Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(551,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.551");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.e (of order \(2\), degree \(1\), 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: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 12 x^{13} + 15 x^{12} - 4 x^{11} + 45 x^{10} - 66 x^{9} - 32 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 551.1 | ||
Root | \(-0.251873 + 1.71364i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 690.551 |
Dual form | 690.2.e.a.551.9 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | −1.71364 | − | 0.251873i | −0.989370 | − | 0.145419i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.251873 | + | 1.71364i | −0.102827 | + | 0.699590i | ||||
\(7\) | − | 0.194278i | − | 0.0734302i | −0.999326 | − | 0.0367151i | \(-0.988311\pi\) | ||
0.999326 | − | 0.0367151i | \(-0.0116894\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 2.87312 | + | 0.863238i | 0.957707 | + | 0.287746i | ||||
\(10\) | 1.00000i | 0.316228i | ||||||||
\(11\) | 3.67639 | 1.10847 | 0.554237 | − | 0.832359i | \(-0.313010\pi\) | ||||
0.554237 | + | 0.832359i | \(0.313010\pi\) | |||||||
\(12\) | 1.71364 | + | 0.251873i | 0.494685 | + | 0.0727094i | ||||
\(13\) | 3.85351 | 1.06877 | 0.534385 | − | 0.845241i | \(-0.320543\pi\) | ||||
0.534385 | + | 0.845241i | \(0.320543\pi\) | |||||||
\(14\) | −0.194278 | −0.0519230 | ||||||||
\(15\) | 1.71364 | + | 0.251873i | 0.442460 | + | 0.0650333i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.71391 | −0.900754 | −0.450377 | − | 0.892838i | \(-0.648710\pi\) | ||||
−0.450377 | + | 0.892838i | \(0.648710\pi\) | |||||||
\(18\) | 0.863238 | − | 2.87312i | 0.203467 | − | 0.677201i | ||||
\(19\) | − | 0.273524i | − | 0.0627507i | −0.999508 | − | 0.0313753i | \(-0.990011\pi\) | ||
0.999508 | − | 0.0313753i | \(-0.00998872\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −0.0489334 | + | 0.332923i | −0.0106781 | + | 0.0726497i | ||||
\(22\) | − | 3.67639i | − | 0.783810i | ||||||
\(23\) | −4.59371 | − | 1.37760i | −0.957856 | − | 0.287250i | ||||
\(24\) | 0.251873 | − | 1.71364i | 0.0514133 | − | 0.349795i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | − | 3.85351i | − | 0.755735i | ||||||
\(27\) | −4.70607 | − | 2.20294i | −0.905683 | − | 0.423956i | ||||
\(28\) | 0.194278i | 0.0367151i | ||||||||
\(29\) | − | 9.11317i | − | 1.69227i | −0.532967 | − | 0.846136i | \(-0.678923\pi\) | ||
0.532967 | − | 0.846136i | \(-0.321077\pi\) | |||||||
\(30\) | 0.251873 | − | 1.71364i | 0.0459855 | − | 0.312866i | ||||
\(31\) | 2.24052 | 0.402410 | 0.201205 | − | 0.979549i | \(-0.435514\pi\) | ||||
0.201205 | + | 0.979549i | \(0.435514\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | −6.30001 | − | 0.925983i | −1.09669 | − | 0.161193i | ||||
\(34\) | 3.71391i | 0.636930i | ||||||||
\(35\) | 0.194278i | 0.0328390i | ||||||||
\(36\) | −2.87312 | − | 0.863238i | −0.478853 | − | 0.143873i | ||||
\(37\) | − | 11.7876i | − | 1.93787i | −0.247321 | − | 0.968934i | \(-0.579550\pi\) | ||
0.247321 | − | 0.968934i | \(-0.420450\pi\) | |||||||
\(38\) | −0.273524 | −0.0443714 | ||||||||
\(39\) | −6.60352 | − | 0.970593i | −1.05741 | − | 0.155419i | ||||
\(40\) | − | 1.00000i | − | 0.158114i | ||||||
\(41\) | − | 9.65442i | − | 1.50777i | −0.657008 | − | 0.753884i | \(-0.728178\pi\) | ||
0.657008 | − | 0.753884i | \(-0.271822\pi\) | |||||||
\(42\) | 0.332923 | + | 0.0489334i | 0.0513711 | + | 0.00755058i | ||||
\(43\) | 10.4535i | 1.59415i | 0.603882 | + | 0.797074i | \(0.293620\pi\) | ||||
−0.603882 | + | 0.797074i | \(0.706380\pi\) | |||||||
\(44\) | −3.67639 | −0.554237 | ||||||||
\(45\) | −2.87312 | − | 0.863238i | −0.428299 | − | 0.128684i | ||||
\(46\) | −1.37760 | + | 4.59371i | −0.203116 | + | 0.677306i | ||||
\(47\) | − | 4.64640i | − | 0.677747i | −0.940832 | − | 0.338874i | \(-0.889954\pi\) | ||
0.940832 | − | 0.338874i | \(-0.110046\pi\) | |||||||
\(48\) | −1.71364 | − | 0.251873i | −0.247343 | − | 0.0363547i | ||||
\(49\) | 6.96226 | 0.994608 | ||||||||
\(50\) | − | 1.00000i | − | 0.141421i | ||||||
\(51\) | 6.36430 | + | 0.935432i | 0.891180 | + | 0.130987i | ||||
\(52\) | −3.85351 | −0.534385 | ||||||||
\(53\) | 4.09935 | 0.563089 | 0.281545 | − | 0.959548i | \(-0.409153\pi\) | ||||
0.281545 | + | 0.959548i | \(0.409153\pi\) | |||||||
\(54\) | −2.20294 | + | 4.70607i | −0.299782 | + | 0.640414i | ||||
\(55\) | −3.67639 | −0.495725 | ||||||||
\(56\) | 0.194278 | 0.0259615 | ||||||||
\(57\) | −0.0688932 | + | 0.468721i | −0.00912513 | + | 0.0620837i | ||||
\(58\) | −9.11317 | −1.19662 | ||||||||
\(59\) | 2.49823i | 0.325242i | 0.986689 | + | 0.162621i | \(0.0519947\pi\) | ||||
−0.986689 | + | 0.162621i | \(0.948005\pi\) | |||||||
\(60\) | −1.71364 | − | 0.251873i | −0.221230 | − | 0.0325166i | ||||
\(61\) | 13.9867i | 1.79082i | 0.445245 | + | 0.895409i | \(0.353117\pi\) | ||||
−0.445245 | + | 0.895409i | \(0.646883\pi\) | |||||||
\(62\) | − | 2.24052i | − | 0.284547i | ||||||
\(63\) | 0.167708 | − | 0.558185i | 0.0211293 | − | 0.0703246i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −3.85351 | −0.477968 | ||||||||
\(66\) | −0.925983 | + | 6.30001i | −0.113981 | + | 0.775478i | ||||
\(67\) | − | 10.9816i | − | 1.34161i | −0.741632 | − | 0.670807i | \(-0.765948\pi\) | ||
0.741632 | − | 0.670807i | \(-0.234052\pi\) | |||||||
\(68\) | 3.71391 | 0.450377 | ||||||||
\(69\) | 7.52499 | + | 3.51774i | 0.905902 | + | 0.423487i | ||||
\(70\) | 0.194278 | 0.0232207 | ||||||||
\(71\) | − | 9.72869i | − | 1.15458i | −0.816538 | − | 0.577291i | \(-0.804110\pi\) | ||
0.816538 | − | 0.577291i | \(-0.195890\pi\) | |||||||
\(72\) | −0.863238 | + | 2.87312i | −0.101734 | + | 0.338600i | ||||
\(73\) | 11.0817 | 1.29702 | 0.648508 | − | 0.761208i | \(-0.275393\pi\) | ||||
0.648508 | + | 0.761208i | \(0.275393\pi\) | |||||||
\(74\) | −11.7876 | −1.37028 | ||||||||
\(75\) | −1.71364 | − | 0.251873i | −0.197874 | − | 0.0290838i | ||||
\(76\) | 0.273524i | 0.0313753i | ||||||||
\(77\) | − | 0.714243i | − | 0.0813955i | ||||||
\(78\) | −0.970593 | + | 6.60352i | −0.109898 | + | 0.747701i | ||||
\(79\) | − | 6.43875i | − | 0.724416i | −0.932097 | − | 0.362208i | \(-0.882023\pi\) | ||
0.932097 | − | 0.362208i | \(-0.117977\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 7.50964 | + | 4.96037i | 0.834404 | + | 0.551153i | ||||
\(82\) | −9.65442 | −1.06615 | ||||||||
\(83\) | −9.42725 | −1.03477 | −0.517387 | − | 0.855751i | \(-0.673095\pi\) | ||||
−0.517387 | + | 0.855751i | \(0.673095\pi\) | |||||||
\(84\) | 0.0489334 | − | 0.332923i | 0.00533907 | − | 0.0363248i | ||||
\(85\) | 3.71391 | 0.402830 | ||||||||
\(86\) | 10.4535 | 1.12723 | ||||||||
\(87\) | −2.29536 | + | 15.6167i | −0.246088 | + | 1.67428i | ||||
\(88\) | 3.67639i | 0.391905i | ||||||||
\(89\) | 9.92316 | 1.05185 | 0.525926 | − | 0.850530i | \(-0.323719\pi\) | ||||
0.525926 | + | 0.850530i | \(0.323719\pi\) | |||||||
\(90\) | −0.863238 | + | 2.87312i | −0.0909933 | + | 0.302853i | ||||
\(91\) | − | 0.748652i | − | 0.0784800i | ||||||
\(92\) | 4.59371 | + | 1.37760i | 0.478928 | + | 0.143625i | ||||
\(93\) | −3.83945 | − | 0.564326i | −0.398132 | − | 0.0585179i | ||||
\(94\) | −4.64640 | −0.479240 | ||||||||
\(95\) | 0.273524i | 0.0280630i | ||||||||
\(96\) | −0.251873 | + | 1.71364i | −0.0257067 | + | 0.174898i | ||||
\(97\) | − | 8.91482i | − | 0.905163i | −0.891723 | − | 0.452582i | \(-0.850503\pi\) | ||
0.891723 | − | 0.452582i | \(-0.149497\pi\) | |||||||
\(98\) | − | 6.96226i | − | 0.703294i | ||||||
\(99\) | 10.5627 | + | 3.17360i | 1.06159 | + | 0.318959i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 8.39174i | 0.835009i | 0.908675 | + | 0.417505i | \(0.137095\pi\) | ||||
−0.908675 | + | 0.417505i | \(0.862905\pi\) | |||||||
\(102\) | 0.935432 | − | 6.36430i | 0.0926215 | − | 0.630159i | ||||
\(103\) | − | 3.35240i | − | 0.330322i | −0.986267 | − | 0.165161i | \(-0.947186\pi\) | ||
0.986267 | − | 0.165161i | \(-0.0528144\pi\) | |||||||
\(104\) | 3.85351i | 0.377867i | ||||||||
\(105\) | 0.0489334 | − | 0.332923i | 0.00477541 | − | 0.0324899i | ||||
\(106\) | − | 4.09935i | − | 0.398164i | ||||||
\(107\) | −17.6874 | −1.70991 | −0.854954 | − | 0.518704i | \(-0.826415\pi\) | ||||
−0.854954 | + | 0.518704i | \(0.826415\pi\) | |||||||
\(108\) | 4.70607 | + | 2.20294i | 0.452841 | + | 0.211978i | ||||
\(109\) | − | 6.90800i | − | 0.661667i | −0.943689 | − | 0.330833i | \(-0.892670\pi\) | ||
0.943689 | − | 0.330833i | \(-0.107330\pi\) | |||||||
\(110\) | 3.67639i | 0.350530i | ||||||||
\(111\) | −2.96897 | + | 20.1997i | −0.281802 | + | 1.91727i | ||||
\(112\) | − | 0.194278i | − | 0.0183576i | ||||||
