Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,6,Mod(107,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.107");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(72.1727189158\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 252 x^{14} + 27174 x^{12} - 1635700 x^{10} + 60061815 x^{8} - 1376564028 x^{6} + \cdots + 498214340649 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{8}\cdot 5^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 107.5 | ||
Root | \(-5.79464 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.107 |
Dual form | 450.6.f.f.143.5 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.82843 | − | 2.82843i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 16.0000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −158.675 | − | 158.675i | −1.22395 | − | 1.22395i | −0.966215 | − | 0.257737i | \(-0.917023\pi\) |
−0.257737 | − | 0.966215i | \(-0.582977\pi\) | |||||||
\(8\) | −45.2548 | − | 45.2548i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 147.071i | − | 0.366476i | −0.983069 | − | 0.183238i | \(-0.941342\pi\) | ||
0.983069 | − | 0.183238i | \(-0.0586579\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −516.434 | + | 516.434i | −0.847532 | + | 0.847532i | −0.989825 | − | 0.142292i | \(-0.954553\pi\) |
0.142292 | + | 0.989825i | \(0.454553\pi\) | |||||||
\(14\) | −897.604 | −1.22395 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −256.000 | −0.250000 | ||||||||
\(17\) | −1093.40 | + | 1093.40i | −0.917607 | + | 0.917607i | −0.996855 | − | 0.0792478i | \(-0.974748\pi\) |
0.0792478 | + | 0.996855i | \(0.474748\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1175.84i | − | 0.747248i | −0.927580 | − | 0.373624i | \(-0.878115\pi\) | ||
0.927580 | − | 0.373624i | \(-0.121885\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −415.980 | − | 415.980i | −0.183238 | − | 0.183238i | ||||
\(23\) | 3134.18 | + | 3134.18i | 1.23539 | + | 1.23539i | 0.961865 | + | 0.273525i | \(0.0881897\pi\) |
0.273525 | + | 0.961865i | \(0.411810\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2921.39i | 0.847532i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2538.81 | + | 2538.81i | −0.611976 | + | 0.611976i | ||||
\(29\) | 1863.75 | 0.411522 | 0.205761 | − | 0.978602i | \(-0.434033\pi\) | ||||
0.205761 | + | 0.978602i | \(0.434033\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3287.55 | −0.614424 | −0.307212 | − | 0.951641i | \(-0.599396\pi\) | ||||
−0.307212 | + | 0.951641i | \(0.599396\pi\) | |||||||
\(32\) | −724.077 | + | 724.077i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6185.20i | 0.917607i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1680.28 | − | 1680.28i | −0.201779 | − | 0.201779i | 0.598983 | − | 0.800762i | \(-0.295572\pi\) |
−0.800762 | + | 0.598983i | \(0.795572\pi\) | |||||||
\(38\) | −3325.78 | − | 3325.78i | −0.373624 | − | 0.373624i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9099.78i | − | 0.845418i | −0.906266 | − | 0.422709i | \(-0.861079\pi\) | ||
0.906266 | − | 0.422709i | \(-0.138921\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13737.1 | − | 13737.1i | 1.13298 | − | 1.13298i | 0.143306 | − | 0.989678i | \(-0.454227\pi\) |
0.989678 | − | 0.143306i | \(-0.0457734\pi\) | |||||||
\(44\) | −2353.14 | −0.183238 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 17729.6 | 1.23539 | ||||||||
\(47\) | 887.609 | − | 887.609i | 0.0586107 | − | 0.0586107i | −0.677194 | − | 0.735805i | \(-0.736804\pi\) |
0.735805 | + | 0.677194i | \(0.236804\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 33548.8i | 1.99612i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 8262.94 | + | 8262.94i | 0.423766 | + | 0.423766i | ||||
\(53\) | 16360.3 | + | 16360.3i | 0.800020 | + | 0.800020i | 0.983098 | − | 0.183078i | \(-0.0586061\pi\) |
−0.183078 | + | 0.983098i | \(0.558606\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 14361.7i | 0.611976i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5271.49 | − | 5271.49i | 0.205761 | − | 0.205761i | ||||
\(59\) | −957.597 | −0.0358140 | −0.0179070 | − | 0.999840i | \(-0.505700\pi\) | ||||
−0.0179070 | + | 0.999840i | \(0.505700\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 19303.4 | 0.664215 | 0.332107 | − | 0.943242i | \(-0.392240\pi\) | ||||
0.332107 | + | 0.943242i | \(0.392240\pi\) | |||||||
\(62\) | −9298.59 | + | 9298.59i | −0.307212 | + | 0.307212i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 35783.9 | + | 35783.9i | 0.973868 | + | 0.973868i | 0.999667 | − | 0.0257987i | \(-0.00821288\pi\) |
−0.0257987 | + | 0.999667i | \(0.508213\pi\) | |||||||
\(68\) | 17494.4 | + | 17494.4i | 0.458804 | + | 0.458804i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 25982.7i | − | 0.611700i | −0.952080 | − | 0.305850i | \(-0.901059\pi\) | ||
0.952080 | − | 0.305850i | \(-0.0989405\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −52858.1 | + | 52858.1i | −1.16093 | + | 1.16093i | −0.176652 | + | 0.984273i | \(0.556527\pi\) |
−0.984273 | + | 0.176652i | \(0.943473\pi\) | |||||||
\(74\) | −9505.07 | −0.201779 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −18813.5 | −0.373624 | ||||||||
\(77\) | −23336.6 | + | 23336.6i | −0.448549 | + | 0.448549i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 16371.2i | − | 0.295130i | −0.989052 | − | 0.147565i | \(-0.952856\pi\) | ||
0.989052 | − | 0.147565i | \(-0.0471436\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −25738.1 | − | 25738.1i | −0.422709 | − | 0.422709i | ||||
\(83\) | 69565.0 | + | 69565.0i | 1.10840 | + | 1.10840i | 0.993361 | + | 0.115036i | \(0.0366983\pi\) |
0.115036 | + | 0.993361i | \(0.463302\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 77708.8i | − | 1.13298i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6655.67 | + | 6655.67i | −0.0916190 | + | 0.0916190i | ||||
\(89\) | −133670. | −1.78879 | −0.894395 | − | 0.447278i | \(-0.852394\pi\) | ||||
−0.894395 | + | 0.447278i | \(0.852394\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 163891. | 2.07468 | ||||||||
\(92\) | 50146.9 | − | 50146.9i | 0.617695 | − | 0.617695i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 5021.08i | − | 0.0586107i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8350.12 | + | 8350.12i | 0.0901080 | + | 0.0901080i | 0.750724 | − | 0.660616i | \(-0.229705\pi\) |
−0.660616 | + | 0.750724i | \(0.729705\pi\) | |||||||
\(98\) | 94890.3 | + | 94890.3i | 0.998060 | + | 0.998060i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 15700.1i | − | 0.153144i | −0.997064 | − | 0.0765718i | \(-0.975603\pi\) | ||
0.997064 | − | 0.0765718i | \(-0.0243975\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −71583.6 | + | 71583.6i | −0.664845 | + | 0.664845i | −0.956518 | − | 0.291673i | \(-0.905788\pi\) |
0.291673 | + | 0.956518i | \(0.405788\pi\) | |||||||
\(104\) | 46742.2 | 0.423766 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 92547.7 | 0.800020 | ||||||||
\(107\) | −71776.6 | + | 71776.6i | −0.606071 | + | 0.606071i | −0.941917 | − | 0.335846i | \(-0.890978\pi\) |
0.335846 | + | 0.941917i | \(0.390978\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 214412.i | 1.72855i | 0.503020 | + | 0.864275i | \(0.332222\pi\) | ||||
