Properties

Label 819.2.bm.f.478.4
Level $819$
Weight $2$
Character 819.478
Analytic conductor $6.540$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.bm (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 478.4
Root \(-1.18541 + 0.771231i\) of defining polynomial
Character \(\chi\) \(=\) 819.478
Dual form 819.2.bm.f.550.3

$q$-expansion

\(f(q)\) \(=\) \(q+0.499987i q^{2} +1.75001 q^{4} +(0.902810 + 0.521238i) q^{5} +(2.63491 + 0.239300i) q^{7} +1.87496i q^{8} +O(q^{10})\) \(q+0.499987i q^{2} +1.75001 q^{4} +(0.902810 + 0.521238i) q^{5} +(2.63491 + 0.239300i) q^{7} +1.87496i q^{8} +(-0.260612 + 0.451393i) q^{10} +(3.43579 + 1.98365i) q^{11} +(-3.57504 - 0.468096i) q^{13} +(-0.119647 + 1.31742i) q^{14} +2.56257 q^{16} -0.142035 q^{17} +(-4.77160 + 2.75488i) q^{19} +(1.57993 + 0.912173i) q^{20} +(-0.991800 + 1.71785i) q^{22} +4.39098 q^{23} +(-1.95662 - 3.38897i) q^{25} +(0.234042 - 1.78747i) q^{26} +(4.61112 + 0.418779i) q^{28} +(-4.19880 - 7.27253i) q^{29} +(2.46516 - 1.42326i) q^{31} +5.03117i q^{32} -0.0710158i q^{34} +(2.25409 + 1.58946i) q^{35} +0.843187i q^{37} +(-1.37740 - 2.38574i) q^{38} +(-0.977298 + 1.69273i) q^{40} +(-10.4766 + 6.04869i) q^{41} +(2.41161 - 4.17704i) q^{43} +(6.01267 + 3.47142i) q^{44} +2.19543i q^{46} +(3.94602 + 2.27824i) q^{47} +(6.88547 + 1.26107i) q^{49} +(1.69444 - 0.978285i) q^{50} +(-6.25636 - 0.819175i) q^{52} +(-0.139800 - 0.242141i) q^{53} +(2.06791 + 3.58172i) q^{55} +(-0.448678 + 4.94034i) q^{56} +(3.63617 - 2.09934i) q^{58} -10.7815i q^{59} +(2.93177 + 5.07797i) q^{61} +(0.711612 + 1.23255i) q^{62} +2.60963 q^{64} +(-2.98359 - 2.28605i) q^{65} +(-4.45524 - 2.57223i) q^{67} -0.248564 q^{68} +(-0.794706 + 1.12701i) q^{70} +(3.20326 + 1.84940i) q^{71} +(5.72686 - 3.30640i) q^{73} -0.421582 q^{74} +(-8.35036 + 4.82108i) q^{76} +(8.57829 + 6.04892i) q^{77} +(-5.96135 + 10.3254i) q^{79} +(2.31352 + 1.33571i) q^{80} +(-3.02426 - 5.23818i) q^{82} -2.87321i q^{83} +(-0.128231 - 0.0740342i) q^{85} +(2.08846 + 1.20578i) q^{86} +(-3.71926 + 6.44195i) q^{88} +1.74765i q^{89} +(-9.30787 - 2.08890i) q^{91} +7.68427 q^{92} +(-1.13909 + 1.97296i) q^{94} -5.74379 q^{95} +(2.34079 + 1.35145i) q^{97} +(-0.630517 + 3.44264i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 8q^{4} + 3q^{5} - 3q^{7} + O(q^{10}) \) \( 12q - 8q^{4} + 3q^{5} - 3q^{7} + 12q^{10} - 12q^{11} - 2q^{13} - 4q^{14} + 16q^{16} + 34q^{17} + 9q^{19} + 3q^{20} - 15q^{22} + 6q^{23} - 5q^{25} + 6q^{26} - 9q^{28} + q^{29} + 18q^{31} + 6q^{35} - 19q^{38} - q^{40} + 6q^{41} + 11q^{43} + 33q^{44} + 15q^{47} - 3q^{49} - 18q^{50} - 7q^{52} + 8q^{53} - 15q^{55} - 27q^{56} - 24q^{58} + 5q^{61} - 41q^{62} + 2q^{64} - 21q^{65} + 15q^{67} - 22q^{68} + 3q^{70} - 30q^{71} + 42q^{73} - 66q^{74} - 45q^{76} + 19q^{77} - 35q^{79} + 63q^{80} + 5q^{82} - 21q^{85} + 57q^{86} - 14q^{88} - 7q^{91} + 66q^{92} + q^{94} + 4q^{95} - 3q^{97} + 18q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

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 \(0.0565655\pi\)
−0.984252 + 0.176772i \(0.943434\pi\)
\(3\) 0 0
\(4\) 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 0
\(7\) 2.63491 + 0.239300i 0.995901 + 0.0904471i
\(8\) 1.87496i 0.662897i
\(9\) 0 0
\(10\) −0.260612 + 0.451393i −0.0824127 + 0.142743i
\(11\) 3.43579 + 1.98365i 1.03593 + 0.598094i 0.918677 0.395009i \(-0.129258\pi\)
0.117251 + 0.993102i \(0.462592\pi\)
\(12\) 0 0
\(13\) −3.57504 0.468096i −0.991537 0.129827i
\(14\) −0.119647 + 1.31742i −0.0319770 + 0.352095i
\(15\) 0 0
\(16\) 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 0
\(19\) −4.77160 + 2.75488i −1.09468 + 0.632014i −0.934818 0.355126i \(-0.884438\pi\)
−0.159861 + 0.987140i \(0.551105\pi\)
\(20\) 1.57993 + 0.912173i 0.353283 + 0.203968i
\(21\) 0 0
