Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,3,Mod(67,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.67");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.k (of order \(6\), degree \(2\), 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: | \(10.6812263629\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + 3 x^{14} + 6 x^{13} - 22 x^{12} + 44 x^{11} - 20 x^{10} - 112 x^{9} + 368 x^{8} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 67.4 | ||
Root | \(1.56937 + 1.23978i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.67 |
Dual form | 392.3.k.n.275.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.288997 | − | 1.97901i | −0.144499 | − | 0.989505i | ||||
\(3\) | 0.0487183 | − | 0.0843825i | 0.0162394 | − | 0.0281275i | −0.857791 | − | 0.513998i | \(-0.828164\pi\) |
0.874031 | + | 0.485870i | \(0.161497\pi\) | |||||||
\(4\) | −3.83296 | + | 1.14386i | −0.958240 | + | 0.285964i | ||||
\(5\) | 3.00119 | − | 1.73274i | 0.600237 | − | 0.346547i | −0.168898 | − | 0.985634i | \(-0.554021\pi\) |
0.769135 | + | 0.639086i | \(0.220687\pi\) | |||||||
\(6\) | −0.181073 | − | 0.0720276i | −0.0301789 | − | 0.0120046i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.37142 | + | 7.25490i | 0.421428 | + | 0.906862i | ||||
\(9\) | 4.49525 | + | 7.78601i | 0.499473 | + | 0.865112i | ||||
\(10\) | −4.29644 | − | 5.43862i | −0.429644 | − | 0.543862i | ||||
\(11\) | 1.46433 | − | 2.53629i | 0.133121 | − | 0.230572i | −0.791757 | − | 0.610836i | \(-0.790833\pi\) |
0.924878 | + | 0.380264i | \(0.124167\pi\) | |||||||
\(12\) | −0.0902137 | + | 0.379162i | −0.00751781 | + | 0.0315968i | ||||
\(13\) | 19.1586i | 1.47374i | 0.676036 | + | 0.736869i | \(0.263696\pi\) | ||||
−0.676036 | + | 0.736869i | \(0.736304\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 0.337664i | − | 0.0225109i | ||||||
\(16\) | 13.3832 | − | 8.76872i | 0.836449 | − | 0.548045i | ||||
\(17\) | −7.19487 | + | 12.4619i | −0.423228 | + | 0.733052i | −0.996253 | − | 0.0864856i | \(-0.972436\pi\) |
0.573025 | + | 0.819538i | \(0.305770\pi\) | |||||||
\(18\) | 14.1095 | − | 11.1463i | 0.783859 | − | 0.619238i | ||||
\(19\) | 4.04872 | + | 7.01259i | 0.213090 | + | 0.369083i | 0.952680 | − | 0.303975i | \(-0.0983138\pi\) |
−0.739590 | + | 0.673058i | \(0.764980\pi\) | |||||||
\(20\) | −9.52143 | + | 10.0744i | −0.476071 | + | 0.503722i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.44254 | − | 2.16494i | −0.247388 | − | 0.0984064i | ||||
\(23\) | 14.5144 | − | 8.37990i | 0.631062 | − | 0.364344i | −0.150101 | − | 0.988671i | \(-0.547960\pi\) |
0.781163 | + | 0.624327i | \(0.214627\pi\) | |||||||
\(24\) | 0.776436 | + | 0.0689571i | 0.0323515 | + | 0.00287321i | ||||
\(25\) | −6.49525 | + | 11.2501i | −0.259810 | + | 0.450004i | ||||
\(26\) | 37.9150 | − | 5.53678i | 1.45827 | − | 0.212953i | ||||
\(27\) | 1.75293 | 0.0649234 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 27.1649i | − | 0.936720i | −0.883538 | − | 0.468360i | \(-0.844845\pi\) | ||
0.883538 | − | 0.468360i | \(-0.155155\pi\) | |||||||
\(30\) | −0.668240 | + | 0.0975839i | −0.0222747 | + | 0.00325280i | ||||
\(31\) | 38.8779 | + | 22.4461i | 1.25412 | + | 0.724069i | 0.971926 | − | 0.235287i | \(-0.0756030\pi\) |
0.282198 | + | 0.959356i | \(0.408936\pi\) | |||||||
\(32\) | −21.2211 | − | 23.9513i | −0.663159 | − | 0.748479i | ||||
\(33\) | −0.142679 | − | 0.247128i | −0.00432362 | − | 0.00748872i | ||||
\(34\) | 26.7415 | + | 10.6373i | 0.786515 | + | 0.312861i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −26.1362 | − | 24.7015i | −0.726006 | − | 0.686154i | ||||
\(37\) | 34.2675 | − | 19.7844i | 0.926149 | − | 0.534713i | 0.0405576 | − | 0.999177i | \(-0.487087\pi\) |
0.885592 | + | 0.464465i | \(0.153753\pi\) | |||||||
\(38\) | 12.7079 | − | 10.0391i | 0.334419 | − | 0.264186i | ||||
\(39\) | 1.61665 | + | 0.933373i | 0.0414526 | + | 0.0239327i | ||||
\(40\) | 22.6891 | + | 15.9315i | 0.567227 | + | 0.398288i | ||||
\(41\) | −45.8766 | −1.11894 | −0.559471 | − | 0.828850i | \(-0.688996\pi\) | ||||
−0.559471 | + | 0.828850i | \(0.688996\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 61.0334 | 1.41938 | 0.709690 | − | 0.704514i | \(-0.248835\pi\) | ||||
0.709690 | + | 0.704514i | \(0.248835\pi\) | |||||||
\(44\) | −2.71156 | + | 11.3965i | −0.0616264 | + | 0.259011i | ||||
\(45\) | 26.9822 | + | 15.5782i | 0.599604 | + | 0.346182i | ||||
\(46\) | −20.7785 | − | 26.3024i | −0.451707 | − | 0.571791i | ||||
\(47\) | 40.0790 | − | 23.1396i | 0.852746 | − | 0.492333i | −0.00883070 | − | 0.999961i | \(-0.502811\pi\) |
0.861576 | + | 0.507628i | \(0.169478\pi\) | |||||||
\(48\) | −0.0879212 | − | 1.55650i | −0.00183169 | − | 0.0324272i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 24.1412 | + | 9.60292i | 0.482824 | + | 0.192058i | ||||
\(51\) | 0.701044 | + | 1.21424i | 0.0137460 | + | 0.0238087i | ||||
\(52\) | −21.9147 | − | 73.4341i | −0.421436 | − | 1.41219i | ||||
\(53\) | −8.39546 | − | 4.84712i | −0.158405 | − | 0.0914551i | 0.418702 | − | 0.908124i | \(-0.362485\pi\) |
−0.577107 | + | 0.816669i | \(0.695818\pi\) | |||||||
\(54\) | −0.506593 | − | 3.46907i | −0.00938135 | − | 0.0642421i | ||||
\(55\) | − | 10.1492i | − | 0.184531i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.788986 | 0.0138419 | ||||||||
\(58\) | −53.7596 | + | 7.85058i | −0.926889 | + | 0.135355i | ||||
\(59\) | −57.2770 | + | 99.2066i | −0.970796 | + | 1.68147i | −0.277632 | + | 0.960687i | \(0.589550\pi\) |
−0.693164 | + | 0.720780i | \(0.743784\pi\) | |||||||
\(60\) | 0.386239 | + | 1.29425i | 0.00643732 | + | 0.0215709i | ||||
\(61\) | 6.47814 | − | 3.74016i | 0.106199 | − | 0.0613141i | −0.445960 | − | 0.895053i | \(-0.647138\pi\) |
0.552159 | + | 0.833739i | \(0.313804\pi\) | |||||||
\(62\) | 33.1855 | − | 83.4265i | 0.535251 | − | 1.34559i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −41.2671 | + | 48.9186i | −0.644798 | + | 0.764353i | ||||
\(65\) | 33.1968 | + | 57.4985i | 0.510720 | + | 0.884592i | ||||
\(66\) | −0.447834 | + | 0.353783i | −0.00678537 | + | 0.00536035i | ||||
\(67\) | 6.02950 | − | 10.4434i | 0.0899925 | − | 0.155872i | −0.817515 | − | 0.575907i | \(-0.804649\pi\) |
0.907508 | + | 0.420035i | \(0.137982\pi\) | |||||||
\(68\) | 13.3231 | − | 55.9958i | 0.195927 | − | 0.823468i | ||||
\(69\) | − | 1.63302i | − | 0.0236669i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 129.187i | − | 1.81953i | −0.415124 | − | 0.909765i | \(-0.636262\pi\) | ||
0.415124 | − | 0.909765i | \(-0.363738\pi\) | |||||||
\(72\) | −41.3313 | + | 58.8625i | −0.574046 | + | 0.817535i | ||||
\(73\) | −9.14268 | + | 15.8356i | −0.125242 | + | 0.216926i | −0.921828 | − | 0.387600i | \(-0.873304\pi\) |
0.796585 | + | 0.604526i | \(0.206637\pi\) | |||||||
\(74\) | −49.0567 | − | 62.0981i | −0.662928 | − | 0.839164i | ||||
\(75\) | 0.632875 | + | 1.09617i | 0.00843833 | + | 0.0146156i | ||||
\(76\) | −23.5400 | − | 22.2478i | −0.309737 | − | 0.292734i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.37995 | − | 3.46911i | 0.0176916 | − | 0.0444758i | ||||
\(79\) | −36.9073 | + | 21.3084i | −0.467180 | + | 0.269727i | −0.715059 | − | 0.699064i | \(-0.753600\pi\) |
0.247878 | + | 0.968791i | \(0.420267\pi\) | |||||||
\(80\) | 24.9716 | − | 49.5061i | 0.312144 | − | 0.618826i | ||||
\(81\) | −40.3719 | + | 69.9261i | −0.498418 | + | 0.863286i | ||||
\(82\) | 13.2582 | + | 90.7903i | 0.161686 | + | 1.10720i | ||||
\(83\) | 109.670 | 1.32133 | 0.660663 | − | 0.750683i | \(-0.270275\pi\) | ||||
0.660663 | + | 0.750683i | \(0.270275\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 49.8673i | 0.586674i | ||||||||
\(86\) | −17.6385 | − | 120.786i | −0.205099 | − | 1.40448i | ||||
\(87\) | −2.29224 | − | 1.32343i | −0.0263476 | − | 0.0152118i | ||||
\(88\) | 23.3374 | + | 2.07265i | 0.265198 | + | 0.0235529i | ||||
\(89\) | −40.4581 | − | 70.0755i | −0.454585 | − | 0.787365i | 0.544079 | − | 0.839034i | \(-0.316879\pi\) |
−0.998664 | + | 0.0516693i | \(0.983546\pi\) | |||||||
\(90\) | 23.0316 | − | 57.9001i | 0.255906 | − | 0.643334i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −46.0478 | + | 48.7223i | −0.500519 | + | 0.529590i | ||||
\(93\) | 3.78812 | − | 2.18707i | 0.0407325 | − | 0.0235169i | ||||
\(94\) | −57.3763 | − | 72.6295i | −0.610386 | − | 0.772655i | ||||
\(95\) | 24.3019 | + | 14.0307i | 0.255810 | + | 0.147692i | ||||
\(96\) | −3.05493 | + | 0.623822i | −0.0318222 | + | 0.00649815i | ||||
\(97\) | −162.086 | −1.67099 | −0.835495 | − | 0.549498i | \(-0.814819\pi\) | ||||
−0.835495 | + | 0.549498i | \(0.814819\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 26.3301 | 0.265961 | ||||||||
\(100\) | 12.0275 | − | 50.5509i | 0.120275 | − | 0.505509i | ||||
\(101\) | 92.5150 | + | 53.4135i | 0.915990 | + | 0.528847i | 0.882354 | − | 0.470587i | \(-0.155958\pi\) |
0.0336364 | + | 0.999434i | \(0.489291\pi\) | |||||||
\(102\) | 2.20040 | − | 1.73829i | 0.0215725 | − | 0.0170420i | ||||
\(103\) | −109.662 | + | 63.3132i | −1.06468 | + | 0.614691i | −0.926722 | − | 0.375748i | \(-0.877386\pi\) |
−0.137954 | + | 0.990439i | \(0.544053\pi\) | |||||||
\(104\) | −138.994 | + | 64.5916i | −1.33648 | + | 0.621074i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.16623 | + | 18.0155i | −0.0676060 | + | 0.169958i | ||||
\(107\) | −43.5096 | − | 75.3608i | −0.406632 | − | 0.704306i | 0.587878 | − | 0.808949i | \(-0.299963\pi\) |
−0.994510 | + | 0.104643i | \(0.966630\pi\) | |||||||
\(108\) | −6.71892 | + | 2.00510i | −0.0622123 | + | 0.0185658i | ||||
\(109\) | 164.477 | + | 94.9607i | 1.50896 | + | 0.871199i | 0.999945 | + | 0.0104412i | \(0.00332359\pi\) |
0.509015 | + | 0.860758i | \(0.330010\pi\) | |||||||
\(110\) | −20.0853 | + | 2.93309i | −0.182594 | + | 0.0266644i | ||||
