Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,6,Mod(193,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.193");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.q (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: | \(53.8889634572\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 564x^{8} + 117814x^{6} + 11067780x^{4} + 427918225x^{2} + 3489248448 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{3}\cdot 7^{2} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 193.4 | ||
Root | \(-14.3017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.193 |
Dual form | 336.6.q.l.289.4 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | −4.50000 | + | 7.79423i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 13.3782 | + | 23.1717i | 0.239316 | + | 0.414508i | 0.960518 | − | 0.278217i | \(-0.0897435\pi\) |
−0.721202 | + | 0.692725i | \(0.756410\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 66.5893 | − | 111.233i | 0.513640 | − | 0.858006i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −40.5000 | − | 70.1481i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −81.6815 | + | 141.477i | −0.203536 | + | 0.352535i | −0.949665 | − | 0.313266i | \(-0.898577\pi\) |
0.746129 | + | 0.665801i | \(0.231910\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −595.608 | −0.977467 | −0.488733 | − | 0.872433i | \(-0.662541\pi\) | ||||
−0.488733 | + | 0.872433i | \(0.662541\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −240.807 | −0.276338 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 301.837 | − | 522.796i | 0.253308 | − | 0.438743i | −0.711126 | − | 0.703064i | \(-0.751815\pi\) |
0.964435 | + | 0.264321i | \(0.0851479\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1240.58 | + | 2148.75i | 0.788389 | + | 1.36553i | 0.926954 | + | 0.375176i | \(0.122418\pi\) |
−0.138565 | + | 0.990353i | \(0.544249\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 567.327 | + | 1019.56i | 0.280728 | + | 0.504505i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 784.296 | + | 1358.44i | 0.309144 | + | 0.535452i | 0.978175 | − | 0.207781i | \(-0.0666243\pi\) |
−0.669032 | + | 0.743234i | \(0.733291\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1204.55 | − | 2086.34i | 0.385456 | − | 0.667629i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2060.19 | −0.454896 | −0.227448 | − | 0.973790i | \(-0.573038\pi\) | ||||
−0.227448 | + | 0.973790i | \(0.573038\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2997.58 | − | 5191.96i | 0.560230 | − | 0.970347i | −0.437246 | − | 0.899342i | \(-0.644046\pi\) |
0.997476 | − | 0.0710050i | \(-0.0226206\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −735.134 | − | 1273.29i | −0.117512 | − | 0.203536i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3468.31 | + | 54.8858i | 0.478572 | + | 0.00757338i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 295.197 | + | 511.297i | 0.0354493 | + | 0.0614000i | 0.883206 | − | 0.468986i | \(-0.155380\pi\) |
−0.847756 | + | 0.530386i | \(0.822047\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2680.24 | − | 4642.30i | 0.282170 | − | 0.488733i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2920.62 | −0.271341 | −0.135670 | − | 0.990754i | \(-0.543319\pi\) | ||||
−0.135670 | + | 0.990754i | \(0.543319\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9413.21 | 0.776366 | 0.388183 | − | 0.921582i | \(-0.373103\pi\) | ||||
0.388183 | + | 0.921582i | \(0.373103\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1083.63 | − | 1876.91i | 0.0797720 | − | 0.138169i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13540.4 | + | 23452.7i | 0.894101 | + | 1.54863i | 0.834913 | + | 0.550382i | \(0.185518\pi\) |
0.0591882 | + | 0.998247i | \(0.481149\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7938.73 | − | 14813.9i | −0.472347 | − | 0.881413i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2716.53 | + | 4705.17i | 0.146248 | + | 0.253308i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −16037.7 | + | 27778.1i | −0.784247 | + | 1.35836i | 0.145201 | + | 0.989402i | \(0.453617\pi\) |
−0.929448 | + | 0.368953i | \(0.879716\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4371.00 | −0.194838 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −22330.4 | −0.910353 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5177.78 | + | 8968.18i | −0.193648 | + | 0.335409i | −0.946457 | − | 0.322831i | \(-0.895365\pi\) |
0.752808 | + | 0.658240i | \(0.228699\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5202.80 | + | 9011.52i | 0.179025 | + | 0.310080i | 0.941547 | − | 0.336882i | \(-0.109372\pi\) |
−0.762522 | + | 0.646962i | \(0.776039\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10499.7 | − | 166.157i | −0.333292 | − | 0.00527432i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7968.15 | − | 13801.2i | −0.233924 | − | 0.405167i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −23318.2 | + | 40388.3i | −0.634611 | + | 1.09918i | 0.351986 | + | 0.936005i | \(0.385506\pi\) |
−0.986597 | + | 0.163174i | \(0.947827\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −14117.3 | −0.356968 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 42000.8 | 0.988807 | 0.494404 | − | 0.869232i | \(-0.335386\pi\) | ||||
0.494404 | + | 0.869232i | \(0.335386\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9583.83 | + | 16599.7i | −0.210490 | + | 0.364580i | −0.951868 | − | 0.306508i | \(-0.900839\pi\) |
0.741378 | + | 0.671088i | \(0.234173\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10840.9 | + | 18777.1i | 0.222543 | + | 0.385456i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10297.8 | + | 18506.5i | 0.197933 | + | 0.355712i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 35576.9 | + | 61621.0i | 0.641358 | + | 1.11086i | 0.985130 | + | 0.171811i | \(0.0549618\pi\) |
−0.343772 | + | 0.939053i | \(0.611705\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3280.50 | + | 5681.99i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7301.98 | 0.116344 | 0.0581722 | − | 0.998307i | \(-0.481473\pi\) | ||||
0.0581722 | + | 0.998307i | \(0.481473\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16152.1 | 0.242483 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9270.85 | − | 16057.6i | 0.131317 | − | 0.227448i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12177.2 | + | 21091.5i | 0.162956 | + | 0.282249i | 0.935928 | − | 0.352192i | \(-0.114564\pi\) |
−0.772971 | + | 0.634441i | \(0.781230\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −39661.1 | + | 66251.5i | −0.502067 | + | 0.838672i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 26978.2 | + | 46727.6i | 0.323449 | + | 0.560230i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −33193.4 | + | 57492.6i | −0.377348 | + | 0.653586i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 92726.4 | 1.00063 | 0.500316 | − | 0.865843i | \(-0.333217\pi\) | ||||
0.500316 | + | 0.865843i | \(0.333217\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13232.4 | 0.135691 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −88097.2 | + | 152589.i | −0.859327 | + | 1.48840i | 0.0132450 | + | 0.999912i | \(0.495784\pi\) |
−0.872572 | + | 0.488486i | \(0.837549\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15806.4 | − | 27377.4i | −0.146804 | − | 0.254272i | 0.783240 | − | 0.621719i | \(-0.213565\pi\) |
−0.930045 | + | 0.367447i | \(0.880232\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −16035.2 | + | 26785.8i | −0.141939 | + | 0.237100i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −39570.7 | − | 68538.5i | −0.334129 | − | 0.578729i | 0.649188 | − | 0.760628i | \(-0.275109\pi\) |
−0.983317 | + | 0.181899i | \(0.941776\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19841.6 | + | 34366.6i | −0.159959 | + | 0.277058i | −0.934854 | − | 0.355033i | \(-0.884470\pi\) |
