Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,6,Mod(6,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.6");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.c (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: | \(6.89650425196\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Relative dimension: | \(17\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 36.9 | ||
Character | \(\chi\) | \(=\) | 43.36 |
Dual form | 43.6.c.a.6.9 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.24721 | −0.220478 | −0.110239 | − | 0.993905i | \(-0.535162\pi\) | ||||
−0.110239 | + | 0.993905i | \(0.535162\pi\) | |||||||
\(3\) | −0.494517 | − | 0.856528i | −0.0317233 | − | 0.0549463i | 0.849728 | − | 0.527222i | \(-0.176766\pi\) |
−0.881451 | + | 0.472275i | \(0.843433\pi\) | |||||||
\(4\) | −30.4445 | −0.951389 | ||||||||
\(5\) | 24.3642 | + | 42.2000i | 0.435840 | + | 0.754896i | 0.997364 | − | 0.0725640i | \(-0.0231182\pi\) |
−0.561524 | + | 0.827460i | \(0.689785\pi\) | |||||||
\(6\) | 0.616768 | + | 1.06827i | 0.00699429 | + | 0.0121145i | ||||
\(7\) | 83.1429 | − | 144.008i | 0.641328 | − | 1.11081i | −0.343809 | − | 0.939040i | \(-0.611717\pi\) |
0.985137 | − | 0.171773i | \(-0.0549495\pi\) | |||||||
\(8\) | 77.8815 | 0.430239 | ||||||||
\(9\) | 121.011 | − | 209.597i | 0.497987 | − | 0.862539i | ||||
\(10\) | −30.3873 | − | 52.6324i | −0.0960931 | − | 0.166438i | ||||
\(11\) | −436.503 | −1.08769 | −0.543846 | − | 0.839185i | \(-0.683032\pi\) | ||||
−0.543846 | + | 0.839185i | \(0.683032\pi\) | |||||||
\(12\) | 15.0553 | + | 26.0765i | 0.0301812 | + | 0.0522753i | ||||
\(13\) | 486.675 | − | 842.946i | 0.798695 | − | 1.38338i | −0.121772 | − | 0.992558i | \(-0.538858\pi\) |
0.920466 | − | 0.390821i | \(-0.127809\pi\) | |||||||
\(14\) | −103.697 | + | 179.608i | −0.141399 | + | 0.244910i | ||||
\(15\) | 24.0970 | − | 41.7372i | 0.0276525 | − | 0.0478956i | ||||
\(16\) | 877.088 | 0.856531 | ||||||||
\(17\) | 375.545 | − | 650.464i | 0.315167 | − | 0.545885i | −0.664306 | − | 0.747460i | \(-0.731273\pi\) |
0.979473 | + | 0.201576i | \(0.0646063\pi\) | |||||||
\(18\) | −150.926 | + | 261.412i | −0.109795 | + | 0.190171i | ||||
\(19\) | 283.197 | + | 490.512i | 0.179972 | + | 0.311721i | 0.941871 | − | 0.335975i | \(-0.109066\pi\) |
−0.761899 | + | 0.647696i | \(0.775733\pi\) | |||||||
\(20\) | −741.754 | − | 1284.76i | −0.414653 | − | 0.718200i | ||||
\(21\) | −164.462 | −0.0813801 | ||||||||
\(22\) | 544.413 | 0.239812 | ||||||||
\(23\) | −498.615 | − | 863.626i | −0.196538 | − | 0.340413i | 0.750866 | − | 0.660455i | \(-0.229636\pi\) |
−0.947404 | + | 0.320042i | \(0.896303\pi\) | |||||||
\(24\) | −38.5137 | − | 66.7078i | −0.0136486 | − | 0.0236400i | ||||
\(25\) | 375.274 | − | 649.994i | 0.120088 | − | 0.207998i | ||||
\(26\) | −606.988 | + | 1051.33i | −0.176095 | + | 0.305005i | ||||
\(27\) | −479.703 | −0.126638 | ||||||||
\(28\) | −2531.24 | + | 4384.24i | −0.610153 | + | 1.05682i | ||||
\(29\) | −1998.43 | + | 3461.38i | −0.441259 | + | 0.764283i | −0.997783 | − | 0.0665481i | \(-0.978801\pi\) |
0.556524 | + | 0.830832i | \(0.312135\pi\) | |||||||
\(30\) | −30.0541 | + | 52.0552i | −0.00609678 | + | 0.0105599i | ||||
\(31\) | 3892.30 | + | 6741.67i | 0.727449 | + | 1.25998i | 0.957958 | + | 0.286909i | \(0.0926276\pi\) |
−0.230509 | + | 0.973070i | \(0.574039\pi\) | |||||||
\(32\) | −3586.12 | −0.619085 | ||||||||
\(33\) | 215.858 | + | 373.877i | 0.0345051 | + | 0.0597647i | ||||
\(34\) | −468.385 | + | 811.267i | −0.0694874 | + | 0.120356i | ||||
\(35\) | 8102.83 | 1.11806 | ||||||||
\(36\) | −3684.11 | + | 6381.07i | −0.473780 | + | 0.820611i | ||||
\(37\) | −6022.45 | − | 10431.2i | −0.723217 | − | 1.25265i | −0.959704 | − | 0.281014i | \(-0.909329\pi\) |
0.236486 | − | 0.971635i | \(-0.424004\pi\) | |||||||
\(38\) | −353.207 | − | 611.773i | −0.0396799 | − | 0.0687276i | ||||
\(39\) | −962.676 | −0.101349 | ||||||||
\(40\) | 1897.52 | + | 3286.60i | 0.187515 | + | 0.324786i | ||||
\(41\) | −15533.0 | −1.44310 | −0.721548 | − | 0.692364i | \(-0.756569\pi\) | ||||
−0.721548 | + | 0.692364i | \(0.756569\pi\) | |||||||
\(42\) | 205.120 | 0.0179425 | ||||||||
\(43\) | 3632.24 | − | 11567.9i | 0.299573 | − | 0.954073i | ||||
\(44\) | 13289.1 | 1.03482 | ||||||||
\(45\) | 11793.3 | 0.868170 | ||||||||
\(46\) | 621.879 | + | 1077.13i | 0.0433323 | + | 0.0750537i | ||||
\(47\) | 8224.60 | 0.543088 | 0.271544 | − | 0.962426i | \(-0.412466\pi\) | ||||
0.271544 | + | 0.962426i | \(0.412466\pi\) | |||||||
\(48\) | −433.735 | − | 751.251i | −0.0271720 | − | 0.0470632i | ||||
\(49\) | −5421.99 | − | 9391.16i | −0.322603 | − | 0.558765i | ||||
\(50\) | −468.047 | + | 810.680i | −0.0264767 | + | 0.0458590i | ||||
\(51\) | −742.854 | −0.0399925 | ||||||||
\(52\) | −14816.6 | + | 25663.0i | −0.759870 | + | 1.31613i | ||||
\(53\) | −2106.28 | − | 3648.19i | −0.102998 | − | 0.178397i | 0.809921 | − | 0.586539i | \(-0.199510\pi\) |
−0.912918 | + | 0.408142i | \(0.866177\pi\) | |||||||
\(54\) | 598.292 | 0.0279209 | ||||||||
\(55\) | −10635.0 | − | 18420.4i | −0.474059 | − | 0.821095i | ||||
\(56\) | 6475.30 | − | 11215.5i | 0.275924 | − | 0.477915i | ||||
\(57\) | 280.092 | − | 485.133i | 0.0114186 | − | 0.0197776i | ||||
\(58\) | 2492.47 | − | 4317.08i | 0.0972880 | − | 0.168508i | ||||
\(59\) | 38108.9 | 1.42527 | 0.712634 | − | 0.701536i | \(-0.247502\pi\) | ||||
0.712634 | + | 0.701536i | \(0.247502\pi\) | |||||||
\(60\) | −733.620 | + | 1270.67i | −0.0263083 | + | 0.0455673i | ||||
\(61\) | 14090.4 | − | 24405.3i | 0.484841 | − | 0.839769i | −0.515007 | − | 0.857186i | \(-0.672211\pi\) |
0.999848 | + | 0.0174167i | \(0.00554417\pi\) | |||||||
\(62\) | −4854.53 | − | 8408.30i | −0.160387 | − | 0.277798i | ||||
\(63\) | −20122.4 | − | 34853.0i | −0.638746 | − | 1.10634i | ||||
\(64\) | −23594.1 | −0.720036 | ||||||||
\(65\) | 47429.7 | 1.39241 | ||||||||
\(66\) | −269.221 | − | 466.305i | −0.00760763 | − | 0.0131768i | ||||
\(67\) | 5914.11 | + | 10243.5i | 0.160954 | + | 0.278781i | 0.935211 | − | 0.354090i | \(-0.115210\pi\) |
−0.774257 | + | 0.632871i | \(0.781876\pi\) | |||||||
\(68\) | −11433.3 | + | 19803.0i | −0.299846 | + | 0.519349i | ||||
\(69\) | −493.147 | + | 854.156i | −0.0124696 | + | 0.0215980i | ||||
\(70\) | −10106.0 | −0.246509 | ||||||||
\(71\) | −37746.3 | + | 65378.5i | −0.888645 | + | 1.53918i | −0.0471673 | + | 0.998887i | \(0.515019\pi\) |
−0.841478 | + | 0.540292i | \(0.818314\pi\) | |||||||
\(72\) | 9424.52 | − | 16323.7i | 0.214253 | − | 0.371098i | ||||
\(73\) | 27806.1 | − | 48161.5i | 0.610707 | − | 1.05777i | −0.380415 | − | 0.924816i | \(-0.624219\pi\) |
0.991122 | − | 0.132959i | \(-0.0424478\pi\) | |||||||
\(74\) | 7511.28 | + | 13009.9i | 0.159454 | + | 0.276182i | ||||
\(75\) | −742.317 | −0.0152383 | ||||||||
\(76\) | −8621.79 | − | 14933.4i | −0.171223 | − | 0.296568i | ||||
\(77\) | −36292.2 | + | 62859.9i | −0.697567 | + | 1.20822i | ||||
\(78\) | 1200.66 | 0.0223452 | ||||||||
\(79\) | −38966.7 | + | 67492.3i | −0.702467 | + | 1.21671i | 0.265131 | + | 0.964212i | \(0.414585\pi\) |
−0.967598 | + | 0.252496i | \(0.918749\pi\) | |||||||
\(80\) | 21369.5 | + | 37013.1i | 0.373310 | + | 0.646592i | ||||
\(81\) | −29168.4 | − | 50521.2i | −0.493970 | − | 0.855581i | ||||
\(82\) | 19372.9 | 0.318171 | ||||||||
\(83\) | 8253.14 | + | 14294.9i | 0.131499 | + | 0.227764i | 0.924255 | − | 0.381776i | \(-0.124688\pi\) |
−0.792755 | + | 0.609540i | \(0.791354\pi\) | |||||||
\(84\) | 5006.97 | 0.0774242 | ||||||||
\(85\) | 36599.4 | 0.549448 | ||||||||
\(86\) | −4530.18 | + | 14427.6i | −0.0660494 | + | 0.210352i | ||||
\(87\) | 3953.03 | 0.0559928 | ||||||||
\(88\) | −33995.6 | −0.467967 | ||||||||
\(89\) | 38194.7 | + | 66155.2i | 0.511126 | + | 0.885296i | 0.999917 | + | 0.0128953i | \(0.00410481\pi\) |
−0.488791 | + | 0.872401i | \(0.662562\pi\) | |||||||
\(90\) | −14708.8 | −0.191413 | ||||||||
\(91\) | −80927.2 | − | 140170.i | −1.02445 | − | 1.77440i | ||||
\(92\) | 15180.1 | + | 26292.6i | 0.186984 | + | 0.323865i | ||||
\(93\) | 3849.62 | − | 6667.74i | 0.0461541 | − | 0.0799413i | ||||
\(94\) | −10257.8 | −0.119739 | ||||||||
\(95\) | −13799.7 | + | 23901.8i | −0.156878 | + | 0.271720i | ||||
\(96\) | 1773.40 | + | 3071.62i | 0.0196394 | + | 0.0340165i | ||||
\(97\) | −1066.68 | −0.0115108 | −0.00575540 | − | 0.999983i | \(-0.501832\pi\) | ||||
−0.00575540 | + | 0.999983i | \(0.501832\pi\) | |||||||
\(98\) | 6762.38 | + | 11712.8i | 0.0711270 | + | 0.123196i | ||||
\(99\) | −52821.7 | + | 91489.8i | −0.541657 | + | 0.938177i | ||||
\(100\) | −11425.0 | + | 19788.7i | −0.114250 | + | 0.197887i | ||||
\(101\) | 31666.0 | − | 54847.0i | 0.308880 | − | 0.534995i | −0.669238 | − | 0.743048i | \(-0.733379\pi\) |
0.978118 | + | 0.208053i | \(0.0667127\pi\) | |||||||
\(102\) | 926.498 | 0.00881747 | ||||||||
\(103\) | −18130.1 | + | 31402.2i | −0.168386 | + | 0.291653i | −0.937853 | − | 0.347034i | \(-0.887189\pi\) |
0.769467 | + | 0.638687i | \(0.220522\pi\) | |||||||
\(104\) | 37903.0 | − | 65649.9i | 0.343629 | − | 0.595184i | ||||
\(105\) | −4006.99 | − | 6940.31i | −0.0354687 | − | 0.0614335i | ||||
\(106\) | 2626.98 | + | 4550.07i | 0.0227087 | + | 0.0393326i | ||||
\(107\) | 117719. | 0.994001 | 0.497000 | − | 0.867750i | \(-0.334435\pi\) | ||||
0.497000 | + | 0.867750i | \(0.334435\pi\) | |||||||
\(108\) | 14604.3 | 0.120482 | ||||||||
\(109\) | 100372. | + | 173850.i | 0.809184 | + | 1.40155i | 0.913430 | + | 0.406997i | \(0.133424\pi\) |
−0.104245 | + | 0.994552i | \(0.533243\pi\) | |||||||
\(110\) | 13264.2 | + | 22974.2i | 0.104520 | + | 0.181033i | ||||
\(111\) | −5956.41 | + | 10316.8i | −0.0458856 | + | 0.0794763i | ||||
\(112\) | 72923.6 | − | 126307.i | 0.549317 | − | 0.951446i | ||||
