Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,4,Mod(4,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(14))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.4");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.e (of order \(7\), degree \(6\), 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: | \(2.53708213025\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{7})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{7}]$ |
Embedding invariants
Embedding label | 11.9 | ||
Character | \(\chi\) | \(=\) | 43.11 |
Dual form | 43.4.e.a.4.9 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{5}{7}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.72209 | + | 3.41339i | 0.962404 | + | 1.20682i | 0.978353 | + | 0.206944i | \(0.0663517\pi\) |
−0.0159488 | + | 0.999873i | \(0.505077\pi\) | |||||||
\(3\) | −2.84196 | + | 3.56370i | −0.546935 | + | 0.685834i | −0.976083 | − | 0.217400i | \(-0.930242\pi\) |
0.429148 | + | 0.903234i | \(0.358814\pi\) | |||||||
\(4\) | −2.46131 | + | 10.7837i | −0.307664 | + | 1.34796i | ||||
\(5\) | 8.30189 | − | 3.99798i | 0.742544 | − | 0.357590i | −0.0240601 | − | 0.999711i | \(-0.507659\pi\) |
0.766604 | + | 0.642120i | \(0.221945\pi\) | |||||||
\(6\) | −19.9004 | −1.35405 | ||||||||
\(7\) | −12.2688 | −0.662455 | −0.331228 | − | 0.943551i | \(-0.607463\pi\) | ||||
−0.331228 | + | 0.943551i | \(0.607463\pi\) | |||||||
\(8\) | −12.0406 | + | 5.79846i | −0.532125 | + | 0.256258i | ||||
\(9\) | 1.38482 | + | 6.06730i | 0.0512897 | + | 0.224715i | ||||
\(10\) | 36.2452 | + | 17.4548i | 1.14617 | + | 0.551968i | ||||
\(11\) | −3.74140 | − | 16.3922i | −0.102552 | − | 0.449311i | −0.999967 | − | 0.00812292i | \(-0.997414\pi\) |
0.897415 | − | 0.441188i | \(-0.145443\pi\) | |||||||
\(12\) | −31.4349 | − | 39.4182i | −0.756207 | − | 0.948253i | ||||
\(13\) | 66.8370 | − | 32.1870i | 1.42594 | − | 0.686697i | 0.447703 | − | 0.894182i | \(-0.352242\pi\) |
0.978238 | + | 0.207485i | \(0.0665278\pi\) | |||||||
\(14\) | −33.3969 | − | 41.8784i | −0.637550 | − | 0.799462i | ||||
\(15\) | −9.34601 | + | 40.9475i | −0.160875 | + | 0.704841i | ||||
\(16\) | 27.1570 | + | 13.0781i | 0.424328 | + | 0.204346i | ||||
\(17\) | −0.640842 | − | 0.308613i | −0.00914277 | − | 0.00440293i | 0.429307 | − | 0.903159i | \(-0.358758\pi\) |
−0.438450 | + | 0.898756i | \(0.644472\pi\) | |||||||
\(18\) | −16.9405 | + | 21.2427i | −0.221828 | + | 0.278164i | ||||
\(19\) | −6.96294 | + | 30.5066i | −0.0840741 | + | 0.368353i | −0.999410 | − | 0.0343378i | \(-0.989068\pi\) |
0.915336 | + | 0.402691i | \(0.131925\pi\) | |||||||
\(20\) | 22.6795 | + | 99.3654i | 0.253564 | + | 1.11094i | ||||
\(21\) | 34.8675 | − | 43.7225i | 0.362320 | − | 0.454335i | ||||
\(22\) | 45.7684 | − | 57.3918i | 0.443539 | − | 0.556180i | ||||
\(23\) | −18.6609 | − | 81.7588i | −0.169177 | − | 0.741213i | −0.986329 | − | 0.164790i | \(-0.947305\pi\) |
0.817152 | − | 0.576423i | \(-0.195552\pi\) | |||||||
\(24\) | 13.5550 | − | 59.3881i | 0.115287 | − | 0.505106i | ||||
\(25\) | −24.9987 | + | 31.3473i | −0.199989 | + | 0.250779i | ||||
\(26\) | 291.803 | + | 140.525i | 2.20105 | + | 1.05997i | ||||
\(27\) | −136.440 | − | 65.7059i | −0.972513 | − | 0.468337i | ||||
\(28\) | 30.1974 | − | 132.304i | 0.203813 | − | 0.892965i | ||||
\(29\) | −142.592 | − | 178.805i | −0.913060 | − | 1.14494i | −0.989013 | − | 0.147829i | \(-0.952771\pi\) |
0.0759532 | − | 0.997111i | \(-0.475800\pi\) | |||||||
\(30\) | −165.211 | + | 79.5613i | −1.00544 | + | 0.484194i | ||||
\(31\) | −151.938 | − | 190.525i | −0.880289 | − | 1.10385i | −0.993896 | − | 0.110321i | \(-0.964812\pi\) |
0.113607 | − | 0.993526i | \(-0.463759\pi\) | |||||||
\(32\) | 53.0733 | + | 232.529i | 0.293192 | + | 1.28456i | ||||
\(33\) | 69.0496 | + | 33.2525i | 0.364242 | + | 0.175410i | ||||
\(34\) | −0.691012 | − | 3.02752i | −0.00348551 | − | 0.0152710i | ||||
\(35\) | −101.855 | + | 49.0506i | −0.491902 | + | 0.236888i | ||||
\(36\) | −68.8364 | −0.318687 | ||||||||
\(37\) | 82.4344 | 0.366274 | 0.183137 | − | 0.983087i | \(-0.441375\pi\) | ||||
0.183137 | + | 0.983087i | \(0.441375\pi\) | |||||||
\(38\) | −123.085 | + | 59.2745i | −0.525447 | + | 0.253042i | ||||
\(39\) | −75.2429 | + | 329.661i | −0.308936 | + | 1.35354i | ||||
\(40\) | −76.7778 | + | 96.2764i | −0.303491 | + | 0.380566i | ||||
\(41\) | 252.021 | + | 316.025i | 0.959979 | + | 1.20378i | 0.978980 | + | 0.203956i | \(0.0653799\pi\) |
−0.0190013 | + | 0.999819i | \(0.506049\pi\) | |||||||
\(42\) | 244.155 | 0.896997 | ||||||||
\(43\) | −163.858 | − | 229.473i | −0.581118 | − | 0.813820i | ||||
\(44\) | 185.977 | 0.637206 | ||||||||
\(45\) | 35.7536 | + | 44.8336i | 0.118441 | + | 0.148520i | ||||
\(46\) | 228.278 | − | 286.252i | 0.731691 | − | 0.917512i | ||||
\(47\) | −78.0998 | + | 342.177i | −0.242383 | + | 1.06195i | 0.696457 | + | 0.717599i | \(0.254759\pi\) |
−0.938840 | + | 0.344353i | \(0.888098\pi\) | |||||||
\(48\) | −123.786 | + | 59.6120i | −0.372227 | + | 0.179255i | ||||
\(49\) | −192.475 | −0.561153 | ||||||||
\(50\) | −175.049 | −0.495114 | ||||||||
\(51\) | 2.92105 | − | 1.40670i | 0.00802018 | − | 0.00386231i | ||||
\(52\) | 182.588 | + | 799.972i | 0.486932 | + | 2.13339i | ||||
\(53\) | −95.6110 | − | 46.0438i | −0.247796 | − | 0.119332i | 0.305864 | − | 0.952075i | \(-0.401055\pi\) |
−0.553660 | + | 0.832743i | \(0.686769\pi\) | |||||||
\(54\) | −147.121 | − | 644.580i | −0.370753 | − | 1.62437i | ||||
\(55\) | −96.5962 | − | 121.128i | −0.236819 | − | 0.296961i | ||||
\(56\) | 147.725 | − | 71.1404i | 0.352509 | − | 0.169760i | ||||
\(57\) | −88.9281 | − | 111.512i | −0.206646 | − | 0.259126i | ||||
\(58\) | 222.183 | − | 973.447i | 0.503001 | − | 2.20379i | ||||
\(59\) | 616.615 | + | 296.946i | 1.36062 | + | 0.655239i | 0.964774 | − | 0.263079i | \(-0.0847381\pi\) |
0.395843 | + | 0.918318i | \(0.370452\pi\) | |||||||
\(60\) | −418.562 | − | 201.569i | −0.900603 | − | 0.433708i | ||||
\(61\) | 315.438 | − | 395.546i | 0.662092 | − | 0.830238i | −0.331477 | − | 0.943463i | \(-0.607547\pi\) |
0.993569 | + | 0.113226i | \(0.0361183\pi\) | |||||||
\(62\) | 236.746 | − | 1037.25i | 0.484947 | − | 2.12469i | ||||
\(63\) | −16.9902 | − | 74.4387i | −0.0339771 | − | 0.148863i | ||||
\(64\) | −498.898 | + | 625.599i | −0.974410 | + | 1.22187i | ||||
\(65\) | 426.190 | − | 534.426i | 0.813268 | − | 1.01981i | ||||
\(66\) | 74.4553 | + | 326.210i | 0.138861 | + | 0.608389i | ||||
\(67\) | −63.7497 | + | 279.306i | −0.116243 | + | 0.509293i | 0.882963 | + | 0.469443i | \(0.155545\pi\) |
−0.999206 | + | 0.0398502i | \(0.987312\pi\) | |||||||
\(68\) | 4.90530 | − | 6.15106i | 0.00874787 | − | 0.0109695i | ||||
\(69\) | 344.397 | + | 165.853i | 0.600878 | + | 0.289368i | ||||
\(70\) | −444.686 | − | 214.150i | −0.759288 | − | 0.365654i | ||||
\(71\) | 29.2594 | − | 128.194i | 0.0489078 | − | 0.214279i | −0.944569 | − | 0.328313i | \(-0.893520\pi\) |
0.993477 | + | 0.114034i | \(0.0363771\pi\) | |||||||
\(72\) | −51.8551 | − | 65.0242i | −0.0848775 | − | 0.106433i | ||||
\(73\) | −656.788 | + | 316.292i | −1.05303 | + | 0.507112i | −0.878601 | − | 0.477557i | \(-0.841522\pi\) |
−0.174429 | + | 0.984670i | \(0.555808\pi\) | |||||||
\(74\) | 224.394 | + | 281.381i | 0.352503 | + | 0.442025i | ||||
\(75\) | −40.6674 | − | 178.175i | −0.0626115 | − | 0.274319i | ||||
\(76\) | −311.836 | − | 150.172i | −0.470659 | − | 0.226657i | ||||
\(77\) | 45.9027 | + | 201.113i | 0.0679363 | + | 0.297648i | ||||
\(78\) | −1330.08 | + | 640.533i | −1.93079 | + | 0.929821i | ||||
\(79\) | 818.448 | 1.16560 | 0.582801 | − | 0.812615i | \(-0.301957\pi\) | ||||
0.582801 | + | 0.812615i | \(0.301957\pi\) | |||||||
\(80\) | 277.741 | 0.388154 | ||||||||
\(81\) | 470.522 | − | 226.592i | 0.645435 | − | 0.310825i | ||||
\(82\) | −392.692 | + | 1720.50i | −0.528848 | + | 2.31704i | ||||
\(83\) | −540.134 | + | 677.307i | −0.714306 | + | 0.895712i | −0.998001 | − | 0.0632031i | \(-0.979868\pi\) |
0.283695 | + | 0.958915i | \(0.408440\pi\) | |||||||
\(84\) | 385.670 | + | 483.615i | 0.500953 | + | 0.628176i | ||||
\(85\) | −6.55403 | −0.00836335 | ||||||||
\(86\) | 337.245 | − | 1183.96i | 0.422861 | − | 1.48453i | ||||
\(87\) | 1042.45 | 1.28462 | ||||||||
\(88\) | 140.098 | + | 175.677i | 0.169710 | + | 0.212810i | ||||
\(89\) | 545.794 | − | 684.404i | 0.650045 | − | 0.815131i | −0.342174 | − | 0.939637i | \(-0.611163\pi\) |
0.992219 | + | 0.124506i | \(0.0397346\pi\) | |||||||
\(90\) | −55.7101 | + | 244.082i | −0.0652485 | + | 0.285872i | ||||
\(91\) | −820.013 | + | 394.897i | −0.944623 | + | 0.454906i | ||||
\(92\) | 927.593 | 1.05118 | ||||||||
\(93\) | 1110.78 | 1.23852 | ||||||||
\(94\) | −1380.58 | + | 664.853i | −1.51485 | + | 0.729514i | ||||
\(95\) | 64.1593 | + | 281.100i | 0.0692906 | + | 0.303582i | ||||
\(96\) | −979.497 | − | 471.701i | −1.04135 | − | 0.501487i | ||||
\(97\) | 207.312 | + | 908.294i | 0.217004 | + | 0.950756i | 0.959678 | + | 0.281103i | \(0.0907001\pi\) |
−0.742674 | + | 0.669653i | \(0.766443\pi\) | |||||||
\(98\) | −523.935 | − | 656.994i | −0.540056 | − | 0.677208i | ||||
\(99\) | 94.2749 | − | 45.4004i | 0.0957069 | − | 0.0460900i | ||||
\(100\) | −276.511 | − | 346.733i | −0.276511 | − | 0.346733i | ||||
\(101\) | −152.349 | + | 667.485i | −0.150092 | + | 0.657597i | 0.842764 | + | 0.538283i | \(0.180927\pi\) |
−0.992857 | + | 0.119314i | \(0.961930\pi\) | |||||||
\(102\) | 12.7530 | + | 6.14152i | 0.0123798 | + | 0.00596177i | ||||
\(103\) | −857.904 | − | 413.145i | −0.820697 | − | 0.395227i | −0.0240793 | − | 0.999710i | \(-0.507665\pi\) |
−0.796618 | + | 0.604483i | \(0.793380\pi\) | |||||||
\(104\) | −618.124 | + | 775.103i | −0.582808 | + | 0.730818i | ||||
\(105\) | 114.665 | − | 502.379i | 0.106573 | − | 0.466925i | ||||
\(106\) | −103.096 | − | 451.693i | −0.0944677 | − | 0.413890i | ||||
\(107\) | −1040.23 | + | 1304.41i | −0.939838 | + | 1.17852i | 0.0439222 | + | 0.999035i | \(0.486015\pi\) |
−0.983761 | + | 0.179485i | \(0.942557\pi\) | |||||||
\(108\) | 1044.37 | − | 1309.60i | 0.930508 | − | 1.16682i | ||||
\(109\) | −483.141 | − | 2116.78i | −0.424555 | − | 1.86010i | −0.504673 | − | 0.863311i | \(-0.668387\pi\) |
