Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,6,Mod(10,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.10");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.c (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.93420133308\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(15\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 10.15 | ||
Character | \(\chi\) | \(=\) | 37.10 |
Dual form | 37.6.c.a.26.15 |
$q$-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 \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.58532 | − | 9.67406i | 0.987355 | − | 1.71015i | 0.356388 | − | 0.934338i | \(-0.384008\pi\) |
0.630966 | − | 0.775810i | \(-0.282659\pi\) | |||||||
\(3\) | −1.95144 | − | 3.38000i | −0.125185 | − | 0.216827i | 0.796620 | − | 0.604480i | \(-0.206619\pi\) |
−0.921805 | + | 0.387653i | \(0.873286\pi\) | |||||||
\(4\) | −46.3916 | − | 80.3526i | −1.44974 | − | 2.51102i | ||||
\(5\) | −1.46163 | − | 2.53162i | −0.0261465 | − | 0.0452871i | 0.852656 | − | 0.522473i | \(-0.174990\pi\) |
−0.878803 | + | 0.477186i | \(0.841657\pi\) | |||||||
\(6\) | −43.5978 | −0.494409 | ||||||||
\(7\) | 81.6887 | + | 141.489i | 0.630110 | + | 1.09138i | 0.987529 | + | 0.157439i | \(0.0503237\pi\) |
−0.357418 | + | 0.933944i | \(0.616343\pi\) | |||||||
\(8\) | −678.988 | −3.75091 | ||||||||
\(9\) | 113.884 | − | 197.252i | 0.468657 | − | 0.811738i | ||||
\(10\) | −32.6548 | −0.103264 | ||||||||
\(11\) | 364.183 | 0.907483 | 0.453742 | − | 0.891133i | \(-0.350089\pi\) | ||||
0.453742 | + | 0.891133i | \(0.350089\pi\) | |||||||
\(12\) | −181.061 | + | 313.607i | −0.362972 | + | 0.628685i | ||||
\(13\) | −397.935 | − | 689.244i | −0.653061 | − | 1.13113i | −0.982376 | − | 0.186915i | \(-0.940151\pi\) |
0.329315 | − | 0.944220i | \(-0.393182\pi\) | |||||||
\(14\) | 1825.03 | 2.48857 | ||||||||
\(15\) | −5.70460 | + | 9.88065i | −0.00654631 | + | 0.0113385i | ||||
\(16\) | −2307.83 | + | 3997.28i | −2.25374 | + | 3.90360i | ||||
\(17\) | 0.520891 | − | 0.902211i | 0.000437144 | − | 0.000757156i | −0.865807 | − | 0.500379i | \(-0.833194\pi\) |
0.866244 | + | 0.499621i | \(0.166528\pi\) | |||||||
\(18\) | −1272.15 | − | 2203.44i | −0.925462 | − | 1.60295i | ||||
\(19\) | 210.290 | + | 364.234i | 0.133640 | + | 0.231471i | 0.925077 | − | 0.379780i | \(-0.124000\pi\) |
−0.791437 | + | 0.611250i | \(0.790667\pi\) | |||||||
\(20\) | −135.615 | + | 234.892i | −0.0758112 | + | 0.131309i | ||||
\(21\) | 318.822 | − | 552.216i | 0.157761 | − | 0.273250i | ||||
\(22\) | 2034.08 | − | 3523.13i | 0.896008 | − | 1.55193i | ||||
\(23\) | 2633.59 | 1.03807 | 0.519037 | − | 0.854752i | \(-0.326291\pi\) | ||||
0.519037 | + | 0.854752i | \(0.326291\pi\) | |||||||
\(24\) | 1325.01 | + | 2294.98i | 0.469559 | + | 0.813300i | ||||
\(25\) | 1558.23 | − | 2698.93i | 0.498633 | − | 0.863657i | ||||
\(26\) | −8890.38 | −2.57921 | ||||||||
\(27\) | −1837.35 | −0.485046 | ||||||||
\(28\) | 7579.34 | − | 13127.8i | 1.82699 | − | 3.16444i | ||||
\(29\) | −2798.83 | −0.617989 | −0.308995 | − | 0.951064i | \(-0.599993\pi\) | ||||
−0.308995 | + | 0.951064i | \(0.599993\pi\) | |||||||
\(30\) | 63.7240 | + | 110.373i | 0.0129271 | + | 0.0223903i | ||||
\(31\) | 5306.84 | 0.991817 | 0.495908 | − | 0.868375i | \(-0.334835\pi\) | ||||
0.495908 | + | 0.868375i | \(0.334835\pi\) | |||||||
\(32\) | 14916.2 | + | 25835.6i | 2.57503 | + | 4.46008i | ||||
\(33\) | −710.684 | − | 1230.94i | −0.113603 | − | 0.196767i | ||||
\(34\) | −5.81869 | − | 10.0783i | −0.000863233 | − | 0.00149516i | ||||
\(35\) | 238.798 | − | 413.610i | 0.0329504 | − | 0.0570717i | ||||
\(36\) | −21133.0 | −2.71772 | ||||||||
\(37\) | 3245.84 | + | 7668.67i | 0.389784 | + | 0.920907i | ||||
\(38\) | 4698.16 | 0.527799 | ||||||||
\(39\) | −1553.10 | + | 2690.04i | −0.163507 | + | 0.283203i | ||||
\(40\) | 992.432 | + | 1718.94i | 0.0980733 | + | 0.169868i | ||||
\(41\) | 6879.84 | + | 11916.2i | 0.639173 | + | 1.10708i | 0.985615 | + | 0.169009i | \(0.0540567\pi\) |
−0.346441 | + | 0.938072i | \(0.612610\pi\) | |||||||
\(42\) | −3561.44 | − | 6168.60i | −0.311532 | − | 0.539590i | ||||
\(43\) | 2630.80 | 0.216978 | 0.108489 | − | 0.994098i | \(-0.465399\pi\) | ||||
0.108489 | + | 0.994098i | \(0.465399\pi\) | |||||||
\(44\) | −16895.1 | − | 29263.1i | −1.31561 | − | 2.27871i | ||||
\(45\) | −665.825 | −0.0490150 | ||||||||
\(46\) | 14709.4 | − | 25477.5i | 1.02495 | − | 1.77526i | ||||
\(47\) | −9382.92 | −0.619575 | −0.309787 | − | 0.950806i | \(-0.600258\pi\) | ||||
−0.309787 | + | 0.950806i | \(0.600258\pi\) | |||||||
\(48\) | 18014.4 | 1.12854 | ||||||||
\(49\) | −4942.58 | + | 8560.79i | −0.294078 | + | 0.509359i | ||||
\(50\) | −17406.4 | − | 30148.8i | −0.984655 | − | 1.70547i | ||||
\(51\) | −4.06596 | −0.000218896 | ||||||||
\(52\) | −36921.7 | + | 63950.3i | −1.89353 | + | 3.27970i | ||||
\(53\) | −125.722 | + | 217.756i | −0.00614781 | + | 0.0106483i | −0.869083 | − | 0.494666i | \(-0.835290\pi\) |
0.862935 | + | 0.505315i | \(0.168624\pi\) | |||||||
\(54\) | −10262.2 | + | 17774.7i | −0.478913 | + | 0.829501i | ||||
\(55\) | −532.303 | − | 921.976i | −0.0237275 | − | 0.0410973i | ||||
\(56\) | −55465.6 | − | 96069.2i | −2.36349 | − | 4.09368i | ||||
\(57\) | 820.740 | − | 1421.56i | 0.0334594 | − | 0.0579534i | ||||
\(58\) | −15632.3 | + | 27076.0i | −0.610175 | + | 1.05685i | ||||
\(59\) | −21769.5 | + | 37705.9i | −0.814177 | + | 1.41020i | 0.0957404 | + | 0.995406i | \(0.469478\pi\) |
−0.909917 | + | 0.414790i | \(0.863855\pi\) | |||||||
\(60\) | 1058.58 | 0.0379618 | ||||||||
\(61\) | 25810.5 | + | 44705.1i | 0.888120 | + | 1.53827i | 0.842096 | + | 0.539328i | \(0.181322\pi\) |
0.0460241 | + | 0.998940i | \(0.485345\pi\) | |||||||
\(62\) | 29640.4 | − | 51338.6i | 0.979275 | − | 1.69615i | ||||
\(63\) | 37212.0 | 1.18122 | ||||||||
\(64\) | 185545. | 5.66239 | ||||||||
\(65\) | −1163.27 | + | 2014.84i | −0.0341505 | + | 0.0591505i | ||||
\(66\) | −15877.6 | −0.448668 | ||||||||
\(67\) | −10987.2 | − | 19030.4i | −0.299020 | − | 0.517918i | 0.676892 | − | 0.736082i | \(-0.263326\pi\) |
−0.975912 | + | 0.218165i | \(0.929993\pi\) | |||||||
\(68\) | −96.6600 | −0.00253498 | ||||||||
\(69\) | −5139.30 | − | 8901.53i | −0.129951 | − | 0.225083i | ||||
\(70\) | −2667.53 | − | 4620.29i | −0.0650674 | − | 0.112700i | ||||
\(71\) | −10357.8 | − | 17940.3i | −0.243850 | − | 0.422361i | 0.717957 | − | 0.696087i | \(-0.245077\pi\) |
−0.961808 | + | 0.273726i | \(0.911744\pi\) | |||||||
\(72\) | −77325.7 | + | 133932.i | −1.75789 | + | 3.04476i | ||||
\(73\) | −62069.4 | −1.36323 | −0.681617 | − | 0.731709i | \(-0.738723\pi\) | ||||
−0.681617 | + | 0.731709i | \(0.738723\pi\) | |||||||
\(74\) | 92316.2 | + | 11431.5i | 1.95974 | + | 0.242674i | ||||
\(75\) | −12163.2 | −0.249686 | ||||||||
\(76\) | 19511.4 | − | 33794.8i | 0.387485 | − | 0.671144i | ||||
\(77\) | 29749.7 | + | 51527.9i | 0.571815 | + | 0.990412i | ||||
\(78\) | 17349.1 | + | 30049.5i | 0.322879 | + | 0.559243i | ||||
\(79\) | −16972.4 | − | 29397.1i | −0.305968 | − | 0.529953i | 0.671508 | − | 0.740997i | \(-0.265647\pi\) |
−0.977476 | + | 0.211045i | \(0.932313\pi\) | |||||||
\(80\) | 13492.8 | 0.235710 | ||||||||
\(81\) | −24088.3 | − | 41722.1i | −0.407937 | − | 0.706567i | ||||
\(82\) | 153704. | 2.52436 | ||||||||
\(83\) | −1882.04 | + | 3259.79i | −0.0299870 | + | 0.0519391i | −0.880629 | − | 0.473806i | \(-0.842880\pi\) |
0.850642 | + | 0.525745i | \(0.176213\pi\) | |||||||
\(84\) | −59162.6 | −0.914849 | ||||||||
\(85\) | −3.04541 | −4.57192e−5 | ||||||||
\(86\) | 14693.9 | − | 25450.5i | 0.214235 | − | 0.371065i | ||||
\(87\) | 5461.76 | + | 9460.04i | 0.0773632 | + | 0.133997i | ||||
\(88\) | −247276. | −3.40389 | ||||||||
\(89\) | 20494.6 | − | 35497.8i | 0.274262 | − | 0.475035i | −0.695687 | − | 0.718345i | \(-0.744900\pi\) |
0.969949 | + | 0.243310i | \(0.0782332\pi\) | |||||||
\(90\) | −3718.85 | + | 6441.24i | −0.0483952 | + | 0.0838229i | ||||
\(91\) | 65013.6 | − | 112607.i | 0.823001 | − | 1.42548i | ||||
\(92\) | −122176. | − | 211616.i | −1.50493 | − | 2.60662i | ||||
\(93\) | −10356.0 | − | 17937.1i | −0.124161 | − | 0.215053i | ||||
\(94\) | −52406.6 | + | 90771.0i | −0.611740 | + | 1.05956i | ||||
\(95\) | 614.735 | − | 1064.75i | 0.00698842 | − | 0.0121043i | ||||
\(96\) | 58216.2 | − | 100833.i | 0.644712 | − | 1.11667i | ||||
\(97\) | 113320. | 1.22286 | 0.611430 | − | 0.791299i | \(-0.290595\pi\) | ||||
0.611430 | + | 0.791299i | \(0.290595\pi\) | |||||||
\(98\) | 55211.7 | + | 95629.5i | 0.580719 | + | 1.00584i | ||||
\(99\) | 41474.6 | − | 71836.1i | 0.425299 | − | 0.736639i | ||||
\(100\) | −289155. | −2.89155 | ||||||||
\(101\) | −119160. | −1.16233 | −0.581163 | − | 0.813787i | \(-0.697402\pi\) | ||||
−0.581163 | + | 0.813787i | \(0.697402\pi\) | |||||||
\(102\) | −22.7097 | + | 39.3344i | −0.000216128 | + | 0.000374345i | ||||
\(103\) | 161486. | 1.49983 | 0.749916 | − | 0.661533i | \(-0.230094\pi\) | ||||
0.749916 | + | 0.661533i | \(0.230094\pi\) | |||||||
\(104\) | 270193. | + | 467988.i | 2.44957 | + | 4.24279i | ||||
\(105\) | −1864.00 | −0.0164996 | ||||||||
\(106\) | 1404.39 | + | 2432.48i | 0.0121401 | + | 0.0210273i | ||||
\(107\) | −59005.8 | − | 102201.i | −0.498236 | − | 0.862971i | 0.501762 | − | 0.865006i | \(-0.332685\pi\) |
−0.999998 | + | 0.00203537i | \(0.999352\pi\) | |||||||
\(108\) | 85237.8 | + | 147636.i | 0.703190 | + | 1.21796i | ||||
\(109\) | −34416.9 | + | 59611.9i | −0.277464 | + | 0.480581i | −0.970754 | − | 0.240078i | \(-0.922827\pi\) |
0.693290 | + | 0.720659i | \(0.256160\pi\) | |||||||
\(110\) | −11892.3 | −0.0937099 | ||||||||
\(111\) | 19586.0 | − | 25935.9i | 0.150882 | − | 0.199800i | ||||
\(112\) | −754095. | −5.68043 | ||||||||
