Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(83,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.83");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.k (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: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 83.1 | ||
Character | \(\chi\) | \(=\) | 210.83 |
Dual form | 210.3.k.a.167.1 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.00000i | −0.500000 | − | 0.500000i | ||||
\(3\) | −2.99336 | + | 0.199427i | −0.997788 | + | 0.0664755i | ||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | 4.37611 | + | 2.41861i | 0.875222 | + | 0.483722i | ||||
\(6\) | 3.19279 | + | 2.79394i | 0.532132 | + | 0.465656i | ||||
\(7\) | −5.12625 | − | 4.76671i | −0.732322 | − | 0.680959i | ||||
\(8\) | 2.00000 | − | 2.00000i | 0.250000 | − | 0.250000i | ||||
\(9\) | 8.92046 | − | 1.19391i | 0.991162 | − | 0.132657i | ||||
\(10\) | −1.95750 | − | 6.79472i | −0.195750 | − | 0.679472i | ||||
\(11\) | − | 6.70149i | − | 0.609226i | −0.952476 | − | 0.304613i | \(-0.901473\pi\) | ||
0.952476 | − | 0.304613i | \(-0.0985271\pi\) | |||||||
\(12\) | −0.398853 | − | 5.98673i | −0.0332378 | − | 0.498894i | ||||
\(13\) | −16.0066 | + | 16.0066i | −1.23128 | + | 1.23128i | −0.267802 | + | 0.963474i | \(0.586297\pi\) |
−0.963474 | + | 0.267802i | \(0.913703\pi\) | |||||||
\(14\) | 0.359544 | + | 9.89296i | 0.0256817 | + | 0.706640i | ||||
\(15\) | −13.5816 | − | 6.36707i | −0.905441 | − | 0.424472i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −7.21482 | + | 7.21482i | −0.424401 | + | 0.424401i | −0.886716 | − | 0.462315i | \(-0.847019\pi\) |
0.462315 | + | 0.886716i | \(0.347019\pi\) | |||||||
\(18\) | −10.1144 | − | 7.72655i | −0.561909 | − | 0.429253i | ||||
\(19\) | −8.06294 | −0.424365 | −0.212183 | − | 0.977230i | \(-0.568057\pi\) | ||||
−0.212183 | + | 0.977230i | \(0.568057\pi\) | |||||||
\(20\) | −4.83722 | + | 8.75222i | −0.241861 | + | 0.437611i | ||||
\(21\) | 16.2954 | + | 13.2462i | 0.775969 | + | 0.630771i | ||||
\(22\) | −6.70149 | + | 6.70149i | −0.304613 | + | 0.304613i | ||||
\(23\) | −11.7195 | + | 11.7195i | −0.509543 | + | 0.509543i | −0.914386 | − | 0.404843i | \(-0.867326\pi\) |
0.404843 | + | 0.914386i | \(0.367326\pi\) | |||||||
\(24\) | −5.58788 | + | 6.38558i | −0.232828 | + | 0.266066i | ||||
\(25\) | 13.3006 | + | 21.1682i | 0.532025 | + | 0.846728i | ||||
\(26\) | 32.0132 | 1.23128 | ||||||||
\(27\) | −26.4641 | + | 5.35279i | −0.980151 | + | 0.198252i | ||||
\(28\) | 9.53342 | − | 10.2525i | 0.340479 | − | 0.366161i | ||||
\(29\) | −6.17789 | −0.213031 | −0.106515 | − | 0.994311i | \(-0.533969\pi\) | ||||
−0.106515 | + | 0.994311i | \(0.533969\pi\) | |||||||
\(30\) | 7.21455 | + | 19.9487i | 0.240485 | + | 0.664956i | ||||
\(31\) | 41.4735i | 1.33785i | 0.743328 | + | 0.668927i | \(0.233246\pi\) | ||||
−0.743328 | + | 0.668927i | \(0.766754\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.125000 | + | 0.125000i | ||||
\(33\) | 1.33645 | + | 20.0600i | 0.0404986 | + | 0.607879i | ||||
\(34\) | 14.4296 | 0.424401 | ||||||||
\(35\) | −10.9042 | − | 33.2581i | −0.311549 | − | 0.950230i | ||||
\(36\) | 2.38782 | + | 17.8409i | 0.0663285 | + | 0.495581i | ||||
\(37\) | −37.8620 | + | 37.8620i | −1.02330 | + | 1.02330i | −0.0235744 | + | 0.999722i | \(0.507505\pi\) |
−0.999722 | + | 0.0235744i | \(0.992495\pi\) | |||||||
\(38\) | 8.06294 | + | 8.06294i | 0.212183 | + | 0.212183i | ||||
\(39\) | 44.7214 | − | 51.1057i | 1.14670 | − | 1.31040i | ||||
\(40\) | 13.5894 | − | 3.91499i | 0.339736 | − | 0.0978748i | ||||
\(41\) | −74.2121 | −1.81005 | −0.905025 | − | 0.425358i | \(-0.860148\pi\) | ||||
−0.905025 | + | 0.425358i | \(0.860148\pi\) | |||||||
\(42\) | −3.04917 | − | 29.5415i | −0.0725992 | − | 0.703370i | ||||
\(43\) | −42.3069 | − | 42.3069i | −0.983882 | − | 0.983882i | 0.0159899 | − | 0.999872i | \(-0.494910\pi\) |
−0.999872 | + | 0.0159899i | \(0.994910\pi\) | |||||||
\(44\) | 13.4030 | 0.304613 | ||||||||
\(45\) | 41.9245 | + | 16.3504i | 0.931655 | + | 0.363343i | ||||
\(46\) | 23.4390 | 0.509543 | ||||||||
\(47\) | 39.4156 | − | 39.4156i | 0.838630 | − | 0.838630i | −0.150049 | − | 0.988679i | \(-0.547943\pi\) |
0.988679 | + | 0.150049i | \(0.0479431\pi\) | |||||||
\(48\) | 11.9735 | − | 0.797706i | 0.249447 | − | 0.0166189i | ||||
\(49\) | 3.55696 | + | 48.8707i | 0.0725910 | + | 0.997362i | ||||
\(50\) | 7.86757 | − | 34.4688i | 0.157351 | − | 0.689377i | ||||
\(51\) | 20.1578 | − | 23.0354i | 0.395250 | − | 0.451675i | ||||
\(52\) | −32.0132 | − | 32.0132i | −0.615638 | − | 0.615638i | ||||
\(53\) | 44.4204 | − | 44.4204i | 0.838121 | − | 0.838121i | −0.150491 | − | 0.988611i | \(-0.548085\pi\) |
0.988611 | + | 0.150491i | \(0.0480854\pi\) | |||||||
\(54\) | 31.8169 | + | 21.1113i | 0.589201 | + | 0.390950i | ||||
\(55\) | 16.2083 | − | 29.3264i | 0.294696 | − | 0.533208i | ||||
\(56\) | −19.7859 | + | 0.719089i | −0.353320 | + | 0.0128409i | ||||
\(57\) | 24.1353 | − | 1.60796i | 0.423427 | − | 0.0282099i | ||||
\(58\) | 6.17789 | + | 6.17789i | 0.106515 | + | 0.106515i | ||||
\(59\) | − | 51.9749i | − | 0.880931i | −0.897769 | − | 0.440466i | \(-0.854813\pi\) | ||
0.897769 | − | 0.440466i | \(-0.145187\pi\) | |||||||
\(60\) | 12.7341 | − | 27.1632i | 0.212236 | − | 0.452721i | ||||
\(61\) | − | 15.0083i | − | 0.246038i | −0.992404 | − | 0.123019i | \(-0.960742\pi\) | ||
0.992404 | − | 0.123019i | \(-0.0392576\pi\) | |||||||
\(62\) | 41.4735 | − | 41.4735i | 0.668927 | − | 0.668927i | ||||
\(63\) | −51.4196 | − | 36.4009i | −0.816184 | − | 0.577793i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | −108.760 | + | 31.3328i | −1.67323 | + | 0.482043i | ||||
\(66\) | 18.7235 | − | 21.3964i | 0.283690 | − | 0.324189i | ||||
\(67\) | −38.7098 | + | 38.7098i | −0.577758 | + | 0.577758i | −0.934285 | − | 0.356527i | \(-0.883961\pi\) |
0.356527 | + | 0.934285i | \(0.383961\pi\) | |||||||
\(68\) | −14.4296 | − | 14.4296i | −0.212201 | − | 0.212201i | ||||
\(69\) | 32.7435 | − | 37.4179i | 0.474544 | − | 0.542288i | ||||
\(70\) | −22.3538 | + | 44.1623i | −0.319340 | + | 0.630890i | ||||
\(71\) | 128.871i | 1.81508i | 0.419962 | + | 0.907542i | \(0.362043\pi\) | ||||
−0.419962 | + | 0.907542i | \(0.637957\pi\) | |||||||
\(72\) | 15.4531 | − | 20.2287i | 0.214626 | − | 0.280955i | ||||
\(73\) | 54.2081 | − | 54.2081i | 0.742576 | − | 0.742576i | −0.230497 | − | 0.973073i | \(-0.574035\pi\) |
0.973073 | + | 0.230497i | \(0.0740352\pi\) | |||||||
\(74\) | 75.7239 | 1.02330 | ||||||||
\(75\) | −44.0351 | − | 60.7117i | −0.587135 | − | 0.809489i | ||||
\(76\) | − | 16.1259i | − | 0.212183i | ||||||
\(77\) | −31.9440 | + | 34.3535i | −0.414858 | + | 0.446150i | ||||
\(78\) | −95.8271 | + | 6.38427i | −1.22855 | + | 0.0818497i | ||||
\(79\) | 25.7821i | 0.326355i | 0.986597 | + | 0.163178i | \(0.0521743\pi\) | ||||
−0.986597 | + | 0.163178i | \(0.947826\pi\) | |||||||
\(80\) | −17.5044 | − | 9.67445i | −0.218805 | − | 0.120931i | ||||
\(81\) | 78.1491 | − | 21.3005i | 0.964804 | − | 0.262969i | ||||
\(82\) | 74.2121 | + | 74.2121i | 0.905025 | + | 0.905025i | ||||
\(83\) | 27.7179 | + | 27.7179i | 0.333950 | + | 0.333950i | 0.854084 | − | 0.520134i | \(-0.174118\pi\) |
−0.520134 | + | 0.854084i | \(0.674118\pi\) | |||||||
\(84\) | −26.4924 | + | 32.5907i | −0.315385 | + | 0.387985i | ||||
\(85\) | −49.0227 | + | 14.1230i | −0.576737 | + | 0.166153i | ||||
\(86\) | 84.6139i | 0.983882i | ||||||||
\(87\) | 18.4927 | − | 1.23203i | 0.212559 | − | 0.0141613i | ||||
\(88\) | −13.4030 | − | 13.4030i | −0.152307 | − | 0.152307i | ||||
\(89\) | − | 32.5020i | − | 0.365191i | −0.983188 | − | 0.182595i | \(-0.941550\pi\) | ||
0.983188 | − | 0.182595i | \(-0.0584498\pi\) | |||||||
\(90\) | −25.5741 | − | 58.2749i | −0.284156 | − | 0.647499i | ||||
\(91\) | 158.353 | − | 5.75508i | 1.74014 | − | 0.0632426i | ||||
\(92\) | −23.4390 | − | 23.4390i | −0.254772 | − | 0.254772i | ||||
\(93\) | −8.27091 | − | 124.145i | −0.0889345 | − | 1.33489i | ||||
\(94\) | −78.8312 | −0.838630 | ||||||||
\(95\) | −35.2843 | − | 19.5011i | −0.371414 | − | 0.205275i | ||||
\(96\) | −12.7712 | − | 11.1758i | −0.133033 | − | 0.116414i | ||||
\(97\) | 56.7224 | + | 56.7224i | 0.584767 | + | 0.584767i | 0.936210 | − | 0.351442i | \(-0.114309\pi\) |
−0.351442 | + | 0.936210i | \(0.614309\pi\) | |||||||
\(98\) | 45.3138 | − | 52.4277i | 0.462385 | − | 0.534976i | ||||
\(99\) | −8.00099 | − | 59.7803i | −0.0808181 | − | 0.603842i | ||||
\(100\) | −42.3364 | + | 26.6013i | −0.423364 | + | 0.266013i | ||||
\(101\) | 63.3063 | 0.626795 | 0.313398 | − | 0.949622i | \(-0.398533\pi\) | ||||
0.313398 | + | 0.949622i | \(0.398533\pi\) | |||||||
\(102\) | −43.1932 | + | 2.87765i | −0.423463 | + | 0.0282123i | ||||
\(103\) | 41.4114 | − | 41.4114i | 0.402052 | − | 0.402052i | −0.476904 | − | 0.878956i | \(-0.658241\pi\) |
0.878956 | + | 0.476904i | \(0.158241\pi\) | |||||||
\(104\) | 64.0263i | 0.615638i | ||||||||
\(105\) | 39.2728 | + | 97.3789i | 0.374027 | + | 0.927418i | ||||
\(106\) | −88.8408 | −0.838121 | ||||||||
\(107\) | 3.96732 | + | 3.96732i | 0.0370777 | + | 0.0370777i | 0.725403 | − | 0.688325i | \(-0.241654\pi\) |
−0.688325 | + | 0.725403i | \(0.741654\pi\) | |||||||
\(108\) | −10.7056 | − | 52.9282i | −0.0991258 | − | 0.490076i | ||||
\(109\) | − | 108.319i | − | 0.993756i | −0.867820 | − | 0.496878i | \(-0.834480\pi\) | ||
0.867820 | − | 0.496878i | \(-0.165520\pi\) | |||||||
\(110\) | −45.5347 | + | 13.1181i | −0.413952 | + | 0.119256i | ||||
\(111\) | 105.784 | − | 120.885i | 0.953009 | − | 1.08906i | ||||
\(112\) | 20.5050 | + | 19.0668i | 0.183080 | + | 0.170240i | ||||
\(113\) | −17.5503 | + | 17.5503i | −0.155312 | + | 0.155312i | −0.780486 | − | 0.625174i | \(-0.785028\pi\) |
0.625174 | + | 0.780486i | \(0.285028\pi\) | |||||||
\(114\) | −25.7433 | − | 22.5274i | −0.225818 | − | 0.197608i | ||||
\(115\) | −79.6307 | + | 22.9409i | −0.692441 | + | 0.199486i | ||||
