Properties

Label 637.2.q.i.589.3
Level $637$
Weight $2$
Character 637.589
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.2346760387617129.1
Defining polynomial: \(x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 589.3
Root \(-1.18541 - 0.771231i\) of defining polynomial
Character \(\chi\) \(=\) 637.589
Dual form 637.2.q.i.491.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.433001 - 0.249993i) q^{2} +(0.424801 - 0.735776i) q^{3} +(-0.875007 - 1.51556i) q^{4} +1.04248i q^{5} +(-0.367878 + 0.212395i) q^{6} +1.87496i q^{8} +(1.13909 + 1.97296i) q^{9} +O(q^{10})\) \(q+(-0.433001 - 0.249993i) q^{2} +(0.424801 - 0.735776i) q^{3} +(-0.875007 - 1.51556i) q^{4} +1.04248i q^{5} +(-0.367878 + 0.212395i) q^{6} +1.87496i q^{8} +(1.13909 + 1.97296i) q^{9} +(0.260612 - 0.451393i) q^{10} +(3.43579 + 1.98365i) q^{11} -1.48681 q^{12} +(3.57504 - 0.468096i) q^{13} +(0.767029 + 0.442844i) q^{15} +(-1.28129 + 2.21925i) q^{16} +(0.0710177 + 0.123006i) q^{17} -1.13906i q^{18} +(-4.77160 + 2.75488i) q^{19} +(1.57993 - 0.912173i) q^{20} +(-0.991800 - 1.71785i) q^{22} +(2.19549 - 3.80270i) q^{23} +(1.37955 + 0.796483i) q^{24} +3.91325 q^{25} +(-1.66502 - 0.691049i) q^{26} +4.48435 q^{27} +(4.19880 - 7.27253i) q^{29} +(-0.221416 - 0.383504i) q^{30} +2.84652i q^{31} +(4.35712 - 2.51558i) q^{32} +(2.91905 - 1.68531i) q^{33} -0.0710158i q^{34} +(1.99342 - 3.45271i) q^{36} +(0.730221 + 0.421593i) q^{37} +2.75481 q^{38} +(1.17426 - 2.82928i) q^{39} -1.95460 q^{40} +(-10.4766 - 6.04869i) q^{41} +(2.41161 + 4.17704i) q^{43} -6.94284i q^{44} +(-2.05676 + 1.18747i) q^{45} +(-1.90130 + 1.09772i) q^{46} +4.55648i q^{47} +(1.08858 + 1.88548i) q^{48} +(-1.69444 - 0.978285i) q^{50} +0.120673 q^{51} +(-3.83761 - 5.00858i) q^{52} -0.279600 q^{53} +(-1.94173 - 1.12106i) q^{54} +(-2.06791 + 3.58172i) q^{55} +4.68111i q^{57} +(-3.63617 + 2.09934i) q^{58} +(9.33705 - 5.39075i) q^{59} -1.54997i q^{60} +(-2.93177 - 5.07797i) q^{61} +(0.711612 - 1.23255i) q^{62} +2.60963 q^{64} +(0.487979 + 3.72689i) q^{65} -1.68527 q^{66} +(4.45524 + 2.57223i) q^{67} +(0.124282 - 0.215263i) q^{68} +(-1.86529 - 3.23078i) q^{69} +(-3.20326 + 1.84940i) q^{71} +(-3.69921 + 2.13574i) q^{72} +6.61281i q^{73} +(-0.210791 - 0.365101i) q^{74} +(1.66235 - 2.87927i) q^{75} +(8.35036 + 4.82108i) q^{76} +(-1.21576 + 0.931521i) q^{78} +11.9227 q^{79} +(-2.31352 - 1.33571i) q^{80} +(-1.51231 + 2.61940i) q^{81} +(3.02426 + 5.23818i) q^{82} +2.87321i q^{83} +(-0.128231 + 0.0740342i) q^{85} -2.41155i q^{86} +(-3.56730 - 6.17875i) q^{87} +(-3.71926 + 6.44195i) q^{88} +(1.51351 + 0.873824i) q^{89} +1.18744 q^{90} -7.68427 q^{92} +(2.09440 + 1.20921i) q^{93} +(1.13909 - 1.97296i) q^{94} +(-2.87190 - 4.97427i) q^{95} -4.27449i q^{96} +(-2.34079 + 1.35145i) q^{97} +9.03822i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 3q^{3} + 4q^{4} + 9q^{6} - q^{9} + O(q^{10}) \) \( 12q + 3q^{3} + 4q^{4} + 9q^{6} - q^{9} - 12q^{10} - 12q^{11} - 2q^{12} + 2q^{13} - 12q^{15} - 8q^{16} - 17q^{17} + 9q^{19} + 3q^{20} - 15q^{22} + 3q^{23} + 15q^{24} + 10q^{25} - 15q^{26} - 12q^{27} - q^{29} + 11q^{30} - 18q^{32} - 6q^{33} - 13q^{36} - 15q^{37} + 38q^{38} + 5q^{39} - 2q^{40} + 6q^{41} + 11q^{43} - 9q^{45} + 30q^{46} - 19q^{48} + 18q^{50} - 8q^{51} + 40q^{52} + 16q^{53} + 6q^{54} + 15q^{55} + 24q^{58} + 27q^{59} - 5q^{61} - 41q^{62} + 2q^{64} - 18q^{65} - 68q^{66} - 15q^{67} + 11q^{68} - 7q^{69} + 30q^{71} - 57q^{72} - 33q^{74} - q^{75} + 45q^{76} + 44q^{78} + 70q^{79} - 63q^{80} + 14q^{81} - 5q^{82} - 21q^{85} - 10q^{87} - 14q^{88} + 48q^{89} - 66q^{92} + 81q^{93} - q^{94} + 2q^{95} + 3q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.433001 0.249993i −0.306178 0.176772i 0.339037 0.940773i \(-0.389899\pi\)
−0.645215 + 0.764001i \(0.723232\pi\)
\(3\) 0.424801 0.735776i 0.245259 0.424801i −0.716946 0.697129i \(-0.754460\pi\)
0.962204 + 0.272328i \(0.0877937\pi\)
\(4\) −0.875007 1.51556i −0.437503 0.757778i
\(5\) 1.04248i 0.466209i 0.972452 + 0.233105i \(0.0748884\pi\)
−0.972452 + 0.233105i \(0.925112\pi\)
\(6\) −0.367878 + 0.212395i −0.150186 + 0.0867098i
\(7\) 0 0
\(8\) 1.87496i 0.662897i
\(9\) 1.13909 + 1.97296i 0.379696 + 0.657653i
\(10\) 0.260612 0.451393i 0.0824127 0.142743i
\(11\) 3.43579 + 1.98365i 1.03593 + 0.598094i 0.918677 0.395009i \(-0.129258\pi\)
0.117251 + 0.993102i \(0.462592\pi\)
\(12\) −1.48681 −0.429206
\(13\) 3.57504 0.468096i 0.991537 0.129827i
\(14\) 0 0
\(15\) 0.767029 + 0.442844i 0.198046 + 0.114342i
\(16\) −1.28129 + 2.21925i −0.320322 + 0.554813i
\(17\) 0.0710177 + 0.123006i 0.0172243 + 0.0298334i 0.874509 0.485009i \(-0.161184\pi\)
−0.857285 + 0.514843i \(0.827850\pi\)
\(18\) 1.13906i 0.268479i
\(19\) −4.77160 + 2.75488i −1.09468 + 0.632014i −0.934818 0.355126i \(-0.884438\pi\)
−0.159861 + 0.987140i \(0.551105\pi\)
\(20\) 1.57993 0.912173i 0.353283 0.203968i
\(21\) 0 0
\(22\) −0.991800 1.71785i −0.211452 0.366246i
\(23\) 2.19549 3.80270i 0.457791 0.792917i −0.541053 0.840989i \(-0.681974\pi\)
0.998844 + 0.0480711i \(0.0153074\pi\)
\(24\) 1.37955 + 0.796483i 0.281599 + 0.162581i
\(25\) 3.91325 0.782649
\(26\) −1.66502 0.691049i −0.326536 0.135526i
\(27\) 4.48435 0.863013
\(28\) 0 0
\(29\) 4.19880 7.27253i 0.779697 1.35047i −0.152419 0.988316i \(-0.548706\pi\)
0.932116 0.362159i \(-0.117960\pi\)
\(30\) −0.221416 0.383504i −0.0404249 0.0700179i
