Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,6,Mod(145,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.145");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.i (of order \(3\), degree \(2\), not 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: | \(69.2858101592\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.47347183152.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 118x^{4} - 231x^{3} + 3700x^{2} - 3585x + 32331 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{9} \) |
Twist minimal: | no (minimal twist has level 18) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 289.1 | ||
Root | \(0.500000 - 5.23712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 432.289 |
Dual form | 432.6.i.b.145.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −33.0434 | − | 57.2329i | −0.591099 | − | 1.02381i | −0.994085 | − | 0.108607i | \(-0.965361\pi\) |
0.402986 | − | 0.915206i | \(-0.367972\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 57.0952 | − | 98.8918i | 0.440407 | − | 0.762808i | −0.557312 | − | 0.830303i | \(-0.688167\pi\) |
0.997720 | + | 0.0674952i | \(0.0215007\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 192.812 | − | 333.961i | 0.480455 | − | 0.832173i | −0.519293 | − | 0.854596i | \(-0.673805\pi\) |
0.999749 | + | 0.0224231i | \(0.00713811\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −516.287 | − | 894.236i | −0.847292 | − | 1.46755i | −0.883616 | − | 0.468212i | \(-0.844898\pi\) |
0.0363242 | − | 0.999340i | \(-0.488435\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −959.020 | −0.804832 | −0.402416 | − | 0.915457i | \(-0.631829\pi\) | ||||
−0.402416 | + | 0.915457i | \(0.631829\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 464.576 | 0.295239 | 0.147619 | − | 0.989044i | \(-0.452839\pi\) | ||||
0.147619 | + | 0.989044i | \(0.452839\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1151.70 | − | 1994.81i | −0.453963 | − | 0.786288i | 0.544664 | − | 0.838654i | \(-0.316657\pi\) |
−0.998628 | + | 0.0523662i | \(0.983324\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −621.235 | + | 1076.01i | −0.198795 | + | 0.344323i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3549.13 | − | 6147.28i | 0.783659 | − | 1.35734i | −0.146138 | − | 0.989264i | \(-0.546684\pi\) |
0.929797 | − | 0.368073i | \(-0.119982\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3881.53 | + | 6723.00i | 0.725435 | + | 1.25649i | 0.958795 | + | 0.284100i | \(0.0916947\pi\) |
−0.233360 | + | 0.972391i | \(0.574972\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7546.48 | −1.04130 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9317.57 | 1.11892 | 0.559459 | − | 0.828858i | \(-0.311009\pi\) | ||||
0.559459 | + | 0.828858i | \(0.311009\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6661.64 | − | 11538.3i | −0.618901 | − | 1.07197i | −0.989687 | − | 0.143250i | \(-0.954245\pi\) |
0.370785 | − | 0.928719i | \(-0.379089\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1056.29 | + | 1829.55i | −0.0871190 | + | 0.150895i | −0.906292 | − | 0.422652i | \(-0.861099\pi\) |
0.819173 | + | 0.573546i | \(0.194433\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1247.40 | + | 2160.56i | −0.0823686 | + | 0.142667i | −0.904267 | − | 0.426968i | \(-0.859582\pi\) |
0.821898 | + | 0.569634i | \(0.192915\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1883.78 | + | 3262.80i | 0.112083 | + | 0.194133i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10044.2 | 0.491163 | 0.245582 | − | 0.969376i | \(-0.421021\pi\) | ||||
0.245582 | + | 0.969376i | \(0.421021\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −25484.7 | −1.13599 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2720.33 | − | 4711.75i | −0.101740 | − | 0.176219i | 0.810662 | − | 0.585515i | \(-0.199108\pi\) |
−0.912402 | + | 0.409296i | \(0.865774\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −17094.4 | + | 29608.4i | −0.588206 | + | 1.01880i | 0.406261 | + | 0.913757i | \(0.366832\pi\) |
−0.994467 | + | 0.105046i | \(0.966501\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −34119.8 | + | 59097.2i | −1.00167 | + | 1.73494i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 26792.6 | + | 46406.2i | 0.729169 | + | 1.26296i | 0.957235 | + | 0.289311i | \(0.0934263\pi\) |
−0.228066 | + | 0.973646i | \(0.573240\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −970.010 | −0.0228365 | −0.0114183 | − | 0.999935i | \(-0.503635\pi\) | ||||
−0.0114183 | + | 0.999935i | \(0.503635\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −72400.3 | −1.59013 | −0.795066 | − | 0.606523i | \(-0.792564\pi\) | ||||
−0.795066 | + | 0.606523i | \(0.792564\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −22017.3 | − | 38135.1i | −0.423192 | − | 0.732990i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16098.9 | − | 27884.0i | 0.290220 | − | 0.502676i | −0.683642 | − | 0.729818i | \(-0.739605\pi\) |
0.973862 | + | 0.227142i | \(0.0729382\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 18046.6 | − | 31257.6i | 0.287541 | − | 0.498036i | −0.685681 | − | 0.727902i | \(-0.740496\pi\) |
0.973222 | + | 0.229866i | \(0.0738289\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 31689.3 | + | 54887.5i | 0.475735 | + | 0.823998i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −42622.2 | −0.570375 | −0.285188 | − | 0.958472i | \(-0.592056\pi\) | ||||
−0.285188 | + | 0.958472i | \(0.592056\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −117910. | −1.49261 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15351.2 | − | 26589.0i | −0.174515 | − | 0.302269i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 21926.9 | − | 37978.6i | 0.236618 | − | 0.409835i | −0.723123 | − | 0.690719i | \(-0.757294\pi\) |
0.959742 | + | 0.280884i | \(0.0906275\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12056.7 | − | 20882.8i | 0.117604 | − | 0.203697i | −0.801213 | − | 0.598379i | \(-0.795812\pi\) |
