Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(218,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.218");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 218.8 | ||
Character | \(\chi\) | \(=\) | 525.218 |
Dual form | 525.2.j.c.407.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.723969 | − | 0.723969i | −0.511923 | − | 0.511923i | 0.403192 | − | 0.915115i | \(-0.367901\pi\) |
−0.915115 | + | 0.403192i | \(0.867901\pi\) | |||||||
\(3\) | 1.41842 | − | 0.994020i | 0.818927 | − | 0.573898i | ||||
\(4\) | − | 0.951738i | − | 0.475869i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.74653 | − | 0.307254i | −0.713020 | − | 0.125436i | ||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | ||||
\(8\) | −2.13697 | + | 2.13697i | −0.755532 | + | 0.755532i | ||||
\(9\) | 1.02385 | − | 2.81988i | 0.341282 | − | 0.939961i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.63664i | − | 1.09649i | −0.836319 | − | 0.548243i | \(-0.815297\pi\) | ||
0.836319 | − | 0.548243i | \(-0.184703\pi\) | |||||||
\(12\) | −0.946047 | − | 1.34997i | −0.273100 | − | 0.389702i | ||||
\(13\) | 4.19487 | + | 4.19487i | 1.16345 | + | 1.16345i | 0.983716 | + | 0.179732i | \(0.0575231\pi\) |
0.179732 | + | 0.983716i | \(0.442477\pi\) | |||||||
\(14\) | −1.02385 | −0.273635 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.19072 | 0.297680 | ||||||||
\(17\) | −4.61300 | − | 4.61300i | −1.11882 | − | 1.11882i | −0.991915 | − | 0.126901i | \(-0.959497\pi\) |
−0.126901 | − | 0.991915i | \(-0.540503\pi\) | |||||||
\(18\) | −2.78274 | + | 1.30027i | −0.655898 | + | 0.306478i | ||||
\(19\) | − | 3.77162i | − | 0.865269i | −0.901569 | − | 0.432635i | \(-0.857584\pi\) | ||
0.901569 | − | 0.432635i | \(-0.142416\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.300098 | − | 1.70586i | 0.0654867 | − | 0.372248i | ||||
\(22\) | −2.63281 | + | 2.63281i | −0.561317 | + | 0.561317i | ||||
\(23\) | −1.81887 | + | 1.81887i | −0.379261 | + | 0.379261i | −0.870836 | − | 0.491574i | \(-0.836422\pi\) |
0.491574 | + | 0.870836i | \(0.336422\pi\) | |||||||
\(24\) | −0.906934 | + | 5.15531i | −0.185127 | + | 1.05232i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 6.07391i | − | 1.19119i | ||||||
\(27\) | −1.35077 | − | 5.01751i | −0.259956 | − | 0.965620i | ||||
\(28\) | −0.672980 | − | 0.672980i | −0.127181 | − | 0.127181i | ||||
\(29\) | 1.13909 | 0.211524 | 0.105762 | − | 0.994391i | \(-0.466272\pi\) | ||||
0.105762 | + | 0.994391i | \(0.466272\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.62492 | 0.651055 | 0.325528 | − | 0.945532i | \(-0.394458\pi\) | ||||
0.325528 | + | 0.945532i | \(0.394458\pi\) | |||||||
\(32\) | 3.41189 | + | 3.41189i | 0.603142 | + | 0.603142i | ||||
\(33\) | −3.61489 | − | 5.15829i | −0.629272 | − | 0.897943i | ||||
\(34\) | 6.67933i | 1.14550i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.68379 | − | 0.974434i | −0.447298 | − | 0.162406i | ||||
\(37\) | −7.24824 | + | 7.24824i | −1.19160 | + | 1.19160i | −0.214987 | + | 0.976617i | \(0.568971\pi\) |
−0.976617 | + | 0.214987i | \(0.931029\pi\) | |||||||
\(38\) | −2.73054 | + | 2.73054i | −0.442951 | + | 0.442951i | ||||
\(39\) | 10.1199 | + | 1.78031i | 1.62048 | + | 0.285078i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.314852i | 0.0491716i | 0.999698 | + | 0.0245858i | \(0.00782669\pi\) | ||||
−0.999698 | + | 0.0245858i | \(0.992173\pi\) | |||||||
\(42\) | −1.45225 | + | 1.01772i | −0.224087 | + | 0.157038i | ||||
\(43\) | 1.06556 | + | 1.06556i | 0.162497 | + | 0.162497i | 0.783672 | − | 0.621175i | \(-0.213344\pi\) |
−0.621175 | + | 0.783672i | \(0.713344\pi\) | |||||||
\(44\) | −3.46112 | −0.521784 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.63362 | 0.388306 | ||||||||
\(47\) | 4.48582 | + | 4.48582i | 0.654324 | + | 0.654324i | 0.954031 | − | 0.299707i | \(-0.0968889\pi\) |
−0.299707 | + | 0.954031i | \(0.596889\pi\) | |||||||
\(48\) | 1.68894 | − | 1.18360i | 0.243778 | − | 0.170838i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.1286 | − | 1.95777i | −1.55831 | − | 0.274142i | ||||
\(52\) | 3.99242 | − | 3.99242i | 0.553648 | − | 0.553648i | ||||
\(53\) | 1.44794 | − | 1.44794i | 0.198890 | − | 0.198890i | −0.600634 | − | 0.799524i | \(-0.705085\pi\) |
0.799524 | + | 0.600634i | \(0.205085\pi\) | |||||||
\(54\) | −2.65460 | + | 4.61044i | −0.361246 | + | 0.627401i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.02213i | 0.403849i | ||||||||
\(57\) | −3.74907 | − | 5.34975i | −0.496576 | − | 0.708592i | ||||
\(58\) | −0.824666 | − | 0.824666i | −0.108284 | − | 0.108284i | ||||
\(59\) | −8.70646 | −1.13348 | −0.566742 | − | 0.823895i | \(-0.691796\pi\) | ||||
−0.566742 | + | 0.823895i | \(0.691796\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.08903 | 0.395509 | 0.197755 | − | 0.980252i | \(-0.436635\pi\) | ||||
0.197755 | + | 0.980252i | \(0.436635\pi\) | |||||||
\(62\) | −2.62433 | − | 2.62433i | −0.333291 | − | 0.333291i | ||||
\(63\) | −1.26999 | − | 2.71793i | −0.160004 | − | 0.342427i | ||||
\(64\) | − | 7.32164i | − | 0.915205i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.11737 | + | 6.35151i | −0.137539 | + | 0.781817i | ||||
\(67\) | 9.67044 | − | 9.67044i | 1.18143 | − | 1.18143i | 0.202060 | − | 0.979373i | \(-0.435237\pi\) |
0.979373 | − | 0.202060i | \(-0.0647635\pi\) | |||||||
\(68\) | −4.39036 | + | 4.39036i | −0.532410 | + | 0.532410i | ||||
\(69\) | −0.771934 | + | 4.38793i | −0.0929300 | + | 0.528245i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.4601i | 1.24138i | 0.784056 | + | 0.620690i | \(0.213147\pi\) | ||||
−0.784056 | + | 0.620690i | \(0.786853\pi\) | |||||||
\(72\) | 3.83807 | + | 8.21392i | 0.452321 | + | 0.968020i | ||||
\(73\) | −0.710104 | − | 0.710104i | −0.0831114 | − | 0.0831114i | 0.664329 | − | 0.747440i | \(-0.268717\pi\) |
−0.747440 | + | 0.664329i | \(0.768717\pi\) | |||||||
\(74\) | 10.4950 | 1.22002 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.58959 | −0.411755 | ||||||||
\(77\) | −2.57149 | − | 2.57149i | −0.293048 | − | 0.293048i | ||||
\(78\) | −6.03759 | − | 8.61538i | −0.683623 | − | 0.975499i | ||||
\(79\) | − | 7.30426i | − | 0.821793i | −0.911682 | − | 0.410897i | \(-0.865216\pi\) | ||
0.911682 | − | 0.410897i | \(-0.134784\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.90348 | − | 5.77426i | −0.767053 | − | 0.641584i | ||||
\(82\) | 0.227943 | − | 0.227943i | 0.0251721 | − | 0.0251721i | ||||
\(83\) | 9.58225 | − | 9.58225i | 1.05179 | − | 1.05179i | 0.0532053 | − | 0.998584i | \(-0.483056\pi\) |
0.998584 | − | 0.0532053i | \(-0.0169438\pi\) | |||||||
\(84\) | −1.62353 | − | 0.285614i | −0.177141 | − | 0.0311631i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 1.54287i | − | 0.166372i | ||||||
\(87\) | 1.61571 | − | 1.13228i | 0.173223 | − | 0.121393i | ||||
\(88\) | 7.77137 | + | 7.77137i | 0.828431 | + | 0.828431i | ||||
\(89\) | 15.5299 | 1.64616 | 0.823082 | − | 0.567923i | \(-0.192253\pi\) | ||||
0.823082 | + | 0.567923i | \(0.192253\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.93244 | 0.621889 | ||||||||
\(92\) | 1.73109 | + | 1.73109i | 0.180479 | + | 0.180479i | ||||
\(93\) | 5.14167 | − | 3.60325i | 0.533167 | − | 0.373639i | ||||
\(94\) | − | 6.49519i | − | 0.669928i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.23099 | + | 1.44801i | 0.840072 | + | 0.147787i | ||||
\(97\) | −5.28841 | + | 5.28841i | −0.536957 | + | 0.536957i | −0.922634 | − | 0.385677i | \(-0.873968\pi\) |
0.385677 | + | 0.922634i | \(0.373968\pi\) | |||||||
\(98\) | −0.723969 | + | 0.723969i | −0.0731319 | + | 0.0731319i | ||||
\(99\) | −10.2549 | − | 3.72336i | −1.03065 | − | 0.374212i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.52857i | 0.550114i | 0.961428 | + | 0.275057i | \(0.0886966\pi\) | ||||
−0.961428 | + | 0.275057i | \(0.911303\pi\) | |||||||
\(102\) | 6.63939 | + | 9.47412i | 0.657398 | + | 0.938078i | ||||
\(103\) | 1.67893 | + | 1.67893i | 0.165430 | + | 0.165430i | 0.784967 | − | 0.619538i | \(-0.212680\pi\) |
−0.619538 | + | 0.784967i | \(0.712680\pi\) | |||||||
\(104\) | −17.9286 | −1.75804 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.09652 | −0.203632 | ||||||||
\(107\) | 6.33012 | + | 6.33012i | 0.611956 | + | 0.611956i | 0.943455 | − | 0.331500i | \(-0.107555\pi\) |
−0.331500 | + | 0.943455i | \(0.607555\pi\) | |||||||
\(108\) | −4.77535 | + | 1.28558i | −0.459509 | + | 0.123705i | ||||
\(109\) | 6.19191i | 0.593078i | 0.955021 | + | 0.296539i | \(0.0958324\pi\) | ||||
−0.955021 | + | 0.296539i | \(0.904168\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.07617 | + | 17.4860i | −0.291977 | + | 1.65970i | ||||
\(112\) | 0.841966 | − | 0.841966i | 0.0795583 | − | 0.0795583i | ||||
\(113\) | 1.87617 | − | 1.87617i | 0.176495 | − | 0.176495i | −0.613331 | − | 0.789826i | \(-0.710171\pi\) |
0.789826 | + | 0.613331i | \(0.210171\pi\) | |||||||
