Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(91,690)]
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, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.91");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.c (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: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.9 | ||
Character | \(\chi\) | \(=\) | 690.91 |
Dual form | 690.3.c.a.91.16 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | − | 2.23607i | − | 0.447214i | ||||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | − | 7.36146i | − | 1.05164i | −0.850597 | − | 0.525818i | \(-0.823759\pi\) | ||
0.850597 | − | 0.525818i | \(-0.176241\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 3.16228i | 0.316228i | ||||||||
\(11\) | − | 16.6371i | − | 1.51247i | −0.654301 | − | 0.756234i | \(-0.727037\pi\) | ||
0.654301 | − | 0.756234i | \(-0.272963\pi\) | |||||||
\(12\) | 3.46410 | 0.288675 | ||||||||
\(13\) | 9.09640 | 0.699723 | 0.349862 | − | 0.936801i | \(-0.386229\pi\) | ||||
0.349862 | + | 0.936801i | \(0.386229\pi\) | |||||||
\(14\) | 10.4107i | 0.743619i | ||||||||
\(15\) | − | 3.87298i | − | 0.258199i | ||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 4.72753i | 0.278090i | 0.990286 | + | 0.139045i | \(0.0444032\pi\) | ||||
−0.990286 | + | 0.139045i | \(0.955597\pi\) | |||||||
\(18\) | −4.24264 | −0.235702 | ||||||||
\(19\) | 11.5103i | 0.605806i | 0.953021 | + | 0.302903i | \(0.0979558\pi\) | ||||
−0.953021 | + | 0.302903i | \(0.902044\pi\) | |||||||
\(20\) | − | 4.47214i | − | 0.223607i | ||||||
\(21\) | − | 12.7504i | − | 0.607163i | ||||||
\(22\) | 23.5285i | 1.06948i | ||||||||
\(23\) | −18.8188 | − | 13.2232i | −0.818207 | − | 0.574924i | ||||
\(24\) | −4.89898 | −0.204124 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | −12.8643 | −0.494779 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | − | 14.7229i | − | 0.525818i | ||||||
\(29\) | −8.88295 | −0.306308 | −0.153154 | − | 0.988202i | \(-0.548943\pi\) | ||||
−0.153154 | + | 0.988202i | \(0.548943\pi\) | |||||||
\(30\) | 5.47723i | 0.182574i | ||||||||
\(31\) | −45.3476 | −1.46283 | −0.731413 | − | 0.681934i | \(-0.761139\pi\) | ||||
−0.731413 | + | 0.681934i | \(0.761139\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | − | 28.8164i | − | 0.873224i | ||||||
\(34\) | − | 6.68573i | − | 0.196639i | ||||||
\(35\) | −16.4607 | −0.470306 | ||||||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | − | 9.59572i | − | 0.259344i | −0.991557 | − | 0.129672i | \(-0.958608\pi\) | ||
0.991557 | − | 0.129672i | \(-0.0413924\pi\) | |||||||
\(38\) | − | 16.2780i | − | 0.428369i | ||||||
\(39\) | 15.7554 | 0.403985 | ||||||||
\(40\) | 6.32456i | 0.158114i | ||||||||
\(41\) | 20.7143 | 0.505228 | 0.252614 | − | 0.967567i | \(-0.418710\pi\) | ||||
0.252614 | + | 0.967567i | \(0.418710\pi\) | |||||||
\(42\) | 18.0318i | 0.429329i | ||||||||
\(43\) | 21.4012i | 0.497702i | 0.968542 | + | 0.248851i | \(0.0800530\pi\) | ||||
−0.968542 | + | 0.248851i | \(0.919947\pi\) | |||||||
\(44\) | − | 33.2743i | − | 0.756234i | ||||||
\(45\) | − | 6.70820i | − | 0.149071i | ||||||
\(46\) | 26.6138 | + | 18.7005i | 0.578560 | + | 0.406532i | ||||
\(47\) | −31.0064 | −0.659712 | −0.329856 | − | 0.944031i | \(-0.607000\pi\) | ||||
−0.329856 | + | 0.944031i | \(0.607000\pi\) | |||||||
\(48\) | 6.92820 | 0.144338 | ||||||||
\(49\) | −5.19104 | −0.105940 | ||||||||
\(50\) | 7.07107 | 0.141421 | ||||||||
\(51\) | 8.18832i | 0.160555i | ||||||||
\(52\) | 18.1928 | 0.349862 | ||||||||
\(53\) | − | 70.7020i | − | 1.33400i | −0.745058 | − | 0.667000i | \(-0.767578\pi\) | ||
0.745058 | − | 0.667000i | \(-0.232422\pi\) | |||||||
\(54\) | −7.34847 | −0.136083 | ||||||||
\(55\) | −37.2018 | −0.676396 | ||||||||
\(56\) | 20.8213i | 0.371810i | ||||||||
\(57\) | 19.9364i | 0.349762i | ||||||||
\(58\) | 12.5624 | 0.216593 | ||||||||
\(59\) | −47.6249 | −0.807201 | −0.403600 | − | 0.914935i | \(-0.632241\pi\) | ||||
−0.403600 | + | 0.914935i | \(0.632241\pi\) | |||||||
\(60\) | − | 7.74597i | − | 0.129099i | ||||||
\(61\) | 16.1273i | 0.264382i | 0.991224 | + | 0.132191i | \(0.0422012\pi\) | ||||
−0.991224 | + | 0.132191i | \(0.957799\pi\) | |||||||
\(62\) | 64.1312 | 1.03437 | ||||||||
\(63\) | − | 22.0844i | − | 0.350546i | ||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | − | 20.3402i | − | 0.312926i | ||||||
\(66\) | 40.7525i | 0.617462i | ||||||||
\(67\) | − | 11.8203i | − | 0.176423i | −0.996102 | − | 0.0882116i | \(-0.971885\pi\) | ||
0.996102 | − | 0.0882116i | \(-0.0281152\pi\) | |||||||
\(68\) | 9.45505i | 0.139045i | ||||||||
\(69\) | −32.5951 | − | 22.9033i | −0.472392 | − | 0.331932i | ||||
\(70\) | 23.2790 | 0.332557 | ||||||||
\(71\) | −2.91130 | −0.0410042 | −0.0205021 | − | 0.999790i | \(-0.506526\pi\) | ||||
−0.0205021 | + | 0.999790i | \(0.506526\pi\) | |||||||
\(72\) | −8.48528 | −0.117851 | ||||||||
\(73\) | 136.473 | 1.86949 | 0.934745 | − | 0.355319i | \(-0.115628\pi\) | ||||
0.934745 | + | 0.355319i | \(0.115628\pi\) | |||||||
\(74\) | 13.5704i | 0.183384i | ||||||||
\(75\) | −8.66025 | −0.115470 | ||||||||
\(76\) | 23.0206i | 0.302903i | ||||||||
\(77\) | −122.474 | −1.59057 | ||||||||
\(78\) | −22.2815 | −0.285661 | ||||||||
\(79\) | 37.4347i | 0.473856i | 0.971527 | + | 0.236928i | \(0.0761406\pi\) | ||||
−0.971527 | + | 0.236928i | \(0.923859\pi\) | |||||||
\(80\) | − | 8.94427i | − | 0.111803i | ||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −29.2945 | −0.357250 | ||||||||
\(83\) | − | 108.327i | − | 1.30514i | −0.757729 | − | 0.652569i | \(-0.773691\pi\) | ||
0.757729 | − | 0.652569i | \(-0.226309\pi\) | |||||||
\(84\) | − | 25.5008i | − | 0.303581i | ||||||
\(85\) | 10.5711 | 0.124366 | ||||||||
\(86\) | − | 30.2659i | − | 0.351929i | ||||||
\(87\) | −15.3857 | −0.176847 | ||||||||
\(88\) | 47.0570i | 0.534738i | ||||||||
\(89\) | − | 10.9382i | − | 0.122901i | −0.998110 | − | 0.0614503i | \(-0.980427\pi\) | ||
0.998110 | − | 0.0614503i | \(-0.0195726\pi\) | |||||||
\(90\) | 9.48683i | 0.105409i | ||||||||
\(91\) | − | 66.9628i | − | 0.735855i | ||||||
\(92\) | −37.6375 | − | 26.4465i | −0.409104 | − | 0.287462i | ||||
\(93\) | −78.5444 | −0.844563 | ||||||||
\(94\) | 43.8497 | 0.466487 | ||||||||
\(95\) | 25.7378 | 0.270924 | ||||||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | − | 70.0663i | − | 0.722333i | −0.932501 | − | 0.361167i | \(-0.882379\pi\) | ||
0.932501 | − | 0.361167i | \(-0.117621\pi\) | |||||||
\(98\) | 7.34124 | 0.0749106 | ||||||||
\(99\) | − | 49.9114i | − | 0.504156i | ||||||
\(100\) | −10.0000 | −0.100000 | ||||||||
\(101\) | −34.4854 | −0.341439 | −0.170720 | − | 0.985320i | \(-0.554609\pi\) | ||||
−0.170720 | + | 0.985320i | \(0.554609\pi\) | |||||||
\(102\) | − | 11.5800i | − | 0.113530i | ||||||
\(103\) | 71.8118i | 0.697202i | 0.937271 | + | 0.348601i | \(0.113343\pi\) | ||||
−0.937271 | + | 0.348601i | \(0.886657\pi\) | |||||||
\(104\) | −25.7285 | −0.247390 | ||||||||
\(105\) | −28.5108 | −0.271531 | ||||||||
\(106\) | 99.9877i | 0.943280i | ||||||||
\(107\) | − | 120.386i | − | 1.12510i | −0.826763 | − | 0.562550i | \(-0.809820\pi\) | ||
0.826763 | − | 0.562550i | \(-0.190180\pi\) | |||||||
\(108\) | 10.3923 | 0.0962250 | ||||||||
\(109\) | − | 115.918i | − | 1.06347i | −0.846912 | − | 0.531734i | \(-0.821541\pi\) | ||
0.846912 | − | 0.531734i | \(-0.178459\pi\) | |||||||
\(110\) | 52.6113 | 0.478284 | ||||||||
\(111\) | − | 16.6203i | − | 0.149732i | ||||||
\(112\) | − | 29.4458i | − | 0.262909i | ||||||
\(113\) | − | 104.989i | − | 0.929108i | −0.885545 | − | 0.464554i | \(-0.846215\pi\) | ||
