Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(227,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([2, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.227");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.bb (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 362.7 | ||
Character | \(\chi\) | \(=\) | 637.362 |
Dual form | 637.2.bb.a.227.7 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.74384 | + | 1.74384i | 1.23308 | + | 1.23308i | 0.962775 | + | 0.270303i | \(0.0871238\pi\) |
0.270303 | + | 0.962775i | \(0.412876\pi\) | |||||||
\(3\) | 0.146239 | + | 0.0844309i | 0.0844309 | + | 0.0487462i | 0.541621 | − | 0.840623i | \(-0.317811\pi\) |
−0.457190 | + | 0.889369i | \(0.651144\pi\) | |||||||
\(4\) | 4.08193i | 2.04096i | ||||||||
\(5\) | 0.638637 | + | 2.38343i | 0.285607 | + | 1.06590i | 0.948394 | + | 0.317093i | \(0.102707\pi\) |
−0.662787 | + | 0.748808i | \(0.730627\pi\) | |||||||
\(6\) | 0.107782 | + | 0.402250i | 0.0440020 | + | 0.164218i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.63054 | + | 3.63054i | −1.28359 | + | 1.28359i | ||||
\(9\) | −1.48574 | − | 2.57338i | −0.495248 | − | 0.857794i | ||||
\(10\) | −3.04263 | + | 5.26998i | −0.962163 | + | 1.66652i | ||||
\(11\) | 1.17950 | + | 4.40195i | 0.355633 | + | 1.32724i | 0.879687 | + | 0.475554i | \(0.157752\pi\) |
−0.524054 | + | 0.851685i | \(0.675581\pi\) | |||||||
\(12\) | −0.344641 | + | 0.596935i | −0.0994892 | + | 0.172320i | ||||
\(13\) | −1.54835 | − | 3.25617i | −0.429434 | − | 0.903098i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.107841 | + | 0.402470i | −0.0278445 | + | 0.103917i | ||||
\(16\) | −4.49827 | −1.12457 | ||||||||
\(17\) | −0.112710 | −0.0273362 | −0.0136681 | − | 0.999907i | \(-0.504351\pi\) | ||||
−0.0136681 | + | 0.999907i | \(0.504351\pi\) | |||||||
\(18\) | 1.89666 | − | 7.07845i | 0.447048 | − | 1.66841i | ||||
\(19\) | 3.32660 | + | 0.891360i | 0.763175 | + | 0.204492i | 0.619354 | − | 0.785112i | \(-0.287395\pi\) |
0.143820 | + | 0.989604i | \(0.454061\pi\) | |||||||
\(20\) | −9.72897 | + | 2.60687i | −2.17546 | + | 0.582914i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.61943 | + | 9.73314i | −1.19807 | + | 2.07511i | ||||
\(23\) | 0.652493i | 0.136054i | 0.997683 | + | 0.0680271i | \(0.0216704\pi\) | ||||
−0.997683 | + | 0.0680271i | \(0.978330\pi\) | |||||||
\(24\) | −0.837454 | + | 0.224395i | −0.170945 | + | 0.0458045i | ||||
\(25\) | −0.942740 | + | 0.544291i | −0.188548 | + | 0.108858i | ||||
\(26\) | 2.97816 | − | 8.37828i | 0.584065 | − | 1.64312i | ||||
\(27\) | − | 1.00836i | − | 0.194058i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.82213 | − | 4.88807i | −0.524056 | − | 0.907691i | −0.999608 | − | 0.0280035i | \(-0.991085\pi\) |
0.475552 | − | 0.879688i | \(-0.342248\pi\) | |||||||
\(30\) | −0.889899 | + | 0.513783i | −0.162473 | + | 0.0938036i | ||||
\(31\) | −5.34937 | − | 1.43336i | −0.960774 | − | 0.257439i | −0.255846 | − | 0.966717i | \(-0.582354\pi\) |
−0.704928 | + | 0.709279i | \(0.749021\pi\) | |||||||
\(32\) | −0.583169 | − | 0.583169i | −0.103091 | − | 0.103091i | ||||
\(33\) | −0.199172 | + | 0.743322i | −0.0346715 | + | 0.129396i | ||||
\(34\) | −0.196548 | − | 0.196548i | −0.0337077 | − | 0.0337077i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 10.5044 | − | 6.06469i | 1.75073 | − | 1.01078i | ||||
\(37\) | 1.09952 | − | 1.09952i | 0.180760 | − | 0.180760i | −0.610927 | − | 0.791687i | \(-0.709203\pi\) |
0.791687 | + | 0.610927i | \(0.209203\pi\) | |||||||
\(38\) | 4.24666 | + | 7.35543i | 0.688899 | + | 1.19321i | ||||
\(39\) | 0.0484931 | − | 0.606906i | 0.00776511 | − | 0.0971827i | ||||
\(40\) | −10.9717 | − | 6.33453i | −1.73478 | − | 1.00158i | ||||
\(41\) | 10.6793 | + | 2.86152i | 1.66783 | + | 0.446894i | 0.964525 | − | 0.263993i | \(-0.0850396\pi\) |
0.703306 | + | 0.710887i | \(0.251706\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.08601 | + | 3.51376i | 0.928108 | + | 0.535843i | 0.886213 | − | 0.463279i | \(-0.153327\pi\) |
0.0418951 | + | 0.999122i | \(0.486660\pi\) | |||||||
\(44\) | −17.9684 | + | 4.81463i | −2.70885 | + | 0.725833i | ||||
\(45\) | 5.18462 | − | 5.18462i | 0.772877 | − | 0.772877i | ||||
\(46\) | −1.13784 | + | 1.13784i | −0.167766 | + | 0.167766i | ||||
\(47\) | 5.72325 | − | 1.53354i | 0.834822 | − | 0.223690i | 0.184006 | − | 0.982925i | \(-0.441093\pi\) |
0.650816 | + | 0.759235i | \(0.274427\pi\) | |||||||
\(48\) | −0.657821 | − | 0.379793i | −0.0949483 | − | 0.0548184i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.59314 | − | 0.694830i | −0.366725 | − | 0.0982637i | ||||
\(51\) | −0.0164826 | − | 0.00951622i | −0.00230802 | − | 0.00133254i | ||||
\(52\) | 13.2914 | − | 6.32024i | 1.84319 | − | 0.876459i | ||||
\(53\) | −2.41079 | − | 4.17561i | −0.331147 | − | 0.573564i | 0.651590 | − | 0.758571i | \(-0.274102\pi\) |
−0.982737 | + | 0.185008i | \(0.940769\pi\) | |||||||
\(54\) | 1.75841 | − | 1.75841i | 0.239289 | − | 0.239289i | ||||
\(55\) | −9.73846 | + | 5.62250i | −1.31313 | + | 0.758138i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.411219 | + | 0.411219i | 0.0544673 | + | 0.0544673i | ||||
\(58\) | 3.60266 | − | 13.4453i | 0.473052 | − | 1.76546i | ||||
\(59\) | −2.79191 | − | 2.79191i | −0.363476 | − | 0.363476i | 0.501615 | − | 0.865091i | \(-0.332739\pi\) |
−0.865091 | + | 0.501615i | \(0.832739\pi\) | |||||||
\(60\) | −1.64285 | − | 0.440201i | −0.212091 | − | 0.0568297i | ||||
\(61\) | −13.2845 | + | 7.66982i | −1.70091 | + | 0.982020i | −0.756067 | + | 0.654495i | \(0.772881\pi\) |
−0.944842 | + | 0.327526i | \(0.893785\pi\) | |||||||
\(62\) | −6.82887 | − | 11.8280i | −0.867268 | − | 1.50215i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.96264i | 0.870330i | ||||||||
\(65\) | 6.77201 | − | 5.76988i | 0.839964 | − | 0.715666i | ||||
\(66\) | −1.64355 | + | 0.948907i | −0.202308 | + | 0.116802i | ||||
\(67\) | −6.07826 | + | 1.62866i | −0.742577 | + | 0.198973i | −0.610223 | − | 0.792230i | \(-0.708920\pi\) |
−0.132354 | + | 0.991203i | \(0.542254\pi\) | |||||||
\(68\) | − | 0.460075i | − | 0.0557923i | ||||||
\(69\) | −0.0550906 | + | 0.0954197i | −0.00663213 | + | 0.0114872i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.56578 | − | 0.955449i | 0.423181 | − | 0.113391i | −0.0409427 | − | 0.999161i | \(-0.513036\pi\) |
0.464123 | + | 0.885771i | \(0.346369\pi\) | |||||||
\(72\) | 14.7368 | + | 3.94872i | 1.73675 | + | 0.465361i | ||||
\(73\) | 0.651157 | − | 2.43015i | 0.0762122 | − | 0.284428i | −0.917293 | − | 0.398212i | \(-0.869631\pi\) |
0.993505 | + | 0.113785i | \(0.0362974\pi\) | |||||||
\(74\) | 3.83477 | 0.445783 | ||||||||
\(75\) | −0.183820 | −0.0212257 | ||||||||
\(76\) | −3.63847 | + | 13.5789i | −0.417361 | + | 1.55761i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.14291 | − | 0.973780i | 0.129409 | − | 0.110259i | ||||
\(79\) | 6.11315 | − | 10.5883i | 0.687783 | − | 1.19128i | −0.284770 | − | 0.958596i | \(-0.591917\pi\) |
0.972553 | − | 0.232680i | \(-0.0747493\pi\) | |||||||
\(80\) | −2.87276 | − | 10.7213i | −0.321185 | − | 1.19868i | ||||
\(81\) | −4.37209 | + | 7.57269i | −0.485788 | + | 0.841410i | ||||
\(82\) | 13.6330 | + | 23.6130i | 1.50551 | + | 2.60762i | ||||
\(83\) | 3.34105 | − | 3.34105i | 0.366728 | − | 0.366728i | −0.499554 | − | 0.866283i | \(-0.666503\pi\) |
0.866283 | + | 0.499554i | \(0.166503\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0719809 | − | 0.268637i | −0.00780743 | − | 0.0291377i | ||||
\(86\) | 4.48558 | + | 16.7404i | 0.483693 | + | 1.80517i | ||||
\(87\) | − | 0.953099i | − | 0.102183i | ||||||
\(88\) | −20.2637 | − | 11.6992i | −2.16011 | − | 1.24714i | ||||
\(89\) | 6.14338 | + | 6.14338i | 0.651197 | + | 0.651197i | 0.953281 | − | 0.302084i | \(-0.0976824\pi\) |
−0.302084 | + | 0.953281i | \(0.597682\pi\) | |||||||
\(90\) | 18.0822 | 1.90604 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.66343 | −0.277682 | ||||||||
\(93\) | −0.661264 | − | 0.661264i | −0.0685699 | − | 0.0685699i | ||||
\(94\) | 12.6547 | + | 7.30617i | 1.30523 | + | 0.753574i | ||||
\(95\) | 8.49797i | 0.871873i | ||||||||
\(96\) | −0.0360444 | − | 0.134519i | −0.00367876 | − | 0.0137293i | ||||
\(97\) | −1.04426 | − | 3.89722i | −0.106028 | − | 0.395703i | 0.892431 | − | 0.451183i | \(-0.148998\pi\) |
−0.998460 | + | 0.0554799i | \(0.982331\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.57547 | − | 9.57547i | 0.962371 | − | 0.962371i | ||||
\(100\) | −2.22176 | − | 3.84820i | −0.222176 | − | 0.384820i | ||||
\(101\) | −2.26018 | + | 3.91475i | −0.224897 | + | 0.389532i | −0.956288 | − | 0.292425i | \(-0.905538\pi\) |
0.731392 | + | 0.681957i | \(0.238871\pi\) | |||||||
\(102\) | −0.0121482 | − | 0.0453376i | −0.00120285 | − | 0.00448910i | ||||
\(103\) | 6.72989 | − | 11.6565i | 0.663115 | − | 1.14855i | −0.316677 | − | 0.948533i | \(-0.602567\pi\) |
0.979793 | − | 0.200016i | \(-0.0640994\pi\) | |||||||
\(104\) | 17.4430 | + | 6.20031i | 1.71042 | + | 0.607990i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.07755 | − | 11.4856i | 0.298919 | − | 1.11558i | ||||
\(107\) | 8.25997 | 0.798521 | 0.399261 | − | 0.916837i | \(-0.369267\pi\) | ||||
0.399261 | + | 0.916837i | \(0.369267\pi\) | |||||||
\(108\) | 4.11603 | 0.396066 | ||||||||
\(109\) | 3.48535 | − | 13.0075i | 0.333836 | − | 1.24589i | −0.571289 | − | 0.820749i | \(-0.693557\pi\) |
0.905125 | − | 0.425145i | \(-0.139777\pi\) | |||||||
\(110\) | −26.7870 | − | 7.17755i | −2.55404 | − | 0.684353i | ||||
\(111\) | 0.253626 | − | 0.0679589i | 0.0240731 | − | 0.00645037i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.14314 | − | 1.97997i | 0.107537 | − | 0.186260i | −0.807235 | − | 0.590231i | \(-0.799037\pi\) |
0.914772 | + | 0.403970i | \(0.132370\pi\) | |||||||