\(31\) 2.84652i 0.511251i 0.966776 + 0.255625i \(0.0822813\pi\)
−0.966776 + 0.255625i \(0.917719\pi\)
\(32\) 4.35712 2.51558i 0.770237 0.444696i
\(33\) 2.91905 1.68531i 0.508141 0.293376i
\(34\) 0.0710158i 0.0121791i
\(35\) 0 0
\(36\) 1.99342 3.45271i 0.332237 0.575451i
\(37\) 0.730221 + 0.421593i 0.120048 + 0.0693095i 0.558821 0.829288i \(-0.311254\pi\)
−0.438774 + 0.898598i \(0.644587\pi\)
\(38\) 2.75481 0.446889
\(39\) 1.17426 2.82928i 0.188033 0.453047i
\(40\) −1.95460 −0.309049
\(41\) −10.4766 6.04869i −1.63618 0.944647i −0.982133 0.188190i \(-0.939738\pi\)
−0.654044 0.756457i \(-0.726929\pi\)
\(42\) 0 0
\(43\) 2.41161 + 4.17704i 0.367768 + 0.636993i 0.989216 0.146463i \(-0.0467888\pi\)
−0.621448 + 0.783455i \(0.713455\pi\)
\(44\) 6.94284i 1.04667i
\(45\) −2.05676 + 1.18747i −0.306604 + 0.177018i
\(46\) −1.90130 + 1.09772i −0.280331 + 0.161849i
\(47\) 4.55648i 0.664630i 0.943168 + 0.332315i \(0.107830\pi\)
−0.943168 + 0.332315i \(0.892170\pi\)
\(48\) 1.08858 + 1.88548i 0.157123 + 0.272146i
\(49\) 0 0
\(50\) −1.69444 0.978285i −0.239630 0.138350i
\(51\) 0.120673 0.0168977
\(52\) −3.83761 5.00858i −0.532180 0.694565i
\(53\) −0.279600 −0.0384060 −0.0192030 0.999816i \(-0.506113\pi\)
−0.0192030 + 0.999816i \(0.506113\pi\)
\(54\) −1.94173 1.12106i −0.264236 0.152557i
\(55\) −2.06791 + 3.58172i −0.278837 + 0.482959i
\(56\) 0 0
\(57\) 4.68111i 0.620028i
\(58\) −3.63617 + 2.09934i −0.477452 + 0.275657i
\(59\) 9.33705 5.39075i 1.21558 0.701815i 0.251611 0.967829i \(-0.419040\pi\)
0.963969 + 0.266013i \(0.0857065\pi\)
\(60\) 1.54997i 0.200100i
\(61\) −2.93177 5.07797i −0.375374 0.650168i 0.615009 0.788520i \(-0.289153\pi\)
−0.990383 + 0.138353i \(0.955819\pi\)
\(62\) 0.711612 1.23255i 0.0903748 0.156534i
\(63\) 0 0
\(64\) 2.60963 0.326204
\(65\) 0.487979 + 3.72689i 0.0605263 + 0.462263i
\(66\) −1.68527 −0.207442
\(67\) 4.45524 + 2.57223i 0.544294 + 0.314248i 0.746818 0.665029i \(-0.231581\pi\)
−0.202523 + 0.979277i \(0.564914\pi\)
\(68\) 0.124282 0.215263i 0.0150714 0.0261044i
\(69\) −1.86529 3.23078i −0.224555 0.388940i
\(70\) 0 0
\(71\) −3.20326 + 1.84940i −0.380157 + 0.219484i −0.677887 0.735167i \(-0.737104\pi\)
0.297730 + 0.954650i \(0.403771\pi\)
\(72\) −3.69921 + 2.13574i −0.435956 + 0.251700i
\(73\) 6.61281i 0.773970i 0.922086 + 0.386985i \(0.126484\pi\)
−0.922086 + 0.386985i \(0.873516\pi\)
\(74\) −0.210791 0.365101i −0.0245040 0.0424421i
\(75\) 1.66235 2.87927i 0.191952 0.332470i
\(76\) 8.35036 + 4.82108i 0.957852 + 0.553016i
\(77\) 0 0
\(78\) −1.21576 + 0.931521i −0.137657 + 0.105474i
\(79\) 11.9227 1.34141 0.670705 0.741725i \(-0.265992\pi\)
0.670705 + 0.741725i \(0.265992\pi\)
\(80\) −2.31352 1.33571i −0.258659 0.149337i
\(81\) −1.51231 + 2.61940i −0.168035 + 0.291045i
\(82\) 3.02426 + 5.23818i 0.333974 + 0.578460i
\(83\) 2.87321i 0.315376i 0.987489 + 0.157688i \(0.0504040\pi\)
−0.987489 + 0.157688i \(0.949596\pi\)
\(84\) 0 0
\(85\) −0.128231 + 0.0740342i −0.0139086 + 0.00803013i
\(86\) 2.41155i 0.260044i
\(87\) −3.56730 6.17875i −0.382455 0.662432i
\(88\) −3.71926 + 6.44195i −0.396475 + 0.686714i
\(89\) 1.51351 + 0.873824i 0.160432 + 0.0926252i 0.578066 0.815990i \(-0.303807\pi\)
−0.417635 + 0.908615i \(0.637141\pi\)
\(90\) 1.18744 0.125167
\(91\) 0 0
\(92\) −7.68427 −0.801141
\(93\) 2.09440 + 1.20921i 0.217180 + 0.125389i
\(94\) 1.13909 1.97296i 0.117488 0.203495i
\(95\) −2.87190 4.97427i −0.294650 0.510350i
\(96\) 4.27449i 0.436263i
\(97\) −2.34079 + 1.35145i −0.237671 + 0.137219i −0.614106 0.789224i \(-0.710483\pi\)
0.376435 + 0.926443i \(0.377150\pi\)
\(98\) 0 0
\(99\) 9.03822i 0.908376i
\(100\) −3.42412 5.93074i −0.342412 0.593074i
\(101\) −5.73612 + 9.93524i −0.570765 + 0.988594i 0.425723 + 0.904854i \(0.360020\pi\)
−0.996488 + 0.0837401i \(0.973313\pi\)
\(102\) −0.0522517 0.0301676i −0.00517369 0.00298703i
\(103\) 4.16950 0.410834 0.205417 0.978675i \(-0.434145\pi\)
0.205417 + 0.978675i \(0.434145\pi\)
\(104\) 0.877660 + 6.70304i 0.0860617 + 0.657287i
\(105\) 0 0
\(106\) 0.121067 + 0.0698982i 0.0117591 + 0.00678911i
\(107\) −4.24371 + 7.35032i −0.410255 + 0.710583i −0.994917 0.100694i \(-0.967894\pi\)
0.584662 + 0.811277i \(0.301227\pi\)
\(108\) −3.92383 6.79628i −0.377571 0.653972i
\(109\) 6.43036i 0.615917i −0.951400 0.307958i \(-0.900354\pi\)
0.951400 0.307958i \(-0.0996458\pi\)
\(110\) 1.79081 1.03393i 0.170747 0.0985810i
\(111\) 0.620397 0.358186i 0.0588855 0.0339975i
\(112\) 0 0
\(113\) −5.48164 9.49448i −0.515670 0.893166i −0.999835 0.0181892i \(-0.994210\pi\)
0.484165 0.874977i \(-0.339123\pi\)
\(114\) 1.17025 2.02692i 0.109603 0.189839i
\(115\) 3.96422 + 2.28874i 0.369665 + 0.213426i
\(116\) −14.6959 −1.36448
\(117\) 4.99582 + 6.52020i 0.461864 + 0.602793i
\(118\) −5.39060 −0.496245
\(119\) 0 0
\(120\) −0.830314 + 1.43815i −0.0757969 + 0.131284i
\(121\) 2.36975 + 4.10453i 0.215432 + 0.373139i
\(122\) 2.93169i 0.265423i
\(123\) −8.90097 + 5.13898i −0.802573 + 0.463366i
\(124\) 4.31406 2.49073i 0.387414 0.223674i
\(125\) 9.29184i 0.831087i
\(126\) 0 0
\(127\) −1.00394 + 1.73887i −0.0890849 + 0.154300i −0.907125 0.420862i \(-0.861728\pi\)
0.818040 + 0.575162i \(0.195061\pi\)
\(128\) −9.84421 5.68356i −0.870113 0.502360i
\(129\) 4.09782 0.360793
\(130\) 0.720401 1.73574i 0.0631834 0.152234i
\(131\) 12.4502 1.08778 0.543890 0.839156i \(-0.316951\pi\)
0.543890 + 0.839156i \(0.316951\pi\)
\(132\) −5.10838 2.94932i −0.444627 0.256706i