\(113\) | −194153. | −1.43037 | −0.715185 | − | 0.698935i | \(-0.753658\pi\) | ||||
−0.715185 | + | 0.698935i | \(0.753658\pi\) | |||||||
\(114\) | −349.334 | + | 605.064i | −0.00251755 | + | 0.00436053i | ||||
\(115\) | 24296.7 | − | 42083.1i | 0.171318 | − | 0.296731i | ||||
\(116\) | 60841.1 | − | 105380.i | 0.419809 | − | 0.727131i | ||||
\(117\) | −117786. | − | 204011.i | −0.795479 | − | 1.37781i | ||||
\(118\) | −47530.0 | −0.314241 | ||||||||
\(119\) | −62447.9 | − | 108163.i | −0.404250 | − | 0.700182i | ||||
\(120\) | 1876.71 | − | 3250.56i | 0.0118972 | − | 0.0206065i | ||||
\(121\) | 29484.1 | 0.183073 | ||||||||
\(122\) | −17573.8 | + | 30438.6i | −0.106897 | + | 0.185151i | ||||
\(123\) | 7681.33 | + | 13304.4i | 0.0457798 | + | 0.0792929i | ||||
\(124\) | −118499. | − | 205246.i | −0.692087 | − | 1.19873i | ||||
\(125\) | 188849. | 1.08104 | ||||||||
\(126\) | 25096.9 | + | 43469.1i | 0.140830 | + | 0.243924i | ||||
\(127\) | 68255.9 | 0.375518 | 0.187759 | − | 0.982215i | \(-0.439878\pi\) | ||||
0.187759 | + | 0.982215i | \(0.439878\pi\) | |||||||
\(128\) | 144183. | 0.777838 | ||||||||
\(129\) | −11704.4 | + | 2609.38i | −0.0619263 | + | 0.0138059i | ||||
\(130\) | −59155.0 | −0.306996 | ||||||||
\(131\) | 202347. | 1.03019 | 0.515095 | − | 0.857133i | \(-0.327757\pi\) | ||||
0.515095 | + | 0.857133i | \(0.327757\pi\) | |||||||
\(132\) | −6571.69 | − | 11382.5i | −0.0328278 | − | 0.0568595i | ||||
\(133\) | 94183.4 | 0.461684 | ||||||||
\(134\) | −7376.16 | − | 12775.9i | −0.0354869 | − | 0.0614651i | ||||
\(135\) | −11687.6 | − | 20243.5i | −0.0551937 | − | 0.0955983i | ||||
\(136\) | 29248.1 | − | 50659.1i | 0.135597 | − | 0.234861i | ||||
\(137\) | −45140.4 | −0.205477 | −0.102739 | − | 0.994708i | \(-0.532761\pi\) | ||||
−0.102739 | + | 0.994708i | \(0.532761\pi\) | |||||||
\(138\) | 615.059 | − | 1065.31i | 0.00274928 | − | 0.00476190i | ||||
\(139\) | 74684.5 | + | 129357.i | 0.327864 | + | 0.567877i | 0.982088 | − | 0.188424i | \(-0.0603379\pi\) |
−0.654224 | + | 0.756301i | \(0.727005\pi\) | |||||||
\(140\) | −246686. | −1.06371 | ||||||||
\(141\) | −4067.20 | − | 7044.60i | −0.0172285 | − | 0.0298407i | ||||
\(142\) | 47077.7 | − | 81540.9i | 0.195927 | − | 0.339355i | ||||
\(143\) | −212435. | + | 367949.i | −0.868734 | + | 1.50469i | ||||
\(144\) | 106137. | − | 183835.i | 0.426542 | − | 0.738792i | ||||
\(145\) | −194760. | −0.769273 | ||||||||
\(146\) | −34680.1 | + | 60067.7i | −0.134647 | + | 0.233216i | ||||
\(147\) | −5362.53 | + | 9288.18i | −0.0204681 | + | 0.0354517i | ||||
\(148\) | 183350. | + | 317572.i | 0.688061 | + | 1.19176i | ||||
\(149\) | 69634.3 | + | 120610.i | 0.256955 | + | 0.445060i | 0.965425 | − | 0.260682i | \(-0.0839474\pi\) |
−0.708469 | + | 0.705741i | \(0.750614\pi\) | |||||||
\(150\) | 925.828 | 0.00335971 | ||||||||
\(151\) | −345221. | −1.23213 | −0.616063 | − | 0.787697i | \(-0.711273\pi\) | ||||
−0.616063 | + | 0.787697i | \(0.711273\pi\) | |||||||
\(152\) | 22055.8 | + | 38201.8i | 0.0774310 | + | 0.134114i | ||||
\(153\) | −90890.2 | − | 157426.i | −0.313898 | − | 0.543687i | ||||
\(154\) | 45264.1 | − | 78399.6i | 0.153798 | − | 0.266387i | ||||
\(155\) | −189666. | + | 328510.i | −0.634102 | + | 1.09830i | ||||
\(156\) | 29308.2 | 0.0964222 | ||||||||
\(157\) | −136168. | + | 235851.i | −0.440887 | + | 0.763638i | −0.997756 | − | 0.0669622i | \(-0.978669\pi\) |
0.556869 | + | 0.830601i | \(0.312003\pi\) | |||||||
\(158\) | 48599.8 | − | 84177.3i | 0.154879 | − | 0.268258i | ||||
\(159\) | −2083.18 | + | 3608.18i | −0.00653484 | + | 0.0113187i | ||||
\(160\) | −87373.0 | − | 151334.i | −0.269822 | − | 0.467345i | ||||
\(161\) | −165825. | −0.504180 | ||||||||
\(162\) | 36379.2 | + | 63010.7i | 0.108910 | + | 0.188637i | ||||
\(163\) | −10413.6 | + | 18036.9i | −0.0306996 | + | 0.0531733i | −0.880967 | − | 0.473178i | \(-0.843107\pi\) |
0.850267 | + | 0.526351i | \(0.176440\pi\) | |||||||
\(164\) | 472893. | 1.37295 | ||||||||
\(165\) | −10518.4 | + | 18218.4i | −0.0300774 | + | 0.0520956i | ||||
\(166\) | −10293.4 | − | 17828.7i | −0.0289928 | − | 0.0502169i | ||||
\(167\) | 288459. | + | 499626.i | 0.800375 | + | 1.38629i | 0.919369 | + | 0.393395i | \(0.128700\pi\) |
−0.118994 | + | 0.992895i | \(0.537967\pi\) | |||||||
\(168\) | −12808.6 | −0.0350129 | ||||||||
\(169\) | −288059. | − | 498932.i | −0.775826 | − | 1.34377i | ||||
\(170\) | −45647.3 | −0.121141 | ||||||||
\(171\) | 137080. | 0.358495 | ||||||||
\(172\) | −110582. | + | 352177.i | −0.285011 | + | 0.907695i | ||||
\(173\) | 677893. | 1.72205 | 0.861026 | − | 0.508562i | \(-0.169823\pi\) | ||||
0.861026 | + | 0.508562i | \(0.169823\pi\) | |||||||
\(174\) | −4930.27 | −0.0123452 | ||||||||
\(175\) | −62402.7 | − | 108085.i | −0.154031 | − | 0.266790i | ||||
\(176\) | −382852. | −0.931642 | ||||||||
\(177\) | −18845.5 | − | 32641.4i | −0.0452142 | − | 0.0783133i | ||||
\(178\) | −47636.9 | − | 82509.6i | −0.112692 | − | 0.195189i | ||||
\(179\) | −171637. | + | 297283.i | −0.400384 | + | 0.693486i | −0.993772 | − | 0.111431i | \(-0.964457\pi\) |
0.593388 | + | 0.804917i | \(0.297790\pi\) | |||||||
\(180\) | −359041. | −0.825968 | ||||||||
\(181\) | 148436. | − | 257098.i | 0.336776 | − | 0.583314i | −0.647048 | − | 0.762449i | \(-0.723997\pi\) |
0.983824 | + | 0.179135i | \(0.0573300\pi\) | |||||||
\(182\) | 100933. | + | 174822.i | 0.225869 | + | 0.391217i | ||||
\(183\) | −27871.8 | −0.0615230 | ||||||||
\(184\) | −38832.9 | − | 67260.6i | −0.0845581 | − | 0.146459i | ||||
\(185\) | 293464. | − | 508295.i | 0.630413 | − | 1.09191i | ||||
\(186\) | −4801.30 | + | 8316.09i | −0.0101760 | + | 0.0176253i | ||||
\(187\) | −163927. | + | 283930.i | −0.342804 | + | 0.593754i | ||||
\(188\) | −250393. | −0.516688 | ||||||||
\(189\) | −39883.9 | + | 69081.0i | −0.0812163 | + | 0.140671i | ||||
\(190\) | 17211.2 | − | 29810.7i | 0.0345882 | − | 0.0599084i | ||||
\(191\) | −360531. | − | 624458.i | −0.715088 | − | 1.23857i | −0.962926 | − | 0.269767i | \(-0.913053\pi\) |
0.247838 | − | 0.968802i | \(-0.420280\pi\) | |||||||
\(192\) | 11667.7 | + | 20209.1i | 0.0228419 | + | 0.0395633i | ||||
\(193\) | 510908. | 0.987300 | 0.493650 | − | 0.869661i | \(-0.335662\pi\) | ||||
0.493650 | + | 0.869661i | \(0.335662\pi\) | |||||||
\(194\) | 1330.38 | 0.00253788 | ||||||||
\(195\) | −23454.8 | − | 40624.9i | −0.0441718 | − | 0.0765079i | ||||
\(196\) | 165070. | + | 285909.i | 0.306921 | + | 0.531603i | ||||
\(197\) | 261799. | − | 453450.i | 0.480621 | − | 0.832460i | −0.519132 | − | 0.854694i | \(-0.673745\pi\) |
0.999753 | + | 0.0222339i | \(0.00707786\pi\) | |||||||
\(198\) | 65879.9 | − | 114107.i | 0.119423 | − | 0.206848i | ||||
\(199\) | 434612. | 0.777980 | 0.388990 | − | 0.921242i | \(-0.372824\pi\) | ||||
0.388990 | + | 0.921242i | \(0.372824\pi\) | |||||||
\(200\) | 29226.9 | − | 50622.5i | 0.0516664 | − | 0.0894888i | ||||
\(201\) | 5849.26 | − | 10131.2i | 0.0102120 | − | 0.0176877i | ||||
\(202\) | −39494.2 | + | 68406.0i | −0.0681012 | + | 0.117955i | ||||
\(203\) | 332311. | + | 575579.i | 0.565984 | + | 0.980313i | ||||
\(204\) | 22615.8 | 0.0380484 | ||||||||
\(205\) | −378448. | − | 655492.i | −0.628959 | − | 1.08939i | ||||
\(206\) | 22612.0 | − | 39165.2i | 0.0371255 | − | 0.0643032i | ||||
\(207\) | −241351. | −0.391493 | ||||||||
\(208\) | 426857. | − | 739338.i | 0.684107 | − | 1.18491i | ||||
\(209\) | −123617. | − | 214110.i | −0.195754 | − | 0.339056i | ||||
\(210\) | 4997.57 | + | 8656.04i | 0.00782007 | + | 0.0135448i | ||||
\(211\) | −544697. | −0.842265 | −0.421133 | − | 0.906999i | \(-0.638367\pi\) | ||||
−0.421133 | + | 0.906999i | \(0.638367\pi\) | |||||||
\(212\) | 64124.6 | + | 111067.i | 0.0979908 | + | 0.169725i | ||||
\(213\) | 74664.7 | 0.112763 | ||||||||
\(214\) | −146821. | −0.219156 | ||||||||
\(215\) | 576660. | − | 128561.i | 0.850792 | − | 0.189676i | ||||
\(216\) | −37360.0 | −0.0544845 | ||||||||
\(217\) | 1.29447e6 | 1.86613 | ||||||||
\(218\) | −125186. | − | 216828.i | −0.178408 | − | 0.309011i | ||||
\(219\) | −55002.3 | −0.0774945 | ||||||||
\(220\) | 323778. | + | 560800.i | 0.451015 | + | 0.781181i | ||||
\(221\) | −365537. | − | 633129.i | −0.503444 | − | 0.871990i | ||||
\(222\) | 7428.91 | − | 12867.2i | 0.0101168 | − | 0.0175228i | ||||
\(223\) | −672053. | −0.904985 | −0.452492 | − | 0.891768i | \(-0.649465\pi\) | ||||
−0.452492 | + | 0.891768i | \(0.649465\pi\) | |||||||
\(224\) | −298161. | + | 516430.i | −0.397037 | + | 0.687688i | ||||
\(225\) | −90824.5 | − | 157313.i | −0.119604 | − | 0.207161i | ||||
\(226\) | 242151. | 0.315366 | ||||||||
\(227\) | −296180. | − | 512999.i | −0.381497 | − | 0.660772i | 0.609780 | − | 0.792571i | \(-0.291258\pi\) |
−0.991276 | + | 0.131799i | \(0.957925\pi\) | |||||||
\(228\) | −8527.24 | + | 14769.6i | −0.0108635 | + | 0.0188162i | ||||
\(229\) | −197566. | + | 342194.i | −0.248956 | + | 0.431205i | −0.963236 | − | 0.268655i | \(-0.913421\pi\) |
0.714280 | + | 0.699860i | \(0.246754\pi\) | |||||||
\(230\) | −30303.1 | + | 52486.6i | −0.0377718 | + | 0.0654227i | ||||
\(231\) | 71788.3 | 0.0885165 | ||||||||
\(232\) | −155641. | + | 269578.i | −0.189847 | + | 0.328824i | ||||
\(233\) | −192132. | + | 332782.i | −0.231851 | + | 0.401578i | −0.958353 | − | 0.285587i | \(-0.907812\pi\) |
0.726502 | + | 0.687165i | \(0.241145\pi\) | |||||||
\(234\) | 146904. | + | 254446.i | 0.175386 | + | 0.303777i | ||||
\(235\) | 200385. | + | 347078.i | 0.236699 | + | 0.409975i | ||||
\(236\) | −1.16021e6 | −1.35599 | ||||||||
\(237\) | 77078.7 | 0.0891382 | ||||||||
\(238\) | 77885.8 | + | 134902.i | 0.0891284 | + | 0.154375i | ||||
\(239\) | 67760.2 | + | 117364.i | 0.0767326 | + | 0.132905i | 0.901838 | − | 0.432073i | \(-0.142218\pi\) |