0.774894 | + | 0.632091i | \(0.217803\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5313.55 | −0.0409334 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 76185.5 | 0.561276 | 0.280638 | − | 0.959814i | \(-0.409454\pi\) | ||||
0.280638 | + | 0.959814i | \(0.409454\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −20984.9 | + | 36346.9i | −0.147966 | + | 0.256285i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 24122.1 | + | 41780.7i | 0.162911 | + | 0.282170i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −38053.3 | − | 68387.0i | −0.246335 | − | 0.442696i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 67181.8 | + | 116362.i | 0.417146 | + | 0.722518i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13142.8 | − | 22763.9i | 0.0783293 | − | 0.135670i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 148072. | 0.847615 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −330407. | −1.81777 | −0.908887 | − | 0.417042i | \(-0.863067\pi\) | ||||
−0.908887 | + | 0.417042i | \(0.863067\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −42359.4 | + | 73368.7i | −0.224118 | + | 0.388183i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 116335. | + | 201498.i | 0.592287 | + | 1.02587i | 0.993924 | + | 0.110072i | \(0.0351082\pi\) |
−0.401636 | + | 0.915799i | \(0.631558\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 321622. | + | 5089.64i | 1.57658 | + | 0.0249493i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9752.69 | + | 16892.2i | 0.0460564 | + | 0.0797720i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −48363.9 | + | 83768.8i | −0.220151 | + | 0.381312i | −0.954854 | − | 0.297077i | \(-0.903988\pi\) |
0.734703 | + | 0.678389i | \(0.237322\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −177589. | −0.779613 | −0.389806 | − | 0.920897i | \(-0.627458\pi\) | ||||
−0.389806 | + | 0.920897i | \(0.627458\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −243727. | −1.03242 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 48650.1 | − | 84264.5i | 0.198950 | − | 0.344592i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −27561.6 | − | 47738.1i | −0.108864 | − | 0.188558i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 151187. | + | 4786.26i | 0.577061 | + | 0.0182685i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23813.2 | + | 41245.7i | 0.0878723 | + | 0.152199i | 0.906612 | − | 0.421966i | \(-0.138660\pi\) |
−0.818739 | + | 0.574166i | \(0.805327\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −252349. | + | 437081.i | −0.900657 | + | 1.55998i | −0.0740127 | + | 0.997257i | \(0.523581\pi\) |
−0.826644 | + | 0.562726i | \(0.809753\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −48897.5 | −0.168872 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 160409. | 0.536288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 128179. | − | 222012.i | 0.415017 | − | 0.718831i | −0.580413 | − | 0.814322i | \(-0.697109\pi\) |
0.995430 | + | 0.0954911i | \(0.0304421\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −144339. | − | 250003.i | −0.452785 | − | 0.784247i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 203330. | + | 3217.68i | 0.618210 | + | 0.00978314i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14351.4 | − | 24857.3i | −0.0423083 | − | 0.0732800i | 0.844096 | − | 0.536192i | \(-0.180138\pi\) |
−0.886404 | + | 0.462912i | \(0.846804\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 19669.5 | − | 34068.6i | 0.0562449 | − | 0.0974190i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 671712. | 1.86377 | 0.931884 | − | 0.362757i | \(-0.118164\pi\) | ||||
0.931884 | + | 0.362757i | \(0.118164\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −16544.3 | −0.0445585 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 100487. | − | 174048.i | 0.262796 | − | 0.455176i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 174668. | + | 302534.i | 0.443709 | + | 0.768526i | 0.997961 | − | 0.0638227i | \(-0.0203292\pi\) |
−0.554253 | + | 0.832348i | \(0.686996\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −151861. | − | 272914.i | −0.374844 | − | 0.673644i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −46600.0 | − | 80713.6i | −0.111803 | − | 0.193648i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9320.90 | + | 16144.3i | −0.0217433 | + | 0.0376605i | −0.876692 | − | 0.481052i | \(-0.840255\pi\) |
0.854949 | + | 0.518712i | \(0.173588\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −317959. | −0.721397 | −0.360699 | − | 0.932682i | \(-0.617462\pi\) | ||||
−0.360699 | + | 0.932682i | \(0.617462\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −93650.5 | −0.206720 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7898.40 | + | 13680.4i | −0.0169672 | + | 0.0293880i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 49308.9 | + | 85405.6i | 0.103115 | + | 0.178600i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 48543.6 | − | 81089.1i | 0.0988502 | − | 0.165123i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4388.68 | + | 7601.42i | 0.00870464 | + | 0.0150769i | 0.870345 | − | 0.492443i | \(-0.163896\pi\) |
−0.861640 | + | 0.507519i | \(0.830563\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 292255. | − | 506200.i | 0.564766 | − | 0.978203i | −0.432306 | − | 0.901727i | \(-0.642300\pi\) |
0.997071 | − | 0.0764758i | \(-0.0243668\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 143427. | 0.270112 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −310165. | −0.569412 | −0.284706 | − | 0.958615i | \(-0.591896\pi\) | ||||
−0.284706 | + | 0.958615i | \(0.591896\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −40846.9 | + | 70749.0i | −0.0731184 | + | 0.126645i | −0.900267 | − | 0.435339i | \(-0.856628\pi\) |
0.827148 | + | 0.561984i | \(0.189962\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −209864. | − | 363494.i | −0.366393 | − | 0.634611i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −137187. | + | 229162.i | −0.233653 | + | 0.390303i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −39072.5 | − | 67675.6i | −0.0649362 | − | 0.112473i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 63528.0 | − | 110034.i | 0.103048 | − | 0.178484i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −405329. | −0.641863 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 700566. | 1.08328 | 0.541642 | − | 0.840609i | \(-0.317803\pi\) | ||||
0.541642 | + | 0.840609i | \(0.317803\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −189004. | + | 327364.i | −0.285444 | + | 0.494404i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 125932. | + | 218120.i | 0.185797 | + | 0.321810i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −377913. | − | 679160.i | −0.544806 | − | 0.979090i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −86254.4 | − | 149397.i | −0.121527 | − | 0.210490i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −179776. | + | 311382.i | −0.247601 | + | 0.428857i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −292308. | −0.393621 | −0.196810 | − | 0.980442i | \(-0.563058\pi\) | ||||
−0.196810 | + | 0.980442i | \(0.563058\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −195137. | −0.256970 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 414937. | − | 718692.i | 0.534463 | − | 0.925717i | −0.464726 | − | 0.885454i | \(-0.653847\pi\) |
0.999189 | − | 0.0402625i | \(-0.0128194\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −438454. | − | 759424.i | −0.552503 | − | 0.956964i | −0.998093 | − | 0.0617267i | \(-0.980339\pi\) |
0.445590 | − | 0.895237i | \(-0.352994\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −190584. | − | 3015.98i | −0.234994 | − | 0.00371877i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 427589. | + | 740606.i | 0.515984 | + | 0.893711i | 0.999828 | + | 0.0185566i | \(0.00590710\pi\) |
