Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(161,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.o (of order \(6\), 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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 161.16 | ||
Character | \(\chi\) | \(=\) | 930.161 |
Dual form | 930.2.o.e.491.6 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.20548 | + | 1.24372i | 0.695982 | + | 0.718059i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.866025 | − | 0.500000i | −0.387298 | − | 0.223607i | ||||
\(6\) | −1.24372 | + | 1.20548i | −0.507745 | + | 0.492133i | ||||
\(7\) | 1.75266 | + | 3.03570i | 0.662443 | + | 1.14739i | 0.979972 | + | 0.199137i | \(0.0638138\pi\) |
−0.317528 | + | 0.948249i | \(0.602853\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.0936563 | + | 2.99854i | −0.0312188 | + | 0.999513i | ||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | −0.508798 | + | 0.881264i | −0.153408 | + | 0.265711i | −0.932478 | − | 0.361226i | \(-0.882358\pi\) |
0.779070 | + | 0.626937i | \(0.215692\pi\) | |||||||
\(12\) | −1.20548 | − | 1.24372i | −0.347991 | − | 0.359030i | ||||
\(13\) | −0.482279 | − | 0.278444i | −0.133760 | − | 0.0772264i | 0.431627 | − | 0.902052i | \(-0.357940\pi\) |
−0.565387 | + | 0.824826i | \(0.691273\pi\) | |||||||
\(14\) | −3.03570 | + | 1.75266i | −0.811324 | + | 0.468418i | ||||
\(15\) | −0.422115 | − | 1.67983i | −0.108990 | − | 0.433729i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.748115 | − | 1.29577i | −0.181445 | − | 0.314271i | 0.760928 | − | 0.648836i | \(-0.224744\pi\) |
−0.942373 | + | 0.334565i | \(0.891411\pi\) | |||||||
\(18\) | −2.99854 | − | 0.0936563i | −0.706762 | − | 0.0220750i | ||||
\(19\) | 2.58309 | + | 4.47405i | 0.592602 | + | 1.02642i | 0.993880 | + | 0.110461i | \(0.0352326\pi\) |
−0.401278 | + | 0.915956i | \(0.631434\pi\) | |||||||
\(20\) | 0.866025 | + | 0.500000i | 0.193649 | + | 0.111803i | ||||
\(21\) | −1.66275 | + | 5.83927i | −0.362843 | + | 1.27423i | ||||
\(22\) | −0.881264 | − | 0.508798i | −0.187886 | − | 0.108476i | ||||
\(23\) | −3.21814 | −0.671029 | −0.335515 | − | 0.942035i | \(-0.608910\pi\) | ||||
−0.335515 | + | 0.942035i | \(0.608910\pi\) | |||||||
\(24\) | 1.24372 | − | 1.20548i | 0.253872 | − | 0.246067i | ||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 0.278444 | − | 0.482279i | 0.0546073 | − | 0.0945827i | ||||
\(27\) | −3.84223 | + | 3.49818i | −0.739437 | + | 0.673226i | ||||
\(28\) | −1.75266 | − | 3.03570i | −0.331222 | − | 0.573693i | ||||
\(29\) | −2.64442 | −0.491056 | −0.245528 | − | 0.969389i | \(-0.578961\pi\) | ||||
−0.245528 | + | 0.969389i | \(0.578961\pi\) | |||||||
\(30\) | 1.67983 | − | 0.422115i | 0.306693 | − | 0.0770673i | ||||
\(31\) | 5.39138 | − | 1.39033i | 0.968320 | − | 0.249711i | ||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −1.70939 | + | 0.429543i | −0.297566 | + | 0.0747738i | ||||
\(34\) | 1.29577 | − | 0.748115i | 0.222223 | − | 0.128301i | ||||
\(35\) | − | 3.50532i | − | 0.592507i | ||||||
\(36\) | 0.0936563 | − | 2.99854i | 0.0156094 | − | 0.499756i | ||||
\(37\) | 2.08724 | − | 1.20507i | 0.343140 | − | 0.198112i | −0.318520 | − | 0.947916i | \(-0.603186\pi\) |
0.661660 | + | 0.749804i | \(0.269852\pi\) | |||||||
\(38\) | −4.47405 | + | 2.58309i | −0.725786 | + | 0.419033i | ||||
\(39\) | −0.235071 | − | 0.935475i | −0.0376414 | − | 0.149796i | ||||
\(40\) | −0.500000 | + | 0.866025i | −0.0790569 | + | 0.136931i | ||||
\(41\) | −7.86397 | − | 4.54027i | −1.22815 | − | 0.709070i | −0.261504 | − | 0.965202i | \(-0.584219\pi\) |
−0.966642 | + | 0.256132i | \(0.917552\pi\) | |||||||
\(42\) | −5.83927 | − | 1.66275i | −0.901019 | − | 0.256568i | ||||
\(43\) | −5.69715 | + | 3.28925i | −0.868807 | + | 0.501606i | −0.866952 | − | 0.498392i | \(-0.833924\pi\) |
−0.00185547 | + | 0.999998i | \(0.500591\pi\) | |||||||
\(44\) | 0.508798 | − | 0.881264i | 0.0767042 | − | 0.132856i | ||||
\(45\) | 1.58038 | − | 2.54998i | 0.235589 | − | 0.380129i | ||||
\(46\) | − | 3.21814i | − | 0.474489i | ||||||
\(47\) | 8.95636i | 1.30642i | 0.757177 | + | 0.653210i | \(0.226578\pi\) | ||||
−0.757177 | + | 0.653210i | \(0.773422\pi\) | |||||||
\(48\) | 1.20548 | + | 1.24372i | 0.173995 | + | 0.179515i | ||||
\(49\) | −2.64364 | + | 4.57892i | −0.377663 | + | 0.654131i | ||||
\(50\) | −0.866025 | + | 0.500000i | −0.122474 | + | 0.0707107i | ||||
\(51\) | 0.709739 | − | 2.49247i | 0.0993833 | − | 0.349015i | ||||
\(52\) | 0.482279 | + | 0.278444i | 0.0668800 | + | 0.0386132i | ||||
\(53\) | −1.80684 | + | 3.12954i | −0.248189 | + | 0.429876i | −0.963023 | − | 0.269418i | \(-0.913169\pi\) |
0.714834 | + | 0.699294i | \(0.246502\pi\) | |||||||
\(54\) | −3.49818 | − | 3.84223i | −0.476042 | − | 0.522861i | ||||
\(55\) | 0.881264 | − | 0.508798i | 0.118830 | − | 0.0686063i | ||||
\(56\) | 3.03570 | − | 1.75266i | 0.405662 | − | 0.234209i | ||||
\(57\) | −2.45059 | + | 8.60599i | −0.324588 | + | 1.13989i | ||||
\(58\) | − | 2.64442i | − | 0.347229i | ||||||
\(59\) | 8.22333 | − | 4.74774i | 1.07059 | − | 0.618103i | 0.142245 | − | 0.989832i | \(-0.454568\pi\) |
0.928342 | + | 0.371728i | \(0.121235\pi\) | |||||||
\(60\) | 0.422115 | + | 1.67983i | 0.0544948 | + | 0.216865i | ||||
\(61\) | 0.662787i | 0.0848612i | 0.999099 | + | 0.0424306i | \(0.0135101\pi\) | ||||
−0.999099 | + | 0.0424306i | \(0.986490\pi\) | |||||||
\(62\) | 1.39033 | + | 5.39138i | 0.176572 | + | 0.684706i | ||||
\(63\) | −9.26680 | + | 4.97111i | −1.16751 | + | 0.626301i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.278444 | + | 0.482279i | 0.0345367 | + | 0.0598193i | ||||
\(66\) | −0.429543 | − | 1.70939i | −0.0528730 | − | 0.210411i | ||||
\(67\) | 0.768714 | − | 1.33145i | 0.0939133 | − | 0.162663i | −0.815241 | − | 0.579122i | \(-0.803396\pi\) |
0.909155 | + | 0.416459i | \(0.136729\pi\) | |||||||
\(68\) | 0.748115 | + | 1.29577i | 0.0907223 | + | 0.157136i | ||||
\(69\) | −3.87939 | − | 4.00245i | −0.467024 | − | 0.481839i | ||||
\(70\) | 3.50532 | 0.418966 | ||||||||
\(71\) | 9.71728 | + | 5.61027i | 1.15323 | + | 0.665817i | 0.949672 | − | 0.313246i | \(-0.101416\pi\) |
0.203557 | + | 0.979063i | \(0.434750\pi\) | |||||||
\(72\) | 2.99854 | + | 0.0936563i | 0.353381 | + | 0.0110375i | ||||
\(73\) | −5.23937 | − | 3.02495i | −0.613222 | − | 0.354044i | 0.161003 | − | 0.986954i | \(-0.448527\pi\) |
−0.774225 | + | 0.632910i | \(0.781860\pi\) | |||||||
\(74\) | 1.20507 | + | 2.08724i | 0.140086 | + | 0.242637i | ||||
\(75\) | −0.474351 | + | 1.66583i | −0.0547734 | + | 0.192354i | ||||
\(76\) | −2.58309 | − | 4.47405i | −0.296301 | − | 0.513208i | ||||
\(77\) | −3.56700 | −0.406498 | ||||||||
\(78\) | 0.935475 | − | 0.235071i | 0.105922 | − | 0.0266165i | ||||
\(79\) | 0.184595 | − | 0.106576i | 0.0207686 | − | 0.0119907i | −0.489580 | − | 0.871959i | \(-0.662850\pi\) |
0.510348 | + | 0.859968i | \(0.329516\pi\) | |||||||
\(80\) | −0.866025 | − | 0.500000i | −0.0968246 | − | 0.0559017i | ||||
\(81\) | −8.98246 | − | 0.561664i | −0.998051 | − | 0.0624071i | ||||
\(82\) | 4.54027 | − | 7.86397i | 0.501389 | − | 0.868430i | ||||
\(83\) | −1.71612 | + | 2.97241i | −0.188369 | + | 0.326264i | −0.944707 | − | 0.327917i | \(-0.893653\pi\) |
0.756338 | + | 0.654181i | \(0.226987\pi\) | |||||||
\(84\) | 1.66275 | − | 5.83927i | 0.181421 | − | 0.637117i | ||||
\(85\) | 1.49623i | 0.162289i | ||||||||
\(86\) | −3.28925 | − | 5.69715i | −0.354689 | − | 0.614339i | ||||
\(87\) | −3.18778 | − | 3.28890i | −0.341766 | − | 0.352608i | ||||
\(88\) | 0.881264 | + | 0.508798i | 0.0939431 | + | 0.0542381i | ||||
\(89\) | 0.779533 | 0.0826303 | 0.0413152 | − | 0.999146i | \(-0.486845\pi\) | ||||
0.0413152 | + | 0.999146i | \(0.486845\pi\) | |||||||
\(90\) | 2.54998 | + | 1.58038i | 0.268792 | + | 0.166586i | ||||
\(91\) | − | 1.95207i | − | 0.204633i | ||||||
\(92\) | 3.21814 | 0.335515 | ||||||||
\(93\) | 8.22835 | + | 5.02933i | 0.853241 | + | 0.521518i | ||||
\(94\) | −8.95636 | −0.923778 | ||||||||
\(95\) | − | 5.16618i | − | 0.530039i | ||||||
\(96\) | −1.24372 | + | 1.20548i | −0.126936 | + | 0.123033i | ||||
\(97\) | 13.2793 | 1.34831 | 0.674155 | − | 0.738590i | \(-0.264508\pi\) | ||||
0.674155 | + | 0.738590i | \(0.264508\pi\) | |||||||
\(98\) | −4.57892 | − | 2.64364i | −0.462540 | − | 0.267048i | ||||
\(99\) | −2.59485 | − | 1.60819i | −0.260792 | − | 0.161629i | ||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | − | 17.5078i | − | 1.74209i | −0.491200 | − | 0.871047i | \(-0.663442\pi\) | ||
0.491200 | − | 0.871047i | \(-0.336558\pi\) | |||||||
\(102\) | 2.49247 | + | 0.709739i | 0.246791 | + | 0.0702746i | ||||
\(103\) | −0.217920 | + | 0.377449i | −0.0214723 | + | 0.0371911i | −0.876562 | − | 0.481289i | \(-0.840169\pi\) |
0.855090 | + | 0.518480i | \(0.173502\pi\) | |||||||
\(104\) | −0.278444 | + | 0.482279i | −0.0273037 | + | 0.0472913i | ||||
\(105\) | 4.35962 | − | 4.22558i | 0.425456 | − | 0.412374i | ||||
\(106\) | −3.12954 | − | 1.80684i | −0.303968 | − | 0.175496i | ||||
\(107\) | 15.5778 | − | 8.99386i | 1.50596 | − | 0.869469i | 0.505988 | − | 0.862540i | \(-0.331128\pi\) |
0.999976 | − | 0.00692852i | \(-0.00220543\pi\) | |||||||
\(108\) | 3.84223 | − | 3.49818i | 0.369719 | − | 0.336613i | ||||
\(109\) | 7.55577 | 0.723711 | 0.361856 | − | 0.932234i | \(-0.382143\pi\) | ||||
0.361856 | + | 0.932234i | \(0.382143\pi\) | |||||||
\(110\) | 0.508798 | + | 0.881264i | 0.0485120 | + | 0.0840252i | ||||
\(111\) | 4.01488 | + | 1.14325i | 0.381075 | + | 0.108513i | ||||
\(112\) | 1.75266 | + | 3.03570i | 0.165611 | + | 0.286846i | ||||
\(113\) | −4.18028 | − | 2.41348i | −0.393247 | − | 0.227041i | 0.290319 | − | 0.956930i | \(-0.406239\pi\) |
−0.683566 | + | 0.729889i | \(0.739572\pi\) | |||||||
\(114\) | −8.60599 | − | 2.45059i | −0.806025 | − | 0.229518i | ||||
\(115\) | 2.78699 | + | 1.60907i | 0.259888 | + | 0.150047i | ||||
\(116\) | 2.64442 | 0.245528 | ||||||||
\(117\) | 0.880093 | − | 1.42005i | 0.0813646 | − | 0.131284i | ||||
