Properties

Label 637.2.u.g.361.4
Level $637$
Weight $2$
Character 637.361
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.u (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 361.4
Root \(-1.18541 - 0.771231i\) of defining polynomial
Character \(\chi\) \(=\) 637.361
Dual form 637.2.u.g.30.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.433001 + 0.249993i) q^{2} -0.849601 q^{3} +(-0.875007 - 1.51556i) q^{4} +(-0.902810 + 0.521238i) q^{5} +(-0.367878 - 0.212395i) q^{6} -1.87496i q^{8} -2.27818 q^{9} +O(q^{10})\) \(q+(0.433001 + 0.249993i) q^{2} -0.849601 q^{3} +(-0.875007 - 1.51556i) q^{4} +(-0.902810 + 0.521238i) q^{5} +(-0.367878 - 0.212395i) q^{6} -1.87496i q^{8} -2.27818 q^{9} -0.521224 q^{10} +3.96730i q^{11} +(0.743407 + 1.28762i) 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} +(-0.986453 - 0.569529i) q^{18} +5.50977i q^{19} +(1.57993 + 0.912173i) q^{20} +(-0.991800 + 1.71785i) q^{22} +(2.19549 - 3.80270i) q^{23} +1.59297i q^{24} +(-1.95662 + 3.38897i) q^{25} +(1.43097 + 1.09642i) q^{26} +4.48435 q^{27} +(4.19880 + 7.27253i) q^{29} +0.442832 q^{30} +(2.46516 + 1.42326i) q^{31} +(-4.35712 + 2.51558i) q^{32} -3.37063i q^{33} +0.0710158i q^{34} +(1.99342 + 3.45271i) q^{36} +(-0.730221 - 0.421593i) q^{37} +(-1.37740 + 2.38574i) q^{38} +(-3.03736 - 0.397695i) 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} +(2.05676 - 1.18747i) q^{45} +(1.90130 - 1.09772i) 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} +(-2.41875 - 5.82776i) q^{52} +(0.139800 - 0.242141i) q^{53} +(1.94173 + 1.12106i) q^{54} +(-2.06791 - 3.58172i) q^{55} -4.68111i q^{57} +4.19868i q^{58} +(-9.33705 + 5.39075i) q^{59} +(-1.34231 - 0.774983i) q^{60} +5.86354 q^{61} +(0.711612 + 1.23255i) q^{62} +2.60963 q^{64} +(-3.47157 + 1.44084i) q^{65} +(0.842634 - 1.45949i) q^{66} +5.14447i q^{67} +(0.124282 - 0.215263i) q^{68} +(-1.86529 + 3.23078i) q^{69} +(-3.20326 - 1.84940i) q^{71} +4.27148i q^{72} +(5.72686 + 3.30640i) 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} +(-5.96135 - 10.3254i) q^{79} -2.67142i q^{80} +3.02462 q^{81} -6.04853 q^{82} -2.87321i q^{83} +(-0.128231 - 0.0740342i) q^{85} +(2.08846 - 1.20578i) q^{86} +(-3.56730 - 6.17875i) q^{87} +7.43852 q^{88} +(-1.51351 - 0.873824i) q^{89} +1.18744 q^{90} -7.68427 q^{92} +(-2.09440 - 1.20921i) q^{93} -2.27818 q^{94} +(-2.87190 - 4.97427i) q^{95} +(3.70181 - 2.13724i) q^{96} +(-2.34079 - 1.35145i) q^{97} -9.03822i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 6q^{3} + 4q^{4} - 3q^{5} + 9q^{6} + 2q^{9} + O(q^{10}) \) \( 12q - 6q^{3} + 4q^{4} - 3q^{5} + 9q^{6} + 2q^{9} + 24q^{10} + q^{12} + 2q^{13} - 12q^{15} - 8q^{16} - 17q^{17} - 3q^{18} + 3q^{20} - 15q^{22} + 3q^{23} - 5q^{25} + 9q^{26} - 12q^{27} - q^{29} - 22q^{30} + 18q^{31} + 18q^{32} - 13q^{36} + 15q^{37} - 19q^{38} - q^{39} + q^{40} + 6q^{41} + 11q^{43} + 33q^{44} + 9q^{45} - 30q^{46} - 15q^{47} - 19q^{48} + 18q^{50} + 4q^{51} - 47q^{52} - 8q^{53} - 6q^{54} + 15q^{55} - 27q^{59} + 30q^{60} + 10q^{61} - 41q^{62} + 2q^{64} - 3q^{65} + 34q^{66} + 11q^{68} - 7q^{69} + 30q^{71} + 42q^{73} - 33q^{74} - q^{75} + 45q^{76} + 44q^{78} - 35q^{79} - 28q^{81} + 10q^{82} - 21q^{85} + 57q^{86} - 10q^{87} + 28q^{88} - 48q^{89} - 66q^{92} - 81q^{93} + 2q^{94} + 2q^{95} + 21q^{96} + 3q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.433001 + 0.249993i 0.306178 + 0.176772i 0.645215 0.764001i \(-0.276768\pi\)
−0.339037 + 0.940773i \(0.610101\pi\)
\(3\) −0.849601 −0.490518 −0.245259 0.969458i \(-0.578873\pi\)
−0.245259 + 0.969458i \(0.578873\pi\)
\(4\) −0.875007 1.51556i −0.437503 0.757778i
\(5\) −0.902810 + 0.521238i −0.403749 + 0.233105i −0.688100 0.725616i \(-0.741555\pi\)
0.284351 + 0.958720i \(0.408222\pi\)
\(6\) −0.367878 0.212395i −0.150186 0.0867098i