−0.483843 | + | 0.875155i | \(0.660760\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −362292. | + | 627507.i | −0.427946 | + | 0.741224i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −640384. | −0.740576 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −61088.9 | −0.0691779 | −0.0345889 | − | 0.999402i | \(-0.511012\pi\) | ||||
−0.0345889 | + | 0.999402i | \(0.511012\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −85910.9 | + | 148802.i | −0.0952808 | + | 0.165031i | −0.909726 | − | 0.415210i | \(-0.863708\pi\) |
0.814445 | + | 0.580241i | \(0.197042\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −29524.5 | − | 51137.9i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 237057. | − | 382137.i | 0.252312 | − | 0.406728i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −738899. | − | 1.27981e6i | −0.770624 | − | 1.33476i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −32858.9 | + | 56913.3i | −0.0335857 | + | 0.0581722i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.87213e6 | 1.87565 | 0.937826 | − | 0.347104i | \(-0.112835\pi\) | ||||
0.937826 | + | 0.347104i | \(0.112835\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −256250. | −0.251688 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −72684.4 | + | 125893.i | −0.0699989 | + | 0.121242i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.03511e6 | − | 1.79287e6i | −0.977588 | − | 1.69323i | −0.671118 | − | 0.741351i | \(-0.734185\pi\) |
−0.306470 | − | 0.951880i | \(-0.599148\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 76530.2 | + | 1211.09i | 0.0708898 | + | 0.00112183i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 83437.7 | + | 144518.i | 0.0758160 | + | 0.131317i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −43069.8 | + | 74599.1i | −0.0383958 | + | 0.0665034i | −0.884585 | − | 0.466380i | \(-0.845558\pi\) |
0.846189 | + | 0.532883i | \(0.178891\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −858221. | −0.750732 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −219189. | −0.188166 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 760410. | − | 1.31707e6i | 0.640718 | − | 1.10976i | −0.344555 | − | 0.938766i | \(-0.611970\pi\) |
0.985273 | − | 0.170990i | \(-0.0546966\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −797683. | − | 1.38163e6i | −0.659792 | − | 1.14279i | −0.980669 | − | 0.195672i | \(-0.937311\pi\) |
0.320877 | − | 0.947121i | \(-0.396022\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −337904. | − | 607259.i | −0.274402 | − | 0.493137i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 196779. | + | 340831.i | 0.156908 | + | 0.271773i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 435077. | − | 753575.i | 0.340695 | − | 0.590102i | −0.643867 | − | 0.765138i | \(-0.722671\pi\) |
0.984562 | + | 0.175036i | \(0.0560042\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −485608. | −0.373487 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.63359e6 | 1.23417 | 0.617087 | − | 0.786895i | \(-0.288313\pi\) | ||||
0.617087 | + | 0.786895i | \(0.288313\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 280329. | − | 485543.i | 0.208066 | − | 0.360381i | −0.743039 | − | 0.669248i | \(-0.766616\pi\) |
0.951105 | + | 0.308867i | \(0.0999498\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −298740. | − | 517433.i | −0.217862 | − | 0.377348i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −194482. | + | 324870.i | −0.139372 | + | 0.232812i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 527718. | + | 914034.i | 0.371670 | + | 0.643751i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −417269. | + | 722731.i | −0.288857 | + | 0.500316i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.01211e6 | 0.688747 | 0.344374 | − | 0.938833i | \(-0.388091\pi\) | ||||
0.344374 | + | 0.938833i | \(0.388091\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −277077. | −0.185373 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −59545.8 | + | 103136.i | −0.0391706 | + | 0.0678455i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −467133. | − | 809098.i | −0.302178 | − | 0.523387i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 626819. | − | 1.04706e6i | 0.398773 | − | 0.666126i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −792874. | − | 1.37330e6i | −0.496133 | − | 0.859327i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −139208. | + | 241115.i | −0.0856869 | + | 0.148414i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.74706e6 | 1.66350 | 0.831749 | − | 0.555153i | \(-0.187340\pi\) | ||||
0.831749 | + | 0.555153i | \(0.187340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 284514. | 0.169515 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 156619. | − | 271272.i | 0.0918213 | − | 0.159039i | −0.816456 | − | 0.577407i | \(-0.804064\pi\) |
0.908278 | + | 0.418368i | \(0.137398\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 61781.7 | + | 107009.i | 0.0356450 | + | 0.0617390i | 0.883298 | − | 0.468813i | \(-0.155318\pi\) |
−0.847653 | + | 0.530552i | \(0.821985\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −136616. | − | 245518.i | −0.0775758 | − | 0.139414i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.24968e6 | + | 2.16450e6i | 0.698472 | + | 1.20979i | 0.968996 | + | 0.247076i | \(0.0794698\pi\) |
−0.270524 | + | 0.962713i | \(0.587197\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 168279. | − | 291468.i | 0.0925879 | − | 0.160367i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 712273. | 0.385819 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.49781e6 | 0.798822 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −717439. | + | 1.24264e6i | −0.376770 | + | 0.652585i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −178574. | − | 309299.i | −0.0923526 | − | 0.159959i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.51036e6 | + | 55551.3i | 1.78798 | + | 0.0282947i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.38949e6 | − | 2.40666e6i | −0.697083 | − | 1.20738i | −0.969473 | − | 0.245197i | \(-0.921147\pi\) |
0.272390 | − | 0.962187i | \(-0.412186\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 23911.0 | − | 41415.0i | 0.0118164 | − | 0.0204667i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.24782e6 | −0.607491 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 737417. | 0.353703 | 0.176851 | − | 0.984238i | \(-0.443409\pi\) | ||||
0.176851 | + | 0.984238i | \(0.443409\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −342835. | + | 593807.i | −0.162026 | + | 0.280638i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 489694. | + | 848174.i | 0.228054 | + | 0.395002i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.17644e6 | − | 103395.i | −0.998873 | − | 0.0474530i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −188864. | − | 327122.i | −0.0854283 | − | 0.147966i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.04336e6 | + | 1.80716e6i | −0.465169 | + | 0.805697i | −0.999209 | − | 0.0397624i | \(-0.987340\pi\) |
0.534040 | + | 0.845459i | \(0.320673\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.35404e6 | −1.47403 | −0.737013 | − | 0.675879i | \(-0.763764\pi\) | ||||
−0.737013 | + | 0.675879i | \(0.763764\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −434198. | −0.188114 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −496079. | + | 859234.i | −0.211892 | + | 0.367007i | −0.952307 | − | 0.305143i | \(-0.901296\pi\) |
0.740415 | + | 0.672150i | \(0.234629\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 561894. | + | 973229.i | 0.236637 | + | 0.409868i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 704264. | + | 11144.9i | 0.292459 | + | 0.00462814i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.22630e6 | − | 3.85606e6i | −0.911689 | − | 1.57909i | −0.811677 | − | 0.584106i | \(-0.801445\pi\) |
−0.100012 | − | 0.994986i | \(-0.531888\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.84002e6 | + | 3.18701e6i | −0.743113 | + | 1.28711i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.20927e6 | −0.481679 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −512856. | −0.201495 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 445316. | − | 771309.i | 0.172585 | − | 0.298926i | −0.766738 | − | 0.641960i | \(-0.778121\pi\) |