0.0801182 | − | 0.996785i | \(-0.474470\pi\) | |||||||
\(110\) | 150.513 | − | 659.442i | 0.130462 | − | 0.571593i | ||||
\(111\) | −234.275 | + | 293.771i | −0.200328 | + | 0.251203i | ||||
\(112\) | −333.185 | − | 160.453i | −0.281099 | − | 0.135370i | ||||
\(113\) | −1496.80 | − | 720.820i | −1.24608 | − | 0.600080i | −0.309621 | − | 0.950860i | \(-0.600202\pi\) |
−0.936458 | + | 0.350780i | \(0.885917\pi\) | |||||||
\(114\) | 138.565 | − | 607.093i | 0.113840 | − | 0.498767i | ||||
\(115\) | −481.791 | − | 604.147i | −0.390672 | − | 0.489887i | ||||
\(116\) | 2279.14 | − | 1097.58i | 1.82425 | − | 0.878513i | ||||
\(117\) | 287.845 | + | 360.947i | 0.227447 | + | 0.285210i | ||||
\(118\) | 664.888 | + | 2913.06i | 0.518711 | + | 2.27262i | ||||
\(119\) | 7.86240 | + | 3.78633i | 0.00605668 | + | 0.00291674i | ||||
\(120\) | −124.901 | − | 547.226i | −0.0950153 | − | 0.416289i | ||||
\(121\) | 944.485 | − | 454.840i | 0.709606 | − | 0.341728i | ||||
\(122\) | 2208.80 | 1.63914 | ||||||||
\(123\) | −1842.45 | −1.35064 | ||||||||
\(124\) | 2428.53 | − | 1169.52i | 1.75878 | − | 0.846982i | ||||
\(125\) | −338.510 | + | 1483.11i | −0.242218 | + | 1.06123i | ||||
\(126\) | 207.840 | − | 260.623i | 0.146951 | − | 0.184271i | ||||
\(127\) | −408.083 | − | 511.720i | −0.285130 | − | 0.357542i | 0.618554 | − | 0.785743i | \(-0.287719\pi\) |
−0.903684 | + | 0.428201i | \(0.859148\pi\) | |||||||
\(128\) | −1585.38 | −1.09476 | ||||||||
\(129\) | 1283.45 | + | 68.2113i | 0.875979 | + | 0.0465556i | ||||
\(130\) | 2984.33 | 2.01341 | ||||||||
\(131\) | 1632.78 | + | 2047.44i | 1.08898 | + | 1.36554i | 0.925392 | + | 0.379011i | \(0.123736\pi\) |
0.163590 | + | 0.986528i | \(0.447693\pi\) | |||||||
\(132\) | −528.538 | + | 662.765i | −0.348510 | + | 0.437017i | ||||
\(133\) | 85.4272 | − | 374.281i | 0.0556953 | − | 0.244017i | ||||
\(134\) | −1126.91 | + | 542.693i | −0.726496 | + | 0.349862i | ||||
\(135\) | −1395.40 | −0.889606 | ||||||||
\(136\) | 9.50562 | 0.00599339 | ||||||||
\(137\) | −374.805 | + | 180.496i | −0.233735 | + | 0.112561i | −0.547086 | − | 0.837077i | \(-0.684263\pi\) |
0.313350 | + | 0.949638i | \(0.398549\pi\) | |||||||
\(138\) | 371.359 | + | 1627.03i | 0.229074 | + | 1.00364i | ||||
\(139\) | 1862.66 | + | 897.010i | 1.13661 | + | 0.547363i | 0.904985 | − | 0.425442i | \(-0.139882\pi\) |
0.231625 | + | 0.972805i | \(0.425596\pi\) | |||||||
\(140\) | −278.251 | − | 1219.10i | −0.167975 | − | 0.735947i | ||||
\(141\) | −997.462 | − | 1250.78i | −0.595755 | − | 0.747053i | ||||
\(142\) | 517.223 | − | 249.082i | 0.305665 | − | 0.147200i | ||||
\(143\) | −777.678 | − | 975.177i | −0.454774 | − | 0.570269i | ||||
\(144\) | −41.7413 | + | 182.880i | −0.0241558 | + | 0.105834i | ||||
\(145\) | −1898.65 | − | 914.340i | −1.08741 | − | 0.523667i | ||||
\(146\) | −2867.46 | − | 1380.90i | −1.62543 | − | 0.782767i | ||||
\(147\) | 547.007 | − | 685.925i | 0.306914 | − | 0.384858i | ||||
\(148\) | −202.896 | + | 888.947i | −0.112689 | + | 0.493723i | ||||
\(149\) | 218.150 | + | 955.778i | 0.119943 | + | 0.525506i | 0.998825 | + | 0.0484659i | \(0.0154332\pi\) |
−0.878882 | + | 0.477040i | \(0.841710\pi\) | |||||||
\(150\) | 497.482 | − | 623.823i | 0.270795 | − | 0.339566i | ||||
\(151\) | 6.78596 | − | 8.50933i | 0.00365718 | − | 0.00458596i | −0.780000 | − | 0.625780i | \(-0.784781\pi\) |
0.783657 | + | 0.621194i | \(0.213352\pi\) | |||||||
\(152\) | −93.0533 | − | 407.693i | −0.0496554 | − | 0.217555i | ||||
\(153\) | 0.984997 | − | 4.31556i | 0.000520473 | − | 0.00228034i | ||||
\(154\) | −561.526 | + | 704.131i | −0.293825 | + | 0.368445i | ||||
\(155\) | −2023.09 | − | 974.269i | −1.04838 | − | 0.504872i | ||||
\(156\) | −3369.77 | − | 1622.79i | −1.72947 | − | 0.832869i | ||||
\(157\) | 229.073 | − | 1003.63i | 0.116446 | − | 0.510182i | −0.882741 | − | 0.469860i | \(-0.844304\pi\) |
0.999187 | − | 0.0403224i | \(-0.0128385\pi\) | |||||||
\(158\) | 2227.89 | + | 2793.68i | 1.12178 | + | 1.40667i | ||||
\(159\) | 435.809 | − | 209.874i | 0.217370 | − | 0.104680i | ||||
\(160\) | 1370.26 | + | 1718.25i | 0.677052 | + | 0.848997i | ||||
\(161\) | 228.948 | + | 1003.09i | 0.112072 | + | 0.491020i | ||||
\(162\) | 2054.25 | + | 989.274i | 0.996278 | + | 0.479782i | ||||
\(163\) | −208.966 | − | 915.539i | −0.100414 | − | 0.439942i | −0.999995 | − | 0.00318810i | \(-0.998985\pi\) |
0.899581 | − | 0.436754i | \(-0.143872\pi\) | |||||||
\(164\) | −4028.22 | + | 1939.89i | −1.91799 | + | 0.923657i | ||||
\(165\) | 706.185 | 0.333191 | ||||||||
\(166\) | −3782.21 | −1.76841 | ||||||||
\(167\) | 1566.03 | − | 754.162i | 0.725649 | − | 0.349454i | −0.0343224 | − | 0.999411i | \(-0.510927\pi\) |
0.759971 | + | 0.649957i | \(0.225213\pi\) | |||||||
\(168\) | −166.304 | + | 728.624i | −0.0763726 | + | 0.334610i | ||||
\(169\) | 2061.37 | − | 2584.88i | 0.938266 | − | 1.17655i | ||||
\(170\) | −17.8407 | − | 22.3715i | −0.00804892 | − | 0.0100930i | ||||
\(171\) | −194.735 | −0.0870864 | ||||||||
\(172\) | 2877.87 | − | 1202.19i | 1.27579 | − | 0.532942i | ||||
\(173\) | −108.791 | −0.0478107 | −0.0239053 | − | 0.999714i | \(-0.507610\pi\) | ||||
−0.0239053 | + | 0.999714i | \(0.507610\pi\) | |||||||
\(174\) | 2837.64 | + | 3558.29i | 1.23633 | + | 1.55031i | ||||
\(175\) | 306.705 | − | 384.596i | 0.132484 | − | 0.166130i | ||||
\(176\) | 112.773 | − | 494.092i | 0.0482989 | − | 0.211611i | ||||
\(177\) | −2810.62 | + | 1353.52i | −1.19355 | + | 0.574785i | ||||
\(178\) | 3821.84 | 1.60932 | ||||||||
\(179\) | −1852.75 | −0.773637 | −0.386819 | − | 0.922156i | \(-0.626426\pi\) | ||||
−0.386819 | + | 0.922156i | \(0.626426\pi\) | |||||||
\(180\) | −571.472 | + | 275.206i | −0.236639 | + | 0.113959i | ||||
\(181\) | 275.636 | + | 1207.64i | 0.113193 | + | 0.495930i | 0.999463 | + | 0.0327617i | \(0.0104303\pi\) |
−0.886270 | + | 0.463168i | \(0.846713\pi\) | |||||||
\(182\) | −3580.09 | − | 1724.08i | −1.45810 | − | 0.702183i | ||||
\(183\) | 513.148 | + | 2248.25i | 0.207284 | + | 0.908172i | ||||
\(184\) | 698.764 | + | 876.223i | 0.279965 | + | 0.351065i | ||||
\(185\) | 684.361 | − | 329.571i | 0.271974 | − | 0.130976i | ||||
\(186\) | 3023.63 | + | 3791.51i | 1.19195 | + | 1.49466i | ||||
\(187\) | −2.66119 | + | 11.6594i | −0.00104067 | + | 0.00455948i | ||||
\(188\) | −3497.71 | − | 1684.41i | −1.35690 | − | 0.653447i | ||||
\(189\) | 1673.96 | + | 806.136i | 0.644246 | + | 0.310253i | ||||
\(190\) | −784.859 | + | 984.182i | −0.299682 | + | 0.375790i | ||||
\(191\) | 649.569 | − | 2845.95i | 0.246079 | − | 1.07814i | −0.689294 | − | 0.724482i | \(-0.742079\pi\) |
0.935373 | − | 0.353662i | \(-0.115064\pi\) | |||||||
\(192\) | −811.599 | − | 3555.85i | −0.305063 | − | 1.33657i | ||||
\(193\) | 1949.53 | − | 2444.63i | 0.727100 | − | 0.911755i | −0.271616 | − | 0.962406i | \(-0.587558\pi\) |
0.998716 | + | 0.0506510i | \(0.0161296\pi\) | |||||||
\(194\) | −2536.04 | + | 3180.10i | −0.938542 | + | 1.17689i | ||||
\(195\) | 693.319 | + | 3037.63i | 0.254613 | + | 1.11553i | ||||
\(196\) | 473.741 | − | 2075.60i | 0.172646 | − | 0.756413i | ||||
\(197\) | −360.369 | + | 451.888i | −0.130331 | + | 0.163430i | −0.842715 | − | 0.538360i | \(-0.819044\pi\) |
0.712384 | + | 0.701790i | \(0.247616\pi\) | |||||||
\(198\) | 411.594 | + | 198.213i | 0.147731 | + | 0.0711434i | ||||
\(199\) | −2813.46 | − | 1354.89i | −1.00221 | − | 0.482641i | −0.140525 | − | 0.990077i | \(-0.544879\pi\) |
−0.861689 | + | 0.507436i | \(0.830593\pi\) | |||||||
\(200\) | 119.233 | − | 522.395i | 0.0421553 | − | 0.184695i | ||||
\(201\) | −814.188 | − | 1020.96i | −0.285713 | − | 0.358273i | ||||
\(202\) | −2693.10 | + | 1296.93i | −0.938048 | + | 0.451740i | ||||
\(203\) | 1749.44 | + | 2193.73i | 0.604861 | + | 0.758472i | ||||
\(204\) | 7.97986 | + | 34.9621i | 0.00273874 | + | 0.0119992i | ||||
\(205\) | 3355.72 | + | 1616.03i | 1.14328 | + | 0.550577i | ||||
\(206\) | −925.067 | − | 4052.98i | −0.312876 | − | 1.37080i | ||||
\(207\) | 470.213 | − | 226.443i | 0.157884 | − | 0.0760331i | ||||
\(208\) | 2236.04 | 0.745391 | ||||||||
\(209\) | 526.120 | 0.174127 | ||||||||
\(210\) | 2026.94 | − | 976.125i | 0.666059 | − | 0.320757i | ||||
\(211\) | 4.05107 | − | 17.7489i | 0.00132174 | − | 0.00579092i | −0.974263 | − | 0.225415i | \(-0.927626\pi\) |
0.975584 | + | 0.219624i | \(0.0704832\pi\) | |||||||
\(212\) | 731.851 | − | 917.712i | 0.237093 | − | 0.297305i | ||||
\(213\) | 373.691 | + | 468.593i | 0.120211 | + | 0.150739i | ||||
\(214\) | −7284.04 | −2.32676 | ||||||||
\(215\) | −2277.76 | − | 1249.96i | −0.722519 | − | 0.396495i | ||||
\(216\) | 2023.81 | 0.637514 | ||||||||
\(217\) | 1864.11 | + | 2337.52i | 0.583152 | + | 0.731249i | ||||
\(218\) | 5910.24 | − | 7411.20i | 1.83620 | − | 2.30252i | ||||
\(219\) | 739.391 | − | 3239.48i | 0.228143 | − | 0.999561i | ||||
\(220\) | 1543.96 | − | 743.531i | 0.473153 | − | 0.227859i | ||||
\(221\) | −52.7653 | −0.0160605 | ||||||||
\(222\) | −1640.47 | −0.495952 | ||||||||
\(223\) | 1731.66 | − | 833.924i | 0.520002 | − | 0.250420i | −0.155423 | − | 0.987848i | \(-0.549674\pi\) |
0.675426 | + | 0.737428i | \(0.263960\pi\) | |||||||
\(224\) | −651.149 | − | 2852.87i | −0.194226 | − | 0.850961i | ||||
\(225\) | −224.812 | − | 108.264i | −0.0666110 | − | 0.0320782i | ||||
\(226\) | −1613.98 | − | 7071.30i | −0.475045 | − | 2.08131i | ||||
\(227\) | −434.006 | − | 544.226i | −0.126899 | − | 0.159126i | 0.714323 | − | 0.699816i | \(-0.246735\pi\) |
−0.841222 | + | 0.540690i | \(0.818163\pi\) | |||||||
\(228\) | 1421.39 | − | 684.508i | 0.412869 | − | 0.198827i | ||||
\(229\) | 1188.11 | + | 1489.84i | 0.342850 | + | 0.429920i | 0.923125 | − | 0.384501i | \(-0.125626\pi\) |
−0.580275 | + | 0.814421i | \(0.697055\pi\) | |||||||
\(230\) | 750.712 | − | 3289.08i | 0.215220 | − | 0.942938i | ||||
\(231\) | −847.159 | − | 407.970i | −0.241294 | − | 0.116201i | ||||
\(232\) | 2753.69 | + | 1326.11i | 0.779263 | + | 0.375273i | ||||
\(233\) | −2115.56 | + | 2652.83i | −0.594829 | + | 0.745892i | −0.984562 | − | 0.175036i | \(-0.943996\pi\) |
0.389733 | + | 0.920928i | \(0.372567\pi\) | |||||||
