Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,3,Mod(391,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, 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("735.391");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.h (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: | \(20.0272994305\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.523596960000.16 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 13x^{6} - 2x^{5} + 91x^{4} - 50x^{3} + 190x^{2} + 100x + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 391.7 | ||
Root | \(1.76021 + 3.04878i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 735.391 |
Dual form | 735.3.h.a.391.8 |
$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.52043 | 1.26021 | 0.630107 | − | 0.776508i | \(-0.283011\pi\) | ||||
0.630107 | + | 0.776508i | \(0.283011\pi\) | |||||||
\(3\) | − 1.73205i | − 0.577350i | ||||||||
\(4\) | 2.35256 | 0.588139 | ||||||||
\(5\) | 2.23607i | 0.447214i | ||||||||
\(6\) | − 4.36551i | − 0.727585i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4.15226 | −0.519033 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 5.63585i | 0.563585i | ||||||||
\(11\) | −8.72072 | −0.792793 | −0.396396 | − | 0.918079i | \(-0.629739\pi\) | ||||
−0.396396 | + | 0.918079i | \(0.629739\pi\) | |||||||
\(12\) | − 4.07475i | − 0.339562i | ||||||||
\(13\) | − 21.5286i | − 1.65605i | −0.560693 | − | 0.828024i | \(-0.689465\pi\) | ||||
0.560693 | − | 0.828024i | \(-0.310535\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.87298 | 0.258199 | ||||||||
\(16\) | −19.8757 | −1.24223 | ||||||||
\(17\) | − 21.6925i | − 1.27603i | −0.770025 | − | 0.638013i | \(-0.779756\pi\) | ||||
0.770025 | − | 0.638013i | \(-0.220244\pi\) | |||||||
\(18\) | −7.56128 | −0.420071 | ||||||||
\(19\) | 3.13605i | 0.165055i | 0.996589 | + | 0.0825276i | \(0.0262993\pi\) | ||||
−0.996589 | + | 0.0825276i | \(0.973701\pi\) | |||||||
\(20\) | 5.26047i | 0.263024i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −21.9799 | −0.999088 | ||||||||
\(23\) | 4.10842 | 0.178627 | 0.0893134 | − | 0.996004i | \(-0.471533\pi\) | ||||
0.0893134 | + | 0.996004i | \(0.471533\pi\) | |||||||
\(24\) | 7.19193i | 0.299664i | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | − 54.2613i | − 2.08697i | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −50.8583 | −1.75373 | −0.876867 | − | 0.480732i | \(-0.840371\pi\) | ||||
−0.876867 | + | 0.480732i | \(0.840371\pi\) | |||||||
\(30\) | 9.76157 | 0.325386 | ||||||||
\(31\) | − 39.1690i | − 1.26352i | −0.775166 | − | 0.631758i | \(-0.782334\pi\) | ||||
0.775166 | − | 0.631758i | \(-0.217666\pi\) | |||||||
\(32\) | −33.4862 | −1.04644 | ||||||||
\(33\) | 15.1047i | 0.457719i | ||||||||
\(34\) | − 54.6743i | − 1.60807i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −7.05767 | −0.196046 | ||||||||
\(37\) | 52.9812 | 1.43192 | 0.715962 | − | 0.698139i | \(-0.245988\pi\) | ||||
0.715962 | + | 0.698139i | \(0.245988\pi\) | |||||||
\(38\) | 7.90419i | 0.208005i | ||||||||
\(39\) | −37.2886 | −0.956119 | ||||||||
\(40\) | − 9.28475i | − 0.232119i | ||||||||
\(41\) | − 36.8122i | − 0.897857i | −0.893568 | − | 0.448929i | \(-0.851806\pi\) | ||||
0.893568 | − | 0.448929i | \(-0.148194\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 17.6504 | 0.410475 | 0.205238 | − | 0.978712i | \(-0.434203\pi\) | ||||
0.205238 | + | 0.978712i | \(0.434203\pi\) | |||||||
\(44\) | −20.5160 | −0.466272 | ||||||||
\(45\) | − 6.70820i | − 0.149071i | ||||||||
\(46\) | 10.3550 | 0.225108 | ||||||||
\(47\) | 4.03919i | 0.0859401i | 0.999076 | + | 0.0429701i | \(0.0136820\pi\) | ||||
−0.999076 | + | 0.0429701i | \(0.986318\pi\) | |||||||
\(48\) | 34.4257i | 0.717203i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −12.6021 | −0.252043 | ||||||||
\(51\) | −37.5724 | −0.736715 | ||||||||
\(52\) | − 50.6473i | − 0.973986i | ||||||||
\(53\) | 4.45186 | 0.0839973 | 0.0419986 | − | 0.999118i | \(-0.486627\pi\) | ||||
0.0419986 | + | 0.999118i | \(0.486627\pi\) | |||||||
\(54\) | 13.0965i | 0.242528i | ||||||||
\(55\) | − 19.5001i | − 0.354548i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.43180 | 0.0952947 | ||||||||
\(58\) | −128.185 | −2.21008 | ||||||||
\(59\) | 94.1118i | 1.59512i | 0.603243 | + | 0.797558i | \(0.293875\pi\) | ||||
−0.603243 | + | 0.797558i | \(0.706125\pi\) | |||||||
\(60\) | 9.11141 | 0.151857 | ||||||||
\(61\) | 73.1827i | 1.19972i | 0.800106 | + | 0.599858i | \(0.204776\pi\) | ||||
−0.800106 | + | 0.599858i | \(0.795224\pi\) | |||||||
\(62\) | − 98.7226i | − 1.59230i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.89677 | −0.0765121 | ||||||||
\(65\) | 48.1394 | 0.740607 | ||||||||
\(66\) | 38.0704i | 0.576824i | ||||||||
\(67\) | −100.532 | −1.50048 | −0.750241 | − | 0.661165i | \(-0.770062\pi\) | ||||
−0.750241 | + | 0.661165i | \(0.770062\pi\) | |||||||
\(68\) | − 51.0327i | − 0.750481i | ||||||||
\(69\) | − 7.11598i | − 0.103130i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −56.6975 | −0.798557 | −0.399278 | − | 0.916830i | \(-0.630739\pi\) | ||||
−0.399278 | + | 0.916830i | \(0.630739\pi\) | |||||||
\(72\) | 12.4568 | 0.173011 | ||||||||
\(73\) | 74.8295i | 1.02506i | 0.858669 | + | 0.512531i | \(0.171292\pi\) | ||||
−0.858669 | + | 0.512531i | \(0.828708\pi\) | |||||||
\(74\) | 133.535 | 1.80453 | ||||||||
\(75\) | 8.66025i | 0.115470i | ||||||||
\(76\) | 7.37773i | 0.0970754i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −93.9833 | −1.20491 | ||||||||
\(79\) | 28.9807 | 0.366844 | 0.183422 | − | 0.983034i | \(-0.441283\pi\) | ||||
0.183422 | + | 0.983034i | \(0.441283\pi\) | |||||||
\(80\) | − 44.4434i | − 0.555543i | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − 92.7824i | − 1.13149i | ||||||||
\(83\) | − 21.1116i | − 0.254357i | −0.991880 | − | 0.127179i | \(-0.959408\pi\) | ||||
0.991880 | − | 0.127179i | \(-0.0405921\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 48.5058 | 0.570657 | ||||||||
\(86\) | 44.4867 | 0.517287 | ||||||||
\(87\) | 88.0892i | 1.01252i | ||||||||
\(88\) | 36.2107 | 0.411486 | ||||||||
\(89\) | − 72.8692i | − 0.818755i | −0.912365 | − | 0.409378i | \(-0.865746\pi\) | ||||
0.912365 | − | 0.409378i | \(-0.134254\pi\) | |||||||
\(90\) | − 16.9075i | − 0.187862i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.66528 | 0.105057 | ||||||||
\(93\) | −67.8427 | −0.729491 | ||||||||
\(94\) | 10.1805i | 0.108303i | ||||||||
\(95\) | −7.01242 | −0.0738150 | ||||||||
\(96\) | 57.9998i | 0.604165i | ||||||||
\(97\) | − 73.7985i | − 0.760809i | −0.924820 | − | 0.380405i | \(-0.875785\pi\) | ||||
0.924820 | − | 0.380405i | \(-0.124215\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 26.1622 | 0.264264 | ||||||||
\(100\) | −11.7628 | −0.117628 | ||||||||
\(101\) | − 106.954i | − 1.05895i | −0.848327 | − | 0.529473i | \(-0.822390\pi\) | ||||
0.848327 | − | 0.529473i | \(-0.177610\pi\) | |||||||
\(102\) | −94.6986 | −0.928418 | ||||||||
\(103\) | − 21.5392i | − 0.209119i | −0.994519 | − | 0.104559i | \(-0.966657\pi\) | ||||
0.994519 | − | 0.104559i | \(-0.0333432\pi\) | |||||||
\(104\) | 89.3925i | 0.859543i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.2206 | 0.105855 | ||||||||
\(107\) | 89.6367 | 0.837726 | 0.418863 | − | 0.908049i | \(-0.362429\pi\) | ||||
