Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(16,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.16");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.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: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.646154928.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 11x^{4} - 8x^{3} + 121x^{2} - 44x + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 46.3 | ||
Root | \(-1.74267 - 3.01840i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.46 |
Dual form | 105.4.i.c.16.3 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.24267 | + | 2.15238i | 0.439352 | + | 0.760980i | 0.997640 | − | 0.0686676i | \(-0.0218748\pi\) |
−0.558288 | + | 0.829647i | \(0.688541\pi\) | |||||||
\(3\) | 1.50000 | − | 2.59808i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0.911519 | − | 1.57880i | 0.113940 | − | 0.197350i | ||||
\(5\) | −2.50000 | − | 4.33013i | −0.223607 | − | 0.387298i | ||||
\(6\) | 7.45605 | 0.507320 | ||||||||
\(7\) | −8.88380 | − | 16.2505i | −0.479680 | − | 0.877443i | ||||
\(8\) | 24.4137 | 1.07894 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 6.21337 | − | 10.7619i | 0.196484 | − | 0.340320i | ||||
\(11\) | 13.0299 | − | 22.5684i | 0.357151 | − | 0.618603i | −0.630333 | − | 0.776325i | \(-0.717082\pi\) |
0.987484 | + | 0.157722i | \(0.0504150\pi\) | |||||||
\(12\) | −2.73456 | − | 4.73639i | −0.0657832 | − | 0.113940i | ||||
\(13\) | 3.20425 | 0.0683614 | 0.0341807 | − | 0.999416i | \(-0.489118\pi\) | ||||
0.0341807 | + | 0.999416i | \(0.489118\pi\) | |||||||
\(14\) | 23.9375 | − | 39.3153i | 0.456968 | − | 0.750533i | ||||
\(15\) | −15.0000 | −0.258199 | ||||||||
\(16\) | 23.0461 | + | 39.9170i | 0.360096 | + | 0.623704i | ||||
\(17\) | 9.01624 | − | 15.6166i | 0.128633 | − | 0.222799i | −0.794514 | − | 0.607245i | \(-0.792274\pi\) |
0.923147 | + | 0.384447i | \(0.125608\pi\) | |||||||
\(18\) | 11.1841 | − | 19.3714i | 0.146451 | − | 0.253660i | ||||
\(19\) | 17.1199 | + | 29.6526i | 0.206715 | + | 0.358041i | 0.950678 | − | 0.310180i | \(-0.100389\pi\) |
−0.743963 | + | 0.668221i | \(0.767056\pi\) | |||||||
\(20\) | −9.11519 | −0.101911 | ||||||||
\(21\) | −55.5457 | − | 1.29492i | −0.577193 | − | 0.0134559i | ||||
\(22\) | 64.7676 | 0.627659 | ||||||||
\(23\) | 49.5912 | + | 85.8945i | 0.449586 | + | 0.778706i | 0.998359 | − | 0.0572653i | \(-0.0182381\pi\) |
−0.548773 | + | 0.835972i | \(0.684905\pi\) | |||||||
\(24\) | 36.6205 | − | 63.4286i | 0.311464 | − | 0.539471i | ||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | 3.98184 | + | 6.89675i | 0.0300347 | + | 0.0520217i | ||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −33.7540 | − | 0.786896i | −0.227818 | − | 0.00531105i | ||||
\(29\) | 212.096 | 1.35811 | 0.679055 | − | 0.734088i | \(-0.262390\pi\) | ||||
0.679055 | + | 0.734088i | \(0.262390\pi\) | |||||||
\(30\) | −18.6401 | − | 32.2856i | −0.113440 | − | 0.196484i | ||||
\(31\) | −146.585 | + | 253.893i | −0.849274 | + | 1.47099i | 0.0325838 | + | 0.999469i | \(0.489626\pi\) |
−0.881857 | + | 0.471516i | \(0.843707\pi\) | |||||||
\(32\) | 40.3771 | − | 69.9352i | 0.223054 | − | 0.386341i | ||||
\(33\) | −39.0896 | − | 67.7052i | −0.206201 | − | 0.357151i | ||||
\(34\) | 44.8170 | 0.226060 | ||||||||
\(35\) | −48.1571 | + | 79.0942i | −0.232573 | + | 0.381982i | ||||
\(36\) | −16.4073 | −0.0759599 | ||||||||
\(37\) | −10.3520 | − | 17.9301i | −0.0459960 | − | 0.0796674i | 0.842111 | − | 0.539304i | \(-0.181313\pi\) |
−0.888107 | + | 0.459637i | \(0.847979\pi\) | |||||||
\(38\) | −42.5490 | + | 73.6971i | −0.181641 | + | 0.314612i | ||||
\(39\) | 4.80637 | − | 8.32488i | 0.0197342 | − | 0.0341807i | ||||
\(40\) | −61.0342 | − | 105.714i | −0.241259 | − | 0.417873i | ||||
\(41\) | −207.842 | −0.791695 | −0.395847 | − | 0.918316i | \(-0.629549\pi\) | ||||
−0.395847 | + | 0.918316i | \(0.629549\pi\) | |||||||
\(42\) | −66.2381 | − | 121.164i | −0.243351 | − | 0.445144i | ||||
\(43\) | 5.96397 | 0.0211511 | 0.0105755 | − | 0.999944i | \(-0.496634\pi\) | ||||
0.0105755 | + | 0.999944i | \(0.496634\pi\) | |||||||
\(44\) | −23.7540 | − | 41.1431i | −0.0813874 | − | 0.140967i | ||||
\(45\) | −22.5000 | + | 38.9711i | −0.0745356 | + | 0.129099i | ||||
\(46\) | −123.252 | + | 213.478i | −0.395053 | + | 0.684252i | ||||
\(47\) | −200.949 | − | 348.055i | −0.623649 | − | 1.08019i | −0.988801 | − | 0.149243i | \(-0.952316\pi\) |
0.365152 | − | 0.930948i | \(-0.381017\pi\) | |||||||
\(48\) | 138.277 | 0.415803 | ||||||||
\(49\) | −185.156 | + | 288.732i | −0.539814 | + | 0.841785i | ||||
\(50\) | −62.1337 | −0.175741 | ||||||||
\(51\) | −27.0487 | − | 46.8497i | −0.0742662 | − | 0.128633i | ||||
\(52\) | 2.92073 | − | 5.05886i | 0.00778909 | − | 0.0134911i | ||||
\(53\) | 3.65770 | − | 6.33533i | 0.00947970 | − | 0.0164193i | −0.861247 | − | 0.508187i | \(-0.830316\pi\) |
0.870726 | + | 0.491768i | \(0.163649\pi\) | |||||||
\(54\) | −33.5522 | − | 58.1141i | −0.0845533 | − | 0.146451i | ||||
\(55\) | −130.299 | −0.319445 | ||||||||
\(56\) | −216.886 | − | 396.734i | −0.517547 | − | 0.946711i | ||||
\(57\) | 102.720 | 0.238694 | ||||||||
\(58\) | 263.566 | + | 456.510i | 0.596688 | + | 1.03349i | ||||
\(59\) | −20.2045 | + | 34.9952i | −0.0445830 | + | 0.0772200i | −0.887456 | − | 0.460893i | \(-0.847529\pi\) |
0.842873 | + | 0.538113i | \(0.180863\pi\) | |||||||
\(60\) | −13.6728 | + | 23.6820i | −0.0294191 | + | 0.0509555i | ||||
\(61\) | 179.242 | + | 310.456i | 0.376223 | + | 0.651637i | 0.990509 | − | 0.137446i | \(-0.0438895\pi\) |
−0.614287 | + | 0.789083i | \(0.710556\pi\) | |||||||
\(62\) | −728.631 | −1.49252 | ||||||||
\(63\) | −86.6828 | + | 142.370i | −0.173349 | + | 0.284712i | ||||
\(64\) | 569.440 | 1.11219 | ||||||||
\(65\) | −8.01062 | − | 13.8748i | −0.0152861 | − | 0.0264763i | ||||
\(66\) | 97.1514 | − | 168.271i | 0.181190 | − | 0.313830i | ||||
\(67\) | −293.731 | + | 508.757i | −0.535597 | + | 0.927681i | 0.463537 | + | 0.886077i | \(0.346580\pi\) |
−0.999134 | + | 0.0416035i | \(0.986753\pi\) | |||||||
\(68\) | −16.4369 | − | 28.4696i | −0.0293128 | − | 0.0507713i | ||||
\(69\) | 297.547 | 0.519138 | ||||||||
\(70\) | −230.084 | − | 5.36388i | −0.392862 | − | 0.00915866i | ||||
\(71\) | 803.405 | 1.34291 | 0.671455 | − | 0.741045i | \(-0.265670\pi\) | ||||
0.671455 | + | 0.741045i | \(0.265670\pi\) | |||||||
\(72\) | −109.862 | − | 190.286i | −0.179824 | − | 0.311464i | ||||
\(73\) | 328.025 | − | 568.157i | 0.525924 | − | 0.910928i | −0.473620 | − | 0.880729i | \(-0.657053\pi\) |
0.999544 | − | 0.0301981i | \(-0.00961381\pi\) | |||||||
\(74\) | 25.7282 | − | 44.5626i | 0.0404168 | − | 0.0700040i | ||||
\(75\) | 37.5000 | + | 64.9519i | 0.0577350 | + | 0.100000i | ||||
\(76\) | 62.4206 | 0.0942123 | ||||||||
\(77\) | −482.502 | − | 11.2484i | −0.714107 | − | 0.0166478i | ||||
\(78\) | 23.8910 | 0.0346811 | ||||||||
\(79\) | 637.780 | + | 1104.67i | 0.908302 | + | 1.57323i | 0.816422 | + | 0.577456i | \(0.195955\pi\) |
0.0918807 | + | 0.995770i | \(0.470712\pi\) | |||||||
\(80\) | 115.231 | − | 199.585i | 0.161040 | − | 0.278929i | ||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −258.280 | − | 447.354i | −0.347832 | − | 0.602464i | ||||
\(83\) | 244.647 | 0.323537 | 0.161768 | − | 0.986829i | \(-0.448280\pi\) | ||||
0.161768 | + | 0.986829i | \(0.448280\pi\) | |||||||
\(84\) | −52.6754 | + | 86.5150i | −0.0684209 | + | 0.112376i | ||||
\(85\) | −90.1624 | −0.115053 | ||||||||
\(86\) | 7.41127 | + | 12.8367i | 0.00929277 | + | 0.0160955i | ||||
\(87\) | 318.144 | − | 551.041i | 0.392053 | − | 0.679055i | ||||
\(88\) | 318.107 | − | 550.978i | 0.385345 | − | 0.667437i | ||||
\(89\) | 705.542 | + | 1222.03i | 0.840307 | + | 1.45545i | 0.889636 | + | 0.456671i | \(0.150958\pi\) |
−0.0493291 | + | 0.998783i | \(0.515708\pi\) | |||||||
\(90\) | −111.841 | −0.130989 | ||||||||
\(91\) | −28.4659 | − | 52.0706i | −0.0327916 | − | 0.0599833i | ||||
\(92\) | 180.813 | 0.204903 | ||||||||
\(93\) | 439.756 | + | 761.679i | 0.490328 | + | 0.849274i | ||||
\(94\) | 499.429 | − | 865.037i | 0.548002 | − | 0.949168i | ||||
\(95\) | 85.5997 | − | 148.263i | 0.0924458 | − | 0.160121i | ||||
\(96\) | −121.131 | − | 209.805i | −0.128780 | − | 0.223054i | ||||
\(97\) | −952.212 | −0.996727 | −0.498363 | − | 0.866968i | \(-0.666065\pi\) | ||||
−0.498363 | + | 0.866968i | \(0.666065\pi\) | |||||||
\(98\) | −851.549 | − | 39.7254i | −0.877749 | − | 0.0409476i | ||||
\(99\) | −234.538 | −0.238100 | ||||||||
\(100\) | 22.7880 | + | 39.4699i | 0.0227880 | + | 0.0394699i | ||||
\(101\) | 720.732 | − | 1248.35i | 0.710055 | − | 1.22985i | −0.254781 | − | 0.966999i | \(-0.582003\pi\) |
0.964836 | − | 0.262852i | \(-0.0846633\pi\) | |||||||
\(102\) | 67.2255 | − | 116.438i | 0.0652580 | − | 0.113030i | ||||
\(103\) | −569.993 | − | 987.257i | −0.545273 | − | 0.944440i | −0.998590 | − | 0.0530906i | \(-0.983093\pi\) |
0.453317 | − | 0.891349i | \(-0.350241\pi\) | |||||||
\(104\) | 78.2275 | 0.0737581 | ||||||||
\(105\) | 133.257 | + | 243.757i | 0.123853 | + | 0.226555i | ||||
\(106\) | 18.1813 | 0.0166597 | ||||||||
\(107\) | −346.702 | − | 600.505i | −0.313242 | − | 0.542552i | 0.665820 | − | 0.746113i | \(-0.268082\pi\) |
−0.979062 | + | 0.203561i | \(0.934749\pi\) | |||||||
\(108\) | −24.6110 | + | 42.6275i | −0.0219277 | + | 0.0379800i | ||||
\(109\) | 570.059 | − | 987.371i | 0.500933 | − | 0.867642i | −0.499066 | − | 0.866564i | \(-0.666324\pi\) |
0.999999 | − | 0.00107792i | \(-0.000343113\pi\) | |||||||
\(110\) | −161.919 | − | 280.452i | −0.140349 | − | 0.243091i | ||||
\(111\) | −62.1117 | −0.0531116 | ||||||||
\(112\) | 443.934 | − | 729.126i | 0.374534 | − | 0.615142i | ||||
\(113\) | 1154.64 | 0.961237 | 0.480618 | − | 0.876930i | \(-0.340412\pi\) | ||||
