Properties

Label 637.2.e.k.508.1
Level $637$
Weight $2$
Character 637.508
Analytic conductor $5.086$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.4406832.1
Defining polynomial: \(x^{6} - x^{5} + 6 x^{4} + 7 x^{3} + 24 x^{2} + 5 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 508.1
Root \(1.43310 - 2.48220i\) of defining polynomial
Character \(\chi\) \(=\) 637.508
Dual form 637.2.e.k.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.933099 - 1.61618i) q^{2} +(-1.67445 + 2.90023i) q^{3} +(-0.741348 + 1.28405i) q^{4} +(0.433099 + 0.750150i) q^{5} +6.24970 q^{6} -0.965392 q^{8} +(-4.10755 - 7.11448i) q^{9} +O(q^{10})\) \(q+(-0.933099 - 1.61618i) q^{2} +(-1.67445 + 2.90023i) q^{3} +(-0.741348 + 1.28405i) q^{4} +(0.433099 + 0.750150i) q^{5} +6.24970 q^{6} -0.965392 q^{8} +(-4.10755 - 7.11448i) q^{9} +(0.808249 - 1.39993i) q^{10} +(1.93310 - 3.34823i) q^{11} +(-2.48270 - 4.30016i) q^{12} -1.00000 q^{13} -2.90081 q^{15} +(2.38350 + 4.12835i) q^{16} +(-1.67445 + 2.90023i) q^{17} +(-7.66550 + 13.2770i) q^{18} +(-2.69175 - 4.66225i) q^{19} -1.28431 q^{20} -7.21509 q^{22} +(2.62485 + 4.54637i) q^{23} +(1.61650 - 2.79986i) q^{24} +(2.12485 - 3.68035i) q^{25} +(0.933099 + 1.61618i) q^{26} +17.4648 q^{27} +1.69779 q^{29} +(2.70674 + 4.68821i) q^{30} +(3.78199 - 6.55060i) q^{31} +(3.48270 - 6.03221i) q^{32} +(6.47374 + 11.2129i) q^{33} +6.24970 q^{34} +12.1805 q^{36} +(2.41580 + 4.18428i) q^{37} +(-5.02334 + 8.70068i) q^{38} +(1.67445 - 2.90023i) q^{39} +(-0.418110 - 0.724188i) q^{40} +4.06922 q^{41} +4.03461 q^{43} +(2.86620 + 4.96440i) q^{44} +(3.55795 - 6.16255i) q^{45} +(4.89849 - 8.48444i) q^{46} +(-1.82555 - 3.16195i) q^{47} -15.9642 q^{48} -7.93078 q^{50} +(-5.60755 - 9.71255i) q^{51} +(0.741348 - 1.28405i) q^{52} +(0.107546 - 0.186276i) q^{53} +(-16.2964 - 28.2262i) q^{54} +3.34889 q^{55} +18.0288 q^{57} +(-1.58420 - 2.74392i) q^{58} +(-1.39245 + 2.41180i) q^{59} +(2.15051 - 3.72479i) q^{60} +(4.51730 + 7.82420i) q^{61} -14.1159 q^{62} -3.46479 q^{64} +(-0.433099 - 0.750150i) q^{65} +(12.0813 - 20.9254i) q^{66} +(3.83159 - 6.63651i) q^{67} +(-2.48270 - 4.30016i) q^{68} -17.5807 q^{69} +4.90081 q^{71} +(3.96539 + 6.86826i) q^{72} +(7.77304 - 13.4633i) q^{73} +(4.50835 - 7.80870i) q^{74} +(7.11590 + 12.3251i) q^{75} +7.98210 q^{76} -6.24970 q^{78} +(-4.71509 - 8.16678i) q^{79} +(-2.06459 + 3.57597i) q^{80} +(-16.9212 + 29.3084i) q^{81} +(-3.79698 - 6.57657i) q^{82} +4.09919 q^{83} -2.90081 q^{85} +(-3.76469 - 6.52063i) q^{86} +(-2.84286 + 4.92397i) q^{87} +(-1.86620 + 3.23235i) q^{88} +(-0.209055 - 0.362094i) q^{89} -13.2797 q^{90} -7.78371 q^{92} +(12.6655 + 21.9373i) q^{93} +(-3.40684 + 5.90083i) q^{94} +(2.33159 - 4.03843i) q^{95} +(11.6632 + 20.2012i) q^{96} +7.11590 q^{97} -31.7612 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 2q^{2} - 4q^{3} - 6q^{4} - 5q^{5} + 4q^{6} - 12q^{8} - 11q^{9} + O(q^{10}) \) \( 6q + 2q^{2} - 4q^{3} - 6q^{4} - 5q^{5} + 4q^{6} - 12q^{8} - 11q^{9} + 14q^{10} + 4q^{11} - 18q^{12} - 6q^{13} + 4q^{15} - 4q^{16} - 4q^{17} - 8q^{18} - 7q^{19} + 32q^{20} - 16q^{22} - q^{23} + 28q^{24} - 4q^{25} - 2q^{26} + 44q^{27} - 14q^{29} + 24q^{30} + 3q^{31} + 24q^{32} + 10q^{33} + 4q^{34} + 52q^{36} + 10q^{37} - 12q^{38} + 4q^{39} + 22q^{40} + 12q^{41} + 18q^{43} + 2q^{44} - 3q^{45} + 28q^{46} - 17q^{47} + 32q^{48} - 60q^{50} - 20q^{51} + 6q^{52} - 13q^{53} - 28q^{54} + 8q^{55} + 8q^{57} - 14q^{58} - 22q^{59} - 42q^{60} + 24q^{61} - 36q^{62} + 40q^{64} + 5q^{65} + 30q^{66} + 14q^{67} - 18q^{68} + 4q^{69} + 8q^{71} + 30q^{72} - 5q^{73} - 8q^{74} - 6q^{75} - 16q^{76} - 4q^{78} - q^{79} - 40q^{80} - 15q^{81} - 20q^{82} + 46q^{83} + 4q^{85} - 6q^{86} - 20q^{87} + 4q^{88} + 11q^{89} - 80q^{90} + 60q^{92} + 38q^{93} + 16q^{94} + 5q^{95} + 52q^{96} - 6q^{97} - 60q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.933099 1.61618i −0.659801 1.14281i −0.980667 0.195684i \(-0.937307\pi\)
0.320866 0.947124i \(-0.396026\pi\)
\(3\) −1.67445 + 2.90023i −0.966742 + 1.67445i −0.261884 + 0.965099i \(0.584344\pi\)
−0.704859 + 0.709348i \(0.748990\pi\)
\(4\) −0.741348 + 1.28405i −0.370674 + 0.642026i
\(5\) 0.433099 + 0.750150i 0.193688 + 0.335477i 0.946470 0.322793i \(-0.104622\pi\)
−0.752782 + 0.658270i \(0.771288\pi\)
\(6\) 6.24970 2.55143
\(7\) 0 0
\(8\) −0.965392 −0.341318
\(9\) −4.10755 7.11448i −1.36918 2.37149i
\(10\) 0.808249 1.39993i 0.255591 0.442696i
\(11\) 1.93310 3.34823i 0.582851 1.00953i −0.412288 0.911053i \(-0.635270\pi\)
0.995140 0.0984746i \(-0.0313963\pi\)
\(12\) −2.48270 4.30016i −0.716693 1.24135i
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −2.90081 −0.748985
\(16\) 2.38350 + 4.12835i 0.595876 + 1.03209i
\(17\) −1.67445 + 2.90023i −0.406113 + 0.703408i −0.994450 0.105207i \(-0.966449\pi\)
0.588337 + 0.808616i \(0.299783\pi\)
\(18\) −7.66550 + 13.2770i −1.80677 + 3.12943i
\(19\) −2.69175 4.66225i −0.617530 1.06959i −0.989935 0.141523i \(-0.954800\pi\)
0.372405 0.928070i \(-0.378533\pi\)
\(20\) −1.28431 −0.287180
\(21\) 0 0
\(22\) −7.21509 −1.53826
\(23\) 2.62485 + 4.54637i 0.547319 + 0.947985i 0.998457 + 0.0555303i \(0.0176849\pi\)
−0.451138 + 0.892454i \(0.648982\pi\)
\(24\) 1.61650 2.79986i 0.329966 0.571518i
\(25\) 2.12485 3.68035i 0.424970 0.736070i
\(26\) 0.933099 + 1.61618i 0.182996 + 0.316958i