0.939323 | + | 0.343034i | \(0.111455\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 118285. | + | 204876.i | 0.0452234 | + | 0.0783293i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.02192e6 | + | 3.63366e6i | 0.762655 | + | 1.37059i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 146486. | + | 253721.i | 0.0545160 | + | 0.0944245i | 0.891996 | − | 0.452044i | \(-0.149305\pi\) |
−0.837480 | + | 0.546469i | \(0.815972\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −666325. | + | 1.15411e6i | −0.244685 | + | 0.423808i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.22707e6 | 0.444646 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.24947e6 | 0.446814 | 0.223407 | − | 0.974725i | \(-0.428282\pi\) | ||||
0.223407 | + | 0.974725i | \(0.428282\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.48683e6 | − | 2.57527e6i | 0.524746 | − | 0.908887i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.05565e6 | + | 1.82843e6i | 0.367723 | + | 0.636915i | 0.989209 | − | 0.146510i | \(-0.0468041\pi\) |
−0.621486 | + | 0.783425i | \(0.713471\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −291062. | + | 486201.i | −0.100077 | + | 0.167172i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −381235. | − | 660318.i | −0.129394 | − | 0.224118i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.73067e6 | − | 2.99761e6i | 0.579883 | − | 1.00439i | −0.415609 | − | 0.909543i | \(-0.636432\pi\) |
0.995492 | − | 0.0948435i | \(-0.0302351\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 946917. | 0.313235 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.09403e6 | −0.683914 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −951908. | + | 1.64875e6i | −0.306974 | + | 0.531695i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.22234e6 | − | 2.11716e6i | −0.389239 | − | 0.674181i | 0.603109 | − | 0.797659i | \(-0.293929\pi\) |
−0.992347 | + | 0.123478i | \(0.960595\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.48697e6 | + | 2.48389e6i | −0.467594 | + | 0.781088i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.66753e6 | + | 4.62030e6i | 0.828416 | + | 1.43486i | 0.899281 | + | 0.437372i | \(0.144091\pi\) |
−0.0708651 | + | 0.997486i | \(0.522576\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.78538e6 | + | 3.09237e6i | −0.547606 | + | 0.948482i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −175548. | −0.0531814 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −96448.6 | −0.0288609 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.09530e6 | + | 3.62916e6i | −0.619352 | + | 1.07275i | 0.370252 | + | 0.928931i | \(0.379271\pi\) |
−0.989604 | + | 0.143818i | \(0.954062\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −435275. | − | 753919.i | −0.127104 | − | 0.220151i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 652776. | + | 1.17313e6i | 0.188317 | + | 0.338431i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 97687.2 | + | 169199.i | 0.0278431 | + | 0.0482256i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 799150. | − | 1.38417e6i | 0.225055 | − | 0.389806i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.21033e6 | 1.44987 | 0.724937 | − | 0.688815i | \(-0.241869\pi\) | ||||
0.724937 | + | 0.688815i | \(0.241869\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.05706e6 | 0.290665 | 0.145333 | − | 0.989383i | \(-0.453575\pi\) | ||||
0.145333 | + | 0.989383i | \(0.453575\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.09677e6 | − | 1.89966e6i | 0.298034 | − | 0.516210i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −727154. | − | 1.25947e6i | −0.195278 | − | 0.338232i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.34883e6 | + | 21345.2i | 0.358004 | + | 0.00566540i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 437851. | + | 758381.i | 0.114864 | + | 0.198950i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.48147e6 | + | 4.29803e6i | −0.643451 | + | 1.11449i | 0.341206 | + | 0.939988i | \(0.389165\pi\) |
−0.984657 | + | 0.174501i | \(0.944169\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.95367e6 | −1.26972 | −0.634859 | − | 0.772628i | \(-0.718942\pi\) | ||||
−0.634859 | + | 0.772628i | \(0.718942\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 496108. | 0.125705 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.94596e6 | + | 3.37050e6i | −0.487451 | + | 0.844289i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.77419e6 | − | 3.07298e6i | −0.439378 | − | 0.761025i | 0.558264 | − | 0.829664i | \(-0.311468\pi\) |
−0.997642 | + | 0.0686387i | \(0.978134\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −717648. | + | 1.15685e6i | −0.175717 | + | 0.283257i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.68493e6 | + | 6.38249e6i | 0.892114 | + | 1.54519i | 0.837337 | + | 0.546688i | \(0.184112\pi\) |
0.0547773 | + | 0.998499i | \(0.482555\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −325817. | + | 564331.i | −0.0779962 | + | 0.135093i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −428638. | −0.101466 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.53641e6 | 0.593750 | 0.296875 | − | 0.954916i | \(-0.404056\pi\) | ||||
0.296875 | + | 0.954916i | \(0.404056\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 238560. | − | 413199.i | 0.0552277 | − | 0.0956571i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.27114e6 | − | 3.93373e6i | −0.519994 | − | 0.900657i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.06575e6 | − | 32690.4i | −0.467789 | − | 0.00740273i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.05909e6 | − | 1.83440e6i | −0.237215 | − | 0.410869i | 0.722699 | − | 0.691163i | \(-0.242901\pi\) |
−0.959914 | + | 0.280294i | \(0.909568\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 220039. | − | 381119.i | 0.0487492 | − | 0.0844362i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.00292e6 | −1.53471 | −0.767356 | − | 0.641221i | \(-0.778428\pi\) | ||||
−0.767356 | + | 0.641221i | \(0.778428\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.94469e6 | 0.855185 | 0.427593 | − | 0.903971i | \(-0.359362\pi\) | ||||
0.427593 | + | 0.903971i | \(0.359362\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −721839. | + | 1.25026e6i | −0.154813 | + | 0.268144i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.15442e6 | + | 3.73156e6i | 0.457128 | + | 0.791769i | 0.998808 | − | 0.0488161i | \(-0.0155448\pi\) |
−0.541680 | + | 0.840585i | \(0.682212\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.93978e6 | + | 5.28319e6i | 0.617139 | + | 1.10908i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.15361e6 | + | 1.99811e6i | 0.239610 | + | 0.415017i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −768885. | + | 1.33175e6i | −0.158019 | + | 0.273696i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.97735e6 | 1.21556 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.59811e6 | 0.522831 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.82969e6 | − | 3.16912e6i | 0.364368 | − | 0.631103i | −0.624307 | − | 0.781179i | \(-0.714619\pi\) |
0.988674 | + | 0.150076i | \(0.0479518\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −175822. | − | 304532.i | −0.0346505 | − | 0.0600165i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −940062. | + | 1.57032e6i | −0.183353 | + | 0.306281i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.24051e6 | + | 2.14863e6i | 0.239467 | + | 0.414769i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.66804e6 | + | 6.35324e6i | −0.700829 | + | 1.21387i | 0.267347 | + | 0.963600i | \(0.413853\pi\) |
−0.968176 | + | 0.250271i | \(0.919480\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 258325. | 0.0488534 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.95510e6 | 1.30197 | 0.650983 | − | 0.759092i | \(-0.274357\pi\) | ||||