\(111\) | − | 3.85544i | − | 0.0347337i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −40.1848 | −0.355617 | −0.177809 | − | 0.984065i | \(-0.556901\pi\) | ||||
−0.177809 | + | 0.984065i | \(0.556901\pi\) | |||||||
\(114\) | −0.228015 | − | 1.56141i | −0.00200013 | − | 0.0136966i | ||||
\(115\) | 29.0403 | − | 50.2993i | 0.252524 | − | 0.437385i | ||||
\(116\) | 31.0728 | + | 104.122i | 0.267869 | + | 0.897603i | ||||
\(117\) | −149.169 | + | 86.1227i | −1.27495 | + | 0.736091i | ||||
\(118\) | 212.884 | + | 84.6812i | 1.80410 | + | 0.717638i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.44971 | − | 1.13841i | 0.0204143 | − | 0.00948672i | ||||
\(121\) | 56.2115 | + | 97.3611i | 0.464558 | + | 0.804637i | ||||
\(122\) | −9.27398 | − | 11.7394i | −0.0760162 | − | 0.0962247i | ||||
\(123\) | −2.23503 | + | 3.87119i | −0.0181710 | + | 0.0314731i | ||||
\(124\) | −174.692 | − | 41.5645i | −1.40881 | − | 0.335197i | ||||
\(125\) | 131.655i | 1.05324i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 153.657i | 1.20989i | 0.796266 | + | 0.604947i | \(0.206806\pi\) | ||||
−0.796266 | + | 0.604947i | \(0.793194\pi\) | |||||||
\(128\) | 108.736 | + | 67.5306i | 0.849504 | + | 0.527583i | ||||
\(129\) | 2.97344 | − | 5.15015i | 0.0230499 | − | 0.0399236i | ||||
\(130\) | 104.196 | − | 82.3137i | 0.801510 | − | 0.633182i | ||||
\(131\) | 30.9325 | + | 53.5766i | 0.236126 | + | 0.408982i | 0.959599 | − | 0.281371i | \(-0.0907890\pi\) |
−0.723474 | + | 0.690352i | \(0.757456\pi\) | |||||||
\(132\) | 0.829563 | + | 0.784026i | 0.00628457 | + | 0.00593959i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −22.4101 | − | 8.91433i | −0.167240 | − | 0.0665248i | ||||
\(135\) | 5.26088 | − | 3.03737i | 0.0389695 | − | 0.0224990i | ||||
\(136\) | −114.667 | − | 10.1838i | −0.843137 | − | 0.0748810i | ||||
\(137\) | −52.9715 | + | 91.7494i | −0.386653 | + | 0.669703i | −0.991997 | − | 0.126261i | \(-0.959702\pi\) |
0.605344 | + | 0.795964i | \(0.293036\pi\) | |||||||
\(138\) | −3.23176 | + | 0.471938i | −0.0234185 | + | 0.00341984i | ||||
\(139\) | 185.384 | 1.33370 | 0.666848 | − | 0.745194i | \(-0.267643\pi\) | ||||
0.666848 | + | 0.745194i | \(0.267643\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 4.50930i | − | 0.0319808i | ||||||
\(142\) | −255.662 | + | 37.3346i | −1.80043 | + | 0.262920i | ||||
\(143\) | 48.5918 | + | 28.0545i | 0.339803 | + | 0.196185i | ||||
\(144\) | 128.434 | + | 64.7839i | 0.891903 | + | 0.449888i | ||||
\(145\) | −47.0696 | − | 81.5269i | −0.324618 | − | 0.562254i | ||||
\(146\) | 33.9810 | + | 13.5170i | 0.232747 | + | 0.0925823i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −108.716 | + | 115.030i | −0.734565 | + | 0.777229i | ||||
\(149\) | 41.0579 | − | 23.7048i | 0.275556 | − | 0.159093i | −0.355854 | − | 0.934542i | \(-0.615810\pi\) |
0.631410 | + | 0.775449i | \(0.282477\pi\) | |||||||
\(150\) | 1.98644 | − | 1.56926i | 0.0132429 | − | 0.0104617i | ||||
\(151\) | −99.2255 | − | 57.2879i | −0.657122 | − | 0.379390i | 0.134057 | − | 0.990974i | \(-0.457199\pi\) |
−0.791180 | + | 0.611584i | \(0.790533\pi\) | |||||||
\(152\) | −37.2257 | + | 53.0154i | −0.244906 | + | 0.348786i | ||||
\(153\) | −129.371 | −0.845563 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 155.573 | 1.00370 | ||||||||
\(156\) | −7.26420 | − | 1.72837i | −0.0465654 | − | 0.0110793i | ||||
\(157\) | −254.694 | − | 147.047i | −1.62225 | − | 0.936608i | −0.986316 | − | 0.164867i | \(-0.947280\pi\) |
−0.635937 | − | 0.771741i | \(-0.719386\pi\) | |||||||
\(158\) | 52.8357 | + | 66.8818i | 0.334403 | + | 0.423302i | ||||
\(159\) | −0.818024 | + | 0.472287i | −0.00514481 | + | 0.00297036i | ||||
\(160\) | −105.190 | − | 35.1118i | −0.657436 | − | 0.219449i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 150.052 | + | 59.6879i | 0.926246 | + | 0.368444i | ||||
\(163\) | −85.5104 | − | 148.108i | −0.524603 | − | 0.908640i | −0.999590 | − | 0.0286465i | \(-0.990880\pi\) |
0.474986 | − | 0.879993i | \(-0.342453\pi\) | |||||||
\(164\) | 175.843 | − | 52.4763i | 1.07222 | − | 0.319977i | ||||
\(165\) | −0.856414 | − | 0.494451i | −0.00519039 | − | 0.00299667i | ||||
\(166\) | −31.6943 | − | 217.038i | −0.190930 | − | 1.30746i | ||||
\(167\) | − | 120.657i | − | 0.722499i | −0.932469 | − | 0.361249i | \(-0.882350\pi\) | ||
0.932469 | − | 0.361249i | \(-0.117650\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −198.052 | −1.17190 | ||||||||
\(170\) | 98.6878 | − | 14.4115i | 0.580516 | − | 0.0847735i | ||||
\(171\) | −36.4000 | + | 63.0467i | −0.212866 | + | 0.368694i | ||||
\(172\) | −233.939 | + | 69.8134i | −1.36011 | + | 0.405892i | ||||
\(173\) | 93.8242 | − | 54.1694i | 0.542336 | − | 0.313118i | −0.203689 | − | 0.979036i | \(-0.565293\pi\) |
0.746025 | + | 0.665918i | \(0.231960\pi\) | |||||||
\(174\) | −1.95662 | + | 4.91884i | −0.0112450 | + | 0.0282692i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.64266 | − | 46.7840i | −0.0150151 | − | 0.265818i | ||||
\(177\) | 5.58087 | + | 9.66635i | 0.0315303 | + | 0.0546121i | ||||
\(178\) | −126.988 | + | 100.319i | −0.713414 | + | 0.563587i | ||||
\(179\) | 80.7188 | − | 139.809i | 0.450943 | − | 0.781056i | −0.547502 | − | 0.836805i | \(-0.684421\pi\) |
0.998445 | + | 0.0557481i | \(0.0177544\pi\) | |||||||
\(180\) | −121.241 | − | 28.8468i | −0.673560 | − | 0.160260i | ||||
\(181\) | 7.14696i | 0.0394860i | 0.999805 | + | 0.0197430i | \(0.00628479\pi\) | ||||
−0.999805 | + | 0.0197430i | \(0.993715\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 0.728856i | − | 0.00398282i | ||||||
\(184\) | 109.730 | + | 77.0484i | 0.596356 | + | 0.418741i | ||||
\(185\) | 68.5621 | − | 118.753i | 0.370606 | − | 0.641909i | ||||
\(186\) | −5.42300 | − | 6.86468i | −0.0291559 | − | 0.0369069i | ||||
\(187\) | 21.0713 | + | 36.4966i | 0.112681 | + | 0.195169i | ||||
\(188\) | −127.153 | + | 134.538i | −0.676346 | + | 0.715628i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 20.7437 | − | 52.1486i | 0.109178 | − | 0.274466i | ||||
\(191\) | −63.4782 | + | 36.6491i | −0.332347 | + | 0.191880i | −0.656882 | − | 0.753993i | \(-0.728125\pi\) |
0.324536 | + | 0.945873i | \(0.394792\pi\) | |||||||
\(192\) | 2.11742 | + | 5.86545i | 0.0110282 | + | 0.0305492i | ||||
\(193\) | 42.5353 | − | 73.6732i | 0.220390 | − | 0.381727i | −0.734536 | − | 0.678569i | \(-0.762600\pi\) |
0.954926 | + | 0.296843i | \(0.0959337\pi\) | |||||||
\(194\) | 46.8424 | + | 320.770i | 0.241456 | + | 1.65345i | ||||
\(195\) | 6.46916 | 0.0331752 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 140.460i | 0.712996i | 0.934296 | + | 0.356498i | \(0.116029\pi\) | ||||
−0.934296 | + | 0.356498i | \(0.883971\pi\) | |||||||
\(198\) | −7.60934 | − | 52.1076i | −0.0384310 | − | 0.263170i | ||||
\(199\) | −123.913 | − | 71.5411i | −0.622677 | − | 0.359503i | 0.155233 | − | 0.987878i | \(-0.450387\pi\) |
−0.777911 | + | 0.628375i | \(0.783720\pi\) | |||||||
\(200\) | −103.517 | − | 9.19355i | −0.517583 | − | 0.0459677i | ||||
\(201\) | −0.587494 | − | 1.01757i | −0.00292285 | − | 0.00506253i | ||||
\(202\) | 78.9694 | − | 198.524i | 0.390937 | − | 0.982794i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −4.07599 | − | 3.85225i | −0.0199804 | − | 0.0188836i | ||||
\(205\) | −137.684 | + | 79.4921i | −0.671631 | + | 0.387766i | ||||
\(206\) | 156.989 | + | 198.724i | 0.762084 | + | 0.964680i | ||||
\(207\) | 130.492 | + | 75.3396i | 0.630396 | + | 0.363959i | ||||
\(208\) | 167.996 | + | 256.403i | 0.807674 | + | 1.23271i | ||||
\(209\) | 23.7146 | 0.113467 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −111.955 | −0.530591 | −0.265295 | − | 0.964167i | \(-0.585469\pi\) | ||||
−0.265295 | + | 0.964167i | \(0.585469\pi\) | |||||||
\(212\) | 37.7239 | + | 8.97562i | 0.177943 | + | 0.0423378i | ||||
\(213\) | −10.9011 | − | 6.29375i | −0.0511788 | − | 0.0295481i | ||||
\(214\) | −136.566 | + | 107.885i | −0.638157 | + | 0.504135i | ||||
\(215\) | 183.173 | − | 105.755i | 0.851965 | − | 0.491882i | ||||
\(216\) | 5.90987 | + | 12.7173i | 0.0273605 | + | 0.0588766i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 140.395 | − | 352.944i | 0.644013 | − | 1.61901i | ||||
\(219\) | 0.890831 | + | 1.54296i | 0.00406772 | + | 0.00704550i | ||||
\(220\) | 11.6092 | + | 38.9014i | 0.0527692 | + | 0.176825i | ||||
\(221\) | −238.752 | − | 137.844i | −1.08033 | − | 0.623727i | ||||
\(222\) | −7.62996 | + | 1.11421i | −0.0343692 | + | 0.00501897i | ||||
\(223\) | − | 311.438i | − | 1.39658i | −0.715814 | − | 0.698291i | \(-0.753944\pi\) | ||
0.715814 | − | 0.698291i | \(-0.246056\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −116.791 | −0.519072 | ||||||||
\(226\) | 11.6133 | + | 79.5261i | 0.0513862 | + | 0.351885i | ||||
\(227\) | 37.1791 | − | 64.3960i | 0.163784 | − | 0.283683i | −0.772439 | − | 0.635090i | \(-0.780963\pi\) |
0.936223 | + | 0.351407i | \(0.114297\pi\) | |||||||
\(228\) | −3.02415 | + | 0.902488i | −0.0132638 | + | 0.00395828i | ||||
\(229\) | 67.7847 | − | 39.1355i | 0.296003 | − | 0.170897i | −0.344643 | − | 0.938734i | \(-0.612000\pi\) |
0.640646 | + | 0.767836i | \(0.278667\pi\) | |||||||
\(230\) | −107.935 | − | 42.9347i | −0.469284 | − | 0.186673i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 197.078 | − | 91.5842i | 0.849476 | − | 0.394760i | ||||
\(233\) | −46.5287 | − | 80.5900i | −0.199694 | − | 0.345880i | 0.748735 | − | 0.662869i | \(-0.230661\pi\) |
−0.948429 | + | 0.316989i | \(0.897328\pi\) | |||||||
\(234\) | 213.547 | + | 270.318i | 0.912594 | + | 1.15520i | ||||
\(235\) | 80.1898 | − | 138.893i | 0.341233 | − | 0.591033i | ||||
\(236\) | 106.062 | − | 445.772i | 0.449416 | − | 1.88886i | ||||
\(237\) | 4.15244i | 0.0175208i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 291.605i | − | 1.22011i | −0.792361 | − | 0.610053i | \(-0.791148\pi\) | ||
0.792361 | − | 0.610053i | \(-0.208852\pi\) | |||||||
