Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(76,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.g (of order \(5\), degree \(4\), not 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: | \(2.99439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 226.4 | ||
Root | \(1.35083i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 375.226 |
Dual form | 375.2.g.e.151.4 |
$q$-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 \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{3}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.417429 | − | 1.28472i | 0.295167 | − | 0.908431i | −0.687998 | − | 0.725712i | \(-0.741510\pi\) |
0.983165 | − | 0.182719i | \(-0.0584897\pi\) | |||||||
\(3\) | −0.809017 | − | 0.587785i | −0.467086 | − | 0.339358i | ||||
\(4\) | 0.141788 | + | 0.103015i | 0.0708938 | + | 0.0515074i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.09284 | + | 0.793998i | −0.446152 | + | 0.324148i | ||||
\(7\) | −1.59580 | −0.603155 | −0.301577 | − | 0.953442i | \(-0.597513\pi\) | ||||
−0.301577 | + | 0.953442i | \(0.597513\pi\) | |||||||
\(8\) | 2.37722 | − | 1.72715i | 0.840474 | − | 0.610640i | ||||
\(9\) | 0.309017 | + | 0.951057i | 0.103006 | + | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.02988 | − | 3.16965i | 0.310521 | − | 0.955686i | −0.667038 | − | 0.745024i | \(-0.732438\pi\) |
0.977559 | − | 0.210662i | \(-0.0675619\pi\) | |||||||
\(12\) | −0.0541581 | − | 0.166681i | −0.0156341 | − | 0.0481168i | ||||
\(13\) | −2.17898 | − | 6.70620i | −0.604339 | − | 1.85997i | −0.501269 | − | 0.865292i | \(-0.667133\pi\) |
−0.103071 | − | 0.994674i | \(-0.532867\pi\) | |||||||
\(14\) | −0.666132 | + | 2.05014i | −0.178031 | + | 0.547924i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.11826 | − | 3.44165i | −0.279565 | − | 0.860413i | ||||
\(17\) | 3.31393 | − | 2.40771i | 0.803747 | − | 0.583957i | −0.108264 | − | 0.994122i | \(-0.534529\pi\) |
0.912011 | + | 0.410166i | \(0.134529\pi\) | |||||||
\(18\) | 1.35083 | 0.318394 | ||||||||
\(19\) | −0.459145 | + | 0.333589i | −0.105335 | + | 0.0765305i | −0.639206 | − | 0.769036i | \(-0.720737\pi\) |
0.533871 | + | 0.845566i | \(0.320737\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.29103 | + | 0.937986i | 0.281725 | + | 0.204685i | ||||
\(22\) | −3.64220 | − | 2.64621i | −0.776519 | − | 0.564174i | ||||
\(23\) | −1.94804 | + | 5.99546i | −0.406195 | + | 1.25014i | 0.513698 | + | 0.857971i | \(0.328275\pi\) |
−0.919893 | + | 0.392169i | \(0.871725\pi\) | |||||||
\(24\) | −2.93840 | −0.599799 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −9.52513 | −1.86803 | ||||||||
\(27\) | 0.309017 | − | 0.951057i | 0.0594703 | − | 0.183031i | ||||
\(28\) | −0.226264 | − | 0.164391i | −0.0427599 | − | 0.0310669i | ||||
\(29\) | 2.25196 | + | 1.63614i | 0.418178 | + | 0.303824i | 0.776904 | − | 0.629619i | \(-0.216789\pi\) |
−0.358726 | + | 0.933443i | \(0.616789\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.805639 | − | 0.585331i | 0.144697 | − | 0.105128i | −0.513082 | − | 0.858340i | \(-0.671496\pi\) |
0.657779 | + | 0.753211i | \(0.271496\pi\) | |||||||
\(32\) | 0.988473 | 0.174739 | ||||||||
\(33\) | −2.69627 | + | 1.95895i | −0.469360 | + | 0.341010i | ||||
\(34\) | −1.70989 | − | 5.26251i | −0.293244 | − | 0.902514i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.0541581 | + | 0.166681i | −0.00902634 | + | 0.0277802i | ||||
\(37\) | 1.09804 | + | 3.37943i | 0.180517 | + | 0.555574i | 0.999842 | − | 0.0177546i | \(-0.00565175\pi\) |
−0.819325 | + | 0.573329i | \(0.805652\pi\) | |||||||
\(38\) | 0.236906 | + | 0.729121i | 0.0384312 | + | 0.118279i | ||||
\(39\) | −2.17898 | + | 6.70620i | −0.348916 | + | 1.07385i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.359364 | + | 1.10601i | 0.0561232 | + | 0.172729i | 0.975189 | − | 0.221376i | \(-0.0710547\pi\) |
−0.919065 | + | 0.394105i | \(0.871055\pi\) | |||||||
\(42\) | 1.74396 | − | 1.26706i | 0.269098 | − | 0.195511i | ||||
\(43\) | −0.117022 | −0.0178456 | −0.00892281 | − | 0.999960i | \(-0.502840\pi\) | ||||
−0.00892281 | + | 0.999960i | \(0.502840\pi\) | |||||||
\(44\) | 0.472545 | − | 0.343324i | 0.0712389 | − | 0.0517581i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.88929 | + | 5.00536i | 1.01577 | + | 0.738001i | ||||
\(47\) | 6.18229 | + | 4.49170i | 0.901780 | + | 0.655182i | 0.938923 | − | 0.344128i | \(-0.111826\pi\) |
−0.0371425 | + | 0.999310i | \(0.511826\pi\) | |||||||
\(48\) | −1.11826 | + | 3.44165i | −0.161407 | + | 0.496760i | ||||
\(49\) | −4.45343 | −0.636205 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.09625 | −0.573589 | ||||||||
\(52\) | 0.381886 | − | 1.17532i | 0.0529580 | − | 0.162988i | ||||
\(53\) | 0.423629 | + | 0.307785i | 0.0581900 | + | 0.0422775i | 0.616500 | − | 0.787355i | \(-0.288550\pi\) |
−0.558310 | + | 0.829632i | \(0.688550\pi\) | |||||||
\(54\) | −1.09284 | − | 0.793998i | −0.148717 | − | 0.108049i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.79356 | + | 2.75618i | −0.506936 | + | 0.368310i | ||||
\(57\) | 0.567535 | 0.0751718 | ||||||||
\(58\) | 3.04201 | − | 2.21015i | 0.399436 | − | 0.290207i | ||||
\(59\) | 0.304072 | + | 0.935838i | 0.0395868 | + | 0.121836i | 0.968897 | − | 0.247465i | \(-0.0795974\pi\) |
−0.929310 | + | 0.369300i | \(0.879597\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.27982 | − | 10.0942i | 0.419937 | − | 1.29243i | −0.487822 | − | 0.872943i | \(-0.662208\pi\) |
0.907759 | − | 0.419491i | \(-0.137792\pi\) | |||||||
\(62\) | −0.415686 | − | 1.27935i | −0.0527922 | − | 0.162478i | ||||
\(63\) | −0.493128 | − | 1.51769i | −0.0621283 | − | 0.191211i | ||||
\(64\) | 2.64914 | − | 8.15321i | 0.331142 | − | 1.01915i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.39120 | + | 4.28166i | 0.171244 | + | 0.527036i | ||||
\(67\) | −12.3099 | + | 8.94370i | −1.50390 | + | 1.09265i | −0.535104 | + | 0.844786i | \(0.679728\pi\) |
−0.968796 | + | 0.247861i | \(0.920272\pi\) | |||||||
\(68\) | 0.717905 | 0.0870588 | ||||||||
\(69\) | 5.10005 | − | 3.70540i | 0.613973 | − | 0.446078i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.62730 | + | 6.26810i | 1.02387 | + | 0.743887i | 0.967073 | − | 0.254499i | \(-0.0819104\pi\) |
0.0567995 | + | 0.998386i | \(0.481910\pi\) | |||||||
\(72\) | 2.37722 | + | 1.72715i | 0.280158 | + | 0.203547i | ||||
\(73\) | −1.71761 | + | 5.28627i | −0.201032 | + | 0.618711i | 0.798821 | + | 0.601568i | \(0.205457\pi\) |
−0.999853 | + | 0.0171433i | \(0.994543\pi\) | |||||||
\(74\) | 4.79996 | 0.557984 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.0994657 | −0.0114095 | ||||||||
\(77\) | −1.64348 | + | 5.05812i | −0.187292 | + | 0.576426i | ||||
\(78\) | 7.70599 | + | 5.59873i | 0.872532 | + | 0.633931i | ||||
\(79\) | 11.8091 | + | 8.57982i | 1.32863 | + | 0.965305i | 0.999781 | + | 0.0209214i | \(0.00665998\pi\) |
0.328847 | + | 0.944383i | \(0.393340\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | 1.57091 | 0.173478 | ||||||||
\(83\) | 4.06448 | − | 2.95302i | 0.446135 | − | 0.324136i | −0.341933 | − | 0.939724i | \(-0.611082\pi\) |
0.788068 | + | 0.615588i | \(0.211082\pi\) | |||||||
\(84\) | 0.0864253 | + | 0.265990i | 0.00942977 | + | 0.0290218i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.0488483 | + | 0.150339i | −0.00526744 | + | 0.0162115i | ||||
\(87\) | −0.860172 | − | 2.64734i | −0.0922201 | − | 0.283824i | ||||
\(88\) | −3.02621 | − | 9.31372i | −0.322595 | − | 0.992846i | ||||
\(89\) | 0.872511 | − | 2.68531i | 0.0924859 | − | 0.284642i | −0.894104 | − | 0.447859i | \(-0.852187\pi\) |
0.986590 | + | 0.163216i | \(0.0521868\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.47720 | + | 10.7017i | 0.364510 | + | 1.12185i | ||||
\(92\) | −0.893830 | + | 0.649405i | −0.0931882 | + | 0.0677052i | ||||
\(93\) | −0.995824 | −0.103262 | ||||||||
\(94\) | 8.35122 | − | 6.06752i | 0.861363 | − | 0.625817i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.799691 | − | 0.581010i | −0.0816182 | − | 0.0592991i | ||||
\(97\) | −1.38012 | − | 1.00271i | −0.140130 | − | 0.101810i | 0.515512 | − | 0.856882i | \(-0.327602\pi\) |
−0.655642 | + | 0.755072i | \(0.727602\pi\) | |||||||
\(98\) | −1.85899 | + | 5.72139i | −0.187787 | + | 0.577948i | ||||
\(99\) | 3.33277 | 0.334956 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.1747 | 1.31093 | 0.655464 | − | 0.755226i | \(-0.272473\pi\) | ||||
0.655464 | + | 0.755226i | \(0.272473\pi\) | |||||||
\(102\) | −1.70989 | + | 5.26251i | −0.169305 | + | 0.521066i | ||||
\(103\) | 8.79562 | + | 6.39039i | 0.866658 | + | 0.629664i | 0.929688 | − | 0.368347i | \(-0.120076\pi\) |
−0.0630298 | + | 0.998012i | \(0.520076\pi\) | |||||||
\(104\) | −16.7625 | − | 12.1787i | −1.64370 | − | 1.19422i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.572251 | − | 0.415765i | 0.0555819 | − | 0.0403826i | ||||
\(107\) | −9.37236 | −0.906060 | −0.453030 | − | 0.891495i | \(-0.649657\pi\) | ||||
−0.453030 | + | 0.891495i | \(0.649657\pi\) | |||||||
\(108\) | 0.141788 | − | 0.103015i | 0.0136435 | − | 0.00991260i | ||||
\(109\) | −4.81755 | − | 14.8269i | −0.461438 | − | 1.42016i | −0.863408 | − | 0.504506i | \(-0.831674\pi\) |
0.401970 | − | 0.915653i | \(-0.368326\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.09804 | − | 3.37943i | 0.104222 | − | 0.320761i | ||||
\(112\) | 1.78452 | + | 5.49218i | 0.168621 | + | 0.518962i | ||||
