Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 148.4 | ||
Root | \(1.60551 - 1.16647i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.148 |
Dual form | 847.2.f.w.372.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.613249 | + | 1.88739i | 0.433632 | + | 1.33458i | 0.894482 | + | 0.447105i | \(0.147545\pi\) |
−0.460849 | + | 0.887478i | \(0.652455\pi\) | |||||||
\(3\) | −2.25424 | − | 1.63780i | −1.30149 | − | 0.945585i | −0.301517 | − | 0.953461i | \(-0.597493\pi\) |
−0.999969 | + | 0.00787594i | \(0.997493\pi\) | |||||||
\(4\) | −1.56812 | + | 1.13930i | −0.784059 | + | 0.569652i | ||||
\(5\) | −0.00832008 | + | 0.0256066i | −0.00372085 | + | 0.0114516i | −0.952900 | − | 0.303286i | \(-0.901916\pi\) |
0.949179 | + | 0.314737i | \(0.101916\pi\) | |||||||
\(6\) | 1.70875 | − | 5.25900i | 0.697595 | − | 2.14698i | ||||
\(7\) | −0.809017 | + | 0.587785i | −0.305780 | + | 0.222162i | ||||
\(8\) | 0.0990607 | + | 0.0719718i | 0.0350232 | + | 0.0254459i | ||||
\(9\) | 1.47215 | + | 4.53082i | 0.490718 | + | 1.51027i | ||||
\(10\) | −0.0534317 | −0.0168966 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 5.40087 | 1.55910 | ||||||||
\(13\) | −1.50835 | − | 4.64222i | −0.418341 | − | 1.28752i | −0.909229 | − | 0.416297i | \(-0.863328\pi\) |
0.490888 | − | 0.871223i | \(-0.336672\pi\) | |||||||
\(14\) | −1.60551 | − | 1.16647i | −0.429090 | − | 0.311752i | ||||
\(15\) | 0.0606939 | − | 0.0440967i | 0.0156711 | − | 0.0113857i | ||||
\(16\) | −1.27302 | + | 3.91797i | −0.318256 | + | 0.979492i | ||||
\(17\) | 0.518771 | − | 1.59661i | 0.125821 | − | 0.387236i | −0.868229 | − | 0.496163i | \(-0.834742\pi\) |
0.994050 | + | 0.108928i | \(0.0347417\pi\) | |||||||
\(18\) | −7.64861 | + | 5.55704i | −1.80280 | + | 1.30981i | ||||
\(19\) | −1.11154 | − | 0.807582i | −0.255005 | − | 0.185272i | 0.452937 | − | 0.891543i | \(-0.350376\pi\) |
−0.707942 | + | 0.706270i | \(0.750376\pi\) | |||||||
\(20\) | −0.0161268 | − | 0.0496332i | −0.00360606 | − | 0.0110983i | ||||
\(21\) | 2.78639 | 0.608041 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.06246 | 1.68114 | 0.840570 | − | 0.541703i | \(-0.182220\pi\) | ||||
0.840570 | + | 0.541703i | \(0.182220\pi\) | |||||||
\(24\) | −0.105431 | − | 0.324483i | −0.0215210 | − | 0.0662349i | ||||
\(25\) | 4.04450 | + | 2.93850i | 0.808900 | + | 0.587700i | ||||
\(26\) | 7.83667 | − | 5.69367i | 1.53690 | − | 1.11662i | ||||
\(27\) | 1.51887 | − | 4.67460i | 0.292307 | − | 0.899628i | ||||
\(28\) | 0.598967 | − | 1.84343i | 0.113194 | − | 0.348376i | ||||
\(29\) | 5.17218 | − | 3.75781i | 0.960449 | − | 0.697807i | 0.00719396 | − | 0.999974i | \(-0.497710\pi\) |
0.953255 | + | 0.302167i | \(0.0977101\pi\) | |||||||
\(30\) | 0.120448 | + | 0.0875106i | 0.0219907 | + | 0.0159772i | ||||
\(31\) | 1.23933 | + | 3.81425i | 0.222589 | + | 0.685060i | 0.998527 | + | 0.0542506i | \(0.0172770\pi\) |
−0.775938 | + | 0.630809i | \(0.782723\pi\) | |||||||
\(32\) | −7.93050 | −1.40193 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.33156 | 0.571358 | ||||||||
\(35\) | −0.00832008 | − | 0.0256066i | −0.00140635 | − | 0.00432830i | ||||
\(36\) | −7.47049 | − | 5.42763i | −1.24508 | − | 0.904605i | ||||
\(37\) | −0.421528 | + | 0.306258i | −0.0692988 | + | 0.0503486i | −0.621895 | − | 0.783100i | \(-0.713637\pi\) |
0.552596 | + | 0.833449i | \(0.313637\pi\) | |||||||
\(38\) | 0.842568 | − | 2.59316i | 0.136683 | − | 0.420665i | ||||
\(39\) | −4.20285 | + | 12.9351i | −0.672995 | + | 2.07127i | ||||
\(40\) | −0.00266714 | + | 0.00193779i | −0.000421712 | + | 0.000306392i | ||||
\(41\) | 8.57456 | + | 6.22978i | 1.33912 | + | 0.972929i | 0.999476 | + | 0.0323754i | \(0.0103072\pi\) |
0.339646 | + | 0.940553i | \(0.389693\pi\) | |||||||
\(42\) | 1.70875 | + | 5.25900i | 0.263666 | + | 0.811481i | ||||
\(43\) | 3.73968 | 0.570296 | 0.285148 | − | 0.958483i | \(-0.407957\pi\) | ||||
0.285148 | + | 0.958483i | \(0.407957\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.128267 | −0.0191209 | ||||||||
\(46\) | 4.94430 | + | 15.2170i | 0.728997 | + | 2.24362i | ||||
\(47\) | 7.24804 | + | 5.26601i | 1.05723 | + | 0.768126i | 0.973575 | − | 0.228368i | \(-0.0733391\pi\) |
0.0836598 | + | 0.996494i | \(0.473339\pi\) | |||||||
\(48\) | 9.28655 | − | 6.74708i | 1.34040 | − | 0.973856i | ||||
\(49\) | 0.309017 | − | 0.951057i | 0.0441453 | − | 0.135865i | ||||
\(50\) | −3.06580 | + | 9.43556i | −0.433570 | + | 1.33439i | ||||
\(51\) | −3.78437 | + | 2.74951i | −0.529918 | + | 0.385008i | ||||
\(52\) | 7.65417 | + | 5.56108i | 1.06144 | + | 0.771183i | ||||
\(53\) | −1.22388 | − | 3.76673i | −0.168114 | − | 0.517400i | 0.831139 | − | 0.556065i | \(-0.187689\pi\) |
−0.999252 | + | 0.0386649i | \(0.987689\pi\) | |||||||
\(54\) | 9.75422 | 1.32738 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.122446 | −0.0163625 | ||||||||
\(57\) | 1.18302 | + | 3.64097i | 0.156695 | + | 0.482258i | ||||
\(58\) | 10.2643 | + | 7.45742i | 1.34776 | + | 0.979207i | ||||
\(59\) | −7.87191 | + | 5.71928i | −1.02484 | + | 0.744587i | −0.967269 | − | 0.253755i | \(-0.918334\pi\) |
−0.0575670 | + | 0.998342i | \(0.518334\pi\) | |||||||
\(60\) | −0.0449356 | + | 0.138298i | −0.00580116 | + | 0.0178541i | ||||
\(61\) | 2.61652 | − | 8.05281i | 0.335011 | − | 1.03106i | −0.631706 | − | 0.775208i | \(-0.717645\pi\) |
0.966717 | − | 0.255849i | \(-0.0823549\pi\) | |||||||
\(62\) | −6.43895 | + | 4.67817i | −0.817747 | + | 0.594128i | ||||
\(63\) | −3.85415 | − | 2.80020i | −0.485577 | − | 0.352792i | ||||
\(64\) | −2.31732 | − | 7.13199i | −0.289665 | − | 0.891499i | ||||
\(65\) | 0.131421 | 0.0163008 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.81285 | 0.343644 | 0.171822 | − | 0.985128i | \(-0.445035\pi\) | ||||
0.171822 | + | 0.985128i | \(0.445035\pi\) | |||||||
\(68\) | 1.00553 | + | 3.09472i | 0.121939 | + | 0.375289i | ||||
\(69\) | −18.1747 | − | 13.2047i | −2.18798 | − | 1.58966i | ||||
\(70\) | 0.0432272 | − | 0.0314064i | 0.00516664 | − | 0.00375378i | ||||
\(71\) | 0.632097 | − | 1.94539i | 0.0750161 | − | 0.230876i | −0.906517 | − | 0.422170i | \(-0.861268\pi\) |
0.981533 | + | 0.191294i | \(0.0612685\pi\) | |||||||
\(72\) | −0.180259 | + | 0.554780i | −0.0212437 | + | 0.0653814i | ||||
\(73\) | 8.46987 | − | 6.15372i | 0.991323 | − | 0.720238i | 0.0311128 | − | 0.999516i | \(-0.490095\pi\) |
0.960210 | + | 0.279277i | \(0.0900949\pi\) | |||||||
\(74\) | −0.836529 | − | 0.607774i | −0.0972446 | − | 0.0706523i | ||||
\(75\) | −4.30459 | − | 13.2482i | −0.497051 | − | 1.52977i | ||||
\(76\) | 2.66311 | 0.305479 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −26.9908 | −3.05611 | ||||||||
\(79\) | 1.80936 | + | 5.56864i | 0.203569 | + | 0.626521i | 0.999769 | + | 0.0214875i | \(0.00684021\pi\) |
−0.796200 | + | 0.605033i | \(0.793160\pi\) | |||||||
\(80\) | −0.0897340 | − | 0.0651956i | −0.0100326 | − | 0.00728909i | ||||
\(81\) | 0.482477 | − | 0.350540i | 0.0536086 | − | 0.0389489i | ||||
\(82\) | −6.49967 | + | 20.0039i | −0.717768 | + | 2.20906i | ||||
\(83\) | 0.805136 | − | 2.47795i | 0.0883752 | − | 0.271991i | −0.897095 | − | 0.441837i | \(-0.854327\pi\) |
0.985471 | + | 0.169846i | \(0.0543270\pi\) | |||||||
\(84\) | −4.36939 | + | 3.17455i | −0.476740 | + | 0.346372i | ||||
\(85\) | 0.0365676 | + | 0.0265679i | 0.00396631 | + | 0.00288169i | ||||
\(86\) | 2.29336 | + | 7.05823i | 0.247299 | + | 0.761108i | ||||
\(87\) | −17.8139 | −1.90985 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.21791 | 0.129099 | 0.0645493 | − | 0.997915i | \(-0.479439\pi\) | ||||
0.0645493 | + | 0.997915i | \(0.479439\pi\) | |||||||
\(90\) | −0.0786597 | − | 0.242090i | −0.00829146 | − | 0.0255185i | ||||
\(91\) | 3.94891 | + | 2.86905i | 0.413958 | + | 0.300758i | ||||
\(92\) | −12.6429 | + | 9.18560i | −1.31811 | + | 0.957665i | ||||
\(93\) | 3.45325 | − | 10.6280i | 0.358085 | − | 1.10207i | ||||
\(94\) | −5.49414 | + | 16.9092i | −0.566677 | + | 1.74405i | ||||
\(95\) | 0.0299275 | − | 0.0217436i | 0.00307050 | − | 0.00223085i | ||||
\(96\) | 17.8773 | + | 12.9886i | 1.82459 | + | 1.32564i | ||||
\(97\) | 1.04964 | + | 3.23046i | 0.106575 | + | 0.328003i | 0.990097 | − | 0.140386i | \(-0.0448344\pi\) |
−0.883522 | + | 0.468389i | \(0.844834\pi\) | |||||||
\(98\) | 1.98451 | 0.200466 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.69009 | −0.969009 | ||||||||
\(101\) | −1.25101 | − | 3.85021i | −0.124480 | − | 0.383111i | 0.869326 | − | 0.494239i | \(-0.164553\pi\) |
−0.993806 | + | 0.111129i | \(0.964553\pi\) | |||||||
\(102\) | −7.51014 | − | 5.45644i | −0.743615 | − | 0.540268i | ||||
\(103\) | 3.19802 | − | 2.32350i | 0.315110 | − | 0.228941i | −0.418976 | − | 0.907997i | \(-0.637611\pi\) |
0.734086 | + | 0.679056i | \(0.237611\pi\) | |||||||
\(104\) | 0.184691 | − | 0.568420i | 0.0181104 | − | 0.0557382i | ||||
\(105\) | −0.0231830 | + | 0.0713500i | −0.00226243 | + | 0.00696304i | ||||
\(106\) | 6.35873 | − | 4.61989i | 0.617614 | − | 0.448723i | ||||
\(107\) | −8.41265 | − | 6.11215i | −0.813281 | − | 0.590883i | 0.101499 | − | 0.994836i | \(-0.467636\pi\) |
−0.914780 | + | 0.403952i | \(0.867636\pi\) | |||||||
\(108\) | 2.94403 | + | 9.06078i | 0.283289 | + | 0.871874i | ||||
\(109\) | −3.77697 | −0.361768 | −0.180884 | − | 0.983504i | \(-0.557896\pi\) | ||||
−0.180884 | + | 0.983504i | \(0.557896\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.45182 | 0.137800 | ||||||||
\(112\) | −1.27302 | − | 3.91797i | −0.120290 | − | 0.370213i | ||||
\(113\) | −5.13619 | − | 3.73166i | −0.483173 | − | 0.351045i | 0.319380 | − | 0.947627i | \(-0.396525\pi\) |
−0.802553 | + | 0.596581i | \(0.796525\pi\) | |||||||
\(114\) | −6.14642 | + | 4.46564i | −0.575665 | + | 0.418245i | ||||
\(115\) | −0.0670803 | + | 0.206452i | −0.00625527 | + | 0.0192517i | ||||
\(116\) | −3.82930 | + | 11.7854i | −0.355541 | + | 1.09424i | ||||
\(117\) | 18.8126 | − | 13.6681i | 1.73922 | − | 1.26362i | ||||