0.418863 | + | 0.908049i | \(0.362429\pi\) | |||||||
\(108\) | 12.2242i | 0.113187i | ||||||||
\(109\) | 27.3501 | 0.250919 | 0.125459 | − | 0.992099i | \(-0.459960\pi\) | ||||
0.125459 | + | 0.992099i | \(0.459960\pi\) | |||||||
\(110\) | − 49.1486i | − 0.446806i | ||||||||
\(111\) | − 91.7661i | − 0.826722i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −92.3372 | −0.817144 | −0.408572 | − | 0.912726i | \(-0.633973\pi\) | ||||
−0.408572 | + | 0.912726i | \(0.633973\pi\) | |||||||
\(114\) | 13.6905 | 0.120092 | ||||||||
\(115\) | 9.18670i | 0.0798843i | ||||||||
\(116\) | −119.647 | −1.03144 | ||||||||
\(117\) | 64.5858i | 0.552016i | ||||||||
\(118\) | 237.202i | 2.01019i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −16.0817 | −0.134014 | ||||||||
\(121\) | −44.9491 | −0.371480 | ||||||||
\(122\) | 184.452i | 1.51190i | ||||||||
\(123\) | −63.7605 | −0.518378 | ||||||||
\(124\) | − 92.1473i | − 0.743123i | ||||||||
\(125\) | − 11.1803i | − 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 191.591 | 1.50859 | 0.754297 | − | 0.656534i | \(-0.227978\pi\) | ||||
0.754297 | + | 0.656534i | \(0.227978\pi\) | |||||||
\(128\) | 121.603 | 0.950023 | ||||||||
\(129\) | − 30.5715i | − 0.236988i | ||||||||
\(130\) | 121.332 | 0.933323 | ||||||||
\(131\) | − 58.8123i | − 0.448949i | −0.974480 | − | 0.224474i | \(-0.927933\pi\) | ||||
0.974480 | − | 0.224474i | \(-0.0720665\pi\) | |||||||
\(132\) | 35.5347i | 0.269202i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −253.384 | −1.89093 | ||||||||
\(135\) | −11.6190 | −0.0860663 | ||||||||
\(136\) | 90.0728i | 0.662300i | ||||||||
\(137\) | 165.914 | 1.21105 | 0.605526 | − | 0.795825i | \(-0.292963\pi\) | ||||
0.605526 | + | 0.795825i | \(0.292963\pi\) | |||||||
\(138\) | − 17.9353i | − 0.129966i | ||||||||
\(139\) | 139.625i | 1.00449i | 0.864724 | + | 0.502247i | \(0.167493\pi\) | ||||
−0.864724 | + | 0.502247i | \(0.832507\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.99607 | 0.0496176 | ||||||||
\(142\) | −142.902 | −1.00635 | ||||||||
\(143\) | 187.745i | 1.31290i | ||||||||
\(144\) | 59.6271 | 0.414077 | ||||||||
\(145\) | − 113.723i | − 0.784294i | ||||||||
\(146\) | 188.602i | 1.29180i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 124.641 | 0.842171 | ||||||||
\(149\) | −14.3372 | −0.0962230 | −0.0481115 | − | 0.998842i | \(-0.515320\pi\) | ||||
−0.0481115 | + | 0.998842i | \(0.515320\pi\) | |||||||
\(150\) | 21.8275i | 0.145517i | ||||||||
\(151\) | 212.374 | 1.40645 | 0.703226 | − | 0.710966i | \(-0.251742\pi\) | ||||
0.703226 | + | 0.710966i | \(0.251742\pi\) | |||||||
\(152\) | − 13.0217i | − 0.0856691i | ||||||||
\(153\) | 65.0774i | 0.425342i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 87.5845 | 0.565062 | ||||||||
\(156\) | −87.7236 | −0.562331 | ||||||||
\(157\) | − 242.918i | − 1.54725i | −0.633645 | − | 0.773624i | \(-0.718442\pi\) | ||||
0.633645 | − | 0.773624i | \(-0.281558\pi\) | |||||||
\(158\) | 73.0437 | 0.462302 | ||||||||
\(159\) | − 7.71084i | − 0.0484959i | ||||||||
\(160\) | − 74.8775i | − 0.467984i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 22.6838 | 0.140024 | ||||||||
\(163\) | 13.2346 | 0.0811936 | 0.0405968 | − | 0.999176i | \(-0.487074\pi\) | ||||
0.0405968 | + | 0.999176i | \(0.487074\pi\) | |||||||
\(164\) | − 86.6026i | − 0.528065i | ||||||||
\(165\) | −33.7752 | −0.204698 | ||||||||
\(166\) | − 53.2104i | − 0.320544i | ||||||||
\(167\) | − 212.616i | − 1.27315i | −0.771216 | − | 0.636574i | \(-0.780351\pi\) | ||||
0.771216 | − | 0.636574i | \(-0.219649\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −294.481 | −1.74249 | ||||||||
\(170\) | 122.255 | 0.719149 | ||||||||
\(171\) | − 9.40815i | − 0.0550184i | ||||||||
\(172\) | 41.5236 | 0.241416 | ||||||||
\(173\) | 248.787i | 1.43807i | 0.694972 | + | 0.719037i | \(0.255417\pi\) | ||||
−0.694972 | + | 0.719037i | \(0.744583\pi\) | |||||||
\(174\) | 222.022i | 1.27599i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 173.330 | 0.984832 | ||||||||
\(177\) | 163.006 | 0.920940 | ||||||||
\(178\) | − 183.662i | − 1.03181i | ||||||||
\(179\) | 55.2703 | 0.308773 | 0.154386 | − | 0.988011i | \(-0.450660\pi\) | ||||
0.154386 | + | 0.988011i | \(0.450660\pi\) | |||||||
\(180\) | − 15.7814i | − 0.0876746i | ||||||||
\(181\) | − 46.9001i | − 0.259117i | −0.991572 | − | 0.129558i | \(-0.958644\pi\) | ||||
0.991572 | − | 0.129558i | \(-0.0413559\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 126.756 | 0.692656 | ||||||||
\(184\) | −17.0592 | −0.0927132 | ||||||||
\(185\) | 118.470i | 0.640376i | ||||||||
\(186\) | −170.993 | −0.919315 | ||||||||
\(187\) | 189.174i | 1.01162i | ||||||||
\(188\) | 9.50241i | 0.0505447i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −17.6743 | −0.0930226 | ||||||||
\(191\) | −20.1123 | −0.105300 | −0.0526499 | − | 0.998613i | \(-0.516767\pi\) | ||||
−0.0526499 | + | 0.998613i | \(0.516767\pi\) | |||||||
\(192\) | 8.48146i | 0.0441743i | ||||||||
\(193\) | 28.7033 | 0.148722 | 0.0743609 | − | 0.997231i | \(-0.476308\pi\) | ||||
0.0743609 | + | 0.997231i | \(0.476308\pi\) | |||||||
\(194\) | − 186.004i | − 0.958783i | ||||||||
\(195\) | − 83.3800i | − 0.427589i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 224.436 | 1.13927 | 0.569636 | − | 0.821897i | \(-0.307084\pi\) | ||||
0.569636 | + | 0.821897i | \(0.307084\pi\) | |||||||
\(198\) | 65.9398 | 0.333029 | ||||||||
\(199\) | − 318.059i | − 1.59829i | −0.601140 | − | 0.799144i | \(-0.705287\pi\) | ||||
0.601140 | − | 0.799144i | \(-0.294713\pi\) | |||||||
\(200\) | 20.7613 | 0.103807 | ||||||||
\(201\) | 174.127i | 0.866303i | ||||||||
\(202\) | − 269.569i | − 1.33450i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −88.3913 | −0.433290 | ||||||||
\(205\) | 82.3145 | 0.401534 | ||||||||
\(206\) | − 54.2881i | − 0.263534i | ||||||||
\(207\) | −12.3252 | −0.0595423 | ||||||||
\(208\) | 427.896i | 2.05719i | ||||||||
\(209\) | − 27.3486i | − 0.130855i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 285.317 | 1.35221 | 0.676107 | − | 0.736804i | \(-0.263666\pi\) | ||||
0.676107 | + | 0.736804i | \(0.263666\pi\) | |||||||
\(212\) | 10.4732 | 0.0494021 | ||||||||
\(213\) | 98.2030i | 0.461047i | ||||||||
\(214\) | 225.923 | 1.05571 | ||||||||
\(215\) | 39.4676i | 0.183570i | ||||||||
\(216\) | − 21.5758i | − 0.0998880i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 68.9341 | 0.316211 | ||||||||
\(219\) | 129.608 | 0.591819 | ||||||||
\(220\) | − 45.8751i | − 0.208523i | ||||||||
\(221\) | −467.009 | −2.11316 | ||||||||
\(222\) | − 231.290i | − 1.04185i | ||||||||
\(223\) | − 57.0977i | − 0.256044i | −0.991771 | − | 0.128022i | \(-0.959137\pi\) | ||||
0.991771 | − | 0.128022i | \(-0.0408627\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.0000 | 0.0666667 | ||||||||
\(226\) | −232.729 | −1.02978 | ||||||||
\(227\) | − 182.656i | − 0.804651i | −0.915497 | − | 0.402325i | \(-0.868202\pi\) | ||||
0.915497 | − | 0.402325i | \(-0.131798\pi\) | |||||||
\(228\) | 12.7786 | 0.0560465 | ||||||||
\(229\) | 16.7832i | 0.0732890i | 0.999328 | + | 0.0366445i | \(0.0116669\pi\) | ||||
−0.999328 | + | 0.0366445i | \(0.988333\pi\) | |||||||
\(230\) | 23.1544i | 0.100671i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 211.177 | 0.910246 | ||||||||
\(233\) | −266.407 | −1.14338 | −0.571688 | − | 0.820471i | \(-0.693711\pi\) | ||||