\(27\) 17.4648 3.36110
\(28\) 0 0
\(29\) 1.69779 0.315271 0.157636 0.987497i \(-0.449613\pi\)
0.157636 + 0.987497i \(0.449613\pi\)
\(30\) 2.70674 + 4.68821i 0.494181 + 0.855946i
\(31\) 3.78199 6.55060i 0.679266 1.17652i −0.295936 0.955208i \(-0.595632\pi\)
0.975202 0.221316i \(-0.0710351\pi\)
\(32\) 3.48270 6.03221i 0.615659 1.06635i
\(33\) 6.47374 + 11.2129i 1.12693 + 1.95191i
\(34\) 6.24970 1.07181
\(35\) 0 0
\(36\) 12.1805 2.03008
\(37\) 2.41580 + 4.18428i 0.397154 + 0.687891i 0.993374 0.114930i \(-0.0366645\pi\)
−0.596219 + 0.802822i \(0.703331\pi\)
\(38\) −5.02334 + 8.70068i −0.814894 + 1.41144i
\(39\) 1.67445 2.90023i 0.268126 0.464408i
\(40\) −0.418110 0.724188i −0.0661091 0.114504i
\(41\) 4.06922 0.635505 0.317752 0.948174i \(-0.397072\pi\)
0.317752 + 0.948174i \(0.397072\pi\)
\(42\) 0 0
\(43\) 4.03461 0.615272 0.307636 0.951504i \(-0.400462\pi\)
0.307636 + 0.951504i \(0.400462\pi\)
\(44\) 2.86620 + 4.96440i 0.432096 + 0.748412i
\(45\) 3.55795 6.16255i 0.530388 0.918659i
\(46\) 4.89849 8.48444i 0.722243 1.25096i
\(47\) −1.82555 3.16195i −0.266284 0.461218i 0.701615 0.712556i \(-0.252463\pi\)
−0.967899 + 0.251338i \(0.919129\pi\)
\(48\) −15.9642 −2.30423
\(49\) 0 0
\(50\) −7.93078 −1.12158
\(51\) −5.60755 9.71255i −0.785214 1.36003i
\(52\) 0.741348 1.28405i 0.102806 0.178066i
\(53\) 0.107546 0.186276i 0.0147726 0.0255869i −0.858545 0.512739i \(-0.828631\pi\)
0.873317 + 0.487152i \(0.161964\pi\)
\(54\) −16.2964 28.2262i −2.21766 3.84109i
\(55\) 3.34889 0.451565
\(56\) 0 0
\(57\) 18.0288 2.38797
\(58\) −1.58420 2.74392i −0.208016 0.360295i
\(59\) −1.39245 + 2.41180i −0.181282 + 0.313990i −0.942317 0.334721i \(-0.891358\pi\)
0.761035 + 0.648710i \(0.224691\pi\)
\(60\) 2.15051 3.72479i 0.277629 0.480868i
\(61\) 4.51730 + 7.82420i 0.578382 + 1.00179i 0.995665 + 0.0930099i \(0.0296488\pi\)
−0.417284 + 0.908776i \(0.637018\pi\)
\(62\) −14.1159 −1.79272
\(63\) 0 0
\(64\) −3.46479 −0.433099
\(65\) −0.433099 0.750150i −0.0537193 0.0930446i
\(66\) 12.0813 20.9254i 1.48710 2.57574i
\(67\) 3.83159 6.63651i 0.468103 0.810779i −0.531232 0.847226i \(-0.678271\pi\)
0.999336 + 0.0364476i \(0.0116042\pi\)
\(68\) −2.48270 4.30016i −0.301071 0.521470i
\(69\) −17.5807 −2.11647
\(70\) 0 0
\(71\) 4.90081 0.581619 0.290809 0.956781i \(-0.406075\pi\)
0.290809 + 0.956781i \(0.406075\pi\)
\(72\) 3.96539 + 6.86826i 0.467326 + 0.809432i
\(73\) 7.77304 13.4633i 0.909766 1.57576i 0.0953766 0.995441i \(-0.469594\pi\)
0.814389 0.580319i \(-0.197072\pi\)
\(74\) 4.50835 7.80870i 0.524085 0.907742i
\(75\) 7.11590 + 12.3251i 0.821673 + 1.42318i
\(76\) 7.98210 0.915609
\(77\) 0 0
\(78\) −6.24970 −0.707639
\(79\) −4.71509 8.16678i −0.530489 0.918835i −0.999367 0.0355715i \(-0.988675\pi\)
0.468878 0.883263i \(-0.344658\pi\)
\(80\) −2.06459 + 3.57597i −0.230828 + 0.399805i
\(81\) −16.9212 + 29.3084i −1.88014 + 3.25649i
\(82\) −3.79698 6.57657i −0.419307 0.726260i
\(83\) 4.09919 0.449945 0.224972 0.974365i \(-0.427771\pi\)
0.224972 + 0.974365i \(0.427771\pi\)
\(84\) 0 0
\(85\) −2.90081 −0.314637
\(86\) −3.76469 6.52063i −0.405957 0.703138i
\(87\) −2.84286 + 4.92397i −0.304786 + 0.527905i
\(88\) −1.86620 + 3.23235i −0.198937 + 0.344570i
\(89\) −0.209055 0.362094i −0.0221598 0.0383819i 0.854733 0.519068i \(-0.173721\pi\)
−0.876893 + 0.480686i \(0.840388\pi\)
\(90\) −13.2797 −1.39980
\(91\) 0 0
\(92\) −7.78371 −0.811508
\(93\) 12.6655 + 21.9373i 1.31335 + 2.27479i
\(94\) −3.40684 + 5.90083i −0.351389 + 0.608624i
\(95\) 2.33159 4.03843i 0.239216 0.414334i
\(96\) 11.6632 + 20.2012i 1.19037 + 2.06178i
\(97\) 7.11590 0.722510 0.361255 0.932467i \(-0.382348\pi\)
0.361255 + 0.932467i \(0.382348\pi\)
\(98\) 0 0
\(99\) −31.7612 −3.19212
\(100\) 3.15051 + 5.45684i 0.315051 + 0.545684i
\(101\) −7.05795 + 12.2247i −0.702292 + 1.21641i 0.265368 + 0.964147i \(0.414507\pi\)
−0.967660 + 0.252259i \(0.918827\pi\)
\(102\) −10.4648 + 18.1256i −1.03617 + 1.79470i
\(103\) −8.43018 14.6015i −0.830651 1.43873i −0.897523 0.440968i \(-0.854635\pi\)
0.0668721 0.997762i \(-0.478698\pi\)
\(104\) 0.965392 0.0946645
\(105\) 0 0
\(106\) −0.401405 −0.0389879
\(107\) −5.09024 8.81656i −0.492092 0.852329i 0.507866 0.861436i \(-0.330434\pi\)
−0.999959 + 0.00910710i \(0.997101\pi\)
\(108\) −12.9475 + 22.4257i −1.24587 + 2.15791i
\(109\) 3.10151 5.37197i 0.297071 0.514542i −0.678394 0.734699i \(-0.737324\pi\)
0.975464 + 0.220157i \(0.0706570\pi\)
\(110\) −3.12485 5.41240i −0.297943 0.516052i
\(111\) −16.1805 −1.53578
\(112\) 0 0
\(113\) 10.2843 0.967466 0.483733 0.875216i \(-0.339281\pi\)
0.483733 + 0.875216i \(0.339281\pi\)
\(114\) −16.8226 29.1377i −1.57558 2.72899i
\(115\) −2.27364 + 3.93806i −0.212018 + 0.367226i
\(116\) −1.25865 + 2.18005i −0.116863 + 0.202412i
\(117\) 4.10755 + 7.11448i 0.379743 + 0.657734i
\(118\) 5.19719 0.478440
\(119\) 0 0
\(120\) 2.80041 0.255642
\(121\) −1.97374 3.41863i −0.179431 0.310784i
\(122\) 8.43018 14.6015i 0.763233 1.32196i
\(123\) −6.81369 + 11.8017i −0.614369 + 1.06412i
\(124\) 5.60755 + 9.71255i 0.503573 + 0.872213i
\(125\) 8.01207 0.716622
\(126\) 0 0
\(127\) −1.91288 −0.169741 −0.0848704 0.996392i \(-0.527048\pi\)
−0.0848704 + 0.996392i \(0.527048\pi\)
\(128\) −3.73240 6.46470i −0.329900 0.571404i
\(129\) −6.75574 + 11.7013i −0.594810 + 1.03024i