\(7\) 0 0
\(8\) 1.87496i 0.662897i
\(9\) −2.27818 −0.759392
\(10\) −0.521224 −0.164825
\(11\) 3.96730i 1.19619i 0.801426 + 0.598094i \(0.204075\pi\)
−0.801426 + 0.598094i \(0.795925\pi\)
\(12\) 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
\(16\) −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 \(0.827850\pi\)
\(18\) −0.986453 0.569529i −0.232509 0.134239i
\(19\) 5.50977i 1.26403i 0.774957 + 0.632014i \(0.217771\pi\)
−0.774957 + 0.632014i \(0.782229\pi\)
\(20\) 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 \(0.0153074\pi\)
\(24\) 1.59297i 0.325163i
\(25\) −1.95662 + 3.38897i −0.391325 + 0.677794i
\(26\) 1.43097 + 1.09642i 0.280637 + 0.215026i
\(27\) 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 \(0.548706\pi\)
\(30\) 0.442832 0.0808498
\(31\) 2.46516 + 1.42326i 0.442756 + 0.255625i 0.704766 0.709440i \(-0.251052\pi\)
−0.262010 + 0.965065i \(0.584385\pi\)
\(32\) −4.35712 + 2.51558i −0.770237 + 0.444696i
\(33\) 3.37063i 0.586751i
\(34\) 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 \(-0.355413\pi\)
−0.558821 + 0.829288i \(0.688746\pi\)
\(38\) −1.37740 + 2.38574i −0.223445 + 0.387017i
\(39\) −3.03736 0.397695i −0.486366 0.0636822i
\(40\) 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
\(45\) 2.05676 1.18747i 0.306604 0.177018i
\(46\) 1.90130 1.09772i 0.280331 0.161849i
\(47\) −3.94602 + 2.27824i −0.575587 + 0.332315i −0.759378 0.650650i \(-0.774496\pi\)
0.183791 + 0.982965i \(0.441163\pi\)
\(48\) 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
\(52\) −2.41875 5.82776i −0.335421 0.808164i
\(53\) 0.139800 0.242141i 0.0192030 0.0332606i −0.856264 0.516538i \(-0.827220\pi\)
0.875467 + 0.483278i \(0.160554\pi\)
\(54\) 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
\(58\) 4.19868i 0.551314i
\(59\) −9.33705 + 5.39075i −1.21558 + 0.701815i −0.963969 0.266013i \(-0.914294\pi\)
−0.251611 + 0.967829i \(0.580960\pi\)
\(60\) −1.34231 0.774983i −0.173292 0.100050i
\(61\) 5.86354 0.750749 0.375374 0.926873i \(-0.377514\pi\)
0.375374 + 0.926873i \(0.377514\pi\)
\(62\) 0.711612 + 1.23255i 0.0903748 + 0.156534i
\(63\) 0 0
\(64\) 2.60963 0.326204
\(65\) −3.47157 + 1.44084i −0.430595 + 0.178714i
\(66\) 0.842634 1.45949i 0.103721 0.179650i
\(67\) 5.14447i 0.628497i 0.949341 + 0.314248i \(0.101753\pi\)
−0.949341 + 0.314248i \(0.898247\pi\)
\(68\) 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 \(0.737104\pi\)
\(72\) 4.27148i 0.503399i
\(73\) 5.72686 + 3.30640i 0.670278 + 0.386985i 0.796182 0.605057i \(-0.206850\pi\)
−0.125904 + 0.992042i \(0.540183\pi\)
\(74\) −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
\(79\) −5.96135 10.3254i −0.670705 1.16169i −0.977705 0.209985i \(-0.932658\pi\)
0.307000 0.951710i \(-0.400675\pi\)
\(80\) 2.67142i 0.298674i
\(81\) 3.02462 0.336069
\(82\) −6.04853 −0.667948
\(83\) 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
\(87\) −3.56730 6.17875i −0.382455 0.662432i
\(88\) 7.43852 0.792949
\(89\) −1.51351 0.873824i −0.160432 0.0926252i 0.417635 0.908615i \(-0.362859\pi\)
−0.578066 + 0.815990i \(0.696193\pi\)
\(90\) 1.18744 0.125167
\(91\) 0 0
\(92\) −7.68427 −0.801141
\(93\) −2.09440 1.20921i −0.217180 0.125389i
\(94\) −2.27818 −0.234976
\(95\) −2.87190 4.97427i −0.294650 0.510350i
\(96\) 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
\(100\) 6.84823 0.684823
\(101\) 11.4722 1.14153 0.570765 0.821114i \(-0.306647\pi\)
0.570765 + 0.821114i \(0.306647\pi\)
\(102\) 0.0603351i 0.00597407i
\(103\) −2.08475 3.61090i −0.205417 0.355792i 0.744849 0.667233i \(-0.232522\pi\)
−0.950265 + 0.311441i \(0.899188\pi\)
\(104\) 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
\(109\) −5.56886 3.21518i −0.533400 0.307958i 0.209000 0.977916i \(-0.432979\pi\)
−0.742400 + 0.669957i \(0.766312\pi\)