\(118\) | −15.6219 | − | 11.3500i | −1.43811 | − | 1.04485i | ||||
\(119\) | 0.518771 | + | 1.59661i | 0.0475557 | + | 0.146361i | ||||
\(120\) | 0.00918610 | 0.000838572 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 16.8033 | 1.52130 | ||||||||
\(123\) | −9.12597 | − | 28.0869i | −0.822861 | − | 2.53251i | ||||
\(124\) | −6.28900 | − | 4.56923i | −0.564769 | − | 0.410329i | ||||
\(125\) | −0.217807 | + | 0.158246i | −0.0194812 | + | 0.0141539i | ||||
\(126\) | 2.92151 | − | 8.99149i | 0.260269 | − | 0.801025i | ||||
\(127\) | −1.55475 | + | 4.78503i | −0.137962 | + | 0.424603i | −0.996039 | − | 0.0889179i | \(-0.971659\pi\) |
0.858077 | + | 0.513521i | \(0.171659\pi\) | |||||||
\(128\) | −0.792108 | + | 0.575500i | −0.0700131 | + | 0.0508675i | ||||
\(129\) | −8.43014 | − | 6.12486i | −0.742233 | − | 0.539264i | ||||
\(130\) | 0.0805937 | + | 0.248042i | 0.00706853 | + | 0.0217547i | ||||
\(131\) | −3.76357 | −0.328825 | −0.164412 | − | 0.986392i | \(-0.552573\pi\) | ||||
−0.164412 | + | 0.986392i | \(0.552573\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.37394 | 0.119136 | ||||||||
\(134\) | 1.72498 | + | 5.30893i | 0.149015 | + | 0.458622i | ||||
\(135\) | 0.107063 | + | 0.0777861i | 0.00921455 | + | 0.00669476i | ||||
\(136\) | 0.166301 | − | 0.120825i | 0.0142602 | − | 0.0103606i | ||||
\(137\) | 5.91393 | − | 18.2012i | 0.505261 | − | 1.55503i | −0.295071 | − | 0.955475i | \(-0.595343\pi\) |
0.800332 | − | 0.599557i | \(-0.204657\pi\) | |||||||
\(138\) | 13.7768 | − | 42.4005i | 1.17276 | − | 3.60937i | ||||
\(139\) | −2.84053 | + | 2.06376i | −0.240930 | + | 0.175046i | −0.701698 | − | 0.712475i | \(-0.747574\pi\) |
0.460767 | + | 0.887521i | \(0.347574\pi\) | |||||||
\(140\) | 0.0422205 | + | 0.0306750i | 0.00356828 | + | 0.00259251i | ||||
\(141\) | −7.71414 | − | 23.7417i | −0.649648 | − | 1.99941i | ||||
\(142\) | 4.05934 | 0.340652 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −19.6257 | −1.63548 | ||||||||
\(145\) | 0.0531916 | + | 0.163707i | 0.00441732 | + | 0.0135951i | ||||
\(146\) | 16.8086 | + | 12.2121i | 1.39109 | + | 1.01068i | ||||
\(147\) | −2.25424 | + | 1.63780i | −0.185927 | + | 0.135084i | ||||
\(148\) | 0.312085 | − | 0.960498i | 0.0256532 | − | 0.0789524i | ||||
\(149\) | −0.966119 | + | 2.97341i | −0.0791476 | + | 0.243591i | −0.982799 | − | 0.184677i | \(-0.940876\pi\) |
0.903652 | + | 0.428268i | \(0.140876\pi\) | |||||||
\(150\) | 22.3646 | − | 16.2488i | 1.82606 | − | 1.32671i | ||||
\(151\) | −15.9550 | − | 11.5920i | −1.29840 | − | 0.943343i | −0.298462 | − | 0.954421i | \(-0.596474\pi\) |
−0.999939 | + | 0.0110780i | \(0.996474\pi\) | |||||||
\(152\) | −0.0519869 | − | 0.159999i | −0.00421669 | − | 0.0129777i | ||||
\(153\) | 7.99769 | 0.646575 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.107981 | −0.00867326 | ||||||||
\(156\) | −8.14639 | − | 25.0720i | −0.652233 | − | 2.00737i | ||||
\(157\) | 18.5706 | + | 13.4924i | 1.48210 | + | 1.07681i | 0.976873 | + | 0.213820i | \(0.0685907\pi\) |
0.505226 | + | 0.862987i | \(0.331409\pi\) | |||||||
\(158\) | −9.40058 | + | 6.82992i | −0.747870 | + | 0.543359i | ||||
\(159\) | −3.41022 | + | 10.4956i | −0.270448 | + | 0.832355i | ||||
\(160\) | 0.0659824 | − | 0.203073i | 0.00521637 | − | 0.0160543i | ||||
\(161\) | −6.52267 | + | 4.73900i | −0.514058 | + | 0.373485i | ||||
\(162\) | 0.957483 | + | 0.695652i | 0.0752270 | + | 0.0546556i | ||||
\(163\) | 5.86795 | + | 18.0597i | 0.459613 | + | 1.41454i | 0.865633 | + | 0.500680i | \(0.166917\pi\) |
−0.406019 | + | 0.913864i | \(0.633083\pi\) | |||||||
\(164\) | −20.5435 | −1.60418 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.17061 | 0.401317 | ||||||||
\(167\) | −0.933366 | − | 2.87260i | −0.0722260 | − | 0.222289i | 0.908427 | − | 0.418044i | \(-0.137284\pi\) |
−0.980653 | + | 0.195755i | \(0.937284\pi\) | |||||||
\(168\) | 0.276022 | + | 0.200542i | 0.0212956 | + | 0.0154721i | ||||
\(169\) | −8.75787 | + | 6.36296i | −0.673682 | + | 0.489459i | ||||
\(170\) | −0.0277189 | + | 0.0853099i | −0.00212594 | + | 0.00654297i | ||||
\(171\) | 2.02265 | − | 6.22508i | 0.154676 | − | 0.476044i | ||||
\(172\) | −5.86426 | + | 4.26064i | −0.447146 | + | 0.324870i | ||||
\(173\) | −7.14871 | − | 5.19384i | −0.543506 | − | 0.394880i | 0.281879 | − | 0.959450i | \(-0.409042\pi\) |
−0.825386 | + | 0.564569i | \(0.809042\pi\) | |||||||
\(174\) | −10.9243 | − | 33.6216i | −0.828171 | − | 2.54885i | ||||
\(175\) | −4.99928 | −0.377910 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 27.1122 | 2.03788 | ||||||||
\(178\) | 0.746884 | + | 2.29867i | 0.0559813 | + | 0.172293i | ||||
\(179\) | −6.84779 | − | 4.97521i | −0.511828 | − | 0.371865i | 0.301689 | − | 0.953407i | \(-0.402450\pi\) |
−0.813517 | + | 0.581542i | \(0.802450\pi\) | |||||||
\(180\) | 0.201138 | − | 0.146135i | 0.0149919 | − | 0.0108923i | ||||
\(181\) | −7.47846 | + | 23.0163i | −0.555869 | + | 1.71079i | 0.137767 | + | 0.990465i | \(0.456007\pi\) |
−0.693637 | + | 0.720325i | \(0.743993\pi\) | |||||||
\(182\) | −2.99334 | + | 9.21255i | −0.221881 | + | 0.682880i | ||||
\(183\) | −19.0872 | + | 13.8676i | −1.41096 | + | 1.02512i | ||||
\(184\) | 0.798673 | + | 0.580270i | 0.0588790 | + | 0.0427781i | ||||
\(185\) | −0.00433507 | − | 0.0133420i | −0.000318721 | − | 0.000980922i | ||||
\(186\) | 22.1769 | 1.62609 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −17.3653 | −1.26650 | ||||||||
\(189\) | 1.51887 | + | 4.67460i | 0.110482 | + | 0.340027i | ||||
\(190\) | 0.0593916 | + | 0.0431505i | 0.00430872 | + | 0.00313047i | ||||
\(191\) | 6.29996 | − | 4.57719i | 0.455849 | − | 0.331194i | −0.336052 | − | 0.941844i | \(-0.609092\pi\) |
0.791901 | + | 0.610650i | \(0.209092\pi\) | |||||||
\(192\) | −6.45698 | + | 19.8725i | −0.465992 | + | 1.43418i | ||||
\(193\) | 5.27296 | − | 16.2285i | 0.379556 | − | 1.16815i | −0.560797 | − | 0.827953i | \(-0.689505\pi\) |
0.940353 | − | 0.340200i | \(-0.110495\pi\) | |||||||
\(194\) | −5.45343 | + | 3.96215i | −0.391533 | + | 0.284466i | ||||
\(195\) | −0.296254 | − | 0.215241i | −0.0212152 | − | 0.0154137i | ||||
\(196\) | 0.598967 | + | 1.84343i | 0.0427834 | + | 0.131674i | ||||
\(197\) | −6.05536 | −0.431426 | −0.215713 | − | 0.976457i | \(-0.569208\pi\) | ||||
−0.215713 | + | 0.976457i | \(0.569208\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.7181 | −0.972451 | −0.486226 | − | 0.873833i | \(-0.661627\pi\) | ||||
−0.486226 | + | 0.873833i | \(0.661627\pi\) | |||||||
\(200\) | 0.189162 | + | 0.582180i | 0.0133757 | + | 0.0411663i | ||||
\(201\) | −6.34083 | − | 4.60688i | −0.447248 | − | 0.324945i | ||||
\(202\) | 6.49966 | − | 4.72228i | 0.457314 | − | 0.332258i | ||||
\(203\) | −1.97560 | + | 6.08026i | −0.138660 | + | 0.426750i | ||||
\(204\) | 2.80181 | − | 8.62310i | 0.196166 | − | 0.603737i | ||||
\(205\) | −0.230864 | + | 0.167733i | −0.0161243 | + | 0.0117150i | ||||
\(206\) | 6.34652 | + | 4.61101i | 0.442183 | + | 0.321265i | ||||
\(207\) | 11.8692 | + | 36.5296i | 0.824965 | + | 2.53898i | ||||
\(208\) | 20.1082 | 1.39425 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.148882 | −0.0102738 | ||||||||
\(211\) | 5.57320 | + | 17.1525i | 0.383675 | + | 1.18083i | 0.937437 | + | 0.348155i | \(0.113192\pi\) |
−0.553762 | + | 0.832675i | \(0.686808\pi\) | |||||||
\(212\) | 6.21065 | + | 4.51230i | 0.426549 | + | 0.309906i | ||||
\(213\) | −4.61107 | + | 3.35014i | −0.315945 | + | 0.229548i | ||||
\(214\) | 6.37693 | − | 19.6262i | 0.435918 | − | 1.34162i | ||||
\(215\) | −0.0311145 | + | 0.0957604i | −0.00212199 | + | 0.00653081i | ||||
\(216\) | 0.486900 | − | 0.353753i | 0.0331293 | − | 0.0240699i | ||||
\(217\) | −3.24460 | − | 2.35734i | −0.220258 | − | 0.160026i | ||||
\(218\) | −2.31622 | − | 7.12860i | −0.156874 | − | 0.482810i | ||||
\(219\) | −29.1717 | −1.97124 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.19432 | −0.551210 | ||||||||
\(222\) | 0.890325 | + | 2.74014i | 0.0597547 | + | 0.183906i | ||||
\(223\) | 5.28542 | + | 3.84008i | 0.353938 | + | 0.257151i | 0.750519 | − | 0.660849i | \(-0.229803\pi\) |
−0.396581 | + | 0.918000i | \(0.629803\pi\) | |||||||
\(224\) | 6.41591 | − | 4.66143i | 0.428681 | − | 0.311455i | ||||
\(225\) | −7.35970 | + | 22.6508i | −0.490647 | + | 1.51006i | ||||
\(226\) | 3.89332 | − | 11.9824i | 0.258980 | − | 0.797059i | ||||
\(227\) | −11.0089 | + | 7.99841i | −0.730684 | + | 0.530873i | −0.889780 | − | 0.456390i | \(-0.849142\pi\) |
0.159096 | + | 0.987263i | \(0.449142\pi\) | |||||||
\(228\) | −6.00329 | − | 4.36164i | −0.397577 | − | 0.288857i | ||||
\(229\) | −6.00144 | − | 18.4705i | −0.396586 | − | 1.22057i | −0.927719 | − | 0.373279i | \(-0.878233\pi\) |
0.531133 | − | 0.847289i | \(-0.321767\pi\) | |||||||
\(230\) | −0.430791 | −0.0284055 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.782815 | 0.0513943 | ||||||||
\(233\) | 1.34778 | + | 4.14803i | 0.0882959 | + | 0.271747i | 0.985449 | − | 0.169974i | \(-0.0543683\pi\) |
−0.897153 | + | 0.441721i | \(0.854368\pi\) | |||||||
\(234\) | 37.3338 | + | 27.1246i | 2.44059 | + | 1.77319i | ||||
\(235\) | −0.195149 | + | 0.141784i | −0.0127301 | + | 0.00924895i | ||||
\(236\) | 5.82808 | − | 17.9370i | 0.379376 | − | 1.16760i | ||||
\(237\) | 5.04159 | − | 15.5164i | 0.327486 | − | 1.00790i | ||||
\(238\) | −2.69529 | + | 1.95824i | −0.174710 | + | 0.126934i | ||||
\(239\) | −8.56758 | − | 6.22471i | −0.554191 | − | 0.402643i | 0.275137 | − | 0.961405i | \(-0.411277\pi\) |
−0.829328 | + | 0.558762i | \(0.811277\pi\) | |||||||
\(240\) | 0.0955046 | + | 0.293933i | 0.00616479 | + | 0.0189733i | ||||
\(241\) | 18.6887 | 1.20384 | 0.601921 | − | 0.798555i | \(-0.294402\pi\) | ||||
0.601921 | + | 0.798555i | \(0.294402\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.4072 | −1.05252 | ||||||||
\(244\) | 5.07159 | + | 15.6088i | 0.324675 | + | 0.999248i | ||||
