Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,6,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.a (trivial) |
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: | yes |
Analytic conductor: | \(167.601091705\) |
Analytic rank: | \(1\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.34806 | −1.29897 | −0.649483 | − | 0.760376i | \(-0.725014\pi\) | ||||
−0.649483 | + | 0.760376i | \(0.725014\pi\) | |||||||
\(3\) | 21.4317 | 1.37485 | 0.687424 | − | 0.726257i | \(-0.258742\pi\) | ||||
0.687424 | + | 0.726257i | \(0.258742\pi\) | |||||||
\(4\) | 21.9939 | 0.687311 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | −157.482 | −1.78588 | ||||||||
\(7\) | 84.2288 | 0.649704 | 0.324852 | − | 0.945765i | \(-0.394686\pi\) | ||||
0.324852 | + | 0.945765i | \(0.394686\pi\) | |||||||
\(8\) | 73.5250 | 0.406172 | ||||||||
\(9\) | 216.320 | 0.890205 | ||||||||
\(10\) | −183.701 | −0.580915 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 471.369 | 0.944948 | ||||||||
\(13\) | −947.397 | −1.55480 | −0.777399 | − | 0.629008i | \(-0.783461\pi\) | ||||
−0.777399 | + | 0.629008i | \(0.783461\pi\) | |||||||
\(14\) | −618.918 | −0.843943 | ||||||||
\(15\) | 535.794 | 0.614850 | ||||||||
\(16\) | −1244.07 | −1.21491 | ||||||||
\(17\) | 938.005 | 0.787196 | 0.393598 | − | 0.919283i | \(-0.371230\pi\) | ||||
0.393598 | + | 0.919283i | \(0.371230\pi\) | |||||||
\(18\) | −1589.53 | −1.15635 | ||||||||
\(19\) | −361.000 | −0.229416 | ||||||||
\(20\) | 549.849 | 0.307375 | ||||||||
\(21\) | 1805.17 | 0.893243 | ||||||||
\(22\) | −889.115 | −0.391653 | ||||||||
\(23\) | −752.093 | −0.296450 | −0.148225 | − | 0.988954i | \(-0.547356\pi\) | ||||
−0.148225 | + | 0.988954i | \(0.547356\pi\) | |||||||
\(24\) | 1575.77 | 0.558425 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 6961.53 | 2.01963 | ||||||||
\(27\) | −571.803 | −0.150951 | ||||||||
\(28\) | 1852.52 | 0.446548 | ||||||||
\(29\) | 2571.32 | 0.567756 | 0.283878 | − | 0.958860i | \(-0.408379\pi\) | ||||
0.283878 | + | 0.958860i | \(0.408379\pi\) | |||||||
\(30\) | −3937.04 | −0.798669 | ||||||||
\(31\) | −2474.20 | −0.462414 | −0.231207 | − | 0.972905i | \(-0.574267\pi\) | ||||
−0.231207 | + | 0.972905i | \(0.574267\pi\) | |||||||
\(32\) | 6788.72 | 1.17196 | ||||||||
\(33\) | 2593.24 | 0.414532 | ||||||||
\(34\) | −6892.52 | −1.02254 | ||||||||
\(35\) | 2105.72 | 0.290556 | ||||||||
\(36\) | 4757.73 | 0.611848 | ||||||||
\(37\) | −8564.08 | −1.02843 | −0.514217 | − | 0.857660i | \(-0.671917\pi\) | ||||
−0.514217 | + | 0.857660i | \(0.671917\pi\) | |||||||
\(38\) | 2652.65 | 0.298003 | ||||||||
\(39\) | −20304.4 | −2.13761 | ||||||||
\(40\) | 1838.13 | 0.181646 | ||||||||
\(41\) | 7460.09 | 0.693082 | 0.346541 | − | 0.938035i | \(-0.387356\pi\) | ||||
0.346541 | + | 0.938035i | \(0.387356\pi\) | |||||||
\(42\) | −13264.5 | −1.16029 | ||||||||
\(43\) | −9669.23 | −0.797482 | −0.398741 | − | 0.917064i | \(-0.630553\pi\) | ||||
−0.398741 | + | 0.917064i | \(0.630553\pi\) | |||||||
\(44\) | 2661.27 | 0.207232 | ||||||||
\(45\) | 5408.00 | 0.398112 | ||||||||
\(46\) | 5526.42 | 0.385079 | ||||||||
\(47\) | 22597.7 | 1.49217 | 0.746087 | − | 0.665849i | \(-0.231930\pi\) | ||||
0.746087 | + | 0.665849i | \(0.231930\pi\) | |||||||
\(48\) | −26662.7 | −1.67032 | ||||||||
\(49\) | −9712.51 | −0.577885 | ||||||||
\(50\) | −4592.54 | −0.259793 | ||||||||
\(51\) | 20103.1 | 1.08227 | ||||||||
\(52\) | −20837.0 | −1.06863 | ||||||||
\(53\) | −37071.2 | −1.81279 | −0.906393 | − | 0.422435i | \(-0.861175\pi\) | ||||
−0.906393 | + | 0.422435i | \(0.861175\pi\) | |||||||
\(54\) | 4201.64 | 0.196080 | ||||||||
\(55\) | 3025.00 | 0.134840 | ||||||||
\(56\) | 6192.92 | 0.263892 | ||||||||
\(57\) | −7736.86 | −0.315412 | ||||||||
\(58\) | −18894.2 | −0.737496 | ||||||||
\(59\) | −9732.55 | −0.363996 | −0.181998 | − | 0.983299i | \(-0.558256\pi\) | ||||
−0.181998 | + | 0.983299i | \(0.558256\pi\) | |||||||
\(60\) | 11784.2 | 0.422593 | ||||||||
\(61\) | −37427.8 | −1.28786 | −0.643932 | − | 0.765082i | \(-0.722698\pi\) | ||||
−0.643932 | + | 0.765082i | \(0.722698\pi\) | |||||||
\(62\) | 18180.6 | 0.600660 | ||||||||
\(63\) | 18220.4 | 0.578370 | ||||||||
\(64\) | −10073.5 | −0.307420 | ||||||||
\(65\) | −23684.9 | −0.695327 | ||||||||
\(66\) | −19055.3 | −0.538463 | ||||||||
\(67\) | 618.633 | 0.0168363 | 0.00841814 | − | 0.999965i | \(-0.497320\pi\) | ||||
0.00841814 | + | 0.999965i | \(0.497320\pi\) | |||||||
\(68\) | 20630.4 | 0.541048 | ||||||||
\(69\) | −16118.7 | −0.407574 | ||||||||
\(70\) | −15472.9 | −0.377423 | ||||||||
\(71\) | 47045.0 | 1.10756 | 0.553780 | − | 0.832663i | \(-0.313185\pi\) | ||||
0.553780 | + | 0.832663i | \(0.313185\pi\) | |||||||
\(72\) | 15904.9 | 0.361577 | ||||||||
\(73\) | −63309.4 | −1.39047 | −0.695234 | − | 0.718783i | \(-0.744699\pi\) | ||||
−0.695234 | + | 0.718783i | \(0.744699\pi\) | |||||||
\(74\) | 62929.3 | 1.33590 | ||||||||
\(75\) | 13394.8 | 0.274969 | ||||||||
\(76\) | −7939.82 | −0.157680 | ||||||||
\(77\) | 10191.7 | 0.195893 | ||||||||
\(78\) | 149198. | 2.77668 | ||||||||
\(79\) | −20032.8 | −0.361139 | −0.180570 | − | 0.983562i | \(-0.557794\pi\) | ||||
−0.180570 | + | 0.983562i | \(0.557794\pi\) | |||||||
\(80\) | −31101.8 | −0.543326 | ||||||||
\(81\) | −64820.5 | −1.09774 | ||||||||
\(82\) | −54817.2 | −0.900289 | ||||||||
\(83\) | 87828.4 | 1.39939 | 0.699697 | − | 0.714440i | \(-0.253318\pi\) | ||||
0.699697 | + | 0.714440i | \(0.253318\pi\) | |||||||
\(84\) | 39702.8 | 0.613936 | ||||||||
\(85\) | 23450.1 | 0.352045 | ||||||||
\(86\) | 71050.0 | 1.03590 | ||||||||
\(87\) | 55108.0 | 0.780578 | ||||||||
\(88\) | 8896.53 | 0.122466 | ||||||||
\(89\) | −10825.3 | −0.144866 | −0.0724329 | − | 0.997373i | \(-0.523076\pi\) | ||||
−0.0724329 | + | 0.997373i | \(0.523076\pi\) | |||||||
\(90\) | −39738.3 | −0.517133 | ||||||||
\(91\) | −79798.1 | −1.01016 | ||||||||
\(92\) | −16541.5 | −0.203754 | ||||||||
\(93\) | −53026.5 | −0.635749 | ||||||||
\(94\) | −166049. | −1.93828 | ||||||||
\(95\) | −9025.00 | −0.102598 | ||||||||
\(96\) | 145494. | 1.61127 | ||||||||
\(97\) | 23614.4 | 0.254829 | 0.127414 | − | 0.991850i | \(-0.459332\pi\) | ||||
0.127414 | + | 0.991850i | \(0.459332\pi\) | |||||||
\(98\) | 71368.1 | 0.750653 | ||||||||
\(99\) | 26174.7 | 0.268407 | ||||||||
\(100\) | 13746.2 | 0.137462 | ||||||||
\(101\) | −100508. | −0.980386 | −0.490193 | − | 0.871614i | \(-0.663074\pi\) | ||||
−0.490193 | + | 0.871614i | \(0.663074\pi\) | |||||||
\(102\) | −147719. | −1.40584 | ||||||||
\(103\) | 76767.1 | 0.712987 | 0.356494 | − | 0.934298i | \(-0.383972\pi\) | ||||
0.356494 | + | 0.934298i | \(0.383972\pi\) | |||||||
\(104\) | −69657.4 | −0.631516 | ||||||||
\(105\) | 45129.2 | 0.399471 | ||||||||
\(106\) | 272401. | 2.35475 | ||||||||
\(107\) | −221627. | −1.87138 | −0.935691 | − | 0.352820i | \(-0.885223\pi\) | ||||
−0.935691 | + | 0.352820i | \(0.885223\pi\) | |||||||
\(108\) | −12576.2 | −0.103750 | ||||||||
\(109\) | −139956. | −1.12831 | −0.564153 | − | 0.825670i | \(-0.690797\pi\) | ||||
−0.564153 | + | 0.825670i | \(0.690797\pi\) | |||||||
\(110\) | −22227.9 | −0.175152 | ||||||||
\(111\) | −183543. | −1.41394 | ||||||||
\(112\) | −104787. | −0.789335 | ||||||||
\(113\) | 10011.3 | 0.0737558 | 0.0368779 | − | 0.999320i | \(-0.488259\pi\) | ||||
