Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [945,2,Mod(433,945)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(945, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("945.433");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 945 = 3^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 945.p (of order \(4\), 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: | \(7.54586299101\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 433.17 | ||
Character | \(\chi\) | \(=\) | 945.433 |
Dual form | 945.2.p.b.622.17 |
$q$-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 \(\left(\mathbb{Z}/945\mathbb{Z}\right)^\times\).
\(n\) | \(136\) | \(596\) | \(757\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.834614 | − | 0.834614i | 0.590161 | − | 0.590161i | −0.347514 | − | 0.937675i | \(-0.612974\pi\) |
0.937675 | + | 0.347514i | \(0.112974\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.606840i | 0.303420i | ||||||||
\(5\) | −1.65237 | − | 1.50655i | −0.738960 | − | 0.673749i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.411321 | + | 2.61358i | −0.155465 | + | 0.987841i | ||||
\(8\) | 2.17570 | + | 2.17570i | 0.769228 | + | 0.769228i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.63647 | + | 0.121701i | −0.833726 | + | 0.0384854i | ||||
\(11\) | −5.36829 | −1.61860 | −0.809300 | − | 0.587396i | \(-0.800153\pi\) | ||||
−0.809300 | + | 0.587396i | \(0.800153\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.211233 | − | 0.211233i | 0.0585856 | − | 0.0585856i | −0.677207 | − | 0.735793i | \(-0.736810\pi\) |
0.735793 | + | 0.677207i | \(0.236810\pi\) | |||||||
\(14\) | 1.83804 | + | 2.52463i | 0.491236 | + | 0.674735i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.41806 | 0.604516 | ||||||||
\(17\) | −4.64565 | − | 4.64565i | −1.12674 | − | 1.12674i | −0.990705 | − | 0.136032i | \(-0.956565\pi\) |
−0.136032 | − | 0.990705i | \(-0.543435\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.27159 | −0.979970 | −0.489985 | − | 0.871731i | \(-0.662998\pi\) | ||||
−0.489985 | + | 0.871731i | \(0.662998\pi\) | |||||||
\(20\) | 0.914234 | − | 1.00272i | 0.204429 | − | 0.224216i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.48045 | + | 4.48045i | −0.955234 | + | 0.955234i | ||||
\(23\) | −4.44100 | − | 4.44100i | −0.926013 | − | 0.926013i | 0.0714324 | − | 0.997445i | \(-0.477243\pi\) |
−0.997445 | + | 0.0714324i | \(0.977243\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.460626 | + | 4.97874i | 0.0921251 | + | 0.995747i | ||||
\(26\) | − | 0.352597i | − | 0.0691499i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.58603 | − | 0.249607i | −0.299731 | − | 0.0471712i | ||||
\(29\) | 4.03028i | 0.748404i | 0.927347 | + | 0.374202i | \(0.122083\pi\) | ||||
−0.927347 | + | 0.374202i | \(0.877917\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.55561i | − | 1.17742i | −0.808344 | − | 0.588711i | \(-0.799636\pi\) | ||
0.808344 | − | 0.588711i | \(-0.200364\pi\) | |||||||
\(32\) | −2.33326 | + | 2.33326i | −0.412466 | + | 0.412466i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.75465 | −1.32991 | ||||||||
\(35\) | 4.61714 | − | 3.69892i | 0.780439 | − | 0.625231i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.85693 | + | 4.85693i | −0.798475 | + | 0.798475i | −0.982855 | − | 0.184380i | \(-0.940972\pi\) |
0.184380 | + | 0.982855i | \(0.440972\pi\) | |||||||
\(38\) | −3.56513 | + | 3.56513i | −0.578340 | + | 0.578340i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.317256 | − | 6.87286i | −0.0501626 | − | 1.08670i | ||||
\(41\) | 1.91696i | 0.299378i | 0.988733 | + | 0.149689i | \(0.0478273\pi\) | ||||
−0.988733 | + | 0.149689i | \(0.952173\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.01165 | + | 5.01165i | 0.764269 | + | 0.764269i | 0.977091 | − | 0.212822i | \(-0.0682654\pi\) |
−0.212822 | + | 0.977091i | \(0.568265\pi\) | |||||||
\(44\) | − | 3.25769i | − | 0.491116i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.41304 | −1.09299 | ||||||||
\(47\) | 7.26539 | + | 7.26539i | 1.05977 | + | 1.05977i | 0.998097 | + | 0.0616689i | \(0.0196423\pi\) |
0.0616689 | + | 0.998097i | \(0.480358\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.66163 | − | 2.15005i | −0.951661 | − | 0.307149i | ||||
\(50\) | 4.53977 | + | 3.77088i | 0.642020 | + | 0.533283i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.128185 | + | 0.128185i | 0.0177761 | + | 0.0177761i | ||||
\(53\) | 1.40312 | + | 1.40312i | 0.192733 | + | 0.192733i | 0.796876 | − | 0.604143i | \(-0.206484\pi\) |
−0.604143 | + | 0.796876i | \(0.706484\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.87037 | + | 8.08758i | 1.19608 | + | 1.09053i | ||||
\(56\) | −6.58130 | + | 4.79147i | −0.879463 | + | 0.640287i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.36373 | + | 3.36373i | 0.441679 | + | 0.441679i | ||||
\(59\) | 1.34247 | 0.174774 | 0.0873872 | − | 0.996174i | \(-0.472148\pi\) | ||||
0.0873872 | + | 0.996174i | \(0.472148\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1.03926i | − | 0.133063i | −0.997784 | − | 0.0665317i | \(-0.978807\pi\) | ||
0.997784 | − | 0.0665317i | \(-0.0211934\pi\) | |||||||
\(62\) | −5.47140 | − | 5.47140i | −0.694868 | − | 0.694868i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.73087i | 1.09136i | ||||||||
\(65\) | −0.667268 | + | 0.0308016i | −0.0827644 | + | 0.00382047i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.23733 | − | 7.23733i | 0.884181 | − | 0.884181i | −0.109776 | − | 0.993956i | \(-0.535013\pi\) |
0.993956 | + | 0.109776i | \(0.0350133\pi\) | |||||||
\(68\) | 2.81917 | − | 2.81917i | 0.341875 | − | 0.341875i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.766361 | − | 6.94070i | 0.0915976 | − | 0.829572i | ||||
\(71\) | 2.92647 | 0.347309 | 0.173654 | − | 0.984807i | \(-0.444442\pi\) | ||||
0.173654 | + | 0.984807i | \(0.444442\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.72270 | + | 9.72270i | −1.13796 | + | 1.13796i | −0.149140 | + | 0.988816i | \(0.547651\pi\) |
−0.988816 | + | 0.149140i | \(0.952349\pi\) | |||||||
\(74\) | 8.10732i | 0.942457i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 2.59217i | − | 0.297343i | ||||||
\(77\) | 2.20809 | − | 14.0305i | 0.251635 | − | 1.59892i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.78130i | 0.312920i | 0.987684 | + | 0.156460i | \(0.0500083\pi\) | ||||
−0.987684 | + | 0.156460i | \(0.949992\pi\) | |||||||
\(80\) | −3.99553 | − | 3.64293i | −0.446713 | − | 0.407292i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.59992 | + | 1.59992i | 0.176681 | + | 0.176681i | ||||
\(83\) | −4.47936 | + | 4.47936i | −0.491674 | + | 0.491674i | −0.908833 | − | 0.417159i | \(-0.863026\pi\) |
0.417159 | + | 0.908833i | \(0.363026\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.677418 | + | 14.6752i | 0.0734764 | + | 1.59175i | ||||
\(86\) | 8.36558 | 0.902084 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −11.6798 | − | 11.6798i | −1.24507 | − | 1.24507i | ||||
\(89\) | 2.53502 | 0.268711 | 0.134356 | − | 0.990933i | \(-0.457104\pi\) | ||||
0.134356 | + | 0.990933i | \(0.457104\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.465191 | + | 0.638961i | 0.0487653 | + | 0.0669813i | ||||
\(92\) | 2.69498 | − | 2.69498i | 0.280971 | − | 0.280971i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.1276 | 1.25086 | ||||||||
\(95\) | 7.05823 | + | 6.43536i | 0.724159 | + | 0.660254i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.1398 | − | 13.1398i | −1.33415 | − | 1.33415i | −0.901621 | − | 0.432527i | \(-0.857622\pi\) |
−0.432527 | − | 0.901621i | \(-0.642378\pi\) | |||||||
\(98\) | −7.35434 | + | 3.76543i | −0.742901 | + | 0.380366i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.02130 | + | 0.279526i | −0.302130 | + | 0.0279526i | ||||
\(101\) | 2.63557i | 0.262249i | 0.991366 | + | 0.131124i | \(0.0418587\pi\) | ||||
−0.991366 | + | 0.131124i | \(0.958141\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.70224 | + | 8.70224i | −0.857457 | + | 0.857457i | −0.991038 | − | 0.133581i | \(-0.957353\pi\) |
0.133581 | + | 0.991038i | \(0.457353\pi\) | |||||||
\(104\) | 0.919163 | 0.0901314 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.34212 | 0.227487 | ||||||||
\(107\) | 10.4154 | − | 10.4154i | 1.00690 | − | 1.00690i | 0.00692307 | − | 0.999976i | \(-0.497796\pi\) |
0.999976 | − | 0.00692307i | \(-0.00220370\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 6.59594i | − | 0.631776i | −0.948796 | − | 0.315888i | \(-0.897698\pi\) | ||