\(113\) | 3.10503 | + | 9.55629i | 0.292096 | + | 0.898980i | 0.984181 | + | 0.177164i | \(0.0566923\pi\) |
−0.692085 | + | 0.721816i | \(0.743308\pi\) | |||||||
\(114\) | 0.236906 | − | 0.729121i | 0.0221883 | − | 0.0682884i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.150753 | + | 0.463970i | 0.0139971 | + | 0.0430785i | ||||
\(117\) | 5.70464 | − | 4.14466i | 0.527394 | − | 0.383174i | ||||
\(118\) | 1.32921 | 0.122364 | ||||||||
\(119\) | −5.28837 | + | 3.84222i | −0.484784 | + | 0.352216i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.0868453 | − | 0.0630968i | −0.00789503 | − | 0.00573608i | ||||
\(122\) | −11.5991 | − | 8.42726i | −1.05014 | − | 0.762968i | ||||
\(123\) | 0.359364 | − | 1.10601i | 0.0324027 | − | 0.0997253i | ||||
\(124\) | 0.174527 | 0.0156730 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.15565 | −0.192041 | ||||||||
\(127\) | −0.301843 | + | 0.928977i | −0.0267842 | + | 0.0824334i | −0.963555 | − | 0.267510i | \(-0.913799\pi\) |
0.936771 | + | 0.349943i | \(0.113799\pi\) | |||||||
\(128\) | −7.76934 | − | 5.64476i | −0.686719 | − | 0.498931i | ||||
\(129\) | 0.0946725 | + | 0.0687836i | 0.00833545 | + | 0.00605606i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.14001 | + | 5.91406i | −0.711196 | + | 0.516714i | −0.883559 | − | 0.468319i | \(-0.844860\pi\) |
0.172363 | + | 0.985033i | \(0.444860\pi\) | |||||||
\(132\) | −0.584098 | −0.0508392 | ||||||||
\(133\) | 0.732703 | − | 0.532340i | 0.0635334 | − | 0.0461597i | ||||
\(134\) | 6.35158 | + | 19.5481i | 0.548693 | + | 1.68870i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.71946 | − | 11.4473i | 0.318941 | − | 0.981600i | ||||
\(137\) | −1.50567 | − | 4.63397i | −0.128638 | − | 0.395907i | 0.865908 | − | 0.500203i | \(-0.166741\pi\) |
−0.994546 | + | 0.104296i | \(0.966741\pi\) | |||||||
\(138\) | −2.63148 | − | 8.09885i | −0.224006 | − | 0.689420i | ||||
\(139\) | 0.0574103 | − | 0.176691i | 0.00486948 | − | 0.0149867i | −0.948592 | − | 0.316501i | \(-0.897492\pi\) |
0.953462 | + | 0.301514i | \(0.0974920\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.36143 | − | 7.26772i | −0.198868 | − | 0.612053i | ||||
\(142\) | 11.6540 | − | 8.46714i | 0.977984 | − | 0.710547i | ||||
\(143\) | −23.5004 | −1.96520 | ||||||||
\(144\) | 2.92764 | − | 2.12706i | 0.243970 | − | 0.177255i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.07437 | + | 4.41329i | 0.502719 | + | 0.365247i | ||||
\(147\) | 3.60290 | + | 2.61766i | 0.297162 | + | 0.215901i | ||||
\(148\) | −0.192442 | + | 0.592276i | −0.0158186 | + | 0.0486847i | ||||
\(149\) | 3.88889 | 0.318590 | 0.159295 | − | 0.987231i | \(-0.449078\pi\) | ||||
0.159295 | + | 0.987231i | \(0.449078\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.1146 | −1.79966 | −0.899829 | − | 0.436242i | \(-0.856309\pi\) | ||||
−0.899829 | + | 0.436242i | \(0.856309\pi\) | |||||||
\(152\) | −0.515331 | + | 1.58603i | −0.0417989 | + | 0.128644i | ||||
\(153\) | 3.31393 | + | 2.40771i | 0.267916 | + | 0.194652i | ||||
\(154\) | 5.81221 | + | 4.22282i | 0.468361 | + | 0.340284i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.999790 | + | 0.726390i | −0.0800472 | + | 0.0581577i | ||||
\(157\) | 13.6058 | 1.08586 | 0.542931 | − | 0.839777i | \(-0.317314\pi\) | ||||
0.542931 | + | 0.839777i | \(0.317314\pi\) | |||||||
\(158\) | 15.9521 | − | 11.5899i | 1.26908 | − | 0.922041i | ||||
\(159\) | −0.161812 | − | 0.498006i | −0.0128325 | − | 0.0394945i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.10868 | − | 9.56754i | 0.244999 | − | 0.754028i | ||||
\(162\) | 0.417429 | + | 1.28472i | 0.0327963 | + | 0.100937i | ||||
\(163\) | 2.66649 | + | 8.20662i | 0.208856 | + | 0.642792i | 0.999533 | + | 0.0305587i | \(0.00972864\pi\) |
−0.790677 | + | 0.612233i | \(0.790271\pi\) | |||||||
\(164\) | −0.0629818 | + | 0.193838i | −0.00491805 | + | 0.0151362i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.09716 | − | 6.45438i | −0.162771 | − | 0.500957i | ||||
\(167\) | −5.33863 | + | 3.87874i | −0.413116 | + | 0.300146i | −0.774862 | − | 0.632131i | \(-0.782181\pi\) |
0.361746 | + | 0.932277i | \(0.382181\pi\) | |||||||
\(168\) | 4.68910 | 0.361772 | ||||||||
\(169\) | −29.7080 | + | 21.5841i | −2.28523 | + | 1.66032i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.459145 | − | 0.333589i | −0.0351117 | − | 0.0255102i | ||||
\(172\) | −0.0165922 | − | 0.0120550i | −0.00126514 | − | 0.000919182i | ||||
\(173\) | 4.22102 | − | 12.9910i | 0.320918 | − | 0.987685i | −0.652331 | − | 0.757934i | \(-0.726209\pi\) |
0.973249 | − | 0.229751i | \(-0.0737912\pi\) | |||||||
\(174\) | −3.76013 | −0.285055 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −12.0605 | −0.909095 | ||||||||
\(177\) | 0.304072 | − | 0.935838i | 0.0228555 | − | 0.0703419i | ||||
\(178\) | −3.08565 | − | 2.24186i | −0.231279 | − | 0.168034i | ||||
\(179\) | −7.95167 | − | 5.77722i | −0.594336 | − | 0.431810i | 0.249528 | − | 0.968368i | \(-0.419724\pi\) |
−0.843864 | + | 0.536557i | \(0.819724\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.4561 | + | 10.5030i | −1.07451 | + | 0.780679i | −0.976718 | − | 0.214528i | \(-0.931179\pi\) |
−0.0977940 | + | 0.995207i | \(0.531179\pi\) | |||||||
\(182\) | 15.2002 | 1.12671 | ||||||||
\(183\) | −8.58667 | + | 6.23858i | −0.634745 | + | 0.461169i | ||||
\(184\) | 5.72414 | + | 17.6171i | 0.421989 | + | 1.29875i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.415686 | + | 1.27935i | −0.0304796 | + | 0.0938065i | ||||
\(187\) | −4.21865 | − | 12.9837i | −0.308498 | − | 0.949461i | ||||
\(188\) | 0.413862 | + | 1.27373i | 0.0301840 | + | 0.0928967i | ||||
\(189\) | −0.493128 | + | 1.51769i | −0.0358698 | + | 0.110396i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.100682 | + | 0.309867i | 0.00728509 | + | 0.0224212i | 0.954633 | − | 0.297785i | \(-0.0962478\pi\) |
−0.947348 | + | 0.320206i | \(0.896248\pi\) | |||||||
\(192\) | −6.93553 | + | 5.03896i | −0.500529 | + | 0.363656i | ||||
\(193\) | −2.90187 | −0.208881 | −0.104441 | − | 0.994531i | \(-0.533305\pi\) | ||||
−0.104441 | + | 0.994531i | \(0.533305\pi\) | |||||||
\(194\) | −1.86430 | + | 1.35450i | −0.133849 | + | 0.0972471i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.631442 | − | 0.458769i | −0.0451030 | − | 0.0327692i | ||||
\(197\) | 14.6610 | + | 10.6518i | 1.04455 | + | 0.758911i | 0.971169 | − | 0.238393i | \(-0.0766205\pi\) |
0.0733829 | + | 0.997304i | \(0.476620\pi\) | |||||||
\(198\) | 1.39120 | − | 4.28166i | 0.0988679 | − | 0.304284i | ||||
\(199\) | 1.53256 | 0.108640 | 0.0543201 | − | 0.998524i | \(-0.482701\pi\) | ||||
0.0543201 | + | 0.998524i | \(0.482701\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.2159 | 1.07325 | ||||||||
\(202\) | 5.49949 | − | 16.9257i | 0.386943 | − | 1.19089i | ||||
\(203\) | −3.59367 | − | 2.61095i | −0.252226 | − | 0.183253i | ||||
\(204\) | −0.580797 | − | 0.421974i | −0.0406640 | − | 0.0295441i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 11.8814 | − | 8.63233i | 0.827816 | − | 0.601443i | ||||
\(207\) | −6.30400 | −0.438158 | ||||||||
\(208\) | −20.6437 | + | 14.9986i | −1.43139 | + | 1.03996i | ||||
\(209\) | 0.584494 | + | 1.79889i | 0.0404303 | + | 0.124432i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.51345 | + | 10.8133i | −0.241876 | + | 0.744418i | 0.754259 | + | 0.656577i | \(0.227996\pi\) |
−0.996135 | + | 0.0878402i | \(0.972004\pi\) | |||||||
\(212\) | 0.0283590 | + | 0.0872802i | 0.00194771 | + | 0.00599443i | ||||
\(213\) | −3.29534 | − | 10.1420i | −0.225793 | − | 0.694919i | ||||
\(214\) | −3.91230 | + | 12.0408i | −0.267439 | + | 0.823093i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.908017 | − | 2.79459i | −0.0617827 | − | 0.190148i | ||||
\(217\) | −1.28564 | + | 0.934069i | −0.0872746 | + | 0.0634087i | ||||
\(218\) | −21.0593 | −1.42632 | ||||||||
\(219\) | 4.49677 | − | 3.26710i | 0.303864 | − | 0.220770i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.3676 | − | 16.9776i | −1.57188 | − | 1.14203i | ||||
\(222\) | −3.88325 | − | 2.82134i | −0.260626 | − | 0.189356i | ||||
\(223\) | 5.23804 | − | 16.1210i | 0.350765 | − | 1.07954i | −0.607659 | − | 0.794198i | \(-0.707891\pi\) |
0.958424 | − | 0.285347i | \(-0.0921087\pi\) | |||||||
\(224\) | −1.57740 | −0.105395 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.5732 | 0.902878 | ||||||||
\(227\) | 4.36076 | − | 13.4210i | 0.289434 | − | 0.890785i | −0.695601 | − | 0.718428i | \(-0.744862\pi\) |
0.985035 | − | 0.172357i | \(-0.0551382\pi\) | |||||||
\(228\) | 0.0804694 | + | 0.0584645i | 0.00532922 | + | 0.00387190i | ||||
\(229\) | −0.0501546 | − | 0.0364394i | −0.00331431 | − | 0.00240799i | 0.586127 | − | 0.810219i | \(-0.300652\pi\) |
−0.589441 | + | 0.807811i | \(0.700652\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.30269 | − | 3.12609i | 0.283096 | − | 0.205682i | ||||
\(232\) | 8.17927 | 0.536995 | ||||||||
\(233\) | 21.0499 | − | 15.2936i | 1.37902 | − | 1.00192i | 0.382052 | − | 0.924141i | \(-0.375218\pi\) |
0.996971 | − | 0.0777775i | \(-0.0247824\pi\) | |||||||
\(234\) | −2.94343 | − | 9.05894i | −0.192418 | − | 0.592201i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.0532914 | + | 0.164014i | −0.00346898 | + | 0.0106764i | ||||
\(237\) | −4.51068 | − | 13.8824i | −0.293000 | − | 0.901761i | ||||
\(238\) | 2.72864 | + | 8.39790i | 0.176872 | + | 0.544355i | ||||