0.885545 | − | 0.464554i | \(-0.153785\pi\) | |||||||
\(114\) | − | 28.1944i | − | 0.247319i | ||||||
\(115\) | −29.5681 | + | 42.0800i | −0.257114 | + | 0.365913i | ||||
\(116\) | −17.7659 | −0.153154 | ||||||||
\(117\) | 27.2892 | 0.233241 | ||||||||
\(118\) | 67.3517 | 0.570777 | ||||||||
\(119\) | 34.8015 | 0.292449 | ||||||||
\(120\) | 10.9545i | 0.0912871i | ||||||||
\(121\) | −155.795 | −1.28756 | ||||||||
\(122\) | − | 22.8074i | − | 0.186946i | ||||||
\(123\) | 35.8783 | 0.291693 | ||||||||
\(124\) | −90.6952 | −0.731413 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 31.2320i | 0.247873i | ||||||||
\(127\) | 26.1241 | 0.205701 | 0.102851 | − | 0.994697i | \(-0.467204\pi\) | ||||
0.102851 | + | 0.994697i | \(0.467204\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 37.0679i | 0.287348i | ||||||||
\(130\) | 28.7653i | 0.221272i | ||||||||
\(131\) | −251.807 | −1.92219 | −0.961096 | − | 0.276216i | \(-0.910920\pi\) | ||||
−0.961096 | + | 0.276216i | \(0.910920\pi\) | |||||||
\(132\) | − | 57.6328i | − | 0.436612i | ||||||
\(133\) | 84.7326 | 0.637087 | ||||||||
\(134\) | 16.7165i | 0.124750i | ||||||||
\(135\) | − | 11.6190i | − | 0.0860663i | ||||||
\(136\) | − | 13.3715i | − | 0.0983196i | ||||||
\(137\) | 51.7087i | 0.377436i | 0.982031 | + | 0.188718i | \(0.0604332\pi\) | ||||
−0.982031 | + | 0.188718i | \(0.939567\pi\) | |||||||
\(138\) | 46.0964 | + | 32.3902i | 0.334032 | + | 0.234712i | ||||
\(139\) | 38.3182 | 0.275670 | 0.137835 | − | 0.990455i | \(-0.455986\pi\) | ||||
0.137835 | + | 0.990455i | \(0.455986\pi\) | |||||||
\(140\) | −32.9214 | −0.235153 | ||||||||
\(141\) | −53.7047 | −0.380885 | ||||||||
\(142\) | 4.11719 | 0.0289943 | ||||||||
\(143\) | − | 151.338i | − | 1.05831i | ||||||
\(144\) | 12.0000 | 0.0833333 | ||||||||
\(145\) | 19.8629i | 0.136985i | ||||||||
\(146\) | −193.002 | −1.32193 | ||||||||
\(147\) | −8.99115 | −0.0611643 | ||||||||
\(148\) | − | 19.1914i | − | 0.129672i | ||||||
\(149\) | − | 46.9760i | − | 0.315275i | −0.987497 | − | 0.157638i | \(-0.949612\pi\) | ||
0.987497 | − | 0.157638i | \(-0.0503878\pi\) | |||||||
\(150\) | 12.2474 | 0.0816497 | ||||||||
\(151\) | −25.8294 | −0.171055 | −0.0855277 | − | 0.996336i | \(-0.527258\pi\) | ||||
−0.0855277 | + | 0.996336i | \(0.527258\pi\) | |||||||
\(152\) | − | 32.5561i | − | 0.214185i | ||||||
\(153\) | 14.1826i | 0.0926966i | ||||||||
\(154\) | 173.204 | 1.12470 | ||||||||
\(155\) | 101.400i | 0.654196i | ||||||||
\(156\) | 31.5109 | 0.201993 | ||||||||
\(157\) | 130.106i | 0.828701i | 0.910117 | + | 0.414351i | \(0.135991\pi\) | ||||
−0.910117 | + | 0.414351i | \(0.864009\pi\) | |||||||
\(158\) | − | 52.9406i | − | 0.335067i | ||||||
\(159\) | − | 122.459i | − | 0.770185i | ||||||
\(160\) | 12.6491i | 0.0790569i | ||||||||
\(161\) | −97.3423 | + | 138.534i | −0.604611 | + | 0.860457i | ||||
\(162\) | −12.7279 | −0.0785674 | ||||||||
\(163\) | 235.517 | 1.44489 | 0.722445 | − | 0.691428i | \(-0.243018\pi\) | ||||
0.722445 | + | 0.691428i | \(0.243018\pi\) | |||||||
\(164\) | 41.4287 | 0.252614 | ||||||||
\(165\) | −64.4354 | −0.390517 | ||||||||
\(166\) | 153.197i | 0.922872i | ||||||||
\(167\) | −9.15117 | −0.0547974 | −0.0273987 | − | 0.999625i | \(-0.508722\pi\) | ||||
−0.0273987 | + | 0.999625i | \(0.508722\pi\) | |||||||
\(168\) | 36.0636i | 0.214664i | ||||||||
\(169\) | −86.2555 | −0.510387 | ||||||||
\(170\) | −14.9497 | −0.0879397 | ||||||||
\(171\) | 34.5309i | 0.201935i | ||||||||
\(172\) | 42.8024i | 0.248851i | ||||||||
\(173\) | 27.8008 | 0.160698 | 0.0803490 | − | 0.996767i | \(-0.474397\pi\) | ||||
0.0803490 | + | 0.996767i | \(0.474397\pi\) | |||||||
\(174\) | 21.7587 | 0.125050 | ||||||||
\(175\) | 36.8073i | 0.210327i | ||||||||
\(176\) | − | 66.5486i | − | 0.378117i | ||||||
\(177\) | −82.4887 | −0.466038 | ||||||||
\(178\) | 15.4689i | 0.0869038i | ||||||||
\(179\) | 243.048 | 1.35781 | 0.678906 | − | 0.734225i | \(-0.262454\pi\) | ||||
0.678906 | + | 0.734225i | \(0.262454\pi\) | |||||||
\(180\) | − | 13.4164i | − | 0.0745356i | ||||||
\(181\) | 2.69386i | 0.0148832i | 0.999972 | + | 0.00744160i | \(0.00236876\pi\) | ||||
−0.999972 | + | 0.00744160i | \(0.997631\pi\) | |||||||
\(182\) | 94.6997i | 0.520328i | ||||||||
\(183\) | 27.9333i | 0.152641i | ||||||||
\(184\) | 53.2275 | + | 37.4010i | 0.289280 | + | 0.203266i | ||||
\(185\) | −21.4567 | −0.115982 | ||||||||
\(186\) | 111.079 | 0.597196 | ||||||||
\(187\) | 78.6525 | 0.420602 | ||||||||
\(188\) | −62.0129 | −0.329856 | ||||||||
\(189\) | − | 38.2513i | − | 0.202388i | ||||||
\(190\) | −36.3988 | −0.191573 | ||||||||
\(191\) | 72.7322i | 0.380797i | 0.981707 | + | 0.190398i | \(0.0609780\pi\) | ||||
−0.981707 | + | 0.190398i | \(0.939022\pi\) | |||||||
\(192\) | 13.8564 | 0.0721688 | ||||||||
\(193\) | −34.1113 | −0.176743 | −0.0883714 | − | 0.996088i | \(-0.528166\pi\) | ||||
−0.0883714 | + | 0.996088i | \(0.528166\pi\) | |||||||
\(194\) | 99.0888i | 0.510767i | ||||||||
\(195\) | − | 35.2302i | − | 0.180668i | ||||||
\(196\) | −10.3821 | −0.0529698 | ||||||||
\(197\) | 352.408 | 1.78887 | 0.894436 | − | 0.447196i | \(-0.147577\pi\) | ||||
0.894436 | + | 0.447196i | \(0.147577\pi\) | |||||||
\(198\) | 70.5854i | 0.356492i | ||||||||
\(199\) | − | 3.97739i | − | 0.0199869i | −0.999950 | − | 0.00999345i | \(-0.996819\pi\) | ||
0.999950 | − | 0.00999345i | \(-0.00318107\pi\) | |||||||
\(200\) | 14.1421 | 0.0707107 | ||||||||
\(201\) | − | 20.4734i | − | 0.101858i | ||||||
\(202\) | 48.7697 | 0.241434 | ||||||||
\(203\) | 65.3914i | 0.322125i | ||||||||
\(204\) | 16.3766i | 0.0802776i | ||||||||
\(205\) | − | 46.3187i | − | 0.225945i | ||||||
\(206\) | − | 101.557i | − | 0.492996i | ||||||
\(207\) | −56.4563 | − | 39.6697i | −0.272736 | − | 0.191641i | ||||
\(208\) | 36.3856 | 0.174931 | ||||||||
\(209\) | 191.499 | 0.916261 | ||||||||
\(210\) | 40.3204 | 0.192002 | ||||||||
\(211\) | 9.97835 | 0.0472907 | 0.0236454 | − | 0.999720i | \(-0.492473\pi\) | ||||
0.0236454 | + | 0.999720i | \(0.492473\pi\) | |||||||
\(212\) | − | 141.404i | − | 0.667000i | ||||||
\(213\) | −5.04251 | −0.0236738 | ||||||||
\(214\) | 170.251i | 0.795566i | ||||||||
\(215\) | 47.8545 | 0.222579 | ||||||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | 333.825i | 1.53836i | ||||||||
\(218\) | 163.933i | 0.751985i | ||||||||
\(219\) | 236.378 | 1.07935 | ||||||||
\(220\) | −74.4036 | −0.338198 | ||||||||
\(221\) | 43.0035i | 0.194586i | ||||||||
\(222\) | 23.5046i | 0.105877i | ||||||||
\(223\) | 239.893 | 1.07575 | 0.537877 | − | 0.843023i | \(-0.319226\pi\) | ||||
0.537877 | + | 0.843023i | \(0.319226\pi\) | |||||||
\(224\) | 41.6427i | 0.185905i | ||||||||
\(225\) | −15.0000 | −0.0666667 | ||||||||
\(226\) | 148.477i | 0.656978i | ||||||||
\(227\) | − | 64.1819i | − | 0.282740i | −0.989957 | − | 0.141370i | \(-0.954849\pi\) | ||
0.989957 | − | 0.141370i | \(-0.0451506\pi\) | |||||||
\(228\) | 39.8729i | 0.174881i | ||||||||
\(229\) | 193.637i | 0.845577i | 0.906228 | + | 0.422789i | \(0.138949\pi\) | ||||
−0.906228 | + | 0.422789i | \(0.861051\pi\) | |||||||
\(230\) | 41.8156 | − | 59.5102i | 0.181807 | − | 0.258740i | ||||
\(231\) | −212.131 | −0.918314 | ||||||||
\(232\) | 25.1248 | 0.108296 | ||||||||
\(233\) | 313.193 | 1.34418 | 0.672088 | − | 0.740472i | \(-0.265398\pi\) | ||||
0.672088 | + | 0.740472i | \(0.265398\pi\) | |||||||
\(234\) | −38.5928 | −0.164926 | ||||||||
\(235\) | 69.3325i | 0.295032i | ||||||||
\(236\) | −95.2497 | −0.403600 | ||||||||
\(237\) | 64.8387i | 0.273581i | ||||||||
