Properties

Label 637.2.q.g.491.3
Level $637$
Weight $2$
Character 637.491
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 491.3
Root \(-1.18541 + 0.771231i\) of defining polynomial
Character \(\chi\) \(=\) 637.491
Dual form 637.2.q.g.589.3

$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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 −0.645215 0.764001i \(-0.723232\pi\)
0.339037 + 0.940773i \(0.389899\pi\)
\(3\) −0.424801 0.735776i −0.245259 0.424801i 0.716946 0.697129i \(-0.245540\pi\)
−0.962204 + 0.272328i \(0.912206\pi\)
\(4\) −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 0.117251 0.993102i \(-0.462592\pi\)
0.918677 + 0.395009i \(0.129258\pi\)
\(12\) 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 \(-0.838816\pi\)
0.857285 + 0.514843i \(0.172150\pi\)
\(18\) 1.13906i 0.268479i
\(19\) 4.77160 + 2.75488i 1.09468 + 0.632014i 0.934818 0.355126i \(-0.115562\pi\)
0.159861 + 0.987140i \(0.448895\pi\)
\(20\) −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 0.998844 0.0480711i \(-0.0153074\pi\)
−0.541053 + 0.840989i \(0.681974\pi\)
\(24\) −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 0.932116 + 0.362159i \(0.117960\pi\)
−0.152419 + 0.988316i \(0.548706\pi\)
\(30\) −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 −0.438774 0.898598i \(-0.644587\pi\)
0.558821 + 0.829288i \(0.311254\pi\)
\(38\) −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 0.654044 0.756457i \(-0.273071\pi\)
0.982133 0.188190i \(-0.0602621\pi\)
\(42\) 0 0
\(43\) 2.41161 4.17704i 0.367768 0.636993i −0.621448 0.783455i \(-0.713455\pi\)
0.989216 + 0.146463i \(0.0467888\pi\)
\(44\) 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 \(-0.580960\pi\)
−0.963969 + 0.266013i \(0.914294\pi\)
\(60\) 1.54997i 0.200100i
\(61\) 2.93177 5.07797i 0.375374 0.650168i −0.615009 0.788520i \(-0.710847\pi\)
0.990383 + 0.138353i \(0.0441808\pi\)
\(62\) −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 −0.202523 0.979277i \(-0.564914\pi\)
0.746818 + 0.665029i \(0.231581\pi\)
\(68\) −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 0.297730 0.954650i \(-0.403771\pi\)
−0.677887 + 0.735167i \(0.737104\pi\)
\(72\) −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 \(-0.696193\pi\)
0.417635 + 0.908615i \(0.362859\pi\)
\(90\) −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 \(-0.289517\pi\)
−0.376435 + 0.926443i \(0.622850\pi\)
\(98\) 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 0.996488 + 0.0837401i \(0.0266866\pi\)
−0.425723 + 0.904854i \(0.639980\pi\)
\(102\) −0.0522517 + 0.0301676i −0.00517369 + 0.00298703i
\(103\) −4.16950 −0.410834 −0.205417 0.978675i \(-0.565855\pi\)
−0.205417 + 0.978675i \(0.565855\pi\)
\(104\) −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 0.584662 0.811277i \(-0.301227\pi\)
−0.994917 + 0.100694i \(0.967894\pi\)
\(108\) 3.92383 6.79628i 0.377571 0.653972i
\(109\) 6.43036i 0.615917i 0.951400 + 0.307958i \(0.0996458\pi\)
−0.951400 + 0.307958i \(0.900354\pi\)
\(110\) −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 0.484165 + 0.874977i \(0.339123\pi\)
−0.999835 + 0.0181892i \(0.994210\pi\)
\(114\) 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 0.818040 0.575162i \(-0.195061\pi\)
−0.907125 + 0.420862i \(0.861728\pi\)
\(128\) −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 \(-0.683049\pi\)
−0.543890 + 0.839156i \(0.683049\pi\)
\(132\) 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 0.293243 0.956038i \(-0.405265\pi\)
−0.681332 + 0.731975i \(0.738599\pi\)
\(138\) 1.86524i 0.158780i
\(139\) 10.3693 17.9601i 0.879510 1.52336i 0.0276301 0.999618i \(-0.491204\pi\)
0.851880 0.523737i \(-0.175463\pi\)
\(140\) 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 0.499596 0.866258i \(-0.333482\pi\)
−0.500403 + 0.865792i \(0.666815\pi\)
\(150\) 1.43960 + 0.831153i 0.117543 + 0.0678633i
\(151\) 18.9054i 1.53850i −0.638947 0.769251i \(-0.720630\pi\)
