Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(76,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.i (of order \(2\), degree \(1\), 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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 76.2 | ||
Character | \(\chi\) | \(=\) | 1155.76 |
Dual form | 1155.2.i.d.76.1 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.26491i | 0.894429i | 0.894427 | + | 0.447215i | \(0.147584\pi\) | ||||
−0.894427 | + | 0.447215i | \(0.852416\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0.399993 | 0.199996 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | −1.26491 | −0.516399 | ||||||||
\(7\) | 0.0556365 | + | 2.64517i | 0.0210286 | + | 0.999779i | ||||
\(8\) | 3.03578i | 1.07331i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −1.26491 | −0.400001 | ||||||||
\(11\) | −0.516444 | + | 3.27617i | −0.155714 | + | 0.987802i | ||||
\(12\) | 0.399993i | 0.115468i | ||||||||
\(13\) | 6.21341 | 1.72329 | 0.861645 | − | 0.507511i | \(-0.169434\pi\) | ||||
0.861645 | + | 0.507511i | \(0.169434\pi\) | |||||||
\(14\) | −3.34591 | + | 0.0703753i | −0.894231 | + | 0.0188086i | ||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −3.04002 | −0.760005 | ||||||||
\(17\) | 1.62680 | 0.394557 | 0.197278 | − | 0.980348i | \(-0.436790\pi\) | ||||
0.197278 | + | 0.980348i | \(0.436790\pi\) | |||||||
\(18\) | − | 1.26491i | − | 0.298143i | ||||||
\(19\) | 4.38730 | 1.00652 | 0.503258 | − | 0.864136i | \(-0.332134\pi\) | ||||
0.503258 | + | 0.864136i | \(0.332134\pi\) | |||||||
\(20\) | 0.399993i | 0.0894411i | ||||||||
\(21\) | −2.64517 | + | 0.0556365i | −0.577223 | + | 0.0121409i | ||||
\(22\) | −4.14407 | − | 0.653257i | −0.883519 | − | 0.139275i | ||||
\(23\) | −1.24003 | −0.258565 | −0.129283 | − | 0.991608i | \(-0.541267\pi\) | ||||
−0.129283 | + | 0.991608i | \(0.541267\pi\) | |||||||
\(24\) | −3.03578 | −0.619677 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 7.85943i | 1.54136i | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0.0222542 | + | 1.05805i | 0.00420564 | + | 0.199952i | ||||
\(29\) | − | 9.91159i | − | 1.84054i | −0.391289 | − | 0.920268i | \(-0.627971\pi\) | ||
0.391289 | − | 0.920268i | \(-0.372029\pi\) | |||||||
\(30\) | − | 1.26491i | − | 0.230941i | ||||||
\(31\) | − | 7.78246i | − | 1.39777i | −0.715233 | − | 0.698886i | \(-0.753680\pi\) | ||
0.715233 | − | 0.698886i | \(-0.246320\pi\) | |||||||
\(32\) | 2.22620i | 0.393541i | ||||||||
\(33\) | −3.27617 | − | 0.516444i | −0.570308 | − | 0.0899014i | ||||
\(34\) | 2.05776i | 0.352903i | ||||||||
\(35\) | −2.64517 | + | 0.0556365i | −0.447115 | + | 0.00940428i | ||||
\(36\) | −0.399993 | −0.0666655 | ||||||||
\(37\) | 1.61516 | 0.265530 | 0.132765 | − | 0.991148i | \(-0.457614\pi\) | ||||
0.132765 | + | 0.991148i | \(0.457614\pi\) | |||||||
\(38\) | 5.54956i | 0.900258i | ||||||||
\(39\) | 6.21341i | 0.994942i | ||||||||
\(40\) | −3.03578 | −0.480000 | ||||||||
\(41\) | −4.95141 | −0.773280 | −0.386640 | − | 0.922231i | \(-0.626364\pi\) | ||||
−0.386640 | + | 0.922231i | \(0.626364\pi\) | |||||||
\(42\) | −0.0703753 | − | 3.34591i | −0.0108592 | − | 0.516285i | ||||
\(43\) | 3.35295i | 0.511320i | 0.966767 | + | 0.255660i | \(0.0822928\pi\) | ||||
−0.966767 | + | 0.255660i | \(0.917707\pi\) | |||||||
\(44\) | −0.206574 | + | 1.31044i | −0.0311422 | + | 0.197557i | ||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | − | 1.56854i | − | 0.231268i | ||||||
\(47\) | − | 4.74958i | − | 0.692797i | −0.938087 | − | 0.346398i | \(-0.887405\pi\) | ||
0.938087 | − | 0.346398i | \(-0.112595\pi\) | |||||||
\(48\) | − | 3.04002i | − | 0.438789i | ||||||
\(49\) | −6.99381 | + | 0.294335i | −0.999116 | + | 0.0420479i | ||||
\(50\) | − | 1.26491i | − | 0.178886i | ||||||
\(51\) | 1.62680i | 0.227797i | ||||||||
\(52\) | 2.48532 | 0.344652 | ||||||||
\(53\) | −8.51450 | −1.16956 | −0.584778 | − | 0.811193i | \(-0.698818\pi\) | ||||
−0.584778 | + | 0.811193i | \(0.698818\pi\) | |||||||
\(54\) | 1.26491 | 0.172133 | ||||||||
\(55\) | −3.27617 | − | 0.516444i | −0.441759 | − | 0.0696373i | ||||
\(56\) | −8.03015 | + | 0.168900i | −1.07307 | + | 0.0225703i | ||||
\(57\) | 4.38730i | 0.581113i | ||||||||
\(58\) | 12.5373 | 1.64623 | ||||||||
\(59\) | 4.49064i | 0.584632i | 0.956322 | + | 0.292316i | \(0.0944259\pi\) | ||||
−0.956322 | + | 0.292316i | \(0.905574\pi\) | |||||||
\(60\) | −0.399993 | −0.0516388 | ||||||||
\(61\) | −6.43034 | −0.823320 | −0.411660 | − | 0.911337i | \(-0.635051\pi\) | ||||
−0.411660 | + | 0.911337i | \(0.635051\pi\) | |||||||
\(62\) | 9.84415 | 1.25021 | ||||||||
\(63\) | −0.0556365 | − | 2.64517i | −0.00700954 | − | 0.333260i | ||||
\(64\) | −8.89600 | −1.11200 | ||||||||
\(65\) | 6.21341i | 0.770679i | ||||||||
\(66\) | 0.653257 | − | 4.14407i | 0.0804104 | − | 0.510100i | ||||
\(67\) | 3.96452 | 0.484343 | 0.242172 | − | 0.970233i | \(-0.422140\pi\) | ||||
0.242172 | + | 0.970233i | \(0.422140\pi\) | |||||||
\(68\) | 0.650708 | 0.0789099 | ||||||||
\(69\) | − | 1.24003i | − | 0.149283i | ||||||
\(70\) | −0.0703753 | − | 3.34591i | −0.00841146 | − | 0.399912i | ||||
\(71\) | 11.2241 | 1.33205 | 0.666025 | − | 0.745929i | \(-0.267994\pi\) | ||||
0.666025 | + | 0.745929i | \(0.267994\pi\) | |||||||
\(72\) | − | 3.03578i | − | 0.357771i | ||||||
\(73\) | 8.16211 | 0.955303 | 0.477651 | − | 0.878549i | \(-0.341488\pi\) | ||||
0.477651 | + | 0.878549i | \(0.341488\pi\) | |||||||
\(74\) | 2.04303i | 0.237498i | ||||||||
\(75\) | − | 1.00000i | − | 0.115470i | ||||||
\(76\) | 1.75489 | 0.201300 | ||||||||
\(77\) | −8.69475 | − | 1.18381i | −0.990858 | − | 0.134907i | ||||
\(78\) | −7.85943 | −0.889905 | ||||||||
\(79\) | 13.4557i | 1.51389i | 0.653481 | + | 0.756943i | \(0.273308\pi\) | ||||
−0.653481 | + | 0.756943i | \(0.726692\pi\) | |||||||
\(80\) | − | 3.04002i | − | 0.339885i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 6.26310i | − | 0.691644i | ||||||
\(83\) | −2.78335 | −0.305512 | −0.152756 | − | 0.988264i | \(-0.548815\pi\) | ||||
−0.152756 | + | 0.988264i | \(0.548815\pi\) | |||||||
\(84\) | −1.05805 | + | 0.0222542i | −0.115442 | + | 0.00242813i | ||||
\(85\) | 1.62680i | 0.176451i | ||||||||
\(86\) | −4.24119 | −0.457340 | ||||||||
\(87\) | 9.91159 | 1.06263 | ||||||||
\(88\) | −9.94574 | − | 1.56781i | −1.06022 | − | 0.167129i | ||||
\(89\) | 2.92087i | 0.309612i | 0.987945 | + | 0.154806i | \(0.0494752\pi\) | ||||
−0.987945 | + | 0.154806i | \(0.950525\pi\) | |||||||
\(90\) | 1.26491 | 0.133334 | ||||||||
\(91\) | 0.345692 | + | 16.4355i | 0.0362384 | + | 1.72291i | ||||
\(92\) | −0.496005 | −0.0517121 | ||||||||
\(93\) | 7.78246 | 0.807004 | ||||||||
\(94\) | 6.00780 | 0.619658 | ||||||||
\(95\) | 4.38730i | 0.450128i | ||||||||
\(96\) | −2.22620 | −0.227211 | ||||||||
\(97\) | − | 15.7071i | − | 1.59482i | −0.603439 | − | 0.797409i | \(-0.706203\pi\) | ||
0.603439 | − | 0.797409i | \(-0.293797\pi\) | |||||||
\(98\) | −0.372309 | − | 8.84657i | −0.0376089 | − | 0.893638i | ||||
\(99\) | 0.516444 | − | 3.27617i | 0.0519046 | − | 0.329267i | ||||
\(100\) | −0.399993 | −0.0399993 | ||||||||
\(101\) | −12.6777 | −1.26148 | −0.630740 | − | 0.775994i | \(-0.717248\pi\) | ||||
−0.630740 | + | 0.775994i | \(0.717248\pi\) | |||||||
\(102\) | −2.05776 | −0.203749 | ||||||||
\(103\) | − | 15.6509i | − | 1.54213i | −0.636756 | − | 0.771065i | \(-0.719724\pi\) | ||
0.636756 | − | 0.771065i | \(-0.280276\pi\) | |||||||
\(104\) | 18.8626i | 1.84963i | ||||||||
\(105\) | −0.0556365 | − | 2.64517i | −0.00542956 | − | 0.258142i | ||||
\(106\) | − | 10.7701i | − | 1.04609i | ||||||
\(107\) | 3.10573i | 0.300242i | 0.988668 | + | 0.150121i | \(0.0479663\pi\) | ||||
−0.988668 | + | 0.150121i | \(0.952034\pi\) | |||||||
\(108\) | − | 0.399993i | − | 0.0384893i | ||||||
\(109\) | − | 3.01992i | − | 0.289256i | −0.989486 | − | 0.144628i | \(-0.953801\pi\) | ||
0.989486 | − | 0.144628i | \(-0.0461985\pi\) | |||||||
\(110\) | 0.653257 | − | 4.14407i | 0.0622856 | − | 0.395122i | ||||
\(111\) | 1.61516i | 0.153304i | ||||||||
\(112\) | −0.169136 | − | 8.04136i | −0.0159818 | − | 0.759837i | ||||
\(113\) | 14.5147 | 1.36543 | 0.682713 | − | 0.730686i | \(-0.260800\pi\) | ||||
