Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(4,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.4");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.t (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: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 33 x^{18} + 455 x^{16} + 3403 x^{14} + 15006 x^{12} + 39799 x^{10} + 62505 x^{8} + 55993 x^{6} + \cdots + 576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 205.10 | ||
Root | \(2.50900i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.205 |
Dual form | 273.2.t.d.4.1 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.50900i | 1.77413i | 0.461642 | + | 0.887066i | \(0.347260\pi\) | ||||
−0.461642 | + | 0.887066i | \(0.652740\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −4.29509 | −2.14755 | ||||||||
\(5\) | −2.97008 | − | 1.71478i | −1.32826 | − | 0.766872i | −0.343231 | − | 0.939251i | \(-0.611521\pi\) |
−0.985031 | + | 0.172379i | \(0.944855\pi\) | |||||||
\(6\) | 2.17286 | + | 1.25450i | 0.887066 | + | 0.512148i | ||||
\(7\) | −0.0473512 | − | 2.64533i | −0.0178971 | − | 0.999840i | ||||
\(8\) | − | 5.75840i | − | 2.03590i | ||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 4.30238 | − | 7.45195i | 1.36053 | − | 2.35651i | ||||
\(11\) | −4.35178 | − | 2.51250i | −1.31211 | − | 0.757547i | −0.329665 | − | 0.944098i | \(-0.606936\pi\) |
−0.982445 | + | 0.186551i | \(0.940269\pi\) | |||||||
\(12\) | −2.14755 | + | 3.71966i | −0.619943 | + | 1.07377i | ||||
\(13\) | 0.135561 | + | 3.60300i | 0.0375977 | + | 0.999293i | ||||
\(14\) | 6.63713 | − | 0.118804i | 1.77385 | − | 0.0317518i | ||||
\(15\) | −2.97008 | + | 1.71478i | −0.766872 | + | 0.442754i | ||||
\(16\) | 5.85764 | 1.46441 | ||||||||
\(17\) | 0.199310 | 0.0483399 | 0.0241699 | − | 0.999708i | \(-0.492306\pi\) | ||||
0.0241699 | + | 0.999708i | \(0.492306\pi\) | |||||||
\(18\) | 2.17286 | − | 1.25450i | 0.512148 | − | 0.295689i | ||||
\(19\) | 3.99823 | − | 2.30838i | 0.917256 | − | 0.529578i | 0.0344977 | − | 0.999405i | \(-0.489017\pi\) |
0.882759 | + | 0.469827i | \(0.155684\pi\) | |||||||
\(20\) | 12.7568 | + | 7.36513i | 2.85250 | + | 1.64689i | ||||
\(21\) | −2.31460 | − | 1.28166i | −0.505086 | − | 0.279680i | ||||
\(22\) | 6.30387 | − | 10.9186i | 1.34399 | − | 2.32786i | ||||
\(23\) | −7.52372 | −1.56880 | −0.784402 | − | 0.620253i | \(-0.787030\pi\) | ||||
−0.784402 | + | 0.620253i | \(0.787030\pi\) | |||||||
\(24\) | −4.98692 | − | 2.87920i | −1.01795 | − | 0.587714i | ||||
\(25\) | 3.38093 | + | 5.85594i | 0.676186 | + | 1.17119i | ||||
\(26\) | −9.03994 | + | 0.340122i | −1.77288 | + | 0.0667034i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.203378 | + | 11.3619i | 0.0384348 | + | 2.14720i | ||||
\(29\) | 1.58334 | + | 2.74243i | 0.294020 | + | 0.509257i | 0.974756 | − | 0.223271i | \(-0.0716736\pi\) |
−0.680737 | + | 0.732528i | \(0.738340\pi\) | |||||||
\(30\) | −4.30238 | − | 7.45195i | −0.785504 | − | 1.36053i | ||||
\(31\) | −3.65876 | + | 2.11239i | −0.657133 | + | 0.379396i | −0.791184 | − | 0.611578i | \(-0.790535\pi\) |
0.134051 | + | 0.990974i | \(0.457202\pi\) | |||||||
\(32\) | 3.18005i | 0.562158i | ||||||||
\(33\) | −4.35178 | + | 2.51250i | −0.757547 | + | 0.437370i | ||||
\(34\) | 0.500070i | 0.0857613i | ||||||||
\(35\) | −4.39551 | + | 7.93804i | −0.742977 | + | 1.34177i | ||||
\(36\) | 2.14755 | + | 3.71966i | 0.357924 | + | 0.619943i | ||||
\(37\) | − | 9.11903i | − | 1.49916i | −0.661914 | − | 0.749580i | \(-0.730256\pi\) | ||
0.661914 | − | 0.749580i | \(-0.269744\pi\) | |||||||
\(38\) | 5.79173 | + | 10.0316i | 0.939542 | + | 1.62733i | ||||
\(39\) | 3.18807 | + | 1.68410i | 0.510500 | + | 0.269672i | ||||
\(40\) | −9.87437 | + | 17.1029i | −1.56128 | + | 2.70421i | ||||
\(41\) | 4.67486 | − | 2.69903i | 0.730090 | − | 0.421517i | −0.0883653 | − | 0.996088i | \(-0.528164\pi\) |
0.818455 | + | 0.574571i | \(0.194831\pi\) | |||||||
\(42\) | 3.21568 | − | 5.80733i | 0.496190 | − | 0.896090i | ||||
\(43\) | 1.27860 | − | 2.21461i | 0.194985 | − | 0.337724i | −0.751910 | − | 0.659265i | \(-0.770867\pi\) |
0.946896 | + | 0.321541i | \(0.104201\pi\) | |||||||
\(44\) | 18.6913 | + | 10.7914i | 2.81782 | + | 1.62687i | ||||
\(45\) | 3.42956i | 0.511248i | ||||||||
\(46\) | − | 18.8770i | − | 2.78327i | ||||||
\(47\) | 6.19804 | + | 3.57844i | 0.904077 | + | 0.521969i | 0.878521 | − | 0.477704i | \(-0.158531\pi\) |
0.0255566 | + | 0.999673i | \(0.491864\pi\) | |||||||
\(48\) | 2.92882 | − | 5.07287i | 0.422739 | − | 0.732205i | ||||
\(49\) | −6.99552 | + | 0.250519i | −0.999359 | + | 0.0357884i | ||||
\(50\) | −14.6926 | + | 8.48276i | −2.07784 | + | 1.19964i | ||||
\(51\) | 0.0996552 | − | 0.172608i | 0.0139545 | − | 0.0241699i | ||||
\(52\) | −0.582245 | − | 15.4752i | −0.0807429 | − | 2.14603i | ||||
\(53\) | −0.215922 | − | 0.373988i | −0.0296592 | − | 0.0513712i | 0.850815 | − | 0.525466i | \(-0.176109\pi\) |
−0.880474 | + | 0.474094i | \(0.842776\pi\) | |||||||
\(54\) | − | 2.50900i | − | 0.341432i | ||||||
\(55\) | 8.61676 | + | 14.9247i | 1.16188 | + | 2.01244i | ||||
\(56\) | −15.2328 | + | 0.272667i | −2.03557 | + | 0.0364366i | ||||
\(57\) | − | 4.61676i | − | 0.611504i | ||||||
\(58\) | −6.88077 | + | 3.97261i | −0.903489 | + | 0.521630i | ||||
\(59\) | − | 0.838256i | − | 0.109132i | −0.998510 | − | 0.0545658i | \(-0.982623\pi\) | ||
0.998510 | − | 0.0545658i | \(-0.0173775\pi\) | |||||||
\(60\) | 12.7568 | − | 7.36513i | 1.64689 | − | 0.950835i | ||||
\(61\) | 1.33262 | + | 2.30816i | 0.170624 | + | 0.295530i | 0.938638 | − | 0.344903i | \(-0.112088\pi\) |
−0.768014 | + | 0.640433i | \(0.778755\pi\) | |||||||
\(62\) | −5.29999 | − | 9.17985i | −0.673099 | − | 1.16584i | ||||
\(63\) | −2.26725 | + | 1.36367i | −0.285646 | + | 0.171806i | ||||
\(64\) | 3.73654 | 0.467068 | ||||||||
\(65\) | 5.77572 | − | 10.9337i | 0.716390 | − | 1.35616i | ||||
\(66\) | −6.30387 | − | 10.9186i | −0.775952 | − | 1.34399i | ||||
\(67\) | −9.67775 | − | 5.58745i | −1.18233 | − | 0.682616i | −0.225774 | − | 0.974180i | \(-0.572491\pi\) |
−0.956551 | + | 0.291564i | \(0.905824\pi\) | |||||||
\(68\) | −0.856057 | −0.103812 | ||||||||
\(69\) | −3.76186 | + | 6.51573i | −0.452875 | + | 0.784402i | ||||
\(70\) | −19.9166 | − | 11.0284i | −2.38048 | − | 1.31814i | ||||
\(71\) | −4.95582 | − | 2.86124i | −0.588148 | − | 0.339567i | 0.176217 | − | 0.984351i | \(-0.443614\pi\) |
−0.764365 | + | 0.644784i | \(0.776947\pi\) | |||||||
\(72\) | −4.98692 | + | 2.87920i | −0.587714 | + | 0.339317i | ||||
\(73\) | 2.73161 | − | 1.57710i | 0.319711 | − | 0.184585i | −0.331553 | − | 0.943437i | \(-0.607573\pi\) |
0.651264 | + | 0.758851i | \(0.274239\pi\) | |||||||
\(74\) | 22.8797 | 2.65971 | ||||||||
\(75\) | 6.76186 | 0.780792 | ||||||||
\(76\) | −17.1728 | + | 9.91470i | −1.96985 | + | 1.13729i | ||||
\(77\) | −6.44032 | + | 11.6308i | −0.733943 | + | 1.32546i | ||||
\(78\) | −4.22542 | + | 7.99888i | −0.478434 | + | 0.905695i | ||||
\(79\) | 2.25566 | − | 3.90692i | 0.253782 | − | 0.439563i | −0.710782 | − | 0.703412i | \(-0.751659\pi\) |
0.964564 | + | 0.263849i | \(0.0849921\pi\) | |||||||
\(80\) | −17.3977 | − | 10.0446i | −1.94512 | − | 1.12302i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 6.77187 | + | 11.7292i | 0.747828 | + | 1.29528i | ||||
\(83\) | − | 14.7167i | − | 1.61537i | −0.589613 | − | 0.807686i | \(-0.700720\pi\) | ||
0.589613 | − | 0.807686i | \(-0.299280\pi\) | |||||||
\(84\) | 9.94141 | + | 5.50483i | 1.08470 | + | 0.600627i | ||||
\(85\) | −0.591968 | − | 0.341773i | −0.0642080 | − | 0.0370705i | ||||
\(86\) | 5.55645 | + | 3.20802i | 0.599168 | + | 0.345930i | ||||
\(87\) | 3.16669 | 0.339505 | ||||||||
\(88\) | −14.4680 | + | 25.0593i | −1.54229 | + | 2.67133i | ||||
\(89\) | 2.34608i | 0.248684i | 0.992239 | + | 0.124342i | \(0.0396820\pi\) | ||||
−0.992239 | + | 0.124342i | \(0.960318\pi\) | |||||||
\(90\) | −8.60477 | −0.907022 | ||||||||
\(91\) | 9.52470 | − | 0.529209i | 0.998460 | − | 0.0554761i | ||||
\(92\) | 32.3151 | 3.36908 | ||||||||
\(93\) | 4.22478i | 0.438089i | ||||||||
\(94\) | −8.97832 | + | 15.5509i | −0.926043 | + | 1.60395i | ||||
\(95\) | −15.8334 | −1.62448 | ||||||||
\(96\) | 2.75400 | + | 1.59002i | 0.281079 | + | 0.162281i | ||||
\(97\) | −5.02047 | − | 2.89857i | −0.509751 | − | 0.294305i | 0.222980 | − | 0.974823i | \(-0.428421\pi\) |
−0.732731 | + | 0.680518i | \(0.761755\pi\) | |||||||
\(98\) | −0.628552 | − | 17.5518i | −0.0634934 | − | 1.77300i | ||||
\(99\) | 5.02500i | 0.505031i | ||||||||
\(100\) | −14.5214 | − | 25.1518i | −1.45214 | − | 2.51518i | ||||
\(101\) | 2.10772 | − | 3.65067i | 0.209726 | − | 0.363256i | −0.741902 | − | 0.670508i | \(-0.766076\pi\) |
0.951628 | + | 0.307252i | \(0.0994095\pi\) | |||||||
\(102\) | 0.433074 | + | 0.250035i | 0.0428807 | + | 0.0247572i | ||||
\(103\) | −2.11287 | + | 3.65960i | −0.208187 | + | 0.360591i | −0.951144 | − | 0.308749i | \(-0.900090\pi\) |
0.742956 | + | 0.669340i | \(0.233423\pi\) | |||||||
\(104\) | 20.7475 | − | 0.780612i | 2.03446 | − | 0.0765453i | ||||
\(105\) | 4.67679 | + | 7.77565i | 0.456408 | + | 0.758825i | ||||
\(106\) | 0.938336 | − | 0.541749i | 0.0911393 | − | 0.0526193i | ||||
\(107\) | 4.65458 | 0.449975 | 0.224988 | − | 0.974362i | \(-0.427766\pi\) | ||||
0.224988 | + | 0.974362i | \(0.427766\pi\) | |||||||
\(108\) | 4.29509 | 0.413296 | ||||||||
\(109\) | −0.524968 | + | 0.303090i | −0.0502828 | + | 0.0290308i | −0.524931 | − | 0.851145i | \(-0.675909\pi\) |
0.474648 | + | 0.880176i | \(0.342575\pi\) | |||||||
\(110\) | −37.4460 | + | 21.6195i | −3.57034 | + | 2.06134i | ||||
\(111\) | −7.89731 | − | 4.55951i | −0.749580 | − | 0.432770i | ||||
\(112\) | −0.277366 | − | 15.4954i | −0.0262086 | − | 1.46418i | ||||
\(113\) | −4.15517 | + | 7.19697i | −0.390886 | + | 0.677034i | −0.992567 | − | 0.121703i | \(-0.961165\pi\) |