\(118\) | 4.74774 | + | 8.22333i | 0.437065 | + | 0.757019i | ||||
\(119\) | 2.62238 | − | 4.54210i | 0.240394 | − | 0.416374i | ||||
\(120\) | −1.67983 | + | 0.422115i | −0.153347 | + | 0.0385336i | ||||
\(121\) | 4.98225 | + | 8.62951i | 0.452932 | + | 0.784501i | ||||
\(122\) | −0.662787 | −0.0600059 | ||||||||
\(123\) | −3.83303 | − | 15.2537i | −0.345613 | − | 1.37538i | ||||
\(124\) | −5.39138 | + | 1.39033i | −0.484160 | + | 0.124855i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | −4.97111 | − | 9.26680i | −0.442861 | − | 0.825552i | ||||
\(127\) | 16.3303 | − | 9.42828i | 1.44908 | − | 0.836624i | 0.450650 | − | 0.892701i | \(-0.351192\pi\) |
0.998426 | + | 0.0560764i | \(0.0178590\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −10.9587 | − | 3.12052i | −0.964857 | − | 0.274747i | ||||
\(130\) | −0.482279 | + | 0.278444i | −0.0422987 | + | 0.0244211i | ||||
\(131\) | 0.711541 | − | 0.410808i | 0.0621676 | − | 0.0358925i | −0.468594 | − | 0.883414i | \(-0.655239\pi\) |
0.530762 | + | 0.847521i | \(0.321906\pi\) | |||||||
\(132\) | 1.70939 | − | 0.429543i | 0.148783 | − | 0.0373869i | ||||
\(133\) | −9.05457 | + | 15.6830i | −0.785131 | + | 1.35989i | ||||
\(134\) | 1.33145 | + | 0.768714i | 0.115020 | + | 0.0664067i | ||||
\(135\) | 5.07656 | − | 1.10840i | 0.436921 | − | 0.0953960i | ||||
\(136\) | −1.29577 | + | 0.748115i | −0.111112 | + | 0.0641503i | ||||
\(137\) | −9.97643 | + | 17.2797i | −0.852344 | + | 1.47630i | 0.0267437 | + | 0.999642i | \(0.491486\pi\) |
−0.879087 | + | 0.476660i | \(0.841847\pi\) | |||||||
\(138\) | 4.00245 | − | 3.87939i | 0.340712 | − | 0.330236i | ||||
\(139\) | − | 1.22089i | − | 0.103555i | −0.998659 | − | 0.0517773i | \(-0.983511\pi\) | ||
0.998659 | − | 0.0517773i | \(-0.0164886\pi\) | |||||||
\(140\) | 3.50532i | 0.296254i | ||||||||
\(141\) | −11.1392 | + | 10.7967i | −0.938087 | + | 0.909244i | ||||
\(142\) | −5.61027 | + | 9.71728i | −0.470804 | + | 0.815456i | ||||
\(143\) | 0.490765 | − | 0.283343i | 0.0410398 | − | 0.0236944i | ||||
\(144\) | −0.0936563 | + | 2.99854i | −0.00780469 | + | 0.249878i | ||||
\(145\) | 2.29013 | + | 1.32221i | 0.190185 | + | 0.109804i | ||||
\(146\) | 3.02495 | − | 5.23937i | 0.250347 | − | 0.433614i | ||||
\(147\) | −8.88171 | + | 2.23184i | −0.732551 | + | 0.184079i | ||||
\(148\) | −2.08724 | + | 1.20507i | −0.171570 | + | 0.0990560i | ||||
\(149\) | 16.6142 | − | 9.59220i | 1.36109 | − | 0.785823i | 0.371317 | − | 0.928506i | \(-0.378906\pi\) |
0.989768 | + | 0.142683i | \(0.0455728\pi\) | |||||||
\(150\) | −1.66583 | − | 0.474351i | −0.136014 | − | 0.0387306i | ||||
\(151\) | 23.3009i | 1.89620i | 0.317971 | + | 0.948100i | \(0.396998\pi\) | ||||
−0.317971 | + | 0.948100i | \(0.603002\pi\) | |||||||
\(152\) | 4.47405 | − | 2.58309i | 0.362893 | − | 0.209516i | ||||
\(153\) | 3.95549 | − | 2.12189i | 0.319783 | − | 0.171545i | ||||
\(154\) | − | 3.56700i | − | 0.287437i | ||||||
\(155\) | −5.36424 | − | 1.49163i | −0.430866 | − | 0.119810i | ||||
\(156\) | 0.235071 | + | 0.935475i | 0.0188207 | + | 0.0748979i | ||||
\(157\) | 10.7418 | 0.857290 | 0.428645 | − | 0.903473i | \(-0.358991\pi\) | ||||
0.428645 | + | 0.903473i | \(0.358991\pi\) | |||||||
\(158\) | 0.106576 | + | 0.184595i | 0.00847874 | + | 0.0146856i | ||||
\(159\) | −6.07037 | + | 1.52539i | −0.481411 | + | 0.120971i | ||||
\(160\) | 0.500000 | − | 0.866025i | 0.0395285 | − | 0.0684653i | ||||
\(161\) | −5.64031 | − | 9.76931i | −0.444519 | − | 0.769929i | ||||
\(162\) | 0.561664 | − | 8.98246i | 0.0441285 | − | 0.705728i | ||||
\(163\) | −3.56174 | −0.278977 | −0.139488 | − | 0.990224i | \(-0.544546\pi\) | ||||
−0.139488 | + | 0.990224i | \(0.544546\pi\) | |||||||
\(164\) | 7.86397 | + | 4.54027i | 0.614073 | + | 0.354535i | ||||
\(165\) | 1.69514 | + | 0.482698i | 0.131967 | + | 0.0375780i | ||||
\(166\) | −2.97241 | − | 1.71612i | −0.230704 | − | 0.133197i | ||||
\(167\) | 5.75062 | + | 9.96036i | 0.444996 | + | 0.770756i | 0.998052 | − | 0.0623883i | \(-0.0198717\pi\) |
−0.553056 | + | 0.833144i | \(0.686538\pi\) | |||||||
\(168\) | 5.83927 | + | 1.66275i | 0.450509 | + | 0.128284i | ||||
\(169\) | −6.34494 | − | 10.9898i | −0.488072 | − | 0.845366i | ||||
\(170\) | −1.49623 | −0.114756 | ||||||||
\(171\) | −13.6575 | + | 7.32648i | −1.04442 | + | 0.560270i | ||||
\(172\) | 5.69715 | − | 3.28925i | 0.434404 | − | 0.250803i | ||||
\(173\) | −2.03876 | − | 1.17708i | −0.155004 | − | 0.0894917i | 0.420492 | − | 0.907296i | \(-0.361858\pi\) |
−0.575496 | + | 0.817805i | \(0.695191\pi\) | |||||||
\(174\) | 3.28890 | − | 3.18778i | 0.249331 | − | 0.241665i | ||||
\(175\) | −1.75266 | + | 3.03570i | −0.132489 | + | 0.229477i | ||||
\(176\) | −0.508798 | + | 0.881264i | −0.0383521 | + | 0.0664278i | ||||
\(177\) | 15.8179 | + | 4.50419i | 1.18894 | + | 0.338556i | ||||
\(178\) | 0.779533i | 0.0584285i | ||||||||
\(179\) | −1.49415 | − | 2.58794i | −0.111678 | − | 0.193432i | 0.804769 | − | 0.593588i | \(-0.202289\pi\) |
−0.916447 | + | 0.400156i | \(0.868956\pi\) | |||||||
\(180\) | −1.58038 | + | 2.54998i | −0.117794 | + | 0.190064i | ||||
\(181\) | 18.9344 | + | 10.9318i | 1.40738 | + | 0.812552i | 0.995135 | − | 0.0985208i | \(-0.0314111\pi\) |
0.412246 | + | 0.911073i | \(0.364744\pi\) | |||||||
\(182\) | 1.95207 | 0.144697 | ||||||||
\(183\) | −0.824318 | + | 0.798974i | −0.0609354 | + | 0.0590618i | ||||
\(184\) | 3.21814i | 0.237245i | ||||||||
\(185\) | −2.41014 | −0.177197 | ||||||||
\(186\) | −5.02933 | + | 8.22835i | −0.368769 | + | 0.603332i | ||||
\(187\) | 1.52256 | 0.111340 | ||||||||
\(188\) | − | 8.95636i | − | 0.653210i | ||||||
\(189\) | −17.3535 | − | 5.53271i | −1.26228 | − | 0.402446i | ||||
\(190\) | 5.16618 | 0.374794 | ||||||||
\(191\) | 8.08961 | + | 4.67054i | 0.585343 | + | 0.337948i | 0.763254 | − | 0.646099i | \(-0.223600\pi\) |
−0.177911 | + | 0.984047i | \(0.556934\pi\) | |||||||
\(192\) | −1.20548 | − | 1.24372i | −0.0869977 | − | 0.0897574i | ||||
\(193\) | −0.846405 | − | 1.46602i | −0.0609256 | − | 0.105526i | 0.833954 | − | 0.551834i | \(-0.186072\pi\) |
−0.894879 | + | 0.446308i | \(0.852739\pi\) | |||||||
\(194\) | 13.2793i | 0.953400i | ||||||||
\(195\) | −0.264160 | + | 0.927680i | −0.0189169 | + | 0.0664326i | ||||
\(196\) | 2.64364 | − | 4.57892i | 0.188831 | − | 0.327065i | ||||
\(197\) | −7.92946 | + | 13.7342i | −0.564951 | + | 0.978524i | 0.432103 | + | 0.901824i | \(0.357772\pi\) |
−0.997054 | + | 0.0766996i | \(0.975562\pi\) | |||||||
\(198\) | 1.60819 | − | 2.59485i | 0.114289 | − | 0.184408i | ||||
\(199\) | −11.7826 | − | 6.80268i | −0.835246 | − | 0.482229i | 0.0203995 | − | 0.999792i | \(-0.493506\pi\) |
−0.855645 | + | 0.517562i | \(0.826840\pi\) | |||||||
\(200\) | 0.866025 | − | 0.500000i | 0.0612372 | − | 0.0353553i | ||||
\(201\) | 2.58261 | − | 0.648971i | 0.182163 | − | 0.0457749i | ||||
\(202\) | 17.5078 | 1.23185 | ||||||||
\(203\) | −4.63477 | − | 8.02765i | −0.325297 | − | 0.563431i | ||||
\(204\) | −0.709739 | + | 2.49247i | −0.0496917 | + | 0.174508i | ||||
\(205\) | 4.54027 | + | 7.86397i | 0.317106 | + | 0.549244i | ||||
\(206\) | −0.377449 | − | 0.217920i | −0.0262981 | − | 0.0151832i | ||||
\(207\) | 0.301399 | − | 9.64972i | 0.0209487 | − | 0.670702i | ||||
\(208\) | −0.482279 | − | 0.278444i | −0.0334400 | − | 0.0193066i | ||||
\(209\) | −5.25709 | −0.363641 | ||||||||
\(210\) | 4.22558 | + | 4.35962i | 0.291593 | + | 0.300843i | ||||
\(211\) | −4.46360 | − | 7.73118i | −0.307287 | − | 0.532236i | 0.670481 | − | 0.741927i | \(-0.266088\pi\) |
−0.977768 | + | 0.209690i | \(0.932754\pi\) | |||||||
\(212\) | 1.80684 | − | 3.12954i | 0.124094 | − | 0.214938i | ||||
\(213\) | 4.73636 | + | 18.8486i | 0.324530 | + | 1.29148i | ||||
\(214\) | 8.99386 | + | 15.5778i | 0.614807 | + | 1.06488i | ||||
\(215\) | 6.57850 | 0.448650 | ||||||||
\(216\) | 3.49818 | + | 3.84223i | 0.238021 | + | 0.261431i | ||||
\(217\) | 13.6699 | + | 13.9298i | 0.927972 | + | 0.945618i | ||||
\(218\) | 7.55577i | 0.511741i | ||||||||
\(219\) | −2.55376 | − | 10.1628i | −0.172567 | − | 0.686738i | ||||
\(220\) | −0.881264 | + | 0.508798i | −0.0594148 | + | 0.0343032i | ||||
\(221\) | 0.833232i | 0.0560493i | ||||||||
\(222\) | −1.14325 | + | 4.01488i | −0.0767300 | + | 0.269461i | ||||
\(223\) | 6.97582 | − | 4.02749i | 0.467136 | − | 0.269701i | −0.247904 | − | 0.968785i | \(-0.579742\pi\) |
0.715040 | + | 0.699084i | \(0.246408\pi\) | |||||||
\(224\) | −3.03570 | + | 1.75266i | −0.202831 | + | 0.117105i | ||||
\(225\) | −2.64364 | + | 1.41816i | −0.176243 | + | 0.0945440i | ||||
\(226\) | 2.41348 | − | 4.18028i | 0.160543 | − | 0.278068i | ||||
\(227\) | 15.0890 | + | 8.71161i | 1.00149 | + | 0.578210i | 0.908689 | − | 0.417475i | \(-0.137085\pi\) |
0.0928007 | + | 0.995685i | \(0.470418\pi\) | |||||||
\(228\) | 2.45059 | − | 8.60599i | 0.162294 | − | 0.569945i | ||||
\(229\) | −12.2125 | + | 7.05087i | −0.807023 | + | 0.465935i | −0.845921 | − | 0.533308i | \(-0.820949\pi\) |
0.0388982 | + | 0.999243i | \(0.487615\pi\) | |||||||
\(230\) | −1.60907 | + | 2.78699i | −0.106099 | + | 0.183769i | ||||
\(231\) | −4.29993 | − | 4.43634i | −0.282915 | − | 0.291889i | ||||
\(232\) | 2.64442i | 0.173615i | ||||||||
\(233\) | 2.39244i | 0.156734i | 0.996925 | + | 0.0783669i | \(0.0249706\pi\) | ||||
−0.996925 | + | 0.0783669i | \(0.975029\pi\) | |||||||
\(234\) | 1.42005 | + | 0.880093i | 0.0928318 | + | 0.0575335i | ||||
\(235\) | 4.47818 | − | 7.75644i | 0.292124 | − | 0.505974i | ||||
\(236\) | −8.22333 | + | 4.74774i | −0.535293 | + | 0.309052i | ||||
\(237\) | 0.355075 | + | 0.101109i | 0.0230646 | + | 0.00656774i | ||||
\(238\) | 4.54210 | + | 2.62238i | 0.294421 | + | 0.169984i | ||||
\(239\) | 5.50979 | − | 9.54323i | 0.356398 | − | 0.617300i | −0.630958 | − | 0.775817i | \(-0.717338\pi\) |
0.987356 | + | 0.158517i | \(0.0506712\pi\) | |||||||
\(240\) | −0.422115 | − | 1.67983i | −0.0272474 | − | 0.108432i | ||||
