Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(229,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.229");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.f (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: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 229.3 | ||
Character | \(\chi\) | \(=\) | 690.229 |
Dual form | 690.3.f.a.229.1 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 0.707107i | ||||||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | −1.71908 | − | 4.69518i | −0.343816 | − | 0.939037i | ||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | −12.9397 | −1.84853 | −0.924263 | − | 0.381757i | \(-0.875319\pi\) | ||||
−0.924263 | + | 0.381757i | \(0.875319\pi\) | |||||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 6.63999 | − | 2.43115i | 0.663999 | − | 0.243115i | ||||
\(11\) | − | 18.3935i | − | 1.67213i | −0.548627 | − | 0.836067i | \(-0.684849\pi\) | ||
0.548627 | − | 0.836067i | \(-0.315151\pi\) | |||||||
\(12\) | 3.46410i | 0.288675i | ||||||||
\(13\) | 7.60366i | 0.584897i | 0.956281 | + | 0.292448i | \(0.0944699\pi\) | ||||
−0.956281 | + | 0.292448i | \(0.905530\pi\) | |||||||
\(14\) | − | 18.2995i | − | 1.30710i | ||||||
\(15\) | −8.13230 | + | 2.97754i | −0.542153 | + | 0.198502i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 19.9407 | 1.17298 | 0.586491 | − | 0.809956i | \(-0.300509\pi\) | ||||
0.586491 | + | 0.809956i | \(0.300509\pi\) | |||||||
\(18\) | − | 4.24264i | − | 0.235702i | ||||||
\(19\) | 24.3487i | 1.28151i | 0.767746 | + | 0.640754i | \(0.221378\pi\) | ||||
−0.767746 | + | 0.640754i | \(0.778622\pi\) | |||||||
\(20\) | 3.43816 | + | 9.39037i | 0.171908 | + | 0.469518i | ||||
\(21\) | 22.4122i | 1.06725i | ||||||||
\(22\) | 26.0123 | 1.18238 | ||||||||
\(23\) | −22.9301 | + | 1.79238i | −0.996959 | + | 0.0779296i | ||||
\(24\) | −4.89898 | −0.204124 | ||||||||
\(25\) | −19.0895 | + | 16.1428i | −0.763581 | + | 0.645712i | ||||
\(26\) | −10.7532 | −0.413584 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 25.8794 | 0.924263 | ||||||||
\(29\) | 32.2461 | 1.11193 | 0.555967 | − | 0.831205i | \(-0.312348\pi\) | ||||
0.555967 | + | 0.831205i | \(0.312348\pi\) | |||||||
\(30\) | −4.21087 | − | 11.5008i | −0.140362 | − | 0.383360i | ||||
\(31\) | 3.18657 | 0.102793 | 0.0513963 | − | 0.998678i | \(-0.483633\pi\) | ||||
0.0513963 | + | 0.998678i | \(0.483633\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | −31.8584 | −0.965407 | ||||||||
\(34\) | 28.2004i | 0.829424i | ||||||||
\(35\) | 22.2444 | + | 60.7542i | 0.635553 | + | 1.73583i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 11.0170 | 0.297758 | 0.148879 | − | 0.988855i | \(-0.452433\pi\) | ||||
0.148879 | + | 0.988855i | \(0.452433\pi\) | |||||||
\(38\) | −34.4342 | −0.906163 | ||||||||
\(39\) | 13.1699 | 0.337690 | ||||||||
\(40\) | −13.2800 | + | 4.86230i | −0.332000 | + | 0.121557i | ||||
\(41\) | −60.4391 | −1.47413 | −0.737063 | − | 0.675824i | \(-0.763788\pi\) | ||||
−0.737063 | + | 0.675824i | \(0.763788\pi\) | |||||||
\(42\) | −31.6956 | −0.754657 | ||||||||
\(43\) | −50.3599 | −1.17116 | −0.585581 | − | 0.810614i | \(-0.699133\pi\) | ||||
−0.585581 | + | 0.810614i | \(0.699133\pi\) | |||||||
\(44\) | 36.7869i | 0.836067i | ||||||||
\(45\) | 5.15724 | + | 14.0856i | 0.114605 | + | 0.313012i | ||||
\(46\) | −2.53481 | − | 32.4280i | −0.0551045 | − | 0.704956i | ||||
\(47\) | 79.4647i | 1.69074i | 0.534182 | + | 0.845369i | \(0.320620\pi\) | ||||
−0.534182 | + | 0.845369i | \(0.679380\pi\) | |||||||
\(48\) | − | 6.92820i | − | 0.144338i | ||||||
\(49\) | 118.435 | 2.41705 | ||||||||
\(50\) | −22.8294 | − | 26.9967i | −0.456588 | − | 0.539933i | ||||
\(51\) | − | 34.5383i | − | 0.677222i | ||||||
\(52\) | − | 15.2073i | − | 0.292448i | ||||||
\(53\) | 92.1165 | 1.73805 | 0.869024 | − | 0.494770i | \(-0.164748\pi\) | ||||
0.869024 | + | 0.494770i | \(0.164748\pi\) | |||||||
\(54\) | −7.34847 | −0.136083 | ||||||||
\(55\) | −86.3608 | + | 31.6199i | −1.57020 | + | 0.574907i | ||||
\(56\) | 36.5989i | 0.653552i | ||||||||
\(57\) | 42.1731 | 0.739879 | ||||||||
\(58\) | 45.6028i | 0.786256i | ||||||||
\(59\) | 5.16200 | 0.0874916 | 0.0437458 | − | 0.999043i | \(-0.486071\pi\) | ||||
0.0437458 | + | 0.999043i | \(0.486071\pi\) | |||||||
\(60\) | 16.2646 | − | 5.95507i | 0.271077 | − | 0.0992512i | ||||
\(61\) | − | 10.5265i | − | 0.172565i | −0.996271 | − | 0.0862827i | \(-0.972501\pi\) | ||
0.996271 | − | 0.0862827i | \(-0.0274988\pi\) | |||||||
\(62\) | 4.50650i | 0.0726854i | ||||||||
\(63\) | 38.8190 | 0.616175 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 35.7006 | − | 13.0713i | 0.549240 | − | 0.201097i | ||||
\(66\) | − | 45.0546i | − | 0.682646i | ||||||
\(67\) | 72.2321 | 1.07809 | 0.539046 | − | 0.842276i | \(-0.318785\pi\) | ||||
0.539046 | + | 0.842276i | \(0.318785\pi\) | |||||||
\(68\) | −39.8814 | −0.586491 | ||||||||
\(69\) | 3.10449 | + | 39.7160i | 0.0449927 | + | 0.575594i | ||||
\(70\) | −85.9194 | + | 31.4583i | −1.22742 | + | 0.449404i | ||||
\(71\) | −8.94916 | −0.126045 | −0.0630223 | − | 0.998012i | \(-0.520074\pi\) | ||||
−0.0630223 | + | 0.998012i | \(0.520074\pi\) | |||||||
\(72\) | 8.48528i | 0.117851i | ||||||||
\(73\) | 70.6321i | 0.967564i | 0.875189 | + | 0.483782i | \(0.160737\pi\) | ||||
−0.875189 | + | 0.483782i | \(0.839263\pi\) | |||||||
\(74\) | 15.5805i | 0.210547i | ||||||||
\(75\) | 27.9602 | + | 33.0640i | 0.372802 | + | 0.440854i | ||||
\(76\) | − | 48.6973i | − | 0.640754i | ||||||
\(77\) | 238.006i | 3.09098i | ||||||||
\(78\) | 18.6251i | 0.238783i | ||||||||
\(79\) | − | 1.35260i | − | 0.0171215i | −0.999963 | − | 0.00856076i | \(-0.997275\pi\) | ||
0.999963 | − | 0.00856076i | \(-0.00272501\pi\) | |||||||
\(80\) | −6.87633 | − | 18.7807i | −0.0859541 | − | 0.234759i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 85.4739i | − | 1.04236i | ||||||
\(83\) | −135.372 | −1.63099 | −0.815494 | − | 0.578765i | \(-0.803535\pi\) | ||||
−0.815494 | + | 0.578765i | \(0.803535\pi\) | |||||||
\(84\) | − | 44.8244i | − | 0.533623i | ||||||
\(85\) | −34.2797 | − | 93.6253i | −0.403291 | − | 1.10147i | ||||
\(86\) | − | 71.2197i | − | 0.828136i | ||||||
\(87\) | − | 55.8518i | − | 0.641975i | ||||||
\(88\) | −52.0246 | −0.591189 | ||||||||
\(89\) | − | 41.9425i | − | 0.471263i | −0.971842 | − | 0.235632i | \(-0.924284\pi\) | ||
0.971842 | − | 0.235632i | \(-0.0757159\pi\) | |||||||
\(90\) | −19.9200 | + | 7.29345i | −0.221333 | + | 0.0810383i | ||||
\(91\) | − | 98.3889i | − | 1.08120i | ||||||
\(92\) | 45.8601 | − | 3.58476i | 0.498479 | − | 0.0389648i | ||||
\(93\) | − | 5.51931i | − | 0.0593474i | ||||||
\(94\) | −112.380 | −1.19553 | ||||||||
\(95\) | 114.321 | − | 41.8573i | 1.20338 | − | 0.440604i | ||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | −165.650 | −1.70773 | −0.853867 | − | 0.520491i | \(-0.825749\pi\) | ||||
−0.853867 | + | 0.520491i | \(0.825749\pi\) | |||||||
\(98\) | 167.493i | 1.70911i | ||||||||
\(99\) | 55.1804i | 0.557378i | ||||||||
\(100\) | 38.1790 | − | 32.2856i | 0.381790 | − | 0.322856i | ||||
\(101\) | 20.2266 | 0.200264 | 0.100132 | − | 0.994974i | \(-0.468074\pi\) | ||||
0.100132 | + | 0.994974i | \(0.468074\pi\) | |||||||
\(102\) | 48.8445 | 0.478868 | ||||||||
\(103\) | −10.1077 | −0.0981328 | −0.0490664 | − | 0.998796i | \(-0.515625\pi\) | ||||
−0.0490664 | + | 0.998796i | \(0.515625\pi\) | |||||||
\(104\) | 21.5064 | 0.206792 | ||||||||
\(105\) | 105.229 | − | 38.5284i | 1.00218 | − | 0.366937i | ||||
\(106\) | 130.272i | 1.22899i | ||||||||
\(107\) | 59.9270 | 0.560065 | 0.280033 | − | 0.959990i | \(-0.409655\pi\) | ||||
0.280033 | + | 0.959990i | \(0.409655\pi\) | |||||||
\(108\) | − | 10.3923i | − | 0.0962250i | ||||||
\(109\) | 44.0489i | 0.404118i | 0.979373 | + | 0.202059i | \(0.0647633\pi\) | ||||
−0.979373 | + | 0.202059i | \(0.935237\pi\) | |||||||
\(110\) | −44.7173 | − | 122.133i | −0.406521 | − | 1.11030i | ||||
\(111\) | − | 19.0821i | − | 0.171911i | ||||||
\(112\) | −51.7587 | −0.462131 | ||||||||
\(113\) | −162.943 | −1.44197 | −0.720987 | − | 0.692948i | \(-0.756311\pi\) | ||||
−0.720987 | + | 0.692948i | \(0.756311\pi\) | |||||||