\(113\) | −3.33657 | −0.313878 | −0.156939 | − | 0.987608i | \(-0.550163\pi\) | ||||
−0.156939 | + | 0.987608i | \(0.550163\pi\) | |||||||
\(114\) | 0.468721 | + | 0.0688932i | 0.0438998 | + | 0.00645244i | ||||
\(115\) | 4.59371 | + | 1.37760i | 0.428366 | + | 0.128462i | ||||
\(116\) | 9.11317i | 0.846136i | ||||||||
\(117\) | 11.0716 | + | 3.32649i | 1.02357 | + | 0.307534i | ||||
\(118\) | 2.49823 | 0.229980 | ||||||||
\(119\) | 0.721531i | 0.0661426i | ||||||||
\(120\) | −0.251873 | + | 1.71364i | −0.0229927 | + | 0.156433i | ||||
\(121\) | 2.51586 | 0.228715 | ||||||||
\(122\) | 13.9867 | 1.26630 | ||||||||
\(123\) | −2.43169 | + | 16.5442i | −0.219258 | + | 1.49174i | ||||
\(124\) | −2.24052 | −0.201205 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −0.558185 | − | 0.167708i | −0.0497270 | − | 0.0149406i | ||||
\(127\) | 13.8315 | 1.22734 | 0.613672 | − | 0.789561i | \(-0.289692\pi\) | ||||
0.613672 | + | 0.789561i | \(0.289692\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 2.63296 | − | 17.9136i | 0.231819 | − | 1.57720i | ||||
\(130\) | 3.85351i | 0.337975i | ||||||||
\(131\) | 11.1092i | 0.970613i | 0.874344 | + | 0.485306i | \(0.161292\pi\) | ||||
−0.874344 | + | 0.485306i | \(0.838708\pi\) | |||||||
\(132\) | 6.30001 | + | 0.925983i | 0.548346 | + | 0.0805965i | ||||
\(133\) | −0.0531397 | −0.00460780 | ||||||||
\(134\) | −10.9816 | −0.948665 | ||||||||
\(135\) | 4.70607 | + | 2.20294i | 0.405034 | + | 0.189599i | ||||
\(136\) | − | 3.71391i | − | 0.318465i | ||||||
\(137\) | 6.61230 | 0.564927 | 0.282463 | − | 0.959278i | \(-0.408848\pi\) | ||||
0.282463 | + | 0.959278i | \(0.408848\pi\) | |||||||
\(138\) | 3.51774 | − | 7.52499i | 0.299450 | − | 0.640570i | ||||
\(139\) | −2.36109 | −0.200265 | −0.100133 | − | 0.994974i | \(-0.531927\pi\) | ||||
−0.100133 | + | 0.994974i | \(0.531927\pi\) | |||||||
\(140\) | − | 0.194278i | − | 0.0164195i | ||||||
\(141\) | −1.17030 | + | 7.96226i | −0.0985572 | + | 0.670543i | ||||
\(142\) | −9.72869 | −0.816413 | ||||||||
\(143\) | 14.1670 | 1.18470 | ||||||||
\(144\) | 2.87312 | + | 0.863238i | 0.239427 | + | 0.0719365i | ||||
\(145\) | 9.11317i | 0.756807i | ||||||||
\(146\) | − | 11.0817i | − | 0.917128i | ||||||
\(147\) | −11.9308 | − | 1.75360i | −0.984036 | − | 0.144635i | ||||
\(148\) | 11.7876i | 0.968934i | ||||||||
\(149\) | 9.03818 | 0.740436 | 0.370218 | − | 0.928945i | \(-0.379283\pi\) | ||||
0.370218 | + | 0.928945i | \(0.379283\pi\) | |||||||
\(150\) | −0.251873 | + | 1.71364i | −0.0205653 | + | 0.139918i | ||||
\(151\) | 7.21414 | 0.587078 | 0.293539 | − | 0.955947i | \(-0.405167\pi\) | ||||
0.293539 | + | 0.955947i | \(0.405167\pi\) | |||||||
\(152\) | 0.273524 | 0.0221857 | ||||||||
\(153\) | −10.6705 | − | 3.20598i | −0.862659 | − | 0.259189i | ||||
\(154\) | −0.714243 | −0.0575553 | ||||||||
\(155\) | −2.24052 | −0.179963 | ||||||||
\(156\) | 6.60352 | + | 0.970593i | 0.528705 | + | 0.0777096i | ||||
\(157\) | 0.699510i | 0.0558270i | 0.999610 | + | 0.0279135i | \(0.00888629\pi\) | ||||
−0.999610 | + | 0.0279135i | \(0.991114\pi\) | |||||||
\(158\) | −6.43875 | −0.512239 | ||||||||
\(159\) | −7.02481 | − | 1.03252i | −0.557104 | − | 0.0818838i | ||||
\(160\) | 1.00000i | 0.0790569i | ||||||||
\(161\) | −0.267638 | + | 0.892458i | −0.0210928 | + | 0.0703356i | ||||
\(162\) | 4.96037 | − | 7.50964i | 0.389724 | − | 0.590013i | ||||
\(163\) | −13.2190 | −1.03539 | −0.517694 | − | 0.855566i | \(-0.673210\pi\) | ||||
−0.517694 | + | 0.855566i | \(0.673210\pi\) | |||||||
\(164\) | 9.65442i | 0.753884i | ||||||||
\(165\) | 6.30001 | + | 0.925983i | 0.490455 | + | 0.0720877i | ||||
\(166\) | 9.42725i | 0.731696i | ||||||||
\(167\) | 10.7904i | 0.834986i | 0.908680 | + | 0.417493i | \(0.137091\pi\) | ||||
−0.908680 | + | 0.417493i | \(0.862909\pi\) | |||||||
\(168\) | −0.332923 | − | 0.0489334i | −0.0256855 | − | 0.00377529i | ||||
\(169\) | 1.84950 | 0.142269 | ||||||||
\(170\) | − | 3.71391i | − | 0.284844i | ||||||
\(171\) | 0.236116 | − | 0.785867i | 0.0180563 | − | 0.0600968i | ||||
\(172\) | − | 10.4535i | − | 0.797074i | ||||||
\(173\) | − | 3.90535i | − | 0.296918i | −0.988919 | − | 0.148459i | \(-0.952569\pi\) | ||
0.988919 | − | 0.148459i | \(-0.0474314\pi\) | |||||||
\(174\) | 15.6167 | + | 2.29536i | 1.18390 | + | 0.174011i | ||||
\(175\) | − | 0.194278i | − | 0.0146860i | ||||||
\(176\) | 3.67639 | 0.277119 | ||||||||
\(177\) | 0.629235 | − | 4.28106i | 0.0472962 | − | 0.321784i | ||||
\(178\) | − | 9.92316i | − | 0.743772i | ||||||
\(179\) | − | 5.90397i | − | 0.441284i | −0.975355 | − | 0.220642i | \(-0.929185\pi\) | ||
0.975355 | − | 0.220642i | \(-0.0708152\pi\) | |||||||
\(180\) | 2.87312 | + | 0.863238i | 0.214150 | + | 0.0643420i | ||||
\(181\) | − | 3.65493i | − | 0.271669i | −0.990732 | − | 0.135834i | \(-0.956628\pi\) | ||
0.990732 | − | 0.135834i | \(-0.0433715\pi\) | |||||||
\(182\) | −0.748652 | −0.0554938 | ||||||||
\(183\) | 3.52288 | − | 23.9682i | 0.260419 | − | 1.77178i | ||||
\(184\) | 1.37760 | − | 4.59371i | 0.101558 | − | 0.338653i | ||||
\(185\) | 11.7876i | 0.866641i | ||||||||
\(186\) | −0.564326 | + | 3.83945i | −0.0413784 | + | 0.281522i | ||||
\(187\) | −13.6538 | −0.998463 | ||||||||
\(188\) | 4.64640i | 0.338874i | ||||||||
\(189\) | −0.427983 | + | 0.914286i | −0.0311312 | + | 0.0665045i | ||||
\(190\) | 0.273524 | 0.0198435 | ||||||||
\(191\) | 12.5903 | 0.911005 | 0.455503 | − | 0.890234i | \(-0.349460\pi\) | ||||
0.455503 | + | 0.890234i | \(0.349460\pi\) | |||||||
\(192\) | 1.71364 | + | 0.251873i | 0.123671 | + | 0.0181773i | ||||
\(193\) | 23.4908 | 1.69090 | 0.845452 | − | 0.534051i | \(-0.179331\pi\) | ||||
0.845452 | + | 0.534051i | \(0.179331\pi\) | |||||||
\(194\) | −8.91482 | −0.640047 | ||||||||
\(195\) | 6.60352 | + | 0.970593i | 0.472888 | + | 0.0695056i | ||||
\(196\) | −6.96226 | −0.497304 | ||||||||
\(197\) | − | 15.4325i | − | 1.09952i | −0.835322 | − | 0.549761i | \(-0.814719\pi\) | ||
0.835322 | − | 0.549761i | \(-0.185281\pi\) | |||||||
\(198\) | 3.17360 | − | 10.5627i | 0.225538 | − | 0.750660i | ||||
\(199\) | 21.1429i | 1.49878i | 0.662127 | + | 0.749391i | \(0.269654\pi\) | ||||
−0.662127 | + | 0.749391i | \(0.730346\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | −2.76596 | + | 18.8185i | −0.195096 | + | 1.32735i | ||||
\(202\) | 8.39174 | 0.590441 | ||||||||
\(203\) | −1.77049 | −0.124264 | ||||||||
\(204\) | −6.36430 | − | 0.935432i | −0.445590 | − | 0.0654933i | ||||
\(205\) | 9.65442i | 0.674294i | ||||||||
\(206\) | −3.35240 | −0.233573 | ||||||||
\(207\) | −12.0091 | − | 7.92349i | −0.834690 | − | 0.550720i | ||||
\(208\) | 3.85351 | 0.267193 | ||||||||
\(209\) | − | 1.00558i | − | 0.0695575i | ||||||
\(210\) | −0.332923 | − | 0.0489334i | −0.0229739 | − | 0.00337672i | ||||
\(211\) | −0.599814 | −0.0412929 | −0.0206464 | − | 0.999787i | \(-0.506572\pi\) | ||||
−0.0206464 | + | 0.999787i | \(0.506572\pi\) | |||||||
\(212\) | −4.09935 | −0.281545 | ||||||||
\(213\) | −2.45039 | + | 16.6715i | −0.167898 | + | 1.14231i | ||||
\(214\) | 17.6874i | 1.20909i | ||||||||
\(215\) | − | 10.4535i | − | 0.712925i | ||||||
\(216\) | 2.20294 | − | 4.70607i | 0.149891 | − | 0.320207i | ||||
\(217\) | − | 0.435285i | − | 0.0295490i | ||||||
\(218\) | −6.90800 | −0.467869 | ||||||||
\(219\) | −18.9900 | − | 2.79118i | −1.28323 | − | 0.188610i | ||||
\(220\) | 3.67639 | 0.247862 | ||||||||
\(221\) | −14.3116 | −0.962699 | ||||||||
\(222\) | 20.1997 | + | 2.96897i | 1.35571 | + | 0.199264i | ||||
\(223\) | −10.6634 | −0.714072 | −0.357036 | − | 0.934091i | \(-0.616213\pi\) | ||||
−0.357036 | + | 0.934091i | \(0.616213\pi\) | |||||||
\(224\) | −0.194278 | −0.0129808 | ||||||||
\(225\) | 2.87312 | + | 0.863238i | 0.191541 | + | 0.0575492i | ||||
\(226\) | 3.33657i | 0.221945i | ||||||||
\(227\) | 5.57422 | 0.369974 | 0.184987 | − | 0.982741i | \(-0.440776\pi\) | ||||
0.184987 | + | 0.982741i | \(0.440776\pi\) | |||||||
\(228\) | 0.0688932 | − | 0.468721i | 0.00456256 | − | 0.0310418i | ||||
\(229\) | − | 14.9060i | − | 0.985015i | −0.870308 | − | 0.492508i | \(-0.836080\pi\) | ||
0.870308 | − | 0.492508i | \(-0.163920\pi\) | |||||||
\(230\) | 1.37760 | − | 4.59371i | 0.0908364 | − | 0.302901i | ||||
\(231\) | −0.179898 | + | 1.22395i | −0.0118364 | + | 0.0805303i | ||||
\(232\) | 9.11317 | 0.598309 | ||||||||
\(233\) | − | 15.3425i | − | 1.00512i | −0.864543 | − | 0.502559i | \(-0.832392\pi\) | ||
0.864543 | − | 0.502559i | \(-0.167608\pi\) | |||||||
\(234\) | 3.32649 | − | 11.0716i | 0.217460 | − | 0.723772i | ||||
\(235\) | 4.64640i | 0.303098i | ||||||||
\(236\) | − | 2.49823i | − | 0.162621i | ||||||