\(114\) | −1.15885 | + | 6.58726i | −0.108536 | + | 0.616954i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 1.08412i | − | 0.100658i | ||||||
\(117\) | 16.1239 | − | 7.53414i | 1.49066 | − | 0.696531i | ||||
\(118\) | 6.30320 | + | 6.30320i | 0.580257 | + | 0.580257i | ||||
\(119\) | −6.52376 | −0.598032 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.22512 | −0.202284 | ||||||||
\(122\) | −2.23636 | − | 2.23636i | −0.202470 | − | 0.202470i | ||||
\(123\) | 0.312969 | + | 0.446593i | 0.0282195 | + | 0.0402680i | ||||
\(124\) | − | 3.44998i | − | 0.309817i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.04826 | + | 2.88713i | −0.0933866 | + | 0.257206i | ||||
\(127\) | −3.43180 | + | 3.43180i | −0.304523 | + | 0.304523i | −0.842781 | − | 0.538257i | \(-0.819083\pi\) |
0.538257 | + | 0.842781i | \(0.319083\pi\) | |||||||
\(128\) | 1.52313 | − | 1.52313i | 0.134627 | − | 0.134627i | ||||
\(129\) | 2.57061 | + | 0.452227i | 0.226329 | + | 0.0398164i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.84637i | 0.336059i | 0.985782 | + | 0.168029i | \(0.0537403\pi\) | ||||
−0.985782 | + | 0.168029i | \(0.946260\pi\) | |||||||
\(132\) | −4.90934 | + | 3.44043i | −0.427303 | + | 0.299451i | ||||
\(133\) | −2.66694 | − | 2.66694i | −0.231253 | − | 0.231253i | ||||
\(134\) | −14.0022 | −1.20961 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 19.7156 | 1.69060 | ||||||||
\(137\) | 13.6056 | + | 13.6056i | 1.16241 | + | 1.16241i | 0.983947 | + | 0.178459i | \(0.0571111\pi\) |
0.178459 | + | 0.983947i | \(0.442889\pi\) | |||||||
\(138\) | 3.73558 | − | 2.61787i | 0.317994 | − | 0.222848i | ||||
\(139\) | − | 9.05369i | − | 0.767924i | −0.923349 | − | 0.383962i | \(-0.874559\pi\) | ||
0.923349 | − | 0.383962i | \(-0.125441\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.8218 | + | 1.90379i | 0.911359 | + | 0.160328i | ||||
\(142\) | 7.57276 | − | 7.57276i | 0.635492 | − | 0.635492i | ||||
\(143\) | 15.2552 | − | 15.2552i | 1.27571 | − | 1.27571i | ||||
\(144\) | 1.21911 | − | 3.35769i | 0.101593 | − | 0.279808i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.02819i | 0.0850934i | ||||||||
\(147\) | −0.994020 | − | 1.41842i | −0.0819854 | − | 0.116990i | ||||
\(148\) | 6.89843 | + | 6.89843i | 0.567047 | + | 0.567047i | ||||
\(149\) | 20.5997 | 1.68759 | 0.843796 | − | 0.536663i | \(-0.180315\pi\) | ||||
0.843796 | + | 0.536663i | \(0.180315\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.9282 | 1.29622 | 0.648109 | − | 0.761547i | \(-0.275560\pi\) | ||||
0.648109 | + | 0.761547i | \(0.275560\pi\) | |||||||
\(152\) | 8.05983 | + | 8.05983i | 0.653738 | + | 0.653738i | ||||
\(153\) | −17.7311 | + | 8.28511i | −1.43348 | + | 0.669811i | ||||
\(154\) | 3.72336i | 0.300037i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.69439 | − | 9.63148i | 0.135660 | − | 0.771135i | ||||
\(157\) | −4.00609 | + | 4.00609i | −0.319721 | + | 0.319721i | −0.848660 | − | 0.528939i | \(-0.822590\pi\) |
0.528939 | + | 0.848660i | \(0.322590\pi\) | |||||||
\(158\) | −5.28806 | + | 5.28806i | −0.420695 | + | 0.420695i | ||||
\(159\) | 0.614508 | − | 3.49307i | 0.0487337 | − | 0.277018i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.57228i | 0.202724i | ||||||||
\(162\) | 0.817520 | + | 9.17828i | 0.0642304 | + | 0.721114i | ||||
\(163\) | 5.18238 | + | 5.18238i | 0.405915 | + | 0.405915i | 0.880311 | − | 0.474396i | \(-0.157334\pi\) |
−0.474396 | + | 0.880311i | \(0.657334\pi\) | |||||||
\(164\) | 0.299656 | 0.0233992 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.8745 | −1.07687 | ||||||||
\(167\) | −7.76731 | − | 7.76731i | −0.601053 | − | 0.601053i | 0.339539 | − | 0.940592i | \(-0.389729\pi\) |
−0.940592 | + | 0.339539i | \(0.889729\pi\) | |||||||
\(168\) | 3.00406 | + | 4.28665i | 0.231768 | + | 0.330723i | ||||
\(169\) | 22.1939i | 1.70722i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.6355 | − | 3.86156i | −0.813319 | − | 0.295301i | ||||
\(172\) | 1.01414 | − | 1.01414i | 0.0773271 | − | 0.0773271i | ||||
\(173\) | 0.953760 | − | 0.953760i | 0.0725131 | − | 0.0725131i | −0.669920 | − | 0.742433i | \(-0.733672\pi\) |
0.742433 | + | 0.669920i | \(0.233672\pi\) | |||||||
\(174\) | −1.98946 | − | 0.349990i | −0.150821 | − | 0.0265327i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 4.33021i | − | 0.326402i | ||||||
\(177\) | −12.3494 | + | 8.65440i | −0.928241 | + | 0.650504i | ||||
\(178\) | −11.2431 | − | 11.2431i | −0.842710 | − | 0.842710i | ||||
\(179\) | 19.1906 | 1.43437 | 0.717187 | − | 0.696881i | \(-0.245429\pi\) | ||||
0.717187 | + | 0.696881i | \(0.245429\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.81119 | 0.506272 | 0.253136 | − | 0.967431i | \(-0.418538\pi\) | ||||
0.253136 | + | 0.967431i | \(0.418538\pi\) | |||||||
\(182\) | −4.29490 | − | 4.29490i | −0.318359 | − | 0.318359i | ||||
\(183\) | 4.38154 | − | 3.07055i | 0.323893 | − | 0.226982i | ||||
\(184\) | − | 7.77374i | − | 0.573088i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.33105 | − | 1.11377i | −0.464215 | − | 0.0816658i | ||||
\(187\) | −16.7758 | + | 16.7758i | −1.22677 | + | 1.22677i | ||||
\(188\) | 4.26933 | − | 4.26933i | 0.311373 | − | 0.311373i | ||||
\(189\) | −4.50306 | − | 2.59277i | −0.327549 | − | 0.188597i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.6052i | 1.78037i | 0.455602 | + | 0.890183i | \(0.349424\pi\) | ||||
−0.455602 | + | 0.890183i | \(0.650576\pi\) | |||||||
\(192\) | −7.27786 | − | 10.3852i | −0.525235 | − | 0.749486i | ||||
\(193\) | −16.1551 | − | 16.1551i | −1.16287 | − | 1.16287i | −0.983844 | − | 0.179026i | \(-0.942705\pi\) |
−0.179026 | − | 0.983844i | \(-0.557295\pi\) | |||||||
\(194\) | 7.65729 | 0.549762 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.951738 | −0.0679813 | ||||||||
\(197\) | −17.2478 | − | 17.2478i | −1.22886 | − | 1.22886i | −0.964397 | − | 0.264459i | \(-0.914807\pi\) |
−0.264459 | − | 0.964397i | \(-0.585193\pi\) | |||||||
\(198\) | 4.72862 | + | 10.1198i | 0.336049 | + | 0.719184i | ||||
\(199\) | 17.1682i | 1.21702i | 0.793547 | + | 0.608509i | \(0.208232\pi\) | ||||
−0.793547 | + | 0.608509i | \(0.791768\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.10416 | − | 23.3294i | 0.289485 | − | 1.64553i | ||||
\(202\) | 4.00252 | − | 4.00252i | 0.281616 | − | 0.281616i | ||||
\(203\) | 0.805459 | − | 0.805459i | 0.0565321 | − | 0.0565321i | ||||
\(204\) | −1.86328 | + | 10.5915i | −0.130456 | + | 0.741554i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 2.43098i | − | 0.169374i | ||||||
\(207\) | 3.26676 | + | 6.99126i | 0.227056 | + | 0.485926i | ||||
\(208\) | 4.99492 | + | 4.99492i | 0.346335 | + | 0.346335i | ||||
\(209\) | −13.7160 | −0.948756 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.4888 | −0.859766 | −0.429883 | − | 0.902884i | \(-0.641445\pi\) | ||||
−0.429883 | + | 0.902884i | \(0.641445\pi\) | |||||||
\(212\) | −1.37806 | − | 1.37806i | −0.0946454 | − | 0.0946454i | ||||
\(213\) | 10.3975 | + | 14.8368i | 0.712426 | + | 1.01660i | ||||
\(214\) | − | 9.16562i | − | 0.626549i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 13.6088 | + | 7.83570i | 0.925962 | + | 0.533152i | ||||
\(217\) | 2.56321 | − | 2.56321i | 0.174002 | − | 0.174002i | ||||
\(218\) | 4.48275 | − | 4.48275i | 0.303610 | − | 0.303610i | ||||
\(219\) | −1.71309 | − | 0.301370i | −0.115760 | − | 0.0203647i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 38.7018i | − | 2.60337i | ||||||
\(222\) | 14.8864 | − | 10.4323i | 0.999107 | − | 0.700167i | ||||
\(223\) | −14.6702 | − | 14.6702i | −0.982386 | − | 0.982386i | 0.0174612 | − | 0.999848i | \(-0.494442\pi\) |
−0.999848 | + | 0.0174612i | \(0.994442\pi\) | |||||||
\(224\) | 4.82514 | 0.322393 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.71657 | −0.180704 | ||||||||
\(227\) | 1.58995 | + | 1.58995i | 0.105528 | + | 0.105528i | 0.757900 | − | 0.652371i | \(-0.226226\pi\) |
−0.652371 | + | 0.757900i | \(0.726226\pi\) | |||||||
\(228\) | −5.09156 | + | 3.56813i | −0.337197 | + | 0.236305i | ||||
\(229\) | 1.35671i | 0.0896541i | 0.998995 | + | 0.0448270i | \(0.0142737\pi\) | ||||
−0.998995 | + | 0.0448270i | \(0.985726\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.20357 | − | 1.09135i | −0.408165 | − | 0.0718053i | ||||
\(232\) | −2.43420 | + | 2.43420i | −0.159813 | + | 0.159813i | ||||
\(233\) | −15.1279 | + | 15.1279i | −0.991061 | + | 0.991061i | −0.999960 | − | 0.00889977i | \(-0.997167\pi\) |
0.00889977 | + | 0.999960i | \(0.497167\pi\) | |||||||
\(234\) | −17.1277 | − | 6.21876i | −1.11967 | − | 0.406533i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.28626i | 0.539390i | ||||||||
\(237\) | −7.26058 | − | 10.3605i | −0.471625 | − | 0.672989i | ||||
\(238\) | 4.72300 | + | 4.72300i | 0.306147 | + | 0.306147i | ||||
\(239\) | 12.4988 | 0.808483 | 0.404242 | − | 0.914652i | \(-0.367535\pi\) | ||||
