Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(161,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.o (of order \(6\), 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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 161.6 | ||
Character | \(\chi\) | \(=\) | 930.161 |
Dual form | 930.2.o.e.491.16 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0.433517 | + | 1.67692i | 0.250291 | + | 0.968171i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.866025 | + | 0.500000i | 0.387298 | + | 0.223607i | ||||
\(6\) | 1.67692 | − | 0.433517i | 0.684600 | − | 0.176983i | ||||
\(7\) | −1.74230 | − | 3.01775i | −0.658527 | − | 1.14060i | −0.980997 | − | 0.194023i | \(-0.937846\pi\) |
0.322469 | − | 0.946580i | \(-0.395487\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −2.62413 | + | 1.45395i | −0.874709 | + | 0.484649i | ||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | 2.28452 | − | 3.95691i | 0.688810 | − | 1.19305i | −0.283413 | − | 0.958998i | \(-0.591467\pi\) |
0.972223 | − | 0.234056i | \(-0.0752000\pi\) | |||||||
\(12\) | −0.433517 | − | 1.67692i | −0.125146 | − | 0.484085i | ||||
\(13\) | −6.16355 | − | 3.55853i | −1.70946 | − | 0.986958i | −0.935219 | − | 0.354070i | \(-0.884797\pi\) |
−0.774243 | − | 0.632888i | \(-0.781869\pi\) | |||||||
\(14\) | −3.01775 | + | 1.74230i | −0.806528 | + | 0.465649i | ||||
\(15\) | −0.463024 | + | 1.66901i | −0.119552 | + | 0.430938i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.01037 | − | 1.75002i | −0.245052 | − | 0.424442i | 0.717095 | − | 0.696976i | \(-0.245472\pi\) |
−0.962146 | + | 0.272534i | \(0.912138\pi\) | |||||||
\(18\) | 1.45395 | + | 2.62413i | 0.342699 | + | 0.618512i | ||||
\(19\) | 3.87530 | + | 6.71222i | 0.889055 | + | 1.53989i | 0.840994 | + | 0.541044i | \(0.181971\pi\) |
0.0480605 | + | 0.998844i | \(0.484696\pi\) | |||||||
\(20\) | −0.866025 | − | 0.500000i | −0.193649 | − | 0.111803i | ||||
\(21\) | 4.30521 | − | 4.22995i | 0.939475 | − | 0.923050i | ||||
\(22\) | −3.95691 | − | 2.28452i | −0.843617 | − | 0.487062i | ||||
\(23\) | −7.42056 | −1.54729 | −0.773647 | − | 0.633617i | \(-0.781570\pi\) | ||||
−0.773647 | + | 0.633617i | \(0.781570\pi\) | |||||||
\(24\) | −1.67692 | + | 0.433517i | −0.342300 | + | 0.0884913i | ||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | −3.55853 | + | 6.16355i | −0.697885 | + | 1.20877i | ||||
\(27\) | −3.57576 | − | 3.77014i | −0.688155 | − | 0.725564i | ||||
\(28\) | 1.74230 | + | 3.01775i | 0.329264 | + | 0.570302i | ||||
\(29\) | −6.35073 | −1.17930 | −0.589650 | − | 0.807659i | \(-0.700734\pi\) | ||||
−0.589650 | + | 0.807659i | \(0.700734\pi\) | |||||||
\(30\) | 1.66901 | + | 0.463024i | 0.304719 | + | 0.0845362i | ||||
\(31\) | −1.29260 | − | 5.41564i | −0.232158 | − | 0.972678i | ||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 7.62581 | + | 2.11558i | 1.32748 | + | 0.368275i | ||||
\(34\) | −1.75002 | + | 1.01037i | −0.300126 | + | 0.173278i | ||||
\(35\) | − | 3.48460i | − | 0.589005i | ||||||
\(36\) | 2.62413 | − | 1.45395i | 0.437354 | − | 0.242325i | ||||
\(37\) | 7.71423 | − | 4.45381i | 1.26821 | − | 0.732202i | 0.293562 | − | 0.955940i | \(-0.405159\pi\) |
0.974649 | + | 0.223738i | \(0.0718260\pi\) | |||||||
\(38\) | 6.71222 | − | 3.87530i | 1.08887 | − | 0.628657i | ||||
\(39\) | 3.29537 | − | 11.8785i | 0.527681 | − | 1.90208i | ||||
\(40\) | −0.500000 | + | 0.866025i | −0.0790569 | + | 0.136931i | ||||
\(41\) | −2.17100 | − | 1.25343i | −0.339053 | − | 0.195752i | 0.320800 | − | 0.947147i | \(-0.396048\pi\) |
−0.659853 | + | 0.751394i | \(0.729382\pi\) | |||||||
\(42\) | −4.22995 | − | 4.30521i | −0.652695 | − | 0.664309i | ||||
\(43\) | −3.21363 | + | 1.85539i | −0.490074 | + | 0.282944i | −0.724605 | − | 0.689164i | \(-0.757978\pi\) |
0.234531 | + | 0.972109i | \(0.424644\pi\) | |||||||
\(44\) | −2.28452 | + | 3.95691i | −0.344405 | + | 0.596527i | ||||
\(45\) | −2.99953 | − | 0.0529076i | −0.447144 | − | 0.00788700i | ||||
\(46\) | 7.42056i | 1.09410i | ||||||||
\(47\) | − | 5.93476i | − | 0.865673i | −0.901472 | − | 0.432837i | \(-0.857513\pi\) | ||
0.901472 | − | 0.432837i | \(-0.142487\pi\) | |||||||
\(48\) | 0.433517 | + | 1.67692i | 0.0625728 | + | 0.242043i | ||||
\(49\) | −2.57122 | + | 4.45348i | −0.367317 | + | 0.636212i | ||||
\(50\) | 0.866025 | − | 0.500000i | 0.122474 | − | 0.0707107i | ||||
\(51\) | 2.49663 | − | 2.45298i | 0.349598 | − | 0.343486i | ||||
\(52\) | 6.16355 | + | 3.55853i | 0.854731 | + | 0.493479i | ||||
\(53\) | 5.09901 | − | 8.83174i | 0.700402 | − | 1.21313i | −0.267923 | − | 0.963440i | \(-0.586337\pi\) |
0.968325 | − | 0.249692i | \(-0.0803294\pi\) | |||||||
\(54\) | −3.77014 | + | 3.57576i | −0.513051 | + | 0.486599i | ||||
\(55\) | 3.95691 | − | 2.28452i | 0.533550 | − | 0.308045i | ||||
\(56\) | 3.01775 | − | 1.74230i | 0.403264 | − | 0.232825i | ||||
\(57\) | −9.57585 | + | 9.40843i | −1.26835 | + | 1.24618i | ||||
\(58\) | 6.35073i | 0.833891i | ||||||||
\(59\) | 7.20993 | − | 4.16265i | 0.938652 | − | 0.541931i | 0.0491148 | − | 0.998793i | \(-0.484360\pi\) |
0.889538 | + | 0.456862i | \(0.151027\pi\) | |||||||
\(60\) | 0.463024 | − | 1.66901i | 0.0597761 | − | 0.215469i | ||||
\(61\) | − | 2.03181i | − | 0.260147i | −0.991504 | − | 0.130073i | \(-0.958479\pi\) | ||
0.991504 | − | 0.130073i | \(-0.0415213\pi\) | |||||||
\(62\) | −5.41564 | + | 1.29260i | −0.687787 | + | 0.164160i | ||||
\(63\) | 8.95967 | + | 5.38575i | 1.12881 | + | 0.678541i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −3.55853 | − | 6.16355i | −0.441381 | − | 0.764495i | ||||
\(66\) | 2.11558 | − | 7.62581i | 0.260410 | − | 0.938672i | ||||
\(67\) | −3.08925 | + | 5.35073i | −0.377412 | + | 0.653696i | −0.990685 | − | 0.136175i | \(-0.956519\pi\) |
0.613273 | + | 0.789871i | \(0.289853\pi\) | |||||||
\(68\) | 1.01037 | + | 1.75002i | 0.122526 | + | 0.212221i | ||||
\(69\) | −3.21694 | − | 12.4437i | −0.387274 | − | 1.49804i | ||||
\(70\) | −3.48460 | −0.416489 | ||||||||
\(71\) | −2.26644 | − | 1.30853i | −0.268977 | − | 0.155294i | 0.359445 | − | 0.933166i | \(-0.382966\pi\) |
−0.628423 | + | 0.777872i | \(0.716299\pi\) | |||||||
\(72\) | −1.45395 | − | 2.62413i | −0.171349 | − | 0.309256i | ||||
\(73\) | 7.81979 | + | 4.51476i | 0.915237 | + | 0.528412i | 0.882113 | − | 0.471039i | \(-0.156121\pi\) |
0.0331247 | + | 0.999451i | \(0.489454\pi\) | |||||||
\(74\) | −4.45381 | − | 7.71423i | −0.517745 | − | 0.896761i | ||||
\(75\) | −1.23550 | + | 1.21390i | −0.142663 | + | 0.140169i | ||||
\(76\) | −3.87530 | − | 6.71222i | −0.444527 | − | 0.769944i | ||||
\(77\) | −15.9213 | −1.81440 | ||||||||
\(78\) | −11.8785 | − | 3.29537i | −1.34497 | − | 0.373127i | ||||
\(79\) | −7.33730 | + | 4.23619i | −0.825511 | + | 0.476609i | −0.852313 | − | 0.523032i | \(-0.824801\pi\) |
0.0268022 | + | 0.999641i | \(0.491468\pi\) | |||||||
\(80\) | 0.866025 | + | 0.500000i | 0.0968246 | + | 0.0559017i | ||||
\(81\) | 4.77207 | − | 7.63068i | 0.530230 | − | 0.847854i | ||||
\(82\) | −1.25343 | + | 2.17100i | −0.138418 | + | 0.239747i | ||||
\(83\) | 4.54612 | − | 7.87412i | 0.499002 | − | 0.864297i | −0.500997 | − | 0.865449i | \(-0.667033\pi\) |
0.999999 | + | 0.00115204i | \(0.000366705\pi\) | |||||||
\(84\) | −4.30521 | + | 4.22995i | −0.469737 | + | 0.461525i | ||||
\(85\) | − | 2.02075i | − | 0.219181i | ||||||
\(86\) | 1.85539 | + | 3.21363i | 0.200072 | + | 0.346534i | ||||
\(87\) | −2.75315 | − | 10.6497i | −0.295168 | − | 1.14176i | ||||
\(88\) | 3.95691 | + | 2.28452i | 0.421808 | + | 0.243531i | ||||
\(89\) | −3.74116 | −0.396562 | −0.198281 | − | 0.980145i | \(-0.563536\pi\) | ||||
−0.198281 | + | 0.980145i | \(0.563536\pi\) | |||||||
\(90\) | −0.0529076 | + | 2.99953i | −0.00557695 | + | 0.316179i | ||||
\(91\) | 24.8001i | 2.59976i | ||||||||
\(92\) | 7.42056 | 0.773647 | ||||||||
\(93\) | 8.52124 | − | 4.51536i | 0.883611 | − | 0.468221i | ||||
\(94\) | −5.93476 | −0.612123 | ||||||||
\(95\) | 7.75060i | 0.795195i | ||||||||
\(96\) | 1.67692 | − | 0.433517i | 0.171150 | − | 0.0442456i | ||||
\(97\) | 5.16445 | 0.524371 | 0.262185 | − | 0.965018i | \(-0.415557\pi\) | ||||
0.262185 | + | 0.965018i | \(0.415557\pi\) | |||||||
\(98\) | 4.45348 | + | 2.57122i | 0.449869 | + | 0.259732i | ||||
\(99\) | −0.241737 | + | 13.7050i | −0.0242955 | + | 1.37741i | ||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | 13.3572i | 1.32909i | 0.747249 | + | 0.664544i | \(0.231374\pi\) | ||||
−0.747249 | + | 0.664544i | \(0.768626\pi\) | |||||||
\(102\) | −2.45298 | − | 2.49663i | −0.242881 | − | 0.247203i | ||||
\(103\) | −5.40064 | + | 9.35418i | −0.532141 | + | 0.921695i | 0.467155 | + | 0.884175i | \(0.345279\pi\) |
−0.999296 | + | 0.0375194i | \(0.988054\pi\) | |||||||
\(104\) | 3.55853 | − | 6.16355i | 0.348942 | − | 0.604386i | ||||
\(105\) | 5.84340 | − | 1.51063i | 0.570257 | − | 0.147423i | ||||
\(106\) | −8.83174 | − | 5.09901i | −0.857814 | − | 0.495259i | ||||
\(107\) | 4.08099 | − | 2.35616i | 0.394524 | − | 0.227779i | −0.289594 | − | 0.957149i | \(-0.593520\pi\) |
0.684119 | + | 0.729371i | \(0.260187\pi\) | |||||||
\(108\) | 3.57576 | + | 3.77014i | 0.344077 | + | 0.362782i | ||||
\(109\) | 7.92947 | 0.759506 | 0.379753 | − | 0.925088i | \(-0.376009\pi\) | ||||
0.379753 | + | 0.925088i | \(0.376009\pi\) | |||||||
\(110\) | −2.28452 | − | 3.95691i | −0.217821 | − | 0.377277i | ||||
\(111\) | 10.8129 | + | 11.0053i | 1.02632 | + | 1.04458i | ||||
\(112\) | −1.74230 | − | 3.01775i | −0.164632 | − | 0.285151i | ||||
\(113\) | −6.53805 | − | 3.77475i | −0.615048 | − | 0.355098i | 0.159890 | − | 0.987135i | \(-0.448886\pi\) |
−0.774939 | + | 0.632037i | \(0.782219\pi\) | |||||||
\(114\) | 9.40843 | + | 9.57585i | 0.881180 | + | 0.896860i | ||||
\(115\) | −6.42639 | − | 3.71028i | −0.599264 | − | 0.345985i | ||||
\(116\) | 6.35073 | 0.589650 | ||||||||
\(117\) | 21.3479 | + | 0.376546i | 1.97361 | + | 0.0348117i | ||||