\(245\) | 0.0217822 | + | 0.0158257i | 0.00139162 | + | 0.00101107i | ||||
\(246\) | 47.4142 | − | 34.4485i | 3.02302 | − | 2.19635i | ||||
\(247\) | −2.07238 | + | 6.37813i | −0.131862 | + | 0.405831i | ||||
\(248\) | −0.151750 | + | 0.467039i | −0.00963614 | + | 0.0296570i | ||||
\(249\) | −5.87337 | + | 4.26725i | −0.372210 | + | 0.270426i | ||||
\(250\) | −0.432241 | − | 0.314041i | −0.0273373 | − | 0.0198617i | ||||
\(251\) | 5.86612 | + | 18.0541i | 0.370266 | + | 1.13956i | 0.946617 | + | 0.322360i | \(0.104476\pi\) |
−0.576351 | + | 0.817202i | \(0.695524\pi\) | |||||||
\(252\) | 9.23404 | 0.581690 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −9.98465 | −0.626493 | ||||||||
\(255\) | −0.0389191 | − | 0.119781i | −0.00243721 | − | 0.00750097i | ||||
\(256\) | −13.7056 | − | 9.95771i | −0.856601 | − | 0.622357i | ||||
\(257\) | 11.0908 | − | 8.05797i | 0.691828 | − | 0.502643i | −0.185432 | − | 0.982657i | \(-0.559369\pi\) |
0.877261 | + | 0.480014i | \(0.159369\pi\) | |||||||
\(258\) | 6.39019 | − | 19.6670i | 0.397836 | − | 1.22441i | ||||
\(259\) | 0.161010 | − | 0.495536i | 0.0100046 | − | 0.0307911i | ||||
\(260\) | −0.206083 | + | 0.149728i | −0.0127807 | + | 0.00928575i | ||||
\(261\) | 24.6402 | + | 17.9021i | 1.52519 | + | 1.10811i | ||||
\(262\) | −2.30801 | − | 7.10332i | −0.142589 | − | 0.438844i | ||||
\(263\) | 16.5767 | 1.02217 | 0.511083 | − | 0.859531i | \(-0.329244\pi\) | ||||
0.511083 | + | 0.859531i | \(0.329244\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.106636 | 0.00655059 | ||||||||
\(266\) | 0.842568 | + | 2.59316i | 0.0516611 | + | 0.158997i | ||||
\(267\) | −2.74547 | − | 1.99470i | −0.168020 | − | 0.122074i | ||||
\(268\) | −4.41087 | + | 3.20469i | −0.269437 | + | 0.195757i | ||||
\(269\) | −2.64012 | + | 8.12546i | −0.160971 | + | 0.495418i | −0.998717 | − | 0.0506426i | \(-0.983873\pi\) |
0.837746 | + | 0.546060i | \(0.183873\pi\) | |||||||
\(270\) | −0.0811559 | + | 0.249772i | −0.00493899 | + | 0.0152006i | ||||
\(271\) | 5.13364 | − | 3.72981i | 0.311846 | − | 0.226570i | −0.420842 | − | 0.907134i | \(-0.638265\pi\) |
0.732688 | + | 0.680564i | \(0.238265\pi\) | |||||||
\(272\) | 5.59507 | + | 4.06506i | 0.339251 | + | 0.246480i | ||||
\(273\) | −4.20285 | − | 12.9351i | −0.254368 | − | 0.782865i | ||||
\(274\) | 37.9794 | 2.29442 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 43.5443 | 2.62106 | ||||||||
\(277\) | −7.41776 | − | 22.8295i | −0.445690 | − | 1.37169i | −0.881725 | − | 0.471763i | \(-0.843618\pi\) |
0.436035 | − | 0.899930i | \(-0.356382\pi\) | |||||||
\(278\) | −5.63707 | − | 4.09557i | −0.338089 | − | 0.245636i | ||||
\(279\) | −15.4572 | + | 11.2303i | −0.925400 | + | 0.672342i | ||||
\(280\) | 0.00101876 | − | 0.00313541i | 6.08824e−5 | − | 0.000187377i | ||||
\(281\) | −0.992389 | + | 3.05426i | −0.0592009 | + | 0.182202i | −0.976284 | − | 0.216495i | \(-0.930537\pi\) |
0.917083 | + | 0.398697i | \(0.130537\pi\) | |||||||
\(282\) | 40.0790 | − | 29.1191i | 2.38667 | − | 1.73402i | ||||
\(283\) | 16.8303 | + | 12.2279i | 1.00046 | + | 0.726875i | 0.962186 | − | 0.272393i | \(-0.0878150\pi\) |
0.0382710 | + | 0.999267i | \(0.487815\pi\) | |||||||
\(284\) | 1.22519 | + | 3.77076i | 0.0727018 | + | 0.223753i | ||||
\(285\) | −0.103075 | −0.00610567 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.5987 | −0.625624 | ||||||||
\(288\) | −11.6749 | − | 35.9317i | −0.687951 | − | 2.11730i | ||||
\(289\) | 11.4732 | + | 8.33579i | 0.674896 | + | 0.490341i | ||||
\(290\) | −0.276358 | + | 0.200786i | −0.0162283 | + | 0.0117906i | ||||
\(291\) | 2.92471 | − | 9.00132i | 0.171449 | − | 0.527667i | ||||
\(292\) | −6.27079 | + | 19.2995i | −0.366970 | + | 1.12942i | ||||
\(293\) | −4.46370 | + | 3.24307i | −0.260772 | + | 0.189462i | −0.710487 | − | 0.703710i | \(-0.751526\pi\) |
0.449715 | + | 0.893172i | \(0.351526\pi\) | |||||||
\(294\) | −4.47357 | − | 3.25024i | −0.260904 | − | 0.189558i | ||||
\(295\) | −0.0809562 | − | 0.249157i | −0.00471345 | − | 0.0145065i | ||||
\(296\) | −0.0637988 | −0.00370823 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.20444 | −0.359414 | ||||||||
\(299\) | −12.1610 | − | 37.4277i | −0.703289 | − | 2.16450i | ||||
\(300\) | 21.8438 | + | 15.8704i | 1.26115 | + | 0.916280i | ||||
\(301\) | −3.02547 | + | 2.19813i | −0.174385 | + | 0.126698i | ||||
\(302\) | 12.0942 | − | 37.2221i | 0.695942 | − | 2.14189i | ||||
\(303\) | −3.48581 | + | 10.7282i | −0.200254 | + | 0.616320i | ||||
\(304\) | 4.57910 | − | 3.32691i | 0.262629 | − | 0.190811i | ||||
\(305\) | 0.184435 | + | 0.134000i | 0.0105607 | + | 0.00767282i | ||||
\(306\) | 4.90457 | + | 15.0947i | 0.280376 | + | 0.862908i | ||||
\(307\) | 8.60991 | 0.491394 | 0.245697 | − | 0.969347i | \(-0.420983\pi\) | ||||
0.245697 | + | 0.969347i | \(0.420983\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.0145 | −0.626594 | ||||||||
\(310\) | −0.0662193 | − | 0.203802i | −0.00376100 | − | 0.0115752i | ||||
\(311\) | −15.4731 | − | 11.2419i | −0.877400 | − | 0.637469i | 0.0551620 | − | 0.998477i | \(-0.482432\pi\) |
−0.932562 | + | 0.361009i | \(0.882432\pi\) | |||||||
\(312\) | −1.34730 | + | 0.978868i | −0.0762756 | + | 0.0554175i | ||||
\(313\) | −0.187498 | + | 0.577058i | −0.0105980 | + | 0.0326173i | −0.956216 | − | 0.292663i | \(-0.905459\pi\) |
0.945618 | + | 0.325280i | \(0.105459\pi\) | |||||||
\(314\) | −14.0769 | + | 43.3241i | −0.794404 | + | 2.44492i | ||||
\(315\) | 0.103770 | − | 0.0753936i | 0.00584680 | − | 0.00424795i | ||||
\(316\) | −9.18166 | − | 6.67087i | −0.516509 | − | 0.375266i | ||||
\(317\) | −1.61085 | − | 4.95769i | −0.0904745 | − | 0.278452i | 0.895573 | − | 0.444914i | \(-0.146766\pi\) |
−0.986048 | + | 0.166462i | \(0.946766\pi\) | |||||||
\(318\) | −21.9005 | −1.22812 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.201906 | 0.0112869 | ||||||||
\(321\) | 8.95364 | + | 27.5565i | 0.499744 | + | 1.53805i | ||||
\(322\) | −12.9443 | − | 9.40461i | −0.721360 | − | 0.524098i | ||||
\(323\) | −1.86603 | + | 1.35575i | −0.103829 | + | 0.0754361i | ||||
\(324\) | −0.357209 | + | 1.09938i | −0.0198449 | + | 0.0610765i | ||||
\(325\) | 7.54065 | − | 23.2077i | 0.418280 | − | 1.28733i | ||||
\(326\) | −30.4871 | + | 22.1502i | −1.68852 | + | 1.22678i | ||||
\(327\) | 8.51420 | + | 6.18593i | 0.470836 | + | 0.342083i | ||||
\(328\) | 0.401033 | + | 1.23425i | 0.0221434 | + | 0.0681502i | ||||
\(329\) | −8.95906 | −0.493929 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.669012 | 0.0367722 | 0.0183861 | − | 0.999831i | \(-0.494147\pi\) | ||||
0.0183861 | + | 0.999831i | \(0.494147\pi\) | |||||||
\(332\) | 1.56060 | + | 4.80302i | 0.0856488 | + | 0.263600i | ||||
\(333\) | −2.00816 | − | 1.45901i | −0.110046 | − | 0.0799533i | ||||
\(334\) | 4.84933 | − | 3.52324i | 0.265343 | − | 0.192783i | ||||
\(335\) | −0.0234031 | + | 0.0720274i | −0.00127865 | + | 0.00393527i | ||||
\(336\) | −3.54715 | + | 10.9170i | −0.193513 | + | 0.595571i | ||||
\(337\) | 5.34125 | − | 3.88065i | 0.290957 | − | 0.211392i | −0.432726 | − | 0.901526i | \(-0.642448\pi\) |
0.723682 | + | 0.690133i | \(0.242448\pi\) | |||||||
\(338\) | −17.3801 | − | 12.6274i | −0.945354 | − | 0.686840i | ||||
\(339\) | 5.46649 | + | 16.8241i | 0.296899 | + | 0.913761i | ||||
\(340\) | −0.0876111 | −0.00475138 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 12.9895 | 0.702393 | ||||||||
\(343\) | 0.309017 | + | 0.951057i | 0.0166853 | + | 0.0513522i | ||||
\(344\) | 0.370456 | + | 0.269152i | 0.0199736 | + | 0.0145117i | ||||
\(345\) | 0.489342 | − | 0.355528i | 0.0263453 | − | 0.0191410i | ||||
\(346\) | 5.41885 | − | 16.6775i | 0.291319 | − | 0.896587i | ||||
\(347\) | 3.77005 | − | 11.6030i | 0.202387 | − | 0.622882i | −0.797424 | − | 0.603420i | \(-0.793804\pi\) |
0.999811 | − | 0.0194628i | \(-0.00619560\pi\) | |||||||
\(348\) | 27.9342 | − | 20.2954i | 1.49743 | − | 1.08795i | ||||
\(349\) | 0.716627 | + | 0.520660i | 0.0383602 | + | 0.0278703i | 0.606800 | − | 0.794854i | \(-0.292453\pi\) |
−0.568440 | + | 0.822725i | \(0.692453\pi\) | |||||||
\(350\) | −3.06580 | − | 9.43556i | −0.163874 | − | 0.504352i | ||||
\(351\) | −23.9915 | −1.28057 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.36012 | 0.285291 | 0.142645 | − | 0.989774i | \(-0.454439\pi\) | ||||
0.142645 | + | 0.989774i | \(0.454439\pi\) | |||||||
\(354\) | 16.6265 | + | 51.1712i | 0.883690 | + | 2.71972i | ||||
\(355\) | 0.0445558 | + | 0.0323717i | 0.00236477 | + | 0.00171811i | ||||
\(356\) | −1.90983 | + | 1.38757i | −0.101221 | + | 0.0735413i | ||||
\(357\) | 1.44550 | − | 4.44879i | 0.0765040 | − | 0.235455i | ||||
\(358\) | 5.19074 | − | 15.9755i | 0.274339 | − | 0.844330i | ||||
\(359\) | −20.9090 | + | 15.1913i | −1.10354 | + | 0.801767i | −0.981634 | − | 0.190775i | \(-0.938900\pi\) |
−0.121903 | + | 0.992542i | \(0.538900\pi\) | |||||||
\(360\) | −0.0127062 | − | 0.00923162i | −0.000669677 | − | 0.000486549i | ||||
\(361\) | −5.28799 | − | 16.2748i | −0.278315 | − | 0.856566i | ||||
\(362\) | −48.0268 | −2.52423 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.46107 | −0.495895 | ||||||||
\(365\) | 0.0871057 | + | 0.268084i | 0.00455932 | + | 0.0140321i | ||||
\(366\) | −37.8787 | − | 27.5205i | −1.97995 | − | 1.43852i | ||||
\(367\) | 16.5448 | − | 12.0205i | 0.863629 | − | 0.627463i | −0.0652408 | − | 0.997870i | \(-0.520782\pi\) |
0.928870 | + | 0.370406i | \(0.120782\pi\) | |||||||
\(368\) | −10.2637 | + | 31.5885i | −0.535033 | + | 1.64666i | ||||
\(369\) | −15.6030 | + | 48.0210i | −0.812259 | + | 2.49987i | ||||
\(370\) | 0.0225230 | − | 0.0163639i | 0.00117091 | − | 0.000850719i | ||||
\(371\) | 3.20417 | + | 2.32797i | 0.166352 | + | 0.120862i | ||||
\(372\) | 6.69343 | + | 20.6003i | 0.347038 | + | 1.06807i | ||||
\(373\) | 9.39109 | 0.486252 | 0.243126 | − | 0.969995i | \(-0.421827\pi\) | ||||