0.638947 0.769251i \(-0.279370\pi\)
\(152\) 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 \(-0.210155\pi\)
0.789856 + 0.613292i \(0.210155\pi\)
\(158\) −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 0.165450 0.986218i \(-0.447092\pi\)
−0.771365 + 0.636393i \(0.780426\pi\)
\(164\) 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 \(-0.590385\pi\)
0.691269 + 0.722597i \(0.257052\pi\)
\(168\) 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 0.126535 0.991962i \(-0.459614\pi\)
0.795797 0.605563i \(-0.207052\pi\)
\(174\) 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 0.778315 0.627874i \(-0.216075\pi\)
−0.932912 + 0.360103i \(0.882741\pi\)
\(180\) −3.59936 + 2.07809i −0.268280 + 0.154892i
\(181\) −7.86568 −0.584651 −0.292326 0.956319i \(-0.594429\pi\)
−0.292326 + 0.956319i \(0.594429\pi\)
\(182\) 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 −0.724705 0.689059i \(-0.758024\pi\)
0.959095 + 0.283084i \(0.0913574\pi\)
\(192\) −1.10857 1.92011i −0.0800044 0.138572i
\(193\) −4.18228 + 2.41464i −0.301047 + 0.173810i −0.642913 0.765939i \(-0.722274\pi\)
0.341866 + 0.939749i \(0.388941\pi\)
\(194\) −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 −0.601554 + 0.798832i \(0.705452\pi\)
−0.992586 + 0.121545i \(0.961215\pi\)
\(198\) 2.25950 + 3.91356i 0.160575 + 0.278125i
\(199\) 8.55731 14.8217i 0.606612 1.05068i −0.385183 0.922840i \(-0.625862\pi\)
0.991795 0.127842i \(-0.0408050\pi\)
\(200\) 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 −0.987631 0.156799i \(-0.949883\pi\)
0.358024 0.933713i \(-0.383451\pi\)
\(212\) 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 \(-0.792582\pi\)
0.127674 + 0.991816i \(0.459249\pi\)
\(224\) 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 \(-0.535857\pi\)
−0.916741 + 0.399481i \(0.869190\pi\)
\(228\) 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 \(0.0812263\pi\)
−0.967618 + 0.252419i \(0.918774\pi\)
\(240\) −1.96557 1.13482i −0.126877 0.0732524i
\(241\) −18.8493 10.8826i −1.21419 0.701012i −0.250519 0.968112i \(-0.580601\pi\)
−0.963669 + 0.267100i \(0.913935\pi\)
\(242\) 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 \(-0.755408\pi\)
0.961390 + 0.275191i \(0.0887411\pi\)
\(252\) 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 \(-0.0269713\pi\)
−0.571499 + 0.820603i \(0.693638\pi\)
\(258\) 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 0.988198 0.153181i \(-0.0489518\pi\)
−0.626758 + 0.779214i \(0.715618\pi\)
\(264\) −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 \(-0.923810\pi\)
0.691061 + 0.722796i \(0.257143\pi\)
\(270\) 1.16867 + 2.02420i 0.0711232 + 0.123189i
\(271\) −2.22022 + 1.28184i −0.134869 + 0.0778665i −0.565916 0.824463i \(-0.691477\pi\)
0.431048 + 0.902329i \(0.358144\pi\)
\(272\) 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 −0.879712 0.475506i \(-0.842265\pi\)
0.851657 + 0.524100i \(0.175598\pi\)
\(278\) 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 \(0.0616509\pi\)
−0.981302 + 0.192473i \(0.938349\pi\)
\(282\) −0.967771 + 1.67623i −0.0576299 + 0.0998180i
\(283\) 11.0873 + 19.2037i 0.659071 + 1.14154i 0.980857 + 0.194731i \(0.0623835\pi\)
−0.321786 + 0.946812i \(0.604283\pi\)
\(284\) 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 \(-0.583269\pi\)
−0.965874 + 0.259014i \(0.916602\pi\)
\(294\) 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 \(-0.536060\pi\)
−0.113044 + 0.993590i \(0.536060\pi\)
\(312\) 5.30477 2.20169i 0.300323 0.124646i
\(313\) 28.4754 1.60953 0.804763 0.593597i \(-0.202293\pi\)
0.804763 + 0.593597i \(0.202293\pi\)
\(314\) −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 \(0.156556\pi\)
−0.881468 + 0.472244i \(0.843444\pi\)
\(318\) −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 0.344885 0.938645i \(-0.387918\pi\)
−0.640448 + 0.768002i \(0.721251\pi\)