\(240\) | −2.96088 | − | 4.51901i | −0.0123370 | − | 0.0188292i | ||||
\(241\) | 111.874 | − | 193.771i | 0.464207 | − | 0.804029i | −0.534959 | − | 0.844878i | \(-0.679673\pi\) |
0.999165 | + | 0.0408488i | \(0.0130062\pi\) | |||||||
\(242\) | 176.434 | − | 139.380i | 0.729065 | − | 0.575951i | ||||
\(243\) | 11.8219 | + | 20.4761i | 0.0486498 | + | 0.0842639i | ||||
\(244\) | −20.5523 | + | 21.7459i | −0.0842306 | + | 0.0891227i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.30703 | + | 3.30438i | 0.0337684 | + | 0.0134325i | ||||
\(247\) | −134.351 | + | 77.5677i | −0.543932 | + | 0.314039i | ||||
\(248\) | −31.7708 | + | 357.730i | −0.128108 | + | 1.44246i | ||||
\(249\) | 5.34294 | − | 9.25424i | 0.0214576 | − | 0.0371656i | ||||
\(250\) | 260.547 | − | 38.0479i | 1.04219 | − | 0.152192i | ||||
\(251\) | 310.605 | 1.23747 | 0.618734 | − | 0.785600i | \(-0.287646\pi\) | ||||
0.618734 | + | 0.785600i | \(0.287646\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 49.0838i | − | 0.194007i | ||||||
\(254\) | 304.088 | − | 44.4063i | 1.19720 | − | 0.174828i | ||||
\(255\) | 4.20793 | + | 2.42945i | 0.0165017 | + | 0.00952724i | ||||
\(256\) | 102.219 | − | 234.707i | 0.399293 | − | 0.916823i | ||||
\(257\) | 87.7358 | + | 151.963i | 0.341385 | + | 0.591295i | 0.984690 | − | 0.174314i | \(-0.0557708\pi\) |
−0.643306 | + | 0.765610i | \(0.722438\pi\) | |||||||
\(258\) | −11.0515 | − | 4.39609i | −0.0428353 | − | 0.0170391i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −193.012 | − | 182.417i | −0.742354 | − | 0.701604i | ||||
\(261\) | 211.506 | − | 122.113i | 0.810368 | − | 0.467866i | ||||
\(262\) | 97.0892 | − | 76.6991i | 0.370569 | − | 0.292745i | ||||
\(263\) | −270.310 | − | 156.064i | −1.02779 | − | 0.593398i | −0.111443 | − | 0.993771i | \(-0.535547\pi\) |
−0.916352 | + | 0.400373i | \(0.868880\pi\) | |||||||
\(264\) | 1.31185 | − | 1.86830i | 0.00496915 | − | 0.00707688i | ||||
\(265\) | −33.5951 | −0.126774 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.88419 | −0.0295288 | ||||||||
\(268\) | −11.1651 | + | 46.9260i | −0.0416607 | + | 0.175097i | ||||
\(269\) | 123.683 | + | 71.4084i | 0.459788 | + | 0.265459i | 0.711955 | − | 0.702225i | \(-0.247810\pi\) |
−0.252167 | + | 0.967684i | \(0.581143\pi\) | |||||||
\(270\) | −7.53137 | − | 9.53354i | −0.0278939 | − | 0.0353094i | ||||
\(271\) | 230.464 | − | 133.059i | 0.850421 | − | 0.490991i | −0.0103718 | − | 0.999946i | \(-0.503301\pi\) |
0.860793 | + | 0.508955i | \(0.169968\pi\) | |||||||
\(272\) | 12.9845 | + | 229.870i | 0.0477371 | + | 0.845108i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 196.882 | + | 78.3158i | 0.718546 | + | 0.285824i | ||||
\(275\) | 19.0224 | + | 32.9477i | 0.0691723 | + | 0.119810i | ||||
\(276\) | 1.86794 | + | 6.25929i | 0.00676789 | + | 0.0226786i | ||||
\(277\) | −317.606 | − | 183.370i | −1.14659 | − | 0.661986i | −0.198539 | − | 0.980093i | \(-0.563620\pi\) |
−0.948055 | + | 0.318107i | \(0.896953\pi\) | |||||||
\(278\) | −53.5754 | − | 366.876i | −0.192717 | − | 1.31970i | ||||
\(279\) | 403.604i | 1.44661i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 147.977 | 0.526607 | 0.263303 | − | 0.964713i | \(-0.415188\pi\) | ||||
0.263303 | + | 0.964713i | \(0.415188\pi\) | |||||||
\(282\) | −8.92394 | + | 1.30317i | −0.0316452 | + | 0.00462118i | ||||
\(283\) | 163.869 | − | 283.830i | 0.579043 | − | 1.00293i | −0.416546 | − | 0.909115i | \(-0.636759\pi\) |
0.995589 | − | 0.0938180i | \(-0.0299072\pi\) | |||||||
\(284\) | 147.771 | + | 495.167i | 0.520320 | + | 1.74355i | ||||
\(285\) | 2.36790 | − | 1.36710i | 0.00830840 | − | 0.00479686i | ||||
\(286\) | 41.4772 | − | 104.271i | 0.145025 | − | 0.364585i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 91.0909 | − | 272.895i | 0.316288 | − | 0.947551i | ||||
\(289\) | 40.9676 | + | 70.9580i | 0.141756 | + | 0.245529i | ||||
\(290\) | −147.740 | + | 116.712i | −0.509447 | + | 0.402456i | ||||
\(291\) | −7.89655 | + | 13.6772i | −0.0271359 | + | 0.0470008i | ||||
\(292\) | 16.9299 | − | 71.1551i | 0.0579791 | − | 0.243682i | ||||
\(293\) | − | 259.881i | − | 0.886966i | −0.896283 | − | 0.443483i | \(-0.853743\pi\) | ||
0.896283 | − | 0.443483i | \(-0.146257\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 396.983i | 1.34571i | ||||||||
\(296\) | 259.064 | + | 181.906i | 0.875215 | + | 0.614547i | ||||
\(297\) | 2.56687 | − | 4.44595i | 0.00864267 | − | 0.0149695i | ||||
\(298\) | −58.7776 | − | 74.4034i | −0.197240 | − | 0.249676i | ||||
\(299\) | 160.547 | + | 278.076i | 0.536947 | + | 0.930019i | ||||
\(300\) | −3.67965 | − | 3.47767i | −0.0122655 | − | 0.0115922i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −84.6974 | + | 212.924i | −0.280455 | + | 0.705047i | ||||
\(303\) | 9.01434 | − | 5.20443i | 0.0297503 | − | 0.0171763i | ||||
\(304\) | 115.676 | + | 58.3486i | 0.380514 | + | 0.191936i | ||||
\(305\) | 12.9614 | − | 22.4498i | 0.0424964 | − | 0.0736060i | ||||
\(306\) | 37.3879 | + | 256.027i | 0.122183 | + | 0.836689i | ||||
\(307\) | −290.462 | −0.946131 | −0.473065 | − | 0.881027i | \(-0.656853\pi\) | ||||
−0.473065 | + | 0.881027i | \(0.656853\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.3380i | 0.0399289i | ||||||||
\(310\) | −44.9602 | − | 307.880i | −0.145033 | − | 0.993162i | ||||
\(311\) | −64.8723 | − | 37.4540i | −0.208593 | − | 0.120431i | 0.392065 | − | 0.919938i | \(-0.371761\pi\) |
−0.600657 | + | 0.799507i | \(0.705094\pi\) | |||||||
\(312\) | −1.32112 | + | 14.8754i | −0.00423436 | + | 0.0476776i | ||||
\(313\) | 142.254 | + | 246.391i | 0.454485 | + | 0.787190i | 0.998658 | − | 0.0517821i | \(-0.0164901\pi\) |
−0.544174 | + | 0.838972i | \(0.683157\pi\) | |||||||
\(314\) | −217.403 | + | 546.538i | −0.692365 | + | 1.74057i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 117.090 | − | 123.891i | 0.370539 | − | 0.392060i | ||||
\(317\) | 10.6202 | − | 6.13157i | 0.0335022 | − | 0.0193425i | −0.483155 | − | 0.875535i | \(-0.660509\pi\) |
0.516658 | + | 0.856192i | \(0.327176\pi\) | |||||||
\(318\) | 1.17107 | + | 1.48239i | 0.00368260 | + | 0.00466160i | ||||
\(319\) | −68.8982 | − | 39.7784i | −0.215982 | − | 0.124697i | ||||
\(320\) | −39.0871 | + | 218.319i | −0.122147 | + | 0.682246i | ||||
\(321\) | −8.47885 | −0.0264139 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −116.520 | −0.360743 | ||||||||
\(324\) | 74.7583 | − | 314.204i | 0.230736 | − | 0.969765i | ||||
\(325\) | −215.536 | − | 124.440i | −0.663188 | − | 0.382892i | ||||
\(326\) | −268.395 | + | 212.029i | −0.823299 | + | 0.650395i | ||||
\(327\) | 16.0260 | − | 9.25264i | 0.0490093 | − | 0.0282955i | ||||
\(328\) | −154.669 | − | 332.830i | −0.471553 | − | 1.01473i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.731022 | + | 1.83775i | −0.00221522 | + | 0.00556893i | ||||
\(331\) | −97.2329 | − | 168.412i | −0.293755 | − | 0.508798i | 0.680940 | − | 0.732340i | \(-0.261572\pi\) |
−0.974694 | + | 0.223541i | \(0.928238\pi\) | |||||||
\(332\) | −420.361 | + | 125.447i | −1.26615 | + | 0.377852i | ||||
\(333\) | 308.082 | + | 177.871i | 0.925172 | + | 0.534148i | ||||
\(334\) | −238.782 | + | 34.8696i | −0.714916 | + | 0.104400i | ||||
\(335\) | − | 41.7901i | − | 0.124747i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.596077 | 0.00176877 | 0.000884387 | − | 1.00000i | \(-0.499718\pi\) | ||||
0.000884387 | 1.00000i | \(0.499718\pi\) | ||||||||
\(338\) | 57.2364 | + | 391.946i | 0.169338 | + | 1.15960i | ||||
\(339\) | −1.95773 | + | 3.39089i | −0.00577502 | + | 0.0100026i | ||||
\(340\) | −57.0410 | − | 191.139i | −0.167768 | − | 0.562174i | ||||
\(341\) | 113.860 | − | 65.7371i | 0.333900 | − | 0.192777i | ||||
\(342\) | 135.290 | + | 53.8157i | 0.395583 | + | 0.157356i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 205.769 | + | 442.791i | 0.598166 | + | 1.28718i | ||||
\(345\) | −2.82959 | − | 4.90099i | −0.00820171 | − | 0.0142058i | ||||
\(346\) | −134.317 | − | 170.024i | −0.388199 | − | 0.491399i | ||||
\(347\) | 102.433 | − | 177.420i | 0.295197 | − | 0.511296i | −0.679834 | − | 0.733366i | \(-0.737948\pi\) |
0.975031 | + | 0.222070i | \(0.0712814\pi\) | |||||||
\(348\) | 10.2999 | + | 2.45065i | 0.0295974 | + | 0.00704208i | ||||
\(349\) | 128.396i | 0.367898i | 0.982936 | + | 0.183949i | \(0.0588882\pi\) | ||||
−0.982936 | + | 0.183949i | \(0.941112\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 33.5837i | 0.0956801i | ||||||||
\(352\) | −91.8223 | + | 18.7503i | −0.260859 | + | 0.0532679i | ||||
\(353\) | −95.4207 | + | 165.274i | −0.270314 | + | 0.468197i | −0.968942 | − | 0.247288i | \(-0.920461\pi\) |
0.698628 | + | 0.715485i | \(0.253794\pi\) | |||||||
\(354\) | 17.5169 | − | 13.8381i | 0.0494829 | − | 0.0390908i | ||||
\(355\) | −223.846 | − | 387.713i | −0.630553 | − | 1.09215i | ||||
\(356\) | 235.231 | + | 222.318i | 0.660760 | + | 0.624489i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −300.011 | − | 119.339i | −0.838020 | − | 0.333349i | ||||
\(359\) | 186.805 | − | 107.852i | 0.520349 | − | 0.300424i | −0.216728 | − | 0.976232i | \(-0.569539\pi\) |
0.737077 | + | 0.675808i | \(0.236205\pi\) | |||||||
\(360\) | −22.0497 | + | 248.274i | −0.0612493 | + | 0.689649i | ||||
\(361\) | 147.716 | − | 255.851i | 0.409185 | − | 0.708729i | ||||
\(362\) | 14.1439 | − | 2.06545i | 0.0390715 | − | 0.00570567i | ||||
\(363\) | 10.9541 | 0.0301766 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 63.3674i | 0.173609i | ||||||||
\(366\) | −1.44241 | + | 0.210637i | −0.00394102 | + | 0.000575512i | ||||
\(367\) | −393.859 | − | 227.395i | −1.07319 | − | 0.619604i | −0.144135 | − | 0.989558i | \(-0.546040\pi\) |
−0.929050 | + | 0.369954i | \(0.879373\pi\) | |||||||
\(368\) | 120.768 | − | 239.423i | 0.328174 | − | 0.650605i | ||||
\(369\) | −206.227 | − | 357.196i | −0.558881 | − | 0.968010i | ||||
