Properties

Label 637.2.k.i.569.3
Level $637$
Weight $2$
Character 637.569
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.k (of order \(6\), degree \(2\), not 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 569.3
Root \(-1.18541 - 0.771231i\) of defining polynomial
Character \(\chi\) \(=\) 637.569
Dual form 637.2.k.i.459.4

$q$-expansion

\(f(q)\) \(=\) \(q-0.499987i q^{2} +(0.424801 - 0.735776i) q^{3} +1.75001 q^{4} +(0.902810 + 0.521238i) q^{5} +(-0.367878 - 0.212395i) q^{6} -1.87496i q^{8} +(1.13909 + 1.97296i) q^{9} +O(q^{10})\) \(q-0.499987i q^{2} +(0.424801 - 0.735776i) q^{3} +1.75001 q^{4} +(0.902810 + 0.521238i) 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} +(0.743407 - 1.28762i) q^{12} +(3.57504 + 0.468096i) q^{13} +(0.767029 - 0.442844i) q^{15} +2.56257 q^{16} -0.142035 q^{17} +(0.986453 - 0.569529i) q^{18} +(4.77160 - 2.75488i) q^{19} +(1.57993 + 0.912173i) q^{20} +(-0.991800 + 1.71785i) q^{22} -4.39098 q^{23} +(-1.37955 - 0.796483i) q^{24} +(-1.95662 - 3.38897i) q^{25} +(0.234042 - 1.78747i) q^{26} +4.48435 q^{27} +(4.19880 + 7.27253i) q^{29} +(-0.221416 - 0.383504i) q^{30} +(-2.46516 + 1.42326i) q^{31} -5.03117i q^{32} +(-2.91905 + 1.68531i) q^{33} +0.0710158i q^{34} +(1.99342 + 3.45271i) q^{36} +0.843187i q^{37} +(-1.37740 - 2.38574i) q^{38} +(1.86309 - 2.43158i) q^{39} +(0.977298 - 1.69273i) q^{40} +(-10.4766 + 6.04869i) q^{41} +(2.41161 - 4.17704i) q^{43} +(-6.01267 - 3.47142i) q^{44} +2.37494i q^{45} +2.19543i q^{46} +(3.94602 + 2.27824i) q^{47} +(1.08858 - 1.88548i) q^{48} +(-1.69444 + 0.978285i) q^{50} +(-0.0603367 + 0.104506i) q^{51} +(6.25636 + 0.819175i) q^{52} +(0.139800 + 0.242141i) q^{53} -2.24211i q^{54} +(-2.06791 - 3.58172i) q^{55} -4.68111i q^{57} +(3.63617 - 2.09934i) q^{58} -10.7815i q^{59} +(1.34231 - 0.774983i) q^{60} +(-2.93177 - 5.07797i) q^{61} +(0.711612 + 1.23255i) q^{62} +2.60963 q^{64} +(2.98359 + 2.28605i) q^{65} +(0.842634 + 1.45949i) q^{66} +(-4.45524 - 2.57223i) q^{67} -0.248564 q^{68} +(-1.86529 + 3.23078i) q^{69} +(-3.20326 - 1.84940i) q^{71} +(3.69921 - 2.13574i) q^{72} +(-5.72686 + 3.30640i) q^{73} +0.421582 q^{74} -3.32470 q^{75} +(8.35036 - 4.82108i) q^{76} +(-1.21576 - 0.931521i) q^{78} +(-5.96135 + 10.3254i) 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} +(-2.08846 - 1.20578i) q^{86} +7.13461 q^{87} +(-3.71926 + 6.44195i) q^{88} +1.74765i q^{89} +1.18744 q^{90} -7.68427 q^{92} +2.41841i q^{93} +(1.13909 - 1.97296i) q^{94} +5.74379 q^{95} +(-3.70181 - 2.13724i) q^{96} +(-2.34079 - 1.35145i) q^{97} -9.03822i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 3q^{3} - 8q^{4} + 3q^{5} + 9q^{6} - q^{9} + O(q^{10}) \) \( 12q + 3q^{3} - 8q^{4} + 3q^{5} + 9q^{6} - q^{9} - 12q^{10} + 12q^{11} + q^{12} + 2q^{13} - 12q^{15} + 16q^{16} + 34q^{17} + 3q^{18} - 9q^{19} + 3q^{20} - 15q^{22} - 6q^{23} - 15q^{24} - 5q^{25} + 6q^{26} - 12q^{27} - q^{29} + 11q^{30} - 18q^{31} + 6q^{33} - 13q^{36} - 19q^{38} - 4q^{39} + q^{40} + 6q^{41} + 11q^{43} - 33q^{44} + 15q^{47} - 19q^{48} + 18q^{50} + 4q^{51} + 7q^{52} - 8q^{53} + 15q^{55} - 24q^{58} - 30q^{60} - 5q^{61} - 41q^{62} + 2q^{64} + 21q^{65} + 34q^{66} + 15q^{67} - 22q^{68} - 7q^{69} + 30q^{71} + 57q^{72} - 42q^{73} + 66q^{74} + 2q^{75} + 45q^{76} + 44q^{78} - 35q^{79} + 63q^{80} + 14q^{81} - 5q^{82} - 21q^{85} - 57q^{86} + 20q^{87} - 14q^{88} - 66q^{92} - q^{94} - 4q^{95} - 21q^{96} + 3q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.499987i 0.353544i −0.984252 0.176772i \(-0.943434\pi\)
0.984252 0.176772i \(-0.0565655\pi\)
\(3\) 0.424801 0.735776i 0.245259 0.424801i −0.716946 0.697129i \(-0.754460\pi\)
0.962204 + 0.272328i \(0.0877937\pi\)
\(4\) 1.75001 0.875007
\(5\) 0.902810 + 0.521238i 0.403749 + 0.233105i 0.688100 0.725616i \(-0.258445\pi\)
−0.284351 + 0.958720i \(0.591778\pi\)
\(6\) −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 \(-0.537408\pi\)
−0.918677 + 0.395009i \(0.870742\pi\)
\(12\) 0.743407 1.28762i 0.214603 0.371703i
\(13\) 3.57504 + 0.468096i 0.991537 + 0.129827i
\(14\) 0 0
\(15\) 0.767029 0.442844i 0.198046 0.114342i
\(16\) 2.56257 0.640643
\(17\) −0.142035 −0.0344486 −0.0172243 0.999852i \(-0.505483\pi\)
−0.0172243 + 0.999852i \(0.505483\pi\)
\(18\) 0.986453 0.569529i 0.232509 0.134239i
\(19\) 4.77160 2.75488i 1.09468 0.632014i 0.159861 0.987140i \(-0.448895\pi\)