\(239\) | 6.02491 | − | 18.5428i | 0.389719 | − | 1.19943i | −0.543279 | − | 0.839552i | \(-0.682817\pi\) |
0.932998 | − | 0.359881i | \(-0.117183\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.26654 | − | 3.89800i | −0.0815848 | − | 0.251092i | 0.901941 | − | 0.431859i | \(-0.142142\pi\) |
−0.983526 | + | 0.180767i | \(0.942142\pi\) | |||||||
\(242\) | −0.117313 | + | 0.0852331i | −0.00754118 | + | 0.00547899i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 1.50489 | − | 1.09337i | 0.0963409 | − | 0.0699957i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.27090 | − | 0.923360i | −0.0810294 | − | 0.0588713i | ||||
\(247\) | 3.23758 | + | 2.35224i | 0.206002 | + | 0.149669i | ||||
\(248\) | 0.904225 | − | 2.78292i | 0.0574184 | − | 0.176716i | ||||
\(249\) | −5.02398 | −0.318382 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.02933 | −0.0649704 | −0.0324852 | − | 0.999472i | \(-0.510342\pi\) | ||||
−0.0324852 | + | 0.999472i | \(0.510342\pi\) | |||||||
\(252\) | 0.0864253 | − | 0.265990i | 0.00544428 | − | 0.0167558i | ||||
\(253\) | 16.9973 | + | 12.3492i | 1.06861 | + | 0.776390i | ||||
\(254\) | 1.06747 | + | 0.775565i | 0.0669792 | + | 0.0486633i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.37601 | − | 2.45281i | 0.211001 | − | 0.153301i | ||||
\(257\) | −18.5597 | −1.15772 | −0.578862 | − | 0.815426i | \(-0.696503\pi\) | ||||
−0.578862 | + | 0.815426i | \(0.696503\pi\) | |||||||
\(258\) | 0.127886 | − | 0.0929149i | 0.00796186 | − | 0.00578463i | ||||
\(259\) | −1.75225 | − | 5.39288i | −0.108880 | − | 0.335097i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.860172 | + | 2.64734i | −0.0532433 | + | 0.163866i | ||||
\(262\) | 4.20001 | + | 12.9263i | 0.259477 | + | 0.798589i | ||||
\(263\) | 3.82988 | + | 11.7872i | 0.236161 | + | 0.726827i | 0.996965 | + | 0.0778466i | \(0.0248044\pi\) |
−0.760805 | + | 0.648981i | \(0.775196\pi\) | |||||||
\(264\) | −3.02621 | + | 9.31372i | −0.186250 | + | 0.573220i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.378053 | − | 1.16353i | −0.0231799 | − | 0.0713405i | ||||
\(267\) | −2.28426 | + | 1.65961i | −0.139795 | + | 0.101567i | ||||
\(268\) | −2.66673 | −0.162897 | ||||||||
\(269\) | 4.28805 | − | 3.11545i | 0.261447 | − | 0.189952i | −0.449338 | − | 0.893362i | \(-0.648340\pi\) |
0.710785 | + | 0.703410i | \(0.248340\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.645132 | − | 0.468716i | −0.0391890 | − | 0.0284725i | 0.568018 | − | 0.823016i | \(-0.307710\pi\) |
−0.607207 | + | 0.794543i | \(0.707710\pi\) | |||||||
\(272\) | −11.9924 | − | 8.71295i | −0.727143 | − | 0.528300i | ||||
\(273\) | 3.47720 | − | 10.7017i | 0.210450 | − | 0.647698i | ||||
\(274\) | −6.58184 | −0.397624 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.10483 | 0.0665032 | ||||||||
\(277\) | −1.46605 | + | 4.51205i | −0.0880867 | + | 0.271103i | −0.985390 | − | 0.170311i | \(-0.945523\pi\) |
0.897304 | + | 0.441414i | \(0.145523\pi\) | |||||||
\(278\) | −0.203033 | − | 0.147512i | −0.0121771 | − | 0.00884717i | ||||
\(279\) | 0.805639 | + | 0.585331i | 0.0482323 | + | 0.0350428i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.1608 | − | 11.0150i | 0.904418 | − | 0.657098i | −0.0351791 | − | 0.999381i | \(-0.511200\pi\) |
0.939597 | + | 0.342283i | \(0.111200\pi\) | |||||||
\(282\) | −10.3227 | −0.614707 | ||||||||
\(283\) | −9.51501 | + | 6.91306i | −0.565608 | + | 0.410939i | −0.833507 | − | 0.552508i | \(-0.813671\pi\) |
0.267899 | + | 0.963447i | \(0.413671\pi\) | |||||||
\(284\) | 0.577538 | + | 1.77748i | 0.0342706 | + | 0.105474i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.80976 | + | 30.1913i | −0.580063 | + | 1.78525i | ||||
\(287\) | −0.573471 | − | 1.76496i | −0.0338509 | − | 0.104182i | ||||
\(288\) | 0.305455 | + | 0.940094i | 0.0179991 | + | 0.0553956i | ||||
\(289\) | −0.0682154 | + | 0.209945i | −0.00401267 | + | 0.0123497i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.527158 | + | 1.62242i | 0.0309025 | + | 0.0951082i | ||||
\(292\) | −0.788101 | + | 0.572589i | −0.0461201 | + | 0.0335082i | ||||
\(293\) | 22.2819 | 1.30172 | 0.650860 | − | 0.759198i | \(-0.274408\pi\) | ||||
0.650860 | + | 0.759198i | \(0.274408\pi\) | |||||||
\(294\) | 4.86691 | − | 3.53602i | 0.283844 | − | 0.206225i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.44707 | + | 6.13715i | 0.490976 | + | 0.356715i | ||||
\(297\) | −2.69627 | − | 1.95895i | −0.156453 | − | 0.113670i | ||||
\(298\) | 1.62333 | − | 4.99611i | 0.0940373 | − | 0.289417i | ||||
\(299\) | 44.4515 | 2.57070 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.186743 | 0.0107637 | ||||||||
\(302\) | −9.23127 | + | 28.4109i | −0.531200 | + | 1.63487i | ||||
\(303\) | −10.6585 | − | 7.74387i | −0.612316 | − | 0.444874i | ||||
\(304\) | 1.66154 | + | 1.20718i | 0.0952958 | + | 0.0692365i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.47656 | − | 3.25241i | 0.255908 | − | 0.185928i | ||||
\(307\) | −15.3063 | −0.873574 | −0.436787 | − | 0.899565i | \(-0.643884\pi\) | ||||
−0.436787 | + | 0.899565i | \(0.643884\pi\) | |||||||
\(308\) | −0.754087 | + | 0.547876i | −0.0429681 | + | 0.0312181i | ||||
\(309\) | −3.35963 | − | 10.3399i | −0.191123 | − | 0.588215i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.97226 | + | 12.2254i | −0.225246 | + | 0.693237i | 0.773020 | + | 0.634382i | \(0.218745\pi\) |
−0.998267 | + | 0.0588556i | \(0.981255\pi\) | |||||||
\(312\) | 6.40272 | + | 19.7055i | 0.362482 | + | 1.11561i | ||||
\(313\) | −3.24690 | − | 9.99293i | −0.183526 | − | 0.564834i | 0.816394 | − | 0.577495i | \(-0.195970\pi\) |
−0.999920 | + | 0.0126612i | \(0.995970\pi\) | |||||||
\(314\) | 5.67947 | − | 17.4796i | 0.320511 | − | 0.986431i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.790537 | + | 2.43302i | 0.0444712 | + | 0.136868i | ||||
\(317\) | 15.7602 | − | 11.4504i | 0.885179 | − | 0.643120i | −0.0494374 | − | 0.998777i | \(-0.515743\pi\) |
0.934617 | + | 0.355657i | \(0.115743\pi\) | |||||||
\(318\) | −0.707341 | −0.0396657 | ||||||||
\(319\) | 7.50526 | − | 5.45289i | 0.420214 | − | 0.305303i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.58240 | + | 5.50893i | 0.423208 | + | 0.307479i | ||||
\(322\) | −10.9939 | − | 7.98754i | −0.612667 | − | 0.445128i | ||||
\(323\) | −0.718392 | + | 2.21098i | −0.0399724 | + | 0.123022i | ||||
\(324\) | −0.175259 | −0.00973662 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.6562 | 0.645579 | ||||||||
\(327\) | −4.81755 | + | 14.8269i | −0.266411 | + | 0.819929i | ||||
\(328\) | 2.76453 | + | 2.00855i | 0.152646 | + | 0.110903i | ||||
\(329\) | −9.86568 | − | 7.16784i | −0.543913 | − | 0.395176i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.7247 | − | 8.51846i | 0.644446 | − | 0.468217i | −0.216929 | − | 0.976187i | \(-0.569604\pi\) |
0.861375 | + | 0.507970i | \(0.169604\pi\) | |||||||
\(332\) | 0.880498 | 0.0483236 | ||||||||
\(333\) | −2.87471 | + | 2.08860i | −0.157533 | + | 0.114455i | ||||
\(334\) | 2.75458 | + | 8.47772i | 0.150724 | + | 0.463880i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.78452 | − | 5.49218i | 0.0973533 | − | 0.299623i | ||||
\(337\) | 2.88382 | + | 8.87550i | 0.157092 | + | 0.483479i | 0.998367 | − | 0.0571283i | \(-0.0181944\pi\) |
−0.841275 | + | 0.540608i | \(0.818194\pi\) | |||||||
\(338\) | 15.3285 | + | 47.1761i | 0.833758 | + | 2.56604i | ||||
\(339\) | 3.10503 | − | 9.55629i | 0.168642 | − | 0.519026i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.02558 | − | 3.15641i | −0.0555383 | − | 0.170929i | ||||
\(342\) | −0.620227 | + | 0.450621i | −0.0335380 | + | 0.0243668i | ||||
\(343\) | 18.2774 | 0.986884 | ||||||||
\(344\) | −0.278186 | + | 0.202114i | −0.0149988 | + | 0.0108973i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.9277 | − | 10.8456i | −0.802519 | − | 0.583064i | ||||
\(347\) | 0.852225 | + | 0.619178i | 0.0457498 | + | 0.0332392i | 0.610425 | − | 0.792074i | \(-0.290999\pi\) |
−0.564675 | + | 0.825313i | \(0.690999\pi\) | |||||||
\(348\) | 0.150753 | − | 0.463970i | 0.00808121 | − | 0.0248714i | ||||
\(349\) | −13.0715 | −0.699700 | −0.349850 | − | 0.936806i | \(-0.613767\pi\) | ||||
−0.349850 | + | 0.936806i | \(0.613767\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.05132 | −0.376371 | ||||||||
\(352\) | 1.01801 | − | 3.13311i | 0.0542602 | − | 0.166996i | ||||
\(353\) | −27.4639 | − | 19.9537i | −1.46176 | − | 1.06203i | −0.982901 | − | 0.184134i | \(-0.941052\pi\) |
−0.478855 | − | 0.877894i | \(-0.658948\pi\) | |||||||
\(354\) | −1.07536 | − | 0.781292i | −0.0571546 | − | 0.0415252i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0.400338 | − | 0.290863i | 0.0212179 | − | 0.0154157i | ||||
\(357\) | 6.53678 | 0.345963 | ||||||||
\(358\) | −10.7413 | + | 7.80405i | −0.567698 | + | 0.412457i | ||||
\(359\) | −1.88331 | − | 5.79622i | −0.0993971 | − | 0.305913i | 0.888978 | − | 0.457951i | \(-0.151416\pi\) |
−0.988375 | + | 0.152038i | \(0.951416\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.77179 | + | 17.7637i | −0.303778 | + | 0.934934i | ||||
\(362\) | 7.45892 | + | 22.9562i | 0.392032 | + | 1.20655i | ||||
\(363\) | 0.0331720 | + | 0.102093i | 0.00174108 | + | 0.00535848i | ||||
\(364\) | −0.609412 | + | 1.87558i | −0.0319419 | + | 0.0983070i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.43047 | + | 13.6356i | 0.231585 | + | 0.712744i | ||||
\(367\) | 17.6881 | − | 12.8511i | 0.923309 | − | 0.670823i | −0.0210364 | − | 0.999779i | \(-0.506697\pi\) |