\(113\) | 65282.5 | − | 113073.i | 0.480951 | − | 0.833032i | −0.518810 | − | 0.854890i | \(-0.673625\pi\) |
0.999761 | + | 0.0218580i | \(0.00695816\pi\) | |||||||
\(114\) | −9168.20 | − | 15879.8i | −0.0660727 | − | 0.114441i | ||||
\(115\) | −3849.34 | − | 6667.26i | −0.0271420 | − | 0.0470113i | ||||
\(116\) | 129842. | + | 224893.i | 0.895923 | + | 1.55178i | ||||
\(117\) | −181273. | −1.22425 | ||||||||
\(118\) | 243180. | + | 421199.i | 1.60776 | + | 2.78473i | ||||
\(119\) | 170.204 | 0.00110180 | ||||||||
\(120\) | 3873.35 | − | 6708.84i | 0.0245547 | − | 0.0425299i | ||||
\(121\) | −28421.4 | −0.176474 | ||||||||
\(122\) | 576639. | 3.50756 | ||||||||
\(123\) | 26851.3 | − | 46507.7i | 0.160030 | − | 0.277180i | ||||
\(124\) | −246193. | − | 426418.i | −1.43787 | − | 2.49047i | ||||
\(125\) | −18245.4 | −0.104443 | ||||||||
\(126\) | 207841. | − | 359991.i | 1.16629 | − | 2.02007i | ||||
\(127\) | −113735. | + | 196995.i | −0.625727 | + | 1.08379i | 0.362673 | + | 0.931916i | \(0.381864\pi\) |
−0.988400 | + | 0.151874i | \(0.951469\pi\) | |||||||
\(128\) | 559011. | − | 968236.i | 3.01575 | − | 5.22344i | ||||
\(129\) | −5133.86 | − | 8892.11i | −0.0271625 | − | 0.0470468i | ||||
\(130\) | 12994.5 | + | 22507.1i | 0.0674374 | + | 0.116805i | ||||
\(131\) | −60077.9 | + | 104058.i | −0.305870 | + | 0.529782i | −0.977455 | − | 0.211146i | \(-0.932280\pi\) |
0.671585 | + | 0.740928i | \(0.265614\pi\) | |||||||
\(132\) | −65939.6 | + | 114211.i | −0.329391 | + | 0.570521i | ||||
\(133\) | −34356.7 | + | 59507.5i | −0.168416 | + | 0.291704i | ||||
\(134\) | −245468. | −1.18095 | ||||||||
\(135\) | 2685.54 | + | 4651.49i | 0.0126823 | + | 0.0219663i | ||||
\(136\) | −353.679 | + | 612.590i | −0.00163969 | + | 0.00284003i | ||||
\(137\) | −154223. | −0.702015 | −0.351008 | − | 0.936373i | \(-0.614161\pi\) | ||||
−0.351008 | + | 0.936373i | \(0.614161\pi\) | |||||||
\(138\) | −114819. | −0.513233 | ||||||||
\(139\) | 15182.2 | − | 26296.3i | 0.0666495 | − | 0.115440i | −0.830775 | − | 0.556608i | \(-0.812102\pi\) |
0.897425 | + | 0.441168i | \(0.145436\pi\) | |||||||
\(140\) | −44312.9 | −0.191078 | ||||||||
\(141\) | 18310.3 | + | 31714.3i | 0.0775616 | + | 0.134341i | ||||
\(142\) | −231407. | −0.963067 | ||||||||
\(143\) | −144921. | − | 251011.i | −0.592642 | − | 1.02649i | ||||
\(144\) | 525649. | + | 910451.i | 2.11247 | + | 3.65890i | ||||
\(145\) | 4090.86 | + | 7085.58i | 0.0161583 | + | 0.0279869i | ||||
\(146\) | −346678. | + | 600463.i | −1.34600 | + | 2.33133i | ||||
\(147\) | 38580.7 | 0.147257 | ||||||||
\(148\) | 465618. | − | 616574.i | 1.74733 | − | 2.31383i | ||||
\(149\) | 86305.1 | 0.318472 | 0.159236 | − | 0.987241i | \(-0.449097\pi\) | ||||
0.159236 | + | 0.987241i | \(0.449097\pi\) | |||||||
\(150\) | −67935.2 | + | 117667.i | −0.246528 | + | 0.427000i | ||||
\(151\) | 73951.5 | + | 128088.i | 0.263940 | + | 0.457157i | 0.967285 | − | 0.253691i | \(-0.0816447\pi\) |
−0.703346 | + | 0.710848i | \(0.748311\pi\) | |||||||
\(152\) | −142785. | − | 247310.i | −0.501271 | − | 0.868227i | ||||
\(153\) | −118.642 | − | 205.494i | −0.000409742 | − | 0.000709694i | ||||
\(154\) | 664646. | 2.25833 | ||||||||
\(155\) | −7756.65 | − | 13434.9i | −0.0259325 | − | 0.0449165i | ||||
\(156\) | 288203. | 0.948170 | ||||||||
\(157\) | −288931. | + | 500444.i | −0.935504 | + | 1.62034i | −0.161771 | + | 0.986828i | \(0.551720\pi\) |
−0.773733 | + | 0.633512i | \(0.781613\pi\) | |||||||
\(158\) | −379186. | −1.20840 | ||||||||
\(159\) | 981.355 | 0.00307846 | ||||||||
\(160\) | 43604.0 | − | 75524.3i | 0.134656 | − | 0.233231i | ||||
\(161\) | 215134. | + | 372623.i | 0.654101 | + | 1.13294i | ||||
\(162\) | −538162. | −1.61111 | ||||||||
\(163\) | 51624.8 | − | 89416.8i | 0.152191 | − | 0.263603i | −0.779842 | − | 0.625977i | \(-0.784700\pi\) |
0.932033 | + | 0.362374i | \(0.118034\pi\) | |||||||
\(164\) | 638334. | − | 1.10563e6i | 1.85327 | − | 3.20995i | ||||
\(165\) | −2077.52 | + | 3598.37i | −0.00594067 | + | 0.0102895i | ||||
\(166\) | 21023.6 | + | 36413.9i | 0.0592157 | + | 0.102565i | ||||
\(167\) | −248945. | − | 431185.i | −0.690735 | − | 1.19639i | −0.971597 | − | 0.236640i | \(-0.923954\pi\) |
0.280863 | − | 0.959748i | \(-0.409379\pi\) | |||||||
\(168\) | −216476. | + | 374948.i | −0.591748 | + | 1.02494i | ||||
\(169\) | −131058. | + | 226999.i | −0.352977 | + | 0.611375i | ||||
\(170\) | −17.0096 | + | 29.4615i | −4.51411e−5 | + | 7.81866e-5i | ||||
\(171\) | 95794.6 | 0.250525 | ||||||||
\(172\) | −122047. | − | 211392.i | −0.314562 | − | 0.544837i | ||||
\(173\) | −130263. | + | 225622.i | −0.330906 | + | 0.573146i | −0.982690 | − | 0.185259i | \(-0.940688\pi\) |
0.651784 | + | 0.758405i | \(0.274021\pi\) | |||||||
\(174\) | 122023. | 0.305539 | ||||||||
\(175\) | 509158. | 1.25677 | ||||||||
\(176\) | −840475. | + | 1.45574e6i | −2.04523 | + | 3.54245i | ||||
\(177\) | 169928. | 0.407692 | ||||||||
\(178\) | −228938. | − | 396533.i | −0.541587 | − | 0.938057i | ||||
\(179\) | 483532. | 1.12796 | 0.563978 | − | 0.825790i | \(-0.309270\pi\) | ||||
0.563978 | + | 0.825790i | \(0.309270\pi\) | |||||||
\(180\) | 30888.7 | + | 53500.8i | 0.0710589 | + | 0.123078i | ||||
\(181\) | 188724. | + | 326880.i | 0.428185 | + | 0.741638i | 0.996712 | − | 0.0810267i | \(-0.0258199\pi\) |
−0.568527 | + | 0.822665i | \(0.692487\pi\) | |||||||
\(182\) | −726243. | − | 1.25789e6i | −1.62519 | − | 2.81491i | ||||
\(183\) | 100735. | − | 174479.i | 0.222359 | − | 0.385137i | ||||
\(184\) | −1.78817e6 | −3.89372 | ||||||||
\(185\) | 14669.9 | − | 19426.0i | 0.0315137 | − | 0.0417306i | ||||
\(186\) | −231366. | −0.490363 | ||||||||
\(187\) | 189.700 | − | 328.570i | 0.000396701 | − | 0.000687107i | ||||
\(188\) | 435289. | + | 753943.i | 0.898221 | + | 1.55576i | ||||
\(189\) | −150091. | − | 259965.i | −0.305633 | − | 0.529372i | ||||
\(190\) | −6866.99 | − | 11894.0i | −0.0138001 | − | 0.0239025i | ||||
\(191\) | −307026. | −0.608964 | −0.304482 | − | 0.952518i | \(-0.598483\pi\) | ||||
−0.304482 | + | 0.952518i | \(0.598483\pi\) | |||||||
\(192\) | −362081. | − | 627143.i | −0.708847 | − | 1.22776i | ||||
\(193\) | −262414. | −0.507099 | −0.253550 | − | 0.967322i | \(-0.581598\pi\) | ||||
−0.253550 | + | 0.967322i | \(0.581598\pi\) | |||||||
\(194\) | 632927. | − | 1.09626e6i | 1.20740 | − | 2.09127i | ||||
\(195\) | 9080.23 | 0.0171006 | ||||||||
\(196\) | 917176. | 1.70535 | ||||||||
\(197\) | 113555. | − | 196683.i | 0.208469 | − | 0.361078i | −0.742764 | − | 0.669554i | \(-0.766485\pi\) |
0.951232 | + | 0.308476i | \(0.0998188\pi\) | |||||||
\(198\) | −463298. | − | 802455.i | −0.839841 | − | 1.45465i | ||||
\(199\) | 438665. | 0.785236 | 0.392618 | − | 0.919702i | \(-0.371570\pi\) | ||||
0.392618 | + | 0.919702i | \(0.371570\pi\) | |||||||
\(200\) | −1.05802e6 | + | 1.83254e6i | −1.87033 | + | 3.23950i | ||||
\(201\) | −42881.8 | + | 74273.5i | −0.0748657 | + | 0.129671i | ||||
\(202\) | −665549. | + | 1.15276e6i | −1.14763 | + | 1.98775i | ||||
\(203\) | −228632. | − | 396003.i | −0.389402 | − | 0.674463i | ||||
\(204\) | 188.627 | + | 326.711i | 0.000317342 | + | 0.000549653i | ||||
\(205\) | 20111.6 | − | 34834.3i | 0.0334243 | − | 0.0578926i | ||||
\(206\) | 901953. | − | 1.56223e6i | 1.48087 | − | 2.56494i | ||||
\(207\) | 299923. | − | 519481.i | 0.486501 | − | 0.842644i | ||||
\(208\) | 3.67347e6 | 5.88733 | ||||||||
\(209\) | 76584.3 | + | 132648.i | 0.121276 | + | 0.210056i | ||||
\(210\) | −10411.1 | + | 18032.5i | −0.0162910 | + | 0.0282168i | ||||
\(211\) | 526124. | 0.813546 | 0.406773 | − | 0.913529i | \(-0.366654\pi\) | ||||
0.406773 | + | 0.913529i | \(0.366654\pi\) | |||||||
\(212\) | 23329.7 | 0.0356509 | ||||||||
\(213\) | −40425.5 | + | 70019.0i | −0.0610529 | + | 0.105747i | ||||
\(214\) | −1.31827e6 | −1.96774 | ||||||||
\(215\) | −3845.27 | − | 6660.20i | −0.00567323 | − | 0.00982632i | ||||
\(216\) | 1.24754e6 | 1.81937 | ||||||||
\(217\) | 433508. | + | 750858.i | 0.624954 | + | 1.08245i | ||||
\(218\) | 384459. | + | 665903.i | 0.547910 | + | 0.949008i | ||||
\(219\) | 121125. | + | 209795.i | 0.170657 | + | 0.295586i | ||||
\(220\) | −49388.8 | + | 85543.9i | −0.0687974 | + | 0.119161i | ||||
\(221\) | −829.124 | −0.00114193 | ||||||||
\(222\) | −141512. | − | 334337.i | −0.192712 | − | 0.455304i | ||||
\(223\) | 110253. | 0.148466 | 0.0742329 | − | 0.997241i | \(-0.476349\pi\) | ||||
0.0742329 | + | 0.997241i | \(0.476349\pi\) | |||||||
\(224\) | −2.43696e6 | + | 4.22095e6i | −3.24511 | + | 5.62069i | ||||
\(225\) | −354913. | − | 614728.i | −0.467376 | − | 0.809519i | ||||
\(226\) | −729248. | − | 1.26309e6i | −0.949738 | − | 1.64499i | ||||
\(227\) | 136713. | + | 236795.i | 0.176095 | + | 0.305005i | 0.940540 | − | 0.339684i | \(-0.110320\pi\) |
−0.764445 | + | 0.644689i | \(0.776987\pi\) | |||||||
\(228\) | −152302. | −0.194030 | ||||||||
\(229\) | −220319. | − | 381603.i | −0.277627 | − | 0.480865i | 0.693167 | − | 0.720777i | \(-0.256215\pi\) |
−0.970795 | + | 0.239912i | \(0.922881\pi\) | |||||||
\(230\) | −85999.2 | −0.107195 | ||||||||
\(231\) | 116110. | − | 201108.i | 0.143165 | − | 0.247970i | ||||
\(232\) | 1.90037e6 | 2.31802 | ||||||||
\(233\) | −1.38173e6 | −1.66738 | −0.833689 | − | 0.552234i | \(-0.813775\pi\) | ||||
−0.833689 | + | 0.552234i | \(0.813775\pi\) | |||||||
\(234\) | −1.01247e6 | + | 1.75365e6i | −1.20877 | + | 2.09364i | ||||
\(235\) | 13714.4 | + | 23754.0i | 0.0161997 | + | 0.0280587i | ||||
\(236\) | 4.03969e6 | 4.72137 | ||||||||
\(237\) | −66241.5 | + | 114734.i | −0.0766054 | + | 0.132685i | ||||
\(238\) | 950.642 | − | 1646.56i | 0.00108786 | − | 0.00188424i | ||||
\(239\) | 318125. | − | 551009.i | 0.360249 | − | 0.623970i | −0.627753 | − | 0.778413i | \(-0.716025\pi\) |