\(118\) | −4.16265 | − | 7.20993i | −0.383203 | − | 0.663727i | ||||
\(119\) | −3.52075 | + | 6.09811i | −0.322746 | + | 0.559013i | ||||
\(120\) | −1.66901 | − | 0.463024i | −0.152359 | − | 0.0422681i | ||||
\(121\) | −4.93811 | − | 8.55305i | −0.448919 | − | 0.777550i | ||||
\(122\) | −2.03181 | −0.183951 | ||||||||
\(123\) | 1.16073 | − | 4.18398i | 0.104660 | − | 0.377256i | ||||
\(124\) | 1.29260 | + | 5.41564i | 0.116079 | + | 0.486339i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 5.38575 | − | 8.95967i | 0.479801 | − | 0.798191i | ||||
\(127\) | −2.02816 | + | 1.17096i | −0.179970 | + | 0.103906i | −0.587279 | − | 0.809385i | \(-0.699801\pi\) |
0.407308 | + | 0.913291i | \(0.366467\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −4.50450 | − | 4.58466i | −0.396599 | − | 0.403657i | ||||
\(130\) | −6.16355 | + | 3.55853i | −0.540579 | + | 0.312104i | ||||
\(131\) | −9.65680 | + | 5.57535i | −0.843718 | + | 0.487121i | −0.858526 | − | 0.512769i | \(-0.828620\pi\) |
0.0148082 | + | 0.999890i | \(0.495286\pi\) | |||||||
\(132\) | −7.62581 | − | 2.11558i | −0.663742 | − | 0.184137i | ||||
\(133\) | 13.5039 | − | 23.3894i | 1.17093 | − | 2.02812i | ||||
\(134\) | 5.35073 | + | 3.08925i | 0.462233 | + | 0.266870i | ||||
\(135\) | −1.21163 | − | 5.05292i | −0.104280 | − | 0.434886i | ||||
\(136\) | 1.75002 | − | 1.01037i | 0.150063 | − | 0.0866388i | ||||
\(137\) | −4.11888 | + | 7.13410i | −0.351899 | + | 0.609508i | −0.986582 | − | 0.163265i | \(-0.947797\pi\) |
0.634683 | + | 0.772773i | \(0.281131\pi\) | |||||||
\(138\) | −12.4437 | + | 3.21694i | −1.05928 | + | 0.273844i | ||||
\(139\) | 7.69544i | 0.652719i | 0.945246 | + | 0.326359i | \(0.105822\pi\) | ||||
−0.945246 | + | 0.326359i | \(0.894178\pi\) | |||||||
\(140\) | 3.48460i | 0.294502i | ||||||||
\(141\) | 9.95212 | − | 2.57282i | 0.838119 | − | 0.216670i | ||||
\(142\) | −1.30853 | + | 2.26644i | −0.109810 | + | 0.190196i | ||||
\(143\) | −28.1616 | + | 16.2591i | −2.35499 | + | 1.35965i | ||||
\(144\) | −2.62413 | + | 1.45395i | −0.218677 | + | 0.121162i | ||||
\(145\) | −5.49989 | − | 3.17536i | −0.456741 | − | 0.263700i | ||||
\(146\) | 4.51476 | − | 7.81979i | 0.373644 | − | 0.647170i | ||||
\(147\) | −8.58280 | − | 2.38107i | −0.707898 | − | 0.196387i | ||||
\(148\) | −7.71423 | + | 4.45381i | −0.634106 | + | 0.366101i | ||||
\(149\) | 10.0333 | − | 5.79275i | 0.821963 | − | 0.474560i | −0.0291300 | − | 0.999576i | \(-0.509274\pi\) |
0.851093 | + | 0.525015i | \(0.175940\pi\) | |||||||
\(150\) | 1.21390 | + | 1.23550i | 0.0991143 | + | 0.100878i | ||||
\(151\) | 3.25609i | 0.264977i | 0.991185 | + | 0.132489i | \(0.0422968\pi\) | ||||
−0.991185 | + | 0.132489i | \(0.957703\pi\) | |||||||
\(152\) | −6.71222 | + | 3.87530i | −0.544433 | + | 0.314328i | ||||
\(153\) | 5.19578 | + | 3.12324i | 0.420054 | + | 0.252499i | ||||
\(154\) | 15.9213i | 1.28298i | ||||||||
\(155\) | 1.58840 | − | 5.33638i | 0.127583 | − | 0.428629i | ||||
\(156\) | −3.29537 | + | 11.8785i | −0.263840 | + | 0.951039i | ||||
\(157\) | −8.65383 | −0.690651 | −0.345326 | − | 0.938483i | \(-0.612231\pi\) | ||||
−0.345326 | + | 0.938483i | \(0.612231\pi\) | |||||||
\(158\) | 4.23619 | + | 7.33730i | 0.337013 | + | 0.583724i | ||||
\(159\) | 17.0206 | + | 4.72192i | 1.34982 | + | 0.374473i | ||||
\(160\) | 0.500000 | − | 0.866025i | 0.0395285 | − | 0.0684653i | ||||
\(161\) | 12.9288 | + | 22.3934i | 1.01894 | + | 1.76485i | ||||
\(162\) | −7.63068 | − | 4.77207i | −0.599523 | − | 0.374930i | ||||
\(163\) | −10.5145 | −0.823559 | −0.411779 | − | 0.911284i | \(-0.635093\pi\) | ||||
−0.411779 | + | 0.911284i | \(0.635093\pi\) | |||||||
\(164\) | 2.17100 | + | 1.25343i | 0.169527 | + | 0.0978762i | ||||
\(165\) | 5.54636 | + | 5.64505i | 0.431783 | + | 0.439466i | ||||
\(166\) | −7.87412 | − | 4.54612i | −0.611150 | − | 0.352848i | ||||
\(167\) | 3.17082 | + | 5.49202i | 0.245365 | + | 0.424985i | 0.962234 | − | 0.272223i | \(-0.0877588\pi\) |
−0.716869 | + | 0.697208i | \(0.754425\pi\) | |||||||
\(168\) | 4.22995 | + | 4.30521i | 0.326347 | + | 0.332154i | ||||
\(169\) | 18.8263 | + | 32.6080i | 1.44817 | + | 2.50831i | ||||
\(170\) | −2.02075 | −0.154984 | ||||||||
\(171\) | −19.9285 | − | 11.9792i | −1.52397 | − | 0.916074i | ||||
\(172\) | 3.21363 | − | 1.85539i | 0.245037 | − | 0.141472i | ||||
\(173\) | 5.87328 | + | 3.39094i | 0.446537 | + | 0.257808i | 0.706367 | − | 0.707846i | \(-0.250333\pi\) |
−0.259829 | + | 0.965655i | \(0.583666\pi\) | |||||||
\(174\) | −10.6497 | + | 2.75315i | −0.807349 | + | 0.208716i | ||||
\(175\) | 1.74230 | − | 3.01775i | 0.131705 | − | 0.228121i | ||||
\(176\) | 2.28452 | − | 3.95691i | 0.172203 | − | 0.298264i | ||||
\(177\) | 10.1061 | + | 10.2859i | 0.759618 | + | 0.773135i | ||||
\(178\) | 3.74116i | 0.280412i | ||||||||
\(179\) | −9.95391 | − | 17.2407i | −0.743990 | − | 1.28863i | −0.950665 | − | 0.310219i | \(-0.899598\pi\) |
0.206675 | − | 0.978410i | \(-0.433736\pi\) | |||||||
\(180\) | 2.99953 | + | 0.0529076i | 0.223572 | + | 0.00394350i | ||||
\(181\) | 0.510977 | + | 0.295013i | 0.0379806 | + | 0.0219281i | 0.518870 | − | 0.854853i | \(-0.326353\pi\) |
−0.480889 | + | 0.876781i | \(0.659686\pi\) | |||||||
\(182\) | 24.8001 | 1.83831 | ||||||||
\(183\) | 3.40719 | − | 0.880825i | 0.251866 | − | 0.0651124i | ||||
\(184\) | − | 7.42056i | − | 0.547051i | ||||||
\(185\) | 8.90762 | 0.654901 | ||||||||
\(186\) | −4.51536 | − | 8.52124i | −0.331082 | − | 0.624808i | ||||
\(187\) | −9.23289 | −0.675176 | ||||||||
\(188\) | 5.93476i | 0.432837i | ||||||||
\(189\) | −5.14731 | + | 17.3595i | −0.374411 | + | 1.26272i | ||||
\(190\) | 7.75060 | 0.562288 | ||||||||
\(191\) | −0.0332892 | − | 0.0192195i | −0.00240872 | − | 0.00139068i | 0.498795 | − | 0.866720i | \(-0.333776\pi\) |
−0.501204 | + | 0.865329i | \(0.667109\pi\) | |||||||
\(192\) | −0.433517 | − | 1.67692i | −0.0312864 | − | 0.121021i | ||||
\(193\) | 0.826680 | + | 1.43185i | 0.0595057 | + | 0.103067i | 0.894244 | − | 0.447581i | \(-0.147714\pi\) |
−0.834738 | + | 0.550647i | \(0.814381\pi\) | |||||||
\(194\) | − | 5.16445i | − | 0.370786i | ||||||
\(195\) | 8.79311 | − | 8.63938i | 0.629687 | − | 0.618679i | ||||
\(196\) | 2.57122 | − | 4.45348i | 0.183658 | − | 0.318106i | ||||
\(197\) | 5.61969 | − | 9.73359i | 0.400386 | − | 0.693490i | −0.593386 | − | 0.804918i | \(-0.702209\pi\) |
0.993772 | + | 0.111428i | \(0.0355426\pi\) | |||||||
\(198\) | 13.7050 | + | 0.241737i | 0.973973 | + | 0.0171795i | ||||
\(199\) | −11.3096 | − | 6.52959i | −0.801715 | − | 0.462870i | 0.0423557 | − | 0.999103i | \(-0.486514\pi\) |
−0.844070 | + | 0.536232i | \(0.819847\pi\) | |||||||
\(200\) | −0.866025 | + | 0.500000i | −0.0612372 | + | 0.0353553i | ||||
\(201\) | −10.3120 | − | 2.86079i | −0.727352 | − | 0.201785i | ||||
\(202\) | 13.3572 | 0.939807 | ||||||||
\(203\) | 11.0649 | + | 19.1649i | 0.776602 | + | 1.34511i | ||||
\(204\) | −2.49663 | + | 2.45298i | −0.174799 | + | 0.171743i | ||||
\(205\) | −1.25343 | − | 2.17100i | −0.0875432 | − | 0.151629i | ||||
\(206\) | 9.35418 | + | 5.40064i | 0.651737 | + | 0.376280i | ||||
\(207\) | 19.4725 | − | 10.7891i | 1.35343 | − | 0.749895i | ||||
\(208\) | −6.16355 | − | 3.55853i | −0.427366 | − | 0.246740i | ||||
\(209\) | 35.4129 | 2.44956 | ||||||||
\(210\) | −1.51063 | − | 5.84340i | −0.104244 | − | 0.403233i | ||||
\(211\) | 10.2150 | + | 17.6930i | 0.703233 | + | 1.21803i | 0.967326 | + | 0.253537i | \(0.0815941\pi\) |
−0.264093 | + | 0.964497i | \(0.585073\pi\) | |||||||
\(212\) | −5.09901 | + | 8.83174i | −0.350201 | + | 0.606566i | ||||
\(213\) | 1.21176 | − | 4.36792i | 0.0830286 | − | 0.299285i | ||||
\(214\) | −2.35616 | − | 4.08099i | −0.161064 | − | 0.278971i | ||||
\(215\) | −3.71078 | −0.253073 | ||||||||
\(216\) | 3.77014 | − | 3.57576i | 0.256526 | − | 0.243300i | ||||
\(217\) | −14.0910 | + | 13.3364i | −0.956558 | + | 0.905335i | ||||
\(218\) | − | 7.92947i | − | 0.537052i | ||||||
\(219\) | −4.18088 | + | 15.0704i | −0.282518 | + | 1.01836i | ||||
\(220\) | −3.95691 | + | 2.28452i | −0.266775 | + | 0.154023i | ||||
\(221\) | 14.3818i | 0.967423i | ||||||||
\(222\) | 11.0053 | − | 10.8129i | 0.738630 | − | 0.725717i | ||||
\(223\) | 4.09323 | − | 2.36323i | 0.274103 | − | 0.158253i | −0.356648 | − | 0.934239i | \(-0.616080\pi\) |
0.630751 | + | 0.775986i | \(0.282747\pi\) | |||||||
\(224\) | −3.01775 | + | 1.74230i | −0.201632 | + | 0.116412i | ||||
\(225\) | −2.57122 | − | 1.54559i | −0.171415 | − | 0.103039i | ||||
\(226\) | −3.77475 | + | 6.53805i | −0.251092 | + | 0.434905i | ||||
\(227\) | 1.98836 | + | 1.14798i | 0.131972 | + | 0.0761942i | 0.564533 | − | 0.825411i | \(-0.309056\pi\) |
−0.432560 | + | 0.901605i | \(0.642390\pi\) | |||||||
\(228\) | 9.57585 | − | 9.40843i | 0.634176 | − | 0.623089i | ||||
\(229\) | 18.1482 | − | 10.4779i | 1.19927 | − | 0.692396i | 0.238874 | − | 0.971051i | \(-0.423222\pi\) |
0.960391 | + | 0.278654i | \(0.0898884\pi\) | |||||||
\(230\) | −3.71028 | + | 6.42639i | −0.244649 | + | 0.423744i | ||||
\(231\) | −6.90216 | − | 26.6988i | −0.454129 | − | 1.75665i | ||||
\(232\) | − | 6.35073i | − | 0.416946i | ||||||
\(233\) | − | 20.5404i | − | 1.34564i | −0.739805 | − | 0.672822i | \(-0.765082\pi\) | ||
0.739805 | − | 0.672822i | \(-0.234918\pi\) | |||||||
\(234\) | 0.376546 | − | 21.3479i | 0.0246156 | − | 1.39555i | ||||
\(235\) | 2.96738 | − | 5.13965i | 0.193570 | − | 0.335274i | ||||
\(236\) | −7.20993 | + | 4.16265i | −0.469326 | + | 0.270966i | ||||
\(237\) | −10.2846 | − | 10.4676i | −0.668057 | − | 0.679944i | ||||
\(238\) | 6.09811 | + | 3.52075i | 0.395282 | + | 0.228216i | ||||
\(239\) | −3.71386 | + | 6.43260i | −0.240230 | + | 0.416090i | −0.960780 | − | 0.277313i | \(-0.910556\pi\) |
0.720550 | + | 0.693403i | \(0.243889\pi\) | |||||||
\(240\) | −0.463024 | + | 1.66901i | −0.0298880 | + | 0.107734i | ||||