\(133\) 0 0
\(134\) −1.28608 2.22756i −0.111101 0.192432i
\(135\) 4.67482i 0.402344i
\(136\) −0.230631 + 0.133155i −0.0197765 + 0.0114180i
\(137\) −4.54246 + 2.62259i −0.388088 + 0.224063i −0.681332 0.731975i \(-0.738599\pi\)
0.293243 + 0.956038i \(0.405265\pi\)
\(138\) 1.86524i 0.158780i
\(139\) −10.3693 17.9601i −0.879510 1.52336i −0.851880 0.523737i \(-0.824537\pi\)
−0.0276301 0.999618i \(-0.508796\pi\)
\(140\) 0 0
\(141\) 3.35255 + 1.93559i 0.282335 + 0.163006i
\(142\) 1.84935 0.155194
\(143\) 13.2116 + 5.48335i 1.10481 + 0.458541i
\(144\) −5.83800 −0.486500
\(145\) 7.58143 + 4.37714i 0.629604 + 0.363502i
\(146\) 1.65316 2.86335i 0.136816 0.236973i
\(147\) 0 0
\(148\) 1.47559i 0.121293i
\(149\) −0.00985188 + 0.00568799i −0.000807098 + 0.000465978i −0.500403 0.865792i \(-0.666815\pi\)
0.499596 + 0.866258i \(0.333482\pi\)
\(150\) −1.43960 + 0.831153i −0.117543 + 0.0678633i
\(151\) 18.9054i 1.53850i 0.638947 + 0.769251i \(0.279370\pi\)
−0.638947 + 0.769251i \(0.720630\pi\)
\(152\) −5.16529 8.94654i −0.418960 0.725660i
\(153\) −0.161791 + 0.280230i −0.0130800 + 0.0226553i
\(154\) 0 0
\(155\) −2.96743 −0.238350
\(156\) −5.31541 + 0.695972i −0.425574 + 0.0557224i
\(157\) −19.7937 −1.57971 −0.789856 0.613292i \(-0.789845\pi\)
−0.789856 + 0.613292i \(0.789845\pi\)
\(158\) −5.16255 2.98060i −0.410710 0.237124i
\(159\) −0.118774 + 0.205723i −0.00941942 + 0.0163149i
\(160\) 2.62243 + 4.54219i 0.207321 + 0.359091i
\(161\) 0 0
\(162\) 1.30967 0.756136i 0.102897 0.0594076i
\(163\) −7.73581 + 4.46627i −0.605915 + 0.349825i −0.771365 0.636393i \(-0.780426\pi\)
0.165450 + 0.986218i \(0.447092\pi\)
\(164\) 21.1706i 1.65314i
\(165\) 1.75690 + 3.04304i 0.136774 + 0.236900i
\(166\) 0.718284 1.24410i 0.0557496 0.0965612i
\(167\) −5.31279 3.06734i −0.411116 0.237358i 0.280153 0.959955i \(-0.409615\pi\)
−0.691269 + 0.722597i \(0.742948\pi\)
\(168\) 0 0
\(169\) 12.5618 3.34692i 0.966290 0.257456i
\(170\) 0.0740322 0.00567801
\(171\) −10.8705 6.27611i −0.831291 0.479946i
\(172\) 4.22036 7.30987i 0.321799 0.557373i
\(173\) −12.1314 21.0122i −0.922332 1.59753i −0.795797 0.605563i \(-0.792948\pi\)
−0.126535 0.991962i \(-0.540386\pi\)
\(174\) 3.56721i 0.270429i
\(175\) 0 0
\(176\) −8.80446 + 5.08325i −0.663661 + 0.383165i
\(177\) 9.15997i 0.688506i
\(178\) −0.436901 0.756734i −0.0327471 0.0567196i
\(179\) −2.06838 + 3.58253i −0.154598 + 0.267771i −0.932912 0.360103i \(-0.882741\pi\)
0.778315 + 0.627874i \(0.216075\pi\)
\(180\) 3.59936 + 2.07809i 0.268280 + 0.154892i
\(181\) 7.86568 0.584651 0.292326 0.956319i \(-0.405571\pi\)
0.292326 + 0.956319i \(0.405571\pi\)
\(182\) 0 0
\(183\) −4.98167 −0.368256
\(184\) 7.12989 + 4.11645i 0.525623 + 0.303468i
\(185\) −0.439501 + 0.761237i −0.0323127 + 0.0559673i
\(186\) −0.604586 1.04717i −0.0443304 0.0767825i
\(187\) 0.563498i 0.0412070i
\(188\) 6.90560 3.98695i 0.503642 0.290778i
\(189\) 0 0
\(190\) 2.87182i 0.208344i
\(191\) 3.23933 + 5.61069i 0.234390 + 0.405975i 0.959095 0.283084i \(-0.0913574\pi\)
−0.724705 + 0.689059i \(0.758024\pi\)
\(192\) 1.10857 1.92011i 0.0800044 0.138572i
\(193\) −4.18228 2.41464i −0.301047 0.173810i 0.341866 0.939749i \(-0.388941\pi\)
−0.642913 + 0.765939i \(0.722274\pi\)
\(194\) 1.35142 0.0970261
\(195\) 2.94945 + 1.22414i 0.211214 + 0.0876626i
\(196\) 0 0
\(197\) −22.3748 12.9181i −1.59414 0.920377i −0.992586 0.121545i \(-0.961215\pi\)
−0.601554 0.798832i \(-0.705452\pi\)
\(198\) 2.25950 3.91356i 0.160575 0.278125i
\(199\) −8.55731 14.8217i −0.606612 1.05068i −0.991795 0.127842i \(-0.959195\pi\)
0.385183 0.922840i \(-0.374138\pi\)
\(200\) 7.33717i 0.518816i
\(201\) 3.78518 2.18537i 0.266986 0.154144i
\(202\) 4.96749 2.86798i 0.349511 0.201790i
\(203\) 0 0
\(204\) −0.105590 0.182887i −0.00739278 0.0128047i
\(205\) 6.30561 10.9216i 0.440403 0.762800i
\(206\) −1.80540 1.04235i −0.125788 0.0726238i
\(207\) 10.0034 0.695286
\(208\) −3.54182 + 8.53368i −0.245581 + 0.591704i
\(209\) −21.8589 −1.51201
\(210\) 0 0
\(211\) −9.14557 + 15.8406i −0.629607 + 1.09051i 0.358024 + 0.933713i \(0.383451\pi\)
−0.987631 + 0.156799i \(0.949883\pi\)
\(212\) 0.244652 + 0.423750i 0.0168028 + 0.0291032i
\(213\) 3.14251i 0.215321i
\(214\) 3.67506 2.12180i 0.251222 0.145043i
\(215\) −4.35446 + 2.51405i −0.296972 + 0.171457i
\(216\) 8.40796i 0.572089i
\(217\) 0 0
\(218\) −1.60755 + 2.78435i −0.108877 + 0.188580i
\(219\) 4.86555 + 2.80912i 0.328783 + 0.189823i
\(220\) 7.23773 0.487968
\(221\) 0.311470 + 0.406509i 0.0209517 + 0.0273447i
\(222\) −0.358177 −0.0240392
\(223\) 9.96682 + 5.75435i 0.667428 + 0.385340i 0.795101 0.606477i \(-0.207418\pi\)
−0.127674 + 0.991816i \(0.540751\pi\)
\(224\) 0 0
\(225\) 4.45753 + 7.72067i 0.297169 + 0.514712i
\(226\) 5.48150i 0.364624i
\(227\) 15.5057 8.95223i 1.02915 0.594181i 0.112410 0.993662i \(-0.464143\pi\)
0.916741 + 0.399481i \(0.130810\pi\)
\(228\) 7.09448 4.09600i 0.469843 0.271264i
\(229\) 3.86350i 0.255307i 0.991819 + 0.127654i \(0.0407446\pi\)
−0.991819 + 0.127654i \(0.959255\pi\)
\(230\) −1.14434 1.98206i −0.0754556 0.130693i
\(231\) 0 0
\(232\) 13.6357 + 7.87256i 0.895226 + 0.516859i
\(233\) −25.0642 −1.64201 −0.821004 0.570922i \(-0.806586\pi\)
−0.821004 + 0.570922i \(0.806586\pi\)
\(234\) −0.533189 4.07217i −0.0348556 0.266206i
\(235\) −4.75001 −0.309857
\(236\) −16.3400 9.43388i −1.06364 0.614093i
\(237\) 5.06477 8.77245i 0.328992 0.569832i