−0.825106 | + | 0.564978i | \(0.808885\pi\) | |||||||
\(240\) | 21135.2 | − | 36607.2i | 0.0236852 | − | 0.0410240i | ||||
\(241\) | 189808. | − | 328757.i | 0.210510 | − | 0.364613i | −0.741365 | − | 0.671103i | \(-0.765821\pi\) |
0.951874 | + | 0.306489i | \(0.0991544\pi\) | |||||||
\(242\) | −36773.0 | −0.0403637 | ||||||||
\(243\) | −87132.5 | + | 150918.i | −0.0946595 | + | 0.163955i | ||||
\(244\) | −428975. | + | 743007.i | −0.461272 | + | 0.798947i | ||||
\(245\) | 264205. | − | 457616.i | 0.281206 | − | 0.487064i | ||||
\(246\) | −9580.25 | − | 16593.5i | −0.0100934 | − | 0.0174823i | ||||
\(247\) | 551300. | 0.574971 | ||||||||
\(248\) | 303139. | + | 525052.i | 0.312977 | + | 0.542092i | ||||
\(249\) | 8162.63 | − | 14138.1i | 0.00834318 | − | 0.0144508i | ||||
\(250\) | −235535. | −0.238345 | ||||||||
\(251\) | 266229. | − | 461122.i | 0.266730 | − | 0.461989i | −0.701286 | − | 0.712880i | \(-0.747390\pi\) |
0.968015 | + | 0.250891i | \(0.0807236\pi\) | |||||||
\(252\) | 612616. | + | 1.06108e6i | 0.607696 | + | 1.05256i | ||||
\(253\) | 217647. | + | 376976.i | 0.213772 | + | 0.370265i | ||||
\(254\) | −85129.7 | −0.0827936 | ||||||||
\(255\) | −18099.0 | − | 31348.4i | −0.0174303 | − | 0.0301902i | ||||
\(256\) | 575186. | 0.548540 | ||||||||
\(257\) | −298033. | −0.281470 | −0.140735 | − | 0.990047i | \(-0.544947\pi\) | ||||
−0.140735 | + | 0.990047i | \(0.544947\pi\) | |||||||
\(258\) | 14597.9 | − | 3254.46i | 0.0136534 | − | 0.00304389i | ||||
\(259\) | −2.00290e6 | −1.85528 | ||||||||
\(260\) | −1.44397e6 | −1.32472 | ||||||||
\(261\) | 483663. | + | 837730.i | 0.439483 | + | 0.761207i | ||||
\(262\) | −252369. | −0.227135 | ||||||||
\(263\) | 267487. | + | 463302.i | 0.238459 | + | 0.413023i | 0.960272 | − | 0.279065i | \(-0.0900243\pi\) |
−0.721813 | + | 0.692088i | \(0.756691\pi\) | |||||||
\(264\) | 16811.4 | + | 29118.2i | 0.0148455 | + | 0.0257131i | ||||
\(265\) | 102636. | − | 177770.i | 0.0897808 | − | 0.155505i | ||||
\(266\) | −117467. | −0.101791 | ||||||||
\(267\) | 37775.8 | − | 65429.7i | 0.0324292 | − | 0.0561690i | ||||
\(268\) | −180052. | − | 311859.i | −0.153130 | − | 0.265229i | ||||
\(269\) | 398325. | 0.335627 | 0.167814 | − | 0.985819i | \(-0.446329\pi\) | ||||
0.167814 | + | 0.985819i | \(0.446329\pi\) | |||||||
\(270\) | 14576.9 | + | 25247.9i | 0.0121690 | + | 0.0210773i | ||||
\(271\) | −276209. | + | 478407.i | −0.228462 | + | 0.395708i | −0.957352 | − | 0.288923i | \(-0.906703\pi\) |
0.728891 | + | 0.684630i | \(0.240036\pi\) | |||||||
\(272\) | 329386. | − | 570514.i | 0.269950 | − | 0.467567i | ||||
\(273\) | −80039.7 | + | 138633.i | −0.0649978 | + | 0.112580i | ||||
\(274\) | 56299.6 | 0.0453032 | ||||||||
\(275\) | −163808. | + | 283724.i | −0.130618 | + | 0.226238i | ||||
\(276\) | 15013.6 | − | 26004.3i | 0.0118635 | − | 0.0205481i | ||||
\(277\) | −53363.6 | − | 92428.5i | −0.0417874 | − | 0.0723780i | 0.844375 | − | 0.535752i | \(-0.179972\pi\) |
−0.886163 | + | 0.463374i | \(0.846639\pi\) | |||||||
\(278\) | −93147.5 | − | 161336.i | −0.0722869 | − | 0.125204i | ||||
\(279\) | 1.88405e6 | 1.44904 | ||||||||
\(280\) | 631061. | 0.481035 | ||||||||
\(281\) | −928899. | − | 1.60890e6i | −0.701783 | − | 1.21552i | −0.967840 | − | 0.251566i | \(-0.919054\pi\) |
0.266057 | − | 0.963957i | \(-0.414279\pi\) | |||||||
\(282\) | 5072.67 | + | 8786.12i | 0.00379851 | + | 0.00657922i | ||||
\(283\) | 688486. | − | 1.19249e6i | 0.511009 | − | 0.885094i | −0.488909 | − | 0.872335i | \(-0.662605\pi\) |
0.999919 | − | 0.0127596i | \(-0.00406163\pi\) | |||||||
\(284\) | 1.14917e6 | − | 1.99041e6i | 0.845448 | − | 1.46436i | ||||
\(285\) | 27296.8 | 0.0199067 | ||||||||
\(286\) | 264952. | − | 458910.i | 0.191537 | − | 0.331751i | ||||
\(287\) | −1.29146e6 | + | 2.23687e6i | −0.925498 | + | 1.60301i | ||||
\(288\) | −433960. | + | 751641.i | −0.308297 | + | 0.533985i | ||||
\(289\) | 427860. | + | 741075.i | 0.301340 | + | 0.521936i | ||||
\(290\) | 242908. | 0.169608 | ||||||||
\(291\) | 527.492 | + | 913.644i | 0.000365161 | + | 0.000632477i | ||||
\(292\) | −846541. | + | 1.46625e6i | −0.581020 | + | 1.00636i | ||||
\(293\) | −2.36069e6 | −1.60646 | −0.803230 | − | 0.595669i | \(-0.796887\pi\) | ||||
−0.803230 | + | 0.595669i | \(0.796887\pi\) | |||||||
\(294\) | 6688.22 | − | 11584.3i | 0.00451276 | − | 0.00781633i | ||||
\(295\) | 928493. | + | 1.60820e6i | 0.621188 | + | 1.07593i | ||||
\(296\) | −469038. | − | 812397.i | −0.311156 | − | 0.538938i | ||||
\(297\) | 209392. | 0.137743 | ||||||||
\(298\) | −86848.8 | − | 150427.i | −0.0566530 | − | 0.0981259i | ||||
\(299\) | −970654. | −0.627894 | ||||||||
\(300\) | 22599.4 | 0.0144976 | ||||||||
\(301\) | −1.36387e6 | − | 1.48486e6i | −0.867672 | − | 0.944644i | ||||
\(302\) | 430564. | 0.271657 | ||||||||
\(303\) | −62637.4 | −0.0391947 | ||||||||
\(304\) | 248389. | + | 430222.i | 0.154152 | + | 0.266999i | ||||
\(305\) | 1.37321e6 | 0.845251 | ||||||||
\(306\) | 113359. | + | 196344.i | 0.0692076 | + | 0.119871i | ||||
\(307\) | 279645. | + | 484360.i | 0.169341 | + | 0.293307i | 0.938188 | − | 0.346125i | \(-0.112503\pi\) |
−0.768847 | + | 0.639432i | \(0.779169\pi\) | |||||||
\(308\) | 1.10490e6 | − | 1.91373e6i | 0.663658 | − | 1.14949i | ||||
\(309\) | 35862.5 | 0.0213670 | ||||||||
\(310\) | 236553. | − | 409723.i | 0.139806 | − | 0.242151i | ||||
\(311\) | −918088. | − | 1.59018e6i | −0.538249 | − | 0.932275i | −0.998998 | − | 0.0447446i | \(-0.985753\pi\) |
0.460749 | − | 0.887530i | \(-0.347581\pi\) | |||||||
\(312\) | −74974.7 | −0.0436042 | ||||||||
\(313\) | 1.10804e6 | + | 1.91919e6i | 0.639286 | + | 1.10728i | 0.985590 | + | 0.169154i | \(0.0541035\pi\) |
−0.346303 | + | 0.938123i | \(0.612563\pi\) | |||||||
\(314\) | 169831. | − | 294156.i | 0.0972059 | − | 0.168366i | ||||
\(315\) | 980531. | − | 1.69833e6i | 0.556782 | − | 0.964375i | ||||
\(316\) | 1.18632e6 | − | 2.05477e6i | 0.668319 | − | 1.15756i | ||||
\(317\) | 2.22654e6 | 1.24447 | 0.622233 | − | 0.782832i | \(-0.286226\pi\) | ||||
0.622233 | + | 0.782832i | \(0.286226\pi\) | |||||||
\(318\) | 2598.17 | − | 4500.17i | 0.00144079 | − | 0.00249552i | ||||
\(319\) | 872321. | − | 1.51090e6i | 0.479954 | − | 0.831305i | ||||
\(320\) | −574852. | − | 995673.i | −0.313820 | − | 0.543553i | ||||
\(321\) | −58214.0 | − | 100830.i | −0.0315330 | − | 0.0546167i | ||||
\(322\) | 206819. | 0.111161 | ||||||||
\(323\) | 425414. | 0.226885 | ||||||||
\(324\) | 888017. | + | 1.53809e6i | 0.469958 | + | 0.813991i | ||||
\(325\) | −365273. | − | 632671.i | −0.191827 | − | 0.332254i | ||||
\(326\) | 12988.0 | − | 22495.9i | 0.00676860 | − | 0.0117236i | ||||
\(327\) | 99271.6 | − | 171943.i | 0.0513400 | − | 0.0889234i | ||||
\(328\) | −1.20973e6 | −0.620876 | ||||||||
\(329\) | 683817. | − | 1.18441e6i | 0.348297 | − | 0.603269i | ||||
\(330\) | 13118.7 | − | 22722.3i | 0.00663141 | − | 0.0114859i | ||||
\(331\) | −1.18476e6 | + | 2.05206e6i | −0.594374 | + | 1.02949i | 0.399261 | + | 0.916837i | \(0.369267\pi\) |
−0.993635 | + | 0.112648i | \(0.964067\pi\) | |||||||
\(332\) | −251262. | − | 435199.i | −0.125107 | − | 0.216692i | ||||
\(333\) | −2.91513e6 | −1.44061 | ||||||||
\(334\) | −359770. | − | 623140.i | −0.176465 | − | 0.305647i | ||||
\(335\) | −288185. | + | 499151.i | −0.140300 | + | 0.243008i | ||||
\(336\) | −144248. | −0.0697046 | ||||||||
\(337\) | 205094. | − | 355233.i | 0.0983735 | − | 0.170388i | −0.812638 | − | 0.582769i | \(-0.801969\pi\) |
0.911012 | + | 0.412381i | \(0.135303\pi\) | |||||||
\(338\) | 359271. | + | 622275.i | 0.171053 | + | 0.296272i | ||||
\(339\) | 96012.1 | + | 166298.i | 0.0453760 | + | 0.0785936i | ||||
\(340\) | −1.11425e6 | −0.522739 | ||||||||
\(341\) | −1.69900e6 | − | 2.94276e6i | −0.791240 | − | 1.37047i | ||||
\(342\) | −170968. | −0.0790404 | ||||||||
\(343\) | 991566. | 0.455078 | ||||||||
\(344\) | 282884. | − | 900922.i | 0.128888 | − | 0.410479i | ||||
\(345\) | −48060.5 | −0.0217390 | ||||||||
\(346\) | −845477. | −0.379675 | ||||||||
\(347\) | 1.99445e6 | + | 3.45449e6i | 0.889201 | + | 1.54014i | 0.840821 | + | 0.541313i | \(0.182072\pi\) |
0.0483798 | + | 0.998829i | \(0.484594\pi\) | |||||||
\(348\) | −120348. | −0.0532709 | ||||||||
\(349\) | 2.04771e6 | + | 3.54674e6i | 0.899921 | + | 1.55871i | 0.827593 | + | 0.561329i | \(0.189710\pi\) |
0.0723287 | + | 0.997381i | \(0.476957\pi\) | |||||||
\(350\) | 77829.5 | + | 134805.i | 0.0339605 | + | 0.0588213i | ||||
\(351\) | −233459. | + | 404364.i | −0.101145 | + | 0.175188i | ||||
\(352\) | 1.56536e6 | 0.673374 | ||||||||
\(353\) | −1.85324e6 | + | 3.20991e6i | −0.791581 | + | 1.37106i | 0.133407 | + | 0.991061i | \(0.457408\pi\) |
−0.924988 | + | 0.379997i | \(0.875925\pi\) | |||||||
\(354\) | 23504.4 | + | 40710.8i | 0.00996874 | + | 0.0172664i | ||||
\(355\) | −3.67863e6 | −1.54923 | ||||||||
\(356\) | −1.16282e6 | − | 2.01406e6i | −0.486280 | − | 0.842262i | ||||
\(357\) | −61763.1 | + | 106977.i | −0.0256483 | + | 0.0444241i | ||||
\(358\) | 214067. | − | 370775.i | 0.0882760 | − | 0.152899i | ||||
\(359\) | −836253. | + | 1.44843e6i | −0.342453 | + | 0.593147i | −0.984888 | − | 0.173194i | \(-0.944591\pi\) |
0.642434 | + | 0.766341i | \(0.277925\pi\) | |||||||
\(360\) | 918482. | 0.373521 | ||||||||
\(361\) | 1.07765e6 | − | 1.86654e6i | 0.435220 | − | 0.753823i | ||||
\(362\) | −185131. | + | 320656.i | −0.0742519 | + | 0.128608i | ||||
\(363\) | −14580.4 | − | 25254.0i | −0.00580769 | − | 0.0100592i | ||||
\(364\) | 2.46378e6 | + | 4.26740e6i | 0.974651 | + | 1.68815i | ||||
\(365\) | 2.70989e6 | 1.06468 | ||||||||
\(366\) | 34762.1 | 0.0135645 | ||||||||
\(367\) | −865343. | − | 1.49882e6i | −0.335369 | − | 0.580876i | 0.648187 | − | 0.761482i | \(-0.275528\pi\) |