0.918818 | + | 0.394682i | \(0.129145\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −68610.4 | − | 118837.i | −0.637231 | − | 1.10372i | −0.986038 | − | 0.166522i | \(-0.946746\pi\) |
0.348807 | − | 0.937195i | \(-0.386587\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −167979. | −1.41839 | −0.709195 | − | 0.705012i | \(-0.750941\pi\) | ||||
−0.709195 | + | 0.705012i | \(0.750941\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −21224.0 | −0.171104 | −0.0855521 | − | 0.996334i | \(-0.527265\pi\) | ||||
−0.0855521 | + | 0.996334i | \(0.527265\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14420.8 | − | 24977.5i | −0.106241 | − | 0.184015i | 0.808003 | − | 0.589178i | \(-0.200548\pi\) |
−0.914245 | + | 0.405163i | \(0.867215\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −76112.4 | + | 131831.i | −0.536674 | + | 0.929547i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −54755.4 | + | 94839.2i | −0.354454 | + | 0.613932i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6172.35 | + | 10690.8i | 0.0383255 | + | 0.0663816i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −124410. | −0.712167 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 215062. | 1.18319 | 0.591594 | − | 0.806236i | \(-0.298499\pi\) | ||||
0.591594 | + | 0.806236i | \(0.298499\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 94654.7 | + | 163947.i | 0.481908 | + | 0.834688i | 0.999784 | − | 0.0207668i | \(-0.00661075\pi\) |
−0.517877 | + | 0.855455i | \(0.673277\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 26525.1 | − | 45942.8i | 0.130025 | − | 0.225210i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1809.78 | + | 3134.63i | −0.00823805 | + | 0.0142687i | −0.870115 | − | 0.492849i | \(-0.835956\pi\) |
0.861877 | + | 0.507117i | \(0.169289\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 60440.1 | + | 104685.i | 0.265331 | + | 0.459567i | 0.967650 | − | 0.252295i | \(-0.0811854\pi\) |
−0.702319 | + | 0.711862i | \(0.747852\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −398186. | −1.62834 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −469102. | −1.85288 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 37408.2 | + | 64792.9i | 0.138039 | + | 0.239090i | 0.926754 | − | 0.375668i | \(-0.122587\pi\) |
−0.788715 | + | 0.614758i | \(0.789254\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −179976. | + | 311728.i | −0.642352 | + | 1.11259i | 0.342554 | + | 0.939498i | \(0.388708\pi\) |
−0.984906 | + | 0.173088i | \(0.944625\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 256518. | − | 444302.i | 0.857607 | − | 1.48542i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23983.3 | − | 41540.3i | −0.0776533 | − | 0.134499i | 0.824584 | − | 0.565740i | \(-0.191409\pi\) |
−0.902237 | + | 0.431241i | \(0.858076\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −263027. | −0.799715 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −361063. | −1.06442 | −0.532212 | − | 0.846611i | \(-0.678639\pi\) | ||||
−0.532212 | + | 0.846611i | \(0.678639\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −58233.2 | − | 100863.i | −0.161577 | − | 0.279860i | 0.773857 | − | 0.633360i | \(-0.218325\pi\) |
−0.935434 | + | 0.353500i | \(0.884991\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −347458. | + | 601816.i | −0.935807 | + | 1.62086i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 51762.9 | − | 89656.0i | 0.131493 | − | 0.227753i | −0.792759 | − | 0.609535i | \(-0.791356\pi\) |
0.924252 | + | 0.381782i | \(0.124689\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 70939.0 | + | 122870.i | 0.175102 | + | 0.303285i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −78941.2 | −0.184150 | −0.0920748 | − | 0.995752i | \(-0.529350\pi\) | ||||
−0.0920748 | + | 0.995752i | \(0.529350\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 586108. | 1.32978 | 0.664892 | − | 0.746940i | \(-0.268478\pi\) | ||||
0.664892 | + | 0.746940i | \(0.268478\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −307884. | − | 533271.i | −0.661391 | − | 1.14556i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −184911. | + | 320275.i | −0.386686 | + | 0.669760i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −386026. | + | 668617.i | −0.765656 | + | 1.32615i | 0.174243 | + | 0.984703i | \(0.444252\pi\) |
−0.939899 | + | 0.341452i | \(0.889081\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8719.67 | + | 15102.9i | 0.0168503 | + | 0.0291855i | 0.874328 | − | 0.485336i | \(-0.161303\pi\) |
−0.857477 | + | 0.514522i | \(0.827969\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −340729. | −0.625524 | −0.312762 | − | 0.949832i | \(-0.601254\pi\) | ||||
−0.312762 | + | 0.949832i | \(0.601254\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14239.7 | −0.0254899 | −0.0127450 | − | 0.999919i | \(-0.504057\pi\) | ||||
−0.0127450 | + | 0.999919i | \(0.504057\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −405277. | − | 701960.i | −0.690258 | − | 1.19556i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −440246. | + | 762529.i | −0.731663 | + | 1.26728i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 89576.0 | − | 155150.i | 0.141849 | − | 0.245690i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24049.2 | − | 41654.4i | −0.0371873 | − | 0.0644102i | 0.846833 | − | 0.531859i | \(-0.178506\pi\) |
−0.884020 | + | 0.467449i | \(0.845173\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 139614. | 0.205984 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 886466. | 1.27795 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 495130. | + | 857590.i | 0.681928 | + | 1.18113i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 391988. | − | 678944.i | 0.527851 | − | 0.914264i | −0.471622 | − | 0.881801i | \(-0.656331\pi\) |
0.999473 | − | 0.0324633i | \(-0.0103352\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 277898. | − | 481334.i | 0.357949 | − | 0.619986i | −0.629669 | − | 0.776863i | \(-0.716810\pi\) |