−0.503020 | + | 0.864275i | \(0.667778\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 40620.9 | + | 40620.9i | 0.305988 | + | 0.305988i | ||||
\(113\) | −60197.8 | − | 60197.8i | −0.443491 | − | 0.443491i | 0.449693 | − | 0.893183i | \(-0.351534\pi\) |
−0.893183 | + | 0.449693i | \(0.851534\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 29820.0i | − | 0.205761i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2708.49 | + | 2708.49i | −0.0179070 | + | 0.0179070i | ||||
\(119\) | 346991. | 2.24622 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 139421. | 0.865695 | ||||||||
\(122\) | 54598.2 | − | 54598.2i | 0.332107 | − | 0.332107i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 52600.8i | 0.307212i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 149979. | + | 149979.i | 0.825125 | + | 0.825125i | 0.986838 | − | 0.161713i | \(-0.0517018\pi\) |
−0.161713 | + | 0.986838i | \(0.551702\pi\) | |||||||
\(128\) | 11585.2 | + | 11585.2i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 296250.i | − | 1.50827i | −0.656717 | − | 0.754137i | \(-0.728055\pi\) | ||
0.656717 | − | 0.754137i | \(-0.271945\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −186577. | + | 186577.i | −0.914596 | + | 0.914596i | ||||
\(134\) | 202424. | 0.973868 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 98963.3 | 0.458804 | ||||||||
\(137\) | 279939. | − | 279939.i | 1.27427 | − | 1.27427i | 0.330448 | − | 0.943824i | \(-0.392800\pi\) |
0.943824 | − | 0.330448i | \(-0.107200\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 271547.i | 1.19209i | 0.802951 | + | 0.596045i | \(0.203262\pi\) | ||||
−0.802951 | + | 0.596045i | \(0.796738\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −73490.1 | − | 73490.1i | −0.305850 | − | 0.305850i | ||||
\(143\) | 75952.4 | + | 75952.4i | 0.310600 | + | 0.310600i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 299010.i | 1.16093i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −26884.4 | + | 26884.4i | −0.100890 | + | 0.100890i | ||||
\(149\) | 74640.5 | 0.275429 | 0.137714 | − | 0.990472i | \(-0.456024\pi\) | ||||
0.137714 | + | 0.990472i | \(0.456024\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 101065. | 0.360711 | 0.180356 | − | 0.983601i | \(-0.442275\pi\) | ||||
0.180356 | + | 0.983601i | \(0.442275\pi\) | |||||||
\(152\) | −53212.5 | + | 53212.5i | −0.186812 | + | 0.186812i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 132011.i | 0.448549i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −179927. | − | 179927.i | −0.582569 | − | 0.582569i | 0.353040 | − | 0.935608i | \(-0.385148\pi\) |
−0.935608 | + | 0.353040i | \(0.885148\pi\) | |||||||
\(158\) | −46304.9 | − | 46304.9i | −0.147565 | − | 0.147565i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 994634.i | − | 3.02412i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −451895. | + | 451895.i | −1.33220 | + | 1.33220i | −0.428796 | + | 0.903402i | \(0.641062\pi\) |
−0.903402 | + | 0.428796i | \(0.858938\pi\) | |||||||
\(164\) | −145597. | −0.422709 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 393519. | 1.10840 | ||||||||
\(167\) | −485733. | + | 485733.i | −1.34774 | + | 1.34774i | −0.459634 | + | 0.888109i | \(0.652019\pi\) |
−0.888109 | + | 0.459634i | \(0.847981\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 162115.i | − | 0.436622i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −219794. | − | 219794.i | −0.566492 | − | 0.566492i | ||||
\(173\) | 258825. | + | 258825.i | 0.657493 | + | 0.657493i | 0.954786 | − | 0.297293i | \(-0.0960839\pi\) |
−0.297293 | + | 0.954786i | \(0.596084\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 37650.2i | 0.0916190i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −378076. | + | 378076.i | −0.894395 | + | 0.894395i | ||||
\(179\) | 643315. | 1.50069 | 0.750345 | − | 0.661046i | \(-0.229887\pi\) | ||||
0.750345 | + | 0.661046i | \(0.229887\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −253825. | −0.575887 | −0.287944 | − | 0.957647i | \(-0.592972\pi\) | ||||
−0.287944 | + | 0.957647i | \(0.592972\pi\) | |||||||
\(182\) | 463553. | − | 463553.i | 1.03734 | − | 1.03734i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 283673.i | − | 0.617695i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 160807. | + | 160807.i | 0.336281 | + | 0.336281i | ||||
\(188\) | −14201.7 | − | 14201.7i | −0.0293054 | − | 0.0293054i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 452729.i | 0.897956i | 0.893543 | + | 0.448978i | \(0.148212\pi\) | ||||
−0.893543 | + | 0.448978i | \(0.851788\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −449759. | + | 449759.i | −0.869133 | + | 0.869133i | −0.992376 | − | 0.123244i | \(-0.960670\pi\) |
0.123244 | + | 0.992376i | \(0.460670\pi\) | |||||||
\(194\) | 47235.4 | 0.0901080 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 536780. | 0.998060 | ||||||||
\(197\) | 142034. | − | 142034.i | 0.260751 | − | 0.260751i | −0.564608 | − | 0.825359i | \(-0.690973\pi\) |
0.825359 | + | 0.564608i | \(0.190973\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 721560.i | − | 1.29163i | −0.763492 | − | 0.645817i | \(-0.776517\pi\) | ||
0.763492 | − | 0.645817i | \(-0.223483\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −44406.6 | − | 44406.6i | −0.0765718 | − | 0.0765718i | ||||
\(203\) | −295732. | − | 295732.i | −0.503683 | − | 0.503683i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 404938.i | 0.664845i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 132207. | − | 132207.i | 0.211883 | − | 0.211883i | ||||
\(209\) | −172932. | −0.273848 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 252159. | 0.389913 | 0.194956 | − | 0.980812i | \(-0.437543\pi\) | ||||
0.194956 | + | 0.980812i | \(0.437543\pi\) | |||||||
\(212\) | 261764. | − | 261764.i | 0.400010 | − | 0.400010i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 406030.i | 0.606071i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 521653. | + | 521653.i | 0.752025 | + | 0.752025i | ||||
\(218\) | 606447. | + | 606447.i | 0.864275 | + | 0.864275i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.12934e6i | − | 1.55540i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 334048. | − | 334048.i | 0.449828 | − | 0.449828i | −0.445469 | − | 0.895297i | \(-0.646963\pi\) |
0.895297 | + | 0.445469i | \(0.146963\pi\) | |||||||
\(224\) | 229787. | 0.305988 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −340530. | −0.443491 | ||||||||
\(227\) | −42990.2 | + | 42990.2i | −0.0553738 | + | 0.0553738i | −0.734251 | − | 0.678878i | \(-0.762467\pi\) |
0.678878 | + | 0.734251i | \(0.262467\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.31576e6i | 1.65801i | 0.559240 | + | 0.829006i | \(0.311093\pi\) | ||||
−0.559240 | + | 0.829006i | \(0.688907\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −84343.8 | − | 84343.8i | −0.102880 | − | 0.102880i | ||||
\(233\) | −842302. | − | 842302.i | −1.01643 | − | 1.01643i | −0.999863 | − | 0.0165689i | \(-0.994726\pi\) |
−0.0165689 | − | 0.999863i | \(-0.505274\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 15321.6i | 0.0179070i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 981440. | − | 981440.i | 1.12311 | − | 1.12311i | ||||
