Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [693,2,Mod(64,693)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(693, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("693.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 693 = 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 693.m (of order \(5\), degree \(4\), 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: | \(5.53363286007\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.13140625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 231) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 64.2 | ||
Root | \(0.418926 - 1.28932i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 693.64 |
Dual form | 693.2.m.f.379.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/693\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(442\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0501062 | + | 0.154211i | −0.0354305 | + | 0.109044i | −0.967208 | − | 0.253987i | \(-0.918258\pi\) |
0.931777 | + | 0.363031i | \(0.118258\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.59676 | + | 1.16012i | 0.798382 | + | 0.580058i | ||||
\(5\) | 1.35567 | + | 4.17234i | 0.606276 | + | 1.86593i | 0.487770 | + | 0.872972i | \(0.337811\pi\) |
0.118506 | + | 0.992953i | \(0.462189\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.809017 | + | 0.587785i | 0.305780 | + | 0.222162i | ||||
\(8\) | −0.521270 | + | 0.378725i | −0.184297 | + | 0.133900i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.711349 | −0.224948 | ||||||||
\(11\) | 3.30902 | + | 0.224514i | 0.997706 | + | 0.0676935i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.517822 | − | 1.59369i | 0.143618 | − | 0.442010i | −0.853213 | − | 0.521563i | \(-0.825349\pi\) |
0.996831 | + | 0.0795526i | \(0.0253492\pi\) | |||||||
\(14\) | −0.131180 | + | 0.0953077i | −0.0350593 | + | 0.0254721i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.18753 | + | 3.65485i | 0.296884 | + | 0.913714i | ||||
\(17\) | −1.91177 | − | 5.88383i | −0.463673 | − | 1.42704i | −0.860644 | − | 0.509208i | \(-0.829938\pi\) |
0.396970 | − | 0.917831i | \(-0.370062\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.81156 | − | 2.04272i | 0.645016 | − | 0.468632i | −0.216554 | − | 0.976271i | \(-0.569482\pi\) |
0.861570 | + | 0.507639i | \(0.169482\pi\) | |||||||
\(20\) | −2.67571 | + | 8.23498i | −0.598306 | + | 1.84140i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.200425 | + | 0.499038i | −0.0427307 | + | 0.106395i | ||||
\(23\) | −0.568595 | −0.118560 | −0.0592801 | − | 0.998241i | \(-0.518881\pi\) | ||||
−0.0592801 | + | 0.998241i | \(0.518881\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.5255 | + | 8.37373i | −2.30509 | + | 1.67475i | ||||
\(26\) | 0.219819 | + | 0.159708i | 0.0431100 | + | 0.0313213i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.609909 | + | 1.87711i | 0.115262 | + | 0.354740i | ||||
\(29\) | −7.17390 | − | 5.21214i | −1.33216 | − | 0.967870i | −0.999694 | − | 0.0247547i | \(-0.992120\pi\) |
−0.332465 | − | 0.943115i | \(-0.607880\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.33943 | − | 4.12233i | 0.240568 | − | 0.740392i | −0.755766 | − | 0.654842i | \(-0.772735\pi\) |
0.996334 | − | 0.0855500i | \(-0.0272647\pi\) | |||||||
\(32\) | −1.91177 | −0.337957 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.00314 | 0.172038 | ||||||||
\(35\) | −1.35567 | + | 4.17234i | −0.229151 | + | 0.705254i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.784298 | − | 0.569826i | −0.128938 | − | 0.0936787i | 0.521447 | − | 0.853284i | \(-0.325392\pi\) |
−0.650385 | + | 0.759605i | \(0.725392\pi\) | |||||||
\(38\) | 0.174133 | + | 0.535927i | 0.0282481 | + | 0.0869388i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.28684 | − | 1.66149i | −0.361581 | − | 0.262704i | ||||
\(41\) | 4.67390 | − | 3.39578i | 0.729940 | − | 0.530332i | −0.159605 | − | 0.987181i | \(-0.551022\pi\) |
0.889544 | + | 0.456849i | \(0.151022\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.04388 | −0.769184 | −0.384592 | − | 0.923087i | \(-0.625658\pi\) | ||||
−0.384592 | + | 0.923087i | \(0.625658\pi\) | |||||||
\(44\) | 5.02326 | + | 4.19734i | 0.757284 | + | 0.632773i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.0284902 | − | 0.0876837i | 0.00420065 | − | 0.0129283i | ||||
\(47\) | 3.78018 | − | 2.74646i | 0.551396 | − | 0.400613i | −0.276904 | − | 0.960898i | \(-0.589308\pi\) |
0.828300 | + | 0.560285i | \(0.189308\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.309017 | + | 0.951057i | 0.0441453 | + | 0.135865i | ||||
\(50\) | −0.713826 | − | 2.19693i | −0.100950 | − | 0.310693i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.67571 | − | 1.94401i | 0.371054 | − | 0.269586i | ||||
\(53\) | 0.735096 | − | 2.26239i | 0.100973 | − | 0.310764i | −0.887791 | − | 0.460247i | \(-0.847761\pi\) |
0.988764 | + | 0.149483i | \(0.0477609\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.54920 | + | 14.1107i | 0.478574 | + | 1.90269i | ||||
\(56\) | −0.644326 | −0.0861016 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.16323 | − | 0.845134i | 0.152739 | − | 0.110972i | ||||
\(59\) | −2.30490 | − | 1.67461i | −0.300072 | − | 0.218015i | 0.427553 | − | 0.903990i | \(-0.359376\pi\) |
−0.727625 | + | 0.685975i | \(0.759376\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.87350 | + | 8.84371i | 0.367913 | + | 1.13232i | 0.948136 | + | 0.317864i | \(0.102965\pi\) |
−0.580223 | + | 0.814458i | \(0.697035\pi\) | |||||||
\(62\) | 0.568595 | + | 0.413109i | 0.0722117 | + | 0.0524648i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.27928 | + | 7.01489i | −0.284910 | + | 0.876861i | ||||
\(65\) | 7.35141 | 0.911830 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.14275 | −0.872626 | −0.436313 | − | 0.899795i | \(-0.643716\pi\) | ||||
−0.436313 | + | 0.899795i | \(0.643716\pi\) | |||||||
\(68\) | 3.77328 | − | 11.6130i | 0.457578 | − | 1.40828i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.575493 | − | 0.418120i | −0.0687846 | − | 0.0499749i | ||||
\(71\) | 0.245510 | + | 0.755602i | 0.0291367 | + | 0.0896734i | 0.964567 | − | 0.263837i | \(-0.0849880\pi\) |
−0.935431 | + | 0.353510i | \(0.884988\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.93117 | − | 1.40308i | −0.226026 | − | 0.164218i | 0.469009 | − | 0.883193i | \(-0.344611\pi\) |
−0.695035 | + | 0.718976i | \(0.744611\pi\) | |||||||
\(74\) | 0.127172 | − | 0.0923956i | 0.0147834 | − | 0.0107408i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.85919 | 0.786803 | ||||||||
\(77\) | 2.54508 | + | 2.12663i | 0.290039 | + | 0.242352i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.207232 | + | 0.637795i | −0.0233154 | + | 0.0717576i | −0.962037 | − | 0.272918i | \(-0.912011\pi\) |
0.938722 | + | 0.344676i | \(0.112011\pi\) | |||||||
\(80\) | −13.6394 | + | 9.90958i | −1.52493 | + | 1.10793i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.289476 | + | 0.890917i | 0.0319673 | + | 0.0983853i | ||||
\(83\) | 2.86923 | + | 8.83059i | 0.314939 | + | 0.969283i | 0.975779 | + | 0.218757i | \(0.0702001\pi\) |
−0.660840 | + | 0.750527i | \(0.729800\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 21.9576 | − | 15.9531i | 2.38164 | − | 1.73036i | ||||
\(86\) | 0.252730 | − | 0.777822i | 0.0272525 | − | 0.0838747i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.80992 | + | 1.13618i | −0.192938 | + | 0.121117i | ||||
\(89\) | 12.2106 | 1.29432 | 0.647161 | − | 0.762354i | \(-0.275956\pi\) | ||||
0.647161 | + | 0.762354i | \(0.275956\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.35567 | − | 0.984955i | 0.142113 | − | 0.103251i | ||||
\(92\) | −0.907912 | − | 0.659637i | −0.0946564 | − | 0.0687719i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.234124 | + | 0.720561i | 0.0241481 | + | 0.0743202i | ||||
\(95\) | 12.3345 | + | 8.96152i | 1.26549 | + | 0.919432i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.65368 | − | 14.3225i | 0.472509 | − | 1.45423i | −0.376778 | − | 0.926304i | \(-0.622968\pi\) |
0.849288 | − | 0.527931i | \(-0.177032\pi\) | |||||||
\(98\) | −0.162147 | −0.0163793 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −28.1179 | −2.81179 | ||||||||
\(101\) | −1.78018 | + | 5.47883i | −0.177135 | + | 0.545164i | −0.999725 | − | 0.0234707i | \(-0.992528\pi\) |
0.822590 | + | 0.568635i | \(0.192528\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.24116 | − | 4.53447i | −0.614959 | − | 0.446794i | 0.236198 | − | 0.971705i | \(-0.424099\pi\) |
−0.851157 | + | 0.524911i | \(0.824099\pi\) | |||||||
\(104\) | 0.333646 | + | 1.02686i | 0.0327167 | + | 0.100692i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.312053 | + | 0.226720i | 0.0303093 | + | 0.0220210i | ||||
\(107\) | −13.3192 | + | 9.67696i | −1.28762 | + | 0.935507i | −0.999754 | − | 0.0221652i | \(-0.992944\pi\) |
