Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(229,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.229");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.k (of order \(6\), 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: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 229.2 | ||
Character | \(\chi\) | \(=\) | 966.229 |
Dual form | 966.2.k.a.367.2 |
$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.52184 | + | 2.63590i | −0.680587 | + | 1.17881i | 0.294216 | + | 0.955739i | \(0.404942\pi\) |
−0.974802 | + | 0.223071i | \(0.928392\pi\) | |||||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | −1.49399 | − | 2.18358i | −0.564673 | − | 0.825315i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −1.52184 | − | 2.63590i | −0.481247 | − | 0.833545i | ||||
\(11\) | −2.07367 | + | 1.19724i | −0.625236 | + | 0.360980i | −0.778905 | − | 0.627142i | \(-0.784224\pi\) |
0.153669 | + | 0.988122i | \(0.450891\pi\) | |||||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | − | 4.32646i | − | 1.19994i | −0.800021 | − | 0.599971i | \(-0.795179\pi\) | ||
0.800021 | − | 0.599971i | \(-0.204821\pi\) | |||||||
\(14\) | 2.63803 | − | 0.202041i | 0.705042 | − | 0.0539976i | ||||
\(15\) | − | 3.04368i | − | 0.785874i | ||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0.399743 | + | 0.692374i | 0.0969518 | + | 0.167925i | 0.910422 | − | 0.413682i | \(-0.135757\pi\) |
−0.813470 | + | 0.581607i | \(0.802424\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | 1.07775 | − | 1.86672i | 0.247254 | − | 0.428256i | −0.715509 | − | 0.698603i | \(-0.753805\pi\) |
0.962763 | + | 0.270347i | \(0.0871386\pi\) | |||||||
\(20\) | 3.04368 | 0.680587 | ||||||||
\(21\) | 2.38562 | + | 1.14404i | 0.520584 | + | 0.249650i | ||||
\(22\) | − | 2.39447i | − | 0.510503i | ||||||
\(23\) | 4.75713 | + | 0.608007i | 0.991931 | + | 0.126778i | ||||
\(24\) | −0.866025 | + | 0.500000i | −0.176777 | + | 0.102062i | ||||
\(25\) | −2.13198 | − | 3.69270i | −0.426396 | − | 0.738540i | ||||
\(26\) | 3.74682 | + | 2.16323i | 0.734812 | + | 0.424244i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −1.14404 | + | 2.38562i | −0.216203 | + | 0.450839i | ||||
\(29\) | −4.78811 | −0.889130 | −0.444565 | − | 0.895747i | \(-0.646642\pi\) | ||||
−0.444565 | + | 0.895747i | \(0.646642\pi\) | |||||||
\(30\) | 2.63590 | + | 1.52184i | 0.481247 | + | 0.277848i | ||||
\(31\) | 3.53448 | − | 2.04063i | 0.634811 | − | 0.366508i | −0.147802 | − | 0.989017i | \(-0.547220\pi\) |
0.782613 | + | 0.622509i | \(0.213887\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 1.19724 | − | 2.07367i | 0.208412 | − | 0.360980i | ||||
\(34\) | −0.799485 | −0.137111 | ||||||||
\(35\) | 8.02929 | − | 0.614946i | 1.35720 | − | 0.103945i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 3.53978 | + | 2.04369i | 0.581937 | + | 0.335981i | 0.761903 | − | 0.647691i | \(-0.224265\pi\) |
−0.179966 | + | 0.983673i | \(0.557599\pi\) | |||||||
\(38\) | 1.07775 | + | 1.86672i | 0.174835 | + | 0.302823i | ||||
\(39\) | 2.16323 | + | 3.74682i | 0.346394 | + | 0.599971i | ||||
\(40\) | −1.52184 | + | 2.63590i | −0.240624 | + | 0.416772i | ||||
\(41\) | − | 7.66774i | − | 1.19750i | −0.800936 | − | 0.598750i | \(-0.795664\pi\) | ||
0.800936 | − | 0.598750i | \(-0.204336\pi\) | |||||||
\(42\) | −2.18358 | + | 1.49399i | −0.336933 | + | 0.230527i | ||||
\(43\) | 3.15309i | 0.480841i | 0.970669 | + | 0.240421i | \(0.0772854\pi\) | ||||
−0.970669 | + | 0.240421i | \(0.922715\pi\) | |||||||
\(44\) | 2.07367 | + | 1.19724i | 0.312618 | + | 0.180490i | ||||
\(45\) | 1.52184 | + | 2.63590i | 0.226862 | + | 0.392937i | ||||
\(46\) | −2.90512 | + | 3.81580i | −0.428336 | + | 0.562608i | ||||
\(47\) | 7.12526 | + | 4.11377i | 1.03933 | + | 0.600055i | 0.919642 | − | 0.392757i | \(-0.128479\pi\) |
0.119683 | + | 0.992812i | \(0.461812\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | −2.53602 | + | 6.52446i | −0.362288 | + | 0.932066i | ||||
\(50\) | 4.26396 | 0.603015 | ||||||||
\(51\) | −0.692374 | − | 0.399743i | −0.0969518 | − | 0.0559752i | ||||
\(52\) | −3.74682 | + | 2.16323i | −0.519590 | + | 0.299986i | ||||
\(53\) | −9.49569 | + | 5.48234i | −1.30433 | + | 0.753057i | −0.981144 | − | 0.193277i | \(-0.938088\pi\) |
−0.323189 | + | 0.946334i | \(0.604755\pi\) | |||||||
\(54\) | −0.866025 | − | 0.500000i | −0.117851 | − | 0.0680414i | ||||
\(55\) | − | 7.28799i | − | 0.982713i | ||||||
\(56\) | −1.49399 | − | 2.18358i | −0.199642 | − | 0.291793i | ||||
\(57\) | 2.15551i | 0.285504i | ||||||||
\(58\) | 2.39406 | − | 4.14663i | 0.314355 | − | 0.544479i | ||||
\(59\) | 10.6576 | − | 6.15319i | 1.38751 | − | 0.801077i | 0.394473 | − | 0.918908i | \(-0.370927\pi\) |
0.993034 | + | 0.117831i | \(0.0375940\pi\) | |||||||
\(60\) | −2.63590 | + | 1.52184i | −0.340293 | + | 0.196468i | ||||
\(61\) | 2.01946 | − | 3.49780i | 0.258565 | − | 0.447848i | −0.707293 | − | 0.706921i | \(-0.750084\pi\) |
0.965858 | + | 0.259073i | \(0.0834171\pi\) | |||||||
\(62\) | 4.08126i | 0.518321i | ||||||||
\(63\) | −2.63803 | + | 0.202041i | −0.332360 | + | 0.0254547i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 11.4041 | + | 6.58416i | 1.41451 | + | 0.816665i | ||||
\(66\) | 1.19724 | + | 2.07367i | 0.147370 | + | 0.255251i | ||||
\(67\) | 4.06092 | − | 2.34457i | 0.496120 | − | 0.286435i | −0.230990 | − | 0.972956i | \(-0.574196\pi\) |
0.727110 | + | 0.686521i | \(0.240863\pi\) | |||||||
\(68\) | 0.399743 | − | 0.692374i | 0.0484759 | − | 0.0839627i | ||||
\(69\) | −4.42380 | + | 1.85202i | −0.532563 | + | 0.222957i | ||||
\(70\) | −3.48209 | + | 7.26105i | −0.416189 | + | 0.867861i | ||||
\(71\) | 6.20671 | 0.736601 | 0.368300 | − | 0.929707i | \(-0.379940\pi\) | ||||
0.368300 | + | 0.929707i | \(0.379940\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 2.21583 | − | 1.27931i | 0.259344 | − | 0.149732i | −0.364691 | − | 0.931128i | \(-0.618826\pi\) |
0.624035 | + | 0.781396i | \(0.285492\pi\) | |||||||
\(74\) | −3.53978 | + | 2.04369i | −0.411491 | + | 0.237575i | ||||
\(75\) | 3.69270 | + | 2.13198i | 0.426396 | + | 0.246180i | ||||
\(76\) | −2.15551 | −0.247254 | ||||||||
\(77\) | 5.71229 | + | 2.73937i | 0.650976 | + | 0.312180i | ||||
\(78\) | −4.32646 | −0.489875 | ||||||||
\(79\) | 7.62601 | + | 4.40288i | 0.857993 | + | 0.495363i | 0.863340 | − | 0.504623i | \(-0.168369\pi\) |
−0.00534663 | + | 0.999986i | \(0.501702\pi\) | |||||||
\(80\) | −1.52184 | − | 2.63590i | −0.170147 | − | 0.294703i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 6.64046 | + | 3.83387i | 0.733316 | + | 0.423380i | ||||
\(83\) | 0.377697 | 0.0414576 | 0.0207288 | − | 0.999785i | \(-0.493401\pi\) | ||||
0.0207288 | + | 0.999785i | \(0.493401\pi\) | |||||||
\(84\) | −0.202041 | − | 2.63803i | −0.0220444 | − | 0.287832i | ||||
\(85\) | −2.43337 | −0.263936 | ||||||||
\(86\) | −2.73065 | − | 1.57654i | −0.294454 | − | 0.170003i | ||||
\(87\) | 4.14663 | − | 2.39406i | 0.444565 | − | 0.256670i | ||||
\(88\) | −2.07367 | + | 1.19724i | −0.221054 | + | 0.127626i | ||||
\(89\) | −0.328941 | + | 0.569742i | −0.0348676 | + | 0.0603925i | −0.882933 | − | 0.469500i | \(-0.844434\pi\) |
0.848065 | + | 0.529892i | \(0.177768\pi\) | |||||||
\(90\) | −3.04368 | −0.320832 | ||||||||
\(91\) | −9.44715 | + | 6.46366i | −0.990330 | + | 0.677576i | ||||
\(92\) | −1.85202 | − | 4.42380i | −0.193086 | − | 0.461213i | ||||
\(93\) | −2.04063 | + | 3.53448i | −0.211604 | + | 0.366508i | ||||
\(94\) | −7.12526 | + | 4.11377i | −0.734914 | + | 0.424303i | ||||
\(95\) | 3.28033 | + | 5.68170i | 0.336555 | + | 0.582930i | ||||
\(96\) | 0.866025 | + | 0.500000i | 0.0883883 | + | 0.0510310i | ||||
\(97\) | 2.07359 | 0.210541 | 0.105271 | − | 0.994444i | \(-0.466429\pi\) | ||||
0.105271 | + | 0.994444i | \(0.466429\pi\) | |||||||
\(98\) | −4.38234 | − | 5.45849i | −0.442683 | − | 0.551390i | ||||
\(99\) | 2.39447i | 0.240653i | ||||||||
\(100\) | −2.13198 | + | 3.69270i | −0.213198 | + | 0.369270i | ||||
\(101\) | 15.0796 | − | 8.70623i | 1.50048 | − | 0.866302i | 0.500480 | − | 0.865748i | \(-0.333157\pi\) |
1.00000 | 0.000554027i | \(-0.000176352\pi\) | ||||||||
\(102\) | 0.692374 | − | 0.399743i | 0.0685553 | − | 0.0395804i | ||||
\(103\) | 7.51800 | − | 13.0216i | 0.740771 | − | 1.28305i | −0.211374 | − | 0.977405i | \(-0.567794\pi\) |
0.952145 | − | 0.305647i | \(-0.0988728\pi\) | |||||||
\(104\) | − | 4.32646i | − | 0.424244i | ||||||
\(105\) | −6.64610 | + | 4.54721i | −0.648593 | + | 0.443762i | ||||
\(106\) | − | 10.9647i | − | 1.06498i | ||||||
\(107\) | −11.7687 | − | 6.79464i | −1.13772 | − | 0.656863i | −0.191855 | − | 0.981423i | \(-0.561450\pi\) |
−0.945865 | + | 0.324560i | \(0.894784\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | −3.63340 | + | 2.09774i | −0.348017 | + | 0.200927i | −0.663811 | − | 0.747900i | \(-0.731062\pi\) |
0.315795 | + | 0.948828i | \(0.397729\pi\) | |||||||
\(110\) | 6.31159 | + | 3.64400i | 0.601786 | + | 0.347441i | ||||
\(111\) | −4.08739 | −0.387958 | ||||||||
\(112\) | 2.63803 | − | 0.202041i | 0.249270 | − | 0.0190910i | ||||
\(113\) | − | 12.0077i | − | 1.12959i | −0.825231 | − | 0.564796i | \(-0.808955\pi\) | ||
0.825231 | − | 0.564796i | \(-0.191045\pi\) | |||||||
\(114\) | −1.86672 | − | 1.07775i | −0.174835 | − | 0.100941i | ||||
\(115\) | −8.84223 | + | 11.6140i | −0.824542 | + | 1.08302i | ||||
\(116\) | 2.39406 | + | 4.14663i | 0.222283 | + | 0.385005i | ||||
\(117\) | −3.74682 | − | 2.16323i | −0.346394 | − | 0.199990i | ||||
\(118\) | 12.3064i | 1.13289i | ||||||||
\(119\) | 0.914643 | − | 1.90727i | 0.0838452 | − | 0.174839i | ||||
\(120\) | − | 3.04368i | − | 0.277848i | ||||||