\(114\) | 59.6418i | 0.523174i | ||||||||
\(115\) | 47.8342 | + | 104.580i | 0.415949 | + | 0.909388i | ||||
\(116\) | −64.4921 | −0.555967 | ||||||||
\(117\) | − | 22.8110i | − | 0.194966i | ||||||
\(118\) | 7.30017i | 0.0618659i | ||||||||
\(119\) | −258.026 | −2.16829 | ||||||||
\(120\) | 8.42175 | + | 23.0016i | 0.0701812 | + | 0.191680i | ||||
\(121\) | −217.320 | −1.79603 | ||||||||
\(122\) | 14.8867 | 0.122022 | ||||||||
\(123\) | 104.684i | 0.851087i | ||||||||
\(124\) | −6.37315 | −0.0513963 | ||||||||
\(125\) | 108.610 | + | 61.8780i | 0.868879 | + | 0.495024i | ||||
\(126\) | 54.8984i | 0.435702i | ||||||||
\(127\) | − | 78.3423i | − | 0.616869i | −0.951246 | − | 0.308434i | \(-0.900195\pi\) | ||
0.951246 | − | 0.308434i | \(-0.0998050\pi\) | |||||||
\(128\) | − | 11.3137i | − | 0.0883883i | ||||||
\(129\) | 87.2260i | 0.676170i | ||||||||
\(130\) | 18.4856 | + | 50.4882i | 0.142197 | + | 0.388371i | ||||
\(131\) | 243.523 | 1.85896 | 0.929479 | − | 0.368876i | \(-0.120257\pi\) | ||||
0.929479 | + | 0.368876i | \(0.120257\pi\) | |||||||
\(132\) | 63.7169 | 0.482704 | ||||||||
\(133\) | − | 315.064i | − | 2.36890i | ||||||
\(134\) | 102.152i | 0.762326i | ||||||||
\(135\) | 24.3969 | − | 8.93261i | 0.180718 | − | 0.0661675i | ||||
\(136\) | − | 56.4008i | − | 0.414712i | ||||||
\(137\) | −68.6757 | −0.501282 | −0.250641 | − | 0.968080i | \(-0.580641\pi\) | ||||
−0.250641 | + | 0.968080i | \(0.580641\pi\) | |||||||
\(138\) | −56.1669 | + | 4.39042i | −0.407007 | + | 0.0318146i | ||||
\(139\) | −136.802 | −0.984184 | −0.492092 | − | 0.870543i | \(-0.663768\pi\) | ||||
−0.492092 | + | 0.870543i | \(0.663768\pi\) | |||||||
\(140\) | −44.4887 | − | 121.508i | −0.317777 | − | 0.867917i | ||||
\(141\) | 137.637 | 0.976148 | ||||||||
\(142\) | − | 12.6560i | − | 0.0891270i | ||||||
\(143\) | 139.858 | 0.978026 | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | −55.4336 | − | 151.401i | −0.382301 | − | 1.04415i | ||||
\(146\) | −99.8889 | −0.684171 | ||||||||
\(147\) | − | 205.136i | − | 1.39548i | ||||||
\(148\) | −22.0341 | −0.148879 | ||||||||
\(149\) | 147.155i | 0.987620i | 0.869570 | + | 0.493810i | \(0.164396\pi\) | ||||
−0.869570 | + | 0.493810i | \(0.835604\pi\) | |||||||
\(150\) | −46.7596 | + | 39.5417i | −0.311731 | + | 0.263611i | ||||
\(151\) | −4.21892 | −0.0279398 | −0.0139699 | − | 0.999902i | \(-0.504447\pi\) | ||||
−0.0139699 | + | 0.999902i | \(0.504447\pi\) | |||||||
\(152\) | 68.8684 | 0.453082 | ||||||||
\(153\) | −59.8221 | −0.390994 | ||||||||
\(154\) | −336.591 | −2.18565 | ||||||||
\(155\) | −5.47798 | − | 14.9616i | −0.0353418 | − | 0.0965261i | ||||
\(156\) | −26.3398 | −0.168845 | ||||||||
\(157\) | 127.989 | 0.815216 | 0.407608 | − | 0.913157i | \(-0.366363\pi\) | ||||
0.407608 | + | 0.913157i | \(0.366363\pi\) | |||||||
\(158\) | 1.91287 | 0.0121067 | ||||||||
\(159\) | − | 159.550i | − | 1.00346i | ||||||
\(160\) | 26.5600 | − | 9.72459i | 0.166000 | − | 0.0607787i | ||||
\(161\) | 296.707 | − | 23.1928i | 1.84290 | − | 0.144055i | ||||
\(162\) | 12.7279i | 0.0785674i | ||||||||
\(163\) | − | 53.8931i | − | 0.330633i | −0.986241 | − | 0.165316i | \(-0.947136\pi\) | ||
0.986241 | − | 0.165316i | \(-0.0528645\pi\) | |||||||
\(164\) | 120.878 | 0.737063 | ||||||||
\(165\) | 54.7672 | + | 149.581i | 0.331923 | + | 0.906553i | ||||
\(166\) | − | 191.445i | − | 1.15328i | ||||||
\(167\) | 189.614i | 1.13541i | 0.823232 | + | 0.567705i | \(0.192169\pi\) | ||||
−0.823232 | + | 0.567705i | \(0.807831\pi\) | |||||||
\(168\) | 63.3912 | 0.377329 | ||||||||
\(169\) | 111.184 | 0.657896 | ||||||||
\(170\) | 132.406 | − | 48.4788i | 0.778860 | − | 0.285169i | ||||
\(171\) | − | 73.0460i | − | 0.427169i | ||||||
\(172\) | 100.720 | 0.585581 | ||||||||
\(173\) | − | 73.4027i | − | 0.424293i | −0.977238 | − | 0.212147i | \(-0.931955\pi\) | ||
0.977238 | − | 0.212147i | \(-0.0680454\pi\) | |||||||
\(174\) | 78.9864 | 0.453945 | ||||||||
\(175\) | 247.012 | − | 208.883i | 1.41150 | − | 1.19362i | ||||
\(176\) | − | 73.5739i | − | 0.418034i | ||||||
\(177\) | − | 8.94085i | − | 0.0505133i | ||||||
\(178\) | 59.3156 | 0.333234 | ||||||||
\(179\) | −279.042 | −1.55889 | −0.779447 | − | 0.626468i | \(-0.784500\pi\) | ||||
−0.779447 | + | 0.626468i | \(0.784500\pi\) | |||||||
\(180\) | −10.3145 | − | 28.1711i | −0.0573027 | − | 0.156506i | ||||
\(181\) | 151.434i | 0.836654i | 0.908296 | + | 0.418327i | \(0.137383\pi\) | ||||
−0.908296 | + | 0.418327i | \(0.862617\pi\) | |||||||
\(182\) | 139.143 | 0.764521 | ||||||||
\(183\) | −18.2324 | −0.0996307 | ||||||||
\(184\) | 5.06962 | + | 64.8560i | 0.0275523 | + | 0.352478i | ||||
\(185\) | −18.9392 | − | 51.7271i | −0.102374 | − | 0.279606i | ||||
\(186\) | 7.80548 | 0.0419649 | ||||||||
\(187\) | − | 366.779i | − | 1.96138i | ||||||
\(188\) | − | 158.929i | − | 0.845369i | ||||||
\(189\) | − | 67.2365i | − | 0.355749i | ||||||
\(190\) | 59.1952 | + | 161.675i | 0.311554 | + | 0.850921i | ||||
\(191\) | 296.805i | 1.55395i | 0.629530 | + | 0.776976i | \(0.283248\pi\) | ||||
−0.629530 | + | 0.776976i | \(0.716752\pi\) | |||||||
\(192\) | 13.8564i | 0.0721688i | ||||||||
\(193\) | 26.9147i | 0.139455i | 0.997566 | + | 0.0697273i | \(0.0222129\pi\) | ||||
−0.997566 | + | 0.0697273i | \(0.977787\pi\) | |||||||
\(194\) | − | 234.265i | − | 1.20755i | ||||||
\(195\) | −22.6402 | − | 61.8352i | −0.116103 | − | 0.317104i | ||||
\(196\) | −236.870 | −1.20852 | ||||||||
\(197\) | 61.5882i | 0.312630i | 0.987707 | + | 0.156315i | \(0.0499615\pi\) | ||||
−0.987707 | + | 0.156315i | \(0.950038\pi\) | |||||||
\(198\) | −78.0369 | −0.394126 | ||||||||
\(199\) | 35.3336i | 0.177556i | 0.996051 | + | 0.0887780i | \(0.0282962\pi\) | ||||
−0.996051 | + | 0.0887780i | \(0.971704\pi\) | |||||||
\(200\) | 45.6588 | + | 53.9933i | 0.228294 | + | 0.269967i | ||||
\(201\) | − | 125.110i | − | 0.622437i | ||||||
\(202\) | 28.6048i | 0.141608i | ||||||||
\(203\) | −417.254 | −2.05544 | ||||||||
\(204\) | 69.0766i | 0.338611i | ||||||||
\(205\) | 103.900 | + | 283.773i | 0.506828 | + | 1.38426i | ||||
\(206\) | − | 14.2944i | − | 0.0693904i | ||||||
\(207\) | 68.7902 | − | 5.37714i | 0.332320 | − | 0.0259765i | ||||
\(208\) | 30.4146i | 0.146224i | ||||||||
\(209\) | 447.856 | 2.14285 | ||||||||
\(210\) | 54.4873 | + | 148.817i | 0.259464 | + | 0.708651i | ||||
\(211\) | −142.017 | −0.673064 | −0.336532 | − | 0.941672i | \(-0.609254\pi\) | ||||
−0.336532 | + | 0.941672i | \(0.609254\pi\) | |||||||
\(212\) | −184.233 | −0.869024 | ||||||||
\(213\) | 15.5004i | 0.0727719i | ||||||||
\(214\) | 84.7496i | 0.396026i | ||||||||
\(215\) | 86.5728 | + | 236.449i | 0.402664 | + | 1.09976i | ||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | −41.2332 | −0.190015 | ||||||||
\(218\) | −62.2945 | −0.285755 | ||||||||
\(219\) | 122.338 | 0.558623 | ||||||||
\(220\) | 172.722 | − | 63.2398i | 0.785098 | − | 0.287453i | ||||
\(221\) | 151.622i | 0.686074i | ||||||||
\(222\) | 26.9861 | 0.121559 | ||||||||
\(223\) | − | 122.920i | − | 0.551211i | −0.961271 | − | 0.275605i | \(-0.911122\pi\) | ||
0.961271 | − | 0.275605i | \(-0.0888783\pi\) | |||||||
\(224\) | − | 73.1979i | − | 0.326776i | ||||||
\(225\) | 57.2685 | − | 48.4284i | 0.254527 | − | 0.215237i | ||||
\(226\) | − | 230.436i | − | 1.01963i | ||||||
\(227\) | −284.494 | −1.25328 | −0.626639 | − | 0.779310i | \(-0.715570\pi\) | ||||
−0.626639 | + | 0.779310i | \(0.715570\pi\) | |||||||
\(228\) | −84.3462 | −0.369940 | ||||||||
\(229\) | 427.020i | 1.86472i | 0.361536 | + | 0.932358i | \(0.382253\pi\) | ||||
−0.361536 | + | 0.932358i | \(0.617747\pi\) | |||||||
\(230\) | −147.898 | + | 67.6478i | −0.643034 | + | 0.294121i | ||||
\(231\) | 412.238 | 1.78458 | ||||||||
\(232\) | − | 91.2056i | − | 0.393128i | ||||||
\(233\) | − | 377.271i | − | 1.61919i | −0.586988 | − | 0.809595i | \(-0.699687\pi\) | ||
0.586988 | − | 0.809595i | \(-0.300313\pi\) | |||||||
\(234\) | 32.2596 | 0.137861 | ||||||||
\(235\) | 373.101 | − | 136.606i | 1.58767 | − | 0.581304i | ||||
\(236\) | −10.3240 | −0.0437458 | ||||||||
\(237\) | −2.34277 | −0.00988511 | ||||||||
\(238\) | − | 364.904i | − | 1.53321i | ||||||
\(239\) | 112.849 | 0.472171 | 0.236086 | − | 0.971732i | \(-0.424135\pi\) | ||||
