Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(201,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.i (of order \(3\), 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: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.1783323.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 201.2 | ||
Root | \(1.09935 + 1.90412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.201 |
Dual form | 1900.2.i.c.501.2 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.182224 | + | 0.315621i | −0.105207 | + | 0.182224i | −0.913823 | − | 0.406113i | \(-0.866884\pi\) |
0.808616 | + | 0.588337i | \(0.200217\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.635552 | −0.240216 | −0.120108 | − | 0.992761i | \(-0.538324\pi\) | ||||
−0.120108 | + | 0.992761i | \(0.538324\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.43359 | + | 2.48305i | 0.477863 | + | 0.827683i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.63555 | 0.493137 | 0.246569 | − | 0.969125i | \(-0.420697\pi\) | ||||
0.246569 | + | 0.969125i | \(0.420697\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.500000 | − | 0.866025i | −0.138675 | − | 0.240192i | 0.788320 | − | 0.615265i | \(-0.210951\pi\) |
−0.926995 | + | 0.375073i | \(0.877618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.29804 | + | 5.71237i | −0.799891 | + | 1.38545i | 0.119795 | + | 0.992799i | \(0.461776\pi\) |
−0.919686 | + | 0.392654i | \(0.871557\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0466721 | − | 4.35865i | 0.0107073 | − | 0.999943i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.115813 | − | 0.200594i | 0.0252724 | − | 0.0437731i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.433589 | + | 0.750998i | 0.0904095 | + | 0.156594i | 0.907684 | − | 0.419655i | \(-0.137849\pi\) |
−0.817274 | + | 0.576249i | \(0.804516\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.13828 | −0.411512 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.54940 | + | 7.87979i | 0.844803 | + | 1.46324i | 0.885792 | + | 0.464082i | \(0.153616\pi\) |
−0.0409898 | + | 0.999160i | \(0.513051\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.86718 | −0.335355 | −0.167677 | − | 0.985842i | \(-0.553627\pi\) | ||||
−0.167677 | + | 0.985842i | \(0.553627\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.298037 | + | 0.516215i | −0.0518816 | + | 0.0898615i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.635552 | −0.104484 | −0.0522420 | − | 0.998634i | \(-0.516637\pi\) | ||||
−0.0522420 | + | 0.998634i | \(0.516637\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.364448 | 0.0583584 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.953328 | + | 1.65121i | −0.148885 | + | 0.257876i | −0.930816 | − | 0.365489i | \(-0.880902\pi\) |
0.781931 | + | 0.623365i | \(0.214235\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.98026 | − | 3.42991i | 0.301987 | − | 0.523057i | −0.674599 | − | 0.738184i | \(-0.735683\pi\) |
0.976586 | + | 0.215128i | \(0.0690168\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.54940 | + | 7.87979i | 0.663598 | + | 1.14939i | 0.979663 | + | 0.200649i | \(0.0643049\pi\) |
−0.316065 | + | 0.948738i | \(0.602362\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.59607 | −0.942296 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.20196 | − | 2.08186i | −0.168309 | − | 0.291519i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.93359 | − | 8.54523i | −0.677681 | − | 1.17378i | −0.975678 | − | 0.219210i | \(-0.929652\pi\) |
0.297997 | − | 0.954567i | \(-0.403681\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.36718 | + | 0.808981i | 0.181087 | + | 0.107152i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.54940 | + | 7.87979i | −0.592282 | + | 1.02586i | 0.401643 | + | 0.915796i | \(0.368439\pi\) |
−0.993924 | + | 0.110065i | \(0.964894\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.13555 | − | 1.96683i | −0.145393 | − | 0.251827i | 0.784127 | − | 0.620601i | \(-0.213111\pi\) |
−0.929519 | + | 0.368773i | \(0.879778\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.911120 | − | 1.57811i | −0.114790 | − | 0.198823i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.23163 | + | 10.7935i | 0.761314 | + | 1.31863i | 0.942173 | + | 0.335126i | \(0.108779\pi\) |
−0.180859 | + | 0.983509i | \(0.557888\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.316041 | −0.0380469 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.25136 | + | 2.16743i | −0.148510 | + | 0.257226i | −0.930677 | − | 0.365842i | \(-0.880781\pi\) |
0.782167 | + | 0.623069i | \(0.214114\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.201963 | + | 0.349810i | −0.0236380 | + | 0.0409422i | −0.877602 | − | 0.479389i | \(-0.840858\pi\) |
0.853964 | + | 0.520331i | \(0.174192\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.03948 | −0.118460 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.36445 | + | 9.29150i | −0.603548 | + | 1.04538i | 0.388732 | + | 0.921351i | \(0.372913\pi\) |
−0.992279 | + | 0.124024i | \(0.960420\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.91112 | + | 6.77426i | −0.434569 | + | 0.752695i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.8672 | 1.74165 | 0.870825 | − | 0.491594i | \(-0.163586\pi\) | ||||
0.870825 | + | 0.491594i | \(0.163586\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.31604 | −0.355517 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.271104 | − | 0.469566i | −0.0287370 | − | 0.0497739i | 0.851299 | − | 0.524680i | \(-0.175815\pi\) |
−0.880036 | + | 0.474907i | \(0.842482\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.317776 | + | 0.550404i | 0.0333120 | + | 0.0576980i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.340245 | − | 0.589321i | 0.0352817 | − | 0.0611097i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.68495 | + | 6.38253i | −0.374150 | + | 0.648047i | −0.990199 | − | 0.139660i | \(-0.955399\pi\) |
0.616049 | + | 0.787708i | \(0.288732\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.34471 | + | 4.06116i | 0.235652 | + | 0.408161i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.66248 | + | 8.07566i | 0.463935 | + | 0.803558i | 0.999153 | − | 0.0411556i | \(-0.0131039\pi\) |
−0.535218 | + | 0.844714i | \(0.679771\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.8672 | 1.07077 | 0.535387 | − | 0.844607i | \(-0.320166\pi\) | ||||
0.535387 | + | 0.844607i | \(0.320166\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.3304 | −1.09535 | −0.547677 | − | 0.836690i | \(-0.684488\pi\) | ||||
−0.547677 | + | 0.836690i | \(0.684488\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.61581 | + | 11.4589i | −0.633680 | + | 1.09757i | 0.353113 | + | 0.935581i | \(0.385123\pi\) |
