Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(19,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.n (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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(84\) |
Relative dimension: | \(42\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 19.8 | ||
Character | \(\chi\) | \(=\) | 756.19 |
Dual form | 756.2.n.b.199.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.17926 | + | 0.780599i | −0.833866 | + | 0.551967i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.781329 | − | 1.84107i | 0.390665 | − | 0.920533i | ||||
\(5\) | 2.00240i | 0.895499i | 0.894159 | + | 0.447749i | \(0.147774\pi\) | ||||
−0.894159 | + | 0.447749i | \(0.852226\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.64523 | + | 0.0525529i | −0.999803 | + | 0.0198631i | ||||
\(8\) | 0.515742 | + | 2.78101i | 0.182342 | + | 0.983235i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.56307 | − | 2.36135i | −0.494286 | − | 0.746726i | ||||
\(11\) | − | 5.03174i | − | 1.51713i | −0.651600 | − | 0.758563i | \(-0.725902\pi\) | ||
0.651600 | − | 0.758563i | \(-0.274098\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.29495 | − | 1.90234i | 0.913854 | − | 0.527614i | 0.0321850 | − | 0.999482i | \(-0.489753\pi\) |
0.881669 | + | 0.471868i | \(0.156420\pi\) | |||||||
\(14\) | 3.07840 | − | 2.12684i | 0.822738 | − | 0.568421i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.77905 | − | 2.87696i | −0.694762 | − | 0.719239i | ||||
\(17\) | −1.61527 | + | 0.932579i | −0.391762 | + | 0.226184i | −0.682923 | − | 0.730490i | \(-0.739292\pi\) |
0.291161 | + | 0.956674i | \(0.405958\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.12744 | − | 5.41689i | 0.717485 | − | 1.24272i | −0.244509 | − | 0.969647i | \(-0.578627\pi\) |
0.961993 | − | 0.273073i | \(-0.0880400\pi\) | |||||||
\(20\) | 3.68654 | + | 1.56453i | 0.824336 | + | 0.349840i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.92777 | + | 5.93375i | 0.837403 | + | 1.26508i | ||||
\(23\) | 6.27581i | 1.30860i | 0.756236 | + | 0.654299i | \(0.227036\pi\) | ||||
−0.756236 | + | 0.654299i | \(0.772964\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.990411 | 0.198082 | ||||||||
\(26\) | −2.40065 | + | 4.81540i | −0.470806 | + | 0.944377i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.97004 | + | 4.91110i | −0.372303 | + | 0.928111i | ||||
\(29\) | 1.23970 | − | 2.14722i | 0.230206 | − | 0.398728i | −0.727663 | − | 0.685935i | \(-0.759393\pi\) |
0.957869 | + | 0.287207i | \(0.0927268\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.557613 | + | 0.965814i | −0.100150 | + | 0.173465i | −0.911746 | − | 0.410753i | \(-0.865266\pi\) |
0.811596 | + | 0.584219i | \(0.198599\pi\) | |||||||
\(32\) | 5.52299 | + | 1.22337i | 0.976335 | + | 0.216263i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.17687 | − | 2.36064i | 0.201831 | − | 0.404846i | ||||
\(35\) | −0.105232 | − | 5.29680i | −0.0177874 | − | 0.895322i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.559132 | − | 0.968445i | 0.0919207 | − | 0.159211i | −0.816399 | − | 0.577489i | \(-0.804033\pi\) |
0.908319 | + | 0.418277i | \(0.137366\pi\) | |||||||
\(38\) | 0.540339 | + | 8.82923i | 0.0876546 | + | 1.43229i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.56868 | + | 1.03272i | −0.880486 | + | 0.163287i | ||||
\(41\) | 6.39139 | − | 3.69007i | 0.998167 | − | 0.576292i | 0.0904619 | − | 0.995900i | \(-0.471166\pi\) |
0.907706 | + | 0.419608i | \(0.137832\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.79358 | + | 3.92228i | 1.03601 | + | 0.598141i | 0.918701 | − | 0.394954i | \(-0.129239\pi\) |
0.117310 | + | 0.993095i | \(0.462573\pi\) | |||||||
\(44\) | −9.26376 | − | 3.93144i | −1.39656 | − | 0.592687i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.89889 | − | 7.40084i | −0.722303 | − | 1.09119i | ||||
\(47\) | −1.95019 | − | 3.37783i | −0.284464 | − | 0.492707i | 0.688015 | − | 0.725697i | \(-0.258482\pi\) |
−0.972479 | + | 0.232990i | \(0.925149\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.99448 | − | 0.278029i | 0.999211 | − | 0.0397184i | ||||
\(50\) | −1.16796 | + | 0.773114i | −0.165174 | + | 0.109335i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.927894 | − | 7.55257i | −0.128676 | − | 1.04735i | ||||
\(53\) | −2.80349 | − | 4.85579i | −0.385089 | − | 0.666994i | 0.606692 | − | 0.794937i | \(-0.292496\pi\) |
−0.991782 | + | 0.127942i | \(0.959163\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.0755 | 1.35858 | ||||||||
\(56\) | −1.51040 | − | 7.32930i | −0.201836 | − | 0.979419i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.214186 | + | 3.49984i | 0.0281241 | + | 0.459552i | ||||
\(59\) | 4.35302 | − | 7.53966i | 0.566715 | − | 0.981580i | −0.430172 | − | 0.902747i | \(-0.641547\pi\) |
0.996888 | − | 0.0788331i | \(-0.0251194\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.83423 | + | 1.05899i | −0.234849 | + | 0.135590i | −0.612807 | − | 0.790232i | \(-0.709960\pi\) |
0.377958 | + | 0.925823i | \(0.376626\pi\) | |||||||
\(62\) | −0.0963407 | − | 1.57422i | −0.0122353 | − | 0.199927i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.46802 | + | 2.86856i | −0.933503 | + | 0.358570i | ||||
\(65\) | 3.80924 | + | 6.59779i | 0.472478 | + | 0.818355i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.4118 | + | 6.01127i | 1.27201 | + | 0.734394i | 0.975366 | − | 0.220595i | \(-0.0707998\pi\) |
0.296642 | + | 0.954989i | \(0.404133\pi\) | |||||||
\(68\) | 0.454879 | + | 3.70248i | 0.0551622 | + | 0.448992i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.25877 | + | 6.16418i | 0.509021 | + | 0.736760i | ||||
\(71\) | 3.84867i | 0.456753i | 0.973573 | + | 0.228377i | \(0.0733417\pi\) | ||||
−0.973573 | + | 0.228377i | \(0.926658\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.499355 | + | 0.288303i | −0.0584450 | + | 0.0337433i | −0.528938 | − | 0.848661i | \(-0.677410\pi\) |
0.470493 | + | 0.882404i | \(0.344076\pi\) | |||||||
\(74\) | 0.0966032 | + | 1.57851i | 0.0112299 | + | 0.183498i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.52929 | − | 9.99021i | −0.863669 | − | 1.14596i | ||||
\(77\) | 0.264432 | + | 13.3101i | 0.0301349 | + | 1.51683i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.42902 | − | 1.97974i | 0.385794 | − | 0.222739i | −0.294542 | − | 0.955639i | \(-0.595167\pi\) |
0.680336 | + | 0.732900i | \(0.261834\pi\) | |||||||
\(80\) | 5.76081 | − | 5.56476i | 0.644078 | − | 0.622159i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.65667 | + | 9.34068i | −0.514243 | + | 1.03151i | ||||
\(83\) | 5.34720 | − | 9.26162i | 0.586931 | − | 1.01660i | −0.407700 | − | 0.913116i | \(-0.633669\pi\) |
0.994632 | − | 0.103479i | \(-0.0329975\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.86739 | − | 3.23442i | −0.202547 | − | 0.350822i | ||||
\(86\) | −11.0732 | + | 0.677665i | −1.19405 | + | 0.0730745i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 13.9933 | − | 2.59508i | 1.49169 | − | 0.276636i | ||||
\(89\) | 5.13938 | + | 2.96722i | 0.544773 | + | 0.314525i | 0.747011 | − | 0.664811i | \(-0.231488\pi\) |
−0.202238 | + | 0.979336i | \(0.564821\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.61592 | + | 5.20528i | −0.903194 | + | 0.545662i | ||||
\(92\) | 11.5542 | + | 4.90347i | 1.20461 | + | 0.511222i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.93652 | + | 2.46103i | 0.509163 | + | 0.253836i | ||||
\(95\) | 10.8468 | + | 6.26238i | 1.11285 | + | 0.642507i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.0382 | − | 8.10496i | −1.42536 | − | 0.822934i | −0.428613 | − | 0.903488i | \(-0.640997\pi\) |
−0.996750 | + | 0.0805547i | \(0.974331\pi\) | |||||||
\(98\) | −8.03131 | + | 5.78775i | −0.811285 | + | 0.584651i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.773837 | − | 1.82341i | 0.0773837 | − | 0.182341i | ||||
\(101\) | − | 3.79391i | − | 0.377508i | −0.982024 | − | 0.188754i | \(-0.939555\pi\) | ||
0.982024 | − | 0.188754i | \(-0.0604449\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.26720 | 0.913125 | 0.456562 | − | 0.889691i | \(-0.349081\pi\) | ||||
0.456562 | + | 0.889691i | \(0.349081\pi\) | |||||||
\(104\) | 6.98976 | + | 8.18217i | 0.685403 | + | 0.802327i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.09649 | + | 3.53786i | 0.689272 | + | 0.343627i | ||||
\(107\) | 6.79221 | + | 3.92148i | 0.656628 | + | 0.379104i | 0.790991 | − | 0.611828i | \(-0.209566\pi\) |
−0.134363 | + | 0.990932i | \(0.542899\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.27240 | + | 14.3282i | 0.792353 | + | 1.37239i | 0.924507 | + | 0.381166i | \(0.124477\pi\) |
−0.132154 | + | 0.991229i | \(0.542189\pi\) | |||||||
\(110\) | −11.8817 | + | 7.86495i | −1.13288 | + | 0.749894i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.50242 | + | 7.46416i | 0.708912 | + | 0.705297i | ||||
\(113\) | −9.70786 | − | 16.8145i | −0.913238 | − | 1.58178i | −0.809460 | − | 0.587175i | \(-0.800240\pi\) |