\(241\) | 19.2359 | − | 11.1059i | 1.23909 | − | 0.715391i | 0.270185 | − | 0.962808i | \(-0.412915\pi\) |
0.968909 | + | 0.247417i | \(0.0795819\pi\) | |||||||
\(242\) | −8.55305 | + | 4.93811i | −0.549811 | + | 0.317434i | ||||
\(243\) | 14.8648 | + | 4.69436i | 0.953579 | + | 0.301143i | ||||
\(244\) | 2.03181i | 0.130073i | ||||||||
\(245\) | −4.45348 | + | 2.57122i | −0.284522 | + | 0.164269i | ||||
\(246\) | −4.18398 | − | 1.16073i | −0.266761 | − | 0.0740056i | ||||
\(247\) | − | 55.1615i | − | 3.50984i | ||||||
\(248\) | 5.41564 | − | 1.29260i | 0.343894 | − | 0.0820801i | ||||
\(249\) | 15.1751 | + | 4.20993i | 0.961683 | + | 0.266793i | ||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −13.1015 | − | 22.6925i | −0.826961 | − | 1.43234i | −0.900411 | − | 0.435040i | \(-0.856734\pi\) |
0.0734504 | − | 0.997299i | \(-0.476599\pi\) | |||||||
\(252\) | −8.95967 | − | 5.38575i | −0.564406 | − | 0.339270i | ||||
\(253\) | −16.9525 | + | 29.3625i | −1.06579 | + | 1.84601i | ||||
\(254\) | 1.17096 | + | 2.02816i | 0.0734726 | + | 0.127258i | ||||
\(255\) | 3.38863 | − | 0.876028i | 0.212204 | − | 0.0548590i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.90822 | + | 1.10171i | 0.119032 | + | 0.0687229i | 0.558334 | − | 0.829616i | \(-0.311441\pi\) |
−0.439302 | + | 0.898339i | \(0.644774\pi\) | |||||||
\(258\) | −4.58466 | + | 4.50450i | −0.285428 | + | 0.280438i | ||||
\(259\) | −26.8810 | − | 15.5197i | −1.67030 | − | 0.964350i | ||||
\(260\) | 3.55853 | + | 6.16355i | 0.220691 | + | 0.382247i | ||||
\(261\) | 16.6651 | − | 9.23362i | 1.03154 | − | 0.571547i | ||||
\(262\) | 5.57535 | + | 9.65680i | 0.344447 | + | 0.596599i | ||||
\(263\) | −26.8127 | −1.65334 | −0.826671 | − | 0.562685i | \(-0.809768\pi\) | ||||
−0.826671 | + | 0.562685i | \(0.809768\pi\) | |||||||
\(264\) | −2.11558 | + | 7.62581i | −0.130205 | + | 0.469336i | ||||
\(265\) | 8.83174 | − | 5.09901i | 0.542529 | − | 0.313229i | ||||
\(266\) | −23.3894 | − | 13.5039i | −1.43410 | − | 0.827976i | ||||
\(267\) | −1.62186 | − | 6.27363i | −0.0992560 | − | 0.383940i | ||||
\(268\) | 3.08925 | − | 5.35073i | 0.188706 | − | 0.326848i | ||||
\(269\) | 8.44253 | − | 14.6229i | 0.514750 | − | 0.891574i | −0.485103 | − | 0.874457i | \(-0.661218\pi\) |
0.999853 | − | 0.0171168i | \(-0.00544870\pi\) | |||||||
\(270\) | −5.05292 | + | 1.21163i | −0.307511 | + | 0.0737373i | ||||
\(271\) | 1.70861i | 0.103791i | 0.998653 | + | 0.0518953i | \(0.0165262\pi\) | ||||
−0.998653 | + | 0.0518953i | \(0.983474\pi\) | |||||||
\(272\) | −1.01037 | − | 1.75002i | −0.0612629 | − | 0.106110i | ||||
\(273\) | −41.5878 | + | 10.7513i | −2.51701 | + | 0.650696i | ||||
\(274\) | 7.13410 | + | 4.11888i | 0.430987 | + | 0.248830i | ||||
\(275\) | 4.56905 | 0.275524 | ||||||||
\(276\) | 3.21694 | + | 12.4437i | 0.193637 | + | 0.749022i | ||||
\(277\) | 10.7229i | 0.644276i | 0.946693 | + | 0.322138i | \(0.104401\pi\) | ||||
−0.946693 | + | 0.322138i | \(0.895599\pi\) | |||||||
\(278\) | 7.69544 | 0.461542 | ||||||||
\(279\) | 11.2660 | + | 12.3320i | 0.674478 | + | 0.738295i | ||||
\(280\) | 3.48460 | 0.208245 | ||||||||
\(281\) | − | 5.39706i | − | 0.321961i | −0.986958 | − | 0.160981i | \(-0.948534\pi\) | ||
0.986958 | − | 0.160981i | \(-0.0514657\pi\) | |||||||
\(282\) | −2.57282 | − | 9.95212i | −0.153209 | − | 0.592640i | ||||
\(283\) | 1.57973 | 0.0939053 | 0.0469527 | − | 0.998897i | \(-0.485049\pi\) | ||||
0.0469527 | + | 0.998897i | \(0.485049\pi\) | |||||||
\(284\) | 2.26644 | + | 1.30853i | 0.134489 | + | 0.0776471i | ||||
\(285\) | −12.9971 | + | 3.36002i | −0.769884 | + | 0.199030i | ||||
\(286\) | 16.2591 | + | 28.1616i | 0.961421 | + | 1.66523i | ||||
\(287\) | 8.73539i | 0.515633i | ||||||||
\(288\) | 1.45395 | + | 2.62413i | 0.0856747 | + | 0.154628i | ||||
\(289\) | 6.45829 | − | 11.1861i | 0.379899 | − | 0.658005i | ||||
\(290\) | −3.17536 | + | 5.49989i | −0.186464 | + | 0.322965i | ||||
\(291\) | 2.23888 | + | 8.66038i | 0.131245 | + | 0.507680i | ||||
\(292\) | −7.81979 | − | 4.51476i | −0.457619 | − | 0.264206i | ||||
\(293\) | 1.57186 | − | 0.907515i | 0.0918292 | − | 0.0530176i | −0.453382 | − | 0.891316i | \(-0.649783\pi\) |
0.545211 | + | 0.838299i | \(0.316449\pi\) | |||||||
\(294\) | −2.38107 | + | 8.58280i | −0.138867 | + | 0.500559i | ||||
\(295\) | 8.32531 | 0.484718 | ||||||||
\(296\) | 4.45381 | + | 7.71423i | 0.258872 | + | 0.448380i | ||||
\(297\) | −23.0870 | + | 5.53598i | −1.33965 | + | 0.321230i | ||||
\(298\) | −5.79275 | − | 10.0333i | −0.335565 | − | 0.581216i | ||||
\(299\) | 45.7370 | + | 26.4063i | 2.64504 | + | 1.52711i | ||||
\(300\) | 1.23550 | − | 1.21390i | 0.0713315 | − | 0.0700844i | ||||
\(301\) | 11.1982 | + | 6.46529i | 0.645454 | + | 0.372653i | ||||
\(302\) | 3.25609 | 0.187367 | ||||||||
\(303\) | −22.3989 | + | 5.79056i | −1.28678 | + | 0.332659i | ||||
\(304\) | 3.87530 | + | 6.71222i | 0.222264 | + | 0.384972i | ||||
\(305\) | 1.01591 | − | 1.75960i | 0.0581706 | − | 0.100754i | ||||
\(306\) | 3.12324 | − | 5.19578i | 0.178544 | − | 0.297023i | ||||
\(307\) | −11.1220 | − | 19.2638i | −0.634764 | − | 1.09944i | −0.986565 | − | 0.163368i | \(-0.947764\pi\) |
0.351802 | − | 0.936075i | \(-0.385569\pi\) | |||||||
\(308\) | 15.9213 | 0.907201 | ||||||||
\(309\) | −18.0275 | − | 5.00125i | −1.02555 | − | 0.284511i | ||||
\(310\) | −5.33638 | − | 1.58840i | −0.303086 | − | 0.0902150i | ||||
\(311\) | − | 7.90128i | − | 0.448040i | −0.974584 | − | 0.224020i | \(-0.928082\pi\) | ||
0.974584 | − | 0.224020i | \(-0.0719182\pi\) | |||||||
\(312\) | 11.8785 | + | 3.29537i | 0.672486 | + | 0.186563i | ||||
\(313\) | 26.2824 | − | 15.1742i | 1.48557 | − | 0.857694i | 0.485704 | − | 0.874123i | \(-0.338563\pi\) |
0.999865 | + | 0.0164291i | \(0.00522980\pi\) | |||||||
\(314\) | 8.65383i | 0.488364i | ||||||||
\(315\) | 5.06643 | + | 9.14403i | 0.285461 | + | 0.515208i | ||||
\(316\) | 7.33730 | − | 4.23619i | 0.412756 | − | 0.238305i | ||||
\(317\) | −2.03734 | + | 1.17626i | −0.114428 | + | 0.0660651i | −0.556122 | − | 0.831101i | \(-0.687711\pi\) |
0.441694 | + | 0.897166i | \(0.354378\pi\) | |||||||
\(318\) | 4.72192 | − | 17.0206i | 0.264792 | − | 0.954470i | ||||
\(319\) | −14.5084 | + | 25.1293i | −0.812314 | + | 1.40697i | ||||
\(320\) | −0.866025 | − | 0.500000i | −0.0484123 | − | 0.0279508i | ||||
\(321\) | 5.72027 | + | 5.82206i | 0.319275 | + | 0.324956i | ||||
\(322\) | 22.3934 | − | 12.9288i | 1.24794 | − | 0.720496i | ||||
\(323\) | 7.83100 | − | 13.5637i | 0.435729 | − | 0.754704i | ||||
\(324\) | −4.77207 | + | 7.63068i | −0.265115 | + | 0.423927i | ||||
\(325\) | − | 7.11706i | − | 0.394783i | ||||||
\(326\) | 10.5145i | 0.582344i | ||||||||
\(327\) | 3.43756 | + | 13.2971i | 0.190098 | + | 0.735331i | ||||
\(328\) | 1.25343 | − | 2.17100i | 0.0692089 | − | 0.119873i | ||||
\(329\) | −17.9096 | + | 10.3401i | −0.987390 | + | 0.570070i | ||||
\(330\) | 5.64505 | − | 5.54636i | 0.310750 | − | 0.305317i | ||||
\(331\) | 28.9498 | + | 16.7142i | 1.59122 | + | 0.918693i | 0.993098 | + | 0.117290i | \(0.0374207\pi\) |
0.598125 | + | 0.801403i | \(0.295913\pi\) | |||||||
\(332\) | −4.54612 | + | 7.87412i | −0.249501 | + | 0.432148i | ||||
\(333\) | −13.7675 | + | 22.9034i | −0.754454 | + | 1.25510i | ||||
\(334\) | 5.49202 | − | 3.17082i | 0.300510 | − | 0.173499i | ||||
\(335\) | −5.35073 | + | 3.08925i | −0.292342 | + | 0.168784i | ||||
\(336\) | 4.30521 | − | 4.22995i | 0.234869 | − | 0.230762i | ||||
\(337\) | − | 20.3539i | − | 1.10875i | −0.832267 | − | 0.554375i | \(-0.812957\pi\) | ||
0.832267 | − | 0.554375i | \(-0.187043\pi\) | |||||||
\(338\) | 32.6080 | − | 18.8263i | 1.77364 | − | 1.02401i | ||||
\(339\) | 3.49559 | − | 12.6002i | 0.189855 | − | 0.684350i | ||||
\(340\) | 2.02075i | 0.109590i | ||||||||
\(341\) | −24.3822 | − | 7.25747i | −1.32037 | − | 0.393014i | ||||
\(342\) | −11.9792 | + | 19.9285i | −0.647762 | + | 1.07761i | ||||
\(343\) | −6.47286 | −0.349502 | ||||||||
\(344\) | −1.85539 | − | 3.21363i | −0.100036 | − | 0.173267i | ||||
\(345\) | 3.43589 | − | 12.3850i | 0.184982 | − | 0.666787i | ||||
\(346\) | 3.39094 | − | 5.87328i | 0.182298 | − | 0.315750i | ||||
\(347\) | −3.41153 | − | 5.90895i | −0.183141 | − | 0.317209i | 0.759808 | − | 0.650148i | \(-0.225293\pi\) |
−0.942948 | + | 0.332939i | \(0.891960\pi\) | |||||||
\(348\) | 2.75315 | + | 10.6497i | 0.147584 | + | 0.570882i | ||||
\(349\) | −22.1151 | −1.18380 | −0.591898 | − | 0.806013i | \(-0.701621\pi\) | ||||
−0.591898 | + | 0.806013i | \(0.701621\pi\) | |||||||
\(350\) | −3.01775 | − | 1.74230i | −0.161306 | − | 0.0931299i | ||||
\(351\) | 8.62322 | + | 35.9619i | 0.460273 | + | 1.91950i | ||||
\(352\) | −3.95691 | − | 2.28452i | −0.210904 | − | 0.121766i | ||||
\(353\) | 7.74400 | + | 13.4130i | 0.412171 | + | 0.713902i | 0.995127 | − | 0.0986022i | \(-0.0314371\pi\) |
−0.582955 | + | 0.812504i | \(0.698104\pi\) | |||||||
\(354\) | 10.2859 | − | 10.1061i | 0.546689 | − | 0.537131i | ||||
\(355\) | −1.30853 | − | 2.26644i | −0.0694497 | − | 0.120290i | ||||
\(356\) | 3.74116 | 0.198281 | ||||||||
\(357\) | −11.7524 | − | 3.26038i | −0.622001 | − | 0.172558i | ||||
\(358\) | −17.2407 | + | 9.95391i | −0.911198 | + | 0.526081i | ||||
\(359\) | 6.07127 | + | 3.50525i | 0.320429 | + | 0.185000i | 0.651584 | − | 0.758577i | \(-0.274105\pi\) |
−0.331155 | + | 0.943577i | \(0.607438\pi\) | |||||||
\(360\) | 0.0529076 | − | 2.99953i | 0.00278847 | − | 0.158089i | ||||
\(361\) | −20.5359 | + | 35.5692i | −1.08084 | + | 1.87207i | ||||
\(362\) | 0.295013 | − | 0.510977i | 0.0155055 | − | 0.0268563i | ||||
\(363\) | 12.2020 | − | 11.9887i | 0.640441 | − | 0.629244i | ||||
\(364\) | − | 24.8001i | − | 1.29988i | ||||||
\(365\) | 4.51476 | + | 7.81979i | 0.236313 | + | 0.409307i | ||||
\(366\) | −0.880825 | − | 3.40719i | −0.0460414 | − | 0.178096i | ||||