0.934818 + 0.355126i \(0.115562\pi\)
\(20\) 1.57993 + 0.912173i 0.353283 + 0.203968i
\(21\) 0 0
\(22\) −0.991800 + 1.71785i −0.211452 + 0.366246i
\(23\) −4.39098 −0.915582 −0.457791 0.889060i \(-0.651359\pi\)
−0.457791 + 0.889060i \(0.651359\pi\)
\(24\) −1.37955 0.796483i −0.281599 0.162581i
\(25\) −1.95662 3.38897i −0.391325 0.677794i
\(26\) 0.234042 1.78747i 0.0458994 0.350552i
\(27\) 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
\(31\) −2.46516 + 1.42326i −0.442756 + 0.255625i −0.704766 0.709440i \(-0.748948\pi\)
0.262010 + 0.965065i \(0.415615\pi\)
\(32\) 5.03117i 0.889393i
\(33\) −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
\(37\) 0.843187i 0.138619i 0.997595 + 0.0693095i \(0.0220796\pi\)
−0.997595 + 0.0693095i \(0.977920\pi\)
\(38\) −1.37740 2.38574i −0.223445 0.387017i
\(39\) 1.86309 2.43158i 0.298334 0.389364i
\(40\) 0.977298 1.69273i 0.154524 0.267644i
\(41\) −10.4766 + 6.04869i −1.63618 + 0.944647i −0.654044 + 0.756457i \(0.726929\pi\)
−0.982133 + 0.188190i \(0.939738\pi\)
\(42\) 0 0
\(43\) 2.41161 4.17704i 0.367768 0.636993i −0.621448 0.783455i \(-0.713455\pi\)
0.989216 + 0.146463i \(0.0467888\pi\)
\(44\) −6.01267 3.47142i −0.906444 0.523336i
\(45\) 2.37494i 0.354036i
\(46\) 2.19543i 0.323699i
\(47\) 3.94602 + 2.27824i 0.575587 + 0.332315i 0.759378 0.650650i \(-0.225504\pi\)
−0.183791 + 0.982965i \(0.558837\pi\)
\(48\) 1.08858 1.88548i 0.157123 0.272146i
\(49\) 0 0
\(50\) −1.69444 + 0.978285i −0.239630 + 0.138350i
\(51\) −0.0603367 + 0.104506i −0.00844883 + 0.0146338i
\(52\) 6.25636 + 0.819175i 0.867601 + 0.113599i
\(53\) 0.139800 + 0.242141i 0.0192030 + 0.0332606i 0.875467 0.483278i \(-0.160554\pi\)
−0.856264 + 0.516538i \(0.827220\pi\)
\(54\) 2.24211i 0.305113i
\(55\) −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
\(59\) 10.7815i 1.40363i −0.712359 0.701815i \(-0.752373\pi\)
0.712359 0.701815i \(-0.247627\pi\)
\(60\) 1.34231 0.774983i 0.173292 0.100050i
\(61\) −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
\(65\) 2.98359 + 2.28605i 0.370069 + 0.283549i
\(66\) 0.842634 + 1.45949i 0.103721 + 0.179650i
\(67\) −4.45524 2.57223i −0.544294 0.314248i 0.202523 0.979277i \(-0.435086\pi\)
−0.746818 + 0.665029i \(0.768419\pi\)
\(68\) −0.248564 −0.0301428
\(69\) −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
\(73\) −5.72686 + 3.30640i −0.670278 + 0.386985i −0.796182 0.605057i \(-0.793150\pi\)
0.125904 + 0.992042i \(0.459817\pi\)
\(74\) 0.421582 0.0490079
\(75\) −3.32470 −0.383903
\(76\) 8.35036 4.82108i 0.957852 0.553016i
\(77\) 0 0
\(78\) −1.21576 0.931521i −0.137657 0.105474i
\(79\) −5.96135 + 10.3254i −0.670705 + 1.16169i 0.307000 + 0.951710i \(0.400675\pi\)
−0.977705 + 0.209985i \(0.932658\pi\)
\(80\) 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 \(-0.949596\pi\)
0.987489 0.157688i \(-0.0504040\pi\)
\(84\) 0 0
\(85\) −0.128231 0.0740342i −0.0139086 0.00803013i
\(86\) −2.08846 1.20578i −0.225205 0.130022i
\(87\) 7.13461 0.764910
\(88\) −3.71926 + 6.44195i −0.396475 + 0.686714i
\(89\) 1.74765i 0.185250i 0.995701 + 0.0926252i \(0.0295258\pi\)
−0.995701 + 0.0926252i \(0.970474\pi\)
\(90\) 1.18744 0.125167
\(91\) 0 0
\(92\) −7.68427 −0.801141
\(93\) 2.41841i 0.250777i
\(94\) 1.13909 1.97296i 0.117488 0.203495i
\(95\) 5.74379 0.589301
\(96\) −3.70181 2.13724i −0.377815 0.218131i
\(97\) −2.34079 1.35145i −0.237671 0.137219i 0.376435 0.926443i \(-0.377150\pi\)
−0.614106 + 0.789224i \(0.710483\pi\)
\(98\) 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
\(103\) −2.08475 + 3.61090i −0.205417 + 0.355792i −0.950265 0.311441i \(-0.899188\pi\)
0.744849 + 0.667233i \(0.232522\pi\)
\(104\) 0.877660 6.70304i 0.0860617 0.657287i
\(105\) 0 0
\(106\) 0.121067 0.0698982i 0.0117591 0.00678911i
\(107\) 8.48742 0.820510 0.410255 0.911971i \(-0.365440\pi\)
0.410255 + 0.911971i \(0.365440\pi\)
\(108\) 7.84767 0.755142
\(109\) 5.56886 3.21518i 0.533400 0.307958i −0.209000 0.977916i \(-0.567021\pi\)
0.742400 + 0.669957i \(0.233688\pi\)
\(110\) −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 \(0.994210\pi\)
\(114\) −2.34049 −0.219207
\(115\) −3.96422 2.28874i −0.369665 0.213426i
\(116\) 7.34795 + 12.7270i 0.682240 + 1.18167i
\(117\) 3.14875 + 7.58661i 0.291102 + 0.701382i
\(118\) −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