\(238\) | −49.2167 | −0.206793 | ||||||||
\(239\) | 211.636 | 0.885508 | 0.442754 | − | 0.896643i | \(-0.354001\pi\) | ||||
0.442754 | + | 0.896643i | \(0.354001\pi\) | |||||||
\(240\) | − | 15.4919i | − | 0.0645497i | ||||||
\(241\) | 305.383i | 1.26715i | 0.773682 | + | 0.633574i | \(0.218413\pi\) | ||||
−0.773682 | + | 0.633574i | \(0.781587\pi\) | |||||||
\(242\) | 220.327 | 0.910441 | ||||||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | 32.2546i | 0.132191i | ||||||||
\(245\) | 11.6075i | 0.0473776i | ||||||||
\(246\) | −50.7395 | −0.206258 | ||||||||
\(247\) | 104.702i | 0.423896i | ||||||||
\(248\) | 128.262 | 0.517187 | ||||||||
\(249\) | − | 187.627i | − | 0.753522i | ||||||
\(250\) | − | 15.8114i | − | 0.0632456i | ||||||
\(251\) | 319.715i | 1.27376i | 0.770962 | + | 0.636882i | \(0.219776\pi\) | ||||
−0.770962 | + | 0.636882i | \(0.780224\pi\) | |||||||
\(252\) | − | 44.1687i | − | 0.175273i | ||||||
\(253\) | −219.997 | + | 313.091i | −0.869553 | + | 1.23751i | ||||
\(254\) | −36.9450 | −0.145453 | ||||||||
\(255\) | 18.3096 | 0.0718025 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 47.3441 | 0.184218 | 0.0921091 | − | 0.995749i | \(-0.470639\pi\) | ||||
0.0921091 | + | 0.995749i | \(0.470639\pi\) | |||||||
\(258\) | − | 52.4220i | − | 0.203186i | ||||||
\(259\) | −70.6385 | −0.272735 | ||||||||
\(260\) | − | 40.6803i | − | 0.156463i | ||||||
\(261\) | −26.6488 | −0.102103 | ||||||||
\(262\) | 356.109 | 1.35919 | ||||||||
\(263\) | 183.744i | 0.698648i | 0.937002 | + | 0.349324i | \(0.113589\pi\) | ||||
−0.937002 | + | 0.349324i | \(0.886411\pi\) | |||||||
\(264\) | 81.5050i | 0.308731i | ||||||||
\(265\) | −158.094 | −0.596583 | ||||||||
\(266\) | −119.830 | −0.450489 | ||||||||
\(267\) | − | 18.9454i | − | 0.0709567i | ||||||
\(268\) | − | 23.6407i | − | 0.0882116i | ||||||
\(269\) | −364.416 | −1.35471 | −0.677354 | − | 0.735657i | \(-0.736873\pi\) | ||||
−0.677354 | + | 0.735657i | \(0.736873\pi\) | |||||||
\(270\) | 16.4317i | 0.0608581i | ||||||||
\(271\) | −345.337 | −1.27431 | −0.637153 | − | 0.770738i | \(-0.719888\pi\) | ||||
−0.637153 | + | 0.770738i | \(0.719888\pi\) | |||||||
\(272\) | 18.9101i | 0.0695224i | ||||||||
\(273\) | − | 115.983i | − | 0.424846i | ||||||
\(274\) | − | 73.1271i | − | 0.266887i | ||||||
\(275\) | 83.1857i | 0.302494i | ||||||||
\(276\) | −65.1901 | − | 45.8067i | −0.236196 | − | 0.165966i | ||||
\(277\) | 209.498 | 0.756310 | 0.378155 | − | 0.925742i | \(-0.376559\pi\) | ||||
0.378155 | + | 0.925742i | \(0.376559\pi\) | |||||||
\(278\) | −54.1901 | −0.194928 | ||||||||
\(279\) | −136.043 | −0.487609 | ||||||||
\(280\) | 46.5579 | 0.166278 | ||||||||
\(281\) | 244.704i | 0.870834i | 0.900229 | + | 0.435417i | \(0.143399\pi\) | ||||
−0.900229 | + | 0.435417i | \(0.856601\pi\) | |||||||
\(282\) | 75.9500 | 0.269326 | ||||||||
\(283\) | − | 292.192i | − | 1.03248i | −0.856444 | − | 0.516240i | \(-0.827331\pi\) | ||
0.856444 | − | 0.516240i | \(-0.172669\pi\) | |||||||
\(284\) | −5.82259 | −0.0205021 | ||||||||
\(285\) | 44.5792 | 0.156418 | ||||||||
\(286\) | 214.024i | 0.748337i | ||||||||
\(287\) | − | 152.488i | − | 0.531316i | ||||||
\(288\) | −16.9706 | −0.0589256 | ||||||||
\(289\) | 266.650 | 0.922666 | ||||||||
\(290\) | − | 28.0903i | − | 0.0968632i | ||||||
\(291\) | − | 121.358i | − | 0.417039i | ||||||
\(292\) | 272.946 | 0.934745 | ||||||||
\(293\) | 180.937i | 0.617533i | 0.951138 | + | 0.308766i | \(0.0999162\pi\) | ||||
−0.951138 | + | 0.308766i | \(0.900084\pi\) | |||||||
\(294\) | 12.7154 | 0.0432497 | ||||||||
\(295\) | 106.492i | 0.360991i | ||||||||
\(296\) | 27.1408i | 0.0916919i | ||||||||
\(297\) | − | 86.4491i | − | 0.291075i | ||||||
\(298\) | 66.4341i | 0.222933i | ||||||||
\(299\) | −171.183 | − | 120.284i | −0.572519 | − | 0.402287i | ||||
\(300\) | −17.3205 | −0.0577350 | ||||||||
\(301\) | 157.544 | 0.523402 | ||||||||
\(302\) | 36.5283 | 0.120954 | ||||||||
\(303\) | −59.7304 | −0.197130 | ||||||||
\(304\) | 46.0412i | 0.151451i | ||||||||
\(305\) | 36.0617 | 0.118235 | ||||||||
\(306\) | − | 20.0572i | − | 0.0655464i | ||||||
\(307\) | 60.1754 | 0.196011 | 0.0980056 | − | 0.995186i | \(-0.468754\pi\) | ||||
0.0980056 | + | 0.995186i | \(0.468754\pi\) | |||||||
\(308\) | −244.947 | −0.795283 | ||||||||
\(309\) | 124.382i | 0.402530i | ||||||||
\(310\) | − | 143.402i | − | 0.462586i | ||||||
\(311\) | −275.681 | −0.886434 | −0.443217 | − | 0.896414i | \(-0.646163\pi\) | ||||
−0.443217 | + | 0.896414i | \(0.646163\pi\) | |||||||
\(312\) | −44.5631 | −0.142830 | ||||||||
\(313\) | − | 110.944i | − | 0.354455i | −0.984170 | − | 0.177227i | \(-0.943287\pi\) | ||
0.984170 | − | 0.177227i | \(-0.0567128\pi\) | |||||||
\(314\) | − | 183.998i | − | 0.585980i | ||||||
\(315\) | −49.3822 | −0.156769 | ||||||||
\(316\) | 74.8693i | 0.236928i | ||||||||
\(317\) | 515.941 | 1.62757 | 0.813787 | − | 0.581163i | \(-0.197402\pi\) | ||||
0.813787 | + | 0.581163i | \(0.197402\pi\) | |||||||
\(318\) | 173.184i | 0.544603i | ||||||||
\(319\) | 147.787i | 0.463282i | ||||||||
\(320\) | − | 17.8885i | − | 0.0559017i | ||||||
\(321\) | − | 208.514i | − | 0.649577i | ||||||
\(322\) | 137.663 | − | 195.916i | 0.427524 | − | 0.608435i | ||||
\(323\) | −54.4153 | −0.168468 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | −45.4820 | −0.139945 | ||||||||
\(326\) | −333.071 | −1.02169 | ||||||||
\(327\) | − | 200.776i | − | 0.613993i | ||||||
\(328\) | −58.5890 | −0.178625 | ||||||||
\(329\) | 228.253i | 0.693777i | ||||||||
\(330\) | 91.1254 | 0.276138 | ||||||||
\(331\) | 559.830 | 1.69133 | 0.845664 | − | 0.533715i | \(-0.179205\pi\) | ||||
0.845664 | + | 0.533715i | \(0.179205\pi\) | |||||||
\(332\) | − | 216.653i | − | 0.652569i | ||||||
\(333\) | − | 28.7872i | − | 0.0864479i | ||||||
\(334\) | 12.9417 | 0.0387476 | ||||||||
\(335\) | −26.4311 | −0.0788988 | ||||||||
\(336\) | − | 51.0017i | − | 0.151791i | ||||||
\(337\) | − | 510.476i | − | 1.51477i | −0.652970 | − | 0.757383i | \(-0.726477\pi\) | ||
0.652970 | − | 0.757383i | \(-0.273523\pi\) | |||||||
\(338\) | 121.984 | 0.360898 | ||||||||
\(339\) | − | 181.847i | − | 0.536421i | ||||||
\(340\) | 21.1421 | 0.0621828 | ||||||||
\(341\) | 754.455i | 2.21248i | ||||||||
\(342\) | − | 48.8341i | − | 0.142790i | ||||||
\(343\) | − | 322.498i | − | 0.940227i | ||||||
\(344\) | − | 60.5317i | − | 0.175964i | ||||||
\(345\) | −51.2134 | + | 72.8848i | −0.148445 | + | 0.211260i | ||||
\(346\) | −39.3162 | −0.113631 | ||||||||
\(347\) | −423.608 | −1.22077 | −0.610386 | − | 0.792104i | \(-0.708986\pi\) | ||||
−0.610386 | + | 0.792104i | \(0.708986\pi\) | |||||||
\(348\) | −30.7714 | −0.0884236 | ||||||||
\(349\) | 206.336 | 0.591220 | 0.295610 | − | 0.955309i | \(-0.404477\pi\) | ||||
0.295610 | + | 0.955309i | \(0.404477\pi\) | |||||||
\(350\) | − | 52.0534i | − | 0.148724i | ||||||
\(351\) | 47.2663 | 0.134662 | ||||||||
\(352\) | 94.1139i | 0.267369i | ||||||||
\(353\) | 458.010 | 1.29748 | 0.648739 | − | 0.761011i | \(-0.275297\pi\) | ||||
0.648739 | + | 0.761011i | \(0.275297\pi\) | |||||||
\(354\) | 116.657 | 0.329538 | ||||||||
\(355\) | 6.50986i | 0.0183376i | ||||||||
\(356\) | − | 21.8763i | − | 0.0614503i | ||||||
\(357\) | 60.2779 | 0.168846 | ||||||||
\(358\) | −343.722 | −0.960118 | ||||||||
\(359\) | 396.012i | 1.10310i | 0.834142 | + | 0.551549i | \(0.185963\pi\) | ||||
−0.834142 | + | 0.551549i | \(0.814037\pi\) | |||||||
\(360\) | 18.9737i | 0.0527046i | ||||||||
\(361\) | 228.513 | 0.633000 | ||||||||
\(362\) | − | 3.80969i | − | 0.0105240i | ||||||
\(363\) | −269.844 | −0.743372 | ||||||||