0.988002 | + | 0.154443i | \(0.0493584\pi\) | |||||||
\(240\) | −26330.5 | − | 45605.8i | −0.0295074 | − | 0.0511083i | ||||
\(241\) | 357584. | + | 619353.i | 0.396584 | + | 0.686903i | 0.993302 | − | 0.115548i | \(-0.0368623\pi\) |
−0.596718 | + | 0.802451i | \(0.703529\pi\) | |||||||
\(242\) | −158743. | + | 274950.i | −0.174243 | + | 0.301798i | ||||
\(243\) | −317252. | + | 549497.i | −0.344658 | + | 0.596966i | ||||
\(244\) | 2.39478e6 | − | 4.14788e6i | 2.57508 | − | 4.46017i | ||||
\(245\) | 28897.0 | 0.0307565 | ||||||||
\(246\) | −299946. | − | 519521.i | −0.316013 | − | 0.547350i | ||||
\(247\) | 167364. | − | 289883.i | 0.174550 | − | 0.302329i | ||||
\(248\) | −3.60328e6 | −3.72022 | ||||||||
\(249\) | 14690.8 | 0.0150157 | ||||||||
\(250\) | −101907. | + | 176508.i | −0.103122 | + | 0.178613i | ||||
\(251\) | −1.47851e6 | −1.48129 | −0.740645 | − | 0.671896i | \(-0.765480\pi\) | ||||
−0.740645 | + | 0.671896i | \(0.765480\pi\) | |||||||
\(252\) | −1.72633e6 | − | 2.99009e6i | −1.71246 | − | 2.96608i | ||||
\(253\) | 959109. | 0.942034 | ||||||||
\(254\) | 1.27049e6 | + | 2.20056e6i | 1.23563 | + | 2.14017i | ||||
\(255\) | 5.94295 | + | 10.2935i | 5.72337e−6 | + | 9.91317e-6i | ||||
\(256\) | −3.27579e6 | − | 5.67384e6i | −3.12404 | − | 5.41100i | ||||
\(257\) | 411533. | − | 712796.i | 0.388662 | − | 0.673182i | −0.603608 | − | 0.797281i | \(-0.706271\pi\) |
0.992270 | + | 0.124099i | \(0.0396042\pi\) | |||||||
\(258\) | −114697. | −0.107276 | ||||||||
\(259\) | −819883. | + | 1.08569e6i | −0.759455 | + | 1.00568i | ||||
\(260\) | 215864. | 0.198037 | ||||||||
\(261\) | −318741. | + | 552075.i | −0.289625 | + | 0.501646i | ||||
\(262\) | 671108. | + | 1.16239e6i | 0.604004 | + | 1.04616i | ||||
\(263\) | 175931. | + | 304721.i | 0.156839 | + | 0.271652i | 0.933727 | − | 0.357986i | \(-0.116536\pi\) |
−0.776888 | + | 0.629638i | \(0.783203\pi\) | |||||||
\(264\) | 482546. | + | 835794.i | 0.426117 | + | 0.738056i | ||||
\(265\) | 735.036 | 0.000642975 | ||||||||
\(266\) | 383786. | + | 664737.i | 0.332572 | + | 0.576031i | ||||
\(267\) | −159977. | −0.137334 | ||||||||
\(268\) | −1.01943e6 | + | 1.76570e6i | −0.867001 | + | 1.50169i | ||||
\(269\) | 324500. | 0.273423 | 0.136711 | − | 0.990611i | \(-0.456347\pi\) | ||||
0.136711 | + | 0.990611i | \(0.456347\pi\) | |||||||
\(270\) | 59998.4 | 0.0500876 | ||||||||
\(271\) | 66098.2 | − | 114485.i | 0.0546722 | − | 0.0946950i | −0.837394 | − | 0.546600i | \(-0.815922\pi\) |
0.892066 | + | 0.451905i | \(0.149255\pi\) | |||||||
\(272\) | 2404.26 | + | 4164.30i | 0.00197042 | + | 0.00341287i | ||||
\(273\) | −507481. | −0.412110 | ||||||||
\(274\) | −861382. | + | 1.49196e6i | −0.693138 | + | 1.20055i | ||||
\(275\) | 567481. | − | 982905.i | 0.452501 | − | 0.783754i | ||||
\(276\) | −476841. | + | 825913.i | −0.376791 | + | 0.652622i | ||||
\(277\) | 265983. | + | 460697.i | 0.208284 | + | 0.360758i | 0.951174 | − | 0.308655i | \(-0.0998789\pi\) |
−0.742890 | + | 0.669413i | \(0.766546\pi\) | |||||||
\(278\) | −169595. | − | 293747.i | −0.131613 | − | 0.227961i | ||||
\(279\) | 604362. | − | 1.04679e6i | 0.464822 | − | 0.805096i | ||||
\(280\) | −162141. | + | 280836.i | −0.123594 | + | 0.214071i | ||||
\(281\) | −682632. | + | 1.18235e6i | −0.515728 | + | 0.893267i | 0.484105 | + | 0.875010i | \(0.339145\pi\) |
−0.999833 | + | 0.0182572i | \(0.994188\pi\) | |||||||
\(282\) | 409075. | 0.306323 | ||||||||
\(283\) | −484759. | − | 839627.i | −0.359799 | − | 0.623190i | 0.628128 | − | 0.778110i | \(-0.283821\pi\) |
−0.987927 | + | 0.154920i | \(0.950488\pi\) | |||||||
\(284\) | −961034. | + | 1.66456e6i | −0.707038 | + | 1.22463i | ||||
\(285\) | −4798.49 | −0.00349939 | ||||||||
\(286\) | −3.23773e6 | −2.34059 | ||||||||
\(287\) | −1.12401e6 | + | 1.94684e6i | −0.805500 | + | 1.39517i | ||||
\(288\) | 6.79484e6 | 4.82723 | ||||||||
\(289\) | 709928. | + | 1.22963e6i | 0.500000 | + | 0.866025i | ||||
\(290\) | 91395.1 | 0.0638158 | ||||||||
\(291\) | −221137. | − | 383021.i | −0.153084 | − | 0.265149i | ||||
\(292\) | 2.87950e6 | + | 4.98744e6i | 1.97633 | + | 3.42311i | ||||
\(293\) | −725040. | − | 1.25581e6i | −0.493393 | − | 0.854582i | 0.506578 | − | 0.862194i | \(-0.330910\pi\) |
−0.999971 | + | 0.00761229i | \(0.997577\pi\) | |||||||
\(294\) | 215485. | − | 373232.i | 0.145395 | − | 0.251831i | ||||
\(295\) | 127276. | 0.0851515 | ||||||||
\(296\) | −2.20389e6 | − | 5.20693e6i | −1.46204 | − | 3.45424i | ||||
\(297\) | −669134. | −0.440171 | ||||||||
\(298\) | 482042. | − | 834921.i | 0.314445 | − | 0.544634i | ||||
\(299\) | −1.04800e6 | − | 1.81518e6i | −0.677925 | − | 1.17420i | ||||
\(300\) | 564269. | + | 977343.i | 0.361979 | + | 0.626966i | ||||
\(301\) | 214907. | + | 372229.i | 0.136720 | + | 0.236807i | ||||
\(302\) | 1.65217e6 | 1.04241 | ||||||||
\(303\) | 232535. | + | 402762.i | 0.145506 | + | 0.252024i | ||||
\(304\) | −1.94126e6 | −1.20476 | ||||||||
\(305\) | 75451.0 | − | 130685.i | 0.0464425 | − | 0.0804407i | ||||
\(306\) | −2650.62 | −0.00161824 | ||||||||
\(307\) | 2.10401e6 | 1.27410 | 0.637049 | − | 0.770823i | \(-0.280155\pi\) | ||||
0.637049 | + | 0.770823i | \(0.280155\pi\) | |||||||
\(308\) | 2.76027e6 | − | 4.78093e6i | 1.65796 | − | 2.87168i | ||||
\(309\) | −315132. | − | 545824.i | −0.187757 | − | 0.325204i | ||||
\(310\) | −173294. | −0.102418 | ||||||||
\(311\) | 600569. | − | 1.04022e6i | 0.352096 | − | 0.609849i | −0.634520 | − | 0.772906i | \(-0.718802\pi\) |
0.986617 | + | 0.163057i | \(0.0521356\pi\) | |||||||
\(312\) | 1.05453e6 | − | 1.82651e6i | 0.613301 | − | 1.06227i | ||||
\(313\) | −303047. | + | 524892.i | −0.174843 | + | 0.302837i | −0.940107 | − | 0.340879i | \(-0.889275\pi\) |
0.765264 | + | 0.643717i | \(0.222609\pi\) | |||||||
\(314\) | 3.22755e6 | + | 5.59028e6i | 1.84735 | + | 3.19970i | ||||
\(315\) | −54390.4 | − | 94206.9i | −0.0308849 | − | 0.0534942i | ||||
\(316\) | −1.57476e6 | + | 2.72756e6i | −0.887148 | + | 1.53659i | ||||
\(317\) | −24603.8 | + | 42615.1i | −0.0137517 | + | 0.0238186i | −0.872819 | − | 0.488043i | \(-0.837711\pi\) |
0.859068 | + | 0.511862i | \(0.171044\pi\) | |||||||
\(318\) | 5481.19 | − | 9493.69i | 0.00303953 | − | 0.00526462i | ||||
\(319\) | −1.01929e6 | −0.560815 | ||||||||
\(320\) | −271199. | − | 469731.i | −0.148052 | − | 0.256433i | ||||
\(321\) | −230293. | + | 398879.i | −0.124744 | + | 0.216062i | ||||
\(322\) | 4.80638e6 | 2.58332 | ||||||||
\(323\) | 438.154 | 0.000233679 | ||||||||
\(324\) | −2.23499e6 | + | 3.87111e6i | −1.18280 | + | 2.04867i | ||||
\(325\) | −2.48029e6 | −1.30255 | ||||||||
\(326\) | −576682. | − | 998843.i | −0.300533 | − | 0.520539i | ||||
\(327\) | 268651. | 0.138937 | ||||||||
\(328\) | −4.67133e6 | − | 8.09097e6i | −2.39748 | − | 4.15256i | ||||
\(329\) | −766479. | − | 1.32758e6i | −0.390400 | − | 0.676193i | ||||
\(330\) | 23207.2 | + | 40196.1i | 0.0117311 | + | 0.0203188i | ||||
\(331\) | 287884. | − | 498631.i | 0.144427 | − | 0.250155i | −0.784732 | − | 0.619835i | \(-0.787199\pi\) |
0.929159 | + | 0.369680i | \(0.120533\pi\) | |||||||
\(332\) | 349244. | 0.173893 | ||||||||
\(333\) | 1.88231e6 | + | 233086.i | 0.930210 | + | 0.115187i | ||||
\(334\) | −5.56174e6 | −2.72800 | ||||||||
\(335\) | −32118.5 | + | 55630.9i | −0.0156366 | + | 0.0270835i | ||||
\(336\) | 1.47157e6 | + | 2.54884e6i | 0.711106 | + | 1.23167i | ||||
\(337\) | −1.33374e6 | − | 2.31010e6i | −0.639728 | − | 1.10804i | −0.985492 | − | 0.169720i | \(-0.945714\pi\) |
0.345765 | − | 0.938321i | \(-0.387620\pi\) | |||||||
\(338\) | 1.46400e6 | + | 2.53573e6i | 0.697027 | + | 1.20729i | ||||
\(339\) | −509581. | −0.240832 | ||||||||
\(340\) | 141.282 | + | 244.707i | 6.62809e−5 | + | 0.000114802i | ||||
\(341\) | 1.93266e6 | 0.900057 | ||||||||
\(342\) | 535044. | − | 926723.i | 0.247357 | − | 0.428435i | ||||
\(343\) | 1.13087e6 | 0.519013 | ||||||||
\(344\) | −1.78628e6 | −0.813867 | ||||||||
\(345\) | −15023.6 | + | 26021.6i | −0.00679556 | + | 0.0117702i | ||||
\(346\) | 1.45512e6 | + | 2.52034e6i | 0.653443 | + | 1.13180i | ||||
\(347\) | −1.50599e6 | −0.671427 | −0.335713 | − | 0.941964i | \(-0.608977\pi\) | ||||
−0.335713 | + | 0.941964i | \(0.608977\pi\) | |||||||
\(348\) | 506759. | − | 877733.i | 0.224313 | − | 0.388521i | ||||
\(349\) | 1.05231e6 | − | 1.82265e6i | 0.462466 | − | 0.801015i | −0.536617 | − | 0.843826i | \(-0.680298\pi\) |
0.999083 | + | 0.0428113i | \(0.0136314\pi\) | |||||||
\(350\) | 2.84381e6 | − | 4.92562e6i | 1.24088 | − | 2.14927i | ||||
\(351\) | 731147. | + | 1.26638e6i | 0.316765 | + | 0.548653i | ||||
\(352\) | 5.43222e6 | + | 9.40889e6i | 2.33680 | + | 4.04745i | ||||
\(353\) | 861986. | − | 1.49300e6i | 0.368183 | − | 0.637711i | −0.621099 | − | 0.783732i | \(-0.713313\pi\) |
0.989281 | + | 0.146021i | \(0.0466468\pi\) | |||||||
\(354\) | 949103. | − | 1.64389e6i | 0.402536 | − | 0.697213i | ||||
\(355\) | −30278.8 | + | 52444.3i | −0.0127517 | + | 0.0220865i | ||||
\(356\) | −3.80312e6 | −1.59043 | ||||||||
\(357\) | −332.143 | − | 575.289i | −0.000137929 | − | 0.000238900i | ||||
\(358\) | 2.70068e6 | − | 4.67771e6i | 1.11369 | − | 1.92897i | ||||
\(359\) | −1.15223e6 | −0.471847 | −0.235924 | − | 0.971772i | \(-0.575812\pi\) | ||||
−0.235924 | + | 0.971772i | \(0.575812\pi\) | |||||||
\(360\) | 452087. | 0.183851 | ||||||||
\(361\) | 1.14961e6 | − | 1.99117e6i | 0.464281 | − | 0.804158i | ||||
\(362\) | 4.21634e6 | 1.69108 | ||||||||
\(363\) | 55462.8 | + | 96064.3i | 0.0220920 | + | 0.0382645i | ||||
\(364\) | −1.20643e7 | −4.77254 | ||||||||
\(365\) | 90722.8 | + | 157137.i | 0.0356438 | + | 0.0617369i | ||||
\(366\) | −1.12528e6 | − | 1.94904e6i | −0.439094 | − | 0.760534i | ||||
\(367\) | 590037. | + | 1.02197e6i | 0.228673 | + | 0.396072i | 0.957415 | − | 0.288715i | \(-0.0932282\pi\) |