\(130\) −0.808249 + 1.39993i −0.0708881 + 0.122782i
\(131\) 5.08129 + 8.80105i 0.443954 + 0.768952i 0.997979 0.0635489i \(-0.0202419\pi\)
−0.554024 + 0.832500i \(0.686909\pi\)
\(132\) −19.1972 −1.67090
\(133\) 0 0
\(134\) −14.3010 −1.23542
\(135\) 7.56399 + 13.1012i 0.651004 + 1.12757i
\(136\) 1.61650 2.79986i 0.138614 0.240086i
\(137\) −3.89849 + 6.75238i −0.333071 + 0.576895i −0.983112 0.183003i \(-0.941418\pi\)
0.650042 + 0.759899i \(0.274751\pi\)
\(138\) 16.4045 + 28.4135i 1.39645 + 2.41872i
\(139\) 5.08129 0.430989 0.215495 0.976505i \(-0.430864\pi\)
0.215495 + 0.976505i \(0.430864\pi\)
\(140\) 0 0
\(141\) 12.2272 1.02971
\(142\) −4.57294 7.92056i −0.383752 0.664679i
\(143\) −1.93310 + 3.34823i −0.161654 + 0.279993i
\(144\) 19.5807 33.9148i 1.63172 2.82623i
\(145\) 0.735311 + 1.27360i 0.0610642 + 0.105766i
\(146\) −29.0121 −2.40106
\(147\) 0 0
\(148\) −7.16378 −0.588859
\(149\) 1.24739 + 2.16053i 0.102190 + 0.176998i 0.912587 0.408884i \(-0.134082\pi\)
−0.810397 + 0.585881i \(0.800748\pi\)
\(150\) 13.2797 23.0011i 1.08428 1.87803i
\(151\) 1.63089 2.82478i 0.132720 0.229877i −0.792004 0.610515i \(-0.790962\pi\)
0.924724 + 0.380638i \(0.124296\pi\)
\(152\) 2.59859 + 4.50090i 0.210774 + 0.365071i
\(153\) 27.5115 2.22417
\(154\) 0 0
\(155\) 6.55191 0.526262
\(156\) 2.48270 + 4.30016i 0.198775 + 0.344288i
\(157\) −0.360161 + 0.623817i −0.0287440 + 0.0497860i −0.880040 0.474900i \(-0.842484\pi\)
0.851296 + 0.524686i \(0.175817\pi\)
\(158\) −8.79930 + 15.2408i −0.700035 + 1.21250i
\(159\) 0.360161 + 0.623817i 0.0285626 + 0.0494719i
\(160\) 6.03341 0.476983
\(161\) 0 0
\(162\) 63.1568 4.96206
\(163\) −0.651106 1.12775i −0.0509985 0.0883321i 0.839399 0.543515i \(-0.182907\pi\)
−0.890398 + 0.455183i \(0.849574\pi\)
\(164\) −3.01671 + 5.22509i −0.235565 + 0.408011i
\(165\) −5.60755 + 9.71255i −0.436547 + 0.756121i
\(166\) −3.82495 6.62501i −0.296874 0.514201i
\(167\) −16.1505 −1.24976 −0.624882 0.780719i \(-0.714853\pi\)
−0.624882 + 0.780719i \(0.714853\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 2.70674 + 4.68821i 0.207597 + 0.359569i
\(171\) −22.1130 + 38.3008i −1.69102 + 2.92894i
\(172\) −2.99105 + 5.18065i −0.228065 + 0.395021i
\(173\) −7.92415 13.7250i −0.602462 1.04349i −0.992447 0.122673i \(-0.960853\pi\)
0.389985 0.920821i \(-0.372480\pi\)
\(174\) 10.6107 0.804393
\(175\) 0 0
\(176\) 18.4302 1.38923
\(177\) −4.66318 8.07687i −0.350506 0.607094i
\(178\) −0.390138 + 0.675740i −0.0292421 + 0.0506488i
\(179\) 10.2324 17.7230i 0.764805 1.32468i −0.175544 0.984472i \(-0.556169\pi\)
0.940349 0.340210i \(-0.110498\pi\)
\(180\) 5.27536 + 9.13719i 0.393202 + 0.681046i
\(181\) 6.58189 0.489228 0.244614 0.969621i \(-0.421339\pi\)
0.244614 + 0.969621i \(0.421339\pi\)
\(182\) 0 0
\(183\) −30.2559 −2.23658
\(184\) −2.53401 4.38903i −0.186810 0.323564i
\(185\) −2.09256 + 3.62442i −0.153848 + 0.266472i
\(186\) 23.6363 40.9393i 1.73310 3.00182i
\(187\) 6.47374 + 11.2129i 0.473407 + 0.819965i
\(188\) 5.41348 0.394819
\(189\) 0 0
\(190\) −8.70242 −0.631340
\(191\) −6.37455 11.0410i −0.461246 0.798902i 0.537777 0.843087i \(-0.319264\pi\)
−0.999023 + 0.0441850i \(0.985931\pi\)
\(192\) 5.80161 10.0487i 0.418695 0.725202i
\(193\) −1.13380 + 1.96380i −0.0816128 + 0.141358i −0.903943 0.427653i \(-0.859340\pi\)
0.822330 + 0.569011i \(0.192674\pi\)
\(194\) −6.63984 11.5005i −0.476713 0.825691i
\(195\) 2.90081 0.207731
\(196\) 0 0
\(197\) −18.6978 −1.33216 −0.666081 0.745879i \(-0.732030\pi\)
−0.666081 + 0.745879i \(0.732030\pi\)
\(198\) 29.6363 + 51.3316i 2.10616 + 3.64798i
\(199\) 9.95876 17.2491i 0.705957 1.22275i −0.260387 0.965504i \(-0.583850\pi\)
0.966345 0.257250i \(-0.0828164\pi\)
\(200\) −2.05131 + 3.55298i −0.145050 + 0.251234i
\(201\) 12.8316 + 22.2250i 0.905071 + 1.56763i
\(202\) 26.3431 1.85349
\(203\) 0 0
\(204\) 16.6286 1.16423
\(205\) 1.76237 + 3.05252i 0.123090 + 0.213197i
\(206\) −15.7324 + 27.2493i −1.09613 + 1.89855i
\(207\) 21.5634 37.3489i 1.49876 2.59593i
\(208\) −2.38350 4.12835i −0.165266 0.286249i
\(209\) −20.8137 −1.43971
\(210\) 0 0
\(211\) 0.645277 0.0444227 0.0222114 0.999753i \(-0.492929\pi\)
0.0222114 + 0.999753i \(0.492929\pi\)
\(212\) 0.159458 + 0.276190i 0.0109516 + 0.0189688i
\(213\) −8.20614 + 14.2135i −0.562276 + 0.973890i
\(214\) −9.49940 + 16.4534i −0.649366 + 1.12473i
\(215\) 1.74739 + 3.02656i 0.119171 + 0.206410i
\(216\) −16.8604 −1.14720
\(217\) 0 0
\(218\) −11.5761 −0.784030
\(219\) 26.0311 + 45.0872i 1.75902 + 3.04671i
\(220\) −2.48270 + 4.30016i −0.167383 + 0.289916i
\(221\) 1.67445 2.90023i 0.112636 0.195090i
\(222\) 15.0980 + 26.1505i 1.01331 + 1.75511i
\(223\) −5.83159 −0.390512 −0.195256 0.980752i \(-0.562554\pi\)
−0.195256 + 0.980752i \(0.562554\pi\)
\(224\) 0 0
\(225\) −34.9117 −2.32745
\(226\) −9.59628 16.6212i −0.638335 1.10563i
\(227\) −7.86620 + 13.6247i −0.522098 + 0.904300i 0.477572 + 0.878593i \(0.341517\pi\)
−0.999670 + 0.0257073i \(0.991816\pi\)
\(228\) −13.3656 + 23.1499i −0.885158 + 1.53314i
\(229\) −4.43914 7.68881i −0.293346 0.508091i 0.681252 0.732049i \(-0.261436\pi\)
−0.974599 + 0.223958i \(0.928102\pi\)
\(230\) 8.48613 0.559559
\(231\) 0 0
\(232\) −1.63903 −0.107608
\(233\) 5.89558 + 10.2114i 0.386232 + 0.668974i 0.991939 0.126714i \(-0.0404431\pi\)
−0.605707 + 0.795688i \(0.707110\pi\)