\(239\) | −1.06608e6 | −1.20725 | −0.603624 | − | 0.797269i | \(-0.706277\pi\) | ||||
−0.603624 | + | 0.797269i | \(0.706277\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 51058.8 | 0.0566275 | 0.0283138 | − | 0.999599i | \(-0.490986\pi\) | ||||
0.0283138 | + | 0.999599i | \(0.490986\pi\) | |||||||
\(242\) | 394342. | − | 394342.i | 0.432848 | − | 0.432848i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 308854.i | − | 0.332107i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 607244. | + | 607244.i | 0.633317 | + | 0.633317i | ||||
\(248\) | 148777. | + | 148777.i | 0.153606 | + | 0.153606i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 516422.i | − | 0.517393i | −0.965959 | − | 0.258697i | \(-0.916707\pi\) | ||
0.965959 | − | 0.258697i | \(-0.0832930\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 460947. | − | 460947.i | 0.452741 | − | 0.452741i | ||||
\(254\) | 848407. | 0.825125 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −887334. | + | 887334.i | −0.838020 | + | 0.838020i | −0.988598 | − | 0.150578i | \(-0.951887\pi\) |
0.150578 | + | 0.988598i | \(0.451887\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 533237.i | 0.493936i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −837922. | − | 837922.i | −0.754137 | − | 0.754137i | ||||
\(263\) | −624251. | − | 624251.i | −0.556506 | − | 0.556506i | 0.371805 | − | 0.928311i | \(-0.378739\pi\) |
−0.928311 | + | 0.371805i | \(0.878739\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.05544e6i | 0.914596i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 572542. | − | 572542.i | 0.486934 | − | 0.486934i | ||||
\(269\) | −341395. | −0.287658 | −0.143829 | − | 0.989603i | \(-0.545942\pi\) | ||||
−0.143829 | + | 0.989603i | \(0.545942\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −706610. | −0.584463 | −0.292231 | − | 0.956348i | \(-0.594398\pi\) | ||||
−0.292231 | + | 0.956348i | \(0.594398\pi\) | |||||||
\(272\) | 279910. | − | 279910.i | 0.229402 | − | 0.229402i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 1.58358e6i | − | 1.27427i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10908.2 | − | 10908.2i | −0.00854186 | − | 0.00854186i | 0.702823 | − | 0.711365i | \(-0.251923\pi\) |
−0.711365 | + | 0.702823i | \(0.751923\pi\) | |||||||
\(278\) | 768052. | + | 768052.i | 0.596045 | + | 0.596045i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.16368e6i | 1.63466i | 0.576171 | + | 0.817329i | \(0.304546\pi\) | ||||
−0.576171 | + | 0.817329i | \(0.695454\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −407593. | + | 407593.i | −0.302524 | + | 0.302524i | −0.842001 | − | 0.539476i | \(-0.818622\pi\) |
0.539476 | + | 0.842001i | \(0.318622\pi\) | |||||||
\(284\) | −415723. | −0.305850 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 429652. | 0.310600 | ||||||||
\(287\) | −1.44391e6 | + | 1.44391e6i | −1.03475 | + | 1.03475i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 971190.i | − | 0.684006i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 845729. | + | 845729.i | 0.580463 | + | 0.580463i | ||||
\(293\) | 60301.5 | + | 60301.5i | 0.0410354 | + | 0.0410354i | 0.727327 | − | 0.686291i | \(-0.240762\pi\) |
−0.686291 | + | 0.727327i | \(0.740762\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 152081.i | 0.100890i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 211115. | − | 211115.i | 0.137714 | − | 0.137714i | ||||
\(299\) | −3.23719e6 | −2.09407 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.35948e6 | −2.77344 | ||||||||
\(302\) | 285856. | − | 285856.i | 0.180356 | − | 0.180356i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 301015.i | 0.186812i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 132817. | + | 132817.i | 0.0804284 | + | 0.0804284i | 0.746177 | − | 0.665748i | \(-0.231887\pi\) |
−0.665748 | + | 0.746177i | \(0.731887\pi\) | |||||||
\(308\) | 373385. | + | 373385.i | 0.224275 | + | 0.224275i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 310276.i | 0.181906i | 0.995855 | + | 0.0909530i | \(0.0289913\pi\) | ||||
−0.995855 | + | 0.0909530i | \(0.971009\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 889368. | − | 889368.i | 0.513122 | − | 0.513122i | −0.402359 | − | 0.915482i | \(-0.631810\pi\) |
0.915482 | + | 0.402359i | \(0.131810\pi\) | |||||||
\(314\) | −1.01782e6 | −0.582569 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −261940. | −0.147565 | ||||||||
\(317\) | −2.29681e6 | + | 2.29681e6i | −1.28374 | + | 1.28374i | −0.345213 | + | 0.938524i | \(0.612193\pi\) |
−0.938524 | + | 0.345213i | \(0.887807\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 274104.i | − | 0.150813i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.81325e6 | − | 2.81325e6i | −1.51206 | − | 1.51206i | ||||
\(323\) | 1.28566e6 | + | 1.28566e6i | 0.685680 | + | 0.685680i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.55630e6i | 1.33220i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −411809. | + | 411809.i | −0.211354 | + | 0.211354i | ||||
\(329\) | −281683. | −0.143473 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.74088e6 | −1.37505 | −0.687527 | − | 0.726159i | \(-0.741304\pi\) | ||||
−0.687527 | + | 0.726159i | \(0.741304\pi\) | |||||||
\(332\) | 1.11304e6 | − | 1.11304e6i | 0.554199 | − | 0.554199i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.74772e6i | 1.34774i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −277606. | − | 277606.i | −0.133154 | − | 0.133154i | 0.637389 | − | 0.770542i | \(-0.280015\pi\) |
−0.770542 | + | 0.637389i | \(0.780015\pi\) | |||||||
\(338\) | −458530. | − | 458530.i | −0.218311 | − | 0.218311i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 483503.i | 0.225171i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.65651e6 | − | 2.65651e6i | 1.21920 | − | 1.21920i | ||||
\(344\) | −1.24334e6 | −0.566492 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.46414e6 | 0.657493 | ||||||||
\(347\) | 1.35770e6 | − | 1.35770e6i | 0.605313 | − | 0.605313i | −0.336405 | − | 0.941717i | \(-0.609211\pi\) |
0.941717 | + | 0.336405i | \(0.109211\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3.94136e6i | − | 1.73214i | −0.499924 | − | 0.866069i | \(-0.666639\pi\) | ||
0.499924 | − | 0.866069i | \(-0.333361\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 106491. | + | 106491.i | 0.0458095 | + | 0.0458095i | ||||
\(353\) | −3.03961e6 | − | 3.03961e6i | −1.29832 | − | 1.29832i | −0.929504 | − | 0.368812i | \(-0.879765\pi\) |
−0.368812 | − | 0.929504i | \(-0.620235\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.13872e6i | 0.894395i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.81957e6 | − | 1.81957e6i | 0.750345 | − | 0.750345i | ||||
\(359\) | 1.62458e6 | 0.665279 | 0.332640 | − | 0.943054i | \(-0.392061\pi\) | ||||
0.332640 | + | 0.943054i | \(0.392061\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.09350e6 | 0.441621 | ||||||||
\(362\) | −717924. | + | 717924.i | −0.287944 | + | 0.287944i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 2.62225e6i | − | 1.03734i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −363952. | − | 363952.i | −0.141052 | − | 0.141052i | 0.633055 | − | 0.774107i | \(-0.281801\pi\) |