0.948796 | − | 0.315888i | \(-0.102302\pi\) | |||||||
\(110\) | 14.1533 | − | 0.653328i | 1.34947 | − | 0.0622924i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.994601 | + | 6.31981i | −0.0939810 | + | 0.597166i | ||||
\(113\) | −10.7735 | − | 10.7735i | −1.01348 | − | 1.01348i | −0.999908 | − | 0.0135748i | \(-0.995679\pi\) |
−0.0135748 | − | 0.999908i | \(-0.504321\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.647577 | + | 14.0287i | 0.0603869 | + | 1.30819i | ||||
\(116\) | −2.44574 | −0.227081 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.12044 | − | 1.12044i | 0.103145 | − | 0.103145i | ||||
\(119\) | 14.0527 | − | 10.2309i | 1.28820 | − | 0.937869i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.8185 | 1.61986 | ||||||||
\(122\) | −0.867380 | − | 0.867380i | −0.0785289 | − | 0.0785289i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.97821 | 0.357254 | ||||||||
\(125\) | 6.73958 | − | 8.92065i | 0.602807 | − | 0.797887i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.88309 | − | 7.88309i | 0.699511 | − | 0.699511i | −0.264794 | − | 0.964305i | \(-0.585304\pi\) |
0.964305 | + | 0.264794i | \(0.0853039\pi\) | |||||||
\(128\) | 2.62038 | + | 2.62038i | 0.231611 | + | 0.231611i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.531204 | + | 0.582619i | −0.0465897 | + | 0.0510990i | ||||
\(131\) | 9.63252i | 0.841598i | 0.907154 | + | 0.420799i | \(0.138250\pi\) | ||||
−0.907154 | + | 0.420799i | \(0.861750\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.75700 | − | 11.1642i | 0.152351 | − | 0.968055i | ||||
\(134\) | − | 12.0807i | − | 1.04362i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 20.2151i | − | 1.73343i | ||||||
\(137\) | −2.81008 | + | 2.81008i | −0.240081 | + | 0.240081i | −0.816884 | − | 0.576803i | \(-0.804300\pi\) |
0.576803 | + | 0.816884i | \(0.304300\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.83253 | 0.749166 | 0.374583 | − | 0.927193i | \(-0.377786\pi\) | ||||
0.374583 | + | 0.927193i | \(0.377786\pi\) | |||||||
\(140\) | 2.24465 | + | 2.80187i | 0.189708 | + | 0.236801i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.44247 | − | 2.44247i | 0.204968 | − | 0.204968i | ||||
\(143\) | −1.13396 | + | 1.13396i | −0.0948267 | + | 0.0948267i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.07181 | − | 6.65950i | 0.504236 | − | 0.553041i | ||||
\(146\) | 16.2294i | 1.34315i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.94738 | − | 2.94738i | −0.242273 | − | 0.242273i | ||||
\(149\) | 2.30798i | 0.189077i | 0.995521 | + | 0.0945387i | \(0.0301376\pi\) | ||||
−0.995521 | + | 0.0945387i | \(0.969862\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.65488 | 0.622945 | 0.311472 | − | 0.950255i | \(-0.399178\pi\) | ||||
0.311472 | + | 0.950255i | \(0.399178\pi\) | |||||||
\(152\) | −9.29372 | − | 9.29372i | −0.753820 | − | 0.753820i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.86711 | − | 13.5529i | −0.795114 | − | 1.09213i | ||||
\(155\) | −9.87634 | + | 10.8323i | −0.793286 | + | 0.870068i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.31345 | − | 1.31345i | −0.104824 | − | 0.104824i | 0.652749 | − | 0.757574i | \(-0.273615\pi\) |
−0.757574 | + | 0.652749i | \(0.773615\pi\) | |||||||
\(158\) | 2.32131 | + | 2.32131i | 0.184673 | + | 0.184673i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.37057 | − | 0.340231i | 0.582695 | − | 0.0268976i | ||||
\(161\) | 13.4336 | − | 9.78025i | 1.05872 | − | 0.770791i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.0280160 | + | 0.0280160i | 0.00219438 | + | 0.00219438i | 0.708203 | − | 0.706009i | \(-0.249506\pi\) |
−0.706009 | + | 0.708203i | \(0.749506\pi\) | |||||||
\(164\) | −1.16329 | −0.0908375 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.47707i | 0.580333i | ||||||||
\(167\) | −6.11313 | − | 6.11313i | −0.473048 | − | 0.473048i | 0.429851 | − | 0.902900i | \(-0.358566\pi\) |
−0.902900 | + | 0.429851i | \(0.858566\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9108i | 0.993135i | ||||||||
\(170\) | 12.8135 | + | 11.6827i | 0.982752 | + | 0.896026i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.04127 | + | 3.04127i | −0.231895 | + | 0.231895i | ||||
\(173\) | −10.1230 | + | 10.1230i | −0.769636 | + | 0.769636i | −0.978042 | − | 0.208406i | \(-0.933172\pi\) |
0.208406 | + | 0.978042i | \(0.433172\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.2018 | − | 0.843978i | −0.997963 | − | 0.0637987i | ||||
\(176\) | −12.9809 | −0.978469 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.11576 | − | 2.11576i | 0.158583 | − | 0.158583i | ||||
\(179\) | 22.9115i | 1.71249i | 0.516571 | + | 0.856244i | \(0.327208\pi\) | ||||
−0.516571 | + | 0.856244i | \(0.672792\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.7359i | 0.797997i | 0.916952 | + | 0.398998i | \(0.130642\pi\) | ||||
−0.916952 | + | 0.398998i | \(0.869358\pi\) | |||||||
\(182\) | 0.921540 | + | 0.145031i | 0.0683091 | + | 0.0107504i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 19.3246i | − | 1.42463i | ||||||
\(185\) | 15.3426 | − | 0.708227i | 1.12801 | − | 0.0520699i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.9392 | + | 24.9392i | 1.82373 | + | 1.82373i | ||||
\(188\) | −4.40893 | + | 4.40893i | −0.321554 | + | 0.321554i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 11.2619 | − | 0.519859i | 0.817026 | − | 0.0377145i | ||||
\(191\) | −17.1890 | −1.24375 | −0.621874 | − | 0.783117i | \(-0.713629\pi\) | ||||
−0.621874 | + | 0.783117i | \(0.713629\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.2279 | − | 11.2279i | −0.808200 | − | 0.808200i | 0.176162 | − | 0.984361i | \(-0.443632\pi\) |
−0.984361 | + | 0.176162i | \(0.943632\pi\) | |||||||
\(194\) | −21.9334 | −1.57472 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.30473 | − | 4.04255i | 0.0931953 | − | 0.288753i | ||||
\(197\) | −4.92276 | + | 4.92276i | −0.350732 | + | 0.350732i | −0.860382 | − | 0.509650i | \(-0.829775\pi\) |
0.509650 | + | 0.860382i | \(0.329775\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.83915 | 0.626591 | 0.313295 | − | 0.949656i | \(-0.398567\pi\) | ||||
0.313295 | + | 0.949656i | \(0.398567\pi\) | |||||||
\(200\) | −9.83007 | + | 11.8344i | −0.695091 | + | 0.836822i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.19968 | + | 2.19968i | 0.154769 | + | 0.154769i | ||||
\(203\) | −10.5335 | − | 1.65774i | −0.739305 | − | 0.116351i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.88799 | − | 3.16751i | 0.201706 | − | 0.221229i | ||||
\(206\) | 14.5260i | 1.01208i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.510776 | − | 0.510776i | 0.0354159 | − | 0.0354159i | ||||
\(209\) | 22.9311 | 1.58618 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.3053 | 1.60440 | 0.802202 | − | 0.597053i | \(-0.203662\pi\) | ||||
0.802202 | + | 0.597053i | \(0.203662\pi\) | |||||||
\(212\) | −0.851469 | + | 0.851469i | −0.0584791 | + | 0.0584791i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 17.3857i | − | 1.18846i | ||||||
\(215\) | −0.730787 | − | 15.8314i | −0.0498393 | − | 1.07969i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.1336 | + | 2.69646i | 1.16311 | + | 0.183048i | ||||
\(218\) | −5.50506 | − | 5.50506i | −0.372850 | − | 0.372850i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.90787 | + | 5.38290i | −0.330889 | + | 0.362915i | ||||
\(221\) | −1.96263 | −0.132021 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.433366 | + | 0.433366i | −0.0290203 | + | 0.0290203i | −0.721468 | − | 0.692448i | \(-0.756532\pi\) |
0.692448 | + | 0.721468i | \(0.256532\pi\) | |||||||
\(224\) | −5.13845 | − | 7.05789i | −0.343327 | − | 0.471575i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −17.9834 | −1.19624 | ||||||||
\(227\) | −5.94890 | − | 5.94890i | −0.394842 | − | 0.394842i | 0.481567 | − | 0.876409i | \(-0.340068\pi\) |
−0.876409 | + | 0.481567i | \(0.840068\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.75108 | 0.115714 | 0.0578572 | − | 0.998325i | \(-0.481573\pi\) | ||||
0.0578572 | + | 0.998325i | \(0.481573\pi\) | |||||||
\(230\) | 12.2491 | + | 11.1681i | 0.807679 | + | 0.736403i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.76870 | + | 8.76870i | −0.575693 | + | 0.575693i | ||||
\(233\) | −14.2334 | − | 14.2334i | −0.932463 | − | 0.932463i | 0.0653964 | − | 0.997859i | \(-0.479169\pi\) |