0.601681 | + | 0.798737i | \(0.294498\pi\) | |||||||
\(114\) | 11.5835 | 1.08489 | ||||||||
\(115\) | 22.3461 | + | 12.9015i | 2.08378 | + | 1.20307i | ||||
\(116\) | −6.80061 | − | 11.7790i | −0.631421 | − | 1.09365i | ||||
\(117\) | 3.05251 | − | 1.91890i | 0.282205 | − | 0.177402i | ||||
\(118\) | 2.10319 | 0.193614 | ||||||||
\(119\) | −0.00943758 | − | 0.527241i | −0.000865142 | − | 0.0483321i | ||||
\(120\) | 9.87437 | + | 17.1029i | 0.901403 | + | 1.56128i | ||||
\(121\) | 7.12531 | + | 12.3414i | 0.647755 | + | 1.12195i | ||||
\(122\) | −5.79118 | + | 3.34354i | −0.524309 | + | 0.302710i | ||||
\(123\) | − | 5.39806i | − | 0.486726i | ||||||
\(124\) | 15.7147 | − | 9.07290i | 1.41122 | − | 0.814771i | ||||
\(125\) | − | 6.04239i | − | 0.540448i | ||||||
\(126\) | −3.42145 | − | 5.68852i | −0.304807 | − | 0.506774i | ||||
\(127\) | 5.03862 | + | 8.72715i | 0.447105 | + | 0.774409i | 0.998196 | − | 0.0600359i | \(-0.0191215\pi\) |
−0.551091 | + | 0.834445i | \(0.685788\pi\) | |||||||
\(128\) | 15.7351i | 1.39080i | ||||||||
\(129\) | −1.27860 | − | 2.21461i | −0.112575 | − | 0.194985i | ||||
\(130\) | 27.4326 | + | 14.4913i | 2.40600 | + | 1.27097i | ||||
\(131\) | 5.52188 | − | 9.56417i | 0.482449 | − | 0.835626i | −0.517348 | − | 0.855775i | \(-0.673081\pi\) |
0.999797 | + | 0.0201493i | \(0.00641417\pi\) | |||||||
\(132\) | 18.6913 | − | 10.7914i | 1.62687 | − | 0.939273i | ||||
\(133\) | −6.29574 | − | 10.4673i | −0.545910 | − | 0.907632i | ||||
\(134\) | 14.0189 | − | 24.2815i | 1.21105 | − | 2.09760i | ||||
\(135\) | 2.97008 | + | 1.71478i | 0.255624 | + | 0.147585i | ||||
\(136\) | − | 1.14771i | − | 0.0984151i | ||||||
\(137\) | 11.3738i | 0.971730i | 0.874034 | + | 0.485865i | \(0.161495\pi\) | ||||
−0.874034 | + | 0.485865i | \(0.838505\pi\) | |||||||
\(138\) | −16.3480 | − | 9.43851i | −1.39163 | − | 0.803459i | ||||
\(139\) | 8.76143 | − | 15.1752i | 0.743135 | − | 1.28715i | −0.207926 | − | 0.978145i | \(-0.566671\pi\) |
0.951061 | − | 0.309003i | \(-0.0999954\pi\) | |||||||
\(140\) | 18.8791 | − | 34.0946i | 1.59558 | − | 2.88152i | ||||
\(141\) | 6.19804 | − | 3.57844i | 0.521969 | − | 0.301359i | ||||
\(142\) | 7.17887 | − | 12.4342i | 0.602437 | − | 1.04345i | ||||
\(143\) | 8.46261 | − | 16.0201i | 0.707679 | − | 1.33966i | ||||
\(144\) | −2.92882 | − | 5.07287i | −0.244068 | − | 0.422739i | ||||
\(145\) | − | 10.8603i | − | 0.901902i | ||||||
\(146\) | 3.95694 | + | 6.85362i | 0.327479 | + | 0.567209i | ||||
\(147\) | −3.28080 | + | 6.18355i | −0.270596 | + | 0.510011i | ||||
\(148\) | 39.1671i | 3.21951i | ||||||||
\(149\) | 10.2864 | − | 5.93887i | 0.842696 | − | 0.486531i | −0.0154836 | − | 0.999880i | \(-0.504929\pi\) |
0.858180 | + | 0.513349i | \(0.171595\pi\) | |||||||
\(150\) | 16.9655i | 1.38523i | ||||||||
\(151\) | −11.5380 | + | 6.66145i | −0.938946 | + | 0.542101i | −0.889630 | − | 0.456682i | \(-0.849038\pi\) |
−0.0493164 | + | 0.998783i | \(0.515704\pi\) | |||||||
\(152\) | −13.2926 | − | 23.0234i | −1.07817 | − | 1.86744i | ||||
\(153\) | −0.0996552 | − | 0.172608i | −0.00805664 | − | 0.0139545i | ||||
\(154\) | −29.1818 | − | 16.1588i | −2.35154 | − | 1.30211i | ||||
\(155\) | 14.4891 | 1.16379 | ||||||||
\(156\) | −13.6931 | − | 7.23338i | −1.09632 | − | 0.579134i | ||||
\(157\) | 5.62062 | + | 9.73519i | 0.448574 | + | 0.776953i | 0.998293 | − | 0.0583963i | \(-0.0185987\pi\) |
−0.549719 | + | 0.835349i | \(0.685265\pi\) | |||||||
\(158\) | 9.80248 | + | 5.65947i | 0.779844 | + | 0.450243i | ||||
\(159\) | −0.431844 | −0.0342474 | ||||||||
\(160\) | 5.45307 | − | 9.44500i | 0.431103 | − | 0.746693i | ||||
\(161\) | 0.356257 | + | 19.9027i | 0.0280770 | + | 1.56855i | ||||
\(162\) | −2.17286 | − | 1.25450i | −0.170716 | − | 0.0985629i | ||||
\(163\) | 3.14511 | − | 1.81583i | 0.246344 | − | 0.142227i | −0.371745 | − | 0.928335i | \(-0.621240\pi\) |
0.618089 | + | 0.786108i | \(0.287907\pi\) | |||||||
\(164\) | −20.0789 | + | 11.5926i | −1.56790 | + | 0.905228i | ||||
\(165\) | 17.2335 | 1.34163 | ||||||||
\(166\) | 36.9243 | 2.86588 | ||||||||
\(167\) | −8.95880 | + | 5.17237i | −0.693253 | + | 0.400250i | −0.804829 | − | 0.593506i | \(-0.797743\pi\) |
0.111577 | + | 0.993756i | \(0.464410\pi\) | |||||||
\(168\) | −7.38028 | + | 13.3284i | −0.569401 | + | 1.02831i | ||||
\(169\) | −12.9632 | + | 0.976850i | −0.997173 | + | 0.0751423i | ||||
\(170\) | 0.857510 | − | 1.48525i | 0.0657680 | − | 0.113913i | ||||
\(171\) | −3.99823 | − | 2.30838i | −0.305752 | − | 0.176526i | ||||
\(172\) | −5.49172 | + | 9.51194i | −0.418740 | + | 0.725279i | ||||
\(173\) | 2.29902 | + | 3.98202i | 0.174791 | + | 0.302747i | 0.940089 | − | 0.340929i | \(-0.110742\pi\) |
−0.765298 | + | 0.643676i | \(0.777408\pi\) | |||||||
\(174\) | 7.94523i | 0.602326i | ||||||||
\(175\) | 15.3308 | − | 9.22095i | 1.15890 | − | 0.697038i | ||||
\(176\) | −25.4911 | − | 14.7173i | −1.92147 | − | 1.10936i | ||||
\(177\) | −0.725951 | − | 0.419128i | −0.0545658 | − | 0.0315036i | ||||
\(178\) | −5.88633 | −0.441199 | ||||||||
\(179\) | −0.453209 | + | 0.784982i | −0.0338745 | + | 0.0586723i | −0.882466 | − | 0.470377i | \(-0.844118\pi\) |
0.848591 | + | 0.529049i | \(0.177451\pi\) | |||||||
\(180\) | − | 14.7303i | − | 1.09793i | ||||||
\(181\) | −18.9155 | −1.40598 | −0.702991 | − | 0.711199i | \(-0.748152\pi\) | ||||
−0.702991 | + | 0.711199i | \(0.748152\pi\) | |||||||
\(182\) | 1.32779 | + | 23.8975i | 0.0984220 | + | 1.77140i | ||||
\(183\) | 2.66523 | 0.197020 | ||||||||
\(184\) | 43.3245i | 3.19393i | ||||||||
\(185\) | −15.6371 | + | 27.0843i | −1.14966 | + | 1.99128i | ||||
\(186\) | −10.6000 | −0.777228 | ||||||||
\(187\) | −0.867354 | − | 0.500767i | −0.0634272 | − | 0.0366197i | ||||
\(188\) | −26.6212 | − | 15.3697i | −1.94155 | − | 1.12095i | ||||
\(189\) | 0.0473512 | + | 2.64533i | 0.00344429 | + | 0.192419i | ||||
\(190\) | − | 39.7261i | − | 2.88203i | ||||||
\(191\) | −7.70584 | − | 13.3469i | −0.557575 | − | 0.965749i | −0.997698 | − | 0.0678112i | \(-0.978398\pi\) |
0.440123 | − | 0.897938i | \(-0.354935\pi\) | |||||||
\(192\) | 1.86827 | − | 3.23594i | 0.134831 | − | 0.233534i | ||||
\(193\) | 6.89839 | + | 3.98279i | 0.496557 | + | 0.286688i | 0.727291 | − | 0.686330i | \(-0.240779\pi\) |
−0.230733 | + | 0.973017i | \(0.574113\pi\) | |||||||
\(194\) | 7.27252 | − | 12.5964i | 0.522136 | − | 0.904366i | ||||
\(195\) | −6.58098 | − | 10.4688i | −0.471273 | − | 0.749683i | ||||
\(196\) | 30.0464 | − | 1.07600i | 2.14617 | − | 0.0768573i | ||||
\(197\) | −11.3638 | + | 6.56087i | −0.809634 | + | 0.467443i | −0.846829 | − | 0.531865i | \(-0.821491\pi\) |
0.0371945 | + | 0.999308i | \(0.488158\pi\) | |||||||
\(198\) | −12.6077 | −0.895993 | ||||||||
\(199\) | 19.5203 | 1.38375 | 0.691877 | − | 0.722015i | \(-0.256784\pi\) | ||||
0.691877 | + | 0.722015i | \(0.256784\pi\) | |||||||
\(200\) | 33.7208 | − | 19.4687i | 2.38442 | − | 1.37665i | ||||
\(201\) | −9.67775 | + | 5.58745i | −0.682616 | + | 0.394108i | ||||
\(202\) | 9.15955 | + | 5.28827i | 0.644464 | + | 0.372081i | ||||
\(203\) | 7.17966 | − | 4.31832i | 0.503913 | − | 0.303087i | ||||
\(204\) | −0.428028 | + | 0.741367i | −0.0299680 | + | 0.0519061i | ||||
\(205\) | −18.5129 | −1.29300 | ||||||||
\(206\) | −9.18195 | − | 5.30120i | −0.639737 | − | 0.369352i | ||||
\(207\) | 3.76186 | + | 6.51573i | 0.261467 | + | 0.452875i | ||||
\(208\) | 0.794065 | + | 21.1051i | 0.0550585 | + | 1.46337i | ||||
\(209\) | −23.1992 | −1.60472 | ||||||||
\(210\) | −19.5091 | + | 11.7341i | −1.34626 | + | 0.809728i | ||||
\(211\) | −11.9554 | − | 20.7074i | −0.823046 | − | 1.42556i | −0.903404 | − | 0.428791i | \(-0.858940\pi\) |
0.0803582 | − | 0.996766i | \(-0.474394\pi\) | |||||||
\(212\) | 0.927405 | + | 1.60631i | 0.0636944 | + | 0.110322i | ||||
\(213\) | −4.95582 | + | 2.86124i | −0.339567 | + | 0.196049i | ||||
\(214\) | 11.6784i | 0.798316i | ||||||||
\(215\) | −7.59512 | + | 4.38504i | −0.517983 | + | 0.299057i | ||||
\(216\) | 5.75840i | 0.391809i | ||||||||
\(217\) | 5.76120 | + | 9.57860i | 0.391096 | + | 0.650238i | ||||
\(218\) | −0.760454 | − | 1.31715i | −0.0515045 | − | 0.0892083i | ||||
\(219\) | − | 3.15419i | − | 0.213141i | ||||||
\(220\) | −37.0098 | − | 64.1028i | −2.49520 | − | 4.32181i | ||||
\(221\) | 0.0270186 | + | 0.718116i | 0.00181747 | + | 0.0483057i | ||||
\(222\) | 11.4398 | − | 19.8144i | 0.767791 | − | 1.32985i | ||||
\(223\) | 9.03870 | − | 5.21849i | 0.605276 | − | 0.349456i | −0.165838 | − | 0.986153i | \(-0.553033\pi\) |
0.771114 | + | 0.636697i | \(0.219700\pi\) | |||||||
\(224\) | 8.41226 | − | 0.150579i | 0.562068 | − | 0.0100610i | ||||
\(225\) | 3.38093 | − | 5.85594i | 0.225395 | − | 0.390396i | ||||
\(226\) | −18.0572 | − | 10.4253i | −1.20115 | − | 0.693483i | ||||
\(227\) | − | 9.90050i | − | 0.657119i | −0.944483 | − | 0.328560i | \(-0.893437\pi\) | ||
0.944483 | − | 0.328560i | \(-0.106563\pi\) | |||||||
\(228\) | 19.8294i | 1.31323i | ||||||||
\(229\) | −13.6564 | − | 7.88453i | −0.902441 | − | 0.521025i | −0.0244498 | − | 0.999701i | \(-0.507783\pi\) |
−0.877991 | + | 0.478676i | \(0.841117\pi\) | |||||||
\(230\) | −32.3699 | + | 56.0663i | −2.13441 | + | 3.69690i | ||||
\(231\) | 6.85245 | + | 11.3929i | 0.450858 | + | 0.749598i | ||||
\(232\) | 15.7920 | − | 9.11752i | 1.03680 | − | 0.598595i | ||||
\(233\) | −0.952488 | + | 1.64976i | −0.0623996 | + | 0.108079i | −0.895538 | − | 0.444986i | \(-0.853209\pi\) |
0.833138 | + | 0.553065i | \(0.186542\pi\) | |||||||
\(234\) | 4.81452 | + | 7.65876i | 0.314735 | + | 0.500669i | ||||
\(235\) | −12.2725 | − | 21.2565i | −0.800567 | − | 1.38662i | ||||
\(236\) | 3.60039i | 0.234365i | ||||||||
\(237\) | −2.25566 | − | 3.90692i | −0.146521 | − | 0.253782i | ||||
\(238\) | 1.32285 | − | 0.0236789i | 0.0857476 | − | 0.00153488i | ||||
