Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,2,Mod(16,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.h (of order \(3\), degree \(2\), 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: | \(0.726638658394\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 16.4 | ||
Root | \(-0.437442 - 0.757672i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.16 |
Dual form | 91.2.h.b.74.4 |
$q$-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 \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(66\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.268125 | −0.189593 | −0.0947966 | − | 0.995497i | \(-0.530220\pi\) | ||||
−0.0947966 | + | 0.995497i | \(0.530220\pi\) | |||||||
\(3\) | 0.571504 | − | 0.989875i | 0.329958 | − | 0.571504i | −0.652545 | − | 0.757750i | \(-0.726299\pi\) |
0.982503 | + | 0.186246i | \(0.0596320\pi\) | |||||||
\(4\) | −1.92811 | −0.964054 | ||||||||
\(5\) | 1.28088 | − | 2.21854i | 0.572826 | − | 0.992163i | −0.423448 | − | 0.905920i | \(-0.639180\pi\) |
0.996274 | − | 0.0862431i | \(-0.0274862\pi\) | |||||||
\(6\) | −0.153235 | + | 0.265410i | −0.0625578 | + | 0.108353i | ||||
\(7\) | 1.80416 | − | 1.93520i | 0.681909 | − | 0.731437i | ||||
\(8\) | 1.05323 | 0.372371 | ||||||||
\(9\) | 0.846765 | + | 1.46664i | 0.282255 | + | 0.488880i | ||||
\(10\) | −0.343436 | + | 0.594848i | −0.108604 | + | 0.188107i | ||||
\(11\) | −1.97300 | + | 3.41734i | −0.594882 | + | 1.03037i | 0.398681 | + | 0.917090i | \(0.369468\pi\) |
−0.993563 | + | 0.113277i | \(0.963865\pi\) | |||||||
\(12\) | −1.10192 | + | 1.90859i | −0.318098 | + | 0.550961i | ||||
\(13\) | −3.15374 | − | 1.74755i | −0.874690 | − | 0.484682i | ||||
\(14\) | −0.483741 | + | 0.518876i | −0.129285 | + | 0.138676i | ||||
\(15\) | −1.46405 | − | 2.53582i | −0.378017 | − | 0.654745i | ||||
\(16\) | 3.57382 | 0.893455 | ||||||||
\(17\) | 0.785100 | 0.190415 | 0.0952073 | − | 0.995457i | \(-0.469649\pi\) | ||||
0.0952073 | + | 0.995457i | \(0.469649\pi\) | |||||||
\(18\) | −0.227039 | − | 0.393243i | −0.0535136 | − | 0.0926883i | ||||
\(19\) | 3.74764 | + | 6.49110i | 0.859767 | + | 1.48916i | 0.872151 | + | 0.489236i | \(0.162724\pi\) |
−0.0123849 | + | 0.999923i | \(0.503942\pi\) | |||||||
\(20\) | −2.46967 | + | 4.27760i | −0.552235 | + | 0.956500i | ||||
\(21\) | −0.884522 | − | 2.89187i | −0.193018 | − | 0.631058i | ||||
\(22\) | 0.529011 | − | 0.916274i | 0.112786 | − | 0.195350i | ||||
\(23\) | −7.95518 | −1.65877 | −0.829384 | − | 0.558678i | \(-0.811309\pi\) | ||||
−0.829384 | + | 0.558678i | \(0.811309\pi\) | |||||||
\(24\) | 0.601923 | − | 1.04256i | 0.122867 | − | 0.212812i | ||||
\(25\) | −0.781294 | − | 1.35324i | −0.156259 | − | 0.270648i | ||||
\(26\) | 0.845598 | + | 0.468561i | 0.165835 | + | 0.0918924i | ||||
\(27\) | 5.36475 | 1.03245 | ||||||||
\(28\) | −3.47862 | + | 3.73128i | −0.657397 | + | 0.705146i | ||||
\(29\) | −1.17586 | − | 2.03666i | −0.218353 | − | 0.378198i | 0.735952 | − | 0.677034i | \(-0.236735\pi\) |
−0.954304 | + | 0.298836i | \(0.903402\pi\) | |||||||
\(30\) | 0.392550 | + | 0.679916i | 0.0716695 | + | 0.124135i | ||||
\(31\) | 1.27718 | + | 2.21215i | 0.229389 | + | 0.397313i | 0.957627 | − | 0.288011i | \(-0.0929939\pi\) |
−0.728238 | + | 0.685324i | \(0.759661\pi\) | |||||||
\(32\) | −3.06468 | −0.541764 | ||||||||
\(33\) | 2.25516 | + | 3.90605i | 0.392573 | + | 0.679956i | ||||
\(34\) | −0.210505 | −0.0361013 | ||||||||
\(35\) | −1.98242 | − | 6.48137i | −0.335091 | − | 1.09555i | ||||
\(36\) | −1.63266 | − | 2.82784i | −0.272109 | − | 0.471307i | ||||
\(37\) | 6.75716 | 1.11087 | 0.555435 | − | 0.831560i | \(-0.312552\pi\) | ||||
0.555435 | + | 0.831560i | \(0.312552\pi\) | |||||||
\(38\) | −1.00484 | − | 1.74043i | −0.163006 | − | 0.282334i | ||||
\(39\) | −3.53223 | + | 2.12308i | −0.565609 | + | 0.339965i | ||||
\(40\) | 1.34905 | − | 2.33663i | 0.213304 | − | 0.369453i | ||||
\(41\) | 1.21874 | + | 2.11091i | 0.190335 | + | 0.329669i | 0.945361 | − | 0.326025i | \(-0.105709\pi\) |
−0.755027 | + | 0.655694i | \(0.772376\pi\) | |||||||
\(42\) | 0.237163 | + | 0.775383i | 0.0365950 | + | 0.119644i | ||||
\(43\) | 1.12473 | − | 1.94809i | 0.171520 | − | 0.297081i | −0.767432 | − | 0.641131i | \(-0.778466\pi\) |
0.938951 | + | 0.344050i | \(0.111799\pi\) | |||||||
\(44\) | 3.80416 | − | 6.58900i | 0.573499 | − | 0.993329i | ||||
\(45\) | 4.33841 | 0.646732 | ||||||||
\(46\) | 2.13298 | 0.314491 | ||||||||
\(47\) | −0.658276 | + | 1.14017i | −0.0960195 | + | 0.166311i | −0.910034 | − | 0.414534i | \(-0.863944\pi\) |
0.814014 | + | 0.580845i | \(0.197278\pi\) | |||||||
\(48\) | 2.04246 | − | 3.53764i | 0.294803 | − | 0.510614i | ||||
\(49\) | −0.490011 | − | 6.98283i | −0.0700016 | − | 0.997547i | ||||
\(50\) | 0.209485 | + | 0.362838i | 0.0296256 | + | 0.0513130i | ||||
\(51\) | 0.448688 | − | 0.777151i | 0.0628289 | − | 0.108823i | ||||
\(52\) | 6.08076 | + | 3.36946i | 0.843249 | + | 0.467260i | ||||
\(53\) | −4.63977 | − | 8.03632i | −0.637321 | − | 1.10387i | −0.986018 | − | 0.166637i | \(-0.946709\pi\) |
0.348697 | − | 0.937236i | \(-0.386624\pi\) | |||||||
\(54\) | −1.43842 | −0.195745 | ||||||||
\(55\) | 5.05434 | + | 8.75438i | 0.681528 | + | 1.18044i | ||||
\(56\) | 1.90019 | − | 2.03820i | 0.253923 | − | 0.272366i | ||||
\(57\) | 8.56716 | 1.13475 | ||||||||
\(58\) | 0.315279 | + | 0.546079i | 0.0413981 | + | 0.0717037i | ||||
\(59\) | −8.96671 | −1.16737 | −0.583683 | − | 0.811982i | \(-0.698389\pi\) | ||||
−0.583683 | + | 0.811982i | \(0.698389\pi\) | |||||||
\(60\) | 2.82286 | + | 4.88933i | 0.364429 | + | 0.631210i | ||||
\(61\) | −4.72273 | − | 8.18002i | −0.604684 | − | 1.04734i | −0.992101 | − | 0.125439i | \(-0.959966\pi\) |
0.387417 | − | 0.921905i | \(-0.373367\pi\) | |||||||
\(62\) | −0.342445 | − | 0.593132i | −0.0434906 | − | 0.0753279i | ||||
\(63\) | 4.36595 | + | 1.00739i | 0.550057 | + | 0.126920i | ||||
\(64\) | −6.32592 | −0.790741 | ||||||||
\(65\) | −7.91657 | + | 4.75832i | −0.981929 | + | 0.590197i | ||||
\(66\) | −0.604665 | − | 1.04731i | −0.0744291 | − | 0.128915i | ||||
\(67\) | 0.676281 | − | 1.17135i | 0.0826209 | − | 0.143104i | −0.821754 | − | 0.569842i | \(-0.807004\pi\) |
0.904375 | + | 0.426739i | \(0.140338\pi\) | |||||||
\(68\) | −1.51376 | −0.183570 | ||||||||
\(69\) | −4.54642 | + | 7.87463i | −0.547324 | + | 0.947994i | ||||
\(70\) | 0.531538 | + | 1.73782i | 0.0635309 | + | 0.207709i | ||||
\(71\) | −6.15808 | + | 10.6661i | −0.730829 | + | 1.26583i | 0.225700 | + | 0.974197i | \(0.427533\pi\) |
−0.956529 | + | 0.291637i | \(0.905800\pi\) | |||||||
\(72\) | 0.891834 | + | 1.54470i | 0.105104 | + | 0.182045i | ||||
\(73\) | −0.384295 | − | 0.665619i | −0.0449783 | − | 0.0779048i | 0.842660 | − | 0.538446i | \(-0.180989\pi\) |
−0.887638 | + | 0.460542i | \(0.847655\pi\) | |||||||
\(74\) | −1.81176 | −0.210613 | ||||||||
\(75\) | −1.78605 | −0.206236 | ||||||||
\(76\) | −7.22585 | − | 12.5155i | −0.828862 | − | 1.43563i | ||||
\(77\) | 3.05363 | + | 9.98358i | 0.347993 | + | 1.13773i | ||||
\(78\) | 0.947080 | − | 0.569251i | 0.107236 | − | 0.0644550i | ||||
\(79\) | −3.09642 | + | 5.36316i | −0.348375 | + | 0.603402i | −0.985961 | − | 0.166976i | \(-0.946600\pi\) |
0.637586 | + | 0.770379i | \(0.279933\pi\) | |||||||
\(80\) | 4.57763 | − | 7.92868i | 0.511794 | − | 0.886454i | ||||
\(81\) | 0.525682 | − | 0.910507i | 0.0584091 | − | 0.101167i | ||||
\(82\) | −0.326774 | − | 0.565989i | −0.0360861 | − | 0.0625030i | ||||
\(83\) | −1.07292 | −0.117768 | −0.0588841 | − | 0.998265i | \(-0.518754\pi\) | ||||
−0.0588841 | + | 0.998265i | \(0.518754\pi\) | |||||||
\(84\) | 1.70545 | + | 5.57584i | 0.186080 | + | 0.608374i | ||||
\(85\) | 1.00562 | − | 1.74178i | 0.109074 | − | 0.188922i | ||||
\(86\) | −0.301568 | + | 0.522332i | −0.0325190 | + | 0.0563245i | ||||
\(87\) | −2.68805 | −0.288189 | ||||||||
\(88\) | −2.07801 | + | 3.59923i | −0.221517 | + | 0.383679i | ||||
\(89\) | 7.66299 | 0.812275 | 0.406138 | − | 0.913812i | \(-0.366875\pi\) | ||||
0.406138 | + | 0.913812i | \(0.366875\pi\) | |||||||
\(90\) | −1.16324 | −0.122616 | ||||||||
\(91\) | −9.07171 | + | 2.95027i | −0.950973 | + | 0.309272i | ||||
\(92\) | 15.3384 | 1.59914 | ||||||||
\(93\) | 2.91966 | 0.302755 | ||||||||
\(94\) | 0.176501 | − | 0.305708i | 0.0182046 | − | 0.0315314i | ||||
\(95\) | 19.2010 | 1.96999 | ||||||||
\(96\) | −1.75148 | + | 3.03365i | −0.178760 | + | 0.309621i | ||||
\(97\) | 1.18601 | − | 2.05423i | 0.120421 | − | 0.208575i | −0.799513 | − | 0.600649i | \(-0.794909\pi\) |
0.919934 | + | 0.392074i | \(0.128242\pi\) | |||||||
\(98\) | 0.131384 | + | 1.87227i | 0.0132718 | + | 0.189128i | ||||
\(99\) | −6.68267 | −0.671634 | ||||||||
\(100\) | 1.50642 | + | 2.60920i | 0.150642 | + | 0.260920i | ||||
\(101\) | 0.398665 | − | 0.690508i | 0.0396686 | − | 0.0687081i | −0.845509 | − | 0.533961i | \(-0.820703\pi\) |
0.885178 | + | 0.465252i | \(0.154036\pi\) | |||||||
\(102\) | −0.120305 | + | 0.208374i | −0.0119119 | + | 0.0206321i | ||||
\(103\) | −1.08309 | + | 1.87597i | −0.106720 | + | 0.184844i | −0.914440 | − | 0.404722i | \(-0.867368\pi\) |
0.807720 | + | 0.589567i | \(0.200701\pi\) | |||||||
\(104\) | −3.32160 | − | 1.84056i | −0.325710 | − | 0.180482i | ||||
\(105\) | −7.54871 | − | 1.74178i | −0.736678 | − | 0.169980i | ||||
\(106\) | 1.24404 | + | 2.15474i | 0.120832 | + | 0.209287i | ||||
\(107\) | −11.5262 | −1.11428 | −0.557141 | − | 0.830418i | \(-0.688102\pi\) | ||||
−0.557141 | + | 0.830418i | \(0.688102\pi\) | |||||||
\(108\) | −10.3438 | −0.995334 | ||||||||
\(109\) | −4.03912 | − | 6.99595i | −0.386877 | − | 0.670091i | 0.605151 | − | 0.796111i | \(-0.293113\pi\) |
−0.992028 | + | 0.126020i | \(0.959780\pi\) | |||||||
\(110\) | −1.35520 | − | 2.34727i | −0.129213 | − | 0.223803i | ||||
\(111\) | 3.86174 | − | 6.68874i | 0.366541 | − | 0.634867i | ||||
\(112\) | 6.44775 | − | 6.91607i | 0.609255 | − | 0.653507i | ||||
\(113\) | −4.02067 | + | 6.96401i | −0.378233 | + | 0.655119i | −0.990805 | − | 0.135296i | \(-0.956802\pi\) |