\(238\) 0 0
\(239\) 7.80462i 0.504839i −0.967618 0.252419i \(-0.918774\pi\)
0.967618 0.252419i \(-0.0812263\pi\)
\(240\) −1.96557 + 1.13482i −0.126877 + 0.0732524i
\(241\) 18.8493 10.8826i 1.21419 0.701012i 0.250519 0.968112i \(-0.419399\pi\)
0.963669 + 0.267100i \(0.0860655\pi\)
\(242\) 2.36969i 0.152329i
\(243\) 8.01138 + 13.8761i 0.513930 + 0.890154i
\(244\) −5.13063 + 8.88652i −0.328455 + 0.568901i
\(245\) 0 0
\(246\) 5.13884 0.327640
\(247\) −15.7691 + 12.0824i −1.00336 + 0.768783i
\(248\) −5.33711 −0.338907
\(249\) 2.11404 + 1.22054i 0.133972 + 0.0773488i
\(250\) 2.32290 4.02338i 0.146913 0.254461i
\(251\) −3.83990 6.65090i −0.242372 0.419801i 0.719017 0.694992i \(-0.244592\pi\)
−0.961390 + 0.275191i \(0.911259\pi\)
\(252\) 0 0
\(253\) 15.0865 8.71017i 0.948478 0.547604i
\(254\) 0.869411 0.501955i 0.0545517 0.0314954i
\(255\) 0.125799i 0.00787784i
\(256\) 0.232070 + 0.401958i 0.0145044 + 0.0251224i
\(257\) −6.81187 + 11.7985i −0.424913 + 0.735971i −0.996412 0.0846316i \(-0.973029\pi\)
0.571499 + 0.820603i \(0.306362\pi\)
\(258\) −1.77436 1.02443i −0.110467 0.0637781i
\(259\) 0 0
\(260\) 5.22132 4.00061i 0.323813 0.248107i
\(261\) 19.1312 1.18419
\(262\) −5.39096 3.11247i −0.333055 0.192289i
\(263\) 5.86158 10.1525i 0.361440 0.626033i −0.626758 0.779214i \(-0.715618\pi\)
0.988198 + 0.153181i \(0.0489518\pi\)
\(264\) 3.15989 + 5.47309i 0.194478 + 0.336845i
\(265\) 0.291476i 0.0179052i
\(266\) 0 0
\(267\) 1.28588 0.742403i 0.0786945 0.0454343i
\(268\) 9.00289i 0.549939i
\(269\) 4.59938 + 7.96636i 0.280429 + 0.485717i 0.971490 0.237079i \(-0.0761899\pi\)
−0.691061 + 0.722796i \(0.742857\pi\)
\(270\) 1.16867 2.02420i 0.0711232 0.123189i
\(271\) 2.22022 + 1.28184i 0.134869 + 0.0778665i 0.565916 0.824463i \(-0.308523\pi\)
−0.431048 + 0.902329i \(0.641856\pi\)
\(272\) −0.363976 −0.0220693
\(273\) 0 0
\(274\) 2.62252 0.158432
\(275\) 13.4451 + 7.76252i 0.810769 + 0.468097i
\(276\) −3.26428 + 5.65391i −0.196487 + 0.340325i
\(277\) −0.466941 0.808765i −0.0280558 0.0485940i 0.851657 0.524100i \(-0.175598\pi\)
−0.879712 + 0.475506i \(0.842265\pi\)
\(278\) 10.3690i 0.621891i
\(279\) −5.61607 + 3.24244i −0.336226 + 0.194120i
\(280\) 0 0
\(281\) 6.45288i 0.384947i −0.981302 0.192473i \(-0.938349\pi\)
0.981302 0.192473i \(-0.0616509\pi\)
\(282\) −0.967771 1.67623i −0.0576299 0.0998180i
\(283\) −11.0873 + 19.2037i −0.659071 + 1.14154i 0.321786 + 0.946812i \(0.395717\pi\)
−0.980857 + 0.194731i \(0.937616\pi\)
\(284\) 5.60575 + 3.23648i 0.332640 + 0.192050i
\(285\) −4.87994 −0.289062
\(286\) −4.34984 5.67711i −0.257211 0.335695i
\(287\) 0 0
\(288\) 9.92629 + 5.73094i 0.584912 + 0.337699i
\(289\) 8.48991 14.7050i 0.499407 0.864998i
\(290\) −2.18851 3.79061i −0.128514 0.222593i
\(291\) 2.29639i 0.134617i
\(292\) 10.0221 5.78625i 0.586498 0.338615i
\(293\) 20.9600 12.1013i 1.22450 0.706964i 0.258624 0.965978i \(-0.416731\pi\)
0.965874 + 0.259014i \(0.0833976\pi\)
\(294\) 0 0
\(295\) 5.61972 + 9.73364i 0.327193 + 0.566714i
\(296\) −0.790469 + 1.36913i −0.0459451 + 0.0795792i
\(297\) 15.4073 + 8.89539i 0.894020 + 0.516163i
\(298\) 0.00568784 0.000329487
\(299\) 6.06892 14.6225i 0.350975 0.845640i
\(300\) −5.81827 −0.335918
\(301\) 0 0
\(302\) 4.72623 8.18607i 0.271964 0.471055i
\(303\) 4.87341 + 8.44100i 0.279970 + 0.484923i
\(304\) 14.1192i 0.809791i
\(305\) 5.29366 3.05630i 0.303114 0.175003i
\(306\) 0.140111 0.0808933i 0.00800963 0.00462436i
\(307\) 24.2924i 1.38644i 0.720726 + 0.693220i \(0.243809\pi\)
−0.720726 + 0.693220i \(0.756191\pi\)
\(308\) 0 0
\(309\) 1.77121 3.06782i 0.100761 0.174522i
\(310\) 1.28490 + 0.741837i 0.0729774 + 0.0421335i
\(311\) 3.98711 0.226088 0.113044 0.993590i \(-0.463940\pi\)
0.113044 + 0.993590i \(0.463940\pi\)
\(312\) 5.30477 + 2.20169i 0.300323 + 0.124646i
\(313\) −28.4754 −1.60953 −0.804763 0.593597i \(-0.797707\pi\)
−0.804763 + 0.593597i \(0.797707\pi\)
\(314\) 8.57071 + 4.94830i 0.483673 + 0.279249i
\(315\) 0 0
\(316\) −10.4324 18.0695i −0.586871 1.01649i
\(317\) 16.8161i 0.944487i −0.881468 0.472244i \(-0.843444\pi\)
0.881468 0.472244i \(-0.156556\pi\)
\(318\) 0.102859 0.0593856i 0.00576804 0.00333018i
\(319\) 28.8523 16.6579i 1.61542 0.932664i
\(320\) 2.72048i 0.152079i
\(321\) 3.60546 + 6.24485i 0.201237 + 0.348553i
\(322\) 0 0
\(323\) −0.677736 0.391291i −0.0377102 0.0217720i
\(324\) 5.29313 0.294063
\(325\) 13.9900 1.83178i 0.776025 0.101609i
\(326\) 4.46615 0.247357
\(327\) −4.73131 2.73162i −0.261642 0.151059i
\(328\) 11.3410 19.6432i 0.626204 1.08462i
\(329\) 0 0
\(330\) 1.75685i 0.0967115i
\(331\) −5.37730 + 3.10459i −0.295563 + 0.170644i −0.640448 0.768002i \(-0.721251\pi\)
0.344885 + 0.938645i \(0.387918\pi\)
\(332\) 4.35451 2.51408i 0.238985 0.137978i
\(333\) 1.92093i 0.105266i
\(334\) 1.53363 + 2.65633i 0.0839165 + 0.145348i
\(335\) −2.68149 + 4.64448i −0.146505 + 0.253755i
\(336\) 0 0
\(337\) 7.69650 0.419255 0.209628 0.977781i \(-0.432775\pi\)
0.209628 + 0.977781i \(0.432775\pi\)
\(338\) −6.27597 1.69114i −0.341368 0.0919858i
\(339\) −9.31442 −0.505890
\(340\) 0.224406 + 0.129561i 0.0121701 + 0.00702642i
\(341\) −5.64651 + 9.78005i −0.305776 + 0.529619i
\(342\) 3.13797 + 5.43513i 0.169682 + 0.293898i
\(343\) 0 0
\(344\) −7.83177 + 4.52167i −0.422261 + 0.243792i
\(345\) 3.36801 1.94452i 0.181327 0.104689i
\(346\) 12.1311i 0.652170i