−0.997859 | + | 0.0653964i | \(0.979169\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.05942 | − | 22.9507i | −0.0691091 | − | 1.49714i | ||||
\(236\) | 0.814663i | 0.0530301i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.18965 | − | 20.2674i | 0.206754 | − | 1.31374i | ||||
\(239\) | 17.1339i | 1.10830i | 0.832416 | + | 0.554151i | \(0.186957\pi\) | ||||
−0.832416 | + | 0.554151i | \(0.813043\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.10083i | 0.0709106i | 0.999371 | + | 0.0354553i | \(0.0112881\pi\) | ||||
−0.999371 | + | 0.0354553i | \(0.988712\pi\) | |||||||
\(242\) | 14.8716 | − | 14.8716i | 0.955980 | − | 0.955980i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.630664 | 0.0403741 | ||||||||
\(245\) | 7.76830 | + | 13.5887i | 0.496299 | + | 0.868152i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.902303 | + | 0.902303i | −0.0574122 | + | 0.0574122i | ||||
\(248\) | 14.2631 | − | 14.2631i | 0.905705 | − | 0.905705i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.82035 | − | 13.0702i | −0.115129 | − | 0.826635i | ||||
\(251\) | − | 17.9236i | − | 1.13133i | −0.824636 | − | 0.565664i | \(-0.808620\pi\) | ||
0.824636 | − | 0.565664i | \(-0.191380\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 23.8406 | + | 23.8406i | 1.49884 | + | 1.49884i | ||||
\(254\) | − | 13.1587i | − | 0.825648i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.0877 | −0.817983 | ||||||||
\(257\) | −15.8529 | − | 15.8529i | −0.988877 | − | 0.988877i | 0.0110616 | − | 0.999939i | \(-0.496479\pi\) |
−0.999939 | + | 0.0110616i | \(0.996479\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.6962 | − | 14.6918i | −0.664632 | − | 0.912901i | ||||
\(260\) | −0.0186917 | − | 0.404925i | −0.00115921 | − | 0.0251124i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.03944 | + | 8.03944i | 0.496678 | + | 0.496678i | ||||
\(263\) | 2.67848 | + | 2.67848i | 0.165162 | + | 0.165162i | 0.784849 | − | 0.619687i | \(-0.212740\pi\) |
−0.619687 | + | 0.784849i | \(0.712740\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.204600 | − | 4.43233i | −0.0125685 | − | 0.272276i | ||||
\(266\) | −7.85134 | − | 10.7842i | −0.481397 | − | 0.661220i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.39191 | + | 4.39191i | 0.268278 | + | 0.268278i | ||||
\(269\) | 7.81764 | 0.476650 | 0.238325 | − | 0.971186i | \(-0.423402\pi\) | ||||
0.238325 | + | 0.971186i | \(0.423402\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 31.7453i | − | 1.92839i | −0.265193 | − | 0.964195i | \(-0.585436\pi\) | ||
0.265193 | − | 0.964195i | \(-0.414564\pi\) | |||||||
\(272\) | −11.2335 | − | 11.2335i | −0.681130 | − | 0.681130i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.69066i | 0.283373i | ||||||||
\(275\) | −2.47277 | − | 26.7273i | −0.149114 | − | 1.61172i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.79671 | − | 8.79671i | 0.528543 | − | 0.528543i | −0.391595 | − | 0.920138i | \(-0.628076\pi\) |
0.920138 | + | 0.391595i | \(0.128076\pi\) | |||||||
\(278\) | 7.37175 | − | 7.37175i | 0.442128 | − | 0.442128i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 18.0933 | + | 1.99778i | 1.08128 | + | 0.119390i | ||||
\(281\) | 1.93492 | 0.115428 | 0.0577138 | − | 0.998333i | \(-0.481619\pi\) | ||||
0.0577138 | + | 0.998333i | \(0.481619\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.96846 | − | 7.96846i | 0.473676 | − | 0.473676i | −0.429426 | − | 0.903102i | \(-0.641284\pi\) |
0.903102 | + | 0.429426i | \(0.141284\pi\) | |||||||
\(284\) | 1.77590i | 0.105380i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.89284i | 0.111926i | ||||||||
\(287\) | −5.01013 | − | 0.788485i | −0.295738 | − | 0.0465428i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 26.1642i | 1.53907i | ||||||||
\(290\) | −0.490491 | − | 10.6257i | −0.0288026 | − | 0.623964i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.90013 | − | 5.90013i | −0.345279 | − | 0.345279i | ||||
\(293\) | −4.45089 | + | 4.45089i | −0.260024 | + | 0.260024i | −0.825064 | − | 0.565040i | \(-0.808861\pi\) |
0.565040 | + | 0.825064i | \(0.308861\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.21825 | − | 2.02249i | −0.129151 | − | 0.117754i | ||||
\(296\) | −21.1345 | −1.22842 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.92627 | + | 1.92627i | 0.111586 | + | 0.111586i | ||||
\(299\) | −1.87618 | −0.108502 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.1598 | + | 11.0370i | −0.873794 | + | 0.636160i | ||||
\(302\) | 6.38886 | − | 6.38886i | 0.367638 | − | 0.367638i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10.3290 | −0.592408 | ||||||||
\(305\) | −1.56569 | + | 1.71724i | −0.0896513 | + | 0.0983286i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.48304 | − | 6.48304i | −0.370007 | − | 0.370007i | 0.497473 | − | 0.867480i | \(-0.334261\pi\) |
−0.867480 | + | 0.497473i | \(0.834261\pi\) | |||||||
\(308\) | 8.51425 | + | 1.33996i | 0.485145 | + | 0.0763513i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.797827 | + | 17.2837i | 0.0453135 | + | 0.981647i | ||||
\(311\) | 23.3314i | 1.32300i | 0.749944 | + | 0.661501i | \(0.230080\pi\) | ||||
−0.749944 | + | 0.661501i | \(0.769920\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.2566 | + | 16.2566i | −0.918879 | + | 0.918879i | −0.996948 | − | 0.0780691i | \(-0.975125\pi\) |
0.0780691 | + | 0.996948i | \(0.475125\pi\) | |||||||
\(314\) | −2.19244 | −0.123727 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.68780 | −0.0949464 | ||||||||
\(317\) | 5.31536 | − | 5.31536i | 0.298540 | − | 0.298540i | −0.541902 | − | 0.840442i | \(-0.682295\pi\) |
0.840442 | + | 0.541902i | \(0.182295\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 21.6357i | − | 1.21137i | ||||||
\(320\) | 13.1535 | − | 14.4266i | 0.735301 | − | 0.806471i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.04914 | − | 19.3746i | 0.169922 | − | 1.07970i | ||||
\(323\) | 19.8443 | + | 19.8443i | 1.10417 | + | 1.10417i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.14898 | + | 0.954376i | 0.0637337 | + | 0.0529393i | ||||
\(326\) | 0.0467651 | 0.00259008 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.17073 | + | 4.17073i | −0.230290 | + | 0.230290i | ||||
\(329\) | −21.9771 | + | 16.0003i | −1.21164 | + | 0.882124i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.24110 | −0.123182 | −0.0615910 | − | 0.998101i | \(-0.519617\pi\) | ||||
−0.0615910 | + | 0.998101i | \(0.519617\pi\) | |||||||
\(332\) | −2.71826 | − | 2.71826i | −0.149184 | − | 0.149184i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −10.2042 | −0.558349 | ||||||||
\(335\) | −22.8621 | + | 1.05533i | −1.24909 | + | 0.0576589i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.05299 | + | 9.05299i | −0.493148 | + | 0.493148i | −0.909297 | − | 0.416149i | \(-0.863380\pi\) |
0.416149 | + | 0.909297i | \(0.363380\pi\) | |||||||
\(338\) | 10.7755 | + | 10.7755i | 0.586110 | + | 0.586110i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.90551 | + | 0.411085i | −0.482969 | + | 0.0222942i | ||||
\(341\) | 35.1924i | 1.90577i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.35939 | − | 16.5264i | 0.451365 | − | 0.892340i | ||||
\(344\) | 21.8077i | 1.17579i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.8976i | 0.908419i | ||||||||
\(347\) | −14.2565 | + | 14.2565i | −0.765331 | + | 0.765331i | −0.977281 | − | 0.211950i | \(-0.932019\pi\) |
0.211950 | + | 0.977281i | \(0.432019\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.0031 | 1.33838 | 0.669192 | − | 0.743090i | \(-0.266640\pi\) | ||||
0.669192 | + | 0.743090i | \(0.266640\pi\) | |||||||
\(350\) | −11.7228 | + | 10.3140i | −0.626610 | + | 0.551307i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 12.5256 | − | 12.5256i | 0.667617 | − | 0.667617i | ||||
\(353\) | −14.1339 | + | 14.1339i | −0.752272 | + | 0.752272i | −0.974903 | − | 0.222631i | \(-0.928536\pi\) |
0.222631 | + | 0.974903i | \(0.428536\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.83561 | − | 4.40887i | −0.256647 | − | 0.233999i | ||||
\(356\) | 1.53835i | 0.0815325i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.1223 | + | 19.1223i | 1.01064 | + | 1.01064i | ||||
\(359\) | 4.56436i | 0.240898i | 0.992720 | + | 0.120449i | \(0.0384334\pi\) | ||||
−0.992720 | + | 0.120449i | \(0.961567\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.753512 | −0.0396585 | ||||||||