0.987618 | + | 0.156878i | \(0.0501428\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −57346.2 | − | 99326.6i | −0.0722630 | − | 0.125163i | 0.827630 | − | 0.561274i | \(-0.189689\pi\) |
−0.899893 | + | 0.436111i | \(0.856355\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 111177. | 0.134161 | 0.0670805 | − | 0.997748i | \(-0.478632\pi\) | ||||
0.0670805 | + | 0.997748i | \(0.478632\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 164874. | 0.194752 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 369523. | + | 640033.i | 0.418453 | + | 0.724782i | 0.995784 | − | 0.0917279i | \(-0.0292390\pi\) |
−0.577331 | + | 0.816510i | \(0.695906\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 645180. | − | 1.11748e6i | 0.715547 | − | 1.23936i | −0.247201 | − | 0.968964i | \(-0.579511\pi\) |
0.962748 | − | 0.270400i | \(-0.0871559\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 124493. | − | 215628.i | 0.132504 | − | 0.229504i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −239855. | − | 415441.i | −0.250153 | − | 0.433278i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.29383e6 | 1.29626 | 0.648129 | − | 0.761530i | \(-0.275552\pi\) | ||||
0.648129 | + | 0.761530i | \(0.275552\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −888250. | −0.872437 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 312181. | + | 540713.i | 0.294831 | + | 0.510663i | 0.974946 | − | 0.222443i | \(-0.0714032\pi\) |
−0.680114 | + | 0.733106i | \(0.738070\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 531988. | − | 921431.i | 0.492780 | − | 0.853519i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 582495. | − | 1.00891e6i | 0.519281 | − | 0.899421i | −0.480468 | − | 0.877012i | \(-0.659533\pi\) |
0.999749 | − | 0.0224089i | \(-0.00713358\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −331895. | − | 574859.i | −0.290326 | − | 0.502859i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.58951e6 | −1.33932 | −0.669659 | − | 0.742669i | \(-0.733560\pi\) | ||||
−0.669659 | + | 0.742669i | \(0.733560\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 977878. | 0.808837 | 0.404419 | − | 0.914574i | \(-0.367474\pi\) | ||||
0.404419 | + | 0.914574i | \(0.367474\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 239563. | + | 414936.i | 0.191024 | + | 0.330864i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 645243. | − | 1.11759e6i | 0.505271 | − | 0.875154i | −0.494711 | − | 0.869058i | \(-0.664726\pi\) |
0.999981 | − | 0.00609677i | \(-0.00194067\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 833662. | − | 1.44395e6i | 0.629831 | − | 1.09090i | −0.357754 | − | 0.933816i | \(-0.616457\pi\) |
0.987585 | − | 0.157084i | \(-0.0502094\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 564568. | + | 977861.i | 0.419035 | + | 0.725790i | 0.995843 | − | 0.0910901i | \(-0.0290351\pi\) |
−0.576808 | + | 0.816880i | \(0.695702\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.52139e6 | −1.09027 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −500138. | −0.352245 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.02815e6 | + | 1.78081e6i | 0.699663 | + | 1.21185i | 0.968583 | + | 0.248689i | \(0.0799997\pi\) |
−0.268921 | + | 0.963162i | \(0.586667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −179778. | + | 311385.i | −0.120277 | + | 0.208325i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.18922e6 | + | 2.05979e6i | −0.769279 | + | 1.33243i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 120618. | + | 208917.i | 0.0767357 | + | 0.132910i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.25943e6 | 1.39075 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.52149e6 | −0.921346 | −0.460673 | − | 0.887570i | \(-0.652392\pi\) | ||||
−0.460673 | + | 0.887570i | \(0.652392\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.35420e6 | + | 2.34554e6i | 0.793928 | + | 1.37512i | 0.923517 | + | 0.383556i | \(0.125301\pi\) |
−0.129589 | + | 0.991568i | \(0.541366\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 325583. | − | 563926.i | 0.187845 | − | 0.325358i | −0.756686 | − | 0.653778i | \(-0.773183\pi\) |
0.944532 | + | 0.328420i | \(0.106516\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −58055.3 | + | 100555.i | −0.0324484 | + | 0.0562024i | −0.881794 | − | 0.471636i | \(-0.843664\pi\) |
0.849345 | + | 0.527838i | \(0.176997\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.36863e6 | − | 2.37054e6i | −0.753026 | − | 1.30428i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −445538. | −0.237618 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.28294e6 | 0.673750 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 142441. | + | 246715.i | 0.0725514 | + | 0.125663i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 158828. | − | 275099.i | 0.0796816 | − | 0.138013i | −0.823431 | − | 0.567416i | \(-0.807943\pi\) |
0.903113 | + | 0.429404i | \(0.141276\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.77064e6 | − | 3.06684e6i | 0.862021 | − | 1.49306i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −215275. | − | 372867.i | −0.103257 | − | 0.178846i | 0.809768 | − | 0.586750i | \(-0.199593\pi\) |
−0.913025 | + | 0.407904i | \(0.866260\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.99363e6 | 1.39416 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.34942e6 | 1.07826 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.07020e6 | + | 3.58569e6i | 0.922971 | + | 1.59863i | 0.794793 | + | 0.606881i | \(0.207580\pi\) |
0.128178 | + | 0.991751i | \(0.459087\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.73048e6 | − | 2.99727e6i | 0.760505 | − | 1.31723i | −0.182085 | − | 0.983283i | \(-0.558285\pi\) |
0.942590 | − | 0.333951i | \(-0.108382\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.32229e6 | − | 2.29027e6i | 0.564792 | − | 0.978249i | −0.432277 | − | 0.901741i | \(-0.642290\pi\) |