\(364\) | − | 133.926i | − | 0.367927i | ||||||
\(365\) | − | 305.162i | − | 0.836061i | ||||||
\(366\) | − | 39.5036i | − | 0.107933i | ||||||
\(367\) | − | 209.492i | − | 0.570824i | −0.958405 | − | 0.285412i | \(-0.907870\pi\) | ||
0.958405 | − | 0.285412i | \(-0.0921304\pi\) | |||||||
\(368\) | −75.2751 | − | 52.8930i | −0.204552 | − | 0.143731i | ||||
\(369\) | 62.1430 | 0.168409 | ||||||||
\(370\) | 30.3443 | 0.0820117 | ||||||||
\(371\) | −520.470 | −1.40288 | ||||||||
\(372\) | −157.089 | −0.422282 | ||||||||
\(373\) | − | 680.917i | − | 1.82552i | −0.408501 | − | 0.912758i | \(-0.633948\pi\) | ||
0.408501 | − | 0.912758i | \(-0.366052\pi\) | |||||||
\(374\) | −111.231 | −0.297410 | ||||||||
\(375\) | 19.3649i | 0.0516398i | ||||||||
\(376\) | 87.6995 | 0.233243 | ||||||||
\(377\) | −80.8028 | −0.214331 | ||||||||
\(378\) | 54.0954i | 0.143110i | ||||||||
\(379\) | − | 354.412i | − | 0.935123i | −0.883960 | − | 0.467562i | \(-0.845133\pi\) | ||
0.883960 | − | 0.467562i | \(-0.154867\pi\) | |||||||
\(380\) | 51.4757 | 0.135462 | ||||||||
\(381\) | 45.2482 | 0.118762 | ||||||||
\(382\) | − | 102.859i | − | 0.269264i | ||||||
\(383\) | − | 211.762i | − | 0.552904i | −0.961028 | − | 0.276452i | \(-0.910841\pi\) | ||
0.961028 | − | 0.276452i | \(-0.0891586\pi\) | |||||||
\(384\) | −19.5959 | −0.0510310 | ||||||||
\(385\) | 273.859i | 0.711323i | ||||||||
\(386\) | 48.2407 | 0.124976 | ||||||||
\(387\) | 64.2036i | 0.165901i | ||||||||
\(388\) | − | 140.133i | − | 0.361167i | ||||||
\(389\) | − | 741.982i | − | 1.90741i | −0.300745 | − | 0.953705i | \(-0.597235\pi\) | ||
0.300745 | − | 0.953705i | \(-0.402765\pi\) | |||||||
\(390\) | 49.8230i | 0.127751i | ||||||||
\(391\) | 62.5132 | − | 88.9662i | 0.159880 | − | 0.227535i | ||||
\(392\) | 14.6825 | 0.0374553 | ||||||||
\(393\) | −436.143 | −1.10978 | ||||||||
\(394\) | −498.380 | −1.26492 | ||||||||
\(395\) | 83.7064 | 0.211915 | ||||||||
\(396\) | − | 99.8229i | − | 0.252078i | ||||||
\(397\) | −308.016 | −0.775859 | −0.387930 | − | 0.921689i | \(-0.626810\pi\) | ||||
−0.387930 | + | 0.921689i | \(0.626810\pi\) | |||||||
\(398\) | 5.62489i | 0.0141329i | ||||||||
\(399\) | 146.761 | 0.367823 | ||||||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | 764.284i | 1.90595i | 0.303055 | + | 0.952973i | \(0.401993\pi\) | ||||
−0.303055 | + | 0.952973i | \(0.598007\pi\) | |||||||
\(402\) | 28.9538i | 0.0720244i | ||||||||
\(403\) | −412.500 | −1.02357 | ||||||||
\(404\) | −68.9707 | −0.170720 | ||||||||
\(405\) | − | 20.1246i | − | 0.0496904i | ||||||
\(406\) | − | 92.4774i | − | 0.227777i | ||||||
\(407\) | −159.645 | −0.392249 | ||||||||
\(408\) | − | 23.1601i | − | 0.0567648i | ||||||
\(409\) | −187.717 | −0.458965 | −0.229483 | − | 0.973313i | \(-0.573703\pi\) | ||||
−0.229483 | + | 0.973313i | \(0.573703\pi\) | |||||||
\(410\) | 65.5045i | 0.159767i | ||||||||
\(411\) | 89.5621i | 0.217913i | ||||||||
\(412\) | 143.624i | 0.348601i | ||||||||
\(413\) | 350.588i | 0.848882i | ||||||||
\(414\) | 79.8413 | + | 56.1015i | 0.192853 | + | 0.135511i | ||||
\(415\) | −242.225 | −0.583676 | ||||||||
\(416\) | −51.4570 | −0.123695 | ||||||||
\(417\) | 66.3690 | 0.159158 | ||||||||
\(418\) | −270.820 | −0.647895 | ||||||||
\(419\) | 271.010i | 0.646801i | 0.946262 | + | 0.323401i | \(0.104826\pi\) | ||||
−0.946262 | + | 0.323401i | \(0.895174\pi\) | |||||||
\(420\) | −57.0216 | −0.135766 | ||||||||
\(421\) | 436.703i | 1.03730i | 0.854987 | + | 0.518650i | \(0.173565\pi\) | ||||
−0.854987 | + | 0.518650i | \(0.826435\pi\) | |||||||
\(422\) | −14.1115 | −0.0334396 | ||||||||
\(423\) | −93.0193 | −0.219904 | ||||||||
\(424\) | 199.975i | 0.471640i | ||||||||
\(425\) | − | 23.6376i | − | 0.0556180i | ||||||
\(426\) | 7.13119 | 0.0167399 | ||||||||
\(427\) | 118.720 | 0.278034 | ||||||||
\(428\) | − | 240.771i | − | 0.562550i | ||||||
\(429\) | − | 262.125i | − | 0.611015i | ||||||
\(430\) | −67.6765 | −0.157387 | ||||||||
\(431\) | − | 785.010i | − | 1.82137i | −0.413103 | − | 0.910684i | \(-0.635555\pi\) | ||
0.413103 | − | 0.910684i | \(-0.364445\pi\) | |||||||
\(432\) | 20.7846 | 0.0481125 | ||||||||
\(433\) | 483.665i | 1.11701i | 0.829502 | + | 0.558504i | \(0.188625\pi\) | ||||
−0.829502 | + | 0.558504i | \(0.811375\pi\) | |||||||
\(434\) | − | 472.099i | − | 1.08779i | ||||||
\(435\) | 34.4035i | 0.0790885i | ||||||||
\(436\) | − | 231.836i | − | 0.531734i | ||||||
\(437\) | 152.204 | − | 216.610i | 0.348292 | − | 0.495674i | ||||
\(438\) | −334.289 | −0.763216 | ||||||||
\(439\) | −727.424 | −1.65700 | −0.828501 | − | 0.559987i | \(-0.810806\pi\) | ||||
−0.828501 | + | 0.559987i | \(0.810806\pi\) | |||||||
\(440\) | 105.223 | 0.239142 | ||||||||
\(441\) | −15.5731 | −0.0353132 | ||||||||
\(442\) | − | 60.8161i | − | 0.137593i | ||||||
\(443\) | −92.6907 | −0.209234 | −0.104617 | − | 0.994513i | \(-0.533362\pi\) | ||||
−0.104617 | + | 0.994513i | \(0.533362\pi\) | |||||||
\(444\) | − | 33.2406i | − | 0.0748661i | ||||||
\(445\) | −24.4585 | −0.0549628 | ||||||||
\(446\) | −339.260 | −0.760673 | ||||||||
\(447\) | − | 81.3648i | − | 0.182024i | ||||||
\(448\) | − | 58.8917i | − | 0.131455i | ||||||
\(449\) | 571.226 | 1.27222 | 0.636109 | − | 0.771599i | \(-0.280543\pi\) | ||||
0.636109 | + | 0.771599i | \(0.280543\pi\) | |||||||
\(450\) | 21.2132 | 0.0471405 | ||||||||
\(451\) | − | 344.627i | − | 0.764140i | ||||||
\(452\) | − | 209.978i | − | 0.464554i | ||||||
\(453\) | −44.7378 | −0.0987589 | ||||||||
\(454\) | 90.7669i | 0.199927i | ||||||||
\(455\) | −149.733 | −0.329084 | ||||||||
\(456\) | − | 56.3888i | − | 0.123660i | ||||||
\(457\) | − | 702.228i | − | 1.53660i | −0.640088 | − | 0.768302i | \(-0.721102\pi\) | ||
0.640088 | − | 0.768302i | \(-0.278898\pi\) | |||||||
\(458\) | − | 273.844i | − | 0.597913i | ||||||
\(459\) | 24.5649i | 0.0535184i | ||||||||
\(460\) | −59.1361 | + | 84.1601i | −0.128557 | + | 0.182957i | ||||
\(461\) | −105.378 | −0.228585 | −0.114292 | − | 0.993447i | \(-0.536460\pi\) | ||||
−0.114292 | + | 0.993447i | \(0.536460\pi\) | |||||||
\(462\) | 299.998 | 0.649346 | ||||||||
\(463\) | 279.994 | 0.604739 | 0.302370 | − | 0.953191i | \(-0.402222\pi\) | ||||
0.302370 | + | 0.953191i | \(0.402222\pi\) | |||||||
\(464\) | −35.5318 | −0.0765771 | ||||||||
\(465\) | 175.631i | 0.377700i | ||||||||
\(466\) | −442.922 | −0.950475 | ||||||||
\(467\) | 580.243i | 1.24249i | 0.783616 | + | 0.621246i | \(0.213373\pi\) | ||||
−0.783616 | + | 0.621246i | \(0.786627\pi\) | |||||||
\(468\) | 54.5784 | 0.116621 | ||||||||
\(469\) | −87.0150 | −0.185533 | ||||||||
\(470\) | − | 98.0510i | − | 0.208619i | ||||||
\(471\) | 225.350i | 0.478451i | ||||||||
\(472\) | 134.703 | 0.285389 | ||||||||
\(473\) | 356.055 | 0.752758 | ||||||||
\(474\) | − | 91.6958i | − | 0.193451i | ||||||
\(475\) | − | 57.5515i | − | 0.121161i | ||||||
\(476\) | 69.6030 | 0.146225 | ||||||||
\(477\) | − | 212.106i | − | 0.444667i | ||||||
\(478\) | −299.299 | −0.626149 | ||||||||
\(479\) | − | 475.037i | − | 0.991727i | −0.868400 | − | 0.495864i | \(-0.834852\pi\) | ||
0.868400 | − | 0.495864i | \(-0.165148\pi\) | |||||||
\(480\) | 21.9089i | 0.0456435i | ||||||||
\(481\) | − | 87.2865i | − | 0.181469i | ||||||
\(482\) | − | 431.876i | − | 0.896008i | ||||||
\(483\) | −168.602 | + | 239.947i | −0.349072 | + | 0.496785i | ||||
\(484\) | −311.589 | −0.643779 | ||||||||
\(485\) | −156.673 | −0.323037 | ||||||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | −68.8375 | −0.141350 | −0.0706751 | − | 0.997499i | \(-0.522515\pi\) | ||||
−0.0706751 | + | 0.997499i | \(0.522515\pi\) | |||||||