0.682713 | + | 0.730686i | \(0.260800\pi\) | |||||||
\(114\) | −5.54956 | −0.519764 | ||||||||
\(115\) | − | 1.24003i | − | 0.115634i | ||||||
\(116\) | − | 3.96456i | − | 0.368100i | ||||||
\(117\) | −6.21341 | −0.574430 | ||||||||
\(118\) | −5.68027 | −0.522912 | ||||||||
\(119\) | 0.0905093 | + | 4.30315i | 0.00829698 | + | 0.394469i | ||||
\(120\) | − | 3.03578i | − | 0.277128i | ||||||
\(121\) | −10.4666 | − | 3.38392i | −0.951506 | − | 0.307629i | ||||
\(122\) | − | 8.13382i | − | 0.736402i | ||||||
\(123\) | − | 4.95141i | − | 0.446453i | ||||||
\(124\) | − | 3.11293i | − | 0.279549i | ||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 3.34591 | − | 0.0703753i | 0.298077 | − | 0.00626953i | ||||
\(127\) | − | 19.3903i | − | 1.72061i | −0.509780 | − | 0.860305i | \(-0.670273\pi\) | ||
0.509780 | − | 0.860305i | \(-0.329727\pi\) | |||||||
\(128\) | − | 6.80026i | − | 0.601064i | ||||||
\(129\) | −3.35295 | −0.295211 | ||||||||
\(130\) | −7.85943 | −0.689318 | ||||||||
\(131\) | −3.50671 | −0.306383 | −0.153192 | − | 0.988197i | \(-0.548955\pi\) | ||||
−0.153192 | + | 0.988197i | \(0.548955\pi\) | |||||||
\(132\) | −1.31044 | − | 0.206574i | −0.114059 | − | 0.0179799i | ||||
\(133\) | 0.244094 | + | 11.6051i | 0.0211656 | + | 1.00629i | ||||
\(134\) | 5.01478i | 0.433211i | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 4.93861i | 0.423482i | ||||||||
\(137\) | 4.53186 | 0.387183 | 0.193591 | − | 0.981082i | \(-0.437986\pi\) | ||||
0.193591 | + | 0.981082i | \(0.437986\pi\) | |||||||
\(138\) | 1.56854 | 0.133523 | ||||||||
\(139\) | 13.8980 | 1.17882 | 0.589408 | − | 0.807836i | \(-0.299361\pi\) | ||||
0.589408 | + | 0.807836i | \(0.299361\pi\) | |||||||
\(140\) | −1.05805 | + | 0.0222542i | −0.0894213 | + | 0.00188082i | ||||
\(141\) | 4.74958 | 0.399986 | ||||||||
\(142\) | 14.1975i | 1.19142i | ||||||||
\(143\) | −3.20888 | + | 20.3562i | −0.268340 | + | 1.70227i | ||||
\(144\) | 3.04002 | 0.253335 | ||||||||
\(145\) | 9.91159 | 0.823113 | ||||||||
\(146\) | 10.3244i | 0.854451i | ||||||||
\(147\) | −0.294335 | − | 6.99381i | −0.0242764 | − | 0.576840i | ||||
\(148\) | 0.646050 | 0.0531050 | ||||||||
\(149\) | − | 4.75210i | − | 0.389307i | −0.980872 | − | 0.194653i | \(-0.937642\pi\) | ||
0.980872 | − | 0.194653i | \(-0.0623582\pi\) | |||||||
\(150\) | 1.26491 | 0.103280 | ||||||||
\(151\) | 3.90311i | 0.317630i | 0.987308 | + | 0.158815i | \(0.0507674\pi\) | ||||
−0.987308 | + | 0.158815i | \(0.949233\pi\) | |||||||
\(152\) | 13.3189i | 1.08031i | ||||||||
\(153\) | −1.62680 | −0.131519 | ||||||||
\(154\) | 1.49741 | − | 10.9981i | 0.120665 | − | 0.886253i | ||||
\(155\) | 7.78246 | 0.625103 | ||||||||
\(156\) | 2.48532i | 0.198985i | ||||||||
\(157\) | − | 11.3424i | − | 0.905223i | −0.891708 | − | 0.452612i | \(-0.850492\pi\) | ||
0.891708 | − | 0.452612i | \(-0.149508\pi\) | |||||||
\(158\) | −17.0203 | −1.35406 | ||||||||
\(159\) | − | 8.51450i | − | 0.675244i | ||||||
\(160\) | −2.22620 | −0.175997 | ||||||||
\(161\) | −0.0689912 | − | 3.28010i | −0.00543727 | − | 0.258508i | ||||
\(162\) | 1.26491i | 0.0993810i | ||||||||
\(163\) | 4.05059 | 0.317267 | 0.158633 | − | 0.987338i | \(-0.449291\pi\) | ||||
0.158633 | + | 0.987338i | \(0.449291\pi\) | |||||||
\(164\) | −1.98053 | −0.154653 | ||||||||
\(165\) | 0.516444 | − | 3.27617i | 0.0402051 | − | 0.255049i | ||||
\(166\) | − | 3.52070i | − | 0.273259i | ||||||
\(167\) | 18.2979 | 1.41593 | 0.707967 | − | 0.706246i | \(-0.249613\pi\) | ||||
0.707967 | + | 0.706246i | \(0.249613\pi\) | |||||||
\(168\) | −0.168900 | − | 8.03015i | −0.0130309 | − | 0.619540i | ||||
\(169\) | 25.6065 | 1.96973 | ||||||||
\(170\) | −2.05776 | −0.157823 | ||||||||
\(171\) | −4.38730 | −0.335505 | ||||||||
\(172\) | 1.34116i | 0.102262i | ||||||||
\(173\) | −5.19325 | −0.394835 | −0.197418 | − | 0.980319i | \(-0.563256\pi\) | ||||
−0.197418 | + | 0.980319i | \(0.563256\pi\) | |||||||
\(174\) | 12.5373i | 0.950451i | ||||||||
\(175\) | −0.0556365 | − | 2.64517i | −0.00420572 | − | 0.199956i | ||||
\(176\) | 1.57000 | − | 9.95962i | 0.118343 | − | 0.750735i | ||||
\(177\) | −4.49064 | −0.337537 | ||||||||
\(178\) | −3.69465 | −0.276926 | ||||||||
\(179\) | −15.8800 | −1.18692 | −0.593462 | − | 0.804862i | \(-0.702239\pi\) | ||||
−0.593462 | + | 0.804862i | \(0.702239\pi\) | |||||||
\(180\) | − | 0.399993i | − | 0.0298137i | ||||||
\(181\) | − | 14.5061i | − | 1.07823i | −0.842232 | − | 0.539115i | \(-0.818759\pi\) | ||
0.842232 | − | 0.539115i | \(-0.181241\pi\) | |||||||
\(182\) | −20.7895 | + | 0.437271i | −1.54102 | + | 0.0324127i | ||||
\(183\) | − | 6.43034i | − | 0.475344i | ||||||
\(184\) | − | 3.76448i | − | 0.277521i | ||||||
\(185\) | 1.61516i | 0.118749i | ||||||||
\(186\) | 9.84415i | 0.721808i | ||||||||
\(187\) | −0.840151 | + | 5.32967i | −0.0614379 | + | 0.389744i | ||||
\(188\) | − | 1.89980i | − | 0.138557i | ||||||
\(189\) | 2.64517 | − | 0.0556365i | 0.192408 | − | 0.00404696i | ||||
\(190\) | −5.54956 | −0.402607 | ||||||||
\(191\) | 15.8476 | 1.14669 | 0.573345 | − | 0.819314i | \(-0.305645\pi\) | ||||
0.573345 | + | 0.819314i | \(0.305645\pi\) | |||||||
\(192\) | − | 8.89600i | − | 0.642013i | ||||||
\(193\) | 8.94943i | 0.644194i | 0.946707 | + | 0.322097i | \(0.104388\pi\) | ||||
−0.946707 | + | 0.322097i | \(0.895612\pi\) | |||||||
\(194\) | 19.8682 | 1.42645 | ||||||||
\(195\) | −6.21341 | −0.444952 | ||||||||
\(196\) | −2.79747 | + | 0.117732i | −0.199819 | + | 0.00840943i | ||||
\(197\) | − | 1.43075i | − | 0.101936i | −0.998700 | − | 0.0509682i | \(-0.983769\pi\) | ||
0.998700 | − | 0.0509682i | \(-0.0162307\pi\) | |||||||
\(198\) | 4.14407 | + | 0.653257i | 0.294506 | + | 0.0464250i | ||||
\(199\) | − | 1.09103i | − | 0.0773410i | −0.999252 | − | 0.0386705i | \(-0.987688\pi\) | ||
0.999252 | − | 0.0386705i | \(-0.0123123\pi\) | |||||||
\(200\) | − | 3.03578i | − | 0.214662i | ||||||
\(201\) | 3.96452i | 0.279636i | ||||||||
\(202\) | − | 16.0362i | − | 1.12830i | ||||||
\(203\) | 26.2178 | − | 0.551446i | 1.84013 | − | 0.0387039i | ||||
\(204\) | 0.650708i | 0.0455586i | ||||||||
\(205\) | − | 4.95141i | − | 0.345821i | ||||||
\(206\) | 19.7971 | 1.37933 | ||||||||
\(207\) | 1.24003 | 0.0861884 | ||||||||
\(208\) | −18.8889 | −1.30971 | ||||||||
\(209\) | −2.26580 | + | 14.3735i | −0.156728 | + | 0.994239i | ||||
\(210\) | 3.34591 | − | 0.0703753i | 0.230890 | − | 0.00485636i | ||||
\(211\) | 7.95189i | 0.547430i | 0.961811 | + | 0.273715i | \(0.0882526\pi\) | ||||
−0.961811 | + | 0.273715i | \(0.911747\pi\) | |||||||
\(212\) | −3.40574 | −0.233907 | ||||||||
\(213\) | 11.2241i | 0.769060i | ||||||||
\(214\) | −3.92848 | −0.268545 | ||||||||
\(215\) | −3.35295 | −0.228669 | ||||||||
\(216\) | 3.03578 | 0.206559 | ||||||||
\(217\) | 20.5859 | − | 0.432989i | 1.39746 | − | 0.0293932i | ||||
\(218\) | 3.81994 | 0.258719 | ||||||||
\(219\) | 8.16211i | 0.551544i | ||||||||
\(220\) | −1.31044 | − | 0.206574i | −0.0883501 | − | 0.0139272i | ||||
\(221\) | 10.1080 | 0.679936 | ||||||||
\(222\) | −2.04303 | −0.137119 | ||||||||
\(223\) | 22.6413i | 1.51618i | 0.652152 | + | 0.758088i | \(0.273866\pi\) | ||||
−0.652152 | + | 0.758088i | \(0.726134\pi\) | |||||||
\(224\) | −5.88868 | + | 0.123858i | −0.393454 | + | 0.00827562i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 18.3598i | 1.22128i | ||||||||
\(227\) | −14.6344 | −0.971317 | −0.485658 | − | 0.874149i | \(-0.661420\pi\) | ||||
−0.485658 | + | 0.874149i | \(0.661420\pi\) | |||||||
\(228\) | 1.75489i | 0.116220i | ||||||||
\(229\) | 25.4139i | 1.67940i | 0.543053 | + | 0.839698i | \(0.317268\pi\) | ||||
−0.543053 | + | 0.839698i | \(0.682732\pi\) | |||||||
\(230\) | 1.56854 | 0.103426 | ||||||||
\(231\) | 1.18381 | − | 8.69475i | 0.0778887 | − | 0.572072i | ||||
\(232\) | 30.0894 | 1.97547 | ||||||||
\(233\) | 26.6512i | 1.74598i | 0.487741 | + | 0.872988i | \(0.337821\pi\) | ||||
−0.487741 | + | 0.872988i | \(0.662179\pi\) | |||||||
\(234\) | − | 7.85943i | − | 0.513787i | ||||||
\(235\) | 4.74958 | 0.309828 | ||||||||
\(236\) | 1.79622i | 0.116924i | ||||||||
\(237\) | −13.4557 | −0.874043 | ||||||||
\(238\) | −5.44312 | + | 0.114487i | −0.352825 | + | 0.00742106i | ||||
