Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,2,Mod(163,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.163");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.z (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.74922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 163.8 | ||
Root | \(0.0376504 + 1.41371i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 720.163 |
Dual form | 720.2.z.g.667.8 |
$q$-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 \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.29924 | − | 0.558542i | 0.918703 | − | 0.394949i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.37606 | − | 1.45136i | 0.688031 | − | 0.725681i | ||||
\(5\) | −1.49107 | + | 1.66635i | −0.666825 | + | 0.745214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.40368 | − | 2.40368i | 0.908504 | − | 0.908504i | −0.0876474 | − | 0.996152i | \(-0.527935\pi\) |
0.996152 | + | 0.0876474i | \(0.0279349\pi\) | |||||||
\(8\) | 0.977191 | − | 2.65426i | 0.345489 | − | 0.938423i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00653 | + | 2.99782i | −0.318293 | + | 0.947992i | ||||
\(11\) | 2.67707 | + | 2.67707i | 0.807167 | + | 0.807167i | 0.984204 | − | 0.177037i | \(-0.0566513\pi\) |
−0.177037 | + | 0.984204i | \(0.556651\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.40164i | − | 0.666094i | −0.942910 | − | 0.333047i | \(-0.891923\pi\) | ||
0.942910 | − | 0.333047i | \(-0.108077\pi\) | |||||||
\(14\) | 1.78040 | − | 4.46551i | 0.475833 | − | 1.19346i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.212908 | − | 3.99433i | −0.0532269 | − | 0.998582i | ||||
\(17\) | 0.0750544 | − | 0.0750544i | 0.0182034 | − | 0.0182034i | −0.697947 | − | 0.716150i | \(-0.745903\pi\) |
0.716150 | + | 0.697947i | \(0.245903\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.67236 | + | 2.67236i | 0.613081 | + | 0.613081i | 0.943748 | − | 0.330666i | \(-0.107274\pi\) |
−0.330666 | + | 0.943748i | \(0.607274\pi\) | |||||||
\(20\) | 0.366678 | + | 4.45708i | 0.0819918 | + | 0.996633i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.97342 | + | 1.98291i | 1.06034 | + | 0.422757i | ||||
\(23\) | −2.12375 | − | 2.12375i | −0.442833 | − | 0.442833i | 0.450130 | − | 0.892963i | \(-0.351378\pi\) |
−0.892963 | + | 0.450130i | \(0.851378\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.553442 | − | 4.96928i | −0.110688 | − | 0.993855i | ||||
\(26\) | −1.34141 | − | 3.12031i | −0.263073 | − | 0.611943i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.180999 | − | 6.79621i | −0.0342056 | − | 1.28436i | ||||
\(29\) | 3.95795 | − | 3.95795i | 0.734974 | − | 0.734974i | −0.236627 | − | 0.971601i | \(-0.576042\pi\) |
0.971601 | + | 0.236627i | \(0.0760419\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.65367i | 0.297008i | 0.988912 | + | 0.148504i | \(0.0474458\pi\) | ||||
−0.988912 | + | 0.148504i | \(0.952554\pi\) | |||||||
\(32\) | −2.50762 | − | 5.07068i | −0.443289 | − | 0.896379i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.0555929 | − | 0.139435i | 0.00953410 | − | 0.0239129i | ||||
\(35\) | 0.421324 | + | 7.58941i | 0.0712168 | + | 1.28284i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.53082i | 0.416064i | 0.978122 | + | 0.208032i | \(0.0667059\pi\) | ||||
−0.978122 | + | 0.208032i | \(0.933294\pi\) | |||||||
\(38\) | 4.96467 | + | 1.97942i | 0.805375 | + | 0.321104i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.96587 | + | 5.58602i | 0.468945 | + | 0.883227i | ||||
\(41\) | 1.70882i | 0.266873i | 0.991057 | + | 0.133436i | \(0.0426012\pi\) | ||||
−0.991057 | + | 0.133436i | \(0.957399\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 3.84601i | − | 0.586510i | −0.956034 | − | 0.293255i | \(-0.905261\pi\) | ||
0.956034 | − | 0.293255i | \(-0.0947386\pi\) | |||||||
\(44\) | 7.56921 | − | 0.201586i | 1.14110 | − | 0.0303902i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.94547 | − | 1.57306i | −0.581728 | − | 0.231936i | ||||
\(47\) | −2.15264 | − | 2.15264i | −0.313995 | − | 0.313995i | 0.532460 | − | 0.846455i | \(-0.321268\pi\) |
−0.846455 | + | 0.532460i | \(0.821268\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 4.55532i | − | 0.650760i | ||||||
\(50\) | −3.49460 | − | 6.14717i | −0.494212 | − | 0.869342i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.48565 | − | 3.30480i | −0.483372 | − | 0.458293i | ||||
\(53\) | 1.29475 | 0.177848 | 0.0889239 | − | 0.996038i | \(-0.471657\pi\) | ||||
0.0889239 | + | 0.996038i | \(0.471657\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.45262 | + | 0.469246i | −1.13975 | + | 0.0632731i | ||||
\(56\) | −4.03113 | − | 8.72883i | −0.538683 | − | 1.16644i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.93166 | − | 7.35302i | 0.384946 | − | 0.965499i | ||||
\(59\) | −5.29614 | + | 5.29614i | −0.689499 | + | 0.689499i | −0.962121 | − | 0.272622i | \(-0.912109\pi\) |
0.272622 | + | 0.962121i | \(0.412109\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.2413 | + | 10.2413i | 1.31126 | + | 1.31126i | 0.920484 | + | 0.390780i | \(0.127795\pi\) |
0.390780 | + | 0.920484i | \(0.372205\pi\) | |||||||
\(62\) | 0.923645 | + | 2.14852i | 0.117303 | + | 0.272862i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.09020 | − | 5.18744i | −0.761274 | − | 0.648430i | ||||
\(65\) | 4.00197 | + | 3.58100i | 0.496383 | + | 0.444168i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.6230i | 1.29780i | 0.760873 | + | 0.648901i | \(0.224771\pi\) | ||||
−0.760873 | + | 0.648901i | \(0.775229\pi\) | |||||||
\(68\) | −0.00565167 | − | 0.212211i | −0.000685365 | − | 0.0257343i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.78640 | + | 9.62515i | 0.572085 | + | 1.15043i | ||||
\(71\) | −2.27322 | −0.269781 | −0.134891 | − | 0.990860i | \(-0.543068\pi\) | ||||
−0.134891 | + | 0.990860i | \(0.543068\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.99096 | + | 9.99096i | −1.16935 | + | 1.16935i | −0.186992 | + | 0.982361i | \(0.559874\pi\) |
−0.982361 | + | 0.186992i | \(0.940126\pi\) | |||||||
\(74\) | 1.41357 | + | 3.28815i | 0.164324 | + | 0.382240i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.55589 | − | 0.201231i | 0.866720 | − | 0.0230828i | ||||
\(77\) | 12.8696 | 1.46663 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.70617 | −0.979520 | −0.489760 | − | 0.871857i | \(-0.662916\pi\) | ||||
−0.489760 | + | 0.871857i | \(0.662916\pi\) | |||||||
\(80\) | 6.97341 | + | 5.60103i | 0.779651 | + | 0.626214i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.954448 | + | 2.22017i | 0.105401 | + | 0.245177i | ||||
\(83\) | −11.1310 | −1.22178 | −0.610890 | − | 0.791715i | \(-0.709188\pi\) | ||||
−0.610890 | + | 0.791715i | \(0.709188\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0131558 | + | 0.236978i | 0.00142695 | + | 0.0257039i | ||||
\(86\) | −2.14816 | − | 4.99689i | −0.231642 | − | 0.538829i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.72165 | − | 4.48963i | 1.03633 | − | 0.478596i | ||||
\(89\) | −15.6390 | −1.65773 | −0.828866 | − | 0.559447i | \(-0.811014\pi\) | ||||
−0.828866 | + | 0.559447i | \(0.811014\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.77276 | − | 5.77276i | −0.605149 | − | 0.605149i | ||||
\(92\) | −6.00475 | + | 0.159920i | −0.626038 | + | 0.0166729i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.99914 | − | 1.59446i | −0.412480 | − | 0.164456i | ||||
\(95\) | −8.43775 | + | 0.468420i | −0.865695 | + | 0.0480589i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.00672 | − | 5.00672i | 0.508355 | − | 0.508355i | −0.405666 | − | 0.914021i | \(-0.632960\pi\) |
0.914021 | + | 0.405666i | \(0.132960\pi\) | |||||||
\(98\) | −2.54434 | − | 5.91846i | −0.257017 | − | 0.597855i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.97379 | − | 6.03478i | −0.797379 | − | 0.603478i | ||||
\(101\) | −6.37101 | + | 6.37101i | −0.633939 | + | 0.633939i | −0.949054 | − | 0.315115i | \(-0.897957\pi\) |
0.315115 | + | 0.949054i | \(0.397957\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.93695 | − | 1.93695i | −0.190854 | − | 0.190854i | 0.605211 | − | 0.796065i | \(-0.293089\pi\) |
−0.796065 | + | 0.605211i | \(0.793089\pi\) | |||||||
\(104\) | −6.37457 | − | 2.34686i | −0.625078 | − | 0.230128i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.68220 | − | 0.723173i | 0.163389 | − | 0.0702408i | ||||
\(107\) | −6.97778 | −0.674568 | −0.337284 | − | 0.941403i | \(-0.609508\pi\) | ||||
−0.337284 | + | 0.941403i | \(0.609508\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.277748 | − | 0.277748i | 0.0266034 | − | 0.0266034i | −0.693680 | − | 0.720283i | \(-0.744012\pi\) |
0.720283 | + | 0.693680i | \(0.244012\pi\) | |||||||
\(110\) | −10.7199 | + | 5.33081i | −1.02210 | + | 0.508273i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −10.1128 | − | 9.08931i | −0.955573 | − | 0.858859i | ||||
\(113\) | 8.75577 | + | 8.75577i | 0.823674 | + | 0.823674i | 0.986633 | − | 0.162959i | \(-0.0521038\pi\) |