\(239\) | − | 26.3087i | − | 1.70177i | −0.525352 | − | 0.850885i | \(-0.676066\pi\) | ||
0.525352 | − | 0.850885i | \(-0.323934\pi\) | |||||||
\(240\) | −17.3977 | + | 10.0446i | −1.12302 | + | 0.648373i | ||||
\(241\) | − | 22.5867i | − | 1.45494i | −0.686139 | − | 0.727470i | \(-0.740696\pi\) | ||
0.686139 | − | 0.727470i | \(-0.259304\pi\) | |||||||
\(242\) | −30.9646 | + | 17.8774i | −1.99048 | + | 1.14920i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −5.72371 | − | 9.91376i | −0.366423 | − | 0.634664i | ||||
\(245\) | 21.2068 | + | 11.2517i | 1.35486 | + | 0.718845i | ||||
\(246\) | 13.5437 | 0.863517 | ||||||||
\(247\) | 8.85909 | + | 14.0927i | 0.563691 | + | 0.896697i | ||||
\(248\) | 12.1640 | + | 21.0686i | 0.772412 | + | 1.33786i | ||||
\(249\) | −12.7451 | − | 7.35837i | −0.807686 | − | 0.466318i | ||||
\(250\) | 15.1604 | 0.958827 | ||||||||
\(251\) | 14.4466 | − | 25.0222i | 0.911859 | − | 1.57939i | 0.100424 | − | 0.994945i | \(-0.467980\pi\) |
0.811436 | − | 0.584442i | \(-0.198686\pi\) | |||||||
\(252\) | 9.73803 | − | 5.85709i | 0.613438 | − | 0.368962i | ||||
\(253\) | 32.7415 | + | 18.9033i | 2.05844 | + | 1.18844i | ||||
\(254\) | −21.8964 | + | 12.6419i | −1.37390 | + | 0.793224i | ||||
\(255\) | −0.591968 | + | 0.341773i | −0.0370705 | + | 0.0214027i | ||||
\(256\) | −32.0063 | −2.00039 | ||||||||
\(257\) | 16.0503 | 1.00119 | 0.500595 | − | 0.865682i | \(-0.333115\pi\) | ||||
0.500595 | + | 0.865682i | \(0.333115\pi\) | |||||||
\(258\) | 5.55645 | − | 3.20802i | 0.345930 | − | 0.199723i | ||||
\(259\) | −24.1228 | + | 0.431797i | −1.49892 | + | 0.0268305i | ||||
\(260\) | −24.8073 | + | 46.9611i | −1.53848 | + | 2.91241i | ||||
\(261\) | 1.58334 | − | 2.74243i | 0.0980065 | − | 0.169752i | ||||
\(262\) | 23.9965 | + | 13.8544i | 1.48251 | + | 0.855928i | ||||
\(263\) | −7.23551 | + | 12.5323i | −0.446161 | + | 0.772773i | −0.998132 | − | 0.0610900i | \(-0.980542\pi\) |
0.551972 | + | 0.833863i | \(0.313876\pi\) | |||||||
\(264\) | 14.4680 | + | 25.0593i | 0.890442 | + | 1.54229i | ||||
\(265\) | 1.48103i | 0.0909791i | ||||||||
\(266\) | 26.2625 | − | 15.7960i | 1.61026 | − | 0.968516i | ||||
\(267\) | 2.03177 | + | 1.17304i | 0.124342 | + | 0.0717890i | ||||
\(268\) | 41.5668 | + | 23.9986i | 2.53910 | + | 1.46595i | ||||
\(269\) | 16.2953 | 0.993542 | 0.496771 | − | 0.867882i | \(-0.334519\pi\) | ||||
0.496771 | + | 0.867882i | \(0.334519\pi\) | |||||||
\(270\) | −4.30238 | + | 7.45195i | −0.261835 | + | 0.453511i | ||||
\(271\) | 11.2296i | 0.682153i | 0.940036 | + | 0.341076i | \(0.110791\pi\) | ||||
−0.940036 | + | 0.341076i | \(0.889209\pi\) | |||||||
\(272\) | 1.16749 | 0.0707894 | ||||||||
\(273\) | 4.30404 | − | 8.51324i | 0.260493 | − | 0.515245i | ||||
\(274\) | −28.5369 | −1.72398 | ||||||||
\(275\) | − | 33.9783i | − | 2.04897i | ||||||
\(276\) | 16.1575 | − | 27.9857i | 0.972569 | − | 1.68454i | ||||
\(277\) | −19.2059 | −1.15397 | −0.576984 | − | 0.816755i | \(-0.695771\pi\) | ||||
−0.576984 | + | 0.816755i | \(0.695771\pi\) | |||||||
\(278\) | 38.0747 | + | 21.9825i | 2.28357 | + | 1.31842i | ||||
\(279\) | 3.65876 | + | 2.11239i | 0.219044 | + | 0.126465i | ||||
\(280\) | 45.7104 | + | 25.3111i | 2.73172 | + | 1.51263i | ||||
\(281\) | − | 21.4527i | − | 1.27976i | −0.768474 | − | 0.639881i | \(-0.778984\pi\) | ||
0.768474 | − | 0.639881i | \(-0.221016\pi\) | |||||||
\(282\) | 8.97832 | + | 15.5509i | 0.534651 | + | 0.926043i | ||||
\(283\) | −4.10738 | + | 7.11419i | −0.244159 | + | 0.422895i | −0.961895 | − | 0.273420i | \(-0.911845\pi\) |
0.717736 | + | 0.696315i | \(0.245178\pi\) | |||||||
\(284\) | 21.2857 | + | 12.2893i | 1.26307 | + | 0.729236i | ||||
\(285\) | −7.91671 | + | 13.7121i | −0.468946 | + | 0.812238i | ||||
\(286\) | 40.1944 | + | 21.2327i | 2.37674 | + | 1.25552i | ||||
\(287\) | −7.36118 | − | 12.2387i | −0.434516 | − | 0.722429i | ||||
\(288\) | 2.75400 | − | 1.59002i | 0.162281 | − | 0.0936930i | ||||
\(289\) | −16.9603 | −0.997663 | ||||||||
\(290\) | 27.2486 | 1.60009 | ||||||||
\(291\) | −5.02047 | + | 2.89857i | −0.294305 | + | 0.169917i | ||||
\(292\) | −11.7325 | + | 6.77378i | −0.686594 | + | 0.396405i | ||||
\(293\) | 8.05762 | + | 4.65207i | 0.470731 | + | 0.271777i | 0.716546 | − | 0.697540i | \(-0.245722\pi\) |
−0.245815 | + | 0.969317i | \(0.579055\pi\) | |||||||
\(294\) | −15.5146 | − | 8.23154i | −0.904827 | − | 0.480073i | ||||
\(295\) | −1.43742 | + | 2.48969i | −0.0836901 | + | 0.144955i | ||||
\(296\) | −52.5110 | −3.05214 | ||||||||
\(297\) | 4.35178 | + | 2.51250i | 0.252516 | + | 0.145790i | ||||
\(298\) | 14.9006 | + | 25.8086i | 0.863170 | + | 1.49505i | ||||
\(299\) | −1.01992 | − | 27.1080i | −0.0589835 | − | 1.56769i | ||||
\(300\) | −29.0428 | −1.67679 | ||||||||
\(301\) | −5.91890 | − | 3.27746i | −0.341160 | − | 0.188910i | ||||
\(302\) | −16.7136 | − | 28.9488i | −0.961759 | − | 1.66582i | ||||
\(303\) | −2.10772 | − | 3.65067i | −0.121085 | − | 0.209726i | ||||
\(304\) | 23.4202 | − | 13.5216i | 1.34324 | − | 0.775520i | ||||
\(305\) | − | 9.14057i | − | 0.523388i | ||||||
\(306\) | 0.433074 | − | 0.250035i | 0.0247572 | − | 0.0142936i | ||||
\(307\) | 17.3759i | 0.991695i | 0.868410 | + | 0.495848i | \(0.165143\pi\) | ||||
−0.868410 | + | 0.495848i | \(0.834857\pi\) | |||||||
\(308\) | 27.6618 | − | 49.9556i | 1.57618 | − | 2.84648i | ||||
\(309\) | 2.11287 | + | 3.65960i | 0.120197 | + | 0.208187i | ||||
\(310\) | 36.3532i | 2.06472i | ||||||||
\(311\) | −2.53895 | − | 4.39760i | −0.143971 | − | 0.249365i | 0.785018 | − | 0.619473i | \(-0.212654\pi\) |
−0.928988 | + | 0.370109i | \(0.879320\pi\) | |||||||
\(312\) | 9.69773 | − | 18.3582i | 0.549026 | − | 1.03933i | ||||
\(313\) | −3.64621 | + | 6.31543i | −0.206096 | + | 0.356969i | −0.950481 | − | 0.310781i | \(-0.899409\pi\) |
0.744385 | + | 0.667750i | \(0.232743\pi\) | |||||||
\(314\) | −24.4256 | + | 14.1021i | −1.37842 | + | 0.795830i | ||||
\(315\) | 9.07230 | − | 0.162394i | 0.511166 | − | 0.00914984i | ||||
\(316\) | −9.68829 | + | 16.7806i | −0.545009 | + | 0.943983i | ||||
\(317\) | −20.5617 | − | 11.8713i | −1.15486 | − | 0.666757i | −0.204791 | − | 0.978806i | \(-0.565652\pi\) |
−0.950066 | + | 0.312048i | \(0.898985\pi\) | |||||||
\(318\) | − | 1.08350i | − | 0.0607595i | ||||||
\(319\) | − | 15.9126i | − | 0.890935i | ||||||
\(320\) | −11.0978 | − | 6.40734i | −0.620388 | − | 0.358181i | ||||
\(321\) | 2.32729 | − | 4.03099i | 0.129897 | − | 0.224988i | ||||
\(322\) | −49.9359 | + | 0.893849i | −2.78282 | + | 0.0498123i | ||||
\(323\) | 0.796888 | − | 0.460084i | 0.0443401 | − | 0.0255997i | ||||
\(324\) | 2.14755 | − | 3.71966i | 0.119308 | − | 0.206648i | ||||
\(325\) | −20.6406 | + | 12.9753i | −1.14494 | + | 0.719742i | ||||
\(326\) | 4.55593 | + | 7.89110i | 0.252330 | + | 0.437048i | ||||
\(327\) | 0.606180i | 0.0335219i | ||||||||
\(328\) | −15.5421 | − | 26.9197i | −0.858167 | − | 1.48639i | ||||
\(329\) | 9.17266 | − | 16.5653i | 0.505705 | − | 0.913274i | ||||
\(330\) | 43.2389i | 2.38023i | ||||||||
\(331\) | −0.0199341 | + | 0.0115089i | −0.00109568 | + | 0.000632589i | −0.500548 | − | 0.865709i | \(-0.666868\pi\) |
0.499452 | + | 0.866342i | \(0.333535\pi\) | |||||||
\(332\) | 63.2097i | 3.46909i | ||||||||
\(333\) | −7.89731 | + | 4.55951i | −0.432770 | + | 0.249860i | ||||
\(334\) | −12.9775 | − | 22.4777i | −0.710096 | − | 1.22992i | ||||
\(335\) | 19.1625 | + | 33.1904i | 1.04696 | + | 1.81338i | ||||
\(336\) | −13.5581 | − | 7.50748i | −0.739654 | − | 0.409567i | ||||
\(337\) | 12.3103 | 0.670583 | 0.335291 | − | 0.942114i | \(-0.391165\pi\) | ||||
0.335291 | + | 0.942114i | \(0.391165\pi\) | |||||||
\(338\) | −2.45092 | − | 32.5248i | −0.133312 | − | 1.76912i | ||||
\(339\) | 4.15517 | + | 7.19697i | 0.225678 | + | 0.390886i | ||||
\(340\) | 2.54256 | + | 1.46795i | 0.137890 | + | 0.0796106i | ||||
\(341\) | 21.2295 | 1.14964 | ||||||||
\(342\) | 5.79173 | − | 10.0316i | 0.313181 | − | 0.542445i | ||||
\(343\) | 0.993950 | + | 18.4936i | 0.0536683 | + | 0.998559i | ||||
\(344\) | −12.7526 | − | 7.36270i | −0.687573 | − | 0.396970i | ||||
\(345\) | 22.3461 | − | 12.9015i | 1.20307 | − | 0.694594i | ||||
\(346\) | −9.99089 | + | 5.76824i | −0.537114 | + | 0.310103i | ||||
\(347\) | 31.5302 | 1.69263 | 0.846315 | − | 0.532683i | \(-0.178816\pi\) | ||||
0.846315 | + | 0.532683i | \(0.178816\pi\) | |||||||
\(348\) | −13.6012 | −0.729102 | ||||||||
\(349\) | 1.69290 | − | 0.977398i | 0.0906191 | − | 0.0523189i | −0.454006 | − | 0.890999i | \(-0.650005\pi\) |
0.544625 | + | 0.838680i | \(0.316672\pi\) | |||||||
\(350\) | 23.1354 | + | 38.4650i | 1.23664 | + | 2.05604i | ||||
\(351\) | −0.135561 | − | 3.60300i | −0.00723569 | − | 0.192314i | ||||
\(352\) | 7.98986 | − | 13.8388i | 0.425861 | − | 0.737613i | ||||
\(353\) | −14.1302 | − | 8.15806i | −0.752073 | − | 0.434210i | 0.0743694 | − | 0.997231i | \(-0.476306\pi\) |
−0.826442 | + | 0.563021i | \(0.809639\pi\) | |||||||
\(354\) | 1.05159 | − | 1.82141i | 0.0558916 | − | 0.0968070i | ||||
\(355\) | 9.81280 | + | 16.9963i | 0.520809 | + | 0.902068i | ||||
\(356\) | − | 10.0766i | − | 0.534061i | ||||||
\(357\) | −0.461323 | − | 0.255447i | −0.0244158 | − | 0.0135197i | ||||
\(358\) | −1.96952 | − | 1.13710i | −0.104092 | − | 0.0600978i | ||||
\(359\) | 19.2335 | + | 11.1044i | 1.01510 | + | 0.586070i | 0.912682 | − | 0.408671i | \(-0.134008\pi\) |
0.102421 | + | 0.994741i | \(0.467341\pi\) | |||||||
\(360\) | 19.7487 | 1.04085 | ||||||||
\(361\) | 1.15722 | − | 2.00436i | 0.0609062 | − | 0.105493i | ||||
\(362\) | − | 47.4592i | − | 2.49440i | ||||||
\(363\) | 14.2506 | 0.747963 | ||||||||
\(364\) | −40.9095 | + | 2.27300i | −2.14424 | + | 0.119138i | ||||
\(365\) | −10.8175 | −0.566213 | ||||||||
\(366\) | 6.68708i | 0.349539i | ||||||||