\(239\) | − | 5.40933i | − | 0.349901i | −0.984577 | − | 0.174950i | \(-0.944024\pi\) | ||
0.984577 | − | 0.174950i | \(-0.0559765\pi\) | |||||||
\(240\) | 3.04002 | 0.196232 | ||||||||
\(241\) | 7.63142 | 0.491583 | 0.245791 | − | 0.969323i | \(-0.420952\pi\) | ||||
0.245791 | + | 0.969323i | \(0.420952\pi\) | |||||||
\(242\) | 4.28036 | − | 13.2393i | 0.275152 | − | 0.851055i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −2.57209 | −0.164661 | ||||||||
\(245\) | −0.294335 | − | 6.99381i | −0.0188044 | − | 0.446818i | ||||
\(246\) | 6.26310 | 0.399321 | ||||||||
\(247\) | 27.2601 | 1.73452 | ||||||||
\(248\) | 23.6259 | 1.50024 | ||||||||
\(249\) | − | 2.78335i | − | 0.176387i | ||||||
\(250\) | 1.26491 | 0.0800002 | ||||||||
\(251\) | − | 6.92390i | − | 0.437033i | −0.975833 | − | 0.218516i | \(-0.929878\pi\) | ||
0.975833 | − | 0.218516i | \(-0.0701217\pi\) | |||||||
\(252\) | −0.0222542 | − | 1.05805i | −0.00140188 | − | 0.0666507i | ||||
\(253\) | 0.640409 | − | 4.06256i | 0.0402621 | − | 0.255411i | ||||
\(254\) | 24.5270 | 1.53896 | ||||||||
\(255\) | −1.62680 | −0.101874 | ||||||||
\(256\) | −9.19025 | −0.574390 | ||||||||
\(257\) | − | 9.73821i | − | 0.607453i | −0.952759 | − | 0.303727i | \(-0.901769\pi\) | ||
0.952759 | − | 0.303727i | \(-0.0982309\pi\) | |||||||
\(258\) | − | 4.24119i | − | 0.264045i | ||||||
\(259\) | 0.0898615 | + | 4.27235i | 0.00558372 | + | 0.265471i | ||||
\(260\) | 2.48532i | 0.154133i | ||||||||
\(261\) | 9.91159i | 0.613512i | ||||||||
\(262\) | − | 4.43569i | − | 0.274038i | ||||||
\(263\) | 28.3755i | 1.74971i | 0.484386 | + | 0.874854i | \(0.339043\pi\) | ||||
−0.484386 | + | 0.874854i | \(0.660957\pi\) | |||||||
\(264\) | 1.56781 | − | 9.94574i | 0.0964922 | − | 0.612118i | ||||
\(265\) | − | 8.51450i | − | 0.523041i | ||||||
\(266\) | −14.6795 | + | 0.308758i | −0.900059 | + | 0.0189312i | ||||
\(267\) | −2.92087 | −0.178754 | ||||||||
\(268\) | 1.58578 | 0.0968669 | ||||||||
\(269\) | − | 2.07759i | − | 0.126673i | −0.997992 | − | 0.0633364i | \(-0.979826\pi\) | ||
0.997992 | − | 0.0633364i | \(-0.0201741\pi\) | |||||||
\(270\) | 1.26491i | 0.0769802i | ||||||||
\(271\) | −15.0097 | −0.911773 | −0.455886 | − | 0.890038i | \(-0.650678\pi\) | ||||
−0.455886 | + | 0.890038i | \(0.650678\pi\) | |||||||
\(272\) | −4.94550 | −0.299865 | ||||||||
\(273\) | −16.4355 | + | 0.345692i | −0.994722 | + | 0.0209222i | ||||
\(274\) | 5.73241i | 0.346308i | ||||||||
\(275\) | 0.516444 | − | 3.27617i | 0.0311427 | − | 0.197560i | ||||
\(276\) | − | 0.496005i | − | 0.0298560i | ||||||
\(277\) | 8.87985i | 0.533539i | 0.963760 | + | 0.266769i | \(0.0859562\pi\) | ||||
−0.963760 | + | 0.266769i | \(0.914044\pi\) | |||||||
\(278\) | 17.5798i | 1.05437i | ||||||||
\(279\) | 7.78246i | 0.465924i | ||||||||
\(280\) | −0.168900 | − | 8.03015i | −0.0100937 | − | 0.479893i | ||||
\(281\) | − | 26.5925i | − | 1.58638i | −0.608976 | − | 0.793189i | \(-0.708419\pi\) | ||
0.608976 | − | 0.793189i | \(-0.291581\pi\) | |||||||
\(282\) | 6.00780i | 0.357760i | ||||||||
\(283\) | 17.3320 | 1.03028 | 0.515141 | − | 0.857105i | \(-0.327739\pi\) | ||||
0.515141 | + | 0.857105i | \(0.327739\pi\) | |||||||
\(284\) | 4.48954 | 0.266405 | ||||||||
\(285\) | −4.38730 | −0.259881 | ||||||||
\(286\) | −25.7488 | − | 4.05896i | −1.52256 | − | 0.240011i | ||||
\(287\) | −0.275479 | − | 13.0973i | −0.0162610 | − | 0.773109i | ||||
\(288\) | − | 2.22620i | − | 0.131180i | ||||||
\(289\) | −14.3535 | −0.844325 | ||||||||
\(290\) | 12.5373i | 0.736216i | ||||||||
\(291\) | 15.7071 | 0.920769 | ||||||||
\(292\) | 3.26478 | 0.191057 | ||||||||
\(293\) | 25.9648 | 1.51688 | 0.758440 | − | 0.651743i | \(-0.225962\pi\) | ||||
0.758440 | + | 0.651743i | \(0.225962\pi\) | |||||||
\(294\) | 8.84657 | − | 0.372309i | 0.515942 | − | 0.0217135i | ||||
\(295\) | −4.49064 | −0.261455 | ||||||||
\(296\) | 4.90326i | 0.284996i | ||||||||
\(297\) | 3.27617 | + | 0.516444i | 0.190103 | + | 0.0299671i | ||||
\(298\) | 6.01099 | 0.348207 | ||||||||
\(299\) | −7.70485 | −0.445583 | ||||||||
\(300\) | − | 0.399993i | − | 0.0230936i | ||||||
\(301\) | −8.86911 | + | 0.186546i | −0.511207 | + | 0.0107524i | ||||
\(302\) | −4.93709 | −0.284098 | ||||||||
\(303\) | − | 12.6777i | − | 0.728316i | ||||||
\(304\) | −13.3375 | −0.764958 | ||||||||
\(305\) | − | 6.43034i | − | 0.368200i | ||||||
\(306\) | − | 2.05776i | − | 0.117634i | ||||||
\(307\) | −20.9514 | −1.19576 | −0.597879 | − | 0.801586i | \(-0.703990\pi\) | ||||
−0.597879 | + | 0.801586i | \(0.703990\pi\) | |||||||
\(308\) | −3.47783 | − | 0.473514i | −0.198168 | − | 0.0269809i | ||||
\(309\) | 15.6509 | 0.890349 | ||||||||
\(310\) | 9.84415i | 0.559110i | ||||||||
\(311\) | 15.3862i | 0.872471i | 0.899832 | + | 0.436236i | \(0.143689\pi\) | ||||
−0.899832 | + | 0.436236i | \(0.856311\pi\) | |||||||
\(312\) | −18.8626 | −1.06788 | ||||||||
\(313\) | 1.85796i | 0.105018i | 0.998620 | + | 0.0525092i | \(0.0167219\pi\) | ||||
−0.998620 | + | 0.0525092i | \(0.983278\pi\) | |||||||
\(314\) | 14.3472 | 0.809658 | ||||||||
\(315\) | 2.64517 | − | 0.0556365i | 0.149038 | − | 0.00313476i | ||||
\(316\) | 5.38219i | 0.302772i | ||||||||
\(317\) | −7.48284 | −0.420278 | −0.210139 | − | 0.977671i | \(-0.567392\pi\) | ||||
−0.210139 | + | 0.977671i | \(0.567392\pi\) | |||||||
\(318\) | 10.7701 | 0.603958 | ||||||||
\(319\) | 32.4720 | + | 5.11878i | 1.81809 | + | 0.286597i | ||||
\(320\) | − | 8.89600i | − | 0.497301i | ||||||
\(321\) | −3.10573 | −0.173345 | ||||||||
\(322\) | 4.14904 | − | 0.0872679i | 0.231217 | − | 0.00486325i | ||||
\(323\) | 7.13726 | 0.397128 | ||||||||
\(324\) | 0.399993 | 0.0222218 | ||||||||
\(325\) | −6.21341 | −0.344658 | ||||||||
\(326\) | 5.12365i | 0.283773i | ||||||||
\(327\) | 3.01992 | 0.167002 | ||||||||
\(328\) | − | 15.0314i | − | 0.829970i | ||||||
\(329\) | 12.5634 | − | 0.264250i | 0.692644 | − | 0.0145686i | ||||
\(330\) | 4.14407 | + | 0.653257i | 0.228124 | + | 0.0359606i | ||||
\(331\) | −5.79400 | −0.318467 | −0.159233 | − | 0.987241i | \(-0.550902\pi\) | ||||
−0.159233 | + | 0.987241i | \(0.550902\pi\) | |||||||
\(332\) | −1.11332 | −0.0611013 | ||||||||
\(333\) | −1.61516 | −0.0885100 | ||||||||
\(334\) | 23.1453i | 1.26645i | ||||||||
\(335\) | 3.96452i | 0.216605i | ||||||||
\(336\) | 8.04136 | − | 0.169136i | 0.438692 | − | 0.00922712i | ||||
\(337\) | − | 29.3608i | − | 1.59938i | −0.600412 | − | 0.799691i | \(-0.704997\pi\) | ||
0.600412 | − | 0.799691i | \(-0.295003\pi\) | |||||||
\(338\) | 32.3900i | 1.76178i | ||||||||
\(339\) | 14.5147i | 0.788329i | ||||||||
\(340\) | 0.650708i | 0.0352896i | ||||||||
\(341\) | 25.4967 | + | 4.01921i | 1.38072 | + | 0.217652i | ||||
\(342\) | − | 5.54956i | − | 0.300086i | ||||||
\(343\) | −1.16768 | − | 18.4834i | −0.0630486 | − | 0.998010i | ||||
\(344\) | −10.1788 | −0.548806 | ||||||||
\(345\) | 1.24003 | 0.0667612 | ||||||||
\(346\) | − | 6.56901i | − | 0.353152i | ||||||
\(347\) | 14.1803i | 0.761241i | 0.924731 | + | 0.380620i | \(0.124289\pi\) | ||||
−0.924731 | + | 0.380620i | \(0.875711\pi\) | |||||||
\(348\) | 3.96456 | 0.212523 | ||||||||
\(349\) | −26.3065 | −1.40815 | −0.704076 | − | 0.710124i | \(-0.748639\pi\) | ||||
−0.704076 | + | 0.710124i | \(0.748639\pi\) | |||||||
\(350\) | 3.34591 | − | 0.0703753i | 0.178846 | − | 0.00376172i | ||||
\(351\) | − | 6.21341i | − | 0.331647i | ||||||
\(352\) | −7.29342 | − | 1.14971i | −0.388741 | − | 0.0612797i | ||||
\(353\) | 6.86576i | 0.365428i | 0.983166 | + | 0.182714i | \(0.0584882\pi\) | ||||
−0.983166 | + | 0.182714i | \(0.941512\pi\) | |||||||
\(354\) | − | 5.68027i | − | 0.301903i | ||||||
\(355\) | 11.2241i | 0.595711i | ||||||||
\(356\) | 1.16833i | 0.0619212i | ||||||||
\(357\) | −4.30315 | + | 0.0905093i | −0.227747 | + | 0.00479026i | ||||
\(358\) | − | 20.0868i | − | 1.06162i | ||||||
\(359\) | 7.03693i | 0.371395i | 0.982607 | + | 0.185697i | \(0.0594544\pi\) | ||||
−0.982607 | + | 0.185697i | \(0.940546\pi\) | |||||||
\(360\) | 3.03578 | 0.160000 | ||||||||
\(361\) | 0.248432 | 0.0130753 | ||||||||
\(362\) | 18.3490 | 0.964401 | ||||||||
\(363\) | 3.38392 | − | 10.4666i | 0.177610 | − | 0.549353i | ||||