0.612572 | + | 0.790415i | \(0.290135\pi\) | |||||||
\(114\) | −2.29707 | −0.215141 | ||||||||
\(115\) | −10.1896 | + | 17.6489i | −0.950186 | + | 1.64577i | ||||
\(116\) | 2.26719 | + | 3.92690i | 0.210504 | + | 0.364603i | ||||
\(117\) | −0.107456 | − | 6.10517i | −0.00993431 | − | 0.564423i | ||||
\(118\) | 2.40420 | 0.221325 | ||||||||
\(119\) | 1.41645 | − | 1.51933i | 0.129845 | − | 0.139276i | ||||
\(120\) | −1.54198 | − | 2.67079i | −0.140763 | − | 0.243808i | ||||
\(121\) | −2.28546 | − | 3.95854i | −0.207769 | − | 0.359867i | ||||
\(122\) | 1.26628 | + | 2.19327i | 0.114644 | + | 0.198569i | ||||
\(123\) | 2.78605 | 0.251210 | ||||||||
\(124\) | −2.46255 | − | 4.26526i | −0.221143 | − | 0.383032i | ||||
\(125\) | 8.80581 | 0.787615 | ||||||||
\(126\) | −1.17062 | − | 0.270107i | −0.104287 | − | 0.0240631i | ||||
\(127\) | −0.894023 | − | 1.54849i | −0.0793317 | − | 0.137406i | 0.823630 | − | 0.567127i | \(-0.191945\pi\) |
−0.902962 | + | 0.429721i | \(0.858612\pi\) | |||||||
\(128\) | 7.82550 | 0.691683 | ||||||||
\(129\) | −1.28558 | − | 2.22668i | −0.113189 | − | 0.196049i | ||||
\(130\) | 2.12263 | − | 1.27583i | 0.186167 | − | 0.111897i | ||||
\(131\) | 3.19545 | − | 5.53469i | 0.279188 | − | 0.483568i | −0.691995 | − | 0.721902i | \(-0.743268\pi\) |
0.971183 | + | 0.238334i | \(0.0766014\pi\) | |||||||
\(132\) | −4.34819 | − | 7.53129i | −0.378461 | − | 0.655514i | ||||
\(133\) | 19.3229 | + | 4.45855i | 1.67551 | + | 0.386605i | ||||
\(134\) | −0.181328 | + | 0.314069i | −0.0156644 | + | 0.0271315i | ||||
\(135\) | 6.87158 | − | 11.9019i | 0.591412 | − | 1.02436i | ||||
\(136\) | 0.826887 | 0.0709050 | ||||||||
\(137\) | 10.0365 | 0.857480 | 0.428740 | − | 0.903428i | \(-0.358958\pi\) | ||||
0.428740 | + | 0.903428i | \(0.358958\pi\) | |||||||
\(138\) | 1.21901 | − | 2.11139i | 0.103769 | − | 0.179733i | ||||
\(139\) | 2.77278 | − | 4.80260i | 0.235184 | − | 0.407351i | −0.724142 | − | 0.689651i | \(-0.757764\pi\) |
0.959326 | + | 0.282300i | \(0.0910972\pi\) | |||||||
\(140\) | 3.82233 | + | 12.4968i | 0.323046 | + | 1.05617i | ||||
\(141\) | 0.752416 | + | 1.30322i | 0.0633648 | + | 0.109751i | ||||
\(142\) | 1.65114 | − | 2.85985i | 0.138560 | − | 0.239993i | ||||
\(143\) | 12.1943 | − | 7.32949i | 1.01974 | − | 0.612922i | ||||
\(144\) | 3.02619 | + | 5.24151i | 0.252182 | + | 0.436793i | ||||
\(145\) | −6.02455 | −0.500312 | ||||||||
\(146\) | 0.103039 | + | 0.178469i | 0.00852759 | + | 0.0147702i | ||||
\(147\) | −7.19217 | − | 3.50567i | −0.593200 | − | 0.289143i | ||||
\(148\) | −13.0285 | −1.07094 | ||||||||
\(149\) | −9.23254 | − | 15.9912i | −0.756359 | − | 1.31005i | −0.944696 | − | 0.327947i | \(-0.893643\pi\) |
0.188337 | − | 0.982104i | \(-0.439690\pi\) | |||||||
\(150\) | 0.478886 | 0.0391009 | ||||||||
\(151\) | −0.803678 | − | 1.39201i | −0.0654024 | − | 0.113280i | 0.831470 | − | 0.555570i | \(-0.187500\pi\) |
−0.896872 | + | 0.442289i | \(0.854166\pi\) | |||||||
\(152\) | 3.94710 | + | 6.83658i | 0.320152 | + | 0.554520i | ||||
\(153\) | 0.664795 | + | 1.15146i | 0.0537455 | + | 0.0930900i | ||||
\(154\) | −0.818755 | − | 2.67685i | −0.0659771 | − | 0.215707i | ||||
\(155\) | 6.54366 | 0.525600 | ||||||||
\(156\) | 6.81052 | − | 4.09353i | 0.545278 | − | 0.327744i | ||||
\(157\) | 0.822967 | + | 1.42542i | 0.0656799 | + | 0.113761i | 0.896995 | − | 0.442040i | \(-0.145745\pi\) |
−0.831315 | + | 0.555801i | \(0.812412\pi\) | |||||||
\(158\) | 0.830229 | − | 1.43800i | 0.0660494 | − | 0.114401i | ||||
\(159\) | −10.6066 | −0.841158 | ||||||||
\(160\) | −3.92548 | + | 6.79913i | −0.310337 | + | 0.537519i | ||||
\(161\) | −14.3524 | + | 15.3949i | −1.13113 | + | 1.21329i | ||||
\(162\) | −0.140949 | + | 0.244130i | −0.0110740 | + | 0.0191807i | ||||
\(163\) | 3.27409 | + | 5.67090i | 0.256447 | + | 0.444179i | 0.965287 | − | 0.261190i | \(-0.0841148\pi\) |
−0.708841 | + | 0.705369i | \(0.750782\pi\) | |||||||
\(164\) | −2.34986 | − | 4.07007i | −0.183493 | − | 0.317819i | ||||
\(165\) | 11.5543 | 0.899503 | ||||||||
\(166\) | 0.287677 | 0.0223281 | ||||||||
\(167\) | −4.77440 | − | 8.26950i | −0.369454 | − | 0.639913i | 0.620026 | − | 0.784581i | \(-0.287122\pi\) |
−0.989480 | + | 0.144668i | \(0.953789\pi\) | |||||||
\(168\) | −0.931600 | − | 3.04579i | −0.0718745 | − | 0.234988i | ||||
\(169\) | 6.89216 | + | 11.0226i | 0.530166 | + | 0.847894i | ||||
\(170\) | −0.269631 | + | 0.467015i | −0.0206798 | + | 0.0358184i | ||||
\(171\) | −6.34673 | + | 10.9929i | −0.485347 | + | 0.840646i | ||||
\(172\) | −2.16860 | + | 3.75613i | −0.165354 | + | 0.286402i | ||||
\(173\) | −5.56582 | − | 9.64028i | −0.423161 | − | 0.732937i | 0.573085 | − | 0.819496i | \(-0.305746\pi\) |
−0.996247 | + | 0.0865588i | \(0.972413\pi\) | |||||||
\(174\) | 0.720733 | 0.0546386 | ||||||||
\(175\) | −4.02837 | − | 0.929502i | −0.304516 | − | 0.0702638i | ||||
\(176\) | −7.05115 | + | 12.2130i | −0.531501 | + | 0.920586i | ||||
\(177\) | −5.12451 | + | 8.87592i | −0.385182 | + | 0.667155i | ||||
\(178\) | −2.05464 | −0.154002 | ||||||||
\(179\) | 6.32173 | − | 10.9496i | 0.472508 | − | 0.818409i | −0.526997 | − | 0.849867i | \(-0.676682\pi\) |
0.999505 | + | 0.0314588i | \(0.0100153\pi\) | |||||||
\(180\) | −8.36493 | −0.623485 | ||||||||
\(181\) | 14.9158 | 1.10868 | 0.554341 | − | 0.832289i | \(-0.312970\pi\) | ||||
0.554341 | + | 0.832289i | \(0.312970\pi\) | |||||||
\(182\) | 2.43235 | − | 0.791042i | 0.180298 | − | 0.0586359i | ||||
\(183\) | −10.7963 | −0.798082 | ||||||||
\(184\) | −8.37859 | −0.617678 | ||||||||
\(185\) | 8.65509 | − | 14.9911i | 0.636335 | − | 1.10216i | ||||
\(186\) | −0.782836 | −0.0574003 | ||||||||
\(187\) | −1.54900 | + | 2.68295i | −0.113274 | + | 0.196197i | ||||
\(188\) | 1.26923 | − | 2.19837i | 0.0925680 | − | 0.160332i | ||||
\(189\) | 9.67886 | − | 10.3819i | 0.704034 | − | 0.755170i | ||||
\(190\) | −5.14829 | −0.373496 | ||||||||
\(191\) | 7.06528 | + | 12.2374i | 0.511226 | + | 0.885469i | 0.999915 | + | 0.0130110i | \(0.00414165\pi\) |
−0.488690 | + | 0.872458i | \(0.662525\pi\) | |||||||
\(192\) | −3.61529 | + | 6.26187i | −0.260911 | + | 0.451912i | ||||
\(193\) | −1.94727 | + | 3.37277i | −0.140167 | + | 0.242777i | −0.927560 | − | 0.373675i | \(-0.878097\pi\) |
0.787392 | + | 0.616452i | \(0.211431\pi\) | |||||||
\(194\) | −0.317999 | + | 0.550790i | −0.0228310 | + | 0.0395444i | ||||
\(195\) | 0.185791 | + | 10.5558i | 0.0133048 | + | 0.755917i | ||||
\(196\) | 0.944795 | + | 13.4637i | 0.0674853 | + | 0.961689i | ||||
\(197\) | 5.85445 | + | 10.1402i | 0.417112 | + | 0.722459i | 0.995648 | − | 0.0931979i | \(-0.0297089\pi\) |
−0.578536 | + | 0.815657i | \(0.696376\pi\) | |||||||
\(198\) | 1.79179 | 0.127337 | ||||||||
\(199\) | 3.49684 | 0.247884 | 0.123942 | − | 0.992289i | \(-0.460446\pi\) | ||||
0.123942 | + | 0.992289i | \(0.460446\pi\) | |||||||
\(200\) | −0.822878 | − | 1.42527i | −0.0581863 | − | 0.100782i | ||||
\(201\) | −0.772995 | − | 1.33887i | −0.0545229 | − | 0.0944364i | ||||
\(202\) | −0.106892 | + | 0.185143i | −0.00752090 | + | 0.0130266i | ||||
\(203\) | −6.06279 | − | 1.39892i | −0.425524 | − | 0.0981850i | ||||
\(204\) | −0.865120 | + | 1.49843i | −0.0605705 | + | 0.104911i | ||||
\(205\) | 6.24421 | 0.436114 | ||||||||
\(206\) | 0.290403 | − | 0.502994i | 0.0202334 | − | 0.0350452i | ||||
\(207\) | −6.73617 | − | 11.6674i | −0.468196 | − | 0.810939i | ||||
\(208\) | −11.2709 | − | 6.24542i | −0.781497 | − | 0.433042i | ||||
\(209\) | −29.5764 | −2.04584 | ||||||||
\(210\) | 2.02400 | + | 0.467015i | 0.139669 | + | 0.0322271i | ||||
\(211\) | −9.50258 | − | 16.4589i | −0.654184 | − | 1.13308i | −0.982098 | − | 0.188373i | \(-0.939679\pi\) |
0.327913 | − | 0.944708i | \(-0.393655\pi\) | |||||||
\(212\) | 8.94598 | + | 15.4949i | 0.614412 | + | 1.06419i | ||||
\(213\) | 7.03874 | + | 12.1915i | 0.482286 | + | 0.835345i | ||||
\(214\) | 3.09047 | 0.211260 | ||||||||
\(215\) | −2.88128 | − | 4.99053i | −0.196502 | − | 0.340351i | ||||
\(216\) | 5.65029 | 0.384453 | ||||||||
\(217\) | 6.58519 | + | 1.51946i | 0.447032 | + | 0.103148i | ||||
\(218\) | 1.08299 | + | 1.87579i | 0.0733492 | + | 0.127045i | ||||
\(219\) | −0.878506 | −0.0593639 | ||||||||
\(220\) | −9.74533 | − | 16.8794i | −0.657030 | − | 1.13801i | ||||
\(221\) | −2.47600 | − | 1.37200i | −0.166554 | − | 0.0922906i | ||||
\(222\) | −1.03543 | + | 1.79342i | −0.0694936 | + | 0.120366i | ||||
\(223\) | 5.98311 | + | 10.3630i | 0.400658 | + | 0.693961i | 0.993805 | − | 0.111133i | \(-0.0354481\pi\) |
−0.593147 | + | 0.805094i | \(0.702115\pi\) | |||||||
\(224\) | −5.52918 | + | 5.93078i | −0.369434 | + | 0.396267i | ||||
\(225\) | 1.32315 | − | 2.29175i | 0.0882097 | − | 0.152784i | ||||
\(226\) | 1.07804 | − | 1.86723i | 0.0717104 | − | 0.124206i | ||||
\(227\) | 15.3842 | 1.02108 | 0.510542 | − | 0.859853i | \(-0.329445\pi\) | ||||
0.510542 | + | 0.859853i | \(0.329445\pi\) | |||||||
\(228\) | −16.5184 | −1.09396 | ||||||||
\(229\) | −4.33084 | + | 7.50123i | −0.286190 | + | 0.495695i | −0.972897 | − | 0.231239i | \(-0.925722\pi\) |
0.686707 | + | 0.726934i | \(0.259055\pi\) | |||||||
\(230\) | 2.73209 | − | 4.73212i | 0.180149 | − | 0.312027i | ||||
\(231\) | 11.6277 | + | 2.68295i | 0.765044 | + | 0.176525i | ||||
\(232\) | −1.23845 | − | 2.14506i | −0.0813082 | − | 0.140830i | ||||
\(233\) | −10.1253 | + | 17.5376i | −0.663333 | + | 1.14893i | 0.316402 | + | 0.948625i | \(0.397525\pi\) |
−0.979734 | + | 0.200301i | \(0.935808\pi\) | |||||||
\(234\) | 0.0288117 | + | 1.63695i | 0.00188348 | + | 0.107011i | ||||
\(235\) | 1.68634 | + | 2.92083i | 0.110005 | + | 0.190534i | ||||
\(236\) | 17.2888 | 1.12540 | ||||||||
\(237\) | 3.53924 | + | 6.13014i | 0.229898 | + | 0.398195i | ||||
\(238\) | −0.379785 | + | 0.407370i | −0.0246178 | + | 0.0264059i | ||||
\(239\) | 16.5526 | 1.07070 | 0.535350 | − | 0.844630i | \(-0.320180\pi\) | ||||
0.535350 | + | 0.844630i | \(0.320180\pi\) | |||||||
\(240\) | −5.23227 | − | 9.06256i | −0.337742 | − | 0.584985i | ||||