\(367\) | 4.00293 | − | 6.93327i | 0.208951 | − | 0.361914i | −0.742433 | − | 0.669920i | \(-0.766328\pi\) |
0.951384 | + | 0.308006i | \(0.0996617\pi\) | |||||||
\(368\) | −44.0712 | −2.29737 | ||||||||
\(369\) | −4.67486 | − | 2.69903i | −0.243363 | − | 0.140506i | ||||
\(370\) | −67.9545 | − | 39.2336i | −3.53279 | − | 2.03966i | ||||
\(371\) | −0.979096 | + | 0.588893i | −0.0508321 | + | 0.0305738i | ||||
\(372\) | − | 18.1458i | − | 0.940816i | ||||||
\(373\) | −14.9023 | − | 25.8116i | −0.771614 | − | 1.33647i | −0.936678 | − | 0.350191i | \(-0.886117\pi\) |
0.165065 | − | 0.986283i | \(-0.447217\pi\) | |||||||
\(374\) | 1.25643 | − | 2.17619i | 0.0649683 | − | 0.112528i | ||||
\(375\) | −5.23287 | − | 3.02120i | −0.270224 | − | 0.156014i | ||||
\(376\) | 20.6061 | − | 35.6908i | 1.06268 | − | 1.84061i | ||||
\(377\) | −9.66635 | + | 6.07656i | −0.497842 | + | 0.312959i | ||||
\(378\) | −6.63713 | + | 0.118804i | −0.341377 | + | 0.00611063i | ||||
\(379\) | 9.17101 | − | 5.29489i | 0.471083 | − | 0.271980i | −0.245610 | − | 0.969369i | \(-0.578988\pi\) |
0.716693 | + | 0.697389i | \(0.245655\pi\) | |||||||
\(380\) | 68.0060 | 3.48864 | ||||||||
\(381\) | 10.0772 | 0.516273 | ||||||||
\(382\) | 33.4874 | − | 19.3340i | 1.71337 | − | 0.989213i | ||||
\(383\) | −24.0899 | + | 13.9083i | −1.23094 | + | 0.710681i | −0.967225 | − | 0.253920i | \(-0.918280\pi\) |
−0.263711 | + | 0.964602i | \(0.584947\pi\) | |||||||
\(384\) | 13.6270 | + | 7.86754i | 0.695399 | + | 0.401489i | ||||
\(385\) | 39.0726 | − | 23.5009i | 1.99132 | − | 1.19771i | ||||
\(386\) | −9.99283 | + | 17.3081i | −0.508622 | + | 0.880959i | ||||
\(387\) | −2.55721 | −0.129990 | ||||||||
\(388\) | 21.5634 | + | 12.4496i | 1.09471 | + | 0.632034i | ||||
\(389\) | −10.2034 | − | 17.6728i | −0.517331 | − | 0.896044i | −0.999797 | − | 0.0201295i | \(-0.993592\pi\) |
0.482466 | − | 0.875915i | \(-0.339741\pi\) | |||||||
\(390\) | 26.2661 | − | 16.5117i | 1.33004 | − | 0.836102i | ||||
\(391\) | −1.49955 | −0.0758357 | ||||||||
\(392\) | 1.44259 | + | 40.2829i | 0.0728616 | + | 2.03460i | ||||
\(393\) | −5.52188 | − | 9.56417i | −0.278542 | − | 0.482449i | ||||
\(394\) | −16.4612 | − | 28.5117i | −0.829305 | − | 1.43640i | ||||
\(395\) | −13.3990 | + | 7.73593i | −0.674178 | + | 0.389237i | ||||
\(396\) | − | 21.5828i | − | 1.08458i | ||||||
\(397\) | −12.1438 | + | 7.01122i | −0.609479 | + | 0.351883i | −0.772762 | − | 0.634696i | \(-0.781125\pi\) |
0.163282 | + | 0.986579i | \(0.447792\pi\) | |||||||
\(398\) | 48.9764i | 2.45496i | ||||||||
\(399\) | −12.2128 | + | 0.218609i | −0.611406 | + | 0.0109441i | ||||
\(400\) | 19.8043 | + | 34.3020i | 0.990213 | + | 1.71510i | ||||
\(401\) | 5.30040i | 0.264689i | 0.991204 | + | 0.132345i | \(0.0422506\pi\) | ||||
−0.991204 | + | 0.132345i | \(0.957749\pi\) | |||||||
\(402\) | −14.0189 | − | 24.2815i | −0.699201 | − | 1.21105i | ||||
\(403\) | −8.10692 | − | 12.8962i | −0.403835 | − | 0.642404i | ||||
\(404\) | −9.05284 | + | 15.6800i | −0.450396 | + | 0.780108i | ||||
\(405\) | 2.97008 | − | 1.71478i | 0.147585 | − | 0.0852080i | ||||
\(406\) | 10.8347 | + | 18.0138i | 0.537716 | + | 0.894009i | ||||
\(407\) | −22.9116 | + | 39.6840i | −1.13568 | + | 1.96706i | ||||
\(408\) | −0.993944 | − | 0.573854i | −0.0492076 | − | 0.0284100i | ||||
\(409\) | 29.0175i | 1.43482i | 0.696649 | + | 0.717412i | \(0.254673\pi\) | ||||
−0.696649 | + | 0.717412i | \(0.745327\pi\) | |||||||
\(410\) | − | 46.4490i | − | 2.29395i | ||||||
\(411\) | 9.85001 | + | 5.68690i | 0.485865 | + | 0.280514i | ||||
\(412\) | 9.07498 | − | 15.7183i | 0.447092 | − | 0.774387i | ||||
\(413\) | −2.21746 | + | 0.0396924i | −0.109114 | + | 0.00195314i | ||||
\(414\) | −16.3480 | + | 9.43851i | −0.803459 | + | 0.463878i | ||||
\(415\) | −25.2359 | + | 43.7099i | −1.23878 | + | 2.14564i | ||||
\(416\) | −11.4577 | + | 0.431089i | −0.561760 | + | 0.0211359i | ||||
\(417\) | −8.76143 | − | 15.1752i | −0.429049 | − | 0.743135i | ||||
\(418\) | − | 58.2068i | − | 2.84699i | ||||||
\(419\) | −6.43099 | − | 11.1388i | −0.314174 | − | 0.544166i | 0.665087 | − | 0.746766i | \(-0.268394\pi\) |
−0.979262 | + | 0.202600i | \(0.935061\pi\) | |||||||
\(420\) | −20.0872 | − | 33.3971i | −0.980157 | − | 1.62961i | ||||
\(421\) | 5.25836i | 0.256277i | 0.991756 | + | 0.128138i | \(0.0409002\pi\) | ||||
−0.991756 | + | 0.128138i | \(0.959100\pi\) | |||||||
\(422\) | 51.9549 | − | 29.9962i | 2.52913 | − | 1.46019i | ||||
\(423\) | − | 7.15688i | − | 0.347980i | ||||||
\(424\) | −2.15357 | + | 1.24336i | −0.104587 | + | 0.0603831i | ||||
\(425\) | 0.673854 | + | 1.16715i | 0.0326867 | + | 0.0566151i | ||||
\(426\) | −7.17887 | − | 12.4342i | −0.347817 | − | 0.602437i | ||||
\(427\) | 6.04274 | − | 3.63450i | 0.292429 | − | 0.175886i | ||||
\(428\) | −19.9919 | −0.966343 | ||||||||
\(429\) | −9.64247 | − | 15.3389i | −0.465543 | − | 0.740567i | ||||
\(430\) | −11.0021 | − | 19.0562i | −0.530568 | − | 0.918970i | ||||
\(431\) | 21.4053 | + | 12.3584i | 1.03106 | + | 0.595281i | 0.917287 | − | 0.398226i | \(-0.130374\pi\) |
0.113770 | + | 0.993507i | \(0.463707\pi\) | |||||||
\(432\) | −5.85764 | −0.281826 | ||||||||
\(433\) | 10.8239 | − | 18.7476i | 0.520166 | − | 0.900953i | −0.479560 | − | 0.877509i | \(-0.659204\pi\) |
0.999725 | − | 0.0234439i | \(-0.00746310\pi\) | |||||||
\(434\) | −24.0327 | + | 14.4549i | −1.15361 | + | 0.693856i | ||||
\(435\) | −9.40533 | − | 5.43017i | −0.450951 | − | 0.260357i | ||||
\(436\) | 2.25479 | − | 1.30180i | 0.107985 | − | 0.0623450i | ||||
\(437\) | −30.0815 | + | 17.3676i | −1.43899 | + | 0.830804i | ||||
\(438\) | 7.91388 | 0.378140 | ||||||||
\(439\) | −7.75058 | −0.369915 | −0.184957 | − | 0.982747i | \(-0.559215\pi\) | ||||
−0.184957 | + | 0.982747i | \(0.559215\pi\) | |||||||
\(440\) | 85.9421 | − | 49.6187i | 4.09713 | − | 2.36548i | ||||
\(441\) | 3.71471 | + | 5.93303i | 0.176891 | + | 0.282525i | ||||
\(442\) | −1.80175 | + | 0.0677898i | −0.0857007 | + | 0.00322443i | ||||
\(443\) | 3.55156 | − | 6.15148i | 0.168740 | − | 0.292265i | −0.769237 | − | 0.638963i | \(-0.779364\pi\) |
0.937977 | + | 0.346698i | \(0.112697\pi\) | |||||||
\(444\) | 33.9197 | + | 19.5835i | 1.60976 | + | 0.929394i | ||||
\(445\) | 4.02301 | − | 6.96806i | 0.190709 | − | 0.330318i | ||||
\(446\) | 13.0932 | + | 22.6781i | 0.619982 | + | 1.07384i | ||||
\(447\) | − | 11.8777i | − | 0.561797i | ||||||
\(448\) | −0.176930 | − | 9.88437i | −0.00835914 | − | 0.466993i | ||||
\(449\) | 25.1353 | + | 14.5119i | 1.18621 | + | 0.684858i | 0.957443 | − | 0.288623i | \(-0.0931974\pi\) |
0.228767 | + | 0.973481i | \(0.426531\pi\) | |||||||
\(450\) | 14.6926 | + | 8.48276i | 0.692614 | + | 0.399881i | ||||
\(451\) | −27.1252 | −1.27728 | ||||||||
\(452\) | 17.8469 | − | 30.9117i | 0.839445 | − | 1.45396i | ||||
\(453\) | 13.3229i | 0.625964i | ||||||||
\(454\) | 24.8404 | 1.16582 | ||||||||
\(455\) | −29.1966 | − | 14.7610i | −1.36876 | − | 0.692004i | ||||
\(456\) | −26.5851 | −1.24496 | ||||||||
\(457\) | 27.0304i | 1.26443i | 0.774794 | + | 0.632213i | \(0.217853\pi\) | ||||
−0.774794 | + | 0.632213i | \(0.782147\pi\) | |||||||
\(458\) | 19.7823 | − | 34.2640i | 0.924367 | − | 1.60105i | ||||
\(459\) | −0.199310 | −0.00930301 | ||||||||
\(460\) | −95.9784 | − | 55.4132i | −4.47502 | − | 2.58365i | ||||
\(461\) | 2.16474 | + | 1.24981i | 0.100822 | + | 0.0582096i | 0.549563 | − | 0.835452i | \(-0.314794\pi\) |
−0.448741 | + | 0.893662i | \(0.648127\pi\) | |||||||
\(462\) | −28.5848 | + | 17.1928i | −1.32989 | + | 0.799882i | ||||
\(463\) | 28.9351i | 1.34473i | 0.740222 | + | 0.672363i | \(0.234721\pi\) | ||||
−0.740222 | + | 0.672363i | \(0.765279\pi\) | |||||||
\(464\) | 9.27466 | + | 16.0642i | 0.430565 | + | 0.745761i | ||||
\(465\) | 7.24455 | − | 12.5479i | 0.335958 | − | 0.581897i | ||||
\(466\) | −4.13925 | − | 2.38979i | −0.191747 | − | 0.110705i | ||||
\(467\) | −4.23383 | + | 7.33321i | −0.195918 | + | 0.339340i | −0.947201 | − | 0.320640i | \(-0.896102\pi\) |
0.751283 | + | 0.659980i | \(0.229435\pi\) | |||||||
\(468\) | −13.1108 | + | 8.24185i | −0.606048 | + | 0.380980i | ||||
\(469\) | −14.3224 | + | 25.8654i | −0.661346 | + | 1.19435i | ||||
\(470\) | 53.3327 | − | 30.7917i | 2.46005 | − | 1.42031i | ||||
\(471\) | 11.2412 | 0.517969 | ||||||||
\(472\) | −4.82701 | −0.222181 | ||||||||
\(473\) | −11.1284 | + | 6.42498i | −0.511684 | + | 0.295421i | ||||
\(474\) | 9.80248 | − | 5.65947i | 0.450243 | − | 0.259948i | ||||
\(475\) | 27.0355 | + | 15.6089i | 1.24047 | + | 0.716187i | ||||
\(476\) | 0.0405353 | + | 2.26455i | 0.00185793 | + | 0.103795i | ||||
\(477\) | −0.215922 | + | 0.373988i | −0.00988639 | + | 0.0171237i | ||||
\(478\) | 66.0087 | 3.01917 | ||||||||
\(479\) | 20.7557 | + | 11.9833i | 0.948351 | + | 0.547531i | 0.892568 | − | 0.450912i | \(-0.148901\pi\) |
0.0557827 | + | 0.998443i | \(0.482235\pi\) | |||||||
\(480\) | −5.45307 | − | 9.44500i | −0.248898 | − | 0.431103i | ||||
\(481\) | 32.8559 | − | 1.23618i | 1.49810 | − | 0.0563650i | ||||
\(482\) | 56.6702 | 2.58126 | ||||||||
\(483\) | 17.4144 | + | 9.64282i | 0.792381 | + | 0.438763i | ||||
\(484\) | −30.6039 | − | 53.0075i | −1.39108 | − | 2.40943i | ||||
\(485\) | 9.94081 | + | 17.2180i | 0.451389 | + | 0.781828i | ||||
\(486\) | −2.17286 | + | 1.25450i | −0.0985629 | + | 0.0569053i | ||||
\(487\) | − | 36.7256i | − | 1.66420i | −0.554628 | − | 0.832099i | \(-0.687139\pi\) | ||
0.554628 | − | 0.832099i | \(-0.312861\pi\) | |||||||
\(488\) | 13.2913 | − | 7.67373i | 0.601669 | − | 0.347374i | ||||
\(489\) | − | 3.63167i | − | 0.164230i | ||||||
\(490\) | −28.2305 | + | 53.2080i | −1.27533 | + | 2.40369i | ||||
\(491\) | 4.83577 | + | 8.37579i | 0.218235 | + | 0.377994i | 0.954268 | − | 0.298951i | \(-0.0966367\pi\) |
−0.736033 | + | 0.676945i | \(0.763303\pi\) | |||||||