0.236086 | + | 0.971732i | \(0.424135\pi\) | |||||||
\(240\) | −32.5292 | + | 11.9101i | −0.135538 | + | 0.0496256i | ||||
\(241\) | − | 149.271i | − | 0.619380i | −0.950838 | − | 0.309690i | \(-0.899775\pi\) | ||
0.950838 | − | 0.309690i | \(-0.100225\pi\) | |||||||
\(242\) | − | 307.337i | − | 1.26999i | ||||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | 21.0530i | 0.0862827i | ||||||||
\(245\) | −203.600 | − | 556.075i | −0.831020 | − | 2.26970i | ||||
\(246\) | −148.045 | −0.601809 | ||||||||
\(247\) | −185.139 | −0.749550 | ||||||||
\(248\) | − | 9.01299i | − | 0.0363427i | ||||||
\(249\) | 234.471i | 0.941652i | ||||||||
\(250\) | −87.5087 | + | 153.598i | −0.350035 | + | 0.614390i | ||||
\(251\) | 357.872i | 1.42579i | 0.701273 | + | 0.712893i | \(0.252615\pi\) | ||||
−0.701273 | + | 0.712893i | \(0.747385\pi\) | |||||||
\(252\) | −77.6381 | −0.308088 | ||||||||
\(253\) | 32.9681 | + | 421.763i | 0.130309 | + | 1.66705i | ||||
\(254\) | 110.793 | 0.436192 | ||||||||
\(255\) | −162.164 | + | 59.3742i | −0.635936 | + | 0.232840i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 58.9536i | − | 0.229391i | −0.993401 | − | 0.114696i | \(-0.963411\pi\) | ||
0.993401 | − | 0.114696i | \(-0.0365893\pi\) | |||||||
\(258\) | −123.356 | −0.478125 | ||||||||
\(259\) | −142.557 | −0.550413 | ||||||||
\(260\) | −71.4011 | + | 26.1426i | −0.274620 | + | 0.100549i | ||||
\(261\) | −96.7382 | −0.370644 | ||||||||
\(262\) | 344.394i | 1.31448i | ||||||||
\(263\) | 121.126 | 0.460557 | 0.230278 | − | 0.973125i | \(-0.426036\pi\) | ||||
0.230278 | + | 0.973125i | \(0.426036\pi\) | |||||||
\(264\) | 90.1093i | 0.341323i | ||||||||
\(265\) | −158.356 | − | 432.504i | −0.597569 | − | 1.63209i | ||||
\(266\) | 445.568 | 1.67507 | ||||||||
\(267\) | −72.6465 | −0.272084 | ||||||||
\(268\) | −144.464 | −0.539046 | ||||||||
\(269\) | 313.321 | 1.16476 | 0.582381 | − | 0.812916i | \(-0.302121\pi\) | ||||
0.582381 | + | 0.812916i | \(0.302121\pi\) | |||||||
\(270\) | 12.6326 | + | 34.5024i | 0.0467875 | + | 0.127787i | ||||
\(271\) | −17.1800 | −0.0633948 | −0.0316974 | − | 0.999498i | \(-0.510091\pi\) | ||||
−0.0316974 | + | 0.999498i | \(0.510091\pi\) | |||||||
\(272\) | 79.7628 | 0.293246 | ||||||||
\(273\) | −170.415 | −0.624229 | ||||||||
\(274\) | − | 97.1221i | − | 0.354460i | ||||||
\(275\) | 296.922 | + | 351.123i | 1.07972 | + | 1.27681i | ||||
\(276\) | −6.20899 | − | 79.4320i | −0.0224963 | − | 0.287797i | ||||
\(277\) | 268.440i | 0.969098i | 0.874764 | + | 0.484549i | \(0.161016\pi\) | ||||
−0.874764 | + | 0.484549i | \(0.838984\pi\) | |||||||
\(278\) | − | 193.467i | − | 0.695923i | ||||||
\(279\) | −9.55972 | −0.0342642 | ||||||||
\(280\) | 171.839 | − | 62.9166i | 0.613710 | − | 0.224702i | ||||
\(281\) | − | 386.651i | − | 1.37598i | −0.725719 | − | 0.687991i | \(-0.758493\pi\) | ||
0.725719 | − | 0.687991i | \(-0.241507\pi\) | |||||||
\(282\) | 194.648i | 0.690241i | ||||||||
\(283\) | 54.5729 | 0.192837 | 0.0964185 | − | 0.995341i | \(-0.469261\pi\) | ||||
0.0964185 | + | 0.995341i | \(0.469261\pi\) | |||||||
\(284\) | 17.8983 | 0.0630223 | ||||||||
\(285\) | −72.4990 | − | 198.011i | −0.254383 | − | 0.694774i | ||||
\(286\) | 197.789i | 0.691569i | ||||||||
\(287\) | 782.063 | 2.72496 | ||||||||
\(288\) | − | 16.9706i | − | 0.0589256i | ||||||
\(289\) | 108.632 | 0.375888 | ||||||||
\(290\) | 214.114 | − | 78.3950i | 0.738323 | − | 0.270327i | ||||
\(291\) | 286.915i | 0.985961i | ||||||||
\(292\) | − | 141.264i | − | 0.483782i | ||||||
\(293\) | 87.8588 | 0.299859 | 0.149930 | − | 0.988697i | \(-0.452095\pi\) | ||||
0.149930 | + | 0.988697i | \(0.452095\pi\) | |||||||
\(294\) | 290.106 | 0.986755 | ||||||||
\(295\) | −8.87390 | − | 24.2366i | −0.0300810 | − | 0.0821578i | ||||
\(296\) | − | 31.1609i | − | 0.105273i | ||||||
\(297\) | 95.5753 | 0.321802 | ||||||||
\(298\) | −208.109 | −0.698353 | ||||||||
\(299\) | −13.6286 | − | 174.352i | −0.0455808 | − | 0.583118i | ||||
\(300\) | −55.9203 | − | 66.1280i | −0.186401 | − | 0.220427i | ||||
\(301\) | 651.641 | 2.16492 | ||||||||
\(302\) | − | 5.96645i | − | 0.0197565i | ||||||
\(303\) | − | 35.0336i | − | 0.115622i | ||||||
\(304\) | 97.3946i | 0.320377i | ||||||||
\(305\) | −49.4238 | + | 18.0959i | −0.162045 | + | 0.0593308i | ||||
\(306\) | − | 84.6012i | − | 0.276475i | ||||||
\(307\) | − | 436.714i | − | 1.42252i | −0.702928 | − | 0.711261i | \(-0.748124\pi\) | ||
0.702928 | − | 0.711261i | \(-0.251876\pi\) | |||||||
\(308\) | − | 476.011i | − | 1.54549i | ||||||
\(309\) | 17.5070i | 0.0566570i | ||||||||
\(310\) | 21.1588 | − | 7.74703i | 0.0682543 | − | 0.0249904i | ||||
\(311\) | −95.4124 | −0.306792 | −0.153396 | − | 0.988165i | \(-0.549021\pi\) | ||||
−0.153396 | + | 0.988165i | \(0.549021\pi\) | |||||||
\(312\) | − | 37.2502i | − | 0.119392i | ||||||
\(313\) | −277.575 | −0.886820 | −0.443410 | − | 0.896319i | \(-0.646231\pi\) | ||||
−0.443410 | + | 0.896319i | \(0.646231\pi\) | |||||||
\(314\) | 181.004i | 0.576445i | ||||||||
\(315\) | −66.7331 | − | 182.263i | −0.211851 | − | 0.578611i | ||||
\(316\) | 2.70520i | 0.00856076i | ||||||||
\(317\) | − | 43.9312i | − | 0.138584i | −0.997596 | − | 0.0692921i | \(-0.977926\pi\) | ||
0.997596 | − | 0.0692921i | \(-0.0220741\pi\) | |||||||
\(318\) | 225.638 | 0.709555 | ||||||||
\(319\) | − | 593.117i | − | 1.85930i | ||||||
\(320\) | 13.7527 | + | 37.5615i | 0.0429770 | + | 0.117380i | ||||
\(321\) | − | 103.797i | − | 0.323354i | ||||||
\(322\) | 32.7996 | + | 419.608i | 0.101862 | + | 1.30313i | ||||
\(323\) | 485.529i | 1.50319i | ||||||||
\(324\) | −18.0000 | −0.0555556 | ||||||||
\(325\) | −122.744 | − | 145.150i | −0.377675 | − | 0.446616i | ||||
\(326\) | 76.2164 | 0.233793 | ||||||||
\(327\) | 76.2949 | 0.233318 | ||||||||
\(328\) | 170.948i | 0.521182i | ||||||||
\(329\) | − | 1028.25i | − | 3.12537i | ||||||
\(330\) | −211.540 | + | 77.4526i | −0.641030 | + | 0.234705i | ||||
\(331\) | −449.865 | −1.35911 | −0.679554 | − | 0.733626i | \(-0.737827\pi\) | ||||
−0.679554 | + | 0.733626i | \(0.737827\pi\) | |||||||
\(332\) | 270.744 | 0.815494 | ||||||||
\(333\) | −33.0511 | −0.0992527 | ||||||||
\(334\) | −268.154 | −0.802857 | ||||||||
\(335\) | −124.173 | − | 339.143i | −0.370666 | − | 1.01237i | ||||
\(336\) | 89.6487i | 0.266812i | ||||||||
\(337\) | −199.863 | −0.593066 | −0.296533 | − | 0.955023i | \(-0.595830\pi\) | ||||
−0.296533 | + | 0.955023i | \(0.595830\pi\) | |||||||
\(338\) | 157.239i | 0.465203i | ||||||||
\(339\) | 282.226i | 0.832525i | ||||||||
\(340\) | 68.5594 | + | 187.251i | 0.201645 | + | 0.550737i | ||||
\(341\) | − | 58.6122i | − | 0.171883i | ||||||
\(342\) | 103.303 | 0.302054 | ||||||||
\(343\) | −898.470 | −2.61945 | ||||||||
\(344\) | 142.439i | 0.414068i | ||||||||
\(345\) | 181.137 | − | 82.8513i | 0.525035 | − | 0.240149i | ||||
\(346\) | 103.807 | 0.300021 | ||||||||
\(347\) | − | 290.365i | − | 0.836786i | −0.908266 | − | 0.418393i | \(-0.862594\pi\) | ||
0.908266 | − | 0.418393i | \(-0.137406\pi\) | |||||||
\(348\) | 111.704i | 0.320987i | ||||||||
\(349\) | −126.648 | −0.362888 | −0.181444 | − | 0.983401i | \(-0.558077\pi\) | ||||
−0.181444 | + | 0.983401i | \(0.558077\pi\) | |||||||
\(350\) | 295.405 | + | 349.328i | 0.844014 | + | 0.998080i | ||||
\(351\) | −39.5098 | −0.112563 | ||||||||
\(352\) | 104.049 | 0.295594 | ||||||||
\(353\) | 497.700i | 1.40992i | 0.709249 | + | 0.704958i | \(0.249034\pi\) | ||||
−0.709249 | + | 0.704958i | \(0.750966\pi\) | |||||||
\(354\) | 12.6443 | 0.0357183 | ||||||||
\(355\) | 15.3843 | + | 42.0180i | 0.0433362 | + | 0.118360i | ||||
\(356\) | 83.8849i | 0.235632i | ||||||||
\(357\) | 446.915i | 1.25186i | ||||||||
\(358\) | − | 394.625i | − | 1.10231i | ||||||
\(359\) | 329.021i | 0.916494i | 0.888825 | + | 0.458247i | \(0.151523\pi\) | ||||
−0.888825 | + | 0.458247i | \(0.848477\pi\) | |||||||
\(360\) | 39.8400 | − | 14.5869i | 0.110667 | − | 0.0405191i | ||||
\(361\) | −231.857 | −0.642264 | ||||||||
\(362\) | −214.161 | −0.591604 | ||||||||
\(363\) | 376.409i | 1.03694i | ||||||||
\(364\) | 196.778i | 0.540598i | ||||||||
\(365\) | 331.631 | − | 121.422i | 0.908578 | − | 0.332664i | ||||