−0.162959 | + | 0.986633i | \(0.552104\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.70557 | − | 0.372258i | 0.625298 | − | 0.0347133i | ||||
\(116\) | −0.298037 | − | 11.1908i | −0.0276721 | − | 1.03904i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.92286 | + | 9.83909i | −0.361128 | + | 0.905762i | ||||
\(119\) | − | 0.360813i | − | 0.0330757i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.33340i | 0.303036i | ||||||||
\(122\) | 19.0261 | + | 7.58574i | 1.72254 | + | 0.686780i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.40008 | + | 2.27555i | 0.215533 | + | 0.204351i | ||||
\(125\) | 9.10577 | + | 6.48729i | 0.814445 | + | 0.580241i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.679502 | − | 0.679502i | −0.0602961 | − | 0.0602961i | 0.676316 | − | 0.736612i | \(-0.263576\pi\) |
−0.736612 | + | 0.676316i | \(0.763576\pi\) | |||||||
\(128\) | −10.8100 | − | 3.33811i | −0.955482 | − | 0.295050i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.19966 | + | 2.41732i | 0.631452 | + | 0.212013i | ||||
\(131\) | 5.43859 | − | 5.43859i | 0.475172 | − | 0.475172i | −0.428412 | − | 0.903584i | \(-0.640927\pi\) |
0.903584 | + | 0.428412i | \(0.140927\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.8470 | 1.11397 | ||||||||
\(134\) | 5.93337 | + | 13.8018i | 0.512565 | + | 1.19229i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.125871 | − | 0.272557i | −0.0107934 | − | 0.0233715i | ||||
\(137\) | 7.47496 | + | 7.47496i | 0.638629 | + | 0.638629i | 0.950217 | − | 0.311588i | \(-0.100861\pi\) |
−0.311588 | + | 0.950217i | \(0.600861\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.5307 | + | 11.5307i | −0.978023 | + | 0.978023i | −0.999764 | − | 0.0217404i | \(-0.993079\pi\) |
0.0217404 | + | 0.999764i | \(0.493079\pi\) | |||||||
\(140\) | 11.5947 | + | 9.83200i | 0.979935 | + | 0.830955i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.95346 | + | 1.26969i | −0.247849 | + | 0.106550i | ||||
\(143\) | 6.42935 | − | 6.42935i | 0.537649 | − | 0.537649i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.693763 | + | 12.4969i | 0.0576139 | + | 1.03781i | ||||
\(146\) | −7.40031 | + | 18.5611i | −0.612454 | + | 1.53612i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.67314 | + | 3.48257i | 0.301930 | + | 0.286265i | ||||
\(149\) | −5.51174 | − | 5.51174i | −0.451539 | − | 0.451539i | 0.444326 | − | 0.895865i | \(-0.353443\pi\) |
−0.895865 | + | 0.444326i | \(0.853443\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.13617 | −0.336597 | −0.168299 | − | 0.985736i | \(-0.553827\pi\) | ||||
−0.168299 | + | 0.985736i | \(0.553827\pi\) | |||||||
\(152\) | 9.70454 | − | 4.48173i | 0.787142 | − | 0.363516i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 16.7207 | − | 7.18822i | 1.34740 | − | 0.579243i | ||||
\(155\) | −2.75559 | − | 2.46573i | −0.221335 | − | 0.198052i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.2700 | 1.61772 | 0.808861 | − | 0.587999i | \(-0.200084\pi\) | ||||
0.808861 | + | 0.587999i | \(0.200084\pi\) | |||||||
\(158\) | −11.3114 | + | 4.86276i | −0.899889 | + | 0.386860i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.1886 | + | 3.38216i | 0.963590 | + | 0.267383i | ||||
\(161\) | −10.2096 | −0.804631 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.1835 | −1.03262 | −0.516308 | − | 0.856403i | \(-0.672694\pi\) | ||||
−0.516308 | + | 0.856403i | \(0.672694\pi\) | |||||||
\(164\) | 2.48012 | + | 2.35144i | 0.193665 | + | 0.183617i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.4618 | + | 6.21710i | −1.12245 | + | 0.482541i | ||||
\(167\) | 11.8190 | − | 11.8190i | 0.914585 | − | 0.914585i | −0.0820441 | − | 0.996629i | \(-0.526145\pi\) |
0.996629 | + | 0.0820441i | \(0.0261448\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.23214 | 0.556319 | ||||||||
\(170\) | 0.149455 | + | 0.300544i | 0.0114627 | + | 0.0230507i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.58195 | − | 5.29234i | −0.425620 | − | 0.403537i | ||||
\(173\) | − | 15.5763i | − | 1.18424i | −0.805849 | − | 0.592120i | \(-0.798291\pi\) | ||
0.805849 | − | 0.592120i | \(-0.201709\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.2748 | − | 10.6142i | −1.00348 | − | 0.802361i | ||||
\(176\) | 10.1231 | − | 11.2631i | 0.763060 | − | 0.848986i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −20.3189 | + | 8.73505i | −1.52296 | + | 0.654719i | ||||
\(179\) | 15.5963 | + | 15.5963i | 1.16572 | + | 1.16572i | 0.983202 | + | 0.182523i | \(0.0584265\pi\) |
0.182523 | + | 0.983202i | \(0.441574\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.98705 | − | 2.98705i | 0.222026 | − | 0.222026i | −0.587325 | − | 0.809351i | \(-0.699819\pi\) |
0.809351 | + | 0.587325i | \(0.199819\pi\) | |||||||
\(182\) | −10.7245 | − | 4.27588i | −0.794955 | − | 0.316950i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.71230 | + | 3.56168i | −0.568559 | + | 0.262571i | ||||
\(185\) | −4.21723 | − | 3.77362i | −0.310057 | − | 0.277442i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.401852 | 0.0293863 | ||||||||
\(188\) | −6.08643 | + | 0.162096i | −0.443899 | + | 0.0118221i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.7010 | + | 5.32143i | −0.776336 | + | 0.386057i | ||||
\(191\) | 6.47168i | 0.468274i | 0.972204 | + | 0.234137i | \(0.0752264\pi\) | ||||
−0.972204 | + | 0.234137i | \(0.924774\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.1131 | − | 11.1131i | −0.799936 | − | 0.799936i | 0.183149 | − | 0.983085i | \(-0.441371\pi\) |
−0.983085 | + | 0.183149i | \(0.941371\pi\) | |||||||
\(194\) | 3.70848 | − | 9.30141i | 0.266253 | − | 0.667802i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.61142 | − | 6.26840i | −0.472244 | − | 0.447743i | ||||
\(197\) | − | 25.0927i | − | 1.78778i | −0.448288 | − | 0.893889i | \(-0.647966\pi\) | ||
0.448288 | − | 0.893889i | \(-0.352034\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.7579i | 1.32972i | 0.746970 | + | 0.664858i | \(0.231508\pi\) | ||||
−0.746970 | + | 0.664858i | \(0.768492\pi\) | |||||||
\(200\) | −13.7306 | − | 3.38695i | −0.970898 | − | 0.239494i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.71901 | + | 11.8360i | −0.332028 | + | 0.832775i | ||||
\(203\) | − | 19.0273i | − | 1.33545i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.84749 | − | 2.54796i | −0.198877 | − | 0.177958i | ||||
\(206\) | −3.59844 | − | 1.43470i | −0.250715 | − | 0.0999604i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −9.59293 | + | 0.511327i | −0.665150 | + | 0.0354541i | ||||
\(209\) | 14.3082i | 0.989718i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.38863 | − | 6.38863i | 0.439811 | − | 0.439811i | −0.452137 | − | 0.891948i | \(-0.649338\pi\) |
0.891948 | + | 0.452137i | \(0.149338\pi\) | |||||||
\(212\) | 1.78166 | − | 1.87915i | 0.122365 | − | 0.129061i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.06583 | + | 3.89738i | −0.619727 | + | 0.266420i | ||||
\(215\) | 6.40879 | + | 5.73465i | 0.437076 | + | 0.391100i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.97489 | + | 3.97489i | 0.269833 | + | 0.269833i | ||||
\(218\) | 0.205728 | − | 0.515996i | 0.0139337 | − | 0.0349476i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −10.9503 | + | 12.9135i | −0.738268 | + | 0.870630i | ||||
\(221\) | −0.180253 | − | 0.180253i | −0.0121252 | − | 0.0121252i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.29779 | + | 4.29779i | −0.287801 | + | 0.287801i | −0.836210 | − | 0.548409i | \(-0.815234\pi\) |
0.548409 | + | 0.836210i | \(0.315234\pi\) | |||||||
\(224\) | −18.2158 | − | 6.16078i | −1.21709 | − | 0.411634i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.2663 | + | 6.48541i | 1.08202 | + | 0.431403i | ||||
\(227\) | 29.1029i | 1.93163i | 0.259241 | + | 0.965813i | \(0.416528\pi\) | ||||
−0.259241 | + | 0.965813i | \(0.583472\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.3405 | − | 18.3405i | −1.21198 | − | 1.21198i | −0.970376 | − | 0.241600i | \(-0.922328\pi\) |
−0.241600 | − | 0.970376i | \(-0.577672\pi\) | |||||||
\(230\) | 8.50424 | − | 4.22900i | 0.560753 | − | 0.278852i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.63776 | − | 14.3731i | −0.435790 | − | 0.943641i | ||||
\(233\) | −1.46663 | + | 1.46663i | −0.0960824 | + | 0.0960824i | −0.753514 | − | 0.657432i | \(-0.771643\pi\) |
0.657432 | + | 0.753514i | \(0.271643\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.79678 | − | 0.377322i | 0.443373 | − | 0.0246138i | ||||
\(236\) | 0.398804 | + | 14.9744i | 0.0259600 | + | 0.974754i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.201529 | − | 0.468784i | −0.0130632 | − | 0.0303867i | ||||
\(239\) | −12.5432 | −0.811352 | −0.405676 | − | 0.914017i | \(-0.632964\pi\) | ||||
−0.405676 | + | 0.914017i | \(0.632964\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.8870 | 0.958954 | 0.479477 | − | 0.877554i | \(-0.340826\pi\) | ||||
0.479477 | + | 0.877554i | \(0.340826\pi\) | |||||||