\(364\) | 0.138274 | + | 6.57408i | 0.00724755 | + | 0.344576i | ||||
\(365\) | 8.16211i | 0.427224i | ||||||||
\(366\) | 8.13382 | 0.425162 | ||||||||
\(367\) | − | 19.8324i | − | 1.03524i | −0.855610 | − | 0.517621i | \(-0.826818\pi\) | ||
0.855610 | − | 0.517621i | \(-0.173182\pi\) | |||||||
\(368\) | 3.76973 | 0.196511 | ||||||||
\(369\) | 4.95141 | 0.257760 | ||||||||
\(370\) | −2.04303 | −0.106212 | ||||||||
\(371\) | −0.473717 | − | 22.5223i | −0.0245941 | − | 1.16930i | ||||
\(372\) | 3.11293 | 0.161398 | ||||||||
\(373\) | 26.5572i | 1.37508i | 0.726146 | + | 0.687540i | \(0.241309\pi\) | ||||
−0.726146 | + | 0.687540i | \(0.758691\pi\) | |||||||
\(374\) | −6.74157 | − | 1.06272i | −0.348598 | − | 0.0549518i | ||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 14.4187 | 0.743587 | ||||||||
\(377\) | − | 61.5848i | − | 3.17178i | ||||||
\(378\) | 0.0703753 | + | 3.34591i | 0.00361972 | + | 0.172095i | ||||
\(379\) | 27.7011 | 1.42291 | 0.711454 | − | 0.702732i | \(-0.248037\pi\) | ||||
0.711454 | + | 0.702732i | \(0.248037\pi\) | |||||||
\(380\) | 1.75489i | 0.0900239i | ||||||||
\(381\) | 19.3903 | 0.993395 | ||||||||
\(382\) | 20.0458i | 1.02563i | ||||||||
\(383\) | − | 8.53084i | − | 0.435906i | −0.975959 | − | 0.217953i | \(-0.930062\pi\) | ||
0.975959 | − | 0.217953i | \(-0.0699379\pi\) | |||||||
\(384\) | 6.80026 | 0.347024 | ||||||||
\(385\) | 1.18381 | − | 8.69475i | 0.0603323 | − | 0.443125i | ||||
\(386\) | −11.3203 | −0.576186 | ||||||||
\(387\) | − | 3.35295i | − | 0.170440i | ||||||
\(388\) | − | 6.28274i | − | 0.318958i | ||||||
\(389\) | 20.8906 | 1.05920 | 0.529598 | − | 0.848249i | \(-0.322343\pi\) | ||||
0.529598 | + | 0.848249i | \(0.322343\pi\) | |||||||
\(390\) | − | 7.85943i | − | 0.397978i | ||||||
\(391\) | −2.01729 | −0.102019 | ||||||||
\(392\) | −0.893539 | − | 21.2317i | −0.0451305 | − | 1.07236i | ||||
\(393\) | − | 3.50671i | − | 0.176890i | ||||||
\(394\) | 1.80977 | 0.0911749 | ||||||||
\(395\) | −13.4557 | −0.677031 | ||||||||
\(396\) | 0.206574 | − | 1.31044i | 0.0103807 | − | 0.0658523i | ||||
\(397\) | 22.2712i | 1.11776i | 0.829249 | + | 0.558879i | \(0.188768\pi\) | ||||
−0.829249 | + | 0.558879i | \(0.811232\pi\) | |||||||
\(398\) | 1.38006 | 0.0691761 | ||||||||
\(399\) | −11.6051 | + | 0.244094i | −0.580984 | + | 0.0122200i | ||||
\(400\) | 3.04002 | 0.152001 | ||||||||
\(401\) | 12.3669 | 0.617574 | 0.308787 | − | 0.951131i | \(-0.400077\pi\) | ||||
0.308787 | + | 0.951131i | \(0.400077\pi\) | |||||||
\(402\) | −5.01478 | −0.250114 | ||||||||
\(403\) | − | 48.3557i | − | 2.40877i | ||||||
\(404\) | −5.07099 | −0.252291 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 0.697531 | + | 33.1633i | 0.0346179 | + | 1.64586i | ||||
\(407\) | −0.834137 | + | 5.29152i | −0.0413467 | + | 0.262291i | ||||
\(408\) | −4.93861 | −0.244498 | ||||||||
\(409\) | −32.5287 | −1.60844 | −0.804221 | − | 0.594331i | \(-0.797417\pi\) | ||||
−0.804221 | + | 0.594331i | \(0.797417\pi\) | |||||||
\(410\) | 6.26310 | 0.309313 | ||||||||
\(411\) | 4.53186i | 0.223540i | ||||||||
\(412\) | − | 6.26025i | − | 0.308420i | ||||||
\(413\) | −11.8785 | + | 0.249843i | −0.584502 | + | 0.0122940i | ||||
\(414\) | 1.56854i | 0.0770894i | ||||||||
\(415\) | − | 2.78335i | − | 0.136629i | ||||||
\(416\) | 13.8323i | 0.678186i | ||||||||
\(417\) | 13.8980i | 0.680589i | ||||||||
\(418\) | −18.1813 | − | 2.86604i | −0.889277 | − | 0.140182i | ||||
\(419\) | 9.85219i | 0.481311i | 0.970611 | + | 0.240656i | \(0.0773624\pi\) | ||||
−0.970611 | + | 0.240656i | \(0.922638\pi\) | |||||||
\(420\) | −0.0222542 | − | 1.05805i | −0.00108589 | − | 0.0516274i | ||||
\(421\) | −8.55665 | −0.417026 | −0.208513 | − | 0.978020i | \(-0.566862\pi\) | ||||
−0.208513 | + | 0.978020i | \(0.566862\pi\) | |||||||
\(422\) | −10.0585 | −0.489638 | ||||||||
\(423\) | 4.74958i | 0.230932i | ||||||||
\(424\) | − | 25.8482i | − | 1.25530i | ||||||
\(425\) | −1.62680 | −0.0789113 | ||||||||
\(426\) | −14.1975 | −0.687869 | ||||||||
\(427\) | −0.357761 | − | 17.0093i | −0.0173133 | − | 0.823138i | ||||
\(428\) | 1.24227i | 0.0600473i | ||||||||
\(429\) | −20.3562 | − | 3.20888i | −0.982806 | − | 0.154926i | ||||
\(430\) | − | 4.24119i | − | 0.204529i | ||||||
\(431\) | − | 10.5938i | − | 0.510284i | −0.966904 | − | 0.255142i | \(-0.917878\pi\) | ||
0.966904 | − | 0.255142i | \(-0.0821222\pi\) | |||||||
\(432\) | 3.04002i | 0.146263i | ||||||||
\(433\) | 40.6553i | 1.95377i | 0.213771 | + | 0.976884i | \(0.431425\pi\) | ||||
−0.213771 | + | 0.976884i | \(0.568575\pi\) | |||||||
\(434\) | 0.547694 | + | 26.0394i | 0.0262901 | + | 1.24993i | ||||
\(435\) | 9.91159i | 0.475224i | ||||||||
\(436\) | − | 1.20795i | − | 0.0578501i | ||||||
\(437\) | −5.44041 | −0.260250 | ||||||||
\(438\) | −10.3244 | −0.493317 | ||||||||
\(439\) | 0.794637 | 0.0379260 | 0.0189630 | − | 0.999820i | \(-0.493964\pi\) | ||||
0.0189630 | + | 0.999820i | \(0.493964\pi\) | |||||||
\(440\) | 1.56781 | − | 9.94574i | 0.0747425 | − | 0.474145i | ||||
\(441\) | 6.99381 | − | 0.294335i | 0.333039 | − | 0.0140160i | ||||
\(442\) | 12.7857i | 0.608154i | ||||||||
\(443\) | −23.4248 | −1.11295 | −0.556473 | − | 0.830866i | \(-0.687846\pi\) | ||||
−0.556473 | + | 0.830866i | \(0.687846\pi\) | |||||||
\(444\) | 0.646050i | 0.0306602i | ||||||||
\(445\) | −2.92087 | −0.138463 | ||||||||
\(446\) | −28.6394 | −1.35611 | ||||||||
\(447\) | 4.75210 | 0.224766 | ||||||||
\(448\) | −0.494942 | − | 23.5314i | −0.0233838 | − | 1.11175i | ||||
\(449\) | −31.4075 | −1.48221 | −0.741106 | − | 0.671388i | \(-0.765698\pi\) | ||||
−0.741106 | + | 0.671388i | \(0.765698\pi\) | |||||||
\(450\) | 1.26491i | 0.0596286i | ||||||||
\(451\) | 2.55712 | − | 16.2216i | 0.120410 | − | 0.763847i | ||||
\(452\) | 5.80577 | 0.273080 | ||||||||
\(453\) | −3.90311 | −0.183384 | ||||||||
\(454\) | − | 18.5112i | − | 0.868774i | ||||||
\(455\) | −16.4355 | + | 0.345692i | −0.770508 | + | 0.0162063i | ||||
\(456\) | −13.3189 | −0.623715 | ||||||||
\(457\) | 35.9351i | 1.68097i | 0.541831 | + | 0.840487i | \(0.317731\pi\) | ||||
−0.541831 | + | 0.840487i | \(0.682269\pi\) | |||||||
\(458\) | −32.1464 | −1.50210 | ||||||||
\(459\) | − | 1.62680i | − | 0.0759325i | ||||||
\(460\) | − | 0.496005i | − | 0.0231264i | ||||||
\(461\) | 26.6282 | 1.24020 | 0.620100 | − | 0.784523i | \(-0.287092\pi\) | ||||
0.620100 | + | 0.784523i | \(0.287092\pi\) | |||||||
\(462\) | 10.9981 | + | 1.49741i | 0.511678 | + | 0.0696659i | ||||
\(463\) | −11.6033 | −0.539253 | −0.269627 | − | 0.962965i | \(-0.586900\pi\) | ||||
−0.269627 | + | 0.962965i | \(0.586900\pi\) | |||||||
\(464\) | 30.1314i | 1.39882i | ||||||||
\(465\) | 7.78246i | 0.360903i | ||||||||
\(466\) | −33.7115 | −1.56165 | ||||||||
\(467\) | 24.2952i | 1.12425i | 0.827054 | + | 0.562123i | \(0.190015\pi\) | ||||
−0.827054 | + | 0.562123i | \(0.809985\pi\) | |||||||
\(468\) | −2.48532 | −0.114884 | ||||||||
\(469\) | 0.220572 | + | 10.4868i | 0.0101851 | + | 0.484236i | ||||
\(470\) | 6.00780i | 0.277119i | ||||||||
\(471\) | 11.3424 | 0.522631 | ||||||||
\(472\) | −13.6326 | −0.627492 | ||||||||
\(473\) | −10.9848 | − | 1.73161i | −0.505083 | − | 0.0796196i | ||||
\(474\) | − | 17.0203i | − | 0.781769i | ||||||
\(475\) | −4.38730 | −0.201303 | ||||||||
\(476\) | 0.0362031 | + | 1.72123i | 0.00165937 | + | 0.0788924i | ||||
\(477\) | 8.51450 | 0.389852 | ||||||||
\(478\) | 6.84234 | 0.312961 | ||||||||
\(479\) | −10.1317 | −0.462929 | −0.231465 | − | 0.972843i | \(-0.574352\pi\) | ||||
−0.231465 | + | 0.972843i | \(0.574352\pi\) | |||||||
\(480\) | − | 2.22620i | − | 0.101612i | ||||||
\(481\) | 10.0356 | 0.457585 | ||||||||
\(482\) | 9.65309i | 0.439686i | ||||||||
\(483\) | 3.28010 | − | 0.0689912i | 0.149250 | − | 0.00313921i | ||||
\(484\) | −4.18655 | − | 1.35354i | −0.190298 | − | 0.0615246i | ||||
\(485\) | 15.7071 | 0.713225 | ||||||||
\(486\) | −1.26491 | −0.0573777 | ||||||||
\(487\) | 1.18274 | 0.0535952 | 0.0267976 | − | 0.999641i | \(-0.491469\pi\) | ||||
0.0267976 | + | 0.999641i | \(0.491469\pi\) | |||||||
\(488\) | − | 19.5211i | − | 0.883679i | ||||||
\(489\) | 4.05059i | 0.183174i | ||||||||
\(490\) | 8.84657 | − | 0.372309i | 0.399647 | − | 0.0168192i | ||||