\(241\) | 21.5818 | − | 12.4602i | 1.39020 | − | 0.802634i | 0.396866 | − | 0.917877i | \(-0.370098\pi\) |
0.993337 | + | 0.115243i | \(0.0367646\pi\) | |||||||
\(242\) | −8.62951 | + | 4.98225i | −0.554726 | + | 0.320271i | ||||
\(243\) | −10.1296 | − | 11.8487i | −0.649813 | − | 0.760094i | ||||
\(244\) | − | 0.662787i | − | 0.0424306i | ||||||
\(245\) | 4.57892 | − | 2.64364i | 0.292536 | − | 0.168896i | ||||
\(246\) | 15.2537 | − | 3.83303i | 0.972542 | − | 0.244385i | ||||
\(247\) | − | 2.87698i | − | 0.183058i | ||||||
\(248\) | −1.39033 | − | 5.39138i | −0.0882861 | − | 0.342353i | ||||
\(249\) | −5.76557 | + | 1.44880i | −0.365378 | + | 0.0918140i | ||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −6.60787 | − | 11.4452i | −0.417085 | − | 0.722413i | 0.578560 | − | 0.815640i | \(-0.303615\pi\) |
−0.995645 | + | 0.0932274i | \(0.970282\pi\) | |||||||
\(252\) | 9.26680 | − | 4.97111i | 0.583754 | − | 0.313150i | ||||
\(253\) | 1.63739 | − | 2.83603i | 0.102942 | − | 0.178300i | ||||
\(254\) | 9.42828 | + | 16.3303i | 0.591583 | + | 1.02465i | ||||
\(255\) | −1.86088 | + | 1.80367i | −0.116533 | + | 0.112950i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 22.1051 | + | 12.7624i | 1.37888 | + | 0.796096i | 0.992025 | − | 0.126044i | \(-0.0402281\pi\) |
0.386855 | + | 0.922141i | \(0.373561\pi\) | |||||||
\(258\) | 3.12052 | − | 10.9587i | 0.194275 | − | 0.682257i | ||||
\(259\) | 7.31644 | + | 4.22415i | 0.454622 | + | 0.262476i | ||||
\(260\) | −0.278444 | − | 0.482279i | −0.0172684 | − | 0.0299097i | ||||
\(261\) | 0.247667 | − | 7.92939i | 0.0153302 | − | 0.490817i | ||||
\(262\) | 0.410808 | + | 0.711541i | 0.0253798 | + | 0.0439591i | ||||
\(263\) | 17.3755 | 1.07142 | 0.535709 | − | 0.844403i | \(-0.320044\pi\) | ||||
0.535709 | + | 0.844403i | \(0.320044\pi\) | |||||||
\(264\) | 0.429543 | + | 1.70939i | 0.0264365 | + | 0.105205i | ||||
\(265\) | 3.12954 | − | 1.80684i | 0.192246 | − | 0.110993i | ||||
\(266\) | −15.6830 | − | 9.05457i | −0.961585 | − | 0.555171i | ||||
\(267\) | 0.939708 | + | 0.969517i | 0.0575092 | + | 0.0593335i | ||||
\(268\) | −0.768714 | + | 1.33145i | −0.0469567 | + | 0.0813313i | ||||
\(269\) | −5.43030 | + | 9.40555i | −0.331091 | + | 0.573466i | −0.982726 | − | 0.185066i | \(-0.940750\pi\) |
0.651635 | + | 0.758533i | \(0.274083\pi\) | |||||||
\(270\) | 1.10840 | + | 5.07656i | 0.0674551 | + | 0.308950i | ||||
\(271\) | 0.444297i | 0.0269891i | 0.999909 | + | 0.0134945i | \(0.00429558\pi\) | ||||
−0.999909 | + | 0.0134945i | \(0.995704\pi\) | |||||||
\(272\) | −0.748115 | − | 1.29577i | −0.0453611 | − | 0.0785678i | ||||
\(273\) | 2.42782 | − | 2.35317i | 0.146938 | − | 0.142421i | ||||
\(274\) | −17.2797 | − | 9.97643i | −1.04390 | − | 0.602698i | ||||
\(275\) | −1.01760 | −0.0613634 | ||||||||
\(276\) | 3.87939 | + | 4.00245i | 0.233512 | + | 0.240919i | ||||
\(277\) | 8.03697i | 0.482895i | 0.970414 | + | 0.241447i | \(0.0776221\pi\) | ||||
−0.970414 | + | 0.241447i | \(0.922378\pi\) | |||||||
\(278\) | 1.22089 | 0.0732242 | ||||||||
\(279\) | 3.66402 | + | 16.2965i | 0.219359 | + | 0.975644i | ||||
\(280\) | −3.50532 | −0.209483 | ||||||||
\(281\) | − | 13.9273i | − | 0.830831i | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||
0.909632 | − | 0.415415i | \(-0.136364\pi\) | |||||||
\(282\) | −10.7967 | − | 11.1392i | −0.642933 | − | 0.663328i | ||||
\(283\) | −28.1351 | −1.67246 | −0.836230 | − | 0.548379i | \(-0.815245\pi\) | ||||
−0.836230 | + | 0.548379i | \(0.815245\pi\) | |||||||
\(284\) | −9.71728 | − | 5.61027i | −0.576614 | − | 0.332909i | ||||
\(285\) | 6.42526 | − | 6.22771i | 0.380600 | − | 0.368898i | ||||
\(286\) | 0.283343 | + | 0.490765i | 0.0167544 | + | 0.0290195i | ||||
\(287\) | − | 31.8302i | − | 1.87888i | ||||||
\(288\) | −2.99854 | − | 0.0936563i | −0.176691 | − | 0.00551875i | ||||
\(289\) | 7.38065 | − | 12.7837i | 0.434156 | − | 0.751980i | ||||
\(290\) | −1.32221 | + | 2.29013i | −0.0776428 | + | 0.134481i | ||||
\(291\) | 16.0079 | + | 16.5157i | 0.938400 | + | 0.968167i | ||||
\(292\) | 5.23937 | + | 3.02495i | 0.306611 | + | 0.177022i | ||||
\(293\) | 19.0627 | − | 11.0058i | 1.11365 | − | 0.642968i | 0.173880 | − | 0.984767i | \(-0.444370\pi\) |
0.939773 | + | 0.341799i | \(0.111036\pi\) | |||||||
\(294\) | −2.23184 | − | 8.88171i | −0.130163 | − | 0.517992i | ||||
\(295\) | −9.49548 | −0.552848 | ||||||||
\(296\) | −1.20507 | − | 2.08724i | −0.0700431 | − | 0.121318i | ||||
\(297\) | −1.12790 | − | 5.16589i | −0.0654477 | − | 0.299755i | ||||
\(298\) | 9.59220 | + | 16.6142i | 0.555661 | + | 0.962433i | ||||
\(299\) | 1.55204 | + | 0.896072i | 0.0897569 | + | 0.0518212i | ||||
\(300\) | 0.474351 | − | 1.66583i | 0.0273867 | − | 0.0961768i | ||||
\(301\) | −19.9703 | − | 11.5299i | −1.15107 | − | 0.664571i | ||||
\(302\) | −23.3009 | −1.34082 | ||||||||
\(303\) | 21.7748 | − | 21.1053i | 1.25093 | − | 1.21247i | ||||
\(304\) | 2.58309 | + | 4.47405i | 0.148151 | + | 0.256604i | ||||
\(305\) | 0.331394 | − | 0.573990i | 0.0189755 | − | 0.0328666i | ||||
\(306\) | 2.12189 | + | 3.95549i | 0.121301 | + | 0.226120i | ||||
\(307\) | −2.89082 | − | 5.00704i | −0.164988 | − | 0.285767i | 0.771663 | − | 0.636031i | \(-0.219425\pi\) |
−0.936651 | + | 0.350264i | \(0.886092\pi\) | |||||||
\(308\) | 3.56700 | 0.203249 | ||||||||
\(309\) | −0.732136 | + | 0.183975i | −0.0416498 | + | 0.0104660i | ||||
\(310\) | 1.49163 | − | 5.36424i | 0.0847188 | − | 0.304668i | ||||
\(311\) | − | 0.448742i | − | 0.0254458i | −0.999919 | − | 0.0127229i | \(-0.995950\pi\) | ||
0.999919 | − | 0.0127229i | \(-0.00404994\pi\) | |||||||
\(312\) | −0.935475 | + | 0.235071i | −0.0529608 | + | 0.0133082i | ||||
\(313\) | 15.1343 | − | 8.73777i | 0.855439 | − | 0.493888i | −0.00704303 | − | 0.999975i | \(-0.502242\pi\) |
0.862482 | + | 0.506087i | \(0.168909\pi\) | |||||||
\(314\) | 10.7418i | 0.606196i | ||||||||
\(315\) | 10.5108 | + | 0.328295i | 0.592219 | + | 0.0184974i | ||||
\(316\) | −0.184595 | + | 0.106576i | −0.0103843 | + | 0.00599537i | ||||
\(317\) | −1.12178 | + | 0.647660i | −0.0630055 | + | 0.0363762i | −0.531172 | − | 0.847264i | \(-0.678248\pi\) |
0.468166 | + | 0.883640i | \(0.344915\pi\) | |||||||
\(318\) | −1.52539 | − | 6.07037i | −0.0855397 | − | 0.340409i | ||||
\(319\) | 1.34548 | − | 2.33043i | 0.0753322 | − | 0.130479i | ||||
\(320\) | 0.866025 | + | 0.500000i | 0.0484123 | + | 0.0279508i | ||||
\(321\) | 29.9645 | + | 8.53249i | 1.67245 | + | 0.476237i | ||||
\(322\) | 9.76931 | − | 5.64031i | 0.544422 | − | 0.314322i | ||||
\(323\) | 3.86490 | − | 6.69421i | 0.215049 | − | 0.372476i | ||||
\(324\) | 8.98246 | + | 0.561664i | 0.499025 | + | 0.0312036i | ||||
\(325\) | − | 0.556888i | − | 0.0308906i | ||||||
\(326\) | − | 3.56174i | − | 0.197266i | ||||||
\(327\) | 9.10829 | + | 9.39723i | 0.503690 | + | 0.519668i | ||||
\(328\) | −4.54027 | + | 7.86397i | −0.250694 | + | 0.434215i | ||||
\(329\) | −27.1888 | + | 15.6975i | −1.49897 | + | 0.865429i | ||||
\(330\) | −0.482698 | + | 1.69514i | −0.0265717 | + | 0.0933145i | ||||
\(331\) | −17.5084 | − | 10.1085i | −0.962351 | − | 0.555614i | −0.0654553 | − | 0.997856i | \(-0.520850\pi\) |
−0.896896 | + | 0.442242i | \(0.854183\pi\) | |||||||
\(332\) | 1.71612 | − | 2.97241i | 0.0941844 | − | 0.163132i | ||||
\(333\) | 3.41796 | + | 6.37153i | 0.187303 | + | 0.349158i | ||||
\(334\) | −9.96036 | + | 5.75062i | −0.545007 | + | 0.314660i | ||||
\(335\) | −1.33145 | + | 0.768714i | −0.0727449 | + | 0.0419993i | ||||
\(336\) | −1.66275 | + | 5.83927i | −0.0907106 | + | 0.318558i | ||||
\(337\) | 11.8084i | 0.643243i | 0.946868 | + | 0.321622i | \(0.104228\pi\) | ||||
−0.946868 | + | 0.321622i | \(0.895772\pi\) | |||||||
\(338\) | 10.9898 | − | 6.34494i | 0.597764 | − | 0.345119i | ||||
\(339\) | −2.03753 | − | 8.10847i | −0.110664 | − | 0.440392i | ||||
\(340\) | − | 1.49623i | − | 0.0811445i | ||||||
\(341\) | −1.51788 | + | 5.45863i | −0.0821976 | + | 0.295601i | ||||
\(342\) | −7.32648 | − | 13.6575i | −0.396171 | − | 0.738514i | ||||
\(343\) | 6.00365 | 0.324166 | ||||||||
\(344\) | 3.28925 | + | 5.69715i | 0.177345 | + | 0.307170i | ||||
\(345\) | 1.35843 | + | 5.40592i | 0.0731352 | + | 0.291045i | ||||
\(346\) | 1.17708 | − | 2.03876i | 0.0632802 | − | 0.109605i | ||||
\(347\) | −2.75581 | − | 4.77321i | −0.147940 | − | 0.256239i | 0.782526 | − | 0.622618i | \(-0.213931\pi\) |
−0.930466 | + | 0.366379i | \(0.880598\pi\) | |||||||
\(348\) | 3.18778 | + | 3.28890i | 0.170883 | + | 0.176304i | ||||
\(349\) | −21.0390 | −1.12619 | −0.563095 | − | 0.826392i | \(-0.690390\pi\) | ||||
−0.563095 | + | 0.826392i | \(0.690390\pi\) | |||||||
\(350\) | −3.03570 | − | 1.75266i | −0.162265 | − | 0.0936836i | ||||
\(351\) | 2.82707 | − | 0.617255i | 0.150898 | − | 0.0329466i | ||||
\(352\) | −0.881264 | − | 0.508798i | −0.0469715 | − | 0.0271190i | ||||
\(353\) | 12.9487 | + | 22.4278i | 0.689189 | + | 1.19371i | 0.972101 | + | 0.234564i | \(0.0753664\pi\) |
−0.282912 | + | 0.959146i | \(0.591300\pi\) | |||||||
\(354\) | −4.50419 | + | 15.8179i | −0.239395 | + | 0.840710i | ||||
\(355\) | −5.61027 | − | 9.71728i | −0.297762 | − | 0.515740i | ||||
\(356\) | −0.779533 | −0.0413152 | ||||||||
\(357\) | 8.81030 | − | 2.21389i | 0.466291 | − | 0.117172i | ||||
\(358\) | 2.58794 | − | 1.49415i | 0.136777 | − | 0.0789683i | ||||
\(359\) | −7.88537 | − | 4.55262i | −0.416174 | − | 0.240278i | 0.277265 | − | 0.960793i | \(-0.410572\pi\) |
−0.693439 | + | 0.720515i | \(0.743905\pi\) | |||||||
\(360\) | −2.54998 | − | 1.58038i | −0.134396 | − | 0.0832932i | ||||
\(361\) | −3.84473 | + | 6.65927i | −0.202354 | + | 0.350488i | ||||
\(362\) | −10.9318 | + | 18.9344i | −0.574561 | + | 0.995169i | ||||
\(363\) | −4.72667 | + | 16.5992i | −0.248086 | + | 0.871230i | ||||
\(364\) | 1.95207i | 0.102316i | ||||||||
\(365\) | 3.02495 | + | 5.23937i | 0.158333 | + | 0.274241i | ||||
\(366\) | −0.798974 | − | 0.824318i | −0.0417630 | − | 0.0430878i | ||||