\(116\) | − | 12.3558i | − | 0.106515i | ||||||
\(117\) | −123.676 | + | 161.897i | −1.05706 | + | 1.38373i | ||||
\(118\) | −51.9749 | + | 51.9749i | −0.440466 | + | 0.440466i | ||||
\(119\) | 71.3760 | − | 2.59405i | 0.599798 | − | 0.0217987i | ||||
\(120\) | −39.8974 | + | 14.4291i | −0.332478 | + | 0.120242i | ||||
\(121\) | 76.0901 | 0.628844 | ||||||||
\(122\) | −15.0083 | + | 15.0083i | −0.123019 | + | 0.123019i | ||||
\(123\) | 222.144 | − | 14.7999i | 1.80605 | − | 0.120324i | ||||
\(124\) | −82.9469 | −0.668927 | ||||||||
\(125\) | 7.00734 | + | 124.803i | 0.0560587 | + | 0.998427i | ||||
\(126\) | 15.0186 | + | 87.8205i | 0.119195 | + | 0.696988i | ||||
\(127\) | −95.1373 | + | 95.1373i | −0.749113 | + | 0.749113i | −0.974313 | − | 0.225200i | \(-0.927696\pi\) |
0.225200 | + | 0.974313i | \(0.427696\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 135.077 | + | 118.203i | 1.04711 | + | 0.916302i | ||||
\(130\) | 140.093 | + | 77.4274i | 1.07764 | + | 0.595596i | ||||
\(131\) | −70.4896 | −0.538088 | −0.269044 | − | 0.963128i | \(-0.586708\pi\) | ||||
−0.269044 | + | 0.963128i | \(0.586708\pi\) | |||||||
\(132\) | −40.1200 | + | 2.67291i | −0.303939 | + | 0.0202493i | ||||
\(133\) | 41.3327 | + | 38.4337i | 0.310772 | + | 0.288975i | ||||
\(134\) | 77.4196 | 0.577758 | ||||||||
\(135\) | −128.756 | − | 40.5819i | −0.953748 | − | 0.300607i | ||||
\(136\) | 28.8593i | 0.212201i | ||||||||
\(137\) | −33.6211 | − | 33.6211i | −0.245409 | − | 0.245409i | 0.573674 | − | 0.819084i | \(-0.305518\pi\) |
−0.819084 | + | 0.573674i | \(0.805518\pi\) | |||||||
\(138\) | −70.1614 | + | 4.67436i | −0.508416 | + | 0.0338722i | ||||
\(139\) | −116.378 | −0.837250 | −0.418625 | − | 0.908159i | \(-0.637488\pi\) | ||||
−0.418625 | + | 0.908159i | \(0.637488\pi\) | |||||||
\(140\) | 66.5161 | − | 21.8084i | 0.475115 | − | 0.155775i | ||||
\(141\) | −110.125 | + | 125.846i | −0.781026 | + | 0.892523i | ||||
\(142\) | 128.871 | − | 128.871i | 0.907542 | − | 0.907542i | ||||
\(143\) | 107.268 | + | 107.268i | 0.750125 | + | 0.750125i | ||||
\(144\) | −35.6818 | + | 4.77565i | −0.247791 | + | 0.0331642i | ||||
\(145\) | −27.0351 | − | 14.9419i | −0.186449 | − | 0.103048i | ||||
\(146\) | −108.416 | −0.742576 | ||||||||
\(147\) | −20.3934 | − | 145.579i | −0.138731 | − | 0.990330i | ||||
\(148\) | −75.7239 | − | 75.7239i | −0.511648 | − | 0.511648i | ||||
\(149\) | −129.115 | −0.866546 | −0.433273 | − | 0.901263i | \(-0.642641\pi\) | ||||
−0.433273 | + | 0.901263i | \(0.642641\pi\) | |||||||
\(150\) | −16.6765 | + | 104.747i | −0.111177 | + | 0.698312i | ||||
\(151\) | −51.7299 | −0.342582 | −0.171291 | − | 0.985220i | \(-0.554794\pi\) | ||||
−0.171291 | + | 0.985220i | \(0.554794\pi\) | |||||||
\(152\) | −16.1259 | + | 16.1259i | −0.106091 | + | 0.106091i | ||||
\(153\) | −55.7456 | + | 72.9734i | −0.364351 | + | 0.476950i | ||||
\(154\) | 66.2976 | − | 2.40948i | 0.430504 | − | 0.0156460i | ||||
\(155\) | −100.308 | + | 181.492i | −0.647150 | + | 1.17092i | ||||
\(156\) | 102.211 | + | 89.4428i | 0.655201 | + | 0.573351i | ||||
\(157\) | −38.1320 | − | 38.1320i | −0.242879 | − | 0.242879i | 0.575161 | − | 0.818040i | \(-0.304939\pi\) |
−0.818040 | + | 0.575161i | \(0.804939\pi\) | |||||||
\(158\) | 25.7821 | − | 25.7821i | 0.163178 | − | 0.163178i | ||||
\(159\) | −124.108 | + | 141.825i | −0.780552 | + | 0.891981i | ||||
\(160\) | 7.82998 | + | 27.1789i | 0.0489374 | + | 0.169868i | ||||
\(161\) | 115.941 | − | 4.21368i | 0.720128 | − | 0.0261719i | ||||
\(162\) | −99.4496 | − | 56.8487i | −0.613887 | − | 0.350918i | ||||
\(163\) | −61.7109 | − | 61.7109i | −0.378594 | − | 0.378594i | 0.492001 | − | 0.870595i | \(-0.336266\pi\) |
−0.870595 | + | 0.492001i | \(0.836266\pi\) | |||||||
\(164\) | − | 148.424i | − | 0.905025i | ||||||
\(165\) | −42.6689 | + | 91.0171i | −0.258599 | + | 0.551618i | ||||
\(166\) | − | 55.4357i | − | 0.333950i | ||||||
\(167\) | 162.253 | − | 162.253i | 0.971575 | − | 0.971575i | −0.0280316 | − | 0.999607i | \(-0.508924\pi\) |
0.999607 | + | 0.0280316i | \(0.00892391\pi\) | |||||||
\(168\) | 59.0831 | − | 6.09833i | 0.351685 | − | 0.0362996i | ||||
\(169\) | − | 343.421i | − | 2.03208i | ||||||
\(170\) | 63.1457 | + | 34.8997i | 0.371445 | + | 0.205292i | ||||
\(171\) | −71.9251 | + | 9.62645i | −0.420615 | + | 0.0562950i | ||||
\(172\) | 84.6139 | − | 84.6139i | 0.491941 | − | 0.491941i | ||||
\(173\) | 90.7208 | + | 90.7208i | 0.524398 | + | 0.524398i | 0.918896 | − | 0.394499i | \(-0.129082\pi\) |
−0.394499 | + | 0.918896i | \(0.629082\pi\) | |||||||
\(174\) | −19.7247 | − | 17.2606i | −0.113360 | − | 0.0991991i | ||||
\(175\) | 32.7203 | − | 171.914i | 0.186973 | − | 0.982365i | ||||
\(176\) | 26.8060i | 0.152307i | ||||||||
\(177\) | 10.3652 | + | 155.580i | 0.0585604 | + | 0.878983i | ||||
\(178\) | −32.5020 | + | 32.5020i | −0.182595 | + | 0.182595i | ||||
\(179\) | 23.3548 | 0.130474 | 0.0652369 | − | 0.997870i | \(-0.479220\pi\) | ||||
0.0652369 | + | 0.997870i | \(0.479220\pi\) | |||||||
\(180\) | −32.7009 | + | 83.8490i | −0.181671 | + | 0.465828i | ||||
\(181\) | 132.268i | 0.730762i | 0.930858 | + | 0.365381i | \(0.119061\pi\) | ||||
−0.930858 | + | 0.365381i | \(0.880939\pi\) | |||||||
\(182\) | −164.108 | − | 152.597i | −0.901690 | − | 0.838448i | ||||
\(183\) | 2.99306 | + | 44.9254i | 0.0163555 | + | 0.245494i | ||||
\(184\) | 46.8780i | 0.254772i | ||||||||
\(185\) | −257.261 | + | 74.1147i | −1.39060 | + | 0.400620i | ||||
\(186\) | −115.874 | + | 132.416i | −0.622980 | + | 0.711915i | ||||
\(187\) | 48.3500 | + | 48.3500i | 0.258556 | + | 0.258556i | ||||
\(188\) | 78.8312 | + | 78.8312i | 0.419315 | + | 0.419315i | ||||
\(189\) | 161.177 | + | 98.7068i | 0.852787 | + | 0.522258i | ||||
\(190\) | 15.7832 | + | 54.7854i | 0.0830693 | + | 0.288344i | ||||
\(191\) | − | 137.668i | − | 0.720774i | −0.932803 | − | 0.360387i | \(-0.882645\pi\) | ||
0.932803 | − | 0.360387i | \(-0.117355\pi\) | |||||||
\(192\) | 1.59541 | + | 23.9469i | 0.00830944 | + | 0.124724i | ||||
\(193\) | 188.004 | + | 188.004i | 0.974116 | + | 0.974116i | 0.999673 | − | 0.0255577i | \(-0.00813615\pi\) |
−0.0255577 | + | 0.999673i | \(0.508136\pi\) | |||||||
\(194\) | − | 113.445i | − | 0.584767i | ||||||
\(195\) | 319.310 | − | 115.480i | 1.63749 | − | 0.592206i | ||||
\(196\) | −97.7415 | + | 7.11392i | −0.498681 | + | 0.0362955i | ||||
\(197\) | −2.30427 | − | 2.30427i | −0.0116968 | − | 0.0116968i | 0.701234 | − | 0.712931i | \(-0.252633\pi\) |
−0.712931 | + | 0.701234i | \(0.752633\pi\) | |||||||
\(198\) | −51.7793 | + | 67.7813i | −0.261512 | + | 0.342330i | ||||
\(199\) | −266.282 | −1.33810 | −0.669051 | − | 0.743217i | \(-0.733299\pi\) | ||||
−0.669051 | + | 0.743217i | \(0.733299\pi\) | |||||||
\(200\) | 68.9377 | + | 15.7351i | 0.344688 | + | 0.0786757i | ||||
\(201\) | 108.153 | − | 123.592i | 0.538073 | − | 0.614887i | ||||
\(202\) | −63.3063 | − | 63.3063i | −0.313398 | − | 0.313398i | ||||
\(203\) | 31.6694 | + | 29.4482i | 0.156007 | + | 0.145065i | ||||
\(204\) | 46.0708 | + | 40.3155i | 0.225837 | + | 0.197625i | ||||
\(205\) | −324.760 | − | 179.490i | −1.58419 | − | 0.875562i | ||||
\(206\) | −82.8227 | −0.402052 | ||||||||
\(207\) | −90.5512 | + | 118.535i | −0.437446 | + | 0.572634i | ||||
\(208\) | 64.0263 | − | 64.0263i | 0.307819 | − | 0.307819i | ||||
\(209\) | 54.0337i | 0.258534i | ||||||||
\(210\) | 58.1060 | − | 136.652i | 0.276695 | − | 0.650722i | ||||
\(211\) | 104.157 | 0.493637 | 0.246819 | − | 0.969062i | \(-0.420615\pi\) | ||||
0.246819 | + | 0.969062i | \(0.420615\pi\) | |||||||
\(212\) | 88.8408 | + | 88.8408i | 0.419060 | + | 0.419060i | ||||
\(213\) | −25.7003 | − | 385.758i | −0.120659 | − | 1.81107i | ||||
\(214\) | − | 7.93464i | − | 0.0370777i | ||||||
\(215\) | −82.8157 | − | 287.464i | −0.385189 | − | 1.33704i | ||||
\(216\) | −42.2226 | + | 63.6337i | −0.195475 | + | 0.294601i | ||||
\(217\) | 197.692 | − | 212.604i | 0.911023 | − | 0.979740i | ||||
\(218\) | −108.319 | + | 108.319i | −0.496878 | + | 0.496878i | ||||
\(219\) | −151.454 | + | 173.075i | −0.691570 | + | 0.790297i | ||||
\(220\) | 58.6529 | + | 32.4166i | 0.266604 | + | 0.147348i | ||||
\(221\) | − | 230.969i | − | 1.04511i | ||||||
\(222\) | −226.669 | + | 15.1014i | −1.02103 | + | 0.0680242i | ||||
\(223\) | −2.59750 | + | 2.59750i | −0.0116480 | + | 0.0116480i | −0.712907 | − | 0.701259i | \(-0.752622\pi\) |
0.701259 | + | 0.712907i | \(0.252622\pi\) | |||||||
\(224\) | −1.43818 | − | 39.5719i | −0.00642044 | − | 0.176660i | ||||
\(225\) | 143.921 | + | 172.950i | 0.639648 | + | 0.768668i | ||||
\(226\) | 35.1005 | 0.155312 | ||||||||
\(227\) | 60.1162 | − | 60.1162i | 0.264829 | − | 0.264829i | −0.562183 | − | 0.827013i | \(-0.690039\pi\) |
0.827013 | + | 0.562183i | \(0.190039\pi\) | |||||||
\(228\) | 3.21593 | + | 48.2706i | 0.0141050 | + | 0.211713i | ||||
\(229\) | 345.368 | 1.50816 | 0.754078 | − | 0.656785i | \(-0.228084\pi\) | ||||
0.754078 | + | 0.656785i | \(0.228084\pi\) | |||||||
\(230\) | 102.572 | + | 56.6898i | 0.445963 | + | 0.246477i | ||||
\(231\) | 88.7692 | − | 109.203i | 0.384282 | − | 0.472741i | ||||
\(232\) | −12.3558 | + | 12.3558i | −0.0532577 | + | 0.0532577i | ||||
\(233\) | 258.641 | − | 258.641i | 1.11005 | − | 1.11005i | 0.116904 | − | 0.993143i | \(-0.462703\pi\) |
0.993143 | − | 0.116904i | \(-0.0372970\pi\) | |||||||
\(234\) | 285.572 | − | 38.2209i | 1.22039 | − | 0.163337i | ||||
\(235\) | 267.818 | − | 77.1559i | 1.13965 | − | 0.328323i | ||||
\(236\) | 103.950 | 0.440466 | ||||||||
\(237\) | −5.14163 | − | 77.1751i | −0.0216946 | − | 0.325633i | ||||
\(238\) | −73.9700 | − | 68.7819i | −0.310798 | − | 0.289000i | ||||
\(239\) | −209.847 | −0.878022 | −0.439011 | − | 0.898482i | \(-0.644671\pi\) | ||||
−0.439011 | + | 0.898482i | \(0.644671\pi\) | |||||||
\(240\) | 54.3265 | + | 25.4683i | 0.226360 | + | 0.106118i | ||||
