Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(151,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.g (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.98878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 24 x^{14} + 94 x^{13} + 262 x^{12} - 936 x^{11} - 1584 x^{10} + 4642 x^{9} + \cdots + 11105 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 5^{6} \) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 301.3 | ||
Root | \(-1.16141 - 0.809017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 750.301 |
Dual form | 750.2.g.f.451.3 |
$q$-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 \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | + | 0.587785i | −0.572061 | + | 0.415627i | ||||
\(3\) | 0.309017 | − | 0.951057i | 0.178411 | − | 0.549093i | ||||
\(4\) | 0.309017 | − | 0.951057i | 0.154508 | − | 0.475528i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.309017 | + | 0.951057i | 0.126156 | + | 0.388267i | ||||
\(7\) | 2.70913 | 1.02395 | 0.511977 | − | 0.858999i | \(-0.328913\pi\) | ||||
0.511977 | + | 0.858999i | \(0.328913\pi\) | |||||||
\(8\) | 0.309017 | + | 0.951057i | 0.109254 | + | 0.336249i | ||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.54704 | + | 3.30361i | −1.37098 | + | 0.996077i | −0.373323 | + | 0.927701i | \(0.621782\pi\) |
−0.997660 | + | 0.0683760i | \(0.978218\pi\) | |||||||
\(12\) | −0.809017 | − | 0.587785i | −0.233543 | − | 0.169679i | ||||
\(13\) | 3.91630 | + | 2.84536i | 1.08619 | + | 0.789161i | 0.978751 | − | 0.205051i | \(-0.0657360\pi\) |
0.107436 | + | 0.994212i | \(0.465736\pi\) | |||||||
\(14\) | −2.19173 | + | 1.59239i | −0.585765 | + | 0.425583i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.809017 | − | 0.587785i | −0.202254 | − | 0.146946i | ||||
\(17\) | 0.323132 | + | 0.994499i | 0.0783711 | + | 0.241202i | 0.982565 | − | 0.185922i | \(-0.0595271\pi\) |
−0.904193 | + | 0.427123i | \(0.859527\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 2.59109 | + | 7.97455i | 0.594437 | + | 1.82949i | 0.557510 | + | 0.830170i | \(0.311757\pi\) |
0.0369263 | + | 0.999318i | \(0.488243\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.837167 | − | 2.57654i | 0.182685 | − | 0.562246i | ||||
\(22\) | 1.73681 | − | 5.34536i | 0.370290 | − | 1.13963i | ||||
\(23\) | 4.28357 | − | 3.11219i | 0.893185 | − | 0.648937i | −0.0435212 | − | 0.999053i | \(-0.513858\pi\) |
0.936707 | + | 0.350115i | \(0.113858\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.84082 | −0.949362 | ||||||||
\(27\) | −0.809017 | + | 0.587785i | −0.155695 | + | 0.113119i | ||||
\(28\) | 0.837167 | − | 2.57654i | 0.158210 | − | 0.486919i | ||||
\(29\) | 1.29490 | − | 3.98530i | 0.240457 | − | 0.740051i | −0.755893 | − | 0.654695i | \(-0.772797\pi\) |
0.996350 | − | 0.0853563i | \(-0.0272028\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.72444 | − | 5.30729i | −0.309719 | − | 0.953218i | −0.977874 | − | 0.209195i | \(-0.932916\pi\) |
0.668155 | − | 0.744022i | \(-0.267084\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.73681 | + | 5.34536i | 0.302340 | + | 0.930508i | ||||
\(34\) | −0.845972 | − | 0.614634i | −0.145083 | − | 0.105409i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.809017 | + | 0.587785i | −0.134836 | + | 0.0979642i | ||||
\(37\) | 2.42041 | + | 1.75853i | 0.397913 | + | 0.289101i | 0.768690 | − | 0.639621i | \(-0.220909\pi\) |
−0.370778 | + | 0.928722i | \(0.620909\pi\) | |||||||
\(38\) | −6.78356 | − | 4.92854i | −1.10044 | − | 0.799516i | ||||
\(39\) | 3.91630 | − | 2.84536i | 0.627110 | − | 0.455622i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.27617 | + | 0.927190i | 0.199304 | + | 0.144803i | 0.682961 | − | 0.730455i | \(-0.260692\pi\) |
−0.483657 | + | 0.875258i | \(0.660692\pi\) | |||||||
\(42\) | 0.837167 | + | 2.57654i | 0.129178 | + | 0.397568i | ||||
\(43\) | 3.29669 | 0.502741 | 0.251370 | − | 0.967891i | \(-0.419119\pi\) | ||||
0.251370 | + | 0.967891i | \(0.419119\pi\) | |||||||
\(44\) | 1.73681 | + | 5.34536i | 0.261834 | + | 0.805843i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.63618 | + | 5.03563i | −0.241241 | + | 0.742464i | ||||
\(47\) | −0.949838 | + | 2.92330i | −0.138548 | + | 0.426407i | −0.996125 | − | 0.0879484i | \(-0.971969\pi\) |
0.857577 | + | 0.514356i | \(0.171969\pi\) | |||||||
\(48\) | −0.809017 | + | 0.587785i | −0.116772 | + | 0.0848395i | ||||
\(49\) | 0.339383 | 0.0484833 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.04568 | 0.146424 | ||||||||
\(52\) | 3.91630 | − | 2.84536i | 0.543094 | − | 0.394581i | ||||
\(53\) | 1.90883 | − | 5.87478i | 0.262198 | − | 0.806962i | −0.730128 | − | 0.683311i | \(-0.760539\pi\) |
0.992326 | − | 0.123652i | \(-0.0394606\pi\) | |||||||
\(54\) | 0.309017 | − | 0.951057i | 0.0420519 | − | 0.129422i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.837167 | + | 2.57654i | 0.111871 | + | 0.344304i | ||||
\(57\) | 8.38494 | 1.11061 | ||||||||
\(58\) | 1.29490 | + | 3.98530i | 0.170029 | + | 0.523295i | ||||
\(59\) | 11.4780 | + | 8.33925i | 1.49431 | + | 1.08568i | 0.972581 | + | 0.232565i | \(0.0747118\pi\) |
0.521726 | + | 0.853113i | \(0.325288\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.218911 | + | 0.159048i | −0.0280286 | + | 0.0203640i | −0.601711 | − | 0.798714i | \(-0.705514\pi\) |
0.573683 | + | 0.819078i | \(0.305514\pi\) | |||||||
\(62\) | 4.51465 | + | 3.28009i | 0.573361 | + | 0.416571i | ||||
\(63\) | −2.19173 | − | 1.59239i | −0.276132 | − | 0.200622i | ||||
\(64\) | −0.809017 | + | 0.587785i | −0.101127 | + | 0.0734732i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.54704 | − | 3.30361i | −0.559701 | − | 0.406647i | ||||
\(67\) | 1.94984 | + | 6.00099i | 0.238211 | + | 0.733137i | 0.996679 | + | 0.0814275i | \(0.0259479\pi\) |
−0.758469 | + | 0.651710i | \(0.774052\pi\) | |||||||
\(68\) | 1.04568 | 0.126807 | ||||||||
\(69\) | −1.63618 | − | 5.03563i | −0.196973 | − | 0.606219i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.40070 | + | 4.31091i | −0.166233 | + | 0.511611i | −0.999125 | − | 0.0418237i | \(-0.986683\pi\) |
0.832892 | + | 0.553435i | \(0.186683\pi\) | |||||||
\(72\) | 0.309017 | − | 0.951057i | 0.0364180 | − | 0.112083i | ||||
\(73\) | 6.60237 | − | 4.79691i | 0.772749 | − | 0.561435i | −0.130045 | − | 0.991508i | \(-0.541512\pi\) |
0.902794 | + | 0.430073i | \(0.141512\pi\) | |||||||
\(74\) | −2.99179 | −0.347788 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.38494 | 0.961819 | ||||||||
\(77\) | −12.3185 | + | 8.94992i | −1.40382 | + | 1.01994i | ||||
\(78\) | −1.49589 | + | 4.60389i | −0.169377 | + | 0.521288i | ||||
\(79\) | 3.85697 | − | 11.8705i | 0.433943 | − | 1.33554i | −0.460223 | − | 0.887804i | \(-0.652230\pi\) |
0.894166 | − | 0.447736i | \(-0.147770\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | −1.57743 | −0.174198 | ||||||||
\(83\) | −0.0415695 | − | 0.127938i | −0.00456285 | − | 0.0140430i | 0.948749 | − | 0.316030i | \(-0.102350\pi\) |
−0.953312 | + | 0.301987i | \(0.902350\pi\) | |||||||
\(84\) | −2.19173 | − | 1.59239i | −0.239138 | − | 0.173744i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.66708 | + | 1.93775i | −0.287599 | + | 0.208953i | ||||
\(87\) | −3.39010 | − | 2.46305i | −0.363456 | − | 0.264067i | ||||
\(88\) | −4.54704 | − | 3.30361i | −0.484716 | − | 0.352167i | ||||
\(89\) | −9.53844 | + | 6.93008i | −1.01107 | + | 0.734587i | −0.964434 | − | 0.264325i | \(-0.914851\pi\) |
−0.0466385 | + | 0.998912i | \(0.514851\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.6098 | + | 7.70845i | 1.11221 | + | 0.808065i | ||||
\(92\) | −1.63618 | − | 5.03563i | −0.170583 | − | 0.525001i | ||||
\(93\) | −5.58042 | −0.578662 | ||||||||
\(94\) | −0.949838 | − | 2.92330i | −0.0979683 | − | 0.301516i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.309017 | − | 0.951057i | 0.0315389 | − | 0.0970668i | ||||
\(97\) | −0.815900 | + | 2.51108i | −0.0828421 | + | 0.254962i | −0.983895 | − | 0.178748i | \(-0.942795\pi\) |
0.901053 | + | 0.433709i | \(0.142795\pi\) | |||||||
\(98\) | −0.274567 | + | 0.199485i | −0.0277354 | + | 0.0201510i | ||||
\(99\) | 5.62045 | 0.564876 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.82844 | −0.380944 | −0.190472 | − | 0.981693i | \(-0.561002\pi\) | ||||
−0.190472 | + | 0.981693i | \(0.561002\pi\) | |||||||
\(102\) | −0.845972 | + | 0.614634i | −0.0837637 | + | 0.0608579i | ||||
\(103\) | −1.82111 | + | 5.60479i | −0.179439 | + | 0.552256i | −0.999808 | − | 0.0195778i | \(-0.993768\pi\) |
0.820369 | + | 0.571834i | \(0.193768\pi\) | |||||||
\(104\) | −1.49589 | + | 4.60389i | −0.146685 | + | 0.451449i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.90883 | + | 5.87478i | 0.185402 | + | 0.570609i | ||||
\(107\) | −5.90758 | −0.571108 | −0.285554 | − | 0.958363i | \(-0.592178\pi\) | ||||
−0.285554 | + | 0.958363i | \(0.592178\pi\) | |||||||
\(108\) | 0.309017 | + | 0.951057i | 0.0297352 | + | 0.0915155i | ||||
\(109\) | −4.56128 | − | 3.31397i | −0.436892 | − | 0.317420i | 0.347507 | − | 0.937677i | \(-0.387028\pi\) |
−0.784399 | + | 0.620257i | \(0.787028\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.42041 | − | 1.75853i | 0.229735 | − | 0.166912i | ||||
\(112\) | −2.19173 | − | 1.59239i | −0.207099 | − | 0.150466i | ||||