\(237\) | −1.62174 | + | 11.0337i | −0.105344 | + | 0.716715i | ||||
\(238\) | 0.721531 | 0.0467699 | ||||||||
\(239\) | 11.6220i | 0.751763i | 0.926668 | + | 0.375881i | \(0.122660\pi\) | ||||
−0.926668 | + | 0.375881i | \(0.877340\pi\) | |||||||
\(240\) | 1.71364 | + | 0.251873i | 0.110615 | + | 0.0162583i | ||||
\(241\) | − | 6.44721i | − | 0.415301i | −0.978203 | − | 0.207651i | \(-0.933418\pi\) | ||
0.978203 | − | 0.207651i | \(-0.0665817\pi\) | |||||||
\(242\) | − | 2.51586i | − | 0.161726i | ||||||
\(243\) | −11.6194 | − | 10.3918i | −0.745387 | − | 0.666632i | ||||
\(244\) | − | 13.9867i | − | 0.895409i | ||||||
\(245\) | −6.96226 | −0.444802 | ||||||||
\(246\) | 16.5442 | + | 2.43169i | 1.05482 | + | 0.155039i | ||||
\(247\) | − | 1.05403i | − | 0.0670661i | ||||||
\(248\) | 2.24052i | 0.142273i | ||||||||
\(249\) | 16.1549 | + | 2.37447i | 1.02378 | + | 0.150476i | ||||
\(250\) | 1.00000i | 0.0632456i | ||||||||
\(251\) | −0.366988 | −0.0231641 | −0.0115820 | − | 0.999933i | \(-0.503687\pi\) | ||||
−0.0115820 | + | 0.999933i | \(0.503687\pi\) | |||||||
\(252\) | −0.167708 | + | 0.558185i | −0.0105646 | + | 0.0351623i | ||||
\(253\) | −16.8883 | − | 5.06461i | −1.06176 | − | 0.318409i | ||||
\(254\) | − | 13.8315i | − | 0.867863i | ||||||
\(255\) | −6.36430 | − | 0.935432i | −0.398548 | − | 0.0585790i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.9857i | 1.30905i | 0.756040 | + | 0.654525i | \(0.227131\pi\) | ||||
−0.756040 | + | 0.654525i | \(0.772869\pi\) | |||||||
\(258\) | −17.9136 | − | 2.63296i | −1.11525 | − | 0.163921i | ||||
\(259\) | −2.29007 | −0.142298 | ||||||||
\(260\) | 3.85351 | 0.238984 | ||||||||
\(261\) | 7.86683 | − | 26.1832i | 0.486945 | − | 1.62070i | ||||
\(262\) | 11.1092 | 0.686327 | ||||||||
\(263\) | 28.4952 | 1.75709 | 0.878544 | − | 0.477661i | \(-0.158515\pi\) | ||||
0.878544 | + | 0.477661i | \(0.158515\pi\) | |||||||
\(264\) | 0.925983 | − | 6.30001i | 0.0569903 | − | 0.387739i | ||||
\(265\) | −4.09935 | −0.251821 | ||||||||
\(266\) | 0.0531397i | 0.00325821i | ||||||||
\(267\) | −17.0047 | − | 2.49937i | −1.04067 | − | 0.152959i | ||||
\(268\) | 10.9816i | 0.670807i | ||||||||
\(269\) | 5.95349i | 0.362991i | 0.983392 | + | 0.181495i | \(0.0580938\pi\) | ||||
−0.983392 | + | 0.181495i | \(0.941906\pi\) | |||||||
\(270\) | 2.20294 | − | 4.70607i | 0.134067 | − | 0.286402i | ||||
\(271\) | −10.8969 | −0.661937 | −0.330969 | − | 0.943642i | \(-0.607375\pi\) | ||||
−0.330969 | + | 0.943642i | \(0.607375\pi\) | |||||||
\(272\) | −3.71391 | −0.225189 | ||||||||
\(273\) | −0.188565 | + | 1.28292i | −0.0114125 | + | 0.0776458i | ||||
\(274\) | − | 6.61230i | − | 0.399463i | ||||||
\(275\) | 3.67639 | 0.221695 | ||||||||
\(276\) | −7.52499 | − | 3.51774i | −0.452951 | − | 0.211743i | ||||
\(277\) | −12.5927 | −0.756623 | −0.378312 | − | 0.925678i | \(-0.623495\pi\) | ||||
−0.378312 | + | 0.925678i | \(0.623495\pi\) | |||||||
\(278\) | 2.36109i | 0.141609i | ||||||||
\(279\) | 6.43729 | + | 1.93410i | 0.385390 | + | 0.115792i | ||||
\(280\) | −0.194278 | −0.0116103 | ||||||||
\(281\) | −10.5936 | −0.631961 | −0.315980 | − | 0.948766i | \(-0.602333\pi\) | ||||
−0.315980 | + | 0.948766i | \(0.602333\pi\) | |||||||
\(282\) | 7.96226 | + | 1.17030i | 0.474145 | + | 0.0696904i | ||||
\(283\) | 31.7364i | 1.88653i | 0.332039 | + | 0.943266i | \(0.392263\pi\) | ||||
−0.332039 | + | 0.943266i | \(0.607737\pi\) | |||||||
\(284\) | 9.72869i | 0.577291i | ||||||||
\(285\) | 0.0688932 | − | 0.468721i | 0.00408088 | − | 0.0277647i | ||||
\(286\) | − | 14.1670i | − | 0.837712i | ||||||
\(287\) | −1.87564 | −0.110716 | ||||||||
\(288\) | 0.863238 | − | 2.87312i | 0.0508668 | − | 0.169300i | ||||
\(289\) | −3.20690 | −0.188641 | ||||||||
\(290\) | 9.11317 | 0.535144 | ||||||||
\(291\) | −2.24540 | + | 15.2768i | −0.131628 | + | 0.895542i | ||||
\(292\) | −11.0817 | −0.648508 | ||||||||
\(293\) | 6.77543 | 0.395825 | 0.197912 | − | 0.980220i | \(-0.436584\pi\) | ||||
0.197912 | + | 0.980220i | \(0.436584\pi\) | |||||||
\(294\) | −1.75360 | + | 11.9308i | −0.102272 | + | 0.695818i | ||||
\(295\) | − | 2.49823i | − | 0.145452i | ||||||
\(296\) | 11.7876 | 0.685139 | ||||||||
\(297\) | −17.3013 | − | 8.09887i | −1.00393 | − | 0.469944i | ||||
\(298\) | − | 9.03818i | − | 0.523567i | ||||||
\(299\) | −17.7019 | − | 5.30860i | −1.02373 | − | 0.307004i | ||||
\(300\) | 1.71364 | + | 0.251873i | 0.0989370 | + | 0.0145419i | ||||
\(301\) | 2.03089 | 0.117059 | ||||||||
\(302\) | − | 7.21414i | − | 0.415127i | ||||||
\(303\) | 2.11365 | − | 14.3804i | 0.121426 | − | 0.826133i | ||||
\(304\) | − | 0.273524i | − | 0.0156877i | ||||||
\(305\) | − | 13.9867i | − | 0.800878i | ||||||
\(306\) | −3.20598 | + | 10.6705i | −0.183274 | + | 0.609992i | ||||
\(307\) | −13.5532 | −0.773522 | −0.386761 | − | 0.922180i | \(-0.626406\pi\) | ||||
−0.386761 | + | 0.922180i | \(0.626406\pi\) | |||||||
\(308\) | 0.714243i | 0.0406978i | ||||||||
\(309\) | −0.844379 | + | 5.74481i | −0.0480350 | + | 0.326811i | ||||
\(310\) | 2.24052i | 0.127253i | ||||||||
\(311\) | 3.63405i | 0.206068i | 0.994678 | + | 0.103034i | \(0.0328550\pi\) | ||||
−0.994678 | + | 0.103034i | \(0.967145\pi\) | |||||||
\(312\) | 0.970593 | − | 6.60352i | 0.0549490 | − | 0.373851i | ||||
\(313\) | − | 20.2986i | − | 1.14734i | −0.819085 | − | 0.573672i | \(-0.805519\pi\) | ||
0.819085 | − | 0.573672i | \(-0.194481\pi\) | |||||||
\(314\) | 0.699510 | 0.0394756 | ||||||||
\(315\) | −0.167708 | + | 0.558185i | −0.00944929 | + | 0.0314501i | ||||
\(316\) | 6.43875i | 0.362208i | ||||||||
\(317\) | 22.0942i | 1.24093i | 0.784233 | + | 0.620467i | \(0.213057\pi\) | ||||
−0.784233 | + | 0.620467i | \(0.786943\pi\) | |||||||
\(318\) | −1.03252 | + | 7.02481i | −0.0579006 | + | 0.393932i | ||||
\(319\) | − | 33.5036i | − | 1.87584i | ||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 30.3099 | + | 4.45498i | 1.69173 | + | 0.248653i | ||||
\(322\) | 0.892458 | + | 0.267638i | 0.0497348 | + | 0.0149149i | ||||
\(323\) | 1.01584i | 0.0565230i | ||||||||
\(324\) | −7.50964 | − | 4.96037i | −0.417202 | − | 0.275576i | ||||
\(325\) | 3.85351 | 0.213754 | ||||||||
\(326\) | 13.2190i | 0.732130i | ||||||||
\(327\) | −1.73994 | + | 11.8378i | −0.0962188 | + | 0.654633i | ||||
\(328\) | 9.65442 | 0.533076 | ||||||||
\(329\) | −0.902694 | −0.0497671 | ||||||||
\(330\) | 0.925983 | − | 6.30001i | 0.0509737 | − | 0.346804i | ||||
\(331\) | −27.8332 | −1.52985 | −0.764925 | − | 0.644120i | \(-0.777224\pi\) | ||||
−0.764925 | + | 0.644120i | \(0.777224\pi\) | |||||||
\(332\) | 9.42725 | 0.517387 | ||||||||
\(333\) | 10.1755 | − | 33.8672i | 0.557614 | − | 1.85591i | ||||
\(334\) | 10.7904 | 0.590424 | ||||||||
\(335\) | 10.9816i | 0.599988i | ||||||||
\(336\) | −0.0489334 | + | 0.332923i | −0.00266953 | + | 0.0181624i | ||||
\(337\) | 27.7015i | 1.50900i | 0.656302 | + | 0.754498i | \(0.272120\pi\) | ||||
−0.656302 | + | 0.754498i | \(0.727880\pi\) | |||||||
\(338\) | − | 1.84950i | − | 0.100600i | ||||||
\(339\) | 5.71767 | + | 0.840390i | 0.310541 | + | 0.0456437i | ||||
\(340\) | −3.71391 | −0.201415 | ||||||||
\(341\) | 8.23704 | 0.446061 | ||||||||
\(342\) | −0.785867 | − | 0.236116i | −0.0424948 | − | 0.0127677i | ||||
\(343\) | − | 2.71256i | − | 0.146465i | ||||||
\(344\) | −10.4535 | −0.563616 | ||||||||
\(345\) | −7.52499 | − | 3.51774i | −0.405132 | − | 0.189389i | ||||
\(346\) | −3.90535 | −0.209953 | ||||||||
\(347\) | 25.4305i | 1.36518i | 0.730801 | + | 0.682590i | \(0.239147\pi\) | ||||
−0.730801 | + | 0.682590i | \(0.760853\pi\) | |||||||
\(348\) | 2.29536 | − | 15.6167i | 0.123044 | − | 0.837142i | ||||
\(349\) | −25.3679 | −1.35791 | −0.678955 | − | 0.734180i | \(-0.737567\pi\) | ||||
−0.678955 | + | 0.734180i | \(0.737567\pi\) | |||||||
\(350\) | −0.194278 | −0.0103846 | ||||||||
\(351\) | −18.1348 | − | 8.48904i | −0.967967 | − | 0.453111i | ||||
\(352\) | − | 3.67639i | − | 0.195952i | ||||||
\(353\) | 6.58726i | 0.350605i | 0.984515 | + | 0.175302i | \(0.0560903\pi\) | ||||
−0.984515 | + | 0.175302i | \(0.943910\pi\) | |||||||
\(354\) | −4.28106 | − | 0.629235i | −0.227536 | − | 0.0334435i | ||||
\(355\) | 9.72869i | 0.516345i | ||||||||
\(356\) | −9.92316 | −0.525926 | ||||||||
\(357\) | 0.181734 | − | 1.23644i | 0.00961838 | − | 0.0654395i | ||||
\(358\) | −5.90397 | −0.312035 | ||||||||
\(359\) | −34.1462 | −1.80217 | −0.901083 | − | 0.433647i | \(-0.857226\pi\) | ||||
−0.901083 | + | 0.433647i | \(0.857226\pi\) | |||||||
\(360\) | 0.863238 | − | 2.87312i | 0.0454966 | − | 0.151427i | ||||
\(361\) | 18.9252 | 0.996062 | ||||||||
\(362\) | −3.65493 | −0.192099 | ||||||||
\(363\) | −4.31128 | − | 0.633677i | −0.226284 | − | 0.0332594i | ||||