0.243126 | + | 0.969995i | \(0.421827\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.750163 | 0.0387383 | ||||||||
\(376\) | 0.338991 | + | 1.04331i | 0.0174821 | + | 0.0538045i | ||||
\(377\) | −25.2460 | − | 18.3423i | −1.30024 | − | 0.944676i | ||||
\(378\) | −7.89133 | + | 5.73339i | −0.405886 | + | 0.294894i | ||||
\(379\) | −1.74160 | + | 5.36009i | −0.0894599 | + | 0.275329i | −0.985770 | − | 0.168098i | \(-0.946238\pi\) |
0.896310 | + | 0.443427i | \(0.146238\pi\) | |||||||
\(380\) | −0.0221573 | + | 0.0681931i | −0.00113664 | + | 0.00349823i | ||||
\(381\) | 11.3417 | − | 8.24024i | 0.581054 | − | 0.422160i | ||||
\(382\) | 12.5024 | + | 9.08350i | 0.639677 | + | 0.464752i | ||||
\(383\) | −0.389189 | − | 1.19780i | −0.0198866 | − | 0.0612047i | 0.940621 | − | 0.339459i | \(-0.110244\pi\) |
−0.960507 | + | 0.278255i | \(0.910244\pi\) | |||||||
\(384\) | 2.72816 | 0.139221 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 33.8631 | 1.72359 | ||||||||
\(387\) | 5.50539 | + | 16.9438i | 0.279855 | + | 0.861304i | ||||
\(388\) | −5.32643 | − | 3.86988i | −0.270408 | − | 0.196463i | ||||
\(389\) | 4.76033 | − | 3.45858i | 0.241358 | − | 0.175357i | −0.460530 | − | 0.887644i | \(-0.652341\pi\) |
0.701888 | + | 0.712287i | \(0.252341\pi\) | |||||||
\(390\) | 0.224566 | − | 0.691142i | 0.0113713 | − | 0.0349974i | ||||
\(391\) | 4.18257 | − | 12.8726i | 0.211522 | − | 0.650997i | ||||
\(392\) | 0.0990607 | − | 0.0719718i | 0.00500332 | − | 0.00363512i | ||||
\(393\) | 8.48400 | + | 6.16399i | 0.427961 | + | 0.310932i | ||||
\(394\) | −3.71344 | − | 11.4288i | −0.187080 | − | 0.575774i | ||||
\(395\) | −0.157648 | −0.00793212 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.86018 | 0.243925 | 0.121963 | − | 0.992535i | \(-0.461081\pi\) | ||||
0.121963 | + | 0.992535i | \(0.461081\pi\) | |||||||
\(398\) | −8.41261 | − | 25.8914i | −0.421686 | − | 1.29782i | ||||
\(399\) | −3.09719 | − | 2.25024i | −0.155054 | − | 0.112653i | ||||
\(400\) | −16.6617 | + | 12.1054i | −0.833085 | + | 0.605271i | ||||
\(401\) | −7.88987 | + | 24.2825i | −0.394001 | + | 1.21261i | 0.535735 | + | 0.844386i | \(0.320035\pi\) |
−0.929736 | + | 0.368226i | \(0.879965\pi\) | |||||||
\(402\) | 4.80646 | − | 14.7928i | 0.239724 | − | 0.737796i | ||||
\(403\) | 15.8373 | − | 11.5064i | 0.788910 | − | 0.573177i | ||||
\(404\) | 6.34830 | + | 4.61231i | 0.315839 | + | 0.229471i | ||||
\(405\) | 0.00496188 | + | 0.0152711i | 0.000246558 | + | 0.000758827i | ||||
\(406\) | −12.6873 | −0.629661 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.572769 | −0.0283563 | ||||||||
\(409\) | 6.49760 | + | 19.9975i | 0.321285 | + | 0.988815i | 0.973090 | + | 0.230427i | \(0.0740124\pi\) |
−0.651804 | + | 0.758387i | \(0.725988\pi\) | |||||||
\(410\) | −0.458154 | − | 0.332868i | −0.0226266 | − | 0.0164392i | ||||
\(411\) | −43.1413 | + | 31.3440i | −2.12801 | + | 1.54609i | ||||
\(412\) | −2.36770 | + | 7.28703i | −0.116648 | + | 0.359006i | ||||
\(413\) | 3.00680 | − | 9.25399i | 0.147955 | − | 0.455359i | ||||
\(414\) | −61.6667 | + | 44.8035i | −3.03075 | + | 2.20197i | ||||
\(415\) | 0.0567531 | + | 0.0412335i | 0.00278590 | + | 0.00202408i | ||||
\(416\) | 11.9620 | + | 36.8151i | 0.586484 | + | 1.80501i | ||||
\(417\) | 9.78326 | 0.479088 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.3141 | −1.52980 | −0.764898 | − | 0.644151i | \(-0.777211\pi\) | ||||
−0.764898 | + | 0.644151i | \(0.777211\pi\) | |||||||
\(420\) | −0.0449356 | − | 0.138298i | −0.00219263 | − | 0.00674823i | ||||
\(421\) | −10.3462 | − | 7.51698i | −0.504244 | − | 0.366355i | 0.306391 | − | 0.951906i | \(-0.400878\pi\) |
−0.810636 | + | 0.585551i | \(0.800878\pi\) | |||||||
\(422\) | −28.9557 | + | 21.0376i | −1.40954 | + | 1.02409i | ||||
\(423\) | −13.1891 | + | 40.5919i | −0.641277 | + | 1.97365i | ||||
\(424\) | 0.149859 | − | 0.461220i | 0.00727782 | − | 0.0223988i | ||||
\(425\) | 6.78982 | − | 4.93309i | 0.329355 | − | 0.239290i | ||||
\(426\) | −9.15073 | − | 6.64839i | −0.443354 | − | 0.322116i | ||||
\(427\) | 2.61652 | + | 8.05281i | 0.126622 | + | 0.389703i | ||||
\(428\) | 20.1556 | 0.974258 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.199818 | −0.00963607 | ||||||||
\(431\) | 6.51033 | + | 20.0367i | 0.313592 | + | 0.965136i | 0.976330 | + | 0.216285i | \(0.0693941\pi\) |
−0.662738 | + | 0.748851i | \(0.730606\pi\) | |||||||
\(432\) | 16.3814 | + | 11.9018i | 0.788149 | + | 0.572624i | ||||
\(433\) | −30.7451 | + | 22.3376i | −1.47752 | + | 1.07348i | −0.499169 | + | 0.866505i | \(0.666361\pi\) |
−0.978347 | + | 0.206973i | \(0.933639\pi\) | |||||||
\(434\) | 2.45946 | − | 7.56944i | 0.118058 | − | 0.363345i | ||||
\(435\) | 0.148213 | − | 0.456152i | 0.00710625 | − | 0.0218708i | ||||
\(436\) | 5.92273 | − | 4.30312i | 0.283647 | − | 0.206082i | ||||
\(437\) | −8.96176 | − | 6.51110i | −0.428699 | − | 0.311468i | ||||
\(438\) | −17.8895 | − | 55.0582i | −0.854793 | − | 2.63078i | ||||
\(439\) | −37.7677 | −1.80256 | −0.901278 | − | 0.433241i | \(-0.857370\pi\) | ||||
−0.901278 | + | 0.433241i | \(0.857370\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.76399 | 0.226857 | ||||||||
\(442\) | −5.02516 | − | 15.4658i | −0.239022 | − | 0.735635i | ||||
\(443\) | 0.831607 | + | 0.604198i | 0.0395108 | + | 0.0287063i | 0.607365 | − | 0.794423i | \(-0.292226\pi\) |
−0.567855 | + | 0.823129i | \(0.692226\pi\) | |||||||
\(444\) | −2.27662 | + | 1.65406i | −0.108044 | + | 0.0784982i | ||||
\(445\) | −0.0101331 | + | 0.0311866i | −0.000480357 | + | 0.00147839i | ||||
\(446\) | −4.00644 | + | 12.3306i | −0.189710 | + | 0.583869i | ||||
\(447\) | 7.04772 | − | 5.12047i | 0.333346 | − | 0.242190i | ||||
\(448\) | 6.06683 | + | 4.40781i | 0.286631 | + | 0.208250i | ||||
\(449\) | 6.22153 | + | 19.1479i | 0.293612 | + | 0.903645i | 0.983684 | + | 0.179904i | \(0.0575789\pi\) |
−0.690072 | + | 0.723741i | \(0.742421\pi\) | |||||||
\(450\) | −47.2642 | −2.22806 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 12.3057 | 0.578809 | ||||||||
\(453\) | 16.9810 | + | 52.2623i | 0.797839 | + | 2.45550i | ||||
\(454\) | −21.8473 | − | 15.8730i | −1.02534 | − | 0.744955i | ||||
\(455\) | −0.106322 | + | 0.0772472i | −0.00498444 | + | 0.00362141i | ||||
\(456\) | −0.144856 | + | 0.445821i | −0.00678350 | + | 0.0208775i | ||||
\(457\) | −7.46140 | + | 22.9638i | −0.349030 | + | 1.07420i | 0.610362 | + | 0.792123i | \(0.291024\pi\) |
−0.959391 | + | 0.282079i | \(0.908976\pi\) | |||||||
\(458\) | 31.1807 | − | 22.6541i | 1.45698 | − | 1.05856i | ||||
\(459\) | −6.67559 | − | 4.85010i | −0.311590 | − | 0.226383i | ||||
\(460\) | −0.130022 | − | 0.400166i | −0.00606229 | − | 0.0186578i | ||||
\(461\) | 11.5885 | 0.539731 | 0.269865 | − | 0.962898i | \(-0.413021\pi\) | ||||
0.269865 | + | 0.962898i | \(0.413021\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.6077 | 1.00419 | 0.502097 | − | 0.864811i | \(-0.332562\pi\) | ||||
0.502097 | + | 0.864811i | \(0.332562\pi\) | |||||||
\(464\) | 8.13865 | + | 25.0482i | 0.377827 | + | 1.16283i | ||||
\(465\) | 0.243415 | + | 0.176852i | 0.0112881 | + | 0.00820130i | ||||
\(466\) | −7.00242 | + | 5.08756i | −0.324381 | + | 0.235676i | ||||
\(467\) | 4.91799 | − | 15.1360i | 0.227577 | − | 0.700411i | −0.770442 | − | 0.637510i | \(-0.779965\pi\) |
0.998020 | − | 0.0629015i | \(-0.0200354\pi\) | |||||||
\(468\) | −13.9281 | + | 42.8664i | −0.643829 | + | 1.98150i | ||||
\(469\) | −2.27564 | + | 1.65335i | −0.105079 | + | 0.0763446i | ||||
\(470\) | −0.387275 | − | 0.281372i | −0.0178637 | − | 0.0129787i | ||||
\(471\) | −19.7649 | − | 60.8300i | −0.910717 | − | 2.80290i | ||||
\(472\) | −1.19142 | −0.0548397 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 32.3772 | 1.48713 | ||||||||
\(475\) | −2.12255 | − | 6.53253i | −0.0973892 | − | 0.299733i | ||||
\(476\) | −2.63252 | − | 1.91264i | −0.120661 | − | 0.0876657i | ||||
\(477\) | 15.2646 | − | 11.0904i | 0.698920 | − | 0.507795i | ||||
\(478\) | 6.49438 | − | 19.9876i | 0.297046 | − | 0.914213i | ||||
\(479\) | 1.63276 | − | 5.02511i | 0.0746026 | − | 0.229603i | −0.906801 | − | 0.421559i | \(-0.861483\pi\) |
0.981404 | + | 0.191956i | \(0.0614830\pi\) | |||||||
\(480\) | −0.481333 | + | 0.349709i | −0.0219698 | + | 0.0159620i | ||||
\(481\) | 2.05753 | + | 1.49488i | 0.0938153 | + | 0.0681608i | ||||
\(482\) | 11.4608 | + | 35.2727i | 0.522025 | + | 1.60663i | ||||
\(483\) | 22.4652 | 1.02220 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.0914540 | −0.00415271 | ||||||||
\(486\) | −10.0617 | − | 30.9668i | −0.456409 | − | 1.40468i | ||||
\(487\) | 21.8965 | + | 15.9087i | 0.992225 | + | 0.720894i | 0.960407 | − | 0.278600i | \(-0.0898704\pi\) |
0.0318177 | + | 0.999494i | \(0.489870\pi\) | |||||||
\(488\) | 0.838769 | − | 0.609401i | 0.0379693 | − | 0.0275863i | ||||
\(489\) | 16.3504 | − | 50.3214i | 0.739391 | − | 2.27561i | ||||
\(490\) | −0.0165113 | + | 0.0508166i | −0.000745905 | + | 0.00229566i | ||||
\(491\) | −15.2095 | + | 11.0503i | −0.686395 | + | 0.498695i | −0.875473 | − | 0.483267i | \(-0.839450\pi\) |
0.189078 | + | 0.981962i | \(0.439450\pi\) | |||||||
\(492\) | 46.3101 | + | 33.6462i | 2.08782 | + | 1.51689i | ||||
\(493\) | −3.31659 | − | 10.2074i | −0.149372 | − | 0.459719i | ||||
\(494\) | −13.3089 | −0.598795 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16.5218 | −0.741851 | ||||||||
\(497\) | 0.632097 | + | 1.94539i | 0.0283534 | + | 0.0872629i | ||||
\(498\) | −11.6558 | − | 8.46842i | −0.522308 | − | 0.379479i | ||||
\(499\) | 32.1719 | − | 23.3743i | 1.44021 | − | 1.04638i | 0.452214 | − | 0.891909i | \(-0.350634\pi\) |
0.987998 | − | 0.154466i | \(-0.0493657\pi\) | |||||||
\(500\) | 0.161256 | − | 0.496296i | 0.00721160 | − | 0.0221950i | ||||
\(501\) | −2.60072 | + | 8.00421i | −0.116192 | + | 0.357602i | ||||
\(502\) | −30.4776 | + | 22.1433i | −1.36028 | + | 0.988302i | ||||