\(370\) | −254.828 | − | 101.366i | −0.688724 | − | 0.273962i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −12.0180 | + | 12.7160i | −0.0323065 | + | 0.0341829i | ||||
\(373\) | −312.417 | + | 180.374i | −0.837579 | + | 0.483576i | −0.856441 | − | 0.516246i | \(-0.827329\pi\) |
0.0188617 | + | 0.999822i | \(0.493996\pi\) | |||||||
\(374\) | 66.1376 | − | 52.2478i | 0.176839 | − | 0.139700i | ||||
\(375\) | 11.1094 | + | 6.41401i | 0.0296250 | + | 0.0171040i | ||||
\(376\) | 302.999 | + | 212.756i | 0.805848 | + | 0.565840i | ||||
\(377\) | 520.441 | 1.38048 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −268.427 | −0.708250 | −0.354125 | − | 0.935198i | \(-0.615221\pi\) | ||||
−0.354125 | + | 0.935198i | \(0.615221\pi\) | |||||||
\(380\) | −109.197 | − | 25.9813i | −0.287362 | − | 0.0683718i | ||||
\(381\) | 12.9659 | + | 7.48589i | 0.0340313 | + | 0.0196480i | ||||
\(382\) | 90.8741 | + | 115.032i | 0.237890 | + | 0.301132i | ||||
\(383\) | −503.621 | + | 290.766i | −1.31494 | + | 0.759180i | −0.982910 | − | 0.184089i | \(-0.941067\pi\) |
−0.332029 | + | 0.943269i | \(0.607733\pi\) | |||||||
\(384\) | 10.9959 | − | 5.88549i | 0.0286350 | − | 0.0153268i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −158.093 | − | 62.8863i | −0.409566 | − | 0.162918i | ||||
\(387\) | 274.360 | + | 475.206i | 0.708942 | + | 1.22792i | ||||
\(388\) | 621.269 | − | 185.403i | 1.60121 | − | 0.477843i | ||||
\(389\) | 443.646 | + | 256.139i | 1.14048 | + | 0.658455i | 0.946549 | − | 0.322560i | \(-0.104543\pi\) |
0.193929 | + | 0.981016i | \(0.437877\pi\) | |||||||
\(390\) | −1.86957 | − | 12.8025i | −0.00479377 | − | 0.0328270i | ||||
\(391\) | 241.169i | 0.616801i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.02790 | 0.0153382 | ||||||||
\(394\) | 277.972 | − | 40.5926i | 0.705513 | − | 0.103027i | ||||
\(395\) | −73.8437 | + | 127.901i | −0.186946 | + | 0.323800i | ||||
\(396\) | −100.922 | + | 30.1179i | −0.254855 | + | 0.0760553i | ||||
\(397\) | 70.4295 | − | 40.6625i | 0.177404 | − | 0.102424i | −0.408668 | − | 0.912683i | \(-0.634007\pi\) |
0.586073 | + | 0.810259i | \(0.300673\pi\) | |||||||
\(398\) | −105.770 | + | 265.900i | −0.265754 | + | 0.668090i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.7219 | + | 207.517i | 0.0293047 | + | 0.518793i | ||||
\(401\) | −263.720 | − | 456.777i | −0.657657 | − | 1.13909i | −0.981221 | − | 0.192888i | \(-0.938215\pi\) |
0.323564 | − | 0.946206i | \(-0.395119\pi\) | |||||||
\(402\) | −1.84399 | + | 1.45673i | −0.00458705 | + | 0.00362371i | ||||
\(403\) | −430.036 | + | 744.845i | −1.06709 | + | 1.84825i | ||||
\(404\) | −415.704 | − | 98.9081i | −1.02897 | − | 0.244822i | ||||
\(405\) | 279.815i | 0.690902i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 115.883i | − | 0.284726i | ||||||
\(408\) | −6.44570 | + | 9.17972i | −0.0157983 | + | 0.0224993i | ||||
\(409\) | −29.3363 | + | 50.8120i | −0.0717270 | + | 0.124235i | −0.899658 | − | 0.436595i | \(-0.856184\pi\) |
0.827931 | + | 0.560830i | \(0.189518\pi\) | |||||||
\(410\) | 197.106 | + | 249.506i | 0.480746 | + | 0.608550i | ||||
\(411\) | 5.16136 | + | 8.93974i | 0.0125581 | + | 0.0217512i | ||||
\(412\) | 347.908 | − | 368.114i | 0.844436 | − | 0.893481i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 111.386 | − | 280.018i | 0.269048 | − | 0.676372i | ||||
\(415\) | 329.140 | − | 190.029i | 0.793109 | − | 0.457902i | ||||
\(416\) | 458.873 | − | 406.566i | 1.10306 | − | 0.977322i | ||||
\(417\) | 9.03158 | − | 15.6432i | 0.0216585 | − | 0.0375136i | ||||
\(418\) | −6.85347 | − | 46.9315i | −0.0163959 | − | 0.112276i | ||||
\(419\) | −760.704 | −1.81552 | −0.907761 | − | 0.419487i | \(-0.862210\pi\) | ||||
−0.907761 | + | 0.419487i | \(0.862210\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 46.2918i | − | 0.109957i | −0.998488 | − | 0.0549784i | \(-0.982491\pi\) | ||
0.998488 | − | 0.0549784i | \(-0.0175090\pi\) | |||||||
\(422\) | 32.3546 | + | 221.559i | 0.0766696 | + | 0.525022i | ||||
\(423\) | 360.331 | + | 208.037i | 0.851846 | + | 0.491814i | ||||
\(424\) | 6.86074 | − | 77.2499i | 0.0161810 | − | 0.182193i | ||||
\(425\) | −93.4650 | − | 161.886i | −0.219918 | − | 0.380909i | ||||
\(426\) | −9.30501 | + | 23.3922i | −0.0218427 | + | 0.0549114i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 252.972 | + | 239.086i | 0.591057 | + | 0.558613i | ||||
\(429\) | 4.73462 | − | 2.73353i | 0.0110364 | − | 0.00637187i | ||||
\(430\) | −262.226 | − | 331.937i | −0.609828 | − | 0.771947i | ||||
\(431\) | 291.137 | + | 168.088i | 0.675492 | + | 0.389996i | 0.798154 | − | 0.602453i | \(-0.205810\pi\) |
−0.122662 | + | 0.992448i | \(0.539143\pi\) | |||||||
\(432\) | 23.4598 | − | 15.3710i | 0.0543051 | − | 0.0355810i | ||||
\(433\) | 372.694 | 0.860725 | 0.430363 | − | 0.902656i | \(-0.358386\pi\) | ||||
0.430363 | + | 0.902656i | \(0.358386\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.17260 | −0.0210864 | ||||||||
\(436\) | −739.054 | − | 175.843i | −1.69508 | − | 0.403309i | ||||
\(437\) | 117.530 | + | 67.8557i | 0.268946 | + | 0.155276i | ||||
\(438\) | 2.79610 | − | 2.20888i | 0.00638378 | − | 0.00504310i | ||||
\(439\) | −344.226 | + | 198.739i | −0.784115 | + | 0.452709i | −0.837887 | − | 0.545844i | \(-0.816209\pi\) |
0.0537719 | + | 0.998553i | \(0.482876\pi\) | |||||||
\(440\) | 73.6313 | − | 34.2172i | 0.167344 | − | 0.0777663i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −203.795 | + | 512.329i | −0.461075 | + | 1.15912i | ||||
\(443\) | −136.765 | − | 236.884i | −0.308725 | − | 0.534727i | 0.669359 | − | 0.742939i | \(-0.266569\pi\) |
−0.978084 | + | 0.208212i | \(0.933236\pi\) | |||||||
\(444\) | 4.41007 | + | 14.7778i | 0.00993260 | + | 0.0332832i | ||||
\(445\) | −242.844 | − | 140.206i | −0.545718 | − | 0.315070i | ||||
\(446\) | −616.339 | + | 90.0047i | −1.38193 | + | 0.201804i | ||||
\(447\) | − | 4.61943i | − | 0.0103343i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 428.702 | 0.954792 | 0.477396 | − | 0.878688i | \(-0.341581\pi\) | ||||
0.477396 | + | 0.878688i | \(0.341581\pi\) | |||||||
\(450\) | 33.7523 | + | 231.131i | 0.0750052 | + | 0.513624i | ||||
\(451\) | −67.1785 | + | 116.357i | −0.148955 | + | 0.257997i | ||||
\(452\) | 154.027 | − | 45.9656i | 0.340767 | − | 0.101694i | ||||
\(453\) | −9.66819 | + | 5.58193i | −0.0213426 | + | 0.0123221i | ||||
\(454\) | −138.185 | − | 54.9674i | −0.304372 | − | 0.121074i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.66000 | + | 5.72401i | 0.00583334 | + | 0.0125527i | ||||
\(457\) | −5.02501 | − | 8.70357i | −0.0109956 | − | 0.0190450i | 0.860475 | − | 0.509492i | \(-0.170167\pi\) |
−0.871471 | + | 0.490447i | \(0.836833\pi\) | |||||||
\(458\) | −97.0392 | − | 122.837i | −0.211876 | − | 0.268202i | ||||
\(459\) | −12.6121 | + | 21.8449i | −0.0274774 | + | 0.0475923i | ||||
\(460\) | −53.7752 | + | 226.013i | −0.116903 | + | 0.491333i | ||||
\(461\) | − | 825.802i | − | 1.79133i | −0.444732 | − | 0.895664i | \(-0.646701\pi\) | ||
0.444732 | − | 0.895664i | \(-0.353299\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 114.707i | 0.247748i | 0.992298 | + | 0.123874i | \(0.0395318\pi\) | ||||
−0.992298 | + | 0.123874i | \(0.960468\pi\) | |||||||
\(464\) | −238.201 | − | 363.553i | −0.513365 | − | 0.783519i | ||||
\(465\) | 7.57924 | − | 13.1276i | 0.0162995 | − | 0.0282315i | ||||
\(466\) | −146.042 | + | 115.371i | −0.313394 | + | 0.247577i | ||||
\(467\) | −100.864 | − | 174.701i | −0.215982 | − | 0.374092i | 0.737594 | − | 0.675245i | \(-0.235962\pi\) |
−0.953576 | + | 0.301153i | \(0.902629\pi\) | |||||||
\(468\) | 473.247 | − | 500.733i | 1.01121 | − | 1.06994i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −298.045 | − | 118.557i | −0.634138 | − | 0.252248i | ||||
\(471\) | −24.8165 | + | 14.3278i | −0.0526889 | + | 0.0304200i | ||||
\(472\) | −912.838 | − | 81.0713i | −1.93398 | − | 0.171761i | ||||
\(473\) | 89.3730 | − | 154.799i | 0.188949 | − | 0.327270i | ||||
\(474\) | 8.21772 | − | 1.20004i | 0.0173370 | − | 0.00253174i | ||||
\(475\) | −105.190 | −0.221452 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 87.1561i | − | 0.182717i | ||||||
\(478\) | −577.090 | + | 84.2732i | −1.20730 | + | 0.176304i | ||||
\(479\) | 517.483 | + | 298.769i | 1.08034 | + | 0.623735i | 0.930988 | − | 0.365050i | \(-0.118948\pi\) |
0.149352 | + | 0.988784i | \(0.452281\pi\) | |||||||
\(480\) | −8.08749 | + | 7.16559i | −0.0168489 | + | 0.0149283i | ||||
\(481\) | 379.040 | + | 656.517i | 0.788026 | + | 1.36490i | ||||
\(482\) | −415.806 | − | 165.400i | −0.862668 | − | 0.343154i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −326.824 | − | 308.884i | −0.675255 | − | 0.638189i | ||||
\(485\) | −486.450 | + | 280.852i | −1.00299 | + | 0.579077i | ||||
\(486\) | 37.1060 | − | 29.3132i | 0.0763497 | − | 0.0603152i | ||||
\(487\) | 298.887 | + | 172.562i | 0.613730 | + | 0.354337i | 0.774424 | − | 0.632667i | \(-0.218040\pi\) |
−0.160694 | + | 0.987004i | \(0.551373\pi\) | |||||||
\(488\) | 48.9750 | + | 34.3886i | 0.100359 | + | 0.0704685i | ||||
\(489\) | −16.6637 | −0.0340770 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 373.498 | 0.760689 | 0.380344 | − | 0.924845i | \(-0.375805\pi\) | ||||
0.380344 | + | 0.924845i | \(0.375805\pi\) | |||||||
\(492\) | 4.13870 | − | 17.3947i | 0.00841199 | − | 0.0353550i | ||||
\(493\) | 338.526 | + | 195.448i | 0.686665 | + | 0.396446i | ||||
\(494\) | 192.334 | + | 243.466i | 0.389341 | + | 0.492845i | ||||
\(495\) | 79.0217 | − | 45.6232i | 0.159640 | − | 0.0921680i | ||||
\(496\) | 717.133 | − | 40.5082i | 1.44583 | − | 0.0816698i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −19.8583 | − | 7.89927i | −0.0398761 | − | 0.0158620i | ||||
\(499\) | 425.158 | + | 736.396i | 0.852021 | + | 1.47574i | 0.879381 | + | 0.476118i | \(0.157956\pi\) |
−0.0273604 | + | 0.999626i | \(0.508710\pi\) | |||||||