\(364\) | 0.748652i | 0.0392400i | ||||||||
\(365\) | −11.0817 | −0.580043 | ||||||||
\(366\) | −23.9682 | − | 3.52288i | −1.25284 | − | 0.184144i | ||||
\(367\) | − | 2.78712i | − | 0.145487i | −0.997351 | − | 0.0727433i | \(-0.976825\pi\) | ||
0.997351 | − | 0.0727433i | \(-0.0231754\pi\) | |||||||
\(368\) | −4.59371 | − | 1.37760i | −0.239464 | − | 0.0718125i | ||||
\(369\) | 8.33407 | − | 27.7383i | 0.433854 | − | 1.44400i | ||||
\(370\) | 11.7876 | 0.612807 | ||||||||
\(371\) | − | 0.796415i | − | 0.0413478i | ||||||
\(372\) | 3.83945 | + | 0.564326i | 0.199066 | + | 0.0292590i | ||||
\(373\) | 36.8414i | 1.90757i | 0.300485 | + | 0.953787i | \(0.402852\pi\) | ||||
−0.300485 | + | 0.953787i | \(0.597148\pi\) | |||||||
\(374\) | 13.6538i | 0.706020i | ||||||||
\(375\) | 1.71364 | + | 0.251873i | 0.0884920 | + | 0.0130067i | ||||
\(376\) | 4.64640 | 0.239620 | ||||||||
\(377\) | − | 35.1176i | − | 1.80865i | ||||||
\(378\) | 0.914286 | + | 0.427983i | 0.0470258 | + | 0.0220131i | ||||
\(379\) | − | 12.8044i | − | 0.657717i | −0.944379 | − | 0.328859i | \(-0.893336\pi\) | ||
0.944379 | − | 0.328859i | \(-0.106664\pi\) | |||||||
\(380\) | − | 0.273524i | − | 0.0140315i | ||||||
\(381\) | −23.7021 | − | 3.48377i | −1.21430 | − | 0.178479i | ||||
\(382\) | − | 12.5903i | − | 0.644178i | ||||||
\(383\) | 14.2092 | 0.726055 | 0.363028 | − | 0.931778i | \(-0.381743\pi\) | ||||
0.363028 | + | 0.931778i | \(0.381743\pi\) | |||||||
\(384\) | 0.251873 | − | 1.71364i | 0.0128533 | − | 0.0874488i | ||||
\(385\) | 0.714243i | 0.0364012i | ||||||||
\(386\) | − | 23.4908i | − | 1.19565i | ||||||
\(387\) | −9.02388 | + | 30.0342i | −0.458710 | + | 1.52673i | ||||
\(388\) | 8.91482i | 0.452582i | ||||||||
\(389\) | 7.98762 | 0.404988 | 0.202494 | − | 0.979283i | \(-0.435095\pi\) | ||||
0.202494 | + | 0.979283i | \(0.435095\pi\) | |||||||
\(390\) | 0.970593 | − | 6.60352i | 0.0491479 | − | 0.334382i | ||||
\(391\) | 17.0606 | + | 5.11629i | 0.862793 | + | 0.258742i | ||||
\(392\) | 6.96226i | 0.351647i | ||||||||
\(393\) | 2.79810 | − | 19.0371i | 0.141145 | − | 0.960295i | ||||
\(394\) | −15.4325 | −0.777479 | ||||||||
\(395\) | 6.43875i | 0.323968i | ||||||||
\(396\) | −10.5627 | − | 3.17360i | −0.530797 | − | 0.159479i | ||||
\(397\) | 6.37102 | 0.319752 | 0.159876 | − | 0.987137i | \(-0.448891\pi\) | ||||
0.159876 | + | 0.987137i | \(0.448891\pi\) | |||||||
\(398\) | 21.1429 | 1.05980 | ||||||||
\(399\) | 0.0910623 | + | 0.0133844i | 0.00455882 | + | 0.000670061i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 4.08280 | 0.203885 | 0.101943 | − | 0.994790i | \(-0.467494\pi\) | ||||
0.101943 | + | 0.994790i | \(0.467494\pi\) | |||||||
\(402\) | 18.8185 | + | 2.76596i | 0.938580 | + | 0.137954i | ||||
\(403\) | 8.63386 | 0.430083 | ||||||||
\(404\) | − | 8.39174i | − | 0.417505i | ||||||
\(405\) | −7.50964 | − | 4.96037i | −0.373157 | − | 0.246483i | ||||
\(406\) | 1.77049i | 0.0878679i | ||||||||
\(407\) | − | 43.3358i | − | 2.14808i | ||||||
\(408\) | −0.935432 | + | 6.36430i | −0.0463108 | + | 0.315080i | ||||
\(409\) | −18.0794 | −0.893971 | −0.446985 | − | 0.894541i | \(-0.647502\pi\) | ||||
−0.446985 | + | 0.894541i | \(0.647502\pi\) | |||||||
\(410\) | 9.65442 | 0.476798 | ||||||||
\(411\) | −11.3311 | − | 1.66546i | −0.558922 | − | 0.0821509i | ||||
\(412\) | 3.35240i | 0.165161i | ||||||||
\(413\) | 0.485351 | 0.0238826 | ||||||||
\(414\) | −7.92349 | + | 12.0091i | −0.389418 | + | 0.590215i | ||||
\(415\) | 9.42725 | 0.462765 | ||||||||
\(416\) | − | 3.85351i | − | 0.188934i | ||||||
\(417\) | 4.04606 | + | 0.594694i | 0.198136 | + | 0.0291223i | ||||
\(418\) | −1.00558 | −0.0491846 | ||||||||
\(419\) | 25.7595 | 1.25843 | 0.629217 | − | 0.777229i | \(-0.283376\pi\) | ||||
0.629217 | + | 0.777229i | \(0.283376\pi\) | |||||||
\(420\) | −0.0489334 | + | 0.332923i | −0.00238770 | + | 0.0162450i | ||||
\(421\) | 13.8562i | 0.675308i | 0.941270 | + | 0.337654i | \(0.109633\pi\) | ||||
−0.941270 | + | 0.337654i | \(0.890367\pi\) | |||||||
\(422\) | 0.599814i | 0.0291985i | ||||||||
\(423\) | 4.01095 | − | 13.3497i | 0.195019 | − | 0.649083i | ||||
\(424\) | 4.09935i | 0.199082i | ||||||||
\(425\) | −3.71391 | −0.180151 | ||||||||
\(426\) | 16.6715 | + | 2.45039i | 0.807735 | + | 0.118722i | ||||
\(427\) | 2.71732 | 0.131500 | ||||||||
\(428\) | 17.6874 | 0.854954 | ||||||||
\(429\) | −24.2771 | − | 3.56828i | −1.17211 | − | 0.172278i | ||||
\(430\) | −10.4535 | −0.504114 | ||||||||
\(431\) | −23.1260 | −1.11394 | −0.556970 | − | 0.830533i | \(-0.688036\pi\) | ||||
−0.556970 | + | 0.830533i | \(0.688036\pi\) | |||||||
\(432\) | −4.70607 | − | 2.20294i | −0.226421 | − | 0.105989i | ||||
\(433\) | 15.8236i | 0.760432i | 0.924898 | + | 0.380216i | \(0.124150\pi\) | ||||
−0.924898 | + | 0.380216i | \(0.875850\pi\) | |||||||
\(434\) | −0.435285 | −0.0208943 | ||||||||
\(435\) | 2.29536 | − | 15.6167i | 0.110054 | − | 0.748763i | ||||
\(436\) | 6.90800i | 0.330833i | ||||||||
\(437\) | −0.376807 | + | 1.25649i | −0.0180251 | + | 0.0601061i | ||||
\(438\) | −2.79118 | + | 18.9900i | −0.133368 | + | 0.907379i | ||||
\(439\) | 31.7678 | 1.51619 | 0.758096 | − | 0.652143i | \(-0.226130\pi\) | ||||
0.758096 | + | 0.652143i | \(0.226130\pi\) | |||||||
\(440\) | − | 3.67639i | − | 0.175265i | ||||||
\(441\) | 20.0034 | + | 6.01008i | 0.952543 | + | 0.286194i | ||||
\(442\) | 14.3116i | 0.680731i | ||||||||
\(443\) | − | 11.4636i | − | 0.544652i | −0.962205 | − | 0.272326i | \(-0.912207\pi\) | ||
0.962205 | − | 0.272326i | \(-0.0877930\pi\) | |||||||
\(444\) | 2.96897 | − | 20.1997i | 0.140901 | − | 0.958634i | ||||
\(445\) | −9.92316 | −0.470403 | ||||||||
\(446\) | 10.6634i | 0.504925i | ||||||||
\(447\) | −15.4882 | − | 2.27647i | −0.732565 | − | 0.107673i | ||||
\(448\) | 0.194278i | 0.00917878i | ||||||||
\(449\) | − | 6.54091i | − | 0.308685i | −0.988017 | − | 0.154342i | \(-0.950674\pi\) | ||
0.988017 | − | 0.154342i | \(-0.0493259\pi\) | |||||||
\(450\) | 0.863238 | − | 2.87312i | 0.0406934 | − | 0.135440i | ||||
\(451\) | − | 35.4935i | − | 1.67132i | ||||||
\(452\) | 3.33657 | 0.156939 | ||||||||
\(453\) | −12.3624 | − | 1.81704i | −0.580838 | − | 0.0853722i | ||||
\(454\) | − | 5.57422i | − | 0.261611i | ||||||
\(455\) | 0.748652i | 0.0350973i | ||||||||
\(456\) | −0.468721 | − | 0.0688932i | −0.0219499 | − | 0.00322622i | ||||
\(457\) | − | 30.6183i | − | 1.43226i | −0.697966 | − | 0.716131i | \(-0.745911\pi\) | ||
0.697966 | − | 0.716131i | \(-0.254089\pi\) | |||||||
\(458\) | −14.9060 | −0.696511 | ||||||||
\(459\) | 17.4779 | + | 8.18151i | 0.815798 | + | 0.381880i | ||||
\(460\) | −4.59371 | − | 1.37760i | −0.214183 | − | 0.0642310i | ||||
\(461\) | 22.9570i | 1.06921i | 0.845101 | + | 0.534606i | \(0.179540\pi\) | ||||
−0.845101 | + | 0.534606i | \(0.820460\pi\) | |||||||
\(462\) | 1.22395 | + | 0.179898i | 0.0569435 | + | 0.00836963i | ||||
\(463\) | 22.2784 | 1.03536 | 0.517682 | − | 0.855573i | \(-0.326795\pi\) | ||||
0.517682 | + | 0.855573i | \(0.326795\pi\) | |||||||
\(464\) | − | 9.11317i | − | 0.423068i | ||||||
\(465\) | 3.83945 | + | 0.564326i | 0.178050 | + | 0.0261700i | ||||
\(466\) | −15.3425 | −0.710726 | ||||||||
\(467\) | −21.8911 | −1.01300 | −0.506500 | − | 0.862240i | \(-0.669061\pi\) | ||||
−0.506500 | + | 0.862240i | \(0.669061\pi\) | |||||||
\(468\) | −11.0716 | − | 3.32649i | −0.511784 | − | 0.153767i | ||||
\(469\) | −2.13348 | −0.0985151 | ||||||||
\(470\) | 4.64640 | 0.214322 | ||||||||
\(471\) | 0.176187 | − | 1.19871i | 0.00811829 | − | 0.0552335i | ||||
\(472\) | −2.49823 | −0.114990 | ||||||||
\(473\) | 38.4313i | 1.76707i | ||||||||
\(474\) | 11.0337 | + | 1.62174i | 0.506794 | + | 0.0744892i | ||||
\(475\) | − | 0.273524i | − | 0.0125501i | ||||||
\(476\) | − | 0.721531i | − | 0.0330713i | ||||||
\(477\) | 11.7779 | + | 3.53872i | 0.539275 | + | 0.162027i | ||||
\(478\) | 11.6220 | 0.531576 | ||||||||
\(479\) | 5.71132 | 0.260957 | 0.130478 | − | 0.991451i | \(-0.458349\pi\) | ||||
0.130478 | + | 0.991451i | \(0.458349\pi\) | |||||||
\(480\) | 0.251873 | − | 1.71364i | 0.0114964 | − | 0.0782166i | ||||
\(481\) | − | 45.4235i | − | 2.07113i | ||||||
\(482\) | −6.44721 | −0.293662 | ||||||||
\(483\) | 0.683421 | − | 1.46194i | 0.0310967 | − | 0.0665206i | ||||
\(484\) | −2.51586 | −0.114357 | ||||||||
\(485\) | 8.91482i | 0.404801i | ||||||||
\(486\) | −10.3918 | + | 11.6194i | −0.471380 | + | 0.527068i | ||||
\(487\) | 22.2185 | 1.00682 | 0.503409 | − | 0.864048i | \(-0.332079\pi\) | ||||
0.503409 | + | 0.864048i | \(0.332079\pi\) | |||||||
\(488\) | −13.9867 | −0.633150 | ||||||||
\(489\) | 22.6525 | + | 3.32949i | 1.02438 | + | 0.150565i | ||||
