91817i −0.940455 0.0883848i
\(472\) 0.859440 + 0.859440i 0.0395589 + 0.0395589i
\(473\) −0.808219 0.808219i −0.0371620 0.0371620i
\(474\) 22.6574 + 2.12937i 1.04069 + 0.0978050i
\(475\) −1.57355 + 4.74594i −0.0721995 + 0.217759i
\(476\) 2.85226i 0.130733i
\(477\) −22.2342 + 15.1456i −1.01803 + 0.693469i
\(478\) −18.3207 + 18.3207i −0.837970 + 0.837970i
\(479\) −33.8055 −1.54461 −0.772307 0.635249i \(-0.780897\pi\)
−0.772307 + 0.635249i \(0.780897\pi\)
\(480\) 0.972374 3.74893i 0.0443826 0.171115i
\(481\) 5.33306 0.243167
\(482\) 16.5076 16.5076i 0.751902 0.751902i
\(483\) 2.50901 + 3.02952i 0.114164 + 0.137848i
\(484\) 5.41865i 0.246302i
\(485\) −14.5590 20.1655i −0.661091 0.915670i
\(486\) 7.03934 13.9085i 0.319311 0.630905i
\(487\) 7.43111 + 7.43111i 0.336736 + 0.336736i 0.855137 0.518402i \(-0.173473\pi\)
−0.518402 + 0.855137i \(0.673473\pi\)
\(488\) −1.03076 1.03076i −0.0466602 0.0466602i
\(489\) 2.18153 23.2124i 0.0986520 1.04970i
\(490\) −4.77546 6.61444i −0.215733 0.298810i
\(491\) 13.2044i 0.595905i 0.954581 + 0.297952i \(0.0963036\pi\)
−0.954581 + 0.297952i \(0.903696\pi\)
\(492\) 2.50296 2.07291i 0.112842 0.0934541i
\(493\) −5.55179 + 5.55179i −0.250040 + 0.250040i
\(494\) 1.24815 0.0561569
\(495\) 25.5570 + 9.25632i 1.14870 + 0.416041i
\(496\) −9.76541 −0.438480
\(497\) 9.35746 9.35746i 0.419740 0.419740i
\(498\) −7.56826 + 6.26792i −0.339142 + 0.280872i
\(499\) 8.93586i 0.400024i −0.979793 0.200012i \(-0.935902\pi\)
0.979793 0.200012i \(-0.0640981\pi\)
\(500\) 5.16510 9.91573i 0.230990 0.443445i
\(501\) −2.15743 + 22.9560i −0.0963869 + 1.02560i
\(502\) −18.7927 18.7927i −0.838758 0.838758i
\(503\) 2.19515 + 2.19515i 0.0978767 + 0.0978767i 0.754350 0.656473i \(-0.227952\pi\)
−0.656473 + 0.754350i \(0.727952\pi\)
\(504\) −5.39600 1.02328i −0.240357 0.0455806i
\(505\) −0.585073 + 3.62370i −0.0260354 + 0.161253i
\(506\) 5.02660i 0.223460i
\(507\) −12.6410 15.2634i −0.561405 0.677873i
\(508\) 1.08300 1.08300i 0.0480505 0.0480505i
\(509\) −3.39889 −0.150653 −0.0753265 0.997159i \(-0.524000\pi\)
−0.0753265 + 0.997159i \(0.524000\pi\)
\(510\) −3.05885 5.20132i −0.135448 0.230318i
\(511\) −7.89577 −0.349288
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −4.54935 + 2.51067i −0.200859 + 0.110849i
\(514\) 4.68583i 0.206683i
\(515\) 17.0850 12.3350i 0.752856 0.543543i
\(516\) −0.486437 0.0457158i −0.0214142 0.00201253i
\(517\) −33.7834 33.7834i −1.48579 1.48579i
\(518\) 5.53118 + 5.53118i 0.243026 + 0.243026i
\(519\) 23.8823 + 2.24448i 1.04832 + 0.0985219i
\(520\) −2.75527 0.444857i −0.120826 0.0195083i
\(521\) 7.98825i 0.349972i −0.984571 0.174986i \(-0.944012\pi\)
0.984571 0.174986i \(-0.0559879\pi\)
\(522\) −8.51128 12.4948i −0.372529 0.546883i