\(488\) | − | 45.6149i | − | 0.0934731i | ||||||
\(489\) | 407.928 | 0.834208 | ||||||||
\(490\) | − | 16.4155i | − | 0.0335011i | ||||||
\(491\) | 473.549 | 0.964459 | 0.482230 | − | 0.876045i | \(-0.339827\pi\) | ||||
0.482230 | + | 0.876045i | \(0.339827\pi\) | |||||||
\(492\) | 71.7566 | 0.145847 | ||||||||
\(493\) | − | 41.9944i | − | 0.0851812i | ||||||
\(494\) | − | 148.072i | − | 0.299740i | ||||||
\(495\) | −111.605 | −0.225465 | ||||||||
\(496\) | −181.390 | −0.365707 | ||||||||
\(497\) | 21.4314i | 0.0431215i | ||||||||
\(498\) | 265.345i | 0.532821i | ||||||||
\(499\) | 730.312 | 1.46355 | 0.731776 | − | 0.681545i | \(-0.238692\pi\) | ||||
0.731776 | + | 0.681545i | \(0.238692\pi\) | |||||||
\(500\) | 22.3607i | 0.0447214i | ||||||||
\(501\) | −15.8503 | −0.0316373 | ||||||||
\(502\) | − | 452.145i | − | 0.900687i | ||||||
\(503\) | − | 506.085i | − | 1.00613i | −0.864247 | − | 0.503067i | \(-0.832205\pi\) | ||
0.864247 | − | 0.503067i | \(-0.167795\pi\) | |||||||
\(504\) | 62.4640i | 0.123937i | ||||||||
\(505\) | 77.1116i | 0.152696i | ||||||||
\(506\) | 311.123 | − | 442.777i | 0.614867 | − | 0.875053i | ||||
\(507\) | −149.399 | −0.294672 | ||||||||
\(508\) | 52.2481 | 0.102851 | ||||||||
\(509\) | 594.057 | 1.16711 | 0.583553 | − | 0.812075i | \(-0.301662\pi\) | ||||
0.583553 | + | 0.812075i | \(0.301662\pi\) | |||||||
\(510\) | −25.8937 | −0.0507720 | ||||||||
\(511\) | − | 1004.64i | − | 1.96602i | ||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 59.8093i | 0.116587i | ||||||||
\(514\) | −66.9546 | −0.130262 | ||||||||
\(515\) | 160.576 | 0.311798 | ||||||||
\(516\) | 74.1359i | 0.143674i | ||||||||
\(517\) | 515.859i | 0.997792i | ||||||||
\(518\) | 99.8979 | 0.192853 | ||||||||
\(519\) | 48.1523 | 0.0927791 | ||||||||
\(520\) | 57.5307i | 0.110636i | ||||||||
\(521\) | − | 151.644i | − | 0.291063i | −0.989354 | − | 0.145531i | \(-0.953511\pi\) | ||
0.989354 | − | 0.145531i | \(-0.0464892\pi\) | |||||||
\(522\) | 37.6871 | 0.0721976 | ||||||||
\(523\) | 460.148i | 0.879824i | 0.898041 | + | 0.439912i | \(0.144990\pi\) | ||||
−0.898041 | + | 0.439912i | \(0.855010\pi\) | |||||||
\(524\) | −503.614 | −0.961096 | ||||||||
\(525\) | 63.7521i | 0.121433i | ||||||||
\(526\) | − | 259.854i | − | 0.494019i | ||||||
\(527\) | − | 214.382i | − | 0.406797i | ||||||
\(528\) | − | 115.266i | − | 0.218306i | ||||||
\(529\) | 179.292 | + | 497.690i | 0.338926 | + | 0.940813i | ||||
\(530\) | 223.579 | 0.421848 | ||||||||
\(531\) | −142.875 | −0.269067 | ||||||||
\(532\) | 169.465 | 0.318544 | ||||||||
\(533\) | 188.426 | 0.353520 | ||||||||
\(534\) | 26.7929i | 0.0501740i | ||||||||
\(535\) | −269.191 | −0.503160 | ||||||||
\(536\) | 33.4330i | 0.0623750i | ||||||||
\(537\) | 420.972 | 0.783933 | ||||||||
\(538\) | 515.363 | 0.957923 | ||||||||
\(539\) | 86.3641i | 0.160230i | ||||||||
\(540\) | − | 23.2379i | − | 0.0430331i | ||||||
\(541\) | −746.487 | −1.37983 | −0.689914 | − | 0.723891i | \(-0.742352\pi\) | ||||
−0.689914 | + | 0.723891i | \(0.742352\pi\) | |||||||
\(542\) | 488.380 | 0.901070 | ||||||||
\(543\) | 4.66590i | 0.00859282i | ||||||||
\(544\) | − | 26.7429i | − | 0.0491598i | ||||||
\(545\) | −259.200 | −0.475597 | ||||||||
\(546\) | 164.025i | 0.300411i | ||||||||
\(547\) | −452.047 | −0.826412 | −0.413206 | − | 0.910638i | \(-0.635591\pi\) | ||||
−0.413206 | + | 0.910638i | \(0.635591\pi\) | |||||||
\(548\) | 103.417i | 0.188718i | ||||||||
\(549\) | 48.3819i | 0.0881273i | ||||||||
\(550\) | − | 117.642i | − | 0.213895i | ||||||
\(551\) | − | 102.245i | − | 0.185563i | ||||||
\(552\) | 92.1927 | + | 64.7804i | 0.167016 | + | 0.117356i | ||||
\(553\) | 275.574 | 0.498325 | ||||||||
\(554\) | −296.275 | −0.534792 | ||||||||
\(555\) | −37.1641 | −0.0669623 | ||||||||
\(556\) | 76.6363 | 0.137835 | ||||||||
\(557\) | 992.369i | 1.78163i | 0.454365 | + | 0.890816i | \(0.349866\pi\) | ||||
−0.454365 | + | 0.890816i | \(0.650134\pi\) | |||||||
\(558\) | 192.394 | 0.344792 | ||||||||
\(559\) | 194.674i | 0.348254i | ||||||||
\(560\) | −65.8429 | −0.117577 | ||||||||
\(561\) | 136.230 | 0.242835 | ||||||||
\(562\) | − | 346.064i | − | 0.615772i | ||||||
\(563\) | 761.693i | 1.35292i | 0.736481 | + | 0.676459i | \(0.236486\pi\) | ||||
−0.736481 | + | 0.676459i | \(0.763514\pi\) | |||||||
\(564\) | −107.409 | −0.190442 | ||||||||
\(565\) | −234.763 | −0.415510 | ||||||||
\(566\) | 413.222i | 0.730074i | ||||||||
\(567\) | − | 66.2531i | − | 0.116849i | ||||||
\(568\) | 8.23439 | 0.0144972 | ||||||||
\(569\) | 444.757i | 0.781647i | 0.920466 | + | 0.390823i | \(0.127810\pi\) | ||||
−0.920466 | + | 0.390823i | \(0.872190\pi\) | |||||||
\(570\) | −63.0445 | −0.110604 | ||||||||
\(571\) | − | 1028.85i | − | 1.80184i | −0.433982 | − | 0.900922i | \(-0.642892\pi\) | ||
0.433982 | − | 0.900922i | \(-0.357108\pi\) | |||||||
\(572\) | − | 302.676i | − | 0.529154i | ||||||
\(573\) | 125.976i | 0.219853i | ||||||||
\(574\) | 215.650i | 0.375697i | ||||||||
\(575\) | 94.0938 | + | 66.1162i | 0.163641 | + | 0.114985i | ||||
\(576\) | 24.0000 | 0.0416667 | ||||||||
\(577\) | −642.647 | −1.11377 | −0.556886 | − | 0.830589i | \(-0.688004\pi\) | ||||
−0.556886 | + | 0.830589i | \(0.688004\pi\) | |||||||
\(578\) | −377.101 | −0.652423 | ||||||||
\(579\) | −59.0826 | −0.102042 | ||||||||
\(580\) | 39.7257i | 0.0684927i | ||||||||
\(581\) | −797.441 | −1.37253 | ||||||||
\(582\) | 171.627i | 0.294891i | ||||||||
\(583\) | −1176.28 | −2.01763 | ||||||||
\(584\) | −386.003 | −0.660965 | ||||||||
\(585\) | − | 61.0205i | − | 0.104309i | ||||||
\(586\) | − | 255.884i | − | 0.436662i | ||||||
\(587\) | 461.581 | 0.786338 | 0.393169 | − | 0.919466i | \(-0.371379\pi\) | ||||
0.393169 | + | 0.919466i | \(0.371379\pi\) | |||||||
\(588\) | −17.9823 | −0.0305821 | ||||||||
\(589\) | − | 521.965i | − | 0.886188i | ||||||
\(590\) | − | 150.603i | − | 0.255259i | ||||||
\(591\) | 610.388 | 1.03281 | ||||||||
\(592\) | − | 38.3829i | − | 0.0648359i | ||||||
\(593\) | 611.226 | 1.03073 | 0.515367 | − | 0.856969i | \(-0.327655\pi\) | ||||
0.515367 | + | 0.856969i | \(0.327655\pi\) | |||||||
\(594\) | 122.258i | 0.205821i | ||||||||
\(595\) | − | 77.8185i | − | 0.130787i | ||||||
\(596\) | − | 93.9520i | − | 0.157638i | ||||||
\(597\) | − | 6.88905i | − | 0.0115394i | ||||||
\(598\) | 242.089 | + | 170.107i | 0.404832 | + | 0.284460i | ||||
\(599\) | 341.070 | 0.569400 | 0.284700 | − | 0.958617i | \(-0.408106\pi\) | ||||
0.284700 | + | 0.958617i | \(0.408106\pi\) | |||||||
\(600\) | 24.4949 | 0.0408248 | ||||||||
\(601\) | 103.870 | 0.172828 | 0.0864142 | − | 0.996259i | \(-0.472459\pi\) | ||||
0.0864142 | + | 0.996259i | \(0.472459\pi\) | |||||||
\(602\) | −222.801 | −0.370101 | ||||||||
\(603\) | − | 35.4610i | − | 0.0588077i | ||||||
\(604\) | −51.6588 | −0.0855277 | ||||||||
\(605\) | 348.367i | 0.575814i | ||||||||
\(606\) | 84.4716 | 0.139392 | ||||||||
\(607\) | −209.656 | −0.345398 | −0.172699 | − | 0.984975i | \(-0.555249\pi\) | ||||
−0.172699 | + | 0.984975i | \(0.555249\pi\) | |||||||
\(608\) | − | 65.1121i | − | 0.107092i | ||||||
\(609\) | 113.261i | 0.185979i | ||||||||
\(610\) | −50.9990 | −0.0836049 | ||||||||
\(611\) | −282.047 | −0.461616 | ||||||||
\(612\) | 28.3652i | 0.0463483i | ||||||||
\(613\) | 790.819i | 1.29008i | 0.764149 | + | 0.645040i | \(0.223159\pi\) | ||||
−0.764149 | + | 0.645040i | \(0.776841\pi\) | |||||||
\(614\) | −85.1009 | −0.138601 | ||||||||
\(615\) | − | 80.2263i | − | 0.130449i | ||||||
\(616\) | 346.408 | 0.562350 | ||||||||