0.650983 | + | 0.759092i | \(0.274357\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −621841. | + | 1.07706e6i | −0.115229 | + | 0.199583i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 177025. | + | 306617.i | 0.0324730 | + | 0.0562449i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.79680e6 | − | 4.67189e6i | 0.507891 | − | 0.848402i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 139655. | + | 241889.i | 0.0251075 | + | 0.0434875i | 0.878306 | − | 0.478099i | \(-0.158674\pi\) |
−0.853199 | + | 0.521586i | \(0.825341\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.02270e6 | + | 5.23548e6i | −0.538023 | + | 0.931884i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.11670e6 | −1.60664 | −0.803318 | − | 0.595550i | \(-0.796934\pi\) | ||||
−0.803318 | + | 0.595550i | \(0.796934\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.71432e6 | −0.822603 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 74449.2 | − | 128950.i | 0.0128629 | − | 0.0222793i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −211761. | − | 366780.i | −0.0362285 | − | 0.0627497i | 0.847343 | − | 0.531047i | \(-0.178201\pi\) |
−0.883571 | + | 0.468297i | \(0.844868\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.20826e6 | + | 2.17140e6i | 0.204695 | + | 0.367865i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 904382. | + | 1.56644e6i | 0.151725 | + | 0.262796i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 422920. | − | 732520.i | 0.0702652 | − | 0.121703i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.42400e6 | −0.727928 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.14402e6 | −0.512350 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.66620e6 | − | 2.88594e6i | 0.268926 | − | 0.465793i | −0.699659 | − | 0.714477i | \(-0.746665\pi\) |
0.968585 | + | 0.248684i | \(0.0799980\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 563848. | + | 976613.i | 0.0901380 | + | 0.156124i | 0.907569 | − | 0.419903i | \(-0.137936\pi\) |
−0.817431 | + | 0.576026i | \(0.804603\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.81053e6 | + | 44476.4i | 0.445030 | + | 0.00704258i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.80956e6 | − | 3.13425e6i | −0.283822 | − | 0.491594i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.98793e6 | − | 3.44320e6i | 0.308860 | − | 0.534962i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 838800. | 0.129099 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.73954e6 | 0.265226 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.05877e6 | − | 1.83384e6i | 0.159925 | − | 0.276998i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −83888.1 | − | 145298.i | −0.0125535 | − | 0.0217433i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.74427e6 | + | 86877.5i | 0.406869 | + | 0.0128806i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 632670. | + | 1.09582e6i | 0.0929360 | + | 0.160970i | 0.908745 | − | 0.417351i | \(-0.137041\pi\) |
−0.815809 | + | 0.578321i | \(0.803708\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.43081e6 | − | 2.47824e6i | 0.208249 | − | 0.360699i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.06178e6 | −0.153123 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.48152e6 | 0.926208 | 0.463104 | − | 0.886304i | \(-0.346736\pi\) | ||||
0.463104 | + | 0.886304i | \(0.346736\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 421427. | − | 729933.i | 0.0596749 | − | 0.103360i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.55583e6 | − | 4.42682e6i | −0.358635 | − | 0.621174i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.22335e6 | + | 145959.i | 1.28255 | + | 0.0202964i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −71085.6 | − | 123124.i | −0.00979601 | − | 0.0169672i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.73942e6 | + | 3.01277e6i | −0.237557 | + | 0.411460i | −0.960013 | − | 0.279957i | \(-0.909680\pi\) |
0.722456 | + | 0.691417i | \(0.243013\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.60658e6 | −0.758872 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −887561. | −0.119067 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.94660e6 | − | 8.56777e6i | 0.657713 | − | 1.13919i | −0.323494 | − | 0.946230i | \(-0.604857\pi\) |
0.981206 | − | 0.192961i | \(-0.0618092\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.01922e6 | + | 1.76535e6i | 0.134322 | + | 0.232653i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 413581. | + | 743261.i | 0.0540260 | + | 0.0970921i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.94944e6 | − | 1.03047e7i | −0.770363 | − | 1.33431i | −0.937364 | − | 0.348351i | \(-0.886742\pi\) |
0.167001 | − | 0.985957i | \(-0.446592\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.85004e6 | + | 4.93642e6i | −0.365815 | + | 0.633610i | −0.988907 | − | 0.148539i | \(-0.952543\pi\) |
0.623092 | + | 0.782149i | \(0.285876\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −78996.3 | −0.0100513 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.77889e6 | 0.476645 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.40787e6 | − | 1.10988e7i | 0.801262 | − | 1.38783i | −0.117524 | − | 0.993070i | \(-0.537496\pi\) |
0.918786 | − | 0.394756i | \(-0.129171\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.63029e6 | + | 4.55580e6i | 0.326068 | + | 0.564766i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 486234. | − | 812224.i | 0.0597592 | − | 0.0998241i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.61997e6 | − | 4.53792e6i | −0.319245 | − | 0.552949i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −645420. | + | 1.11790e6i | −0.0779745 | + | 0.135056i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.06067e7 | −1.27053 | −0.635267 | − | 0.772293i | \(-0.719110\pi\) | ||||
−0.635267 | + | 0.772293i | \(0.719110\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.48749e7 | 1.76672 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.39574e6 | − | 2.41749e6i | 0.164375 | − | 0.284706i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.03390e6 | − | 1.79076e6i | −0.120737 | − | 0.209123i | 0.799322 | − | 0.600904i | \(-0.205192\pi\) |
−0.920059 | + | 0.391781i | \(0.871859\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.07556e6 | − | 1.79665e6i | 0.124549 | − | 0.208052i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −367623. | − | 636741.i | −0.0422150 | − | 0.0731184i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.35372e6 | + | 5.80881e6i | −0.381909 | + | 0.661485i | −0.991335 | − | 0.131357i | \(-0.958066\pi\) |
0.609426 | + | 0.792843i | \(0.291400\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −762575. | −0.0861185 | −0.0430592 | − | 0.999073i | \(-0.513710\pi\) | ||||
−0.0430592 | + | 0.999073i | \(0.513710\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.77755e6 | 0.423074 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.79754e6 | + | 3.11343e6i | −0.199659 | + | 0.345820i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.35168e6 | − | 5.80529e6i | −0.369225 | − | 0.639517i | 0.620219 | − | 0.784428i | \(-0.287044\pi\) |
−0.989445 | + | 0.144912i | \(0.953710\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.16880e6 | − | 2.10049e6i | −0.127702 | − | 0.229497i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.06477e6 | − | 1.39686e7i | −0.873954 | − | 1.51373i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.64607e6 | − | 6.31518e6i | 0.391899 | − | 0.678788i | −0.600801 | − | 0.799398i | \(-0.705152\pi\) |
0.992700 | + | 0.120610i | \(0.0384851\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 703305. | 0.0749818 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.70607e6 | −0.391923 | −0.195962 | − | 0.980612i | \(-0.562783\pi\) | ||||
−0.195962 | + | 0.980612i | \(0.562783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.46700e6 | + | 4.27296e6i | −0.258787 | + | 0.448232i | −0.965917 | − | 0.258851i | \(-0.916656\pi\) |