\(122\) −2.53892 + 1.46584i −0.229863 + 0.132711i
\(123\) 10.2780i 0.926732i
\(124\) −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 \(0.861728\pi\)
\(128\) 11.3671i 1.00472i
\(129\) −2.04891 3.54882i −0.180397 0.312456i
\(130\) 1.14299 1.49175i 0.100247 0.130836i
\(131\) −6.22511 + 10.7822i −0.543890 + 0.942046i 0.454785 + 0.890601i \(0.349716\pi\)
−0.998676 + 0.0514449i \(0.983617\pi\)
\(132\) −5.10838 + 2.94932i −0.444627 + 0.256706i
\(133\) 0 0
\(134\) −1.28608 + 2.22756i −0.111101 + 0.192432i
\(135\) 4.04851 + 2.33741i 0.348441 + 0.201172i
\(136\) 0.266310i 0.0228359i
\(137\) 5.24518i 0.448126i 0.974575 + 0.224063i \(0.0719321\pi\)
−0.974575 + 0.224063i \(0.928068\pi\)
\(138\) 1.61535 + 0.932620i 0.137507 + 0.0793899i
\(139\) −10.3693 + 17.9601i −0.879510 + 1.52336i −0.0276301 + 0.999618i \(0.508796\pi\)
−0.851880 + 0.523737i \(0.824537\pi\)
\(140\) 0 0
\(141\) 3.35255 1.93559i 0.282335 0.163006i
\(142\) −0.924676 + 1.60159i −0.0775971 + 0.134402i
\(143\) −11.3545 8.69991i −0.949513 0.727523i
\(144\) 2.91900 + 5.05585i 0.243250 + 0.421321i
\(145\) 8.75428i 0.727004i
\(146\) 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 \(-0.666518\pi\)
0.500403 + 0.865792i \(0.333185\pi\)
\(150\) 1.66231i 0.135727i
\(151\) −16.3726 + 9.45271i −1.33238 + 0.769251i −0.985664 0.168719i \(-0.946037\pi\)
−0.346717 + 0.937970i \(0.612704\pi\)
\(152\) −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
\(156\) 3.26044 4.25530i 0.261044 0.340696i
\(157\) 9.89687 + 17.1419i 0.789856 + 1.36807i 0.926054 + 0.377390i \(0.123178\pi\)
−0.136198 + 0.990682i \(0.543488\pi\)
\(158\) 5.16255 + 2.98060i 0.410710 + 0.237124i
\(159\) 0.237549 0.0188388
\(160\) 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 \(-0.552908\pi\)
0.771365 + 0.636393i \(0.219574\pi\)
\(164\) −18.3343 + 10.5853i −1.43167 + 0.826572i
\(165\) −3.51380 −0.273549
\(166\) −1.43657 −0.111499
\(167\) −5.31279 + 3.06734i −0.411116 + 0.237358i −0.691269 0.722597i \(-0.742948\pi\)
0.280153 + 0.959955i \(0.409615\pi\)
\(168\) 0 0
\(169\) 12.5618 + 3.34692i 0.966290 + 0.257456i
\(170\) −0.0370161 + 0.0641138i −0.00283900 + 0.00491730i
\(171\) 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
\(177\) −7.93277 4.57999i −0.596263 0.344253i
\(178\) 0.873801 0.0654942
\(179\) −2.06838 + 3.58253i −0.154598 + 0.267771i −0.932912 0.360103i \(-0.882741\pi\)
0.778315 + 0.627874i \(0.216075\pi\)
\(180\) 4.15618i 0.309784i
\(181\) 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
\(184\) 8.23289i 0.606937i
\(185\) −0.439501 + 0.761237i −0.0323127 + 0.0559673i
\(186\) 1.20917 0.0886608
\(187\) 0.488003 + 0.281749i 0.0356863 + 0.0206035i
\(188\) 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 0.642913 0.765939i \(-0.277726\pi\)
−0.341866 + 0.939749i \(0.611059\pi\)
\(194\) −0.675708 + 1.17036i −0.0485130 + 0.0840270i
\(195\) 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 \(0.961215\pi\)
\(198\) −4.51899 −0.321151
\(199\) 17.1146 1.21322 0.606612 0.794998i \(-0.292528\pi\)
0.606612 + 0.794998i \(0.292528\pi\)
\(200\) −6.35417 + 3.66858i −0.449308 + 0.259408i
\(201\) −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
\(205\) −12.6112 −0.880806
\(206\) 1.80540 + 1.04235i 0.125788 + 0.0726238i
\(207\) −5.00171 8.66322i −0.347643 0.602136i
\(208\) 9.16129 + 1.19953i 0.635221 + 0.0831725i
\(209\) −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
\(213\) −2.72149 + 1.57125i −0.186474 + 0.107661i
\(214\) 4.24360i 0.290086i
\(215\) 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
\(219\) 5.61825i 0.379646i
\(220\) −3.61887 6.26806i −0.243984 0.422593i
\(221\) −0.507782 0.0664862i −0.0341571 0.00447235i
\(222\) 0.179088 0.310190i 0.0120196 0.0208186i
\(223\) 9.96682 5.75435i 0.667428 0.385340i −0.127674 0.991816i \(-0.540751\pi\)
0.795101 + 0.606477i \(0.207418\pi\)
\(224\) 0 0
\(225\) 4.45753 7.72067i 0.297169 0.514712i
\(226\) 4.74711 + 2.74075i 0.315773 + 0.182312i
\(227\) 17.9045i 1.18836i −0.804332 0.594181i \(-0.797476\pi\)
0.804332 0.594181i \(-0.202524\pi\)
\(228\) 8.19200i 0.542528i
\(229\) 3.34589 + 1.93175i 0.221103 + 0.127654i 0.606461 0.795113i \(-0.292589\pi\)
−0.385358 + 0.922767i \(0.625922\pi\)
\(230\) −1.14434 + 1.98206i −0.0754556 + 0.130693i
\(231\) 0 0
\(232\) 13.6357 7.87256i 0.895226 0.516859i