\(114\) | 1.43420i | 0.134325i | ||||||||
\(115\) | −1.55517 | + | 0.416707i | −0.145020 | + | 0.0388581i | ||||
\(116\) | 19.9527 | − | 11.5197i | 1.85256 | − | 1.06958i | ||||
\(117\) | −6.07892 | + | 8.82231i | −0.561996 | + | 0.815623i | ||||
\(118\) | − | 9.73726i | − | 0.896388i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.06966 | − | 1.85270i | −0.0976461 | − | 0.169128i | ||||
\(121\) | −8.45969 | + | 4.88420i | −0.769063 | + | 0.444018i | ||||
\(122\) | −36.5409 | − | 9.79112i | −3.30826 | − | 0.886446i | ||||
\(123\) | 1.32013 | + | 1.32013i | 0.119032 | + | 0.119032i | ||||
\(124\) | 5.85086 | − | 21.8357i | 0.525423 | − | 1.96091i | ||||
\(125\) | 6.82460 | + | 6.82460i | 0.610411 | + | 0.610411i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.38857 | + | 2.53374i | −0.389422 | + | 0.224833i | −0.681910 | − | 0.731436i | \(-0.738850\pi\) |
0.292488 | + | 0.956269i | \(0.405517\pi\) | |||||||
\(128\) | −13.3080 | + | 13.3080i | −1.17628 | + | 1.17628i | ||||
\(129\) | 0.593340 | + | 1.02769i | 0.0522406 | + | 0.0904834i | ||||
\(130\) | 21.8710 | + | 1.74754i | 1.91821 | + | 0.153269i | ||||
\(131\) | 4.92213 | + | 2.84179i | 0.430048 | + | 0.248288i | 0.699367 | − | 0.714763i | \(-0.253465\pi\) |
−0.269319 | + | 0.963051i | \(0.586799\pi\) | |||||||
\(132\) | −3.03418 | − | 0.813007i | −0.264092 | − | 0.0707632i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −13.4396 | − | 7.75936i | −1.16100 | − | 0.670306i | ||||
\(135\) | 2.40334 | − | 0.643974i | 0.206847 | − | 0.0554244i | ||||
\(136\) | 0.409199 | − | 0.409199i | 0.0350885 | − | 0.0350885i | ||||
\(137\) | −6.04202 | + | 6.04202i | −0.516205 | + | 0.516205i | −0.916421 | − | 0.400216i | \(-0.868935\pi\) |
0.400216 | + | 0.916421i | \(0.368935\pi\) | |||||||
\(138\) | −0.262465 | + | 0.0703274i | −0.0223425 | + | 0.00598666i | ||||
\(139\) | −9.91348 | − | 5.72355i | −0.840850 | − | 0.485465i | 0.0167030 | − | 0.999860i | \(-0.494683\pi\) |
−0.857553 | + | 0.514395i | \(0.828016\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.966439 | + | 0.258957i | 0.0813888 | + | 0.0218081i | ||||
\(142\) | 7.88429 | + | 4.55200i | 0.661635 | + | 0.381995i | ||||
\(143\) | 12.5072 | − | 10.6564i | 1.04591 | − | 0.891133i | ||||
\(144\) | 6.68327 | + | 11.5758i | 0.556939 | + | 0.964647i | ||||
\(145\) | 9.84803 | − | 9.84803i | 0.817835 | − | 0.817835i | ||||
\(146\) | 5.37330 | − | 3.10227i | 0.444697 | − | 0.256746i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.48817 | + | 4.48817i | 0.368925 | + | 0.368925i | ||||
\(149\) | −1.97417 | + | 7.36771i | −0.161730 | + | 0.603586i | 0.836704 | + | 0.547655i | \(0.184479\pi\) |
−0.998435 | + | 0.0559311i | \(0.982187\pi\) | |||||||
\(150\) | −0.320552 | − | 0.320552i | −0.0261730 | − | 0.0261730i | ||||
\(151\) | 6.37363 | + | 1.70781i | 0.518679 | + | 0.138980i | 0.508656 | − | 0.860970i | \(-0.330143\pi\) |
0.0100235 | + | 0.999950i | \(0.496809\pi\) | |||||||
\(152\) | −15.3135 | + | 8.84123i | −1.24209 | + | 0.717119i | ||||
\(153\) | 0.167458 | + | 0.290046i | 0.0135382 | + | 0.0234489i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 13.6652i | − | 1.09762i | ||||||
\(156\) | 2.47734 | + | 0.197945i | 0.198346 | + | 0.0158483i | ||||
\(157\) | −8.20626 | + | 4.73788i | −0.654931 | + | 0.378124i | −0.790343 | − | 0.612665i | \(-0.790097\pi\) |
0.135412 | + | 0.990789i | \(0.456764\pi\) | |||||||
\(158\) | 29.1246 | − | 7.80390i | 2.31703 | − | 0.620845i | ||||
\(159\) | − | 0.814180i | − | 0.0645687i | ||||||
\(160\) | 1.01751 | − | 1.76238i | 0.0804411 | − | 0.139328i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −20.8297 | + | 5.58131i | −1.63654 | + | 0.438509i | ||||
\(163\) | −17.8485 | − | 4.78249i | −1.39800 | − | 0.374594i | −0.520376 | − | 0.853937i | \(-0.674208\pi\) |
−0.877627 | + | 0.479344i | \(0.840875\pi\) | |||||||
\(164\) | −11.6805 | + | 43.5922i | −0.912094 | + | 3.40398i | ||||
\(165\) | −1.89885 | −0.147825 | ||||||||
\(166\) | 11.6525 | 0.904409 | ||||||||
\(167\) | 4.24807 | − | 15.8540i | 0.328725 | − | 1.22682i | −0.581788 | − | 0.813341i | \(-0.697647\pi\) |
0.910513 | − | 0.413480i | \(-0.135687\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.20525 | + | 10.0833i | −0.631173 | + | 0.775642i | ||||
\(170\) | 0.342935 | − | 0.593981i | 0.0263019 | − | 0.0455563i | ||||
\(171\) | −2.64866 | − | 9.88495i | −0.202548 | − | 0.755921i | ||||
\(172\) | −14.3429 | + | 24.8426i | −1.09364 | + | 1.89423i | ||||
\(173\) | −9.11872 | − | 15.7941i | −0.693283 | − | 1.20080i | −0.970756 | − | 0.240068i | \(-0.922830\pi\) |
0.277473 | − | 0.960733i | \(-0.410503\pi\) | |||||||
\(174\) | 1.66205 | − | 1.66205i | 0.125999 | − | 0.125999i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.30571 | − | 19.8012i | −0.399933 | − | 1.49257i | ||||
\(177\) | −0.172561 | − | 0.644008i | −0.0129705 | − | 0.0484066i | ||||
\(178\) | 21.4261i | 1.60595i | ||||||||
\(179\) | −20.4226 | − | 11.7910i | −1.52645 | − | 0.881299i | −0.999507 | − | 0.0314008i | \(-0.990003\pi\) |
−0.526947 | − | 0.849898i | \(-0.676663\pi\) | |||||||
\(180\) | 21.1632 | + | 21.1632i | 1.57741 | + | 1.57741i | ||||
\(181\) | −4.65138 | −0.345735 | −0.172867 | − | 0.984945i | \(-0.555303\pi\) | ||||
−0.172867 | + | 0.984945i | \(0.555303\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.59028 | −0.191479 | ||||||||
\(184\) | −2.36890 | − | 2.36890i | −0.174638 | − | 0.174638i | ||||
\(185\) | 3.32282 | + | 1.91843i | 0.244299 | + | 0.141046i | ||||
\(186\) | − | 2.30627i | − | 0.169104i | ||||||
\(187\) | −0.132942 | − | 0.496145i | −0.00972165 | − | 0.0362817i | ||||
\(188\) | 6.25980 | + | 23.3619i | 0.456543 | + | 1.70384i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −14.8191 | + | 14.8191i | −1.07509 | + | 1.07509i | ||||
\(191\) | −3.84978 | − | 6.66801i | −0.278560 | − | 0.482480i | 0.692467 | − | 0.721450i | \(-0.256524\pi\) |
−0.971027 | + | 0.238969i | \(0.923190\pi\) | |||||||
\(192\) | −0.587862 | + | 1.01821i | −0.0424253 | + | 0.0734827i | ||||
\(193\) | 0.0645055 | + | 0.240738i | 0.00464321 | + | 0.0173287i | 0.968209 | − | 0.250144i | \(-0.0804781\pi\) |
−0.963565 | + | 0.267473i | \(0.913811\pi\) | |||||||
\(194\) | 4.97510 | − | 8.61713i | 0.357192 | − | 0.618674i | ||||
\(195\) | 1.47748 | − | 0.272013i | 0.105805 | − | 0.0194792i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.72653 | + | 6.44350i | −0.123010 | + | 0.459081i | −0.999761 | − | 0.0218645i | \(-0.993040\pi\) |
0.876751 | + | 0.480945i | \(0.159706\pi\) | |||||||
\(198\) | 33.3961 | 2.37336 | ||||||||
\(199\) | 5.38835 | 0.381970 | 0.190985 | − | 0.981593i | \(-0.438832\pi\) | ||||
0.190985 | + | 0.981593i | \(0.438832\pi\) | |||||||
\(200\) | 1.44658 | − | 5.39873i | 0.102289 | − | 0.381748i | ||||
\(201\) | −1.02639 | − | 0.275019i | −0.0723956 | − | 0.0193984i | ||||
\(202\) | −10.7681 | + | 2.88530i | −0.757639 | + | 0.203009i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.0388445 | − | 0.0672807i | 0.00271966 | − | 0.00471059i | ||||
\(205\) | 27.2809i | 1.90538i | ||||||||
\(206\) | 32.0628 | − | 8.59121i | 2.23392 | − | 0.598578i | ||||
\(207\) | 1.67912 | − | 0.969438i | 0.116707 | − | 0.0673806i | ||||
\(208\) | 6.96488 | + | 14.6471i | 0.482928 | + | 1.01560i | ||||
\(209\) | 15.6949i | 1.08564i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.44964 | − | 2.51085i | −0.0997974 | − | 0.172854i | 0.811803 | − | 0.583931i | \(-0.198486\pi\) |
−0.911601 | + | 0.411077i | \(0.865153\pi\) | |||||||
\(212\) | 17.0445 | − | 9.84066i | 1.17062 | − | 0.675859i | ||||
\(213\) | 0.602125 | + | 0.161339i | 0.0412569 | + | 0.0110548i | ||||
\(214\) | 14.4040 | + | 14.4040i | 0.984639 | + | 0.984639i | ||||
\(215\) | −4.48804 | + | 16.7496i | −0.306081 | + | 1.14231i | ||||
\(216\) | 3.66087 | + | 3.66087i | 0.249091 | + | 0.249091i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 28.7608 | − | 16.6051i | 1.94793 | − | 1.12464i | ||||
\(219\) | 0.300404 | − | 0.300404i | 0.0202994 | − | 0.0202994i | ||||
\(220\) | −22.9506 | − | 39.7517i | −1.54733 | − | 2.68006i | ||||
\(221\) | 0.174514 | + | 0.367003i | 0.0117391 | + | 0.0246873i | ||||
\(222\) | 0.560791 | + | 0.323773i | 0.0376379 | + | 0.0217302i | ||||
\(223\) | 18.1024 | + | 4.85053i | 1.21223 | + | 0.324816i | 0.807636 | − | 0.589681i | \(-0.200747\pi\) |
0.404593 | + | 0.914497i | \(0.367413\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.80134 | + | 1.61735i | 0.186756 | + | 0.107824i | ||||
\(226\) | 5.44619 | − | 1.45930i | 0.362275 | − | 0.0970714i | ||||
\(227\) | −4.51374 | + | 4.51374i | −0.299587 | + | 0.299587i | −0.840852 | − | 0.541265i | \(-0.817946\pi\) |
0.541265 | + | 0.840852i | \(0.317946\pi\) | |||||||
\(228\) | −1.67857 | + | 1.67857i | −0.111166 | + | 0.111166i | ||||
\(229\) | −16.7169 | + | 4.47928i | −1.10468 | + | 0.295999i | −0.764671 | − | 0.644421i | \(-0.777098\pi\) |
−0.340014 | + | 0.940420i | \(0.610432\pi\) | |||||||
\(230\) | −3.43863 | − | 1.98529i | −0.226737 | − | 0.130906i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 27.9921 | + | 7.50047i | 1.83777 | + | 0.492430i | ||||
\(233\) | 1.08707 | + | 0.627620i | 0.0712163 | + | 0.0411167i | 0.535185 | − | 0.844735i | \(-0.320242\pi\) |
−0.463969 | + | 0.885851i | \(0.653575\pi\) | |||||||
\(234\) | −25.9853 | + | 4.78403i | −1.69871 | + | 0.312742i | ||||
\(235\) | 7.31017 | + | 12.6616i | 0.476863 | + | 0.825950i | ||||
\(236\) | 11.3964 | − | 11.3964i | 0.741840 | − | 0.741840i | ||||
\(237\) | 1.78796 | − | 1.03228i | 0.116140 | − | 0.0670536i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.59429 | − | 8.59429i | −0.555918 | − | 0.555918i | 0.372225 | − | 0.928143i | \(-0.378595\pi\) |
−0.928143 | + | 0.372225i | \(0.878595\pi\) | |||||||