−0.774107 | + | 0.633055i | \(0.781801\pi\) | |||||||
\(368\) | −802350. | − | 802350.i | −0.308848 | − | 0.308848i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 5.19195e6i | − | 1.95837i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.54530e6 | − | 1.54530e6i | 0.575096 | − | 0.575096i | −0.358452 | − | 0.933548i | \(-0.616695\pi\) |
0.933548 | + | 0.358452i | \(0.116695\pi\) | |||||||
\(374\) | 909664. | 0.336281 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −80337.2 | −0.0293054 | ||||||||
\(377\) | −962504. | + | 962504.i | −0.348778 | + | 0.348778i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.52657e6i | 0.903512i | 0.892142 | + | 0.451756i | \(0.149202\pi\) | ||||
−0.892142 | + | 0.451756i | \(0.850798\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.28051e6 | + | 1.28051e6i | 0.448978 | + | 0.448978i | ||||
\(383\) | −1.81889e6 | − | 1.81889e6i | −0.633592 | − | 0.633592i | 0.315375 | − | 0.948967i | \(-0.397870\pi\) |
−0.948967 | + | 0.315375i | \(0.897870\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.54422e6i | 0.869133i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 133602. | − | 133602.i | 0.0450540 | − | 0.0450540i | ||||
\(389\) | 3.17134e6 | 1.06260 | 0.531299 | − | 0.847185i | \(-0.321704\pi\) | ||||
0.531299 | + | 0.847185i | \(0.321704\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.85382e6 | −2.26721 | ||||||||
\(392\) | 1.51824e6 | − | 1.51824e6i | 0.499030 | − | 0.499030i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 803465.i | − | 0.260751i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.79311e6 | + | 3.79311e6i | 1.20787 | + | 1.20787i | 0.971716 | + | 0.236150i | \(0.0758858\pi\) |
0.236150 | + | 0.971716i | \(0.424114\pi\) | |||||||
\(398\) | −2.04088e6 | − | 2.04088e6i | −0.645817 | − | 0.645817i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.97722e6i | 0.924592i | 0.886726 | + | 0.462296i | \(0.152974\pi\) | ||||
−0.886726 | + | 0.462296i | \(0.847026\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.69780e6 | − | 1.69780e6i | 0.520744 | − | 0.520744i | ||||
\(404\) | −251202. | −0.0765718 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.67291e6 | −0.503683 | ||||||||
\(407\) | −247120. | + | 247120.i | −0.0739472 | + | 0.0739472i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 149571.i | 0.0442118i | 0.999756 | + | 0.0221059i | \(0.00703710\pi\) | ||||
−0.999756 | + | 0.0221059i | \(0.992963\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.14534e6 | + | 1.14534e6i | 0.332423 | + | 0.332423i | ||||
\(413\) | 151947. | + | 151947.i | 0.0438346 | + | 0.0438346i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 747876.i | − | 0.211883i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −489126. | + | 489126.i | −0.136924 | + | 0.136924i | ||||
\(419\) | −6.06070e6 | −1.68650 | −0.843252 | − | 0.537518i | \(-0.819362\pi\) | ||||
−0.843252 | + | 0.537518i | \(0.819362\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.60024e6 | 0.989979 | 0.494989 | − | 0.868899i | \(-0.335172\pi\) | ||||
0.494989 | + | 0.868899i | \(0.335172\pi\) | |||||||
\(422\) | 713212. | − | 713212.i | 0.194956 | − | 0.194956i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 1.48076e6i | − | 0.400010i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.06297e6 | − | 3.06297e6i | −0.812967 | − | 0.812967i | ||||
\(428\) | 1.14843e6 | + | 1.14843e6i | 0.303035 | + | 0.303035i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.61379e6i | 0.418460i | 0.977866 | + | 0.209230i | \(0.0670958\pi\) | ||||
−0.977866 | + | 0.209230i | \(0.932904\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.69226e6 | + | 4.69226e6i | −1.20271 | + | 1.20271i | −0.229376 | + | 0.973338i | \(0.573669\pi\) |
−0.973338 | + | 0.229376i | \(0.926331\pi\) | |||||||
\(434\) | 2.95092e6 | 0.752025 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.43058e6 | 0.864275 | ||||||||
\(437\) | 3.68530e6 | − | 3.68530e6i | 0.923142 | − | 0.923142i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.32229e6i | − | 0.575117i | −0.957763 | − | 0.287558i | \(-0.907156\pi\) | ||
0.957763 | − | 0.287558i | \(-0.0928435\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.19425e6 | − | 3.19425e6i | −0.777702 | − | 0.777702i | ||||
\(443\) | −3.43425e6 | − | 3.43425e6i | −0.831424 | − | 0.831424i | 0.156288 | − | 0.987712i | \(-0.450047\pi\) |
−0.987712 | + | 0.156288i | \(0.950047\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 1.88966e6i | − | 0.449828i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 649935. | − | 649935.i | 0.152994 | − | 0.152994i | ||||
\(449\) | 152617. | 0.0357262 | 0.0178631 | − | 0.999840i | \(-0.494314\pi\) | ||||
0.0178631 | + | 0.999840i | \(0.494314\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.33831e6 | −0.309825 | ||||||||
\(452\) | −963165. | + | 963165.i | −0.221745 | + | 0.221745i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 243189.i | 0.0553738i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.56661e6 | − | 2.56661e6i | −0.574870 | − | 0.574870i | 0.358616 | − | 0.933485i | \(-0.383249\pi\) |
−0.933485 | + | 0.358616i | \(0.883249\pi\) | |||||||
\(458\) | 3.72153e6 | + | 3.72153e6i | 0.829006 | + | 0.829006i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 4.24935e6i | − | 0.931257i | −0.884980 | − | 0.465629i | \(-0.845828\pi\) | ||
0.884980 | − | 0.465629i | \(-0.154172\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.95866e6 | + | 3.95866e6i | −0.858215 | + | 0.858215i | −0.991128 | − | 0.132913i | \(-0.957567\pi\) |
0.132913 | + | 0.991128i | \(0.457567\pi\) | |||||||
\(464\) | −477120. | −0.102880 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.76478e6 | −1.01643 | ||||||||
\(467\) | −246422. | + | 246422.i | −0.0522862 | + | 0.0522862i | −0.732766 | − | 0.680480i | \(-0.761771\pi\) |
0.680480 | + | 0.732766i | \(0.261771\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1.13560e7i | − | 2.38394i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 43335.9 | + | 43335.9i | 0.00895350 | + | 0.00895350i | ||||
\(473\) | −2.02033e6 | − | 2.02033e6i | −0.415212 | − | 0.415212i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 5.55186e6i | − | 1.12311i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.01534e6 | + | 3.01534e6i | −0.603624 | + | 0.603624i | ||||
\(479\) | 311522. | 0.0620369 | 0.0310184 | − | 0.999519i | \(-0.490125\pi\) | ||||
0.0310184 | + | 0.999519i | \(0.490125\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.73550e6 | 0.342029 | ||||||||
\(482\) | 144416. | − | 144416.i | 0.0283138 | − | 0.0283138i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 2.23074e6i | − | 0.432848i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.12519e6 | + | 1.12519e6i | 0.214983 | + | 0.214983i | 0.806380 | − | 0.591397i | \(-0.201423\pi\) |
−0.591397 | + | 0.806380i | \(0.701423\pi\) | |||||||
\(488\) | −873570. | − | 873570.i | −0.166054 | − | 0.166054i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.48585e6i | 1.21412i | 0.794654 | + | 0.607062i | \(0.207652\pi\) | ||||