0.404242 | + | 0.914652i | \(0.367535\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.0373 | −1.16188 | −0.580942 | − | 0.813945i | \(-0.697316\pi\) | ||||
−0.580942 | + | 0.813945i | \(0.697316\pi\) | |||||||
\(242\) | 1.61092 | + | 1.61092i | 0.103554 | + | 0.103554i | ||||
\(243\) | −15.5318 | − | 1.32814i | −0.996364 | − | 0.0852003i | ||||
\(244\) | − | 2.93994i | − | 0.188210i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.0967396 | − | 0.549900i | 0.00616789 | − | 0.0350603i | ||||
\(247\) | 15.8215 | − | 15.8215i | 1.00670 | − | 1.00670i | ||||
\(248\) | −7.74634 | + | 7.74634i | −0.491893 | + | 0.491893i | ||||
\(249\) | 4.06673 | − | 23.1166i | 0.257719 | − | 1.46496i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 5.34538i | − | 0.337398i | −0.985668 | − | 0.168699i | \(-0.946043\pi\) | ||
0.985668 | − | 0.168699i | \(-0.0539565\pi\) | |||||||
\(252\) | −2.58675 | + | 1.20870i | −0.162950 | + | 0.0761407i | ||||
\(253\) | 6.61458 | + | 6.61458i | 0.415855 | + | 0.415855i | ||||
\(254\) | 4.96904 | 0.311785 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.8487 | −1.05304 | ||||||||
\(257\) | −11.6091 | − | 11.6091i | −0.724155 | − | 0.724155i | 0.245294 | − | 0.969449i | \(-0.421115\pi\) |
−0.969449 | + | 0.245294i | \(0.921115\pi\) | |||||||
\(258\) | −1.53364 | − | 2.18844i | −0.0954803 | − | 0.136246i | ||||
\(259\) | 10.2506i | 0.636939i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.16625 | − | 3.21210i | 0.0721893 | − | 0.198824i | ||||
\(262\) | 2.78465 | − | 2.78465i | 0.172036 | − | 0.172036i | ||||
\(263\) | 3.90300 | − | 3.90300i | 0.240669 | − | 0.240669i | −0.576458 | − | 0.817127i | \(-0.695565\pi\) |
0.817127 | + | 0.576458i | \(0.195565\pi\) | |||||||
\(264\) | 18.7480 | + | 3.29819i | 1.15386 | + | 0.202989i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.86156i | 0.236768i | ||||||||
\(267\) | 22.0279 | − | 15.4370i | 1.34809 | − | 0.944730i | ||||
\(268\) | −9.20373 | − | 9.20373i | −0.562207 | − | 0.562207i | ||||
\(269\) | −31.1948 | −1.90198 | −0.950989 | − | 0.309225i | \(-0.899930\pi\) | ||||
−0.950989 | + | 0.309225i | \(0.899930\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.4757 | −1.18306 | −0.591532 | − | 0.806282i | \(-0.701477\pi\) | ||||
−0.591532 | + | 0.806282i | \(0.701477\pi\) | |||||||
\(272\) | −5.49279 | − | 5.49279i | −0.333049 | − | 0.333049i | ||||
\(273\) | 8.41471 | − | 5.89697i | 0.509282 | − | 0.356901i | ||||
\(274\) | − | 19.7001i | − | 1.19013i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.17616 | + | 0.734679i | 0.251375 | + | 0.0442225i | ||||
\(277\) | −1.91736 | + | 1.91736i | −0.115203 | + | 0.115203i | −0.762358 | − | 0.647155i | \(-0.775959\pi\) |
0.647155 | + | 0.762358i | \(0.275959\pi\) | |||||||
\(278\) | −6.55459 | + | 6.55459i | −0.393118 | + | 0.393118i | ||||
\(279\) | 3.71137 | − | 10.2219i | 0.222194 | − | 0.611967i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 0.320414i | − | 0.0191143i | −0.999954 | − | 0.00955715i | \(-0.996958\pi\) | ||
0.999954 | − | 0.00955715i | \(-0.00304218\pi\) | |||||||
\(282\) | −6.45635 | − | 9.21293i | −0.384470 | − | 0.548622i | ||||
\(283\) | −1.20675 | − | 1.20675i | −0.0717340 | − | 0.0717340i | 0.670330 | − | 0.742064i | \(-0.266153\pi\) |
−0.742064 | + | 0.670330i | \(0.766153\pi\) | |||||||
\(284\) | 9.95523 | 0.590734 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −22.0886 | −1.30613 | ||||||||
\(287\) | 0.222634 | + | 0.222634i | 0.0131417 | + | 0.0131417i | ||||
\(288\) | 13.1144 | − | 6.12787i | 0.772772 | − | 0.361088i | ||||
\(289\) | 25.5595i | 1.50350i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.24441 | + | 12.7580i | −0.131570 | + | 0.747887i | ||||
\(292\) | −0.675833 | + | 0.675833i | −0.0395501 | + | 0.0395501i | ||||
\(293\) | −11.2016 | + | 11.2016i | −0.654402 | + | 0.654402i | −0.954050 | − | 0.299648i | \(-0.903131\pi\) |
0.299648 | + | 0.954050i | \(0.403131\pi\) | |||||||
\(294\) | −0.307254 | + | 1.74653i | −0.0179194 | + | 0.101860i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 30.9785i | − | 1.80059i | ||||||
\(297\) | −18.2469 | + | 4.91227i | −1.05879 | + | 0.285039i | ||||
\(298\) | −14.9135 | − | 14.9135i | −0.863918 | − | 0.863918i | ||||
\(299\) | −15.2599 | −0.882502 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.50693 | 0.0868581 | ||||||||
\(302\) | −11.5315 | − | 11.5315i | −0.663565 | − | 0.663565i | ||||
\(303\) | 5.49551 | + | 7.84185i | 0.315709 | + | 0.450503i | ||||
\(304\) | − | 4.49094i | − | 0.257573i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 18.8349 | + | 6.83862i | 1.07672 | + | 0.390938i | ||||
\(307\) | −16.0589 | + | 16.0589i | −0.916529 | + | 0.916529i | −0.996775 | − | 0.0802463i | \(-0.974429\pi\) |
0.0802463 | + | 0.996775i | \(0.474429\pi\) | |||||||
\(308\) | −2.44738 | + | 2.44738i | −0.139453 | + | 0.139453i | ||||
\(309\) | 4.05031 | + | 0.712540i | 0.230414 | + | 0.0405350i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.709997i | 0.0402602i | 0.999797 | + | 0.0201301i | \(0.00640805\pi\) | ||||
−0.999797 | + | 0.0201301i | \(0.993592\pi\) | |||||||
\(312\) | −25.4303 | + | 17.8214i | −1.43971 | + | 1.00894i | ||||
\(313\) | 14.9431 | + | 14.9431i | 0.844632 | + | 0.844632i | 0.989457 | − | 0.144826i | \(-0.0462621\pi\) |
−0.144826 | + | 0.989457i | \(0.546262\pi\) | |||||||
\(314\) | 5.80057 | 0.327345 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.95174 | −0.391066 | ||||||||
\(317\) | −3.83925 | − | 3.83925i | −0.215634 | − | 0.215634i | 0.591022 | − | 0.806656i | \(-0.298725\pi\) |
−0.806656 | + | 0.591022i | \(0.798725\pi\) | |||||||
\(318\) | −2.97376 | + | 2.08399i | −0.166760 | + | 0.116864i | ||||
\(319\) | − | 4.14246i | − | 0.231933i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.2711 | + | 2.68652i | 0.852347 | + | 0.149947i | ||||
\(322\) | 1.86225 | − | 1.86225i | 0.103779 | − | 0.103779i | ||||
\(323\) | −17.3985 | + | 17.3985i | −0.968077 | + | 0.968077i | ||||
\(324\) | −5.49558 | + | 6.57030i | −0.305310 | + | 0.365017i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 7.50376i | − | 0.415595i | ||||||
\(327\) | 6.15489 | + | 8.78275i | 0.340366 | + | 0.485687i | ||||
\(328\) | −0.672828 | − | 0.672828i | −0.0371507 | − | 0.0371507i | ||||
\(329\) | 6.34391 | 0.349751 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.8078 | 1.74831 | 0.874157 | − | 0.485644i | \(-0.161415\pi\) | ||||
0.874157 | + | 0.485644i | \(0.161415\pi\) | |||||||
\(332\) | −9.11979 | − | 9.11979i | −0.500514 | − | 0.500514i | ||||
\(333\) | 13.0181 | + | 27.8603i | 0.713388 | + | 1.52673i | ||||
\(334\) | 11.2466i | 0.615386i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.357333 | − | 2.03120i | 0.0194941 | − | 0.110811i | ||||
\(337\) | 12.8338 | − | 12.8338i | 0.699104 | − | 0.699104i | −0.265113 | − | 0.964217i | \(-0.585409\pi\) |
0.964217 | + | 0.265113i | \(0.0854093\pi\) | |||||||
\(338\) | 16.0677 | − | 16.0677i | 0.873966 | − | 0.873966i | ||||
\(339\) | 0.796250 | − | 4.52615i | 0.0432464 | − | 0.245827i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 13.1825i | − | 0.713874i | ||||||
\(342\) | 4.90414 | + | 10.4954i | 0.265186 | + | 0.567529i | ||||
\(343\) | −0.707107 | − | 0.707107i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | −4.55414 | −0.245543 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.38099 | −0.0742423 | ||||||||
\(347\) | 17.4728 | + | 17.4728i | 0.937989 | + | 0.937989i | 0.998187 | − | 0.0601971i | \(-0.0191729\pi\) |
−0.0601971 | + | 0.998187i | \(0.519173\pi\) | |||||||
\(348\) | −1.07763 | − | 1.53773i | −0.0577672 | − | 0.0824312i | ||||
\(349\) | 2.27784i | 0.121930i | 0.998140 | + | 0.0609649i | \(0.0194178\pi\) | ||||
−0.998140 | + | 0.0609649i | \(0.980582\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 15.3815 | − | 26.7141i | 0.821003 | − | 1.42589i | ||||
\(352\) | 12.4078 | − | 12.4078i | 0.661338 | − | 0.661338i | ||||
\(353\) | −0.992444 | + | 0.992444i | −0.0528225 | + | 0.0528225i | −0.733025 | − | 0.680202i | \(-0.761892\pi\) |
0.680202 | + | 0.733025i | \(0.261892\pi\) | |||||||
\(354\) | 15.2061 | + | 2.67510i | 0.808196 | + | 0.142180i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 14.7804i | − | 0.783358i | ||||||
\(357\) | −9.25346 | + | 6.48475i | −0.489745 | + | 0.343210i | ||||
\(358\) | −13.8934 | − | 13.8934i | −0.734289 | − | 0.734289i | ||||
\(359\) | −4.68580 | −0.247307 | −0.123654 | − | 0.992325i | \(-0.539461\pi\) | ||||
−0.123654 | + | 0.992325i | \(0.539461\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.77488 | 0.251310 | ||||||||
\(362\) | −4.93109 | − | 4.93109i | −0.259172 | − | 0.259172i | ||||
\(363\) | −3.15616 | + | 2.21181i | −0.165655 | + | 0.116090i | ||||
\(364\) | − | 5.64613i | − | 0.295938i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.39509 | − | 0.949116i | −0.282006 | − | 0.0496111i | ||||
\(367\) | −8.68225 | + | 8.68225i | −0.453210 | + | 0.453210i | −0.896418 | − | 0.443209i | \(-0.853840\pi\) |