−0.103778 | − | 0.994600i | \(-0.533093\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.5667 | −1.17185 | ||||||||
\(116\) | −2.98456 | − | 3.96004i | −0.277109 | − | 0.367681i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.752087 | + | 12.2892i | 0.0692352 | + | 1.13131i | ||||
\(119\) | 4.22376 | − | 2.55177i | 0.387192 | − | 0.233921i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.3184 | −1.30167 | ||||||||
\(122\) | 1.33639 | − | 2.68063i | 0.120991 | − | 0.242693i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.34245 | + | 1.78122i | 0.120555 | + | 0.159958i | ||||
\(125\) | 11.9952i | 1.07288i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.21609i | − | 0.196646i | −0.995155 | − | 0.0983232i | \(-0.968652\pi\) | ||
0.995155 | − | 0.0983232i | \(-0.0313479\pi\) | |||||||
\(128\) | 6.56757 | − | 9.21233i | 0.580497 | − | 0.814262i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.64233 | − | 4.80705i | −0.845688 | − | 0.421606i | ||||
\(131\) | −15.9027 | −1.38943 | −0.694714 | − | 0.719286i | \(-0.744469\pi\) | ||||
−0.694714 | + | 0.719286i | \(0.744469\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.98813 | + | 14.4933i | −0.692659 | + | 1.25673i | ||||
\(134\) | −16.9707 | + | 1.03859i | −1.46605 | + | 0.0897204i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.42658 | − | 4.01112i | −0.293826 | − | 0.343951i | ||||
\(137\) | 4.30171 | 0.367520 | 0.183760 | − | 0.982971i | \(-0.441173\pi\) | ||||
0.183760 | + | 0.982971i | \(0.441173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.19727 | − | 3.80579i | −0.186370 | − | 0.322803i | 0.757667 | − | 0.652641i | \(-0.226339\pi\) |
−0.944037 | + | 0.329838i | \(0.893006\pi\) | |||||||
\(140\) | −9.83397 | − | 3.94480i | −0.831122 | − | 0.333397i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.00427 | − | 4.53860i | −0.252113 | − | 0.380871i | ||||
\(143\) | −9.57207 | − | 16.5793i | −0.800457 | − | 1.38643i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.29958 | + | 2.48236i | 0.357060 | + | 0.206149i | ||||
\(146\) | 0.363822 | − | 0.729781i | 0.0301102 | − | 0.0603971i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.34611 | − | 1.78607i | −0.110649 | − | 0.146814i | ||||
\(149\) | −4.58475 | −0.375597 | −0.187799 | − | 0.982208i | \(-0.560135\pi\) | ||||
−0.187799 | + | 0.982208i | \(0.560135\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 23.4942i | − | 1.91193i | −0.293475 | − | 0.955967i | \(-0.594812\pi\) | ||
0.293475 | − | 0.955967i | \(-0.405188\pi\) | |||||||
\(152\) | 16.6774 | + | 5.90373i | 1.35271 | + | 0.478856i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.7017 | − | 15.4897i | −0.862367 | − | 1.24820i | ||||
\(155\) | −1.93394 | − | 1.11656i | −0.155338 | − | 0.0896844i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.1976 | − | 8.19699i | −1.13309 | − | 0.654191i | −0.188381 | − | 0.982096i | \(-0.560324\pi\) |
−0.944711 | + | 0.327905i | \(0.893657\pi\) | |||||||
\(158\) | −2.49833 | + | 5.01133i | −0.198756 | + | 0.398680i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.44967 | + | 11.0592i | −0.193663 | + | 0.874307i | ||||
\(161\) | −0.329812 | − | 16.6010i | −0.0259928 | − | 1.30834i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.37894 | − | 2.52818i | −0.342985 | − | 0.198022i | 0.318606 | − | 0.947887i | \(-0.396785\pi\) |
−0.661591 | + | 0.749865i | \(0.730119\pi\) | |||||||
\(164\) | −1.79989 | − | 14.6501i | −0.140547 | − | 1.14398i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.923854 | + | 15.0959i | 0.0717050 | + | 1.17167i | ||||
\(167\) | 4.45705 | + | 7.71983i | 0.344897 | + | 0.597378i | 0.985335 | − | 0.170631i | \(-0.0545806\pi\) |
−0.640438 | + | 0.768010i | \(0.721247\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.737790 | − | 1.27789i | 0.0567530 | − | 0.0982992i | ||||
\(170\) | 4.72694 | + | 2.35655i | 0.362539 | + | 0.180739i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 12.5292 | − | 9.44284i | 0.955342 | − | 0.720010i | ||||
\(173\) | −2.63021 | + | 1.51855i | −0.199971 | + | 0.115453i | −0.596642 | − | 0.802508i | \(-0.703499\pi\) |
0.396671 | + | 0.917961i | \(0.370165\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.61986 | + | 0.0520490i | −0.198043 | + | 0.00393453i | ||||
\(176\) | −14.4761 | + | 13.9834i | −1.09118 | + | 1.05404i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.37690 | + | 0.512657i | −0.627875 | + | 0.0384253i | ||||
\(179\) | 4.01804 | − | 2.31982i | 0.300323 | − | 0.173391i | −0.342265 | − | 0.939603i | \(-0.611194\pi\) |
0.642588 | + | 0.766212i | \(0.277861\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.81679i | − | 0.283700i | −0.989888 | − | 0.141850i | \(-0.954695\pi\) | ||
0.989888 | − | 0.141850i | \(-0.0453050\pi\) | |||||||
\(182\) | 6.09721 | − | 12.8640i | 0.451955 | − | 0.953542i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −17.4531 | + | 3.23670i | −1.28666 | + | 0.238612i | ||||
\(185\) | 1.93921 | + | 1.11960i | 0.142574 | + | 0.0823149i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.69249 | + | 8.12764i | 0.343149 | + | 0.594352i | ||||
\(188\) | −7.74254 | + | 0.951233i | −0.564683 | + | 0.0693758i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −17.6796 | + | 1.08197i | −1.28261 | + | 0.0784946i | ||||
\(191\) | −3.26838 | + | 1.88700i | −0.236492 | + | 0.136539i | −0.613563 | − | 0.789645i | \(-0.710264\pi\) |
0.377071 | + | 0.926184i | \(0.376931\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.06896 | − | 10.5117i | 0.436853 | − | 0.756652i | −0.560592 | − | 0.828092i | \(-0.689426\pi\) |
0.997445 | + | 0.0714404i | \(0.0227596\pi\) | |||||||
\(194\) | 22.8815 | − | 1.40032i | 1.64279 | − | 0.100537i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.95312 | − | 13.0945i | 0.353794 | − | 0.935323i | ||||
\(197\) | 6.35688 | 0.452909 | 0.226455 | − | 0.974022i | \(-0.427287\pi\) | ||||
0.226455 | + | 0.974022i | \(0.427287\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.00759 | − | 1.74520i | −0.0714262 | − | 0.123714i | 0.828100 | − | 0.560580i | \(-0.189422\pi\) |
−0.899527 | + | 0.436866i | \(0.856088\pi\) | |||||||
\(200\) | 0.510796 | + | 2.75434i | 0.0361187 | + | 0.194761i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.96152 | + | 4.47402i | 0.208372 | + | 0.314791i | ||||
\(203\) | −3.16644 | + | 5.74503i | −0.222240 | + | 0.403222i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.38898 | + | 12.7981i | 0.516069 | + | 0.893858i | ||||
\(206\) | −10.9285 | + | 7.23397i | −0.761424 | + | 0.504015i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −14.6298 | − | 4.19273i | −1.01439 | − | 0.290714i | ||||
\(209\) | −27.2564 | − | 15.7365i | −1.88536 | − | 1.08851i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.8266 | + | 9.13752i | −1.08955 | + | 0.629053i | −0.933457 | − | 0.358690i | \(-0.883224\pi\) |
−0.156094 | + | 0.987742i | \(0.549890\pi\) | |||||||
\(212\) | −11.1303 | + | 1.36744i | −0.764431 | + | 0.0939165i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −11.0709 | + | 0.677528i | −0.756792 | + | 0.0463149i | ||||
\(215\) | −7.85395 | + | 13.6034i | −0.535635 | + | 0.927747i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.42426 | − | 2.58410i | 0.0966850 | − | 0.175420i | ||||
\(218\) | −20.9400 | − | 10.4393i | −1.41823 | − | 0.707041i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.87230 | − | 18.5497i | 0.530751 | − | 1.25062i | ||||
\(221\) | −3.54816 | + | 6.14560i | −0.238675 | + | 0.413398i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.23280 | + | 14.2596i | −0.551309 | + | 0.954896i | 0.446871 | + | 0.894598i | \(0.352538\pi\) |
−0.998180 | + | 0.0602974i | \(0.980795\pi\) | |||||||
\(224\) | −14.6739 | − | 2.94584i | −0.980438 | − | 0.196827i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 24.5735 | + | 12.2508i | 1.63461 | + | 0.814911i | ||||
\(227\) | −0.441421 | −0.0292982 | −0.0146491 | − | 0.999893i | \(-0.504663\pi\) | ||||
−0.0146491 | + | 0.999893i | \(0.504663\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 5.37457i | − | 0.355161i | −0.984106 | − | 0.177581i | \(-0.943173\pi\) | ||
0.984106 | − | 0.177581i | \(-0.0568271\pi\) | |||||||
\(230\) | 14.8194 | − | 9.80953i | 0.977163 | − | 0.646821i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.61079 | + | 2.34020i | 0.434020 | + | 0.153641i | ||||
\(233\) | −3.38198 | + | 5.85776i | −0.221561 | + | 0.383754i | −0.955282 | − | 0.295696i | \(-0.904448\pi\) |
0.733721 | + | 0.679450i | \(0.237782\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.76375 | − | 3.90505i | 0.441218 | − | 0.254737i | ||||
\(236\) | −10.4799 | − | 13.9052i | −0.682181 | − | 0.905149i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.98902 | + | 6.30628i | −0.193749 | + | 0.408776i | ||||
\(239\) | −0.169520 | + | 0.0978724i | −0.0109653 | + | 0.00633084i | −0.505473 | − | 0.862843i | \(-0.668682\pi\) |