−0.571688 | + | 0.820471i | \(0.693711\pi\) | |||||||
\(234\) | 162.784i | 0.695658i | ||||||||
\(235\) | −9.03189 | −0.0384336 | ||||||||
\(236\) | 221.403i | 0.938150i | ||||||||
\(237\) | − 50.1960i | − 0.211797i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −39.7012 | −0.166114 | −0.0830568 | − | 0.996545i | \(-0.526468\pi\) | ||||
−0.0830568 | + | 0.996545i | \(0.526468\pi\) | |||||||
\(240\) | −76.9783 | −0.320743 | ||||||||
\(241\) | 83.3574i | 0.345881i | 0.984932 | + | 0.172941i | \(0.0553269\pi\) | ||||
−0.984932 | + | 0.172941i | \(0.944673\pi\) | |||||||
\(242\) | −113.291 | −0.468144 | ||||||||
\(243\) | − 15.5885i | − 0.0641500i | ||||||||
\(244\) | 172.166i | 0.705600i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −160.704 | −0.653267 | ||||||||
\(247\) | 67.5148 | 0.273339 | ||||||||
\(248\) | 162.640i | 0.655807i | ||||||||
\(249\) | −36.5664 | −0.146853 | ||||||||
\(250\) | − 28.1792i | − 0.112717i | ||||||||
\(251\) | 111.464i | 0.444079i | 0.975038 | + | 0.222039i | \(0.0712713\pi\) | ||||
−0.975038 | + | 0.222039i | \(0.928729\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −35.8283 | −0.141614 | ||||||||
\(254\) | 482.892 | 1.90115 | ||||||||
\(255\) | − 84.0145i | − 0.329469i | ||||||||
\(256\) | 326.078 | 1.27374 | ||||||||
\(257\) | 222.907i | 0.867343i | 0.901071 | + | 0.433672i | \(0.142782\pi\) | ||||
−0.901071 | + | 0.433672i | \(0.857218\pi\) | |||||||
\(258\) | − 77.0531i | − 0.298656i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 113.251 | 0.435580 | ||||||||
\(261\) | 152.575 | 0.584578 | ||||||||
\(262\) | − 148.232i | − 0.565772i | ||||||||
\(263\) | −426.500 | −1.62167 | −0.810837 | − | 0.585272i | \(-0.800988\pi\) | ||||
−0.810837 | + | 0.585272i | \(0.800988\pi\) | |||||||
\(264\) | − 62.7188i | − 0.237571i | ||||||||
\(265\) | 9.95465i | 0.0375647i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −126.213 | −0.472709 | ||||||||
\(268\) | −236.508 | −0.882492 | ||||||||
\(269\) | − 59.4913i | − 0.221157i | −0.993867 | − | 0.110579i | \(-0.964730\pi\) | ||||
0.993867 | − | 0.110579i | \(-0.0352704\pi\) | |||||||
\(270\) | −29.2847 | −0.108462 | ||||||||
\(271\) | 54.4810i | 0.201037i | 0.994935 | + | 0.100518i | \(0.0320501\pi\) | ||||
−0.994935 | + | 0.100518i | \(0.967950\pi\) | |||||||
\(272\) | 431.153i | 1.58512i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 418.175 | 1.52618 | ||||||||
\(275\) | 43.6036 | 0.158559 | ||||||||
\(276\) | − 16.7407i | − 0.0606549i | ||||||||
\(277\) | −472.378 | −1.70534 | −0.852669 | − | 0.522452i | \(-0.825017\pi\) | ||||
−0.852669 | + | 0.522452i | \(0.825017\pi\) | |||||||
\(278\) | 351.914i | 1.26588i | ||||||||
\(279\) | 117.507i | 0.421172i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −534.544 | −1.90229 | −0.951146 | − | 0.308743i | \(-0.900092\pi\) | ||||
−0.951146 | + | 0.308743i | \(0.900092\pi\) | |||||||
\(282\) | 17.6331 | 0.0625287 | ||||||||
\(283\) | − 447.275i | − 1.58048i | −0.612799 | − | 0.790239i | \(-0.709957\pi\) | ||||
0.612799 | − | 0.790239i | \(-0.290043\pi\) | |||||||
\(284\) | −133.384 | −0.469662 | ||||||||
\(285\) | 12.1459i | 0.0426171i | ||||||||
\(286\) | 473.198i | 1.65454i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 100.459 | 0.348815 | ||||||||
\(289\) | −181.563 | −0.628245 | ||||||||
\(290\) | − 286.630i | − 0.988378i | ||||||||
\(291\) | −127.823 | −0.439254 | ||||||||
\(292\) | 176.040i | 0.602878i | ||||||||
\(293\) | 504.200i | 1.72082i | 0.509604 | + | 0.860409i | \(0.329792\pi\) | ||||
−0.509604 | + | 0.860409i | \(0.670208\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −210.440 | −0.713357 | ||||||||
\(296\) | −219.992 | −0.743216 | ||||||||
\(297\) | − 45.3142i | − 0.152573i | ||||||||
\(298\) | −36.1359 | −0.121262 | ||||||||
\(299\) | − 88.4485i | − 0.295814i | ||||||||
\(300\) | 20.3737i | 0.0679124i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 535.274 | 1.77243 | ||||||||
\(303\) | −185.249 | −0.611383 | ||||||||
\(304\) | − 62.3312i | − 0.205037i | ||||||||
\(305\) | −163.641 | −0.536529 | ||||||||
\(306\) | 164.023i | 0.536022i | ||||||||
\(307\) | − 398.792i | − 1.29900i | −0.760363 | − | 0.649499i | \(-0.774979\pi\) | ||||
0.760363 | − | 0.649499i | \(-0.225021\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −37.3070 | −0.120735 | ||||||||
\(310\) | 220.751 | 0.712098 | ||||||||
\(311\) | − 239.122i | − 0.768880i | −0.923150 | − | 0.384440i | \(-0.874395\pi\) | ||||
0.923150 | − | 0.384440i | \(-0.125605\pi\) | |||||||
\(312\) | 154.832 | 0.496257 | ||||||||
\(313\) | − 223.199i | − 0.713095i | −0.934277 | − | 0.356548i | \(-0.883954\pi\) | ||||
0.934277 | − | 0.356548i | \(-0.116046\pi\) | |||||||
\(314\) | − 612.257i | − 1.94986i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 68.1786 | 0.215755 | ||||||||
\(317\) | −286.014 | −0.902252 | −0.451126 | − | 0.892460i | \(-0.648978\pi\) | ||||
−0.451126 | + | 0.892460i | \(0.648978\pi\) | |||||||
\(318\) | − 19.4346i | − 0.0611152i | ||||||||
\(319\) | 443.521 | 1.39035 | ||||||||
\(320\) | − 10.9495i | − 0.0342172i | ||||||||
\(321\) | − 155.255i | − 0.483662i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 68.0286 | 0.210615 | ||||||||
\(324\) | 21.1730 | 0.0653488 | ||||||||
\(325\) | 107.643i | 0.331209i | ||||||||
\(326\) | 33.3568 | 0.102321 | ||||||||
\(327\) | − 47.3718i | − 0.144868i | ||||||||
\(328\) | 152.854i | 0.466018i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −85.1279 | −0.257963 | ||||||||
\(331\) | 539.024 | 1.62847 | 0.814236 | − | 0.580534i | \(-0.197156\pi\) | ||||
0.814236 | + | 0.580534i | \(0.197156\pi\) | |||||||
\(332\) | − 49.6663i | − 0.149597i | ||||||||
\(333\) | −158.944 | −0.477308 | ||||||||
\(334\) | − 535.883i | − 1.60444i | ||||||||
\(335\) | − 224.797i | − 0.671036i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 68.2484 | 0.202518 | 0.101259 | − | 0.994860i | \(-0.467713\pi\) | ||||
0.101259 | + | 0.994860i | \(0.467713\pi\) | |||||||
\(338\) | −742.218 | −2.19591 | ||||||||
\(339\) | 159.933i | 0.471778i | ||||||||
\(340\) | 114.113 | 0.335625 | ||||||||
\(341\) | 341.582i | 1.00171i | ||||||||
\(342\) | − 23.7126i | − 0.0693350i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −73.2893 | −0.213050 | ||||||||
\(345\) | 15.9118 | 0.0461212 | ||||||||
\(346\) | 627.049i | 1.81228i | ||||||||
\(347\) | 381.895 | 1.10056 | 0.550281 | − | 0.834980i | \(-0.314521\pi\) | ||||
0.550281 | + | 0.834980i | \(0.314521\pi\) | |||||||
\(348\) | 207.235i | 0.595502i | ||||||||
\(349\) | − 301.869i | − 0.864953i | −0.901645 | − | 0.432477i | \(-0.857640\pi\) | ||||
0.901645 | − | 0.432477i | \(-0.142360\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 111.866 | 0.318706 | ||||||||
\(352\) | 292.024 | 0.829613 | ||||||||
\(353\) | 128.045i | 0.362735i | 0.983415 | + | 0.181367i | \(0.0580523\pi\) | ||||
−0.983415 | + | 0.181367i | \(0.941948\pi\) | |||||||
\(354\) | 410.846 | 1.16058 | ||||||||
\(355\) | − 126.780i | − 0.357125i | ||||||||
\(356\) | − 171.429i | − 0.481542i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 139.305 | 0.389120 | ||||||||
\(359\) | −524.226 | −1.46024 | −0.730119 | − | 0.683320i | \(-0.760535\pi\) | ||||
−0.730119 | + | 0.683320i | \(0.760535\pi\) | |||||||
\(360\) | 27.8542i | 0.0773729i | ||||||||