−0.794654 | + | 0.607062i | \(0.792348\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.03783e6 | + | 2.03783e6i | −0.377615 | + | 0.377615i | ||||
\(494\) | 3.43509e6 | 0.633317 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 841612. | 0.153606 | ||||||||
\(497\) | −4.12281e6 | + | 4.12281e6i | −0.748691 | + | 0.748691i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.91058e6i | 1.06262i | 0.847177 | + | 0.531311i | \(0.178300\pi\) | ||||
−0.847177 | + | 0.531311i | \(0.821700\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.46066e6 | − | 1.46066e6i | −0.258697 | − | 0.258697i | ||||
\(503\) | 4.45794e6 | + | 4.45794e6i | 0.785623 | + | 0.785623i | 0.980773 | − | 0.195150i | \(-0.0625194\pi\) |
−0.195150 | + | 0.980773i | \(0.562519\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 2.60751e6i | − | 0.452741i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.39966e6 | − | 2.39966e6i | 0.412563 | − | 0.412563i | ||||
\(509\) | 1.00967e7 | 1.72736 | 0.863681 | − | 0.504038i | \(-0.168153\pi\) | ||||
0.863681 | + | 0.504038i | \(0.168153\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.67746e7 | 2.84183 | ||||||||
\(512\) | 185364. | − | 185364.i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.01952e6i | 0.838020i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −130542. | − | 130542.i | −0.0214794 | − | 0.0214794i | ||||
\(518\) | 1.50822e6 | + | 1.50822e6i | 0.246968 | + | 0.246968i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.57041e6i | 0.576266i | 0.957590 | + | 0.288133i | \(0.0930346\pi\) | ||||
−0.957590 | + | 0.288133i | \(0.906965\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −527646. | + | 527646.i | −0.0843506 | + | 0.0843506i | −0.748023 | − | 0.663673i | \(-0.768997\pi\) |
0.663673 | + | 0.748023i | \(0.268997\pi\) | |||||||
\(524\) | −4.74000e6 | −0.754137 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.53130e6 | −0.556506 | ||||||||
\(527\) | 3.59460e6 | − | 3.59460e6i | 0.563799 | − | 0.563799i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.32098e7i | 2.05238i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.98523e6 | + | 2.98523e6i | 0.457298 | + | 0.457298i | ||||
\(533\) | 4.69944e6 | + | 4.69944e6i | 0.716519 | + | 0.716519i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 3.23879e6i | − | 0.486934i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −965611. | + | 965611.i | −0.143829 | + | 0.143829i | ||||
\(539\) | 4.93405e6 | 0.731530 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.31558e6 | −1.07462 | −0.537311 | − | 0.843384i | \(-0.680560\pi\) | ||||
−0.537311 | + | 0.843384i | \(0.680560\pi\) | |||||||
\(542\) | −1.99860e6 | + | 1.99860e6i | −0.292231 | + | 0.292231i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 1.58341e6i | − | 0.229402i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.05132e6 | + | 2.05132e6i | 0.293133 | + | 0.293133i | 0.838317 | − | 0.545183i | \(-0.183540\pi\) |
−0.545183 | + | 0.838317i | \(0.683540\pi\) | |||||||
\(548\) | −4.47903e6 | − | 4.47903e6i | −0.637136 | − | 0.637136i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2.19148e6i | − | 0.307509i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.59771e6 | + | 2.59771e6i | −0.361226 | + | 0.361226i | ||||
\(554\) | −61705.9 | −0.00854186 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.34476e6 | 0.596045 | ||||||||
\(557\) | 7.01106e6 | − | 7.01106e6i | 0.957515 | − | 0.957515i | −0.0416185 | − | 0.999134i | \(-0.513251\pi\) |
0.999134 | + | 0.0416185i | \(0.0132514\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.41886e7i | 1.92048i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.11981e6 | + | 6.11981e6i | 0.817329 | + | 0.817329i | ||||
\(563\) | 5.99030e6 | + | 5.99030e6i | 0.796485 | + | 0.796485i | 0.982539 | − | 0.186055i | \(-0.0595702\pi\) |
−0.186055 | + | 0.982539i | \(0.559570\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.30569e6i | 0.302524i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.17584e6 | + | 1.17584e6i | −0.152925 | + | 0.152925i | ||||
\(569\) | 1.44748e6 | 0.187426 | 0.0937132 | − | 0.995599i | \(-0.470126\pi\) | ||||
0.0937132 | + | 0.995599i | \(0.470126\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.36363e6 | 1.20186 | 0.600930 | − | 0.799301i | \(-0.294797\pi\) | ||||
0.600930 | + | 0.799301i | \(0.294797\pi\) | |||||||
\(572\) | 1.21524e6 | − | 1.21524e6i | 0.155300 | − | 0.155300i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.16800e6i | 1.03475i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.33073e6 | − | 3.33073e6i | −0.416486 | − | 0.416486i | 0.467505 | − | 0.883991i | \(-0.345153\pi\) |
−0.883991 | + | 0.467505i | \(0.845153\pi\) | |||||||
\(578\) | −2.74694e6 | − | 2.74694e6i | −0.342003 | − | 0.342003i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 2.20765e7i | − | 2.71325i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.40612e6 | − | 2.40612e6i | 0.293188 | − | 0.293188i | ||||
\(584\) | 4.78417e6 | 0.580463 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 341117. | 0.0410354 | ||||||||
\(587\) | −2.42159e6 | + | 2.42159e6i | −0.290072 | + | 0.290072i | −0.837109 | − | 0.547037i | \(-0.815756\pi\) |
0.547037 | + | 0.837109i | \(0.315756\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.86563e6i | 0.459127i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 430151. | + | 430151.i | 0.0504448 | + | 0.0504448i | ||||
\(593\) | −3.52839e6 | − | 3.52839e6i | −0.412041 | − | 0.412041i | 0.470408 | − | 0.882449i | \(-0.344107\pi\) |
−0.882449 | + | 0.470408i | \(0.844107\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 1.19425e6i | − | 0.137714i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.15616e6 | + | 9.15616e6i | −1.04703 | + | 1.04703i | ||||
\(599\) | −8.61219e6 | −0.980723 | −0.490362 | − | 0.871519i | \(-0.663135\pi\) | ||||
−0.490362 | + | 0.871519i | \(0.663135\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.25949e7 | 1.42235 | 0.711176 | − | 0.703014i | \(-0.248163\pi\) | ||||
0.711176 | + | 0.703014i | \(0.248163\pi\) | |||||||
\(602\) | −1.23305e7 | + | 1.23305e7i | −1.38672 | + | 1.38672i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 1.61704e6i | − | 0.180356i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.82263e6 | + | 7.82263e6i | 0.861749 | + | 0.861749i | 0.991541 | − | 0.129792i | \(-0.0414309\pi\) |
−0.129792 | + | 0.991541i | \(0.541431\pi\) | |||||||
\(608\) | 851400. | + | 851400.i | 0.0934060 | + | 0.0934060i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 916783.i | 0.0993490i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.39579e6 | − | 5.39579e6i | 0.579967 | − | 0.579967i | −0.354927 | − | 0.934894i | \(-0.615494\pi\) |
0.934894 | + | 0.354927i | \(0.115494\pi\) | |||||||
\(614\) | 751329. | 0.0804284 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.11218e6 | 0.224275 | ||||||||
\(617\) | 7.83798e6 | − | 7.83798e6i | 0.828880 | − | 0.828880i | −0.158482 | − | 0.987362i | \(-0.550660\pi\) |
0.987362 | + | 0.158482i | \(0.0506600\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.59378e7i | − | 1.67187i | −0.548828 | − | 0.835935i | \(-0.684926\pi\) | ||
0.548828 | − | 0.835935i | \(-0.315074\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 877593. | + | 877593.i | 0.0909530 | + | 0.0909530i | ||||