0.494507 | + | 0.869173i | \(0.335349\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.8524i | 0.827897i | 0.910300 | + | 0.413948i | \(0.135851\pi\) | ||||
−0.910300 | + | 0.413948i | \(0.864149\pi\) | |||||||
\(242\) | 16.8851 | − | 11.1769i | 1.08542 | − | 0.718479i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.516540 | + | 4.20437i | 0.0330681 | + | 0.269157i | ||||
\(245\) | 0.556724 | + | 14.0057i | 0.0355678 | + | 0.894792i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 23.7978i | − | 1.51422i | ||||||
\(248\) | −2.97352 | − | 1.05262i | −0.188819 | − | 0.0668412i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.36343 | − | 14.1455i | −0.592195 | − | 0.894639i | ||||
\(251\) | −13.7723 | −0.869299 | −0.434650 | − | 0.900600i | \(-0.643128\pi\) | ||||
−0.434650 | + | 0.900600i | \(0.643128\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 31.5782 | 1.98531 | ||||||||
\(254\) | 1.72988 | + | 2.61336i | 0.108542 | + | 0.163977i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.553766 | + | 15.9904i | −0.0346104 | + | 0.999401i | ||||
\(257\) | − | 13.8537i | − | 0.864170i | −0.901833 | − | 0.432085i | \(-0.857778\pi\) | ||
0.901833 | − | 0.432085i | \(-0.142222\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.42814 | + | 2.59114i | −0.0887402 | + | 0.161006i | ||||
\(260\) | 15.1232 | − | 1.85801i | 0.937903 | − | 0.115229i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 18.7535 | − | 12.4137i | 1.15860 | − | 0.766919i | ||||
\(263\) | 1.61839i | 0.0997945i | 0.998754 | + | 0.0498972i | \(0.0158894\pi\) | ||||
−0.998754 | + | 0.0498972i | \(0.984111\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.72322 | − | 5.61370i | 0.597293 | − | 0.344847i | ||||
\(266\) | −1.89332 | − | 23.3269i | −0.116087 | − | 1.43027i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 19.2022 | − | 14.4721i | 1.17296 | − | 0.884024i | ||||
\(269\) | 3.95786 | − | 2.28507i | 0.241315 | − | 0.139323i | −0.374466 | − | 0.927241i | \(-0.622174\pi\) |
0.615781 | + | 0.787917i | \(0.288841\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.9451 | + | 20.6896i | −0.725615 | + | 1.25680i | 0.233105 | + | 0.972452i | \(0.425111\pi\) |
−0.958720 | + | 0.284351i | \(0.908222\pi\) | |||||||
\(272\) | 7.17192 | + | 2.05539i | 0.434861 | + | 0.124626i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.07285 | + | 3.35791i | −0.306462 | + | 0.202859i | ||||
\(275\) | − | 4.98349i | − | 0.300516i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.3054 | 0.739363 | 0.369681 | − | 0.929159i | \(-0.379467\pi\) | ||||
0.369681 | + | 0.929159i | \(0.379467\pi\) | |||||||
\(278\) | 5.56196 | + | 2.77284i | 0.333584 | + | 0.166304i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 14.6762 | − | 3.02443i | 0.877069 | − | 0.180744i | ||||
\(281\) | 6.68674 | − | 11.5818i | 0.398897 | − | 0.690910i | −0.594693 | − | 0.803953i | \(-0.702726\pi\) |
0.993590 | + | 0.113043i | \(0.0360597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.22533 | + | 5.58643i | −0.191726 | + | 0.332079i | −0.945822 | − | 0.324685i | \(-0.894742\pi\) |
0.754097 | + | 0.656764i | \(0.228075\pi\) | |||||||
\(284\) | 7.08566 | + | 3.00708i | 0.420456 | + | 0.178437i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 24.2298 | + | 12.0794i | 1.43274 | + | 0.714272i | ||||
\(287\) | −16.7128 | + | 10.0970i | −0.986524 | + | 0.596005i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.76059 | + | 11.7097i | −0.397682 | + | 0.688805i | ||||
\(290\) | −7.00807 | + | 0.428886i | −0.411528 | + | 0.0251851i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.140624 | + | 1.14460i | 0.00822938 | + | 0.0669829i | ||||
\(293\) | −18.9236 | + | 10.9255i | −1.10553 | + | 0.638277i | −0.937668 | − | 0.347534i | \(-0.887019\pi\) |
−0.167861 | + | 0.985811i | \(0.553686\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.0974 | + | 8.71648i | 0.879003 | + | 0.507493i | ||||
\(296\) | 2.98162 | + | 1.05548i | 0.173303 | + | 0.0613487i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.40663 | − | 3.57885i | 0.313198 | − | 0.207317i | ||||
\(299\) | 11.9387 | + | 20.6785i | 0.690434 | + | 1.19587i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.1767 | − | 10.0183i | −1.04769 | − | 0.577445i | ||||
\(302\) | 18.3396 | + | 27.7059i | 1.05532 | + | 1.59430i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −24.2755 | + | 6.05629i | −1.39229 | + | 0.347352i | ||||
\(305\) | −2.12053 | − | 3.67286i | −0.121421 | − | 0.210307i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.00234 | 0.285499 | 0.142749 | − | 0.989759i | \(-0.454406\pi\) | ||||
0.142749 | + | 0.989759i | \(0.454406\pi\) | |||||||
\(308\) | 24.7114 | + | 9.91273i | 1.40806 | + | 0.564830i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.15222 | − | 0.192912i | 0.179034 | − | 0.0109567i | ||||
\(311\) | 10.1968 | − | 17.6613i | 0.578206 | − | 1.00148i | −0.417479 | − | 0.908687i | \(-0.637086\pi\) |
0.995685 | − | 0.0927962i | \(-0.0295805\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.2484 | + | 10.5357i | −1.03146 | + | 0.595515i | −0.917403 | − | 0.397959i | \(-0.869718\pi\) |
−0.114059 | + | 0.993474i | \(0.536385\pi\) | |||||||
\(314\) | 23.1413 | − | 1.41622i | 1.30594 | − | 0.0799220i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.965649 | − | 7.85988i | −0.0543220 | − | 0.442153i | ||||
\(317\) | 6.03814 | + | 10.4584i | 0.339136 | + | 0.587400i | 0.984270 | − | 0.176669i | \(-0.0565321\pi\) |
−0.645135 | + | 0.764069i | \(0.723199\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.8042 | − | 6.23782i | −0.604920 | − | 0.349251i | ||||
\(320\) | −5.74400 | − | 14.9539i | −0.321099 | − | 0.835950i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 13.3476 | + | 19.3195i | 0.743835 | + | 1.07663i | ||||
\(323\) | 11.6664i | 0.649133i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.26335 | − | 1.88410i | 0.181018 | − | 0.104511i | ||||
\(326\) | 7.13742 | − | 0.436802i | 0.395305 | − | 0.0241922i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 13.5584 | + | 15.8714i | 0.748639 | + | 0.876351i | ||||
\(329\) | 5.33621 | + | 8.83264i | 0.294195 | + | 0.486959i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.10382 | − | 0.637288i | 0.0606712 | − | 0.0350285i | −0.469358 | − | 0.883008i | \(-0.655514\pi\) |
0.530029 | + | 0.847980i | \(0.322181\pi\) | |||||||
\(332\) | −12.8733 | − | 17.0809i | −0.706516 | − | 0.937437i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.2821 | − | 5.62455i | −0.617331 | − | 0.307762i | ||||
\(335\) | −12.0370 | + | 20.8486i | −0.657649 | + | 1.13908i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.12539 | − | 10.6095i | −0.333671 | − | 0.577935i | 0.649558 | − | 0.760312i | \(-0.274954\pi\) |
−0.983229 | + | 0.182377i | \(0.941621\pi\) | |||||||
\(338\) | 0.127470 | + | 2.08289i | 0.00693348 | + | 0.113294i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7.41383 | + | 0.910848i | −0.402071 | + | 0.0493977i | ||||
\(341\) | 4.85972 | + | 2.80576i | 0.263169 | + | 0.151941i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.4874 | + | 1.10303i | −0.998225 | + | 0.0595581i | ||||
\(344\) | −7.40415 | + | 20.9159i | −0.399205 | + | 1.12771i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.91633 | − | 3.84391i | 0.103023 | − | 0.206650i | ||||
\(347\) | 7.47885 | + | 4.31792i | 0.401486 | + | 0.231798i | 0.687125 | − | 0.726539i | \(-0.258873\pi\) |
−0.285639 | + | 0.958337i | \(0.592206\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.91380 | − | 3.99168i | −0.370087 | − | 0.213670i | 0.303409 | − | 0.952860i | \(-0.401875\pi\) |
−0.673497 | + | 0.739190i | \(0.735208\pi\) | |||||||
\(350\) | 3.04888 | − | 2.10644i | 0.162970 | − | 0.112594i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.15567 | − | 27.7902i | 0.328098 | − | 1.48122i | ||||
\(353\) | 18.9233i | 1.00719i | 0.863941 | + | 0.503594i | \(0.167989\pi\) | ||||
−0.863941 | + | 0.503594i | \(0.832011\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.70656 | −0.409022 | ||||||||
\(356\) | 9.47840 | − | 7.14356i | 0.502354 | − | 0.378608i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.92749 | + | 5.87216i | −0.154722 | + | 0.310353i | ||||
\(359\) | 22.7971 | + | 13.1619i | 1.20319 | + | 0.694659i | 0.961262 | − | 0.275636i | \(-0.0888885\pi\) |
0.241923 | + | 0.970295i | \(0.422222\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.0618 | − | 17.4276i | −0.529569 | − | 0.917240i | ||||
\(362\) | 2.97939 | + | 4.50101i | 0.156593 | + | 0.236568i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.85140 | + | 19.9295i | 0.149454 | + | 1.04459i | ||||
\(365\) | −0.577296 | − | 0.999906i | −0.0302170 | − | 0.0523375i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.55991 | −0.0814269 | −0.0407134 | − | 0.999171i | \(-0.512963\pi\) | ||||
−0.0407134 | + | 0.999171i | \(0.512963\pi\) | |||||||