\(361\) | 351.165 | 0.972757 | ||||||||
\(362\) | − 118.208i | − 0.326542i | ||||||||
\(363\) | 77.8541i | 0.214474i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −167.324 | −0.458421 | ||||||||
\(366\) | 319.480 | 0.872895 | ||||||||
\(367\) | 35.5881i | 0.0969704i | 0.998824 | + | 0.0484852i | \(0.0154394\pi\) | ||||
−0.998824 | + | 0.0484852i | \(0.984561\pi\) | |||||||
\(368\) | −81.6576 | −0.221896 | ||||||||
\(369\) | 110.436i | 0.299286i | ||||||||
\(370\) | 298.594i | 0.807011i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −159.604 | −0.429042 | ||||||||
\(373\) | −267.091 | −0.716063 | −0.358031 | − | 0.933710i | \(-0.616552\pi\) | ||||
−0.358031 | + | 0.933710i | \(0.616552\pi\) | |||||||
\(374\) | 476.799i | 1.27486i | ||||||||
\(375\) | −19.3649 | −0.0516398 | ||||||||
\(376\) | − 16.7718i | − 0.0446058i | ||||||||
\(377\) | 1094.91i | 2.90427i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −125.687 | −0.331627 | −0.165813 | − | 0.986157i | \(-0.553025\pi\) | ||||
−0.165813 | + | 0.986157i | \(0.553025\pi\) | |||||||
\(380\) | −16.4971 | −0.0434135 | ||||||||
\(381\) | − 331.846i | − 0.870987i | ||||||||
\(382\) | −50.6915 | −0.132700 | ||||||||
\(383\) | 356.520i | 0.930861i | 0.885084 | + | 0.465430i | \(0.154100\pi\) | ||||
−0.885084 | + | 0.465430i | \(0.845900\pi\) | |||||||
\(384\) | − 210.622i | − 0.548496i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 72.3446 | 0.187421 | ||||||||
\(387\) | −52.9513 | −0.136825 | ||||||||
\(388\) | − 173.615i | − 0.447462i | ||||||||
\(389\) | 446.632 | 1.14816 | 0.574078 | − | 0.818801i | \(-0.305361\pi\) | ||||
0.574078 | + | 0.818801i | \(0.305361\pi\) | |||||||
\(390\) | − 210.153i | − 0.538854i | ||||||||
\(391\) | − 89.1216i | − 0.227933i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −101.866 | −0.259201 | ||||||||
\(394\) | 565.676 | 1.43573 | ||||||||
\(395\) | 64.8027i | 0.164058i | ||||||||
\(396\) | 61.5479 | 0.155424 | ||||||||
\(397\) | − 606.320i | − 1.52725i | −0.645657 | − | 0.763627i | \(-0.723417\pi\) | ||||
0.645657 | − | 0.763627i | \(-0.276583\pi\) | |||||||
\(398\) | − 801.645i | − 2.01418i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 99.3785 | 0.248446 | ||||||||
\(401\) | −728.804 | −1.81747 | −0.908734 | − | 0.417377i | \(-0.862950\pi\) | ||||
−0.908734 | + | 0.417377i | \(0.862950\pi\) | |||||||
\(402\) | 438.874i | 1.09173i | ||||||||
\(403\) | −843.254 | −2.09244 | ||||||||
\(404\) | − 251.614i | − 0.622808i | ||||||||
\(405\) | 20.1246i | 0.0496904i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −462.034 | −1.13522 | ||||||||
\(408\) | 156.011 | 0.382379 | ||||||||
\(409\) | − 530.657i | − 1.29745i | −0.761023 | − | 0.648725i | \(-0.775302\pi\) | ||||
0.761023 | − | 0.648725i | \(-0.224698\pi\) | |||||||
\(410\) | 207.468 | 0.506019 | ||||||||
\(411\) | − 287.372i | − 0.699201i | ||||||||
\(412\) | − 50.6722i | − 0.122991i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −31.0649 | −0.0750360 | ||||||||
\(415\) | 47.2071 | 0.113752 | ||||||||
\(416\) | 720.912i | 1.73296i | ||||||||
\(417\) | 241.837 | 0.579945 | ||||||||
\(418\) | − 68.9302i | − 0.164905i | ||||||||
\(419\) | 282.637i | 0.674552i | 0.941406 | + | 0.337276i | \(0.109506\pi\) | ||||
−0.941406 | + | 0.337276i | \(0.890494\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 440.590 | 1.04653 | 0.523267 | − | 0.852169i | \(-0.324713\pi\) | ||||
0.523267 | + | 0.852169i | \(0.324713\pi\) | |||||||
\(422\) | 719.121 | 1.70408 | ||||||||
\(423\) | − 12.1176i | − 0.0286467i | ||||||||
\(424\) | −18.4853 | −0.0435974 | ||||||||
\(425\) | 108.462i | 0.255205i | ||||||||
\(426\) | 247.514i | 0.581018i | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 210.875 | 0.492700 | ||||||||
\(429\) | 325.184 | 0.758004 | ||||||||
\(430\) | 99.4752i | 0.231338i | ||||||||
\(431\) | −127.435 | −0.295672 | −0.147836 | − | 0.989012i | \(-0.547231\pi\) | ||||
−0.147836 | + | 0.989012i | \(0.547231\pi\) | |||||||
\(432\) | − 103.277i | − 0.239068i | ||||||||
\(433\) | − 433.284i | − 1.00066i | −0.865836 | − | 0.500328i | \(-0.833213\pi\) | ||||
0.865836 | − | 0.500328i | \(-0.166787\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −196.973 | −0.452812 | ||||||||
\(436\) | 64.3427 | 0.147575 | ||||||||
\(437\) | 12.8842i | 0.0294833i | ||||||||
\(438\) | 326.669 | 0.745819 | ||||||||
\(439\) | 63.2288i | 0.144029i | 0.997404 | + | 0.0720146i | \(0.0229428\pi\) | ||||
−0.997404 | + | 0.0720146i | \(0.977057\pi\) | |||||||
\(440\) | 80.9697i | 0.184022i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1177.06 | −2.66303 | ||||||||
\(443\) | 438.379 | 0.989570 | 0.494785 | − | 0.869016i | \(-0.335247\pi\) | ||||
0.494785 | + | 0.869016i | \(0.335247\pi\) | |||||||
\(444\) | − 215.885i | − 0.486227i | ||||||||
\(445\) | 162.941 | 0.366159 | ||||||||
\(446\) | − 143.911i | − 0.322670i | ||||||||
\(447\) | 24.8328i | 0.0555544i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 214.986 | 0.478810 | 0.239405 | − | 0.970920i | \(-0.423048\pi\) | ||||
0.239405 | + | 0.970920i | \(0.423048\pi\) | |||||||
\(450\) | 37.8064 | 0.0840143 | ||||||||
\(451\) | 321.028i | 0.711815i | ||||||||
\(452\) | −217.228 | −0.480594 | ||||||||
\(453\) | − 367.843i | − 0.812016i | ||||||||
\(454\) | − 460.371i | − 1.01403i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −22.5543 | −0.0494611 | ||||||||
\(457\) | −241.199 | −0.527789 | −0.263894 | − | 0.964552i | \(-0.585007\pi\) | ||||
−0.263894 | + | 0.964552i | \(0.585007\pi\) | |||||||
\(458\) | 42.3008i | 0.0923598i | ||||||||
\(459\) | 112.717 | 0.245572 | ||||||||
\(460\) | 21.6122i | 0.0469831i | ||||||||
\(461\) | − 343.383i | − 0.744865i | −0.928059 | − | 0.372432i | \(-0.878524\pi\) | ||||
0.928059 | − | 0.372432i | \(-0.121476\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 74.7714 | 0.161493 | 0.0807467 | − | 0.996735i | \(-0.474270\pi\) | ||||
0.0807467 | + | 0.996735i | \(0.474270\pi\) | |||||||
\(464\) | 1010.84 | 2.17854 | ||||||||
\(465\) | − 151.701i | − 0.326238i | ||||||||
\(466\) | −671.459 | −1.44090 | ||||||||
\(467\) | 356.190i | 0.762720i | 0.924427 | + | 0.381360i | \(0.124544\pi\) | ||||
−0.924427 | + | 0.381360i | \(0.875456\pi\) | |||||||
\(468\) | 151.942i | 0.324662i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −22.7642 | −0.0484345 | ||||||||
\(471\) | −420.746 | −0.893304 | ||||||||
\(472\) | − 390.777i | − 0.827918i | ||||||||
\(473\) | −153.925 | −0.325422 | ||||||||
\(474\) | − 126.515i | − 0.266910i | ||||||||
\(475\) | − 15.6803i | − 0.0330111i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.3556 | −0.0279991 | ||||||||
\(478\) | −100.064 | −0.209339 | ||||||||
\(479\) | 373.751i | 0.780274i | 0.920757 | + | 0.390137i | \(0.127572\pi\) | ||||
−0.920757 | + | 0.390137i | \(0.872428\pi\) | |||||||
\(480\) | −129.692 | −0.270191 | ||||||||
\(481\) | − 1140.61i | − 2.37133i | ||||||||
\(482\) | 210.096i | 0.435884i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −105.745 | −0.218482 | ||||||||
\(485\) | 165.019 | 0.340244 | ||||||||
\(486\) | − 39.2896i | − 0.0808428i | ||||||||
\(487\) | 777.563 | 1.59664 | 0.798319 | − | 0.602235i | \(-0.205723\pi\) | ||||
0.798319 | + | 0.602235i | \(0.205723\pi\) | |||||||
\(488\) | − 303.874i | − 0.622692i | ||||||||