\(366\) | − | 25.7845i | − | 0.0704496i | ||||||
\(367\) | −172.395 | −0.469742 | −0.234871 | − | 0.972027i | \(-0.575467\pi\) | ||||
−0.234871 | + | 0.972027i | \(0.575467\pi\) | |||||||
\(368\) | −91.7202 | + | 7.16952i | −0.249240 | + | 0.0194824i | ||||
\(369\) | 181.317 | 0.491375 | ||||||||
\(370\) | 73.1531 | − | 26.7841i | 0.197711 | − | 0.0723894i | ||||
\(371\) | −1191.96 | −3.21282 | ||||||||
\(372\) | 11.0386i | 0.0296737i | ||||||||
\(373\) | −175.718 | −0.471095 | −0.235548 | − | 0.971863i | \(-0.575688\pi\) | ||||
−0.235548 | + | 0.971863i | \(0.575688\pi\) | |||||||
\(374\) | 518.704 | 1.38691 | ||||||||
\(375\) | 107.176 | − | 188.118i | 0.285802 | − | 0.501648i | ||||
\(376\) | 224.760 | 0.597766 | ||||||||
\(377\) | 245.188i | 0.650366i | ||||||||
\(378\) | 95.0868 | 0.251552 | ||||||||
\(379\) | 423.074i | 1.11629i | 0.829744 | + | 0.558145i | \(0.188487\pi\) | ||||
−0.829744 | + | 0.558145i | \(0.811513\pi\) | |||||||
\(380\) | −228.643 | + | 83.7147i | −0.601692 | + | 0.220302i | ||||
\(381\) | −135.693 | −0.356149 | ||||||||
\(382\) | −419.746 | −1.09881 | ||||||||
\(383\) | −401.734 | −1.04891 | −0.524457 | − | 0.851437i | \(-0.675732\pi\) | ||||
−0.524457 | + | 0.851437i | \(0.675732\pi\) | |||||||
\(384\) | −19.5959 | −0.0510310 | ||||||||
\(385\) | 1117.48 | − | 409.151i | 2.90255 | − | 1.06273i | ||||
\(386\) | −38.0632 | −0.0986092 | ||||||||
\(387\) | 151.080 | 0.390387 | ||||||||
\(388\) | 331.300 | 0.853867 | ||||||||
\(389\) | − | 346.765i | − | 0.891427i | −0.895176 | − | 0.445714i | \(-0.852950\pi\) | ||
0.895176 | − | 0.445714i | \(-0.147050\pi\) | |||||||
\(390\) | 87.4482 | − | 32.0180i | 0.224226 | − | 0.0820975i | ||||
\(391\) | −457.241 | + | 35.7413i | −1.16942 | + | 0.0914100i | ||||
\(392\) | − | 334.985i | − | 0.854555i | ||||||
\(393\) | − | 421.795i | − | 1.07327i | ||||||
\(394\) | −87.0988 | −0.221063 | ||||||||
\(395\) | −6.35071 | + | 2.32523i | −0.0160777 | + | 0.00588666i | ||||
\(396\) | − | 110.361i | − | 0.278689i | ||||||
\(397\) | 98.9151i | 0.249157i | 0.992210 | + | 0.124578i | \(0.0397578\pi\) | ||||
−0.992210 | + | 0.124578i | \(0.960242\pi\) | |||||||
\(398\) | −49.9693 | −0.125551 | ||||||||
\(399\) | −545.707 | −1.36769 | ||||||||
\(400\) | −76.3581 | + | 64.5712i | −0.190895 | + | 0.161428i | ||||
\(401\) | 625.874i | 1.56078i | 0.625291 | + | 0.780392i | \(0.284980\pi\) | ||||
−0.625291 | + | 0.780392i | \(0.715020\pi\) | |||||||
\(402\) | 176.932 | 0.440129 | ||||||||
\(403\) | 24.2296i | 0.0601231i | ||||||||
\(404\) | −40.4533 | −0.100132 | ||||||||
\(405\) | −15.4717 | − | 42.2567i | −0.0382018 | − | 0.104337i | ||||
\(406\) | − | 590.086i | − | 1.45341i | ||||||
\(407\) | − | 202.642i | − | 0.497891i | ||||||
\(408\) | −97.6891 | −0.239434 | ||||||||
\(409\) | 410.570 | 1.00384 | 0.501920 | − | 0.864914i | \(-0.332627\pi\) | ||||
0.501920 | + | 0.864914i | \(0.332627\pi\) | |||||||
\(410\) | −401.316 | + | 146.937i | −0.978818 | + | 0.358382i | ||||
\(411\) | 118.950i | 0.289415i | ||||||||
\(412\) | 20.2154 | 0.0490664 | ||||||||
\(413\) | −66.7946 | −0.161730 | ||||||||
\(414\) | 7.60443 | + | 97.2840i | 0.0183682 | + | 0.234985i | ||||
\(415\) | 232.716 | + | 635.597i | 0.560761 | + | 1.53156i | ||||
\(416\) | −43.0128 | −0.103396 | ||||||||
\(417\) | 236.947i | 0.568219i | ||||||||
\(418\) | 633.365i | 1.51523i | ||||||||
\(419\) | 36.3204i | 0.0866834i | 0.999060 | + | 0.0433417i | \(0.0138004\pi\) | ||||
−0.999060 | + | 0.0433417i | \(0.986200\pi\) | |||||||
\(420\) | −210.459 | + | 77.0567i | −0.501092 | + | 0.183468i | ||||
\(421\) | 545.508i | 1.29574i | 0.761750 | + | 0.647871i | \(0.224341\pi\) | ||||
−0.761750 | + | 0.647871i | \(0.775659\pi\) | |||||||
\(422\) | − | 200.842i | − | 0.475928i | ||||||
\(423\) | − | 238.394i | − | 0.563580i | ||||||
\(424\) | − | 260.545i | − | 0.614493i | ||||||
\(425\) | −380.658 | + | 321.899i | −0.895667 | + | 0.757409i | ||||
\(426\) | −21.9209 | −0.0514575 | ||||||||
\(427\) | 136.209i | 0.318992i | ||||||||
\(428\) | −119.854 | −0.280033 | ||||||||
\(429\) | − | 242.241i | − | 0.564663i | ||||||
\(430\) | −334.390 | + | 122.432i | −0.777650 | + | 0.284727i | ||||
\(431\) | 156.738i | 0.363662i | 0.983330 | + | 0.181831i | \(0.0582024\pi\) | ||||
−0.983330 | + | 0.181831i | \(0.941798\pi\) | |||||||
\(432\) | 20.7846i | 0.0481125i | ||||||||
\(433\) | 10.8320 | 0.0250162 | 0.0125081 | − | 0.999922i | \(-0.496018\pi\) | ||||
0.0125081 | + | 0.999922i | \(0.496018\pi\) | |||||||
\(434\) | − | 58.3126i | − | 0.134361i | ||||||
\(435\) | −262.235 | + | 96.0138i | −0.602838 | + | 0.220721i | ||||
\(436\) | − | 88.0978i | − | 0.202059i | ||||||
\(437\) | −43.6421 | − | 558.316i | −0.0998674 | − | 1.27761i | ||||
\(438\) | 173.013i | 0.395006i | ||||||||
\(439\) | 10.1988 | 0.0232319 | 0.0116159 | − | 0.999933i | \(-0.496302\pi\) | ||||
0.0116159 | + | 0.999933i | \(0.496302\pi\) | |||||||
\(440\) | 89.4345 | + | 244.265i | 0.203260 | + | 0.555148i | ||||
\(441\) | −355.306 | −0.805682 | ||||||||
\(442\) | −214.426 | −0.485127 | ||||||||
\(443\) | 23.7800i | 0.0536794i | 0.999640 | + | 0.0268397i | \(0.00854437\pi\) | ||||
−0.999640 | + | 0.0268397i | \(0.991456\pi\) | |||||||
\(444\) | 38.1642i | 0.0859553i | ||||||||
\(445\) | −196.928 | + | 72.1025i | −0.442534 | + | 0.162028i | ||||
\(446\) | 173.835 | 0.389765 | ||||||||
\(447\) | 254.881 | 0.570203 | ||||||||
\(448\) | 103.517 | 0.231066 | ||||||||
\(449\) | −417.771 | −0.930448 | −0.465224 | − | 0.885193i | \(-0.654026\pi\) | ||||
−0.465224 | + | 0.885193i | \(0.654026\pi\) | |||||||
\(450\) | 68.4881 | + | 80.9900i | 0.152196 | + | 0.179978i | ||||
\(451\) | 1111.69i | 2.46494i | ||||||||
\(452\) | 325.886 | 0.720987 | ||||||||
\(453\) | 7.30738i | 0.0161311i | ||||||||
\(454\) | − | 402.335i | − | 0.886201i | ||||||
\(455\) | −461.954 | + | 169.138i | −1.01528 | + | 0.371733i | ||||
\(456\) | − | 119.284i | − | 0.261587i | ||||||
\(457\) | −197.215 | −0.431543 | −0.215772 | − | 0.976444i | \(-0.569227\pi\) | ||||
−0.215772 | + | 0.976444i | \(0.569227\pi\) | |||||||
\(458\) | −603.898 | −1.31855 | ||||||||
\(459\) | 103.615i | 0.225741i | ||||||||
\(460\) | −95.6684 | − | 209.159i | −0.207975 | − | 0.454694i | ||||
\(461\) | −791.818 | −1.71761 | −0.858805 | − | 0.512303i | \(-0.828792\pi\) | ||||
−0.858805 | + | 0.512303i | \(0.828792\pi\) | |||||||
\(462\) | 582.992i | 1.26189i | ||||||||
\(463\) | 225.166i | 0.486320i | 0.969986 | + | 0.243160i | \(0.0781840\pi\) | ||||
−0.969986 | + | 0.243160i | \(0.921816\pi\) | |||||||
\(464\) | 128.984 | 0.277983 | ||||||||
\(465\) | −25.9142 | + | 9.48814i | −0.0557294 | + | 0.0204046i | ||||
\(466\) | 533.542 | 1.14494 | ||||||||
\(467\) | 4.35994 | 0.00933607 | 0.00466803 | − | 0.999989i | \(-0.498514\pi\) | ||||
0.00466803 | + | 0.999989i | \(0.498514\pi\) | |||||||
\(468\) | 45.6219i | 0.0974828i | ||||||||
\(469\) | −934.661 | −1.99288 | ||||||||
\(470\) | 193.191 | + | 527.645i | 0.411044 | + | 1.12265i | ||||
\(471\) | − | 221.683i | − | 0.470665i | ||||||
\(472\) | − | 14.6003i | − | 0.0309329i | ||||||
\(473\) | 926.294i | 1.95834i | ||||||||
\(474\) | − | 3.31318i | − | 0.00698983i | ||||||
\(475\) | −393.056 | − | 464.804i | −0.827486 | − | 0.978535i | ||||
\(476\) | 516.053 | 1.08414 | ||||||||
\(477\) | −276.350 | −0.579349 | ||||||||
\(478\) | 159.593i | 0.333876i | ||||||||
\(479\) | − | 262.797i | − | 0.548637i | −0.961639 | − | 0.274318i | \(-0.911548\pi\) | ||
0.961639 | − | 0.274318i | \(-0.0884522\pi\) | |||||||
\(480\) | −16.8435 | − | 46.0032i | −0.0350906 | − | 0.0958401i | ||||
\(481\) | 83.7698i | 0.174158i | ||||||||
\(482\) | 211.100 | 0.437968 | ||||||||
\(483\) | −40.1712 | − | 513.912i | −0.0831701 | − | 1.06400i | ||||
\(484\) | 434.640 | 0.898016 | ||||||||
\(485\) | 284.766 | + | 777.758i | 0.587147 | + | 1.60363i | ||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | − | 320.366i | − | 0.657835i | −0.944359 | − | 0.328917i | \(-0.893316\pi\) | ||
0.944359 | − | 0.328917i | \(-0.106684\pi\) | |||||||
\(488\) | −29.7734 | −0.0610111 | ||||||||
\(489\) | −93.3456 | −0.190891 | ||||||||
\(490\) | 786.409 | − | 287.934i | 1.60492 | − | 0.587620i | ||||