0.707131 | + | 0.707083i | \(0.249989\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 571752. | + | 990303.i | 0.0594947 | + | 0.103048i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.15695e6 | + | 49958.5i | 0.325872 | + | 0.00515691i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.78328e6 | − | 3.08873e6i | −0.182608 | − | 0.316286i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.82398e6 | − | 3.15923e6i | 0.185290 | − | 0.320932i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 356405. | 0.0359185 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.30887e7 | −1.30865 | −0.654326 | − | 0.756213i | \(-0.727047\pi\) | ||||
−0.654326 | + | 0.756213i | \(0.727047\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.15255e6 | + | 5.46037e6i | −0.312717 | + | 0.541642i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.42024e6 | − | 7.65609e6i | −0.435023 | − | 0.753482i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.72837e6 | + | 8.82328e6i | 0.461703 | + | 0.861552i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.70103e6 | − | 2.94627e6i | −0.164801 | − | 0.285444i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.27660e6 | + | 1.60675e7i | −0.891751 | + | 1.54456i | −0.0539767 | + | 0.998542i | \(0.517190\pi\) |
−0.837775 | + | 0.546016i | \(0.816144\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.07346e7 | −1.02390 | −0.511949 | − | 0.859016i | \(-0.671076\pi\) | ||||
−0.511949 | + | 0.859016i | \(0.671076\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.26677e6 | −0.214540 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.63282e6 | − | 2.82812e6i | 0.153348 | − | 0.265606i | −0.779109 | − | 0.626889i | \(-0.784328\pi\) |
0.932456 | + | 0.361283i | \(0.117661\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −845858. | − | 1.46507e6i | −0.0788289 | − | 0.136536i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.99413e6 | + | 110682.i | 0.646817 | + | 0.0102358i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.41947e6 | − | 2.45859e6i | −0.130270 | − | 0.225633i | 0.793511 | − | 0.608556i | \(-0.208251\pi\) |
−0.923780 | + | 0.382923i | \(0.874918\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.11270e6 | + | 5.39136e6i | −0.283488 | + | 0.491015i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.55258e6 | 0.140327 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.20588e7 | −1.08166 | −0.540828 | − | 0.841133i | \(-0.681889\pi\) | ||||
−0.540828 | + | 0.841133i | \(0.681889\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.99879e6 | − | 5.19405e6i | 0.266957 | − | 0.462384i | −0.701117 | − | 0.713046i | \(-0.747315\pi\) |
0.968075 | + | 0.250662i | \(0.0806484\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.61799e6 | − | 2.80244e6i | −0.142952 | − | 0.247601i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.18477e6 | + | 7.52060e6i | 0.366959 | + | 0.659475i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.61580e6 | − | 2.79864e6i | −0.140628 | − | 0.243575i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.31538e6 | − | 2.27831e6i | 0.113628 | − | 0.196810i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.69989e6 | −0.145752 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.89426e7 | 1.61214 | 0.806069 | − | 0.591822i | \(-0.201591\pi\) | ||||
0.806069 | + | 0.591822i | \(0.201591\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 878116. | − | 1.52094e6i | 0.0741810 | − | 0.128485i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.22818e6 | − | 3.85931e6i | −0.186843 | − | 0.323622i | 0.757353 | − | 0.653006i | \(-0.226492\pi\) |
−0.944196 | + | 0.329384i | \(0.893159\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.17459e6 | − | 1.03143e7i | 0.513965 | − | 0.858547i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.73443e6 | + | 6.46823e6i | 0.308572 | + | 0.534463i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.21187e6 | − | 3.83106e6i | 0.181429 | − | 0.314245i | −0.760938 | − | 0.648824i | \(-0.775261\pi\) |
0.942367 | + | 0.334580i | \(0.108594\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.58808e6 | −0.210742 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.89217e6 | 0.637976 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.55219e6 | − | 1.65449e7i | 0.766575 | − | 1.32775i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.37228e6 | − | 4.10890e6i | −0.189004 | − | 0.327364i | 0.755915 | − | 0.654670i | \(-0.227192\pi\) |
−0.944918 | + | 0.327306i | \(0.893859\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 881136. | − | 1.47189e6i | 0.0696963 | − | 0.116424i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.37582e6 | − | 4.11503e6i | −0.186574 | − | 0.323155i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −881549. | + | 1.52689e6i | −0.0687329 | + | 0.119049i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.69660e6 | −0.595807 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.02431e7 | −1.55590 | −0.777952 | − | 0.628324i | \(-0.783741\pi\) | ||||
−0.777952 | + | 0.628324i | \(0.783741\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −732431. | + | 1.26861e6i | −0.0558957 | + | 0.0968142i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.26062e6 | − | 5.64757e6i | −0.247075 | − | 0.427946i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.11066e7 | + | 1.99601e7i | 0.835668 | + | 1.50181i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.08834e7 | − | 1.88507e7i | −0.813112 | − | 1.40835i | −0.910676 | − | 0.413121i | \(-0.864439\pi\) |
0.0975645 | − | 0.995229i | \(-0.468895\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.88173e6 | − | 4.99130e6i | 0.213786 | − | 0.370288i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.40395e6 | 0.692766 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.60340e6 | 0.190448 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 274900. | − | 476141.i | 0.0199699 | − | 0.0345889i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.70313e6 | − | 9.87812e6i | −0.411426 | − | 0.712610i | 0.583620 | − | 0.812027i | \(-0.301636\pi\) |
−0.995046 | + | 0.0994167i | \(0.968302\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.09782e6 | − | 64847.7i | −0.293572 | − | 0.00464576i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −773198. | − | 1.33922e6i | −0.0550104 | − | 0.0952808i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.48160e6 | + | 4.29826e6i | −0.175342 | + | 0.303702i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −635734. | −0.0446107 | −0.0223054 | − | 0.999751i | \(-0.507101\pi\) | ||||
−0.0223054 | + | 0.999751i | \(0.507101\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.84125e6 | − | 4.92119e6i | 0.196660 | − | 0.340625i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.20000e6 | − | 7.27462e6i | −0.288729 | − | 0.500093i | 0.684778 | − | 0.728752i | \(-0.259899\pi\) |
−0.973507 | + | 0.228659i | \(0.926566\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.91170e6 | + | 3.56729e6i | 0.130528 | + | 0.243568i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.80933e6 | − | 6.59795e6i | −0.258333 | − | 0.447446i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.90264e6 | − | 5.02752e6i | 0.195516 | − | 0.338644i | −0.751554 | − | 0.659672i | \(-0.770695\pi\) |
0.947070 | + | 0.321028i | \(0.104029\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.33002e7 | 0.889840 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.80938e7 | 1.20242 | 0.601212 | − | 0.799090i | \(-0.294685\pi\) | ||||
0.601212 | + | 0.799090i | \(0.294685\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −637154. | + | 1.10358e6i | −0.0420585 | + | 0.0728475i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −295730. | − | 512220.i | −0.0193907 | − | 0.0335857i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.02588e7 | − | 162344.i | −0.668175 | − | 0.0105738i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.45350e7 | + | 2.51753e7i | 0.940404 | + | 1.62883i | 0.764703 | + | 0.644383i | \(0.222886\pi\) |