−0.986793 | + | 0.161985i | \(0.948210\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.115813 | − | 0.200594i | 0.0109925 | − | 0.0190395i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.09334 | −0.667286 | −0.333643 | − | 0.942700i | \(-0.608278\pi\) | ||||
−0.333643 | + | 0.942700i | \(0.608278\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.43359 | − | 2.48305i | 0.132535 | − | 0.229558i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.09607 | − | 3.63051i | 0.192147 | − | 0.332808i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.32497 | −0.756815 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.347439 | − | 0.601781i | −0.0313275 | − | 0.0542608i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.13828 | + | 14.0959i | 0.722156 | + | 1.25081i | 0.960134 | + | 0.279540i | \(0.0901819\pi\) |
−0.237978 | + | 0.971270i | \(0.576485\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.721702 | + | 1.25002i | 0.0635423 | + | 0.110059i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.31778 | − | 9.21066i | 0.464616 | − | 0.804739i | −0.534568 | − | 0.845126i | \(-0.679526\pi\) |
0.999184 | + | 0.0403866i | \(0.0128590\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0296625 | + | 2.77015i | −0.00257207 | + | 0.240202i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.74864 | + | 3.02873i | 0.149396 | + | 0.258761i | 0.931004 | − | 0.365008i | \(-0.118934\pi\) |
−0.781608 | + | 0.623769i | \(0.785600\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.367178 | − | 0.635970i | −0.0311436 | − | 0.0539423i | 0.850034 | − | 0.526729i | \(-0.176582\pi\) |
−0.881177 | + | 0.472786i | \(0.843248\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.31604 | −0.279261 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.817776 | − | 1.41643i | −0.0683859 | − | 0.118448i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.20196 | − | 2.08186i | 0.0991362 | − | 0.171709i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.06914 | + | 8.78001i | −0.415280 | + | 0.719286i | −0.995458 | − | 0.0952036i | \(-0.969650\pi\) |
0.580178 | + | 0.814490i | \(0.302983\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.81331 | 0.228944 | 0.114472 | − | 0.993426i | \(-0.463482\pi\) | ||||
0.114472 | + | 0.993426i | \(0.463482\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −18.9121 | −1.52895 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.480261 | − | 0.831836i | 0.0383290 | − | 0.0663878i | −0.846225 | − | 0.532826i | \(-0.821130\pi\) |
0.884554 | + | 0.466439i | \(0.154463\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.59607 | 0.285187 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.275568 | − | 0.477298i | −0.0217178 | − | 0.0376164i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.13828 | −0.245809 | −0.122905 | − | 0.992418i | \(-0.539221\pi\) | ||||
−0.122905 | + | 0.992418i | \(0.539221\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.31778 | − | 9.21066i | −0.411502 | − | 0.712742i | 0.583552 | − | 0.812076i | \(-0.301662\pi\) |
−0.995054 | + | 0.0993334i | \(0.968329\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.8896 | − | 6.13262i | 0.832752 | − | 0.468973i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.18495 | − | 10.7127i | 0.470233 | − | 0.814468i | −0.529187 | − | 0.848505i | \(-0.677503\pi\) |
0.999421 | + | 0.0340371i | \(0.0108364\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.65802 | − | 2.87178i | −0.124624 | − | 0.215856i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.324970 | −0.0242894 | −0.0121447 | − | 0.999926i | \(-0.503866\pi\) | ||||
−0.0121447 | + | 0.999926i | \(0.503866\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.40666 | − | 7.63255i | −0.327544 | − | 0.567323i | 0.654480 | − | 0.756079i | \(-0.272888\pi\) |
−0.982024 | + | 0.188756i | \(0.939554\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.827699 | 0.0611853 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.39411 | + | 9.34287i | −0.394456 | + | 0.683219i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.35899 | 0.0988519 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.1921 | 1.82284 | 0.911420 | − | 0.411478i | \(-0.134987\pi\) | ||||
0.911420 | + | 0.411478i | \(0.134987\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.43632 | + | 16.3442i | −0.679241 | + | 1.17648i | 0.295969 | + | 0.955198i | \(0.404358\pi\) |
−0.975210 | + | 0.221282i | \(0.928976\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.36445 | 0.524695 | 0.262348 | − | 0.964973i | \(-0.415503\pi\) | ||||
0.262348 | + | 0.964973i | \(0.415503\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.38419 | − | 2.39748i | −0.0981224 | − | 0.169953i | 0.812785 | − | 0.582564i | \(-0.197950\pi\) |
−0.910907 | + | 0.412611i | \(0.864617\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.54221 | −0.320383 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.89138 | − | 5.00802i | −0.202935 | − | 0.351494i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.24318 | + | 2.15324i | −0.0864067 | + | 0.149661i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.0763346 | − | 7.12880i | 0.00528018 | − | 0.493109i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.46325 | + | 14.6588i | −0.582634 | + | 1.00915i | 0.412532 | + | 0.910943i | \(0.364645\pi\) |
−0.995166 | + | 0.0982088i | \(0.968689\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.456057 | − | 0.789915i | −0.0312485 | − | 0.0541241i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.18669 | 0.0805577 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.0736051 | − | 0.127488i | −0.00497377 | − | 0.00861482i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.59607 | 0.443700 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.32051 | − | 7.48334i | 0.289322 | − | 0.501121i | −0.684326 | − | 0.729176i | \(-0.739903\pi\) |
0.973648 | + | 0.228055i | \(0.0732367\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.9265 | −1.38894 | −0.694470 | − | 0.719521i | \(-0.744361\pi\) | ||||
−0.694470 | + | 0.719521i | \(0.744361\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.3754 | 1.47861 | 0.739303 | − | 0.673373i | \(-0.235155\pi\) | ||||
0.739303 | + | 0.673373i | \(0.235155\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.189418 | − | 0.328081i | 0.0124628 | − | 0.0215862i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.61854 | + | 16.6598i | −0.630132 | + | 1.09142i | 0.357393 | + | 0.933954i | \(0.383666\pi\) |
−0.987524 | + | 0.157466i | \(0.949668\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.95506 | − | 3.38627i | −0.126995 | − | 0.219962i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.13282 | −0.137961 | −0.0689804 | − | 0.997618i | \(-0.521975\pi\) | ||||