\(121\) | −2.63325 | + | 4.56093i | −0.239387 | + | 0.414630i | ||||
\(122\) | 2.01946 | + | 3.49780i | 0.182833 | + | 0.316676i | ||||
\(123\) | 3.83387 | + | 6.64046i | 0.345688 | + | 0.598750i | ||||
\(124\) | −3.53448 | − | 2.04063i | −0.317405 | − | 0.183254i | ||||
\(125\) | −2.24027 | −0.200376 | ||||||||
\(126\) | 1.14404 | − | 2.38562i | 0.101919 | − | 0.212528i | ||||
\(127\) | 9.00515 | 0.799078 | 0.399539 | − | 0.916716i | \(-0.369170\pi\) | ||||
0.399539 | + | 0.916716i | \(0.369170\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −1.57654 | − | 2.73065i | −0.138807 | − | 0.240421i | ||||
\(130\) | −11.4041 | + | 6.58416i | −1.00021 | + | 0.577469i | ||||
\(131\) | 5.63863 | + | 3.25546i | 0.492649 | + | 0.284431i | 0.725673 | − | 0.688040i | \(-0.241529\pi\) |
−0.233024 | + | 0.972471i | \(0.574862\pi\) | |||||||
\(132\) | −2.39447 | −0.208412 | ||||||||
\(133\) | −5.68628 | + | 0.435500i | −0.493063 | + | 0.0377626i | ||||
\(134\) | 4.68915i | 0.405080i | ||||||||
\(135\) | −2.63590 | − | 1.52184i | −0.226862 | − | 0.130979i | ||||
\(136\) | 0.399743 | + | 0.692374i | 0.0342776 | + | 0.0593706i | ||||
\(137\) | 7.83359 | − | 4.52273i | 0.669269 | − | 0.386403i | −0.126531 | − | 0.991963i | \(-0.540384\pi\) |
0.795800 | + | 0.605560i | \(0.207051\pi\) | |||||||
\(138\) | 0.608007 | − | 4.75713i | 0.0517570 | − | 0.404954i | ||||
\(139\) | − | 10.5668i | − | 0.896264i | −0.893967 | − | 0.448132i | \(-0.852090\pi\) | ||
0.893967 | − | 0.448132i | \(-0.147910\pi\) | |||||||
\(140\) | −4.54721 | − | 6.64610i | −0.384309 | − | 0.561698i | ||||
\(141\) | −8.22754 | −0.692884 | ||||||||
\(142\) | −3.10335 | + | 5.37517i | −0.260428 | + | 0.451074i | ||||
\(143\) | 5.17979 | + | 8.97165i | 0.433156 | + | 0.750247i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 7.28673 | − | 12.6210i | 0.605130 | − | 1.04812i | ||||
\(146\) | 2.55863i | 0.211753i | ||||||||
\(147\) | −1.06598 | − | 6.91836i | −0.0879202 | − | 0.570617i | ||||
\(148\) | − | 4.08739i | − | 0.335981i | ||||||
\(149\) | 3.19186 | + | 1.84282i | 0.261487 | + | 0.150970i | 0.625013 | − | 0.780614i | \(-0.285094\pi\) |
−0.363526 | + | 0.931584i | \(0.618427\pi\) | |||||||
\(150\) | −3.69270 | + | 2.13198i | −0.301507 | + | 0.174075i | ||||
\(151\) | −12.2114 | − | 21.1507i | −0.993747 | − | 1.72122i | −0.593568 | − | 0.804783i | \(-0.702281\pi\) |
−0.400179 | − | 0.916437i | \(-0.631052\pi\) | |||||||
\(152\) | 1.07775 | − | 1.86672i | 0.0874174 | − | 0.151411i | ||||
\(153\) | 0.799485 | 0.0646345 | ||||||||
\(154\) | −5.22851 | + | 3.57730i | −0.421326 | + | 0.288267i | ||||
\(155\) | 12.4220i | 0.997762i | ||||||||
\(156\) | 2.16323 | − | 3.74682i | 0.173197 | − | 0.299986i | ||||
\(157\) | 4.68552 | + | 8.11555i | 0.373945 | + | 0.647692i | 0.990169 | − | 0.139880i | \(-0.0446715\pi\) |
−0.616223 | + | 0.787571i | \(0.711338\pi\) | |||||||
\(158\) | −7.62601 | + | 4.40288i | −0.606693 | + | 0.350274i | ||||
\(159\) | 5.48234 | − | 9.49569i | 0.434778 | − | 0.753057i | ||||
\(160\) | 3.04368 | 0.240624 | ||||||||
\(161\) | −5.77946 | − | 11.2959i | −0.455485 | − | 0.890243i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −5.92061 | + | 10.2548i | −0.463738 | + | 0.803217i | −0.999144 | − | 0.0413775i | \(-0.986825\pi\) |
0.535406 | + | 0.844595i | \(0.320159\pi\) | |||||||
\(164\) | −6.64046 | + | 3.83387i | −0.518533 | + | 0.299375i | ||||
\(165\) | 3.64400 | + | 6.31159i | 0.283685 | + | 0.491356i | ||||
\(166\) | −0.188848 | + | 0.327095i | −0.0146575 | + | 0.0253875i | ||||
\(167\) | − | 0.104509i | − | 0.00808712i | −0.999992 | − | 0.00404356i | \(-0.998713\pi\) | ||
0.999992 | − | 0.00404356i | \(-0.00128711\pi\) | |||||||
\(168\) | 2.38562 | + | 1.14404i | 0.184054 | + | 0.0882647i | ||||
\(169\) | −5.71822 | −0.439863 | ||||||||
\(170\) | 1.21669 | − | 2.10736i | 0.0933156 | − | 0.161627i | ||||
\(171\) | −1.07775 | − | 1.86672i | −0.0824179 | − | 0.142752i | ||||
\(172\) | 2.73065 | − | 1.57654i | 0.208210 | − | 0.120210i | ||||
\(173\) | −3.02723 | − | 1.74777i | −0.230156 | − | 0.132880i | 0.380488 | − | 0.924786i | \(-0.375756\pi\) |
−0.610644 | + | 0.791905i | \(0.709089\pi\) | |||||||
\(174\) | 4.78811i | 0.362986i | ||||||||
\(175\) | −4.87814 | + | 10.1722i | −0.368753 | + | 0.768944i | ||||
\(176\) | − | 2.39447i | − | 0.180490i | ||||||
\(177\) | −6.15319 | + | 10.6576i | −0.462502 | + | 0.801077i | ||||
\(178\) | −0.328941 | − | 0.569742i | −0.0246551 | − | 0.0427040i | ||||
\(179\) | −10.1370 | − | 17.5577i | −0.757672 | − | 1.31233i | −0.944035 | − | 0.329845i | \(-0.893003\pi\) |
0.186363 | − | 0.982481i | \(-0.440330\pi\) | |||||||
\(180\) | 1.52184 | − | 2.63590i | 0.113431 | − | 0.196468i | ||||
\(181\) | −5.28828 | −0.393075 | −0.196537 | − | 0.980496i | \(-0.562970\pi\) | ||||
−0.196537 | + | 0.980496i | \(0.562970\pi\) | |||||||
\(182\) | −0.874119 | − | 11.4133i | −0.0647940 | − | 0.846010i | ||||
\(183\) | 4.03891i | 0.298565i | ||||||||
\(184\) | 4.75713 | + | 0.608007i | 0.350701 | + | 0.0448229i | ||||
\(185\) | −10.7740 | + | 6.22034i | −0.792117 | + | 0.457329i | ||||
\(186\) | −2.04063 | − | 3.53448i | −0.149626 | − | 0.259160i | ||||
\(187\) | −1.65787 | − | 0.957172i | −0.121236 | − | 0.0699954i | ||||
\(188\) | − | 8.22754i | − | 0.600055i | ||||||
\(189\) | 2.18358 | − | 1.49399i | 0.158832 | − | 0.108671i | ||||
\(190\) | −6.56067 | −0.475961 | ||||||||
\(191\) | 18.1430 | + | 10.4748i | 1.31278 | + | 0.757933i | 0.982555 | − | 0.185970i | \(-0.0595426\pi\) |
0.330223 | + | 0.943903i | \(0.392876\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | −6.27262 | − | 10.8645i | −0.451513 | − | 0.782043i | 0.546967 | − | 0.837154i | \(-0.315782\pi\) |
−0.998480 | + | 0.0551106i | \(0.982449\pi\) | |||||||
\(194\) | −1.03680 | + | 1.79578i | −0.0744377 | + | 0.128930i | ||||
\(195\) | −13.1683 | −0.943003 | ||||||||
\(196\) | 6.91836 | − | 1.06598i | 0.494169 | − | 0.0761412i | ||||
\(197\) | −20.6843 | −1.47370 | −0.736849 | − | 0.676057i | \(-0.763687\pi\) | ||||
−0.736849 | + | 0.676057i | \(0.763687\pi\) | |||||||
\(198\) | −2.07367 | − | 1.19724i | −0.147370 | − | 0.0850838i | ||||
\(199\) | −9.53909 | − | 16.5222i | −0.676208 | − | 1.17123i | −0.976114 | − | 0.217258i | \(-0.930289\pi\) |
0.299906 | − | 0.953969i | \(-0.403045\pi\) | |||||||
\(200\) | −2.13198 | − | 3.69270i | −0.150754 | − | 0.261113i | ||||
\(201\) | −2.34457 | + | 4.06092i | −0.165373 | + | 0.286435i | ||||
\(202\) | 17.4125i | 1.22514i | ||||||||
\(203\) | 7.15337 | + | 10.4552i | 0.502068 | + | 0.733812i | ||||
\(204\) | 0.799485i | 0.0559752i | ||||||||
\(205\) | 20.2114 | + | 11.6691i | 1.41162 | + | 0.815002i | ||||
\(206\) | 7.51800 | + | 13.0216i | 0.523804 | + | 0.907255i | ||||
\(207\) | 2.90512 | − | 3.81580i | 0.201920 | − | 0.265216i | ||||
\(208\) | 3.74682 | + | 2.16323i | 0.259795 | + | 0.149993i | ||||
\(209\) | 5.16130i | 0.357015i | ||||||||
\(210\) | −0.614946 | − | 8.02929i | −0.0424353 | − | 0.554074i | ||||
\(211\) | 20.7862 | 1.43098 | 0.715491 | − | 0.698622i | \(-0.246203\pi\) | ||||
0.715491 | + | 0.698622i | \(0.246203\pi\) | |||||||
\(212\) | 9.49569 | + | 5.48234i | 0.652167 | + | 0.376529i | ||||
\(213\) | −5.37517 | + | 3.10335i | −0.368300 | + | 0.212638i | ||||
\(214\) | 11.7687 | − | 6.79464i | 0.804489 | − | 0.464472i | ||||
\(215\) | −8.31122 | − | 4.79849i | −0.566821 | − | 0.327254i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | −9.73633 | − | 4.66913i | −0.660945 | − | 0.316961i | ||||
\(218\) | − | 4.19549i | − | 0.284154i | ||||||
\(219\) | −1.27931 | + | 2.21583i | −0.0864479 | + | 0.149732i | ||||
\(220\) | −6.31159 | + | 3.64400i | −0.425527 | + | 0.245678i | ||||
\(221\) | 2.99553 | − | 1.72947i | 0.201501 | − | 0.116337i | ||||
\(222\) | 2.04369 | − | 3.53978i | 0.137164 | − | 0.237575i | ||||
\(223\) | 15.2414i | 1.02064i | 0.859985 | + | 0.510319i | \(0.170473\pi\) | ||||
−0.859985 | + | 0.510319i | \(0.829527\pi\) | |||||||
\(224\) | −1.14404 | + | 2.38562i | −0.0764394 | + | 0.159396i | ||||
\(225\) | −4.26396 | −0.284264 | ||||||||
\(226\) | 10.3990 | + | 6.00386i | 0.691731 | + | 0.399371i | ||||
\(227\) | −4.63162 | − | 8.02220i | −0.307412 | − | 0.532452i | 0.670384 | − | 0.742015i | \(-0.266129\pi\) |
−0.977795 | + | 0.209562i | \(0.932796\pi\) | |||||||
\(228\) | 1.86672 | − | 1.07775i | 0.123627 | − | 0.0713760i | ||||
\(229\) | 7.25789 | − | 12.5710i | 0.479615 | − | 0.830717i | −0.520112 | − | 0.854098i | \(-0.674110\pi\) |
0.999727 | + | 0.0233811i | \(0.00744312\pi\) | |||||||
\(230\) | −5.63694 | − | 13.4646i | −0.371689 | − | 0.887831i | ||||
\(231\) | −6.31668 | + | 0.483780i | −0.415607 | + | 0.0318304i | ||||
\(232\) | −4.78811 | −0.314355 | ||||||||
\(233\) | −5.45759 | + | 9.45282i | −0.357539 | + | 0.619275i | −0.987549 | − | 0.157312i | \(-0.949717\pi\) |
0.630010 | + | 0.776587i | \(0.283051\pi\) | |||||||
\(234\) | 3.74682 | − | 2.16323i | 0.244937 | − | 0.141415i | ||||
\(235\) | −21.6870 | + | 12.5210i | −1.41470 | + | 0.816778i | ||||
\(236\) | −10.6576 | − | 6.15319i | −0.693753 | − | 0.400539i | ||||
\(237\) | −8.80576 | −0.571995 | ||||||||
\(238\) | 1.19442 | + | 1.74574i | 0.0774227 | + | 0.113159i | ||||
\(239\) | 20.1227 | 1.30163 | 0.650816 | − | 0.759236i | \(-0.274427\pi\) | ||||
0.650816 | + | 0.759236i | \(0.274427\pi\) | |||||||
\(240\) | 2.63590 | + | 1.52184i | 0.170147 | + | 0.0982342i | ||||
\(241\) | −12.5697 | − | 21.7713i | −0.809683 | − | 1.40241i | −0.913084 | − | 0.407772i | \(-0.866306\pi\) |
0.103401 | − | 0.994640i | \(-0.467027\pi\) | |||||||
\(242\) | −2.63325 | − | 4.56093i | −0.169272 | − | 0.293188i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | −4.03891 | −0.258565 | ||||||||