0.443209 | + | 0.896418i | \(0.353840\pi\) | |||||||
\(368\) | −2.16577 | + | 2.16577i | −0.112899 | + | 0.112899i | ||||
\(369\) | 0.887846 | + | 0.322360i | 0.0462194 | + | 0.0167814i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 2.04769i | − | 0.106311i | ||||||
\(372\) | −3.42935 | − | 4.89353i | −0.177803 | − | 0.253717i | ||||
\(373\) | −14.4089 | − | 14.4089i | −0.746062 | − | 0.746062i | 0.227675 | − | 0.973737i | \(-0.426888\pi\) |
−0.973737 | + | 0.227675i | \(0.926888\pi\) | |||||||
\(374\) | 24.2903 | 1.25602 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −19.1721 | −0.988726 | ||||||||
\(377\) | 4.77834 | + | 4.77834i | 0.246097 | + | 0.246097i | ||||
\(378\) | 1.38298 | + | 5.13716i | 0.0711331 | + | 0.264227i | ||||
\(379\) | 14.3572i | 0.737482i | 0.929532 | + | 0.368741i | \(0.120211\pi\) | ||||
−0.929532 | + | 0.368741i | \(0.879789\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.45647 | + | 8.27903i | −0.0746170 | + | 0.424148i | ||||
\(382\) | 17.8134 | − | 17.8134i | 0.911411 | − | 0.911411i | ||||
\(383\) | 10.9175 | − | 10.9175i | 0.557860 | − | 0.557860i | −0.370838 | − | 0.928698i | \(-0.620929\pi\) |
0.928698 | + | 0.370838i | \(0.120929\pi\) | |||||||
\(384\) | 0.646422 | − | 3.67448i | 0.0329876 | − | 0.187512i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 23.3916i | 1.19060i | ||||||||
\(387\) | 4.09573 | − | 1.91379i | 0.208198 | − | 0.0972832i | ||||
\(388\) | 5.03318 | + | 5.03318i | 0.255521 | + | 0.255521i | ||||
\(389\) | −14.3250 | −0.726304 | −0.363152 | − | 0.931730i | \(-0.618299\pi\) | ||||
−0.363152 | + | 0.931730i | \(0.618299\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.7809 | 0.848648 | ||||||||
\(392\) | 2.13697 | + | 2.13697i | 0.107933 | + | 0.107933i | ||||
\(393\) | 3.82337 | + | 5.45577i | 0.192863 | + | 0.275207i | ||||
\(394\) | 24.9738i | 1.25816i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.54366 | + | 9.75996i | −0.178076 | + | 0.490456i | ||||
\(397\) | −21.0767 | + | 21.0767i | −1.05781 | + | 1.05781i | −0.0595859 | + | 0.998223i | \(0.518978\pi\) |
−0.998223 | + | 0.0595859i | \(0.981022\pi\) | |||||||
\(398\) | 12.4292 | − | 12.4292i | 0.623020 | − | 0.623020i | ||||
\(399\) | −6.43384 | − | 1.13186i | −0.322095 | − | 0.0566636i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.9494i | 0.546788i | 0.961902 | + | 0.273394i | \(0.0881463\pi\) | ||||
−0.961902 | + | 0.273394i | \(0.911854\pi\) | |||||||
\(402\) | −19.8610 | + | 13.9185i | −0.990579 | + | 0.694191i | ||||
\(403\) | 15.2061 | + | 15.2061i | 0.757469 | + | 0.757469i | ||||
\(404\) | 5.26175 | 0.261782 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.16625 | −0.0578802 | ||||||||
\(407\) | 26.3592 | + | 26.3592i | 1.30658 | + | 1.30658i | ||||
\(408\) | 27.9651 | − | 19.5978i | 1.38448 | − | 0.970233i | ||||
\(409\) | − | 19.4500i | − | 0.961739i | −0.876792 | − | 0.480870i | \(-0.840321\pi\) | ||
0.876792 | − | 0.480870i | \(-0.159679\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 32.8228 | + | 5.77426i | 1.61903 | + | 0.284823i | ||||
\(412\) | 1.59790 | − | 1.59790i | 0.0787227 | − | 0.0787227i | ||||
\(413\) | −6.15639 | + | 6.15639i | −0.302936 | + | 0.302936i | ||||
\(414\) | 2.69642 | − | 7.42649i | 0.132522 | − | 0.364992i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 28.6249i | 1.40345i | ||||||||
\(417\) | −8.99956 | − | 12.8420i | −0.440710 | − | 0.628874i | ||||
\(418\) | 9.92997 | + | 9.92997i | 0.485690 | + | 0.485690i | ||||
\(419\) | −25.9297 | −1.26675 | −0.633373 | − | 0.773846i | \(-0.718330\pi\) | ||||
−0.633373 | + | 0.773846i | \(0.718330\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.79961 | −0.282656 | −0.141328 | − | 0.989963i | \(-0.545137\pi\) | ||||
−0.141328 | + | 0.989963i | \(0.545137\pi\) | |||||||
\(422\) | 9.04153 | + | 9.04153i | 0.440135 | + | 0.440135i | ||||
\(423\) | 17.2423 | − | 8.05670i | 0.838349 | − | 0.391730i | ||||
\(424\) | 6.18839i | 0.300535i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.21390 | − | 18.2688i | 0.155714 | − | 0.885128i | ||||
\(427\) | 2.18427 | − | 2.18427i | 0.105704 | − | 0.105704i | ||||
\(428\) | 6.02461 | − | 6.02461i | 0.291211 | − | 0.291211i | ||||
\(429\) | 6.47435 | − | 36.8023i | 0.312585 | − | 1.77683i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.8759i | 0.716545i | 0.933617 | + | 0.358272i | \(0.116634\pi\) | ||||
−0.933617 | + | 0.358272i | \(0.883366\pi\) | |||||||
\(432\) | −1.60839 | − | 5.97445i | −0.0773838 | − | 0.287446i | ||||
\(433\) | −18.5862 | − | 18.5862i | −0.893198 | − | 0.893198i | 0.101625 | − | 0.994823i | \(-0.467596\pi\) |
−0.994823 | + | 0.101625i | \(0.967596\pi\) | |||||||
\(434\) | −3.71137 | −0.178151 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.89308 | 0.282227 | ||||||||
\(437\) | 6.86010 | + | 6.86010i | 0.328163 | + | 0.328163i | ||||
\(438\) | 1.02204 | + | 1.45840i | 0.0488349 | + | 0.0696852i | ||||
\(439\) | − | 15.6687i | − | 0.747828i | −0.927463 | − | 0.373914i | \(-0.878016\pi\) | ||
0.927463 | − | 0.373914i | \(-0.121984\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.81988 | − | 1.02385i | −0.134280 | − | 0.0487546i | ||||
\(442\) | −28.0189 | + | 28.0189i | −1.33273 | + | 1.33273i | ||||
\(443\) | −17.4278 | + | 17.4278i | −0.828021 | + | 0.828021i | −0.987243 | − | 0.159222i | \(-0.949102\pi\) |
0.159222 | + | 0.987243i | \(0.449102\pi\) | |||||||
\(444\) | 16.6421 | + | 2.92771i | 0.789797 | + | 0.138943i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 21.2415i | 1.00581i | ||||||||
\(447\) | 29.2191 | − | 20.4765i | 1.38202 | − | 0.968506i | ||||
\(448\) | −5.17718 | − | 5.17718i | −0.244599 | − | 0.244599i | ||||
\(449\) | −0.620804 | −0.0292975 | −0.0146488 | − | 0.999893i | \(-0.504663\pi\) | ||||
−0.0146488 | + | 0.999893i | \(0.504663\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.14500 | 0.0539160 | ||||||||
\(452\) | −1.78562 | − | 1.78562i | −0.0839885 | − | 0.0839885i | ||||
\(453\) | 22.5929 | − | 15.8330i | 1.06151 | − | 0.743897i | ||||
\(454\) | − | 2.30214i | − | 0.108045i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 19.4439 | + | 3.42061i | 0.910543 | + | 0.160185i | ||||
\(457\) | 9.10965 | − | 9.10965i | 0.426131 | − | 0.426131i | −0.461177 | − | 0.887308i | \(-0.652573\pi\) |
0.887308 | + | 0.461177i | \(0.152573\pi\) | |||||||
\(458\) | 0.982218 | − | 0.982218i | 0.0458960 | − | 0.0458960i | ||||
\(459\) | −16.9147 | + | 29.3769i | −0.789508 | + | 1.37120i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.78274i | 0.129605i | 0.997898 | + | 0.0648025i | \(0.0206418\pi\) | ||||
−0.997898 | + | 0.0648025i | \(0.979358\pi\) | |||||||
\(462\) | 3.70109 | + | 5.28130i | 0.172190 | + | 0.245708i | ||||
\(463\) | 10.4466 | + | 10.4466i | 0.485495 | + | 0.485495i | 0.906881 | − | 0.421386i | \(-0.138456\pi\) |
−0.421386 | + | 0.906881i | \(0.638456\pi\) | |||||||
\(464\) | 1.35634 | 0.0629664 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 21.9042 | 1.01469 | ||||||||
\(467\) | 15.9720 | + | 15.9720i | 0.739097 | + | 0.739097i | 0.972403 | − | 0.233306i | \(-0.0749544\pi\) |
−0.233306 | + | 0.972403i | \(0.574954\pi\) | |||||||
\(468\) | −7.17052 | − | 15.3458i | −0.331457 | − | 0.709358i | ||||
\(469\) | − | 13.6761i | − | 0.631502i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.70020 | + | 9.66447i | −0.0783409 | + | 0.445315i | ||||
\(472\) | 18.6054 | − | 18.6054i | 0.856383 | − | 0.856383i | ||||
\(473\) | 3.87506 | − | 3.87506i | 0.178175 | − | 0.178175i | ||||
\(474\) | −2.24426 | + | 12.7571i | −0.103082 | + | 0.585955i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.20891i | 0.284585i | ||||||||
\(477\) | −2.60055 | − | 5.56548i | −0.119071 | − | 0.254826i | ||||
\(478\) | −9.04878 | − | 9.04878i | −0.413882 | − | 0.413882i | ||||
\(479\) | 10.8945 | 0.497782 | 0.248891 | − | 0.968531i | \(-0.419934\pi\) | ||||
0.248891 | + | 0.968531i | \(0.419934\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −60.8109 | −2.77274 | ||||||||
\(482\) | 13.0584 | + | 13.0584i | 0.594796 | + | 0.594796i | ||||
\(483\) | 2.55689 | + | 3.64857i | 0.116343 | + | 0.166016i | ||||
\(484\) | 2.11773i | 0.0962604i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 10.2830 | + | 12.2061i | 0.466446 | + | 0.553678i | ||||
\(487\) | 5.03387 | − | 5.03387i | 0.228107 | − | 0.228107i | −0.583795 | − | 0.811901i | \(-0.698433\pi\) |
0.811901 | + | 0.583795i | \(0.198433\pi\) | |||||||
\(488\) | −6.60114 | + | 6.60114i | −0.298820 | + | 0.298820i | ||||
\(489\) | 12.5022 | + | 2.19941i | 0.565368 | + | 0.0994609i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.9196i | 0.537922i | 0.963151 | + | 0.268961i | \(0.0866803\pi\) | ||||
−0.963151 | + | 0.268961i | \(0.913320\pi\) | |||||||
\(492\) | 0.425040 | − | 0.297865i | 0.0191623 | − | 0.0134288i | ||||