\(367\) | −0.917271 | − | 0.529587i | −0.0478812 | − | 0.0276442i | 0.475868 | − | 0.879517i | \(-0.342134\pi\) |
−0.523749 | + | 0.851872i | \(0.675467\pi\) | |||||||
\(368\) | −7.42056 | −0.386824 | ||||||||
\(369\) | 7.51939 | + | 0.132632i | 0.391444 | + | 0.00690453i | ||||
\(370\) | − | 8.90762i | − | 0.463085i | ||||||
\(371\) | −35.5360 | −1.84494 | ||||||||
\(372\) | −8.52124 | + | 4.51536i | −0.441806 | + | 0.234110i | ||||
\(373\) | −9.78720 | −0.506762 | −0.253381 | − | 0.967367i | \(-0.581543\pi\) | ||||
−0.253381 | + | 0.967367i | \(0.581543\pi\) | |||||||
\(374\) | 9.23289i | 0.477422i | ||||||||
\(375\) | −1.67692 | + | 0.433517i | −0.0865958 | + | 0.0223867i | ||||
\(376\) | 5.93476 | 0.306062 | ||||||||
\(377\) | 39.1430 | + | 22.5992i | 2.01597 | + | 1.16392i | ||||
\(378\) | 17.3595 | + | 5.14731i | 0.892875 | + | 0.264749i | ||||
\(379\) | 3.22853 | + | 5.59198i | 0.165838 | + | 0.287241i | 0.936953 | − | 0.349456i | \(-0.113634\pi\) |
−0.771114 | + | 0.636697i | \(0.780300\pi\) | |||||||
\(380\) | − | 7.75060i | − | 0.397597i | ||||||
\(381\) | −2.84285 | − | 2.89344i | −0.145644 | − | 0.148235i | ||||
\(382\) | −0.0192195 | + | 0.0332892i | −0.000983358 | + | 0.00170323i | ||||
\(383\) | −6.78475 | + | 11.7515i | −0.346684 | + | 0.600475i | −0.985658 | − | 0.168753i | \(-0.946026\pi\) |
0.638974 | + | 0.769228i | \(0.279359\pi\) | |||||||
\(384\) | −1.67692 | + | 0.433517i | −0.0855750 | + | 0.0221228i | ||||
\(385\) | −13.7883 | − | 7.96066i | −0.702715 | − | 0.405713i | ||||
\(386\) | 1.43185 | − | 0.826680i | 0.0728793 | − | 0.0420769i | ||||
\(387\) | 5.73533 | − | 9.54122i | 0.291543 | − | 0.485008i | ||||
\(388\) | −5.16445 | −0.262185 | ||||||||
\(389\) | −8.50667 | − | 14.7340i | −0.431306 | − | 0.747043i | 0.565681 | − | 0.824624i | \(-0.308614\pi\) |
−0.996986 | + | 0.0775814i | \(0.975280\pi\) | |||||||
\(390\) | −8.63938 | − | 8.79311i | −0.437472 | − | 0.445256i | ||||
\(391\) | 7.49754 | + | 12.9861i | 0.379167 | + | 0.656736i | ||||
\(392\) | −4.45348 | − | 2.57122i | −0.224935 | − | 0.129866i | ||||
\(393\) | −13.5358 | − | 13.7767i | −0.682791 | − | 0.694941i | ||||
\(394\) | −9.73359 | − | 5.61969i | −0.490371 | − | 0.283116i | ||||
\(395\) | −8.47239 | −0.426292 | ||||||||
\(396\) | 0.241737 | − | 13.7050i | 0.0121478 | − | 0.688703i | ||||
\(397\) | 1.89196 | + | 3.27696i | 0.0949546 | + | 0.164466i | 0.909590 | − | 0.415508i | \(-0.136396\pi\) |
−0.814635 | + | 0.579974i | \(0.803063\pi\) | |||||||
\(398\) | −6.52959 | + | 11.3096i | −0.327299 | + | 0.566898i | ||||
\(399\) | 45.0763 | + | 12.5052i | 2.25664 | + | 0.626044i | ||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | 6.86891 | 0.343017 | 0.171509 | − | 0.985183i | \(-0.445136\pi\) | ||||
0.171509 | + | 0.985183i | \(0.445136\pi\) | |||||||
\(402\) | −2.86079 | + | 10.3120i | −0.142683 | + | 0.514316i | ||||
\(403\) | −11.3047 | + | 37.9794i | −0.563128 | + | 1.89189i | ||||
\(404\) | − | 13.3572i | − | 0.664544i | ||||||
\(405\) | 7.94808 | − | 4.22233i | 0.394943 | − | 0.209809i | ||||
\(406\) | 19.1649 | − | 11.0649i | 0.951139 | − | 0.549140i | ||||
\(407\) | − | 40.6994i | − | 2.01739i | ||||||
\(408\) | 2.45298 | + | 2.49663i | 0.121441 | + | 0.123602i | ||||
\(409\) | 5.16441 | − | 2.98167i | 0.255364 | − | 0.147434i | −0.366854 | − | 0.930278i | \(-0.619565\pi\) |
0.622218 | + | 0.782844i | \(0.286232\pi\) | |||||||
\(410\) | −2.17100 | + | 1.25343i | −0.107218 | + | 0.0619024i | ||||
\(411\) | −13.7489 | − | 3.81427i | −0.678185 | − | 0.188144i | ||||
\(412\) | 5.40064 | − | 9.35418i | 0.266070 | − | 0.460847i | ||||
\(413\) | −25.1237 | − | 14.5052i | −1.23626 | − | 0.713753i | ||||
\(414\) | −10.7891 | − | 19.4725i | −0.530256 | − | 0.957021i | ||||
\(415\) | 7.87412 | − | 4.54612i | 0.386525 | − | 0.223160i | ||||
\(416\) | −3.55853 | + | 6.16355i | −0.174471 | + | 0.302193i | ||||
\(417\) | −12.9046 | + | 3.33611i | −0.631943 | + | 0.163370i | ||||
\(418\) | − | 35.4129i | − | 1.73210i | ||||||
\(419\) | 1.08088i | 0.0528046i | 0.999651 | + | 0.0264023i | \(0.00840510\pi\) | ||||
−0.999651 | + | 0.0264023i | \(0.991595\pi\) | |||||||
\(420\) | −5.84340 | + | 1.51063i | −0.285129 | + | 0.0737114i | ||||
\(421\) | 6.53199 | − | 11.3137i | 0.318350 | − | 0.551398i | −0.661794 | − | 0.749686i | \(-0.730205\pi\) |
0.980144 | + | 0.198288i | \(0.0635380\pi\) | |||||||
\(422\) | 17.6930 | − | 10.2150i | 0.861281 | − | 0.497261i | ||||
\(423\) | 8.62883 | + | 15.5736i | 0.419548 | + | 0.757212i | ||||
\(424\) | 8.83174 | + | 5.09901i | 0.428907 | + | 0.247630i | ||||
\(425\) | 1.01037 | − | 1.75002i | 0.0490103 | − | 0.0848884i | ||||
\(426\) | −4.36792 | − | 1.21176i | −0.211626 | − | 0.0587101i | ||||
\(427\) | −6.13150 | + | 3.54002i | −0.296724 | + | 0.171314i | ||||
\(428\) | −4.08099 | + | 2.35616i | −0.197262 | + | 0.113889i | ||||
\(429\) | −39.4737 | − | 40.1761i | −1.90581 | − | 1.93972i | ||||
\(430\) | 3.71078i | 0.178950i | ||||||||
\(431\) | −6.28123 | + | 3.62647i | −0.302556 | + | 0.174681i | −0.643591 | − | 0.765370i | \(-0.722556\pi\) |
0.341035 | + | 0.940051i | \(0.389223\pi\) | |||||||
\(432\) | −3.57576 | − | 3.77014i | −0.172039 | − | 0.181391i | ||||
\(433\) | − | 19.0811i | − | 0.916977i | −0.888700 | − | 0.458488i | \(-0.848391\pi\) | ||
0.888700 | − | 0.458488i | \(-0.151609\pi\) | |||||||
\(434\) | 13.3364 | + | 14.0910i | 0.640168 | + | 0.676388i | ||||
\(435\) | 2.94054 | − | 10.5995i | 0.140988 | − | 0.508205i | ||||
\(436\) | −7.92947 | −0.379753 | ||||||||
\(437\) | −28.7569 | − | 49.8084i | −1.37563 | − | 2.38266i | ||||
\(438\) | 15.0704 | + | 4.18088i | 0.720091 | + | 0.199770i | ||||
\(439\) | −16.8037 | + | 29.1048i | −0.801995 | + | 1.38910i | 0.116306 | + | 0.993213i | \(0.462895\pi\) |
−0.918301 | + | 0.395883i | \(0.870439\pi\) | |||||||
\(440\) | 2.28452 | + | 3.95691i | 0.108910 | + | 0.188638i | ||||
\(441\) | 0.272074 | − | 15.4249i | 0.0129559 | − | 0.734520i | ||||
\(442\) | 14.3818 | 0.684071 | ||||||||
\(443\) | −6.93043 | − | 4.00128i | −0.329275 | − | 0.190107i | 0.326244 | − | 0.945285i | \(-0.394217\pi\) |
−0.655519 | + | 0.755179i | \(0.727550\pi\) | |||||||
\(444\) | −10.8129 | − | 11.0053i | −0.513159 | − | 0.522290i | ||||
\(445\) | −3.23994 | − | 1.87058i | −0.153588 | − | 0.0886739i | ||||
\(446\) | −2.36323 | − | 4.09323i | −0.111902 | − | 0.193820i | ||||
\(447\) | 14.0636 | + | 14.3139i | 0.665186 | + | 0.677022i | ||||
\(448\) | 1.74230 | + | 3.01775i | 0.0823159 | + | 0.142575i | ||||
\(449\) | 20.3595 | 0.960824 | 0.480412 | − | 0.877043i | \(-0.340487\pi\) | ||||
0.480412 | + | 0.877043i | \(0.340487\pi\) | |||||||
\(450\) | −1.54559 | + | 2.57122i | −0.0728596 | + | 0.121208i | ||||
\(451\) | −9.91941 | + | 5.72697i | −0.467087 | + | 0.269673i | ||||
\(452\) | 6.53805 | + | 3.77475i | 0.307524 | + | 0.177549i | ||||
\(453\) | −5.46021 | + | 1.41157i | −0.256543 | + | 0.0663214i | ||||
\(454\) | 1.14798 | − | 1.98836i | 0.0538774 | − | 0.0933184i | ||||
\(455\) | −12.4000 | + | 21.4775i | −0.581323 | + | 1.00688i | ||||
\(456\) | −9.40843 | − | 9.57585i | −0.440590 | − | 0.448430i | ||||
\(457\) | 11.2885i | 0.528052i | 0.964516 | + | 0.264026i | \(0.0850504\pi\) | ||||
−0.964516 | + | 0.264026i | \(0.914950\pi\) | |||||||
\(458\) | −10.4779 | − | 18.1482i | −0.489598 | − | 0.848009i | ||||
\(459\) | −2.98496 | + | 10.0669i | −0.139326 | + | 0.469882i | ||||
\(460\) | 6.42639 | + | 3.71028i | 0.299632 | + | 0.172993i | ||||
\(461\) | −16.9753 | −0.790617 | −0.395308 | − | 0.918548i | \(-0.629362\pi\) | ||||
−0.395308 | + | 0.918548i | \(0.629362\pi\) | |||||||
\(462\) | −26.6988 | + | 6.90216i | −1.24214 | + | 0.321118i | ||||
\(463\) | 7.96544i | 0.370186i | 0.982721 | + | 0.185093i | \(0.0592586\pi\) | ||||
−0.982721 | + | 0.185093i | \(0.940741\pi\) | |||||||
\(464\) | −6.35073 | −0.294825 | ||||||||
\(465\) | 9.63729 | + | 0.350205i | 0.446919 | + | 0.0162404i | ||||
\(466\) | −20.5404 | −0.951513 | ||||||||
\(467\) | − | 17.5704i | − | 0.813063i | −0.913637 | − | 0.406532i | \(-0.866738\pi\) | ||
0.913637 | − | 0.406532i | \(-0.133262\pi\) | |||||||
\(468\) | −21.3479 | − | 0.376546i | −0.986805 | − | 0.0174059i | ||||
\(469\) | 21.5296 | 0.994144 | ||||||||
\(470\) | −5.13965 | − | 2.96738i | −0.237074 | − | 0.136875i | ||||
\(471\) | −3.75158 | − | 14.5118i | −0.172864 | − | 0.668668i | ||||
\(472\) | 4.16265 | + | 7.20993i | 0.191602 | + | 0.331864i | ||||
\(473\) | 16.9547i | 0.779579i | ||||||||
\(474\) | −10.4676 | + | 10.2846i | −0.480793 | + | 0.472388i | ||||
\(475\) | −3.87530 | + | 6.71222i | −0.177811 | + | 0.307978i | ||||
\(476\) | 3.52075 | − | 6.09811i | 0.161373 | − | 0.279507i | ||||
\(477\) | −0.539552 | + | 30.5893i | −0.0247044 | + | 1.40059i | ||||
\(478\) | 6.43260 | + | 3.71386i | 0.294220 | + | 0.169868i | ||||
\(479\) | 34.7418 | − | 20.0582i | 1.58739 | − | 0.916481i | 0.593658 | − | 0.804718i | \(-0.297683\pi\) |
0.993735 | − | 0.111764i | \(-0.0356500\pi\) | |||||||
\(480\) | 1.66901 | + | 0.463024i | 0.0761797 | + | 0.0211340i | ||||
\(481\) | −63.3961 | −2.89061 | ||||||||
\(482\) | −11.1059 | − | 19.2359i | −0.505858 | − | 0.876172i | ||||
\(483\) | −31.9471 | + | 31.3886i | −1.45364 | + | 1.42823i | ||||
\(484\) | 4.93811 | + | 8.55305i | 0.224459 | + | 0.388775i | ||||
\(485\) | 4.47255 | + | 2.58223i | 0.203088 | + | 0.117253i | ||||
\(486\) | 4.69436 | − | 14.8648i | 0.212940 | − | 0.674282i | ||||
\(487\) | 11.2285 | + | 6.48275i | 0.508810 | + | 0.293761i | 0.732344 | − | 0.680935i | \(-0.238426\pi\) |
−0.223535 | + | 0.974696i | \(0.571760\pi\) | |||||||
\(488\) | 2.03181 | 0.0919757 | ||||||||
\(489\) | −4.55821 | − | 17.6320i | −0.206130 | − | 0.797346i | ||||
\(490\) | 2.57122 | + | 4.45348i | 0.116156 | + | 0.201188i | ||||
\(491\) | −5.53082 | + | 9.57967i | −0.249603 | + | 0.432324i | −0.963416 | − | 0.268012i | \(-0.913633\pi\) |
0.713813 | + | 0.700336i | \(0.246967\pi\) | |||||||