\(234\) 7.66550 13.2770i 0.501109 0.867946i
\(235\) 1.58129 2.73888i 0.103152 0.178665i
\(236\) −2.06459 3.57597i −0.134393 0.232776i
\(237\) 31.5807 2.05139
\(238\) 0 0
\(239\) −16.0692 −1.03943 −0.519716 0.854339i \(-0.673962\pi\)
−0.519716 + 0.854339i \(0.673962\pi\)
\(240\) −6.91408 11.9755i −0.446302 0.773017i
\(241\) 2.46771 4.27419i 0.158959 0.275325i −0.775535 0.631305i \(-0.782520\pi\)
0.934494 + 0.355980i \(0.115853\pi\)
\(242\) −3.68340 + 6.37983i −0.236778 + 0.410111i
\(243\) −30.4702 52.7760i −1.95467 3.38558i
\(244\) −13.3956 −0.857564
\(245\) 0 0
\(246\) 25.4314 1.62145
\(247\) 2.69175 + 4.66225i 0.171272 + 0.296652i
\(248\) −3.65111 + 6.32390i −0.231845 + 0.401568i
\(249\) −6.86388 + 11.8886i −0.434981 + 0.753409i
\(250\) −7.47606 12.9489i −0.472828 0.818961i
\(251\) −15.2439 −0.962185 −0.481092 0.876670i \(-0.659760\pi\)
−0.481092 + 0.876670i \(0.659760\pi\)
\(252\) 0 0
\(253\) 20.2964 1.27602
\(254\) 1.78491 + 3.09155i 0.111995 + 0.193981i
\(255\) 4.85725 8.41300i 0.304173 0.526842i
\(256\) −10.4302 + 18.0656i −0.651887 + 1.12910i
\(257\) −7.80825 13.5243i −0.487065 0.843622i 0.512824 0.858494i \(-0.328599\pi\)
−0.999889 + 0.0148720i \(0.995266\pi\)
\(258\) 25.2151 1.56982
\(259\) 0 0
\(260\) 1.28431 0.0796494
\(261\) −6.97374 12.0789i −0.431664 0.747664i
\(262\) 9.48270 16.4245i 0.585843 1.01471i
\(263\) −8.54668 + 14.8033i −0.527011 + 0.912810i 0.472493 + 0.881334i \(0.343354\pi\)
−0.999505 + 0.0314757i \(0.989979\pi\)
\(264\) −6.24970 10.8248i −0.384642 0.666220i
\(265\) 0.186313 0.0114451
\(266\) 0 0
\(267\) 1.40021 0.0856913
\(268\) 5.68108 + 9.83992i 0.347027 + 0.601069i
\(269\) 8.16841 14.1481i 0.498037 0.862625i −0.501961 0.864890i \(-0.667388\pi\)
0.999997 + 0.00226550i \(0.000721131\pi\)
\(270\) 14.1159 24.4495i 0.859066 1.48795i
\(271\) −6.24970 10.8248i −0.379642 0.657560i 0.611368 0.791347i \(-0.290620\pi\)
−0.991010 + 0.133787i \(0.957286\pi\)
\(272\) −15.9642 −0.967971
\(273\) 0 0
\(274\) 14.5507 0.879041
\(275\) −8.21509 14.2290i −0.495389 0.858038i
\(276\) 13.0334 22.5745i 0.784519 1.35883i
\(277\) 1.50000 2.59808i 0.0901263 0.156103i −0.817438 0.576017i \(-0.804606\pi\)
0.907564 + 0.419914i \(0.137940\pi\)
\(278\) −4.74135 8.21226i −0.284367 0.492538i
\(279\) −62.1389 −3.72016
\(280\) 0 0
\(281\) 0.831590 0.0496085 0.0248043 0.999692i \(-0.492104\pi\)
0.0248043 + 0.999692i \(0.492104\pi\)
\(282\) −11.4092 19.7612i −0.679406 1.17676i
\(283\) 5.52938 9.57716i 0.328687 0.569303i −0.653564 0.756871i \(-0.726727\pi\)
0.982252 + 0.187568i \(0.0600604\pi\)
\(284\) −3.63320 + 6.29289i −0.215591 + 0.373414i
\(285\) 7.80825 + 13.5243i 0.462521 + 0.801109i
\(286\) 7.21509 0.426637
\(287\) 0 0
\(288\) −57.2213 −3.37180
\(289\) 2.89245 + 5.00988i 0.170144 + 0.294699i
\(290\) 1.37224 2.37678i 0.0805804 0.139569i
\(291\) −11.9152 + 20.6377i −0.698481 + 1.20980i
\(292\) 11.5251 + 19.9620i 0.674453 + 1.16819i
\(293\) 26.9175 1.57254 0.786269 0.617884i \(-0.212010\pi\)
0.786269 + 0.617884i \(0.212010\pi\)
\(294\) 0 0
\(295\) −2.41228 −0.140448
\(296\) −2.33219 4.03947i −0.135556 0.234789i
\(297\) 33.7612 58.4761i 1.95902 3.39313i
\(298\) 2.32787 4.03199i 0.134850 0.233567i
\(299\) −2.62485 4.54637i −0.151799 0.262924i
\(300\) −21.1014 −1.21829
\(301\) 0 0
\(302\) −6.08712 −0.350274
\(303\) −23.6363 40.9393i −1.35787 2.35190i
\(304\) 12.8316 22.2250i 0.735942 1.27469i
\(305\) −3.91288 + 6.77731i −0.224051 + 0.388068i
\(306\) −25.6709 44.4634i −1.46751 2.54180i
\(307\) 15.1580 0.865110 0.432555 0.901608i \(-0.357612\pi\)
0.432555 + 0.901608i \(0.357612\pi\)
\(308\) 0 0
\(309\) 56.4636 3.21210
\(310\) −6.11358 10.5890i −0.347228 0.601417i
\(311\) 2.12253 3.67634i 0.120358 0.208466i −0.799551 0.600598i \(-0.794929\pi\)
0.919909 + 0.392132i \(0.128262\pi\)
\(312\) −1.61650 + 2.79986i −0.0915162 + 0.158511i
\(313\) 8.97666 + 15.5480i 0.507391 + 0.878827i 0.999963 + 0.00855523i \(0.00272325\pi\)
−0.492573 + 0.870271i \(0.663943\pi\)
\(314\) 1.34426 0.0758612
\(315\) 0 0
\(316\) 13.9821 0.786554
\(317\) 7.63320 + 13.2211i 0.428723 + 0.742571i 0.996760 0.0804326i \(-0.0256302\pi\)
−0.568037 + 0.823003i \(0.692297\pi\)
\(318\) 0.672132 1.16417i 0.0376913 0.0652832i
\(319\) 3.28199 5.68458i 0.183756 0.318275i
\(320\) −1.50060 2.59911i −0.0838860 0.145295i
\(321\) 34.0934 1.90291
\(322\) 0 0
\(323\) 18.0288 1.00315
\(324\) −25.0890 43.4555i −1.39384 2.41419i
\(325\) −2.12485 + 3.68035i −0.117865 + 0.204149i
\(326\) −1.21509 + 2.10460i −0.0672977 + 0.116563i
\(327\) 10.3866 + 17.9902i 0.574382 + 0.994858i
\(328\) −3.92839 −0.216909
\(329\) 0 0
\(330\) 20.9296 1.15214
\(331\) −8.63320 14.9531i −0.474524 0.821899i 0.525051 0.851071i \(-0.324046\pi\)
−0.999574 + 0.0291717i \(0.990713\pi\)
\(332\) −3.03893 + 5.26358i −0.166783 + 0.288876i
\(333\) 19.8460 34.3742i 1.08755 1.88370i
\(334\) 15.0700 + 26.1020i 0.824595 + 1.42824i
\(335\) 6.63783 0.362664
\(336\) 0 0
\(337\) −25.5415 −1.39133 −0.695666 0.718366i \(-0.744891\pi\)
−0.695666 + 0.718366i \(0.744891\pi\)
\(338\) −0.933099 1.61618i −0.0507539 0.0879083i
\(339\) −17.2205 + 29.8268i −0.935291 + 1.61997i
\(340\) 2.15051 3.72479i 0.116628 0.202005i
\(341\) −14.6219 25.3259i −0.791822 1.37148i
\(342\) 82.5344 4.46295
\(343\) 0 0
\(344\) −3.89498 −0.210003