0.0368779 | + | 0.999320i | \(0.488259\pi\) | |||||||
\(114\) | 56850.9 | 0.409709 | ||||||||
\(115\) | −18802.3 | −0.132577 | ||||||||
\(116\) | 56553.6 | 0.390225 | ||||||||
\(117\) | −204941. | −1.38409 | ||||||||
\(118\) | 71515.3 | 0.472818 | ||||||||
\(119\) | 79007.0 | 0.511444 | ||||||||
\(120\) | 39394.3 | 0.249735 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 275022. | 1.67289 | ||||||||
\(123\) | 159883. | 0.952882 | ||||||||
\(124\) | −54417.5 | −0.317822 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | −133884. | −0.751282 | ||||||||
\(127\) | −352689. | −1.94036 | −0.970181 | − | 0.242381i | \(-0.922072\pi\) | ||||
−0.970181 | + | 0.242381i | \(0.922072\pi\) | |||||||
\(128\) | −143218. | −0.772631 | ||||||||
\(129\) | −207228. | −1.09642 | ||||||||
\(130\) | 174038. | 0.903205 | ||||||||
\(131\) | −219577. | −1.11792 | −0.558958 | − | 0.829196i | \(-0.688799\pi\) | ||||
−0.558958 | + | 0.829196i | \(0.688799\pi\) | |||||||
\(132\) | 57035.6 | 0.284912 | ||||||||
\(133\) | −30406.6 | −0.149052 | ||||||||
\(134\) | −4545.75 | −0.0218698 | ||||||||
\(135\) | −14295.1 | −0.0675075 | ||||||||
\(136\) | 68966.9 | 0.319737 | ||||||||
\(137\) | 79257.9 | 0.360779 | 0.180389 | − | 0.983595i | \(-0.442264\pi\) | ||||
0.180389 | + | 0.983595i | \(0.442264\pi\) | |||||||
\(138\) | 118441. | 0.529424 | ||||||||
\(139\) | −152220. | −0.668244 | −0.334122 | − | 0.942530i | \(-0.608440\pi\) | ||||
−0.334122 | + | 0.942530i | \(0.608440\pi\) | |||||||
\(140\) | 46313.1 | 0.199703 | ||||||||
\(141\) | 484308. | 2.05151 | ||||||||
\(142\) | −345689. | −1.43868 | ||||||||
\(143\) | −114635. | −0.468789 | ||||||||
\(144\) | −269118. | −1.08152 | ||||||||
\(145\) | 64283.1 | 0.253908 | ||||||||
\(146\) | 465201. | 1.80617 | ||||||||
\(147\) | −208156. | −0.794504 | ||||||||
\(148\) | −188358. | −0.706854 | ||||||||
\(149\) | 224953. | 0.830093 | 0.415046 | − | 0.909800i | \(-0.363765\pi\) | ||||
0.415046 | + | 0.909800i | \(0.363765\pi\) | |||||||
\(150\) | −98426.1 | −0.357176 | ||||||||
\(151\) | 14688.3 | 0.0524241 | 0.0262120 | − | 0.999656i | \(-0.491655\pi\) | ||||
0.0262120 | + | 0.999656i | \(0.491655\pi\) | |||||||
\(152\) | −26542.5 | −0.0931823 | ||||||||
\(153\) | 202909. | 0.700766 | ||||||||
\(154\) | −74889.1 | −0.254458 | ||||||||
\(155\) | −61855.0 | −0.206798 | ||||||||
\(156\) | −446574. | −1.46920 | ||||||||
\(157\) | 32994.6 | 0.106830 | 0.0534151 | − | 0.998572i | \(-0.482989\pi\) | ||||
0.0534151 | + | 0.998572i | \(0.482989\pi\) | |||||||
\(158\) | 147202. | 0.469107 | ||||||||
\(159\) | −794500. | −2.49230 | ||||||||
\(160\) | 169718. | 0.524116 | ||||||||
\(161\) | −63347.9 | −0.192605 | ||||||||
\(162\) | 476304. | 1.42593 | ||||||||
\(163\) | 110502. | 0.325762 | 0.162881 | − | 0.986646i | \(-0.447921\pi\) | ||||
0.162881 | + | 0.986646i | \(0.447921\pi\) | |||||||
\(164\) | 164077. | 0.476363 | ||||||||
\(165\) | 64831.0 | 0.185384 | ||||||||
\(166\) | −645368. | −1.81776 | ||||||||
\(167\) | 256704. | 0.712264 | 0.356132 | − | 0.934436i | \(-0.384095\pi\) | ||||
0.356132 | + | 0.934436i | \(0.384095\pi\) | |||||||
\(168\) | 132725. | 0.362811 | ||||||||
\(169\) | 526269. | 1.41739 | ||||||||
\(170\) | −172313. | −0.457294 | ||||||||
\(171\) | −78091.5 | −0.204227 | ||||||||
\(172\) | −212664. | −0.548118 | ||||||||
\(173\) | 565322. | 1.43609 | 0.718043 | − | 0.695999i | \(-0.245038\pi\) | ||||
0.718043 | + | 0.695999i | \(0.245038\pi\) | |||||||
\(174\) | −404937. | −1.01394 | ||||||||
\(175\) | 52643.0 | 0.129941 | ||||||||
\(176\) | −150533. | −0.366311 | ||||||||
\(177\) | −208586. | −0.500439 | ||||||||
\(178\) | 79545.1 | 0.188176 | ||||||||
\(179\) | 758958. | 1.77046 | 0.885228 | − | 0.465157i | \(-0.154002\pi\) | ||||
0.885228 | + | 0.465157i | \(0.154002\pi\) | |||||||
\(180\) | 118943. | 0.273627 | ||||||||
\(181\) | −558952. | −1.26817 | −0.634086 | − | 0.773263i | \(-0.718623\pi\) | ||||
−0.634086 | + | 0.773263i | \(0.718623\pi\) | |||||||
\(182\) | 586361. | 1.31216 | ||||||||
\(183\) | −802144. | −1.77062 | ||||||||
\(184\) | −55297.7 | −0.120410 | ||||||||
\(185\) | −214102. | −0.459929 | ||||||||
\(186\) | 389642. | 0.825815 | ||||||||
\(187\) | 113499. | 0.237349 | ||||||||
\(188\) | 497012. | 1.02559 | ||||||||
\(189\) | −48162.2 | −0.0980736 | ||||||||
\(190\) | 66316.2 | 0.133271 | ||||||||
\(191\) | 330907. | 0.656330 | 0.328165 | − | 0.944620i | \(-0.393570\pi\) | ||||
0.328165 | + | 0.944620i | \(0.393570\pi\) | |||||||
\(192\) | −215894. | −0.422656 | ||||||||
\(193\) | 504756. | 0.975411 | 0.487706 | − | 0.873008i | \(-0.337834\pi\) | ||||
0.487706 | + | 0.873008i | \(0.337834\pi\) | |||||||
\(194\) | −173520. | −0.331014 | ||||||||
\(195\) | −507610. | −0.955968 | ||||||||
\(196\) | −213617. | −0.397187 | ||||||||
\(197\) | 768297. | 1.41047 | 0.705234 | − | 0.708974i | \(-0.250842\pi\) | ||||
0.705234 | + | 0.708974i | \(0.250842\pi\) | |||||||
\(198\) | −192333. | −0.348651 | ||||||||
\(199\) | 390726. | 0.699422 | 0.349711 | − | 0.936858i | \(-0.386280\pi\) | ||||
0.349711 | + | 0.936858i | \(0.386280\pi\) | |||||||
\(200\) | 45953.2 | 0.0812345 | ||||||||
\(201\) | 13258.4 | 0.0231473 | ||||||||
\(202\) | 738538. | 1.27349 | ||||||||
\(203\) | 216580. | 0.368873 | ||||||||
\(204\) | 442146. | 0.743859 | ||||||||
\(205\) | 186502. | 0.309956 | ||||||||
\(206\) | −564089. | −0.926146 | ||||||||
\(207\) | −162693. | −0.263902 | ||||||||
\(208\) | 1.17863e6 | 1.88895 | ||||||||
\(209\) | −43681.0 | −0.0691714 | ||||||||
\(210\) | −331612. | −0.518898 | ||||||||
\(211\) | −604166. | −0.934222 | −0.467111 | − | 0.884199i | \(-0.654705\pi\) | ||||
−0.467111 | + | 0.884199i | \(0.654705\pi\) | |||||||
\(212\) | −815341. | −1.24595 | ||||||||
\(213\) | 1.00826e6 | 1.52273 | ||||||||
\(214\) | 1.62853e6 | 2.43086 | ||||||||
\(215\) | −241731. | −0.356645 | ||||||||
\(216\) | −42041.8 | −0.0613122 | ||||||||
\(217\) | −208399. | −0.300432 | ||||||||
\(218\) | 1.02841e6 | 1.46563 | ||||||||
\(219\) | −1.35683e6 | −1.91168 | ||||||||
\(220\) | 66531.7 | 0.0926770 | ||||||||
\(221\) | −888664. | −1.22393 | ||||||||
\(222\) | 1.34869e6 | 1.83666 | ||||||||
\(223\) | 976246. | 1.31461 | 0.657305 | − | 0.753624i | \(-0.271696\pi\) | ||||
0.657305 | + | 0.753624i | \(0.271696\pi\) | |||||||
\(224\) | 571805. | 0.761427 | ||||||||
\(225\) | 135200. | 0.178041 | ||||||||
\(226\) | −73563.9 | −0.0958063 | ||||||||
\(227\) | −1.09207e6 | −1.40665 | −0.703326 | − | 0.710868i | \(-0.748302\pi\) | ||||
−0.703326 | + | 0.710868i | \(0.748302\pi\) | |||||||
\(228\) | −170164. | −0.216786 | ||||||||
\(229\) | 57325.7 | 0.0722372 | 0.0361186 | − | 0.999348i | \(-0.488501\pi\) | ||||
0.0361186 | + | 0.999348i | \(0.488501\pi\) | |||||||
\(230\) | 138161. | 0.172212 | ||||||||
\(231\) | 218426. | 0.269323 | ||||||||
\(232\) | 189057. | 0.230607 | ||||||||
\(233\) | −117833. | −0.142193 | −0.0710965 | − | 0.997469i | \(-0.522650\pi\) | ||||
−0.0710965 | + | 0.997469i | \(0.522650\pi\) | |||||||
\(234\) | 1.50592e6 | 1.79788 | ||||||||
\(235\) | 564942. | 0.667320 | ||||||||
\(236\) | −214057. | −0.250178 | ||||||||
\(237\) | −429338. | −0.496511 | ||||||||
\(238\) | −580548. | −0.664348 | ||||||||
\(239\) | 60104.5 | 0.0680631 | 0.0340316 | − | 0.999421i | \(-0.489165\pi\) | ||||