\(617\) | 446.127i | 0.723059i | 0.932361 | + | 0.361529i | \(0.117745\pi\) | ||||
−0.932361 | + | 0.361529i | \(0.882255\pi\) | |||||||
\(618\) | − | 175.902i | − | 0.284632i | ||||||
\(619\) | − | 931.416i | − | 1.50471i | −0.658758 | − | 0.752355i | \(-0.728918\pi\) | ||
0.658758 | − | 0.752355i | \(-0.271082\pi\) | |||||||
\(620\) | 202.801i | 0.327098i | ||||||||
\(621\) | −97.7852 | − | 68.7100i | −0.157464 | − | 0.110644i | ||||
\(622\) | 389.872 | 0.626803 | ||||||||
\(623\) | −80.5207 | −0.129247 | ||||||||
\(624\) | 63.0217 | 0.100996 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 156.899i | 0.250637i | ||||||||
\(627\) | 331.685 | 0.529004 | ||||||||
\(628\) | 260.212i | 0.414351i | ||||||||
\(629\) | 45.3640 | 0.0721209 | ||||||||
\(630\) | 69.8369 | 0.110852 | ||||||||
\(631\) | 578.467i | 0.916747i | 0.888760 | + | 0.458373i | \(0.151568\pi\) | ||||
−0.888760 | + | 0.458373i | \(0.848432\pi\) | |||||||
\(632\) | − | 105.881i | − | 0.167534i | ||||||
\(633\) | 17.2830 | 0.0273033 | ||||||||
\(634\) | −729.651 | −1.15087 | ||||||||
\(635\) | − | 58.4152i | − | 0.0919925i | ||||||
\(636\) | − | 244.919i | − | 0.385092i | ||||||
\(637\) | −47.2198 | −0.0741284 | ||||||||
\(638\) | − | 209.002i | − | 0.327590i | ||||||
\(639\) | −8.73389 | −0.0136681 | ||||||||
\(640\) | 25.2982i | 0.0395285i | ||||||||
\(641\) | 198.212i | 0.309223i | 0.987975 | + | 0.154611i | \(0.0494125\pi\) | ||||
−0.987975 | + | 0.154611i | \(0.950587\pi\) | |||||||
\(642\) | 294.884i | 0.459320i | ||||||||
\(643\) | 91.4978i | 0.142298i | 0.997466 | + | 0.0711491i | \(0.0226666\pi\) | ||||
−0.997466 | + | 0.0711491i | \(0.977333\pi\) | |||||||
\(644\) | −194.685 | + | 277.067i | −0.302305 | + | 0.430228i | ||||
\(645\) | 82.8864 | 0.128506 | ||||||||
\(646\) | 76.9548 | 0.119125 | ||||||||
\(647\) | −178.939 | −0.276568 | −0.138284 | − | 0.990393i | \(-0.544159\pi\) | ||||
−0.138284 | + | 0.990393i | \(0.544159\pi\) | |||||||
\(648\) | −25.4558 | −0.0392837 | ||||||||
\(649\) | 792.342i | 1.22087i | ||||||||
\(650\) | 64.3213 | 0.0989558 | ||||||||
\(651\) | 578.201i | 0.888174i | ||||||||
\(652\) | 471.034 | 0.722445 | ||||||||
\(653\) | 298.195 | 0.456654 | 0.228327 | − | 0.973585i | \(-0.426674\pi\) | ||||
0.228327 | + | 0.973585i | \(0.426674\pi\) | |||||||
\(654\) | 283.940i | 0.434159i | ||||||||
\(655\) | 563.058i | 0.859630i | ||||||||
\(656\) | 82.8573 | 0.126307 | ||||||||
\(657\) | 409.418 | 0.623163 | ||||||||
\(658\) | − | 322.798i | − | 0.490574i | ||||||
\(659\) | − | 686.401i | − | 1.04158i | −0.853685 | − | 0.520790i | \(-0.825638\pi\) | ||
0.853685 | − | 0.520790i | \(-0.174362\pi\) | |||||||
\(660\) | −128.871 | −0.195259 | ||||||||
\(661\) | − | 1101.62i | − | 1.66660i | −0.552823 | − | 0.833299i | \(-0.686449\pi\) | ||
0.552823 | − | 0.833299i | \(-0.313551\pi\) | |||||||
\(662\) | −791.719 | −1.19595 | ||||||||
\(663\) | 74.4842i | 0.112344i | ||||||||
\(664\) | 306.394i | 0.461436i | ||||||||
\(665\) | − | 189.468i | − | 0.284914i | ||||||
\(666\) | 40.7112i | 0.0611279i | ||||||||
\(667\) | 167.166 | + | 117.461i | 0.250624 | + | 0.176104i | ||||
\(668\) | −18.3023 | −0.0273987 | ||||||||
\(669\) | 415.507 | 0.621087 | ||||||||
\(670\) | 37.3792 | 0.0557899 | ||||||||
\(671\) | 268.312 | 0.399869 | ||||||||
\(672\) | 72.1272i | 0.107332i | ||||||||
\(673\) | 963.161 | 1.43114 | 0.715572 | − | 0.698539i | \(-0.246166\pi\) | ||||
0.715572 | + | 0.698539i | \(0.246166\pi\) | |||||||
\(674\) | 721.923i | 1.07110i | ||||||||
\(675\) | −25.9808 | −0.0384900 | ||||||||
\(676\) | −172.511 | −0.255194 | ||||||||
\(677\) | 1066.82i | 1.57581i | 0.615799 | + | 0.787903i | \(0.288833\pi\) | ||||
−0.615799 | + | 0.787903i | \(0.711167\pi\) | |||||||
\(678\) | 257.170i | 0.379307i | ||||||||
\(679\) | −515.790 | −0.759632 | ||||||||
\(680\) | −29.8995 | −0.0439699 | ||||||||
\(681\) | − | 111.166i | − | 0.163240i | ||||||
\(682\) | − | 1066.96i | − | 1.56446i | ||||||
\(683\) | −280.062 | −0.410047 | −0.205024 | − | 0.978757i | \(-0.565727\pi\) | ||||
−0.205024 | + | 0.978757i | \(0.565727\pi\) | |||||||
\(684\) | 69.0618i | 0.100968i | ||||||||
\(685\) | 115.624 | 0.168794 | ||||||||
\(686\) | 456.081i | 0.664841i | ||||||||
\(687\) | 335.389i | 0.488194i | ||||||||
\(688\) | 85.6048i | 0.124426i | ||||||||
\(689\) | − | 643.134i | − | 0.933430i | ||||||
\(690\) | 72.4267 | − | 103.075i | 0.104966 | − | 0.149383i | ||||
\(691\) | 1165.91 | 1.68727 | 0.843637 | − | 0.536914i | \(-0.180410\pi\) | ||||
0.843637 | + | 0.536914i | \(0.180410\pi\) | |||||||
\(692\) | 55.6015 | 0.0803490 | ||||||||
\(693\) | −367.421 | −0.530189 | ||||||||
\(694\) | 599.072 | 0.863217 | ||||||||
\(695\) | − | 85.6820i | − | 0.123284i | ||||||
\(696\) | 43.5174 | 0.0625250 | ||||||||
\(697\) | 97.9275i | 0.140499i | ||||||||
\(698\) | −291.803 | −0.418055 | ||||||||
\(699\) | 542.466 | 0.776060 | ||||||||
\(700\) | 73.6146i | 0.105164i | ||||||||
\(701\) | 508.137i | 0.724875i | 0.932008 | + | 0.362437i | \(0.118055\pi\) | ||||
−0.932008 | + | 0.362437i | \(0.881945\pi\) | |||||||
\(702\) | −66.8446 | −0.0952203 | ||||||||
\(703\) | 110.450 | 0.157112 | ||||||||
\(704\) | − | 133.097i | − | 0.189058i | ||||||
\(705\) | 120.087i | 0.170337i | ||||||||
\(706\) | −647.724 | −0.917456 | ||||||||
\(707\) | 253.863i | 0.359070i | ||||||||
\(708\) | −164.977 | −0.233019 | ||||||||
\(709\) | − | 51.5395i | − | 0.0726932i | −0.999339 | − | 0.0363466i | \(-0.988428\pi\) | ||
0.999339 | − | 0.0363466i | \(-0.0115720\pi\) | |||||||
\(710\) | − | 9.20633i | − | 0.0129667i | ||||||
\(711\) | 112.304i | 0.157952i | ||||||||
\(712\) | 30.9378i | 0.0434519i | ||||||||
\(713\) | 853.386 | + | 599.643i | 1.19690 | + | 0.841013i | ||||
\(714\) | −85.2459 | −0.119392 | ||||||||
\(715\) | −338.402 | −0.473290 | ||||||||
\(716\) | 486.097 | 0.678906 | ||||||||
\(717\) | 366.565 | 0.511248 | ||||||||
\(718\) | − | 560.046i | − | 0.780008i | ||||||
\(719\) | 849.242 | 1.18114 | 0.590571 | − | 0.806985i | \(-0.298902\pi\) | ||||
0.590571 | + | 0.806985i | \(0.298902\pi\) | |||||||
\(720\) | − | 26.8328i | − | 0.0372678i | ||||||
\(721\) | 528.640 | 0.733203 | ||||||||
\(722\) | −323.166 | −0.447598 | ||||||||
\(723\) | 528.938i | 0.731588i | ||||||||
\(724\) | 5.38772i | 0.00744160i | ||||||||
\(725\) | 44.4147 | 0.0612617 | ||||||||
\(726\) | 381.617 | 0.525644 | ||||||||
\(727\) | − | 467.357i | − | 0.642858i | −0.946934 | − | 0.321429i | \(-0.895837\pi\) | ||
0.946934 | − | 0.321429i | \(-0.104163\pi\) | |||||||
\(728\) | 189.399i | 0.260164i | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 431.565i | 0.591185i | ||||||||
\(731\) | −101.175 | −0.138406 | ||||||||
\(732\) | 55.8666i | 0.0763205i | ||||||||
\(733\) | − | 1031.67i | − | 1.40746i | −0.710469 | − | 0.703729i | \(-0.751517\pi\) | ||
0.710469 | − | 0.703729i | \(-0.248483\pi\) | |||||||
\(734\) | 296.267i | 0.403634i | ||||||||
\(735\) | 20.1048i | 0.0273535i | ||||||||
\(736\) | 106.455 | + | 74.8020i | 0.144640 | + | 0.101633i | ||||
\(737\) | −196.657 | −0.266834 | ||||||||
\(738\) | −87.8835 | −0.119083 | ||||||||
\(739\) | −561.453 | −0.759747 | −0.379873 | − | 0.925039i | \(-0.624032\pi\) | ||||
−0.379873 | + | 0.925039i | \(0.624032\pi\) | |||||||
\(740\) | −42.9134 | −0.0579910 | ||||||||
\(741\) | 181.350i | 0.244737i | ||||||||
\(742\) | 736.055 | 0.991988 | ||||||||
\(743\) | − | 878.524i | − | 1.18240i | −0.806524 | − | 0.591201i | \(-0.798654\pi\) | ||
0.806524 | − | 0.591201i | \(-0.201346\pi\) | |||||||
\(744\) | 222.157 | 0.298598 | ||||||||
\(745\) | −105.042 | −0.140995 | ||||||||
\(746\) | 962.963i | 1.29083i | ||||||||