0.480618 | + | 0.876930i | \(0.340412\pi\) | |||||||
\(114\) | 127.647 | + | 221.091i | 0.104871 | + | 0.181641i | ||||
\(115\) | 247.956 | − | 429.473i | 0.201061 | − | 0.348248i | ||||
\(116\) | 193.329 | − | 334.856i | 0.154743 | − | 0.268022i | ||||
\(117\) | −14.4191 | − | 24.9746i | −0.0113936 | − | 0.0197342i | ||||
\(118\) | −100.430 | −0.0783505 | ||||||||
\(119\) | −333.875 | − | 7.78353i | −0.257196 | − | 0.00599593i | ||||
\(120\) | −366.205 | −0.278582 | ||||||||
\(121\) | 325.945 | + | 564.552i | 0.244887 | + | 0.424157i | ||||
\(122\) | −445.479 | + | 771.592i | −0.330588 | + | 0.572595i | ||||
\(123\) | −311.763 | + | 539.990i | −0.228543 | + | 0.395847i | ||||
\(124\) | 267.230 | + | 462.857i | 0.193532 | + | 0.335208i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | −414.151 | − | 9.65498i | −0.292822 | − | 0.00682646i | ||||
\(127\) | −1453.32 | −1.01544 | −0.507722 | − | 0.861521i | \(-0.669512\pi\) | ||||
−0.507722 | + | 0.861521i | \(0.669512\pi\) | |||||||
\(128\) | 384.612 | + | 666.168i | 0.265588 | + | 0.460012i | ||||
\(129\) | 8.94595 | − | 15.4948i | 0.00610579 | − | 0.0105755i | ||||
\(130\) | 19.9092 | − | 34.4837i | 0.0134319 | − | 0.0232648i | ||||
\(131\) | 769.788 | + | 1333.31i | 0.513410 | + | 0.889252i | 0.999879 | + | 0.0155543i | \(0.00495129\pi\) |
−0.486469 | + | 0.873698i | \(0.661715\pi\) | |||||||
\(132\) | −142.524 | −0.0939781 | ||||||||
\(133\) | 329.779 | − | 541.635i | 0.215003 | − | 0.353126i | ||||
\(134\) | −1460.05 | −0.941262 | ||||||||
\(135\) | 67.5000 | + | 116.913i | 0.0430331 | + | 0.0745356i | ||||
\(136\) | 220.120 | − | 381.258i | 0.138787 | − | 0.240387i | ||||
\(137\) | −1457.77 | + | 2524.93i | −0.909093 | + | 1.57460i | −0.0937658 | + | 0.995594i | \(0.529891\pi\) |
−0.815327 | + | 0.579001i | \(0.803443\pi\) | |||||||
\(138\) | 369.755 | + | 640.434i | 0.228084 | + | 0.395053i | ||||
\(139\) | −2338.76 | −1.42713 | −0.713565 | − | 0.700589i | \(-0.752920\pi\) | ||||
−0.713565 | + | 0.700589i | \(0.752920\pi\) | |||||||
\(140\) | 80.9775 | + | 148.126i | 0.0488847 | + | 0.0894211i | ||||
\(141\) | −1205.70 | −0.720127 | ||||||||
\(142\) | 998.371 | + | 1729.23i | 0.590010 | + | 1.02193i | ||||
\(143\) | 41.7510 | − | 72.3148i | 0.0244153 | − | 0.0422886i | ||||
\(144\) | 207.415 | − | 359.253i | 0.120032 | − | 0.207901i | ||||
\(145\) | −530.239 | − | 918.401i | −0.303683 | − | 0.525994i | ||||
\(146\) | 1630.52 | 0.924263 | ||||||||
\(147\) | 472.414 | + | 914.148i | 0.265061 | + | 0.512909i | ||||
\(148\) | −37.7440 | −0.0209631 | ||||||||
\(149\) | 246.088 | + | 426.237i | 0.135304 | + | 0.234354i | 0.925714 | − | 0.378225i | \(-0.123466\pi\) |
−0.790409 | + | 0.612579i | \(0.790132\pi\) | |||||||
\(150\) | −93.2006 | + | 161.428i | −0.0507320 | + | 0.0878704i | ||||
\(151\) | −540.975 | + | 936.996i | −0.291549 | + | 0.504978i | −0.974176 | − | 0.225789i | \(-0.927504\pi\) |
0.682627 | + | 0.730767i | \(0.260837\pi\) | |||||||
\(152\) | 417.961 | + | 723.930i | 0.223034 | + | 0.386306i | ||||
\(153\) | −162.292 | −0.0857552 | ||||||||
\(154\) | −575.383 | − | 1052.50i | −0.301076 | − | 0.550735i | ||||
\(155\) | 1465.85 | 0.759613 | ||||||||
\(156\) | −8.76220 | − | 15.1766i | −0.00449703 | − | 0.00778909i | ||||
\(157\) | 1445.65 | − | 2503.95i | 0.734877 | − | 1.27284i | −0.219900 | − | 0.975522i | \(-0.570573\pi\) |
0.954777 | − | 0.297322i | \(-0.0960936\pi\) | |||||||
\(158\) | −1585.11 | + | 2745.49i | −0.798129 | + | 1.38240i | ||||
\(159\) | −10.9731 | − | 19.0060i | −0.00547311 | − | 0.00947970i | ||||
\(160\) | −403.771 | −0.199506 | ||||||||
\(161\) | 955.268 | − | 1568.95i | 0.467613 | − | 0.768017i | ||||
\(162\) | −201.313 | −0.0976337 | ||||||||
\(163\) | −1262.53 | − | 2186.76i | −0.606680 | − | 1.05080i | −0.991784 | − | 0.127927i | \(-0.959168\pi\) |
0.385104 | − | 0.922873i | \(-0.374166\pi\) | |||||||
\(164\) | −189.452 | + | 328.140i | −0.0902056 | + | 0.156241i | ||||
\(165\) | −195.448 | + | 338.526i | −0.0922159 | + | 0.159723i | ||||
\(166\) | 304.017 | + | 526.573i | 0.142146 | + | 0.246205i | ||||
\(167\) | −2891.98 | −1.34005 | −0.670025 | − | 0.742338i | \(-0.733717\pi\) | ||||
−0.670025 | + | 0.742338i | \(0.733717\pi\) | |||||||
\(168\) | −1356.07 | − | 31.6138i | −0.622759 | − | 0.0145182i | ||||
\(169\) | −2186.73 | −0.995327 | ||||||||
\(170\) | −112.042 | − | 194.063i | −0.0505486 | − | 0.0875528i | ||||
\(171\) | 154.080 | − | 266.874i | 0.0689050 | − | 0.119347i | ||||
\(172\) | 5.43627 | − | 9.41589i | 0.00240995 | − | 0.00417416i | ||||
\(173\) | 1452.47 | + | 2515.75i | 0.638320 | + | 1.10560i | 0.985801 | + | 0.167916i | \(0.0537037\pi\) |
−0.347481 | + | 0.937687i | \(0.612963\pi\) | |||||||
\(174\) | 1581.40 | 0.688996 | ||||||||
\(175\) | 462.881 | + | 10.7910i | 0.199946 | + | 0.00466127i | ||||
\(176\) | 1201.15 | 0.514433 | ||||||||
\(177\) | 60.6134 | + | 104.985i | 0.0257400 | + | 0.0445830i | ||||
\(178\) | −1753.52 | + | 3037.18i | −0.738380 | + | 1.27891i | ||||
\(179\) | −11.5520 | + | 20.0087i | −0.00482369 | + | 0.00835487i | −0.868427 | − | 0.495817i | \(-0.834869\pi\) |
0.863603 | + | 0.504172i | \(0.168202\pi\) | |||||||
\(180\) | 41.0184 | + | 71.0459i | 0.0169852 | + | 0.0294191i | ||||
\(181\) | −3024.01 | −1.24184 | −0.620919 | − | 0.783875i | \(-0.713240\pi\) | ||||
−0.620919 | + | 0.783875i | \(0.713240\pi\) | |||||||
\(182\) | 76.7016 | − | 125.976i | 0.0312390 | − | 0.0513075i | ||||
\(183\) | 1075.45 | 0.434424 | ||||||||
\(184\) | 1210.70 | + | 2097.00i | 0.485078 | + | 0.840179i | ||||
\(185\) | −51.7598 | + | 89.6506i | −0.0205700 | + | 0.0356283i | ||||
\(186\) | −1092.95 | + | 1893.04i | −0.430853 | + | 0.746260i | ||||
\(187\) | −234.961 | − | 406.964i | −0.0918826 | − | 0.159145i | ||||
\(188\) | −732.677 | −0.284234 | ||||||||
\(189\) | 239.863 | + | 438.763i | 0.0923145 | + | 0.168864i | ||||
\(190\) | 425.490 | 0.162465 | ||||||||
\(191\) | −1948.45 | − | 3374.81i | −0.738140 | − | 1.27850i | −0.953332 | − | 0.301924i | \(-0.902371\pi\) |
0.215192 | − | 0.976572i | \(-0.430962\pi\) | |||||||
\(192\) | 854.160 | − | 1479.45i | 0.321061 | − | 0.556094i | ||||
\(193\) | 2304.64 | − | 3991.76i | 0.859543 | − | 1.48877i | −0.0128229 | − | 0.999918i | \(-0.504082\pi\) |
0.872366 | − | 0.488854i | \(-0.162585\pi\) | |||||||
\(194\) | −1183.29 | − | 2049.52i | −0.437914 | − | 0.758489i | ||||
\(195\) | −48.0637 | −0.0176508 | ||||||||
\(196\) | 287.076 | + | 555.509i | 0.104620 | + | 0.202445i | ||||
\(197\) | 3119.11 | 1.12806 | 0.564029 | − | 0.825755i | \(-0.309251\pi\) | ||||
0.564029 | + | 0.825755i | \(0.309251\pi\) | |||||||
\(198\) | −291.454 | − | 504.814i | −0.104610 | − | 0.181190i | ||||
\(199\) | 2074.47 | − | 3593.08i | 0.738970 | − | 1.27993i | −0.213990 | − | 0.976836i | \(-0.568646\pi\) |
0.952960 | − | 0.303098i | \(-0.0980208\pi\) | |||||||
\(200\) | −305.171 | + | 528.572i | −0.107894 | + | 0.186878i | ||||
\(201\) | 881.194 | + | 1526.27i | 0.309227 | + | 0.535597i | ||||
\(202\) | 3582.54 | 1.24786 | ||||||||
\(203\) | −1884.22 | − | 3446.66i | −0.651458 | − | 1.19166i | ||||
\(204\) | −98.6216 | −0.0338475 | ||||||||
\(205\) | 519.605 | + | 899.983i | 0.177028 | + | 0.306622i | ||||
\(206\) | 1416.63 | − | 2453.68i | 0.479133 | − | 0.829883i | ||||
\(207\) | 446.321 | − | 773.051i | 0.149862 | − | 0.259569i | ||||
\(208\) | 73.8455 | + | 127.904i | 0.0246166 | + | 0.0426373i | ||||
\(209\) | 892.283 | 0.295314 | ||||||||
\(210\) | −359.062 | + | 589.730i | −0.117989 | + | 0.193787i | ||||
\(211\) | −3835.74 | −1.25148 | −0.625742 | − | 0.780030i | \(-0.715204\pi\) | ||||
−0.625742 | + | 0.780030i | \(0.715204\pi\) | |||||||
\(212\) | −6.66813 | − | 11.5495i | −0.00216023 | − | 0.00374163i | ||||
\(213\) | 1205.11 | − | 2087.31i | 0.387665 | − | 0.671455i | ||||
\(214\) | 861.675 | − | 1492.47i | 0.275247 | − | 0.476742i | ||||
\(215\) | −14.9099 | − | 25.8247i | −0.00472953 | − | 0.00819178i | ||||
\(216\) | −659.169 | −0.207643 | ||||||||
\(217\) | 5428.12 | + | 126.544i | 1.69809 | + | 0.0395870i | ||||
\(218\) | 2833.59 | 0.880344 | ||||||||
\(219\) | −984.076 | − | 1704.47i | −0.303643 | − | 0.525924i | ||||
\(220\) | −118.770 | + | 205.715i | −0.0363975 | + | 0.0630424i | ||||
\(221\) | 28.8903 | − | 50.0394i | 0.00879353 | − | 0.0152308i | ||||
\(222\) | −77.1847 | − | 133.688i | −0.0233347 | − | 0.0404168i | ||||
\(223\) | −750.330 | −0.225318 | −0.112659 | − | 0.993634i | \(-0.535937\pi\) | ||||
−0.112659 | + | 0.993634i | \(0.535937\pi\) | |||||||
\(224\) | −1495.18 | − | 34.8567i | −0.445987 | − | 0.0103972i | ||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | 1434.85 | + | 2485.23i | 0.422321 | + | 0.731482i | ||||
\(227\) | 314.420 | − | 544.591i | 0.0919329 | − | 0.159232i | −0.816392 | − | 0.577499i | \(-0.804029\pi\) |
0.908324 | + | 0.418266i | \(0.137362\pi\) | |||||||
\(228\) | 93.6309 | − | 162.174i | 0.0271968 | − | 0.0471062i | ||||
\(229\) | 1223.66 | + | 2119.45i | 0.353109 | + | 0.611603i | 0.986792 | − | 0.161989i | \(-0.0517910\pi\) |
−0.633683 | + | 0.773593i | \(0.718458\pi\) | |||||||
\(230\) | 1232.52 | 0.353346 | ||||||||
\(231\) | −752.978 | + | 1236.71i | −0.214469 | + | 0.352248i | ||||
\(232\) | 5178.04 | 1.46532 | ||||||||
\(233\) | −1580.58 | − | 2737.65i | −0.444409 | − | 0.769739i | 0.553602 | − | 0.832782i | \(-0.313253\pi\) |
−0.998011 | + | 0.0630423i | \(0.979920\pi\) | |||||||
\(234\) | 35.8365 | − | 62.0707i | 0.0100116 | − | 0.0173406i | ||||
\(235\) | −1004.75 | + | 1740.27i | −0.278904 | + | 0.483076i | ||||
\(236\) | 36.8335 | + | 63.7975i | 0.0101596 | + | 0.0175969i | ||||
\(237\) | 3826.68 | 1.04882 | ||||||||
\(238\) | −398.145 | − | 728.298i | −0.108437 | − | 0.198355i | ||||