0.0340316 | + | 0.999421i | \(0.489165\pi\) | |||||||
\(240\) | −666566. | −0.746991 | ||||||||
\(241\) | −836662. | −0.927913 | −0.463956 | − | 0.885858i | \(-0.653571\pi\) | ||||
−0.463956 | + | 0.885858i | \(0.653571\pi\) | |||||||
\(242\) | −107583. | −0.118088 | ||||||||
\(243\) | −1.25027e6 | −1.35827 | ||||||||
\(244\) | −823186. | −0.885163 | ||||||||
\(245\) | −242813. | −0.258438 | ||||||||
\(246\) | −1.17483e6 | −1.23776 | ||||||||
\(247\) | 342010. | 0.356695 | ||||||||
\(248\) | −181916. | −0.187820 | ||||||||
\(249\) | 1.88232e6 | 1.92395 | ||||||||
\(250\) | −114813. | −0.116183 | ||||||||
\(251\) | 277631. | 0.278153 | 0.139077 | − | 0.990282i | \(-0.455587\pi\) | ||||
0.139077 | + | 0.990282i | \(0.455587\pi\) | |||||||
\(252\) | 400737. | 0.397520 | ||||||||
\(253\) | −91003.2 | −0.0893831 | ||||||||
\(254\) | 2.59158e6 | 2.52046 | ||||||||
\(255\) | 502577. | 0.484008 | ||||||||
\(256\) | 1.37473e6 | 1.31104 | ||||||||
\(257\) | 1.15289e6 | 1.08882 | 0.544409 | − | 0.838820i | \(-0.316754\pi\) | ||||
0.544409 | + | 0.838820i | \(0.316754\pi\) | |||||||
\(258\) | 1.52273e6 | 1.42421 | ||||||||
\(259\) | −721342. | −0.668177 | ||||||||
\(260\) | −520925. | −0.477905 | ||||||||
\(261\) | 556229. | 0.505419 | ||||||||
\(262\) | 1.61347e6 | 1.45213 | ||||||||
\(263\) | −80717.3 | −0.0719577 | −0.0359788 | − | 0.999353i | \(-0.511455\pi\) | ||||
−0.0359788 | + | 0.999353i | \(0.511455\pi\) | |||||||
\(264\) | 190668. | 0.168371 | ||||||||
\(265\) | −926779. | −0.810703 | ||||||||
\(266\) | 223429. | 0.193614 | ||||||||
\(267\) | −232006. | −0.199168 | ||||||||
\(268\) | 13606.2 | 0.0115718 | ||||||||
\(269\) | −1.72261e6 | −1.45146 | −0.725732 | − | 0.687977i | \(-0.758499\pi\) | ||||
−0.725732 | + | 0.687977i | \(0.758499\pi\) | |||||||
\(270\) | 105041. | 0.0876899 | ||||||||
\(271\) | 513468. | 0.424708 | 0.212354 | − | 0.977193i | \(-0.431887\pi\) | ||||
0.212354 | + | 0.977193i | \(0.431887\pi\) | |||||||
\(272\) | −1.16695e6 | −0.956376 | ||||||||
\(273\) | −1.71021e6 | −1.38881 | ||||||||
\(274\) | −582391. | −0.468639 | ||||||||
\(275\) | 75625.0 | 0.0603023 | ||||||||
\(276\) | −354513. | −0.280130 | ||||||||
\(277\) | −597435. | −0.467833 | −0.233917 | − | 0.972257i | \(-0.575154\pi\) | ||||
−0.233917 | + | 0.972257i | \(0.575154\pi\) | |||||||
\(278\) | 1.11852e6 | 0.868025 | ||||||||
\(279\) | −535219. | −0.411643 | ||||||||
\(280\) | 154823. | 0.118016 | ||||||||
\(281\) | −1.00075e6 | −0.756068 | −0.378034 | − | 0.925792i | \(-0.623400\pi\) | ||||
−0.378034 | + | 0.925792i | \(0.623400\pi\) | |||||||
\(282\) | −3.55872e6 | −2.66484 | ||||||||
\(283\) | 178437. | 0.132440 | 0.0662201 | − | 0.997805i | \(-0.478906\pi\) | ||||
0.0662201 | + | 0.997805i | \(0.478906\pi\) | |||||||
\(284\) | 1.03470e6 | 0.761238 | ||||||||
\(285\) | −193422. | −0.141056 | ||||||||
\(286\) | 842345. | 0.608941 | ||||||||
\(287\) | 628354. | 0.450298 | ||||||||
\(288\) | 1.46853e6 | 1.04328 | ||||||||
\(289\) | −540003. | −0.380322 | ||||||||
\(290\) | −472356. | −0.329818 | ||||||||
\(291\) | 506099. | 0.350351 | ||||||||
\(292\) | −1.39242e6 | −0.955684 | ||||||||
\(293\) | −634516. | −0.431791 | −0.215896 | − | 0.976416i | \(-0.569267\pi\) | ||||
−0.215896 | + | 0.976416i | \(0.569267\pi\) | |||||||
\(294\) | 1.52954e6 | 1.03203 | ||||||||
\(295\) | −243314. | −0.162784 | ||||||||
\(296\) | −629674. | −0.417721 | ||||||||
\(297\) | −69188.1 | −0.0455135 | ||||||||
\(298\) | −1.65297e6 | −1.07826 | ||||||||
\(299\) | 712531. | 0.460920 | ||||||||
\(300\) | 294605. | 0.188990 | ||||||||
\(301\) | −814427. | −0.518127 | ||||||||
\(302\) | −107931. | −0.0680970 | ||||||||
\(303\) | −2.15406e6 | −1.34788 | ||||||||
\(304\) | 449110. | 0.278721 | ||||||||
\(305\) | −935696. | −0.575951 | ||||||||
\(306\) | −1.49099e6 | −0.910271 | ||||||||
\(307\) | −1.20427e6 | −0.729255 | −0.364628 | − | 0.931153i | \(-0.618804\pi\) | ||||
−0.364628 | + | 0.931153i | \(0.618804\pi\) | |||||||
\(308\) | 224155. | 0.134639 | ||||||||
\(309\) | 1.64525e6 | 0.980249 | ||||||||
\(310\) | 454514. | 0.268623 | ||||||||
\(311\) | −773440. | −0.453446 | −0.226723 | − | 0.973959i | \(-0.572801\pi\) | ||||
−0.226723 | + | 0.973959i | \(0.572801\pi\) | |||||||
\(312\) | −1.49288e6 | −0.868238 | ||||||||
\(313\) | −1.71303e6 | −0.988333 | −0.494166 | − | 0.869367i | \(-0.664527\pi\) | ||||
−0.494166 | + | 0.869367i | \(0.664527\pi\) | |||||||
\(314\) | −242447. | −0.138769 | ||||||||
\(315\) | 455509. | 0.258655 | ||||||||
\(316\) | −440601. | −0.248215 | ||||||||
\(317\) | −2.30187e6 | −1.28657 | −0.643285 | − | 0.765627i | \(-0.722429\pi\) | ||||
−0.643285 | + | 0.765627i | \(0.722429\pi\) | |||||||
\(318\) | 5.83803e6 | 3.23742 | ||||||||
\(319\) | 311130. | 0.171185 | ||||||||
\(320\) | −251839. | −0.137483 | ||||||||
\(321\) | −4.74985e6 | −2.57286 | ||||||||
\(322\) | 465484. | 0.250187 | ||||||||
\(323\) | −338620. | −0.180595 | ||||||||
\(324\) | −1.42566e6 | −0.754489 | ||||||||
\(325\) | −592123. | −0.310959 | ||||||||
\(326\) | −811975. | −0.423154 | ||||||||
\(327\) | −2.99951e6 | −1.55125 | ||||||||
\(328\) | 548504. | 0.281511 | ||||||||
\(329\) | 1.90338e6 | 0.969471 | ||||||||
\(330\) | −476382. | −0.240808 | ||||||||
\(331\) | −1.01111e6 | −0.507259 | −0.253630 | − | 0.967301i | \(-0.581624\pi\) | ||||
−0.253630 | + | 0.967301i | \(0.581624\pi\) | |||||||
\(332\) | 1.93169e6 | 0.961819 | ||||||||
\(333\) | −1.85258e6 | −0.915517 | ||||||||
\(334\) | −1.88628e6 | −0.925207 | ||||||||
\(335\) | 15465.8 | 0.00752942 | ||||||||
\(336\) | −2.24576e6 | −1.08521 | ||||||||
\(337\) | 2.52958e6 | 1.21331 | 0.606657 | − | 0.794964i | \(-0.292510\pi\) | ||||
0.606657 | + | 0.794964i | \(0.292510\pi\) | |||||||
\(338\) | −3.86705e6 | −1.84115 | ||||||||
\(339\) | 214561. | 0.101403 | ||||||||
\(340\) | 515761. | 0.241964 | ||||||||
\(341\) | −299378. | −0.139423 | ||||||||
\(342\) | 573821. | 0.265284 | ||||||||
\(343\) | −2.23371e6 | −1.02516 | ||||||||
\(344\) | −710930. | −0.323915 | ||||||||
\(345\) | −402967. | −0.182273 | ||||||||
\(346\) | −4.15401e6 | −1.86543 | ||||||||
\(347\) | −1.80606e6 | −0.805207 | −0.402603 | − | 0.915375i | \(-0.631895\pi\) | ||||
−0.402603 | + | 0.915375i | \(0.631895\pi\) | |||||||
\(348\) | 1.21204e6 | 0.536500 | ||||||||
\(349\) | −2.24094e6 | −0.984843 | −0.492421 | − | 0.870357i | \(-0.663888\pi\) | ||||
−0.492421 | + | 0.870357i | \(0.663888\pi\) | |||||||
\(350\) | −386824. | −0.168789 | ||||||||
\(351\) | 541724. | 0.234699 | ||||||||
\(352\) | 821435. | 0.353359 | ||||||||
\(353\) | 2.21799e6 | 0.947375 | 0.473687 | − | 0.880693i | \(-0.342923\pi\) | ||||
0.473687 | + | 0.880693i | \(0.342923\pi\) | |||||||
\(354\) | 1.53270e6 | 0.650053 | ||||||||
\(355\) | 1.17612e6 | 0.495316 | ||||||||
\(356\) | −238092. | −0.0995679 | ||||||||
\(357\) | 1.69326e6 | 0.703158 | ||||||||
\(358\) | −5.57687e6 | −2.29976 | ||||||||
\(359\) | 3.63641e6 | 1.48914 | 0.744572 | − | 0.667542i | \(-0.232654\pi\) | ||||
0.744572 | + | 0.667542i | \(0.232654\pi\) | |||||||
\(360\) | 397623. | 0.161702 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | 4.10721e6 | 1.64731 | ||||||||
\(363\) | 313782. | 0.124986 | ||||||||
\(364\) | −1.75508e6 | −0.694292 | ||||||||
\(365\) | −1.58274e6 | −0.621836 | ||||||||
\(366\) | 5.89420e6 | 2.29997 | ||||||||