\(523\) 26.3556 26.3556i 1.15245 1.15245i 0.166388 0.986060i \(-0.446790\pi\)
0.986060 0.166388i \(-0.0532105\pi\)
\(524\) 6.00990 0.262544
\(525\) −14.5160 6.37580i −0.633532 0.278263i
\(526\) −12.0296 −0.524517
\(527\) −10.7583 + 10.7583i −0.468637 + 0.468637i
\(528\) 4.47654 + 5.40524i 0.194816 + 0.235233i
\(529\) 21.4611i 0.933091i
\(530\) −19.7956 3.19614i −0.859866 0.138832i
\(531\) −0.679364 + 3.58245i −0.0294819 + 0.155465i
\(532\) 1.29452 + 1.29452i 0.0561245 + 0.0561245i
\(533\) −1.65600 1.65600i −0.0717291 0.0717291i
\(534\) 2.51268 26.7361i 0.108734 1.15698i
\(535\) −33.5462 + 24.2195i −1.45033 + 1.04710i
\(536\) 3.19333i 0.137931i
\(537\) −3.61343 + 2.99259i −0.155931 + 0.129140i
\(538\) 13.5151 13.5151i 0.582676 0.582676i
\(539\) 14.7835 0.636770
\(540\) 10.9374 3.92080i 0.470672 0.168724i
\(541\) 6.97397 0.299834 0.149917 0.988699i \(-0.452099\pi\)
0.149917 + 0.988699i \(0.452099\pi\)
\(542\) 11.3585 11.3585i 0.487890 0.487890i
\(543\) −17.7860 + 14.7301i −0.763269 + 0.632128i
\(544\) 1.55800i 0.0667986i
\(545\) 4.69778 29.0961i 0.201231 1.24634i
\(546\) −0.370323 + 3.94040i −0.0158484 + 0.168634i
\(547\) −2.68199 2.68199i −0.114674 0.114674i 0.647442 0.762115i \(-0.275839\pi\)
−0.762115 + 0.647442i \(0.775839\pi\)
\(548\) −1.40049 1.40049i −0.0598258 0.0598258i
\(549\) 0.814787 4.29656i 0.0347743 0.183373i
\(550\) 9.08950 + 18.1066i 0.387578 + 0.772066i
\(551\) 5.03943i 0.214687i
\(552\) −1.37050 1.65482i −0.0583324 0.0704339i
\(553\) 17.0086 17.0086i 0.723277 0.723277i
\(554\) −14.5571 −0.618473
\(555\) −16.0183 4.15474i −0.679940 0.176359i
\(556\) −23.4290 −0.993610
\(557\) −6.84374 + 6.84374i −0.289979 + 0.289979i −0.837072 0.547093i \(-0.815734\pi\)
0.547093 + 0.837072i \(0.315734\pi\)
\(558\) −16.4932 24.2125i −0.698212 1.02500i
\(559\) 0.352081i 0.0148914i
\(560\) −2.39624 3.31901i −0.101260 0.140254i
\(561\) 10.8865 + 1.02312i 0.459626 + 0.0431961i
\(562\) −15.8138 15.8138i −0.667063 0.667063i
\(563\) 24.0154 + 24.0154i 1.01213 + 1.01213i 0.999926 + 0.0122028i \(0.00388437\pi\)
0.0122028 + 0.999926i \(0.496116\pi\)
\(564\) −20.3330 1.91091i −0.856173 0.0804639i
\(565\) −14.0044 19.3974i −0.589171 0.816054i
\(566\) 32.3336i 1.35908i
\(567\) −6.57639 15.1072i −0.276182 0.634442i
\(568\) −5.11134 + 5.11134i −0.214467 + 0.214467i
\(569\) −12.3367 −0.517182 −0.258591 0.965987i \(-0.583258\pi\)
−0.258591 + 0.965987i \(0.583258\pi\)
\(570\) −3.74893 0.972374i −0.157025 0.0407283i
\(571\) −2.43566 −0.101929 −0.0509646 0.998700i \(-0.516230\pi\)
−0.0509646 + 0.998700i \(0.516230\pi\)
\(572\) 3.57619 3.57619i 0.149528 0.149528i
\(573\) −17.2649 20.8466i −0.721250 0.870880i
\(574\) 3.43503i 0.143375i
\(575\) −2.78277 5.54335i −0.116049 0.231174i
\(576\) 2.94747 + 0.558949i 0.122811 + 0.0232895i