\(239\) | −6018.30 | −1.62884 | −0.814418 | − | 0.580279i | \(-0.802944\pi\) | ||||
−0.814418 | + | 0.580279i | \(0.802944\pi\) | |||||||
\(240\) | −345.692 | − | 598.756i | −0.0929763 | − | 0.161040i | ||||
\(241\) | −2859.22 | + | 4952.31i | −0.764225 | + | 1.32368i | 0.176430 | + | 0.984313i | \(0.443545\pi\) |
−0.940655 | + | 0.339364i | \(0.889788\pi\) | |||||||
\(242\) | −810.086 | + | 1403.11i | −0.215183 | + | 0.372708i | ||||
\(243\) | 121.500 | + | 210.444i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 653.530 | 0.171467 | ||||||||
\(245\) | 1713.14 | + | 79.9191i | 0.446728 | + | 0.0208402i | ||||
\(246\) | −1549.68 | −0.401642 | ||||||||
\(247\) | 54.8566 | + | 95.0143i | 0.0141313 | + | 0.0244762i | ||||
\(248\) | −3578.69 | + | 6198.46i | −0.916317 | + | 1.58711i | ||||
\(249\) | 366.971 | − | 635.612i | 0.0933970 | − | 0.161768i | ||||
\(250\) | 155.334 | + | 269.047i | 0.0392968 | + | 0.0680641i | ||||
\(251\) | 1236.06 | 0.310834 | 0.155417 | − | 0.987849i | \(-0.450328\pi\) | ||||
0.155417 | + | 0.987849i | \(0.450328\pi\) | |||||||
\(252\) | 145.760 | + | 266.627i | 0.0364365 | + | 0.0666505i | ||||
\(253\) | 2584.67 | 0.642280 | ||||||||
\(254\) | −1806.01 | − | 3128.09i | −0.446137 | − | 0.772733i | ||||
\(255\) | −135.244 | + | 234.249i | −0.0332129 | + | 0.0575264i | ||||
\(256\) | 1321.86 | − | 2289.54i | 0.322721 | − | 0.558969i | ||||
\(257\) | 549.467 | + | 951.705i | 0.133365 | + | 0.230995i | 0.924972 | − | 0.380036i | \(-0.124088\pi\) |
−0.791607 | + | 0.611031i | \(0.790755\pi\) | |||||||
\(258\) | 44.4676 | 0.0107304 | ||||||||
\(259\) | −199.408 | + | 327.512i | −0.0478402 | + | 0.0785737i | ||||
\(260\) | −29.2073 | −0.00696678 | ||||||||
\(261\) | −954.431 | − | 1653.12i | −0.226352 | − | 0.392053i | ||||
\(262\) | −1913.19 | + | 3313.75i | −0.451135 | + | 0.781389i | ||||
\(263\) | 3361.74 | − | 5822.70i | 0.788189 | − | 1.36518i | −0.138886 | − | 0.990308i | \(-0.544352\pi\) |
0.927075 | − | 0.374875i | \(-0.122314\pi\) | |||||||
\(264\) | −954.322 | − | 1652.93i | −0.222479 | − | 0.385345i | ||||
\(265\) | −36.5770 | −0.00847891 | ||||||||
\(266\) | 1575.61 | + | 36.7317i | 0.363184 | + | 0.00846679i | ||||
\(267\) | 4233.25 | 0.970302 | ||||||||
\(268\) | 535.483 | + | 927.484i | 0.122052 | + | 0.211400i | ||||
\(269\) | −2570.07 | + | 4451.49i | −0.582527 | + | 1.00897i | 0.412652 | + | 0.910889i | \(0.364603\pi\) |
−0.995179 | + | 0.0980772i | \(0.968731\pi\) | |||||||
\(270\) | −167.761 | + | 290.571i | −0.0378134 | + | 0.0654947i | ||||
\(271\) | −1457.50 | − | 2524.47i | −0.326705 | − | 0.565870i | 0.655151 | − | 0.755498i | \(-0.272605\pi\) |
−0.981856 | + | 0.189628i | \(0.939272\pi\) | |||||||
\(272\) | 831.157 | 0.185280 | ||||||||
\(273\) | −177.982 | − | 4.14924i | −0.0394578 | − | 0.000919867i | ||||
\(274\) | −7246.14 | −1.59765 | ||||||||
\(275\) | 325.747 | + | 564.210i | 0.0714301 | + | 0.123721i | ||||
\(276\) | 271.220 | − | 469.767i | 0.0591505 | − | 0.102452i | ||||
\(277\) | −892.967 | + | 1546.66i | −0.193694 | + | 0.335488i | −0.946472 | − | 0.322787i | \(-0.895380\pi\) |
0.752778 | + | 0.658275i | \(0.228714\pi\) | |||||||
\(278\) | −2906.32 | − | 5033.89i | −0.627012 | − | 1.08602i | ||||
\(279\) | 2638.53 | 0.566182 | ||||||||
\(280\) | −1175.69 | + | 1930.98i | −0.250932 | + | 0.412136i | ||||
\(281\) | 1264.76 | 0.268503 | 0.134252 | − | 0.990947i | \(-0.457137\pi\) | ||||
0.134252 | + | 0.990947i | \(0.457137\pi\) | |||||||
\(282\) | −1498.29 | − | 2595.11i | −0.316389 | − | 0.548002i | ||||
\(283\) | −4183.20 | + | 7245.52i | −0.878677 | + | 1.52191i | −0.0258826 | + | 0.999665i | \(0.508240\pi\) |
−0.852794 | + | 0.522247i | \(0.825094\pi\) | |||||||
\(284\) | 732.319 | − | 1268.41i | 0.153011 | − | 0.265023i | ||||
\(285\) | −256.799 | − | 444.789i | −0.0533736 | − | 0.0924458i | ||||
\(286\) | 207.532 | 0.0429077 | ||||||||
\(287\) | 1846.43 | + | 3377.53i | 0.379760 | + | 0.694667i | ||||
\(288\) | −726.787 | −0.148703 | ||||||||
\(289\) | 2293.91 | + | 3973.18i | 0.466907 | + | 0.808707i | ||||
\(290\) | 1317.83 | − | 2282.55i | 0.266847 | − | 0.462193i | ||||
\(291\) | −1428.32 | + | 2473.92i | −0.287730 | + | 0.498363i | ||||
\(292\) | −598.003 | − | 1035.77i | −0.119847 | − | 0.207582i | ||||
\(293\) | −1552.76 | −0.309602 | −0.154801 | − | 0.987946i | \(-0.549474\pi\) | ||||
−0.154801 | + | 0.987946i | \(0.549474\pi\) | |||||||
\(294\) | −1380.53 | + | 2152.80i | −0.273858 | + | 0.427054i | ||||
\(295\) | 202.045 | 0.0398762 | ||||||||
\(296\) | −252.729 | − | 437.740i | −0.0496270 | − | 0.0859565i | ||||
\(297\) | −351.807 | + | 609.347i | −0.0687337 | + | 0.119050i | ||||
\(298\) | −611.615 | + | 1059.35i | −0.118892 | + | 0.205927i | ||||
\(299\) | 158.903 | + | 275.227i | 0.0307344 | + | 0.0532335i | ||||
\(300\) | 136.728 | 0.0263133 | ||||||||
\(301\) | −52.9827 | − | 96.9173i | −0.0101458 | − | 0.0185589i | ||||
\(302\) | −2689.02 | −0.512370 | ||||||||
\(303\) | −2162.20 | − | 3745.04i | −0.409950 | − | 0.710055i | ||||
\(304\) | −789.096 | + | 1366.76i | −0.148874 | + | 0.257858i | ||||
\(305\) | 896.210 | − | 1552.28i | 0.168252 | − | 0.291421i | ||||
\(306\) | −201.676 | − | 349.314i | −0.0376767 | − | 0.0652580i | ||||
\(307\) | −6847.06 | −1.27291 | −0.636453 | − | 0.771315i | \(-0.719599\pi\) | ||||
−0.636453 | + | 0.771315i | \(0.719599\pi\) | |||||||
\(308\) | −457.569 | + | 751.520i | −0.0846507 | + | 0.139032i | ||||
\(309\) | −3419.96 | −0.629627 | ||||||||
\(310\) | 1821.58 | + | 3155.06i | 0.333738 | + | 0.578050i | ||||
\(311\) | −1175.13 | + | 2035.38i | −0.214262 | + | 0.371113i | −0.953044 | − | 0.302832i | \(-0.902068\pi\) |
0.738782 | + | 0.673944i | \(0.235401\pi\) | |||||||
\(312\) | 117.341 | − | 203.241i | 0.0212921 | − | 0.0368790i | ||||
\(313\) | 2045.92 | + | 3543.64i | 0.369465 | + | 0.639931i | 0.989482 | − | 0.144657i | \(-0.0462078\pi\) |
−0.620017 | + | 0.784588i | \(0.712874\pi\) | |||||||
\(314\) | 7185.91 | 1.29148 | ||||||||
\(315\) | 833.185 | + | 19.4238i | 0.149031 | + | 0.00347431i | ||||
\(316\) | 2325.40 | 0.413967 | ||||||||
\(317\) | 496.845 | + | 860.562i | 0.0880304 | + | 0.152473i | 0.906678 | − | 0.421822i | \(-0.138609\pi\) |
−0.818648 | + | 0.574295i | \(0.805276\pi\) | |||||||
\(318\) | 27.2720 | − | 47.2365i | 0.00480924 | − | 0.00832985i | ||||
\(319\) | 2763.58 | − | 4786.66i | 0.485050 | − | 0.840131i | ||||
\(320\) | −1423.60 | − | 2465.75i | −0.248693 | − | 0.430748i | ||||
\(321\) | −2080.21 | −0.361701 | ||||||||
\(322\) | 4564.06 | + | 106.401i | 0.789892 | + | 0.0184145i | ||||
\(323\) | 617.430 | 0.106361 | ||||||||
\(324\) | 73.8330 | + | 127.883i | 0.0126600 | + | 0.0219277i | ||||
\(325\) | −40.0531 | + | 69.3740i | −0.00683614 | + | 0.0118405i | ||||
\(326\) | 3137.82 | − | 5434.87i | 0.533092 | − | 0.923342i | ||||
\(327\) | −1710.18 | − | 2962.11i | −0.289214 | − | 0.500933i | ||||
\(328\) | −5074.19 | −0.854193 | ||||||||
\(329\) | −3870.86 | + | 6357.57i | −0.648654 | + | 1.06536i | ||||
\(330\) | −971.514 | −0.162061 | ||||||||
\(331\) | −1530.07 | − | 2650.16i | −0.254079 | − | 0.440078i | 0.710566 | − | 0.703631i | \(-0.248439\pi\) |
−0.964645 | + | 0.263553i | \(0.915106\pi\) | |||||||
\(332\) | 223.001 | − | 386.249i | 0.0368637 | − | 0.0638498i | ||||
\(333\) | −93.1676 | + | 161.371i | −0.0153320 | + | 0.0265558i | ||||
\(334\) | −3593.80 | − | 6224.64i | −0.588754 | − | 1.01975i | ||||
\(335\) | 2937.31 | 0.479052 | ||||||||
\(336\) | −1228.42 | − | 2247.06i | −0.199452 | − | 0.364843i | ||||
\(337\) | −2761.72 | −0.446411 | −0.223205 | − | 0.974771i | \(-0.571652\pi\) | ||||
−0.223205 | + | 0.974771i | \(0.571652\pi\) | |||||||
\(338\) | −2717.40 | − | 4706.67i | −0.437299 | − | 0.757423i | ||||
\(339\) | 1731.97 | − | 2999.85i | 0.277485 | − | 0.480618i | ||||
\(340\) | −82.1847 | + | 142.348i | −0.0131091 | + | 0.0227056i | ||||
\(341\) | 3819.98 | + | 6616.39i | 0.606637 | + | 1.05073i | ||||
\(342\) | 765.883 | 0.121094 | ||||||||
\(343\) | 6336.92 | + | 443.836i | 0.997556 | + | 0.0698684i | ||||
\(344\) | 145.602 | 0.0228208 | ||||||||
\(345\) | −743.868 | − | 1288.42i | −0.116083 | − | 0.201061i | ||||
\(346\) | −3609.90 | + | 6252.53i | −0.560894 | + | 0.971497i | ||||
\(347\) | −6265.03 | + | 10851.4i | −0.969235 | + | 1.67876i | −0.271456 | + | 0.962451i | \(0.587505\pi\) |
−0.697779 | + | 0.716313i | \(0.745828\pi\) | |||||||
\(348\) | −579.988 | − | 1004.57i | −0.0893408 | − | 0.154743i | ||||
\(349\) | 3744.12 | 0.574263 | 0.287132 | − | 0.957891i | \(-0.407298\pi\) | ||||
0.287132 | + | 0.957891i | \(0.407298\pi\) | |||||||
\(350\) | 551.984 | + | 1009.70i | 0.0842994 | + | 0.154203i | ||||
\(351\) | −86.5147 | −0.0131562 | ||||||||
\(352\) | −1052.22 | − | 1822.49i | −0.159328 | − | 0.275964i | ||||
\(353\) | 1122.02 | − | 1943.39i | 0.169175 | − | 0.293020i | −0.768955 | − | 0.639303i | \(-0.779223\pi\) |
0.938130 | + | 0.346283i | \(0.112556\pi\) | |||||||
\(354\) | −150.645 | + | 260.926i | −0.0226178 | + | 0.0391752i | ||||
\(355\) | −2008.51 | − | 3478.84i | −0.300284 | − | 0.520107i | ||||
\(356\) | 2572.46 | 0.382978 | ||||||||
\(357\) | −521.035 | + | 855.758i | −0.0772440 | + | 0.126867i | ||||
\(358\) | −57.4217 | −0.00847718 | ||||||||
\(359\) | 470.588 | + | 815.083i | 0.0691830 | + | 0.119828i | 0.898542 | − | 0.438888i | \(-0.144627\pi\) |
−0.829359 | + | 0.558716i | \(0.811294\pi\) | |||||||
\(360\) | −549.308 | + | 951.429i | −0.0804196 | + | 0.139291i | ||||
\(361\) | 2843.31 | − | 4924.77i | 0.414538 | − | 0.718001i | ||||
\(362\) | −3757.86 | − | 6508.80i | −0.545604 | − | 0.945013i | ||||
\(363\) | 1955.67 | 0.282771 | ||||||||
\(364\) | −108.156 | − | 2.52141i | −0.0155740 | − | 0.000363071i | ||||