\(22\) −0.991800 + 1.71785i −0.211452 + 0.366246i
\(23\) 4.39098 0.915582 0.457791 0.889060i \(-0.348641\pi\)
0.457791 + 0.889060i \(0.348641\pi\)
\(24\) 0 0
\(25\) −1.95662 3.38897i −0.391325 0.677794i
\(26\) 0.234042 1.78747i 0.0458994 0.350552i
\(27\) 0 0
\(28\) 4.61112 + 0.418779i 0.871420 + 0.0791418i
\(29\) −4.19880 7.27253i −0.779697 1.35047i −0.932116 0.362159i \(-0.882040\pi\)
0.152419 0.988316i \(-0.451294\pi\)
\(30\) 0 0
\(31\) 2.46516 1.42326i 0.442756 0.255625i −0.262010 0.965065i \(-0.584385\pi\)
0.704766 + 0.709440i \(0.251052\pi\)
\(32\) 5.03117i 0.889393i
\(33\) 0 0
\(34\) 0.0710158i 0.0121791i
\(35\) 2.25409 + 1.58946i 0.381010 + 0.268667i
\(36\) 0 0
\(37\) 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
\(39\) 0 0
\(40\) −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
\(45\) 0 0
\(46\) 2.19543i 0.323699i
\(47\) 3.94602 + 2.27824i 0.575587 + 0.332315i 0.759378 0.650650i \(-0.225504\pi\)
−0.183791 + 0.982965i \(0.558837\pi\)
\(48\) 0 0
\(49\) 6.88547 + 1.26107i 0.983639 + 0.180153i
\(50\) 1.69444 0.978285i 0.239630 0.138350i
\(51\) 0 0
\(52\) −6.25636 0.819175i −0.867601 0.113599i
\(53\) −0.139800 0.242141i −0.0192030 0.0332606i 0.856264 0.516538i \(-0.172780\pi\)
−0.875467 + 0.483278i \(0.839446\pi\)
\(54\) 0 0
\(55\) 2.06791 + 3.58172i 0.278837 + 0.482959i
\(56\) −0.448678 + 4.94034i −0.0599571 + 0.660180i
\(57\) 0 0
\(58\) 3.63617 2.09934i 0.477452 0.275657i
\(59\) 10.7815i 1.40363i −0.712359 0.701815i \(-0.752373\pi\)
0.712359 0.701815i \(-0.247627\pi\)
\(60\) 0 0
\(61\) 2.93177 + 5.07797i 0.375374 + 0.650168i 0.990383 0.138353i \(-0.0441808\pi\)
−0.615009 + 0.788520i \(0.710847\pi\)
\(62\) 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 0
\(67\) −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
\(69\) 0 0
\(70\) −0.794706 + 1.12701i −0.0949856 + 0.134704i
\(71\) 3.20326 + 1.84940i 0.380157 + 0.219484i 0.677887 0.735167i \(-0.262896\pi\)
−0.297730 + 0.954650i \(0.596229\pi\)
\(72\) 0 0
\(73\) 5.72686 3.30640i 0.670278 0.386985i −0.125904 0.992042i \(-0.540183\pi\)
0.796182 + 0.605057i \(0.206850\pi\)
\(74\) −0.421582 −0.0490079
\(75\) 0 0
\(76\) −8.35036 + 4.82108i −0.957852 + 0.553016i
\(77\) 8.57829 + 6.04892i 0.977587 + 0.689339i
\(78\) 0 0
\(79\) −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
\(81\) 0 0
\(82\) −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
\(87\) 0 0
\(88\) −3.71926 + 6.44195i −0.396475 + 0.686714i
\(89\) 1.74765i 0.185250i 0.995701 + 0.0926252i \(0.0295258\pi\)
−0.995701 + 0.0926252i \(0.970474\pi\)
\(90\) 0 0
\(91\) −9.30787 2.08890i −0.975730 0.218976i
\(92\) 7.68427 0.801141
\(93\) 0 0
\(94\) −1.13909 + 1.97296i −0.117488 + 0.203495i
\(95\) −5.74379 −0.589301
\(96\) 0 0
\(97\) 2.34079 + 1.35145i 0.237671 + 0.137219i 0.614106 0.789224i \(-0.289517\pi\)
−0.376435 + 0.926443i \(0.622850\pi\)
\(98\) −0.630517 + 3.44264i −0.0636919 + 0.347759i
\(99\) 0 0
\(100\) −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 0
\(103\) 2.08475 3.61090i 0.205417 0.355792i −0.744849 0.667233i \(-0.767478\pi\)
0.950265 + 0.311441i \(0.100812\pi\)
\(104\) 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 \(-0.634560\pi\)
−0.410255 + 0.911971i \(0.634560\pi\)
\(108\) 0 0
\(109\) 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 0
\(112\) 6.75214 + 0.613225i 0.638018 + 0.0579443i
\(113\) 5.48164 9.49448i 0.515670 0.893166i −0.484165 0.874977i \(-0.660877\pi\)
0.999835 0.0181892i \(-0.00579012\pi\)
\(114\) 0 0
\(115\) 3.96422 + 2.28874i 0.369665 + 0.213426i
\(116\) −7.34795 12.7270i −0.682240 1.18167i
\(117\) 0 0
\(118\) 5.39060 0.496245
\(119\) −0.374250 0.0339891i −0.0343074 0.00311578i
\(120\) 0 0
\(121\) 2.36975 + 4.10453i 0.215432 + 0.373139i
\(122\) −2.53892 + 1.46584i −0.229863 + 0.132711i