\(367\) | −1.69594e6 | −0.657271 | −0.328636 | − | 0.944457i | \(-0.606589\pi\) | ||||
−0.328636 | + | 0.944457i | \(0.606589\pi\) | |||||||
\(368\) | 935658. | 0.360162 | ||||||||
\(369\) | 1.61377e6 | 0.616985 | ||||||||
\(370\) | 1.57323e6 | 0.597432 | ||||||||
\(371\) | −3.12246e6 | −1.17777 | ||||||||
\(372\) | −1.16626e6 | −0.436957 | ||||||||
\(373\) | −4.78535e6 | −1.78091 | −0.890454 | − | 0.455072i | \(-0.849613\pi\) | ||||
−0.890454 | + | 0.455072i | \(0.849613\pi\) | |||||||
\(374\) | −833994. | −0.308308 | ||||||||
\(375\) | 334871. | 0.122970 | ||||||||
\(376\) | 1.66150e6 | 0.606080 | ||||||||
\(377\) | −2.43607e6 | −0.882746 | ||||||||
\(378\) | 353899. | 0.127394 | ||||||||
\(379\) | −223946. | −0.0800840 | −0.0400420 | − | 0.999198i | \(-0.512749\pi\) | ||||
−0.0400420 | + | 0.999198i | \(0.512749\pi\) | |||||||
\(380\) | −198495. | −0.0705166 | ||||||||
\(381\) | −7.55875e6 | −2.66770 | ||||||||
\(382\) | −2.43152e6 | −0.852550 | ||||||||
\(383\) | 873082. | 0.304129 | 0.152065 | − | 0.988371i | \(-0.451408\pi\) | ||||
0.152065 | + | 0.988371i | \(0.451408\pi\) | |||||||
\(384\) | −3.06941e6 | −1.06225 | ||||||||
\(385\) | 254792. | 0.0876060 | ||||||||
\(386\) | −3.70897e6 | −1.26703 | ||||||||
\(387\) | −2.09165e6 | −0.709922 | ||||||||
\(388\) | 519375. | 0.175147 | ||||||||
\(389\) | −1.29218e6 | −0.432960 | −0.216480 | − | 0.976287i | \(-0.569458\pi\) | ||||
−0.216480 | + | 0.976287i | \(0.569458\pi\) | |||||||
\(390\) | 3.72994e6 | 1.24177 | ||||||||
\(391\) | −705467. | −0.233364 | ||||||||
\(392\) | −714113. | −0.234721 | ||||||||
\(393\) | −4.70592e6 | −1.53696 | ||||||||
\(394\) | −5.64549e6 | −1.83215 | ||||||||
\(395\) | −500821. | −0.161506 | ||||||||
\(396\) | 575685. | 0.184479 | ||||||||
\(397\) | 1.90173e6 | 0.605582 | 0.302791 | − | 0.953057i | \(-0.402082\pi\) | ||||
0.302791 | + | 0.953057i | \(0.402082\pi\) | |||||||
\(398\) | −2.87108e6 | −0.908526 | ||||||||
\(399\) | −651666. | −0.204924 | ||||||||
\(400\) | −777545. | −0.242983 | ||||||||
\(401\) | −3.27319e6 | −1.01651 | −0.508253 | − | 0.861208i | \(-0.669709\pi\) | ||||
−0.508253 | + | 0.861208i | \(0.669709\pi\) | |||||||
\(402\) | −97423.5 | −0.0300676 | ||||||||
\(403\) | 2.34405e6 | 0.718960 | ||||||||
\(404\) | −2.21057e6 | −0.673830 | ||||||||
\(405\) | −1.62051e6 | −0.490924 | ||||||||
\(406\) | −1.59144e6 | −0.479154 | ||||||||
\(407\) | −1.03625e6 | −0.310084 | ||||||||
\(408\) | 1.47808e6 | 0.439590 | ||||||||
\(409\) | −2.46121e6 | −0.727511 | −0.363755 | − | 0.931494i | \(-0.618506\pi\) | ||||
−0.363755 | + | 0.931494i | \(0.618506\pi\) | |||||||
\(410\) | −1.37043e6 | −0.402622 | ||||||||
\(411\) | 1.69863e6 | 0.496016 | ||||||||
\(412\) | 1.68841e6 | 0.490044 | ||||||||
\(413\) | −819761. | −0.236490 | ||||||||
\(414\) | 1.19547e6 | 0.342799 | ||||||||
\(415\) | 2.19571e6 | 0.625828 | ||||||||
\(416\) | −6.43161e6 | −1.82216 | ||||||||
\(417\) | −3.26234e6 | −0.918733 | ||||||||
\(418\) | 320970. | 0.0898513 | ||||||||
\(419\) | 2.05556e6 | 0.572000 | 0.286000 | − | 0.958230i | \(-0.407674\pi\) | ||||
0.286000 | + | 0.958230i | \(0.407674\pi\) | |||||||
\(420\) | 992570. | 0.274560 | ||||||||
\(421\) | 820076. | 0.225501 | 0.112751 | − | 0.993623i | \(-0.464034\pi\) | ||||
0.112751 | + | 0.993623i | \(0.464034\pi\) | |||||||
\(422\) | 4.43945e6 | 1.21352 | ||||||||
\(423\) | 4.88833e6 | 1.32834 | ||||||||
\(424\) | −2.72566e6 | −0.736304 | ||||||||
\(425\) | 586253. | 0.157439 | ||||||||
\(426\) | −7.40872e6 | −1.97797 | ||||||||
\(427\) | −3.15250e6 | −0.836730 | ||||||||
\(428\) | −4.87444e6 | −1.28622 | ||||||||
\(429\) | −2.45683e6 | −0.644513 | ||||||||
\(430\) | 1.77625e6 | 0.463269 | ||||||||
\(431\) | −4.59815e6 | −1.19231 | −0.596156 | − | 0.802869i | \(-0.703306\pi\) | ||||
−0.596156 | + | 0.802869i | \(0.703306\pi\) | |||||||
\(432\) | 711364. | 0.183393 | ||||||||
\(433\) | 3.67289e6 | 0.941431 | 0.470715 | − | 0.882285i | \(-0.343996\pi\) | ||||
0.470715 | + | 0.882285i | \(0.343996\pi\) | |||||||
\(434\) | 1.53133e6 | 0.390251 | ||||||||
\(435\) | 1.37770e6 | 0.349085 | ||||||||
\(436\) | −3.07819e6 | −0.775497 | ||||||||
\(437\) | 271506. | 0.0680104 | ||||||||
\(438\) | 9.97008e6 | 2.48321 | ||||||||
\(439\) | 1.01093e6 | 0.250356 | 0.125178 | − | 0.992134i | \(-0.460050\pi\) | ||||
0.125178 | + | 0.992134i | \(0.460050\pi\) | |||||||
\(440\) | 222413. | 0.0547683 | ||||||||
\(441\) | −2.10101e6 | −0.514436 | ||||||||
\(442\) | 6.52995e6 | 1.58984 | ||||||||
\(443\) | 67001.0 | 0.0162208 | 0.00811040 | − | 0.999967i | \(-0.497418\pi\) | ||||
0.00811040 | + | 0.999967i | \(0.497418\pi\) | |||||||
\(444\) | −4.03684e6 | −0.971816 | ||||||||
\(445\) | −270633. | −0.0647860 | ||||||||
\(446\) | −7.17351e6 | −1.70763 | ||||||||
\(447\) | 4.82114e6 | 1.14125 | ||||||||
\(448\) | −848483. | −0.199732 | ||||||||
\(449\) | −1.86511e6 | −0.436606 | −0.218303 | − | 0.975881i | \(-0.570052\pi\) | ||||
−0.218303 | + | 0.975881i | \(0.570052\pi\) | |||||||
\(450\) | −993457. | −0.231269 | ||||||||
\(451\) | 902671. | 0.208972 | ||||||||
\(452\) | 220189. | 0.0506932 | ||||||||
\(453\) | 314797. | 0.0720751 | ||||||||
\(454\) | 8.02460e6 | 1.82719 | ||||||||
\(455\) | −1.99495e6 | −0.451756 | ||||||||
\(456\) | −568853. | −0.128111 | ||||||||
\(457\) | −5.27822e6 | −1.18222 | −0.591109 | − | 0.806592i | \(-0.701310\pi\) | ||||
−0.591109 | + | 0.806592i | \(0.701310\pi\) | |||||||
\(458\) | −421233. | −0.0938336 | ||||||||
\(459\) | −536354. | −0.118828 | ||||||||
\(460\) | −413537. | −0.0911213 | ||||||||
\(461\) | 2.01902e6 | 0.442475 | 0.221238 | − | 0.975220i | \(-0.428990\pi\) | ||||
0.221238 | + | 0.975220i | \(0.428990\pi\) | |||||||
\(462\) | −1.60500e6 | −0.349841 | ||||||||
\(463\) | 6.33610e6 | 1.37363 | 0.686814 | − | 0.726833i | \(-0.259009\pi\) | ||||
0.686814 | + | 0.726833i | \(0.259009\pi\) | |||||||
\(464\) | −3.19891e6 | −0.689775 | ||||||||
\(465\) | −1.32566e6 | −0.284315 | ||||||||
\(466\) | 865846. | 0.184704 | ||||||||
\(467\) | −8.47933e6 | −1.79916 | −0.899579 | − | 0.436759i | \(-0.856126\pi\) | ||||
−0.899579 | + | 0.436759i | \(0.856126\pi\) | |||||||
\(468\) | −4.50746e6 | −0.951299 | ||||||||
\(469\) | 52106.7 | 0.0109386 | ||||||||
\(470\) | −4.15123e6 | −0.866826 | ||||||||
\(471\) | 707133. | 0.146875 | ||||||||
\(472\) | −715586. | −0.147845 | ||||||||
\(473\) | −1.16998e6 | −0.240450 | ||||||||
\(474\) | 3.15480e6 | 0.644951 | ||||||||
\(475\) | −225625. | −0.0458831 | ||||||||
\(476\) | 1.73768e6 | 0.351521 | ||||||||
\(477\) | −8.01923e6 | −1.61375 | ||||||||
\(478\) | −441651. | −0.0884117 | ||||||||
\(479\) | 5.40868e6 | 1.07709 | 0.538546 | − | 0.842596i | \(-0.318974\pi\) | ||||
0.538546 | + | 0.842596i | \(0.318974\pi\) | |||||||
\(480\) | 3.63735e6 | 0.720580 | ||||||||
\(481\) | 8.11358e6 | 1.59901 | ||||||||
\(482\) | 6.14784e6 | 1.20533 | ||||||||
\(483\) | −1.35766e6 | −0.264802 | ||||||||
\(484\) | 322013. | 0.0624828 | ||||||||
\(485\) | 590361. | 0.113963 | ||||||||
\(486\) | 9.18704e6 | 1.76435 | ||||||||
\(487\) | −2.56793e6 | −0.490637 | −0.245318 | − | 0.969443i | \(-0.578892\pi\) | ||||
−0.245318 | + | 0.969443i | \(0.578892\pi\) | |||||||
\(488\) | −2.75188e6 | −0.523095 | ||||||||
\(489\) | 2.36825e6 | 0.447874 | ||||||||
\(490\) | 1.78420e6 | 0.335702 | ||||||||