\(241\) | −16.4008 | −1.05647 | −0.528233 | − | 0.849100i | \(-0.677145\pi\) | ||||
−0.528233 | + | 0.849100i | \(0.677145\pi\) | |||||||
\(242\) | 0.612791 | + | 1.06138i | 0.0393917 | + | 0.0682284i | ||||
\(243\) | 7.44626 | + | 12.8973i | 0.477678 | + | 0.827362i | ||||
\(244\) | 9.10595 | + | 15.7720i | 0.582949 | + | 1.00970i | ||||
\(245\) | −16.1194 | − | 7.85704i | −1.02983 | − | 0.501968i | ||||
\(246\) | −0.747011 | −0.0476277 | ||||||||
\(247\) | −0.475582 | − | 27.0204i | −0.0302605 | − | 1.71927i | ||||
\(248\) | 1.34516 | + | 2.32989i | 0.0854178 | + | 0.147948i | ||||
\(249\) | −0.613178 | + | 1.06206i | −0.0388586 | + | 0.0673051i | ||||
\(250\) | −2.36106 | −0.149326 | ||||||||
\(251\) | 10.2154 | − | 17.6935i | 0.644788 | − | 1.11681i | −0.339563 | − | 0.940583i | \(-0.610279\pi\) |
0.984350 | − | 0.176222i | \(-0.0563876\pi\) | |||||||
\(252\) | −8.41802 | − | 1.94236i | −0.530285 | − | 0.122357i | ||||
\(253\) | 15.6956 | − | 27.1855i | 0.986772 | − | 1.70914i | ||||
\(254\) | 0.239710 | + | 0.415190i | 0.0150407 | + | 0.0260513i | ||||
\(255\) | −1.14943 | − | 1.99087i | −0.0719800 | − | 0.124673i | ||||
\(256\) | 10.5536 | 0.659602 | ||||||||
\(257\) | 13.7779 | 0.859442 | 0.429721 | − | 0.902962i | \(-0.358612\pi\) | ||||
0.429721 | + | 0.902962i | \(0.358612\pi\) | |||||||
\(258\) | 0.344695 | + | 0.597030i | 0.0214598 | + | 0.0371695i | ||||
\(259\) | 12.1910 | − | 13.0765i | 0.757511 | − | 0.812532i | ||||
\(260\) | 15.2640 | − | 9.17456i | 0.946633 | − | 0.568982i | ||||
\(261\) | 1.99136 | − | 3.44914i | 0.123262 | − | 0.213496i | ||||
\(262\) | −0.856782 | + | 1.48399i | −0.0529321 | + | 0.0916812i | ||||
\(263\) | −12.9587 | + | 22.4451i | −0.799065 | + | 1.38402i | 0.121160 | + | 0.992633i | \(0.461338\pi\) |
−0.920225 | + | 0.391389i | \(0.871995\pi\) | |||||||
\(264\) | 2.37519 | + | 4.11395i | 0.146183 | + | 0.253196i | ||||
\(265\) | −23.7719 | −1.46030 | ||||||||
\(266\) | −5.18096 | − | 1.19545i | −0.317665 | − | 0.0732977i | ||||
\(267\) | 4.37943 | − | 7.58540i | 0.268017 | − | 0.464219i | ||||
\(268\) | −1.30394 | + | 2.25850i | −0.0796510 | + | 0.137960i | ||||
\(269\) | −30.0666 | −1.83319 | −0.916596 | − | 0.399814i | \(-0.869075\pi\) | ||||
−0.916596 | + | 0.399814i | \(0.869075\pi\) | |||||||
\(270\) | −1.84245 | + | 3.19121i | −0.112128 | + | 0.194211i | ||||
\(271\) | 14.4505 | 0.877808 | 0.438904 | − | 0.898534i | \(-0.355367\pi\) | ||||
0.438904 | + | 0.898534i | \(0.355367\pi\) | |||||||
\(272\) | 2.80581 | 0.170127 | ||||||||
\(273\) | −2.26412 | + | 10.6659i | −0.137031 | + | 0.645533i | ||||
\(274\) | −2.69105 | −0.162572 | ||||||||
\(275\) | 6.16598 | 0.371822 | ||||||||
\(276\) | 8.76599 | − | 15.1831i | 0.527651 | − | 0.913918i | ||||
\(277\) | −15.3255 | −0.920819 | −0.460409 | − | 0.887707i | \(-0.652297\pi\) | ||||
−0.460409 | + | 0.887707i | \(0.652297\pi\) | |||||||
\(278\) | −0.743453 | + | 1.28770i | −0.0445894 | + | 0.0772310i | ||||
\(279\) | −2.16295 | + | 3.74634i | −0.129492 | + | 0.224287i | ||||
\(280\) | −2.08794 | − | 6.82634i | −0.124778 | − | 0.407952i | ||||
\(281\) | 5.29279 | 0.315741 | 0.157871 | − | 0.987460i | \(-0.449537\pi\) | ||||
0.157871 | + | 0.987460i | \(0.449537\pi\) | |||||||
\(282\) | −0.201742 | − | 0.349427i | −0.0120135 | − | 0.0208081i | ||||
\(283\) | 15.3923 | − | 26.6602i | 0.914975 | − | 1.58478i | 0.108036 | − | 0.994147i | \(-0.465544\pi\) |
0.806938 | − | 0.590636i | \(-0.201123\pi\) | |||||||
\(284\) | 11.8734 | − | 20.5654i | 0.704559 | − | 1.22033i | ||||
\(285\) | 10.9735 | − | 19.0066i | 0.650013 | − | 1.12586i | ||||
\(286\) | −3.26960 | + | 1.96522i | −0.193335 | + | 0.116206i | ||||
\(287\) | 6.28384 | + | 1.44992i | 0.370923 | + | 0.0855864i | ||||
\(288\) | −2.59507 | − | 4.49479i | −0.152916 | − | 0.264858i | ||||
\(289\) | −16.3836 | −0.963742 | ||||||||
\(290\) | 1.61533 | 0.0948557 | ||||||||
\(291\) | −1.35562 | − | 2.34800i | −0.0794677 | − | 0.137642i | ||||
\(292\) | 0.740963 | + | 1.28339i | 0.0433616 | + | 0.0751044i | ||||
\(293\) | 8.75864 | − | 15.1704i | 0.511685 | − | 0.886265i | −0.488223 | − | 0.872719i | \(-0.662355\pi\) |
0.999908 | − | 0.0135461i | \(-0.00431197\pi\) | |||||||
\(294\) | 1.92840 | + | 0.939958i | 0.112467 | + | 0.0548195i | ||||
\(295\) | −11.4853 | + | 19.8930i | −0.668697 | + | 1.15822i | ||||
\(296\) | 7.11681 | 0.413656 | ||||||||
\(297\) | −10.5847 | + | 18.3332i | −0.614184 | + | 1.06380i | ||||
\(298\) | 2.47548 | + | 4.28765i | 0.143400 | + | 0.248377i | ||||
\(299\) | 25.0886 | + | 13.9020i | 1.45091 | + | 0.803976i | ||||
\(300\) | 3.44370 | 0.198822 | ||||||||
\(301\) | −1.74075 | − | 5.69124i | −0.100335 | − | 0.328038i | ||||
\(302\) | 0.215486 | + | 0.373233i | 0.0123998 | + | 0.0214772i | ||||
\(303\) | −0.455678 | − | 0.789257i | −0.0261780 | − | 0.0453416i | ||||
\(304\) | 13.3934 | + | 23.1980i | 0.768163 | + | 1.33050i | ||||
\(305\) | −24.1970 | −1.38551 | ||||||||
\(306\) | −0.178248 | − | 0.308735i | −0.0101898 | − | 0.0176492i | ||||
\(307\) | −8.63573 | −0.492867 | −0.246434 | − | 0.969160i | \(-0.579259\pi\) | ||||
−0.246434 | + | 0.969160i | \(0.579259\pi\) | |||||||
\(308\) | −5.88773 | − | 19.2494i | −0.335484 | − | 1.09684i | ||||
\(309\) | 1.23798 | + | 2.14425i | 0.0704262 | + | 0.121982i | ||||
\(310\) | −1.75452 | −0.0996501 | ||||||||
\(311\) | 8.21130 | + | 14.2224i | 0.465620 | + | 0.806478i | 0.999229 | − | 0.0392535i | \(-0.0124980\pi\) |
−0.533609 | + | 0.845731i | \(0.679165\pi\) | |||||||
\(312\) | −3.72023 | + | 2.23608i | −0.210617 | + | 0.126593i | ||||
\(313\) | −5.02308 | + | 8.70024i | −0.283921 | + | 0.491766i | −0.972347 | − | 0.233541i | \(-0.924969\pi\) |
0.688426 | + | 0.725307i | \(0.258302\pi\) | |||||||
\(314\) | −0.220658 | − | 0.382191i | −0.0124525 | − | 0.0215683i | ||||
\(315\) | 7.82719 | − | 8.39570i | 0.441012 | − | 0.473044i | ||||
\(316\) | 5.97024 | − | 10.3408i | 0.335852 | − | 0.581713i | ||||
\(317\) | −5.07249 | + | 8.78581i | −0.284899 | + | 0.493460i | −0.972585 | − | 0.232549i | \(-0.925294\pi\) |
0.687685 | + | 0.726009i | \(0.258627\pi\) | |||||||
\(318\) | 2.84390 | 0.159478 | ||||||||
\(319\) | 9.27992 | 0.519576 | ||||||||
\(320\) | −8.10273 | + | 14.0343i | −0.452957 | + | 0.784544i | ||||
\(321\) | −6.58729 | + | 11.4095i | −0.367667 | + | 0.636817i | ||||
\(322\) | 3.84824 | − | 4.12775i | 0.214454 | − | 0.230031i | ||||
\(323\) | 2.94227 | + | 5.09616i | 0.163712 | + | 0.283558i | ||||
\(324\) | −1.01357 | + | 1.75556i | −0.0563095 | + | 0.0975310i | ||||
\(325\) | 0.0991476 | + | 5.63312i | 0.00549972 | + | 0.312469i | ||||
\(326\) | −0.877867 | − | 1.52051i | −0.0486206 | − | 0.0842133i | ||||
\(327\) | −9.23349 | −0.510613 | ||||||||
\(328\) | 1.28360 | + | 2.22327i | 0.0708751 | + | 0.122759i | ||||
\(329\) | 1.01882 | + | 3.33094i | 0.0561693 | + | 0.183641i | ||||
\(330\) | −3.09801 | −0.170540 | ||||||||
\(331\) | −1.15958 | − | 2.00845i | −0.0637363 | − | 0.110395i | 0.832396 | − | 0.554181i | \(-0.186968\pi\) |
−0.896133 | + | 0.443786i | \(0.853635\pi\) | |||||||
\(332\) | 2.06871 | 0.113535 | ||||||||
\(333\) | 5.72172 | + | 9.91032i | 0.313549 | + | 0.543082i | ||||
\(334\) | 1.28014 | + | 2.21726i | 0.0700460 | + | 0.121323i | ||||
\(335\) | −1.73247 | − | 3.00072i | −0.0946547 | − | 0.163947i | ||||
\(336\) | −3.16112 | − | 10.3350i | −0.172453 | − | 0.563822i | ||||
\(337\) | −15.9998 | −0.871565 | −0.435783 | − | 0.900052i | \(-0.643528\pi\) | ||||
−0.435783 | + | 0.900052i | \(0.643528\pi\) | |||||||
\(338\) | −1.84796 | − | 2.95544i | −0.100516 | − | 0.160755i | ||||
\(339\) | 4.59567 | + | 7.95993i | 0.249602 | + | 0.432324i | ||||
\(340\) | −1.93894 | + | 3.35834i | −0.105154 | + | 0.182132i | ||||
\(341\) | −10.0795 | −0.545837 | ||||||||
\(342\) | 1.70172 | − | 2.94747i | 0.0920185 | − | 0.159381i | ||||
\(343\) | −14.3972 | − | 11.6499i | −0.777378 | − | 0.629034i | ||||
\(344\) | 1.18459 | − | 2.05178i | 0.0638690 | − | 0.110624i | ||||
\(345\) | 11.6468 | + | 20.1729i | 0.627043 | + | 1.08607i | ||||
\(346\) | 1.49234 | + | 2.58480i | 0.0802285 | + | 0.138960i | ||||
\(347\) | −22.8208 | −1.22509 | −0.612543 | − | 0.790437i | \(-0.709853\pi\) | ||||
−0.612543 | + | 0.790437i | \(0.709853\pi\) | |||||||
\(348\) | 5.18285 | 0.277830 | ||||||||
\(349\) | 11.3511 | + | 19.6607i | 0.607612 | + | 1.05241i | 0.991633 | + | 0.129090i | \(0.0412056\pi\) |
−0.384021 | + | 0.923324i | \(0.625461\pi\) | |||||||
\(350\) | 1.08011 | + | 0.249223i | 0.0577342 | + | 0.0133215i | ||||
\(351\) | −16.9190 | − | 9.37515i | −0.903071 | − | 0.500408i | ||||
\(352\) | 6.04662 | − | 10.4731i | 0.322286 | − | 0.558216i | ||||
\(353\) | 13.6322 | − | 23.6116i | 0.725568 | − | 1.25672i | −0.233171 | − | 0.972436i | \(-0.574910\pi\) |
0.958740 | − | 0.284286i | \(-0.0917564\pi\) | |||||||
\(354\) | 1.37401 | − | 2.37986i | 0.0730279 | − | 0.126488i | ||||
\(355\) | 15.7755 | + | 27.3239i | 0.837276 | + | 1.45020i | ||||
\(356\) | −14.7751 | −0.783077 | ||||||||
\(357\) | −0.694438 | − | 2.27041i | −0.0367535 | − | 0.120163i | ||||
\(358\) | −1.69502 | + | 2.93585i | −0.0895844 | + | 0.155165i | ||||
\(359\) | 7.21309 | − | 12.4934i | 0.380692 | − | 0.659378i | −0.610469 | − | 0.792040i | \(-0.709019\pi\) |
0.991161 | + | 0.132662i | \(0.0423524\pi\) | |||||||
\(360\) | 4.56932 | 0.240824 | ||||||||
\(361\) | −18.5895 | + | 32.1980i | −0.978397 | + | 1.69463i | ||||
\(362\) | −3.99930 | −0.210199 | ||||||||
\(363\) | −5.22461 | −0.274221 | ||||||||
\(364\) | 17.4912 | − | 5.68844i | 0.916790 | − | 0.298155i | ||||
\(365\) | −1.96894 | −0.103059 | ||||||||
\(366\) | 2.89475 | 0.151311 | ||||||||
\(367\) | 5.69586 | − | 9.86553i | 0.297322 | − | 0.514976i | −0.678201 | − | 0.734877i | \(-0.737240\pi\) |
0.975522 | + | 0.219901i | \(0.0705733\pi\) | |||||||
\(368\) | −28.4304 | −1.48204 | ||||||||
\(369\) | −2.06397 | + | 3.57489i | −0.107446 | + | 0.186102i | ||||
\(370\) | −2.32065 | + | 4.01948i | −0.120645 | + | 0.208963i | ||||
\(371\) | −23.9228 | − | 5.51991i | −1.24201 | − | 0.286580i | ||||