\(240\) | 0.485100 | − | 1.81042i | 0.0313131 | − | 0.116862i | ||||
\(241\) | 1.71820 | + | 1.71820i | 0.110679 | + | 0.110679i | 0.760277 | − | 0.649599i | \(-0.225063\pi\) |
−0.649599 | + | 0.760277i | \(0.725063\pi\) | |||||||
\(242\) | −23.2696 | − | 6.23506i | −1.49582 | − | 0.400805i | ||||
\(243\) | −3.89852 | + | 2.25081i | −0.250090 | + | 0.144390i | ||||
\(244\) | −31.3077 | − | 54.2264i | −2.00427 | − | 3.47149i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.60418i | 0.293552i | ||||||||
\(247\) | −2.24831 | − | 12.2121i | −0.143057 | − | 0.777037i | ||||
\(248\) | 24.6249 | − | 14.2172i | 1.56368 | − | 0.902794i | ||||
\(249\) | 0.770679 | − | 0.206503i | 0.0488398 | − | 0.0130866i | ||||
\(250\) | 23.8020i | 1.50537i | ||||||||
\(251\) | −7.94802 | + | 13.7664i | −0.501675 | + | 0.868926i | 0.498323 | + | 0.866991i | \(0.333949\pi\) |
−0.999998 | + | 0.00193499i | \(0.999384\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.87225 | + | 0.769616i | −0.180577 | + | 0.0483853i | ||||
\(254\) | −12.0714 | − | 3.23451i | −0.757425 | − | 0.202951i | ||||
\(255\) | 0.0121548 | − | 0.0453624i | 0.000761165 | − | 0.00284071i | ||||
\(256\) | −32.4888 | −2.03055 | ||||||||
\(257\) | −14.1941 | −0.885401 | −0.442701 | − | 0.896670i | \(-0.645980\pi\) | ||||
−0.442701 | + | 0.896670i | \(0.645980\pi\) | |||||||
\(258\) | −0.757443 | + | 2.82682i | −0.0471564 | + | 0.175990i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 23.5522 | + | 27.6428i | 1.46065 | + | 1.71434i | ||||
\(261\) | −8.38591 | + | 14.5248i | −0.519075 | + | 0.899064i | ||||
\(262\) | 3.62776 | + | 13.5390i | 0.224124 | + | 0.836442i | ||||
\(263\) | 9.46835 | − | 16.3997i | 0.583843 | − | 1.01125i | −0.411175 | − | 0.911556i | \(-0.634882\pi\) |
0.995019 | − | 0.0996901i | \(-0.0317851\pi\) | |||||||
\(264\) | −1.97555 | − | 3.42176i | −0.121587 | − | 0.210595i | ||||
\(265\) | 8.41264 | − | 8.41264i | 0.516784 | − | 0.516784i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.379708 | + | 1.41709i | 0.0232378 | + | 0.0867245i | ||||
\(268\) | −6.64809 | − | 24.8110i | −0.406096 | − | 1.51557i | ||||
\(269\) | − | 24.2202i | − | 1.47673i | −0.674400 | − | 0.738366i | \(-0.735598\pi\) | ||
0.674400 | − | 0.738366i | \(-0.264402\pi\) | |||||||
\(270\) | 5.31402 | + | 3.06805i | 0.323401 | + | 0.186716i | ||||
\(271\) | −11.1386 | − | 11.1386i | −0.676624 | − | 0.676624i | 0.282610 | − | 0.959235i | \(-0.408800\pi\) |
−0.959235 | + | 0.282610i | \(0.908800\pi\) | |||||||
\(272\) | 0.507001 | 0.0307414 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −21.0726 | −1.27304 | ||||||||
\(275\) | −3.50791 | − | 3.50791i | −0.211535 | − | 0.211535i | ||||
\(276\) | −0.389496 | − | 0.224876i | −0.0234449 | − | 0.0135359i | ||||
\(277\) | 0.746768i | 0.0448689i | 0.999748 | + | 0.0224345i | \(0.00714171\pi\) | ||||
−0.999748 | + | 0.0224345i | \(0.992858\pi\) | |||||||
\(278\) | −7.30655 | − | 27.2684i | −0.438218 | − | 1.63545i | ||||
\(279\) | 4.25920 | + | 15.8956i | 0.254992 | + | 0.951643i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.536856 | + | 0.536856i | −0.0320261 | + | 0.0320261i | −0.722939 | − | 0.690912i | \(-0.757209\pi\) |
0.690912 | + | 0.722939i | \(0.257209\pi\) | |||||||
\(282\) | 1.23373 | + | 2.13689i | 0.0734677 | + | 0.127250i | ||||
\(283\) | −9.63432 | + | 16.6871i | −0.572701 | + | 0.991947i | 0.423587 | + | 0.905856i | \(0.360771\pi\) |
−0.996287 | + | 0.0860911i | \(0.972562\pi\) | |||||||
\(284\) | 3.90007 | + | 14.5553i | 0.231427 | + | 0.863696i | ||||
\(285\) | −0.717491 | + | 1.24273i | −0.0425005 | + | 0.0736130i | ||||
\(286\) | 40.3935 | + | 3.22753i | 2.38852 | + | 0.190848i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.634278 | + | 2.36716i | −0.0373752 | + | 0.139486i | ||||
\(289\) | −16.9873 | −0.999253 | ||||||||
\(290\) | 34.3467 | 2.01691 | ||||||||
\(291\) | 0.176335 | − | 0.658092i | 0.0103370 | − | 0.0385780i | ||||
\(292\) | 9.91970 | + | 2.65798i | 0.580507 | + | 0.155546i | ||||
\(293\) | −14.0543 | + | 3.76584i | −0.821062 | + | 0.220003i | −0.644811 | − | 0.764342i | \(-0.723064\pi\) |
−0.176251 | + | 0.984345i | \(0.556397\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.87129 | − | 8.43733i | 0.283618 | − | 0.491240i | ||||
\(296\) | 7.98371i | 0.464044i | ||||||||
\(297\) | 4.43873 | − | 1.18936i | 0.257562 | − | 0.0690134i | ||||
\(298\) | −16.2907 | + | 9.40544i | −0.943695 | + | 0.544843i | ||||
\(299\) | 2.12463 | − | 1.01029i | 0.122870 | − | 0.0584263i | ||||
\(300\) | − | 0.750340i | − | 0.0433209i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.13643 | + | 14.0927i | 0.468199 | + | 0.810944i | ||||
\(303\) | −0.661052 | + | 0.381659i | −0.0379764 | + | 0.0219257i | ||||
\(304\) | −14.9639 | − | 4.00958i | −0.858241 | − | 0.229965i | ||||
\(305\) | −26.7645 | − | 26.7645i | −1.53253 | − | 1.53253i | ||||
\(306\) | −0.213773 | + | 0.797813i | −0.0122206 | + | 0.0456079i | ||||
\(307\) | −9.47209 | − | 9.47209i | −0.540601 | − | 0.540601i | 0.383104 | − | 0.923705i | \(-0.374855\pi\) |
−0.923705 | + | 0.383104i | \(0.874855\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.96834 | − | 1.13642i | 0.111975 | − | 0.0646487i | ||||
\(310\) | 23.8299 | − | 23.8299i | 1.35345 | − | 1.35345i | ||||
\(311\) | 4.14087 | + | 7.17220i | 0.234807 | + | 0.406698i | 0.959217 | − | 0.282672i | \(-0.0912207\pi\) |
−0.724409 | + | 0.689370i | \(0.757887\pi\) | |||||||
\(312\) | 2.02734 | + | 2.37945i | 0.114775 | + | 0.134710i | ||||
\(313\) | 4.98156 | + | 2.87611i | 0.281574 | + | 0.162567i | 0.634136 | − | 0.773222i | \(-0.281356\pi\) |
−0.352562 | + | 0.935789i | \(0.614689\pi\) | |||||||
\(314\) | −22.5725 | − | 6.04827i | −1.27384 | − | 0.341324i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 43.2206 | + | 24.9534i | 2.43135 | + | 1.40374i | ||||
\(317\) | 9.94515 | − | 2.66479i | 0.558575 | − | 0.149670i | 0.0315235 | − | 0.999503i | \(-0.489964\pi\) |
0.527052 | + | 0.849833i | \(0.323297\pi\) | |||||||
\(318\) | 1.41980 | − | 1.41980i | 0.0796182 | − | 0.0796182i | ||||
\(319\) | 18.1883 | − | 18.1883i | 1.01835 | − | 1.01835i | ||||
\(320\) | −16.5949 | + | 4.44660i | −0.927685 | + | 0.248573i | ||||
\(321\) | 1.20793 | + | 0.697397i | 0.0674199 | + | 0.0389249i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.374942 | − | 0.100465i | −0.0208623 | − | 0.00559004i | ||||
\(324\) | −30.9111 | − | 17.8466i | −1.71729 | − | 0.991475i | ||||
\(325\) | 3.23199 | + | 2.22697i | 0.179279 | + | 0.123530i | ||||
\(326\) | −22.7850 | − | 39.4647i | −1.26194 | − | 2.18575i | ||||
\(327\) | 1.60793 | − | 1.60793i | 0.0889186 | − | 0.0889186i | ||||
\(328\) | −49.1605 | + | 28.3829i | −2.71444 | + | 1.56718i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.31129 | − | 3.31129i | −0.182280 | − | 0.182280i | ||||
\(331\) | −4.48552 | + | 16.7402i | −0.246547 | + | 0.920125i | 0.726053 | + | 0.687639i | \(0.241353\pi\) |
−0.972600 | + | 0.232486i | \(0.925314\pi\) | |||||||
\(332\) | 13.6379 | + | 13.6379i | 0.748479 | + | 0.748479i | ||||
\(333\) | −4.46309 | − | 1.19588i | −0.244576 | − | 0.0655340i | ||||
\(334\) | 35.0547 | − | 20.2389i | 1.91811 | − | 1.10742i | ||||
\(335\) | −7.76360 | − | 13.4470i | −0.424171 | − | 0.734686i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.1069i | 0.659506i | 0.944067 | + | 0.329753i | \(0.106965\pi\) | ||||
−0.944067 | + | 0.329753i | \(0.893035\pi\) | |||||||
\(338\) | −31.8923 | + | 3.27510i | −1.73471 | + | 0.178142i | ||||
\(339\) | 0.334342 | − | 0.193032i | 0.0181589 | − | 0.0104841i | ||||
\(340\) | 1.09655 | − | 0.293821i | 0.0594690 | − | 0.0159347i | ||||
\(341\) | − | 25.2383i | − | 1.36673i | ||||||
\(342\) | 12.6189 | − | 21.8566i | 0.682351 | − | 1.18187i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −34.8523 | + | 9.33865i | −1.87911 | + | 0.503506i | ||||
\(345\) | −0.262609 | − | 0.0703659i | −0.0141384 | − | 0.00378837i | ||||
\(346\) | 11.6407 | − | 43.4438i | 0.625810 | − | 2.33555i | ||||
\(347\) | −2.86789 | −0.153957 | −0.0769783 | − | 0.997033i | \(-0.524527\pi\) | ||||
−0.0769783 | + | 0.997033i | \(0.524527\pi\) | |||||||
\(348\) | 3.89048 | 0.208552 | ||||||||
\(349\) | −3.12009 | + | 11.6443i | −0.167014 | + | 0.623306i | 0.830760 | + | 0.556630i | \(0.187906\pi\) |
−0.997775 | + | 0.0666760i | \(0.978761\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.28338 | + | 1.56128i | −0.175254 | + | 0.0833352i | ||||
\(352\) | 1.87924 | − | 3.25493i | 0.100164 | − | 0.173488i | ||||
\(353\) | −7.89564 | − | 29.4669i | −0.420242 | − | 1.56837i | −0.774098 | − | 0.633066i | \(-0.781796\pi\) |
0.353856 | − | 0.935300i | \(-0.384870\pi\) | |||||||
\(354\) | 0.822126 | − | 1.42396i | 0.0436955 | − | 0.0756828i | ||||
\(355\) | 4.55449 | + | 7.88860i | 0.241727 | + | 0.418683i | ||||
\(356\) | −25.0768 | + | 25.0768i | −1.32907 | + | 1.32907i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15.0521 | − | 56.1751i | −0.795527 | − | 2.96895i | ||||
\(359\) | −4.63302 | − | 17.2907i | −0.244521 | − | 0.912566i | −0.973623 | − | 0.228161i | \(-0.926729\pi\) |
0.729102 | − | 0.684405i | \(-0.239938\pi\) | |||||||
\(360\) | 37.6459i | 1.98411i | ||||||||
\(361\) | −6.18273 | − | 3.56960i | −0.325407 | − | 0.187874i | ||||
\(362\) | −8.11125 | − | 8.11125i | −0.426318 | − | 0.426318i | ||||
\(363\) | −1.64951 | −0.0865769 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.20794 | 0.324939 | ||||||||
\(366\) | −4.51702 | − | 4.51702i | −0.236109 | − | 0.236109i | ||||
\(367\) | 6.26259 | + | 3.61571i | 0.326905 | + | 0.188738i | 0.654466 | − | 0.756091i | \(-0.272893\pi\) |
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(368\) | − | 2.93509i | − | 0.153002i | ||||||
\(369\) | −8.50296 | − | 31.7335i | −0.442646 | − | 1.65198i | ||||