\(245\) | −13.3384 | − | 16.6139i | −0.852161 | − | 1.06142i | ||||
\(246\) | −7.66774 | −0.488877 | ||||||||
\(247\) | −8.07630 | − | 4.66285i | −0.513883 | − | 0.296690i | ||||
\(248\) | 3.53448 | − | 2.04063i | 0.224439 | − | 0.129580i | ||||
\(249\) | −0.327095 | + | 0.188848i | −0.0207288 | + | 0.0119678i | ||||
\(250\) | 1.12013 | − | 1.94013i | 0.0708435 | − | 0.122704i | ||||
\(251\) | 7.54744 | 0.476390 | 0.238195 | − | 0.971217i | \(-0.423444\pi\) | ||||
0.238195 | + | 0.971217i | \(0.423444\pi\) | |||||||
\(252\) | 1.49399 | + | 2.18358i | 0.0941122 | + | 0.137552i | ||||
\(253\) | −10.5927 | + | 4.43460i | −0.665955 | + | 0.278801i | ||||
\(254\) | −4.50257 | + | 7.79869i | −0.282517 | + | 0.489333i | ||||
\(255\) | 2.10736 | − | 1.21669i | 0.131968 | − | 0.0761919i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −13.1071 | − | 7.56741i | −0.817601 | − | 0.472042i | 0.0319873 | − | 0.999488i | \(-0.489816\pi\) |
−0.849589 | + | 0.527446i | \(0.823150\pi\) | |||||||
\(258\) | 3.15309 | 0.196303 | ||||||||
\(259\) | −0.825818 | − | 10.7826i | −0.0513139 | − | 0.670001i | ||||
\(260\) | − | 13.1683i | − | 0.816665i | ||||||
\(261\) | −2.39406 | + | 4.14663i | −0.148188 | + | 0.256670i | ||||
\(262\) | −5.63863 | + | 3.25546i | −0.348356 | + | 0.201123i | ||||
\(263\) | 11.4148 | − | 6.59033i | 0.703866 | − | 0.406377i | −0.104920 | − | 0.994481i | \(-0.533459\pi\) |
0.808786 | + | 0.588104i | \(0.200125\pi\) | |||||||
\(264\) | 1.19724 | − | 2.07367i | 0.0736848 | − | 0.127626i | ||||
\(265\) | − | 33.3729i | − | 2.05008i | ||||||
\(266\) | 2.46599 | − | 5.14222i | 0.151199 | − | 0.315290i | ||||
\(267\) | − | 0.657881i | − | 0.0402617i | ||||||
\(268\) | −4.06092 | − | 2.34457i | −0.248060 | − | 0.143218i | ||||
\(269\) | 10.8165 | − | 6.24489i | 0.659492 | − | 0.380758i | −0.132591 | − | 0.991171i | \(-0.542330\pi\) |
0.792083 | + | 0.610413i | \(0.208996\pi\) | |||||||
\(270\) | 2.63590 | − | 1.52184i | 0.160416 | − | 0.0926161i | ||||
\(271\) | 2.91636 | + | 1.68376i | 0.177156 | + | 0.102281i | 0.585956 | − | 0.810343i | \(-0.300719\pi\) |
−0.408800 | + | 0.912624i | \(0.634053\pi\) | |||||||
\(272\) | −0.799485 | −0.0484759 | ||||||||
\(273\) | 4.94964 | − | 10.3213i | 0.299566 | − | 0.624672i | ||||
\(274\) | 9.04546i | 0.546456i | ||||||||
\(275\) | 8.84206 | + | 5.10496i | 0.533196 | + | 0.307841i | ||||
\(276\) | 3.81580 | + | 2.90512i | 0.229684 | + | 0.174867i | ||||
\(277\) | −0.782895 | − | 1.35601i | −0.0470396 | − | 0.0814750i | 0.841547 | − | 0.540184i | \(-0.181645\pi\) |
−0.888587 | + | 0.458709i | \(0.848312\pi\) | |||||||
\(278\) | 9.15111 | + | 5.28340i | 0.548847 | + | 0.316877i | ||||
\(279\) | − | 4.08126i | − | 0.244339i | ||||||
\(280\) | 8.02929 | − | 0.614946i | 0.479842 | − | 0.0367500i | ||||
\(281\) | − | 24.0099i | − | 1.43231i | −0.697940 | − | 0.716156i | \(-0.745900\pi\) | ||
0.697940 | − | 0.716156i | \(-0.254100\pi\) | |||||||
\(282\) | 4.11377 | − | 7.12526i | 0.244971 | − | 0.424303i | ||||
\(283\) | −13.8760 | − | 24.0340i | −0.824845 | − | 1.42867i | −0.902038 | − | 0.431657i | \(-0.857929\pi\) |
0.0771934 | − | 0.997016i | \(-0.475404\pi\) | |||||||
\(284\) | −3.10335 | − | 5.37517i | −0.184150 | − | 0.318958i | ||||
\(285\) | −5.68170 | − | 3.28033i | −0.336555 | − | 0.194310i | ||||
\(286\) | −10.3596 | −0.612574 | ||||||||
\(287\) | −16.7431 | + | 11.4555i | −0.988314 | + | 0.676196i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 8.18041 | − | 14.1689i | 0.481201 | − | 0.833464i | ||||
\(290\) | 7.28673 | + | 12.6210i | 0.427891 | + | 0.741130i | ||||
\(291\) | −1.79578 | + | 1.03680i | −0.105271 | + | 0.0607781i | ||||
\(292\) | −2.21583 | − | 1.27931i | −0.129672 | − | 0.0748661i | ||||
\(293\) | −23.9833 | −1.40112 | −0.700560 | − | 0.713594i | \(-0.747066\pi\) | ||||
−0.700560 | + | 0.713594i | \(0.747066\pi\) | |||||||
\(294\) | 6.52446 | + | 2.53602i | 0.380514 | + | 0.147904i | ||||
\(295\) | 37.4566i | 2.18081i | ||||||||
\(296\) | 3.53978 | + | 2.04369i | 0.205746 | + | 0.118787i | ||||
\(297\) | −1.19724 | − | 2.07367i | −0.0694707 | − | 0.120327i | ||||
\(298\) | −3.19186 | + | 1.84282i | −0.184899 | + | 0.106752i | ||||
\(299\) | 2.63052 | − | 20.5815i | 0.152127 | − | 1.19026i | ||||
\(300\) | − | 4.26396i | − | 0.246180i | ||||||
\(301\) | 6.88501 | − | 4.71067i | 0.396845 | − | 0.271518i | ||||
\(302\) | 24.4227 | 1.40537 | ||||||||
\(303\) | −8.70623 | + | 15.0796i | −0.500160 | + | 0.866302i | ||||
\(304\) | 1.07775 | + | 1.86672i | 0.0618134 | + | 0.107064i | ||||
\(305\) | 6.14657 | + | 10.6462i | 0.351952 | + | 0.609598i | ||||
\(306\) | −0.399743 | + | 0.692374i | −0.0228518 | + | 0.0395804i | ||||
\(307\) | 32.7277i | 1.86787i | 0.357444 | + | 0.933935i | \(0.383648\pi\) | ||||
−0.357444 | + | 0.933935i | \(0.616352\pi\) | |||||||
\(308\) | −0.483780 | − | 6.31668i | −0.0275659 | − | 0.359926i | ||||
\(309\) | 15.0360i | 0.855368i | ||||||||
\(310\) | −10.7578 | − | 6.21102i | −0.611002 | − | 0.352762i | ||||
\(311\) | −15.7420 | + | 9.08865i | −0.892647 | + | 0.515370i | −0.874807 | − | 0.484471i | \(-0.839012\pi\) |
−0.0178397 | + | 0.999841i | \(0.505679\pi\) | |||||||
\(312\) | 2.16323 | + | 3.74682i | 0.122469 | + | 0.212122i | ||||
\(313\) | 13.1187 | − | 22.7223i | 0.741514 | − | 1.28434i | −0.210292 | − | 0.977639i | \(-0.567441\pi\) |
0.951806 | − | 0.306701i | \(-0.0992253\pi\) | |||||||
\(314\) | −9.37104 | −0.528838 | ||||||||
\(315\) | 3.48209 | − | 7.26105i | 0.196193 | − | 0.409114i | ||||
\(316\) | − | 8.80576i | − | 0.495363i | ||||||
\(317\) | −11.2001 | + | 19.3992i | −0.629062 | + | 1.08957i | 0.358678 | + | 0.933461i | \(0.383228\pi\) |
−0.987740 | + | 0.156106i | \(0.950106\pi\) | |||||||
\(318\) | 5.48234 | + | 9.49569i | 0.307434 | + | 0.532492i | ||||
\(319\) | 9.92898 | − | 5.73250i | 0.555916 | − | 0.320958i | ||||
\(320\) | −1.52184 | + | 2.63590i | −0.0850733 | + | 0.147351i | ||||
\(321\) | 13.5893 | 0.758480 | ||||||||
\(322\) | 12.6723 | + | 0.642805i | 0.706199 | + | 0.0358221i | ||||
\(323\) | 1.72330 | 0.0958868 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −15.9763 | + | 9.22392i | −0.886205 | + | 0.511651i | ||||
\(326\) | −5.92061 | − | 10.2548i | −0.327912 | − | 0.567961i | ||||
\(327\) | 2.09774 | − | 3.63340i | 0.116006 | − | 0.200927i | ||||
\(328\) | − | 7.66774i | − | 0.423380i | ||||||
\(329\) | −1.66230 | − | 21.7045i | −0.0916454 | − | 1.19661i | ||||
\(330\) | −7.28799 | −0.401191 | ||||||||
\(331\) | 0.644942 | − | 1.11707i | 0.0354492 | − | 0.0613998i | −0.847756 | − | 0.530386i | \(-0.822047\pi\) |
0.883206 | + | 0.468986i | \(0.155380\pi\) | |||||||
\(332\) | −0.188848 | − | 0.327095i | −0.0103644 | − | 0.0179517i | ||||
\(333\) | 3.53978 | − | 2.04369i | 0.193979 | − | 0.111994i | ||||
\(334\) | 0.0905071 | + | 0.0522543i | 0.00495233 | + | 0.00285923i | ||||
\(335\) | 14.2722i | 0.779776i | ||||||||
\(336\) | −2.18358 | + | 1.49399i | −0.119124 | + | 0.0815036i | ||||
\(337\) | 5.47567i | 0.298279i | 0.988816 | + | 0.149139i | \(0.0476503\pi\) | ||||
−0.988816 | + | 0.149139i | \(0.952350\pi\) | |||||||
\(338\) | 2.85911 | − | 4.95212i | 0.155515 | − | 0.269360i | ||||
\(339\) | 6.00386 | + | 10.3990i | 0.326085 | + | 0.564796i | ||||
\(340\) | 1.21669 | + | 2.10736i | 0.0659841 | + | 0.114288i | ||||
\(341\) | −4.88623 | + | 8.46320i | −0.264604 | + | 0.458308i | ||||
\(342\) | 2.15551 | 0.116557 | ||||||||
\(343\) | 18.0354 | − | 4.20986i | 0.973822 | − | 0.227311i | ||||
\(344\) | 3.15309i | 0.170003i | ||||||||
\(345\) | 1.85058 | − | 14.4792i | 0.0996317 | − | 0.779532i | ||||
\(346\) | 3.02723 | − | 1.74777i | 0.162745 | − | 0.0939607i | ||||
\(347\) | 14.8210 | + | 25.6708i | 0.795635 | + | 1.37808i | 0.922435 | + | 0.386152i | \(0.126196\pi\) |
−0.126801 | + | 0.991928i | \(0.540471\pi\) | |||||||
\(348\) | −4.14663 | − | 2.39406i | −0.222283 | − | 0.128335i | ||||
\(349\) | − | 3.81383i | − | 0.204150i | −0.994777 | − | 0.102075i | \(-0.967452\pi\) | ||
0.994777 | − | 0.102075i | \(-0.0325481\pi\) | |||||||
\(350\) | −6.37029 | − | 9.31068i | −0.340506 | − | 0.497677i | ||||
\(351\) | 4.32646 | 0.230929 | ||||||||
\(352\) | 2.07367 | + | 1.19724i | 0.110527 | + | 0.0638129i | ||||
\(353\) | −5.74580 | + | 3.31734i | −0.305818 | + | 0.176564i | −0.645054 | − | 0.764137i | \(-0.723165\pi\) |
0.339235 | + | 0.940701i | \(0.389832\pi\) | |||||||
\(354\) | −6.15319 | − | 10.6576i | −0.327038 | − | 0.566447i | ||||
\(355\) | −9.44560 | + | 16.3603i | −0.501321 | + | 0.868313i | ||||
\(356\) | 0.657881 | 0.0348676 | ||||||||
\(357\) | 0.161528 | + | 2.10906i | 0.00854899 | + | 0.111623i | ||||
\(358\) | 20.2739 | 1.07151 | ||||||||
\(359\) | 23.6674 | + | 13.6644i | 1.24912 | + | 0.721178i | 0.970933 | − | 0.239350i | \(-0.0769342\pi\) |
0.278184 | + | 0.960528i | \(0.410268\pi\) | |||||||
\(360\) | 1.52184 | + | 2.63590i | 0.0802079 | + | 0.138924i | ||||
\(361\) | 7.17689 | + | 12.4307i | 0.377731 | + | 0.654250i | ||||
\(362\) | 2.64414 | − | 4.57978i | 0.138973 | − | 0.240708i | ||||
\(363\) | − | 5.26651i | − | 0.276420i | ||||||
\(364\) | 10.3213 | + | 4.94964i | 0.540981 | + | 0.259432i | ||||
\(365\) | 7.78762i | 0.407623i | ||||||||
\(366\) | −3.49780 | − | 2.01946i | −0.182833 | − | 0.105559i | ||||
\(367\) | 5.10915 | + | 8.84930i | 0.266695 | + | 0.461930i | 0.968006 | − | 0.250926i | \(-0.0807349\pi\) |
−0.701311 | + | 0.712855i | \(0.747402\pi\) | |||||||
\(368\) | −2.90512 | + | 3.81580i | −0.151440 | + | 0.198912i | ||||
\(369\) | −6.64046 | − | 3.83387i | −0.345688 | − | 0.199583i | ||||
\(370\) | − | 12.4407i | − | 0.646761i | ||||||