0.997069 | − | 0.0765076i | \(-0.0243770\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 32052.5 | + | 55516.5i | 0.0134987 | + | 0.0233804i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.13123e6 | 0.872761 | 0.436380 | − | 0.899762i | \(-0.356260\pi\) | ||||
0.436380 | + | 0.899762i | \(0.356260\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.26027e6 | −0.912834 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.39235e6 | + | 4.14368e6i | 0.939925 | + | 1.62800i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −640035. | + | 1.10857e6i | −0.248049 | + | 0.429634i | −0.962985 | − | 0.269557i | \(-0.913123\pi\) |
0.714935 | + | 0.699191i | \(0.246456\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 573476. | − | 993289.i | 0.216312 | − | 0.374663i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.94733e6 | + | 3.37288e6i | 0.724716 | + | 1.25524i | 0.959091 | + | 0.283099i | \(0.0913623\pi\) |
−0.234375 | + | 0.972146i | \(0.575304\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.32949e6 | −2.65595 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.83335e6 | 1.01322 | 0.506609 | − | 0.862176i | \(-0.330899\pi\) | ||||
0.506609 | + | 0.862176i | \(0.330899\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.18249e6 | − | 2.04814e6i | −0.411909 | − | 0.713448i | 0.583189 | − | 0.812336i | \(-0.301805\pi\) |
−0.995099 | + | 0.0988883i | \(0.968471\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.45505e6 | + | 2.52023e6i | −0.500296 | + | 0.866539i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −871692. | + | 1.50981e6i | −0.292071 | + | 0.505882i | −0.974299 | − | 0.225257i | \(-0.927678\pi\) |
0.682228 | + | 0.731139i | \(0.261011\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.10451e6 | + | 1.91306e6i | 0.365364 | + | 0.632830i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.12785e6 | −0.686195 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.81109e6 | 1.53203 | 0.766015 | − | 0.642823i | \(-0.222237\pi\) | ||||
0.766015 | + | 0.642823i | \(0.222237\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.27703e6 | − | 3.94394e6i | −0.707145 | − | 1.22481i | −0.965912 | − | 0.258871i | \(-0.916649\pi\) |
0.258767 | − | 0.965940i | \(-0.416684\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00797e6 | − | 6.94200e6i | 1.22931 | − | 2.12923i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.79654e6 | − | 3.11170e6i | 0.537590 | − | 0.931133i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −956414. | − | 1.65656e6i | −0.282708 | − | 0.489664i | 0.689343 | − | 0.724435i | \(-0.257899\pi\) |
−0.972051 | + | 0.234771i | \(0.924566\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −621271. | −0.179228 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.38528e6 | −0.679860 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.20697e6 | − | 3.82259e6i | −0.614132 | − | 1.06371i | −0.990536 | − | 0.137252i | \(-0.956173\pi\) |
0.376404 | − | 0.926456i | \(-0.377161\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 872253. | − | 1.51079e6i | 0.239848 | − | 0.415430i | −0.720822 | − | 0.693120i | \(-0.756236\pi\) |
0.960671 | + | 0.277690i | \(0.0895689\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 595777. | − | 1.03192e6i | 0.159997 | − | 0.277122i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.95202e6 | + | 3.38099e6i | 0.518100 | + | 0.897376i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.21740e6 | −0.574976 | −0.287488 | − | 0.957784i | \(-0.592820\pi\) | ||||
−0.287488 | + | 0.957784i | \(0.592820\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.63511e6 | −0.931746 | −0.465873 | − | 0.884851i | \(-0.654260\pi\) | ||||
−0.465873 | + | 0.884851i | \(0.654260\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −535054. | − | 926741.i | −0.134028 | − | 0.232143i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.54413e6 | + | 2.67452e6i | −0.382405 | + | 0.662345i | −0.991405 | − | 0.130825i | \(-0.958237\pi\) |
0.609001 | + | 0.793170i | \(0.291571\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.50048e6 | − | 6.06302e6i | 0.847459 | − | 1.46784i | −0.0360092 | − | 0.999351i | \(-0.511465\pi\) |
0.883468 | − | 0.468491i | \(-0.155202\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.40838e6 | + | 2.43939e6i | 0.337148 | + | 0.583958i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.00196e6 | 1.17091 | 0.585456 | − | 0.810704i | \(-0.300916\pi\) | ||||
0.585456 | + | 0.810704i | \(0.300916\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.13778e6 | −1.18942 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.89615e6 | + | 6.74833e6i | 0.882282 | + | 1.52816i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.78581e6 | + | 3.09311e6i | −0.399985 | + | 0.692795i | −0.993724 | − | 0.111863i | \(-0.964318\pi\) |
0.593738 | + | 0.804658i | \(0.297651\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.75061e6 | − | 4.76420e6i | 0.602805 | − | 1.04409i | −0.389589 | − | 0.920989i | \(-0.627383\pi\) |
0.992394 | − | 0.123100i | \(-0.0392837\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.42708e6 | − | 2.47177e6i | −0.309382 | − | 0.535866i | 0.668845 | − | 0.743402i | \(-0.266789\pi\) |
−0.978227 | + | 0.207536i | \(0.933456\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.16552e6 | −1.52039 | −0.760196 | − | 0.649694i | \(-0.774897\pi\) | ||||
−0.760196 | + | 0.649694i | \(0.774897\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.11892e6 | 1.28452 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 407332. | + | 705520.i | 0.0837136 | + | 0.144996i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −288611. | + | 499889.i | −0.0586920 | + | 0.101658i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.64185e6 | + | 2.84377e6i | −0.326961 | + | 0.566312i | −0.981907 | − | 0.189363i | \(-0.939358\pi\) |
0.654947 | + | 0.755675i | \(0.272691\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.81054e6 | − | 8.33210e6i | −0.948050 | − | 1.64207i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.89816e6 | −0.559459 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.18097e6 | −0.416704 | −0.208352 | − | 0.978054i | \(-0.566810\pi\) | ||||