\(234\) | −448.512 | + | 1965.06i | −0.125300 | + | 0.548974i | ||||
\(235\) | 719.643 | + | 3152.96i | 0.199763 | + | 0.875219i | ||||
\(236\) | −4719.86 | + | 5918.51i | −1.30185 | + | 1.63247i | ||||
\(237\) | −2325.99 | + | 2916.70i | −0.637508 | + | 0.799410i | ||||
\(238\) | 8.47791 | + | 37.1442i | 0.00230900 | + | 0.0101164i | ||||
\(239\) | −946.024 | + | 4144.80i | −0.256039 | + | 1.12178i | 0.669406 | + | 0.742896i | \(0.266549\pi\) |
−0.925445 | + | 0.378882i | \(0.876309\pi\) | |||||||
\(240\) | −789.327 | + | 989.784i | −0.212295 | + | 0.266210i | ||||
\(241\) | −6322.84 | − | 3044.92i | −1.69000 | − | 0.813860i | −0.995541 | − | 0.0943265i | \(-0.969930\pi\) |
−0.694457 | − | 0.719534i | \(-0.744355\pi\) | |||||||
\(242\) | 4123.52 | + | 1985.78i | 1.09533 | + | 0.527483i | ||||
\(243\) | 380.142 | − | 1665.51i | 0.100355 | − | 0.439682i | ||||
\(244\) | 3489.06 | + | 4375.14i | 0.915427 | + | 1.14791i | ||||
\(245\) | −1597.91 | + | 769.513i | −0.416681 | + | 0.200663i | ||||
\(246\) | −5015.32 | − | 6289.01i | −1.29986 | − | 1.62997i | ||||
\(247\) | 516.535 | + | 2263.09i | 0.133062 | + | 0.582983i | ||||
\(248\) | 2934.18 | + | 1413.03i | 0.751294 | + | 0.361804i | ||||
\(249\) | −878.681 | − | 3849.75i | −0.223631 | − | 0.979791i | ||||
\(250\) | −5983.89 | + | 2881.69i | −1.51382 | + | 0.729016i | ||||
\(251\) | 2690.62 | 0.676616 | 0.338308 | − | 0.941035i | \(-0.390145\pi\) | ||||
0.338308 | + | 0.941035i | \(0.390145\pi\) | |||||||
\(252\) | 844.543 | 0.211116 | ||||||||
\(253\) | −1270.39 | + | 611.785i | −0.315685 | + | 0.152026i | ||||
\(254\) | 635.862 | − | 2785.89i | 0.157077 | − | 0.688199i | ||||
\(255\) | 18.6263 | − | 23.3566i | 0.00457421 | − | 0.00573587i | ||||
\(256\) | −324.370 | − | 406.748i | −0.0791920 | − | 0.0993036i | ||||
\(257\) | 652.543 | 0.158383 | 0.0791917 | − | 0.996859i | \(-0.474766\pi\) | ||||
0.0791917 | + | 0.996859i | \(0.474766\pi\) | |||||||
\(258\) | 3260.83 | + | 4566.59i | 0.786861 | + | 1.10195i | ||||
\(259\) | −1011.37 | −0.242640 | ||||||||
\(260\) | 4714.10 | + | 5911.29i | 1.12445 | + | 1.41001i | ||||
\(261\) | 887.399 | − | 1112.76i | 0.210455 | − | 0.263902i | ||||
\(262\) | −2544.15 | + | 11146.6i | −0.599916 | + | 2.62840i | ||||
\(263\) | 4463.63 | − | 2149.57i | 1.04654 | − | 0.503986i | 0.170063 | − | 0.985433i | \(-0.445603\pi\) |
0.876475 | + | 0.481447i | \(0.159889\pi\) | |||||||
\(264\) | −1024.21 | −0.238773 | ||||||||
\(265\) | −977.834 | −0.226671 | ||||||||
\(266\) | 1510.11 | − | 727.230i | 0.348085 | − | 0.167629i | ||||
\(267\) | 887.888 | + | 3890.09i | 0.203512 | + | 0.891646i | ||||
\(268\) | −2855.04 | − | 1374.92i | −0.650744 | − | 0.313382i | ||||
\(269\) | 1566.00 | + | 6861.10i | 0.354947 | + | 1.55513i | 0.765590 | + | 0.643329i | \(0.222447\pi\) |
−0.410642 | + | 0.911797i | \(0.634695\pi\) | |||||||
\(270\) | −3798.40 | − | 4763.04i | −0.856161 | − | 1.07359i | ||||
\(271\) | 77.0982 | − | 37.1285i | 0.0172819 | − | 0.00832250i | −0.425223 | − | 0.905089i | \(-0.639804\pi\) |
0.442505 | + | 0.896766i | \(0.354090\pi\) | |||||||
\(272\) | −13.3673 | − | 16.7620i | −0.00297982 | − | 0.00373657i | ||||
\(273\) | 923.144 | − | 4044.56i | 0.204657 | − | 0.896659i | ||||
\(274\) | −1636.36 | − | 788.028i | −0.360788 | − | 0.173746i | ||||
\(275\) | 607.380 | + | 292.499i | 0.133187 | + | 0.0641394i | ||||
\(276\) | −2636.18 | + | 3305.66i | −0.574925 | + | 0.720933i | ||||
\(277\) | −1665.04 | + | 7295.02i | −0.361165 | + | 1.58237i | 0.389079 | + | 0.921204i | \(0.372793\pi\) |
−0.750244 | + | 0.661161i | \(0.770064\pi\) | |||||||
\(278\) | 2008.48 | + | 8799.74i | 0.433312 | + | 1.89846i | ||||
\(279\) | 945.563 | − | 1185.70i | 0.202901 | − | 0.254430i | ||||
\(280\) | 941.975 | − | 1181.20i | 0.201049 | − | 0.252108i | ||||
\(281\) | 609.148 | + | 2668.85i | 0.129319 | + | 0.566585i | 0.997521 | + | 0.0703730i | \(0.0224190\pi\) |
−0.868201 | + | 0.496212i | \(0.834724\pi\) | |||||||
\(282\) | 1554.21 | − | 6809.46i | 0.328199 | − | 1.43793i | ||||
\(283\) | 4625.89 | − | 5800.68i | 0.971663 | − | 1.21843i | −0.00418792 | − | 0.999991i | \(-0.501333\pi\) |
0.975851 | − | 0.218436i | \(-0.0700955\pi\) | |||||||
\(284\) | 1310.39 | + | 631.050i | 0.273793 | + | 0.131852i | ||||
\(285\) | −1184.10 | − | 570.230i | −0.246104 | − | 0.118518i | ||||
\(286\) | 1211.75 | − | 5309.04i | 0.250533 | − | 1.09766i | ||||
\(287\) | −3092.01 | − | 3877.26i | −0.635943 | − | 0.797448i | ||||
\(288\) | −1337.33 | + | 644.023i | −0.273621 | + | 0.131769i | ||||
\(289\) | −3062.89 | − | 3840.74i | −0.623426 | − | 0.781751i | ||||
\(290\) | −2047.28 | − | 8969.74i | −0.414554 | − | 1.81628i | ||||
\(291\) | −3826.06 | − | 1842.53i | −0.770748 | − | 0.371173i | ||||
\(292\) | −1794.24 | − | 7861.09i | −0.359589 | − | 1.57546i | ||||
\(293\) | −1617.83 | + | 779.105i | −0.322575 | + | 0.155344i | −0.588162 | − | 0.808743i | \(-0.700148\pi\) |
0.265587 | + | 0.964087i | \(0.414434\pi\) | |||||||
\(294\) | 3830.33 | 0.759828 | ||||||||
\(295\) | 6306.26 | 1.24463 | ||||||||
\(296\) | −992.561 | + | 477.992i | −0.194904 | + | 0.0938606i | ||||
\(297\) | −566.585 | + | 2482.37i | −0.110696 | + | 0.484990i | ||||
\(298\) | −2668.62 | + | 3346.35i | −0.518755 | + | 0.650499i | ||||
\(299\) | −3878.81 | − | 4863.87i | −0.750225 | − | 0.940753i | ||||
\(300\) | 2021.49 | 0.389035 | ||||||||
\(301\) | 2010.34 | + | 2815.36i | 0.384965 | + | 0.539119i | ||||
\(302\) | 47.5177 | 0.00905409 | ||||||||
\(303\) | −1945.75 | − | 2439.89i | −0.368912 | − | 0.462601i | ||||
\(304\) | −588.062 | + | 737.407i | −0.110946 | + | 0.139122i | ||||
\(305\) | 1037.34 | − | 4544.89i | 0.194748 | − | 0.853246i | ||||
\(306\) | 17.4119 | − | 8.38515i | 0.00325286 | − | 0.00156649i | ||||
\(307\) | −1176.57 | −0.218731 | −0.109365 | − | 0.994002i | \(-0.534882\pi\) | ||||
−0.109365 | + | 0.994002i | \(0.534882\pi\) | |||||||
\(308\) | −2281.72 | −0.422120 | ||||||||
\(309\) | 3910.45 | − | 1883.17i | 0.719928 | − | 0.346699i | ||||
\(310\) | −2181.47 | − | 9557.65i | −0.399675 | − | 1.75109i | ||||
\(311\) | 5673.77 | + | 2732.34i | 1.03450 | + | 0.498190i | 0.872507 | − | 0.488602i | \(-0.162493\pi\) |
0.161995 | + | 0.986792i | \(0.448207\pi\) | |||||||
\(312\) | −1005.55 | − | 4405.62i | −0.182462 | − | 0.799420i | ||||
\(313\) | 731.410 | + | 917.159i | 0.132082 | + | 0.165626i | 0.843474 | − | 0.537169i | \(-0.180506\pi\) |
−0.711392 | + | 0.702795i | \(0.751935\pi\) | |||||||
\(314\) | 4049.35 | − | 1950.06i | 0.727765 | − | 0.350473i | ||||
\(315\) | −438.655 | − | 550.056i | −0.0784616 | − | 0.0983878i | ||||
\(316\) | −2014.45 | + | 8825.90i | −0.358613 | + | 1.57119i | ||||
\(317\) | 1122.29 | + | 540.467i | 0.198846 | + | 0.0957591i | 0.530657 | − | 0.847587i | \(-0.321945\pi\) |
−0.331811 | + | 0.943346i | \(0.607660\pi\) | |||||||
\(318\) | 1902.69 | + | 916.289i | 0.335528 | + | 0.161582i | ||||
\(319\) | −2397.51 | + | 3006.38i | −0.420798 | + | 0.527664i | ||||
\(320\) | −1640.67 | + | 7188.24i | −0.286613 | + | 1.25573i | ||||
\(321\) | −1692.23 | − | 7414.13i | −0.294239 | − | 1.28915i | ||||
\(322\) | −2800.71 | + | 3511.98i | −0.484713 | + | 0.607811i | ||||
\(323\) | 13.8769 | − | 17.4011i | 0.00239050 | − | 0.00299759i | ||||
\(324\) | 1285.39 | + | 5631.68i | 0.220404 | + | 0.965652i | ||||
\(325\) | −661.859 | + | 2899.79i | −0.112964 | + | 0.494928i | ||||
\(326\) | 2556.27 | − | 3205.46i | 0.434291 | − | 0.544583i | ||||
\(327\) | 8916.62 | + | 4294.02i | 1.50792 | + | 0.726177i | ||||
\(328\) | −4866.95 | − | 2343.80i | −0.819306 | − | 0.394557i | ||||
\(329\) | 958.194 | − | 4198.12i | 0.160568 | − | 0.703495i | ||||
\(330\) | 1922.30 | + | 2410.49i | 0.320664 | + | 0.402100i | ||||
\(331\) | −888.205 | + | 427.737i | −0.147493 | + | 0.0710288i | −0.506174 | − | 0.862431i | \(-0.668941\pi\) |
0.358681 | + | 0.933460i | \(0.383226\pi\) | |||||||
\(332\) | −5974.43 | − | 7491.70i | −0.987619 | − | 1.23844i | ||||
\(333\) | 114.157 | + | 500.154i | 0.0187861 | + | 0.0823071i | ||||
\(334\) | 6837.14 | + | 3292.59i | 1.12009 | + | 0.539409i | ||||
\(335\) | 587.416 | + | 2573.64i | 0.0958029 | + | 0.419740i | ||||
\(336\) | 1518.71 | − | 731.370i | 0.246584 | − | 0.118749i | ||||
\(337\) | −11334.6 | −1.83214 | −0.916072 | − | 0.401014i | \(-0.868658\pi\) | ||||
−0.916072 | + | 0.401014i | \(0.868658\pi\) | |||||||
\(338\) | 14434.4 | 2.32287 | ||||||||
\(339\) | 6822.62 | − | 3285.60i | 1.09308 | − | 0.526399i | ||||
\(340\) | 16.1315 | − | 70.6767i | 0.00257310 | − | 0.0112735i | ||||
\(341\) | −2554.65 | + | 3203.43i | −0.405695 | + | 0.508725i | ||||
\(342\) | −530.087 | − | 664.708i | −0.0838123 | − | 0.105097i | ||||
\(343\) | 6569.67 | 1.03419 | ||||||||
\(344\) | 3303.54 | + | 1812.87i | 0.517775 | + | 0.284138i | ||||
\(345\) | 3522.23 | 0.549653 | ||||||||
\(346\) | −296.140 | − | 371.347i | −0.0460132 | − | 0.0576987i | ||||
\(347\) | 3244.83 | − | 4068.89i | 0.501994 | − | 0.629480i | −0.464684 | − | 0.885476i | \(-0.653832\pi\) |
0.966678 | + | 0.255997i | \(0.0824036\pi\) | |||||||
\(348\) | −2565.79 | + | 11241.5i | −0.395232 | + | 1.73162i | ||||
\(349\) | −4995.61 | + | 2405.76i | −0.766214 | + | 0.368989i | −0.775812 | − | 0.630965i | \(-0.782659\pi\) |
0.00959725 | + | 0.999954i | \(0.496945\pi\) | |||||||
\(350\) | 2147.65 | 0.327991 | ||||||||
\(351\) | −11234.1 | −1.70835 | ||||||||
\(352\) | 3613.09 | − | 1739.97i | 0.547098 | − | 0.263468i | ||||
\(353\) | −613.931 | − | 2689.81i | −0.0925672 | − | 0.405563i | 0.907322 | − | 0.420436i | \(-0.138123\pi\) |
−0.999889 | + | 0.0148726i | \(0.995266\pi\) | |||||||
\(354\) | −12270.9 | − | 5909.34i | −1.84234 | − | 0.887225i | ||||
\(355\) | −269.608 | − | 1181.23i | −0.0403080 | − | 0.176601i | ||||
\(356\) | 6037.03 | + | 7570.20i | 0.898770 | + | 1.12702i | ||||
\(357\) | −35.8379 | + | 17.2586i | −0.00531301 | + | 0.00255861i | ||||
\(358\) | −5043.35 | − | 6324.16i | −0.744552 | − | 0.933638i | ||||
\(359\) | 92.3117 | − | 404.444i | 0.0135711 | − | 0.0594588i | −0.967689 | − | 0.252147i | \(-0.918863\pi\) |
0.981260 | + | 0.192688i | \(0.0617205\pi\) | |||||||
\(360\) | −690.461 | − | 332.508i | −0.101085 | − | 0.0486798i | ||||