\(370\) | 2.44903 | + | 9.13989i | 0.127319 | + | 0.475160i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.69923 | − | 2.69923i | 0.139949 | − | 0.139949i | ||||
\(373\) | 12.2087 | + | 21.1462i | 0.632145 | + | 1.09491i | 0.987112 | + | 0.160029i | \(0.0511586\pi\) |
−0.354967 | + | 0.934879i | \(0.615508\pi\) | |||||||
\(374\) | 0.633367 | − | 1.09702i | 0.0327506 | − | 0.0567257i | ||||
\(375\) | 0.421813 | + | 1.57423i | 0.0217823 | + | 0.0812927i | ||||
\(376\) | −15.2109 | + | 26.3461i | −0.784443 | + | 1.35869i | ||||
\(377\) | −11.5467 | + | 16.7577i | −0.594687 | + | 0.863067i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.27080 | + | 8.47475i | −0.116643 | + | 0.435319i | −0.999405 | − | 0.0345031i | \(-0.989015\pi\) |
0.882761 | + | 0.469822i | \(0.155682\pi\) | |||||||
\(380\) | −34.6881 | −1.77946 | ||||||||
\(381\) | −0.855704 | −0.0438390 | ||||||||
\(382\) | 4.91454 | − | 18.3413i | 0.251449 | − | 0.938422i | ||||
\(383\) | 16.9913 | + | 4.55280i | 0.868213 | + | 0.232637i | 0.665315 | − | 0.746563i | \(-0.268297\pi\) |
0.202898 | + | 0.979200i | \(0.434964\pi\) | |||||||
\(384\) | −3.06976 | + | 0.822539i | −0.156653 | + | 0.0419750i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.307320 | + | 0.532294i | −0.0156422 | + | 0.0270931i | ||||
\(387\) | − | 20.8822i | − | 1.06150i | ||||||
\(388\) | 15.9082 | − | 4.26258i | 0.807615 | − | 0.216400i | ||||
\(389\) | 8.77740 | − | 5.06764i | 0.445032 | − | 0.256939i | −0.260698 | − | 0.965420i | \(-0.583953\pi\) |
0.705730 | + | 0.708481i | \(0.250619\pi\) | |||||||
\(390\) | 3.05084 | + | 2.10215i | 0.154485 | + | 0.106446i | ||||
\(391\) | − | 0.0735427i | − | 0.00371921i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.479870 | + | 0.831159i | 0.0242062 | + | 0.0419264i | ||||
\(394\) | −14.2472 | + | 8.22563i | −0.717764 | + | 0.414401i | ||||
\(395\) | 29.1405 | + | 7.80817i | 1.46622 | + | 0.392872i | ||||
\(396\) | 39.0864 | + | 39.0864i | 1.96416 | + | 1.96416i | ||||
\(397\) | −2.18723 | + | 8.16286i | −0.109774 | + | 0.409682i | −0.998843 | − | 0.0480910i | \(-0.984686\pi\) |
0.889069 | + | 0.457773i | \(0.151353\pi\) | |||||||
\(398\) | 9.39641 | + | 9.39641i | 0.470999 | + | 0.470999i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.24070 | − | 2.44837i | 0.212035 | − | 0.122419i | ||||
\(401\) | 6.65097 | − | 6.65097i | 0.332134 | − | 0.332134i | −0.521263 | − | 0.853396i | \(-0.674539\pi\) |
0.853396 | + | 0.521263i | \(0.174539\pi\) | |||||||
\(402\) | −1.31026 | − | 2.26944i | −0.0653498 | − | 0.113189i | ||||
\(403\) | 3.61542 | + | 19.6378i | 0.180097 | + | 0.978227i | ||||
\(404\) | −15.9797 | − | 9.22590i | −0.795021 | − | 0.459006i | ||||
\(405\) | −20.8411 | − | 5.58436i | −1.03560 | − | 0.277489i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.13693 | + | 3.54316i | 0.304196 | + | 0.175628i | ||||
\(408\) | 0.0943896 | − | 0.0252916i | 0.00467298 | − | 0.00125212i | ||||
\(409\) | −17.9666 | + | 17.9666i | −0.888390 | + | 0.888390i | −0.994368 | − | 0.105979i | \(-0.966203\pi\) |
0.105979 | + | 0.994368i | \(0.466203\pi\) | |||||||
\(410\) | −47.5734 | + | 47.5734i | −2.34948 | + | 2.34948i | ||||
\(411\) | −1.39371 | + | 0.373444i | −0.0687467 | + | 0.0184206i | ||||
\(412\) | 47.5810 | + | 27.4709i | 2.34415 | + | 1.35339i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.61864 | + | 1.23756i | 0.226994 | + | 0.0608228i | ||||
\(415\) | 10.0969 | + | 5.82944i | 0.495636 | + | 0.286156i | ||||
\(416\) | −0.995948 | + | 2.80184i | −0.0488304 | + | 0.137372i | ||||
\(417\) | −0.966489 | − | 1.67401i | −0.0473292 | − | 0.0819765i | ||||
\(418\) | −27.3693 | + | 27.3693i | −1.33868 | + | 1.33868i | ||||
\(419\) | 17.4075 | − | 10.0503i | 0.850414 | − | 0.490987i | −0.0103762 | − | 0.999946i | \(-0.503303\pi\) |
0.860791 | + | 0.508959i | \(0.169970\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.51951 | − | 2.51951i | −0.122793 | − | 0.122793i | 0.643040 | − | 0.765833i | \(-0.277673\pi\) |
−0.765833 | + | 0.643040i | \(0.777673\pi\) | |||||||
\(422\) | 1.85058 | − | 6.90645i | 0.0900847 | − | 0.336201i | ||||
\(423\) | −12.4497 | − | 12.4497i | −0.605324 | − | 0.605324i | ||||
\(424\) | 23.9122 | + | 6.40724i | 1.16128 | + | 0.311163i | ||||
\(425\) | 0.106256 | − | 0.0613472i | 0.00515419 | − | 0.00297578i | ||||
\(426\) | 0.768658 | + | 1.33135i | 0.0372416 | + | 0.0645044i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 33.7166i | 1.62975i | ||||||||
\(429\) | 2.72877 | − | 0.502381i | 0.131746 | − | 0.0242552i | ||||
\(430\) | −37.0349 | + | 21.3821i | −1.78598 | + | 1.03114i | ||||
\(431\) | 23.1558 | − | 6.20458i | 1.11538 | − | 0.298864i | 0.346365 | − | 0.938100i | \(-0.387416\pi\) |
0.769011 | + | 0.639236i | \(0.220749\pi\) | |||||||
\(432\) | 4.53586i | 0.218232i | ||||||||
\(433\) | 11.7141 | − | 20.2893i | 0.562941 | − | 0.975043i | −0.434296 | − | 0.900770i | \(-0.643003\pi\) |
0.997238 | − | 0.0742732i | \(-0.0236637\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.27164 | − | 0.608684i | 0.108917 | − | 0.0291842i | ||||
\(436\) | 53.0957 | + | 14.2269i | 2.54282 | + | 0.681347i | ||||
\(437\) | −0.581607 | + | 2.17059i | −0.0278220 | + | 0.103833i | ||||
\(438\) | 1.04771 | 0.0500616 | ||||||||
\(439\) | 33.7642 | 1.61148 | 0.805738 | − | 0.592272i | \(-0.201769\pi\) | ||||
0.805738 | + | 0.592272i | \(0.201769\pi\) | |||||||
\(440\) | 14.9431 | − | 55.7686i | 0.712386 | − | 2.65866i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.335669 | + | 0.944318i | −0.0159661 | + | 0.0449166i | ||||
\(443\) | −15.5134 | + | 26.8699i | −0.737062 | + | 1.27663i | 0.216750 | + | 0.976227i | \(0.430454\pi\) |
−0.953813 | + | 0.300402i | \(0.902879\pi\) | |||||||
\(444\) | 0.277403 | + | 1.03528i | 0.0131650 | + | 0.0491324i | ||||
\(445\) | −10.7189 | + | 18.5657i | −0.508125 | + | 0.880098i | ||||
\(446\) | 23.1091 | + | 40.0262i | 1.09425 | + | 1.89530i | ||||
\(447\) | −0.910762 | + | 0.910762i | −0.0430776 | + | 0.0430776i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.388197 | − | 1.44877i | −0.0183202 | − | 0.0683718i | 0.956161 | − | 0.292843i | \(-0.0946013\pi\) |
−0.974481 | + | 0.224471i | \(0.927935\pi\) | |||||||
\(450\) | 2.06468 | + | 7.70548i | 0.0973298 | + | 0.363240i | ||||
\(451\) | 50.3851i | 2.37254i | ||||||||
\(452\) | 8.08210 | + | 4.66620i | 0.380150 | + | 0.219480i | ||||
\(453\) | 0.787880 | + | 0.787880i | 0.0370178 | + | 0.0370178i | ||||
\(454\) | −15.7424 | −0.738829 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.98589 | −0.139827 | ||||||||
\(457\) | 21.6961 | + | 21.6961i | 1.01490 | + | 1.01490i | 0.999887 | + | 0.0150158i | \(0.00477986\pi\) |
0.0150158 | + | 0.999887i | \(0.495220\pi\) | |||||||
\(458\) | −36.9627 | − | 21.3404i | −1.72715 | − | 0.997172i | ||||
\(459\) | 0.113652i | 0.00530482i | ||||||||
\(460\) | −1.70097 | − | 6.34809i | −0.0793080 | − | 0.295981i | ||||
\(461\) | −6.69670 | − | 24.9924i | −0.311896 | − | 1.16401i | −0.926845 | − | 0.375445i | \(-0.877490\pi\) |
0.614948 | − | 0.788568i | \(-0.289177\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.5381 | + | 26.5381i | −1.23333 | + | 1.23333i | −0.270652 | + | 0.962677i | \(0.587239\pi\) |
−0.962677 | + | 0.270652i | \(0.912761\pi\) | |||||||
\(464\) | 12.6947 | + | 21.9878i | 0.589336 | + | 1.02076i | ||||
\(465\) | 1.15377 | − | 1.99838i | 0.0535047 | − | 0.0926728i | ||||
\(466\) | 0.801205 | + | 2.99014i | 0.0371151 | + | 0.138515i | ||||
\(467\) | −4.11119 | + | 7.12080i | −0.190243 | + | 0.329511i | −0.945331 | − | 0.326113i | \(-0.894261\pi\) |
0.755087 | + | 0.655624i | \(0.227594\pi\) | |||||||
\(468\) | −36.0120 | − | 24.8137i | −1.66466 | − | 1.14701i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −9.33199 | + | 34.8274i | −0.430452 | + | 1.60647i | ||||
\(471\) | −1.60010 | −0.0737285 | ||||||||
\(472\) | 20.2723 | 0.933106 | ||||||||
\(473\) | −8.28895 | + | 30.9348i | −0.381127 | + | 1.42238i | ||||
\(474\) | 4.91803 | + | 1.31778i | 0.225892 | + | 0.0605277i | ||||
\(475\) | −3.62128 | + | 0.970319i | −0.166156 | + | 0.0445213i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.16362 | + | 12.4078i | −0.328000 | + | 0.568112i | ||||
\(478\) | − | 29.9740i | − | 1.37098i | ||||||
\(479\) | −20.9972 | + | 5.62619i | −0.959388 | + | 0.257067i | −0.704342 | − | 0.709861i | \(-0.748758\pi\) |
−0.255047 | + | 0.966929i | \(0.582091\pi\) | |||||||
\(480\) | 0.297598 | − | 0.171818i | 0.0135834 | − | 0.00784239i | ||||
\(481\) | −5.28267 | − | 1.87779i | −0.240869 | − | 0.0856196i | ||||
\(482\) | 5.99250i | 0.272951i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −19.9370 | − | 34.5318i | −0.906225 | − | 1.56963i | ||||
\(485\) | 8.62185 | − | 4.97782i | 0.391498 | − | 0.226031i | ||||
\(486\) | −10.7234 | − | 2.87333i | −0.486425 | − | 0.130337i | ||||
\(487\) | 12.7599 | + | 12.7599i | 0.578206 | + | 0.578206i | 0.934409 | − | 0.356202i | \(-0.115929\pi\) |
−0.356202 | + | 0.934409i | \(0.615929\pi\) | |||||||
\(488\) | 20.3844 | − | 76.0755i | 0.922758 | − | 3.44378i | ||||
\(489\) | −2.20635 | − | 2.20635i | −0.0997746 | − | 0.0997746i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.63350 | − | 3.25250i | 0.254236 | − | 0.146783i | −0.367466 | − | 0.930037i | \(-0.619775\pi\) |
0.621703 | + | 0.783253i | \(0.286441\pi\) | |||||||
\(492\) | −5.38867 | + | 5.38867i | −0.242940 | + | 0.242940i | ||||
\(493\) | 0.318082 | + | 0.550935i | 0.0143257 | + | 0.0248129i | ||||
\(494\) | 17.3752 | − | 25.2166i | 0.781748 | − | 1.13455i | ||||
\(495\) | 28.9377 | + | 16.7072i | 1.30065 | + | 0.750932i | ||||
\(496\) | 24.0629 | + | 6.44763i | 1.08046 | + | 0.289507i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.70405 | + | 0.983831i | 0.0763601 | + | 0.0440865i | ||||
