Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,6,Mod(49,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, 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("144.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.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: | \(23.0952700531\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 18) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(0.500000 + 5.23712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.49 |
Dual form | 144.6.i.b.97.1 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −15.5145 | + | 1.51695i | −0.995254 | + | 0.0973126i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 33.0434 | − | 57.2329i | 0.591099 | − | 1.02381i | −0.402986 | − | 0.915206i | \(-0.632028\pi\) |
0.994085 | − | 0.108607i | \(-0.0346389\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 57.0952 | + | 98.8918i | 0.440407 | + | 0.762808i | 0.997720 | − | 0.0674952i | \(-0.0215007\pi\) |
−0.557312 | + | 0.830303i | \(0.688167\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 238.398 | − | 47.0695i | 0.981061 | − | 0.193702i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −192.812 | − | 333.961i | −0.480455 | − | 0.832173i | 0.519293 | − | 0.854596i | \(-0.326195\pi\) |
−0.999749 | + | 0.0224231i | \(0.992862\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −516.287 | + | 894.236i | −0.847292 | + | 1.46755i | 0.0363242 | + | 0.999340i | \(0.488435\pi\) |
−0.883616 | + | 0.468212i | \(0.844898\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −425.832 | + | 938.063i | −0.488663 | + | 1.07648i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 959.020 | 0.804832 | 0.402416 | − | 0.915457i | \(-0.368171\pi\) | ||||
0.402416 | + | 0.915457i | \(0.368171\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 464.576 | 0.295239 | 0.147619 | − | 0.989044i | \(-0.452839\pi\) | ||||
0.147619 | + | 0.989044i | \(0.452839\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1035.82 | − | 1447.64i | −0.512548 | − | 0.716330i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1151.70 | − | 1994.81i | 0.453963 | − | 0.786288i | −0.544664 | − | 0.838654i | \(-0.683343\pi\) |
0.998628 | + | 0.0523662i | \(0.0166763\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −621.235 | − | 1076.01i | −0.198795 | − | 0.344323i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3627.21 | + | 1091.90i | −0.957555 | + | 0.288252i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3549.13 | − | 6147.28i | −0.783659 | − | 1.35734i | −0.929797 | − | 0.368073i | \(-0.880018\pi\) |
0.146138 | − | 0.989264i | \(-0.453316\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3881.53 | − | 6723.00i | 0.725435 | − | 1.25649i | −0.233360 | − | 0.972391i | \(-0.574972\pi\) |
0.958795 | − | 0.284100i | \(-0.0916947\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3497.98 | + | 4888.74i | 0.559156 | + | 0.781469i | ||||
\(34\) | 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 | ||||||||
\(39\) | 6653.41 | − | 14656.8i | 0.700459 | − | 1.54304i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6661.64 | − | 11538.3i | 0.618901 | − | 1.07197i | −0.370785 | − | 0.928719i | \(-0.620911\pi\) |
0.989687 | − | 0.143250i | \(-0.0457552\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1056.29 | − | 1829.55i | −0.0871190 | − | 0.150895i | 0.819173 | − | 0.573546i | \(-0.194433\pi\) |
−0.906292 | + | 0.422652i | \(0.861099\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5183.55 | − | 15199.5i | 0.381589 | − | 1.11892i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1247.40 | + | 2160.56i | 0.0823686 | + | 0.142667i | 0.904267 | − | 0.426968i | \(-0.140418\pi\) |
−0.821898 | + | 0.569634i | \(0.807085\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1883.78 | − | 3262.80i | 0.112083 | − | 0.194133i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −14878.7 | + | 1454.79i | −0.801012 | + | 0.0783203i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10044.2 | −0.491163 | −0.245582 | − | 0.969376i | \(-0.578979\pi\) | ||||
−0.245582 | + | 0.969376i | \(0.578979\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −25484.7 | −1.13599 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7207.66 | + | 704.741i | −0.293837 | + | 0.0287304i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2720.33 | − | 4711.75i | 0.101740 | − | 0.176219i | −0.810662 | − | 0.585515i | \(-0.800892\pi\) |
0.912402 | + | 0.409296i | \(0.134226\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −17094.4 | − | 29608.4i | −0.588206 | − | 1.01880i | −0.994467 | − | 0.105046i | \(-0.966501\pi\) |
0.406261 | − | 0.913757i | \(-0.366832\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 18266.1 | + | 20888.1i | 0.579823 | + | 0.663053i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 34119.8 | + | 59097.2i | 1.00167 | + | 1.73494i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 26792.6 | − | 46406.2i | 0.729169 | − | 1.26296i | −0.228066 | − | 0.973646i | \(-0.573240\pi\) |
0.957235 | − | 0.289311i | \(-0.0934263\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −14842.0 | + | 32695.5i | −0.375293 | + | 0.826732i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 970.010 | 0.0228365 | 0.0114183 | − | 0.999935i | \(-0.496365\pi\) | ||||
0.0114183 | + | 0.999935i | \(0.496365\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −72400.3 | −1.59013 | −0.795066 | − | 0.606523i | \(-0.792564\pi\) | ||||
−0.795066 | + | 0.606523i | \(0.792564\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11270.4 | + | 15751.3i | 0.231359 | + | 0.323344i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 22017.3 | − | 38135.1i | 0.423192 | − | 0.732990i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16098.9 | + | 27884.0i | 0.290220 | + | 0.502676i | 0.973862 | − | 0.227142i | \(-0.0729382\pi\) |
−0.683642 | + | 0.729818i | \(0.739605\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 54617.9 | − | 22442.5i | 0.924959 | − | 0.380066i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −18046.6 | − | 31257.6i | −0.287541 | − | 0.498036i | 0.685681 | − | 0.727902i | \(-0.259504\pi\) |
−0.973222 | + | 0.229866i | \(0.926171\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 31689.3 | − | 54887.5i | 0.475735 | − | 0.823998i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 64388.1 | + | 89987.9i | 0.912026 | + | 1.27464i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 42622.2 | 0.570375 | 0.285188 | − | 0.958472i | \(-0.407944\pi\) | ||||
0.285188 | + | 0.958472i | \(0.407944\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −117910. | −1.49261 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −50021.4 | + | 110192.i | −0.599720 | + | 1.32112i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15351.2 | − | 26589.0i | 0.174515 | − | 0.302269i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 21926.9 | + | 37978.6i | 0.236618 | + | 0.409835i | 0.959742 | − | 0.280884i | \(-0.0906275\pi\) |
−0.723123 | + | 0.690719i | \(0.757294\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −61685.4 | − | 70539.9i | −0.632549 | − | 0.723347i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12056.7 | − | 20882.8i | −0.117604 | − | 0.203697i | 0.801213 | − | 0.598379i | \(-0.204188\pi\) |