−0.208352 | + | 0.978054i | \(0.566810\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.96974e6 | + | 8.60785e6i | 0.930315 | + | 1.61135i | 0.782782 | + | 0.622297i | \(0.213800\pi\) |
0.147534 | + | 0.989057i | \(0.452866\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.40369e6 | + | 5.89536e6i | −0.630714 | + | 1.09243i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −55382.9 | + | 95926.0i | −0.0100574 | + | 0.0174199i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.26386e6 | − | 3.92112e6i | −0.407004 | − | 0.704951i | 0.587549 | − | 0.809189i | \(-0.300093\pi\) |
−0.994552 | + | 0.104238i | \(0.966760\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.40282e6 | −0.775909 | −0.387955 | − | 0.921679i | \(-0.626818\pi\) | ||||
−0.387955 | + | 0.921679i | \(0.626818\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.59357e6 | −0.278063 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.91063e6 | + | 5.04135e6i | 0.497957 | + | 0.862487i | 0.999997 | − | 0.00235703i | \(-0.000750266\pi\) |
−0.502040 | + | 0.864844i | \(0.667417\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.13371e6 | + | 7.15979e6i | −0.700306 | + | 1.21296i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.53424e6 | + | 7.85354e6i | −0.753333 | + | 1.30481i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 481028. | + | 833166.i | 0.0791488 | + | 0.137090i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.09649e7 | −1.76975 | −0.884875 | − | 0.465829i | \(-0.845756\pi\) | ||||
−0.884875 | + | 0.465829i | \(0.845756\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.83705e6 | 0.613399 | 0.306700 | − | 0.951806i | \(-0.400775\pi\) | ||||
0.306700 | + | 0.951806i | \(0.400775\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.72246e6 | − | 6.44750e6i | −0.583854 | − | 1.01126i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 565332. | − | 979183.i | 0.0878343 | − | 0.152133i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.87864e6 | + | 1.19141e7i | −1.04878 | + | 1.81654i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.55060e6 | + | 9.61392e6i | 0.838408 | + | 1.45217i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.45286e6 | 0.215403 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.88767e6 | −0.717974 | −0.358987 | − | 0.933343i | \(-0.616878\pi\) | ||||
−0.358987 | + | 0.933343i | \(0.616878\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 701313. | + | 1.21471e6i | 0.101139 | + | 0.175179i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.46672e6 | + | 6.00454e6i | −0.495394 | + | 0.858047i | −0.999986 | − | 0.00531061i | \(-0.998310\pi\) |
0.504592 | + | 0.863358i | \(0.331643\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.64884e6 | − | 2.85588e6i | 0.231366 | − | 0.400739i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.83834e6 | − | 3.18409e6i | −0.255630 | − | 0.442764i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.83771e6 | 1.34356 | 0.671778 | − | 0.740752i | \(-0.265531\pi\) | ||||
0.671778 | + | 0.740752i | \(0.265531\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.18140e6 | 0.295261 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.36609e6 | − | 2.36613e6i | −0.181638 | − | 0.314607i | 0.760800 | − | 0.648986i | \(-0.224807\pi\) |
−0.942439 | + | 0.334379i | \(0.891473\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −953024. | + | 1.65069e6i | −0.125598 | + | 0.217542i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.71998e6 | − | 8.17525e6i | 0.611167 | − | 1.05857i | −0.379877 | − | 0.925037i | \(-0.624034\pi\) |
0.991044 | − | 0.133535i | \(-0.0426329\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.33948e6 | − | 1.09803e7i | −0.813698 | − | 1.40937i | −0.910259 | − | 0.414039i | \(-0.864118\pi\) |
0.0965611 | − | 0.995327i | \(-0.469216\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.86191e6 | 0.360983 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.51657e7 | −1.89637 | −0.948187 | − | 0.317712i | \(-0.897086\pi\) | ||||
−0.948187 | + | 0.317712i | \(0.897086\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.06075e6 | − | 3.56932e6i | −0.253270 | − | 0.438677i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.93665e6 | − | 3.35437e6i | 0.235982 | − | 0.408733i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −911702. | + | 1.57911e6i | −0.109209 | + | 0.189155i | −0.915450 | − | 0.402432i | \(-0.868165\pi\) |
0.806241 | + | 0.591587i | \(0.201498\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.80327e6 | + | 3.12335e6i | 0.214176 | + | 0.370965i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.27957e7 | −1.49427 | −0.747133 | − | 0.664674i | \(-0.768570\pi\) | ||||
−0.747133 | + | 0.664674i | \(0.768570\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.23723e6 | 0.838069 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.38212e6 | − | 7.59006e6i | −0.499020 | − | 0.864327i | 0.500980 | − | 0.865459i | \(-0.332973\pi\) |
−0.999999 | + | 0.00113166i | \(0.999640\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −834793. | + | 1.44590e6i | −0.0942741 | + | 0.163288i | −0.909305 | − | 0.416129i | \(-0.863386\pi\) |
0.815031 | + | 0.579417i | \(0.196720\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 407911. | − | 706523.i | 0.0453082 | − | 0.0784762i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.08535e6 | − | 8.80809e6i | −0.560208 | − | 0.970308i | −0.997478 | − | 0.0709782i | \(-0.977388\pi\) |
0.437270 | − | 0.899330i | \(-0.355945\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.57607e6 | 0.279161 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.37829e7 | 1.48146 | 0.740730 | − | 0.671803i | \(-0.234480\pi\) | ||||
0.740730 | + | 0.671803i | \(0.234480\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.05409e6 | − | 1.04860e7i | −0.640230 | − | 1.10891i | −0.985381 | − | 0.170363i | \(-0.945506\pi\) |