\(499\) | 19.4522 | − | 5.21221i | 0.870802 | − | 0.233331i | 0.204367 | − | 0.978894i | \(-0.434486\pi\) |
0.666434 | + | 0.745564i | \(0.267820\pi\) | |||||||
\(500\) | −27.8575 | + | 27.8575i | −1.24583 | + | 1.24583i | ||||
\(501\) | 1.95980 | − | 1.95980i | 0.0875574 | − | 0.0875574i | ||||
\(502\) | −37.8664 | + | 10.1463i | −1.69006 | + | 0.452850i | ||||
\(503\) | 17.1138 | + | 9.88067i | 0.763068 | + | 0.440557i | 0.830396 | − | 0.557173i | \(-0.188114\pi\) |
−0.0673282 | + | 0.997731i | \(0.521447\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.7740 | − | 2.88687i | −0.479435 | − | 0.128464i | ||||
\(506\) | −6.35081 | − | 3.66664i | −0.282328 | − | 0.163002i | ||||
\(507\) | −2.05127 | + | 0.781798i | −0.0911001 | + | 0.0347209i | ||||
\(508\) | −10.3425 | − | 17.9138i | −0.458876 | − | 0.794796i | ||||
\(509\) | −21.0947 | + | 21.0947i | −0.935004 | + | 0.935004i | −0.998013 | − | 0.0630085i | \(-0.979930\pi\) |
0.0630085 | + | 0.998013i | \(0.479930\pi\) | |||||||
\(510\) | 0.100301 | − | 0.0579086i | 0.00444139 | − | 0.00256424i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −30.0390 | − | 30.0390i | −1.32755 | − | 1.32755i | ||||
\(513\) | 0.898808 | − | 3.35440i | 0.0396833 | − | 0.148100i | ||||
\(514\) | −24.7521 | − | 24.7521i | −1.09177 | − | 1.09177i | ||||
\(515\) | 32.0804 | + | 8.59591i | 1.41363 | + | 0.378781i | ||||
\(516\) | −4.19497 | + | 2.42197i | −0.184673 | + | 0.106621i | ||||
\(517\) | 13.5012 | + | 23.3847i | 0.593780 | + | 1.02846i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 3.07961i | − | 0.135180i | ||||||
\(520\) | −3.63825 | + | 45.5338i | −0.159548 | + | 1.99679i | ||||
\(521\) | −6.67564 | + | 3.85418i | −0.292465 | + | 0.168855i | −0.639053 | − | 0.769163i | \(-0.720674\pi\) |
0.346588 | + | 0.938018i | \(0.387340\pi\) | |||||||
\(522\) | −39.9525 | + | 10.7053i | −1.74868 | + | 0.468556i | ||||
\(523\) | − | 0.0152739i | − | 0.000667882i | −1.00000 | 0.000333941i | \(-0.999894\pi\) | |||
1.00000 | 0.000333941i | \(-0.000106297\pi\) | ||||||||
\(524\) | −11.6000 | + | 20.0918i | −0.506748 | + | 0.877713i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 45.1096 | − | 12.0871i | 1.96687 | − | 0.527021i | ||||
\(527\) | 0.602928 | + | 0.161554i | 0.0262640 | + | 0.00703741i | ||||
\(528\) | 0.895931 | − | 3.34366i | 0.0389904 | − | 0.145514i | ||||
\(529\) | 22.5743 | 0.981489 | ||||||||
\(530\) | 29.3405 | 1.27447 | ||||||||
\(531\) | −3.03659 | + | 11.3327i | −0.131777 | + | 0.491798i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.21772 | − | 39.2043i | −0.312634 | − | 1.69813i | ||||
\(534\) | −1.80902 | + | 3.13332i | −0.0782841 | + | 0.135592i | ||||
\(535\) | 5.27513 | + | 19.6870i | 0.228064 | + | 0.851145i | ||||
\(536\) | 16.1544 | − | 27.9803i | 0.697764 | − | 1.20856i | ||||
\(537\) | −1.99105 | − | 3.44859i | −0.0859199 | − | 0.148818i | ||||
\(538\) | 42.2361 | − | 42.2361i | 1.82093 | − | 1.82093i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.62865 | + | 9.81027i | 0.113119 | + | 0.422167i | ||||
\(541\) | −12.0108 | − | 44.8251i | −0.516386 | − | 1.92718i | −0.325325 | − | 0.945602i | \(-0.605474\pi\) |
−0.191061 | − | 0.981578i | \(-0.561193\pi\) | |||||||
\(542\) | − | 38.8479i | − | 1.66866i | ||||||
\(543\) | −0.680212 | − | 0.392720i | −0.0291907 | − | 0.0168532i | ||||
\(544\) | 0.0657291 | + | 0.0657291i | 0.00281811 | + | 0.00281811i | ||||
\(545\) | 33.2283 | 1.42334 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.9225 | 0.980097 | 0.490049 | − | 0.871695i | \(-0.336979\pi\) | ||||
0.490049 | + | 0.871695i | \(0.336979\pi\) | |||||||
\(548\) | −24.6631 | − | 24.6631i | −1.05355 | − | 1.05355i | ||||
\(549\) | 39.4748 | + | 22.7908i | 1.68474 | + | 0.972686i | ||||
\(550\) | − | 12.2344i | − | 0.521678i | ||||||
\(551\) | −5.03106 | − | 18.7762i | −0.214330 | − | 0.799892i | ||||
\(552\) | −0.146416 | − | 0.546434i | −0.00623190 | − | 0.0232578i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.30224 | + | 1.30224i | −0.0553269 | + | 0.0553269i | ||||
\(555\) | 0.323950 | + | 0.561098i | 0.0137509 | + | 0.0238173i | ||||
\(556\) | 23.3631 | − | 40.4661i | 0.990816 | − | 1.71614i | ||||
\(557\) | −4.20224 | − | 15.6830i | −0.178055 | − | 0.664509i | −0.996011 | − | 0.0892288i | \(-0.971560\pi\) |
0.817957 | − | 0.575280i | \(-0.195107\pi\) | |||||||
\(558\) | −20.2919 | + | 35.1466i | −0.859025 | + | 1.48787i | ||||
\(559\) | 2.01814 | − | 25.2576i | 0.0853581 | − | 1.06828i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.0224488 | − | 0.0837799i | 0.000947788 | − | 0.00353719i | ||||
\(562\) | −1.87238 | −0.0789814 | ||||||||
\(563\) | −10.5234 | −0.443507 | −0.221753 | − | 0.975103i | \(-0.571178\pi\) | ||||
−0.221753 | + | 0.975103i | \(0.571178\pi\) | |||||||
\(564\) | −1.05704 | + | 3.94493i | −0.0445095 | + | 0.166112i | ||||
\(565\) | 5.44917 | + | 1.46010i | 0.229248 | + | 0.0614269i | ||||
\(566\) | −45.9003 | + | 12.2989i | −1.92933 | + | 0.516963i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.47692 | + | 16.4145i | −0.397643 | + | 0.688737i | ||||
\(569\) | 35.6613i | 1.49500i | 0.664262 | + | 0.747500i | \(0.268746\pi\) | ||||
−0.664262 | + | 0.747500i | \(0.731254\pi\) | |||||||
\(570\) | −3.41830 | + | 0.915932i | −0.143177 | + | 0.0383642i | ||||
\(571\) | 9.54352 | − | 5.50995i | 0.399384 | − | 0.230584i | −0.286834 | − | 0.957980i | \(-0.592603\pi\) |
0.686218 | + | 0.727396i | \(0.259270\pi\) | |||||||
\(572\) | 43.4986 | + | 51.0535i | 1.81877 | + | 2.13466i | ||||
\(573\) | − | 1.30016i | − | 0.0543150i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.355147 | − | 0.615132i | −0.0148106 | − | 0.0256528i | ||||
\(576\) | 17.9175 | − | 10.3447i | 0.746564 | − | 0.431029i | ||||
\(577\) | 26.6870 | + | 7.15076i | 1.11099 | + | 0.297690i | 0.767234 | − | 0.641367i | \(-0.221633\pi\) |
0.343760 | + | 0.939057i | \(0.388299\pi\) | |||||||
\(578\) | −29.6231 | − | 29.6231i | −1.23216 | − | 1.23216i | ||||
\(579\) | −0.0108925 | + | 0.0406514i | −0.000452677 | + | 0.00168942i | ||||
\(580\) | 40.1989 | + | 40.1989i | 1.66917 | + | 1.66917i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.45510 | − | 0.840105i | 0.0603160 | − | 0.0348235i | ||||
\(583\) | 15.5373 | − | 15.5373i | 0.643489 | − | 0.643489i | ||||
\(584\) | 6.45871 | + | 11.1868i | 0.267263 | + | 0.462914i | ||||
\(585\) | −24.9096 | − | 8.85440i | −1.02988 | − | 0.366084i | ||||
\(586\) | −31.0754 | − | 17.9414i | −1.28371 | − | 0.741153i | ||||
\(587\) | 7.45089 | + | 1.99646i | 0.307531 | + | 0.0824027i | 0.409284 | − | 0.912407i | \(-0.365778\pi\) |
−0.101753 | + | 0.994810i | \(0.532445\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.5176 | − | 9.53642i | −0.680594 | − | 0.392941i | ||||
\(590\) | 23.2081 | − | 6.21858i | 0.955460 | − | 0.256015i | ||||
\(591\) | −0.796517 | + | 0.796517i | −0.0327643 | + | 0.0327643i | ||||
\(592\) | −4.94594 | + | 4.94594i | −0.203277 | + | 0.203277i | ||||
\(593\) | −9.89297 | + | 2.65081i | −0.406256 | + | 0.108856i | −0.456159 | − | 0.889898i | \(-0.650775\pi\) |
0.0499035 | + | 0.998754i | \(0.484109\pi\) | |||||||
\(594\) | 9.81446 | + | 5.66638i | 0.402692 | + | 0.232495i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −30.0744 | − | 8.05842i | −1.23190 | − | 0.330086i | ||||
\(597\) | 0.787985 | + | 0.454944i | 0.0322501 | + | 0.0186196i | ||||
\(598\) | 5.46677 | + | 1.94323i | 0.223553 | + | 0.0794646i | ||||
\(599\) | 19.8784 | + | 34.4305i | 0.812211 | + | 1.40679i | 0.911313 | + | 0.411714i | \(0.135070\pi\) |
−0.0991022 | + | 0.995077i | \(0.531597\pi\) | |||||||
\(600\) | 0.667366 | − | 0.667366i | 0.0272451 | − | 0.0272451i | ||||
\(601\) | −5.65826 | + | 3.26680i | −0.230805 | + | 0.133255i | −0.610943 | − | 0.791674i | \(-0.709210\pi\) |
0.380138 | + | 0.924930i | \(0.375876\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.2219 | + | 13.2219i | 0.538437 | + | 0.538437i | ||||
\(604\) | −6.97116 | + | 26.0167i | −0.283652 | + | 1.05860i | ||||
\(605\) | −17.0438 | − | 17.0438i | −0.692930 | − | 0.692930i | ||||
\(606\) | −1.81832 | − | 0.487216i | −0.0738640 | − | 0.0197918i | ||||
\(607\) | −5.87637 | + | 3.39272i | −0.238514 | + | 0.137706i | −0.614494 | − | 0.788922i | \(-0.710640\pi\) |
0.375979 | + | 0.926628i | \(0.377306\pi\) | |||||||
\(608\) | −1.42016 | − | 2.45979i | −0.0575950 | − | 0.0997575i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 93.3456i | − | 3.77945i | ||||||
\(611\) | −13.8550 | − | 16.2614i | −0.560515 | − | 0.657866i | ||||
\(612\) | −1.18395 | + | 0.683553i | −0.0478583 | + | 0.0276310i | ||||
\(613\) | 19.0899 | − | 5.11512i | 0.771034 | − | 0.206598i | 0.148206 | − | 0.988957i | \(-0.452650\pi\) |
0.622828 | + | 0.782359i | \(0.285984\pi\) | |||||||
\(614\) | − | 33.0355i | − | 1.33321i | ||||||
\(615\) | −2.30335 | + | 3.98952i | −0.0928800 | + | 0.160873i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.05438 | + | 0.550470i | −0.0827063 | + | 0.0221611i | −0.299935 | − | 0.953960i | \(-0.596965\pi\) |
0.217229 | + | 0.976121i | \(0.430298\pi\) | |||||||
\(618\) | 5.41419 | + | 1.45073i | 0.217791 | + | 0.0583568i | ||||
\(619\) | 7.70516 | − | 28.7560i | 0.309696 | − | 1.15580i | −0.619130 | − | 0.785288i | \(-0.712515\pi\) |
0.928827 | − | 0.370514i | \(-0.120819\pi\) | |||||||
\(620\) | 55.7804 | 2.24020 | ||||||||
\(621\) | 0.657946 | 0.0264024 | ||||||||
\(622\) | −5.28614 | + | 19.7281i | −0.211955 | + | 0.791027i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.218135 | + | 2.73003i | −0.00873239 | + | 0.109288i | ||||
\(625\) | −14.6290 | + | 25.3381i | −0.585158 | + | 1.01352i | ||||
\(626\) | 3.67157 | + | 13.7025i | 0.146745 | + | 0.547661i | ||||