\(372\) | −5.62943 | −0.291872 | ||||||||
\(373\) | 15.4815 | + | 26.8147i | 0.801599 | + | 1.38841i | 0.918563 | + | 0.395274i | \(0.129351\pi\) |
−0.116964 | + | 0.993136i | \(0.537316\pi\) | |||||||
\(374\) | 0.415327 | − | 0.719367i | 0.0214760 | − | 0.0371976i | ||||
\(375\) | 5.03256 | − | 8.71665i | 0.259880 | − | 0.450126i | ||||
\(376\) | −0.693313 | + | 1.20085i | −0.0357549 | + | 0.0619293i | ||||
\(377\) | 0.149219 | + | 8.47796i | 0.00768518 | + | 0.436637i | ||||
\(378\) | −2.59515 | + | 2.78364i | −0.133480 | + | 0.143175i | ||||
\(379\) | −5.29330 | − | 9.16826i | −0.271898 | − | 0.470942i | 0.697450 | − | 0.716634i | \(-0.254318\pi\) |
−0.969348 | + | 0.245692i | \(0.920985\pi\) | |||||||
\(380\) | −37.0217 | −1.89917 | ||||||||
\(381\) | −2.04375 | −0.104705 | ||||||||
\(382\) | −1.89438 | − | 3.28116i | −0.0969249 | − | 0.167879i | ||||
\(383\) | −15.3758 | − | 26.6317i | −0.785668 | − | 1.36082i | −0.928599 | − | 0.371084i | \(-0.878986\pi\) |
0.142931 | − | 0.989733i | \(-0.454347\pi\) | |||||||
\(384\) | 4.47231 | − | 7.74627i | 0.228227 | − | 0.395300i | ||||
\(385\) | 26.0603 | + | 6.01313i | 1.32816 | + | 0.306458i | ||||
\(386\) | 0.522112 | − | 0.904324i | 0.0265748 | − | 0.0460289i | ||||
\(387\) | 3.80953 | 0.193649 | ||||||||
\(388\) | −2.28675 | + | 3.96077i | −0.116092 | + | 0.201078i | ||||
\(389\) | 8.18978 | + | 14.1851i | 0.415239 | + | 0.719214i | 0.995453 | − | 0.0952492i | \(-0.0303648\pi\) |
−0.580215 | + | 0.814463i | \(0.697031\pi\) | |||||||
\(390\) | −0.0498153 | − | 2.83028i | −0.00252249 | − | 0.143317i | ||||
\(391\) | −6.24561 | −0.315854 | ||||||||
\(392\) | −0.516092 | − | 7.35449i | −0.0260666 | − | 0.371458i | ||||
\(393\) | −3.65243 | − | 6.32620i | −0.184241 | − | 0.319114i | ||||
\(394\) | −1.56972 | − | 2.71884i | −0.0790816 | − | 0.136973i | ||||
\(395\) | 7.93227 | + | 13.7391i | 0.399116 | + | 0.691289i | ||||
\(396\) | 12.8849 | 0.647492 | ||||||||
\(397\) | 7.94133 | + | 13.7548i | 0.398564 | + | 0.690333i | 0.993549 | − | 0.113404i | \(-0.0361755\pi\) |
−0.594985 | + | 0.803737i | \(0.702842\pi\) | |||||||
\(398\) | −0.937591 | −0.0469972 | ||||||||
\(399\) | 15.4565 | − | 16.5792i | 0.773795 | − | 0.829997i | ||||
\(400\) | −2.79221 | − | 4.83624i | −0.139610 | − | 0.241812i | ||||
\(401\) | 6.63573 | 0.331373 | 0.165686 | − | 0.986178i | \(-0.447016\pi\) | ||||
0.165686 | + | 0.986178i | \(0.447016\pi\) | |||||||
\(402\) | 0.207259 | + | 0.358984i | 0.0103372 | + | 0.0179045i | ||||
\(403\) | −0.162077 | − | 9.20847i | −0.00807362 | − | 0.458707i | ||||
\(404\) | −0.768670 | + | 1.33137i | −0.0382427 | + | 0.0662384i | ||||
\(405\) | −1.34667 | − | 2.33250i | −0.0669164 | − | 0.115903i | ||||
\(406\) | 1.62559 | + | 0.375086i | 0.0806765 | + | 0.0186152i | ||||
\(407\) | −13.3319 | + | 23.0915i | −0.660836 | + | 1.14460i | ||||
\(408\) | 0.472570 | − | 0.818515i | 0.0233957 | − | 0.0405225i | ||||
\(409\) | 5.87235 | 0.290369 | 0.145184 | − | 0.989405i | \(-0.453622\pi\) | ||||
0.145184 | + | 0.989405i | \(0.453622\pi\) | |||||||
\(410\) | −1.67423 | −0.0826843 | ||||||||
\(411\) | 5.73593 | − | 9.93492i | 0.282933 | − | 0.490053i | ||||
\(412\) | 2.08831 | − | 3.61707i | 0.102884 | − | 0.178200i | ||||
\(413\) | −16.1774 | + | 17.3524i | −0.796037 | + | 0.853855i | ||||
\(414\) | 1.80614 | + | 3.12832i | 0.0887667 | + | 0.153749i | ||||
\(415\) | −1.37428 | + | 2.38032i | −0.0674607 | + | 0.116845i | ||||
\(416\) | 9.66521 | + | 5.35567i | 0.473876 | + | 0.262584i | ||||
\(417\) | −3.16932 | − | 5.48942i | −0.155202 | − | 0.268818i | ||||
\(418\) | 7.93017 | 0.387877 | ||||||||
\(419\) | 15.0712 | + | 26.1040i | 0.736274 | + | 1.27526i | 0.954162 | + | 0.299290i | \(0.0967499\pi\) |
−0.217888 | + | 0.975974i | \(0.569917\pi\) | |||||||
\(420\) | 14.5547 | + | 3.35834i | 0.710198 | + | 0.163870i | ||||
\(421\) | 40.0580 | 1.95231 | 0.976153 | − | 0.217083i | \(-0.0696543\pi\) | ||||
0.976153 | + | 0.217083i | \(0.0696543\pi\) | |||||||
\(422\) | 2.54788 | + | 4.41306i | 0.124029 | + | 0.214824i | ||||
\(423\) | −2.22962 | −0.108408 | ||||||||
\(424\) | −4.88672 | − | 8.46405i | −0.237320 | − | 0.411051i | ||||
\(425\) | −0.613394 | − | 1.06243i | −0.0297540 | − | 0.0515354i | ||||
\(426\) | −1.88726 | − | 3.26884i | −0.0914382 | − | 0.158376i | ||||
\(427\) | −24.3506 | − | 5.61862i | −1.17841 | − | 0.271904i | ||||
\(428\) | 22.2238 | 1.07423 | ||||||||
\(429\) | −0.286184 | − | 16.2597i | −0.0138171 | − | 0.785024i | ||||
\(430\) | 0.772544 | + | 1.33809i | 0.0372554 | + | 0.0645282i | ||||
\(431\) | 1.95793 | − | 3.39124i | 0.0943104 | − | 0.163350i | −0.815010 | − | 0.579447i | \(-0.803269\pi\) |
0.909321 | + | 0.416096i | \(0.136602\pi\) | |||||||
\(432\) | 19.1726 | 0.922445 | ||||||||
\(433\) | 20.3963 | − | 35.3274i | 0.980182 | − | 1.69772i | 0.318532 | − | 0.947912i | \(-0.396810\pi\) |
0.661650 | − | 0.749813i | \(-0.269856\pi\) | |||||||
\(434\) | −1.76566 | − | 0.407405i | −0.0847542 | − | 0.0195561i | ||||
\(435\) | −3.44306 | + | 5.96355i | −0.165082 | + | 0.285930i | ||||
\(436\) | 7.78785 | + | 13.4890i | 0.372971 | + | 0.646004i | ||||
\(437\) | −29.8131 | − | 51.6378i | −1.42615 | − | 2.47017i | ||||
\(438\) | 0.235549 | 0.0112550 | ||||||||
\(439\) | −25.5623 | −1.22002 | −0.610010 | − | 0.792394i | \(-0.708835\pi\) | ||||
−0.610010 | + | 0.792394i | \(0.708835\pi\) | |||||||
\(440\) | 5.32336 | + | 9.22033i | 0.253781 | + | 0.439562i | ||||
\(441\) | 9.82637 | − | 6.63149i | 0.467923 | − | 0.315785i | ||||
\(442\) | 0.663878 | + | 0.367867i | 0.0315775 | + | 0.0174977i | ||||
\(443\) | 13.7282 | − | 23.7779i | 0.652247 | − | 1.12972i | −0.330330 | − | 0.943866i | \(-0.607160\pi\) |
0.982576 | − | 0.185859i | \(-0.0595067\pi\) | |||||||
\(444\) | −7.44586 | + | 12.8966i | −0.353365 | + | 0.612046i | ||||
\(445\) | 9.81535 | − | 17.0007i | 0.465292 | − | 0.805910i | ||||
\(446\) | −1.60422 | − | 2.77859i | −0.0759621 | − | 0.131570i | ||||
\(447\) | −21.1057 | −0.998267 | ||||||||
\(448\) | −11.4130 | + | 12.2419i | −0.539213 | + | 0.578377i | ||||
\(449\) | 7.40181 | − | 12.8203i | 0.349313 | − | 0.605028i | −0.636815 | − | 0.771017i | \(-0.719748\pi\) |
0.986128 | + | 0.165989i | \(0.0530816\pi\) | |||||||
\(450\) | −0.354769 | + | 0.614477i | −0.0167240 | + | 0.0289667i | ||||
\(451\) | −9.61827 | −0.452907 | ||||||||
\(452\) | 7.75230 | − | 13.4274i | 0.364637 | − | 0.631571i | ||||
\(453\) | −1.83722 | −0.0863203 | ||||||||
\(454\) | −4.12489 | −0.193590 | ||||||||
\(455\) | −5.07444 | + | 23.9049i | −0.237893 | + | 1.12068i | ||||
\(456\) | 9.02315 | 0.422548 | ||||||||
\(457\) | −0.651951 | −0.0304970 | −0.0152485 | − | 0.999884i | \(-0.504854\pi\) | ||||
−0.0152485 | + | 0.999884i | \(0.504854\pi\) | |||||||
\(458\) | 1.16121 | − | 2.01127i | 0.0542596 | − | 0.0939805i | ||||
\(459\) | 4.21186 | 0.196593 | ||||||||
\(460\) | 19.6467 | − | 34.0290i | 0.916031 | − | 1.58661i | ||||
\(461\) | −6.24774 | + | 10.8214i | −0.290986 | + | 0.504003i | −0.974043 | − | 0.226362i | \(-0.927317\pi\) |
0.683057 | + | 0.730365i | \(0.260650\pi\) | |||||||
\(462\) | −3.11767 | − | 0.719367i | −0.145047 | − | 0.0334680i | ||||
\(463\) | −0.309503 | −0.0143838 | −0.00719190 | − | 0.999974i | \(-0.502289\pi\) | ||||
−0.00719190 | + | 0.999974i | \(0.502289\pi\) | |||||||
\(464\) | −4.20233 | − | 7.27865i | −0.195088 | − | 0.337903i | ||||
\(465\) | 3.73973 | − | 6.47741i | 0.173426 | − | 0.300382i | ||||
\(466\) | 2.71486 | − | 4.70227i | 0.125763 | − | 0.217829i | ||||
\(467\) | −12.2387 | + | 21.1980i | −0.566338 | + | 0.980926i | 0.430586 | + | 0.902549i | \(0.358307\pi\) |
−0.996924 | + | 0.0783762i | \(0.975026\pi\) | |||||||
\(468\) | 0.207187 | + | 11.7714i | 0.00957722 | + | 0.544134i | ||||
\(469\) | −1.04668 | − | 3.42205i | −0.0483314 | − | 0.158016i | ||||
\(470\) | −0.452151 | − | 0.783149i | −0.0208562 | − | 0.0361240i | ||||
\(471\) | 1.88132 | 0.0866865 | ||||||||
\(472\) | −9.44396 | −0.434694 | ||||||||
\(473\) | 4.43818 | + | 7.68716i | 0.204068 | + | 0.353456i | ||||
\(474\) | −0.948959 | − | 1.64364i | −0.0435871 | − | 0.0754951i | ||||
\(475\) | 5.85601 | − | 10.1429i | 0.268692 | − | 0.465389i | ||||
\(476\) | −2.73106 | + | 2.92943i | −0.125178 | + | 0.134270i | ||||
\(477\) | 7.85759 | − | 13.6097i | 0.359774 | − | 0.623147i | ||||
\(478\) | −4.43817 | −0.202997 | ||||||||
\(479\) | −4.06925 | + | 7.04815i | −0.185929 | + | 0.322038i | −0.943889 | − | 0.330262i | \(-0.892863\pi\) |
0.757960 | + | 0.652301i | \(0.226196\pi\) | |||||||
\(480\) | 4.48686 | + | 7.77147i | 0.204796 | + | 0.354718i | ||||
\(481\) | −21.3103 | − | 11.8084i | −0.971667 | − | 0.538419i | ||||
\(482\) | 4.39746 | 0.200299 | ||||||||
\(483\) | 7.03653 | + | 23.0053i | 0.320173 | + | 1.04678i | ||||
\(484\) | 4.40662 | + | 7.63250i | 0.200301 | + | 0.346932i | ||||
\(485\) | −3.03826 | − | 5.26243i | −0.137960 | − | 0.238954i | ||||
\(486\) | −1.99653 | − | 3.45809i | −0.0905645 | − | 0.156862i | ||||
\(487\) | 4.60960 | 0.208881 | 0.104440 | − | 0.994531i | \(-0.466695\pi\) | ||||
0.104440 | + | 0.994531i | \(0.466695\pi\) | |||||||
\(488\) | −4.97410 | − | 8.61540i | −0.225167 | − | 0.390001i | ||||
\(489\) | 7.48464 | 0.338467 | ||||||||
\(490\) | 4.32201 | + | 2.10667i | 0.195248 | + | 0.0951696i | ||||
\(491\) | −6.50947 | − | 11.2747i | −0.293768 | − | 0.508822i | 0.680929 | − | 0.732349i | \(-0.261576\pi\) |
−0.974698 | + | 0.223527i | \(0.928243\pi\) | |||||||
\(492\) | −5.37181 | −0.242180 | ||||||||
\(493\) | −0.923171 | − | 1.59898i | −0.0415775 | − | 0.0720144i | ||||
\(494\) | 0.127515 | + | 7.24485i | 0.00573719 | + | 0.325961i | ||||
\(495\) | −8.55969 | + | 14.8258i | −0.384729 | + | 0.666371i | ||||
\(496\) | 4.56443 | + | 7.90582i | 0.204949 | + | 0.354982i | ||||
\(497\) | 9.53090 | + | 31.1605i | 0.427519 | + | 1.39774i | ||||
\(498\) | 0.164409 | − | 0.284764i | 0.00736733 | − | 0.0127606i | ||||
\(499\) | 16.1603 | − | 27.9905i | 0.723436 | − | 1.25303i | −0.236178 | − | 0.971710i | \(-0.575895\pi\) |
0.959614 | − | 0.281319i | \(-0.0907717\pi\) | |||||||