\(492\) | −1.16073 | + | 4.18398i | −0.0523299 | + | 0.188628i | ||||
\(493\) | 6.41661 | + | 11.1139i | 0.288989 | + | 0.500544i | ||||
\(494\) | −55.1615 | −2.48183 | ||||||||
\(495\) | −7.06186 | + | 11.7480i | −0.317407 | + | 0.528034i | ||||
\(496\) | −1.29260 | − | 5.41564i | −0.0580394 | − | 0.243170i | ||||
\(497\) | 9.11942i | 0.409062i | ||||||||
\(498\) | 4.20993 | − | 15.1751i | 0.188651 | − | 0.680012i | ||||
\(499\) | −20.9146 | + | 12.0750i | −0.936264 | + | 0.540552i | −0.888787 | − | 0.458320i | \(-0.848451\pi\) |
−0.0474768 | + | 0.998872i | \(0.515118\pi\) | |||||||
\(500\) | − | 1.00000i | − | 0.0447214i | ||||||
\(501\) | −7.83507 | + | 7.69809i | −0.350045 | + | 0.343925i | ||||
\(502\) | −22.6925 | + | 13.1015i | −1.01282 | + | 0.584750i | ||||
\(503\) | 1.02268 | − | 0.590446i | 0.0455991 | − | 0.0263267i | −0.477027 | − | 0.878889i | \(-0.658286\pi\) |
0.522626 | + | 0.852562i | \(0.324952\pi\) | |||||||
\(504\) | −5.38575 | + | 8.95967i | −0.239900 | + | 0.399095i | ||||
\(505\) | −6.67859 | + | 11.5677i | −0.297193 | + | 0.514754i | ||||
\(506\) | 29.3625 | + | 16.9525i | 1.30532 | + | 0.753629i | ||||
\(507\) | −46.5196 | + | 45.7063i | −2.06601 | + | 2.02989i | ||||
\(508\) | 2.02816 | − | 1.17096i | 0.0899852 | − | 0.0519530i | ||||
\(509\) | 14.3823 | − | 24.9109i | 0.637484 | − | 1.10416i | −0.348498 | − | 0.937309i | \(-0.613308\pi\) |
0.985983 | − | 0.166846i | \(-0.0533583\pi\) | |||||||
\(510\) | −0.876028 | − | 3.38863i | −0.0387912 | − | 0.150051i | ||||
\(511\) | − | 31.4643i | − | 1.39190i | ||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 11.4489 | − | 38.6117i | 0.505480 | − | 1.70475i | ||||
\(514\) | 1.10171 | − | 1.90822i | 0.0485944 | − | 0.0841680i | ||||
\(515\) | −9.35418 | + | 5.40064i | −0.412194 | + | 0.237981i | ||||
\(516\) | 4.50450 | + | 4.58466i | 0.198300 | + | 0.201828i | ||||
\(517\) | −23.4833 | − | 13.5581i | −1.03280 | − | 0.596285i | ||||
\(518\) | −15.5197 | + | 26.8810i | −0.681899 | + | 1.18108i | ||||
\(519\) | −3.14017 | + | 11.3191i | −0.137838 | + | 0.496852i | ||||
\(520\) | 6.16355 | − | 3.55853i | 0.270290 | − | 0.156052i | ||||
\(521\) | −7.38345 | + | 4.26284i | −0.323475 | + | 0.186758i | −0.652940 | − | 0.757409i | \(-0.726465\pi\) |
0.329465 | + | 0.944168i | \(0.393131\pi\) | |||||||
\(522\) | −9.23362 | − | 16.6651i | −0.404145 | − | 0.729412i | ||||
\(523\) | − | 16.0030i | − | 0.699764i | −0.936794 | − | 0.349882i | \(-0.886222\pi\) | ||
0.936794 | − | 0.349882i | \(-0.113778\pi\) | |||||||
\(524\) | 9.65680 | − | 5.57535i | 0.421859 | − | 0.243560i | ||||
\(525\) | 5.81585 | + | 1.61345i | 0.253824 | + | 0.0704168i | ||||
\(526\) | 26.8127i | 1.16909i | ||||||||
\(527\) | −8.17147 | + | 7.73389i | −0.355955 | + | 0.336894i | ||||
\(528\) | 7.62581 | + | 2.11558i | 0.331871 | + | 0.0920687i | ||||
\(529\) | 32.0647 | 1.39412 | ||||||||
\(530\) | −5.09901 | − | 8.83174i | −0.221487 | − | 0.383626i | ||||
\(531\) | −12.8675 | + | 21.4062i | −0.558401 | + | 0.928949i | ||||
\(532\) | −13.5039 | + | 23.3894i | −0.585467 | + | 1.01406i | ||||
\(533\) | 8.92071 | + | 15.4511i | 0.386399 | + | 0.669263i | ||||
\(534\) | −6.27363 | + | 1.62186i | −0.271486 | + | 0.0701846i | ||||
\(535\) | 4.71232 | 0.203731 | ||||||||
\(536\) | −5.35073 | − | 3.08925i | −0.231117 | − | 0.133435i | ||||
\(537\) | 24.5961 | − | 24.1660i | 1.06140 | − | 1.04284i | ||||
\(538\) | −14.6229 | − | 8.44253i | −0.630438 | − | 0.363983i | ||||
\(539\) | 11.7480 | + | 20.3482i | 0.506023 | + | 0.876458i | ||||
\(540\) | 1.21163 | + | 5.05292i | 0.0521401 | + | 0.217443i | ||||
\(541\) | −11.1843 | − | 19.3718i | −0.480850 | − | 0.832857i | 0.518908 | − | 0.854830i | \(-0.326339\pi\) |
−0.999759 | + | 0.0219728i | \(0.993005\pi\) | |||||||
\(542\) | 1.70861 | 0.0733911 | ||||||||
\(543\) | −0.273196 | + | 0.984761i | −0.0117239 | + | 0.0422601i | ||||
\(544\) | −1.75002 | + | 1.01037i | −0.0750314 | + | 0.0433194i | ||||
\(545\) | 6.86713 | + | 3.96474i | 0.294155 | + | 0.169831i | ||||
\(546\) | 10.7513 | + | 41.5878i | 0.460112 | + | 1.77979i | ||||
\(547\) | −4.94232 | + | 8.56034i | −0.211318 | + | 0.366014i | −0.952127 | − | 0.305702i | \(-0.901109\pi\) |
0.740809 | + | 0.671716i | \(0.234442\pi\) | |||||||
\(548\) | 4.11888 | − | 7.13410i | 0.175950 | − | 0.304754i | ||||
\(549\) | 2.95415 | + | 5.33173i | 0.126080 | + | 0.227553i | ||||
\(550\) | − | 4.56905i | − | 0.194825i | ||||||
\(551\) | −24.6110 | − | 42.6275i | −1.04846 | − | 1.81599i | ||||
\(552\) | 12.4437 | − | 3.21694i | 0.529639 | − | 0.136922i | ||||
\(553\) | 25.5676 | + | 14.7614i | 1.08724 | + | 0.627720i | ||||
\(554\) | 10.7229 | 0.455572 | ||||||||
\(555\) | 3.86161 | + | 14.9374i | 0.163916 | + | 0.634056i | ||||
\(556\) | − | 7.69544i | − | 0.326359i | ||||||
\(557\) | 29.2677 | 1.24011 | 0.620056 | − | 0.784557i | \(-0.287110\pi\) | ||||
0.620056 | + | 0.784557i | \(0.287110\pi\) | |||||||
\(558\) | 12.3320 | − | 11.2660i | 0.522053 | − | 0.476928i | ||||
\(559\) | 26.4098 | 1.11702 | ||||||||
\(560\) | − | 3.48460i | − | 0.147251i | ||||||
\(561\) | −4.00262 | − | 15.4828i | −0.168991 | − | 0.653686i | ||||
\(562\) | −5.39706 | −0.227661 | ||||||||
\(563\) | −11.1094 | − | 6.41401i | −0.468205 | − | 0.270318i | 0.247283 | − | 0.968943i | \(-0.420462\pi\) |
−0.715488 | + | 0.698625i | \(0.753796\pi\) | |||||||
\(564\) | −9.95212 | + | 2.57282i | −0.419060 | + | 0.108335i | ||||
\(565\) | −3.77475 | − | 6.53805i | −0.158805 | − | 0.275058i | ||||
\(566\) | − | 1.57973i | − | 0.0664011i | ||||||
\(567\) | −31.3419 | − | 1.10600i | −1.31624 | − | 0.0464476i | ||||
\(568\) | 1.30853 | − | 2.26644i | 0.0549048 | − | 0.0950979i | ||||
\(569\) | −11.5367 | + | 19.9822i | −0.483644 | + | 0.837696i | −0.999824 | − | 0.0187841i | \(-0.994020\pi\) |
0.516179 | + | 0.856481i | \(0.327354\pi\) | |||||||
\(570\) | 3.36002 | + | 12.9971i | 0.140736 | + | 0.544390i | ||||
\(571\) | −36.0606 | − | 20.8196i | −1.50909 | − | 0.871273i | −0.999944 | − | 0.0105924i | \(-0.996628\pi\) |
−0.509145 | − | 0.860681i | \(-0.670038\pi\) | |||||||
\(572\) | 28.1616 | − | 16.2591i | 1.17749 | − | 0.679827i | ||||
\(573\) | 0.0177982 | − | 0.0641554i | 0.000743531 | − | 0.00268013i | ||||
\(574\) | 8.73539 | 0.364608 | ||||||||
\(575\) | −3.71028 | − | 6.42639i | −0.154729 | − | 0.267999i | ||||
\(576\) | 2.62413 | − | 1.45395i | 0.109339 | − | 0.0605811i | ||||
\(577\) | 1.28776 | + | 2.23047i | 0.0536102 | + | 0.0928556i | 0.891585 | − | 0.452853i | \(-0.149594\pi\) |
−0.837975 | + | 0.545709i | \(0.816260\pi\) | |||||||
\(578\) | −11.1861 | − | 6.45829i | −0.465280 | − | 0.268629i | ||||
\(579\) | −2.04272 | + | 2.00701i | −0.0848926 | + | 0.0834084i | ||||
\(580\) | 5.49989 | + | 3.17536i | 0.228370 | + | 0.131850i | ||||
\(581\) | −31.6828 | −1.31443 | ||||||||
\(582\) | 8.66038 | − | 2.23888i | 0.358984 | − | 0.0928045i | ||||
\(583\) | −23.2976 | − | 40.3526i | −0.964889 | − | 1.67124i | ||||
\(584\) | −4.51476 | + | 7.81979i | −0.186822 | + | 0.323585i | ||||
\(585\) | 18.2995 | + | 11.0000i | 0.756592 | + | 0.454795i | ||||
\(586\) | −0.907515 | − | 1.57186i | −0.0374891 | − | 0.0649330i | ||||
\(587\) | 34.5548 | 1.42623 | 0.713115 | − | 0.701047i | \(-0.247284\pi\) | ||||
0.713115 | + | 0.701047i | \(0.247284\pi\) | |||||||
\(588\) | 8.58280 | + | 2.38107i | 0.353949 | + | 0.0981936i | ||||
\(589\) | 31.3418 | − | 29.6634i | 1.29141 | − | 1.22226i | ||||
\(590\) | − | 8.32531i | − | 0.342747i | ||||||
\(591\) | 18.7587 | + | 5.20410i | 0.771629 | + | 0.214068i | ||||
\(592\) | 7.71423 | − | 4.45381i | 0.317053 | − | 0.183050i | ||||
\(593\) | − | 38.0833i | − | 1.56389i | −0.623345 | − | 0.781947i | \(-0.714227\pi\) | ||
0.623345 | − | 0.781947i | \(-0.285773\pi\) | |||||||
\(594\) | 5.53598 | + | 23.0870i | 0.227144 | + | 0.947272i | ||||
\(595\) | −6.09811 | + | 3.52075i | −0.249998 | + | 0.144337i | ||||
\(596\) | −10.0333 | + | 5.79275i | −0.410981 | + | 0.237280i | ||||
\(597\) | 6.04671 | − | 21.7960i | 0.247475 | − | 0.892049i | ||||
\(598\) | 26.4063 | − | 45.7370i | 1.07983 | − | 1.87033i | ||||
\(599\) | 20.5428 | + | 11.8604i | 0.839355 | + | 0.484602i | 0.857045 | − | 0.515242i | \(-0.172298\pi\) |
−0.0176899 | + | 0.999844i | \(0.505631\pi\) | |||||||
\(600\) | −1.21390 | − | 1.23550i | −0.0495571 | − | 0.0504390i | ||||
\(601\) | 27.7430 | − | 16.0174i | 1.13166 | − | 0.653365i | 0.187309 | − | 0.982301i | \(-0.440023\pi\) |
0.944352 | + | 0.328936i | \(0.106690\pi\) | |||||||
\(602\) | 6.46529 | − | 11.1982i | 0.263506 | − | 0.456405i | ||||
\(603\) | 0.326889 | − | 18.5326i | 0.0133120 | − | 0.754706i | ||||
\(604\) | − | 3.25609i | − | 0.132489i | ||||||
\(605\) | − | 9.87622i | − | 0.401525i | ||||||
\(606\) | 5.79056 | + | 22.3989i | 0.235226 | + | 0.909894i | ||||
\(607\) | 11.3836 | − | 19.7170i | 0.462047 | − | 0.800289i | −0.537016 | − | 0.843572i | \(-0.680448\pi\) |
0.999063 | + | 0.0432830i | \(0.0137817\pi\) | |||||||
\(608\) | 6.71222 | − | 3.87530i | 0.272216 | − | 0.157164i | ||||
\(609\) | −27.3412 | + | 26.8632i | −1.10792 | + | 1.08855i | ||||
\(610\) | −1.75960 | − | 1.01591i | −0.0712441 | − | 0.0411328i | ||||
\(611\) | −21.1190 | + | 36.5792i | −0.854384 | + | 1.47984i | ||||
\(612\) | −5.19578 | − | 3.12324i | −0.210027 | − | 0.126249i | ||||
\(613\) | −31.6497 | + | 18.2730i | −1.27832 | + | 0.738038i | −0.976539 | − | 0.215340i | \(-0.930914\pi\) |
−0.301780 | + | 0.953378i | \(0.597581\pi\) | |||||||
\(614\) | −19.2638 | + | 11.1220i | −0.777423 | + | 0.448846i | ||||
\(615\) | 3.09721 | − | 3.04306i | 0.124892 | − | 0.122708i | ||||
\(616\) | − | 15.9213i | − | 0.641488i | ||||||
\(617\) | 24.1598 | − | 13.9487i | 0.972638 | − | 0.561553i | 0.0725987 | − | 0.997361i | \(-0.476871\pi\) |
0.900040 | + | 0.435808i | \(0.143537\pi\) | |||||||
\(618\) | −5.00125 | + | 18.0275i | −0.201180 | + | 0.725172i | ||||