\(490\) | 6.96226i | 0.314523i | ||||||||
\(491\) | − | 9.94225i | − | 0.448688i | −0.974510 | − | 0.224344i | \(-0.927976\pi\) | ||
0.974510 | − | 0.224344i | \(-0.0720239\pi\) | |||||||
\(492\) | 2.43169 | − | 16.5442i | 0.109629 | − | 0.745870i | ||||
\(493\) | 33.8454i | 1.52432i | ||||||||
\(494\) | −1.05403 | −0.0474229 | ||||||||
\(495\) | −10.5627 | − | 3.17360i | −0.474759 | − | 0.142643i | ||||
\(496\) | 2.24052 | 0.100602 | ||||||||
\(497\) | −1.89007 | −0.0847813 | ||||||||
\(498\) | 2.37447 | − | 16.1549i | 0.106402 | − | 0.723919i | ||||
\(499\) | 5.95037 | 0.266375 | 0.133187 | − | 0.991091i | \(-0.457479\pi\) | ||||
0.133187 | + | 0.991091i | \(0.457479\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 2.71781 | − | 18.4908i | 0.121423 | − | 0.826110i | ||||
\(502\) | 0.366988i | 0.0163795i | ||||||||
\(503\) | 27.9653 | 1.24691 | 0.623455 | − | 0.781859i | \(-0.285728\pi\) | ||||
0.623455 | + | 0.781859i | \(0.285728\pi\) | |||||||
\(504\) | 0.558185 | + | 0.167708i | 0.0248635 | + | 0.00747032i | ||||
\(505\) | − | 8.39174i | − | 0.373427i | ||||||
\(506\) | −5.06461 | + | 16.8883i | −0.225149 | + | 0.750776i | ||||
\(507\) | −3.16938 | − | 0.465839i | −0.140757 | − | 0.0206886i | ||||
\(508\) | −13.8315 | −0.613672 | ||||||||
\(509\) | 3.52122i | 0.156075i | 0.996950 | + | 0.0780376i | \(0.0248654\pi\) | ||||
−0.996950 | + | 0.0780376i | \(0.975135\pi\) | |||||||
\(510\) | −0.935432 | + | 6.36430i | −0.0414216 | + | 0.281816i | ||||
\(511\) | − | 2.15293i | − | 0.0952402i | ||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −0.602557 | + | 1.28722i | −0.0266035 | + | 0.0568322i | ||||
\(514\) | 20.9857 | 0.925638 | ||||||||
\(515\) | 3.35240i | 0.147724i | ||||||||
\(516\) | −2.63296 | + | 17.9136i | −0.115910 | + | 0.788601i | ||||
\(517\) | − | 17.0820i | − | 0.751265i | ||||||
\(518\) | 2.29007i | 0.100620i | ||||||||
\(519\) | −0.983651 | + | 6.69236i | −0.0431775 | + | 0.293762i | ||||
\(520\) | − | 3.85351i | − | 0.168987i | ||||||
\(521\) | −25.1110 | −1.10013 | −0.550067 | − | 0.835121i | \(-0.685398\pi\) | ||||
−0.550067 | + | 0.835121i | \(0.685398\pi\) | |||||||
\(522\) | −26.1832 | − | 7.86683i | −1.14601 | − | 0.344322i | ||||
\(523\) | − | 23.9422i | − | 1.04692i | −0.852050 | − | 0.523460i | \(-0.824641\pi\) | ||
0.852050 | − | 0.523460i | \(-0.175359\pi\) | |||||||
\(524\) | − | 11.1092i | − | 0.485306i | ||||||
\(525\) | −0.0489334 | + | 0.332923i | −0.00213563 | + | 0.0145299i | ||||
\(526\) | − | 28.4952i | − | 1.24245i | ||||||
\(527\) | −8.32109 | −0.362472 | ||||||||
\(528\) | −6.30001 | − | 0.925983i | −0.274173 | − | 0.0402982i | ||||
\(529\) | 19.2044 | + | 12.6566i | 0.834975 | + | 0.550288i | ||||
\(530\) | 4.09935i | 0.178065i | ||||||||
\(531\) | −2.15656 | + | 7.17771i | −0.0935869 | + | 0.311486i | ||||
\(532\) | 0.0531397 | 0.00230390 | ||||||||
\(533\) | − | 37.2034i | − | 1.61146i | ||||||
\(534\) | −2.49937 | + | 17.0047i | −0.108158 | + | 0.735866i | ||||
\(535\) | 17.6874 | 0.764694 | ||||||||
\(536\) | 10.9816 | 0.474332 | ||||||||
\(537\) | −1.48705 | + | 10.1173i | −0.0641709 | + | 0.436593i | ||||
\(538\) | 5.95349 | 0.256673 | ||||||||
\(539\) | 25.5960 | 1.10250 | ||||||||
\(540\) | −4.70607 | − | 2.20294i | −0.202517 | − | 0.0947994i | ||||
\(541\) | −3.04910 | −0.131091 | −0.0655455 | − | 0.997850i | \(-0.520879\pi\) | ||||
−0.0655455 | + | 0.997850i | \(0.520879\pi\) | |||||||
\(542\) | 10.8969i | 0.468060i | ||||||||
\(543\) | −0.920578 | + | 6.26324i | −0.0395058 | + | 0.268781i | ||||
\(544\) | 3.71391i | 0.159232i | ||||||||
\(545\) | 6.90800i | 0.295906i | ||||||||
\(546\) | 1.28292 | + | 0.188565i | 0.0549039 | + | 0.00806984i | ||||
\(547\) | 23.7201 | 1.01420 | 0.507099 | − | 0.861888i | \(-0.330718\pi\) | ||||
0.507099 | + | 0.861888i | \(0.330718\pi\) | |||||||
\(548\) | −6.61230 | −0.282463 | ||||||||
\(549\) | −12.0739 | + | 40.1856i | −0.515301 | + | 1.71508i | ||||
\(550\) | − | 3.67639i | − | 0.156762i | ||||||
\(551\) | −2.49267 | −0.106191 | ||||||||
\(552\) | −3.51774 | + | 7.52499i | −0.149725 | + | 0.320285i | ||||
\(553\) | −1.25091 | −0.0531940 | ||||||||
\(554\) | 12.5927i | 0.535013i | ||||||||
\(555\) | 2.96897 | − | 20.1997i | 0.126026 | − | 0.857428i | ||||
\(556\) | 2.36109 | 0.100133 | ||||||||
\(557\) | 3.97743 | 0.168529 | 0.0842645 | − | 0.996443i | \(-0.473146\pi\) | ||||
0.0842645 | + | 0.996443i | \(0.473146\pi\) | |||||||
\(558\) | 1.93410 | − | 6.43729i | 0.0818772 | − | 0.272512i | ||||
\(559\) | 40.2827i | 1.70378i | ||||||||
\(560\) | 0.194278i | 0.00820975i | ||||||||
\(561\) | 23.3976 | + | 3.43901i | 0.987849 | + | 0.145195i | ||||
\(562\) | 10.5936i | 0.446864i | ||||||||
\(563\) | 19.2899 | 0.812971 | 0.406486 | − | 0.913657i | \(-0.366754\pi\) | ||||
0.406486 | + | 0.913657i | \(0.366754\pi\) | |||||||
\(564\) | 1.17030 | − | 7.96226i | 0.0492786 | − | 0.335271i | ||||
\(565\) | 3.33657 | 0.140370 | ||||||||
\(566\) | 31.7364 | 1.33398 | ||||||||
\(567\) | 0.963692 | − | 1.45896i | 0.0404713 | − | 0.0612705i | ||||
\(568\) | 9.72869 | 0.408207 | ||||||||
\(569\) | 10.8881 | 0.456454 | 0.228227 | − | 0.973608i | \(-0.426707\pi\) | ||||
0.228227 | + | 0.973608i | \(0.426707\pi\) | |||||||
\(570\) | −0.468721 | − | 0.0688932i | −0.0196326 | − | 0.00288562i | ||||
\(571\) | 4.04576i | 0.169310i | 0.996410 | + | 0.0846549i | \(0.0269788\pi\) | ||||
−0.996410 | + | 0.0846549i | \(0.973021\pi\) | |||||||
\(572\) | −14.1670 | −0.592352 | ||||||||
\(573\) | −21.5753 | − | 3.17116i | −0.901321 | − | 0.132477i | ||||
\(574\) | 1.87564i | 0.0782879i | ||||||||
\(575\) | −4.59371 | − | 1.37760i | −0.191571 | − | 0.0574500i | ||||
\(576\) | −2.87312 | − | 0.863238i | −0.119713 | − | 0.0359683i | ||||
\(577\) | −35.0273 | −1.45821 | −0.729103 | − | 0.684404i | \(-0.760062\pi\) | ||||
−0.729103 | + | 0.684404i | \(0.760062\pi\) | |||||||
\(578\) | 3.20690i | 0.133390i | ||||||||
\(579\) | −40.2548 | − | 5.91669i | −1.67293 | − | 0.245889i | ||||
\(580\) | − | 9.11317i | − | 0.378404i | ||||||
\(581\) | 1.83151i | 0.0759838i | ||||||||
\(582\) | 15.2768 | + | 2.24540i | 0.633244 | + | 0.0930749i | ||||
\(583\) | 15.0708 | 0.624170 | ||||||||
\(584\) | 11.0817i | 0.458564i | ||||||||
\(585\) | −11.0716 | − | 3.32649i | −0.457754 | − | 0.137534i | ||||
\(586\) | − | 6.77543i | − | 0.279890i | ||||||
\(587\) | 39.2631i | 1.62056i | 0.586043 | + | 0.810280i | \(0.300685\pi\) | ||||
−0.586043 | + | 0.810280i | \(0.699315\pi\) | |||||||
\(588\) | 11.9308 | + | 1.75360i | 0.492018 | + | 0.0723173i | ||||
\(589\) | − | 0.612836i | − | 0.0252515i | ||||||
\(590\) | −2.49823 | −0.102850 | ||||||||
\(591\) | −3.88703 | + | 26.4458i | −0.159891 | + | 1.08783i | ||||
\(592\) | − | 11.7876i | − | 0.484467i | ||||||
\(593\) | 20.0039i | 0.821461i | 0.911757 | + | 0.410730i | \(0.134726\pi\) | ||||
−0.911757 | + | 0.410730i | \(0.865274\pi\) | |||||||
\(594\) | −8.09887 | + | 17.3013i | −0.332301 | + | 0.709883i | ||||
\(595\) | − | 0.721531i | − | 0.0295799i | ||||||
\(596\) | −9.03818 | −0.370218 | ||||||||
\(597\) | 5.32533 | − | 36.2314i | 0.217951 | − | 1.48285i | ||||
\(598\) | −5.30860 | + | 17.7019i | −0.217085 | + | 0.723885i | ||||
\(599\) | − | 9.77816i | − | 0.399525i | −0.979844 | − | 0.199762i | \(-0.935983\pi\) | ||
0.979844 | − | 0.199762i | \(-0.0640170\pi\) | |||||||
\(600\) | 0.251873 | − | 1.71364i | 0.0102827 | − | 0.0699590i | ||||
\(601\) | −33.3197 | −1.35914 | −0.679569 | − | 0.733612i | \(-0.737833\pi\) | ||||
−0.679569 | + | 0.733612i | \(0.737833\pi\) | |||||||
\(602\) | − | 2.03089i | − | 0.0827730i | ||||||
\(603\) | 9.47972 | − | 31.5514i | 0.386044 | − | 1.28487i | ||||
\(604\) | −7.21414 | −0.293539 | ||||||||
\(605\) | −2.51586 | −0.102284 | ||||||||
\(606\) | −14.3804 | − | 2.11365i | −0.584164 | − | 0.0858612i | ||||
\(607\) | −6.68091 | −0.271170 | −0.135585 | − | 0.990766i | \(-0.543291\pi\) | ||||
−0.135585 | + | 0.990766i | \(0.543291\pi\) | |||||||
\(608\) | −0.273524 | −0.0110929 | ||||||||
\(609\) | 3.03398 | + | 0.445938i | 0.122943 | + | 0.0180703i | ||||
\(610\) | −13.9867 | −0.566306 | ||||||||
\(611\) | − | 17.9049i | − | 0.724356i | ||||||
\(612\) | 10.6705 | + | 3.20598i | 0.431329 | + | 0.129594i | ||||
\(613\) | 2.66775i | 0.107749i | 0.998548 | + | 0.0538746i | \(0.0171571\pi\) | ||||
−0.998548 | + | 0.0538746i | \(0.982843\pi\) | |||||||
\(614\) | 13.5532i | 0.546962i | ||||||||
\(615\) | 2.43169 | − | 16.5442i | 0.0980550 | − | 0.667127i | ||||
\(616\) | 0.714243 | 0.0287777 | ||||||||
\(617\) | 39.4541 | 1.58836 | 0.794182 | − | 0.607680i | \(-0.207900\pi\) | ||||
0.794182 | + | 0.607680i | \(0.207900\pi\) | |||||||