\(110\) 2.06785i 0.197162i
\(111\) 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
\(115\) 4.57749i 0.426853i
\(116\) 7.34795 12.7270i 0.682240 1.18167i
\(117\) −8.14457 1.06641i −0.752965 0.0985893i
\(118\) −5.39060 −0.496245
\(119\) 0 0
\(120\) −0.830314 1.43815i −0.0757969 0.131284i
\(121\) −4.73951 −0.430864
\(122\) 2.53892 + 1.46584i 0.229863 + 0.132711i
\(123\) 8.90097 5.13898i 0.802573 0.463366i
\(124\) 4.98145i 0.447348i
\(125\) 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
\(129\) −2.04891 + 3.54882i −0.180397 + 0.312456i
\(130\) −1.86339 0.243983i −0.163430 0.0213987i
\(131\) −6.22511 10.7822i −0.543890 0.942046i −0.998676 0.0514449i \(-0.983617\pi\)
0.454785 0.890601i \(-0.349716\pi\)
\(132\) −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
\(136\) 0.230631 0.133155i 0.0197765 0.0114180i
\(137\) 4.54246 2.62259i 0.388088 0.224063i −0.293243 0.956038i \(-0.594735\pi\)
0.681332 + 0.731975i \(0.261401\pi\)
\(138\) −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
\(143\) −1.85708 + 14.1833i −0.155297 + 1.18606i
\(144\) 2.91900 5.05585i 0.243250 0.421321i
\(145\) −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
\(149\) 0.0113760i 0.000931956i 1.00000 0.000465978i \(0.000148325\pi\)
−1.00000 0.000465978i \(0.999852\pi\)
\(150\) 1.43960 0.831153i 0.117543 0.0678633i
\(151\) 16.3726 + 9.45271i 1.33238 + 0.769251i 0.985664 0.168719i \(-0.0539631\pi\)
0.346717 + 0.937970i \(0.387296\pi\)
\(152\) 10.3306 0.837920
\(153\) −0.161791 0.280230i −0.0130800 0.0226553i
\(154\) 0 0
\(155\) −2.96743 −0.238350
\(156\) 2.05498 + 4.95127i 0.164530 + 0.396419i
\(157\) 9.89687 17.1419i 0.789856 1.36807i −0.136198 0.990682i \(-0.543488\pi\)
0.926054 0.377390i \(-0.123178\pi\)
\(158\) 5.96119i 0.474247i
\(159\) −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
\(163\) 8.93255i 0.699651i 0.936815 + 0.349825i \(0.113759\pi\)
−0.936815 + 0.349825i \(0.886241\pi\)
\(164\) 18.3343 + 10.5853i 1.43167 + 0.826572i
\(165\) 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 −0.691269 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
\(171\) 12.5522i 0.959893i
\(172\) −8.44072 −0.643599
\(173\) 24.2628 1.84466 0.922332 0.386399i \(-0.126281\pi\)
0.922332 + 0.386399i \(0.126281\pi\)
\(174\) 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
\(178\) −0.436901 0.756734i −0.0327471 0.0567196i
\(179\) 4.13675 0.309195 0.154598 0.987978i \(-0.450592\pi\)
0.154598 + 0.987978i \(0.450592\pi\)
\(180\) −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
\(185\) 0.879001 0.0646254
\(186\) −0.604586 1.04717i −0.0443304 0.0767825i
\(187\) −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
\(191\) −6.47866 −0.468780 −0.234390 0.972143i \(-0.575309\pi\)
−0.234390 + 0.972143i \(0.575309\pi\)
\(192\) −2.21715 −0.160009
\(193\) 4.82928i 0.347619i −0.984779 0.173810i \(-0.944392\pi\)
0.984779 0.173810i \(-0.0556077\pi\)
\(194\) −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 \(0.961215\pi\)
\(198\) 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 \(-0.374138\pi\)
\(200\) 6.35417 + 3.66858i 0.449308 + 0.259408i
\(201\) 4.37075i 0.308289i
\(202\) 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
\(206\) 2.08470i 0.145248i
\(207\) −5.00171 + 8.66322i −0.347643 + 0.602136i
\(208\) −5.61947 + 7.33415i −0.389640 + 0.508532i
\(209\) −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 \(-0.383451\pi\)
\(212\) −0.489304 −0.0336055
\(213\) 2.72149 + 1.57125i 0.186474 + 0.107661i
\(214\) −3.67506 + 2.12180i −0.251222 + 0.145043i
\(215\) 5.02810i 0.342913i
\(216\) 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
\(220\) −3.61887 + 6.26806i −0.243984 + 0.422593i
\(221\) 0.196312 + 0.472995i 0.0132054 + 0.0318171i