\(123\) 0 0
\(124\) 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
\(129\) 0 0
\(130\) 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 \(0.983617\pi\)
\(132\) 0 0
\(133\) −13.2320 + 6.11702i −1.14736 + 0.530413i
\(134\) 1.28608 2.22756i 0.111101 0.192432i
\(135\) 0 0
\(136\) 0.266310i 0.0228359i
\(137\) 5.24518i 0.448126i −0.974575 0.224063i \(-0.928068\pi\)
0.974575 0.224063i \(-0.0719321\pi\)
\(138\) 0 0
\(139\) 10.3693 17.9601i 0.879510 1.52336i 0.0276301 0.999618i \(-0.491204\pi\)
0.851880 0.523737i \(-0.175463\pi\)
\(140\) 3.94468 + 2.78157i 0.333387 + 0.235085i
\(141\) 0 0
\(142\) −0.924676 + 1.60159i −0.0775971 + 0.134402i
\(143\) −11.3545 8.69991i −0.949513 0.727523i
\(144\) 0 0
\(145\) 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 −0.500403 0.865792i \(-0.666815\pi\)
0.499596 + 0.866258i \(0.333482\pi\)
\(150\) 0 0
\(151\) −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 0
\(154\) −3.02438 + 4.28903i −0.243712 + 0.345620i
\(155\) 2.96743 0.238350
\(156\) 0 0
\(157\) −9.89687 17.1419i −0.789856 1.36807i −0.926054 0.377390i \(-0.876822\pi\)
0.136198 0.990682i \(-0.456512\pi\)
\(158\) −5.16255 2.98060i −0.410710 0.237124i
\(159\) 0 0
\(160\) −2.62243 + 4.54219i −0.207321 + 0.359091i
\(161\) 11.5698 + 1.05076i 0.911830 + 0.0828117i
\(162\) 0 0
\(163\) 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
\(165\) 0 0
\(166\) 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
\(171\) 0 0
\(172\) 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 \(-0.540386\pi\)
\(174\) 0 0
\(175\) −4.34454 9.39784i −0.328416 0.710410i
\(176\) 8.80446 + 5.08325i 0.663661 + 0.383165i
\(177\) 0 0
\(178\) −0.873801 −0.0654942
\(179\) 2.06838 3.58253i 0.154598 0.267771i −0.778315 0.627874i \(-0.783925\pi\)
0.932912 + 0.360103i \(0.117259\pi\)
\(180\) 0 0
\(181\) −7.86568 −0.584651 −0.292326 0.956319i \(-0.594429\pi\)
−0.292326 + 0.956319i \(0.594429\pi\)
\(182\) 1.04442 4.65381i 0.0774176 0.344964i
\(183\) 0 0
\(184\) 8.23289i 0.606937i
\(185\) −0.439501 + 0.761237i −0.0323127 + 0.0559673i
\(186\) 0 0
\(187\) −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 0.724705 0.689059i \(-0.241976\pi\)
−0.959095 + 0.283084i \(0.908643\pi\)
\(192\) 0 0
\(193\) 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
\(195\) 0 0
\(196\) 12.0497 + 2.20689i 0.860690 + 0.157635i
\(197\) 22.3748 12.9181i 1.59414 0.920377i 0.601554 0.798832i \(-0.294548\pi\)
0.992586 0.121545i \(-0.0387850\pi\)
\(198\) 0 0
\(199\) −17.1146 −1.21322 −0.606612 0.794998i \(-0.707472\pi\)
−0.606612 + 0.794998i \(0.707472\pi\)
\(200\) 6.35417 3.66858i 0.449308 0.259408i
\(201\) 0 0
\(202\) −4.96749 2.86798i −0.349511 0.201790i
\(203\) −9.32312 20.1672i −0.654355 1.41546i
\(204\) 0 0
\(205\) −12.6112 −0.880806
\(206\) 1.80540 + 1.04235i 0.125788 + 0.0726238i
\(207\) 0 0
\(208\) −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
\(213\) 0 0
\(214\) 4.24360i 0.290086i
\(215\) 4.35446 2.51405i 0.296972 0.171457i
\(216\) 0 0
\(217\) 6.83606 3.16025i 0.464062 0.214532i
\(218\) 1.60755 + 2.78435i 0.108877 + 0.188580i
\(219\) 0 0
\(220\) 3.61887 + 6.26806i 0.243984 + 0.422593i
\(221\) 0.507782 + 0.0664862i 0.0341571 + 0.00447235i
\(222\) 0 0
\(223\) −9.96682 + 5.75435i −0.667428 + 0.385340i −0.795101 0.606477i \(-0.792582\pi\)
0.127674 + 0.991816i \(0.459249\pi\)
\(224\) −1.20396 + 13.2567i −0.0804430 + 0.885747i
\(225\) 0 0
\(226\) 4.74711 + 2.74075i 0.315773 + 0.182312i
\(227\) 17.9045i 1.18836i −0.804332 0.594181i \(-0.797476\pi\)
0.804332 0.594181i \(-0.202524\pi\)
\(228\) 0 0
\(229\) −3.34589 1.93175i −0.221103 0.127654i 0.385358 0.922767i \(-0.374078\pi\)
−0.606461 + 0.795113i \(0.707411\pi\)
\(230\) −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 \(0.473252\pi\)