\(365\) | −3280.25 | −0.470401 | ||||||||
\(366\) | 1336.44 | + | 2314.78i | 0.190865 | + | 0.330588i | ||||
\(367\) | −242.112 | + | 419.350i | −0.0344363 | + | 0.0596455i | −0.882730 | − | 0.469881i | \(-0.844297\pi\) |
0.848294 | + | 0.529526i | \(0.177630\pi\) | |||||||
\(368\) | −2285.77 | + | 3959.07i | −0.323788 | + | 0.560817i | ||||
\(369\) | 935.289 | + | 1619.97i | 0.131949 | + | 0.228543i | ||||
\(370\) | −257.282 | −0.0361499 | ||||||||
\(371\) | −135.446 | − | 3.15762i | −0.0189543 | − | 0.000441875i | ||||
\(372\) | 1603.38 | 0.223472 | ||||||||
\(373\) | 5211.12 | + | 9025.93i | 0.723383 | + | 1.25294i | 0.959636 | + | 0.281244i | \(0.0907471\pi\) |
−0.236253 | + | 0.971691i | \(0.575920\pi\) | |||||||
\(374\) | 583.960 | − | 1011.45i | 0.0807376 | − | 0.139842i | ||||
\(375\) | 187.500 | − | 324.760i | 0.0258199 | − | 0.0447214i | ||||
\(376\) | −4905.91 | − | 8497.29i | −0.672881 | − | 1.16546i | ||||
\(377\) | 679.607 | 0.0928423 | ||||||||
\(378\) | −646.311 | + | 1061.51i | −0.0879436 | + | 0.144440i | ||||
\(379\) | −6388.05 | −0.865784 | −0.432892 | − | 0.901446i | \(-0.642507\pi\) | ||||
−0.432892 | + | 0.901446i | \(0.642507\pi\) | |||||||
\(380\) | −156.052 | − | 270.289i | −0.0210665 | − | 0.0364883i | ||||
\(381\) | −2179.98 | + | 3775.84i | −0.293134 | + | 0.507722i | ||||
\(382\) | 4842.57 | − | 8387.58i | 0.648606 | − | 1.12342i | ||||
\(383\) | 2491.40 | + | 4315.22i | 0.332387 | + | 0.575712i | 0.982979 | − | 0.183716i | \(-0.0588125\pi\) |
−0.650592 | + | 0.759427i | \(0.725479\pi\) | |||||||
\(384\) | 2307.67 | 0.306674 | ||||||||
\(385\) | 1157.55 | + | 2117.42i | 0.153232 | + | 0.280295i | ||||
\(386\) | 11455.7 | 1.51057 | ||||||||
\(387\) | −26.8379 | − | 46.4845i | −0.00352518 | − | 0.00610579i | ||||
\(388\) | −867.960 | + | 1503.35i | −0.113567 | + | 0.196704i | ||||
\(389\) | 3374.32 | − | 5844.50i | 0.439807 | − | 0.761769i | −0.557867 | − | 0.829930i | \(-0.688380\pi\) |
0.997674 | + | 0.0681618i | \(0.0217134\pi\) | |||||||
\(390\) | −59.7276 | − | 103.451i | −0.00775493 | − | 0.0134319i | ||||
\(391\) | 1788.50 | 0.231326 | ||||||||
\(392\) | −4520.34 | + | 7049.01i | −0.582428 | + | 0.908237i | ||||
\(393\) | 4618.73 | 0.592835 | ||||||||
\(394\) | 3876.04 | + | 6713.49i | 0.495614 | + | 0.858429i | ||||
\(395\) | 3188.90 | − | 5523.34i | 0.406205 | − | 0.703568i | ||||
\(396\) | −213.786 | + | 370.288i | −0.0271291 | + | 0.0469890i | ||||
\(397\) | −1991.14 | − | 3448.76i | −0.251720 | − | 0.435991i | 0.712280 | − | 0.701896i | \(-0.247663\pi\) |
−0.963999 | + | 0.265904i | \(0.914329\pi\) | |||||||
\(398\) | 10311.5 | 1.29867 | ||||||||
\(399\) | −912.541 | − | 1669.24i | −0.114497 | − | 0.209440i | ||||
\(400\) | −1152.31 | −0.144038 | ||||||||
\(401\) | −3284.14 | − | 5688.29i | −0.408982 | − | 0.708378i | 0.585794 | − | 0.810460i | \(-0.300783\pi\) |
−0.994776 | + | 0.102082i | \(0.967450\pi\) | |||||||
\(402\) | −2190.07 | + | 3793.32i | −0.271719 | + | 0.470631i | ||||
\(403\) | −469.695 | + | 813.536i | −0.0580576 | + | 0.100559i | ||||
\(404\) | −1313.92 | − | 2275.78i | −0.161807 | − | 0.280258i | ||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 5077.03 | − | 8338.61i | 0.620613 | − | 1.01931i | ||||
\(407\) | −539.539 | −0.0657100 | ||||||||
\(408\) | −660.359 | − | 1143.77i | −0.0801290 | − | 0.138787i | ||||
\(409\) | 2478.39 | − | 4292.69i | 0.299629 | − | 0.518973i | −0.676422 | − | 0.736514i | \(-0.736470\pi\) |
0.976051 | + | 0.217541i | \(0.0698037\pi\) | |||||||
\(410\) | −1291.40 | + | 2236.77i | −0.155555 | + | 0.269430i | ||||
\(411\) | 4373.31 | + | 7574.80i | 0.524865 | + | 0.909093i | ||||
\(412\) | −2078.24 | −0.248513 | ||||||||
\(413\) | 748.180 | + | 17.4421i | 0.0891418 | + | 0.00207813i | ||||
\(414\) | 2218.53 | 0.263369 | ||||||||
\(415\) | −611.618 | − | 1059.35i | −0.0723450 | − | 0.125305i | ||||
\(416\) | 129.378 | − | 224.090i | 0.0152483 | − | 0.0264108i | ||||
\(417\) | −3508.14 | + | 6076.27i | −0.411977 | + | 0.713565i | ||||
\(418\) | 1108.82 | + | 1920.53i | 0.129747 | + | 0.224728i | ||||
\(419\) | 5778.60 | 0.673754 | 0.336877 | − | 0.941549i | \(-0.390629\pi\) | ||||
0.336877 | + | 0.941549i | \(0.390629\pi\) | |||||||
\(420\) | 506.309 | + | 11.8034i | 0.0588223 | + | 0.00137131i | ||||
\(421\) | 7463.23 | 0.863980 | 0.431990 | − | 0.901878i | \(-0.357812\pi\) | ||||
0.431990 | + | 0.901878i | \(0.357812\pi\) | |||||||
\(422\) | −4766.58 | − | 8255.96i | −0.549842 | − | 0.952355i | ||||
\(423\) | −1808.54 | + | 3132.49i | −0.207883 | + | 0.360064i | ||||
\(424\) | 89.2980 | − | 154.669i | 0.0102281 | − | 0.0177155i | ||||
\(425\) | 225.406 | + | 390.414i | 0.0257266 | + | 0.0445597i | ||||
\(426\) | 5990.22 | 0.681285 | ||||||||
\(427\) | 3452.71 | − | 5670.80i | 0.391308 | − | 0.642691i | ||||
\(428\) | −1264.10 | −0.142763 | ||||||||
\(429\) | −125.253 | − | 216.944i | −0.0140962 | − | 0.0244153i | ||||
\(430\) | 37.0564 | − | 64.1835i | 0.00415585 | − | 0.00719815i | ||||
\(431\) | −1520.79 | + | 2634.09i | −0.169963 | + | 0.294384i | −0.938406 | − | 0.345533i | \(-0.887698\pi\) |
0.768444 | + | 0.639917i | \(0.221031\pi\) | |||||||
\(432\) | −622.245 | − | 1077.76i | −0.0693004 | − | 0.120032i | ||||
\(433\) | 4047.48 | 0.449214 | 0.224607 | − | 0.974449i | \(-0.427890\pi\) | ||||
0.224607 | + | 0.974449i | \(0.427890\pi\) | |||||||
\(434\) | 6473.01 | + | 11840.6i | 0.715932 | + | 1.30960i | ||||
\(435\) | −3181.44 | −0.350662 | ||||||||
\(436\) | −1039.24 | − | 1800.01i | −0.114153 | − | 0.197718i | ||||
\(437\) | −1698.00 | + | 2941.02i | −0.185872 | + | 0.321941i | ||||
\(438\) | 2445.77 | − | 4236.20i | 0.266812 | − | 0.462132i | ||||
\(439\) | 1366.46 | + | 2366.77i | 0.148559 | + | 0.257312i | 0.930695 | − | 0.365796i | \(-0.119203\pi\) |
−0.782136 | + | 0.623108i | \(0.785870\pi\) | |||||||
\(440\) | −3181.07 | −0.344663 | ||||||||
\(441\) | 3083.65 | + | 143.854i | 0.332971 | + | 0.0155334i | ||||
\(442\) | 143.605 | 0.0154538 | ||||||||
\(443\) | −3199.52 | − | 5541.73i | −0.343146 | − | 0.594347i | 0.641869 | − | 0.766814i | \(-0.278159\pi\) |
−0.985015 | + | 0.172468i | \(0.944826\pi\) | |||||||
\(444\) | −56.6160 | + | 98.0618i | −0.00605153 | + | 0.0104816i | ||||
\(445\) | 3527.71 | − | 6110.17i | 0.375797 | − | 0.650899i | ||||
\(446\) | −932.416 | − | 1614.99i | −0.0989937 | − | 0.171462i | ||||
\(447\) | 1476.53 | 0.156236 | ||||||||
\(448\) | −5058.79 | − | 9253.67i | −0.533495 | − | 0.975882i | ||||
\(449\) | −16489.7 | −1.73318 | −0.866588 | − | 0.499024i | \(-0.833692\pi\) | ||||
−0.866588 | + | 0.499024i | \(0.833692\pi\) | |||||||
\(450\) | 279.602 | + | 484.285i | 0.0292901 | + | 0.0507320i | ||||
\(451\) | −2708.16 | + | 4690.67i | −0.282754 | + | 0.489745i | ||||
\(452\) | 1052.48 | − | 1822.95i | 0.109523 | − | 0.189700i | ||||
\(453\) | 1622.92 | + | 2810.99i | 0.168326 | + | 0.291549i | ||||
\(454\) | 1562.89 | 0.161564 | ||||||||
\(455\) | −154.307 | + | 253.437i | −0.0158990 | + | 0.0261128i | ||||
\(456\) | 2507.77 | 0.257537 | ||||||||
\(457\) | −7187.97 | − | 12449.9i | −0.735753 | − | 1.27436i | −0.954392 | − | 0.298556i | \(-0.903495\pi\) |
0.218639 | − | 0.975806i | \(-0.429838\pi\) | |||||||
\(458\) | −3041.23 | + | 5267.57i | −0.310278 | + | 0.537418i | ||||
\(459\) | −243.438 | + | 421.648i | −0.0247554 | + | 0.0428776i | ||||
\(460\) | −452.033 | − | 782.945i | −0.0458178 | − | 0.0793587i | ||||
\(461\) | 1000.39 | 0.101069 | 0.0505346 | − | 0.998722i | \(-0.483907\pi\) | ||||
0.0505346 | + | 0.998722i | \(0.483907\pi\) | |||||||
\(462\) | −3597.56 | − | 83.8688i | −0.362281 | − | 0.00844574i | ||||
\(463\) | −626.125 | −0.0628477 | −0.0314239 | − | 0.999506i | \(-0.510004\pi\) | ||||
−0.0314239 | + | 0.999506i | \(0.510004\pi\) | |||||||
\(464\) | 4887.98 | + | 8466.23i | 0.489049 | + | 0.847058i | ||||
\(465\) | 2198.78 | − | 3808.40i | 0.219282 | − | 0.379807i | ||||
\(466\) | 3928.30 | − | 6804.01i | 0.390504 | − | 0.676373i | ||||
\(467\) | −459.520 | − | 795.912i | −0.0455333 | − | 0.0788659i | 0.842361 | − | 0.538914i | \(-0.181165\pi\) |
−0.887894 | + | 0.460048i | \(0.847832\pi\) | |||||||
\(468\) | −52.5732 | −0.00519273 | ||||||||
\(469\) | 10877.0 | + | 253.572i | 1.07090 | + | 0.0249656i | ||||
\(470\) | −4994.29 | −0.490148 | ||||||||
\(471\) | −4336.96 | − | 7511.84i | −0.424282 | − | 0.734877i | ||||
\(472\) | −493.265 | + | 854.361i | −0.0481025 | + | 0.0833160i | ||||
\(473\) | 77.7098 | − | 134.597i | 0.00755412 | − | 0.0130841i | ||||
\(474\) | 4755.32 | + | 8236.46i | 0.460800 | + | 0.798129i | ||||
\(475\) | −855.997 | −0.0826860 | ||||||||
\(476\) | −316.622 | + | 520.027i | −0.0304882 | + | 0.0500743i | ||||
\(477\) | −65.8387 | −0.00631980 | ||||||||
\(478\) | −7478.80 | − | 12953.7i | −0.715632 | − | 1.23951i | ||||
\(479\) | 7831.84 | − | 13565.1i | 0.747068 | − | 1.29396i | −0.202154 | − | 0.979354i | \(-0.564794\pi\) |
0.949222 | − | 0.314606i | \(-0.101873\pi\) | |||||||
\(480\) | −605.656 | + | 1049.03i | −0.0575923 | + | 0.0997528i | ||||
\(481\) | −33.1702 | − | 57.4525i | −0.00314435 | − | 0.00544618i | ||||
\(482\) | −14212.3 | −1.34305 | ||||||||
\(483\) | −2643.35 | − | 4835.29i | −0.249020 | − | 0.455514i | ||||
\(484\) | 1188.42 | 0.111610 | ||||||||
\(485\) | 2380.53 | + | 4123.20i | 0.222875 | + | 0.386031i | ||||
\(486\) | −301.970 | + | 523.027i | −0.0281844 | + | 0.0488169i | ||||
\(487\) | −7220.23 | + | 12505.8i | −0.671827 | + | 1.16364i | 0.305558 | + | 0.952173i | \(0.401157\pi\) |
−0.977385 | + | 0.211466i | \(0.932176\pi\) | |||||||
\(488\) | 4375.95 | + | 7579.38i | 0.405922 | + | 0.703078i | ||||
\(489\) | −7575.16 | −0.700533 | ||||||||
\(490\) | 1956.86 | + | 3786.63i | 0.180412 | + | 0.349107i | ||||