\(491\) | − | 36.8069i | − | 1.66107i | −0.556964 | − | 0.830536i | \(-0.688034\pi\) | ||
0.556964 | − | 0.830536i | \(-0.311966\pi\) | |||||||
\(492\) | − | 1.98053i | − | 0.0892890i | ||||||
\(493\) | − | 16.1242i | − | 0.726196i | ||||||
\(494\) | 34.4817i | 1.55141i | ||||||||
\(495\) | 3.27617 | + | 0.516444i | 0.147253 | + | 0.0232124i | ||||
\(496\) | 23.6588i | 1.06231i | ||||||||
\(497\) | 0.624467 | + | 29.6895i | 0.0280112 | + | 1.33176i | ||||
\(498\) | 3.52070 | 0.157766 | ||||||||
\(499\) | 3.70034 | 0.165650 | 0.0828250 | − | 0.996564i | \(-0.473606\pi\) | ||||
0.0828250 | + | 0.996564i | \(0.473606\pi\) | |||||||
\(500\) | − | 0.399993i | − | 0.0178882i | ||||||
\(501\) | 18.2979i | 0.817490i | ||||||||
\(502\) | 8.75814 | 0.390895 | ||||||||
\(503\) | −14.2284 | −0.634412 | −0.317206 | − | 0.948357i | \(-0.602745\pi\) | ||||
−0.317206 | + | 0.948357i | \(0.602745\pi\) | |||||||
\(504\) | 8.03015 | − | 0.168900i | 0.357691 | − | 0.00752342i | ||||
\(505\) | − | 12.6777i | − | 0.564151i | ||||||
\(506\) | 5.13879 | + | 0.810062i | 0.228447 | + | 0.0360116i | ||||
\(507\) | 25.6065i | 1.13722i | ||||||||
\(508\) | − | 7.75597i | − | 0.344116i | ||||||
\(509\) | − | 30.1161i | − | 1.33487i | −0.744666 | − | 0.667437i | \(-0.767391\pi\) | ||
0.744666 | − | 0.667437i | \(-0.232609\pi\) | |||||||
\(510\) | − | 2.05776i | − | 0.0911192i | ||||||
\(511\) | 0.454111 | + | 21.5901i | 0.0200887 | + | 0.955091i | ||||
\(512\) | − | 25.2254i | − | 1.11482i | ||||||
\(513\) | − | 4.38730i | − | 0.193704i | ||||||
\(514\) | 12.3180 | 0.543324 | ||||||||
\(515\) | 15.6509 | 0.689662 | ||||||||
\(516\) | −1.34116 | −0.0590411 | ||||||||
\(517\) | 15.5604 | + | 2.45289i | 0.684346 | + | 0.107878i | ||||
\(518\) | −5.40416 | + | 0.113667i | −0.237445 | + | 0.00499425i | ||||
\(519\) | − | 5.19325i | − | 0.227958i | ||||||
\(520\) | −18.8626 | −0.827179 | ||||||||
\(521\) | − | 40.1175i | − | 1.75758i | −0.477210 | − | 0.878790i | \(-0.658352\pi\) | ||
0.477210 | − | 0.878790i | \(-0.341648\pi\) | |||||||
\(522\) | −12.5373 | −0.548743 | ||||||||
\(523\) | 34.5565 | 1.51105 | 0.755526 | − | 0.655119i | \(-0.227381\pi\) | ||||
0.755526 | + | 0.655119i | \(0.227381\pi\) | |||||||
\(524\) | −1.40266 | −0.0612755 | ||||||||
\(525\) | 2.64517 | − | 0.0556365i | 0.115445 | − | 0.00242817i | ||||
\(526\) | −35.8926 | −1.56499 | ||||||||
\(527\) | − | 12.6605i | − | 0.551500i | ||||||
\(528\) | 9.95962 | + | 1.57000i | 0.433437 | + | 0.0683255i | ||||
\(529\) | −21.4623 | −0.933144 | ||||||||
\(530\) | 10.7701 | 0.467824 | ||||||||
\(531\) | − | 4.49064i | − | 0.194877i | ||||||
\(532\) | 0.0976358 | + | 4.64197i | 0.00423305 | + | 0.201255i | ||||
\(533\) | −30.7651 | −1.33259 | ||||||||
\(534\) | − | 3.69465i | − | 0.159883i | ||||||
\(535\) | −3.10573 | −0.134272 | ||||||||
\(536\) | 12.0354i | 0.519851i | ||||||||
\(537\) | − | 15.8800i | − | 0.685271i | ||||||
\(538\) | 2.62797 | 0.113300 | ||||||||
\(539\) | 2.64762 | − | 23.0649i | 0.114041 | − | 0.993476i | ||||
\(540\) | 0.399993 | 0.0172129 | ||||||||
\(541\) | 12.9976i | 0.558809i | 0.960174 | + | 0.279404i | \(0.0901370\pi\) | ||||
−0.960174 | + | 0.279404i | \(0.909863\pi\) | |||||||
\(542\) | − | 18.9859i | − | 0.815516i | ||||||
\(543\) | 14.5061 | 0.622516 | ||||||||
\(544\) | 3.62159i | 0.155274i | ||||||||
\(545\) | 3.01992 | 0.129359 | ||||||||
\(546\) | −0.437271 | − | 20.7895i | −0.0187135 | − | 0.889709i | ||||
\(547\) | − | 17.7677i | − | 0.759690i | −0.925050 | − | 0.379845i | \(-0.875977\pi\) | ||
0.925050 | − | 0.379845i | \(-0.124023\pi\) | |||||||
\(548\) | 1.81271 | 0.0774351 | ||||||||
\(549\) | 6.43034 | 0.274440 | ||||||||
\(550\) | 4.14407 | + | 0.653257i | 0.176704 | + | 0.0278550i | ||||
\(551\) | − | 43.4851i | − | 1.85253i | ||||||
\(552\) | 3.76448 | 0.160227 | ||||||||
\(553\) | −35.5926 | + | 0.748629i | −1.51355 | + | 0.0318349i | ||||
\(554\) | −11.2323 | −0.477213 | ||||||||
\(555\) | −1.61516 | −0.0685595 | ||||||||
\(556\) | 5.55911 | 0.235759 | ||||||||
\(557\) | − | 40.3959i | − | 1.71163i | −0.517283 | − | 0.855814i | \(-0.673057\pi\) | ||
0.517283 | − | 0.855814i | \(-0.326943\pi\) | |||||||
\(558\) | −9.84415 | −0.416736 | ||||||||
\(559\) | 20.8333i | 0.881153i | ||||||||
\(560\) | 8.04136 | − | 0.169136i | 0.339809 | − | 0.00714730i | ||||
\(561\) | −5.32967 | − | 0.840151i | −0.225019 | − | 0.0354712i | ||||
\(562\) | 33.6373 | 1.41890 | ||||||||
\(563\) | 26.5897 | 1.12062 | 0.560311 | − | 0.828282i | \(-0.310682\pi\) | ||||
0.560311 | + | 0.828282i | \(0.310682\pi\) | |||||||
\(564\) | 1.89980 | 0.0799958 | ||||||||
\(565\) | 14.5147i | 0.610637i | ||||||||
\(566\) | 21.9235i | 0.921515i | ||||||||
\(567\) | 0.0556365 | + | 2.64517i | 0.00233651 | + | 0.111087i | ||||
\(568\) | 34.0738i | 1.42971i | ||||||||
\(569\) | − | 18.6104i | − | 0.780188i | −0.920775 | − | 0.390094i | \(-0.872442\pi\) | ||
0.920775 | − | 0.390094i | \(-0.127558\pi\) | |||||||
\(570\) | − | 5.54956i | − | 0.232446i | ||||||
\(571\) | 24.0931i | 1.00826i | 0.863627 | + | 0.504132i | \(0.168187\pi\) | ||||
−0.863627 | + | 0.504132i | \(0.831813\pi\) | |||||||
\(572\) | −1.28353 | + | 8.14233i | −0.0536670 | + | 0.340448i | ||||
\(573\) | 15.8476i | 0.662042i | ||||||||
\(574\) | 16.5669 | − | 0.348457i | 0.691491 | − | 0.0145443i | ||||
\(575\) | 1.24003 | 0.0517130 | ||||||||
\(576\) | 8.89600 | 0.370667 | ||||||||
\(577\) | − | 2.60480i | − | 0.108439i | −0.998529 | − | 0.0542195i | \(-0.982733\pi\) | ||
0.998529 | − | 0.0542195i | \(-0.0172671\pi\) | |||||||
\(578\) | − | 18.1560i | − | 0.755189i | ||||||
\(579\) | −8.94943 | −0.371926 | ||||||||
\(580\) | 3.96456 | 0.164620 | ||||||||
\(581\) | −0.154856 | − | 7.36242i | −0.00642449 | − | 0.305445i | ||||
\(582\) | 19.8682i | 0.823563i | ||||||||
\(583\) | 4.39726 | − | 27.8949i | 0.182116 | − | 1.15529i | ||||
\(584\) | 24.7784i | 1.02534i | ||||||||
\(585\) | − | 6.21341i | − | 0.256893i | ||||||
\(586\) | 32.8432i | 1.35674i | ||||||||
\(587\) | 10.3722i | 0.428107i | 0.976822 | + | 0.214054i | \(0.0686667\pi\) | ||||
−0.976822 | + | 0.214054i | \(0.931333\pi\) | |||||||
\(588\) | −0.117732 | − | 2.79747i | −0.00485519 | − | 0.115366i | ||||
\(589\) | − | 34.1440i | − | 1.40688i | ||||||
\(590\) | − | 5.68027i | − | 0.233853i | ||||||
\(591\) | 1.43075 | 0.0588530 | ||||||||
\(592\) | −4.91010 | −0.201804 | ||||||||
\(593\) | −2.87360 | −0.118005 | −0.0590024 | − | 0.998258i | \(-0.518792\pi\) | ||||
−0.0590024 | + | 0.998258i | \(0.518792\pi\) | |||||||
\(594\) | −0.653257 | + | 4.14407i | −0.0268035 | + | 0.170033i | ||||
\(595\) | −4.30315 | + | 0.0905093i | −0.176412 | + | 0.00371052i | ||||
\(596\) | − | 1.90080i | − | 0.0778600i | ||||||
\(597\) | 1.09103 | 0.0446529 | ||||||||
\(598\) | − | 9.74597i | − | 0.398542i | ||||||
\(599\) | 6.32064 | 0.258254 | 0.129127 | − | 0.991628i | \(-0.458782\pi\) | ||||
0.129127 | + | 0.991628i | \(0.458782\pi\) | |||||||
\(600\) | 3.03578 | 0.123935 | ||||||||
\(601\) | 17.0259 | 0.694502 | 0.347251 | − | 0.937772i | \(-0.387115\pi\) | ||||
0.347251 | + | 0.937772i | \(0.387115\pi\) | |||||||
\(602\) | −0.235965 | − | 11.2187i | −0.00961722 | − | 0.457239i | ||||
\(603\) | −3.96452 | −0.161448 | ||||||||
\(604\) | 1.56121i | 0.0635249i | ||||||||
\(605\) | 3.38392 | − | 10.4666i | 0.137576 | − | 0.425527i | ||||
\(606\) | 16.0362 | 0.651427 | ||||||||
\(607\) | −17.1498 | −0.696089 | −0.348044 | − | 0.937478i | \(-0.613154\pi\) | ||||
−0.348044 | + | 0.937478i | \(0.613154\pi\) | |||||||
\(608\) | 9.76703i | 0.396106i | ||||||||
\(609\) | 0.551446 | + | 26.2178i | 0.0223457 | + | 1.06240i | ||||
\(610\) | 8.13382 | 0.329329 | ||||||||
\(611\) | − | 29.5111i | − | 1.19389i | ||||||
\(612\) | −0.650708 | −0.0263033 | ||||||||
\(613\) | 16.9312i | 0.683844i | 0.939728 | + | 0.341922i | \(0.111078\pi\) | ||||
−0.939728 | + | 0.341922i | \(0.888922\pi\) | |||||||
\(614\) | − | 26.5017i | − | 1.06952i | ||||||
\(615\) | 4.95141 | 0.199660 | ||||||||
\(616\) | 3.59378 | − | 26.3954i | 0.144797 | − | 1.06350i | ||||
\(617\) | −40.9282 | −1.64771 | −0.823854 | − | 0.566803i | \(-0.808180\pi\) | ||||
−0.823854 | + | 0.566803i | \(0.808180\pi\) | |||||||