0.175701 | + | 0.984444i | \(0.443781\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.42460e6 | + | 1.45918e7i | −0.541454 | + | 0.937826i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.35039e7 | −0.862166 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.75384e7 | 1.74662 | 0.873311 | − | 0.487163i | \(-0.161968\pi\) | ||||
0.873311 | + | 0.487163i | \(0.161968\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.15312e6 | − | 1.99727e6i | 0.0726560 | − | 0.125844i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.27683e7 | − | 2.21153e7i | −0.799229 | − | 1.38430i | −0.920119 | − | 0.391639i | \(-0.871908\pi\) |
0.120890 | − | 0.992666i | \(-0.461425\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.50148e6 | + | 4.49549e6i | 0.155555 | + | 0.279554i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −654160. | − | 1.13304e6i | −0.0404139 | − | 0.0699989i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.08393e6 | − | 5.34152e6i | 0.189285 | − | 0.327851i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.51037e7 | −0.921015 | −0.460507 | − | 0.887656i | \(-0.652332\pi\) | ||||
−0.460507 | + | 0.887656i | \(0.652332\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.86321e7 | 1.12882 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.50268e6 | − | 7.79887e6i | 0.271033 | − | 0.469443i | −0.698094 | − | 0.716006i | \(-0.745968\pi\) |
0.969127 | + | 0.246564i | \(0.0793014\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.22146e6 | − | 1.25079e7i | −0.431888 | − | 0.748051i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −353826. | + | 591044.i | −0.0210250 | + | 0.0351211i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.62325e6 | − | 6.27566e6i | −0.213922 | − | 0.370524i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.43069e6 | + | 5.94213e6i | −0.201258 | + | 0.348589i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.50188e6 | −0.0875448 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.85918e6 | 0.397281 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.17443e7 | + | 2.03417e7i | −0.675912 | + | 1.17071i | 0.300289 | + | 0.953848i | \(0.402917\pi\) |
−0.976201 | + | 0.216866i | \(0.930417\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −387628. | − | 671392.i | −0.0221678 | − | 0.0383958i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.07314e6 | − | 8.47437e6i | 0.288294 | − | 0.481578i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.09883e6 | − | 5.36733e6i | −0.174991 | − | 0.303093i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.86200e6 | − | 6.68917e6i | 0.216718 | − | 0.375366i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.81831e7 | −1.57160 | −0.785802 | − | 0.618478i | \(-0.787750\pi\) | ||||
−0.785802 | + | 0.618478i | \(0.787750\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.63480e7 | 0.905934 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 986351. | − | 1.70841e6i | 0.0543188 | − | 0.0940829i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.56564e6 | − | 2.71177e6i | −0.0856848 | − | 0.148410i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.64562e6 | + | 4.75453e6i | 0.143892 | + | 0.258594i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.84369e6 | + | 1.18536e7i | 0.369919 | + | 0.640718i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.66312e6 | + | 1.15409e7i | −0.357937 | + | 0.619965i | −0.987616 | − | 0.156890i | \(-0.949853\pi\) |
0.629679 | + | 0.776855i | \(0.283186\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.58038e7 | 1.91151 | 0.955757 | − | 0.294158i | \(-0.0950391\pi\) | ||||
0.955757 | + | 0.294158i | \(0.0950391\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.43583e7 | 0.761862 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 383991. | − | 665092.i | 0.0202501 | − | 0.0350742i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.16778e7 | + | 2.02266e7i | 0.612078 | + | 1.06015i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.25369e6 | + | 98964.3i | 0.325781 | + | 0.00515547i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.26845e7 | − | 2.19702e7i | −0.656772 | − | 1.13756i | −0.981446 | − | 0.191737i | \(-0.938588\pi\) |
0.324674 | − | 0.945826i | \(-0.394745\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.33837e7 | + | 2.31813e7i | −0.688774 | + | 1.19299i | 0.283461 | + | 0.958984i | \(0.408517\pi\) |
−0.972235 | + | 0.234008i | \(0.924816\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.54202e6 | −0.181182 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.81253e7 | −1.93843 | −0.969213 | − | 0.246224i | \(-0.920810\pi\) | ||||
−0.969213 | + | 0.246224i | \(0.920810\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.06070e7 | − | 1.83719e7i | 0.536051 | − | 0.928468i | −0.463061 | − | 0.886327i | \(-0.653249\pi\) |
0.999112 | − | 0.0421411i | \(-0.0134179\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.91569e6 | + | 6.78217e6i | 0.196701 | + | 0.340695i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.01409e7 | − | 321037.i | −0.506363 | − | 0.0160304i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.98628e6 | + | 1.55647e7i | 0.446030 | + | 0.772546i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.18524e6 | − | 3.78494e6i | 0.107816 | − | 0.186743i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.95969e6 | −0.341338 | −0.170669 | − | 0.985328i | \(-0.554593\pi\) | ||||
−0.170669 | + | 0.985328i | \(0.554593\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.62668e7 | −0.793070 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.35114e6 | + | 1.27325e7i | −0.356275 | + | 0.617087i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −221332. | − | 383358.i | −0.0106636 | − | 0.0184698i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.74170e7 | + | 275622.i | 0.834187 | + | 0.0132010i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.52296e6 | + | 4.36989e6i | 0.120127 | + | 0.208066i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −463044. | + | 802016.i | −0.0219179 | + | 0.0379629i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.50813e6 | −0.306255 | −0.153128 | − | 0.988206i | \(-0.548935\pi\) | ||||
−0.153128 | + | 0.988206i | \(0.548935\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.37732e6 | 0.251565 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.67971e6 | − | 1.50337e7i | 0.403695 | − | 0.699220i | −0.590474 | − | 0.807057i | \(-0.701059\pi\) |
0.994169 | + | 0.107837i | \(0.0343924\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.06441e7 | − | 3.57566e7i | −0.954580 | − | 1.65338i | −0.735325 | − | 0.677714i | \(-0.762971\pi\) |
−0.219255 | − | 0.975668i | \(-0.570363\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.65694e6 | − | 2.97775e6i | −0.0761728 | − | 0.136893i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.34758e6 | + | 1.09943e7i | 0.290123 | + | 0.502507i | 0.973838 | − | 0.227241i | \(-0.0729706\pi\) |
−0.683716 | + | 0.729748i | \(0.739637\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.67347e6 | + | 8.09470e6i | −0.212373 | + | 0.367841i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.49892e6 | −0.429167 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.16239e7 | −0.522158 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.38885e7 | − | 2.40556e7i | 0.620311 | − | 1.07441i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.75542e6 | − | 6.50458e6i | −0.166772 | − | 0.288857i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.86003e6 | − | 1.64706e7i | 0.435369 | − | 0.727258i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.51380e6 | + | 1.64784e7i | 0.417691 | + | 0.723462i | 0.995707 | − | 0.0925634i | \(-0.0295061\pi\) |