\(503\) | −32.8157 | − | 23.8420i | −1.46318 | − | 1.06306i | −0.982521 | − | 0.186154i | \(-0.940398\pi\) |
−0.480658 | − | 0.876908i | \(-0.659602\pi\) | |||||||
\(504\) | −0.180259 | − | 0.554780i | −0.00802937 | − | 0.0247119i | ||||
\(505\) | 0.108999 | 0.00485040 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 30.1636 | 1.33961 | ||||||||
\(508\) | −3.01357 | − | 9.27483i | −0.133706 | − | 0.411504i | ||||
\(509\) | 12.5243 | + | 9.09945i | 0.555131 | + | 0.403326i | 0.829674 | − | 0.558249i | \(-0.188527\pi\) |
−0.274543 | + | 0.961575i | \(0.588527\pi\) | |||||||
\(510\) | 0.202206 | − | 0.146911i | 0.00895381 | − | 0.00650532i | ||||
\(511\) | −3.23520 | + | 9.95693i | −0.143117 | + | 0.440469i | ||||
\(512\) | 9.78397 | − | 30.1120i | 0.432395 | − | 1.33077i | ||||
\(513\) | −5.46341 | + | 3.96940i | −0.241216 | + | 0.175253i | ||||
\(514\) | 22.0100 | + | 15.9912i | 0.970817 | + | 0.705340i | ||||
\(515\) | 0.0328890 | + | 0.101222i | 0.00144926 | + | 0.00446037i | ||||
\(516\) | 20.1975 | 0.889147 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 1.03401 | 0.0454317 | ||||||||
\(519\) | 7.60843 | + | 23.4163i | 0.333973 | + | 1.02786i | ||||
\(520\) | 0.0130186 | + | 0.00945859i | 0.000570905 | + | 0.000414787i | ||||
\(521\) | −30.3169 | + | 22.0265i | −1.32821 | + | 0.965000i | −0.328418 | + | 0.944532i | \(0.606516\pi\) |
−0.999791 | + | 0.0204678i | \(0.993484\pi\) | |||||||
\(522\) | −18.6777 | + | 57.4840i | −0.817500 | + | 2.51601i | ||||
\(523\) | −6.43111 | + | 19.7929i | −0.281213 | + | 0.865484i | 0.706295 | + | 0.707917i | \(0.250365\pi\) |
−0.987508 | + | 0.157567i | \(0.949635\pi\) | |||||||
\(524\) | 5.90172 | − | 4.28785i | 0.257818 | − | 0.187316i | ||||
\(525\) | 11.2696 | + | 8.18782i | 0.491844 | + | 0.357346i | ||||
\(526\) | 10.1657 | + | 31.2867i | 0.443244 | + | 1.36417i | ||||
\(527\) | 6.73281 | 0.293286 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 42.0033 | 1.82623 | ||||||||
\(530\) | 0.0653943 | + | 0.201263i | 0.00284055 | + | 0.00874230i | ||||
\(531\) | −37.5017 | − | 27.2466i | −1.62744 | − | 1.18240i | ||||
\(532\) | −2.15450 | + | 1.56534i | −0.0934094 | + | 0.0678659i | ||||
\(533\) | 15.9866 | − | 49.2017i | 0.692456 | − | 2.13116i | ||||
\(534\) | 2.08111 | − | 6.40501i | 0.0900586 | − | 0.277172i | ||||
\(535\) | 0.226505 | − | 0.164565i | 0.00979266 | − | 0.00711478i | ||||
\(536\) | 0.278643 | + | 0.202446i | 0.0120355 | + | 0.00874432i | ||||
\(537\) | 7.28816 | + | 22.4306i | 0.314507 | + | 0.967954i | ||||
\(538\) | −16.9549 | −0.730979 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.256510 | −0.0110384 | ||||||||
\(541\) | −5.38488 | − | 16.5730i | −0.231514 | − | 0.712528i | −0.997565 | − | 0.0697472i | \(-0.977781\pi\) |
0.766050 | − | 0.642780i | \(-0.222219\pi\) | |||||||
\(542\) | 10.1878 | + | 7.40186i | 0.437603 | + | 0.317937i | ||||
\(543\) | 54.5544 | − | 39.6361i | 2.34115 | − | 1.70095i | ||||
\(544\) | −4.11412 | + | 12.6620i | −0.176391 | + | 0.542877i | ||||
\(545\) | 0.0314247 | − | 0.0967152i | 0.00134609 | − | 0.00414283i | ||||
\(546\) | 21.8360 | − | 15.8648i | 0.934496 | − | 0.678951i | ||||
\(547\) | 12.7792 | + | 9.28463i | 0.546399 | + | 0.396982i | 0.826456 | − | 0.563001i | \(-0.190353\pi\) |
−0.280057 | + | 0.959983i | \(0.590353\pi\) | |||||||
\(548\) | 11.4630 | + | 35.2794i | 0.489673 | + | 1.50706i | ||||
\(549\) | 40.3378 | 1.72157 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.78382 | −0.374203 | ||||||||
\(552\) | −0.850034 | − | 2.61613i | −0.0361798 | − | 0.111350i | ||||
\(553\) | −4.73697 | − | 3.44161i | −0.201436 | − | 0.146352i | ||||
\(554\) | 38.5392 | − | 28.0004i | 1.63737 | − | 1.18962i | ||||
\(555\) | −0.0120792 | + | 0.0371760i | −0.000512734 | + | 0.00157803i | ||||
\(556\) | 2.10303 | − | 6.47245i | 0.0891881 | − | 0.274493i | ||||
\(557\) | 13.6199 | − | 9.89541i | 0.577092 | − | 0.419282i | −0.260582 | − | 0.965452i | \(-0.583915\pi\) |
0.837675 | + | 0.546170i | \(0.183915\pi\) | |||||||
\(558\) | −30.6751 | − | 22.2868i | −1.29858 | − | 0.943474i | ||||
\(559\) | −5.64075 | − | 17.3604i | −0.238578 | − | 0.734268i | ||||
\(560\) | 0.110917 | 0.00468711 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.37315 | −0.268835 | ||||||||
\(563\) | −11.5666 | − | 35.5984i | −0.487475 | − | 1.50029i | −0.828364 | − | 0.560190i | \(-0.810728\pi\) |
0.340889 | − | 0.940104i | \(-0.389272\pi\) | |||||||
\(564\) | 39.1457 | + | 28.4410i | 1.64833 | + | 1.19758i | ||||
\(565\) | 0.138289 | − | 0.100473i | 0.00581785 | − | 0.00422691i | ||||
\(566\) | −12.7577 | + | 39.2640i | −0.536244 | + | 1.65039i | ||||
\(567\) | −0.184290 | + | 0.567186i | −0.00773945 | + | 0.0238196i | ||||
\(568\) | 0.202629 | − | 0.147219i | 0.00850214 | − | 0.00617717i | ||||
\(569\) | 2.24025 | + | 1.62763i | 0.0939160 | + | 0.0682340i | 0.633752 | − | 0.773536i | \(-0.281514\pi\) |
−0.539836 | + | 0.841770i | \(0.681514\pi\) | |||||||
\(570\) | −0.0632109 | − | 0.194543i | −0.00264761 | − | 0.00814852i | ||||
\(571\) | −8.85289 | −0.370482 | −0.185241 | − | 0.982693i | \(-0.559307\pi\) | ||||
−0.185241 | + | 0.982693i | \(0.559307\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.6981 | −0.906453 | ||||||||
\(574\) | −6.49967 | − | 20.0039i | −0.271291 | − | 0.834947i | ||||
\(575\) | 32.6086 | + | 23.6916i | 1.35987 | + | 0.988006i | ||||
\(576\) | 28.9023 | − | 20.9988i | 1.20426 | − | 0.874949i | ||||
\(577\) | 11.4856 | − | 35.3491i | 0.478152 | − | 1.47160i | −0.363506 | − | 0.931592i | \(-0.618420\pi\) |
0.841659 | − | 0.540010i | \(-0.181580\pi\) | |||||||
\(578\) | −8.69691 | + | 26.7663i | −0.361744 | + | 1.11333i | ||||
\(579\) | −38.4656 | + | 27.9469i | −1.59857 | + | 1.16143i | ||||
\(580\) | −0.269922 | − | 0.196110i | −0.0112079 | − | 0.00814303i | ||||
\(581\) | 0.805136 | + | 2.47795i | 0.0334027 | + | 0.102803i | ||||
\(582\) | 18.7825 | 0.778562 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.28193 | 0.0530464 | ||||||||
\(585\) | 0.193472 | + | 0.595445i | 0.00799907 | + | 0.0246186i | ||||
\(586\) | −8.85829 | − | 6.43592i | −0.365933 | − | 0.265866i | ||||
\(587\) | 28.5736 | − | 20.7599i | 1.17936 | − | 0.856854i | 0.187259 | − | 0.982311i | \(-0.440040\pi\) |
0.992099 | + | 0.125457i | \(0.0400396\pi\) | |||||||
\(588\) | 1.66896 | − | 5.13653i | 0.0688267 | − | 0.211827i | ||||
\(589\) | 1.70276 | − | 5.24056i | 0.0701610 | − | 0.215933i | ||||
\(590\) | 0.420610 | − | 0.305591i | 0.0173162 | − | 0.0125810i | ||||
\(591\) | 13.6502 | + | 9.91747i | 0.561495 | + | 0.407950i | ||||
\(592\) | −0.663294 | − | 2.04141i | −0.0272612 | − | 0.0839014i | ||||
\(593\) | −8.09224 | −0.332308 | −0.166154 | − | 0.986100i | \(-0.553135\pi\) | ||||
−0.166154 | + | 0.986100i | \(0.553135\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0452000 | −0.00185302 | ||||||||
\(596\) | −1.87263 | − | 5.76336i | −0.0767058 | − | 0.236076i | ||||
\(597\) | 30.9239 | + | 22.4675i | 1.26563 | + | 0.919535i | ||||
\(598\) | 63.1828 | − | 45.9050i | 2.58374 | − | 1.87720i | ||||
\(599\) | 1.18544 | − | 3.64841i | 0.0484357 | − | 0.149070i | −0.923913 | − | 0.382601i | \(-0.875028\pi\) |
0.972349 | + | 0.233532i | \(0.0750282\pi\) | |||||||
\(600\) | 0.527079 | − | 1.62218i | 0.0215179 | − | 0.0662253i | ||||
\(601\) | 11.5986 | − | 8.42687i | 0.473116 | − | 0.343739i | −0.325538 | − | 0.945529i | \(-0.605545\pi\) |
0.798655 | + | 0.601790i | \(0.205545\pi\) | |||||||
\(602\) | −6.00409 | − | 4.36222i | −0.244708 | − | 0.177791i | ||||
\(603\) | 4.14094 | + | 12.7445i | 0.168632 | + | 0.518997i | ||||
\(604\) | 38.2261 | 1.55540 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −22.3859 | −0.909367 | ||||||||
\(607\) | 4.25781 | + | 13.1042i | 0.172819 | + | 0.531883i | 0.999527 | − | 0.0307486i | \(-0.00978911\pi\) |
−0.826708 | + | 0.562631i | \(0.809789\pi\) | |||||||
\(608\) | 8.81508 | + | 6.40453i | 0.357499 | + | 0.259738i | ||||
\(609\) | 14.4117 | − | 10.4707i | 0.583992 | − | 0.424295i | ||||
\(610\) | −0.139805 | + | 0.430276i | −0.00566054 | + | 0.0174214i | ||||
\(611\) | 13.5134 | − | 41.5899i | 0.546693 | − | 1.68255i | ||||
\(612\) | −12.5413 | + | 9.11179i | −0.506952 | + | 0.368322i | ||||
\(613\) | 7.72154 | + | 5.61003i | 0.311870 | + | 0.226587i | 0.732699 | − | 0.680553i | \(-0.238261\pi\) |
−0.420828 | + | 0.907140i | \(0.638261\pi\) | |||||||
\(614\) | 5.28002 | + | 16.2502i | 0.213084 | + | 0.655806i | ||||
\(615\) | 0.795137 | 0.0320630 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.5153 | −1.26876 | −0.634379 | − | 0.773023i | \(-0.718744\pi\) | ||||
−0.634379 | + | 0.773023i | \(0.718744\pi\) | |||||||
\(618\) | −6.75464 | − | 20.7887i | −0.271712 | − | 0.836243i | ||||
\(619\) | −16.6089 | − | 12.0671i | −0.667568 | − | 0.485016i | 0.201642 | − | 0.979459i | \(-0.435372\pi\) |
−0.869210 | + | 0.494443i | \(0.835372\pi\) | |||||||
\(620\) | 0.169327 | − | 0.123023i | 0.00680034 | − | 0.00494074i | ||||
\(621\) | 12.2458 | − | 37.6888i | 0.491409 | − | 1.51240i | ||||
\(622\) | 11.7289 | − | 36.0978i | 0.470286 | − | 1.44739i | ||||
\(623\) | −0.985313 | + | 0.715872i | −0.0394757 | + | 0.0286808i | ||||
\(624\) | −45.3288 | − | 32.9333i | −1.81460 | − | 1.31839i | ||||
\(625\) | 7.72206 | + | 23.7661i | 0.308883 | + | 0.950643i | ||||
\(626\) | −1.20411 | −0.0481261 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −44.4928 | −1.77546 | ||||||||
\(629\) | 0.270299 | + | 0.831896i | 0.0107775 | + | 0.0331699i | ||||
\(630\) | 0.205934 | + | 0.149620i | 0.00820460 | + | 0.00596099i | ||||
\(631\) | −29.0970 | + | 21.1402i | −1.15833 | + | 0.841578i | −0.989566 | − | 0.144078i | \(-0.953978\pi\) |
−0.168766 | + | 0.985656i | \(0.553978\pi\) | |||||||
\(632\) | −0.221548 | + | 0.681856i | −0.00881272 | + | 0.0271228i | ||||
\(633\) | 15.5291 | − | 47.7937i | 0.617227 | − | 1.89963i | ||||
\(634\) | 8.36923 | − | 6.08060i | 0.332384 | − | 0.241491i | ||||