\(491\) | −19320.8 | −1.77584 | −0.887918 | − | 0.460001i | \(-0.847849\pi\) | ||||
−0.887918 | + | 0.460001i | \(0.847849\pi\) | |||||||
\(492\) | 568.356 | + | 984.421i | 0.0520802 | + | 0.0902056i | ||||
\(493\) | 1912.30 | − | 3312.21i | 0.174698 | − | 0.302585i | ||||
\(494\) | −136.338 | + | 236.144i | −0.0124173 | + | 0.0215073i | ||||
\(495\) | 586.345 | + | 1015.58i | 0.0532409 | + | 0.0922159i | ||||
\(496\) | −13512.9 | −1.22328 | ||||||||
\(497\) | −7137.29 | − | 13055.7i | −0.644167 | − | 1.17833i | ||||
\(498\) | 1824.10 | 0.164137 | ||||||||
\(499\) | 2266.59 | + | 3925.86i | 0.203340 | + | 0.352195i | 0.949603 | − | 0.313456i | \(-0.101487\pi\) |
−0.746263 | + | 0.665652i | \(0.768154\pi\) | |||||||
\(500\) | 113.940 | − | 197.350i | 0.0101911 | − | 0.0176515i | ||||
\(501\) | −4337.98 | + | 7513.60i | −0.386839 | + | 0.670025i | ||||
\(502\) | 1536.02 | + | 2660.47i | 0.136566 | + | 0.236539i | ||||
\(503\) | 1296.32 | 0.114911 | 0.0574554 | − | 0.998348i | \(-0.481701\pi\) | ||||
0.0574554 | + | 0.998348i | \(0.481701\pi\) | |||||||
\(504\) | −2116.25 | + | 3475.76i | −0.187034 | + | 0.307188i | ||||
\(505\) | −7207.32 | −0.635092 | ||||||||
\(506\) | 3211.90 | + | 5563.18i | 0.282187 | + | 0.488762i | ||||
\(507\) | −3280.10 | + | 5681.30i | −0.287326 | + | 0.497663i | ||||
\(508\) | −1324.73 | + | 2294.50i | −0.115700 | + | 0.200398i | ||||
\(509\) | 3266.81 | + | 5658.28i | 0.284477 | + | 0.492728i | 0.972482 | − | 0.232977i | \(-0.0748468\pi\) |
−0.688005 | + | 0.725706i | \(0.741513\pi\) | |||||||
\(510\) | −672.255 | −0.0583685 | ||||||||
\(511\) | −12146.9 | − | 283.178i | −1.05156 | − | 0.0245148i | ||||
\(512\) | 12724.4 | 1.09833 | ||||||||
\(513\) | −462.239 | − | 800.621i | −0.0397823 | − | 0.0689050i | ||||
\(514\) | −1365.62 | + | 2365.32i | −0.117188 | + | 0.202976i | ||||
\(515\) | −2849.97 | + | 4936.28i | −0.243853 | + | 0.422366i | ||||
\(516\) | −16.3088 | − | 28.2477i | −0.00139139 | − | 0.00240995i | ||||
\(517\) | −10473.4 | −0.890946 | ||||||||
\(518\) | −952.728 | − | 22.2107i | −0.0808117 | − | 0.00188394i | ||||
\(519\) | 8714.83 | 0.737068 | ||||||||
\(520\) | −195.569 | − | 338.735i | −0.0164928 | − | 0.0285664i | ||||
\(521\) | −411.791 | + | 713.244i | −0.0346275 | + | 0.0599765i | −0.882820 | − | 0.469712i | \(-0.844358\pi\) |
0.848192 | + | 0.529688i | \(0.177691\pi\) | |||||||
\(522\) | 2372.09 | − | 4108.59i | 0.198896 | − | 0.344498i | ||||
\(523\) | 8626.23 | + | 14941.1i | 0.721221 | + | 1.24919i | 0.960511 | + | 0.278243i | \(0.0897522\pi\) |
−0.239289 | + | 0.970948i | \(0.576914\pi\) | |||||||
\(524\) | 2806.71 | 0.233991 | ||||||||
\(525\) | 722.357 | − | 1186.41i | 0.0600500 | − | 0.0986272i | ||||
\(526\) | 16710.2 | 1.38517 | ||||||||
\(527\) | 2643.29 | + | 4578.32i | 0.218489 | + | 0.378434i | ||||
\(528\) | 1801.73 | − | 3120.69i | 0.148504 | − | 0.257217i | ||||
\(529\) | 1164.92 | − | 2017.70i | 0.0957443 | − | 0.165834i | ||||
\(530\) | −45.4534 | − | 78.7275i | −0.00372522 | − | 0.00645228i | ||||
\(531\) | 363.680 | 0.0297220 | ||||||||
\(532\) | −554.532 | − | 1014.36i | −0.0451918 | − | 0.0826660i | ||||
\(533\) | −665.978 | −0.0541214 | ||||||||
\(534\) | 5260.55 | + | 9111.55i | 0.426304 | + | 0.738380i | ||||
\(535\) | −1733.51 | + | 3002.53i | −0.140086 | + | 0.242637i | ||||
\(536\) | −7171.06 | + | 12420.6i | −0.577878 | + | 1.00091i | ||||
\(537\) | 34.6561 | + | 60.0261i | 0.00278496 | + | 0.00482369i | ||||
\(538\) | −12775.0 | −1.02374 | ||||||||
\(539\) | 4103.66 | + | 7940.82i | 0.327936 | + | 0.634574i | ||||
\(540\) | 246.110 | 0.0196128 | ||||||||
\(541\) | 8572.43 | + | 14847.9i | 0.681252 | + | 1.17996i | 0.974599 | + | 0.223957i | \(0.0718976\pi\) |
−0.293347 | + | 0.956006i | \(0.594769\pi\) | |||||||
\(542\) | 3622.41 | − | 6274.19i | 0.287077 | − | 0.497232i | ||||
\(543\) | −4536.01 | + | 7856.60i | −0.358488 | + | 0.620919i | ||||
\(544\) | −728.099 | − | 1261.10i | −0.0573841 | − | 0.0993922i | ||||
\(545\) | −5700.59 | −0.448048 | ||||||||
\(546\) | −212.243 | − | 388.241i | −0.0166358 | − | 0.0304307i | ||||
\(547\) | −14217.3 | −1.11131 | −0.555656 | − | 0.831412i | \(-0.687533\pi\) | ||||
−0.555656 | + | 0.831412i | \(0.687533\pi\) | |||||||
\(548\) | 2657.57 | + | 4603.05i | 0.207164 | + | 0.358818i | ||||
\(549\) | 1613.18 | − | 2794.10i | 0.125408 | − | 0.217212i | ||||
\(550\) | −809.595 | + | 1402.26i | −0.0627659 | + | 0.108714i | ||||
\(551\) | 3631.07 | + | 6289.19i | 0.280742 | + | 0.486259i | ||||
\(552\) | 7264.23 | 0.560120 | ||||||||
\(553\) | 12285.5 | − | 20177.9i | 0.944722 | − | 1.55163i | ||||
\(554\) | −4438.67 | −0.340399 | ||||||||
\(555\) | 155.279 | + | 268.952i | 0.0118761 | + | 0.0205700i | ||||
\(556\) | −2131.82 | + | 3692.43i | −0.162607 | + | 0.281643i | ||||
\(557\) | 9695.91 | − | 16793.8i | 0.737575 | − | 1.27752i | −0.216010 | − | 0.976391i | \(-0.569304\pi\) |
0.953584 | − | 0.301126i | \(-0.0973623\pi\) | |||||||
\(558\) | 3278.84 | + | 5679.12i | 0.248753 | + | 0.430853i | ||||
\(559\) | 19.1100 | 0.00144592 | ||||||||
\(560\) | −4267.04 | − | 99.4762i | −0.321992 | − | 0.00750649i | ||||
\(561\) | −1409.77 | −0.106097 | ||||||||
\(562\) | 1571.69 | + | 2722.24i | 0.117967 | + | 0.204325i | ||||
\(563\) | 2081.20 | − | 3604.75i | 0.155794 | − | 0.269844i | −0.777554 | − | 0.628817i | \(-0.783540\pi\) |
0.933348 | + | 0.358973i | \(0.116873\pi\) | |||||||
\(564\) | −1099.02 | + | 1903.55i | −0.0820512 | + | 0.142117i | ||||
\(565\) | −2886.61 | − | 4999.76i | −0.214939 | − | 0.372285i | ||||
\(566\) | −20793.4 | −1.54419 | ||||||||
\(567\) | 1499.73 | + | 34.9628i | 0.111081 | + | 0.00258960i | ||||
\(568\) | 19614.1 | 1.44892 | ||||||||
\(569\) | 5348.05 | + | 9263.10i | 0.394028 | + | 0.682477i | 0.992977 | − | 0.118311i | \(-0.0377479\pi\) |
−0.598948 | + | 0.800788i | \(0.704415\pi\) | |||||||
\(570\) | 638.236 | − | 1105.46i | 0.0468996 | − | 0.0812324i | ||||
\(571\) | −6235.48 | + | 10800.2i | −0.456999 | + | 0.791546i | −0.998801 | − | 0.0489606i | \(-0.984409\pi\) |
0.541801 | + | 0.840506i | \(0.317742\pi\) | |||||||
\(572\) | −76.1136 | − | 131.833i | −0.00556376 | − | 0.00963671i | ||||
\(573\) | −11690.7 | −0.852331 | ||||||||
\(574\) | −4975.21 | + | 8171.38i | −0.361779 | + | 0.594193i | ||||
\(575\) | −2479.56 | −0.179835 | ||||||||
\(576\) | −2562.48 | − | 4438.35i | −0.185365 | − | 0.321061i | ||||
\(577\) | 7851.02 | − | 13598.4i | 0.566451 | − | 0.981122i | −0.430462 | − | 0.902609i | \(-0.641649\pi\) |
0.996913 | − | 0.0785131i | \(-0.0250173\pi\) | |||||||
\(578\) | −5701.18 | + | 9874.73i | −0.410273 | + | 0.710614i | ||||
\(579\) | −6913.93 | − | 11975.3i | −0.496257 | − | 0.859543i | ||||
\(580\) | −1933.29 | −0.138406 | ||||||||
\(581\) | −2173.40 | − | 3975.64i | −0.155194 | − | 0.283885i | ||||
\(582\) | −7099.74 | −0.505659 | ||||||||
\(583\) | −95.3189 | − | 165.097i | −0.00677136 | − | 0.0117283i | ||||
\(584\) | 8008.31 | − | 13870.8i | 0.567442 | − | 0.982838i | ||||
\(585\) | −72.0956 | + | 124.873i | −0.00509536 | + | 0.00882542i | ||||
\(586\) | −1929.58 | − | 3342.13i | −0.136024 | − | 0.235601i | ||||
\(587\) | 22423.3 | 1.57668 | 0.788339 | − | 0.615241i | \(-0.210941\pi\) | ||||
0.788339 | + | 0.615241i | \(0.210941\pi\) | |||||||
\(588\) | 1873.87 | + | 87.4173i | 0.131423 | + | 0.00613100i | ||||
\(589\) | −10038.1 | −0.702230 | ||||||||
\(590\) | 251.076 | + | 434.876i | 0.0175197 | + | 0.0303450i | ||||
\(591\) | 4678.66 | − | 8103.68i | 0.325642 | − | 0.564029i | ||||
\(592\) | 477.145 | − | 826.439i | 0.0331259 | − | 0.0573757i | ||||
\(593\) | −266.968 | − | 462.403i | −0.0184875 | − | 0.0320213i | 0.856634 | − | 0.515925i | \(-0.172552\pi\) |
−0.875121 | + | 0.483904i | \(0.839218\pi\) | |||||||
\(594\) | −1748.73 | −0.120793 | ||||||||
\(595\) | 800.985 | + | 1465.18i | 0.0551885 | + | 0.100952i | ||||
\(596\) | 897.255 | 0.0616661 | ||||||||
\(597\) | −6223.40 | − | 10779.2i | −0.426645 | − | 0.738970i | ||||
\(598\) | −394.929 | + | 684.036i | −0.0270064 | + | 0.0467765i | ||||
\(599\) | 2813.30 | − | 4872.78i | 0.191900 | − | 0.332381i | −0.753980 | − | 0.656898i | \(-0.771868\pi\) |
0.945880 | + | 0.324517i | \(0.105202\pi\) | |||||||
\(600\) | 915.513 | + | 1585.72i | 0.0622928 | + | 0.107894i | ||||
\(601\) | 8563.09 | 0.581191 | 0.290596 | − | 0.956846i | \(-0.406147\pi\) | ||||
0.290596 | + | 0.956846i | \(0.406147\pi\) | |||||||
\(602\) | 142.762 | − | 234.475i | 0.00966537 | − | 0.0158746i | ||||
\(603\) | 5287.16 | 0.357065 | ||||||||
\(604\) | 986.217 | + | 1708.18i | 0.0664381 | + | 0.115074i | ||||
\(605\) | 1629.72 | − | 2822.76i | 0.109517 | − | 0.189689i | ||||
\(606\) | 5373.82 | − | 9307.72i | 0.360225 | − | 0.623928i | ||||
\(607\) | 10366.6 | + | 17955.5i | 0.693194 | + | 1.20065i | 0.970786 | + | 0.239948i | \(0.0771304\pi\) |
−0.277592 | + | 0.960699i | \(0.589536\pi\) | |||||||
\(608\) | 2765.01 | 0.184434 | ||||||||
\(609\) | −11781.0 | − | 274.647i | −0.783892 | − | 0.0182746i | ||||
\(610\) | 4454.79 | 0.295687 | ||||||||
\(611\) | −643.892 | − | 1115.25i | −0.0426335 | − | 0.0738434i | ||||
\(612\) | −147.932 | + | 256.227i | −0.00977094 | + | 0.0169238i | ||||
\(613\) | −6225.28 | + | 10782.5i | −0.410174 | + | 0.710443i | −0.994909 | − | 0.100782i | \(-0.967865\pi\) |
0.584734 | + | 0.811225i | \(0.301199\pi\) | |||||||
\(614\) | −8508.67 | − | 14737.4i | −0.559254 | − | 0.968656i | ||||
\(615\) | 3117.63 | 0.204415 | ||||||||
\(616\) | −11779.7 | − | 274.616i | −0.770481 | − | 0.0179620i | ||||
\(617\) | 6173.86 | 0.402837 | 0.201418 | − | 0.979505i | \(-0.435445\pi\) | ||||
0.201418 | + | 0.979505i | \(0.435445\pi\) | |||||||
\(618\) | −4249.90 | − | 7361.04i | −0.276628 | − | 0.479133i | ||||
\(619\) | 13335.8 | − | 23098.3i | 0.865930 | − | 1.49984i | −0.000189984 | − | 1.00000i | \(-0.500060\pi\) |