\(489\) | − 22.9229i | − 0.0468772i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 458.794 | 0.934407 | 0.467203 | − | 0.884150i | \(-0.345262\pi\) | ||||
0.467203 | + | 0.884150i | \(0.345262\pi\) | |||||||
\(492\) | −150.000 | −0.304878 | ||||||||
\(493\) | 1103.24i | 2.23781i | ||||||||
\(494\) | 170.166 | 0.344466 | ||||||||
\(495\) | 58.5004i | 0.118183i | ||||||||
\(496\) | 778.511i | 1.56958i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −92.1631 | −0.185066 | ||||||||
\(499\) | 635.543 | 1.27363 | 0.636817 | − | 0.771015i | \(-0.280251\pi\) | ||||
0.636817 | + | 0.771015i | \(0.280251\pi\) | |||||||
\(500\) | − 26.3024i | − 0.0526047i | ||||||||
\(501\) | −368.261 | −0.735052 | ||||||||
\(502\) | 280.936i | 0.559634i | ||||||||
\(503\) | 10.6561i | 0.0211852i | 0.999944 | + | 0.0105926i | \(0.00337179\pi\) | ||||
−0.999944 | + | 0.0105926i | \(0.996628\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 239.156 | 0.473575 | ||||||||
\(506\) | −90.3027 | −0.178464 | ||||||||
\(507\) | 510.056i | 1.00603i | ||||||||
\(508\) | 450.729 | 0.887262 | ||||||||
\(509\) | − 815.315i | − 1.60180i | −0.598799 | − | 0.800899i | \(-0.704355\pi\) | ||||
0.598799 | − | 0.800899i | \(-0.295645\pi\) | |||||||
\(510\) | − 211.753i | − 0.415201i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 335.445 | 0.655167 | ||||||||
\(513\) | −16.2954 | −0.0317649 | ||||||||
\(514\) | 561.822i | 1.09304i | ||||||||
\(515\) | 48.1632 | 0.0935207 | ||||||||
\(516\) | − 71.9211i | − 0.139382i | ||||||||
\(517\) | − 35.2246i | − 0.0681327i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 430.911 | 0.830273 | ||||||||
\(520\) | −199.888 | −0.384399 | ||||||||
\(521\) | − 443.325i | − 0.850911i | −0.904979 | − | 0.425456i | \(-0.860114\pi\) | ||||
0.904979 | − | 0.425456i | \(-0.139886\pi\) | |||||||
\(522\) | 384.554 | 0.736694 | ||||||||
\(523\) | 634.102i | 1.21243i | 0.795300 | + | 0.606216i | \(0.207313\pi\) | ||||
−0.795300 | + | 0.606216i | \(0.792687\pi\) | |||||||
\(524\) | − 138.359i | − 0.264044i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1074.96 | −2.04366 | ||||||||
\(527\) | −849.672 | −1.61228 | ||||||||
\(528\) | − 300.217i | − 0.568593i | ||||||||
\(529\) | −512.121 | −0.968092 | ||||||||
\(530\) | 25.0900i | 0.0473396i | ||||||||
\(531\) | − 282.335i | − 0.531705i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −792.515 | −1.48689 | ||||||||
\(534\) | −318.111 | −0.595714 | ||||||||
\(535\) | 200.434i | 0.374643i | ||||||||
\(536\) | 417.437 | 0.778799 | ||||||||
\(537\) | − 95.7310i | − 0.178270i | ||||||||
\(538\) | − 149.944i | − 0.278706i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −27.3342 | −0.0506189 | ||||||||
\(541\) | −175.150 | −0.323752 | −0.161876 | − | 0.986811i | \(-0.551755\pi\) | ||||
−0.161876 | + | 0.986811i | \(0.551755\pi\) | |||||||
\(542\) | 137.315i | 0.253349i | ||||||||
\(543\) | −81.2333 | −0.149601 | ||||||||
\(544\) | 726.398i | 1.33529i | ||||||||
\(545\) | 61.1568i | 0.112214i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −773.543 | −1.41416 | −0.707078 | − | 0.707136i | \(-0.749987\pi\) | ||||
−0.707078 | + | 0.707136i | \(0.749987\pi\) | |||||||
\(548\) | 390.322 | 0.712267 | ||||||||
\(549\) | − 219.548i | − 0.399905i | ||||||||
\(550\) | 109.900 | 0.199818 | ||||||||
\(551\) | − 159.494i | − 0.289463i | ||||||||
\(552\) | 29.5474i | 0.0535280i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1190.60 | −2.14909 | ||||||||
\(555\) | 205.195 | 0.369721 | ||||||||
\(556\) | 328.475i | 0.590782i | ||||||||
\(557\) | −756.528 | −1.35822 | −0.679110 | − | 0.734037i | \(-0.737634\pi\) | ||||
−0.679110 | + | 0.734037i | \(0.737634\pi\) | |||||||
\(558\) | 296.168i | 0.530767i | ||||||||
\(559\) | − 379.989i | − 0.679766i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 327.659 | 0.584062 | ||||||||
\(562\) | −1347.28 | −2.39729 | ||||||||
\(563\) | − 520.983i | − 0.925370i | −0.886523 | − | 0.462685i | \(-0.846886\pi\) | ||||
0.886523 | − | 0.462685i | \(-0.153114\pi\) | |||||||
\(564\) | 16.4587 | 0.0291820 | ||||||||
\(565\) | − 206.472i | − 0.365438i | ||||||||
\(566\) | − 1127.32i | − 1.99174i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 235.423 | 0.414477 | ||||||||
\(569\) | −183.066 | −0.321733 | −0.160867 | − | 0.986976i | \(-0.551429\pi\) | ||||
−0.160867 | + | 0.986976i | \(0.551429\pi\) | |||||||
\(570\) | 30.6128i | 0.0537066i | ||||||||
\(571\) | 997.600 | 1.74711 | 0.873555 | − | 0.486725i | \(-0.161808\pi\) | ||||
0.873555 | + | 0.486725i | \(0.161808\pi\) | |||||||
\(572\) | 441.680i | 0.772169i | ||||||||
\(573\) | 34.8355i | 0.0607949i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −20.5421 | −0.0357254 | ||||||||
\(576\) | 14.6903 | 0.0255040 | ||||||||
\(577\) | 322.317i | 0.558608i | 0.960203 | + | 0.279304i | \(0.0901038\pi\) | ||||
−0.960203 | + | 0.279304i | \(0.909896\pi\) | |||||||
\(578\) | −457.616 | −0.791723 | ||||||||
\(579\) | − 49.7156i | − 0.0858645i | ||||||||
\(580\) | − 267.539i | − 0.461274i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −322.168 | −0.553553 | ||||||||
\(583\) | −38.8234 | −0.0665924 | ||||||||
\(584\) | − 310.712i | − 0.532041i | ||||||||
\(585\) | −144.418 | −0.246869 | ||||||||
\(586\) | 1270.80i | 2.16860i | ||||||||
\(587\) | 406.391i | 0.692318i | 0.938176 | + | 0.346159i | \(0.112514\pi\) | ||||
−0.938176 | + | 0.346159i | \(0.887486\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 122.836 | 0.208550 | ||||||||
\(590\) | −530.400 | −0.898983 | ||||||||
\(591\) | − 388.735i | − 0.657759i | ||||||||
\(592\) | −1053.04 | −1.77878 | ||||||||
\(593\) | − 385.309i | − 0.649763i | −0.945755 | − | 0.324881i | \(-0.894676\pi\) | ||||
0.945755 | − | 0.324881i | \(-0.105324\pi\) | |||||||
\(594\) | − 114.211i | − 0.192275i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −33.7291 | −0.0565925 | ||||||||
\(597\) | −550.895 | −0.922772 | ||||||||
\(598\) | − 222.928i | − 0.372789i | ||||||||
\(599\) | −896.544 | −1.49673 | −0.748367 | − | 0.663285i | \(-0.769162\pi\) | ||||
−0.748367 | + | 0.663285i | \(0.769162\pi\) | |||||||
\(600\) | − 35.9597i | − 0.0599328i | ||||||||
\(601\) | 599.296i | 0.997166i | 0.866842 | + | 0.498583i | \(0.166146\pi\) | ||||
−0.866842 | + | 0.498583i | \(0.833854\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 301.597 | 0.500161 | ||||||||
\(604\) | 499.622 | 0.827189 | ||||||||
\(605\) | − 100.509i | − 0.166131i | ||||||||
\(606\) | −466.907 | −0.770474 | ||||||||
\(607\) | 492.970i | 0.812142i | 0.913841 | + | 0.406071i | \(0.133101\pi\) | ||||
−0.913841 | + | 0.406071i | \(0.866899\pi\) | |||||||
\(608\) | − 105.014i | − 0.172721i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −412.446 | −0.676142 | ||||||||
\(611\) | 86.9581 | 0.142321 | ||||||||
\(612\) | 153.098i | 0.250160i | ||||||||
\(613\) | −140.964 | −0.229958 | −0.114979 | − | 0.993368i | \(-0.536680\pi\) | ||||
−0.114979 | + | 0.993368i | \(0.536680\pi\) | |||||||
\(614\) | − 1005.13i | − 1.63701i | ||||||||
\(615\) | − 142.573i | − 0.231826i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 61.9853 | 0.100462 | 0.0502312 | − | 0.998738i | \(-0.484004\pi\) | ||||
0.0502312 | + | 0.998738i | \(0.484004\pi\) | |||||||
\(618\) | −94.0297 | −0.152152 | ||||||||
\(619\) | − 634.457i | − 1.02497i | −0.858696 | − | 0.512485i | \(-0.828725\pi\) | ||||