\(362\) | 8.96037 | + | 8.96037i | 0.470947 | + | 0.470947i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.387747 | + | 0.282297i | −0.0203235 | + | 0.0147964i | ||||
\(365\) | 30.7132 | − | 1.41774i | 1.60760 | − | 0.0742080i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.77553 | + | 1.77553i | 0.0926819 | + | 0.0926819i | 0.751928 | − | 0.659246i | \(-0.229124\pi\) |
−0.659246 | + | 0.751928i | \(0.729124\pi\) | |||||||
\(368\) | −10.7386 | − | 10.7386i | −0.559790 | − | 0.559790i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 12.2141 | − | 13.3963i | 0.634980 | − | 0.696439i | ||||
\(371\) | −4.24430 | + | 3.09003i | −0.220353 | + | 0.160427i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.44065 | − | 9.44065i | −0.488818 | − | 0.488818i | 0.419115 | − | 0.907933i | \(-0.362340\pi\) |
−0.907933 | + | 0.419115i | \(0.862340\pi\) | |||||||
\(374\) | 41.6292 | 2.15259 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 31.6147i | 1.63040i | ||||||||
\(377\) | 0.851330 | + | 0.851330i | 0.0438457 | + | 0.0438457i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.1510i | 0.829619i | 0.909908 | + | 0.414809i | \(0.136152\pi\) | ||||
−0.909908 | + | 0.414809i | \(0.863848\pi\) | |||||||
\(380\) | −3.90524 | + | 4.28322i | −0.200334 | + | 0.219725i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −14.3461 | + | 14.3461i | −0.734012 | + | 0.734012i | ||||
\(383\) | −14.1980 | + | 14.1980i | −0.725482 | + | 0.725482i | −0.969716 | − | 0.244234i | \(-0.921464\pi\) |
0.244234 | + | 0.969716i | \(0.421464\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.7861 | + | 19.8569i | −1.26322 | + | 1.01200i | ||||
\(386\) | −18.7419 | −0.953936 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.97378 | − | 7.97378i | 0.404807 | − | 0.404807i | ||||
\(389\) | − | 26.2759i | − | 1.33224i | −0.745844 | − | 0.666121i | \(-0.767954\pi\) | ||
0.745844 | − | 0.666121i | \(-0.232046\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.2627i | 2.08674i | ||||||||
\(392\) | −9.81587 | − | 19.1716i | −0.495776 | − | 0.968312i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.21721i | 0.413977i | ||||||||
\(395\) | 4.19016 | − | 4.59572i | 0.210830 | − | 0.231236i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.5891 | − | 25.5891i | −1.28428 | − | 1.28428i | −0.938209 | − | 0.346068i | \(-0.887517\pi\) |
−0.346068 | − | 0.938209i | \(-0.612483\pi\) | |||||||
\(398\) | 7.37727 | − | 7.37727i | 0.369789 | − | 0.369789i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.11382 | + | 12.0389i | 0.0556911 | + | 0.601945i | ||||
\(401\) | 7.82242 | 0.390633 | 0.195317 | − | 0.980740i | \(-0.437427\pi\) | ||||
0.195317 | + | 0.980740i | \(0.437427\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.38476 | − | 1.38476i | −0.0689800 | − | 0.0689800i | ||||
\(404\) | −1.59937 | −0.0795716 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.1749 | + | 7.40780i | −0.504974 | + | 0.367643i | ||||
\(407\) | 26.0734 | − | 26.0734i | 1.29241 | − | 1.29241i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.9780 | −0.987848 | −0.493924 | − | 0.869505i | \(-0.664438\pi\) | ||||
−0.493924 | + | 0.869505i | \(0.664438\pi\) | |||||||
\(410\) | −0.233296 | − | 5.05400i | −0.0115217 | − | 0.249599i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.28087 | − | 5.28087i | −0.260170 | − | 0.260170i | ||||
\(413\) | −0.552185 | + | 3.50865i | −0.0271713 | + | 0.172649i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14.1499 | − | 0.653170i | 0.694592 | − | 0.0320629i | ||||
\(416\) | 0.985725i | 0.0483292i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 19.1386 | − | 19.1386i | 0.936101 | − | 0.936101i | ||||
\(419\) | 24.0861 | 1.17668 | 0.588341 | − | 0.808613i | \(-0.299781\pi\) | ||||
0.588341 | + | 0.808613i | \(0.299781\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.9909 | 0.535662 | 0.267831 | − | 0.963466i | \(-0.413693\pi\) | ||||
0.267831 | + | 0.963466i | \(0.413693\pi\) | |||||||
\(422\) | 19.4509 | − | 19.4509i | 0.946857 | − | 0.946857i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.10554i | 0.296511i | ||||||||
\(425\) | 20.9896 | − | 25.2694i | 1.01814 | − | 1.22575i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.71619 | + | 0.427469i | 0.131446 | + | 0.0206867i | ||||
\(428\) | 6.32051 | + | 6.32051i | 0.305514 | + | 0.305514i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −13.8230 | − | 12.6031i | −0.666604 | − | 0.607778i | ||||
\(431\) | −15.5845 | −0.750681 | −0.375340 | − | 0.926887i | \(-0.622474\pi\) | ||||
−0.375340 | + | 0.926887i | \(0.622474\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.9396 | + | 26.9396i | −1.29464 | + | 1.29464i | −0.362748 | + | 0.931887i | \(0.618161\pi\) |
−0.931887 | + | 0.362748i | \(0.881839\pi\) | |||||||
\(434\) | 16.5505 | − | 12.0494i | 0.794447 | − | 0.578392i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.00268 | 0.191694 | ||||||||
\(437\) | 18.9701 | + | 18.9701i | 0.907465 | + | 0.907465i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.4369 | 1.50040 | 0.750201 | − | 0.661210i | \(-0.229957\pi\) | ||||
0.750201 | + | 0.661210i | \(0.229957\pi\) | |||||||
\(440\) | 1.70312 | + | 36.8955i | 0.0811932 | + | 1.75892i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.63804 | + | 1.63804i | −0.0779137 | + | 0.0779137i | ||||
\(443\) | 2.32611 | + | 2.32611i | 0.110517 | + | 0.110517i | 0.760203 | − | 0.649686i | \(-0.225100\pi\) |
−0.649686 | + | 0.760203i | \(0.725100\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.18878 | − | 3.81913i | −0.198567 | − | 0.181044i | ||||
\(446\) | 0.723386i | 0.0342533i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −22.8188 | − | 3.59119i | −1.07809 | − | 0.169668i | ||||
\(449\) | − | 10.7504i | − | 0.507344i | −0.967290 | − | 0.253672i | \(-0.918362\pi\) | ||
0.967290 | − | 0.253672i | \(-0.0816384\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 10.2908i | − | 0.484574i | ||||||
\(452\) | 6.53778 | − | 6.53778i | 0.307511 | − | 0.307511i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.93007 | −0.466041 | ||||||||
\(455\) | 0.193959 | − | 1.75663i | 0.00909295 | − | 0.0823521i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.9180 | + | 17.9180i | −0.838170 | + | 0.838170i | −0.988618 | − | 0.150448i | \(-0.951929\pi\) |
0.150448 | + | 0.988618i | \(0.451929\pi\) | |||||||
\(458\) | 1.46147 | − | 1.46147i | 0.0682901 | − | 0.0682901i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.51321 | + | 0.392976i | −0.396930 | + | 0.0183226i | ||||
\(461\) | − | 14.6856i | − | 0.683974i | −0.939705 | − | 0.341987i | \(-0.888900\pi\) | ||
0.939705 | − | 0.341987i | \(-0.111100\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.08950 | + | 5.08950i | 0.236529 | + | 0.236529i | 0.815411 | − | 0.578882i | \(-0.196511\pi\) |
−0.578882 | + | 0.815411i | \(0.696511\pi\) | |||||||
\(464\) | 9.74547i | 0.452422i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −23.7588 | −1.10061 | ||||||||
\(467\) | 22.3186 | + | 22.3186i | 1.03278 | + | 1.03278i | 0.999444 | + | 0.0333391i | \(0.0106141\pi\) |
0.0333391 | + | 0.999444i | \(0.489386\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.9385 | + | 21.8922i | 0.735971 | + | 1.01089i | ||||
\(470\) | −20.0392 | − | 18.2708i | −0.924339 | − | 0.842768i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.92081 | + | 2.92081i | 0.134441 | + | 0.134441i | ||||
\(473\) | −26.9040 | − | 26.9040i | −1.23705 | − | 1.23705i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.96760 | − | 21.2671i | −0.0902799 | − | 0.975803i | ||||
\(476\) | 6.20855 | + | 8.52772i | 0.284568 | + | 0.390867i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.3002 | + | 14.3002i | 0.654076 | + | 0.654076i | ||||
\(479\) | −37.1494 | −1.69740 | −0.848700 | − | 0.528874i | \(-0.822614\pi\) | ||||
−0.848700 | + | 0.528874i | \(0.822614\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.05189i | 0.0935583i | ||||||||
\(482\) | 0.918767 | + | 0.918767i | 0.0418487 | + | 0.0418487i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.8130i | 0.491500i | ||||||||
\(485\) | 1.91602 | + | 41.5076i | 0.0870020 | + | 1.88476i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.41260 | + | 4.41260i | −0.199954 | + | 0.199954i | −0.799980 | − | 0.600026i | \(-0.795157\pi\) |
0.600026 | + | 0.799980i | \(0.295157\pi\) | |||||||
\(488\) | 2.26112 | − | 2.26112i | 0.102356 | − | 0.102356i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 17.8249 | + | 4.85780i | 0.805245 | + | 0.219453i | ||||