\(242\) | 1.86184 | + | 4.33089i | 0.119684 | + | 0.278400i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 28.9565 | − | 0.771179i | 1.85375 | − | 0.0493697i | ||||
\(245\) | 7.59075 | + | 6.79228i | 0.484955 | + | 0.433943i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.41803 | − | 6.41803i | 0.408370 | − | 0.408370i | ||||
\(248\) | 4.38927 | + | 1.61595i | 0.278719 | + | 0.102613i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 15.4540 | + | 3.34261i | 0.977399 | + | 0.211405i | ||||
\(251\) | 5.38459 | + | 5.38459i | 0.339872 | + | 0.339872i | 0.856319 | − | 0.516447i | \(-0.172746\pi\) |
−0.516447 | + | 0.856319i | \(0.672746\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 11.3709i | − | 0.714880i | ||||||
\(254\) | −1.26237 | − | 0.503308i | −0.0792081 | − | 0.0315803i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.9093 | + | 1.70085i | −0.994334 | + | 0.106303i | ||||
\(257\) | 3.88657 | − | 3.88657i | 0.242437 | − | 0.242437i | −0.575420 | − | 0.817858i | \(-0.695162\pi\) |
0.817858 | + | 0.575420i | \(0.195162\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.08327 | + | 6.08327i | 0.377996 | + | 0.377996i | ||||
\(260\) | 10.7043 | − | 0.880628i | 0.663851 | − | 0.0546142i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.02836 | − | 10.1037i | 0.248873 | − | 0.624210i | ||||
\(263\) | −16.9658 | − | 16.9658i | −1.04615 | − | 1.04615i | −0.998882 | − | 0.0472716i | \(-0.984947\pi\) |
−0.0472716 | − | 0.998882i | \(-0.515053\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.93056 | + | 2.15751i | −0.118593 | + | 0.132535i | ||||
\(266\) | 16.6913 | − | 7.17557i | 1.02341 | − | 0.439963i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.4178 | + | 14.6179i | 0.941791 | + | 0.892928i | ||||
\(269\) | −2.55482 | + | 2.55482i | −0.155770 | + | 0.155770i | −0.780689 | − | 0.624919i | \(-0.785132\pi\) |
0.624919 | + | 0.780689i | \(0.285132\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.33684i | 0.202698i | 0.994851 | + | 0.101349i | \(0.0323159\pi\) | ||||
−0.994851 | + | 0.101349i | \(0.967684\pi\) | |||||||
\(272\) | −0.315772 | − | 0.283813i | −0.0191465 | − | 0.0172087i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.8869 | + | 5.53671i | 0.838937 | + | 0.334485i | ||||
\(275\) | 11.8215 | − | 14.7847i | 0.712863 | − | 0.891551i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 4.60736i | − | 0.276830i | −0.990374 | − | 0.138415i | \(-0.955799\pi\) | ||
0.990374 | − | 0.138415i | \(-0.0442007\pi\) | |||||||
\(278\) | −8.54081 | + | 21.4216i | −0.512244 | + | 1.28478i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 20.5560 | + | 6.29799i | 1.22845 | + | 0.376377i | ||||
\(281\) | − | 22.1178i | − | 1.31944i | −0.751513 | − | 0.659718i | \(-0.770676\pi\) | ||
0.751513 | − | 0.659718i | \(-0.229324\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 10.8629i | − | 0.645734i | −0.946444 | − | 0.322867i | \(-0.895353\pi\) | ||
0.946444 | − | 0.322867i | \(-0.104647\pi\) | |||||||
\(284\) | −3.12809 | + | 3.29926i | −0.185618 | + | 0.195775i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.76222 | − | 11.9443i | 0.281596 | − | 0.706284i | ||||
\(287\) | 4.10745 | + | 4.10745i | 0.242455 | + | 0.242455i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9887i | 0.999337i | ||||||||
\(290\) | 7.88141 | + | 15.8490i | 0.462813 | + | 0.930686i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.752328 | + | 28.2487i | 0.0440267 | + | 1.65313i | ||||
\(293\) | 18.4067 | 1.07533 | 0.537665 | − | 0.843159i | \(-0.319307\pi\) | ||||
0.537665 | + | 0.843159i | \(0.319307\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.928326 | − | 16.7221i | −0.0540492 | − | 0.973600i | ||||
\(296\) | 6.71746 | + | 2.47309i | 0.390444 | + | 0.143746i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.2396 | − | 4.08255i | −0.593166 | − | 0.236496i | ||||
\(299\) | −5.10048 | + | 5.10048i | −0.294968 | + | 0.294968i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.24455 | − | 9.24455i | −0.532847 | − | 0.532847i | ||||
\(302\) | −5.37389 | + | 2.31023i | −0.309233 | + | 0.132939i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 10.1053 | − | 11.2432i | 0.579580 | − | 0.644845i | ||||
\(305\) | −32.3360 | + | 1.79513i | −1.85156 | + | 0.102789i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.60872i | 0.377180i | 0.982056 | + | 0.188590i | \(0.0603917\pi\) | ||||
−0.982056 | + | 0.188590i | \(0.939608\pi\) | |||||||
\(308\) | 17.7094 | − | 18.6785i | 1.00909 | − | 1.06431i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.95740 | − | 1.66447i | −0.281561 | − | 0.0945356i | ||||
\(311\) | 0.606102 | 0.0343689 | 0.0171845 | − | 0.999852i | \(-0.494530\pi\) | ||||
0.0171845 | + | 0.999852i | \(0.494530\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.3708 | − | 19.3708i | 1.09490 | − | 1.09490i | 0.0999032 | − | 0.994997i | \(-0.468147\pi\) |
0.994997 | − | 0.0999032i | \(-0.0318533\pi\) | |||||||
\(314\) | 26.3357 | − | 11.3216i | 1.48621 | − | 0.638918i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.9802 | + | 12.6358i | −0.673940 | + | 0.710820i | ||||
\(317\) | 7.04328 | 0.395590 | 0.197795 | − | 0.980243i | \(-0.436622\pi\) | ||||
0.197795 | + | 0.980243i | \(0.436622\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.1914 | 1.18649 | ||||||||
\(320\) | 17.7250 | − | 2.41358i | 0.990856 | − | 0.134923i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −13.2648 | + | 5.70250i | −0.739217 | + | 0.317788i | ||||
\(323\) | 0.401145 | 0.0223203 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.9344 | + | 1.32917i | −0.662001 | + | 0.0737290i | ||||
\(326\) | −17.1286 | + | 7.36356i | −0.948667 | + | 0.407830i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.53565 | + | 1.66984i | 0.250440 | + | 0.0922017i | ||||
\(329\) | −10.3485 | −0.570532 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.2275 | − | 13.2275i | −0.727047 | − | 0.727047i | 0.242983 | − | 0.970031i | \(-0.421874\pi\) |
−0.970031 | + | 0.242983i | \(0.921874\pi\) | |||||||
\(332\) | −15.3169 | + | 16.1550i | −0.840623 | + | 0.886624i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.75437 | − | 21.9572i | 0.479018 | − | 1.20145i | ||||
\(335\) | −17.7016 | − | 15.8395i | −0.967140 | − | 0.865407i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.73287 | − | 7.73287i | 0.421236 | − | 0.421236i | −0.464393 | − | 0.885629i | \(-0.653727\pi\) |
0.885629 | + | 0.464393i | \(0.153727\pi\) | |||||||
\(338\) | 9.39631 | − | 4.03945i | 0.511092 | − | 0.219717i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.362044 | + | 0.307003i | 0.0196346 | + | 0.0166496i | ||||
\(341\) | −4.42699 | + | 4.42699i | −0.239735 | + | 0.239735i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.87623 | + | 5.87623i | 0.317286 | + | 0.317286i | ||||
\(344\) | −10.2083 | − | 3.75828i | −0.550395 | − | 0.202633i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.69999 | − | 20.2373i | −0.467714 | − | 1.08797i | ||||
\(347\) | 11.3945 | 0.611691 | 0.305845 | − | 0.952081i | \(-0.401061\pi\) | ||||
0.305845 | + | 0.952081i | \(0.401061\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.0508 | + | 12.0508i | −0.645066 | + | 0.645066i | −0.951796 | − | 0.306730i | \(-0.900765\pi\) |
0.306730 | + | 0.951796i | \(0.400765\pi\) | |||||||
\(350\) | −23.1757 | − | 6.37591i | −1.23879 | − | 0.340807i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.86150 | − | 20.2876i | 0.365719 | − | 1.08134i | ||||
\(353\) | 6.47876 | + | 6.47876i | 0.344830 | + | 0.344830i | 0.858179 | − | 0.513350i | \(-0.171596\pi\) |
−0.513350 | + | 0.858179i | \(0.671596\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.38952 | − | 3.78798i | 0.179897 | − | 0.201045i | ||||
\(356\) | −21.5203 | + | 22.6979i | −1.14057 | + | 1.20299i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 28.9746 | + | 11.5522i | 1.53136 | + | 0.610553i | ||||
\(359\) | − | 3.25098i | − | 0.171580i | −0.996313 | − | 0.0857902i | \(-0.972659\pi\) | ||
0.996313 | − | 0.0857902i | \(-0.0273415\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 4.71699i | − | 0.248263i | ||||||
\(362\) | 2.21251 | − | 5.54929i | 0.116287 | − | 0.291664i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −16.3220 | + | 0.434694i | −0.855507 | + | 0.0227841i | ||||
\(365\) | −1.75125 | − | 31.5456i | −0.0916646 | − | 1.65117i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.7038 | − | 12.7038i | −0.663132 | − | 0.663132i | 0.292985 | − | 0.956117i | \(-0.405351\pi\) |
−0.956117 | + | 0.292985i | \(0.905351\pi\) | |||||||
\(368\) | −8.03080 | + | 8.93513i | −0.418635 | + | 0.465776i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.58693 | − | 2.54735i | −0.394426 | − | 0.132430i | ||||
\(371\) | 3.11216 | − | 3.11216i | 0.161575 | − | 0.161575i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.9761 | 1.13788 | 0.568939 | − | 0.822379i | \(-0.307354\pi\) | ||||
0.568939 | + | 0.822379i | \(0.307354\pi\) | |||||||