\(222\) 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
\(227\) −15.5057 + 8.95223i −1.02915 + 0.594181i −0.916741 0.399481i \(-0.869190\pi\)
−0.112410 + 0.993662i \(0.535857\pi\)
\(228\) −7.09448 + 4.09600i −0.469843 + 0.271264i
\(229\) −3.34589 + 1.93175i −0.221103 + 0.127654i −0.606461 0.795113i \(-0.707411\pi\)
0.385358 + 0.922767i \(0.374078\pi\)
\(230\) −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 0.904935 + 0.425549i \(0.139919\pi\)
−0.0839312 + 0.996472i \(0.526748\pi\)
\(234\) −3.26001 2.49784i −0.213114 0.163289i
\(235\) 2.37501 4.11363i 0.154928 0.268344i
\(236\) 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 \(0.918774\pi\)
\(240\) 2.26964i 0.146505i
\(241\) −18.8493 + 10.8826i −1.21419 + 0.701012i −0.963669 0.267100i \(-0.913935\pi\)
−0.250519 + 0.968112i \(0.580601\pi\)
\(242\) −2.05221 1.18484i −0.131921 0.0761647i
\(243\) −16.0228 −1.02786
\(244\) −5.13063 8.88652i −0.328455 0.568901i
\(245\) 0 0
\(246\) 5.13884 0.327640
\(247\) −2.57910 + 19.6976i −0.164104 + 1.25333i
\(248\) 2.66855 4.62207i 0.169453 0.293502i
\(249\) 2.44109i 0.154698i
\(250\) 2.32290 4.02338i 0.146913 0.254461i
\(251\) −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
\(254\) 1.00391i 0.0629909i
\(255\) 0.108945 + 0.0628995i 0.00682241 + 0.00393892i
\(256\) 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
\(261\) −9.56560 16.5681i −0.592096 1.02554i
\(262\) 6.22494i 0.384578i
\(263\) −11.7232 −0.722880 −0.361440 0.932395i \(-0.617715\pi\)
−0.361440 + 0.932395i \(0.617715\pi\)
\(264\) −6.31978 −0.388956
\(265\) 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
\(269\) 4.59938 + 7.96636i 0.280429 + 0.485717i 0.971490 0.237079i \(-0.0761899\pi\)
−0.691061 + 0.722796i \(0.742857\pi\)
\(270\) −2.33735 −0.142246
\(271\) −2.22022 1.28184i −0.134869 0.0778665i 0.431048 0.902329i \(-0.358144\pi\)
−0.565916 + 0.824463i \(0.691477\pi\)
\(272\) −0.363976 −0.0220693
\(273\) 0 0
\(274\) 2.62252 0.158432
\(275\) −13.4451 7.76252i −0.810769 0.468097i
\(276\) 6.52857 0.392974
\(277\) −0.466941 0.808765i −0.0280558 0.0485940i 0.851657 0.524100i \(-0.175598\pi\)
−0.879712 + 0.475506i \(0.842265\pi\)
\(278\) −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 \(0.938349\pi\)
\(282\) 1.93554 0.115260
\(283\) 22.1746 1.31814 0.659071 0.752081i \(-0.270950\pi\)
0.659071 + 0.752081i \(0.270950\pi\)
\(284\) 6.47296i 0.384099i
\(285\) 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
\(289\) 8.48991 14.7050i 0.499407 0.864998i
\(290\) −2.18851 3.79061i −0.128514 0.222593i
\(291\) 1.98873 + 1.14820i 0.116582 + 0.0673085i
\(292\) 11.5725i 0.677229i
\(293\) 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
\(296\) −0.790469 + 1.36913i −0.0459451 + 0.0795792i
\(297\) 17.7908i 1.03233i
\(298\) −0.00284392 + 0.00492581i −0.000164744 + 0.000285345i
\(299\) 9.62898 12.5671i 0.556858 0.726773i
\(300\) −5.81827 −0.335918
\(301\) 0 0
\(302\) 4.72623 + 8.18607i 0.271964 + 0.471055i
\(303\) −9.74683 −0.559940
\(304\) −12.2276 7.05959i −0.701299 0.404895i
\(305\) −5.29366 + 3.05630i −0.303114 + 0.175003i
\(306\) 0.161787i 0.00924872i
\(307\) 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
\(310\) −1.28490 0.741837i −0.0729774 0.0421335i
\(311\) −1.99355 + 3.45294i −0.113044 + 0.195798i −0.916996 0.398896i \(-0.869393\pi\)
0.803952 + 0.594694i \(0.202727\pi\)
\(312\) −0.745661 + 5.69491i −0.0422148 + 0.322411i
\(313\) 14.2377 + 24.6604i 0.804763 + 1.39389i 0.916451 + 0.400147i \(0.131041\pi\)
−0.111688 + 0.993743i \(0.535626\pi\)
\(314\) 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 \(-0.510111\pi\)
0.849709 + 0.527252i \(0.176778\pi\)
\(318\) −0.102859 + 0.0593856i −0.00576804 + 0.00333018i
\(319\) −28.8523 + 16.6579i −1.61542 + 0.932664i