\(371\) | 26.1575 | + | 12.5440i | 1.35803 | + | 0.651254i | ||||
\(372\) | 4.08126 | 0.211604 | ||||||||
\(373\) | −8.16295 | − | 4.71288i | −0.422662 | − | 0.244024i | 0.273554 | − | 0.961857i | \(-0.411801\pi\) |
−0.696215 | + | 0.717833i | \(0.745134\pi\) | |||||||
\(374\) | 1.65787 | − | 0.957172i | 0.0857265 | − | 0.0494942i | ||||
\(375\) | 1.94013 | − | 1.12013i | 0.100188 | − | 0.0578435i | ||||
\(376\) | 7.12526 | + | 4.11377i | 0.367457 | + | 0.212151i | ||||
\(377\) | 20.7156i | 1.06691i | ||||||||
\(378\) | 0.202041 | + | 2.63803i | 0.0103918 | + | 0.135685i | ||||
\(379\) | 5.25144i | 0.269748i | 0.990863 | + | 0.134874i | \(0.0430630\pi\) | ||||
−0.990863 | + | 0.134874i | \(0.956937\pi\) | |||||||
\(380\) | 3.28033 | − | 5.68170i | 0.168278 | − | 0.291465i | ||||
\(381\) | −7.79869 | + | 4.50257i | −0.399539 | + | 0.230674i | ||||
\(382\) | −18.1430 | + | 10.4748i | −0.928275 | + | 0.535940i | ||||
\(383\) | 1.43797 | − | 2.49064i | 0.0734768 | − | 0.127266i | −0.826946 | − | 0.562281i | \(-0.809924\pi\) |
0.900423 | + | 0.435016i | \(0.143257\pi\) | |||||||
\(384\) | − | 1.00000i | − | 0.0510310i | ||||||
\(385\) | −15.9139 | + | 10.8882i | −0.811047 | + | 0.554912i | ||||
\(386\) | 12.5452 | 0.638536 | ||||||||
\(387\) | 2.73065 | + | 1.57654i | 0.138807 | + | 0.0801402i | ||||
\(388\) | −1.03680 | − | 1.79578i | −0.0526354 | − | 0.0911671i | ||||
\(389\) | −5.89494 | + | 3.40344i | −0.298885 | + | 0.172561i | −0.641942 | − | 0.766753i | \(-0.721871\pi\) |
0.343057 | + | 0.939315i | \(0.388538\pi\) | |||||||
\(390\) | 6.58416 | − | 11.4041i | 0.333402 | − | 0.577469i | ||||
\(391\) | 1.48066 | + | 3.53676i | 0.0748802 | + | 0.178862i | ||||
\(392\) | −2.53602 | + | 6.52446i | −0.128088 | + | 0.329535i | ||||
\(393\) | −6.51093 | −0.328433 | ||||||||
\(394\) | 10.3422 | − | 17.9132i | 0.521031 | − | 0.902453i | ||||
\(395\) | −23.2111 | + | 13.4009i | −1.16788 | + | 0.674274i | ||||
\(396\) | 2.07367 | − | 1.19724i | 0.104206 | − | 0.0601634i | ||||
\(397\) | 30.7424 | + | 17.7492i | 1.54292 | + | 0.890804i | 0.998653 | + | 0.0518916i | \(0.0165250\pi\) |
0.544266 | + | 0.838913i | \(0.316808\pi\) | |||||||
\(398\) | 19.0782 | 0.956302 | ||||||||
\(399\) | 4.70672 | − | 3.22030i | 0.235631 | − | 0.161216i | ||||
\(400\) | 4.26396 | 0.213198 | ||||||||
\(401\) | 19.3925 | + | 11.1963i | 0.968417 | + | 0.559116i | 0.898753 | − | 0.438455i | \(-0.144474\pi\) |
0.0696637 | + | 0.997571i | \(0.477807\pi\) | |||||||
\(402\) | −2.34457 | − | 4.06092i | −0.116937 | − | 0.202540i | ||||
\(403\) | −8.82870 | − | 15.2918i | −0.439789 | − | 0.761737i | ||||
\(404\) | −15.0796 | − | 8.70623i | −0.750240 | − | 0.433151i | ||||
\(405\) | 3.04368 | 0.151241 | ||||||||
\(406\) | −12.6312 | + | 0.967393i | −0.626874 | + | 0.0480109i | ||||
\(407\) | −9.78714 | −0.485130 | ||||||||
\(408\) | −0.692374 | − | 0.399743i | −0.0342776 | − | 0.0197902i | ||||
\(409\) | 5.06658 | − | 2.92519i | 0.250526 | − | 0.144641i | −0.369479 | − | 0.929239i | \(-0.620464\pi\) |
0.620005 | + | 0.784598i | \(0.287131\pi\) | |||||||
\(410\) | −20.2114 | + | 11.6691i | −0.998170 | + | 0.576293i | ||||
\(411\) | −4.52273 | + | 7.83359i | −0.223090 | + | 0.386403i | ||||
\(412\) | −15.0360 | −0.740771 | ||||||||
\(413\) | −29.3583 | − | 14.0790i | −1.44463 | − | 0.692782i | ||||
\(414\) | 1.85202 | + | 4.42380i | 0.0910217 | + | 0.217418i | ||||
\(415\) | −0.574793 | + | 0.995571i | −0.0282155 | + | 0.0488707i | ||||
\(416\) | −3.74682 | + | 2.16323i | −0.183703 | + | 0.106061i | ||||
\(417\) | 5.28340 | + | 9.15111i | 0.258729 | + | 0.448132i | ||||
\(418\) | −4.46982 | − | 2.58065i | −0.218626 | − | 0.126224i | ||||
\(419\) | 10.4963 | 0.512776 | 0.256388 | − | 0.966574i | \(-0.417467\pi\) | ||||
0.256388 | + | 0.966574i | \(0.417467\pi\) | |||||||
\(420\) | 7.26105 | + | 3.48209i | 0.354303 | + | 0.169909i | ||||
\(421\) | 14.1358i | 0.688937i | 0.938798 | + | 0.344469i | \(0.111941\pi\) | ||||
−0.938798 | + | 0.344469i | \(0.888059\pi\) | |||||||
\(422\) | −10.3931 | + | 18.0014i | −0.505929 | + | 0.876294i | ||||
\(423\) | 7.12526 | − | 4.11377i | 0.346442 | − | 0.200018i | ||||
\(424\) | −9.49569 | + | 5.48234i | −0.461151 | + | 0.266246i | ||||
\(425\) | 1.70449 | − | 2.95226i | 0.0826797 | − | 0.143205i | ||||
\(426\) | − | 6.20671i | − | 0.300716i | ||||||
\(427\) | −10.6548 | + | 0.816024i | −0.515620 | + | 0.0394902i | ||||
\(428\) | 13.5893i | 0.656863i | ||||||||
\(429\) | −8.97165 | − | 5.17979i | −0.433156 | − | 0.250082i | ||||
\(430\) | 8.31122 | − | 4.79849i | 0.400803 | − | 0.231404i | ||||
\(431\) | −5.07838 | + | 2.93200i | −0.244617 | + | 0.141230i | −0.617297 | − | 0.786730i | \(-0.711772\pi\) |
0.372680 | + | 0.927960i | \(0.378439\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | 15.8861 | 0.763438 | 0.381719 | − | 0.924278i | \(-0.375332\pi\) | ||||
0.381719 | + | 0.924278i | \(0.375332\pi\) | |||||||
\(434\) | 8.91175 | − | 6.09734i | 0.427778 | − | 0.292682i | ||||
\(435\) | 14.5735i | 0.698744i | ||||||||
\(436\) | 3.63340 | + | 2.09774i | 0.174008 | + | 0.100464i | ||||
\(437\) | 6.26200 | − | 8.22498i | 0.299552 | − | 0.393454i | ||||
\(438\) | −1.27931 | − | 2.21583i | −0.0611279 | − | 0.105877i | ||||
\(439\) | 17.8490 | + | 10.3051i | 0.851888 | + | 0.491838i | 0.861287 | − | 0.508118i | \(-0.169659\pi\) |
−0.00939944 | + | 0.999956i | \(0.502992\pi\) | |||||||
\(440\) | − | 7.28799i | − | 0.347441i | ||||||
\(441\) | 4.38234 | + | 5.45849i | 0.208683 | + | 0.259928i | ||||
\(442\) | 3.45894i | 0.164525i | ||||||||
\(443\) | 5.21749 | − | 9.03695i | 0.247890 | − | 0.429358i | −0.715050 | − | 0.699073i | \(-0.753596\pi\) |
0.962940 | + | 0.269715i | \(0.0869294\pi\) | |||||||
\(444\) | 2.04369 | + | 3.53978i | 0.0969895 | + | 0.167991i | ||||
\(445\) | −1.00119 | − | 1.73411i | −0.0474609 | − | 0.0822047i | ||||
\(446\) | −13.1994 | − | 7.62069i | −0.625011 | − | 0.360850i | ||||
\(447\) | −3.68564 | −0.174325 | ||||||||
\(448\) | −1.49399 | − | 2.18358i | −0.0705842 | − | 0.103164i | ||||
\(449\) | −7.05546 | −0.332968 | −0.166484 | − | 0.986044i | \(-0.553241\pi\) | ||||
−0.166484 | + | 0.986044i | \(0.553241\pi\) | |||||||
\(450\) | 2.13198 | − | 3.69270i | 0.100502 | − | 0.174075i | ||||
\(451\) | 9.18009 | + | 15.9004i | 0.432274 | + | 0.748720i | ||||
\(452\) | −10.3990 | + | 6.00386i | −0.489127 | + | 0.282398i | ||||
\(453\) | 21.1507 | + | 12.2114i | 0.993747 | + | 0.573740i | ||||
\(454\) | 9.26324 | 0.434746 | ||||||||
\(455\) | −2.66054 | − | 34.7384i | −0.124728 | − | 1.62856i | ||||
\(456\) | 2.15551i | 0.100941i | ||||||||
\(457\) | 17.6738 | + | 10.2040i | 0.826746 | + | 0.477322i | 0.852737 | − | 0.522340i | \(-0.174941\pi\) |
−0.0259910 | + | 0.999662i | \(0.508274\pi\) | |||||||
\(458\) | 7.25789 | + | 12.5710i | 0.339139 | + | 0.587406i | ||||
\(459\) | −0.692374 | + | 0.399743i | −0.0323173 | + | 0.0186584i | ||||
\(460\) | 14.4792 | + | 1.85058i | 0.675095 | + | 0.0862836i | ||||
\(461\) | 19.2906i | 0.898452i | 0.893418 | + | 0.449226i | \(0.148300\pi\) | ||||
−0.893418 | + | 0.449226i | \(0.851700\pi\) | |||||||
\(462\) | 2.73937 | − | 5.71229i | 0.127447 | − | 0.265760i | ||||
\(463\) | −16.9180 | −0.786248 | −0.393124 | − | 0.919486i | \(-0.628606\pi\) | ||||
−0.393124 | + | 0.919486i | \(0.628606\pi\) | |||||||
\(464\) | 2.39406 | − | 4.14663i | 0.111141 | − | 0.192502i | ||||
\(465\) | −6.21102 | − | 10.7578i | −0.288029 | − | 0.498881i | ||||
\(466\) | −5.45759 | − | 9.45282i | −0.252818 | − | 0.437894i | ||||
\(467\) | −13.4093 | + | 23.2256i | −0.620508 | + | 1.07475i | 0.368883 | + | 0.929476i | \(0.379740\pi\) |
−0.989391 | + | 0.145276i | \(0.953593\pi\) | |||||||
\(468\) | 4.32646i | 0.199990i | ||||||||
\(469\) | −11.1865 | − | 5.36457i | −0.516545 | − | 0.247713i | ||||
\(470\) | − | 25.0420i | − | 1.15510i | ||||||
\(471\) | −8.11555 | − | 4.68552i | −0.373945 | − | 0.215897i | ||||
\(472\) | 10.6576 | − | 6.15319i | 0.490558 | − | 0.283224i | ||||
\(473\) | −3.77499 | − | 6.53847i | −0.173574 | − | 0.300639i | ||||
\(474\) | 4.40288 | − | 7.62601i | 0.202231 | − | 0.350274i | ||||
\(475\) | −9.19100 | −0.421712 | ||||||||
\(476\) | −2.10906 | + | 0.161528i | −0.0966687 | + | 0.00740364i | ||||
\(477\) | 10.9647i | 0.502038i | ||||||||
\(478\) | −10.0614 | + | 17.4268i | −0.460196 | + | 0.797083i | ||||
\(479\) | 8.04405 | + | 13.9327i | 0.367542 | + | 0.636601i | 0.989181 | − | 0.146703i | \(-0.0468661\pi\) |
−0.621639 | + | 0.783304i | \(0.713533\pi\) | |||||||
\(480\) | −2.63590 | + | 1.52184i | −0.120312 | + | 0.0694621i | ||||
\(481\) | 8.84195 | − | 15.3147i | 0.403158 | − | 0.698291i | ||||
\(482\) | 25.1393 | 1.14506 | ||||||||
\(483\) | 10.6531 | + | 6.89283i | 0.484734 | + | 0.313635i | ||||
\(484\) | 5.26651 | 0.239387 | ||||||||
\(485\) | −3.15567 | + | 5.46578i | −0.143292 | + | 0.248188i | ||||
\(486\) | −0.866025 | + | 0.500000i | −0.0392837 | + | 0.0226805i | ||||
\(487\) | 13.3255 | + | 23.0804i | 0.603834 | + | 1.04587i | 0.992235 | + | 0.124381i | \(0.0396944\pi\) |
−0.388401 | + | 0.921491i | \(0.626972\pi\) | |||||||
\(488\) | 2.01946 | − | 3.49780i | 0.0914165 | − | 0.158338i | ||||
\(489\) | − | 11.8412i | − | 0.535478i | ||||||
\(490\) | 21.0572 | − | 3.24449i | 0.951269 | − | 0.146571i | ||||
\(491\) | 22.4635 | 1.01376 | 0.506882 | − | 0.862015i | \(-0.330798\pi\) | ||||
0.506882 | + | 0.862015i | \(0.330798\pi\) | |||||||
\(492\) | 3.83387 | − | 6.64046i | 0.172844 | − | 0.299375i | ||||
\(493\) | −1.91401 | − | 3.31517i | −0.0862028 | − | 0.149308i | ||||
\(494\) | 8.07630 | − | 4.66285i | 0.363370 | − | 0.209792i | ||||
\(495\) | −6.31159 | − | 3.64400i | −0.283685 | − | 0.163785i | ||||