\(374\) | 0.522103 | − | 0.224451i | 0.0269973 | − | 0.0116061i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.81721 | + | 3.61013i | −0.403142 | + | 0.186178i | ||||
\(377\) | −9.50557 | − | 9.50557i | −0.489562 | − | 0.489562i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.0642 | + | 17.0642i | −0.876527 | + | 0.876527i | −0.993174 | − | 0.116646i | \(-0.962786\pi\) |
0.116646 | + | 0.993174i | \(0.462786\pi\) | |||||||
\(380\) | −10.9310 | + | 12.8908i | −0.560749 | + | 0.661285i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.61470 | + | 8.40828i | 0.184944 | + | 0.430205i | ||||
\(383\) | 0.228058 | − | 0.228058i | 0.0116532 | − | 0.0116532i | −0.701256 | − | 0.712909i | \(-0.747377\pi\) |
0.712909 | + | 0.701256i | \(0.247377\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.1894 | + | 21.4453i | −0.977985 | + | 1.09295i | ||||
\(386\) | −20.6457 | − | 8.23145i | −1.05084 | − | 0.418970i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.377011 | − | 14.1561i | −0.0191398 | − | 0.718668i | ||||
\(389\) | 14.3036 | + | 14.3036i | 0.725221 | + | 0.725221i | 0.969664 | − | 0.244443i | \(-0.0786050\pi\) |
−0.244443 | + | 0.969664i | \(0.578605\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.318794 | −0.0161221 | ||||||||
\(392\) | −12.0910 | − | 4.45141i | −0.610688 | − | 0.224830i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.0153 | − | 32.6015i | −0.706081 | − | 1.64244i | ||||
\(395\) | 12.9815 | − | 14.5075i | 0.653169 | − | 0.729953i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.11618 | 0.256774 | 0.128387 | − | 0.991724i | \(-0.459020\pi\) | ||||
0.128387 | + | 0.991724i | \(0.459020\pi\) | |||||||
\(398\) | 10.4771 | + | 24.3711i | 0.525170 | + | 1.22161i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −19.7311 | + | 3.26863i | −0.986555 | + | 0.163431i | ||||
\(401\) | 16.2837 | 0.813170 | 0.406585 | − | 0.913613i | \(-0.366719\pi\) | ||||
0.406585 | + | 0.913613i | \(0.366719\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.97152 | 0.197835 | ||||||||
\(404\) | 0.479742 | + | 18.0135i | 0.0238681 | + | 0.896207i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.6275 | − | 24.7210i | −0.527436 | − | 1.22688i | ||||
\(407\) | −6.77518 | + | 6.77518i | −0.335833 | + | 0.335833i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.4256 | −0.861640 | −0.430820 | − | 0.902438i | \(-0.641776\pi\) | ||||
−0.430820 | + | 0.902438i | \(0.641776\pi\) | |||||||
\(410\) | −5.12273 | − | 1.71998i | −0.252993 | − | 0.0849438i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.47659 | + | 0.145854i | −0.269812 | + | 0.00718573i | ||||
\(413\) | 25.4604i | 1.25283i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.5970 | − | 18.5481i | 0.814714 | − | 0.910488i | ||||
\(416\) | −12.1779 | + | 6.02239i | −0.597073 | + | 0.295272i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.99172 | + | 18.5898i | 0.390888 | + | 0.909257i | ||||
\(419\) | 11.7257 | + | 11.7257i | 0.572837 | + | 0.572837i | 0.932920 | − | 0.360083i | \(-0.117252\pi\) |
−0.360083 | + | 0.932920i | \(0.617252\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.5406 | + | 23.5406i | −1.14730 | + | 1.14730i | −0.160216 | + | 0.987082i | \(0.551219\pi\) |
−0.987082 | + | 0.160216i | \(0.948781\pi\) | |||||||
\(422\) | 4.73206 | − | 11.8687i | 0.230353 | − | 0.577759i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.26522 | − | 3.43661i | 0.0614445 | − | 0.166896i | ||||
\(425\) | −0.414505 | − | 0.331428i | −0.0201064 | − | 0.0160766i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 49.2335 | 2.38258 | ||||||||
\(428\) | −9.60186 | + | 10.1273i | −0.464123 | + | 0.489521i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.5296 | + | 3.87112i | 0.556008 | + | 0.186682i | ||||
\(431\) | − | 35.0243i | − | 1.68706i | −0.537079 | − | 0.843532i | \(-0.680472\pi\) | ||
0.537079 | − | 0.843532i | \(-0.319528\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.1094 | + | 10.1094i | 0.485828 | + | 0.485828i | 0.906987 | − | 0.421159i | \(-0.138376\pi\) |
−0.421159 | + | 0.906987i | \(0.638376\pi\) | |||||||
\(434\) | 7.38449 | + | 2.94420i | 0.354467 | + | 0.141326i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.0209147 | − | 0.785311i | −0.00100163 | − | 0.0376096i | ||||
\(437\) | − | 11.3509i | − | 0.542985i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 22.6071i | − | 1.07898i | −0.841993 | − | 0.539488i | \(-0.818618\pi\) | ||
0.841993 | − | 0.539488i | \(-0.181382\pi\) | |||||||
\(440\) | −7.01433 | + | 22.8940i | −0.334395 | + | 1.09143i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.334872 | − | 0.133514i | −0.0159282 | − | 0.00635061i | ||||
\(443\) | 10.9178i | 0.518721i | 0.965781 | + | 0.259360i | \(0.0835118\pi\) | ||||
−0.965781 | + | 0.259360i | \(0.916488\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.3188 | − | 26.0601i | 1.10542 | − | 1.23537i | ||||
\(446\) | −3.18337 | + | 7.98436i | −0.150737 | + | 0.378071i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −27.1078 | + | 2.16993i | −1.28072 | + | 0.102520i | ||||
\(449\) | − | 28.8112i | − | 1.35969i | −0.733358 | − | 0.679843i | \(-0.762048\pi\) | ||
0.733358 | − | 0.679843i | \(-0.237952\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.57463 | + | 4.57463i | −0.215411 | + | 0.215411i | ||||
\(452\) | 24.7563 | − | 0.659318i | 1.16444 | − | 0.0310117i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 16.2552 | + | 37.8117i | 0.762893 | + | 1.77459i | ||||
\(455\) | 18.2270 | − | 1.01187i | 0.854495 | − | 0.0474371i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.1653 | − | 19.1653i | −0.896513 | − | 0.896513i | 0.0986128 | − | 0.995126i | \(-0.468559\pi\) |
−0.995126 | + | 0.0986128i | \(0.968559\pi\) | |||||||
\(458\) | −34.0727 | − | 13.5848i | −1.59211 | − | 0.634778i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.68700 | − | 10.2445i | 0.405033 | − | 0.477651i | ||||
\(461\) | −4.43227 | − | 4.43227i | −0.206431 | − | 0.206431i | 0.596317 | − | 0.802749i | \(-0.296630\pi\) |
−0.802749 | + | 0.596317i | \(0.796630\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.1518 | − | 20.1518i | 0.936534 | − | 0.936534i | −0.0615691 | − | 0.998103i | \(-0.519610\pi\) |
0.998103 | + | 0.0615691i | \(0.0196105\pi\) | |||||||
\(464\) | −16.6521 | − | 14.9667i | −0.773052 | − | 0.694811i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.08634 | + | 2.72469i | −0.0503236 | + | 0.126219i | ||||
\(467\) | − | 3.89858i | − | 0.180405i | −0.995923 | − | 0.0902025i | \(-0.971249\pi\) | ||
0.995923 | − | 0.0902025i | \(-0.0287514\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.5342 | + | 25.5342i | 1.17906 | + | 1.17906i | ||||
\(470\) | 8.61992 | − | 4.28652i | 0.397607 | − | 0.197723i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.88200 | + | 19.2327i | 0.408827 | + | 0.885256i | ||||
\(473\) | 10.2960 | − | 10.2960i | 0.473412 | − | 0.473412i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 11.8007 | − | 14.7587i | 0.541453 | − | 0.677175i | ||||
\(476\) | −0.523671 | − | 0.496501i | −0.0240024 | − | 0.0227571i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −16.2967 | + | 7.00590i | −0.745392 | + | 0.320443i | ||||
\(479\) | −9.85299 | −0.450194 | −0.225097 | − | 0.974336i | \(-0.572270\pi\) | ||||
−0.225097 | + | 0.974336i | \(0.572270\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.07811 | 0.277138 | ||||||||
\(482\) | 19.3418 | − | 8.31500i | 0.880994 | − | 0.378738i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.83797 | + | 4.58696i | 0.219908 | + | 0.208498i | ||||
\(485\) | 0.877595 | + | 15.8083i | 0.0398495 | + | 0.717818i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.9164 | + | 13.9164i | −0.630611 | + | 0.630611i | −0.948221 | − | 0.317610i | \(-0.897120\pi\) |
0.317610 | + | 0.948221i | \(0.397120\pi\) | |||||||
\(488\) | 37.1908 | − | 17.1754i | 1.68355 | − | 0.777492i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 13.6560 | + | 4.58507i | 0.616915 | + | 0.207132i | ||||
\(491\) | −2.39213 | − | 2.39213i | −0.107955 | − | 0.107955i | 0.651066 | − | 0.759021i | \(-0.274322\pi\) |
−0.759021 | + | 0.651066i | \(0.774322\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 0.594124i | − | 0.0267580i | ||||||
\(494\) | 4.75384 | − | 11.9233i | 0.213885 | − | 0.536456i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.60531 | − | 0.352079i | 0.296587 | − | 0.0158088i | ||||
\(497\) | −5.46408 | + | 5.46408i | −0.245098 | + | 0.245098i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.87034 | − | 9.87034i | −0.441857 | − | 0.441857i | 0.450779 | − | 0.892636i | \(-0.351146\pi\) |
−0.892636 | + | 0.450779i | \(0.851146\pi\) | |||||||
\(500\) | 21.9455 | − | 4.28886i | 0.981433 | − | 0.191804i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.0034 | + | 3.98837i | 0.446474 | + | 0.178010i | ||||
\(503\) | −9.29035 | − | 9.29035i | −0.414236 | − | 0.414236i | 0.468975 | − | 0.883211i | \(-0.344623\pi\) |