\(320\) −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
\(325\) −8.58136 + 11.1998i −0.476008 + 0.621253i
\(326\) −2.23308 + 3.86780i −0.123679 + 0.214218i
\(327\) 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
\(331\) 6.20917i 0.341287i 0.985333 + 0.170644i \(0.0545846\pi\)
−0.985333 + 0.170644i \(0.945415\pi\)
\(332\) −4.35451 + 2.51408i −0.238985 + 0.137978i
\(333\) 1.66357 + 0.960464i 0.0911632 + 0.0526331i
\(334\) −3.06726 −0.167833
\(335\) −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 \(0.432775\pi\)
\(338\) 4.60255 + 4.58958i 0.250346 + 0.249640i
\(339\) 4.65721 8.06653i 0.252945 0.438114i
\(340\) 0.259122i 0.0140528i
\(341\) −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
\(345\) 3.88904i 0.209379i
\(346\) 10.5058 + 6.06553i 0.564795 + 0.326085i
\(347\) −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 −0.0763028 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
\(353\) 11.8424i 0.630306i −0.949041 0.315153i \(-0.897944\pi\)
0.949041 0.315153i \(-0.102056\pi\)
\(354\) 4.57986 0.243417
\(355\) 3.85591 0.204651
\(356\) 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 \(-0.356317\pi\)
0.997394 + 0.0721417i \(0.0229834\pi\)
\(360\) −2.22646 3.85634i −0.117345 0.203247i
\(361\) −11.3575 −0.597765
\(362\) 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
\(367\) −24.0774 −1.25683 −0.628415 0.777878i \(-0.716296\pi\)
−0.628415 + 0.777878i \(0.716296\pi\)
\(368\) 5.62610 + 9.74470i 0.293281 + 0.507977i
\(369\) 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
\(373\) −18.3922 −0.952314 −0.476157 0.879360i \(-0.657971\pi\)
−0.476157 + 0.879360i \(0.657971\pi\)
\(374\) −0.281741 −0.0145685
\(375\) 7.89436i 0.407663i
\(376\) 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 \(0.400353\pi\)
\(380\) −5.02586 + 8.70504i −0.257821 + 0.446559i
\(381\) 0.852946 + 1.47735i 0.0436977 + 0.0756867i
\(382\) −2.80527 1.61962i −0.143530 0.0828671i
\(383\) 22.3711i 1.14311i 0.820564 + 0.571555i \(0.193660\pi\)
−0.820564 + 0.571555i \(0.806340\pi\)
\(384\) −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
\(388\) 4.73012i 0.240136i
\(389\) −10.6973 + 18.5283i −0.542374 + 0.939420i 0.456393 + 0.889778i \(0.349141\pi\)
−0.998767 + 0.0496415i \(0.984192\pi\)
\(390\) 1.58314 + 0.207288i 0.0801655 + 0.0104964i
\(391\) 0.623674 0.0315406
\(392\) 0 0
\(393\) 5.28886 + 9.16058i 0.266788 + 0.462090i
\(394\) −12.9178 −0.650788
\(395\) 10.7639 + 6.21456i 0.541592 + 0.312689i
\(396\) −13.6979 + 7.90851i −0.688347 + 0.397417i
\(397\) 1.19673i 0.0600622i −0.999549 0.0300311i \(-0.990439\pi\)
0.999549 0.0300311i \(-0.00956063\pi\)
\(398\) 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 \(0.0273516\pi\)
0.572479 + 0.819919i \(0.305982\pi\)
\(402\) 1.09266 1.89254i 0.0544968 0.0943913i
\(403\) 8.14682 + 6.24214i 0.405822 + 0.310943i
\(404\) −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
\(409\) 12.7066 7.33616i 0.628301 0.362750i −0.151793 0.988412i \(-0.548505\pi\)
0.780094 + 0.625662i \(0.215171\pi\)
\(410\) 5.46067 3.15272i 0.269683 0.155702i
\(411\) −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
\(416\) −16.7544 + 6.95375i −0.821451 + 0.340936i
\(417\) 8.80975 15.2589i 0.431415 0.747233i
\(418\) −9.46494 5.46458i −0.462945 0.267282i
\(419\) −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 \(-0.0204278\pi\)
\(422\) 9.14532i 0.445187i
\(423\) 8.98974 5.19023i 0.437096 0.252358i
\(424\) −0.454004 0.262119i −0.0220484 0.0127296i
\(425\) −0.555819 −0.0269612
\(426\) 0.785606 + 1.36071i 0.0380628 + 0.0659266i
\(427\) 0 0
\(428\) 14.8531 0.717952
\(429\) 1.57778 12.0501i 0.0761759 0.581785i
\(430\) −1.25699 + 2.17717i −0.0606175 + 0.104993i
\(431\) 18.8377i 0.907378i −0.891160 0.453689i \(-0.850108\pi\)
0.891160 0.453689i \(-0.149892\pi\)