−0.728742 | + | 0.684788i | \(0.759895\pi\) | |||||||
\(368\) | −6.07788e6 | + | 1.05272e7i | −2.33955 | + | 4.05222i | ||||
\(369\) | 3.13401e6 | 1.19821 | ||||||||
\(370\) | −105992. | − | 250419.i | −0.0402504 | − | 0.0950960i | ||||
\(371\) | −41080.1 | −0.0154952 | ||||||||
\(372\) | −960863. | + | 1.66426e6i | −0.360001 | + | 0.623541i | ||||
\(373\) | 352006. | + | 609692.i | 0.131002 | + | 0.226902i | 0.924063 | − | 0.382240i | \(-0.124847\pi\) |
−0.793061 | + | 0.609142i | \(0.791514\pi\) | |||||||
\(374\) | −2119.07 | − | 3670.34i | −0.000783369 | − | 0.00135684i | ||||
\(375\) | 35605.0 | + | 61669.6i | 0.0130747 | + | 0.0226461i | ||||
\(376\) | 6.37089e6 | 2.32397 | ||||||||
\(377\) | 1.11375e6 | + | 1.92907e6i | 0.403585 | + | 0.699029i | ||||
\(378\) | −3.35322e6 | −1.20707 | ||||||||
\(379\) | −1.39302e6 | + | 2.41278e6i | −0.498150 | + | 0.862820i | −0.999998 | − | 0.00213540i | \(-0.999320\pi\) |
0.501848 | + | 0.864956i | \(0.332654\pi\) | |||||||
\(380\) | −114074. | −0.0405255 | ||||||||
\(381\) | 887790. | 0.313327 | ||||||||
\(382\) | −1.71484e6 | + | 2.97019e6i | −0.601263 | + | 1.04142i | ||||
\(383\) | 1.55836e6 | + | 2.69916e6i | 0.542839 | + | 0.940224i | 0.998740 | + | 0.0501935i | \(0.0159838\pi\) |
−0.455901 | + | 0.890031i | \(0.650683\pi\) | |||||||
\(384\) | −4.36352e6 | −1.51011 | ||||||||
\(385\) | 86966.3 | − | 150630.i | 0.0299019 | − | 0.0517916i | ||||
\(386\) | −1.46566e6 | + | 2.53861e6i | −0.500687 | + | 0.867215i | ||||
\(387\) | 299605. | − | 518932.i | 0.101689 | − | 0.176130i | ||||
\(388\) | −5.25709e6 | − | 9.10554e6i | −1.77283 | − | 3.07062i | ||||
\(389\) | −771047. | − | 1.33549e6i | −0.258349 | − | 0.447473i | 0.707451 | − | 0.706763i | \(-0.249845\pi\) |
−0.965800 | + | 0.259289i | \(0.916512\pi\) | |||||||
\(390\) | 50716.0 | − | 87842.7i | 0.0168843 | − | 0.0292445i | ||||
\(391\) | 1371.81 | − | 2376.05i | 0.000453788 | − | 0.000785984i | ||||
\(392\) | 3.35595e6 | − | 5.81267e6i | 1.10306 | − | 1.91056i | ||||
\(393\) | 468955. | 0.153161 | ||||||||
\(394\) | −1.26848e6 | − | 2.19707e6i | −0.411665 | − | 0.713024i | ||||
\(395\) | −49615.0 | + | 85935.7i | −0.0160000 | + | 0.0277128i | ||||
\(396\) | −7.69629e6 | −2.46629 | ||||||||
\(397\) | −957673. | −0.304959 | −0.152479 | − | 0.988307i | \(-0.548726\pi\) | ||||
−0.152479 | + | 0.988307i | \(0.548726\pi\) | |||||||
\(398\) | 2.45008e6 | − | 4.24367e6i | 0.775306 | − | 1.34287i | ||||
\(399\) | 268181. | 0.0843326 | ||||||||
\(400\) | 7.19226e6 | + | 1.24574e7i | 2.24758 | + | 3.89292i | ||||
\(401\) | 979169. | 0.304086 | 0.152043 | − | 0.988374i | \(-0.451415\pi\) | ||||
0.152043 | + | 0.988374i | \(0.451415\pi\) | |||||||
\(402\) | 479017. | + | 829683.i | 0.147838 | + | 0.256063i | ||||
\(403\) | −2.11178e6 | − | 3.65770e6i | −0.647717 | − | 1.12188i | ||||
\(404\) | 5.52804e6 | + | 9.57485e6i | 1.68507 | + | 2.91863i | ||||
\(405\) | −70416.4 | + | 121965.i | −0.0213322 | + | 0.0369485i | ||||
\(406\) | −5.10794e6 | −1.53791 | ||||||||
\(407\) | 1.18208e6 | + | 2.79280e6i | 0.353722 | + | 0.835707i | ||||
\(408\) | 2760.74 | 0.000821060 | ||||||||
\(409\) | 2.00983e6 | − | 3.48112e6i | 0.594087 | − | 1.02899i | −0.399588 | − | 0.916695i | \(-0.630847\pi\) |
0.993675 | − | 0.112294i | \(-0.0358198\pi\) | |||||||
\(410\) | −224660. | − | 389122.i | −0.0660033 | − | 0.114321i | ||||
\(411\) | 300957. | + | 521272.i | 0.0878819 | + | 0.152216i | ||||
\(412\) | −7.49161e6 | − | 1.29759e7i | −2.17436 | − | 3.76611i | ||||
\(413\) | −7.11329e6 | −2.05209 | ||||||||
\(414\) | −3.35033e6 | − | 5.80294e6i | −0.960698 | − | 1.66398i | ||||
\(415\) | 11003.4 | 0.00313623 | ||||||||
\(416\) | 1.18713e7 | − | 2.05617e7i | 3.36330 | − | 5.82541i | ||||
\(417\) | −118509. | −0.0333741 | ||||||||
\(418\) | 1.71099e6 | 0.478969 | ||||||||
\(419\) | −965336. | + | 1.67201e6i | −0.268623 | + | 0.465269i | −0.968506 | − | 0.248988i | \(-0.919902\pi\) |
0.699883 | + | 0.714257i | \(0.253235\pi\) | |||||||
\(420\) | 86474.1 | + | 149778.i | 0.0239201 | + | 0.0414308i | ||||
\(421\) | 4.99175e6 | 1.37261 | 0.686305 | − | 0.727314i | \(-0.259232\pi\) | ||||
0.686305 | + | 0.727314i | \(0.259232\pi\) | |||||||
\(422\) | 2.93857e6 | − | 5.08975e6i | 0.803258 | − | 1.39128i | ||||
\(423\) | −1.06856e6 | + | 1.85080e6i | −0.290368 | + | 0.502932i | ||||
\(424\) | 85363.5 | − | 147854.i | 0.0230599 | − | 0.0399409i | ||||
\(425\) | −1623.33 | − | 2811.70i | −0.000435949 | − | 0.000755086i | ||||
\(426\) | 451579. | + | 782158.i | 0.120562 | + | 0.208819i | ||||
\(427\) | −4.21685e6 | + | 7.30379e6i | −1.11923 | + | 1.93856i | ||||
\(428\) | −5.47475e6 | + | 9.48255e6i | −1.44462 | + | 2.50216i | ||||
\(429\) | −565612. | + | 979669.i | −0.148380 | + | 0.257002i | ||||
\(430\) | −85908.2 | −0.0224060 | ||||||||
\(431\) | 2.43420e6 | + | 4.21615e6i | 0.631194 | + | 1.09326i | 0.987308 | + | 0.158817i | \(0.0507680\pi\) |
−0.356115 | + | 0.934442i | \(0.615899\pi\) | |||||||
\(432\) | 4.24030e6 | − | 7.34442e6i | 1.09317 | − | 1.89343i | ||||
\(433\) | −941882. | −0.241422 | −0.120711 | − | 0.992688i | \(-0.538517\pi\) | ||||
−0.120711 | + | 0.992688i | \(0.538517\pi\) | |||||||
\(434\) | 9.68513e6 | 2.46821 | ||||||||
\(435\) | 15966.2 | − | 27654.2i | 0.00404555 | − | 0.00700710i | ||||
\(436\) | 6.38663e6 | 1.60900 | ||||||||
\(437\) | 553818. | + | 959241.i | 0.138728 | + | 0.240284i | ||||
\(438\) | 2.70609e6 | 0.673995 | ||||||||
\(439\) | 1.77079e6 | + | 3.06710e6i | 0.438537 | + | 0.759568i | 0.997577 | − | 0.0695727i | \(-0.0221636\pi\) |
−0.559040 | + | 0.829141i | \(0.688830\pi\) | |||||||
\(440\) | 361427. | + | 626010.i | 0.0889998 | + | 0.154152i | ||||
\(441\) | 1.12576e6 | + | 1.94987e6i | 0.275644 | + | 0.477429i | ||||
\(442\) | −4630.92 | + | 8020.99i | −0.00112749 | + | 0.00195287i | ||||
\(443\) | −4.67617e6 | −1.13209 | −0.566046 | − | 0.824374i | \(-0.691527\pi\) | ||||
−0.566046 | + | 0.824374i | \(0.691527\pi\) | |||||||
\(444\) | −2.99265e6 | − | 370578.i | −0.720441 | − | 0.0892118i | ||||
\(445\) | −119823. | −0.0286840 | ||||||||
\(446\) | 615796. | − | 1.06659e6i | 0.146588 | − | 0.253899i | ||||
\(447\) | −168420. | − | 291711.i | −0.0398680 | − | 0.0690533i | ||||
\(448\) | 1.51569e7 | + | 2.62526e7i | 3.56793 | + | 6.17983i | ||||
\(449\) | −643194. | − | 1.11404e6i | −0.150566 | − | 0.260787i | 0.780870 | − | 0.624694i | \(-0.214776\pi\) |
−0.931436 | + | 0.363906i | \(0.881443\pi\) | |||||||
\(450\) | −7.92922e6 | −1.84586 | ||||||||
\(451\) | 2.50552e6 | + | 4.33969e6i | 0.580039 | + | 1.00466i | ||||
\(452\) | −1.21142e7 | −2.78901 | ||||||||
\(453\) | 288625. | − | 499912.i | 0.0660827 | − | 0.114459i | ||||
\(454\) | 3.05435e6 | 0.695472 | ||||||||
\(455\) | −380104. | −0.0860744 | ||||||||
\(456\) | −557273. | + | 965224.i | −0.125503 | + | 0.217378i | ||||
\(457\) | −1.28737e6 | − | 2.22979e6i | −0.288346 | − | 0.499430i | 0.685069 | − | 0.728478i | \(-0.259772\pi\) |
−0.973415 | + | 0.229048i | \(0.926439\pi\) | |||||||
\(458\) | −4.92220e6 | −1.09647 | ||||||||
\(459\) | −957.062 | + | 1657.68i | −0.000212035 | + | 0.000367256i | ||||
\(460\) | −357154. | + | 618610.i | −0.0786976 | + | 0.136308i | ||||
\(461\) | −3.57807e6 | + | 6.19741e6i | −0.784146 | + | 1.35818i | 0.145362 | + | 0.989379i | \(0.453565\pi\) |
−0.929508 | + | 0.368803i | \(0.879768\pi\) | |||||||
\(462\) | −1.29702e6 | − | 2.24650e6i | −0.282710 | − | 0.489668i | ||||
\(463\) | −3.18060e6 | − | 5.50896e6i | −0.689535 | − | 1.19431i | −0.971988 | − | 0.235029i | \(-0.924481\pi\) |
0.282453 | − | 0.959281i | \(-0.408852\pi\) | |||||||
\(464\) | 6.45923e6 | − | 1.11877e7i | 1.39279 | − | 2.41238i | ||||
\(465\) | −30273.4 | + | 52435.0i | −0.00649274 | + | 0.0112458i | ||||
\(466\) | −7.71742e6 | + | 1.33670e7i | −1.64629 | + | 2.85146i | ||||
\(467\) | −1.38751e6 | −0.294405 | −0.147202 | − | 0.989106i | \(-0.547027\pi\) | ||||
−0.147202 | + | 0.989106i | \(0.547027\pi\) | |||||||
\(468\) | 8.40956e6 | + | 1.45658e7i | 1.77484 | + | 3.07411i | ||||
\(469\) | 1.79506e6 | − | 3.10913e6i | 0.376831 | − | 0.652691i | ||||
\(470\) | 306397. | 0.0639794 | ||||||||
\(471\) | 2.25533e6 | 0.468445 | ||||||||
\(472\) | 1.47812e7 | − | 2.56019e7i | 3.05391 | − | 5.28952i | ||||
\(473\) | 958094. | 0.196904 | ||||||||
\(474\) | 739961. | + | 1.28165e6i | 0.151273 | + | 0.262013i | ||||
\(475\) | 1.31072e6 | 0.266549 | ||||||||
\(476\) | −7896.03 | − | 13676.3i | −0.00159732 | − | 0.00276663i | ||||
\(477\) | 28635.3 | + | 49597.8i | 0.00576243 | + | 0.00998082i | ||||
\(478\) | −3.55366e6 | − | 6.15512e6i | −0.711387 | − | 1.23216i | ||||
\(479\) | −457553. | + | 792505.i | −0.0911177 | + | 0.157820i | −0.907982 | − | 0.419010i | \(-0.862377\pi\) |
0.816864 | + | 0.576830i | \(0.195711\pi\) | |||||||
\(480\) | −340363. | −0.0674278 | ||||||||
\(481\) | 3.99394e6 | − | 5.28881e6i | 0.787117 | − | 1.04231i | ||||
\(482\) | 7.98887e6 | 1.56628 | ||||||||
\(483\) | 839645. | − | 1.45431e6i | 0.163768 | − | 0.283654i | ||||
\(484\) | 1.31851e6 | + | 2.28373e6i | 0.255842 | + | 0.443131i | ||||
\(485\) | −165632. | − | 286883.i | −0.0319735 | − | 0.0553797i | ||||
\(486\) | 3.54391e6 | + | 6.13823e6i | 0.680600 | + | 1.17883i | ||||
\(487\) | 7.47578e6 | 1.42835 | 0.714174 | − | 0.699969i | \(-0.246803\pi\) | ||||
0.714174 | + | 0.699969i | \(0.246803\pi\) | |||||||
\(488\) | −1.75250e7 | − | 3.03542e7i | −3.33126 | − | 5.76991i | ||||
\(489\) | −402972. | −0.0762083 | ||||||||
\(490\) | 161399. | − | 279551.i | 0.0303676 | − | 0.0525982i | ||||
\(491\) | −6.03053e6 | −1.12889 | −0.564445 | − | 0.825471i | \(-0.690910\pi\) | ||||
−0.564445 | + | 0.825471i | \(0.690910\pi\) | |||||||
\(492\) | −4.98269e6 | −0.928007 | ||||||||