\(496\) | 4.08126i | 0.183254i | ||||||||
\(497\) | −9.27273 | − | 13.5528i | −0.415939 | − | 0.607927i | ||||
\(498\) | − | 0.377697i | − | 0.0169250i | ||||||
\(499\) | −2.37249 | + | 4.10928i | −0.106207 | + | 0.183956i | −0.914231 | − | 0.405194i | \(-0.867204\pi\) |
0.808024 | + | 0.589150i | \(0.200537\pi\) | |||||||
\(500\) | 1.12013 | + | 1.94013i | 0.0500939 | + | 0.0867652i | ||||
\(501\) | 0.0522543 | + | 0.0905071i | 0.00233455 | + | 0.00404356i | ||||
\(502\) | −3.77372 | + | 6.53628i | −0.168429 | + | 0.291728i | ||||
\(503\) | −40.9737 | −1.82693 | −0.913463 | − | 0.406922i | \(-0.866602\pi\) | ||||
−0.913463 | + | 0.406922i | \(0.866602\pi\) | |||||||
\(504\) | −2.63803 | + | 0.202041i | −0.117507 | + | 0.00899960i | ||||
\(505\) | 52.9979i | 2.35837i | ||||||||
\(506\) | 1.45586 | − | 11.3908i | 0.0647207 | − | 0.506384i | ||||
\(507\) | 4.95212 | − | 2.85911i | 0.219931 | − | 0.126977i | ||||
\(508\) | −4.50257 | − | 7.79869i | −0.199769 | − | 0.346011i | ||||
\(509\) | −16.3212 | − | 9.42303i | −0.723423 | − | 0.417668i | 0.0925884 | − | 0.995704i | \(-0.470486\pi\) |
−0.816011 | + | 0.578036i | \(0.803819\pi\) | |||||||
\(510\) | 2.43337i | 0.107752i | ||||||||
\(511\) | −6.10390 | − | 2.92717i | −0.270021 | − | 0.129490i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.86672 | + | 1.07775i | 0.0824179 | + | 0.0475840i | ||||
\(514\) | 13.1071 | − | 7.56741i | 0.578131 | − | 0.333784i | ||||
\(515\) | 22.8824 | + | 39.6334i | 1.00832 | + | 1.74646i | ||||
\(516\) | −1.57654 | + | 2.73065i | −0.0694035 | + | 0.120210i | ||||
\(517\) | −19.7006 | −0.866431 | ||||||||
\(518\) | 9.75095 | + | 4.67614i | 0.428432 | + | 0.205458i | ||||
\(519\) | 3.49554 | 0.153437 | ||||||||
\(520\) | 11.4041 | + | 6.58416i | 0.500103 | + | 0.288735i | ||||
\(521\) | 1.23201 | + | 2.13390i | 0.0539751 | + | 0.0934877i | 0.891751 | − | 0.452527i | \(-0.149477\pi\) |
−0.837775 | + | 0.546015i | \(0.816144\pi\) | |||||||
\(522\) | −2.39406 | − | 4.14663i | −0.104785 | − | 0.181493i | ||||
\(523\) | 10.2857 | − | 17.8154i | 0.449764 | − | 0.779014i | −0.548606 | − | 0.836081i | \(-0.684841\pi\) |
0.998370 | + | 0.0570665i | \(0.0181747\pi\) | |||||||
\(524\) | − | 6.51093i | − | 0.284431i | ||||||
\(525\) | −0.861493 | − | 11.2484i | −0.0375986 | − | 0.490922i | ||||
\(526\) | 13.1807i | 0.574704i | ||||||||
\(527\) | 2.82576 | + | 1.63145i | 0.123092 | + | 0.0710673i | ||||
\(528\) | 1.19724 | + | 2.07367i | 0.0521030 | + | 0.0902450i | ||||
\(529\) | 22.2607 | + | 5.78474i | 0.967855 | + | 0.251511i | ||||
\(530\) | 28.9018 | + | 16.6865i | 1.25541 | + | 0.724813i | ||||
\(531\) | − | 12.3064i | − | 0.534051i | ||||||
\(532\) | 3.22030 | + | 4.70672i | 0.139618 | + | 0.204062i | ||||
\(533\) | −33.1741 | −1.43693 | ||||||||
\(534\) | 0.569742 | + | 0.328941i | 0.0246551 | + | 0.0142347i | ||||
\(535\) | 35.8200 | − | 20.6807i | 1.54863 | − | 0.894104i | ||||
\(536\) | 4.06092 | − | 2.34457i | 0.175405 | − | 0.101270i | ||||
\(537\) | 17.5577 | + | 10.1370i | 0.757672 | + | 0.437442i | ||||
\(538\) | 12.4898i | 0.538473i | ||||||||
\(539\) | −2.55245 | − | 16.5658i | −0.109942 | − | 0.713540i | ||||
\(540\) | 3.04368i | 0.130979i | ||||||||
\(541\) | −8.91227 | + | 15.4365i | −0.383168 | + | 0.663667i | −0.991513 | − | 0.130006i | \(-0.958500\pi\) |
0.608345 | + | 0.793673i | \(0.291834\pi\) | |||||||
\(542\) | −2.91636 | + | 1.68376i | −0.125268 | + | 0.0723236i | ||||
\(543\) | 4.57978 | − | 2.64414i | 0.196537 | − | 0.113471i | ||||
\(544\) | 0.399743 | − | 0.692374i | 0.0171388 | − | 0.0296853i | ||||
\(545\) | − | 12.7697i | − | 0.546994i | ||||||
\(546\) | 6.46366 | + | 9.44715i | 0.276619 | + | 0.404301i | ||||
\(547\) | −1.99506 | −0.0853026 | −0.0426513 | − | 0.999090i | \(-0.513580\pi\) | ||||
−0.0426513 | + | 0.999090i | \(0.513580\pi\) | |||||||
\(548\) | −7.83359 | − | 4.52273i | −0.334635 | − | 0.193201i | ||||
\(549\) | −2.01946 | − | 3.49780i | −0.0861883 | − | 0.149283i | ||||
\(550\) | −8.84206 | + | 5.10496i | −0.377027 | + | 0.217676i | ||||
\(551\) | −5.16041 | + | 8.93809i | −0.219841 | + | 0.380775i | ||||
\(552\) | −4.42380 | + | 1.85202i | −0.188290 | + | 0.0788271i | ||||
\(553\) | −1.77912 | − | 23.2298i | −0.0756559 | − | 0.987832i | ||||
\(554\) | 1.56579 | 0.0665241 | ||||||||
\(555\) | 6.22034 | − | 10.7740i | 0.264039 | − | 0.457329i | ||||
\(556\) | −9.15111 | + | 5.28340i | −0.388094 | + | 0.224066i | ||||
\(557\) | 0.0975129 | − | 0.0562991i | 0.00413175 | − | 0.00238547i | −0.497933 | − | 0.867216i | \(-0.665907\pi\) |
0.502064 | + | 0.864830i | \(0.332574\pi\) | |||||||
\(558\) | 3.53448 | + | 2.04063i | 0.149626 | + | 0.0863868i | ||||
\(559\) | 13.6417 | 0.576982 | ||||||||
\(560\) | −3.48209 | + | 7.26105i | −0.147145 | + | 0.306835i | ||||
\(561\) | 1.91434 | 0.0808237 | ||||||||
\(562\) | 20.7932 | + | 12.0050i | 0.877108 | + | 0.506399i | ||||
\(563\) | −14.9248 | − | 25.8506i | −0.629007 | − | 1.08947i | −0.987751 | − | 0.156036i | \(-0.950128\pi\) |
0.358745 | − | 0.933436i | \(-0.383205\pi\) | |||||||
\(564\) | 4.11377 | + | 7.12526i | 0.173221 | + | 0.300027i | ||||
\(565\) | 31.6512 | + | 18.2738i | 1.33157 | + | 0.768785i | ||||
\(566\) | 27.7521 | 1.16651 | ||||||||
\(567\) | −1.14404 | + | 2.38562i | −0.0480452 | + | 0.100187i | ||||
\(568\) | 6.20671 | 0.260428 | ||||||||
\(569\) | −30.8972 | − | 17.8385i | −1.29528 | − | 0.747829i | −0.315693 | − | 0.948861i | \(-0.602237\pi\) |
−0.979585 | + | 0.201032i | \(0.935570\pi\) | |||||||
\(570\) | 5.68170 | − | 3.28033i | 0.237980 | − | 0.137398i | ||||
\(571\) | 29.9445 | − | 17.2885i | 1.25314 | − | 0.723499i | 0.281406 | − | 0.959589i | \(-0.409199\pi\) |
0.971731 | + | 0.236089i | \(0.0758657\pi\) | |||||||
\(572\) | 5.17979 | − | 8.97165i | 0.216578 | − | 0.375124i | ||||
\(573\) | −20.9497 | −0.875186 | ||||||||
\(574\) | −1.54919 | − | 20.2277i | −0.0646621 | − | 0.844288i | ||||
\(575\) | −7.89693 | − | 18.8629i | −0.329325 | − | 0.786638i | ||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | 16.5610 | − | 9.56149i | 0.689443 | − | 0.398050i | −0.113961 | − | 0.993485i | \(-0.536354\pi\) |
0.803403 | + | 0.595435i | \(0.203020\pi\) | |||||||
\(578\) | 8.18041 | + | 14.1689i | 0.340260 | + | 0.589348i | ||||
\(579\) | 10.8645 | + | 6.27262i | 0.451513 | + | 0.260681i | ||||
\(580\) | −14.5735 | −0.605130 | ||||||||
\(581\) | −0.564273 | − | 0.824730i | −0.0234100 | − | 0.0342156i | ||||
\(582\) | − | 2.07359i | − | 0.0859532i | ||||||
\(583\) | 13.1273 | − | 22.7372i | 0.543677 | − | 0.941677i | ||||
\(584\) | 2.21583 | − | 1.27931i | 0.0916919 | − | 0.0529383i | ||||
\(585\) | 11.4041 | − | 6.58416i | 0.471502 | − | 0.272222i | ||||
\(586\) | 11.9916 | − | 20.7701i | 0.495370 | − | 0.858007i | ||||
\(587\) | 38.6271i | 1.59431i | 0.603774 | + | 0.797155i | \(0.293663\pi\) | ||||
−0.603774 | + | 0.797155i | \(0.706337\pi\) | |||||||
\(588\) | −5.45849 | + | 4.38234i | −0.225104 | + | 0.180725i | ||||
\(589\) | − | 8.79719i | − | 0.362482i | ||||||
\(590\) | −32.4384 | − | 18.7283i | −1.33547 | − | 0.771032i | ||||
\(591\) | 17.9132 | − | 10.3422i | 0.736849 | − | 0.425420i | ||||
\(592\) | −3.53978 | + | 2.04369i | −0.145484 | + | 0.0839953i | ||||
\(593\) | −0.782667 | − | 0.451873i | −0.0321403 | − | 0.0185562i | 0.483844 | − | 0.875154i | \(-0.339240\pi\) |
−0.515984 | + | 0.856598i | \(0.672574\pi\) | |||||||
\(594\) | 2.39447 | 0.0982463 | ||||||||
\(595\) | 3.63542 | + | 5.31346i | 0.149038 | + | 0.217831i | ||||
\(596\) | − | 3.68564i | − | 0.150970i | ||||||
\(597\) | 16.5222 | + | 9.53909i | 0.676208 | + | 0.390409i | ||||
\(598\) | 16.5089 | + | 12.5689i | 0.675098 | + | 0.513979i | ||||
\(599\) | −13.8142 | − | 23.9269i | −0.564434 | − | 0.977628i | −0.997102 | − | 0.0760748i | \(-0.975761\pi\) |
0.432668 | − | 0.901553i | \(-0.357572\pi\) | |||||||
\(600\) | 3.69270 | + | 2.13198i | 0.150754 | + | 0.0870377i | ||||
\(601\) | − | 43.6360i | − | 1.77995i | −0.456009 | − | 0.889975i | \(-0.650721\pi\) | ||
0.456009 | − | 0.889975i | \(-0.349279\pi\) | |||||||
\(602\) | 0.637052 | + | 8.31793i | 0.0259643 | + | 0.339013i | ||||
\(603\) | − | 4.68915i | − | 0.190957i | ||||||
\(604\) | −12.2114 | + | 21.1507i | −0.496874 | + | 0.860610i | ||||
\(605\) | −8.01477 | − | 13.8820i | −0.325847 | − | 0.564383i | ||||
\(606\) | −8.70623 | − | 15.0796i | −0.353666 | − | 0.612568i | ||||
\(607\) | 4.23392 | + | 2.44445i | 0.171849 | + | 0.0992173i | 0.583458 | − | 0.812144i | \(-0.301699\pi\) |
−0.411608 | + | 0.911361i | \(0.635033\pi\) | |||||||
\(608\) | −2.15551 | −0.0874174 | ||||||||
\(609\) | −11.4226 | − | 5.47779i | −0.462867 | − | 0.221971i | ||||
\(610\) | −12.2931 | −0.497735 | ||||||||
\(611\) | 17.7980 | − | 30.8271i | 0.720032 | − | 1.24713i | ||||
\(612\) | −0.399743 | − | 0.692374i | −0.0161586 | − | 0.0279876i | ||||
\(613\) | −6.30762 | + | 3.64171i | −0.254762 | + | 0.147087i | −0.621943 | − | 0.783063i | \(-0.713656\pi\) |
0.367181 | + | 0.930150i | \(0.380323\pi\) | |||||||
\(614\) | −28.3430 | − | 16.3639i | −1.14383 | − | 0.660392i | ||||
\(615\) | −23.3381 | −0.941083 | ||||||||
\(616\) | 5.71229 | + | 2.73937i | 0.230155 | + | 0.110372i | ||||
\(617\) | 33.9874i | 1.36828i | 0.729350 | + | 0.684141i | \(0.239823\pi\) | ||||
−0.729350 | + | 0.684141i | \(0.760177\pi\) | |||||||
\(618\) | −13.0216 | − | 7.51800i | −0.523804 | − | 0.302418i | ||||
\(619\) | −8.69677 | − | 15.0632i | −0.349553 | − | 0.605443i | 0.636617 | − | 0.771180i | \(-0.280333\pi\) |
−0.986170 | + | 0.165737i | \(0.947000\pi\) | |||||||
\(620\) | 10.7578 | − | 6.21102i | 0.432044 | − | 0.249440i | ||||
\(621\) | −0.608007 | + | 4.75713i | −0.0243985 | + | 0.190897i | ||||