\(491\) | 1.13750e6 | 0.212935 | 0.106467 | − | 0.994316i | \(-0.466046\pi\) | ||||
0.106467 | + | 0.994316i | \(0.466046\pi\) | |||||||
\(492\) | 3.51645e6 | 0.654926 | ||||||||
\(493\) | 2.41192e6 | 0.446935 | ||||||||
\(494\) | −2.51311e6 | −0.463334 | ||||||||
\(495\) | 654367. | 0.120035 | ||||||||
\(496\) | 3.07809e6 | 0.561793 | ||||||||
\(497\) | 3.96254e6 | 0.719586 | ||||||||
\(498\) | −1.38314e7 | −2.49915 | ||||||||
\(499\) | 6.62654e6 | 1.19134 | 0.595670 | − | 0.803230i | \(-0.296887\pi\) | ||||
0.595670 | + | 0.803230i | \(0.296887\pi\) | |||||||
\(500\) | 343655. | 0.0614750 | ||||||||
\(501\) | 5.50161e6 | 0.979255 | ||||||||
\(502\) | −2.04005e6 | −0.361311 | ||||||||
\(503\) | −8.10433e6 | −1.42823 | −0.714113 | − | 0.700030i | \(-0.753170\pi\) | ||||
−0.714113 | + | 0.700030i | \(0.753170\pi\) | |||||||
\(504\) | 1.33965e6 | 0.234918 | ||||||||
\(505\) | −2.51270e6 | −0.438442 | ||||||||
\(506\) | 668697. | 0.116106 | ||||||||
\(507\) | 1.12789e7 | 1.94870 | ||||||||
\(508\) | −7.75703e6 | −1.33363 | ||||||||
\(509\) | 1.09648e7 | 1.87588 | 0.937939 | − | 0.346802i | \(-0.112732\pi\) | ||||
0.937939 | + | 0.346802i | \(0.112732\pi\) | |||||||
\(510\) | −3.69297e6 | −0.628709 | ||||||||
\(511\) | −5.33247e6 | −0.903393 | ||||||||
\(512\) | −5.51860e6 | −0.930366 | ||||||||
\(513\) | 206421. | 0.0346306 | ||||||||
\(514\) | −8.47150e6 | −1.41434 | ||||||||
\(515\) | 1.91918e6 | 0.318858 | ||||||||
\(516\) | −4.55777e6 | −0.753578 | ||||||||
\(517\) | 2.73432e6 | 0.449907 | ||||||||
\(518\) | 5.30046e6 | 0.867939 | ||||||||
\(519\) | 1.21158e7 | 1.97440 | ||||||||
\(520\) | −1.74144e6 | −0.282422 | ||||||||
\(521\) | −4.35822e6 | −0.703420 | −0.351710 | − | 0.936109i | \(-0.614400\pi\) | ||||
−0.351710 | + | 0.936109i | \(0.614400\pi\) | |||||||
\(522\) | −4.08720e6 | −0.656522 | ||||||||
\(523\) | 2.19655e6 | 0.351145 | 0.175573 | − | 0.984466i | \(-0.443822\pi\) | ||||
0.175573 | + | 0.984466i | \(0.443822\pi\) | |||||||
\(524\) | −4.82937e6 | −0.768356 | ||||||||
\(525\) | 1.12823e6 | 0.178649 | ||||||||
\(526\) | 593115. | 0.0934705 | ||||||||
\(527\) | −2.32081e6 | −0.364010 | ||||||||
\(528\) | −3.22618e6 | −0.503621 | ||||||||
\(529\) | −5.87070e6 | −0.912117 | ||||||||
\(530\) | 6.81003e6 | 1.05307 | ||||||||
\(531\) | −2.10534e6 | −0.324031 | ||||||||
\(532\) | −668761. | −0.102445 | ||||||||
\(533\) | −7.06767e6 | −1.07760 | ||||||||
\(534\) | 1.70479e6 | 0.258713 | ||||||||
\(535\) | −5.54067e6 | −0.836908 | ||||||||
\(536\) | 45485.0 | 0.00683843 | ||||||||
\(537\) | 1.62658e7 | 2.43411 | ||||||||
\(538\) | 1.26578e7 | 1.88540 | ||||||||
\(539\) | −1.17521e6 | −0.174239 | ||||||||
\(540\) | −314405. | −0.0463986 | ||||||||
\(541\) | 5.41278e6 | 0.795109 | 0.397555 | − | 0.917578i | \(-0.369859\pi\) | ||||
0.397555 | + | 0.917578i | \(0.369859\pi\) | |||||||
\(542\) | −3.77299e6 | −0.551681 | ||||||||
\(543\) | −1.19793e7 | −1.74354 | ||||||||
\(544\) | 6.36785e6 | 0.922562 | ||||||||
\(545\) | −3.49891e6 | −0.504593 | ||||||||
\(546\) | 1.25667e7 | 1.80402 | ||||||||
\(547\) | −1.20209e7 | −1.71778 | −0.858889 | − | 0.512162i | \(-0.828845\pi\) | ||||
−0.858889 | + | 0.512162i | \(0.828845\pi\) | |||||||
\(548\) | 1.74319e6 | 0.247967 | ||||||||
\(549\) | −8.09638e6 | −1.14646 | ||||||||
\(550\) | −555697. | −0.0783306 | ||||||||
\(551\) | −928248. | −0.130252 | ||||||||
\(552\) | −1.18513e6 | −0.165545 | ||||||||
\(553\) | −1.68734e6 | −0.234633 | ||||||||
\(554\) | 4.38998e6 | 0.607699 | ||||||||
\(555\) | −4.58858e6 | −0.632333 | ||||||||
\(556\) | −3.34792e6 | −0.459291 | ||||||||
\(557\) | 1.29791e7 | 1.77258 | 0.886291 | − | 0.463128i | \(-0.153273\pi\) | ||||
0.886291 | + | 0.463128i | \(0.153273\pi\) | |||||||
\(558\) | 3.93282e6 | 0.534710 | ||||||||
\(559\) | 9.16060e6 | 1.23992 | ||||||||
\(560\) | −2.61967e6 | −0.353001 | ||||||||
\(561\) | 2.43247e6 | 0.326318 | ||||||||
\(562\) | 7.35359e6 | 0.982106 | ||||||||
\(563\) | −1.83258e6 | −0.243665 | −0.121832 | − | 0.992551i | \(-0.538877\pi\) | ||||
−0.121832 | + | 0.992551i | \(0.538877\pi\) | |||||||
\(564\) | 1.06518e7 | 1.41003 | ||||||||
\(565\) | 250284. | 0.0329846 | ||||||||
\(566\) | −1.31117e6 | −0.172035 | ||||||||
\(567\) | −5.45975e6 | −0.713206 | ||||||||
\(568\) | 3.45898e6 | 0.449860 | ||||||||
\(569\) | −5.51647e6 | −0.714300 | −0.357150 | − | 0.934047i | \(-0.616251\pi\) | ||||
−0.357150 | + | 0.934047i | \(0.616251\pi\) | |||||||
\(570\) | 1.42127e6 | 0.183227 | ||||||||
\(571\) | −2.25143e6 | −0.288980 | −0.144490 | − | 0.989506i | \(-0.546154\pi\) | ||||
−0.144490 | + | 0.989506i | \(0.546154\pi\) | |||||||
\(572\) | −2.52128e6 | −0.322204 | ||||||||
\(573\) | 7.09191e6 | 0.902354 | ||||||||
\(574\) | −4.61718e6 | −0.584921 | ||||||||
\(575\) | −470058. | −0.0592901 | ||||||||
\(576\) | −2.17911e6 | −0.273667 | ||||||||
\(577\) | −1.38710e6 | −0.173447 | −0.0867236 | − | 0.996232i | \(-0.527640\pi\) | ||||
−0.0867236 | + | 0.996232i | \(0.527640\pi\) | |||||||
\(578\) | 3.96798e6 | 0.494026 | ||||||||
\(579\) | 1.08178e7 | 1.34104 | ||||||||
\(580\) | 1.41384e6 | 0.174514 | ||||||||
\(581\) | 7.39768e6 | 0.909191 | ||||||||
\(582\) | −3.71884e6 | −0.455093 | ||||||||
\(583\) | −4.48561e6 | −0.546576 | ||||||||
\(584\) | −4.65483e6 | −0.564770 | ||||||||
\(585\) | −5.12352e6 | −0.618983 | ||||||||
\(586\) | 4.66246e6 | 0.560882 | ||||||||
\(587\) | −159778. | −0.0191391 | −0.00956955 | − | 0.999954i | \(-0.503046\pi\) | ||||
−0.00956955 | + | 0.999954i | \(0.503046\pi\) | |||||||
\(588\) | −4.57818e6 | −0.546071 | ||||||||
\(589\) | 893187. | 0.106085 | ||||||||
\(590\) | 1.78788e6 | 0.211451 | ||||||||
\(591\) | 1.64659e7 | 1.93918 | ||||||||
\(592\) | 1.06543e7 | 1.24946 | ||||||||
\(593\) | −1.18442e7 | −1.38314 | −0.691572 | − | 0.722308i | \(-0.743081\pi\) | ||||
−0.691572 | + | 0.722308i | \(0.743081\pi\) | |||||||
\(594\) | 508398. | 0.0591205 | ||||||||
\(595\) | 1.97518e6 | 0.228725 | ||||||||
\(596\) | 4.94761e6 | 0.570532 | ||||||||
\(597\) | 8.37394e6 | 0.961599 | ||||||||
\(598\) | −5.23572e6 | −0.598719 | ||||||||
\(599\) | −1.87540e6 | −0.213564 | −0.106782 | − | 0.994282i | \(-0.534055\pi\) | ||||
−0.106782 | + | 0.994282i | \(0.534055\pi\) | |||||||
\(600\) | 984856. | 0.111685 | ||||||||
\(601\) | −1.59381e7 | −1.79991 | −0.899954 | − | 0.435985i | \(-0.856400\pi\) | ||||
−0.899954 | + | 0.435985i | \(0.856400\pi\) | |||||||
\(602\) | 5.98446e6 | 0.673029 | ||||||||
\(603\) | 133823. | 0.0149877 | ||||||||
\(604\) | 323055. | 0.0360316 | ||||||||
\(605\) | 366025. | 0.0406558 | ||||||||
\(606\) | 1.58282e7 | 1.75085 | ||||||||
\(607\) | 1.35588e7 | 1.49365 | 0.746825 | − | 0.665021i | \(-0.231577\pi\) | ||||
0.746825 | + | 0.665021i | \(0.231577\pi\) | |||||||
\(608\) | −2.45073e6 | −0.268866 | ||||||||
\(609\) | 4.64168e6 | 0.507145 | ||||||||
\(610\) | 6.87555e6 | 0.748140 | ||||||||
\(611\) | −2.14090e7 | −2.32003 | ||||||||
\(612\) | 4.46277e6 | 0.481644 | ||||||||
\(613\) | −7.25709e6 | −0.780030 | −0.390015 | − | 0.920809i | \(-0.627530\pi\) | ||||
−0.390015 | + | 0.920809i | \(0.627530\pi\) | |||||||
\(614\) | 8.84908e6 | 0.947277 | ||||||||
\(615\) | 3.99707e6 | 0.426142 | ||||||||
\(616\) | 749344. | 0.0795663 | ||||||||
\(617\) | −1.82352e7 | −1.92840 | −0.964199 | − | 0.265181i | \(-0.914568\pi\) | ||||