\(747\) | − | 324.980i | − | 0.435046i | ||||||
\(748\) | 157.305 | 0.210301 | ||||||||
\(749\) | −886.214 | −1.18320 | ||||||||
\(750\) | − | 27.3861i | − | 0.0365148i | ||||||
\(751\) | − | 59.7825i | − | 0.0796038i | −0.999208 | − | 0.0398019i | \(-0.987327\pi\) | ||
0.999208 | − | 0.0398019i | \(-0.0126727\pi\) | |||||||
\(752\) | −124.026 | −0.164928 | ||||||||
\(753\) | 553.762i | 0.735408i | ||||||||
\(754\) | 114.272 | 0.151555 | ||||||||
\(755\) | 57.7562i | 0.0764983i | ||||||||
\(756\) | − | 76.5025i | − | 0.101194i | ||||||
\(757\) | − | 666.974i | − | 0.881076i | −0.897734 | − | 0.440538i | \(-0.854788\pi\) | ||
0.897734 | − | 0.440538i | \(-0.145212\pi\) | |||||||
\(758\) | 501.214i | 0.661232i | ||||||||
\(759\) | −381.046 | + | 542.289i | −0.502037 | + | 0.714478i | ||||
\(760\) | −72.7976 | −0.0957863 | ||||||||
\(761\) | 520.271 | 0.683668 | 0.341834 | − | 0.939760i | \(-0.388952\pi\) | ||||
0.341834 | + | 0.939760i | \(0.388952\pi\) | |||||||
\(762\) | −63.9907 | −0.0839772 | ||||||||
\(763\) | −853.325 | −1.11838 | ||||||||
\(764\) | 145.464i | 0.190398i | ||||||||
\(765\) | 31.7132 | 0.0414552 | ||||||||
\(766\) | 299.477i | 0.390962i | ||||||||
\(767\) | −433.215 | −0.564817 | ||||||||
\(768\) | 27.7128 | 0.0360844 | ||||||||
\(769\) | − | 417.949i | − | 0.543497i | −0.962368 | − | 0.271749i | \(-0.912398\pi\) | ||
0.962368 | − | 0.271749i | \(-0.0876019\pi\) | |||||||
\(770\) | − | 387.296i | − | 0.502981i | ||||||
\(771\) | 82.0023 | 0.106358 | ||||||||
\(772\) | −68.2227 | −0.0883714 | ||||||||
\(773\) | − | 308.047i | − | 0.398509i | −0.979948 | − | 0.199254i | \(-0.936148\pi\) | ||
0.979948 | − | 0.199254i | \(-0.0638520\pi\) | |||||||
\(774\) | − | 90.7976i | − | 0.117310i | ||||||
\(775\) | 226.738 | 0.292565 | ||||||||
\(776\) | 198.178i | 0.255383i | ||||||||
\(777\) | −122.349 | −0.157464 | ||||||||
\(778\) | 1049.32i | 1.34874i | ||||||||
\(779\) | 238.428i | 0.306070i | ||||||||
\(780\) | − | 70.4604i | − | 0.0903339i | ||||||
\(781\) | 48.4356i | 0.0620175i | ||||||||
\(782\) | −88.4070 | + | 125.817i | −0.113052 | + | 0.160892i | ||||
\(783\) | −46.1571 | −0.0589491 | ||||||||
\(784\) | −20.7642 | −0.0264849 | ||||||||
\(785\) | 290.926 | 0.370607 | ||||||||
\(786\) | 616.799 | 0.784731 | ||||||||
\(787\) | 444.989i | 0.565424i | 0.959205 | + | 0.282712i | \(0.0912341\pi\) | ||||
−0.959205 | + | 0.282712i | \(0.908766\pi\) | |||||||
\(788\) | 704.815 | 0.894436 | ||||||||
\(789\) | 318.255i | 0.403365i | ||||||||
\(790\) | −118.379 | −0.149847 | ||||||||
\(791\) | −772.873 | −0.977084 | ||||||||
\(792\) | 141.171i | 0.178246i | ||||||||
\(793\) | 146.700i | 0.184994i | ||||||||
\(794\) | 435.600 | 0.548615 | ||||||||
\(795\) | −273.828 | −0.344437 | ||||||||
\(796\) | − | 7.95479i | − | 0.00999345i | ||||||
\(797\) | 445.698i | 0.559219i | 0.960114 | + | 0.279610i | \(0.0902050\pi\) | ||||
−0.960114 | + | 0.279610i | \(0.909795\pi\) | |||||||
\(798\) | −207.552 | −0.260090 | ||||||||
\(799\) | − | 146.584i | − | 0.183459i | ||||||
\(800\) | 28.2843 | 0.0353553 | ||||||||
\(801\) | − | 32.8145i | − | 0.0409669i | ||||||
\(802\) | − | 1080.86i | − | 1.34771i | ||||||
\(803\) | − | 2270.52i | − | 2.82754i | ||||||
\(804\) | − | 40.9469i | − | 0.0509290i | ||||||
\(805\) | 309.770 | + | 217.664i | 0.384808 | + | 0.270390i | ||||
\(806\) | 583.363 | 0.723776 | ||||||||
\(807\) | −631.188 | −0.782141 | ||||||||
\(808\) | 97.5393 | 0.120717 | ||||||||
\(809\) | 308.829 | 0.381741 | 0.190871 | − | 0.981615i | \(-0.438869\pi\) | ||||
0.190871 | + | 0.981615i | \(0.438869\pi\) | |||||||
\(810\) | 28.4605i | 0.0351364i | ||||||||
\(811\) | 1459.27 | 1.79934 | 0.899672 | − | 0.436567i | \(-0.143806\pi\) | ||||
0.899672 | + | 0.436567i | \(0.143806\pi\) | |||||||
\(812\) | 130.783i | 0.161063i | ||||||||
\(813\) | −598.141 | −0.735721 | ||||||||
\(814\) | 225.773 | 0.277362 | ||||||||
\(815\) | − | 526.632i | − | 0.646175i | ||||||
\(816\) | 32.7533i | 0.0401388i | ||||||||
\(817\) | −246.334 | −0.301511 | ||||||||
\(818\) | 265.472 | 0.324537 | ||||||||
\(819\) | − | 200.888i | − | 0.245285i | ||||||
\(820\) | − | 92.6373i | − | 0.112972i | ||||||
\(821\) | −875.617 | −1.06653 | −0.533263 | − | 0.845950i | \(-0.679034\pi\) | ||||
−0.533263 | + | 0.845950i | \(0.679034\pi\) | |||||||
\(822\) | − | 126.660i | − | 0.154087i | ||||||
\(823\) | −1246.88 | −1.51505 | −0.757523 | − | 0.652808i | \(-0.773591\pi\) | ||||
−0.757523 | + | 0.652808i | \(0.773591\pi\) | |||||||
\(824\) | − | 203.115i | − | 0.246498i | ||||||
\(825\) | 144.082i | 0.174645i | ||||||||
\(826\) | − | 495.807i | − | 0.600250i | ||||||
\(827\) | − | 789.157i | − | 0.954240i | −0.878838 | − | 0.477120i | \(-0.841681\pi\) | ||
0.878838 | − | 0.477120i | \(-0.158319\pi\) | |||||||
\(828\) | −112.913 | − | 79.3395i | −0.136368 | − | 0.0958206i | ||||
\(829\) | −182.486 | −0.220128 | −0.110064 | − | 0.993924i | \(-0.535106\pi\) | ||||
−0.110064 | + | 0.993924i | \(0.535106\pi\) | |||||||
\(830\) | 342.558 | 0.412721 | ||||||||
\(831\) | 362.861 | 0.436656 | ||||||||
\(832\) | 72.7712 | 0.0874654 | ||||||||
\(833\) | − | 24.5408i | − | 0.0294607i | ||||||
\(834\) | −93.8600 | −0.112542 | ||||||||
\(835\) | 20.4626i | 0.0245061i | ||||||||
\(836\) | 382.997 | 0.458131 | ||||||||
\(837\) | −235.633 | −0.281521 | ||||||||
\(838\) | − | 383.266i | − | 0.457357i | ||||||
\(839\) | − | 471.140i | − | 0.561550i | −0.959774 | − | 0.280775i | \(-0.909409\pi\) | ||
0.959774 | − | 0.280775i | \(-0.0905914\pi\) | |||||||
\(840\) | 80.6407 | 0.0960009 | ||||||||
\(841\) | −762.093 | −0.906175 | ||||||||
\(842\) | − | 617.591i | − | 0.733481i | ||||||
\(843\) | 423.840i | 0.502776i | ||||||||
\(844\) | 19.9567 | 0.0236454 | ||||||||
\(845\) | 192.873i | 0.228252i | ||||||||
\(846\) | 131.549 | 0.155496 | ||||||||
\(847\) | 1146.88i | 1.35404i | ||||||||
\(848\) | − | 282.808i | − | 0.333500i | ||||||
\(849\) | − | 506.091i | − | 0.596103i | ||||||
\(850\) | 33.4287i | 0.0393278i | ||||||||
\(851\) | −126.887 | + | 180.580i | −0.149103 | + | 0.212197i | ||||
\(852\) | −10.0850 | −0.0118369 | ||||||||
\(853\) | 884.542 | 1.03698 | 0.518489 | − | 0.855085i | \(-0.326495\pi\) | ||||
0.518489 | + | 0.855085i | \(0.326495\pi\) | |||||||
\(854\) | −167.896 | −0.196600 | ||||||||
\(855\) | 77.2135 | 0.0903082 | ||||||||
\(856\) | 340.502i | 0.397783i | ||||||||
\(857\) | −1025.63 | −1.19676 | −0.598382 | − | 0.801211i | \(-0.704190\pi\) | ||||
−0.598382 | + | 0.801211i | \(0.704190\pi\) | |||||||
\(858\) | 370.701i | 0.432053i | ||||||||
\(859\) | 46.7953 | 0.0544765 | 0.0272383 | − | 0.999629i | \(-0.491329\pi\) | ||||
0.0272383 | + | 0.999629i | \(0.491329\pi\) | |||||||
\(860\) | 95.7090 | 0.111290 | ||||||||
\(861\) | − | 264.116i | − | 0.306755i | ||||||
\(862\) | 1110.17i | 1.28790i | ||||||||
\(863\) | 369.087 | 0.427679 | 0.213839 | − | 0.976869i | \(-0.431403\pi\) | ||||
0.213839 | + | 0.976869i | \(0.431403\pi\) | |||||||
\(864\) | −29.3939 | −0.0340207 | ||||||||
\(865\) | − | 62.1644i | − | 0.0718663i | ||||||
\(866\) | − | 684.005i | − | 0.789845i | ||||||
\(867\) | 461.852 | 0.532702 | ||||||||
\(868\) | 667.649i | 0.769181i | ||||||||
\(869\) | 622.806 | 0.716693 | ||||||||
\(870\) | − | 48.6539i | − | 0.0559240i | ||||||
\(871\) | − | 107.523i | − | 0.123447i | ||||||
\(872\) | 327.866i | 0.375993i | ||||||||
\(873\) | − | 210.199i | − | 0.240778i | ||||||
\(874\) | −215.248 | + | 306.332i | −0.246280 | + | 0.350495i | ||||
\(875\) | 82.3036 | 0.0940612 | ||||||||
\(876\) | 472.756 | 0.539675 | ||||||||