\(500\) | −16.9786 | −0.759304 | ||||||||
\(501\) | −10.9144 | −0.487618 | ||||||||
\(502\) | −2.73900 | + | 4.74408i | −0.122247 | + | 0.211739i | ||||
\(503\) | 15.9126 | − | 27.5615i | 0.709509 | − | 1.22891i | −0.255531 | − | 0.966801i | \(-0.582250\pi\) |
0.965039 | − | 0.262105i | \(-0.0844165\pi\) | |||||||
\(504\) | 4.59832 | + | 1.06101i | 0.204826 | + | 0.0472612i | ||||
\(505\) | −1.02128 | − | 1.76891i | −0.0454465 | − | 0.0787156i | ||||
\(506\) | −4.20838 | + | 7.28912i | −0.187085 | + | 0.324041i | ||||
\(507\) | 14.8499 | − | 0.522904i | 0.659508 | − | 0.0232230i | ||||
\(508\) | 1.72377 | + | 2.98566i | 0.0764801 | + | 0.132467i | ||||
\(509\) | 2.25575 | 0.0999845 | 0.0499922 | − | 0.998750i | \(-0.484080\pi\) | ||||
0.0499922 | + | 0.998750i | \(0.484080\pi\) | |||||||
\(510\) | 0.308191 | + | 0.533802i | 0.0136469 | + | 0.0236372i | ||||
\(511\) | −1.98144 | − | 0.457194i | −0.0876536 | − | 0.0202251i | ||||
\(512\) | −18.4807 | −0.816739 | ||||||||
\(513\) | 20.1051 | + | 34.8231i | 0.887663 | + | 1.53748i | ||||
\(514\) | −3.69420 | −0.162944 | ||||||||
\(515\) | 2.77461 | + | 4.80576i | 0.122264 | + | 0.211767i | ||||
\(516\) | 2.47873 | + | 4.29329i | 0.109120 | + | 0.189001i | ||||
\(517\) | −2.59756 | − | 4.49911i | −0.114241 | − | 0.197870i | ||||
\(518\) | −3.26871 | + | 3.50613i | −0.143619 | + | 0.154050i | ||||
\(519\) | −12.7236 | −0.558502 | ||||||||
\(520\) | −8.33793 | + | 5.01158i | −0.365642 | + | 0.219773i | ||||
\(521\) | −5.38562 | − | 9.32817i | −0.235948 | − | 0.408675i | 0.723600 | − | 0.690220i | \(-0.242486\pi\) |
−0.959548 | + | 0.281546i | \(0.909153\pi\) | |||||||
\(522\) | −0.533934 | + | 0.924801i | −0.0233697 | + | 0.0404775i | ||||
\(523\) | 7.40793 | 0.323926 | 0.161963 | − | 0.986797i | \(-0.448217\pi\) | ||||
0.161963 | + | 0.986797i | \(0.448217\pi\) | |||||||
\(524\) | −6.16118 | + | 10.6715i | −0.269152 | + | 0.466186i | ||||
\(525\) | −3.22232 | + | 3.45637i | −0.140634 | + | 0.150848i | ||||
\(526\) | 3.47454 | − | 6.01809i | 0.151497 | − | 0.262401i | ||||
\(527\) | 1.00272 | + | 1.73676i | 0.0436790 | + | 0.0756543i | ||||
\(528\) | 8.05953 | + | 13.9595i | 0.350746 | + | 0.607510i | ||||
\(529\) | 40.2848 | 1.75151 | ||||||||
\(530\) | 6.37385 | 0.276862 | ||||||||
\(531\) | −7.59270 | − | 13.1509i | −0.329495 | − | 0.570702i | ||||
\(532\) | −37.2567 | − | 8.59656i | −1.61528 | − | 0.372708i | ||||
\(533\) | −0.154660 | − | 8.78707i | −0.00669906 | − | 0.380610i | ||||
\(534\) | −1.17424 | + | 2.03384i | −0.0508142 | + | 0.0880127i | ||||
\(535\) | −14.7637 | + | 25.5715i | −0.638290 | + | 1.10555i | ||||
\(536\) | 0.712276 | − | 1.23370i | 0.0307656 | − | 0.0532876i | ||||
\(537\) | −7.22580 | − | 12.5154i | −0.311816 | − | 0.540081i | ||||
\(538\) | 8.06161 | 0.347561 | ||||||||
\(539\) | 24.8295 | + | 12.1026i | 1.06948 | + | 0.521296i | ||||
\(540\) | −13.2492 | + | 22.9482i | −0.570153 | + | 0.987534i | ||||
\(541\) | −16.2741 | + | 28.1875i | −0.699676 | + | 1.21188i | 0.268902 | + | 0.963168i | \(0.413339\pi\) |
−0.968579 | + | 0.248708i | \(0.919994\pi\) | |||||||
\(542\) | −3.87455 | −0.166426 | ||||||||
\(543\) | 8.52445 | − | 14.7648i | 0.365819 | − | 0.633617i | ||||
\(544\) | −2.40608 | −0.103160 | ||||||||
\(545\) | −20.6944 | −0.886453 | ||||||||
\(546\) | 0.607069 | − | 2.85981i | 0.0259801 | − | 0.122389i | ||||
\(547\) | −13.4997 | −0.577206 | −0.288603 | − | 0.957449i | \(-0.593191\pi\) | ||||
−0.288603 | + | 0.957449i | \(0.593191\pi\) | |||||||
\(548\) | −19.3515 | −0.826657 | ||||||||
\(549\) | 7.99810 | − | 13.8531i | 0.341350 | − | 0.591236i | ||||
\(550\) | −1.65325 | −0.0704950 | ||||||||
\(551\) | 8.81342 | − | 15.2653i | 0.375464 | − | 0.650323i | ||||
\(552\) | −4.78840 | + | 8.29376i | −0.203808 | + | 0.353006i | ||||
\(553\) | 4.79235 | + | 15.6682i | 0.203792 | + | 0.666280i | ||||
\(554\) | 4.10915 | 0.174581 | ||||||||
\(555\) | −9.89284 | − | 17.1349i | −0.419928 | − | 0.727336i | ||||
\(556\) | −5.34623 | + | 9.25994i | −0.226731 | + | 0.392709i | ||||
\(557\) | 14.8851 | − | 25.7818i | 0.630703 | − | 1.09241i | −0.356705 | − | 0.934217i | \(-0.616100\pi\) |
0.987408 | − | 0.158193i | \(-0.0505668\pi\) | |||||||
\(558\) | 0.579941 | − | 1.00449i | 0.0245509 | − | 0.0425233i | ||||
\(559\) | −6.95148 | + | 4.17825i | −0.294016 | + | 0.176721i | ||||
\(560\) | −7.08483 | − | 23.1632i | −0.299389 | − | 0.978826i | ||||
\(561\) | 1.77052 | + | 3.06664i | 0.0747516 | + | 0.129474i | ||||
\(562\) | −1.41913 | −0.0598624 | ||||||||
\(563\) | 14.1326 | 0.595617 | 0.297809 | − | 0.954626i | \(-0.403744\pi\) | ||||
0.297809 | + | 0.954626i | \(0.403744\pi\) | |||||||
\(564\) | −1.45074 | − | 2.51275i | −0.0610872 | − | 0.105806i | ||||
\(565\) | 10.3000 | + | 17.8401i | 0.433324 | + | 0.750538i | ||||
\(566\) | −4.12705 | + | 7.14826i | −0.173473 | + | 0.300464i | ||||
\(567\) | −0.813601 | − | 2.66000i | −0.0341680 | − | 0.111710i | ||||
\(568\) | −6.48584 | + | 11.2338i | −0.272140 | + | 0.471360i | ||||
\(569\) | −24.2540 | −1.01678 | −0.508391 | − | 0.861127i | \(-0.669759\pi\) | ||||
−0.508391 | + | 0.861127i | \(0.669759\pi\) | |||||||
\(570\) | −2.94227 | + | 5.09616i | −0.123238 | + | 0.213455i | ||||
\(571\) | −0.604159 | − | 1.04643i | −0.0252832 | − | 0.0437919i | 0.853107 | − | 0.521736i | \(-0.174715\pi\) |
−0.878390 | + | 0.477944i | \(0.841382\pi\) | |||||||
\(572\) | −23.5119 | + | 14.1320i | −0.983083 | + | 0.590891i | ||||
\(573\) | 16.1514 | 0.674732 | ||||||||
\(574\) | −1.68486 | − | 0.388761i | −0.0703245 | − | 0.0162266i | ||||
\(575\) | 6.21533 | + | 10.7653i | 0.259197 | + | 0.448943i | ||||
\(576\) | −5.35657 | − | 9.27786i | −0.223191 | − | 0.386577i | ||||
\(577\) | 7.30518 | + | 12.6529i | 0.304119 | + | 0.526749i | 0.977065 | − | 0.212943i | \(-0.0683047\pi\) |
−0.672946 | + | 0.739692i | \(0.734971\pi\) | |||||||
\(578\) | 4.39286 | 0.182719 | ||||||||
\(579\) | 2.22575 | + | 3.85510i | 0.0924988 | + | 0.160213i | ||||
\(580\) | 11.6160 | 0.482328 | ||||||||
\(581\) | −1.93572 | + | 2.07632i | −0.0803072 | + | 0.0861401i | ||||
\(582\) | 0.363475 | + | 0.629558i | 0.0150665 | + | 0.0260960i | ||||
\(583\) | 36.6171 | 1.51652 | ||||||||
\(584\) | −0.404749 | − | 0.701046i | −0.0167486 | − | 0.0290095i | ||||
\(585\) | −13.6822 | − | 7.58157i | −0.565690 | − | 0.313459i | ||||
\(586\) | −2.34841 | + | 4.06757i | −0.0970120 | + | 0.168030i | ||||
\(587\) | −10.7548 | − | 18.6278i | −0.443897 | − | 0.768852i | 0.554078 | − | 0.832465i | \(-0.313071\pi\) |
−0.997975 | + | 0.0636132i | \(0.979738\pi\) | |||||||
\(588\) | 13.8673 | + | 6.75931i | 0.571877 | + | 0.278749i | ||||
\(589\) | −9.57284 | + | 16.5806i | −0.394442 | + | 0.683193i | ||||
\(590\) | 3.07949 | − | 5.33383i | 0.126780 | − | 0.219590i | ||||
\(591\) | 13.3834 | 0.550518 | ||||||||
\(592\) | 24.1489 | 0.992512 | ||||||||
\(593\) | 1.32429 | − | 2.29373i | 0.0543820 | − | 0.0941923i | −0.837553 | − | 0.546356i | \(-0.816014\pi\) |
0.891935 | + | 0.452164i | \(0.149348\pi\) | |||||||
\(594\) | 2.83801 | − | 4.91558i | 0.116445 | − | 0.201689i | ||||
\(595\) | −1.55640 | − | 5.08852i | −0.0638062 | − | 0.208609i | ||||
\(596\) | 17.8013 | + | 30.8328i | 0.729171 | + | 1.26296i | ||||
\(597\) | 1.99846 | − | 3.46143i | 0.0817915 | − | 0.141667i | ||||
\(598\) | −6.72688 | − | 3.72749i | −0.275082 | − | 0.152428i | ||||
\(599\) | 20.1250 | + | 34.8576i | 0.822287 | + | 1.42424i | 0.903975 | + | 0.427584i | \(0.140635\pi\) |
−0.0816889 | + | 0.996658i | \(0.526031\pi\) | |||||||
\(600\) | −1.88112 | −0.0767962 | ||||||||
\(601\) | −19.1725 | − | 33.2077i | −0.782061 | − | 1.35457i | −0.930739 | − | 0.365683i | \(-0.880835\pi\) |
0.148679 | − | 0.988886i | \(-0.452498\pi\) | |||||||
\(602\) | 0.466740 | + | 1.52597i | 0.0190229 | + | 0.0621937i | ||||
\(603\) | 2.29060 | 0.0932806 | ||||||||
\(604\) | 1.54958 | + | 2.68395i | 0.0630515 | + | 0.109208i | ||||
\(605\) | −11.7096 | −0.476063 | ||||||||
\(606\) | 0.122179 | + | 0.211620i | 0.00496317 | + | 0.00859646i | ||||
\(607\) | −21.2773 | − | 36.8534i | −0.863620 | − | 1.49583i | −0.868411 | − | 0.495845i | \(-0.834858\pi\) |
0.00479063 | − | 0.999989i | \(-0.498475\pi\) | |||||||
\(608\) | −11.4853 | − | 19.8931i | −0.465791 | − | 0.806773i | ||||
\(609\) | −4.84967 | + | 5.20191i | −0.196518 | + | 0.210792i | ||||
\(610\) | 6.48782 | 0.262684 | ||||||||
\(611\) | 4.06853 | − | 2.44543i | 0.164595 | − | 0.0989314i | ||||
\(612\) | −1.28180 | − | 2.22014i | −0.0518136 | − | 0.0897438i | ||||
\(613\) | −7.63261 | + | 13.2201i | −0.308278 | + | 0.533953i | −0.977986 | − | 0.208672i | \(-0.933086\pi\) |
0.669708 | + | 0.742625i | \(0.266419\pi\) | |||||||
\(614\) | 2.31546 | 0.0934442 | ||||||||
\(615\) | 3.56859 | − | 6.18098i | 0.143899 | − | 0.249241i | ||||
\(616\) | 3.21616 | + | 10.5150i | 0.129583 | + | 0.423660i | ||||
\(617\) | −6.99061 | + | 12.1081i | −0.281431 | + | 0.487453i | −0.971737 | − | 0.236064i | \(-0.924142\pi\) |
0.690306 | + | 0.723517i | \(0.257476\pi\) | |||||||
\(618\) | −0.331934 | − | 0.574926i | −0.0133523 | − | 0.0231269i | ||||
\(619\) | 4.25792 | + | 7.37494i | 0.171140 | + | 0.296424i | 0.938819 | − | 0.344411i | \(-0.111921\pi\) |
−0.767678 | + | 0.640835i | \(0.778588\pi\) | |||||||
\(620\) | −12.6169 | −0.506707 | ||||||||
\(621\) | −42.6775 | −1.71259 | ||||||||
\(622\) | −2.20166 | − | 3.81338i | −0.0882784 | − | 0.152903i | ||||
\(623\) | 13.8253 | − | 14.8294i | 0.553897 | − | 0.594129i | ||||
\(624\) | −12.6236 | + | 7.58750i | −0.505347 | + | 0.303743i | ||||
\(625\) | 15.1856 | − | 26.3023i | 0.607425 | − | 1.05209i | ||||
\(626\) | 1.34682 | − | 2.33275i | 0.0538296 | − | 0.0932356i | ||||
\(627\) | −16.9030 | + | 29.2769i | −0.675042 | + | 1.16921i | ||||
\(628\) | −1.58677 | − | 2.74837i | −0.0633190 | − | 0.109672i | ||||
\(629\) | 5.30504 | 0.211526 | ||||||||
\(630\) | −2.09867 | + | 2.25110i | −0.0836129 | + | 0.0896859i | ||||
\(631\) | −18.4146 | + | 31.8950i | −0.733074 | + | 1.26972i | 0.222490 | + | 0.974935i | \(0.428582\pi\) |