0.944345 | + | 0.328955i | \(0.106697\pi\) | |||||||
\(368\) | 22.8127 | 1.18919 | ||||||||
\(369\) | −0.940826 | + | 0.683550i | −0.0489775 | + | 0.0355842i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.676026 | − | 0.491162i | −0.0350975 | − | 0.0254999i | ||||
\(372\) | −0.141196 | − | 0.102585i | −0.00732065 | − | 0.00531876i | ||||
\(373\) | −7.55730 | + | 23.2590i | −0.391302 | + | 1.20430i | 0.540502 | + | 0.841343i | \(0.318234\pi\) |
−0.931804 | + | 0.362961i | \(0.881766\pi\) | |||||||
\(374\) | −18.4413 | −0.953578 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 22.4545 | 1.15800 | ||||||||
\(377\) | 6.06534 | − | 18.6672i | 0.312381 | − | 0.961410i | ||||
\(378\) | 1.74396 | + | 1.26706i | 0.0896995 | + | 0.0651705i | ||||
\(379\) | 5.07918 | + | 3.69024i | 0.260900 | + | 0.189555i | 0.710544 | − | 0.703653i | \(-0.248449\pi\) |
−0.449644 | + | 0.893208i | \(0.648449\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.790235 | − | 0.574140i | 0.0404850 | − | 0.0294141i | ||||
\(382\) | 0.440118 | 0.0225184 | ||||||||
\(383\) | −19.9727 | + | 14.5110i | −1.02056 | + | 0.741477i | −0.966397 | − | 0.257055i | \(-0.917248\pi\) |
−0.0541589 | + | 0.998532i | \(0.517248\pi\) | |||||||
\(384\) | 2.96762 | + | 9.13341i | 0.151441 | + | 0.466087i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.21133 | + | 3.72808i | −0.0616549 | + | 0.189754i | ||||
\(387\) | −0.0361617 | − | 0.111294i | −0.00183820 | − | 0.00565740i | ||||
\(388\) | −0.0923892 | − | 0.284345i | −0.00469035 | − | 0.0144354i | ||||
\(389\) | −3.99360 | + | 12.2910i | −0.202484 | + | 0.623181i | 0.797324 | + | 0.603552i | \(0.206248\pi\) |
−0.999807 | + | 0.0196288i | \(0.993752\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.97967 | + | 24.5589i | 0.403549 | + | 1.24200i | ||||
\(392\) | −10.5868 | + | 7.69175i | −0.534713 | + | 0.388492i | ||||
\(393\) | 10.0616 | 0.507541 | ||||||||
\(394\) | 19.8045 | − | 14.3888i | 0.997736 | − | 0.724897i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.472545 | + | 0.343324i | 0.0237463 | + | 0.0172527i | ||||
\(397\) | 23.4788 | + | 17.0584i | 1.17837 | + | 0.856135i | 0.991987 | − | 0.126342i | \(-0.0403236\pi\) |
0.186383 | + | 0.982477i | \(0.440324\pi\) | |||||||
\(398\) | 0.639734 | − | 1.96890i | 0.0320670 | − | 0.0986921i | ||||
\(399\) | −0.905670 | −0.0453402 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.3926 | 1.16817 | 0.584084 | − | 0.811693i | \(-0.301454\pi\) | ||||
0.584084 | + | 0.811693i | \(0.301454\pi\) | |||||||
\(402\) | 6.35158 | − | 19.5481i | 0.316788 | − | 0.974973i | ||||
\(403\) | −5.68081 | − | 4.12735i | −0.282981 | − | 0.205598i | ||||
\(404\) | 1.86800 | + | 1.35719i | 0.0929367 | + | 0.0675225i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.85443 | + | 3.52695i | −0.240921 | + | 0.175040i | ||||
\(407\) | 11.8425 | 0.587009 | ||||||||
\(408\) | −9.73768 | + | 7.07484i | −0.482087 | + | 0.350257i | ||||
\(409\) | −4.94173 | − | 15.2091i | −0.244353 | − | 0.752040i | −0.995742 | − | 0.0921815i | \(-0.970616\pi\) |
0.751389 | − | 0.659859i | \(-0.229384\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.50567 | + | 4.63397i | −0.0742691 | + | 0.228577i | ||||
\(412\) | 0.588806 | + | 1.81216i | 0.0290084 | + | 0.0892786i | ||||
\(413\) | −0.485237 | − | 1.49341i | −0.0238770 | − | 0.0734858i | ||||
\(414\) | −2.63148 | + | 8.09885i | −0.129330 | + | 0.398037i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.15386 | − | 6.62890i | −0.105602 | − | 0.325008i | ||||
\(417\) | −0.150302 | + | 0.109201i | −0.00736033 | + | 0.00534759i | ||||
\(418\) | 2.55504 | 0.124971 | ||||||||
\(419\) | −26.1935 | + | 19.0307i | −1.27964 | + | 0.929710i | −0.999542 | − | 0.0302627i | \(-0.990366\pi\) |
−0.280094 | + | 0.959973i | \(0.590366\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.6044 | − | 10.6107i | −0.711774 | − | 0.517134i | 0.171972 | − | 0.985102i | \(-0.444986\pi\) |
−0.883745 | + | 0.467968i | \(0.844986\pi\) | |||||||
\(422\) | 12.4254 | + | 9.02757i | 0.604858 | + | 0.439455i | ||||
\(423\) | −2.36143 | + | 7.26772i | −0.114816 | + | 0.353369i | ||||
\(424\) | 1.53865 | 0.0747235 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −14.4052 | −0.697932 | ||||||||
\(427\) | −5.23392 | + | 16.1084i | −0.253287 | + | 0.779538i | ||||
\(428\) | −1.32888 | − | 0.965491i | −0.0642340 | − | 0.0466688i | ||||
\(429\) | 19.0122 | + | 13.8132i | 0.917919 | + | 0.666907i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.8070 | + | 19.4764i | −1.29125 | + | 0.938146i | −0.999830 | − | 0.0184500i | \(-0.994127\pi\) |
−0.291417 | + | 0.956596i | \(0.594127\pi\) | |||||||
\(432\) | −3.61877 | −0.174108 | ||||||||
\(433\) | 18.3366 | − | 13.3223i | 0.881201 | − | 0.640230i | −0.0523682 | − | 0.998628i | \(-0.516677\pi\) |
0.933569 | + | 0.358398i | \(0.116677\pi\) | |||||||
\(434\) | 0.663351 | + | 2.04158i | 0.0318419 | + | 0.0979991i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.844320 | − | 2.59855i | 0.0404356 | − | 0.124448i | ||||
\(437\) | −1.10558 | − | 3.40263i | −0.0528872 | − | 0.162770i | ||||
\(438\) | −2.32020 | − | 7.14085i | −0.110864 | − | 0.341203i | ||||
\(439\) | −2.62799 | + | 8.08812i | −0.125427 | + | 0.386025i | −0.993979 | − | 0.109574i | \(-0.965051\pi\) |
0.868551 | + | 0.495599i | \(0.165051\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.37619 | − | 4.23547i | −0.0655327 | − | 0.201689i | ||||
\(442\) | −31.5657 | + | 22.9338i | −1.50142 | + | 1.09085i | ||||
\(443\) | 6.35768 | 0.302063 | 0.151031 | − | 0.988529i | \(-0.451741\pi\) | ||||
0.151031 | + | 0.988529i | \(0.451741\pi\) | |||||||
\(444\) | 0.503820 | − | 0.366046i | 0.0239102 | − | 0.0173718i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −18.5244 | − | 13.4588i | −0.877157 | − | 0.637292i | ||||
\(447\) | −3.14617 | − | 2.28583i | −0.148809 | − | 0.108116i | ||||
\(448\) | −4.22749 | + | 13.0109i | −0.199730 | + | 0.614706i | ||||
\(449\) | −6.25726 | −0.295298 | −0.147649 | − | 0.989040i | \(-0.547171\pi\) | ||||
−0.147649 | + | 0.989040i | \(0.547171\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.87576 | 0.182502 | ||||||||
\(452\) | −0.544184 | + | 1.67483i | −0.0255963 | + | 0.0787772i | ||||
\(453\) | 17.8911 | + | 12.9986i | 0.840596 | + | 0.610729i | ||||
\(454\) | −15.4219 | − | 11.2047i | −0.723786 | − | 0.525861i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.34915 | − | 0.980218i | 0.0631800 | − | 0.0459029i | ||||
\(457\) | −11.0441 | −0.516620 | −0.258310 | − | 0.966062i | \(-0.583166\pi\) | ||||
−0.258310 | + | 0.966062i | \(0.583166\pi\) | |||||||
\(458\) | −0.0677503 | + | 0.0492235i | −0.00316576 | + | 0.00230006i | ||||
\(459\) | −1.26581 | − | 3.89576i | −0.0590830 | − | 0.181839i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.31202 | + | 22.5041i | −0.340555 | + | 1.04812i | 0.623366 | + | 0.781930i | \(0.285765\pi\) |
−0.963921 | + | 0.266189i | \(0.914235\pi\) | |||||||
\(462\) | −2.22007 | − | 6.83266i | −0.103287 | − | 0.317884i | ||||
\(463\) | −1.92345 | − | 5.91977i | −0.0893903 | − | 0.275115i | 0.896361 | − | 0.443325i | \(-0.146201\pi\) |
−0.985751 | + | 0.168210i | \(0.946201\pi\) | |||||||
\(464\) | 3.11276 | − | 9.58009i | 0.144506 | − | 0.444744i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.8611 | − | 33.4271i | −0.503132 | − | 1.54848i | ||||
\(467\) | −4.00204 | + | 2.90765i | −0.185192 | + | 0.134550i | −0.676519 | − | 0.736425i | \(-0.736512\pi\) |
0.491326 | + | 0.870976i | \(0.336512\pi\) | |||||||
\(468\) | 1.23581 | 0.0571252 | ||||||||
\(469\) | 19.6442 | − | 14.2723i | 0.907084 | − | 0.659035i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.0073 | − | 7.99730i | −0.507191 | − | 0.368496i | ||||
\(472\) | 2.33918 | + | 1.69951i | 0.107669 | + | 0.0782264i | ||||
\(473\) | −0.120518 | + | 0.370918i | −0.00554144 | + | 0.0170548i | ||||
\(474\) | −19.7179 | −0.905671 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.14563 | −0.0525099 | ||||||||
\(477\) | −0.161812 | + | 0.498006i | −0.00740886 | + | 0.0228021i | ||||
\(478\) | −21.3072 | − | 15.4806i | −0.974569 | − | 0.708066i | ||||
\(479\) | 24.3432 | + | 17.6863i | 1.11227 | + | 0.808109i | 0.983019 | − | 0.183503i | \(-0.0587436\pi\) |
0.129248 | + | 0.991612i | \(0.458744\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.2705 | − | 14.7274i | 0.924256 | − | 0.671511i | ||||
\(482\) | −5.53651 | −0.252181 | ||||||||
\(483\) | −8.13864 | + | 5.91307i | −0.370321 | + | 0.269054i | ||||
\(484\) | −0.00581369 | − | 0.0178927i | −0.000264259 | − | 0.000813305i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.417429 | − | 1.28472i | 0.0189350 | − | 0.0582759i | ||||
\(487\) | −10.5838 | − | 32.5736i | −0.479598 | − | 1.47605i | −0.839655 | − | 0.543120i | \(-0.817243\pi\) |
0.360057 | − | 0.932930i | \(-0.382757\pi\) | |||||||
\(488\) | −9.63743 | − | 29.6609i | −0.436266 | − | 1.34269i | ||||
\(489\) | 2.66649 | − | 8.20662i | 0.120583 | − | 0.371116i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.21975 | − | 9.90938i | −0.145305 | − | 0.447204i | 0.851745 | − | 0.523957i | \(-0.175545\pi\) |
−0.997050 | + | 0.0767530i | \(0.975545\pi\) | |||||||
\(492\) | 0.164888 | − | 0.119798i | 0.00743374 | − | 0.00540093i | ||||
\(493\) | 11.4022 | 0.513530 | ||||||||