\(233\) 12.5321 21.7062i 0.821004 1.42202i −0.0839312 0.996472i \(-0.526748\pi\)
0.904935 0.425549i \(-0.139919\pi\)
\(234\) 3.79320 1.57433i 0.247969 0.102917i
\(235\) 2.37501 + 4.11363i 0.154928 + 0.268344i
\(236\) 18.8678i 1.22819i
\(237\) 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
\(241\) 21.7653i 1.40202i −0.713150 0.701012i \(-0.752732\pi\)
0.713150 0.701012i \(-0.247268\pi\)
\(242\) 2.05221 1.18484i 0.131921 0.0761647i
\(243\) 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
\(247\) 18.3482 7.61524i 1.16747 0.484546i
\(248\) 2.66855 + 4.62207i 0.169453 + 0.293502i
\(249\) −2.11404 1.22054i −0.133972 0.0773488i
\(250\) −4.64579 −0.293826
\(251\) −3.83990 + 6.65090i −0.242372 + 0.419801i −0.961390 0.275191i \(-0.911259\pi\)
0.719017 + 0.694992i \(0.244592\pi\)
\(252\) 0 0
\(253\) 15.0865 + 8.71017i 0.948478 + 0.547604i
\(254\) −0.869411 + 0.501955i −0.0545517 + 0.0314954i
\(255\) −0.108945 + 0.0628995i −0.00682241 + 0.00393892i
\(256\) −0.464141 −0.0290088
\(257\) 13.6237 0.849826 0.424913 0.905234i \(-0.360305\pi\)
0.424913 + 0.905234i \(0.360305\pi\)
\(258\) −1.77436 + 1.02443i −0.110467 + 0.0637781i
\(259\) 0 0
\(260\) 5.22132 + 4.00061i 0.323813 + 0.248107i
\(261\) −9.56560 + 16.5681i −0.592096 + 1.02554i
\(262\) 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
\(268\) −7.79673 4.50144i −0.476261 0.274970i
\(269\) −9.19876 −0.560858 −0.280429 0.959875i \(-0.590477\pi\)
−0.280429 + 0.959875i \(0.590477\pi\)
\(270\) 1.16867 2.02420i 0.0711232 0.123189i
\(271\) 2.56369i 0.155733i 0.996964 + 0.0778665i \(0.0248108\pi\)
−0.996964 + 0.0778665i \(0.975189\pi\)
\(272\) −0.363976 −0.0220693
\(273\) 0 0
\(274\) 2.62252 0.158432
\(275\) 15.5250i 0.936195i
\(276\) −3.26428 + 5.65391i −0.196487 + 0.340325i
\(277\) 0.933882 0.0561115 0.0280558 0.999606i \(-0.491068\pi\)
0.0280558 + 0.999606i \(0.491068\pi\)
\(278\) 8.97981 + 5.18450i 0.538573 + 0.310945i
\(279\) −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 0.321786 + 0.946812i \(0.395717\pi\)
−0.980857 + 0.194731i \(0.937616\pi\)
\(284\) −5.60575 3.23648i −0.332640 0.192050i
\(285\) 2.43997 4.22615i 0.144531 0.250335i
\(286\) −4.34984 + 5.67711i −0.257211 + 0.335695i
\(287\) 0 0
\(288\) 9.92629 5.73094i 0.584912 0.337699i
\(289\) −16.9798 −0.998813
\(290\) 4.37702 0.257028
\(291\) −1.98873 + 1.14820i −0.116582 + 0.0673085i
\(292\) −10.0221 + 5.78625i −0.586498 + 0.338615i
\(293\) 20.9600 + 12.1013i 1.22450 + 0.706964i 0.965874 0.259014i \(-0.0833976\pi\)
0.258624 + 0.965978i \(0.416731\pi\)
\(294\) 0 0
\(295\) 5.61972 9.73364i 0.327193 0.566714i
\(296\) 1.58094 0.0918902
\(297\) −15.4073 8.89539i −0.894020 0.516163i
\(298\) −0.00284392 0.00492581i −0.000164744 0.000285345i
\(299\) −15.6979 2.05540i −0.907833 0.118867i
\(300\) −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
\(304\) 12.2276 7.05959i 0.701299 0.404895i
\(305\) 6.11259i 0.350006i
\(306\) −0.140111 + 0.0808933i −0.00800963 + 0.00462436i
\(307\) 24.2924i 1.38644i −0.720726 0.693220i \(-0.756191\pi\)
0.720726 0.693220i \(-0.243809\pi\)
\(308\) 0 0
\(309\) 1.77121 + 3.06782i 0.100761 + 0.174522i
\(310\) 1.48367i 0.0842671i
\(311\) −1.99355 3.45294i −0.113044 0.195798i 0.803952 0.594694i \(-0.202727\pi\)
−0.916996 + 0.398896i \(0.869393\pi\)
\(312\) −4.55911 3.49322i −0.258109 0.197764i
\(313\) 14.2377 24.6604i 0.804763 1.39389i −0.111688 0.993743i \(-0.535626\pi\)
0.916451 0.400147i \(-0.131041\pi\)
\(314\) 8.57071 4.94830i 0.483673 0.279249i
\(315\) 0 0
\(316\) −10.4324 + 18.0695i −0.586871 + 1.01649i
\(317\) −14.5632 8.40806i −0.817950 0.472244i 0.0317591 0.999496i \(-0.489889\pi\)
−0.849709 + 0.527252i \(0.823222\pi\)
\(318\) 0.118771i 0.00666036i
\(319\) 33.3158i 1.86533i
\(320\) 2.35600 + 1.36024i 0.131704 + 0.0760396i
\(321\) 3.60546 6.24485i 0.201237 0.348553i
\(322\) 0 0
\(323\) −0.677736 + 0.391291i −0.0377102 + 0.0217720i
\(324\) −2.64657 + 4.58399i −0.147031 + 0.254666i
\(325\) −5.40863 13.0316i −0.300017 0.722862i
\(326\) −2.23308 3.86780i −0.123679 0.214218i
\(327\) 5.46324i 0.302118i
\(328\) 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 \(-0.612082\pi\)
0.640448 + 0.768002i \(0.278749\pi\)
\(332\) 5.02816i 0.275956i
\(333\) −1.66357 + 0.960464i −0.0911632 + 0.0526331i
\(334\) 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 \(0.432775\pi\)