\(577\) 20.3964 + 20.3964i 0.849115 + 0.849115i 0.990023 0.140908i \(-0.0450021\pi\)
−0.140908 + 0.990023i \(0.545002\pi\)
\(578\) 10.3044 + 10.3044i 0.428607 + 0.428607i
\(579\) 2.69030 28.6260i 0.111805 1.18966i
\(580\) 1.79612 11.1244i 0.0745798 0.461917i
\(581\) 10.3866i 0.430909i
\(582\) 14.8378 12.2885i 0.615048 0.509374i
\(583\) 25.6936 25.6936i 1.06412 1.06412i
\(584\) 4.31292 0.178470
\(585\) −3.55049 7.58278i −0.146795 0.313509i
\(586\) 23.6769 0.978084
\(587\) 7.30666 7.30666i 0.301578 0.301578i −0.540053 0.841631i \(-0.681596\pi\)
0.841631 + 0.540053i \(0.181596\pi\)
\(588\) 4.86692 4.03071i 0.200708 0.166224i
\(589\) 9.76541i 0.402377i
\(590\) −2.20351 + 1.59088i −0.0907172 + 0.0654955i
\(591\) −2.39294 + 25.4620i −0.0984325 + 1.04737i
\(592\) −3.02131 3.02131i −0.124175 0.124175i
\(593\) 30.5679 + 30.5679i 1.25527 + 1.25527i 0.953324 + 0.301950i \(0.0976377\pi\)
0.301950 + 0.953324i \(0.402362\pi\)
\(594\) −5.84121 + 20.2283i −0.239668 + 0.829977i
\(595\) −6.29631 1.01658i −0.258124 0.0416759i
\(596\) 4.36654i 0.178861i
\(597\) −8.04915 9.71902i −0.329430 0.397773i
\(598\) −1.09486 + 1.09486i −0.0447720 + 0.0447720i
\(599\) −23.0022 −0.939843 −0.469921 0.882708i \(-0.655718\pi\)
−0.469921 + 0.882708i \(0.655718\pi\)
\(600\) 7.92913 + 3.48267i 0.323705 + 0.142179i
\(601\) −13.6513 −0.556847 −0.278423 0.960458i \(-0.589812\pi\)
−0.278423 + 0.960458i \(0.589812\pi\)
\(602\) −0.365160 + 0.365160i −0.0148828 + 0.0148828i
\(603\) −7.91758 + 5.39334i −0.322429 + 0.219634i
\(604\) 20.3330i 0.827340i
\(605\) −11.9616 1.93128i −0.486307 0.0785177i
\(606\) −2.83079 0.266040i −0.114993 0.0108071i
\(607\) 1.96645 + 1.96645i 0.0798158 + 0.0798158i 0.745888 0.666072i \(-0.232026\pi\)
−0.666072 + 0.745888i \(0.732026\pi\)
\(608\) −0.707107 0.707107i −0.0286770 0.0286770i
\(609\) −15.9095 1.49519i −0.644684 0.0605880i
\(610\) 2.64276 1.90800i 0.107002 0.0772528i
\(611\) 14.7169i 0.595382i
\(612\) 3.86292 2.63136i 0.156149 0.106366i
\(613\) −12.1077 + 12.1077i −0.489025 + 0.489025i −0.907999 0.418973i \(-0.862390\pi\)
0.418973 + 0.907999i \(0.362390\pi\)
\(614\) 0.545878 0.0220298
\(615\) 3.68382 + 6.26404i 0.148546 + 0.252590i
\(616\) 7.41808 0.298883
\(617\) 30.8463 30.8463i 1.24183 1.24183i 0.282582 0.959243i \(-0.408809\pi\)
0.959243 0.282582i \(-0.0911911\pi\)
\(618\) 10.4113 + 12.5712i 0.418803 + 0.505687i
\(619\) 28.1904i 1.13307i −0.824039 0.566534i \(-0.808284\pi\)
0.824039 0.566534i \(-0.191716\pi\)
\(620\) 3.48052 21.5569i 0.139781 0.865748i
\(621\) 1.78830 6.19293i 0.0717619 0.248514i
\(622\) 21.0708 + 21.0708i 0.844862 + 0.844862i
\(623\) −20.0703 20.0703i −0.804101 0.804101i
\(624\) 0.202282 2.15237i 0.00809777 0.0861639i