−0.883211 | + | 0.468975i | \(0.844623\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.11673 | − | 20.1159i | −0.0496939 | − | 0.895146i | ||||
\(506\) | −6.35110 | − | 14.7735i | −0.282341 | − | 0.656763i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.92124 | + | 0.0511671i | −0.0852413 | + | 0.00227017i | ||||
\(509\) | 6.53818 | − | 6.53818i | 0.289800 | − | 0.289800i | −0.547201 | − | 0.837001i | \(-0.684307\pi\) |
0.837001 | + | 0.547201i | \(0.184307\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 48.0301i | 2.12473i | ||||||||
\(512\) | −19.7201 | + | 11.0958i | −0.871513 | + | 0.490372i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.87878 | − | 7.22040i | 0.126978 | − | 0.318478i | ||||
\(515\) | 6.11577 | − | 0.339516i | 0.269493 | − | 0.0149608i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 11.5255i | − | 0.506893i | ||||||
\(518\) | 11.3014 | + | 4.50588i | 0.496555 | + | 0.197977i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 13.4156 | − | 7.12294i | 0.588312 | − | 0.312362i | ||||
\(521\) | 14.2961i | 0.626324i | 0.949700 | + | 0.313162i | \(0.101388\pi\) | ||||
−0.949700 | + | 0.313162i | \(0.898612\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.0319i | 0.701027i | 0.936558 | + | 0.350513i | \(0.113993\pi\) | ||||
−0.936558 | + | 0.350513i | \(0.886007\pi\) | |||||||
\(524\) | −0.409530 | − | 15.3772i | −0.0178904 | − | 0.671756i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −31.5187 | − | 12.5665i | −1.37428 | − | 0.547928i | ||||
\(527\) | 0.124115 | + | 0.124115i | 0.00540655 | + | 0.00540655i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 13.9794i | − | 0.607798i | ||||||
\(530\) | −1.30321 | + | 3.88143i | −0.0566077 | + | 0.168598i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 17.6782 | − | 18.6456i | 0.766448 | − | 0.808390i | ||||
\(533\) | 4.10397 | 0.177762 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.4043 | − | 11.6274i | 0.449819 | − | 0.502697i | ||||
\(536\) | 28.1961 | + | 10.3807i | 1.21789 | + | 0.448376i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.89236 | + | 4.74631i | −0.0815854 | + | 0.204628i | ||||
\(539\) | 12.1949 | − | 12.1949i | 0.525271 | − | 0.525271i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.3926 | − | 14.3926i | −0.618785 | − | 0.618785i | 0.326435 | − | 0.945220i | \(-0.394153\pi\) |
−0.945220 | + | 0.326435i | \(0.894153\pi\) | |||||||
\(542\) | 1.86376 | + | 4.33536i | 0.0800555 | + | 0.186220i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.568785 | − | 0.192369i | −0.0243865 | − | 0.00824777i | ||||
\(545\) | 0.0486846 | + | 0.876965i | 0.00208542 | + | 0.0375651i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.6741i | 0.499148i | 0.968356 | + | 0.249574i | \(0.0802905\pi\) | ||||
−0.968356 | + | 0.249574i | \(0.919709\pi\) | |||||||
\(548\) | 21.1349 | − | 0.562871i | 0.902838 | − | 0.0240447i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.10111 | − | 25.8117i | 0.302792 | − | 1.10061i | ||||
\(551\) | 21.1541 | 0.901197 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.9268 | + | 20.9268i | −0.889898 | + | 0.889898i | ||||
\(554\) | −2.57340 | − | 5.98608i | −0.109333 | − | 0.254324i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.868274 | + | 32.6023i | 0.0368230 | + | 1.38264i | ||||
\(557\) | 39.6712 | 1.68092 | 0.840460 | − | 0.541873i | \(-0.182285\pi\) | ||||
0.840460 | + | 0.541873i | \(0.182285\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.23671 | −0.390671 | ||||||||
\(560\) | 30.2249 | − | 3.29875i | 1.27723 | − | 0.139398i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.3537 | − | 28.7364i | −0.521110 | − | 1.21217i | ||||
\(563\) | 12.4534 | 0.524850 | 0.262425 | − | 0.964952i | \(-0.415478\pi\) | ||||
0.262425 | + | 0.964952i | \(0.415478\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.6456 | + | 1.53474i | −1.16306 | + | 0.0645671i | ||||
\(566\) | −6.06740 | − | 14.1136i | −0.255032 | − | 0.593238i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.22137 | + | 6.03371i | −0.0932066 | + | 0.253169i | ||||
\(569\) | 5.62622 | 0.235863 | 0.117932 | − | 0.993022i | \(-0.462374\pi\) | ||||
0.117932 | + | 0.993022i | \(0.462374\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.1808 | + | 23.1808i | 0.970086 | + | 0.970086i | 0.999565 | − | 0.0294797i | \(-0.00938505\pi\) |
−0.0294797 | + | 0.999565i | \(0.509385\pi\) | |||||||
\(572\) | −0.484136 | − | 18.1785i | −0.0202427 | − | 0.760081i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.63076 | + | 3.04239i | 0.318502 | + | 0.126987i | ||||
\(575\) | −9.37814 | + | 11.7289i | −0.391095 | + | 0.489128i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.6307 | + | 25.6307i | −1.06702 | + | 1.06702i | −0.0694322 | + | 0.997587i | \(0.522119\pi\) |
−0.997587 | + | 0.0694322i | \(0.977881\pi\) | |||||||
\(578\) | 9.48892 | + | 22.0725i | 0.394687 | + | 0.918094i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 19.0922 | + | 16.1896i | 0.792761 | + | 0.672237i | ||||
\(581\) | −26.7552 | + | 26.7552i | −1.10999 | + | 1.10999i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.46614 | + | 3.46614i | 0.143553 | + | 0.143553i | ||||
\(584\) | 16.7555 | + | 36.2817i | 0.693349 | + | 1.50135i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 23.9147 | − | 10.2809i | 0.987908 | − | 0.424700i | ||||
\(587\) | −25.5579 | −1.05489 | −0.527444 | − | 0.849590i | \(-0.676849\pi\) | ||||
−0.527444 | + | 0.849590i | \(0.676849\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.41920 | + | 4.41920i | −0.182090 | + | 0.182090i | ||||
\(590\) | −10.5461 | − | 21.2076i | −0.434177 | − | 0.873103i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.1089 | − | 0.538831i | 0.415474 | − | 0.0221458i | ||||
\(593\) | −2.96607 | − | 2.96607i | −0.121802 | − | 0.121802i | 0.643578 | − | 0.765380i | \(-0.277449\pi\) |
−0.765380 | + | 0.643578i | \(0.777449\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.601241 | + | 0.537996i | 0.0246485 | + | 0.0220557i | ||||
\(596\) | −15.5840 | + | 0.415039i | −0.638347 | + | 0.0170007i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.77793 | + | 9.47559i | −0.154491 | + | 0.387486i | ||||
\(599\) | 5.14724i | 0.210311i | 0.994456 | + | 0.105155i | \(0.0335340\pi\) | ||||
−0.994456 | + | 0.105155i | \(0.966466\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.5619i | 1.36902i | 0.729005 | + | 0.684509i | \(0.239983\pi\) | ||||
−0.729005 | + | 0.684509i | \(0.760017\pi\) | |||||||
\(602\) | −17.1744 | − | 6.84745i | −0.699976 | − | 0.279081i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.69163 | + | 6.00309i | −0.231589 | + | 0.244262i | ||||
\(605\) | −5.55461 | − | 4.97032i | −0.225827 | − | 0.202072i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.29572 | − | 3.29572i | −0.133769 | − | 0.133769i | 0.637052 | − | 0.770821i | \(-0.280154\pi\) |
−0.770821 | + | 0.637052i | \(0.780154\pi\) | |||||||
\(608\) | 6.84943 | − | 20.2519i | 0.277781 | − | 0.821325i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −41.0097 | + | 20.3933i | −1.66043 | + | 0.825702i | ||||
\(611\) | −5.16986 | + | 5.16986i | −0.209150 | + | 0.209150i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.261903 | 0.0105781 | 0.00528907 | − | 0.999986i | \(-0.498316\pi\) | ||||
0.00528907 | + | 0.999986i | \(0.498316\pi\) | |||||||
\(614\) | 3.69125 | + | 8.58633i | 0.148967 | + | 0.346516i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.5761 | − | 34.1593i | 0.506704 | − | 1.37632i | ||||
\(617\) | −12.1529 | − | 12.1529i | −0.489259 | − | 0.489259i | 0.418813 | − | 0.908072i | \(-0.362446\pi\) |
−0.908072 | + | 0.418813i | \(0.862446\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −12.1134 | + | 12.1134i | −0.486877 | + | 0.486877i | −0.907319 | − | 0.420442i | \(-0.861875\pi\) |
0.420442 | + | 0.907319i | \(0.361875\pi\) | |||||||
\(620\) | −7.37054 | + | 0.606366i | −0.296008 | + | 0.0243522i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.787474 | − | 0.338534i | 0.0315748 | − | 0.0135740i | ||||
\(623\) | −37.5911 | + | 37.5911i | −1.50606 | + | 1.50606i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.3874 | + | 5.50042i | −0.975496 | + | 0.220017i | ||||
\(626\) | 14.3479 | − | 35.9867i | 0.573459 | − | 1.43832i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 27.8928 | − | 29.4191i | 1.11304 | − | 1.17395i | ||||
\(629\) | 0.189949 | + | 0.189949i | 0.00757377 | + | 0.00757377i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 49.8568 | 1.98477 | 0.992384 | − | 0.123179i | \(-0.0393090\pi\) | ||||
0.992384 | + | 0.123179i | \(0.0393090\pi\) | |||||||
\(632\) | −8.50759 | + | 23.1084i | −0.338414 | + | 0.919204i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.15093 | − | 3.93397i | 0.363430 | − | 0.156238i | ||||
\(635\) | 2.14547 | − | 0.119105i | 0.0851404 | − | 0.00472656i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.9402 | −0.433467 | ||||||||