\(345\) −7.61418 13.1882i −0.409934 0.710026i
\(346\) −14.7880 + 25.6136i −0.795009 + 1.37700i
\(347\) 6.31429 10.9367i 0.338969 0.587111i −0.645270 0.763954i \(-0.723255\pi\)
0.984239 + 0.176843i \(0.0565886\pi\)
\(348\) −4.21509 7.30075i −0.225953 0.391362i
\(349\) −35.6394 −1.90774 −0.953868 0.300226i \(-0.902938\pi\)
−0.953868 + 0.300226i \(0.902938\pi\)
\(350\) 0 0
\(351\) −17.4648 −0.932202
\(352\) −13.4648 23.3217i −0.717676 1.24305i
\(353\) 2.70674 4.68821i 0.144065 0.249528i −0.784959 0.619548i \(-0.787316\pi\)
0.929024 + 0.370020i \(0.120649\pi\)
\(354\) −8.70242 + 15.0730i −0.462528 + 0.801123i
\(355\) 2.12253 + 3.67634i 0.112652 + 0.195120i
\(356\) 0.619931 0.0328563
\(357\) 0 0
\(358\) −38.1914 −2.01848
\(359\) 9.41580 + 16.3086i 0.496947 + 0.860737i 0.999994 0.00352211i \(-0.00112113\pi\)
−0.503047 + 0.864259i \(0.667788\pi\)
\(360\) −3.43482 + 5.94928i −0.181031 + 0.313554i
\(361\) −4.99105 + 8.64475i −0.262687 + 0.454987i
\(362\) −6.14156 10.6375i −0.322793 0.559094i
\(363\) 13.2197 0.693856
\(364\) 0 0
\(365\) 13.4660 0.704842
\(366\) 28.2318 + 48.8989i 1.47570 + 2.55599i
\(367\) −11.5753 + 20.0489i −0.604223 + 1.04655i 0.387950 + 0.921680i \(0.373183\pi\)
−0.992174 + 0.124865i \(0.960150\pi\)
\(368\) −12.5127 + 21.6726i −0.652268 + 1.12976i
\(369\) −16.7145 28.9504i −0.870122 1.50710i
\(370\) 7.81025 0.406036
\(371\) 0 0
\(372\) −37.5582 −1.94730
\(373\) 16.5896 + 28.7341i 0.858979 + 1.48780i 0.872904 + 0.487893i \(0.162234\pi\)
−0.0139245 + 0.999903i \(0.504432\pi\)
\(374\) 12.0813 20.9254i 0.624709 1.08203i
\(375\) −13.4158 + 23.2368i −0.692789 + 1.19995i
\(376\) 1.76237 + 3.05252i 0.0908875 + 0.157422i
\(377\) −1.69779 −0.0874406
\(378\) 0 0
\(379\) 37.7853 1.94090 0.970451 0.241299i \(-0.0775733\pi\)
0.970451 + 0.241299i \(0.0775733\pi\)
\(380\) 3.45704 + 5.98777i 0.177342 + 0.307166i
\(381\) 3.20302 5.54779i 0.164096 0.284222i
\(382\) −11.8962 + 20.6048i −0.608661 + 1.05423i
\(383\) 0.115899 + 0.200743i 0.00592215 + 0.0102575i 0.868971 0.494862i \(-0.164782\pi\)
−0.863049 + 0.505120i \(0.831448\pi\)
\(384\) 24.9988 1.27571
\(385\) 0 0
\(386\) 4.23180 0.215393
\(387\) −16.5723 28.7041i −0.842419 1.45911i
\(388\) −5.27536 + 9.13719i −0.267816 + 0.463870i
\(389\) −4.67676 + 8.10039i −0.237121 + 0.410706i −0.959887 0.280387i \(-0.909537\pi\)
0.722766 + 0.691093i \(0.242871\pi\)
\(390\) −2.70674 4.68821i −0.137061 0.237397i
\(391\) −17.5807 −0.889094
\(392\) 0 0
\(393\) −34.0334 −1.71676
\(394\) 17.4469 + 30.2189i 0.878962 + 1.52241i
\(395\) 4.08420 7.07405i 0.205499 0.355934i
\(396\) 23.5461 40.7830i 1.18324 2.04942i
\(397\) 4.87224 + 8.43896i 0.244530 + 0.423539i 0.962000 0.273051i \(-0.0880328\pi\)
−0.717469 + 0.696590i \(0.754700\pi\)
\(398\) −37.1700 −1.86317
\(399\) 0 0
\(400\) 20.2583 1.01292
\(401\) −4.86620 8.42850i −0.243006 0.420899i 0.718563 0.695462i \(-0.244800\pi\)
−0.961569 + 0.274563i \(0.911467\pi\)
\(402\) 23.9463 41.4762i 1.19433 2.06864i
\(403\) −3.78199 + 6.55060i −0.188395 + 0.326309i
\(404\) −10.4648 18.1256i −0.520643 0.901780i
\(405\) −29.3143 −1.45664
\(406\) 0 0
\(407\) 18.6799 0.925928
\(408\) 5.41348 + 9.37642i 0.268007 + 0.464202i
\(409\) −6.18652 + 10.7154i −0.305904 + 0.529841i −0.977462 0.211111i \(-0.932292\pi\)
0.671558 + 0.740952i \(0.265625\pi\)
\(410\) 3.28894 5.69661i 0.162429 0.281336i
\(411\) −13.0556 22.6130i −0.643987 1.11542i
\(412\) 24.9988 1.23160
\(413\) 0 0
\(414\) −80.4831 −3.95553
\(415\) 1.77536 + 3.07501i 0.0871489 + 0.150946i
\(416\) −3.48270 + 6.03221i −0.170753 + 0.295753i
\(417\) −8.50835 + 14.7369i −0.416656 + 0.721669i
\(418\) 19.4212 + 33.6386i 0.949924 + 1.64532i
\(419\) 21.1054 1.03107 0.515534 0.856869i \(-0.327594\pi\)
0.515534 + 0.856869i \(0.327594\pi\)
\(420\) 0 0
\(421\) 23.2618 1.13371 0.566855 0.823818i \(-0.308160\pi\)
0.566855 + 0.823818i \(0.308160\pi\)
\(422\) −0.602108 1.04288i −0.0293102 0.0507667i
\(423\) −14.9971 + 25.9757i −0.729183 + 1.26298i
\(424\) −0.103824 + 0.179829i −0.00504215 + 0.00873326i
\(425\) 7.11590 + 12.3251i 0.345172 + 0.597855i
\(426\) 30.6286 1.48396
\(427\) 0 0
\(428\) 15.0946 0.729623
\(429\) −6.47374 11.2129i −0.312555 0.541362i
\(430\) 3.26097 5.64816i 0.157258 0.272379i
\(431\) 8.49477 14.7134i 0.409179 0.708718i −0.585619 0.810586i \(-0.699149\pi\)
0.994798 + 0.101868i \(0.0324819\pi\)
\(432\) 41.6274 + 72.1007i 2.00280 + 3.46895i
\(433\) −30.8604 −1.48305 −0.741527 0.670923i \(-0.765898\pi\)
−0.741527 + 0.670923i \(0.765898\pi\)
\(434\) 0 0
\(435\) −4.92496 −0.236134
\(436\) 4.59859 + 7.96500i 0.220233 + 0.381454i
\(437\) 14.1309 24.4754i 0.675972 1.17082i
\(438\) 48.5792 84.1416i 2.32120 4.02044i
\(439\) −9.59859 16.6253i −0.458116 0.793480i 0.540745 0.841186i \(-0.318142\pi\)
−0.998861 + 0.0477062i \(0.984809\pi\)
\(440\) −3.23300 −0.154127
\(441\) 0 0
\(442\) −6.24970 −0.297268
\(443\) 17.1888 + 29.7719i 0.816666 + 1.41451i 0.908125 + 0.418699i \(0.137514\pi\)
−0.0914589 + 0.995809i \(0.529153\pi\)
\(444\) 11.9954 20.7766i 0.569275 0.986013i
\(445\) 0.181083 0.313645i 0.00858417 0.0148682i
\(446\) 5.44145 + 9.42487i 0.257660 + 0.446281i
\(447\) −8.35472 −0.395165
\(448\) 0 0
\(449\) 29.6274 1.39820 0.699101 0.715023i \(-0.253584\pi\)
0.699101 + 0.715023i \(0.253584\pi\)
\(450\) 32.5761 + 56.4234i 1.53565 + 2.65982i