−0.918818 | + | 0.394682i | \(0.870855\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −68610.4 | + | 118837.i | −0.637231 | + | 1.10372i | 0.348807 | + | 0.937195i | \(0.386587\pi\) |
−0.986038 | + | 0.166522i | \(0.946746\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −117080. | + | 11447.7i | −1.03635 | + | 0.101331i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 167979. | 1.41839 | 0.709195 | − | 0.705012i | \(-0.249059\pi\) | ||||
0.709195 | + | 0.705012i | \(0.249059\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −21224.0 | −0.171104 | −0.0855521 | − | 0.996334i | \(-0.527265\pi\) | ||||
−0.0855521 | + | 0.996334i | \(0.527265\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −144557. | + | 14134.3i | −1.11361 | + | 0.108885i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14420.8 | − | 24977.5i | 0.106241 | − | 0.184015i | −0.808003 | − | 0.589178i | \(-0.799452\pi\) |
0.914245 | + | 0.405163i | \(0.132785\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −76112.4 | − | 131831.i | −0.536674 | − | 0.929547i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −80990.5 | + | 237485.i | −0.546977 | + | 1.60388i | ||||
\(118\) | 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 | ||||||||
\(123\) | −85848.7 | + | 189116.i | −0.511648 | + | 1.12711i | ||||
\(124\) | 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 | ||||||||
\(129\) | 19163.2 | + | 26782.2i | 0.101389 | + | 0.141701i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −94654.7 | + | 163947.i | −0.481908 | + | 0.834688i | −0.999784 | − | 0.0207668i | \(-0.993389\pi\) |
0.517877 | + | 0.855455i | \(0.326723\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 26525.1 | + | 45942.8i | 0.130025 | + | 0.225210i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −57363.1 | + | 243676.i | −0.270893 | + | 1.15074i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1809.78 | + | 3134.63i | 0.00823805 | + | 0.0142687i | 0.870115 | − | 0.492849i | \(-0.164044\pi\) |
−0.861877 | + | 0.507117i | \(0.830711\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 60440.1 | − | 104685.i | 0.265331 | − | 0.459567i | −0.702319 | − | 0.711862i | \(-0.747852\pi\) |
0.967650 | + | 0.252295i | \(0.0811854\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −22630.2 | − | 31627.7i | −0.0958609 | − | 0.133974i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 398186. | 1.62834 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −469102. | −1.85288 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −24276.3 | + | 53478.2i | −0.0926594 | + | 0.204119i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −37408.2 | + | 64792.9i | −0.138039 | + | 0.239090i | −0.926754 | − | 0.375668i | \(-0.877413\pi\) |
0.788715 | + | 0.614758i | \(0.210746\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −179976. | − | 311728.i | −0.642352 | − | 1.11259i | −0.984906 | − | 0.173088i | \(-0.944625\pi\) |
0.342554 | − | 0.939498i | \(-0.388708\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 228628. | − | 45140.6i | 0.789589 | − | 0.155897i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −256518. | − | 444302.i | −0.857607 | − | 1.48542i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23983.3 | + | 41540.3i | −0.0776533 | + | 0.134499i | −0.902237 | − | 0.431241i | \(-0.858076\pi\) |
0.824584 | + | 0.565740i | \(0.191409\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 155831. | − | 15236.6i | 0.488832 | − | 0.0477964i | ||||
\(160\) | 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 | ||||||||
\(165\) | 395382. | − | 38659.1i | 1.13059 | − | 0.110546i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 58233.2 | − | 100863.i | 0.161577 | − | 0.279860i | −0.773857 | − | 0.633360i | \(-0.781675\pi\) |
0.935434 | + | 0.353500i | \(0.115009\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −347458. | − | 601816.i | −0.935807 | − | 1.62086i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 110754. | − | 21867.4i | 0.289647 | − | 0.0571882i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −51762.9 | − | 89656.0i | −0.131493 | − | 0.227753i | 0.792759 | − | 0.609535i | \(-0.208644\pi\) |
−0.924252 | + | 0.381782i | \(0.875311\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 70939.0 | − | 122870.i | 0.175102 | − | 0.303285i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −35057.0 | + | 77226.9i | −0.0841088 | + | 0.185283i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 78941.2 | 0.184150 | 0.0920748 | − | 0.995752i | \(-0.470650\pi\) | ||||
0.0920748 | + | 0.995752i | \(0.470650\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 586108. | 1.32978 | 0.664892 | − | 0.746940i | \(-0.268478\pi\) | ||||
0.664892 | + | 0.746940i | \(0.268478\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 310125. | + | 433427.i | 0.684557 | + | 0.956728i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 307884. | − | 533271.i | 0.661391 | − | 1.14556i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −184911. | − | 320275.i | −0.386686 | − | 0.669760i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −315076. | − | 296359.i | −0.641595 | − | 0.603482i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 386026. | + | 668617.i | 0.765656 | + | 1.32615i | 0.939899 | + | 0.341452i | \(0.110919\pi\) |
−0.174243 | + | 0.984703i | \(0.555748\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8719.67 | − | 15102.9i | 0.0168503 | − | 0.0291855i | −0.857477 | − | 0.514522i | \(-0.827969\pi\) |
0.874328 | + | 0.485336i | \(0.161303\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −618998. | − | 865104.i | −1.16574 | − | 1.62923i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 340729. | 0.625524 | 0.312762 | − | 0.949832i | \(-0.398746\pi\) | ||||
0.312762 | + | 0.949832i | \(0.398746\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14239.7 | −0.0254899 | −0.0127450 | − | 0.999919i | \(-0.504057\pi\) | ||||
−0.0127450 | + | 0.999919i | \(0.504057\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −345277. | + | 760610.i | −0.602806 | + | 1.32792i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 405277. | − | 701960.i | 0.690258 | − | 1.19556i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −440246. | − | 762529.i | −0.731663 | − | 1.26728i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 180669. | − | 529768.i | 0.293061 | − | 0.859329i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −89576.0 | − | 155150.i | −0.141849 | − | 0.245690i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24049.2 | + | 41654.4i | −0.0371873 | + | 0.0644102i | −0.884020 | − | 0.467449i | \(-0.845173\pi\) |
0.846833 | + | 0.531859i | \(0.178506\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15049.2 | + | 1471.46i | −0.0227282 | + | 0.00222228i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −139614. | −0.205984 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 886466. | 1.27795 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.12325e6 | − | 109828.i | 1.58258 | − | 0.154740i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −495130. | + | 857590.i | −0.681928 | + | 1.18113i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 391988. | + | 678944.i | 0.527851 | + | 0.914264i | 0.999473 | + | 0.0324633i | \(0.0103352\pi\) |