\(361\) | 5297.57 | + | 2551.18i | 0.772354 | + | 0.371946i | ||||
\(362\) | −3371.85 | + | 4228.16i | −0.489559 | + | 0.613888i | ||||
\(363\) | −1063.27 | + | 4658.50i | −0.153739 | + | 0.673575i | ||||
\(364\) | −2240.15 | − | 9814.73i | −0.322571 | − | 1.41327i | ||||
\(365\) | −4188.05 | + | 5251.65i | −0.600582 | + | 0.753106i | ||||
\(366\) | −6277.32 | + | 7871.51i | −0.896505 | + | 1.12418i | ||||
\(367\) | −475.812 | − | 2084.67i | −0.0676762 | − | 0.296509i | 0.929752 | − | 0.368187i | \(-0.120022\pi\) |
−0.997428 | + | 0.0716787i | \(0.977164\pi\) | |||||||
\(368\) | 562.477 | − | 2464.37i | 0.0796771 | − | 0.349088i | ||||
\(369\) | −1568.41 | + | 1966.73i | −0.221269 | + | 0.277463i | ||||
\(370\) | 2987.85 | + | 1438.87i | 0.419813 | + | 0.202171i | ||||
\(371\) | 1173.04 | + | 564.905i | 0.164154 | + | 0.0790523i | ||||
\(372\) | −2733.96 | + | 11978.3i | −0.381046 | + | 1.66947i | ||||
\(373\) | 3295.55 | + | 4132.49i | 0.457472 | + | 0.573651i | 0.956054 | − | 0.293191i | \(-0.0947172\pi\) |
−0.498582 | + | 0.866842i | \(0.666146\pi\) | |||||||
\(374\) | −47.0422 | + | 22.6543i | −0.00650400 | + | 0.00313216i | ||||
\(375\) | −4323.32 | − | 5421.28i | −0.595348 | − | 0.746543i | ||||
\(376\) | −1043.73 | − | 4572.89i | −0.143155 | − | 0.627204i | ||||
\(377\) | −15285.6 | − | 7361.18i | −2.08820 | − | 1.00562i | ||||
\(378\) | 1805.01 | + | 7908.25i | 0.245607 | + | 1.07608i | ||||
\(379\) | 11184.1 | − | 5385.99i | 1.51581 | − | 0.729973i | 0.523297 | − | 0.852150i | \(-0.324702\pi\) |
0.992508 | + | 0.122177i | \(0.0389875\pi\) | |||||||
\(380\) | −3189.22 | −0.430535 | ||||||||
\(381\) | 2983.37 | 0.401162 | ||||||||
\(382\) | 11482.5 | − | 5529.69i | 1.53795 | − | 0.740637i | ||||
\(383\) | −1854.07 | + | 8123.21i | −0.247359 | + | 1.08375i | 0.686786 | + | 0.726859i | \(0.259021\pi\) |
−0.934146 | + | 0.356892i | \(0.883836\pi\) | |||||||
\(384\) | 4505.59 | − | 5649.83i | 0.598763 | − | 0.750825i | ||||
\(385\) | 1185.12 | + | 1486.10i | 0.156882 | + | 0.196724i | ||||
\(386\) | 13651.3 | 1.80008 | ||||||||
\(387\) | 1165.36 | − | 1311.95i | 0.153072 | − | 0.172326i | ||||
\(388\) | −10305.0 | −1.34835 | ||||||||
\(389\) | −4564.21 | − | 5723.34i | −0.594896 | − | 0.745976i | 0.389677 | − | 0.920952i | \(-0.372587\pi\) |
−0.984573 | + | 0.174976i | \(0.944015\pi\) | |||||||
\(390\) | −8481.34 | + | 10635.3i | −1.10120 | + | 1.38087i | ||||
\(391\) | −13.2732 | + | 58.1535i | −0.00171676 | + | 0.00752161i | ||||
\(392\) | 2317.52 | − | 1116.06i | 0.298604 | − | 0.143800i | ||||
\(393\) | −11936.8 | −1.53214 | ||||||||
\(394\) | −2523.43 | −0.322661 | ||||||||
\(395\) | 6794.67 | − | 3272.14i | 0.865511 | − | 0.416808i | ||||
\(396\) | 257.544 | + | 1128.38i | 0.0326821 | + | 0.143189i | ||||
\(397\) | 3464.66 | + | 1668.49i | 0.438001 | + | 0.210930i | 0.639871 | − | 0.768482i | \(-0.278988\pi\) |
−0.201870 | + | 0.979412i | \(0.564702\pi\) | |||||||
\(398\) | −3033.71 | − | 13291.6i | −0.382076 | − | 1.67398i | ||||
\(399\) | 1091.05 | + | 1368.13i | 0.136894 | + | 0.171659i | ||||
\(400\) | −1088.85 | + | 524.364i | −0.136107 | + | 0.0655455i | ||||
\(401\) | 3121.68 | + | 3914.46i | 0.388751 | + | 0.487478i | 0.937243 | − | 0.348678i | \(-0.113369\pi\) |
−0.548492 | + | 0.836156i | \(0.684798\pi\) | |||||||
\(402\) | 1268.64 | − | 5558.29i | 0.157398 | − | 0.689607i | ||||
\(403\) | −16287.5 | − | 7843.66i | −2.01325 | − | 0.969530i | ||||
\(404\) | −6822.98 | − | 3285.77i | −0.840238 | − | 0.404637i | ||||
\(405\) | 3000.32 | − | 3762.28i | 0.368116 | − | 0.461603i | ||||
\(406\) | −2725.93 | + | 11943.1i | −0.333216 | + | 1.45991i | ||||
\(407\) | −308.420 | − | 1351.28i | −0.0375622 | − | 0.164571i | ||||
\(408\) | −27.0146 | + | 33.8752i | −0.00327799 | + | 0.00411047i | ||||
\(409\) | 8370.93 | − | 10496.8i | 1.01202 | − | 1.26903i | 0.0492267 | − | 0.998788i | \(-0.484324\pi\) |
0.962792 | − | 0.270244i | \(-0.0871043\pi\) | |||||||
\(410\) | 3618.42 | + | 15853.3i | 0.435856 | + | 1.90961i | ||||
\(411\) | 421.943 | − | 1848.65i | 0.0506397 | − | 0.221867i | ||||
\(412\) | 6566.80 | − | 8234.50i | 0.785250 | − | 0.984672i | ||||
\(413\) | −7565.15 | − | 3643.19i | −0.901348 | − | 0.434067i | ||||
\(414\) | 2052.90 | + | 988.625i | 0.243707 | + | 0.117363i | ||||
\(415\) | −1776.28 | + | 7782.37i | −0.210106 | + | 0.920534i | ||||
\(416\) | 11031.7 | + | 13833.3i | 1.30018 | + | 1.63037i | ||||
\(417\) | −8490.28 | + | 4088.70i | −0.997052 | + | 0.480155i | ||||
\(418\) | 1432.15 | + | 1795.86i | 0.167580 | + | 0.210139i | ||||
\(419\) | 431.243 | + | 1889.40i | 0.0502807 | + | 0.220294i | 0.993826 | − | 0.110949i | \(-0.0353891\pi\) |
−0.943545 | + | 0.331243i | \(0.892532\pi\) | |||||||
\(420\) | 5135.28 | + | 2473.02i | 0.596609 | + | 0.287312i | ||||
\(421\) | 2894.60 | + | 12682.1i | 0.335093 | + | 1.46814i | 0.809129 | + | 0.587632i | \(0.199940\pi\) |
−0.474036 | + | 0.880505i | \(0.657203\pi\) | |||||||
\(422\) | 71.6113 | − | 34.4862i | 0.00826063 | − | 0.00397811i | ||||
\(423\) | −2184.25 | −0.251068 | ||||||||
\(424\) | 1418.20 | 0.162438 | ||||||||
\(425\) | 25.6944 | − | 12.3738i | 0.00293262 | − | 0.00141227i | ||||
\(426\) | −582.273 | + | 2551.11i | −0.0662236 | + | 0.290144i | ||||
\(427\) | −3870.05 | + | 4852.90i | −0.438607 | + | 0.549995i | ||||
\(428\) | −11506.0 | − | 14428.1i | −1.29945 | − | 1.62945i | ||||
\(429\) | 5685.37 | 0.639842 | ||||||||
\(430\) | −1933.66 | − | 11177.4i | −0.216859 | − | 1.25354i | ||||
\(431\) | 445.930 | 0.0498368 | 0.0249184 | − | 0.999689i | \(-0.492067\pi\) | ||||
0.0249184 | + | 0.999689i | \(0.492067\pi\) | |||||||
\(432\) | −2845.98 | − | 3568.75i | −0.316962 | − | 0.397458i | ||||
\(433\) | −3091.47 | + | 3876.58i | −0.343110 | + | 0.430246i | −0.923208 | − | 0.384300i | \(-0.874443\pi\) |
0.580098 | + | 0.814547i | \(0.303014\pi\) | |||||||
\(434\) | −2904.60 | + | 12725.9i | −0.321256 | + | 1.40751i | ||||
\(435\) | 8654.30 | − | 4167.69i | 0.953889 | − | 0.459369i | ||||
\(436\) | 24015.8 | 2.63796 | ||||||||
\(437\) | 2624.12 | 0.287251 | ||||||||
\(438\) | 13070.3 | − | 6294.33i | 1.42585 | − | 0.686655i | ||||
\(439\) | −499.408 | − | 2188.05i | −0.0542949 | − | 0.237881i | 0.940498 | − | 0.339799i | \(-0.110359\pi\) |
−0.994793 | + | 0.101918i | \(0.967502\pi\) | |||||||
\(440\) | 1865.43 | + | 898.345i | 0.202116 | + | 0.0973339i | ||||
\(441\) | −266.544 | − | 1167.81i | −0.0287813 | − | 0.126099i | ||||
\(442\) | −143.632 | − | 180.109i | −0.0154567 | − | 0.0193821i | ||||
\(443\) | −1375.31 | + | 662.315i | −0.147501 | + | 0.0710328i | −0.506178 | − | 0.862429i | \(-0.668942\pi\) |
0.358677 | + | 0.933462i | \(0.383228\pi\) | |||||||
\(444\) | −2591.32 | − | 3249.41i | −0.276979 | − | 0.347320i | ||||
\(445\) | 1794.89 | − | 7863.92i | 0.191204 | − | 0.837720i | ||||
\(446\) | 7560.24 | + | 3640.82i | 0.802663 | + | 0.386542i | ||||
\(447\) | −4026.08 | − | 1938.86i | −0.426011 | − | 0.205156i | ||||
\(448\) | 6120.90 | − | 7675.37i | 0.645504 | − | 0.809436i | ||||
\(449\) | −1871.60 | + | 8200.00i | −0.196717 | + | 0.861875i | 0.776157 | + | 0.630540i | \(0.217167\pi\) |
−0.972874 | + | 0.231335i | \(0.925691\pi\) | |||||||
\(450\) | −242.412 | − | 1062.08i | −0.0253942 | − | 0.111259i | ||||
\(451\) | 4237.41 | − | 5313.55i | 0.442421 | − | 0.554779i | ||||
\(452\) | 11457.2 | − | 14366.9i | 1.19226 | − | 1.49504i | ||||
\(453\) | 11.0393 | + | 48.3663i | 0.00114497 | + | 0.00501644i | ||||
\(454\) | 676.255 | − | 2962.87i | 0.0699080 | − | 0.306287i | ||||
\(455\) | −5228.86 | + | 6556.79i | −0.538754 | + | 0.675576i | ||||
\(456\) | 1717.35 | + | 827.032i | 0.176365 | + | 0.0849327i | ||||
\(457\) | 13711.3 | + | 6603.03i | 1.40348 | + | 0.675879i | 0.973864 | − | 0.227134i | \(-0.0729354\pi\) |
0.429614 | + | 0.903013i | \(0.358650\pi\) | |||||||
\(458\) | −1851.28 | + | 8110.98i | −0.188875 | + | 0.827514i | ||||
\(459\) | 67.1586 | + | 84.2143i | 0.00682940 | + | 0.00856380i | ||||
\(460\) | 7700.77 | − | 3708.50i | 0.780544 | − | 0.375890i | ||||
\(461\) | −9474.08 | − | 11880.1i | −0.957162 | − | 1.20024i | −0.979694 | − | 0.200497i | \(-0.935744\pi\) |
0.0225322 | − | 0.999746i | \(-0.492827\pi\) | |||||||
\(462\) | −913.480 | − | 4002.22i | −0.0919890 | − | 0.403030i | ||||
\(463\) | −16427.2 | − | 7910.91i | −1.64889 | − | 0.794063i | −0.999433 | − | 0.0336624i | \(-0.989283\pi\) |
−0.649455 | − | 0.760400i | \(-0.725003\pi\) | |||||||
\(464\) | −1533.94 | − | 6720.65i | −0.153473 | − | 0.672410i | ||||
\(465\) | 9221.54 | − | 4440.86i | 0.919653 | − | 0.442881i | ||||
\(466\) | −14813.9 | −1.47262 | ||||||||
\(467\) | 358.288 | 0.0355024 | 0.0177512 | − | 0.999842i | \(-0.494349\pi\) | ||||
0.0177512 | + | 0.999842i | \(0.494349\pi\) | |||||||
\(468\) | −4600.81 | + | 2215.64i | −0.454429 | + | 0.218841i | ||||
\(469\) | 782.136 | − | 3426.76i | 0.0770057 | − | 0.337384i | ||||
\(470\) | −8803.36 | + | 11039.1i | −0.863976 | + | 1.08339i | ||||
\(471\) | 2925.63 | + | 3668.63i | 0.286212 | + | 0.358899i | ||||
\(472\) | −9146.26 | −0.891929 | ||||||||
\(473\) | −3148.49 | + | 3544.53i | −0.306063 | + | 0.344562i | ||||
\(474\) | −16287.4 | −1.57828 | ||||||||
\(475\) | −782.237 | − | 980.895i | −0.0755611 | − | 0.0947506i | ||||
\(476\) | −60.1824 | + | 75.4664i | −0.00579508 | + | 0.00726680i | ||||
\(477\) | 146.957 | − | 643.863i | 0.0141063 | − | 0.0618039i | ||||
\(478\) | −16723.0 | + | 8053.37i | −1.60019 | + | 0.770613i | ||||
\(479\) | 9899.32 | 0.944283 | 0.472141 | − | 0.881523i | \(-0.343481\pi\) | ||||
0.472141 | + | 0.881523i | \(0.343481\pi\) | |||||||
\(480\) | −10017.5 | −0.952574 | ||||||||
\(481\) | 5509.66 | − | 2653.31i | 0.522285 | − | 0.251519i | ||||
\(482\) | −6817.83 | − | 29870.9i | −0.644281 | − | 2.82278i | ||||
\(483\) | −4225.36 | − | 2034.83i | −0.398055 | − | 0.191693i | ||||
\(484\) | 2580.19 | + | 11304.5i | 0.242317 | + | 1.06166i | ||||
\(485\) | 5352.43 | + | 6711.73i | 0.501116 | + | 0.628379i | ||||
\(486\) | 6719.83 | − | 3236.10i | 0.627197 | − | 0.302042i | ||||
\(487\) | 7565.88 | + | 9487.31i | 0.703989 | + | 0.882775i | 0.997314 | − | 0.0732381i | \(-0.0233333\pi\) |
−0.293325 | + | 0.956013i | \(0.594762\pi\) | |||||||