\(338\) 1.67342 6.28072i 0.0910219 0.341626i
\(339\) 4.65721 + 8.06653i 0.252945 + 0.438114i
\(340\) −0.224406 0.129561i −0.0121701 0.00702642i
\(341\) 11.2930 0.611552
\(342\) 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
\(346\) −10.5058 + 6.06553i −0.564795 + 0.326085i
\(347\) 30.4094 1.63246 0.816231 0.577725i \(-0.196059\pi\)
0.816231 + 0.577725i \(0.196059\pi\)
\(348\) 12.4857 0.669302
\(349\) 13.9933 8.07906i 0.749046 0.432462i −0.0763028 0.997085i \(-0.524312\pi\)
0.825349 + 0.564623i \(0.190978\pi\)
\(350\) 0 0
\(351\) 16.0317 + 2.09911i 0.855709 + 0.112042i
\(352\) −9.98008 + 17.2860i −0.531940 + 0.921347i
\(353\) 10.2558 + 5.92119i 0.545861 + 0.315153i 0.747451 0.664317i \(-0.231277\pi\)
−0.201590 + 0.979470i \(0.564611\pi\)
\(354\) −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
\(359\) −27.1631 15.6826i −1.43362 0.827698i −0.436221 0.899840i \(-0.643683\pi\)
−0.997394 + 0.0721417i \(0.977017\pi\)
\(360\) 4.45292 0.234689
\(361\) 5.67876 9.83591i 0.298882 0.517679i
\(362\) 3.93273i 0.206700i
\(363\) 4.02669 0.211346
\(364\) 0 0
\(365\) −6.89369 −0.360832
\(366\) 2.49077i 0.130195i
\(367\) 12.0387 20.8517i 0.628415 1.08845i −0.359454 0.933163i \(-0.617037\pi\)
0.987870 0.155285i \(-0.0496295\pi\)
\(368\) −11.2522 −0.586562
\(369\) −23.8676 13.7800i −1.24250 0.717358i
\(370\) 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
\(376\) 4.27160 7.39862i 0.220291 0.381555i
\(377\) 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 \(0.400353\pi\)
\(380\) 10.0517 0.515642
\(381\) −1.70589 −0.0873955
\(382\) 2.80527 1.61962i 0.143530 0.0828671i
\(383\) 19.3739 11.1856i 0.989962 0.571555i 0.0846992 0.996407i \(-0.473007\pi\)
0.905263 + 0.424852i \(0.139674\pi\)
\(384\) −8.36365 4.82876i −0.426806 0.246417i
\(385\) 0 0
\(386\) 1.20729 2.09108i 0.0614493 0.106433i
\(387\) 10.9882 0.558560
\(388\) −4.09641 2.36506i −0.207963 0.120068i
\(389\) −10.6973 18.5283i −0.542374 0.939420i −0.998767 0.0496415i \(-0.984192\pi\)
0.456393 0.889778i \(-0.349141\pi\)
\(390\) −0.612054 1.47469i −0.0309926 0.0746736i
\(391\) 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
\(395\) −10.7639 + 6.21456i −0.541592 + 0.312689i
\(396\) 15.8170i 0.794835i
\(397\) −1.03640 + 0.598365i −0.0520154 + 0.0300311i −0.525782 0.850619i \(-0.676227\pi\)
0.473767 + 0.880650i \(0.342894\pi\)
\(398\) 8.55708i 0.428928i
\(399\) 0 0
\(400\) −5.01399 8.68449i −0.250699 0.434224i
\(401\) 36.2749i 1.81148i −0.423831 0.905741i \(-0.639315\pi\)
0.423831 0.905741i \(-0.360685\pi\)
\(402\) 1.09266 + 1.89254i 0.0544968 + 0.0943913i
\(403\) −9.47926 + 3.93428i −0.472196 + 0.195980i
\(404\) −10.0383 + 17.3868i −0.499423 + 0.865026i
\(405\) −2.73066 + 1.57655i −0.135688 + 0.0783393i
\(406\) 0 0
\(407\) 1.67259 2.89701i 0.0829072 0.143599i
\(408\) 0.195945 + 0.113129i 0.00970071 + 0.00560071i
\(409\) 14.6723i 0.725500i 0.931887 + 0.362750i \(0.118162\pi\)
−0.931887 + 0.362750i \(0.881838\pi\)
\(410\) 6.30544i 0.311404i
\(411\) 3.85928 + 2.22816i 0.190364 + 0.109907i
\(412\) −3.64834 + 6.31912i −0.179741 + 0.311321i
\(413\) 0 0
\(414\) −4.33150 + 2.50079i −0.212881 + 0.122907i
\(415\) 1.49763 2.59397i 0.0735156 0.127333i
\(416\) 2.35507 17.9866i 0.115467 0.881866i
\(417\) 8.80975 + 15.2589i 0.431415 + 0.747233i
\(418\) 10.9292i 0.534563i
\(419\) −2.96674 5.13855i −0.144935 0.251034i 0.784414 0.620238i \(-0.212964\pi\)
−0.929349 + 0.369203i \(0.879631\pi\)
\(420\) 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
\(423\) 10.3805i 0.504715i
\(424\) 0.454004 0.262119i 0.0220484 0.0127296i
\(425\) 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
\(429\) −11.2246 + 4.65866i −0.541929 + 0.224922i
\(430\) −1.25699 2.17717i −0.0606175 0.104993i
\(431\) 16.3139 + 9.41883i 0.785812 + 0.453689i 0.838486 0.544923i \(-0.183441\pi\)
−0.0526738 + 0.998612i \(0.516774\pi\)
\(432\) 11.4915 0.552884
\(433\) −9.56773 + 16.5718i −0.459796 + 0.796389i −0.998950 0.0458176i \(-0.985411\pi\)
0.539154 + 0.842207i \(0.318744\pi\)
\(434\) 0 0
\(435\) 6.44119 + 3.71883i 0.308832 + 0.178304i
\(436\) 9.74557 5.62661i 0.466728 0.269466i
\(437\) −20.9520 + 12.0966i −1.00227 + 0.578660i
\(438\) 2.80905 0.134222
\(439\) −1.26511 −0.0603803 −0.0301901 0.999544i \(-0.509611\pi\)
−0.0301901 + 0.999544i \(0.509611\pi\)