−0.471622 | + | 0.881801i | \(0.656331\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −198748. | − | 227277.i | −0.261726 | − | 0.299295i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −277898. | − | 481334.i | −0.357949 | − | 0.619986i | 0.629669 | − | 0.776863i | \(-0.283190\pi\) |
−0.987618 | + | 0.156878i | \(0.949857\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −57346.2 | + | 99326.6i | −0.0722630 | + | 0.125163i | −0.899893 | − | 0.436111i | \(-0.856355\pi\) |
0.827630 | + | 0.561274i | \(0.189689\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −283738. | + | 625045.i | −0.349854 | + | 0.770693i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −111177. | −0.134161 | −0.0670805 | − | 0.997748i | \(-0.521368\pi\) | ||||
−0.0670805 | + | 0.997748i | \(0.521368\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 164874. | 0.194752 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −292064. | − | 408185.i | −0.337759 | − | 0.472048i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −369523. | + | 640033.i | −0.418453 | + | 0.724782i | −0.995784 | − | 0.0917279i | \(-0.970761\pi\) |
0.577331 | + | 0.816510i | \(0.304094\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 645180. | + | 1.11748e6i | 0.715547 | + | 1.23936i | 0.962748 | + | 0.270400i | \(0.0871559\pi\) |
−0.247201 | + | 0.968964i | \(0.579511\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −813324. | + | 431036.i | −0.883584 | + | 0.468272i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −124493. | − | 215628.i | −0.132504 | − | 0.229504i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −239855. | + | 415441.i | −0.250153 | + | 0.433278i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 327400. | + | 457569.i | 0.334641 | + | 0.467690i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.29383e6 | −1.29626 | −0.648129 | − | 0.761530i | \(-0.724448\pi\) | ||||
−0.648129 | + | 0.761530i | \(0.724448\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −888250. | −0.872437 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −408381. | + | 899621.i | −0.393292 | + | 0.866382i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −312181. | + | 540713.i | −0.294831 | + | 0.510663i | −0.974946 | − | 0.222443i | \(-0.928597\pi\) |
0.680114 | + | 0.733106i | \(0.261930\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 531988. | + | 921431.i | 0.492780 | + | 0.853519i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.13545e6 | − | 1.29844e6i | −1.03174 | − | 1.17983i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −582495. | − | 1.00891e6i | −0.519281 | − | 0.899421i | −0.999749 | − | 0.0224089i | \(-0.992866\pi\) |
0.480468 | − | 0.877012i | \(-0.340467\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −331895. | + | 574859.i | −0.290326 | + | 0.502859i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −661261. | + | 64655.9i | −0.567668 | + | 0.0555047i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.58951e6 | 1.33932 | 0.669659 | − | 0.742669i | \(-0.266440\pi\) | ||||
0.669659 | + | 0.742669i | \(0.266440\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 977878. | 0.808837 | 0.404419 | − | 0.914574i | \(-0.367474\pi\) | ||||
0.404419 | + | 0.914574i | \(0.367474\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.82931e6 | − | 178864.i | 1.48553 | − | 0.145250i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −239563. | + | 414936.i | −0.191024 | + | 0.330864i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 645243. | + | 1.11759e6i | 0.505271 | + | 0.875154i | 0.999981 | + | 0.00609677i | \(0.00194067\pi\) |
−0.494711 | + | 0.869058i | \(0.664726\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 608899. | − | 1.78545e6i | 0.468312 | − | 1.37321i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −833662. | − | 1.44395e6i | −0.629831 | − | 1.09090i | −0.987585 | − | 0.157084i | \(-0.949791\pi\) |
0.357754 | − | 0.933816i | \(-0.383543\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 564568. | − | 977861.i | 0.419035 | − | 0.725790i | −0.576808 | − | 0.816880i | \(-0.695702\pi\) |
0.995843 | + | 0.0910901i | \(0.0290351\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −197831. | + | 435802.i | −0.144272 | + | 0.317817i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.52139e6 | 1.09027 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −500138. | −0.352245 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −397797. | − | 555955.i | −0.275378 | − | 0.384864i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.02815e6 | + | 1.78081e6i | −0.699663 | + | 1.21185i | 0.268921 | + | 0.963162i | \(0.413333\pi\) |
−0.968583 | + | 0.248689i | \(0.920000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −179778. | − | 311385.i | −0.120277 | − | 0.208325i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.06402e6 | + | 1.00082e6i | 0.699937 | + | 0.658359i | ||||
\(298\) | 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 | ||||||||
\(303\) | 218731. | + | 305696.i | 0.136869 | + | 0.191286i | ||||
\(304\) | 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 | ||||||||
\(309\) | 884184. | − | 1.94777e6i | 0.526801 | − | 1.16049i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.35420e6 | + | 2.34554e6i | −0.793928 | + | 1.37512i | 0.129589 | + | 0.991568i | \(0.458634\pi\) |
−0.923517 | + | 0.383556i | \(0.874699\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 325583. | + | 563926.i | 0.187845 | + | 0.325358i | 0.944532 | − | 0.328420i | \(-0.106516\pi\) |
−0.756686 | + | 0.653778i | \(0.773183\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.79906e6 | − | 355209.i | 1.02157 | − | 0.201701i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 58055.3 | + | 100555.i | 0.0324484 | + | 0.0562024i | 0.881794 | − | 0.471636i | \(-0.156336\pi\) |
−0.849345 | + | 0.527838i | \(0.823003\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.36863e6 | + | 2.37054e6i | −0.753026 | + | 1.30428i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.60611e6 | + | 254816.i | −1.41166 | + | 0.138027i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 445538. | 0.237618 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.28294e6 | 0.673750 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 329279. | − | 32195.8i | 0.170292 | − | 0.0166506i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −142441. | + | 246715.i | −0.0725514 | + | 0.125663i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 158828. | + | 275099.i | 0.0796816 | + | 0.138013i | 0.903113 | − | 0.429404i | \(-0.141276\pi\) |
−0.823431 | + | 0.567416i | \(0.807943\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.22129e6 | − | 438573.i | 1.09773 | − | 0.216736i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.77064e6 | − | 3.06684e6i | −0.862021 | − | 1.49306i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −215275. | + | 372867.i | −0.103257 | + | 0.178846i | −0.913025 | − | 0.407904i | \(-0.866260\pi\) |
0.809768 | + | 0.586750i | \(0.199593\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −185841. | + | 409389.i | −0.0878299 | + | 0.193480i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.99363e6 | −1.39416 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.34942e6 | 1.07826 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.38082e6 | + | 1.92982e6i | 0.624584 | + | 0.872910i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.07020e6 | + | 3.58569e6i | −0.922971 | + | 1.59863i | −0.128178 | + | 0.991751i | \(0.540913\pi\) |