−0.0689804 | + | 0.997618i | \(0.521975\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.2316 | − | 21.1858i | −0.787908 | − | 1.36470i | −0.927246 | − | 0.374452i | \(-0.877831\pi\) |
0.139338 | − | 0.990245i | \(-0.455503\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.63282 | − | 8.02428i | −0.297196 | − | 0.514758i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.79804 | + | 2.13891i | −0.241663 | + | 0.136095i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.89138 | + | 5.00802i | −0.183234 | + | 0.317370i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.64002 | − | 2.84059i | −0.103517 | − | 0.179297i | 0.809614 | − | 0.586962i | \(-0.199676\pi\) |
−0.913131 | + | 0.407666i | \(0.866343\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.709157 | + | 1.22830i | 0.0445843 | + | 0.0772223i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.81778 | − | 6.61258i | −0.238146 | − | 0.412482i | 0.722036 | − | 0.691855i | \(-0.243206\pi\) |
−0.960182 | + | 0.279374i | \(0.909873\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.403926 | 0.0250988 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.0439 | + | 22.5928i | −0.807400 | + | 1.39846i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.36445 | − | 12.7556i | 0.454111 | − | 0.786544i | −0.544525 | − | 0.838744i | \(-0.683290\pi\) |
0.998637 | + | 0.0522005i | \(0.0166235\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.197607 | 0.0120933 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.73163 | − | 11.6595i | 0.410434 | − | 0.710893i | −0.584503 | − | 0.811392i | \(-0.698710\pi\) |
0.994937 | + | 0.100498i | \(0.0320437\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.93086 | + | 3.34435i | −0.117291 | + | 0.203155i | −0.918693 | − | 0.394971i | \(-0.870754\pi\) |
0.801402 | + | 0.598126i | \(0.204088\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.231626 | −0.0140186 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.2766 | 1.45864 | 0.729319 | − | 0.684174i | \(-0.239837\pi\) | ||||
0.729319 | + | 0.684174i | \(0.239837\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.67676 | − | 4.63629i | −0.160254 | − | 0.277568i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.248635 | − | 0.430649i | −0.0148323 | − | 0.0256904i | 0.858514 | − | 0.512790i | \(-0.171388\pi\) |
−0.873346 | + | 0.487100i | \(0.838055\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.57906 | + | 13.1273i | −0.450529 | + | 0.780338i | −0.998419 | − | 0.0562118i | \(-0.982098\pi\) |
0.547890 | + | 0.836550i | \(0.315431\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.605889 | − | 1.04943i | 0.0357645 | − | 0.0619460i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.2541 | − | 22.9568i | −0.779653 | − | 1.35040i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.34297 | − | 2.32610i | −0.0787265 | − | 0.136358i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.4094 | 0.783385 | 0.391692 | − | 0.920096i | \(-0.371890\pi\) | ||||
0.391692 | + | 0.920096i | \(0.371890\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.49727 | −0.202932 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.433589 | − | 0.750998i | 0.0250751 | − | 0.0434313i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.25856 | + | 2.17989i | −0.0725421 | + | 0.125647i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.39847 | −0.195237 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.1033 | − | 27.8917i | 0.919062 | − | 1.59186i | 0.118219 | − | 0.992988i | \(-0.462281\pi\) |
0.800843 | − | 0.598875i | \(-0.204385\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.98026 | + | 3.42991i | −0.112653 | + | 0.195121i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.3699 | 0.701433 | 0.350717 | − | 0.936482i | \(-0.385938\pi\) | ||||
0.350717 | + | 0.936482i | \(0.385938\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.3941 | + | 21.4672i | 0.700557 | + | 1.21340i | 0.968271 | + | 0.249901i | \(0.0803982\pi\) |
−0.267715 | + | 0.963498i | \(0.586268\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.65529 | + | 6.33115i | 0.205302 | + | 0.355593i | 0.950229 | − | 0.311553i | \(-0.100849\pi\) |
−0.744927 | + | 0.667146i | \(0.767516\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.44078 | + | 12.8878i | 0.416604 | + | 0.721579i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.06468 | − | 3.57612i | 0.115239 | − | 0.199600i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.7443 | + | 14.6416i | 1.37681 | + | 0.814680i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.41112 | − | 4.17618i | −0.133335 | − | 0.230943i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.89138 | − | 5.00802i | −0.159407 | − | 0.276101i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.4722 | 1.01532 | 0.507661 | − | 0.861557i | \(-0.330510\pi\) | ||||
0.507661 | + | 0.861557i | \(0.330510\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.911120 | − | 1.57811i | −0.0499291 | − | 0.0864797i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.2316 | − | 26.3819i | 0.829720 | − | 1.43712i | −0.0685388 | − | 0.997648i | \(-0.521834\pi\) |
0.898258 | − | 0.439468i | \(-0.144833\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.29258 | − | 2.23881i | 0.0702032 | − | 0.121595i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.05387 | −0.165376 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.64101 | 0.466571 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.6608 | − | 20.1970i | 0.625982 | − | 1.08423i | −0.362368 | − | 0.932035i | \(-0.618032\pi\) |
0.988350 | − | 0.152197i | \(-0.0486349\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.6894 | −0.946893 | −0.473446 | − | 0.880823i | \(-0.656990\pi\) | ||||
−0.473446 | + | 0.880823i | \(0.656990\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.06914 | + | 1.85181i | 0.0570665 | + | 0.0988421i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.13828 | 0.379932 | 0.189966 | − | 0.981791i | \(-0.439162\pi\) | ||||
0.189966 | + | 0.981791i | \(0.439162\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.763910 | + | 1.32313i | 0.0404304 | + | 0.0700275i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.0719 | − | 26.1052i | 0.795463 | − | 1.37778i | −0.127082 | − | 0.991892i | \(-0.540561\pi\) |
0.922545 | − | 0.385890i | \(-0.126106\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9956 | − | 0.406855i | −0.999771 | − | 0.0214134i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.51701 | − | 2.62754i | 0.0796224 | − | 0.137910i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.1015 | − | 26.1566i | −0.788294 | − | 1.36536i | −0.927012 | − | 0.375033i | \(-0.877631\pi\) |