\(625\) 20.0479 + 14.9360i 0.801915 + 0.597438i
\(626\) 20.6787i 0.826486i
\(627\) 5.40524 4.47654i 0.215864 0.178776i
\(628\) 8.36917 8.36917i 0.333966 0.333966i
\(629\) −6.65697 −0.265431
\(630\) 4.18208 11.5469i 0.166618 0.460038i
\(631\) −44.8116 −1.78392 −0.891961 0.452113i \(-0.850670\pi\)
−0.891961 + 0.452113i \(0.850670\pi\)
\(632\) −9.29061 + 9.29061i −0.369561 + 0.369561i
\(633\) −1.70566 + 1.41260i −0.0677939 + 0.0561459i
\(634\) 3.80868i 0.151262i
\(635\) 2.00471 + 2.77671i 0.0795546 + 0.110190i
\(636\) 1.45333 15.4640i 0.0576281 0.613189i
\(637\) −3.22003 3.22003i −0.127582 0.127582i
\(638\) 14.4389 + 14.4389i 0.571643 + 0.571643i
\(639\) −21.3059 4.04038i −0.842848 0.159835i
\(640\) 1.30890 + 1.81295i 0.0517389 + 0.0716630i
\(641\) 9.11894i 0.360176i −0.983650 0.180088i \(-0.942362\pi\)
0.983650 0.180088i \(-0.0576383\pi\)
\(642\) −20.4424 24.6833i −0.806796 0.974173i
\(643\) 12.0846 12.0846i 0.476572 0.476572i −0.427462 0.904034i \(-0.640592\pi\)
0.904034 + 0.427462i \(0.140592\pi\)
\(644\) −2.27106 −0.0894923
\(645\) 0.274289 1.05751i 0.0108001 0.0416393i
\(646\) −1.55800 −0.0612986
\(647\) −1.21178 + 1.21178i −0.0476399 + 0.0476399i −0.730525 0.682886i \(-0.760725\pi\)
0.682886 + 0.730525i \(0.260725\pi\)
\(648\) 3.59223 + 8.25202i 0.141116 + 0.324170i
\(649\) 4.92492i 0.193320i
\(650\) 1.96403 5.92364i 0.0770355 0.232344i
\(651\) −30.8294 2.89737i −1.20830 0.113557i
\(652\) 9.51819 + 9.51819i 0.372761 + 0.372761i
\(653\) 7.87945 + 7.87945i 0.308347 + 0.308347i 0.844268 0.535921i \(-0.180036\pi\)
−0.535921 + 0.844268i \(0.680036\pi\)
\(654\) 22.7295 + 2.13614i 0.888793 + 0.0835296i
\(655\) −2.14201 + 13.2667i −0.0836952 + 0.518374i
\(656\) 1.87632i 0.0732581i
\(657\) 7.28426 + 10.6935i 0.284186 + 0.417193i
\(658\) −15.2636 + 15.2636i −0.595038 + 0.595038i
\(659\) −30.2646 −1.17894 −0.589471 0.807789i \(-0.700664\pi\)
−0.589471 + 0.807789i \(0.700664\pi\)
\(660\) −13.5275 + 7.95537i −0.526555 + 0.309662i
\(661\) −21.0286 −0.817917 −0.408958 0.912553i \(-0.634108\pi\)
−0.408958 + 0.912553i \(0.634108\pi\)
\(662\) −2.22309 + 2.22309i −0.0864027 + 0.0864027i
\(663\) −2.14836 2.59405i −0.0834353 0.100745i
\(664\) 5.67349i 0.220174i
\(665\) −3.31901 + 2.39624i −0.128706 + 0.0929222i
\(666\) 2.38826 12.5939i 0.0925433 0.488002i
\(667\) −4.42050 4.42050i −0.171163 0.171163i
\(668\) −9.41306 9.41306i −0.364202 0.364202i
\(669\) −4.48930 + 47.7682i −0.173566 + 1.84682i
\(670\) −7.04921 1.13815i −0.272335 0.0439704i
\(671\) 5.90664i 0.228023i
\(672\) 2.44213 2.02254i 0.0942072 0.0780210i
\(673\) −22.0700 + 22.0700i −0.850736 + 0.850736i −0.990224 0.139488i \(-0.955454\pi\)
0.139488 + 0.990224i \(0.455454\pi\)
\(674\) −0.569824 −0.0219488
\(675\) 4.75684 + 25.5416i 0.183091 + 0.983096i