\(432\) −5.74573 + 9.95190i −0.276442 + 0.478811i
\(433\) −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
\(436\) 11.2532i 0.538931i
\(437\) 20.9520 + 12.0966i 1.00227 + 0.578660i
\(438\) −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
\(443\) 10.4696 + 18.1339i 0.497426 + 0.861568i 0.999996 0.00296930i \(-0.000945159\pi\)
−0.502569 + 0.864537i \(0.667612\pi\)
\(444\) 1.25366i 0.0594961i
\(445\) 1.82188 0.0863654
\(446\) 5.75419 0.272469
\(447\) 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
\(451\) −23.9970 41.5640i −1.12997 1.95717i
\(452\) 19.1859 0.902429
\(453\) −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 \(-0.382411\pi\)
−0.627066 + 0.778966i \(0.715744\pi\)
\(458\) −1.93170 −0.0902624
\(459\) 0.318468 + 0.551603i 0.0148648 + 0.0257466i
\(460\) 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 \(-0.281921\pi\)
\(464\) −21.5194 −0.999015
\(465\) 2.52113 0.116915
\(466\) 12.5317i 0.580522i
\(467\) 6.47472 + 11.2145i 0.299614 + 0.518947i 0.976048 0.217557i \(-0.0698087\pi\)
−0.676433 + 0.736504i \(0.736475\pi\)
\(468\) 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
\(473\) 16.5716 + 9.56761i 0.761962 + 0.439919i
\(474\) 5.06464i 0.232627i
\(475\) −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
\(479\) 27.0119i 1.23421i 0.786882 + 0.617104i \(0.211694\pi\)
−0.786882 + 0.617104i \(0.788306\pi\)
\(480\) −2.22802 + 3.85905i −0.101695 + 0.176141i
\(481\) −2.41322 1.84903i −0.110033 0.0843083i
\(482\) −10.8823 −0.495677
\(483\) 0 0
\(484\) 4.14710 + 7.18299i 0.188505 + 0.326499i
\(485\) 2.81771 0.127946
\(486\) −6.93788 4.00558i −0.314708 0.181697i
\(487\) 27.7854 16.0419i 1.25908 0.726928i 0.286182 0.958175i \(-0.407614\pi\)
0.972895 + 0.231247i \(0.0742805\pi\)
\(488\) 10.9939i 0.497669i
\(489\) 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
\(493\) −0.596378 + 1.03296i −0.0268595 + 0.0465220i
\(494\) −6.04103 + 7.88433i −0.271799 + 0.354733i
\(495\) 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 \(-0.679482\pi\)
0.464739 + 0.885448i \(0.346148\pi\)
\(500\) −14.0823 + 8.13042i −0.629780 + 0.363603i
\(501\) 4.51376 2.60602i 0.201660 0.116428i
\(502\) −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
\(507\) −10.6725 2.84355i −0.473982 0.126287i
\(508\) −1.75690 + 3.04304i −0.0779499 + 0.135013i
\(509\) −20.0843 11.5957i −0.890220 0.513969i −0.0162054 0.999869i \(-0.505159\pi\)
−0.874014 + 0.485900i \(0.838492\pi\)
\(510\) 0.0314489 + 0.0544711i 0.00139258 + 0.00241202i
\(511\) 0 0
\(512\) 22.5022i 0.994464i
\(513\) 24.7077i 1.09087i
\(514\) −5.89910 + 3.40585i −0.260198 + 0.150225i
\(515\) 3.76427 + 2.17330i 0.165874 + 0.0957671i
\(516\) 7.17125 0.315696
\(517\) −9.03847 15.6551i −0.397511 0.688510i
\(518\) 0 0
\(519\) −20.6137 −0.904840
\(520\) 2.70151 + 6.50904i 0.118469 + 0.285440i
\(521\) 16.6255 28.7962i 0.728376 1.26158i −0.229193 0.973381i \(-0.573609\pi\)
0.957569 0.288203i \(-0.0930579\pi\)
\(522\) 9.56535i 0.418664i
\(523\) 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
\(527\) 0.404307i 0.0176119i
\(528\) 7.48028 + 4.31874i 0.325537 + 0.187949i
\(529\) 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
\(534\) 0.371191 + 0.642922i 0.0160630 + 0.0278220i
\(535\) 8.84793i 0.382529i
\(536\) 9.64566 0.416629
\(537\) −3.51459 −0.151666
\(538\) 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 \(-0.504657\pi\)
0.858617 + 0.512618i \(0.171324\pi\)
\(542\) −0.640905 1.11008i −0.0275292 0.0476820i
\(543\) −6.68269 −0.286782
\(544\) −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
\(549\) −13.3582 −0.570113
\(550\) −3.88116 6.72236i −0.165493 0.286642i
\(551\) −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
\(555\) −0.746801 −0.0316999
\(556\) 36.2927 1.53915