−0.287861 | + | 0.957672i | \(0.592944\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.74355 | 0.933263 | 0.466632 | − | 0.884452i | \(-0.345467\pi\) | ||||
0.466632 | + | 0.884452i | \(0.345467\pi\) | |||||||
\(110\) | −2.35386 | − | 0.159708i | −0.224432 | − | 0.0152275i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.18753 | + | 3.65485i | −0.112211 | + | 0.345351i | ||||
\(113\) | −2.31156 | + | 1.67945i | −0.217453 | + | 0.157989i | −0.691180 | − | 0.722683i | \(-0.742909\pi\) |
0.473726 | + | 0.880672i | \(0.342909\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.770830 | − | 2.37237i | −0.0718803 | − | 0.221225i | ||||
\(116\) | −5.40832 | − | 16.6451i | −0.502150 | − | 1.54546i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.373733 | − | 0.271533i | 0.0344049 | − | 0.0249966i | ||||
\(119\) | 1.91177 | − | 5.88383i | 0.175252 | − | 0.539370i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.8992 | + | 1.48584i | 0.990835 | + | 0.135076i | ||||
\(122\) | −1.50778 | −0.136508 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.92112 | − | 5.02849i | 0.621535 | − | 0.451572i | ||||
\(125\) | −32.8168 | − | 23.8428i | −2.93522 | − | 2.13256i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.96015 | − | 15.2658i | −0.440142 | − | 1.35462i | −0.887724 | − | 0.460375i | \(-0.847715\pi\) |
0.447582 | − | 0.894243i | \(-0.352285\pi\) | |||||||
\(128\) | −4.06088 | − | 2.95040i | −0.358935 | − | 0.260781i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.368352 | + | 1.13367i | −0.0323066 | + | 0.0994294i | ||||
\(131\) | −0.750136 | −0.0655397 | −0.0327699 | − | 0.999463i | \(-0.510433\pi\) | ||||
−0.0327699 | + | 0.999463i | \(0.510433\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.47528 | 0.301345 | ||||||||
\(134\) | 0.357897 | − | 1.10149i | 0.0309176 | − | 0.0951544i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.22491 | + | 2.34303i | 0.276533 | + | 0.200913i | ||||
\(137\) | 4.01977 | + | 12.3716i | 0.343432 | + | 1.05697i | 0.962418 | + | 0.271572i | \(0.0875436\pi\) |
−0.618986 | + | 0.785402i | \(0.712456\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.15607 | − | 2.29302i | −0.267695 | − | 0.194492i | 0.445838 | − | 0.895114i | \(-0.352906\pi\) |
−0.713532 | + | 0.700622i | \(0.752906\pi\) | |||||||
\(140\) | −7.00509 | + | 5.08949i | −0.592038 | + | 0.430141i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.128824 | −0.0108107 | ||||||||
\(143\) | 2.07129 | − | 5.15729i | 0.173210 | − | 0.431274i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.0213 | − | 36.9979i | 0.998318 | − | 3.07251i | ||||
\(146\) | 0.313133 | − | 0.227505i | 0.0259151 | − | 0.0188284i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.591274 | − | 1.81975i | −0.0486024 | − | 0.149583i | ||||
\(149\) | −5.73023 | − | 17.6358i | −0.469439 | − | 1.44478i | −0.853313 | − | 0.521399i | \(-0.825410\pi\) |
0.383874 | − | 0.923385i | \(-0.374590\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.8259 | + | 12.2247i | −1.36927 | + | 0.994832i | −0.371475 | + | 0.928443i | \(0.621148\pi\) |
−0.997794 | + | 0.0663888i | \(0.978852\pi\) | |||||||
\(152\) | −0.691955 | + | 2.12962i | −0.0561249 | + | 0.172735i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.455474 | + | 0.285923i | −0.0367032 | + | 0.0230403i | ||||
\(155\) | 19.0156 | 1.52737 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.70019 | + | 3.41489i | −0.375116 | + | 0.272538i | −0.759329 | − | 0.650707i | \(-0.774473\pi\) |
0.384213 | + | 0.923244i | \(0.374473\pi\) | |||||||
\(158\) | −0.0879715 | − | 0.0639150i | −0.00699864 | − | 0.00508481i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.59174 | − | 7.97656i | −0.204895 | − | 0.630603i | ||||
\(161\) | −0.460003 | − | 0.334212i | −0.0362533 | − | 0.0263396i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.75120 | + | 8.46732i | −0.215491 | + | 0.663212i | 0.783628 | + | 0.621230i | \(0.213367\pi\) |
−0.999118 | + | 0.0419811i | \(0.986633\pi\) | |||||||
\(164\) | 11.4026 | 0.890394 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.50554 | −0.116853 | ||||||||
\(167\) | 1.18154 | − | 3.63641i | 0.0914304 | − | 0.281394i | −0.894877 | − | 0.446314i | \(-0.852737\pi\) |
0.986307 | + | 0.164920i | \(0.0527366\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.24551 | + | 5.99071i | 0.634270 | + | 0.460824i | ||||
\(170\) | 1.35994 | + | 4.18546i | 0.104302 | + | 0.321010i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.05388 | − | 5.85148i | −0.614102 | − | 0.446171i | ||||
\(173\) | 1.41627 | − | 1.02898i | 0.107677 | − | 0.0782322i | −0.532644 | − | 0.846340i | \(-0.678801\pi\) |
0.640321 | + | 0.768107i | \(0.278801\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.2462 | −1.07691 | ||||||||
\(176\) | 3.10900 | + | 12.3606i | 0.234350 | + | 0.931715i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.611827 | + | 1.88301i | −0.0458584 | + | 0.141138i | ||||
\(179\) | −10.3992 | + | 7.55545i | −0.777272 | + | 0.564721i | −0.904159 | − | 0.427196i | \(-0.859501\pi\) |
0.126887 | + | 0.991917i | \(0.459501\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.82406 | − | 21.0023i | −0.507228 | − | 1.56109i | −0.796992 | − | 0.603990i | \(-0.793577\pi\) |
0.289764 | − | 0.957098i | \(-0.406423\pi\) | |||||||
\(182\) | 0.0839633 | + | 0.258413i | 0.00622377 | + | 0.0191548i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.296392 | − | 0.215341i | 0.0218503 | − | 0.0158752i | ||||
\(185\) | 1.31425 | − | 4.04485i | 0.0966257 | − | 0.297383i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.00509 | − | 19.8989i | −0.366008 | − | 1.45515i | ||||
\(188\) | 9.22227 | 0.672603 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.00000 | + | 1.45309i | −0.145095 | + | 0.105418i | ||||
\(191\) | 11.9055 | + | 8.64983i | 0.861449 | + | 0.625879i | 0.928279 | − | 0.371885i | \(-0.121288\pi\) |
−0.0668297 | + | 0.997764i | \(0.521288\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.63062 | + | 8.09622i | 0.189356 | + | 0.582779i | 0.999996 | − | 0.00276642i | \(-0.000880579\pi\) |
−0.810640 | + | 0.585545i | \(0.800881\pi\) | |||||||
\(194\) | 1.97552 | + | 1.43530i | 0.141834 | + | 0.103048i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.609909 | + | 1.87711i | −0.0435650 | + | 0.134079i | ||||
\(197\) | 4.72273 | 0.336480 | 0.168240 | − | 0.985746i | \(-0.446192\pi\) | ||||
0.168240 | + | 0.985746i | \(0.446192\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.7620 | 1.18822 | 0.594112 | − | 0.804382i | \(-0.297504\pi\) | ||||
0.594112 | + | 0.804382i | \(0.297504\pi\) | |||||||
\(200\) | 2.83654 | − | 8.72996i | 0.200573 | − | 0.617301i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.755699 | − | 0.549048i | −0.0531708 | − | 0.0386309i | ||||
\(203\) | −2.74018 | − | 8.43342i | −0.192323 | − | 0.591910i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.5046 | + | 14.8975i | 1.43211 | + | 1.04049i | ||||
\(206\) | 1.01199 | − | 0.735251i | 0.0705084 | − | 0.0512274i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.43964 | 0.446509 | ||||||||
\(209\) | 9.76212 | − | 6.12816i | 0.675260 | − | 0.423893i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.13511 | + | 9.64887i | −0.215830 | + | 0.664256i | 0.783264 | + | 0.621689i | \(0.213553\pi\) |
−0.999094 | + | 0.0425663i | \(0.986447\pi\) | |||||||
\(212\) | 3.79842 | − | 2.75971i | 0.260876 | − | 0.189538i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.824921 | − | 2.53884i | −0.0563904 | − | 0.173552i | ||||
\(215\) | −6.83785 | − | 21.0447i | −0.466338 | − | 1.43524i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.50666 | − | 2.54774i | 0.238048 | − | 0.172952i | ||||
\(218\) | −0.488213 | + | 1.50256i | −0.0330659 | + | 0.101767i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −10.7028 | + | 26.6489i | −0.721584 | + | 1.79667i | ||||
\(221\) | −10.3670 | −0.697358 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.94449 | − | 3.59238i | 0.331107 | − | 0.240564i | −0.409793 | − | 0.912179i | \(-0.634399\pi\) |
0.740900 | + | 0.671615i | \(0.234399\pi\) | |||||||
\(224\) | −1.54666 | − | 1.12371i | −0.103340 | − | 0.0750812i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.143166 | − | 0.440619i | −0.00952325 | − | 0.0293096i | ||||
\(227\) | 11.4953 | + | 8.35181i | 0.762969 | + | 0.554329i | 0.899819 | − | 0.436262i | \(-0.143698\pi\) |
−0.136851 | + | 0.990592i | \(0.543698\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.842941 | + | 2.59431i | −0.0557031 | + | 0.171437i | −0.975037 | − | 0.222041i | \(-0.928728\pi\) |
0.919334 | + | 0.393478i | \(0.128728\pi\) | |||||||
\(230\) | 0.404469 | 0.0266699 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.71351 | 0.375110 | ||||||||