\(451\) 7.86620 13.6247i 0.370405 0.641560i
\(452\) −7.62425 + 13.2056i −0.358615 + 0.621139i
\(453\) 5.46167 + 9.45989i 0.256612 + 0.444464i
\(454\) 29.3598 1.37792
\(455\) 0 0
\(456\) −17.4048 −0.815056
\(457\) 8.51962 + 14.7564i 0.398531 + 0.690276i 0.993545 0.113439i \(-0.0361868\pi\)
−0.595014 + 0.803715i \(0.702853\pi\)
\(458\) −8.28431 + 14.3488i −0.387100 + 0.670477i
\(459\) −29.2439 + 50.6519i −1.36499 + 2.36423i
\(460\) −3.37112 5.83895i −0.157179 0.272242i
\(461\) 15.1280 0.704580 0.352290 0.935891i \(-0.385403\pi\)
0.352290 + 0.935891i \(0.385403\pi\)
\(462\) 0 0
\(463\) 26.1221 1.21400 0.607000 0.794702i \(-0.292373\pi\)
0.607000 + 0.794702i \(0.292373\pi\)
\(464\) 4.04668 + 7.00906i 0.187863 + 0.325387i
\(465\) −10.9708 + 19.0020i −0.508760 + 0.881198i
\(466\) 11.0023 19.0566i 0.509672 0.882779i
\(467\) −11.4594 19.8482i −0.530276 0.918464i −0.999376 0.0353196i \(-0.988755\pi\)
0.469100 0.883145i \(-0.344578\pi\)
\(468\) −12.1805 −0.563043
\(469\) 0 0
\(470\) −5.90200 −0.272239
\(471\) −1.20614 2.08910i −0.0555760 0.0962605i
\(472\) 1.34426 2.32833i 0.0618747 0.107170i
\(473\) 7.79930 13.5088i 0.358612 0.621134i
\(474\) −29.4679 51.0399i −1.35351 2.34434i
\(475\) −22.8783 −1.04973
\(476\) 0 0
\(477\) −1.76700 −0.0809056
\(478\) 14.9942 + 25.9707i 0.685817 + 1.18787i
\(479\) −17.5957 + 30.4766i −0.803967 + 1.39251i 0.113019 + 0.993593i \(0.463948\pi\)
−0.916986 + 0.398919i \(0.869385\pi\)
\(480\) −10.1026 + 17.4983i −0.461120 + 0.798683i
\(481\) −2.41580 4.18428i −0.110151 0.190787i
\(482\) −9.21046 −0.419525
\(483\) 0 0
\(484\) 5.85293 0.266042
\(485\) 3.08189 + 5.33799i 0.139941 + 0.242386i
\(486\) −56.8635 + 98.4905i −2.57938 + 4.46762i
\(487\) 14.1505 24.5094i 0.641221 1.11063i −0.343940 0.938992i \(-0.611762\pi\)
0.985161 0.171635i \(-0.0549050\pi\)
\(488\) −4.36097 7.55342i −0.197412 0.341927i
\(489\) 4.36097 0.197210
\(490\) 0 0
\(491\) 8.24970 0.372304 0.186152 0.982521i \(-0.440398\pi\)
0.186152 + 0.982521i \(0.440398\pi\)
\(492\) −10.1026 17.4983i −0.455462 0.788883i
\(493\) −2.84286 + 4.92397i −0.128036 + 0.221765i
\(494\) 5.02334 8.70068i 0.226011 0.391462i
\(495\) −13.7557 23.8256i −0.618274 1.07088i
\(496\) 36.0576 1.61903
\(497\) 0 0
\(498\) 25.6187 1.14800
\(499\) 8.36328 + 14.4856i 0.374392 + 0.648466i 0.990236 0.139402i \(-0.0445181\pi\)
−0.615844 + 0.787868i \(0.711185\pi\)
\(500\) −5.93974 + 10.2879i −0.265633 + 0.460090i
\(501\) 27.0432 46.8401i 1.20820 2.09266i
\(502\) 14.2240 + 24.6368i 0.634850 + 1.09959i
\(503\) 21.2213 0.946213 0.473106 0.881005i \(-0.343133\pi\)
0.473106 + 0.881005i \(0.343133\pi\)
\(504\) 0 0
\(505\) −12.2272 −0.544102
\(506\) −18.9385 32.8025i −0.841921 1.45825i
\(507\) −1.67445 + 2.90023i −0.0743648 + 0.128804i
\(508\) 1.41811 2.45624i 0.0629185 0.108978i
\(509\) 20.3024 + 35.1648i 0.899889 + 1.55865i 0.827635 + 0.561267i \(0.189686\pi\)
0.0722543 + 0.997386i \(0.476981\pi\)
\(510\) −18.1292 −0.802773
\(511\) 0 0
\(512\) 24.0000 1.06066
\(513\) −47.0109 81.4252i −2.07558 3.59501i
\(514\) −14.5717 + 25.2390i −0.642732 + 1.11324i
\(515\) 7.30221 12.6478i 0.321774 0.557329i
\(516\) −10.0167 17.3494i −0.440961 0.763767i
\(517\) −14.1159 −0.620817
\(518\) 0 0
\(519\) 53.0743 2.32970
\(520\) 0.418110 + 0.724188i 0.0183354 + 0.0317578i
\(521\) −1.73240 + 3.00060i −0.0758977 + 0.131459i −0.901476 0.432828i \(-0.857516\pi\)
0.825579 + 0.564287i \(0.190849\pi\)
\(522\) −13.0144 + 22.5416i −0.569624 + 0.986618i
\(523\) −2.78491 4.82360i −0.121776 0.210921i 0.798692 0.601740i \(-0.205525\pi\)
−0.920468 + 0.390818i \(0.872192\pi\)
\(524\) −15.0680 −0.658249
\(525\) 0 0
\(526\) 31.8996 1.39089
\(527\) 12.6655 + 21.9373i 0.551718 + 0.955603i
\(528\) −30.8604 + 53.4517i −1.34303 + 2.32619i
\(529\) −2.27968 + 3.94852i −0.0991164 + 0.171675i
\(530\) −0.173848 0.301114i −0.00755149 0.0130796i
\(531\) 22.8783 0.992832
\(532\) 0 0
\(533\) −4.06922 −0.176257
\(534\) −1.30653 2.26298i −0.0565392 0.0979287i
\(535\) 4.40916 7.63689i 0.190625 0.330171i
\(536\) −3.69899 + 6.40683i −0.159772 + 0.276733i
\(537\) 34.2672 + 59.3526i 1.47874 + 2.56125i
\(538\) −30.4877 −1.31442
\(539\) 0 0
\(540\) −22.4302 −0.965241
\(541\) −12.1182 20.9894i −0.521003 0.902403i −0.999702 0.0244241i \(-0.992225\pi\)
0.478699 0.877979i \(-0.341109\pi\)
\(542\) −11.6632 + 20.2012i −0.500976 + 0.867717i
\(543\) −11.0210 + 19.0890i −0.472957 + 0.819186i
\(544\) 11.6632 + 20.2012i 0.500055 + 0.866120i
\(545\) 5.37304 0.230156
\(546\) 0 0
\(547\) 15.7733 0.674416 0.337208 0.941430i \(-0.390518\pi\)
0.337208 + 0.941430i \(0.390518\pi\)
\(548\) −5.78028 10.0117i −0.246921 0.427680i
\(549\) 37.1101 64.2765i 1.58382 2.74326i
\(550\) −15.3310 + 26.5541i −0.653716 + 1.13227i
\(551\) −4.57002 7.91551i −0.194690 0.337212i
\(552\) 16.9723 0.722387
\(553\) 0 0
\(554\) −5.59859 −0.237861
\(555\) −7.00775 12.1378i −0.297463 0.515220i
\(556\) −3.76700 + 6.52464i −0.159757 + 0.276707i
\(557\) 8.61067 14.9141i 0.364846 0.631931i −0.623906 0.781500i \(-0.714455\pi\)
0.988751 + 0.149568i \(0.0477884\pi\)
\(558\) 57.9817 + 100.427i 2.45456 + 4.25143i
\(559\) −4.03461 −0.170646
\(560\) 0 0
\(561\) −43.3598 −1.83065
\(562\) −0.775956 1.34400i −0.0327317 0.0566930i
\(563\) 7.67989 13.3020i 0.323669 0.560610i −0.657573 0.753390i \(-0.728417\pi\)