\(494\) | 4.37342 | − | 3.17747i | 0.196769 | − | 0.142961i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.91542 | − | 2.11817i | −0.130906 | − | 0.0951088i | ||||
\(497\) | −13.7674 | − | 10.0026i | −0.617553 | − | 0.448679i | ||||
\(498\) | −2.09716 | + | 6.45438i | −0.0939758 | + | 0.289228i | ||||
\(499\) | 8.83514 | 0.395515 | 0.197757 | − | 0.980251i | \(-0.436634\pi\) | ||||
0.197757 | + | 0.980251i | \(0.436634\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.59891 | 0.294818 | ||||||||
\(502\) | −0.429671 | + | 1.32239i | −0.0191771 | + | 0.0590211i | ||||
\(503\) | −17.2915 | − | 12.5630i | −0.770988 | − | 0.560156i | 0.131273 | − | 0.991346i | \(-0.458094\pi\) |
−0.902261 | + | 0.431190i | \(0.858094\pi\) | |||||||
\(504\) | −3.79356 | − | 2.75618i | −0.168979 | − | 0.122770i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 22.9604 | − | 16.6817i | 1.02072 | − | 0.741593i | ||||
\(507\) | 36.7211 | 1.63084 | ||||||||
\(508\) | −0.138496 | + | 0.100623i | −0.00614477 | + | 0.00446443i | ||||
\(509\) | −5.18529 | − | 15.9587i | −0.229834 | − | 0.707356i | −0.997765 | − | 0.0668236i | \(-0.978714\pi\) |
0.767931 | − | 0.640533i | \(-0.221286\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.74096 | − | 8.43582i | 0.121253 | − | 0.373179i | ||||
\(512\) | −7.67717 | − | 23.6279i | −0.339286 | − | 1.04422i | ||||
\(513\) | 0.175378 | + | 0.539758i | 0.00774312 | + | 0.0238309i | ||||
\(514\) | −7.74737 | + | 23.8440i | −0.341722 | + | 1.05171i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.00633766 | + | 0.0195053i | 0.000279000 | + | 0.000858674i | ||||
\(517\) | 20.6042 | − | 14.9698i | 0.906170 | − | 0.658371i | ||||
\(518\) | −7.65976 | −0.336550 | ||||||||
\(519\) | −11.0508 | + | 8.02886i | −0.485075 | + | 0.352428i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.72559 | + | 2.70680i | 0.163221 | + | 0.118587i | 0.666397 | − | 0.745597i | \(-0.267835\pi\) |
−0.503176 | + | 0.864184i | \(0.667835\pi\) | |||||||
\(522\) | 3.04201 | + | 2.21015i | 0.133145 | + | 0.0967357i | ||||
\(523\) | 4.00592 | − | 12.3290i | 0.175167 | − | 0.539108i | −0.824474 | − | 0.565899i | \(-0.808529\pi\) |
0.999641 | + | 0.0267915i | \(0.00852902\pi\) | |||||||
\(524\) | −1.76339 | −0.0770340 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.7418 | 0.729979 | ||||||||
\(527\) | 1.26052 | − | 3.87949i | 0.0549093 | − | 0.168993i | ||||
\(528\) | 9.75716 | + | 7.08899i | 0.424626 | + | 0.308509i | ||||
\(529\) | −13.5433 | − | 9.83979i | −0.588840 | − | 0.427817i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.796071 | + | 0.578380i | −0.0345465 | + | 0.0250995i | ||||
\(532\) | 0.158727 | 0.00688169 | ||||||||
\(533\) | 6.63406 | − | 4.81993i | 0.287353 | − | 0.208774i | ||||
\(534\) | 1.17861 | + | 3.62740i | 0.0510036 | + | 0.156973i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −13.8163 | + | 42.5223i | −0.596774 | + | 1.83668i | ||||
\(537\) | 3.03727 | + | 9.34775i | 0.131068 | + | 0.403385i | ||||
\(538\) | −2.21251 | − | 6.80940i | −0.0953880 | − | 0.293574i | ||||
\(539\) | −4.58651 | + | 14.1158i | −0.197555 | + | 0.608012i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.45597 | − | 26.0248i | −0.363551 | − | 1.11889i | −0.950884 | − | 0.309548i | \(-0.899822\pi\) |
0.587333 | − | 0.809345i | \(-0.300178\pi\) | |||||||
\(542\) | −0.871464 | + | 0.633156i | −0.0374326 | + | 0.0271964i | ||||
\(543\) | 17.8687 | 0.766819 | ||||||||
\(544\) | 3.27573 | − | 2.37996i | 0.140446 | − | 0.102040i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −12.2972 | − | 8.93444i | −0.526271 | − | 0.382359i | ||||
\(547\) | −22.3656 | − | 16.2495i | −0.956282 | − | 0.694779i | −0.00399765 | − | 0.999992i | \(-0.501272\pi\) |
−0.952284 | + | 0.305213i | \(0.901272\pi\) | |||||||
\(548\) | 0.263882 | − | 0.812146i | 0.0112725 | − | 0.0346931i | ||||
\(549\) | 10.6137 | 0.452982 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.57978 | −0.0673007 | ||||||||
\(552\) | 5.72414 | − | 17.6171i | 0.243636 | − | 0.749833i | ||||
\(553\) | −18.8449 | − | 13.6916i | −0.801368 | − | 0.582228i | ||||
\(554\) | 5.18473 | + | 3.76692i | 0.220278 | + | 0.160041i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.0263418 | − | 0.0191385i | 0.00111714 | − | 0.000811652i | ||||
\(557\) | −6.17333 | −0.261572 | −0.130786 | − | 0.991411i | \(-0.541750\pi\) | ||||
−0.130786 | + | 0.991411i | \(0.541750\pi\) | |||||||
\(558\) | 1.08828 | − | 0.790682i | 0.0460706 | − | 0.0334722i | ||||
\(559\) | 0.254987 | + | 0.784770i | 0.0107848 | + | 0.0331923i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.21865 | + | 12.9837i | −0.178112 | + | 0.548171i | ||||
\(562\) | −7.82254 | − | 24.0753i | −0.329974 | − | 1.01555i | ||||
\(563\) | 1.76119 | + | 5.42039i | 0.0742254 | + | 0.228442i | 0.981285 | − | 0.192559i | \(-0.0616787\pi\) |
−0.907060 | + | 0.421001i | \(0.861679\pi\) | |||||||
\(564\) | 0.413862 | − | 1.27373i | 0.0174267 | − | 0.0536339i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.90947 | + | 15.1098i | 0.206360 | + | 0.635112i | ||||
\(567\) | 1.29103 | − | 0.937986i | 0.0542180 | − | 0.0393917i | ||||
\(568\) | 31.3350 | 1.31479 | ||||||||
\(569\) | −16.3185 | + | 11.8561i | −0.684109 | + | 0.497034i | −0.874718 | − | 0.484632i | \(-0.838954\pi\) |
0.190610 | + | 0.981666i | \(0.438954\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.7464 | + | 9.26077i | 0.533418 | + | 0.387551i | 0.821635 | − | 0.570014i | \(-0.193062\pi\) |
−0.288217 | + | 0.957565i | \(0.593062\pi\) | |||||||
\(572\) | −3.33207 | − | 2.42089i | −0.139321 | − | 0.101222i | ||||
\(573\) | 0.100682 | − | 0.309867i | 0.00420605 | − | 0.0129449i | ||||
\(574\) | −2.50686 | −0.104634 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 8.57279 | 0.357200 | ||||||||
\(577\) | −4.97709 | + | 15.3179i | −0.207199 | + | 0.637692i | 0.792417 | + | 0.609980i | \(0.208822\pi\) |
−0.999616 | + | 0.0277128i | \(0.991178\pi\) | |||||||
\(578\) | 0.241245 | + | 0.175275i | 0.0100345 | + | 0.00729047i | ||||
\(579\) | 2.34766 | + | 1.70568i | 0.0975656 | + | 0.0708855i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.48609 | + | 4.71242i | −0.269088 | + | 0.195504i | ||||
\(582\) | 2.30441 | 0.0955207 | ||||||||
\(583\) | 1.41186 | − | 1.02578i | 0.0584732 | − | 0.0424833i | ||||
\(584\) | 5.04705 | + | 15.5332i | 0.208848 | + | 0.642769i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.30110 | − | 28.6258i | 0.384225 | − | 1.18252i | ||||
\(587\) | 0.618257 | + | 1.90280i | 0.0255182 | + | 0.0785369i | 0.963005 | − | 0.269485i | \(-0.0868535\pi\) |
−0.937486 | + | 0.348022i | \(0.886853\pi\) | |||||||
\(588\) | 0.241189 | + | 0.742304i | 0.00994648 | + | 0.0306121i | ||||
\(589\) | −0.174646 | + | 0.537504i | −0.00719614 | + | 0.0221475i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.60000 | − | 17.2350i | −0.230353 | − | 0.708954i | ||||
\(592\) | 10.4029 | − | 7.55816i | 0.427557 | − | 0.310638i | ||||
\(593\) | −26.8231 | −1.10149 | −0.550747 | − | 0.834672i | \(-0.685657\pi\) | ||||
−0.550747 | + | 0.834672i | \(0.685657\pi\) | |||||||
\(594\) | −3.64220 | + | 2.64621i | −0.149441 | + | 0.108575i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.551396 | + | 0.400613i | 0.0225861 | + | 0.0164097i | ||||
\(597\) | −1.23987 | − | 0.900815i | −0.0507443 | − | 0.0368679i | ||||
\(598\) | 18.5554 | − | 57.1076i | 0.758786 | − | 2.33530i | ||||
\(599\) | −44.8025 | −1.83058 | −0.915290 | − | 0.402796i | \(-0.868038\pi\) | ||||
−0.915290 | + | 0.402796i | \(0.868038\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.2298 | −0.580446 | −0.290223 | − | 0.956959i | \(-0.593729\pi\) | ||||
−0.290223 | + | 0.956959i | \(0.593729\pi\) | |||||||
\(602\) | 0.0779519 | − | 0.239911i | 0.00317708 | − | 0.00977805i | ||||
\(603\) | −12.3099 | − | 8.94370i | −0.501300 | − | 0.364216i | ||||
\(604\) | −3.13557 | − | 2.27813i | −0.127585 | − | 0.0926957i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −14.3979 | + | 10.4607i | −0.584873 | + | 0.424935i | ||||
\(607\) | −20.3346 | −0.825356 | −0.412678 | − | 0.910877i | \(-0.635406\pi\) | ||||
−0.412678 | + | 0.910877i | \(0.635406\pi\) | |||||||
\(608\) | −0.453853 | + | 0.329743i | −0.0184062 | + | 0.0133729i | ||||
\(609\) | 1.37266 | + | 4.22461i | 0.0556230 | + | 0.171190i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.6512 | − | 51.2470i | 0.673634 | − | 2.07323i | ||||
\(612\) | 0.221845 | + | 0.682768i | 0.00896755 | + | 0.0275993i | ||||
\(613\) | −6.42510 | − | 19.7744i | −0.259507 | − | 0.798681i | −0.992908 | − | 0.118885i | \(-0.962068\pi\) |
0.733401 | − | 0.679797i | \(-0.237932\pi\) | |||||||
\(614\) | −6.38928 | + | 19.6642i | −0.257850 | + | 0.793582i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.82922 | + | 14.8628i | 0.194575 | + | 0.598839i | ||||
\(617\) | −4.00167 | + | 2.90738i | −0.161101 | + | 0.117047i | −0.665415 | − | 0.746474i | \(-0.731745\pi\) |
0.504314 | + | 0.863520i | \(0.331745\pi\) | |||||||
\(618\) | −14.6862 | −0.590766 | ||||||||
\(619\) | 37.1765 | − | 27.0103i | 1.49425 | − | 1.08564i | 0.521650 | − | 0.853160i | \(-0.325317\pi\) |
0.972602 | − | 0.232477i | \(-0.0746832\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.10005 | + | 3.70540i | 0.204658 | + | 0.148693i | ||||
\(622\) | 14.0480 | + | 10.2065i | 0.563273 | + | 0.409242i | ||||
\(623\) | −1.39235 | + | 4.28521i | −0.0557833 | + | 0.171683i | ||||