\(676\) 11.4421 0.440082
\(677\) −18.2077 + 18.2077i −0.699780 + 0.699780i −0.964363 0.264583i \(-0.914766\pi\)
0.264583 + 0.964363i \(0.414766\pi\)
\(678\) 14.2726 11.8204i 0.548137 0.453959i
\(679\) 20.3633i 0.781471i
\(680\) 3.43925 + 0.555291i 0.131889 + 0.0212944i
\(681\) 0.491785 5.23282i 0.0188452 0.200522i
\(682\) 27.9798 + 27.9798i 1.07140 + 1.07140i
\(683\) −27.5676 27.5676i −1.05484 1.05484i −0.998406 0.0564381i \(-0.982026\pi\)
−0.0564381 0.998406i \(-0.517974\pi\)
\(684\) 0.558949 2.94747i 0.0213719 0.112699i
\(685\) 3.59070 2.59239i 0.137194 0.0990503i
\(686\) 19.4944i 0.744299i
\(687\) 20.0891 + 24.2568i 0.766447 + 0.925454i
\(688\) 0.199462 0.199462i 0.00760442 0.00760442i
\(689\) −11.1928 −0.426412
\(690\) 4.14145 2.43555i 0.157662 0.0927198i
\(691\) 16.3113 0.620510 0.310255 0.950653i \(-0.399586\pi\)
0.310255 + 0.950653i \(0.399586\pi\)
\(692\) −9.79289 + 9.79289i −0.372270 + 0.372270i
\(693\) 12.5287 + 18.3925i 0.475926 + 0.698673i
\(694\) 20.6395i 0.783464i
\(695\) 8.35040 51.7190i 0.316749 1.96181i
\(696\) 8.69025 + 0.816718i 0.329403 + 0.0309576i
\(697\) 2.06709 + 2.06709i 0.0782965 + 0.0782965i
\(698\) 4.42467 + 4.42467i 0.167476 + 0.167476i
\(699\) 12.5308 + 1.17766i 0.473960 + 0.0445432i
\(700\) 8.18069 4.10671i 0.309201 0.155219i
\(701\) 16.2155i 0.612453i −0.951959 0.306226i \(-0.900934\pi\)
0.951959 0.306226i \(-0.0990664\pi\)
\(702\) 5.67827 3.13369i 0.214312 0.118273i
\(703\) −3.02131 + 3.02131i −0.113951 + 0.113951i
\(704\) −4.05199 −0.152715
\(705\) 11.4652 44.2036i 0.431806 1.66480i
\(706\) 1.27025 0.0478065
\(707\) −2.12502 + 2.12502i −0.0799198 + 0.0799198i
\(708\) −1.34278 1.62135i −0.0504646 0.0609340i
\(709\) 27.2559i 1.02362i 0.859100 + 0.511808i \(0.171024\pi\)
−0.859100 + 0.511808i \(0.828976\pi\)
\(710\) −9.46144 13.1049i −0.355082 0.491820i
\(711\) −38.7265 7.34398i −1.45236 0.275421i
\(712\) 10.9631 + 10.9631i 0.410858 + 0.410858i
\(713\) −8.56606 8.56606i −0.320801 0.320801i
\(714\) 0.462254 4.91859i 0.0172994 0.184074i
\(715\) 6.61977 + 9.16897i 0.247565 + 0.342900i
\(716\) 2.70878i 0.101232i
\(717\) 34.5624 28.6240i 1.29076 1.06898i
\(718\) −0.683791 + 0.683791i −0.0255188 + 0.0255188i
\(719\) −27.9463 −1.04222 −0.521111 0.853489i \(-0.674482\pi\)
−0.521111 + 0.853489i \(0.674482\pi\)
\(720\) −2.28439 + 6.30726i −0.0851340 + 0.235058i
\(721\) 17.2526 0.642519
\(722\) −0.707107 + 0.707107i −0.0263158 + 0.0263158i
\(723\) −31.1419 + 25.7913i −1.15818 + 0.959189i
\(724\) 13.3331i 0.495522i
\(725\) 23.9168 + 7.92979i 0.888248 + 0.294505i
\(726\) 0.878178 9.34421i 0.0325922 0.346796i
\(727\) 0.785783 + 0.785783i 0.0291431 + 0.0291431i 0.721528 0.692385i \(-0.243440\pi\)
−0.692385 + 0.721528i \(0.743440\pi\)