0.981242 + 0.192780i \(0.0617504\pi\)
\(564\) −9.06459 + 15.7003i −0.381688 + 0.661103i
\(565\) 4.45413 + 7.71477i 0.187386 + 0.324563i
\(566\) −20.6378 −0.867473
\(567\) 0 0
\(568\) −4.73120 −0.198517
\(569\) −11.8610 20.5438i −0.497238 0.861241i 0.502757 0.864428i \(-0.332319\pi\)
−0.999995 + 0.00318672i \(0.998986\pi\)
\(570\) 14.5717 25.2390i 0.610343 1.05715i
\(571\) 13.6595 23.6589i 0.571631 0.990093i −0.424768 0.905302i \(-0.639644\pi\)
0.996399 0.0847910i \(-0.0270223\pi\)
\(572\) −2.86620 4.96440i −0.119842 0.207572i
\(573\) 42.6954 1.78363
\(574\) 0 0
\(575\) 22.3097 0.930377
\(576\) 14.2318 + 24.6502i 0.592992 + 1.02709i
\(577\) 11.6332 20.1493i 0.484297 0.838826i −0.515541 0.856865i \(-0.672409\pi\)
0.999837 + 0.0180388i \(0.00574224\pi\)
\(578\) 5.39789 9.34942i 0.224523 0.388885i
\(579\) −3.79698 6.57657i −0.157797 0.273313i
\(580\) −2.18048 −0.0905397
\(581\) 0 0
\(582\) 44.4722 1.84343
\(583\) −0.415795 0.720178i −0.0172205 0.0298267i
\(584\) −7.50403 + 12.9974i −0.310519 + 0.537835i
\(585\) −3.55795 + 6.16255i −0.147103 + 0.254790i
\(586\) −25.1167 43.5034i −1.03756 1.79711i
\(587\) 45.7266 1.88734 0.943669 0.330892i \(-0.107349\pi\)
0.943669 + 0.330892i \(0.107349\pi\)
\(588\) 0 0
\(589\) −40.7207 −1.67787
\(590\) 2.25090 + 3.89867i 0.0926680 + 0.160506i
\(591\) 31.3085 54.2278i 1.28786 2.23064i
\(592\) −11.5161 + 19.9465i −0.473309 + 0.819795i
\(593\) −14.6949 25.4523i −0.603446 1.04520i −0.992295 0.123898i \(-0.960460\pi\)
0.388849 0.921302i \(-0.372873\pi\)
\(594\) −126.010 −5.17026
\(595\) 0 0
\(596\) −3.69899 −0.151516
\(597\) 33.3508 + 57.7653i 1.36496 + 2.36418i
\(598\) −4.89849 + 8.48444i −0.200314 + 0.346954i
\(599\) −11.0294 + 19.1034i −0.450648 + 0.780546i −0.998426 0.0560780i \(-0.982140\pi\)
0.547778 + 0.836624i \(0.315474\pi\)
\(600\) −6.86963 11.8986i −0.280452 0.485756i
\(601\) −30.8604 −1.25882 −0.629410 0.777073i \(-0.716704\pi\)
−0.629410 + 0.777073i \(0.716704\pi\)
\(602\) 0 0
\(603\) −62.9537 −2.56367
\(604\) 2.41811 + 4.18829i 0.0983915 + 0.170419i
\(605\) 1.70965 2.96121i 0.0695073 0.120390i
\(606\) −44.1101 + 76.4009i −1.79185 + 3.10357i
\(607\) 18.2431 + 31.5979i 0.740463 + 1.28252i 0.952285 + 0.305211i \(0.0987271\pi\)
−0.211821 + 0.977308i \(0.567940\pi\)
\(608\) −37.4982 −1.52075
\(609\) 0 0
\(610\) 14.6044 0.591316
\(611\) 1.82555 + 3.16195i 0.0738540 + 0.127919i
\(612\) −20.3956 + 35.3262i −0.824442 + 1.42798i
\(613\) −14.4994 + 25.1137i −0.585625 + 1.01433i 0.409172 + 0.912457i \(0.365818\pi\)
−0.994797 + 0.101875i \(0.967516\pi\)
\(614\) −14.1439 24.4979i −0.570800 0.988655i
\(615\) −11.8040 −0.475984
\(616\) 0 0
\(617\) −41.6515 −1.67683 −0.838414 0.545035i \(-0.816517\pi\)
−0.838414 + 0.545035i \(0.816517\pi\)
\(618\) −52.6861 91.2551i −2.11935 3.67082i
\(619\) 6.24970 10.8248i 0.251197 0.435085i −0.712659 0.701511i \(-0.752509\pi\)
0.963856 + 0.266425i \(0.0858426\pi\)
\(620\) −4.85725 + 8.41300i −0.195072 + 0.337874i
\(621\) 45.8425 + 79.4015i 1.83959 + 3.18627i
\(622\) −7.92214 −0.317649
\(623\) 0 0
\(624\) 15.9642 0.639079
\(625\) −7.15423 12.3915i −0.286169 0.495660i
\(626\) 16.7522 29.0157i 0.669554 1.15970i
\(627\) 34.8514 60.3644i 1.39183 2.41072i
\(628\) −0.534009 0.924931i −0.0213093 0.0369088i
\(629\) −16.1805 −0.645158
\(630\) 0 0
\(631\) −35.5582 −1.41555 −0.707774 0.706439i \(-0.750300\pi\)
−0.707774 + 0.706439i \(0.750300\pi\)
\(632\) 4.55191 + 7.88414i 0.181065 + 0.313614i
\(633\) −1.08048 + 1.87145i −0.0429453 + 0.0743835i
\(634\) 14.2451 24.6732i 0.565744 0.979897i
\(635\) −0.828467 1.43495i −0.0328767 0.0569441i
\(636\) −1.06802 −0.0423497
\(637\) 0 0
\(638\) −12.2497 −0.484970
\(639\) −20.1303 34.8667i −0.796342 1.37930i
\(640\) 3.23300 5.59971i 0.127795 0.221348i
\(641\) −0.680484 + 1.17863i −0.0268775 + 0.0465532i −0.879151 0.476543i \(-0.841890\pi\)
0.852274 + 0.523096i \(0.175223\pi\)
\(642\) −31.8125 55.1008i −1.25554 2.17466i
\(643\) −12.1867 −0.480598 −0.240299 0.970699i \(-0.577245\pi\)
−0.240299 + 0.970699i \(0.577245\pi\)
\(644\) 0 0
\(645\) −11.7036 −0.460829
\(646\) −16.8226 29.1377i −0.661878 1.14641i
\(647\) −1.86076 + 3.22293i −0.0731540 + 0.126706i −0.900282 0.435307i \(-0.856640\pi\)
0.827128 + 0.562014i \(0.189973\pi\)
\(648\) 16.3356 28.2941i 0.641724 1.11150i
\(649\) 5.38350 + 9.32450i 0.211321 + 0.366019i
\(650\) 7.93078 0.311071
\(651\) 0 0
\(652\) 1.93078 0.0756153
\(653\) 22.5294 + 39.0220i 0.881643 + 1.52705i 0.849514 + 0.527566i \(0.176895\pi\)
0.0321288 + 0.999484i \(0.489771\pi\)
\(654\) 19.3835 33.5732i 0.757955 1.31282i
\(655\) −4.40141 + 7.62346i −0.171977 + 0.297873i
\(656\) 9.69899 + 16.7991i 0.378682 + 0.655896i
\(657\) −127.713 −4.98254
\(658\) 0 0
\(659\) 5.37887 0.209531 0.104766 0.994497i \(-0.466591\pi\)
0.104766 + 0.994497i \(0.466591\pi\)
\(660\) −8.31429 14.4008i −0.323633 0.560549i
\(661\) −21.2468 + 36.8005i −0.826404 + 1.43137i 0.0744372 + 0.997226i \(0.476284\pi\)
−0.900841 + 0.434148i \(0.857049\pi\)
\(662\) −16.1113 + 27.9055i −0.626182 + 1.08458i
\(663\) 5.60755 + 9.71255i 0.217779 + 0.377204i
\(664\) −3.95733 −0.153574
\(665\) 0 0
\(666\) −74.0731 −2.87027
\(667\) 4.45644 + 7.71878i 0.172554 + 0.298872i
\(668\) 11.9731 20.7381i 0.463255 0.802381i
\(669\) 9.76469 16.9129i 0.377525 0.653892i
\(670\) −6.19376 10.7279i −0.239286 0.414455i