\(241\) | 174.145i | 0.722592i | 0.932451 | + | 0.361296i | \(0.117666\pi\) | ||||
−0.932451 | + | 0.361296i | \(0.882334\pi\) | |||||||
\(242\) | −76.0901 | − | 76.0901i | −0.314422 | − | 0.314422i | ||||
\(243\) | −229.681 | + | 79.3451i | −0.945189 | + | 0.326523i | ||||
\(244\) | 30.0166 | 0.123019 | ||||||||
\(245\) | −102.634 | + | 222.466i | −0.418913 | + | 0.908026i | ||||
\(246\) | −236.944 | − | 207.344i | −0.963185 | − | 0.842861i | ||||
\(247\) | 129.060 | − | 129.060i | 0.522511 | − | 0.522511i | ||||
\(248\) | 82.9469 | + | 82.9469i | 0.334464 | + | 0.334464i | ||||
\(249\) | −88.4973 | − | 77.4420i | −0.355411 | − | 0.311012i | ||||
\(250\) | 117.796 | − | 131.811i | 0.471184 | − | 0.527243i | ||||
\(251\) | −425.295 | −1.69440 | −0.847202 | − | 0.531271i | \(-0.821715\pi\) | ||||
−0.847202 | + | 0.531271i | \(0.821715\pi\) | |||||||
\(252\) | 72.8019 | − | 102.839i | 0.288896 | − | 0.408092i | ||||
\(253\) | 78.5381 | + | 78.5381i | 0.310427 | + | 0.310427i | ||||
\(254\) | 190.275 | 0.749113 | ||||||||
\(255\) | 143.926 | − | 52.0517i | 0.564417 | − | 0.204124i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −24.8379 | + | 24.8379i | −0.0966454 | + | 0.0966454i | −0.753776 | − | 0.657131i | \(-0.771770\pi\) |
0.657131 | + | 0.753776i | \(0.271770\pi\) | |||||||
\(258\) | −16.8743 | − | 253.280i | −0.0654041 | − | 0.981706i | ||||
\(259\) | 374.567 | − | 13.6131i | 1.44620 | − | 0.0525601i | ||||
\(260\) | −62.6656 | − | 217.520i | −0.241022 | − | 0.836617i | ||||
\(261\) | −55.1096 | + | 7.37586i | −0.211148 | + | 0.0282600i | ||||
\(262\) | 70.4896 | + | 70.4896i | 0.269044 | + | 0.269044i | ||||
\(263\) | −220.211 | + | 220.211i | −0.837302 | + | 0.837302i | −0.988503 | − | 0.151201i | \(-0.951686\pi\) |
0.151201 | + | 0.988503i | \(0.451686\pi\) | |||||||
\(264\) | 42.7929 | + | 37.4471i | 0.162094 | + | 0.141845i | ||||
\(265\) | 301.824 | − | 86.9527i | 1.13896 | − | 0.328124i | ||||
\(266\) | −2.89899 | − | 79.7664i | −0.0108984 | − | 0.299874i | ||||
\(267\) | 6.48175 | + | 97.2902i | 0.0242762 | + | 0.364383i | ||||
\(268\) | −77.4196 | − | 77.4196i | −0.288879 | − | 0.288879i | ||||
\(269\) | − | 251.260i | − | 0.934053i | −0.884243 | − | 0.467026i | \(-0.845325\pi\) | ||
0.884243 | − | 0.467026i | \(-0.154675\pi\) | |||||||
\(270\) | 88.1740 | + | 169.338i | 0.326571 | + | 0.627178i | ||||
\(271\) | − | 101.261i | − | 0.373657i | −0.982393 | − | 0.186829i | \(-0.940179\pi\) | ||
0.982393 | − | 0.186829i | \(-0.0598209\pi\) | |||||||
\(272\) | 28.8593 | − | 28.8593i | 0.106100 | − | 0.106100i | ||||
\(273\) | −472.859 | + | 48.8067i | −1.73208 | + | 0.178779i | ||||
\(274\) | 67.2421i | 0.245409i | ||||||||
\(275\) | 141.858 | − | 89.1340i | 0.515849 | − | 0.324124i | ||||
\(276\) | 74.8358 | + | 65.4871i | 0.271144 | + | 0.237272i | ||||
\(277\) | −298.311 | + | 298.311i | −1.07693 | + | 1.07693i | −0.0801518 | + | 0.996783i | \(0.525541\pi\) |
−0.996783 | + | 0.0801518i | \(0.974459\pi\) | |||||||
\(278\) | 116.378 | + | 116.378i | 0.418625 | + | 0.418625i | ||||
\(279\) | 49.5157 | + | 369.962i | 0.177476 | + | 1.32603i | ||||
\(280\) | −88.3245 | − | 44.7077i | −0.315445 | − | 0.159670i | ||||
\(281\) | 105.319i | 0.374801i | 0.982284 | + | 0.187400i | \(0.0600062\pi\) | ||||
−0.982284 | + | 0.187400i | \(0.939994\pi\) | |||||||
\(282\) | 235.970 | − | 15.7210i | 0.836775 | − | 0.0557483i | ||||
\(283\) | −205.970 | + | 205.970i | −0.727811 | + | 0.727811i | −0.970183 | − | 0.242372i | \(-0.922074\pi\) |
0.242372 | + | 0.970183i | \(0.422074\pi\) | |||||||
\(284\) | −257.742 | −0.907542 | ||||||||
\(285\) | 109.508 | + | 51.3373i | 0.384238 | + | 0.180131i | ||||
\(286\) | − | 214.536i | − | 0.750125i | ||||||
\(287\) | 380.430 | + | 353.747i | 1.32554 | + | 1.23257i | ||||
\(288\) | 40.4575 | + | 30.9062i | 0.140477 | + | 0.107313i | ||||
\(289\) | 184.893i | 0.639767i | ||||||||
\(290\) | 12.0932 | + | 41.9770i | 0.0417007 | + | 0.144748i | ||||
\(291\) | −181.103 | − | 158.479i | −0.622346 | − | 0.544601i | ||||
\(292\) | 108.416 | + | 108.416i | 0.371288 | + | 0.371288i | ||||
\(293\) | −123.123 | − | 123.123i | −0.420216 | − | 0.420216i | 0.465062 | − | 0.885278i | \(-0.346032\pi\) |
−0.885278 | + | 0.465062i | \(0.846032\pi\) | |||||||
\(294\) | −125.185 | + | 165.972i | −0.425800 | + | 0.564530i | ||||
\(295\) | 125.707 | − | 227.448i | 0.426126 | − | 0.771010i | ||||
\(296\) | 151.448i | 0.511648i | ||||||||
\(297\) | 35.8717 | + | 177.349i | 0.120780 | + | 0.597134i | ||||
\(298\) | 129.115 | + | 129.115i | 0.433273 | + | 0.433273i | ||||
\(299\) | − | 375.178i | − | 1.25478i | ||||||
\(300\) | 121.423 | − | 88.0703i | 0.404744 | − | 0.293568i | ||||
\(301\) | 15.2112 | + | 418.541i | 0.0505356 | + | 1.39050i | ||||
\(302\) | 51.7299 | + | 51.7299i | 0.171291 | + | 0.171291i | ||||
\(303\) | −189.499 | + | 12.6250i | −0.625409 | + | 0.0416665i | ||||
\(304\) | 32.2518 | 0.106091 | ||||||||
\(305\) | 36.2993 | − | 65.6780i | 0.119014 | − | 0.215338i | ||||
\(306\) | 128.719 | − | 17.2277i | 0.420650 | − | 0.0562998i | ||||
\(307\) | −234.650 | − | 234.650i | −0.764331 | − | 0.764331i | 0.212771 | − | 0.977102i | \(-0.431751\pi\) |
−0.977102 | + | 0.212771i | \(0.931751\pi\) | |||||||
\(308\) | −68.7071 | − | 63.8881i | −0.223075 | − | 0.207429i | ||||
\(309\) | −115.701 | + | 132.218i | −0.374436 | + | 0.427889i | ||||
\(310\) | 281.801 | − | 81.1842i | 0.909034 | − | 0.261884i | ||||
\(311\) | 312.785 | 1.00574 | 0.502870 | − | 0.864362i | \(-0.332277\pi\) | ||||
0.502870 | + | 0.864362i | \(0.332277\pi\) | |||||||
\(312\) | −12.7685 | − | 191.654i | −0.0409248 | − | 0.614276i | ||||
\(313\) | 240.526 | − | 240.526i | 0.768452 | − | 0.768452i | −0.209382 | − | 0.977834i | \(-0.567145\pi\) |
0.977834 | + | 0.209382i | \(0.0671451\pi\) | |||||||
\(314\) | 76.2640i | 0.242879i | ||||||||
\(315\) | −136.978 | − | 283.658i | −0.434850 | − | 0.900503i | ||||
\(316\) | −51.5641 | −0.163178 | ||||||||
\(317\) | −170.827 | − | 170.827i | −0.538887 | − | 0.538887i | 0.384315 | − | 0.923202i | \(-0.374438\pi\) |
−0.923202 | + | 0.384315i | \(0.874438\pi\) | |||||||
\(318\) | 265.933 | − | 17.7172i | 0.836267 | − | 0.0557145i | ||||
\(319\) | 41.4010i | 0.129784i | ||||||||
\(320\) | 19.3489 | − | 35.0089i | 0.0604653 | − | 0.109403i | ||||
\(321\) | −12.6668 | − | 11.0844i | −0.0394605 | − | 0.0345310i | ||||
\(322\) | −120.154 | − | 111.727i | −0.373150 | − | 0.346978i | ||||
\(323\) | 58.1727 | − | 58.1727i | 0.180101 | − | 0.180101i | ||||
\(324\) | 42.6010 | + | 156.298i | 0.131485 | + | 0.482402i | ||||
\(325\) | −551.728 | − | 125.933i | −1.69763 | − | 0.387486i | ||||
\(326\) | 123.422i | 0.378594i | ||||||||
\(327\) | 21.6018 | + | 324.240i | 0.0660605 | + | 0.991558i | ||||
\(328\) | −148.424 | + | 148.424i | −0.452513 | + | 0.452513i | ||||
\(329\) | −389.937 | + | 14.1717i | −1.18522 | + | 0.0430749i | ||||
\(330\) | 133.686 | − | 48.3482i | 0.405109 | − | 0.146510i | ||||
\(331\) | −421.233 | −1.27261 | −0.636303 | − | 0.771439i | \(-0.719537\pi\) | ||||
−0.636303 | + | 0.771439i | \(0.719537\pi\) | |||||||
\(332\) | −55.4357 | + | 55.4357i | −0.166975 | + | 0.166975i | ||||
\(333\) | −292.542 | + | 382.950i | −0.878505 | + | 1.15000i | ||||
\(334\) | −324.506 | −0.971575 | ||||||||
\(335\) | −263.022 | + | 75.7743i | −0.785141 | + | 0.226192i | ||||
\(336\) | −65.1814 | − | 52.9847i | −0.193992 | − | 0.157693i | ||||
\(337\) | 159.190 | − | 159.190i | 0.472375 | − | 0.472375i | −0.430307 | − | 0.902682i | \(-0.641595\pi\) |
0.902682 | + | 0.430307i | \(0.141595\pi\) | |||||||
\(338\) | −343.421 | + | 343.421i | −1.01604 | + | 1.01604i | ||||
\(339\) | 49.0343 | − | 56.0343i | 0.144644 | − | 0.165293i | ||||
\(340\) | −28.2460 | − | 98.0454i | −0.0830764 | − | 0.288369i | ||||
\(341\) | 277.934 | 0.815056 | ||||||||
\(342\) | 81.5516 | + | 62.2987i | 0.238455 | + | 0.182160i | ||||
\(343\) | 214.719 | − | 267.479i | 0.626002 | − | 0.779821i | ||||
\(344\) | −169.228 | −0.491941 | ||||||||
\(345\) | 233.789 | − | 84.5508i | 0.677648 | − | 0.245075i | ||||
\(346\) | − | 181.442i | − | 0.524398i | ||||||
\(347\) | 280.509 | + | 280.509i | 0.808384 | + | 0.808384i | 0.984389 | − | 0.176005i | \(-0.0563175\pi\) |
−0.176005 | + | 0.984389i | \(0.556318\pi\) | |||||||
\(348\) | 2.46407 | + | 36.9853i | 0.00708066 | + | 0.106280i | ||||
\(349\) | −504.442 | −1.44539 | −0.722697 | − | 0.691165i | \(-0.757098\pi\) | ||||
−0.722697 | + | 0.691165i | \(0.757098\pi\) | |||||||
\(350\) | −204.634 | + | 139.194i | −0.584669 | + | 0.397696i | ||||
\(351\) | 337.920 | − | 509.279i | 0.962734 | − | 1.45094i | ||||
\(352\) | 26.8060 | − | 26.8060i | 0.0761533 | − | 0.0761533i | ||||
\(353\) | 205.433 | + | 205.433i | 0.581964 | + | 0.581964i | 0.935443 | − | 0.353479i | \(-0.115001\pi\) |
−0.353479 | + | 0.935443i | \(0.615001\pi\) | |||||||
\(354\) | 145.215 | − | 165.945i | 0.410211 | − | 0.468772i | ||||
\(355\) | −311.689 | + | 563.953i | −0.877996 | + | 1.58860i | ||||
\(356\) | 65.0039 | 0.182595 | ||||||||
\(357\) | −213.137 | + | 21.9992i | −0.597022 | + | 0.0616224i | ||||
\(358\) | −23.3548 | − | 23.3548i | −0.0652369 | − | 0.0652369i | ||||
\(359\) | 428.176 | 1.19269 | 0.596346 | − | 0.802727i | \(-0.296619\pi\) | ||||
0.596346 | + | 0.802727i | \(0.296619\pi\) | |||||||
\(360\) | 116.550 | − | 51.1481i | 0.323750 | − | 0.142078i | ||||
\(361\) | −295.989 | −0.819914 | ||||||||
\(362\) | 132.268 | − | 132.268i | 0.365381 | − | 0.365381i | ||||
\(363\) | −227.765 | + | 15.1744i | −0.627453 | + | 0.0418027i | ||||
\(364\) | 11.5102 | + | 316.705i | 0.0316213 | + | 0.870069i | ||||
\(365\) | 368.329 | − | 106.112i | 1.00912 | − | 0.290718i | ||||
\(366\) | 41.9323 | − | 47.9184i | 0.114569 | − | 0.130925i | ||||
\(367\) | −152.654 | − | 152.654i | −0.415952 | − | 0.415952i | 0.467854 | − | 0.883806i | \(-0.345027\pi\) |
−0.883806 | + | 0.467854i | \(0.845027\pi\) | |||||||