\(368\) | 18.0552 | − | 17.4408i | 0.941194 | − | 0.909164i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.16080 | + | 0.193438i | −0.164322 | + | 0.0100564i | ||||
\(371\) | 7.67107 | + | 12.6974i | 0.398262 | + | 0.659214i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 35.9979 | 1.86390 | 0.931950 | − | 0.362588i | \(-0.118107\pi\) | ||||
0.931950 | + | 0.362588i | \(0.118107\pi\) | |||||||
\(374\) | −11.8781 | − | 5.92168i | −0.614203 | − | 0.306203i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.38797 | − | 7.16558i | 0.432577 | − | 0.369537i | ||||
\(377\) | − | 9.43329i | − | 0.485839i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.4764i | 1.00044i | 0.865899 | + | 0.500219i | \(0.166747\pi\) | ||||
−0.865899 | + | 0.500219i | \(0.833253\pi\) | |||||||
\(380\) | 20.0043 | − | 15.0766i | 1.02620 | − | 0.773414i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.38130 | − | 4.77657i | 0.121838 | − | 0.244391i | ||||
\(383\) | 0.0991517 | 0.00506641 | 0.00253321 | − | 0.999997i | \(-0.499194\pi\) | ||||
0.00253321 | + | 0.999997i | \(0.499194\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −26.6521 | + | 0.529498i | −1.35832 | + | 0.0269857i | ||||
\(386\) | 1.04855 | + | 17.1336i | 0.0533700 | + | 0.872075i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −25.8902 | + | 19.5126i | −1.31438 | + | 0.990603i | ||||
\(389\) | 26.5662 | 1.34696 | 0.673481 | − | 0.739204i | \(-0.264798\pi\) | ||||
0.673481 | + | 0.739204i | \(0.264798\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.85269 | − | 10.1372i | −0.295983 | − | 0.512658i | ||||
\(392\) | 4.38054 | + | 19.3083i | 0.221251 | + | 0.975217i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.49645 | + | 4.96218i | −0.377665 | + | 0.249991i | ||||
\(395\) | 3.96423 | + | 6.86625i | 0.199462 | + | 0.345478i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.4405 | + | 13.5334i | 1.17645 | + | 0.679221i | 0.955190 | − | 0.295995i | \(-0.0956511\pi\) |
0.221256 | + | 0.975216i | \(0.428984\pi\) | |||||||
\(398\) | 2.55052 | + | 1.27153i | 0.127846 | + | 0.0637358i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.75240 | − | 2.84937i | −0.137620 | − | 0.142469i | ||||
\(401\) | 31.9981 | 1.59791 | 0.798954 | − | 0.601392i | \(-0.205387\pi\) | ||||
0.798954 | + | 0.601392i | \(0.205387\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.24308i | 0.211363i | ||||||||
\(404\) | −6.98484 | − | 2.96429i | −0.347509 | − | 0.147479i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.750499 | − | 9.24662i | −0.0372466 | − | 0.458902i | ||||
\(407\) | −4.87296 | − | 2.81340i | −0.241544 | − | 0.139455i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.9401 | + | 10.9351i | 0.936527 | + | 0.540704i | 0.888870 | − | 0.458160i | \(-0.151491\pi\) |
0.0476569 | + | 0.998864i | \(0.484825\pi\) | |||||||
\(410\) | −18.7037 | − | 9.32450i | −0.923712 | − | 0.460504i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.24074 | − | 17.0615i | 0.356726 | − | 0.840562i | ||||
\(413\) | −11.1185 | + | 20.1729i | −0.547106 | + | 0.992643i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.5454 | + | 10.7072i | 0.910359 | + | 0.525596i | ||||
\(416\) | 20.5252 | − | 6.47566i | 1.00633 | − | 0.317495i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 44.4263 | − | 2.71884i | 2.17296 | − | 0.132983i | ||||
\(419\) | −9.62802 | − | 16.6762i | −0.470360 | − | 0.814687i | 0.529066 | − | 0.848581i | \(-0.322542\pi\) |
−0.999425 | + | 0.0338939i | \(0.989209\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.8866 | − | 29.2484i | 0.823002 | − | 1.42548i | −0.0804343 | − | 0.996760i | \(-0.525631\pi\) |
0.903437 | − | 0.428722i | \(-0.141036\pi\) | |||||||
\(422\) | 11.5311 | − | 23.1298i | 0.561323 | − | 1.12594i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.0581 | − | 10.3009i | 0.585594 | − | 0.500255i | ||||
\(425\) | −1.59979 | + | 0.923637i | −0.0776010 | + | 0.0448030i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.79631 | − | 2.89768i | 0.232110 | − | 0.140228i | ||||
\(428\) | 12.5267 | − | 9.44094i | 0.605499 | − | 0.456345i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.35695 | − | 22.1728i | −0.0654381 | − | 1.06927i | ||||
\(431\) | 2.57782 | − | 1.48830i | 0.124169 | − | 0.0716890i | −0.436629 | − | 0.899642i | \(-0.643828\pi\) |
0.560798 | + | 0.827953i | \(0.310494\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 25.5918i | − | 1.22986i | −0.788580 | − | 0.614932i | \(-0.789183\pi\) | ||
0.788580 | − | 0.614932i | \(-0.210817\pi\) | |||||||
\(434\) | 0.337573 | + | 4.15912i | 0.0162040 | + | 0.199644i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 32.8427 | − | 4.03498i | 1.57288 | − | 0.193241i | ||||
\(437\) | 33.9954 | + | 19.6272i | 1.62622 | + | 0.938898i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.5655 | − | 25.2282i | −0.695174 | − | 1.20408i | −0.970122 | − | 0.242618i | \(-0.921994\pi\) |
0.274947 | − | 0.961459i | \(-0.411340\pi\) | |||||||
\(440\) | 5.19637 | + | 28.0201i | 0.247727 | + | 1.33581i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.613029 | − | 10.0170i | −0.0291588 | − | 0.476459i | ||||
\(443\) | −21.9919 | + | 12.6970i | −1.04487 | + | 0.603254i | −0.921208 | − | 0.389070i | \(-0.872796\pi\) |
−0.123659 | + | 0.992325i | \(0.539463\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.94155 | + | 10.2911i | −0.281657 | + | 0.487844i | ||||
\(446\) | −1.42241 | − | 23.2424i | −0.0673530 | − | 1.10056i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 19.6039 | − | 7.98048i | 0.926196 | − | 0.377042i | ||||
\(449\) | −30.7532 | −1.45133 | −0.725667 | − | 0.688046i | \(-0.758469\pi\) | ||||
−0.725667 | + | 0.688046i | \(0.758469\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.5675 | − | 32.1598i | −0.874308 | − | 1.51435i | ||||
\(452\) | −38.5416 | + | 4.73515i | −1.81285 | + | 0.222723i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.520552 | − | 0.344573i | 0.0244307 | − | 0.0161716i | ||||
\(455\) | −10.4230 | − | 17.2525i | −0.488639 | − | 0.808809i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.49304 | + | 9.51423i | 0.256954 | + | 0.445057i | 0.965424 | − | 0.260683i | \(-0.0839479\pi\) |
−0.708471 | + | 0.705740i | \(0.750615\pi\) | |||||||
\(458\) | 4.19538 | + | 6.33804i | 0.196037 | + | 0.296157i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.81870 | + | 23.1360i | −0.457799 | + | 1.07872i | ||||
\(461\) | −14.3875 | − | 8.30665i | −0.670095 | − | 0.386879i | 0.126018 | − | 0.992028i | \(-0.459780\pi\) |
−0.796113 | + | 0.605149i | \(0.793114\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.92387 | + | 3.99750i | −0.321779 | + | 0.185779i | −0.652185 | − | 0.758059i | \(-0.726148\pi\) |
0.330406 | + | 0.943839i | \(0.392814\pi\) | |||||||
\(464\) | −9.62262 | + | 2.40067i | −0.446719 | + | 0.111448i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.584316 | − | 9.54781i | −0.0270679 | − | 0.442294i | ||||
\(467\) | 12.6639 | − | 21.9346i | 0.586017 | − | 1.01501i | −0.408731 | − | 0.912655i | \(-0.634029\pi\) |
0.994748 | − | 0.102356i | \(-0.0326381\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −27.8576 | − | 15.3540i | −1.28634 | − | 0.708983i | ||||
\(470\) | −4.92797 | + | 9.88487i | −0.227310 | + | 0.455955i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 23.2129 | + | 8.21728i | 1.06846 | + | 0.378231i | ||||
\(473\) | 19.7359 | − | 34.1835i | 0.907456 | − | 1.57176i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.09745 | − | 5.36495i | 0.142121 | − | 0.246161i | ||||
\(476\) | −1.39784 | − | 9.77000i | −0.0640697 | − | 0.447807i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.123510 | − | 0.247745i | 0.00564920 | − | 0.0113316i | ||||
\(479\) | 4.18768 | 0.191340 | 0.0956701 | − | 0.995413i | \(-0.469501\pi\) | ||||
0.0956701 | + | 0.995413i | \(0.469501\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 4.25464i | − | 0.193995i | ||||||
\(482\) | −10.0326 | − | 15.1564i | −0.456972 | − | 0.690355i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.1874 | + | 26.3611i | −0.508516 | + | 1.19823i | ||||
\(485\) | 16.2293 | − | 28.1100i | 0.736936 | − | 1.27641i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.8039 | + | 17.2073i | −1.35054 | + | 0.779737i | −0.988326 | − | 0.152356i | \(-0.951314\pi\) |
−0.362219 | + | 0.932093i | \(0.617981\pi\) | |||||||
\(488\) | −3.89106 | − | 4.55485i | −0.176140 | − | 0.206188i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −11.5894 | − | 16.0819i | −0.523555 | − | 0.726504i | ||||
\(491\) | −12.1909 | + | 7.03839i | −0.550166 | + | 0.317638i | −0.749189 | − | 0.662357i | \(-0.769556\pi\) |
0.199023 | + | 0.979995i | \(0.436223\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.62446i | 0.208275i | ||||||||
\(494\) | 18.5766 | + | 28.0639i | 0.835800 | + | 1.26266i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.32824 | − | 1.07982i | 0.194344 | − | 0.0484852i | ||||