\(618\) | 5.74481 | + | 0.844379i | 0.231090 | + | 0.0339659i | ||||
\(619\) | 2.35902i | 0.0948171i | 0.998876 | + | 0.0474086i | \(0.0150963\pi\) | ||||
−0.998876 | + | 0.0474086i | \(0.984904\pi\) | |||||||
\(620\) | 2.24052 | 0.0899815 | ||||||||
\(621\) | 18.5835 | + | 16.6028i | 0.745732 | + | 0.666246i | ||||
\(622\) | 3.63405 | 0.145712 | ||||||||
\(623\) | − | 1.92785i | − | 0.0772378i | ||||||
\(624\) | −6.60352 | − | 0.970593i | −0.264352 | − | 0.0388548i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −20.2986 | −0.811294 | ||||||||
\(627\) | −0.253279 | + | 1.72320i | −0.0101150 | + | 0.0688181i | ||||
\(628\) | − | 0.699510i | − | 0.0279135i | ||||||
\(629\) | 43.7780i | 1.74554i | ||||||||
\(630\) | 0.558185 | + | 0.167708i | 0.0222386 | + | 0.00668166i | ||||
\(631\) | − | 0.472138i | − | 0.0187955i | −0.999956 | − | 0.00939776i | \(-0.997009\pi\) | ||
0.999956 | − | 0.00939776i | \(-0.00299144\pi\) | |||||||
\(632\) | 6.43875 | 0.256120 | ||||||||
\(633\) | 1.02786 | + | 0.151077i | 0.0408540 | + | 0.00600476i | ||||
\(634\) | 22.0942 | 0.877472 | ||||||||
\(635\) | −13.8315 | −0.548884 | ||||||||
\(636\) | 7.02481 | + | 1.03252i | 0.278552 | + | 0.0409419i | ||||
\(637\) | 26.8291 | 1.06301 | ||||||||
\(638\) | −33.5036 | −1.32642 | ||||||||
\(639\) | 8.39817 | − | 27.9517i | 0.332227 | − | 1.10575i | ||||
\(640\) | − | 1.00000i | − | 0.0395285i | ||||||
\(641\) | −17.5371 | −0.692675 | −0.346337 | − | 0.938110i | \(-0.612575\pi\) | ||||
−0.346337 | + | 0.938110i | \(0.612575\pi\) | |||||||
\(642\) | 4.45498 | − | 30.3099i | 0.175824 | − | 1.19623i | ||||
\(643\) | − | 3.71442i | − | 0.146482i | −0.997314 | − | 0.0732412i | \(-0.976666\pi\) | ||
0.997314 | − | 0.0732412i | \(-0.0233343\pi\) | |||||||
\(644\) | 0.267638 | − | 0.892458i | 0.0105464 | − | 0.0351678i | ||||
\(645\) | −2.63296 | + | 17.9136i | −0.103673 | + | 0.705346i | ||||
\(646\) | 1.01584 | 0.0399678 | ||||||||
\(647\) | 37.9848i | 1.49334i | 0.665197 | + | 0.746668i | \(0.268347\pi\) | ||||
−0.665197 | + | 0.746668i | \(0.731653\pi\) | |||||||
\(648\) | −4.96037 | + | 7.50964i | −0.194862 | + | 0.295007i | ||||
\(649\) | 9.18446i | 0.360522i | ||||||||
\(650\) | − | 3.85351i | − | 0.151147i | ||||||
\(651\) | −0.109636 | + | 0.745921i | −0.00429699 | + | 0.0292349i | ||||
\(652\) | 13.2190 | 0.517694 | ||||||||
\(653\) | 28.7963i | 1.12689i | 0.826155 | + | 0.563443i | \(0.190524\pi\) | ||||
−0.826155 | + | 0.563443i | \(0.809476\pi\) | |||||||
\(654\) | 11.8378 | + | 1.73994i | 0.462896 | + | 0.0680369i | ||||
\(655\) | − | 11.1092i | − | 0.434071i | ||||||
\(656\) | − | 9.65442i | − | 0.376942i | ||||||
\(657\) | 31.8391 | + | 9.56615i | 1.24216 | + | 0.373211i | ||||
\(658\) | 0.902694i | 0.0351907i | ||||||||
\(659\) | −6.49917 | −0.253172 | −0.126586 | − | 0.991956i | \(-0.540402\pi\) | ||||
−0.126586 | + | 0.991956i | \(0.540402\pi\) | |||||||
\(660\) | −6.30001 | − | 0.925983i | −0.245228 | − | 0.0360438i | ||||
\(661\) | − | 39.1114i | − | 1.52126i | −0.649187 | − | 0.760629i | \(-0.724891\pi\) | ||
0.649187 | − | 0.760629i | \(-0.275109\pi\) | |||||||
\(662\) | 27.8332i | 1.08177i | ||||||||
\(663\) | 24.5248 | + | 3.60469i | 0.952466 | + | 0.139995i | ||||
\(664\) | − | 9.42725i | − | 0.365848i | ||||||
\(665\) | 0.0531397 | 0.00206067 | ||||||||
\(666\) | −33.8672 | − | 10.1755i | −1.31233 | − | 0.394292i | ||||
\(667\) | −12.5543 | + | 41.8633i | −0.486105 | + | 1.62095i | ||||
\(668\) | − | 10.7904i | − | 0.417493i | ||||||
\(669\) | 18.2732 | + | 2.68581i | 0.706481 | + | 0.103839i | ||||
\(670\) | 10.9816 | 0.424256 | ||||||||
\(671\) | 51.4207i | 1.98507i | ||||||||
\(672\) | 0.332923 | + | 0.0489334i | 0.0128428 | + | 0.00188765i | ||||
\(673\) | −13.0249 | −0.502071 | −0.251036 | − | 0.967978i | \(-0.580771\pi\) | ||||
−0.251036 | + | 0.967978i | \(0.580771\pi\) | |||||||
\(674\) | 27.7015 | 1.06702 | ||||||||
\(675\) | −4.70607 | − | 2.20294i | −0.181137 | − | 0.0847912i | ||||
\(676\) | −1.84950 | −0.0711347 | ||||||||
\(677\) | 26.1392 | 1.00461 | 0.502305 | − | 0.864691i | \(-0.332485\pi\) | ||||
0.502305 | + | 0.864691i | \(0.332485\pi\) | |||||||
\(678\) | 0.840390 | − | 5.71767i | 0.0322750 | − | 0.219586i | ||||
\(679\) | −1.73196 | −0.0664664 | ||||||||
\(680\) | 3.71391i | 0.142422i | ||||||||
\(681\) | −9.55221 | − | 1.40399i | −0.366041 | − | 0.0538012i | ||||
\(682\) | − | 8.23704i | − | 0.315413i | ||||||
\(683\) | 15.5123i | 0.593560i | 0.954946 | + | 0.296780i | \(0.0959128\pi\) | ||||
−0.954946 | + | 0.296780i | \(0.904087\pi\) | |||||||
\(684\) | −0.236116 | + | 0.785867i | −0.00902813 | + | 0.0300484i | ||||
\(685\) | −6.61230 | −0.252643 | ||||||||
\(686\) | −2.71256 | −0.103566 | ||||||||
\(687\) | −3.75441 | + | 25.5435i | −0.143240 | + | 0.974545i | ||||
\(688\) | 10.4535i | 0.398537i | ||||||||
\(689\) | 15.7969 | 0.601813 | ||||||||
\(690\) | −3.51774 | + | 7.52499i | −0.133918 | + | 0.286471i | ||||
\(691\) | 31.1673 | 1.18566 | 0.592830 | − | 0.805327i | \(-0.298010\pi\) | ||||
0.592830 | + | 0.805327i | \(0.298010\pi\) | |||||||
\(692\) | 3.90535i | 0.148459i | ||||||||
\(693\) | 0.616562 | − | 2.05211i | 0.0234212 | − | 0.0779530i | ||||
\(694\) | 25.4305 | 0.965329 | ||||||||
\(695\) | 2.36109 | 0.0895612 | ||||||||
\(696\) | −15.6167 | − | 2.29536i | −0.591949 | − | 0.0870053i | ||||
\(697\) | 35.8556i | 1.35813i | ||||||||
\(698\) | 25.3679i | 0.960188i | ||||||||
\(699\) | −3.86435 | + | 26.2915i | −0.146163 | + | 0.994434i | ||||
\(700\) | 0.194278i | 0.00734302i | ||||||||
\(701\) | 39.7108 | 1.49986 | 0.749929 | − | 0.661519i | \(-0.230088\pi\) | ||||
0.749929 | + | 0.661519i | \(0.230088\pi\) | |||||||
\(702\) | −8.48904 | + | 18.1348i | −0.320398 | + | 0.684456i | ||||
\(703\) | −3.22419 | −0.121603 | ||||||||
\(704\) | −3.67639 | −0.138559 | ||||||||
\(705\) | 1.17030 | − | 7.96226i | 0.0440761 | − | 0.299876i | ||||
\(706\) | 6.58726 | 0.247915 | ||||||||
\(707\) | 1.63033 | 0.0613149 | ||||||||
\(708\) | −0.629235 | + | 4.28106i | −0.0236481 | + | 0.160892i | ||||
\(709\) | 29.9453i | 1.12462i | 0.826926 | + | 0.562311i | \(0.190087\pi\) | ||||
−0.826926 | + | 0.562311i | \(0.809913\pi\) | |||||||
\(710\) | 9.72869 | 0.365111 | ||||||||
\(711\) | 5.55817 | − | 18.4993i | 0.208448 | − | 0.693778i | ||||
\(712\) | 9.92316i | 0.371886i | ||||||||
\(713\) | −10.2923 | − | 3.08655i | −0.385450 | − | 0.115592i | ||||
\(714\) | −1.23644 | − | 0.181734i | −0.0462727 | − | 0.00680122i | ||||
\(715\) | −14.1670 | −0.529816 | ||||||||
\(716\) | 5.90397i | 0.220642i | ||||||||
\(717\) | 2.92726 | − | 19.9159i | 0.109320 | − | 0.743772i | ||||
\(718\) | 34.1462i | 1.27432i | ||||||||
\(719\) | 19.0401i | 0.710077i | 0.934852 | + | 0.355038i | \(0.115532\pi\) | ||||
−0.934852 | + | 0.355038i | \(0.884468\pi\) | |||||||
\(720\) | −2.87312 | − | 0.863238i | −0.107075 | − | 0.0321710i | ||||
\(721\) | −0.651299 | −0.0242556 | ||||||||
\(722\) | − | 18.9252i | − | 0.704322i | ||||||
\(723\) | −1.62388 | + | 11.0482i | −0.0603926 | + | 0.410886i | ||||
\(724\) | 3.65493i | 0.135834i | ||||||||
\(725\) | − | 9.11317i | − | 0.338454i | ||||||
\(726\) | −0.633677 | + | 4.31128i | −0.0235180 | + | 0.160007i | ||||
\(727\) | − | 28.0357i | − | 1.03979i | −0.854231 | − | 0.519893i | \(-0.825972\pi\) | ||
0.854231 | − | 0.519893i | \(-0.174028\pi\) | |||||||
\(728\) | 0.748652 | 0.0277469 | ||||||||
\(729\) | 17.2941 | + | 20.7344i | 0.640523 | + | 0.767939i | ||||
\(730\) | 11.0817i | 0.410152i | ||||||||
\(731\) | − | 38.8234i | − | 1.43594i | ||||||
\(732\) | −3.52288 | + | 23.9682i | −0.130209 | + | 0.885891i | ||||
\(733\) | − | 33.0849i | − | 1.22202i | −0.791623 | − | 0.611010i | \(-0.790763\pi\) | ||
0.791623 | − | 0.611010i | \(-0.209237\pi\) | |||||||
\(734\) | −2.78712 | −0.102875 | ||||||||
\(735\) | 11.9308 | + | 1.75360i | 0.440074 | + | 0.0646826i | ||||
\(736\) | −1.37760 | + | 4.59371i | −0.0507791 | + | 0.169327i | ||||
\(737\) | − | 40.3726i | − | 1.48714i | ||||||
\(738\) | −27.7383 | − | 8.33407i | −1.02106 | − | 0.306781i | ||||
\(739\) | 0.332871 | 0.0122449 | 0.00612243 | − | 0.999981i | \(-0.498051\pi\) | ||||
0.00612243 | + | 0.999981i | \(0.498051\pi\) | |||||||
\(740\) | − | 11.7876i | − | 0.433320i | ||||||
\(741\) | −0.265480 | + | 1.80622i | −0.00975266 | + | 0.0663532i | ||||
\(742\) | −0.796415 | −0.0292373 | ||||||||
\(743\) | −16.2658 | −0.596734 | −0.298367 | − | 0.954451i | \(-0.596442\pi\) | ||||
−0.298367 | + | 0.954451i | \(0.596442\pi\) | |||||||
\(744\) | 0.564326 | − | 3.83945i | 0.0206892 | − | 0.140761i | ||||
\(745\) | −9.03818 | −0.331133 | ||||||||
\(746\) | 36.8414 | 1.34886 | ||||||||