\(622\) | − | 18.1773i | − | 0.728843i | ||||||
\(623\) | 1.73551 | − | 0.132919i | 0.0695316 | − | 0.00532527i | ||||
\(624\) | −4.32646 | −0.173197 | ||||||||
\(625\) | 14.0692 | − | 24.3686i | 0.562769 | − | 0.974744i | ||||
\(626\) | 13.1187 | + | 22.7223i | 0.524330 | + | 0.908166i | ||||
\(627\) | −2.58065 | − | 4.46982i | −0.103061 | − | 0.178507i | ||||
\(628\) | 4.68552 | − | 8.11555i | 0.186973 | − | 0.323846i | ||||
\(629\) | 3.26781i | 0.130296i | ||||||||
\(630\) | 4.54721 | + | 6.64610i | 0.181165 | + | 0.264787i | ||||
\(631\) | − | 28.9833i | − | 1.15381i | −0.816812 | − | 0.576903i | \(-0.804261\pi\) | ||
0.816812 | − | 0.576903i | \(-0.195739\pi\) | |||||||
\(632\) | 7.62601 | + | 4.40288i | 0.303346 | + | 0.175137i | ||||
\(633\) | −18.0014 | + | 10.3931i | −0.715491 | + | 0.413089i | ||||
\(634\) | −11.2001 | − | 19.3992i | −0.444814 | − | 0.770441i | ||||
\(635\) | −13.7044 | + | 23.7367i | −0.543841 | + | 0.941961i | ||||
\(636\) | −10.9647 | −0.434778 | ||||||||
\(637\) | 28.2278 | + | 10.9720i | 1.11843 | + | 0.434725i | ||||
\(638\) | 11.4650i | 0.453904i | ||||||||
\(639\) | 3.10335 | − | 5.37517i | 0.122767 | − | 0.212638i | ||||
\(640\) | −1.52184 | − | 2.63590i | −0.0601559 | − | 0.104193i | ||||
\(641\) | −16.3277 | + | 9.42678i | −0.644904 | + | 0.372335i | −0.786501 | − | 0.617589i | \(-0.788110\pi\) |
0.141597 | + | 0.989924i | \(0.454776\pi\) | |||||||
\(642\) | −6.79464 | + | 11.7687i | −0.268163 | + | 0.464472i | ||||
\(643\) | 48.6652 | 1.91917 | 0.959584 | − | 0.281422i | \(-0.0908062\pi\) | ||||
0.959584 | + | 0.281422i | \(0.0908062\pi\) | |||||||
\(644\) | −6.89283 | + | 10.6531i | −0.271615 | + | 0.419792i | ||||
\(645\) | 9.59698 | 0.377881 | ||||||||
\(646\) | −0.861648 | + | 1.49242i | −0.0339011 | + | 0.0587184i | ||||
\(647\) | 11.4722 | − | 6.62349i | 0.451020 | − | 0.260396i | −0.257241 | − | 0.966347i | \(-0.582813\pi\) |
0.708261 | + | 0.705951i | \(0.249480\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −14.7336 | + | 25.5194i | −0.578346 | + | 1.00172i | ||||
\(650\) | − | 18.4478i | − | 0.723584i | ||||||
\(651\) | 10.7665 | − | 0.824580i | 0.421971 | − | 0.0323178i | ||||
\(652\) | 11.8412 | 0.463738 | ||||||||
\(653\) | −14.8034 | + | 25.6402i | −0.579300 | + | 1.00338i | 0.416259 | + | 0.909246i | \(0.363341\pi\) |
−0.995560 | + | 0.0941318i | \(0.969992\pi\) | |||||||
\(654\) | 2.09774 | + | 3.63340i | 0.0820283 | + | 0.142077i | ||||
\(655\) | −17.1622 | + | 9.90857i | −0.670581 | + | 0.387160i | ||||
\(656\) | 6.64046 | + | 3.83387i | 0.259266 | + | 0.149687i | ||||
\(657\) | − | 2.55863i | − | 0.0998215i | ||||||
\(658\) | 19.6278 | + | 9.41264i | 0.765170 | + | 0.366943i | ||||
\(659\) | − | 39.8104i | − | 1.55079i | −0.631474 | − | 0.775397i | \(-0.717550\pi\) | ||
0.631474 | − | 0.775397i | \(-0.282450\pi\) | |||||||
\(660\) | 3.64400 | − | 6.31159i | 0.141842 | − | 0.245678i | ||||
\(661\) | 14.0002 | + | 24.2490i | 0.544544 | + | 0.943178i | 0.998635 | + | 0.0522226i | \(0.0166305\pi\) |
−0.454092 | + | 0.890955i | \(0.650036\pi\) | |||||||
\(662\) | 0.644942 | + | 1.11707i | 0.0250664 | + | 0.0434162i | ||||
\(663\) | −1.72947 | + | 2.99553i | −0.0671670 | + | 0.116337i | ||||
\(664\) | 0.377697 | 0.0146575 | ||||||||
\(665\) | 7.50567 | − | 15.6512i | 0.291057 | − | 0.606929i | ||||
\(666\) | 4.08739i | 0.158383i | ||||||||
\(667\) | −22.7777 | − | 2.91121i | −0.881956 | − | 0.112722i | ||||
\(668\) | −0.0905071 | + | 0.0522543i | −0.00350183 | + | 0.00202178i | ||||
\(669\) | −7.62069 | − | 13.1994i | −0.294633 | − | 0.510319i | ||||
\(670\) | −12.3601 | − | 7.13612i | −0.477513 | − | 0.275692i | ||||
\(671\) | 9.67106i | 0.373347i | ||||||||
\(672\) | −0.202041 | − | 2.63803i | −0.00779388 | − | 0.101764i | ||||
\(673\) | −25.5988 | −0.986760 | −0.493380 | − | 0.869814i | \(-0.664239\pi\) | ||||
−0.493380 | + | 0.869814i | \(0.664239\pi\) | |||||||
\(674\) | −4.74207 | − | 2.73784i | −0.182658 | − | 0.105458i | ||||
\(675\) | 3.69270 | − | 2.13198i | 0.142132 | − | 0.0820599i | ||||
\(676\) | 2.85911 | + | 4.95212i | 0.109966 | + | 0.190466i | ||||
\(677\) | −23.6160 | + | 40.9042i | −0.907638 | + | 1.57208i | −0.0903020 | + | 0.995914i | \(0.528783\pi\) |
−0.817336 | + | 0.576161i | \(0.804550\pi\) | |||||||
\(678\) | −12.0077 | −0.461154 | ||||||||
\(679\) | −3.09792 | − | 4.52785i | −0.118887 | − | 0.173763i | ||||
\(680\) | −2.43337 | −0.0933156 | ||||||||
\(681\) | 8.02220 | + | 4.63162i | 0.307412 | + | 0.177484i | ||||
\(682\) | −4.88623 | − | 8.46320i | −0.187103 | − | 0.324073i | ||||
\(683\) | −22.2497 | − | 38.5377i | −0.851362 | − | 1.47460i | −0.879979 | − | 0.475013i | \(-0.842443\pi\) |
0.0286165 | − | 0.999590i | \(-0.490890\pi\) | |||||||
\(684\) | −1.07775 | + | 1.86672i | −0.0412089 | + | 0.0713760i | ||||
\(685\) | 27.5314i | 1.05192i | ||||||||
\(686\) | −5.37187 | + | 17.7241i | −0.205099 | + | 0.676708i | ||||
\(687\) | 14.5158i | 0.553811i | ||||||||
\(688\) | −2.73065 | − | 1.57654i | −0.104105 | − | 0.0601052i | ||||
\(689\) | 23.7191 | + | 41.0827i | 0.903625 | + | 1.56513i | ||||
\(690\) | 11.6140 | + | 8.84223i | 0.442139 | + | 0.336618i | ||||
\(691\) | −29.3090 | − | 16.9215i | −1.11497 | − | 0.643726i | −0.174855 | − | 0.984594i | \(-0.555946\pi\) |
−0.940111 | + | 0.340869i | \(0.889279\pi\) | |||||||
\(692\) | 3.49554i | 0.132880i | ||||||||
\(693\) | 5.22851 | − | 3.57730i | 0.198615 | − | 0.135891i | ||||
\(694\) | −29.6421 | −1.12520 | ||||||||
\(695\) | 27.8530 | + | 16.0809i | 1.05653 | + | 0.609985i | ||||
\(696\) | 4.14663 | − | 2.39406i | 0.157177 | − | 0.0907465i | ||||
\(697\) | 5.30895 | − | 3.06512i | 0.201091 | − | 0.116100i | ||||
\(698\) | 3.30287 | + | 1.90691i | 0.125016 | + | 0.0721778i | ||||
\(699\) | − | 10.9152i | − | 0.412850i | ||||||
\(700\) | 11.2484 | − | 0.861493i | 0.425151 | − | 0.0325614i | ||||
\(701\) | − | 26.6557i | − | 1.00677i | −0.864062 | − | 0.503386i | \(-0.832087\pi\) | ||
0.864062 | − | 0.503386i | \(-0.167913\pi\) | |||||||
\(702\) | −2.16323 | + | 3.74682i | −0.0816458 | + | 0.141415i | ||||
\(703\) | 7.63003 | − | 4.40520i | 0.287772 | − | 0.166145i | ||||
\(704\) | −2.07367 | + | 1.19724i | −0.0781545 | + | 0.0451225i | ||||
\(705\) | 12.5210 | − | 21.6870i | 0.471567 | − | 0.816778i | ||||
\(706\) | − | 6.63468i | − | 0.249700i | ||||||
\(707\) | −41.5395 | − | 19.9206i | −1.56225 | − | 0.749190i | ||||
\(708\) | 12.3064 | 0.462502 | ||||||||
\(709\) | 27.0586 | + | 15.6223i | 1.01621 | + | 0.586708i | 0.913003 | − | 0.407952i | \(-0.133757\pi\) |
0.103205 | + | 0.994660i | \(0.467090\pi\) | |||||||
\(710\) | −9.44560 | − | 16.3603i | −0.354487 | − | 0.613990i | ||||
\(711\) | 7.62601 | − | 4.40288i | 0.285998 | − | 0.165121i | ||||
\(712\) | −0.328941 | + | 0.569742i | −0.0123276 | + | 0.0213520i | ||||
\(713\) | 18.0547 | − | 7.55857i | 0.676154 | − | 0.283071i | ||||
\(714\) | −1.90727 | − | 0.914643i | −0.0713776 | − | 0.0342297i | ||||
\(715\) | −31.5312 | −1.17920 | ||||||||
\(716\) | −10.1370 | + | 17.5577i | −0.378836 | + | 0.656163i | ||||
\(717\) | −17.4268 | + | 10.0614i | −0.650816 | + | 0.375749i | ||||
\(718\) | −23.6674 | + | 13.6644i | −0.883259 | + | 0.509950i | ||||
\(719\) | 2.92333 | + | 1.68779i | 0.109022 | + | 0.0629438i | 0.553519 | − | 0.832836i | \(-0.313284\pi\) |
−0.444498 | + | 0.895780i | \(0.646618\pi\) | |||||||
\(720\) | −3.04368 | −0.113431 | ||||||||
\(721\) | −39.6654 | + | 3.03788i | −1.47722 | + | 0.113137i | ||||
\(722\) | −14.3538 | −0.534193 | ||||||||
\(723\) | 21.7713 | + | 12.5697i | 0.809683 | + | 0.467471i | ||||
\(724\) | 2.64414 | + | 4.57978i | 0.0982687 | + | 0.170206i | ||||
\(725\) | 10.2082 | + | 17.6810i | 0.379122 | + | 0.656658i | ||||
\(726\) | 4.56093 | + | 2.63325i | 0.169272 | + | 0.0977292i | ||||
\(727\) | −23.0380 | −0.854433 | −0.427216 | − | 0.904149i | \(-0.640506\pi\) | ||||
−0.427216 | + | 0.904149i | \(0.640506\pi\) | |||||||
\(728\) | −9.44715 | + | 6.46366i | −0.350135 | + | 0.239559i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −6.74428 | − | 3.89381i | −0.249617 | − | 0.144116i | ||||
\(731\) | −2.18312 | + | 1.26042i | −0.0807455 | + | 0.0466184i | ||||
\(732\) | 3.49780 | − | 2.01946i | 0.129282 | − | 0.0746413i | ||||
\(733\) | −8.86114 | + | 15.3479i | −0.327294 | + | 0.566889i | −0.981974 | − | 0.189017i | \(-0.939470\pi\) |
0.654680 | + | 0.755906i | \(0.272803\pi\) | |||||||
\(734\) | −10.2183 | −0.377164 | ||||||||
\(735\) | 19.8583 | + | 7.71881i | 0.732486 | + | 0.284713i | ||||
\(736\) | −1.85202 | − | 4.42380i | −0.0682663 | − | 0.163064i | ||||
\(737\) | −5.61401 | + | 9.72375i | −0.206795 | + | 0.358179i | ||||
\(738\) | 6.64046 | − | 3.83387i | 0.244439 | − | 0.141127i | ||||
\(739\) | 18.7794 | + | 32.5269i | 0.690812 | + | 1.19652i | 0.971572 | + | 0.236744i | \(0.0760801\pi\) |
−0.280760 | + | 0.959778i | \(0.590587\pi\) | |||||||
\(740\) | 10.7740 | + | 6.22034i | 0.396058 | + | 0.228664i | ||||
\(741\) | 9.32571 | 0.342588 | ||||||||
\(742\) | −23.9422 | + | 16.3811i | −0.878946 | + | 0.601368i | ||||
\(743\) | 40.0707i | 1.47005i | 0.678040 | + | 0.735025i | \(0.262830\pi\) | ||||
−0.678040 | + | 0.735025i | \(0.737170\pi\) | |||||||
\(744\) | −2.04063 | + | 3.53448i | −0.0748132 | + | 0.129580i | ||||
\(745\) | −9.71498 | + | 5.60895i | −0.355929 | + | 0.205496i | ||||
\(746\) | 8.16295 | − | 4.71288i | 0.298867 | − | 0.172551i | ||||
\(747\) | 0.188848 | − | 0.327095i | 0.00690960 | − | 0.0119678i | ||||
\(748\) | 1.91434i | 0.0699954i | ||||||||
\(749\) | 2.74559 | + | 35.8489i | 0.100322 | + | 1.30989i | ||||
\(750\) | 2.24027i | 0.0818030i | ||||||||