\(491\) | 179.242 | 0.365055 | 0.182528 | − | 0.983201i | \(-0.441572\pi\) | ||||
0.182528 | + | 0.983201i | \(0.441572\pi\) | |||||||
\(492\) | − | 209.367i | − | 0.425543i | ||||||
\(493\) | 643.009 | 1.30428 | ||||||||
\(494\) | − | 261.826i | − | 0.530012i | ||||||
\(495\) | 259.082 | − | 94.8597i | 0.523399 | − | 0.191636i | ||||
\(496\) | 12.7463 | 0.0256982 | ||||||||
\(497\) | 115.799 | 0.232997 | ||||||||
\(498\) | −331.593 | −0.665848 | ||||||||
\(499\) | −14.9582 | −0.0299763 | −0.0149882 | − | 0.999888i | \(-0.504771\pi\) | ||||
−0.0149882 | + | 0.999888i | \(0.504771\pi\) | |||||||
\(500\) | −217.220 | − | 123.756i | −0.434440 | − | 0.247512i | ||||
\(501\) | 328.420 | 0.655530 | ||||||||
\(502\) | −506.108 | −1.00818 | ||||||||
\(503\) | −694.560 | −1.38084 | −0.690418 | − | 0.723411i | \(-0.742573\pi\) | ||||
−0.690418 | + | 0.723411i | \(0.742573\pi\) | |||||||
\(504\) | − | 109.797i | − | 0.217851i | ||||||
\(505\) | −34.7713 | − | 94.9678i | −0.0688540 | − | 0.188055i | ||||
\(506\) | −596.463 | + | 46.6239i | −1.17878 | + | 0.0921422i | ||||
\(507\) | − | 192.577i | − | 0.379836i | ||||||
\(508\) | 156.685i | 0.308434i | ||||||||
\(509\) | −401.121 | −0.788057 | −0.394028 | − | 0.919098i | \(-0.628919\pi\) | ||||
−0.394028 | + | 0.919098i | \(0.628919\pi\) | |||||||
\(510\) | −83.9678 | − | 229.334i | −0.164643 | − | 0.449675i | ||||
\(511\) | − | 913.957i | − | 1.78857i | ||||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | −126.519 | −0.246626 | ||||||||
\(514\) | 83.3730 | 0.162204 | ||||||||
\(515\) | 17.3759 | + | 47.4574i | 0.0337397 | + | 0.0921503i | ||||
\(516\) | − | 174.452i | − | 0.338085i | ||||||
\(517\) | 1461.63 | 2.82714 | ||||||||
\(518\) | − | 201.606i | − | 0.389201i | ||||||
\(519\) | −127.137 | −0.244966 | ||||||||
\(520\) | −36.9712 | − | 100.976i | −0.0710985 | − | 0.194186i | ||||
\(521\) | 832.880i | 1.59862i | 0.600920 | + | 0.799309i | \(0.294801\pi\) | ||||
−0.600920 | + | 0.799309i | \(0.705199\pi\) | |||||||
\(522\) | − | 136.808i | − | 0.262085i | ||||||
\(523\) | −303.690 | −0.580670 | −0.290335 | − | 0.956925i | \(-0.593767\pi\) | ||||
−0.290335 | + | 0.956925i | \(0.593767\pi\) | |||||||
\(524\) | −487.047 | −0.929479 | ||||||||
\(525\) | −361.796 | − | 427.838i | −0.689134 | − | 0.814929i | ||||
\(526\) | 171.299i | 0.325663i | ||||||||
\(527\) | 63.5425 | 0.120574 | ||||||||
\(528\) | −127.434 | −0.241352 | ||||||||
\(529\) | 522.575 | − | 82.1988i | 0.987854 | − | 0.155385i | ||||
\(530\) | 611.653 | − | 223.949i | 1.15406 | − | 0.422545i | ||||
\(531\) | −15.4860 | −0.0291639 | ||||||||
\(532\) | 630.128i | 1.18445i | ||||||||
\(533\) | − | 459.558i | − | 0.862211i | ||||||
\(534\) | − | 102.738i | − | 0.192393i | ||||||
\(535\) | −103.019 | − | 281.368i | −0.192560 | − | 0.525922i | ||||
\(536\) | − | 204.303i | − | 0.381163i | ||||||
\(537\) | 483.315i | 0.900028i | ||||||||
\(538\) | 443.103i | 0.823612i | ||||||||
\(539\) | − | 2178.44i | − | 4.04162i | ||||||
\(540\) | −48.7938 | + | 17.8652i | −0.0903589 | + | 0.0330837i | ||||
\(541\) | 802.731 | 1.48379 | 0.741896 | − | 0.670515i | \(-0.233927\pi\) | ||||
0.741896 | + | 0.670515i | \(0.233927\pi\) | |||||||
\(542\) | − | 24.2962i | − | 0.0448269i | ||||||
\(543\) | 262.292 | 0.483043 | ||||||||
\(544\) | 112.802i | 0.207356i | ||||||||
\(545\) | 206.818 | − | 75.7236i | 0.379482 | − | 0.138942i | ||||
\(546\) | − | 241.003i | − | 0.441397i | ||||||
\(547\) | 555.494i | 1.01553i | 0.861496 | + | 0.507764i | \(0.169528\pi\) | ||||
−0.861496 | + | 0.507764i | \(0.830472\pi\) | |||||||
\(548\) | 137.351 | 0.250641 | ||||||||
\(549\) | 31.5795i | 0.0575218i | ||||||||
\(550\) | −496.562 | + | 419.912i | −0.902840 | + | 0.763476i | ||||
\(551\) | 785.148i | 1.42495i | ||||||||
\(552\) | 112.334 | − | 8.78084i | 0.203503 | − | 0.0159073i | ||||
\(553\) | 17.5022i | 0.0316496i | ||||||||
\(554\) | −379.632 | −0.685256 | ||||||||
\(555\) | −89.5939 | + | 32.8037i | −0.161430 | + | 0.0591057i | ||||
\(556\) | 273.603 | 0.492092 | ||||||||
\(557\) | −697.030 | −1.25140 | −0.625700 | − | 0.780064i | \(-0.715187\pi\) | ||||
−0.625700 | + | 0.780064i | \(0.715187\pi\) | |||||||
\(558\) | − | 13.5195i | − | 0.0242285i | ||||||
\(559\) | − | 382.920i | − | 0.685008i | ||||||
\(560\) | 88.9774 | + | 243.017i | 0.158888 | + | 0.433958i | ||||
\(561\) | −635.280 | −1.13241 | ||||||||
\(562\) | 546.807 | 0.972966 | ||||||||
\(563\) | 24.7377 | 0.0439390 | 0.0219695 | − | 0.999759i | \(-0.493006\pi\) | ||||
0.0219695 | + | 0.999759i | \(0.493006\pi\) | |||||||
\(564\) | −275.274 | −0.488074 | ||||||||
\(565\) | 280.113 | + | 765.048i | 0.495775 | + | 1.35407i | ||||
\(566\) | 77.1777i | 0.136356i | ||||||||
\(567\) | −116.457 | −0.205392 | ||||||||
\(568\) | 25.3121i | 0.0445635i | ||||||||
\(569\) | 475.965i | 0.836495i | 0.908333 | + | 0.418247i | \(0.137355\pi\) | ||||
−0.908333 | + | 0.418247i | \(0.862645\pi\) | |||||||
\(570\) | 280.029 | − | 102.529i | 0.491279 | − | 0.179876i | ||||
\(571\) | − | 558.821i | − | 0.978671i | −0.872096 | − | 0.489336i | \(-0.837239\pi\) | ||
0.872096 | − | 0.489336i | \(-0.162761\pi\) | |||||||
\(572\) | −279.715 | −0.489013 | ||||||||
\(573\) | 514.081 | 0.897175 | ||||||||
\(574\) | 1106.00i | 1.92684i | ||||||||
\(575\) | 408.790 | − | 404.371i | 0.710938 | − | 0.703254i | ||||
\(576\) | 24.0000 | 0.0416667 | ||||||||
\(577\) | 1114.51i | 1.93156i | 0.259365 | + | 0.965779i | \(0.416487\pi\) | ||||
−0.259365 | + | 0.965779i | \(0.583513\pi\) | |||||||
\(578\) | 153.628i | 0.265793i | ||||||||
\(579\) | 46.6177 | 0.0805141 | ||||||||
\(580\) | 110.867 | + | 302.802i | 0.191150 | + | 0.522073i | ||||
\(581\) | 1751.67 | 3.01492 | ||||||||
\(582\) | −405.758 | −0.697179 | ||||||||
\(583\) | − | 1694.34i | − | 2.90625i | ||||||
\(584\) | 199.778 | 0.342085 | ||||||||
\(585\) | −107.102 | + | 39.2139i | −0.183080 | + | 0.0670323i | ||||
\(586\) | 124.251i | 0.212032i | ||||||||
\(587\) | 396.273i | 0.675082i | 0.941311 | + | 0.337541i | \(0.109595\pi\) | ||||
−0.941311 | + | 0.337541i | \(0.890405\pi\) | |||||||
\(588\) | 410.272i | 0.697741i | ||||||||
\(589\) | 77.5888i | 0.131730i | ||||||||
\(590\) | 34.2757 | − | 12.5496i | 0.0580943 | − | 0.0212705i | ||||
\(591\) | 106.674 | 0.180497 | ||||||||
\(592\) | 44.0682 | 0.0744395 | ||||||||
\(593\) | − | 888.386i | − | 1.49812i | −0.662501 | − | 0.749061i | \(-0.730505\pi\) | ||
0.662501 | − | 0.749061i | \(-0.269495\pi\) | |||||||
\(594\) | 135.164i | 0.227549i | ||||||||
\(595\) | 443.568 | + | 1211.48i | 0.745493 | + | 2.03610i | ||||
\(596\) | − | 294.311i | − | 0.493810i | ||||||
\(597\) | 61.1997 | 0.102512 | ||||||||
\(598\) | 246.571 | − | 19.2738i | 0.412327 | − | 0.0322305i | ||||
\(599\) | −902.768 | −1.50713 | −0.753563 | − | 0.657376i | \(-0.771666\pi\) | ||||
−0.753563 | + | 0.657376i | \(0.771666\pi\) | |||||||
\(600\) | 93.5192 | − | 79.0833i | 0.155865 | − | 0.131806i | ||||
\(601\) | 685.970 | 1.14138 | 0.570691 | − | 0.821165i | \(-0.306675\pi\) | ||||
0.570691 | + | 0.821165i | \(0.306675\pi\) | |||||||
\(602\) | 921.560i | 1.53083i | ||||||||
\(603\) | −216.696 | −0.359364 | ||||||||
\(604\) | 8.43783 | 0.0139699 | ||||||||
\(605\) | 373.591 | + | 1020.36i | 0.617505 | + | 1.68654i | ||||
\(606\) | 49.5450 | 0.0817574 | ||||||||
\(607\) | − | 790.719i | − | 1.30267i | −0.758791 | − | 0.651334i | \(-0.774210\pi\) | ||
0.758791 | − | 0.651334i | \(-0.225790\pi\) | |||||||
\(608\) | −137.737 | −0.226541 | ||||||||
\(609\) | 722.705i | 1.18671i | ||||||||
\(610\) | −25.5915 | − | 69.8959i | −0.0419532 | − | 0.114583i | ||||
\(611\) | −604.222 | −0.988907 | ||||||||
\(612\) | 119.644 | 0.195497 | ||||||||
\(613\) | −563.868 | −0.919850 | −0.459925 | − | 0.887958i | \(-0.652124\pi\) | ||||
−0.459925 | + | 0.887958i | \(0.652124\pi\) | |||||||
\(614\) | 617.607 | 1.00587 | ||||||||
\(615\) | 491.509 | − | 179.960i | 0.799202 | − | 0.292618i | ||||
\(616\) | 673.182 | 1.09283 | ||||||||
\(617\) | 803.130 | 1.30167 | 0.650835 | − | 0.759219i | \(-0.274419\pi\) | ||||
0.650835 | + | 0.759219i | \(0.274419\pi\) | |||||||
\(618\) | −24.7587 | −0.0400625 | ||||||||