\(618\) | 19.7971i | 0.796354i | ||||||||
\(619\) | − | 4.37850i | − | 0.175987i | −0.996121 | − | 0.0879934i | \(-0.971955\pi\) | ||
0.996121 | − | 0.0879934i | \(-0.0280455\pi\) | |||||||
\(620\) | 3.11293 | 0.125018 | ||||||||
\(621\) | 1.24003i | 0.0497609i | ||||||||
\(622\) | −19.4622 | −0.780364 | ||||||||
\(623\) | −7.72619 | + | 0.162507i | −0.309543 | + | 0.00651070i | ||||
\(624\) | − | 18.8889i | − | 0.756161i | ||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −2.35017 | −0.0939315 | ||||||||
\(627\) | −14.3735 | − | 2.26580i | −0.574024 | − | 0.0904872i | ||||
\(628\) | − | 4.53688i | − | 0.181041i | ||||||
\(629\) | 2.62753 | 0.104767 | ||||||||
\(630\) | 0.0703753 | + | 3.34591i | 0.00280382 | + | 0.133304i | ||||
\(631\) | −25.8773 | −1.03016 | −0.515079 | − | 0.857143i | \(-0.672237\pi\) | ||||
−0.515079 | + | 0.857143i | \(0.672237\pi\) | |||||||
\(632\) | −40.8487 | −1.62487 | ||||||||
\(633\) | −7.95189 | −0.316059 | ||||||||
\(634\) | − | 9.46515i | − | 0.375909i | ||||||
\(635\) | 19.3903 | 0.769480 | ||||||||
\(636\) | − | 3.40574i | − | 0.135046i | ||||||
\(637\) | −43.4554 | + | 1.82883i | −1.72177 | + | 0.0724608i | ||||
\(638\) | −6.47482 | + | 41.0743i | −0.256340 | + | 1.62615i | ||||
\(639\) | −11.2241 | −0.444017 | ||||||||
\(640\) | 6.80026 | 0.268804 | ||||||||
\(641\) | −29.0849 | −1.14879 | −0.574393 | − | 0.818580i | \(-0.694762\pi\) | ||||
−0.574393 | + | 0.818580i | \(0.694762\pi\) | |||||||
\(642\) | − | 3.92848i | − | 0.155045i | ||||||
\(643\) | 17.5627i | 0.692606i | 0.938123 | + | 0.346303i | \(0.112563\pi\) | ||||
−0.938123 | + | 0.346303i | \(0.887437\pi\) | |||||||
\(644\) | −0.0275960 | − | 1.31202i | −0.00108743 | − | 0.0517007i | ||||
\(645\) | − | 3.35295i | − | 0.132022i | ||||||
\(646\) | 9.02802i | 0.355203i | ||||||||
\(647\) | 34.6069i | 1.36054i | 0.732962 | + | 0.680270i | \(0.238137\pi\) | ||||
−0.732962 | + | 0.680270i | \(0.761863\pi\) | |||||||
\(648\) | 3.03578i | 0.119257i | ||||||||
\(649\) | −14.7121 | − | 2.31916i | −0.577500 | − | 0.0910352i | ||||
\(650\) | − | 7.85943i | − | 0.308272i | ||||||
\(651\) | 0.432989 | + | 20.5859i | 0.0169702 | + | 0.806825i | ||||
\(652\) | 1.62021 | 0.0634522 | ||||||||
\(653\) | 6.83133 | 0.267331 | 0.133665 | − | 0.991027i | \(-0.457325\pi\) | ||||
0.133665 | + | 0.991027i | \(0.457325\pi\) | |||||||
\(654\) | 3.81994i | 0.149371i | ||||||||
\(655\) | − | 3.50671i | − | 0.137019i | ||||||
\(656\) | 15.0524 | 0.587697 | ||||||||
\(657\) | −8.16211 | −0.318434 | ||||||||
\(658\) | 0.334253 | + | 15.8916i | 0.0130305 | + | 0.619521i | ||||
\(659\) | − | 13.2657i | − | 0.516759i | −0.966044 | − | 0.258379i | \(-0.916812\pi\) | ||
0.966044 | − | 0.258379i | \(-0.0831884\pi\) | |||||||
\(660\) | 0.206574 | − | 1.31044i | 0.00804088 | − | 0.0510090i | ||||
\(661\) | − | 26.8096i | − | 1.04277i | −0.853321 | − | 0.521385i | \(-0.825415\pi\) | ||
0.853321 | − | 0.521385i | \(-0.174585\pi\) | |||||||
\(662\) | − | 7.32891i | − | 0.284846i | ||||||
\(663\) | 10.1080i | 0.392561i | ||||||||
\(664\) | − | 8.44964i | − | 0.327910i | ||||||
\(665\) | −11.6051 | + | 0.244094i | −0.450028 | + | 0.00946556i | ||||
\(666\) | − | 2.04303i | − | 0.0791659i | ||||||
\(667\) | 12.2907i | 0.475898i | ||||||||
\(668\) | 7.31902 | 0.283182 | ||||||||
\(669\) | −22.6413 | −0.875365 | ||||||||
\(670\) | −5.01478 | −0.193738 | ||||||||
\(671\) | 3.32091 | − | 21.0669i | 0.128202 | − | 0.813277i | ||||
\(672\) | −0.123858 | − | 5.88868i | −0.00477793 | − | 0.227161i | ||||
\(673\) | − | 4.86973i | − | 0.187714i | −0.995586 | − | 0.0938572i | \(-0.970080\pi\) | ||
0.995586 | − | 0.0938572i | \(-0.0299197\pi\) | |||||||
\(674\) | 37.1388 | 1.43053 | ||||||||
\(675\) | 1.00000i | 0.0384900i | ||||||||
\(676\) | 10.2424 | 0.393939 | ||||||||
\(677\) | −28.7691 | −1.10569 | −0.552844 | − | 0.833285i | \(-0.686457\pi\) | ||||
−0.552844 | + | 0.833285i | \(0.686457\pi\) | |||||||
\(678\) | −18.3598 | −0.705105 | ||||||||
\(679\) | 41.5480 | − | 0.873890i | 1.59447 | − | 0.0335368i | ||||
\(680\) | −4.93861 | −0.189387 | ||||||||
\(681\) | − | 14.6344i | − | 0.560790i | ||||||
\(682\) | −5.08395 | + | 32.2511i | −0.194675 | + | 1.23496i | ||||
\(683\) | 42.3628 | 1.62097 | 0.810484 | − | 0.585761i | \(-0.199204\pi\) | ||||
0.810484 | + | 0.585761i | \(0.199204\pi\) | |||||||
\(684\) | −1.75489 | −0.0670999 | ||||||||
\(685\) | 4.53186i | 0.173153i | ||||||||
\(686\) | 23.3799 | − | 1.47701i | 0.892650 | − | 0.0563925i | ||||
\(687\) | −25.4139 | −0.969600 | ||||||||
\(688\) | − | 10.1930i | − | 0.388606i | ||||||
\(689\) | −52.9041 | −2.01549 | ||||||||
\(690\) | 1.56854i | 0.0597132i | ||||||||
\(691\) | − | 5.30501i | − | 0.201812i | −0.994896 | − | 0.100906i | \(-0.967826\pi\) | ||
0.994896 | − | 0.100906i | \(-0.0321742\pi\) | |||||||
\(692\) | −2.07726 | −0.0789656 | ||||||||
\(693\) | 8.69475 | + | 1.18381i | 0.330286 | + | 0.0449691i | ||||
\(694\) | −17.9369 | −0.680876 | ||||||||
\(695\) | 13.8980i | 0.527182i | ||||||||
\(696\) | 30.0894i | 1.14054i | ||||||||
\(697\) | −8.05494 | −0.305103 | ||||||||
\(698\) | − | 33.2754i | − | 1.25949i | ||||||
\(699\) | −26.6512 | −1.00804 | ||||||||
\(700\) | −0.0222542 | − | 1.05805i | −0.000841129 | − | 0.0399904i | ||||
\(701\) | 20.2558i | 0.765053i | 0.923945 | + | 0.382526i | \(0.124946\pi\) | ||||
−0.923945 | + | 0.382526i | \(0.875054\pi\) | |||||||
\(702\) | 7.85943 | 0.296635 | ||||||||
\(703\) | 7.08618 | 0.267260 | ||||||||
\(704\) | 4.59428 | − | 29.1448i | 0.173154 | − | 1.09844i | ||||
\(705\) | 4.74958i | 0.178879i | ||||||||
\(706\) | −8.68460 | −0.326849 | ||||||||
\(707\) | −0.705343 | − | 33.5347i | −0.0265272 | − | 1.26120i | ||||
\(708\) | −1.79622 | −0.0675062 | ||||||||
\(709\) | −11.0545 | −0.415160 | −0.207580 | − | 0.978218i | \(-0.566559\pi\) | ||||
−0.207580 | + | 0.978218i | \(0.566559\pi\) | |||||||
\(710\) | −14.1975 | −0.532821 | ||||||||
\(711\) | − | 13.4557i | − | 0.504629i | ||||||
\(712\) | −8.86713 | −0.332310 | ||||||||
\(713\) | 9.65053i | 0.361415i | ||||||||
\(714\) | −0.114487 | − | 5.44312i | −0.00428455 | − | 0.203704i | ||||
\(715\) | −20.3562 | − | 3.20888i | −0.761278 | − | 0.120005i | ||||
\(716\) | −6.35187 | −0.237380 | ||||||||
\(717\) | 5.40933 | 0.202015 | ||||||||
\(718\) | −8.90111 | −0.332186 | ||||||||
\(719\) | − | 51.4013i | − | 1.91694i | −0.285188 | − | 0.958472i | \(-0.592056\pi\) | ||
0.285188 | − | 0.958472i | \(-0.407944\pi\) | |||||||
\(720\) | 3.04002i | 0.113295i | ||||||||
\(721\) | 41.3993 | − | 0.870761i | 1.54179 | − | 0.0324289i | ||||
\(722\) | 0.314245i | 0.0116950i | ||||||||
\(723\) | 7.63142i | 0.283815i | ||||||||
\(724\) | − | 5.80234i | − | 0.215642i | ||||||
\(725\) | 9.91159i | 0.368107i | ||||||||
\(726\) | 13.2393 | + | 4.28036i | 0.491357 | + | 0.158859i | ||||
\(727\) | 20.4356i | 0.757915i | 0.925414 | + | 0.378958i | \(0.123717\pi\) | ||||
−0.925414 | + | 0.378958i | \(0.876283\pi\) | |||||||
\(728\) | −49.8947 | + | 1.04945i | −1.84922 | + | 0.0388951i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −10.3244 | −0.382122 | ||||||||
\(731\) | 5.45458i | 0.201745i | ||||||||
\(732\) | − | 2.57209i | − | 0.0950671i | ||||||
\(733\) | −26.7268 | −0.987178 | −0.493589 | − | 0.869695i | \(-0.664315\pi\) | ||||
−0.493589 | + | 0.869695i | \(0.664315\pi\) | |||||||
\(734\) | 25.0863 | 0.925951 | ||||||||
\(735\) | 6.99381 | − | 0.294335i | 0.257971 | − | 0.0108567i | ||||
\(736\) | − | 2.76057i | − | 0.101756i | ||||||
\(737\) | −2.04745 | + | 12.9884i | −0.0754189 | + | 0.478435i | ||||
\(738\) | 6.26310i | 0.230548i | ||||||||
\(739\) | 34.5733i | 1.27180i | 0.771772 | + | 0.635899i | \(0.219371\pi\) | ||||
−0.771772 | + | 0.635899i | \(0.780629\pi\) | |||||||
\(740\) | 0.646050i | 0.0237493i | ||||||||
\(741\) | 27.2601i | 1.00143i | ||||||||
\(742\) | 28.4887 | − | 0.599211i | 1.04585 | − | 0.0219977i | ||||
\(743\) | 22.7283i | 0.833821i | 0.908948 | + | 0.416911i | \(0.136887\pi\) | ||||
−0.908948 | + | 0.416911i | \(0.863113\pi\) | |||||||
\(744\) | 23.6259i | 0.866167i | ||||||||
\(745\) | 4.75210 | 0.174103 | ||||||||
\(746\) | −33.5926 | −1.22991 | ||||||||
\(747\) | 2.78335 | 0.101837 | ||||||||