\(627\) | −1.32513 | + | 2.29520i | −0.0529208 | + | 0.0916615i | ||||
\(628\) | −19.3397 | − | 33.4973i | −0.771738 | − | 1.33669i | ||||
\(629\) | −0.123927 | + | 0.123927i | −0.00494130 | + | 0.00494130i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.04595 | + | 22.5638i | 0.240686 | + | 0.898251i | 0.975503 | + | 0.219986i | \(0.0706011\pi\) |
−0.734817 | + | 0.678265i | \(0.762732\pi\) | |||||||
\(632\) | 16.2472 | + | 60.6352i | 0.646277 | + | 2.41194i | ||||
\(633\) | − | 0.489578i | − | 0.0194590i | ||||||
\(634\) | 21.9897 | + | 12.6957i | 0.873321 | + | 0.504212i | ||||
\(635\) | −8.84168 | − | 8.84168i | −0.350872 | − | 0.350872i | ||||
\(636\) | 3.32342 | 0.131782 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 63.4349 | 2.51141 | ||||||||
\(639\) | −7.75657 | − | 7.75657i | −0.306845 | − | 0.306845i | ||||
\(640\) | −40.2177 | − | 23.2197i | −1.58975 | − | 0.917840i | ||||
\(641\) | − | 25.5854i | − | 1.01056i | −0.862955 | − | 0.505280i | \(-0.831389\pi\) | ||
0.862955 | − | 0.505280i | \(-0.168611\pi\) | |||||||
\(642\) | 0.890280 | + | 3.32257i | 0.0351366 | + | 0.131131i | ||||
\(643\) | 7.72960 | + | 28.8473i | 0.304826 | + | 1.13763i | 0.933095 | + | 0.359630i | \(0.117097\pi\) |
−0.628269 | + | 0.777996i | \(0.716236\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.07051 | + | 2.07051i | −0.0815261 | + | 0.0815261i | ||||
\(646\) | −0.478642 | − | 0.829032i | −0.0188319 | − | 0.0326178i | ||||
\(647\) | −1.41318 | + | 2.44770i | −0.0555577 | + | 0.0962288i | −0.892467 | − | 0.451113i | \(-0.851027\pi\) |
0.836909 | + | 0.547342i | \(0.184360\pi\) | |||||||
\(648\) | −11.6199 | − | 43.3660i | −0.456472 | − | 1.70358i | ||||
\(649\) | 8.99679 | − | 15.5829i | 0.353155 | − | 0.611683i | ||||
\(650\) | 1.75260 | + | 9.51953i | 0.0687425 | + | 0.373387i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 19.5218 | − | 72.8563i | 0.764532 | − | 2.85327i | ||||
\(653\) | 26.1013 | 1.02142 | 0.510711 | − | 0.859753i | \(-0.329382\pi\) | ||||
0.510711 | + | 0.859753i | \(0.329382\pi\) | |||||||
\(654\) | 5.60793 | 0.219287 | ||||||||
\(655\) | −3.62975 | + | 13.5464i | −0.141826 | + | 0.529302i | ||||
\(656\) | −48.0385 | − | 12.8719i | −1.87559 | − | 0.502562i | ||||
\(657\) | −7.22116 | + | 1.93490i | −0.281724 | + | 0.0754878i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.04837 | + | 15.6722i | −0.352475 | + | 0.610504i | −0.986682 | − | 0.162659i | \(-0.947993\pi\) |
0.634208 | + | 0.773163i | \(0.281326\pi\) | |||||||
\(660\) | − | 7.75097i | − | 0.301706i | ||||||
\(661\) | 1.36965 | − | 0.366997i | 0.0532733 | − | 0.0142745i | −0.232084 | − | 0.972696i | \(-0.574554\pi\) |
0.285357 | + | 0.958421i | \(0.407888\pi\) | |||||||
\(662\) | −37.0142 | + | 21.3702i | −1.43860 | + | 0.830574i | ||||
\(663\) | −0.00546567 | + | 0.0684044i | −0.000212269 | + | 0.00265661i | ||||
\(664\) | 24.2596i | 0.941457i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.69748 | − | 9.86833i | −0.220773 | − | 0.382390i | ||||
\(667\) | 3.18943 | − | 1.84142i | 0.123495 | − | 0.0713000i | ||||
\(668\) | 64.7149 | + | 17.3403i | 2.50389 | + | 0.670917i | ||||
\(669\) | 2.23774 | + | 2.23774i | 0.0865160 | + | 0.0865160i | ||||
\(670\) | 9.91083 | − | 36.9877i | 0.382889 | − | 1.42896i | ||||
\(671\) | −49.4313 | − | 49.4313i | −1.90827 | − | 1.90827i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.78674 | + | 2.18627i | −0.145968 | + | 0.0842747i | −0.571205 | − | 0.820807i | \(-0.693524\pi\) |
0.425237 | + | 0.905082i | \(0.360191\pi\) | |||||||
\(674\) | −21.1125 | + | 21.1125i | −0.813222 | + | 0.813222i | ||||
\(675\) | 0.548839 | + | 0.950618i | 0.0211248 | + | 0.0365893i | ||||
\(676\) | −41.1595 | − | 33.4932i | −1.58306 | − | 1.28820i | ||||
\(677\) | 40.1930 | + | 23.2054i | 1.54474 | + | 0.891857i | 0.998530 | + | 0.0542097i | \(0.0172639\pi\) |
0.546212 | + | 0.837647i | \(0.316069\pi\) | |||||||
\(678\) | 0.919654 | + | 0.246420i | 0.0353191 | + | 0.00946372i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.23662 | + | 0.713966i | 0.0474224 | + | 0.0273793i | ||||
\(681\) | −1.04118 | + | 0.278984i | −0.0398982 | + | 0.0106907i | ||||
\(682\) | 44.0115 | − | 44.0115i | 1.68529 | − | 1.68529i | ||||
\(683\) | 2.74654 | − | 2.74654i | 0.105094 | − | 0.105094i | −0.652605 | − | 0.757698i | \(-0.726324\pi\) |
0.757698 | + | 0.652605i | \(0.226324\pi\) | |||||||
\(684\) | 40.3496 | − | 10.8116i | 1.54281 | − | 0.413394i | ||||
\(685\) | −18.2594 | − | 10.5421i | −0.697655 | − | 0.402791i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.82285 | − | 0.756380i | −0.107698 | − | 0.0288577i | ||||
\(688\) | −27.3765 | − | 15.8058i | −1.04372 | − | 0.602592i | ||||
\(689\) | −9.86374 | + | 14.3152i | −0.375779 | + | 0.545366i | ||||
\(690\) | −0.335240 | − | 0.580653i | −0.0127624 | − | 0.0221051i | ||||
\(691\) | 30.7245 | − | 30.7245i | 1.16882 | − | 1.16882i | 0.186329 | − | 0.982487i | \(-0.440341\pi\) |
0.982487 | − | 0.186329i | \(-0.0596590\pi\) | |||||||
\(692\) | 64.4703 | − | 37.2219i | 2.45079 | − | 1.41497i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.00114 | − | 5.00114i | −0.189841 | − | 0.189841i | ||||
\(695\) | 7.31054 | − | 27.2833i | 0.277305 | − | 1.03492i | ||||
\(696\) | 3.46026 | + | 3.46026i | 0.131161 | + | 0.131161i | ||||
\(697\) | −1.20367 | − | 0.322522i | −0.0455922 | − | 0.0122164i | ||||
\(698\) | −25.7467 | + | 14.8649i | −0.974527 | + | 0.562644i | ||||
\(699\) | 0.105981 | + | 0.183564i | 0.00400857 | + | 0.00694305i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33.2095i | 1.25430i | 0.778897 | + | 0.627152i | \(0.215780\pi\) | ||||
−0.778897 | + | 0.627152i | \(0.784220\pi\) | |||||||
\(702\) | −8.44829 | − | 3.00304i | −0.318860 | − | 0.113343i | ||||
\(703\) | 4.63774 | − | 2.67760i | 0.174916 | − | 0.100988i | ||||
\(704\) | −30.6492 | + | 8.21243i | −1.15514 | + | 0.309518i | ||||
\(705\) | 2.46882i | 0.0929810i | ||||||||
\(706\) | 37.6168 | − | 65.1542i | 1.41573 | − | 2.45211i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.62879 | − | 0.704383i | 0.0987961 | − | 0.0264723i | ||||
\(709\) | −21.4384 | − | 5.74441i | −0.805138 | − | 0.215736i | −0.167299 | − | 0.985906i | \(-0.553505\pi\) |
−0.637838 | + | 0.770170i | \(0.720171\pi\) | |||||||
\(710\) | −5.81415 | + | 21.6987i | −0.218201 | + | 0.814338i | ||||
\(711\) | −36.3303 | −1.36249 | ||||||||
\(712\) | −44.6075 | −1.67174 | ||||||||
\(713\) | 0.935257 | − | 3.49043i | 0.0350256 | − | 0.130717i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 33.3863 | + | 23.0045i | 1.24858 | + | 0.860319i | ||||
\(716\) | 48.1299 | − | 83.3634i | 1.79870 | − | 3.11544i | ||||
\(717\) | −0.531193 | − | 1.98244i | −0.0198378 | − | 0.0740356i | ||||
\(718\) | 22.0728 | − | 38.2313i | 0.823751 | − | 1.42678i | ||||
\(719\) | 14.2145 | + | 24.6202i | 0.530111 | + | 0.918180i | 0.999383 | + | 0.0351257i | \(0.0111832\pi\) |
−0.469272 | + | 0.883054i | \(0.655484\pi\) | |||||||
\(720\) | −23.3218 | + | 23.3218i | −0.869153 | + | 0.869153i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −4.55687 | − | 17.0065i | −0.169589 | − | 0.632915i | ||||
\(723\) | 0.106198 | + | 0.396335i | 0.00394953 | + | 0.0147399i | ||||
\(724\) | − | 18.9866i | − | 0.705632i | ||||||
\(725\) | 5.32106 | + | 3.07212i | 0.197619 | + | 0.114096i | ||||
\(726\) | −2.87648 | − | 2.87648i | −0.106756 | − | 0.106756i | ||||
\(727\) | 0.462661 | 0.0171591 | 0.00857957 | − | 0.999963i | \(-0.497269\pi\) | ||||
0.00857957 | + | 0.999963i | \(0.497269\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.4724 | 0.943422 | ||||||||
\(730\) | 10.8256 | + | 10.8256i | 0.400675 | + | 0.400675i | ||||
\(731\) | −0.685955 | − | 0.396036i | −0.0253710 | − | 0.0146479i | ||||
\(732\) | − | 10.5733i | − | 0.390802i | ||||||
\(733\) | 9.38272 | + | 35.0168i | 0.346559 | + | 1.29337i | 0.890781 | + | 0.454433i | \(0.150158\pi\) |
−0.544222 | + | 0.838941i | \(0.683175\pi\) | |||||||
\(734\) | 4.61573 | + | 17.2261i | 0.170370 | + | 0.635828i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.380514 | − | 0.380514i | 0.0140259 | − | 0.0140259i | ||||
\(737\) | −14.3386 | − | 24.8352i | −0.528169 | − | 0.914816i | ||||
\(738\) | 40.5102 | − | 70.1657i | 1.49120 | − | 2.58284i | ||||
\(739\) | −0.379862 | − | 1.41767i | −0.0139735 | − | 0.0521497i | 0.958587 | − | 0.284800i | \(-0.0919270\pi\) |
−0.972561 | + | 0.232650i | \(0.925260\pi\) | |||||||
\(740\) | −7.83091 | + | 13.5635i | −0.287870 | + | 0.498605i | ||||
\(741\) | 0.702289 | − | 1.97571i | 0.0257992 | − | 0.0725794i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.513502 | − | 1.91642i | 0.0188386 | − | 0.0703065i | −0.955867 | − | 0.293801i | \(-0.905080\pi\) |
0.974705 | + | 0.223494i | \(0.0717464\pi\) | |||||||
\(744\) | 4.80149 | 0.176031 | ||||||||
\(745\) | −18.8212 | −0.689555 | ||||||||
\(746\) | −15.5854 | + | 58.1655i | −0.570622 | + | 2.12959i | ||||
\(747\) | −13.5618 | − | 3.63386i | −0.496199 | − | 0.132956i | ||||
\(748\) | 2.02523 | − | 0.542658i | 0.0740496 | − | 0.0198415i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.00962 | + | 3.48077i | −0.0733810 | + | 0.127100i | ||||
\(751\) | − | 18.1843i | − | 0.663555i | −0.943358 | − | 0.331778i | \(-0.892352\pi\) | ||
0.943358 | − | 0.331778i | \(-0.107648\pi\) | |||||||
\(752\) | −25.7447 | + | 6.89828i | −0.938814 | + | 0.251554i | ||||
\(753\) | −2.32462 | + | 1.34212i | −0.0847137 | + | 0.0489095i | ||||
\(754\) | −49.3583 | + | 9.08713i | −1.79752 | + | 0.330934i | ||||
\(755\) | 16.2818i | 0.592554i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.77153 | + | 4.80044i | 0.100733 | + | 0.174475i | 0.911987 | − | 0.410219i | \(-0.134548\pi\) |
−0.811254 | + | 0.584694i | \(0.801215\pi\) | |||||||
\(758\) | −18.7385 | + | 10.8187i | −0.680612 | + | 0.392952i | ||||