−0.955563 | + | 0.294786i | \(0.904752\pi\) | |||||||
\(632\) | −3.26123 | + | 5.64861i | −0.129725 | + | 0.224690i | ||||
\(633\) | −21.7231 | −0.863414 | ||||||||
\(634\) | 1.36006 | − | 2.35570i | 0.0540150 | − | 0.0935567i | ||||
\(635\) | −4.58053 | −0.181773 | ||||||||
\(636\) | 20.4507 | 0.810922 | ||||||||
\(637\) | −10.6574 | + | 22.8783i | −0.422263 | + | 0.906473i | ||||
\(638\) | −2.48818 | −0.0985081 | ||||||||
\(639\) | −20.8578 | −0.825121 | ||||||||
\(640\) | 10.0235 | − | 17.3612i | 0.396214 | − | 0.686263i | ||||
\(641\) | 25.8747 | 1.02199 | 0.510996 | − | 0.859583i | \(-0.329277\pi\) | ||||
0.510996 | + | 0.859583i | \(0.329277\pi\) | |||||||
\(642\) | 1.76622 | − | 3.05918i | 0.0697071 | − | 0.120736i | ||||
\(643\) | −20.2626 | + | 35.0958i | −0.799078 | + | 1.38404i | 0.121139 | + | 0.992636i | \(0.461345\pi\) |
−0.920217 | + | 0.391408i | \(0.871988\pi\) | |||||||
\(644\) | 27.6730 | − | 29.6830i | 1.09047 | − | 1.16967i | ||||
\(645\) | −6.58666 | −0.259350 | ||||||||
\(646\) | −0.788896 | − | 1.36641i | −0.0310387 | − | 0.0537606i | ||||
\(647\) | −0.892002 | + | 1.54499i | −0.0350682 | + | 0.0607399i | −0.883027 | − | 0.469322i | \(-0.844498\pi\) |
0.847959 | + | 0.530062i | \(0.177832\pi\) | |||||||
\(648\) | 0.553661 | − | 0.958969i | 0.0217499 | − | 0.0376719i | ||||
\(649\) | 17.6913 | − | 30.6423i | 0.694445 | − | 1.20281i | ||||
\(650\) | −0.0265840 | − | 1.51038i | −0.00104271 | − | 0.0592420i | ||||
\(651\) | 5.26754 | − | 5.65014i | 0.206451 | − | 0.221446i | ||||
\(652\) | −6.31281 | − | 10.9341i | −0.247229 | − | 0.428213i | ||||
\(653\) | 12.4042 | 0.485414 | 0.242707 | − | 0.970100i | \(-0.421965\pi\) | ||||
0.242707 | + | 0.970100i | \(0.421965\pi\) | |||||||
\(654\) | 2.47573 | 0.0968088 | ||||||||
\(655\) | −8.18597 | − | 14.1785i | −0.319852 | − | 0.554000i | ||||
\(656\) | 4.35554 | + | 7.54402i | 0.170055 | + | 0.294545i | ||||
\(657\) | 0.650815 | − | 1.12725i | 0.0253907 | − | 0.0439780i | ||||
\(658\) | −0.273171 | − | 0.893110i | −0.0106493 | − | 0.0348171i | ||||
\(659\) | 0.564336 | − | 0.977458i | 0.0219834 | − | 0.0380764i | −0.854824 | − | 0.518917i | \(-0.826335\pi\) |
0.876808 | + | 0.480841i | \(0.159669\pi\) | |||||||
\(660\) | −22.2780 | −0.867170 | ||||||||
\(661\) | 14.4627 | − | 25.0502i | 0.562534 | − | 0.974338i | −0.434740 | − | 0.900556i | \(-0.643160\pi\) |
0.997274 | − | 0.0737821i | \(-0.0235069\pi\) | |||||||
\(662\) | 0.310913 | + | 0.538517i | 0.0120840 | + | 0.0209301i | ||||
\(663\) | −2.77315 | + | 1.66683i | −0.107700 | + | 0.0647342i | ||||
\(664\) | −1.13003 | −0.0438535 | ||||||||
\(665\) | 34.6418 | − | 37.1579i | 1.34335 | − | 1.44092i | ||||
\(666\) | −1.53414 | − | 2.65721i | −0.0594467 | − | 0.102965i | ||||
\(667\) | 9.35421 | + | 16.2020i | 0.362196 | + | 0.627342i | ||||
\(668\) | 9.20556 | + | 15.9445i | 0.356174 | + | 0.616911i | ||||
\(669\) | 13.6775 | 0.528802 | ||||||||
\(670\) | 0.464518 | + | 0.804568i | 0.0179459 | + | 0.0310832i | ||||
\(671\) | 37.2718 | 1.43886 | ||||||||
\(672\) | 2.71078 | + | 8.86266i | 0.104571 | + | 0.341885i | ||||
\(673\) | 3.54980 | + | 6.14843i | 0.136835 | + | 0.237005i | 0.926297 | − | 0.376795i | \(-0.122974\pi\) |
−0.789462 | + | 0.613799i | \(0.789640\pi\) | |||||||
\(674\) | 4.28995 | 0.165243 | ||||||||
\(675\) | −4.19145 | − | 7.25980i | −0.161329 | − | 0.279430i | ||||
\(676\) | −13.2888 | − | 21.2528i | −0.511109 | − | 0.817416i | ||||
\(677\) | 25.2010 | − | 43.6494i | 0.968552 | − | 1.67758i | 0.268800 | − | 0.963196i | \(-0.413373\pi\) |
0.699752 | − | 0.714386i | \(-0.253294\pi\) | |||||||
\(678\) | −1.23221 | − | 2.13426i | −0.0473229 | − | 0.0819657i | ||||
\(679\) | −1.83559 | − | 6.00132i | −0.0704436 | − | 0.230310i | ||||
\(680\) | 1.05914 | − | 1.83449i | 0.0406162 | − | 0.0703493i | ||||
\(681\) | 8.79213 | − | 15.2284i | 0.336915 | − | 0.583554i | ||||
\(682\) | 2.70258 | 0.103487 | ||||||||
\(683\) | 27.5282 | 1.05334 | 0.526669 | − | 0.850070i | \(-0.323441\pi\) | ||||
0.526669 | + | 0.850070i | \(0.323441\pi\) | |||||||
\(684\) | 12.2372 | − | 21.1954i | 0.467901 | − | 0.810428i | ||||
\(685\) | 12.8556 | − | 22.2665i | 0.491186 | − | 0.850760i | ||||
\(686\) | 3.86026 | + | 3.12362i | 0.147386 | + | 0.119261i | ||||
\(687\) | 4.95019 | + | 8.57398i | 0.188861 | + | 0.327118i | ||||
\(688\) | 4.01958 | − | 6.96212i | 0.153245 | − | 0.265428i | ||||
\(689\) | 0.588795 | + | 33.4527i | 0.0224313 | + | 1.27445i | ||||
\(690\) | −3.12280 | − | 5.40885i | −0.118883 | − | 0.205912i | ||||
\(691\) | −24.3338 | −0.925702 | −0.462851 | − | 0.886436i | \(-0.653174\pi\) | ||||
−0.462851 | + | 0.886436i | \(0.653174\pi\) | |||||||
\(692\) | 10.7315 | + | 18.5875i | 0.407950 | + | 0.706591i | ||||
\(693\) | −12.0566 | + | 12.9323i | −0.457993 | + | 0.491258i | ||||
\(694\) | 6.11884 | 0.232268 | ||||||||
\(695\) | −7.10319 | − | 12.3031i | −0.269439 | − | 0.466683i | ||||
\(696\) | −2.83112 | −0.107313 | ||||||||
\(697\) | 0.956829 | + | 1.65728i | 0.0362425 | + | 0.0627738i | ||||
\(698\) | −3.04352 | − | 5.27153i | −0.115199 | − | 0.199531i | ||||
\(699\) | 11.5733 | + | 20.0456i | 0.437744 | + | 0.758195i | ||||
\(700\) | 7.76714 | + | 1.79218i | 0.293570 | + | 0.0677381i | ||||
\(701\) | −20.5588 | −0.776495 | −0.388248 | − | 0.921555i | \(-0.626919\pi\) | ||||
−0.388248 | + | 0.921555i | \(0.626919\pi\) | |||||||
\(702\) | 4.53642 | + | 2.51371i | 0.171216 | + | 0.0948740i | ||||
\(703\) | 25.3234 | + | 43.8613i | 0.955088 | + | 1.65426i | ||||
\(704\) | 12.4811 | − | 21.6178i | 0.470397 | − | 0.814752i | ||||
\(705\) | 3.85501 | 0.145188 | ||||||||
\(706\) | −3.65513 | + | 6.33088i | −0.137563 | + | 0.238266i | ||||
\(707\) | −0.617017 | − | 2.01728i | −0.0232053 | − | 0.0758678i | ||||
\(708\) | 9.88062 | − | 17.1137i | 0.371336 | − | 0.643174i | ||||
\(709\) | −20.4544 | − | 35.4281i | −0.768183 | − | 1.33053i | −0.938547 | − | 0.345151i | \(-0.887828\pi\) |
0.170364 | − | 0.985381i | \(-0.445506\pi\) | |||||||
\(710\) | −4.22981 | − | 7.32624i | −0.158742 | − | 0.274949i | ||||
\(711\) | −10.4878 | −0.393322 | ||||||||
\(712\) | 8.07085 | 0.302468 | ||||||||
\(713\) | −10.1602 | − | 17.5980i | −0.380503 | − | 0.659051i | ||||
\(714\) | 0.186196 | + | 0.608753i | 0.00696822 | + | 0.0227820i | ||||
\(715\) | −0.641405 | − | 36.4418i | −0.0239872 | − | 1.36284i | ||||
\(716\) | −12.1890 | + | 21.1119i | −0.455524 | + | 0.788990i | ||||
\(717\) | 9.45989 | − | 16.3850i | 0.353286 | − | 0.611910i | ||||
\(718\) | −1.93401 | + | 3.34981i | −0.0721767 | + | 0.125014i | ||||
\(719\) | 0.599734 | + | 1.03877i | 0.0223663 | + | 0.0387396i | 0.876992 | − | 0.480505i | \(-0.159547\pi\) |
−0.854626 | + | 0.519245i | \(0.826213\pi\) | |||||||
\(720\) | 15.5047 | 0.577826 | ||||||||
\(721\) | 1.67630 | + | 5.48054i | 0.0624289 | + | 0.204106i | ||||
\(722\) | 4.98433 | − | 8.63311i | 0.185497 | − | 0.321291i | ||||
\(723\) | −9.37311 | + | 16.2347i | −0.348590 | + | 0.603775i | ||||
\(724\) | −28.7593 | −1.06883 | ||||||||
\(725\) | −1.83739 | + | 3.18246i | −0.0682390 | + | 0.118193i | ||||
\(726\) | 1.40085 | 0.0519904 | ||||||||
\(727\) | −2.06230 | −0.0764865 | −0.0382433 | − | 0.999268i | \(-0.512176\pi\) | ||||
−0.0382433 | + | 0.999268i | \(0.512176\pi\) | |||||||
\(728\) | −9.55455 | + | 3.10730i | −0.354115 | + | 0.115164i | ||||
\(729\) | 20.1764 | 0.747273 | ||||||||
\(730\) | 0.527922 | 0.0195393 | ||||||||
\(731\) | 0.883025 | − | 1.52944i | 0.0326599 | − | 0.0565685i | ||||
\(732\) | 20.8164 | 0.769395 | ||||||||
\(733\) | −15.0310 | + | 26.0345i | −0.555184 | + | 0.961606i | 0.442706 | + | 0.896667i | \(0.354019\pi\) |
−0.997889 | + | 0.0649392i | \(0.979315\pi\) | |||||||
\(734\) | −1.52720 | + | 2.64520i | −0.0563702 | + | 0.0976360i | ||||
\(735\) | −16.9898 | + | 11.4658i | −0.626677 | + | 0.422923i | ||||
\(736\) | 24.3801 | 0.898662 | ||||||||
\(737\) | 2.66861 | + | 4.62216i | 0.0982993 | + | 0.170259i | ||||
\(738\) | 0.553401 | − | 0.958519i | 0.0203710 | − | 0.0352836i | ||||
\(739\) | −22.1274 | + | 38.3257i | −0.813969 | + | 1.40984i | 0.0960970 | + | 0.995372i | \(0.469364\pi\) |
−0.910066 | + | 0.414464i | \(0.863969\pi\) | |||||||
\(740\) | −16.6880 | + | 28.9044i | −0.613461 | + | 1.06255i | ||||
\(741\) | −27.0186 | − | 14.9715i | −0.992553 | − | 0.549992i | ||||
\(742\) | 6.41430 | + | 1.48003i | 0.235476 | + | 0.0543335i | ||||
\(743\) | 4.31326 | + | 7.47078i | 0.158238 | + | 0.274076i | 0.934233 | − | 0.356662i | \(-0.116085\pi\) |
−0.775995 | + | 0.630739i | \(0.782752\pi\) | |||||||
\(744\) | 3.07506 | 0.112737 | ||||||||
\(745\) | −47.3030 | −1.73305 | ||||||||
\(746\) | −4.15097 | − | 7.18969i | −0.151978 | − | 0.263233i | ||||
\(747\) | −0.908511 | − | 1.57359i | −0.0332407 | − | 0.0575746i | ||||
\(748\) | 2.98665 | − | 5.17302i | 0.109203 | − | 0.189144i | ||||
\(749\) | −20.7952 | + | 22.3056i | −0.759839 | + | 0.815028i | ||||
\(750\) | −1.34936 | + | 2.33715i | −0.0492715 | + | 0.0853408i | ||||
\(751\) | 5.72211 | 0.208803 | 0.104401 | − | 0.994535i | \(-0.466707\pi\) | ||||
0.104401 | + | 0.994535i | \(0.466707\pi\) | |||||||
\(752\) | −2.35256 | + | 4.07476i | −0.0857891 | + | 0.148591i | ||||
\(753\) | −11.6763 | − | 20.2239i | −0.425506 | − | 0.736998i | ||||
\(754\) | −0.0400094 | − | 2.27316i | −0.00145706 | − | 0.0827835i | ||||
\(755\) | −4.11765 | −0.149857 | ||||||||
\(756\) | −18.6619 | + | 20.0174i | −0.678727 | + | 0.728025i | ||||
\(757\) | 17.3611 | + | 30.0703i | 0.631000 | + | 1.09292i | 0.987348 | + | 0.158571i | \(0.0506887\pi\) |
−0.356347 | + | 0.934354i | \(0.615978\pi\) | |||||||
\(758\) | 1.41927 | + | 2.45824i | 0.0515501 | + | 0.0892873i | ||||
\(759\) | −17.9402 | − | 31.0733i | −0.651187 | − | 1.12789i | ||||
\(760\) | 20.2230 | 0.733566 | ||||||||
\(761\) | 26.5867 | + | 46.0496i | 0.963768 | + | 1.66930i | 0.712888 | + | 0.701278i | \(0.247387\pi\) |
0.250880 | + | 0.968018i | \(0.419280\pi\) | |||||||
\(762\) | 0.547981 | 0.0198513 | ||||||||
\(763\) | −20.8258 | − | 4.80532i | −0.753944 | − | 0.173964i | ||||