\(619\) | 242.335i | 0.391494i | 0.980654 | + | 0.195747i | \(0.0627131\pi\) | ||||
−0.980654 | + | 0.195747i | \(0.937287\pi\) | |||||||
\(620\) | 10.9560 | + | 29.9231i | 0.0176709 | + | 0.0482631i | ||||
\(621\) | −9.31348 | − | 119.148i | −0.0149976 | − | 0.191865i | ||||
\(622\) | − | 134.934i | − | 0.216935i | ||||||
\(623\) | 542.722i | 0.871142i | ||||||||
\(624\) | 52.6797 | 0.0844226 | ||||||||
\(625\) | 103.819 | − | 616.317i | 0.166111 | − | 0.986107i | ||||
\(626\) | − | 392.550i | − | 0.627076i | ||||||
\(627\) | − | 775.710i | − | 1.23718i | ||||||
\(628\) | −255.978 | −0.407608 | ||||||||
\(629\) | 219.688 | 0.349265 | ||||||||
\(630\) | 257.758 | − | 94.3748i | 0.409140 | − | 0.149801i | ||||
\(631\) | 713.068i | 1.13006i | 0.825070 | + | 0.565031i | \(0.191136\pi\) | ||||
−0.825070 | + | 0.565031i | \(0.808864\pi\) | |||||||
\(632\) | −3.82573 | −0.00605337 | ||||||||
\(633\) | 245.980i | 0.388594i | ||||||||
\(634\) | 62.1281 | 0.0979939 | ||||||||
\(635\) | −367.832 | + | 134.677i | −0.579263 | + | 0.212090i | ||||
\(636\) | 319.101i | 0.501731i | ||||||||
\(637\) | 900.541i | 1.41372i | ||||||||
\(638\) | 838.794 | 1.31472 | ||||||||
\(639\) | 26.8475 | 0.0420149 | ||||||||
\(640\) | −53.1199 | + | 19.4492i | −0.0829999 | + | 0.0303894i | ||||
\(641\) | 320.213i | 0.499553i | 0.968304 | + | 0.249776i | \(0.0803571\pi\) | ||||
−0.968304 | + | 0.249776i | \(0.919643\pi\) | |||||||
\(642\) | 146.791 | 0.228646 | ||||||||
\(643\) | 441.300 | 0.686315 | 0.343157 | − | 0.939278i | \(-0.388504\pi\) | ||||
0.343157 | + | 0.939278i | \(0.388504\pi\) | |||||||
\(644\) | −593.415 | + | 46.3857i | −0.921452 | + | 0.0720274i | ||||
\(645\) | 409.542 | − | 149.949i | 0.634949 | − | 0.232478i | ||||
\(646\) | −686.642 | −1.06291 | ||||||||
\(647\) | 935.951i | 1.44660i | 0.690533 | + | 0.723301i | \(0.257376\pi\) | ||||
−0.690533 | + | 0.723301i | \(0.742624\pi\) | |||||||
\(648\) | − | 25.4558i | − | 0.0392837i | ||||||
\(649\) | − | 94.9472i | − | 0.146298i | ||||||
\(650\) | 205.273 | − | 173.587i | 0.315805 | − | 0.267057i | ||||
\(651\) | 71.4181i | 0.109705i | ||||||||
\(652\) | 107.786i | 0.165316i | ||||||||
\(653\) | 779.044i | 1.19302i | 0.802604 | + | 0.596512i | \(0.203447\pi\) | ||||
−0.802604 | + | 0.596512i | \(0.796553\pi\) | |||||||
\(654\) | 107.897i | 0.164981i | ||||||||
\(655\) | −418.637 | − | 1143.39i | −0.639140 | − | 1.74563i | ||||
\(656\) | −241.757 | −0.368531 | ||||||||
\(657\) | − | 211.896i | − | 0.322521i | ||||||
\(658\) | 1454.16 | 2.20997 | ||||||||
\(659\) | − | 990.231i | − | 1.50263i | −0.659946 | − | 0.751313i | \(-0.729421\pi\) | ||
0.659946 | − | 0.751313i | \(-0.270579\pi\) | |||||||
\(660\) | −109.534 | − | 299.162i | −0.165961 | − | 0.453276i | ||||
\(661\) | 82.8711i | 0.125372i | 0.998033 | + | 0.0626862i | \(0.0199667\pi\) | ||||
−0.998033 | + | 0.0626862i | \(0.980033\pi\) | |||||||
\(662\) | − | 636.205i | − | 0.961034i | ||||||
\(663\) | 262.617 | 0.396105 | ||||||||
\(664\) | 382.890i | 0.576642i | ||||||||
\(665\) | −1479.28 | + | 541.620i | −2.22449 | + | 0.814467i | ||||
\(666\) | − | 46.7414i | − | 0.0701822i | ||||||
\(667\) | −739.404 | + | 57.7972i | −1.10855 | + | 0.0866525i | ||||
\(668\) | − | 379.227i | − | 0.567705i | ||||||
\(669\) | −212.904 | −0.318242 | ||||||||
\(670\) | 479.621 | − | 175.607i | 0.715852 | − | 0.262100i | ||||
\(671\) | −193.619 | −0.288553 | ||||||||
\(672\) | −126.782 | −0.188664 | ||||||||
\(673\) | − | 461.012i | − | 0.685010i | −0.939516 | − | 0.342505i | \(-0.888725\pi\) | ||
0.939516 | − | 0.342505i | \(-0.111275\pi\) | |||||||
\(674\) | − | 282.649i | − | 0.419361i | ||||||
\(675\) | −83.8805 | − | 99.1920i | −0.124267 | − | 0.146951i | ||||
\(676\) | −222.369 | −0.328948 | ||||||||
\(677\) | 1137.48 | 1.68017 | 0.840085 | − | 0.542454i | \(-0.182505\pi\) | ||||
0.840085 | + | 0.542454i | \(0.182505\pi\) | |||||||
\(678\) | −399.128 | −0.588684 | ||||||||
\(679\) | 2143.46 | 3.15679 | ||||||||
\(680\) | −264.812 | + | 96.9576i | −0.389430 | + | 0.142585i | ||||
\(681\) | 492.758i | 0.723580i | ||||||||
\(682\) | 82.8901 | 0.121540 | ||||||||
\(683\) | 27.4834i | 0.0402393i | 0.999798 | + | 0.0201196i | \(0.00640471\pi\) | ||||
−0.999798 | + | 0.0201196i | \(0.993595\pi\) | |||||||
\(684\) | 146.092i | 0.213585i | ||||||||
\(685\) | 118.059 | + | 322.445i | 0.172349 | + | 0.470723i | ||||
\(686\) | − | 1270.63i | − | 1.85223i | ||||||
\(687\) | 739.621 | 1.07659 | ||||||||
\(688\) | −201.440 | −0.292790 | ||||||||
\(689\) | 700.422i | 1.01658i | ||||||||
\(690\) | 117.169 | + | 256.167i | 0.169811 | + | 0.371256i | ||||
\(691\) | 202.309 | 0.292777 | 0.146388 | − | 0.989227i | \(-0.453235\pi\) | ||||
0.146388 | + | 0.989227i | \(0.453235\pi\) | |||||||
\(692\) | 146.805i | 0.212147i | ||||||||
\(693\) | − | 714.017i | − | 1.03033i | ||||||
\(694\) | 410.638 | 0.591697 | ||||||||
\(695\) | 235.173 | + | 642.309i | 0.338378 | + | 0.924185i | ||||
\(696\) | −157.973 | −0.226972 | ||||||||
\(697\) | −1205.20 | −1.72912 | ||||||||
\(698\) | − | 179.107i | − | 0.256600i | ||||||
\(699\) | −653.453 | −0.934840 | ||||||||
\(700\) | −494.024 | + | 417.766i | −0.705749 | + | 0.596808i | ||||
\(701\) | − | 720.064i | − | 1.02719i | −0.858031 | − | 0.513597i | \(-0.828313\pi\) | ||
0.858031 | − | 0.513597i | \(-0.171687\pi\) | |||||||
\(702\) | − | 55.8752i | − | 0.0795944i | ||||||
\(703\) | 268.250i | 0.381579i | ||||||||
\(704\) | 147.148i | 0.209017i | ||||||||
\(705\) | −236.609 | − | 646.231i | −0.335616 | − | 0.916639i | ||||
\(706\) | −703.855 | −0.996961 | ||||||||
\(707\) | −261.726 | −0.370193 | ||||||||
\(708\) | 17.8817i | 0.0252566i | ||||||||
\(709\) | − | 1116.63i | − | 1.57493i | −0.616357 | − | 0.787467i | \(-0.711392\pi\) | ||
0.616357 | − | 0.787467i | \(-0.288608\pi\) | |||||||
\(710\) | −59.4224 | + | 21.7567i | −0.0836935 | + | 0.0306433i | ||||
\(711\) | 4.05780i | 0.00570717i | ||||||||
\(712\) | −118.631 | −0.166617 | ||||||||
\(713\) | −73.0683 | + | 5.71155i | −0.102480 | + | 0.00801059i | ||||
\(714\) | −632.033 | −0.885200 | ||||||||
\(715\) | −240.427 | − | 656.658i | −0.336261 | − | 0.918402i | ||||
\(716\) | 558.084 | 0.779447 | ||||||||
\(717\) | − | 195.460i | − | 0.272608i | ||||||
\(718\) | −465.307 | −0.648059 | ||||||||
\(719\) | −276.958 | −0.385199 | −0.192600 | − | 0.981277i | \(-0.561692\pi\) | ||||
−0.192600 | + | 0.981277i | \(0.561692\pi\) | |||||||
\(720\) | 20.6290 | + | 56.3422i | 0.0286514 | + | 0.0782531i | ||||
\(721\) | 130.790 | 0.181401 | ||||||||
\(722\) | − | 327.896i | − | 0.454149i | ||||||
\(723\) | −258.544 | −0.357599 | ||||||||
\(724\) | − | 302.869i | − | 0.418327i | ||||||
\(725\) | −615.562 | + | 520.542i | −0.849051 | + | 0.717989i | ||||
\(726\) | −532.323 | −0.733227 | ||||||||
\(727\) | −1175.60 | −1.61706 | −0.808530 | − | 0.588455i | \(-0.799736\pi\) | ||||
−0.808530 | + | 0.588455i | \(0.799736\pi\) | |||||||
\(728\) | −278.286 | −0.382261 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 171.717 | + | 468.997i | 0.235229 | + | 0.642462i | ||||
\(731\) | −1004.21 | −1.37375 | ||||||||
\(732\) | 36.4648 | 0.0498154 | ||||||||
\(733\) | −620.255 | −0.846187 | −0.423093 | − | 0.906086i | \(-0.639056\pi\) | ||||
−0.423093 | + | 0.906086i | \(0.639056\pi\) | |||||||
\(734\) | − | 243.804i | − | 0.332158i | ||||||
\(735\) | −963.151 | + | 352.645i | −1.31041 | + | 0.479790i | ||||
\(736\) | −10.1392 | − | 129.712i | −0.0137761 | − | 0.176239i | ||||
\(737\) | − | 1328.60i | − | 1.80271i | ||||||
\(738\) | 256.422i | 0.347455i | ||||||||
\(739\) | −147.282 | −0.199298 | −0.0996492 | − | 0.995023i | \(-0.531772\pi\) | ||||
−0.0996492 | + | 0.995023i | \(0.531772\pi\) | |||||||
\(740\) | 37.8784 | + | 103.454i | 0.0511870 | + | 0.139803i | ||||
\(741\) | 320.670i | 0.432753i | ||||||||
\(742\) | − | 1685.68i | − | 2.27181i | ||||||
\(743\) | 722.303 | 0.972143 | 0.486072 | − | 0.873919i | \(-0.338429\pi\) | ||||
0.486072 | + | 0.873919i | \(0.338429\pi\) | |||||||
\(744\) | −15.6110 | −0.0209825 | ||||||||
\(745\) | 690.922 | − | 252.972i | 0.927412 | − | 0.339560i | ||||
\(746\) | − | 248.503i | − | 0.333114i | ||||||
\(747\) | 406.116 | 0.543663 | ||||||||