\(113\) | −4.09923 | − | 2.97826i | −0.385623 | − | 0.280171i | 0.378037 | − | 0.925791i | \(-0.376599\pi\) |
−0.763659 | + | 0.645619i | \(0.776599\pi\) | |||||||
\(114\) | −6.78356 | + | 4.92854i | −0.635339 | + | 0.461601i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.39010 | − | 2.46305i | −0.314763 | − | 0.228688i | ||||
\(117\) | −1.49589 | − | 4.60389i | −0.138296 | − | 0.425630i | ||||
\(118\) | −14.1876 | −1.30607 | ||||||||
\(119\) | 0.875408 | + | 2.69423i | 0.0802485 | + | 0.246979i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.36248 | − | 19.5817i | 0.578407 | − | 1.78015i | ||||
\(122\) | 0.0836164 | − | 0.257345i | 0.00757027 | − | 0.0232989i | ||||
\(123\) | 1.27617 | − | 0.927190i | 0.115068 | − | 0.0836019i | ||||
\(124\) | −5.58042 | −0.501136 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.70913 | 0.241348 | ||||||||
\(127\) | 7.70919 | − | 5.60106i | 0.684080 | − | 0.497013i | −0.190628 | − | 0.981662i | \(-0.561053\pi\) |
0.874709 | + | 0.484649i | \(0.161053\pi\) | |||||||
\(128\) | 0.309017 | − | 0.951057i | 0.0273135 | − | 0.0840623i | ||||
\(129\) | 1.01873 | − | 3.13534i | 0.0896945 | − | 0.276051i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.0460083 | + | 0.141599i | 0.00401976 | + | 0.0123716i | 0.953046 | − | 0.302825i | \(-0.0979297\pi\) |
−0.949027 | + | 0.315196i | \(0.897930\pi\) | |||||||
\(132\) | 5.62045 | 0.489197 | ||||||||
\(133\) | 7.01960 | + | 21.6041i | 0.608676 | + | 1.87331i | ||||
\(134\) | −5.10474 | − | 3.70881i | −0.440983 | − | 0.320393i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.845972 | + | 0.614634i | −0.0725415 | + | 0.0527045i | ||||
\(137\) | −7.30072 | − | 5.30429i | −0.623743 | − | 0.453176i | 0.230484 | − | 0.973076i | \(-0.425969\pi\) |
−0.854227 | + | 0.519900i | \(0.825969\pi\) | |||||||
\(138\) | 4.28357 | + | 3.11219i | 0.364641 | + | 0.264927i | ||||
\(139\) | −5.75420 | + | 4.18067i | −0.488065 | + | 0.354600i | −0.804440 | − | 0.594034i | \(-0.797534\pi\) |
0.316375 | + | 0.948634i | \(0.397534\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.48671 | + | 1.80670i | 0.209419 | + | 0.152152i | ||||
\(142\) | −1.40070 | − | 4.31091i | −0.117544 | − | 0.361764i | ||||
\(143\) | −27.2075 | −2.27521 | ||||||||
\(144\) | 0.309017 | + | 0.951057i | 0.0257514 | + | 0.0792547i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.52188 | + | 7.76156i | −0.208712 | + | 0.642351i | ||||
\(147\) | 0.104875 | − | 0.322773i | 0.00864996 | − | 0.0266218i | ||||
\(148\) | 2.42041 | − | 1.75853i | 0.198956 | − | 0.144550i | ||||
\(149\) | 15.4351 | 1.26449 | 0.632246 | − | 0.774768i | \(-0.282133\pi\) | ||||
0.632246 | + | 0.774768i | \(0.282133\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.99801 | −0.650868 | −0.325434 | − | 0.945565i | \(-0.605510\pi\) | ||||
−0.325434 | + | 0.945565i | \(0.605510\pi\) | |||||||
\(152\) | −6.78356 | + | 4.92854i | −0.550219 | + | 0.399758i | ||||
\(153\) | 0.323132 | − | 0.994499i | 0.0261237 | − | 0.0804005i | ||||
\(154\) | 4.70525 | − | 14.4813i | 0.379160 | − | 1.16693i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.49589 | − | 4.60389i | −0.119767 | − | 0.368606i | ||||
\(157\) | −15.6147 | −1.24619 | −0.623095 | − | 0.782146i | \(-0.714125\pi\) | ||||
−0.623095 | + | 0.782146i | \(0.714125\pi\) | |||||||
\(158\) | 3.85697 | + | 11.8705i | 0.306844 | + | 0.944369i | ||||
\(159\) | −4.99738 | − | 3.63081i | −0.396318 | − | 0.287942i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.6047 | − | 8.43133i | 0.914581 | − | 0.664482i | ||||
\(162\) | −0.809017 | − | 0.587785i | −0.0635624 | − | 0.0461808i | ||||
\(163\) | −2.95881 | − | 2.14970i | −0.231752 | − | 0.168378i | 0.465849 | − | 0.884864i | \(-0.345749\pi\) |
−0.697601 | + | 0.716487i | \(0.745749\pi\) | |||||||
\(164\) | 1.27617 | − | 0.927190i | 0.0996519 | − | 0.0724014i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.108830 | + | 0.0790699i | 0.00844688 | + | 0.00613702i | ||||
\(167\) | 1.94776 | + | 5.99458i | 0.150722 | + | 0.463874i | 0.997702 | − | 0.0677496i | \(-0.0215819\pi\) |
−0.846980 | + | 0.531624i | \(0.821582\pi\) | |||||||
\(168\) | 2.70913 | 0.209014 | ||||||||
\(169\) | 3.22413 | + | 9.92286i | 0.248010 | + | 0.763297i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.59109 | − | 7.97455i | 0.198146 | − | 0.609829i | ||||
\(172\) | 1.01873 | − | 3.13534i | 0.0776777 | − | 0.239068i | ||||
\(173\) | 8.61237 | − | 6.25725i | 0.654786 | − | 0.475730i | −0.210112 | − | 0.977677i | \(-0.567383\pi\) |
0.864898 | + | 0.501947i | \(0.167383\pi\) | |||||||
\(174\) | 4.19039 | 0.317673 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.62045 | 0.423657 | ||||||||
\(177\) | 11.4780 | − | 8.33925i | 0.862739 | − | 0.626816i | ||||
\(178\) | 3.64336 | − | 11.2131i | 0.273081 | − | 0.840458i | ||||
\(179\) | −0.246999 | + | 0.760184i | −0.0184615 | + | 0.0568188i | −0.959863 | − | 0.280470i | \(-0.909510\pi\) |
0.941401 | + | 0.337288i | \(0.109510\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.04439 | − | 15.5250i | −0.374946 | − | 1.15397i | −0.943515 | − | 0.331330i | \(-0.892503\pi\) |
0.568568 | − | 0.822636i | \(-0.307497\pi\) | |||||||
\(182\) | −13.1144 | −0.972104 | ||||||||
\(183\) | 0.0836164 | + | 0.257345i | 0.00618110 | + | 0.0190235i | ||||
\(184\) | 4.28357 | + | 3.11219i | 0.315789 | + | 0.229434i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.51465 | − | 3.28009i | 0.331030 | − | 0.240508i | ||||
\(187\) | −4.75474 | − | 3.45452i | −0.347701 | − | 0.252619i | ||||
\(188\) | 2.48671 | + | 1.80670i | 0.181362 | + | 0.131767i | ||||
\(189\) | −2.19173 | + | 1.59239i | −0.159425 | + | 0.115829i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.5641 | + | 9.12835i | 0.909106 | + | 0.660504i | 0.940789 | − | 0.338994i | \(-0.110087\pi\) |
−0.0316826 | + | 0.999498i | \(0.510087\pi\) | |||||||
\(192\) | 0.309017 | + | 0.951057i | 0.0223014 | + | 0.0686366i | ||||
\(193\) | −21.0202 | −1.51307 | −0.756533 | − | 0.653956i | \(-0.773108\pi\) | ||||
−0.756533 | + | 0.653956i | \(0.773108\pi\) | |||||||
\(194\) | −0.815900 | − | 2.51108i | −0.0585782 | − | 0.180285i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.104875 | − | 0.322773i | 0.00749109 | − | 0.0230552i | ||||
\(197\) | 7.46505 | − | 22.9751i | 0.531863 | − | 1.63691i | −0.218468 | − | 0.975844i | \(-0.570106\pi\) |
0.750331 | − | 0.661062i | \(-0.229894\pi\) | |||||||
\(198\) | −4.54704 | + | 3.30361i | −0.323144 | + | 0.234778i | ||||
\(199\) | −25.4930 | −1.80715 | −0.903574 | − | 0.428432i | \(-0.859066\pi\) | ||||
−0.903574 | + | 0.428432i | \(0.859066\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.30981 | 0.445060 | ||||||||
\(202\) | 3.09727 | − | 2.25030i | 0.217923 | − | 0.158331i | ||||
\(203\) | 3.50806 | − | 10.7967i | 0.246217 | − | 0.757779i | ||||
\(204\) | 0.323132 | − | 0.994499i | 0.0226238 | − | 0.0696289i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.82111 | − | 5.60479i | −0.126882 | − | 0.390504i | ||||
\(207\) | −5.29478 | −0.368013 | ||||||||
\(208\) | −1.49589 | − | 4.60389i | −0.103722 | − | 0.319222i | ||||
\(209\) | −38.1266 | − | 27.7006i | −2.63727 | − | 1.91609i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.24669 | + | 3.08540i | −0.292354 | + | 0.212408i | −0.724288 | − | 0.689498i | \(-0.757831\pi\) |
0.431934 | + | 0.901905i | \(0.357831\pi\) | |||||||
\(212\) | −4.99738 | − | 3.63081i | −0.343222 | − | 0.249365i | ||||
\(213\) | 3.66708 | + | 2.66429i | 0.251264 | + | 0.182554i | ||||
\(214\) | 4.77934 | − | 3.47239i | 0.326709 | − | 0.237368i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.809017 | − | 0.587785i | −0.0550466 | − | 0.0399937i | ||||
\(217\) | −4.67174 | − | 14.3781i | −0.317139 | − | 0.976052i | ||||
\(218\) | 5.63805 | 0.381857 | ||||||||
\(219\) | −2.52188 | − | 7.76156i | −0.170413 | − | 0.524477i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.56423 | + | 4.81419i | −0.105221 | + | 0.323837i | ||||
\(222\) | −0.924514 | + | 2.84536i | −0.0620493 | + | 0.190968i | ||||
\(223\) | 11.9710 | − | 8.69743i | 0.801637 | − | 0.582423i | −0.109757 | − | 0.993958i | \(-0.535007\pi\) |
0.911394 | + | 0.411535i | \(0.135007\pi\) | |||||||
\(224\) | 2.70913 | 0.181011 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.06692 | 0.337047 | ||||||||
\(227\) | −9.60986 | + | 6.98197i | −0.637829 | + | 0.463410i | −0.859104 | − | 0.511802i | \(-0.828978\pi\) |
0.221275 | + | 0.975211i | \(0.428978\pi\) | |||||||
\(228\) | 2.59109 | − | 7.97455i | 0.171599 | − | 0.528128i | ||||
\(229\) | 5.64177 | − | 17.3636i | 0.372819 | − | 1.14742i | −0.572119 | − | 0.820170i | \(-0.693879\pi\) |
0.944938 | − | 0.327248i | \(-0.106121\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.70525 | + | 14.4813i | 0.309583 | + | 0.952798i | ||||
\(232\) | 4.19039 | 0.275113 | ||||||||
\(233\) | −0.883301 | − | 2.71852i | −0.0578669 | − | 0.178096i | 0.917945 | − | 0.396708i | \(-0.129847\pi\) |
−0.975812 | + | 0.218611i | \(0.929847\pi\) | |||||||
\(234\) | 3.91630 | + | 2.84536i | 0.256017 | + | 0.186007i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 11.4780 | − | 8.33925i | 0.747154 | − | 0.542839i | ||||
\(237\) | −10.0977 | − | 7.33640i | −0.655915 | − | 0.476550i | ||||
\(238\) | −2.29185 | − | 1.66512i | −0.148558 | − | 0.107934i | ||||