\(493\) | −1457.89 | + | 2525.13i | −0.000270151 | + | 0.000467915i | ||||
\(494\) | −1.86956e6 | − | 3.23818e6i | −0.344685 | − | 0.597012i | ||||
\(495\) | −242483. | −0.0444803 | ||||||||
\(496\) | −1.22473e7 | + | 2.12129e7i | −2.23530 | + | 3.87165i | ||||
\(497\) | 1.69224e6 | − | 2.93104e6i | 0.307305 | − | 0.532268i | ||||
\(498\) | 82052.8 | − | 142120.i | 0.0148259 | − | 0.0256791i | ||||
\(499\) | 405296. | + | 701993.i | 0.0728653 | + | 0.126206i | 0.900156 | − | 0.435568i | \(-0.143452\pi\) |
−0.827291 | + | 0.561774i | \(0.810119\pi\) | |||||||
\(500\) | 846436. | + | 1.46607e6i | 0.151415 | + | 0.262259i | ||||
\(501\) | −971603. | + | 1.68287e6i | −0.172940 | + | 0.299540i | ||||
\(502\) | −8.25796e6 | + | 1.43032e7i | −1.46256 | + | 2.53323i | ||||
\(503\) | 1.39895e6 | − | 2.42306e6i | 0.246538 | − | 0.427016i | −0.716025 | − | 0.698075i | \(-0.754040\pi\) |
0.962563 | + | 0.271058i | \(0.0873737\pi\) | |||||||
\(504\) | −2.52665e7 | −4.43067 | ||||||||
\(505\) | 174169. | + | 301669.i | 0.0303908 | + | 0.0526384i | ||||
\(506\) | 5.35693e6 | − | 9.27848e6i | 0.930122 | − | 1.61102i | ||||
\(507\) | 1.02301e6 | 0.176750 | ||||||||
\(508\) | 2.11054e7 | 3.62856 | ||||||||
\(509\) | −838785. | + | 1.45282e6i | −0.143501 | + | 0.248552i | −0.928813 | − | 0.370549i | \(-0.879169\pi\) |
0.785311 | + | 0.619101i | \(0.212503\pi\) | |||||||
\(510\) | 132.773 | 2.26040e−5 | ||||||||
\(511\) | −5.07037e6 | − | 8.78214e6i | −0.858988 | − | 1.48781i | ||||
\(512\) | −3.74087e7 | −6.30664 | ||||||||
\(513\) | −386378. | − | 669226.i | −0.0648215 | − | 0.112274i | ||||
\(514\) | −4.59709e6 | − | 7.96239e6i | −0.767494 | − | 1.32934i | ||||
\(515\) | −236034. | − | 408823.i | −0.0392154 | − | 0.0679230i | ||||
\(516\) | −476336. | + | 825038.i | −0.0787570 | + | 0.136411i | ||||
\(517\) | −3.41711e6 | −0.562253 | ||||||||
\(518\) | 5.92376e6 | + | 1.39955e7i | 0.970003 | + | 2.29174i | ||||
\(519\) | 1.01680e6 | 0.165698 | ||||||||
\(520\) | 789847. | − | 1.36805e6i | 0.128096 | − | 0.221868i | ||||
\(521\) | 3.49607e6 | + | 6.05537e6i | 0.564269 | + | 0.977342i | 0.997117 | + | 0.0758754i | \(0.0241751\pi\) |
−0.432849 | + | 0.901467i | \(0.642492\pi\) | |||||||
\(522\) | 3.56054e6 | + | 6.16704e6i | 0.571926 | + | 0.990604i | ||||
\(523\) | −5.60809e6 | − | 9.71349e6i | −0.896521 | − | 1.55282i | −0.831911 | − | 0.554909i | \(-0.812753\pi\) |
−0.0646101 | − | 0.997911i | \(-0.520580\pi\) | |||||||
\(524\) | 1.11484e7 | 1.77372 | ||||||||
\(525\) | −993594. | − | 1.72095e6i | −0.157330 | − | 0.272503i | ||||
\(526\) | 3.93052e6 | 0.619421 | ||||||||
\(527\) | 2764.29 | − | 4787.88i | 0.000433567 | − | 0.000750960i | ||||
\(528\) | 6.56056e6 | 1.02413 | ||||||||
\(529\) | 499440. | 0.0775969 | ||||||||
\(530\) | 4105.41 | − | 7110.79i | 0.000634844 | − | 0.00109958i | ||||
\(531\) | 4.95839e6 | + | 8.58818e6i | 0.763140 | + | 1.32180i | ||||
\(532\) | 6.37545e6 | 0.976634 | ||||||||
\(533\) | 5.47546e6 | − | 9.48377e6i | 0.834838 | − | 1.44598i | ||||
\(534\) | −893521. | + | 1.54762e6i | −0.135597 | + | 0.234862i | ||||
\(535\) | −172490. | + | 298761.i | −0.0260543 | + | 0.0451273i | ||||
\(536\) | 7.46017e6 | + | 1.29214e7i | 1.12160 | + | 1.94266i | ||||
\(537\) | −943585. | − | 1.63434e6i | −0.141203 | − | 0.244572i | ||||
\(538\) | 1.81244e6 | − | 3.13923e6i | 0.269965 | − | 0.467593i | ||||
\(539\) | −1.80000e6 | + | 3.11770e6i | −0.266871 | + | 0.462234i | ||||
\(540\) | 249173. | − | 431580.i | 0.0367719 | − | 0.0636909i | ||||
\(541\) | −3.70126e6 | −0.543697 | −0.271848 | − | 0.962340i | \(-0.587635\pi\) | ||||
−0.271848 | + | 0.962340i | \(0.587635\pi\) | |||||||
\(542\) | −738359. | − | 1.27888e6i | −0.107962 | − | 0.186995i | ||||
\(543\) | 736570. | − | 1.27578e6i | 0.107205 | − | 0.185684i | ||||
\(544\) | 31078.8 | 0.00450264 | ||||||||
\(545\) | 201220. | 0.0290188 | ||||||||
\(546\) | −2.83445e6 | + | 4.90941e6i | −0.406899 | + | 0.704770i | ||||
\(547\) | −6.62509e6 | −0.946724 | −0.473362 | − | 0.880868i | \(-0.656960\pi\) | ||||
−0.473362 | + | 0.880868i | \(0.656960\pi\) | |||||||
\(548\) | 7.15463e6 | + | 1.23922e7i | 1.01774 | + | 1.76277i | ||||
\(549\) | 1.17576e7 | 1.66490 | ||||||||
\(550\) | −6.33912e6 | − | 1.09797e7i | −0.893557 | − | 1.54769i | ||||
\(551\) | −588567. | − | 1.01943e6i | −0.0825879 | − | 0.143046i | ||||
\(552\) | 3.48952e6 | + | 6.04403e6i | 0.487437 | + | 0.844265i | ||||
\(553\) | 2.77291e6 | − | 4.80282e6i | 0.385588 | − | 0.667857i | ||||
\(554\) | 5.94241e6 | 0.822599 | ||||||||
\(555\) | −94287.7 | − | 11675.6i | −0.0129934 | − | 0.00160896i | ||||
\(556\) | −2.81730e6 | −0.386497 | ||||||||
\(557\) | 6.65904e6 | − | 1.15338e7i | 0.909439 | − | 1.57520i | 0.0945948 | − | 0.995516i | \(-0.469844\pi\) |
0.814845 | − | 0.579679i | \(-0.196822\pi\) | |||||||
\(558\) | −6.75111e6 | − | 1.16933e7i | −0.917889 | − | 1.58983i | ||||
\(559\) | −1.04689e6 | − | 1.81326e6i | −0.141700 | − | 0.245432i | ||||
\(560\) | 1.10221e6 | + | 1.90909e6i | 0.148523 | + | 0.257250i | ||||
\(561\) | −1480.76 | −0.000198645 | ||||||||
\(562\) | 7.62543e6 | + | 1.32076e7i | 1.01841 | + | 1.76394i | ||||
\(563\) | −1.20161e7 | −1.59769 | −0.798845 | − | 0.601536i | \(-0.794556\pi\) | ||||
−0.798845 | + | 0.601536i | \(0.794556\pi\) | |||||||
\(564\) | 1.69889e6 | − | 2.94256e6i | 0.224888 | − | 0.389517i | ||||
\(565\) | −381677. | −0.0503008 | ||||||||
\(566\) | −1.08301e7 | −1.42100 | ||||||||
\(567\) | 3.93547e6 | − | 6.81644e6i | 0.514090 | − | 0.890431i | ||||
\(568\) | 7.03285e6 | + | 1.21813e7i | 0.914662 | + | 1.58424i | ||||
\(569\) | −1.19419e6 | −0.154629 | −0.0773146 | − | 0.997007i | \(-0.524635\pi\) | ||||
−0.0773146 | + | 0.997007i | \(0.524635\pi\) | |||||||
\(570\) | −26801.1 | + | 46420.9i | −0.00345514 | + | 0.00598448i | ||||
\(571\) | −134175. | + | 232397.i | −0.0172219 | + | 0.0298291i | −0.874508 | − | 0.485011i | \(-0.838815\pi\) |
0.857286 | + | 0.514840i | \(0.172149\pi\) | |||||||
\(572\) | −1.34463e7 | + | 2.32896e7i | −1.71835 | + | 2.97627i | ||||
\(573\) | 599144. | + | 1.03775e6i | 0.0762333 | + | 0.132040i | ||||
\(574\) | 1.25559e7 | + | 2.17475e7i | 1.59063 | + | 2.75505i | ||||
\(575\) | 4.10373e6 | − | 7.10787e6i | 0.517617 | − | 0.896540i | ||||
\(576\) | 2.11306e7 | − | 3.65992e7i | 2.65372 | − | 4.59638i | ||||
\(577\) | −3.64014e6 | + | 6.30491e6i | −0.455175 | + | 0.788386i | −0.998698 | − | 0.0510078i | \(-0.983757\pi\) |
0.543523 | + | 0.839394i | \(0.317090\pi\) | |||||||
\(578\) | 1.58607e7 | 1.97471 | ||||||||
\(579\) | 512086. | + | 886958.i | 0.0634814 | + | 0.109953i | ||||
\(580\) | 379563. | − | 657423.i | 0.0468505 | − | 0.0811475i | ||||
\(581\) | −614965. | −0.0755806 | ||||||||
\(582\) | −4.94049e6 | −0.604592 | ||||||||
\(583\) | −45785.7 | + | 79303.2i | −0.00557903 | + | 0.00966317i | ||||
\(584\) | 4.21444e7 | 5.11337 | ||||||||
\(585\) | 264955. | + | 458916.i | 0.0320098 | + | 0.0554426i | ||||
\(586\) | −1.61983e7 | −1.94862 | ||||||||
\(587\) | 2.61325e6 | + | 4.52628e6i | 0.313029 | + | 0.542183i | 0.979017 | − | 0.203780i | \(-0.0653228\pi\) |
−0.665987 | + | 0.745963i | \(0.731990\pi\) | |||||||
\(588\) | −1.78982e6 | − | 3.10006e6i | −0.213484 | − | 0.369766i | ||||
\(589\) | 1.11598e6 | + | 1.93293e6i | 0.132546 | + | 0.229577i | ||||
\(590\) | 710879. | − | 1.23128e6i | 0.0840748 | − | 0.145622i | ||||
\(591\) | −886385. | −0.104389 | ||||||||
\(592\) | −3.81447e7 | − | 4.72344e6i | −4.47332 | − | 0.553929i | ||||
\(593\) | −1.44351e7 | −1.68571 | −0.842853 | − | 0.538143i | \(-0.819126\pi\) | ||||
−0.842853 | + | 0.538143i | \(0.819126\pi\) | |||||||
\(594\) | −3.73733e6 | + | 6.47324e6i | −0.434605 | + | 0.752758i | ||||
\(595\) | −248.776 | − | 430.892i | −2.88082e−5 | − | 4.98972e-5i | ||||
\(596\) | −4.00383e6 | − | 6.93485e6i | −0.461701 | − | 0.799689i | ||||
\(597\) | −856030. | − | 1.48269e6i | −0.0982999 | − | 0.170260i | ||||
\(598\) | −2.34136e7 | −2.67741 | ||||||||
\(599\) | 8.14606e6 | + | 1.41094e7i | 0.927642 | + | 1.60672i | 0.787255 | + | 0.616627i | \(0.211501\pi\) |
0.140387 | + | 0.990097i | \(0.455165\pi\) | |||||||
\(600\) | 8.25865e6 | 0.936550 | ||||||||
\(601\) | 3.92446e6 | − | 6.79737e6i | 0.443194 | − | 0.767635i | −0.554730 | − | 0.832030i | \(-0.687179\pi\) |
0.997924 | + | 0.0643953i | \(0.0205118\pi\) | |||||||
\(602\) | 4.80129e6 | 0.539966 | ||||||||
\(603\) | −5.00505e6 | −0.560551 | ||||||||
\(604\) | 6.86146e6 | − | 1.18844e7i | 0.765287 | − | 1.32552i | ||||
\(605\) | 41541.7 | + | 71952.3i | 0.00461419 | + | 0.00799201i | ||||
\(606\) | 5.19513e6 | 0.574665 | ||||||||
\(607\) | −633076. | + | 1.09652e6i | −0.0697404 | + | 0.120794i | −0.898787 | − | 0.438386i | \(-0.855550\pi\) |
0.829047 | + | 0.559180i | \(0.188884\pi\) | |||||||
\(608\) | −6.27346e6 | + | 1.08659e7i | −0.688253 | + | 1.19209i | ||||
\(609\) | −892327. | + | 1.54556e6i | −0.0974947 | + | 0.168866i | ||||
\(610\) | −842836. | − | 1.45983e6i | −0.0917104 | − | 0.158847i | ||||
\(611\) | 3.73379e6 | + | 6.46712e6i | 0.404620 | + | 0.700822i | ||||
\(612\) | −11008.0 | + | 19066.4i | −0.00118804 | + | 0.00205774i | ||||
\(613\) | −1.26207e6 | + | 2.18597e6i | −0.135654 | + | 0.234960i | −0.925847 | − | 0.377898i | \(-0.876647\pi\) |
0.790193 | + | 0.612858i | \(0.209980\pi\) | |||||||
\(614\) | 1.17516e7 | − | 2.03544e7i | 1.25799 | − | 2.17890i | ||||
\(615\) | −156987. | −0.0167369 | ||||||||
\(616\) | −2.01997e7 | − | 3.49868e7i | −2.14483 | − | 3.71495i | ||||
\(617\) | −2.10647e6 | + | 3.64852e6i | −0.222763 | + | 0.385837i | −0.955646 | − | 0.294518i | \(-0.904841\pi\) |
0.732883 | + | 0.680355i | \(0.238174\pi\) | |||||||
\(618\) | −7.04044e6 | −0.741530 | ||||||||
\(619\) | −1.54773e7 | −1.62356 | −0.811781 | − | 0.583961i | \(-0.801502\pi\) | ||||