\(233\) | 5.49731 | − | 16.9190i | 0.360141 | − | 1.10840i | −0.592828 | − | 0.805329i | \(-0.701988\pi\) |
0.952968 | − | 0.303070i | \(-0.0980115\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.5839 | + | 12.0489i | 1.08181 | + | 0.785982i | ||||
\(236\) | −1.73764 | − | 5.34791i | −0.113111 | − | 0.348119i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.811561 | + | 0.589634i | 0.0526057 | + | 0.0382203i | ||||
\(239\) | 10.2792 | − | 7.46827i | 0.664906 | − | 0.483082i | −0.203410 | − | 0.979094i | \(-0.565202\pi\) |
0.868316 | + | 0.496011i | \(0.165202\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.6604 | −1.20202 | −0.601012 | − | 0.799240i | \(-0.705235\pi\) | ||||
−0.601012 | + | 0.799240i | \(0.705235\pi\) | |||||||
\(242\) | −0.775251 | + | 1.60633i | −0.0498350 | + | 0.103259i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.67144 | + | 17.4549i | −0.363077 | + | 1.11744i | ||||
\(245\) | −3.54920 | + | 2.57865i | −0.226750 | + | 0.164744i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.79958 | − | 5.53852i | −0.114504 | − | 0.352408i | ||||
\(248\) | 0.863026 | + | 2.65612i | 0.0548022 | + | 0.168664i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.32115 | − | 3.86604i | 0.336539 | − | 0.244510i | ||||
\(251\) | −5.82475 | + | 17.9267i | −0.367655 | + | 1.13153i | 0.580647 | + | 0.814155i | \(0.302800\pi\) |
−0.948302 | + | 0.317370i | \(0.897200\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.88149 | − | 0.127658i | −0.118288 | − | 0.00802576i | ||||
\(254\) | 2.60269 | 0.163307 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.2760 | + | 8.19248i | −0.704749 | + | 0.512030i | ||||
\(257\) | −8.36076 | − | 6.07445i | −0.521530 | − | 0.378914i | 0.295650 | − | 0.955296i | \(-0.404464\pi\) |
−0.817180 | + | 0.576383i | \(0.804464\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.299575 | − | 0.921997i | −0.0186147 | − | 0.0572901i | ||||
\(260\) | 11.7385 | + | 8.52849i | 0.727989 | + | 0.528915i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.0375865 | − | 0.115679i | 0.00232210 | − | 0.00714670i | ||||
\(263\) | 4.14979 | 0.255887 | 0.127943 | − | 0.991781i | \(-0.459162\pi\) | ||||
0.127943 | + | 0.991781i | \(0.459162\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.4360 | 0.641079 | ||||||||
\(266\) | −0.174133 | + | 0.535927i | −0.0106768 | + | 0.0328598i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −11.4053 | − | 8.28643i | −0.696689 | − | 0.506174i | ||||
\(269\) | 1.56433 | + | 4.81452i | 0.0953790 | + | 0.293546i | 0.987352 | − | 0.158542i | \(-0.0506792\pi\) |
−0.891973 | + | 0.452088i | \(0.850679\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.2901 | + | 15.4682i | 1.29328 | + | 0.939625i | 0.999866 | − | 0.0163598i | \(-0.00520772\pi\) |
0.293417 | + | 0.955985i | \(0.405208\pi\) | |||||||
\(272\) | 19.2343 | − | 13.9745i | 1.16625 | − | 0.847329i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.10925 | −0.127424 | ||||||||
\(275\) | −40.0179 | + | 25.1212i | −2.41317 | + | 1.51487i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.97843 | − | 24.5551i | 0.479377 | − | 1.47537i | −0.360585 | − | 0.932726i | \(-0.617423\pi\) |
0.839962 | − | 0.542645i | \(-0.182577\pi\) | |||||||
\(278\) | 0.511749 | − | 0.371807i | 0.0306926 | − | 0.0222995i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.873496 | − | 2.68834i | −0.0522014 | − | 0.160659i | ||||
\(281\) | 1.68057 | + | 5.17226i | 0.100254 | + | 0.308551i | 0.988587 | − | 0.150649i | \(-0.0481362\pi\) |
−0.888333 | + | 0.459200i | \(0.848136\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.5360 | + | 14.9203i | −1.22074 | + | 0.886919i | −0.996161 | − | 0.0875371i | \(-0.972100\pi\) |
−0.224578 | + | 0.974456i | \(0.572100\pi\) | |||||||
\(284\) | −0.484565 | + | 1.49134i | −0.0287536 | + | 0.0884946i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.691528 | + | 0.577828i | 0.0408909 | + | 0.0341677i | ||||
\(287\) | 5.77725 | 0.341020 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.2113 | + | 12.5048i | −1.01243 | + | 0.735575i | ||||
\(290\) | 5.10314 | + | 3.70765i | 0.299667 | + | 0.217721i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.45589 | − | 4.48076i | −0.0851993 | − | 0.262217i | ||||
\(293\) | 5.46412 | + | 3.96992i | 0.319217 | + | 0.231925i | 0.735841 | − | 0.677154i | \(-0.236787\pi\) |
−0.416624 | + | 0.909079i | \(0.636787\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.86233 | − | 11.8870i | 0.224874 | − | 0.692090i | ||||
\(296\) | 0.624638 | 0.0363064 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.00676 | 0.174177 | ||||||||
\(299\) | −0.294431 | + | 0.906165i | −0.0170274 | + | 0.0524049i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.08058 | − | 2.96472i | −0.235201 | − | 0.170883i | ||||
\(302\) | −1.04210 | − | 3.20727i | −0.0599664 | − | 0.184558i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 10.8047 | + | 7.85005i | 0.619690 | + | 0.450231i | ||||
\(305\) | −33.0034 | + | 23.9784i | −1.88977 | + | 1.37300i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.6396 | −1.00674 | −0.503372 | − | 0.864070i | \(-0.667908\pi\) | ||||
−0.503372 | + | 0.864070i | \(0.667908\pi\) | |||||||
\(308\) | 1.59676 | + | 6.34832i | 0.0909840 | + | 0.361729i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.952798 | + | 2.93241i | −0.0541153 | + | 0.166550i | ||||
\(311\) | −9.90354 | + | 7.19534i | −0.561578 | + | 0.408010i | −0.832036 | − | 0.554721i | \(-0.812825\pi\) |
0.270458 | + | 0.962732i | \(0.412825\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.976343 | + | 3.00487i | 0.0551862 | + | 0.169846i | 0.974851 | − | 0.222860i | \(-0.0715392\pi\) |
−0.919664 | + | 0.392705i | \(0.871539\pi\) | |||||||
\(314\) | −0.291105 | − | 0.895928i | −0.0164280 | − | 0.0505602i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.07082 | + | 0.777994i | −0.0602382 | + | 0.0437656i | ||||
\(317\) | −2.60614 | + | 8.02087i | −0.146375 | + | 0.450497i | −0.997185 | − | 0.0749766i | \(-0.976112\pi\) |
0.850810 | + | 0.525473i | \(0.176112\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.5683 | − | 18.8577i | −1.26358 | − | 1.05583i | ||||
\(320\) | −32.3584 | −1.80889 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.0745882 | − | 0.0541915i | 0.00415664 | − | 0.00301998i | ||||
\(323\) | −17.3941 | − | 12.6375i | −0.967833 | − | 0.703172i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.37701 | + | 22.7041i | 0.409203 | + | 1.25940i | ||||
\(326\) | −1.16790 | − | 0.848531i | −0.0646842 | − | 0.0469958i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.15029 | + | 3.54024i | −0.0635144 | + | 0.195477i | ||||
\(329\) | 4.67256 | 0.257607 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.13284 | 0.337092 | 0.168546 | − | 0.985694i | \(-0.446093\pi\) | ||||
0.168546 | + | 0.985694i | \(0.446093\pi\) | |||||||
\(332\) | −5.66303 | + | 17.4290i | −0.310799 | + | 0.956541i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.501572 | + | 0.364414i | 0.0274448 | + | 0.0199398i | ||||
\(335\) | −9.68325 | − | 29.8020i | −0.529052 | − | 1.62826i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.1728 | + | 17.5626i | 1.31678 | + | 0.956695i | 0.999966 | + | 0.00820616i | \(0.00261213\pi\) |
0.316811 | + | 0.948489i | \(0.397388\pi\) | |||||||
\(338\) | −1.33699 | + | 0.971377i | −0.0727225 | + | 0.0528360i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 53.5686 | 2.90516 | ||||||||
\(341\) | 5.35770 | − | 13.3401i | 0.290136 | − | 0.722408i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.309017 | + | 0.951057i | −0.0166853 | + | 0.0513522i | ||||
\(344\) | 2.62922 | − | 1.91024i | 0.141758 | − | 0.102993i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.0877165 | + | 0.269964i | 0.00471567 | + | 0.0145133i | ||||
\(347\) | 9.01453 | + | 27.7439i | 0.483925 | + | 1.48937i | 0.833531 | + | 0.552472i | \(0.186315\pi\) |
−0.349606 | + | 0.936897i | \(0.613685\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.8347 | + | 7.87188i | −0.579969 | + | 0.421372i | −0.838713 | − | 0.544574i | \(-0.816691\pi\) |
0.258744 | + | 0.965946i | \(0.416691\pi\) | |||||||
\(350\) | 0.713826 | − | 2.19693i | 0.0381556 | − | 0.117431i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.32609 | − | 0.429220i | −0.337182 | − | 0.0228775i | ||||
\(353\) | 21.3175 | 1.13462 | 0.567309 | − | 0.823505i | \(-0.307985\pi\) | ||||
0.567309 | + | 0.823505i | \(0.307985\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.81979 | + | 2.04870i | −0.149659 | + | 0.108734i | ||||
\(356\) | 19.4974 | + | 14.1657i | 1.03336 | + | 0.750782i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.644071 | − | 1.98225i | −0.0340402 | − | 0.104765i | ||||
\(359\) | −16.6847 | − | 12.1221i | −0.880584 | − | 0.639782i | 0.0528216 | − | 0.998604i | \(-0.483179\pi\) |