\(488\) | −1504.51 | + | 6591.67i | −0.139561 | + | 0.611457i | ||||
\(489\) | 3856.58 | + | 1857.23i | 0.356647 | + | 0.171752i | ||||
\(490\) | −6976.30 | − | 3359.61i | −0.643178 | − | 0.309738i | ||||
\(491\) | −9408.62 | + | 11798.0i | −0.864776 | + | 1.08440i | 0.130890 | + | 0.991397i | \(0.458217\pi\) |
−0.995666 | + | 0.0929984i | \(0.970355\pi\) | |||||||
\(492\) | 4534.84 | − | 19868.4i | 0.415542 | − | 1.82061i | ||||
\(493\) | 36.1975 | + | 158.592i | 0.00330681 | + | 0.0144881i | ||||
\(494\) | −6318.75 | + | 7923.46i | −0.575494 | + | 0.721647i | ||||
\(495\) | 601.150 | − | 753.818i | 0.0545852 | − | 0.0684477i | ||||
\(496\) | −1634.49 | − | 7161.15i | −0.147965 | − | 0.648277i | ||||
\(497\) | −358.980 | + | 1572.79i | −0.0323993 | + | 0.141950i | ||||
\(498\) | 10748.9 | − | 13478.6i | 0.967205 | − | 1.21284i | ||||
\(499\) | −2430.19 | − | 1170.32i | −0.218017 | − | 0.104991i | 0.321688 | − | 0.946846i | \(-0.395750\pi\) |
−0.539705 | + | 0.841854i | \(0.681464\pi\) | |||||||
\(500\) | −15160.2 | − | 7300.78i | −1.35597 | − | 0.653001i | ||||
\(501\) | −1762.99 | + | 7724.17i | −0.157215 | + | 0.688803i | ||||
\(502\) | 7324.12 | + | 9184.15i | 0.651178 | + | 0.816551i | ||||
\(503\) | 1243.30 | − | 598.744i | 0.110211 | − | 0.0530749i | −0.377966 | − | 0.925820i | \(-0.623376\pi\) |
0.488177 | + | 0.872745i | \(0.337662\pi\) | |||||||
\(504\) | 636.202 | + | 797.772i | 0.0562276 | + | 0.0705071i | ||||
\(505\) | 1403.81 | + | 6150.48i | 0.123700 | + | 0.541966i | ||||
\(506\) | −5546.36 | − | 2670.99i | −0.487285 | − | 0.234664i | ||||
\(507\) | 3353.40 | + | 14692.2i | 0.293747 | + | 1.28699i | ||||
\(508\) | 6522.65 | − | 3141.14i | 0.569677 | − | 0.274342i | ||||
\(509\) | 21509.0 | 1.87302 | 0.936512 | − | 0.350636i | \(-0.114035\pi\) | ||||
0.936512 | + | 0.350636i | \(0.114035\pi\) | |||||||
\(510\) | 130.428 | 0.0113244 | ||||||||
\(511\) | 8058.03 | − | 3880.54i | 0.697585 | − | 0.335939i | ||||
\(512\) | −2316.82 | + | 10150.7i | −0.199981 | + | 0.876173i | ||||
\(513\) | 2954.49 | − | 3704.81i | 0.254276 | − | 0.318853i | ||||
\(514\) | 1776.28 | + | 2227.39i | 0.152429 | + | 0.191140i | ||||
\(515\) | −8773.97 | −0.750733 | ||||||||
\(516\) | −3894.53 | + | 13672.4i | −0.332262 | + | 1.16646i | ||||
\(517\) | 5901.23 | 0.502003 | ||||||||
\(518\) | −2753.05 | − | 3452.22i | −0.233518 | − | 0.292822i | ||||
\(519\) | 309.180 | − | 387.699i | 0.0261493 | − | 0.0327902i | ||||
\(520\) | −2032.75 | + | 8906.07i | −0.171427 | + | 0.751071i | ||||
\(521\) | 10369.4 | − | 4993.63i | 0.871959 | − | 0.419913i | 0.0562779 | − | 0.998415i | \(-0.482077\pi\) |
0.815681 | + | 0.578502i | \(0.196362\pi\) | |||||||
\(522\) | 6213.88 | 0.521023 | ||||||||
\(523\) | 7328.63 | 0.612732 | 0.306366 | − | 0.951914i | \(-0.400887\pi\) | ||||
0.306366 | + | 0.951914i | \(0.400887\pi\) | |||||||
\(524\) | −26097.8 | + | 12568.0i | −2.17574 | + | 1.04778i | ||||
\(525\) | 498.942 | + | 2186.01i | 0.0414774 | + | 0.181724i | ||||
\(526\) | 19487.7 | + | 9384.80i | 1.61541 | + | 0.777941i | ||||
\(527\) | 38.5701 | + | 168.987i | 0.00318812 | + | 0.0139681i | ||||
\(528\) | 1440.30 | + | 1806.08i | 0.118714 | + | 0.148863i | ||||
\(529\) | 4625.81 | − | 2227.67i | 0.380193 | − | 0.183091i | ||||
\(530\) | −2661.75 | − | 3337.73i | −0.218149 | − | 0.273551i | ||||
\(531\) | −947.759 | + | 4152.40i | −0.0774562 | + | 0.339358i | ||||
\(532\) | 3825.87 | + | 1842.44i | 0.311791 | + | 0.150150i | ||||
\(533\) | 27016.2 | + | 13010.3i | 2.19550 | + | 1.05730i | ||||
\(534\) | −10861.5 | + | 13619.9i | −0.880192 | + | 1.10373i | ||||
\(535\) | −3420.88 | + | 14987.9i | −0.276444 | + | 1.21118i | ||||
\(536\) | −851.957 | − | 3732.67i | −0.0686547 | − | 0.300796i | ||||
\(537\) | 5265.43 | − | 6602.65i | 0.423129 | − | 0.530587i | ||||
\(538\) | −19156.8 | + | 24021.9i | −1.53515 | + | 1.92502i | ||||
\(539\) | 720.128 | + | 3155.09i | 0.0575475 | + | 0.252132i | ||||
\(540\) | 3434.51 | − | 15047.6i | 0.273699 | − | 1.19916i | ||||
\(541\) | −4490.93 | + | 5631.45i | −0.356895 | + | 0.447532i | −0.927573 | − | 0.373642i | \(-0.878109\pi\) |
0.570678 | + | 0.821174i | \(0.306680\pi\) | |||||||
\(542\) | 336.603 | + | 162.099i | 0.0266759 | + | 0.0128464i | ||||
\(543\) | −5087.02 | − | 2449.78i | −0.402035 | − | 0.193610i | ||||
\(544\) | 37.7501 | − | 165.394i | 0.00297522 | − | 0.0130353i | ||||
\(545\) | −12473.8 | − | 15641.7i | −0.980403 | − | 1.22939i | ||||
\(546\) | 16318.5 | − | 7858.60i | 1.27906 | − | 0.615965i | ||||
\(547\) | −2592.19 | − | 3250.51i | −0.202622 | − | 0.254080i | 0.670130 | − | 0.742244i | \(-0.266238\pi\) |
−0.872752 | + | 0.488164i | \(0.837667\pi\) | |||||||
\(548\) | −1023.91 | − | 4486.04i | −0.0798161 | − | 0.349697i | ||||
\(549\) | 2836.72 | + | 1366.09i | 0.220525 | + | 0.106199i | ||||
\(550\) | 654.930 | + | 2869.43i | 0.0507751 | + | 0.222460i | ||||
\(551\) | 6447.60 | − | 3105.00i | 0.498507 | − | 0.240068i | ||||
\(552\) | −5108.45 | −0.393895 | ||||||||
\(553\) | −10041.4 | −0.772160 | ||||||||
\(554\) | −29433.2 | + | 14174.3i | −2.25721 | + | 1.08702i | ||||
\(555\) | −770.432 | + | 3375.48i | −0.0589244 | + | 0.258165i | ||||
\(556\) | −14257.7 | + | 17878.6i | −1.08752 | + | 1.36370i | ||||
\(557\) | −13921.1 | − | 17456.6i | −1.05899 | − | 1.32793i | −0.942302 | − | 0.334763i | \(-0.891344\pi\) |
−0.116688 | − | 0.993169i | \(-0.537228\pi\) | |||||||
\(558\) | 6621.16 | 0.502323 | ||||||||
\(559\) | −18337.8 | − | 10063.2i | −1.38749 | − | 0.761407i | ||||
\(560\) | −3407.56 | −0.257135 | ||||||||
\(561\) | −33.9877 | − | 42.6193i | −0.00255787 | − | 0.00320746i | ||||
\(562\) | −7451.68 | + | 9344.12i | −0.559307 | + | 0.701348i | ||||
\(563\) | 3020.32 | − | 13232.9i | 0.226095 | − | 0.990586i | −0.726696 | − | 0.686959i | \(-0.758945\pi\) |
0.952791 | − | 0.303627i | \(-0.0981976\pi\) | |||||||
\(564\) | 15943.1 | − | 7677.78i | 1.19029 | − | 0.573214i | ||||
\(565\) | −15308.1 | −1.13985 | ||||||||
\(566\) | 32392.1 | 2.40555 | ||||||||
\(567\) | −5772.76 | + | 2780.02i | −0.427572 | + | 0.205908i | ||||
\(568\) | 391.026 | + | 1713.19i | 0.0288857 | + | 0.126556i | ||||
\(569\) | −5067.93 | − | 2440.59i | −0.373390 | − | 0.179815i | 0.237771 | − | 0.971321i | \(-0.423583\pi\) |
−0.611161 | + | 0.791506i | \(0.709297\pi\) | |||||||
\(570\) | −1276.79 | − | 5594.00i | −0.0938229 | − | 0.411065i | ||||
\(571\) | −9489.95 | − | 11900.0i | −0.695520 | − | 0.872155i | 0.301160 | − | 0.953574i | \(-0.402626\pi\) |
−0.996680 | + | 0.0814190i | \(0.974055\pi\) | |||||||
\(572\) | 12430.1 | − | 5986.03i | 0.908618 | − | 0.437567i | ||||
\(573\) | 8296.05 | + | 10402.9i | 0.604839 | + | 0.758444i | ||||
\(574\) | 4817.88 | − | 21108.5i | 0.350339 | − | 1.53493i | ||||
\(575\) | 3029.42 | + | 1458.89i | 0.219714 | + | 0.105809i | ||||
\(576\) | −4486.58 | − | 2160.62i | −0.324550 | − | 0.156295i | ||||
\(577\) | 425.039 | − | 532.982i | 0.0306666 | − | 0.0384547i | −0.766262 | − | 0.642529i | \(-0.777885\pi\) |
0.796928 | + | 0.604074i | \(0.206457\pi\) | |||||||
\(578\) | 4772.50 | − | 20909.7i | 0.343443 | − | 1.50472i | ||||
\(579\) | 3171.46 | + | 13895.1i | 0.227636 | + | 0.997340i | ||||
\(580\) | 14533.1 | − | 18223.9i | 1.04044 | − | 1.30467i | ||||
\(581\) | 6626.82 | − | 8309.77i | 0.473196 | − | 0.593369i | ||||
\(582\) | −4125.59 | − | 18075.4i | −0.293834 | − | 1.28737i | ||||
\(583\) | −397.038 | + | 1739.54i | −0.0282052 | + | 0.123575i | ||||
\(584\) | 6074.13 | − | 7616.71i | 0.430392 | − | 0.539695i | ||||
\(585\) | 3832.72 | + | 1845.74i | 0.270878 | + | 0.130448i | ||||
\(586\) | −7063.26 | − | 3401.49i | −0.497919 | − | 0.239785i | ||||
\(587\) | 1188.47 | − | 5207.05i | 0.0835666 | − | 0.366129i | −0.915803 | − | 0.401627i | \(-0.868445\pi\) |
0.999370 | + | 0.0354982i | \(0.0113018\pi\) | |||||||
\(588\) | 6050.45 | + | 7587.03i | 0.424348 | + | 0.532115i | ||||
\(589\) | 6870.21 | − | 3308.52i | 0.480615 | − | 0.231452i | ||||
\(590\) | 17166.2 | + | 21525.7i | 1.19783 | + | 1.50203i | ||||
\(591\) | −586.242 | − | 2568.49i | −0.0408033 | − | 0.178771i | ||||
\(592\) | 2238.67 | + | 1078.09i | 0.155420 | + | 0.0748464i | ||||
\(593\) | −4785.69 | − | 20967.5i | −0.331408 | − | 1.45199i | −0.816406 | − | 0.577478i | \(-0.804037\pi\) |
0.484999 | − | 0.874515i | \(-0.338820\pi\) | |||||||
\(594\) | −10015.6 | + | 4823.26i | −0.691827 | + | 0.333166i | ||||
\(595\) | 80.4104 | 0.00554035 | ||||||||
\(596\) | −10843.8 | −0.745264 | ||||||||
\(597\) | 12824.1 | − | 6175.78i | 0.879157 | − | 0.423380i | ||||
\(598\) | 6043.84 | − | 26479.8i | 0.413296 | − | 1.81077i | ||||
\(599\) | 8819.93 | − | 11059.8i | 0.601624 | − | 0.754413i | −0.384006 | − | 0.923331i | \(-0.625456\pi\) |
0.985630 | + | 0.168918i | \(0.0540273\pi\) | |||||||
\(600\) | 1522.80 | + | 1909.54i | 0.103614 | + | 0.129927i | ||||
\(601\) | −1655.86 | −0.112386 | −0.0561930 | − | 0.998420i | \(-0.517896\pi\) | ||||
−0.0561930 | + | 0.998420i | \(0.517896\pi\) | |||||||
\(602\) | −4137.60 | + | 14525.8i | −0.280126 | + | 0.983432i | ||||
\(603\) | −1782.91 | −0.120408 | ||||||||
\(604\) | 75.0597 | + | 94.1219i | 0.00505651 | + | 0.00634067i | ||||
\(605\) | 6022.57 | − | 7552.07i | 0.404715 | − | 0.507496i | ||||
\(606\) | 3031.80 | − | 13283.2i | 0.203232 | − | 0.890418i | ||||
\(607\) | −14307.3 | + | 6890.03i | −0.956697 | + | 0.460721i | −0.846029 | − | 0.533136i | \(-0.821013\pi\) |
−0.110668 | + | 0.993857i | \(0.535299\pi\) | |||||||
\(608\) | −7463.24 | −0.497820 | ||||||||
\(609\) | −12789.6 | −0.851006 | ||||||||
\(610\) | 18337.2 | − | 8830.75i | 1.21714 | − | 0.586142i | ||||
\(611\) | 5793.71 | + | 25383.9i | 0.383614 | + | 1.68072i | ||||
\(612\) | 44.1133 | + | 21.2438i | 0.00291368 | + | 0.00140315i | ||||
\(613\) | 3733.91 | + | 16359.3i | 0.246021 | + | 1.07789i | 0.935428 | + | 0.353516i | \(0.115014\pi\) |
−0.689407 | + | 0.724374i | \(0.742129\pi\) | |||||||
\(614\) | −3202.73 | − | 4016.10i | −0.210508 | − | 0.263968i | ||||
\(615\) | −15295.8 | + | 7366.08i | −1.00291 | + | 0.482974i | ||||
\(616\) | −1718.84 | − | 2155.36i | −0.112425 | − | 0.140977i | ||||