\(623\) | 2.12102e7 | + | 2.12102e7i | 2.18939 | + | 2.18939i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 5.03103e6i | − | 0.513122i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.87883e6 | + | 2.87883e6i | −0.291284 | + | 0.291284i | ||||
\(629\) | 3.67443e6 | 0.370308 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.00728e7 | 1.00711 | 0.503555 | − | 0.863963i | \(-0.332025\pi\) | ||||
0.503555 | + | 0.863963i | \(0.332025\pi\) | |||||||
\(632\) | −740878. | + | 740878.i | −0.0737826 | + | 0.0737826i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.29927e7i | 1.28374i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.73257e7 | − | 1.73257e7i | −1.69178 | − | 1.69178i | ||||
\(638\) | −775283. | − | 775283.i | −0.0754064 | − | 0.0754064i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.57715e7i | 1.51610i | 0.652196 | + | 0.758050i | \(0.273848\pi\) | ||||
−0.652196 | + | 0.758050i | \(0.726152\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −516496. | + | 516496.i | −0.0492651 | + | 0.0492651i | −0.731310 | − | 0.682045i | \(-0.761091\pi\) |
0.682045 | + | 0.731310i | \(0.261091\pi\) | |||||||
\(644\) | −1.59141e7 | −1.51206 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.27282e6 | 0.685680 | ||||||||
\(647\) | −9.00208e6 | + | 9.00208e6i | −0.845439 | + | 0.845439i | −0.989560 | − | 0.144121i | \(-0.953965\pi\) |
0.144121 | + | 0.989560i | \(0.453965\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 140835.i | 0.0131250i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.23032e6 | + | 7.23032e6i | 0.666099 | + | 0.666099i | ||||
\(653\) | 1.28977e7 | + | 1.28977e7i | 1.18367 | + | 1.18367i | 0.978786 | + | 0.204884i | \(0.0656816\pi\) |
0.204884 | + | 0.978786i | \(0.434318\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.32954e6i | 0.211354i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −796721. | + | 796721.i | −0.0717367 | + | 0.0717367i | ||||
\(659\) | 4.33804e6 | 0.389117 | 0.194558 | − | 0.980891i | \(-0.437673\pi\) | ||||
0.194558 | + | 0.980891i | \(0.437673\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.05066e6 | −0.538641 | −0.269321 | − | 0.963051i | \(-0.586799\pi\) | ||||
−0.269321 | + | 0.963051i | \(0.586799\pi\) | |||||||
\(662\) | −7.75238e6 | + | 7.75238e6i | −0.687527 | + | 0.687527i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 6.29630e6i | − | 0.554199i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.84133e6 | + | 5.84133e6i | 0.508390 | + | 0.508390i | ||||
\(668\) | 7.77174e6 | + | 7.77174e6i | 0.673871 | + | 0.673871i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.83897e6i | − | 0.243419i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.05580e7 | + | 1.05580e7i | −0.898558 | + | 0.898558i | −0.995309 | − | 0.0967510i | \(-0.969155\pi\) |
0.0967510 | + | 0.995309i | \(0.469155\pi\) | |||||||
\(674\) | −1.57037e6 | −0.133154 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.59383e6 | −0.218311 | ||||||||
\(677\) | 1.56712e7 | − | 1.56712e7i | 1.31410 | − | 1.31410i | 0.395740 | − | 0.918362i | \(-0.370488\pi\) |
0.918362 | − | 0.395740i | \(-0.129512\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 2.64992e6i | − | 0.220576i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.36755e6 | + | 1.36755e6i | 0.112586 | + | 0.112586i | ||||
\(683\) | 7.35948e6 | + | 7.35948e6i | 0.603664 | + | 0.603664i | 0.941283 | − | 0.337619i | \(-0.109622\pi\) |
−0.337619 | + | 0.941283i | \(0.609622\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 1.50275e7i | − | 1.21920i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.51670e6 | + | 3.51670e6i | −0.283246 | + | 0.283246i | ||||
\(689\) | −1.68980e7 | −1.35609 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.57697e6 | 0.284984 | 0.142492 | − | 0.989796i | \(-0.454488\pi\) | ||||
0.142492 | + | 0.989796i | \(0.454488\pi\) | |||||||
\(692\) | 4.14120e6 | − | 4.14120e6i | 0.328747 | − | 0.328747i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 7.68030e6i | − | 0.605313i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.94970e6 | + | 9.94970e6i | 0.775761 | + | 0.775761i | ||||
\(698\) | −1.11479e7 | − | 1.11479e7i | −0.866069 | − | 0.866069i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.49735e6i | − | 0.115087i | −0.998343 | − | 0.0575437i | \(-0.981673\pi\) | ||
0.998343 | − | 0.0575437i | \(-0.0183269\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.97574e6 | + | 1.97574e6i | −0.150779 | + | 0.150779i | ||||
\(704\) | 602403. | 0.0458095 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.71946e7 | −1.29832 | ||||||||
\(707\) | −2.49122e6 | + | 2.49122e6i | −0.187441 | + | 0.187441i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.18203e6i | 0.387154i | 0.981085 | + | 0.193577i | \(0.0620090\pi\) | ||||
−0.981085 | + | 0.193577i | \(0.937991\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.04922e6 | + | 6.04922e6i | 0.447198 | + | 0.447198i | ||||
\(713\) | −1.03038e7 | − | 1.03038e7i | −0.759053 | − | 0.759053i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 1.02930e7i | − | 0.750345i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.59500e6 | − | 4.59500e6i | 0.332640 | − | 0.332640i | ||||
\(719\) | 6.23048e6 | 0.449468 | 0.224734 | − | 0.974420i | \(-0.427849\pi\) | ||||
0.224734 | + | 0.974420i | \(0.427849\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.27171e7 | 1.62748 | ||||||||
\(722\) | 3.09288e6 | − | 3.09288e6i | 0.220810 | − | 0.220810i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.06119e6i | 0.287944i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.01394e7 | − | 1.01394e7i | −0.711503 | − | 0.711503i | 0.255347 | − | 0.966850i | \(-0.417810\pi\) |
−0.966850 | + | 0.255347i | \(0.917810\pi\) | |||||||
\(728\) | −7.41685e6 | − | 7.41685e6i | −0.518670 | − | 0.518670i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.00403e7i | 2.07927i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.81889e6 | + | 2.81889e6i | −0.193784 | + | 0.193784i | −0.797329 | − | 0.603545i | \(-0.793754\pi\) |
0.603545 | + | 0.797329i | \(0.293754\pi\) | |||||||
\(734\) | −2.05882e6 | −0.141052 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.53877e6 | −0.308848 | ||||||||
\(737\) | 5.26277e6 | − | 5.26277e6i | 0.356899 | − | 0.356899i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.51555e7i | 1.02085i | 0.859924 | + | 0.510423i | \(0.170511\pi\) | ||||
−0.859924 | + | 0.510423i | \(0.829489\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.46850e7 | − | 1.46850e7i | −0.979187 | − | 0.979187i | ||||
\(743\) | −1.08129e7 | − | 1.08129e7i | −0.718570 | − | 0.718570i | 0.249742 | − | 0.968312i | \(-0.419654\pi\) |
−0.968312 | + | 0.249742i | \(0.919654\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 8.74153e6i | − | 0.575096i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.57292e6 | − | 2.57292e6i | 0.168140 | − | 0.168140i | ||||
\(749\) | 2.27784e7 | 1.48360 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.14862e6 | 0.268413 | 0.134207 | − | 0.990953i | \(-0.457151\pi\) | ||||
0.134207 | + | 0.990953i | \(0.457151\pi\) | |||||||