0.138718 | − | 0.990332i | \(-0.455702\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.46672 | −0.284586 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.13555 | + | 5.43094i | 0.162790 | + | 0.281960i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.0449 | −1.50389 | −0.751945 | − | 0.659226i | \(-0.770884\pi\) | ||||
−0.751945 | + | 0.659226i | \(0.770884\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.54940 | − | 7.87979i | 0.234306 | − | 0.405830i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.76837 | 0.142202 | 0.0711009 | − | 0.997469i | \(-0.477349\pi\) | ||||
0.0711009 | + | 0.997469i | \(0.477349\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.93196 | −0.303904 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.3052 | − | 23.0453i | 0.679866 | − | 1.17756i | −0.295156 | − | 0.955449i | \(-0.595371\pi\) |
0.975021 | − | 0.222112i | \(-0.0712952\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.3555 | 0.577233 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.77830 | + | 4.81215i | 0.140865 | + | 0.243986i | 0.927823 | − | 0.373021i | \(-0.121678\pi\) |
−0.786957 | + | 0.617007i | \(0.788345\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.71997 | −0.289271 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.93805 | + | 3.35681i | 0.0977618 | + | 0.169328i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.35725 | − | 2.35083i | 0.0681186 | − | 0.117985i | −0.829955 | − | 0.557831i | \(-0.811634\pi\) |
0.898073 | + | 0.439846i | \(0.144967\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.868912 | − | 0.514150i | −0.0435000 | − | 0.0257397i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.94078 | − | 15.4859i | 0.446481 | − | 0.773328i | −0.551673 | − | 0.834061i | \(-0.686010\pi\) |
0.998154 | + | 0.0607322i | \(0.0193436\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.933589 | + | 1.61702i | 0.0465054 | + | 0.0805497i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.03948 | −0.0515250 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.1625 | − | 22.7981i | −0.650843 | − | 1.12729i | −0.982919 | − | 0.184040i | \(-0.941082\pi\) |
0.332076 | − | 0.943253i | \(-0.392251\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.27457 | −0.0628701 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.89138 | − | 5.00802i | 0.142276 | − | 0.246428i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.267634 | 0.0131061 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.3250 | 0.748674 | 0.374337 | − | 0.927293i | \(-0.377870\pi\) | ||||
0.374337 | + | 0.927293i | \(0.377870\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.9166 | + | 18.9081i | −0.532042 | + | 0.921523i | 0.467259 | + | 0.884121i | \(0.345242\pi\) |
−0.999300 | + | 0.0374023i | \(0.988092\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.0439 | + | 22.5928i | −0.634218 | + | 1.09850i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.721702 | + | 1.25002i | 0.0349256 | + | 0.0604929i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.596074 | 0.0287787 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.6427 | − | 20.1658i | −0.560811 | − | 0.971354i | −0.997426 | − | 0.0717050i | \(-0.977156\pi\) |
0.436615 | − | 0.899649i | \(-0.356177\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.95060 | − | 3.37854i | −0.0937398 | − | 0.162362i | 0.815342 | − | 0.578979i | \(-0.196549\pi\) |
−0.909082 | + | 0.416617i | \(0.863216\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.29357 | − | 1.85481i | 0.157553 | − | 0.0887276i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.73882 | − | 16.8681i | 0.464808 | − | 0.805072i | −0.534384 | − | 0.845242i | \(-0.679457\pi\) |
0.999193 | + | 0.0401697i | \(0.0127898\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.45606 | − | 16.3784i | −0.450288 | − | 0.779922i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.953328 | + | 1.65121i | 0.0452940 | + | 0.0784515i | 0.887784 | − | 0.460261i | \(-0.152244\pi\) |
−0.842490 | + | 0.538713i | \(0.818911\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.84744 | − | 3.19986i | −0.0873808 | − | 0.151348i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.05933 | −0.380343 | −0.190172 | − | 0.981751i | \(-0.560904\pi\) | ||||
−0.190172 | + | 0.981751i | \(0.560904\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.55922 | + | 2.70064i | −0.0734207 | + | 0.127168i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.512653 | + | 0.887941i | −0.0240865 | + | 0.0417191i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.3250 | −0.529760 | −0.264880 | − | 0.964281i | \(-0.585332\pi\) | ||||
−0.264880 | + | 0.964281i | \(0.585332\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.05213 | − | 12.2146i | 0.329165 | − | 0.570131i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.0521 | + | 17.4108i | −0.468174 | + | 0.810902i | −0.999338 | − | 0.0363671i | \(-0.988421\pi\) |
0.531164 | + | 0.847269i | \(0.321755\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.33043 | −0.0618303 | −0.0309151 | − | 0.999522i | \(-0.509842\pi\) | ||||
−0.0309151 | + | 0.999522i | \(0.509842\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.0844 | −0.466651 | −0.233326 | − | 0.972399i | \(-0.574961\pi\) | ||||
−0.233326 | + | 0.972399i | \(0.574961\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.96052 | − | 6.85982i | −0.182880 | − | 0.316757i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.175030 | + | 0.303161i | 0.00806496 | + | 0.0139689i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.23882 | − | 5.60980i | 0.148921 | − | 0.257939i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.1455 | − | 24.5007i | 0.647677 | − | 1.12181i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.44078 | − | 7.69166i | −0.202905 | − | 0.351441i | 0.746559 | − | 0.665320i | \(-0.231705\pi\) |
−0.949463 | + | 0.313879i | \(0.898371\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.317776 | + | 0.550404i | 0.0144893 | + | 0.0250963i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.200861 | 0.00913947 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.32497 | −0.241297 | −0.120649 | − | 0.992695i | \(-0.538497\pi\) | ||||
−0.120649 | + | 0.992695i | \(0.538497\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.571870 | − | 0.990508i | 0.0258609 | − | 0.0447923i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.70469 | − | 16.8090i | 0.437967 | − | 0.758580i | −0.559566 | − | 0.828786i | \(-0.689032\pi\) |