\(619\) | − | 30.8511i | − | 1.24001i | −0.784598 | − | 0.620004i | \(-0.787131\pi\) | ||
0.784598 | − | 0.620004i | \(-0.212869\pi\) | |||||||
\(620\) | −1.58840 | + | 5.33638i | −0.0637916 | + | 0.214314i | ||||
\(621\) | 26.5341 | + | 27.9766i | 1.06478 | + | 1.12266i | ||||
\(622\) | −7.90128 | −0.316812 | ||||||||
\(623\) | 6.51822 | + | 11.2899i | 0.261147 | + | 0.452320i | ||||
\(624\) | 3.29537 | − | 11.8785i | 0.131920 | − | 0.475519i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −15.1742 | − | 26.2824i | −0.606481 | − | 1.05046i | ||||
\(627\) | 15.3521 | + | 59.3846i | 0.613103 | + | 2.37159i | ||||
\(628\) | 8.65383 | 0.345326 | ||||||||
\(629\) | −15.5885 | − | 9.00003i | −0.621554 | − | 0.358855i | ||||
\(630\) | 9.14403 | − | 5.06643i | 0.364307 | − | 0.201851i | ||||
\(631\) | 10.5170 | + | 6.07200i | 0.418676 | + | 0.241723i | 0.694511 | − | 0.719483i | \(-0.255621\pi\) |
−0.275835 | + | 0.961205i | \(0.588954\pi\) | |||||||
\(632\) | −4.23619 | − | 7.33730i | −0.168507 | − | 0.291862i | ||||
\(633\) | −25.2413 | + | 24.8000i | −1.00325 | + | 0.985713i | ||||
\(634\) | 1.17626 | + | 2.03734i | 0.0467151 | + | 0.0809129i | ||||
\(635\) | −2.34192 | −0.0929363 | ||||||||
\(636\) | −17.0206 | − | 4.72192i | −0.674912 | − | 0.187236i | ||||
\(637\) | 31.6957 | − | 18.2995i | 1.25583 | − | 0.725053i | ||||
\(638\) | 25.1293 | + | 14.5084i | 0.994877 | + | 0.574393i | ||||
\(639\) | 7.84997 | + | 0.138463i | 0.310540 | + | 0.00547749i | ||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | 1.90290 | − | 3.29593i | 0.0751602 | − | 0.130181i | −0.825996 | − | 0.563676i | \(-0.809387\pi\) |
0.901156 | + | 0.433495i | \(0.142720\pi\) | |||||||
\(642\) | 5.82206 | − | 5.72027i | 0.229778 | − | 0.225761i | ||||
\(643\) | − | 20.2527i | − | 0.798687i | −0.916801 | − | 0.399344i | \(-0.869238\pi\) | ||
0.916801 | − | 0.399344i | \(-0.130762\pi\) | |||||||
\(644\) | −12.9288 | − | 22.3934i | −0.509468 | − | 0.882424i | ||||
\(645\) | −1.60869 | − | 6.22268i | −0.0633419 | − | 0.245018i | ||||
\(646\) | −13.5637 | − | 7.83100i | −0.533656 | − | 0.308107i | ||||
\(647\) | 16.2899 | 0.640422 | 0.320211 | − | 0.947346i | \(-0.396246\pi\) | ||||
0.320211 | + | 0.947346i | \(0.396246\pi\) | |||||||
\(648\) | 7.63068 | + | 4.77207i | 0.299762 | + | 0.187465i | ||||
\(649\) | − | 38.0387i | − | 1.49315i | ||||||
\(650\) | −7.11706 | −0.279154 | ||||||||
\(651\) | −28.4728 | − | 17.8479i | −1.11594 | − | 0.699514i | ||||
\(652\) | 10.5145 | 0.411779 | ||||||||
\(653\) | − | 17.8196i | − | 0.697335i | −0.937247 | − | 0.348667i | \(-0.886634\pi\) | ||
0.937247 | − | 0.348667i | \(-0.113366\pi\) | |||||||
\(654\) | 13.2971 | − | 3.43756i | 0.519958 | − | 0.134419i | ||||
\(655\) | −11.1507 | −0.435694 | ||||||||
\(656\) | −2.17100 | − | 1.25343i | −0.0847633 | − | 0.0489381i | ||||
\(657\) | −27.0843 | − | 0.477730i | −1.05666 | − | 0.0186380i | ||||
\(658\) | 10.3401 | + | 17.9096i | 0.403100 | + | 0.698190i | ||||
\(659\) | − | 41.5819i | − | 1.61980i | −0.586567 | − | 0.809901i | \(-0.699521\pi\) | ||
0.586567 | − | 0.809901i | \(-0.300479\pi\) | |||||||
\(660\) | −5.54636 | − | 5.64505i | −0.215892 | − | 0.219733i | ||||
\(661\) | 19.3681 | − | 33.5466i | 0.753334 | − | 1.30481i | −0.192865 | − | 0.981225i | \(-0.561778\pi\) |
0.946199 | − | 0.323587i | \(-0.104889\pi\) | |||||||
\(662\) | 16.7142 | − | 28.9498i | 0.649614 | − | 1.12516i | ||||
\(663\) | −24.1171 | + | 6.23474i | −0.936630 | + | 0.242137i | ||||
\(664\) | 7.87412 | + | 4.54612i | 0.305575 | + | 0.176424i | ||||
\(665\) | 23.3894 | − | 13.5039i | 0.907002 | − | 0.523658i | ||||
\(666\) | 22.9034 | + | 13.7675i | 0.887490 | + | 0.533480i | ||||
\(667\) | 47.1260 | 1.82472 | ||||||||
\(668\) | −3.17082 | − | 5.49202i | −0.122683 | − | 0.212492i | ||||
\(669\) | 5.73742 | + | 5.83952i | 0.221822 | + | 0.225769i | ||||
\(670\) | 3.08925 | + | 5.35073i | 0.119348 | + | 0.206717i | ||||
\(671\) | −8.03970 | − | 4.64172i | −0.310369 | − | 0.179192i | ||||
\(672\) | −4.22995 | − | 4.30521i | −0.163174 | − | 0.166077i | ||||
\(673\) | −6.95179 | − | 4.01362i | −0.267972 | − | 0.154714i | 0.359994 | − | 0.932955i | \(-0.382779\pi\) |
−0.627966 | + | 0.778241i | \(0.716112\pi\) | |||||||
\(674\) | −20.3539 | −0.784004 | ||||||||
\(675\) | 1.47716 | − | 4.98177i | 0.0568558 | − | 0.191748i | ||||
\(676\) | −18.8263 | − | 32.6080i | −0.724087 | − | 1.25416i | ||||
\(677\) | −14.9097 | + | 25.8244i | −0.573028 | + | 0.992513i | 0.423225 | + | 0.906024i | \(0.360898\pi\) |
−0.996253 | + | 0.0864884i | \(0.972435\pi\) | |||||||
\(678\) | −12.6002 | − | 3.49559i | −0.483908 | − | 0.134247i | ||||
\(679\) | −8.99803 | − | 15.5850i | −0.345313 | − | 0.598099i | ||||
\(680\) | 2.02075 | 0.0774921 | ||||||||
\(681\) | −1.06308 | + | 3.83199i | −0.0407375 | + | 0.146842i | ||||
\(682\) | −7.25747 | + | 24.3822i | −0.277903 | + | 0.933643i | ||||
\(683\) | 30.4194i | 1.16397i | 0.813201 | + | 0.581983i | \(0.197723\pi\) | ||||
−0.813201 | + | 0.581983i | \(0.802277\pi\) | |||||||
\(684\) | 19.9285 | + | 11.9792i | 0.761985 | + | 0.458037i | ||||
\(685\) | −7.13410 | + | 4.11888i | −0.272580 | + | 0.157374i | ||||
\(686\) | 6.47286i | 0.247135i | ||||||||
\(687\) | 25.4381 | + | 25.8907i | 0.970523 | + | 0.987793i | ||||
\(688\) | −3.21363 | + | 1.85539i | −0.122518 | + | 0.0707361i | ||||
\(689\) | −62.8560 | + | 36.2899i | −2.39462 | + | 1.38254i | ||||
\(690\) | −12.3850 | − | 3.43589i | −0.471490 | − | 0.130802i | ||||
\(691\) | −14.7285 | + | 25.5106i | −0.560300 | + | 0.970467i | 0.437170 | + | 0.899379i | \(0.355981\pi\) |
−0.997470 | + | 0.0710887i | \(0.977353\pi\) | |||||||
\(692\) | −5.87328 | − | 3.39094i | −0.223269 | − | 0.128904i | ||||
\(693\) | 41.7795 | − | 23.1487i | 1.58707 | − | 0.879348i | ||||
\(694\) | −5.90895 | + | 3.41153i | −0.224301 | + | 0.129500i | ||||
\(695\) | −3.84772 | + | 6.66445i | −0.145952 | + | 0.252797i | ||||
\(696\) | 10.6497 | − | 2.75315i | 0.403674 | − | 0.104358i | ||||
\(697\) | 5.06572i | 0.191878i | ||||||||
\(698\) | 22.1151i | 0.837070i | ||||||||
\(699\) | 34.4445 | − | 8.90459i | 1.30281 | − | 0.336803i | ||||
\(700\) | −1.74230 | + | 3.01775i | −0.0658527 | + | 0.114060i | ||||
\(701\) | 10.4353 | − | 6.02480i | 0.394134 | − | 0.227553i | −0.289816 | − | 0.957082i | \(-0.593594\pi\) |
0.683950 | + | 0.729529i | \(0.260261\pi\) | |||||||
\(702\) | 35.9619 | − | 8.62322i | 1.35729 | − | 0.325462i | ||||
\(703\) | 59.7899 | + | 34.5197i | 2.25502 | + | 1.30194i | ||||
\(704\) | −2.28452 | + | 3.95691i | −0.0861013 | + | 0.149132i | ||||
\(705\) | 9.90520 | + | 2.74793i | 0.373051 | + | 0.103493i | ||||
\(706\) | 13.4130 | − | 7.74400i | 0.504805 | − | 0.291449i | ||||
\(707\) | 40.3086 | − | 23.2722i | 1.51596 | − | 0.875241i | ||||
\(708\) | −10.1061 | − | 10.2859i | −0.379809 | − | 0.386568i | ||||
\(709\) | 13.5805i | 0.510025i | 0.966938 | + | 0.255012i | \(0.0820795\pi\) | ||||
−0.966938 | + | 0.255012i | \(0.917920\pi\) | |||||||
\(710\) | −2.26644 | + | 1.30853i | −0.0850581 | + | 0.0491083i | ||||
\(711\) | 13.0948 | − | 21.7844i | 0.491093 | − | 0.816977i | ||||
\(712\) | − | 3.74116i | − | 0.140206i | ||||||
\(713\) | 9.59181 | + | 40.1871i | 0.359216 | + | 1.50502i | ||||
\(714\) | −3.26038 | + | 11.7524i | −0.122017 | + | 0.439821i | ||||
\(715\) | −32.5182 | −1.21611 | ||||||||
\(716\) | 9.95391 | + | 17.2407i | 0.371995 | + | 0.644314i | ||||
\(717\) | −12.3970 | − | 3.43921i | −0.462974 | − | 0.128440i | ||||
\(718\) | 3.50525 | − | 6.07127i | 0.130815 | − | 0.226578i | ||||
\(719\) | −14.0046 | − | 24.2566i | −0.522282 | − | 0.904619i | −0.999664 | − | 0.0259233i | \(-0.991747\pi\) |
0.477382 | − | 0.878696i | \(-0.341586\pi\) | |||||||
\(720\) | −2.99953 | − | 0.0529076i | −0.111786 | − | 0.00197175i | ||||
\(721\) | 37.6381 | 1.40172 | ||||||||
\(722\) | 35.5692 | + | 20.5359i | 1.32375 | + | 0.764267i | ||||
\(723\) | 26.9627 | + | 27.4425i | 1.00275 | + | 1.02060i | ||||
\(724\) | −0.510977 | − | 0.295013i | −0.0189903 | − | 0.0109641i | ||||
\(725\) | −3.17536 | − | 5.49989i | −0.117930 | − | 0.204261i | ||||
\(726\) | −11.9887 | − | 12.2020i | −0.444943 | − | 0.452860i | ||||
\(727\) | 5.94479 | + | 10.2967i | 0.220480 | + | 0.381883i | 0.954954 | − | 0.296754i | \(-0.0959042\pi\) |
−0.734474 | + | 0.678637i | \(0.762571\pi\) | |||||||
\(728\) | −24.8001 | −0.919153 | ||||||||
\(729\) | −1.42791 | + | 26.9622i | −0.0528856 | + | 0.998601i | ||||
\(730\) | 7.81979 | − | 4.51476i | 0.289423 | − | 0.167099i | ||||
\(731\) | 6.49393 | + | 3.74927i | 0.240187 | + | 0.138672i | ||||
\(732\) | −3.40719 | + | 0.880825i | −0.125933 | + | 0.0325562i | ||||
\(733\) | −14.6598 | + | 25.3916i | −0.541474 | + | 0.937860i | 0.457346 | + | 0.889289i | \(0.348800\pi\) |
−0.998820 | + | 0.0485712i | \(0.984533\pi\) | |||||||
\(734\) | −0.529587 | + | 0.917271i | −0.0195474 | + | 0.0338571i | ||||
\(735\) | −6.24239 | − | 6.35347i | −0.230254 | − | 0.234351i | ||||
\(736\) | 7.42056i | 0.273526i | ||||||||
\(737\) | 14.1149 | + | 24.4478i | 0.519930 | + | 0.900545i | ||||
\(738\) | 0.132632 | − | 7.51939i | 0.00488224 | − | 0.276793i | ||||
\(739\) | 17.4177 | + | 10.0561i | 0.640719 | + | 0.369919i | 0.784892 | − | 0.619633i | \(-0.212719\pi\) |
−0.144172 | + | 0.989553i | \(0.546052\pi\) | |||||||
\(740\) | −8.90762 | −0.327451 | ||||||||
\(741\) | 92.5014 | − | 23.9134i | 3.39812 | − | 0.878482i | ||||
\(742\) | 35.5360i | 1.30457i | ||||||||
\(743\) | 37.1326 | 1.36226 | 0.681131 | − | 0.732162i | \(-0.261489\pi\) | ||||
0.681131 | + | 0.732162i | \(0.261489\pi\) | |||||||
\(744\) | 4.51536 | + | 8.52124i | 0.165541 | + | 0.312404i | ||||
\(745\) | 11.5855 | 0.424460 | ||||||||
\(746\) | 9.78720i | 0.358335i | ||||||||
\(747\) | −0.481049 | + | 27.2725i | −0.0176007 | + | 0.997849i | ||||
\(748\) | 9.23289 | 0.337588 | ||||||||
\(749\) | −14.2206 | − | 8.21028i | −0.519610 | − | 0.299997i | ||||