−0.933406 | + | 0.358822i | \(0.883179\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.13915 | + | 6.58362i | −0.112587 | + | 0.346506i | ||||
\(362\) | 3.58072 | 0.188198 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.30735 | 0.173352 | ||||||||
\(365\) | 3.23607 | − | 9.95959i | 0.169384 | − | 0.521309i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.5799 | − | 19.3114i | −1.38746 | − | 1.00805i | −0.996139 | − | 0.0877934i | \(-0.972018\pi\) |
−0.391320 | − | 0.920255i | \(-0.627982\pi\) | |||||||
\(368\) | −0.675226 | − | 2.07813i | −0.0351986 | − | 0.108330i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.557909 | + | 0.405345i | 0.0290043 | + | 0.0210729i | ||||
\(371\) | 1.92451 | − | 1.39824i | 0.0999154 | − | 0.0725928i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.0979 | 1.35130 | 0.675650 | − | 0.737223i | \(-0.263863\pi\) | ||||
0.675650 | + | 0.737223i | \(0.263863\pi\) | |||||||
\(374\) | 3.31942 | + | 0.225220i | 0.171643 | + | 0.0116458i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.930342 | + | 2.86330i | −0.0479787 | + | 0.147663i | ||||
\(377\) | −12.0213 | + | 8.73401i | −0.619130 | + | 0.449825i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.60724 | − | 11.1020i | −0.185292 | − | 0.570269i | 0.814662 | − | 0.579937i | \(-0.196923\pi\) |
−0.999953 | + | 0.00966747i | \(0.996923\pi\) | |||||||
\(380\) | 9.29883 | + | 28.6188i | 0.477020 | + | 1.46812i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.93044 | + | 1.40255i | −0.0987698 | + | 0.0717604i | ||||
\(383\) | 4.74963 | − | 14.6178i | 0.242695 | − | 0.746937i | −0.753313 | − | 0.657663i | \(-0.771545\pi\) |
0.996007 | − | 0.0892743i | \(-0.0284548\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.42270 | + | 13.5020i | −0.276366 | + | 0.688124i | ||||
\(386\) | −1.38034 | −0.0702573 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 24.0466 | − | 17.4709i | 1.22078 | − | 0.886951i | ||||
\(389\) | −7.80236 | − | 5.66874i | −0.395595 | − | 0.287417i | 0.372149 | − | 0.928173i | \(-0.378621\pi\) |
−0.767744 | + | 0.640756i | \(0.778621\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.08703 | + | 3.34552i | 0.0549732 | + | 0.169190i | ||||
\(392\) | −0.521270 | − | 0.378725i | −0.0263281 | − | 0.0191285i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.236638 | + | 0.728297i | −0.0119217 | + | 0.0366911i | ||||
\(395\) | −2.94203 | −0.148030 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.2855 | 1.01810 | 0.509050 | − | 0.860737i | \(-0.329997\pi\) | ||||
0.509050 | + | 0.860737i | \(0.329997\pi\) | |||||||
\(398\) | −0.839879 | + | 2.58488i | −0.0420993 | + | 0.129568i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −44.2916 | − | 32.1798i | −2.21458 | − | 1.60899i | ||||
\(401\) | 2.52051 | + | 7.75734i | 0.125868 | + | 0.387383i | 0.994058 | − | 0.108849i | \(-0.0347165\pi\) |
−0.868190 | + | 0.496232i | \(0.834717\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.87613 | − | 4.26926i | −0.292711 | − | 0.212667i | ||||
\(404\) | −9.19862 | + | 6.68319i | −0.457648 | + | 0.332501i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.43783 | 0.0713582 | ||||||||
\(407\) | −2.46732 | − | 2.06165i | −0.122301 | − | 0.102192i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.98884 | + | 9.19870i | −0.147789 | + | 0.454846i | −0.997359 | − | 0.0726287i | \(-0.976861\pi\) |
0.849570 | + | 0.527475i | \(0.176861\pi\) | |||||||
\(410\) | −3.32477 | + | 2.41559i | −0.164199 | + | 0.119297i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.70514 | − | 14.4809i | −0.231806 | − | 0.713425i | ||||
\(413\) | −0.880394 | − | 2.70957i | −0.0433213 | − | 0.133329i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −32.9544 | + | 23.9428i | −1.61767 | + | 1.17531i | ||||
\(416\) | −0.989957 | + | 3.04678i | −0.0485367 | + | 0.149380i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.455887 | + | 1.81249i | 0.0222982 | + | 0.0886516i | ||||
\(419\) | 18.9357 | 0.925072 | 0.462536 | − | 0.886601i | \(-0.346940\pi\) | ||||
0.462536 | + | 0.886601i | \(0.346940\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.5940 | − | 7.69703i | 0.516322 | − | 0.375130i | −0.298894 | − | 0.954286i | \(-0.596618\pi\) |
0.815217 | + | 0.579156i | \(0.196618\pi\) | |||||||
\(422\) | −1.33088 | − | 0.966937i | −0.0647860 | − | 0.0470698i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.473641 | + | 1.45772i | 0.0230021 | + | 0.0707931i | ||||
\(425\) | 71.3037 | + | 51.8052i | 3.45874 | + | 2.51292i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.87350 | + | 8.84371i | −0.139058 | + | 0.427977i | ||||
\(428\) | −32.4940 | −1.57066 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.58795 | 0.173027 | ||||||||
\(431\) | 5.03804 | − | 15.5055i | 0.242674 | − | 0.746873i | −0.753336 | − | 0.657635i | \(-0.771557\pi\) |
0.996010 | − | 0.0892381i | \(-0.0284432\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.45274 | − | 6.86782i | −0.454270 | − | 0.330046i | 0.337009 | − | 0.941501i | \(-0.390585\pi\) |
−0.791279 | + | 0.611455i | \(0.790585\pi\) | |||||||
\(434\) | 0.217184 | + | 0.668424i | 0.0104252 | + | 0.0320854i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.5582 | + | 11.3037i | 0.745100 | + | 0.541347i | ||||
\(437\) | −1.59864 | + | 1.16148i | −0.0764733 | + | 0.0555611i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.7172 | 0.559230 | 0.279615 | − | 0.960112i | \(-0.409793\pi\) | ||||
0.279615 | + | 0.960112i | \(0.409793\pi\) | |||||||
\(440\) | −7.19417 | − | 6.01132i | −0.342969 | − | 0.286578i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.519450 | − | 1.59870i | 0.0247077 | − | 0.0760425i | ||||
\(443\) | −10.1670 | + | 7.38676i | −0.483049 | + | 0.350955i | −0.802505 | − | 0.596646i | \(-0.796500\pi\) |
0.319456 | + | 0.947601i | \(0.396500\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.5536 | + | 50.9467i | 0.784716 | + | 2.41511i | ||||
\(446\) | 0.306236 | + | 0.942496i | 0.0145007 | + | 0.0446285i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5.96722 | + | 4.33544i | −0.281925 | + | 0.204830i | ||||
\(449\) | 4.92451 | − | 15.1561i | 0.232402 | − | 0.715259i | −0.765054 | − | 0.643967i | \(-0.777288\pi\) |
0.997455 | − | 0.0712927i | \(-0.0227124\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.2284 | − | 10.1874i | 0.764166 | − | 0.479704i | ||||
\(452\) | −5.63937 | −0.265254 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.86393 | + | 1.35422i | −0.0874785 | + | 0.0635568i | ||||
\(455\) | 5.94742 | + | 4.32105i | 0.278819 | + | 0.202574i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.35290 | − | 22.6299i | −0.343954 | − | 1.05858i | −0.962141 | − | 0.272551i | \(-0.912133\pi\) |
0.618187 | − | 0.786031i | \(-0.287867\pi\) | |||||||
\(458\) | −0.357834 | − | 0.259982i | −0.0167205 | − | 0.0121482i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.52139 | − | 4.68237i | 0.0709353 | − | 0.218317i | ||||
\(461\) | 22.6035 | 1.05275 | 0.526375 | − | 0.850252i | \(-0.323551\pi\) | ||||
0.526375 | + | 0.850252i | \(0.323551\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.03759 | 0.141169 | 0.0705843 | − | 0.997506i | \(-0.477514\pi\) | ||||
0.0705843 | + | 0.997506i | \(0.477514\pi\) | |||||||
\(464\) | 10.5304 | − | 32.4091i | 0.488860 | − | 1.50456i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.33365 | + | 1.69549i | 0.108104 | + | 0.0785422i | ||||
\(467\) | 7.10896 | + | 21.8791i | 0.328963 | + | 1.01244i | 0.969620 | + | 0.244617i | \(0.0786623\pi\) |
−0.640657 | + | 0.767828i | \(0.721338\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.77861 | − | 4.19841i | −0.266831 | − | 0.193864i | ||||
\(470\) | −2.68903 | + | 1.95369i | −0.124036 | + | 0.0901171i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.83569 | 0.0844946 | ||||||||
\(473\) | −16.6903 | − | 1.13242i | −0.767419 | − | 0.0520688i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.2993 | + | 47.0865i | −0.701982 | + | 2.16048i | ||||
\(476\) | 9.87858 | − | 7.17721i | 0.452784 | − | 0.328967i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.636639 | + | 1.95937i | 0.0291192 | + | 0.0896197i | ||||
\(479\) | −2.52554 | − | 7.77283i | −0.115395 | − | 0.355150i | 0.876634 | − | 0.481158i | \(-0.159783\pi\) |
−0.992029 | + | 0.126008i | \(0.959783\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.31425 | + | 0.954860i | −0.0599247 | + | 0.0435379i | ||||
\(482\) | 0.935003 | − | 2.87764i | 0.0425882 | − | 0.131073i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15.6797 | + | 15.0169i | 0.712713 | + | 0.682585i | ||||
\(485\) | 66.0673 | 2.99996 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.808395 | − | 0.587334i | 0.0366319 | − | 0.0266146i | −0.569319 | − | 0.822117i | \(-0.692793\pi\) |