\(500\) | −150.595 | − | 504.629i | −0.301189 | − | 1.00926i | ||||
\(501\) | −10.1814 | − | 5.87822i | −0.0203221 | − | 0.0117330i | ||||
\(502\) | −89.7639 | − | 614.689i | −0.178812 | − | 1.22448i | ||||
\(503\) | − | 459.256i | − | 0.913033i | −0.889715 | − | 0.456517i | \(-0.849097\pi\) | ||
0.889715 | − | 0.456517i | \(-0.150903\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 370.206 | 0.733082 | ||||||||
\(506\) | −97.1373 | + | 14.1851i | −0.191971 | + | 0.0280338i | ||||
\(507\) | −9.64873 | + | 16.7121i | −0.0190310 | + | 0.0329627i | ||||
\(508\) | −175.761 | − | 588.960i | −0.345987 | − | 1.15937i | ||||
\(509\) | −583.623 | + | 336.955i | −1.14661 | + | 0.661994i | −0.948058 | − | 0.318097i | \(-0.896956\pi\) |
−0.198549 | + | 0.980091i | \(0.563623\pi\) | |||||||
\(510\) | 3.59182 | − | 9.02963i | 0.00704279 | − | 0.0177052i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −494.028 | − | 134.463i | −0.964898 | − | 0.262623i | ||||
\(513\) | 7.09713 | + | 12.2926i | 0.0138346 | + | 0.0239622i | ||||
\(514\) | 275.381 | − | 217.547i | 0.535760 | − | 0.423243i | ||||
\(515\) | −219.410 | + | 380.029i | −0.426039 | + | 0.737921i | ||||
\(516\) | −5.50605 | + | 23.1415i | −0.0106706 | + | 0.0448479i | ||||
\(517\) | − | 135.536i | − | 0.262159i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 10.5562i | − | 0.0203394i | ||||||
\(520\) | −305.225 | + | 434.691i | −0.586972 | + | 0.835944i | ||||
\(521\) | −243.236 | + | 421.298i | −0.466864 | + | 0.808633i | −0.999284 | − | 0.0378482i | \(-0.987950\pi\) |
0.532419 | + | 0.846481i | \(0.321283\pi\) | |||||||
\(522\) | −302.788 | − | 383.282i | −0.580053 | − | 0.734257i | ||||
\(523\) | −340.043 | − | 588.973i | −0.650179 | − | 1.12614i | −0.983079 | − | 0.183181i | \(-0.941361\pi\) |
0.332900 | − | 0.942962i | \(-0.391973\pi\) | |||||||
\(524\) | −179.847 | − | 169.975i | −0.343219 | − | 0.324379i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −230.732 | + | 580.048i | −0.438655 | + | 1.10275i | ||||
\(527\) | −559.442 | + | 322.994i | −1.06156 | + | 0.612892i | ||||
\(528\) | −4.07650 | − | 2.05624i | −0.00772064 | − | 0.00389440i | ||||
\(529\) | −124.054 | + | 214.869i | −0.234507 | + | 0.406179i | ||||
\(530\) | 9.70890 | + | 66.4851i | 0.0183187 | + | 0.125444i | ||||
\(531\) | −1029.90 | −1.93954 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 878.931i | − | 1.64903i | ||||||
\(534\) | 2.27851 | + | 15.6029i | 0.00426687 | + | 0.0292189i | ||||
\(535\) | −261.161 | − | 150.781i | −0.488151 | − | 0.281834i | ||||
\(536\) | 96.0938 | + | 8.53431i | 0.179279 | + | 0.0159222i | ||||
\(537\) | −7.86496 | − | 13.6225i | −0.0146461 | − | 0.0253678i | ||||
\(538\) | 105.574 | − | 265.407i | 0.196234 | − | 0.493321i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −16.6904 | + | 17.6598i | −0.0309082 | + | 0.0327034i | ||||
\(541\) | 688.489 | − | 397.499i | 1.27262 | − | 0.734749i | 0.297142 | − | 0.954833i | \(-0.403966\pi\) |
0.975481 | + | 0.220084i | \(0.0706331\pi\) | |||||||
\(542\) | −329.928 | − | 417.637i | −0.608723 | − | 0.770548i | ||||
\(543\) | 0.603078 | + | 0.348187i | 0.00111064 | + | 0.000641229i | ||||
\(544\) | 451.162 | − | 92.1281i | 0.829341 | − | 0.169353i | ||||
\(545\) | 658.167 | 1.20765 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −736.752 | −1.34690 | −0.673448 | − | 0.739235i | \(-0.735187\pi\) | ||||
−0.673448 | + | 0.739235i | \(0.735187\pi\) | |||||||
\(548\) | 98.0896 | − | 412.264i | 0.178996 | − | 0.752306i | ||||
\(549\) | 58.2418 | + | 33.6259i | 0.106087 | + | 0.0612494i | ||||
\(550\) | 59.7065 | − | 47.1673i | 0.108557 | − | 0.0857587i | ||||
\(551\) | 190.496 | − | 109.983i | 0.345728 | − | 0.199606i | ||||
\(552\) | 11.8474 | − | 5.50559i | 0.0214626 | − | 0.00997389i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −271.104 | + | 681.540i | −0.489357 | + | 1.23022i | ||||
\(555\) | −6.68046 | − | 11.5709i | −0.0120369 | − | 0.0208485i | ||||
\(556\) | −710.569 | + | 212.053i | −1.27800 | + | 0.381389i | ||||
\(557\) | −360.057 | − | 207.879i | −0.646421 | − | 0.373212i | 0.140662 | − | 0.990058i | \(-0.455077\pi\) |
−0.787084 | + | 0.616846i | \(0.788410\pi\) | |||||||
\(558\) | 798.737 | − | 116.641i | 1.43143 | − | 0.209033i | ||||
\(559\) | 1169.31i | 2.09179i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.10624 | 0.00731950 | ||||||||
\(562\) | −42.7648 | − | 292.847i | −0.0760940 | − | 0.521080i | ||||
\(563\) | −48.2498 | + | 83.5711i | −0.0857012 | + | 0.148439i | −0.905690 | − | 0.423941i | \(-0.860646\pi\) |
0.819989 | + | 0.572380i | \(0.193980\pi\) | |||||||
\(564\) | 5.15799 | + | 17.2840i | 0.00914537 | + | 0.0306453i | ||||
\(565\) | −120.602 | + | 69.6296i | −0.213455 | + | 0.123238i | ||||
\(566\) | −609.060 | − | 242.273i | −1.07608 | − | 0.428044i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 937.235 | − | 435.542i | 1.65006 | − | 0.766800i | ||||
\(569\) | −173.977 | − | 301.336i | −0.305759 | − | 0.529589i | 0.671671 | − | 0.740849i | \(-0.265577\pi\) |
−0.977430 | + | 0.211260i | \(0.932243\pi\) | |||||||
\(570\) | −3.38983 | − | 4.29100i | −0.00594707 | − | 0.00752807i | ||||
\(571\) | 6.86255 | − | 11.8863i | 0.0120185 | − | 0.0208166i | −0.859954 | − | 0.510372i | \(-0.829508\pi\) |
0.871972 | + | 0.489556i | \(0.162841\pi\) | |||||||
\(572\) | −218.341 | − | 51.9497i | −0.381715 | − | 0.0908212i | ||||
\(573\) | 7.14193i | 0.0124641i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 217.718i | 0.378641i | ||||||||
\(576\) | −566.386 | − | 101.404i | −0.983310 | − | 0.176049i | ||||
\(577\) | −413.660 | + | 716.480i | −0.716915 | + | 1.24173i | 0.245302 | + | 0.969447i | \(0.421113\pi\) |
−0.962216 | + | 0.272286i | \(0.912220\pi\) | |||||||
\(578\) | 128.587 | − | 101.582i | 0.222469 | − | 0.175747i | ||||
\(579\) | −4.14449 | − | 7.17846i | −0.00715801 | − | 0.0123980i | ||||
\(580\) | 273.671 | + | 258.649i | 0.471847 | + | 0.445946i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 29.3495 | + | 11.6747i | 0.0504286 | + | 0.0200596i | ||||
\(583\) | −24.5874 | + | 14.1956i | −0.0421740 | + | 0.0243492i | ||||
\(584\) | −145.709 | − | 12.9408i | −0.249502 | − | 0.0221589i | ||||
\(585\) | −298.456 | + | 516.941i | −0.510181 | + | 0.883659i | ||||
\(586\) | −514.307 | + | 75.1049i | −0.877657 | + | 0.128165i | ||||
\(587\) | 675.987 | 1.15160 | 0.575798 | − | 0.817592i | \(-0.304692\pi\) | ||||
0.575798 | + | 0.817592i | \(0.304692\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 363.512i | 0.617169i | ||||||||
\(590\) | 785.634 | − | 114.727i | 1.33158 | − | 0.194453i | ||||
\(591\) | 11.8524 | + | 6.84298i | 0.0200548 | + | 0.0115786i | ||||
\(592\) | 285.125 | − | 565.260i | 0.481630 | − | 0.954831i | ||||
\(593\) | −207.058 | − | 358.635i | −0.349171 | − | 0.604781i | 0.636932 | − | 0.770920i | \(-0.280203\pi\) |
−0.986102 | + | 0.166139i | \(0.946870\pi\) | |||||||
\(594\) | −9.54041 | − | 3.79500i | −0.0160613 | − | 0.00638889i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −130.258 | + | 137.824i | −0.218554 | + | 0.231248i | ||||
\(597\) | −12.0736 | + | 6.97072i | −0.0202238 | + | 0.0116762i | ||||
\(598\) | 503.917 | − | 398.087i | 0.842671 | − | 0.665698i | ||||
\(599\) | 626.399 | + | 361.652i | 1.04574 | + | 0.603759i | 0.921454 | − | 0.388487i | \(-0.127002\pi\) |
0.124287 | + | 0.992246i | \(0.460336\pi\) | |||||||
\(600\) | −5.81893 | + | 8.28710i | −0.00969821 | + | 0.0138118i | ||||
\(601\) | −68.7503 | −0.114393 | −0.0571966 | − | 0.998363i | \(-0.518216\pi\) | ||||
−0.0571966 | + | 0.998363i | \(0.518216\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 108.416 | 0.179795 | ||||||||
\(604\) | 445.857 | + | 106.082i | 0.738173 | + | 0.175633i | ||||
\(605\) | 337.402 | + | 194.799i | 0.557690 | + | 0.321982i | ||||
\(606\) | −12.9047 | − | 16.3354i | −0.0212950 | − | 0.0269561i | ||||
\(607\) | 122.338 | − | 70.6317i | 0.201545 | − | 0.116362i | −0.395831 | − | 0.918323i | \(-0.629543\pi\) |
0.597376 | + | 0.801961i | \(0.296210\pi\) | |||||||
\(608\) | 82.0424 | − | 245.787i | 0.134938 | − | 0.404255i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −48.1742 | − | 19.1628i | −0.0789742 | − | 0.0314145i | ||||
\(611\) | 443.323 | + | 767.858i | 0.725569 | + | 1.25672i | ||||
\(612\) | 495.874 | − | 147.982i | 0.810252 | − | 0.241801i | ||||
\(613\) | 83.7767 | + | 48.3685i | 0.136667 | + | 0.0789046i | 0.566774 | − | 0.823873i | \(-0.308191\pi\) |
−0.430108 | + | 0.902778i | \(0.641524\pi\) | |||||||
\(614\) | 83.9428 | + | 574.828i | 0.136715 | + | 0.936201i | ||||
\(615\) | 15.4909i | 0.0251884i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 580.418 | 0.940709 | 0.470355 | − | 0.882478i | \(-0.344126\pi\) | ||||
0.470355 | + | 0.882478i | \(0.344126\pi\) | |||||||
\(618\) | 24.4171 | − | 3.56566i | 0.0395099 | − | 0.00576967i | ||||
\(619\) | 78.9725 | − | 136.784i | 0.127581 | − | 0.220976i | −0.795158 | − | 0.606402i | \(-0.792612\pi\) |
0.922739 | + | 0.385426i | \(0.125945\pi\) | |||||||
\(620\) | −596.305 | + | 177.953i | −0.961782 | + | 0.287021i | ||||
\(621\) | 25.4428 | − | 14.6894i | 0.0409707 | − | 0.0236544i | ||||
\(622\) | −55.3740 | + | 139.207i | −0.0890257 | + | 0.223806i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 29.8204 | − | 1.68445i | 0.0477891 | − | 0.00269943i | ||||
\(625\) | 65.7420 | + | 113.869i | 0.105187 | + | 0.182190i | ||||
\(626\) | 446.498 | − | 352.728i | 0.713256 | − | 0.563463i | ||||
\(627\) | 1.15534 | − | 2.00110i | 0.00184264 | − | 0.00319155i | ||||
\(628\) | 1144.43 | + | 272.294i | 1.82234 | + | 0.433589i | ||||
\(629\) | 569.384i | 0.905221i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 771.793i | − | 1.22313i | −0.791195 | − | 0.611564i | \(-0.790541\pi\) | ||
0.791195 | − | 0.611564i | \(-0.209459\pi\) | |||||||