\(752\) | −227228. | + | 227228.i | −0.0146527 | + | 0.0146527i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.44475e6i | 0.348778i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.78607e6 | − | 3.78607e6i | −0.240131 | − | 0.240131i | 0.576773 | − | 0.816904i | \(-0.304312\pi\) |
−0.816904 | + | 0.576773i | \(0.804312\pi\) | |||||||
\(758\) | 7.14623e6 | + | 7.14623e6i | 0.451756 | + | 0.451756i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 5.97949e6i | − | 0.374285i | −0.982333 | − | 0.187142i | \(-0.940077\pi\) | ||
0.982333 | − | 0.187142i | \(-0.0599226\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.40218e7 | − | 3.40218e7i | 2.11566 | − | 2.11566i | ||||
\(764\) | 7.24367e6 | 0.448978 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.02892e7 | −0.633592 | ||||||||
\(767\) | 494536. | − | 494536.i | 0.0303535 | − | 0.0303535i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 9.77362e6i | − | 0.595991i | −0.954567 | − | 0.297995i | \(-0.903682\pi\) | ||
0.954567 | − | 0.297995i | \(-0.0963180\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.19614e6 | + | 7.19614e6i | 0.434566 | + | 0.434566i | ||||
\(773\) | −1.78140e7 | − | 1.78140e7i | −1.07229 | − | 1.07229i | −0.997175 | − | 0.0751134i | \(-0.976068\pi\) |
−0.0751134 | − | 0.997175i | \(-0.523932\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 755767.i | − | 0.0450540i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.96990e6 | − | 8.96990e6i | 0.531299 | − | 0.531299i | ||||
\(779\) | −1.06999e7 | −0.631737 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.82130e6 | −0.224173 | ||||||||
\(782\) | −1.93855e7 | + | 1.93855e7i | −1.13360 | + | 1.13360i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 8.58849e6i | − | 0.499030i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.48699e6 | + | 9.48699e6i | 0.545999 | + | 0.545999i | 0.925281 | − | 0.379282i | \(-0.123829\pi\) |
−0.379282 | + | 0.925281i | \(0.623829\pi\) | |||||||
\(788\) | −2.27254e6 | − | 2.27254e6i | −0.130376 | − | 0.130376i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.91038e7i | 1.08562i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.96891e6 | + | 9.96891e6i | −0.562943 | + | 0.562943i | ||||
\(794\) | 2.14571e7 | 1.20787 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.15450e7 | −0.645817 | ||||||||
\(797\) | 1.21012e7 | − | 1.21012e7i | 0.674812 | − | 0.674812i | −0.284010 | − | 0.958821i | \(-0.591665\pi\) |
0.958821 | + | 0.284010i | \(0.0916648\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.94102e6i | 0.107563i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 8.42085e6 | + | 8.42085e6i | 0.462296 | + | 0.462296i | ||||
\(803\) | 7.77389e6 | + | 7.77389e6i | 0.425451 | + | 0.425451i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 9.60421e6i | − | 0.520744i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −710505. | + | 710505.i | −0.0382859 | + | 0.0382859i | ||||
\(809\) | 707664. | 0.0380151 | 0.0190075 | − | 0.999819i | \(-0.493949\pi\) | ||||
0.0190075 | + | 0.999819i | \(0.493949\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.78088e7 | −1.48467 | −0.742335 | − | 0.670029i | \(-0.766282\pi\) | ||||
−0.742335 | + | 0.670029i | \(0.766282\pi\) | |||||||
\(812\) | −4.73170e6 | + | 4.73170e6i | −0.251842 | + | 0.251842i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.39792e6i | 0.0739472i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.61527e7 | − | 1.61527e7i | −0.846620 | − | 0.846620i | ||||
\(818\) | 423050. | + | 423050.i | 0.0221059 | + | 0.0221059i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.29079e7i | 0.668343i | 0.942512 | + | 0.334171i | \(0.108456\pi\) | ||||
−0.942512 | + | 0.334171i | \(0.891544\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.17626e6 | − | 6.17626e6i | 0.317853 | − | 0.317853i | −0.530089 | − | 0.847942i | \(-0.677842\pi\) |
0.847942 | + | 0.530089i | \(0.177842\pi\) | |||||||
\(824\) | 6.47901e6 | 0.332423 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 859543. | 0.0438346 | ||||||||
\(827\) | −1.93860e7 | + | 1.93860e7i | −0.985656 | + | 0.985656i | −0.999899 | − | 0.0142426i | \(-0.995466\pi\) |
0.0142426 | + | 0.999899i | \(0.495466\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1.85346e7i | − | 0.936693i | −0.883545 | − | 0.468346i | \(-0.844850\pi\) | ||
0.883545 | − | 0.468346i | \(-0.155150\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.11531e6 | − | 2.11531e6i | −0.105942 | − | 0.105942i | ||||
\(833\) | −3.66822e7 | − | 3.66822e7i | −1.83165 | − | 1.83165i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.76691e6i | 0.136924i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.71422e7 | + | 1.71422e7i | −0.843252 | + | 0.843252i | ||||
\(839\) | −2.29948e6 | −0.112778 | −0.0563891 | − | 0.998409i | \(-0.517959\pi\) | ||||
−0.0563891 | + | 0.998409i | \(0.517959\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.70376e7 | −0.830650 | ||||||||
\(842\) | 1.01830e7 | − | 1.01830e7i | 0.494989 | − | 0.494989i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 4.03454e6i | − | 0.194956i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.21227e7 | − | 2.21227e7i | −1.05957 | − | 1.05957i | ||||
\(848\) | −4.18823e6 | − | 4.18823e6i | −0.200005 | − | 0.200005i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.05326e7i | − | 0.498552i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.39924e6 | + | 6.39924e6i | −0.301131 | + | 0.301131i | −0.841456 | − | 0.540325i | \(-0.818301\pi\) |
0.540325 | + | 0.841456i | \(0.318301\pi\) | |||||||
\(854\) | −1.73268e7 | −0.812967 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.49648e6 | 0.303035 | ||||||||
\(857\) | 2.04306e7 | − | 2.04306e7i | 0.950232 | − | 0.950232i | −0.0485865 | − | 0.998819i | \(-0.515472\pi\) |
0.998819 | + | 0.0485865i | \(0.0154717\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 2.14389e7i | − | 0.991335i | −0.868512 | − | 0.495668i | \(-0.834923\pi\) | ||
0.868512 | − | 0.495668i | \(-0.165077\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.56449e6 | + | 4.56449e6i | 0.209230 | + | 0.209230i | ||||
\(863\) | 1.26808e7 | + | 1.26808e7i | 0.579587 | + | 0.579587i | 0.934789 | − | 0.355203i | \(-0.115588\pi\) |
−0.355203 | + | 0.934789i | \(0.615588\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.65434e7i | 1.20271i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.34645e6 | − | 8.34645e6i | 0.376013 | − | 0.376013i | ||||
\(869\) | −2.40774e6 | −0.108158 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.69600e7 | −1.65077 | ||||||||
\(872\) | 9.70316e6 | − | 9.70316e6i | 0.432137 | − | 0.432137i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 2.08472e7i | − | 0.923142i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.90955e7 | − | 1.90955e7i | −0.838361 | − | 0.838361i | 0.150282 | − | 0.988643i | \(-0.451982\pi\) |
−0.988643 | + | 0.150282i | \(0.951982\pi\) | |||||||
\(878\) | −6.56844e6 | − | 6.56844e6i | −0.287558 | − | 0.287558i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.44332e7i | 1.92871i | 0.264605 | + | 0.964357i | \(0.414759\pi\) | ||||
−0.264605 | + | 0.964357i | \(0.585241\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.91929e6 | + | 4.91929e6i | −0.212325 | + | 0.212325i | −0.805254 | − | 0.592929i | \(-0.797971\pi\) |