0.605951 | + | 0.795502i | \(0.292793\pi\) | |||||||
\(488\) | −4.84720 | − | 3.52170i | −0.219423 | − | 0.159420i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.219819 | − | 0.676533i | −0.00993040 | − | 0.0305626i | ||||
\(491\) | 19.6556 | + | 14.2806i | 0.887046 | + | 0.644476i | 0.935106 | − | 0.354368i | \(-0.115304\pi\) |
−0.0480603 | + | 0.998844i | \(0.515304\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.9525 | + | 52.1744i | −0.763502 | + | 2.34982i | ||||
\(494\) | 0.944272 | 0.0424848 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16.6571 | 0.747927 | ||||||||
\(497\) | −0.245510 | + | 0.755602i | −0.0110126 | + | 0.0338934i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.2350 | + | 24.1466i | 1.48780 | + | 1.08095i | 0.974937 | + | 0.222482i | \(0.0714160\pi\) |
0.512865 | + | 0.858469i | \(0.328584\pi\) | |||||||
\(500\) | −24.7402 | − | 76.1426i | −1.10642 | − | 3.40520i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.47265 | − | 1.79648i | −0.110360 | − | 0.0801809i | ||||
\(503\) | −8.35469 | + | 6.07004i | −0.372517 | + | 0.270650i | −0.758254 | − | 0.651959i | \(-0.773947\pi\) |
0.385737 | + | 0.922609i | \(0.373947\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25.2729 | −1.12463 | ||||||||
\(506\) | 0.113961 | − | 0.283750i | 0.00506617 | − | 0.0126142i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.78989 | − | 30.1302i | 0.434356 | − | 1.33681i | ||||
\(509\) | −32.8546 | + | 23.8703i | −1.45625 | + | 1.05803i | −0.471935 | + | 0.881633i | \(0.656444\pi\) |
−0.984319 | + | 0.176397i | \(0.943556\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.737640 | − | 2.27022i | −0.0326313 | − | 0.100429i | ||||
\(512\) | −3.80061 | − | 11.6971i | −0.167965 | − | 0.516943i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.35567 | − | 0.984955i | 0.0597962 | − | 0.0434445i | ||||
\(515\) | 10.4583 | − | 32.1875i | 0.460850 | − | 1.41835i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.1253 | − | 8.23939i | 0.577250 | − | 0.362368i | ||||
\(518\) | 0.157193 | 0.00690666 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.83207 | + | 2.78416i | −0.168048 | + | 0.122094i | ||||
\(521\) | −17.9719 | − | 13.0573i | −0.787363 | − | 0.572053i | 0.119817 | − | 0.992796i | \(-0.461769\pi\) |
−0.907180 | + | 0.420743i | \(0.861769\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.00397 | − | 21.5560i | −0.306262 | − | 0.942578i | −0.979203 | − | 0.202882i | \(-0.934969\pi\) |
0.672941 | − | 0.739696i | \(-0.265031\pi\) | |||||||
\(524\) | −1.19779 | − | 0.870246i | −0.0523257 | − | 0.0380169i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.207930 | + | 0.639943i | −0.00906618 | + | 0.0279028i | ||||
\(527\) | −26.8158 | −1.16811 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6767 | −0.985943 | ||||||||
\(530\) | −0.522910 | + | 1.60935i | −0.0227137 | + | 0.0699057i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.54920 | + | 4.03173i | 0.240588 | + | 0.174798i | ||||
\(533\) | −2.99159 | − | 9.20715i | −0.129580 | − | 0.398806i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −58.4320 | − | 42.4533i | −2.52624 | − | 1.83542i | ||||
\(536\) | 3.72331 | − | 2.70514i | 0.160822 | − | 0.116844i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.820835 | −0.0353887 | ||||||||
\(539\) | 0.809017 | + | 3.21644i | 0.0348468 | + | 0.138542i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.93649 | + | 5.95991i | −0.0832563 | + | 0.256237i | −0.984016 | − | 0.178082i | \(-0.943011\pi\) |
0.900759 | + | 0.434319i | \(0.143011\pi\) | |||||||
\(542\) | −3.45213 | + | 2.50812i | −0.148282 | + | 0.107733i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.65488 | + | 11.2486i | 0.156702 | + | 0.482278i | ||||
\(545\) | 13.2091 | + | 40.6534i | 0.565815 | + | 1.74140i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.5807 | + | 20.0386i | −1.17927 | + | 0.856787i | −0.992089 | − | 0.125539i | \(-0.959934\pi\) |
−0.187178 | + | 0.982326i | \(0.559934\pi\) | |||||||
\(548\) | −7.93384 | + | 24.4179i | −0.338917 | + | 1.04308i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.86882 | − | 7.42994i | −0.0796868 | − | 0.316814i | ||||
\(551\) | −30.8168 | −1.31284 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.542541 | + | 0.394179i | −0.0230712 | + | 0.0167622i | ||||
\(554\) | 3.38690 | + | 2.46072i | 0.143895 | + | 0.104546i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.37933 | − | 7.32283i | −0.100906 | − | 0.310557i | ||||
\(557\) | −21.3574 | − | 15.5170i | −0.904941 | − | 0.657478i | 0.0347891 | − | 0.999395i | \(-0.488924\pi\) |
−0.939730 | + | 0.341916i | \(0.888924\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.61183 | + | 8.03838i | −0.110469 | + | 0.339987i | ||||
\(560\) | −16.8592 | −0.712431 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.881827 | −0.0371976 | ||||||||
\(563\) | 2.11715 | − | 6.51593i | 0.0892274 | − | 0.274614i | −0.896479 | − | 0.443086i | \(-0.853884\pi\) |
0.985706 | + | 0.168473i | \(0.0538835\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.1409 | − | 7.36783i | −0.426633 | − | 0.309967i | ||||
\(566\) | −1.27189 | − | 3.91448i | −0.0534616 | − | 0.164538i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.414143 | − | 0.300892i | −0.0173770 | − | 0.0126252i | ||||
\(569\) | 14.8866 | − | 10.8157i | 0.624079 | − | 0.453420i | −0.230265 | − | 0.973128i | \(-0.573959\pi\) |
0.854344 | + | 0.519708i | \(0.173959\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.336889 | 0.0140984 | 0.00704918 | − | 0.999975i | \(-0.497756\pi\) | ||||
0.00704918 | + | 0.999975i | \(0.497756\pi\) | |||||||
\(572\) | 9.29041 | − | 5.83204i | 0.388452 | − | 0.243850i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.289476 | + | 0.890917i | −0.0120825 | + | 0.0371862i | ||||
\(575\) | 6.55332 | − | 4.76126i | 0.273292 | − | 0.198558i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.98337 | − | 24.5703i | −0.332352 | − | 1.02288i | −0.968012 | − | 0.250905i | \(-0.919272\pi\) |
0.635659 | − | 0.771970i | \(-0.280728\pi\) | |||||||
\(578\) | −1.06598 | − | 3.28075i | −0.0443389 | − | 0.136461i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 62.1171 | − | 45.1307i | 2.57927 | − | 1.87395i | ||||
\(581\) | −2.86923 | + | 8.83059i | −0.119036 | + | 0.366355i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.94038 | − | 7.32126i | 0.121778 | − | 0.303216i | ||||
\(584\) | 1.53804 | 0.0636446 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.885992 | + | 0.643711i | −0.0366000 | + | 0.0265914i | ||||
\(587\) | −3.02099 | − | 2.19488i | −0.124689 | − | 0.0905922i | 0.523693 | − | 0.851907i | \(-0.324554\pi\) |
−0.648382 | + | 0.761315i | \(0.724554\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.65488 | − | 14.3262i | −0.191801 | − | 0.590303i | ||||
\(590\) | 1.63959 | + | 1.19123i | 0.0675008 | + | 0.0490422i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.15125 | − | 3.54318i | 0.0473160 | − | 0.145624i | ||||
\(593\) | −17.5647 | −0.721295 | −0.360648 | − | 0.932702i | \(-0.617444\pi\) | ||||
−0.360648 | + | 0.932702i | \(0.617444\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27.1411 | 1.11268 | ||||||||
\(596\) | 11.3098 | − | 34.8080i | 0.463268 | − | 1.42579i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.124988 | − | 0.0908090i | −0.00511114 | − | 0.00371346i | ||||
\(599\) | −3.49462 | − | 10.7553i | −0.142786 | − | 0.439451i | 0.853933 | − | 0.520382i | \(-0.174211\pi\) |
−0.996720 | + | 0.0809314i | \(0.974211\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.4470 | + | 17.0353i | 0.956424 | + | 0.694883i | 0.952317 | − | 0.305109i | \(-0.0986929\pi\) |
0.00410642 | + | 0.999992i | \(0.498693\pi\) | |||||||
\(602\) | 0.661655 | − | 0.480720i | 0.0269670 | − | 0.0195927i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −41.0490 | −1.67026 | ||||||||
\(605\) | 8.57632 | + | 47.4894i | 0.348677 | + | 1.93072i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.26926 | − | 6.98406i | 0.0921063 | − | 0.283474i | −0.894382 | − | 0.447303i | \(-0.852385\pi\) |
0.986489 | + | 0.163829i | \(0.0523845\pi\) | |||||||
\(608\) | −5.37507 | + | 3.90522i | −0.217988 | + | 0.158377i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.04406 | − | 6.29096i | −0.0827615 | − | 0.254714i | ||||
\(611\) | −2.41955 | − | 7.44662i | −0.0978846 | − | 0.301258i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.3337 | + | 11.1406i | −0.619323 | + | 0.449965i | −0.852685 | − | 0.522425i | \(-0.825027\pi\) |
0.233362 | + | 0.972390i | \(0.425027\pi\) | |||||||
\(614\) | 0.883853 | − | 2.72022i | 0.0356694 | − | 0.109779i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.13208 | − | 0.144660i | −0.0859041 | − | 0.00582852i | ||||
\(617\) | −25.2571 | −1.01681 | −0.508407 | − | 0.861117i | \(-0.669766\pi\) | ||||