0.997533 | + | 0.0702054i | \(0.0223655\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −60.0164 | −2.70300 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.795307 | − | 1.37751i | 0.0356744 | − | 0.0617899i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.79357 | + | 10.0348i | −0.259356 | + | 0.449218i | −0.966070 | − | 0.258282i | \(-0.916844\pi\) |
0.706714 | + | 0.707500i | \(0.250177\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.87611 | 0.173172 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.5521 | + | 30.4012i | 0.782611 | + | 1.35552i | 0.930416 | + | 0.366505i | \(0.119446\pi\) |
−0.147805 | + | 0.989017i | \(0.547221\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.18669 | + | 3.78746i | 0.0971142 | + | 0.168207i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.93359 | + | 13.7414i | 0.351650 | + | 0.609076i | 0.986539 | − | 0.163528i | \(-0.0522873\pi\) |
−0.634889 | + | 0.772604i | \(0.718954\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.128358 | − | 0.222323i | 0.00567823 | − | 0.00983498i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.0997981 | + | 9.32002i | −0.00440619 | + | 0.411489i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.44078 | + | 12.8878i | 0.327245 | + | 0.566805i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.25409 | + | 3.90421i | 0.0989438 | + | 0.171376i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.6949 | 1.60763 | 0.803816 | − | 0.594878i | \(-0.202800\pi\) | ||||
0.803816 | + | 0.594878i | \(0.202800\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.5127 | − | 26.8687i | −0.678321 | − | 1.17489i | −0.975486 | − | 0.220060i | \(-0.929375\pi\) |
0.297165 | − | 0.954826i | \(-0.403959\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.15802 | − | 10.6660i | 0.268248 | − | 0.464618i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.1240 | − | 19.2673i | 0.483652 | − | 0.837710i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −26.0879 | −1.13212 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.90666 | 0.0825864 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.0592173 | − | 0.102567i | 0.00255542 | − | 0.00442611i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.7882 | −0.464682 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.79357 | + | 6.57066i | 0.163098 | + | 0.282495i | 0.935978 | − | 0.352058i | \(-0.114518\pi\) |
−0.772880 | + | 0.634552i | \(0.781185\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.21199 | 0.137840 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.3914 | − | 26.6587i | −0.658088 | − | 1.13984i | −0.981110 | − | 0.193450i | \(-0.938032\pi\) |
0.323022 | − | 0.946391i | \(-0.395301\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.25583 | − | 5.63926i | 0.138955 | − | 0.240678i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.5576 | − | 19.4615i | 1.47220 | − | 0.829087i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.40939 | − | 5.90523i | 0.144982 | − | 0.251116i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.5369 | + | 26.9106i | 0.658318 | + | 1.14024i | 0.981051 | + | 0.193750i | \(0.0620650\pi\) |
−0.322733 | + | 0.946490i | \(0.604602\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.96052 | −0.167512 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.96587 | − | 3.40499i | −0.0829992 | − | 0.143759i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.2766 | 0.980990 | 0.490495 | − | 0.871444i | \(-0.336816\pi\) | ||||
0.490495 | + | 0.871444i | \(0.336816\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.48572 | − | 4.30539i | 0.104390 | − | 0.180810i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.1976 | 1.01442 | 0.507208 | − | 0.861824i | \(-0.330678\pi\) | ||||
0.507208 | + | 0.861824i | \(0.330678\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.8475 | 1.24908 | 0.624540 | − | 0.780992i | \(-0.285286\pi\) | ||||
0.624540 | + | 0.780992i | \(0.285286\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.59061 | + | 7.95118i | −0.191776 | + | 0.332165i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.7882 | −1.40662 | −0.703311 | − | 0.710882i | \(-0.748296\pi\) | ||||
−0.703311 | + | 0.710882i | \(0.748296\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.43905 | − | 5.95661i | −0.142922 | − | 0.247548i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.0844 | −0.418372 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.06914 | − | 13.9762i | −0.334190 | − | 0.578833i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −15.3474 | + | 26.5825i | −0.633457 | + | 1.09718i | 0.353383 | + | 0.935479i | \(0.385031\pi\) |
−0.986840 | + | 0.161700i | \(0.948302\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0871451 | + | 8.13837i | −0.00359075 | + | 0.335336i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.34198 | + | 2.32438i | −0.0552017 | + | 0.0956121i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.49727 | + | 6.05745i | 0.143616 | + | 0.248750i | 0.928856 | − | 0.370442i | \(-0.120794\pi\) |
−0.785240 | + | 0.619192i | \(0.787460\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.00893 | 0.0412927 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.26837 | + | 3.92894i | 0.0926833 | + | 0.160532i | 0.908639 | − | 0.417582i | \(-0.137122\pi\) |
−0.815956 | + | 0.578114i | \(0.803789\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.0790 | 0.655874 | 0.327937 | − | 0.944700i | \(-0.393647\pi\) | ||||
0.327937 | + | 0.944700i | \(0.393647\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.8672 | + | 30.9469i | −0.727608 | + | 1.26025i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.0702 | 1.38287 | 0.691434 | − | 0.722439i | \(-0.256979\pi\) | ||||
0.691434 | + | 0.722439i | \(0.256979\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.10752 | 0.0854009 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.54940 | − | 7.87979i | 0.184049 | − | 0.318782i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.7191 | + | 34.1544i | −0.796446 | + | 1.37949i | 0.125471 | + | 0.992097i | \(0.459956\pi\) |
−0.921917 | + | 0.387388i | \(0.873377\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.6257 | − | 33.9928i | −0.790102 | − | 1.36850i | −0.925903 | − | 0.377761i | \(-0.876694\pi\) |
0.135801 | − | 0.990736i | \(-0.456639\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.3644 | 0.979290 | 0.489645 | − | 0.871922i | \(-0.337126\pi\) | ||||
0.489645 | + | 0.871922i | \(0.337126\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.927135 | − | 1.60584i | −0.0372046 | − | 0.0644403i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.172301 | + | 0.298433i | 0.00690308 | + | 0.0119565i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.23609 | + | 1.32313i | 0.0893008 | + | 0.0528408i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.09607 | − | 3.63051i | 0.0835759 | − | 0.144758i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.6949 | + | 30.6484i | 0.704422 | + | 1.22009i | 0.966900 | + | 0.255157i | \(0.0821270\pi\) |