\(632\) | −279.020 | − | 195.919i | −0.441488 | − | 0.309998i | ||||
\(633\) | −5.45424 | + | 9.44701i | −0.00861649 | + | 0.0149242i | ||||
\(634\) | −15.2036 | − | 19.2455i | −0.0239805 | − | 0.0303556i | ||||
\(635\) | 266.246 | + | 461.152i | 0.419286 | + | 0.726224i | ||||
\(636\) | 2.59523 | − | 2.74596i | 0.00408055 | − | 0.00431755i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −58.8104 | + | 147.846i | −0.0921793 | + | 0.231733i | ||||
\(639\) | 1005.85 | − | 580.726i | 1.57410 | − | 0.908805i | ||||
\(640\) | 443.351 | + | 14.2602i | 0.692736 | + | 0.0222816i | ||||
\(641\) | 293.451 | − | 508.273i | 0.457802 | − | 0.792937i | −0.541042 | − | 0.840996i | \(-0.681970\pi\) |
0.998845 | + | 0.0480584i | \(0.0153034\pi\) | |||||||
\(642\) | 2.45036 | + | 16.7797i | 0.00381677 | + | 0.0261366i | ||||
\(643\) | −865.328 | −1.34577 | −0.672883 | − | 0.739749i | \(-0.734944\pi\) | ||||
−0.672883 | + | 0.739749i | \(0.734944\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 20.6087i | − | 0.0319515i | ||||||
\(646\) | 33.6740 | + | 230.594i | 0.0521269 | + | 0.356957i | ||||
\(647\) | 115.080 | + | 66.4414i | 0.177867 | + | 0.102691i | 0.586290 | − | 0.810101i | \(-0.300588\pi\) |
−0.408423 | + | 0.912793i | \(0.633921\pi\) | |||||||
\(648\) | −643.418 | − | 57.1434i | −0.992928 | − | 0.0881843i | ||||
\(649\) | 167.745 | + | 290.542i | 0.258466 | + | 0.447677i | ||||
\(650\) | −183.978 | + | 462.511i | −0.283044 | + | 0.711555i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 497.173 | + | 469.882i | 0.762535 | + | 0.720677i | ||||
\(653\) | −315.501 | + | 182.155i | −0.483156 | + | 0.278950i | −0.721731 | − | 0.692174i | \(-0.756653\pi\) |
0.238575 | + | 0.971124i | \(0.423320\pi\) | |||||||
\(654\) | −22.9426 | − | 29.0417i | −0.0350804 | − | 0.0444063i | ||||
\(655\) | 185.668 | + | 107.196i | 0.283463 | + | 0.163657i | ||||
\(656\) | −613.975 | + | 402.279i | −0.935938 | + | 0.613231i | ||||
\(657\) | −164.395 | −0.250220 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.8972 | −0.0286756 | −0.0143378 | − | 0.999897i | \(-0.504564\pi\) | ||||
−0.0143378 | + | 0.999897i | \(0.504564\pi\) | |||||||
\(660\) | 3.84818 | + | 0.915596i | 0.00583058 | + | 0.00138727i | ||||
\(661\) | 293.674 | + | 169.553i | 0.444288 | + | 0.256510i | 0.705415 | − | 0.708795i | \(-0.250761\pi\) |
−0.261127 | + | 0.965304i | \(0.584094\pi\) | |||||||
\(662\) | −305.190 | + | 241.096i | −0.461011 | + | 0.364193i | ||||
\(663\) | −23.2632 | + | 13.4310i | −0.0350878 | + | 0.0202579i | ||||
\(664\) | 369.744 | + | 795.645i | 0.556843 | + | 1.19826i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 262.974 | − | 661.102i | 0.394856 | − | 0.992646i | ||||
\(667\) | −227.639 | − | 394.283i | −0.341288 | − | 0.591128i | ||||
\(668\) | 138.015 | + | 462.475i | 0.206609 | + | 0.692328i | ||||
\(669\) | −26.2799 | − | 15.1727i | −0.0392824 | − | 0.0226797i | ||||
\(670\) | −82.7031 | + | 12.0772i | −0.123437 | + | 0.0180257i | ||||
\(671\) | − | 21.9073i | − | 0.0326487i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 674.869 | 1.00278 | 0.501389 | − | 0.865222i | \(-0.332823\pi\) | ||||
0.501389 | + | 0.865222i | \(0.332823\pi\) | |||||||
\(674\) | −0.172265 | − | 1.17964i | −0.000255585 | − | 0.00175021i | ||||
\(675\) | −11.3857 | + | 19.7207i | −0.0168678 | + | 0.0292158i | ||||
\(676\) | 759.124 | − | 226.543i | 1.12296 | − | 0.335122i | ||||
\(677\) | 856.280 | − | 494.374i | 1.26482 | − | 0.730242i | 0.290813 | − | 0.956780i | \(-0.406074\pi\) |
0.974002 | + | 0.226538i | \(0.0727408\pi\) | |||||||
\(678\) | 7.27639 | + | 2.89441i | 0.0107321 | + | 0.00426905i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −361.782 | + | 168.123i | −0.532032 | + | 0.247240i | ||||
\(681\) | −3.62260 | − | 6.27453i | −0.00531953 | − | 0.00921369i | ||||
\(682\) | −163.000 | − | 206.332i | −0.239002 | − | 0.302540i | ||||
\(683\) | 259.062 | − | 448.709i | 0.379301 | − | 0.656968i | −0.611660 | − | 0.791121i | \(-0.709498\pi\) |
0.990961 | + | 0.134153i | \(0.0428312\pi\) | |||||||
\(684\) | 67.4035 | − | 283.292i | 0.0985431 | − | 0.414170i | ||||
\(685\) | 367.143i | 0.535975i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 7.62646i | − | 0.0111011i | ||||||
\(688\) | 816.821 | − | 535.184i | 1.18724 | − | 0.777884i | ||||
\(689\) | 92.8640 | − | 160.845i | 0.134781 | − | 0.233447i | ||||
\(690\) | −8.88137 | + | 7.01616i | −0.0128715 | + | 0.0101683i | ||||
\(691\) | −308.511 | − | 534.356i | −0.446470 | − | 0.773309i | 0.551683 | − | 0.834054i | \(-0.313986\pi\) |
−0.998153 | + | 0.0607450i | \(0.980652\pi\) | |||||||
\(692\) | −297.662 | + | 314.951i | −0.430148 | + | 0.455131i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −380.718 | − | 151.443i | −0.548585 | − | 0.218217i | ||||
\(695\) | 556.371 | − | 321.221i | 0.800534 | − | 0.462189i | ||||
\(696\) | 1.87321 | − | 21.0918i | 0.00269140 | − | 0.0303043i | ||||
\(697\) | 330.076 | − | 571.709i | 0.473567 | − | 0.820243i | ||||
\(698\) | 254.098 | − | 37.1062i | 0.364037 | − | 0.0531608i | ||||
\(699\) | −9.06718 | −0.0129717 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 97.6954i | − | 0.139366i | −0.997569 | − | 0.0696829i | \(-0.977801\pi\) | ||
0.997569 | − | 0.0696829i | \(-0.0221987\pi\) | |||||||
\(702\) | 66.4625 | − | 9.70561i | 0.0946760 | − | 0.0138256i | ||||
\(703\) | 277.479 | + | 160.203i | 0.394707 | + | 0.227884i | ||||
\(704\) | 63.6434 | + | 176.298i | 0.0904025 | + | 0.250424i | ||||
\(705\) | −7.81342 | − | 13.5332i | −0.0110829 | − | 0.0191961i | ||||
\(706\) | 354.654 | + | 141.075i | 0.502343 | + | 0.199823i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −32.4482 | − | 30.6670i | −0.0458308 | − | 0.0433150i | ||||
\(709\) | 1082.31 | − | 624.872i | 1.52653 | − | 0.881343i | 0.527028 | − | 0.849848i | \(-0.323306\pi\) |
0.999504 | − | 0.0314953i | \(-0.0100269\pi\) | |||||||
\(710\) | −702.597 | + | 555.042i | −0.989573 | + | 0.781749i | ||||
\(711\) | −331.815 | − | 191.573i | −0.466688 | − | 0.269442i | ||||
\(712\) | 371.989 | − | 529.773i | 0.522456 | − | 0.744063i | ||||
\(713\) | 752.386 | 1.05524 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 194.444 | 0.271950 | ||||||||
\(716\) | −149.470 | + | 628.214i | −0.208758 | + | 0.877393i | ||||
\(717\) | −24.6064 | − | 14.2065i | −0.0343186 | − | 0.0198138i | ||||
\(718\) | −267.427 | − | 338.521i | −0.372460 | − | 0.471477i | ||||
\(719\) | 367.839 | − | 212.372i | 0.511599 | − | 0.295372i | −0.221892 | − | 0.975071i | \(-0.571223\pi\) |
0.733491 | + | 0.679700i | \(0.237890\pi\) | |||||||
\(720\) | 497.708 | − | 28.1137i | 0.691261 | − | 0.0390468i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −549.022 | − | 218.391i | −0.760418 | − | 0.302480i | ||||
\(723\) | −10.9006 | − | 18.8804i | −0.0150769 | − | 0.0261140i | ||||
\(724\) | −8.17510 | − | 27.3940i | −0.0112916 | − | 0.0378370i | ||||
\(725\) | 305.608 | + | 176.443i | 0.421528 | + | 0.243369i | ||||
\(726\) | −3.16571 | − | 21.6783i | −0.00436048 | − | 0.0298599i | ||||
\(727\) | 79.1445i | 0.108865i | 0.998517 | + | 0.0544323i | \(0.0173349\pi\) | ||||
−0.998517 | + | 0.0544323i | \(0.982665\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −724.390 | −0.993676 | ||||||||
\(730\) | 125.405 | − | 18.3130i | 0.171787 | − | 0.0250863i | ||||
\(731\) | −439.127 | + | 760.591i | −0.600721 | + | 1.04048i | ||||
\(732\) | 0.833707 | + | 2.79368i | 0.00113894 | + | 0.00381650i | ||||
\(733\) | 574.839 | − | 331.883i | 0.784227 | − | 0.452774i | −0.0536990 | − | 0.998557i | \(-0.517101\pi\) |
0.837926 | + | 0.545783i | \(0.183768\pi\) | |||||||
\(734\) | −336.192 | + | 845.167i | −0.458027 | + | 1.15145i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −508.721 | − | 169.809i | −0.691198 | − | 0.230718i | ||||
\(737\) | −17.6584 | − | 30.5852i | −0.0239598 | − | 0.0414996i | ||||
\(738\) | −647.295 | + | 511.354i | −0.877093 | + | 0.692892i | ||||
\(739\) | −416.056 | + | 720.630i | −0.562998 | + | 0.975142i | 0.434235 | + | 0.900800i | \(0.357019\pi\) |
−0.997233 | + | 0.0743418i | \(0.976314\pi\) | |||||||
\(740\) | −126.959 | + | 533.601i | −0.171567 | + | 0.721083i | ||||
\(741\) | 15.1159i | 0.0203993i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 283.217i | 0.381180i | 0.981670 | + | 0.190590i | \(0.0610401\pi\) | ||||
−0.981670 | + | 0.190590i | \(0.938960\pi\) | |||||||
\(744\) | 28.6384 | + | 20.1089i | 0.0384924 | + | 0.0270281i | ||||
\(745\) | 82.1483 | − | 142.285i | 0.110266 | − | 0.190987i | ||||
\(746\) | 447.250 | + | 566.149i | 0.599530 | + | 0.758912i | ||||
\(747\) | 492.995 | + | 853.892i | 0.659966 | + | 1.14309i | ||||
\(748\) | −122.513 | − | 115.788i | −0.163787 | − | 0.154796i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 9.48280 | − | 23.8392i | 0.0126437 | − | 0.0317856i | ||||
\(751\) | −324.743 | + | 187.490i | −0.432414 | + | 0.249654i | −0.700375 | − | 0.713776i | \(-0.746984\pi\) |
0.267960 | + | 0.963430i | \(0.413650\pi\) | |||||||
\(752\) | 333.480 | − | 661.124i | 0.443458 | − | 0.879154i | ||||
\(753\) | 15.1321 | − | 26.2096i | 0.0200958 | − | 0.0348069i | ||||
\(754\) | −150.406 | − | 1029.96i | −0.199477 | − | 1.36599i | ||||
\(755\) | −397.059 | −0.525906 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 63.0951i | − | 0.0833488i | −0.999131 | − | 0.0416744i | \(-0.986731\pi\) | ||
0.999131 | − | 0.0416744i | \(-0.0132692\pi\) | |||||||
\(758\) | 77.5746 | + | 531.220i | 0.102341 | + | 0.700817i | ||||
\(759\) | −4.14181 | − | 2.39128i | −0.00545694 | − | 0.00315056i | ||||
\(760\) | −19.8594 | + | 223.611i | −0.0261308 | + | 0.294225i | ||||
\(761\) | 233.753 | + | 404.871i | 0.307165 | + | 0.532025i | 0.977741 | − | 0.209815i | \(-0.0672863\pi\) |
−0.670576 | + | 0.741841i | \(0.733953\pi\) | |||||||