\(557\) 11.3281i 0.479986i −0.970775 0.239993i \(-0.922855\pi\)
0.970775 0.239993i \(-0.0771451\pi\)
\(558\) −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
\(562\) −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 \(-0.408080\pi\)
\(564\) −5.86700 3.38732i −0.247045 0.142632i
\(565\) 11.4290i 0.480820i
\(566\) 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 \(-0.0956019\pi\)
\(570\) 2.43990i 0.102196i
\(571\) 13.1273 22.7371i 0.549360 0.951519i −0.448959 0.893552i \(-0.648205\pi\)
0.998319 0.0579663i \(-0.0184616\pi\)
\(572\) 23.1205 9.59594i 0.966716 0.401226i
\(573\) 5.50428 0.229945
\(574\) 0 0
\(575\) 8.59149 + 14.8809i 0.358290 + 0.620576i
\(576\) −5.94520 −0.247717
\(577\) 21.2806 + 12.2863i 0.885922 + 0.511487i 0.872606 0.488424i \(-0.162428\pi\)
0.0133154 + 0.999911i \(0.495761\pi\)
\(578\) 7.35228 4.24484i 0.305815 0.176562i
\(579\) 4.10296i 0.170513i
\(580\) 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
\(584\) 6.19936 10.7376i 0.256531 0.444325i
\(585\) 7.90885 3.28249i 0.326991 0.135714i
\(586\) 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
\(591\) 19.0097 10.9752i 0.781954 0.451461i
\(592\) 1.87124 1.08036i 0.0769077 0.0444027i
\(593\) 33.1545 19.1417i 1.36149 0.786057i 0.371669 0.928365i \(-0.378786\pi\)
0.989822 + 0.142308i \(0.0454524\pi\)
\(594\) −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
\(598\) 7.31105 3.03438i 0.298971 0.124085i
\(599\) −7.03567 + 12.1861i −0.287470 + 0.497912i −0.973205 0.229939i \(-0.926147\pi\)
0.685735 + 0.727851i \(0.259481\pi\)
\(600\) −5.39851 3.11683i −0.220393 0.127244i
\(601\) −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
\(604\) 33.0847i 1.34620i
\(605\) 4.27887 2.47041i 0.173961 0.100436i
\(606\) −4.22039 2.43664i −0.171441 0.0989818i
\(607\) −6.55127 −0.265908 −0.132954 0.991122i \(-0.542446\pi\)
−0.132954 + 0.991122i \(0.542446\pi\)
\(608\) −13.8603 24.0067i −0.562108 0.973600i
\(609\) 0 0
\(610\) −3.05621 −0.123742
\(611\) −15.1736 + 6.29767i −0.613859 + 0.254776i
\(612\) −0.283136 + 0.490406i −0.0114451 + 0.0198235i
\(613\) 33.3244i 1.34596i −0.739660 0.672980i \(-0.765014\pi\)
0.739660 0.672980i \(-0.234986\pi\)
\(614\) 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 \(0.623216\pi\)
\(618\) 1.77116i 0.0712466i
\(619\) 15.2582 + 8.80931i 0.613278 + 0.354076i 0.774247 0.632883i \(-0.218129\pi\)
−0.160970 + 0.986959i \(0.551462\pi\)
\(620\) 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
\(625\) −4.93986 8.55609i −0.197594 0.342244i
\(626\) 14.2373i 0.569038i
\(627\) 18.5714 0.741669
\(628\) −34.6393 −1.38226
\(629\) 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
\(633\) 7.77009 + 13.4582i 0.308833 + 0.534915i
\(634\) 8.40783 0.333918
\(635\) 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
\(640\) −11.8499 −0.468410
\(641\) −10.4702 18.1350i −0.413550 0.716289i 0.581725 0.813385i \(-0.302378\pi\)
−0.995275 + 0.0970962i \(0.969045\pi\)
\(642\) 3.12234 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
\(646\) −0.391280 −0.0153947
\(647\) −37.6768 −1.48123 −0.740614 0.671930i \(-0.765465\pi\)
−0.740614 + 0.671930i \(0.765465\pi\)
\(648\) 5.67104i 0.222779i
\(649\) −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
\(653\) −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
\(655\) 11.2402 + 6.48952i 0.439190 + 0.253567i
\(656\) 31.0004i 1.21036i
\(657\) −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
\(661\) 4.59298i 0.178646i −0.996003 0.0893231i \(-0.971530\pi\)
0.996003 0.0893231i \(-0.0284704\pi\)
\(662\) −1.55225 + 2.68858i −0.0603300 + 0.104495i
\(663\) −0.166787 0.401857i −0.00647747 0.0156068i
\(664\) −5.38715 −0.209062
\(665\) 0 0
\(666\) 0.480219 + 0.831764i 0.0186081 + 0.0322302i
\(667\) 36.8736 1.42775