0.345152 | − | 0.938547i | \(-0.387827\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.48665e6 | + | 1.46993e7i | −0.890245 | + | 1.54195i | −0.0506641 | + | 0.998716i | \(0.516134\pi\) |
−0.839581 | + | 0.543234i | \(0.817200\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.43352e6 | + | 4.21498e6i | −0.251197 | + | 0.435087i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.05231e6 | + | 1.04829e7i | 0.619756 | + | 1.07345i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.93574e6 | −0.900541 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.90092e6 | −0.789958 | −0.394979 | − | 0.918690i | \(-0.629248\pi\) | ||||
−0.394979 | + | 0.918690i | \(0.629248\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.10637e6 | − | 1.23086e7i | −0.699381 | − | 1.21136i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.94514e6 | − | 3.36908e6i | 0.189934 | − | 0.328975i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.33807e6 | − | 9.24581e6i | 0.513144 | − | 0.888792i | −0.486740 | − | 0.873547i | \(-0.661814\pi\) |
0.999884 | − | 0.0152446i | \(-0.00485269\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.68885e6 | + | 8.12132e6i | 0.447238 | + | 0.774639i | 0.998205 | − | 0.0598882i | \(-0.0190744\pi\) |
−0.550967 | + | 0.834527i | \(0.685741\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.44013e6 | −0.886579 | −0.443289 | − | 0.896379i | \(-0.646189\pi\) | ||||
−0.443289 | + | 0.896379i | \(0.646189\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.09805e6 | −0.195526 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.44455e6 | + | 1.28943e7i | 0.683212 | + | 1.18336i | 0.973995 | + | 0.226569i | \(0.0727509\pi\) |
−0.290783 | + | 0.956789i | \(0.593916\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.25543e6 | − | 1.08347e7i | 0.569710 | − | 0.986766i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.82391e6 | − | 6.62320e6i | 0.343000 | − | 0.594093i | −0.641989 | − | 0.766714i | \(-0.721890\pi\) |
0.984988 | + | 0.172621i | \(0.0552237\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.50269e6 | + | 4.33479e6i | 0.222794 | + | 0.385891i | 0.955655 | − | 0.294487i | \(-0.0951489\pi\) |
−0.732861 | + | 0.680378i | \(0.761816\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.50592e6 | −0.307431 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.63502e7 | −1.42301 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.59202e6 | + | 1.14177e7i | 0.565214 | + | 0.978979i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.07220e6 | + | 1.85710e6i | −0.0912511 | + | 0.158051i | −0.908038 | − | 0.418888i | \(-0.862420\pi\) |
0.816787 | + | 0.576940i | \(0.195753\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.75463e6 | + | 8.23526e6i | −0.398699 | + | 0.690567i | −0.993566 | − | 0.113257i | \(-0.963871\pi\) |
0.594867 | + | 0.803824i | \(0.297205\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.50385e6 | − | 4.33679e6i | −0.208417 | − | 0.360989i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.47266e6 | −0.448897 | −0.224449 | − | 0.974486i | \(-0.572058\pi\) | ||||
−0.224449 | + | 0.974486i | \(0.572058\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 239205. | 0.0194780 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.18570e6 | − | 8.98189e6i | −0.416159 | − | 0.720808i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.44084e6 | − | 5.95970e6i | 0.274138 | − | 0.474821i | −0.695779 | − | 0.718255i | \(-0.744941\pi\) |
0.969917 | + | 0.243435i | \(0.0782742\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.99430e6 | − | 6.91832e6i | 0.313674 | − | 0.543299i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.38864e6 | + | 1.10655e7i | 0.498112 | + | 0.862755i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.19615e6 | −0.399380 | −0.199690 | − | 0.979859i | \(-0.563994\pi\) | ||||
−0.199690 | + | 0.979859i | \(0.563994\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.32872e6 | 0.330348 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.37676e6 | − | 2.38461e6i | −0.103588 | − | 0.179419i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −287410. | + | 497809.i | −0.0214727 | + | 0.0371918i | −0.876562 | − | 0.481289i | \(-0.840169\pi\) |
0.855089 | + | 0.518481i | \(0.173502\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.94074e6 | − | 1.54858e7i | 0.658642 | − | 1.14080i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.31574e7 | + | 2.27893e7i | 0.962511 | + | 1.66712i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −400906. | −0.0289215 | −0.0144607 | − | 0.999895i | \(-0.504603\pi\) | ||||
−0.0144607 | + | 0.999895i | \(0.504603\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.56693e7 | −1.12256 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.40969e6 | + | 7.63781e6i | 0.311575 | + | 0.539664i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.27154e6 | − | 9.13058e6i | 0.369915 | − | 0.640711i | −0.619637 | − | 0.784889i | \(-0.712720\pi\) |
0.989552 | + | 0.144177i | \(0.0460535\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.01301e6 | − | 1.75458e6i | 0.0701162 | − | 0.121445i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.96868e6 | − | 1.20701e7i | −0.479061 | − | 0.829758i | 0.520651 | − | 0.853770i | \(-0.325689\pi\) |
−0.999712 | + | 0.0240119i | \(0.992356\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.06638e7 | 1.40133 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.88034e6 | 0.665519 | 0.332760 | − | 0.943012i | \(-0.392020\pi\) | ||||
0.332760 | + | 0.943012i | \(0.392020\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.66695e6 | + | 8.08339e6i | 0.310142 | + | 0.537182i | 0.978393 | − | 0.206754i | \(-0.0662899\pi\) |
−0.668251 | + | 0.743936i | \(0.732957\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.47219e6 | − | 4.28195e6i | 0.163189 | − | 0.282652i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.59080e6 | + | 1.66117e7i | −0.624669 | + | 1.08196i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.43761e7 | + | 2.49001e7i | 0.930124 | + | 1.61102i | 0.783106 | + | 0.621888i | \(0.213634\pi\) |