\(491\) | 14.8666 | 0.670922 | 0.335461 | − | 0.942054i | \(-0.391108\pi\) | ||||
0.335461 | + | 0.942054i | \(0.391108\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.7233 | − | 18.7233i | 0.843254 | − | 0.843254i | ||||
\(494\) | 1.50615i | 0.0677648i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 15.8519i | − | 0.711770i | ||||||
\(497\) | −1.20372 | + | 7.64858i | −0.0539943 | + | 0.343086i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.4873i | 1.40956i | 0.709424 | + | 0.704782i | \(0.248955\pi\) | ||||
−0.709424 | + | 0.704782i | \(0.751045\pi\) | |||||||
\(500\) | 5.41341 | + | 4.08985i | 0.242095 | + | 0.182904i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −14.9593 | − | 14.9593i | −0.667665 | − | 0.667665i | ||||
\(503\) | −8.21640 | + | 8.21640i | −0.366351 | + | 0.366351i | −0.866145 | − | 0.499794i | \(-0.833409\pi\) |
0.499794 | + | 0.866145i | \(0.333409\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.97061 | − | 4.35492i | 0.176690 | − | 0.193791i | ||||
\(506\) | 39.7953 | 1.76912 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.78378 | + | 4.78378i | 0.212246 | + | 0.212246i | ||||
\(509\) | −34.3815 | −1.52393 | −0.761966 | − | 0.647616i | \(-0.775766\pi\) | ||||
−0.761966 | + | 0.647616i | \(0.775766\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.4119 | − | 29.4102i | −0.947208 | − | 1.30103i | ||||
\(512\) | −16.1640 | + | 16.1640i | −0.714353 | + | 0.714353i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −26.4621 | −1.16719 | ||||||||
\(515\) | 27.4896 | − | 1.26894i | 1.21134 | − | 0.0559162i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −39.0027 | − | 39.0027i | −1.71534 | − | 1.71534i | ||||
\(518\) | −21.1892 | − | 3.33472i | −0.930998 | − | 0.146519i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.51879 | − | 1.38476i | −0.0666035 | − | 0.0607259i | ||||
\(521\) | − | 9.07830i | − | 0.397727i | −0.980027 | − | 0.198864i | \(-0.936275\pi\) | ||
0.980027 | − | 0.198864i | \(-0.0637251\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.1622 | + | 16.1622i | −0.706724 | + | 0.706724i | −0.965845 | − | 0.259121i | \(-0.916567\pi\) |
0.259121 | + | 0.965845i | \(0.416567\pi\) | |||||||
\(524\) | −5.84541 | −0.255358 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.47100 | 0.194945 | ||||||||
\(527\) | −30.4551 | + | 30.4551i | −1.32664 | + | 1.32664i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.4450i | 0.715000i | ||||||||
\(530\) | −3.87004 | − | 3.52852i | −0.168104 | − | 0.153269i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.77486 | + | 1.06622i | 0.293728 | + | 0.0462264i | ||||
\(533\) | 0.404925 | + | 0.404925i | 0.0175393 | + | 0.0175393i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −32.9015 | + | 1.51876i | −1.42246 | + | 0.0656616i | ||||
\(536\) | 31.4926 | 1.36027 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 6.52470 | − | 6.52470i | 0.281300 | − | 0.281300i | ||||
\(539\) | 35.7615 | + | 11.5421i | 1.54036 | + | 0.497152i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −41.1554 | −1.76941 | −0.884704 | − | 0.466152i | \(-0.845640\pi\) | ||||
−0.884704 | + | 0.466152i | \(0.845640\pi\) | |||||||
\(542\) | −26.4951 | − | 26.4951i | −1.13806 | − | 1.13806i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 21.6790 | 0.929481 | ||||||||
\(545\) | −9.93709 | + | 10.8989i | −0.425658 | + | 0.466858i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.803089 | − | 0.803089i | 0.0343376 | − | 0.0343376i | −0.689730 | − | 0.724067i | \(-0.742271\pi\) |
0.724067 | + | 0.689730i | \(0.242271\pi\) | |||||||
\(548\) | −1.70527 | − | 1.70527i | −0.0728455 | − | 0.0728455i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −24.3708 | − | 20.2432i | −1.03917 | − | 0.863171i | ||||
\(551\) | − | 17.2157i | − | 0.733414i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.26915 | − | 1.14401i | −0.309116 | − | 0.0486481i | ||||
\(554\) | − | 14.6837i | − | 0.623851i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.35994i | 0.227312i | ||||||||
\(557\) | 6.69005 | − | 6.69005i | 0.283466 | − | 0.283466i | −0.551023 | − | 0.834490i | \(-0.685762\pi\) |
0.834490 | + | 0.551023i | \(0.185762\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.11726 | 0.0895504 | ||||||||
\(560\) | 11.1645 | − | 8.94422i | 0.471788 | − | 0.377962i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.61491 | − | 1.61491i | 0.0681209 | − | 0.0681209i | ||||
\(563\) | 13.5785 | − | 13.5785i | 0.572267 | − | 0.572267i | −0.360494 | − | 0.932761i | \(-0.617392\pi\) |
0.932761 | + | 0.360494i | \(0.117392\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.57096 | + | 34.0325i | 0.0660909 | + | 1.43176i | ||||
\(566\) | − | 13.3012i | − | 0.559090i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.36714 | + | 6.36714i | 0.267159 | + | 0.267159i | ||||
\(569\) | 22.3363i | 0.936388i | 0.883626 | + | 0.468194i | \(0.155095\pi\) | ||||
−0.883626 | + | 0.468194i | \(0.844905\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.9515 | 1.54637 | 0.773186 | − | 0.634179i | \(-0.218662\pi\) | ||||
0.773186 | + | 0.634179i | \(0.218662\pi\) | |||||||
\(572\) | −0.688134 | − | 0.688134i | −0.0287723 | − | 0.0287723i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.83960 | + | 3.52344i | −0.202001 | + | 0.147065i | ||||
\(575\) | 20.0649 | − | 24.1562i | 0.836766 | − | 1.00738i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.2142 | + | 14.2142i | 0.591745 | + | 0.591745i | 0.938103 | − | 0.346357i | \(-0.112582\pi\) |
−0.346357 | + | 0.938103i | \(0.612582\pi\) | |||||||
\(578\) | 21.8370 | + | 21.8370i | 0.908298 | + | 0.908298i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.04125 | + | 3.68462i | 0.167804 | + | 0.152996i | ||||
\(581\) | −9.86473 | − | 13.5496i | −0.409258 | − | 0.562134i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.53234 | − | 7.53234i | −0.311958 | − | 0.311958i | ||||
\(584\) | −42.3074 | −1.75069 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.42955i | 0.306912i | ||||||||
\(587\) | −15.4368 | − | 15.4368i | −0.637146 | − | 0.637146i | 0.312704 | − | 0.949851i | \(-0.398765\pi\) |
−0.949851 | + | 0.312704i | \(0.898765\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28.0029i | 1.15384i | ||||||||
\(590\) | −3.53938 | + | 0.163380i | −0.145714 | + | 0.00672626i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11.7444 | + | 11.7444i | −0.482691 | + | 0.482691i | ||||
\(593\) | 10.3544 | − | 10.3544i | 0.425205 | − | 0.425205i | −0.461786 | − | 0.886991i | \(-0.652791\pi\) |
0.886991 | + | 0.461786i | \(0.152791\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −38.6335 | − | 4.26574i | −1.58382 | − | 0.174878i | ||||
\(596\) | −1.40058 | −0.0573699 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.56588 | + | 1.56588i | −0.0640337 | + | 0.0640337i | ||||
\(599\) | − | 26.9396i | − | 1.10072i | −0.834927 | − | 0.550361i | \(-0.814490\pi\) | ||
0.834927 | − | 0.550361i | \(-0.185510\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.0891997i | 0.00363853i | 0.999998 | + | 0.00181926i | \(0.000579090\pi\) | ||||
−0.999998 | + | 0.00181926i | \(0.999421\pi\) | |||||||
\(602\) | −3.44094 | + | 21.8641i | −0.140242 | + | 0.891116i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.64529i | 0.189014i | ||||||||
\(605\) | −29.4427 | − | 26.8444i | −1.19702 | − | 1.09138i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.0616 | − | 10.0616i | −0.408389 | − | 0.408389i | 0.472787 | − | 0.881177i | \(-0.343248\pi\) |
−0.881177 | + | 0.472787i | \(0.843248\pi\) | |||||||
\(608\) | 9.96673 | − | 9.96673i | 0.404204 | − | 0.404204i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.126479 | + | 2.73998i | 0.00512100 | + | 0.110938i | ||||
\(611\) | 3.06939 | 0.124174 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.0621 | + | 16.0621i | 0.648743 | + | 0.648743i | 0.952689 | − | 0.303946i | \(-0.0983044\pi\) |
−0.303946 | + | 0.952689i | \(0.598304\pi\) | |||||||
\(614\) | −10.8217 | −0.436727 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 35.3303 | − | 25.7220i | 1.42350 | − | 1.03637i | ||||
\(617\) | −2.97487 | + | 2.97487i | −0.119764 | + | 0.119764i | −0.764448 | − | 0.644685i | \(-0.776989\pi\) |
0.644685 | + | 0.764448i | \(0.276989\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.85389 | 0.114707 | 0.0573537 | − | 0.998354i | \(-0.481734\pi\) | ||||