−0.811781 | + | 0.583961i | \(0.801502\pi\) | |||||||
\(620\) | −719687. | + | 1.24654e6i | −0.0751908 | + | 0.130234i | ||||
\(621\) | −4.83883e6 | −0.503514 | ||||||||
\(622\) | −6.70874e6 | − | 1.16199e7i | −0.695288 | − | 1.20427i | ||||
\(623\) | 6.69672e6 | 0.691261 | ||||||||
\(624\) | −7.16857e6 | − | 1.24163e7i | −0.737006 | − | 1.27653i | ||||
\(625\) | −4.84279e6 | − | 8.38796e6i | −0.495902 | − | 0.858927i | ||||
\(626\) | 3.38523e6 | + | 5.86339e6i | 0.345265 | + | 0.598016i | ||||
\(627\) | 298900. | − | 517710.i | 0.0303639 | − | 0.0525918i | ||||
\(628\) | 5.36160e7 | 5.42494 | ||||||||
\(629\) | 8609.48 | + | 1066.11i | 0.000867662 | + | 0.000107442i | ||||
\(630\) | −1.21515e6 | −0.121977 | ||||||||
\(631\) | 6.45032e6 | − | 1.11723e7i | 0.644923 | − | 1.11704i | −0.339397 | − | 0.940643i | \(-0.610223\pi\) |
0.984319 | − | 0.176395i | \(-0.0564437\pi\) | |||||||
\(632\) | 1.15241e7 | + | 1.99603e7i | 1.14766 | + | 1.98781i | ||||
\(633\) | −1.02670e6 | − | 1.77830e6i | −0.101844 | − | 0.176399i | ||||
\(634\) | 274841. | + | 476038.i | 0.0271555 | + | 0.0470347i | ||||
\(635\) | 664956. | 0.0654423 | ||||||||
\(636\) | −45526.7 | − | 78854.5i | −0.00446296 | − | 0.00773007i | ||||
\(637\) | 7.86730e6 | 0.768205 | ||||||||
\(638\) | −5.69304e6 | + | 9.86064e6i | −0.553723 | + | 0.959077i | ||||
\(639\) | −4.71836e6 | −0.457129 | ||||||||
\(640\) | −3.26828e6 | −0.315406 | ||||||||
\(641\) | −7.46246e6 | + | 1.29254e7i | −0.717360 | + | 1.24250i | 0.244682 | + | 0.969603i | \(0.421316\pi\) |
−0.962042 | + | 0.272901i | \(0.912017\pi\) | |||||||
\(642\) | 2.57252e6 | + | 4.45574e6i | 0.246332 | + | 0.426660i | ||||
\(643\) | 9.16285e6 | 0.873983 | 0.436992 | − | 0.899466i | \(-0.356044\pi\) | ||||
0.436992 | + | 0.899466i | \(0.356044\pi\) | |||||||
\(644\) | 1.99609e7 | − | 3.45732e7i | 1.89655 | − | 3.28492i | ||||
\(645\) | −15007.7 | + | 25994.0i | −0.00142041 | + | 0.00246022i | ||||
\(646\) | 2447.23 | − | 4238.73i | 0.000230724 | − | 0.000399626i | ||||
\(647\) | 9.68563e6 | + | 1.67760e7i | 0.909635 | + | 1.57553i | 0.814571 | + | 0.580064i | \(0.196972\pi\) |
0.0950643 | + | 0.995471i | \(0.469694\pi\) | |||||||
\(648\) | 1.63556e7 | + | 2.83288e7i | 1.53013 | + | 2.65027i | ||||
\(649\) | −7.92810e6 | + | 1.37319e7i | −0.738852 | + | 1.27973i | ||||
\(650\) | −1.38532e7 | + | 2.39945e7i | −1.28608 | + | 2.22755i | ||||
\(651\) | 1.69194e6 | − | 2.93052e6i | 0.156470 | − | 0.271014i | ||||
\(652\) | −9.57983e6 | −0.882549 | ||||||||
\(653\) | −5.00319e6 | − | 8.66578e6i | −0.459160 | − | 0.795289i | 0.539757 | − | 0.841821i | \(-0.318516\pi\) |
−0.998917 | + | 0.0465323i | \(0.985183\pi\) | |||||||
\(654\) | 1.50050e6 | − | 2.59895e6i | 0.137180 | − | 0.237603i | ||||
\(655\) | 351248. | 0.0319897 | ||||||||
\(656\) | −6.35101e7 | −5.76213 | ||||||||
\(657\) | −7.06870e6 | + | 1.22433e7i | −0.638890 | + | 1.10659i | ||||
\(658\) | −1.71241e7 | −1.54185 | ||||||||
\(659\) | −6.78824e6 | − | 1.17576e7i | −0.608897 | − | 1.05464i | −0.991423 | − | 0.130695i | \(-0.958279\pi\) |
0.382526 | − | 0.923945i | \(-0.375054\pi\) | |||||||
\(660\) | 385518. | 0.0344497 | ||||||||
\(661\) | 9.12568e6 | + | 1.58061e7i | 0.812384 | + | 1.40709i | 0.911191 | + | 0.411984i | \(0.135164\pi\) |
−0.0988070 | + | 0.995107i | \(0.531503\pi\) | |||||||
\(662\) | −3.21585e6 | − | 5.57002e6i | −0.285201 | − | 0.493983i | ||||
\(663\) | 1617.99 | + | 2802.44i | 0.000142953 | + | 0.000247601i | ||||
\(664\) | 1.27788e6 | − | 2.21336e6i | 0.112479 | − | 0.194819i | ||||
\(665\) | 200868. | 0.0176139 | ||||||||
\(666\) | 1.27682e7 | − | 1.69077e7i | 1.11543 | − | 1.47707i | ||||
\(667\) | −7.37096e6 | −0.641519 | ||||||||
\(668\) | −2.30979e7 | + | 4.00067e7i | −2.00277 | + | 3.46890i | ||||
\(669\) | −215152. | − | 372654.i | −0.0185857 | − | 0.0321914i | ||||
\(670\) | 358785. | + | 621433.i | 0.0308778 | + | 0.0534820i | ||||
\(671\) | 9.39975e6 | + | 1.62808e7i | 0.805954 | + | 1.39595i | ||||
\(672\) | 1.90224e7 | 1.62496 | ||||||||
\(673\) | 1.91614e6 | + | 3.31885e6i | 0.163076 | + | 0.282455i | 0.935970 | − | 0.352079i | \(-0.114525\pi\) |
−0.772895 | + | 0.634534i | \(0.781192\pi\) | |||||||
\(674\) | −2.97974e7 | −2.52655 | ||||||||
\(675\) | −2.86301e6 | + | 4.95889e6i | −0.241860 | + | 0.418914i | ||||
\(676\) | 2.43200e7 | 2.04690 | ||||||||
\(677\) | −1.26925e7 | −1.06433 | −0.532164 | − | 0.846641i | \(-0.678621\pi\) | ||||
−0.532164 | + | 0.846641i | \(0.678621\pi\) | |||||||
\(678\) | −2.84617e6 | + | 4.92972e6i | −0.237786 | + | 0.411858i | ||||
\(679\) | 9.25694e6 | + | 1.60335e7i | 0.770536 | + | 1.33461i | ||||
\(680\) | 2067.80 | 0.000171489 | ||||||||
\(681\) | 533578. | − | 924183.i | 0.0440890 | − | 0.0763643i | ||||
\(682\) | 1.07945e7 | − | 1.86967e7i | 0.888675 | − | 1.53923i | ||||
\(683\) | 9.60314e6 | − | 1.66331e7i | 0.787701 | − | 1.36434i | −0.139671 | − | 0.990198i | \(-0.544605\pi\) |
0.927372 | − | 0.374140i | \(-0.122062\pi\) | |||||||
\(684\) | −4.44407e6 | − | 7.69735e6i | −0.363195 | − | 0.629073i | ||||
\(685\) | 225417. | + | 390434.i | 0.0183552 | + | 0.0317922i | ||||
\(686\) | 6.31629e6 | − | 1.09401e7i | 0.512450 | − | 0.887590i | ||||
\(687\) | −859879. | + | 1.48935e6i | −0.0695097 | + | 0.120394i | ||||
\(688\) | −6.07145e6 | + | 1.05161e7i | −0.489014 | + | 0.846997i | ||||
\(689\) | 200116. | 0.0160596 | ||||||||
\(690\) | 167823. | + | 290678.i | 0.0134192 | + | 0.0232428i | ||||
\(691\) | 9.21884e6 | − | 1.59675e7i | 0.734482 | − | 1.27216i | −0.220469 | − | 0.975394i | \(-0.570759\pi\) |
0.954950 | − | 0.296766i | \(-0.0959080\pi\) | |||||||
\(692\) | 2.41724e7 | 1.91891 | ||||||||
\(693\) | 1.35520e7 | 1.07194 | ||||||||
\(694\) | −8.41144e6 | + | 1.45690e7i | −0.662936 | + | 1.14824i | ||||
\(695\) | −88763.1 | −0.00697061 | ||||||||
\(696\) | −3.70847e6 | − | 6.42325e6i | −0.290182 | − | 0.502611i | ||||
\(697\) | 14334.6 | 0.00111764 | ||||||||
\(698\) | −1.17550e7 | − | 2.03602e7i | −0.913236 | − | 1.58177i | ||||
\(699\) | 2.69637e6 | + | 4.67026e6i | 0.208731 | + | 0.361533i | ||||
\(700\) | −2.36207e7 | − | 4.09122e7i | −1.82199 | − | 3.15579i | ||||
\(701\) | 5.49806e6 | − | 9.52292e6i | 0.422585 | − | 0.731939i | −0.573606 | − | 0.819131i | \(-0.694456\pi\) |
0.996192 | + | 0.0871920i | \(0.0277894\pi\) | |||||||
\(702\) | 1.63348e7 | 1.25104 | ||||||||
\(703\) | −2.11062e6 | + | 2.79489e6i | −0.161072 | + | 0.213293i | ||||
\(704\) | 6.75724e7 | 5.13852 | ||||||||
\(705\) | 53525.8 | − | 92709.4i | 0.00405593 | − | 0.00702508i | ||||
\(706\) | −9.62893e6 | − | 1.66778e7i | −0.727054 | − | 1.25929i | ||||
\(707\) | −9.73405e6 | − | 1.68599e7i | −0.732394 | − | 1.26854i | ||||
\(708\) | −7.88324e6 | − | 1.36542e7i | −0.591046 | − | 1.02372i | ||||
\(709\) | −5.13350e6 | −0.383529 | −0.191764 | − | 0.981441i | \(-0.561421\pi\) | ||||
−0.191764 | + | 0.981441i | \(0.561421\pi\) | |||||||
\(710\) | 338233. | + | 585837.i | 0.0251808 | + | 0.0436145i | ||||
\(711\) | −7.73154e6 | −0.573577 | ||||||||
\(712\) | −1.39156e7 | + | 2.41025e7i | −1.02873 | + | 1.78182i | ||||
\(713\) | 1.39760e7 | 1.02958 | ||||||||
\(714\) | −7420.50 | −0.000544738 | ||||||||
\(715\) | −423644. | + | 733773.i | −0.0309910 | + | 0.0536780i | ||||
\(716\) | −2.24318e7 | − | 3.88530e7i | −1.63524 | − | 2.83232i | ||||
\(717\) | −2.48321e6 | −0.180391 | ||||||||
\(718\) | −6.43555e6 | + | 1.11467e7i | −0.465881 | + | 0.806929i | ||||
\(719\) | 5.89947e6 | − | 1.02182e7i | 0.425589 | − | 0.737142i | −0.570886 | − | 0.821029i | \(-0.693400\pi\) |
0.996475 | + | 0.0838874i | \(0.0267336\pi\) | |||||||
\(720\) | 1.53661e6 | − | 2.66149e6i | 0.110467 | − | 0.191335i | ||||
\(721\) | 1.31916e7 | + | 2.28485e7i | 0.945060 | + | 1.63689i | ||||
\(722\) | −1.28418e7 | − | 2.22427e7i | −0.916820 | − | 1.58798i | ||||
\(723\) | 1.39561e6 | − | 2.41727e6i | 0.0992929 | − | 0.171980i | ||||
\(724\) | 1.75104e7 | − | 3.03290e7i | 1.24151 | − | 2.15036i | ||||
\(725\) | −4.36121e6 | + | 7.55384e6i | −0.308150 | + | 0.533731i | ||||
\(726\) | 1.23911e6 | 0.0872506 | ||||||||
\(727\) | −107117. | − | 185533.i | −0.00751665 | − | 0.0130192i | 0.862243 | − | 0.506495i | \(-0.169059\pi\) |
−0.869759 | + | 0.493476i | \(0.835726\pi\) | |||||||
\(728\) | −4.41434e7 | + | 7.64586e7i | −3.08701 | + | 5.34685i | ||||
\(729\) | −9.23049e6 | −0.643289 | ||||||||
\(730\) | 2.02686e6 | 0.140772 | ||||||||
\(731\) | 1370.36 | − | 2373.54i | 9.48509e−5 | − | 0.000164287i | ||||
\(732\) | −1.86931e7 | −1.28945 | ||||||||
\(733\) | 5.77161e6 | + | 9.99672e6i | 0.396768 | + | 0.687223i | 0.993325 | − | 0.115348i | \(-0.0367984\pi\) |
−0.596557 | + | 0.802571i | \(0.703465\pi\) | |||||||
\(734\) | 1.31822e7 | 0.903124 | ||||||||
\(735\) | −56390.8 | − | 97671.7i | −0.00385026 | − | 0.00666884i | ||||
\(736\) | 3.92830e7 | + | 6.80402e7i | 2.67307 | + | 4.62990i | ||||
\(737\) | −4.00136e6 | − | 6.93055e6i | −0.271355 | − | 0.470001i | ||||
\(738\) | 1.75044e7 | − | 3.03186e7i | 1.18306 | − | 2.04912i | ||||
\(739\) | −2.35473e7 | −1.58610 | −0.793048 | − | 0.609159i | \(-0.791507\pi\) | ||||
−0.793048 | + | 0.609159i | \(0.791507\pi\) | |||||||
\(740\) | −2.24150e6 | − | 277563.i | −0.150473 | − | 0.0186330i | ||||
\(741\) | −1.30641e6 | −0.0874042 | ||||||||
\(742\) | −229446. | + | 397412.i | −0.0152993 | + | 0.0264991i | ||||
\(743\) | −1.38303e7 | − | 2.39547e7i | −0.919091 | − | 1.59191i | −0.800798 | − | 0.598934i | \(-0.795591\pi\) |
−0.118293 | − | 0.992979i | \(-0.537742\pi\) | |||||||
\(744\) | 7.03160e6 | + | 1.21791e7i | 0.465716 | + | 0.806644i | ||||
\(745\) | −126147. | − | 218492.i | −0.00832693 | − | 0.0144227i | ||||
\(746\) | 7.86426e6 | 0.517382 | ||||||||