\(617\) | 3117.65 | − | 13659.3i | 0.203423 | − | 0.891254i | −0.765411 | − | 0.643542i | \(-0.777464\pi\) |
0.968834 | − | 0.247712i | \(-0.0796786\pi\) | |||||||
\(618\) | 17072.6 | + | 8221.74i | 1.11126 | + | 0.535156i | ||||
\(619\) | 735.485 | + | 354.191i | 0.0477571 | + | 0.0229986i | 0.457610 | − | 0.889153i | \(-0.348706\pi\) |
−0.409853 | + | 0.912152i | \(0.634420\pi\) | |||||||
\(620\) | 15485.7 | − | 19418.4i | 1.00310 | − | 1.25784i | ||||
\(621\) | −2825.95 | + | 12381.3i | −0.182611 | + | 0.800071i | ||||
\(622\) | 6117.95 | + | 26804.5i | 0.394385 | + | 1.72791i | ||||
\(623\) | −6696.26 | + | 8396.84i | −0.430626 | + | 0.539988i | ||||
\(624\) | −6354.72 | + | 7968.57i | −0.407680 | + | 0.511215i | ||||
\(625\) | 2003.93 | + | 8779.78i | 0.128251 | + | 0.561906i | ||||
\(626\) | −1139.66 | + | 4993.18i | −0.0727635 | + | 0.318798i | ||||
\(627\) | −1495.21 | + | 1874.94i | −0.0952360 | + | 0.119422i | ||||
\(628\) | 10259.1 | + | 4940.50i | 0.651881 | + | 0.313929i | ||||
\(629\) | −52.8274 | − | 25.4403i | −0.00334876 | − | 0.00161268i | ||||
\(630\) | 683.499 | − | 2994.60i | 0.0432242 | − | 0.189378i | ||||
\(631\) | −7468.39 | − | 9365.07i | −0.471176 | − | 0.590836i | 0.488283 | − | 0.872685i | \(-0.337623\pi\) |
−0.959459 | + | 0.281850i | \(0.909052\pi\) | |||||||
\(632\) | −9854.63 | + | 4745.74i | −0.620247 | + | 0.298695i | ||||
\(633\) | 51.7388 | + | 64.8784i | 0.00324871 | + | 0.00407375i | ||||
\(634\) | 1210.15 | + | 5302.02i | 0.0758064 | + | 0.332129i | ||||
\(635\) | −5433.71 | − | 2616.73i | −0.339575 | − | 0.163531i | ||||
\(636\) | 1190.56 | + | 5216.19i | 0.0742278 | + | 0.325213i | ||||
\(637\) | −12864.5 | + | 6195.20i | −0.800171 | + | 0.385342i | ||||
\(638\) | −16788.2 | −1.04177 | ||||||||
\(639\) | 818.310 | 0.0506602 | ||||||||
\(640\) | −13161.7 | + | 6338.33i | −0.812908 | + | 0.391476i | ||||
\(641\) | 3240.50 | − | 14197.6i | 0.199676 | − | 0.874836i | −0.771454 | − | 0.636285i | \(-0.780470\pi\) |
0.971130 | − | 0.238551i | \(-0.0766724\pi\) | |||||||
\(642\) | 20700.9 | − | 25958.1i | 1.27259 | − | 1.59577i | ||||
\(643\) | 2111.82 | + | 2648.14i | 0.129521 | + | 0.162415i | 0.842363 | − | 0.538910i | \(-0.181164\pi\) |
−0.712842 | + | 0.701325i | \(0.752592\pi\) | |||||||
\(644\) | −11380.5 | −0.696357 | ||||||||
\(645\) | 10927.8 | − | 4564.92i | 0.667100 | − | 0.278672i | ||||
\(646\) | 97.1709 | 0.00591817 | ||||||||
\(647\) | −10156.2 | − | 12735.5i | −0.617127 | − | 0.773853i | 0.370810 | − | 0.928709i | \(-0.379080\pi\) |
−0.987937 | + | 0.154856i | \(0.950509\pi\) | |||||||
\(648\) | −4351.50 | + | 5456.61i | −0.263801 | + | 0.330796i | ||||
\(649\) | 2560.58 | − | 11218.6i | 0.154871 | − | 0.678536i | ||||
\(650\) | −11699.8 | + | 5634.31i | −0.706004 | + | 0.339994i | ||||
\(651\) | −13627.9 | −0.820462 | ||||||||
\(652\) | 10387.2 | 0.623919 | ||||||||
\(653\) | −14308.7 | + | 6890.73i | −0.857495 | + | 0.412948i | −0.810354 | − | 0.585940i | \(-0.800725\pi\) |
−0.0471411 | + | 0.998888i | \(0.515011\pi\) | |||||||
\(654\) | 9614.67 | + | 42124.6i | 0.574868 | + | 2.51866i | ||||
\(655\) | 21740.8 | + | 10469.8i | 1.29692 | + | 0.624564i | ||||
\(656\) | 2711.13 | + | 11878.3i | 0.161360 | + | 0.706963i | ||||
\(657\) | −2828.57 | − | 3546.92i | −0.167965 | − | 0.210622i | ||||
\(658\) | 16938.1 | − | 8156.97i | 1.00352 | − | 0.483270i | ||||
\(659\) | 17874.5 | + | 22413.9i | 1.05659 | + | 1.32492i | 0.943514 | + | 0.331331i | \(0.107498\pi\) |
0.113072 | + | 0.993587i | \(0.463931\pi\) | |||||||
\(660\) | −1738.14 | + | 7615.29i | −0.102511 | + | 0.449128i | ||||
\(661\) | −28338.8 | − | 13647.2i | −1.66755 | − | 0.803050i | −0.998192 | − | 0.0601107i | \(-0.980855\pi\) |
−0.669359 | − | 0.742939i | \(-0.733431\pi\) | |||||||
\(662\) | −3877.81 | − | 1867.45i | −0.227667 | − | 0.109638i | ||||
\(663\) | 149.957 | − | 188.040i | 0.00878406 | − | 0.0110149i | ||||
\(664\) | 2576.22 | − | 11287.1i | 0.150567 | − | 0.659678i | ||||
\(665\) | −787.161 | − | 3448.78i | −0.0459020 | − | 0.201110i | ||||
\(666\) | −1396.48 | + | 1751.13i | −0.0812498 | + | 0.101884i | ||||
\(667\) | −11958.0 | + | 14994.9i | −0.694176 | + | 0.870469i | ||||
\(668\) | 4278.16 | + | 18743.9i | 0.247795 | + | 1.08566i | ||||
\(669\) | −1949.45 | + | 8541.09i | −0.112661 | + | 0.493599i | ||||
\(670\) | −7185.83 | + | 9010.75i | −0.414348 | + | 0.519576i | ||||
\(671\) | −7664.03 | − | 3690.80i | −0.440934 | − | 0.212343i | ||||
\(672\) | 12017.3 | + | 5787.23i | 0.689848 | + | 0.332213i | ||||
\(673\) | 2791.50 | − | 12230.4i | 0.159888 | − | 0.700514i | −0.829894 | − | 0.557921i | \(-0.811599\pi\) |
0.989782 | − | 0.142592i | \(-0.0455438\pi\) | |||||||
\(674\) | −30853.7 | − | 38689.3i | −1.76326 | − | 2.21106i | ||||
\(675\) | 5470.52 | − | 2634.46i | 0.311941 | − | 0.150223i | ||||
\(676\) | 22800.9 | + | 28591.4i | 1.29727 | + | 1.62673i | ||||
\(677\) | 3217.63 | + | 14097.4i | 0.182664 | + | 0.800304i | 0.980356 | + | 0.197238i | \(0.0631973\pi\) |
−0.797691 | + | 0.603066i | \(0.793946\pi\) | |||||||
\(678\) | 29786.8 | + | 14344.6i | 1.68725 | + | 0.812537i | ||||
\(679\) | −2543.48 | − | 11143.7i | −0.143755 | − | 0.629833i | ||||
\(680\) | 78.9147 | − | 38.0033i | 0.00445035 | − | 0.00214318i | ||||
\(681\) | 3172.89 | 0.178539 | ||||||||
\(682\) | −17888.5 | −1.00438 | ||||||||
\(683\) | −18601.3 | + | 8957.93i | −1.04211 | + | 0.501853i | −0.875019 | − | 0.484089i | \(-0.839151\pi\) |
−0.167089 | + | 0.985942i | \(0.553437\pi\) | |||||||
\(684\) | 479.304 | − | 2099.97i | 0.0267933 | − | 0.117389i | ||||
\(685\) | −2389.97 | + | 2996.92i | −0.133308 | + | 0.167163i | ||||
\(686\) | 17883.2 | + | 22424.8i | 0.995313 | + | 1.24808i | ||||
\(687\) | −8685.92 | −0.482370 | ||||||||
\(688\) | −1448.81 | − | 8374.74i | −0.0802841 | − | 0.464075i | ||||
\(689\) | −7872.36 | −0.435287 | ||||||||
\(690\) | 9587.82 | + | 12022.7i | 0.528988 | + | 0.663331i | ||||
\(691\) | 17952.3 | − | 22511.5i | 0.988334 | − | 1.23933i | 0.0174342 | − | 0.999848i | \(-0.494450\pi\) |
0.970900 | − | 0.239484i | \(-0.0769783\pi\) | |||||||
\(692\) | 267.769 | − | 1173.17i | 0.0147096 | − | 0.0644470i | ||||
\(693\) | −1156.64 | + | 557.010i | −0.0634016 | + | 0.0305326i | ||||
\(694\) | 22721.4 | 1.24279 | ||||||||
\(695\) | 19049.8 | 1.03971 | ||||||||
\(696\) | −12551.7 | + | 6044.60i | −0.683581 | + | 0.329195i | ||||
\(697\) | −63.9765 | − | 280.299i | −0.00347673 | − | 0.0152326i | ||||
\(698\) | −21810.3 | − | 10503.3i | −1.18271 | − | 0.569563i | ||||
\(699\) | −3441.56 | − | 15078.5i | −0.186226 | − | 0.815908i | ||||
\(700\) | 3392.47 | + | 4254.02i | 0.183176 | + | 0.229695i | ||||
\(701\) | −30214.8 | + | 14550.7i | −1.62795 | + | 0.783981i | −0.627970 | + | 0.778238i | \(0.716114\pi\) |
−0.999984 | + | 0.00574352i | \(0.998172\pi\) | |||||||
\(702\) | −30580.2 | − | 38346.4i | −1.64413 | − | 2.06167i | ||||
\(703\) | −573.985 | + | 2514.79i | −0.0307941 | + | 0.134918i | ||||
\(704\) | 12121.5 | + | 5837.40i | 0.648928 | + | 0.312507i | ||||
\(705\) | −13281.4 | − | 6395.99i | −0.709513 | − | 0.341683i | ||||
\(706\) | 7510.19 | − | 9417.48i | 0.400354 | − | 0.502028i | ||||
\(707\) | 1869.15 | − | 8189.27i | 0.0994294 | − | 0.435628i | ||||
\(708\) | −7678.18 | − | 33640.3i | −0.407576 | − | 1.78571i | ||||
\(709\) | 20668.0 | − | 25916.8i | 1.09478 | − | 1.37282i | 0.173087 | − | 0.984907i | \(-0.444626\pi\) |
0.921697 | − | 0.387910i | \(-0.126803\pi\) | |||||||
\(710\) | 3298.11 | − | 4135.70i | 0.174332 | − | 0.218605i | ||||
\(711\) | 1133.40 | + | 4965.77i | 0.0597834 | + | 0.261928i | ||||
\(712\) | −2603.21 | + | 11405.4i | −0.137022 | + | 0.600331i | ||||
\(713\) | −12741.8 | + | 15977.7i | −0.669261 | + | 0.839227i | ||||
\(714\) | −156.465 | − | 75.3493i | −0.00820103 | − | 0.00394941i | ||||
\(715\) | −10354.9 | − | 4986.67i | −0.541612 | − | 0.260827i | ||||
\(716\) | 4560.19 | − | 19979.5i | 0.238020 | − | 1.04283i | ||||
\(717\) | −12082.3 | − | 15150.7i | −0.629318 | − | 0.789140i | ||||
\(718\) | 1631.81 | − | 785.836i | 0.0848168 | − | 0.0408456i | ||||
\(719\) | 18412.9 | + | 23089.1i | 0.955058 | + | 1.19760i | 0.980218 | + | 0.197921i | \(0.0634189\pi\) |
−0.0251604 | + | 0.999683i | \(0.508010\pi\) | |||||||
\(720\) | 384.621 | + | 1685.13i | 0.0199083 | + | 0.0872240i | ||||
\(721\) | 10525.5 | + | 5068.81i | 0.543675 | + | 0.261820i | ||||
\(722\) | 5712.30 | + | 25027.2i | 0.294446 | + | 1.29005i | ||||
\(723\) | 28820.4 | − | 13879.2i | 1.48249 | − | 0.713931i | ||||
\(724\) | −13701.3 | −0.703320 | ||||||||
\(725\) | 9169.68 | 0.469729 | ||||||||
\(726\) | −18795.6 | + | 9051.48i | −0.960840 | + | 0.462716i | ||||
\(727\) | 5450.30 | − | 23879.3i | 0.278047 | − | 1.21820i | −0.622211 | − | 0.782849i | \(-0.713766\pi\) |
0.900259 | − | 0.435356i | \(-0.143377\pi\) | |||||||
\(728\) | 7583.67 | − | 9509.62i | 0.386084 | − | 0.484134i | ||||
\(729\) | 13646.6 | + | 17112.2i | 0.693317 | + | 0.869392i | ||||
\(730\) | −29326.2 | −1.48686 | ||||||||
\(731\) | 34.1886 | + | 197.624i | 0.00172984 | + | 0.00999918i | ||||
\(732\) | −25507.5 | −1.28795 | ||||||||
\(733\) | 5246.15 | + | 6578.46i | 0.264353 | + | 0.331488i | 0.896238 | − | 0.443574i | \(-0.146290\pi\) |
−0.631884 | + | 0.775063i | \(0.717718\pi\) | |||||||
\(734\) | 5820.58 | − | 7298.78i | 0.292700 | − | 0.367034i | ||||
\(735\) | 1798.88 | − | 7881.39i | 0.0902756 | − | 0.395523i | ||||
\(736\) | 18020.9 | − | 8678.43i | 0.902528 | − | 0.434635i | ||||
\(737\) | 4816.94 | 0.240752 | ||||||||
\(738\) | −10982.6 | −0.547797 | ||||||||
\(739\) | −22447.9 | + | 10810.4i | −1.11740 | + | 0.538113i | −0.899089 | − | 0.437766i | \(-0.855770\pi\) |
−0.218314 | + | 0.975879i | \(0.570056\pi\) | |||||||
\(740\) | 1869.57 | + | 8191.12i | 0.0928740 | + | 0.406907i | ||||
\(741\) | −9532.93 | − | 4590.82i | −0.472606 | − | 0.227595i | ||||
\(742\) | 1264.87 | + | 5541.75i | 0.0625806 | + | 0.274184i | ||||
\(743\) | 2771.96 | + | 3475.92i | 0.136868 | + | 0.171628i | 0.845542 | − | 0.533909i | \(-0.179277\pi\) |
−0.708674 | + | 0.705537i | \(0.750706\pi\) | |||||||
\(744\) | −13374.4 | + | 6440.79i | −0.659046 | + | 0.317380i | ||||