0.0573537 | + | 0.998354i | \(0.481734\pi\) | |||||||
\(620\) | −6.57345 | − | 5.99336i | −0.263996 | − | 0.240699i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 19.4727 | + | 19.4727i | 0.780784 | + | 0.780784i | ||||
\(623\) | −1.04271 | + | 6.62548i | −0.0417752 | + | 0.265444i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.5756 | + | 4.58667i | −0.983026 | + | 0.183467i | ||||
\(626\) | 27.1360i | 1.08457i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.797053 | − | 0.797053i | 0.0318059 | − | 0.0318059i | ||||
\(629\) | 45.1272 | 1.79934 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −43.5592 | −1.73406 | −0.867031 | − | 0.498253i | \(-0.833975\pi\) | ||||
−0.867031 | + | 0.498253i | \(0.833975\pi\) | |||||||
\(632\) | −6.05128 | + | 6.05128i | −0.240707 | + | 0.240707i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 8.87254i | − | 0.352374i | ||||||
\(635\) | −24.9020 | + | 1.14949i | −0.988206 | + | 0.0456163i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.86132 | + | 0.952998i | −0.0737482 | + | 0.0377591i | ||||
\(638\) | −18.0574 | − | 18.0574i | −0.714901 | − | 0.714901i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.382098 | − | 8.27756i | −0.0151038 | − | 0.327199i | ||||
\(641\) | 3.15773 | 0.124723 | 0.0623615 | − | 0.998054i | \(-0.480137\pi\) | ||||
0.0623615 | + | 0.998054i | \(0.480137\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.6478 | − | 20.6478i | 0.814270 | − | 0.814270i | −0.171001 | − | 0.985271i | \(-0.554700\pi\) |
0.985271 | + | 0.171001i | \(0.0547001\pi\) | |||||||
\(644\) | 5.93505 | + | 8.15206i | 0.233874 | + | 0.321236i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 33.1247 | 1.30327 | ||||||||
\(647\) | 15.9052 | + | 15.9052i | 0.625299 | + | 0.625299i | 0.946882 | − | 0.321583i | \(-0.104215\pi\) |
−0.321583 | + | 0.946882i | \(0.604215\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.20675 | −0.282890 | ||||||||
\(650\) | 1.75549 | − | 0.162415i | 0.0688558 | − | 0.00637044i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.0170012 | + | 0.0170012i | −0.000665820 | + | 0.000665820i | ||||
\(653\) | 1.09464 | + | 1.09464i | 0.0428366 | + | 0.0428366i | 0.728201 | − | 0.685364i | \(-0.240357\pi\) |
−0.685364 | + | 0.728201i | \(0.740357\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.5119 | − | 15.9165i | 0.567025 | − | 0.621907i | ||||
\(656\) | 4.63532i | 0.180979i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.98833 | + | 31.6964i | −0.194465 | + | 1.23566i | ||||
\(659\) | − | 10.3823i | − | 0.404438i | −0.979340 | − | 0.202219i | \(-0.935185\pi\) | ||
0.979340 | − | 0.202219i | \(-0.0648153\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1.17964i | − | 0.0458826i | −0.999737 | − | 0.0229413i | \(-0.992697\pi\) | ||
0.999737 | − | 0.0229413i | \(-0.00730308\pi\) | |||||||
\(662\) | −1.87045 | + | 1.87045i | −0.0726972 | + | 0.0726972i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −19.4915 | −0.756418 | ||||||||
\(665\) | −19.7225 | + | 15.8003i | −0.764807 | + | 0.612708i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.8985 | − | 17.8985i | 0.693032 | − | 0.693032i | ||||
\(668\) | 3.70970 | − | 3.70970i | 0.143532 | − | 0.143532i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −18.2002 | + | 19.9618i | −0.703136 | + | 0.771192i | ||||
\(671\) | 5.57904i | 0.215376i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.04729 | + | 5.04729i | 0.194559 | + | 0.194559i | 0.797663 | − | 0.603104i | \(-0.206070\pi\) |
−0.603104 | + | 0.797663i | \(0.706070\pi\) | |||||||
\(674\) | 15.1115i | 0.582073i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.83477 | −0.301337 | ||||||||
\(677\) | 35.4227 | + | 35.4227i | 1.36140 | + | 1.36140i | 0.872131 | + | 0.489272i | \(0.162738\pi\) |
0.489272 | + | 0.872131i | \(0.337262\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 39.7467 | − | 28.9373i | 1.52534 | − | 1.11051i | ||||
\(680\) | −30.4551 | + | 33.4028i | −1.16790 | + | 1.28094i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 29.3720 | + | 29.3720i | 1.12471 | + | 1.12471i | ||||
\(683\) | 15.7912 | + | 15.7912i | 0.604235 | + | 0.604235i | 0.941433 | − | 0.337199i | \(-0.109479\pi\) |
−0.337199 | + | 0.941433i | \(0.609479\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.87679 | − | 0.409759i | 0.339165 | − | 0.0156561i | ||||
\(686\) | −6.81626 | − | 20.7700i | −0.260246 | − | 0.793002i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 12.1185 | + | 12.1185i | 0.462013 | + | 0.462013i | ||||
\(689\) | 0.592771 | 0.0225828 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.7766i | 0.486043i | 0.970021 | + | 0.243022i | \(0.0781386\pi\) | ||||
−0.970021 | + | 0.243022i | \(0.921861\pi\) | |||||||
\(692\) | −6.14304 | − | 6.14304i | −0.233523 | − | 0.233523i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 23.7974i | 0.903337i | ||||||||
\(695\) | −14.5946 | − | 13.3066i | −0.553604 | − | 0.504749i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.90551 | − | 8.90551i | 0.337320 | − | 0.337320i | ||||
\(698\) | 20.8679 | − | 20.8679i | 0.789862 | − | 0.789862i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.512160 | − | 8.01139i | 0.0193578 | − | 0.302802i | ||||
\(701\) | 0.236603 | 0.00893637 | 0.00446819 | − | 0.999990i | \(-0.498578\pi\) | ||||
0.00446819 | + | 0.999990i | \(0.498578\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.7468 | − | 20.7468i | 0.782482 | − | 0.782482i | ||||
\(704\) | − | 46.8698i | − | 1.76647i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23.5927i | 0.887923i | ||||||||
\(707\) | −6.88827 | − | 1.08407i | −0.259060 | − | 0.0407705i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 21.9016i | − | 0.822531i | −0.911516 | − | 0.411266i | \(-0.865087\pi\) | ||
0.911516 | − | 0.411266i | \(-0.134913\pi\) | |||||||
\(710\) | −7.71557 | + | 0.356156i | −0.289560 | + | 0.0133663i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.51545 | + | 5.51545i | 0.206700 | + | 0.206700i | ||||
\(713\) | −29.1135 | + | 29.1135i | −1.09031 | + | 1.09031i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.58209 | − | 0.165352i | 0.133962 | − | 0.00618381i | ||||
\(716\) | −13.9036 | −0.519604 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.80948 | + | 3.80948i | 0.142168 | + | 0.142168i | ||||
\(719\) | −22.0183 | −0.821143 | −0.410571 | − | 0.911829i | \(-0.634671\pi\) | ||||
−0.410571 | + | 0.911829i | \(0.634671\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.1646 | − | 26.3234i | −0.713727 | − | 0.980336i | ||||
\(722\) | −0.628891 | + | 0.628891i | −0.0234049 | + | 0.0234049i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.51501 | −0.242128 | ||||||||
\(725\) | −20.0657 | + | 1.85645i | −0.745222 | + | 0.0689468i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.8625 | − | 20.8625i | −0.773748 | − | 0.773748i | 0.205012 | − | 0.978760i | \(-0.434277\pi\) |
−0.978760 | + | 0.205012i | \(0.934277\pi\) | |||||||
\(728\) | −0.378072 | + | 2.40231i | −0.0140123 | + | 0.0890355i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 24.4504 | − | 26.8169i | 0.904949 | − | 0.992538i | ||||
\(731\) | − | 46.5647i | − | 1.72226i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.6466 | − | 24.6466i | 0.910342 | − | 0.910342i | −0.0859573 | − | 0.996299i | \(-0.527395\pi\) |
0.996299 | + | 0.0859573i | \(0.0273949\pi\) | |||||||
\(734\) | 2.96376 | 0.109394 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 20.7240 | 0.763898 | ||||||||
\(737\) | −38.8521 | + | 38.8521i | −1.43113 | + | 1.43113i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 13.8298i | − | 0.508738i | −0.967107 | − | 0.254369i | \(-0.918132\pi\) | ||
0.967107 | − | 0.254369i | \(-0.0818678\pi\) | |||||||
\(740\) | 0.429781 | + | 9.31053i | 0.0157991 | + | 0.342262i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.963365 | + | 6.12133i | −0.0353663 | + | 0.224721i | ||||
\(743\) | −23.9640 | − | 23.9640i | −0.879156 | − | 0.879156i | 0.114292 | − | 0.993447i | \(-0.463540\pi\) |
−0.993447 | + | 0.114292i | \(0.963540\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.47709 | − | 3.81363i | 0.127391 | − | 0.139721i | ||||
\(746\) | −15.7586 | −0.576963 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −15.1341 | + | 15.1341i | −0.553358 | + | 0.553358i | ||||
\(749\) | 22.9375 | + | 31.5057i | 0.838119 | + | 1.15119i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.8695 | −0.725049 | −0.362525 | − | 0.931974i | \(-0.618085\pi\) | ||||