\(748\) | 733.558i | 0.980692i | ||||||||
\(749\) | −775.436 | −1.03529 | ||||||||
\(750\) | 266.039 | + | 151.570i | 0.354719 | + | 0.202093i | ||||
\(751\) | − | 1411.00i | − | 1.87883i | −0.342781 | − | 0.939415i | \(-0.611369\pi\) | ||
0.342781 | − | 0.939415i | \(-0.388631\pi\) | |||||||
\(752\) | 317.859i | 0.422685i | ||||||||
\(753\) | 619.853 | 0.823178 | ||||||||
\(754\) | −346.748 | −0.459878 | ||||||||
\(755\) | 7.25266 | + | 19.8086i | 0.00960618 | + | 0.0262365i | ||||
\(756\) | 134.473i | 0.177874i | ||||||||
\(757\) | −407.669 | −0.538532 | −0.269266 | − | 0.963066i | \(-0.586781\pi\) | ||||
−0.269266 | + | 0.963066i | \(0.586781\pi\) | |||||||
\(758\) | −598.317 | −0.789336 | ||||||||
\(759\) | 730.516 | − | 57.1024i | 0.962471 | − | 0.0752338i | ||||
\(760\) | −118.390 | − | 323.350i | −0.155777 | − | 0.425460i | ||||
\(761\) | 696.139 | 0.914769 | 0.457385 | − | 0.889269i | \(-0.348786\pi\) | ||||
0.457385 | + | 0.889269i | \(0.348786\pi\) | |||||||
\(762\) | − | 191.899i | − | 0.251836i | ||||||
\(763\) | − | 569.978i | − | 0.747023i | ||||||
\(764\) | − | 593.610i | − | 0.776976i | ||||||
\(765\) | 102.839 | + | 280.876i | 0.134430 | + | 0.367158i | ||||
\(766\) | − | 568.138i | − | 0.741694i | ||||||
\(767\) | 39.2501i | 0.0511735i | ||||||||
\(768\) | − | 27.7128i | − | 0.0360844i | ||||||
\(769\) | 320.918i | 0.417319i | 0.977988 | + | 0.208659i | \(0.0669100\pi\) | ||||
−0.977988 | + | 0.208659i | \(0.933090\pi\) | |||||||
\(770\) | 578.627 | + | 1580.36i | 0.751464 | + | 2.05241i | ||||
\(771\) | −102.111 | −0.132439 | ||||||||
\(772\) | − | 53.8294i | − | 0.0697273i | ||||||
\(773\) | −582.738 | −0.753865 | −0.376933 | − | 0.926241i | \(-0.623021\pi\) | ||||
−0.376933 | + | 0.926241i | \(0.623021\pi\) | |||||||
\(774\) | 213.659i | 0.276045i | ||||||||
\(775\) | −60.8301 | + | 51.4403i | −0.0784905 | + | 0.0663745i | ||||
\(776\) | 468.529i | 0.603775i | ||||||||
\(777\) | 246.916i | 0.317781i | ||||||||
\(778\) | 490.400 | 0.630334 | ||||||||
\(779\) | − | 1471.61i | − | 1.88910i | ||||||
\(780\) | 45.2803 | + | 123.670i | 0.0580517 | + | 0.158552i | ||||
\(781\) | 164.606i | 0.210763i | ||||||||
\(782\) | −50.5459 | − | 646.637i | −0.0646367 | − | 0.826902i | ||||
\(783\) | 167.555i | 0.213992i | ||||||||
\(784\) | 473.741 | 0.604261 | ||||||||
\(785\) | −220.023 | − | 600.932i | −0.280285 | − | 0.765518i | ||||
\(786\) | 596.508 | 0.758916 | ||||||||
\(787\) | −463.279 | −0.588665 | −0.294333 | − | 0.955703i | \(-0.595097\pi\) | ||||
−0.294333 | + | 0.955703i | \(0.595097\pi\) | |||||||
\(788\) | − | 123.176i | − | 0.156315i | ||||||
\(789\) | − | 209.797i | − | 0.265903i | ||||||
\(790\) | −3.28837 | − | 8.98125i | −0.00416250 | − | 0.0113687i | ||||
\(791\) | 2108.43 | 2.66553 | ||||||||
\(792\) | 156.074 | 0.197063 | ||||||||
\(793\) | 80.0399 | 0.100933 | ||||||||
\(794\) | −139.887 | −0.176180 | ||||||||
\(795\) | −749.119 | + | 274.280i | −0.942288 | + | 0.345007i | ||||
\(796\) | − | 70.6673i | − | 0.0887780i | ||||||
\(797\) | 831.050 | 1.04272 | 0.521362 | − | 0.853336i | \(-0.325424\pi\) | ||||
0.521362 | + | 0.853336i | \(0.325424\pi\) | |||||||
\(798\) | − | 771.746i | − | 0.967100i | ||||||
\(799\) | 1584.58i | 1.98321i | ||||||||
\(800\) | −91.3175 | − | 107.987i | −0.114147 | − | 0.134983i | ||||
\(801\) | 125.827i | 0.157088i | ||||||||
\(802\) | −885.120 | −1.10364 | ||||||||
\(803\) | 1299.17 | 1.61790 | ||||||||
\(804\) | 250.220i | 0.311218i | ||||||||
\(805\) | −618.959 | − | 1353.23i | −0.768893 | − | 1.68103i | ||||
\(806\) | −34.2658 | −0.0425135 | ||||||||
\(807\) | − | 542.688i | − | 0.672476i | ||||||
\(808\) | − | 57.2096i | − | 0.0708040i | ||||||
\(809\) | 618.152 | 0.764094 | 0.382047 | − | 0.924143i | \(-0.375219\pi\) | ||||
0.382047 | + | 0.924143i | \(0.375219\pi\) | |||||||
\(810\) | 59.7599 | − | 21.8803i | 0.0737777 | − | 0.0270128i | ||||
\(811\) | −668.575 | −0.824383 | −0.412192 | − | 0.911097i | \(-0.635237\pi\) | ||||
−0.412192 | + | 0.911097i | \(0.635237\pi\) | |||||||
\(812\) | 834.507 | 1.02772 | ||||||||
\(813\) | 29.7566i | 0.0366010i | ||||||||
\(814\) | 286.579 | 0.352062 | ||||||||
\(815\) | −253.038 | + | 92.6467i | −0.310476 | + | 0.113677i | ||||
\(816\) | − | 138.153i | − | 0.169305i | ||||||
\(817\) | − | 1226.20i | − | 1.50085i | ||||||
\(818\) | 580.634i | 0.709822i | ||||||||
\(819\) | 295.167i | 0.360399i | ||||||||
\(820\) | −207.800 | − | 567.546i | −0.253414 | − | 0.692129i | ||||
\(821\) | −1377.11 | −1.67736 | −0.838681 | − | 0.544623i | \(-0.816673\pi\) | ||||
−0.838681 | + | 0.544623i | \(0.816673\pi\) | |||||||
\(822\) | −168.220 | −0.204648 | ||||||||
\(823\) | 976.421i | 1.18642i | 0.805049 | + | 0.593208i | \(0.202139\pi\) | ||||
−0.805049 | + | 0.593208i | \(0.797861\pi\) | |||||||
\(824\) | 28.5888i | 0.0346952i | ||||||||
\(825\) | 608.162 | − | 514.285i | 0.737166 | − | 0.623375i | ||||
\(826\) | − | 94.4619i | − | 0.114361i | ||||||
\(827\) | 438.021 | 0.529650 | 0.264825 | − | 0.964296i | \(-0.414686\pi\) | ||||
0.264825 | + | 0.964296i | \(0.414686\pi\) | |||||||
\(828\) | −137.580 | + | 10.7543i | −0.166160 | + | 0.0129883i | ||||
\(829\) | 541.852 | 0.653621 | 0.326810 | − | 0.945090i | \(-0.394026\pi\) | ||||
0.326810 | + | 0.945090i | \(0.394026\pi\) | |||||||
\(830\) | −898.870 | + | 329.110i | −1.08298 | + | 0.396518i | ||||
\(831\) | 464.952 | 0.559509 | ||||||||
\(832\) | − | 60.8293i | − | 0.0731121i | ||||||
\(833\) | 2361.68 | 2.83515 | ||||||||
\(834\) | −335.094 | −0.401791 | ||||||||
\(835\) | 890.271 | − | 325.961i | 1.06619 | − | 0.390373i | ||||
\(836\) | −895.713 | −1.07143 | ||||||||
\(837\) | 16.5579i | 0.0197825i | ||||||||
\(838\) | −51.3647 | −0.0612944 | ||||||||
\(839\) | 537.167i | 0.640247i | 0.947376 | + | 0.320123i | \(0.103724\pi\) | ||||
−0.947376 | + | 0.320123i | \(0.896276\pi\) | |||||||
\(840\) | −108.975 | − | 297.633i | −0.129732 | − | 0.354326i | ||||
\(841\) | 198.809 | 0.236395 | ||||||||
\(842\) | −771.464 | −0.916228 | ||||||||
\(843\) | −669.699 | −0.794423 | ||||||||
\(844\) | 284.033 | 0.336532 | ||||||||
\(845\) | −191.135 | − | 522.031i | −0.226195 | − | 0.617789i | ||||
\(846\) | 337.140 | 0.398511 | ||||||||
\(847\) | 2812.05 | 3.32001 | ||||||||
\(848\) | 368.466 | 0.434512 | ||||||||
\(849\) | − | 94.5230i | − | 0.111335i | ||||||
\(850\) | −455.234 | − | 538.332i | −0.535569 | − | 0.633332i | ||||
\(851\) | −252.622 | + | 19.7467i | −0.296853 | + | 0.0232042i | ||||
\(852\) | − | 31.0008i | − | 0.0363859i | ||||||
\(853\) | − | 198.433i | − | 0.232630i | −0.993212 | − | 0.116315i | \(-0.962892\pi\) | ||
0.993212 | − | 0.116315i | \(-0.0371081\pi\) | |||||||
\(854\) | −192.629 | −0.225561 | ||||||||
\(855\) | −342.964 | + | 125.572i | −0.401128 | + | 0.146868i | ||||
\(856\) | − | 169.499i | − | 0.198013i | ||||||
\(857\) | − | 984.927i | − | 1.14927i | −0.818409 | − | 0.574637i | \(-0.805143\pi\) | ||
0.818409 | − | 0.574637i | \(-0.194857\pi\) | |||||||
\(858\) | 342.580 | 0.399277 | ||||||||
\(859\) | 332.809 | 0.387437 | 0.193719 | − | 0.981057i | \(-0.437945\pi\) | ||||
0.193719 | + | 0.981057i | \(0.437945\pi\) | |||||||
\(860\) | −173.146 | − | 472.898i | −0.201332 | − | 0.549882i | ||||
\(861\) | − | 1354.57i | − | 1.57326i | ||||||
\(862\) | −221.661 | −0.257148 | ||||||||
\(863\) | − | 22.3010i | − | 0.0258412i | −0.999917 | − | 0.0129206i | \(-0.995887\pi\) | ||
0.999917 | − | 0.0129206i | \(-0.00411287\pi\) | |||||||
\(864\) | −29.3939 | −0.0340207 | ||||||||
\(865\) | −344.639 | + | 126.185i | −0.398427 | + | 0.145879i | ||||
\(866\) | 15.3188i | 0.0176891i | ||||||||
\(867\) | − | 188.156i | − | 0.217019i | ||||||
\(868\) | 82.4665 | 0.0950075 | ||||||||
\(869\) | −24.8790 | −0.0286295 | ||||||||
\(870\) | −135.784 | − | 370.856i | −0.156074 | − | 0.426271i | ||||
\(871\) | 549.228i | 0.630572i | ||||||||
\(872\) | 124.589 | 0.142877 | ||||||||
\(873\) | 496.951 | 0.569245 | ||||||||
\(874\) | 789.578 | − | 61.7192i | 0.903408 | − | 0.0706169i | ||||
\(875\) | −1405.38 | − | 800.681i | −1.60615 | − | 0.915064i | ||||
\(876\) | −244.677 | −0.279312 | ||||||||
\(877\) | 298.806i | 0.340714i | 0.985382 | + | 0.170357i | \(0.0544921\pi\) | ||||