\(638\) | 27.5328 | − | 11.8363i | 1.09003 | − | 0.468604i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 21.6810 | − | 13.0360i | 0.857015 | − | 0.515292i | ||||
\(641\) | 4.10036 | 0.161954 | 0.0809772 | − | 0.996716i | \(-0.474196\pi\) | ||||
0.0809772 | + | 0.996716i | \(0.474196\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.7451 | −0.739233 | −0.369617 | − | 0.929184i | \(-0.620511\pi\) | ||||
−0.369617 | + | 0.929184i | \(0.620511\pi\) | |||||||
\(644\) | −14.0491 | + | 14.8179i | −0.553611 | + | 0.583906i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.521184 | − | 0.224056i | 0.0205057 | − | 0.00881537i | ||||
\(647\) | −5.46529 | + | 5.46529i | −0.214863 | + | 0.214863i | −0.806330 | − | 0.591467i | \(-0.798549\pi\) |
0.591467 | + | 0.806330i | \(0.298549\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.3563 | −1.11308 | ||||||||
\(650\) | −14.7633 | + | 8.39277i | −0.579063 | + | 0.329192i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18.1414 | + | 19.1341i | −0.710471 | + | 0.749350i | ||||
\(653\) | 33.9219i | 1.32747i | 0.747970 | + | 0.663733i | \(0.231029\pi\) | ||||
−0.747970 | + | 0.663733i | \(0.768971\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.953294 | + | 17.1719i | 0.0372483 | + | 0.670961i | ||||
\(656\) | 6.82559 | − | 0.363821i | 0.266495 | − | 0.0142048i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −13.4452 | + | 5.78007i | −0.524149 | + | 0.225331i | ||||
\(659\) | −26.4961 | − | 26.4961i | −1.03214 | − | 1.03214i | −0.999466 | − | 0.0326746i | \(-0.989598\pi\) |
−0.0326746 | − | 0.999466i | \(-0.510402\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.6974 | − | 10.6974i | 0.416081 | − | 0.416081i | −0.467769 | − | 0.883851i | \(-0.654942\pi\) |
0.883851 | + | 0.467769i | \(0.154942\pi\) | |||||||
\(662\) | −24.5738 | − | 9.79759i | −0.955087 | − | 0.380794i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10.8771 | + | 29.5444i | −0.422112 | + | 1.14655i | ||||
\(665\) | −19.1557 | + | 21.4075i | −0.742826 | + | 0.830149i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.8114 | −0.650941 | ||||||||
\(668\) | −0.889984 | − | 33.4174i | −0.0344345 | − | 1.29296i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −31.8457 | − | 10.6923i | −1.23031 | − | 0.413081i | ||||
\(671\) | 54.8333i | 2.11682i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.70854 | − | 6.70854i | −0.258595 | − | 0.258595i | 0.565887 | − | 0.824483i | \(-0.308534\pi\) |
−0.824483 | + | 0.565887i | \(0.808534\pi\) | |||||||
\(674\) | 5.72774 | − | 14.3660i | 0.220624 | − | 0.553358i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.95188 | − | 10.4965i | 0.382764 | − | 0.403710i | ||||
\(677\) | 13.1970i | 0.507200i | 0.967309 | + | 0.253600i | \(0.0816147\pi\) | ||||
−0.967309 | + | 0.253600i | \(0.918385\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 24.0691i | − | 0.923686i | ||||||
\(680\) | 0.641857 | + | 0.196654i | 0.0246141 | + | 0.00754134i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.27908 | + | 8.22440i | −0.125562 | + | 0.314928i | ||||
\(683\) | 37.9089i | 1.45054i | 0.688462 | + | 0.725272i | \(0.258286\pi\) | ||||
−0.688462 | + | 0.725272i | \(0.741714\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23.6016 | + | 1.31024i | −0.901770 | + | 0.0500616i | ||||
\(686\) | 10.9168 | + | 4.35252i | 0.416804 | + | 0.166180i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −15.3622 | + | 0.818844i | −0.585679 | + | 0.0312181i | ||||
\(689\) | − | 3.10952i | − | 0.118463i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.8280 | − | 20.8280i | 0.792335 | − | 0.792335i | −0.189538 | − | 0.981873i | \(-0.560699\pi\) |
0.981873 | + | 0.189538i | \(0.0606991\pi\) | |||||||
\(692\) | −22.6068 | − | 21.4339i | −0.859382 | − | 0.814794i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.8043 | − | 6.36433i | 0.561962 | − | 0.241586i | ||||
\(695\) | −2.02114 | − | 36.4073i | −0.0766664 | − | 1.38101i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.128255 | + | 0.128255i | 0.00485799 | + | 0.00485799i | ||||
\(698\) | −8.92605 | + | 22.3878i | −0.337856 | + | 0.847392i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −33.6721 | + | 4.66075i | −1.27269 | + | 0.176160i | ||||
\(701\) | −19.9053 | − | 19.9053i | −0.751812 | − | 0.751812i | 0.223005 | − | 0.974817i | \(-0.428413\pi\) |
−0.974817 | + | 0.223005i | \(0.928413\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.76326 | + | 6.76326i | −0.255081 | + | 0.255081i | ||||
\(704\) | −2.41674 | − | 30.1910i | −0.0910844 | − | 1.13787i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 12.0361 | + | 4.79882i | 0.452986 | + | 0.180606i | ||||
\(707\) | 30.6277i | 1.15187i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.57112 | − | 8.57112i | −0.321895 | − | 0.321895i | 0.527599 | − | 0.849494i | \(-0.323092\pi\) |
−0.849494 | + | 0.527599i | \(0.823092\pi\) | |||||||
\(710\) | 2.28806 | − | 6.81469i | 0.0858695 | − | 0.255751i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −15.2823 | + | 41.5100i | −0.572729 | + | 1.55565i | ||||
\(713\) | 3.51199 | − | 3.51199i | 0.131525 | − | 0.131525i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.12696 | + | 20.3001i | 0.0421458 | + | 0.759182i | ||||
\(716\) | 44.0975 | − | 1.17442i | 1.64800 | − | 0.0438901i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.81581 | − | 4.22382i | −0.0677655 | − | 0.157631i | ||||
\(719\) | 33.1900 | 1.23778 | 0.618889 | − | 0.785478i | \(-0.287583\pi\) | ||||
0.618889 | + | 0.785478i | \(0.287583\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.31162 | −0.346783 | ||||||||
\(722\) | −2.63464 | − | 6.12852i | −0.0980511 | − | 0.228080i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.224927 | − | 8.44566i | −0.00835936 | − | 0.313880i | ||||
\(725\) | −21.8587 | − | 17.4777i | −0.811810 | − | 0.649104i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.06503 | − | 5.06503i | 0.187852 | − | 0.187852i | −0.606915 | − | 0.794767i | \(-0.707593\pi\) |
0.794767 | + | 0.606915i | \(0.207593\pi\) | |||||||
\(728\) | −20.9635 | + | 9.68131i | −0.776958 | + | 0.358813i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −19.8949 | − | 40.0073i | −0.736341 | − | 1.48074i | ||||
\(731\) | −0.288660 | − | 0.288660i | −0.0106765 | − | 0.0106765i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.0744i | 1.59099i | 0.605961 | + | 0.795494i | \(0.292789\pi\) | ||||
−0.605961 | + | 0.795494i | \(0.707211\pi\) | |||||||
\(734\) | −23.6009 | − | 9.40969i | −0.871124 | − | 0.347318i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.44332 | + | 16.0944i | −0.200643 | + | 0.593249i | ||||
\(737\) | −28.4384 | + | 28.4384i | −1.04754 | + | 1.04754i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.3838 | + | 11.3838i | 0.418762 | + | 0.418762i | 0.884777 | − | 0.466015i | \(-0.154311\pi\) |
−0.466015 | + | 0.884777i | \(0.654311\pi\) | |||||||
\(740\) | −11.2801 | + | 0.927997i | −0.414663 | + | 0.0341138i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.30518 | − | 5.78173i | 0.0846258 | − | 0.212254i | ||||
\(743\) | −1.54795 | − | 1.54795i | −0.0567888 | − | 0.0567888i | 0.678142 | − | 0.734931i | \(-0.262785\pi\) |
−0.734931 | + | 0.678142i | \(0.762785\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.4029 | − | 0.966116i | 0.637591 | − | 0.0353958i | ||||
\(746\) | 28.5523 | − | 12.2746i | 1.04537 | − | 0.449404i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.552973 | − | 0.583233i | 0.0202187 | − | 0.0213251i | ||||
\(749\) | −16.7723 | + | 16.7723i | −0.612847 | + | 0.612847i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1.49244i | − | 0.0544600i | −0.999629 | − | 0.0272300i | \(-0.991331\pi\) | ||
0.999629 | − | 0.0272300i | \(-0.00866865\pi\) | |||||||
\(752\) | −8.14005 | + | 9.05667i | −0.296837 | + | 0.330263i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −17.6593 | − | 7.04078i | −0.643113 | − | 0.256410i | ||||
\(755\) | 6.16731 | − | 6.89231i | 0.224451 | − | 0.250837i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.7030i | 0.825154i | 0.910923 | + | 0.412577i | \(0.135371\pi\) | ||||
−0.910923 | + | 0.412577i | \(0.864629\pi\) | |||||||
\(758\) | −12.6394 | + | 31.7015i | −0.459085 | + | 1.15145i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7.00198 | + | 22.8537i | −0.253989 | + | 0.828991i | ||||
\(761\) | 33.6599i | 1.22017i | 0.792335 | + | 0.610086i | \(0.208865\pi\) | ||||
−0.792335 | + | 0.610086i | \(0.791135\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1.33523i | − | 0.0483386i | ||||||
\(764\) | 9.39275 | + | 8.90543i | 0.339818 | + | 0.322187i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.168923 | − | 0.423683i | 0.00610343 | − | 0.0153083i | ||||
\(767\) | 12.7194 | + | 12.7194i | 0.459271 | + | 0.459271i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 10.1943i | − | 0.367615i | −0.982962 | − | 0.183808i | \(-0.941158\pi\) | ||
0.982962 | − | 0.183808i | \(-0.0588423\pi\) | |||||||