\(759\) | −0.485013 | − | 0.129959i | −0.0176048 | − | 0.00471720i | ||||
\(760\) | −30.8522 | − | 30.8522i | −1.11913 | − | 1.11913i | ||||
\(761\) | −11.4195 | + | 42.6182i | −0.413957 | + | 1.54491i | 0.372960 | + | 0.927848i | \(0.378343\pi\) |
−0.786916 | + | 0.617060i | \(0.788324\pi\) | |||||||
\(762\) | −1.49221 | − | 1.49221i | −0.0540569 | − | 0.0540569i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 27.2183 | − | 15.7145i | 0.984725 | − | 0.568531i | ||||
\(765\) | −0.584359 | + | 0.584359i | −0.0211276 | + | 0.0211276i | ||||
\(766\) | 21.6907 | + | 37.5693i | 0.783715 | + | 1.35743i | ||||
\(767\) | −4.76808 | + | 13.4138i | −0.172165 | + | 0.484343i | ||||
\(768\) | −4.75111 | − | 2.74306i | −0.171441 | − | 0.0989815i | ||||
\(769\) | −27.2136 | − | 7.29187i | −0.981348 | − | 0.262951i | −0.267736 | − | 0.963492i | \(-0.586275\pi\) |
−0.713612 | + | 0.700541i | \(0.752942\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.07572 | − | 1.19842i | −0.0747552 | − | 0.0431599i | ||||
\(772\) | −0.982674 | + | 0.263307i | −0.0353672 | + | 0.00947661i | ||||
\(773\) | −14.6663 | + | 14.6663i | −0.527511 | + | 0.527511i | −0.919829 | − | 0.392319i | \(-0.871673\pi\) |
0.392319 | + | 0.919829i | \(0.371673\pi\) | |||||||
\(774\) | 36.4151 | − | 36.4151i | 1.30891 | − | 1.30891i | ||||
\(775\) | 5.82323 | − | 1.56033i | 0.209177 | − | 0.0560487i | ||||
\(776\) | 17.9402 | + | 10.3578i | 0.644017 | + | 0.371823i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24.1435 | + | 6.46922i | 0.865585 | + | 0.231933i | ||||
\(779\) | 32.9752 | + | 19.0383i | 1.18146 | + | 0.682116i | ||||
\(780\) | 1.11034 | + | 6.03098i | 0.0397564 | + | 0.215944i | ||||
\(781\) | 8.41168 | + | 14.5695i | 0.300994 | + | 0.521336i | ||||
\(782\) | 0.128246 | − | 0.128246i | 0.00458608 | − | 0.00458608i | ||||
\(783\) | −4.92891 | + | 2.84571i | −0.176145 | + | 0.101697i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.5332 | − | 16.5332i | −0.590096 | − | 0.590096i | ||||
\(786\) | −0.612591 | + | 2.28622i | −0.0218504 | + | 0.0815467i | ||||
\(787\) | −32.1068 | − | 32.1068i | −1.14448 | − | 1.14448i | −0.987620 | − | 0.156863i | \(-0.949862\pi\) |
−0.156863 | − | 0.987620i | \(-0.550138\pi\) | |||||||
\(788\) | −26.3019 | − | 7.04758i | −0.936967 | − | 0.251060i | ||||
\(789\) | 2.76928 | − | 1.59884i | 0.0985888 | − | 0.0569203i | ||||
\(790\) | 37.2001 | + | 64.4324i | 1.32352 | + | 2.29240i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 69.5282i | 2.47058i | ||||||||
\(793\) | 45.5433 | + | 31.3811i | 1.61729 | + | 1.11438i | ||||
\(794\) | −18.0489 | + | 10.4205i | −0.640530 | + | 0.369810i | ||||
\(795\) | 1.94054 | − | 0.519966i | 0.0688238 | − | 0.0184413i | ||||
\(796\) | 21.9949i | 0.779587i | ||||||||
\(797\) | 15.9452 | − | 27.6179i | 0.564809 | − | 0.978277i | −0.432259 | − | 0.901750i | \(-0.642283\pi\) |
0.997067 | − | 0.0765277i | \(-0.0243834\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.645069 | + | 0.172846i | −0.0228209 | + | 0.00611484i | ||||
\(800\) | 0.867191 | + | 0.232363i | 0.0306598 | + | 0.00821528i | ||||
\(801\) | 6.68178 | − | 24.9367i | 0.236089 | − | 0.881096i | ||||
\(802\) | 23.1964 | 0.819094 | ||||||||
\(803\) | 11.4655 | 0.404607 | ||||||||
\(804\) | 1.12261 | − | 4.18963i | 0.0395913 | − | 0.147757i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −27.9403 | + | 40.5497i | −0.984157 | + | 1.42830i | ||||
\(807\) | 2.04494 | − | 3.54193i | 0.0719851 | − | 0.124682i | ||||
\(808\) | −6.00697 | − | 22.4183i | −0.211325 | − | 0.788674i | ||||
\(809\) | −14.6403 | + | 25.3577i | −0.514726 | + | 0.891531i | 0.485128 | + | 0.874443i | \(0.338773\pi\) |
−0.999854 | + | 0.0170879i | \(0.994560\pi\) | |||||||
\(810\) | −26.6053 | − | 46.0817i | −0.934815 | − | 1.61915i | ||||
\(811\) | −35.8857 | + | 35.8857i | −1.26012 | + | 1.26012i | −0.309082 | + | 0.951035i | \(0.600022\pi\) |
−0.951035 | + | 0.309082i | \(0.899978\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.688454 | − | 2.56935i | −0.0241451 | − | 0.0901109i | ||||
\(814\) | 4.52311 | + | 16.8805i | 0.158535 | + | 0.591660i | ||||
\(815\) | − | 45.5949i | − | 1.59712i | ||||||
\(816\) | 0.0741431 | + | 0.0428065i | 0.00259553 | + | 0.00149853i | ||||
\(817\) | 17.1137 | + | 17.1137i | 0.598732 | + | 0.598732i | ||||
\(818\) | −62.6615 | −2.19091 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −111.359 | −3.88881 | ||||||||
\(821\) | −6.93408 | − | 6.93408i | −0.242001 | − | 0.242001i | 0.575677 | − | 0.817678i | \(-0.304739\pi\) |
−0.817678 | + | 0.575677i | \(0.804739\pi\) | |||||||
\(822\) | −3.08163 | − | 1.77918i | −0.107484 | − | 0.0620559i | ||||
\(823\) | − | 27.5693i | − | 0.961006i | −0.876993 | − | 0.480503i | \(-0.840454\pi\) | ||
0.876993 | − | 0.480503i | \(-0.159546\pi\) | |||||||
\(824\) | 17.8863 | + | 66.7525i | 0.623098 | + | 2.32543i | ||||
\(825\) | −0.216816 | − | 0.809167i | −0.00754855 | − | 0.0281716i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.9789 | − | 18.9789i | 0.659961 | − | 0.659961i | −0.295410 | − | 0.955371i | \(-0.595456\pi\) |
0.955371 | + | 0.295410i | \(0.0954562\pi\) | |||||||
\(828\) | 3.95717 | + | 6.85402i | 0.137521 | + | 0.238194i | ||||
\(829\) | −14.8153 | + | 25.6608i | −0.514556 | + | 0.891238i | 0.485301 | + | 0.874347i | \(0.338710\pi\) |
−0.999857 | + | 0.0168908i | \(0.994623\pi\) | |||||||
\(830\) | 7.44172 | + | 27.7729i | 0.258306 | + | 0.964011i | ||||
\(831\) | −0.0630503 | + | 0.109206i | −0.00218719 | + | 0.00378832i | ||||
\(832\) | 22.6715 | − | 10.7806i | 0.785993 | − | 0.373749i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.23380 | − | 4.60459i | 0.0427229 | − | 0.159444i | ||||
\(835\) | 40.4999 | 1.40156 | ||||||||
\(836\) | −64.0654 | −2.21575 | ||||||||
\(837\) | −1.44534 | + | 5.39406i | −0.0499581 | + | 0.186446i | ||||
\(838\) | 47.8819 | + | 12.8299i | 1.65405 | + | 0.443202i | ||||
\(839\) | 51.8608 | − | 13.8961i | 1.79043 | − | 0.479745i | 0.798014 | − | 0.602638i | \(-0.205884\pi\) |
0.992420 | + | 0.122893i | \(0.0392172\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.42879 | + | 2.47474i | −0.0492686 | + | 0.0853357i | ||||
\(842\) | − | 8.78721i | − | 0.302827i | ||||||
\(843\) | −0.123836 | + | 0.0331818i | −0.00426515 | + | 0.00114284i | ||||
\(844\) | 10.2491 | − | 5.91733i | 0.352789 | − | 0.203683i | ||||
\(845\) | −29.2731 | − | 13.1170i | −1.00703 | − | 0.451239i | ||||
\(846\) | − | 43.4204i | − | 1.49282i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10.8444 | + | 18.7830i | 0.372397 | + | 0.645011i | ||||
\(849\) | −2.81782 | + | 1.62687i | −0.0967073 | + | 0.0558340i | ||||
\(850\) | 0.292273 | + | 0.0783144i | 0.0100249 | + | 0.00268616i | ||||
\(851\) | 0.717431 | + | 0.717431i | 0.0245932 | + | 0.0245932i | ||||
\(852\) | −0.658573 | + | 2.45783i | −0.0225623 | + | 0.0842038i | ||||
\(853\) | 36.2761 | + | 36.2761i | 1.24207 | + | 1.24207i | 0.959140 | + | 0.282930i | \(0.0913066\pi\) |
0.282930 | + | 0.959140i | \(0.408693\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 21.8685 | − | 12.6258i | 0.747887 | − | 0.431793i | ||||
\(856\) | −29.9881 | + | 29.9881i | −1.02497 | + | 1.02497i | ||||
\(857\) | 23.1941 | + | 40.1733i | 0.792295 | + | 1.37230i | 0.924543 | + | 0.381079i | \(0.124447\pi\) |
−0.132247 | + | 0.991217i | \(0.542219\pi\) | |||||||
\(858\) | 5.63459 | + | 3.88245i | 0.192362 | + | 0.132545i | ||||
\(859\) | 6.53039 | + | 3.77032i | 0.222814 | + | 0.128642i | 0.607253 | − | 0.794509i | \(-0.292272\pi\) |
−0.384439 | + | 0.923151i | \(0.625605\pi\) | |||||||
\(860\) | −68.3705 | − | 18.3198i | −2.33142 | − | 0.624701i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 51.1997 | + | 29.5601i | 1.74387 | + | 1.00682i | ||||
\(863\) | 18.4118 | − | 4.93343i | 0.626745 | − | 0.167936i | 0.0685528 | − | 0.997647i | \(-0.478162\pi\) |
0.558192 | + | 0.829712i | \(0.311495\pi\) | |||||||
\(864\) | −0.588042 | + | 0.588042i | −0.0200056 | + | 0.0200056i | ||||
\(865\) | 31.8205 | − | 31.8205i | 1.08193 | − | 1.08193i | ||||
\(866\) | 55.8087 | − | 14.9539i | 1.89646 | − | 0.508154i | ||||
\(867\) | −2.48420 | − | 1.43425i | −0.0843678 | − | 0.0487098i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 53.8196 | + | 14.4209i | 1.82570 | + | 0.489196i | ||||
\(870\) | 5.02281 | + | 2.89992i | 0.170289 | + | 0.0983166i | ||||
\(871\) | 14.7144 | + | 17.2701i | 0.498580 | + | 0.585174i | ||||
\(872\) | 34.5705 | + | 59.8779i | 1.17071 | + | 2.02772i | ||||
\(873\) | −8.47755 | + | 8.47755i | −0.286921 | + | 0.286921i | ||||
\(874\) | −4.79937 | + | 2.77092i | −0.162341 | + | 0.0937277i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.22623 | + | 1.22623i | 0.0414304 | + | 0.0414304i | ||||
\(877\) | −4.25400 | + | 15.8761i | −0.143647 | + | 0.536099i | 0.856165 | + | 0.516703i | \(0.172841\pi\) |
−0.999812 | + | 0.0193959i | \(0.993826\pi\) | |||||||
\(878\) | 58.8792 | + | 58.8792i | 1.98708 | + | 1.98708i | ||||
\(879\) | −2.37324 | − | 0.635907i | −0.0800473 | − | 0.0214486i | ||||
\(880\) | 43.8062 | − | 25.2915i | 1.47671 | − | 0.852578i | ||||
\(881\) | −6.33542 | − | 10.9733i | −0.213446 | − | 0.369699i | 0.739345 | − | 0.673327i | \(-0.235135\pi\) |
−0.952791 | + | 0.303628i | \(0.901802\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 48.6526i | − | 1.63729i | −0.574300 | − | 0.818645i | \(-0.694726\pi\) | ||
0.574300 | − | 0.818645i | \(-0.305274\pi\) | |||||||
\(884\) | −1.49808 | + | 0.712355i | −0.0503859 | + | 0.0239591i | ||||
\(885\) | 1.42474 | − | 0.822575i | 0.0478922 | − | 0.0276506i | ||||
\(886\) | −73.9095 | + | 19.8040i | −2.48304 | + | 0.665328i | ||||
\(887\) | − | 11.4213i | − | 0.383489i | −0.981445 | − | 0.191744i | \(-0.938586\pi\) | ||