\(635\) | −0.109593 | − | 0.0796237i | −0.00434905 | − | 0.00315977i | ||||
\(636\) | −6.61004 | − | 20.3436i | −0.262105 | − | 0.806676i | ||||
\(637\) | −4.88112 | −0.193397 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.74478 | 0.385498 | ||||||||
\(640\) | −0.00814618 | − | 0.0250714i | −0.000322006 | − | 0.000991033i | ||||
\(641\) | −11.0192 | − | 8.00590i | −0.435232 | − | 0.316214i | 0.348506 | − | 0.937307i | \(-0.386689\pi\) |
−0.783737 | + | 0.621092i | \(0.786689\pi\) | |||||||
\(642\) | −46.5189 | + | 33.7980i | −1.83595 | + | 1.33390i | ||||
\(643\) | 6.79501 | − | 20.9129i | 0.267969 | − | 0.824724i | −0.723026 | − | 0.690821i | \(-0.757249\pi\) |
0.990995 | − | 0.133902i | \(-0.0427509\pi\) | |||||||
\(644\) | 4.82915 | − | 14.8626i | 0.190295 | − | 0.585669i | ||||
\(645\) | 0.226976 | − | 0.164908i | 0.00893717 | − | 0.00649323i | ||||
\(646\) | −3.70317 | − | 2.69051i | −0.145699 | − | 0.105857i | ||||
\(647\) | −4.57971 | − | 14.0949i | −0.180047 | − | 0.554128i | 0.819781 | − | 0.572677i | \(-0.194095\pi\) |
−0.999828 | + | 0.0185496i | \(0.994095\pi\) | |||||||
\(648\) | 0.0730235 | 0.00286863 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 48.4262 | 1.89943 | ||||||||
\(651\) | 3.45325 | + | 10.6280i | 0.135343 | + | 0.416544i | ||||
\(652\) | −29.7771 | − | 21.6343i | −1.16616 | − | 0.847266i | ||||
\(653\) | −35.0932 | + | 25.4967i | −1.37330 | + | 0.997763i | −0.375832 | + | 0.926688i | \(0.622643\pi\) |
−0.997471 | + | 0.0710750i | \(0.977357\pi\) | |||||||
\(654\) | −6.45391 | + | 19.8631i | −0.252368 | + | 0.776708i | ||||
\(655\) | 0.0313132 | − | 0.0963722i | 0.00122351 | − | 0.00376557i | ||||
\(656\) | −35.3237 | + | 25.6642i | −1.37916 | + | 1.00202i | ||||
\(657\) | 40.3504 | + | 29.3163i | 1.57422 | + | 1.14374i | ||||
\(658\) | −5.49414 | − | 16.9092i | −0.214184 | − | 0.659190i | ||||
\(659\) | 42.2093 | 1.64424 | 0.822121 | − | 0.569313i | \(-0.192791\pi\) | ||||
0.822121 | + | 0.569313i | \(0.192791\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.2794 | 0.633197 | 0.316599 | − | 0.948560i | \(-0.397459\pi\) | ||||
0.316599 | + | 0.948560i | \(0.397459\pi\) | |||||||
\(662\) | 0.410271 | + | 1.26268i | 0.0159456 | + | 0.0490756i | ||||
\(663\) | 18.4720 | + | 13.4207i | 0.717392 | + | 0.521215i | ||||
\(664\) | 0.258100 | − | 0.187521i | 0.0100162 | − | 0.00727722i | ||||
\(665\) | −0.0114313 | + | 0.0351819i | −0.000443286 | + | 0.00136430i | ||||
\(666\) | 1.52222 | − | 4.68490i | 0.0589847 | − | 0.181536i | ||||
\(667\) | 41.7005 | − | 30.2972i | 1.61465 | − | 1.17311i | ||||
\(668\) | 4.73640 | + | 3.44119i | 0.183257 | + | 0.133144i | ||||
\(669\) | −5.62531 | − | 17.3129i | −0.217487 | − | 0.669357i | ||||
\(670\) | −0.150295 | −0.00580642 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −22.0975 | −0.852430 | ||||||||
\(673\) | −1.64103 | − | 5.05056i | −0.0632569 | − | 0.194685i | 0.914433 | − | 0.404736i | \(-0.132637\pi\) |
−0.977690 | + | 0.210052i | \(0.932637\pi\) | |||||||
\(674\) | 10.5998 | + | 7.70120i | 0.408289 | + | 0.296639i | ||||
\(675\) | 19.8794 | − | 14.4432i | 0.765158 | − | 0.555920i | ||||
\(676\) | 6.48401 | − | 19.9557i | 0.249385 | − | 0.767529i | ||||
\(677\) | −10.4431 | + | 32.1407i | −0.401363 | + | 1.23527i | 0.522532 | + | 0.852620i | \(0.324988\pi\) |
−0.923894 | + | 0.382648i | \(0.875012\pi\) | |||||||
\(678\) | −28.4013 | + | 20.6348i | −1.09075 | + | 0.792473i | ||||
\(679\) | −2.74799 | − | 1.99653i | −0.105458 | − | 0.0766199i | ||||
\(680\) | 0.00171027 | + | 0.00526367i | 6.55858e−5 | + | 0.000201852i | ||||
\(681\) | 37.9164 | 1.45296 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.8834 | −0.607761 | −0.303880 | − | 0.952710i | \(-0.598282\pi\) | ||||
−0.303880 | + | 0.952710i | \(0.598282\pi\) | |||||||
\(684\) | 3.92050 | + | 12.0661i | 0.149904 | + | 0.461358i | ||||
\(685\) | 0.416866 | + | 0.302871i | 0.0159276 | + | 0.0115721i | ||||
\(686\) | −1.60551 | + | 1.16647i | −0.0612985 | + | 0.0445360i | ||||
\(687\) | −16.7224 | + | 51.4662i | −0.637999 | + | 1.96356i | ||||
\(688\) | −4.76071 | + | 14.6520i | −0.181500 | + | 0.558601i | ||||
\(689\) | −15.6399 | + | 11.3631i | −0.595834 | + | 0.432899i | ||||
\(690\) | 0.971107 | + | 0.705551i | 0.0369694 | + | 0.0268599i | ||||
\(691\) | 7.89151 | + | 24.2876i | 0.300207 | + | 0.923942i | 0.981422 | + | 0.191859i | \(0.0614517\pi\) |
−0.681215 | + | 0.732083i | \(0.738548\pi\) | |||||||
\(692\) | 17.1274 | 0.651085 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.2113 | 0.919050 | ||||||||
\(695\) | −0.0292125 | − | 0.0899068i | −0.00110809 | − | 0.00341036i | ||||
\(696\) | −1.76465 | − | 1.28210i | −0.0668890 | − | 0.0485977i | ||||
\(697\) | 14.3948 | − | 10.4584i | 0.545242 | − | 0.396141i | ||||
\(698\) | −0.543216 | + | 1.67185i | −0.0205610 | + | 0.0632803i | ||||
\(699\) | 3.75544 | − | 11.5581i | 0.142044 | − | 0.437166i | ||||
\(700\) | 7.83945 | − | 5.69569i | 0.296303 | − | 0.215277i | ||||
\(701\) | 2.66600 | + | 1.93696i | 0.100693 | + | 0.0731579i | 0.636993 | − | 0.770870i | \(-0.280178\pi\) |
−0.536299 | + | 0.844028i | \(0.680178\pi\) | |||||||
\(702\) | −14.7128 | − | 45.2813i | −0.555298 | − | 1.70903i | ||||
\(703\) | 0.715875 | 0.0269997 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.672125 | 0.0253137 | ||||||||
\(706\) | 3.28709 | + | 10.1166i | 0.123711 | + | 0.380744i | ||||
\(707\) | 3.27519 | + | 2.37956i | 0.123176 | + | 0.0894927i | ||||
\(708\) | −42.5151 | + | 30.8891i | −1.59782 | + | 1.16088i | ||||
\(709\) | −13.8757 | + | 42.7049i | −0.521111 | + | 1.60382i | 0.250768 | + | 0.968047i | \(0.419317\pi\) |
−0.771880 | + | 0.635769i | \(0.780683\pi\) | |||||||
\(710\) | −0.0337740 | + | 0.103946i | −0.00126752 | + | 0.00390102i | ||||
\(711\) | −22.5669 | + | 16.3958i | −0.846323 | + | 0.614890i | ||||
\(712\) | 0.120647 | + | 0.0876554i | 0.00452145 | + | 0.00328503i | ||||
\(713\) | 9.99202 | + | 30.7523i | 0.374204 | + | 1.15168i | ||||
\(714\) | 9.28304 | 0.347409 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.4064 | 0.613137 | ||||||||
\(717\) | 9.11855 | + | 28.0640i | 0.340538 | + | 1.04807i | ||||
\(718\) | −41.4943 | − | 30.1474i | −1.54855 | − | 1.12509i | ||||
\(719\) | −2.58290 | + | 1.87659i | −0.0963259 | + | 0.0699849i | −0.634906 | − | 0.772590i | \(-0.718961\pi\) |
0.538580 | + | 0.842575i | \(0.318961\pi\) | |||||||
\(720\) | 0.163287 | − | 0.502547i | 0.00608536 | − | 0.0187288i | ||||
\(721\) | −1.22153 | + | 3.75950i | −0.0454923 | + | 0.140011i | ||||
\(722\) | 27.4739 | − | 19.9609i | 1.02247 | − | 0.742869i | ||||
\(723\) | −42.1287 | − | 30.6083i | −1.56678 | − | 1.13834i | ||||
\(724\) | −14.4955 | − | 44.6125i | −0.538721 | − | 1.65801i | ||||
\(725\) | 31.9612 | 1.18701 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.1654 | 0.747891 | 0.373946 | − | 0.927451i | \(-0.378005\pi\) | ||||
0.373946 | + | 0.927451i | \(0.378005\pi\) | |||||||
\(728\) | 0.184691 | + | 0.568420i | 0.00684510 | + | 0.0210670i | ||||
\(729\) | 35.5384 | + | 25.8202i | 1.31624 | + | 0.956303i | ||||
\(730\) | −0.452560 | + | 0.328804i | −0.0167500 | + | 0.0121696i | ||||
\(731\) | 1.94004 | − | 5.97083i | 0.0717550 | − | 0.220839i | ||||
\(732\) | 14.1315 | − | 43.4921i | 0.522314 | − | 1.60752i | ||||
\(733\) | 15.9453 | − | 11.5849i | 0.588952 | − | 0.427899i | −0.252988 | − | 0.967469i | \(-0.581413\pi\) |
0.841940 | + | 0.539571i | \(0.181413\pi\) | |||||||
\(734\) | 32.8333 | + | 23.8548i | 1.21190 | + | 0.880496i | ||||
\(735\) | −0.0231830 | − | 0.0713500i | −0.000855118 | − | 0.00263178i | ||||
\(736\) | −63.9394 | −2.35684 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −100.203 | −3.68851 | ||||||||
\(739\) | −10.6789 | − | 32.8662i | −0.392829 | − | 1.20900i | −0.930640 | − | 0.365937i | \(-0.880749\pi\) |
0.537811 | − | 0.843065i | \(-0.319251\pi\) | |||||||
\(740\) | 0.0219985 | + | 0.0159828i | 0.000808680 | + | 0.000587541i | ||||
\(741\) | 15.1178 | − | 10.9837i | 0.555365 | − | 0.403496i | ||||
\(742\) | −2.42882 | + | 7.47513i | −0.0891647 | + | 0.274421i | ||||
\(743\) | −7.98443 | + | 24.5735i | −0.292920 | + | 0.901516i | 0.690992 | + | 0.722862i | \(0.257174\pi\) |
−0.983912 | + | 0.178653i | \(0.942826\pi\) | |||||||
\(744\) | 1.10700 | − | 0.804281i | 0.0405845 | − | 0.0294864i | ||||
\(745\) | −0.0681006 | − | 0.0494780i | −0.00249501 | − | 0.00181273i | ||||
\(746\) | 5.75907 | + | 17.7246i | 0.210855 | + | 0.648944i | ||||
\(747\) | 12.4125 | 0.454148 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.3986 | 0.379957 | ||||||||
\(750\) | 0.460037 | + | 1.41585i | 0.0167982 | + | 0.0516995i | ||||
\(751\) | 28.8980 | + | 20.9956i | 1.05450 | + | 0.766142i | 0.973064 | − | 0.230536i | \(-0.0740480\pi\) |
0.0814404 | + | 0.996678i | \(0.474048\pi\) | |||||||
\(752\) | −29.8590 | + | 21.6938i | −1.08884 | + | 0.791092i | ||||
\(753\) | 16.3453 | − | 50.3057i | 0.595656 | − | 1.83324i | ||||
\(754\) | 19.1369 | − | 58.8973i | 0.696925 | − | 2.14491i | ||||
\(755\) | 0.429578 | − | 0.312107i | 0.0156340 | − | 0.0113587i | ||||
\(756\) | −7.70756 | − | 5.59987i | −0.280321 | − | 0.203665i | ||||
\(757\) | −4.57952 | − | 14.0943i | −0.166446 | − | 0.512267i | 0.832694 | − | 0.553733i | \(-0.186797\pi\) |
−0.999140 | + | 0.0414660i | \(0.986797\pi\) | |||||||
\(758\) | −11.1846 | −0.406242 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.00452957 | 0.000164305 | ||||||||
\(761\) | −6.72913 | − | 20.7101i | −0.243931 | − | 0.750742i | −0.995810 | − | 0.0914417i | \(-0.970852\pi\) |
0.751879 | − | 0.659301i | \(-0.229148\pi\) | |||||||
\(762\) | 22.5078 | + | 16.3529i | 0.815372 | + | 0.592402i | ||||
\(763\) | 3.05563 | − | 2.22005i | 0.110621 | − | 0.0803711i | ||||
\(764\) | −4.66427 | + | 14.3551i | −0.168747 | + | 0.519351i | ||||
\(765\) | −0.0665414 | + | 0.204793i | −0.00240581 | + | 0.00740431i | ||||
\(766\) | 2.02204 | − | 1.46910i | 0.0730593 | − | 0.0530807i | ||||