\(493\) | −5.25462 | − | 5.25462i | −0.236656 | − | 0.236656i | ||||
\(494\) | −22.9085 | −1.03070 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.31627 | 0.193806 | ||||||||
\(497\) | 7.39638 | + | 7.39638i | 0.331773 | + | 0.331773i | ||||
\(498\) | −19.6799 | + | 13.7915i | −0.881878 | + | 0.618014i | ||||
\(499\) | − | 0.966794i | − | 0.0432797i | −0.999766 | − | 0.0216398i | \(-0.993111\pi\) | ||
0.999766 | − | 0.0216398i | \(-0.00688871\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.7382 | − | 3.29647i | −0.837161 | − | 0.147275i | ||||
\(502\) | −3.86989 | + | 3.86989i | −0.172722 | + | 0.172722i | ||||
\(503\) | 3.21397 | − | 3.21397i | 0.143304 | − | 0.143304i | −0.631815 | − | 0.775119i | \(-0.717690\pi\) |
0.775119 | + | 0.631815i | \(0.217690\pi\) | |||||||
\(504\) | 8.52204 | + | 3.09420i | 0.379602 | + | 0.137826i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 9.57750i | − | 0.425772i | ||||||
\(507\) | 22.0612 | + | 31.4803i | 0.979771 | + | 1.39809i | ||||
\(508\) | 3.26618 | + | 3.26618i | 0.144913 | + | 0.144913i | ||||
\(509\) | −24.1223 | −1.06920 | −0.534601 | − | 0.845104i | \(-0.679538\pi\) | ||||
−0.534601 | + | 0.845104i | \(0.679538\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.00424 | −0.0444249 | ||||||||
\(512\) | 9.15166 | + | 9.15166i | 0.404450 | + | 0.404450i | ||||
\(513\) | −18.9241 | + | 5.09460i | −0.835521 | + | 0.224932i | ||||
\(514\) | 16.8092i | 0.741423i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.430401 | − | 2.44654i | 0.0189474 | − | 0.107703i | ||||
\(517\) | 16.3133 | − | 16.3133i | 0.717458 | − | 0.717458i | ||||
\(518\) | 7.42109 | − | 7.42109i | 0.326064 | − | 0.326064i | ||||
\(519\) | 0.404778 | − | 2.30089i | 0.0177678 | − | 0.100998i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 43.5258i | − | 1.90690i | −0.301554 | − | 0.953449i | \(-0.597505\pi\) | ||
0.301554 | − | 0.953449i | \(-0.402495\pi\) | |||||||
\(522\) | −3.16979 | + | 1.48113i | −0.138738 | + | 0.0648273i | ||||
\(523\) | −7.55731 | − | 7.55731i | −0.330458 | − | 0.330458i | 0.522302 | − | 0.852760i | \(-0.325073\pi\) |
−0.852760 | + | 0.522302i | \(0.825073\pi\) | |||||||
\(524\) | 3.66073 | 0.159920 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.65130 | −0.246408 | ||||||||
\(527\) | −16.7218 | − | 16.7218i | −0.728411 | − | 0.728411i | ||||
\(528\) | −4.30432 | − | 6.14208i | −0.187322 | − | 0.267300i | ||||
\(529\) | 16.3834i | 0.712322i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.91408 | + | 24.5512i | −0.386838 | + | 1.06543i | ||||
\(532\) | −2.53823 | + | 2.53823i | −0.110046 | + | 0.110046i | ||||
\(533\) | −1.32076 | + | 1.32076i | −0.0572086 | + | 0.0572086i | ||||
\(534\) | −27.1235 | − | 4.77162i | −1.17375 | − | 0.206488i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 41.3308i | 1.78522i | ||||||||
\(537\) | 27.2204 | − | 19.0759i | 1.17465 | − | 0.823184i | ||||
\(538\) | 22.5840 | + | 22.5840i | 0.973667 | + | 0.973667i | ||||
\(539\) | −3.63664 | −0.156641 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.5120 | 0.924873 | 0.462436 | − | 0.886652i | \(-0.346975\pi\) | ||||
0.462436 | + | 0.886652i | \(0.346975\pi\) | |||||||
\(542\) | 14.0998 | + | 14.0998i | 0.605638 | + | 0.605638i | ||||
\(543\) | 9.66115 | − | 6.77046i | 0.414600 | − | 0.290548i | ||||
\(544\) | − | 31.4781i | − | 1.34961i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −10.3612 | − | 1.82277i | −0.443419 | − | 0.0780073i | ||||
\(547\) | −4.12772 | + | 4.12772i | −0.176489 | + | 0.176489i | −0.789823 | − | 0.613335i | \(-0.789828\pi\) |
0.613335 | + | 0.789823i | \(0.289828\pi\) | |||||||
\(548\) | 12.9490 | − | 12.9490i | 0.553153 | − | 0.553153i | ||||
\(549\) | 3.16269 | − | 8.71069i | 0.134980 | − | 0.371763i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 4.29622i | − | 0.183025i | ||||||
\(552\) | −7.72726 | − | 11.0265i | −0.328894 | − | 0.469317i | ||||
\(553\) | −5.16489 | − | 5.16489i | −0.219633 | − | 0.219633i | ||||
\(554\) | 2.77622 | 0.117950 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.61674 | −0.365431 | ||||||||
\(557\) | −30.3025 | − | 30.3025i | −1.28396 | − | 1.28396i | −0.938396 | − | 0.345560i | \(-0.887689\pi\) |
−0.345560 | − | 0.938396i | \(-0.612311\pi\) | |||||||
\(558\) | −10.0872 | + | 4.71339i | −0.427026 | + | 0.199534i | ||||
\(559\) | 8.93978i | 0.378113i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.11969 | + | 40.4706i | −0.300593 | + | 1.70867i | ||||
\(562\) | −0.231970 | + | 0.231970i | −0.00978505 | + | 0.00978505i | ||||
\(563\) | −8.67504 | + | 8.67504i | −0.365609 | + | 0.365609i | −0.865873 | − | 0.500264i | \(-0.833236\pi\) |
0.500264 | + | 0.865873i | \(0.333236\pi\) | |||||||
\(564\) | 1.81191 | − | 10.2995i | 0.0762953 | − | 0.433687i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.74730i | 0.0734447i | ||||||||
\(567\) | −8.96451 | + | 0.798479i | −0.376474 | + | 0.0335330i | ||||
\(568\) | −22.3528 | − | 22.3528i | −0.937902 | − | 0.937902i | ||||
\(569\) | −7.88148 | −0.330409 | −0.165205 | − | 0.986259i | \(-0.552828\pi\) | ||||
−0.165205 | + | 0.986259i | \(0.552828\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.5764 | −0.484459 | −0.242230 | − | 0.970219i | \(-0.577879\pi\) | ||||
−0.242230 | + | 0.970219i | \(0.577879\pi\) | |||||||
\(572\) | −14.5190 | − | 14.5190i | −0.607068 | − | 0.607068i | ||||
\(573\) | 24.4580 | + | 34.9005i | 1.02175 | + | 1.45799i | ||||
\(574\) | − | 0.322360i | − | 0.0134551i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −20.6462 | − | 7.49624i | −0.860257 | − | 0.312343i | ||||
\(577\) | 15.8784 | − | 15.8784i | 0.661027 | − | 0.661027i | −0.294595 | − | 0.955622i | \(-0.595185\pi\) |
0.955622 | + | 0.294595i | \(0.0951849\pi\) | |||||||
\(578\) | 18.5043 | − | 18.5043i | 0.769677 | − | 0.769677i | ||||
\(579\) | −38.9733 | − | 6.85627i | −1.61967 | − | 0.284937i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 13.5514i | − | 0.562205i | ||||||
\(582\) | 10.8613 | − | 7.61150i | 0.450214 | − | 0.315507i | ||||
\(583\) | −5.26562 | − | 5.26562i | −0.218080 | − | 0.218080i | ||||
\(584\) | 3.03494 | 0.125587 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.2192 | 0.670007 | ||||||||
\(587\) | 9.87937 | + | 9.87937i | 0.407765 | + | 0.407765i | 0.880959 | − | 0.473193i | \(-0.156899\pi\) |
−0.473193 | + | 0.880959i | \(0.656899\pi\) | |||||||
\(588\) | −1.34997 | + | 0.946047i | −0.0556717 | + | 0.0390143i | ||||
\(589\) | − | 13.6718i | − | 0.563338i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −41.6094 | − | 7.32001i | −1.71158 | − | 0.301105i | ||||
\(592\) | −8.63063 | + | 8.63063i | −0.354717 | + | 0.354717i | ||||
\(593\) | 0.614696 | − | 0.614696i | 0.0252426 | − | 0.0252426i | −0.694373 | − | 0.719615i | \(-0.744318\pi\) |
0.719615 | + | 0.694373i | \(0.244318\pi\) | |||||||
\(594\) | 16.7665 | + | 9.65383i | 0.687937 | + | 0.396101i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 19.6055i | − | 0.803073i | ||||||
\(597\) | 17.0655 | + | 24.3517i | 0.698445 | + | 0.996649i | ||||
\(598\) | 11.0477 | + | 11.0477i | 0.451773 | + | 0.451773i | ||||
\(599\) | −15.3650 | −0.627797 | −0.313898 | − | 0.949457i | \(-0.601635\pi\) | ||||
−0.313898 | + | 0.949457i | \(0.601635\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.6232 | −1.08598 | −0.542991 | − | 0.839738i | \(-0.682708\pi\) | ||||
−0.542991 | + | 0.839738i | \(0.682708\pi\) | |||||||
\(602\) | −1.09097 | − | 1.09097i | −0.0444647 | − | 0.0444647i | ||||
\(603\) | −17.3685 | − | 37.1706i | −0.707299 | − | 1.51370i | ||||
\(604\) | − | 15.1595i | − | 0.616830i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.69868 | − | 9.65584i | 0.0690040 | − | 0.392242i | ||||
\(607\) | −12.5800 | + | 12.5800i | −0.510606 | + | 0.510606i | −0.914712 | − | 0.404106i | \(-0.867583\pi\) |
0.404106 | + | 0.914712i | \(0.367583\pi\) | |||||||
\(608\) | 12.8683 | − | 12.8683i | 0.521880 | − | 0.521880i | ||||
\(609\) | 0.341839 | − | 1.94312i | 0.0138520 | − | 0.0787393i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 37.6349i | 1.52254i | ||||||||
\(612\) | 7.88525 | + | 16.8754i | 0.318742 | + | 0.682146i | ||||
\(613\) | −26.4562 | − | 26.4562i | −1.06856 | − | 1.06856i | −0.997470 | − | 0.0710867i | \(-0.977353\pi\) |
−0.0710867 | − | 0.997470i | \(-0.522647\pi\) | |||||||
\(614\) | 23.2523 | 0.938385 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.9904 | 0.442815 | ||||||||
\(617\) | −8.96074 | − | 8.96074i | −0.360746 | − | 0.360746i | 0.503342 | − | 0.864088i | \(-0.332104\pi\) |
−0.864088 | + | 0.503342i | \(0.832104\pi\) | |||||||
\(618\) | −2.41644 | − | 3.44816i | −0.0972037 | − | 0.138705i | ||||
\(619\) | 23.8205i | 0.957426i | 0.877971 | + | 0.478713i | \(0.158897\pi\) | ||||
−0.877971 | + | 0.478713i | \(0.841103\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.5831 | + | 6.66933i | 0.464814 | + | 0.267631i | ||||