0.858696 | − | 0.512485i | \(-0.171275\pi\) | |||||||
\(620\) | 206.048 | 0.332335 | ||||||||
\(621\) | 21.3480i | 0.0343767i | ||||||||
\(622\) | − 602.689i | − 0.968953i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 741.138 | 1.18772 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | − 562.557i | − 0.898653i | ||||||||
\(627\) | −47.3692 | −0.0755489 | ||||||||
\(628\) | − 571.478i | − 0.909997i | ||||||||
\(629\) | − 1149.29i | − 1.82717i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 93.3216 | 0.147895 | 0.0739474 | − | 0.997262i | \(-0.476440\pi\) | ||||
0.0739474 | + | 0.997262i | \(0.476440\pi\) | |||||||
\(632\) | −120.335 | −0.190404 | ||||||||
\(633\) | − 494.184i | − 0.780701i | ||||||||
\(634\) | −720.878 | −1.13703 | ||||||||
\(635\) | 428.411i | 0.674663i | ||||||||
\(636\) | − 18.1402i | − 0.0285223i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1117.86 | 1.75214 | ||||||||
\(639\) | 170.093 | 0.266186 | ||||||||
\(640\) | 271.912i | 0.424863i | ||||||||
\(641\) | 307.921 | 0.480377 | 0.240188 | − | 0.970726i | \(-0.422791\pi\) | ||||
0.240188 | + | 0.970726i | \(0.422791\pi\) | |||||||
\(642\) | − 391.310i | − 0.609517i | ||||||||
\(643\) | − 296.519i | − 0.461150i | −0.973055 | − | 0.230575i | \(-0.925939\pi\) | ||||
0.973055 | − | 0.230575i | \(-0.0740607\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 68.3599 | 0.105984 | ||||||||
\(646\) | 171.461 | 0.265420 | ||||||||
\(647\) | 235.244i | 0.363592i | 0.983336 | + | 0.181796i | \(0.0581911\pi\) | ||||
−0.983336 | + | 0.181796i | \(0.941809\pi\) | |||||||
\(648\) | −37.3704 | −0.0576703 | ||||||||
\(649\) | − 820.723i | − 1.26460i | ||||||||
\(650\) | 271.307i | 0.417395i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 31.1350 | 0.0477531 | ||||||||
\(653\) | 297.646 | 0.455813 | 0.227906 | − | 0.973683i | \(-0.426812\pi\) | ||||
0.227906 | + | 0.973683i | \(0.426812\pi\) | |||||||
\(654\) | − 119.397i | − 0.182565i | ||||||||
\(655\) | 131.508 | 0.200776 | ||||||||
\(656\) | 731.668i | 1.11535i | ||||||||
\(657\) | − 224.488i | − 0.341687i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −127.740 | −0.193839 | −0.0969197 | − | 0.995292i | \(-0.530899\pi\) | ||||
−0.0969197 | + | 0.995292i | \(0.530899\pi\) | |||||||
\(660\) | −79.4580 | −0.120391 | ||||||||
\(661\) | − 951.023i | − 1.43876i | −0.694614 | − | 0.719382i | \(-0.744425\pi\) | ||||
0.694614 | − | 0.719382i | \(-0.255575\pi\) | |||||||
\(662\) | 1358.57 | 2.05222 | ||||||||
\(663\) | 808.882i | 1.22003i | ||||||||
\(664\) | 87.6611i | 0.132020i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −400.606 | −0.601510 | ||||||||
\(667\) | −208.947 | −0.313264 | ||||||||
\(668\) | − 500.190i | − 0.748788i | ||||||||
\(669\) | −98.8962 | −0.147827 | ||||||||
\(670\) | − 566.585i | − 0.845649i | ||||||||
\(671\) | − 638.206i | − 0.951126i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1003.39 | −1.49092 | −0.745460 | − | 0.666550i | \(-0.767770\pi\) | ||||
−0.745460 | + | 0.666550i | \(0.767770\pi\) | |||||||
\(674\) | 172.015 | 0.255215 | ||||||||
\(675\) | − 25.9808i | − 0.0384900i | ||||||||
\(676\) | −692.783 | −1.02483 | ||||||||
\(677\) | − 471.815i | − 0.696920i | −0.937324 | − | 0.348460i | \(-0.886705\pi\) | ||||
0.937324 | − | 0.348460i | \(-0.113295\pi\) | |||||||
\(678\) | 403.099i | 0.594541i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −201.409 | −0.296190 | ||||||||
\(681\) | −316.369 | −0.464565 | ||||||||
\(682\) | 860.932i | 1.26236i | ||||||||
\(683\) | 417.228 | 0.610876 | 0.305438 | − | 0.952212i | \(-0.401197\pi\) | ||||
0.305438 | + | 0.952212i | \(0.401197\pi\) | |||||||
\(684\) | − 22.1332i | − 0.0323585i | ||||||||
\(685\) | 370.995i | 0.541599i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.0693 | 0.0423134 | ||||||||
\(688\) | −350.815 | −0.509905 | ||||||||
\(689\) | − 95.8423i | − 0.139103i | ||||||||
\(690\) | 40.1046 | 0.0581226 | ||||||||
\(691\) | − 185.799i | − 0.268884i | −0.990921 | − | 0.134442i | \(-0.957076\pi\) | ||||
0.990921 | − | 0.134442i | \(-0.0429242\pi\) | |||||||
\(692\) | 585.285i | 0.845787i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 962.538 | 1.38694 | ||||||||
\(695\) | −312.210 | −0.449223 | ||||||||
\(696\) | − 365.770i | − 0.525531i | ||||||||
\(697\) | −798.546 | −1.14569 | ||||||||
\(698\) | − 760.838i | − 1.09003i | ||||||||
\(699\) | 461.430i | 0.660129i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1034.80 | 1.47618 | 0.738089 | − | 0.674704i | \(-0.235729\pi\) | ||||
0.738089 | + | 0.674704i | \(0.235729\pi\) | |||||||
\(702\) | 281.950 | 0.401638 | ||||||||
\(703\) | 166.152i | 0.236347i | ||||||||
\(704\) | 42.7034 | 0.0606582 | ||||||||
\(705\) | 15.6437i | 0.0221896i | ||||||||
\(706\) | 322.729i | 0.457123i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 383.482 | 0.541641 | ||||||||
\(709\) | −216.642 | −0.305560 | −0.152780 | − | 0.988260i | \(-0.548823\pi\) | ||||
−0.152780 | + | 0.988260i | \(0.548823\pi\) | |||||||
\(710\) | − 319.539i | − 0.450054i | ||||||||
\(711\) | −86.9420 | −0.122281 | ||||||||
\(712\) | 302.572i | 0.424961i | ||||||||
\(713\) | − 160.923i | − 0.225698i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −419.811 | −0.587148 | ||||||||
\(716\) | 130.027 | 0.181601 | ||||||||
\(717\) | 68.7644i | 0.0959057i | ||||||||
\(718\) | −1321.27 | −1.84021 | ||||||||
\(719\) | − 0.375796i | 0 0.000522665i | −1.00000 | 0.000261332i | \(-0.999917\pi\) | |||||
1.00000 | 0.000261332i | \(-8.31847e-5\pi\) | ||||||||
\(720\) | 133.330i | 0.185181i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 885.086 | 1.22588 | ||||||||
\(723\) | 144.379 | 0.199695 | ||||||||
\(724\) | − 110.335i | − 0.152397i | ||||||||
\(725\) | 254.292 | 0.350747 | ||||||||
\(726\) | 196.226i | 0.270283i | ||||||||
\(727\) | 174.857i | 0.240518i | 0.992743 | + | 0.120259i | \(0.0383726\pi\) | ||||
−0.992743 | + | 0.120259i | \(0.961627\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | −421.727 | −0.577709 | ||||||||
\(731\) | − 382.881i | − 0.523778i | ||||||||
\(732\) | 298.201 | 0.407378 | ||||||||
\(733\) | 852.412i | 1.16291i | 0.813579 | + | 0.581454i | \(0.197516\pi\) | ||||
−0.813579 | + | 0.581454i | \(0.802484\pi\) | |||||||
\(734\) | 89.6973i | 0.122203i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −137.575 | −0.186923 | ||||||||
\(737\) | 876.714 | 1.18957 | ||||||||
\(738\) | 278.347i | 0.377164i | ||||||||
\(739\) | −1168.25 | −1.58086 | −0.790428 | − | 0.612555i | \(-0.790142\pi\) | ||||
−0.790428 | + | 0.612555i | \(0.790142\pi\) | |||||||
\(740\) | 278.706i | 0.376630i | ||||||||
\(741\) | − 116.939i | − 0.157813i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −558.877 | −0.752190 | −0.376095 | − | 0.926581i | \(-0.622733\pi\) | ||||
−0.376095 | + | 0.926581i | \(0.622733\pi\) | |||||||
\(744\) | 281.701 | 0.378630 | ||||||||
\(745\) | − 32.0590i | − 0.0430322i | ||||||||
\(746\) | −673.184 | −0.902392 | ||||||||
\(747\) | 63.3349i | 0.0847857i | ||||||||
\(748\) | 445.042i | 0.594976i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −48.8079 | −0.0650772 | ||||||||
\(751\) | 1261.31 | 1.67950 | 0.839752 | − | 0.542970i | \(-0.182700\pi\) | ||||
0.839752 | + | 0.542970i | \(0.182700\pi\) | |||||||
\(752\) | − 80.2817i | − 0.106758i | ||||||||