\(497\) | −0.202259 | − | 10.1806i | −0.00907255 | − | 0.456663i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.6889i | 0.702331i | 0.936313 | + | 0.351166i | \(0.114215\pi\) | ||||
−0.936313 | + | 0.351166i | \(0.885785\pi\) | |||||||
\(500\) | 22.0839 | + | 9.37218i | 0.987622 | + | 0.419137i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 16.2412 | − | 10.7506i | 0.724879 | − | 0.479825i | ||||
\(503\) | 9.76063 | 0.435205 | 0.217603 | − | 0.976037i | \(-0.430176\pi\) | ||||
0.217603 | + | 0.976037i | \(0.430176\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.59691 | 0.338058 | ||||||||
\(506\) | −37.2391 | + | 24.6499i | −1.65548 | + | 1.09582i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.07997 | − | 1.73150i | −0.181019 | − | 0.0768228i | ||||
\(509\) | − | 33.1208i | − | 1.46806i | −0.679120 | − | 0.734028i | \(-0.737638\pi\) | ||
0.679120 | − | 0.734028i | \(-0.262362\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.30576 | − | 0.788869i | 0.0577633 | − | 0.0348975i | ||||
\(512\) | −11.8291 | − | 19.2892i | −0.522776 | − | 0.852470i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.8142 | + | 16.3372i | 0.476993 | + | 0.720602i | ||||
\(515\) | 18.5566i | 0.817702i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.9963 | + | 9.81284i | −0.747498 | + | 0.431568i | ||||
\(518\) | −0.338493 | − | 4.17045i | −0.0148725 | − | 0.183239i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −16.3839 | + | 13.9963i | −0.718483 | + | 0.613777i | ||||
\(521\) | −12.6595 | + | 7.30899i | −0.554624 | + | 0.320213i | −0.750985 | − | 0.660319i | \(-0.770421\pi\) |
0.196361 | + | 0.980532i | \(0.437088\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.22510 | − | 10.7822i | 0.272205 | − | 0.471472i | −0.697221 | − | 0.716856i | \(-0.745581\pi\) |
0.969426 | + | 0.245383i | \(0.0789139\pi\) | |||||||
\(524\) | −12.4253 | + | 29.2780i | −0.542800 | + | 1.27901i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.26332 | − | 1.90852i | −0.0550833 | − | 0.0832152i | ||||
\(527\) | − | 2.08007i | − | 0.0906094i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.3858 | −0.712426 | ||||||||
\(530\) | −7.08419 | + | 14.2100i | −0.307718 | + | 0.617242i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 20.4417 | + | 26.0307i | 0.886261 | + | 1.12857i | ||||
\(533\) | 14.0395 | − | 24.3172i | 0.608120 | − | 1.05329i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.85236 | + | 13.6007i | −0.339487 | + | 0.588009i | ||||
\(536\) | −11.3476 | + | 32.0557i | −0.490141 | + | 1.38459i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.88364 | + | 5.78420i | −0.124322 | + | 0.249375i | ||||
\(539\) | −1.39897 | − | 35.1944i | −0.0602579 | − | 1.51593i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.8784 | + | 32.6984i | −0.811647 | + | 1.40581i | 0.100064 | + | 0.994981i | \(0.468095\pi\) |
−0.911711 | + | 0.410832i | \(0.865238\pi\) | |||||||
\(542\) | −2.06380 | − | 33.7229i | −0.0886479 | − | 1.44852i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −10.0620 | + | 3.17455i | −0.431406 | + | 0.136108i | ||||
\(545\) | −28.6908 | + | 16.5646i | −1.22898 | + | 0.709551i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.46357 | + | 2.57704i | 0.190848 | + | 0.110186i | 0.592380 | − | 0.805659i | \(-0.298189\pi\) |
−0.401531 | + | 0.915845i | \(0.631522\pi\) | |||||||
\(548\) | 3.36105 | − | 7.91973i | 0.143577 | − | 0.338314i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.89011 | + | 5.87685i | 0.165875 | + | 0.250590i | ||||
\(551\) | −7.75416 | − | 13.4306i | −0.330338 | − | 0.572162i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.96649 | + | 5.41708i | −0.381294 | + | 0.230358i | ||||
\(554\) | −14.5114 | + | 9.60562i | −0.616529 | + | 0.408104i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.72350 | + | 1.07175i | −0.369959 | + | 0.0454524i | ||||
\(557\) | 21.0386 | + | 36.4399i | 0.891434 | + | 1.54401i | 0.838156 | + | 0.545430i | \(0.183634\pi\) |
0.0532780 | + | 0.998580i | \(0.483033\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.8460 | 1.26235 | ||||||||
\(560\) | −14.9462 | + | 15.0228i | −0.631593 | + | 0.634829i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.15529 | + | 18.8776i | 0.0487330 | + | 0.796305i | ||||
\(563\) | −16.2896 | + | 28.2145i | −0.686526 | + | 1.18910i | 0.286429 | + | 0.958102i | \(0.407532\pi\) |
−0.972955 | + | 0.230996i | \(0.925801\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 33.6693 | − | 19.4390i | 1.41648 | − | 0.817804i | ||||
\(566\) | −0.557251 | − | 9.10556i | −0.0234230 | − | 0.382735i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.7032 | + | 1.98492i | −0.449096 | + | 0.0832854i | ||||
\(569\) | 20.3694 | + | 35.2808i | 0.853930 | + | 1.47905i | 0.877635 | + | 0.479330i | \(0.159120\pi\) |
−0.0237050 | + | 0.999719i | \(0.507546\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.1787 | + | 13.3822i | 0.969998 | + | 0.560029i | 0.899236 | − | 0.437465i | \(-0.144123\pi\) |
0.0707624 | + | 0.997493i | \(0.477457\pi\) | |||||||
\(572\) | −38.0025 | + | 4.66892i | −1.58897 | + | 0.195217i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.8271 | − | 24.9530i | 0.493653 | − | 1.04152i | ||||
\(575\) | 6.21563i | 0.259210i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.34065 | − | 2.50607i | 0.180704 | − | 0.104329i | −0.406920 | − | 0.913464i | \(-0.633397\pi\) |
0.587623 | + | 0.809135i | \(0.300064\pi\) | |||||||
\(578\) | −1.16805 | − | 19.0861i | −0.0485845 | − | 0.793878i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.92957 | − | 5.97626i | 0.329258 | − | 0.248151i | ||||
\(581\) | −13.6578 | + | 24.7801i | −0.566623 | + | 1.02805i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.4331 | + | 14.1064i | −1.01191 | + | 0.584229i | ||||
\(584\) | −1.05931 | − | 1.24002i | −0.0438346 | − | 0.0513124i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.7875 | − | 27.6559i | 0.569554 | − | 1.14245i | ||||
\(587\) | 10.2852 | − | 17.8145i | 0.424517 | − | 0.735285i | −0.571858 | − | 0.820352i | \(-0.693777\pi\) |
0.996375 | + | 0.0850676i | \(0.0271106\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.48781 | + | 6.04106i | 0.143713 | + | 0.248918i | ||||
\(590\) | −24.6079 | + | 1.50598i | −1.01309 | + | 0.0620000i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.34003 | + | 1.08276i | −0.178374 | + | 0.0445011i | ||||
\(593\) | 15.5093 | + | 8.95431i | 0.636891 | + | 0.367709i | 0.783416 | − | 0.621498i | \(-0.213475\pi\) |
−0.146525 | + | 0.989207i | \(0.546809\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.10966 | + | 8.45764i | 0.209476 | + | 0.346730i | ||||
\(596\) | −3.58220 | + | 8.44082i | −0.146732 | + | 0.345750i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −30.2205 | − | 15.0660i | −1.23581 | − | 0.616096i | ||||
\(599\) | −18.2010 | − | 10.5083i | −0.743672 | − | 0.429360i | 0.0797306 | − | 0.996816i | \(-0.474594\pi\) |
−0.823403 | + | 0.567457i | \(0.807927\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.3571 | − | 10.0211i | −0.708012 | − | 0.408771i | 0.102312 | − | 0.994752i | \(-0.467376\pi\) |
−0.810325 | + | 0.585981i | \(0.800709\pi\) | |||||||
\(602\) | 29.2554 | − | 2.37451i | 1.19236 | − | 0.0967776i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −43.2544 | − | 18.3567i | −1.76000 | − | 0.746925i | ||||
\(605\) | − | 28.6710i | − | 1.16564i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.5971 | 0.754833 | 0.377417 | − | 0.926044i | \(-0.376812\pi\) | ||||
0.377417 | + | 0.926044i | \(0.376812\pi\) | |||||||
\(608\) | 23.8997 | − | 26.0914i | 0.969260 | − | 1.05815i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.36769 | + | 2.67599i | 0.217331 | + | 0.108348i | ||||
\(611\) | −12.8515 | − | 7.41984i | −0.519918 | − | 0.300175i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.7357 | + | 28.9871i | 0.675949 | + | 1.17078i | 0.976191 | + | 0.216915i | \(0.0695993\pi\) |
−0.300242 | + | 0.953863i | \(0.597067\pi\) | |||||||
\(614\) | −5.89908 | + | 3.90483i | −0.238068 | + | 0.157586i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −36.8791 | + | 7.59996i | −1.48590 | + | 0.306211i | ||||
\(617\) | 12.3643 | + | 21.4156i | 0.497769 | + | 0.862161i | 0.999997 | − | 0.00257408i | \(-0.000819356\pi\) |
−0.502228 | + | 0.864735i | \(0.667486\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 42.6300 | 1.71345 | 0.856723 | − | 0.515777i | \(-0.172497\pi\) | ||||
0.856723 | + | 0.515777i | \(0.172497\pi\) | |||||||
\(620\) | −3.56671 | + | 2.68811i | −0.143243 | + | 0.107957i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.76173 | + | 28.7870i | 0.0706391 | + | 1.15425i | ||||
\(623\) | −13.7508 | − | 7.57889i | −0.550913 | − | 0.303642i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0670 | −0.762681 | ||||||||
\(626\) | 13.2955 | − | 26.6691i | 0.531396 | − | 1.06591i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −26.1842 | + | 19.7342i | −1.04486 | + | 0.787479i | ||||