−0.904935 + 0.425549i \(0.860081\pi\)
\(234\) 0 0
\(235\) 2.37501 + 4.11363i 0.154928 + 0.268344i
\(236\) 18.8678i 1.22819i
\(237\) 0 0
\(238\) 0.0169941 0.187120i 0.00110156 0.0121292i
\(239\) 7.80462i 0.504839i −0.967618 0.252419i \(-0.918774\pi\)
0.967618 0.252419i \(-0.0812263\pi\)
\(240\) 0 0
\(241\) 21.7653i 1.40202i 0.713150 + 0.701012i \(0.247268\pi\)
−0.713150 + 0.701012i \(0.752732\pi\)
\(242\) −2.05221 + 1.18484i −0.131921 + 0.0761647i
\(243\) 0 0
\(244\) 5.13063 + 8.88652i 0.328455 + 0.568901i
\(245\) 5.55895 + 4.72747i 0.355149 + 0.302027i
\(246\) 0 0
\(247\) 18.3482 7.61524i 1.16747 0.484546i
\(248\) 2.66855 + 4.62207i 0.169453 + 0.293502i
\(249\) 0 0
\(250\) 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 0
\(256\) −0.464141 −0.0290088
\(257\) 13.6237 0.849826 0.424913 0.905234i \(-0.360305\pi\)
0.424913 + 0.905234i \(0.360305\pi\)
\(258\) 0 0
\(259\) −0.201775 + 2.22172i −0.0125377 + 0.138051i
\(260\) −5.22132 4.00061i −0.323813 0.248107i
\(261\) 0 0
\(262\) −5.39096 3.11247i −0.333055 0.192289i
\(263\) −5.86158 + 10.1525i −0.361440 + 0.626033i −0.988198 0.153181i \(-0.951048\pi\)
0.626758 + 0.779214i \(0.284382\pi\)
\(264\) 0 0
\(265\) 0.291476i 0.0179052i
\(266\) −3.05843 6.61580i −0.187524 0.405641i
\(267\) 0 0
\(268\) −7.79673 4.50144i −0.476261 0.274970i
\(269\) −9.19876 −0.560858 −0.280429 0.959875i \(-0.590477\pi\)
−0.280429 + 0.959875i \(0.590477\pi\)
\(270\) 0 0
\(271\) 2.56369i 0.155733i −0.996964 0.0778665i \(-0.975189\pi\)
0.996964 0.0778665i \(-0.0248108\pi\)
\(272\) −0.363976 −0.0220693
\(273\) 0 0
\(274\) 2.62252 0.158432
\(275\) 15.5250i 0.936195i
\(276\) 0 0
\(277\) 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
\(279\) 0 0
\(280\) −2.98016 + 4.22632i −0.178099 + 0.252571i
\(281\) 6.45288i 0.384947i −0.981302 0.192473i \(-0.938349\pi\)
0.981302 0.192473i \(-0.0616509\pi\)
\(282\) 0 0
\(283\) 11.0873 19.2037i 0.659071 1.14154i −0.321786 0.946812i \(-0.604283\pi\)
0.980857 0.194731i \(-0.0623835\pi\)
\(284\) 5.60575 + 3.23648i 0.332640 + 0.192050i
\(285\) 0 0
\(286\) 4.34984 5.67711i 0.257211 0.335695i
\(287\) −29.0524 + 13.4307i −1.71491 + 0.792788i
\(288\) 0 0
\(289\) −16.9798 −0.998813
\(290\) 4.37702 0.257028
\(291\) 0 0
\(292\) 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
\(297\) 0 0
\(298\) −0.00284392 0.00492581i −0.000164744 0.000285345i
\(299\) −15.6979 2.05540i −0.907833 0.118867i
\(300\) 0 0
\(301\) 7.35395 10.4290i 0.423875 0.601118i
\(302\) −4.72623 8.18607i −0.271964 0.471055i
\(303\) 0 0
\(304\) −12.2276 + 7.05959i −0.701299 + 0.404895i
\(305\) 6.11259i 0.350006i
\(306\) 0 0
\(307\) 24.2924i 1.38644i 0.720726 + 0.693220i \(0.243809\pi\)
−0.720726 + 0.693220i \(0.756191\pi\)
\(308\) 15.0121 + 10.5857i 0.855395 + 0.603176i
\(309\) 0 0
\(310\) 1.48367i 0.0842671i
\(311\) −1.99355 3.45294i −0.113044 0.195798i 0.803952 0.594694i \(-0.202727\pi\)
−0.916996 + 0.398896i \(0.869393\pi\)
\(312\) 0 0
\(313\) −14.2377 + 24.6604i −0.804763 + 1.39389i 0.111688 + 0.993743i \(0.464374\pi\)
−0.916451 + 0.400147i \(0.868959\pi\)
\(314\) 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 0.849709 0.527252i \(-0.176778\pi\)
−0.0317591 + 0.999496i \(0.510111\pi\)
\(318\) 0 0
\(319\) 33.3158i 1.86533i
\(320\) 2.35600 + 1.36024i 0.131704 + 0.0760396i
\(321\) 0 0
\(322\) −0.525367 + 5.78476i −0.0292776 + 0.322372i
\(323\) 0.677736 0.391291i 0.0377102 0.0217720i
\(324\) 0 0
\(325\) 5.40863 + 13.0316i 0.300017 + 0.722862i
\(326\) 2.23308 + 3.86780i 0.123679 + 0.214218i
\(327\) 0 0
\(328\) −11.3410 19.6432i −0.626204 1.08462i
\(329\) 9.85222 + 6.94723i 0.543171 + 0.383013i
\(330\) 0 0
\(331\) 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
\(333\) 0 0
\(334\) −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