\(748\) | −0.336054 | + | 2.13183i | −0.0122874 | + | 0.0779474i | ||||
\(749\) | −8.21517 | + | 0.172792i | −0.300176 | + | 0.00631367i | ||||
\(750\) | 1.26491i | 0.0461881i | ||||||||
\(751\) | 15.5678 | 0.568076 | 0.284038 | − | 0.958813i | \(-0.408326\pi\) | ||||
0.284038 | + | 0.958813i | \(0.408326\pi\) | |||||||
\(752\) | 14.4388i | 0.526529i | ||||||||
\(753\) | 6.92390 | 0.252321 | ||||||||
\(754\) | 77.8994 | 2.83693 | ||||||||
\(755\) | −3.90311 | −0.142049 | ||||||||
\(756\) | 1.05805 | − | 0.0222542i | 0.0384808 | − | 0.000809377i | ||||
\(757\) | 2.20307 | 0.0800718 | 0.0400359 | − | 0.999198i | \(-0.487253\pi\) | ||||
0.0400359 | + | 0.999198i | \(0.487253\pi\) | |||||||
\(758\) | 35.0395i | 1.27269i | ||||||||
\(759\) | 4.06256 | + | 0.640409i | 0.147462 | + | 0.0232454i | ||||
\(760\) | −13.3189 | −0.483128 | ||||||||
\(761\) | 31.3430 | 1.13618 | 0.568092 | − | 0.822965i | \(-0.307682\pi\) | ||||
0.568092 | + | 0.822965i | \(0.307682\pi\) | |||||||
\(762\) | 24.5270i | 0.888521i | ||||||||
\(763\) | 7.98819 | − | 0.168018i | 0.289192 | − | 0.00608265i | ||||
\(764\) | 6.33891 | 0.229334 | ||||||||
\(765\) | − | 1.62680i | − | 0.0588170i | ||||||
\(766\) | 10.7908 | 0.389887 | ||||||||
\(767\) | 27.9022i | 1.00749i | ||||||||
\(768\) | − | 9.19025i | − | 0.331625i | ||||||
\(769\) | −17.8883 | −0.645069 | −0.322535 | − | 0.946558i | \(-0.604535\pi\) | ||||
−0.322535 | + | 0.946558i | \(0.604535\pi\) | |||||||
\(770\) | 10.9981 | + | 1.49741i | 0.396344 | + | 0.0539630i | ||||
\(771\) | 9.73821 | 0.350713 | ||||||||
\(772\) | 3.57971i | 0.128837i | ||||||||
\(773\) | − | 37.4966i | − | 1.34866i | −0.738430 | − | 0.674330i | \(-0.764433\pi\) | ||
0.738430 | − | 0.674330i | \(-0.235567\pi\) | |||||||
\(774\) | 4.24119 | 0.152447 | ||||||||
\(775\) | 7.78246i | 0.279554i | ||||||||
\(776\) | 47.6835 | 1.71174 | ||||||||
\(777\) | −4.27235 | + | 0.0898615i | −0.153270 | + | 0.00322376i | ||||
\(778\) | 26.4248i | 0.947376i | ||||||||
\(779\) | −21.7233 | −0.778319 | ||||||||
\(780\) | −2.48532 | −0.0889887 | ||||||||
\(781\) | −5.79660 | + | 36.7719i | −0.207419 | + | 1.31580i | ||||
\(782\) | − | 2.55169i | − | 0.0912484i | ||||||
\(783\) | −9.91159 | −0.354211 | ||||||||
\(784\) | 21.2613 | − | 0.894786i | 0.759333 | − | 0.0319566i | ||||
\(785\) | 11.3424 | 0.404828 | ||||||||
\(786\) | 4.43569 | 0.158216 | ||||||||
\(787\) | 1.23343 | 0.0439671 | 0.0219835 | − | 0.999758i | \(-0.493002\pi\) | ||||
0.0219835 | + | 0.999758i | \(0.493002\pi\) | |||||||
\(788\) | − | 0.572288i | − | 0.0203869i | ||||||
\(789\) | −28.3755 | −1.01019 | ||||||||
\(790\) | − | 17.0203i | − | 0.605556i | ||||||
\(791\) | 0.807546 | + | 38.3937i | 0.0287130 | + | 1.36512i | ||||
\(792\) | 9.94574 | + | 1.56781i | 0.353407 | + | 0.0557098i | ||||
\(793\) | −39.9543 | −1.41882 | ||||||||
\(794\) | −28.1711 | −0.999755 | ||||||||
\(795\) | 8.51450 | 0.301978 | ||||||||
\(796\) | − | 0.436404i | − | 0.0154679i | ||||||
\(797\) | − | 27.5155i | − | 0.974651i | −0.873220 | − | 0.487325i | \(-0.837973\pi\) | ||
0.873220 | − | 0.487325i | \(-0.162027\pi\) | |||||||
\(798\) | −0.308758 | − | 14.6795i | −0.0109299 | − | 0.519649i | ||||
\(799\) | − | 7.72660i | − | 0.273348i | ||||||
\(800\) | − | 2.22620i | − | 0.0787082i | ||||||
\(801\) | − | 2.92087i | − | 0.103204i | ||||||
\(802\) | 15.6431i | 0.552376i | ||||||||
\(803\) | −4.21527 | + | 26.7405i | −0.148754 | + | 0.943650i | ||||
\(804\) | 1.58578i | 0.0559261i | ||||||||
\(805\) | 3.28010 | − | 0.0689912i | 0.115608 | − | 0.00243162i | ||||
\(806\) | 61.1657 | 2.15447 | ||||||||
\(807\) | 2.07759 | 0.0731345 | ||||||||
\(808\) | − | 38.4868i | − | 1.35396i | ||||||
\(809\) | 39.7878i | 1.39886i | 0.714699 | + | 0.699432i | \(0.246564\pi\) | ||||
−0.714699 | + | 0.699432i | \(0.753436\pi\) | |||||||
\(810\) | −1.26491 | −0.0444445 | ||||||||
\(811\) | 23.6701 | 0.831170 | 0.415585 | − | 0.909554i | \(-0.363577\pi\) | ||||
0.415585 | + | 0.909554i | \(0.363577\pi\) | |||||||
\(812\) | 10.4869 | − | 0.220574i | 0.368019 | − | 0.00774064i | ||||
\(813\) | − | 15.0097i | − | 0.526412i | ||||||
\(814\) | −6.69332 | − | 1.05511i | −0.234601 | − | 0.0369817i | ||||
\(815\) | 4.05059i | 0.141886i | ||||||||
\(816\) | − | 4.94550i | − | 0.173127i | ||||||
\(817\) | 14.7104i | 0.514652i | ||||||||
\(818\) | − | 41.1460i | − | 1.43864i | ||||||
\(819\) | −0.345692 | − | 16.4355i | −0.0120795 | − | 0.574303i | ||||
\(820\) | − | 1.98053i | − | 0.0691630i | ||||||
\(821\) | 36.8760i | 1.28698i | 0.765454 | + | 0.643490i | \(0.222514\pi\) | ||||
−0.765454 | + | 0.643490i | \(0.777486\pi\) | |||||||
\(822\) | −5.73241 | −0.199941 | ||||||||
\(823\) | 40.0752 | 1.39693 | 0.698467 | − | 0.715642i | \(-0.253866\pi\) | ||||
0.698467 | + | 0.715642i | \(0.253866\pi\) | |||||||
\(824\) | 47.5128 | 1.65519 | ||||||||
\(825\) | 3.27617 | + | 0.516444i | 0.114062 | + | 0.0179803i | ||||
\(826\) | −0.316030 | − | 15.0253i | −0.0109961 | − | 0.522796i | ||||
\(827\) | − | 2.31803i | − | 0.0806058i | −0.999188 | − | 0.0403029i | \(-0.987168\pi\) | ||
0.999188 | − | 0.0403029i | \(-0.0128323\pi\) | |||||||
\(828\) | 0.496005 | 0.0172374 | ||||||||
\(829\) | 47.9666i | 1.66595i | 0.553311 | + | 0.832975i | \(0.313364\pi\) | ||||
−0.553311 | + | 0.832975i | \(0.686636\pi\) | |||||||
\(830\) | 3.52070 | 0.122205 | ||||||||
\(831\) | −8.87985 | −0.308039 | ||||||||
\(832\) | −55.2745 | −1.91630 | ||||||||
\(833\) | −11.3775 | + | 0.478824i | −0.394208 | + | 0.0165903i | ||||
\(834\) | −17.5798 | −0.608739 | ||||||||
\(835\) | 18.2979i | 0.633225i | ||||||||
\(836\) | −0.906302 | + | 5.74931i | −0.0313451 | + | 0.198844i | ||||
\(837\) | −7.78246 | −0.269001 | ||||||||
\(838\) | −12.4622 | −0.430499 | ||||||||
\(839\) | − | 6.13941i | − | 0.211956i | −0.994368 | − | 0.105978i | \(-0.966203\pi\) | ||
0.994368 | − | 0.105978i | \(-0.0337973\pi\) | |||||||
\(840\) | 8.03015 | − | 0.168900i | 0.277067 | − | 0.00582761i | ||||
\(841\) | −69.2396 | −2.38757 | ||||||||
\(842\) | − | 10.8234i | − | 0.373000i | ||||||
\(843\) | 26.5925 | 0.915896 | ||||||||
\(844\) | 3.18070i | 0.109484i | ||||||||
\(845\) | 25.6065i | 0.880890i | ||||||||
\(846\) | −6.00780 | −0.206553 | ||||||||
\(847\) | 8.36870 | − | 27.8741i | 0.287552 | − | 0.957765i | ||||
\(848\) | 25.8842 | 0.888869 | ||||||||
\(849\) | 17.3320i | 0.594834i | ||||||||
\(850\) | − | 2.05776i | − | 0.0705806i | ||||||
\(851\) | −2.00285 | −0.0686568 | ||||||||
\(852\) | 4.48954i | 0.153809i | ||||||||
\(853\) | 9.43350 | 0.322997 | 0.161498 | − | 0.986873i | \(-0.448367\pi\) | ||||
0.161498 | + | 0.986873i | \(0.448367\pi\) | |||||||
\(854\) | 21.5153 | − | 0.452537i | 0.736239 | − | 0.0154855i | ||||
\(855\) | − | 4.38730i | − | 0.150043i | ||||||
\(856\) | −9.42832 | −0.322253 | ||||||||
\(857\) | −48.1302 | −1.64410 | −0.822049 | − | 0.569417i | \(-0.807169\pi\) | ||||
−0.822049 | + | 0.569417i | \(0.807169\pi\) | |||||||
\(858\) | 4.05896 | − | 25.7488i | 0.138570 | − | 0.879051i | ||||
\(859\) | − | 46.8091i | − | 1.59711i | −0.601924 | − | 0.798553i | \(-0.705599\pi\) | ||
0.601924 | − | 0.798553i | \(-0.294401\pi\) | |||||||
\(860\) | −1.34116 | −0.0457330 | ||||||||
\(861\) | 13.0973 | − | 0.275479i | 0.446355 | − | 0.00938829i | ||||
\(862\) | 13.4002 | 0.456413 | ||||||||
\(863\) | −30.9748 | −1.05440 | −0.527198 | − | 0.849743i | \(-0.676757\pi\) | ||||
−0.527198 | + | 0.849743i | \(0.676757\pi\) | |||||||
\(864\) | 2.22620 | 0.0757370 | ||||||||
\(865\) | − | 5.19325i | − | 0.176576i | ||||||
\(866\) | −51.4254 | −1.74751 | ||||||||
\(867\) | − | 14.3535i | − | 0.487471i | ||||||
\(868\) | 8.23421 | − | 0.173192i | 0.279487 | − | 0.00587853i | ||||
\(869\) | −44.0832 | − | 6.94912i | −1.49542 | − | 0.235733i | ||||
\(870\) | −12.5373 | −0.425054 | ||||||||
\(871\) | 24.6332 | 0.834664 | ||||||||
\(872\) | 9.16782 | 0.310462 | ||||||||
\(873\) | 15.7071i | 0.531606i | ||||||||
\(874\) | − | 6.88165i | − | 0.232775i | ||||||
\(875\) | 2.64517 | − | 0.0556365i | 0.0894229 | − | 0.00188086i | ||||
\(876\) | 3.26478i | 0.110307i | ||||||||
\(877\) | − | 34.3921i | − | 1.16134i | −0.814140 | − | 0.580669i | \(-0.802791\pi\) | ||