−0.983556 | + | 0.180605i | \(0.942194\pi\) | |||||||
\(368\) | −437329. | − | 757476.i | −0.168341 | − | 0.291574i | ||||
\(369\) | −1.87966e6 | + | 3.25567e6i | −0.718644 | + | 1.24473i | ||||
\(370\) | −366012. | + | 633952.i | −0.138992 | + | 0.240742i | ||||
\(371\) | −700490. | −0.264221 | ||||||||
\(372\) | −117200. | + | 202996.i | −0.0439106 | + | 0.0760553i | ||||
\(373\) | 1.07620e6 | − | 1.86403e6i | 0.400517 | − | 0.693716i | −0.593271 | − | 0.805003i | \(-0.702164\pi\) |
0.993788 | + | 0.111287i | \(0.0354971\pi\) | |||||||
\(374\) | 204452. | − | 354121.i | 0.0755808 | − | 0.130910i | ||||
\(375\) | −93389.1 | − | 161755.i | −0.0342940 | − | 0.0593989i | ||||
\(376\) | 640544. | 0.233657 | ||||||||
\(377\) | 1.94517e6 | + | 3.36914e6i | 0.704863 | + | 1.22086i | ||||
\(378\) | 49743.7 | − | 86158.7i | 0.0179064 | − | 0.0310148i | ||||
\(379\) | −526611. | −0.188318 | −0.0941591 | − | 0.995557i | \(-0.530016\pi\) | ||||
−0.0941591 | + | 0.995557i | \(0.530016\pi\) | |||||||
\(380\) | 420126. | − | 727679.i | 0.149252 | − | 0.258512i | ||||
\(381\) | −33753.7 | − | 58463.1i | −0.0119127 | − | 0.0206333i | ||||
\(382\) | 449659. | + | 778832.i | 0.157661 | + | 0.273077i | ||||
\(383\) | −3.64301e6 | −1.26900 | −0.634502 | − | 0.772921i | \(-0.718795\pi\) | ||||
−0.634502 | + | 0.772921i | \(0.718795\pi\) | |||||||
\(384\) | −71300.9 | − | 123497.i | −0.0246756 | − | 0.0427393i | ||||
\(385\) | −3.53691e6 | −1.21611 | ||||||||
\(386\) | −637211. | −0.217678 | ||||||||
\(387\) | −1.98505e6 | − | 2.16114e6i | −0.673742 | − | 0.733510i | ||||
\(388\) | 32474.6 | 0.0109513 | ||||||||
\(389\) | 1.77768e6 | 0.595636 | 0.297818 | − | 0.954623i | \(-0.403741\pi\) | ||||
0.297818 | + | 0.954623i | \(0.403741\pi\) | |||||||
\(390\) | 29253.1 | + | 50667.9i | 0.00973893 | + | 0.0168683i | ||||
\(391\) | −749010. | −0.247768 | ||||||||
\(392\) | −422273. | − | 731398.i | −0.138796 | − | 0.240402i | ||||
\(393\) | −100064. | − | 173316.i | −0.0326810 | − | 0.0566052i | ||||
\(394\) | −326520. | + | 565548.i | −0.105967 | + | 0.183539i | ||||
\(395\) | −3.79756e6 | −1.22465 | ||||||||
\(396\) | 1.60813e6 | − | 2.78536e6i | 0.515326 | − | 0.892571i | ||||
\(397\) | 69822.7 | + | 120937.i | 0.0222342 | + | 0.0385107i | 0.876928 | − | 0.480621i | \(-0.159589\pi\) |
−0.854694 | + | 0.519132i | \(0.826255\pi\) | |||||||
\(398\) | −542053. | −0.171528 | ||||||||
\(399\) | −46575.3 | − | 80670.8i | −0.0146461 | − | 0.0253679i | ||||
\(400\) | 329148. | − | 570101.i | 0.102859 | − | 0.178157i | ||||
\(401\) | −2.81406e6 | + | 4.87410e6i | −0.873923 | + | 1.51368i | −0.0160174 | + | 0.999872i | \(0.505099\pi\) |
−0.857906 | + | 0.513807i | \(0.828235\pi\) | |||||||
\(402\) | −7295.27 | + | 12635.8i | −0.00225152 | + | 0.00389975i | ||||
\(403\) | 7.57715e6 | 2.32404 | ||||||||
\(404\) | −964053. | + | 1.66979e6i | −0.293865 | + | 0.508989i | ||||
\(405\) | 1.42133e6 | − | 2.46181e6i | 0.430583 | − | 0.745792i | ||||
\(406\) | −414462. | − | 717869.i | −0.124787 | − | 0.216138i | ||||
\(407\) | 2.62882e6 | + | 4.55325e6i | 0.786637 | + | 1.36250i | ||||
\(408\) | −57854.6 | −0.0172063 | ||||||||
\(409\) | 269707. | 0.0797232 | 0.0398616 | − | 0.999205i | \(-0.487308\pi\) | ||||
0.0398616 | + | 0.999205i | \(0.487308\pi\) | |||||||
\(410\) | 472006. | + | 817538.i | 0.138672 | + | 0.240186i | ||||
\(411\) | 22322.7 | + | 38664.0i | 0.00651841 | + | 0.0112902i | ||||
\(412\) | 551960. | − | 956022.i | 0.160201 | − | 0.277476i | ||||
\(413\) | 3.16849e6 | − | 5.48798e6i | 0.914065 | − | 1.58321i | ||||
\(414\) | 301017. | 0.0863157 | ||||||||
\(415\) | −402162. | + | 696564.i | −0.114625 | + | 0.198537i | ||||
\(416\) | −1.74528e6 | + | 3.02291e6i | −0.494460 | + | 0.856430i | ||||
\(417\) | 73865.5 | − | 127939.i | 0.0208018 | − | 0.0360298i | ||||
\(418\) | 154176. | + | 267041.i | 0.0431595 | + | 0.0747545i | ||||
\(419\) | 1.57291e6 | 0.437692 | 0.218846 | − | 0.975759i | \(-0.429771\pi\) | ||||
0.218846 | + | 0.975759i | \(0.429771\pi\) | |||||||
\(420\) | 121991. | + | 211294.i | 0.0337445 | + | 0.0584472i | ||||
\(421\) | −134897. | + | 233649.i | −0.0370935 | + | 0.0642478i | −0.883976 | − | 0.467532i | \(-0.845143\pi\) |
0.846883 | + | 0.531780i | \(0.178477\pi\) | |||||||
\(422\) | 679353. | 0.185701 | ||||||||
\(423\) | 995266. | − | 1.72385e6i | 0.270451 | − | 0.468434i | ||||
\(424\) | −164040. | − | 284126.i | −0.0443135 | − | 0.0767533i | ||||
\(425\) | −281865. | − | 488204.i | −0.0756952 | − | 0.131108i | ||||
\(426\) | −93122.8 | −0.0248618 | ||||||||
\(427\) | −2.34304e6 | − | 4.05826e6i | −0.621884 | − | 1.07713i | ||||
\(428\) | −3.58389e6 | −0.945682 | ||||||||
\(429\) | 420211. | 0.110236 | ||||||||
\(430\) | −719218. | + | 160343.i | −0.187581 | + | 0.0418194i | ||||
\(431\) | 6.42657e6 | 1.66643 | 0.833213 | − | 0.552952i | \(-0.186499\pi\) | ||||
0.833213 | + | 0.552952i | \(0.186499\pi\) | |||||||
\(432\) | −420742. | −0.108469 | ||||||||
\(433\) | −683599. | − | 1.18403e6i | −0.175219 | − | 0.303489i | 0.765018 | − | 0.644009i | \(-0.222730\pi\) |
−0.940237 | + | 0.340520i | \(0.889397\pi\) | |||||||
\(434\) | −1.61448e6 | −0.411442 | ||||||||
\(435\) | 96312.3 | + | 166818.i | 0.0244039 | + | 0.0422687i | ||||
\(436\) | −3.05578e6 | − | 5.29277e6i | −0.769849 | − | 1.33342i | ||||
\(437\) | 282413. | − | 489153.i | 0.0707426 | − | 0.122530i | ||||
\(438\) | 68599.6 | 0.0170858 | ||||||||
\(439\) | 563506. | − | 976022.i | 0.139552 | − | 0.241712i | −0.787775 | − | 0.615963i | \(-0.788767\pi\) |
0.927327 | + | 0.374251i | \(0.122100\pi\) | |||||||
\(440\) | −828274. | − | 1.43461e6i | −0.203959 | − | 0.353267i | ||||
\(441\) | −2.62448e6 | −0.642609 | ||||||||
\(442\) | 455903. | + | 789647.i | 0.110998 | + | 0.192255i | ||||
\(443\) | 3.37733e6 | − | 5.84971e6i | 0.817644 | − | 1.41620i | −0.0897697 | − | 0.995963i | \(-0.528613\pi\) |
0.907414 | − | 0.420238i | \(-0.138054\pi\) | |||||||
\(444\) | 181340. | − | 314089.i | 0.0436551 | − | 0.0756129i | ||||
\(445\) | −1.86116e6 | + | 3.22363e6i | −0.445538 | + | 0.771694i | ||||
\(446\) | 838193. | 0.199529 | ||||||||
\(447\) | 68870.7 | − | 119288.i | 0.0163029 | − | 0.0282375i | ||||
\(448\) | −1.96169e6 | + | 3.39774e6i | −0.461779 | + | 0.799825i | ||||
\(449\) | −2.34313e6 | − | 4.05843e6i | −0.548506 | − | 0.950040i | −0.998377 | − | 0.0569469i | \(-0.981863\pi\) |
0.449871 | − | 0.893093i | \(-0.351470\pi\) | |||||||
\(450\) | 113277. | + | 196202.i | 0.0263701 | + | 0.0456744i | ||||
\(451\) | 6.78020e6 | 1.56964 | ||||||||
\(452\) | 5.91089e6 | 1.36084 | ||||||||
\(453\) | 170718. | + | 295692.i | 0.0390871 | + | 0.0677008i | ||||
\(454\) | 369399. | + | 639819.i | 0.0841117 | + | 0.145686i | ||||
\(455\) | 3.94345e6 | − | 6.83025e6i | 0.892992 | − | 1.54671i | ||||
\(456\) | 21814.0 | − | 37782.9i | 0.00491273 | − | 0.00850909i | ||||
\(457\) | −1.94840e6 | −0.436403 | −0.218202 | − | 0.975904i | \(-0.570019\pi\) | ||||
−0.218202 | + | 0.975904i | \(0.570019\pi\) | |||||||
\(458\) | 246406. | − | 426789.i | 0.0548894 | − | 0.0950712i | ||||
\(459\) | −180150. | + | 312029.i | −0.0399120 | + | 0.0691296i | ||||
\(460\) | −739699. | + | 1.28120e6i | −0.162990 | + | 0.282307i | ||||
\(461\) | −1.47382e6 | − | 2.55272e6i | −0.322991 | − | 0.559437i | 0.658112 | − | 0.752920i | \(-0.271355\pi\) |
−0.981104 | + | 0.193482i | \(0.938022\pi\) | |||||||
\(462\) | −89535.4 | −0.0195159 | ||||||||
\(463\) | −3.81961e6 | − | 6.61576e6i | −0.828069 | − | 1.43426i | −0.899551 | − | 0.436815i | \(-0.856106\pi\) |
0.0714825 | − | 0.997442i | \(-0.477227\pi\) | |||||||
\(464\) | −1.75280e6 | + | 3.03594e6i | −0.377952 | + | 0.654632i | ||||
\(465\) | 375171. | 0.0804632 | ||||||||
\(466\) | 239629. | − | 415050.i | 0.0511181 | − | 0.0885391i | ||||
\(467\) | 850970. | + | 1.47392e6i | 0.180560 | + | 0.312740i | 0.942071 | − | 0.335412i | \(-0.108876\pi\) |
−0.761511 | + | 0.648152i | \(0.775542\pi\) | |||||||
\(468\) | 3.58593e6 | + | 6.21101e6i | 0.756811 | + | 1.31083i | ||||
\(469\) | 1.96687e6 | 0.412898 | ||||||||
\(470\) | −249923. | − | 432880.i | −0.0521870 | − | 0.0903905i | ||||
\(471\) | 269350. | 0.0559455 | ||||||||
\(472\) | 2.96798e6 | 0.613206 | ||||||||
\(473\) | −1.58548e6 | + | 5.04941e6i | −0.325843 | + | 1.03774i | ||||
\(474\) | −96133.6 | −0.0196530 | ||||||||
\(475\) | 425106. | 0.0864497 | ||||||||
\(476\) | 1.90119e6 | + | 3.29296e6i | 0.384599 | + | 0.666146i | ||||
\(477\) | −1.01953e6 | −0.205166 | ||||||||
\(478\) | −84511.4 | − | 146378.i | −0.0169179 | − | 0.0293026i | ||||
\(479\) | 730267. | + | 1.26486e6i | 0.145426 | + | 0.251886i | 0.929532 | − | 0.368742i | \(-0.120211\pi\) |
−0.784106 | + | 0.620627i | \(0.786878\pi\) | |||||||
\(480\) | −86414.8 | + | 149675.i | −0.0171193 | + | 0.0296514i | ||||
\(481\) | −1.17239e7 | −2.31052 | ||||||||
\(482\) | −236731. | + | 410030.i | −0.0464128 | + | 0.0803893i | ||||
\(483\) | 82003.4 | + | 142034.i | 0.0159943 | + | 0.0277029i | ||||
\(484\) | −897629. | −0.174174 | ||||||||
\(485\) | −25988.8 | − | 45014.0i | −0.00501687 | − | 0.00868947i | ||||
\(486\) | 108673. | − | 188227.i | 0.0208704 | − | 0.0361485i | ||||
\(487\) | −4.30934e6 | + | 7.46399e6i | −0.823357 | + | 1.42610i | 0.0798119 | + | 0.996810i | \(0.474568\pi\) |
−0.903169 | + | 0.429286i | \(0.858765\pi\) | |||||||
\(488\) | 1.09738e6 | − | 1.90072e6i | 0.208597 | − | 0.361301i | ||||
\(489\) | 20598.9 | 0.00389557 | ||||||||
\(490\) | −329520. | + | 570745.i | −0.0619999 | + | 0.107387i | ||||
\(491\) | −2.38488e6 | + | 4.13072e6i | −0.446439 | + | 0.773255i | −0.998151 | − | 0.0607798i | \(-0.980641\pi\) |
0.551712 | + | 0.834034i | \(0.313975\pi\) | |||||||
\(492\) | −233854. | − | 405047.i | −0.0435544 | − | 0.0754384i | ||||