0.147018 | + | 0.989134i | \(0.453032\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.37881e7 | 1.51877 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.94587e6 | −0.313691 | −0.156846 | − | 0.987623i | \(-0.550133\pi\) | ||||
−0.156846 | + | 0.987623i | \(0.550133\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.56829e6 | + | 7.91251e6i | 0.285951 | + | 0.495282i | 0.972839 | − | 0.231481i | \(-0.0743571\pi\) |
−0.686888 | + | 0.726763i | \(0.741024\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.21179e6 | + | 2.09888e6i | −0.0753555 | + | 0.130520i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.80894e6 | + | 4.86523e6i | −0.172407 | + | 0.298617i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.26221e6 | − | 1.43106e7i | −0.503826 | − | 0.872652i | −0.999990 | − | 0.00442349i | \(-0.998592\pi\) |
0.496164 | − | 0.868229i | \(-0.334741\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.01763e7 | −0.612550 | −0.306275 | − | 0.951943i | \(-0.599083\pi\) | ||||
−0.306275 | + | 0.951943i | \(0.599083\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.64536e6 | −0.576852 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.09484e6 | − | 5.36042e6i | −0.182724 | − | 0.316486i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −187030. | + | 323945.i | −0.0109719 | + | 0.0190040i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.58498e6 | + | 2.74527e6i | −0.0918015 | + | 0.159005i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.38173e6 | − | 1.62496e7i | −0.539941 | − | 0.935205i | −0.998907 | − | 0.0467507i | \(-0.985113\pi\) |
0.458966 | − | 0.888454i | \(-0.348220\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.29343e6 | −0.187158 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.53025e7 | 1.99353 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.23982e6 | − | 2.14744e6i | −0.0691376 | − | 0.119750i | 0.829384 | − | 0.558678i | \(-0.188691\pi\) |
−0.898522 | + | 0.438929i | \(0.855358\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.19628e6 | − | 2.07202e6i | 0.0662929 | − | 0.114823i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.39597e7 | + | 2.41788e7i | −0.763987 | + | 1.32326i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.69130e6 | + | 1.50538e7i | 0.472711 | + | 0.818759i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.50880e7 | 1.34770 | 0.673852 | − | 0.738867i | \(-0.264639\pi\) | ||||
0.673852 | + | 0.738867i | \(0.264639\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.28465e6 | 0.228751 | 0.114376 | − | 0.993438i | \(-0.463513\pi\) | ||||
0.114376 | + | 0.993438i | \(0.463513\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.19308e7 | + | 2.06647e7i | 0.629179 | + | 1.08977i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −490728. | + | 849967.i | −0.0257209 | + | 0.0445499i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.01563e7 | − | 1.75913e7i | 0.525871 | − | 0.910836i | −0.473675 | − | 0.880700i | \(-0.657073\pi\) |
0.999546 | − | 0.0301356i | \(-0.00959392\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.58313e6 | − | 1.14023e7i | −0.338792 | − | 0.586804i | 0.645414 | − | 0.763833i | \(-0.276685\pi\) |
−0.984206 | + | 0.177029i | \(0.943351\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.82859e7 | 1.43816 | 0.719079 | − | 0.694928i | \(-0.244564\pi\) | ||||
0.719079 | + | 0.694928i | \(0.244564\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.36608e7 | 0.690381 | 0.345190 | − | 0.938533i | \(-0.387814\pi\) | ||||
0.345190 | + | 0.938533i | \(0.387814\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.80658e6 | − | 3.12909e6i | −0.0902080 | − | 0.156245i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.84845e6 | + | 6.66571e6i | −0.191016 | + | 0.330849i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 75641.6 | − | 131015.i | 0.00370984 | − | 0.00642564i | −0.864165 | − | 0.503209i | \(-0.832152\pi\) |
0.867874 | + | 0.496784i | \(0.165486\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.49371e7 | − | 2.58718e7i | −0.728244 | − | 1.26135i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.59249e7 | 2.21262 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.40965e6 | 0.0675152 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.07311e7 | − | 1.85868e7i | −0.507948 | − | 0.879792i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.38831e7 | − | 2.40462e7i | 0.653301 | − | 1.13155i | −0.329015 | − | 0.944325i | \(-0.606717\pi\) |
0.982317 | − | 0.187226i | \(-0.0599498\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.76136e7 | + | 3.05077e7i | −0.819212 | + | 1.41892i | 0.0870512 | + | 0.996204i | \(0.472256\pi\) |
−0.906263 | + | 0.422713i | \(0.861078\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.02341e7 | − | 3.50464e7i | −0.935622 | − | 1.62054i | −0.773522 | − | 0.633770i | \(-0.781507\pi\) |
−0.162100 | − | 0.986774i | \(-0.551827\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.96865e7 | −0.899789 | −0.449895 | − | 0.893082i | \(-0.648538\pi\) | ||||
−0.449895 | + | 0.893082i | \(0.648538\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.84170e6 | −0.310902 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.20812e6 | − | 1.07528e7i | −0.278876 | − | 0.483027i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.76654e7 | − | 4.79178e7i | 1.23564 | − | 2.14019i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.10324e6 | + | 1.23032e7i | −0.313644 | + | 0.543247i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.31221e7 | − | 2.27282e7i | −0.576109 | − | 0.997850i | −0.995920 | − | 0.0902384i | \(-0.971237\pi\) |
0.419811 | − | 0.907611i | \(-0.362096\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.29423e7 | 0.561786 | 0.280893 | − | 0.959739i | \(-0.409369\pi\) | ||||
0.280893 | + | 0.959739i | \(0.409369\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.39097e6 | −0.146360 | −0.0731800 | − | 0.997319i | \(-0.523315\pi\) | ||||