\(770\) | −12.9537 | + | 38.5807i | −0.466817 | + | 1.39035i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −31.4213 | + | 0.836823i | −1.13088 | + | 0.0301179i | ||||
\(773\) | −7.34419 | −0.264152 | −0.132076 | − | 0.991240i | \(-0.542164\pi\) | ||||
−0.132076 | + | 0.991240i | \(0.542164\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.21755 | − | 0.915212i | 0.295183 | − | 0.0328754i | ||||
\(776\) | −8.39662 | − | 18.1817i | −0.301421 | − | 0.652684i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 26.5730 | + | 10.5947i | 0.952688 | + | 0.379838i | ||||
\(779\) | −4.56658 | + | 4.56658i | −0.163615 | + | 0.163615i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.08556 | − | 6.08556i | −0.217759 | − | 0.217759i | ||||
\(782\) | −0.414191 | + | 0.178060i | −0.0148114 | + | 0.00636741i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −18.1954 | + | 0.969861i | −0.649837 | + | 0.0346379i | ||||
\(785\) | −30.2239 | + | 33.7769i | −1.07874 | + | 1.20555i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 29.4359i | − | 1.04928i | −0.851326 | − | 0.524638i | \(-0.824201\pi\) | ||
0.851326 | − | 0.524638i | \(-0.175799\pi\) | |||||||
\(788\) | −36.4186 | − | 34.5291i | −1.29736 | − | 1.23005i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.76302 | − | 26.0995i | 0.311774 | − | 0.928578i | ||||
\(791\) | 42.0921 | 1.49662 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.5959 | − | 24.5959i | 0.873425 | − | 0.873425i | ||||
\(794\) | 6.64715 | − | 2.85760i | 0.235899 | − | 0.101412i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 27.2246 | + | 25.8121i | 0.964950 | + | 0.914886i | ||||
\(797\) | −50.3934 | −1.78503 | −0.892513 | − | 0.451022i | \(-0.851060\pi\) | ||||
−0.892513 | + | 0.451022i | \(0.851060\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.323131 | −0.0114315 | ||||||||
\(800\) | −23.8098 | + | 15.2674i | −0.841804 | + | 0.539784i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21.1565 | − | 9.09514i | 0.747062 | − | 0.321161i | ||||
\(803\) | −53.4930 | −1.88773 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.2232 | − | 17.0128i | 0.536548 | − | 0.599623i | ||||
\(806\) | 5.15996 | − | 2.21826i | 0.181752 | − | 0.0781348i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.6846 | + | 23.1360i | 0.375884 | + | 0.813922i | ||||
\(809\) | 27.1588 | 0.954851 | 0.477426 | − | 0.878672i | \(-0.341570\pi\) | ||||
0.477426 | + | 0.878672i | \(0.341570\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.5416 | − | 11.5416i | −0.405280 | − | 0.405280i | 0.474809 | − | 0.880089i | \(-0.342517\pi\) |
−0.880089 | + | 0.474809i | \(0.842517\pi\) | |||||||
\(812\) | −27.6155 | − | 26.1827i | −0.969113 | − | 0.918833i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.01838 | + | 12.5868i | −0.175894 | + | 0.441168i | ||||
\(815\) | 19.6575 | − | 21.9684i | 0.688574 | − | 0.769520i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.2779 | − | 10.2779i | 0.359579 | − | 0.359579i | ||||
\(818\) | −22.6401 | + | 9.73292i | −0.791591 | + | 0.340304i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.61635 | + | 0.626587i | −0.265974 | + | 0.0218814i | ||||
\(821\) | 20.2900 | − | 20.2900i | 0.708126 | − | 0.708126i | −0.258015 | − | 0.966141i | \(-0.583068\pi\) |
0.966141 | + | 0.258015i | \(0.0830684\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −31.4540 | − | 31.4540i | −1.09642 | − | 1.09642i | −0.994826 | − | 0.101592i | \(-0.967606\pi\) |
−0.101592 | − | 0.994826i | \(-0.532394\pi\) | |||||||
\(824\) | −7.03395 | + | 3.24840i | −0.245039 | + | 0.113164i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.2207 | + | 33.0793i | 0.494802 | + | 1.15098i | ||||
\(827\) | −15.3304 | −0.533090 | −0.266545 | − | 0.963822i | \(-0.585882\pi\) | ||||
−0.266545 | + | 0.963822i | \(0.585882\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.896046 | + | 0.896046i | −0.0311210 | + | 0.0311210i | −0.722496 | − | 0.691375i | \(-0.757005\pi\) |
0.691375 | + | 0.722496i | \(0.257005\pi\) | |||||||
\(830\) | 11.2036 | − | 33.3685i | 0.388884 | − | 1.15824i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −12.4583 | + | 14.6264i | −0.431915 | + | 0.507080i | ||||
\(833\) | −0.341897 | − | 0.341897i | −0.0118460 | − | 0.0118460i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.07168 | + | 37.3176i | 0.0716935 | + | 1.29143i | ||||
\(836\) | 20.7664 | + | 19.6889i | 0.718220 | + | 0.680956i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 21.7838 | + | 8.68522i | 0.752508 | + | 0.300026i | ||||
\(839\) | 48.1891i | 1.66367i | 0.555021 | + | 0.831837i | \(0.312710\pi\) | ||||
−0.555021 | + | 0.831837i | \(0.687290\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 2.33080i | − | 0.0803723i | ||||||
\(842\) | −17.4365 | + | 43.7333i | −0.600902 | + | 1.50715i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.481069 | − | 18.0634i | −0.0165591 | − | 0.621767i | ||||
\(845\) | −10.7836 | + | 12.0513i | −0.370967 | + | 0.414577i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.01241 | + | 8.01241i | 0.275310 | + | 0.275310i | ||||
\(848\) | −0.275662 | − | 5.17166i | −0.00946628 | − | 0.177596i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.723658 | − | 0.199087i | −0.0248213 | − | 0.00682863i | ||||
\(851\) | 5.37484 | − | 5.37484i | 0.184247 | − | 0.184247i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.7426 | −0.470537 | −0.235268 | − | 0.971930i | \(-0.575597\pi\) | ||||
−0.235268 | + | 0.971930i | \(0.575597\pi\) | |||||||
\(854\) | 63.9663 | − | 27.4990i | 2.18888 | − | 0.940996i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.81862 | + | 18.5208i | −0.233056 | + | 0.633029i | ||||
\(857\) | 13.4366 | + | 13.4366i | 0.458986 | + | 0.458986i | 0.898323 | − | 0.439336i | \(-0.144786\pi\) |
−0.439336 | + | 0.898323i | \(0.644786\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.00719 | − | 7.00719i | 0.239082 | − | 0.239082i | −0.577388 | − | 0.816470i | \(-0.695928\pi\) |
0.816470 | + | 0.577388i | \(0.195928\pi\) | |||||||
\(860\) | 17.1420 | − | 1.41025i | 0.584536 | − | 0.0480890i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −19.5626 | − | 45.5051i | −0.666304 | − | 1.54991i | ||||
\(863\) | 41.4708 | − | 41.4708i | 1.41168 | − | 1.41168i | 0.663560 | − | 0.748123i | \(-0.269045\pi\) |
0.748123 | − | 0.663560i | \(-0.230955\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.9555 | + | 23.2252i | 0.882513 | + | 0.789682i | ||||
\(866\) | 18.7811 | + | 7.48806i | 0.638209 | + | 0.254455i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11.2387 | − | 0.299313i | 0.381466 | − | 0.0101593i | ||||
\(869\) | −23.3070 | − | 23.3070i | −0.790636 | − | 0.790636i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.5125 | 0.864458 | ||||||||
\(872\) | −0.465802 | − | 1.00863i | −0.0157741 | − | 0.0341564i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.33993 | − | 14.7475i | −0.214451 | − | 0.498842i | ||||
\(875\) | 37.4807 | − | 6.29398i | 1.26708 | − | 0.212775i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.34168 | −0.180376 | −0.0901879 | − | 0.995925i | \(-0.528747\pi\) | ||||
−0.0901879 | + | 0.995925i | \(0.528747\pi\) | |||||||
\(878\) | −12.6270 | − | 29.3721i | −0.426141 | − | 0.991259i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.67395 | + | 33.6627i | 0.123849 | + | 1.13477i | ||||
\(881\) | 45.9723 | 1.54885 | 0.774423 | − | 0.632668i | \(-0.218040\pi\) | ||||
0.774423 | + | 0.632668i | \(0.218040\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.64739 | 0.0890918 | 0.0445459 | − | 0.999007i | \(-0.485816\pi\) | ||||
0.0445459 | + | 0.999007i | \(0.485816\pi\) | |||||||
\(884\) | −0.509653 | + | 0.0135732i | −0.0171415 | + | 0.000456518i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.09806 | + | 14.1849i | 0.204868 | + | 0.476551i | ||||
\(887\) | −3.87171 | + | 3.87171i | −0.129999 | + | 0.129999i | −0.769113 | − | 0.639113i | \(-0.779301\pi\) |
0.639113 | + | 0.769113i | \(0.279301\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.26661 | −0.109558 | ||||||||
\(890\) | 15.7411 | − | 46.8829i | 0.527644 | − | 1.57152i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.323627 | + | 12.1517i | 0.0108358 | + | 0.406868i | ||||
\(893\) | − | 11.5053i | − | 0.385009i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −49.2441 | + | 2.73378i | −1.64605 | + | 0.0913801i | ||||
\(896\) | −34.0076 | + | 17.9601i | −1.13611 | + | 0.600005i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16.0923 | − | 37.4328i | −0.537006 | − | 1.24915i | ||||
\(899\) | 6.54516 | + | 6.54516i | 0.218293 | + | 0.218293i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.0971768 | − | 0.0971768i | 0.00323743 | − | 0.00323743i | ||||
\(902\) | −3.38843 | + | 8.49868i | −0.112822 | + | 0.282975i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 31.7962 | − | 14.6840i | 1.05752 | − | 0.488384i | ||||