\(440\) −6.71557 + 3.87724i −0.320152 + 0.184840i
\(441\) 0 0
\(442\) −0.0332422 + 0.253884i −0.00158117 + 0.0120760i
\(443\) 10.4696 18.1339i 0.497426 0.861568i −0.502569 0.864537i \(-0.667612\pi\)
0.999996 + 0.00296930i \(0.000945159\pi\)
\(444\) 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 \(0.528167\pi\)
\(450\) −3.86023 2.22871i −0.181973 0.105062i
\(451\) 47.9940 2.25995
\(452\) −9.59295 + 16.6155i −0.451214 + 0.781526i
\(453\) 16.0621i 0.754662i
\(454\) −8.95199 −0.420138
\(455\) 0 0
\(456\) −8.77687 −0.411015
\(457\) 6.56597i 0.307143i 0.988138 + 0.153571i \(0.0490775\pi\)
−0.988138 + 0.153571i \(0.950922\pi\)
\(458\) 0.965850 1.67290i 0.0451312 0.0781695i
\(459\) −0.636936 −0.0297296
\(460\) −6.93744 4.00533i −0.323460 0.186749i
\(461\) 4.42854 + 2.55682i 0.206258 + 0.119083i 0.599571 0.800322i \(-0.295338\pi\)
−0.393313 + 0.919404i \(0.628671\pi\)
\(462\) 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
\(467\) 6.47472 11.2145i 0.299614 0.518947i −0.676433 0.736504i \(-0.736475\pi\)
0.976048 + 0.217557i \(0.0698087\pi\)
\(468\) 5.51035 + 13.2767i 0.254716 + 0.613714i
\(469\) 0 0
\(470\) 2.05676 1.18747i 0.0948713 0.0547740i
\(471\) 16.8168 0.774877
\(472\) −20.2148 −0.930463
\(473\) −16.5716 + 9.56761i −0.761962 + 0.439919i
\(474\) 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
\(478\) 3.90221 0.178483
\(479\) −23.3930 13.5060i −1.06885 0.617104i −0.140987 0.990012i \(-0.545027\pi\)
−0.927868 + 0.372908i \(0.878361\pi\)
\(480\) −2.22802 3.85905i −0.101695 0.176141i
\(481\) −0.394692 + 3.01442i −0.0179964 + 0.137446i
\(482\) −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
\(486\) 6.93788 4.00558i 0.314708 0.181697i
\(487\) 32.0838i 1.45386i 0.686713 + 0.726928i \(0.259053\pi\)
−0.686713 + 0.726928i \(0.740947\pi\)
\(488\) −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 \(-0.389992\pi\)
\(492\) 17.9866i 0.810897i
\(493\) −0.596378 1.03296i −0.0268595 0.0465220i
\(494\) −3.80752 9.17385i −0.171308 0.412751i
\(495\) 4.71106 8.15980i 0.211746 0.366756i
\(496\) −6.31716 + 3.64721i −0.283649 + 0.163765i
\(497\) 0 0
\(498\) −0.610255 + 1.05699i −0.0273462 + 0.0473650i
\(499\) 1.55726 + 0.899082i 0.0697123 + 0.0402484i 0.534451 0.845199i \(-0.320518\pi\)
−0.464739 + 0.885448i \(0.653852\pi\)
\(500\) 16.2608i 0.727207i
\(501\) 5.21204i 0.232857i
\(502\) 3.32536 + 1.91990i 0.148418 + 0.0856893i
\(503\) 14.5386 25.1816i 0.648245 1.12279i −0.335297 0.942112i \(-0.608837\pi\)
0.983542 0.180681i \(-0.0578300\pi\)
\(504\) 0 0
\(505\) −10.3572 + 5.97976i −0.460891 + 0.266096i
\(506\) 4.35497 7.54303i 0.193602 0.335329i
\(507\) 7.79884 7.82088i 0.346359 0.347338i
\(508\) −1.75690 3.04304i −0.0779499 0.135013i
\(509\) 23.1913i 1.02794i 0.857809 + 0.513969i \(0.171825\pi\)
−0.857809 + 0.513969i \(0.828175\pi\)
\(510\) 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
\(514\) 6.81169i 0.300451i
\(515\) −3.76427 + 2.17330i −0.165874 + 0.0957671i
\(516\) −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
\(520\) 4.28624 5.59410i 0.187964 0.245318i
\(521\) 16.6255 + 28.7962i 0.728376 + 1.26158i 0.957569 + 0.288203i \(0.0930579\pi\)
−0.229193 + 0.973381i \(0.573609\pi\)
\(522\) 8.28383 + 4.78267i 0.362574 + 0.209332i
\(523\) −38.7121 −1.69276 −0.846380 0.532579i \(-0.821223\pi\)
−0.846380 + 0.532579i \(0.821223\pi\)
\(524\) −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
\(528\) −7.48028 + 4.31874i −0.325537 + 0.187949i
\(529\) −3.71931 −0.161709
\(530\) 0.145734 0.00633029
\(531\) 21.2714 12.2811i 0.923102 0.532953i
\(532\) 0 0
\(533\) −40.2857 + 16.7202i −1.74497 + 0.724233i
\(534\) 0.371191 0.642922i 0.0160630 0.0278220i
\(535\) 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
\(541\) −19.6306 11.3337i −0.843986 0.487275i 0.0146313 0.999893i \(-0.495343\pi\)
−0.858617 + 0.512618i \(0.828676\pi\)
\(542\) 1.28181 0.0550585
\(543\) 3.34135 5.78738i 0.143391 0.248360i
\(544\) 0.714603i 0.0306384i
\(545\) 6.70349 0.287146
\(546\) 0 0
\(547\) −9.21134 −0.393848 −0.196924 0.980419i \(-0.563095\pi\)
−0.196924 + 0.980419i \(0.563095\pi\)
\(548\) 9.17913i 0.392113i
\(549\) 6.67909 11.5685i 0.285056 0.493732i
\(550\) 7.76231 0.330986
\(551\) 40.0699 + 23.1344i 1.70704 + 0.985558i
\(552\) 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 \(-0.256188\pi\)