\(767\) | 38.4237 | + | 27.9165i | 1.38740 | + | 1.00801i | ||||
\(768\) | 14.5870 | + | 44.8941i | 0.526363 | + | 1.61998i | ||||
\(769\) | −35.6991 | −1.28734 | −0.643672 | − | 0.765302i | \(-0.722590\pi\) | ||||
−0.643672 | + | 0.765302i | \(0.722590\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −38.1988 | −1.37570 | ||||||||
\(772\) | 10.2206 | + | 31.4557i | 0.367847 | + | 1.13212i | ||||
\(773\) | −34.4827 | − | 25.0531i | −1.24026 | − | 0.901098i | −0.242640 | − | 0.970116i | \(-0.578013\pi\) |
−0.997615 | + | 0.0690182i | \(0.978013\pi\) | |||||||
\(774\) | −28.6034 | + | 20.7816i | −1.02813 | + | 0.746979i | ||||
\(775\) | −6.19573 | + | 19.0685i | −0.222557 | + | 0.684961i | ||||
\(776\) | −0.128524 | + | 0.395556i | −0.00461374 | + | 0.0141996i | ||||
\(777\) | −1.17454 | + | 0.853356i | −0.0421365 | + | 0.0306140i | ||||
\(778\) | 9.44694 | + | 6.86361i | 0.338689 | + | 0.246072i | ||||
\(779\) | −4.49992 | − | 13.8493i | −0.161226 | − | 0.496204i | ||||
\(780\) | 0.709786 | 0.0254144 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 26.8606 | 0.960533 | ||||||||
\(783\) | −9.71038 | − | 29.8855i | −0.347021 | − | 1.06802i | ||||
\(784\) | 3.33282 | + | 2.42144i | 0.119029 | + | 0.0864799i | ||||
\(785\) | −0.500002 | + | 0.363273i | −0.0178458 | + | 0.0129658i | ||||
\(786\) | −6.43102 | + | 19.7926i | −0.229387 | + | 0.705980i | ||||
\(787\) | −14.5506 | + | 44.7821i | −0.518672 | + | 1.59631i | 0.257827 | + | 0.966191i | \(0.416994\pi\) |
−0.776499 | + | 0.630118i | \(0.783006\pi\) | |||||||
\(788\) | 9.49551 | − | 6.89889i | 0.338263 | − | 0.245763i | ||||
\(789\) | −37.3680 | − | 27.1494i | −1.33033 | − | 0.966545i | ||||
\(790\) | −0.0966773 | − | 0.297542i | −0.00343962 | − | 0.0105861i | ||||
\(791\) | 6.34869 | 0.225733 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41.3295 | −1.46765 | ||||||||
\(794\) | 2.98050 | + | 9.17303i | 0.105774 | + | 0.325538i | ||||
\(795\) | −0.240383 | − | 0.174648i | −0.00852550 | − | 0.00619414i | ||||
\(796\) | 21.5116 | − | 15.6291i | 0.762459 | − | 0.553959i | ||||
\(797\) | −2.31226 | + | 7.11641i | −0.0819045 | + | 0.252076i | −0.983620 | − | 0.180253i | \(-0.942308\pi\) |
0.901716 | + | 0.432329i | \(0.142308\pi\) | |||||||
\(798\) | 2.34772 | − | 7.22555i | 0.0831086 | − | 0.255782i | ||||
\(799\) | 12.1679 | − | 8.84046i | 0.430468 | − | 0.312753i | ||||
\(800\) | −32.0749 | − | 23.3038i | −1.13402 | − | 0.823913i | ||||
\(801\) | 1.79296 | + | 5.51815i | 0.0633510 | + | 0.194974i | ||||
\(802\) | −50.6690 | −1.78918 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 15.1918 | 0.535774 | ||||||||
\(805\) | −0.0670803 | − | 0.206452i | −0.00236427 | − | 0.00727648i | ||||
\(806\) | 31.4293 | + | 22.8347i | 1.10705 | + | 0.804318i | ||||
\(807\) | 19.2593 | − | 13.9927i | 0.677961 | − | 0.492568i | ||||
\(808\) | 0.153181 | − | 0.471442i | 0.00538888 | − | 0.0165853i | ||||
\(809\) | 10.7380 | − | 33.0483i | 0.377529 | − | 1.16191i | −0.564228 | − | 0.825619i | \(-0.690826\pi\) |
0.941757 | − | 0.336295i | \(-0.109174\pi\) | |||||||
\(810\) | −0.0257796 | + | 0.0187300i | −0.000905803 | + | 0.000658104i | ||||
\(811\) | −10.3662 | − | 7.53146i | −0.364005 | − | 0.264465i | 0.390715 | − | 0.920511i | \(-0.372228\pi\) |
−0.754721 | + | 0.656046i | \(0.772228\pi\) | |||||||
\(812\) | −3.82930 | − | 11.7854i | −0.134382 | − | 0.413585i | ||||
\(813\) | −17.6811 | −0.620105 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.511268 | −0.0179089 | ||||||||
\(816\) | −5.95488 | − | 18.3272i | −0.208462 | − | 0.641581i | ||||
\(817\) | −4.15681 | − | 3.02010i | −0.145428 | − | 0.105660i | ||||
\(818\) | −33.7584 | + | 24.5269i | −1.18034 | + | 0.857564i | ||||
\(819\) | −7.18576 | + | 22.1155i | −0.251091 | + | 0.772778i | ||||
\(820\) | 0.170924 | − | 0.526049i | 0.00596892 | − | 0.0183704i | ||||
\(821\) | 43.9478 | − | 31.9300i | 1.53379 | − | 1.11436i | 0.579705 | − | 0.814826i | \(-0.303168\pi\) |
0.954085 | − | 0.299538i | \(-0.0968324\pi\) | |||||||
\(822\) | −85.6146 | − | 62.2027i | −2.98615 | − | 2.16957i | ||||
\(823\) | −6.10918 | − | 18.8021i | −0.212953 | − | 0.655401i | −0.999293 | − | 0.0376067i | \(-0.988027\pi\) |
0.786340 | − | 0.617794i | \(-0.211973\pi\) | |||||||
\(824\) | 0.484024 | 0.0168618 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19.3098 | 0.671873 | ||||||||
\(827\) | 3.80395 | + | 11.7074i | 0.132276 | + | 0.407105i | 0.995156 | − | 0.0983040i | \(-0.0313418\pi\) |
−0.862880 | + | 0.505409i | \(0.831342\pi\) | |||||||
\(828\) | −60.2306 | − | 43.7601i | −2.09316 | − | 1.52077i | ||||
\(829\) | 20.8127 | − | 15.1213i | 0.722854 | − | 0.525184i | −0.164441 | − | 0.986387i | \(-0.552582\pi\) |
0.887295 | + | 0.461203i | \(0.152582\pi\) | |||||||
\(830\) | −0.0430198 | + | 0.132401i | −0.00149324 | + | 0.00459572i | ||||
\(831\) | −20.6688 | + | 63.6120i | −0.716993 | + | 2.20668i | ||||
\(832\) | −29.6129 | + | 21.5151i | −1.02664 | + | 0.745900i | ||||
\(833\) | −1.35816 | − | 0.986762i | −0.0470575 | − | 0.0341893i | ||||
\(834\) | 5.99957 | + | 18.4648i | 0.207748 | + | 0.639383i | ||||
\(835\) | 0.0813232 | 0.00281431 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.7125 | 0.681363 | ||||||||
\(838\) | −19.2034 | − | 59.1019i | −0.663369 | − | 2.04164i | ||||
\(839\) | 37.7112 | + | 27.3988i | 1.30194 | + | 0.945912i | 0.999973 | − | 0.00740804i | \(-0.00235807\pi\) |
0.301963 | + | 0.953320i | \(0.402358\pi\) | |||||||
\(840\) | −0.00743171 | + | 0.00539945i | −0.000256418 | + | 0.000186299i | ||||
\(841\) | 3.66881 | − | 11.2914i | 0.126511 | − | 0.389359i | ||||
\(842\) | 7.84262 | − | 24.1371i | 0.270275 | − | 0.831820i | ||||
\(843\) | 7.23935 | − | 5.25970i | 0.249336 | − | 0.181154i | ||||
\(844\) | −28.2814 | − | 20.5476i | −0.973485 | − | 0.707279i | ||||
\(845\) | −0.0900675 | − | 0.277199i | −0.00309842 | − | 0.00953594i | ||||
\(846\) | −84.7009 | −2.91208 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 16.3160 | 0.560292 | ||||||||
\(849\) | −17.9126 | − | 55.1293i | −0.614759 | − | 1.89203i | ||||
\(850\) | 13.4745 | + | 9.78980i | 0.462171 | + | 0.335787i | ||||
\(851\) | −3.39856 | + | 2.46920i | −0.116501 | + | 0.0846430i | ||||
\(852\) | 3.41387 | − | 10.5068i | 0.116957 | − | 0.359957i | ||||
\(853\) | −3.03109 | + | 9.32873i | −0.103782 | + | 0.319410i | −0.989443 | − | 0.144924i | \(-0.953706\pi\) |
0.885660 | + | 0.464334i | \(0.153706\pi\) | |||||||
\(854\) | −13.5942 | + | 9.87675i | −0.465183 | + | 0.337976i | ||||
\(855\) | 0.142574 | + | 0.103586i | 0.00487594 | + | 0.00354258i | ||||
\(856\) | −0.393460 | − | 1.21095i | −0.0134482 | − | 0.0413893i | ||||
\(857\) | −32.9168 | −1.12442 | −0.562208 | − | 0.826996i | \(-0.690048\pi\) | ||||
−0.562208 | + | 0.826996i | \(0.690048\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.4747 | −0.971543 | −0.485772 | − | 0.874086i | \(-0.661461\pi\) | ||||
−0.485772 | + | 0.874086i | \(0.661461\pi\) | |||||||
\(860\) | −0.0603091 | − | 0.185612i | −0.00205652 | − | 0.00632933i | ||||
\(861\) | 23.8921 | + | 17.3586i | 0.814241 | + | 0.591581i | ||||
\(862\) | −33.8246 | + | 24.5750i | −1.15207 | + | 0.837029i | ||||
\(863\) | 9.04709 | − | 27.8441i | 0.307966 | − | 0.947823i | −0.670587 | − | 0.741831i | \(-0.733958\pi\) |
0.978554 | − | 0.205992i | \(-0.0660422\pi\) | |||||||
\(864\) | −12.0454 | + | 37.0720i | −0.409793 | + | 1.26121i | ||||
\(865\) | 0.192474 | − | 0.139841i | 0.00654432 | − | 0.00475473i | ||||
\(866\) | −61.0141 | − | 44.3293i | −2.07334 | − | 1.50637i | ||||
\(867\) | −12.2111 | − | 37.5818i | −0.414709 | − | 1.27634i | ||||
\(868\) | 7.77363 | 0.263854 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.951826 | 0.0322699 | ||||||||
\(871\) | −4.24275 | − | 13.0579i | −0.143760 | − | 0.442449i | ||||
\(872\) | −0.374149 | − | 0.271835i | −0.0126703 | − | 0.00920551i | ||||
\(873\) | −13.0914 | + | 9.51146i | −0.443077 | + | 0.321914i | ||||
\(874\) | 6.79317 | − | 20.9072i | 0.229782 | − | 0.707198i | ||||
\(875\) | 0.0831947 | − | 0.256047i | 0.00281250 | − | 0.00865597i | ||||
\(876\) | 45.7446 | − | 33.2354i | 1.54557 | − | 1.12292i | ||||
\(877\) | 18.2858 | + | 13.2854i | 0.617468 | + | 0.448617i | 0.852036 | − | 0.523483i | \(-0.175368\pi\) |
−0.234568 | + | 0.972100i | \(0.575368\pi\) | |||||||
\(878\) | −23.1610 | − | 71.2823i | −0.781647 | − | 2.40566i | ||||
\(879\) | 15.3738 | 0.518544 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.1102 | −1.18289 | −0.591447 | − | 0.806344i | \(-0.701443\pi\) | ||||
−0.591447 | + | 0.806344i | \(0.701443\pi\) | |||||||
\(882\) | 2.92151 | + | 8.99149i | 0.0983724 | + | 0.302759i | ||||
\(883\) | −12.2996 | − | 8.93621i | −0.413916 | − | 0.300727i | 0.361269 | − | 0.932461i | \(-0.382343\pi\) |
−0.775185 | + | 0.631734i | \(0.782343\pi\) | |||||||
\(884\) | 12.8497 | − | 9.33582i | 0.432181 | − | 0.313998i | ||||
\(885\) | −0.225576 | + | 0.694251i | −0.00758264 | + | 0.0233370i | ||||
\(886\) | −0.630372 | + | 1.94009i | −0.0211778 | + | 0.0651785i | ||||
\(887\) | 31.1728 | − | 22.6483i | 1.04668 | − | 0.760457i | 0.0751006 | − | 0.997176i | \(-0.476072\pi\) |
0.971578 | + | 0.236719i | \(0.0760722\pi\) | |||||||
\(888\) | 0.143818 | + | 0.104490i | 0.00482621 | + | 0.00350645i | ||||
\(889\) | −1.55475 | − | 4.78503i | −0.0521447 | − | 0.160485i | ||||
\(890\) | −0.0650753 | −0.00218133 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.6632 | −0.423995 | ||||||||
\(893\) | −3.80376 | − | 11.7068i | −0.127288 | − | 0.391752i | ||||
\(894\) | 13.9863 | + | 10.1616i | 0.467772 | + | 0.339856i | ||||
\(895\) | 0.184372 | − | 0.133954i | 0.00616288 | − | 0.00447760i | ||||
\(896\) | 0.302558 | − | 0.931179i | 0.0101078 | − | 0.0311085i | ||||
\(897\) | −33.8853 | + | 104.288i | −1.13140 | + | 3.48209i | ||||
\(898\) | −32.3241 | + | 23.4849i | −1.07867 | + | 0.783700i | ||||