\(624\) | 25.5171 | 1.02150 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −14.1934 | −0.567283 | ||||||||
\(627\) | 0.584494 | − | 1.79889i | 0.0233424 | − | 0.0718407i | ||||
\(628\) | 1.92914 | + | 1.40160i | 0.0769810 | + | 0.0559299i | ||||
\(629\) | 11.7755 | + | 8.55543i | 0.469521 | + | 0.341127i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.5262 | − | 12.7335i | 0.697707 | − | 0.506914i | −0.181477 | − | 0.983395i | \(-0.558088\pi\) |
0.879185 | + | 0.476481i | \(0.158088\pi\) | |||||||
\(632\) | 42.8915 | 1.70613 | ||||||||
\(633\) | 9.19833 | − | 6.68298i | 0.365601 | − | 0.265625i | ||||
\(634\) | −8.13179 | − | 25.0271i | −0.322955 | − | 0.993952i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0.0283590 | − | 0.0872802i | 0.00112451 | − | 0.00346088i | ||||
\(637\) | 9.70393 | + | 29.8656i | 0.384484 | + | 1.18332i | ||||
\(638\) | −3.87249 | − | 11.9183i | −0.153314 | − | 0.471851i | ||||
\(639\) | −3.29534 | + | 10.1420i | −0.130362 | + | 0.401211i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.2442 | + | 34.6061i | 0.444119 | + | 1.36686i | 0.883447 | + | 0.468531i | \(0.155217\pi\) |
−0.439328 | + | 0.898327i | \(0.644783\pi\) | |||||||
\(642\) | 10.2425 | − | 7.44163i | 0.404240 | − | 0.293698i | ||||
\(643\) | −1.01349 | −0.0399682 | −0.0199841 | − | 0.999800i | \(-0.506362\pi\) | ||||
−0.0199841 | + | 0.999800i | \(0.506362\pi\) | |||||||
\(644\) | 1.42637 | − | 1.03632i | 0.0562069 | − | 0.0408367i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.54060 | + | 1.84586i | 0.0999587 | + | 0.0726243i | ||||
\(647\) | −11.0841 | − | 8.05306i | −0.435760 | − | 0.316598i | 0.348188 | − | 0.937425i | \(-0.386797\pi\) |
−0.783948 | + | 0.620826i | \(0.786797\pi\) | |||||||
\(648\) | −0.908017 | + | 2.79459i | −0.0356703 | + | 0.109782i | ||||
\(649\) | 3.27944 | 0.128729 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.58913 | 0.0622830 | ||||||||
\(652\) | −0.467327 | + | 1.43829i | −0.0183019 | + | 0.0563276i | ||||
\(653\) | 19.2847 | + | 14.0112i | 0.754669 | + | 0.548299i | 0.897271 | − | 0.441481i | \(-0.145547\pi\) |
−0.142601 | + | 0.989780i | \(0.545547\pi\) | |||||||
\(654\) | 17.0374 | + | 12.3784i | 0.666213 | + | 0.484032i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.40463 | − | 2.47361i | 0.132928 | − | 0.0965782i | ||||
\(657\) | −5.55832 | −0.216851 | ||||||||
\(658\) | −13.3269 | + | 9.68253i | −0.519535 | + | 0.377464i | ||||
\(659\) | 4.56597 | + | 14.0526i | 0.177865 | + | 0.547412i | 0.999753 | − | 0.0222376i | \(-0.00707903\pi\) |
−0.821888 | + | 0.569649i | \(0.807079\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.33453 | − | 7.18496i | 0.0908029 | − | 0.279463i | −0.895334 | − | 0.445395i | \(-0.853063\pi\) |
0.986137 | + | 0.165932i | \(0.0530633\pi\) | |||||||
\(662\) | −6.04958 | − | 18.6187i | −0.235124 | − | 0.723637i | ||||
\(663\) | 8.92563 | + | 27.4703i | 0.346643 | + | 1.06686i | ||||
\(664\) | 4.56186 | − | 14.0399i | 0.177034 | − | 0.544856i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.48327 | + | 4.56503i | 0.0574755 | + | 0.176891i | ||||
\(667\) | −14.1964 | + | 10.3143i | −0.549685 | + | 0.399369i | ||||
\(668\) | −1.15652 | −0.0447471 | ||||||||
\(669\) | −13.7134 | + | 9.96335i | −0.530190 | + | 0.385205i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.6174 | − | 20.7917i | −1.10476 | − | 0.802656i | ||||
\(672\) | 1.27615 | + | 0.927174i | 0.0492284 | + | 0.0357665i | ||||
\(673\) | −3.76836 | + | 11.5978i | −0.145259 | + | 0.447063i | −0.997044 | − | 0.0768292i | \(-0.975520\pi\) |
0.851785 | + | 0.523892i | \(0.175520\pi\) | |||||||
\(674\) | 12.6063 | 0.485576 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.43571 | −0.247527 | ||||||||
\(677\) | 5.54706 | − | 17.0721i | 0.213191 | − | 0.656134i | −0.786086 | − | 0.618117i | \(-0.787896\pi\) |
0.999277 | − | 0.0380172i | \(-0.0121042\pi\) | |||||||
\(678\) | −10.9810 | − | 7.97815i | −0.421722 | − | 0.306399i | ||||
\(679\) | 2.20239 | + | 1.60013i | 0.0845198 | + | 0.0614073i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.4166 | + | 8.29466i | −0.437486 | + | 0.317852i | ||||
\(682\) | −4.48320 | −0.171671 | ||||||||
\(683\) | −8.11227 | + | 5.89391i | −0.310407 | + | 0.225524i | −0.732071 | − | 0.681228i | \(-0.761446\pi\) |
0.421664 | + | 0.906752i | \(0.361446\pi\) | |||||||
\(684\) | −0.0307366 | − | 0.0945975i | −0.00117524 | − | 0.00361703i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.62950 | − | 23.4812i | 0.291296 | − | 0.896516i | ||||
\(687\) | 0.0191573 | + | 0.0589602i | 0.000730898 | + | 0.00224947i | ||||
\(688\) | 0.130861 | + | 0.402748i | 0.00498901 | + | 0.0153546i | ||||
\(689\) | 1.14099 | − | 3.51160i | 0.0434682 | − | 0.133781i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.91136 | + | 18.1933i | 0.224879 | + | 0.692105i | 0.998304 | + | 0.0582177i | \(0.0185418\pi\) |
−0.773425 | + | 0.633887i | \(0.781458\pi\) | |||||||
\(692\) | 1.93675 | − | 1.40713i | 0.0736242 | − | 0.0534911i | ||||
\(693\) | −5.31842 | −0.202030 | ||||||||
\(694\) | 1.15121 | − | 0.836404i | 0.0436994 | − | 0.0317494i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.61716 | − | 4.80765i | −0.250823 | − | 0.182234i | ||||
\(697\) | 3.85386 | + | 2.79999i | 0.145975 | + | 0.106057i | ||||
\(698\) | −5.45642 | + | 16.7931i | −0.206528 | + | 0.635629i | ||||
\(699\) | −26.0191 | −0.984131 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.81920 | −0.144249 | −0.0721246 | − | 0.997396i | \(-0.522978\pi\) | ||||
−0.0721246 | + | 0.997396i | \(0.522978\pi\) | |||||||
\(702\) | −2.94343 | + | 9.05894i | −0.111092 | + | 0.341907i | ||||
\(703\) | −1.63150 | − | 1.18535i | −0.0615332 | − | 0.0447065i | ||||
\(704\) | −23.1145 | − | 16.7937i | −0.871162 | − | 0.632936i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −37.0991 | + | 26.9540i | −1.39624 | + | 1.01443i | ||||
\(707\) | −21.0241 | −0.790692 | ||||||||
\(708\) | 0.139519 | − | 0.101366i | 0.00524344 | − | 0.00380958i | ||||
\(709\) | 11.7592 | + | 36.1911i | 0.441626 | + | 1.35918i | 0.886142 | + | 0.463413i | \(0.153375\pi\) |
−0.444517 | + | 0.895771i | \(0.646625\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.51068 | + | 13.8824i | −0.169164 | + | 0.520632i | ||||
\(712\) | −2.56379 | − | 7.89053i | −0.0960821 | − | 0.295710i | ||||
\(713\) | 1.93991 | + | 5.97043i | 0.0726502 | + | 0.223594i | ||||
\(714\) | 2.72864 | − | 8.39790i | 0.102117 | − | 0.314284i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −0.532309 | − | 1.63828i | −0.0198933 | − | 0.0612253i | ||||
\(717\) | −15.7734 | + | 11.4601i | −0.589070 | + | 0.427984i | ||||
\(718\) | −8.23264 | −0.307239 | ||||||||
\(719\) | −15.7224 | + | 11.4230i | −0.586348 | + | 0.426007i | −0.841007 | − | 0.541024i | \(-0.818037\pi\) |
0.254659 | + | 0.967031i | \(0.418037\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.0360 | − | 10.1978i | −0.522729 | − | 0.379785i | ||||
\(722\) | 20.4120 | + | 14.8302i | 0.759657 | + | 0.551923i | ||||
\(723\) | −1.26654 | + | 3.89800i | −0.0471030 | + | 0.144968i | ||||
\(724\) | −3.13165 | −0.116387 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.145007 | 0.00538172 | ||||||||
\(727\) | −11.7655 | + | 36.2104i | −0.436358 | + | 1.34297i | 0.455331 | + | 0.890322i | \(0.349521\pi\) |
−0.891689 | + | 0.452649i | \(0.850479\pi\) | |||||||
\(728\) | 26.7496 | + | 19.4347i | 0.991406 | + | 0.720298i | ||||
\(729\) | −0.809017 | − | 0.587785i | −0.0299636 | − | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.387802 | + | 0.281755i | −0.0143434 | + | 0.0104211i | ||||
\(732\) | −1.86015 | −0.0687531 | ||||||||
\(733\) | −13.7202 | + | 9.96833i | −0.506768 | + | 0.368189i | −0.811596 | − | 0.584219i | \(-0.801401\pi\) |
0.304828 | + | 0.952407i | \(0.401401\pi\) | |||||||
\(734\) | −9.12653 | − | 28.0886i | −0.336866 | − | 1.03677i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.92559 | + | 5.92635i | −0.0709781 | + | 0.218448i | ||||
\(737\) | 15.6706 | + | 48.2292i | 0.577235 | + | 1.77655i | ||||
\(738\) | 0.485439 | + | 1.49403i | 0.0178693 | + | 0.0549959i | ||||
\(739\) | 4.08025 | − | 12.5577i | 0.150095 | − | 0.461944i | −0.847536 | − | 0.530737i | \(-0.821915\pi\) |
0.997631 | + | 0.0687937i | \(0.0219150\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.23665 | − | 3.80600i | −0.0454293 | − | 0.139817i | ||||
\(742\) | −0.913197 | + | 0.663476i | −0.0335245 | + | 0.0243570i | ||||
\(743\) | 42.2364 | 1.54950 | 0.774752 | − | 0.632265i | \(-0.217875\pi\) | ||||
0.774752 | + | 0.632265i | \(0.217875\pi\) | |||||||
\(744\) | −2.36729 | + | 1.71994i | −0.0867891 | + | 0.0630560i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 26.7265 | + | 19.4180i | 0.978528 | + | 0.710942i | ||||
\(747\) | 4.06448 | + | 2.95302i | 0.148712 | + | 0.108045i | ||||
\(748\) | 0.739358 | − | 2.27551i | 0.0270336 | − | 0.0832008i | ||||
\(749\) | 14.9564 | 0.546494 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.04801 | −0.0382426 | −0.0191213 | − | 0.999817i | \(-0.506087\pi\) | ||||
−0.0191213 | + | 0.999817i | \(0.506087\pi\) | |||||||
\(752\) | 8.54545 | − | 26.3002i | 0.311620 | − | 0.959069i | ||||
\(753\) | 0.832742 | + | 0.605022i | 0.0303468 | + | 0.0220482i | ||||
\(754\) | −21.4502 | − | 15.5845i | −0.781170 | − | 0.567553i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.226264 | + | 0.164391i | −0.00822915 | + | 0.00597883i | ||||