\(764\) | −13.6226 | − | 23.5951i | −0.492849 | − | 0.853640i | ||||
\(765\) | 3.40609 | 0.123147 | ||||||||
\(766\) | 4.12265 | + | 7.14063i | 0.148957 | + | 0.258002i | ||||
\(767\) | 28.2787 | + | 15.6697i | 1.02108 | + | 0.565801i | ||||
\(768\) | 6.03145 | − | 10.4468i | 0.217641 | − | 0.376966i | ||||
\(769\) | −2.45578 | − | 4.25354i | −0.0885578 | − | 0.153387i | 0.818344 | − | 0.574729i | \(-0.194892\pi\) |
−0.906902 | + | 0.421342i | \(0.861559\pi\) | |||||||
\(770\) | −6.98744 | − | 1.61227i | −0.251810 | − | 0.0581023i | ||||
\(771\) | 7.87414 | − | 13.6384i | 0.283580 | − | 0.491175i | ||||
\(772\) | 3.75455 | − | 6.50306i | 0.135129 | − | 0.234050i | ||||
\(773\) | −22.9807 | −0.826557 | −0.413279 | − | 0.910605i | \(-0.635616\pi\) | ||||
−0.413279 | + | 0.910605i | \(0.635616\pi\) | |||||||
\(774\) | −1.02143 | −0.0367146 | ||||||||
\(775\) | 1.99571 | − | 3.45667i | 0.0716881 | − | 0.124167i | ||||
\(776\) | 1.24913 | − | 2.16356i | 0.0448413 | − | 0.0776674i | ||||
\(777\) | −5.97685 | − | 19.5408i | −0.214418 | − | 0.701023i | ||||
\(778\) | −2.19589 | − | 3.80339i | −0.0787264 | − | 0.136358i | ||||
\(779\) | −9.13476 | + | 15.8219i | −0.327287 | + | 0.566877i | ||||
\(780\) | −0.358225 | − | 20.3528i | −0.0128265 | − | 0.728745i | ||||
\(781\) | −24.2998 | − | 42.0885i | −0.869515 | − | 1.50604i | ||||
\(782\) | 1.67460 | 0.0598837 | ||||||||
\(783\) | −6.30821 | − | 10.9261i | −0.225437 | − | 0.390469i | ||||
\(784\) | −1.75121 | − | 24.9554i | −0.0625433 | − | 0.891264i | ||||
\(785\) | 4.21648 | 0.150493 | ||||||||
\(786\) | 0.979309 | + | 1.69621i | 0.0349308 | + | 0.0605019i | ||||
\(787\) | −3.18774 | −0.113631 | −0.0568154 | − | 0.998385i | \(-0.518095\pi\) | ||||
−0.0568154 | + | 0.998385i | \(0.518095\pi\) | |||||||
\(788\) | −11.2880 | − | 19.5514i | −0.402119 | − | 0.696490i | ||||
\(789\) | 14.8119 | + | 25.6549i | 0.527316 | + | 0.913339i | ||||
\(790\) | −2.12684 | − | 3.68380i | −0.0756696 | − | 0.131064i | ||||
\(791\) | 6.22283 | + | 20.3450i | 0.221258 | + | 0.723385i | ||||
\(792\) | −7.03836 | −0.250097 | ||||||||
\(793\) | 0.599323 | + | 34.0509i | 0.0212826 | + | 1.20918i | ||||
\(794\) | −2.12927 | − | 3.68800i | −0.0755650 | − | 0.130882i | ||||
\(795\) | −13.5857 | + | 23.5312i | −0.481837 | + | 0.834566i | ||||
\(796\) | −6.74229 | −0.238974 | ||||||||
\(797\) | −27.3255 | + | 47.3291i | −0.967918 | + | 1.67648i | −0.266355 | + | 0.963875i | \(0.585820\pi\) |
−0.701562 | + | 0.712608i | \(0.747514\pi\) | |||||||
\(798\) | −4.14429 | + | 4.44530i | −0.146706 | + | 0.157362i | ||||
\(799\) | −0.516813 | + | 0.895146i | −0.0182835 | + | 0.0316680i | ||||
\(800\) | 2.39442 | + | 4.14725i | 0.0846554 | + | 0.146628i | ||||
\(801\) | 6.48875 | + | 11.2388i | 0.229269 | + | 0.397105i | ||||
\(802\) | −1.77921 | −0.0628260 | ||||||||
\(803\) | 3.03286 | 0.107027 | ||||||||
\(804\) | 1.49042 | + | 2.58148i | 0.0525630 | + | 0.0910418i | ||||
\(805\) | 15.7705 | + | 51.5604i | 0.555838 | + | 1.81727i | ||||
\(806\) | 0.0434569 | + | 2.46902i | 0.00153070 | + | 0.0869677i | ||||
\(807\) | −17.1832 | + | 29.7622i | −0.604877 | + | 1.04768i | ||||
\(808\) | 0.419884 | − | 0.727260i | 0.0147715 | − | 0.0255849i | ||||
\(809\) | 10.1498 | − | 17.5799i | 0.356847 | − | 0.618077i | −0.630585 | − | 0.776120i | \(-0.717185\pi\) |
0.987432 | + | 0.158043i | \(0.0505185\pi\) | |||||||
\(810\) | 0.361076 | + | 0.625401i | 0.0126869 | + | 0.0219744i | ||||
\(811\) | 2.43587 | 0.0855350 | 0.0427675 | − | 0.999085i | \(-0.486383\pi\) | ||||
0.0427675 | + | 0.999085i | \(0.486383\pi\) | |||||||
\(812\) | 11.6897 | + | 2.69727i | 0.410229 | + | 0.0946557i | ||||
\(813\) | 8.25855 | − | 14.3042i | 0.289640 | − | 0.501671i | ||||
\(814\) | 3.57461 | − | 6.19141i | 0.125290 | − | 0.217009i | ||||
\(815\) | 16.7748 | 0.587597 | ||||||||
\(816\) | 1.60353 | − | 2.77740i | 0.0561348 | − | 0.0972284i | ||||
\(817\) | 16.8603 | 0.589867 | ||||||||
\(818\) | −1.57452 | −0.0550519 | ||||||||
\(819\) | −12.0086 | − | 10.8067i | −0.419614 | − | 0.377618i | ||||
\(820\) | −12.0395 | −0.420438 | ||||||||
\(821\) | 45.3524 | 1.58281 | 0.791405 | − | 0.611292i | \(-0.209350\pi\) | ||||
0.791405 | + | 0.611292i | \(0.209350\pi\) | |||||||
\(822\) | −1.53795 | + | 2.66380i | −0.0536421 | + | 0.0929108i | ||||
\(823\) | −2.75742 | −0.0961177 | −0.0480588 | − | 0.998845i | \(-0.515303\pi\) | ||||
−0.0480588 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(824\) | −1.14074 | + | 1.97581i | −0.0397394 | + | 0.0688307i | ||||
\(825\) | 3.52388 | − | 6.10354i | 0.122686 | − | 0.212498i | ||||
\(826\) | 4.33756 | − | 4.65261i | 0.150923 | − | 0.161885i | ||||
\(827\) | −8.64504 | −0.300618 | −0.150309 | − | 0.988639i | \(-0.548027\pi\) | ||||
−0.150309 | + | 0.988639i | \(0.548027\pi\) | |||||||
\(828\) | 12.9881 | + | 22.4960i | 0.451366 | + | 0.781789i | ||||
\(829\) | 14.7871 | − | 25.6119i | 0.513576 | − | 0.889540i | −0.486300 | − | 0.873792i | \(-0.661654\pi\) |
0.999876 | − | 0.0157478i | \(-0.00501289\pi\) | |||||||
\(830\) | 0.368479 | − | 0.638224i | 0.0127901 | − | 0.0221531i | ||||
\(831\) | −8.75858 | + | 15.1703i | −0.303832 | + | 0.526252i | ||||
\(832\) | 19.9503 | + | 11.0548i | 0.691653 | + | 0.383258i | ||||
\(833\) | −0.384708 | − | 5.48222i | −0.0133293 | − | 0.189948i | ||||
\(834\) | 0.849774 | + | 1.47185i | 0.0294253 | + | 0.0509660i | ||||
\(835\) | −24.4617 | −0.846531 | ||||||||
\(836\) | 57.0264 | 1.97230 | ||||||||
\(837\) | 6.85177 | + | 11.8676i | 0.236832 | + | 0.410204i | ||||
\(838\) | −4.04096 | − | 6.99914i | −0.139593 | − | 0.241781i | ||||
\(839\) | −12.6236 | + | 21.8648i | −0.435817 | + | 0.754857i | −0.997362 | − | 0.0725895i | \(-0.976874\pi\) |
0.561545 | + | 0.827446i | \(0.310207\pi\) | |||||||
\(840\) | −7.95049 | − | 1.83449i | −0.274318 | − | 0.0632958i | ||||
\(841\) | 11.7347 | − | 20.3251i | 0.404644 | − | 0.700865i | ||||
\(842\) | −10.7406 | −0.370144 | ||||||||
\(843\) | 3.02485 | − | 5.23920i | 0.104182 | − | 0.180448i | ||||
\(844\) | 18.3220 | + | 31.7346i | 0.630669 | + | 1.09235i | ||||
\(845\) | 33.2822 | − | 1.17195i | 1.14494 | − | 0.0403164i | ||||
\(846\) | 0.597818 | 0.0205534 | ||||||||
\(847\) | −11.7839 | − | 2.71901i | −0.404900 | − | 0.0934262i | ||||
\(848\) | −16.5817 | − | 28.7204i | −0.569418 | − | 0.986261i | ||||
\(849\) | −17.5935 | − | 30.4728i | −0.603807 | − | 1.04582i | ||||
\(850\) | 0.164466 | + | 0.284864i | 0.00564115 | + | 0.00977076i | ||||
\(851\) | −53.7544 | −1.84268 | ||||||||
\(852\) | −13.5715 | − | 23.5064i | −0.464950 | − | 0.805318i | ||||
\(853\) | −35.1368 | −1.20306 | −0.601531 | − | 0.798850i | \(-0.705442\pi\) | ||||
−0.601531 | + | 0.798850i | \(0.705442\pi\) | |||||||
\(854\) | 6.52900 | + | 1.50649i | 0.223418 | + | 0.0515511i | ||||
\(855\) | 16.2588 | + | 28.1610i | 0.556039 | + | 0.963087i | ||||
\(856\) | −12.1397 | −0.414927 | ||||||||
\(857\) | 0.671345 | + | 1.16280i | 0.0229327 | + | 0.0397206i | 0.877264 | − | 0.480008i | \(-0.159366\pi\) |
−0.854331 | + | 0.519729i | \(0.826033\pi\) | |||||||
\(858\) | 0.0767330 | + | 4.35962i | 0.00261962 | + | 0.148835i | ||||
\(859\) | −2.38386 | + | 4.12897i | −0.0813363 | + | 0.140879i | −0.903824 | − | 0.427904i | \(-0.859252\pi\) |
0.822488 | + | 0.568783i | \(0.192585\pi\) | |||||||
\(860\) | 5.55542 | + | 9.62228i | 0.189438 | + | 0.328117i | ||||
\(861\) | 5.02648 | − | 5.39157i | 0.171302 | − | 0.183744i | ||||
\(862\) | −0.524972 | + | 0.909278i | −0.0178806 | + | 0.0309701i | ||||
\(863\) | 13.3052 | − | 23.0453i | 0.452915 | − | 0.784472i | −0.545650 | − | 0.838013i | \(-0.683717\pi\) |
0.998566 | + | 0.0535407i | \(0.0170507\pi\) | |||||||
\(864\) | −16.4412 | −0.559343 | ||||||||
\(865\) | −28.5165 | −0.969591 | ||||||||
\(866\) | −5.46875 | + | 9.47216i | −0.185836 | + | 0.321877i | ||||
\(867\) | −9.36331 | + | 16.2177i | −0.317995 | + | 0.550783i | ||||
\(868\) | −12.6970 | − | 2.92968i | −0.430963 | − | 0.0994399i | ||||
\(869\) | −12.2185 | − | 21.1630i | −0.414484 | − | 0.717907i | ||||
\(870\) | 0.923171 | − | 1.59898i | 0.0312984 | − | 0.0542105i | ||||
\(871\) | −4.17981 | + | 2.51231i | −0.141627 | + | 0.0851264i | ||||
\(872\) | −4.25410 | − | 7.36831i | −0.144062 | − | 0.249523i | ||||
\(873\) | 4.01708 | 0.135958 | ||||||||
\(874\) | 7.99364 | + | 13.8454i | 0.270389 | + | 0.468328i | ||||
\(875\) | 15.8871 | − | 17.0410i | 0.537082 | − | 0.576091i | ||||
\(876\) | 1.69385 | 0.0572300 | ||||||||
\(877\) | −4.01848 | − | 6.96022i | −0.135695 | − | 0.235030i | 0.790168 | − | 0.612890i | \(-0.209993\pi\) |
−0.925863 | + | 0.377860i | \(0.876660\pi\) | |||||||
\(878\) | 6.85389 | 0.231307 | ||||||||
\(879\) | −10.0112 | − | 17.3399i | −0.337670 | − | 0.584861i | ||||
\(880\) | 18.0633 | + | 31.2866i | 0.608915 | + | 1.05467i | ||||
\(881\) | 27.3349 | + | 47.3454i | 0.920935 | + | 1.59511i | 0.797971 | + | 0.602695i | \(0.205907\pi\) |
0.122964 | + | 0.992411i | \(0.460760\pi\) | |||||||
\(882\) | −2.63470 | + | 1.77807i | −0.0887149 | + | 0.0598707i | ||||
\(883\) | −8.45085 | −0.284394 | −0.142197 | − | 0.989838i | \(-0.545417\pi\) | ||||
−0.142197 | + | 0.989838i | \(0.545417\pi\) | |||||||
\(884\) | 4.77400 | + | 2.64536i | 0.160567 | + | 0.0889732i | ||||
\(885\) | 13.1277 | + | 22.7379i | 0.441284 | + | 0.764327i | ||||
\(886\) | −3.68088 | + | 6.37547i | −0.123662 | + | 0.214188i | ||||
\(887\) | −10.3557 | −0.347710 | −0.173855 | − | 0.984771i | \(-0.555622\pi\) | ||||
−0.173855 | + | 0.984771i | \(0.555622\pi\) | |||||||
\(888\) | 4.06729 | − | 7.04475i | 0.136489 | − | 0.236406i | ||||
\(889\) | −4.60961 | − | 1.06361i | −0.154601 | − | 0.0356725i | ||||
\(890\) | −2.63174 | + | 4.55831i | −0.0882162 | + | 0.152795i | ||||
\(891\) | 2.07434 | + | 3.59286i | 0.0694930 | + | 0.120365i | ||||
\(892\) | −11.5361 | − | 19.9811i | −0.386256 | − | 0.669016i | ||||
\(893\) | −9.86792 | −0.330217 | ||||||||
\(894\) | 5.65898 | 0.189265 | ||||||||
\(895\) | −16.1947 | − | 28.0501i | −0.541330 | − | 0.937611i | ||||