\(239\) | −13.2548 | + | 9.63014i | −0.857379 | + | 0.622922i | −0.927171 | − | 0.374640i | \(-0.877766\pi\) |
0.0697919 | + | 0.997562i | \(0.477766\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.2995 | − | 15.4750i | −1.37202 | − | 0.996831i | −0.997576 | − | 0.0695808i | \(-0.977834\pi\) |
−0.374443 | − | 0.927250i | \(-0.622166\pi\) | |||||||
\(242\) | 6.36248 | + | 19.5817i | 0.408995 | + | 1.25876i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0.0836164 | + | 0.257345i | 0.00535299 | + | 0.0164748i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.487453 | + | 1.50022i | −0.0310788 | + | 0.0956508i | ||||
\(247\) | −12.5430 | + | 38.6034i | −0.798091 | + | 2.45627i | ||||
\(248\) | 4.51465 | − | 3.28009i | 0.286681 | − | 0.208286i | ||||
\(249\) | −0.134522 | −0.00852497 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.8356 | −0.873295 | −0.436647 | − | 0.899633i | \(-0.643834\pi\) | ||||
−0.436647 | + | 0.899633i | \(0.643834\pi\) | |||||||
\(252\) | −2.19173 | + | 1.59239i | −0.138066 | + | 0.100311i | ||||
\(253\) | −9.19604 | + | 28.3025i | −0.578150 | + | 1.77936i | ||||
\(254\) | −2.94465 | + | 9.06270i | −0.184764 | + | 0.568644i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.309017 | + | 0.951057i | 0.0193136 | + | 0.0594410i | ||||
\(257\) | 28.6204 | 1.78529 | 0.892647 | − | 0.450756i | \(-0.148846\pi\) | ||||
0.892647 | + | 0.450756i | \(0.148846\pi\) | |||||||
\(258\) | 1.01873 | + | 3.13534i | 0.0634236 | + | 0.195198i | ||||
\(259\) | 6.55720 | + | 4.76409i | 0.407445 | + | 0.296026i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.39010 | + | 2.46305i | −0.209842 | + | 0.152459i | ||||
\(262\) | −0.120451 | − | 0.0875130i | −0.00744150 | − | 0.00540657i | ||||
\(263\) | −2.52661 | − | 1.83569i | −0.155798 | − | 0.113194i | 0.507155 | − | 0.861855i | \(-0.330697\pi\) |
−0.662953 | + | 0.748661i | \(0.730697\pi\) | |||||||
\(264\) | −4.54704 | + | 3.30361i | −0.279851 | + | 0.203323i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −18.3775 | − | 13.3521i | −1.12680 | − | 0.818668i | ||||
\(267\) | 3.64336 | + | 11.2131i | 0.222970 | + | 0.686231i | ||||
\(268\) | 6.30981 | 0.385433 | ||||||||
\(269\) | 2.85284 | + | 8.78015i | 0.173941 | + | 0.535335i | 0.999584 | − | 0.0288583i | \(-0.00918715\pi\) |
−0.825643 | + | 0.564194i | \(0.809187\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.70088 | + | 20.6232i | −0.407050 | + | 1.25277i | 0.512122 | + | 0.858913i | \(0.328860\pi\) |
−0.919172 | + | 0.393857i | \(0.871140\pi\) | |||||||
\(272\) | 0.323132 | − | 0.994499i | 0.0195928 | − | 0.0603004i | ||||
\(273\) | 10.6098 | − | 7.70845i | 0.642133 | − | 0.466537i | ||||
\(274\) | 9.02419 | 0.545171 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.29478 | −0.318708 | ||||||||
\(277\) | 8.32889 | − | 6.05129i | 0.500434 | − | 0.363587i | −0.308749 | − | 0.951144i | \(-0.599910\pi\) |
0.809183 | + | 0.587557i | \(0.199910\pi\) | |||||||
\(278\) | 2.19791 | − | 6.76447i | 0.131822 | − | 0.405706i | ||||
\(279\) | −1.72444 | + | 5.30729i | −0.103240 | + | 0.317739i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.246763 | − | 0.759459i | −0.0147207 | − | 0.0453055i | 0.943426 | − | 0.331582i | \(-0.107582\pi\) |
−0.958147 | + | 0.286277i | \(0.907582\pi\) | |||||||
\(282\) | −3.07374 | −0.183039 | ||||||||
\(283\) | 0.225781 | + | 0.694882i | 0.0134213 | + | 0.0413064i | 0.957543 | − | 0.288291i | \(-0.0930870\pi\) |
−0.944122 | + | 0.329597i | \(0.893087\pi\) | |||||||
\(284\) | 3.66708 | + | 2.66429i | 0.217601 | + | 0.158097i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 22.0114 | − | 15.9922i | 1.30156 | − | 0.945638i | ||||
\(287\) | 3.45730 | + | 2.51188i | 0.204078 | + | 0.148271i | ||||
\(288\) | −0.809017 | − | 0.587785i | −0.0476718 | − | 0.0346356i | ||||
\(289\) | 12.8687 | − | 9.34964i | 0.756981 | − | 0.549979i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.13605 | + | 1.55193i | 0.125218 | + | 0.0909759i | ||||
\(292\) | −2.52188 | − | 7.76156i | −0.147582 | − | 0.454211i | ||||
\(293\) | 18.4842 | 1.07986 | 0.539929 | − | 0.841711i | \(-0.318451\pi\) | ||||
0.539929 | + | 0.841711i | \(0.318451\pi\) | |||||||
\(294\) | 0.104875 | + | 0.322773i | 0.00611645 | + | 0.0188245i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.924514 | + | 2.84536i | −0.0537363 | + | 0.165383i | ||||
\(297\) | 1.73681 | − | 5.34536i | 0.100780 | − | 0.310169i | ||||
\(298\) | −12.4872 | + | 9.07251i | −0.723367 | + | 0.525557i | ||||
\(299\) | 25.6311 | 1.48228 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.93117 | 0.514784 | ||||||||
\(302\) | 6.47052 | − | 4.70111i | 0.372337 | − | 0.270518i | ||||
\(303\) | −1.18305 | + | 3.64106i | −0.0679646 | + | 0.209173i | ||||
\(304\) | 2.59109 | − | 7.97455i | 0.148609 | − | 0.457372i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.323132 | + | 0.994499i | 0.0184723 | + | 0.0568518i | ||||
\(307\) | 14.1923 | 0.809998 | 0.404999 | − | 0.914317i | \(-0.367272\pi\) | ||||
0.404999 | + | 0.914317i | \(0.367272\pi\) | |||||||
\(308\) | 4.70525 | + | 14.4813i | 0.268107 | + | 0.825147i | ||||
\(309\) | 4.76772 | + | 3.46395i | 0.271226 | + | 0.197057i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.18254 | + | 5.94496i | −0.463989 | + | 0.337108i | −0.795094 | − | 0.606486i | \(-0.792579\pi\) |
0.331105 | + | 0.943594i | \(0.392579\pi\) | |||||||
\(312\) | 3.91630 | + | 2.84536i | 0.221717 | + | 0.161087i | ||||
\(313\) | −5.66348 | − | 4.11476i | −0.320119 | − | 0.232580i | 0.416107 | − | 0.909316i | \(-0.363394\pi\) |
−0.736226 | + | 0.676735i | \(0.763394\pi\) | |||||||
\(314\) | 12.6326 | − | 9.17810i | 0.712898 | − | 0.517950i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.0977 | − | 7.33640i | −0.568039 | − | 0.412704i | ||||
\(317\) | −4.73987 | − | 14.5878i | −0.266218 | − | 0.819333i | −0.991410 | − | 0.130788i | \(-0.958249\pi\) |
0.725193 | − | 0.688546i | \(-0.241751\pi\) | |||||||
\(318\) | 6.17710 | 0.346395 | ||||||||
\(319\) | 7.27792 | + | 22.3991i | 0.407485 | + | 1.25411i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.82554 | + | 5.61845i | −0.101892 | + | 0.313591i | ||||
\(322\) | −4.43261 | + | 13.6422i | −0.247020 | + | 0.760249i | ||||
\(323\) | −7.09342 | + | 5.15367i | −0.394689 | + | 0.286758i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.65730 | 0.202559 | ||||||||
\(327\) | −4.56128 | + | 3.31397i | −0.252239 | + | 0.183263i | ||||
\(328\) | −0.487453 | + | 1.50022i | −0.0269151 | + | 0.0828361i | ||||
\(329\) | −2.57324 | + | 7.91960i | −0.141867 | + | 0.436622i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.30737 | + | 22.4898i | 0.401650 | + | 1.23615i | 0.923661 | + | 0.383212i | \(0.125182\pi\) |
−0.522011 | + | 0.852939i | \(0.674818\pi\) | |||||||
\(332\) | −0.134522 | −0.00738284 | ||||||||
\(333\) | −0.924514 | − | 2.84536i | −0.0506630 | − | 0.155925i | ||||
\(334\) | −5.09929 | − | 3.70485i | −0.279021 | − | 0.202721i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.19173 | + | 1.59239i | −0.119569 | + | 0.0868718i | ||||
\(337\) | 22.4196 | + | 16.2888i | 1.22127 | + | 0.887306i | 0.996205 | − | 0.0870374i | \(-0.0277400\pi\) |
0.225067 | + | 0.974343i | \(0.427740\pi\) | |||||||
\(338\) | −8.44089 | − | 6.13266i | −0.459124 | − | 0.333573i | ||||
\(339\) | −4.09923 | + | 2.97826i | −0.222639 | + | 0.161757i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.3744 | + | 18.4355i | 1.37410 | + | 0.998341i | ||||
\(342\) | 2.59109 | + | 7.97455i | 0.140110 | + | 0.431214i | ||||
\(343\) | −18.0445 | −0.974310 | ||||||||
\(344\) | 1.01873 | + | 3.13534i | 0.0549265 | + | 0.169046i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.28963 | + | 10.1244i | −0.176852 | + | 0.544294i | ||||
\(347\) | 8.24643 | − | 25.3799i | 0.442692 | − | 1.36246i | −0.442304 | − | 0.896865i | \(-0.645839\pi\) |
0.884996 | − | 0.465600i | \(-0.154161\pi\) | |||||||
\(348\) | −3.39010 | + | 2.46305i | −0.181728 | + | 0.132033i | ||||
\(349\) | −5.73576 | −0.307028 | −0.153514 | − | 0.988146i | \(-0.549059\pi\) | ||||
−0.153514 | + | 0.988146i | \(0.549059\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.84082 | −0.258384 | ||||||||
\(352\) | −4.54704 | + | 3.30361i | −0.242358 | + | 0.176083i | ||||
\(353\) | −8.99327 | + | 27.6785i | −0.478664 | + | 1.47318i | 0.362288 | + | 0.932066i | \(0.381996\pi\) |
−0.840952 | + | 0.541109i | \(0.818004\pi\) | |||||||
\(354\) | −4.38420 | + | 13.4932i | −0.233018 | + | 0.717155i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.64336 | + | 11.2131i | 0.193098 | + | 0.594293i | ||||
\(357\) | 2.83288 | 0.149932 | ||||||||
\(358\) | −0.246999 | − | 0.760184i | −0.0130543 | − | 0.0401770i | ||||
\(359\) | 10.5088 | + | 7.63506i | 0.554631 | + | 0.402963i | 0.829490 | − | 0.558521i | \(-0.188631\pi\) |
−0.274859 | + | 0.961485i | \(0.588631\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −41.5084 | + | 30.1576i | −2.18465 | + | 1.58724i | ||||
\(362\) | 13.2064 | + | 9.59500i | 0.694112 | + | 0.504302i | ||||
\(363\) | −16.6572 | − | 12.1021i | −0.874275 | − | 0.635198i | ||||
\(364\) | 10.6098 | − | 7.70845i | 0.556103 | − | 0.404033i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.218911 | − | 0.159048i | −0.0114426 | − | 0.00831356i | ||||
\(367\) | −1.13968 | − | 3.50756i | −0.0594906 | − | 0.183093i | 0.916895 | − | 0.399129i | \(-0.130687\pi\) |