\(905\) | 0.523580 | + | 9.43136i | 0.0174044 | + | 0.313509i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.2062 | 0.870163 | 0.435081 | − | 0.900391i | \(-0.356720\pi\) | ||||
0.435081 | + | 0.900391i | \(0.356720\pi\) | |||||||
\(908\) | 42.2388 | + | 40.0473i | 1.40174 | + | 1.32902i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 23.1161 | − | 11.4952i | 0.766292 | − | 0.381062i | ||||
\(911\) | 24.2898i | 0.804757i | 0.915473 | + | 0.402378i | \(0.131816\pi\) | ||||
−0.915473 | + | 0.402378i | \(0.868184\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −29.7983 | − | 29.7983i | −0.986181 | − | 0.986181i | ||||
\(914\) | −35.6049 | − | 14.1957i | −1.17771 | − | 0.469553i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −51.8564 | + | 1.38106i | −1.71339 | + | 0.0456314i | ||||
\(917\) | − | 26.1452i | − | 0.863391i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41.1294i | 1.35673i | 0.734723 | + | 0.678367i | \(0.237312\pi\) | ||||
−0.734723 | + | 0.678367i | \(0.762688\pi\) | |||||||
\(920\) | 5.56455 | − | 18.1621i | 0.183458 | − | 0.598787i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −8.23420 | − | 3.28298i | −0.271179 | − | 0.108119i | ||||
\(923\) | 5.45944i | 0.179700i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.5763 | − | 1.40066i | 0.413508 | − | 0.0460535i | ||||
\(926\) | 14.9265 | − | 37.4377i | 0.490514 | − | 1.23028i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −29.9946 | − | 10.1445i | −0.984620 | − | 0.333009i | ||||
\(929\) | − | 43.4799i | − | 1.42653i | −0.700894 | − | 0.713265i | \(-0.747215\pi\) | ||
0.700894 | − | 0.713265i | \(-0.252785\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.1734 | − | 12.1734i | 0.398968 | − | 0.398968i | ||||
\(932\) | 0.110439 | + | 4.14680i | 0.00361754 | + | 0.135833i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.17752 | − | 5.06521i | −0.0712507 | − | 0.165739i | ||||
\(935\) | −0.599188 | + | 0.669626i | −0.0195955 | + | 0.0218991i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.0565 | + | 13.0565i | 0.426537 | + | 0.426537i | 0.887447 | − | 0.460910i | \(-0.152477\pi\) |
−0.460910 | + | 0.887447i | \(0.652477\pi\) | |||||||
\(938\) | 47.4370 | + | 18.9132i | 1.54887 | + | 0.617537i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.80516 | − | 10.3838i | 0.287193 | − | 0.338683i | ||||
\(941\) | 5.53494 | + | 5.53494i | 0.180434 | + | 0.180434i | 0.791545 | − | 0.611111i | \(-0.209277\pi\) |
−0.611111 | + | 0.791545i | \(0.709277\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.62911 | − | 3.62911i | 0.118180 | − | 0.118180i | ||||
\(944\) | 22.2821 | + | 20.0270i | 0.725222 | + | 0.651822i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.62627 | − | 19.1278i | 0.247951 | − | 0.621898i | ||||
\(947\) | − | 31.6905i | − | 1.02980i | −0.857249 | − | 0.514902i | \(-0.827828\pi\) | ||
0.857249 | − | 0.514902i | \(-0.172172\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.9947 | + | 23.9947i | 0.778900 | + | 0.778900i | ||||
\(950\) | 7.08861 | − | 25.7663i | 0.229985 | − | 0.835969i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.957692 | − | 0.352583i | −0.0310390 | − | 0.0114273i | ||||
\(953\) | −2.85543 | + | 2.85543i | −0.0924965 | + | 0.0924965i | −0.751841 | − | 0.659344i | \(-0.770834\pi\) |
0.659344 | + | 0.751841i | \(0.270834\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.7841 | − | 9.64970i | −0.348964 | − | 0.312257i | ||||
\(956\) | −17.2602 | + | 18.2047i | −0.558235 | + | 0.588783i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.8014 | + | 5.50331i | −0.413595 | + | 0.177804i | ||||
\(959\) | 35.9348 | 1.16039 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.2654 | 0.911786 | ||||||||
\(962\) | 7.89694 | − | 3.39488i | 0.254608 | − | 0.109455i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 20.4854 | − | 21.6064i | 0.659790 | − | 0.695895i | ||||
\(965\) | 35.0886 | − | 1.94793i | 1.12954 | − | 0.0627062i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.1144 | + | 40.1144i | −1.28999 | + | 1.28999i | −0.355202 | + | 0.934790i | \(0.615588\pi\) |
−0.934790 | + | 0.355202i | \(0.884412\pi\) | |||||||
\(968\) | 8.84771 | + | 3.25737i | 0.284376 | + | 0.104696i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.96981 | + | 20.0486i | 0.320111 | + | 0.643723i | ||||
\(971\) | 17.3439 | + | 17.3439i | 0.556592 | + | 0.556592i | 0.928335 | − | 0.371743i | \(-0.121240\pi\) |
−0.371743 | + | 0.928335i | \(0.621240\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 55.4322i | 1.77708i | ||||||||
\(974\) | −10.3079 | + | 25.8536i | −0.330285 | + | 0.828404i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 38.7267 | − | 43.0876i | 1.23961 | − | 1.37920i | ||||
\(977\) | 12.2234 | − | 12.2234i | 0.391060 | − | 0.391060i | −0.484005 | − | 0.875065i | \(-0.660818\pi\) |
0.875065 | + | 0.484005i | \(0.160818\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −41.8667 | − | 41.8667i | −1.33807 | − | 1.33807i | ||||
\(980\) | 20.3034 | − | 1.67034i | 0.648568 | − | 0.0533569i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.44406 | − | 1.77185i | −0.141816 | − | 0.0565421i | ||||
\(983\) | −13.6091 | − | 13.6091i | −0.434063 | − | 0.434063i | 0.455945 | − | 0.890008i | \(-0.349301\pi\) |
−0.890008 | + | 0.455945i | \(0.849301\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41.8132 | + | 37.4148i | 1.33228 | + | 1.19214i | ||||
\(986\) | −0.331843 | − | 0.771911i | −0.0105680 | − | 0.0245827i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.483284 | − | 18.1465i | −0.0153753 | − | 0.577317i | ||||
\(989\) | −8.16797 | + | 8.16797i | −0.259726 | + | 0.259726i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.9400i | 1.68169i | 0.541273 | + | 0.840847i | \(0.317942\pi\) | ||||
−0.541273 | + | 0.840847i | \(0.682058\pi\) | |||||||
\(992\) | 8.38525 | − | 4.14678i | 0.266232 | − | 0.131660i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.04725 | + | 10.1511i | −0.128371 | + | 0.321973i | ||||
\(995\) | −31.2573 | − | 27.9693i | −0.990923 | − | 0.886688i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 3.67381i | − | 0.116351i | −0.998306 | − | 0.0581754i | \(-0.981472\pi\) | ||
0.998306 | − | 0.0581754i | \(-0.0185283\pi\) | |||||||
\(998\) | −18.3370 | − | 7.31097i | −0.580446 | − | 0.231425i | ||||
\(999\) | 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 | 720.2.z.g.163.8 | 18 | ||
3.2 | odd | 2 | 80.2.s.b.3.2 | yes | 18 | ||
5.2 | odd | 4 | 720.2.bd.g.307.6 | 18 | |||
12.11 | even | 2 | 320.2.s.b.303.8 | 18 | |||
15.2 | even | 4 | 80.2.j.b.67.4 | yes | 18 | ||
15.8 | even | 4 | 400.2.j.d.307.6 | 18 | |||
15.14 | odd | 2 | 400.2.s.d.243.8 | 18 | |||
16.11 | odd | 4 | 720.2.bd.g.523.6 | 18 | |||
24.5 | odd | 2 | 640.2.s.d.223.8 | 18 | |||
24.11 | even | 2 | 640.2.s.c.223.2 | 18 | |||
48.5 | odd | 4 | 320.2.j.b.143.8 | 18 | |||
48.11 | even | 4 | 80.2.j.b.43.4 | ✓ | 18 | ||
48.29 | odd | 4 | 640.2.j.c.543.2 | 18 | |||
48.35 | even | 4 | 640.2.j.d.543.8 | 18 | |||
60.23 | odd | 4 | 1600.2.j.d.1007.8 | 18 | |||
60.47 | odd | 4 | 320.2.j.b.47.2 | 18 | |||
60.59 | even | 2 | 1600.2.s.d.943.2 | 18 | |||
80.27 | even | 4 | inner | 720.2.z.g.667.8 | 18 | ||
120.77 | even | 4 | 640.2.j.d.607.2 | 18 | |||
120.107 | odd | 4 | 640.2.j.c.607.8 | 18 | |||
240.53 | even | 4 | 1600.2.s.d.207.2 | 18 | |||
240.59 | even | 4 | 400.2.j.d.43.6 | 18 | |||
240.77 | even | 4 | 640.2.s.c.287.2 | 18 | |||
240.107 | odd | 4 | 80.2.s.b.27.2 | yes | 18 | ||
240.149 | odd | 4 | 1600.2.j.d.143.2 | 18 | |||
240.197 | even | 4 | 320.2.s.b.207.8 | 18 | |||
240.203 | odd | 4 | 400.2.s.d.107.8 | 18 | |||
240.227 | odd | 4 | 640.2.s.d.287.8 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.j.b.43.4 | ✓ | 18 | 48.11 | even | 4 | ||
80.2.j.b.67.4 | yes | 18 | 15.2 | even | 4 | ||
80.2.s.b.3.2 | yes | 18 | 3.2 | odd | 2 | ||
80.2.s.b.27.2 | yes | 18 | 240.107 | odd | 4 | ||
320.2.j.b.47.2 | 18 | 60.47 | odd | 4 | |||
320.2.j.b.143.8 | 18 | 48.5 | odd | 4 | |||
320.2.s.b.207.8 | 18 | 240.197 | even | 4 | |||
320.2.s.b.303.8 | 18 | 12.11 | even | 2 | |||
400.2.j.d.43.6 | 18 | 240.59 | even | 4 | |||
400.2.j.d.307.6 | 18 | 15.8 | even | 4 | |||
400.2.s.d.107.8 | 18 | 240.203 | odd | 4 | |||
400.2.s.d.243.8 | 18 | 15.14 | odd | 2 | |||
640.2.j.c.543.2 | 18 | 48.29 | odd | 4 | |||
640.2.j.c.607.8 | 18 | 120.107 | odd | 4 | |||
640.2.j.d.543.8 | 18 | 48.35 | even | 4 | |||
640.2.j.d.607.2 | 18 | 120.77 | even | 4 | |||
640.2.s.c.223.2 | 18 | 24.11 | even | 2 | |||
640.2.s.c.287.2 | 18 | 240.77 | even | 4 | |||
640.2.s.d.223.8 | 18 | 24.5 | odd | 2 | |||
640.2.s.d.287.8 | 18 | 240.227 | odd | 4 | |||
720.2.z.g.163.8 | 18 | 1.1 | even | 1 | trivial | ||
720.2.z.g.667.8 | 18 | 80.27 | even | 4 | inner | ||
720.2.bd.g.307.6 | 18 | 5.2 | odd | 4 | |||
720.2.bd.g.523.6 | 18 | 16.11 | odd | 4 | |||
1600.2.j.d.143.2 | 18 | 240.149 | odd | 4 | |||
1600.2.j.d.1007.8 | 18 | 60.23 | odd | 4 | |||
1600.2.s.d.207.2 | 18 | 240.53 | even | 4 | |||
1600.2.s.d.943.2 | 18 | 60.59 | even | 2 |