0.592929 | + | 0.805254i | \(0.297971\pi\) | |||||||
\(884\) | −1.80694e7 | −0.777702 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.94270e7 | −0.831424 | ||||||||
\(887\) | 2.51992e7 | − | 2.51992e7i | 1.07542 | − | 1.07542i | 0.0785053 | − | 0.996914i | \(-0.474985\pi\) |
0.996914 | − | 0.0785053i | \(-0.0250147\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 4.75958e7i | − | 2.01983i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.34477e6 | − | 5.34477e6i | −0.224914 | − | 0.224914i | ||||
\(893\) | −1.04369e6 | − | 1.04369e6i | −0.0437967 | − | 0.0437967i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 3.67658e6i | − | 0.152994i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 431666. | − | 431666.i | 0.0178631 | − | 0.0178631i | ||||
\(899\) | −6.12717e6 | −0.252849 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.57767e7 | −1.46821 | ||||||||
\(902\) | −3.78532e6 | + | 3.78532e6i | −0.154913 | + | 0.154913i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.44848e6i | 0.221745i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.60527e6 | − | 1.60527e6i | −0.0647933 | − | 0.0647933i | 0.673968 | − | 0.738761i | \(-0.264589\pi\) |
−0.738761 | + | 0.673968i | \(0.764589\pi\) | |||||||
\(908\) | 687843. | + | 687843.i | 0.0276869 | + | 0.0276869i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.28125e7i | − | 0.511493i | −0.966744 | − | 0.255746i | \(-0.917679\pi\) | ||
0.966744 | − | 0.255746i | \(-0.0823212\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.02310e7 | − | 1.02310e7i | 0.406201 | − | 0.406201i | ||||
\(914\) | −1.45189e7 | −0.574870 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.10521e7 | 0.829006 | ||||||||
\(917\) | −4.70076e7 | + | 4.70076e7i | −1.84606 | + | 1.84606i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.73416e7i | 1.06791i | 0.845512 | + | 0.533956i | \(0.179295\pi\) | ||||
−0.845512 | + | 0.533956i | \(0.820705\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.20190e7 | − | 1.20190e7i | −0.465629 | − | 0.465629i | ||||
\(923\) | 1.34183e7 | + | 1.34183e7i | 0.518435 | + | 0.518435i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.23936e7i | 0.858215i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.34950e6 | + | 1.34950e6i | −0.0514402 | + | 0.0514402i | ||||
\(929\) | 2.92776e7 | 1.11300 | 0.556502 | − | 0.830846i | \(-0.312143\pi\) | ||||
0.556502 | + | 0.830846i | \(0.312143\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.94480e7 | 1.49160 | ||||||||
\(932\) | −1.34768e7 | + | 1.34768e7i | −0.508216 | + | 0.508216i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.39397e6i | 0.0522862i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.60245e7 | + | 1.60245e7i | 0.596260 | + | 0.596260i | 0.939315 | − | 0.343055i | \(-0.111462\pi\) |
−0.343055 | + | 0.939315i | \(0.611462\pi\) | |||||||
\(938\) | −3.21197e7 | − | 3.21197e7i | −1.19197 | − | 1.19197i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 3.40359e7i | − | 1.25304i | −0.779407 | − | 0.626518i | \(-0.784479\pi\) | ||
0.779407 | − | 0.626518i | \(-0.215521\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.85203e7 | − | 2.85203e7i | 1.04442 | − | 1.04442i | ||||
\(944\) | 245145. | 0.00895350 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.14287e7 | −0.415212 | ||||||||
\(947\) | −1.66968e7 | + | 1.66968e7i | −0.605003 | + | 0.605003i | −0.941636 | − | 0.336633i | \(-0.890712\pi\) |
0.336633 | + | 0.941636i | \(0.390712\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 5.45954e7i | − | 1.96784i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.57030e7 | − | 1.57030e7i | −0.561554 | − | 0.561554i | ||||
\(953\) | −8.06226e6 | − | 8.06226e6i | −0.287558 | − | 0.287558i | 0.548556 | − | 0.836114i | \(-0.315178\pi\) |
−0.836114 | + | 0.548556i | \(0.815178\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.70573e7i | 0.603624i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 881117. | − | 881117.i | 0.0310184 | − | 0.0310184i | ||||
\(959\) | −8.88389e7 | −3.11930 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.78212e7 | −0.622484 | ||||||||
\(962\) | 4.90874e6 | − | 4.90874e6i | 0.171014 | − | 0.171014i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 816940.i | − | 0.0283138i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.67667e7 | + | 3.67667e7i | 1.26441 | + | 1.26441i | 0.948932 | + | 0.315481i | \(0.102166\pi\) |
0.315481 | + | 0.948932i | \(0.397834\pi\) | |||||||
\(968\) | −6.30948e6 | − | 6.30948e6i | −0.216424 | − | 0.216424i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.24102e7i | 0.422408i | 0.977442 | + | 0.211204i | \(0.0677384\pi\) | ||||
−0.977442 | + | 0.211204i | \(0.932262\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.30879e7 | − | 4.30879e7i | 1.45906 | − | 1.45906i | ||||
\(974\) | 6.36506e6 | 0.214983 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.94166e6 | −0.166054 | ||||||||
\(977\) | 1.37859e7 | − | 1.37859e7i | 0.462059 | − | 0.462059i | −0.437271 | − | 0.899330i | \(-0.644055\pi\) |
0.899330 | + | 0.437271i | \(0.144055\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.96590e7i | 0.655548i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.83448e7 | + | 1.83448e7i | 0.607062 | + | 0.607062i | ||||
\(983\) | −1.44300e7 | − | 1.44300e7i | −0.476303 | − | 0.476303i | 0.427644 | − | 0.903947i | \(-0.359344\pi\) |
−0.903947 | + | 0.427644i | \(0.859344\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.15277e7i | 0.377615i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.71590e6 | − | 9.71590e6i | 0.316658 | − | 0.316658i | ||||
\(989\) | 8.61091e7 | 2.79936 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.26137e6 | −0.105491 | −0.0527455 | − | 0.998608i | \(-0.516797\pi\) | ||||
−0.0527455 | + | 0.998608i | \(0.516797\pi\) | |||||||
\(992\) | 2.38044e6 | − | 2.38044e6i | 0.0768029 | − | 0.0768029i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.33222e7i | 0.748691i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.93241e7 | + | 1.93241e7i | 0.615689 | + | 0.615689i | 0.944423 | − | 0.328733i | \(-0.106622\pi\) |
−0.328733 | + | 0.944423i | \(0.606622\pi\) | |||||||
\(998\) | 1.67177e7 | + | 1.67177e7i | 0.531311 | + | 0.531311i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 450.6.f.f.107.5 | yes | 16 | |
3.2 | odd | 2 | inner | 450.6.f.f.107.1 | ✓ | 16 | |
5.2 | odd | 4 | 450.6.f.g.143.8 | yes | 16 | ||
5.3 | odd | 4 | inner | 450.6.f.f.143.1 | yes | 16 | |
5.4 | even | 2 | 450.6.f.g.107.4 | yes | 16 | ||
15.2 | even | 4 | 450.6.f.g.143.4 | yes | 16 | ||
15.8 | even | 4 | inner | 450.6.f.f.143.5 | yes | 16 | |
15.14 | odd | 2 | 450.6.f.g.107.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.6.f.f.107.1 | ✓ | 16 | 3.2 | odd | 2 | inner | |
450.6.f.f.107.5 | yes | 16 | 1.1 | even | 1 | trivial | |
450.6.f.f.143.1 | yes | 16 | 5.3 | odd | 4 | inner | |
450.6.f.f.143.5 | yes | 16 | 15.8 | even | 4 | inner | |
450.6.f.g.107.4 | yes | 16 | 5.4 | even | 2 | ||
450.6.f.g.107.8 | yes | 16 | 15.14 | odd | 2 | ||
450.6.f.g.143.4 | yes | 16 | 15.2 | even | 4 | ||
450.6.f.g.143.8 | yes | 16 | 5.2 | odd | 4 |