\(762\) | 11.0675 | − | 27.8231i | 0.0145243 | − | 0.0365133i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 201.388 | − | 213.085i | 0.263597 | − | 0.278907i | ||||
\(765\) | −388.267 | + | 224.166i | −0.507538 | + | 0.293027i | ||||
\(766\) | 720.974 | + | 912.641i | 0.941219 | + | 1.19144i | ||||
\(767\) | −1900.66 | − | 1097.35i | −2.47804 | − | 1.43070i | ||||
\(768\) | −14.8252 | − | 20.0600i | −0.0193037 | − | 0.0261198i | ||||
\(769\) | −900.573 | −1.17110 | −0.585548 | − | 0.810638i | \(-0.699121\pi\) | ||||
−0.585548 | + | 0.810638i | \(0.699121\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.0974 | 0.0221756 | ||||||||
\(772\) | −78.7643 | + | 331.041i | −0.102026 | + | 0.428809i | ||||
\(773\) | −1058.94 | − | 611.381i | −1.36991 | − | 0.790919i | −0.378996 | − | 0.925398i | \(-0.623731\pi\) |
−0.990916 | + | 0.134479i | \(0.957064\pi\) | |||||||
\(774\) | 861.148 | − | 680.295i | 1.11259 | − | 0.878935i | ||||
\(775\) | −505.043 | + | 291.587i | −0.651668 | + | 0.376241i | ||||
\(776\) | −546.460 | − | 1175.92i | −0.704201 | − | 1.51536i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 378.689 | − | 952.003i | 0.486747 | − | 1.22365i | ||||
\(779\) | −185.742 | − | 321.714i | −0.238436 | − | 0.412983i | ||||
\(780\) | −24.7960 | + | 7.39979i | −0.0317898 | + | 0.00948691i | ||||
\(781\) | −327.655 | − | 189.172i | −0.419533 | − | 0.242217i | ||||
\(782\) | 477.277 | − | 69.6973i | 0.610328 | − | 0.0891270i | ||||
\(783\) | − | 47.6182i | − | 0.0608151i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1019.18 | −1.29832 | ||||||||
\(786\) | −1.74205 | − | 11.9293i | −0.00221635 | − | 0.0151772i | ||||
\(787\) | 431.471 | − | 747.330i | 0.548248 | − | 0.949593i | −0.450147 | − | 0.892954i | \(-0.648628\pi\) |
0.998395 | − | 0.0566385i | \(-0.0180383\pi\) | |||||||
\(788\) | −160.666 | − | 538.378i | −0.203891 | − | 0.683221i | ||||
\(789\) | −26.3381 | + | 15.2063i | −0.0333816 | + | 0.0192729i | ||||
\(790\) | 274.458 | + | 109.174i | 0.347415 | + | 0.138195i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 88.7700 | + | 191.022i | 0.112083 | + | 0.241190i | ||||
\(793\) | 71.6561 | + | 124.112i | 0.0903608 | + | 0.156510i | ||||
\(794\) | −100.825 | − | 127.629i | −0.126984 | − | 0.160742i | ||||
\(795\) | −1.63670 | + | 2.83484i | −0.00205874 | + | 0.00356584i | ||||
\(796\) | 556.786 | + | 132.476i | 0.699479 | + | 0.166427i | ||||
\(797\) | − | 1078.34i | − | 1.35300i | −0.736442 | − | 0.676500i | \(-0.763496\pi\) | ||
0.736442 | − | 0.676500i | \(-0.236504\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 665.947i | 0.833476i | ||||||||
\(800\) | 407.291 | − | 83.1697i | 0.509114 | − | 0.103962i | ||||
\(801\) | 363.739 | − | 630.014i | 0.454106 | − | 0.786534i | ||||
\(802\) | −827.752 | + | 653.912i | −1.03211 | + | 0.815352i | ||||
\(803\) | 26.7758 | + | 46.3771i | 0.0333447 | + | 0.0577547i | ||||
\(804\) | 3.41579 | + | 3.22829i | 0.00424850 | + | 0.00401529i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1598.33 | + | 635.788i | 1.98305 | + | 0.788819i | ||||
\(807\) | 12.0512 | − | 6.95779i | 0.0149334 | − | 0.00862180i | ||||
\(808\) | −75.6029 | + | 851.266i | −0.0935680 | + | 1.05355i | ||||
\(809\) | −166.694 | + | 288.723i | −0.206050 | + | 0.356888i | −0.950467 | − | 0.310827i | \(-0.899394\pi\) |
0.744417 | + | 0.667715i | \(0.232727\pi\) | |||||||
\(810\) | 553.757 | − | 80.8658i | 0.683651 | − | 0.0998344i | ||||
\(811\) | 1246.04 | 1.53642 | 0.768211 | − | 0.640197i | \(-0.221147\pi\) | ||||
0.768211 | + | 0.640197i | \(0.221147\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 25.9295i | − | 0.0318936i | ||||||
\(814\) | −229.334 | + | 33.4900i | −0.281737 | + | 0.0411425i | ||||
\(815\) | −513.265 | − | 296.334i | −0.629773 | − | 0.363600i | ||||
\(816\) | 20.0296 | + | 10.1032i | 0.0245460 | + | 0.0123814i | ||||
\(817\) | 247.107 | + | 428.002i | 0.302456 | + | 0.523870i | ||||
\(818\) | 109.036 | + | 43.3724i | 0.133295 | + | 0.0530224i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 436.811 | − | 462.181i | 0.532696 | − | 0.563636i | ||||
\(821\) | −1263.25 | + | 729.338i | −1.53867 | + | 0.888353i | −0.539755 | + | 0.841822i | \(0.681483\pi\) |
−0.998917 | + | 0.0465306i | \(0.985184\pi\) | |||||||
\(822\) | 16.2002 | − | 12.7979i | 0.0197083 | − | 0.0155693i | ||||
\(823\) | 401.876 | + | 232.023i | 0.488306 | + | 0.281924i | 0.723872 | − | 0.689935i | \(-0.242361\pi\) |
−0.235565 | + | 0.971859i | \(0.575694\pi\) | |||||||
\(824\) | −829.046 | − | 582.129i | −1.00612 | − | 0.706467i | ||||
\(825\) | 3.70695 | 0.00449328 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1077.41 | 1.30279 | 0.651394 | − | 0.758739i | \(-0.274184\pi\) | ||||
0.651394 | + | 0.758739i | \(0.274184\pi\) | |||||||
\(828\) | −586.348 | − | 139.509i | −0.708150 | − | 0.168490i | ||||
\(829\) | 31.1210 | + | 17.9677i | 0.0375404 | + | 0.0216740i | 0.518653 | − | 0.854985i | \(-0.326434\pi\) |
−0.481112 | + | 0.876659i | \(0.659767\pi\) | |||||||
\(830\) | −471.190 | − | 596.454i | −0.567699 | − | 0.718619i | ||||
\(831\) | −30.9465 | + | 17.8670i | −0.0372400 | + | 0.0215006i | ||||
\(832\) | −937.211 | − | 790.619i | −1.12646 | − | 0.950263i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −33.5681 | − | 13.3528i | −0.0402495 | − | 0.0160105i | ||||
\(835\) | −209.067 | − | 362.115i | −0.250380 | − | 0.433671i | ||||
\(836\) | −90.8973 | + | 27.1262i | −0.108729 | + | 0.0324476i | ||||
\(837\) | 68.1503 | + | 39.3466i | 0.0814221 | + | 0.0470091i | ||||
\(838\) | 219.841 | + | 1505.44i | 0.262341 | + | 1.79647i | ||||
\(839\) | − | 734.676i | − | 0.875656i | −0.899059 | − | 0.437828i | \(-0.855748\pi\) | ||
0.899059 | − | 0.437828i | \(-0.144252\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 103.069 | 0.122555 | ||||||||
\(842\) | −91.6119 | + | 13.3782i | −0.108803 | + | 0.0158886i | ||||
\(843\) | 7.20916 | − | 12.4866i | 0.00855179 | − | 0.0148121i | ||||
\(844\) | 429.118 | − | 128.060i | 0.508433 | − | 0.151730i | ||||
\(845\) | −594.390 | + | 343.171i | −0.703420 | + | 0.406119i | ||||
\(846\) | 307.573 | − | 773.221i | 0.363561 | − | 0.913972i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −154.861 | + | 8.74753i | −0.182619 | + | 0.0103155i | ||||
\(849\) | −15.9669 | − | 27.6554i | −0.0188067 | − | 0.0325741i | ||||
\(850\) | −293.363 | + | 231.753i | −0.345133 | + | 0.272651i | ||||
\(851\) | 331.582 | − | 574.317i | 0.389638 | − | 0.674873i | ||||
\(852\) | 48.9826 | + | 11.6544i | 0.0574913 | + | 0.0136789i | ||||
\(853\) | − | 402.566i | − | 0.471942i | −0.971760 | − | 0.235971i | \(-0.924173\pi\) | ||
0.971760 | − | 0.235971i | \(-0.0758270\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 252.287i | 0.295072i | ||||||||
\(856\) | 400.046 | − | 569.730i | 0.467343 | − | 0.665573i | ||||
\(857\) | 276.001 | − | 478.048i | 0.322055 | − | 0.557816i | −0.658857 | − | 0.752268i | \(-0.728960\pi\) |
0.980912 | + | 0.194453i | \(0.0622930\pi\) | |||||||
\(858\) | −6.77798 | − | 8.57988i | −0.00789975 | − | 0.00999986i | ||||
\(859\) | −165.058 | − | 285.889i | −0.192152 | − | 0.332817i | 0.753811 | − | 0.657091i | \(-0.228213\pi\) |
−0.945963 | + | 0.324274i | \(0.894880\pi\) | |||||||
\(860\) | −581.125 | + | 614.877i | −0.675727 | + | 0.714973i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 248.510 | − | 624.740i | 0.288295 | − | 0.724757i | ||||
\(863\) | −967.063 | + | 558.334i | −1.12058 | + | 0.646969i | −0.941550 | − | 0.336874i | \(-0.890630\pi\) |
−0.179033 | + | 0.983843i | \(0.557297\pi\) | |||||||
\(864\) | −37.1991 | − | 41.9851i | −0.0430546 | − | 0.0485938i | ||||
\(865\) | 187.723 | − | 325.145i | 0.217020 | − | 0.375890i | ||||
\(866\) | −107.708 | − | 737.565i | −0.124374 | − | 0.851692i | ||||
\(867\) | 7.98348 | 0.00920817 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 124.810i | 0.143625i | ||||||||
\(870\) | 2.65086 | + | 18.1527i | 0.00304696 | + | 0.0208651i | ||||
\(871\) | 200.081 | + | 115.517i | 0.229714 | + | 0.132625i | ||||
\(872\) | −134.410 | + | 1513.41i | −0.154140 | + | 1.73557i | ||||
\(873\) | −728.618 | − | 1262.00i | −0.834614 | − | 1.44559i | ||||
\(874\) | 100.321 | − | 252.202i | 0.114784 | − | 0.288561i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.17945 | − | 4.89514i | −0.00591262 | − | 0.00558806i | ||||
\(877\) | 0.647303 | − | 0.373720i | 0.000738087 | − | 0.000426135i | −0.499631 | − | 0.866238i | \(-0.666531\pi\) |
0.500369 | + | 0.865812i | \(0.333198\pi\) | |||||||
\(878\) | 492.787 | + | 623.792i | 0.561261 | + | 0.710469i | ||||
\(879\) | −21.9294 | − | 12.6610i | −0.0249481 | − | 0.0144038i | ||||
\(880\) | −88.9954 | − | 135.828i | −0.101131 | − | 0.154351i | ||||
\(881\) | 247.826 | 0.281301 | 0.140650 | − | 0.990059i | \(-0.455081\pi\) | ||||
0.140650 | + | 0.990059i | \(0.455081\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1613.74 | −1.82757 | −0.913784 | − | 0.406200i | \(-0.866854\pi\) | ||||
−0.913784 | + | 0.406200i | \(0.866854\pi\) | |||||||
\(884\) | 1072.80 | + | 255.251i | 1.21358 | + | 0.288745i | ||||
\(885\) | 33.4985 | + | 19.3403i | 0.0378514 | + | 0.0218535i | ||||
\(886\) | −429.271 | + | 339.118i | −0.484505 | + | 0.382752i | ||||
\(887\) | 961.795 | − | 555.293i | 1.08432 | − | 0.626034i | 0.152264 | − | 0.988340i | \(-0.451344\pi\) |
0.932059 | + | 0.362305i | \(0.118010\pi\) | |||||||
\(888\) | 27.9708 | − | 12.9983i | 0.0314987 | − | 0.0146377i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −207.288 | + | 521.111i | −0.232908 | + | 0.585518i | ||||
\(891\) | 118.236 | + | 204.790i | 0.132700 | + | 0.229843i | ||||
\(892\) | 356.240 | + | 1193.73i | 0.399373 | + | 1.33826i | ||||
\(893\) | 324.538 | + | 187.372i | 0.363424 | + | 0.209823i | ||||
\(894\) | −9.14189 | + | 1.33500i | −0.0102258 | + | 0.00149329i | ||||
\(895\) | − | 559.458i | − | 0.625092i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 31.2863 | 0.0348788 | ||||||||