0.866120 | − | 0.499835i | \(-0.166606\pi\) | |||||||
\(620\) | 1336.15 | − | 2314.28i | 0.0865503 | − | 0.149909i | ||||
\(621\) | −1338.96 | − | 2319.15i | −0.0865229 | − | 0.149862i | ||||
\(622\) | −5841.22 | −0.376546 | ||||||||
\(623\) | 13590.7 | − | 22321.7i | 0.874000 | − | 1.43547i | ||||
\(624\) | 443.073 | 0.0284249 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −5084.83 | + | 8807.19i | −0.324650 | + | 0.562310i | ||||
\(627\) | 1338.42 | − | 2318.22i | 0.0852497 | − | 0.147657i | ||||
\(628\) | −2635.48 | − | 4564.79i | −0.167464 | − | 0.290056i | ||||
\(629\) | −373.343 | −0.0236664 | ||||||||
\(630\) | 993.571 | + | 1817.47i | 0.0628330 | + | 0.114936i | ||||
\(631\) | 25175.3 | 1.58829 | 0.794147 | − | 0.607726i | \(-0.207918\pi\) | ||||
0.794147 | + | 0.607726i | \(0.207918\pi\) | |||||||
\(632\) | 15570.6 | + | 26969.0i | 0.980006 | + | 1.69742i | ||||
\(633\) | −5753.61 | + | 9965.55i | −0.361273 | + | 0.625742i | ||||
\(634\) | −1234.83 | + | 2138.80i | −0.0773526 | + | 0.133979i | ||||
\(635\) | 3633.30 | + | 6293.07i | 0.227060 | + | 0.393280i | ||||
\(636\) | −40.0088 | −0.00249442 | ||||||||
\(637\) | −593.286 | + | 925.169i | −0.0369024 | + | 0.0575456i | ||||
\(638\) | 13736.9 | 0.852430 | ||||||||
\(639\) | −3615.32 | − | 6261.92i | −0.223818 | − | 0.387665i | ||||
\(640\) | 1923.06 | − | 3330.84i | 0.118774 | − | 0.205723i | ||||
\(641\) | 3951.07 | − | 6843.45i | 0.243460 | − | 0.421685i | −0.718238 | − | 0.695798i | \(-0.755051\pi\) |
0.961697 | + | 0.274113i | \(0.0883842\pi\) | |||||||
\(642\) | −2585.03 | − | 4477.40i | −0.158914 | − | 0.275247i | ||||
\(643\) | −18223.2 | −1.11766 | −0.558828 | − | 0.829284i | \(-0.688749\pi\) | ||||
−0.558828 | + | 0.829284i | \(0.688749\pi\) | |||||||
\(644\) | −1606.31 | − | 2938.30i | −0.0982880 | − | 0.179791i | ||||
\(645\) | −89.4595 | −0.00546119 | ||||||||
\(646\) | 767.264 | + | 1328.94i | 0.0467301 | + | 0.0809388i | ||||
\(647\) | 11989.7 | − | 20766.8i | 0.728539 | − | 1.26187i | −0.228961 | − | 0.973436i | \(-0.573533\pi\) |
0.957500 | − | 0.288432i | \(-0.0931338\pi\) | |||||||
\(648\) | −988.754 | + | 1712.57i | −0.0599413 | + | 0.103821i | ||||
\(649\) | 526.523 | + | 911.965i | 0.0318457 | + | 0.0551583i | ||||
\(650\) | −199.092 | −0.0120139 | ||||||||
\(651\) | 8470.95 | − | 13912.8i | 0.509989 | − | 0.837615i | ||||
\(652\) | −4603.27 | −0.276500 | ||||||||
\(653\) | −5459.18 | − | 9455.57i | −0.327158 | − | 0.566654i | 0.654789 | − | 0.755812i | \(-0.272758\pi\) |
−0.981947 | + | 0.189158i | \(0.939424\pi\) | |||||||
\(654\) | 4250.39 | − | 7361.88i | 0.254133 | − | 0.440172i | ||||
\(655\) | 3848.94 | − | 6666.56i | 0.229604 | − | 0.397686i | ||||
\(656\) | −4789.95 | − | 8296.44i | −0.285086 | − | 0.493783i | ||||
\(657\) | −5904.46 | −0.350616 | ||||||||
\(658\) | −18494.1 | − | 431.147i | −1.09571 | − | 0.0255439i | ||||
\(659\) | −910.217 | −0.0538043 | −0.0269021 | − | 0.999638i | \(-0.508564\pi\) | ||||
−0.0269021 | + | 0.999638i | \(0.508564\pi\) | |||||||
\(660\) | 356.309 | + | 617.146i | 0.0210141 | + | 0.0363975i | ||||
\(661\) | 5321.44 | − | 9217.00i | 0.313132 | − | 0.542360i | −0.665907 | − | 0.746035i | \(-0.731955\pi\) |
0.979039 | + | 0.203675i | \(0.0652886\pi\) | |||||||
\(662\) | 3802.76 | − | 6586.57i | 0.223260 | − | 0.386698i | ||||
\(663\) | −86.6708 | − | 150.118i | −0.00507694 | − | 0.00879353i | ||||
\(664\) | 5972.74 | 0.349077 | ||||||||
\(665\) | −3169.80 | − | 73.8965i | −0.184841 | − | 0.00430915i | ||||
\(666\) | −463.108 | −0.0269446 | ||||||||
\(667\) | 10518.1 | + | 18217.9i | 0.610588 | + | 1.05757i | ||||
\(668\) | −2636.10 | + | 4565.86i | −0.152685 | + | 0.264459i | ||||
\(669\) | −1125.49 | + | 1949.41i | −0.0650436 | + | 0.112659i | ||||
\(670\) | 3650.12 | + | 6322.20i | 0.210473 | + | 0.364549i | ||||
\(671\) | 9342.00 | 0.537472 | ||||||||
\(672\) | −2333.33 | + | 3832.31i | −0.133944 | + | 0.219992i | ||||
\(673\) | 12314.8 | 0.705351 | 0.352676 | − | 0.935746i | \(-0.385272\pi\) | ||||
0.352676 | + | 0.935746i | \(0.385272\pi\) | |||||||
\(674\) | −3431.92 | − | 5944.25i | −0.196131 | − | 0.339709i | ||||
\(675\) | 337.500 | − | 584.567i | 0.0192450 | − | 0.0333333i | ||||
\(676\) | −1993.25 | + | 3452.41i | −0.113407 | + | 0.196427i | ||||
\(677\) | −4907.95 | − | 8500.81i | −0.278623 | − | 0.482589i | 0.692420 | − | 0.721495i | \(-0.256545\pi\) |
−0.971043 | + | 0.238906i | \(0.923211\pi\) | |||||||
\(678\) | 8609.08 | 0.487655 | ||||||||
\(679\) | 8459.27 | + | 15473.9i | 0.478110 | + | 0.874571i | ||||
\(680\) | −2201.20 | −0.124135 | ||||||||
\(681\) | −943.259 | − | 1633.77i | −0.0530775 | − | 0.0919329i | ||||
\(682\) | −9493.97 | + | 16444.0i | −0.533054 | + | 0.923277i | ||||
\(683\) | −2177.36 | + | 3771.29i | −0.121983 | + | 0.211281i | −0.920550 | − | 0.390626i | \(-0.872259\pi\) |
0.798567 | + | 0.601906i | \(0.205592\pi\) | |||||||
\(684\) | −280.893 | − | 486.521i | −0.0157021 | − | 0.0271968i | ||||
\(685\) | 14577.7 | 0.813117 | ||||||||
\(686\) | 6919.44 | + | 14191.0i | 0.385110 | + | 0.789817i | ||||
\(687\) | 7341.99 | 0.407735 | ||||||||
\(688\) | 137.446 | + | 238.064i | 0.00761641 | + | 0.0131920i | ||||
\(689\) | 11.7202 | − | 20.3000i | 0.000648046 | − | 0.00112245i | ||||
\(690\) | 1848.77 | − | 3202.17i | 0.102002 | − | 0.176673i | ||||
\(691\) | −6744.58 | − | 11682.0i | −0.371311 | − | 0.643130i | 0.618456 | − | 0.785819i | \(-0.287758\pi\) |
−0.989768 | + | 0.142689i | \(0.954425\pi\) | |||||||
\(692\) | 5295.82 | 0.290920 | ||||||||
\(693\) | 2083.59 | + | 3811.35i | 0.114212 | + | 0.208920i | ||||
\(694\) | −31141.6 | −1.70334 | ||||||||
\(695\) | 5846.90 | + | 10127.1i | 0.319116 | + | 0.552725i | ||||
\(696\) | 7767.06 | − | 13452.9i | 0.423002 | − | 0.732661i | ||||
\(697\) | −1873.95 | + | 3245.78i | −0.101838 | + | 0.176388i | ||||
\(698\) | 4652.72 | + | 8058.75i | 0.252304 | + | 0.437003i | ||||
\(699\) | −9483.49 | −0.513160 | ||||||||
\(700\) | 438.961 | − | 720.959i | 0.0237017 | − | 0.0389281i | ||||
\(701\) | −17175.4 | −0.925399 | −0.462700 | − | 0.886515i | \(-0.653119\pi\) | ||||
−0.462700 | + | 0.886515i | \(0.653119\pi\) | |||||||
\(702\) | −107.510 | − | 186.212i | −0.00578019 | − | 0.0100116i | ||||
\(703\) | 354.450 | − | 613.925i | 0.0190161 | − | 0.0329369i | ||||
\(704\) | 7419.74 | − | 12851.4i | 0.397219 | − | 0.688003i | ||||
\(705\) | 3014.24 | + | 5220.82i | 0.161025 | + | 0.278904i | ||||
\(706\) | 5577.21 | 0.297310 | ||||||||
\(707\) | −26689.0 | − | 622.194i | −1.41972 | − | 0.0330976i | ||||
\(708\) | 221.001 | 0.0117313 | ||||||||
\(709\) | −906.735 | − | 1570.51i | −0.0480298 | − | 0.0831901i | 0.841011 | − | 0.541018i | \(-0.181961\pi\) |
−0.889041 | + | 0.457828i | \(0.848628\pi\) | |||||||
\(710\) | 4991.85 | − | 8646.14i | 0.263860 | − | 0.457020i | ||||
\(711\) | 5740.02 | − | 9942.01i | 0.302767 | − | 0.524409i | ||||
\(712\) | 17224.9 | + | 29834.4i | 0.906642 | + | 1.57035i | ||||
\(713\) | −29077.4 | −1.52729 | ||||||||
\(714\) | −2489.39 | − | 58.0344i | −0.130481 | − | 0.00304185i | ||||
\(715\) | −417.510 | −0.0218377 | ||||||||
\(716\) | 21.0598 | + | 36.4766i | 0.00109922 | + | 0.00190391i | ||||
\(717\) | −9027.46 | + | 15636.0i | −0.470204 | + | 0.814418i | ||||
\(718\) | −1169.58 | + | 2025.77i | −0.0607914 | + | 0.105294i | ||||
\(719\) | −11350.9 | − | 19660.4i | −0.588760 | − | 1.01976i | −0.994395 | − | 0.105727i | \(-0.966283\pi\) |
0.405636 | − | 0.914035i | \(-0.367050\pi\) | |||||||
\(720\) | −2074.15 | −0.107360 | ||||||||
\(721\) | −10979.7 | + | 18033.3i | −0.567136 | + | 0.931475i | ||||
\(722\) | 14133.3 | 0.728512 | ||||||||
\(723\) | 8577.65 | + | 14856.9i | 0.441226 | + | 0.764225i | ||||
\(724\) | −2756.44 | + | 4774.29i | −0.141495 | + | 0.245076i | ||||
\(725\) | −2651.20 | + | 4592.01i | −0.135811 | + | 0.235232i | ||||
\(726\) | 2430.26 | + | 4209.33i | 0.124236 | + | 0.215183i | ||||
\(727\) | 29667.1 | 1.51347 | 0.756734 | − | 0.653723i | \(-0.226794\pi\) | ||||
0.756734 | + | 0.653723i | \(0.226794\pi\) | |||||||
\(728\) | −694.958 | − | 1271.23i | −0.0353803 | − | 0.0647185i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −4076.29 | − | 7060.34i | −0.206672 | − | 0.357966i | ||||
\(731\) | 53.7725 | − | 93.1368i | 0.00272072 | − | 0.00471243i | ||||
\(732\) | 980.294 | − | 1697.92i | 0.0494983 | − | 0.0857335i | ||||
\(733\) | −5287.33 | − | 9157.92i | −0.266428 | − | 0.461467i | 0.701509 | − | 0.712661i | \(-0.252510\pi\) |
−0.967937 | + | 0.251194i | \(0.919177\pi\) | |||||||
\(734\) | −1203.46 | −0.0605187 | ||||||||
\(735\) | 2777.34 | − | 4330.98i | 0.139379 | − | 0.217348i | ||||
\(736\) | 8009.39 | 0.401128 | ||||||||
\(737\) | 7654.57 | + | 13258.1i | 0.382577 | + | 0.662643i | ||||
\(738\) | −2324.52 | + | 4026.19i | −0.115944 | + | 0.200821i | ||||
\(739\) | −15764.8 | + | 27305.4i | −0.784730 | + | 1.35919i | 0.144429 | + | 0.989515i | \(0.453865\pi\) |
−0.929160 | + | 0.369678i | \(0.879468\pi\) | |||||||
\(740\) | 94.3600 | + | 163.436i | 0.00468749 | + | 0.00811897i | ||||
\(741\) | 329.139 | 0.0163175 | ||||||||
\(742\) | −161.520 | − | 295.456i | −0.00799133 | − | 0.0146179i | ||||
\(743\) | 8886.27 | 0.438769 | 0.219385 | − | 0.975638i | \(-0.429595\pi\) | ||||
0.219385 | + | 0.975638i | \(0.429595\pi\) | |||||||
\(744\) | 10736.1 | + | 18595.4i | 0.529036 | + | 0.916317i | ||||
\(745\) | 1230.44 | − | 2131.18i | 0.0605098 | − | 0.104806i | ||||
\(746\) | −12951.5 | + | 22432.6i | −0.635639 | + | 1.10096i | ||||
\(747\) | −1100.91 | − | 1906.84i | −0.0539228 | − | 0.0933970i | ||||
\(748\) | −856.685 | −0.0418764 | ||||||||
\(749\) | −6678.47 | + | 10968.8i | −0.325802 | + | 0.535104i | ||||