\(750\) | 0.433517 | + | 1.67692i | 0.0158298 | + | 0.0612325i | ||||
\(751\) | 17.9527 | + | 31.0951i | 0.655105 | + | 1.13467i | 0.981868 | + | 0.189568i | \(0.0607089\pi\) |
−0.326763 | + | 0.945106i | \(0.605958\pi\) | |||||||
\(752\) | − | 5.93476i | − | 0.216418i | ||||||
\(753\) | 32.3738 | − | 31.8078i | 1.17977 | − | 1.15914i | ||||
\(754\) | 22.5992 | − | 39.1430i | 0.823016 | − | 1.42551i | ||||
\(755\) | −1.62805 | + | 2.81986i | −0.0592507 | + | 0.102625i | ||||
\(756\) | 5.14731 | − | 17.3595i | 0.187206 | − | 0.631358i | ||||
\(757\) | 45.7000 | + | 26.3849i | 1.66099 | + | 0.958975i | 0.972242 | + | 0.233977i | \(0.0751741\pi\) |
0.688751 | + | 0.724998i | \(0.258159\pi\) | |||||||
\(758\) | 5.59198 | − | 3.22853i | 0.203110 | − | 0.117265i | ||||
\(759\) | −56.5878 | − | 15.6988i | −2.05401 | − | 0.569829i | ||||
\(760\) | −7.75060 | −0.281144 | ||||||||
\(761\) | 2.24987 | + | 3.89689i | 0.0815578 | + | 0.141262i | 0.903919 | − | 0.427703i | \(-0.140677\pi\) |
−0.822361 | + | 0.568965i | \(0.807344\pi\) | |||||||
\(762\) | −2.89344 | + | 2.84285i | −0.104818 | + | 0.102986i | ||||
\(763\) | −13.8155 | − | 23.9292i | −0.500155 | − | 0.866295i | ||||
\(764\) | 0.0332892 | + | 0.0192195i | 0.00120436 | + | 0.000695339i | ||||
\(765\) | 2.93806 | + | 5.30270i | 0.106226 | + | 0.191719i | ||||
\(766\) | 11.7515 | + | 6.78475i | 0.424600 | + | 0.245143i | ||||
\(767\) | −59.2517 | −2.13945 | ||||||||
\(768\) | 0.433517 | + | 1.67692i | 0.0156432 | + | 0.0605107i | ||||
\(769\) | −23.4372 | − | 40.5944i | −0.845166 | − | 1.46387i | −0.885477 | − | 0.464684i | \(-0.846168\pi\) |
0.0403101 | − | 0.999187i | \(-0.487165\pi\) | |||||||
\(770\) | −7.96066 | + | 13.7883i | −0.286882 | + | 0.496894i | ||||
\(771\) | −1.02024 | + | 3.67754i | −0.0367429 | + | 0.132444i | ||||
\(772\) | −0.826680 | − | 1.43185i | −0.0297529 | − | 0.0515335i | ||||
\(773\) | −23.1884 | −0.834030 | −0.417015 | − | 0.908900i | \(-0.636924\pi\) | ||||
−0.417015 | + | 0.908900i | \(0.636924\pi\) | |||||||
\(774\) | −9.54122 | − | 5.73533i | −0.342952 | − | 0.206152i | ||||
\(775\) | 4.04379 | − | 3.82724i | 0.145257 | − | 0.137479i | ||||
\(776\) | 5.16445i | 0.185393i | ||||||||
\(777\) | 14.3720 | − | 51.8054i | 0.515593 | − | 1.85851i | ||||
\(778\) | −14.7340 | + | 8.50667i | −0.528239 | + | 0.304979i | ||||
\(779\) | − | 19.4296i | − | 0.696139i | ||||||
\(780\) | −8.79311 | + | 8.63938i | −0.314844 | + | 0.309339i | ||||
\(781\) | −10.3555 | + | 5.97875i | −0.370549 | + | 0.213936i | ||||
\(782\) | 12.9861 | − | 7.49754i | 0.464383 | − | 0.268111i | ||||
\(783\) | 22.7087 | + | 23.9431i | 0.811541 | + | 0.855658i | ||||
\(784\) | −2.57122 | + | 4.45348i | −0.0918292 | + | 0.159053i | ||||
\(785\) | −7.49444 | − | 4.32692i | −0.267488 | − | 0.154434i | ||||
\(786\) | −13.7767 | + | 13.5358i | −0.491398 | + | 0.482806i | ||||
\(787\) | 13.6572 | − | 7.88500i | 0.486828 | − | 0.281070i | −0.236430 | − | 0.971649i | \(-0.575977\pi\) |
0.723257 | + | 0.690579i | \(0.242644\pi\) | |||||||
\(788\) | −5.61969 | + | 9.73359i | −0.200193 | + | 0.346745i | ||||
\(789\) | −11.6238 | − | 44.9628i | −0.413817 | − | 1.60072i | ||||
\(790\) | 8.47239i | 0.301434i | ||||||||
\(791\) | 26.3070i | 0.935368i | ||||||||
\(792\) | −13.7050 | − | 0.241737i | −0.486987 | − | 0.00858976i | ||||
\(793\) | −7.23026 | + | 12.5232i | −0.256754 | + | 0.444711i | ||||
\(794\) | 3.27696 | − | 1.89196i | 0.116295 | − | 0.0671430i | ||||
\(795\) | 12.3793 | + | 12.5996i | 0.439050 | + | 0.446862i | ||||
\(796\) | 11.3096 | + | 6.52959i | 0.400857 | + | 0.231435i | ||||
\(797\) | −18.5401 | + | 32.1125i | −0.656726 | + | 1.13748i | 0.324732 | + | 0.945806i | \(0.394726\pi\) |
−0.981458 | + | 0.191676i | \(0.938608\pi\) | |||||||
\(798\) | 12.5052 | − | 45.0763i | 0.442680 | − | 1.59568i | ||||
\(799\) | −10.3859 | + | 5.99632i | −0.367428 | + | 0.212135i | ||||
\(800\) | 0.866025 | − | 0.500000i | 0.0306186 | − | 0.0176777i | ||||
\(801\) | 9.81727 | − | 5.43945i | 0.346876 | − | 0.192193i | ||||
\(802\) | − | 6.86891i | − | 0.242550i | ||||||
\(803\) | 35.7290 | − | 20.6282i | 1.26085 | − | 0.727952i | ||||
\(804\) | 10.3120 | + | 2.86079i | 0.363676 | + | 0.100892i | ||||
\(805\) | 25.8577i | 0.911364i | ||||||||
\(806\) | 37.9794 | + | 11.3047i | 1.33777 | + | 0.398192i | ||||
\(807\) | 28.1814 | + | 7.81818i | 0.992033 | + | 0.275213i | ||||
\(808\) | −13.3572 | −0.469904 | ||||||||
\(809\) | −1.42684 | − | 2.47135i | −0.0501649 | − | 0.0868881i | 0.839853 | − | 0.542815i | \(-0.182641\pi\) |
−0.890017 | + | 0.455926i | \(0.849308\pi\) | |||||||
\(810\) | −4.22233 | − | 7.94808i | −0.148357 | − | 0.279267i | ||||
\(811\) | 21.0007 | − | 36.3744i | 0.737436 | − | 1.27728i | −0.216211 | − | 0.976347i | \(-0.569370\pi\) |
0.953646 | − | 0.300930i | \(-0.0972969\pi\) | |||||||
\(812\) | −11.0649 | − | 19.1649i | −0.388301 | − | 0.672557i | ||||
\(813\) | −2.86520 | + | 0.740711i | −0.100487 | + | 0.0259779i | ||||
\(814\) | −40.6994 | −1.42651 | ||||||||
\(815\) | −9.10582 | − | 5.25725i | −0.318963 | − | 0.184153i | ||||
\(816\) | 2.49663 | − | 2.45298i | 0.0873995 | − | 0.0858715i | ||||
\(817\) | −24.9076 | − | 14.3804i | −0.871405 | − | 0.503106i | ||||
\(818\) | −2.98167 | − | 5.16441i | −0.104252 | − | 0.180569i | ||||
\(819\) | −36.0580 | − | 65.0786i | −1.25997 | − | 2.27403i | ||||
\(820\) | 1.25343 | + | 2.17100i | 0.0437716 | + | 0.0758146i | ||||
\(821\) | 0.760718 | 0.0265492 | 0.0132746 | − | 0.999912i | \(-0.495774\pi\) | ||||
0.0132746 | + | 0.999912i | \(0.495774\pi\) | |||||||
\(822\) | −3.81427 | + | 13.7489i | −0.133038 | + | 0.479549i | ||||
\(823\) | 42.5908 | − | 24.5898i | 1.48462 | − | 0.857147i | 0.484775 | − | 0.874639i | \(-0.338901\pi\) |
0.999847 | + | 0.0174918i | \(0.00556811\pi\) | |||||||
\(824\) | −9.35418 | − | 5.40064i | −0.325868 | − | 0.188140i | ||||
\(825\) | 1.98076 | + | 7.66193i | 0.0689612 | + | 0.266754i | ||||
\(826\) | −14.5052 | + | 25.1237i | −0.504700 | + | 0.874166i | ||||
\(827\) | −19.0147 | + | 32.9345i | −0.661207 | + | 1.14524i | 0.319092 | + | 0.947724i | \(0.396622\pi\) |
−0.980299 | + | 0.197521i | \(0.936711\pi\) | |||||||
\(828\) | −19.4725 | + | 10.7891i | −0.676716 | + | 0.374947i | ||||
\(829\) | 34.4080i | 1.19504i | 0.801854 | + | 0.597520i | \(0.203847\pi\) | ||||
−0.801854 | + | 0.597520i | \(0.796153\pi\) | |||||||
\(830\) | −4.54612 | − | 7.87412i | −0.157798 | − | 0.273315i | ||||
\(831\) | −17.9814 | + | 4.64855i | −0.623769 | + | 0.161256i | ||||
\(832\) | 6.16355 | + | 3.55853i | 0.213683 | + | 0.123370i | ||||
\(833\) | 10.3916 | 0.360046 | ||||||||
\(834\) | 3.33611 | + | 12.9046i | 0.115520 | + | 0.446851i | ||||
\(835\) | 6.34163i | 0.219461i | ||||||||
\(836\) | −35.4129 | −1.22478 | ||||||||
\(837\) | −15.7957 | + | 24.2383i | −0.545980 | + | 0.837798i | ||||
\(838\) | 1.08088 | 0.0373385 | ||||||||
\(839\) | − | 55.2028i | − | 1.90581i | −0.303267 | − | 0.952906i | \(-0.598077\pi\) | ||
0.303267 | − | 0.952906i | \(-0.401923\pi\) | |||||||
\(840\) | 1.51063 | + | 5.84340i | 0.0521218 | + | 0.201616i | ||||
\(841\) | 11.3317 | 0.390749 | ||||||||
\(842\) | −11.3137 | − | 6.53199i | −0.389897 | − | 0.225107i | ||||
\(843\) | 9.05044 | − | 2.33972i | 0.311714 | − | 0.0805841i | ||||
\(844\) | −10.2150 | − | 17.6930i | −0.351616 | − | 0.609017i | ||||
\(845\) | 37.6525i | 1.29529i | ||||||||
\(846\) | 15.5736 | − | 8.62883i | 0.535430 | − | 0.296665i | ||||
\(847\) | −17.2073 | + | 29.8040i | −0.591251 | + | 1.02408i | ||||
\(848\) | 5.09901 | − | 8.83174i | 0.175101 | − | 0.303283i | ||||
\(849\) | 0.684841 | + | 2.64908i | 0.0235037 | + | 0.0909164i | ||||
\(850\) | −1.75002 | − | 1.01037i | −0.0600251 | − | 0.0346555i | ||||
\(851\) | −57.2439 | + | 33.0498i | −1.96230 | + | 1.13293i | ||||
\(852\) | −1.21176 | + | 4.36792i | −0.0415143 | + | 0.149642i | ||||
\(853\) | −3.59004 | −0.122920 | −0.0614602 | − | 0.998110i | \(-0.519576\pi\) | ||||
−0.0614602 | + | 0.998110i | \(0.519576\pi\) | |||||||
\(854\) | 3.54002 | + | 6.13150i | 0.121137 | + | 0.209816i | ||||
\(855\) | −11.2690 | − | 20.3386i | −0.385391 | − | 0.695564i | ||||
\(856\) | 2.35616 | + | 4.08099i | 0.0805319 | + | 0.139485i | ||||
\(857\) | −17.3013 | − | 9.98890i | −0.591000 | − | 0.341214i | 0.174493 | − | 0.984658i | \(-0.444172\pi\) |
−0.765493 | + | 0.643444i | \(0.777505\pi\) | |||||||
\(858\) | −40.1761 | + | 39.4737i | −1.37159 | + | 1.34761i | ||||
\(859\) | 2.15684 | + | 1.24525i | 0.0735903 | + | 0.0424874i | 0.536344 | − | 0.844000i | \(-0.319805\pi\) |
−0.462753 | + | 0.886487i | \(0.653138\pi\) | |||||||
\(860\) | 3.71078 | 0.126536 | ||||||||
\(861\) | −14.6485 | + | 3.78694i | −0.499221 | + | 0.129059i | ||||
\(862\) | 3.62647 | + | 6.28123i | 0.123518 | + | 0.213939i | ||||
\(863\) | 2.86348 | − | 4.95970i | 0.0974741 | − | 0.168830i | −0.813164 | − | 0.582034i | \(-0.802257\pi\) |
0.910639 | + | 0.413204i | \(0.135590\pi\) | |||||||
\(864\) | −3.77014 | + | 3.57576i | −0.128263 | + | 0.121650i | ||||
\(865\) | 3.39094 | + | 5.87328i | 0.115295 | + | 0.199698i | ||||
\(866\) | −19.0811 | −0.648401 | ||||||||
\(867\) | 21.5580 | + | 5.98068i | 0.732147 | + | 0.203115i | ||||
\(868\) | 14.0910 | − | 13.3364i | 0.478279 | − | 0.452667i | ||||
\(869\) | 38.7108i | 1.31317i | ||||||||
\(870\) | −10.5995 | − | 2.94054i | −0.359355 | − | 0.0996935i | ||||
\(871\) | 38.0815 | − | 21.9864i | 1.29034 | − | 0.744979i | ||||
\(872\) | 7.92947i | 0.268526i | ||||||||
\(873\) | −13.5522 | + | 7.50884i | −0.458672 | + | 0.254136i | ||||
\(874\) | −49.8084 | + | 28.7569i | −1.68480 | + | 0.972717i | ||||
\(875\) | 3.01775 | − | 1.74230i | 0.102019 | − | 0.0589005i | ||||
\(876\) | 4.18088 | − | 15.0704i | 0.141259 | − | 0.509181i | ||||
\(877\) | −16.6119 | + | 28.7726i | −0.560943 | + | 0.971582i | 0.436471 | + | 0.899718i | \(0.356228\pi\) |