−0.262478 | + | 0.964938i | \(0.584540\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.08442 | − | 5.34236i | −0.122595 | − | 0.212340i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.29804 | + | 5.71237i | 0.130673 | + | 0.226332i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.17577 | −0.283869 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.8546 | + | 30.9251i | −0.705216 | + | 1.22147i | 0.261398 | + | 0.965231i | \(0.415816\pi\) |
−0.966614 | + | 0.256238i | \(0.917517\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.5549 | − | 18.2816i | 0.416243 | − | 0.720954i | −0.579315 | − | 0.815104i | \(-0.696680\pi\) |
0.995558 | + | 0.0941496i | \(0.0300132\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −43.7058 | −1.71825 | −0.859126 | − | 0.511764i | \(-0.828992\pi\) | ||||
−0.859126 | + | 0.511764i | \(0.828992\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.44078 | + | 12.8878i | −0.292076 | + | 0.505891i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.216243 | + | 0.374544i | −0.00847524 | + | 0.0146795i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.1887 | 0.946576 | 0.473288 | − | 0.880908i | \(-0.343067\pi\) | ||||
0.473288 | + | 0.880908i | \(0.343067\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.15813 | −0.0451829 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.9956 | − | 29.4373i | −0.662056 | − | 1.14672i | −0.980074 | − | 0.198630i | \(-0.936351\pi\) |
0.318018 | − | 0.948085i | \(-0.396983\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.27830 | − | 3.94613i | −0.0886155 | − | 0.153487i | 0.818311 | − | 0.574776i | \(-0.194911\pi\) |
−0.906926 | + | 0.421290i | \(0.861578\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.20196 | + | 2.08186i | −0.0466804 | + | 0.0808528i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.94514 | + | 6.83318i | −0.152756 | + | 0.264582i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.57460 | + | 2.72729i | 0.0608775 | + | 0.105443i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.85725 | − | 3.21686i | −0.0716985 | − | 0.124185i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.7487 | 0.876900 | 0.438450 | − | 0.898756i | \(-0.355528\pi\) | ||||
0.438450 | + | 0.898756i | \(0.355528\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.6949 | 0.603203 | 0.301602 | − | 0.953434i | \(-0.402479\pi\) | ||||
0.301602 | + | 0.953434i | \(0.402479\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.34198 | − | 4.05643i | 0.0898769 | − | 0.155671i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.81331 | − | 6.60485i | 0.146126 | − | 0.253098i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.82770 | 0.337783 | 0.168891 | − | 0.985635i | \(-0.445981\pi\) | ||||
0.168891 | + | 0.985635i | \(0.445981\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.07733 | + | 7.06214i | −0.155560 | + | 0.269438i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.93359 | + | 8.54523i | −0.187955 | + | 0.325547i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.0198 | −0.875716 | −0.437858 | − | 0.899044i | \(-0.644263\pi\) | ||||
−0.437858 | + | 0.899044i | \(0.644263\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.49018 | − | 2.58107i | −0.0566074 | − | 0.0980469i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.28822 | − | 10.8915i | −0.238183 | − | 0.412546i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.50546 | − | 6.07163i | −0.132589 | − | 0.229650i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.95606 | − | 8.58414i | 0.187188 | − | 0.324219i | −0.757124 | − | 0.653271i | \(-0.773396\pi\) |
0.944312 | + | 0.329053i | \(0.106729\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.0296625 | + | 2.77015i | −0.00111874 | + | 0.104478i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.96325 | − | 5.13250i | −0.111445 | − | 0.193028i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.0521 | + | 31.2672i | 0.677962 | + | 1.17426i | 0.975594 | + | 0.219584i | \(0.0704700\pi\) |
−0.297632 | + | 0.954681i | \(0.596197\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −30.7617 | −1.15365 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.809587 | − | 1.40225i | −0.0303193 | − | 0.0525145i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.388651 | − | 0.673164i | 0.0145145 | − | 0.0251398i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.50546 | − | 16.4639i | 0.354494 | − | 0.614001i | −0.632537 | − | 0.774530i | \(-0.717987\pi\) |
0.987031 | + | 0.160529i | \(0.0513199\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.90666 | −0.257217 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.91558 | 0.331574 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.44351 | + | 2.50024i | −0.0535369 | + | 0.0927286i | −0.891552 | − | 0.452919i | \(-0.850383\pi\) |
0.838015 | + | 0.545647i | \(0.183716\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.0899 | −0.744069 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.0619 | + | 22.6240i | 0.483114 | + | 0.836777i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −44.9463 | −1.66013 | −0.830066 | − | 0.557666i | \(-0.811697\pi\) | ||||
−0.830066 | + | 0.557666i | \(0.811697\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.1921 | + | 17.6533i | 0.375433 | + | 0.650268i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.4956 | + | 44.1597i | −0.937872 | + | 1.62444i | −0.168442 | + | 0.985711i | \(0.553874\pi\) |
−0.769430 | + | 0.638731i | \(0.779460\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0170096 | − | 1.58850i | 0.000624862 | − | 0.0583550i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.43805 | − | 16.3472i | 0.346249 | − | 0.599720i | −0.639331 | − | 0.768931i | \(-0.720789\pi\) |
0.985580 | + | 0.169211i | \(0.0541220\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 22.7470 | + | 39.3990i | 0.832270 | + | 1.44153i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.20108 | 0.263122 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.0127 | − | 22.5386i | −0.474838 | − | 0.822444i | 0.524746 | − | 0.851259i | \(-0.324160\pi\) |
−0.999585 | + | 0.0288143i | \(0.990827\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.19540 | 0.0435629 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.95779 | + | 10.3192i | −0.216540 | + | 0.375058i | −0.953748 | − | 0.300608i | \(-0.902810\pi\) |