\(492\) | 23.1852i | 1.04527i | ||||||||
\(493\) | 0.315577 | + | 0.546595i | 0.0142129 | + | 0.0246174i | ||||
\(494\) | −35.3586 | + | 22.2275i | −1.59086 | + | 1.00006i | ||||
\(495\) | 8.61676 | − | 14.9247i | 0.387295 | − | 0.670814i | ||||
\(496\) | −21.4317 | + | 12.3736i | −0.962313 | + | 0.555591i | ||||
\(497\) | −7.33426 | + | 13.2453i | −0.328987 | + | 0.594131i | ||||
\(498\) | 18.4622 | − | 31.9774i | 0.827309 | − | 1.43294i | ||||
\(499\) | −24.0357 | − | 13.8770i | −1.07599 | − | 0.621221i | −0.146176 | − | 0.989259i | \(-0.546697\pi\) |
−0.929811 | + | 0.368037i | \(0.880030\pi\) | |||||||
\(500\) | 25.9526i | 1.16064i | ||||||||
\(501\) | 10.3447i | 0.462169i | ||||||||
\(502\) | 62.7807 | + | 36.2465i | 2.80204 | + | 1.61776i | ||||
\(503\) | 6.56936 | − | 11.3785i | 0.292913 | − | 0.507341i | −0.681584 | − | 0.731740i | \(-0.738709\pi\) |
0.974497 | + | 0.224399i | \(0.0720419\pi\) | |||||||
\(504\) | 7.85256 | + | 13.0557i | 0.349781 | + | 0.581547i | ||||
\(505\) | −12.5202 | + | 7.22854i | −0.557141 | + | 0.321666i | ||||
\(506\) | −47.4285 | + | 82.1486i | −2.10845 | + | 3.65195i | ||||
\(507\) | −5.63565 | + | 11.7149i | −0.250288 | + | 0.520278i | ||||
\(508\) | −21.6414 | − | 37.4839i | −0.960180 | − | 1.66308i | ||||
\(509\) | 29.1555i | 1.29230i | 0.763212 | + | 0.646148i | \(0.223621\pi\) | ||||
−0.763212 | + | 0.646148i | \(0.776379\pi\) | |||||||
\(510\) | −0.857510 | − | 1.48525i | −0.0379712 | − | 0.0657680i | ||||
\(511\) | −4.30128 | − | 7.15133i | −0.190277 | − | 0.316356i | ||||
\(512\) | − | 48.8337i | − | 2.15816i | ||||||
\(513\) | −3.99823 | + | 2.30838i | −0.176526 | + | 0.101917i | ||||
\(514\) | 40.2702i | 1.77624i | ||||||||
\(515\) | 12.5508 | − | 7.24621i | 0.553055 | − | 0.319306i | ||||
\(516\) | 5.49172 | + | 9.51194i | 0.241760 | + | 0.418740i | ||||
\(517\) | −17.9817 | − | 31.1452i | −0.790833 | − | 1.36976i | ||||
\(518\) | −1.08338 | − | 60.5242i | −0.0476010 | − | 2.65928i | ||||
\(519\) | 4.59804 | 0.201831 | ||||||||
\(520\) | −62.9604 | − | 33.2589i | −2.76100 | − | 1.45850i | ||||
\(521\) | 7.62747 | + | 13.2112i | 0.334166 | + | 0.578792i | 0.983324 | − | 0.181861i | \(-0.0582122\pi\) |
−0.649159 | + | 0.760653i | \(0.724879\pi\) | |||||||
\(522\) | 6.88077 | + | 3.97261i | 0.301163 | + | 0.173877i | ||||
\(523\) | −24.9370 | −1.09042 | −0.545209 | − | 0.838300i | \(-0.683550\pi\) | ||||
−0.545209 | + | 0.838300i | \(0.683550\pi\) | |||||||
\(524\) | −23.7170 | + | 41.0790i | −1.03608 | + | 1.79454i | ||||
\(525\) | −0.320182 | − | 17.8873i | −0.0139739 | − | 0.780667i | ||||
\(526\) | −31.4435 | − | 18.1539i | −1.37100 | − | 0.791548i | ||||
\(527\) | −0.729229 | + | 0.421021i | −0.0317657 | + | 0.0183400i | ||||
\(528\) | −25.4911 | + | 14.7173i | −1.10936 | + | 0.640489i | ||||
\(529\) | 33.6063 | 1.46114 | ||||||||
\(530\) | −3.71592 | −0.161409 | ||||||||
\(531\) | −0.725951 | + | 0.419128i | −0.0315036 | + | 0.0181886i | ||||
\(532\) | 27.0408 | + | 44.9581i | 1.17237 | + | 1.94918i | ||||
\(533\) | 10.3583 | + | 16.4776i | 0.448669 | + | 0.713725i | ||||
\(534\) | −2.94316 | + | 5.09771i | −0.127363 | + | 0.220600i | ||||
\(535\) | −13.8245 | − | 7.98158i | −0.597685 | − | 0.345074i | ||||
\(536\) | −32.1748 | + | 55.7283i | −1.38974 | + | 2.40710i | ||||
\(537\) | 0.453209 | + | 0.784982i | 0.0195574 | + | 0.0338745i | ||||
\(538\) | 40.8849i | 1.76267i | ||||||||
\(539\) | 31.0724 | + | 16.4860i | 1.33838 | + | 0.710104i | ||||
\(540\) | −12.7568 | − | 7.36513i | −0.548965 | − | 0.316945i | ||||
\(541\) | −21.8817 | − | 12.6334i | −0.940767 | − | 0.543152i | −0.0505664 | − | 0.998721i | \(-0.516103\pi\) |
−0.890201 | + | 0.455569i | \(0.849436\pi\) | |||||||
\(542\) | −28.1752 | −1.21023 | ||||||||
\(543\) | −9.45777 | + | 16.3813i | −0.405872 | + | 0.702991i | ||||
\(544\) | 0.633816i | 0.0271746i | ||||||||
\(545\) | 2.07893 | 0.0890516 | ||||||||
\(546\) | 21.3597 | + | 10.7989i | 0.914112 | + | 0.462148i | ||||
\(547\) | 31.0477 | 1.32750 | 0.663752 | − | 0.747953i | \(-0.268963\pi\) | ||||
0.663752 | + | 0.747953i | \(0.268963\pi\) | |||||||
\(548\) | − | 48.8516i | − | 2.08684i | ||||||
\(549\) | 1.33262 | − | 2.30816i | 0.0568747 | − | 0.0985099i | ||||
\(550\) | 85.2517 | 3.63515 | ||||||||
\(551\) | 12.6611 | + | 7.30991i | 0.539383 | + | 0.311413i | ||||
\(552\) | 37.5201 | + | 21.6623i | 1.59696 | + | 0.922007i | ||||
\(553\) | −10.4419 | − | 5.78197i | −0.444035 | − | 0.245874i | ||||
\(554\) | − | 48.1876i | − | 2.04729i | ||||||
\(555\) | 15.6371 | + | 27.0843i | 0.663759 | + | 1.14966i | ||||
\(556\) | −37.6312 | + | 65.1791i | −1.59592 | + | 2.76421i | ||||
\(557\) | 22.2174 | + | 12.8272i | 0.941380 | + | 0.543506i | 0.890393 | − | 0.455193i | \(-0.150430\pi\) |
0.0509872 | + | 0.998699i | \(0.483763\pi\) | |||||||
\(558\) | −5.29999 | + | 9.17985i | −0.224366 | + | 0.388614i | ||||
\(559\) | 8.15256 | + | 4.30660i | 0.344816 | + | 0.182150i | ||||
\(560\) | −25.7473 | + | 46.4982i | −1.08802 | + | 1.96491i | ||||
\(561\) | −0.867354 | + | 0.500767i | −0.0366197 | + | 0.0211424i | ||||
\(562\) | 53.8249 | 2.27047 | ||||||||
\(563\) | 9.04397 | 0.381158 | 0.190579 | − | 0.981672i | \(-0.438964\pi\) | ||||
0.190579 | + | 0.981672i | \(0.438964\pi\) | |||||||
\(564\) | −26.6212 | + | 15.3697i | −1.12095 | + | 0.647183i | ||||
\(565\) | 24.6824 | − | 14.2504i | 1.03840 | − | 0.599519i | ||||
\(566\) | −17.8495 | − | 10.3054i | −0.750272 | − | 0.433170i | ||||
\(567\) | 2.31460 | + | 1.28166i | 0.0972039 | + | 0.0538245i | ||||
\(568\) | −16.4762 | + | 28.5376i | −0.691325 | + | 1.19741i | ||||
\(569\) | 43.9957 | 1.84440 | 0.922198 | − | 0.386719i | \(-0.126391\pi\) | ||||
0.922198 | + | 0.386719i | \(0.126391\pi\) | |||||||
\(570\) | −34.4038 | − | 19.8631i | −1.44102 | − | 0.831972i | ||||
\(571\) | −8.12709 | − | 14.0765i | −0.340108 | − | 0.589085i | 0.644344 | − | 0.764735i | \(-0.277130\pi\) |
−0.984453 | + | 0.175651i | \(0.943797\pi\) | |||||||
\(572\) | −36.3477 | + | 68.8076i | −1.51977 | + | 2.87699i | ||||
\(573\) | −15.4117 | −0.643833 | ||||||||
\(574\) | 30.7070 | − | 18.4692i | 1.28168 | − | 0.770890i | ||||
\(575\) | −25.4372 | − | 44.0584i | −1.06080 | − | 1.83736i | ||||
\(576\) | −1.86827 | − | 3.23594i | −0.0778446 | − | 0.134831i | ||||
\(577\) | 2.00627 | − | 1.15832i | 0.0835222 | − | 0.0482216i | −0.457657 | − | 0.889129i | \(-0.651311\pi\) |
0.541179 | + | 0.840907i | \(0.317978\pi\) | |||||||
\(578\) | − | 42.5534i | − | 1.76999i | ||||||
\(579\) | 6.89839 | − | 3.98279i | 0.286688 | − | 0.165519i | ||||
\(580\) | 46.6462i | 1.93688i | ||||||||
\(581\) | −38.9306 | + | 0.696855i | −1.61511 | + | 0.0289104i | ||||
\(582\) | −7.27252 | − | 12.5964i | −0.301455 | − | 0.522136i | ||||
\(583\) | 2.17001i | 0.0898728i | ||||||||
\(584\) | −9.08154 | − | 15.7297i | −0.375797 | − | 0.650899i | ||||
\(585\) | −12.3567 | + | 0.464913i | −0.510887 | + | 0.0192218i | ||||
\(586\) | −11.6720 | + | 20.2166i | −0.482168 | + | 0.835139i | ||||
\(587\) | −29.7041 | + | 17.1497i | −1.22602 | + | 0.707843i | −0.966195 | − | 0.257813i | \(-0.916998\pi\) |
−0.259825 | + | 0.965656i | \(0.583665\pi\) | |||||||
\(588\) | 14.0914 | − | 26.5589i | 0.581118 | − | 1.09527i | ||||
\(589\) | −9.75238 | + | 16.8916i | −0.401840 | + | 0.696007i | ||||
\(590\) | −6.24664 | − | 3.60650i | −0.257170 | − | 0.148477i | ||||
\(591\) | 13.1217i | 0.539756i | ||||||||
\(592\) | − | 53.4160i | − | 2.19538i | ||||||
\(593\) | −21.2551 | − | 12.2717i | −0.872844 | − | 0.503937i | −0.00455184 | − | 0.999990i | \(-0.501449\pi\) |
−0.868292 | + | 0.496053i | \(0.834782\pi\) | |||||||
\(594\) | −6.30387 | + | 10.9186i | −0.258651 | + | 0.447996i | ||||
\(595\) | −0.876071 | + | 1.58213i | −0.0359154 | + | 0.0648612i | ||||
\(596\) | −44.1811 | + | 25.5080i | −1.80973 | + | 1.04485i | ||||
\(597\) | 9.76013 | − | 16.9050i | 0.399456 | − | 0.691877i | ||||
\(598\) | 68.0140 | − | 2.55898i | 2.78130 | − | 0.104644i | ||||
\(599\) | 8.47361 | + | 14.6767i | 0.346222 | + | 0.599675i | 0.985575 | − | 0.169239i | \(-0.0541309\pi\) |
−0.639353 | + | 0.768914i | \(0.720798\pi\) | |||||||
\(600\) | − | 38.9375i | − | 1.58961i | ||||||
\(601\) | 20.0508 | + | 34.7290i | 0.817888 | + | 1.41662i | 0.907235 | + | 0.420624i | \(0.138189\pi\) |
−0.0893467 | + | 0.996001i | \(0.528478\pi\) | |||||||
\(602\) | 8.22316 | − | 14.8505i | 0.335151 | − | 0.605263i | ||||
\(603\) | 11.1749i | 0.455077i | ||||||||
\(604\) | 49.5566 | − | 28.6115i | 2.01643 | − | 1.16419i | ||||
\(605\) | − | 48.8733i | − | 1.98698i | ||||||
\(606\) | 9.15955 | − | 5.28827i | 0.372081 | − | 0.214821i | ||||
\(607\) | 21.9043 | + | 37.9393i | 0.889067 | + | 1.53991i | 0.840980 | + | 0.541066i | \(0.181979\pi\) |
0.0480874 | + | 0.998843i | \(0.484687\pi\) | |||||||
\(608\) | 7.34075 | + | 12.7145i | 0.297707 | + | 0.515643i | ||||
\(609\) | −0.149946 | − | 8.37693i | −0.00607614 | − | 0.339450i | ||||
\(610\) | 22.9337 | 0.928559 | ||||||||
\(611\) | −12.0529 | + | 22.8167i | −0.487609 | + | 0.923063i | ||||
\(612\) | 0.428028 | + | 0.741367i | 0.0173020 | + | 0.0299680i | ||||
\(613\) | −8.91783 | − | 5.14871i | −0.360188 | − | 0.207954i | 0.308975 | − | 0.951070i | \(-0.400014\pi\) |
−0.669163 | + | 0.743116i | \(0.733347\pi\) | |||||||
\(614\) | −43.5962 | −1.75940 | ||||||||
\(615\) | −9.25647 | + | 16.0327i | −0.373257 | + | 0.646500i | ||||
\(616\) | 66.9750 | + | 37.0859i | 2.69850 | + | 1.49423i | ||||
\(617\) | 12.1246 | + | 7.00015i | 0.488119 | + | 0.281815i | 0.723794 | − | 0.690017i | \(-0.242397\pi\) |
−0.235675 | + | 0.971832i | \(0.575730\pi\) | |||||||
\(618\) | −9.18195 | + | 5.30120i | −0.369352 | + | 0.213246i | ||||
\(619\) | 25.0425 | − | 14.4583i | 1.00654 | − | 0.581127i | 0.0963641 | − | 0.995346i | \(-0.469279\pi\) |
0.910177 | + | 0.414219i | \(0.135945\pi\) | |||||||