\(629\) | 2.08574i | 0.0831639i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 43.8344i | − | 1.74502i | −0.488596 | − | 0.872510i | \(-0.662491\pi\) | ||
0.488596 | − | 0.872510i | \(-0.337509\pi\) | |||||||
\(632\) | 7.27417 | + | 8.51509i | 0.289351 | + | 0.338712i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −15.2844 | − | 7.61981i | −0.607019 | − | 0.302621i | ||||
\(635\) | 4.43749 | 0.176097 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.5175 | − | 14.2220i | 0.892177 | − | 0.563495i | ||||
\(638\) | 17.6103 | − | 1.07773i | 0.697197 | − | 0.0426677i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 18.4467 | + | 13.1509i | 0.729171 | + | 0.519834i | ||||
\(641\) | −26.2084 | −1.03517 | −0.517584 | − | 0.855632i | \(-0.673168\pi\) | ||||
−0.517584 | + | 0.855632i | \(0.673168\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.8988 | − | 43.1259i | −0.981911 | − | 1.70072i | −0.654930 | − | 0.755690i | \(-0.727302\pi\) |
−0.326981 | − | 0.945031i | \(-0.606031\pi\) | |||||||
\(644\) | −30.8212 | − | 12.3636i | −1.21452 | − | 0.487194i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.10675 | − | 13.7577i | −0.358300 | − | 0.541290i | ||||
\(647\) | 7.44967 | + | 12.9032i | 0.292877 | + | 0.507277i | 0.974489 | − | 0.224436i | \(-0.0720541\pi\) |
−0.681612 | + | 0.731714i | \(0.738721\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −37.9376 | − | 21.9033i | −1.48918 | − | 0.859778i | ||||
\(650\) | −2.37763 | + | 4.76922i | −0.0932583 | + | 0.187064i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.07594 | + | 6.08657i | −0.316278 | + | 0.238369i | ||||
\(653\) | −43.2148 | −1.69113 | −0.845563 | − | 0.533876i | \(-0.820735\pi\) | ||||
−0.845563 | + | 0.533876i | \(0.820735\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 31.8436i | − | 1.24423i | ||||||
\(656\) | −28.3782 | − | 8.13287i | −1.10798 | − | 0.317535i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −13.1876 | − | 6.25057i | −0.514105 | − | 0.243673i | ||||
\(659\) | 28.1704 | + | 16.2642i | 1.09736 | + | 0.633562i | 0.935527 | − | 0.353256i | \(-0.114925\pi\) |
0.161835 | + | 0.986818i | \(0.448259\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.1675 | + | 15.1078i | 1.01780 | + | 0.587627i | 0.913466 | − | 0.406916i | \(-0.133396\pi\) |
0.104333 | + | 0.994542i | \(0.466729\pi\) | |||||||
\(662\) | −0.804223 | + | 1.61317i | −0.0312570 | + | 0.0626976i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 28.5144 | + | 10.0940i | 1.10657 | + | 0.391723i | ||||
\(665\) | −29.0213 | − | 15.9954i | −1.12540 | − | 0.620275i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.4755 | + | 7.78009i | 0.521774 | + | 0.301246i | ||||
\(668\) | 17.6951 | − | 2.17399i | 0.684646 | − | 0.0841142i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.07967 | − | 33.9821i | −0.0803445 | − | 1.31284i | ||||
\(671\) | 5.32858 | + | 9.22937i | 0.205708 | + | 0.356296i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.60245 | + | 13.1678i | −0.293053 | + | 0.507582i | −0.974530 | − | 0.224257i | \(-0.928005\pi\) |
0.681477 | + | 0.731839i | \(0.261338\pi\) | |||||||
\(674\) | 15.5052 | + | 7.72991i | 0.597238 | + | 0.297745i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.77622 | − | 2.35677i | −0.0683162 | − | 0.0906451i | ||||
\(677\) | −35.2936 | + | 20.3768i | −1.35644 | + | 0.783143i | −0.989143 | − | 0.146959i | \(-0.953052\pi\) |
−0.367301 | + | 0.930102i | \(0.619718\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 37.5602 | + | 20.7017i | 1.44143 | + | 0.794459i | ||||
\(680\) | 8.03186 | − | 6.86136i | 0.308008 | − | 0.263121i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.92108 | + | 0.484761i | −0.303314 | + | 0.0185625i | ||||
\(683\) | 1.67736 | − | 0.968424i | 0.0641824 | − | 0.0370557i | −0.467565 | − | 0.883958i | \(-0.654869\pi\) |
0.531748 | + | 0.846903i | \(0.321535\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.61373i | 0.329114i | ||||||||
\(686\) | 20.9405 | − | 15.7320i | 0.799512 | − | 0.600651i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.59548 | − | 30.4450i | −0.289575 | − | 1.16071i | ||||
\(689\) | −18.4747 | − | 10.6664i | −0.703831 | − | 0.406357i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.02376 | + | 13.8976i | 0.305238 | + | 0.528688i | 0.977314 | − | 0.211794i | \(-0.0679306\pi\) |
−0.672076 | + | 0.740482i | \(0.734597\pi\) | |||||||
\(692\) | 0.740696 | + | 6.02888i | 0.0281570 | + | 0.229184i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.1901 | + | 0.746021i | −0.462730 | + | 0.0283186i | ||||
\(695\) | 7.62070 | − | 4.39981i | 0.289069 | − | 0.166894i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.88257 | + | 11.9210i | −0.260696 | + | 0.451538i | ||||
\(698\) | 11.2691 | − | 0.689657i | 0.426542 | − | 0.0261039i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.95115 | + | 4.86401i | −0.0737466 | + | 0.183842i | ||||
\(701\) | 15.9608 | 0.602830 | 0.301415 | − | 0.953493i | \(-0.402541\pi\) | ||||
0.301415 | + | 0.953493i | \(0.402541\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.49731 | − | 6.05751i | −0.131903 | − | 0.228463i | ||||
\(704\) | 14.4339 | + | 37.5771i | 0.543996 | + | 1.41624i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.7715 | − | 22.3156i | −0.555934 | − | 0.839859i | ||||
\(707\) | 0.199381 | + | 10.0358i | 0.00749849 | + | 0.377433i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.54644 | + | 2.67851i | 0.0580776 | + | 0.100593i | 0.893602 | − | 0.448859i | \(-0.148170\pi\) |
−0.835525 | + | 0.549453i | \(0.814836\pi\) | |||||||
\(710\) | 9.08807 | − | 6.01574i | 0.341069 | − | 0.225767i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.60128 | + | 15.8230i | −0.209917 | + | 0.592991i | ||||
\(713\) | −6.06127 | − | 3.49947i | −0.226996 | − | 0.131056i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 33.1983 | − | 19.1671i | 1.24155 | − | 0.716808i | ||||
\(716\) | −1.13152 | − | 9.21002i | −0.0422871 | − | 0.344195i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −37.1580 | + | 2.27403i | −1.38672 | + | 0.0848660i | ||||
\(719\) | 12.5658 | − | 21.7645i | 0.468624 | − | 0.811680i | −0.530733 | − | 0.847539i | \(-0.678083\pi\) |
0.999357 | + | 0.0358588i | \(0.0114167\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.5139 | + | 0.487019i | −0.912945 | + | 0.0181375i | ||||
\(722\) | 25.4695 | + | 12.6975i | 0.947876 | + | 0.472551i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.02697 | − | 2.98217i | −0.261155 | − | 0.110831i | ||||
\(725\) | 1.22781 | − | 2.12663i | 0.0455996 | − | 0.0789809i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.4226 | + | 45.7653i | −0.979960 | + | 1.69734i | −0.317474 | + | 0.948267i | \(0.602835\pi\) |
−0.662486 | + | 0.749074i | \(0.730499\pi\) | |||||||
\(728\) | −18.9195 | − | 21.2764i | −0.701204 | − | 0.788555i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.46131 | + | 0.728516i | 0.0540855 | + | 0.0269636i | ||||
\(731\) | −14.6313 | −0.541159 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.85524i | 0.142397i | 0.997462 | + | 0.0711983i | \(0.0226823\pi\) | ||||
−0.997462 | + | 0.0711983i | \(0.977318\pi\) | |||||||
\(734\) | 1.83955 | − | 1.21767i | 0.0678991 | − | 0.0449450i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.67763 | + | 34.6612i | −0.283001 | + | 1.27763i | ||||
\(737\) | 30.2471 | − | 52.3896i | 1.11417 | − | 1.92980i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.15539 | + | 1.82177i | −0.116073 | + | 0.0670148i | −0.556912 | − | 0.830571i | \(-0.688014\pi\) |
0.440840 | + | 0.897586i | \(0.354681\pi\) | |||||||
\(740\) | 3.57643 | − | 2.69544i | 0.131472 | − | 0.0990862i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −18.9578 | − | 8.98551i | −0.695961 | − | 0.329868i | ||||
\(743\) | 10.9054 | − | 6.29626i | 0.400082 | − | 0.230987i | −0.286437 | − | 0.958099i | \(-0.592471\pi\) |
0.686519 | + | 0.727112i | \(0.259138\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 9.18048i | − | 0.336347i | ||||||
\(746\) | −42.4510 | + | 28.0999i | −1.55424 | + | 1.02881i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 18.6299 | − | 2.28883i | 0.681177 | − | 0.0836880i | ||||
\(749\) | −18.1730 | − | 10.0163i | −0.664028 | − | 0.365987i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.3856i | 0.488447i | 0.969719 | + | 0.244223i | \(0.0785330\pi\) | ||||
−0.969719 | + | 0.244223i | \(0.921467\pi\) | |||||||
\(752\) | −4.29819 | + | 14.9978i | −0.156739 | + | 0.546912i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.36362 | + | 11.1243i | 0.268167 | + | 0.405125i | ||||
\(755\) | 47.0448 | 1.71213 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.72257 | 0.0626080 | 0.0313040 | − | 0.999510i | \(-0.490034\pi\) | ||||
0.0313040 | + | 0.999510i | \(0.490034\pi\) | |||||||
\(758\) | −15.2033 | − | 22.9679i | −0.552208 | − | 0.834230i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −11.8216 | + | 33.3947i | −0.428815 | + | 1.21135i | ||||