−0.794793 | + | 0.606881i | \(0.792420\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.73048e6 | + | 2.99727e6i | 0.760505 | + | 1.31723i | 0.942590 | + | 0.333951i | \(0.108382\pi\) |
−0.182085 | + | 0.983283i | \(0.558285\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 896271. | − | 3.80731e6i | 0.388304 | − | 1.64949i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.32229e6 | − | 2.29027e6i | −0.564792 | − | 0.978249i | −0.997069 | − | 0.0765076i | \(-0.975623\pi\) |
0.432277 | − | 0.901741i | \(-0.357710\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 32052.5 | − | 55516.5i | 0.0134987 | − | 0.0233804i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −993368. | − | 1.38832e6i | −0.412515 | − | 0.576526i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.13123e6 | −0.872761 | −0.436380 | − | 0.899762i | \(-0.643740\pi\) | ||||
−0.436380 | + | 0.899762i | \(0.643740\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.26027e6 | −0.912834 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −79543.3 | + | 175226.i | −0.0316838 | + | 0.0697961i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.39235e6 | + | 4.14368e6i | −0.939925 | + | 1.62800i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −640035. | − | 1.10857e6i | −0.248049 | − | 0.429634i | 0.714935 | − | 0.699191i | \(-0.246456\pi\) |
−0.962985 | + | 0.269557i | \(0.913123\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.04502e6 | − | 3.06426e6i | 0.399538 | − | 1.17155i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −573476. | − | 993289.i | −0.216312 | − | 0.374663i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.94733e6 | − | 3.37288e6i | 0.724716 | − | 1.25524i | −0.234375 | − | 0.972146i | \(-0.575304\pi\) |
0.959091 | − | 0.283099i | \(-0.0913623\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.93016e6 | + | 188725.i | −0.708787 | + | 0.0693028i | ||||
\(376\) | 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 | ||||||||
\(381\) | −3.33657e6 | + | 326239.i | −1.17757 | + | 0.115139i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.18249e6 | − | 2.04814e6i | 0.411909 | − | 0.713448i | −0.583189 | − | 0.812336i | \(-0.698195\pi\) |
0.995099 | + | 0.0988883i | \(0.0315287\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.45505e6 | − | 2.52023e6i | −0.500296 | − | 0.866539i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −337934. | − | 386442.i | −0.114698 | − | 0.131162i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 871692. | + | 1.50981e6i | 0.292071 | + | 0.505882i | 0.974299 | − | 0.225257i | \(-0.0723222\pi\) |
−0.682228 | + | 0.731139i | \(0.738989\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.10451e6 | − | 1.91306e6i | 0.365364 | − | 0.632830i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.21982e6 | − | 2.68713e6i | 0.398395 | − | 0.877623i | ||||
\(394\) | 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 | ||||||||
\(399\) | −481216. | − | 672541.i | −0.151324 | − | 0.211488i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.27703e6 | − | 3.94394e6i | 0.707145 | − | 1.22481i | −0.258767 | − | 0.965940i | \(-0.583316\pi\) |
0.965912 | − | 0.258871i | \(-0.0833506\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00797e6 | + | 6.94200e6i | 1.22931 | + | 2.12923i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 520314. | − | 3.86752e6i | 0.157626 | − | 1.17164i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.79654e6 | − | 3.11170e6i | −0.537590 | − | 0.931133i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −956414. | + | 1.65656e6i | −0.282708 | + | 0.489664i | −0.972051 | − | 0.234771i | \(-0.924566\pi\) |
0.689343 | + | 0.724435i | \(0.257899\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −32832.9 | − | 45886.8i | −0.00958748 | − | 0.0133993i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 621271. | 0.179228 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.38528e6 | −0.679860 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −778894. | + | 1.71582e6i | −0.219350 | + | 0.483206i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.20697e6 | − | 3.82259e6i | 0.614132 | − | 1.06371i | −0.376404 | − | 0.926456i | \(-0.622839\pi\) |
0.990536 | − | 0.137252i | \(-0.0438272\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 872253. | + | 1.51079e6i | 0.239848 | + | 0.415430i | 0.960671 | − | 0.277690i | \(-0.0895689\pi\) |
−0.720822 | + | 0.693120i | \(0.756236\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 399074. | + | 456359.i | 0.108443 | + | 0.124010i | ||||
\(424\) | 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 | ||||||||
\(429\) | −6.17765e6 | + | 604030.i | −1.62061 | + | 0.158458i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.21740e6 | 0.574976 | 0.287488 | − | 0.957784i | \(-0.407180\pi\) | ||||
0.287488 | + | 0.957784i | \(0.407180\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.63511e6 | −0.931746 | −0.465873 | − | 0.884851i | \(-0.654260\pi\) | ||||
−0.465873 | + | 0.884851i | \(0.654260\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.27787e6 | − | 711606.i | 1.84409 | − | 0.180309i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 535054. | − | 926741.i | 0.134028 | − | 0.232143i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.54413e6 | − | 2.67452e6i | −0.382405 | − | 0.662345i | 0.609001 | − | 0.793170i | \(-0.291571\pi\) |
−0.991405 | + | 0.130825i | \(0.958237\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 295510. | − | 866512.i | 0.0723562 | − | 0.212167i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.50048e6 | − | 6.06302e6i | −0.847459 | − | 1.46784i | −0.883468 | − | 0.468491i | \(-0.844798\pi\) |
0.0360092 | − | 0.999351i | \(-0.488535\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.40838e6 | − | 2.43939e6i | 0.337148 | − | 0.583958i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 482080. | − | 1.06197e6i | 0.114117 | − | 0.251388i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.00196e6 | −1.17091 | −0.585456 | − | 0.810704i | \(-0.699084\pi\) | ||||
−0.585456 | + | 0.810704i | \(0.699084\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.13778e6 | −1.18942 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.26511e6 | + | 4.56328e6i | 0.747572 | + | 1.04480i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.89615e6 | + | 6.74833e6i | −0.882282 | + | 1.52816i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.78581e6 | − | 3.09311e6i | −0.399985 | − | 0.692795i | 0.593738 | − | 0.804658i | \(-0.297651\pi\) |
−0.993724 | + | 0.111863i | \(0.964318\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.47857e6 | + | 1.04715e6i | −0.770671 | + | 0.231994i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.75061e6 | − | 4.76420e6i | −0.602805 | − | 1.04409i | −0.992394 | − | 0.123100i | \(-0.960716\pi\) |
0.389589 | − | 0.920989i | \(-0.372617\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.42708e6 | + | 2.47177e6i | −0.309382 | + | 0.535866i | −0.978227 | − | 0.207536i | \(-0.933456\pi\) |
0.668845 | + | 0.743402i | \(0.266789\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.65373e6 | + | 6.50399e6i | 0.998087 | + | 1.39491i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.16552e6 | 1.52039 | 0.760196 | − | 0.649694i | \(-0.225103\pi\) | ||||