\(368\) | 46.8780 | − | 46.8780i | 0.127386 | − | 0.127386i | ||||
\(369\) | −662.006 | + | 88.6027i | −1.79405 | + | 0.240116i | ||||
\(370\) | 331.376 | + | 183.147i | 0.895611 | + | 0.494991i | ||||
\(371\) | −439.449 | + | 15.9711i | −1.18450 | + | 0.0430488i | ||||
\(372\) | 248.290 | − | 16.5418i | 0.667447 | − | 0.0444673i | ||||
\(373\) | 382.613 | + | 382.613i | 1.02577 | + | 1.02577i | 0.999659 | + | 0.0261145i | \(0.00831345\pi\) |
0.0261145 | + | 0.999659i | \(0.491687\pi\) | |||||||
\(374\) | − | 96.7001i | − | 0.258556i | ||||||
\(375\) | −45.8646 | − | 372.185i | −0.122306 | − | 0.992492i | ||||
\(376\) | − | 157.662i | − | 0.419315i | ||||||
\(377\) | 98.8869 | − | 98.8869i | 0.262299 | − | 0.262299i | ||||
\(378\) | −62.4700 | − | 259.884i | −0.165264 | − | 0.687523i | ||||
\(379\) | 726.851i | 1.91781i | 0.283721 | + | 0.958907i | \(0.408431\pi\) | ||||
−0.283721 | + | 0.958907i | \(0.591569\pi\) | |||||||
\(380\) | 39.0022 | − | 70.5686i | 0.102637 | − | 0.185707i | ||||
\(381\) | 265.808 | − | 303.753i | 0.697658 | − | 0.797253i | ||||
\(382\) | −137.668 | + | 137.668i | −0.360387 | + | 0.360387i | ||||
\(383\) | 465.105 | + | 465.105i | 1.21437 | + | 1.21437i | 0.969573 | + | 0.244801i | \(0.0787225\pi\) |
0.244801 | + | 0.969573i | \(0.421277\pi\) | |||||||
\(384\) | 22.3515 | − | 25.5423i | 0.0582070 | − | 0.0665165i | ||||
\(385\) | −222.878 | + | 73.0745i | −0.578905 | + | 0.189804i | ||||
\(386\) | − | 376.009i | − | 0.974116i | ||||||
\(387\) | −427.908 | − | 326.886i | −1.10571 | − | 0.844668i | ||||
\(388\) | −113.445 | + | 113.445i | −0.292384 | + | 0.292384i | ||||
\(389\) | 120.366 | 0.309424 | 0.154712 | − | 0.987960i | \(-0.450555\pi\) | ||||
0.154712 | + | 0.987960i | \(0.450555\pi\) | |||||||
\(390\) | −434.791 | − | 203.830i | −1.11485 | − | 0.522641i | ||||
\(391\) | − | 169.108i | − | 0.432502i | ||||||
\(392\) | 104.855 | + | 90.6275i | 0.267488 | + | 0.231193i | ||||
\(393\) | 211.001 | − | 14.0575i | 0.536898 | − | 0.0357697i | ||||
\(394\) | 4.60854i | 0.0116968i | ||||||||
\(395\) | −62.3568 | + | 112.825i | −0.157865 | + | 0.285633i | ||||
\(396\) | 119.561 | − | 16.0020i | 0.301921 | − | 0.0404090i | ||||
\(397\) | 312.868 | + | 312.868i | 0.788080 | + | 0.788080i | 0.981179 | − | 0.193100i | \(-0.0618541\pi\) |
−0.193100 | + | 0.981179i | \(0.561854\pi\) | |||||||
\(398\) | 266.282 | + | 266.282i | 0.669051 | + | 0.669051i | ||||
\(399\) | −131.388 | − | 106.803i | −0.329294 | − | 0.267677i | ||||
\(400\) | −53.2025 | − | 84.6728i | −0.133006 | − | 0.211682i | ||||
\(401\) | − | 641.900i | − | 1.60075i | −0.599501 | − | 0.800374i | \(-0.704634\pi\) | ||
0.599501 | − | 0.800374i | \(-0.295366\pi\) | |||||||
\(402\) | −231.745 | + | 15.4395i | −0.576480 | + | 0.0384068i | ||||
\(403\) | −663.849 | − | 663.849i | −1.64727 | − | 1.64727i | ||||
\(404\) | 126.613i | 0.313398i | ||||||||
\(405\) | 393.507 | + | 95.7992i | 0.971621 | + | 0.236541i | ||||
\(406\) | −2.22122 | − | 61.1176i | −0.00547100 | − | 0.150536i | ||||
\(407\) | 253.732 | + | 253.732i | 0.623419 | + | 0.623419i | ||||
\(408\) | −5.75531 | − | 86.3864i | −0.0141061 | − | 0.211731i | ||||
\(409\) | −134.590 | −0.329071 | −0.164535 | − | 0.986371i | \(-0.552612\pi\) | ||||
−0.164535 | + | 0.986371i | \(0.552612\pi\) | |||||||
\(410\) | 145.270 | + | 504.250i | 0.354317 | + | 1.22988i | ||||
\(411\) | 107.345 | + | 93.9351i | 0.261180 | + | 0.228553i | ||||
\(412\) | 82.8227 | + | 82.8227i | 0.201026 | + | 0.201026i | ||||
\(413\) | −247.749 | + | 266.437i | −0.599878 | + | 0.645125i | ||||
\(414\) | 209.087 | − | 27.9841i | 0.505040 | − | 0.0675945i | ||||
\(415\) | 54.2576 | + | 188.335i | 0.130741 | + | 0.453819i | ||||
\(416\) | −128.053 | −0.307819 | ||||||||
\(417\) | 348.361 | − | 23.2088i | 0.835398 | − | 0.0556566i | ||||
\(418\) | 54.0337 | − | 54.0337i | 0.129267 | − | 0.129267i | ||||
\(419\) | 268.374i | 0.640510i | 0.947331 | + | 0.320255i | \(0.103769\pi\) | ||||
−0.947331 | + | 0.320255i | \(0.896231\pi\) | |||||||
\(420\) | −194.758 | + | 78.5457i | −0.463709 | + | 0.187014i | ||||
\(421\) | −28.9266 | −0.0687092 | −0.0343546 | − | 0.999410i | \(-0.510938\pi\) | ||||
−0.0343546 | + | 0.999410i | \(0.510938\pi\) | |||||||
\(422\) | −104.157 | − | 104.157i | −0.246819 | − | 0.246819i | ||||
\(423\) | 304.546 | − | 398.664i | 0.719968 | − | 0.942468i | ||||
\(424\) | − | 177.682i | − | 0.419060i | ||||||
\(425\) | −248.687 | − | 56.7631i | −0.585145 | − | 0.133560i | ||||
\(426\) | −360.057 | + | 411.458i | −0.845205 | + | 0.965864i | ||||
\(427\) | −71.5403 | + | 76.9365i | −0.167542 | + | 0.180179i | ||||
\(428\) | −7.93464 | + | 7.93464i | −0.0185389 | + | 0.0185389i | ||||
\(429\) | −342.484 | − | 299.700i | −0.798331 | − | 0.698601i | ||||
\(430\) | −204.648 | + | 370.279i | −0.475926 | + | 0.861115i | ||||
\(431\) | − | 276.630i | − | 0.641833i | −0.947107 | − | 0.320917i | \(-0.896009\pi\) | ||
0.947107 | − | 0.320917i | \(-0.103991\pi\) | |||||||
\(432\) | 105.856 | − | 21.4112i | 0.245038 | − | 0.0495629i | ||||
\(433\) | −249.817 | + | 249.817i | −0.576945 | + | 0.576945i | −0.934060 | − | 0.357116i | \(-0.883760\pi\) |
0.357116 | + | 0.934060i | \(0.383760\pi\) | |||||||
\(434\) | −410.296 | + | 14.9116i | −0.945381 | + | 0.0343584i | ||||
\(435\) | 83.9057 | + | 39.3351i | 0.192887 | + | 0.0904254i | ||||
\(436\) | 216.639 | 0.496878 | ||||||||
\(437\) | 94.4936 | − | 94.4936i | 0.216233 | − | 0.216233i | ||||
\(438\) | 324.529 | − | 21.6210i | 0.740934 | − | 0.0493631i | ||||
\(439\) | 519.817 | 1.18409 | 0.592047 | − | 0.805903i | \(-0.298320\pi\) | ||||
0.592047 | + | 0.805903i | \(0.298320\pi\) | |||||||
\(440\) | −26.2363 | − | 91.0695i | −0.0596279 | − | 0.206976i | ||||
\(441\) | 90.0771 | + | 431.703i | 0.204256 | + | 0.978917i | ||||
\(442\) | −230.969 | + | 230.969i | −0.522555 | + | 0.522555i | ||||
\(443\) | −388.588 | + | 388.588i | −0.877173 | + | 0.877173i | −0.993241 | − | 0.116068i | \(-0.962971\pi\) |
0.116068 | + | 0.993241i | \(0.462971\pi\) | |||||||
\(444\) | 241.771 | + | 211.568i | 0.544529 | + | 0.476504i | ||||
\(445\) | 78.6096 | − | 142.232i | 0.176651 | − | 0.319623i | ||||
\(446\) | 5.19500 | 0.0116480 | ||||||||
\(447\) | 386.489 | − | 25.7490i | 0.864629 | − | 0.0576041i | ||||
\(448\) | −38.1337 | + | 41.0100i | −0.0851198 | + | 0.0915402i | ||||
\(449\) | 283.968 | 0.632445 | 0.316223 | − | 0.948685i | \(-0.397585\pi\) | ||||
0.316223 | + | 0.948685i | \(0.397585\pi\) | |||||||
\(450\) | 29.0296 | − | 316.871i | 0.0645102 | − | 0.704158i | ||||
\(451\) | 497.331i | 1.10273i | ||||||||
\(452\) | −35.1005 | − | 35.1005i | −0.0776560 | − | 0.0776560i | ||||
\(453\) | 154.846 | − | 10.3163i | 0.341824 | − | 0.0227733i | ||||
\(454\) | −120.232 | −0.264829 | ||||||||
\(455\) | 706.887 | + | 357.808i | 1.55360 | + | 0.786392i | ||||
\(456\) | 45.0547 | − | 51.4866i | 0.0988042 | − | 0.112909i | ||||
\(457\) | −201.368 | + | 201.368i | −0.440630 | + | 0.440630i | −0.892224 | − | 0.451594i | \(-0.850856\pi\) |
0.451594 | + | 0.892224i | \(0.350856\pi\) | |||||||
\(458\) | −345.368 | − | 345.368i | −0.754078 | − | 0.754078i | ||||
\(459\) | 152.314 | − | 229.553i | 0.331839 | − | 0.500116i | ||||
\(460\) | −45.8817 | − | 159.261i | −0.0997429 | − | 0.346220i | ||||
\(461\) | −553.509 | −1.20067 | −0.600335 | − | 0.799749i | \(-0.704966\pi\) | ||||
−0.600335 | + | 0.799749i | \(0.704966\pi\) | |||||||
\(462\) | −197.972 | + | 20.4340i | −0.428511 | + | 0.0442293i | ||||
\(463\) | 574.866 | + | 574.866i | 1.24161 | + | 1.24161i | 0.959333 | + | 0.282278i | \(0.0910902\pi\) |
0.282278 | + | 0.959333i | \(0.408910\pi\) | |||||||
\(464\) | 24.7116 | 0.0532577 | ||||||||
\(465\) | 264.065 | − | 563.277i | 0.567881 | − | 1.21135i | ||||
\(466\) | −517.282 | −1.11005 | ||||||||
\(467\) | −628.925 | + | 628.925i | −1.34673 | + | 1.34673i | −0.457549 | + | 0.889184i | \(0.651273\pi\) |
−0.889184 | + | 0.457549i | \(0.848727\pi\) | |||||||
\(468\) | −323.793 | − | 247.351i | −0.691865 | − | 0.528528i | ||||
\(469\) | 382.955 | − | 13.9179i | 0.816534 | − | 0.0296757i | ||||
\(470\) | −344.974 | − | 190.662i | −0.733987 | − | 0.405664i | ||||
\(471\) | 121.748 | + | 106.538i | 0.258487 | + | 0.226196i | ||||
\(472\) | −103.950 | − | 103.950i | −0.220233 | − | 0.220233i | ||||
\(473\) | −283.519 | + | 283.519i | −0.599407 | + | 0.599407i | ||||
\(474\) | −72.0335 | + | 82.3167i | −0.151969 | + | 0.173664i | ||||
\(475\) | −107.242 | − | 170.678i | −0.225773 | − | 0.359322i | ||||
\(476\) | 5.18810 | + | 142.752i | 0.0108994 | + | 0.299899i | ||||
\(477\) | 343.216 | − | 449.284i | 0.719531 | − | 0.941896i | ||||
\(478\) | 209.847 | + | 209.847i | 0.439011 | + | 0.439011i | ||||
\(479\) | 229.796i | 0.479742i | 0.970805 | + | 0.239871i | \(0.0771051\pi\) | ||||
−0.970805 | + | 0.239871i | \(0.922895\pi\) | |||||||
\(480\) | −28.8582 | − | 79.7948i | −0.0601212 | − | 0.166239i | ||||
\(481\) | − | 1212.08i | − | 2.51992i | ||||||
\(482\) | 174.145 | − | 174.145i | 0.361296 | − | 0.361296i | ||||
\(483\) | −346.212 | + | 35.7347i | −0.716795 | + | 0.0739849i | ||||
\(484\) | 152.180i | 0.314422i | ||||||||
\(485\) | 111.034 | + | 385.413i | 0.228936 | + | 0.794666i | ||||
\(486\) | 309.026 | + | 150.336i | 0.635856 | + | 0.309333i | ||||
\(487\) | 58.0212 | − | 58.0212i | 0.119140 | − | 0.119140i | −0.645023 | − | 0.764163i | \(-0.723152\pi\) |
0.764163 | + | 0.645023i | \(0.223152\pi\) | |||||||
\(488\) | −30.0166 | − | 30.0166i | −0.0615095 | − | 0.0615095i | ||||
\(489\) | 197.030 | + | 172.416i | 0.402924 | + | 0.352590i | ||||
\(490\) | 325.100 | − | 119.833i | 0.663470 | − | 0.244557i | ||||
\(491\) | 105.182i | 0.214221i | 0.994247 | + | 0.107110i | \(0.0341598\pi\) | ||||
−0.994247 | + | 0.107110i | \(0.965840\pi\) | |||||||
\(492\) | 29.5997 | + | 444.287i | 0.0601620 | + | 0.903023i | ||||
\(493\) | 44.5724 | − | 44.5724i | 0.0904105 | − | 0.0904105i | ||||