\(339\) 0 0
\(340\) −0.224406 0.129561i −0.0121701 0.00702642i
\(341\) 11.2930 0.611552
\(342\) 0 0
\(343\) 17.8408 + 4.97049i 0.963313 + 0.268381i
\(344\) 7.83177 + 4.52167i 0.422261 + 0.243792i
\(345\) 0 0
\(346\) 10.5058 6.06553i 0.564795 0.326085i
\(347\) −30.4094 −1.63246 −0.816231 0.577725i \(-0.803941\pi\)
−0.816231 + 0.577725i \(0.803941\pi\)
\(348\) 0 0
\(349\) −13.9933 + 8.07906i −0.749046 + 0.432462i −0.825349 0.564623i \(-0.809022\pi\)
0.0763028 + 0.997085i \(0.475688\pi\)
\(350\) 4.69880 2.17221i 0.251161 0.116110i
\(351\) 0 0
\(352\) −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 \(0.564611\pi\)
\(354\) 0 0
\(355\) 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 0.997394 0.0721417i \(-0.0229834\pi\)
0.436221 + 0.899840i \(0.356317\pi\)
\(360\) 0 0
\(361\) 5.67876 9.83591i 0.298882 0.517679i
\(362\) 3.93273i 0.206700i
\(363\) 0 0
\(364\) −16.2889 3.65560i −0.853770 0.191605i
\(365\) 6.89369 0.360832
\(366\) 0 0
\(367\) −12.0387 + 20.8517i −0.628415 + 1.08845i 0.359454 + 0.933163i \(0.382963\pi\)
−0.987870 + 0.155285i \(0.950370\pi\)
\(368\) 11.2522 0.586562
\(369\) 0 0
\(370\) −0.380608 0.219744i −0.0197869 0.0114240i
\(371\) −0.310416 0.671473i −0.0161160 0.0348611i
\(372\) 0 0
\(373\) 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
\(375\) 0 0
\(376\) −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
\(381\) 0 0
\(382\) 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 \(0.139674\pi\)
\(384\) 0 0
\(385\) 4.59164 + 9.93236i 0.234012 + 0.506200i
\(386\) −1.20729 + 2.09108i −0.0614493 + 0.106433i
\(387\) 0 0
\(388\) 4.09641 + 2.36506i 0.207963 + 0.120068i
\(389\) 10.6973 + 18.5283i 0.542374 + 0.939420i 0.998767 + 0.0496415i \(0.0158079\pi\)
−0.456393 + 0.889778i \(0.650859\pi\)
\(390\) 0 0
\(391\) −0.623674 −0.0315406
\(392\) −2.36445 + 12.9100i −0.119423 + 0.652051i
\(393\) 0 0
\(394\) 6.45888 + 11.1871i 0.325394 + 0.563599i
\(395\) −10.7639 + 6.21456i −0.541592 + 0.312689i
\(396\) 0 0
\(397\) 1.03640 0.598365i 0.0520154 0.0300311i −0.473767 0.880650i \(-0.657106\pi\)
0.525782 + 0.850619i \(0.323773\pi\)
\(398\) 8.55708i 0.428928i
\(399\) 0 0
\(400\) −5.01399 8.68449i −0.250699 0.434224i
\(401\) 36.2749i 1.81148i 0.423831 + 0.905741i \(0.360685\pi\)
−0.423831 + 0.905741i \(0.639315\pi\)
\(402\) 0 0
\(403\) −9.47926 + 3.93428i −0.472196 + 0.195980i
\(404\) −10.0383 + 17.3868i −0.499423 + 0.865026i
\(405\) 0 0
\(406\) 10.0833 4.66144i 0.500428 0.231343i
\(407\) −1.67259 + 2.89701i −0.0829072 + 0.143599i
\(408\) 0 0
\(409\) 14.6723i 0.725500i −0.931887 0.362750i \(-0.881838\pi\)
0.931887 0.362750i \(-0.118162\pi\)
\(410\) 6.30544i 0.311404i
\(411\) 0 0
\(412\) 3.64834 6.31912i 0.179741 0.311321i
\(413\) 2.58002 28.4082i 0.126954 1.39788i
\(414\) 0 0
\(415\) 1.49763 2.59397i 0.0735156 0.127333i
\(416\) 2.35507 17.9866i 0.115467 0.881866i
\(417\) 0 0
\(418\) 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
\(423\) 0 0
\(424\) 0.454004 0.262119i 0.0220484 0.0127296i
\(425\) 0.277910 + 0.481354i 0.0134806 + 0.0233491i
\(426\) 0 0
\(427\) 6.50978 + 14.0816i 0.315030 + 0.681454i
\(428\) −14.8531 −0.717952
\(429\) 0 0
\(430\) 1.25699 + 2.17717i 0.0606175 + 0.104993i
\(431\) −16.3139 9.41883i −0.785812 0.453689i 0.0526738 0.998612i \(-0.483226\pi\)
−0.838486 + 0.544923i \(0.816559\pi\)
\(432\) 0 0
\(433\) 9.56773 16.5718i 0.459796 0.796389i −0.539154 0.842207i \(-0.681256\pi\)
0.998950 + 0.0458176i \(0.0145893\pi\)
\(434\) 1.58008 + 3.41794i 0.0758463 + 0.164066i
\(435\) 0 0
\(436\) 9.74557 5.62661i 0.466728 0.269466i
\(437\) −20.9520 + 12.0966i −1.00227 + 0.578660i
\(438\) 0 0
\(439\) 1.26511 0.0603803 0.0301901 0.999544i \(-0.490389\pi\)
0.0301901 + 0.999544i \(0.490389\pi\)