0.760196 | + | 0.649694i | \(0.225103\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.11892e6 | 1.28452 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 309074. | − | 680857.i | 0.0641962 | − | 0.141418i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −407332. | + | 705520.i | −0.0837136 | + | 0.144996i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −288611. | − | 499889.i | −0.0586920 | − | 0.101658i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.39452e6 | + | 472775.i | −0.481861 | + | 0.0951391i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.64185e6 | + | 2.84377e6i | 0.326961 | + | 0.566312i | 0.981907 | − | 0.189363i | \(-0.0606423\pi\) |
−0.654947 | + | 0.755675i | \(0.727309\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.81054e6 | + | 8.33210e6i | −0.948050 | + | 1.64207i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.08072e6 | + | 398999.i | −0.795920 | + | 0.0778224i | ||||
\(484\) | 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 | ||||||||
\(489\) | 5.60171e6 | − | 547716.i | 1.05937 | − | 0.103582i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.96974e6 | + | 8.60785e6i | −0.930315 | + | 1.61135i | −0.147534 | + | 0.989057i | \(0.547134\pi\) |
−0.782782 | + | 0.622297i | \(0.786200\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.40369e6 | − | 5.89536e6i | −0.630714 | − | 1.09243i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.07550e6 | + | 1.19955e6i | −1.11447 | + | 0.220042i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 55382.9 | + | 95926.0i | 0.0100574 | + | 0.0174199i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.26386e6 | + | 3.92112e6i | −0.407004 | + | 0.704951i | −0.994552 | − | 0.104238i | \(-0.966760\pi\) |
0.587549 | + | 0.809189i | \(0.300093\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −750453. | + | 1.65317e6i | −0.133576 | + | 0.294255i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.40282e6 | 0.775909 | 0.387955 | − | 0.921679i | \(-0.373182\pi\) | ||||
0.387955 | + | 0.921679i | \(0.373182\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.59357e6 | −0.278063 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.30356e6 | + | 8.80977e6i | 1.08910 | + | 1.52211i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.91063e6 | + | 5.04135e6i | −0.497957 | + | 0.862487i | −0.999997 | − | 0.00235703i | \(-0.999250\pi\) |
0.502040 | + | 0.864844i | \(0.332583\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.13371e6 | − | 7.15979e6i | −0.700306 | − | 1.21296i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.68512e6 | + | 507269.i | −0.282707 | + | 0.0851030i | ||||
\(514\) | 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 | ||||||||
\(519\) | 939078. | + | 1.31244e6i | 0.153032 | + | 0.213876i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.09649e7 | 1.76975 | 0.884875 | − | 0.465829i | \(-0.154244\pi\) | ||||
0.884875 | + | 0.465829i | \(0.154244\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.83705e6 | 0.613399 | 0.306700 | − | 0.951806i | \(-0.400775\pi\) | ||||
0.306700 | + | 0.951806i | \(0.400775\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −914194. | + | 2.01387e6i | −0.144757 | + | 0.318885i | ||||
\(526\) | 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 | ||||||||
\(531\) | 426741. | − | 1.25131e6i | 0.0656792 | − | 0.192588i | ||||
\(532\) | 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 | ||||||||
\(537\) | −1.22473e6 | + | 119750.i | −0.183276 | + | 0.0179201i | ||||
\(538\) | 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 | ||||||||
\(543\) | −9.09315e6 | + | 889098.i | −1.32347 | + | 0.129405i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −701313. | + | 1.21471e6i | −0.101139 | + | 0.175179i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.46672e6 | − | 6.00454e6i | −0.495394 | − | 0.858047i | 0.504592 | − | 0.863358i | \(-0.331643\pi\) |
−0.999986 | + | 0.00531061i | \(0.998310\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.46892e6 | − | 6.25395e6i | −0.774410 | − | 0.885571i | ||||
\(550\) | 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 | ||||||||
\(555\) | −3.96772e6 | + | 8.74047e6i | −0.546774 | + | 1.20449i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.83771e6 | −1.34356 | −0.671778 | − | 0.740752i | \(-0.734469\pi\) | ||||
−0.671778 | + | 0.740752i | \(0.734469\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.18140e6 | 0.295261 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.35464e6 | + | 4.68840e6i | 0.450027 | + | 0.628951i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.36609e6 | − | 2.36613e6i | 0.181638 | − | 0.314607i | −0.760800 | − | 0.648986i | \(-0.775193\pi\) |
0.942439 | + | 0.334379i | \(0.108527\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −953024. | − | 1.65069e6i | −0.125598 | − | 0.217542i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.33780e6 | + | 4.11990e6i | 0.697276 | + | 0.538182i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.71998e6 | − | 8.17525e6i | −0.611167 | − | 1.05857i | −0.991044 | − | 0.133535i | \(-0.957367\pi\) |
0.379877 | − | 0.925037i | \(-0.375966\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.33948e6 | + | 1.09803e7i | −0.813698 | + | 1.40937i | 0.0965611 | + | 0.995327i | \(0.469216\pi\) |
−0.910259 | + | 0.414039i | \(0.864118\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.00326e6 | − | 9.78766e6i | −0.891073 | − | 1.24535i | ||||
\(574\) | 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 | ||||||||
\(579\) | −112371. | + | 247541.i | −0.0139302 | + | 0.0306867i | ||||
\(580\) | 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 | ||||||||
\(585\) | 1.09158e7 | + | 1.24826e7i | 1.31875 | + | 1.50805i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 911702. | + | 1.57911e6i | 0.109209 | + | 0.189155i | 0.915450 | − | 0.402432i | \(-0.131835\pi\) |
−0.806241 | + | 0.591587i | \(0.798502\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.80327e6 | − | 3.12335e6i | 0.214176 | − | 0.370965i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.28623e6 | + | 516870.i | −0.622555 | + | 0.0608713i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.27957e7 | 1.49427 | 0.747133 | − | 0.664674i | \(-0.231430\pi\) | ||||
0.747133 | + | 0.664674i | \(0.231430\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.23723e6 | 0.838069 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 220922. | − | 21601.0i | 0.0253689 | − | 0.00248049i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.38212e6 | − | 7.59006e6i | 0.499020 | − | 0.864327i | −0.500980 | − | 0.865459i | \(-0.667027\pi\) |
0.999999 | + | 0.00113166i | \(0.000360218\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −834793. | − | 1.44590e6i | −0.0942741 | − | 0.163288i | 0.815031 | − | 0.579417i | \(-0.196720\pi\) |
−0.909305 | + | 0.416129i | \(0.863386\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.20298e6 | − | 1.23242e7i | 0.470722 | − | 1.38028i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −407911. | − | 706523.i | −0.0453082 | − | 0.0784762i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.08535e6 | + | 8.80809e6i | −0.560208 | + | 0.970308i | 0.437270 | + | 0.899330i | \(0.355945\pi\) |