\(493\) | 1.50100e6 | + | 2.59981e6i | 0.278140 | + | 0.481753i | ||||
\(494\) | −687589. | −0.126769 | ||||||||
\(495\) | −5.14782e6 | −0.944302 | ||||||||
\(496\) | 3.41389e6 | + | 5.91304e6i | 0.623083 | + | 1.07921i | ||||
\(497\) | 6.27667e6 | + | 1.08715e7i | 1.13983 | + | 1.97424i | ||||
\(498\) | −10180.5 | + | 17633.2i | −0.00183949 | + | 0.00318609i | ||||
\(499\) | 2.58239e6 | − | 4.47283e6i | 0.464269 | − | 0.804138i | −0.534899 | − | 0.844916i | \(-0.679650\pi\) |
0.999168 | + | 0.0407780i | \(0.0129837\pi\) | |||||||
\(500\) | −5.74941e6 | −1.02849 | ||||||||
\(501\) | 285296. | − | 494147.i | 0.0507810 | − | 0.0879553i | ||||
\(502\) | −332044. | + | 575118.i | −0.0588081 | + | 0.101859i | ||||
\(503\) | 4.79895e6 | − | 8.31202e6i | 0.845719 | − | 1.46483i | −0.0392764 | − | 0.999228i | \(-0.512505\pi\) |
0.884995 | − | 0.465600i | \(-0.154161\pi\) | |||||||
\(504\) | −1.56716e6 | − | 2.71441e6i | −0.274813 | − | 0.475991i | ||||
\(505\) | 3.08606e6 | 0.538488 | ||||||||
\(506\) | −271452. | − | 470169.i | −0.0471321 | − | 0.0816353i | ||||
\(507\) | −284900. | + | 493461.i | −0.0492235 | + | 0.0852576i | ||||
\(508\) | −2.07801e6 | −0.357264 | ||||||||
\(509\) | 1.08351e6 | − | 1.87670e6i | 0.185370 | − | 0.321070i | −0.758331 | − | 0.651869i | \(-0.773985\pi\) |
0.943701 | + | 0.330800i | \(0.107318\pi\) | |||||||
\(510\) | 22573.3 | + | 39098.2i | 0.00384300 | + | 0.00665627i | ||||
\(511\) | −4.62376e6 | − | 8.00858e6i | −0.783326 | − | 1.35676i | ||||
\(512\) | −5.33123e6 | −0.898779 | ||||||||
\(513\) | −135851. | − | 235300.i | −0.0227912 | − | 0.0394756i | ||||
\(514\) | 371711. | 0.0620580 | ||||||||
\(515\) | −1.76690e6 | −0.293557 | ||||||||
\(516\) | 356334. | − | 79441.3i | 0.0589160 | − | 0.0131348i | ||||
\(517\) | −3.59006e6 | −0.590712 | ||||||||
\(518\) | 2.49804e6 | 0.409048 | ||||||||
\(519\) | −335230. | − | 580635.i | −0.0546291 | − | 0.0946204i | ||||
\(520\) | 3.69390e6 | 0.599069 | ||||||||
\(521\) | 5.48802e6 | + | 9.50552e6i | 0.885770 | + | 1.53420i | 0.844828 | + | 0.535037i | \(0.179702\pi\) |
0.0409416 | + | 0.999162i | \(0.486964\pi\) | |||||||
\(522\) | −603231. | − | 1.04483e6i | −0.0968964 | − | 0.167830i | ||||
\(523\) | −1.04582e6 | + | 1.81142e6i | −0.167188 | + | 0.289578i | −0.937430 | − | 0.348174i | \(-0.886802\pi\) |
0.770242 | + | 0.637751i | \(0.220135\pi\) | |||||||
\(524\) | −6.16033e6 | −0.980112 | ||||||||
\(525\) | −61718.4 | + | 106899.i | −0.00977275 | + | 0.0169269i | ||||
\(526\) | −333614. | − | 577836.i | −0.0525751 | − | 0.0910627i | ||||
\(527\) | 5.84695e6 | 0.917071 | ||||||||
\(528\) | 189327. | + | 327923.i | 0.0295547 | + | 0.0511903i | ||||
\(529\) | 2.72094e6 | − | 4.71280e6i | 0.422746 | − | 0.732217i | ||||
\(530\) | −128009. | + | 221717.i | −0.0197947 | + | 0.0342854i | ||||
\(531\) | 4.61160e6 | − | 7.98752e6i | 0.709766 | − | 1.22935i | ||||
\(532\) | −2.86736e6 | −0.439242 | ||||||||
\(533\) | −7.55952e6 | + | 1.30935e7i | −1.15259 | + | 1.99635i | ||||
\(534\) | −47114.5 | + | 81604.8i | −0.00714993 | + | 0.0123840i | ||||
\(535\) | 2.86812e6 | + | 4.96774e6i | 0.433225 | + | 0.750368i | ||||
\(536\) | 460600. | + | 797783.i | 0.0692488 | + | 0.119942i | ||||
\(537\) | 339509. | 0.0508060 | ||||||||
\(538\) | −496796. | −0.0739985 | ||||||||
\(539\) | 2.36672e6 | + | 4.09927e6i | 0.350893 | + | 0.607764i | ||||
\(540\) | 355822. | + | 616301.i | 0.0525107 | + | 0.0909512i | ||||
\(541\) | 5.17791e6 | − | 8.96840e6i | 0.760608 | − | 1.31741i | −0.181929 | − | 0.983312i | \(-0.558234\pi\) |
0.942538 | − | 0.334100i | \(-0.108432\pi\) | |||||||
\(542\) | 344491. | − | 596676.i | 0.0503709 | − | 0.0872449i | ||||
\(543\) | −293616. | −0.0427346 | ||||||||
\(544\) | −1.34675e6 | + | 2.33264e6i | −0.195115 | + | 0.337949i | ||||
\(545\) | −4.89098e6 | + | 8.47142e6i | −0.705349 | + | 1.22170i | ||||
\(546\) | 99826.6 | − | 172905.i | 0.0143306 | − | 0.0248213i | ||||
\(547\) | −1.59753e6 | − | 2.76700e6i | −0.228287 | − | 0.395404i | 0.729014 | − | 0.684499i | \(-0.239979\pi\) |
−0.957300 | + | 0.289095i | \(0.906646\pi\) | |||||||
\(548\) | 1.37427e6 | 0.195489 | ||||||||
\(549\) | −3.41019e6 | − | 5.90662e6i | −0.482889 | − | 0.836389i | ||||
\(550\) | 204304. | − | 353865.i | 0.0287985 | − | 0.0498805i | ||||
\(551\) | −2.26380e6 | −0.317657 | ||||||||
\(552\) | −38407.1 | + | 66523.0i | −0.00536492 | + | 0.00929232i | ||||
\(553\) | 6.47961e6 | + | 1.12230e7i | 0.901023 | + | 1.56062i | ||||
\(554\) | 66555.8 | + | 115278.i | 0.00921322 | + | 0.0159578i | ||||
\(555\) | −580492. | −0.0799951 | ||||||||
\(556\) | −2.27373e6 | − | 3.93822e6i | −0.311926 | − | 0.540272i | ||||
\(557\) | 7.52794e6 | 1.02811 | 0.514053 | − | 0.857758i | \(-0.328143\pi\) | ||||
0.514053 | + | 0.857758i | \(0.328143\pi\) | |||||||
\(558\) | −2.34981e6 | −0.319482 | ||||||||
\(559\) | −7.98336e6 | − | 8.69157e6i | −1.08058 | − | 1.17644i | ||||
\(560\) | 7.10690e6 | 0.957657 | ||||||||
\(561\) | 324258. | 0.0434995 | ||||||||
\(562\) | 1.15853e6 | + | 2.00664e6i | 0.154728 | + | 0.267996i | ||||
\(563\) | −1.99120e6 | −0.264754 | −0.132377 | − | 0.991199i | \(-0.542261\pi\) | ||||
−0.132377 | + | 0.991199i | \(0.542261\pi\) | |||||||
\(564\) | 123824. | + | 214469.i | 0.0163910 | + | 0.0283901i | ||||
\(565\) | −4.73038e6 | − | 8.19327e6i | −0.623412 | − | 1.07978i | ||||
\(566\) | −858689. | + | 1.48729e6i | −0.112666 | + | 0.195144i | ||||
\(567\) | −9.70059e6 | −1.26719 | ||||||||
\(568\) | −2.93974e6 | + | 5.09178e6i | −0.382330 | + | 0.662214i | ||||
\(569\) | 2.63816e6 | + | 4.56943e6i | 0.341602 | + | 0.591672i | 0.984730 | − | 0.174086i | \(-0.0556972\pi\) |
−0.643128 | + | 0.765758i | \(0.722364\pi\) | |||||||
\(570\) | −34044.9 | −0.00438900 | ||||||||
\(571\) | 2.48880e6 | + | 4.31072e6i | 0.319447 | + | 0.553299i | 0.980373 | − | 0.197153i | \(-0.0631695\pi\) |
−0.660926 | + | 0.750451i | \(0.729836\pi\) | |||||||
\(572\) | 6.46748e6 | − | 1.12020e7i | 0.826504 | − | 1.43155i | ||||
\(573\) | −356577. | + | 617610.i | −0.0453699 | + | 0.0785829i | ||||
\(574\) | 1.61072e6 | − | 2.78985e6i | 0.204052 | − | 0.353429i | ||||
\(575\) | −748469. | −0.0944070 | ||||||||
\(576\) | −2.85515e6 | + | 4.94526e6i | −0.358569 | + | 0.621060i | ||||
\(577\) | 7.73379e6 | − | 1.33953e7i | 0.967059 | − | 1.67499i | 0.263080 | − | 0.964774i | \(-0.415262\pi\) |
0.703979 | − | 0.710221i | \(-0.251405\pi\) | |||||||
\(578\) | −533632. | − | 924278.i | −0.0664389 | − | 0.115076i | ||||
\(579\) | −252652. | − | 437607.i | −0.0313204 | − | 0.0542485i | ||||
\(580\) | 5.92937e6 | 0.731878 | ||||||||
\(581\) | 2.74476e6 | 0.337337 | ||||||||
\(582\) | −657.896 | − | 1139.51i | −8.05099e−5 | − | 0.000139447i | ||||
\(583\) | 919399. | + | 1.59245e6i | 0.112030 | + | 0.194041i | ||||
\(584\) | 2.16558e6 | − | 3.75090e6i | 0.262750 | − | 0.455096i | ||||
\(585\) | 5.73952e6 | − | 9.94113e6i | 0.693403 | − | 1.20101i | ||||
\(586\) | 2.94428e6 | 0.354189 | ||||||||
\(587\) | −1.72030e6 | + | 2.97965e6i | −0.206068 | + | 0.356920i | −0.950472 | − | 0.310809i | \(-0.899400\pi\) |
0.744405 | + | 0.667729i | \(0.232733\pi\) | |||||||
\(588\) | 163259. | − | 282774.i | 0.0194731 | − | 0.0337284i | ||||
\(589\) | −2.20458e6 | + | 3.81844e6i | −0.261841 | + | 0.453522i | ||||
\(590\) | −1.15803e6 | − | 2.00576e6i | −0.136959 | − | 0.237219i | ||||
\(591\) | −517857. | −0.0609875 | ||||||||
\(592\) | −5.28222e6 | − | 9.14907e6i | −0.619458 | − | 1.07293i | ||||
\(593\) | −5.95063e6 | + | 1.03068e7i | −0.694906 | + | 1.20361i | 0.275307 | + | 0.961356i | \(0.411221\pi\) |
−0.970212 | + | 0.242256i | \(0.922113\pi\) | |||||||
\(594\) | −261156. | −0.0303693 | ||||||||
\(595\) | 3.04298e6 | − | 5.27060e6i | 0.352377 | − | 0.610334i | ||||
\(596\) | −2.11998e6 | − | 3.67191e6i | −0.244465 | − | 0.423425i | ||||
\(597\) | −214923. | − | 372257.i | −0.0246801 | − | 0.0427472i | ||||
\(598\) | 1.21061e6 | 0.138437 | ||||||||
\(599\) | −2.25127e6 | − | 3.89931e6i | −0.256366 | − | 0.444039i | 0.708900 | − | 0.705309i | \(-0.249192\pi\) |
−0.965266 | + | 0.261270i | \(0.915859\pi\) | |||||||
\(600\) | −57812.8 | −0.00655611 | ||||||||
\(601\) | 2.84128e6 | 0.320869 | 0.160434 | − | 0.987047i | \(-0.448711\pi\) | ||||
0.160434 | + | 0.987047i | \(0.448711\pi\) | |||||||
\(602\) | 1.70103e6 | + | 1.85193e6i | 0.191303 | + | 0.208273i | ||||
\(603\) | 2.86269e6 | 0.320613 | ||||||||
\(604\) | 1.05101e7 | 1.17223 | ||||||||
\(605\) | 718357. | + | 1.24423e6i | 0.0797906 | + | 0.138201i | ||||
\(606\) | 78122.2 | 0.00864157 | ||||||||
\(607\) | −4.72627e6 | − | 8.18614e6i | −0.520651 | − | 0.901794i | −0.999712 | − | 0.0240121i | \(-0.992356\pi\) |
0.479061 | − | 0.877782i | \(-0.340977\pi\) | |||||||
\(608\) | −1.01558e6 | − | 1.75904e6i | −0.111418 | − | 0.192982i | ||||
\(609\) | 328666. | − | 569267.i | 0.0359097 | − | 0.0621975i | ||||
\(610\) | −1.71268e6 | −0.186360 | ||||||||
\(611\) | 4.00271e6 | − | 6.93289e6i | 0.433761 | − | 0.751296i | ||||
\(612\) | 2.76710e6 | + | 4.79276e6i | 0.298639 | + | 0.517258i | ||||
\(613\) | −9.44159e6 | −1.01483 | −0.507416 | − | 0.861701i | \(-0.669399\pi\) | ||||
−0.507416 | + | 0.861701i | \(0.669399\pi\) | |||||||
\(614\) | −348777. | − | 604100.i | −0.0373360 | − | 0.0646678i | ||||
\(615\) | −374298. | + | 648304.i | −0.0399053 | + | 0.0691179i | ||||
\(616\) | −2.82649e6 | + | 4.89562e6i | −0.300120 | + | 0.519824i | ||||
\(617\) | −1.55546e6 | + | 2.69414e6i | −0.164493 | + | 0.284909i | −0.936475 | − | 0.350734i | \(-0.885932\pi\) |
0.771982 | + | 0.635644i | \(0.219265\pi\) | |||||||
\(618\) | −44728.2 | −0.00471096 | ||||||||
\(619\) | −1.44636e6 | + | 2.50517e6i | −0.151722 | + | 0.262791i | −0.931861 | − | 0.362816i | \(-0.881815\pi\) |