−0.578016 | + | 0.816026i | \(0.696173\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.55451e6 | + | 7.88864e6i | −0.198824 | + | 0.344374i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.60494e7 | 1.56480 | 0.782399 | − | 0.622778i | \(-0.213996\pi\) | ||||
0.782399 | + | 0.622778i | \(0.213996\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.13710e7 | −0.490790 | −0.245395 | − | 0.969423i | \(-0.578918\pi\) | ||||
−0.245395 | + | 0.969423i | \(0.578918\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.24685e6 | − | 2.15960e6i | 0.0535124 | − | 0.0926863i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.56953e7 | + | 2.71850e7i | 0.669823 | + | 1.16017i | 0.977953 | + | 0.208823i | \(0.0669633\pi\) |
−0.308131 | + | 0.951344i | \(0.599703\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.20016e7 | + | 3.67523e7i | −0.933683 | + | 1.55966i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −535912. | − | 928227.i | −0.0226152 | − | 0.0391706i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.35959e7 | + | 5.81897e7i | −1.40980 | + | 2.44184i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −498787. | −0.0208141 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.40839e6 | 0.348925 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.17558e6 | + | 1.06964e7i | −0.254846 | + | 0.441407i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.68154e6 | + | 1.67689e7i | 0.397313 | + | 0.688166i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.34036e6 | + | 9.59735e6i | 0.217947 | + | 0.391681i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.25371e6 | − | 7.36764e6i | −0.172642 | − | 0.299025i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.94598e7 | + | 3.37054e7i | −0.785454 | + | 1.36045i | 0.143273 | + | 0.989683i | \(0.454237\pi\) |
−0.928727 | + | 0.370763i | \(0.879096\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.42717e7 | 0.572885 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.37630e7 | 0.549437 | 0.274719 | − | 0.961525i | \(-0.411415\pi\) | ||||
0.274719 | + | 0.961525i | \(0.411415\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −596437. | + | 1.03306e6i | −0.0236803 | + | 0.0410155i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.25287e6 | − | 2.17004e6i | −0.0494714 | − | 0.0856869i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.01600e7 | + | 477280.i | 1.18443 | + | 0.0187435i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.06989e7 | + | 3.58515e7i | 0.808460 | + | 1.40029i | 0.913930 | + | 0.405871i | \(0.133032\pi\) |
−0.105470 | + | 0.994422i | \(0.533635\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.23618e7 | + | 2.14112e7i | −0.480210 | + | 0.831749i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.50160e7 | −0.966526 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.42232e6 | 0.0546566 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.28031e6 | + | 2.21757e6i | −0.0489348 | + | 0.0847575i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.29015e6 | − | 2.23460e6i | −0.0490456 | − | 0.0849494i | 0.840460 | − | 0.541873i | \(-0.182285\pi\) |
−0.889506 | + | 0.456924i | \(0.848951\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.19827e7 | − | 3.54361e7i | 0.831202 | − | 1.33990i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.40957e6 | + | 2.44145e6i | 0.0530131 | + | 0.0918213i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.31933e6 | + | 2.28514e6i | −0.0493541 | + | 0.0854839i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.18054e7 | 0.439269 | 0.219634 | − | 0.975582i | \(-0.429514\pi\) | ||||
0.219634 | + | 0.975582i | \(0.429514\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.11207e6 | −0.0411593 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.61777e7 | + | 2.80206e7i | −0.595583 | + | 1.03158i | 0.397881 | + | 0.917437i | \(0.369746\pi\) |
−0.993464 | + | 0.114143i | \(0.963588\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.29063e6 | − | 3.96748e6i | −0.0838832 | − | 0.145290i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.52840e6 | + | 40011.7i | 0.0921013 | + | 0.00145750i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −415142. | − | 719047.i | −0.0150426 | − | 0.0260545i | 0.858406 | − | 0.512971i | \(-0.171455\pi\) |
−0.873449 | + | 0.486916i | \(0.838122\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.70820e6 | − | 9.88690e6i | 0.205747 | − | 0.356365i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.24942e7 | −0.806526 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.26012e7 | 1.87613 | 0.938066 | − | 0.346457i | \(-0.112615\pi\) | ||||
0.938066 | + | 0.346457i | \(0.112615\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −117425. | + | 203386.i | −0.00416632 | + | 0.00721628i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.51451e6 | + | 2.62322e6i | 0.0534556 | + | 0.0925879i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.09737e6 | + | 1.09578e7i | 0.214090 | + | 0.384748i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.65639e6 | − | 6.33305e6i | −0.127715 | − | 0.221210i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.20523e6 | + | 5.55162e6i | −0.111376 | + | 0.192910i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.56393e7 | 0.540630 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.79449e7 | 0.961029 | 0.480514 | − | 0.876987i | \(-0.340450\pi\) | ||||
0.480514 | + | 0.876987i | \(0.340450\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.74014e6 | + | 1.16743e7i | −0.230600 | + | 0.399411i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.66081e7 | − | 2.87661e7i | −0.565291 | − | 0.979113i | −0.997023 | − | 0.0771108i | \(-0.975430\pi\) |
0.431731 | − | 0.902002i | \(-0.357903\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.18255e7 | + | 1.97538e7i | −0.400441 | + | 0.668912i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.45695e6 | − | 1.11838e7i | −0.217528 | − | 0.376770i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.04933e7 | − | 1.81750e7i | 0.351704 | − | 0.609169i | −0.634844 | − | 0.772640i | \(-0.718936\pi\) |
0.986548 | + | 0.163471i | \(0.0522691\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.97860e6 | −0.132670 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.21433e6 | 0.106640 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.70372e7 | + | 2.95092e7i | −0.562359 | + | 0.974034i | 0.434931 | + | 0.900464i | \(0.356773\pi\) |
−0.997290 | + | 0.0735703i | \(0.976561\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.14944e6 | − | 7.18704e6i | −0.136269 | − | 0.236026i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.62296e7 | + | 2.71106e7i | −0.530292 | + | 0.885821i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.38274e6 | + | 1.27873e7i | 0.240009 | + | 0.415707i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.42227e6 | − | 9.39165e6i | 0.175387 | − | 0.303779i | −0.764908 | − | 0.644139i | \(-0.777216\pi\) |
0.940295 | + | 0.340360i | \(0.110549\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.50108e7 | 0.804922 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.18583e6 | −0.0699937 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.78414e6 | − | 1.17505e7i | 0.216151 | − | 0.374384i | −0.737477 | − | 0.675372i | \(-0.763983\pi\) |
0.953628 | + | 0.300988i | \(0.0973163\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 215199. | + | 372735.i | 0.00682223 | + | 0.0118164i |
(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 | 336.6.q.l.193.4 | 10 | ||
4.3 | odd | 2 | 168.6.q.c.25.4 | ✓ | 10 | ||
7.2 | even | 3 | inner | 336.6.q.l.289.4 | 10 | ||
12.11 | even | 2 | 504.6.s.c.361.2 | 10 | |||
28.23 | odd | 6 | 168.6.q.c.121.4 | yes | 10 | ||
84.23 | even | 6 | 504.6.s.c.289.2 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.6.q.c.25.4 | ✓ | 10 | 4.3 | odd | 2 | ||
168.6.q.c.121.4 | yes | 10 | 28.23 | odd | 6 | ||
336.6.q.l.193.4 | 10 | 1.1 | even | 1 | trivial | ||
336.6.q.l.289.4 | 10 | 7.2 | even | 3 | inner | ||
504.6.s.c.289.2 | 10 | 84.23 | even | 6 | |||
504.6.s.c.361.2 | 10 | 12.11 | even | 2 |