\(440\) −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 \(-0.999055\pi\)
0.502569 + 0.864537i \(0.332388\pi\)
\(444\) 0 0
\(445\) −0.910940 + 1.57779i −0.0431827 + 0.0747946i
\(446\) −2.87710 4.98328i −0.136234 0.235965i
\(447\) 0 0
\(448\) 6.87614 + 0.624486i 0.324867 + 0.0295042i
\(449\) −15.4700 8.93162i −0.730075 0.421509i 0.0883746 0.996087i \(-0.471833\pi\)
−0.818450 + 0.574578i \(0.805166\pi\)
\(450\) 0 0
\(451\) −47.9940 −2.25995
\(452\) 9.59295 16.6155i 0.451214 0.781526i
\(453\) 0 0
\(454\) 8.95199 0.420138
\(455\) −7.31443 6.73749i −0.342906 0.315858i
\(456\) 0 0
\(457\) 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 0
\(460\) 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
\(465\) 0 0
\(466\) −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 \(0.0698087\pi\)
\(468\) 0 0
\(469\) −11.1236 7.84374i −0.513641 0.362190i
\(470\) −2.05676 + 1.18747i −0.0948713 + 0.0547740i
\(471\) 0 0
\(472\) 20.2148 0.930463
\(473\) 16.5716 9.56761i 0.761962 0.439919i
\(474\) 0 0
\(475\) 18.6724 + 10.7805i 0.856750 + 0.494645i
\(476\) −0.654942 0.0594814i −0.0300192 0.00272633i
\(477\) 0 0
\(478\) 3.90221 0.178483
\(479\) −23.3930 13.5060i −1.06885 0.617104i −0.140987 0.990012i \(-0.545027\pi\)
−0.927868 + 0.372908i \(0.878361\pi\)
\(480\) 0 0
\(481\) 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
\(486\) 0 0
\(487\) 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
\(489\) 0 0
\(490\) −2.36367 + 2.77940i −0.106780 + 0.125561i
\(491\) 14.3020 + 24.7718i 0.645440 + 1.11793i 0.984200 + 0.177061i \(0.0566591\pi\)
−0.338760 + 0.940873i \(0.610008\pi\)
\(492\) 0 0
\(493\) 0.596378 + 1.03296i 0.0268595 + 0.0465220i
\(494\) 3.80752 + 9.17385i 0.171308 + 0.412751i
\(495\) 0 0
\(496\) 6.31716 3.64721i 0.283649 0.163765i
\(497\) 7.99773 + 5.63954i 0.358747 + 0.252968i
\(498\) 0 0
\(499\) 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
\(501\) 0 0
\(502\) −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
\(507\) 0 0
\(508\) −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 0
\(511\) 15.8810 7.34163i 0.702532 0.324774i
\(512\) 22.5022i 0.994464i
\(513\) 0 0
\(514\) 6.81169i 0.300451i
\(515\) 3.76427 2.17330i 0.165874 0.0957671i
\(516\) 0 0
\(517\) 9.03847 + 15.6551i 0.397511 + 0.688510i
\(518\) −1.11083 0.100885i −0.0488070 0.00443262i
\(519\) 0 0
\(520\) 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 \(0.573609\pi\)
\(522\) 0 0
\(523\) 38.7121 1.69276 0.846380 0.532579i \(-0.178777\pi\)
0.846380 + 0.532579i \(0.178777\pi\)
\(524\) −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
\(528\) 0 0
\(529\) −3.71931 −0.161709
\(530\) 0.145734 0.00633029
\(531\) 0 0
\(532\) −23.1561 + 10.7049i −1.00394 + 0.464115i
\(533\) 40.2857 16.7202i 1.74497 0.724233i
\(534\) 0 0
\(535\) −7.66253 4.42396i −0.331280 0.191265i
\(536\) 4.82283 8.35338i 0.208314 0.360811i
\(537\) 0 0
\(538\) 4.59926i 0.198288i
\(539\) 21.1555 + 17.9911i 0.911231 + 0.774933i
\(540\) 0 0
\(541\) −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
\(543\) 0 0
\(544\) 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
\(549\) 0 0
\(550\) 7.76231 0.330986
\(551\) 40.0699 + 23.1344i 1.70704 + 0.985558i
\(552\) 0 0
\(553\) −18.1785 + 25.7798i −0.773027 + 1.09627i
\(554\) 0.466928i 0.0198379i
\(555\) 0 0
\(556\) 18.1464 31.4304i 0.769577 1.33295i
\(557\) −9.81039 5.66403i −0.415680 0.239993i 0.277547 0.960712i \(-0.410478\pi\)
−0.693227 + 0.720719i \(0.743812\pi\)
\(558\) 0 0
\(559\) −10.5769 + 13.8042i −0.447354 + 0.583855i
\(560\) 5.77627 + 4.07310i 0.244092 + 0.172120i
\(561\) 0 0
\(562\) 3.22636 0.136096
\(563\) 32.6386 1.37555 0.687777 0.725922i \(-0.258586\pi\)
0.687777 + 0.725922i \(0.258586\pi\)
\(564\) 0 0
\(565\) 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 \(-0.237731\pi\)