−0.277547 + 0.960712i \(0.589522\pi\)
\(558\) −1.62118 + 2.80796i −0.0686299 + 0.118871i
\(559\) 10.5769 13.8042i 0.447354 0.583855i
\(560\) 0 0
\(561\) 0.414608 0.239374i 0.0175048 0.0101064i
\(562\) 3.22636 0.136096
\(563\) 32.6386 1.37555 0.687777 0.725922i \(-0.258586\pi\)
0.687777 + 0.725922i \(0.258586\pi\)
\(564\) 5.86700 3.38732i 0.247045 0.142632i
\(565\) −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
\(569\) −35.0091 −1.46766 −0.733829 0.679335i \(-0.762269\pi\)
−0.733829 + 0.679335i \(0.762269\pi\)
\(570\) −2.11302 1.21995i −0.0885046 0.0510981i
\(571\) 13.1273 + 22.7371i 0.549360 + 0.951519i 0.998319 + 0.0579663i \(0.0184616\pi\)
−0.448959 + 0.893552i \(0.648205\pi\)
\(572\) −19.8706 15.2250i −0.830830 0.636587i
\(573\) 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
\(577\) −21.2806 + 12.2863i −0.885922 + 0.511487i −0.872606 0.488424i \(-0.837572\pi\)
−0.0133154 + 0.999911i \(0.504239\pi\)
\(578\) 8.48969i 0.353124i
\(579\) 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
\(583\) 1.10926i 0.0459408i
\(584\) 6.19936 + 10.7376i 0.256531 + 0.444325i
\(585\) −1.11170 + 8.49051i −0.0459632 + 0.351039i
\(586\) 6.05048 10.4797i 0.249943 0.432914i
\(587\) −17.7777 + 10.2640i −0.733765 + 0.423639i −0.819798 0.572653i \(-0.805914\pi\)
0.0860331 + 0.996292i \(0.472581\pi\)
\(588\) 0 0
\(589\) −7.84184 + 13.5825i −0.323117 + 0.559656i
\(590\) −4.86669 2.80978i −0.200358 0.115677i
\(591\) 21.9505i 0.902923i
\(592\) 2.16073i 0.0888054i
\(593\) −33.1545 19.1417i −1.36149 0.786057i −0.371669 0.928365i \(-0.621214\pi\)
−0.989822 + 0.142308i \(0.954548\pi\)
\(594\) −4.44757 + 7.70342i −0.182486 + 0.316075i
\(595\) 0 0
\(596\) 0.0172409 0.00995405i 0.000706216 0.000407734i
\(597\) 7.27030 12.5925i 0.297554 0.515378i
\(598\) −1.02767 + 7.84874i −0.0420247 + 0.320959i
\(599\) −7.03567 12.1861i −0.287470 0.497912i 0.685735 0.727851i \(-0.259481\pi\)
−0.973205 + 0.229939i \(0.926147\pi\)
\(600\) 6.23367i 0.254488i
\(601\) −10.1171 17.5233i −0.412685 0.714791i 0.582498 0.812832i \(-0.302075\pi\)
−0.995182 + 0.0980417i \(0.968742\pi\)
\(602\) 0 0
\(603\) 11.7200i 0.477276i
\(604\) −28.6522 + 16.5424i −1.16584 + 0.673099i
\(605\) 4.94082i 0.200873i
\(606\) 4.22039 2.43664i 0.171441 0.0989818i
\(607\) 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
\(611\) 13.0407 + 9.99190i 0.527572 + 0.404229i
\(612\) −0.283136 0.490406i −0.0114451 0.0198235i
\(613\) 28.8598 + 16.6622i 1.16564 + 0.672980i 0.952648 0.304075i \(-0.0983472\pi\)
0.212988 + 0.977055i \(0.431681\pi\)
\(614\) −12.1459 −0.490168
\(615\) −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
\(619\) −15.2582 + 8.80931i −0.613278 + 0.354076i −0.774247 0.632883i \(-0.781871\pi\)
0.160970 + 0.986959i \(0.448538\pi\)
\(620\) −5.19304 −0.208558
\(621\) −19.6907 −0.790159
\(622\) −1.72642 + 0.996751i −0.0692233 + 0.0399661i
\(623\) 0 0
\(624\) 4.77431 6.23110i 0.191125 0.249444i
\(625\) −4.93986 + 8.55609i −0.197594 + 0.342244i
\(626\) −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 \(0.565153\pi\)
\(632\) 19.3596 + 11.1773i 0.770084 + 0.444608i
\(633\) −15.5402 −0.617667
\(634\) −4.20392 + 7.28140i −0.166959 + 0.289181i
\(635\) 2.09316i 0.0830644i
\(636\) 0.415713 0.0164841
\(637\) 0 0
\(638\) −16.6575 −0.659475
\(639\) 8.42653i 0.333348i
\(640\) 5.92497 10.2623i 0.234205 0.405655i
\(641\) 20.9405 0.827099 0.413550 0.910482i \(-0.364289\pi\)
0.413550 + 0.910482i \(0.364289\pi\)
\(642\) −3.12234 1.80268i −0.123229 0.0711463i
\(643\) 16.3952 + 9.46576i 0.646563 + 0.373293i 0.787138 0.616777i \(-0.211562\pi\)
−0.140575 + 0.990070i \(0.544895\pi\)
\(644\) 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
\(649\) −21.3867 + 37.0429i −0.839503 + 1.45406i
\(650\) −6.51562 + 2.70424i −0.255563 + 0.106069i
\(651\) 0 0
\(652\) 13.5378 7.81604i 0.530180 0.306100i
\(653\) 29.0326 1.13613 0.568066 0.822983i \(-0.307692\pi\)
0.568066 + 0.822983i \(0.307692\pi\)
\(654\) −2.73155 −0.106812
\(655\) −11.2402 + 6.48952i −0.439190 + 0.253567i
\(656\) −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 \(0.157872\pi\)
\(660\) −6.14919 −0.239357
\(661\) 3.97764 + 2.29649i 0.154712 + 0.0893231i 0.575357 0.817902i \(-0.304863\pi\)
−0.420645 + 0.907225i \(0.638196\pi\)
\(662\) −1.55225 2.68858i −0.0603300 0.104495i