\(622\) | 0.514016 | − | 0.514016i | 0.0206101 | − | 0.0206101i | ||||
\(623\) | 10.9813 | − | 10.9813i | 0.439956 | − | 0.439956i | ||||
\(624\) | 12.0500 | + | 2.11985i | 0.482384 | + | 0.0848621i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 21.6366i | − | 0.864773i | ||||||
\(627\) | −19.4551 | + | 13.6340i | −0.776962 | + | 0.544489i | ||||
\(628\) | 3.81275 | + | 3.81275i | 0.152145 | + | 0.152145i | ||||
\(629\) | 66.8723 | 2.66637 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.2819 | 0.807410 | 0.403705 | − | 0.914889i | \(-0.367722\pi\) | ||||
0.403705 | + | 0.914889i | \(0.367722\pi\) | |||||||
\(632\) | 15.6090 | + | 15.6090i | 0.620891 | + | 0.620891i | ||||
\(633\) | −17.7144 | + | 12.4142i | −0.704086 | + | 0.493418i | ||||
\(634\) | 5.55900i | 0.220776i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.32448 | − | 0.584851i | −0.131824 | − | 0.0231908i | ||||
\(637\) | 4.19487 | − | 4.19487i | 0.166207 | − | 0.166207i | ||||
\(638\) | −2.99901 | + | 2.99901i | −0.118732 | + | 0.118732i | ||||
\(639\) | 29.4961 | + | 10.7095i | 1.16685 | + | 0.423661i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.5041i | 1.08635i | 0.839620 | + | 0.543174i | \(0.182778\pi\) | ||||
−0.839620 | + | 0.543174i | \(0.817222\pi\) | |||||||
\(642\) | −9.11081 | − | 13.0007i | −0.359575 | − | 0.513098i | ||||
\(643\) | 17.2643 | + | 17.2643i | 0.680839 | + | 0.680839i | 0.960189 | − | 0.279350i | \(-0.0901190\pi\) |
−0.279350 | + | 0.960189i | \(0.590119\pi\) | |||||||
\(644\) | 2.44813 | 0.0964699 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 25.1919 | 0.991163 | ||||||||
\(647\) | 2.92523 | + | 2.92523i | 0.115003 | + | 0.115003i | 0.762266 | − | 0.647264i | \(-0.224087\pi\) |
−0.647264 | + | 0.762266i | \(0.724087\pi\) | |||||||
\(648\) | 27.0919 | − | 2.41310i | 1.06427 | − | 0.0947957i | ||||
\(649\) | 31.6622i | 1.24285i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.08783 | − | 6.18359i | 0.0426355 | − | 0.242354i | ||||
\(652\) | 4.93226 | − | 4.93226i | 0.193162 | − | 0.193162i | ||||
\(653\) | −25.2123 | + | 25.2123i | −0.986635 | + | 0.986635i | −0.999912 | − | 0.0132769i | \(-0.995774\pi\) |
0.0132769 | + | 0.999912i | \(0.495774\pi\) | |||||||
\(654\) | 1.90249 | − | 10.8144i | 0.0743933 | − | 0.422876i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.374901i | 0.0146374i | ||||||||
\(657\) | −2.72945 | + | 1.27537i | −0.106486 | + | 0.0497570i | ||||
\(658\) | −4.59280 | − | 4.59280i | −0.179046 | − | 0.179046i | ||||
\(659\) | 20.3603 | 0.793125 | 0.396563 | − | 0.918008i | \(-0.370203\pi\) | ||||
0.396563 | + | 0.918008i | \(0.370203\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.8508 | 0.694314 | 0.347157 | − | 0.937807i | \(-0.387147\pi\) | ||||
0.347157 | + | 0.937807i | \(0.387147\pi\) | |||||||
\(662\) | −23.0278 | − | 23.0278i | −0.895002 | − | 0.895002i | ||||
\(663\) | −38.4704 | − | 54.8956i | −1.49407 | − | 2.13197i | ||||
\(664\) | 40.9539i | 1.58932i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.7453 | − | 29.5947i | 0.416371 | − | 1.14677i | ||||
\(667\) | −2.07186 | + | 2.07186i | −0.0802228 | + | 0.0802228i | ||||
\(668\) | −7.39244 | + | 7.39244i | −0.286022 | + | 0.286022i | ||||
\(669\) | −35.3909 | − | 6.22605i | −1.36829 | − | 0.240713i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 11.2337i | − | 0.433671i | ||||||
\(672\) | 6.84409 | − | 4.79629i | 0.264016 | − | 0.185021i | ||||
\(673\) | 22.7637 | + | 22.7637i | 0.877476 | + | 0.877476i | 0.993273 | − | 0.115797i | \(-0.0369421\pi\) |
−0.115797 | + | 0.993273i | \(0.536942\pi\) | |||||||
\(674\) | −18.5826 | −0.715776 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 21.1227 | 0.812413 | ||||||||
\(677\) | 10.9347 | + | 10.9347i | 0.420256 | + | 0.420256i | 0.885292 | − | 0.465036i | \(-0.153959\pi\) |
−0.465036 | + | 0.885292i | \(0.653959\pi\) | |||||||
\(678\) | −3.85325 | + | 2.70033i | −0.147983 | + | 0.103706i | ||||
\(679\) | 7.47894i | 0.287015i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.83566 | + | 0.674777i | 0.146983 | + | 0.0258575i | ||||
\(682\) | −9.54374 | + | 9.54374i | −0.365449 | + | 0.365449i | ||||
\(683\) | −6.50227 | + | 6.50227i | −0.248802 | + | 0.248802i | −0.820479 | − | 0.571677i | \(-0.806293\pi\) |
0.571677 | + | 0.820479i | \(0.306293\pi\) | |||||||
\(684\) | −3.67519 | + | 10.1222i | −0.140525 | + | 0.387033i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.02385i | 0.0390907i | ||||||||
\(687\) | 1.34860 | + | 1.92439i | 0.0514523 | + | 0.0734201i | ||||
\(688\) | 1.26879 | + | 1.26879i | 0.0483720 | + | 0.0483720i | ||||
\(689\) | 12.1478 | 0.462795 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.4621 | 1.04471 | 0.522353 | − | 0.852729i | \(-0.325054\pi\) | ||||
0.522353 | + | 0.852729i | \(0.325054\pi\) | |||||||
\(692\) | −0.907730 | − | 0.907730i | −0.0345067 | − | 0.0345067i | ||||
\(693\) | −9.88411 | + | 4.61849i | −0.375466 | + | 0.175442i | ||||
\(694\) | − | 25.2995i | − | 0.960357i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.03308 | + | 5.87237i | −0.0391588 | + | 0.222591i | ||||
\(697\) | 1.45241 | − | 1.45241i | 0.0550140 | − | 0.0550140i | ||||
\(698\) | 1.64908 | − | 1.64908i | 0.0624187 | − | 0.0624187i | ||||
\(699\) | −6.42031 | + | 36.4952i | −0.242838 | + | 1.38037i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 22.1998i | − | 0.838473i | −0.907877 | − | 0.419237i | \(-0.862298\pi\) | ||
0.907877 | − | 0.419237i | \(-0.137702\pi\) | |||||||
\(702\) | −30.4759 | + | 8.20448i | −1.15024 | + | 0.309658i | ||||
\(703\) | 27.3376 | + | 27.3376i | 1.03106 | + | 1.03106i | ||||
\(704\) | −26.6262 | −1.00351 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.43700 | 0.0540821 | ||||||||
\(707\) | 3.90929 | + | 3.90929i | 0.147024 | + | 0.147024i | ||||
\(708\) | 8.23671 | + | 11.7534i | 0.309555 | + | 0.441721i | ||||
\(709\) | − | 29.2448i | − | 1.09831i | −0.835721 | − | 0.549155i | \(-0.814950\pi\) | ||
0.835721 | − | 0.549155i | \(-0.185050\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.5972 | − | 7.47844i | −0.772453 | − | 0.280463i | ||||
\(712\) | −33.1868 | + | 33.1868i | −1.24373 | + | 1.24373i | ||||
\(713\) | −6.59328 | + | 6.59328i | −0.246920 | + | 0.246920i | ||||
\(714\) | 11.3940 | + | 2.00445i | 0.426409 | + | 0.0750148i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 18.2644i | − | 0.682574i | ||||||
\(717\) | 17.7287 | − | 12.4241i | 0.662089 | − | 0.463987i | ||||
\(718\) | 3.39237 | + | 3.39237i | 0.126602 | + | 0.126602i | ||||
\(719\) | −20.4862 | −0.764006 | −0.382003 | − | 0.924161i | \(-0.624766\pi\) | ||||
−0.382003 | + | 0.924161i | \(0.624766\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.37436 | 0.0884258 | ||||||||
\(722\) | −3.45687 | − | 3.45687i | −0.128651 | − | 0.128651i | ||||
\(723\) | −25.5845 | + | 17.9294i | −0.951498 | + | 0.666803i | ||||
\(724\) | − | 6.48247i | − | 0.240919i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.88625 | + | 0.683677i | 0.144232 | + | 0.0253736i | ||||
\(727\) | −17.3682 | + | 17.3682i | −0.644150 | + | 0.644150i | −0.951573 | − | 0.307423i | \(-0.900533\pi\) |
0.307423 | + | 0.951573i | \(0.400533\pi\) | |||||||
\(728\) | −12.6774 | + | 12.6774i | −0.469857 | + | 0.469857i | ||||
\(729\) | −23.3508 | + | 13.5550i | −0.864845 | + | 0.502038i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 9.83087i | − | 0.363608i | ||||||
\(732\) | −2.92236 | − | 4.17008i | −0.108014 | − | 0.154131i | ||||
\(733\) | 7.68183 | + | 7.68183i | 0.283735 | + | 0.283735i | 0.834597 | − | 0.550862i | \(-0.185701\pi\) |
−0.550862 | + | 0.834597i | \(0.685701\pi\) | |||||||
\(734\) | 12.5714 | 0.464017 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.4116 | −0.457497 | ||||||||
\(737\) | −35.1679 | − | 35.1679i | −1.29543 | − | 1.29543i | ||||
\(738\) | −0.409394 | − | 0.876152i | −0.0150700 | − | 0.0322516i | ||||
\(739\) | − | 9.51894i | − | 0.350160i | −0.984554 | − | 0.175080i | \(-0.943982\pi\) | ||
0.984554 | − | 0.175080i | \(-0.0560184\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.71467 | − | 38.1684i | 0.246669 | − | 1.40215i | ||||
\(742\) | −1.48247 | + | 1.48247i | −0.0544231 | + | 0.0544231i | ||||
\(743\) | 3.56000 | − | 3.56000i | 0.130604 | − | 0.130604i | −0.638783 | − | 0.769387i | \(-0.720562\pi\) |
0.769387 | + | 0.638783i | \(0.220562\pi\) | |||||||
\(744\) | −3.28757 | + | 18.6876i | −0.120528 | + | 0.685121i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 20.8631i | 0.763854i | ||||||||
\(747\) | −17.2101 | − | 36.8316i | −0.629683 | − | 1.34760i | ||||
\(748\) | 15.9662 | + | 15.9662i | 0.583780 | + | 0.583780i | ||||
\(749\) | 8.95214 | 0.327104 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.8113 | −1.01485 | −0.507424 | − | 0.861696i | \(-0.669402\pi\) | ||||
−0.507424 | + | 0.861696i | \(0.669402\pi\) | |||||||
\(752\) | 5.34136 | + | 5.34136i | 0.194779 | + | 0.194779i | ||||