0.814140 | − | 0.580669i | \(-0.197209\pi\) | |||||||
\(878\) | 1.00515i | 0.0339221i | ||||||||
\(879\) | 25.9648i | 0.875771i | ||||||||
\(880\) | 9.95962 | + | 1.57000i | 0.335739 | + | 0.0529247i | ||||
\(881\) | − | 40.8658i | − | 1.37680i | −0.725330 | − | 0.688401i | \(-0.758313\pi\) | ||
0.725330 | − | 0.688401i | \(-0.241687\pi\) | |||||||
\(882\) | 0.372309 | + | 8.84657i | 0.0125363 | + | 0.297879i | ||||
\(883\) | 0.236721 | 0.00796629 | 0.00398314 | − | 0.999992i | \(-0.498732\pi\) | ||||
0.00398314 | + | 0.999992i | \(0.498732\pi\) | |||||||
\(884\) | 4.04311 | 0.135985 | ||||||||
\(885\) | − | 4.49064i | − | 0.150951i | ||||||
\(886\) | − | 29.6304i | − | 0.995451i | ||||||
\(887\) | 13.3787 | 0.449211 | 0.224606 | − | 0.974450i | \(-0.427891\pi\) | ||||
0.224606 | + | 0.974450i | \(0.427891\pi\) | |||||||
\(888\) | −4.90326 | −0.164543 | ||||||||
\(889\) | 51.2905 | − | 1.07881i | 1.72023 | − | 0.0361820i | ||||
\(890\) | − | 3.69465i | − | 0.123845i | ||||||
\(891\) | −0.516444 | + | 3.27617i | −0.0173015 | + | 0.109756i | ||||
\(892\) | 9.05637i | 0.303230i | ||||||||
\(893\) | − | 20.8378i | − | 0.697311i | ||||||
\(894\) | 6.01099i | 0.201038i | ||||||||
\(895\) | − | 15.8800i | − | 0.530808i | ||||||
\(896\) | 17.9878 | − | 0.378343i | 0.600931 | − | 0.0126395i | ||||
\(897\) | − | 7.70485i | − | 0.257257i | ||||||
\(898\) | − | 39.7278i | − | 1.32573i | ||||||
\(899\) | −77.1366 | −2.57265 | ||||||||
\(900\) | 0.399993 | 0.0133331 | ||||||||
\(901\) | −13.8514 | −0.461456 | ||||||||
\(902\) | 20.5190 | + | 3.23454i | 0.683207 | + | 0.107698i | ||||
\(903\) | −0.186546 | − | 8.86911i | −0.00620787 | − | 0.295146i | ||||
\(904\) | 44.0634i | 1.46553i | ||||||||
\(905\) | 14.5061 | 0.482199 | ||||||||
\(906\) | − | 4.93709i | − | 0.164024i | ||||||
\(907\) | 42.2499 | 1.40288 | 0.701442 | − | 0.712726i | \(-0.252540\pi\) | ||||
0.701442 | + | 0.712726i | \(0.252540\pi\) | |||||||
\(908\) | −5.85364 | −0.194260 | ||||||||
\(909\) | 12.6777 | 0.420493 | ||||||||
\(910\) | −0.437271 | − | 20.7895i | −0.0144954 | − | 0.689165i | ||||
\(911\) | 45.9937 | 1.52384 | 0.761919 | − | 0.647672i | \(-0.224257\pi\) | ||||
0.761919 | + | 0.647672i | \(0.224257\pi\) | |||||||
\(912\) | − | 13.3375i | − | 0.441648i | ||||||
\(913\) | 1.43744 | − | 9.11872i | 0.0475724 | − | 0.301786i | ||||
\(914\) | −45.4549 | −1.50351 | ||||||||
\(915\) | 6.43034 | 0.212580 | ||||||||
\(916\) | 10.1654i | 0.335873i | ||||||||
\(917\) | −0.195101 | − | 9.27584i | −0.00644281 | − | 0.306315i | ||||
\(918\) | 2.05776 | 0.0679162 | ||||||||
\(919\) | 13.7556i | 0.453755i | 0.973923 | + | 0.226878i | \(0.0728518\pi\) | ||||
−0.973923 | + | 0.226878i | \(0.927148\pi\) | |||||||
\(920\) | 3.76448 | 0.124111 | ||||||||
\(921\) | − | 20.9514i | − | 0.690371i | ||||||
\(922\) | 33.6824i | 1.10927i | ||||||||
\(923\) | 69.7397 | 2.29551 | ||||||||
\(924\) | 0.473514 | − | 3.47783i | 0.0155775 | − | 0.114412i | ||||
\(925\) | −1.61516 | −0.0531060 | ||||||||
\(926\) | − | 14.6772i | − | 0.482324i | ||||||
\(927\) | 15.6509i | 0.514043i | ||||||||
\(928\) | 22.0652 | 0.724326 | ||||||||
\(929\) | − | 40.1490i | − | 1.31725i | −0.752473 | − | 0.658624i | \(-0.771139\pi\) | ||
0.752473 | − | 0.658624i | \(-0.228861\pi\) | |||||||
\(930\) | −9.84415 | −0.322802 | ||||||||
\(931\) | −30.6840 | + | 1.29134i | −1.00563 | + | 0.0423219i | ||||
\(932\) | 10.6603i | 0.349189i | ||||||||
\(933\) | −15.3862 | −0.503722 | ||||||||
\(934\) | −30.7313 | −1.00556 | ||||||||
\(935\) | −5.32967 | − | 0.840151i | −0.174299 | − | 0.0274759i | ||||
\(936\) | − | 18.8626i | − | 0.616543i | ||||||
\(937\) | 49.9501 | 1.63180 | 0.815899 | − | 0.578195i | \(-0.196243\pi\) | ||||
0.815899 | + | 0.578195i | \(0.196243\pi\) | |||||||
\(938\) | −13.2649 | + | 0.279004i | −0.433115 | + | 0.00910982i | ||||
\(939\) | −1.85796 | −0.0606324 | ||||||||
\(940\) | 1.89980 | 0.0619645 | ||||||||
\(941\) | −4.24177 | −0.138278 | −0.0691388 | − | 0.997607i | \(-0.522025\pi\) | ||||
−0.0691388 | + | 0.997607i | \(0.522025\pi\) | |||||||
\(942\) | 14.3472i | 0.467456i | ||||||||
\(943\) | 6.13992 | 0.199943 | ||||||||
\(944\) | − | 13.6516i | − | 0.444323i | ||||||
\(945\) | 0.0556365 | + | 2.64517i | 0.00180985 | + | 0.0860473i | ||||
\(946\) | 2.19034 | − | 13.8949i | 0.0712141 | − | 0.451761i | ||||
\(947\) | −11.5681 | −0.375912 | −0.187956 | − | 0.982177i | \(-0.560186\pi\) | ||||
−0.187956 | + | 0.982177i | \(0.560186\pi\) | |||||||
\(948\) | −5.38219 | −0.174805 | ||||||||
\(949\) | 50.7146 | 1.64626 | ||||||||
\(950\) | − | 5.54956i | − | 0.180052i | ||||||
\(951\) | − | 7.48284i | − | 0.242648i | ||||||
\(952\) | −13.0634 | + | 0.274767i | −0.423389 | + | 0.00890524i | ||||
\(953\) | − | 24.5357i | − | 0.794790i | −0.917648 | − | 0.397395i | \(-0.869914\pi\) | ||
0.917648 | − | 0.397395i | \(-0.130086\pi\) | |||||||
\(954\) | 10.7701i | 0.348695i | ||||||||
\(955\) | 15.8476i | 0.512815i | ||||||||
\(956\) | − | 2.16369i | − | 0.0699789i | ||||||
\(957\) | −5.11878 | + | 32.4720i | −0.165467 | + | 1.04967i | ||||
\(958\) | − | 12.8157i | − | 0.414057i | ||||||
\(959\) | 0.252137 | + | 11.9875i | 0.00814191 | + | 0.387097i | ||||
\(960\) | 8.89600 | 0.287117 | ||||||||
\(961\) | −29.5667 | −0.953766 | ||||||||
\(962\) | 12.6942i | 0.409278i | ||||||||
\(963\) | − | 3.10573i | − | 0.100081i | ||||||
\(964\) | 3.05251 | 0.0983148 | ||||||||
\(965\) | −8.94943 | −0.288092 | ||||||||
\(966\) | 0.0872679 | + | 4.14904i | 0.00280780 | + | 0.133493i | ||||
\(967\) | 13.9191i | 0.447609i | 0.974634 | + | 0.223805i | \(0.0718478\pi\) | ||||
−0.974634 | + | 0.223805i | \(0.928152\pi\) | |||||||
\(968\) | 10.2728 | − | 31.7743i | 0.330182 | − | 1.02126i | ||||
\(969\) | 7.13726i | 0.229282i | ||||||||
\(970\) | 19.8682i | 0.637929i | ||||||||
\(971\) | 40.5634i | 1.30174i | 0.759189 | + | 0.650870i | \(0.225596\pi\) | ||||
−0.759189 | + | 0.650870i | \(0.774404\pi\) | |||||||
\(972\) | 0.399993i | 0.0128298i | ||||||||
\(973\) | 0.773237 | + | 36.7626i | 0.0247888 | + | 1.17855i | ||||
\(974\) | 1.49607i | 0.0479371i | ||||||||
\(975\) | − | 6.21341i | − | 0.198988i | ||||||
\(976\) | 19.5484 | 0.625728 | ||||||||
\(977\) | 26.2257 | 0.839036 | 0.419518 | − | 0.907747i | \(-0.362199\pi\) | ||||
0.419518 | + | 0.907747i | \(0.362199\pi\) | |||||||
\(978\) | −5.12365 | −0.163836 | ||||||||
\(979\) | −9.56927 | − | 1.50847i | −0.305835 | − | 0.0482108i | ||||
\(980\) | −0.117732 | − | 2.79747i | −0.00376081 | − | 0.0893620i | ||||
\(981\) | 3.01992i | 0.0964186i | ||||||||
\(982\) | 46.5576 | 1.48571 | ||||||||
\(983\) | − | 41.6641i | − | 1.32888i | −0.747343 | − | 0.664439i | \(-0.768671\pi\) | ||
0.747343 | − | 0.664439i | \(-0.231329\pi\) | |||||||
\(984\) | 15.0314 | 0.479184 | ||||||||
\(985\) | 1.43075 | 0.0455873 | ||||||||
\(986\) | 20.3957 | 0.649531 | ||||||||
\(987\) | 0.264250 | + | 12.5634i | 0.00841116 | + | 0.399898i | ||||
\(988\) | 10.9039 | 0.346898 | ||||||||
\(989\) | − | 4.15778i | − | 0.132210i | ||||||
\(990\) | −0.653257 | + | 4.14407i | −0.0207619 | + | 0.131707i | ||||
\(991\) | 13.5033 | 0.428946 | 0.214473 | − | 0.976730i | \(-0.431197\pi\) | ||||
0.214473 | + | 0.976730i | \(0.431197\pi\) | |||||||
\(992\) | 17.3254 | 0.550081 | ||||||||
\(993\) | − | 5.79400i | − | 0.183867i | ||||||
\(994\) | −37.5546 | + | 0.789897i | −1.19116 | + | 0.0250540i | ||||
\(995\) | 1.09103 | 0.0345880 | ||||||||
\(996\) | − | 1.11332i | − | 0.0352769i | ||||||
\(997\) | 41.4277 | 1.31203 | 0.656014 | − | 0.754749i | \(-0.272241\pi\) | ||||
0.656014 | + | 0.754749i | \(0.272241\pi\) | |||||||
\(998\) | 4.68061i | 0.148162i | ||||||||
\(999\) | − | 1.61516i | − | 0.0511013i |
(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 | 1155.2.i.d.76.2 | yes | 32 | |
7.6 | odd | 2 | inner | 1155.2.i.d.76.32 | yes | 32 | |
11.10 | odd | 2 | inner | 1155.2.i.d.76.31 | yes | 32 | |
77.76 | even | 2 | inner | 1155.2.i.d.76.1 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.i.d.76.1 | ✓ | 32 | 77.76 | even | 2 | inner | |
1155.2.i.d.76.2 | yes | 32 | 1.1 | even | 1 | trivial | |
1155.2.i.d.76.31 | yes | 32 | 11.10 | odd | 2 | inner | |
1155.2.i.d.76.32 | yes | 32 | 7.6 | odd | 2 | inner |