−0.362525 | + | 0.931974i | \(0.618085\pi\) | |||||||
\(752\) | 17.5682 | + | 17.5682i | 0.640645 | + | 0.640645i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.42106 | 0.0517521 | ||||||||
\(755\) | −12.6487 | − | 11.5324i | −0.460332 | − | 0.419708i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.3668 | − | 12.3668i | 0.449480 | − | 0.449480i | −0.445701 | − | 0.895182i | \(-0.647046\pi\) |
0.895182 | + | 0.445701i | \(0.147046\pi\) | |||||||
\(758\) | 13.4798 | + | 13.4798i | 0.489609 | + | 0.489609i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.35519 | + | 29.3581i | 0.0491579 | + | 1.06493i | ||||
\(761\) | − | 5.77211i | − | 0.209239i | −0.994512 | − | 0.104619i | \(-0.966638\pi\) | ||
0.994512 | − | 0.104619i | \(-0.0333624\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.2390 | + | 2.71305i | 0.624095 | + | 0.0982190i | ||||
\(764\) | − | 10.4310i | − | 0.377379i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23.6996i | 0.856303i | ||||||||
\(767\) | 0.283574 | − | 0.283574i | 0.0102393 | − | 0.0102393i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.2996 | 1.20081 | 0.600407 | − | 0.799694i | \(-0.295005\pi\) | ||||
0.600407 | + | 0.799694i | \(0.295005\pi\) | |||||||
\(770\) | −4.11404 | + | 37.2597i | −0.148260 | + | 1.34274i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.81353 | − | 6.81353i | 0.245224 | − | 0.245224i | ||||
\(773\) | −16.3711 | + | 16.3711i | −0.588829 | + | 0.588829i | −0.937314 | − | 0.348485i | \(-0.886696\pi\) |
0.348485 | + | 0.937314i | \(0.386696\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32.6386 | − | 3.01968i | 1.17241 | − | 0.108470i | ||||
\(776\) | − | 57.1768i | − | 2.05253i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −21.9302 | − | 21.9302i | −0.786237 | − | 0.786237i | ||||
\(779\) | − | 8.18846i | − | 0.293382i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.7102 | −0.562153 | ||||||||
\(782\) | 34.4384 | + | 34.4384i | 1.23151 | + | 1.23151i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −16.1082 | − | 5.19895i | −0.575294 | − | 0.185677i | ||||
\(785\) | 0.191524 | + | 4.14907i | 0.00683578 | + | 0.148087i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.5165 | + | 25.5165i | 0.909564 | + | 0.909564i | 0.996237 | − | 0.0866724i | \(-0.0276233\pi\) |
−0.0866724 | + | 0.996237i | \(0.527623\pi\) | |||||||
\(788\) | −2.98733 | − | 2.98733i | −0.106419 | − | 0.106419i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.338488 | − | 7.33281i | −0.0120429 | − | 0.260890i | ||||
\(791\) | 32.5887 | − | 23.7260i | 1.15872 | − | 0.843599i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.219526 | − | 0.219526i | −0.00779561 | − | 0.00779561i | ||||
\(794\) | −42.7139 | −1.51586 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.36395i | 0.190120i | ||||||||
\(797\) | −4.81872 | − | 4.81872i | −0.170688 | − | 0.170688i | 0.616594 | − | 0.787281i | \(-0.288512\pi\) |
−0.787281 | + | 0.616594i | \(0.788512\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 67.5049i | − | 2.38815i | ||||||
\(800\) | −12.6914 | − | 10.5419i | −0.448710 | − | 0.372713i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.52870 | − | 6.52870i | 0.230536 | − | 0.230536i | ||||
\(803\) | 52.1943 | − | 52.1943i | 1.84190 | − | 1.84190i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −36.9316 | − | 4.07783i | −1.30167 | − | 0.143725i | ||||
\(806\) | −2.31148 | −0.0814186 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.73421 | + | 5.73421i | −0.201729 | + | 0.201729i | ||||
\(809\) | 11.9948i | 0.421715i | 0.977517 | + | 0.210858i | \(0.0676256\pi\) | ||||
−0.977517 | + | 0.210858i | \(0.932374\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.1121i | 1.58410i | 0.610457 | + | 0.792049i | \(0.290986\pi\) | ||||
−0.610457 | + | 0.792049i | \(0.709014\pi\) | |||||||
\(812\) | 1.00598 | − | 6.39214i | 0.0353031 | − | 0.224320i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 43.5224i | − | 1.52546i | ||||||
\(815\) | −0.00408523 | − | 0.0885001i | −0.000143099 | − | 0.00310002i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.4077 | − | 21.4077i | −0.748961 | − | 0.748961i | ||||
\(818\) | −16.6739 | + | 16.6739i | −0.582989 | + | 0.582989i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.92218 | + | 1.75255i | 0.0671253 | + | 0.0612016i | ||||
\(821\) | −19.1184 | −0.667237 | −0.333619 | − | 0.942708i | \(-0.608270\pi\) | ||||
−0.333619 | + | 0.942708i | \(0.608270\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.7028 | − | 26.7028i | −0.930802 | − | 0.930802i | 0.0669541 | − | 0.997756i | \(-0.478672\pi\) |
−0.997756 | + | 0.0669541i | \(0.978672\pi\) | |||||||
\(824\) | −37.8670 | −1.31916 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.46750 | + | 3.38923i | 0.0858554 | + | 0.117926i | ||||
\(827\) | −38.9060 | + | 38.9060i | −1.35289 | + | 1.35289i | −0.470489 | + | 0.882406i | \(0.655922\pi\) |
−0.882406 | + | 0.470489i | \(0.844078\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −50.9527 | −1.76966 | −0.884830 | − | 0.465915i | \(-0.845725\pi\) | ||||
−0.884830 | + | 0.465915i | \(0.845725\pi\) | |||||||
\(830\) | 11.2646 | − | 12.3549i | 0.390999 | − | 0.428843i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.84425 | + | 1.84425i | 0.0639379 | + | 0.0639379i | ||||
\(833\) | 20.9592 | + | 40.9360i | 0.726195 | + | 1.41835i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.891403 | + | 19.3109i | 0.0308483 | + | 0.668280i | ||||
\(836\) | 13.9155i | 0.481279i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 20.1026 | − | 20.1026i | 0.694432 | − | 0.694432i | ||||
\(839\) | −18.9255 | −0.653382 | −0.326691 | − | 0.945131i | \(-0.605934\pi\) | ||||
−0.326691 | + | 0.945131i | \(0.605934\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.7568 | 0.439891 | ||||||||
\(842\) | 9.17313 | − | 9.17313i | 0.316127 | − | 0.316127i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.1426i | 0.486809i | ||||||||
\(845\) | 19.4507 | − | 21.3333i | 0.669124 | − | 0.733888i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.32913 | + | 46.5701i | −0.251832 | + | 1.60017i | ||||
\(848\) | 3.39283 | + | 3.39283i | 0.116510 | + | 0.116510i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.57199 | − | 38.6084i | −0.122518 | − | 1.32426i | ||||
\(851\) | 43.1393 | 1.47880 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.3473 | + | 10.3473i | −0.354285 | + | 0.354285i | −0.861701 | − | 0.507416i | \(-0.830601\pi\) |
0.507416 | + | 0.861701i | \(0.330601\pi\) | |||||||
\(854\) | 2.62374 | − | 1.91020i | 0.0897825 | − | 0.0653656i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 45.3219 | 1.54907 | ||||||||
\(857\) | −6.66606 | − | 6.66606i | −0.227708 | − | 0.227708i | 0.584026 | − | 0.811735i | \(-0.301476\pi\) |
−0.811735 | + | 0.584026i | \(0.801476\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.54137 | −0.291428 | −0.145714 | − | 0.989327i | \(-0.546548\pi\) | ||||
−0.145714 | + | 0.989327i | \(0.546548\pi\) | |||||||
\(860\) | 9.60711 | − | 0.443471i | 0.327600 | − | 0.0151222i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13.0071 | + | 13.0071i | −0.443023 | + | 0.443023i | ||||
\(863\) | −15.3649 | − | 15.3649i | −0.523026 | − | 0.523026i | 0.395458 | − | 0.918484i | \(-0.370586\pi\) |
−0.918484 | + | 0.395458i | \(0.870586\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.9776 | − | 1.47611i | 1.08727 | − | 0.0501893i | ||||
\(866\) | 44.9683i | 1.52809i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.63632 | + | 10.3974i | −0.0555404 | + | 0.352910i | ||||
\(869\) | − | 14.9308i | − | 0.506493i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 3.05753i | − | 0.103601i | ||||||
\(872\) | 14.3508 | − | 14.3508i | 0.485980 | − | 0.485980i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 31.6655 | 1.07110 | ||||||||
\(875\) | 20.5427 | + | 21.2837i | 0.694471 | + | 0.719521i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.4460 | + | 13.4460i | −0.454040 | + | 0.454040i | −0.896693 | − | 0.442653i | \(-0.854037\pi\) |
0.442653 | + | 0.896693i | \(0.354037\pi\) | |||||||
\(878\) | 26.2377 | − | 26.2377i | 0.885478 | − | 0.885478i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 21.4491 | + | 19.5563i | 0.723050 | + | 0.659242i | ||||
\(881\) | 38.9446i | 1.31208i | 0.754727 | + | 0.656039i | \(0.227769\pi\) | ||||