−0.508407 | + | 0.861117i | \(0.669766\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.5984 | − | 9.15329i | 0.506373 | − | 0.367902i | −0.305073 | − | 0.952329i | \(-0.598681\pi\) |
0.811446 | + | 0.584427i | \(0.198681\pi\) | |||||||
\(620\) | 30.3633 | + | 22.0603i | 1.21942 | + | 0.885962i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.613373 | − | 1.88777i | −0.0245940 | − | 0.0756926i | ||||
\(623\) | 9.87858 | + | 7.17721i | 0.395777 | + | 0.287549i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 32.9796 | − | 101.501i | 1.31918 | − | 4.06003i | ||||
\(626\) | −0.512306 | −0.0204759 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.4668 | −0.457573 | ||||||||
\(629\) | −1.85336 | + | 5.70405i | −0.0738983 | + | 0.227436i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.1383 | + | 21.1702i | 1.15998 | + | 0.842773i | 0.989775 | − | 0.142636i | \(-0.0455579\pi\) |
0.170202 | + | 0.985409i | \(0.445558\pi\) | |||||||
\(632\) | −0.133525 | − | 0.410948i | −0.00531134 | − | 0.0163466i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.10632 | − | 0.803791i | −0.0439377 | − | 0.0319226i | ||||
\(635\) | 56.9696 | − | 41.3908i | 2.26077 | − | 1.64254i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.67571 | 0.0663939 | ||||||||
\(638\) | 4.03888 | − | 2.53540i | 0.159901 | − | 0.100378i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.80484 | − | 20.9432i | 0.268985 | − | 0.827851i | ||||
\(641\) | −21.6339 | + | 15.7179i | −0.854487 | + | 0.620821i | −0.926380 | − | 0.376591i | \(-0.877096\pi\) |
0.0718924 | + | 0.997412i | \(0.477096\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.26004 | + | 6.95569i | 0.0891273 | + | 0.274306i | 0.985679 | − | 0.168634i | \(-0.0539356\pi\) |
−0.896551 | + | 0.442940i | \(0.853936\pi\) | |||||||
\(644\) | −0.346792 | − | 1.06731i | −0.0136655 | − | 0.0420581i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.82040 | − | 2.04914i | 0.110967 | − | 0.0806224i | ||||
\(647\) | 10.8224 | − | 33.3080i | 0.425474 | − | 1.30947i | −0.477067 | − | 0.878867i | \(-0.658300\pi\) |
0.902540 | − | 0.430606i | \(-0.141700\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.25098 | − | 6.05879i | −0.284626 | − | 0.237828i | ||||
\(650\) | −3.87086 | −0.151828 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.2161 | + | 10.3286i | −0.556745 | + | 0.404499i | ||||
\(653\) | −3.27764 | − | 2.38134i | −0.128264 | − | 0.0931891i | 0.521804 | − | 0.853066i | \(-0.325259\pi\) |
−0.650067 | + | 0.759877i | \(0.725259\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.01694 | − | 3.12982i | −0.0397352 | − | 0.122292i | ||||
\(656\) | 17.9615 | + | 13.0498i | 0.701279 | + | 0.509509i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.234124 | + | 0.720561i | −0.00912712 | + | 0.0280904i | ||||
\(659\) | −28.6360 | −1.11550 | −0.557750 | − | 0.830009i | \(-0.688335\pi\) | ||||
−0.557750 | + | 0.830009i | \(0.688335\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.2741 | 1.76096 | 0.880479 | − | 0.474085i | \(-0.157221\pi\) | ||||
0.880479 | + | 0.474085i | \(0.157221\pi\) | |||||||
\(662\) | −0.307294 | + | 0.945753i | −0.0119433 | + | 0.0367577i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.84001 | − | 3.51648i | −0.187829 | − | 0.136466i | ||||
\(665\) | 4.71135 | + | 14.5000i | 0.182698 | + | 0.562287i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.07904 | + | 2.96360i | 0.157941 | + | 0.114751i | ||||
\(668\) | 6.10530 | − | 4.43576i | 0.236221 | − | 0.171625i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.08099 | 0.196296 | ||||||||
\(671\) | 7.52291 | + | 29.9091i | 0.290419 | + | 1.15463i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.0157313 | − | 0.0484159i | 0.000606396 | − | 0.00186630i | −0.950753 | − | 0.309950i | \(-0.899688\pi\) |
0.951359 | + | 0.308084i | \(0.0996877\pi\) | |||||||
\(674\) | −3.91956 | + | 2.84772i | −0.150976 | + | 0.109690i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.21620 | + | 19.1315i | 0.239085 | + | 0.735827i | ||||
\(677\) | −12.0961 | − | 37.2279i | −0.464890 | − | 1.43079i | −0.859121 | − | 0.511773i | \(-0.828989\pi\) |
0.394230 | − | 0.919012i | \(-0.371011\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.1835 | − | 8.85182i | 0.467559 | − | 0.339702i | ||||
\(680\) | −5.40399 | + | 16.6318i | −0.207234 | + | 0.637800i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.78874 | + | 1.49464i | 0.0684945 | + | 0.0572328i | ||||
\(683\) | −15.4140 | −0.589800 | −0.294900 | − | 0.955528i | \(-0.595286\pi\) | ||||
−0.294900 | + | 0.955528i | \(0.595286\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −46.1688 | + | 33.5436i | −1.76402 | + | 1.28164i | ||||
\(686\) | −0.131180 | − | 0.0953077i | −0.00500847 | − | 0.00363887i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.98977 | − | 18.4346i | −0.228358 | − | 0.702814i | ||||
\(689\) | −3.22491 | − | 2.34303i | −0.122859 | − | 0.0892624i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.8275 | + | 36.4013i | −0.449939 | + | 1.38477i | 0.427036 | + | 0.904235i | \(0.359558\pi\) |
−0.876975 | + | 0.480536i | \(0.840442\pi\) | |||||||
\(692\) | 3.45520 | 0.131347 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.73010 | −0.179552 | ||||||||
\(695\) | 5.28865 | − | 16.2768i | 0.200610 | − | 0.617414i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.9157 | − | 21.0085i | −1.09526 | − | 0.795752i | ||||
\(698\) | −0.671045 | − | 2.06526i | −0.0253994 | − | 0.0781714i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −22.7479 | − | 16.5273i | −0.859789 | − | 0.624673i | ||||
\(701\) | −1.12351 | + | 0.816275i | −0.0424342 | + | 0.0308303i | −0.608800 | − | 0.793324i | \(-0.708349\pi\) |
0.566366 | + | 0.824154i | \(0.308349\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.36909 | −0.127068 | ||||||||
\(704\) | −9.11711 | + | 22.7007i | −0.343614 | + | 0.855564i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.06814 | + | 3.28740i | −0.0402000 | + | 0.123723i | ||||
\(707\) | −4.66057 | + | 3.38611i | −0.175279 | + | 0.127348i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.96659 | − | 12.2079i | −0.148968 | − | 0.458477i | 0.848532 | − | 0.529145i | \(-0.177487\pi\) |
−0.997500 | + | 0.0706674i | \(0.977487\pi\) | |||||||
\(710\) | −0.174643 | − | 0.537496i | −0.00655424 | − | 0.0201719i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.36503 | + | 4.62446i | −0.238539 | + | 0.173309i | ||||
\(713\) | −0.761591 | + | 2.34394i | −0.0285218 | + | 0.0877811i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.3259 | + | 1.65049i | 0.909739 | + | 0.0617250i | ||||
\(716\) | −25.3702 | −0.948131 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.70538 | − | 1.96557i | 0.100964 | − | 0.0733545i | ||||
\(719\) | −17.3983 | − | 12.6406i | −0.648849 | − | 0.471416i | 0.214030 | − | 0.976827i | \(-0.431341\pi\) |
−0.862879 | + | 0.505411i | \(0.831341\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.38391 | − | 7.33692i | −0.0887814 | − | 0.273241i | ||||
\(722\) | −0.908083 | − | 0.659761i | −0.0337953 | − | 0.0245537i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.4687 | − | 41.4524i | 0.500560 | − | 1.54057i | ||||
\(725\) | 126.327 | 4.69168 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.35770 | −0.198706 | −0.0993531 | − | 0.995052i | \(-0.531677\pi\) | ||||
−0.0993531 | + | 0.995052i | \(0.531677\pi\) | |||||||
\(728\) | −0.333646 | + | 1.02686i | −0.0123657 | + | 0.0380578i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.37373 | + | 0.998076i | 0.0508441 | + | 0.0369404i | ||||
\(731\) | 9.64275 | + | 29.6773i | 0.356650 | + | 1.09766i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.5342 | − | 24.3640i | −1.23861 | − | 0.899906i | −0.241109 | − | 0.970498i | \(-0.577511\pi\) |
−0.997505 | + | 0.0705923i | \(0.977511\pi\) | |||||||
\(734\) | 4.30985 | − | 3.13129i | 0.159080 | − | 0.115578i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.08703 | 0.0400683 | ||||||||
\(737\) | −23.6355 | − | 1.60365i | −0.870625 | − | 0.0590711i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.1668 | − | 40.5231i | 0.484347 | − | 1.49067i | −0.348576 | − | 0.937280i | \(-0.613335\pi\) |
0.832924 | − | 0.553388i | \(-0.186665\pi\) | |||||||
\(740\) | 6.79105 | − | 4.93399i | 0.249644 | − | 0.181377i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.119194 | + | 0.366841i | 0.00437574 | + | 0.0134671i | ||||
\(743\) | 9.40891 | + | 28.9576i | 0.345179 | + | 1.06235i | 0.961488 | + | 0.274848i | \(0.0886275\pi\) |
−0.616308 | + | 0.787505i | \(0.711372\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 65.8143 | − | 47.8169i | 2.41125 | − | 1.75188i | ||||
\(746\) | −1.30767 | + | 4.02459i | −0.0478772 | + | 0.147351i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 15.0931 | − | 37.5804i | 0.551860 | − | 1.37407i | ||||