\(757\) | 17.0074 | 0.618146 | 0.309073 | − | 0.951038i | \(-0.399981\pi\) | ||||
0.309073 | + | 0.951038i | \(0.399981\pi\) | |||||||
\(758\) | 6.86110 | − | 4.98488i | 0.249207 | − | 0.181059i | ||||
\(759\) | −6.49238 | − | 19.9815i | −0.235658 | − | 0.725282i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.45484 | + | 22.9436i | −0.270238 | + | 0.831706i | 0.720203 | + | 0.693764i | \(0.244049\pi\) |
−0.990440 | + | 0.137942i | \(0.955951\pi\) | |||||||
\(762\) | −0.407738 | − | 1.25489i | −0.0147708 | − | 0.0454599i | ||||
\(763\) | 7.68783 | + | 23.6607i | 0.278318 | + | 0.856575i | ||||
\(764\) | −0.0176454 | + | 0.0543070i | −0.000638389 | + | 0.00196476i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.3053 | + | 31.7165i | 0.372346 | + | 1.14596i | ||||
\(767\) | 5.61335 | − | 4.07834i | 0.202686 | − | 0.147260i | ||||
\(768\) | −4.17298 | −0.150579 | ||||||||
\(769\) | −40.2744 | + | 29.2611i | −1.45233 | + | 1.05518i | −0.467053 | + | 0.884230i | \(0.654684\pi\) |
−0.985279 | + | 0.170952i | \(0.945316\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.0151 | + | 10.9091i | 0.540757 | + | 0.392883i | ||||
\(772\) | −0.411450 | − | 0.298936i | −0.0148084 | − | 0.0107589i | ||||
\(773\) | −9.72608 | + | 29.9338i | −0.349823 | + | 1.07664i | 0.609128 | + | 0.793072i | \(0.291520\pi\) |
−0.958951 | + | 0.283572i | \(0.908480\pi\) | |||||||
\(774\) | −0.158076 | −0.00568193 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.01268 | −0.179945 | ||||||||
\(777\) | −1.75225 | + | 5.39288i | −0.0628617 | + | 0.193468i | ||||
\(778\) | 14.1235 | + | 10.2613i | 0.506350 | + | 0.367885i | ||||
\(779\) | −0.533952 | − | 0.387939i | −0.0191308 | − | 0.0138993i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.7528 | − | 20.8901i | 1.02886 | − | 0.747508i | ||||
\(782\) | 34.8822 | 1.24738 | ||||||||
\(783\) | 2.25196 | − | 1.63614i | 0.0804784 | − | 0.0584710i | ||||
\(784\) | 4.98010 | + | 15.3272i | 0.177861 | + | 0.547399i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.20001 | − | 12.9263i | 0.149809 | − | 0.461066i | ||||
\(787\) | −5.91505 | − | 18.2047i | −0.210849 | − | 0.648926i | −0.999422 | − | 0.0339855i | \(-0.989180\pi\) |
0.788573 | − | 0.614941i | \(-0.210820\pi\) | |||||||
\(788\) | 0.981451 | + | 3.02060i | 0.0349627 | + | 0.107604i | ||||
\(789\) | 3.82988 | − | 11.7872i | 0.136347 | − | 0.419634i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.95499 | − | 15.2499i | −0.176179 | − | 0.542224i | ||||
\(792\) | 7.92272 | − | 5.75619i | 0.281522 | − | 0.204537i | ||||
\(793\) | −74.8406 | −2.65767 | ||||||||
\(794\) | 31.7159 | − | 23.0430i | 1.12556 | − | 0.817764i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.217298 | + | 0.157876i | 0.00770191 | + | 0.00559577i | ||||
\(797\) | 5.83655 | + | 4.24050i | 0.206741 | + | 0.150206i | 0.686338 | − | 0.727283i | \(-0.259217\pi\) |
−0.479597 | + | 0.877489i | \(0.659217\pi\) | |||||||
\(798\) | −0.378053 | + | 1.16353i | −0.0133829 | + | 0.0411885i | ||||
\(799\) | 31.3024 | 1.10740 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.82350 | 0.0997636 | ||||||||
\(802\) | 9.76474 | − | 30.0528i | 0.344805 | − | 1.06120i | ||||
\(803\) | 14.9867 | + | 10.8885i | 0.528869 | + | 0.384246i | ||||
\(804\) | 2.15743 | + | 1.56747i | 0.0760867 | + | 0.0552802i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.67381 | + | 5.57535i | −0.270298 | + | 0.196383i | ||||
\(807\) | −5.30032 | −0.186580 | ||||||||
\(808\) | 31.3191 | − | 22.7546i | 1.10180 | − | 0.800505i | ||||
\(809\) | 0.327376 | + | 1.00756i | 0.0115099 | + | 0.0354239i | 0.956647 | − | 0.291251i | \(-0.0940716\pi\) |
−0.945137 | + | 0.326675i | \(0.894072\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.68712 | − | 20.5808i | 0.234817 | − | 0.722691i | −0.762329 | − | 0.647190i | \(-0.775944\pi\) |
0.997146 | − | 0.0755016i | \(-0.0240558\pi\) | |||||||
\(812\) | −0.240571 | − | 0.740402i | −0.00844239 | − | 0.0259830i | ||||
\(813\) | 0.246419 | + | 0.758399i | 0.00864228 | + | 0.0265982i | ||||
\(814\) | 4.94339 | − | 15.2142i | 0.173266 | − | 0.533257i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4.58067 | + | 14.0979i | 0.160356 | + | 0.493524i | ||||
\(817\) | 0.0537299 | − | 0.0390371i | 0.00187977 | − | 0.00136573i | ||||
\(818\) | −21.6022 | −0.755302 | ||||||||
\(819\) | −9.10344 | + | 6.61404i | −0.318100 | + | 0.231113i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.7553 | + | 13.6265i | 0.654564 | + | 0.475568i | 0.864823 | − | 0.502077i | \(-0.167431\pi\) |
−0.210259 | + | 0.977646i | \(0.567431\pi\) | |||||||
\(822\) | 5.32482 | + | 3.86871i | 0.185724 | + | 0.134937i | ||||
\(823\) | −8.64534 | + | 26.6076i | −0.301358 | + | 0.927483i | 0.679654 | + | 0.733533i | \(0.262130\pi\) |
−0.981011 | + | 0.193950i | \(0.937870\pi\) | |||||||
\(824\) | 31.9463 | 1.11290 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.12116 | −0.0738044 | ||||||||
\(827\) | −12.7638 | + | 39.2829i | −0.443841 | + | 1.36600i | 0.439909 | + | 0.898042i | \(0.355011\pi\) |
−0.883750 | + | 0.467959i | \(0.844989\pi\) | |||||||
\(828\) | −0.893830 | − | 0.649405i | −0.0310627 | − | 0.0225684i | ||||
\(829\) | −38.4838 | − | 27.9602i | −1.33660 | − | 0.971096i | −0.999562 | − | 0.0296051i | \(-0.990575\pi\) |
−0.337038 | − | 0.941491i | \(-0.609425\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.83818 | − | 2.78860i | 0.133145 | − | 0.0967355i | ||||
\(832\) | −60.4495 | −2.09571 | ||||||||
\(833\) | −14.7584 | + | 10.7226i | −0.511348 | + | 0.371516i | ||||
\(834\) | 0.0775516 | + | 0.238679i | 0.00268539 | + | 0.00826478i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.102438 | + | 0.315272i | −0.00354289 | + | 0.0109039i | ||||
\(837\) | −0.307727 | − | 0.947085i | −0.0106366 | − | 0.0327360i | ||||
\(838\) | 13.5151 | + | 41.5951i | 0.466871 | + | 1.43688i | ||||
\(839\) | 15.1518 | − | 46.6324i | 0.523097 | − | 1.60993i | −0.244950 | − | 0.969536i | \(-0.578772\pi\) |
0.768048 | − | 0.640393i | \(-0.221228\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.56714 | − | 20.2116i | −0.226453 | − | 0.696951i | ||||
\(842\) | −19.7280 | + | 14.3332i | −0.679872 | + | 0.493956i | ||||
\(843\) | −18.7398 | −0.645433 | ||||||||
\(844\) | −1.61209 | + | 1.17125i | −0.0554905 | + | 0.0403162i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8.35122 | + | 6.06752i | 0.287121 | + | 0.208606i | ||||
\(847\) | 0.138588 | + | 0.100690i | 0.00476192 | + | 0.00345974i | ||||
\(848\) | 0.585560 | − | 1.80217i | 0.0201082 | − | 0.0618867i | ||||
\(849\) | 11.7612 | 0.403643 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.4003 | −0.767871 | ||||||||
\(852\) | 0.577538 | − | 1.77748i | 0.0197861 | − | 0.0608954i | ||||
\(853\) | 26.3235 | + | 19.1251i | 0.901299 | + | 0.654832i | 0.938799 | − | 0.344464i | \(-0.111939\pi\) |
−0.0375002 | + | 0.999297i | \(0.511939\pi\) | |||||||
\(854\) | 18.5099 | + | 13.4482i | 0.633394 | + | 0.460188i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −22.2801 | + | 16.1875i | −0.761520 | + | 0.553276i | ||||
\(857\) | −30.4813 | −1.04122 | −0.520610 | − | 0.853794i | \(-0.674296\pi\) | ||||
−0.520610 | + | 0.853794i | \(0.674296\pi\) | |||||||
\(858\) | 25.6823 | − | 18.6593i | 0.876779 | − | 0.637017i | ||||
\(859\) | 1.27382 | + | 3.92040i | 0.0434620 | + | 0.133762i | 0.970433 | − | 0.241371i | \(-0.0775970\pi\) |
−0.926971 | + | 0.375133i | \(0.877597\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.573471 | + | 1.76496i | −0.0195439 | + | 0.0601498i | ||||
\(862\) | 13.8316 | + | 42.5694i | 0.471107 | + | 1.44992i | ||||
\(863\) | −5.69159 | − | 17.5169i | −0.193744 | − | 0.596283i | −0.999989 | − | 0.00470109i | \(-0.998504\pi\) |
0.806245 | − | 0.591582i | \(-0.201496\pi\) | |||||||
\(864\) | 0.305455 | − | 0.940094i | 0.0103918 | − | 0.0319826i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −9.46115 | − | 29.1184i | −0.321503 | − | 0.989485i | ||||
\(867\) | 0.178590 | − | 0.129753i | 0.00606524 | − | 0.00440666i | ||||
\(868\) | −0.278510 | −0.00945325 | ||||||||
\(869\) | 39.3570 | − | 28.5945i | 1.33510 | − | 0.970003i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 86.8013 | + | 63.0649i | 2.94115 | + | 2.13687i | ||||
\(872\) | −37.0607 | − | 26.9261i | −1.25503 | − | 0.911834i | ||||
\(873\) | 0.527158 | − | 1.62242i | 0.0178416 | − | 0.0549108i | ||||
\(874\) | −4.83292 | −0.163476 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.974146 | 0.0329133 | ||||||||
\(877\) | −5.84432 | + | 17.9870i | −0.197349 | + | 0.607377i | 0.802593 | + | 0.596528i | \(0.203453\pi\) |
−0.999941 | + | 0.0108490i | \(0.996547\pi\) | |||||||
\(878\) | 9.29394 | + | 6.75244i | 0.313655 | + | 0.227884i | ||||
\(879\) | −18.0264 | − | 13.0969i | −0.608015 | − | 0.441749i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.0192 | + | 20.3571i | −0.943990 | + | 0.685849i | −0.949378 | − | 0.314137i | \(-0.898285\pi\) |
0.00538802 | + | 0.999985i | \(0.498285\pi\) | |||||||
\(882\) | −6.01583 | −0.202563 | ||||||||
\(883\) | 26.4447 | − | 19.2132i | 0.889934 | − | 0.646575i | −0.0459269 | − | 0.998945i | \(-0.514624\pi\) |
0.935861 | + | 0.352370i | \(0.114624\pi\) | |||||||
\(884\) | −1.56430 | − | 4.81442i | −0.0526131 | − | 0.161926i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.65388 | − | 8.16781i | 0.0891589 | − | 0.274403i | ||||
\(887\) | 15.0775 | + | 46.4037i | 0.506253 | + | 1.55809i | 0.798655 | + | 0.601790i | \(0.205545\pi\) |