\(367\) | −29.0390 | − | 16.7657i | −1.51582 | − | 0.875162i | −0.999828 | − | 0.0185717i | \(-0.994088\pi\) |
−0.515997 | − | 0.856590i | \(-0.672579\pi\) | |||||||
\(368\) | −3.21814 | −0.167757 | ||||||||
\(369\) | 14.3507 | − | 23.1552i | 0.747066 | − | 1.20541i | ||||
\(370\) | − | 2.41014i | − | 0.125297i | ||||||
\(371\) | −12.6671 | −0.657645 | ||||||||
\(372\) | −8.22835 | − | 5.02933i | −0.426620 | − | 0.260759i | ||||
\(373\) | −23.3875 | −1.21096 | −0.605479 | − | 0.795862i | \(-0.707018\pi\) | ||||
−0.605479 | + | 0.795862i | \(0.707018\pi\) | |||||||
\(374\) | 1.52256i | 0.0787296i | ||||||||
\(375\) | 1.24372 | − | 1.20548i | 0.0642252 | − | 0.0622505i | ||||
\(376\) | 8.95636 | 0.461889 | ||||||||
\(377\) | 1.27535 | + | 0.736322i | 0.0656837 | + | 0.0379225i | ||||
\(378\) | 5.53271 | − | 17.3535i | 0.284572 | − | 0.892570i | ||||
\(379\) | −5.80353 | − | 10.0520i | −0.298107 | − | 0.516337i | 0.677596 | − | 0.735435i | \(-0.263022\pi\) |
−0.975703 | + | 0.219098i | \(0.929689\pi\) | |||||||
\(380\) | 5.16618i | 0.265020i | ||||||||
\(381\) | 31.4118 | + | 8.94463i | 1.60928 | + | 0.458247i | ||||
\(382\) | −4.67054 | + | 8.08961i | −0.238965 | + | 0.413900i | ||||
\(383\) | −1.14352 | + | 1.98063i | −0.0584311 | + | 0.101206i | −0.893761 | − | 0.448543i | \(-0.851943\pi\) |
0.835330 | + | 0.549749i | \(0.185276\pi\) | |||||||
\(384\) | 1.24372 | − | 1.20548i | 0.0634681 | − | 0.0615167i | ||||
\(385\) | 3.08911 | + | 1.78350i | 0.157436 | + | 0.0908956i | ||||
\(386\) | 1.46602 | − | 0.846405i | 0.0746183 | − | 0.0430809i | ||||
\(387\) | −9.32937 | − | 17.3912i | −0.474238 | − | 0.884043i | ||||
\(388\) | −13.2793 | −0.674155 | ||||||||
\(389\) | −1.40760 | − | 2.43804i | −0.0713684 | − | 0.123614i | 0.828133 | − | 0.560532i | \(-0.189403\pi\) |
−0.899501 | + | 0.436918i | \(0.856070\pi\) | |||||||
\(390\) | −0.927680 | − | 0.264160i | −0.0469749 | − | 0.0133763i | ||||
\(391\) | 2.40754 | + | 4.16998i | 0.121755 | + | 0.210885i | ||||
\(392\) | 4.57892 | + | 2.64364i | 0.231270 | + | 0.133524i | ||||
\(393\) | 1.36867 | + | 0.389735i | 0.0690405 | + | 0.0196595i | ||||
\(394\) | −13.7342 | − | 7.92946i | −0.691921 | − | 0.399481i | ||||
\(395\) | −0.213152 | −0.0107248 | ||||||||
\(396\) | 2.59485 | + | 1.60819i | 0.130396 | + | 0.0808144i | ||||
\(397\) | −2.67976 | − | 4.64148i | −0.134493 | − | 0.232949i | 0.790910 | − | 0.611932i | \(-0.209607\pi\) |
−0.925404 | + | 0.378983i | \(0.876274\pi\) | |||||||
\(398\) | 6.80268 | − | 11.7826i | 0.340988 | − | 0.590608i | ||||
\(399\) | −30.4202 | + | 7.64414i | −1.52292 | + | 0.382685i | ||||
\(400\) | 0.500000 | + | 0.866025i | 0.0250000 | + | 0.0433013i | ||||
\(401\) | −11.7824 | −0.588384 | −0.294192 | − | 0.955746i | \(-0.595050\pi\) | ||||
−0.294192 | + | 0.955746i | \(0.595050\pi\) | |||||||
\(402\) | 0.648971 | + | 2.58261i | 0.0323677 | + | 0.128809i | ||||
\(403\) | −2.98728 | − | 0.830669i | −0.148807 | − | 0.0413786i | ||||
\(404\) | 17.5078i | 0.871047i | ||||||||
\(405\) | 7.49820 | + | 4.97764i | 0.372589 | + | 0.247341i | ||||
\(406\) | 8.02765 | − | 4.63477i | 0.398406 | − | 0.230020i | ||||
\(407\) | 2.45255i | 0.121568i | ||||||||
\(408\) | −2.49247 | − | 0.709739i | −0.123395 | − | 0.0351373i | ||||
\(409\) | −0.573155 | + | 0.330911i | −0.0283407 | + | 0.0163625i | −0.514103 | − | 0.857728i | \(-0.671875\pi\) |
0.485763 | + | 0.874091i | \(0.338542\pi\) | |||||||
\(410\) | −7.86397 | + | 4.54027i | −0.388374 | + | 0.224228i | ||||
\(411\) | −33.5173 | + | 8.42240i | −1.65329 | + | 0.415446i | ||||
\(412\) | 0.217920 | − | 0.377449i | 0.0107362 | − | 0.0185956i | ||||
\(413\) | 28.8254 | + | 16.6424i | 1.41841 | + | 0.818917i | ||||
\(414\) | 9.64972 | + | 0.301399i | 0.474258 | + | 0.0148130i | ||||
\(415\) | 2.97241 | − | 1.71612i | 0.145910 | − | 0.0842411i | ||||
\(416\) | 0.278444 | − | 0.482279i | 0.0136518 | − | 0.0236457i | ||||
\(417\) | 1.51844 | − | 1.47176i | 0.0743584 | − | 0.0720722i | ||||
\(418\) | − | 5.25709i | − | 0.257133i | ||||||
\(419\) | − | 4.45152i | − | 0.217471i | −0.994071 | − | 0.108736i | \(-0.965320\pi\) | ||
0.994071 | − | 0.108736i | \(-0.0346802\pi\) | |||||||
\(420\) | −4.35962 | + | 4.22558i | −0.212728 | + | 0.206187i | ||||
\(421\) | 5.24985 | − | 9.09301i | 0.255862 | − | 0.443166i | −0.709267 | − | 0.704940i | \(-0.750974\pi\) |
0.965129 | + | 0.261774i | \(0.0843073\pi\) | |||||||
\(422\) | 7.73118 | − | 4.46360i | 0.376348 | − | 0.217285i | ||||
\(423\) | −26.8560 | − | 0.838820i | −1.30578 | − | 0.0407848i | ||||
\(424\) | 3.12954 | + | 1.80684i | 0.151984 | + | 0.0877480i | ||||
\(425\) | 0.748115 | − | 1.29577i | 0.0362889 | − | 0.0628542i | ||||
\(426\) | −18.8486 | + | 4.73636i | −0.913217 | + | 0.229477i | ||||
\(427\) | −2.01202 | + | 1.16164i | −0.0973685 | + | 0.0562157i | ||||
\(428\) | −15.5778 | + | 8.99386i | −0.752982 | + | 0.434734i | ||||
\(429\) | 0.944004 | + | 0.268809i | 0.0455769 | + | 0.0129782i | ||||
\(430\) | 6.57850i | 0.317244i | ||||||||
\(431\) | −10.1716 | + | 5.87257i | −0.489948 | + | 0.282872i | −0.724553 | − | 0.689219i | \(-0.757954\pi\) |
0.234605 | + | 0.972091i | \(0.424620\pi\) | |||||||
\(432\) | −3.84223 | + | 3.49818i | −0.184859 | + | 0.168306i | ||||
\(433\) | − | 0.986441i | − | 0.0474053i | −0.999719 | − | 0.0237027i | \(-0.992455\pi\) | ||
0.999719 | − | 0.0237027i | \(-0.00754550\pi\) | |||||||
\(434\) | −13.9298 | + | 13.6699i | −0.668653 | + | 0.656175i | ||||
\(435\) | 1.11625 | + | 4.44217i | 0.0535200 | + | 0.212986i | ||||
\(436\) | −7.55577 | −0.361856 | ||||||||
\(437\) | −8.31276 | − | 14.3981i | −0.397653 | − | 0.688756i | ||||
\(438\) | 10.1628 | − | 2.55376i | 0.485597 | − | 0.122023i | ||||
\(439\) | −0.755941 | + | 1.30933i | −0.0360791 | + | 0.0624909i | −0.883501 | − | 0.468429i | \(-0.844820\pi\) |
0.847422 | + | 0.530920i | \(0.178153\pi\) | |||||||
\(440\) | −0.508798 | − | 0.881264i | −0.0242560 | − | 0.0420126i | ||||
\(441\) | −13.4825 | − | 8.35589i | −0.642022 | − | 0.397900i | ||||
\(442\) | −0.833232 | −0.0396328 | ||||||||
\(443\) | −32.6594 | − | 18.8559i | −1.55169 | − | 0.895871i | −0.998004 | − | 0.0631476i | \(-0.979886\pi\) |
−0.553690 | − | 0.832723i | \(-0.686781\pi\) | |||||||
\(444\) | −4.01488 | − | 1.14325i | −0.190538 | − | 0.0542563i | ||||
\(445\) | −0.675095 | − | 0.389767i | −0.0320026 | − | 0.0184767i | ||||
\(446\) | 4.02749 | + | 6.97582i | 0.190707 | + | 0.330315i | ||||
\(447\) | 31.9579 | + | 9.10014i | 1.51156 | + | 0.430422i | ||||
\(448\) | −1.75266 | − | 3.03570i | −0.0828054 | − | 0.143423i | ||||
\(449\) | −19.1329 | −0.902938 | −0.451469 | − | 0.892287i | \(-0.649100\pi\) | ||||
−0.451469 | + | 0.892287i | \(0.649100\pi\) | |||||||
\(450\) | −1.41816 | − | 2.64364i | −0.0668527 | − | 0.124622i | ||||
\(451\) | 8.00235 | − | 4.62016i | 0.376816 | − | 0.217555i | ||||
\(452\) | 4.18028 | + | 2.41348i | 0.196624 | + | 0.113521i | ||||
\(453\) | −28.9797 | + | 28.0887i | −1.36158 | + | 1.31972i | ||||
\(454\) | −8.71161 | + | 15.0890i | −0.408856 | + | 0.708160i | ||||
\(455\) | −0.976035 | + | 1.69054i | −0.0457572 | + | 0.0792538i | ||||
\(456\) | 8.60599 | + | 2.45059i | 0.403012 | + | 0.114759i | ||||
\(457\) | 33.8765i | 1.58468i | 0.610082 | + | 0.792338i | \(0.291136\pi\) | ||||
−0.610082 | + | 0.792338i | \(0.708864\pi\) | |||||||
\(458\) | −7.05087 | − | 12.2125i | −0.329466 | − | 0.570651i | ||||
\(459\) | 7.40728 | + | 2.36161i | 0.345742 | + | 0.110231i | ||||
\(460\) | −2.78699 | − | 1.60907i | −0.129944 | − | 0.0750233i | ||||
\(461\) | 20.2187 | 0.941678 | 0.470839 | − | 0.882219i | \(-0.343951\pi\) | ||||
0.470839 | + | 0.882219i | \(0.343951\pi\) | |||||||
\(462\) | 4.43634 | − | 4.29993i | 0.206397 | − | 0.200051i | ||||
\(463\) | 4.75152i | 0.220822i | 0.993886 | + | 0.110411i | \(0.0352167\pi\) | ||||
−0.993886 | + | 0.110411i | \(0.964783\pi\) | |||||||
\(464\) | −2.64442 | −0.122764 | ||||||||
\(465\) | −4.61130 | − | 8.46971i | −0.213844 | − | 0.392773i | ||||
\(466\) | −2.39244 | −0.110828 | ||||||||
\(467\) | − | 4.46882i | − | 0.206792i | −0.994640 | − | 0.103396i | \(-0.967029\pi\) | ||
0.994640 | − | 0.103396i | \(-0.0329709\pi\) | |||||||
\(468\) | −0.880093 | + | 1.42005i | −0.0406823 | + | 0.0656420i | ||||
\(469\) | 5.38918 | 0.248849 | ||||||||
\(470\) | 7.75644 | + | 4.47818i | 0.357778 | + | 0.206563i | ||||
\(471\) | 12.9490 | + | 13.3598i | 0.596658 | + | 0.615585i | ||||
\(472\) | −4.74774 | − | 8.22333i | −0.218533 | − | 0.378509i | ||||
\(473\) | − | 6.69426i | − | 0.307802i | ||||||
\(474\) | −0.101109 | + | 0.355075i | −0.00464409 | + | 0.0163092i | ||||
\(475\) | −2.58309 | + | 4.47405i | −0.118520 | + | 0.205283i | ||||
\(476\) | −2.62238 | + | 4.54210i | −0.120197 | + | 0.208187i | ||||
\(477\) | −9.21483 | − | 5.71099i | −0.421918 | − | 0.261488i | ||||
\(478\) | 9.54323 | + | 5.50979i | 0.436497 | + | 0.252012i | ||||
\(479\) | 7.32007 | − | 4.22624i | 0.334463 | − | 0.193102i | −0.323358 | − | 0.946277i | \(-0.604812\pi\) |
0.657821 | + | 0.753175i | \(0.271478\pi\) | |||||||
\(480\) | 1.67983 | − | 0.422115i | 0.0766733 | − | 0.0192668i | ||||
\(481\) | −1.34217 | −0.0611979 | ||||||||
\(482\) | 12.4602 | + | 21.5818i | 0.567548 | + | 0.983022i | ||||
\(483\) | 5.35098 | − | 18.7916i | 0.243478 | − | 0.855048i | ||||
\(484\) | −4.98225 | − | 8.62951i | −0.226466 | − | 0.392250i | ||||
\(485\) | −11.5002 | − | 6.63966i | −0.522198 | − | 0.301491i | ||||
\(486\) | 11.8487 | − | 10.1296i | 0.537468 | − | 0.459487i | ||||
\(487\) | −29.2380 | − | 16.8806i | −1.32490 | − | 0.764931i | −0.340394 | − | 0.940283i | \(-0.610560\pi\) |
−0.984506 | + | 0.175352i | \(0.943894\pi\) | |||||||
\(488\) | 0.662787 | 0.0300030 | ||||||||
\(489\) | −4.29359 | − | 4.42979i | −0.194163 | − | 0.200322i | ||||
\(490\) | 2.64364 | + | 4.57892i | 0.119427 | + | 0.206854i | ||||
\(491\) | −3.86335 | + | 6.69152i | −0.174351 | + | 0.301984i | −0.939936 | − | 0.341350i | \(-0.889116\pi\) |