\(896\) | 14.1185 | − | 15.1439i | 0.471665 | − | 0.505923i | ||||
\(897\) | 28.0995 | − | 16.8895i | 0.938215 | − | 0.563923i | ||||
\(898\) | −1.98461 | + | 3.43745i | −0.0662274 | + | 0.114709i | ||||
\(899\) | 3.00359 | − | 5.20237i | 0.100175 | − | 0.173509i | ||||
\(900\) | −2.55117 | + | 4.41875i | −0.0850389 | + | 0.147292i | ||||
\(901\) | −3.64268 | − | 6.30931i | −0.121355 | − | 0.210194i | ||||
\(902\) | 2.57890 | 0.0858680 | ||||||||
\(903\) | −6.62847 | − | 1.52944i | −0.220582 | − | 0.0508967i | ||||
\(904\) | −4.23468 | + | 7.33467i | −0.140843 | + | 0.243948i | ||||
\(905\) | 19.1053 | − | 33.0914i | 0.635082 | − | 1.09999i | ||||
\(906\) | 0.492606 | 0.0163657 | ||||||||
\(907\) | −9.24019 | + | 16.0045i | −0.306815 | + | 0.531420i | −0.977664 | − | 0.210175i | \(-0.932597\pi\) |
0.670849 | + | 0.741594i | \(0.265930\pi\) | |||||||
\(908\) | −29.6624 | −0.984380 | ||||||||
\(909\) | 1.35030 | 0.0447867 | ||||||||
\(910\) | 1.36059 | − | 6.40951i | 0.0451030 | − | 0.212473i | ||||
\(911\) | −26.6282 | −0.882230 | −0.441115 | − | 0.897451i | \(-0.645417\pi\) | ||||
−0.441115 | + | 0.897451i | \(0.645417\pi\) | |||||||
\(912\) | 30.6175 | 1.01385 | ||||||||
\(913\) | 2.11687 | − | 3.66653i | 0.0700582 | − | 0.121344i | ||||
\(914\) | 0.174804 | 0.00578202 | ||||||||
\(915\) | −13.8287 | + | 23.9520i | −0.457162 | + | 0.791828i | ||||
\(916\) | 8.35033 | − | 14.4632i | 0.275903 | − | 0.477877i | ||||
\(917\) | −4.94563 | − | 16.1693i | −0.163319 | − | 0.533958i | ||||
\(918\) | −1.12931 | −0.0372727 | ||||||||
\(919\) | 5.57467 | + | 9.65561i | 0.183891 | + | 0.318509i | 0.943202 | − | 0.332219i | \(-0.107797\pi\) |
−0.759311 | + | 0.650728i | \(0.774464\pi\) | |||||||
\(920\) | −10.7319 | + | 18.5883i | −0.353822 | + | 0.612837i | ||||
\(921\) | −4.93536 | + | 8.54829i | −0.162626 | + | 0.281676i | ||||
\(922\) | 1.67518 | − | 2.90149i | 0.0551690 | − | 0.0955555i | ||||
\(923\) | 38.0605 | − | 22.8766i | 1.25278 | − | 0.752993i | ||||
\(924\) | −22.4194 | − | 5.17302i | −0.737544 | − | 0.170180i | ||||
\(925\) | −5.27933 | − | 9.14406i | −0.173583 | − | 0.300655i | ||||
\(926\) | 0.0829855 | 0.00272707 | ||||||||
\(927\) | −3.66849 | −0.120489 | ||||||||
\(928\) | 3.60365 | + | 6.24170i | 0.118296 | + | 0.204894i | ||||
\(929\) | −3.87255 | − | 6.70745i | −0.127054 | − | 0.220064i | 0.795480 | − | 0.605980i | \(-0.207219\pi\) |
−0.922534 | + | 0.385916i | \(0.873886\pi\) | |||||||
\(930\) | −1.00272 | + | 1.73676i | −0.0328804 | + | 0.0569505i | ||||
\(931\) | 43.4898 | − | 29.3498i | 1.42532 | − | 0.961901i | ||||
\(932\) | 19.5227 | − | 33.8144i | 0.639489 | − | 1.10763i | ||||
\(933\) | 18.7712 | 0.614541 | ||||||||
\(934\) | 3.28149 | − | 5.68371i | 0.107374 | − | 0.185977i | ||||
\(935\) | 3.96817 | + | 6.87306i | 0.129773 | + | 0.224773i | ||||
\(936\) | −0.113175 | − | 6.43011i | −0.00369925 | − | 0.210175i | ||||
\(937\) | 36.4239 | 1.18992 | 0.594959 | − | 0.803756i | \(-0.297168\pi\) | ||||
0.594959 | + | 0.803756i | \(0.297168\pi\) | |||||||
\(938\) | 0.280643 | + | 0.917537i | 0.00916331 | + | 0.0299587i | ||||
\(939\) | 5.74143 | + | 9.94445i | 0.187364 | + | 0.324525i | ||||
\(940\) | −3.25145 | − | 5.63168i | −0.106051 | − | 0.183685i | ||||
\(941\) | 9.89466 | + | 17.1381i | 0.322557 | + | 0.558685i | 0.981015 | − | 0.193933i | \(-0.0621243\pi\) |
−0.658458 | + | 0.752617i | \(0.728791\pi\) | |||||||
\(942\) | −0.504429 | −0.0164352 | ||||||||
\(943\) | −9.69526 | − | 16.7927i | −0.315721 | − | 0.546845i | ||||
\(944\) | −32.0454 | −1.04299 | ||||||||
\(945\) | −10.6352 | − | 34.7709i | −0.345963 | − | 1.13110i | ||||
\(946\) | −1.18999 | − | 2.06112i | −0.0386899 | − | 0.0670129i | ||||
\(947\) | 9.94796 | 0.323265 | 0.161633 | − | 0.986851i | \(-0.448324\pi\) | ||||
0.161633 | + | 0.986851i | \(0.448324\pi\) | |||||||
\(948\) | −6.82403 | − | 11.8196i | −0.221634 | − | 0.383882i | ||||
\(949\) | 0.0487677 | + | 2.77076i | 0.00158307 | + | 0.0899427i | ||||
\(950\) | −1.57014 | + | 2.71957i | −0.0509422 | + | 0.0882345i | ||||
\(951\) | 5.79790 | + | 10.0423i | 0.188010 | + | 0.325643i | ||||
\(952\) | 1.49184 | − | 1.60019i | 0.0483507 | − | 0.0518625i | ||||
\(953\) | −0.0105567 | + | 0.0182847i | −0.000341965 | + | 0.000592300i | −0.866196 | − | 0.499704i | \(-0.833442\pi\) |
0.865854 | + | 0.500296i | \(0.166776\pi\) | |||||||
\(954\) | −2.10682 | + | 3.64912i | −0.0682108 | + | 0.118144i | ||||
\(955\) | 36.1990 | 1.17137 | ||||||||
\(956\) | −31.9152 | −1.03221 | ||||||||
\(957\) | 5.30352 | − | 9.18596i | 0.171438 | − | 0.296940i | ||||
\(958\) | 1.09107 | − | 1.88979i | 0.0352508 | − | 0.0610562i | ||||
\(959\) | 18.1075 | − | 19.4227i | 0.584723 | − | 0.627193i | ||||
\(960\) | 9.26150 | + | 16.0414i | 0.298914 | + | 0.517733i | ||||
\(961\) | 12.2376 | − | 21.1962i | 0.394761 | − | 0.683747i | ||||
\(962\) | 5.71383 | + | 3.16614i | 0.184221 | + | 0.102081i | ||||
\(963\) | −9.76001 | − | 16.9048i | −0.314512 | − | 0.544751i | ||||
\(964\) | 31.6224 | 1.01849 | ||||||||
\(965\) | 4.98842 | + | 8.64020i | 0.160583 | + | 0.278138i | ||||
\(966\) | −1.88667 | − | 6.16831i | −0.0607026 | − | 0.198462i | ||||
\(967\) | −19.8102 | −0.637053 | −0.318526 | − | 0.947914i | \(-0.603188\pi\) | ||||
−0.318526 | + | 0.947914i | \(0.603188\pi\) | |||||||
\(968\) | −2.40711 | − | 4.16923i | −0.0773674 | − | 0.134004i | ||||
\(969\) | 6.72608 | 0.216073 | ||||||||
\(970\) | 0.814635 | + | 1.41099i | 0.0261563 | + | 0.0453041i | ||||
\(971\) | 1.80887 | + | 3.13305i | 0.0580493 | + | 0.100544i | 0.893590 | − | 0.448885i | \(-0.148179\pi\) |
−0.835540 | + | 0.549429i | \(0.814845\pi\) | |||||||
\(972\) | −14.3572 | − | 24.8674i | −0.460508 | − | 0.797622i | ||||
\(973\) | −4.29146 | − | 14.0306i | −0.137578 | − | 0.449799i | ||||
\(974\) | −1.23595 | −0.0396024 | ||||||||
\(975\) | 5.63275 | + | 3.12121i | 0.180392 | + | 0.0999587i | ||||
\(976\) | −16.8782 | − | 29.2339i | −0.540258 | − | 0.935755i | ||||
\(977\) | −1.08085 | + | 1.87208i | −0.0345793 | + | 0.0598931i | −0.882797 | − | 0.469754i | \(-0.844342\pi\) |
0.848218 | + | 0.529648i | \(0.177676\pi\) | |||||||
\(978\) | −2.00682 | −0.0641710 | ||||||||
\(979\) | −15.1191 | + | 26.1870i | −0.483208 | + | 0.836941i | ||||
\(980\) | 31.0799 | + | 15.1492i | 0.992810 | + | 0.483924i | ||||
\(981\) | 6.84036 | − | 11.8479i | 0.218396 | − | 0.378273i | ||||
\(982\) | 1.74535 | + | 3.02304i | 0.0556965 | + | 0.0964692i | ||||
\(983\) | 15.0545 | + | 26.0752i | 0.480165 | + | 0.831671i | 0.999741 | − | 0.0227535i | \(-0.00724329\pi\) |
−0.519576 | + | 0.854424i | \(0.673910\pi\) | |||||||
\(984\) | 2.93434 | 0.0935433 | ||||||||
\(985\) | 29.9953 | 0.955730 | ||||||||
\(986\) | 0.247525 | + | 0.428727i | 0.00788281 | + | 0.0136534i | ||||
\(987\) | 3.87948 | + | 0.895146i | 0.123485 | + | 0.0284928i | ||||
\(988\) | 0.916973 | + | 52.0983i | 0.0291728 | + | 1.65747i | ||||
\(989\) | −8.94742 | + | 15.4974i | −0.284511 | + | 0.492788i | ||||
\(990\) | 2.29507 | − | 3.97517i | 0.0729420 | − | 0.126339i | ||||
\(991\) | 13.5730 | − | 23.5092i | 0.431161 | − | 0.746793i | −0.565812 | − | 0.824534i | \(-0.691437\pi\) |
0.996974 | + | 0.0777408i | \(0.0247706\pi\) | |||||||
\(992\) | −3.91416 | − | 6.77953i | −0.124275 | − | 0.215250i | ||||
\(993\) | −2.65082 | −0.0841213 | ||||||||
\(994\) | −2.55548 | − | 8.35491i | −0.0810548 | − | 0.265002i | ||||
\(995\) | 4.47902 | − | 7.75790i | 0.141995 | − | 0.245942i | ||||
\(996\) | 1.18227 | − | 2.04776i | 0.0374618 | − | 0.0648858i | ||||
\(997\) | 50.8009 | 1.60888 | 0.804441 | − | 0.594033i | \(-0.202465\pi\) | ||||
0.804441 | + | 0.594033i | \(0.202465\pi\) | |||||||
\(998\) | −4.33300 | + | 7.50497i | −0.137159 | + | 0.237566i | ||||
\(999\) | 36.2504 | 1.14691 |
(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 | 91.2.h.b.16.4 | yes | 12 | |
3.2 | odd | 2 | 819.2.s.d.289.3 | 12 | |||
7.2 | even | 3 | 637.2.f.k.393.3 | 12 | |||
7.3 | odd | 6 | 637.2.g.l.263.3 | 12 | |||
7.4 | even | 3 | 91.2.g.b.81.3 | yes | 12 | ||
7.5 | odd | 6 | 637.2.f.j.393.3 | 12 | |||
7.6 | odd | 2 | 637.2.h.l.471.4 | 12 | |||
13.3 | even | 3 | 1183.2.e.h.170.3 | 12 | |||
13.9 | even | 3 | 91.2.g.b.9.3 | ✓ | 12 | ||
13.10 | even | 6 | 1183.2.e.g.170.4 | 12 | |||
21.11 | odd | 6 | 819.2.n.d.172.4 | 12 | |||
39.35 | odd | 6 | 819.2.n.d.100.4 | 12 | |||
91.9 | even | 3 | 637.2.f.k.295.3 | 12 | |||
91.16 | even | 3 | 8281.2.a.bz.1.4 | 6 | |||
91.23 | even | 6 | 8281.2.a.ce.1.3 | 6 | |||
91.48 | odd | 6 | 637.2.g.l.373.3 | 12 | |||
91.61 | odd | 6 | 637.2.f.j.295.3 | 12 | |||
91.68 | odd | 6 | 8281.2.a.ca.1.4 | 6 | |||
91.74 | even | 3 | inner | 91.2.h.b.74.4 | yes | 12 | |
91.75 | odd | 6 | 8281.2.a.cf.1.3 | 6 | |||
91.81 | even | 3 | 1183.2.e.h.508.3 | 12 | |||
91.87 | odd | 6 | 637.2.h.l.165.4 | 12 | |||
91.88 | even | 6 | 1183.2.e.g.508.4 | 12 | |||
273.74 | odd | 6 | 819.2.s.d.802.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.g.b.9.3 | ✓ | 12 | 13.9 | even | 3 | ||
91.2.g.b.81.3 | yes | 12 | 7.4 | even | 3 | ||
91.2.h.b.16.4 | yes | 12 | 1.1 | even | 1 | trivial | |
91.2.h.b.74.4 | yes | 12 | 91.74 | even | 3 | inner | |
637.2.f.j.295.3 | 12 | 91.61 | odd | 6 | |||
637.2.f.j.393.3 | 12 | 7.5 | odd | 6 | |||
637.2.f.k.295.3 | 12 | 91.9 | even | 3 | |||
637.2.f.k.393.3 | 12 | 7.2 | even | 3 | |||
637.2.g.l.263.3 | 12 | 7.3 | odd | 6 | |||
637.2.g.l.373.3 | 12 | 91.48 | odd | 6 | |||
637.2.h.l.165.4 | 12 | 91.87 | odd | 6 | |||
637.2.h.l.471.4 | 12 | 7.6 | odd | 2 | |||
819.2.n.d.100.4 | 12 | 39.35 | odd | 6 | |||
819.2.n.d.172.4 | 12 | 21.11 | odd | 6 | |||
819.2.s.d.289.3 | 12 | 3.2 | odd | 2 | |||
819.2.s.d.802.3 | 12 | 273.74 | odd | 6 | |||
1183.2.e.g.170.4 | 12 | 13.10 | even | 6 | |||
1183.2.e.g.508.4 | 12 | 91.88 | even | 6 | |||
1183.2.e.h.170.3 | 12 | 13.3 | even | 3 | |||
1183.2.e.h.508.3 | 12 | 91.81 | even | 3 | |||
8281.2.a.bz.1.4 | 6 | 91.16 | even | 3 | |||
8281.2.a.ca.1.4 | 6 | 91.68 | odd | 6 | |||
8281.2.a.ce.1.3 | 6 | 91.23 | even | 6 | |||
8281.2.a.cf.1.3 | 6 | 91.75 | odd | 6 |