−0.292402 | + | 0.956296i | \(0.594455\pi\) | |||||||
\(888\) | −3.22649 | − | 9.93012i | −0.108274 | − | 0.333233i | ||||
\(889\) | 0.481680 | − | 1.48246i | 0.0161550 | − | 0.0497201i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.02988 | + | 3.16965i | 0.0345024 | + | 0.106187i | ||||
\(892\) | 2.40340 | − | 1.74617i | 0.0804716 | − | 0.0584661i | ||||
\(893\) | −4.33695 | −0.145131 | ||||||||
\(894\) | −4.24995 | + | 3.08777i | −0.142139 | + | 0.103270i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 12.3983 | + | 9.00789i | 0.414198 | + | 0.300932i | ||||
\(897\) | −35.9620 | − | 26.1280i | −1.20074 | − | 0.872387i | ||||
\(898\) | −2.61196 | + | 8.03879i | −0.0871623 | + | 0.268258i | ||||
\(899\) | 2.77195 | 0.0924497 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.14494 | 0.0714582 | ||||||||
\(902\) | 1.61786 | − | 4.97925i | 0.0538687 | − | 0.165791i | ||||
\(903\) | −0.151078 | − | 0.109765i | −0.00502756 | − | 0.00365274i | ||||
\(904\) | 23.8865 | + | 17.3545i | 0.794452 | + | 0.577203i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 24.1678 | − | 17.5589i | 0.802921 | − | 0.583356i | ||||
\(907\) | 45.0367 | 1.49542 | 0.747710 | − | 0.664025i | \(-0.231153\pi\) | ||||
0.747710 | + | 0.664025i | \(0.231153\pi\) | |||||||
\(908\) | 2.00087 | − | 1.45371i | 0.0664011 | − | 0.0482432i | ||||
\(909\) | 4.07120 | + | 12.5299i | 0.135033 | + | 0.415589i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.00018 | − | 12.3113i | 0.132532 | − | 0.407891i | −0.862666 | − | 0.505774i | \(-0.831207\pi\) |
0.995198 | + | 0.0978826i | \(0.0312070\pi\) | |||||||
\(912\) | −0.634652 | − | 1.95326i | −0.0210154 | − | 0.0646788i | ||||
\(913\) | −5.17410 | − | 15.9243i | −0.171238 | − | 0.527016i | ||||
\(914\) | −4.61012 | + | 14.1885i | −0.152489 | + | 0.469314i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.00335750 | − | 0.0103333i | −0.000110935 | − | 0.000341423i | ||||
\(917\) | 12.9898 | − | 9.43764i | 0.428961 | − | 0.311658i | ||||
\(918\) | −5.53333 | −0.182627 | ||||||||
\(919\) | −11.7889 | + | 8.56513i | −0.388880 | + | 0.282538i | −0.764996 | − | 0.644035i | \(-0.777259\pi\) |
0.376117 | + | 0.926572i | \(0.377259\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.3830 | + | 8.99679i | 0.408034 | + | 0.296454i | ||||
\(922\) | 25.8591 | + | 18.7877i | 0.851623 | + | 0.618741i | ||||
\(923\) | 23.2365 | − | 71.5145i | 0.764838 | − | 2.35393i | ||||
\(924\) | 0.932102 | 0.0306639 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.40813 | −0.276308 | ||||||||
\(927\) | −3.35963 | + | 10.3399i | −0.110345 | + | 0.339606i | ||||
\(928\) | 2.22600 | + | 1.61728i | 0.0730720 | + | 0.0530899i | ||||
\(929\) | 25.3701 | + | 18.4324i | 0.832365 | + | 0.604749i | 0.920227 | − | 0.391384i | \(-0.128004\pi\) |
−0.0878623 | + | 0.996133i | \(0.528004\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.04477 | − | 1.48561i | 0.0670147 | − | 0.0486890i | ||||
\(932\) | 4.56008 | 0.149370 | ||||||||
\(933\) | 10.3995 | − | 7.55569i | 0.340465 | − | 0.247362i | ||||
\(934\) | 2.06494 | + | 6.35522i | 0.0675668 | + | 0.207949i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.40272 | − | 19.7055i | 0.209279 | − | 0.644095i | ||||
\(937\) | −15.0716 | − | 46.3855i | −0.492367 | − | 1.51535i | −0.821021 | − | 0.570898i | \(-0.806595\pi\) |
0.328654 | − | 0.944450i | \(-0.393405\pi\) | |||||||
\(938\) | −10.1358 | − | 31.1949i | −0.330946 | − | 1.01855i | ||||
\(939\) | −3.24690 | + | 9.99293i | −0.105959 | + | 0.326107i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −9.96145 | − | 30.6582i | −0.324734 | − | 0.999429i | −0.971561 | − | 0.236791i | \(-0.923904\pi\) |
0.646827 | − | 0.762637i | \(-0.276096\pi\) | |||||||
\(942\) | −14.8690 | + | 10.8030i | −0.484460 | + | 0.351980i | ||||
\(943\) | −7.33108 | −0.238733 | ||||||||
\(944\) | 2.88080 | − | 2.09302i | 0.0937619 | − | 0.0681220i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.426216 | + | 0.309664i | 0.0138575 | + | 0.0100680i | ||||
\(947\) | 42.0070 | + | 30.5199i | 1.36505 | + | 0.991763i | 0.998106 | + | 0.0615183i | \(0.0195942\pi\) |
0.366939 | + | 0.930245i | \(0.380406\pi\) | |||||||
\(948\) | 0.790537 | − | 2.43302i | 0.0256755 | − | 0.0790209i | ||||
\(949\) | 39.1935 | 1.27227 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.4806 | −0.631703 | ||||||||
\(952\) | −5.93551 | + | 18.2676i | −0.192371 | + | 0.592057i | ||||
\(953\) | 32.1817 | + | 23.3814i | 1.04247 | + | 0.757398i | 0.970766 | − | 0.240028i | \(-0.0771567\pi\) |
0.0717028 | + | 0.997426i | \(0.477157\pi\) | |||||||
\(954\) | 0.572251 | + | 0.415765i | 0.0185273 | + | 0.0134609i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.76444 | − | 2.00848i | 0.0894083 | − | 0.0649590i | ||||
\(957\) | −9.27701 | −0.299883 | ||||||||
\(958\) | 32.8835 | − | 23.8912i | 1.06242 | − | 0.771891i | ||||
\(959\) | 2.40274 | + | 7.39487i | 0.0775885 | + | 0.238793i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.27309 | + | 28.5396i | −0.299132 | + | 0.920633i | ||||
\(962\) | −10.4590 | − | 32.1895i | −0.337211 | − | 1.03783i | ||||
\(963\) | −2.89622 | − | 8.91364i | −0.0933293 | − | 0.287238i | ||||
\(964\) | 0.221972 | − | 0.683160i | 0.00714924 | − | 0.0220031i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.19930 | + | 12.9241i | 0.135110 | + | 0.415827i | ||||
\(967\) | 16.0847 | − | 11.6862i | 0.517248 | − | 0.375802i | −0.298318 | − | 0.954466i | \(-0.596426\pi\) |
0.815566 | + | 0.578664i | \(0.196426\pi\) | |||||||
\(968\) | −0.315428 | −0.0101382 | ||||||||
\(969\) | 1.88077 | − | 1.36646i | 0.0604191 | − | 0.0438971i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 33.4804 | + | 24.3250i | 1.07444 | + | 0.780625i | 0.976705 | − | 0.214588i | \(-0.0688407\pi\) |
0.0977335 | + | 0.995213i | \(0.468841\pi\) | |||||||
\(972\) | 0.141788 | + | 0.103015i | 0.00454784 | + | 0.00330420i | ||||
\(973\) | −0.0916152 | + | 0.281963i | −0.00293705 | + | 0.00903931i | ||||
\(974\) | −46.2658 | −1.48245 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −38.4085 | −1.22943 | ||||||||
\(977\) | −1.11861 | + | 3.44274i | −0.0357876 | + | 0.110143i | −0.967355 | − | 0.253427i | \(-0.918442\pi\) |
0.931567 | + | 0.363570i | \(0.118442\pi\) | |||||||
\(978\) | −9.43010 | − | 6.85137i | −0.301541 | − | 0.219083i | ||||
\(979\) | −7.61292 | − | 5.53111i | −0.243310 | − | 0.176775i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.6125 | − | 9.16353i | 0.402686 | − | 0.292569i | ||||
\(982\) | −14.0747 | −0.449143 | ||||||||
\(983\) | −16.2692 | + | 11.8203i | −0.518907 | + | 0.377008i | −0.816192 | − | 0.577781i | \(-0.803919\pi\) |
0.297285 | + | 0.954789i | \(0.403919\pi\) | |||||||
\(984\) | −1.05596 | − | 3.24990i | −0.0336626 | − | 0.103603i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.75962 | − | 14.6486i | 0.151577 | − | 0.466506i | ||||
\(987\) | 3.76836 | + | 11.5978i | 0.119948 | + | 0.369162i | ||||
\(988\) | 0.216733 | + | 0.667037i | 0.00689521 | + | 0.0212213i | ||||
\(989\) | 0.227963 | − | 0.701599i | 0.00724881 | − | 0.0223095i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.29905 | + | 7.07576i | 0.0730319 | + | 0.224769i | 0.980909 | − | 0.194467i | \(-0.0622978\pi\) |
−0.907877 | + | 0.419236i | \(0.862298\pi\) | |||||||
\(992\) | 0.796352 | − | 0.578584i | 0.0252842 | − | 0.0183700i | ||||
\(993\) | −14.4925 | −0.459905 | ||||||||
\(994\) | −18.5974 | + | 13.5118i | −0.589875 | + | 0.428569i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.712338 | − | 0.517544i | −0.0225713 | − | 0.0163990i | ||||
\(997\) | −37.3338 | − | 27.1246i | −1.18237 | − | 0.859045i | −0.189937 | − | 0.981796i | \(-0.560828\pi\) |
−0.992438 | + | 0.122751i | \(0.960828\pi\) | |||||||
\(998\) | 3.68804 | − | 11.3506i | 0.116743 | − | 0.359298i | ||||
\(999\) | 3.55334 | 0.112423 |
(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 | 375.2.g.e.226.4 | 16 | ||
5.2 | odd | 4 | 75.2.i.a.4.3 | ✓ | 16 | ||
5.3 | odd | 4 | 375.2.i.c.274.2 | 16 | |||
5.4 | even | 2 | 375.2.g.d.226.1 | 16 | |||
15.2 | even | 4 | 225.2.m.b.154.2 | 16 | |||
25.6 | even | 5 | inner | 375.2.g.e.151.4 | 16 | ||
25.8 | odd | 20 | 75.2.i.a.19.3 | yes | 16 | ||
25.9 | even | 10 | 1875.2.a.p.1.2 | 8 | |||
25.12 | odd | 20 | 1875.2.b.h.1249.12 | 16 | |||
25.13 | odd | 20 | 1875.2.b.h.1249.5 | 16 | |||
25.16 | even | 5 | 1875.2.a.m.1.7 | 8 | |||
25.17 | odd | 20 | 375.2.i.c.349.2 | 16 | |||
25.19 | even | 10 | 375.2.g.d.151.1 | 16 | |||
75.8 | even | 20 | 225.2.m.b.19.2 | 16 | |||
75.41 | odd | 10 | 5625.2.a.bd.1.2 | 8 | |||
75.59 | odd | 10 | 5625.2.a.t.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.i.a.4.3 | ✓ | 16 | 5.2 | odd | 4 | ||
75.2.i.a.19.3 | yes | 16 | 25.8 | odd | 20 | ||
225.2.m.b.19.2 | 16 | 75.8 | even | 20 | |||
225.2.m.b.154.2 | 16 | 15.2 | even | 4 | |||
375.2.g.d.151.1 | 16 | 25.19 | even | 10 | |||
375.2.g.d.226.1 | 16 | 5.4 | even | 2 | |||
375.2.g.e.151.4 | 16 | 25.6 | even | 5 | inner | ||
375.2.g.e.226.4 | 16 | 1.1 | even | 1 | trivial | ||
375.2.i.c.274.2 | 16 | 5.3 | odd | 4 | |||
375.2.i.c.349.2 | 16 | 25.17 | odd | 20 | |||
1875.2.a.m.1.7 | 8 | 25.16 | even | 5 | |||
1875.2.a.p.1.2 | 8 | 25.9 | even | 10 | |||
1875.2.b.h.1249.5 | 16 | 25.13 | odd | 20 | |||
1875.2.b.h.1249.12 | 16 | 25.12 | odd | 20 | |||
5625.2.a.t.1.7 | 8 | 75.59 | odd | 10 | |||
5625.2.a.bd.1.2 | 8 | 75.41 | odd | 10 |