\(751\) | −36.9816 | − | 21.3513i | −1.34948 | − | 0.779122i | −0.361303 | − | 0.932449i | \(-0.617668\pi\) |
−0.988176 | + | 0.153327i | \(0.951001\pi\) | |||||||
\(752\) | −7.12526 | + | 4.11377i | −0.259831 | + | 0.150014i | ||||
\(753\) | −6.53628 | + | 3.77372i | −0.238195 | + | 0.137522i | ||||
\(754\) | −17.9402 | − | 10.3578i | −0.653343 | − | 0.377208i | ||||
\(755\) | 74.3349 | 2.70532 | ||||||||
\(756\) | −2.38562 | − | 1.14404i | −0.0867641 | − | 0.0416084i | ||||
\(757\) | − | 16.6847i | − | 0.606417i | −0.952924 | − | 0.303208i | \(-0.901942\pi\) | ||
0.952924 | − | 0.303208i | \(-0.0980578\pi\) | |||||||
\(758\) | −4.54788 | − | 2.62572i | −0.165187 | − | 0.0953705i | ||||
\(759\) | 6.95622 | − | 9.13681i | 0.252495 | − | 0.331645i | ||||
\(760\) | 3.28033 | + | 5.68170i | 0.118990 | + | 0.206097i | ||||
\(761\) | 22.1967 | + | 12.8153i | 0.804631 | + | 0.464554i | 0.845088 | − | 0.534627i | \(-0.179548\pi\) |
−0.0404567 | + | 0.999181i | \(0.512881\pi\) | |||||||
\(762\) | − | 9.00515i | − | 0.326222i | ||||||
\(763\) | 10.0088 | + | 4.79981i | 0.362344 | + | 0.173765i | ||||
\(764\) | − | 20.9497i | − | 0.757933i | ||||||
\(765\) | −1.21669 | + | 2.10736i | −0.0439894 | + | 0.0761919i | ||||
\(766\) | 1.43797 | + | 2.49064i | 0.0519560 | + | 0.0899904i | ||||
\(767\) | −26.6215 | − | 46.1098i | −0.961247 | − | 1.66493i | ||||
\(768\) | 0.866025 | + | 0.500000i | 0.0312500 | + | 0.0180422i | ||||
\(769\) | −4.61225 | −0.166322 | −0.0831610 | − | 0.996536i | \(-0.526502\pi\) | ||||
−0.0831610 | + | 0.996536i | \(0.526502\pi\) | |||||||
\(770\) | −1.47247 | − | 19.2259i | −0.0530641 | − | 0.692854i | ||||
\(771\) | 15.1348 | 0.545067 | ||||||||
\(772\) | −6.27262 | + | 10.8645i | −0.225756 | + | 0.391022i | ||||
\(773\) | 22.1352 | + | 38.3393i | 0.796147 | + | 1.37897i | 0.922108 | + | 0.386933i | \(0.126465\pi\) |
−0.125961 | + | 0.992035i | \(0.540201\pi\) | |||||||
\(774\) | −2.73065 | + | 1.57654i | −0.0981513 | + | 0.0566677i | ||||
\(775\) | −15.0709 | − | 8.70117i | −0.541361 | − | 0.312555i | ||||
\(776\) | 2.07359 | 0.0744377 | ||||||||
\(777\) | 6.10650 | + | 8.92513i | 0.219069 | + | 0.320187i | ||||
\(778\) | − | 6.80689i | − | 0.244039i | ||||||
\(779\) | −14.3136 | − | 8.26393i | −0.512836 | − | 0.296086i | ||||
\(780\) | 6.58416 | + | 11.4041i | 0.235751 | + | 0.408332i | ||||
\(781\) | −12.8707 | + | 7.43089i | −0.460549 | + | 0.265898i | ||||
\(782\) | −3.80326 | − | 0.486093i | −0.136004 | − | 0.0173826i | ||||
\(783\) | − | 4.78811i | − | 0.171113i | ||||||
\(784\) | −4.38234 | − | 5.45849i | −0.156512 | − | 0.194946i | ||||
\(785\) | −28.5224 | −1.01801 | ||||||||
\(786\) | 3.25546 | − | 5.63863i | 0.116119 | − | 0.201123i | ||||
\(787\) | −24.1723 | − | 41.8676i | −0.861649 | − | 1.49242i | −0.870336 | − | 0.492458i | \(-0.836099\pi\) |
0.00868697 | − | 0.999962i | \(-0.497235\pi\) | |||||||
\(788\) | 10.3422 | + | 17.9132i | 0.368425 | + | 0.638130i | ||||
\(789\) | −6.59033 | + | 11.4148i | −0.234622 | + | 0.406377i | ||||
\(790\) | − | 26.8019i | − | 0.953568i | ||||||
\(791\) | −26.2198 | + | 17.9394i | −0.932268 | + | 0.637850i | ||||
\(792\) | 2.39447i | 0.0850838i | ||||||||
\(793\) | −15.1331 | − | 8.73709i | −0.537392 | − | 0.310263i | ||||
\(794\) | −30.7424 | + | 17.7492i | −1.09101 | + | 0.629894i | ||||
\(795\) | 16.6865 | + | 28.9018i | 0.591808 | + | 1.02504i | ||||
\(796\) | −9.53909 | + | 16.5222i | −0.338104 | + | 0.585613i | ||||
\(797\) | 54.2267 | 1.92081 | 0.960404 | − | 0.278612i | \(-0.0898743\pi\) | ||||
0.960404 | + | 0.278612i | \(0.0898743\pi\) | |||||||
\(798\) | 0.435500 | + | 5.68628i | 0.0154165 | + | 0.201292i | ||||
\(799\) | 6.57779i | 0.232706i | ||||||||
\(800\) | −2.13198 | + | 3.69270i | −0.0753769 | + | 0.130557i | ||||
\(801\) | 0.328941 | + | 0.569742i | 0.0116225 | + | 0.0201308i | ||||
\(802\) | −19.3925 | + | 11.1963i | −0.684774 | + | 0.395355i | ||||
\(803\) | −3.06328 | + | 5.30575i | −0.108101 | + | 0.187236i | ||||
\(804\) | 4.68915 | 0.165373 | ||||||||
\(805\) | 38.5703 | + | 1.95649i | 1.35943 | + | 0.0689572i | ||||
\(806\) | 17.6574 | 0.621955 | ||||||||
\(807\) | −6.24489 | + | 10.8165i | −0.219831 | + | 0.380758i | ||||
\(808\) | 15.0796 | − | 8.70623i | 0.530500 | − | 0.306284i | ||||
\(809\) | −22.9145 | − | 39.6890i | −0.805629 | − | 1.39539i | −0.915865 | − | 0.401485i | \(-0.868494\pi\) |
0.110236 | − | 0.993905i | \(-0.464839\pi\) | |||||||
\(810\) | −1.52184 | + | 2.63590i | −0.0534719 | + | 0.0926161i | ||||
\(811\) | 14.0502i | 0.493368i | 0.969096 | + | 0.246684i | \(0.0793409\pi\) | ||||
−0.969096 | + | 0.246684i | \(0.920659\pi\) | |||||||
\(812\) | 5.47779 | − | 11.4226i | 0.192233 | − | 0.400855i | ||||
\(813\) | −3.36752 | −0.118104 | ||||||||
\(814\) | 4.89357 | − | 8.47591i | 0.171519 | − | 0.297080i | ||||
\(815\) | −18.0204 | − | 31.2123i | −0.631227 | − | 1.09332i | ||||
\(816\) | 0.692374 | − | 0.399743i | 0.0242380 | − | 0.0139938i | ||||
\(817\) | 5.88595 | + | 3.39825i | 0.205923 | + | 0.118890i | ||||
\(818\) | 5.85038i | 0.204554i | ||||||||
\(819\) | 0.874119 | + | 11.4133i | 0.0305442 | + | 0.398813i | ||||
\(820\) | − | 23.3381i | − | 0.815002i | ||||||
\(821\) | 4.84622 | − | 8.39390i | 0.169134 | − | 0.292949i | −0.768981 | − | 0.639271i | \(-0.779236\pi\) |
0.938116 | + | 0.346322i | \(0.112570\pi\) | |||||||
\(822\) | −4.52273 | − | 7.83359i | −0.157748 | − | 0.273228i | ||||
\(823\) | −2.12993 | − | 3.68915i | −0.0742448 | − | 0.128596i | 0.826513 | − | 0.562918i | \(-0.190321\pi\) |
−0.900758 | + | 0.434322i | \(0.856988\pi\) | |||||||
\(824\) | 7.51800 | − | 13.0216i | 0.261902 | − | 0.453627i | ||||
\(825\) | −10.2099 | −0.355464 | ||||||||
\(826\) | 26.8719 | − | 18.3855i | 0.934994 | − | 0.639715i | ||||
\(827\) | − | 40.2206i | − | 1.39861i | −0.714825 | − | 0.699304i | \(-0.753494\pi\) | ||
0.714825 | − | 0.699304i | \(-0.246506\pi\) | |||||||
\(828\) | −4.75713 | − | 0.608007i | −0.165322 | − | 0.0211297i | ||||
\(829\) | 22.7148 | − | 13.1144i | 0.788917 | − | 0.455481i | −0.0506642 | − | 0.998716i | \(-0.516134\pi\) |
0.839581 | + | 0.543234i | \(0.182800\pi\) | |||||||
\(830\) | −0.574793 | − | 0.995571i | −0.0199514 | − | 0.0345568i | ||||
\(831\) | 1.35601 | + | 0.782895i | 0.0470396 | + | 0.0271583i | ||||
\(832\) | − | 4.32646i | − | 0.149993i | ||||||
\(833\) | −5.53113 | + | 0.852232i | −0.191642 | + | 0.0295281i | ||||
\(834\) | −10.5668 | −0.365898 | ||||||||
\(835\) | 0.275474 | + | 0.159045i | 0.00953318 | + | 0.00550398i | ||||
\(836\) | 4.46982 | − | 2.58065i | 0.154592 | − | 0.0892537i | ||||
\(837\) | 2.04063 | + | 3.53448i | 0.0705345 | + | 0.122169i | ||||
\(838\) | −5.24814 | + | 9.09004i | −0.181294 | + | 0.314010i | ||||
\(839\) | −24.1849 | −0.834954 | −0.417477 | − | 0.908687i | \(-0.637086\pi\) | ||||
−0.417477 | + | 0.908687i | \(0.637086\pi\) | |||||||
\(840\) | −6.64610 | + | 4.54721i | −0.229312 | + | 0.156893i | ||||
\(841\) | −6.07398 | −0.209448 | ||||||||
\(842\) | −12.2420 | − | 7.06791i | −0.421886 | − | 0.243576i | ||||
\(843\) | 12.0050 | + | 20.7932i | 0.413473 | + | 0.716156i | ||||
\(844\) | −10.3931 | − | 18.0014i | −0.357746 | − | 0.619634i | ||||
\(845\) | 8.70220 | − | 15.0726i | 0.299365 | − | 0.518515i | ||||
\(846\) | 8.22754i | 0.282869i | ||||||||
\(847\) | 13.8932 | − | 1.06405i | 0.477375 | − | 0.0365611i | ||||
\(848\) | − | 10.9647i | − | 0.376529i | ||||||
\(849\) | 24.0340 | + | 13.8760i | 0.824845 | + | 0.476224i | ||||
\(850\) | 1.70449 | + | 2.95226i | 0.0584634 | + | 0.101262i | ||||
\(851\) | 15.5966 | + | 11.8743i | 0.534646 | + | 0.407047i | ||||
\(852\) | 5.37517 | + | 3.10335i | 0.184150 | + | 0.106319i | ||||
\(853\) | − | 39.8471i | − | 1.36434i | −0.731193 | − | 0.682170i | \(-0.761036\pi\) | ||
0.731193 | − | 0.682170i | \(-0.238964\pi\) | |||||||
\(854\) | 4.62068 | − | 9.63530i | 0.158116 | − | 0.329713i | ||||
\(855\) | 6.56067 | 0.224370 | ||||||||
\(856\) | −11.7687 | − | 6.79464i | −0.402245 | − | 0.232236i | ||||
\(857\) | −20.6008 | + | 11.8939i | −0.703709 | + | 0.406287i | −0.808728 | − | 0.588183i | \(-0.799843\pi\) |
0.105018 | + | 0.994470i | \(0.466510\pi\) | |||||||
\(858\) | 8.97165 | − | 5.17979i | 0.306287 | − | 0.176835i | ||||
\(859\) | −24.2200 | − | 13.9834i | −0.826377 | − | 0.477109i | 0.0262339 | − | 0.999656i | \(-0.491649\pi\) |
−0.852610 | + | 0.522547i | \(0.824982\pi\) | |||||||
\(860\) | 9.59698i | 0.327254i | ||||||||
\(861\) | 8.77220 | − | 18.2923i | 0.298956 | − | 0.623400i | ||||
\(862\) | − | 5.86400i | − | 0.199729i | ||||||
\(863\) | −7.98752 | + | 13.8348i | −0.271898 | + | 0.470942i | −0.969348 | − | 0.245692i | \(-0.920985\pi\) |
0.697450 | + | 0.716634i | \(0.254318\pi\) | |||||||
\(864\) | 0.866025 | − | 0.500000i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | 9.21389 | − | 5.31964i | 0.313282 | − | 0.180873i | ||||
\(866\) | −7.94306 | + | 13.7578i | −0.269916 | + | 0.467508i | ||||
\(867\) | 16.3608i | 0.555643i | ||||||||
\(868\) | 0.824580 | + | 10.7665i | 0.0279881 | + | 0.365438i | ||||
\(869\) | −21.0851 | −0.715264 | ||||||||
\(870\) | −12.6210 | − | 7.28673i | −0.427891 | − | 0.247043i | ||||
\(871\) | −10.1437 | − | 17.5694i | −0.343706 | − | 0.595316i | ||||
\(872\) | −3.63340 | + | 2.09774i | −0.123042 | + | 0.0710386i | ||||
\(873\) | 1.03680 | − | 1.79578i | 0.0350902 | − | 0.0607781i | ||||
\(874\) | 3.99204 | + | 9.53554i | 0.135033 | + | 0.322544i | ||||
\(875\) | 3.34693 | + | 4.89180i | 0.113147 | + | 0.165373i | ||||
\(876\) | 2.55863 | 0.0864479 | ||||||||
\(877\) | 14.0832 | − | 24.3928i | 0.475555 | − | 0.823686i | −0.524053 | − | 0.851686i | \(-0.675581\pi\) |
0.999608 | + | 0.0280001i | \(0.00891386\pi\) | |||||||