−0.976386 | + | 0.216035i | \(0.930687\pi\) | |||||||
\(368\) | −5.29478 | −0.276009 | ||||||||
\(369\) | −0.487453 | − | 1.50022i | −0.0253758 | − | 0.0780986i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.17127 | − | 15.9155i | 0.268479 | − | 0.826293i | ||||
\(372\) | −1.72444 | + | 5.30729i | −0.0894083 | + | 0.275170i | ||||
\(373\) | 21.0383 | − | 15.2853i | 1.08932 | − | 0.791440i | 0.110039 | − | 0.993927i | \(-0.464902\pi\) |
0.979285 | + | 0.202487i | \(0.0649024\pi\) | |||||||
\(374\) | 5.87718 | 0.303902 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.07374 | −0.158516 | ||||||||
\(377\) | 16.4108 | − | 11.9232i | 0.845201 | − | 0.614074i | ||||
\(378\) | 0.837167 | − | 2.57654i | 0.0430592 | − | 0.132523i | ||||
\(379\) | −9.32153 | + | 28.6887i | −0.478815 | + | 1.47364i | 0.361929 | + | 0.932206i | \(0.382118\pi\) |
−0.840743 | + | 0.541434i | \(0.817882\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.94465 | − | 9.06270i | −0.150859 | − | 0.464296i | ||||
\(382\) | −15.5301 | −0.794588 | ||||||||
\(383\) | −4.13001 | − | 12.7109i | −0.211034 | − | 0.649495i | −0.999411 | − | 0.0343033i | \(-0.989079\pi\) |
0.788378 | − | 0.615191i | \(-0.210921\pi\) | |||||||
\(384\) | −0.809017 | − | 0.587785i | −0.0412850 | − | 0.0299953i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.0057 | − | 12.3554i | 0.865567 | − | 0.628871i | ||||
\(387\) | −2.66708 | − | 1.93775i | −0.135575 | − | 0.0985012i | ||||
\(388\) | 2.13605 | + | 1.55193i | 0.108442 | + | 0.0787875i | ||||
\(389\) | 7.84772 | − | 5.70170i | 0.397895 | − | 0.289088i | −0.370788 | − | 0.928718i | \(-0.620912\pi\) |
0.768683 | + | 0.639630i | \(0.220912\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.47923 | + | 3.25435i | 0.226525 | + | 0.164580i | ||||
\(392\) | 0.104875 | + | 0.322773i | 0.00529700 | + | 0.0163025i | ||||
\(393\) | 0.148886 | 0.00751030 | ||||||||
\(394\) | 7.46505 | + | 22.9751i | 0.376084 | + | 1.15747i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.73681 | − | 5.34536i | 0.0872781 | − | 0.268614i | ||||
\(397\) | −2.44508 | + | 7.52519i | −0.122715 | + | 0.377679i | −0.993478 | − | 0.114025i | \(-0.963626\pi\) |
0.870763 | + | 0.491704i | \(0.163626\pi\) | |||||||
\(398\) | 20.6242 | − | 14.9844i | 1.03380 | − | 0.751100i | ||||
\(399\) | 22.7159 | 1.13722 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.1362 | −1.00555 | −0.502777 | − | 0.864416i | \(-0.667688\pi\) | ||||
−0.502777 | + | 0.864416i | \(0.667688\pi\) | |||||||
\(402\) | −5.10474 | + | 3.70881i | −0.254601 | + | 0.184979i | ||||
\(403\) | 8.34772 | − | 25.6916i | 0.415829 | − | 1.27979i | ||||
\(404\) | −1.18305 | + | 3.64106i | −0.0588591 | + | 0.181150i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.50806 | + | 10.7967i | 0.174102 | + | 0.535831i | ||||
\(407\) | −16.8152 | −0.833498 | ||||||||
\(408\) | 0.323132 | + | 0.994499i | 0.0159974 | + | 0.0492351i | ||||
\(409\) | 2.27125 | + | 1.65016i | 0.112306 | + | 0.0815951i | 0.642521 | − | 0.766268i | \(-0.277889\pi\) |
−0.530215 | + | 0.847863i | \(0.677889\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.30072 | + | 5.30429i | −0.360118 | + | 0.261641i | ||||
\(412\) | 4.76772 | + | 3.46395i | 0.234889 | + | 0.170657i | ||||
\(413\) | 31.0954 | + | 22.5921i | 1.53010 | + | 1.11168i | ||||
\(414\) | 4.28357 | − | 3.11219i | 0.210526 | − | 0.152956i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.91630 | + | 2.84536i | 0.192013 | + | 0.139505i | ||||
\(417\) | 2.19791 | + | 6.76447i | 0.107632 | + | 0.331258i | ||||
\(418\) | 47.1271 | 2.30506 | ||||||||
\(419\) | −10.2582 | − | 31.5714i | −0.501144 | − | 1.54236i | −0.807157 | − | 0.590337i | \(-0.798995\pi\) |
0.306013 | − | 0.952027i | \(-0.401005\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.91384 | − | 18.2009i | 0.288223 | − | 0.887059i | −0.697191 | − | 0.716885i | \(-0.745567\pi\) |
0.985414 | − | 0.170174i | \(-0.0544329\pi\) | |||||||
\(422\) | 1.62209 | − | 4.99228i | 0.0789622 | − | 0.243021i | ||||
\(423\) | 2.48671 | − | 1.80670i | 0.120908 | − | 0.0878447i | ||||
\(424\) | 6.17710 | 0.299987 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.53276 | −0.219613 | ||||||||
\(427\) | −0.593057 | + | 0.430881i | −0.0287000 | + | 0.0208518i | ||||
\(428\) | −1.82554 | + | 5.61845i | −0.0882410 | + | 0.271578i | ||||
\(429\) | −8.40759 | + | 25.8759i | −0.405922 | + | 1.24930i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.19003 | − | 19.0510i | −0.298163 | − | 0.917652i | −0.982141 | − | 0.188149i | \(-0.939751\pi\) |
0.683977 | − | 0.729503i | \(-0.260249\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −10.0003 | − | 30.7778i | −0.480585 | − | 1.47909i | −0.838275 | − | 0.545247i | \(-0.816436\pi\) |
0.357691 | − | 0.933840i | \(-0.383564\pi\) | |||||||
\(434\) | 12.2308 | + | 8.88618i | 0.587096 | + | 0.426550i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.56128 | + | 3.31397i | −0.218446 | + | 0.158710i | ||||
\(437\) | 35.9175 | + | 26.0956i | 1.71816 | + | 1.24832i | ||||
\(438\) | 6.60237 | + | 4.79691i | 0.315474 | + | 0.229205i | ||||
\(439\) | −14.0178 | + | 10.1846i | −0.669035 | + | 0.486083i | −0.869702 | − | 0.493577i | \(-0.835689\pi\) |
0.200667 | + | 0.979660i | \(0.435689\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.274567 | − | 0.199485i | −0.0130746 | − | 0.00949926i | ||||
\(442\) | −1.56423 | − | 4.81419i | −0.0744026 | − | 0.228988i | ||||
\(443\) | −16.5326 | −0.785489 | −0.392745 | − | 0.919648i | \(-0.628474\pi\) | ||||
−0.392745 | + | 0.919648i | \(0.628474\pi\) | |||||||
\(444\) | −0.924514 | − | 2.84536i | −0.0438755 | − | 0.135035i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.57251 | + | 14.0727i | −0.216515 | + | 0.666364i | ||||
\(447\) | 4.76970 | − | 14.6796i | 0.225599 | − | 0.694323i | ||||
\(448\) | −2.19173 | + | 1.59239i | −0.103550 | + | 0.0752332i | ||||
\(449\) | 2.51289 | 0.118591 | 0.0592954 | − | 0.998240i | \(-0.481115\pi\) | ||||
0.0592954 | + | 0.998240i | \(0.481115\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.86586 | −0.417477 | ||||||||
\(452\) | −4.09923 | + | 2.97826i | −0.192811 | + | 0.140086i | ||||
\(453\) | −2.47152 | + | 7.60655i | −0.116122 | + | 0.357387i | ||||
\(454\) | 3.67064 | − | 11.2971i | 0.172272 | − | 0.530198i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.59109 | + | 7.97455i | 0.121339 | + | 0.373443i | ||||
\(457\) | −36.7686 | −1.71996 | −0.859982 | − | 0.510324i | \(-0.829525\pi\) | ||||
−0.859982 | + | 0.510324i | \(0.829525\pi\) | |||||||
\(458\) | 5.64177 | + | 17.3636i | 0.263623 | + | 0.811347i | ||||
\(459\) | −0.845972 | − | 0.614634i | −0.0394866 | − | 0.0286887i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.91129 | + | 3.56826i | −0.228741 | + | 0.166190i | −0.696253 | − | 0.717797i | \(-0.745151\pi\) |
0.467511 | + | 0.883987i | \(0.345151\pi\) | |||||||
\(462\) | −12.3185 | − | 8.94992i | −0.573109 | − | 0.416388i | ||||
\(463\) | 26.9502 | + | 19.5805i | 1.25248 | + | 0.909982i | 0.998363 | − | 0.0571903i | \(-0.0182142\pi\) |
0.254120 | + | 0.967173i | \(0.418214\pi\) | |||||||
\(464\) | −3.39010 | + | 2.46305i | −0.157381 | + | 0.114344i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.31251 | + | 1.68014i | 0.107125 | + | 0.0778309i | ||||
\(467\) | 2.82334 | + | 8.68934i | 0.130648 | + | 0.402094i | 0.994888 | − | 0.100986i | \(-0.0321998\pi\) |
−0.864239 | + | 0.503081i | \(0.832200\pi\) | |||||||
\(468\) | −4.84082 | −0.223767 | ||||||||
\(469\) | 5.28236 | + | 16.2574i | 0.243917 | + | 0.750699i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.82522 | + | 14.8505i | −0.222334 | + | 0.684274i | ||||
\(472\) | −4.38420 | + | 13.4932i | −0.201799 | + | 0.621074i | ||||
\(473\) | −14.9902 | + | 10.8910i | −0.689249 | + | 0.500769i | ||||
\(474\) | 12.4814 | 0.573291 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.83288 | 0.129845 | ||||||||
\(477\) | −4.99738 | + | 3.63081i | −0.228814 | + | 0.166243i | ||||
\(478\) | 5.06286 | − | 15.5819i | 0.231570 | − | 0.712699i | ||||
\(479\) | 6.44637 | − | 19.8399i | 0.294542 | − | 0.906507i | −0.688833 | − | 0.724920i | \(-0.741877\pi\) |
0.983375 | − | 0.181587i | \(-0.0581233\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.47540 | + | 13.7739i | 0.204061 | + | 0.628034i | ||||
\(482\) | 26.3276 | 1.19919 | ||||||||
\(483\) | −4.43261 | − | 13.6422i | −0.201691 | − | 0.620741i | ||||
\(484\) | −16.6572 | − | 12.1021i | −0.757144 | − | 0.550098i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.809017 | + | 0.587785i | −0.0366978 | + | 0.0266625i | ||||
\(487\) | −1.02981 | − | 0.748202i | −0.0466652 | − | 0.0339043i | 0.564208 | − | 0.825633i | \(-0.309182\pi\) |
−0.610873 | + | 0.791728i | \(0.709182\pi\) | |||||||
\(488\) | −0.218911 | − | 0.159048i | −0.00990961 | − | 0.00719976i | ||||
\(489\) | −2.95881 | + | 2.14970i | −0.133802 | + | 0.0972130i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.65507 | − | 6.28827i | −0.390598 | − | 0.283786i | 0.375103 | − | 0.926983i | \(-0.377607\pi\) |
−0.765700 | + | 0.643197i | \(0.777607\pi\) | |||||||
\(492\) | −0.487453 | − | 1.50022i | −0.0219761 | − | 0.0676354i | ||||
\(493\) | 4.38180 | 0.197346 | ||||||||