0.780138 | + | 0.625607i | \(0.215149\pi\) | |||||||
\(620\) | 5.77427e6 | − | 1.00013e7i | 0.603278 | − | 1.04491i | ||||
\(621\) | 239187. | + | 414284.i | 0.0248891 | + | 0.0431091i | ||||
\(622\) | 1.14505e6 | + | 1.98329e6i | 0.118672 | + | 0.205546i | ||||
\(623\) | 1.27025e7 | 1.31120 | ||||||||
\(624\) | −844352. | −0.0868084 | ||||||||
\(625\) | 3.42842e6 | + | 5.93820e6i | 0.351070 | + | 0.608071i | ||||
\(626\) | −1.38196e6 | − | 2.39363e6i | −0.140949 | − | 0.244130i | ||||
\(627\) | −122261. | + | 211762.i | −0.0124199 | + | 0.0215119i | ||||
\(628\) | 4.14557e6 | − | 7.18034e6i | 0.419455 | − | 0.726517i | ||||
\(629\) | −9.04681e6 | −0.911736 | ||||||||
\(630\) | −1.22293e6 | + | 2.11818e6i | −0.122758 | + | 0.212624i | ||||
\(631\) | −3.76998e6 | + | 6.52979e6i | −0.376934 | + | 0.652868i | −0.990614 | − | 0.136686i | \(-0.956355\pi\) |
0.613681 | + | 0.789554i | \(0.289688\pi\) | |||||||
\(632\) | −3.03479e6 | + | 5.25640e6i | −0.302228 | + | 0.523475i | ||||
\(633\) | 269362. | + | 466549.i | 0.0267194 | + | 0.0462794i | ||||
\(634\) | −2.77697e6 | −0.274378 | ||||||||
\(635\) | 1.66300e6 | + | 2.88040e6i | 0.163666 | + | 0.283477i | ||||
\(636\) | 63421.4 | − | 109849.i | 0.00621718 | − | 0.0107685i | ||||
\(637\) | −1.05550e7 | −1.03065 | ||||||||
\(638\) | −1.08797e6 | + | 1.88442e6i | −0.105819 | + | 0.183285i | ||||
\(639\) | 9.13543e6 | + | 1.58230e7i | 0.885068 | + | 1.53298i | ||||
\(640\) | 3.51290e6 | + | 6.08452e6i | 0.339012 | + | 0.587187i | ||||
\(641\) | −6.12124e6 | −0.588429 | −0.294214 | − | 0.955739i | \(-0.595058\pi\) | ||||
−0.294214 | + | 0.955739i | \(0.595058\pi\) | |||||||
\(642\) | 72605.3 | + | 125756.i | 0.00695233 | + | 0.0120418i | ||||
\(643\) | −8.80693e6 | −0.840035 | −0.420017 | − | 0.907516i | \(-0.637976\pi\) | ||||
−0.420017 | + | 0.907516i | \(0.637976\pi\) | |||||||
\(644\) | 5.04846e6 | 0.479672 | ||||||||
\(645\) | −395284. | − | 430350.i | −0.0374119 | − | 0.0407308i | ||||
\(646\) | −530582. | −0.0500231 | ||||||||
\(647\) | 1.51956e7 | 1.42711 | 0.713557 | − | 0.700598i | \(-0.247083\pi\) | ||||
0.713557 | + | 0.700598i | \(0.247083\pi\) | |||||||
\(648\) | −2.27168e6 | − | 3.93467e6i | −0.212525 | − | 0.368104i | ||||
\(649\) | −1.66347e7 | −1.55025 | ||||||||
\(650\) | 455573. | + | 789076.i | 0.0422936 | + | 0.0732547i | ||||
\(651\) | −640137. | − | 1.10875e6i | −0.0591999 | − | 0.102537i | ||||
\(652\) | 317037. | − | 549125.i | 0.0292073 | − | 0.0505885i | ||||
\(653\) | 1.10998e7 | 1.01867 | 0.509335 | − | 0.860568i | \(-0.329891\pi\) | ||||
0.509335 | + | 0.860568i | \(0.329891\pi\) | |||||||
\(654\) | −123813. | + | 214450.i | −0.0113193 | + | 0.0196057i | ||||
\(655\) | 4.93001e6 | + | 8.53902e6i | 0.448998 | + | 0.777687i | ||||
\(656\) | −1.36238e7 | −1.23606 | ||||||||
\(657\) | −6.72968e6 | − | 1.16561e7i | −0.608248 | − | 1.05352i | ||||
\(658\) | −852865. | + | 1.47721e6i | −0.0767920 | + | 0.133008i | ||||
\(659\) | 654712. | − | 1.13399e6i | 0.0587268 | − | 0.101718i | −0.835167 | − | 0.549996i | \(-0.814629\pi\) |
0.893894 | + | 0.448278i | \(0.147963\pi\) | |||||||
\(660\) | 320228. | − | 554650.i | 0.0286153 | − | 0.0495632i | ||||
\(661\) | 7.77181e6 | 0.691861 | 0.345930 | − | 0.938260i | \(-0.387563\pi\) | ||||
0.345930 | + | 0.938260i | \(0.387563\pi\) | |||||||
\(662\) | 1.47765e6 | − | 2.55936e6i | 0.131046 | − | 0.226979i | ||||
\(663\) | −361529. | + | 626186.i | −0.0319418 | + | 0.0553248i | ||||
\(664\) | 642767. | + | 1.11331e6i | 0.0565761 | + | 0.0979928i | ||||
\(665\) | 2.29470e6 | + | 3.97454e6i | 0.201220 | + | 0.348524i | ||||
\(666\) | 3.63579e6 | 0.317624 | ||||||||
\(667\) | 3.98579e6 | 0.346896 | ||||||||
\(668\) | −8.78199e6 | − | 1.52109e7i | −0.761468 | − | 1.31890i | ||||
\(669\) | 332341. | + | 575632.i | 0.0287091 | + | 0.0497256i | ||||
\(670\) | 359428. | − | 622547.i | 0.0309332 | − | 0.0535779i | ||||
\(671\) | −6.15051e6 | + | 1.06530e7i | −0.527357 | + | 0.913410i | ||||
\(672\) | 589782. | 0.0503812 | ||||||||
\(673\) | −3.86953e6 | + | 6.70222e6i | −0.329322 | + | 0.570402i | −0.982377 | − | 0.186908i | \(-0.940153\pi\) |
0.653056 | + | 0.757310i | \(0.273487\pi\) | |||||||
\(674\) | −255796. | + | 443052.i | −0.0216892 | + | 0.0375668i | ||||
\(675\) | −180020. | + | 311804.i | −0.0152076 | + | 0.0263404i | ||||
\(676\) | 8.76979e6 | + | 1.51897e7i | 0.738113 | + | 1.27845i | ||||
\(677\) | −2.00333e7 | −1.67989 | −0.839944 | − | 0.542673i | \(-0.817412\pi\) | ||||
−0.839944 | + | 0.542673i | \(0.817412\pi\) | |||||||
\(678\) | −119748. | − | 207409.i | −0.0100044 | − | 0.0173282i | ||||
\(679\) | −88687.1 | + | 153611.i | −0.00738220 | + | 0.0127864i | ||||
\(680\) | 2.85042e6 | 0.236394 | ||||||||
\(681\) | −292932. | + | 507373.i | −0.0242047 | + | 0.0419237i | ||||
\(682\) | 2.11902e6 | + | 3.67025e6i | 0.174451 | + | 0.302158i | ||||
\(683\) | −2.04056e6 | − | 3.53435e6i | −0.167377 | − | 0.289906i | 0.770120 | − | 0.637900i | \(-0.220197\pi\) |
−0.937497 | + | 0.347993i | \(0.886863\pi\) | |||||||
\(684\) | −4.17332e6 | −0.341068 | ||||||||
\(685\) | −1.09981e6 | − | 1.90492e6i | −0.0895551 | − | 0.155114i | ||||
\(686\) | −1.23669e6 | −0.100335 | ||||||||
\(687\) | 390798. | 0.0315908 | ||||||||
\(688\) | 3.18579e6 | − | 1.01460e7i | 0.256594 | − | 0.817193i | ||||
\(689\) | −4.10030e6 | −0.329054 | ||||||||
\(690\) | 59941.7 | 0.00479299 | ||||||||
\(691\) | 1.14627e7 | + | 1.98540e7i | 0.913254 | + | 1.58180i | 0.809438 | + | 0.587205i | \(0.199772\pi\) |
0.103816 | + | 0.994597i | \(0.466895\pi\) | |||||||
\(692\) | −2.06381e7 | −1.63834 | ||||||||
\(693\) | 8.78349e6 | + | 1.52135e7i | 0.694759 | + | 1.20336i | ||||
\(694\) | −2.48751e6 | − | 4.30849e6i | −0.196049 | − | 0.339568i | ||||
\(695\) | −3.63925e6 | + | 6.30337e6i | −0.285792 | + | 0.495007i | ||||
\(696\) | 307868. | 0.0240903 | ||||||||
\(697\) | −5.83334e6 | + | 1.01036e7i | −0.454816 | + | 0.787764i | ||||
\(698\) | −2.55393e6 | − | 4.42353e6i | −0.198413 | − | 0.343662i | ||||
\(699\) | 380049. | 0.0294203 | ||||||||
\(700\) | 1.89982e6 | + | 3.29058e6i | 0.146544 | + | 0.253821i | ||||
\(701\) | 7.78266e6 | − | 1.34800e7i | 0.598182 | − | 1.03608i | −0.394908 | − | 0.918721i | \(-0.629223\pi\) |
0.993089 | − | 0.117360i | \(-0.0374432\pi\) | |||||||
\(702\) | 291174. | − | 504328.i | 0.0223002 | − | 0.0386251i | ||||
\(703\) | 3.41108e6 | − | 5.90817e6i | 0.260318 | − | 0.450884i | ||||
\(704\) | 1.02989e7 | 0.783178 | ||||||||
\(705\) | 198188. | − | 343272.i | 0.0150177 | − | 0.0260115i | ||||
\(706\) | 2.31139e6 | − | 4.00344e6i | 0.174526 | − | 0.302288i | ||||
\(707\) | −5.26560e6 | − | 9.12029e6i | −0.396186 | − | 0.686215i | ||||
\(708\) | 573741. | + | 993749.i | 0.0430163 | + | 0.0745064i | ||||
\(709\) | 2.09179e7 | 1.56279 | 0.781397 | − | 0.624034i | \(-0.214507\pi\) | ||||
0.781397 | + | 0.624034i | \(0.214507\pi\) | |||||||
\(710\) | 4.58803e6 | 0.341571 | ||||||||
\(711\) | 9.43079e6 | + | 1.63346e7i | 0.699639 | + | 1.21181i | ||||
\(712\) | 2.97466e6 | + | 5.15227e6i | 0.219906 | + | 0.380889i | ||||
\(713\) | 3.88152e6 | − | 6.72299e6i | 0.285942 | − | 0.495267i | ||||
\(714\) | 77031.7 | − | 133423.i | 0.00565489 | − | 0.00979455i | ||||
\(715\) | −2.07032e7 | −1.51451 | ||||||||
\(716\) | 5.22538e6 | − | 9.05063e6i | 0.380921 | − | 0.659775i | ||||
\(717\) | 67017.2 | − | 116077.i | 0.00486842 | − | 0.00843235i | ||||
\(718\) | 1.04299e6 | − | 1.80650e6i | 0.0755035 | − | 0.130776i | ||||
\(719\) | −3.53782e6 | − | 6.12768e6i | −0.255219 | − | 0.442052i | 0.709736 | − | 0.704468i | \(-0.248814\pi\) |
−0.964955 | + | 0.262416i | \(0.915481\pi\) | |||||||
\(720\) | 1.03438e7 | 0.743615 | ||||||||
\(721\) | 3.01477e6 | + | 5.22174e6i | 0.215981 | + | 0.374091i | ||||
\(722\) | −1.34406e6 | + | 2.32797e6i | −0.0959565 | + | 0.166202i | ||||
\(723\) | −375453. | −0.0267122 | ||||||||
\(724\) | −4.51904e6 | + | 7.82721e6i | −0.320406 | + | 0.554959i | ||||
\(725\) | 1.49992e6 | + | 2.59793e6i | 0.105980 | + | 0.183562i | ||||
\(726\) | 18184.9 | + | 31497.1i | 0.00128047 | + | 0.00221784i | ||||
\(727\) | −1.38648e7 | −0.972919 | −0.486460 | − | 0.873703i | \(-0.661712\pi\) | ||||
−0.486460 | + | 0.873703i | \(0.661712\pi\) | |||||||
\(728\) | −6.30273e6 | − | 1.09167e7i | −0.440758 | − | 0.763416i | ||||
\(729\) | −1.40035e7 | −0.975928 | ||||||||
\(730\) | −3.37981e6 | −0.234739 | ||||||||
\(731\) | −6.16040e6 | − | 6.70689e6i | −0.426398 | − | 0.464224i | ||||
\(732\) | 848542. | 0.0585323 | ||||||||
\(733\) | −5.59992e6 | −0.384965 | −0.192483 | − | 0.981300i | \(-0.561654\pi\) | ||||
−0.192483 | + | 0.981300i | \(0.561654\pi\) | |||||||
\(734\) | 1.07927e6 | + | 1.86934e6i | 0.0739416 | + | 0.128071i | ||||
\(735\) | −522615. | −0.0356832 | ||||||||
\(736\) | 1.78810e6 | + | 3.09707e6i | 0.121674 | + | 0.210745i | ||||
\(737\) | −2.58153e6 | − | 4.47134e6i | −0.175069 | − | 0.303228i | ||||
\(738\) | 2.34434e6 | − | 4.06051e6i | 0.158445 | − | 0.274435i | ||||
\(739\) | 9.61223e6 | 0.647460 | 0.323730 | − | 0.946149i | \(-0.395063\pi\) | ||||
0.323730 | + | 0.946149i | \(0.395063\pi\) | |||||||
\(740\) | −8.93435e6 | + | 1.54748e7i | −0.599769 | + | 1.03883i | ||||
\(741\) | −272627. | − | 472204.i | −0.0182400 | − | 0.0315925i | ||||
\(742\) | 873660. | 0.0582549 | ||||||||
\(743\) | −1.22155e7 | − | 2.11579e7i | −0.811783 | − | 1.40605i | −0.911615 | − | 0.411045i | \(-0.865164\pi\) |
0.0998321 | − | 0.995004i | \(-0.468169\pi\) | |||||||
\(744\) | 299814. | − | 519294.i | 0.0198573 | − | 0.0343939i | ||||
\(745\) | −3.39316e6 | + | 5.87713e6i | −0.223983 | + | 0.387949i | ||||
\(746\) | −1.34225e6 | + | 2.32485e6i | −0.0883053 | + | 0.152949i | ||||
\(747\) | 3.99488e6 | 0.261940 | ||||||||