−0.964199 | + | 0.265181i | \(0.914568\pi\) | |||||||
\(618\) | −1.20894e7 | −1.27331 | ||||||||
\(619\) | 4.92013e6 | 0.516119 | 0.258060 | − | 0.966129i | \(-0.416917\pi\) | ||||
0.258060 | + | 0.966129i | \(0.416917\pi\) | |||||||
\(620\) | −1.36044e6 | −0.142134 | ||||||||
\(621\) | 430049. | 0.0447496 | ||||||||
\(622\) | 5.68328e6 | 0.589010 | ||||||||
\(623\) | −911804. | −0.0941199 | ||||||||
\(624\) | 2.52601e7 | 2.59701 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 1.25874e7 | 1.28381 | ||||||||
\(627\) | −936160. | −0.0951002 | ||||||||
\(628\) | 725682. | 0.0734256 | ||||||||
\(629\) | −8.03315e6 | −0.809579 | ||||||||
\(630\) | −3.34710e6 | −0.335983 | ||||||||
\(631\) | −8.54707e6 | −0.854562 | −0.427281 | − | 0.904119i | \(-0.640529\pi\) | ||||
−0.427281 | + | 0.904119i | \(0.640529\pi\) | |||||||
\(632\) | −1.47291e6 | −0.146685 | ||||||||
\(633\) | −1.29483e7 | −1.28441 | ||||||||
\(634\) | 1.69143e7 | 1.67121 | ||||||||
\(635\) | −8.81723e6 | −0.867756 | ||||||||
\(636\) | −1.74742e7 | −1.71299 | ||||||||
\(637\) | 9.20161e6 | 0.898494 | ||||||||
\(638\) | −2.28620e6 | −0.222363 | ||||||||
\(639\) | 1.01768e7 | 0.985956 | ||||||||
\(640\) | −3.58045e6 | −0.345531 | ||||||||
\(641\) | 4.12709e6 | 0.396734 | 0.198367 | − | 0.980128i | \(-0.436436\pi\) | ||||
0.198367 | + | 0.980128i | \(0.436436\pi\) | |||||||
\(642\) | 3.49021e7 | 3.34206 | ||||||||
\(643\) | −1.02660e7 | −0.979201 | −0.489601 | − | 0.871947i | \(-0.662857\pi\) | ||||
−0.489601 | + | 0.871947i | \(0.662857\pi\) | |||||||
\(644\) | −1.39327e6 | −0.132379 | ||||||||
\(645\) | −5.18071e6 | −0.490332 | ||||||||
\(646\) | 2.48820e6 | 0.234587 | ||||||||
\(647\) | −1.07012e7 | −1.00502 | −0.502508 | − | 0.864573i | \(-0.667589\pi\) | ||||
−0.502508 | + | 0.864573i | \(0.667589\pi\) | |||||||
\(648\) | −4.76593e6 | −0.445872 | ||||||||
\(649\) | −1.17764e6 | −0.109749 | ||||||||
\(650\) | 4.35096e6 | 0.403926 | ||||||||
\(651\) | −4.46635e6 | −0.413048 | ||||||||
\(652\) | 2.43037e6 | 0.223900 | ||||||||
\(653\) | −2.06722e7 | −1.89716 | −0.948579 | − | 0.316540i | \(-0.897479\pi\) | ||||
−0.948579 | + | 0.316540i | \(0.897479\pi\) | |||||||
\(654\) | 2.20406e7 | 2.01502 | ||||||||
\(655\) | −5.48943e6 | −0.499947 | ||||||||
\(656\) | −9.28090e6 | −0.842035 | ||||||||
\(657\) | −1.36951e7 | −1.23780 | ||||||||
\(658\) | −1.39861e7 | −1.25931 | ||||||||
\(659\) | 7.97936e6 | 0.715739 | 0.357870 | − | 0.933772i | \(-0.383503\pi\) | ||||
0.357870 | + | 0.933772i | \(0.383503\pi\) | |||||||
\(660\) | 1.42589e6 | 0.127417 | ||||||||
\(661\) | 7.50235e6 | 0.667872 | 0.333936 | − | 0.942596i | \(-0.391623\pi\) | ||||
0.333936 | + | 0.942596i | \(0.391623\pi\) | |||||||
\(662\) | 7.42972e6 | 0.658912 | ||||||||
\(663\) | −1.90456e7 | −1.68272 | ||||||||
\(664\) | 6.45759e6 | 0.568395 | ||||||||
\(665\) | −760165. | −0.0666582 | ||||||||
\(666\) | 1.36129e7 | 1.18922 | ||||||||
\(667\) | −1.93387e6 | −0.168312 | ||||||||
\(668\) | 5.64593e6 | 0.489547 | ||||||||
\(669\) | 2.09227e7 | 1.80739 | ||||||||
\(670\) | −113644. | −0.00978045 | ||||||||
\(671\) | −4.52877e6 | −0.388306 | ||||||||
\(672\) | 1.22548e7 | 1.04685 | ||||||||
\(673\) | −9.47243e6 | −0.806164 | −0.403082 | − | 0.915164i | \(-0.632061\pi\) | ||||
−0.403082 | + | 0.915164i | \(0.632061\pi\) | |||||||
\(674\) | −1.85875e7 | −1.57605 | ||||||||
\(675\) | −357377. | −0.0301903 | ||||||||
\(676\) | 1.15747e7 | 0.974191 | ||||||||
\(677\) | −9.79457e6 | −0.821323 | −0.410661 | − | 0.911788i | \(-0.634702\pi\) | ||||
−0.410661 | + | 0.911788i | \(0.634702\pi\) | |||||||
\(678\) | −1.57660e6 | −0.131719 | ||||||||
\(679\) | 1.98902e6 | 0.165563 | ||||||||
\(680\) | 1.72417e6 | 0.142991 | ||||||||
\(681\) | −2.34050e7 | −1.93393 | ||||||||
\(682\) | 2.19985e6 | 0.181106 | ||||||||
\(683\) | 5.50489e6 | 0.451540 | 0.225770 | − | 0.974181i | \(-0.427510\pi\) | ||||
0.225770 | + | 0.974181i | \(0.427510\pi\) | |||||||
\(684\) | −1.71754e6 | −0.140367 | ||||||||
\(685\) | 1.98145e6 | 0.161345 | ||||||||
\(686\) | 1.64134e7 | 1.33164 | ||||||||
\(687\) | 1.22859e6 | 0.0993151 | ||||||||
\(688\) | 1.20292e7 | 0.968872 | ||||||||
\(689\) | 3.51211e7 | 2.81852 | ||||||||
\(690\) | 2.96102e6 | 0.236766 | ||||||||
\(691\) | −1.22205e6 | −0.0973630 | −0.0486815 | − | 0.998814i | \(-0.515502\pi\) | ||||
−0.0486815 | + | 0.998814i | \(0.515502\pi\) | |||||||
\(692\) | 1.24337e7 | 0.987037 | ||||||||
\(693\) | 2.20466e6 | 0.174385 | ||||||||
\(694\) | 1.32710e7 | 1.04594 | ||||||||
\(695\) | −3.80550e6 | −0.298848 | ||||||||
\(696\) | 4.05182e6 | 0.317049 | ||||||||
\(697\) | 6.99760e6 | 0.545591 | ||||||||
\(698\) | 1.64666e7 | 1.27928 | ||||||||
\(699\) | −2.52537e6 | −0.195494 | ||||||||
\(700\) | 1.15783e6 | 0.0893097 | ||||||||
\(701\) | −1.24814e7 | −0.959331 | −0.479665 | − | 0.877451i | \(-0.659242\pi\) | ||||
−0.479665 | + | 0.877451i | \(0.659242\pi\) | |||||||
\(702\) | −3.98062e6 | −0.304865 | ||||||||
\(703\) | 3.09163e6 | 0.235939 | ||||||||
\(704\) | −1.21890e6 | −0.0926907 | ||||||||
\(705\) | 1.21077e7 | 0.917463 | ||||||||
\(706\) | −1.62979e7 | −1.23061 | ||||||||
\(707\) | −8.46566e6 | −0.636960 | ||||||||
\(708\) | −4.58762e6 | −0.343957 | ||||||||
\(709\) | −2.21328e7 | −1.65356 | −0.826782 | − | 0.562522i | \(-0.809831\pi\) | ||||
−0.826782 | + | 0.562522i | \(0.809831\pi\) | |||||||
\(710\) | −8.64223e6 | −0.643398 | ||||||||
\(711\) | −4.33350e6 | −0.321488 | ||||||||
\(712\) | −795933. | −0.0588405 | ||||||||
\(713\) | 1.86083e6 | 0.137083 | ||||||||
\(714\) | −1.24422e7 | −0.913377 | ||||||||
\(715\) | −2.86588e6 | −0.209649 | ||||||||
\(716\) | 1.66925e7 | 1.21685 | ||||||||
\(717\) | 1.28814e6 | 0.0935764 | ||||||||
\(718\) | −2.67205e7 | −1.93435 | ||||||||
\(719\) | 2.39803e7 | 1.72995 | 0.864973 | − | 0.501819i | \(-0.167336\pi\) | ||||
0.864973 | + | 0.501819i | \(0.167336\pi\) | |||||||
\(720\) | −6.72794e6 | −0.483672 | ||||||||
\(721\) | 6.46600e6 | 0.463231 | ||||||||
\(722\) | −957606. | −0.0683666 | ||||||||
\(723\) | −1.79311e7 | −1.27574 | ||||||||
\(724\) | −1.22936e7 | −0.871628 | ||||||||
\(725\) | 1.60708e6 | 0.113551 | ||||||||
\(726\) | −2.30569e6 | −0.162353 | ||||||||
\(727\) | 2.14734e7 | 1.50683 | 0.753417 | − | 0.657543i | \(-0.228404\pi\) | ||||
0.753417 | + | 0.657543i | \(0.228404\pi\) | |||||||
\(728\) | −5.86716e6 | −0.410298 | ||||||||
\(729\) | −1.10440e7 | −0.769679 | ||||||||
\(730\) | 1.16300e7 | 0.807744 | ||||||||
\(731\) | −9.06979e6 | −0.627774 | ||||||||
\(732\) | −1.76423e7 | −1.21696 | ||||||||
\(733\) | −718866. | −0.0494183 | −0.0247092 | − | 0.999695i | \(-0.507866\pi\) | ||||
−0.0247092 | + | 0.999695i | \(0.507866\pi\) | |||||||
\(734\) | 1.24618e7 | 0.853772 | ||||||||
\(735\) | −5.20390e6 | −0.355313 | ||||||||
\(736\) | −5.10574e6 | −0.347428 | ||||||||
\(737\) | 74854.6 | 0.00507633 | ||||||||
\(738\) | −1.18580e7 | −0.801442 | ||||||||
\(739\) | 2.57636e7 | 1.73538 | 0.867692 | − | 0.497101i | \(-0.165602\pi\) | ||||
0.867692 | + | 0.497101i | \(0.165602\pi\) | |||||||
\(740\) | −4.70895e6 | −0.316115 | ||||||||
\(741\) | 7.32988e6 | 0.490401 | ||||||||
\(742\) | 2.29440e7 | 1.52989 | ||||||||
\(743\) | 1.72902e7 | 1.14902 | 0.574511 | − | 0.818497i | \(-0.305192\pi\) | ||||
0.574511 | + | 0.818497i | \(0.305192\pi\) | |||||||
\(744\) | −3.89877e6 | −0.258223 | ||||||||