\(494\) | −12.5430 | − | 38.6034i | −0.564336 | − | 1.73685i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.72444 | + | 5.30729i | −0.0774298 | + | 0.238304i | ||||
\(497\) | −3.79468 | + | 11.6788i | −0.170215 | + | 0.523867i | ||||
\(498\) | 0.108830 | − | 0.0790699i | 0.00487681 | − | 0.00354321i | ||||
\(499\) | −7.08035 | −0.316960 | −0.158480 | − | 0.987362i | \(-0.550659\pi\) | ||||
−0.158480 | + | 0.987362i | \(0.550659\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.30307 | 0.281601 | ||||||||
\(502\) | 11.1932 | − | 8.13236i | 0.499578 | − | 0.362965i | ||||
\(503\) | 1.70912 | − | 5.26012i | 0.0762058 | − | 0.234537i | −0.905696 | − | 0.423928i | \(-0.860651\pi\) |
0.981902 | + | 0.189390i | \(0.0606511\pi\) | |||||||
\(504\) | 0.837167 | − | 2.57654i | 0.0372904 | − | 0.114768i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.19604 | − | 28.3025i | −0.408814 | − | 1.25820i | ||||
\(507\) | 10.4335 | 0.463368 | ||||||||
\(508\) | −2.94465 | − | 9.06270i | −0.130648 | − | 0.402092i | ||||
\(509\) | −7.79724 | − | 5.66503i | −0.345607 | − | 0.251098i | 0.401417 | − | 0.915895i | \(-0.368518\pi\) |
−0.747024 | + | 0.664798i | \(0.768518\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.8867 | − | 12.9954i | 0.791260 | − | 0.574884i | ||||
\(512\) | −0.809017 | − | 0.587785i | −0.0357538 | − | 0.0259767i | ||||
\(513\) | −6.78356 | − | 4.92854i | −0.299501 | − | 0.217601i | ||||
\(514\) | −23.1544 | + | 16.8227i | −1.02130 | + | 0.742016i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.66708 | − | 1.93775i | −0.117412 | − | 0.0853046i | ||||
\(517\) | −5.33851 | − | 16.4303i | −0.234788 | − | 0.722602i | ||||
\(518\) | −8.10515 | −0.356120 | ||||||||
\(519\) | −3.28963 | − | 10.1244i | −0.144399 | − | 0.444414i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.26109 | − | 19.2697i | 0.274304 | − | 0.844219i | −0.715099 | − | 0.699023i | \(-0.753619\pi\) |
0.989403 | − | 0.145197i | \(-0.0463814\pi\) | |||||||
\(522\) | 1.29490 | − | 3.98530i | 0.0566763 | − | 0.174432i | ||||
\(523\) | −20.7659 | + | 15.0873i | −0.908030 | + | 0.659722i | −0.940516 | − | 0.339750i | \(-0.889658\pi\) |
0.0324859 | + | 0.999472i | \(0.489658\pi\) | |||||||
\(524\) | 0.148886 | 0.00650411 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.12306 | 0.136172 | ||||||||
\(527\) | 4.72088 | − | 3.42992i | 0.205645 | − | 0.149410i | ||||
\(528\) | 1.73681 | − | 5.34536i | 0.0755851 | − | 0.232627i | ||||
\(529\) | 1.55580 | − | 4.78827i | 0.0676436 | − | 0.208186i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.38420 | − | 13.4932i | −0.190258 | − | 0.585554i | ||||
\(532\) | 22.7159 | 0.984859 | ||||||||
\(533\) | 2.35967 | + | 7.26231i | 0.102209 | + | 0.314566i | ||||
\(534\) | −9.53844 | − | 6.93008i | −0.412769 | − | 0.299894i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.10474 | + | 3.70881i | −0.220491 | + | 0.160196i | ||||
\(537\) | 0.646651 | + | 0.469819i | 0.0279050 | + | 0.0202742i | ||||
\(538\) | −7.46884 | − | 5.42643i | −0.322005 | − | 0.233950i | ||||
\(539\) | −1.54319 | + | 1.12119i | −0.0664698 | + | 0.0482932i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.20447 | + | 2.32818i | 0.137771 | + | 0.100096i | 0.654536 | − | 0.756031i | \(-0.272864\pi\) |
−0.516765 | + | 0.856127i | \(0.672864\pi\) | |||||||
\(542\) | −6.70088 | − | 20.6232i | −0.287828 | − | 0.885842i | ||||
\(543\) | −16.3240 | −0.700529 | ||||||||
\(544\) | 0.323132 | + | 0.994499i | 0.0138542 | + | 0.0426388i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.05257 | + | 12.4725i | −0.173434 | + | 0.533775i | ||||
\(547\) | 3.07502 | − | 9.46392i | 0.131478 | − | 0.404648i | −0.863547 | − | 0.504268i | \(-0.831763\pi\) |
0.995026 | + | 0.0996194i | \(0.0317625\pi\) | |||||||
\(548\) | −7.30072 | + | 5.30429i | −0.311871 | + | 0.226588i | ||||
\(549\) | 0.270588 | 0.0115484 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 35.1362 | 1.49685 | ||||||||
\(552\) | 4.28357 | − | 3.11219i | 0.182321 | − | 0.132464i | ||||
\(553\) | 10.4490 | − | 32.1588i | 0.444338 | − | 1.36753i | ||||
\(554\) | −3.18135 | + | 9.79119i | −0.135163 | + | 0.415988i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.19791 | + | 6.76447i | 0.0932122 | + | 0.286878i | ||||
\(557\) | −18.7017 | −0.792415 | −0.396207 | − | 0.918161i | \(-0.629674\pi\) | ||||
−0.396207 | + | 0.918161i | \(0.629674\pi\) | |||||||
\(558\) | −1.72444 | − | 5.30729i | −0.0730015 | − | 0.224676i | ||||
\(559\) | 12.9108 | + | 9.38028i | 0.546071 | + | 0.396744i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.75474 | + | 3.45452i | −0.200745 | + | 0.145850i | ||||
\(562\) | 0.646034 | + | 0.469371i | 0.0272513 | + | 0.0197992i | ||||
\(563\) | 31.0553 | + | 22.5630i | 1.30882 | + | 0.950917i | 1.00000 | 0.000202039i | \(-6.43111e-5\pi\) | |
0.308825 | + | 0.951119i | \(0.400064\pi\) | |||||||
\(564\) | 2.48671 | − | 1.80670i | 0.104709 | − | 0.0760758i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.591102 | − | 0.429461i | −0.0248459 | − | 0.0180516i | ||||
\(567\) | 0.837167 | + | 2.57654i | 0.0351577 | + | 0.108204i | ||||
\(568\) | −4.53276 | −0.190190 | ||||||||
\(569\) | −4.90344 | − | 15.0913i | −0.205563 | − | 0.632658i | −0.999690 | − | 0.0249059i | \(-0.992071\pi\) |
0.794127 | − | 0.607752i | \(-0.207929\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.96877 | − | 30.6807i | 0.417180 | − | 1.28395i | −0.493106 | − | 0.869969i | \(-0.664139\pi\) |
0.910286 | − | 0.413979i | \(-0.135861\pi\) | |||||||
\(572\) | −8.40759 | + | 25.8759i | −0.351539 | + | 1.08193i | ||||
\(573\) | 12.5641 | − | 9.12835i | 0.524873 | − | 0.381342i | ||||
\(574\) | −4.27346 | −0.178371 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 22.6848 | − | 16.4815i | 0.944379 | − | 0.686132i | −0.00509145 | − | 0.999987i | \(-0.501621\pi\) |
0.949471 | + | 0.313855i | \(0.101621\pi\) | |||||||
\(578\) | −4.91540 | + | 15.1280i | −0.204454 | + | 0.629243i | ||||
\(579\) | −6.49559 | + | 19.9914i | −0.269948 | + | 0.830813i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.112617 | − | 0.346600i | −0.00467215 | − | 0.0143794i | ||||
\(582\) | −2.64031 | −0.109444 | ||||||||
\(583\) | 10.7285 | + | 33.0189i | 0.444328 | + | 1.36750i | ||||
\(584\) | 6.60237 | + | 4.79691i | 0.273208 | + | 0.198497i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.9540 | + | 10.8647i | −0.617745 | + | 0.448818i | ||||
\(587\) | −9.21228 | − | 6.69311i | −0.380231 | − | 0.276254i | 0.381209 | − | 0.924489i | \(-0.375508\pi\) |
−0.761441 | + | 0.648234i | \(0.775508\pi\) | |||||||
\(588\) | −0.274567 | − | 0.199485i | −0.0113229 | − | 0.00822660i | ||||
\(589\) | 37.8551 | − | 27.5033i | 1.55979 | − | 1.13326i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.5438 | − | 14.1994i | −0.803923 | − | 0.584084i | ||||
\(592\) | −0.924514 | − | 2.84536i | −0.0379973 | − | 0.116944i | ||||
\(593\) | 34.9063 | 1.43343 | 0.716715 | − | 0.697366i | \(-0.245645\pi\) | ||||
0.716715 | + | 0.697366i | \(0.245645\pi\) | |||||||
\(594\) | 1.73681 | + | 5.34536i | 0.0712623 | + | 0.219323i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.76970 | − | 14.6796i | 0.195375 | − | 0.601301i | ||||
\(597\) | −7.87776 | + | 24.2453i | −0.322415 | + | 0.992292i | ||||
\(598\) | −20.7360 | + | 15.0656i | −0.847957 | + | 0.616076i | ||||
\(599\) | 21.2325 | 0.867535 | 0.433768 | − | 0.901025i | \(-0.357184\pi\) | ||||
0.433768 | + | 0.901025i | \(0.357184\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.6617 | −0.924389 | −0.462195 | − | 0.886779i | \(-0.652938\pi\) | ||||
−0.462195 | + | 0.886779i | \(0.652938\pi\) | |||||||
\(602\) | −7.22547 | + | 5.24961i | −0.294488 | + | 0.213958i | ||||
\(603\) | 1.94984 | − | 6.00099i | 0.0794036 | − | 0.244379i | ||||
\(604\) | −2.47152 | + | 7.60655i | −0.100565 | + | 0.309506i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.18305 | − | 3.64106i | −0.0480582 | − | 0.147908i | ||||
\(607\) | 21.3752 | 0.867591 | 0.433796 | − | 0.901011i | \(-0.357174\pi\) | ||||
0.433796 | + | 0.901011i | \(0.357174\pi\) | |||||||
\(608\) | 2.59109 | + | 7.97455i | 0.105083 | + | 0.323411i | ||||
\(609\) | −9.18421 | − | 6.67272i | −0.372163 | − | 0.270392i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.0377 | + | 8.74590i | −0.486993 | + | 0.353821i | ||||
\(612\) | −0.845972 | − | 0.614634i | −0.0341964 | − | 0.0248451i | ||||
\(613\) | −27.5136 | − | 19.9898i | −1.11126 | − | 0.807380i | −0.128401 | − | 0.991722i | \(-0.540985\pi\) |
−0.982862 | + | 0.184342i | \(0.940985\pi\) | |||||||
\(614\) | −11.4818 | + | 8.34203i | −0.463368 | + | 0.336657i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.3185 | − | 8.94992i | −0.496327 | − | 0.360603i | ||||
\(617\) | −7.53787 | − | 23.1992i | −0.303463 | − | 0.933963i | −0.980246 | − | 0.197781i | \(-0.936627\pi\) |
0.676783 | − | 0.736182i | \(-0.263373\pi\) | |||||||
\(618\) | −5.89322 | −0.237060 | ||||||||
\(619\) | −7.50529 | − | 23.0989i | −0.301663 | − | 0.928423i | −0.980901 | − | 0.194505i | \(-0.937690\pi\) |
0.679239 | − | 0.733918i | \(-0.262310\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.63618 | + | 5.03563i | −0.0656575 | + | 0.202073i | ||||
\(622\) | 3.12545 | − | 9.61915i | 0.125319 | − | 0.385693i | ||||
\(623\) | −25.8409 | + | 18.7745i | −1.03529 | + | 0.752184i | ||||