\(663\) −0.264625 + 0.345370i −0.0102772 + 0.0134131i
\(664\) −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
\(668\) −9.29746 + 5.36789i −0.359730 + 0.207690i
\(669\) 9.77780i 0.378032i
\(670\) −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 \(0.859142\pi\)
\(674\) 3.84815i 0.148225i
\(675\) −8.77418 15.1973i −0.337718 0.584945i
\(676\) 21.9833 + 5.85716i 0.845510 + 0.225275i
\(677\) 4.04354 7.00361i 0.155406 0.269171i −0.777801 0.628511i \(-0.783665\pi\)
0.933207 + 0.359340i \(0.116998\pi\)
\(678\) 4.03316 2.32854i 0.154892 0.0894272i
\(679\) 0 0
\(680\) −0.138811 + 0.240427i −0.00532315 + 0.00921997i
\(681\) −13.1737 7.60583i −0.504817 0.291456i
\(682\) 5.64636i 0.216210i
\(683\) 24.6865i 0.944604i 0.881437 + 0.472302i \(0.156577\pi\)
−0.881437 + 0.472302i \(0.843423\pi\)
\(684\) 19.0236 + 10.9833i 0.727386 + 0.419956i
\(685\) −2.73398 + 4.73540i −0.104460 + 0.180930i
\(686\) 0 0
\(687\) 2.84267 1.64122i 0.108455 0.0626164i
\(688\) 6.17994 10.7040i 0.235608 0.408085i
\(689\) 0.386445 + 0.931102i 0.0147224 + 0.0354722i
\(690\) 0.972234 + 1.68396i 0.0370123 + 0.0641072i
\(691\) 11.2567i 0.428225i −0.976809 0.214113i \(-0.931314\pi\)
0.976809 0.214113i \(-0.0686859\pi\)
\(692\) −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
\(696\) 13.3771i 0.507057i
\(697\) 1.48805 0.859128i 0.0563640 0.0325418i
\(698\) −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 \(0.362094\pi\)
\(702\) 1.04953 8.01564i 0.0396118 0.302531i
\(703\) 2.32288 + 4.02335i 0.0876091 + 0.151743i
\(704\) −8.96614 5.17660i −0.337924 0.195101i
\(705\) 4.03562 0.151990
\(706\) 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 \(-0.519363\pi\)
0.834027 + 0.551723i \(0.186030\pi\)
\(710\) −1.66961 + 0.963952i −0.0626595 + 0.0361765i
\(711\) −27.1620 −1.01866
\(712\) 3.27677 0.122802
\(713\) 10.8245 6.24951i 0.405380 0.234046i
\(714\) 0 0
\(715\) −5.71626 13.7728i −0.213776 0.515072i
\(716\) −3.61969 + 6.26948i −0.135274 + 0.234301i
\(717\) 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
\(723\) −16.0144 9.24589i −0.595580 0.343859i
\(724\) 13.7650 0.511574
\(725\) 16.4309 28.4592i 0.610229 1.05695i
\(726\) 2.01329i 0.0747203i
\(727\) 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
\(730\) 3.44675i 0.127570i
\(731\) −0.342535 + 0.593287i −0.0126691 + 0.0219435i
\(732\) −8.71799 −0.322226
\(733\) −4.55224 2.62824i −0.168141 0.0970761i 0.413568 0.910473i \(-0.364282\pi\)
−0.581709 + 0.813397i \(0.697616\pi\)
\(734\) −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 \(-0.291351\pi\)
−0.381768 + 0.924258i \(0.624685\pi\)
\(740\) −0.769132 + 1.33218i −0.0282738 + 0.0489717i
\(741\) 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 \(0.337500\pi\)
\(744\) 4.53441 0.166240
\(745\) 0.0118592 0.000434486
\(746\) 7.96386 4.59794i 0.291578 0.168342i
\(747\) 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
\(751\) 25.7013 0.937854 0.468927 0.883237i \(-0.344641\pi\)
0.468927 + 0.883237i \(0.344641\pi\)
\(752\) 10.1120 + 5.83815i 0.368746 + 0.212896i
\(753\) 3.26238 + 5.65062i 0.118888 + 0.205920i
\(754\) 13.9821 5.80315i 0.509199 0.211338i
\(755\) −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
\(759\) 12.8175 7.40018i 0.465245 0.268609i
\(760\) 10.7694i 0.390646i
\(761\) −7.20531 + 4.15999i −0.261192 + 0.150800i −0.624878 0.780722i \(-0.714851\pi\)
0.363686 + 0.931522i \(0.381518\pi\)
\(762\) 0.852923i 0.0308981i
\(763\) 0 0
\(764\) 5.66888 + 9.81878i 0.205093 + 0.355231i
\(765\) 0.337326i 0.0121960i
\(766\) −5.59263 9.68671i −0.202070 0.349995i
\(767\) 5.04678 38.5442i 0.182229 1.39175i
\(768\) −0.197167 + 0.341504i −0.00711466 + 0.0123230i
\(769\) −22.1346 + 12.7794i −0.798194 + 0.460838i −0.842839 0.538165i \(-0.819118\pi\)
0.0446452 + 0.999003i \(0.485784\pi\)
\(770\) 0 0
\(771\) 5.78738 10.0240i 0.208427 0.361007i
\(772\) 7.31905 + 4.22565i 0.263418 + 0.152085i
\(773\) 8.40077i 0.302155i −0.988522 0.151077i \(-0.951726\pi\)
0.988522 0.151077i \(-0.0482742\pi\)
\(774\) 5.49394i 0.197476i
\(775\) 9.64678 + 5.56957i 0.346523 + 0.200065i
\(776\) −2.53392 + 4.38887i −0.0909623 + 0.157551i
\(777\) 0 0
\(778\) −9.26388 + 5.34850i −0.332126 + 0.191753i
\(779\) −33.3269 + 57.7238i −1.19406 + 2.06817i
\(780\) 5.16158 2.14226i 0.184814 0.0767053i
\(781\) 7.33714 + 12.7083i 0.262544 + 0.454739i
\(782\)