0.737208 | + | 0.675666i | \(0.236144\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.516902 | −0.0187623 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.39500 | −0.0868186 | −0.0434093 | − | 0.999057i | \(-0.513822\pi\) | ||||
−0.0434093 | + | 0.999057i | \(0.513822\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.20469 | − | 7.28274i | 0.152220 | − | 0.263653i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.09880 | 0.328539 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.66248 | − | 4.61156i | −0.0960117 | − | 0.166297i | 0.814019 | − | 0.580839i | \(-0.197275\pi\) |
−0.910030 | + | 0.414542i | \(0.863942\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.78276 | 0.100219 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.2486 | − | 21.2153i | −0.440553 | − | 0.763060i | 0.557178 | − | 0.830393i | \(-0.311884\pi\) |
−0.997731 | + | 0.0673334i | \(0.978551\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.0736051 | + | 0.127488i | −0.00264057 | + | 0.00457360i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.15256 | + | 4.23229i | 0.256267 | + | 0.151637i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.04667 | + | 3.54494i | −0.0732357 | + | 0.126848i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.72790 | − | 16.8492i | −0.347647 | − | 0.602142i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.5171 | 0.731356 | 0.365678 | − | 0.930741i | \(-0.380837\pi\) | ||||
0.365678 | + | 0.930741i | \(0.380837\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.68396 | + | 4.64875i | 0.0955515 | + | 0.165500i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.50819 | 0.160293 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.13555 | + | 1.96683i | −0.0403246 | + | 0.0698443i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.0144 | 0.815211 | 0.407606 | − | 0.913158i | \(-0.366364\pi\) | ||||
0.407606 | + | 0.913158i | \(0.366364\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −60.0164 | −2.12323 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.777303 | − | 1.34633i | 0.0274647 | − | 0.0475702i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.330321 | + | 0.572133i | −0.0116568 | + | 0.0201901i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.45333 | + | 4.24929i | 0.0863612 | + | 0.149582i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.3195 | −0.995661 | −0.497830 | − | 0.867274i | \(-0.665870\pi\) | ||||
−0.497830 | + | 0.867274i | \(0.665870\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.7766 | − | 34.2540i | −0.694449 | − | 1.20282i | −0.970366 | − | 0.241640i | \(-0.922315\pi\) |
0.275917 | − | 0.961181i | \(-0.411019\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.703698 | − | 1.21884i | −0.0246798 | − | 0.0427466i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.8574 | − | 8.79134i | −0.519793 | − | 0.307570i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.911120 | + | 1.57811i | −0.0318371 | + | 0.0551435i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.4013 | − | 26.6758i | −0.537509 | − | 0.930993i | −0.999037 | − | 0.0438677i | \(-0.986032\pi\) |
0.461528 | − | 0.887126i | \(-0.347301\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.00000 | − | 13.8564i | −0.278862 | − | 0.483004i | 0.692240 | − | 0.721668i | \(-0.256624\pi\) |
−0.971102 | + | 0.238664i | \(0.923291\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.1427 | + | 17.5678i | 0.352698 | + | 0.610891i | 0.986721 | − | 0.162423i | \(-0.0519310\pi\) |
−0.634023 | + | 0.773314i | \(0.718598\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.0792 | 1.53093 | 0.765466 | − | 0.643476i | \(-0.222508\pi\) | ||||
0.765466 | + | 0.643476i | \(0.222508\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.42377 | + | 7.66220i | −0.153459 | + | 0.265799i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21.7541 | − | 37.6792i | 0.753735 | − | 1.30551i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.99255 | 0.138003 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.9534 | + | 46.6847i | −0.930536 | + | 1.61174i | −0.148129 | + | 0.988968i | \(0.547325\pi\) |
−0.782407 | + | 0.622767i | \(0.786008\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.8941 | + | 46.5820i | −0.927383 | + | 1.60627i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.181229 | 0.00624187 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.29095 | 0.181799 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.76218 | − | 4.78423i | −0.0947976 | − | 0.164194i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.275568 | − | 0.477298i | −0.00944636 | − | 0.0163616i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.5324 | − | 23.4388i | 0.463340 | − | 0.802529i | −0.535785 | − | 0.844355i | \(-0.679984\pi\) |
0.999125 | + | 0.0418258i | \(0.0133174\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.67676 | + | 2.90424i | −0.0572772 | + | 0.0992070i | −0.893242 | − | 0.449576i | \(-0.851575\pi\) |
0.835965 | + | 0.548783i | \(0.184909\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.8529 | + | 46.5106i | 0.916209 | + | 1.58692i | 0.805121 | + | 0.593110i | \(0.202100\pi\) |
0.111088 | + | 0.993811i | \(0.464567\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.220815 | + | 0.382463i | 0.00752536 | + | 0.0130343i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.1527 | 1.33277 | 0.666386 | − | 0.745607i | \(-0.267840\pi\) | ||||
0.666386 | + | 0.745607i | \(0.267840\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.66086 | 0.328100 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.77383 | + | 15.1967i | −0.297632 | + | 0.515514i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.23163 | − | 10.7935i | 0.211151 | − | 0.365724i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21.1308 | −0.715170 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.8260 | + | 25.6793i | −0.500637 | + | 0.867129i | 0.499362 | + | 0.866393i | \(0.333568\pi\) |
−1.00000 | 0.000735993i | \(0.999766\pi\) | ||||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.44351 | + | 4.23229i | −0.0824176 | + | 0.142752i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.2820 | 1.45821 | 0.729104 | − | 0.684403i | \(-0.239937\pi\) | ||||
0.729104 | + | 0.684403i | \(0.239937\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.4830 | + | 49.3340i | 0.958529 | + | 1.66022i | 0.726078 | + | 0.687613i | \(0.241341\pi\) |
0.232451 | + | 0.972608i | \(0.425325\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.1158 | + | 17.5211i | 0.339656 | + | 0.588301i | 0.984368 | − | 0.176124i | \(-0.0563561\pi\) |