0.765586 | + | 0.643334i | \(0.222449\pi\) | |||||||
\(492\) | 3.83303 | + | 15.2537i | 0.172806 | + | 0.687691i | ||||
\(493\) | 1.97833 | + | 3.42657i | 0.0890995 | + | 0.154325i | ||||
\(494\) | 2.87698 | 0.129442 | ||||||||
\(495\) | 1.44311 | + | 2.69016i | 0.0648632 | + | 0.120914i | ||||
\(496\) | 5.39138 | − | 1.39033i | 0.242080 | − | 0.0624277i | ||||
\(497\) | 39.3316i | 1.76426i | ||||||||
\(498\) | −1.44880 | − | 5.76557i | −0.0649223 | − | 0.258362i | ||||
\(499\) | 28.3347 | − | 16.3590i | 1.26843 | − | 0.732330i | 0.293742 | − | 0.955885i | \(-0.405099\pi\) |
0.974691 | + | 0.223554i | \(0.0717660\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | −5.45563 | + | 19.1591i | −0.243739 | + | 0.855966i | ||||
\(502\) | 11.4452 | − | 6.60787i | 0.510823 | − | 0.294924i | ||||
\(503\) | −25.7137 | + | 14.8458i | −1.14652 | + | 0.661942i | −0.948036 | − | 0.318162i | \(-0.896934\pi\) |
−0.198482 | + | 0.980105i | \(0.563601\pi\) | |||||||
\(504\) | 4.97111 | + | 9.26680i | 0.221431 | + | 0.412776i | ||||
\(505\) | −8.75391 | + | 15.1622i | −0.389544 | + | 0.674710i | ||||
\(506\) | 2.83603 | + | 1.63739i | 0.126077 | + | 0.0727906i | ||||
\(507\) | 6.01946 | − | 21.1392i | 0.267334 | − | 0.938824i | ||||
\(508\) | −16.3303 | + | 9.42828i | −0.724538 | + | 0.418312i | ||||
\(509\) | 13.1355 | − | 22.7513i | 0.582219 | − | 1.00843i | −0.412997 | − | 0.910733i | \(-0.635518\pi\) |
0.995216 | − | 0.0977008i | \(-0.0311488\pi\) | |||||||
\(510\) | −1.80367 | − | 1.86088i | −0.0798678 | − | 0.0824014i | ||||
\(511\) | − | 21.2069i | − | 0.938137i | ||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −25.5759 | − | 8.15418i | −1.12920 | − | 0.360016i | ||||
\(514\) | −12.7624 | + | 22.1051i | −0.562925 | + | 0.975015i | ||||
\(515\) | 0.377449 | − | 0.217920i | 0.0166324 | − | 0.00960271i | ||||
\(516\) | 10.9587 | + | 3.12052i | 0.482428 | + | 0.137373i | ||||
\(517\) | −7.89292 | − | 4.55698i | −0.347130 | − | 0.200416i | ||||
\(518\) | −4.22415 | + | 7.31644i | −0.185598 | + | 0.321466i | ||||
\(519\) | −0.993726 | − | 3.95458i | −0.0436197 | − | 0.173587i | ||||
\(520\) | 0.482279 | − | 0.278444i | 0.0211493 | − | 0.0122106i | ||||
\(521\) | −33.3101 | + | 19.2316i | −1.45934 | + | 0.842552i | −0.998979 | − | 0.0451783i | \(-0.985614\pi\) |
−0.460364 | + | 0.887730i | \(0.652281\pi\) | |||||||
\(522\) | 7.92939 | + | 0.247667i | 0.347060 | + | 0.0108401i | ||||
\(523\) | − | 7.33956i | − | 0.320937i | −0.987041 | − | 0.160468i | \(-0.948700\pi\) | ||
0.987041 | − | 0.160468i | \(-0.0513004\pi\) | |||||||
\(524\) | −0.711541 | + | 0.410808i | −0.0310838 | + | 0.0179462i | ||||
\(525\) | −5.88833 | + | 1.47965i | −0.256988 | + | 0.0645771i | ||||
\(526\) | 17.3755i | 0.757607i | ||||||||
\(527\) | −5.83493 | − | 5.94588i | −0.254173 | − | 0.259007i | ||||
\(528\) | −1.70939 | + | 0.429543i | −0.0743915 | + | 0.0186934i | ||||
\(529\) | −12.6436 | −0.549720 | ||||||||
\(530\) | 1.80684 | + | 3.12954i | 0.0784842 | + | 0.135939i | ||||
\(531\) | 13.4661 | + | 25.1026i | 0.584380 | + | 1.08936i | ||||
\(532\) | 9.05457 | − | 15.6830i | 0.392565 | − | 0.679943i | ||||
\(533\) | 2.52842 | + | 4.37935i | 0.109518 | + | 0.189691i | ||||
\(534\) | −0.969517 | + | 0.939708i | −0.0419551 | + | 0.0406651i | ||||
\(535\) | −17.9877 | −0.777677 | ||||||||
\(536\) | −1.33145 | − | 0.768714i | −0.0575099 | − | 0.0332034i | ||||
\(537\) | 1.41750 | − | 4.97800i | 0.0611698 | − | 0.214817i | ||||
\(538\) | −9.40555 | − | 5.43030i | −0.405502 | − | 0.234117i | ||||
\(539\) | −2.69016 | − | 4.65949i | −0.115873 | − | 0.200698i | ||||
\(540\) | −5.07656 | + | 1.10840i | −0.218460 | + | 0.0476980i | ||||
\(541\) | −13.7846 | − | 23.8755i | −0.592644 | − | 1.02649i | −0.993875 | − | 0.110513i | \(-0.964751\pi\) |
0.401231 | − | 0.915977i | \(-0.368583\pi\) | |||||||
\(542\) | −0.444297 | −0.0190842 | ||||||||
\(543\) | 9.22892 | + | 36.7270i | 0.396051 | + | 1.57610i | ||||
\(544\) | 1.29577 | − | 0.748115i | 0.0555558 | − | 0.0320752i | ||||
\(545\) | −6.54349 | − | 3.77788i | −0.280292 | − | 0.161827i | ||||
\(546\) | 2.35317 | + | 2.42782i | 0.100707 | + | 0.103901i | ||||
\(547\) | 17.8437 | − | 30.9062i | 0.762941 | − | 1.32145i | −0.178387 | − | 0.983960i | \(-0.557088\pi\) |
0.941328 | − | 0.337493i | \(-0.109579\pi\) | |||||||
\(548\) | 9.97643 | − | 17.2797i | 0.426172 | − | 0.738151i | ||||
\(549\) | −1.98739 | − | 0.0620742i | −0.0848198 | − | 0.00264926i | ||||
\(550\) | − | 1.01760i | − | 0.0433905i | ||||||
\(551\) | −6.83078 | − | 11.8313i | −0.291001 | − | 0.504028i | ||||
\(552\) | −4.00245 | + | 3.87939i | −0.170356 | + | 0.165118i | ||||
\(553\) | 0.647065 | + | 0.373583i | 0.0275160 | + | 0.0158864i | ||||
\(554\) | −8.03697 | −0.341458 | ||||||||
\(555\) | −2.90536 | − | 2.99752i | −0.123326 | − | 0.127238i | ||||
\(556\) | 1.22089i | 0.0517773i | ||||||||
\(557\) | 7.54761 | 0.319803 | 0.159901 | − | 0.987133i | \(-0.448882\pi\) | ||||
0.159901 | + | 0.987133i | \(0.448882\pi\) | |||||||
\(558\) | −16.2965 | + | 3.66402i | −0.689885 | + | 0.155110i | ||||
\(559\) | 3.66349 | 0.154949 | ||||||||
\(560\) | − | 3.50532i | − | 0.148127i | ||||||
\(561\) | 1.83541 | + | 1.89363i | 0.0774910 | + | 0.0799491i | ||||
\(562\) | 13.9273 | 0.587486 | ||||||||
\(563\) | 14.7599 | + | 8.52162i | 0.622054 | + | 0.359143i | 0.777668 | − | 0.628675i | \(-0.216402\pi\) |
−0.155614 | + | 0.987818i | \(0.549736\pi\) | |||||||
\(564\) | 11.1392 | − | 10.7967i | 0.469043 | − | 0.454622i | ||||
\(565\) | 2.41348 | + | 4.18028i | 0.101536 | + | 0.175866i | ||||
\(566\) | − | 28.1351i | − | 1.18261i | ||||||
\(567\) | −14.0382 | − | 28.2524i | −0.589547 | − | 1.18649i | ||||
\(568\) | 5.61027 | − | 9.71728i | 0.235402 | − | 0.407728i | ||||
\(569\) | 16.3440 | − | 28.3087i | 0.685178 | − | 1.18676i | −0.288203 | − | 0.957569i | \(-0.593058\pi\) |
0.973381 | − | 0.229194i | \(-0.0736090\pi\) | |||||||
\(570\) | 6.22771 | + | 6.42526i | 0.260850 | + | 0.269125i | ||||
\(571\) | −36.0942 | − | 20.8390i | −1.51049 | − | 0.872084i | −0.999925 | − | 0.0122468i | \(-0.996102\pi\) |
−0.510569 | − | 0.859837i | \(-0.670565\pi\) | |||||||
\(572\) | −0.490765 | + | 0.283343i | −0.0205199 | + | 0.0118472i | ||||
\(573\) | 3.94301 | + | 15.6914i | 0.164721 | + | 0.655517i | ||||
\(574\) | 31.8302 | 1.32857 | ||||||||
\(575\) | −1.60907 | − | 2.78699i | −0.0671029 | − | 0.116226i | ||||
\(576\) | 0.0936563 | − | 2.99854i | 0.00390235 | − | 0.124939i | ||||
\(577\) | −18.9525 | − | 32.8266i | −0.789002 | − | 1.36659i | −0.926579 | − | 0.376100i | \(-0.877265\pi\) |
0.137577 | − | 0.990491i | \(-0.456069\pi\) | |||||||
\(578\) | 12.7837 | + | 7.38065i | 0.531730 | + | 0.306994i | ||||
\(579\) | 0.802986 | − | 2.81993i | 0.0333710 | − | 0.117192i | ||||
\(580\) | −2.29013 | − | 1.32221i | −0.0950926 | − | 0.0549018i | ||||
\(581\) | −12.0311 | −0.499135 | ||||||||
\(582\) | −16.5157 | + | 16.0079i | −0.684598 | + | 0.663549i | ||||
\(583\) | −1.83864 | − | 3.18461i | −0.0761485 | − | 0.131893i | ||||
\(584\) | −3.02495 | + | 5.23937i | −0.125173 | + | 0.216807i | ||||
\(585\) | −1.47221 | + | 0.789756i | −0.0608684 | + | 0.0326524i | ||||
\(586\) | 11.0058 | + | 19.0627i | 0.454647 | + | 0.787471i | ||||
\(587\) | −26.0324 | −1.07447 | −0.537237 | − | 0.843431i | \(-0.680532\pi\) | ||||
−0.537237 | + | 0.843431i | \(0.680532\pi\) | |||||||
\(588\) | 8.88171 | − | 2.23184i | 0.366276 | − | 0.0920394i | ||||
\(589\) | 20.1468 | + | 20.5299i | 0.830136 | + | 0.845921i | ||||
\(590\) | − | 9.49548i | − | 0.390923i | ||||||
\(591\) | −26.6403 | + | 6.69429i | −1.09583 | + | 0.275366i | ||||
\(592\) | 2.08724 | − | 1.20507i | 0.0857850 | − | 0.0495280i | ||||
\(593\) | 16.4572i | 0.675817i | 0.941179 | + | 0.337908i | \(0.109719\pi\) | ||||
−0.941179 | + | 0.337908i | \(0.890281\pi\) | |||||||
\(594\) | 5.16589 | − | 1.12790i | 0.211959 | − | 0.0462785i | ||||
\(595\) | −4.54210 | + | 2.62238i | −0.186208 | + | 0.107507i | ||||
\(596\) | −16.6142 | + | 9.59220i | −0.680543 | + | 0.392912i | ||||
\(597\) | −5.74303 | − | 22.8547i | −0.235047 | − | 0.935379i | ||||
\(598\) | −0.896072 | + | 1.55204i | −0.0366431 | + | 0.0634677i | ||||
\(599\) | 17.7128 | + | 10.2265i | 0.723724 | + | 0.417842i | 0.816122 | − | 0.577880i | \(-0.196120\pi\) |
−0.0923976 | + | 0.995722i | \(0.529453\pi\) | |||||||
\(600\) | 1.66583 | + | 0.474351i | 0.0680072 | + | 0.0193653i | ||||
\(601\) | −10.8743 | + | 6.27830i | −0.443573 | + | 0.256097i | −0.705112 | − | 0.709096i | \(-0.749103\pi\) |
0.261539 | + | 0.965193i | \(0.415770\pi\) | |||||||
\(602\) | 11.5299 | − | 19.9703i | 0.469923 | − | 0.813930i | ||||
\(603\) | 3.92041 | + | 2.42972i | 0.159651 | + | 0.0989457i | ||||
\(604\) | − | 23.3009i | − | 0.948100i | ||||||
\(605\) | − | 9.96450i | − | 0.405114i | ||||||
\(606\) | 21.1053 | + | 21.7748i | 0.857343 | + | 0.884539i | ||||
\(607\) | −8.27295 | + | 14.3292i | −0.335789 | + | 0.581603i | −0.983636 | − | 0.180167i | \(-0.942336\pi\) |
0.647847 | + | 0.761770i | \(0.275669\pi\) | |||||||
\(608\) | −4.47405 | + | 2.58309i | −0.181447 | + | 0.104758i | ||||
\(609\) | 4.39702 | − | 15.4415i | 0.178176 | − | 0.625720i | ||||
\(610\) | 0.573990 | + | 0.331394i | 0.0232402 | + | 0.0134177i | ||||
\(611\) | 2.49384 | − | 4.31946i | 0.100890 | − | 0.174747i | ||||
\(612\) | −3.95549 | + | 2.12189i | −0.159891 | + | 0.0857725i | ||||
\(613\) | 28.1131 | − | 16.2311i | 1.13548 | − | 0.655568i | 0.190171 | − | 0.981751i | \(-0.439096\pi\) |
0.945307 | + | 0.326183i | \(0.105763\pi\) | |||||||
\(614\) | 5.00704 | − | 2.89082i | 0.202068 | − | 0.116664i | ||||
\(615\) | −4.30736 | + | 15.1266i | −0.173690 | + | 0.609964i | ||||
\(616\) | 3.56700i | 0.143719i | ||||||||
\(617\) | 0.546152 | − | 0.315321i | 0.0219873 | − | 0.0126943i | −0.488966 | − | 0.872303i | \(-0.662626\pi\) |
0.510953 | + | 0.859608i | \(0.329292\pi\) | |||||||
\(618\) | −0.183975 | − | 0.732136i | −0.00740055 | − | 0.0294508i | ||||