\(898\) | −123.894 | − | 848.405i | −0.137966 | − | 0.944771i | ||||
\(899\) | 609.747 | − | 1056.11i | 0.678250 | − | 1.17476i | ||||
\(900\) | 447.656 | − | 133.592i | 0.497396 | − | 0.148436i | ||||
\(901\) | 120.808 | − | 69.7488i | 0.134083 | − | 0.0774127i | ||||
\(902\) | 249.685 | + | 99.3202i | 0.276813 | + | 0.110111i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −135.480 | − | 291.536i | −0.149867 | − | 0.322496i | ||||
\(905\) | 12.3838 | + | 21.4494i | 0.0136837 | + | 0.0237009i | ||||
\(906\) | 13.8408 | + | 17.5203i | 0.0152768 | + | 0.0193381i | ||||
\(907\) | 259.004 | − | 448.609i | 0.285562 | − | 0.494607i | −0.687184 | − | 0.726484i | \(-0.741153\pi\) |
0.972745 | + | 0.231876i | \(0.0744865\pi\) | |||||||
\(908\) | −68.8460 | + | 289.355i | −0.0758216 | + | 0.318673i | ||||
\(909\) | 960.430i | 1.05658i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1065.61i | − | 1.16972i | −0.811135 | − | 0.584860i | \(-0.801150\pi\) | ||
0.811135 | − | 0.584860i | \(-0.198850\pi\) | |||||||
\(912\) | 10.5591 | − | 6.91840i | 0.0115780 | − | 0.00758597i | ||||
\(913\) | 160.593 | − | 278.155i | 0.175896 | − | 0.304661i | ||||
\(914\) | −15.7722 | + | 12.4598i | −0.0172563 | + | 0.0136322i | ||||
\(915\) | −1.26292 | − | 2.18743i | −0.00138024 | − | 0.00239064i | ||||
\(916\) | −215.051 | + | 227.541i | −0.234772 | + | 0.248407i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 46.8761 | + | 18.6464i | 0.0510632 | + | 0.0203120i | ||||
\(919\) | −1025.08 | + | 591.831i | −1.11543 | + | 0.643994i | −0.940231 | − | 0.340538i | \(-0.889391\pi\) |
−0.175200 | + | 0.984533i | \(0.556057\pi\) | |||||||
\(920\) | 462.823 | + | 41.1044i | 0.503069 | + | 0.0446787i | ||||
\(921\) | −14.1508 | + | 24.5099i | −0.0153646 | + | 0.0266123i | ||||
\(922\) | −1634.27 | + | 238.654i | −1.77253 | + | 0.258844i | ||||
\(923\) | 2475.03 | 2.68151 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 514.018i | 0.555695i | ||||||||
\(926\) | 227.007 | − | 33.1501i | 0.245148 | − | 0.0357992i | ||||
\(927\) | −985.914 | − | 569.217i | −1.06355 | − | 0.614043i | ||||
\(928\) | −650.635 | + | 576.468i | −0.701115 | + | 0.621194i | ||||
\(929\) | −189.509 | − | 328.240i | −0.203993 | − | 0.353326i | 0.745818 | − | 0.666149i | \(-0.232059\pi\) |
−0.949811 | + | 0.312823i | \(0.898725\pi\) | |||||||
\(930\) | −28.1701 | − | 11.2055i | −0.0302904 | − | 0.0120490i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 270.526 | + | 255.676i | 0.290264 | + | 0.274331i | ||||
\(933\) | −6.32093 | + | 3.64939i | −0.00677485 | + | 0.00391146i | ||||
\(934\) | −316.585 | + | 250.098i | −0.338957 | + | 0.267771i | ||||
\(935\) | 126.478 | + | 73.0221i | 0.135271 | + | 0.0780985i | ||||
\(936\) | −1127.72 | − | 791.849i | −1.20483 | − | 0.845993i | ||||
\(937\) | −1316.09 | −1.40458 | −0.702289 | − | 0.711892i | \(-0.747839\pi\) | ||||
−0.702289 | + | 0.711892i | \(0.747839\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.7214 | 0.0295223 | ||||||||
\(940\) | −148.491 | + | 624.096i | −0.157969 | + | 0.663932i | ||||
\(941\) | −430.441 | − | 248.515i | −0.457430 | − | 0.264097i | 0.253533 | − | 0.967327i | \(-0.418407\pi\) |
−0.710963 | + | 0.703230i | \(0.751741\pi\) | |||||||
\(942\) | 35.5268 | + | 44.9714i | 0.0377142 | + | 0.0477403i | ||||
\(943\) | −665.872 | + | 384.442i | −0.706121 | + | 0.407679i | ||||
\(944\) | 103.367 | + | 1829.95i | 0.109499 | + | 1.93850i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −332.176 | − | 132.134i | −0.351138 | − | 0.139676i | ||||
\(947\) | −404.243 | − | 700.170i | −0.426867 | − | 0.739356i | 0.569726 | − | 0.821835i | \(-0.307050\pi\) |
−0.996593 | + | 0.0824792i | \(0.973716\pi\) | |||||||
\(948\) | −4.74980 | − | 15.9161i | −0.00501033 | − | 0.0167892i | ||||
\(949\) | −303.387 | − | 175.161i | −0.319692 | − | 0.184574i | ||||
\(950\) | 30.3996 | + | 208.172i | 0.0319995 | + | 0.219128i | ||||
\(951\) | − | 1.19488i | − | 0.00125644i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1345.58 | −1.41194 | −0.705969 | − | 0.708243i | \(-0.749488\pi\) | ||||
−0.705969 | + | 0.708243i | \(0.749488\pi\) | |||||||
\(954\) | −172.483 | + | 25.1879i | −0.180800 | + | 0.0264024i | ||||
\(955\) | −127.007 | + | 219.982i | −0.132991 | + | 0.230347i | ||||
\(956\) | 333.555 | + | 1117.71i | 0.348907 | + | 1.16915i | ||||
\(957\) | −6.71320 | + | 3.87587i | −0.00701484 | + | 0.00405002i | ||||
\(958\) | 441.715 | − | 1110.45i | 0.461081 | − | 1.15913i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 16.5180 | + | 13.9344i | 0.0172063 | + | 0.0145150i | ||||
\(961\) | 527.158 | + | 913.065i | 0.548552 | + | 0.950119i | ||||
\(962\) | 1189.71 | − | 939.857i | 1.23671 | − | 0.976982i | ||||
\(963\) | 391.173 | − | 677.532i | 0.406203 | − | 0.703564i | ||||
\(964\) | −207.161 | + | 870.685i | −0.214898 | + | 0.903200i | ||||
\(965\) | − | 294.809i | − | 0.305502i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 140.279i | − | 0.145066i | −0.997366 | − | 0.0725330i | \(-0.976892\pi\) | ||
0.997366 | − | 0.0725330i | \(-0.0231083\pi\) | |||||||
\(968\) | −516.832 | + | 736.054i | −0.533918 | + | 0.760386i | ||||
\(969\) | −5.67666 | + | 9.83226i | −0.00585826 | + | 0.0101468i | ||||
\(970\) | 696.392 | + | 881.525i | 0.717930 | + | 0.908788i | ||||
\(971\) | 719.336 | + | 1245.93i | 0.740820 | + | 1.28314i | 0.952122 | + | 0.305717i | \(0.0988961\pi\) |
−0.211303 | + | 0.977421i | \(0.567771\pi\) | |||||||
\(972\) | −68.7346 | − | 64.9616i | −0.0707146 | − | 0.0668330i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 255.125 | − | 641.370i | 0.261935 | − | 0.658491i | ||||
\(975\) | −21.0011 | + | 12.1250i | −0.0215396 | + | 0.0124359i | ||||
\(976\) | 53.9018 | − | 106.860i | 0.0552272 | − | 0.109488i | ||||
\(977\) | −451.095 | + | 781.319i | −0.461714 | + | 0.799712i | −0.999047 | − | 0.0436581i | \(-0.986099\pi\) |
0.537332 | + | 0.843371i | \(0.319432\pi\) | |||||||
\(978\) | 4.81576 | + | 32.9776i | 0.00492409 | + | 0.0337194i | ||||
\(979\) | −236.976 | −0.242059 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1707.49i | 1.74056i | ||||||||
\(982\) | −107.940 | − | 739.157i | −0.109918 | − | 0.752705i | ||||
\(983\) | −435.778 | − | 251.597i | −0.443315 | − | 0.255948i | 0.261688 | − | 0.965153i | \(-0.415721\pi\) |
−0.705003 | + | 0.709205i | \(0.749054\pi\) | |||||||
\(984\) | −35.6203 | − | 3.16352i | −0.0361995 | − | 0.00321496i | ||||
\(985\) | 243.380 | + | 421.547i | 0.247087 | + | 0.427967i | ||||
\(986\) | 288.960 | − | 726.430i | 0.293063 | − | 0.736744i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 426.237 | − | 450.993i | 0.431414 | − | 0.456470i | ||||
\(989\) | 885.864 | − | 511.454i | 0.895717 | − | 0.517142i | ||||
\(990\) | −113.126 | − | 143.200i | −0.114268 | − | 0.144646i | ||||
\(991\) | 784.898 | + | 453.161i | 0.792026 | + | 0.457277i | 0.840675 | − | 0.541539i | \(-0.182158\pi\) |
−0.0486491 | + | 0.998816i | \(0.515492\pi\) | |||||||
\(992\) | −287.416 | − | 1407.51i | −0.289734 | − | 1.41886i | ||||
\(993\) | −18.9481 | −0.0190816 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −495.847 | −0.498339 | ||||||||
\(996\) | −9.89374 | + | 41.5827i | −0.00993347 | + | 0.0417497i | ||||
\(997\) | 527.085 | + | 304.313i | 0.528671 | + | 0.305228i | 0.740475 | − | 0.672084i | \(-0.234601\pi\) |
−0.211804 | + | 0.977312i | \(0.567934\pi\) | |||||||
\(998\) | 1334.47 | − | 1054.21i | 1.33714 | − | 1.05632i | ||||
\(999\) | 60.0687 | − | 34.6807i | 0.0601288 | − | 0.0347154i |
(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 | 392.3.k.n.67.4 | 16 | ||
7.2 | even | 3 | inner | 392.3.k.n.275.2 | 16 | ||
7.3 | odd | 6 | 56.3.g.b.43.8 | yes | 8 | ||
7.4 | even | 3 | 392.3.g.m.99.8 | 8 | |||
7.5 | odd | 6 | 392.3.k.o.275.2 | 16 | |||
7.6 | odd | 2 | 392.3.k.o.67.4 | 16 | |||
8.3 | odd | 2 | inner | 392.3.k.n.67.2 | 16 | ||
21.17 | even | 6 | 504.3.g.b.379.1 | 8 | |||
28.3 | even | 6 | 224.3.g.b.15.3 | 8 | |||
28.11 | odd | 6 | 1568.3.g.m.687.6 | 8 | |||
56.3 | even | 6 | 56.3.g.b.43.7 | ✓ | 8 | ||
56.11 | odd | 6 | 392.3.g.m.99.7 | 8 | |||
56.19 | even | 6 | 392.3.k.o.275.4 | 16 | |||
56.27 | even | 2 | 392.3.k.o.67.2 | 16 | |||
56.45 | odd | 6 | 224.3.g.b.15.4 | 8 | |||
56.51 | odd | 6 | inner | 392.3.k.n.275.4 | 16 | ||
56.53 | even | 6 | 1568.3.g.m.687.5 | 8 | |||
84.59 | odd | 6 | 2016.3.g.b.1135.5 | 8 | |||
112.3 | even | 12 | 1792.3.d.j.1023.7 | 16 | |||
112.45 | odd | 12 | 1792.3.d.j.1023.9 | 16 | |||
112.59 | even | 12 | 1792.3.d.j.1023.10 | 16 | |||
112.101 | odd | 12 | 1792.3.d.j.1023.8 | 16 | |||
168.59 | odd | 6 | 504.3.g.b.379.2 | 8 | |||
168.101 | even | 6 | 2016.3.g.b.1135.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.g.b.43.7 | ✓ | 8 | 56.3 | even | 6 | ||
56.3.g.b.43.8 | yes | 8 | 7.3 | odd | 6 | ||
224.3.g.b.15.3 | 8 | 28.3 | even | 6 | |||
224.3.g.b.15.4 | 8 | 56.45 | odd | 6 | |||
392.3.g.m.99.7 | 8 | 56.11 | odd | 6 | |||
392.3.g.m.99.8 | 8 | 7.4 | even | 3 | |||
392.3.k.n.67.2 | 16 | 8.3 | odd | 2 | inner | ||
392.3.k.n.67.4 | 16 | 1.1 | even | 1 | trivial | ||
392.3.k.n.275.2 | 16 | 7.2 | even | 3 | inner | ||
392.3.k.n.275.4 | 16 | 56.51 | odd | 6 | inner | ||
392.3.k.o.67.2 | 16 | 56.27 | even | 2 | |||
392.3.k.o.67.4 | 16 | 7.6 | odd | 2 | |||
392.3.k.o.275.2 | 16 | 7.5 | odd | 6 | |||
392.3.k.o.275.4 | 16 | 56.19 | even | 6 | |||
504.3.g.b.379.1 | 8 | 21.17 | even | 6 | |||
504.3.g.b.379.2 | 8 | 168.59 | odd | 6 | |||
1568.3.g.m.687.5 | 8 | 56.53 | even | 6 | |||
1568.3.g.m.687.6 | 8 | 28.11 | odd | 6 | |||
1792.3.d.j.1023.7 | 16 | 112.3 | even | 12 | |||
1792.3.d.j.1023.8 | 16 | 112.101 | odd | 12 | |||
1792.3.d.j.1023.9 | 16 | 112.45 | odd | 12 | |||
1792.3.d.j.1023.10 | 16 | 112.59 | even | 12 | |||
2016.3.g.b.1135.4 | 8 | 168.101 | even | 6 | |||
2016.3.g.b.1135.5 | 8 | 84.59 | odd | 6 |