−0.997478 | + | 0.0709782i | \(0.977388\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.22282e6 | + | 1.15053e7i | −0.570639 | + | 1.25706i | ||||
\(610\) | 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 | ||||||||
\(615\) | 7.98691e6 | + | 1.11624e7i | 0.851513 | + | 1.19006i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.05409e6 | − | 1.04860e7i | 0.640230 | − | 1.10891i | −0.345152 | − | 0.938547i | \(-0.612173\pi\) |
0.985381 | − | 0.170363i | \(-0.0544942\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.48665e6 | − | 1.46993e7i | −0.890245 | − | 1.54195i | −0.839581 | − | 0.543234i | \(-0.817200\pi\) |
−0.0506641 | − | 0.998716i | \(-0.516134\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.99935e6 | + | 8.49313e6i | −0.208046 | + | 0.883769i | ||||
\(622\) | 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 | ||||||||
\(627\) | 1.62508e6 | + | 2.27119e6i | 0.165084 | + | 0.230720i | ||||
\(628\) | 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 | ||||||||
\(633\) | 309923. | − | 682728.i | 0.0307428 | − | 0.0677233i | ||||
\(634\) | 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 | ||||||||
\(639\) | 231248. | − | 45657.9i | 0.0224040 | − | 0.00442347i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.33807e6 | − | 9.24581e6i | −0.513144 | − | 0.888792i | −0.999884 | − | 0.0152446i | \(-0.995147\pi\) |
0.486740 | − | 0.873547i | \(-0.338186\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.68885e6 | − | 8.12132e6i | 0.447238 | − | 0.774639i | −0.550967 | − | 0.834527i | \(-0.685741\pi\) |
0.998205 | + | 0.0598882i | \(0.0190744\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.16604e6 | − | 211788.i | 0.205006 | − | 0.0200448i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.44013e6 | 0.886579 | 0.443289 | − | 0.896379i | \(-0.353811\pi\) | ||||
0.443289 | + | 0.896379i | \(0.353811\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.09805e6 | −0.195526 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.37531e7 | + | 1.34473e6i | −1.27188 | + | 0.124360i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.44455e6 | + | 1.28943e7i | −0.683212 | + | 1.18336i | 0.290783 | + | 0.956789i | \(0.406084\pi\) |
−0.973995 | + | 0.226569i | \(0.927249\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.25543e6 | + | 1.08347e7i | 0.569710 | + | 0.986766i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.72601e7 | + | 3.40784e6i | −1.56002 | + | 0.308011i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.82391e6 | − | 6.62320e6i | −0.343000 | − | 0.594093i | 0.641989 | − | 0.766714i | \(-0.278110\pi\) |
−0.984988 | + | 0.172621i | \(0.944776\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.50269e6 | − | 4.33479e6i | 0.222794 | − | 0.385891i | −0.732861 | − | 0.680378i | \(-0.761816\pi\) |
0.955655 | + | 0.294487i | \(0.0951489\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.38075e6 | − | 1.40561e7i | 0.563752 | − | 1.24189i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.50592e6 | 0.307431 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.63502e7 | −1.42301 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.11142e6 | − | 9.93882e6i | −0.614315 | − | 0.858558i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.59202e6 | + | 1.14177e7i | −0.565214 | + | 0.978979i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.07220e6 | − | 1.85710e6i | −0.0912511 | − | 0.158051i | 0.816787 | − | 0.576940i | \(-0.195753\pi\) |
−0.908038 | + | 0.418888i | \(0.862420\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.42824e6 | + | 3.22459e6i | 0.289609 | + | 0.272405i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.75463e6 | + | 8.23526e6i | 0.398699 | + | 0.690567i | 0.993566 | − | 0.113257i | \(-0.0361285\pi\) |
−0.594867 | + | 0.803824i | \(0.702795\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.50385e6 | + | 4.33679e6i | −0.208417 | + | 0.360989i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.04161e6 | + | 7.04608e6i | 0.416583 | + | 0.582210i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.47266e6 | 0.448897 | 0.224449 | − | 0.974486i | \(-0.427942\pi\) | ||||
0.224449 | + | 0.974486i | \(0.427942\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 239205. | 0.0194780 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 739023. | − | 1.62799e6i | 0.0597401 | − | 0.131601i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.18570e6 | − | 8.98189e6i | 0.416159 | − | 0.720808i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.44084e6 | + | 5.95970e6i | 0.274138 | + | 0.474821i | 0.969917 | − | 0.243435i | \(-0.0782742\pi\) |
−0.695779 | + | 0.718255i | \(0.744941\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.45388e6 | − | 1.01277e7i | 0.273196 | − | 0.801080i | ||||
\(694\) | 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 | ||||||||
\(699\) | 1.72486e6 | − | 168651.i | 0.133524 | − | 0.0130556i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.19615e6 | 0.399380 | 0.199690 | − | 0.979859i | \(-0.436006\pi\) | ||||
0.199690 | + | 0.979859i | \(0.436006\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.32872e6 | 0.330348 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.55793e6 | + | 250106.i | −0.193827 | + | 0.0189518i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.37676e6 | − | 2.38461e6i | 0.103588 | − | 0.179419i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −287410. | − | 497809.i | −0.0214727 | − | 0.0371918i | 0.855089 | − | 0.518481i | \(-0.173502\pi\) |
−0.876562 | + | 0.481289i | \(0.840169\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.15042e6 | + | 5.88973e6i | 0.382093 | + | 0.436939i | ||||
\(712\) | 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 | ||||||||
\(717\) | 4.76206e6 | − | 1.04903e7i | 0.345937 | − | 0.762063i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 400906. | 0.0289215 | 0.0144607 | − | 0.999895i | \(-0.495397\pi\) | ||||
0.0144607 | + | 0.999895i | \(0.495397\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.56693e7 | −1.12256 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.17048e7 | − | 1.63585e7i | −0.832757 | − | 1.16385i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.40969e6 | + | 7.63781e6i | −0.311575 | + | 0.539664i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.27154e6 | + | 9.13058e6i | 0.369915 | + | 0.640711i | 0.989552 | − | 0.144177i | \(-0.0460535\pi\) |
−0.619637 | + | 0.784889i | \(0.712720\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.19644e7 | − | 7.92108e6i | 0.833822 | − | 0.552034i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.01301e6 | − | 1.75458e6i | −0.0701162 | − | 0.121445i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.96868e6 | + | 1.20701e7i | −0.479061 | + | 0.829758i | −0.999712 | − | 0.0240119i | \(-0.992356\pi\) |
0.520651 | + | 0.853770i | \(0.325689\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.25854e6 | + | 3.15651e6i | 0.154209 | + | 0.215520i | ||||
\(736\) | 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 | ||||||||
\(741\) | 3.09102e6 | − | 6.80919e6i | 0.206803 | − | 0.455565i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.66695e6 | + | 8.08339e6i | −0.310142 | + | 0.537182i | −0.978393 | − | 0.206754i | \(-0.933710\pi\) |