\(749\) | −16.4634 | −0.601561 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.33483 | + | 5.32907i | −0.267652 | + | 0.194460i | −0.713514 | − | 0.700641i | \(-0.752897\pi\) |
0.445862 | + | 0.895102i | \(0.352897\pi\) | |||||||
\(752\) | 14.5270 | + | 10.5545i | 0.529746 | + | 0.384883i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.744538 | − | 2.29145i | −0.0271145 | − | 0.0834498i | ||||
\(755\) | −73.8159 | − | 53.6304i | −2.68644 | − | 1.95181i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.41984 | − | 7.44750i | 0.0879505 | − | 0.270684i | −0.897402 | − | 0.441214i | \(-0.854548\pi\) |
0.985352 | + | 0.170530i | \(0.0545480\pi\) | |||||||
\(758\) | 1.89279 | 0.0687493 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9.82355 | −0.356338 | ||||||||
\(761\) | −8.18844 | + | 25.2014i | −0.296831 | + | 0.913551i | 0.685770 | + | 0.727819i | \(0.259466\pi\) |
−0.982600 | + | 0.185732i | \(0.940534\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.88270 | + | 5.72712i | 0.285373 | + | 0.207336i | ||||
\(764\) | 8.97540 | + | 27.6235i | 0.324719 | + | 0.999381i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.01625 | + | 1.46489i | 0.0728500 | + | 0.0529287i | ||||
\(767\) | −3.86233 | + | 2.80615i | −0.139461 | + | 0.101324i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.3995 | −0.951989 | −0.475995 | − | 0.879448i | \(-0.657912\pi\) | ||||
−0.475995 | + | 0.879448i | \(0.657912\pi\) | |||||||
\(770\) | −1.81044 | − | 1.51277i | −0.0652438 | − | 0.0545166i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.19208 | + | 15.9796i | −0.186867 | + | 0.575117i | ||||
\(773\) | 27.6333 | − | 20.0768i | 0.993901 | − | 0.722111i | 0.0331288 | − | 0.999451i | \(-0.489453\pi\) |
0.960772 | + | 0.277340i | \(0.0894528\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19.0818 | + | 58.7277i | 0.685438 | + | 2.10956i | ||||
\(776\) | 2.99848 | + | 9.22838i | 0.107639 | + | 0.331280i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.26513 | − | 0.919171i | 0.0453571 | − | 0.0329539i | ||||
\(779\) | 6.20431 | − | 19.0949i | 0.222293 | − | 0.684146i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.642753 | + | 2.55542i | 0.0229995 | + | 0.0914401i | ||||
\(782\) | −0.570383 | −0.0203969 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.10900 | + | 2.25882i | −0.111036 | + | 0.0806723i | ||||
\(785\) | −20.6200 | − | 14.9813i | −0.735959 | − | 0.534705i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.63104 | + | 11.1752i | 0.129433 | + | 0.398353i | 0.994683 | − | 0.102988i | \(-0.0328404\pi\) |
−0.865250 | + | 0.501341i | \(0.832840\pi\) | |||||||
\(788\) | 7.54108 | + | 5.47891i | 0.268640 | + | 0.195178i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.147414 | − | 0.453695i | 0.00524477 | − | 0.0161417i | ||||
\(791\) | −2.85725 | −0.101592 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.5821 | 0.553337 | ||||||||
\(794\) | −1.01643 | + | 3.12825i | −0.0360718 | + | 0.111017i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26.7649 | + | 19.4458i | 0.948656 | + | 0.689239i | ||||
\(797\) | −4.72880 | − | 14.5537i | −0.167503 | − | 0.515520i | 0.831709 | − | 0.555211i | \(-0.187363\pi\) |
−0.999212 | + | 0.0396911i | \(0.987363\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.3866 | − | 16.9913i | −0.827358 | − | 0.601111i | ||||
\(800\) | 22.0341 | − | 16.0087i | 0.779022 | − | 0.565992i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.32256 | −0.0467013 | ||||||||
\(803\) | −6.07526 | − | 5.07637i | −0.214391 | − | 0.179141i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.770830 | − | 2.37237i | 0.0271682 | − | 0.0836151i | ||||
\(806\) | 0.952798 | − | 0.692248i | 0.0335609 | − | 0.0243834i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.14702 | − | 3.53015i | −0.0403519 | − | 0.124190i | ||||
\(809\) | −5.63373 | − | 17.3388i | −0.198071 | − | 0.609601i | −0.999927 | − | 0.0120833i | \(-0.996154\pi\) |
0.801856 | − | 0.597518i | \(-0.203846\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.04254 | + | 3.66362i | −0.177068 | + | 0.128647i | −0.672789 | − | 0.739835i | \(-0.734904\pi\) |
0.495721 | + | 0.868482i | \(0.334904\pi\) | |||||||
\(812\) | 5.40832 | − | 16.6451i | 0.189795 | − | 0.584129i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.441557 | − | 0.277187i | 0.0154766 | − | 0.00971539i | ||||
\(815\) | −39.0582 | −1.36815 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.1812 | + | 10.3032i | −0.496136 | + | 0.360464i | ||||
\(818\) | −1.26878 | − | 0.921825i | −0.0443619 | − | 0.0322308i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15.4582 | + | 47.5755i | 0.539825 | + | 1.66141i | ||||
\(821\) | −23.9791 | − | 17.4219i | −0.836878 | − | 0.608027i | 0.0846188 | − | 0.996413i | \(-0.473033\pi\) |
−0.921497 | + | 0.388386i | \(0.873033\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.09698 | + | 18.7646i | −0.212527 | + | 0.654092i | 0.786793 | + | 0.617217i | \(0.211740\pi\) |
−0.999320 | + | 0.0368743i | \(0.988260\pi\) | |||||||
\(824\) | 4.97065 | 0.173161 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.461960 | 0.0160736 | ||||||||
\(827\) | −12.7225 | + | 39.1560i | −0.442406 | + | 1.36159i | 0.442897 | + | 0.896572i | \(0.353951\pi\) |
−0.885303 | + | 0.465014i | \(0.846049\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.4424 | − | 13.3992i | −0.640532 | − | 0.465374i | 0.219501 | − | 0.975612i | \(-0.429557\pi\) |
−0.860033 | + | 0.510238i | \(0.829557\pi\) | |||||||
\(830\) | −2.04102 | − | 6.28163i | −0.0708450 | − | 0.218038i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 9.99931 | + | 7.26492i | 0.346664 | + | 0.251866i | ||||
\(833\) | 5.00509 | − | 3.63641i | 0.173416 | − | 0.125994i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.7741 | 0.580492 | ||||||||
\(836\) | 22.6972 | + | 1.53998i | 0.784998 | + | 0.0532615i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.948799 | + | 2.92010i | −0.0327757 | + | 0.100873i | ||||
\(839\) | −38.2442 | + | 27.7861i | −1.32034 | + | 0.959281i | −0.320409 | + | 0.947279i | \(0.603820\pi\) |
−0.999928 | + | 0.0120017i | \(0.996180\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.3369 | + | 47.2021i | 0.528858 | + | 1.62766i | ||||
\(842\) | 0.656139 | + | 2.01939i | 0.0226121 | + | 0.0695928i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.1998 | + | 11.7699i | −0.557622 | + | 0.405136i | ||||
\(845\) | −13.8170 | + | 42.5245i | −0.475321 | + | 1.46289i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.94427 | + | 7.60845i | 0.272968 | + | 0.261430i | ||||
\(848\) | 9.14167 | 0.313926 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −11.5617 | + | 8.40006i | −0.396563 | + | 0.288120i | ||||
\(851\) | 0.445948 | + | 0.324000i | 0.0152869 | + | 0.0111066i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.35434 | + | 10.3236i | 0.114850 | + | 0.353473i | 0.991916 | − | 0.126898i | \(-0.0405020\pi\) |
−0.877065 | + | 0.480371i | \(0.840502\pi\) | |||||||
\(854\) | −1.21982 | − | 0.886250i | −0.0417413 | − | 0.0303269i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.27799 | − | 10.0886i | 0.112040 | − | 0.344822i | ||||
\(857\) | −28.5431 | −0.975014 | −0.487507 | − | 0.873119i | \(-0.662094\pi\) | ||||
−0.487507 | + | 0.873119i | \(0.662094\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.8034 | −1.25572 | −0.627858 | − | 0.778328i | \(-0.716068\pi\) | ||||
−0.627858 | + | 0.778328i | \(0.716068\pi\) | |||||||
\(860\) | 13.4959 | − | 41.5362i | 0.460207 | − | 1.41637i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.13868 | + | 1.55384i | 0.0728438 | + | 0.0529241i | ||||
\(863\) | 13.9537 | + | 42.9451i | 0.474990 | + | 1.46187i | 0.845972 | + | 0.533228i | \(0.179021\pi\) |
−0.370982 | + | 0.928640i | \(0.620979\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.21327 | + | 4.51421i | 0.211258 | + | 0.153488i | ||||
\(866\) | 1.53274 | − | 1.11360i | 0.0520845 | − | 0.0378416i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.55498 | 0.290375 | ||||||||
\(869\) | −0.828929 | + | 2.06395i | −0.0281195 | + | 0.0700146i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.69867 | + | 11.3833i | −0.125325 | + | 0.385710i | ||||
\(872\) | −5.07903 | + | 3.69013i | −0.171998 | + | 0.124964i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.0990113 | − | 0.304726i | −0.00334911 | − | 0.0103075i | ||||
\(875\) | −12.5349 | − | 38.5784i | −0.423757 | − | 1.30419i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.1956 | + | 20.4853i | −0.952097 | + | 0.691739i | −0.951302 | − | 0.308261i | \(-0.900253\pi\) |
−0.000795243 | 1.00000i | \(0.500253\pi\) | ||||||||
\(878\) | −0.587103 | + | 1.80692i | −0.0198138 | + | 0.0609805i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −47.3578 | + | 29.7287i | −1.59643 | + | 1.00216i | ||||