\(745\) | 5632.24 | + | 7062.61i | 0.276979 | + | 0.347321i | ||||
\(746\) | −5135.02 | + | 22498.0i | −0.252019 | + | 1.10417i | ||||
\(747\) | −4857.41 | − | 2339.21i | −0.237916 | − | 0.114574i | ||||
\(748\) | −119.182 | − | 57.3949i | −0.00582582 | − | 0.00280557i | ||||
\(749\) | 12762.4 | − | 16003.6i | 0.622601 | − | 0.780717i | ||||
\(750\) | 6736.47 | − | 29514.4i | 0.327975 | − | 1.43695i | ||||
\(751\) | −1140.76 | − | 4997.99i | −0.0554286 | − | 0.242848i | 0.939623 | − | 0.342213i | \(-0.111176\pi\) |
−0.995051 | + | 0.0993641i | \(0.968319\pi\) | |||||||
\(752\) | −6596.00 | + | 8271.12i | −0.319855 | + | 0.401086i | ||||
\(753\) | −7646.63 | + | 9588.57i | −0.370065 | + | 0.464047i | ||||
\(754\) | −16482.3 | − | 72213.7i | −0.796087 | − | 3.48789i | ||||
\(755\) | 22.3162 | − | 97.7737i | 0.00107572 | − | 0.00471304i | ||||
\(756\) | −12813.3 | + | 16067.3i | −0.616420 | + | 0.772966i | ||||
\(757\) | 6032.34 | + | 2905.02i | 0.289629 | + | 0.139478i | 0.573057 | − | 0.819516i | \(-0.305757\pi\) |
−0.283428 | + | 0.958994i | \(0.591472\pi\) | |||||||
\(758\) | 48828.7 | + | 23514.7i | 2.33976 | + | 1.12677i | ||||
\(759\) | 1430.16 | − | 6265.94i | 0.0683946 | − | 0.299656i | ||||
\(760\) | −2402.47 | − | 3012.60i | −0.114667 | − | 0.143787i | ||||
\(761\) | −25622.8 | + | 12339.3i | −1.22054 | + | 0.587779i | −0.929461 | − | 0.368922i | \(-0.879727\pi\) |
−0.291075 | + | 0.956700i | \(0.594013\pi\) | |||||||
\(762\) | 8121.00 | + | 10183.4i | 0.386080 | + | 0.484129i | ||||
\(763\) | 5927.58 | + | 25970.4i | 0.281249 | + | 1.23223i | ||||
\(764\) | 29091.0 | + | 14009.5i | 1.37759 | + | 0.663411i | ||||
\(765\) | −9.07616 | − | 39.7653i | −0.000428953 | − | 0.00187937i | ||||
\(766\) | −32774.7 | + | 15783.4i | −1.54595 | + | 0.744490i | ||||
\(767\) | 50770.5 | 2.39011 | ||||||||
\(768\) | 2371.37 | 0.111419 | ||||||||
\(769\) | 30040.4 | − | 14466.7i | 1.40869 | − | 0.678390i | 0.433788 | − | 0.901015i | \(-0.357177\pi\) |
0.974904 | + | 0.222625i | \(0.0714625\pi\) | |||||||
\(770\) | −1846.62 | + | 8090.59i | −0.0864256 | + | 0.378655i | ||||
\(771\) | −1854.50 | + | 2325.47i | −0.0866254 | + | 0.108625i | ||||
\(772\) | 21563.8 | + | 27040.1i | 1.00531 | + | 1.26062i | ||||
\(773\) | 31381.8 | 1.46019 | 0.730094 | − | 0.683347i | \(-0.239476\pi\) | ||||
0.730094 | + | 0.683347i | \(0.239476\pi\) | |||||||
\(774\) | 7650.43 | + | 406.597i | 0.355283 | + | 0.0188822i | ||||
\(775\) | 9770.70 | 0.452870 | ||||||||
\(776\) | −7762.87 | − | 9734.34i | −0.359112 | − | 0.450312i | ||||
\(777\) | 2874.28 | − | 3604.23i | 0.132708 | − | 0.166411i | ||||
\(778\) | 7111.81 | − | 31158.9i | 0.327726 | − | 1.43586i | ||||
\(779\) | −11395.7 | + | 5487.86i | −0.524123 | + | 0.252404i | ||||
\(780\) | −34463.3 | −1.58203 | ||||||||
\(781\) | −2210.85 | −0.101294 | ||||||||
\(782\) | −234.632 | + | 112.993i | −0.0107294 | + | 0.00516702i | ||||
\(783\) | 7706.71 | + | 33765.3i | 0.351744 | + | 1.54109i | ||||
\(784\) | −5227.06 | − | 2517.22i | −0.238113 | − | 0.114669i | ||||
\(785\) | −2110.77 | − | 9247.88i | −0.0959702 | − | 0.420473i | ||||
\(786\) | −32492.9 | − | 40744.8i | −1.47453 | − | 1.84901i | ||||
\(787\) | −552.575 | + | 266.106i | −0.0250282 | + | 0.0120529i | −0.446356 | − | 0.894855i | \(-0.647278\pi\) |
0.421328 | + | 0.906908i | \(0.361564\pi\) | |||||||
\(788\) | −3986.05 | − | 4998.35i | −0.180199 | − | 0.225963i | ||||
\(789\) | −5025.02 | + | 22016.0i | −0.226737 | + | 0.993399i | ||||
\(790\) | 29664.8 | + | 14285.8i | 1.33598 | + | 0.643375i | ||||
\(791\) | 18364.0 | + | 8843.63i | 0.825472 | + | 0.397526i | ||||
\(792\) | −871.876 | + | 1093.30i | −0.0391171 | + | 0.0490513i | ||||
\(793\) | 8351.45 | − | 36590.1i | 0.373983 | − | 1.63853i | ||||
\(794\) | 3735.90 | + | 16368.0i | 0.166980 | + | 0.731587i | ||||
\(795\) | 2778.96 | − | 3484.71i | 0.123974 | − | 0.155459i | ||||
\(796\) | 21535.5 | − | 27004.7i | 0.958926 | − | 1.20246i | ||||
\(797\) | −743.793 | − | 3258.77i | −0.0330571 | − | 0.144833i | 0.955706 | − | 0.294323i | \(-0.0950940\pi\) |
−0.988763 | + | 0.149490i | \(0.952237\pi\) | |||||||
\(798\) | −1700.03 | + | 7448.33i | −0.0754142 | + | 0.330411i | ||||
\(799\) | 155.650 | − | 195.179i | 0.00689175 | − | 0.00864198i | ||||
\(800\) | −8615.94 | − | 4149.22i | −0.380774 | − | 0.183371i | ||||
\(801\) | 4908.31 | + | 2363.72i | 0.216512 | + | 0.104267i | ||||
\(802\) | −4864.10 | + | 21311.0i | −0.214161 | + | 0.938302i | ||||
\(803\) | 7642.02 | + | 9582.79i | 0.335842 | + | 0.421132i | ||||
\(804\) | 13013.7 | − | 6267.06i | 0.570843 | − | 0.274903i | ||||
\(805\) | 5911.02 | + | 7412.19i | 0.258803 | + | 0.324528i | ||||
\(806\) | −17562.6 | − | 76946.8i | −0.767515 | − | 3.36270i | ||||
\(807\) | −28901.4 | − | 13918.2i | −1.26069 | − | 0.607117i | ||||
\(808\) | −2036.01 | − | 8920.33i | −0.0886466 | − | 0.388386i | ||||
\(809\) | −4116.04 | + | 1982.18i | −0.178878 | + | 0.0861430i | −0.521180 | − | 0.853447i | \(-0.674508\pi\) |
0.342302 | + | 0.939590i | \(0.388794\pi\) | |||||||
\(810\) | 21009.3 | 0.911346 | ||||||||
\(811\) | −42027.8 | −1.81972 | −0.909861 | − | 0.414913i | \(-0.863812\pi\) | ||||
−0.909861 | + | 0.414913i | \(0.863812\pi\) | |||||||
\(812\) | −27962.5 | + | 13466.0i | −1.20849 | + | 0.581976i | ||||
\(813\) | −86.7947 | + | 380.273i | −0.00374419 | + | 0.0164044i | ||||
\(814\) | 3772.89 | − | 4731.05i | 0.162457 | − | 0.203714i | ||||
\(815\) | −5395.12 | − | 6765.26i | −0.231881 | − | 0.290769i | ||||
\(816\) | 97.7240 | 0.00419243 | ||||||||
\(817\) | 8141.37 | − | 3400.94i | 0.348630 | − | 0.145635i | ||||
\(818\) | 58616.1 | 2.50546 | ||||||||
\(819\) | −3531.53 | − | 4428.40i | −0.150674 | − | 0.188939i | ||||
\(820\) | −25686.2 | + | 32209.5i | −1.09390 | + | 1.37171i | ||||
\(821\) | 4613.95 | − | 20215.0i | 0.196136 | − | 0.859329i | −0.777073 | − | 0.629410i | \(-0.783297\pi\) |
0.973210 | − | 0.229919i | \(-0.0738462\pi\) | |||||||
\(822\) | 7458.75 | − | 3591.94i | 0.316489 | − | 0.152413i | ||||
\(823\) | −25400.2 | −1.07582 | −0.537908 | − | 0.843003i | \(-0.680785\pi\) | ||||
−0.537908 | + | 0.843003i | \(0.680785\pi\) | |||||||
\(824\) | 12725.3 | 0.537994 | ||||||||
\(825\) | −2768.53 | + | 1333.25i | −0.116834 | + | 0.0562641i | ||||
\(826\) | −8157.40 | − | 35739.9i | −0.343623 | − | 1.50551i | ||||
\(827\) | −1089.89 | − | 524.861i | −0.0458271 | − | 0.0220692i | 0.410830 | − | 0.911712i | \(-0.365239\pi\) |
−0.456657 | + | 0.889643i | \(0.650953\pi\) | |||||||
\(828\) | 1284.55 | + | 5627.98i | 0.0539145 | + | 0.236215i | ||||
\(829\) | 9201.80 | + | 11538.7i | 0.385515 | + | 0.483420i | 0.936287 | − | 0.351235i | \(-0.114238\pi\) |
−0.550772 | + | 0.834655i | \(0.685667\pi\) | |||||||
\(830\) | −31399.5 | + | 15121.2i | −1.31312 | + | 0.632366i | ||||
\(831\) | −21265.3 | − | 26665.8i | −0.887707 | − | 1.11315i | ||||
\(832\) | −13208.7 | + | 57871.1i | −0.550396 | + | 2.41144i | ||||
\(833\) | 123.346 | + | 59.4005i | 0.00513049 | + | 0.00247071i | ||||
\(834\) | −37067.6 | − | 17850.8i | −1.53903 | − | 0.741156i | ||||
\(835\) | 9985.92 | − | 12521.9i | 0.413865 | − | 0.518970i | ||||
\(836\) | −1294.94 | + | 5673.52i | −0.0535725 | + | 0.234716i | ||||
\(837\) | 8211.84 | + | 35978.4i | 0.339119 | + | 1.48578i | ||||
\(838\) | −5275.38 | + | 6615.12i | −0.217464 | + | 0.272692i | ||||
\(839\) | 26601.6 | − | 33357.3i | 1.09462 | − | 1.37261i | 0.172819 | − | 0.984954i | \(-0.444712\pi\) |
0.921803 | − | 0.387659i | \(-0.126716\pi\) | |||||||
\(840\) | 1532.39 | + | 6713.84i | 0.0629434 | + | 0.275773i | ||||
\(841\) | −6211.64 | + | 27215.0i | −0.254690 | + | 1.11587i | ||||
\(842\) | −35409.5 | + | 44402.1i | −1.44928 | + | 1.81734i | ||||
\(843\) | −11242.2 | − | 5413.94i | −0.459313 | − | 0.221193i | ||||
\(844\) | 181.428 | + | 87.3710i | 0.00739929 | + | 0.00356331i | ||||
\(845\) | 6778.99 | − | 29700.7i | 0.275981 | − | 1.20915i | ||||
\(846\) | −5945.72 | − | 7455.69i | −0.241629 | − | 0.302993i | ||||
\(847\) | −11587.7 | + | 5580.36i | −0.470082 | + | 0.226380i | ||||
\(848\) | −1994.34 | − | 2500.82i | −0.0807617 | − | 0.101272i | ||||
\(849\) | 7525.32 | + | 32970.6i | 0.304203 | + | 1.33280i | ||||
\(850\) | 112.179 | + | 54.0226i | 0.00452672 | + | 0.00217995i | ||||
\(851\) | −1538.30 | − | 6739.74i | −0.0619651 | − | 0.271487i | ||||
\(852\) | −5972.94 | + | 2876.42i | −0.240175 | + | 0.115662i | ||||
\(853\) | −5852.96 | −0.234937 | −0.117469 | − | 0.993077i | \(-0.537478\pi\) | ||||
−0.117469 | + | 0.993077i | \(0.537478\pi\) | |||||||
\(854\) | −27099.5 | −1.08586 | ||||||||
\(855\) | −1616.67 | + | 778.548i | −0.0646655 | + | 0.0311413i | ||||
\(856\) | 4961.46 | − | 21737.6i | 0.198107 | − | 0.867962i | ||||
\(857\) | −2129.85 | + | 2670.75i | −0.0848943 | + | 0.106454i | −0.822465 | − | 0.568816i | \(-0.807402\pi\) |
0.737570 | + | 0.675270i | \(0.235973\pi\) | |||||||
\(858\) | 15476.1 | + | 19406.4i | 0.615786 | + | 0.772171i | ||||
\(859\) | −4064.51 | −0.161443 | −0.0807213 | − | 0.996737i | \(-0.525722\pi\) | ||||
−0.0807213 | + | 0.996737i | \(0.525722\pi\) | |||||||
\(860\) | 19085.4 | − | 21486.1i | 0.756753 | − | 0.851942i | ||||
\(861\) | 22604.8 | 0.894736 | ||||||||
\(862\) | 1213.86 | + | 1522.13i | 0.0479632 | + | 0.0601439i | ||||
\(863\) | −15256.2 | + | 19130.6i | −0.601769 | + | 0.754594i | −0.985652 | − | 0.168787i | \(-0.946015\pi\) |
0.383884 | + | 0.923381i | \(0.374586\pi\) | |||||||
\(864\) | 8037.25 | − | 35213.5i | 0.316473 | − | 1.38656i | ||||
\(865\) | −903.173 | + | 434.945i | −0.0355015 | + | 0.0170966i | ||||
\(866\) | −21647.6 | −0.849439 | ||||||||
\(867\) | 22391.9 | 0.877125 | ||||||||
\(868\) | −29795.2 | + | 14348.6i | −1.16511 | + | 0.561088i | ||||
\(869\) | −3062.14 | − | 13416.1i | −0.119535 | − | 0.523718i | ||||
\(870\) | 37783.7 | + | 18195.7i | 1.47240 | + | 0.709071i | ||||
\(871\) | 4729.17 | + | 20719.9i | 0.183975 | + | 0.806046i | ||||
\(872\) | 18091.4 | + | 22685.8i | 0.702581 | + | 0.881009i | ||||
\(873\) | −5223.80 | + | 2515.65i | −0.202519 | + | 0.0975279i | ||||
\(874\) | 7143.09 | + | 8957.16i | 0.276452 | + | 0.346659i | ||||
\(875\) | 4153.13 | − | 18196.0i | 0.160459 | − | 0.703015i | ||||