0.733829 + 0.679335i \(0.237731\pi\)
\(570\) 0 0
\(571\) 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
\(573\) 0 0
\(574\) −6.71516 14.5258i −0.280285 0.606296i
\(575\) −8.59149 14.8809i −0.358290 0.620576i
\(576\) 0 0
\(577\) 21.2806 12.2863i 0.885922 0.511487i 0.0133154 0.999911i \(-0.495761\pi\)
0.872606 + 0.488424i \(0.162428\pi\)
\(578\) 8.48969i 0.353124i
\(579\) 0 0
\(580\) 15.3201i 0.636133i
\(581\) 0.687561 7.57065i 0.0285248 0.314083i
\(582\) 0 0
\(583\) 1.10926i 0.0459408i
\(584\) 6.19936 + 10.7376i 0.256531 + 0.444325i
\(585\) 0 0
\(586\) −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
\(591\) 0 0
\(592\) 2.16073i 0.0888054i
\(593\) −33.1545 19.1417i −1.36149 0.786057i −0.371669 0.928365i \(-0.621214\pi\)
−0.989822 + 0.142308i \(0.954548\pi\)
\(594\) 0 0
\(595\) −0.320160 0.225759i −0.0131253 0.00925521i
\(596\) −0.0172409 + 0.00995405i −0.000706216 + 0.000407734i
\(597\) 0 0
\(598\) 1.02767 7.84874i 0.0420247 0.320959i
\(599\) 7.03567 + 12.1861i 0.287470 + 0.497912i 0.973205 0.229939i \(-0.0738526\pi\)
−0.685735 + 0.727851i \(0.740519\pi\)
\(600\) 0 0
\(601\) 10.1171 + 17.5233i 0.412685 + 0.714791i 0.995182 0.0980417i \(-0.0312579\pi\)
−0.582498 + 0.812832i \(0.697925\pi\)
\(602\) 5.21437 + 3.67688i 0.212522 + 0.149858i
\(603\) 0 0
\(604\) −28.6522 + 16.5424i −1.16584 + 0.673099i
\(605\) 4.94082i 0.200873i
\(606\) 0 0
\(607\) −3.27563 5.67356i −0.132954 0.230283i 0.791860 0.610703i \(-0.209113\pi\)
−0.924814 + 0.380420i \(0.875780\pi\)
\(608\) −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 0
\(613\) 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
\(615\) 0 0
\(616\) −11.3415 + 16.0839i −0.456961 + 0.648040i
\(617\) −5.85466 3.38019i −0.235700 0.136081i 0.377499 0.926010i \(-0.376784\pi\)
−0.613199 + 0.789929i \(0.710117\pi\)
\(618\) 0 0
\(619\) 15.2582 8.80931i 0.613278 0.354076i −0.160970 0.986959i \(-0.551462\pi\)
0.774247 + 0.632883i \(0.218129\pi\)
\(620\) 5.19304 0.208558
\(621\) 0 0
\(622\) 1.72642 0.996751i 0.0692233 0.0399661i
\(623\) −0.418213 + 4.60489i −0.0167554 + 0.184491i
\(624\) 0 0
\(625\) −4.93986 + 8.55609i −0.197594 + 0.342244i
\(626\) −12.3299 7.11866i −0.492801 0.284519i
\(627\) 0 0
\(628\) −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
\(633\) 0 0
\(634\) −4.20392 + 7.28140i −0.166959 + 0.289181i
\(635\) 2.09316i 0.0830644i
\(636\) 0 0
\(637\) −24.0255 7.73143i −0.951925 0.306330i
\(638\) 16.6575 0.659475
\(639\) 0 0
\(640\) −5.92497 + 10.2623i −0.234205 + 0.405655i
\(641\) −20.9405 −0.827099 −0.413550 0.910482i \(-0.635711\pi\)
−0.413550 + 0.910482i \(0.635711\pi\)
\(642\) 0 0
\(643\) −16.3952 9.46576i −0.646563 0.373293i 0.140575 0.990070i \(-0.455105\pi\)
−0.787138 + 0.616777i \(0.788438\pi\)
\(644\) 20.2473 + 1.83885i 0.797857 + 0.0724608i
\(645\) 0 0
\(646\) 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 \(-0.0987988\pi\)
\(648\) 0 0
\(649\) 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 \(-0.692308\pi\)
−0.568066 + 0.822983i \(0.692308\pi\)
\(654\) 0 0
\(655\) −11.2402 + 6.48952i −0.439190 + 0.253567i
\(656\) −26.8472 + 15.5002i −1.04821 + 0.605182i
\(657\) 0 0
\(658\) −3.47352 + 4.92598i −0.135412 + 0.192035i
\(659\) −0.709152 + 1.22829i −0.0276247 + 0.0478473i −0.879507 0.475886i \(-0.842128\pi\)
0.851883 + 0.523733i \(0.175461\pi\)
\(660\) 0 0
\(661\) −3.97764 2.29649i −0.154712 0.0893231i 0.420645 0.907225i \(-0.361804\pi\)
−0.575357 + 0.817902i \(0.695137\pi\)
\(662\) 1.55225 + 2.68858i 0.0603300 + 0.104495i
\(663\) 0 0
\(664\) 5.38715 0.209062
\(665\) −15.1344 1.37449i −0.586885 0.0533005i
\(666\) 0 0
\(667\) −18.4368 31.9335i −0.713877 1.23647i
\(668\) −9.29746 + 5.36789i −0.359730 + 0.207690i
\(669\) 0 0
\(670\) 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