−0.0731800 | + | 0.997319i | \(0.523315\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.83796e6 | − | 6.64753e6i | −0.163791 | − | 0.283695i | 0.772434 | − | 0.635095i | \(-0.219039\pi\) |
−0.936225 | + | 0.351400i | \(0.885706\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.22790e7 | − | 2.12678e7i | 0.521085 | − | 0.902545i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −579513. | + | 1.00375e6i | −0.0243184 | + | 0.0421207i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.60849e6 | + | 4.51803e6i | 0.108851 | + | 0.188535i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.51042e7 | 2.27398 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.63260e6 | −0.395304 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.93670e7 | − | 3.35446e7i | −0.786033 | − | 1.36145i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.44435e6 | − | 9.42990e6i | 0.219750 | − | 0.380618i | −0.734982 | − | 0.678087i | \(-0.762809\pi\) |
0.954731 | + | 0.297469i | \(0.0961426\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 90239.2 | − | 156299.i | 0.00360246 | − | 0.00623964i | −0.864219 | − | 0.503117i | \(-0.832187\pi\) |
0.867821 | + | 0.496877i | \(0.165520\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.95920e6 | − | 1.20537e7i | −0.276301 | − | 0.478568i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.16173e7 | 0.848942 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.24831e7 | 0.878148 | 0.439074 | − | 0.898451i | \(-0.355307\pi\) | ||||
0.439074 | + | 0.898451i | \(0.355307\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 500804. | + | 867418.i | 0.0193492 | + | 0.0335138i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.78840e6 | + | 1.00258e7i | −0.222436 | + | 0.385270i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.06620e7 | + | 3.57877e7i | −0.785477 | + | 1.36049i | 0.143237 | + | 0.989688i | \(0.454249\pi\) |
−0.928714 | + | 0.370797i | \(0.879084\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 875159. | + | 1.51582e6i | 0.0330912 | + | 0.0573157i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.44403e7 | 0.914278 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.56470e7 | 0.954305 | 0.477153 | − | 0.878820i | \(-0.341669\pi\) | ||||
0.477153 | + | 0.878820i | \(0.341669\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.99880e6 | + | 1.55864e7i | 0.331292 | + | 0.573814i | 0.982765 | − | 0.184857i | \(-0.0591823\pi\) |
−0.651474 | + | 0.758671i | \(0.725849\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.53445e7 | + | 2.65774e7i | −0.561917 | + | 0.973269i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.25398e7 | − | 3.90400e7i | 0.816723 | − | 1.41461i | −0.0913614 | − | 0.995818i | \(-0.529122\pi\) |
0.908084 | − | 0.418788i | \(-0.137545\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.73793e7 | + | 6.47429e7i | 1.34731 | + | 2.33360i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.21374e7 | −0.789577 | −0.394788 | − | 0.918772i | \(-0.629182\pi\) | ||||
−0.394788 | + | 0.918772i | \(0.629182\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.10225e7 | 1.81031 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 206660. | + | 357945.i | 0.00725619 | + | 0.0125681i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.58180e7 | + | 2.73975e7i | −0.552512 | + | 0.956979i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 576255. | − | 998103.i | 0.0199203 | − | 0.0345030i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.81614e6 | − | 1.70020e7i | −0.337578 | − | 0.584703i | 0.646398 | − | 0.763000i | \(-0.276274\pi\) |
−0.983977 | + | 0.178297i | \(0.942941\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.46539e7 | −1.17952 | −0.589758 | − | 0.807580i | \(-0.700777\pi\) | ||||
−0.589758 | + | 0.807580i | \(0.700777\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.38034e7 | 0.467415 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.34006e7 | + | 2.32106e7i | 0.449148 | + | 0.777947i | 0.998331 | − | 0.0577553i | \(-0.0183943\pi\) |
−0.549183 | + | 0.835702i | \(0.685061\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.21808e6 | + | 1.42341e7i | −0.274040 | + | 0.474651i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.19040e7 | − | 2.06183e7i | 0.392924 | − | 0.680565i | −0.599910 | − | 0.800068i | \(-0.704797\pi\) |
0.992834 | + | 0.119503i | \(0.0381301\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.12589e7 | + | 1.95009e7i | 0.369746 | + | 0.640419i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.86614e6 | 0.158195 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.37156e7 | 0.767096 | 0.383548 | − | 0.923521i | \(-0.374702\pi\) | ||||
0.383548 | + | 0.923521i | \(0.374702\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 470529. | + | 814980.i | 0.0150671 | + | 0.0260969i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.04170e7 | − | 3.53633e7i | 0.650511 | − | 1.12672i | −0.332488 | − | 0.943107i | \(-0.607888\pi\) |
0.982999 | − | 0.183610i | \(-0.0587785\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 432.6.i.b.289.1 | 6 | ||
3.2 | odd | 2 | 144.6.i.b.97.1 | 6 | |||
4.3 | odd | 2 | 54.6.c.b.19.1 | 6 | |||
9.4 | even | 3 | inner | 432.6.i.b.145.1 | 6 | ||
9.5 | odd | 6 | 144.6.i.b.49.1 | 6 | |||
12.11 | even | 2 | 18.6.c.b.7.3 | ✓ | 6 | ||
36.7 | odd | 6 | 162.6.a.i.1.3 | 3 | |||
36.11 | even | 6 | 162.6.a.j.1.1 | 3 | |||
36.23 | even | 6 | 18.6.c.b.13.3 | yes | 6 | ||
36.31 | odd | 6 | 54.6.c.b.37.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
18.6.c.b.7.3 | ✓ | 6 | 12.11 | even | 2 | ||
18.6.c.b.13.3 | yes | 6 | 36.23 | even | 6 | ||
54.6.c.b.19.1 | 6 | 4.3 | odd | 2 | |||
54.6.c.b.37.1 | 6 | 36.31 | odd | 6 | |||
144.6.i.b.49.1 | 6 | 9.5 | odd | 6 | |||
144.6.i.b.97.1 | 6 | 3.2 | odd | 2 | |||
162.6.a.i.1.3 | 3 | 36.7 | odd | 6 | |||
162.6.a.j.1.1 | 3 | 36.11 | even | 6 | |||
432.6.i.b.145.1 | 6 | 9.4 | even | 3 | inner | ||
432.6.i.b.289.1 | 6 | 1.1 | even | 1 | trivial |