\(494\) | −258.120 | −0.522511 | ||||||||
\(495\) | 109.572 | − | 280.956i | 0.221358 | − | 0.567589i | ||||
\(496\) | − | 165.894i | − | 0.334464i | ||||||
\(497\) | 614.290 | − | 660.625i | 1.23600 | − | 1.32923i | ||||
\(498\) | 11.0554 | + | 165.939i | 0.0221995 | + | 0.333211i | ||||
\(499\) | − | 29.9809i | − | 0.0600819i | −0.999549 | − | 0.0300409i | \(-0.990436\pi\) | ||
0.999549 | − | 0.0300409i | \(-0.00956377\pi\) | |||||||
\(500\) | −249.607 | + | 14.0147i | −0.499214 | + | 0.0280293i | ||||
\(501\) | −453.325 | + | 518.040i | −0.904840 | + | 1.03401i | ||||
\(502\) | 425.295 | + | 425.295i | 0.847202 | + | 0.847202i | ||||
\(503\) | 159.113 | + | 159.113i | 0.316328 | + | 0.316328i | 0.847355 | − | 0.531027i | \(-0.178194\pi\) |
−0.531027 | + | 0.847355i | \(0.678194\pi\) | |||||||
\(504\) | −175.641 | + | 30.0373i | −0.348494 | + | 0.0595977i | ||||
\(505\) | 277.035 | + | 153.113i | 0.548585 | + | 0.303195i | ||||
\(506\) | − | 157.076i | − | 0.310427i | ||||||
\(507\) | 68.4873 | + | 1027.99i | 0.135084 | + | 2.02758i | ||||
\(508\) | −190.275 | − | 190.275i | −0.374556 | − | 0.374556i | ||||
\(509\) | − | 782.408i | − | 1.53715i | −0.639761 | − | 0.768574i | \(-0.720967\pi\) | ||
0.639761 | − | 0.768574i | \(-0.279033\pi\) | |||||||
\(510\) | −195.978 | − | 91.8746i | −0.384270 | − | 0.180146i | ||||
\(511\) | −536.278 | + | 19.4902i | −1.04947 | + | 0.0381413i | ||||
\(512\) | −16.0000 | − | 16.0000i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 213.378 | − | 43.1592i | 0.415942 | − | 0.0841311i | ||||
\(514\) | 49.6757 | 0.0966454 | ||||||||
\(515\) | 281.379 | − | 81.0626i | 0.546366 | − | 0.157403i | ||||
\(516\) | −236.406 | + | 270.154i | −0.458151 | + | 0.523555i | ||||
\(517\) | −264.143 | − | 264.143i | −0.510915 | − | 0.510915i | ||||
\(518\) | −388.180 | − | 360.954i | −0.749383 | − | 0.696822i | ||||
\(519\) | −289.653 | − | 253.468i | −0.558097 | − | 0.488378i | ||||
\(520\) | −154.855 | + | 280.186i | −0.297798 | + | 0.538819i | ||||
\(521\) | 224.244 | 0.430411 | 0.215205 | − | 0.976569i | \(-0.430958\pi\) | ||||
0.215205 | + | 0.976569i | \(0.430958\pi\) | |||||||
\(522\) | 62.4855 | + | 47.7337i | 0.119704 | + | 0.0914439i | ||||
\(523\) | 278.114 | − | 278.114i | 0.531767 | − | 0.531767i | −0.389331 | − | 0.921098i | \(-0.627294\pi\) |
0.921098 | + | 0.389331i | \(0.127294\pi\) | |||||||
\(524\) | − | 140.979i | − | 0.269044i | ||||||
\(525\) | −63.6595 | + | 521.126i | −0.121256 | + | 0.992621i | ||||
\(526\) | 440.421 | 0.837302 | ||||||||
\(527\) | −299.224 | − | 299.224i | −0.567787 | − | 0.567787i | ||||
\(528\) | −5.34582 | − | 80.2400i | −0.0101247 | − | 0.151970i | ||||
\(529\) | 254.307i | 0.480731i | ||||||||
\(530\) | −388.777 | − | 214.871i | −0.733541 | − | 0.405418i | ||||
\(531\) | −62.0535 | − | 463.640i | −0.116862 | − | 0.873146i | ||||
\(532\) | −76.8674 | + | 82.6654i | −0.144488 | + | 0.155386i | ||||
\(533\) | 1187.88 | − | 1187.88i | 2.22867 | − | 2.22867i | ||||
\(534\) | 90.8084 | − | 103.772i | 0.170053 | − | 0.194329i | ||||
\(535\) | 7.76601 | + | 26.9568i | 0.0145159 | + | 0.0503866i | ||||
\(536\) | 154.839i | 0.288879i | ||||||||
\(537\) | −69.9095 | + | 4.65757i | −0.130185 | + | 0.00867331i | ||||
\(538\) | −251.260 | + | 251.260i | −0.467026 | + | 0.467026i | ||||
\(539\) | 327.507 | − | 23.8369i | 0.607619 | − | 0.0442243i | ||||
\(540\) | 81.1639 | − | 257.512i | 0.150304 | − | 0.476874i | ||||
\(541\) | 135.498 | 0.250458 | 0.125229 | − | 0.992128i | \(-0.460033\pi\) | ||||
0.125229 | + | 0.992128i | \(0.460033\pi\) | |||||||
\(542\) | −101.261 | + | 101.261i | −0.186829 | + | 0.186829i | ||||
\(543\) | −26.3777 | − | 395.926i | −0.0485778 | − | 0.729146i | ||||
\(544\) | −57.7186 | −0.106100 | ||||||||
\(545\) | 261.983 | − | 474.018i | 0.480702 | − | 0.869757i | ||||
\(546\) | 521.666 | + | 424.052i | 0.955432 | + | 0.776653i | ||||
\(547\) | −15.9985 | + | 15.9985i | −0.0292477 | + | 0.0292477i | −0.721579 | − | 0.692332i | \(-0.756584\pi\) |
0.692332 | + | 0.721579i | \(0.256584\pi\) | |||||||
\(548\) | 67.2421 | − | 67.2421i | 0.122705 | − | 0.122705i | ||||
\(549\) | −17.9186 | − | 133.881i | −0.0326387 | − | 0.243864i | ||||
\(550\) | −230.993 | − | 52.7244i | −0.419986 | − | 0.0958626i | ||||
\(551\) | 49.8120 | 0.0904028 | ||||||||
\(552\) | −9.34871 | − | 140.323i | −0.0169361 | − | 0.254208i | ||||
\(553\) | 122.896 | − | 132.165i | 0.222234 | − | 0.238997i | ||||
\(554\) | 596.622 | 1.07693 | ||||||||
\(555\) | 755.297 | − | 273.157i | 1.36090 | − | 0.492175i | ||||
\(556\) | − | 232.756i | − | 0.418625i | ||||||
\(557\) | −502.514 | − | 502.514i | −0.902180 | − | 0.902180i | 0.0934442 | − | 0.995625i | \(-0.470212\pi\) |
−0.995625 | + | 0.0934442i | \(0.970212\pi\) | |||||||
\(558\) | 320.447 | − | 419.478i | 0.574277 | − | 0.751753i | ||||
\(559\) | 1354.38 | 2.42286 | ||||||||
\(560\) | 43.6169 | + | 133.032i | 0.0778873 | + | 0.237558i | ||||
\(561\) | −154.372 | − | 135.087i | −0.275172 | − | 0.240797i | ||||
\(562\) | 105.319 | − | 105.319i | 0.187400 | − | 0.187400i | ||||
\(563\) | −502.281 | − | 502.281i | −0.892150 | − | 0.892150i | 0.102575 | − | 0.994725i | \(-0.467292\pi\) |
−0.994725 | + | 0.102575i | \(0.967292\pi\) | |||||||
\(564\) | −251.691 | − | 220.249i | −0.446261 | − | 0.390513i | ||||
\(565\) | −119.249 | + | 34.3546i | −0.211060 | + | 0.0608046i | ||||
\(566\) | 411.941 | 0.727811 | ||||||||
\(567\) | −502.146 | − | 263.323i | −0.885618 | − | 0.464414i | ||||
\(568\) | 257.742 | + | 257.742i | 0.453771 | + | 0.453771i | ||||
\(569\) | −359.729 | −0.632212 | −0.316106 | − | 0.948724i | \(-0.602376\pi\) | ||||
−0.316106 | + | 0.948724i | \(0.602376\pi\) | |||||||
\(570\) | −58.1705 | − | 160.845i | −0.102053 | − | 0.282184i | ||||
\(571\) | 583.678 | 1.02220 | 0.511102 | − | 0.859520i | \(-0.329238\pi\) | ||||
0.511102 | + | 0.859520i | \(0.329238\pi\) | |||||||
\(572\) | −214.536 | + | 214.536i | −0.375063 | + | 0.375063i | ||||
\(573\) | 27.4546 | + | 412.090i | 0.0479138 | + | 0.719180i | ||||
\(574\) | −26.6825 | − | 734.177i | −0.0464852 | − | 1.27905i | ||||
\(575\) | −403.958 | − | 92.2040i | −0.702535 | − | 0.160355i | ||||
\(576\) | −9.55130 | − | 71.3637i | −0.0165821 | − | 0.123895i | ||||
\(577\) | −194.662 | − | 194.662i | −0.337369 | − | 0.337369i | 0.518007 | − | 0.855376i | \(-0.326674\pi\) |
−0.855376 | + | 0.518007i | \(0.826674\pi\) | |||||||
\(578\) | 184.893 | − | 184.893i | 0.319884 | − | 0.319884i | ||||
\(579\) | −600.258 | − | 525.272i | −1.03672 | − | 0.907206i | ||||
\(580\) | 29.8838 | − | 54.0702i | 0.0515238 | − | 0.0932245i | ||||
\(581\) | −9.96580 | − | 274.212i | −0.0171528 | − | 0.471965i | ||||
\(582\) | 22.6239 | + | 339.582i | 0.0388727 | + | 0.583474i | ||||
\(583\) | −297.683 | − | 297.683i | −0.510605 | − | 0.510605i | ||||
\(584\) | − | 216.832i | − | 0.371288i | ||||||
\(585\) | −932.783 | + | 409.353i | −1.59450 | + | 0.699749i | ||||
\(586\) | 246.246i | 0.420216i | ||||||||
\(587\) | 505.473 | − | 505.473i | 0.861113 | − | 0.861113i | −0.130355 | − | 0.991467i | \(-0.541612\pi\) |
0.991467 | + | 0.130355i | \(0.0416115\pi\) | |||||||
\(588\) | 291.157 | − | 40.7868i | 0.495165 | − | 0.0693653i | ||||
\(589\) | − | 334.398i | − | 0.567739i | ||||||
\(590\) | −353.155 | + | 101.741i | −0.598568 | + | 0.172442i | ||||
\(591\) | 7.35705 | + | 6.43798i | 0.0124485 | + | 0.0108934i | ||||
\(592\) | 151.448 | − | 151.448i | 0.255824 | − | 0.255824i | ||||
\(593\) | 78.0986 | + | 78.0986i | 0.131701 | + | 0.131701i | 0.769884 | − | 0.638183i | \(-0.220314\pi\) |
−0.638183 | + | 0.769884i | \(0.720314\pi\) | |||||||
\(594\) | 141.477 | − | 213.220i | 0.238177 | − | 0.358957i | ||||
\(595\) | 318.623 | + | 161.279i | 0.535501 | + | 0.271057i | ||||
\(596\) | − | 258.231i | − | 0.433273i | ||||||
\(597\) | 797.080 | − | 53.1037i | 1.33514 | − | 0.0889510i | ||||
\(598\) | −375.178 | + | 375.178i | −0.627388 | + | 0.627388i | ||||
\(599\) | 516.399 | 0.862102 | 0.431051 | − | 0.902328i | \(-0.358143\pi\) | ||||
0.431051 | + | 0.902328i | \(0.358143\pi\) | |||||||
\(600\) | −209.494 | − | 33.3530i | −0.349156 | − | 0.0555884i | ||||
\(601\) | 894.037i | 1.48758i | 0.668412 | + | 0.743791i | \(0.266974\pi\) | ||||
−0.668412 | + | 0.743791i | \(0.733026\pi\) | |||||||
\(602\) | 403.330 | − | 433.752i | 0.669983 | − | 0.720519i | ||||
\(603\) | −299.093 | + | 391.525i | −0.496008 | + | 0.649296i | ||||
\(604\) | − | 103.460i | − | 0.171291i | ||||||
\(605\) | 332.978 | + | 184.032i | 0.550377 | + | 0.304186i | ||||
\(606\) | 202.124 | + | 176.874i | 0.333538 | + | 0.291871i | ||||
\(607\) | 71.3484 | + | 71.3484i | 0.117543 | + | 0.117543i | 0.763431 | − | 0.645889i | \(-0.223513\pi\) |
−0.645889 | + | 0.763431i | \(0.723513\pi\) | |||||||
\(608\) | −32.2518 | − | 32.2518i | −0.0530457 | − | 0.0530457i | ||||
\(609\) | −100.671 | − | 81.8335i | −0.165305 | − | 0.134374i | ||||
\(610\) | −101.977 | + | 29.3787i | −0.167176 | + | 0.0481618i | ||||
\(611\) | 1261.82i | 2.06517i | ||||||||
\(612\) | −145.947 | − | 111.491i | −0.238475 | − | 0.182175i | ||||
\(613\) | −32.1532 | − | 32.1532i | −0.0524522 | − | 0.0524522i | 0.680394 | − | 0.732846i | \(-0.261809\pi\) |
−0.732846 | + | 0.680394i | \(0.761809\pi\) | |||||||
\(614\) | 469.299i | 0.764331i | ||||||||
\(615\) | 1007.92 | + | 472.514i | 1.63889 | + | 0.768315i | ||||
\(616\) | 4.81896 | + | 132.595i | 0.00782299 | + | 0.215252i | ||||
\(617\) | −771.937 | − | 771.937i | −1.25111 | − | 1.25111i | −0.955221 | − | 0.295892i | \(-0.904383\pi\) |
−0.295892 | − | 0.955221i | \(-0.595617\pi\) | |||||||
\(618\) | 247.919 | − | 16.5170i | 0.401163 | − | 0.0267266i | ||||
\(619\) | −245.518 | −0.396636 | −0.198318 | − | 0.980138i | \(-0.563548\pi\) | ||||
−0.198318 | + | 0.980138i | \(0.563548\pi\) | |||||||
\(620\) | −362.985 | − | 200.616i | −0.585459 | − | 0.323575i | ||||
\(621\) | 247.414 | − | 372.878i | 0.398412 | − | 0.600447i | ||||