0.981445 | − | 0.191744i | \(-0.0614144\pi\) | |||||||
\(888\) | −0.674072 | + | 1.16753i | −0.0226204 | + | 0.0391796i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −51.0675 | + | 13.6835i | −1.71179 | + | 0.458672i | ||||
\(891\) | −38.4915 | − | 10.3138i | −1.28951 | − | 0.345524i | ||||
\(892\) | −19.7995 | + | 73.8928i | −0.662937 | + | 2.47411i | ||||
\(893\) | 20.4059 | 0.682858 | ||||||||
\(894\) | −3.17644 | −0.106236 | ||||||||
\(895\) | 15.0603 | − | 56.2059i | 0.503411 | − | 1.87875i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.396002 | + | 0.0316414i | 0.0132221 | + | 0.00105648i | ||||
\(898\) | 1.84947 | − | 3.20337i | 0.0617176 | − | 0.106898i | ||||
\(899\) | 8.09024 | + | 30.1932i | 0.269824 | + | 1.00700i | ||||
\(900\) | −6.60192 | + | 11.4349i | −0.220064 | + | 0.381162i | ||||
\(901\) | 0.271720 | + | 0.470633i | 0.00905232 | + | 0.0156791i | ||||
\(902\) | −87.8633 | + | 87.8633i | −2.92553 | + | 2.92553i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.03816 | + | 11.3386i | 0.101048 | + | 0.377115i | ||||
\(905\) | −2.97055 | − | 11.0862i | −0.0987443 | − | 0.368519i | ||||
\(906\) | 2.74786i | 0.0912917i | ||||||||
\(907\) | 23.0490 | + | 13.3073i | 0.765328 | + | 0.441862i | 0.831205 | − | 0.555965i | \(-0.187651\pi\) |
−0.0658773 | + | 0.997828i | \(0.520985\pi\) | |||||||
\(908\) | −18.4247 | − | 18.4247i | −0.611447 | − | 0.611447i | ||||
\(909\) | 13.4322 | 0.445518 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −57.5752 | −1.90755 | −0.953775 | − | 0.300520i | \(-0.902840\pi\) | ||||
−0.953775 | + | 0.300520i | \(0.902840\pi\) | |||||||
\(912\) | −1.84977 | − | 1.84977i | −0.0612522 | − | 0.0612522i | ||||
\(913\) | 18.6479 | + | 10.7664i | 0.617157 | + | 0.356316i | ||||
\(914\) | 75.6690i | 2.50291i | ||||||||
\(915\) | −1.65425 | − | 6.17374i | −0.0546878 | − | 0.204098i | ||||
\(916\) | −18.2841 | − | 68.2372i | −0.604124 | − | 2.25462i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.198190 | + | 0.198190i | −0.00654126 | + | 0.00654126i | ||||
\(919\) | −18.1716 | − | 31.4741i | −0.599424 | − | 1.03823i | −0.992906 | − | 0.118901i | \(-0.962063\pi\) |
0.393482 | − | 0.919332i | \(-0.371270\pi\) | |||||||
\(920\) | 4.13324 | − | 7.15898i | 0.136269 | − | 0.236024i | ||||
\(921\) | −0.585448 | − | 2.18492i | −0.0192912 | − | 0.0719956i | ||||
\(922\) | 31.9047 | − | 55.2606i | 1.05073 | − | 1.81991i | ||||
\(923\) | −8.63217 | − | 10.1314i | −0.284131 | − | 0.333480i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.438103 | + | 1.63502i | −0.0144047 | + | 0.0537592i | ||||
\(926\) | −92.5561 | −3.04158 | ||||||||
\(927\) | −39.9955 | −1.31363 | ||||||||
\(928\) | −1.20479 | + | 4.49635i | −0.0395492 | + | 0.147600i | ||||
\(929\) | −49.1711 | − | 13.1754i | −1.61325 | − | 0.432269i | −0.664242 | − | 0.747518i | \(-0.731246\pi\) |
−0.949009 | + | 0.315248i | \(0.897912\pi\) | |||||||
\(930\) | 5.49683 | − | 1.47287i | 0.180248 | − | 0.0482974i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.56190 | + | 4.43734i | −0.0839177 | + | 0.145350i | ||||
\(933\) | 1.39847i | 0.0457839i | ||||||||
\(934\) | −19.5867 | + | 5.24825i | −0.640898 | + | 0.171728i | ||||
\(935\) | 1.09762 | − | 0.633713i | 0.0358961 | − | 0.0207246i | ||||
\(936\) | −9.96000 | − | 54.0995i | −0.325553 | − | 1.76830i | ||||
\(937\) | 55.7488i | 1.82123i | 0.413251 | + | 0.910617i | \(0.364393\pi\) | ||||
−0.413251 | + | 0.910617i | \(0.635607\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.485664 | + | 0.841195i | 0.0158491 | + | 0.0274514i | ||||
\(940\) | −51.6836 | + | 29.8396i | −1.68573 | + | 0.973259i | ||||
\(941\) | −7.44082 | − | 1.99376i | −0.242564 | − | 0.0649948i | 0.135489 | − | 0.990779i | \(-0.456740\pi\) |
−0.378053 | + | 0.925784i | \(0.623406\pi\) | |||||||
\(942\) | −2.79030 | − | 2.79030i | −0.0909130 | − | 0.0909130i | ||||
\(943\) | −1.86712 | + | 6.96819i | −0.0608018 | + | 0.226916i | ||||
\(944\) | 12.5588 | + | 12.5588i | 0.408753 | + | 0.408753i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −68.3998 | + | 39.4906i | −2.22387 | + | 1.28395i | ||||
\(947\) | −27.7853 | + | 27.7853i | −0.902900 | + | 0.902900i | −0.995686 | − | 0.0927863i | \(-0.970423\pi\) |
0.0927863 | + | 0.995686i | \(0.470423\pi\) | |||||||
\(948\) | 4.21368 | + | 7.29831i | 0.136854 | + | 0.237038i | ||||
\(949\) | −8.92120 | + | 1.64244i | −0.289594 | + | 0.0533159i | ||||
\(950\) | −8.00700 | − | 4.62284i | −0.259781 | − | 0.149985i | ||||
\(951\) | 1.67936 | + | 0.449982i | 0.0544568 | + | 0.0145917i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.9303 | − | 20.1670i | −1.13150 | − | 0.653275i | −0.187192 | − | 0.982323i | \(-0.559939\pi\) |
−0.944313 | + | 0.329049i | \(0.893272\pi\) | |||||||
\(954\) | −34.1293 | + | 9.14491i | −1.10498 | + | 0.296077i | ||||
\(955\) | 13.4341 | − | 13.4341i | 0.434717 | − | 0.434717i | ||||
\(956\) | 35.0812 | − | 35.0812i | 1.13461 | − | 1.13461i | ||||
\(957\) | 4.19549 | − | 1.12418i | 0.135621 | − | 0.0363396i | ||||
\(958\) | −46.4269 | − | 26.8046i | −1.49999 | − | 0.866017i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.80225 | − | 0.750861i | −0.0904423 | − | 0.0242339i | ||||
\(961\) | −0.285588 | − | 0.164884i | −0.00921252 | − | 0.00531885i | ||||
\(962\) | −5.93755 | − | 12.4867i | −0.191434 | − | 0.402586i | ||||
\(963\) | −12.2722 | − | 21.2561i | −0.395466 | − | 0.684967i | ||||
\(964\) | −7.01355 | + | 7.01355i | −0.225891 | + | 0.225891i | ||||
\(965\) | −0.532585 | + | 0.307488i | −0.0171445 | + | 0.00989840i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.13971 | − | 1.13971i | −0.0366507 | − | 0.0366507i | 0.688544 | − | 0.725195i | \(-0.258250\pi\) |
−0.725195 | + | 0.688544i | \(0.758250\pi\) | |||||||
\(968\) | 12.9809 | − | 48.4455i | 0.417223 | − | 1.55710i | ||||
\(969\) | −0.0463486 | − | 0.0463486i | −0.00148893 | − | 0.00148893i | ||||
\(970\) | 23.7156 | + | 6.35457i | 0.761462 | + | 0.204033i | ||||
\(971\) | 22.6332 | − | 13.0673i | 0.726333 | − | 0.419348i | −0.0907462 | − | 0.995874i | \(-0.528925\pi\) |
0.817079 | + | 0.576526i | \(0.195592\pi\) | |||||||
\(972\) | −9.18765 | − | 15.9135i | −0.294694 | − | 0.510425i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 44.5023i | 1.42595i | ||||||||
\(975\) | 0.284617 | + | 0.598549i | 0.00911504 | + | 0.0191689i | ||||
\(976\) | 59.7574 | − | 34.5009i | 1.91279 | − | 1.10435i | ||||
\(977\) | 15.3729 | − | 4.11917i | 0.491824 | − | 0.131784i | −0.00437887 | − | 0.999990i | \(-0.501394\pi\) |
0.496203 | + | 0.868207i | \(0.334727\pi\) | |||||||
\(978\) | − | 7.69503i | − | 0.246060i | ||||||
\(979\) | −19.7967 | + | 34.2890i | −0.632707 | + | 1.09588i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −38.6516 | + | 10.3567i | −1.23405 | + | 0.330663i | ||||
\(982\) | 15.4957 | + | 4.15207i | 0.494489 | + | 0.132498i | ||||
\(983\) | −2.03290 | + | 7.58689i | −0.0648395 | + | 0.241984i | −0.990738 | − | 0.135788i | \(-0.956643\pi\) |
0.925898 | + | 0.377773i | \(0.123310\pi\) | |||||||
\(984\) | −9.58556 | −0.305577 | ||||||||
\(985\) | −16.4603 | −0.524467 | ||||||||
\(986\) | −0.406056 | + | 1.51542i | −0.0129315 | + | 0.0482609i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 49.8489 | − | 9.17745i | 1.58590 | − | 0.291974i | ||||
\(989\) | −2.29270 | + | 3.97108i | −0.0729038 | + | 0.126273i | ||||
\(990\) | 21.3280 | + | 79.5972i | 0.677848 | + | 2.52976i | ||||
\(991\) | −2.27497 | + | 3.94037i | −0.0722669 | + | 0.125170i | −0.899894 | − | 0.436108i | \(-0.856357\pi\) |
0.827628 | + | 0.561278i | \(0.189690\pi\) | |||||||
\(992\) | 2.28370 | + | 3.95548i | 0.0725074 | + | 0.125586i | ||||
\(993\) | −2.06935 | + | 2.06935i | −0.0656688 | + | 0.0656688i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.44120 | + | 12.8428i | 0.109094 | + | 0.407143i | ||||
\(996\) | 0.842930 | + | 3.14586i | 0.0267093 | + | 0.0996803i | ||||
\(997\) | − | 20.0987i | − | 0.636534i | −0.948001 | − | 0.318267i | \(-0.896899\pi\) | ||
0.948001 | − | 0.318267i | \(-0.103101\pi\) | |||||||
\(998\) | 43.0108 | + | 24.8323i | 1.36148 | + | 0.786052i | ||||
\(999\) | −1.10871 | − | 1.10871i | −0.0350780 | − | 0.0350780i |
(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 | 637.2.bb.a.362.7 | 28 | ||
7.2 | even | 3 | 637.2.bd.a.440.7 | 28 | |||
7.3 | odd | 6 | 637.2.x.a.570.1 | 28 | |||
7.4 | even | 3 | 91.2.w.a.24.1 | yes | 28 | ||
7.5 | odd | 6 | 637.2.bd.b.440.7 | 28 | |||
7.6 | odd | 2 | 91.2.ba.a.89.7 | yes | 28 | ||
13.6 | odd | 12 | 637.2.x.a.19.1 | 28 | |||
21.11 | odd | 6 | 819.2.gh.b.388.7 | 28 | |||
21.20 | even | 2 | 819.2.et.b.271.1 | 28 | |||
91.6 | even | 12 | 91.2.w.a.19.1 | ✓ | 28 | ||
91.19 | even | 12 | 637.2.bd.a.97.7 | 28 | |||
91.32 | odd | 12 | 91.2.ba.a.45.7 | yes | 28 | ||
91.45 | even | 12 | inner | 637.2.bb.a.227.7 | 28 | ||
91.58 | odd | 12 | 637.2.bd.b.97.7 | 28 | |||
273.32 | even | 12 | 819.2.et.b.136.1 | 28 | |||
273.188 | odd | 12 | 819.2.gh.b.19.7 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.w.a.19.1 | ✓ | 28 | 91.6 | even | 12 | ||
91.2.w.a.24.1 | yes | 28 | 7.4 | even | 3 | ||
91.2.ba.a.45.7 | yes | 28 | 91.32 | odd | 12 | ||
91.2.ba.a.89.7 | yes | 28 | 7.6 | odd | 2 | ||
637.2.x.a.19.1 | 28 | 13.6 | odd | 12 | |||
637.2.x.a.570.1 | 28 | 7.3 | odd | 6 | |||
637.2.bb.a.227.7 | 28 | 91.45 | even | 12 | inner | ||
637.2.bb.a.362.7 | 28 | 1.1 | even | 1 | trivial | ||
637.2.bd.a.97.7 | 28 | 91.19 | even | 12 | |||
637.2.bd.a.440.7 | 28 | 7.2 | even | 3 | |||
637.2.bd.b.97.7 | 28 | 91.58 | odd | 12 | |||
637.2.bd.b.440.7 | 28 | 7.5 | odd | 6 | |||
819.2.et.b.136.1 | 28 | 273.32 | even | 12 | |||
819.2.et.b.271.1 | 28 | 21.20 | even | 2 | |||
819.2.gh.b.19.7 | 28 | 273.188 | odd | 12 | |||
819.2.gh.b.388.7 | 28 | 21.11 | odd | 6 |