\(624\) | −4.84082 | −0.193788 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.00045 | 0.279794 | ||||||||
\(627\) | −38.1266 | + | 27.7006i | −1.52263 | + | 1.10626i | ||||
\(628\) | −4.82522 | + | 14.8505i | −0.192547 | + | 0.592599i | ||||
\(629\) | −0.966744 | + | 2.97533i | −0.0385466 | + | 0.118634i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.319506 | + | 0.983337i | 0.0127193 | + | 0.0391460i | 0.957215 | − | 0.289379i | \(-0.0934486\pi\) |
−0.944495 | + | 0.328525i | \(0.893449\pi\) | |||||||
\(632\) | 12.4814 | 0.496484 | ||||||||
\(633\) | 1.62209 | + | 4.99228i | 0.0644723 | + | 0.198425i | ||||
\(634\) | 12.4091 | + | 9.01577i | 0.492830 | + | 0.358062i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.99738 | + | 3.63081i | −0.198159 | + | 0.143971i | ||||
\(637\) | 1.32913 | + | 0.965668i | 0.0526620 | + | 0.0382612i | ||||
\(638\) | −19.0538 | − | 13.8434i | −0.754349 | − | 0.548067i | ||||
\(639\) | 3.66708 | − | 2.66429i | 0.145067 | − | 0.105398i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.99638 | − | 2.90354i | −0.157847 | − | 0.114683i | 0.506058 | − | 0.862499i | \(-0.331102\pi\) |
−0.663905 | + | 0.747817i | \(0.731102\pi\) | |||||||
\(642\) | −1.82554 | − | 5.61845i | −0.0720485 | − | 0.221742i | ||||
\(643\) | 36.3220 | 1.43240 | 0.716199 | − | 0.697896i | \(-0.245880\pi\) | ||||
0.716199 | + | 0.697896i | \(0.245880\pi\) | |||||||
\(644\) | −4.43261 | − | 13.6422i | −0.174669 | − | 0.537577i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.70945 | − | 8.33882i | 0.106602 | − | 0.328086i | ||||
\(647\) | 4.41077 | − | 13.5750i | 0.173405 | − | 0.533687i | −0.826152 | − | 0.563448i | \(-0.809475\pi\) |
0.999557 | + | 0.0297610i | \(0.00947462\pi\) | |||||||
\(648\) | −0.809017 | + | 0.587785i | −0.0317812 | + | 0.0230904i | ||||
\(649\) | −79.7405 | −3.13009 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.1181 | −0.592524 | ||||||||
\(652\) | −2.95881 | + | 2.14970i | −0.115876 | + | 0.0841889i | ||||
\(653\) | 1.78195 | − | 5.48428i | 0.0697331 | − | 0.214616i | −0.910117 | − | 0.414352i | \(-0.864008\pi\) |
0.979850 | + | 0.199736i | \(0.0640083\pi\) | |||||||
\(654\) | 1.74225 | − | 5.36211i | 0.0681275 | − | 0.209675i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.487453 | − | 1.50022i | −0.0190318 | − | 0.0585739i | ||||
\(657\) | −8.16098 | −0.318390 | ||||||||
\(658\) | −2.57324 | − | 7.91960i | −0.100315 | − | 0.308738i | ||||
\(659\) | −8.14688 | − | 5.91906i | −0.317357 | − | 0.230574i | 0.417690 | − | 0.908590i | \(-0.362840\pi\) |
−0.735047 | + | 0.678016i | \(0.762840\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.8762 | − | 21.7064i | 1.16205 | − | 0.844279i | 0.172015 | − | 0.985094i | \(-0.444972\pi\) |
0.990036 | + | 0.140815i | \(0.0449723\pi\) | |||||||
\(662\) | −19.1310 | − | 13.8995i | −0.743546 | − | 0.540218i | ||||
\(663\) | 4.09519 | + | 2.97533i | 0.159044 | + | 0.115552i | ||||
\(664\) | 0.108830 | − | 0.0790699i | 0.00422344 | − | 0.00306851i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.42041 | + | 1.75853i | 0.0937889 | + | 0.0681416i | ||||
\(667\) | −6.85622 | − | 21.1013i | −0.265474 | − | 0.817044i | ||||
\(668\) | 6.30307 | 0.243873 | ||||||||
\(669\) | −4.57251 | − | 14.0727i | −0.176783 | − | 0.544084i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.469961 | − | 1.44639i | 0.0181427 | − | 0.0558373i | ||||
\(672\) | 0.837167 | − | 2.57654i | 0.0322944 | − | 0.0993920i | ||||
\(673\) | −21.8708 | + | 15.8901i | −0.843059 | + | 0.612518i | −0.923223 | − | 0.384263i | \(-0.874455\pi\) |
0.0801645 | + | 0.996782i | \(0.474455\pi\) | |||||||
\(674\) | −27.7121 | −1.06743 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.4335 | 0.401289 | ||||||||
\(677\) | 6.99862 | − | 5.08479i | 0.268979 | − | 0.195425i | −0.445117 | − | 0.895472i | \(-0.646838\pi\) |
0.714096 | + | 0.700048i | \(0.246838\pi\) | |||||||
\(678\) | 1.56576 | − | 4.81893i | 0.0601328 | − | 0.185070i | ||||
\(679\) | −2.21038 | + | 6.80284i | −0.0848265 | + | 0.261069i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.67064 | + | 11.2971i | 0.140659 | + | 0.432904i | ||||
\(682\) | −31.3644 | −1.20101 | ||||||||
\(683\) | −14.3605 | − | 44.1971i | −0.549489 | − | 1.69115i | −0.710069 | − | 0.704132i | \(-0.751336\pi\) |
0.160580 | − | 0.987023i | \(-0.448664\pi\) | |||||||
\(684\) | −6.78356 | − | 4.92854i | −0.259376 | − | 0.188448i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 14.5983 | − | 10.6063i | 0.557365 | − | 0.404949i | ||||
\(687\) | −14.7704 | − | 10.7313i | −0.563524 | − | 0.409424i | ||||
\(688\) | −2.66708 | − | 1.93775i | −0.101681 | − | 0.0738759i | ||||
\(689\) | 24.1914 | − | 17.5761i | 0.921619 | − | 0.669596i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.2570 | + | 27.7954i | 1.45537 | + | 1.05739i | 0.984540 | + | 0.175159i | \(0.0560440\pi\) |
0.470826 | + | 0.882226i | \(0.343956\pi\) | |||||||
\(692\) | −3.28963 | − | 10.1244i | −0.125053 | − | 0.384874i | ||||
\(693\) | 15.2265 | 0.578407 | ||||||||
\(694\) | 8.24643 | + | 25.3799i | 0.313030 | + | 0.963408i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.29490 | − | 3.98530i | 0.0490831 | − | 0.151062i | ||||
\(697\) | −0.509719 | + | 1.56875i | −0.0193070 | + | 0.0594208i | ||||
\(698\) | 4.64032 | − | 3.37139i | 0.175639 | − | 0.127609i | ||||
\(699\) | −2.85842 | −0.108115 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.1858 | 1.14010 | 0.570052 | − | 0.821609i | \(-0.306923\pi\) | ||||
0.570052 | + | 0.821609i | \(0.306923\pi\) | |||||||
\(702\) | 3.91630 | − | 2.84536i | 0.147811 | − | 0.107391i | ||||
\(703\) | −7.75199 | + | 23.8582i | −0.292372 | + | 0.899828i | ||||
\(704\) | 1.73681 | − | 5.34536i | 0.0654586 | − | 0.201461i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.99327 | − | 27.6785i | −0.338466 | − | 1.04169i | ||||
\(707\) | −10.3717 | −0.390069 | ||||||||
\(708\) | −4.38420 | − | 13.4932i | −0.164768 | − | 0.507105i | ||||
\(709\) | 14.0202 | + | 10.1862i | 0.526538 | + | 0.382553i | 0.819061 | − | 0.573706i | \(-0.194495\pi\) |
−0.292523 | + | 0.956259i | \(0.594495\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10.0977 | + | 7.33640i | −0.378693 | + | 0.275136i | ||||
\(712\) | −9.53844 | − | 6.93008i | −0.357468 | − | 0.259716i | ||||
\(713\) | −23.9041 | − | 17.3673i | −0.895215 | − | 0.650412i | ||||
\(714\) | −2.29185 | + | 1.66512i | −0.0857702 | + | 0.0623157i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.646651 | + | 0.469819i | 0.0241665 | + | 0.0175580i | ||||
\(717\) | 5.06286 | + | 15.5819i | 0.189076 | + | 0.581917i | ||||
\(718\) | −12.9895 | −0.484765 | ||||||||
\(719\) | −5.82077 | − | 17.9145i | −0.217078 | − | 0.668098i | −0.999000 | − | 0.0447207i | \(-0.985760\pi\) |
0.781921 | − | 0.623377i | \(-0.214240\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.93361 | + | 15.1841i | −0.183737 | + | 0.565485i | ||||
\(722\) | 15.8548 | − | 48.7961i | 0.590055 | − | 1.81600i | ||||
\(723\) | −21.2995 | + | 15.4750i | −0.792136 | + | 0.575520i | ||||
\(724\) | −16.3240 | −0.606676 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 20.5894 | 0.764144 | ||||||||
\(727\) | −17.2593 | + | 12.5396i | −0.640111 | + | 0.465068i | −0.859888 | − | 0.510482i | \(-0.829467\pi\) |
0.219777 | + | 0.975550i | \(0.429467\pi\) | |||||||
\(728\) | −4.05257 | + | 12.4725i | −0.150198 | + | 0.462263i | ||||
\(729\) | 0.309017 | − | 0.951057i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.06527 | + | 3.27856i | 0.0394004 | + | 0.121262i | ||||
\(732\) | 0.270588 | 0.0100012 | ||||||||
\(733\) | −6.44956 | − | 19.8497i | −0.238220 | − | 0.733165i | −0.996678 | − | 0.0814434i | \(-0.974047\pi\) |
0.758458 | − | 0.651722i | \(-0.225953\pi\) | |||||||
\(734\) | 2.98371 | + | 2.16779i | 0.110131 | + | 0.0800147i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.28357 | − | 3.11219i | 0.157894 | − | 0.114717i | ||||
\(737\) | −28.6909 | − | 20.8452i | −1.05684 | − | 0.767842i | ||||
\(738\) | 1.27617 | + | 0.927190i | 0.0469764 | + | 0.0341303i | ||||
\(739\) | 13.1129 | − | 9.52707i | 0.482365 | − | 0.350459i | −0.319875 | − | 0.947460i | \(-0.603641\pi\) |
0.802241 | + | 0.597001i | \(0.203641\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 32.8380 | + | 23.8582i | 1.20633 | + | 0.876452i | ||||
\(742\) | 5.17127 | + | 15.9155i | 0.189843 | + | 0.584277i | ||||
\(743\) | 34.7758 | 1.27580 | 0.637900 | − | 0.770120i | \(-0.279803\pi\) | ||||
0.637900 | + | 0.770120i | \(0.279803\pi\) | |||||||
\(744\) | −1.72444 | − | 5.30729i | −0.0632212 | − | 0.194575i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −8.03593 | + | 24.7321i | −0.294216 | + | 0.905505i | ||||
\(747\) | −0.0415695 | + | 0.127938i | −0.00152095 | + | 0.00468100i | ||||
\(748\) | −4.75474 | + | 3.45452i | −0.173850 | + | 0.126310i | ||||
\(749\) | −16.0044 | −0.584788 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.2393 | 0.775034 | 0.387517 | − | 0.921863i | \(-0.373333\pi\) | ||||
0.387517 | + | 0.921863i | \(0.373333\pi\) | |||||||
\(752\) | 2.48671 | − | 1.80670i | 0.0906809 | − | 0.0658836i | ||||
\(753\) | −4.27543 | + | 13.1584i | −0.155805 | + | 0.479520i | ||||
\(754\) | −6.26838 | + | 19.2921i | −0.228281 | + | 0.702577i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.837167 | + | 2.57654i | 0.0304475 | + | 0.0937077i | ||||