\(619\) | − | 45.8973i | − | 1.84477i | −0.386274 | − | 0.922384i | \(-0.626238\pi\) | ||
0.386274 | − | 0.922384i | \(-0.373762\pi\) | |||||||
\(620\) | 5.36424 | + | 1.49163i | 0.215433 | + | 0.0599052i | ||||
\(621\) | 12.3648 | − | 11.2577i | 0.496184 | − | 0.451754i | ||||
\(622\) | 0.448742 | 0.0179929 | ||||||||
\(623\) | 1.36626 | + | 2.36643i | 0.0547379 | + | 0.0948089i | ||||
\(624\) | −0.235071 | − | 0.935475i | −0.00941035 | − | 0.0374490i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 8.73777 | + | 15.1343i | 0.349232 | + | 0.604887i | ||||
\(627\) | −6.33730 | − | 6.53832i | −0.253087 | − | 0.261116i | ||||
\(628\) | −10.7418 | −0.428645 | ||||||||
\(629\) | −3.12299 | − | 1.80306i | −0.124522 | − | 0.0718927i | ||||
\(630\) | −0.328295 | + | 10.5108i | −0.0130796 | + | 0.418762i | ||||
\(631\) | 16.2083 | + | 9.35789i | 0.645244 | + | 0.372532i | 0.786632 | − | 0.617423i | \(-0.211823\pi\) |
−0.141388 | + | 0.989954i | \(0.545156\pi\) | |||||||
\(632\) | −0.106576 | − | 0.184595i | −0.00423937 | − | 0.00734280i | ||||
\(633\) | 4.23463 | − | 14.8712i | 0.168311 | − | 0.591077i | ||||
\(634\) | −0.647660 | − | 1.12178i | −0.0257219 | − | 0.0445516i | ||||
\(635\) | −18.8566 | −0.748300 | ||||||||
\(636\) | 6.07037 | − | 1.52539i | 0.240706 | − | 0.0604857i | ||||
\(637\) | 2.54994 | − | 1.47221i | 0.101032 | − | 0.0583311i | ||||
\(638\) | 2.33043 | + | 1.34548i | 0.0922627 | + | 0.0532679i | ||||
\(639\) | −17.7327 | + | 28.6122i | −0.701495 | + | 1.13188i | ||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | −3.71167 | + | 6.42881i | −0.146602 | + | 0.253923i | −0.929970 | − | 0.367636i | \(-0.880167\pi\) |
0.783367 | + | 0.621559i | \(0.213500\pi\) | |||||||
\(642\) | −8.53249 | + | 29.9645i | −0.336751 | + | 1.18260i | ||||
\(643\) | 17.2741i | 0.681222i | 0.940204 | + | 0.340611i | \(0.110634\pi\) | ||||
−0.940204 | + | 0.340611i | \(0.889366\pi\) | |||||||
\(644\) | 5.64031 | + | 9.76931i | 0.222259 | + | 0.384965i | ||||
\(645\) | 7.93022 | + | 8.18178i | 0.312252 | + | 0.322157i | ||||
\(646\) | 6.69421 | + | 3.86490i | 0.263380 | + | 0.152062i | ||||
\(647\) | 8.93872 | 0.351418 | 0.175709 | − | 0.984442i | \(-0.443778\pi\) | ||||
0.175709 | + | 0.984442i | \(0.443778\pi\) | |||||||
\(648\) | −0.561664 | + | 8.98246i | −0.0220642 | + | 0.352864i | ||||
\(649\) | 9.66257i | 0.379289i | ||||||||
\(650\) | 0.556888 | 0.0218429 | ||||||||
\(651\) | −0.846021 | + | 33.7935i | −0.0331582 | + | 1.32447i | ||||
\(652\) | 3.56174 | 0.139488 | ||||||||
\(653\) | 22.3040i | 0.872823i | 0.899747 | + | 0.436411i | \(0.143751\pi\) | ||||
−0.899747 | + | 0.436411i | \(0.856249\pi\) | |||||||
\(654\) | −9.39723 | + | 9.10829i | −0.367461 | + | 0.356163i | ||||
\(655\) | −0.821617 | −0.0321032 | ||||||||
\(656\) | −7.86397 | − | 4.54027i | −0.307037 | − | 0.177268i | ||||
\(657\) | 9.56114 | − | 15.4272i | 0.373016 | − | 0.601871i | ||||
\(658\) | −15.6975 | − | 27.1888i | −0.611951 | − | 1.05993i | ||||
\(659\) | − | 23.8067i | − | 0.927377i | −0.885998 | − | 0.463688i | \(-0.846526\pi\) | ||
0.885998 | − | 0.463688i | \(-0.153474\pi\) | |||||||
\(660\) | −1.69514 | − | 0.482698i | −0.0659833 | − | 0.0187890i | ||||
\(661\) | −20.5693 | + | 35.6271i | −0.800054 | + | 1.38573i | 0.119527 | + | 0.992831i | \(0.461862\pi\) |
−0.919580 | + | 0.392902i | \(0.871471\pi\) | |||||||
\(662\) | 10.1085 | − | 17.5084i | 0.392878 | − | 0.680485i | ||||
\(663\) | −1.03630 | + | 1.00444i | −0.0402467 | + | 0.0390093i | ||||
\(664\) | 2.97241 | + | 1.71612i | 0.115352 | + | 0.0665984i | ||||
\(665\) | 15.6830 | − | 9.05457i | 0.608160 | − | 0.351121i | ||||
\(666\) | −6.37153 | + | 3.41796i | −0.246892 | + | 0.132443i | ||||
\(667\) | 8.51012 | 0.329513 | ||||||||
\(668\) | −5.75062 | − | 9.96036i | −0.222498 | − | 0.385378i | ||||
\(669\) | 13.4182 | + | 3.82089i | 0.518779 | + | 0.147724i | ||||
\(670\) | −0.768714 | − | 1.33145i | −0.0296980 | − | 0.0514384i | ||||
\(671\) | −0.584090 | − | 0.337225i | −0.0225486 | − | 0.0130184i | ||||
\(672\) | −5.83927 | − | 1.66275i | −0.225255 | − | 0.0641421i | ||||
\(673\) | −40.8232 | − | 23.5693i | −1.57362 | − | 0.908529i | −0.995720 | − | 0.0924207i | \(-0.970540\pi\) |
−0.577899 | − | 0.816109i | \(-0.696127\pi\) | |||||||
\(674\) | −11.8084 | −0.454842 | ||||||||
\(675\) | −4.95063 | − | 1.57838i | −0.190550 | − | 0.0607517i | ||||
\(676\) | 6.34494 | + | 10.9898i | 0.244036 | + | 0.422683i | ||||
\(677\) | −9.59632 | + | 16.6213i | −0.368816 | + | 0.638809i | −0.989381 | − | 0.145347i | \(-0.953570\pi\) |
0.620564 | + | 0.784155i | \(0.286904\pi\) | |||||||
\(678\) | 8.10847 | − | 2.03753i | 0.311404 | − | 0.0782511i | ||||
\(679\) | 23.2741 | + | 40.3120i | 0.893179 | + | 1.54703i | ||||
\(680\) | 1.49623 | 0.0573778 | ||||||||
\(681\) | 7.35460 | + | 29.2680i | 0.281829 | + | 1.12155i | ||||
\(682\) | −5.45863 | − | 1.51788i | −0.209022 | − | 0.0581225i | ||||
\(683\) | 28.8541i | 1.10407i | 0.833821 | + | 0.552035i | \(0.186148\pi\) | ||||
−0.833821 | + | 0.552035i | \(0.813852\pi\) | |||||||
\(684\) | 13.6575 | − | 7.32648i | 0.522208 | − | 0.280135i | ||||
\(685\) | 17.2797 | − | 9.97643i | 0.660223 | − | 0.381180i | ||||
\(686\) | 6.00365i | 0.229220i | ||||||||
\(687\) | −23.4911 | − | 6.68918i | −0.896242 | − | 0.255208i | ||||
\(688\) | −5.69715 | + | 3.28925i | −0.217202 | + | 0.125402i | ||||
\(689\) | 1.74280 | − | 1.00621i | 0.0663955 | − | 0.0383335i | ||||
\(690\) | −5.40592 | + | 1.35843i | −0.205800 | + | 0.0517144i | ||||
\(691\) | 20.3713 | − | 35.2841i | 0.774959 | − | 1.34227i | −0.159858 | − | 0.987140i | \(-0.551104\pi\) |
0.934817 | − | 0.355129i | \(-0.115563\pi\) | |||||||
\(692\) | 2.03876 | + | 1.17708i | 0.0775021 | + | 0.0447459i | ||||
\(693\) | 0.334072 | − | 10.6958i | 0.0126904 | − | 0.406299i | ||||
\(694\) | 4.77321 | − | 2.75581i | 0.181188 | − | 0.104609i | ||||
\(695\) | −0.610446 | + | 1.05732i | −0.0231555 | + | 0.0401065i | ||||
\(696\) | −3.28890 | + | 3.18778i | −0.124666 | + | 0.120833i | ||||
\(697\) | 13.5866i | 0.514628i | ||||||||
\(698\) | − | 21.0390i | − | 0.796337i | ||||||
\(699\) | −2.97551 | + | 2.88403i | −0.112544 | + | 0.109084i | ||||
\(700\) | 1.75266 | − | 3.03570i | 0.0662443 | − | 0.114739i | ||||
\(701\) | 6.09463 | − | 3.51874i | 0.230191 | − | 0.132901i | −0.380469 | − | 0.924794i | \(-0.624237\pi\) |
0.610660 | + | 0.791893i | \(0.290904\pi\) | |||||||
\(702\) | 0.617255 | + | 2.82707i | 0.0232968 | + | 0.106701i | ||||
\(703\) | 10.7831 | + | 6.22560i | 0.406691 | + | 0.234803i | ||||
\(704\) | 0.508798 | − | 0.881264i | 0.0191761 | − | 0.0332139i | ||||
\(705\) | 15.0451 | − | 3.78061i | 0.566633 | − | 0.142386i | ||||
\(706\) | −22.4278 | + | 12.9487i | −0.844081 | + | 0.487330i | ||||
\(707\) | 53.1485 | − | 30.6853i | 1.99885 | − | 1.15404i | ||||
\(708\) | −15.8179 | − | 4.50419i | −0.594472 | − | 0.169278i | ||||
\(709\) | − | 22.0251i | − | 0.827169i | −0.910466 | − | 0.413585i | \(-0.864277\pi\) | ||
0.910466 | − | 0.413585i | \(-0.135723\pi\) | |||||||
\(710\) | 9.71728 | − | 5.61027i | 0.364683 | − | 0.210550i | ||||
\(711\) | 0.302284 | + | 0.563497i | 0.0113365 | + | 0.0211328i | ||||
\(712\) | − | 0.779533i | − | 0.0292142i | ||||||
\(713\) | −17.3502 | + | 4.47428i | −0.649771 | + | 0.167563i | ||||
\(714\) | 2.21389 | + | 8.81030i | 0.0828529 | + | 0.329717i | ||||
\(715\) | −0.566687 | −0.0211929 | ||||||||
\(716\) | 1.49415 | + | 2.58794i | 0.0558390 | + | 0.0967160i | ||||
\(717\) | 18.5110 | − | 4.65153i | 0.691305 | − | 0.173714i | ||||
\(718\) | 4.55262 | − | 7.88537i | 0.169902 | − | 0.294279i | ||||
\(719\) | 18.1976 | + | 31.5191i | 0.678656 | + | 1.17547i | 0.975386 | + | 0.220505i | \(0.0707704\pi\) |
−0.296730 | + | 0.954961i | \(0.595896\pi\) | |||||||
\(720\) | 1.58038 | − | 2.54998i | 0.0588972 | − | 0.0950322i | ||||
\(721\) | −1.52776 | −0.0568968 | ||||||||
\(722\) | −6.65927 | − | 3.84473i | −0.247832 | − | 0.143086i | ||||
\(723\) | 41.5133 | + | 11.8211i | 1.54389 | + | 0.439630i | ||||
\(724\) | −18.9344 | − | 10.9318i | −0.703690 | − | 0.406276i | ||||
\(725\) | −1.32221 | − | 2.29013i | −0.0491056 | − | 0.0850534i | ||||
\(726\) | −16.5992 | − | 4.72667i | −0.616053 | − | 0.175423i | ||||
\(727\) | 3.84543 | + | 6.66048i | 0.142619 | + | 0.247024i | 0.928482 | − | 0.371377i | \(-0.121114\pi\) |
−0.785863 | + | 0.618401i | \(0.787781\pi\) | |||||||
\(728\) | −1.95207 | −0.0723485 | ||||||||
\(729\) | 2.52543 | − | 26.8816i | 0.0935346 | − | 0.995616i | ||||
\(730\) | −5.23937 | + | 3.02495i | −0.193918 | + | 0.111959i | ||||
\(731\) | 8.52425 | + | 4.92148i | 0.315281 | + | 0.182027i | ||||
\(732\) | 0.824318 | − | 0.798974i | 0.0304677 | − | 0.0295309i | ||||
\(733\) | 2.30501 | − | 3.99239i | 0.0851374 | − | 0.147462i | −0.820312 | − | 0.571916i | \(-0.806200\pi\) |
0.905450 | + | 0.424454i | \(0.139534\pi\) | |||||||
\(734\) | 16.7657 | − | 29.0390i | 0.618833 | − | 1.07185i | ||||
\(735\) | 8.80770 | + | 2.50803i | 0.324877 | + | 0.0925099i | ||||
\(736\) | − | 3.21814i | − | 0.118622i | ||||||
\(737\) | 0.782240 | + | 1.35488i | 0.0288142 | + | 0.0499076i | ||||
\(738\) | 23.1552 | + | 14.3507i | 0.852354 | + | 0.528255i | ||||
\(739\) | 2.74609 | + | 1.58546i | 0.101017 | + | 0.0583220i | 0.549657 | − | 0.835390i | \(-0.314758\pi\) |
−0.448641 | + | 0.893712i | \(0.648092\pi\) | |||||||
\(740\) | 2.41014 | 0.0885984 | ||||||||
\(741\) | 3.57815 | − | 3.46813i | 0.131447 | − | 0.127405i | ||||
\(742\) | − | 12.6671i | − | 0.465025i | ||||||
\(743\) | 30.5226 | 1.11977 | 0.559883 | − | 0.828571i | \(-0.310846\pi\) | ||||
0.559883 | + | 0.828571i | \(0.310846\pi\) | |||||||
\(744\) | 5.02933 | − | 8.22835i | 0.184384 | − | 0.301666i | ||||
\(745\) | −19.1844 | −0.702862 | ||||||||
\(746\) | − | 23.3875i | − | 0.856276i | ||||||
\(747\) | −8.75216 | − | 5.42424i | −0.320225 | − | 0.198463i | ||||
\(748\) | −1.52256 | −0.0556702 | ||||||||
\(749\) | 54.6052 | + | 31.5264i | 1.99523 | + | 1.15195i | ||||