\(747\) | −27.0856 | − | 8.13796i | −0.991011 | − | 0.297752i | ||||
\(748\) | 13.6538 | 0.499231 | ||||||||
\(749\) | 3.43628i | 0.125559i | ||||||||
\(750\) | 0.251873 | − | 1.71364i | 0.00919709 | − | 0.0625733i | ||||
\(751\) | − | 40.0221i | − | 1.46043i | −0.683218 | − | 0.730214i | \(-0.739420\pi\) | ||
0.683218 | − | 0.730214i | \(-0.260580\pi\) | |||||||
\(752\) | − | 4.64640i | − | 0.169437i | ||||||
\(753\) | 0.628885 | + | 0.0924342i | 0.0229178 | + | 0.00336849i | ||||
\(754\) | −35.1176 | −1.27891 | ||||||||
\(755\) | −7.21414 | −0.262549 | ||||||||
\(756\) | 0.427983 | − | 0.914286i | 0.0155656 | − | 0.0332523i | ||||
\(757\) | 20.5788i | 0.747950i | 0.927439 | + | 0.373975i | \(0.122005\pi\) | ||||
−0.927439 | + | 0.373975i | \(0.877995\pi\) | |||||||
\(758\) | −12.8044 | −0.465076 | ||||||||
\(759\) | 27.6648 | + | 12.9326i | 1.00417 | + | 0.469424i | ||||
\(760\) | −0.273524 | −0.00992176 | ||||||||
\(761\) | 5.93470i | 0.215133i | 0.994198 | + | 0.107566i | \(0.0343058\pi\) | ||||
−0.994198 | + | 0.107566i | \(0.965694\pi\) | |||||||
\(762\) | −3.48377 | + | 23.7021i | −0.126204 | + | 0.858637i | ||||
\(763\) | −1.34207 | −0.0485864 | ||||||||
\(764\) | −12.5903 | −0.455503 | ||||||||
\(765\) | 10.6705 | + | 3.20598i | 0.385793 | + | 0.115913i | ||||
\(766\) | − | 14.2092i | − | 0.513399i | ||||||
\(767\) | 9.62693i | 0.347608i | ||||||||
\(768\) | −1.71364 | − | 0.251873i | −0.0618356 | − | 0.00908867i | ||||
\(769\) | 9.97467i | 0.359696i | 0.983694 | + | 0.179848i | \(0.0575606\pi\) | ||||
−0.983694 | + | 0.179848i | \(0.942439\pi\) | |||||||
\(770\) | 0.714243 | 0.0257395 | ||||||||
\(771\) | 5.28572 | − | 35.9619i | 0.190361 | − | 1.29514i | ||||
\(772\) | −23.4908 | −0.845452 | ||||||||
\(773\) | −44.7513 | −1.60959 | −0.804796 | − | 0.593552i | \(-0.797725\pi\) | ||||
−0.804796 | + | 0.593552i | \(0.797725\pi\) | |||||||
\(774\) | 30.0342 | + | 9.02388i | 1.07956 | + | 0.324357i | ||||
\(775\) | 2.24052 | 0.0804819 | ||||||||
\(776\) | 8.91482 | 0.320024 | ||||||||
\(777\) | 3.92436 | + | 0.576806i | 0.140785 | + | 0.0206928i | ||||
\(778\) | − | 7.98762i | − | 0.286370i | ||||||
\(779\) | −2.64072 | −0.0946135 | ||||||||
\(780\) | −6.60352 | − | 0.970593i | −0.236444 | − | 0.0347528i | ||||
\(781\) | − | 35.7665i | − | 1.27983i | ||||||
\(782\) | 5.11629 | − | 17.0606i | 0.182958 | − | 0.610087i | ||||
\(783\) | −20.0758 | + | 42.8872i | −0.717449 | + | 1.53266i | ||||
\(784\) | 6.96226 | 0.248652 | ||||||||
\(785\) | − | 0.699510i | − | 0.0249666i | ||||||
\(786\) | −19.0371 | − | 2.79810i | −0.679031 | − | 0.0998048i | ||||
\(787\) | 23.8924i | 0.851671i | 0.904801 | + | 0.425835i | \(0.140020\pi\) | ||||
−0.904801 | + | 0.425835i | \(0.859980\pi\) | |||||||
\(788\) | 15.4325i | 0.549761i | ||||||||
\(789\) | −48.8305 | − | 7.17716i | −1.73841 | − | 0.255514i | ||||
\(790\) | 6.43875 | 0.229080 | ||||||||
\(791\) | 0.648222i | 0.0230481i | ||||||||
\(792\) | −3.17360 | + | 10.5627i | −0.112769 | + | 0.375330i | ||||
\(793\) | 53.8979i | 1.91397i | ||||||||
\(794\) | − | 6.37102i | − | 0.226099i | ||||||
\(795\) | 7.02481 | + | 1.03252i | 0.249144 | + | 0.0366195i | ||||
\(796\) | − | 21.1429i | − | 0.749391i | ||||||
\(797\) | −16.9611 | −0.600793 | −0.300396 | − | 0.953814i | \(-0.597119\pi\) | ||||
−0.300396 | + | 0.953814i | \(0.597119\pi\) | |||||||
\(798\) | 0.0133844 | − | 0.0910623i | 0.000473804 | − | 0.00322357i | ||||
\(799\) | 17.2563i | 0.610484i | ||||||||
\(800\) | − | 1.00000i | − | 0.0353553i | ||||||
\(801\) | 28.5104 | + | 8.56605i | 1.00737 | + | 0.302666i | ||||
\(802\) | − | 4.08280i | − | 0.144169i | ||||||
\(803\) | 40.7407 | 1.43771 | ||||||||
\(804\) | 2.76596 | − | 18.8185i | 0.0975480 | − | 0.663677i | ||||
\(805\) | 0.267638 | − | 0.892458i | 0.00943300 | − | 0.0314550i | ||||
\(806\) | − | 8.63386i | − | 0.304115i | ||||||
\(807\) | 1.49952 | − | 10.2021i | 0.0527857 | − | 0.359132i | ||||
\(808\) | −8.39174 | −0.295220 | ||||||||
\(809\) | − | 18.7429i | − | 0.658965i | −0.944162 | − | 0.329483i | \(-0.893126\pi\) | ||
0.944162 | − | 0.329483i | \(-0.106874\pi\) | |||||||
\(810\) | −4.96037 | + | 7.50964i | −0.174290 | + | 0.263862i | ||||
\(811\) | −38.4375 | −1.34972 | −0.674861 | − | 0.737944i | \(-0.735797\pi\) | ||||
−0.674861 | + | 0.737944i | \(0.735797\pi\) | |||||||
\(812\) | 1.77049 | 0.0621320 | ||||||||
\(813\) | 18.6733 | + | 2.74462i | 0.654901 | + | 0.0962581i | ||||
\(814\) | −43.3358 | −1.51892 | ||||||||
\(815\) | 13.2190 | 0.463040 | ||||||||
\(816\) | 6.36430 | + | 0.935432i | 0.222795 | + | 0.0327467i | ||||
\(817\) | 2.85929 | 0.100034 | ||||||||
\(818\) | 18.0794i | 0.632133i | ||||||||
\(819\) | 0.646265 | − | 2.15097i | 0.0225823 | − | 0.0751609i | ||||
\(820\) | − | 9.65442i | − | 0.337147i | ||||||
\(821\) | − | 32.7980i | − | 1.14466i | −0.820023 | − | 0.572330i | \(-0.806040\pi\) | ||
0.820023 | − | 0.572330i | \(-0.193960\pi\) | |||||||
\(822\) | −1.66546 | + | 11.3311i | −0.0580895 | + | 0.395217i | ||||
\(823\) | 36.3523 | 1.26716 | 0.633581 | − | 0.773676i | \(-0.281584\pi\) | ||||
0.633581 | + | 0.773676i | \(0.281584\pi\) | |||||||
\(824\) | 3.35240 | 0.116786 | ||||||||
\(825\) | −6.30001 | − | 0.925983i | −0.219338 | − | 0.0322386i | ||||
\(826\) | − | 0.485351i | − | 0.0168875i | ||||||
\(827\) | 1.85363 | 0.0644572 | 0.0322286 | − | 0.999481i | \(-0.489740\pi\) | ||||
0.0322286 | + | 0.999481i | \(0.489740\pi\) | |||||||
\(828\) | 12.0091 | + | 7.92349i | 0.417345 | + | 0.275360i | ||||
\(829\) | −23.4117 | −0.813124 | −0.406562 | − | 0.913623i | \(-0.633272\pi\) | ||||
−0.406562 | + | 0.913623i | \(0.633272\pi\) | |||||||
\(830\) | − | 9.42725i | − | 0.327225i | ||||||
\(831\) | 21.5794 | + | 3.17176i | 0.748580 | + | 0.110027i | ||||
\(832\) | −3.85351 | −0.133596 | ||||||||
\(833\) | −25.8572 | −0.895898 | ||||||||
\(834\) | 0.594694 | − | 4.04606i | 0.0205926 | − | 0.140103i | ||||
\(835\) | − | 10.7904i | − | 0.373417i | ||||||
\(836\) | 1.00558i | 0.0347788i | ||||||||
\(837\) | −10.5440 | − | 4.93573i | −0.364456 | − | 0.170604i | ||||
\(838\) | − | 25.7595i | − | 0.889848i | ||||||
\(839\) | −19.0303 | −0.656998 | −0.328499 | − | 0.944504i | \(-0.606543\pi\) | ||||
−0.328499 | + | 0.944504i | \(0.606543\pi\) | |||||||
\(840\) | 0.332923 | + | 0.0489334i | 0.0114869 | + | 0.00168836i | ||||
\(841\) | −54.0498 | −1.86379 | ||||||||
\(842\) | 13.8562 | 0.477515 | ||||||||
\(843\) | 18.1536 | + | 2.66824i | 0.625243 | + | 0.0918990i | ||||
\(844\) | 0.599814 | 0.0206464 | ||||||||
\(845\) | −1.84950 | −0.0636248 | ||||||||
\(846\) | −13.3497 | − | 4.01095i | −0.458971 | − | 0.137899i | ||||
\(847\) | − | 0.488777i | − | 0.0167946i | ||||||
\(848\) | 4.09935 | 0.140772 | ||||||||
\(849\) | 7.99352 | − | 54.3847i | 0.274337 | − | 1.86648i | ||||
\(850\) | 3.71391i | 0.127386i | ||||||||
\(851\) | −16.2386 | + | 54.1488i | −0.556652 | + | 1.85620i | ||||
\(852\) | 2.45039 | − | 16.6715i | 0.0839490 | − | 0.571155i | ||||
\(853\) | −8.98937 | −0.307790 | −0.153895 | − | 0.988087i | \(-0.549182\pi\) | ||||
−0.153895 | + | 0.988087i | \(0.549182\pi\) | |||||||
\(854\) | − | 2.71732i | − | 0.0929847i | ||||||
\(855\) | −0.236116 | + | 0.785867i | −0.00807501 | + | 0.0268761i | ||||
\(856\) | − | 17.6874i | − | 0.604544i | ||||||
\(857\) | 35.0879i | 1.19858i | 0.800532 | + | 0.599290i | \(0.204550\pi\) | ||||
−0.800532 | + | 0.599290i | \(0.795450\pi\) | |||||||
\(858\) | −3.56828 | + | 24.2771i | −0.121819 | + | 0.828807i | ||||
\(859\) | −20.3531 | −0.694439 | −0.347220 | − | 0.937784i | \(-0.612874\pi\) | ||||
−0.347220 | + | 0.937784i | \(0.612874\pi\) | |||||||
\(860\) | 10.4535i | 0.356462i | ||||||||
\(861\) | 3.21418 | + | 0.472424i | 0.109539 | + | 0.0161002i | ||||
\(862\) | 23.1260i | 0.787674i | ||||||||
\(863\) | − | 55.7757i | − | 1.89863i | −0.314333 | − | 0.949313i | \(-0.601781\pi\) | ||
0.314333 | − | 0.949313i | \(-0.398219\pi\) | |||||||
\(864\) | −2.20294 | + | 4.70607i | −0.0749455 | + | 0.160104i | ||||
\(865\) | 3.90535i | 0.132786i | ||||||||
\(866\) | 15.8236 | 0.537707 | ||||||||
\(867\) | 5.49548 | + | 0.807732i | 0.186636 | + | 0.0274320i | ||||
\(868\) | 0.435285i | 0.0147745i | ||||||||
\(869\) | − | 23.6714i | − | 0.802996i | ||||||
\(870\) | −15.6167 | − | 2.29536i | −0.529455 | − | 0.0778199i | ||||
\(871\) | − | 42.3176i | − | 1.43388i | ||||||
\(872\) | 6.90800 | 0.233935 | ||||||||
\(873\) | 7.69562 | − | 25.6134i | 0.260457 | − | 0.866881i | ||||
\(874\) | 1.25649 | + | 0.376807i | 0.0425014 | + | 0.0127457i | ||||
\(875\) | 0.194278i | 0.00656780i | ||||||||
\(876\) | 18.9900 | + | 2.79118i | 0.641614 | + | 0.0943052i | ||||