\(881\) | 35.3563 | 1.19118 | 0.595592 | − | 0.803287i | \(-0.296917\pi\) | ||||
0.595592 | + | 0.803287i | \(0.296917\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.1340 | − | 14.6282i | 0.677565 | − | 0.492279i | −0.194984 | − | 0.980806i | \(-0.562466\pi\) |
0.872549 | + | 0.488527i | \(0.162466\pi\) | |||||||
\(884\) | −16.5536 | − | 12.0269i | −0.556758 | − | 0.404508i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.629690 | − | 1.93799i | −0.0211549 | − | 0.0651080i | ||||
\(887\) | −40.1036 | − | 29.1370i | −1.34655 | − | 0.978324i | −0.999176 | − | 0.0405971i | \(-0.987074\pi\) |
−0.347372 | − | 0.937727i | \(-0.612926\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.96015 | − | 15.2658i | 0.166358 | − | 0.511998i | ||||
\(890\) | −8.68599 | −0.291155 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.0628 | 0.403891 | ||||||||
\(893\) | 5.01796 | − | 15.4437i | 0.167920 | − | 0.516804i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −45.6218 | − | 33.1462i | −1.52497 | − | 1.10795i | ||||
\(896\) | −1.55112 | − | 4.77385i | −0.0518193 | − | 0.159483i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.09049 | + | 1.51883i | 0.0697605 | + | 0.0506839i | ||||
\(899\) | −31.0950 | + | 22.5919i | −1.03708 | + | 0.753481i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.7169 | −0.490291 | ||||||||
\(902\) | 0.757859 | + | 3.01305i | 0.0252340 | + | 0.100324i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.568899 | − | 1.75089i | 0.0189213 | − | 0.0582338i | ||||
\(905\) | 78.3774 | − | 56.9445i | 2.60535 | − | 1.89290i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.441357 | − | 1.35836i | −0.0146550 | − | 0.0451035i | 0.943462 | − | 0.331482i | \(-0.107549\pi\) |
−0.958117 | + | 0.286378i | \(0.907549\pi\) | |||||||
\(908\) | 8.66617 | + | 26.6717i | 0.287597 | + | 0.885133i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.964357 | + | 0.700646i | −0.0319681 | + | 0.0232262i | ||||
\(911\) | −16.7402 | + | 51.5211i | −0.554628 | + | 1.70697i | 0.142294 | + | 0.989824i | \(0.454552\pi\) |
−0.696922 | + | 0.717147i | \(0.745448\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.51175 | + | 29.8648i | 0.248603 | + | 0.988379i | ||||
\(914\) | 3.85821 | 0.127618 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.35567 | + | 3.16458i | −0.143916 | + | 0.104561i | ||||
\(917\) | −0.606873 | − | 0.440919i | −0.0200407 | − | 0.0145604i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.07678 | − | 21.7801i | −0.233441 | − | 0.718459i | −0.997324 | − | 0.0731040i | \(-0.976710\pi\) |
0.763883 | − | 0.645355i | \(-0.223290\pi\) | |||||||
\(920\) | 1.30029 | + | 0.944714i | 0.0428692 | + | 0.0311463i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.13258 | + | 3.48571i | −0.0372994 | + | 0.114796i | ||||
\(923\) | 1.33133 | 0.0438211 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.8110 | 0.454101 | ||||||||
\(926\) | −0.152202 | + | 0.468430i | −0.00500167 | + | 0.0153936i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 13.7149 | + | 9.96443i | 0.450212 | + | 0.327099i | ||||
\(929\) | 4.49019 | + | 13.8194i | 0.147319 | + | 0.453400i | 0.997302 | − | 0.0734098i | \(-0.0233881\pi\) |
−0.849983 | + | 0.526810i | \(0.823388\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.81156 | + | 2.04272i | 0.0921452 | + | 0.0669474i | ||||
\(932\) | 28.4059 | − | 20.6381i | 0.930466 | − | 0.676023i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.73021 | −0.122056 | ||||||||
\(935\) | 76.2397 | − | 47.8594i | 2.49331 | − | 1.56517i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.46675 | − | 29.1357i | 0.309265 | − | 0.951821i | −0.668786 | − | 0.743455i | \(-0.733186\pi\) |
0.978051 | − | 0.208366i | \(-0.0668144\pi\) | |||||||
\(938\) | 0.936985 | − | 0.680760i | 0.0305937 | − | 0.0222276i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12.5024 | + | 38.4784i | 0.407783 | + | 1.25503i | ||||
\(941\) | −6.50584 | − | 20.0229i | −0.212084 | − | 0.652728i | −0.999348 | − | 0.0361114i | \(-0.988503\pi\) |
0.787264 | − | 0.616617i | \(-0.211497\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.65755 | + | 1.93083i | −0.0865419 | + | 0.0628764i | ||||
\(944\) | 3.38330 | − | 10.4127i | 0.110117 | − | 0.338905i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.01092 | − | 2.51708i | 0.0328678 | − | 0.0818375i | ||||
\(947\) | −0.729464 | −0.0237044 | −0.0118522 | − | 0.999930i | \(-0.503773\pi\) | ||||
−0.0118522 | + | 0.999930i | \(0.503773\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.23607 | + | 2.35114i | −0.105047 | + | 0.0763213i | ||||
\(950\) | −6.49467 | − | 4.71866i | −0.210715 | − | 0.153093i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.23180 | + | 3.79111i | 0.0399230 | + | 0.122870i | ||||
\(953\) | 31.5638 | + | 22.9325i | 1.02245 | + | 0.742856i | 0.966784 | − | 0.255594i | \(-0.0822709\pi\) |
0.0556689 | + | 0.998449i | \(0.482271\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.9501 | + | 61.3999i | −0.645569 | + | 1.98686i | ||||
\(956\) | 25.0775 | 0.811065 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.32520 | 0.0428153 | ||||||||
\(959\) | −4.01977 | + | 12.3716i | −0.129805 | + | 0.399499i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.88001 | + | 7.17825i | 0.318710 | + | 0.231556i | ||||
\(962\) | −0.0813978 | − | 0.250517i | −0.00262437 | − | 0.00807698i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −29.7963 | − | 21.6483i | −0.959673 | − | 0.697243i | ||||
\(965\) | −30.2139 | + | 21.9517i | −0.972619 | + | 0.706649i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.46386 | 0.0792324 | 0.0396162 | − | 0.999215i | \(-0.487386\pi\) | ||||
0.0396162 | + | 0.999215i | \(0.487386\pi\) | |||||||
\(968\) | −6.24415 | + | 3.35327i | −0.200695 | + | 0.107778i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.31039 | + | 10.1883i | −0.106290 | + | 0.327127i | ||||
\(971\) | 28.0562 | − | 20.3840i | 0.900367 | − | 0.654155i | −0.0381935 | − | 0.999270i | \(-0.512160\pi\) |
0.938560 | + | 0.345116i | \(0.112160\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.20551 | − | 3.71019i | −0.0386470 | − | 0.118943i | ||||
\(974\) | 0.0500677 | + | 0.154093i | 0.00160427 | + | 0.00493745i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −28.9101 | + | 21.0044i | −0.925390 | + | 0.672335i | ||||
\(977\) | 7.76676 | − | 23.9036i | 0.248481 | − | 0.764745i | −0.746564 | − | 0.665314i | \(-0.768298\pi\) |
0.995044 | − | 0.0994308i | \(-0.0317022\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 40.4051 | + | 2.74145i | 1.29135 | + | 0.0876171i | ||||
\(980\) | −8.65877 | −0.276594 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.18710 | + | 2.31557i | −0.101705 | + | 0.0738927i | ||||
\(983\) | 24.5860 | + | 17.8628i | 0.784172 | + | 0.569734i | 0.906228 | − | 0.422789i | \(-0.138949\pi\) |
−0.122056 | + | 0.992523i | \(0.538949\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.40248 | + | 19.7048i | 0.204000 | + | 0.627847i | ||||
\(986\) | −7.19646 | − | 5.22853i | −0.229182 | − | 0.166510i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.55184 | − | 10.9314i | 0.112999 | − | 0.347775i | ||||
\(989\) | 2.86792 | 0.0911947 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.09793 | −0.257239 | −0.128620 | − | 0.991694i | \(-0.541055\pi\) | ||||
−0.128620 | + | 0.991694i | \(0.541055\pi\) | |||||||
\(992\) | −2.56068 | + | 7.88096i | −0.0813016 | + | 0.250221i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.104221 | − | 0.0757207i | −0.00330568 | − | 0.00240172i | ||||
\(995\) | 22.7238 | + | 69.9365i | 0.720392 | + | 2.21714i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.1230 | + | 26.9715i | 1.17570 | + | 0.854194i | 0.991680 | − | 0.128728i | \(-0.0410896\pi\) |
0.184018 | + | 0.982923i | \(0.441090\pi\) | |||||||
\(998\) | −5.38896 | + | 3.91531i | −0.170585 | + | 0.123937i | ||||
\(999\) | 0 | 0 |
(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 | 693.2.m.f.64.2 | 8 | ||
3.2 | odd | 2 | 231.2.j.f.64.1 | ✓ | 8 | ||
11.4 | even | 5 | 7623.2.a.ci.1.3 | 4 | |||
11.5 | even | 5 | inner | 693.2.m.f.379.2 | 8 | ||
11.7 | odd | 10 | 7623.2.a.cl.1.2 | 4 | |||
33.5 | odd | 10 | 231.2.j.f.148.1 | yes | 8 | ||
33.26 | odd | 10 | 2541.2.a.bn.1.2 | 4 | |||
33.29 | even | 10 | 2541.2.a.bm.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.j.f.64.1 | ✓ | 8 | 3.2 | odd | 2 | ||
231.2.j.f.148.1 | yes | 8 | 33.5 | odd | 10 | ||
693.2.m.f.64.2 | 8 | 1.1 | even | 1 | trivial | ||
693.2.m.f.379.2 | 8 | 11.5 | even | 5 | inner | ||
2541.2.a.bm.1.3 | 4 | 33.29 | even | 10 | |||
2541.2.a.bn.1.2 | 4 | 33.26 | odd | 10 | |||
7623.2.a.ci.1.3 | 4 | 11.4 | even | 5 | |||
7623.2.a.cl.1.2 | 4 | 11.7 | odd | 10 |