\(878\) | −17.8490 | + | 10.3051i | −0.602376 | + | 0.347782i | ||||
\(879\) | 20.7701 | − | 11.9916i | 0.700560 | − | 0.404468i | ||||
\(880\) | 6.31159 | + | 3.64400i | 0.212764 | + | 0.122839i | ||||
\(881\) | 35.4459 | 1.19420 | 0.597102 | − | 0.802166i | \(-0.296319\pi\) | ||||
0.597102 | + | 0.802166i | \(0.296319\pi\) | |||||||
\(882\) | −6.91836 | + | 1.06598i | −0.232953 | + | 0.0358933i | ||||
\(883\) | −23.4131 | −0.787913 | −0.393957 | − | 0.919129i | \(-0.628894\pi\) | ||||
−0.393957 | + | 0.919129i | \(0.628894\pi\) | |||||||
\(884\) | −2.99553 | − | 1.72947i | −0.100750 | − | 0.0581683i | ||||
\(885\) | −18.7283 | − | 32.4384i | −0.629545 | − | 1.09040i | ||||
\(886\) | 5.21749 | + | 9.03695i | 0.175285 | + | 0.303602i | ||||
\(887\) | −2.04900 | − | 1.18299i | −0.0687987 | − | 0.0397209i | 0.465206 | − | 0.885202i | \(-0.345980\pi\) |
−0.534005 | + | 0.845481i | \(0.679314\pi\) | |||||||
\(888\) | −4.08739 | −0.137164 | ||||||||
\(889\) | −13.4536 | − | 19.6634i | −0.451218 | − | 0.659490i | ||||
\(890\) | 2.00238 | 0.0671198 | ||||||||
\(891\) | 2.07367 | + | 1.19724i | 0.0694707 | + | 0.0401089i | ||||
\(892\) | 13.1994 | − | 7.62069i | 0.441950 | − | 0.255160i | ||||
\(893\) | 15.3585 | − | 8.86726i | 0.513954 | − | 0.296732i | ||||
\(894\) | 1.84282 | − | 3.19186i | 0.0616331 | − | 0.106752i | ||||
\(895\) | 61.7072 | 2.06265 | ||||||||
\(896\) | 2.63803 | − | 0.202041i | 0.0881303 | − | 0.00674970i | ||||
\(897\) | 8.01267 | + | 19.1394i | 0.267535 | + | 0.639045i | ||||
\(898\) | 3.52773 | − | 6.11021i | 0.117722 | − | 0.203900i | ||||
\(899\) | −16.9235 | + | 9.77077i | −0.564429 | + | 0.325873i | ||||
\(900\) | 2.13198 | + | 3.69270i | 0.0710660 | + | 0.123090i | ||||
\(901\) | −7.59166 | − | 4.38305i | −0.252915 | − | 0.146020i | ||||
\(902\) | −18.3602 | −0.611327 | ||||||||
\(903\) | −3.60726 | + | 7.52206i | −0.120042 | + | 0.250319i | ||||
\(904\) | − | 12.0077i | − | 0.399371i | ||||||
\(905\) | 8.04790 | − | 13.9394i | 0.267521 | − | 0.463361i | ||||
\(906\) | −21.1507 | + | 12.2114i | −0.702685 | + | 0.405696i | ||||
\(907\) | −33.1958 | + | 19.1656i | −1.10225 | + | 0.636383i | −0.936810 | − | 0.349838i | \(-0.886237\pi\) |
−0.165437 | + | 0.986220i | \(0.552903\pi\) | |||||||
\(908\) | −4.63162 | + | 8.02220i | −0.153706 | + | 0.266226i | ||||
\(909\) | − | 17.4125i | − | 0.577535i | ||||||
\(910\) | 31.4146 | + | 15.0651i | 1.04138 | + | 0.499403i | ||||
\(911\) | 27.5063i | 0.911324i | 0.890153 | + | 0.455662i | \(0.150597\pi\) | ||||
−0.890153 | + | 0.455662i | \(0.849403\pi\) | |||||||
\(912\) | −1.86672 | − | 1.07775i | −0.0618134 | − | 0.0356880i | ||||
\(913\) | −0.783219 | + | 0.452192i | −0.0259208 | + | 0.0149654i | ||||
\(914\) | −17.6738 | + | 10.2040i | −0.584598 | + | 0.337518i | ||||
\(915\) | −10.6462 | − | 6.14657i | −0.351952 | − | 0.203199i | ||||
\(916\) | −14.5158 | −0.479615 | ||||||||
\(917\) | −1.31547 | − | 17.1760i | −0.0434407 | − | 0.567201i | ||||
\(918\) | − | 0.799485i | − | 0.0263869i | ||||||
\(919\) | −41.4042 | − | 23.9047i | −1.36580 | − | 0.788544i | −0.375410 | − | 0.926859i | \(-0.622498\pi\) |
−0.990388 | + | 0.138315i | \(0.955831\pi\) | |||||||
\(920\) | −8.84223 | + | 11.6140i | −0.291520 | + | 0.382904i | ||||
\(921\) | −16.3639 | − | 28.3430i | −0.539207 | − | 0.933935i | ||||
\(922\) | −16.7061 | − | 9.64529i | −0.550187 | − | 0.317651i | ||||
\(923\) | − | 26.8531i | − | 0.883879i | ||||||
\(924\) | 3.57730 | + | 5.22851i | 0.117685 | + | 0.172005i | ||||
\(925\) | − | 17.4285i | − | 0.573044i | ||||||
\(926\) | 8.45902 | − | 14.6514i | 0.277981 | − | 0.481476i | ||||
\(927\) | −7.51800 | − | 13.0216i | −0.246924 | − | 0.427684i | ||||
\(928\) | 2.39406 | + | 4.14663i | 0.0785887 | + | 0.136120i | ||||
\(929\) | −18.2769 | − | 10.5522i | −0.599647 | − | 0.346206i | 0.169256 | − | 0.985572i | \(-0.445864\pi\) |
−0.768903 | + | 0.639366i | \(0.779197\pi\) | |||||||
\(930\) | 12.4220 | 0.407335 | ||||||||
\(931\) | 9.44617 | + | 11.7658i | 0.309586 | + | 0.385609i | ||||
\(932\) | 10.9152 | 0.357539 | ||||||||
\(933\) | 9.08865 | − | 15.7420i | 0.297549 | − | 0.515370i | ||||
\(934\) | −13.4093 | − | 23.2256i | −0.438766 | − | 0.759964i | ||||
\(935\) | 5.04602 | − | 2.91332i | 0.165023 | − | 0.0952758i | ||||
\(936\) | −3.74682 | − | 2.16323i | −0.122469 | − | 0.0707073i | ||||
\(937\) | −53.7539 | −1.75606 | −0.878032 | − | 0.478603i | \(-0.841143\pi\) | ||||
−0.878032 | + | 0.478603i | \(0.841143\pi\) | |||||||
\(938\) | 10.2391 | − | 7.00551i | 0.334319 | − | 0.228738i | ||||
\(939\) | 26.2374i | 0.856227i | ||||||||
\(940\) | 21.6870 | + | 12.5210i | 0.707351 | + | 0.408389i | ||||
\(941\) | −19.2827 | − | 33.3986i | −0.628597 | − | 1.08876i | −0.987833 | − | 0.155516i | \(-0.950296\pi\) |
0.359236 | − | 0.933247i | \(-0.383037\pi\) | |||||||
\(942\) | 8.11555 | − | 4.68552i | 0.264419 | − | 0.152662i | ||||
\(943\) | 4.66204 | − | 36.4765i | 0.151817 | − | 1.18784i | ||||
\(944\) | 12.3064i | 0.400539i | ||||||||
\(945\) | 0.614946 | + | 8.02929i | 0.0200042 | + | 0.261193i | ||||
\(946\) | 7.54998 | 0.245471 | ||||||||
\(947\) | 20.6952 | − | 35.8451i | 0.672503 | − | 1.16481i | −0.304689 | − | 0.952452i | \(-0.598552\pi\) |
0.977192 | − | 0.212358i | \(-0.0681142\pi\) | |||||||
\(948\) | 4.40288 | + | 7.62601i | 0.142999 | + | 0.247681i | ||||
\(949\) | −5.53489 | − | 9.58671i | −0.179670 | − | 0.311198i | ||||
\(950\) | 4.59550 | − | 7.95964i | 0.149098 | − | 0.258245i | ||||
\(951\) | − | 22.4003i | − | 0.726378i | ||||||
\(952\) | 0.914643 | − | 1.90727i | 0.0296438 | − | 0.0618148i | ||||
\(953\) | − | 26.9984i | − | 0.874564i | −0.899324 | − | 0.437282i | \(-0.855941\pi\) | ||
0.899324 | − | 0.437282i | \(-0.144059\pi\) | |||||||
\(954\) | −9.49569 | − | 5.48234i | −0.307434 | − | 0.177497i | ||||
\(955\) | −55.2213 | + | 31.8820i | −1.78692 | + | 1.03168i | ||||
\(956\) | −10.0614 | − | 17.4268i | −0.325408 | − | 0.563623i | ||||
\(957\) | −5.73250 | + | 9.92898i | −0.185305 | + | 0.320958i | ||||
\(958\) | −16.0881 | −0.519783 | ||||||||
\(959\) | −21.5790 | − | 10.3484i | −0.696822 | − | 0.334166i | ||||
\(960\) | − | 3.04368i | − | 0.0982342i | ||||||
\(961\) | −7.17165 | + | 12.4217i | −0.231344 | + | 0.400699i | ||||
\(962\) | 8.84195 | + | 15.3147i | 0.285076 | + | 0.493766i | ||||
\(963\) | −11.7687 | + | 6.79464i | −0.379240 | + | 0.218954i | ||||
\(964\) | −12.5697 | + | 21.7713i | −0.404841 | + | 0.701206i | ||||
\(965\) | 38.1836 | 1.22917 | ||||||||
\(966\) | −11.2959 | + | 5.77946i | −0.363440 | + | 0.185951i | ||||
\(967\) | 7.63681 | 0.245583 | 0.122792 | − | 0.992432i | \(-0.460815\pi\) | ||||
0.122792 | + | 0.992432i | \(0.460815\pi\) | |||||||
\(968\) | −2.63325 | + | 4.56093i | −0.0846360 | + | 0.146594i | ||||
\(969\) | −1.49242 | + | 0.861648i | −0.0479434 | + | 0.0276801i | ||||
\(970\) | −3.15567 | − | 5.46578i | −0.101323 | − | 0.175496i | ||||
\(971\) | −14.3330 | + | 24.8254i | −0.459967 | + | 0.796686i | −0.998959 | − | 0.0456248i | \(-0.985472\pi\) |
0.538992 | + | 0.842311i | \(0.318805\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | −23.0734 | + | 15.7866i | −0.739699 | + | 0.506096i | ||||
\(974\) | −26.6509 | −0.853950 | ||||||||
\(975\) | 9.22392 | − | 15.9763i | 0.295402 | − | 0.511651i | ||||
\(976\) | 2.01946 | + | 3.49780i | 0.0646412 | + | 0.111962i | ||||
\(977\) | 6.00035 | − | 3.46430i | 0.191968 | − | 0.110833i | −0.400936 | − | 0.916106i | \(-0.631315\pi\) |
0.592904 | + | 0.805273i | \(0.297982\pi\) | |||||||
\(978\) | 10.2548 | + | 5.92061i | 0.327912 | + | 0.189320i | ||||
\(979\) | − | 1.57528i | − | 0.0503461i | ||||||
\(980\) | −7.71881 | + | 19.8583i | −0.246568 | + | 0.634352i | ||||
\(981\) | 4.19549i | 0.133952i | ||||||||
\(982\) | −11.2318 | + | 19.4540i | −0.358420 | + | 0.620801i | ||||
\(983\) | −13.2988 | − | 23.0343i | −0.424167 | − | 0.734679i | 0.572175 | − | 0.820131i | \(-0.306100\pi\) |
−0.996342 | + | 0.0854527i | \(0.972766\pi\) | |||||||
\(984\) | 3.83387 | + | 6.64046i | 0.122219 | + | 0.211690i | ||||
\(985\) | 31.4782 | − | 54.5219i | 1.00298 | − | 1.73721i | ||||
\(986\) | 3.82802 | 0.121909 | ||||||||
\(987\) | 12.2918 | + | 17.9655i | 0.391253 | + | 0.571847i | ||||
\(988\) | 9.32571i | 0.296690i | ||||||||
\(989\) | −1.91710 | + | 14.9997i | −0.0609602 | + | 0.476961i | ||||
\(990\) | 6.31159 | − | 3.64400i | 0.200595 | − | 0.115814i | ||||
\(991\) | 8.16021 | + | 14.1339i | 0.259217 | + | 0.448978i | 0.966033 | − | 0.258421i | \(-0.0832020\pi\) |
−0.706815 | + | 0.707398i | \(0.749869\pi\) | |||||||
\(992\) | −3.53448 | − | 2.04063i | −0.112220 | − | 0.0647901i | ||||
\(993\) | 1.28988i | 0.0409332i | ||||||||
\(994\) | 16.3735 | − | 1.25401i | 0.519335 | − | 0.0397747i | ||||
\(995\) | 58.0678 | 1.84087 | ||||||||
\(996\) | 0.327095 | + | 0.188848i | 0.0103644 | + | 0.00598389i | ||||
\(997\) | 20.7618 | − | 11.9868i | 0.657533 | − | 0.379627i | −0.133803 | − | 0.991008i | \(-0.542719\pi\) |
0.791336 | + | 0.611381i | \(0.209386\pi\) | |||||||
\(998\) | −2.37249 | − | 4.10928i | −0.0750999 | − | 0.130077i | ||||
\(999\) | −2.04369 | + | 3.53978i | −0.0646596 | + | 0.111994i |
(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 | 966.2.k.a.229.2 | ✓ | 32 | |
7.3 | odd | 6 | inner | 966.2.k.a.367.7 | yes | 32 | |
23.22 | odd | 2 | inner | 966.2.k.a.229.7 | yes | 32 | |
161.45 | even | 6 | inner | 966.2.k.a.367.2 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.k.a.229.2 | ✓ | 32 | 1.1 | even | 1 | trivial | |
966.2.k.a.229.7 | yes | 32 | 23.22 | odd | 2 | inner | |
966.2.k.a.367.2 | yes | 32 | 161.45 | even | 6 | inner | |
966.2.k.a.367.7 | yes | 32 | 7.3 | odd | 6 | inner |