\(750\) | 932.006 | 0.0453761 | ||||||||
\(751\) | 10241.2 | + | 17738.2i | 0.497610 | + | 0.861886i | 0.999996 | − | 0.00275714i | \(-0.000877627\pi\) |
−0.502386 | + | 0.864644i | \(0.667544\pi\) | |||||||
\(752\) | 9262.21 | − | 16042.6i | 0.449146 | − | 0.777944i | ||||
\(753\) | 1854.09 | − | 3211.38i | 0.0897301 | − | 0.155417i | ||||
\(754\) | 844.531 | + | 1462.77i | 0.0407905 | + | 0.0706511i | ||||
\(755\) | 5409.75 | 0.260769 | ||||||||
\(756\) | 911.357 | + | 21.2462i | 0.0438436 | + | 0.00102211i | ||||
\(757\) | −9959.68 | −0.478191 | −0.239096 | − | 0.970996i | \(-0.576851\pi\) | ||||
−0.239096 | + | 0.970996i | \(0.576851\pi\) | |||||||
\(758\) | −7938.27 | − | 13749.5i | −0.380384 | − | 0.658844i | ||||
\(759\) | 3877.01 | − | 6715.17i | 0.185410 | − | 0.321140i | ||||
\(760\) | 2089.80 | − | 3619.65i | 0.0997437 | − | 0.172761i | ||||
\(761\) | 2278.35 | + | 3946.21i | 0.108528 | + | 0.187976i | 0.915174 | − | 0.403058i | \(-0.132053\pi\) |
−0.806646 | + | 0.591035i | \(0.798720\pi\) | |||||||
\(762\) | −10836.0 | −0.515155 | ||||||||
\(763\) | −21109.5 | − | 492.120i | −1.00159 | − | 0.0233499i | ||||
\(764\) | −7104.19 | −0.336414 | ||||||||
\(765\) | 405.731 | + | 702.746i | 0.0191755 | + | 0.0332129i | ||||
\(766\) | −6191.99 | + | 10724.8i | −0.292070 | + | 0.505880i | ||||
\(767\) | −64.7401 | + | 112.133i | −0.00304776 | + | 0.00527887i | ||||
\(768\) | −3965.59 | − | 6868.61i | −0.186323 | − | 0.322721i | ||||
\(769\) | −23304.9 | −1.09284 | −0.546421 | − | 0.837511i | \(-0.684010\pi\) | ||||
−0.546421 | + | 0.837511i | \(0.684010\pi\) | |||||||
\(770\) | −3119.02 | + | 5122.74i | −0.145976 | + | 0.239754i | ||||
\(771\) | 3296.80 | 0.153997 | ||||||||
\(772\) | −4201.45 | − | 7277.12i | −0.195872 | − | 0.339261i | ||||
\(773\) | −19795.7 | + | 34287.2i | −0.921090 | + | 1.59537i | −0.123359 | + | 0.992362i | \(0.539367\pi\) |
−0.797732 | + | 0.603013i | \(0.793967\pi\) | |||||||
\(774\) | 66.7014 | − | 115.530i | 0.00309759 | − | 0.00536518i | ||||
\(775\) | −3664.63 | − | 6347.33i | −0.169855 | − | 0.294197i | ||||
\(776\) | −23247.0 | −1.07541 | ||||||||
\(777\) | 551.788 | + | 1009.35i | 0.0254766 | + | 0.0466024i | ||||
\(778\) | 16772.8 | 0.772921 | ||||||||
\(779\) | −3558.24 | − | 6163.06i | −0.163655 | − | 0.283459i | ||||
\(780\) | −43.8110 | + | 75.8829i | −0.00201114 | + | 0.00348339i | ||||
\(781\) | 10468.3 | − | 18131.6i | 0.479621 | − | 0.830728i | ||||
\(782\) | 2222.53 | + | 3849.53i | 0.101634 | + | 0.176035i | ||||
\(783\) | −5726.58 | −0.261368 | ||||||||
\(784\) | −15792.5 | − | 736.730i | −0.719409 | − | 0.0335609i | ||||
\(785\) | −14456.5 | −0.657294 | ||||||||
\(786\) | 5739.58 | + | 9941.24i | 0.260463 | + | 0.451135i | ||||
\(787\) | −11195.6 | + | 19391.3i | −0.507089 | + | 0.878304i | 0.492877 | + | 0.870099i | \(0.335945\pi\) |
−0.999966 | + | 0.00820496i | \(0.997388\pi\) | |||||||
\(788\) | 2843.13 | − | 4924.44i | 0.128531 | − | 0.222622i | ||||
\(789\) | −10085.2 | − | 17468.1i | −0.455061 | − | 0.788189i | ||||
\(790\) | 15851.1 | 0.713868 | ||||||||
\(791\) | −10257.6 | − | 18763.5i | −0.461086 | − | 0.843431i | ||||
\(792\) | −5725.93 | −0.256897 | ||||||||
\(793\) | 574.336 | + | 994.778i | 0.0257191 | + | 0.0445468i | ||||
\(794\) | 4948.69 | − | 8571.38i | 0.221187 | − | 0.383107i | ||||
\(795\) | −54.8656 | + | 95.0299i | −0.00244765 | + | 0.00423945i | ||||
\(796\) | −3781.83 | − | 6550.32i | −0.168396 | − | 0.291671i | ||||
\(797\) | −16409.1 | −0.729285 | −0.364642 | − | 0.931148i | \(-0.618809\pi\) | ||||
−0.364642 | + | 0.931148i | \(0.618809\pi\) | |||||||
\(798\) | 2458.85 | − | 4038.46i | 0.109076 | − | 0.179148i | ||||
\(799\) | −7247.23 | −0.320887 | ||||||||
\(800\) | 1009.43 | + | 1748.38i | 0.0446108 | + | 0.0772682i | ||||
\(801\) | 6349.88 | − | 10998.3i | 0.280102 | − | 0.485151i | ||||
\(802\) | 8162.22 | − | 14137.4i | 0.359374 | − | 0.622454i | ||||
\(803\) | −8548.26 | − | 14806.0i | −0.375668 | − | 0.650677i | ||||
\(804\) | 3212.90 | 0.140933 | ||||||||
\(805\) | −9181.93 | − | 214.055i | −0.402013 | − | 0.00937200i | ||||
\(806\) | −2334.71 | −0.102031 | ||||||||
\(807\) | 7710.20 | + | 13354.5i | 0.336322 | + | 0.582527i | ||||
\(808\) | 17595.7 | − | 30476.7i | 0.766108 | − | 1.32694i | ||||
\(809\) | −21773.8 | + | 37713.3i | −0.946260 | + | 1.63897i | −0.193052 | + | 0.981188i | \(0.561839\pi\) |
−0.753208 | + | 0.657782i | \(0.771495\pi\) | |||||||
\(810\) | 503.283 | + | 871.712i | 0.0218316 | + | 0.0378134i | ||||
\(811\) | 23780.0 | 1.02963 | 0.514814 | − | 0.857302i | \(-0.327861\pi\) | ||||
0.514814 | + | 0.857302i | \(0.327861\pi\) | |||||||
\(812\) | −7159.07 | − | 166.897i | −0.309402 | − | 0.00721298i | ||||
\(813\) | −8745.02 | −0.377246 | ||||||||
\(814\) | −670.471 | − | 1161.29i | −0.0288698 | − | 0.0500039i | ||||
\(815\) | −6312.64 | + | 10933.8i | −0.271315 | + | 0.469932i | ||||
\(816\) | 1246.74 | − | 2159.41i | 0.0534859 | − | 0.0926402i | ||||
\(817\) | 102.103 | + | 176.847i | 0.00437225 | + | 0.00757295i | ||||
\(818\) | 12319.3 | 0.526571 | ||||||||
\(819\) | −277.753 | + | 456.187i | −0.0118504 | + | 0.0194633i | ||||
\(820\) | 1894.52 | 0.0806823 | ||||||||
\(821\) | −15615.7 | − | 27047.2i | −0.663814 | − | 1.14976i | −0.979605 | − | 0.200931i | \(-0.935603\pi\) |
0.315792 | − | 0.948829i | \(-0.397730\pi\) | |||||||
\(822\) | −10869.2 | + | 18826.0i | −0.461201 | + | 0.798823i | ||||
\(823\) | −1667.96 | + | 2889.00i | −0.0706458 | + | 0.122362i | −0.899185 | − | 0.437570i | \(-0.855839\pi\) |
0.828539 | + | 0.559932i | \(0.189173\pi\) | |||||||
\(824\) | −13915.6 | − | 24102.6i | −0.588318 | − | 1.01900i | ||||
\(825\) | 1954.48 | 0.0824804 | ||||||||
\(826\) | 892.203 | + | 1632.04i | 0.0375832 | + | 0.0687481i | ||||
\(827\) | 32281.3 | 1.35735 | 0.678677 | − | 0.734437i | \(-0.262554\pi\) | ||||
0.678677 | + | 0.734437i | \(0.262554\pi\) | |||||||
\(828\) | −813.660 | − | 1409.30i | −0.0341505 | − | 0.0591505i | ||||
\(829\) | 14756.4 | − | 25558.9i | 0.618230 | − | 1.07081i | −0.371579 | − | 0.928401i | \(-0.621184\pi\) |
0.989809 | − | 0.142404i | \(-0.0454831\pi\) | |||||||
\(830\) | 1520.09 | − | 2632.87i | 0.0635698 | − | 0.110106i | ||||
\(831\) | 2678.90 | + | 4639.99i | 0.111829 | + | 0.193694i | ||||
\(832\) | 1824.63 | 0.0760308 | ||||||||
\(833\) | 2839.60 | + | 5494.78i | 0.118111 | + | 0.228551i | ||||
\(834\) | −17437.9 | −0.724011 | ||||||||
\(835\) | 7229.96 | + | 12522.7i | 0.299644 | + | 0.518999i | ||||
\(836\) | 813.333 | − | 1408.73i | 0.0336480 | − | 0.0582800i | ||||
\(837\) | 3957.80 | − | 6855.11i | 0.163443 | − | 0.283091i | ||||
\(838\) | 7180.91 | + | 12437.7i | 0.296015 | + | 0.512713i | ||||
\(839\) | 17025.0 | 0.700558 | 0.350279 | − | 0.936645i | \(-0.386087\pi\) | ||||
0.350279 | + | 0.936645i | \(0.386087\pi\) | |||||||
\(840\) | 3253.30 | + | 5951.01i | 0.133630 | + | 0.244440i | ||||
\(841\) | 20595.6 | 0.844462 | ||||||||
\(842\) | 9274.37 | + | 16063.7i | 0.379591 | + | 0.657471i | ||||
\(843\) | 1897.14 | − | 3285.95i | 0.0775102 | − | 0.134252i | ||||
\(844\) | −3496.35 | + | 6055.86i | −0.142594 | + | 0.246980i | ||||
\(845\) | 5466.83 | + | 9468.83i | 0.222562 | + | 0.385488i | ||||
\(846\) | −8989.73 | −0.365335 | ||||||||
\(847\) | 6278.62 | − | 10312.1i | 0.254706 | − | 0.418334i | ||||
\(848\) | 337.184 | 0.0136544 | ||||||||
\(849\) | 12549.6 | + | 21736.5i | 0.507304 | + | 0.878677i | ||||
\(850\) | −560.212 | + | 970.316i | −0.0226060 | + | 0.0391548i | ||||
\(851\) | 1026.73 | − | 1778.35i | 0.0413583 | − | 0.0716347i | ||||
\(852\) | −2196.96 | − | 3805.24i | −0.0883409 | − | 0.153011i | ||||
\(853\) | −19970.0 | −0.801593 | −0.400796 | − | 0.916167i | \(-0.631267\pi\) | ||||
−0.400796 | + | 0.916167i | \(0.631267\pi\) | |||||||
\(854\) | 16496.3 | + | 384.573i | 0.660997 | + | 0.0154096i | ||||
\(855\) | −1540.80 | −0.0616305 | ||||||||
\(856\) | −8464.27 | − | 14660.5i | −0.337971 | − | 0.585382i | ||||
\(857\) | −2344.96 | + | 4061.60i | −0.0934685 | + | 0.161892i | −0.908968 | − | 0.416865i | \(-0.863129\pi\) |
0.815500 | + | 0.578757i | \(0.196462\pi\) | |||||||
\(858\) | 311.297 | − | 539.183i | 0.0123864 | − | 0.0214538i | ||||
\(859\) | −17201.2 | − | 29793.4i | −0.683235 | − | 1.18340i | −0.973988 | − | 0.226600i | \(-0.927239\pi\) |
0.290753 | − | 0.956798i | \(-0.406094\pi\) | |||||||
\(860\) | −54.3627 | −0.00215553 | ||||||||
\(861\) | 11544.7 | + | 269.139i | 0.456961 | + | 0.0106530i | ||||
\(862\) | −7559.39 | −0.298694 | ||||||||
\(863\) | −1658.93 | − | 2873.35i | −0.0654351 | − | 0.113337i | 0.831452 | − | 0.555597i | \(-0.187510\pi\) |
−0.896887 | + | 0.442260i | \(0.854177\pi\) | |||||||
\(864\) | −1090.18 | + | 1888.25i | −0.0429268 | + | 0.0743513i | ||||
\(865\) | 7262.36 | − | 12578.8i | 0.285465 | − | 0.494441i | ||||
\(866\) | 5029.71 | + | 8711.71i | 0.197363 | + | 0.341843i | ||||
\(867\) | 13763.5 | 0.539138 | ||||||||
\(868\) | 5147.62 | − | 8454.55i | 0.201292 | − | 0.330606i | ||||
\(869\) | 33240.8 | 1.29760 | ||||||||
\(870\) | −3953.49 | − | 6847.64i | −0.154064 | − | 0.266847i | ||||
\(871\) | −941.188 | + | 1630.19i | −0.0366142 | + | 0.0634176i | ||||
\(872\) | 13917.2 | − | 24105.4i | 0.540478 | − | 0.936136i | ||||
\(873\) | 4284.96 | + | 7421.76i | 0.166121 | + | 0.287730i | ||||
\(874\) | −8440.24 | −0.326654 | ||||||||
\(875\) | −1110.48 | − | 2031.31i | −0.0429039 | − | 0.0784809i | ||||
\(876\) | −3588.02 | −0.138388 | ||||||||
\(877\) | −13434.1 | − | 23268.6i | −0.517261 | − | 0.895922i | −0.999799 | − | 0.0200472i | \(-0.993618\pi\) |
0.482538 | − | 0.875875i | \(-0.339715\pi\) | |||||||
\(878\) | −3396.12 | + | 5882.25i | −0.130539 | + | 0.226101i | ||||
\(879\) | −2329.15 | + | 4034.20i | −0.0893744 | + | 0.154801i | ||||