−0.754727 | + | 0.656039i | \(0.772231\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −41.0363 | − | 41.0363i | −1.38098 | − | 1.38098i | −0.842878 | − | 0.538104i | \(-0.819141\pi\) |
−0.538104 | − | 0.842878i | \(-0.680859\pi\) | |||||||
\(884\) | − | 1.19101i | − | 0.0400579i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.88280 | 0.130445 | ||||||||
\(887\) | 24.0739 | + | 24.0739i | 0.808321 | + | 0.808321i | 0.984380 | − | 0.176058i | \(-0.0563348\pi\) |
−0.176058 | + | 0.984380i | \(0.556335\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.3606 | + | 23.8456i | 0.582257 | + | 0.799756i | ||||
\(890\) | −6.68350 | + | 0.308515i | −0.224032 | + | 0.0103415i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.262984 | − | 0.262984i | −0.00880535 | − | 0.00880535i | ||||
\(893\) | −31.0348 | − | 31.0348i | −1.03854 | − | 1.03854i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34.5173 | − | 37.8582i | 1.15379 | − | 1.26546i | ||||
\(896\) | −7.92640 | + | 5.77076i | −0.264802 | + | 0.192788i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.97246 | − | 8.97246i | −0.299415 | − | 0.299415i | ||||
\(899\) | 26.4209 | 0.881187 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 13.0368i | − | 0.434319i | ||||||
\(902\) | −8.58882 | − | 8.58882i | −0.285976 | − | 0.285976i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 46.8798i | − | 1.55920i | ||||||
\(905\) | 16.1742 | − | 17.7397i | 0.537649 | − | 0.589688i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.8310 | − | 39.8310i | 1.32257 | − | 1.32257i | 0.410874 | − | 0.911692i | \(-0.365224\pi\) |
0.911692 | − | 0.410874i | \(-0.134776\pi\) | |||||||
\(908\) | 3.61003 | − | 3.61003i | 0.119803 | − | 0.119803i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.30423 | − | 1.62799i | −0.0432347 | − | 0.0539673i | ||||
\(911\) | 43.1171 | 1.42853 | 0.714267 | − | 0.699874i | \(-0.246760\pi\) | ||||
0.714267 | + | 0.699874i | \(0.246760\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.0465 | − | 24.0465i | 0.795823 | − | 0.795823i | ||||
\(914\) | 29.9093i | 0.989311i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.06262i | 0.0351101i | ||||||||
\(917\) | −25.1754 | − | 3.96206i | −0.831365 | − | 0.130839i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 18.4346i | − | 0.608101i | −0.952656 | − | 0.304051i | \(-0.901661\pi\) | ||
0.952656 | − | 0.304051i | \(-0.0983392\pi\) | |||||||
\(920\) | −29.1135 | + | 31.9313i | −0.959842 | + | 1.05274i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.2568 | − | 12.2568i | −0.403655 | − | 0.403655i | ||||
\(923\) | 0.618169 | − | 0.618169i | 0.0203473 | − | 0.0203473i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −26.4186 | − | 21.9442i | −0.868639 | − | 0.721520i | ||||
\(926\) | 8.49552 | 0.279180 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9.40369 | − | 9.40369i | −0.308691 | − | 0.308691i | ||||
\(929\) | 7.44762 | 0.244349 | 0.122174 | − | 0.992509i | \(-0.461013\pi\) | ||||
0.122174 | + | 0.992509i | \(0.461013\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28.4558 | + | 9.18411i | 0.932600 | + | 0.300997i | ||||
\(932\) | 8.63742 | − | 8.63742i | 0.282928 | − | 0.282928i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 37.2549 | 1.21902 | ||||||||
\(935\) | −3.63658 | − | 78.7808i | −0.118929 | − | 2.57641i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.21948 | − | 2.21948i | −0.0725073 | − | 0.0725073i | 0.669923 | − | 0.742430i | \(-0.266327\pi\) |
−0.742430 | + | 0.669923i | \(0.766327\pi\) | |||||||
\(938\) | 31.5740 | + | 4.96907i | 1.03093 | + | 0.162246i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 13.9274 | − | 0.642900i | 0.454263 | − | 0.0209691i | ||||
\(941\) | − | 39.7630i | − | 1.29624i | −0.761540 | − | 0.648118i | \(-0.775557\pi\) | ||
0.761540 | − | 0.648118i | \(-0.224443\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.51321 | − | 8.51321i | 0.277228 | − | 0.277228i | ||||
\(944\) | 3.24617 | 0.105654 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −44.9088 | −1.46011 | ||||||||
\(947\) | 15.8124 | − | 15.8124i | 0.513835 | − | 0.513835i | −0.401864 | − | 0.915699i | \(-0.631638\pi\) |
0.915699 | + | 0.401864i | \(0.131638\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.10752i | 0.133336i | ||||||||
\(950\) | −19.3920 | − | 16.1076i | −0.629160 | − | 0.522601i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 52.8339 | + | 8.31492i | 1.71236 | + | 0.269488i | ||||
\(953\) | 24.9374 | + | 24.9374i | 0.807803 | + | 0.807803i | 0.984301 | − | 0.176498i | \(-0.0564769\pi\) |
−0.176498 | + | 0.984301i | \(0.556477\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.4024 | + | 25.8960i | 0.919081 | + | 0.837974i | ||||
\(956\) | −10.3976 | −0.336281 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −31.0054 | + | 31.0054i | −1.00174 | + | 1.00174i | ||||
\(959\) | −6.18852 | − | 8.50021i | −0.199838 | − | 0.274486i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.9760 | −0.386322 | ||||||||
\(962\) | 1.71254 | + | 1.71254i | 0.0552145 | + | 0.0552145i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.668028 | −0.0215157 | ||||||||
\(965\) | 1.63722 | + | 35.4679i | 0.0527041 | + | 1.14175i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.3820 | − | 32.3820i | 1.04133 | − | 1.04133i | 0.0422262 | − | 0.999108i | \(-0.486555\pi\) |
0.999108 | − | 0.0422262i | \(-0.0134450\pi\) | |||||||
\(968\) | 38.7678 | + | 38.7678i | 1.24604 | + | 1.24604i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 36.2419 | + | 33.0437i | 1.16366 | + | 1.06097i | ||||
\(971\) | − | 12.9902i | − | 0.416877i | −0.978036 | − | 0.208438i | \(-0.933162\pi\) | ||
0.978036 | − | 0.208438i | \(-0.0668380\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.63301 | + | 23.0846i | −0.116469 | + | 0.740057i | ||||
\(974\) | 7.36563i | 0.236010i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 2.51299i | − | 0.0804390i | ||||||
\(977\) | 35.1310 | − | 35.1310i | 1.12394 | − | 1.12394i | 0.132798 | − | 0.991143i | \(-0.457604\pi\) |
0.991143 | − | 0.132798i | \(-0.0423961\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.6087 | −0.434936 | ||||||||
\(980\) | −8.24619 | + | 4.71412i | −0.263415 | + | 0.150587i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.4079 | − | 12.4079i | 0.395952 | − | 0.395952i | ||||
\(983\) | 4.28795 | − | 4.28795i | 0.136764 | − | 0.136764i | −0.635410 | − | 0.772175i | \(-0.719169\pi\) |
0.772175 | + | 0.635410i | \(0.219169\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.5506 | − | 0.717826i | 0.495483 | − | 0.0228719i | ||||
\(986\) | − | 31.2534i | − | 0.995311i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.547554 | − | 0.547554i | −0.0174200 | − | 0.0174200i | ||||
\(989\) | − | 44.5135i | − | 1.41545i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.67606 | −0.0850080 | −0.0425040 | − | 0.999096i | \(-0.513534\pi\) | ||||
−0.0425040 | + | 0.999096i | \(0.513534\pi\) | |||||||
\(992\) | 15.2959 | + | 15.2959i | 0.485646 | + | 0.485646i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.37897 | + | 7.38825i | 0.170610 | + | 0.234341i | ||||
\(995\) | −14.6055 | − | 13.3166i | −0.463026 | − | 0.422165i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.09258 | + | 3.09258i | 0.0979429 | + | 0.0979429i | 0.754380 | − | 0.656437i | \(-0.227937\pi\) |
−0.656437 | + | 0.754380i | \(0.727937\pi\) | |||||||
\(998\) | 26.2797 | + | 26.2797i | 0.831869 | + | 0.831869i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 945.2.p.b.433.17 | yes | 48 | |
3.2 | odd | 2 | inner | 945.2.p.b.433.8 | yes | 48 | |
5.2 | odd | 4 | inner | 945.2.p.b.622.18 | yes | 48 | |
7.6 | odd | 2 | inner | 945.2.p.b.433.18 | yes | 48 | |
15.2 | even | 4 | inner | 945.2.p.b.622.7 | yes | 48 | |
21.20 | even | 2 | inner | 945.2.p.b.433.7 | ✓ | 48 | |
35.27 | even | 4 | inner | 945.2.p.b.622.17 | yes | 48 | |
105.62 | odd | 4 | inner | 945.2.p.b.622.8 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
945.2.p.b.433.7 | ✓ | 48 | 21.20 | even | 2 | inner | |
945.2.p.b.433.8 | yes | 48 | 3.2 | odd | 2 | inner | |
945.2.p.b.433.17 | yes | 48 | 1.1 | even | 1 | trivial | |
945.2.p.b.433.18 | yes | 48 | 7.6 | odd | 2 | inner | |
945.2.p.b.622.7 | yes | 48 | 15.2 | even | 4 | inner | |
945.2.p.b.622.8 | yes | 48 | 105.62 | odd | 4 | inner | |
945.2.p.b.622.17 | yes | 48 | 35.27 | even | 4 | inner | |
945.2.p.b.622.18 | yes | 48 | 5.2 | odd | 4 | inner |