\(761\) | − | 20.7093i | − | 0.750710i | −0.926881 | − | 0.375355i | \(-0.877521\pi\) | ||
0.926881 | − | 0.375355i | \(-0.122479\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.6354 | − | 37.4667i | −0.819456 | − | 1.35639i | ||||
\(764\) | 0.920413 | + | 7.49168i | 0.0332994 | + | 0.271040i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.116926 | + | 0.0773977i | −0.00422471 | + | 0.00279649i | ||||
\(767\) | − | 33.1237i | − | 1.19603i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.19700 | + | 3.57784i | −0.223470 | + | 0.129020i | −0.607556 | − | 0.794277i | \(-0.707850\pi\) |
0.384086 | + | 0.923297i | \(0.374517\pi\) | |||||||
\(770\) | 31.0165 | − | 21.4290i | 1.11776 | − | 0.772248i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.6110 | − | 19.3865i | −0.525860 | − | 0.697735i | ||||
\(773\) | −28.6131 | + | 16.5198i | −1.02914 | + | 0.594176i | −0.916739 | − | 0.399487i | \(-0.869188\pi\) |
−0.112404 | + | 0.993663i | \(0.535855\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.552266 | + | 0.956553i | −0.0198380 | + | 0.0343604i | ||||
\(776\) | 15.2999 | − | 43.2204i | 0.549233 | − | 1.55152i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −31.3286 | + | 20.7376i | −1.12319 | + | 0.743479i | ||||
\(779\) | − | 46.1620i | − | 1.65392i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.3655 | 0.692952 | ||||||||
\(782\) | 14.8149 | + | 7.38578i | 0.529781 | + | 0.264115i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −20.2379 | − | 19.3502i | −0.722781 | − | 0.691077i | ||||
\(785\) | 16.4136 | − | 28.4292i | 0.585827 | − | 1.01468i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.7413 | + | 20.3366i | −0.418533 | + | 0.724920i | −0.995792 | − | 0.0916406i | \(-0.970789\pi\) |
0.577259 | + | 0.816561i | \(0.304122\pi\) | |||||||
\(788\) | 4.96682 | − | 11.7034i | 0.176936 | − | 0.416918i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −10.0347 | − | 5.00265i | −0.357017 | − | 0.177986i | ||||
\(791\) | 26.5632 | + | 43.9680i | 0.944477 | + | 1.56332i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.02913 | + | 6.97866i | −0.143079 | + | 0.247820i | ||||
\(794\) | −38.2067 | + | 2.33821i | −1.35591 | + | 0.0829799i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.00029 | + | 0.491467i | −0.141786 | + | 0.0174196i | ||||
\(797\) | −15.6061 | + | 9.01016i | −0.552795 | + | 0.319156i | −0.750248 | − | 0.661156i | \(-0.770066\pi\) |
0.197454 | + | 0.980312i | \(0.436733\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.30018 | + | 3.63741i | 0.222884 | + | 0.128682i | ||||
\(800\) | 5.47003 | + | 1.21164i | 0.193395 | + | 0.0428379i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −37.7342 | + | 24.9777i | −1.33244 | + | 0.881993i | ||||
\(803\) | 1.45066 | + | 2.51262i | 0.0511928 | + | 0.0886685i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 33.2417 | − | 0.660415i | 1.17162 | − | 0.0232766i | ||||
\(806\) | −3.31214 | − | 5.00371i | −0.116665 | − | 0.176248i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.5509 | − | 1.95668i | 0.371179 | − | 0.0688356i | ||||
\(809\) | −6.22093 | − | 10.7750i | −0.218716 | − | 0.378828i | 0.735699 | − | 0.677308i | \(-0.236854\pi\) |
−0.954416 | + | 0.298480i | \(0.903520\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.5370 | 0.405118 | 0.202559 | − | 0.979270i | \(-0.435074\pi\) | ||||
0.202559 | + | 0.979270i | \(0.435074\pi\) | |||||||
\(812\) | 8.10295 | + | 10.3184i | 0.284358 | + | 0.362104i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.94265 | − | 0.486082i | 0.278390 | − | 0.0170372i | ||||
\(815\) | 5.06242 | − | 8.76836i | 0.177329 | − | 0.307142i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 42.4931 | − | 24.5334i | 1.48664 | − | 0.858315i | ||||
\(818\) | −30.8713 | + | 1.88929i | −1.07939 | + | 0.0660574i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 29.3354 | − | 3.60408i | 1.02444 | − | 0.125860i | ||||
\(821\) | 15.3484 | + | 26.5841i | 0.535661 | + | 0.927792i | 0.999131 | + | 0.0416797i | \(0.0132709\pi\) |
−0.463470 | + | 0.886113i | \(0.653396\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.4029 | + | 21.5946i | 1.30378 | + | 0.752740i | 0.981051 | − | 0.193749i | \(-0.0620649\pi\) |
0.322734 | + | 0.946490i | \(0.395398\pi\) | |||||||
\(824\) | 4.77948 | + | 25.7722i | 0.166501 | + | 0.897816i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.63528 | − | 32.4683i | −0.0916930 | − | 1.12972i | ||||
\(827\) | − | 24.5381i | − | 0.853273i | −0.904423 | − | 0.426637i | \(-0.859698\pi\) | ||
0.904423 | − | 0.426637i | \(-0.140302\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44.2845 | + | 25.5676i | −1.53806 | + | 0.888001i | −0.539110 | + | 0.842235i | \(0.681239\pi\) |
−0.998952 | + | 0.0457657i | \(0.985427\pi\) | |||||||
\(830\) | −30.2280 | + | 1.84992i | −1.04923 | + | 0.0642117i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −19.1498 | + | 23.6585i | −0.663899 | + | 0.820210i | ||||
\(833\) | −11.0387 | + | 6.97200i | −0.382469 | + | 0.241565i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.4582 | + | 8.92477i | −0.534952 | + | 0.308854i | ||||
\(836\) | −50.2681 | + | 37.8854i | −1.73856 | + | 1.31029i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 24.3714 | + | 12.1500i | 0.841897 | + | 0.419717i | ||||
\(839\) | 14.4267 | − | 24.9878i | 0.498066 | − | 0.862675i | −0.501932 | − | 0.864907i | \(-0.667377\pi\) |
0.999998 | + | 0.00223194i | \(0.000710448\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.4263 | + | 19.7909i | 0.394011 | + | 0.682447i | ||||
\(842\) | 2.91755 | + | 47.6733i | 0.100546 | + | 1.64293i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.45696 | + | 36.2773i | 0.153415 | + | 1.24872i | ||||
\(845\) | 2.55884 | + | 1.47735i | 0.0880268 | + | 0.0508223i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.8754 | − | 0.752472i | 1.30141 | − | 0.0258552i | ||||
\(848\) | −6.17886 | + | 21.5600i | −0.212183 | + | 0.740374i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.16558 | − | 2.33800i | 0.0399791 | − | 0.0801929i | ||||
\(851\) | 6.07778 | + | 3.50901i | 0.208344 | + | 0.120287i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.27160 | − | 1.31151i | −0.0777781 | − | 0.0449052i | 0.460607 | − | 0.887604i | \(-0.347632\pi\) |
−0.538385 | + | 0.842699i | \(0.680965\pi\) | |||||||
\(854\) | −3.39419 | + | 7.16113i | −0.116147 | + | 0.245049i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.40266 | + | 20.9117i | −0.253018 | + | 0.714746i | ||||
\(857\) | − | 20.7061i | − | 0.707307i | −0.935376 | − | 0.353654i | \(-0.884939\pi\) | ||
0.935376 | − | 0.353654i | \(-0.115061\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −54.5095 | −1.85984 | −0.929920 | − | 0.367763i | \(-0.880124\pi\) | ||||
−0.929920 | + | 0.367763i | \(0.880124\pi\) | |||||||
\(860\) | 18.9083 | + | 25.0884i | 0.644768 | + | 0.855507i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.87816 | + | 3.76734i | −0.0639703 | + | 0.128316i | ||||
\(863\) | −27.4054 | − | 15.8225i | −0.932891 | − | 0.538605i | −0.0451662 | − | 0.998979i | \(-0.514382\pi\) |
−0.887725 | + | 0.460375i | \(0.847715\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.04074 | − | 5.26672i | −0.103388 | − | 0.179074i | ||||
\(866\) | 19.9770 | + | 30.1795i | 0.678845 | + | 1.02554i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.64469 | − | 4.64119i | −0.123709 | − | 0.157532i | ||||
\(869\) | −9.96155 | − | 17.2539i | −0.337922 | − | 0.585299i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 45.7419 | 1.54991 | ||||||||
\(872\) | −35.5805 | + | 30.3953i | −1.20491 | + | 1.02931i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −55.4106 | + | 3.39107i | −1.87429 | + | 0.114705i | ||||
\(875\) | −0.630381 | − | 31.7300i | −0.0213108 | − | 1.07267i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.91019 | 0.267108 | 0.133554 | − | 0.991042i | \(-0.457361\pi\) | ||||
0.133554 | + | 0.991042i | \(0.457361\pi\) | |||||||
\(878\) | 36.8697 | + | 18.3809i | 1.24429 | + | 0.620326i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −28.0004 | − | 28.9869i | −0.943893 | − | 0.977147i | ||||
\(881\) | 22.7935i | 0.767932i | 0.923347 | + | 0.383966i | \(0.125442\pi\) | ||||
−0.923347 | + | 0.383966i | \(0.874558\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 13.4192i | − | 0.451591i | −0.974175 | − | 0.225795i | \(-0.927502\pi\) | ||
0.974175 | − | 0.225795i | \(-0.0724981\pi\) | |||||||
\(884\) | 8.54217 | + | 11.3341i | 0.287304 | + | 0.381208i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.0230 | − | 32.1400i | 0.538303 | − | 1.07977i | ||||
\(887\) | 58.3174 | 1.95811 | 0.979053 | − | 0.203605i | \(-0.0652659\pi\) | ||||
0.979053 | + | 0.203605i | \(0.0652659\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.116462 | + | 5.86207i | 0.00390601 | + | 0.196608i | ||||