\(753\) | 193.061 | 0.256389 | ||||||||
\(754\) | 2759.64i | 3.66000i | ||||||||
\(755\) | 474.883i | 0.628985i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1269.13 | −1.67652 | −0.838262 | − | 0.545268i | \(-0.816428\pi\) | ||||
−0.838262 | + | 0.545268i | \(0.816428\pi\) | |||||||
\(758\) | −316.784 | −0.417921 | ||||||||
\(759\) | 62.0565i | 0.0817609i | ||||||||
\(760\) | 29.1174 | 0.0383124 | ||||||||
\(761\) | 182.117i | 0.239313i | 0.992815 | + | 0.119656i | \(0.0381793\pi\) | ||||
−0.992815 | + | 0.119656i | \(0.961821\pi\) | |||||||
\(762\) | − 836.394i | − 1.09763i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −47.3152 | −0.0619309 | ||||||||
\(765\) | −145.517 | −0.190219 | ||||||||
\(766\) | 898.582i | 1.17308i | ||||||||
\(767\) | 2026.10 | 2.64159 | ||||||||
\(768\) | − 564.784i | − 0.735396i | ||||||||
\(769\) | 810.237i | 1.05362i | 0.849982 | + | 0.526812i | \(0.176613\pi\) | ||||
−0.849982 | + | 0.526812i | \(0.823387\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 386.087 | 0.500761 | ||||||||
\(772\) | 67.5261 | 0.0874690 | ||||||||
\(773\) | 245.365i | 0.317419i | 0.987325 | + | 0.158709i | \(0.0507333\pi\) | ||||
−0.987325 | + | 0.158709i | \(0.949267\pi\) | |||||||
\(774\) | −133.460 | −0.172429 | ||||||||
\(775\) | 195.845i | 0.252703i | ||||||||
\(776\) | 306.431i | 0.394885i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1125.70 | 1.44692 | ||||||||
\(779\) | 115.445 | 0.148196 | ||||||||
\(780\) | − 196.156i | − 0.251482i | ||||||||
\(781\) | 494.443 | 0.633090 | ||||||||
\(782\) | − 224.625i | − 0.287244i | ||||||||
\(783\) | − 264.268i | − 0.337506i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 543.181 | 0.691950 | ||||||||
\(786\) | −256.746 | −0.326648 | ||||||||
\(787\) | − 430.726i | − 0.547302i | −0.961829 | − | 0.273651i | \(-0.911769\pi\) | ||||
0.961829 | − | 0.273651i | \(-0.0882312\pi\) | |||||||
\(788\) | 527.999 | 0.670050 | ||||||||
\(789\) | 738.720i | 0.936274i | ||||||||
\(790\) | 163.331i | 0.206748i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −108.632 | −0.137162 | ||||||||
\(793\) | 1575.52 | 1.98679 | ||||||||
\(794\) | − 1528.19i | − 1.92467i | ||||||||
\(795\) | 17.2420 | 0.0216880 | ||||||||
\(796\) | − 748.252i | − 0.940015i | ||||||||
\(797\) | 1137.61i | 1.42737i | 0.700468 | + | 0.713684i | \(0.252975\pi\) | ||||
−0.700468 | + | 0.713684i | \(0.747025\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 87.6199 | 0.109662 | ||||||||
\(800\) | 167.431 | 0.209289 | ||||||||
\(801\) | 218.608i | 0.272918i | ||||||||
\(802\) | −1836.90 | −2.29040 | ||||||||
\(803\) | − 652.567i | − 0.812661i | ||||||||
\(804\) | 409.643i | 0.509507i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2125.36 | −2.63692 | ||||||||
\(807\) | −103.042 | −0.127685 | ||||||||
\(808\) | 444.100i | 0.549628i | ||||||||
\(809\) | 910.672 | 1.12568 | 0.562838 | − | 0.826567i | \(-0.309710\pi\) | ||||
0.562838 | + | 0.826567i | \(0.309710\pi\) | |||||||
\(810\) | 50.7226i | 0.0626205i | ||||||||
\(811\) | − 546.361i | − 0.673688i | −0.941560 | − | 0.336844i | \(-0.890640\pi\) | ||||
0.941560 | − | 0.336844i | \(-0.109360\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 94.3638 | 0.116069 | ||||||||
\(814\) | −1164.52 | −1.43062 | ||||||||
\(815\) | 29.5934i | 0.0363109i | ||||||||
\(816\) | 746.779 | 0.915170 | ||||||||
\(817\) | 55.3527i | 0.0677511i | ||||||||
\(818\) | − 1337.48i | − 1.63507i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 193.649 | 0.236158 | ||||||||
\(821\) | 644.300 | 0.784775 | 0.392388 | − | 0.919800i | \(-0.371649\pi\) | ||||
0.392388 | + | 0.919800i | \(0.371649\pi\) | |||||||
\(822\) | − 724.300i | − 0.881143i | ||||||||
\(823\) | 769.321 | 0.934777 | 0.467388 | − | 0.884052i | \(-0.345195\pi\) | ||||
0.467388 | + | 0.884052i | \(0.345195\pi\) | |||||||
\(824\) | 89.4365i | 0.108539i | ||||||||
\(825\) | − 75.5236i | − 0.0915438i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 715.404 | 0.865060 | 0.432530 | − | 0.901620i | \(-0.357621\pi\) | ||||
0.432530 | + | 0.901620i | \(0.357621\pi\) | |||||||
\(828\) | −28.9958 | −0.0350191 | ||||||||
\(829\) | 78.8630i | 0.0951303i | 0.998868 | + | 0.0475651i | \(0.0151462\pi\) | ||||
−0.998868 | + | 0.0475651i | \(0.984854\pi\) | |||||||
\(830\) | 118.982 | 0.143352 | ||||||||
\(831\) | 818.184i | 0.984577i | ||||||||
\(832\) | 105.421i | 0.126708i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 609.533 | 0.730855 | ||||||||
\(835\) | 475.423 | 0.569369 | ||||||||
\(836\) | − 64.3391i | − 0.0769607i | ||||||||
\(837\) | 203.528 | 0.243164 | ||||||||
\(838\) | 712.367i | 0.850080i | ||||||||
\(839\) | 165.698i | 0.197494i | 0.995113 | + | 0.0987471i | \(0.0314835\pi\) | ||||
−0.995113 | + | 0.0987471i | \(0.968517\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1745.57 | 2.07559 | ||||||||
\(842\) | 1110.48 | 1.31886 | ||||||||
\(843\) | 925.857i | 1.09829i | ||||||||
\(844\) | 671.224 | 0.795289 | ||||||||
\(845\) | − 658.480i | − 0.779266i | ||||||||
\(846\) | − 30.5414i | − 0.0361010i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −88.4838 | −0.104344 | ||||||||
\(849\) | −774.703 | −0.912489 | ||||||||
\(850\) | 273.371i | 0.321613i | ||||||||
\(851\) | 217.669 | 0.255780 | ||||||||
\(852\) | 231.028i | 0.271160i | ||||||||
\(853\) | 1066.17i | 1.24991i | 0.780661 | + | 0.624955i | \(0.214883\pi\) | ||||
−0.780661 | + | 0.624955i | \(0.785117\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 21.0373 | 0.0246050 | ||||||||
\(856\) | −372.195 | −0.434808 | ||||||||
\(857\) | 222.650i | 0.259802i | 0.991527 | + | 0.129901i | \(0.0414659\pi\) | ||||
−0.991527 | + | 0.129901i | \(0.958534\pi\) | |||||||
\(858\) | 819.602 | 0.955247 | ||||||||
\(859\) | − 1516.66i | − 1.76561i | −0.469740 | − | 0.882805i | \(-0.655652\pi\) | ||||
0.469740 | − | 0.882805i | \(-0.344348\pi\) | |||||||
\(860\) | 92.8497i | 0.107965i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −321.190 | −0.372610 | ||||||||
\(863\) | 138.036 | 0.159949 | 0.0799745 | − | 0.996797i | \(-0.474516\pi\) | ||||
0.0799745 | + | 0.996797i | \(0.474516\pi\) | |||||||
\(864\) | − 173.999i | − 0.201388i | ||||||||
\(865\) | −556.304 | −0.643126 | ||||||||
\(866\) | − 1092.06i | − 1.26104i | ||||||||
\(867\) | 314.476i | 0.362717i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −252.732 | −0.290831 | ||||||||
\(870\) | −496.457 | −0.570640 | ||||||||
\(871\) | 2164.32i | 2.48487i | ||||||||
\(872\) | −113.565 | −0.130235 | ||||||||
\(873\) | 221.396i | 0.253603i | ||||||||
\(874\) | 32.4737i | 0.0371552i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 304.911 | 0.348072 | ||||||||
\(877\) | −617.621 | −0.704243 | −0.352121 | − | 0.935954i | \(-0.614540\pi\) | ||||
−0.352121 | + | 0.935954i | \(0.614540\pi\) | |||||||
\(878\) | 159.364i | 0.181508i | ||||||||
\(879\) | 873.300 | 0.993515 | ||||||||
\(880\) | 387.579i | 0.440430i | ||||||||
\(881\) | − 425.629i | − 0.483120i | −0.970386 | − | 0.241560i | \(-0.922341\pi\) | ||||
0.970386 | − | 0.241560i | \(-0.0776591\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 295.270 | 0.334394 | 0.167197 | − | 0.985923i | \(-0.446528\pi\) | ||||
0.167197 | + | 0.985923i | \(0.446528\pi\) | |||||||
\(884\) | −1098.66 | −1.24283 | ||||||||