\(876\) | 33113.7 | + | 15946.7i | 1.27718 | + | 0.615057i | ||||
\(877\) | −11535.6 | − | 5555.25i | −0.444161 | − | 0.213897i | 0.198416 | − | 0.980118i | \(-0.436420\pi\) |
−0.642577 | + | 0.766221i | \(0.722135\pi\) | |||||||
\(878\) | 6109.24 | − | 7660.74i | 0.234825 | − | 0.294462i | ||||
\(879\) | 1821.30 | − | 7979.64i | 0.0698873 | − | 0.306196i | ||||
\(880\) | −1039.14 | − | 4552.77i | −0.0398061 | − | 0.174402i | ||||
\(881\) | −16750.4 | + | 21004.3i | −0.640561 | + | 0.803238i | −0.991073 | − | 0.133320i | \(-0.957436\pi\) |
0.350512 | + | 0.936558i | \(0.386008\pi\) | |||||||
\(882\) | 3260.62 | − | 4088.69i | 0.124479 | − | 0.156092i | ||||
\(883\) | 3136.18 | + | 13740.5i | 0.119525 | + | 0.523675i | 0.998872 | + | 0.0474922i | \(0.0151229\pi\) |
−0.879346 | + | 0.476183i | \(0.842020\pi\) | |||||||
\(884\) | 129.872 | − | 569.005i | 0.00494124 | − | 0.0216490i | ||||
\(885\) | −17922.1 | + | 22473.6i | −0.680729 | + | 0.853607i | ||||
\(886\) | −6004.46 | − | 2891.60i | −0.227679 | − | 0.109645i | ||||
\(887\) | −2305.26 | − | 1110.15i | −0.0872637 | − | 0.0420240i | 0.389743 | − | 0.920924i | \(-0.372564\pi\) |
−0.477007 | + | 0.878900i | \(0.658278\pi\) | |||||||
\(888\) | 1117.39 | − | 4895.62i | 0.0422267 | − | 0.185007i | ||||
\(889\) | 5006.71 | + | 6278.21i | 0.188886 | + | 0.236855i | ||||
\(890\) | 31728.5 | − | 15279.6i | 1.19499 | − | 0.575477i | ||||
\(891\) | −5474.74 | − | 6865.10i | −0.205848 | − | 0.258125i | ||||
\(892\) | 4730.63 | + | 20726.2i | 0.177571 | + | 0.777989i | ||||
\(893\) | −9894.88 | − | 4765.12i | −0.370794 | − | 0.178565i | ||||
\(894\) | −4341.27 | − | 19020.3i | −0.162409 | − | 0.711560i | ||||
\(895\) | −15381.3 | + | 7407.26i | −0.574459 | + | 0.276645i | ||||
\(896\) | 19450.8 | 0.725230 | ||||||||
\(897\) | 28356.8 | 1.05552 | ||||||||
\(898\) | −33084.5 | + | 15932.6i | −1.22945 | + | 0.592071i | ||||
\(899\) | −12401.6 | + | 54334.7i | −0.460083 | + | 2.01576i | ||||
\(900\) | 1720.82 | − | 2157.84i | 0.0637340 | − | 0.0799199i | ||||
\(901\) | 47.0618 | + | 59.0137i | 0.00174013 | + | 0.00218205i | ||||
\(902\) | 29671.8 | 1.09530 | ||||||||
\(903\) | −15746.4 | − | 836.874i | −0.580297 | − | 0.0308410i | ||||
\(904\) | 22202.0 | 0.816846 | ||||||||
\(905\) | 7116.43 | + | 8923.72i | 0.261390 | + | 0.327773i | ||||
\(906\) | −135.043 | + | 169.339i | −0.00495200 | + | 0.00620961i | ||||
\(907\) | −5101.35 | + | 22350.5i | −0.186756 | + | 0.818231i | 0.791557 | + | 0.611096i | \(0.209271\pi\) |
−0.978312 | + | 0.207135i | \(0.933586\pi\) | |||||||
\(908\) | 6937.00 | − | 3340.68i | 0.253538 | − | 0.122097i | ||||
\(909\) | −4260.81 | −0.155470 | ||||||||
\(910\) | −36614.3 | −1.33379 | ||||||||
\(911\) | 4400.08 | − | 2118.97i | 0.160023 | − | 0.0770631i | −0.352158 | − | 0.935941i | \(-0.614552\pi\) |
0.512181 | + | 0.858878i | \(0.328838\pi\) | |||||||
\(912\) | −956.649 | − | 4191.35i | −0.0347344 | − | 0.152182i | ||||
\(913\) | 13123.4 | + | 6319.88i | 0.475707 | + | 0.229088i | ||||
\(914\) | 14784.7 | + | 64776.2i | 0.535050 | + | 2.34421i | ||||
\(915\) | 13248.6 | + | 16613.2i | 0.478671 | + | 0.600234i | ||||
\(916\) | −18990.3 | + | 9145.27i | −0.684998 | + | 0.329878i | ||||
\(917\) | −20032.3 | − | 25119.7i | −0.721402 | − | 0.904609i | ||||
\(918\) | −104.645 | + | 458.478i | −0.00376229 | + | 0.0164837i | ||||
\(919\) | 14504.5 | + | 6984.98i | 0.520629 | + | 0.250722i | 0.675694 | − | 0.737183i | \(-0.263844\pi\) |
−0.155064 | + | 0.987904i | \(0.549558\pi\) | |||||||
\(920\) | 9304.19 | + | 4480.66i | 0.333424 | + | 0.160568i | ||||
\(921\) | 3343.76 | − | 4192.94i | 0.119632 | − | 0.150013i | ||||
\(922\) | 14762.2 | − | 64677.5i | 0.527297 | − | 2.31024i | ||||
\(923\) | −2170.57 | − | 9509.87i | −0.0774052 | − | 0.339135i | ||||
\(924\) | 6484.55 | − | 8131.36i | 0.230872 | − | 0.289505i | ||||
\(925\) | −2060.75 | + | 2584.10i | −0.0732508 | + | 0.0918536i | ||||
\(926\) | −17713.2 | − | 77606.6i | −0.628609 | − | 2.75411i | ||||
\(927\) | 1318.63 | − | 5777.29i | 0.0467200 | − | 0.204694i | ||||
\(928\) | 34009.6 | − | 42646.7i | 1.20304 | − | 1.50856i | ||||
\(929\) | −22902.2 | − | 11029.1i | −0.808822 | − | 0.389508i | −0.0166919 | − | 0.999861i | \(-0.505313\pi\) |
−0.792130 | + | 0.610353i | \(0.791028\pi\) | |||||||
\(930\) | 40260.2 | + | 19388.3i | 1.41955 | + | 0.683621i | ||||
\(931\) | 1340.19 | − | 5871.78i | 0.0471784 | − | 0.206702i | ||||
\(932\) | −23400.3 | − | 29343.0i | −0.822427 | − | 1.03129i | ||||
\(933\) | −25861.9 | + | 12454.4i | −0.907481 | + | 0.437020i | ||||
\(934\) | 975.293 | + | 1222.98i | 0.0341676 | + | 0.0428448i | ||||
\(935\) | 24.5213 | + | 107.435i | 0.000857681 | + | 0.00375774i | ||||
\(936\) | −5558.77 | − | 2676.96i | −0.194118 | − | 0.0934821i | ||||
\(937\) | 4180.34 | + | 18315.3i | 0.145748 | + | 0.638564i | 0.994038 | + | 0.109032i | \(0.0347751\pi\) |
−0.848290 | + | 0.529532i | \(0.822368\pi\) | |||||||
\(938\) | 13825.9 | − | 6658.21i | 0.481271 | − | 0.231768i | ||||
\(939\) | −5347.11 | −0.185832 | ||||||||
\(940\) | −35771.8 | −1.24122 | ||||||||
\(941\) | 11586.0 | − | 5579.51i | 0.401373 | − | 0.193291i | −0.222297 | − | 0.974979i | \(-0.571355\pi\) |
0.623670 | + | 0.781688i | \(0.285641\pi\) | |||||||
\(942\) | −4558.63 | + | 19972.7i | −0.157673 | + | 0.690812i | ||||
\(943\) | 21134.9 | − | 26502.3i | 0.729847 | − | 0.915200i | ||||
\(944\) | 12861.9 | + | 16128.3i | 0.443453 | + | 0.556073i | ||||
\(945\) | 17119.9 | 0.589324 | ||||||||
\(946\) | −20669.3 | − | 1098.51i | −0.710379 | − | 0.0377544i | ||||
\(947\) | 56380.9 | 1.93467 | 0.967336 | − | 0.253498i | \(-0.0815813\pi\) | ||||
0.967336 | + | 0.253498i | \(0.0815813\pi\) | |||||||
\(948\) | −25727.9 | − | 32261.7i | −0.881437 | − | 1.10529i | ||||
\(949\) | −33717.2 | + | 42280.0i | −1.15333 | + | 1.44623i | ||||
\(950\) | 1218.86 | − | 5340.17i | 0.0416263 | − | 0.182377i | ||||
\(951\) | −5115.56 | + | 2463.53i | −0.174431 | + | 0.0840014i | ||||
\(952\) | −116.623 | −0.00397035 | ||||||||
\(953\) | −7899.32 | −0.268504 | −0.134252 | − | 0.990947i | \(-0.542863\pi\) | ||||
−0.134252 | + | 0.990947i | \(0.542863\pi\) | |||||||
\(954\) | 2597.79 | − | 1251.03i | 0.0881619 | − | 0.0424565i | ||||
\(955\) | −5985.39 | − | 26223.7i | −0.202809 | − | 0.888564i | ||||
\(956\) | −42367.8 | − | 20403.3i | −1.43334 | − | 0.690261i | ||||
\(957\) | −3900.22 | − | 17088.0i | −0.131741 | − | 0.577195i | ||||
\(958\) | 26946.8 | + | 33790.3i | 0.908781 | + | 1.13958i | ||||
\(959\) | 4598.42 | − | 2214.48i | 0.154839 | − | 0.0745666i | ||||
\(960\) | −20954.0 | − | 26275.5i | −0.704466 | − | 0.883373i | ||||
\(961\) | −6585.28 | + | 28852.0i | −0.221049 | + | 0.968480i | ||||
\(962\) | 24054.6 | + | 11584.1i | 0.806186 | + | 0.388239i | ||||
\(963\) | −9354.75 | − | 4505.01i | −0.313035 | − | 0.150750i | ||||
\(964\) | 48397.9 | − | 60689.1i | 1.61700 | − | 2.02766i | ||||
\(965\) | 6411.19 | − | 28089.3i | 0.213869 | − | 0.937022i | ||||
\(966\) | −4556.15 | − | 19961.8i | −0.151751 | − | 0.664865i | ||||
\(967\) | 28717.7 | − | 36010.8i | 0.955014 | − | 1.19755i | −0.0252145 | − | 0.999682i | \(-0.508027\pi\) |
0.980229 | − | 0.197868i | \(-0.0634017\pi\) | |||||||
\(968\) | −8734.82 | + | 10953.1i | −0.290029 | + | 0.363684i | ||||
\(969\) | 22.5747 | + | 98.9062i | 0.000748404 | + | 0.00327897i | ||||
\(970\) | −8339.99 | + | 36539.9i | −0.276063 | + | 1.20951i | ||||
\(971\) | 29781.9 | − | 37345.3i | 0.984291 | − | 1.23426i | 0.0121353 | − | 0.999926i | \(-0.496137\pi\) |
0.972156 | − | 0.234336i | \(-0.0752914\pi\) | |||||||
\(972\) | 17024.7 | + | 8198.68i | 0.561799 | + | 0.270548i | ||||
\(973\) | −22852.7 | − | 11005.3i | −0.752954 | − | 0.362603i | ||||
\(974\) | −11788.9 | + | 51650.6i | −0.387825 | + | 1.69917i | ||||
\(975\) | −8453.02 | − | 10599.7i | −0.277655 | − | 0.348168i | ||||
\(976\) | 13739.3 | − | 6616.52i | 0.450600 | − | 0.216998i | ||||
\(977\) | −10974.5 | − | 13761.6i | −0.359372 | − | 0.450639i | 0.568974 | − | 0.822356i | \(-0.307341\pi\) |
−0.928346 | + | 0.371717i | \(0.878769\pi\) | |||||||
\(978\) | 4158.50 | + | 18219.6i | 0.135965 | + | 0.595703i | ||||
\(979\) | −13260.9 | − | 6386.10i | −0.432911 | − | 0.208479i | ||||
\(980\) | −4365.24 | − | 19125.4i | −0.142288 | − | 0.623406i | ||||
\(981\) | 12174.1 | − | 5862.71i | 0.396216 | − | 0.190807i | ||||
\(982\) | −65882.5 | −2.14093 | ||||||||
\(983\) | 35830.0 | 1.16256 | 0.581281 | − | 0.813703i | \(-0.302552\pi\) | ||||
0.581281 | + | 0.813703i | \(0.302552\pi\) | |||||||
\(984\) | 22184.3 | − | 10683.4i | 0.718708 | − | 0.346111i | ||||
\(985\) | −1185.10 | + | 5192.28i | −0.0383356 | + | 0.167959i | ||||
\(986\) | −442.803 | + | 555.257i | −0.0143019 | + | 0.0179341i | ||||
\(987\) | 12237.7 | + | 15345.6i | 0.394661 | + | 0.494889i | ||||
\(988\) | −25675.8 | −0.826777 | ||||||||
\(989\) | −15703.7 | + | 17679.0i | −0.504902 | + | 0.568411i | ||||
\(990\) | 4209.46 | 0.135137 | ||||||||
\(991\) | −10240.0 | − | 12840.5i | −0.328237 | − | 0.411596i | 0.590141 | − | 0.807300i | \(-0.299072\pi\) |
−0.918378 | + | 0.395704i | \(0.870501\pi\) | |||||||
\(992\) | 36238.7 | − | 45441.9i | 1.15986 | − | 1.45442i | ||||
\(993\) | 999.913 | − | 4380.90i | 0.0319550 | − | 0.140004i | ||||
\(994\) | −6345.73 | + | 3055.94i | −0.202489 | + | 0.0975137i | ||||
\(995\) | −28773.8 | −0.916776 | ||||||||
\(996\) | 43677.3 | 1.38952 | ||||||||
\(997\) | −21226.8 | + | 10222.3i | −0.674282 | + | 0.324717i | −0.739503 | − | 0.673154i | \(-0.764939\pi\) |
0.0652205 | + | 0.997871i | \(0.479225\pi\) | |||||||
\(998\) | −2620.45 | − | 11480.9i | −0.0831150 | − | 0.364150i | ||||
\(999\) | −11247.3 | − | 5416.42i | −0.356206 | − | 0.171540i |
(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 | 43.4.e.a.11.9 | yes | 60 | |
43.2 | odd | 14 | 1849.4.a.g.1.6 | 30 | |||
43.4 | even | 7 | inner | 43.4.e.a.4.9 | ✓ | 60 | |
43.41 | even | 7 | 1849.4.a.h.1.25 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.4.e.a.4.9 | ✓ | 60 | 43.4 | even | 7 | inner | |
43.4.e.a.11.9 | yes | 60 | 1.1 | even | 1 | trivial | |
1849.4.a.g.1.6 | 30 | 43.2 | odd | 14 | |||
1849.4.a.h.1.25 | 30 | 43.41 | even | 7 |