\(880\) | −3002.88 | − | 5201.14i | −0.115031 | − | 0.199239i | ||||
\(881\) | −12933.5 | −0.494599 | −0.247300 | − | 0.968939i | \(-0.579543\pi\) | ||||
−0.247300 | + | 0.968939i | \(0.579543\pi\) | |||||||
\(882\) | 3522.34 | + | 6815.93i | 0.134471 | + | 0.260209i | ||||
\(883\) | −17537.5 | −0.668386 | −0.334193 | − | 0.942505i | \(-0.608464\pi\) | ||||
−0.334193 | + | 0.942505i | \(0.608464\pi\) | |||||||
\(884\) | −52.6680 | − | 91.2237i | −0.00200387 | − | 0.00347080i | ||||
\(885\) | 303.067 | − | 524.927i | 0.0115113 | − | 0.0199381i | ||||
\(886\) | 7951.93 | − | 13773.1i | 0.301524 | − | 0.522255i | ||||
\(887\) | 17647.2 | + | 30565.9i | 0.668022 | + | 1.15705i | 0.978456 | + | 0.206453i | \(0.0661921\pi\) |
−0.310435 | + | 0.950595i | \(0.600475\pi\) | |||||||
\(888\) | −1516.38 | −0.0573043 | ||||||||
\(889\) | 12911.0 | + | 23617.2i | 0.487089 | + | 0.890995i | ||||
\(890\) | 17535.2 | 0.660428 | ||||||||
\(891\) | 1055.42 | + | 1828.04i | 0.0396834 | + | 0.0687337i | ||||
\(892\) | −683.940 | + | 1184.62i | −0.0256726 | + | 0.0444663i | ||||
\(893\) | 6880.49 | − | 11917.3i | 0.257835 | − | 0.446583i | ||||
\(894\) | 1834.84 | + | 3178.04i | 0.0686425 | + | 0.118892i | ||||
\(895\) | 115.520 | 0.00431444 | ||||||||
\(896\) | 7408.73 | − | 12168.2i | 0.276237 | − | 0.453697i | ||||
\(897\) | 953.416 | 0.0354890 | ||||||||
\(898\) | −20491.3 | − | 35492.0i | −0.761474 | − | 1.31891i | ||||
\(899\) | −31090.1 | + | 53849.6i | −1.15341 | + | 1.99776i | ||||
\(900\) | 205.092 | − | 355.229i | 0.00759599 | − | 0.0131566i | ||||
\(901\) | −65.9575 | − | 114.242i | −0.00243880 | − | 0.00422413i | ||||
\(902\) | −13461.4 | −0.496914 | ||||||||
\(903\) | −331.273 | − | 7.72286i | −0.0122083 | − | 0.000284608i | ||||
\(904\) | 28189.1 | 1.03712 | ||||||||
\(905\) | 7560.02 | + | 13094.3i | 0.277683 | + | 0.480962i | ||||
\(906\) | −4033.53 | + | 6986.29i | −0.147909 | + | 0.256185i | ||||
\(907\) | −15307.9 | + | 26514.0i | −0.560408 | + | 0.970655i | 0.437053 | + | 0.899436i | \(0.356022\pi\) |
−0.997461 | + | 0.0712189i | \(0.977311\pi\) | |||||||
\(908\) | −573.199 | − | 992.810i | −0.0209496 | − | 0.0362859i | ||||
\(909\) | −12973.2 | −0.473370 | ||||||||
\(910\) | −737.247 | − | 17.1872i | −0.0268566 | − | 0.000626099i | ||||
\(911\) | 28971.0 | 1.05362 | 0.526812 | − | 0.849982i | \(-0.323387\pi\) | ||||
0.526812 | + | 0.849982i | \(0.323387\pi\) | |||||||
\(912\) | 2367.29 | + | 4100.27i | 0.0859526 | + | 0.148874i | ||||
\(913\) | 3187.73 | − | 5521.30i | 0.115551 | − | 0.200141i | ||||
\(914\) | 17864.6 | − | 30942.4i | 0.646509 | − | 1.11979i | ||||
\(915\) | −2688.63 | − | 4656.84i | −0.0971402 | − | 0.168252i | ||||
\(916\) | 4461.57 | 0.160933 | ||||||||
\(917\) | 14828.3 | − | 24354.3i | 0.533996 | − | 0.877045i | ||||
\(918\) | −1210.06 | −0.0435053 | ||||||||
\(919\) | −13119.7 | − | 22724.0i | −0.470924 | − | 0.815664i | 0.528523 | − | 0.848919i | \(-0.322746\pi\) |
−0.999447 | + | 0.0332552i | \(0.989413\pi\) | |||||||
\(920\) | 6053.52 | − | 10485.0i | 0.216933 | − | 0.375740i | ||||
\(921\) | −10270.6 | + | 17789.2i | −0.367456 | + | 0.636453i | ||||
\(922\) | 1243.16 | + | 2153.22i | 0.0444049 | + | 0.0769116i | ||||
\(923\) | 2574.31 | 0.0918032 | ||||||||
\(924\) | 1266.15 | + | 2316.08i | 0.0450794 | + | 0.0824604i | ||||
\(925\) | 517.598 | 0.0183984 | ||||||||
\(926\) | −778.070 | − | 1347.66i | −0.0276123 | − | 0.0478258i | ||||
\(927\) | −5129.94 | + | 8885.31i | −0.181758 | + | 0.314813i | ||||
\(928\) | 8563.80 | − | 14832.9i | 0.302932 | − | 0.524693i | ||||
\(929\) | 8971.61 | + | 15539.3i | 0.316845 | + | 0.548792i | 0.979828 | − | 0.199843i | \(-0.0640431\pi\) |
−0.662983 | + | 0.748635i | \(0.730710\pi\) | |||||||
\(930\) | 10929.5 | 0.385367 | ||||||||
\(931\) | −11731.5 | − | 547.284i | −0.412981 | − | 0.0192659i | ||||
\(932\) | −5762.92 | −0.202544 | ||||||||
\(933\) | 3525.39 | + | 6106.15i | 0.123704 | + | 0.214262i | ||||
\(934\) | 1142.07 | − | 1978.12i | 0.0400103 | − | 0.0692998i | ||||
\(935\) | −1174.80 | + | 2034.82i | −0.0410911 | + | 0.0711719i | ||||
\(936\) | −352.024 | − | 609.723i | −0.0122930 | − | 0.0212921i | ||||
\(937\) | 43418.1 | 1.51378 | 0.756888 | − | 0.653545i | \(-0.226719\pi\) | ||||
0.756888 | + | 0.653545i | \(0.226719\pi\) | |||||||
\(938\) | 12970.8 | + | 23726.5i | 0.451505 | + | 0.825904i | ||||
\(939\) | 12275.5 | 0.426621 | ||||||||
\(940\) | 1831.69 | + | 3172.58i | 0.0635566 | + | 0.110083i | ||||
\(941\) | −15447.5 | + | 26755.8i | −0.535146 | + | 0.926901i | 0.464010 | + | 0.885830i | \(0.346410\pi\) |
−0.999156 | + | 0.0410706i | \(0.986923\pi\) | |||||||
\(942\) | 10778.9 | − | 18669.5i | 0.372818 | − | 0.645739i | ||||
\(943\) | −10307.1 | − | 17852.5i | −0.355935 | − | 0.616498i | ||||
\(944\) | −1862.54 | −0.0642166 | ||||||||
\(945\) | 1300.24 | − | 2135.54i | 0.0447586 | − | 0.0735124i | ||||
\(946\) | 386.272 | 0.0132757 | ||||||||
\(947\) | −3876.31 | − | 6713.97i | −0.133013 | − | 0.230385i | 0.791824 | − | 0.610750i | \(-0.209132\pi\) |
−0.924837 | + | 0.380365i | \(0.875798\pi\) | |||||||
\(948\) | 3488.09 | − | 6041.55i | 0.119502 | − | 0.206984i | ||||
\(949\) | 1051.07 | − | 1820.52i | 0.0359529 | − | 0.0622723i | ||||
\(950\) | −1063.73 | − | 1842.43i | −0.0363282 | − | 0.0629224i | ||||
\(951\) | 2981.07 | 0.101649 | ||||||||
\(952\) | −8151.13 | − | 190.025i | −0.277499 | − | 0.00646926i | ||||
\(953\) | 21377.5 | 0.726638 | 0.363319 | − | 0.931665i | \(-0.381644\pi\) | ||||
0.363319 | + | 0.931665i | \(0.381644\pi\) | |||||||
\(954\) | −81.8161 | − | 141.710i | −0.00277662 | − | 0.00480924i | ||||
\(955\) | −9742.24 | + | 16874.1i | −0.330106 | + | 0.571761i | ||||
\(956\) | −5485.80 | + | 9501.68i | −0.185589 | + | 0.321450i | ||||
\(957\) | −8290.74 | − | 14360.0i | −0.280044 | − | 0.485050i | ||||
\(958\) | 38929.7 | 1.31290 | ||||||||
\(959\) | 53981.9 | + | 1258.46i | 1.81769 | + | 0.0423753i | ||||
\(960\) | −8541.60 | −0.287166 | ||||||||
\(961\) | −28079.0 | − | 48634.2i | −0.942532 | − | 1.63251i | ||||
\(962\) | 82.4396 | − | 142.790i | 0.00276295 | − | 0.00478557i | ||||
\(963\) | −3120.32 | + | 5404.55i | −0.104414 | + | 0.180851i | ||||
\(964\) | 5212.46 | + | 9028.24i | 0.174151 | + | 0.301639i | ||||
\(965\) | −23046.4 | −0.768798 | ||||||||
\(966\) | 7122.53 | − | 11698.2i | 0.237229 | − | 0.389630i | ||||
\(967\) | −47707.3 | −1.58652 | −0.793259 | − | 0.608885i | \(-0.791617\pi\) | ||||
−0.793259 | + | 0.608885i | \(0.791617\pi\) | |||||||
\(968\) | 7957.51 | + | 13782.8i | 0.264219 | + | 0.457641i | ||||
\(969\) | 926.145 | − | 1604.13i | 0.0307039 | − | 0.0531807i | ||||
\(970\) | −5916.45 | + | 10247.6i | −0.195841 | + | 0.339207i | ||||
\(971\) | 21717.3 | + | 37615.4i | 0.717756 | + | 1.24319i | 0.961887 | + | 0.273447i | \(0.0881640\pi\) |
−0.244131 | + | 0.969742i | \(0.578503\pi\) | |||||||
\(972\) | 442.998 | 0.0146185 | ||||||||
\(973\) | 20777.1 | + | 38006.0i | 0.684566 | + | 1.25222i | ||||
\(974\) | −35889.6 | −1.18067 | ||||||||
\(975\) | 120.159 | + | 208.122i | 0.00394685 | + | 0.00683614i | ||||
\(976\) | −8261.66 | + | 14309.6i | −0.270952 | + | 0.469303i | ||||
\(977\) | 16743.8 | − | 29001.1i | 0.548292 | − | 0.949669i | −0.450100 | − | 0.892978i | \(-0.648612\pi\) |
0.998392 | − | 0.0566908i | \(-0.0180549\pi\) | |||||||
\(978\) | −9413.46 | − | 16304.6i | −0.307781 | − | 0.533092i | ||||
\(979\) | 36772.5 | 1.20046 | ||||||||
\(980\) | 1687.73 | − | 2631.85i | 0.0550129 | − | 0.0857870i | ||||
\(981\) | −10261.1 | −0.333955 | ||||||||
\(982\) | −24009.5 | − | 41585.6i | −0.780217 | − | 1.35138i | ||||
\(983\) | −7883.76 | + | 13655.1i | −0.255802 | + | 0.443061i | −0.965113 | − | 0.261834i | \(-0.915673\pi\) |
0.709311 | + | 0.704895i | \(0.249006\pi\) | |||||||
\(984\) | −7611.29 | + | 13183.1i | −0.246584 | + | 0.427096i | ||||
\(985\) | −7797.77 | − | 13506.1i | −0.252241 | − | 0.436895i | ||||
\(986\) | 9505.49 | 0.307015 | ||||||||
\(987\) | 10711.2 | + | 19593.1i | 0.345431 | + | 0.631871i | ||||
\(988\) | 200.011 | 0.00644049 | ||||||||
\(989\) | 295.760 | + | 512.272i | 0.00950924 | + | 0.0164705i | ||||
\(990\) | −1457.27 | + | 2524.07i | −0.0467829 | + | 0.0810304i | ||||
\(991\) | 1792.30 | − | 3104.35i | 0.0574512 | − | 0.0995084i | −0.835869 | − | 0.548928i | \(-0.815036\pi\) |
0.893321 | + | 0.449420i | \(0.148369\pi\) | |||||||
\(992\) | 11837.4 | + | 20502.9i | 0.378868 | + | 0.656218i | ||||
\(993\) | −9180.42 | −0.293386 | ||||||||
\(994\) | 19231.5 | − | 31586.1i | 0.613667 | − | 1.00790i | ||||
\(995\) | −20744.7 | −0.660955 | ||||||||
\(996\) | −669.002 | − | 1158.75i | −0.0212833 | − | 0.0368637i | ||||
\(997\) | 18006.7 | − | 31188.6i | 0.571995 | − | 0.990724i | −0.424366 | − | 0.905491i | \(-0.639503\pi\) |
0.996361 | − | 0.0852334i | \(-0.0271636\pi\) | |||||||
\(998\) | −5633.28 | + | 9757.13i | −0.178676 | + | 0.309475i | ||||
\(999\) | 279.503 | + | 484.113i | 0.00885193 | + | 0.0153320i |
(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 | 105.4.i.c.46.3 | yes | 6 | |
3.2 | odd | 2 | 315.4.j.e.46.1 | 6 | |||
7.2 | even | 3 | inner | 105.4.i.c.16.3 | ✓ | 6 | |
7.3 | odd | 6 | 735.4.a.s.1.1 | 3 | |||
7.4 | even | 3 | 735.4.a.r.1.1 | 3 | |||
21.2 | odd | 6 | 315.4.j.e.226.1 | 6 | |||
21.11 | odd | 6 | 2205.4.a.bi.1.3 | 3 | |||
21.17 | even | 6 | 2205.4.a.bj.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.i.c.16.3 | ✓ | 6 | 7.2 | even | 3 | inner | |
105.4.i.c.46.3 | yes | 6 | 1.1 | even | 1 | trivial | |
315.4.j.e.46.1 | 6 | 3.2 | odd | 2 | |||
315.4.j.e.226.1 | 6 | 21.2 | odd | 6 | |||
735.4.a.r.1.1 | 3 | 7.4 | even | 3 | |||
735.4.a.s.1.1 | 3 | 7.3 | odd | 6 | |||
2205.4.a.bi.1.3 | 3 | 21.11 | odd | 6 | |||
2205.4.a.bj.1.3 | 3 | 21.17 | even | 6 |