\(347\) −15.2047 26.3353i −0.816231 1.41375i −0.908440 0.418015i \(-0.862726\pi\)
0.0922088 0.995740i \(-0.470607\pi\)
\(348\) −6.24283 + 10.8129i −0.334651 + 0.579632i
\(349\) 13.9933 + 8.07906i 0.749046 + 0.432462i 0.825349 0.564623i \(-0.190978\pi\)
−0.0763028 + 0.997085i \(0.524312\pi\)
\(350\) 0 0
\(351\) 16.0317 2.09911i 0.855709 0.112042i
\(352\) 19.9602 1.06388
\(353\) −10.2558 5.92119i −0.545861 0.315153i 0.201590 0.979470i \(-0.435389\pi\)
−0.747451 + 0.664317i \(0.768723\pi\)
\(354\) −2.28993 + 3.96628i −0.121709 + 0.210805i
\(355\) −1.92796 3.33932i −0.102325 0.177233i
\(356\) 3.05841i 0.162095i
\(357\) 0 0
\(358\) 1.79122 1.03416i 0.0946688 0.0546571i
\(359\) 31.3653i 1.65540i −0.561174 0.827698i \(-0.689650\pi\)
0.561174 0.827698i \(-0.310350\pi\)
\(360\) −2.22646 3.85634i −0.117345 0.203247i
\(361\) 5.67876 9.83591i 0.298882 0.517679i
\(362\) −3.40585 1.96637i −0.179007 0.103350i
\(363\) 4.02669 0.211346
\(364\) 0 0
\(365\) −6.89369 −0.360832
\(366\) 2.15707 + 1.24538i 0.112752 + 0.0650973i
\(367\) 12.0387 20.8517i 0.628415 1.08845i −0.359454 0.933163i \(-0.617037\pi\)
0.987870 0.155285i \(-0.0496295\pi\)
\(368\) 5.62610 + 9.74470i 0.293281 + 0.507977i
\(369\) 27.5600i 1.43472i
\(370\) 0.380608 0.219744i 0.0197869 0.0114240i
\(371\) 0 0
\(372\) 4.23225i 0.219432i
\(373\) 9.19612 + 15.9281i 0.476157 + 0.824728i 0.999627 0.0273160i \(-0.00869604\pi\)
−0.523470 + 0.852044i \(0.675363\pi\)
\(374\) 0.140871 0.243995i 0.00728425 0.0126167i
\(375\) 6.83672 + 3.94718i 0.353046 + 0.203831i
\(376\) −8.54320 −0.440582
\(377\) 11.6066 27.9650i 0.597771 1.44027i
\(378\) 0 0
\(379\) −7.04719 4.06870i −0.361990 0.208995i 0.307963 0.951398i \(-0.400353\pi\)
−0.669953 + 0.742403i \(0.733686\pi\)
\(380\) −5.02586 + 8.70504i −0.257821 + 0.446559i
\(381\) 0.852946 + 1.47735i 0.0436977 + 0.0756867i
\(382\) 3.23925i 0.165734i
\(383\) −19.3739 + 11.1856i −0.989962 + 0.571555i −0.905263 0.424852i \(-0.860326\pi\)
−0.0846992 + 0.996407i \(0.526993\pi\)
\(384\) −8.36365 + 4.82876i −0.426806 + 0.246417i
\(385\) 0 0
\(386\) 1.20729 + 2.09108i 0.0614493 + 0.106433i
\(387\) −5.49409 + 9.51604i −0.279280 + 0.483727i
\(388\) 4.09641 + 2.36506i 0.207963 + 0.120068i
\(389\) 21.3946 1.08475 0.542374 0.840137i \(-0.317525\pi\)
0.542374 + 0.840137i \(0.317525\pi\)
\(390\) −0.971088 1.26740i −0.0491729 0.0641771i
\(391\) 0.623674 0.0315406
\(392\) 0 0
\(393\) 5.28886 9.16058i 0.266788 0.462090i
\(394\) 6.45888 + 11.1871i 0.325394 + 0.563599i
\(395\) 12.4291i 0.625377i
\(396\) 13.6979 7.90851i 0.688347 0.397417i
\(397\) 1.03640 0.598365i 0.0520154 0.0300311i −0.473767 0.880650i \(-0.657106\pi\)
0.525782 + 0.850619i \(0.323773\pi\)
\(398\) 8.55708i 0.428928i
\(399\) 0 0
\(400\) −5.01399 + 8.68449i −0.250699 + 0.434224i
\(401\) −31.4150 18.1375i −1.56879 0.905741i −0.996310 0.0858220i \(-0.972648\pi\)
−0.572479 0.819919i \(-0.694018\pi\)
\(402\) −2.18532 −0.108994
\(403\) 1.33245 + 10.1764i 0.0663739 + 0.506924i
\(404\) 20.0766 0.998846
\(405\) −2.73066 1.57655i −0.135688 0.0783393i
\(406\) 0 0
\(407\) 1.67259 + 2.89701i 0.0829072 + 0.143599i
\(408\) 0.226257i 0.0112014i
\(409\) −12.7066 + 7.33616i −0.628301 + 0.362750i −0.780094 0.625662i \(-0.784829\pi\)
0.151793 + 0.988412i \(0.451495\pi\)
\(410\) −5.46067 + 3.15272i −0.269683 + 0.155702i
\(411\) 4.45631i 0.219814i
\(412\) −3.64834 6.31912i −0.179741 0.311321i
\(413\) 0 0
\(414\) −4.33150 2.50079i −0.212881 0.122907i
\(415\) −2.99525 −0.147031
\(416\) 14.3993 11.0329i 0.705985 0.540930i
\(417\) −17.6195 −0.862830
\(418\) 9.46494 + 5.46458i 0.462945 + 0.267282i
\(419\) −2.96674 + 5.13855i −0.144935 + 0.251034i −0.929349 0.369203i \(-0.879631\pi\)
0.784414 + 0.620238i \(0.212964\pi\)
\(420\) 0 0
\(421\) 2.63174i 0.128263i 0.997941 + 0.0641317i \(0.0204278\pi\)
−0.997941 + 0.0641317i \(0.979572\pi\)
\(422\) 7.92008 4.57266i 0.385544 0.222594i
\(423\) −8.98974 + 5.19023i −0.437096 + 0.252358i
\(424\) 0.524238i 0.0254593i
\(425\) 0.277910 + 0.481354i 0.0134806 + 0.0233491i
\(426\) 0.785606 1.36071i 0.0380628 0.0659266i
\(427\) 0 0
\(428\) 14.8531 0.717952
\(429\) 9.64682 7.39146i 0.465753 0.356863i
\(430\) 2.51398 0.121235
\(431\) −16.3139 9.41883i −0.785812 0.453689i 0.0526738 0.998612i \(-0.483226\pi\)
−0.838486 + 0.544923i \(0.816559\pi\)
\(432\) −5.74573 + 9.95190i −0.276442 + 0.478811i
\(433\) −9.56773 16.5718i −0.459796 0.796389i 0.539154 0.842207i \(-0.318744\pi\)
−0.998950 + 0.0458176i \(0.985411\pi\)
\(434\) 0 0
\(435\) 6.44119 3.71883i 0.308832 0.178304i
\(436\) −9.74557 + 5.62661i −0.466728 + 0.269466i
\(437\) 24.1933i 1.15732i
\(438\) −1.40452 2.43271i −0.0671108 0.116239i
\(439\) 0.632554 1.09561i 0.0301901 0.0522908i −0.850536 0.525918i \(-0.823722\pi\)
0.880726 + 0.473627i \(0.157055\pi\)
\(440\) −6.71557 3.87724i −0.320152 0.184840i
\(441\) 0 0
\(442\) −0.0332422 0.253884i −0.00158117 0.0120760i
\(443\) −20.9392 −0.994853 −0.497426 0.867506i \(-0.665722\pi\)
−0.497426 + 0.867506i \(0.665722\pi\)
\(444\) −1.08570 0.626831i −0.0515252 0.0297481i
\(445\) −0.910940 + 1.57779i −0.0431827 + 0.0747946i
\(446\) −2.87710 4.98328i −0.136234 0.235965i
\(447\) 0.00966505i 0.000457141i
\(448\) 0 0
\(449\) 15.4700 8.93162i 0.730075 0.421509i −0.0883746 0.996087i \(-0.528167\pi\)
0.818450 + 0.574578i \(0.194834\pi\)
\(450\) 4.45741i 0.210125i
\(451\) −23.9970 41.5640i −1.12997 1.95717i
\(452\) −9.59295 + 16.6155i −0.451214 + 0.781526i