\(622\) | −312.785 | − | 312.785i | −0.502870 | − | 0.502870i | ||||
\(623\) | −154.927 | + | 166.613i | −0.248680 | + | 0.267437i | ||||
\(624\) | −178.886 | + | 204.423i | −0.286676 | + | 0.327600i | ||||
\(625\) | −271.186 | + | 563.101i | −0.433898 | + | 0.900962i | ||||
\(626\) | −481.051 | −0.768452 | ||||||||
\(627\) | −10.7758 | − | 161.743i | −0.0171862 | − | 0.257963i | ||||
\(628\) | 76.2640 | − | 76.2640i | 0.121440 | − | 0.121440i | ||||
\(629\) | − | 546.335i | − | 0.868577i | ||||||
\(630\) | −146.681 | + | 420.636i | −0.232826 | + | 0.667677i | ||||
\(631\) | 405.528 | 0.642675 | 0.321337 | − | 0.946965i | \(-0.395868\pi\) | ||||
0.321337 | + | 0.946965i | \(0.395868\pi\) | |||||||
\(632\) | 51.5641 | + | 51.5641i | 0.0815888 | + | 0.0815888i | ||||
\(633\) | −311.781 | + | 20.7718i | −0.492545 | + | 0.0328148i | ||||
\(634\) | 341.654i | 0.538887i | ||||||||
\(635\) | −646.431 | + | 186.231i | −1.01800 | + | 0.293277i | ||||
\(636\) | −283.650 | − | 248.216i | −0.445991 | − | 0.390276i | ||||
\(637\) | −839.188 | − | 725.319i | −1.31741 | − | 1.13865i | ||||
\(638\) | 41.4010 | − | 41.4010i | 0.0648919 | − | 0.0648919i | ||||
\(639\) | 153.861 | + | 1149.59i | 0.240783 | + | 1.79904i | ||||
\(640\) | −54.3578 | + | 15.6600i | −0.0849340 | + | 0.0244687i | ||||
\(641\) | 891.470i | 1.39075i | 0.718648 | + | 0.695374i | \(0.244761\pi\) | ||||
−0.718648 | + | 0.695374i | \(0.755239\pi\) | |||||||
\(642\) | 1.58238 | + | 23.7513i | 0.00246476 | + | 0.0369957i | ||||
\(643\) | −319.764 | + | 319.764i | −0.497300 | + | 0.497300i | −0.910596 | − | 0.413297i | \(-0.864377\pi\) |
0.413297 | + | 0.910596i | \(0.364377\pi\) | |||||||
\(644\) | 8.42736 | + | 231.881i | 0.0130860 | + | 0.360064i | ||||
\(645\) | 305.225 | + | 843.968i | 0.473218 | + | 1.30848i | ||||
\(646\) | −116.345 | −0.180101 | ||||||||
\(647\) | −185.628 | + | 185.628i | −0.286906 | + | 0.286906i | −0.835855 | − | 0.548950i | \(-0.815028\pi\) |
0.548950 | + | 0.835855i | \(0.315028\pi\) | |||||||
\(648\) | 113.697 | − | 198.899i | 0.175459 | − | 0.306943i | ||||
\(649\) | −348.309 | −0.536686 | ||||||||
\(650\) | 425.795 | + | 677.661i | 0.655070 | + | 1.04256i | ||||
\(651\) | −549.365 | + | 675.825i | −0.843879 | + | 1.03813i | ||||
\(652\) | 123.422 | − | 123.422i | 0.189297 | − | 0.189297i | ||||
\(653\) | 528.502 | − | 528.502i | 0.809345 | − | 0.809345i | −0.175190 | − | 0.984535i | \(-0.556054\pi\) |
0.984535 | + | 0.175190i | \(0.0560540\pi\) | |||||||
\(654\) | 302.638 | − | 345.841i | 0.462749 | − | 0.528809i | ||||
\(655\) | −308.470 | − | 170.487i | −0.470947 | − | 0.260285i | ||||
\(656\) | 296.848 | 0.452513 | ||||||||
\(657\) | 418.841 | − | 548.280i | 0.637505 | − | 0.834521i | ||||
\(658\) | 404.109 | + | 375.765i | 0.614147 | + | 0.571072i | ||||
\(659\) | −101.666 | −0.154274 | −0.0771369 | − | 0.997021i | \(-0.524578\pi\) | ||||
−0.0771369 | + | 0.997021i | \(0.524578\pi\) | |||||||
\(660\) | −182.034 | − | 85.3377i | −0.275809 | − | 0.129300i | ||||
\(661\) | 563.886i | 0.853080i | 0.904469 | + | 0.426540i | \(0.140268\pi\) | ||||
−0.904469 | + | 0.426540i | \(0.859732\pi\) | |||||||
\(662\) | 421.233 | + | 421.233i | 0.636303 | + | 0.636303i | ||||
\(663\) | 46.0614 | + | 691.375i | 0.0694742 | + | 1.04280i | ||||
\(664\) | 110.871 | 0.166975 | ||||||||
\(665\) | 87.9201 | + | 268.158i | 0.132211 | + | 0.403245i | ||||
\(666\) | 675.492 | − | 90.4078i | 1.01425 | − | 0.135747i | ||||
\(667\) | 72.4017 | − | 72.4017i | 0.108548 | − | 0.108548i | ||||
\(668\) | 324.506 | + | 324.506i | 0.485788 | + | 0.485788i | ||||
\(669\) | 7.25725 | − | 8.29327i | 0.0108479 | − | 0.0123965i | ||||
\(670\) | 338.796 | + | 187.248i | 0.505666 | + | 0.279475i | ||||
\(671\) | −100.578 | −0.149893 | ||||||||
\(672\) | 12.1967 | + | 118.166i | 0.0181498 | + | 0.175842i | ||||
\(673\) | −835.168 | − | 835.168i | −1.24096 | − | 1.24096i | −0.959602 | − | 0.281361i | \(-0.909214\pi\) |
−0.281361 | − | 0.959602i | \(-0.590786\pi\) | |||||||
\(674\) | −318.381 | −0.472375 | ||||||||
\(675\) | −465.298 | − | 489.002i | −0.689331 | − | 0.724447i | ||||
\(676\) | 686.843 | 1.01604 | ||||||||
\(677\) | −710.321 | + | 710.321i | −1.04922 | + | 1.04922i | −0.0504936 | + | 0.998724i | \(0.516079\pi\) |
−0.998724 | + | 0.0504936i | \(0.983921\pi\) | |||||||
\(678\) | −105.069 | + | 6.99998i | −0.154969 | + | 0.0103245i | ||||
\(679\) | −20.3942 | − | 561.153i | −0.0300357 | − | 0.826440i | ||||
\(680\) | −69.7994 | + | 126.291i | −0.102646 | + | 0.185723i | ||||
\(681\) | −167.961 | + | 191.938i | −0.246639 | + | 0.281848i | ||||
\(682\) | −277.934 | − | 277.934i | −0.407528 | − | 0.407528i | ||||
\(683\) | −228.514 | + | 228.514i | −0.334573 | + | 0.334573i | −0.854320 | − | 0.519747i | \(-0.826026\pi\) |
0.519747 | + | 0.854320i | \(0.326026\pi\) | |||||||
\(684\) | −19.2529 | − | 143.850i | −0.0281475 | − | 0.210307i | ||||
\(685\) | −65.8131 | − | 228.446i | −0.0960775 | − | 0.333497i | ||||
\(686\) | −482.197 | + | 52.7601i | −0.702912 | + | 0.0769097i | ||||
\(687\) | −1033.81 | + | 68.8755i | −1.50482 | + | 0.100255i | ||||
\(688\) | 169.228 | + | 169.228i | 0.245971 | + | 0.245971i | ||||
\(689\) | 1422.04i | 2.06391i | ||||||||
\(690\) | −318.339 | − | 149.238i | −0.461362 | − | 0.216287i | ||||
\(691\) | 334.468i | 0.484034i | 0.970272 | + | 0.242017i | \(0.0778090\pi\) | ||||
−0.970272 | + | 0.242017i | \(0.922191\pi\) | |||||||
\(692\) | −181.442 | + | 181.442i | −0.262199 | + | 0.262199i | ||||
\(693\) | −243.940 | + | 344.588i | −0.352006 | + | 0.497240i | ||||
\(694\) | − | 561.019i | − | 0.808384i | ||||||
\(695\) | −509.282 | − | 281.473i | −0.732780 | − | 0.404997i | ||||
\(696\) | 34.5213 | − | 39.4494i | 0.0495995 | − | 0.0566802i | ||||
\(697\) | 535.427 | − | 535.427i | 0.768188 | − | 0.768188i | ||||
\(698\) | 504.442 | + | 504.442i | 0.722697 | + | 0.722697i | ||||
\(699\) | −722.627 | + | 825.787i | −1.03380 | + | 1.18138i | ||||
\(700\) | 343.828 | + | 65.4405i | 0.491183 | + | 0.0934865i | ||||
\(701\) | 786.818i | 1.12242i | 0.827673 | + | 0.561211i | \(0.189664\pi\) | ||||
−0.827673 | + | 0.561211i | \(0.810336\pi\) | |||||||
\(702\) | −847.199 | + | 171.360i | −1.20684 | + | 0.244102i | ||||
\(703\) | 305.279 | − | 305.279i | 0.434252 | − | 0.434252i | ||||
\(704\) | −53.6119 | −0.0761533 | ||||||||
\(705\) | −786.290 | + | 284.366i | −1.11530 | + | 0.403355i | ||||
\(706\) | − | 410.867i | − | 0.581964i | ||||||
\(707\) | −324.524 | − | 301.763i | −0.459016 | − | 0.426821i | ||||
\(708\) | −311.160 | + | 20.7304i | −0.439491 | + | 0.0292802i | ||||
\(709\) | − | 1314.72i | − | 1.85434i | −0.374647 | − | 0.927168i | \(-0.622236\pi\) | ||
0.374647 | − | 0.927168i | \(-0.377764\pi\) | |||||||
\(710\) | 875.642 | − | 252.264i | 1.23330 | − | 0.355302i | ||||
\(711\) | 30.7815 | + | 229.988i | 0.0432933 | + | 0.323471i | ||||
\(712\) | −65.0039 | − | 65.0039i | −0.0912976 | − | 0.0912976i | ||||
\(713\) | −486.048 | − | 486.048i | −0.681695 | − | 0.681695i | ||||
\(714\) | 235.136 | + | 191.138i | 0.329322 | + | 0.267700i | ||||
\(715\) | 209.977 | + | 728.855i | 0.293673 | + | 1.01938i | ||||
\(716\) | 46.7096i | 0.0652369i | ||||||||
\(717\) | 628.149 | − | 41.8491i | 0.876080 | − | 0.0583670i | ||||
\(718\) | −428.176 | − | 428.176i | −0.596346 | − | 0.596346i | ||||
\(719\) | 678.749i | 0.944018i | 0.881594 | + | 0.472009i | \(0.156471\pi\) | ||||
−0.881594 | + | 0.472009i | \(0.843529\pi\) | |||||||
\(720\) | −167.698 | − | 65.4017i | −0.232914 | − | 0.0908357i | ||||
\(721\) | −409.681 | + | 14.8892i | −0.568212 | + | 0.0206508i | ||||
\(722\) | 295.989 | + | 295.989i | 0.409957 | + | 0.409957i | ||||
\(723\) | −34.7291 | − | 521.279i | −0.0480347 | − | 0.720994i | ||||
\(724\) | −264.536 | −0.365381 | ||||||||
\(725\) | −82.1698 | − | 130.775i | −0.113338 | − | 0.180379i | ||||
\(726\) | 242.940 | + | 212.591i | 0.334628 | + | 0.292825i | ||||
\(727\) | −167.875 | − | 167.875i | −0.230915 | − | 0.230915i | 0.582160 | − | 0.813074i | \(-0.302208\pi\) |
−0.813074 | + | 0.582160i | \(0.802208\pi\) | |||||||
\(728\) | 305.195 | − | 328.215i | 0.419224 | − | 0.450845i | ||||
\(729\) | 671.695 | − | 283.313i | 0.921393 | − | 0.388633i | ||||
\(730\) | −474.441 | − | 262.216i | −0.649919 | − | 0.359201i | ||||
\(731\) | 610.474 | 0.835122 | ||||||||
\(732\) | −89.8507 | + | 5.98611i | −0.122747 | + | 0.00817775i | ||||
\(733\) | 138.636 | − | 138.636i | 0.189135 | − | 0.189135i | −0.606187 | − | 0.795322i | \(-0.707302\pi\) |
0.795322 | + | 0.606187i | \(0.207302\pi\) | |||||||
\(734\) | 305.309i | 0.415952i | ||||||||
\(735\) | 262.854 | − | 686.391i | 0.357625 | − | 0.933865i | ||||
\(736\) | −93.7560 | −0.127386 | ||||||||
\(737\) | 259.413 | + | 259.413i | 0.351985 | + | 0.351985i | ||||
\(738\) | 750.608 | + | 573.403i | 1.01708 | + | 0.776969i | ||||
\(739\) | 467.931i | 0.633195i | 0.948560 | + | 0.316598i | \(0.102540\pi\) | ||||
−0.948560 | + | 0.316598i | \(0.897460\pi\) | |||||||
\(740\) | −148.229 | − | 514.523i | −0.200310 | − | 0.695301i | ||||
\(741\) | −360.586 | + | 412.062i | −0.486621 | + | 0.556089i | ||||
\(742\) | 455.420 | + | 423.478i | 0.613774 | + | 0.570725i | ||||
\(743\) | −164.867 | + | 164.867i | −0.221893 | + | 0.221893i | −0.809295 | − | 0.587402i | \(-0.800151\pi\) |
0.587402 | + | 0.809295i | \(0.300151\pi\) | |||||||
\(744\) | −264.832 | − | 231.749i | −0.355957 | − | 0.311490i | ||||
\(745\) | −565.023 | − | 312.280i | −0.758419 | − | 0.419168i | ||||
\(746\) | − | 765.227i | − | 1.02577i | ||||||
\(747\) | 280.349 | + | 214.163i | 0.375299 | + | 0.286698i | ||||
\(748\) | −96.7001 | + | 96.7001i | −0.129278 | + | 0.129278i | ||||
\(749\) | −1.42643 | − | 39.2485i | −0.00190444 | − | 0.0524013i | ||||
\(750\) | −326.320 | + | 418.049i | −0.435093 | + | 0.557399i | ||||
\(751\) | 661.864 | 0.881310 | 0.440655 | − | 0.897677i | \(-0.354746\pi\) | ||||