\(745\) | 5.62383e6 | 0.371229 | ||||||||
\(746\) | 3.51630e7 | 2.31334 | ||||||||
\(747\) | 1.89990e7 | 1.24575 | ||||||||
\(748\) | 2.49628e6 | 0.163132 | ||||||||
\(749\) | −1.86673e7 | −1.21584 | ||||||||
\(750\) | −2.46065e6 | −0.159734 | ||||||||
\(751\) | 2.42401e7 | 1.56832 | 0.784161 | − | 0.620558i | \(-0.213094\pi\) | ||||
0.784161 | + | 0.620558i | \(0.213094\pi\) | |||||||
\(752\) | −2.81132e7 | −1.81286 | ||||||||
\(753\) | 5.95012e6 | 0.382418 | ||||||||
\(754\) | 1.79004e7 | 1.14666 | ||||||||
\(755\) | 367209. | 0.0234448 | ||||||||
\(756\) | −1.05928e6 | −0.0674071 | ||||||||
\(757\) | −2.34776e6 | −0.148906 | −0.0744532 | − | 0.997225i | \(-0.523721\pi\) | ||||
−0.0744532 | + | 0.997225i | \(0.523721\pi\) | |||||||
\(758\) | 1.64557e6 | 0.104026 | ||||||||
\(759\) | −1.95036e6 | −0.122888 | ||||||||
\(760\) | −663563. | −0.0416724 | ||||||||
\(761\) | 1.11190e7 | 0.695993 | 0.347996 | − | 0.937496i | \(-0.386862\pi\) | ||||
0.347996 | + | 0.937496i | \(0.386862\pi\) | |||||||
\(762\) | 5.55421e7 | 3.46525 | ||||||||
\(763\) | −1.17884e7 | −0.733064 | ||||||||
\(764\) | 7.27795e6 | 0.451103 | ||||||||
\(765\) | 5.07273e6 | 0.313392 | ||||||||
\(766\) | −6.41545e6 | −0.395053 | ||||||||
\(767\) | 9.22059e6 | 0.565940 | ||||||||
\(768\) | 2.94628e7 | 1.80248 | ||||||||
\(769\) | 1.74490e7 | 1.06403 | 0.532017 | − | 0.846734i | \(-0.321434\pi\) | ||||
0.532017 | + | 0.846734i | \(0.321434\pi\) | |||||||
\(770\) | −1.87223e6 | −0.113797 | ||||||||
\(771\) | 2.47085e7 | 1.49696 | ||||||||
\(772\) | 1.11016e7 | 0.670411 | ||||||||
\(773\) | 5.91190e6 | 0.355860 | 0.177930 | − | 0.984043i | \(-0.443060\pi\) | ||||
0.177930 | + | 0.984043i | \(0.443060\pi\) | |||||||
\(774\) | 1.53695e7 | 0.922164 | ||||||||
\(775\) | −1.54638e6 | −0.0924828 | ||||||||
\(776\) | 1.73625e6 | 0.103504 | ||||||||
\(777\) | −1.54596e7 | −0.918641 | ||||||||
\(778\) | 9.49498e6 | 0.562400 | ||||||||
\(779\) | −2.69309e6 | −0.159004 | ||||||||
\(780\) | −1.11643e7 | −0.657047 | ||||||||
\(781\) | 5.69244e6 | 0.333942 | ||||||||
\(782\) | 5.18381e6 | 0.303132 | ||||||||
\(783\) | −1.47029e6 | −0.0857035 | ||||||||
\(784\) | 1.20831e7 | 0.702081 | ||||||||
\(785\) | 824866. | 0.0477759 | ||||||||
\(786\) | 3.45794e7 | 1.99646 | ||||||||
\(787\) | −8.19379e6 | −0.471572 | −0.235786 | − | 0.971805i | \(-0.575766\pi\) | ||||
−0.235786 | + | 0.971805i | \(0.575766\pi\) | |||||||
\(788\) | 1.68979e7 | 0.969430 | ||||||||
\(789\) | −1.72991e6 | −0.0989308 | ||||||||
\(790\) | 3.68006e6 | 0.209791 | ||||||||
\(791\) | 843243. | 0.0479194 | ||||||||
\(792\) | 1.92450e6 | 0.109019 | ||||||||
\(793\) | 3.54590e7 | 2.00237 | ||||||||
\(794\) | −1.39740e7 | −0.786630 | ||||||||
\(795\) | −1.98625e7 | −1.11459 | ||||||||
\(796\) | 8.59361e6 | 0.480721 | ||||||||
\(797\) | 2.73550e6 | 0.152543 | 0.0762714 | − | 0.997087i | \(-0.475698\pi\) | ||||
0.0762714 | + | 0.997087i | \(0.475698\pi\) | |||||||
\(798\) | 4.78848e6 | 0.266189 | ||||||||
\(799\) | 2.11967e7 | 1.17463 | ||||||||
\(800\) | 4.24295e6 | 0.234392 | ||||||||
\(801\) | −2.34173e6 | −0.128960 | ||||||||
\(802\) | 2.40516e7 | 1.32041 | ||||||||
\(803\) | −7.66044e6 | −0.419242 | ||||||||
\(804\) | 291604. | 0.0159094 | ||||||||
\(805\) | −1.58370e6 | −0.0861355 | ||||||||
\(806\) | −1.72242e7 | −0.933904 | ||||||||
\(807\) | −3.69186e7 | −1.99554 | ||||||||
\(808\) | −7.38985e6 | −0.398206 | ||||||||
\(809\) | 3.16480e7 | 1.70010 | 0.850051 | − | 0.526701i | \(-0.176571\pi\) | ||||
0.850051 | + | 0.526701i | \(0.176571\pi\) | |||||||
\(810\) | 1.19076e7 | 0.637694 | ||||||||
\(811\) | 1.23445e7 | 0.659056 | 0.329528 | − | 0.944146i | \(-0.393110\pi\) | ||||
0.329528 | + | 0.944146i | \(0.393110\pi\) | |||||||
\(812\) | 4.76344e6 | 0.253531 | ||||||||
\(813\) | 1.10045e7 | 0.583908 | ||||||||
\(814\) | 7.61445e6 | 0.402789 | ||||||||
\(815\) | 2.76255e6 | 0.145685 | ||||||||
\(816\) | −2.50097e7 | −1.31487 | ||||||||
\(817\) | 3.49059e6 | 0.182955 | ||||||||
\(818\) | 1.80851e7 | 0.945011 | ||||||||
\(819\) | −1.72619e7 | −0.899247 | ||||||||
\(820\) | 4.10192e6 | 0.213036 | ||||||||
\(821\) | 1.32448e7 | 0.685786 | 0.342893 | − | 0.939374i | \(-0.388593\pi\) | ||||
0.342893 | + | 0.939374i | \(0.388593\pi\) | |||||||
\(822\) | −1.24817e7 | −0.644307 | ||||||||
\(823\) | −1.49357e7 | −0.768648 | −0.384324 | − | 0.923198i | \(-0.625565\pi\) | ||||
−0.384324 | + | 0.923198i | \(0.625565\pi\) | |||||||
\(824\) | 5.64430e6 | 0.289596 | ||||||||
\(825\) | 1.62078e6 | 0.0829064 | ||||||||
\(826\) | 6.02365e6 | 0.307192 | ||||||||
\(827\) | 1.00695e7 | 0.511970 | 0.255985 | − | 0.966681i | \(-0.417600\pi\) | ||||
0.255985 | + | 0.966681i | \(0.417600\pi\) | |||||||
\(828\) | −3.57825e6 | −0.181382 | ||||||||
\(829\) | −1.10311e7 | −0.557483 | −0.278741 | − | 0.960366i | \(-0.589917\pi\) | ||||
−0.278741 | + | 0.960366i | \(0.589917\pi\) | |||||||
\(830\) | −1.61342e7 | −0.812929 | ||||||||
\(831\) | −1.28041e7 | −0.643199 | ||||||||
\(832\) | 9.54365e6 | 0.477976 | ||||||||
\(833\) | −9.11039e6 | −0.454909 | ||||||||
\(834\) | 2.39719e7 | 1.19340 | ||||||||
\(835\) | 6.41760e6 | 0.318534 | ||||||||
\(836\) | −960718. | −0.0475423 | ||||||||
\(837\) | 1.41476e6 | 0.0698020 | ||||||||
\(838\) | −1.51044e7 | −0.743008 | ||||||||
\(839\) | 1.60476e7 | 0.787053 | 0.393526 | − | 0.919313i | \(-0.371255\pi\) | ||||
0.393526 | + | 0.919313i | \(0.371255\pi\) | |||||||
\(840\) | 3.31813e6 | 0.162254 | ||||||||
\(841\) | −1.38994e7 | −0.677653 | ||||||||
\(842\) | −6.02597e6 | −0.292918 | ||||||||
\(843\) | −2.14479e7 | −1.03948 | ||||||||
\(844\) | −1.32880e7 | −0.642101 | ||||||||
\(845\) | 1.31567e7 | 0.633878 | ||||||||
\(846\) | −3.59197e7 | −1.72547 | ||||||||
\(847\) | 1.23319e6 | 0.0590640 | ||||||||
\(848\) | 4.61192e7 | 2.20238 | ||||||||
\(849\) | 3.82422e6 | 0.182085 | ||||||||
\(850\) | −4.30782e6 | −0.204508 | ||||||||
\(851\) | 6.44098e6 | 0.304879 | ||||||||
\(852\) | 2.21755e7 | 1.04659 | ||||||||
\(853\) | −4.31366e6 | −0.202989 | −0.101495 | − | 0.994836i | \(-0.532362\pi\) | ||||
−0.101495 | + | 0.994836i | \(0.532362\pi\) | |||||||
\(854\) | 2.31648e7 | 1.08688 | ||||||||
\(855\) | −1.95229e6 | −0.0913331 | ||||||||
\(856\) | −1.62951e7 | −0.760104 | ||||||||
\(857\) | 2.80413e6 | 0.130421 | 0.0652103 | − | 0.997872i | \(-0.479228\pi\) | ||||
0.0652103 | + | 0.997872i | \(0.479228\pi\) | |||||||
\(858\) | 1.80529e7 | 0.837200 | ||||||||
\(859\) | 4.08154e7 | 1.88730 | 0.943649 | − | 0.330947i | \(-0.107368\pi\) | ||||
0.943649 | + | 0.330947i | \(0.107368\pi\) | |||||||
\(860\) | −5.31661e6 | −0.245126 | ||||||||
\(861\) | 1.34667e7 | 0.619091 | ||||||||
\(862\) | 3.37875e7 | 1.54877 | ||||||||
\(863\) | 2.39288e7 | 1.09369 | 0.546844 | − | 0.837235i | \(-0.315829\pi\) | ||||
0.546844 | + | 0.837235i | \(0.315829\pi\) | |||||||
\(864\) | −3.88181e6 | −0.176909 | ||||||||
\(865\) | 1.41330e7 | 0.642237 | ||||||||
\(866\) | −2.69886e7 | −1.22289 | ||||||||
\(867\) | −1.15732e7 | −0.522885 | ||||||||
\(868\) | −4.58352e6 | −0.206490 | ||||||||
\(869\) | −2.42397e6 | −0.108888 | ||||||||
\(870\) | −1.01234e7 | −0.453450 | ||||||||
\(871\) | −586092. | −0.0261770 | ||||||||
\(872\) | −1.02903e7 | −0.458286 | ||||||||
\(873\) | 5.10827e6 | 0.226850 | ||||||||
\(874\) | −1.99504e6 | −0.0883431 | ||||||||