\(885\) | 364.494i | 0.411857i | ||||||||
\(886\) | 1104.90 | 1.24707 | ||||||||
\(887\) | 1689.77i | 1.90504i | 0.304481 | + | 0.952519i | \(0.401517\pi\) | ||||
−0.304481 | + | 0.952519i | \(0.598483\pi\) | |||||||
\(888\) | 381.037i | 0.429096i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 410.680 | 0.461438 | ||||||||
\(891\) | −78.4865 | −0.0880881 | ||||||||
\(892\) | − 134.326i | − 0.150589i | ||||||||
\(893\) | −12.6671 | −0.0141849 | ||||||||
\(894\) | 62.5893i | 0.0700104i | ||||||||
\(895\) | 123.588i | 0.138087i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −153.197 | −0.170788 | ||||||||
\(898\) | 541.856 | 0.603403 | ||||||||
\(899\) | 1992.07i | 2.21587i | ||||||||
\(900\) | 35.2883 | 0.0392093 | ||||||||
\(901\) | − 96.5717i | − 0.107183i | ||||||||
\(902\) | 809.129i | 0.897039i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 383.409 | 0.424124 | ||||||||
\(905\) | 104.872 | 0.115880 | ||||||||
\(906\) | − 927.122i | − 1.02331i | ||||||||
\(907\) | 442.075 | 0.487404 | 0.243702 | − | 0.969850i | \(-0.421638\pi\) | ||||
0.243702 | + | 0.969850i | \(0.421638\pi\) | |||||||
\(908\) | − 429.708i | − 0.473246i | ||||||||
\(909\) | 320.861i | 0.352982i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 998.378 | 1.09591 | 0.547957 | − | 0.836507i | \(-0.315406\pi\) | ||||
0.547957 | + | 0.836507i | \(0.315406\pi\) | |||||||
\(912\) | −107.961 | −0.118378 | ||||||||
\(913\) | 184.109i | 0.201653i | ||||||||
\(914\) | −607.926 | −0.665127 | ||||||||
\(915\) | 283.435i | 0.309765i | ||||||||
\(916\) | 39.4834i | 0.0431041i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 284.096 | 0.309473 | ||||||||
\(919\) | 309.594 | 0.336881 | 0.168441 | − | 0.985712i | \(-0.446127\pi\) | ||||
0.168441 | + | 0.985712i | \(0.446127\pi\) | |||||||
\(920\) | − 38.1456i | − 0.0414626i | ||||||||
\(921\) | −690.728 | −0.749976 | ||||||||
\(922\) | − 865.471i | − 0.938689i | ||||||||
\(923\) | 1220.62i | 1.32245i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −264.906 | −0.286385 | ||||||||
\(926\) | 188.456 | 0.203516 | ||||||||
\(927\) | 64.6177i | 0.0697062i | ||||||||
\(928\) | 1703.05 | 1.83519 | ||||||||
\(929\) | 511.843i | 0.550961i | 0.961307 | + | 0.275480i | \(0.0888369\pi\) | ||||
−0.961307 | + | 0.275480i | \(0.911163\pi\) | |||||||
\(930\) | − 382.351i | − 0.411130i | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −626.737 | −0.672464 | ||||||||
\(933\) | −414.171 | −0.443913 | ||||||||
\(934\) | 897.752i | 0.961190i | ||||||||
\(935\) | −423.006 | −0.452412 | ||||||||
\(936\) | − 268.177i | − 0.286514i | ||||||||
\(937\) | 592.935i | 0.632801i | 0.948626 | + | 0.316401i | \(0.102474\pi\) | ||||
−0.948626 | + | 0.316401i | \(0.897526\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −386.592 | −0.411706 | ||||||||
\(940\) | −21.2480 | −0.0226043 | ||||||||
\(941\) | − 634.459i | − 0.674240i | −0.941462 | − | 0.337120i | \(-0.890547\pi\) | ||||
0.941462 | − | 0.337120i | \(-0.109453\pi\) | |||||||
\(942\) | −1060.46 | −1.12575 | ||||||||
\(943\) | − 151.240i | − 0.160381i | ||||||||
\(944\) | − 1870.54i | − 1.98150i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −387.956 | −0.410101 | ||||||||
\(947\) | 659.609 | 0.696525 | 0.348263 | − | 0.937397i | \(-0.386772\pi\) | ||||
0.348263 | + | 0.937397i | \(0.386772\pi\) | |||||||
\(948\) | − 118.089i | − 0.124566i | ||||||||
\(949\) | 1610.97 | 1.69755 | ||||||||
\(950\) | − 39.5209i | − 0.0416010i | ||||||||
\(951\) | 495.391i | 0.520916i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −615.571 | −0.645930 | −0.322965 | − | 0.946411i | \(-0.604680\pi\) | ||||
−0.322965 | + | 0.946411i | \(0.604680\pi\) | |||||||
\(954\) | −33.6617 | −0.0352849 | ||||||||
\(955\) | − 44.9724i | − 0.0470915i | ||||||||
\(956\) | −93.3992 | −0.0976979 | ||||||||
\(957\) | − 768.201i | − 0.802718i | ||||||||
\(958\) | 942.013i | 0.983312i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −18.9651 | −0.0197553 | ||||||||
\(961\) | −573.211 | −0.596473 | ||||||||
\(962\) | − 2874.83i | − 2.98839i | ||||||||
\(963\) | −268.910 | −0.279242 | ||||||||
\(964\) | 196.103i | 0.203426i | ||||||||
\(965\) | 64.1825i | 0.0665104i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 386.702 | 0.399899 | 0.199949 | − | 0.979806i | \(-0.435922\pi\) | ||||
0.199949 | + | 0.979806i | \(0.435922\pi\) | |||||||
\(968\) | 186.640 | 0.192810 | ||||||||
\(969\) | − 117.829i | − 0.121599i | ||||||||
\(970\) | 415.917 | 0.428781 | ||||||||
\(971\) | − 562.498i | − 0.579298i | −0.957133 | − | 0.289649i | \(-0.906461\pi\) | ||||
0.957133 | − | 0.289649i | \(-0.0935386\pi\) | |||||||
\(972\) | − 36.6727i | − 0.0377291i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1959.79 | 2.01211 | ||||||||
\(975\) | 186.443 | 0.191224 | ||||||||
\(976\) | − 1454.56i | − 1.49033i | ||||||||
\(977\) | 712.083 | 0.728846 | 0.364423 | − | 0.931234i | \(-0.381266\pi\) | ||||
0.364423 | + | 0.931234i | \(0.381266\pi\) | |||||||
\(978\) | − 57.7756i | − 0.0590753i | ||||||||
\(979\) | 635.472i | 0.649103i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −82.0504 | −0.0836396 | ||||||||
\(982\) | 1156.36 | 1.17755 | ||||||||
\(983\) | 1228.81i | 1.25006i | 0.780599 | + | 0.625032i | \(0.214914\pi\) | ||||
−0.780599 | + | 0.625032i | \(0.785086\pi\) | |||||||
\(984\) | 264.751 | 0.269055 | ||||||||
\(985\) | 501.855i | 0.509498i | ||||||||
\(986\) | 2780.64i | 2.82012i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 158.832 | 0.160761 | ||||||||
\(989\) | 72.5153 | 0.0733219 | ||||||||
\(990\) | 147.446i | 0.148935i | ||||||||
\(991\) | −1242.50 | −1.25378 | −0.626892 | − | 0.779107i | \(-0.715673\pi\) | ||||
−0.626892 | + | 0.779107i | \(0.715673\pi\) | |||||||
\(992\) | 1311.62i | 1.32220i | ||||||||
\(993\) | − 933.617i | − 0.940199i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 711.202 | 0.714776 | ||||||||
\(996\) | −86.0246 | −0.0863701 | ||||||||
\(997\) | − 801.766i | − 0.804178i | −0.915601 | − | 0.402089i | \(-0.868284\pi\) | ||||
0.915601 | − | 0.402089i | \(-0.131716\pi\) | |||||||
\(998\) | 1601.84 | 1.60505 | ||||||||
\(999\) | 275.298i | 0.275574i |
(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 | 735.3.h.a.391.7 | 8 | ||
7.4 | even | 3 | 105.3.n.a.61.1 | yes | 8 | ||
7.5 | odd | 6 | 105.3.n.a.31.1 | ✓ | 8 | ||
7.6 | odd | 2 | inner | 735.3.h.a.391.8 | 8 | ||
21.5 | even | 6 | 315.3.w.a.136.4 | 8 | |||
21.11 | odd | 6 | 315.3.w.a.271.4 | 8 | |||
35.4 | even | 6 | 525.3.o.l.376.4 | 8 | |||
35.12 | even | 12 | 525.3.s.h.199.7 | 16 | |||
35.18 | odd | 12 | 525.3.s.h.124.7 | 16 | |||
35.19 | odd | 6 | 525.3.o.l.451.4 | 8 | |||
35.32 | odd | 12 | 525.3.s.h.124.2 | 16 | |||
35.33 | even | 12 | 525.3.s.h.199.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.n.a.31.1 | ✓ | 8 | 7.5 | odd | 6 | ||
105.3.n.a.61.1 | yes | 8 | 7.4 | even | 3 | ||
315.3.w.a.136.4 | 8 | 21.5 | even | 6 | |||
315.3.w.a.271.4 | 8 | 21.11 | odd | 6 | |||
525.3.o.l.376.4 | 8 | 35.4 | even | 6 | |||
525.3.o.l.451.4 | 8 | 35.19 | odd | 6 | |||
525.3.s.h.124.2 | 16 | 35.32 | odd | 12 | |||
525.3.s.h.124.7 | 16 | 35.18 | odd | 12 | |||
525.3.s.h.199.2 | 16 | 35.33 | even | 12 | |||
525.3.s.h.199.7 | 16 | 35.12 | even | 12 | |||
735.3.h.a.391.7 | 8 | 1.1 | even | 1 | trivial | ||
735.3.h.a.391.8 | 8 | 7.6 | odd | 2 | inner |