0.440655 | + | 0.897677i | \(0.354746\pi\) | |||||||
\(752\) | −157.662 | + | 157.662i | −0.209657 | + | 0.209657i | ||||
\(753\) | 1273.06 | − | 84.8152i | 1.69066 | − | 0.112636i | ||||
\(754\) | −197.774 | −0.262299 | ||||||||
\(755\) | −226.376 | − | 125.114i | −0.299835 | − | 0.165715i | ||||
\(756\) | −197.414 | + | 322.354i | −0.261129 | + | 0.426394i | ||||
\(757\) | 846.245 | − | 846.245i | 1.11789 | − | 1.11789i | 0.125843 | − | 0.992050i | \(-0.459837\pi\) |
0.992050 | − | 0.125843i | \(-0.0401635\pi\) | |||||||
\(758\) | 726.851 | − | 726.851i | 0.958907 | − | 0.958907i | ||||
\(759\) | −250.756 | − | 219.430i | −0.330376 | − | 0.289105i | ||||
\(760\) | −109.571 | + | 31.5664i | −0.144172 | + | 0.0415347i | ||||
\(761\) | −29.8430 | −0.0392155 | −0.0196078 | − | 0.999808i | \(-0.506242\pi\) | ||||
−0.0196078 | + | 0.999808i | \(0.506242\pi\) | |||||||
\(762\) | −569.561 | + | 37.9458i | −0.747456 | + | 0.0497976i | ||||
\(763\) | −516.327 | + | 555.273i | −0.676707 | + | 0.727750i | ||||
\(764\) | 275.336 | 0.360387 | ||||||||
\(765\) | −420.443 | + | 184.512i | −0.549599 | + | 0.241193i | ||||
\(766\) | − | 930.211i | − | 1.21437i | ||||||
\(767\) | 831.941 | + | 831.941i | 1.08467 | + | 1.08467i | ||||
\(768\) | −47.8938 | + | 3.19082i | −0.0623618 | + | 0.00415472i | ||||
\(769\) | −331.944 | −0.431656 | −0.215828 | − | 0.976431i | \(-0.569245\pi\) | ||||
−0.215828 | + | 0.976431i | \(0.569245\pi\) | |||||||
\(770\) | 295.953 | + | 149.804i | 0.384354 | + | 0.194551i | ||||
\(771\) | 69.3954 | − | 79.3021i | 0.0900071 | − | 0.102856i | ||||
\(772\) | −376.009 | + | 376.009i | −0.487058 | + | 0.487058i | ||||
\(773\) | 221.297 | + | 221.297i | 0.286284 | + | 0.286284i | 0.835609 | − | 0.549325i | \(-0.185115\pi\) |
−0.549325 | + | 0.835609i | \(0.685115\pi\) | |||||||
\(774\) | 101.022 | + | 754.795i | 0.130519 | + | 0.975187i | ||||
\(775\) | −877.919 | + | 551.624i | −1.13280 | + | 0.711772i | ||||
\(776\) | 226.890 | 0.292384 | ||||||||
\(777\) | −1118.50 | + | 115.447i | −1.43951 | + | 0.148581i | ||||
\(778\) | −120.366 | − | 120.366i | −0.154712 | − | 0.154712i | ||||
\(779\) | 598.367 | 0.768123 | ||||||||
\(780\) | 230.960 | + | 638.621i | 0.296103 | + | 0.818745i | ||||
\(781\) | 863.627 | 1.10580 | ||||||||
\(782\) | −169.108 | + | 169.108i | −0.216251 | + | 0.216251i | ||||
\(783\) | 163.492 | − | 33.0689i | 0.208802 | − | 0.0422336i | ||||
\(784\) | −14.2278 | − | 195.483i | −0.0181478 | − | 0.249340i | ||||
\(785\) | −74.6433 | − | 259.096i | −0.0950870 | − | 0.330059i | ||||
\(786\) | −225.058 | − | 196.943i | −0.286334 | − | 0.250564i | ||||
\(787\) | 866.889 | + | 866.889i | 1.10151 | + | 1.10151i | 0.994229 | + | 0.107282i | \(0.0342149\pi\) |
0.107282 | + | 0.994229i | \(0.465785\pi\) | |||||||
\(788\) | 4.60854 | − | 4.60854i | 0.00584840 | − | 0.00584840i | ||||
\(789\) | 615.254 | − | 703.086i | 0.779790 | − | 0.891110i | ||||
\(790\) | 175.182 | − | 50.4683i | 0.221749 | − | 0.0638839i | ||||
\(791\) | 173.624 | − | 6.31010i | 0.219500 | − | 0.00797737i | ||||
\(792\) | −135.563 | − | 103.559i | −0.171165 | − | 0.130756i | ||||
\(793\) | 240.232 | + | 240.232i | 0.302941 | + | 0.302941i | ||||
\(794\) | − | 625.735i | − | 0.788080i | ||||||
\(795\) | −886.129 | + | 320.473i | −1.11463 | + | 0.403111i | ||||
\(796\) | − | 532.564i | − | 0.669051i | ||||||
\(797\) | −258.945 | + | 258.945i | −0.324900 | + | 0.324900i | −0.850643 | − | 0.525743i | \(-0.823787\pi\) |
0.525743 | + | 0.850643i | \(0.323787\pi\) | |||||||
\(798\) | 24.5853 | + | 238.192i | 0.0308086 | + | 0.298486i | ||||
\(799\) | 568.753i | 0.711831i | ||||||||
\(800\) | −31.4703 | + | 137.875i | −0.0393379 | + | 0.172344i | ||||
\(801\) | −38.8045 | − | 289.932i | −0.0484451 | − | 0.361963i | ||||
\(802\) | −641.900 | + | 641.900i | −0.800374 | + | 0.800374i | ||||
\(803\) | −363.275 | − | 363.275i | −0.452397 | − | 0.452397i | ||||
\(804\) | 247.185 | + | 216.306i | 0.307443 | + | 0.269037i | ||||
\(805\) | 517.560 | + | 261.976i | 0.642931 | + | 0.325436i | ||||
\(806\) | 1327.70i | 1.64727i | ||||||||
\(807\) | 50.1080 | + | 752.113i | 0.0620916 | + | 0.931987i | ||||
\(808\) | 126.613 | − | 126.613i | 0.156699 | − | 0.156699i | ||||
\(809\) | −1378.37 | −1.70380 | −0.851898 | − | 0.523707i | \(-0.824549\pi\) | ||||
−0.851898 | + | 0.523707i | \(0.824549\pi\) | |||||||
\(810\) | −297.708 | − | 489.306i | −0.367540 | − | 0.604081i | ||||
\(811\) | 1011.53i | 1.24726i | 0.781720 | + | 0.623630i | \(0.214343\pi\) | ||||
−0.781720 | + | 0.623630i | \(0.785657\pi\) | |||||||
\(812\) | −58.8964 | + | 63.3388i | −0.0725325 | + | 0.0780035i | ||||
\(813\) | 20.1941 | + | 303.111i | 0.0248391 | + | 0.372831i | ||||
\(814\) | − | 507.463i | − | 0.623419i | ||||||
\(815\) | −120.799 | − | 419.308i | −0.148219 | − | 0.514488i | ||||
\(816\) | −80.6310 | + | 92.1417i | −0.0988126 | + | 0.112919i | ||||
\(817\) | 341.118 | + | 341.118i | 0.417526 | + | 0.417526i | ||||
\(818\) | 134.590 | + | 134.590i | 0.164535 | + | 0.164535i | ||||
\(819\) | 1405.71 | − | 240.397i | 1.71637 | − | 0.293525i | ||||
\(820\) | 358.980 | − | 649.520i | 0.437781 | − | 0.792097i | ||||
\(821\) | 423.217i | 0.515490i | 0.966213 | + | 0.257745i | \(0.0829794\pi\) | ||||
−0.966213 | + | 0.257745i | \(0.917021\pi\) | |||||||
\(822\) | −13.4099 | − | 201.280i | −0.0163137 | − | 0.244866i | ||||
\(823\) | −538.152 | − | 538.152i | −0.653891 | − | 0.653891i | 0.300037 | − | 0.953928i | \(-0.403001\pi\) |
−0.953928 | + | 0.300037i | \(0.903001\pi\) | |||||||
\(824\) | − | 165.645i | − | 0.201026i | ||||||
\(825\) | −406.858 | + | 295.101i | −0.493162 | + | 0.357698i | ||||
\(826\) | 514.186 | − | 18.6873i | 0.622502 | − | 0.0226238i | ||||
\(827\) | −632.746 | − | 632.746i | −0.765110 | − | 0.765110i | 0.212131 | − | 0.977241i | \(-0.431960\pi\) |
−0.977241 | + | 0.212131i | \(0.931960\pi\) | |||||||
\(828\) | −237.071 | − | 181.102i | −0.286317 | − | 0.218723i | ||||
\(829\) | −376.988 | −0.454750 | −0.227375 | − | 0.973807i | \(-0.573014\pi\) | ||||
−0.227375 | + | 0.973807i | \(0.573014\pi\) | |||||||
\(830\) | 134.077 | − | 242.593i | 0.161539 | − | 0.292280i | ||||
\(831\) | 833.462 | − | 952.444i | 1.00296 | − | 1.14614i | ||||
\(832\) | 128.053 | + | 128.053i | 0.153909 | + | 0.153909i | ||||
\(833\) | −378.256 | − | 326.931i | −0.454089 | − | 0.392474i | ||||
\(834\) | −371.570 | − | 325.152i | −0.445528 | − | 0.389871i | ||||
\(835\) | 1102.46 | − | 317.610i | 1.32032 | − | 0.380371i | ||||
\(836\) | −108.067 | −0.129267 | ||||||||
\(837\) | −221.999 | − | 1097.56i | −0.265232 | − | 1.31130i | ||||
\(838\) | 268.374 | − | 268.374i | 0.320255 | − | 0.320255i | ||||
\(839\) | − | 30.3808i | − | 0.0362107i | −0.999836 | − | 0.0181054i | \(-0.994237\pi\) | ||
0.999836 | − | 0.0181054i | \(-0.00576343\pi\) | |||||||
\(840\) | 273.303 | + | 116.212i | 0.325361 | + | 0.138348i | ||||
\(841\) | −802.834 | −0.954618 | ||||||||
\(842\) | 28.9266 | + | 28.9266i | 0.0343546 | + | 0.0343546i | ||||
\(843\) | −21.0034 | − | 315.258i | −0.0249151 | − | 0.373972i | ||||
\(844\) | 208.315i | 0.246819i | ||||||||
\(845\) | 830.603 | − | 1502.85i | 0.982962 | − | 1.77852i | ||||
\(846\) | −703.210 | + | 94.1175i | −0.831218 | + | 0.111250i | ||||
\(847\) | −390.057 | − | 362.699i | −0.460516 | − | 0.428216i | ||||
\(848\) | −177.682 | + | 177.682i | −0.209530 | + | 0.209530i | ||||
\(849\) | 575.469 | − | 657.621i | 0.677819 | − | 0.774583i | ||||
\(850\) | 191.923 | + | 305.450i | 0.225792 | + | 0.359353i | ||||
\(851\) | − | 887.446i | − | 1.04283i | ||||||
\(852\) | 771.515 | − | 51.4006i | 0.905534 | − | 0.0603293i | ||||
\(853\) | 396.677 | − | 396.677i | 0.465038 | − | 0.465038i | −0.435265 | − | 0.900303i | \(-0.643345\pi\) |
0.900303 | + | 0.435265i | \(0.143345\pi\) | |||||||
\(854\) | 148.477 | − | 5.39616i | 0.173860 | − | 0.00631868i | ||||
\(855\) | −338.035 | − | 131.833i | −0.395362 | − | 0.154190i | ||||
\(856\) | 15.8693 | 0.0185389 | ||||||||
\(857\) | 303.815 | − | 303.815i | 0.354510 | − | 0.354510i | −0.507274 | − | 0.861785i | \(-0.669347\pi\) |
0.861785 | + | 0.507274i | \(0.169347\pi\) | |||||||
\(858\) | 42.7841 | + | 642.184i | 0.0498650 | + | 0.748466i | ||||
\(859\) | −139.382 | −0.162261 | −0.0811304 | − | 0.996703i | \(-0.525853\pi\) | ||||
−0.0811304 | + | 0.996703i | \(0.525853\pi\) | |||||||
\(860\) | 574.928 | − | 165.631i | 0.668520 | − | 0.192595i | ||||
\(861\) | −1209.31 | − | 983.027i | −1.40454 | − | 1.14173i | ||||
\(862\) | −276.630 | + | 276.630i | −0.320917 | + | 0.320917i | ||||
\(863\) | −698.585 | + | 698.585i | −0.809484 | + | 0.809484i | −0.984556 | − | 0.175072i | \(-0.943984\pi\) |
0.175072 | + | 0.984556i | \(0.443984\pi\) | |||||||
\(864\) | −127.267 | − | 84.4452i | −0.147300 | − | 0.0977375i | ||||
\(865\) | 177.586 | + | 616.422i | 0.205301 | + | 0.712627i | ||||
\(866\) | 499.634 | 0.576945 | ||||||||
\(867\) | −36.8725 | − | 553.451i | −0.0425288 | − | 0.638352i | ||||
\(868\) | 425.207 | + | 395.384i | 0.489870 | + | 0.455512i | ||||
\(869\) | 172.778 | 0.198824 | ||||||||
\(870\) | −44.5707 | − | 123.241i | −0.0512306 | − | 0.141656i | ||||
\(871\) | − | 1239.22i | − | 1.42276i | ||||||
\(872\) | −216.639 | − | 216.639i | −0.248439 | − | 0.248439i | ||||
\(873\) | 573.712 | + | 438.268i | 0.657172 | + | 0.502026i | ||||
\(874\) | −188.987 | −0.216233 | ||||||||
\(875\) | 558.980 | − | 673.176i | 0.638835 | − | 0.769344i | ||||
\(876\) | −346.150 | − | 302.908i | −0.395148 | − | 0.345785i | ||||
\(877\) | 122.285 | − | 122.285i | 0.139435 | − | 0.139435i | −0.633944 | − | 0.773379i | \(-0.718565\pi\) |
0.773379 | + | 0.633944i | \(0.218565\pi\) | |||||||
\(878\) | −519.817 | − | 519.817i | −0.592047 | − | 0.592047i | ||||
\(879\) | 393.107 | + | 343.999i | 0.447220 | + | 0.391352i | ||||
\(880\) | −64.8332 | + | 117.306i | −0.0736741 | + | 0.133302i | ||||
\(881\) | −75.7345 | −0.0859643 | −0.0429821 | − | 0.999076i | \(-0.513686\pi\) | ||||