\(748\) | 4.99066e6 | − | 8.64408e6i | 0.326140 | − | 0.564891i | ||||
\(749\) | 9.78749e6 | − | 1.69524e7i | 0.637481 | − | 1.10415i | ||||
\(750\) | 116476. | + | 201742.i | 0.00756107 | + | 0.0130962i | ||||
\(751\) | −23719.0 | − | 41082.5i | −0.00153461 | − | 0.00265802i | 0.865257 | − | 0.501328i | \(-0.167155\pi\) |
−0.866792 | + | 0.498670i | \(0.833822\pi\) | |||||||
\(752\) | 7.21369e6 | 0.465171 | ||||||||
\(753\) | −526619. | −0.0338461 | ||||||||
\(754\) | −2.42604e6 | − | 4.20203e6i | −0.155407 | − | 0.269173i | ||||
\(755\) | −8.41103e6 | − | 1.45683e7i | −0.537009 | − | 0.930128i | ||||
\(756\) | 1.21424e6 | − | 2.10313e6i | 0.0772683 | − | 0.133833i | ||||
\(757\) | 1.24520e7 | − | 2.15675e7i | 0.789769 | − | 1.36792i | −0.136339 | − | 0.990662i | \(-0.543534\pi\) |
0.926108 | − | 0.377258i | \(-0.123133\pi\) | |||||||
\(758\) | 656797. | 0.0415200 | ||||||||
\(759\) | 215260. | − | 372842.i | 0.0135631 | − | 0.0234920i | ||||
\(760\) | −1.07474e6 | + | 1.86151e6i | −0.0674950 | + | 0.116905i | ||||
\(761\) | −1.01477e7 | + | 1.75763e7i | −0.635193 | + | 1.10019i | 0.351282 | + | 0.936270i | \(0.385746\pi\) |
−0.986474 | + | 0.163916i | \(0.947587\pi\) | |||||||
\(762\) | 42098.1 | + | 72916.0i | 0.00262648 | + | 0.00454920i | ||||
\(763\) | 3.33810e7 | 2.07581 | ||||||||
\(764\) | 1.09762e7 | + | 1.90113e7i | 0.680327 | + | 1.17836i | ||||
\(765\) | 4.42893e6 | − | 7.67113e6i | 0.273618 | − | 0.473921i | ||||
\(766\) | 4.54360e6 | 0.279788 | ||||||||
\(767\) | 1.85467e7 | − | 3.21238e7i | 1.13835 | − | 1.97169i | ||||
\(768\) | −284439. | − | 492663.i | −0.0174015 | − | 0.0301403i | ||||
\(769\) | 4.80391e6 | + | 8.32062e6i | 0.292940 | + | 0.507388i | 0.974504 | − | 0.224372i | \(-0.0720329\pi\) |
−0.681563 | + | 0.731759i | \(0.738700\pi\) | |||||||
\(770\) | 4.41129e6 | 0.268126 | ||||||||
\(771\) | 147383. | + | 255274.i | 0.00892915 | + | 0.0154657i | ||||
\(772\) | −1.55543e7 | −0.939307 | ||||||||
\(773\) | 1.99799e7 | 1.20267 | 0.601333 | − | 0.798998i | \(-0.294636\pi\) | ||||
0.601333 | + | 0.798998i | \(0.294636\pi\) | |||||||
\(774\) | 2.47578e6 | + | 2.69541e6i | 0.148545 | + | 0.161723i | ||||
\(775\) | 5.84272e6 | 0.349431 | ||||||||
\(776\) | −83074.9 | −0.00495240 | ||||||||
\(777\) | 990466. | + | 1.71554e6i | 0.0588555 | + | 0.101941i | ||||
\(778\) | −2.21715e6 | −0.131325 | ||||||||
\(779\) | −4.39890e6 | − | 7.61912e6i | −0.259717 | − | 0.449843i | ||||
\(780\) | 714069. | + | 1.23680e6i | 0.0420246 | + | 0.0727888i | ||||
\(781\) | 1.64764e7 | − | 2.85379e7i | 0.966572 | − | 1.67415i | ||||
\(782\) | 934175. | 0.0546275 | ||||||||
\(783\) | 958653. | − | 1.66043e6i | 0.0558801 | − | 0.0967871i | ||||
\(784\) | −4.75556e6 | − | 8.23688e6i | −0.276320 | − | 0.478600i | ||||
\(785\) | −1.32705e7 | −0.768624 | ||||||||
\(786\) | 124801. | + | 216161.i | 0.00720545 | + | 0.0124802i | ||||
\(787\) | −2.75984e6 | + | 4.78018e6i | −0.158835 | + | 0.275111i | −0.934449 | − | 0.356097i | \(-0.884107\pi\) |
0.775614 | + | 0.631208i | \(0.217441\pi\) | |||||||
\(788\) | −7.97034e6 | + | 1.38050e7i | −0.457258 | + | 0.791994i | ||||
\(789\) | 264554. | − | 458221.i | 0.0151294 | − | 0.0262049i | ||||
\(790\) | 4.73637e6 | 0.270009 | ||||||||
\(791\) | −1.61425e7 | + | 2.79596e7i | −0.917337 | + | 1.58887i | ||||
\(792\) | −4.11383e6 | + | 7.12537e6i | −0.233042 | + | 0.403640i | ||||
\(793\) | −1.37149e7 | − | 2.37549e7i | −0.774480 | − | 1.34144i | ||||
\(794\) | −87083.8 | − | 150834.i | −0.00490215 | − | 0.00849077i | ||||
\(795\) | −203020. | −0.0113926 | ||||||||
\(796\) | −1.32315e7 | −0.740162 | ||||||||
\(797\) | 4.77048e6 | + | 8.26272e6i | 0.266021 | + | 0.460763i | 0.967831 | − | 0.251602i | \(-0.0809575\pi\) |
−0.701809 | + | 0.712365i | \(0.747624\pi\) | |||||||
\(798\) | 58089.3 | + | 100614.i | 0.00322916 | + | 0.00559306i | ||||
\(799\) | 3.08871e6 | − | 5.34980e6i | 0.171163 | − | 0.296463i | ||||
\(800\) | −1.34578e6 | + | 2.33096e6i | −0.0743445 | + | 0.128768i | ||||
\(801\) | 1.84879e7 | 1.01814 | ||||||||
\(802\) | 3.50974e6 | − | 6.07905e6i | 0.192681 | − | 0.333733i | ||||
\(803\) | −1.21374e7 | + | 2.10227e7i | −0.664261 | + | 1.15053i | ||||
\(804\) | −178077. | + | 308439.i | −0.00971558 | + | 0.0168279i | ||||
\(805\) | −4.04019e6 | − | 6.99782e6i | −0.219742 | − | 0.380604i | ||||
\(806\) | −9.45032e6 | −0.512400 | ||||||||
\(807\) | −196979. | − | 341177.i | −0.0106472 | − | 0.0184415i | ||||
\(808\) | 2.46619e6 | − | 4.27157e6i | 0.132892 | − | 0.230176i | ||||
\(809\) | −2.31166e7 | −1.24180 | −0.620900 | − | 0.783889i | \(-0.713233\pi\) | ||||
−0.620900 | + | 0.783889i | \(0.713233\pi\) | |||||||
\(810\) | −1.77270e6 | + | 3.07041e6i | −0.0949342 | + | 0.164431i | ||||
\(811\) | 5.72963e6 | + | 9.92401e6i | 0.305897 | + | 0.529828i | 0.977461 | − | 0.211118i | \(-0.0677105\pi\) |
−0.671564 | + | 0.740947i | \(0.734377\pi\) | |||||||
\(812\) | −1.01170e7 | − | 1.75232e7i | −0.538471 | − | 0.932659i | ||||
\(813\) | 546359. | 0.0289902 | ||||||||
\(814\) | −3.27870e6 | − | 5.67887e6i | −0.173436 | − | 0.300401i | ||||
\(815\) | −1.01488e6 | −0.0535205 | ||||||||
\(816\) | −651548. | −0.0342548 | ||||||||
\(817\) | 6.70281e6 | − | 1.49433e6i | 0.351319 | − | 0.0783233i | ||||
\(818\) | −336383. | −0.0175772 | ||||||||
\(819\) | −3.91723e7 | −2.04065 | ||||||||
\(820\) | 1.15217e7 | + | 1.99561e7i | 0.598385 | + | 1.03643i | ||||
\(821\) | 2.73375e7 | 1.41547 | 0.707736 | − | 0.706477i | \(-0.249717\pi\) | ||||
0.707736 | + | 0.706477i | \(0.249717\pi\) | |||||||
\(822\) | −27841.1 | − | 48222.2i | −0.00143717 | − | 0.00248925i | ||||
\(823\) | 5.51095e6 | + | 9.54525e6i | 0.283614 | + | 0.491233i | 0.972272 | − | 0.233853i | \(-0.0751333\pi\) |
−0.688658 | + | 0.725086i | \(0.741800\pi\) | |||||||
\(824\) | −1.41200e6 | + | 2.44565e6i | −0.0724462 | + | 0.125481i | ||||
\(825\) | 324024. | 0.0165746 | ||||||||
\(826\) | −3.95178e6 | + | 6.84468e6i | −0.201531 | + | 0.349062i | ||||
\(827\) | −5.50128e6 | − | 9.52849e6i | −0.279705 | − | 0.484463i | 0.691607 | − | 0.722274i | \(-0.256903\pi\) |
−0.971311 | + | 0.237812i | \(0.923570\pi\) | |||||||
\(828\) | 7.34781e6 | 0.372462 | ||||||||
\(829\) | 1.11216e7 | + | 1.92632e7i | 0.562060 | + | 0.973516i | 0.997317 | + | 0.0732096i | \(0.0233242\pi\) |
−0.435257 | + | 0.900306i | \(0.643342\pi\) | |||||||
\(830\) | 501581. | − | 868764.i | 0.0252724 | − | 0.0437730i | ||||
\(831\) | −52778.4 | + | 91414.9i | −0.00265127 | + | 0.00459213i | ||||
\(832\) | −1.14827e7 | + | 1.98886e7i | −0.575089 | + | 0.996084i | ||||
\(833\) | −8.14482e6 | −0.406695 | ||||||||
\(834\) | −92126.0 | + | 159567.i | −0.00458635 | + | 0.00794379i | ||||
\(835\) | −1.40562e7 | + | 2.43460e7i | −0.697670 | + | 1.20840i | ||||
\(836\) | 3.76344e6 | + | 6.51847e6i | 0.186238 | + | 0.322574i | ||||
\(837\) | −1.86715e6 | − | 3.23400e6i | −0.0921225 | − | 0.159561i | ||||
\(838\) | −1.96175e6 | −0.0965014 | ||||||||
\(839\) | 2.10834e7 | 1.03404 | 0.517018 | − | 0.855974i | \(-0.327042\pi\) | ||||
0.517018 | + | 0.855974i | \(0.327042\pi\) | |||||||
\(840\) | −312070. | − | 540522.i | −0.0152600 | − | 0.0264311i | ||||
\(841\) | 2.26813e6 | + | 3.92852e6i | 0.110581 | + | 0.191531i | ||||
\(842\) | 168246. | − | 291410.i | 0.00817830 | − | 0.0141652i | ||||
\(843\) | −918712. | + | 1.59126e6i | −0.0445257 | + | 0.0771208i | ||||
\(844\) | 1.65830e7 | 0.801322 | ||||||||
\(845\) | 1.40366e7 | − | 2.43122e7i | 0.676271 | − | 1.17134i | ||||
\(846\) | −1.24131e6 | + | 2.15001e6i | −0.0596285 | + | 0.103280i | ||||
\(847\) | 2.45140e6 | − | 4.24595e6i | 0.117410 | − | 0.203360i | ||||
\(848\) | −1.84739e6 | − | 3.19978e6i | −0.0882206 | − | 0.152803i | ||||
\(849\) | −1.36187e6 | −0.0648436 | ||||||||
\(850\) | 351545. | + | 608895.i | 0.0166892 | + | 0.0289065i | ||||
\(851\) | −6.00577e6 | + | 1.04023e7i | −0.284279 | + | 0.492385i | ||||
\(852\) | −2.27313e6 | −0.107281 | ||||||||
\(853\) | −1.58980e7 | + | 2.75361e7i | −0.748116 | + | 1.29578i | 0.200609 | + | 0.979671i | \(0.435708\pi\) |
−0.948725 | + | 0.316104i | \(0.897625\pi\) | |||||||
\(854\) | 2.92227e6 | + | 5.06151e6i | 0.137112 | + | 0.237485i | ||||
\(855\) | 3.33984e6 | + | 5.78477e6i | 0.156246 | + | 0.270627i | ||||
\(856\) | 9.16813e6 | 0.427658 | ||||||||
\(857\) | −811149. | − | 1.40495e6i | −0.0377267 | − | 0.0653445i | 0.846546 | − | 0.532316i | \(-0.178678\pi\) |
−0.884272 | + | 0.466972i | \(0.845345\pi\) | |||||||
\(858\) | −524093. | −0.0243047 | ||||||||
\(859\) | −1.58611e7 | −0.733418 | −0.366709 | − | 0.930336i | \(-0.619515\pi\) | ||||
−0.366709 | + | 0.930336i | \(0.619515\pi\) | |||||||
\(860\) | −1.75561e7 | + | 3.91397e6i | −0.809435 | + | 0.180456i | ||||
\(861\) | 2.55459e6 | 0.117439 | ||||||||
\(862\) | −8.01530e6 | −0.367411 | ||||||||
\(863\) | 472608. | + | 818582.i | 0.0216010 | + | 0.0374141i | 0.876624 | − | 0.481176i | \(-0.159790\pi\) |
−0.855023 | + | 0.518590i | \(0.826457\pi\) | |||||||
\(864\) | 1.72027e6 | 0.0783995 | ||||||||
\(865\) | 1.65163e7 | + | 2.86071e7i | 0.750538 | + | 1.29997i | ||||
\(866\) | 852594. | + | 1.47674e6i | 0.0386320 | + | 0.0669126i | ||||
\(867\) | 423168. | − | 732948.i | 0.0191190 | − | 0.0331151i | ||||
\(868\) | −3.94095e7 | −1.77542 | ||||||||
\(869\) | 1.70091e7 | − | 2.94606e7i | 0.764067 | − | 1.32340i | ||||
\(870\) | −120122. | − | 208057.i | −0.00538052 | − | 0.00931933i | ||||
\(871\) | 1.15130e7 | 0.514213 | ||||||||
\(872\) | 7.81715e6 | + | 1.35397e7i | 0.348143 | + | 0.603001i | ||||
\(873\) | −129080. | + | 223573.i | −0.00573224 | + | 0.00992852i | ||||
\(874\) | −352229. | + | 610078.i | −0.0155972 | + | 0.0270151i | ||||
\(875\) | 1.57015e7 | − | 2.71957e7i | 0.693298 | − | 1.20083i | ||||
\(876\) | 1.67452e6 | 0.0737274 | ||||||||