\(453\) 13.9102 + 8.03104i 0.653557 + 0.377331i
\(454\) −8.95199 −0.420138
\(455\) 0 0
\(456\) −8.77687 −0.411015
\(457\) 5.68629 + 3.28298i 0.265994 + 0.153571i 0.627066 0.778966i \(-0.284256\pi\)
−0.361072 + 0.932538i \(0.617589\pi\)
\(458\) 0.965850 1.67290i 0.0451312 0.0781695i
\(459\) 0.318468 + 0.551603i 0.0148648 + 0.0257466i
\(460\) 8.01066i 0.373499i
\(461\) 4.42854 2.55682i 0.206258 0.119083i −0.393313 0.919404i \(-0.628671\pi\)
0.599571 + 0.800322i \(0.295338\pi\)
\(462\) 0 0
\(463\) 33.3239i 1.54869i 0.632761 + 0.774347i \(0.281921\pi\)
−0.632761 + 0.774347i \(0.718079\pi\)
\(464\) 10.7597 + 18.6364i 0.499508 + 0.865173i
\(465\) −1.26057 + 2.18336i −0.0584574 + 0.101251i
\(466\) 10.8528 + 6.26587i 0.502747 + 0.290261i
\(467\) −12.9494 −0.599229 −0.299614 0.954060i \(-0.596858\pi\)
−0.299614 + 0.954060i \(0.596858\pi\)
\(468\) 5.51035 13.2767i 0.254716 0.613714i
\(469\) 0 0
\(470\) 2.05676 + 1.18747i 0.0948713 + 0.0547740i
\(471\) −8.40840 + 14.5638i −0.387439 + 0.671063i
\(472\) 10.1074 + 17.5066i 0.465231 + 0.805805i
\(473\) 19.1352i 0.879838i
\(474\) −4.38611 + 2.53232i −0.201461 + 0.116313i
\(475\) −18.6724 + 10.7805i −0.856750 + 0.494645i
\(476\) 0 0
\(477\) −0.318489 0.551640i −0.0145826 0.0252578i
\(478\) −1.95110 + 3.37941i −0.0892414 + 0.154571i
\(479\) 23.3930 + 13.5060i 1.06885 + 0.617104i 0.927868 0.372908i \(-0.121639\pi\)
0.140987 + 0.990012i \(0.454973\pi\)
\(480\) 4.45605 0.203390
\(481\) 2.80791 + 1.16540i 0.128030 + 0.0531376i
\(482\) −10.8823 −0.495677
\(483\) 0 0
\(484\) 4.14710 7.18299i 0.188505 0.326499i
\(485\) −1.40886 2.44021i −0.0639729 0.110804i
\(486\) 8.01117i 0.363394i
\(487\) −27.7854 + 16.0419i −1.25908 + 0.726928i −0.972895 0.231247i \(-0.925720\pi\)
−0.286182 + 0.958175i \(0.592386\pi\)
\(488\) 9.52097 5.49694i 0.430994 0.248835i
\(489\) 7.58910i 0.343191i
\(490\) 0 0
\(491\) −14.3020 + 24.7718i −0.645440 + 1.11793i 0.338760 + 0.940873i \(0.389992\pi\)
−0.984200 + 0.177061i \(0.943341\pi\)
\(492\) 15.5768 + 8.99328i 0.702257 + 0.405448i
\(493\) 1.19276 0.0537190
\(494\) 9.84854 1.28952i 0.443107 0.0580181i
\(495\) −9.42212 −0.423493
\(496\) −6.31716 3.64721i −0.283649 0.163765i
\(497\) 0 0
\(498\) −0.610255 1.05699i −0.0273462 0.0473650i
\(499\) 1.79816i 0.0804969i 0.999190 + 0.0402484i \(0.0128149\pi\)
−0.999190 + 0.0402484i \(0.987185\pi\)
\(500\) 14.0823 8.13042i 0.629780 0.363603i
\(501\) −4.51376 + 2.60602i −0.201660 + 0.116428i
\(502\) 3.83980i 0.171379i
\(503\) 14.5386 + 25.1816i 0.648245 + 1.12279i 0.983542 + 0.180681i \(0.0578300\pi\)
−0.335297 + 0.942112i \(0.608837\pi\)
\(504\) 0 0
\(505\) −10.3572 5.97976i −0.460891 0.266096i
\(506\) −8.70994 −0.387204
\(507\) 2.87366 10.6644i 0.127624 0.473624i
\(508\) 3.51380 0.155900
\(509\) 20.0843 + 11.5957i 0.890220 + 0.513969i 0.874014 0.485900i \(-0.161508\pi\)
0.0162054 + 0.999869i \(0.494841\pi\)
\(510\) 0.0314489 0.0544711i 0.00139258 0.00241202i
\(511\) 0 0
\(512\) 22.5022i 0.994464i
\(513\) −21.3975 + 12.3539i −0.944723 + 0.545436i
\(514\) 5.89910 3.40585i 0.260198 0.150225i
\(515\) 4.34660i 0.191534i
\(516\) −3.58562 6.21048i −0.157848 0.273401i
\(517\) −9.03847 + 15.6551i −0.397511 + 0.688510i
\(518\) 0 0
\(519\) −20.6137 −0.904840
\(520\) −6.98775 + 0.914939i −0.306433 + 0.0401227i
\(521\) −33.2510 −1.45675 −0.728376 0.685178i \(-0.759725\pi\)
−0.728376 + 0.685178i \(0.759725\pi\)
\(522\) −8.28383 4.78267i −0.362574 0.209332i
\(523\) 19.3560 33.5256i 0.846380 1.46597i −0.0380367 0.999276i \(-0.512110\pi\)
0.884417 0.466697i \(-0.154556\pi\)
\(524\) −10.8940 18.8690i −0.475908 0.824296i
\(525\) 0 0
\(526\) −5.07614 + 2.93071i −0.221330 + 0.127785i
\(527\) −0.350140 + 0.202153i −0.0152523 + 0.00880594i
\(528\) 8.63748i 0.375898i
\(529\) 1.85966 + 3.22102i 0.0808546 + 0.140044i
\(530\) −0.0728671 + 0.126210i −0.00316514 + 0.00548219i
\(531\) 21.2714 + 12.2811i 0.923102 + 0.532953i
\(532\) 0 0
\(533\) −40.2857 16.7202i −1.74497 0.724233i
\(534\) −0.742383 −0.0321260
\(535\) −7.66253 4.42396i −0.331280 0.191265i
\(536\) −4.82283 + 8.35338i −0.208314 + 0.360811i
\(537\) 1.75730 + 3.04372i 0.0758329 + 0.131346i
\(538\) 4.59926i 0.198288i
\(539\) 0 0
\(540\) 7.08495 4.09050i 0.304888 0.176027i
\(541\) 22.6675i 0.974551i −0.873248 0.487275i \(-0.837991\pi\)
0.873248 0.487275i \(-0.162009\pi\)
\(542\) −0.640905 1.11008i −0.0275292 0.0476820i
\(543\) 3.34135 5.78738i 0.143391 0.248360i
\(544\) 0.618865 + 0.357302i 0.0265336 + 0.0153192i
\(545\) 6.70349 0.287146
\(546\) 0 0
\(547\) −9.21134 −0.393848 −0.196924 0.980419i \(-0.563095\pi\)
−0.196924 + 0.980419i \(0.563095\pi\)
\(548\) 7.94936 + 4.58957i 0.339580 + 0.196057i
\(549\) 6.67909 11.5685i 0.285056 0.493732i
\(550\) −3.88116 6.72236i −0.165493 0.286642i
\(551\) 46.2688i 1.97112i
\(552\) 6.05757 3.49734i 0.257827 0.148857i
\(553\) 0 0
\(554\) 0.466928i 0.0198379i
\(555\) 0.373400 + 0.646748i 0.0158500 + 0.0274529i
\(556\) −18.1464 + 31.4304i −0.769577 + 1.33295i
\(557\) −9.81039 5.66403i −0.415680 0.239993i 0.277547 0.960712i \(-0.410478\pi\)
−0.693227 + 0.720719i \(0.743812\pi\)
\(558\) 3.24236 0.137260
\(559\) 10.5769 + 13.8042i 0.447354 + 0.583855i
\(560\) 0 0
\(561\) 0.414608 + 0.239374i 0.0175048 + 0.0101064i
\(562\) −1.61318 + 2.79411i −0.0680478 + 0.117862i
\(563\) −16.3193 28.2659i −0.687777 1.19127i −0.972555 0.232672i \(-0.925253\pi\)