0.668251 | + | 0.743936i | \(0.267043\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.47219e6 | + | 4.28195e6i | 0.163189 | + | 0.282652i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.77354e6 | − | 6.60230e6i | −0.378565 | − | 0.432906i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.59080e6 | + | 1.66117e7i | 0.624669 | + | 1.08196i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.43761e7 | − | 2.49001e7i | 0.930124 | − | 1.61102i | 0.147018 | − | 0.989134i | \(-0.453032\pi\) |
0.783106 | − | 0.621888i | \(-0.213634\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.00730e7 | − | 1.96267e6i | 1.29011 | − | 0.126142i | ||||
\(754\) | 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 | ||||||||
\(759\) | 1.37807e7 | − | 1.34743e6i | 0.868296 | − | 0.0848991i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.56829e6 | + | 7.91251e6i | −0.285951 | + | 0.495282i | −0.972839 | − | 0.231481i | \(-0.925643\pi\) |
0.686888 | + | 0.726763i | \(0.258976\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.21179e6 | − | 2.09888e6i | −0.0753555 | − | 0.130520i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.97113e6 | − | 1.45766e7i | 0.307115 | − | 0.900542i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.80894e6 | + | 4.86523e6i | 0.172407 | + | 0.298617i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.26221e6 | + | 1.43106e7i | −0.503826 | + | 0.872652i | 0.496164 | + | 0.868229i | \(0.334741\pi\) |
−0.999990 | + | 0.00442349i | \(0.998592\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.02309e6 | − | 8.86244e6i | 0.243738 | − | 0.536930i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.01763e7 | 0.612550 | 0.306275 | − | 0.951943i | \(-0.400917\pi\) | ||||
0.306275 | + | 0.951943i | \(0.400917\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.64536e6 | −0.576852 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.65129e6 | − | 1.34885e7i | −0.573499 | − | 0.801515i | ||||
\(778\) | 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 | ||||||||
\(783\) | 1.95856e7 | + | 1.84222e7i | 1.14165 | + | 1.07383i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.58498e6 | + | 2.74527e6i | 0.0918015 | + | 0.159005i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.38173e6 | + | 1.62496e7i | −0.539941 | + | 0.935205i | 0.458966 | + | 0.888454i | \(0.348220\pi\) |
−0.998907 | + | 0.0467507i | \(0.985113\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.05676e7 | + | 1.47691e7i | 0.604342 | + | 0.844620i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.29343e6 | 0.187158 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.53025e7 | 1.99353 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.27714e6 | − | 9.42210e6i | 0.240014 | − | 0.528725i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.23982e6 | − | 2.14744e6i | 0.0691376 | − | 0.119750i | −0.829384 | − | 0.558678i | \(-0.811309\pi\) |
0.898522 | + | 0.438929i | \(0.144642\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.19628e6 | + | 2.07202e6i | 0.0662929 | + | 0.114823i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.01610e7 | − | 2.00620e6i | 0.559573 | − | 0.110483i | ||||
\(802\) | 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 | ||||||||
\(807\) | −2.46605e7 | + | 2.41122e6i | −1.33296 | + | 0.130332i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.50880e7 | −1.34770 | −0.673852 | − | 0.738867i | \(-0.735361\pi\) | ||||
−0.673852 | + | 0.738867i | \(0.735361\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.28465e6 | 0.228751 | 0.114376 | − | 0.993438i | \(-0.463513\pi\) | ||||
0.114376 | + | 0.993438i | \(0.463513\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.51713e7 | + | 1.48339e6i | −0.804999 | + | 0.0787101i | ||||
\(814\) | 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 | ||||||||
\(819\) | −2.81095e7 | + | 5.54996e6i | −1.46434 | + | 0.289121i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.01563e7 | − | 1.75913e7i | −0.525871 | − | 0.910836i | −0.999546 | − | 0.0301356i | \(-0.990406\pi\) |
0.473675 | − | 0.880700i | \(-0.342927\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.58313e6 | + | 1.14023e7i | −0.338792 | + | 0.586804i | −0.984206 | − | 0.177029i | \(-0.943351\pi\) |
0.645414 | + | 0.763833i | \(0.276685\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.08726e6 | − | 6.80092e6i | 0.157920 | − | 0.347883i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.82859e7 | −1.43816 | −0.719079 | − | 0.694928i | \(-0.755436\pi\) | ||||
−0.719079 | + | 0.694928i | \(0.755436\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.36608e7 | 0.690381 | 0.345190 | − | 0.938533i | \(-0.387814\pi\) | ||||
0.345190 | + | 0.938533i | \(0.387814\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.17059e7 | − | 1.63601e7i | −0.588036 | − | 0.821832i | ||||
\(832\) | 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 | ||||||||
\(837\) | −6.73831e6 | + | 2.86240e7i | −0.332458 | + | 1.41227i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −75641.6 | − | 131015.i | −0.00370984 | − | 0.00642564i | 0.864165 | − | 0.503209i | \(-0.167848\pi\) |
−0.867874 | + | 0.496784i | \(0.834514\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.49371e7 | + | 2.58718e7i | −0.728244 | + | 1.26135i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.51242e7 | + | 2.11374e7i | 0.733000 | + | 1.02443i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.59249e7 | −2.21262 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.40965e6 | 0.0675152 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.27561e6 | + | 1.60274e7i | −0.346418 | + | 0.763123i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.07311e7 | − | 1.85868e7i | 0.507948 | − | 0.879792i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.38831e7 | + | 2.40462e7i | 0.653301 | + | 1.13155i | 0.982317 | + | 0.187226i | \(0.0599498\pi\) |
−0.329015 | + | 0.944325i | \(0.606717\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.40816e6 | − | 7.06134e6i | 0.112660 | − | 0.330348i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.76136e7 | + | 3.05077e7i | 0.819212 | + | 1.41892i | 0.906263 | + | 0.422713i | \(0.138922\pi\) |
−0.0870512 | + | 0.996204i | \(0.527744\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.02341e7 | + | 3.50464e7i | −0.935622 | + | 1.62054i | −0.162100 | + | 0.986774i | \(0.551827\pi\) |
−0.773522 | + | 0.633770i | \(0.781507\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.36036e7 | + | 2.30788e6i | −1.08510 | + | 0.106097i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.96865e7 | 0.899789 | 0.449895 | − | 0.893082i | \(-0.351462\pi\) | ||||
0.449895 | + | 0.893082i | \(0.351462\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.84170e6 | −0.310902 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.75937e6 | − | 758686.i | 0.350573 | − | 0.0342779i | ||||
\(868\) | 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 | ||||||||
\(873\) | 7.01496e6 | + | 8.02191e6i | 0.311523 | + | 0.356240i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.10324e6 | + | 1.23032e7i | 0.313644 | + | 0.543247i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.31221e7 | + | 2.27282e7i | −0.576109 | + | 0.997850i | 0.419811 | + | 0.907611i | \(0.362096\pi\) |