\(747\) | 428667. | + | 742474.i | 0.0281073 | + | 0.0486833i | ||||
\(748\) | −35202.0 | −0.00230045 | ||||||||
\(749\) | 9.64021e6 | − | 1.66973e7i | 0.627888 | − | 1.08753i | ||||
\(750\) | 795461. | 0.0516376 | ||||||||
\(751\) | 2.45156e7 | 1.58614 | 0.793072 | − | 0.609128i | \(-0.208480\pi\) | ||||
0.793072 | + | 0.609128i | \(0.208480\pi\) | |||||||
\(752\) | 2.16542e7 | − | 3.75062e7i | 1.39636 | − | 2.41857i | ||||
\(753\) | 2.88523e6 | + | 4.99737e6i | 0.185436 | + | 0.321184i | ||||
\(754\) | 2.48826e7 | 1.59393 | ||||||||
\(755\) | 216180. | − | 374435.i | 0.0138022 | − | 0.0239061i | ||||
\(756\) | −1.39259e7 | + | 2.41204e7i | −0.886175 | + | 1.53490i | ||||
\(757\) | −1.33213e7 | + | 2.30732e7i | −0.844906 | + | 1.46342i | 0.0407977 | + | 0.999167i | \(0.487010\pi\) |
−0.885703 | + | 0.464252i | \(0.846323\pi\) | |||||||
\(758\) | 1.55609e7 | + | 2.69523e7i | 0.983700 | + | 1.70382i | ||||
\(759\) | −1.87165e6 | − | 3.24179e6i | −0.117929 | − | 0.204259i | ||||
\(760\) | −417398. | + | 722954.i | −0.0262130 | + | 0.0454022i | ||||
\(761\) | −6.27905e6 | + | 1.08756e7i | −0.393036 | + | 0.680758i | −0.992848 | − | 0.119383i | \(-0.961908\pi\) |
0.599813 | + | 0.800141i | \(0.295242\pi\) | |||||||
\(762\) | 4.95859e6 | − | 8.58853e6i | 0.309365 | − | 0.535836i | ||||
\(763\) | −1.12459e7 | −0.699331 | ||||||||
\(764\) | 1.42434e7 | + | 2.46703e7i | 0.882838 | + | 1.52912i | ||||
\(765\) | −346.823 | + | 600.715i | −2.14266e−5 | + | 3.71120e-5i | ||||
\(766\) | 3.48158e7 | 2.14390 | ||||||||
\(767\) | 3.46514e7 | 2.12683 | ||||||||
\(768\) | −1.27851e7 | + | 2.21444e7i | −0.782168 | + | 1.35475i | ||||
\(769\) | 2.46945e6 | 0.150586 | 0.0752930 | − | 0.997161i | \(-0.476011\pi\) | ||||
0.0752930 | + | 0.997161i | \(0.476011\pi\) | |||||||
\(770\) | −971469. | − | 1.68263e6i | −0.0590476 | − | 0.102273i | ||||
\(771\) | −3.21233e6 | −0.194619 | ||||||||
\(772\) | 1.21738e7 | + | 2.10856e7i | 0.735161 | + | 1.27334i | ||||
\(773\) | −1.09133e7 | − | 1.89024e7i | −0.656913 | − | 1.13781i | −0.981411 | − | 0.191920i | \(-0.938529\pi\) |
0.324498 | − | 0.945886i | \(-0.394805\pi\) | |||||||
\(774\) | −3.34678e6 | − | 5.79680e6i | −0.200805 | − | 0.347805i | ||||
\(775\) | 8.26926e6 | − | 1.43228e7i | 0.494552 | − | 0.856590i | ||||
\(776\) | −7.69427e7 | −4.58684 | ||||||||
\(777\) | 5.26960e6 | + | 652532.i | 0.313131 | + | 0.0387748i | ||||
\(778\) | −1.72262e7 | −1.02033 | ||||||||
\(779\) | −2.89353e6 | + | 5.01174e6i | −0.170838 | + | 0.295900i | ||||
\(780\) | −421247. | − | 729621.i | −0.0247913 | − | 0.0429399i | ||||
\(781\) | −3.77215e6 | − | 6.53356e6i | −0.221290 | − | 0.383286i | ||||
\(782\) | −15324.0 | − | 26542.0i | −0.000896100 | − | 0.00155209i | ||||
\(783\) | 5.14243e6 | 0.299754 | ||||||||
\(784\) | −2.28133e7 | − | 3.95138e7i | −1.32555 | − | 2.29593i | ||||
\(785\) | 1.68925e6 | 0.0978406 | ||||||||
\(786\) | 2.61926e6 | − | 4.53669e6i | 0.151225 | − | 0.261929i | ||||
\(787\) | 1.00902e7 | 0.580714 | 0.290357 | − | 0.956918i | \(-0.406226\pi\) | ||||
0.290357 | + | 0.956918i | \(0.406226\pi\) | |||||||
\(788\) | −2.10720e7 | −1.20890 | ||||||||
\(789\) | 686639. | − | 1.18929e6i | 0.0392677 | − | 0.0680137i | ||||
\(790\) | 554231. | + | 959957.i | 0.0315954 | + | 0.0547248i | ||||
\(791\) | 2.13314e7 | 1.21221 | ||||||||
\(792\) | −2.81607e7 | + | 4.87758e7i | −1.59526 | + | 2.76307i | ||||
\(793\) | 2.05418e7 | − | 3.55794e7i | 1.15999 | − | 2.00917i | ||||
\(794\) | −5.34891e6 | + | 9.26458e6i | −0.301102 | + | 0.521524i | ||||
\(795\) | −1434.38 | − | 2484.42i | −8.04910e−5 | − | 0.000139414i | ||||
\(796\) | −2.03504e7 | − | 3.52479e7i | −1.13839 | − | 1.97174i | ||||
\(797\) | −1.04554e7 | + | 1.81092e7i | −0.583034 | + | 1.00984i | 0.412084 | + | 0.911146i | \(0.364801\pi\) |
−0.995117 | + | 0.0986979i | \(0.968532\pi\) | |||||||
\(798\) | 1.49788e6 | − | 2.59440e6i | 0.0832661 | − | 0.144221i | ||||
\(799\) | −4887.49 | + | 8465.37i | −0.000270844 | + | 0.000469115i | ||||
\(800\) | 9.29711e7 | 5.13598 | ||||||||
\(801\) | −4.66801e6 | − | 8.08524e6i | −0.257070 | − | 0.445258i | ||||
\(802\) | 5.46898e6 | − | 9.47254e6i | 0.300241 | − | 0.520033i | ||||
\(803\) | −2.26047e7 | −1.23711 | ||||||||
\(804\) | 7.95743e6 | 0.434143 | ||||||||
\(805\) | 628895. | − | 1.08928e6i | 0.0342049 | − | 0.0592447i | ||||
\(806\) | −4.71798e7 | −2.55810 | ||||||||
\(807\) | −633244. | − | 1.09681e6i | −0.0342285 | − | 0.0592854i | ||||
\(808\) | 8.09084e7 | 4.35979 | ||||||||
\(809\) | 1.03848e7 | + | 1.79870e7i | 0.557863 | + | 0.966248i | 0.997675 | + | 0.0681574i | \(0.0217120\pi\) |
−0.439811 | + | 0.898090i | \(0.644955\pi\) | |||||||
\(810\) | 786597. | + | 1.36243e6i | 0.0421250 | + | 0.0729626i | ||||
\(811\) | 6.40458e6 | + | 1.10931e7i | 0.341931 | + | 0.592242i | 0.984791 | − | 0.173741i | \(-0.0555857\pi\) |
−0.642860 | + | 0.765984i | \(0.722252\pi\) | |||||||
\(812\) | −2.12133e7 | + | 3.67424e7i | −1.12906 | + | 1.95559i | ||||
\(813\) | −515948. | −0.0273766 | ||||||||
\(814\) | 3.36200e7 | + | 4.16315e6i | 1.77843 | + | 0.220222i | ||||
\(815\) | −301826. | −0.0159171 | ||||||||
\(816\) | 9383.56 | − | 16252.8i | 0.000493336 | − | 0.000854482i | ||||
\(817\) | 553232. | + | 958226.i | 0.0289969 | + | 0.0502242i | ||||
\(818\) | −2.24510e7 | − | 3.88863e7i | −1.17315 | − | 2.03195i | ||||
\(819\) | −1.48080e7 | − | 2.56482e7i | −0.771411 | − | 1.33612i | ||||
\(820\) | −3.73204e6 | −0.193826 | ||||||||
\(821\) | 4.94783e6 | + | 8.56988e6i | 0.256187 | + | 0.443728i | 0.965217 | − | 0.261450i | \(-0.0842005\pi\) |
−0.709031 | + | 0.705178i | \(0.750867\pi\) | |||||||
\(822\) | 6.72376e6 | 0.347082 | ||||||||
\(823\) | −2.59111e6 | + | 4.48794e6i | −0.133348 | + | 0.230966i | −0.924965 | − | 0.380052i | \(-0.875906\pi\) |
0.791617 | + | 0.611017i | \(0.209239\pi\) | |||||||
\(824\) | −1.09647e8 | −5.62574 | ||||||||
\(825\) | −4.42963e6 | −0.226586 | ||||||||
\(826\) | −3.97300e7 | + | 6.88144e7i | −2.02614 | + | 3.50937i | ||||
\(827\) | 8.56896e6 | + | 1.48419e7i | 0.435677 | + | 0.754614i | 0.997351 | − | 0.0727444i | \(-0.0231757\pi\) |
−0.561674 | + | 0.827359i | \(0.689842\pi\) | |||||||
\(828\) | −5.56556e7 | −2.82120 | ||||||||
\(829\) | 150003. | − | 259813.i | 0.00758078 | − | 0.0131303i | −0.862210 | − | 0.506551i | \(-0.830920\pi\) |
0.869791 | + | 0.493420i | \(0.164254\pi\) | |||||||
\(830\) | 61457.6 | − | 106448.i | 0.00309657 | − | 0.00536341i | ||||
\(831\) | 1.03810e6 | − | 1.79805e6i | 0.0521481 | − | 0.0903231i | ||||
\(832\) | −7.38349e7 | − | 1.27886e8i | −3.69788 | − | 6.40492i | ||||
\(833\) | 5149.09 | + | 8918.49i | 0.000257109 | + | 0.000445327i | ||||
\(834\) | −661909. | + | 1.14646e6i | −0.0329521 | + | 0.0570747i | ||||
\(835\) | −727732. | + | 1.26047e6i | −0.0361206 | + | 0.0625627i | ||||
\(836\) | 7.10574e6 | − | 1.23075e7i | 0.351636 | − | 0.609052i | ||||
\(837\) | −9.75053e6 | −0.481077 | ||||||||
\(838\) | 1.07834e7 | + | 1.86774e7i | 0.530452 | + | 0.918770i | ||||
\(839\) | 1.13452e7 | − | 1.96505e7i | 0.556428 | − | 0.963761i | −0.441363 | − | 0.897329i | \(-0.645505\pi\) |
0.997791 | − | 0.0664325i | \(-0.0211617\pi\) | |||||||
\(840\) | 1.26564e6 | 0.0618886 | ||||||||
\(841\) | −1.26777e7 | −0.618089 | ||||||||
\(842\) | 2.78805e7 | − | 4.82904e7i | 1.35525 | − | 2.34737i | ||||
\(843\) | 5.32847e6 | 0.258246 | ||||||||
\(844\) | −2.44077e7 | − | 4.22754e7i | −1.17943 | − | 2.04283i | ||||
\(845\) | 766235. | 0.0369165 | ||||||||
\(846\) | 1.19365e7 | + | 2.06747e7i | 0.573393 | + | 0.993145i | ||||
\(847\) | −2.32171e6 | − | 4.02131e6i | −0.111198 | − | 0.192601i | ||||
\(848\) | −580289. | − | 1.00509e6i | −0.0277112 | − | 0.0479971i | ||||
\(849\) | −1.89196e6 | + | 3.27697e6i | −0.0900830 | + | 0.156028i | ||||
\(850\) | −36267.4 | −0.00172175 | ||||||||
\(851\) | 8.54822e6 | + | 2.01961e7i | 0.404624 | + | 0.955969i | ||||
\(852\) | 7.50162e6 | 0.354043 | ||||||||
\(853\) | −1.38424e7 | + | 2.39758e7i | −0.651388 | + | 1.12824i | 0.331398 | + | 0.943491i | \(0.392480\pi\) |
−0.982786 | + | 0.184746i | \(0.940854\pi\) | |||||||
\(854\) | 4.71049e7 | + | 8.15881e7i | 2.21015 | + | 3.82809i | ||||
\(855\) | −140017. | − | 242516.i | −0.00655035 | − | 0.0113455i | ||||
\(856\) | 4.00642e7 | + | 6.93933e7i | 1.86884 | + | 3.23693i | ||||
\(857\) | −2.40254e7 | −1.11743 | −0.558714 | − | 0.829361i | \(-0.688705\pi\) | ||||
−0.558714 | + | 0.829361i | \(0.688705\pi\) | |||||||
\(858\) | 6.31825e6 | + | 1.09435e7i | 0.293007 | + | 0.507504i | ||||
\(859\) | −1.54867e7 | −0.716106 | −0.358053 | − | 0.933701i | \(-0.616559\pi\) | ||||
−0.358053 | + | 0.933701i | \(0.616559\pi\) | |||||||
\(860\) | −356776. | + | 617955.i | −0.0164494 | + | 0.0284912i | ||||
\(861\) | 8.77377e6 | 0.403347 | ||||||||
\(862\) | 5.43831e7 | 2.49285 | ||||||||
\(863\) | 4.76679e6 | − | 8.25633e6i | 0.217871 | − | 0.377364i | −0.736286 | − | 0.676671i | \(-0.763422\pi\) |
0.954157 | + | 0.299307i | \(0.0967555\pi\) | |||||||
\(864\) | −2.74063e7 | − | 4.74691e7i | −1.24901 | − | 2.16335i | ||||
\(865\) | 761586. | 0.0346082 | ||||||||
\(866\) | −5.26071e6 | + | 9.11182e6i | −0.238369 | + | 0.412867i | ||||
\(867\) | 2.77077e6 | − | 4.79911e6i | 0.125185 | − | 0.216827i | ||||
\(868\) | 4.02223e7 | − | 6.96671e7i | 1.81204 | − | 3.13854i | ||||
\(869\) | −6.18108e6 | − | 1.07059e7i | −0.277661 | − | 0.480923i | ||||
\(870\) | −178352. | − | 308916.i | −0.00798879 | − | 0.0138370i | ||||
\(871\) | −8.74438e6 | + | 1.51457e7i | −0.390556 | + | 0.676463i | ||||
\(872\) | 2.33687e7 | − | 4.04757e7i | 1.04074 | − | 1.80262i | ||||
\(873\) | 1.29053e7 | − | 2.23526e7i | 0.573102 | − | 0.992641i | ||||
\(874\) | 1.23730e7 | 0.547894 | ||||||||
\(875\) | −1.49045e6 | − | 2.58153e6i | −0.0658107 | − | 0.113987i | ||||