\(757\) | −53.9563 | −1.96107 | −0.980537 | − | 0.196335i | \(-0.937096\pi\) | ||||
−0.980537 | + | 0.196335i | \(0.937096\pi\) | |||||||
\(758\) | −9.32153 | − | 28.6887i | −0.338573 | − | 1.04202i | ||||
\(759\) | 24.0755 | + | 17.4919i | 0.873887 | + | 0.634916i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.2990 | − | 24.9197i | 1.24334 | − | 0.903339i | 0.245523 | − | 0.969391i | \(-0.421040\pi\) |
0.997816 | + | 0.0660520i | \(0.0210403\pi\) | |||||||
\(762\) | 7.70919 | + | 5.60106i | 0.279275 | + | 0.202905i | ||||
\(763\) | −12.3571 | − | 8.97796i | −0.447357 | − | 0.325024i | ||||
\(764\) | 12.5641 | − | 9.12835i | 0.454553 | − | 0.330252i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.8125 | + | 7.85574i | 0.390672 | + | 0.283840i | ||||
\(767\) | 21.2231 | + | 65.3181i | 0.766323 | + | 2.35850i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 1.55943 | + | 4.79943i | 0.0562345 | + | 0.173072i | 0.975229 | − | 0.221199i | \(-0.0709971\pi\) |
−0.918994 | + | 0.394271i | \(0.870997\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.84420 | − | 27.2197i | 0.318516 | − | 0.980292i | ||||
\(772\) | −6.49559 | + | 19.9914i | −0.233782 | + | 0.719506i | ||||
\(773\) | −28.1938 | + | 20.4840i | −1.01406 | + | 0.736758i | −0.965057 | − | 0.262041i | \(-0.915605\pi\) |
−0.0490036 | + | 0.998799i | \(0.515605\pi\) | |||||||
\(774\) | 3.29669 | 0.118497 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.64031 | −0.0947815 | ||||||||
\(777\) | 6.55720 | − | 4.76409i | 0.235238 | − | 0.170911i | ||||
\(778\) | −2.99756 | + | 9.22554i | −0.107468 | + | 0.330752i | ||||
\(779\) | −4.08726 | + | 12.5793i | −0.146441 | + | 0.450700i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.87256 | − | 24.2292i | −0.281702 | − | 0.866990i | ||||
\(782\) | −5.53664 | −0.197990 | ||||||||
\(783\) | 1.29490 | + | 3.98530i | 0.0462760 | + | 0.142423i | ||||
\(784\) | −0.274567 | − | 0.199485i | −0.00980596 | − | 0.00712445i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.120451 | + | 0.0875130i | −0.00429635 | + | 0.00312148i | ||||
\(787\) | 12.9790 | + | 9.42980i | 0.462652 | + | 0.336136i | 0.794571 | − | 0.607172i | \(-0.207696\pi\) |
−0.331919 | + | 0.943308i | \(0.607696\pi\) | |||||||
\(788\) | −19.5438 | − | 14.1994i | −0.696218 | − | 0.505832i | ||||
\(789\) | −2.52661 | + | 1.83569i | −0.0899497 | + | 0.0653523i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.1053 | − | 8.06850i | −0.394860 | − | 0.286883i | ||||
\(792\) | 1.73681 | + | 5.34536i | 0.0617150 | + | 0.189939i | ||||
\(793\) | −1.30987 | −0.0465148 | ||||||||
\(794\) | −2.44508 | − | 7.52519i | −0.0867728 | − | 0.267059i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.87776 | + | 24.2453i | −0.279220 | + | 0.859350i | ||||
\(797\) | −11.5093 | + | 35.4218i | −0.407679 | + | 1.25471i | 0.510959 | + | 0.859605i | \(0.329290\pi\) |
−0.918638 | + | 0.395101i | \(0.870710\pi\) | |||||||
\(798\) | −18.3775 | + | 13.3521i | −0.650558 | + | 0.472658i | ||||
\(799\) | −3.21415 | −0.113708 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.7902 | 0.416585 | ||||||||
\(802\) | 16.2905 | − | 11.8358i | 0.575239 | − | 0.417935i | ||||
\(803\) | −14.1741 | + | 43.6234i | −0.500193 | + | 1.53944i | ||||
\(804\) | 1.94984 | − | 6.00099i | 0.0687655 | − | 0.211638i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.34772 | + | 25.6916i | 0.294036 | + | 0.904949i | ||||
\(807\) | 9.23200 | 0.324982 | ||||||||
\(808\) | −1.18305 | − | 3.64106i | −0.0416196 | − | 0.128092i | ||||
\(809\) | 6.97671 | + | 5.06888i | 0.245288 | + | 0.178212i | 0.703636 | − | 0.710561i | \(-0.251559\pi\) |
−0.458348 | + | 0.888773i | \(0.651559\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.148704 | + | 0.108040i | −0.00522171 | + | 0.00379379i | −0.590393 | − | 0.807116i | \(-0.701027\pi\) |
0.585171 | + | 0.810910i | \(0.301027\pi\) | |||||||
\(812\) | −9.18421 | − | 6.67272i | −0.322303 | − | 0.234167i | ||||
\(813\) | 17.5431 | + | 12.7458i | 0.615265 | + | 0.447016i | ||||
\(814\) | 13.6038 | − | 9.88372i | 0.476812 | − | 0.346424i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.845972 | − | 0.614634i | −0.0296149 | − | 0.0215165i | ||||
\(817\) | 8.54203 | + | 26.2897i | 0.298848 | + | 0.919758i | ||||
\(818\) | −2.80742 | −0.0981591 | ||||||||
\(819\) | −4.05257 | − | 12.4725i | −0.141608 | − | 0.435826i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.46892 | − | 26.0647i | 0.295567 | − | 0.909663i | −0.687463 | − | 0.726220i | \(-0.741276\pi\) |
0.983030 | − | 0.183443i | \(-0.0587244\pi\) | |||||||
\(822\) | 2.78863 | − | 8.58252i | 0.0972646 | − | 0.299350i | ||||
\(823\) | 26.3728 | − | 19.1609i | 0.919296 | − | 0.667908i | −0.0240525 | − | 0.999711i | \(-0.507657\pi\) |
0.943349 | + | 0.331803i | \(0.107657\pi\) | |||||||
\(824\) | −5.89322 | −0.205300 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −38.4360 | −1.33736 | ||||||||
\(827\) | −31.2347 | + | 22.6934i | −1.08614 | + | 0.789125i | −0.978743 | − | 0.205091i | \(-0.934251\pi\) |
−0.107395 | + | 0.994216i | \(0.534251\pi\) | |||||||
\(828\) | −1.63618 | + | 5.03563i | −0.0568611 | + | 0.175000i | ||||
\(829\) | 11.1557 | − | 34.3338i | 0.387455 | − | 1.19246i | −0.547229 | − | 0.836983i | \(-0.684317\pi\) |
0.934684 | − | 0.355480i | \(-0.115683\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.18135 | − | 9.79119i | −0.110360 | − | 0.339653i | ||||
\(832\) | −4.84082 | −0.167825 | ||||||||
\(833\) | 0.109666 | + | 0.337517i | 0.00379969 | + | 0.0116943i | ||||
\(834\) | −5.75420 | − | 4.18067i | −0.199252 | − | 0.144765i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −38.1266 | + | 27.7006i | −1.31864 | + | 0.958046i | ||||
\(837\) | 4.51465 | + | 3.28009i | 0.156049 | + | 0.113376i | ||||
\(838\) | 26.8562 | + | 19.5122i | 0.927733 | + | 0.674038i | ||||
\(839\) | −26.7665 | + | 19.4470i | −0.924081 | + | 0.671384i | −0.944536 | − | 0.328407i | \(-0.893488\pi\) |
0.0204558 | + | 0.999791i | \(0.493488\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.25567 | + | 6.72464i | 0.319161 | + | 0.231884i | ||||
\(842\) | 5.91384 | + | 18.2009i | 0.203804 | + | 0.627246i | ||||
\(843\) | −0.798542 | −0.0275033 | ||||||||
\(844\) | 1.62209 | + | 4.99228i | 0.0558347 | + | 0.171841i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.949838 | + | 2.92330i | −0.0326561 | + | 0.100505i | ||||
\(847\) | 17.2368 | − | 53.0493i | 0.592262 | − | 1.82280i | ||||
\(848\) | −4.99738 | + | 3.63081i | −0.171611 | + | 0.124683i | ||||
\(849\) | 0.730642 | 0.0250756 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.8409 | 0.543018 | ||||||||
\(852\) | 3.66708 | − | 2.66429i | 0.125632 | − | 0.0912771i | ||||
\(853\) | −6.22591 | + | 19.1614i | −0.213171 | + | 0.656073i | 0.786107 | + | 0.618090i | \(0.212093\pi\) |
−0.999278 | + | 0.0379832i | \(0.987907\pi\) | |||||||
\(854\) | 0.226528 | − | 0.697180i | 0.00775162 | − | 0.0238570i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.82554 | − | 5.61845i | −0.0623958 | − | 0.192035i | ||||
\(857\) | 55.8400 | 1.90746 | 0.953729 | − | 0.300668i | \(-0.0972098\pi\) | ||||
0.953729 | + | 0.300668i | \(0.0972098\pi\) | |||||||
\(858\) | −8.40759 | − | 25.8759i | −0.287031 | − | 0.883389i | ||||
\(859\) | 41.2044 | + | 29.9368i | 1.40588 | + | 1.02143i | 0.993906 | + | 0.110232i | \(0.0351595\pi\) |
0.411971 | + | 0.911197i | \(0.364841\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.45730 | − | 2.51188i | 0.117825 | − | 0.0856046i | ||||
\(862\) | 16.2057 | + | 11.7741i | 0.551969 | + | 0.401029i | ||||
\(863\) | 22.3882 | + | 16.2660i | 0.762104 | + | 0.553701i | 0.899555 | − | 0.436808i | \(-0.143891\pi\) |
−0.137451 | + | 0.990509i | \(0.543891\pi\) | |||||||
\(864\) | −0.809017 | + | 0.587785i | −0.0275233 | + | 0.0199969i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 26.1812 | + | 19.0217i | 0.889672 | + | 0.646385i | ||||
\(867\) | −4.91540 | − | 15.1280i | −0.166936 | − | 0.513775i | ||||
\(868\) | −15.1181 | −0.513141 | ||||||||
\(869\) | 21.6779 | + | 66.7177i | 0.735372 | + | 2.26324i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.43881 | + | 29.0497i | −0.319822 | + | 0.984311i | ||||
\(872\) | 1.74225 | − | 5.36211i | 0.0590002 | − | 0.181584i | ||||
\(873\) | 2.13605 | − | 1.55193i | 0.0722944 | − | 0.0525250i | ||||
\(874\) | −44.3964 | −1.50173 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.16098 | −0.275734 | ||||||||
\(877\) | −27.1845 | + | 19.7507i | −0.917956 | + | 0.666934i | −0.943015 | − | 0.332752i | \(-0.892023\pi\) |
0.0250581 | + | 0.999686i | \(0.492023\pi\) | |||||||
\(878\) | 5.35434 | − | 16.4790i | 0.180700 | − | 0.556138i | ||||
\(879\) | 5.71193 | − | 17.5795i | 0.192659 | − | 0.592942i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.801894 | + | 2.46798i | 0.0270165 | + | 0.0831482i | 0.963656 | − | 0.267147i | \(-0.0860811\pi\) |
−0.936639 | + | 0.350296i | \(0.886081\pi\) | |||||||
\(882\) | 0.339383 | 0.0114276 | ||||||||
\(883\) | −12.3541 | − | 38.0222i | −0.415750 | − | 1.27955i | −0.911578 | − | 0.411127i | \(-0.865135\pi\) |
0.495828 | − | 0.868421i | \(-0.334865\pi\) | |||||||
\(884\) | 4.09519 | + | 2.97533i | 0.137736 | + | 0.100071i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.3752 | − | 9.71764i | 0.449348 | − | 0.326470i | ||||