\(877\) | 26.1377 | 0.882608 | 0.441304 | − | 0.897358i | \(-0.354516\pi\) | ||||
0.441304 | + | 0.897358i | \(0.354516\pi\) | |||||||
\(878\) | − | 31.7678i | − | 1.07211i | ||||||
\(879\) | −11.6106 | − | 1.70655i | −0.391617 | − | 0.0575604i | ||||
\(880\) | −3.67639 | −0.123931 | ||||||||
\(881\) | −15.6301 | −0.526590 | −0.263295 | − | 0.964715i | \(-0.584809\pi\) | ||||
−0.263295 | + | 0.964715i | \(0.584809\pi\) | |||||||
\(882\) | 6.01008 | − | 20.0034i | 0.202370 | − | 0.673549i | ||||
\(883\) | 26.2855 | 0.884577 | 0.442289 | − | 0.896873i | \(-0.354167\pi\) | ||||
0.442289 | + | 0.896873i | \(0.354167\pi\) | |||||||
\(884\) | 14.3116 | 0.481350 | ||||||||
\(885\) | −0.629235 | + | 4.28106i | −0.0211515 | + | 0.143906i | ||||
\(886\) | −11.4636 | −0.385127 | ||||||||
\(887\) | − | 21.1883i | − | 0.711435i | −0.934594 | − | 0.355717i | \(-0.884237\pi\) | ||
0.934594 | − | 0.355717i | \(-0.115763\pi\) | |||||||
\(888\) | −20.1997 | − | 2.96897i | −0.677857 | − | 0.0996321i | ||||
\(889\) | − | 2.68715i | − | 0.0901241i | ||||||
\(890\) | 9.92316i | 0.332625i | ||||||||
\(891\) | 27.6084 | + | 18.2363i | 0.924916 | + | 0.610938i | ||||
\(892\) | 10.6634 | 0.357036 | ||||||||
\(893\) | −1.27090 | −0.0425291 | ||||||||
\(894\) | −2.27647 | + | 15.4882i | −0.0761365 | + | 0.518002i | ||||
\(895\) | 5.90397i | 0.197348i | ||||||||
\(896\) | 0.194278 | 0.00649038 | ||||||||
\(897\) | 28.9976 | + | 13.5556i | 0.968201 | + | 0.452610i | ||||
\(898\) | −6.54091 | −0.218273 | ||||||||
\(899\) | − | 20.4183i | − | 0.680987i | ||||||
\(900\) | −2.87312 | − | 0.863238i | −0.0957707 | − | 0.0287746i | ||||
\(901\) | −15.2246 | −0.507205 | ||||||||
\(902\) | −35.4935 | −1.18180 | ||||||||
\(903\) | −3.48022 | − | 0.511526i | −0.115814 | − | 0.0170225i | ||||
\(904\) | − | 3.33657i | − | 0.110973i | ||||||
\(905\) | 3.65493i | 0.121494i | ||||||||
\(906\) | −1.81704 | + | 12.3624i | −0.0603672 | + | 0.410714i | ||||
\(907\) | 30.7874i | 1.02228i | 0.859498 | + | 0.511140i | \(0.170777\pi\) | ||||
−0.859498 | + | 0.511140i | \(0.829223\pi\) | |||||||
\(908\) | −5.57422 | −0.184987 | ||||||||
\(909\) | −7.24407 | + | 24.1105i | −0.240271 | + | 0.799694i | ||||
\(910\) | 0.748652 | 0.0248176 | ||||||||
\(911\) | −43.6844 | −1.44733 | −0.723664 | − | 0.690152i | \(-0.757544\pi\) | ||||
−0.723664 | + | 0.690152i | \(0.757544\pi\) | |||||||
\(912\) | −0.0688932 | + | 0.468721i | −0.00228128 | + | 0.0155209i | ||||
\(913\) | −34.6583 | −1.14702 | ||||||||
\(914\) | −30.6183 | −1.01276 | ||||||||
\(915\) | −3.52288 | + | 23.9682i | −0.116463 | + | 0.792365i | ||||
\(916\) | 14.9060i | 0.492508i | ||||||||
\(917\) | 2.15827 | 0.0712723 | ||||||||
\(918\) | 8.18151 | − | 17.4779i | 0.270030 | − | 0.576856i | ||||
\(919\) | − | 53.3411i | − | 1.75956i | −0.475381 | − | 0.879780i | \(-0.657690\pi\) | ||
0.475381 | − | 0.879780i | \(-0.342310\pi\) | |||||||
\(920\) | −1.37760 | + | 4.59371i | −0.0454182 | + | 0.151450i | ||||
\(921\) | 23.2253 | + | 3.41368i | 0.765299 | + | 0.112485i | ||||
\(922\) | 22.9570 | 0.756047 | ||||||||
\(923\) | − | 37.4895i | − | 1.23398i | ||||||
\(924\) | 0.179898 | − | 1.22395i | 0.00591822 | − | 0.0402652i | ||||
\(925\) | − | 11.7876i | − | 0.387573i | ||||||
\(926\) | − | 22.2784i | − | 0.732114i | ||||||
\(927\) | 2.89392 | − | 9.63185i | 0.0950488 | − | 0.316352i | ||||
\(928\) | −9.11317 | −0.299154 | ||||||||
\(929\) | − | 40.8893i | − | 1.34153i | −0.741668 | − | 0.670767i | \(-0.765965\pi\) | ||
0.741668 | − | 0.670767i | \(-0.234035\pi\) | |||||||
\(930\) | 0.564326 | − | 3.83945i | 0.0185050 | − | 0.125900i | ||||
\(931\) | − | 1.90434i | − | 0.0624123i | ||||||
\(932\) | 15.3425i | 0.502559i | ||||||||
\(933\) | 0.915317 | − | 6.22745i | 0.0299661 | − | 0.203877i | ||||
\(934\) | 21.8911i | 0.716299i | ||||||||
\(935\) | 13.6538 | 0.446526 | ||||||||
\(936\) | −3.32649 | + | 11.0716i | −0.108730 | + | 0.361886i | ||||
\(937\) | 12.8925i | 0.421181i | 0.977574 | + | 0.210590i | \(0.0675386\pi\) | ||||
−0.977574 | + | 0.210590i | \(0.932461\pi\) | |||||||
\(938\) | 2.13348i | 0.0696607i | ||||||||
\(939\) | −5.11266 | + | 34.7844i | −0.166845 | + | 1.13515i | ||||
\(940\) | − | 4.64640i | − | 0.151549i | ||||||
\(941\) | 28.2649 | 0.921410 | 0.460705 | − | 0.887553i | \(-0.347597\pi\) | ||||
0.460705 | + | 0.887553i | \(0.347597\pi\) | |||||||
\(942\) | −1.19871 | − | 0.176187i | −0.0390560 | − | 0.00574050i | ||||
\(943\) | −13.3000 | + | 44.3497i | −0.433106 | + | 1.44422i | ||||
\(944\) | 2.49823i | 0.0813104i | ||||||||
\(945\) | 0.427983 | − | 0.914286i | 0.0139223 | − | 0.0297417i | ||||
\(946\) | 38.4313 | 1.24951 | ||||||||
\(947\) | − | 53.6576i | − | 1.74364i | −0.489829 | − | 0.871818i | \(-0.662941\pi\) | ||
0.489829 | − | 0.871818i | \(-0.337059\pi\) | |||||||
\(948\) | 1.62174 | − | 11.0337i | 0.0526718 | − | 0.358358i | ||||
\(949\) | 42.7034 | 1.38621 | ||||||||
\(950\) | −0.273524 | −0.00887429 | ||||||||
\(951\) | 5.56492 | − | 37.8615i | 0.180455 | − | 1.22774i | ||||
\(952\) | −0.721531 | −0.0233849 | ||||||||
\(953\) | −47.7407 | −1.54647 | −0.773236 | − | 0.634118i | \(-0.781363\pi\) | ||||
−0.773236 | + | 0.634118i | \(0.781363\pi\) | |||||||
\(954\) | 3.53872 | − | 11.7779i | 0.114570 | − | 0.381325i | ||||
\(955\) | −12.5903 | −0.407414 | ||||||||
\(956\) | − | 11.6220i | − | 0.375881i | ||||||
\(957\) | −8.43864 | + | 57.4130i | −0.272782 | + | 1.85590i | ||||
\(958\) | − | 5.71132i | − | 0.184524i | ||||||
\(959\) | − | 1.28462i | − | 0.0414827i | ||||||
\(960\) | −1.71364 | − | 0.251873i | −0.0553075 | − | 0.00812916i | ||||
\(961\) | −25.9801 | −0.838066 | ||||||||
\(962\) | −45.4235 | −1.46451 | ||||||||
\(963\) | −50.8181 | − | 15.2685i | −1.63759 | − | 0.492019i | ||||
\(964\) | 6.44721i | 0.207651i | ||||||||
\(965\) | −23.4908 | −0.756196 | ||||||||
\(966\) | −1.46194 | − | 0.683421i | −0.0470372 | − | 0.0219887i | ||||
\(967\) | −7.74638 | −0.249107 | −0.124553 | − | 0.992213i | \(-0.539750\pi\) | ||||
−0.124553 | + | 0.992213i | \(0.539750\pi\) | |||||||
\(968\) | 2.51586i | 0.0808629i | ||||||||
\(969\) | 0.255863 | − | 1.74079i | 0.00821950 | − | 0.0559221i | ||||
\(970\) | 8.91482 | 0.286238 | ||||||||
\(971\) | 54.7216 | 1.75610 | 0.878051 | − | 0.478568i | \(-0.158844\pi\) | ||||
0.878051 | + | 0.478568i | \(0.158844\pi\) | |||||||
\(972\) | 11.6194 | + | 10.3918i | 0.372693 | + | 0.333316i | ||||
\(973\) | 0.458708i | 0.0147055i | ||||||||
\(974\) | − | 22.2185i | − | 0.711928i | ||||||
\(975\) | −6.60352 | − | 0.970593i | −0.211482 | − | 0.0310838i | ||||
\(976\) | 13.9867i | 0.447704i | ||||||||
\(977\) | 30.6187 | 0.979578 | 0.489789 | − | 0.871841i | \(-0.337074\pi\) | ||||
0.489789 | + | 0.871841i | \(0.337074\pi\) | |||||||
\(978\) | 3.32949 | − | 22.6525i | 0.106465 | − | 0.724348i | ||||
\(979\) | 36.4814 | 1.16595 | ||||||||
\(980\) | 6.96226 | 0.222401 | ||||||||
\(981\) | 5.96325 | − | 19.8475i | 0.190392 | − | 0.633683i | ||||
\(982\) | −9.94225 | −0.317270 | ||||||||
\(983\) | 18.1788 | 0.579812 | 0.289906 | − | 0.957055i | \(-0.406376\pi\) | ||||
0.289906 | + | 0.957055i | \(0.406376\pi\) | |||||||
\(984\) | −16.5442 | − | 2.43169i | −0.527410 | − | 0.0775193i | ||||
\(985\) | 15.4325i | 0.491721i | ||||||||
\(986\) | 33.8454 | 1.07786 | ||||||||
\(987\) | 1.54689 | + | 0.227364i | 0.0492381 | + | 0.00723708i | ||||
\(988\) | 1.05403i | 0.0335330i | ||||||||
\(989\) | 14.4008 | − | 48.0205i | 0.457919 | − | 1.52696i | ||||
\(990\) | −3.17360 | + | 10.5627i | −0.100864 | + | 0.335705i | ||||
\(991\) | 28.0460 | 0.890912 | 0.445456 | − | 0.895304i | \(-0.353042\pi\) | ||||
0.445456 | + | 0.895304i | \(0.353042\pi\) | |||||||
\(992\) | − | 2.24052i | − | 0.0711367i | ||||||
\(993\) | 47.6960 | + | 7.01042i | 1.51359 | + | 0.222469i | ||||
\(994\) | 1.89007i | 0.0599494i | ||||||||
\(995\) | − | 21.1429i | − | 0.670276i | ||||||
\(996\) | −16.1549 | − | 2.37447i | −0.511888 | − | 0.0752379i | ||||
\(997\) | −34.7005 | −1.09898 | −0.549488 | − | 0.835502i | \(-0.685177\pi\) | ||||
−0.549488 | + | 0.835502i | \(0.685177\pi\) | |||||||
\(998\) | − | 5.95037i | − | 0.188356i | ||||||
\(999\) | −25.9673 | + | 55.4732i | −0.821570 | + | 1.75509i |
(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 | 690.2.e.a.551.1 | ✓ | 16 | |
3.2 | odd | 2 | 690.2.e.b.551.9 | yes | 16 | ||
23.22 | odd | 2 | 690.2.e.b.551.1 | yes | 16 | ||
69.68 | even | 2 | inner | 690.2.e.a.551.9 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.e.a.551.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
690.2.e.a.551.9 | yes | 16 | 69.68 | even | 2 | inner | |
690.2.e.b.551.1 | yes | 16 | 23.22 | odd | 2 | ||
690.2.e.b.551.9 | yes | 16 | 3.2 | odd | 2 |