\(875\) | 1.31607e6 | 0.0581113 | ||||||||
\(876\) | −2.98421e7 | −1.31392 | ||||||||
\(877\) | −2.09756e7 | −0.920907 | −0.460454 | − | 0.887684i | \(-0.652313\pi\) | ||||
−0.460454 | + | 0.887684i | \(0.652313\pi\) | |||||||
\(878\) | −7.42834e6 | −0.325204 | ||||||||
\(879\) | −1.35988e7 | −0.593647 | ||||||||
\(880\) | −3.76332e6 | −0.163819 | ||||||||
\(881\) | −966060. | −0.0419338 | −0.0209669 | − | 0.999780i | \(-0.506674\pi\) | ||||
−0.0209669 | + | 0.999780i | \(0.506674\pi\) | |||||||
\(882\) | 1.54383e7 | 0.668235 | ||||||||
\(883\) | −1.30372e7 | −0.562709 | −0.281355 | − | 0.959604i | \(-0.590784\pi\) | ||||
−0.281355 | + | 0.959604i | \(0.590784\pi\) | |||||||
\(884\) | −1.95452e7 | −0.841221 | ||||||||
\(885\) | −5.21464e6 | −0.223803 | ||||||||
\(886\) | −492328. | −0.0210703 | ||||||||
\(887\) | −9.46650e6 | −0.403999 | −0.202000 | − | 0.979386i | \(-0.564744\pi\) | ||||
−0.202000 | + | 0.979386i | \(0.564744\pi\) | |||||||
\(888\) | −1.34950e7 | −0.574303 | ||||||||
\(889\) | −2.97066e7 | −1.26066 | ||||||||
\(890\) | 1.98863e6 | 0.0841548 | ||||||||
\(891\) | −7.84327e6 | −0.330981 | ||||||||
\(892\) | 2.14715e7 | 0.903546 | ||||||||
\(893\) | −8.15776e6 | −0.342328 | ||||||||
\(894\) | −3.54260e7 | −1.48244 | ||||||||
\(895\) | 1.89740e7 | 0.791772 | ||||||||
\(896\) | −1.20631e7 | −0.501981 | ||||||||
\(897\) | 1.52708e7 | 0.633695 | ||||||||
\(898\) | 1.37050e7 | 0.567136 | ||||||||
\(899\) | −6.36198e6 | −0.262538 | ||||||||
\(900\) | 2.97358e6 | 0.122370 | ||||||||
\(901\) | −3.47729e7 | −1.42702 | ||||||||
\(902\) | −6.63288e6 | −0.271447 | ||||||||
\(903\) | −1.74546e7 | −0.712345 | ||||||||
\(904\) | 736085. | 0.0299576 | ||||||||
\(905\) | −1.39738e7 | −0.567143 | ||||||||
\(906\) | −2.31315e6 | −0.0936230 | ||||||||
\(907\) | −4.28420e7 | −1.72923 | −0.864613 | − | 0.502438i | \(-0.832436\pi\) | ||||
−0.864613 | + | 0.502438i | \(0.832436\pi\) | |||||||
\(908\) | −2.40190e7 | −0.966807 | ||||||||
\(909\) | −2.17419e7 | −0.872745 | ||||||||
\(910\) | 1.46590e7 | 0.586816 | ||||||||
\(911\) | 4.32180e7 | 1.72532 | 0.862658 | − | 0.505788i | \(-0.168798\pi\) | ||||
0.862658 | + | 0.505788i | \(0.168798\pi\) | |||||||
\(912\) | 9.62522e6 | 0.383198 | ||||||||
\(913\) | 1.06272e7 | 0.421933 | ||||||||
\(914\) | 3.87847e7 | 1.53566 | ||||||||
\(915\) | −2.00536e7 | −0.791844 | ||||||||
\(916\) | 1.26082e6 | 0.0496494 | ||||||||
\(917\) | −1.84947e7 | −0.726314 | ||||||||
\(918\) | 3.94116e6 | 0.154354 | ||||||||
\(919\) | −7.50162e6 | −0.292999 | −0.146500 | − | 0.989211i | \(-0.546801\pi\) | ||||
−0.146500 | + | 0.989211i | \(0.546801\pi\) | |||||||
\(920\) | −1.38244e6 | −0.0538489 | ||||||||
\(921\) | −2.58097e7 | −1.00261 | ||||||||
\(922\) | −1.48359e7 | −0.574760 | ||||||||
\(923\) | −4.45703e7 | −1.72203 | ||||||||
\(924\) | 4.80404e6 | 0.185109 | ||||||||
\(925\) | −5.35255e6 | −0.205687 | ||||||||
\(926\) | −4.65580e7 | −1.78430 | ||||||||
\(927\) | 1.66062e7 | 0.634705 | ||||||||
\(928\) | 1.74560e7 | 0.665387 | ||||||||
\(929\) | −4.62847e7 | −1.75954 | −0.879768 | − | 0.475404i | \(-0.842302\pi\) | ||||
−0.879768 | + | 0.475404i | \(0.842302\pi\) | |||||||
\(930\) | 9.74104e6 | 0.369316 | ||||||||
\(931\) | 3.50622e6 | 0.132576 | ||||||||
\(932\) | −2.59162e6 | −0.0977308 | ||||||||
\(933\) | −1.65762e7 | −0.623419 | ||||||||
\(934\) | 6.23066e7 | 2.33704 | ||||||||
\(935\) | 2.83747e6 | 0.106145 | ||||||||
\(936\) | −1.50683e7 | −0.562178 | ||||||||
\(937\) | 1.19512e7 | 0.444696 | 0.222348 | − | 0.974967i | \(-0.428628\pi\) | ||||
0.222348 | + | 0.974967i | \(0.428628\pi\) | |||||||
\(938\) | −382883. | −0.0142089 | ||||||||
\(939\) | −3.67132e7 | −1.35881 | ||||||||
\(940\) | 1.24253e7 | 0.458656 | ||||||||
\(941\) | 1.48031e6 | 0.0544976 | 0.0272488 | − | 0.999629i | \(-0.491325\pi\) | ||||
0.0272488 | + | 0.999629i | \(0.491325\pi\) | |||||||
\(942\) | −5.19605e6 | −0.190786 | ||||||||
\(943\) | −5.61068e6 | −0.205464 | ||||||||
\(944\) | 1.21080e7 | 0.442224 | ||||||||
\(945\) | −1.20406e6 | −0.0438599 | ||||||||
\(946\) | 8.59706e6 | 0.312336 | ||||||||
\(947\) | 1.06634e7 | 0.386385 | 0.193193 | − | 0.981161i | \(-0.438116\pi\) | ||||
0.193193 | + | 0.981161i | \(0.438116\pi\) | |||||||
\(948\) | −9.44285e6 | −0.341257 | ||||||||
\(949\) | 5.99792e7 | 2.16190 | ||||||||
\(950\) | 1.65791e6 | 0.0596006 | ||||||||
\(951\) | −4.93332e7 | −1.76884 | ||||||||
\(952\) | 5.80899e6 | 0.207734 | ||||||||
\(953\) | −7.45014e6 | −0.265725 | −0.132862 | − | 0.991134i | \(-0.542417\pi\) | ||||
−0.132862 | + | 0.991134i | \(0.542417\pi\) | |||||||
\(954\) | 5.89258e7 | 2.09621 | ||||||||
\(955\) | 8.27267e6 | 0.293520 | ||||||||
\(956\) | 1.32193e6 | 0.0467805 | ||||||||
\(957\) | 6.66807e6 | 0.235353 | ||||||||
\(958\) | −3.97433e7 | −1.39910 | ||||||||
\(959\) | 6.67579e6 | 0.234399 | ||||||||
\(960\) | −5.39734e6 | −0.189018 | ||||||||
\(961\) | −2.25075e7 | −0.786173 | ||||||||
\(962\) | −5.96191e7 | −2.07705 | ||||||||
\(963\) | −4.79422e7 | −1.66591 | ||||||||
\(964\) | −1.84015e7 | −0.637765 | ||||||||
\(965\) | 1.26189e7 | 0.436217 | ||||||||
\(966\) | 9.97613e6 | 0.343969 | ||||||||
\(967\) | 7.81001e6 | 0.268587 | 0.134294 | − | 0.990942i | \(-0.457123\pi\) | ||||
0.134294 | + | 0.990942i | \(0.457123\pi\) | |||||||
\(968\) | 1.07648e6 | 0.0369248 | ||||||||
\(969\) | −7.25722e6 | −0.248291 | ||||||||
\(970\) | −4.33801e6 | −0.148034 | ||||||||
\(971\) | 5.69979e7 | 1.94004 | 0.970021 | − | 0.243021i | \(-0.0781385\pi\) | ||||
0.970021 | + | 0.243021i | \(0.0781385\pi\) | |||||||
\(972\) | −2.74983e7 | −0.933556 | ||||||||
\(973\) | −1.28213e7 | −0.434160 | ||||||||
\(974\) | 1.88693e7 | 0.637320 | ||||||||
\(975\) | −1.26902e7 | −0.427522 | ||||||||
\(976\) | 4.65630e7 | 1.56465 | ||||||||
\(977\) | −392600. | −0.0131587 | −0.00657936 | − | 0.999978i | \(-0.502094\pi\) | ||||
−0.00657936 | + | 0.999978i | \(0.502094\pi\) | |||||||
\(978\) | −1.74020e7 | −0.581772 | ||||||||
\(979\) | −1.30986e6 | −0.0436787 | ||||||||
\(980\) | −5.34041e6 | −0.177627 | ||||||||
\(981\) | −3.02754e7 | −1.00442 | ||||||||
\(982\) | −8.35840e6 | −0.276595 | ||||||||
\(983\) | 2.60437e7 | 0.859645 | 0.429822 | − | 0.902914i | \(-0.358576\pi\) | ||||
0.429822 | + | 0.902914i | \(0.358576\pi\) | |||||||
\(984\) | 1.17554e7 | 0.387034 | ||||||||
\(985\) | 1.92074e7 | 0.630781 | ||||||||
\(986\) | −1.77229e7 | −0.580554 | ||||||||
\(987\) | 4.07927e7 | 1.33287 | ||||||||
\(988\) | 7.52216e6 | 0.245160 | ||||||||
\(989\) | 7.27216e6 | 0.236414 | ||||||||
\(990\) | −4.80833e6 | −0.155922 | ||||||||
\(991\) | 1.64529e7 | 0.532179 | 0.266090 | − | 0.963948i | \(-0.414268\pi\) | ||||
0.266090 | + | 0.963948i | \(0.414268\pi\) | |||||||
\(992\) | −1.67967e7 | −0.541930 | ||||||||
\(993\) | −2.16699e7 | −0.697404 | ||||||||
\(994\) | −2.91170e7 | −0.934717 | ||||||||
\(995\) | 9.76815e6 | 0.312791 | ||||||||
\(996\) | 4.13996e7 | 1.32235 | ||||||||
\(997\) | 3.71006e6 | 0.118207 | 0.0591034 | − | 0.998252i | \(-0.481176\pi\) | ||||
0.0591034 | + | 0.998252i | \(0.481176\pi\) | |||||||
\(998\) | −4.86922e7 | −1.54751 | ||||||||
\(999\) | 4.89696e6 | 0.155243 |
(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 | 1045.6.a.e.1.10 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.6.a.e.1.10 | ✓ | 38 | 1.1 | even | 1 | trivial |