−0.0429821 | + | 0.999076i | \(0.513686\pi\) | |||||||
\(882\) | 341.626 | − | 521.780i | 0.387331 | − | 0.591587i | ||||
\(883\) | −1004.90 | − | 1004.90i | −1.13805 | − | 1.13805i | −0.988799 | − | 0.149255i | \(-0.952313\pi\) |
−0.149255 | − | 0.988799i | \(-0.547687\pi\) | |||||||
\(884\) | 461.939 | 0.522555 | ||||||||
\(885\) | −330.928 | + | 705.904i | −0.373930 | + | 0.797632i | ||||
\(886\) | 777.176 | 0.877173 | ||||||||
\(887\) | −265.442 | + | 265.442i | −0.299258 | + | 0.299258i | −0.840723 | − | 0.541465i | \(-0.817870\pi\) |
0.541465 | + | 0.840723i | \(0.317870\pi\) | |||||||
\(888\) | −30.2027 | − | 453.339i | −0.0340121 | − | 0.510517i | ||||
\(889\) | 941.190 | − | 34.2061i | 1.05871 | − | 0.0384770i | ||||
\(890\) | −220.842 | + | 63.6224i | −0.248137 | + | 0.0714859i | ||||
\(891\) | −142.745 | − | 523.716i | −0.160208 | − | 0.587784i | ||||
\(892\) | −5.19500 | − | 5.19500i | −0.00582399 | − | 0.00582399i | ||||
\(893\) | −317.806 | + | 317.806i | −0.355885 | + | 0.355885i | ||||
\(894\) | −412.238 | − | 360.740i | −0.461117 | − | 0.403512i | ||||
\(895\) | 102.203 | + | 56.4862i | 0.114193 | + | 0.0631131i | ||||
\(896\) | 79.1437 | − | 2.87635i | 0.0883300 | − | 0.00321022i | ||||
\(897\) | 74.8205 | + | 1123.05i | 0.0834119 | + | 1.25200i | ||||
\(898\) | −283.968 | − | 283.968i | −0.316223 | − | 0.316223i | ||||
\(899\) | − | 256.218i | − | 0.285004i | ||||||
\(900\) | −345.901 | + | 287.842i | −0.384334 | + | 0.319824i | ||||
\(901\) | 640.970i | 0.711399i | ||||||||
\(902\) | 497.331 | − | 497.331i | 0.551365 | − | 0.551365i | ||||
\(903\) | −129.001 | − | 1249.81i | −0.142858 | − | 1.38407i | ||||
\(904\) | 70.2011i | 0.0776560i | ||||||||
\(905\) | −319.905 | + | 578.819i | −0.353486 | + | 0.639579i | ||||
\(906\) | −165.163 | − | 144.530i | −0.182299 | − | 0.159525i | ||||
\(907\) | 149.728 | − | 149.728i | 0.165081 | − | 0.165081i | −0.619732 | − | 0.784813i | \(-0.712759\pi\) |
0.784813 | + | 0.619732i | \(0.212759\pi\) | |||||||
\(908\) | 120.232 | + | 120.232i | 0.132415 | + | 0.132415i | ||||
\(909\) | 564.721 | − | 75.5822i | 0.621255 | − | 0.0831487i | ||||
\(910\) | −349.079 | − | 1064.70i | −0.383603 | − | 1.17000i | ||||
\(911\) | 1426.12i | 1.56544i | 0.622373 | + | 0.782721i | \(0.286169\pi\) | ||||
−0.622373 | + | 0.782721i | \(0.713831\pi\) | |||||||
\(912\) | −96.5413 | + | 6.43186i | −0.105857 | + | 0.00705248i | ||||
\(913\) | 185.751 | − | 185.751i | 0.203451 | − | 0.203451i | ||||
\(914\) | 402.736 | 0.440630 | ||||||||
\(915\) | −95.5591 | + | 203.837i | −0.104436 | + | 0.222773i | ||||
\(916\) | 690.735i | 0.754078i | ||||||||
\(917\) | 361.347 | + | 336.003i | 0.394054 | + | 0.366416i | ||||
\(918\) | −381.867 | + | 77.2389i | −0.415977 | + | 0.0841382i | ||||
\(919\) | − | 816.634i | − | 0.888612i | −0.895875 | − | 0.444306i | \(-0.853450\pi\) | ||
0.895875 | − | 0.444306i | \(-0.146550\pi\) | |||||||
\(920\) | −113.380 | + | 205.143i | −0.123239 | + | 0.222982i | ||||
\(921\) | 749.187 | + | 655.596i | 0.813450 | + | 0.711831i | ||||
\(922\) | 553.509 | + | 553.509i | 0.600335 | + | 0.600335i | ||||
\(923\) | −2062.78 | − | 2062.78i | −2.23487 | − | 2.23487i | ||||
\(924\) | 218.406 | + | 177.538i | 0.236370 | + | 0.192141i | ||||
\(925\) | −1305.06 | − | 297.882i | −1.41087 | − | 0.322034i | ||||
\(926\) | − | 1149.73i | − | 1.24161i | ||||||
\(927\) | 319.967 | − | 418.850i | 0.345164 | − | 0.451834i | ||||
\(928\) | −24.7116 | − | 24.7116i | −0.0266288 | − | 0.0266288i | ||||
\(929\) | − | 238.799i | − | 0.257050i | −0.991706 | − | 0.128525i | \(-0.958976\pi\) | ||
0.991706 | − | 0.128525i | \(-0.0410242\pi\) | |||||||
\(930\) | −827.342 | + | 299.212i | −0.889615 | + | 0.321734i | ||||
\(931\) | −28.6796 | − | 394.042i | −0.0308051 | − | 0.423246i | ||||
\(932\) | 517.282 | + | 517.282i | 0.555024 | + | 0.555024i | ||||
\(933\) | −936.280 | + | 62.3777i | −1.00352 | + | 0.0668571i | ||||
\(934\) | 1257.85 | 1.34673 | ||||||||
\(935\) | 94.6450 | + | 328.525i | 0.101225 | + | 0.351364i | ||||
\(936\) | 76.4418 | + | 571.144i | 0.0816686 | + | 0.610197i | ||||
\(937\) | 397.595 | + | 397.595i | 0.424328 | + | 0.424328i | 0.886691 | − | 0.462363i | \(-0.152998\pi\) |
−0.462363 | + | 0.886691i | \(0.652998\pi\) | |||||||
\(938\) | −396.873 | − | 369.037i | −0.423105 | − | 0.393429i | ||||
\(939\) | −672.013 | + | 767.948i | −0.715669 | + | 0.817836i | ||||
\(940\) | 154.312 | + | 535.636i | 0.164161 | + | 0.569825i | ||||
\(941\) | −64.3259 | −0.0683591 | −0.0341796 | − | 0.999416i | \(-0.510882\pi\) | ||||
−0.0341796 | + | 0.999416i | \(0.510882\pi\) | |||||||
\(942\) | −15.2091 | − | 228.286i | −0.0161455 | − | 0.242342i | ||||
\(943\) | 869.728 | − | 869.728i | 0.922299 | − | 0.922299i | ||||
\(944\) | 207.900i | 0.220233i | ||||||||
\(945\) | 466.594 | + | 821.776i | 0.493750 | + | 0.869604i | ||||
\(946\) | 567.039 | 0.599407 | ||||||||
\(947\) | 74.9155 | + | 74.9155i | 0.0791083 | + | 0.0791083i | 0.745554 | − | 0.666445i | \(-0.232185\pi\) |
−0.666445 | + | 0.745554i | \(0.732185\pi\) | |||||||
\(948\) | 154.350 | − | 10.2833i | 0.162817 | − | 0.0108473i | ||||
\(949\) | 1735.37i | 1.82863i | ||||||||
\(950\) | −63.4358 | + | 277.920i | −0.0667745 | + | 0.292548i | ||||
\(951\) | 545.416 | + | 477.281i | 0.573518 | + | 0.501872i | ||||
\(952\) | 137.564 | − | 147.940i | 0.144500 | − | 0.155399i | ||||
\(953\) | −445.618 | + | 445.618i | −0.467595 | + | 0.467595i | −0.901134 | − | 0.433540i | \(-0.857264\pi\) |
0.433540 | + | 0.901134i | \(0.357264\pi\) | |||||||
\(954\) | −792.500 | + | 106.068i | −0.830713 | + | 0.111183i | ||||
\(955\) | 332.965 | − | 602.449i | 0.348655 | − | 0.630837i | ||||
\(956\) | − | 419.695i | − | 0.439011i | ||||||
\(957\) | −8.25647 | − | 123.928i | −0.00862745 | − | 0.129497i | ||||
\(958\) | 229.796 | − | 229.796i | 0.239871 | − | 0.239871i | ||||
\(959\) | 12.0883 | + | 332.612i | 0.0126051 | + | 0.346832i | ||||
\(960\) | −50.9366 | + | 108.653i | −0.0530589 | + | 0.113180i | ||||
\(961\) | −759.049 | −0.789853 | ||||||||
\(962\) | −1212.08 | + | 1212.08i | −1.25996 | + | 1.25996i | ||||
\(963\) | 40.1269 | + | 30.6537i | 0.0416687 | + | 0.0318314i | ||||
\(964\) | −348.289 | −0.361296 | ||||||||
\(965\) | 368.018 | + | 1277.44i | 0.381366 | + | 1.32377i | ||||
\(966\) | 381.947 | + | 310.477i | 0.395390 | + | 0.321405i | ||||
\(967\) | −1035.26 | + | 1035.26i | −1.07059 | + | 1.07059i | −0.0732796 | + | 0.997311i | \(0.523347\pi\) |
−0.997311 | + | 0.0732796i | \(0.976653\pi\) | |||||||
\(968\) | 152.180 | − | 152.180i | 0.157211 | − | 0.157211i | ||||
\(969\) | −162.531 | + | 185.733i | −0.167731 | + | 0.191675i | ||||
\(970\) | 274.379 | − | 496.447i | 0.282865 | − | 0.511801i | ||||
\(971\) | 1533.72 | 1.57952 | 0.789762 | − | 0.613413i | \(-0.210204\pi\) | ||||
0.789762 | + | 0.613413i | \(0.210204\pi\) | |||||||
\(972\) | −158.690 | − | 459.362i | −0.163262 | − | 0.472595i | ||||
\(973\) | 596.582 | + | 554.739i | 0.613137 | + | 0.570133i | ||||
\(974\) | −116.042 | −0.119140 | ||||||||
\(975\) | 1676.64 | + | 266.934i | 1.71963 | + | 0.273778i | ||||
\(976\) | 60.0333i | 0.0615095i | ||||||||
\(977\) | −975.493 | − | 975.493i | −0.998458 | − | 0.998458i | 0.00154127 | − | 0.999999i | \(-0.499509\pi\) |
−0.999999 | + | 0.00154127i | \(0.999509\pi\) | |||||||
\(978\) | −24.6136 | − | 369.446i | −0.0251672 | − | 0.377757i | ||||
\(979\) | −217.811 | −0.222484 | ||||||||
\(980\) | −444.933 | − | 205.267i | −0.454013 | − | 0.209456i | ||||
\(981\) | −129.324 | − | 966.259i | −0.131829 | − | 0.984973i | ||||
\(982\) | 105.182 | − | 105.182i | 0.107110 | − | 0.107110i | ||||
\(983\) | 518.969 | + | 518.969i | 0.527944 | + | 0.527944i | 0.919959 | − | 0.392015i | \(-0.128222\pi\) |
−0.392015 | + | 0.919959i | \(0.628222\pi\) | |||||||
\(984\) | 414.688 | − | 473.887i | 0.421431 | − | 0.481593i | ||||
\(985\) | −4.51060 | − | 15.6569i | −0.00457928 | − | 0.0158953i | ||||
\(986\) | −89.1447 | −0.0904105 | ||||||||
\(987\) | 1164.40 | − | 120.185i | 1.17973 | − | 0.121768i | ||||
\(988\) | 258.120 | + | 258.120i | 0.261255 | + | 0.261255i | ||||
\(989\) | 991.632 | 1.00266 | ||||||||
\(990\) | −390.529 | + | 171.384i | −0.394473 | + | 0.173115i | ||||
\(991\) | 398.566 | 0.402185 | 0.201093 | − | 0.979572i | \(-0.435551\pi\) | ||||
0.201093 | + | 0.979572i | \(0.435551\pi\) | |||||||
\(992\) | −165.894 | + | 165.894i | −0.167232 | + | 0.167232i | ||||
\(993\) | 1260.90 | − | 84.0050i | 1.26979 | − | 0.0845972i | ||||
\(994\) | −1274.92 | + | 46.3348i | −1.28261 | + | 0.0466145i | ||||
\(995\) | −1165.28 | − | 644.033i | −1.17114 | − | 0.647270i | ||||
\(996\) | 154.884 | − | 176.995i | 0.155506 | − | 0.177705i | ||||
\(997\) | 1068.24 | + | 1068.24i | 1.07146 | + | 1.07146i | 0.997242 | + | 0.0742170i | \(0.0236457\pi\) |
0.0742170 | + | 0.997242i | \(0.476354\pi\) | |||||||
\(998\) | −29.9809 | + | 29.9809i | −0.0300409 | + | 0.0300409i | ||||
\(999\) | 799.315 | − | 1204.65i | 0.800115 | − | 1.20586i |
(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 | 210.3.k.a.83.1 | ✓ | 32 | |
3.2 | odd | 2 | 210.3.k.b.83.8 | yes | 32 | ||
5.2 | odd | 4 | 210.3.k.b.167.9 | yes | 32 | ||
7.6 | odd | 2 | inner | 210.3.k.a.83.16 | yes | 32 | |
15.2 | even | 4 | inner | 210.3.k.a.167.16 | yes | 32 | |
21.20 | even | 2 | 210.3.k.b.83.9 | yes | 32 | ||
35.27 | even | 4 | 210.3.k.b.167.8 | yes | 32 | ||
105.62 | odd | 4 | inner | 210.3.k.a.167.1 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.k.a.83.1 | ✓ | 32 | 1.1 | even | 1 | trivial | |
210.3.k.a.83.16 | yes | 32 | 7.6 | odd | 2 | inner | |
210.3.k.a.167.1 | yes | 32 | 105.62 | odd | 4 | inner | |
210.3.k.a.167.16 | yes | 32 | 15.2 | even | 4 | inner | |
210.3.k.b.83.8 | yes | 32 | 3.2 | odd | 2 | ||
210.3.k.b.83.9 | yes | 32 | 21.20 | even | 2 | ||
210.3.k.b.167.8 | yes | 32 | 35.27 | even | 4 | ||
210.3.k.b.167.9 | yes | 32 | 5.2 | odd | 4 |