\(671\) 34.9296 1.34844
\(672\) 0 0
\(673\) −37.3765 −1.44076 −0.720379 0.693581i \(-0.756032\pi\)
−0.720379 + 0.693581i \(0.756032\pi\)
\(674\) 23.8327 + 41.2795i 0.918002 + 1.59003i
\(675\) 37.1101 64.2765i 1.42837 2.47400i
\(676\) −0.741348 + 1.28405i −0.0285134 + 0.0493866i
\(677\) −21.7378 37.6510i −0.835453 1.44705i −0.893661 0.448742i \(-0.851872\pi\)
0.0582083 0.998304i \(-0.481461\pi\)
\(678\) 64.2738 2.46842
\(679\) 0 0
\(680\) 2.80041 0.107391
\(681\) −26.3431 45.6275i −1.00947 1.74845i
\(682\) −27.2874 + 47.2632i −1.04489 + 1.80980i
\(683\) −15.6978 + 27.1894i −0.600659 + 1.04037i 0.392062 + 0.919939i \(0.371762\pi\)
−0.992721 + 0.120434i \(0.961572\pi\)
\(684\) −32.7868 56.7885i −1.25364 2.17136i
\(685\) −6.75373 −0.258047
\(686\) 0 0
\(687\) 29.7324 1.13436
\(688\) 9.61650 + 16.6563i 0.366626 + 0.635014i
\(689\) −0.107546 + 0.186276i −0.00409719 + 0.00709653i
\(690\) −14.2096 + 24.6117i −0.540949 + 0.936952i
\(691\) 6.72053 + 11.6403i 0.255661 + 0.442818i 0.965075 0.261974i \(-0.0843736\pi\)
−0.709414 + 0.704792i \(0.751040\pi\)
\(692\) 23.4982 0.893268
\(693\) 0 0
\(694\) −23.5674 −0.894607
\(695\) 2.20070 + 3.81173i 0.0834774 + 0.144587i
\(696\) 2.74447 4.75356i 0.104029 0.180183i
\(697\) −6.81369 + 11.8017i −0.258087 + 0.447019i
\(698\) 33.2551 + 57.5996i 1.25873 + 2.18018i
\(699\) −39.4873 −1.49355
\(700\) 0 0
\(701\) −28.0346 −1.05885 −0.529426 0.848356i \(-0.677593\pi\)
−0.529426 + 0.848356i \(0.677593\pi\)
\(702\) 16.2964 + 28.2262i 0.615067 + 1.06533i
\(703\) 13.0054 22.5261i 0.490509 0.849587i
\(704\) −6.69779 + 11.6009i −0.252432 + 0.437226i
\(705\) 5.29558 + 9.17221i 0.199443 + 0.345445i
\(706\) −10.1026 −0.380217
\(707\) 0 0
\(708\) 13.8282 0.519694
\(709\) 20.1424 + 34.8876i 0.756462 + 1.31023i 0.944644 + 0.328097i \(0.106407\pi\)
−0.188182 + 0.982134i \(0.560259\pi\)
\(710\) 3.96107 6.86078i 0.148656 0.257480i
\(711\) −38.7349 + 67.0909i −1.45267 + 2.51610i
\(712\) 0.201820 + 0.349563i 0.00756353 + 0.0131004i
\(713\) 39.7087 1.48710
\(714\) 0 0
\(715\) −3.34889 −0.125242
\(716\) 15.1715 + 26.2779i 0.566987 + 0.982050i
\(717\) 26.9071 46.6044i 1.00486 1.74047i
\(718\) 17.5717 30.4351i 0.655772 1.13583i
\(719\) 8.37224 + 14.5011i 0.312232 + 0.540801i 0.978845 0.204602i \(-0.0655901\pi\)
−0.666613 + 0.745404i \(0.732257\pi\)
\(720\) 33.9215 1.26418
\(721\) 0 0
\(722\) 18.6286 0.693284
\(723\) 8.26409 + 14.3138i 0.307345 + 0.532337i
\(724\) −4.87947 + 8.45149i −0.181344 + 0.314097i
\(725\) 3.60755 6.24845i 0.133981 0.232062i
\(726\) −12.3353 21.3654i −0.457806 0.792944i
\(727\) −51.4982 −1.90996 −0.954981 0.296666i \(-0.904125\pi\)
−0.954981 + 0.296666i \(0.904125\pi\)
\(728\) 0 0
\(729\) 102.556 3.79836
\(730\) −12.5651 21.7634i −0.465055 0.805500i
\(731\) −6.75574 + 11.7013i −0.249870 + 0.432788i
\(732\) 22.4302 38.8502i 0.829043 1.43595i
\(733\) 16.9158 + 29.2990i 0.624799 + 1.08218i 0.988580 + 0.150699i \(0.0481525\pi\)
−0.363781 + 0.931485i \(0.618514\pi\)
\(734\) 43.2034 1.59467
\(735\) 0 0
\(736\) 36.5662 1.34785
\(737\) −14.8137 25.6581i −0.545669 0.945127i
\(738\) −31.1926 + 54.0271i −1.14821 + 1.98876i
\(739\) −10.3345 + 17.8999i −0.380161 + 0.658458i −0.991085 0.133231i \(-0.957465\pi\)
0.610924 + 0.791689i \(0.290798\pi\)
\(740\) −3.10263 5.37391i −0.114055 0.197549i
\(741\) −18.0288 −0.662304
\(742\) 0 0
\(743\) −29.6966 −1.08946 −0.544731 0.838611i \(-0.683368\pi\)
−0.544731 + 0.838611i \(0.683368\pi\)
\(744\) −12.2272 21.1781i −0.448270 0.776426i
\(745\) −1.08048 + 1.87145i −0.0395858 + 0.0685647i
\(746\) 30.9596 53.6235i 1.13351 1.96330i
\(747\) −16.8376 29.1636i −0.616057 1.06704i
\(748\) −19.1972 −0.701919
\(749\) 0 0
\(750\) 50.0731 1.82841
\(751\) 6.01148 + 10.4122i 0.219362 + 0.379946i 0.954613 0.297849i \(-0.0962691\pi\)
−0.735251 + 0.677795i \(0.762936\pi\)
\(752\) 8.70242 15.0730i 0.317345 0.549657i
\(753\) 25.5251 44.2107i 0.930185 1.61113i
\(754\) 1.58420 + 2.74392i 0.0576933 + 0.0999278i
\(755\) 2.82534 0.102825
\(756\) 0 0
\(757\) −30.2906 −1.10093 −0.550464 0.834859i \(-0.685549\pi\)
−0.550464 + 0.834859i \(0.685549\pi\)
\(758\) −35.2575 61.0677i −1.28061 2.21808i
\(759\) −33.9852 + 58.8641i −1.23359 + 2.13663i
\(760\) −2.25090 + 3.89867i −0.0816487 + 0.141420i
\(761\) 22.9792 + 39.8011i 0.832995 + 1.44279i 0.895653 + 0.444754i \(0.146709\pi\)
−0.0626580 + 0.998035i \(0.519958\pi\)
\(762\) −11.9549 −0.433082
\(763\) 0 0
\(764\) 18.9030 0.683888
\(765\) 11.9152 + 20.6377i 0.430795 + 0.746159i
\(766\) 0.216290 0.374626i 0.00781488 0.0135358i
\(767\) 1.39245 2.41180i 0.0502786 0.0870851i
\(768\) −34.9296 60.4998i −1.26041 2.18310i
\(769\) 4.03924 0.145659 0.0728293 0.997344i \(-0.476797\pi\)
0.0728293 + 0.997344i \(0.476797\pi\)
\(770\) 0 0
\(771\) 52.2980 1.88347
\(772\) −1.68108 2.91172i −0.0605035 0.104795i
\(773\) −18.0588 + 31.2787i −0.649528 + 1.12502i 0.333707 + 0.942677i \(0.391700\pi\)
−0.983236 + 0.182339i \(0.941633\pi\)
\(774\) −30.9273 + 53.5676i −1.11166 + 1.92545i
\(775\) −16.0723 27.8381i −0.577335 0.999974i
\(776\) −6.86963 −0.246605
\(777\) 0 0
\(778\) 17.4555 0.625811
\(779\) −10.9533 18.9717i −0.392443 0.679732i
\(780\) −2.15051 + 3.72479i −0.0770005 + 0.133369i
\(781\) 9.47374 16.4090i 0.338997 0.587160i
\(782\) 16.4045 + 28.4135i 0.586625 + 1.01606i
\(783\)