\(332\) −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 0.0922088 + 0.995740i \(0.470607\pi\)
−0.908440 + 0.418015i \(0.862726\pi\)
\(348\) 6.24283 + 10.8129i 0.334651 + 0.579632i
\(349\) −13.9933 + 8.07906i −0.749046 + 0.432462i −0.825349 0.564623i \(-0.809022\pi\)
0.0763028 + 0.997085i \(0.475688\pi\)
\(350\) 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 \(-0.564611\pi\)
0.747451 + 0.664317i \(0.231277\pi\)
\(354\) −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 \(0.310350\pi\)
−0.561174 + 0.827698i \(0.689650\pi\)
\(360\) 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 −0.987870 0.155285i \(-0.950370\pi\)
0.359454 0.933163i \(-0.382963\pi\)
\(368\) 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 −0.523470 0.852044i \(-0.675363\pi\)
0.999627 + 0.0273160i \(0.00869604\pi\)
\(374\) −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 −0.669953 0.742403i \(-0.733686\pi\)
0.307963 + 0.951398i \(0.400353\pi\)
\(380\) −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 \(-0.139674\pi\)
0.0846992 + 0.996407i \(0.473007\pi\)
\(384\) 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 \(-0.342894\pi\)
−0.525782 + 0.850619i \(0.676227\pi\)
\(398\) 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 −0.572479 + 0.819919i \(0.694018\pi\)
−0.996310 + 0.0858220i \(0.972648\pi\)
\(402\) 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 \(-0.215171\pi\)
−0.151793 + 0.988412i \(0.548505\pi\)
\(410\) −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 \(-0.120369\pi\)
−0.784414 + 0.620238i \(0.787036\pi\)
\(420\) 0 0
\(421\) 2.63174i 0.128263i −0.997941 0.0641317i \(-0.979572\pi\)
0.997941 0.0641317i \(-0.0204278\pi\)
\(422\) 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 −0.838486 0.544923i \(-0.816559\pi\)
0.0526738 + 0.998612i \(0.483226\pi\)
\(432\) 5.74573 + 9.95190i 0.276442 + 0.478811i
\(433\) 9.56773 16.5718i 0.459796 0.796389i −0.539154 0.842207i \(-0.681256\pi\)
0.998950 + 0.0458176i \(0.0145893\pi\)
\(434\) 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 \(-0.176278\pi\)
−0.880726 + 0.473627i \(0.842945\pi\)
\(440\) 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 0.818450 0.574578i \(-0.194834\pi\)
−0.0883746 + 0.996087i \(0.528167\pi\)
\(450\) 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 −0.361072 0.932538i \(-0.617589\pi\)
0.627066 + 0.778966i \(0.284256\pi\)
\(458\) −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 \(-0.371329\pi\)
−0.599571 + 0.800322i \(0.704662\pi\)
\(462\) 0 0
\(463\) 33.3239i 1.54869i −0.632761 0.774347i \(-0.718079\pi\)
0.632761 0.774347i \(-0.281921\pi\)
\(464\) 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 \(-0.403142\pi\)
0.299614 + 0.954060i \(0.403142\pi\)
\(468\) −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 \(-0.878361\pi\)
−0.140987 + 0.990012i \(0.545027\pi\)
\(480\) 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 −0.286182 0.958175i \(-0.592386\pi\)
−0.972895 + 0.231247i \(0.925720\pi\)
\(488\) −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 −0.984200 0.177061i \(-0.943341\pi\)
0.338760 0.940873i \(-0.389992\pi\)
\(492\) 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 \(-0.987185\pi\)
0.999190 0.0402484i \(-0.0128149\pi\)
\(500\) −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 0.335297 + 0.942112i \(0.391163\pi\)
−0.983542 + 0.180681i \(0.942170\pi\)
\(504\) 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 \(-0.838492\pi\)
−0.0162054 + 0.999869i \(0.505159\pi\)
\(510\) −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 \(-0.240275\pi\)
0.728376 + 0.685178i \(0.240275\pi\)
\(522\) −8.28383 + 4.78267i −0.362574 + 0.209332i
\(523\) −19.3560 33.5256i −0.846380 1.46597i −0.884417 0.466697i \(-0.845444\pi\)
0.0380367 0.999276i \(-0.487890\pi\)
\(524\) 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 \(0.162009\pi\)
−0.873248 + 0.487275i \(0.837991\pi\)