−0.644712 | + | 0.764425i | \(0.723023\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.17230 | − | 8.95869i | −0.173473 | − | 0.300465i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.39684 | + | 11.0797i | −0.214302 | + | 0.371182i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 34.5576 | − | 19.4615i | 1.15643 | − | 0.651254i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.158021 | + | 0.273700i | 0.00527615 | + | 0.00913857i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.49454 | − | 14.7130i | −0.283309 | − | 0.490705i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 65.0846 | 2.16828 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.458679 | − | 0.794456i | −0.0152639 | − | 0.0264378i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.00000 | + | 8.66025i | −0.166022 | + | 0.287559i | −0.937018 | − | 0.349281i | \(-0.886426\pi\) |
0.770996 | + | 0.636841i | \(0.219759\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.3682 | + | 23.1544i | −0.443394 | + | 0.767981i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −55.0109 | −1.82259 | −0.911297 | − | 0.411751i | \(-0.864917\pi\) | ||||
−0.911297 | + | 0.411751i | \(0.864917\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.9516 | 0.858872 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.37972 | + | 5.85385i | −0.111608 | + | 0.193311i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48.6159 | 1.60369 | 0.801846 | − | 0.597531i | \(-0.203852\pi\) | ||||
0.801846 | + | 0.597531i | \(0.203852\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.86880 | + | 10.1651i | 0.193384 | + | 0.334950i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.50273 | 0.0823783 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15.5791 | + | 26.9837i | 0.511684 | + | 0.886262i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.66075 | + | 9.80471i | −0.185723 | + | 0.321682i | −0.943820 | − | 0.330460i | \(-0.892796\pi\) |
0.758097 | + | 0.652142i | \(0.226129\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.307853 | + | 28.7500i | −0.0100895 | + | 0.942242i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.25409 | + | 3.90421i | −0.0737957 | + | 0.127818i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.24864 | − | 9.09090i | −0.171465 | − | 0.296987i | 0.767467 | − | 0.641088i | \(-0.221517\pi\) |
−0.938932 | + | 0.344102i | \(0.888184\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.03402 | −0.294814 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.40939 | + | 2.44113i | 0.0459447 | + | 0.0795785i | 0.888083 | − | 0.459683i | \(-0.152037\pi\) |
−0.842139 | + | 0.539261i | \(0.818704\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.65341 | −0.0538424 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.7568 | + | 39.4160i | −0.739497 | + | 1.28085i | 0.213224 | + | 0.977003i | \(0.431603\pi\) |
−0.952722 | + | 0.303844i | \(0.901730\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.403926 | 0.0131120 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.66433 | −0.0863967 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.3600 | + | 17.9440i | −0.335593 | + | 0.581264i | −0.983599 | − | 0.180372i | \(-0.942270\pi\) |
0.648006 | + | 0.761635i | \(0.275603\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.42356 | −0.175319 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.11135 | − | 1.92491i | −0.0358873 | − | 0.0621587i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.5136 | −0.887537 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.2432 | − | 28.1340i | −0.523429 | − | 0.906606i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.73436 | + | 11.6642i | −0.216562 | + | 0.375097i | −0.953755 | − | 0.300586i | \(-0.902818\pi\) |
0.737192 | + | 0.675683i | \(0.236151\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.13020 | + | 5.14177i | −0.293304 | + | 0.165177i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.5252 | − | 40.7468i | 0.754960 | − | 1.30763i | −0.190435 | − | 0.981700i | \(-0.560990\pi\) |
0.945394 | − | 0.325928i | \(-0.105677\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.233360 | + | 0.404192i | 0.00748119 | + | 0.0129578i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.0648 | −1.37776 | −0.688882 | − | 0.724873i | \(-0.741898\pi\) | ||||
−0.688882 | + | 0.724873i | \(0.741898\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.443404 | − | 0.767999i | −0.0141713 | − | 0.0245454i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −37.9374 | −1.21125 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −27.0396 | + | 46.8339i | −0.862429 | + | 1.49377i | 0.00714884 | + | 0.999974i | \(0.497724\pi\) |
−0.869578 | + | 0.493796i | \(0.835609\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.10752 | 0.0670830 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.43448 | 0.109210 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.6356 | + | 35.7418i | −0.655510 | + | 1.13538i | 0.326256 | + | 0.945282i | \(0.394213\pi\) |
−0.981766 | + | 0.190095i | \(0.939120\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.36608 | + | 5.83021i | −0.106819 | + | 0.185016i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.544937 | − | 0.943859i | −0.0172583 | − | 0.0298923i | 0.857267 | − | 0.514872i | \(-0.172160\pi\) |
−0.874526 | + | 0.484979i | \(0.838827\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.35899 | 0.0429965 |
(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 | 1900.2.i.c.201.2 | 6 | ||
5.2 | odd | 4 | 1900.2.s.c.49.4 | 12 | |||
5.3 | odd | 4 | 1900.2.s.c.49.3 | 12 | |||
5.4 | even | 2 | 380.2.i.b.201.2 | yes | 6 | ||
15.14 | odd | 2 | 3420.2.t.v.3241.2 | 6 | |||
19.7 | even | 3 | inner | 1900.2.i.c.501.2 | 6 | ||
20.19 | odd | 2 | 1520.2.q.i.961.2 | 6 | |||
95.7 | odd | 12 | 1900.2.s.c.349.3 | 12 | |||
95.49 | even | 6 | 7220.2.a.n.1.2 | 3 | |||
95.64 | even | 6 | 380.2.i.b.121.2 | ✓ | 6 | ||
95.83 | odd | 12 | 1900.2.s.c.349.4 | 12 | |||
95.84 | odd | 6 | 7220.2.a.o.1.2 | 3 | |||
285.254 | odd | 6 | 3420.2.t.v.1261.2 | 6 | |||
380.159 | odd | 6 | 1520.2.q.i.881.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.i.b.121.2 | ✓ | 6 | 95.64 | even | 6 | ||
380.2.i.b.201.2 | yes | 6 | 5.4 | even | 2 | ||
1520.2.q.i.881.2 | 6 | 380.159 | odd | 6 | |||
1520.2.q.i.961.2 | 6 | 20.19 | odd | 2 | |||
1900.2.i.c.201.2 | 6 | 1.1 | even | 1 | trivial | ||
1900.2.i.c.501.2 | 6 | 19.7 | even | 3 | inner | ||
1900.2.s.c.49.3 | 12 | 5.3 | odd | 4 | |||
1900.2.s.c.49.4 | 12 | 5.2 | odd | 4 | |||
1900.2.s.c.349.3 | 12 | 95.7 | odd | 12 | |||
1900.2.s.c.349.4 | 12 | 95.83 | odd | 12 | |||
3420.2.t.v.1261.2 | 6 | 285.254 | odd | 6 | |||
3420.2.t.v.3241.2 | 6 | 15.14 | odd | 2 | |||
7220.2.a.n.1.2 | 3 | 95.49 | even | 6 | |||
7220.2.a.o.1.2 | 3 | 95.84 | odd | 6 |