−0.985382 | + | 0.170357i | \(0.945508\pi\) | |||||||
\(878\) | 14.4233i | 0.0164274i | ||||||||
\(879\) | − | 152.176i | − | 0.173124i | ||||||
\(880\) | −345.443 | + | 126.480i | −0.392549 | + | 0.143727i | ||||
\(881\) | − | 392.975i | − | 0.446056i | −0.974812 | − | 0.223028i | \(-0.928406\pi\) | ||
0.974812 | − | 0.223028i | \(-0.0715941\pi\) | |||||||
\(882\) | − | 502.478i | − | 0.569703i | ||||||
\(883\) | − | 565.810i | − | 0.640781i | −0.947286 | − | 0.320391i | \(-0.896186\pi\) | ||
0.947286 | − | 0.320391i | \(-0.103814\pi\) | |||||||
\(884\) | − | 303.245i | − | 0.343037i | ||||||
\(885\) | −41.9789 | + | 15.3701i | −0.0474338 | + | 0.0173673i | ||||
\(886\) | −33.6300 | −0.0379571 | ||||||||
\(887\) | − | 233.861i | − | 0.263654i | −0.991273 | − | 0.131827i | \(-0.957916\pi\) | ||
0.991273 | − | 0.131827i | \(-0.0420844\pi\) | |||||||
\(888\) | −53.9723 | −0.0607796 | ||||||||
\(889\) | 1013.72i | 1.14030i | ||||||||
\(890\) | −101.968 | − | 278.498i | −0.114571 | − | 0.312919i | ||||
\(891\) | − | 165.541i | − | 0.185793i | ||||||
\(892\) | 245.840i | 0.275605i | ||||||||
\(893\) | −1934.86 | −2.16670 | ||||||||
\(894\) | 360.456i | 0.403194i | ||||||||
\(895\) | 479.696 | + | 1310.15i | 0.535974 | + | 1.46386i | ||||
\(896\) | 146.396i | 0.163388i | ||||||||
\(897\) | −301.987 | + | 23.6055i | −0.336663 | + | 0.0263161i | ||||
\(898\) | − | 590.818i | − | 0.657926i | ||||||
\(899\) | 102.754 | 0.114299 | ||||||||
\(900\) | −114.537 | + | 96.8569i | −0.127263 | + | 0.107619i | ||||
\(901\) | 1836.87 | 2.03870 | ||||||||
\(902\) | −1572.16 | −1.74297 | ||||||||
\(903\) | − | 1128.68i | − | 1.24992i | ||||||
\(904\) | 460.873i | 0.509815i | ||||||||
\(905\) | 711.013 | − | 260.328i | 0.785649 | − | 0.287655i | ||||
\(906\) | −10.3342 | −0.0114064 | ||||||||
\(907\) | 1359.32 | 1.49870 | 0.749350 | − | 0.662174i | \(-0.230366\pi\) | ||||
0.749350 | + | 0.662174i | \(0.230366\pi\) | |||||||
\(908\) | 568.988 | 0.626639 | ||||||||
\(909\) | −60.6799 | −0.0667546 | ||||||||
\(910\) | −239.198 | − | 653.301i | −0.262855 | − | 0.717914i | ||||
\(911\) | 413.072i | 0.453427i | 0.973961 | + | 0.226714i | \(0.0727982\pi\) | ||||
−0.973961 | + | 0.226714i | \(0.927202\pi\) | |||||||
\(912\) | 168.692 | 0.184970 | ||||||||
\(913\) | 2489.96i | 2.72723i | ||||||||
\(914\) | − | 278.904i | − | 0.305147i | ||||||
\(915\) | 31.3430 | + | 85.6046i | 0.0342547 | + | 0.0935569i | ||||
\(916\) | − | 854.040i | − | 0.932358i | ||||||
\(917\) | −3151.11 | −3.43633 | ||||||||
\(918\) | −146.534 | −0.159623 | ||||||||
\(919\) | − | 88.1481i | − | 0.0959174i | −0.998849 | − | 0.0479587i | \(-0.984728\pi\) | ||
0.998849 | − | 0.0479587i | \(-0.0152716\pi\) | |||||||
\(920\) | 295.796 | − | 135.296i | 0.321517 | − | 0.147060i | ||||
\(921\) | −756.411 | −0.821293 | ||||||||
\(922\) | − | 1119.80i | − | 1.21453i | ||||||
\(923\) | − | 68.0464i | − | 0.0737230i | ||||||
\(924\) | −824.476 | −0.892290 | ||||||||
\(925\) | −210.310 | + | 177.846i | −0.227362 | + | 0.192266i | ||||
\(926\) | −318.433 | −0.343880 | ||||||||
\(927\) | 30.3230 | 0.0327109 | ||||||||
\(928\) | 182.411i | 0.196564i | ||||||||
\(929\) | 1331.41 | 1.43317 | 0.716584 | − | 0.697501i | \(-0.245705\pi\) | ||||
0.716584 | + | 0.697501i | \(0.245705\pi\) | |||||||
\(930\) | −13.4183 | − | 36.6482i | −0.0144282 | − | 0.0394066i | ||||
\(931\) | 2883.74i | 3.09746i | ||||||||
\(932\) | 754.543i | 0.809595i | ||||||||
\(933\) | 165.259i | 0.177127i | ||||||||
\(934\) | 6.16589i | 0.00660160i | ||||||||
\(935\) | −1722.09 | + | 630.523i | −1.84181 | + | 0.674356i | ||||
\(936\) | −64.5192 | −0.0689307 | ||||||||
\(937\) | −547.333 | −0.584134 | −0.292067 | − | 0.956398i | \(-0.594343\pi\) | ||||
−0.292067 | + | 0.956398i | \(0.594343\pi\) | |||||||
\(938\) | − | 1321.81i | − | 1.40918i | ||||||
\(939\) | 480.773i | 0.512006i | ||||||||
\(940\) | −746.203 | + | 273.213i | −0.793833 | + | 0.290652i | ||||
\(941\) | 1213.44i | 1.28952i | 0.764383 | + | 0.644762i | \(0.223043\pi\) | ||||
−0.764383 | + | 0.644762i | \(0.776957\pi\) | |||||||
\(942\) | 313.508 | 0.332811 | ||||||||
\(943\) | 1385.87 | − | 108.330i | 1.46964 | − | 0.114878i | ||||
\(944\) | 20.6480 | 0.0218729 | ||||||||
\(945\) | −315.688 | + | 115.585i | −0.334061 | + | 0.122312i | ||||
\(946\) | −1309.98 | −1.38475 | ||||||||
\(947\) | − | 320.019i | − | 0.337929i | −0.985622 | − | 0.168964i | \(-0.945958\pi\) | ||
0.985622 | − | 0.168964i | \(-0.0540423\pi\) | |||||||
\(948\) | 4.68554 | 0.00494256 | ||||||||
\(949\) | −537.063 | −0.565925 | ||||||||
\(950\) | 657.332 | − | 555.865i | 0.691929 | − | 0.585121i | ||||
\(951\) | −76.0911 | −0.0800117 | ||||||||
\(952\) | 729.809i | 0.766606i | ||||||||
\(953\) | 9.42027 | 0.00988486 | 0.00494243 | − | 0.999988i | \(-0.498427\pi\) | ||||
0.00494243 | + | 0.999988i | \(0.498427\pi\) | |||||||
\(954\) | − | 390.817i | − | 0.409662i | ||||||
\(955\) | 1393.55 | − | 510.232i | 1.45922 | − | 0.534274i | ||||
\(956\) | −225.698 | −0.236086 | ||||||||
\(957\) | −1027.31 | −1.07347 | ||||||||
\(958\) | 371.651 | 0.387945 | ||||||||
\(959\) | 888.641 | 0.926633 | ||||||||
\(960\) | 65.0584 | − | 23.8203i | 0.0677692 | − | 0.0248128i | ||||
\(961\) | −950.846 | −0.989434 | ||||||||
\(962\) | −118.468 | −0.123148 | ||||||||
\(963\) | −179.781 | −0.186688 | ||||||||
\(964\) | 298.541i | 0.309690i | ||||||||
\(965\) | 126.370 | − | 46.2686i | 0.130953 | − | 0.0479467i | ||||
\(966\) | 726.782 | − | 56.8106i | 0.752362 | − | 0.0588101i | ||||
\(967\) | − | 1077.67i | − | 1.11445i | −0.830363 | − | 0.557223i | \(-0.811867\pi\) | ||
0.830363 | − | 0.557223i | \(-0.188133\pi\) | |||||||
\(968\) | 614.673i | 0.634993i | ||||||||
\(969\) | 840.962 | 0.867865 | ||||||||
\(970\) | −1099.92 | + | 402.720i | −1.13393 | + | 0.415175i | ||||
\(971\) | − | 492.034i | − | 0.506729i | −0.967371 | − | 0.253365i | \(-0.918463\pi\) | ||
0.967371 | − | 0.253365i | \(-0.0815373\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | 1770.17 | 1.81929 | ||||||||
\(974\) | 453.065 | 0.465159 | ||||||||
\(975\) | −251.407 | + | 212.600i | −0.257854 | + | 0.218051i | ||||
\(976\) | − | 42.1060i | − | 0.0431414i | ||||||
\(977\) | −528.771 | −0.541219 | −0.270610 | − | 0.962689i | \(-0.587225\pi\) | ||||
−0.270610 | + | 0.962689i | \(0.587225\pi\) | |||||||
\(978\) | − | 132.011i | − | 0.134980i | ||||||
\(979\) | −771.467 | −0.788016 | ||||||||
\(980\) | 407.200 | + | 1112.15i | 0.415510 | + | 1.13485i | ||||
\(981\) | − | 132.147i | − | 0.134706i | ||||||
\(982\) | 253.487i | 0.258133i | ||||||||
\(983\) | 883.852 | 0.899137 | 0.449569 | − | 0.893246i | \(-0.351578\pi\) | ||||
0.449569 | + | 0.893246i | \(0.351578\pi\) | |||||||
\(984\) | 296.090 | 0.300905 | ||||||||
\(985\) | 289.168 | − | 105.875i | 0.293571 | − | 0.107487i | ||||
\(986\) | 909.352i | 0.922264i | ||||||||
\(987\) | −1780.98 | −1.80443 | ||||||||
\(988\) | 370.278 | 0.374775 | ||||||||
\(989\) | 1154.76 | − | 90.2642i | 1.16760 | − | 0.0912681i | ||||
\(990\) | 134.152 | + | 366.398i | 0.135507 | + | 0.370099i | ||||
\(991\) | −1016.15 | −1.02537 | −0.512687 | − | 0.858576i | \(-0.671350\pi\) | ||||
−0.512687 | + | 0.858576i | \(0.671350\pi\) | |||||||
\(992\) | 18.0260i | 0.0181714i | ||||||||
\(993\) | 779.188i | 0.784681i | ||||||||
\(994\) | 163.765i | 0.164753i | ||||||||
\(995\) | 165.898 | − | 60.7414i | 0.166732 | − | 0.0610466i | ||||
\(996\) | − | 468.943i | − | 0.470826i | ||||||
\(997\) | 811.334i | 0.813776i | 0.913478 | + | 0.406888i | \(0.133386\pi\) | ||||
−0.913478 | + | 0.406888i | \(0.866614\pi\) | |||||||
\(998\) | − | 21.1541i | − | 0.0211965i | ||||||
\(999\) | 57.2463i | 0.0573036i |
(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 | 690.3.f.a.229.3 | yes | 48 | |
5.4 | even | 2 | inner | 690.3.f.a.229.2 | yes | 48 | |
23.22 | odd | 2 | inner | 690.3.f.a.229.4 | yes | 48 | |
115.114 | odd | 2 | inner | 690.3.f.a.229.1 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.f.a.229.1 | ✓ | 48 | 115.114 | odd | 2 | inner | |
690.3.f.a.229.2 | yes | 48 | 5.4 | even | 2 | inner | |
690.3.f.a.229.3 | yes | 48 | 1.1 | even | 1 | trivial | |
690.3.f.a.229.4 | yes | 48 | 23.22 | odd | 2 | inner |