\(620\) | −62.2321 | −2.49930 | ||||||||
\(621\) | 7.52372 | 0.301916 | ||||||||
\(622\) | 11.0336 | − | 6.37024i | 0.442406 | − | 0.255423i | ||||
\(623\) | 6.20616 | − | 0.111090i | 0.248645 | − | 0.00445072i | ||||
\(624\) | 18.6746 | + | 9.86487i | 0.747581 | + | 0.394911i | ||||
\(625\) | 6.54328 | − | 11.3333i | 0.261731 | − | 0.453332i | ||||
\(626\) | −15.8454 | − | 9.14836i | −0.633310 | − | 0.365642i | ||||
\(627\) | −11.5996 | + | 20.0911i | −0.463243 | + | 0.802361i | ||||
\(628\) | −24.1411 | − | 41.8136i | −0.963334 | − | 1.66854i | ||||
\(629\) | − | 1.81752i | − | 0.0724692i | ||||||
\(630\) | 0.407446 | + | 22.7624i | 0.0162330 | + | 0.906877i | ||||
\(631\) | −36.5812 | − | 21.1202i | −1.45628 | − | 0.840782i | −0.457451 | − | 0.889235i | \(-0.651237\pi\) |
−0.998825 | + | 0.0484534i | \(0.984571\pi\) | |||||||
\(632\) | −22.4976 | − | 12.9890i | −0.894907 | − | 0.516675i | ||||
\(633\) | −23.9109 | −0.950371 | ||||||||
\(634\) | 29.7851 | − | 51.5892i | 1.18292 | − | 2.04887i | ||||
\(635\) | − | 34.5605i | − | 1.37149i | ||||||
\(636\) | 1.85481 | 0.0735480 | ||||||||
\(637\) | −1.85094 | − | 25.1709i | −0.0733368 | − | 0.997307i | ||||
\(638\) | 39.9248 | 1.58064 | ||||||||
\(639\) | 5.72249i | 0.226378i | ||||||||
\(640\) | 26.9822 | − | 46.7345i | 1.06656 | − | 1.84734i | ||||
\(641\) | −22.6364 | −0.894086 | −0.447043 | − | 0.894512i | \(-0.647523\pi\) | ||||
−0.447043 | + | 0.894512i | \(0.647523\pi\) | |||||||
\(642\) | 10.1138 | + | 5.83918i | 0.399158 | + | 0.230454i | ||||
\(643\) | 21.1425 | + | 12.2066i | 0.833778 | + | 0.481382i | 0.855145 | − | 0.518389i | \(-0.173468\pi\) |
−0.0213662 | + | 0.999772i | \(0.506802\pi\) | |||||||
\(644\) | −1.53016 | − | 85.4839i | −0.0602966 | − | 3.36854i | ||||
\(645\) | 8.77009i | 0.345322i | ||||||||
\(646\) | 1.15435 | + | 1.99939i | 0.0454173 | + | 0.0786651i | ||||
\(647\) | 13.1968 | − | 22.8574i | 0.518818 | − | 0.898619i | −0.480943 | − | 0.876752i | \(-0.659706\pi\) |
0.999761 | − | 0.0218670i | \(-0.00696104\pi\) | |||||||
\(648\) | 4.98692 | + | 2.87920i | 0.195905 | + | 0.113106i | ||||
\(649\) | −2.10612 | + | 3.64790i | −0.0826724 | + | 0.143193i | ||||
\(650\) | −32.5551 | − | 51.7874i | −1.27692 | − | 2.03127i | ||||
\(651\) | 11.1759 | − | 0.200048i | 0.438019 | − | 0.00784050i | ||||
\(652\) | −13.5086 | + | 7.79917i | −0.529036 | + | 0.305439i | ||||
\(653\) | 15.9908 | 0.625766 | 0.312883 | − | 0.949792i | \(-0.398705\pi\) | ||||
0.312883 | + | 0.949792i | \(0.398705\pi\) | |||||||
\(654\) | −1.52091 | −0.0594722 | ||||||||
\(655\) | −32.8009 | + | 18.9376i | −1.28164 | + | 0.739953i | ||||
\(656\) | 27.3836 | − | 15.8099i | 1.06915 | − | 0.617275i | ||||
\(657\) | −2.73161 | − | 1.57710i | −0.106570 | − | 0.0615284i | ||||
\(658\) | 41.5624 | + | 23.0142i | 1.62027 | + | 0.897188i | ||||
\(659\) | 1.71887 | − | 2.97717i | 0.0669576 | − | 0.115974i | −0.830603 | − | 0.556865i | \(-0.812004\pi\) |
0.897561 | + | 0.440891i | \(0.145337\pi\) | |||||||
\(660\) | −74.0196 | −2.88121 | ||||||||
\(661\) | 7.12554 | + | 4.11393i | 0.277151 | + | 0.160013i | 0.632133 | − | 0.774860i | \(-0.282180\pi\) |
−0.354982 | + | 0.934873i | \(0.615513\pi\) | |||||||
\(662\) | −0.0288760 | − | 0.0500147i | −0.00112230 | − | 0.00194388i | ||||
\(663\) | 0.635416 | + | 0.335659i | 0.0246775 | + | 0.0130359i | ||||
\(664\) | −84.7448 | −3.28873 | ||||||||
\(665\) | 0.749731 | + | 41.8846i | 0.0290733 | + | 1.62422i | ||||
\(666\) | −11.4398 | − | 19.8144i | −0.443285 | − | 0.767791i | ||||
\(667\) | −11.9126 | − | 20.6333i | −0.461259 | − | 0.798924i | ||||
\(668\) | 38.4789 | − | 22.2158i | 1.48879 | − | 0.859555i | ||||
\(669\) | − | 10.4370i | − | 0.403517i | ||||||
\(670\) | −83.2748 | + | 48.0787i | −3.21719 | + | 1.85744i | ||||
\(671\) | − | 13.3928i | − | 0.517023i | ||||||
\(672\) | 4.07573 | − | 7.36052i | 0.157225 | − | 0.283938i | ||||
\(673\) | −12.6425 | − | 21.8974i | −0.487332 | − | 0.844084i | 0.512562 | − | 0.858650i | \(-0.328697\pi\) |
−0.999894 | + | 0.0145663i | \(0.995363\pi\) | |||||||
\(674\) | 30.8865i | 1.18970i | ||||||||
\(675\) | −3.38093 | − | 5.85594i | −0.130132 | − | 0.225395i | ||||
\(676\) | 55.6784 | − | 4.19566i | 2.14148 | − | 0.161372i | ||||
\(677\) | 3.17568 | − | 5.50044i | 0.122051 | − | 0.211399i | −0.798525 | − | 0.601961i | \(-0.794386\pi\) |
0.920576 | + | 0.390562i | \(0.127719\pi\) | |||||||
\(678\) | −18.0572 | + | 10.4253i | −0.693483 | + | 0.400383i | ||||
\(679\) | −7.42994 | + | 13.4180i | −0.285135 | + | 0.514937i | ||||
\(680\) | −1.96806 | + | 3.40879i | −0.0754718 | + | 0.130721i | ||||
\(681\) | −8.57408 | − | 4.95025i | −0.328560 | − | 0.189694i | ||||
\(682\) | 53.2649i | 2.03962i | ||||||||
\(683\) | 47.9352i | 1.83419i | 0.398671 | + | 0.917094i | \(0.369471\pi\) | ||||
−0.398671 | + | 0.917094i | \(0.630529\pi\) | |||||||
\(684\) | 17.1728 | + | 9.91470i | 0.656617 | + | 0.379098i | ||||
\(685\) | 19.5036 | − | 33.7812i | 0.745193 | − | 1.29071i | ||||
\(686\) | −46.4004 | + | 2.49382i | −1.77158 | + | 0.0952146i | ||||
\(687\) | −13.6564 | + | 7.88453i | −0.521025 | + | 0.300814i | ||||
\(688\) | 7.48960 | − | 12.9724i | 0.285538 | − | 0.494567i | ||||
\(689\) | 1.31821 | − | 0.828665i | 0.0502197 | − | 0.0315696i | ||||
\(690\) | 32.3699 | + | 56.0663i | 1.23230 | + | 2.13441i | ||||
\(691\) | − | 25.5592i | − | 0.972317i | −0.873871 | − | 0.486159i | \(-0.838398\pi\) | ||
0.873871 | − | 0.486159i | \(-0.161602\pi\) | |||||||
\(692\) | −9.87450 | − | 17.1031i | −0.375372 | − | 0.650164i | ||||
\(693\) | 13.2928 | − | 0.237940i | 0.504951 | − | 0.00903858i | ||||
\(694\) | 79.1094i | 3.00295i | ||||||||
\(695\) | −52.0444 | + | 30.0478i | −1.97416 | + | 1.13978i | ||||
\(696\) | − | 18.2350i | − | 0.691198i | ||||||
\(697\) | 0.931747 | − | 0.537944i | 0.0352924 | − | 0.0203761i | ||||
\(698\) | 2.45230 | + | 4.24750i | 0.0928207 | + | 0.160770i | ||||
\(699\) | 0.952488 | + | 1.64976i | 0.0360264 | + | 0.0623996i | ||||
\(700\) | −65.8472 | + | 39.6048i | −2.48879 | + | 1.49692i | ||||
\(701\) | −14.6478 | −0.553238 | −0.276619 | − | 0.960980i | \(-0.589214\pi\) | ||||
−0.276619 | + | 0.960980i | \(0.589214\pi\) | |||||||
\(702\) | 9.03994 | − | 0.340122i | 0.341191 | − | 0.0128371i | ||||
\(703\) | −21.0502 | − | 36.4600i | −0.793922 | − | 1.37511i | ||||
\(704\) | −16.2606 | − | 9.38806i | −0.612844 | − | 0.353826i | ||||
\(705\) | −24.5449 | −0.924416 | ||||||||
\(706\) | 20.4686 | − | 35.4526i | 0.770345 | − | 1.33428i | ||||
\(707\) | −9.75703 | − | 5.40274i | −0.366951 | − | 0.203191i | ||||
\(708\) | 3.11803 | + | 1.80019i | 0.117183 | + | 0.0676555i | ||||
\(709\) | 16.2182 | − | 9.36357i | 0.609087 | − | 0.351656i | −0.163521 | − | 0.986540i | \(-0.552285\pi\) |
0.772608 | + | 0.634883i | \(0.218952\pi\) | |||||||
\(710\) | −42.6437 | + | 24.6203i | −1.60039 | + | 0.923985i | ||||
\(711\) | −4.51133 | −0.169188 | ||||||||
\(712\) | 13.5097 | 0.506297 | ||||||||
\(713\) | 27.5275 | − | 15.8930i | 1.03091 | − | 0.595198i | ||||
\(714\) | 0.640918 | − | 1.15746i | 0.0239858 | − | 0.0433169i | ||||
\(715\) | −52.6055 | + | 33.0694i | −1.96733 | + | 1.23673i | ||||
\(716\) | 1.94658 | − | 3.37157i | 0.0727470 | − | 0.126001i | ||||
\(717\) | −22.7840 | − | 13.1544i | −0.850885 | − | 0.491259i | ||||
\(718\) | −27.8611 | + | 48.2568i | −1.03977 | + | 1.80093i | ||||
\(719\) | −8.57680 | − | 14.8555i | −0.319861 | − | 0.554015i | 0.660598 | − | 0.750740i | \(-0.270303\pi\) |
−0.980459 | + | 0.196725i | \(0.936969\pi\) | |||||||
\(720\) | 20.0891i | 0.748677i | ||||||||
\(721\) | 9.78089 | + | 5.41595i | 0.364259 | + | 0.201701i | ||||
\(722\) | 5.02895 | + | 2.90346i | 0.187158 | + | 0.108056i | ||||
\(723\) | −19.5607 | − | 11.2934i | −0.727470 | − | 0.420005i | ||||
\(724\) | 81.2440 | 3.01941 | ||||||||
\(725\) | −10.7063 | + | 18.5439i | −0.397624 | + | 0.688705i | ||||
\(726\) | 35.7548i | 1.32699i | ||||||||
\(727\) | 7.13494 | 0.264620 | 0.132310 | − | 0.991208i | \(-0.457760\pi\) | ||||
0.132310 | + | 0.991208i | \(0.457760\pi\) | |||||||
\(728\) | −3.04739 | − | 54.8470i | −0.112944 | − | 2.03276i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − | 27.1411i | − | 1.00454i | ||||||
\(731\) | 0.254839 | − | 0.441394i | 0.00942556 | − | 0.0163255i | ||||
\(732\) | −11.4474 | −0.423109 | ||||||||
\(733\) | 17.0588 | + | 9.84891i | 0.630082 | + | 0.363778i | 0.780784 | − | 0.624801i | \(-0.214820\pi\) |
−0.150702 | + | 0.988579i | \(0.548153\pi\) | |||||||
\(734\) | 17.3956 | + | 10.0434i | 0.642083 | + | 0.370707i | ||||
\(735\) | 20.3477 | − | 12.7398i | 0.750535 | − | 0.469915i | ||||
\(736\) | − | 23.9258i | − | 0.881915i | ||||||
\(737\) | 28.0769 | + | 48.6307i | 1.03423 | + | 1.79133i | ||||
\(738\) | 6.77187 | − | 11.7292i | 0.249276 | − | 0.431759i | ||||
\(739\) | 9.67092 | + | 5.58351i | 0.355751 | + | 0.205393i | 0.667215 | − | 0.744865i | \(-0.267486\pi\) |
−0.311464 | + | 0.950258i | \(0.600819\pi\) | |||||||
\(740\) | 67.1629 | − | 116.329i | 2.46896 | − | 4.27636i | ||||
\(741\) | 16.6342 | − | 0.625850i | 0.611072 | − | 0.0229912i | ||||
\(742\) | −1.47753 | − | 2.45655i | −0.0542420 | − | 0.0901829i | ||||
\(743\) | −19.2388 | + | 11.1075i | −0.705802 | + | 0.407495i | −0.809505 | − | 0.587114i | \(-0.800264\pi\) |
0.103703 | + | 0.994608i | \(0.466931\pi\) | |||||||
\(744\) | 24.3279 | 0.891905 | ||||||||
\(745\) | −40.7354 | −1.49243 | ||||||||
\(746\) | 64.7614 | − | 37.3900i | 2.37108 | − | 1.36895i | ||||
\(747\) | −12.7451 | + | 7.35837i | −0.466318 | + | 0.269229i | ||||
\(748\) | 3.72537 | + | 2.15084i | 0.136213 | + | 0.0786426i | ||||
\(749\) | −0.220400 | − | 12.3129i | −0.00805324 | − | 0.449903i | ||||
\(750\) | 7.58019 | − | 13.1293i | 0.276789 | − | 0.479413i | ||||