\(753\) | −5.31342 | − | 7.58201i | −0.193632 | − | 0.276304i | ||||
\(754\) | − | 6.91874i | − | 0.251966i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.46764 | + | 4.28573i | −0.0897473 | + | 0.155870i | ||||
\(757\) | −17.0932 | + | 17.0932i | −0.621262 | + | 0.621262i | −0.945854 | − | 0.324592i | \(-0.894773\pi\) |
0.324592 | + | 0.945854i | \(0.394773\pi\) | |||||||
\(758\) | 10.3942 | − | 10.3942i | 0.377534 | − | 0.377534i | ||||
\(759\) | 15.9573 | + | 2.80724i | 0.579213 | + | 0.101897i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 19.0016i | − | 0.688809i | −0.938821 | − | 0.344404i | \(-0.888081\pi\) | ||
0.938821 | − | 0.344404i | \(-0.111919\pi\) | |||||||
\(762\) | 7.04820 | − | 4.93933i | 0.255329 | − | 0.178933i | ||||
\(763\) | 4.37834 | + | 4.37834i | 0.158507 | + | 0.158507i | ||||
\(764\) | 23.4177 | 0.847221 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.8079 | −0.571163 | ||||||||
\(767\) | −36.5225 | − | 36.5225i | −1.31875 | − | 1.31875i | ||||
\(768\) | −23.8986 | + | 16.7479i | −0.862365 | + | 0.604339i | ||||
\(769\) | − | 45.4833i | − | 1.64017i | −0.572242 | − | 0.820085i | \(-0.693926\pi\) | ||
0.572242 | − | 0.820085i | \(-0.306074\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.0063 | − | 4.92692i | −1.00862 | − | 0.177439i | ||||
\(772\) | −15.3754 | + | 15.3754i | −0.553374 | + | 0.553374i | ||||
\(773\) | 31.5448 | − | 31.5448i | 1.13459 | − | 1.13459i | 0.145183 | − | 0.989405i | \(-0.453623\pi\) |
0.989405 | − | 0.145183i | \(-0.0463772\pi\) | |||||||
\(774\) | −4.35070 | − | 1.57966i | −0.156383 | − | 0.0567797i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 22.6023i | − | 0.811376i | ||||||
\(777\) | 10.1893 | + | 14.5396i | 0.365538 | + | 0.521606i | ||||
\(778\) | 10.3708 | + | 10.3708i | 0.371812 | + | 0.371812i | ||||
\(779\) | 1.18750 | 0.0425467 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 38.0394 | 1.36116 | ||||||||
\(782\) | −12.1489 | − | 12.1489i | −0.434443 | − | 0.434443i | ||||
\(783\) | −1.53865 | − | 5.71540i | −0.0549870 | − | 0.204252i | ||||
\(784\) | − | 1.19072i | − | 0.0425257i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.18181 | − | 6.71781i | 0.0421538 | − | 0.239616i | ||||
\(787\) | 29.4500 | − | 29.4500i | 1.04978 | − | 1.04978i | 0.0510863 | − | 0.998694i | \(-0.483732\pi\) |
0.998694 | − | 0.0510863i | \(-0.0162683\pi\) | |||||||
\(788\) | −16.4154 | + | 16.4154i | −0.584774 | + | 0.584774i | ||||
\(789\) | 1.65644 | − | 9.41576i | 0.0589709 | − | 0.335210i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 2.65330i | − | 0.0943406i | ||||||
\(792\) | 29.8710 | − | 13.9577i | 1.06142 | − | 0.495964i | ||||
\(793\) | 12.9581 | + | 12.9581i | 0.460154 | + | 0.460154i | ||||
\(794\) | 30.5178 | 1.08303 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.3396 | 0.579141 | ||||||||
\(797\) | 12.4688 | + | 12.4688i | 0.441668 | + | 0.441668i | 0.892572 | − | 0.450905i | \(-0.148899\pi\) |
−0.450905 | + | 0.892572i | \(0.648899\pi\) | |||||||
\(798\) | 3.83847 | + | 5.47733i | 0.135880 | + | 0.193895i | ||||
\(799\) | − | 41.3862i | − | 1.46414i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.9002 | − | 43.7924i | 0.561806 | − | 1.54733i | ||||
\(802\) | 7.92704 | − | 7.92704i | 0.279914 | − | 0.279914i | ||||
\(803\) | −2.58239 | + | 2.58239i | −0.0911306 | + | 0.0911306i | ||||
\(804\) | −22.2035 | − | 3.90608i | −0.783056 | − | 0.137757i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 22.0175i | − | 0.775532i | ||||||
\(807\) | −44.2474 | + | 31.0082i | −1.55758 | + | 1.09154i | ||||
\(808\) | −11.8144 | − | 11.8144i | −0.415628 | − | 0.415628i | ||||
\(809\) | −24.8749 | −0.874556 | −0.437278 | − | 0.899326i | \(-0.644057\pi\) | ||||
−0.437278 | + | 0.899326i | \(0.644057\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.91973 | 0.242984 | 0.121492 | − | 0.992592i | \(-0.461232\pi\) | ||||
0.121492 | + | 0.992592i | \(0.461232\pi\) | |||||||
\(812\) | −0.766585 | − | 0.766585i | −0.0269019 | − | 0.0269019i | ||||
\(813\) | −27.6248 | + | 19.3592i | −0.968842 | + | 0.678958i | ||||
\(814\) | − | 38.1665i | − | 1.33774i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −13.2510 | − | 2.33115i | −0.463879 | − | 0.0816067i | ||||
\(817\) | 4.01889 | − | 4.01889i | 0.140603 | − | 0.140603i | ||||
\(818\) | −14.0812 | + | 14.0812i | −0.492337 | + | 0.492337i | ||||
\(819\) | 6.07391 | − | 16.7288i | 0.212240 | − | 0.584551i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.31823i | 0.115807i | 0.998322 | + | 0.0579034i | \(0.0184415\pi\) | ||||
−0.998322 | + | 0.0579034i | \(0.981558\pi\) | |||||||
\(822\) | −19.5823 | − | 27.9431i | −0.683011 | − | 0.974626i | ||||
\(823\) | 8.02010 | + | 8.02010i | 0.279563 | + | 0.279563i | 0.832935 | − | 0.553371i | \(-0.186659\pi\) |
−0.553371 | + | 0.832935i | \(0.686659\pi\) | |||||||
\(824\) | −7.17562 | −0.249975 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.91408 | 0.310160 | ||||||||
\(827\) | 26.6136 | + | 26.6136i | 0.925444 | + | 0.925444i | 0.997407 | − | 0.0719628i | \(-0.0229263\pi\) |
−0.0719628 | + | 0.997407i | \(0.522926\pi\) | |||||||
\(828\) | 6.65384 | − | 3.10910i | 0.231237 | − | 0.108049i | ||||
\(829\) | 16.8759i | 0.586125i | 0.956093 | + | 0.293062i | \(0.0946744\pi\) | ||||
−0.956093 | + | 0.293062i | \(0.905326\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.813734 | + | 4.62553i | −0.0282281 | + | 0.160458i | ||||
\(832\) | 30.7133 | − | 30.7133i | 1.06479 | − | 1.06479i | ||||
\(833\) | −4.61300 | + | 4.61300i | −0.159831 | + | 0.159831i | ||||
\(834\) | −2.78179 | + | 15.8126i | −0.0963254 | + | 0.547545i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 13.0540i | 0.451483i | ||||||||
\(837\) | −4.89645 | − | 18.1881i | −0.169246 | − | 0.628672i | ||||
\(838\) | 18.7723 | + | 18.7723i | 0.648477 | + | 0.648477i | ||||
\(839\) | 38.5483 | 1.33084 | 0.665418 | − | 0.746471i | \(-0.268253\pi\) | ||||
0.665418 | + | 0.746471i | \(0.268253\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.7025 | −0.955258 | ||||||||
\(842\) | 4.19874 | + | 4.19874i | 0.144698 | + | 0.144698i | ||||
\(843\) | −0.318498 | − | 0.454482i | −0.0109697 | − | 0.0156532i | ||||
\(844\) | 11.8861i | 0.409136i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −18.3157 | − | 6.65008i | −0.629706 | − | 0.228635i | ||||
\(847\) | −1.57340 | + | 1.57340i | −0.0540626 | + | 0.0540626i | ||||
\(848\) | 1.72409 | − | 1.72409i | 0.0592055 | − | 0.0592055i | ||||
\(849\) | −2.91122 | − | 0.512149i | −0.0999129 | − | 0.0175769i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 26.3673i | − | 0.903859i | ||||||
\(852\) | 14.1207 | − | 9.89570i | 0.483768 | − | 0.339021i | ||||
\(853\) | 18.1797 | + | 18.1797i | 0.622462 | + | 0.622462i | 0.946160 | − | 0.323699i | \(-0.104926\pi\) |
−0.323699 | + | 0.946160i | \(0.604926\pi\) | |||||||
\(854\) | −3.16269 | −0.108225 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −27.0545 | −0.924704 | ||||||||
\(857\) | −32.6389 | − | 32.6389i | −1.11492 | − | 1.11492i | −0.992475 | − | 0.122447i | \(-0.960926\pi\) |
−0.122447 | − | 0.992475i | \(-0.539074\pi\) | |||||||
\(858\) | −31.3310 | + | 21.9565i | −1.06962 | + | 0.749583i | ||||
\(859\) | − | 22.2340i | − | 0.758615i | −0.925271 | − | 0.379308i | \(-0.876162\pi\) | ||
0.925271 | − | 0.379308i | \(-0.123838\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.537092 | + | 0.0944864i | 0.0183040 | + | 0.00322009i | ||||
\(862\) | 10.7697 | − | 10.7697i | 0.366816 | − | 0.366816i | ||||
\(863\) | 41.1315 | − | 41.1315i | 1.40013 | − | 1.40013i | 0.600534 | − | 0.799599i | \(-0.294955\pi\) |
0.799599 | − | 0.600534i | \(-0.205045\pi\) | |||||||
\(864\) | 12.5105 | − | 21.7279i | 0.425616 | − | 0.739197i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 26.9117i | 0.914498i | ||||||||
\(867\) | 25.4067 | + | 36.2542i | 0.862855 | + | 1.23126i | ||||
\(868\) | −2.43950 | − | 2.43950i | −0.0828021 | − | 0.0828021i | ||||
\(869\) | −26.5629 | −0.901086 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 81.1325 | 2.74907 | ||||||||
\(872\) | −13.2319 | − | 13.2319i | −0.448089 | − | 0.448089i | ||||
\(873\) | 9.49818 | + | 20.3272i | 0.321465 | + | 0.687972i | ||||
\(874\) | − | 9.93300i | − | 0.335989i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.286825 | + | 1.63041i | −0.00969092 | + | 0.0550864i | ||||
\(877\) | 11.3627 | − | 11.3627i | 0.383690 | − | 0.383690i | −0.488740 | − | 0.872430i | \(-0.662543\pi\) |
0.872430 | + | 0.488740i | \(0.162543\pi\) | |||||||
\(878\) | −11.3437 | + | 11.3437i | −0.382831 | + | 0.382831i | ||||
\(879\) | −4.75397 | + | 27.0231i | −0.160347 | + | 0.911467i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.3402i | 0.516823i | 0.966035 | + | 0.258412i | \(0.0831991\pi\) | ||||
−0.966035 | + | 0.258412i | \(0.916801\pi\) | |||||||
\(882\) | 1.30027 | + | 2.78274i | 0.0437825 | + | 0.0936998i | ||||