\(542\) 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 −0.693227 0.720719i \(-0.743812\pi\)
0.277547 + 0.960712i \(0.410478\pi\)
\(558\) −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 −0.284778 0.958594i \(-0.591920\pi\)
0.972555 0.232672i \(-0.0747469\pi\)
\(564\) 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 0.955235 + 0.295847i \(0.0956019\pi\)
−0.221407 + 0.975182i \(0.571065\pi\)
\(570\) −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 \(-0.527419\pi\)
0.819798 + 0.572653i \(0.194086\pi\)
\(588\) 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 \(-0.0312579\pi\)
−0.582498 + 0.812832i \(0.697925\pi\)
\(602\) 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 \(-0.875780\pi\)
0.791860 + 0.610703i \(0.209113\pi\)
\(608\) 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 −0.952648 0.304075i \(-0.901653\pi\)
−0.212988 + 0.977055i \(0.568319\pi\)
\(614\) −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 0.613199 0.789929i \(-0.289883\pi\)
−0.377499 + 0.926010i \(0.623216\pi\)
\(618\) −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 0.746319 0.665588i \(-0.231819\pi\)
−0.203257 + 0.979125i \(0.565153\pi\)
\(632\) 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 −0.995275 0.0970962i \(-0.969045\pi\)
0.581725 + 0.813385i \(0.302378\pi\)
\(642\) 3.60537i 0.142293i
\(643\) −16.3952 9.46576i −0.646563 0.373293i 0.140575 0.990070i \(-0.455105\pi\)
−0.787138 + 0.616777i \(0.788438\pi\)
\(644\) 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 −0.952216 0.305426i \(-0.901201\pi\)
0.211601 0.977356i \(-0.432132\pi\)
\(648\) −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 −0.996757 0.0804686i \(-0.974358\pi\)
0.428691 0.903451i \(-0.358975\pi\)
\(654\) −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 −0.851883 0.523733i \(-0.824539\pi\)
0.879507 + 0.475886i \(0.157872\pi\)
\(660\) 3.07459 + 5.32535i 0.119678 + 0.207289i
\(661\) 3.97764 2.29649i 0.154712 0.0893231i −0.420645 0.907225i \(-0.638196\pi\)
0.575357 + 0.817902i \(0.304863\pi\)
\(662\) 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 0.822684 0.568499i \(-0.192475\pi\)
−0.903676 + 0.428216i \(0.859142\pi\)
\(674\) −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 \(-0.450331\pi\)
0.155406 + 0.987851i \(0.450331\pi\)
\(678\) −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 0.0316929 0.999498i \(-0.489910\pi\)
−0.849744 + 0.527196i \(0.823243\pi\)
\(684\) 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 \(-0.597981\pi\)
0.673831 + 0.738885i \(0.264647\pi\)
\(692\) 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 0.0607929 0.998150i \(-0.480637\pi\)
−0.834027 + 0.551723i \(0.813970\pi\)
\(710\) 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 \(-0.706673\pi\)
0.992112 + 0.125354i \(0.0400068\pi\)
\(720\) 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 \(-0.665366\pi\)
−0.496457 + 0.868061i \(0.665366\pi\)
\(728\) 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 −0.609547 0.792750i \(-0.708649\pi\)
0.381768 + 0.924258i \(0.375315\pi\)
\(740\) −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 −0.511294 0.859406i \(-0.670834\pi\)
0.488620 + 0.872496i \(0.337500\pi\)
\(744\) −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 0.530442 0.847721i \(-0.322026\pi\)
−0.999369 + 0.0355158i \(0.988693\pi\)
\(752\) 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 0.677813 0.735234i \(-0.262928\pi\)
−0.975638 + 0.219386i \(0.929594\pi\)
\(758\) 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 \(-0.381518\pi\)
−0.624878 + 0.780722i \(0.714851\pi\)
\(762\) 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 \(-0.514216\pi\)
0.842839 + 0.538165i \(0.180882\pi\)
\(770\) 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 \(-0.381608\pi\)
−0.625098 + 0.780546i \(0.714941\pi\)
\(774\) 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