\(751\) | −29.2653 | −1.06791 | −0.533954 | − | 0.845514i | \(-0.679294\pi\) | ||||
−0.533954 | + | 0.845514i | \(0.679294\pi\) | |||||||
\(752\) | 36.3059 | + | 20.9612i | 1.32394 | + | 0.764377i | ||||
\(753\) | −14.4466 | − | 25.0222i | −0.526462 | − | 0.911859i | ||||
\(754\) | −15.2461 | − | 24.2529i | −0.555230 | − | 0.883238i | ||||
\(755\) | 45.6916 | 1.66289 | ||||||||
\(756\) | −0.203378 | − | 11.3619i | −0.00739678 | − | 0.413229i | ||||
\(757\) | 26.6911 | + | 46.2303i | 0.970104 | + | 1.68027i | 0.695226 | + | 0.718791i | \(0.255304\pi\) |
0.274878 | + | 0.961479i | \(0.411363\pi\) | |||||||
\(758\) | 13.2849 | + | 23.0101i | 0.482529 | + | 0.835764i | ||||
\(759\) | 32.7415 | − | 18.9033i | 1.18844 | − | 0.686148i | ||||
\(760\) | 91.1751i | 3.30727i | ||||||||
\(761\) | −8.96431 | + | 5.17555i | −0.324956 | + | 0.187613i | −0.653599 | − | 0.756841i | \(-0.726742\pi\) |
0.328644 | + | 0.944454i | \(0.393409\pi\) | |||||||
\(762\) | 25.2838i | 0.915937i | ||||||||
\(763\) | 0.826631 | + | 1.37436i | 0.0299260 | + | 0.0497552i | ||||
\(764\) | 33.0973 | + | 57.3262i | 1.19742 | + | 2.07399i | ||||
\(765\) | 0.683546i | 0.0247137i | ||||||||
\(766\) | −34.8960 | − | 60.4416i | −1.26084 | − | 2.18384i | ||||
\(767\) | 3.02024 | − | 0.113635i | 0.109055 | − | 0.00410311i | ||||
\(768\) | −16.0031 | + | 27.7182i | −0.577463 | + | 1.00020i | ||||
\(769\) | 11.0010 | − | 6.35144i | 0.396707 | − | 0.229039i | −0.288355 | − | 0.957523i | \(-0.593108\pi\) |
0.685062 | + | 0.728485i | \(0.259775\pi\) | |||||||
\(770\) | 58.9637 | + | 98.0333i | 2.12490 | + | 3.53287i | ||||
\(771\) | 8.02514 | − | 13.9000i | 0.289018 | − | 0.500595i | ||||
\(772\) | −29.6292 | − | 17.1065i | −1.06638 | − | 0.615675i | ||||
\(773\) | − | 52.0546i | − | 1.87227i | −0.351637 | − | 0.936137i | \(-0.614375\pi\) | ||
0.351637 | − | 0.936137i | \(-0.385625\pi\) | |||||||
\(774\) | − | 6.41604i | − | 0.230620i | ||||||
\(775\) | −24.7400 | − | 14.2837i | −0.888688 | − | 0.513085i | ||||
\(776\) | −16.6911 | + | 28.9098i | −0.599176 | + | 1.03780i | ||||
\(777\) | −11.6875 | + | 21.1069i | −0.419285 | + | 0.757205i | ||||
\(778\) | 44.3410 | − | 25.6003i | 1.58970 | − | 0.917814i | ||||
\(779\) | 12.4608 | − | 21.5827i | 0.446453 | − | 0.773279i | ||||
\(780\) | 28.2659 | + | 44.9643i | 1.01208 | + | 1.60998i | ||||
\(781\) | 14.3777 | + | 24.9030i | 0.514476 | + | 0.891099i | ||||
\(782\) | − | 3.76239i | − | 0.134543i | ||||||
\(783\) | −1.58334 | − | 2.74243i | −0.0565841 | − | 0.0980065i | ||||
\(784\) | −40.9772 | + | 1.46745i | −1.46347 | + | 0.0524089i | ||||
\(785\) | − | 38.5524i | − | 1.37600i | ||||||
\(786\) | 23.9965 | − | 13.8544i | 0.855928 | − | 0.494170i | ||||
\(787\) | 28.6226i | 1.02028i | 0.860090 | + | 0.510142i | \(0.170407\pi\) | ||||
−0.860090 | + | 0.510142i | \(0.829593\pi\) | |||||||
\(788\) | 48.8084 | − | 28.1795i | 1.73873 | − | 1.00385i | ||||
\(789\) | 7.23551 | + | 12.5323i | 0.257591 | + | 0.446161i | ||||
\(790\) | −19.4095 | − | 33.6182i | −0.690558 | − | 1.19608i | ||||
\(791\) | 19.2351 | + | 10.6510i | 0.683921 | + | 0.378706i | ||||
\(792\) | 28.9359 | 1.02819 | ||||||||
\(793\) | −8.13566 | + | 5.11432i | −0.288906 | + | 0.181615i | ||||
\(794\) | −17.5912 | − | 30.4688i | −0.624287 | − | 1.08130i | ||||
\(795\) | 1.28261 | + | 0.740516i | 0.0454896 | + | 0.0262634i | ||||
\(796\) | −83.8414 | −2.97168 | ||||||||
\(797\) | −7.72007 | + | 13.3715i | −0.273459 | + | 0.473644i | −0.969745 | − | 0.244120i | \(-0.921501\pi\) |
0.696286 | + | 0.717764i | \(0.254834\pi\) | |||||||
\(798\) | −0.548490 | − | 30.6420i | −0.0194163 | − | 1.08472i | ||||
\(799\) | 1.23533 | + | 0.713220i | 0.0437030 | + | 0.0252319i | ||||
\(800\) | −18.6222 | + | 10.7515i | −0.658393 | + | 0.380123i | ||||
\(801\) | 2.03177 | − | 1.17304i | 0.0717890 | − | 0.0414474i | ||||
\(802\) | −13.2987 | −0.469594 | ||||||||
\(803\) | −15.8498 | −0.559328 | ||||||||
\(804\) | 41.5668 | − | 23.9986i | 1.46595 | − | 0.846366i | ||||
\(805\) | 33.0706 | − | 59.7236i | 1.16559 | − | 2.10498i | ||||
\(806\) | 32.3565 | − | 20.3403i | 1.13971 | − | 0.716456i | ||||
\(807\) | 8.14765 | − | 14.1121i | 0.286811 | − | 0.496771i | ||||
\(808\) | −21.0220 | − | 12.1371i | −0.739552 | − | 0.426981i | ||||
\(809\) | −1.85814 | + | 3.21840i | −0.0653289 | + | 0.113153i | −0.896840 | − | 0.442355i | \(-0.854143\pi\) |
0.831511 | + | 0.555508i | \(0.187476\pi\) | |||||||
\(810\) | 4.30238 | + | 7.45195i | 0.151170 | + | 0.261835i | ||||
\(811\) | 22.6432i | 0.795111i | 0.917578 | + | 0.397555i | \(0.130141\pi\) | ||||
−0.917578 | + | 0.397555i | \(0.869859\pi\) | |||||||
\(812\) | −30.8373 | + | 18.5476i | −1.08218 | + | 0.650893i | ||||
\(813\) | 9.72516 | + | 5.61482i | 0.341076 | + | 0.196920i | ||||
\(814\) | −99.5672 | − | 57.4852i | −3.48983 | − | 2.01485i | ||||
\(815\) | −12.4550 | −0.436280 | ||||||||
\(816\) | 0.583744 | − | 1.01107i | 0.0204351 | − | 0.0353947i | ||||
\(817\) | − | 11.8060i | − | 0.413040i | ||||||
\(818\) | −72.8050 | −2.54557 | ||||||||
\(819\) | −5.22066 | − | 7.98403i | −0.182425 | − | 0.278985i | ||||
\(820\) | 79.5148 | 2.77678 | ||||||||
\(821\) | − | 0.279111i | − | 0.00974104i | −0.999988 | − | 0.00487052i | \(-0.998450\pi\) | ||
0.999988 | − | 0.00487052i | \(-0.00155034\pi\) | |||||||
\(822\) | −14.2685 | + | 24.7137i | −0.497669 | + | 0.861989i | ||||
\(823\) | 12.0751 | 0.420913 | 0.210456 | − | 0.977603i | \(-0.432505\pi\) | ||||
0.210456 | + | 0.977603i | \(0.432505\pi\) | |||||||
\(824\) | 21.0734 | + | 12.1668i | 0.734128 | + | 0.423849i | ||||
\(825\) | −29.4261 | − | 16.9892i | −1.02449 | − | 0.591487i | ||||
\(826\) | −0.0995884 | − | 5.56362i | −0.00346512 | − | 0.193583i | ||||
\(827\) | − | 8.62027i | − | 0.299756i | −0.988704 | − | 0.149878i | \(-0.952112\pi\) | ||
0.988704 | − | 0.149878i | \(-0.0478881\pi\) | |||||||
\(828\) | −16.1575 | − | 27.9857i | −0.561513 | − | 0.972569i | ||||
\(829\) | −6.28936 | + | 10.8935i | −0.218438 | + | 0.378346i | −0.954331 | − | 0.298752i | \(-0.903430\pi\) |
0.735892 | + | 0.677099i | \(0.236763\pi\) | |||||||
\(830\) | −109.668 | − | 63.3170i | −3.80664 | − | 2.19777i | ||||
\(831\) | −9.60293 | + | 16.6328i | −0.333122 | + | 0.576984i | ||||
\(832\) | 0.506528 | + | 13.4628i | 0.0175607 | + | 0.466737i | ||||
\(833\) | −1.39428 | + | 0.0499310i | −0.0483089 | + | 0.00173001i | ||||
\(834\) | 38.0747 | − | 21.9825i | 1.31842 | − | 0.761190i | ||||
\(835\) | 35.4778 | 1.22776 | ||||||||
\(836\) | 99.6427 | 3.44622 | ||||||||
\(837\) | 3.65876 | − | 2.11239i | 0.126465 | − | 0.0730148i | ||||
\(838\) | 27.9473 | − | 16.1354i | 0.965423 | − | 0.557387i | ||||
\(839\) | −21.7367 | − | 12.5497i | −0.750435 | − | 0.433264i | 0.0754160 | − | 0.997152i | \(-0.475972\pi\) |
−0.825851 | + | 0.563888i | \(0.809305\pi\) | |||||||
\(840\) | 44.7752 | − | 26.9308i | 1.54489 | − | 0.929201i | ||||
\(841\) | 9.48604 | − | 16.4303i | 0.327105 | − | 0.566562i | ||||
\(842\) | −13.1932 | −0.454669 | ||||||||
\(843\) | −18.5786 | − | 10.7264i | −0.639881 | − | 0.369435i | ||||
\(844\) | 51.3497 | + | 88.9403i | 1.76753 | + | 3.06145i | ||||
\(845\) | 40.1770 | + | 19.3278i | 1.38213 | + | 0.664895i | ||||
\(846\) | 17.9566 | 0.617362 | ||||||||
\(847\) | 32.3096 | − | 19.4332i | 1.11017 | − | 0.667731i | ||||
\(848\) | −1.26479 | − | 2.19069i | −0.0434332 | − | 0.0752285i | ||||
\(849\) | 4.10738 | + | 7.11419i | 0.140965 | + | 0.244159i | ||||
\(850\) | −2.92838 | + | 1.69070i | −0.100443 | + | 0.0579906i | ||||
\(851\) | 68.6090i | 2.35189i | ||||||||
\(852\) | 21.2857 | − | 12.2893i | 0.729236 | − | 0.421025i | ||||
\(853\) | − | 41.0459i | − | 1.40538i | −0.711494 | − | 0.702692i | \(-0.751981\pi\) | ||
0.711494 | − | 0.702692i | \(-0.248019\pi\) | |||||||
\(854\) | 9.11898 | + | 15.1612i | 0.312045 | + | 0.518807i | ||||
\(855\) | 7.91671 | + | 13.7121i | 0.270746 | + | 0.468946i | ||||
\(856\) | − | 26.8029i | − | 0.916105i | ||||||
\(857\) | 5.36867 | + | 9.29880i | 0.183390 | + | 0.317641i | 0.943033 | − | 0.332700i | \(-0.107959\pi\) |
−0.759643 | + | 0.650341i | \(0.774626\pi\) | |||||||
\(858\) | 38.4853 | − | 24.1930i | 1.31386 | − | 0.825935i | ||||
\(859\) | 26.1491 | − | 45.2917i | 0.892197 | − | 1.54533i | 0.0549622 | − | 0.998488i | \(-0.482496\pi\) |
0.837235 | − | 0.546843i | \(-0.184171\pi\) | |||||||
\(860\) | 32.6217 | − | 18.8342i | 1.11239 | − | 0.642240i | ||||
\(861\) | −14.2796 | + | 0.255604i | −0.486649 | + | 0.00871098i | ||||
\(862\) | −31.0072 | + | 53.7060i | −1.05611 | + | 1.82923i | ||||
\(863\) | −37.4567 | − | 21.6256i | −1.27504 | − | 0.736145i | −0.299109 | − | 0.954219i | \(-0.596689\pi\) |
−0.975932 | + | 0.218073i | \(0.930023\pi\) | |||||||
\(864\) | − | 3.18005i | − | 0.108187i | ||||||
\(865\) | − | 15.7692i | − | 0.536170i | ||||||
\(866\) | 47.0378 | + | 27.1573i | 1.59841 | + | 0.922843i | ||||
\(867\) | −8.48014 | + | 14.6880i | −0.288001 | + | 0.498832i | ||||
\(868\) | −24.7449 | − | 41.1410i | −0.839897 | − | 1.39642i | ||||
\(869\) | −19.6323 | + | 11.3347i | −0.665980 | + | 0.384504i | ||||
\(870\) | 13.6243 | − | 23.5980i | 0.461907 | − | 0.800047i | ||||
\(871\) | 18.8197 | − | 35.6264i | 0.637680 | − | 1.20715i | ||||
\(872\) | 1.74531 | + | 3.02297i | 0.0591038 | + | 0.102371i | ||||
\(873\) | 5.79714i | 0.196203i | ||||||||
\(874\) | −43.5753 | − | 75.4746i | −1.47396 | − | 2.55297i | ||||
\(875\) | −15.9841 | + | 0.286115i | −0.540362 | + | 0.00967244i | ||||
\(876\) | 13.5476i | 0.457729i | ||||||||
\(877\) | −30.7866 | + | 17.7747i | −1.03959 | + | 0.600208i | −0.919717 | − | 0.392582i | \(-0.871582\pi\) |
−0.119873 | + | 0.992789i | \(0.538249\pi\) | |||||||
\(878\) | − | 19.4462i | − | 0.656278i | ||||||
\(879\) | 8.05762 | − | 4.65207i | 0.271777 | − | 0.156910i | ||||
\(880\) | 50.4739 | + | 87.4233i | 1.70147 | + | 2.94704i | ||||