\(728\) −1.61575 1.61575i −0.0598837 0.0598837i
\(729\) −14.3931 + 22.8438i −0.533078 + 0.846066i
\(730\) −1.53718 + 9.52068i −0.0568937 + 0.352376i
\(731\) 0.439483i 0.0162549i
\(732\) 1.61044 + 1.94454i 0.0595237 + 0.0718724i
\(733\) 32.5824 32.5824i 1.20346 1.20346i 0.230353 0.973107i \(-0.426012\pi\)
0.973107 0.230353i \(-0.0739880\pi\)
\(734\) −27.9364 −1.03115
\(735\) 7.16308 + 12.1802i 0.264214 + 0.449274i
\(736\) 1.24053 0.0457264
\(737\) 9.14951 9.14951i 0.337026 0.337026i
\(738\) −4.65218 + 3.16899i −0.171249 + 0.116652i
\(739\) 29.4181i 1.08216i 0.840970 + 0.541082i \(0.181985\pi\)
−0.840970 + 0.541082i \(0.818015\pi\)
\(740\) 7.74631 5.59264i 0.284760 0.205590i
\(741\) −2.15237 0.202282i −0.0790694 0.00743102i
\(742\) −11.6086 11.6086i −0.426165 0.426165i
\(743\) 15.5044 + 15.5044i 0.568802 + 0.568802i 0.931793 0.362991i \(-0.118244\pi\)
−0.362991 + 0.931793i \(0.618244\pi\)
\(744\) 16.8400 + 1.58264i 0.617384 + 0.0580223i
\(745\) 9.63905 + 1.55629i 0.353148 + 0.0570182i
\(746\) 14.0261i 0.513532i
\(747\) 14.0669 9.58218i 0.514682 0.350594i
\(748\) −4.46396 + 4.46396i −0.163219 + 0.163219i
\(749\) −33.8751 −1.23777
\(750\) −10.5140 + 16.2621i −0.383916 + 0.593809i
\(751\) −30.2158 −1.10259 −0.551295 0.834311i \(-0.685866\pi\)
−0.551295 + 0.834311i \(0.685866\pi\)
\(752\) 8.33748 8.33748i 0.304037 0.304037i
\(753\) 29.3614 + 35.4527i 1.06999 + 1.29197i
\(754\) 6.28996i 0.229067i
\(755\) −44.8848 7.24697i −1.63353 0.263744i
\(756\) 9.13931 + 2.63911i 0.332394 + 0.0959834i
\(757\) 26.1455 + 26.1455i 0.950273 + 0.950273i 0.998821 0.0485482i \(-0.0154594\pi\)
−0.0485482 + 0.998821i \(0.515459\pi\)
\(758\) 15.2776 + 15.2776i 0.554906 + 0.554906i
\(759\) −0.814639 + 8.66813i −0.0295695 + 0.314633i
\(760\) 1.81295 1.30890i 0.0657625 0.0474789i
\(761\) 21.4239i 0.776614i 0.921530 + 0.388307i \(0.126940\pi\)
−0.921530 + 0.388307i \(0.873060\pi\)
\(762\) −2.04311 + 1.69207i −0.0740139 + 0.0612972i
\(763\) 17.0626 17.0626i 0.617709 0.617709i
\(764\) 15.6275 0.565383
\(765\) 4.43188 + 9.46516i 0.160235 + 0.342214i
\(766\) −30.0023 −1.08403
\(767\) −1.07271 + 1.07271i −0.0387333 + 0.0387333i
\(768\) −1.33397 + 1.10477i −0.0481355 + 0.0398651i
\(769\) 5.25678i 0.189564i −0.995498 0.0947821i \(-0.969785\pi\)
0.995498 0.0947821i \(-0.0302154\pi\)
\(770\) −2.64390 + 16.3753i −0.0952797 + 0.590124i
\(771\) −0.759413 + 8.08049i −0.0273496 + 0.291012i
\(772\) 11.7380 + 11.7380i 0.422461 + 0.422461i
\(773\) 28.7467 + 28.7467i 1.03395 + 1.03395i 0.999403 + 0.0345431i \(0.0109976\pi\)
0.0345431 + 0.999403i \(0.489002\pi\)
\(774\) 0.831428 + 0.157669i 0.0298851 + 0.00566731i
\(775\) 46.3460 + 15.3664i 1.66480 + 0.551976i
\(776\) 11.1231i 0.399295i
\(777\) −8.64184 10.4347i −0.310024 0.374342i
\(778\) </