\(899\) | 20.7432 | + | 15.0708i | 0.691825 | + | 0.502641i | ||||
\(900\) | −14.2653 | − | 43.9041i | −0.475510 | − | 1.46347i | ||||
\(901\) | −6.64893 | −0.221508 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.4202 | 0.346764 | ||||||||
\(904\) | −0.240220 | − | 0.739322i | −0.00798961 | − | 0.0245895i | ||||
\(905\) | −0.527148 | − | 0.382995i | −0.0175230 | − | 0.0127312i | ||||
\(906\) | −88.2255 | + | 64.0996i | −2.93110 | + | 2.12957i | ||||
\(907\) | −17.4352 | + | 53.6600i | −0.578926 | + | 1.78175i | 0.0434788 | + | 0.999054i | \(0.486156\pi\) |
−0.622405 | + | 0.782696i | \(0.713844\pi\) | |||||||
\(908\) | 8.15058 | − | 25.0849i | 0.270486 | − | 0.832471i | ||||
\(909\) | 15.6030 | − | 11.3362i | 0.517518 | − | 0.375998i | ||||
\(910\) | −0.210997 | − | 0.153298i | −0.00699448 | − | 0.00508179i | ||||
\(911\) | −9.45295 | − | 29.0932i | −0.313190 | − | 0.963900i | −0.976493 | − | 0.215549i | \(-0.930846\pi\) |
0.663303 | − | 0.748351i | \(-0.269154\pi\) | |||||||
\(912\) | −15.7712 | −0.522237 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −47.9173 | −1.58496 | ||||||||
\(915\) | −0.196296 | − | 0.604136i | −0.00648934 | − | 0.0199721i | ||||
\(916\) | 30.4545 | + | 22.1265i | 1.00625 | + | 0.731080i | ||||
\(917\) | 3.04480 | − | 2.21217i | 0.100548 | − | 0.0730524i | ||||
\(918\) | 5.06021 | − | 15.5737i | 0.167012 | − | 0.514010i | ||||
\(919\) | 10.1637 | − | 31.2806i | 0.335269 | − | 1.03185i | −0.631320 | − | 0.775522i | \(-0.717487\pi\) |
0.966589 | − | 0.256330i | \(-0.0825133\pi\) | |||||||
\(920\) | −0.0215037 | + | 0.0156234i | −0.000708957 | + | 0.000515088i | ||||
\(921\) | −19.4088 | − | 14.1013i | −0.639542 | − | 0.464654i | ||||
\(922\) | 7.10664 | + | 21.8720i | 0.234045 | + | 0.720316i | ||||
\(923\) | −9.98437 | −0.328640 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.60481 | −0.0856457 | ||||||||
\(926\) | 13.2509 | + | 40.7820i | 0.435451 | + | 1.34018i | ||||
\(927\) | 15.2353 | + | 11.0691i | 0.500394 | + | 0.363557i | ||||
\(928\) | −41.0180 | + | 29.8013i | −1.34648 | + | 0.978275i | ||||
\(929\) | 6.74665 | − | 20.7641i | 0.221350 | − | 0.681246i | −0.777291 | − | 0.629141i | \(-0.783407\pi\) |
0.998642 | − | 0.0521055i | \(-0.0165932\pi\) | |||||||
\(930\) | −0.184513 | + | 0.567873i | −0.00605042 | + | 0.0186213i | ||||
\(931\) | −1.11154 | + | 0.807582i | −0.0364293 | + | 0.0264674i | ||||
\(932\) | −6.83935 | − | 4.96908i | −0.224030 | − | 0.162767i | ||||
\(933\) | 16.4682 | + | 50.6838i | 0.539144 | + | 1.65931i | ||||
\(934\) | 31.5835 | 1.03344 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.84730 | 0.0930670 | ||||||||
\(937\) | −10.8008 | − | 33.2416i | −0.352848 | − | 1.08596i | −0.957247 | − | 0.289273i | \(-0.906586\pi\) |
0.604398 | − | 0.796682i | \(-0.293414\pi\) | |||||||
\(938\) | −4.51604 | − | 3.28110i | −0.147454 | − | 0.107132i | ||||
\(939\) | 1.36777 | − | 0.993744i | 0.0446355 | − | 0.0324296i | ||||
\(940\) | 0.144481 | − | 0.444667i | 0.00471245 | − | 0.0145034i | ||||
\(941\) | −6.31028 | + | 19.4210i | −0.205709 | + | 0.633108i | 0.793974 | + | 0.607951i | \(0.208008\pi\) |
−0.999684 | + | 0.0251567i | \(0.991992\pi\) | |||||||
\(942\) | 102.689 | − | 74.6079i | 3.34579 | − | 2.43086i | ||||
\(943\) | 69.1321 | + | 50.2274i | 2.25125 | + | 1.63563i | ||||
\(944\) | −12.3868 | − | 38.1227i | −0.403156 | − | 1.24079i | ||||
\(945\) | −0.132338 | −0.00430494 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.3122 | −0.367597 | −0.183799 | − | 0.982964i | \(-0.558839\pi\) | ||||
−0.183799 | + | 0.982964i | \(0.558839\pi\) | |||||||
\(948\) | 9.77211 | + | 30.0755i | 0.317383 | + | 0.976806i | ||||
\(949\) | −41.3424 | − | 30.0370i | −1.34203 | − | 0.975044i | ||||
\(950\) | 11.0278 | − | 8.01213i | 0.357788 | − | 0.259948i | ||||
\(951\) | −4.48847 | + | 13.8141i | −0.145549 | + | 0.447952i | ||||
\(952\) | −0.0635213 | + | 0.195499i | −0.00205874 | + | 0.00633614i | ||||
\(953\) | 3.68847 | − | 2.67983i | 0.119481 | − | 0.0868081i | −0.526440 | − | 0.850212i | \(-0.676474\pi\) |
0.645921 | + | 0.763404i | \(0.276474\pi\) | |||||||
\(954\) | 30.2929 | + | 22.0091i | 0.980769 | + | 0.712570i | ||||
\(955\) | 0.0647899 | + | 0.199403i | 0.00209655 | + | 0.00645252i | ||||
\(956\) | 20.5268 | 0.663885 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.4856 | 0.338775 | ||||||||
\(959\) | 5.91393 | + | 18.2012i | 0.190971 | + | 0.587747i | ||||
\(960\) | −0.455145 | − | 0.330682i | −0.0146897 | − | 0.0106727i | ||||
\(961\) | 12.0669 | − | 8.76714i | 0.389256 | − | 0.282811i | ||||
\(962\) | −1.55964 | + | 4.80009i | −0.0502849 | + | 0.154761i | ||||
\(963\) | 15.3083 | − | 47.1142i | 0.493304 | − | 1.51823i | ||||
\(964\) | −29.3060 | + | 21.2921i | −0.943883 | + | 0.685771i | ||||
\(965\) | 0.371685 | + | 0.270045i | 0.0119650 | + | 0.00869305i | ||||
\(966\) | 13.7768 | + | 42.4005i | 0.443260 | + | 1.36421i | ||||
\(967\) | −38.9153 | −1.25143 | −0.625715 | − | 0.780052i | \(-0.715193\pi\) | ||||
−0.625715 | + | 0.780052i | \(0.715193\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.42694 | 0.206463 | ||||||||
\(970\) | −0.0560840 | − | 0.172609i | −0.00180075 | − | 0.00554214i | ||||
\(971\) | −34.2545 | − | 24.8874i | −1.09928 | − | 0.798674i | −0.118338 | − | 0.992973i | \(-0.537757\pi\) |
−0.980942 | + | 0.194300i | \(0.937757\pi\) | |||||||
\(972\) | 25.7285 | − | 18.6928i | 0.825241 | − | 0.599573i | ||||
\(973\) | 1.08498 | − | 3.33924i | 0.0347830 | − | 0.107051i | ||||
\(974\) | −16.5979 | + | 51.0831i | −0.531832 | + | 1.63681i | ||||
\(975\) | −55.0081 | + | 39.9657i | −1.76167 | + | 1.27993i | ||||
\(976\) | 28.2198 | + | 20.5028i | 0.903292 | + | 0.656280i | ||||
\(977\) | 11.0188 | + | 33.9123i | 0.352522 | + | 1.08495i | 0.957433 | + | 0.288657i | \(0.0932088\pi\) |
−0.604911 | + | 0.796293i | \(0.706791\pi\) | |||||||
\(978\) | 105.003 | 3.35762 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −0.0521874 | −0.00166707 | ||||||||
\(981\) | −5.56028 | − | 17.1128i | −0.177526 | − | 0.546369i | ||||
\(982\) | −30.1835 | − | 21.9296i | −0.963193 | − | 0.699801i | ||||
\(983\) | 23.8832 | − | 17.3522i | 0.761756 | − | 0.553448i | −0.137692 | − | 0.990475i | \(-0.543968\pi\) |
0.899449 | + | 0.437027i | \(0.143968\pi\) | |||||||
\(984\) | 1.11744 | − | 3.43911i | 0.0356226 | − | 0.109635i | ||||
\(985\) | 0.0503810 | − | 0.155057i | 0.00160527 | − | 0.00494052i | ||||
\(986\) | 17.2314 | − | 12.5194i | 0.548760 | − | 0.398698i | ||||
\(987\) | 20.1959 | + | 14.6732i | 0.642842 | + | 0.467052i | ||||
\(988\) | −4.01690 | − | 12.3627i | −0.127794 | − | 0.393311i | ||||
\(989\) | 30.1511 | 0.958748 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.7292 | −0.976145 | −0.488072 | − | 0.872803i | \(-0.662300\pi\) | ||||
−0.488072 | + | 0.872803i | \(0.662300\pi\) | |||||||
\(992\) | −9.82848 | − | 30.2489i | −0.312054 | − | 0.960405i | ||||
\(993\) | −1.50811 | − | 1.09571i | −0.0478586 | − | 0.0347713i | ||||
\(994\) | −3.28408 | + | 2.38602i | −0.104165 | + | 0.0756800i | ||||
\(995\) | 0.114136 | − | 0.351274i | 0.00361835 | − | 0.0111361i | ||||
\(996\) | 4.34843 | − | 13.3831i | 0.137785 | − | 0.424060i | ||||
\(997\) | −40.4474 | + | 29.3868i | −1.28098 | + | 0.930688i | −0.999582 | − | 0.0289020i | \(-0.990799\pi\) |
−0.281400 | + | 0.959590i | \(0.590799\pi\) | |||||||
\(998\) | 63.8456 | + | 46.3866i | 2.02100 | + | 1.46834i | ||||
\(999\) | 0.791389 | + | 2.43564i | 0.0250384 | + | 0.0770604i |
(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 | 847.2.f.w.148.4 | 16 | ||
11.2 | odd | 10 | 847.2.f.v.372.1 | 16 | |||
11.3 | even | 5 | 847.2.a.p.1.7 | 8 | |||
11.4 | even | 5 | 77.2.f.b.36.1 | yes | 16 | ||
11.5 | even | 5 | 77.2.f.b.15.1 | ✓ | 16 | ||
11.6 | odd | 10 | 847.2.f.x.323.4 | 16 | |||
11.7 | odd | 10 | 847.2.f.x.729.4 | 16 | |||
11.8 | odd | 10 | 847.2.a.o.1.2 | 8 | |||
11.9 | even | 5 | inner | 847.2.f.w.372.4 | 16 | ||
11.10 | odd | 2 | 847.2.f.v.148.1 | 16 | |||
33.5 | odd | 10 | 693.2.m.i.631.4 | 16 | |||
33.8 | even | 10 | 7623.2.a.cw.1.7 | 8 | |||
33.14 | odd | 10 | 7623.2.a.ct.1.2 | 8 | |||
33.26 | odd | 10 | 693.2.m.i.190.4 | 16 | |||
77.4 | even | 15 | 539.2.q.g.520.1 | 32 | |||
77.5 | odd | 30 | 539.2.q.f.312.1 | 32 | |||
77.16 | even | 15 | 539.2.q.g.312.1 | 32 | |||
77.26 | odd | 30 | 539.2.q.f.410.4 | 32 | |||
77.27 | odd | 10 | 539.2.f.e.246.1 | 16 | |||
77.37 | even | 15 | 539.2.q.g.410.4 | 32 | |||
77.38 | odd | 30 | 539.2.q.f.422.4 | 32 | |||
77.41 | even | 10 | 5929.2.a.bs.1.2 | 8 | |||
77.48 | odd | 10 | 539.2.f.e.344.1 | 16 | |||
77.59 | odd | 30 | 539.2.q.f.520.1 | 32 | |||
77.60 | even | 15 | 539.2.q.g.422.4 | 32 | |||
77.69 | odd | 10 | 5929.2.a.bt.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.b.15.1 | ✓ | 16 | 11.5 | even | 5 | ||
77.2.f.b.36.1 | yes | 16 | 11.4 | even | 5 | ||
539.2.f.e.246.1 | 16 | 77.27 | odd | 10 | |||
539.2.f.e.344.1 | 16 | 77.48 | odd | 10 | |||
539.2.q.f.312.1 | 32 | 77.5 | odd | 30 | |||
539.2.q.f.410.4 | 32 | 77.26 | odd | 30 | |||
539.2.q.f.422.4 | 32 | 77.38 | odd | 30 | |||
539.2.q.f.520.1 | 32 | 77.59 | odd | 30 | |||
539.2.q.g.312.1 | 32 | 77.16 | even | 15 | |||
539.2.q.g.410.4 | 32 | 77.37 | even | 15 | |||
539.2.q.g.422.4 | 32 | 77.60 | even | 15 | |||
539.2.q.g.520.1 | 32 | 77.4 | even | 15 | |||
693.2.m.i.190.4 | 16 | 33.26 | odd | 10 | |||
693.2.m.i.631.4 | 16 | 33.5 | odd | 10 | |||
847.2.a.o.1.2 | 8 | 11.8 | odd | 10 | |||
847.2.a.p.1.7 | 8 | 11.3 | even | 5 | |||
847.2.f.v.148.1 | 16 | 11.10 | odd | 2 | |||
847.2.f.v.372.1 | 16 | 11.2 | odd | 10 | |||
847.2.f.w.148.4 | 16 | 1.1 | even | 1 | trivial | ||
847.2.f.w.372.4 | 16 | 11.9 | even | 5 | inner | ||
847.2.f.x.323.4 | 16 | 11.6 | odd | 10 | |||
847.2.f.x.729.4 | 16 | 11.7 | odd | 10 | |||
5929.2.a.bs.1.2 | 8 | 77.41 | even | 10 | |||
5929.2.a.bt.1.7 | 8 | 77.69 | odd | 10 | |||
7623.2.a.ct.1.2 | 8 | 33.14 | odd | 10 | |||
7623.2.a.cw.1.7 | 8 | 33.8 | even | 10 |