\(668\) 9.29746 + 5.36789i 0.359730 + 0.207690i
\(669\) −8.46782 + 4.88890i −0.327385 + 0.189016i
\(670\) 2.68142i 0.103592i
\(671\) 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
\(675\) −8.77418 + 15.1973i −0.337718 + 0.584945i
\(676\) −5.91919 21.9666i −0.227661 0.844871i
\(677\) 4.04354 + 7.00361i 0.155406 + 0.269171i 0.933207 0.359340i \(-0.116998\pi\)
−0.777801 + 0.628511i \(0.783665\pi\)
\(678\) 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
\(682\) −4.88989 + 2.82318i −0.187244 + 0.108105i
\(683\) 21.3792 12.3433i 0.818051 0.472302i −0.0316929 0.999498i \(-0.510090\pi\)
0.849744 + 0.527196i \(0.176757\pi\)
\(684\) −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
\(689\) 0.613136 0.800222i 0.0233586 0.0304860i
\(690\) 0.972234 1.68396i 0.0370123 0.0641072i
\(691\) 9.74859 + 5.62835i 0.370854 + 0.214113i 0.673831 0.738885i \(-0.264647\pi\)
−0.302978 + 0.952998i \(0.597981\pi\)
\(692\) −21.2301 36.7716i −0.807047 1.39785i
\(693\) 0 0
\(694\) 15.2043i 0.577147i
\(695\) 21.6194i 0.820071i
\(696\) −11.5849 + 6.68854i −0.439124 + 0.253528i
\(697\) −1.48805 0.859128i −0.0563640 0.0325418i
\(698\) 8.07884 0.305789
\(699\) −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 \(0.362094\pi\)
\(702\) 6.41698 + 4.91673i 0.242193 + 0.185570i
\(703\) 2.32288 4.02335i 0.0876091 0.151743i
\(704\) 10.3532i 0.390201i
\(705\) −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
\(709\) 23.7741i 0.892854i 0.894820 + 0.446427i \(0.147304\pi\)
−0.894820 + 0.446427i \(0.852696\pi\)
\(710\) 1.66961 + 0.963952i 0.0626595 + 0.0361765i
\(711\) 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
\(716\) −3.61969 6.26948i −0.135274 0.234301i
\(717\) 6.63082i 0.247632i
\(718\) 15.6822 0.585255
\(719\) 20.7808 0.774992 0.387496 0.921871i \(-0.373340\pi\)
0.387496 + 0.921871i \(0.373340\pi\)
\(720\) 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
\(724\) −6.88252 11.9209i −0.255787 0.443036i
\(725\) −32.8618 −1.22046
\(726\) 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
\(731\) 0.685069 0.0253382
\(732\) 4.35899 + 7.55000i 0.161113 + 0.279056i
\(733\) 4.55224 2.62824i 0.168141 0.0970761i −0.413568 0.910473i \(-0.635718\pi\)
0.581709 + 0.813397i \(0.302384\pi\)
\(734\) −10.4255 6.01919i −0.384814 0.222172i
\(735\) 0 0
\(736\) 22.0917i 0.814312i
\(737\) −20.4097 −0.751800
\(738\) 13.7796 0.507235
\(739\) 7.15001i 0.263017i −0.991315 0.131509i \(-0.958018\pi\)
0.991315 0.131509i \(-0.0419821\pi\)
\(740\) −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 \(0.337500\pi\)
\(744\) −2.26721 + 3.92692i −0.0831198 + 0.143968i
\(745\) −0.00592959 0.0102703i −0.000217243 0.000376276i
\(746\) −7.96386 4.59794i −0.291578 0.168342i
\(747\) 6.54569i 0.239494i
\(748\) 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 \(0.322026\pi\)
\(752\) 11.6763i 0.425791i
\(753\) 3.26238 5.65062i 0.118888 0.205920i
\(754\) −1.96539 + 15.0104i −0.0715752 + 0.546648i
\(755\) −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 \(0.929594\pi\)
\(758\) −4.06859 −0.147778
\(759\) −12.8175 7.40018i −0.465245 0.268609i
\(760\) −9.32654 + 5.38468i −0.338309 + 0.195323i
\(761\) 8.31998i 0.301599i −0.988564 0.150800i \(-0.951815\pi\)
0.988564 0.150800i \(-0.0481848\pi\)
\(762\) 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
\(766\) −5.59263 + 9.68671i −0.202070 + 0.349995i
\(767\) −35.9037 + 14.9015i −1.29641 + 0.538061i
\(768\) −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
\(773\) −7.27528 + 4.20038i −0.261674 + 0.151077i −0.625098 0.780546i \(-0.714941\pi\)
0.363424 + 0.931624i \(0.381608\pi\)
\(774\) −4.75789 + 2.74697i −0.171019 + 0.0987378i
\(775\) −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
\(780\) −4.43604 3.39892i −0.158836 0.121701i
\(781\)