\(675\) 0 0
\(676\) 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 \(0.116998\pi\)
\(678\) 0 0
\(679\) 5.84435 + 4.12110i 0.224285 + 0.158153i
\(680\) 0.138811 0.240427i 0.00532315 0.00921997i
\(681\) 0 0
\(682\) 5.64636i 0.216210i
\(683\) 24.6865i 0.944604i −0.881437 0.472302i \(-0.843423\pi\)
0.881437 0.472302i \(-0.156577\pi\)
\(684\) 0 0
\(685\) 2.73398 4.73540i 0.104460 0.180930i
\(686\) −2.48518 + 8.92016i −0.0948846 + 0.340573i
\(687\) 0 0
\(688\) 6.17994 10.7040i 0.235608 0.408085i
\(689\) 0.386445 + 0.931102i 0.0147224 + 0.0354722i
\(690\) 0 0
\(691\) 11.2567i 0.428225i 0.976809 + 0.214113i \(0.0686859\pi\)
−0.976809 + 0.214113i \(0.931314\pi\)
\(692\) −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
\(696\) 0 0
\(697\) 1.48805 0.859128i 0.0563640 0.0325418i
\(698\) −4.03942 6.99648i −0.152894 0.264821i
\(699\) 0 0
\(700\) −7.60300 16.4463i −0.287366 0.621614i
\(701\) −22.2305 −0.839635 −0.419818 0.907608i \(-0.637906\pi\)
−0.419818 + 0.907608i \(0.637906\pi\)
\(702\) 0 0
\(703\) −2.32288 4.02335i −0.0876091 0.151743i
\(704\) 8.96614 + 5.17660i 0.337924 + 0.195101i
\(705\) 0 0
\(706\) −2.96052 + 5.12776i −0.111420 + 0.192986i
\(707\) −17.4916 + 24.8058i −0.657841 + 0.932918i
\(708\) 0 0
\(709\) 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
\(711\) 0 0
\(712\) −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
\(717\) 0 0
\(718\) −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 \(0.959993\pi\)
\(720\) 0 0
\(721\) 6.35722 9.01550i 0.236755 0.335755i
\(722\) 4.91782 + 2.83931i 0.183022 + 0.105668i
\(723\) 0 0
\(724\) −13.7650 −0.511574
\(725\) −16.4309 + 28.4592i −0.610229 + 1.05695i
\(726\) 0 0
\(727\) −26.7719 −0.992915 −0.496457 0.868061i \(-0.665366\pi\)
−0.496457 + 0.868061i \(0.665366\pi\)
\(728\) 3.91659 17.4519i 0.145159 0.646809i
\(729\) 0 0
\(730\) 3.44675i 0.127570i
\(731\) −0.342535 + 0.593287i −0.0126691 + 0.0219435i
\(732\) 0 0
\(733\) 4.55224 + 2.62824i 0.168141 + 0.0970761i 0.581709 0.813397i \(-0.302384\pi\)
−0.413568 + 0.910473i \(0.635718\pi\)
\(734\) −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
\(738\) 0 0
\(739\) 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
\(741\) 0 0
\(742\) 0.335727 0.155204i 0.0123249 0.00569771i
\(743\) 0.618032 0.356821i 0.0226734 0.0130905i −0.488620 0.872496i \(-0.662500\pi\)
0.511294 + 0.859406i \(0.329166\pi\)
\(744\) 0 0
\(745\) −0.0118592 −0.000434486
\(746\) −7.96386 + 4.59794i −0.291578 + 0.168342i
\(747\) 0 0
\(748\) −0.854012 0.493064i −0.0312258 0.0180282i
\(749\) −22.3636 2.03104i −0.817147 0.0742127i
\(750\) 0 0
\(751\) 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
\(753\) 0 0
\(754\) −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
\(759\) 0 0
\(760\) 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 0
\(763\) 15.4428 7.13907i 0.559067 0.258452i
\(764\) −5.66888 9.81878i −0.205093 0.355231i
\(765\) 0 0
\(766\) 5.59263 + 9.68671i 0.202070 + 0.349995i
\(767\) −5.04678 + 38.5442i −0.182229 + 1.39175i
\(768\) 0 0
\(769\) 22.1346 12.7794i 0.798194 0.460838i −0.0446452 0.999003i \(-0.514216\pi\)
0.842839 + 0.538165i \(0.180882\pi\)
\(770\) −4.96605 + 2.29576i −0.178964 + 0.0827334i
\(771\) 0 0
\(772\) 7.31905 + 4.22565i 0.263418 + 0.152085i
\(773\) 8.40077i 0.302155i −0.988522 0.151077i \(-0.951726\pi\)
0.988522 0.151077i \(-0.0482742\pi\)
\(774\) 0 0
\(775\) −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
\(780\) 0 0
\(781\) 7.33714 + 12.7083i 0.262544 + 0.454739i
\(782\) 0.311829i 0.0111510i
\(783\) 0 0
\(784\) 17.6445 + 3.23158i 0.630162 + 0.115414i
\(785\) 20.6345i 0.736476i
\(786\) 0 0
\(787\) 35.0644i 1.24991i −0.780660 0.624956i \(-0.785117\pi\)
0.780660 0.624956i \(-0.214883\pi\)
\(788\) 39.1562 22.6069i