\(881\) | 16.3098 | + | 28.2494i | 0.549491 | + | 0.951746i | 0.998309 | + | 0.0581231i | \(0.0185116\pi\) |
−0.448819 | + | 0.893623i | \(0.648155\pi\) | |||||||
\(882\) | −14.8860 | + | 9.32023i | −0.501238 | + | 0.313828i | ||||
\(883\) | 26.9860 | 0.908151 | 0.454075 | − | 0.890963i | \(-0.349970\pi\) | ||||
0.454075 | + | 0.890963i | \(0.349970\pi\) | |||||||
\(884\) | −0.116048 | − | 3.08437i | −0.00390310 | − | 0.103739i | ||||
\(885\) | 1.43742 | + | 2.48969i | 0.0483185 | + | 0.0836901i | ||||
\(886\) | 15.4341 | + | 8.91086i | 0.518518 | + | 0.299366i | ||||
\(887\) | 28.8798 | 0.969687 | 0.484844 | − | 0.874601i | \(-0.338877\pi\) | ||||
0.484844 | + | 0.874601i | \(0.338877\pi\) | |||||||
\(888\) | −26.2555 | + | 45.4758i | −0.881076 | + | 1.52607i | ||||
\(889\) | 22.8476 | − | 13.7420i | 0.766283 | − | 0.460893i | ||||
\(890\) | 17.4829 | + | 10.0937i | 0.586028 | + | 0.338343i | ||||
\(891\) | 4.35178 | − | 2.51250i | 0.145790 | − | 0.0841719i | ||||
\(892\) | −38.8220 | + | 22.4139i | −1.29986 | + | 0.750473i | ||||
\(893\) | 33.0416 | 1.10569 | ||||||||
\(894\) | 29.8013 | 0.996703 | ||||||||
\(895\) | 2.69214 | − | 1.55431i | 0.0899883 | − | 0.0519548i | ||||
\(896\) | 41.6244 | − | 0.745075i | 1.39057 | − | 0.0248912i | ||||
\(897\) | −23.9861 | − | 12.6707i | −0.800874 | − | 0.423063i | ||||
\(898\) | −36.4104 | + | 63.0646i | −1.21503 | + | 2.10449i | ||||
\(899\) | −11.5862 | − | 6.68927i | −0.386420 | − | 0.223100i | ||||
\(900\) | −14.5214 | + | 25.1518i | −0.484047 | + | 0.838394i | ||||
\(901\) | −0.0430355 | − | 0.0745396i | −0.00143372 | − | 0.00248328i | ||||
\(902\) | − | 68.0573i | − | 2.26606i | ||||||
\(903\) | −5.79782 | + | 3.48719i | −0.192939 | + | 0.116046i | ||||
\(904\) | 41.4430 | + | 23.9271i | 1.37837 | + | 0.795804i | ||||
\(905\) | 56.1807 | + | 32.4360i | 1.86751 | + | 1.07821i | ||||
\(906\) | −33.4272 | −1.11054 | ||||||||
\(907\) | 0.289244 | − | 0.500985i | 0.00960418 | − | 0.0166349i | −0.861183 | − | 0.508294i | \(-0.830276\pi\) |
0.870788 | + | 0.491659i | \(0.163610\pi\) | |||||||
\(908\) | 42.5236i | 1.41119i | ||||||||
\(909\) | −4.21544 | −0.139817 | ||||||||
\(910\) | 37.0353 | − | 73.2544i | 1.22771 | − | 2.42836i | ||||
\(911\) | −46.6019 | −1.54399 | −0.771994 | − | 0.635629i | \(-0.780741\pi\) | ||||
−0.771994 | + | 0.635629i | \(0.780741\pi\) | |||||||
\(912\) | − | 27.0433i | − | 0.895493i | ||||||
\(913\) | −36.9758 | + | 64.0439i | −1.22372 | + | 2.11955i | ||||
\(914\) | −67.8192 | −2.24326 | ||||||||
\(915\) | −7.91597 | − | 4.57029i | −0.261694 | − | 0.151089i | ||||
\(916\) | 58.6556 | + | 33.8648i | 1.93803 | + | 1.11892i | ||||
\(917\) | −25.5618 | − | 14.1543i | −0.844126 | − | 0.467416i | ||||
\(918\) | − | 0.500070i | − | 0.0165048i | ||||||
\(919\) | 7.80769 | + | 13.5233i | 0.257552 | + | 0.446093i | 0.965586 | − | 0.260086i | \(-0.0837508\pi\) |
−0.708034 | + | 0.706179i | \(0.750417\pi\) | |||||||
\(920\) | 74.2920 | − | 128.677i | 2.44933 | − | 4.24237i | ||||
\(921\) | 15.0480 | + | 8.68795i | 0.495848 | + | 0.286278i | ||||
\(922\) | −3.13579 | + | 5.43134i | −0.103272 | + | 0.178872i | ||||
\(923\) | 9.63725 | − | 18.2437i | 0.317214 | − | 0.600499i | ||||
\(924\) | −29.4319 | − | 48.9336i | −0.968238 | − | 1.60980i | ||||
\(925\) | 53.4005 | − | 30.8308i | 1.75580 | − | 1.01371i | ||||
\(926\) | −72.5981 | −2.38572 | ||||||||
\(927\) | 4.22574 | 0.138792 | ||||||||
\(928\) | −8.72106 | + | 5.03511i | −0.286283 | + | 0.165285i | ||||
\(929\) | 9.06186 | − | 5.23187i | 0.297310 | − | 0.171652i | −0.343924 | − | 0.938998i | \(-0.611756\pi\) |
0.641234 | + | 0.767346i | \(0.278423\pi\) | |||||||
\(930\) | 31.4828 | + | 18.1766i | 1.03236 | + | 0.596034i | ||||
\(931\) | −27.3914 | + | 17.1499i | −0.897716 | + | 0.562066i | ||||
\(932\) | 4.09102 | − | 7.08586i | 0.134006 | − | 0.232105i | ||||
\(933\) | −5.07791 | −0.166243 | ||||||||
\(934\) | −18.3990 | − | 10.6227i | −0.602035 | − | 0.347585i | ||||
\(935\) | 1.71741 | + | 2.97464i | 0.0561653 | + | 0.0972812i | ||||
\(936\) | −11.0498 | − | 17.5776i | −0.361173 | − | 0.574541i | ||||
\(937\) | −37.2603 | −1.21724 | −0.608621 | − | 0.793461i | \(-0.708277\pi\) | ||||
−0.608621 | + | 0.793461i | \(0.708277\pi\) | |||||||
\(938\) | −64.8963 | − | 35.9349i | −2.11894 | − | 1.17332i | ||||
\(939\) | 3.64621 | + | 6.31543i | 0.118990 | + | 0.206096i | ||||
\(940\) | 52.7114 | + | 91.2988i | 1.71926 | + | 2.97784i | ||||
\(941\) | 9.05253 | − | 5.22648i | 0.295104 | − | 0.170378i | −0.345137 | − | 0.938552i | \(-0.612168\pi\) |
0.640241 | + | 0.768174i | \(0.278834\pi\) | |||||||
\(942\) | 28.2043i | 0.918945i | ||||||||
\(943\) | −35.1723 | + | 20.3067i | −1.14537 | + | 0.661278i | ||||
\(944\) | − | 4.91020i | − | 0.159814i | ||||||
\(945\) | 4.39551 | − | 7.93804i | 0.142986 | − | 0.258224i | ||||
\(946\) | −16.1203 | − | 27.9212i | −0.524116 | − | 0.907796i | ||||
\(947\) | 10.7568i | 0.349549i | 0.984609 | + | 0.174774i | \(0.0559196\pi\) | ||||
−0.984609 | + | 0.174774i | \(0.944080\pi\) | |||||||
\(948\) | 9.68829 | + | 16.7806i | 0.314661 | + | 0.545009i | ||||
\(949\) | 6.05258 | + | 9.62821i | 0.196475 | + | 0.312545i | ||||
\(950\) | −39.1628 | + | 67.8320i | −1.27061 | + | 2.20076i | ||||
\(951\) | −20.5617 | + | 11.8713i | −0.666757 | + | 0.384953i | ||||
\(952\) | −3.03606 | + | 0.0543453i | −0.0983994 | + | 0.00176134i | ||||
\(953\) | −22.9984 | + | 39.8344i | −0.744992 | + | 1.29036i | 0.205207 | + | 0.978719i | \(0.434213\pi\) |
−0.950199 | + | 0.311645i | \(0.899120\pi\) | |||||||
\(954\) | −0.938336 | − | 0.541749i | −0.0303798 | − | 0.0175398i | ||||
\(955\) | 52.8553i | 1.71036i | ||||||||
\(956\) | 112.998i | 3.65463i | ||||||||
\(957\) | −13.7807 | − | 7.95630i | −0.445467 | − | 0.257191i | ||||
\(958\) | −30.0661 | + | 52.0760i | −0.971392 | + | 1.68250i | ||||
\(959\) | 30.0874 | − | 0.538563i | 0.971574 | − | 0.0173911i | ||||
\(960\) | −11.0978 | + | 6.40734i | −0.358181 | + | 0.206796i | ||||
\(961\) | −6.57564 | + | 11.3893i | −0.212117 | + | 0.367398i | ||||
\(962\) | 3.10158 | + | 82.4355i | 0.0999990 | + | 2.65783i | ||||
\(963\) | −2.32729 | − | 4.03099i | −0.0749959 | − | 0.129897i | ||||
\(964\) | 97.0122i | 3.12455i | ||||||||
\(965\) | −13.6592 | − | 23.6584i | −0.439705 | − | 0.761592i | ||||
\(966\) | −24.1939 | + | 43.6927i | −0.778425 | + | 1.40579i | ||||
\(967\) | − | 54.8212i | − | 1.76293i | −0.472250 | − | 0.881465i | \(-0.656558\pi\) | ||
0.472250 | − | 0.881465i | \(-0.343442\pi\) | |||||||
\(968\) | 71.0666 | − | 41.0303i | 2.28417 | − | 1.31877i | ||||
\(969\) | − | 0.920167i | − | 0.0295600i | ||||||
\(970\) | −43.2000 | + | 24.9415i | −1.38707 | + | 0.800823i | ||||
\(971\) | −18.9408 | − | 32.8064i | −0.607838 | − | 1.05281i | −0.991596 | − | 0.129373i | \(-0.958704\pi\) |
0.383758 | − | 0.923434i | \(-0.374630\pi\) | |||||||
\(972\) | −2.14755 | − | 3.71966i | −0.0688826 | − | 0.119308i | ||||
\(973\) | −40.5584 | − | 22.4583i | −1.30024 | − | 0.719980i | ||||
\(974\) | 92.1447 | 2.95251 | ||||||||
\(975\) | 0.916642 | + | 24.3630i | 0.0293560 | + | 0.780240i | ||||
\(976\) | 7.80599 | + | 13.5204i | 0.249864 | + | 0.432777i | ||||
\(977\) | −45.3003 | − | 26.1541i | −1.44928 | − | 0.836745i | −0.450846 | − | 0.892602i | \(-0.648877\pi\) |
−0.998439 | + | 0.0558573i | \(0.982211\pi\) | |||||||
\(978\) | 9.11186 | 0.291365 | ||||||||
\(979\) | 5.89453 | − | 10.2096i | 0.188390 | − | 0.326301i | ||||
\(980\) | −91.0854 | − | 48.3271i | −2.90962 | − | 1.54375i | ||||
\(981\) | 0.524968 | + | 0.303090i | 0.0167609 | + | 0.00967693i | ||||
\(982\) | −21.0149 | + | 12.1330i | −0.670612 | + | 0.387178i | ||||
\(983\) | −29.7363 | + | 17.1683i | −0.948442 | + | 0.547583i | −0.892597 | − | 0.450856i | \(-0.851119\pi\) |
−0.0558452 | + | 0.998439i | \(0.517785\pi\) | |||||||
\(984\) | −31.0841 | −0.990926 | ||||||||
\(985\) | 45.0018 | 1.43388 | ||||||||
\(986\) | −1.37141 | + | 0.791783i | −0.0436746 | + | 0.0252155i | ||||
\(987\) | −9.75963 | − | 16.2264i | −0.310653 | − | 0.516492i | ||||
\(988\) | −38.0506 | − | 60.5295i | −1.21055 | − | 1.92570i | ||||
\(989\) | −9.61985 | + | 16.6621i | −0.305893 | + | 0.529823i | ||||
\(990\) | 37.4460 | + | 21.6195i | 1.19011 | + | 0.687112i | ||||
\(991\) | 16.2263 | − | 28.1048i | 0.515446 | − | 0.892778i | −0.484393 | − | 0.874850i | \(-0.660960\pi\) |
0.999839 | − | 0.0179281i | \(-0.00570701\pi\) | |||||||
\(992\) | −6.71749 | − | 11.6350i | −0.213280 | − | 0.369413i | ||||
\(993\) | 0.0230179i | 0.000730451i | ||||||||
\(994\) | −33.2324 | − | 18.4017i | −1.05407 | − | 0.583666i | ||||
\(995\) | −57.9768 | − | 33.4729i | −1.83799 | − | 1.06116i | ||||
\(996\) | 54.7412 | + | 31.6049i | 1.73454 | + | 1.00144i | ||||
\(997\) | −2.32191 | −0.0735355 | −0.0367677 | − | 0.999324i | \(-0.511706\pi\) | ||||
−0.0367677 | + | 0.999324i | \(0.511706\pi\) | |||||||
\(998\) | 34.8175 | − | 60.3057i | 1.10213 | − | 1.90894i | ||||
\(999\) | 9.11903i | 0.288513i |
(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 | 273.2.t.d.205.10 | yes | 20 | |
3.2 | odd | 2 | 819.2.bm.g.478.1 | 20 | |||
7.4 | even | 3 | 273.2.bl.d.88.1 | yes | 20 | ||
13.4 | even | 6 | 273.2.bl.d.121.1 | yes | 20 | ||
21.11 | odd | 6 | 819.2.do.g.361.10 | 20 | |||
39.17 | odd | 6 | 819.2.do.g.667.10 | 20 | |||
91.4 | even | 6 | inner | 273.2.t.d.4.1 | ✓ | 20 | |
273.95 | odd | 6 | 819.2.bm.g.550.10 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.t.d.4.1 | ✓ | 20 | 91.4 | even | 6 | inner | |
273.2.t.d.205.10 | yes | 20 | 1.1 | even | 1 | trivial | |
273.2.bl.d.88.1 | yes | 20 | 7.4 | even | 3 | ||
273.2.bl.d.121.1 | yes | 20 | 13.4 | even | 6 | ||
819.2.bm.g.478.1 | 20 | 3.2 | odd | 2 | |||
819.2.bm.g.550.10 | 20 | 273.95 | odd | 6 | |||
819.2.do.g.361.10 | 20 | 21.11 | odd | 6 | |||
819.2.do.g.667.10 | 20 | 39.17 | odd | 6 |