−0.997414 | + | 0.0718639i | \(0.977105\pi\) | |||||||
\(878\) | 29.1048 | + | 16.8037i | 0.982240 | + | 0.567096i | ||||
\(879\) | 2.20326 | + | 2.24246i | 0.0743141 | + | 0.0756365i | ||||
\(880\) | 3.95691 | − | 2.28452i | 0.133388 | − | 0.0770113i | ||||
\(881\) | −0.720751 | + | 1.24838i | −0.0242827 | + | 0.0420589i | −0.877911 | − | 0.478823i | \(-0.841064\pi\) |
0.853629 | + | 0.520882i | \(0.174397\pi\) | |||||||
\(882\) | −15.4249 | − | 0.272074i | −0.519384 | − | 0.00916120i | ||||
\(883\) | 17.4463i | 0.587116i | 0.955941 | + | 0.293558i | \(0.0948393\pi\) | ||||
−0.955941 | + | 0.293558i | \(0.905161\pi\) | |||||||
\(884\) | − | 14.3818i | − | 0.483711i | ||||||
\(885\) | 3.60916 | + | 13.9609i | 0.121321 | + | 0.469290i | ||||
\(886\) | −4.00128 | + | 6.93043i | −0.134426 | + | 0.232832i | ||||
\(887\) | −33.7458 | + | 19.4831i | −1.13307 | + | 0.654180i | −0.944706 | − | 0.327919i | \(-0.893653\pi\) |
−0.188367 | + | 0.982099i | \(0.560319\pi\) | |||||||
\(888\) | −11.0053 | + | 10.8129i | −0.369315 | + | 0.362858i | ||||
\(889\) | 7.06733 | + | 4.08033i | 0.237031 | + | 0.136850i | ||||
\(890\) | −1.87058 | + | 3.23994i | −0.0627020 | + | 0.108603i | ||||
\(891\) | −19.2920 | − | 36.3152i | −0.646307 | − | 1.21660i | ||||
\(892\) | −4.09323 | + | 2.36323i | −0.137051 | + | 0.0791266i | ||||
\(893\) | 39.8354 | − | 22.9990i | 1.33304 | − | 0.769631i | ||||
\(894\) | 14.3139 | − | 14.0636i | 0.478727 | − | 0.470357i | ||||
\(895\) | − | 19.9078i | − | 0.665445i | ||||||
\(896\) | 3.01775 | − | 1.74230i | 0.100816 | − | 0.0582062i | ||||
\(897\) | −24.4535 | + | 88.1449i | −0.816477 | + | 2.94307i | ||||
\(898\) | − | 20.3595i | − | 0.679405i | ||||||
\(899\) | 8.20894 | + | 34.3933i | 0.273783 | + | 1.14708i | ||||
\(900\) | 2.57122 | + | 1.54559i | 0.0857073 | + | 0.0515195i | ||||
\(901\) | −20.6076 | −0.686539 | ||||||||
\(902\) | 5.72697 | + | 9.91941i | 0.190687 | + | 0.330280i | ||||
\(903\) | −5.98716 | + | 21.5813i | −0.199240 | + | 0.718181i | ||||
\(904\) | 3.77475 | − | 6.53805i | 0.125546 | − | 0.217452i | ||||
\(905\) | 0.295013 | + | 0.510977i | 0.00980655 | + | 0.0169854i | ||||
\(906\) | 1.41157 | + | 5.46021i | 0.0468963 | + | 0.181403i | ||||
\(907\) | −16.4320 | −0.545616 | −0.272808 | − | 0.962068i | \(-0.587952\pi\) | ||||
−0.272808 | + | 0.962068i | \(0.587952\pi\) | |||||||
\(908\) | −1.98836 | − | 1.14798i | −0.0659861 | − | 0.0380971i | ||||
\(909\) | −19.4206 | − | 35.0509i | −0.644142 | − | 1.16257i | ||||
\(910\) | 21.4775 | + | 12.4000i | 0.711973 | + | 0.411058i | ||||
\(911\) | 9.31914 | + | 16.1412i | 0.308757 | + | 0.534783i | 0.978091 | − | 0.208179i | \(-0.0667537\pi\) |
−0.669334 | + | 0.742962i | \(0.733420\pi\) | |||||||
\(912\) | −9.57585 | + | 9.40843i | −0.317088 | + | 0.311544i | ||||
\(913\) | −20.7715 | − | 35.9772i | −0.687435 | − | 1.19067i | ||||
\(914\) | 11.2885 | 0.373389 | ||||||||
\(915\) | 3.39112 | + | 0.940776i | 0.112107 | + | 0.0311011i | ||||
\(916\) | −18.1482 | + | 10.4779i | −0.599633 | + | 0.346198i | ||||
\(917\) | 33.6501 | + | 19.4279i | 1.11122 | + | 0.641565i | ||||
\(918\) | 10.0669 | + | 2.98496i | 0.332257 | + | 0.0985185i | ||||
\(919\) | 25.9040 | − | 44.8671i | 0.854495 | − | 1.48003i | −0.0226174 | − | 0.999744i | \(-0.507200\pi\) |
0.877113 | − | 0.480285i | \(-0.159467\pi\) | |||||||
\(920\) | 3.71028 | − | 6.42639i | 0.122324 | − | 0.211872i | ||||
\(921\) | 27.4823 | − | 27.0018i | 0.905572 | − | 0.889740i | ||||
\(922\) | 16.9753i | 0.559050i | ||||||||
\(923\) | 9.31290 | + | 16.1304i | 0.306538 | + | 0.530939i | ||||
\(924\) | 6.90216 | + | 26.6988i | 0.227064 | + | 0.878325i | ||||
\(925\) | 7.71423 | + | 4.45381i | 0.253642 | + | 0.146440i | ||||
\(926\) | 7.96544 | 0.261761 | ||||||||
\(927\) | 0.571469 | − | 32.3988i | 0.0187695 | − | 1.06412i | ||||
\(928\) | 6.35073i | 0.208473i | ||||||||
\(929\) | 25.7853 | 0.845990 | 0.422995 | − | 0.906132i | \(-0.360979\pi\) | ||||
0.422995 | + | 0.906132i | \(0.360979\pi\) | |||||||
\(930\) | 0.350205 | − | 9.63729i | 0.0114837 | − | 0.316019i | ||||
\(931\) | −39.8570 | −1.30626 | ||||||||
\(932\) | 20.5404i | 0.672822i | ||||||||
\(933\) | 13.2498 | − | 3.42534i | 0.433780 | − | 0.112141i | ||||
\(934\) | −17.5704 | −0.574923 | ||||||||
\(935\) | −7.99592 | − | 4.61645i | −0.261495 | − | 0.150974i | ||||
\(936\) | −0.376546 | + | 21.3479i | −0.0123078 | + | 0.697776i | ||||
\(937\) | −20.7134 | − | 35.8767i | −0.676679 | − | 1.17204i | −0.975975 | − | 0.217882i | \(-0.930085\pi\) |
0.299296 | − | 0.954160i | \(-0.403248\pi\) | |||||||
\(938\) | − | 21.5296i | − | 0.702966i | ||||||
\(939\) | 36.8397 | + | 37.4953i | 1.20222 | + | 1.22361i | ||||
\(940\) | −2.96738 | + | 5.13965i | −0.0967852 | + | 0.167637i | ||||
\(941\) | 29.2558 | − | 50.6725i | 0.953711 | − | 1.65188i | 0.216421 | − | 0.976300i | \(-0.430562\pi\) |
0.737290 | − | 0.675576i | \(-0.236105\pi\) | |||||||
\(942\) | −14.5118 | + | 3.75158i | −0.472820 | + | 0.122233i | ||||
\(943\) | 16.1100 | + | 9.30113i | 0.524615 | + | 0.302887i | ||||
\(944\) | 7.20993 | − | 4.16265i | 0.234663 | − | 0.135483i | ||||
\(945\) | −13.1374 | + | 12.4601i | −0.427361 | + | 0.405327i | ||||
\(946\) | 16.9547 | 0.551246 | ||||||||
\(947\) | 3.87757 | + | 6.71615i | 0.126004 | + | 0.218246i | 0.922125 | − | 0.386892i | \(-0.126451\pi\) |
−0.796121 | + | 0.605138i | \(0.793118\pi\) | |||||||
\(948\) | 10.2846 | + | 10.4676i | 0.334028 | + | 0.339972i | ||||
\(949\) | −32.1318 | − | 55.6539i | −1.04304 | − | 1.80660i | ||||
\(950\) | 6.71222 | + | 3.87530i | 0.217773 | + | 0.125731i | ||||
\(951\) | −2.85571 | − | 2.90652i | −0.0926027 | − | 0.0942504i | ||||
\(952\) | −6.09811 | − | 3.52075i | −0.197641 | − | 0.114108i | ||||
\(953\) | −27.8491 | −0.902120 | −0.451060 | − | 0.892494i | \(-0.648954\pi\) | ||||
−0.451060 | + | 0.892494i | \(0.648954\pi\) | |||||||
\(954\) | 30.5893 | + | 0.539552i | 0.990364 | + | 0.0174686i | ||||
\(955\) | −0.0192195 | − | 0.0332892i | −0.000621930 | − | 0.00107721i | ||||
\(956\) | 3.71386 | − | 6.43260i | 0.120115 | − | 0.208045i | ||||
\(957\) | −48.4294 | − | 13.4355i | −1.56550 | − | 0.434307i | ||||
\(958\) | −20.0582 | − | 34.7418i | −0.648050 | − | 1.12246i | ||||
\(959\) | 28.7053 | 0.926942 | ||||||||
\(960\) | 0.463024 | − | 1.66901i | 0.0149440 | − | 0.0538672i | ||||
\(961\) | −27.6584 | + | 14.0005i | −0.892206 | + | 0.451629i | ||||
\(962\) | 63.3961i | 2.04397i | ||||||||
\(963\) | −7.28330 | + | 12.1164i | −0.234701 | + | 0.390446i | ||||
\(964\) | −19.2359 | + | 11.1059i | −0.619547 | + | 0.357696i | ||||
\(965\) | 1.65336i | 0.0532235i | ||||||||
\(966\) | 31.3886 | + | 31.9471i | 1.00991 | + | 1.02788i | ||||
\(967\) | −13.1444 | + | 7.58893i | −0.422696 | + | 0.244043i | −0.696230 | − | 0.717819i | \(-0.745141\pi\) |
0.273534 | + | 0.961862i | \(0.411807\pi\) | |||||||
\(968\) | 8.55305 | − | 4.93811i | 0.274906 | − | 0.158717i | ||||
\(969\) | 26.1401 | + | 7.25188i | 0.839741 | + | 0.232964i | ||||
\(970\) | 2.58223 | − | 4.47255i | 0.0829103 | − | 0.143605i | ||||
\(971\) | 25.4154 | + | 14.6736i | 0.815619 | + | 0.470898i | 0.848903 | − | 0.528548i | \(-0.177263\pi\) |
−0.0332846 | + | 0.999446i | \(0.510597\pi\) | |||||||
\(972\) | −14.8648 | − | 4.69436i | −0.476789 | − | 0.150572i | ||||
\(973\) | 23.2229 | − | 13.4078i | 0.744493 | − | 0.429833i | ||||
\(974\) | 6.48275 | − | 11.2285i | 0.207721 | − | 0.359783i | ||||
\(975\) | 11.9347 | − | 3.08537i | 0.382218 | − | 0.0988108i | ||||
\(976\) | − | 2.03181i | − | 0.0650367i | ||||||
\(977\) | − | 12.5882i | − | 0.402731i | −0.979516 | − | 0.201366i | \(-0.935462\pi\) | ||
0.979516 | − | 0.201366i | \(-0.0645379\pi\) | |||||||
\(978\) | −17.6320 | + | 4.55821i | −0.563808 | + | 0.145756i | ||||
\(979\) | −8.54677 | + | 14.8034i | −0.273156 | + | 0.473120i | ||||
\(980\) | 4.45348 | − | 2.57122i | 0.142261 | − | 0.0821346i | ||||
\(981\) | −20.8079 | + | 11.5290i | −0.664346 | + | 0.368094i | ||||
\(982\) | 9.57967 | + | 5.53082i | 0.305700 | + | 0.176496i | ||||
\(983\) | 22.8887 | − | 39.6444i | 0.730036 | − | 1.26446i | −0.226832 | − | 0.973934i | \(-0.572837\pi\) |
0.956867 | − | 0.290525i | \(-0.0938300\pi\) | |||||||
\(984\) | 4.18398 | + | 1.16073i | 0.133380 | + | 0.0370028i | ||||
\(985\) | 9.73359 | − | 5.61969i | 0.310138 | − | 0.179058i | ||||
\(986\) | 11.1139 | − | 6.41661i | 0.353938 | − | 0.204346i | ||||
\(987\) | −25.1037 | − | 25.5504i | −0.799060 | − | 0.813278i | ||||
\(988\) | 55.1615i | 1.75492i | ||||||||
\(989\) | 23.8469 | − | 13.7680i | 0.758288 | − | 0.437798i | ||||
\(990\) | 11.7480 | + | 7.06186i | 0.373377 | + | 0.224441i | ||||
\(991\) | − | 53.5869i | − | 1.70224i | −0.524967 | − | 0.851122i | \(-0.675922\pi\) | ||
0.524967 | − | 0.851122i | \(-0.324078\pi\) | |||||||
\(992\) | −5.41564 | + | 1.29260i | −0.171947 | + | 0.0410400i | ||||
\(993\) | −15.4781 | + | 55.7923i | −0.491182 | + | 1.77052i | ||||
\(994\) | 9.11942 | 0.289251 | ||||||||
\(995\) | −6.52959 | − | 11.3096i | −0.207002 | − | 0.358538i | ||||
\(996\) | −15.1751 | − | 4.20993i | −0.480841 | − | 0.133397i | ||||
\(997\) | −25.7953 | + | 44.6787i | −0.816945 | + | 1.41499i | 0.0909780 | + | 0.995853i | \(0.471001\pi\) |
−0.907923 | + | 0.419137i | \(0.862333\pi\) | |||||||
\(998\) | 12.0750 | + | 20.9146i | 0.382228 | + | 0.662039i | ||||
\(999\) | −44.3757 | − | 13.1580i | −1.40398 | − | 0.416300i |
(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 | 930.2.o.e.161.6 | ✓ | 40 | |
3.2 | odd | 2 | inner | 930.2.o.e.161.13 | yes | 40 | |
31.26 | odd | 6 | inner | 930.2.o.e.491.3 | yes | 40 | |
93.26 | even | 6 | inner | 930.2.o.e.491.16 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.o.e.161.6 | ✓ | 40 | 1.1 | even | 1 | trivial | |
930.2.o.e.161.13 | yes | 40 | 3.2 | odd | 2 | inner | |
930.2.o.e.491.3 | yes | 40 | 31.26 | odd | 6 | inner | |
930.2.o.e.491.16 | yes | 40 | 93.26 | even | 6 | inner |