\(883\) | −0.509152 | − | 0.509152i | −0.0171343 | − | 0.0171343i | 0.698488 | − | 0.715622i | \(-0.253857\pi\) |
−0.715622 | + | 0.698488i | \(0.753857\pi\) | |||||||
\(884\) | −36.8340 | −1.23886 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25.2344 | 0.847767 | ||||||||
\(887\) | −35.3019 | − | 35.3019i | −1.18532 | − | 1.18532i | −0.978346 | − | 0.206974i | \(-0.933638\pi\) |
−0.206974 | − | 0.978346i | \(-0.566362\pi\) | |||||||
\(888\) | −30.7933 | − | 43.9406i | −1.03335 | − | 1.47455i | ||||
\(889\) | 4.85330i | 0.162775i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.9989 | + | 25.1054i | −0.703488 | + | 0.841063i | ||||
\(892\) | −13.9621 | + | 13.9621i | −0.467487 | + | 0.467487i | ||||
\(893\) | 16.9188 | − | 16.9188i | 0.566167 | − | 0.566167i | ||||
\(894\) | −35.9781 | − | 6.32934i | −1.20329 | − | 0.211685i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 2.15404i | − | 0.0719613i | ||||||
\(897\) | −21.6450 | + | 15.1686i | −0.722704 | + | 0.506466i | ||||
\(898\) | 0.449443 | + | 0.449443i | 0.0149981 | + | 0.0149981i | ||||
\(899\) | 4.12912 | 0.137714 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.3587 | −0.445042 | ||||||||
\(902\) | −0.828946 | − | 0.828946i | −0.0276009 | − | 0.0276009i | ||||
\(903\) | 2.13747 | − | 1.49792i | 0.0711304 | − | 0.0498477i | ||||
\(904\) | 8.01862i | 0.266695i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −27.8192 | − | 4.89401i | −0.924229 | − | 0.162593i | ||||
\(907\) | 6.84363 | − | 6.84363i | 0.227239 | − | 0.227239i | −0.584299 | − | 0.811538i | \(-0.698631\pi\) |
0.811538 | + | 0.584299i | \(0.198631\pi\) | |||||||
\(908\) | 1.51321 | − | 1.51321i | 0.0502177 | − | 0.0502177i | ||||
\(909\) | 15.5899 | + | 5.66041i | 0.517085 | + | 0.187744i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 33.2065i | − | 1.10018i | −0.835105 | − | 0.550090i | \(-0.814593\pi\) | ||
0.835105 | − | 0.550090i | \(-0.185407\pi\) | |||||||
\(912\) | −4.46409 | − | 6.37006i | −0.147821 | − | 0.210934i | ||||
\(913\) | −34.8472 | − | 34.8472i | −1.15327 | − | 1.15327i | ||||
\(914\) | −13.1902 | −0.436293 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.29123 | 0.0426636 | ||||||||
\(917\) | 2.71979 | + | 2.71979i | 0.0898154 | + | 0.0898154i | ||||
\(918\) | 33.5136 | − | 9.02227i | 1.10611 | − | 0.297779i | ||||
\(919\) | 48.0196i | 1.58402i | 0.610507 | + | 0.792011i | \(0.290966\pi\) | ||||
−0.610507 | + | 0.792011i | \(0.709034\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.81543 | + | 38.7411i | −0.224576 | + | 1.27656i | ||||
\(922\) | 2.01462 | − | 2.01462i | 0.0663479 | − | 0.0663479i | ||||
\(923\) | −43.8786 | + | 43.8786i | −1.44428 | + | 1.44428i | ||||
\(924\) | −1.03868 | + | 5.90417i | −0.0341699 | + | 0.194233i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 15.1261i | − | 0.497073i | ||||||
\(927\) | 6.45334 | − | 3.01541i | 0.211955 | − | 0.0990391i | ||||
\(928\) | 3.88645 | + | 3.88645i | 0.127579 | + | 0.127579i | ||||
\(929\) | 29.7649 | 0.976555 | 0.488277 | − | 0.872688i | \(-0.337625\pi\) | ||||
0.488277 | + | 0.872688i | \(0.337625\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.77162 | −0.123610 | ||||||||
\(932\) | 14.3978 | + | 14.3978i | 0.471615 | + | 0.471615i | ||||
\(933\) | 0.705751 | + | 1.00708i | 0.0231053 | + | 0.0329702i | ||||
\(934\) | − | 23.1265i | − | 0.756722i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −18.3561 | + | 50.5565i | −0.599989 | + | 1.65249i | ||||
\(937\) | −16.2931 | + | 16.2931i | −0.532273 | + | 0.532273i | −0.921248 | − | 0.388975i | \(-0.872829\pi\) |
0.388975 | + | 0.921248i | \(0.372829\pi\) | |||||||
\(938\) | −9.90105 | + | 9.90105i | −0.323281 | + | 0.323281i | ||||
\(939\) | 36.0493 | + | 6.34187i | 1.17642 | + | 0.206959i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.9179i | 1.26869i | 0.773052 | + | 0.634343i | \(0.218729\pi\) | ||||
−0.773052 | + | 0.634343i | \(0.781271\pi\) | |||||||
\(942\) | 8.22767 | − | 5.76589i | 0.268072 | − | 0.187863i | ||||
\(943\) | −0.572676 | − | 0.572676i | −0.0186489 | − | 0.0186489i | ||||
\(944\) | −10.3670 | −0.337416 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.61085 | −0.182424 | ||||||||
\(947\) | −2.32343 | − | 2.32343i | −0.0755014 | − | 0.0755014i | 0.668348 | − | 0.743849i | \(-0.267002\pi\) |
−0.743849 | + | 0.668348i | \(0.767002\pi\) | |||||||
\(948\) | −9.86050 | + | 6.91017i | −0.320254 | + | 0.224432i | ||||
\(949\) | − | 5.95759i | − | 0.193392i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.26198 | − | 1.62939i | −0.300340 | − | 0.0528366i | ||||
\(952\) | 13.9411 | − | 13.9411i | 0.451833 | − | 0.451833i | ||||
\(953\) | 4.77849 | − | 4.77849i | 0.154791 | − | 0.154791i | −0.625463 | − | 0.780254i | \(-0.715090\pi\) |
0.780254 | + | 0.625463i | \(0.215090\pi\) | |||||||
\(954\) | −2.14652 | + | 5.91195i | −0.0694962 | + | 0.191407i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 11.8956i | − | 0.384732i | ||||||
\(957\) | −4.11769 | − | 5.87576i | −0.133106 | − | 0.189936i | ||||
\(958\) | −7.88727 | − | 7.88727i | −0.254826 | − | 0.254826i | ||||
\(959\) | 19.2412 | 0.621332 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.8599 | −0.576127 | ||||||||
\(962\) | 44.0252 | + | 44.0252i | 1.41943 | + | 1.41943i | ||||
\(963\) | 24.3313 | − | 11.3691i | 0.784064 | − | 0.366365i | ||||
\(964\) | 17.1668i | 0.552904i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.790343 | − | 4.49257i | 0.0254289 | − | 0.144546i | ||||
\(967\) | −26.7726 | + | 26.7726i | −0.860949 | + | 0.860949i | −0.991448 | − | 0.130499i | \(-0.958342\pi\) |
0.130499 | + | 0.991448i | \(0.458342\pi\) | |||||||
\(968\) | 4.75501 | − | 4.75501i | 0.152832 | − | 0.152832i | ||||
\(969\) | −7.38396 | + | 41.9728i | −0.237207 | + | 1.34836i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 10.3583i | − | 0.332413i | −0.986091 | − | 0.166206i | \(-0.946848\pi\) | ||
0.986091 | − | 0.166206i | \(-0.0531518\pi\) | |||||||
\(972\) | −1.26404 | + | 14.7822i | −0.0405442 | + | 0.474139i | ||||
\(973\) | −6.40193 | − | 6.40193i | −0.205236 | − | 0.205236i | ||||
\(974\) | −7.28874 | −0.233546 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.67816 | 0.117735 | ||||||||
\(977\) | 11.0435 | + | 11.0435i | 0.353311 | + | 0.353311i | 0.861340 | − | 0.508029i | \(-0.169626\pi\) |
−0.508029 | + | 0.861340i | \(0.669626\pi\) | |||||||
\(978\) | −7.45889 | − | 10.6435i | −0.238509 | − | 0.340342i | ||||
\(979\) | − | 56.4765i | − | 1.80500i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.4605 | + | 6.33957i | 0.557470 | + | 0.202407i | ||||
\(982\) | 8.62939 | − | 8.62939i | 0.275375 | − | 0.275375i | ||||
\(983\) | −9.03917 | + | 9.03917i | −0.288305 | + | 0.288305i | −0.836410 | − | 0.548105i | \(-0.815349\pi\) |
0.548105 | + | 0.836410i | \(0.315349\pi\) | |||||||
\(984\) | −1.62316 | − | 0.285550i | −0.0517444 | − | 0.00910300i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.60837i | 0.242300i | ||||||||
\(987\) | 8.99835 | − | 6.30598i | 0.286421 | − | 0.200721i | ||||
\(988\) | −15.0579 | − | 15.0579i | −0.479055 | − | 0.479055i | ||||
\(989\) | −3.87624 | −0.123257 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.41165 | 0.298971 | 0.149485 | − | 0.988764i | \(-0.452238\pi\) | ||||
0.149485 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(992\) | 12.3678 | + | 12.3678i | 0.392679 | + | 0.392679i | ||||
\(993\) | 45.1169 | − | 31.6176i | 1.43174 | − | 1.00335i | ||||
\(994\) | − | 10.7095i | − | 0.339685i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −22.0010 | − | 3.87046i | −0.697128 | − | 0.122640i | ||||
\(997\) | −14.3463 | + | 14.3463i | −0.454351 | + | 0.454351i | −0.896796 | − | 0.442445i | \(-0.854111\pi\) |
0.442445 | + | 0.896796i | \(0.354111\pi\) | |||||||
\(998\) | −0.699929 | + | 0.699929i | −0.0221559 | + | 0.0221559i | ||||
\(999\) | 46.1589 | + | 26.5774i | 1.46040 | + | 0.840872i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 525.2.j.c.218.8 | yes | 32 | |
3.2 | odd | 2 | inner | 525.2.j.c.218.10 | yes | 32 | |
5.2 | odd | 4 | inner | 525.2.j.c.407.10 | yes | 32 | |
5.3 | odd | 4 | inner | 525.2.j.c.407.7 | yes | 32 | |
5.4 | even | 2 | inner | 525.2.j.c.218.9 | yes | 32 | |
15.2 | even | 4 | inner | 525.2.j.c.407.8 | yes | 32 | |
15.8 | even | 4 | inner | 525.2.j.c.407.9 | yes | 32 | |
15.14 | odd | 2 | inner | 525.2.j.c.218.7 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.j.c.218.7 | ✓ | 32 | 15.14 | odd | 2 | inner | |
525.2.j.c.218.8 | yes | 32 | 1.1 | even | 1 | trivial | |
525.2.j.c.218.9 | yes | 32 | 5.4 | even | 2 | inner | |
525.2.j.c.218.10 | yes | 32 | 3.2 | odd | 2 | inner | |
525.2.j.c.407.7 | yes | 32 | 5.3 | odd | 4 | inner | |
525.2.j.c.407.8 | yes | 32 | 15.2 | even | 4 | inner | |
525.2.j.c.407.9 | yes | 32 | 15.8 | even | 4 | inner | |
525.2.j.c.407.10 | yes | 32 | 5.2 | odd | 4 | inner |