\(877\) | 8.16402e6 | − | 1.41405e7i | 0.358430 | − | 0.620820i | −0.629268 | − | 0.777188i | \(-0.716645\pi\) |
0.987699 | + | 0.156368i | \(0.0499787\pi\) | |||||||
\(878\) | −702812. | + | 1.21731e6i | −0.0307683 | + | 0.0532922i | ||||
\(879\) | 1.16740e6 | + | 2.02200e6i | 0.0509622 | + | 0.0882691i | ||||
\(880\) | −9.32787e6 | − | 1.61563e7i | −0.406046 | − | 0.703293i | ||||
\(881\) | −2.47571e7 | −1.07463 | −0.537317 | − | 0.843380i | \(-0.680562\pi\) | ||||
−0.537317 | + | 0.843380i | \(0.680562\pi\) | |||||||
\(882\) | 3.27329e6 | 0.141681 | ||||||||
\(883\) | −8.45869e6 | − | 1.46509e7i | −0.365091 | − | 0.632356i | 0.623700 | − | 0.781664i | \(-0.285629\pi\) |
−0.988791 | + | 0.149308i | \(0.952295\pi\) | |||||||
\(884\) | 1.11286e7 | + | 1.92753e7i | 0.478971 | + | 0.829602i | ||||
\(885\) | 918311. | − | 1.59056e6i | 0.0394123 | − | 0.0682640i | ||||
\(886\) | −4.21225e6 | + | 7.29583e6i | −0.180273 | + | 0.312241i | ||||
\(887\) | −3.53502e7 | −1.50863 | −0.754315 | − | 0.656513i | \(-0.772031\pi\) | ||||
−0.754315 | + | 0.656513i | \(0.772031\pi\) | |||||||
\(888\) | −463894. | + | 803488.i | −0.0197418 | + | 0.0341938i | ||||
\(889\) | 5.67500e6 | − | 9.82938e6i | 0.240830 | − | 0.417130i | ||||
\(890\) | 2.32127e6 | − | 4.02056e6i | 0.0982314 | − | 0.170142i | ||||
\(891\) | 1.27321e7 | + | 2.20527e7i | 0.537287 | + | 0.930608i | ||||
\(892\) | 2.04603e7 | 0.860993 | ||||||||
\(893\) | 2.32918e6 | + | 4.03426e6i | 0.0977406 | + | 0.169292i | ||||
\(894\) | −85896.4 | + | 148777.i | −0.00359444 | + | 0.00622575i | ||||
\(895\) | −1.67271e7 | −0.698014 | ||||||||
\(896\) | 1.19878e7 | − | 2.07635e7i | 0.498849 | − | 0.864032i | ||||
\(897\) | 480005. | + | 831393.i | 0.0199189 | + | 0.0345005i | ||||
\(898\) | 2.92239e6 | + | 5.06172e6i | 0.120934 | + | 0.209463i | ||||
\(899\) | −3.11140e7 | −1.28397 | ||||||||
\(900\) | 2.76510e6 | + | 4.78930e6i | 0.113790 | + | 0.197090i | ||||
\(901\) | −3.16402e6 | −0.129846 | ||||||||
\(902\) | −8.45636e6 | −0.346072 | ||||||||
\(903\) | −597366. | + | 1.90248e6i | −0.0243793 | + | 0.0776426i | ||||
\(904\) | −1.51210e7 | −0.615401 | ||||||||
\(905\) | 1.44660e7 | 0.587122 | ||||||||
\(906\) | −212921. | − | 368791.i | −0.00861785 | − | 0.0149266i | ||||
\(907\) | −8.14027e6 | −0.328565 | −0.164282 | − | 0.986413i | \(-0.552531\pi\) | ||||
−0.164282 | + | 0.986413i | \(0.552531\pi\) | |||||||
\(908\) | 9.01704e6 | + | 1.56180e7i | 0.362952 | + | 0.628651i | ||||
\(909\) | −7.66385e6 | − | 1.32742e7i | −0.307636 | − | 0.532842i | ||||
\(910\) | −4.91832e6 | + | 8.51878e6i | −0.196885 | + | 0.341015i | ||||
\(911\) | 7.97527e6 | 0.318383 | 0.159191 | − | 0.987248i | \(-0.449111\pi\) | ||||
0.159191 | + | 0.987248i | \(0.449111\pi\) | |||||||
\(912\) | 245665. | − | 425504.i | 0.00978039 | − | 0.0169401i | ||||
\(913\) | −3.60252e6 | − | 6.23975e6i | −0.143031 | − | 0.247737i | ||||
\(914\) | 2.43007e6 | 0.0962174 | ||||||||
\(915\) | −679073. | − | 1.17619e6i | −0.0268141 | − | 0.0464435i | ||||
\(916\) | 6.01478e6 | − | 1.04179e7i | 0.236854 | − | 0.410243i | ||||
\(917\) | 1.68237e7 | − | 2.91395e7i | 0.660690 | − | 1.14435i | ||||
\(918\) | 224686. | − | 389167.i | 0.00879972 | − | 0.0152416i | ||||
\(919\) | 1.09074e7 | 0.426023 | 0.213012 | − | 0.977050i | \(-0.431673\pi\) | ||||
0.213012 | + | 0.977050i | \(0.431673\pi\) | |||||||
\(920\) | 1.89226e6 | − | 3.27750e6i | 0.0737076 | − | 0.127665i | ||||
\(921\) | 276579. | − | 479049.i | 0.0107441 | − | 0.0186093i | ||||
\(922\) | 1.83816e6 | + | 3.18379e6i | 0.0712126 | + | 0.123344i | ||||
\(923\) | 3.67404e7 | + | 6.36362e7i | 1.41951 | + | 2.45867i | ||||
\(924\) | −2.18556e6 | −0.0842136 | ||||||||
\(925\) | −9.04027e6 | −0.347398 | ||||||||
\(926\) | 4.76387e6 | + | 8.25126e6i | 0.182571 | + | 0.316222i | ||||
\(927\) | 4.38787e6 | + | 7.60001e6i | 0.167708 | + | 0.290479i | ||||
\(928\) | 7.16662e6 | − | 1.24129e7i | 0.273177 | − | 0.473157i | ||||
\(929\) | 1.84508e7 | − | 3.19577e7i | 0.701415 | − | 1.21489i | −0.266555 | − | 0.963820i | \(-0.585885\pi\) |
0.967970 | − | 0.251067i | \(-0.0807814\pi\) | |||||||
\(930\) | −467919. | −0.0177404 | ||||||||
\(931\) | 3.07099e6 | − | 5.31910e6i | 0.116119 | − | 0.201124i | ||||
\(932\) | 5.84934e6 | − | 1.01314e7i | 0.220581 | − | 0.382057i | ||||
\(933\) | −908020. | + | 1.57274e6i | −0.0341501 | + | 0.0591496i | ||||
\(934\) | −1.06134e6 | − | 1.83830e6i | −0.0398096 | − | 0.0689523i | ||||
\(935\) | −1.59758e7 | −0.597630 | ||||||||
\(936\) | −9.17335e6 | − | 1.58887e7i | −0.342246 | − | 0.592788i | ||||
\(937\) | 4.68836e6 | − | 8.12049e6i | 0.174451 | − | 0.302157i | −0.765520 | − | 0.643412i | \(-0.777518\pi\) |
0.939971 | + | 0.341254i | \(0.110852\pi\) | |||||||
\(938\) | −2.45310e6 | −0.0910350 | ||||||||
\(939\) | 1.09589e6 | − | 1.89814e6i | 0.0405605 | − | 0.0702529i | ||||
\(940\) | −6.10063e6 | − | 1.05666e7i | −0.225193 | − | 0.390046i | ||||
\(941\) | −9.07361e6 | − | 1.57160e7i | −0.334046 | − | 0.578584i | 0.649255 | − | 0.760571i | \(-0.275081\pi\) |
−0.983301 | + | 0.181986i | \(0.941747\pi\) | |||||||
\(942\) | −335937. | −0.0123348 | ||||||||
\(943\) | 7.74498e6 | + | 1.34147e7i | 0.283623 | + | 0.491249i | ||||
\(944\) | 3.34249e7 | 1.22079 | ||||||||
\(945\) | −3.88695e6 | −0.141589 | ||||||||
\(946\) | 1.97744e6 | − | 6.29769e6i | 0.0718414 | − | 0.228799i | ||||
\(947\) | −2.49691e6 | −0.0904748 | −0.0452374 | − | 0.998976i | \(-0.514404\pi\) | ||||
−0.0452374 | + | 0.998976i | \(0.514404\pi\) | |||||||
\(948\) | −2.34662e6 | −0.0848051 | ||||||||
\(949\) | −2.70651e7 | − | 4.68780e7i | −0.975536 | − | 1.68968i | ||||
\(950\) | −530198. | −0.0190603 | ||||||||
\(951\) | −1.10106e6 | − | 1.90710e6i | −0.0394785 | − | 0.0683788i | ||||
\(952\) | −4.86354e6 | − | 8.42389e6i | −0.173924 | − | 0.301246i | ||||
\(953\) | −1.87480e7 | + | 3.24725e7i | −0.668686 | + | 1.15820i | 0.309585 | + | 0.950872i | \(0.399810\pi\) |
−0.978272 | + | 0.207327i | \(0.933524\pi\) | |||||||
\(954\) | 1.27157e6 | 0.0452346 | ||||||||
\(955\) | 1.75681e7 | − | 3.04288e7i | 0.623327 | − | 1.07963i | ||||
\(956\) | −2.06292e6 | − | 3.57309e6i | −0.0730026 | − | 0.126444i | ||||
\(957\) | −1.72551e6 | −0.0609029 | ||||||||
\(958\) | −910798. | − | 1.57755e6i | −0.0320633 | − | 0.0555353i | ||||
\(959\) | −3.75310e6 | + | 6.50056e6i | −0.131778 | + | 0.228247i | ||||
\(960\) | −568548. | + | 984754.i | −0.0199108 | + | 0.0344865i | ||||
\(961\) | −1.59855e7 | + | 2.76877e7i | −0.558364 | + | 0.967115i | ||||
\(962\) | 1.46222e7 | 0.509419 | ||||||||
\(963\) | 1.42453e7 | − | 2.46735e7i | 0.495000 | − | 0.857365i | ||||
\(964\) | −5.77860e6 | + | 1.00088e7i | −0.200277 | + | 0.346889i | ||||
\(965\) | 1.24478e7 | + | 2.15603e7i | 0.430304 | + | 0.745309i | ||||
\(966\) | −102276. | − | 177147.i | −0.00352638 | − | 0.00610788i | ||||
\(967\) | 7.25545e6 | 0.249516 | 0.124758 | − | 0.992187i | \(-0.460185\pi\) | ||||
0.124758 | + | 0.992187i | \(0.460185\pi\) | |||||||
\(968\) | 2.29627e6 | 0.0787653 | ||||||||
\(969\) | −210374. | − | 364379.i | −0.00719753 | − | 0.0124665i | ||||
\(970\) | 32413.6 | + | 56142.0i | 0.00110611 | + | 0.00191584i | ||||
\(971\) | −1.87048e7 | + | 3.23976e7i | −0.636655 | + | 1.10272i | 0.349507 | + | 0.936934i | \(0.386349\pi\) |
−0.986162 | + | 0.165785i | \(0.946984\pi\) | |||||||
\(972\) | 2.65270e6 | − | 4.59461e6i | 0.0900581 | − | 0.155985i | ||||
\(973\) | 2.48380e7 | 0.841073 | ||||||||
\(974\) | 5.37466e6 | − | 9.30919e6i | 0.181532 | − | 0.314423i | ||||
\(975\) | −361267. | + | 625733.i | −0.0121707 | + | 0.0210803i | ||||
\(976\) | 1.23585e7 | − | 2.14056e7i | 0.415281 | − | 0.719288i | ||||
\(977\) | −1.81876e7 | − | 3.15018e7i | −0.609591 | − | 1.05584i | −0.991308 | − | 0.131564i | \(-0.958000\pi\) |
0.381717 | − | 0.924279i | \(-0.375333\pi\) | |||||||
\(978\) | −25691.2 | −0.000858888 | ||||||||
\(979\) | −1.66721e7 | − | 2.88769e7i | −0.555948 | − | 0.962930i | ||||
\(980\) | −8.04357e6 | + | 1.39319e7i | −0.267537 | + | 0.463387i | ||||
\(981\) | 4.85846e7 | 1.61185 | ||||||||
\(982\) | 2.97445e6 | − | 5.15189e6i | 0.0984300 | − | 0.170486i | ||||
\(983\) | −1.35121e7 | − | 2.34037e7i | −0.446005 | − | 0.772503i | 0.552117 | − | 0.833767i | \(-0.313820\pi\) |
−0.998122 | + | 0.0612638i | \(0.980487\pi\) | |||||||
\(984\) | 598234. | + | 1.03617e6i | 0.0196962 | + | 0.0341149i | ||||
\(985\) | 2.55141e7 | 0.837895 | ||||||||
\(986\) | −1.87207e6 | − | 3.24252e6i | −0.0613239 | − | 0.106216i | ||||
\(987\) | −1.35264e6 | −0.0441965 | ||||||||
\(988\) | −1.67840e7 | −0.547021 | ||||||||
\(989\) | −1.18014e7 | + | 2.63101e6i | −0.383657 | + | 0.0855326i | ||||
\(990\) | 6.42043e6 | 0.208198 | ||||||||
\(991\) | 3.91081e7 | 1.26498 | 0.632488 | − | 0.774570i | \(-0.282034\pi\) | ||||
0.632488 | + | 0.774570i | \(0.282034\pi\) | |||||||
\(992\) | −1.39583e7 | − | 2.41765e7i | −0.450353 | − | 0.780034i | ||||
\(993\) | 2.34353e6 | 0.0754219 | ||||||||
\(994\) | −7.82835e6 | − | 1.35591e7i | −0.251307 | − | 0.435276i | ||||
\(995\) | 1.05890e7 | + | 1.83406e7i | 0.339075 | + | 0.587295i | ||||
\(996\) | −248507. | + | 430427.i | −0.00793762 | + | 0.0137484i | ||||
\(997\) | −5.56148e7 | −1.77195 | −0.885977 | − | 0.463730i | \(-0.846511\pi\) | ||||
−0.885977 | + | 0.463730i | \(0.846511\pi\) | |||||||
\(998\) | −3.22079e6 | + | 5.57857e6i | −0.102361 | + | 0.177295i | ||||
\(999\) | 2.88899e6 | + | 5.00387e6i | 0.0915866 | + | 0.158633i |
(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 | 43.6.c.a.36.9 | yes | 34 | |
43.6 | even | 3 | inner | 43.6.c.a.6.9 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.c.a.6.9 | ✓ | 34 | 43.6 | even | 3 | inner | |
43.6.c.a.36.9 | yes | 34 | 1.1 | even | 1 | trivial |