\(887\) | −17.7050 | − | 12.8634i | −0.594475 | − | 0.431911i | 0.249439 | − | 0.968391i | \(-0.419754\pi\) |
−0.843913 | + | 0.536480i | \(0.819754\pi\) | |||||||
\(888\) | 2.42041 | + | 1.75853i | 0.0812236 | + | 0.0590124i | ||||
\(889\) | 20.8852 | − | 15.1740i | 0.700467 | − | 0.508919i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.54704 | − | 3.30361i | −0.152331 | − | 0.110675i | ||||
\(892\) | −4.57251 | − | 14.0727i | −0.153099 | − | 0.471190i | ||||
\(893\) | −25.7731 | −0.862465 | ||||||||
\(894\) | 4.76970 | + | 14.6796i | 0.159523 | + | 0.490961i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.837167 | − | 2.57654i | 0.0279678 | − | 0.0860760i | ||||
\(897\) | 7.92043 | − | 24.3766i | 0.264456 | − | 0.813910i | ||||
\(898\) | −2.03297 | + | 1.47704i | −0.0678412 | + | 0.0492895i | ||||
\(899\) | −23.3841 | −0.779904 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.45927 | 0.215189 | ||||||||
\(902\) | 7.17263 | − | 5.21122i | 0.238822 | − | 0.173515i | ||||
\(903\) | 2.75988 | − | 8.49405i | 0.0918431 | − | 0.282664i | ||||
\(904\) | 1.56576 | − | 4.81893i | 0.0520766 | − | 0.160275i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.47152 | − | 7.60655i | −0.0821107 | − | 0.252711i | ||||
\(907\) | 22.6784 | 0.753025 | 0.376512 | − | 0.926412i | \(-0.377123\pi\) | ||||
0.376512 | + | 0.926412i | \(0.377123\pi\) | |||||||
\(908\) | 3.67064 | + | 11.2971i | 0.121814 | + | 0.374906i | ||||
\(909\) | 3.09727 | + | 2.25030i | 0.102730 | + | 0.0746377i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −39.1006 | + | 28.4082i | −1.29546 | + | 0.941207i | −0.999900 | − | 0.0141173i | \(-0.995506\pi\) |
−0.295560 | + | 0.955324i | \(0.595506\pi\) | |||||||
\(912\) | −6.78356 | − | 4.92854i | −0.224626 | − | 0.163200i | ||||
\(913\) | 0.611676 | + | 0.444408i | 0.0202435 | + | 0.0147078i | ||||
\(914\) | 29.7465 | − | 21.6121i | 0.983925 | − | 0.714863i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.7704 | − | 10.7313i | −0.488026 | − | 0.354572i | ||||
\(917\) | 0.124642 | + | 0.383610i | 0.00411606 | + | 0.0126679i | ||||
\(918\) | 1.04568 | 0.0345125 | ||||||||
\(919\) | −13.3112 | − | 40.9678i | −0.439097 | − | 1.35140i | −0.888829 | − | 0.458239i | \(-0.848481\pi\) |
0.449732 | − | 0.893164i | \(-0.351519\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.38566 | − | 13.4977i | 0.144513 | − | 0.444764i | ||||
\(922\) | 1.87594 | − | 5.77356i | 0.0617809 | − | 0.190142i | ||||
\(923\) | −17.7517 | + | 12.8973i | −0.584303 | + | 0.424521i | ||||
\(924\) | 15.2265 | 0.500916 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −33.3123 | −1.09471 | ||||||||
\(927\) | 4.76772 | − | 3.46395i | 0.156592 | − | 0.113771i | ||||
\(928\) | 1.29490 | − | 3.98530i | 0.0425072 | − | 0.130824i | ||||
\(929\) | −11.7192 | + | 36.0680i | −0.384495 | + | 1.18335i | 0.552351 | + | 0.833612i | \(0.313731\pi\) |
−0.936846 | + | 0.349742i | \(0.886269\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.879373 | + | 2.70643i | 0.0288203 | + | 0.0886997i | ||||
\(932\) | −2.85842 | −0.0936307 | ||||||||
\(933\) | 3.12545 | + | 9.61915i | 0.102323 | + | 0.314917i | ||||
\(934\) | −7.39159 | − | 5.37030i | −0.241860 | − | 0.175722i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.91630 | − | 2.84536i | 0.128008 | − | 0.0930035i | ||||
\(937\) | −13.4115 | − | 9.74401i | −0.438134 | − | 0.318323i | 0.346759 | − | 0.937954i | \(-0.387282\pi\) |
−0.784893 | + | 0.619631i | \(0.787282\pi\) | |||||||
\(938\) | −13.8294 | − | 10.0477i | −0.451546 | − | 0.328068i | ||||
\(939\) | −5.66348 | + | 4.11476i | −0.184821 | + | 0.134280i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.7160 | − | 15.0510i | −0.675321 | − | 0.490650i | 0.196481 | − | 0.980508i | \(-0.437049\pi\) |
−0.871802 | + | 0.489858i | \(0.837049\pi\) | |||||||
\(942\) | −4.82522 | − | 14.8505i | −0.157214 | − | 0.483855i | ||||
\(943\) | 8.35214 | 0.271983 | ||||||||
\(944\) | −4.38420 | − | 13.4932i | −0.142694 | − | 0.439166i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.72574 | − | 17.6220i | 0.186160 | − | 0.572941i | ||||
\(947\) | −6.16914 | + | 18.9867i | −0.200470 | + | 0.616984i | 0.799399 | + | 0.600801i | \(0.205151\pi\) |
−0.999869 | + | 0.0161830i | \(0.994849\pi\) | |||||||
\(948\) | −10.0977 | + | 7.33640i | −0.327957 | + | 0.238275i | ||||
\(949\) | 39.5058 | 1.28241 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.3385 | −0.497386 | ||||||||
\(952\) | −2.29185 | + | 1.66512i | −0.0742792 | + | 0.0539670i | ||||
\(953\) | 13.9470 | − | 42.9246i | 0.451789 | − | 1.39046i | −0.423075 | − | 0.906094i | \(-0.639049\pi\) |
0.874864 | − | 0.484368i | \(-0.160951\pi\) | |||||||
\(954\) | 1.90883 | − | 5.87478i | 0.0618007 | − | 0.190203i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.06286 | + | 15.5819i | 0.163745 | + | 0.503955i | ||||
\(957\) | 23.5519 | 0.761323 | ||||||||
\(958\) | 6.44637 | + | 19.8399i | 0.208273 | + | 0.640997i | ||||
\(959\) | −19.7786 | − | 14.3700i | −0.638685 | − | 0.464031i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.114121 | + | 0.0829138i | −0.00368132 | + | 0.00267464i | ||||
\(962\) | −11.7168 | − | 8.51272i | −0.377763 | − | 0.274461i | ||||
\(963\) | 4.77934 | + | 3.47239i | 0.154012 | + | 0.111896i | ||||
\(964\) | −21.2995 | + | 15.4750i | −0.686010 | + | 0.498415i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 11.6047 | + | 8.43133i | 0.373376 | + | 0.271274i | ||||
\(967\) | 2.42552 | + | 7.46499i | 0.0779995 | + | 0.240058i | 0.982452 | − | 0.186517i | \(-0.0597200\pi\) |
−0.904452 | + | 0.426575i | \(0.859720\pi\) | |||||||
\(968\) | 20.5894 | 0.661768 | ||||||||
\(969\) | 2.70945 | + | 8.33882i | 0.0870400 | + | 0.267881i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.32948 | − | 4.09171i | 0.0426649 | − | 0.131309i | −0.927455 | − | 0.373934i | \(-0.878009\pi\) |
0.970120 | + | 0.242625i | \(0.0780085\pi\) | |||||||
\(972\) | 0.309017 | − | 0.951057i | 0.00991172 | − | 0.0305052i | ||||
\(973\) | −15.5889 | + | 11.3260i | −0.499757 | + | 0.363095i | ||||
\(974\) | 1.27292 | 0.0407869 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.270588 | 0.00866132 | ||||||||
\(977\) | −0.344912 | + | 0.250593i | −0.0110347 | + | 0.00801720i | −0.593289 | − | 0.804990i | \(-0.702171\pi\) |
0.582254 | + | 0.813007i | \(0.302171\pi\) | |||||||
\(978\) | 1.13017 | − | 3.47829i | 0.0361387 | − | 0.111224i | ||||
\(979\) | 20.4773 | − | 63.0226i | 0.654457 | − | 2.01421i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.74225 | + | 5.36211i | 0.0556259 | + | 0.171199i | ||||
\(982\) | 10.6983 | 0.341395 | ||||||||
\(983\) | −18.4146 | − | 56.6743i | −0.587335 | − | 1.80763i | −0.589685 | − | 0.807634i | \(-0.700748\pi\) |
0.00234965 | − | 0.999997i | \(-0.499252\pi\) | |||||||
\(984\) | 1.27617 | + | 0.927190i | 0.0406827 | + | 0.0295577i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.54495 | + | 2.57556i | −0.112894 | + | 0.0820225i | ||||
\(987\) | 6.73682 | + | 4.89458i | 0.214435 | + | 0.155796i | ||||
\(988\) | 32.8380 | + | 23.8582i | 1.04472 | + | 0.759030i | ||||
\(989\) | 14.1216 | − | 10.2599i | 0.449041 | − | 0.326247i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.7809 | − | 12.9186i | −0.564830 | − | 0.410373i | 0.268393 | − | 0.963309i | \(-0.413507\pi\) |
−0.833224 | + | 0.552936i | \(0.813507\pi\) | |||||||
\(992\) | −1.72444 | − | 5.30729i | −0.0547511 | − | 0.168507i | ||||
\(993\) | 23.6472 | 0.750420 | ||||||||
\(994\) | −3.79468 | − | 11.6788i | −0.120360 | − | 0.370430i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −0.0415695 | + | 0.127938i | −0.00131718 | + | 0.00405387i | ||||
\(997\) | −13.8580 | + | 42.6506i | −0.438887 | + | 1.35076i | 0.450163 | + | 0.892947i | \(0.351366\pi\) |
−0.889050 | + | 0.457810i | \(0.848634\pi\) | |||||||
\(998\) | 5.72812 | − | 4.16172i | 0.181320 | − | 0.131737i | ||||
\(999\) | −2.99179 | −0.0946560 |
(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 | 750.2.g.f.301.3 | 16 | ||
5.2 | odd | 4 | 750.2.h.d.199.2 | 16 | |||
5.3 | odd | 4 | 150.2.h.b.139.4 | yes | 16 | ||
5.4 | even | 2 | 750.2.g.g.301.2 | 16 | |||
15.8 | even | 4 | 450.2.l.c.289.1 | 16 | |||
25.3 | odd | 20 | 3750.2.c.k.1249.3 | 16 | |||
25.4 | even | 10 | 3750.2.a.u.1.3 | 8 | |||
25.9 | even | 10 | 750.2.g.g.451.2 | 16 | |||
25.12 | odd | 20 | 150.2.h.b.109.4 | ✓ | 16 | ||
25.13 | odd | 20 | 750.2.h.d.49.1 | 16 | |||
25.16 | even | 5 | inner | 750.2.g.f.451.3 | 16 | ||
25.21 | even | 5 | 3750.2.a.v.1.6 | 8 | |||
25.22 | odd | 20 | 3750.2.c.k.1249.14 | 16 | |||
75.62 | even | 20 | 450.2.l.c.109.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.h.b.109.4 | ✓ | 16 | 25.12 | odd | 20 | ||
150.2.h.b.139.4 | yes | 16 | 5.3 | odd | 4 | ||
450.2.l.c.109.1 | 16 | 75.62 | even | 20 | |||
450.2.l.c.289.1 | 16 | 15.8 | even | 4 | |||
750.2.g.f.301.3 | 16 | 1.1 | even | 1 | trivial | ||
750.2.g.f.451.3 | 16 | 25.16 | even | 5 | inner | ||
750.2.g.g.301.2 | 16 | 5.4 | even | 2 | |||
750.2.g.g.451.2 | 16 | 25.9 | even | 10 | |||
750.2.h.d.49.1 | 16 | 25.13 | odd | 20 | |||
750.2.h.d.199.2 | 16 | 5.2 | odd | 4 | |||
3750.2.a.u.1.3 | 8 | 25.4 | even | 10 | |||
3750.2.a.v.1.6 | 8 | 25.21 | even | 5 | |||
3750.2.c.k.1249.3 | 16 | 25.3 | odd | 20 | |||
3750.2.c.k.1249.14 | 16 | 25.22 | odd | 20 |