\(890\) | −1.02654 | − | 16.7739i | −0.0344098 | − | 0.562261i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 19.8204 | + | 26.2986i | 0.663636 | + | 0.880542i | ||||
\(893\) | −24.3964 | −0.816395 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.64519 | + | 8.04571i | 0.155272 | + | 0.268938i | ||||
\(896\) | −16.8886 | + | 24.7139i | −0.564209 | + | 0.825632i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 36.2662 | − | 24.0060i | 1.21022 | − | 0.801089i | ||||
\(899\) | 1.38254 | + | 2.39463i | 0.0461103 | + | 0.0798654i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.05682 | + | 5.22896i | 0.301727 | + | 0.174202i | ||||
\(902\) | 46.9999 | + | 23.4311i | 1.56492 | + | 0.780172i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 41.7545 | − | 35.6696i | 1.38874 | − | 1.18635i | ||||
\(905\) | 7.64273 | 0.254053 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 2.07741i | − | 0.0689794i | −0.999405 | − | 0.0344897i | \(-0.989019\pi\) | ||
0.999405 | − | 0.0344897i | \(-0.0109806\pi\) | |||||||
\(908\) | −0.344895 | + | 0.812686i | −0.0114457 | + | 0.0269699i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 25.7588 | + | 12.2090i | 0.853896 | + | 0.404725i | ||||
\(911\) | −39.6927 | − | 22.9166i | −1.31508 | − | 0.759261i | −0.332147 | − | 0.943228i | \(-0.607773\pi\) |
−0.982933 | + | 0.183966i | \(0.941106\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −46.6020 | − | 26.9057i | −1.54230 | − | 0.890449i | ||||
\(914\) | −13.9046 | − | 6.93193i | −0.459922 | − | 0.229288i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.89494 | − | 4.19931i | −0.326938 | − | 0.138749i | ||||
\(917\) | 42.0664 | − | 0.835735i | 1.38915 | − | 0.0275984i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.35149 | + | 1.93498i | 0.110555 | + | 0.0638292i | 0.554258 | − | 0.832345i | \(-0.313002\pi\) |
−0.443703 | + | 0.896174i | \(0.646335\pi\) | |||||||
\(920\) | −6.48115 | − | 34.9480i | −0.213677 | − | 1.15220i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 23.4509 | − | 1.43517i | 0.772314 | − | 0.0472648i | ||||
\(923\) | 7.32148 | + | 12.6812i | 0.240989 | + | 0.417406i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.553771 | − | 0.959159i | 0.0182079 | − | 0.0315369i | ||||
\(926\) | 5.04463 | − | 10.1189i | 0.165777 | − | 0.332527i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.47366 | − | 10.3424i | 0.310988 | − | 0.339507i | ||||
\(929\) | −6.96346 | + | 4.02036i | −0.228464 | + | 0.131904i | −0.609863 | − | 0.792507i | \(-0.708776\pi\) |
0.381399 | + | 0.924410i | \(0.375442\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.3688 | − | 38.7578i | 0.667560 | − | 1.27024i | ||||
\(932\) | 8.14208 | + | 10.8033i | 0.266703 | + | 0.353873i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.18799 | + | 35.7521i | 0.0715932 | + | 1.16985i | ||||
\(935\) | −16.2747 | + | 9.39623i | −0.532241 | + | 0.307290i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 51.2010i | − | 1.67267i | −0.548222 | − | 0.836333i | \(-0.684695\pi\) | ||
0.548222 | − | 0.836333i | \(-0.315305\pi\) | |||||||
\(938\) | 44.8368 | − | 3.63916i | 1.46397 | − | 0.118823i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.90475 | − | 15.5036i | −0.0621259 | − | 0.505673i | ||||
\(941\) | 48.6046 | + | 28.0619i | 1.58446 | + | 0.914790i | 0.994196 | + | 0.107582i | \(0.0343108\pi\) |
0.590267 | + | 0.807208i | \(0.299023\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.1582 | + | 40.1112i | 0.754134 | + | 1.30620i | ||||
\(944\) | −33.7885 | + | 8.42962i | −1.09972 | + | 0.274361i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.40983 | + | 55.7172i | 0.110863 | + | 1.81152i | ||||
\(947\) | 7.57213 | − | 4.37177i | 0.246061 | − | 0.142063i | −0.371898 | − | 0.928274i | \(-0.621293\pi\) |
0.617959 | + | 0.786210i | \(0.287960\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.09690 | + | 1.89988i | −0.0356068 | + | 0.0616728i | ||||
\(950\) | 0.535158 | + | 8.74456i | 0.0173628 | + | 0.283711i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.27487 | + | 10.4303i | 0.300600 | + | 0.338047i | ||||
\(953\) | 0.861914 | 0.0279201 | 0.0139601 | − | 0.999903i | \(-0.495556\pi\) | ||||
0.0139601 | + | 0.999903i | \(0.495556\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.77853 | − | 6.54460i | −0.122270 | − | 0.211778i | ||||
\(956\) | 0.0477387 | + | 0.388568i | 0.00154398 | + | 0.0125672i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.93839 | + | 3.26890i | −0.159552 | + | 0.105613i | ||||
\(959\) | −11.3790 | + | 0.226067i | −0.367447 | + | 0.00730010i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.8781 | + | 25.7697i | 0.479940 | + | 0.831280i | ||||
\(962\) | 3.32117 | + | 5.01734i | 0.107079 | + | 0.161766i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 23.6622 | + | 10.0420i | 0.762107 | + | 0.323430i | ||||
\(965\) | 21.0487 | + | 12.1525i | 0.677581 | + | 0.391201i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.3142 | + | 19.8113i | −1.10347 | + | 0.637090i | −0.937131 | − | 0.348979i | \(-0.886529\pi\) |
−0.166341 | + | 0.986068i | \(0.553195\pi\) | |||||||
\(968\) | −7.38458 | − | 39.8195i | −0.237349 | − | 1.27985i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.80400 | + | 45.8178i | 0.0900309 | + | 1.47112i | ||||
\(971\) | −5.76791 | + | 9.99031i | −0.185101 | + | 0.320604i | −0.943611 | − | 0.331058i | \(-0.892595\pi\) |
0.758510 | + | 0.651662i | \(0.225928\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.01230 | + | 9.95171i | 0.192745 | + | 0.319037i | ||||
\(974\) | 21.7147 | − | 43.5569i | 0.695784 | − | 1.39565i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.14410 | + | 2.33401i | 0.260686 | + | 0.0747098i | ||||
\(977\) | −2.46473 | + | 4.26903i | −0.0788536 | + | 0.136578i | −0.902756 | − | 0.430154i | \(-0.858459\pi\) |
0.823902 | + | 0.566732i | \(0.191793\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.9303 | − | 25.8600i | 0.477174 | − | 0.826489i | ||||
\(980\) | 26.2204 | + | 9.91810i | 0.837581 | + | 0.316822i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 8.88207 | − | 17.8163i | 0.283438 | − | 0.568541i | ||||
\(983\) | −6.53487 | −0.208430 | −0.104215 | − | 0.994555i | \(-0.533233\pi\) | ||||
−0.104215 | + | 0.994555i | \(0.533233\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.7290i | 0.405579i | ||||||||
\(986\) | −3.60985 | − | 5.45346i | −0.114961 | − | 0.173673i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −43.8134 | − | 18.5939i | −1.39389 | − | 0.591552i | ||||
\(989\) | −24.6155 | + | 42.6352i | −0.782726 | + | 1.35572i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.59915 | + | 5.54207i | −0.304927 | + | 0.176050i | −0.644654 | − | 0.764474i | \(-0.722999\pi\) |
0.339727 | + | 0.940524i | \(0.389665\pi\) | |||||||
\(992\) | −4.26124 | + | 4.65201i | −0.135294 | + | 0.147702i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.18550 | + | 11.8478i | 0.259628 | + | 0.375788i | ||||
\(995\) | 3.49458 | − | 2.01760i | 0.110786 | − | 0.0639621i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 12.6388i | − | 0.400275i | −0.979768 | − | 0.200138i | \(-0.935861\pi\) | ||
0.979768 | − | 0.200138i | \(-0.0641389\pi\) | |||||||
\(998\) | −12.2467 | − | 18.5014i | −0.387664 | − | 0.585650i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 756.2.n.b.19.8 | 84 | ||
3.2 | odd | 2 | 252.2.n.b.187.35 | yes | 84 | ||
4.3 | odd | 2 | inner | 756.2.n.b.19.36 | 84 | ||
7.3 | odd | 6 | 756.2.bj.b.451.21 | 84 | |||
9.4 | even | 3 | 756.2.bj.b.523.21 | 84 | |||
9.5 | odd | 6 | 252.2.bj.b.103.22 | yes | 84 | ||
12.11 | even | 2 | 252.2.n.b.187.7 | yes | 84 | ||
21.17 | even | 6 | 252.2.bj.b.115.22 | yes | 84 | ||
28.3 | even | 6 | 756.2.bj.b.451.22 | 84 | |||
36.23 | even | 6 | 252.2.bj.b.103.21 | yes | 84 | ||
36.31 | odd | 6 | 756.2.bj.b.523.22 | 84 | |||
63.31 | odd | 6 | inner | 756.2.n.b.199.36 | 84 | ||
63.59 | even | 6 | 252.2.n.b.31.7 | ✓ | 84 | ||
84.59 | odd | 6 | 252.2.bj.b.115.21 | yes | 84 | ||
252.31 | even | 6 | inner | 756.2.n.b.199.8 | 84 | ||
252.59 | odd | 6 | 252.2.n.b.31.35 | yes | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.n.b.31.7 | ✓ | 84 | 63.59 | even | 6 | ||
252.2.n.b.31.35 | yes | 84 | 252.59 | odd | 6 | ||
252.2.n.b.187.7 | yes | 84 | 12.11 | even | 2 | ||
252.2.n.b.187.35 | yes | 84 | 3.2 | odd | 2 | ||
252.2.bj.b.103.21 | yes | 84 | 36.23 | even | 6 | ||
252.2.bj.b.103.22 | yes | 84 | 9.5 | odd | 6 | ||
252.2.bj.b.115.21 | yes | 84 | 84.59 | odd | 6 | ||
252.2.bj.b.115.22 | yes | 84 | 21.17 | even | 6 | ||
756.2.n.b.19.8 | 84 | 1.1 | even | 1 | trivial | ||
756.2.n.b.19.36 | 84 | 4.3 | odd | 2 | inner | ||
756.2.n.b.199.8 | 84 | 252.31 | even | 6 | inner | ||
756.2.n.b.199.36 | 84 | 63.31 | odd | 6 | inner | ||
756.2.bj.b.451.21 | 84 | 7.3 | odd | 6 | |||
756.2.bj.b.451.22 | 84 | 28.3 | even | 6 | |||
756.2.bj.b.523.21 | 84 | 9.4 | even | 3 | |||
756.2.bj.b.523.22 | 84 | 36.31 | odd | 6 |