0.284778 0.958594i \(-0.408080\pi\)
\(564\) 6.77463i 0.285264i
\(565\) 9.89776 5.71448i 0.416402 0.240410i
\(566\) 9.60161 5.54349i 0.403586 0.233010i
\(567\) 0 0
\(568\) −3.46755 6.00597i −0.145495 0.252005i
\(569\) 17.5045 30.3188i 0.733829 1.27103i −0.221407 0.975182i \(-0.571065\pi\)
0.955235 0.295847i \(-0.0956019\pi\)
\(570\) 2.11302 + 1.21995i 0.0885046 + 0.0510981i
\(571\) −26.2546 −1.09872 −0.549360 0.835586i \(-0.685128\pi\)
−0.549360 + 0.835586i \(0.685128\pi\)
\(572\) −3.24992 24.8209i −0.135886 1.03781i
\(573\) 5.50428 0.229945
\(574\) 0 0
\(575\) 8.59149 14.8809i 0.358290 0.620576i
\(576\) 2.97260 + 5.14870i 0.123858 + 0.214529i
\(577\) 24.5727i 1.02297i 0.859291 + 0.511487i \(0.170905\pi\)
−0.859291 + 0.511487i \(0.829095\pi\)
\(578\) −7.35228 + 4.24484i −0.305815 + 0.176562i
\(579\) −3.55327 + 2.05148i −0.147669 + 0.0852567i
\(580\) 15.3201i 0.636133i
\(581\) 0 0
\(582\) 0.574083 0.994341i 0.0237965 0.0412167i
\(583\) −0.960646 0.554629i −0.0397859 0.0229704i
\(584\) −12.3987 −0.513063
\(585\) −6.79714 + 5.20802i −0.281027 + 0.215325i
\(586\) −12.1010 −0.499886
\(587\) −17.7777 10.2640i −0.733765 0.423639i 0.0860331 0.996292i \(-0.472581\pi\)
−0.819798 + 0.572653i \(0.805914\pi\)
\(588\) 0 0
\(589\) −7.84184 13.5825i −0.323117 0.559656i
\(590\) 5.61957i 0.231354i
\(591\) −19.0097 + 10.9752i −0.781954 + 0.451461i
\(592\) −1.87124 + 1.08036i −0.0769077 + 0.0444027i
\(593\) 38.2835i 1.57211i −0.618154 0.786057i \(-0.712119\pi\)
0.618154 0.786057i \(-0.287881\pi\)
\(594\) −4.44757 7.70342i −0.182486 0.316075i
\(595\) 0 0
\(596\) 0.0172409 + 0.00995405i 0.000706216 + 0.000407734i
\(597\) −14.5406 −0.595107
\(598\) −6.28338 + 4.81436i −0.256946 + 0.196874i
\(599\) 14.0713 0.574939 0.287470 0.957790i \(-0.407186\pi\)
0.287470 + 0.957790i \(0.407186\pi\)
\(600\) 5.39851 + 3.11683i 0.220393 + 0.127244i
\(601\) −10.1171 + 17.5233i −0.412685 + 0.714791i −0.995182 0.0980417i \(-0.968742\pi\)
0.582498 + 0.812832i \(0.302075\pi\)
\(602\) 0 0
\(603\) 11.7200i 0.477276i
\(604\) 28.6522 16.5424i 1.16584 0.673099i
\(605\) −4.27887 + 2.47041i −0.173961 + 0.100436i
\(606\) 4.87328i 0.197964i
\(607\) 3.27563 + 5.67356i 0.132954 + 0.230283i 0.924814 0.380420i \(-0.124220\pi\)
−0.791860 + 0.610703i \(0.790887\pi\)
\(608\) −13.8603 + 24.0067i −0.562108 + 0.973600i
\(609\) 0 0
\(610\) −3.05621 −0.123742
\(611\) 2.13287 + 16.2896i 0.0862867 + 0.659005i
\(612\) 0.566272 0.0228902
\(613\) −28.8598 16.6622i −1.16564 0.672980i −0.212988 0.977055i \(-0.568319\pi\)
−0.952648 + 0.304075i \(0.901653\pi\)
\(614\) 6.07294 10.5186i 0.245084 0.424498i
\(615\) −5.35726 9.27904i −0.216025 0.374167i
\(616\) 0 0
\(617\) 5.85466 3.38019i 0.235700 0.136081i −0.377499 0.926010i \(-0.623216\pi\)
0.613199 + 0.789929i \(0.289883\pi\)
\(618\) −1.53387 + 0.885581i −0.0617013 + 0.0356233i
\(619\) 17.6186i 0.708152i 0.935217 + 0.354076i \(0.115205\pi\)
−0.935217 + 0.354076i \(0.884795\pi\)
\(620\) 2.59652 + 4.49731i 0.104279 + 0.180616i
\(621\) 9.84534 17.0526i 0.395080 0.684298i
\(622\) −1.72642 0.996751i −0.0692233 0.0399661i
\(623\) 0 0
\(624\) 4.77431 + 6.23110i 0.191125 + 0.249444i
\(625\) 9.87972 0.395189
\(626\) 12.3299 + 7.11866i 0.492801 + 0.284519i
\(627\) −9.28569 + 16.0833i −0.370835 + 0.642304i
\(628\) 17.3197 + 29.9985i 0.691130 + 1.19707i
\(629\) 0.119762i 0.00477524i
\(630\) 0 0
\(631\) 13.6416 7.87596i 0.543062 0.313537i −0.203257 0.979125i \(-0.565153\pi\)
0.746319 + 0.665588i \(0.231819\pi\)
\(632\) 22.3546i 0.889216i
\(633\) 7.77009 + 13.4582i 0.308833 + 0.534915i
\(634\) −4.20392 + 7.28140i −0.166959 + 0.289181i
\(635\) −1.81273 1.04658i −0.0719359 0.0415322i
\(636\) 0.415713 0.0164841
\(637\) 0 0
\(638\) −16.6575 −0.659475
\(639\) −7.29759 4.21327i −0.288688 0.166674i
\(640\) 5.92497 10.2623i 0.234205 0.405655i
\(641\) −10.4702 18.1350i −0.413550 0.716289i 0.581725 0.813385i \(-0.302378\pi\)
−0.995275 + 0.0970962i \(0.969045\pi\)
\(642\) 3.60537i 0.142293i
\(643\) 16.3952 9.46576i 0.646563 0.373293i −0.140575 0.990070i \(-0.544895\pi\)
0.787138 + 0.616777i \(0.211562\pi\)
\(644\) 0 0
\(645\) 4.27188i 0.168205i
\(646\) 0.195640 + 0.338859i 0.00769736 + 0.0133322i
\(647\) 18.8384 32.6291i 0.740614 1.28278i −0.211601 0.977356i \(-0.567868\pi\)
0.952216 0.305426i \(-0.0987988\pi\)
\(648\) −4.91126 2.83552i −0.192933 0.111390i
\(649\) 42.7735 1.67901
\(650\) −6.51562 2.70424i −0.255563 0.106069i
\(651\) 0 0
\(652\) 13.5378 + 7.81604i 0.530180 + 0.306100i
\(653\) −14.5163 + 25.1430i −0.568066 + 0.983920i 0.428691 + 0.903451i \(0.358975\pi\)
−0.996757 + 0.0804686i \(0.974358\pi\)
\(654\) 1.36577 + 2.36559i 0.0534060 + 0.0925019i
\(655\) 12.9790i 0.507133i
\(656\) 26.8472 15.5002i 1.04821 0.605182i
\(657\) −13.0468 + 7.53257i −0.509004 + 0.293874i
\(658\) 0 0
\(659\) 0.709152 + 1.22829i 0.0276247 + 0.0478473i 0.879507 0.475886i \(-0.157872\pi\)
−0.851883 + 0.523733i \(0.824539\pi\)
\(660\) 3.07459 5.32535i 0.119678 0.207289i
\(661\) −3.97764 2.29649i −0.154712 0.0893231i 0.420645 0.907225i \(-0.361804\pi\)
−0.575357 + 0.817902i \(0.695137\pi\)
\(662\) 3.10450 0.120660
\(663\) 0.431412 0.0564868i 0.0167547 0.00219377i
\(664\) −5.38715 −0.209062
\(665\) 0 0
\(666\) 0.480219 0.831764i 0.0186081 0.0322302i
\(667\) −18.4368 31.9335i −0.713877 1.23647i
\(668\) 10.7358i 0.415380i
\(669\) 8.46782 4.88890i 0.327385 0.189016i