\(750\) | 1.20548 | + | 1.24372i | 0.0440178 | + | 0.0454141i | ||||
\(751\) | 19.5846 | + | 33.9216i | 0.714654 | + | 1.23782i | 0.963093 | + | 0.269169i | \(0.0867490\pi\) |
−0.248439 | + | 0.968647i | \(0.579918\pi\) | |||||||
\(752\) | 8.95636i | 0.326605i | ||||||||
\(753\) | 6.26890 | − | 22.0152i | 0.228452 | − | 0.802278i | ||||
\(754\) | −0.736322 | + | 1.27535i | −0.0268153 | + | 0.0464454i | ||||
\(755\) | 11.6505 | − | 20.1792i | 0.424003 | − | 0.734395i | ||||
\(756\) | 17.3535 | + | 5.53271i | 0.631142 | + | 0.201223i | ||||
\(757\) | 37.5703 | + | 21.6912i | 1.36552 | + | 0.788382i | 0.990352 | − | 0.138576i | \(-0.0442526\pi\) |
0.375165 | + | 0.926958i | \(0.377586\pi\) | |||||||
\(758\) | 10.0520 | − | 5.80353i | 0.365105 | − | 0.210794i | ||||
\(759\) | 5.50105 | − | 1.38233i | 0.199675 | − | 0.0501754i | ||||
\(760\) | −5.16618 | −0.187397 | ||||||||
\(761\) | −20.1815 | − | 34.9553i | −0.731577 | − | 1.26713i | −0.956209 | − | 0.292685i | \(-0.905451\pi\) |
0.224632 | − | 0.974444i | \(-0.427882\pi\) | |||||||
\(762\) | −8.94463 | + | 31.4118i | −0.324030 | + | 1.13793i | ||||
\(763\) | 13.2427 | + | 22.9370i | 0.479418 | + | 0.830376i | ||||
\(764\) | −8.08961 | − | 4.67054i | −0.292672 | − | 0.168974i | ||||
\(765\) | −4.48650 | − | 0.140131i | −0.162210 | − | 0.00506646i | ||||
\(766\) | −1.98063 | − | 1.14352i | −0.0715632 | − | 0.0413170i | ||||
\(767\) | −5.28792 | −0.190936 | ||||||||
\(768\) | 1.20548 | + | 1.24372i | 0.0434989 | + | 0.0448787i | ||||
\(769\) | 7.20267 | + | 12.4754i | 0.259735 | + | 0.449874i | 0.966171 | − | 0.257903i | \(-0.0830315\pi\) |
−0.706436 | + | 0.707777i | \(0.749698\pi\) | |||||||
\(770\) | −1.78350 | + | 3.08911i | −0.0642729 | + | 0.111324i | ||||
\(771\) | 10.7744 | + | 42.8772i | 0.388030 | + | 1.54419i | ||||
\(772\) | 0.846405 | + | 1.46602i | 0.0304628 | + | 0.0527631i | ||||
\(773\) | −0.596764 | −0.0214641 | −0.0107321 | − | 0.999942i | \(-0.503416\pi\) | ||||
−0.0107321 | + | 0.999942i | \(0.503416\pi\) | |||||||
\(774\) | 17.3912 | − | 9.32937i | 0.625113 | − | 0.335337i | ||||
\(775\) | 3.89975 | + | 3.97391i | 0.140083 | + | 0.142747i | ||||
\(776\) | − | 13.2793i | − | 0.476700i | ||||||
\(777\) | 3.56615 | + | 14.1917i | 0.127935 | + | 0.509124i | ||||
\(778\) | 2.43804 | − | 1.40760i | 0.0874080 | − | 0.0504650i | ||||
\(779\) | − | 46.9117i | − | 1.68079i | ||||||
\(780\) | 0.264160 | − | 0.927680i | 0.00945846 | − | 0.0332163i | ||||
\(781\) | −9.88827 | + | 5.70899i | −0.353830 | + | 0.204284i | ||||
\(782\) | −4.16998 | + | 2.40754i | −0.149118 | + | 0.0860935i | ||||
\(783\) | 10.1605 | − | 9.25066i | 0.363105 | − | 0.330592i | ||||
\(784\) | −2.64364 | + | 4.57892i | −0.0944156 | + | 0.163533i | ||||
\(785\) | −9.30268 | − | 5.37091i | −0.332027 | − | 0.191696i | ||||
\(786\) | −0.389735 | + | 1.36867i | −0.0139014 | + | 0.0488190i | ||||
\(787\) | −44.6959 | + | 25.8052i | −1.59324 | + | 0.919856i | −0.600490 | + | 0.799632i | \(0.705028\pi\) |
−0.992747 | + | 0.120224i | \(0.961639\pi\) | |||||||
\(788\) | 7.92946 | − | 13.7342i | 0.282475 | − | 0.489262i | ||||
\(789\) | 20.9457 | + | 21.6101i | 0.745687 | + | 0.769342i | ||||
\(790\) | − | 0.213152i | − | 0.00758361i | ||||||
\(791\) | − | 16.9201i | − | 0.601608i | ||||||
\(792\) | −1.60819 | + | 2.59485i | −0.0571444 | + | 0.0922040i | ||||
\(793\) | 0.184549 | − | 0.319648i | 0.00655353 | − | 0.0113510i | ||||
\(794\) | 4.64148 | − | 2.67976i | 0.164720 | − | 0.0951011i | ||||
\(795\) | 6.01979 | + | 1.71416i | 0.213500 | + | 0.0607949i | ||||
\(796\) | 11.7826 | + | 6.80268i | 0.417623 | + | 0.241115i | ||||
\(797\) | −23.5456 | + | 40.7822i | −0.834028 | + | 1.44458i | 0.0607919 | + | 0.998150i | \(0.480637\pi\) |
−0.894820 | + | 0.446428i | \(0.852696\pi\) | |||||||
\(798\) | −7.64414 | − | 30.4202i | −0.270600 | − | 1.07686i | ||||
\(799\) | 11.6054 | − | 6.70039i | 0.410570 | − | 0.237043i | ||||
\(800\) | −0.866025 | + | 0.500000i | −0.0306186 | + | 0.0176777i | ||||
\(801\) | −0.0730082 | + | 2.33746i | −0.00257962 | + | 0.0825901i | ||||
\(802\) | − | 11.7824i | − | 0.416050i | ||||||
\(803\) | 5.33157 | − | 3.07818i | 0.188147 | − | 0.108627i | ||||
\(804\) | −2.58261 | + | 0.648971i | −0.0910817 | + | 0.0228874i | ||||
\(805\) | 11.2806i | 0.397590i | ||||||||
\(806\) | 0.830669 | − | 2.98728i | 0.0292591 | − | 0.105222i | ||||
\(807\) | −18.2439 | + | 4.58442i | −0.642216 | + | 0.161379i | ||||
\(808\) | −17.5078 | −0.615923 | ||||||||
\(809\) | 4.47657 | + | 7.75365i | 0.157388 | + | 0.272604i | 0.933926 | − | 0.357467i | \(-0.116359\pi\) |
−0.776538 | + | 0.630070i | \(0.783026\pi\) | |||||||
\(810\) | −4.97764 | + | 7.49820i | −0.174897 | + | 0.263460i | ||||
\(811\) | 19.0738 | − | 33.0368i | 0.669772 | − | 1.16008i | −0.308195 | − | 0.951323i | \(-0.599725\pi\) |
0.977968 | − | 0.208756i | \(-0.0669416\pi\) | |||||||
\(812\) | 4.63477 | + | 8.02765i | 0.162648 | + | 0.281715i | ||||
\(813\) | −0.552579 | + | 0.535589i | −0.0193798 | + | 0.0187839i | ||||
\(814\) | −2.45255 | −0.0859617 | ||||||||
\(815\) | 3.08456 | + | 1.78087i | 0.108047 | + | 0.0623811i | ||||
\(816\) | 0.709739 | − | 2.49247i | 0.0248458 | − | 0.0872538i | ||||
\(817\) | −29.4325 | − | 16.9929i | −1.02971 | − | 0.594506i | ||||
\(818\) | −0.330911 | − | 0.573155i | −0.0115700 | − | 0.0200399i | ||||
\(819\) | 5.85336 | + | 0.182824i | 0.204533 | + | 0.00638838i | ||||
\(820\) | −4.54027 | − | 7.86397i | −0.158553 | − | 0.274622i | ||||
\(821\) | −1.33931 | −0.0467422 | −0.0233711 | − | 0.999727i | \(-0.507440\pi\) | ||||
−0.0233711 | + | 0.999727i | \(0.507440\pi\) | |||||||
\(822\) | −8.42240 | − | 33.5173i | −0.293765 | − | 1.16905i | ||||
\(823\) | −21.0797 | + | 12.1704i | −0.734792 | + | 0.424233i | −0.820173 | − | 0.572116i | \(-0.806123\pi\) |
0.0853804 | + | 0.996348i | \(0.472789\pi\) | |||||||
\(824\) | 0.377449 | + | 0.217920i | 0.0131491 | + | 0.00759161i | ||||
\(825\) | −1.22669 | − | 1.26560i | −0.0427078 | − | 0.0440625i | ||||
\(826\) | −16.6424 | + | 28.8254i | −0.579062 | + | 1.00296i | ||||
\(827\) | 17.0711 | − | 29.5680i | 0.593621 | − | 1.02818i | −0.400119 | − | 0.916463i | \(-0.631031\pi\) |
0.993740 | − | 0.111718i | \(-0.0356353\pi\) | |||||||
\(828\) | −0.301399 | + | 9.64972i | −0.0104744 | + | 0.335351i | ||||
\(829\) | 32.3395i | 1.12320i | 0.827409 | + | 0.561599i | \(0.189814\pi\) | ||||
−0.827409 | + | 0.561599i | \(0.810186\pi\) | |||||||
\(830\) | 1.71612 | + | 2.97241i | 0.0595674 | + | 0.103174i | ||||
\(831\) | −9.99570 | + | 9.68837i | −0.346747 | + | 0.336086i | ||||
\(832\) | 0.482279 | + | 0.278444i | 0.0167200 | + | 0.00965330i | ||||
\(833\) | 7.91098 | 0.274099 | ||||||||
\(834\) | 1.47176 | + | 1.51844i | 0.0509627 | + | 0.0525793i | ||||
\(835\) | − | 11.5012i | − | 0.398017i | ||||||
\(836\) | 5.25709 | 0.181820 | ||||||||
\(837\) | −15.8513 | + | 24.2020i | −0.547900 | + | 0.836544i | ||||
\(838\) | 4.45152 | 0.153775 | ||||||||
\(839\) | − | 23.2464i | − | 0.802555i | −0.915956 | − | 0.401278i | \(-0.868566\pi\) | ||
0.915956 | − | 0.401278i | \(-0.131434\pi\) | |||||||
\(840\) | −4.22558 | − | 4.35962i | −0.145796 | − | 0.150421i | ||||
\(841\) | −22.0070 | −0.758864 | ||||||||
\(842\) | 9.09301 | + | 5.24985i | 0.313366 | + | 0.180922i | ||||
\(843\) | 17.3216 | − | 16.7890i | 0.596586 | − | 0.578243i | ||||
\(844\) | 4.46360 | + | 7.73118i | 0.153643 | + | 0.266118i | ||||
\(845\) | 12.6899i | 0.436545i | ||||||||
\(846\) | 0.838820 | − | 26.8560i | 0.0288392 | − | 0.923328i | ||||
\(847\) | −17.4644 | + | 30.2492i | −0.600083 | + | 1.03937i | ||||
\(848\) | −1.80684 | + | 3.12954i | −0.0620472 | + | 0.107469i | ||||
\(849\) | −33.9162 | − | 34.9921i | −1.16400 | − | 1.20093i | ||||
\(850\) | 1.29577 | + | 0.748115i | 0.0444447 | + | 0.0256601i | ||||
\(851\) | −6.71703 | + | 3.87808i | −0.230257 | + | 0.132939i | ||||
\(852\) | −4.73636 | − | 18.8486i | −0.162265 | − | 0.645742i | ||||
\(853\) | 27.9332 | 0.956415 | 0.478207 | − | 0.878247i | \(-0.341287\pi\) | ||||
0.478207 | + | 0.878247i | \(0.341287\pi\) | |||||||
\(854\) | −1.16164 | − | 2.01202i | −0.0397505 | − | 0.0688499i | ||||
\(855\) | 15.4910 | + | 0.483846i | 0.529781 | + | 0.0165472i | ||||
\(856\) | −8.99386 | − | 15.5778i | −0.307404 | − | 0.532439i | ||||
\(857\) | 30.8970 | + | 17.8384i | 1.05542 | + | 0.609348i | 0.924162 | − | 0.382000i | \(-0.124765\pi\) |
0.131259 | + | 0.991348i | \(0.458098\pi\) | |||||||
\(858\) | −0.268809 | + | 0.944004i | −0.00917697 | + | 0.0322278i | ||||
\(859\) | −27.9755 | − | 16.1517i | −0.954512 | − | 0.551088i | −0.0600327 | − | 0.998196i | \(-0.519120\pi\) |
−0.894480 | + | 0.447108i | \(0.852454\pi\) | |||||||
\(860\) | −6.57850 | −0.224325 | ||||||||
\(861\) | 39.5877 | − | 38.3705i | 1.34914 | − | 1.30766i | ||||
\(862\) | −5.87257 | − | 10.1716i | −0.200020 | − | 0.346446i | ||||
\(863\) | 10.9154 | − | 18.9061i | 0.371565 | − | 0.643570i | −0.618241 | − | 0.785988i | \(-0.712155\pi\) |
0.989807 | + | 0.142418i | \(0.0454879\pi\) | |||||||
\(864\) | −3.49818 | − | 3.84223i | −0.119011 | − | 0.130715i | ||||
\(865\) | 1.17708 | + | 2.03876i | 0.0400219 | + | 0.0693200i | ||||
\(866\) | 0.986441 | 0.0335206 | ||||||||
\(867\) | 24.7964 | − | 6.23096i | 0.842131 | − | 0.211615i | ||||
\(868\) | −13.6699 | − | 13.9298i | −0.463986 | − | 0.472809i | ||||
\(869\) | 0.216903i | 0.00735792i | ||||||||
\(870\) | −4.44217 | + | 1.11625i | −0.150604 | + | 0.0378444i | ||||
\(871\) | −0.741469 | + | 0.428087i | −0.0251237 | + | 0.0145052i | ||||
\(872\) | − | 7.55577i | − | 0.255871i | ||||||
\(873\) | −1.24369 | + | 39.8185i | −0.0420926 | + | 1.34765i | ||||
\(874\) | 14.3981 | − | 8.31276i | 0.487024 | − | 0.281183i | ||||
\(875\) | 3.03570 | − | 1.75266i | 0.102625 | − | 0.0592507i | ||||
\(876\) | 2.55376 | + | 10.1628i | 0.0862834 | + | 0.343369i | ||||
\(877\) | −14.0024 | + | 24.2529i | −0.472829 | + | 0.818963i | −0.999516 | − | 0.0310954i | \(-0.990100\pi\) |