−0.995920 | + | 0.0902384i | \(0.971237\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.32498e7 | − | 2.91880e7i | 0.578414 | − | 1.27419i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.29423e7 | −0.561786 | −0.280893 | − | 0.959739i | \(-0.590631\pi\) | ||||
−0.280893 | + | 0.959739i | \(0.590631\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.39097e6 | −0.146360 | −0.0731800 | − | 0.997319i | \(-0.523315\pi\) | ||||
−0.0731800 | + | 0.997319i | \(0.523315\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.26152e6 | + | 4.55825e6i | 0.139979 | + | 0.195632i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.83796e6 | − | 6.64753e6i | 0.163791 | − | 0.283695i | −0.772434 | − | 0.635095i | \(-0.780961\pi\) |
0.936225 | + | 0.351400i | \(0.114294\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.22790e7 | + | 2.12678e7i | 0.521085 | + | 0.902545i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.80259e7 | − | 1.39130e7i | −0.760682 | − | 0.587122i | ||||
\(892\) | 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 | ||||||||
\(897\) | −2.15747e7 | − | 3.01525e7i | −0.895290 | − | 1.25125i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.51042e7 | −2.27398 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.63260e6 | −0.395304 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.55441e6 | + | 3.42421e6i | −0.0634377 | + | 0.139747i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.93670e7 | − | 3.35446e7i | 0.786033 | − | 1.36145i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.44435e6 | + | 9.42990e6i | 0.219750 | + | 0.380618i | 0.954731 | − | 0.297469i | \(-0.0961426\pi\) |
−0.734982 | + | 0.678087i | \(0.762809\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.85722e6 | − | 4.41090e6i | −0.154834 | − | 0.177059i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −90239.2 | − | 156299.i | −0.00360246 | − | 0.00623964i | 0.864219 | − | 0.503117i | \(-0.167813\pi\) |
−0.867821 | + | 0.496877i | \(0.834480\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.95920e6 | + | 1.20537e7i | −0.276301 | + | 0.478568i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.50539e7 | − | 3.42745e6i | 1.38415 | − | 0.135338i | ||||
\(916\) | 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 | ||||||||
\(921\) | 2.36051e7 | − | 2.30803e6i | 0.916973 | − | 0.0896586i | ||||
\(922\) | 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 | ||||||||
\(927\) | −1.07630e7 | + | 3.15598e7i | −0.411371 | + | 1.20625i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.06620e7 | + | 3.57877e7i | 0.785477 | + | 1.36049i | 0.928714 | + | 0.370797i | \(0.120916\pi\) |
−0.143237 | + | 0.989688i | \(0.545751\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 875159. | − | 1.51582e6i | 0.0330912 | − | 0.0573157i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.74516e7 | − | 3.84441e7i | 0.656343 | − | 1.44586i | ||||
\(934\) | 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 | ||||||||
\(939\) | −5.90670e6 | − | 8.25512e6i | −0.218615 | − | 0.305534i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.99880e6 | + | 1.55864e7i | −0.331292 | + | 0.573814i | −0.982765 | − | 0.184857i | \(-0.940818\pi\) |
0.651474 | + | 0.758671i | \(0.274151\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.53445e7 | − | 2.65774e7i | −0.561917 | − | 0.973269i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.73727e7 | + | 8.23997e6i | −0.997098 | + | 0.300155i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.25398e7 | − | 3.90400e7i | −0.816723 | − | 1.41461i | −0.908084 | − | 0.418788i | \(-0.862455\pi\) |
0.0913614 | − | 0.995818i | \(-0.470878\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.73793e7 | − | 6.47429e7i | 1.34731 | − | 2.33360i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.05323e6 | − | 1.47199e6i | −0.0377636 | − | 0.0527780i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.21374e7 | 0.789577 | 0.394788 | − | 0.918772i | \(-0.370818\pi\) | ||||
0.394788 | + | 0.918772i | \(0.370818\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.10225e7 | 1.81031 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.76376e7 | − | 3.88539e7i | 0.622530 | − | 1.37137i | ||||
\(958\) | 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 | ||||||||
\(963\) | 4.00458e7 | − | 7.90668e6i | 1.39153 | − | 0.274744i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −576255. | − | 998103.i | −0.0199203 | − | 0.0345030i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.81614e6 | + | 1.70020e7i | −0.337578 | + | 0.584703i | −0.983977 | − | 0.178297i | \(-0.942941\pi\) |
0.646398 | + | 0.763000i | \(0.276274\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.91229e6 | + | 675861.i | −0.236490 | + | 0.0231232i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.46539e7 | 1.17952 | 0.589758 | − | 0.807580i | \(-0.299223\pi\) | ||||
0.589758 | + | 0.807580i | \(0.299223\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.38034e7 | 0.467415 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.99042e7 | + | 1.94616e6i | −0.670552 | + | 0.0655644i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.34006e7 | + | 2.32106e7i | −0.449148 | + | 0.777947i | −0.998331 | − | 0.0577553i | \(-0.981606\pi\) |
0.549183 | + | 0.835702i | \(0.314939\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.21808e6 | − | 1.42341e7i | −0.274040 | − | 0.474651i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.05975e6 | + | 999002.i | −0.167864 | + | 0.0331431i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.19040e7 | − | 2.06183e7i | −0.392924 | − | 0.680565i | 0.599910 | − | 0.800068i | \(-0.295203\pi\) |
−0.992834 | + | 0.119503i | \(0.961870\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.12589e7 | − | 1.95009e7i | 0.369746 | − | 0.640419i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.83564e6 | − | 4.04374e6i | 0.0599785 | − | 0.132126i | ||||
\(988\) | 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 | ||||||||
\(993\) | −2.88145e6 | − | 4.02708e6i | −0.0927338 | − | 0.129603i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −470529. | + | 814980.i | −0.0150671 | + | 0.0260969i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.04170e7 | + | 3.53633e7i | 0.650511 | + | 1.12672i | 0.982999 | + | 0.183610i | \(0.0587785\pi\) |
−0.332488 | + | 0.943107i | \(0.607888\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.37968e7 | + | 1.01738e7i | −1.07143 | + | 0.322530i |
(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 | 144.6.i.b.49.1 | 6 | ||
3.2 | odd | 2 | 432.6.i.b.145.1 | 6 | |||
4.3 | odd | 2 | 18.6.c.b.13.3 | yes | 6 | ||
9.2 | odd | 6 | 432.6.i.b.289.1 | 6 | |||
9.7 | even | 3 | inner | 144.6.i.b.97.1 | 6 | ||
12.11 | even | 2 | 54.6.c.b.37.1 | 6 | |||
36.7 | odd | 6 | 18.6.c.b.7.3 | ✓ | 6 | ||
36.11 | even | 6 | 54.6.c.b.19.1 | 6 | |||
36.23 | even | 6 | 162.6.a.i.1.3 | 3 | |||
36.31 | odd | 6 | 162.6.a.j.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
18.6.c.b.7.3 | ✓ | 6 | 36.7 | odd | 6 | ||
18.6.c.b.13.3 | yes | 6 | 4.3 | odd | 2 | ||
54.6.c.b.19.1 | 6 | 36.11 | even | 6 | |||
54.6.c.b.37.1 | 6 | 12.11 | even | 2 | |||
144.6.i.b.49.1 | 6 | 1.1 | even | 1 | trivial | ||
144.6.i.b.97.1 | 6 | 9.7 | even | 3 | inner | ||
162.6.a.i.1.3 | 3 | 36.23 | even | 6 | |||
162.6.a.j.1.1 | 3 | 36.31 | odd | 6 | |||
432.6.i.b.145.1 | 6 | 3.2 | odd | 2 | |||
432.6.i.b.289.1 | 6 | 9.2 | odd | 6 |