\(876\) | 1.12384e7 | − | 1.94654e7i | 0.494815 | − | 0.857046i | ||||
\(877\) | −2.76664e7 | −1.21466 | −0.607328 | − | 0.794451i | \(-0.707759\pi\) | ||||
−0.607328 | + | 0.794451i | \(0.707759\pi\) | |||||||
\(878\) | 3.95617e7 | 1.73196 | ||||||||
\(879\) | −2.82975e6 | + | 4.90127e6i | −0.123531 | + | 0.213962i | ||||
\(880\) | 4.91387e6 | 0.213903 | ||||||||
\(881\) | 9.76484e6 | + | 1.69132e7i | 0.423863 | + | 0.734152i | 0.996314 | − | 0.0857870i | \(-0.0273404\pi\) |
−0.572450 | + | 0.819939i | \(0.694007\pi\) | |||||||
\(882\) | 2.51509e7 | 1.08863 | ||||||||
\(883\) | 217317. | + | 376405.i | 0.00937978 | + | 0.0162463i | 0.870677 | − | 0.491855i | \(-0.163681\pi\) |
−0.861297 | + | 0.508101i | \(0.830348\pi\) | |||||||
\(884\) | 38464.4 | + | 66622.3i | 0.00165550 | + | 0.00286740i | ||||
\(885\) | −248373. | − | 430194.i | −0.0106597 | − | 0.0184632i | ||||
\(886\) | −2.61179e7 | + | 4.52376e7i | −1.11778 | + | 1.93604i | ||||
\(887\) | −1.99392e7 | −0.850942 | −0.425471 | − | 0.904972i | \(-0.639891\pi\) | ||||
−0.425471 | + | 0.904972i | \(0.639891\pi\) | |||||||
\(888\) | −1.32987e7 | + | 1.76102e7i | −0.565947 | + | 0.749431i | ||||
\(889\) | −3.71634e7 | −1.57711 | ||||||||
\(890\) | −669248. | + | 1.15917e6i | −0.0283212 | + | 0.0490538i | ||||
\(891\) | −8.77254e6 | − | 1.51945e7i | −0.370196 | − | 0.641198i | ||||
\(892\) | −5.11480e6 | − | 8.85909e6i | −0.215237 | − | 0.372801i | ||||
\(893\) | −1.97314e6 | − | 3.41758e6i | −0.0827998 | − | 0.143413i | ||||
\(894\) | −3.76271e6 | −0.157455 | ||||||||
\(895\) | −706746. | − | 1.22412e6i | −0.0294921 | − | 0.0510818i | ||||
\(896\) | 1.82660e8 | 7.60103 | ||||||||
\(897\) | −4.09021e6 | + | 7.08446e6i | −0.169733 | + | 0.293985i | ||||
\(898\) | −1.43698e7 | −0.594647 | ||||||||
\(899\) | −1.48529e7 | −0.612932 | ||||||||
\(900\) | −3.29300e7 | + | 5.70365e7i | −1.35514 | + | 2.34718i | ||||
\(901\) | 130.975 | + | 226.855i | 5.37496e−6 | + | 9.30971e-6i | ||||
\(902\) | 5.59766e7 | 2.29082 | ||||||||
\(903\) | 838756. | − | 1.45277e6i | 0.0342308 | − | 0.0592894i | ||||
\(904\) | −4.43260e7 | + | 7.67749e7i | −1.80401 | + | 3.12463i | ||||
\(905\) | 551692. | − | 955558.i | 0.0223911 | − | 0.0387825i | ||||
\(906\) | −3.22412e6 | − | 5.58434e6i | −0.130494 | − | 0.226022i | ||||
\(907\) | −4.34752e6 | − | 7.53013e6i | −0.175478 | − | 0.303938i | 0.764848 | − | 0.644210i | \(-0.222814\pi\) |
−0.940327 | + | 0.340273i | \(0.889481\pi\) | |||||||
\(908\) | 1.26847e7 | − | 2.19706e7i | 0.510583 | − | 0.884355i | ||||
\(909\) | −1.35704e7 | + | 2.35047e7i | −0.544733 | + | 0.943505i | ||||
\(910\) | −2.12300e6 | + | 3.67715e6i | −0.0849860 | + | 0.147200i | ||||
\(911\) | 1.01465e7 | 0.405061 | 0.202531 | − | 0.979276i | \(-0.435083\pi\) | ||||
0.202531 | + | 0.979276i | \(0.435083\pi\) | |||||||
\(912\) | 3.78826e6 | + | 6.56146e6i | 0.150818 | + | 0.261224i | ||||
\(913\) | −685408. | + | 1.18716e6i | −0.0272127 | + | 0.0471338i | ||||
\(914\) | −2.87615e7 | −1.13880 | ||||||||
\(915\) | −588954. | −0.0232556 | ||||||||
\(916\) | −2.04419e7 | + | 3.54064e7i | −0.804974 | + | 1.39426i | ||||
\(917\) | −1.96307e7 | −0.770927 | ||||||||
\(918\) | 10691.0 | + | 18517.3i | 0.000418708 | + | 0.000725224i | ||||
\(919\) | 3.60671e7 | 1.40871 | 0.704355 | − | 0.709847i | \(-0.251236\pi\) | ||||
0.704355 | + | 0.709847i | \(0.251236\pi\) | |||||||
\(920\) | 2.61366e6 | + | 4.52699e6i | 0.101807 | + | 0.176335i | ||||
\(921\) | −4.10587e6 | − | 7.11157e6i | −0.159498 | − | 0.276259i | ||||
\(922\) | 3.99694e7 | + | 6.92290e7i | 1.54846 | + | 2.68201i | ||||
\(923\) | −8.24350e6 | + | 1.42782e7i | −0.318498 | + | 0.551655i | ||||
\(924\) | −2.15461e7 | −0.830210 | ||||||||
\(925\) | 2.57549e7 | + | 3.18922e6i | 0.989706 | + | 0.122555i | ||||
\(926\) | −7.10587e7 | −2.72326 | ||||||||
\(927\) | 1.83907e7 | − | 3.18536e7i | 0.702907 | − | 1.21747i | ||||
\(928\) | −4.17478e7 | − | 7.23093e7i | −1.59134 | − | 2.75628i | ||||
\(929\) | 878565. | + | 1.52172e6i | 0.0333991 | + | 0.0578489i | 0.882242 | − | 0.470797i | \(-0.156033\pi\) |
−0.848843 | + | 0.528646i | \(0.822700\pi\) | |||||||
\(930\) | 338173. | + | 585733.i | 0.0128213 | + | 0.0222071i | ||||
\(931\) | −4.15751e6 | −0.157202 | ||||||||
\(932\) | 6.41008e7 | + | 1.11026e8i | 2.41726 | + | 4.18682i | ||||
\(933\) | −4.68791e6 | −0.176309 | ||||||||
\(934\) | −7.74971e6 | + | 1.34229e7i | −0.290682 | + | 0.503476i | ||||
\(935\) | −1109.09 | −4.14894e−5 | ||||||||
\(936\) | 1.23082e8 | 4.59204 | ||||||||
\(937\) | 1.23212e7 | − | 2.13409e7i | 0.458461 | − | 0.794078i | −0.540419 | − | 0.841396i | \(-0.681734\pi\) |
0.998880 | + | 0.0473181i | \(0.0150675\pi\) | |||||||
\(938\) | −2.00520e7 | − | 3.47310e7i | −0.744132 | − | 1.28887i | ||||
\(939\) | 2.36552e6 | 0.0875512 | ||||||||
\(940\) | 1.27247e6 | − | 2.20398e6i | 0.0469707 | − | 0.0813556i | ||||
\(941\) | 2.13160e7 | − | 3.69204e7i | 0.784751 | − | 1.35923i | −0.144397 | − | 0.989520i | \(-0.546124\pi\) |
0.929148 | − | 0.369709i | \(-0.120543\pi\) | |||||||
\(942\) | 1.25968e7 | − | 2.18182e7i | 0.462521 | − | 0.801110i | ||||
\(943\) | 1.81187e7 | + | 3.13824e7i | 0.663509 | + | 1.14923i | ||||
\(944\) | −1.00481e8 | − | 1.74038e8i | −3.66989 | − | 6.35644i | ||||
\(945\) | −438756. | + | 759948.i | −0.0159825 | + | 0.0276824i | ||||
\(946\) | 5.35126e6 | − | 9.26866e6i | 0.194414 | − | 0.336736i | ||||
\(947\) | −9.10385e6 | + | 1.57683e7i | −0.329875 | + | 0.571361i | −0.982487 | − | 0.186332i | \(-0.940340\pi\) |
0.652611 | + | 0.757693i | \(0.273673\pi\) | |||||||
\(948\) | 1.22922e7 | 0.444231 | ||||||||
\(949\) | 2.46996e7 | + | 4.27810e7i | 0.890275 | + | 1.54200i | ||||
\(950\) | 7.32080e6 | − | 1.26800e7i | 0.263178 | − | 0.455837i | ||||
\(951\) | 192052. | 0.00688601 | ||||||||
\(952\) | −115566. | −0.00413275 | ||||||||
\(953\) | −1.64848e7 | + | 2.85525e7i | −0.587964 | + | 1.01838i | 0.406534 | + | 0.913635i | \(0.366737\pi\) |
−0.994499 | + | 0.104749i | \(0.966596\pi\) | |||||||
\(954\) | 639749. | 0.0227583 | ||||||||
\(955\) | 448759. | + | 777274.i | 0.0159223 | + | 0.0275782i | ||||
\(956\) | −5.90333e7 | −2.08907 | ||||||||
\(957\) | 1.98908e6 | + | 3.44519e6i | 0.0702058 | + | 0.121600i | ||||
\(958\) | 5.11116e6 | + | 8.85279e6i | 0.179931 | + | 0.311649i | ||||
\(959\) | −1.25982e7 | − | 2.18208e7i | −0.442347 | − | 0.766168i | ||||
\(960\) | −1.05846e6 | + | 1.83331e6i | −0.0370678 | + | 0.0642032i | ||||
\(961\) | −466646. | −0.0162997 | ||||||||
\(962\) | −2.88568e7 | − | 6.81773e7i | −1.00533 | − | 2.37521i | ||||
\(963\) | −2.68792e7 | −0.934008 | ||||||||
\(964\) | 3.31778e7 | − | 5.74656e7i | 1.14989 | − | 1.99166i | ||||
\(965\) | 383553. | + | 664333.i | 0.0132589 | + | 0.0229651i | ||||
\(966\) | −9.37938e6 | − | 1.62456e7i | −0.323393 | − | 0.560134i | ||||
\(967\) | −2.48466e7 | − | 4.30356e7i | −0.854478 | − | 1.48000i | −0.877128 | − | 0.480257i | \(-0.840544\pi\) |
0.0226496 | − | 0.999743i | \(-0.492790\pi\) | |||||||
\(968\) | 1.92978e7 | 0.661940 | ||||||||
\(969\) | −855.033 | − | 1480.96i | −2.92532e−5 | − | 5.06681e-5i | ||||
\(970\) | −3.70043e6 | −0.126277 | ||||||||
\(971\) | 1.13766e7 | − | 1.97049e7i | 0.387226 | − | 0.670696i | −0.604849 | − | 0.796340i | \(-0.706767\pi\) |
0.992075 | + | 0.125644i | \(0.0400998\pi\) | |||||||
\(972\) | 5.88714e7 | 1.99866 | ||||||||
\(973\) | 4.96085e6 | 0.167986 | ||||||||
\(974\) | 4.17546e7 | − | 7.23211e7i | 1.41029 | − | 2.44269i | ||||
\(975\) | 4.84015e6 | + | 8.38339e6i | 0.163060 | + | 0.282428i | ||||
\(976\) | −2.38265e8 | −8.00637 | ||||||||
\(977\) | 2.62371e7 | − | 4.54439e7i | 0.879385 | − | 1.52314i | 0.0273674 | − | 0.999625i | \(-0.491288\pi\) |
0.852017 | − | 0.523514i | \(-0.175379\pi\) | |||||||
\(978\) | −2.25073e6 | + | 3.89837e6i | −0.0752446 | + | 0.130328i | ||||
\(979\) | 7.46381e6 | − | 1.29277e7i | 0.248888 | − | 0.431087i | ||||
\(980\) | −1.34058e6 | − | 2.32195e6i | −0.0445889 | − | 0.0772302i | ||||
\(981\) | 7.83906e6 | + | 1.35776e7i | 0.260071 | + | 0.450456i | ||||
\(982\) | −3.36824e7 | + | 5.83397e7i | −1.11461 | + | 1.93057i | ||||
\(983\) | −2.71054e7 | + | 4.69479e7i | −0.894689 | + | 1.54965i | −0.0605002 | + | 0.998168i | \(0.519270\pi\) |
−0.834189 | + | 0.551479i | \(0.814064\pi\) | |||||||
\(984\) | −1.82317e7 | + | 3.15782e7i | −0.600259 | + | 1.03968i | ||||
\(985\) | −663903. | −0.0218029 | ||||||||
\(986\) | 16285.5 | + | 28207.3i | 0.000533469 | + | 0.000923995i | ||||
\(987\) | −2.99148e6 | + | 5.18140e6i | −0.0977447 | + | 0.169299i | ||||
\(988\) | −3.10571e7 | −1.01221 | ||||||||
\(989\) | 6.92844e6 | 0.225240 | ||||||||
\(990\) | −1.35434e6 | + | 2.34579e6i | −0.0439178 | + | 0.0760679i | ||||
\(991\) | 4.13018e7 | 1.33593 | 0.667966 | − | 0.744191i | \(-0.267165\pi\) | ||||
0.667966 | + | 0.744191i | \(0.267165\pi\) | |||||||
\(992\) | 7.91577e7 | + | 1.37105e8i | 2.55396 | + | 4.42359i | ||||
\(993\) | −2.24716e6 | −0.0723205 | ||||||||
\(994\) | −1.89034e7 | − | 3.27416e7i | −0.606839 | − | 1.05108i | ||||
\(995\) | −641167. | − | 1.11053e6i | −0.0205312 | − | 0.0355610i | ||||
\(996\) | −681529. | − | 1.18044e6i | −0.0217689 | − | 0.0377048i | ||||
\(997\) | 6.24004e6 | − | 1.08081e7i | 0.198815 | − | 0.344358i | −0.749329 | − | 0.662197i | \(-0.769624\pi\) |
0.948145 | + | 0.317840i | \(0.102957\pi\) | |||||||
\(998\) | 9.05483e6 | 0.287776 | ||||||||
\(999\) | −5.96376e6 | − | 1.40901e7i | −0.189063 | − | 0.446682i |
(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 | 37.6.c.a.10.15 | ✓ | 30 | |
37.26 | even | 3 | inner | 37.6.c.a.26.15 | yes | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.6.c.a.10.15 | ✓ | 30 | 1.1 | even | 1 | trivial | |
37.6.c.a.26.15 | yes | 30 | 37.26 | even | 3 | inner |