0.526688 | + | 0.850059i | \(0.323434\pi\) | |||||||
\(878\) | −1.30933 | − | 0.755941i | −0.0441877 | − | 0.0255118i | ||||
\(879\) | 36.6677 | + | 10.4413i | 1.23677 | + | 0.352175i | ||||
\(880\) | 0.881264 | − | 0.508798i | 0.0297074 | − | 0.0171516i | ||||
\(881\) | 6.16441 | − | 10.6771i | 0.207684 | − | 0.359720i | −0.743300 | − | 0.668958i | \(-0.766741\pi\) |
0.950985 | + | 0.309238i | \(0.100074\pi\) | |||||||
\(882\) | 8.35589 | − | 13.4825i | 0.281358 | − | 0.453978i | ||||
\(883\) | 26.1480i | 0.879951i | 0.898010 | + | 0.439976i | \(0.145013\pi\) | ||||
−0.898010 | + | 0.439976i | \(0.854987\pi\) | |||||||
\(884\) | − | 0.833232i | − | 0.0280246i | ||||||
\(885\) | −11.4466 | − | 11.8097i | −0.384772 | − | 0.396978i | ||||
\(886\) | 18.8559 | − | 32.6594i | 0.633476 | − | 1.09721i | ||||
\(887\) | −7.69703 | + | 4.44388i | −0.258441 | + | 0.149211i | −0.623623 | − | 0.781725i | \(-0.714340\pi\) |
0.365182 | + | 0.930936i | \(0.381007\pi\) | |||||||
\(888\) | 1.14325 | − | 4.01488i | 0.0383650 | − | 0.134730i | ||||
\(889\) | 57.2428 | + | 33.0491i | 1.91986 | + | 1.10843i | ||||
\(890\) | 0.389767 | − | 0.675095i | 0.0130650 | − | 0.0226292i | ||||
\(891\) | 5.06523 | − | 7.63014i | 0.169692 | − | 0.255619i | ||||
\(892\) | −6.97582 | + | 4.02749i | −0.233568 | + | 0.134850i | ||||
\(893\) | −40.0712 | + | 23.1351i | −1.34093 | + | 0.774187i | ||||
\(894\) | −9.10014 | + | 31.9579i | −0.304354 | + | 1.06883i | ||||
\(895\) | 2.98830i | 0.0998878i | ||||||||
\(896\) | 3.03570 | − | 1.75266i | 0.101416 | − | 0.0585523i | ||||
\(897\) | 0.756491 | + | 3.01049i | 0.0252585 | + | 0.100517i | ||||
\(898\) | − | 19.1329i | − | 0.638474i | ||||||
\(899\) | −14.2571 | + | 3.67662i | −0.475500 | + | 0.122622i | ||||
\(900\) | 2.64364 | − | 1.41816i | 0.0881213 | − | 0.0472720i | ||||
\(901\) | 5.40691 | 0.180130 | ||||||||
\(902\) | 4.62016 | + | 8.00235i | 0.153834 | + | 0.266449i | ||||
\(903\) | −9.73387 | − | 38.7364i | −0.323923 | − | 1.28907i | ||||
\(904\) | −2.41348 | + | 4.18028i | −0.0802713 | + | 0.139034i | ||||
\(905\) | −10.9318 | − | 18.9344i | −0.363384 | − | 0.629400i | ||||
\(906\) | −28.0887 | − | 28.9797i | −0.933184 | − | 0.962786i | ||||
\(907\) | −22.6580 | −0.752347 | −0.376174 | − | 0.926549i | \(-0.622760\pi\) | ||||
−0.376174 | + | 0.926549i | \(0.622760\pi\) | |||||||
\(908\) | −15.0890 | − | 8.71161i | −0.500745 | − | 0.289105i | ||||
\(909\) | 52.4979 | + | 1.63972i | 1.74124 | + | 0.0543860i | ||||
\(910\) | −1.69054 | − | 0.976035i | −0.0560409 | − | 0.0323552i | ||||
\(911\) | 20.8726 | + | 36.1524i | 0.691539 | + | 1.19778i | 0.971333 | + | 0.237721i | \(0.0764004\pi\) |
−0.279794 | + | 0.960060i | \(0.590266\pi\) | |||||||
\(912\) | −2.45059 | + | 8.60599i | −0.0811470 | + | 0.284973i | ||||
\(913\) | −1.74632 | − | 3.02471i | −0.0577947 | − | 0.100103i | ||||
\(914\) | −33.8765 | −1.12054 | ||||||||
\(915\) | 1.11337 | − | 0.279772i | 0.0368068 | − | 0.00924899i | ||||
\(916\) | 12.2125 | − | 7.05087i | 0.403511 | − | 0.232967i | ||||
\(917\) | 2.49418 | + | 1.44001i | 0.0823650 | + | 0.0475535i | ||||
\(918\) | −2.36161 | + | 7.40728i | −0.0779449 | + | 0.244477i | ||||
\(919\) | 27.6822 | − | 47.9471i | 0.913153 | − | 1.58163i | 0.103570 | − | 0.994622i | \(-0.466973\pi\) |
0.809583 | − | 0.587005i | \(-0.199693\pi\) | |||||||
\(920\) | 1.60907 | − | 2.78699i | 0.0530495 | − | 0.0918845i | ||||
\(921\) | 2.74252 | − | 9.63122i | 0.0903693 | − | 0.317359i | ||||
\(922\) | 20.2187i | 0.665867i | ||||||||
\(923\) | −3.12429 | − | 5.41143i | −0.102837 | − | 0.178119i | ||||
\(924\) | 4.29993 | + | 4.43634i | 0.141457 | + | 0.145945i | ||||
\(925\) | 2.08724 | + | 1.20507i | 0.0686280 | + | 0.0396224i | ||||
\(926\) | −4.75152 | −0.156145 | ||||||||
\(927\) | −1.11138 | − | 0.688792i | −0.0365027 | − | 0.0226229i | ||||
\(928\) | − | 2.64442i | − | 0.0868073i | ||||||
\(929\) | 13.1951 | 0.432917 | 0.216459 | − | 0.976292i | \(-0.430549\pi\) | ||||
0.216459 | + | 0.976292i | \(0.430549\pi\) | |||||||
\(930\) | 8.46971 | − | 4.61130i | 0.277733 | − | 0.151210i | ||||
\(931\) | −27.3150 | −0.895214 | ||||||||
\(932\) | − | 2.39244i | − | 0.0783669i | ||||||
\(933\) | 0.558107 | − | 0.540947i | 0.0182716 | − | 0.0177098i | ||||
\(934\) | 4.46882 | 0.146224 | ||||||||
\(935\) | −1.31857 | − | 0.761279i | −0.0431220 | − | 0.0248965i | ||||
\(936\) | −1.42005 | − | 0.880093i | −0.0464159 | − | 0.0287667i | ||||
\(937\) | −12.0937 | − | 20.9469i | −0.395083 | − | 0.684304i | 0.598029 | − | 0.801475i | \(-0.295951\pi\) |
−0.993112 | + | 0.117171i | \(0.962618\pi\) | |||||||
\(938\) | 5.38918i | 0.175963i | ||||||||
\(939\) | 29.1113 | + | 8.28955i | 0.950011 | + | 0.270519i | ||||
\(940\) | −4.47818 | + | 7.75644i | −0.146062 | + | 0.252987i | ||||
\(941\) | 23.1741 | − | 40.1388i | 0.755455 | − | 1.30849i | −0.189693 | − | 0.981843i | \(-0.560749\pi\) |
0.945148 | − | 0.326643i | \(-0.105917\pi\) | |||||||
\(942\) | −13.3598 | + | 12.9490i | −0.435284 | + | 0.421901i | ||||
\(943\) | 25.3074 | + | 14.6112i | 0.824122 | + | 0.475807i | ||||
\(944\) | 8.22333 | − | 4.74774i | 0.267647 | − | 0.154526i | ||||
\(945\) | 12.2623 | + | 13.4682i | 0.398891 | + | 0.438122i | ||||
\(946\) | 6.69426 | 0.217649 | ||||||||
\(947\) | −12.4511 | − | 21.5659i | −0.404605 | − | 0.700796i | 0.589670 | − | 0.807644i | \(-0.299258\pi\) |
−0.994275 | + | 0.106848i | \(0.965924\pi\) | |||||||
\(948\) | −0.355075 | − | 0.101109i | −0.0115323 | − | 0.00328387i | ||||
\(949\) | 1.68456 | + | 2.91774i | 0.0546831 | + | 0.0947139i | ||||
\(950\) | −4.47405 | − | 2.58309i | −0.145157 | − | 0.0838066i | ||||
\(951\) | −2.15778 | − | 0.614437i | −0.0699710 | − | 0.0199245i | ||||
\(952\) | −4.54210 | − | 2.62238i | −0.147210 | − | 0.0849919i | ||||
\(953\) | −54.5547 | −1.76720 | −0.883600 | − | 0.468243i | \(-0.844887\pi\) | ||||
−0.883600 | + | 0.468243i | \(0.844887\pi\) | |||||||
\(954\) | 5.71099 | − | 9.21483i | 0.184900 | − | 0.298341i | ||||
\(955\) | −4.67054 | − | 8.08961i | −0.151135 | − | 0.261773i | ||||
\(956\) | −5.50979 | + | 9.54323i | −0.178199 | + | 0.308650i | ||||
\(957\) | 4.52033 | − | 1.13589i | 0.146122 | − | 0.0367181i | ||||
\(958\) | 4.22624 | + | 7.32007i | 0.136544 | + | 0.236501i | ||||
\(959\) | −69.9412 | −2.25852 | ||||||||
\(960\) | 0.422115 | + | 1.67983i | 0.0136237 | + | 0.0542162i | ||||
\(961\) | 27.1340 | − | 14.9916i | 0.875289 | − | 0.483600i | ||||
\(962\) | − | 1.34217i | − | 0.0432735i | ||||||
\(963\) | 25.5095 | + | 47.5530i | 0.822031 | + | 1.53237i | ||||
\(964\) | −21.5818 | + | 12.4602i | −0.695101 | + | 0.401317i | ||||
\(965\) | 1.69281i | 0.0544935i | ||||||||
\(966\) | 18.7916 | + | 5.35098i | 0.604610 | + | 0.172165i | ||||
\(967\) | −35.0773 | + | 20.2519i | −1.12801 | + | 0.651257i | −0.943434 | − | 0.331561i | \(-0.892425\pi\) |
−0.184576 | + | 0.982818i | \(0.559091\pi\) | |||||||
\(968\) | 8.62951 | − | 4.98225i | 0.277363 | − | 0.160136i | ||||
\(969\) | 12.9847 | − | 3.26286i | 0.417130 | − | 0.104818i | ||||
\(970\) | 6.63966 | − | 11.5002i | 0.213187 | − | 0.369250i | ||||
\(971\) | 47.5688 | + | 27.4639i | 1.52656 | + | 0.881358i | 0.999503 | + | 0.0315255i | \(0.0100365\pi\) |
0.527053 | + | 0.849832i | \(0.323297\pi\) | |||||||
\(972\) | 10.1296 | + | 11.8487i | 0.324907 | + | 0.380047i | ||||
\(973\) | 3.70626 | − | 2.13981i | 0.118817 | − | 0.0685991i | ||||
\(974\) | 16.8806 | − | 29.2380i | 0.540888 | − | 0.936846i | ||||
\(975\) | 0.692610 | − | 0.671315i | 0.0221813 | − | 0.0214993i | ||||
\(976\) | 0.662787i | 0.0212153i | ||||||||
\(977\) | 9.01668i | 0.288469i | 0.989544 | + | 0.144235i | \(0.0460720\pi\) | ||||
−0.989544 | + | 0.144235i | \(0.953928\pi\) | |||||||
\(978\) | 4.42979 | − | 4.29359i | 0.141649 | − | 0.137294i | ||||
\(979\) | −0.396625 | + | 0.686975i | −0.0126762 | + | 0.0219558i | ||||
\(980\) | −4.57892 | + | 2.64364i | −0.146268 | + | 0.0844479i | ||||
\(981\) | −0.707645 | + | 22.6563i | −0.0225934 | + | 0.723359i | ||||
\(982\) | −6.69152 | − | 3.86335i | −0.213535 | − | 0.123284i | ||||
\(983\) | −10.0029 | + | 17.3255i | −0.319042 | + | 0.552596i | −0.980288 | − | 0.197572i | \(-0.936694\pi\) |
0.661247 | + | 0.750168i | \(0.270028\pi\) | |||||||
\(984\) | −15.2537 | + | 3.83303i | −0.486271 | + | 0.122192i | ||||
\(985\) | 13.7342 | − | 7.92946i | 0.437609 | − | 0.252654i | ||||
\(986\) | −3.42657 | + | 1.97833i | −0.109124 | + | 0.0630029i | ||||
\(987\) | −52.2986 | − | 14.8922i | −1.66468 | − | 0.474025i | ||||
\(988\) | 2.87698i | 0.0915291i | ||||||||
\(989\) | 18.3342 | − | 10.5853i | 0.582995 | − | 0.336592i | ||||
\(990\) | −2.69016 | + | 1.44311i | −0.0854988 | + | 0.0458652i | ||||
\(991\) | 53.7889i | 1.70866i | 0.519730 | + | 0.854330i | \(0.326032\pi\) | ||||
−0.519730 | + | 0.854330i | \(0.673968\pi\) | |||||||
\(992\) | 1.39033 | + | 5.39138i | 0.0441430 | + | 0.171176i | ||||
\(993\) | −8.53390 | − | 33.9611i | −0.270815 | − | 1.07772i | ||||
\(994\) | −39.3316 | −1.24752 | ||||||||
\(995\) | 6.80268 | + | 11.7826i | 0.215660 | + | 0.373533i | ||||
\(996\) | 5.76557 | − | 1.44880i | 0.182689 | − | 0.0459070i | ||||
\(997\) | 5.51236 | − | 9.54769i | 0.174578 | − | 0.302378i | −0.765437 | − | 0.643511i | \(-0.777477\pi\) |
0.940015 | + | 0.341133i | \(0.110810\pi\) | |||||||
\(998\) | 16.3590 | + | 28.3347i | 0.517836 | + | 0.896918i | ||||
\(999\) | −3.80410 | + | 11.9317i | −0.120356 | + | 0.377502i |
(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 | 930.2.o.e.161.16 | yes | 40 | |
3.2 | odd | 2 | inner | 930.2.o.e.161.4 | ✓ | 40 | |
31.26 | odd | 6 | inner | 930.2.o.e.491.14 | yes | 40 | |
93.26 | even | 6 | inner | 930.2.o.e.491.6 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.o.e.161.4 | ✓ | 40 | 3.2 | odd | 2 | inner | |
930.2.o.e.161.16 | yes | 40 | 1.1 | even | 1 | trivial | |
930.2.o.e.491.6 | yes | 40 | 93.26 | even | 6 | inner | |
930.2.o.e.491.14 | yes | 40 | 31.26 | odd | 6 | inner |