\(877\) | −648.975 | −0.739994 | −0.369997 | − | 0.929033i | \(-0.620641\pi\) | ||||
−0.369997 | + | 0.929033i | \(0.620641\pi\) | |||||||
\(878\) | 1028.73 | 1.17168 | ||||||||
\(879\) | 313.392i | 0.356533i | ||||||||
\(880\) | −148.807 | −0.169099 | ||||||||
\(881\) | 940.494i | 1.06753i | 0.845633 | + | 0.533765i | \(0.179223\pi\) | ||||
−0.845633 | + | 0.533765i | \(0.820777\pi\) | |||||||
\(882\) | 22.0237 | 0.0249702 | ||||||||
\(883\) | 599.839 | 0.679320 | 0.339660 | − | 0.940548i | \(-0.389688\pi\) | ||||
0.339660 | + | 0.940548i | \(0.389688\pi\) | |||||||
\(884\) | 86.0070i | 0.0972929i | ||||||||
\(885\) | 184.450i | 0.208418i | ||||||||
\(886\) | 131.084 | 0.147951 | ||||||||
\(887\) | −1396.51 | −1.57442 | −0.787212 | − | 0.616683i | \(-0.788476\pi\) | ||||
−0.787212 | + | 0.616683i | \(0.788476\pi\) | |||||||
\(888\) | 47.0092i | 0.0529383i | ||||||||
\(889\) | − | 192.311i | − | 0.216323i | ||||||
\(890\) | 34.5895 | 0.0388646 | ||||||||
\(891\) | − | 149.734i | − | 0.168052i | ||||||
\(892\) | 479.787 | 0.537877 | ||||||||
\(893\) | − | 356.894i | − | 0.399657i | ||||||
\(894\) | 115.067i | 0.128711i | ||||||||
\(895\) | − | 543.473i | − | 0.607232i | ||||||
\(896\) | 83.2854i | 0.0929524i | ||||||||
\(897\) | −296.498 | − | 208.338i | −0.330544 | − | 0.232261i | ||||
\(898\) | −807.835 | −0.899594 | ||||||||
\(899\) | 402.820 | 0.448076 | ||||||||
\(900\) | −30.0000 | −0.0333333 | ||||||||
\(901\) | 334.245 | 0.370972 | ||||||||
\(902\) | 487.377i | 0.540329i | ||||||||
\(903\) | 272.874 | 0.302186 | ||||||||
\(904\) | 296.954i | 0.328489i | ||||||||
\(905\) | 6.02365 | 0.00665597 | ||||||||
\(906\) | 63.2688 | 0.0698331 | ||||||||
\(907\) | 1427.22i | 1.57356i | 0.617233 | + | 0.786781i | \(0.288254\pi\) | ||||
−0.617233 | + | 0.786781i | \(0.711746\pi\) | |||||||
\(908\) | − | 128.364i | − | 0.141370i | ||||||
\(909\) | −103.456 | −0.113813 | ||||||||
\(910\) | 211.755 | 0.232698 | ||||||||
\(911\) | − | 1127.16i | − | 1.23728i | −0.785675 | − | 0.618639i | \(-0.787684\pi\) | ||
0.785675 | − | 0.618639i | \(-0.212316\pi\) | |||||||
\(912\) | 79.7457i | 0.0874405i | ||||||||
\(913\) | −1802.24 | −1.97398 | ||||||||
\(914\) | 993.100i | 1.08654i | ||||||||
\(915\) | 62.4607 | 0.0682631 | ||||||||
\(916\) | 387.274i | 0.422789i | ||||||||
\(917\) | 1853.67i | 2.02145i | ||||||||
\(918\) | − | 34.7401i | − | 0.0378432i | ||||||
\(919\) | − | 801.735i | − | 0.872400i | −0.899850 | − | 0.436200i | \(-0.856324\pi\) | ||
0.899850 | − | 0.436200i | \(-0.143676\pi\) | |||||||
\(920\) | 83.6311 | − | 119.020i | 0.0909034 | − | 0.129370i | ||||
\(921\) | 104.227 | 0.113167 | ||||||||
\(922\) | 149.027 | 0.161634 | ||||||||
\(923\) | −26.4823 | −0.0286916 | ||||||||
\(924\) | −424.261 | −0.459157 | ||||||||
\(925\) | 47.9786i | 0.0518688i | ||||||||
\(926\) | −395.972 | −0.427615 | ||||||||
\(927\) | 215.435i | 0.232401i | ||||||||
\(928\) | 50.2495 | 0.0541482 | ||||||||
\(929\) | 126.765 | 0.136453 | 0.0682267 | − | 0.997670i | \(-0.478266\pi\) | ||||
0.0682267 | + | 0.997670i | \(0.478266\pi\) | |||||||
\(930\) | − | 248.379i | − | 0.267074i | ||||||
\(931\) | − | 59.7505i | − | 0.0641788i | ||||||
\(932\) | 626.386 | 0.672088 | ||||||||
\(933\) | −477.493 | −0.511783 | ||||||||
\(934\) | − | 820.588i | − | 0.878574i | ||||||
\(935\) | − | 175.872i | − | 0.188099i | ||||||
\(936\) | −77.1855 | −0.0824632 | ||||||||
\(937\) | 267.683i | 0.285681i | 0.989746 | + | 0.142840i | \(0.0456236\pi\) | ||||
−0.989746 | + | 0.142840i | \(0.954376\pi\) | |||||||
\(938\) | 123.058 | 0.131192 | ||||||||
\(939\) | − | 192.161i | − | 0.204645i | ||||||
\(940\) | 138.665i | 0.147516i | ||||||||
\(941\) | − | 862.078i | − | 0.916130i | −0.888919 | − | 0.458065i | \(-0.848543\pi\) | ||
0.888919 | − | 0.458065i | \(-0.151457\pi\) | |||||||
\(942\) | − | 318.694i | − | 0.338316i | ||||||
\(943\) | −389.818 | − | 273.911i | −0.413381 | − | 0.290467i | ||||
\(944\) | −190.499 | −0.201800 | ||||||||
\(945\) | −85.5324 | −0.0905105 | ||||||||
\(946\) | −503.537 | −0.532281 | ||||||||
\(947\) | −1624.54 | −1.71546 | −0.857732 | − | 0.514097i | \(-0.828127\pi\) | ||||
−0.857732 | + | 0.514097i | \(0.828127\pi\) | |||||||
\(948\) | 129.677i | 0.136791i | ||||||||
\(949\) | 1241.41 | 1.30813 | ||||||||
\(950\) | 81.3902i | 0.0856738i | ||||||||
\(951\) | 893.636 | 0.939680 | ||||||||
\(952\) | −98.4334 | −0.103396 | ||||||||
\(953\) | 1336.93i | 1.40286i | 0.712738 | + | 0.701430i | \(0.247455\pi\) | ||||
−0.712738 | + | 0.701430i | \(0.752545\pi\) | |||||||
\(954\) | 299.963i | 0.314427i | ||||||||
\(955\) | 162.634 | 0.170297 | ||||||||
\(956\) | 423.273 | 0.442754 | ||||||||
\(957\) | 255.974i | 0.267476i | ||||||||
\(958\) | 671.804i | 0.701257i | ||||||||
\(959\) | 380.651 | 0.396925 | ||||||||
\(960\) | − | 30.9839i | − | 0.0322749i | ||||||
\(961\) | 1095.41 | 1.13986 | ||||||||
\(962\) | 123.442i | 0.128318i | ||||||||
\(963\) | − | 361.157i | − | 0.375033i | ||||||
\(964\) | 610.765i | 0.633574i | ||||||||
\(965\) | 76.2753i | 0.0790418i | ||||||||
\(966\) | 238.439 | − | 339.336i | 0.246831 | − | 0.351280i | ||||
\(967\) | −816.485 | −0.844348 | −0.422174 | − | 0.906515i | \(-0.638733\pi\) | ||||
−0.422174 | + | 0.906515i | \(0.638733\pi\) | |||||||
\(968\) | 440.654 | 0.455221 | ||||||||
\(969\) | −94.2500 | −0.0972652 | ||||||||
\(970\) | 221.569 | 0.228422 | ||||||||
\(971\) | 387.663i | 0.399241i | 0.979873 | + | 0.199621i | \(0.0639710\pi\) | ||||
−0.979873 | + | 0.199621i | \(0.936029\pi\) | |||||||
\(972\) | 31.1769 | 0.0320750 | ||||||||
\(973\) | − | 282.078i | − | 0.289905i | ||||||
\(974\) | 97.3509 | 0.0999496 | ||||||||
\(975\) | −78.7772 | −0.0807971 | ||||||||
\(976\) | 64.5092i | 0.0660955i | ||||||||
\(977\) | − | 1127.70i | − | 1.15425i | −0.816655 | − | 0.577126i | \(-0.804174\pi\) | ||
0.816655 | − | 0.577126i | \(-0.195826\pi\) | |||||||
\(978\) | −576.897 | −0.589874 | ||||||||
\(979\) | −181.980 | −0.185883 | ||||||||
\(980\) | 23.2150i | 0.0236888i | ||||||||
\(981\) | − | 347.754i | − | 0.354489i | ||||||
\(982\) | −669.700 | −0.681976 | ||||||||
\(983\) | − | 1302.78i | − | 1.32531i | −0.748923 | − | 0.662657i | \(-0.769429\pi\) | ||
0.748923 | − | 0.662657i | \(-0.230571\pi\) | |||||||
\(984\) | −101.479 | −0.103129 | ||||||||
\(985\) | − | 788.008i | − | 0.800008i | ||||||
\(986\) | 59.3890i | 0.0602322i | ||||||||
\(987\) | 395.345i | 0.400552i | ||||||||
\(988\) | 209.405i | 0.211948i | ||||||||
\(989\) | 282.993 | − | 402.744i | 0.286141 | − | 0.407223i | ||||
\(990\) | 157.834 | 0.159428 | ||||||||
\(991\) | 1394.73 | 1.40739 | 0.703696 | − | 0.710501i | \(-0.251532\pi\) | ||||
0.703696 | + | 0.710501i | \(0.251532\pi\) | |||||||
\(992\) | 256.525 | 0.258594 | ||||||||
\(993\) | 969.654 | 0.976489 | ||||||||
\(994\) | − | 30.3085i | − | 0.0304915i | ||||||
\(995\) | −8.89372 | −0.00893842 | ||||||||
\(996\) | − | 375.254i | − | 0.376761i | ||||||
\(997\) | −330.604 | −0.331599 | −0.165800 | − | 0.986159i | \(-0.553020\pi\) | ||||
−0.165800 | + | 0.986159i | \(0.553020\pi\) | |||||||
\(998\) | −1032.82 | −1.03489 | ||||||||
\(999\) | − | 49.8608i | − | 0.0499107i |
(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.c.a.91.9 | ✓ | 32 | |
3.2 | odd | 2 | 2070.3.c.b.91.27 | 32 | |||
23.22 | odd | 2 | inner | 690.3.c.a.91.16 | yes | 32 | |
69.68 | even | 2 | 2070.3.c.b.91.22 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.c.a.91.9 | ✓ | 32 | 1.1 | even | 1 | trivial | |
690.3.c.a.91.16 | yes | 32 | 23.22 | odd | 2 | inner | |
2070.3.c.b.91.22 | 32 | 69.68 | even | 2 | |||
2070.3.c.b.91.27 | 32 | 3.2 | odd | 2 |