\(670\) 2.32218 1.34071i 0.0897135 0.0517961i
\(671\) 23.2624i 0.898036i
\(672\) 0 0
\(673\) −2.10111 + 3.63924i −0.0809920 + 0.140282i −0.903676 0.428216i \(-0.859142\pi\)
0.822684 + 0.568499i \(0.192475\pi\)
\(674\) −3.33259 1.92407i −0.128367 0.0741126i
\(675\) 17.5484 0.675436
\(676\) −16.0641 16.1095i −0.617849 0.619596i
\(677\) −8.08708 −0.310812 −0.155406 0.987851i \(-0.549669\pi\)
−0.155406 + 0.987851i \(0.549669\pi\)
\(678\) 4.03316 + 2.32854i 0.154892 + 0.0894272i
\(679\) 0 0
\(680\) −0.138811 0.240427i −0.00532315 0.00921997i
\(681\) 15.2117i 0.582912i
\(682\) 4.88989 2.82318i 0.187244 0.108105i
\(683\) −21.3792 + 12.3433i −0.818051 + 0.472302i −0.849744 0.527196i \(-0.823243\pi\)
0.0316929 + 0.999498i \(0.489910\pi\)
\(684\) 21.9666i 0.839912i
\(685\) −2.73398 4.73540i −0.104460 0.180930i
\(686\) 0 0
\(687\) 2.84267 + 1.64122i 0.108455 + 0.0626164i
\(688\) −12.3599 −0.471216
\(689\) −0.999581 + 0.130880i −0.0380810 + 0.00498612i
\(690\) −1.94447 −0.0740246
\(691\) −9.74859 5.62835i −0.370854 0.214113i 0.302978 0.952998i \(-0.402019\pi\)
−0.673831 + 0.738885i \(0.735353\pi\)
\(692\) −21.2301 + 36.7716i −0.807047 + 1.39785i
\(693\) 0 0
\(694\) 15.2043i 0.577147i
\(695\) 18.7230 10.8097i 0.710202 0.410035i
\(696\) 11.5849 6.68854i 0.439124 0.253528i
\(697\) 1.71826i 0.0650836i
\(698\) −4.03942 6.99648i −0.152894 0.264821i
\(699\) −10.6473 + 18.4416i −0.402717 + 0.697526i
\(700\) 0 0
\(701\) 22.2305 0.839635 0.419818 0.907608i \(-0.362094\pi\)
0.419818 + 0.907608i \(0.362094\pi\)
\(702\) −7.46651 3.09890i −0.281805 0.116961i
\(703\) −4.64576 −0.175218
\(704\) 8.96614 + 5.17660i 0.337924 + 0.195101i
\(705\) −2.01781 + 3.49495i −0.0759951 + 0.131627i
\(706\) 2.96052 + 5.12776i 0.111420 + 0.192986i
\(707\) 0 0
\(708\) −13.8825 + 8.01504i −0.521734 + 0.301224i
\(709\) −20.5889 + 11.8870i −0.773234 + 0.446427i −0.834027 0.551723i \(-0.813970\pi\)
0.0607929 + 0.998150i \(0.480637\pi\)
\(710\) 1.92790i 0.0723530i
\(711\) 13.5810 + 23.5230i 0.509328 + 0.882182i
\(712\) −1.63838 + 2.83776i −0.0614010 + 0.106350i
\(713\) 10.8245 + 6.24951i 0.405380 + 0.234046i
\(714\) 0 0
\(715\) −5.71626 + 13.7728i −0.213776 + 0.515072i
\(716\) 7.23937 0.270548
\(717\) −5.74246 3.31541i −0.214456 0.123816i
\(718\) −7.84111 + 13.5812i −0.292628 + 0.506846i
\(719\) −10.3904 17.9967i −0.387496 0.671163i 0.604616 0.796517i \(-0.293327\pi\)
−0.992112 + 0.125354i \(0.959993\pi\)
\(720\) 6.08597i 0.226811i
\(721\) 0 0
\(722\) −4.91782 + 2.83931i −0.183022 + 0.105668i
\(723\) 18.4918i 0.687717i
\(724\) −6.88252 11.9209i −0.255787 0.443036i
\(725\) 16.4309 28.4592i 0.610229 1.05695i
\(726\) −1.74356 1.00665i −0.0647097 0.0373601i
\(727\) 26.7719 0.992915 0.496457 0.868061i \(-0.334634\pi\)
0.496457 + 0.868061i \(0.334634\pi\)
\(728\) 0 0
\(729\) 4.53910 0.168115
\(730\) 2.98497 + 1.72338i 0.110479 + 0.0637850i
\(731\) −0.342535 + 0.593287i −0.0126691 + 0.0219435i
\(732\) 4.35899 + 7.55000i 0.161113 + 0.279056i
\(733\) 5.25647i 0.194152i −0.995277 0.0970761i \(-0.969051\pi\)
0.995277 0.0970761i \(-0.0309490\pi\)
\(734\) −10.4255 + 6.01919i −0.384814 + 0.222172i
\(735\) 0 0
\(736\) 22.0917i 0.814312i
\(737\) 10.2048 + 17.6753i 0.375900 + 0.651078i
\(738\) −6.88981 + 11.9335i −0.253617 + 0.439278i
\(739\) −6.19209 3.57501i −0.227780 0.131509i 0.381768 0.924258i \(-0.375315\pi\)
−0.609547 + 0.792750i \(0.708649\pi\)
\(740\) 1.53826 0.0565477
\(741\) 2.19121 + 16.7351i 0.0804960 + 0.614780i
\(742\) 0 0
\(743\) −0.618032 0.356821i −0.0226734 0.0130905i 0.488620 0.872496i \(-0.337500\pi\)
−0.511294 + 0.859406i \(0.670834\pi\)
\(744\) −2.26721 + 3.92692i −0.0831198 + 0.143968i
\(745\) −0.00592959 0.0102703i −0.000217243 0.000376276i
\(746\) 9.19587i 0.336685i
\(747\) −5.66873 + 3.27284i −0.207408 + 0.119747i
\(748\) 0.854012 0.493064i 0.0312258 0.0180282i
\(749\) 0 0
\(750\) −1.97354 3.41827i −0.0720634 0.124817i
\(751\) −12.8507 + 22.2580i −0.468927 + 0.812205i −0.999369 0.0355158i \(-0.988693\pi\)
0.530442 + 0.847721i \(0.322026\pi\)
\(752\) −10.1120 5.83815i −0.368746 0.212896i
\(753\) −6.52477 −0.237776
\(754\) −12.0167 + 9.20730i −0.437624 + 0.335310i
\(755\) −19.7084 −0.717263
\(756\) 0 0
\(757\) −8.19425 + 14.1928i −0.297825 + 0.515848i −0.975638 0.219386i \(-0.929594\pi\)
0.677813 + 0.735234i \(0.262928\pi\)
\(758\) 2.03430 + 3.52350i 0.0738889 + 0.127979i
\(759\) 14.8004i 0.537219i
\(760\) 9.32654 5.38468i 0.338309 0.195323i
\(761\) 7.20531 4.15999i 0.261192 0.150800i −0.363686 0.931522i \(-0.618482\pi\)
0.624878 + 0.780722i \(0.285149\pi\)
\(762\) 0.852923i 0.0308981i
\(763\) 0 0
\(764\) 5.66888 9.81878i 0.205093 0.355231i
\(765\) −0.292133 0.168663i −0.0105621 0.00609802i
\(766\) 11.1853 0.404140
\(767\) 30.8569 23.6428i 1.11418 0.853690i
\(768\) 0.394335 0.0142293
\(769\) −22.1346 12.7794i −0.798194 0.460838i 0.0446452 0.999003i \(-0.485784\pi\)
−0.842839 + 0.538165i \(0.819118\pi\)
\(770\) 0 0
\(771\) 5.78738 + 10.0240i 0.208427 + 0.361007i
\(772\) 8.45131i 0.304169i
\(773\) 7.27528 4.20038i 0.261674 0.151077i −0.363424 0.931624i \(-0.618392\pi\)
0.625098 + 0.780546i \(0.285059\pi\)
\(774\) 4.75789 2.74697i 0.171019 0.0987378i
\(775\) 11.1391i 0.400130i
\(776\) −2.53392 4.38887i −0.0909623 0.157551i
\(777\) 0 0
\(778\) −9.26388 5.34850i −0.332126 0.191753i
\(779\) 66.6537 2.38812
\(780\) −0.725534 5.54119i −0.0259783 0.198406i
\(781\) −14.6743 −0.525087