Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(364,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.364");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.b (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: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + x^{10} + 34 x^{9} - 123 x^{8} - 20 x^{7} + 516 x^{6} - 668 x^{5} - 67 x^{4} + 3848 x^{3} + 6697 x^{2} + 4398 x + 1089 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 364.2 | ||
Root | \(1.15541 + 2.37379i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.364 |
Dual form | 605.2.b.h.364.11 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.60777i | − | 1.84397i | −0.387227 | − | 0.921984i | \(-0.626567\pi\) | ||
0.387227 | − | 0.921984i | \(-0.373433\pi\) | |||||||
\(3\) | 2.13980i | 1.23542i | 0.786407 | + | 0.617708i | \(0.211939\pi\) | ||||
−0.786407 | + | 0.617708i | \(0.788061\pi\) | |||||||
\(4\) | −4.80044 | −2.40022 | ||||||||
\(5\) | −2.11084 | − | 0.737808i | −0.943996 | − | 0.329958i | ||||
\(6\) | 5.58011 | 2.27807 | ||||||||
\(7\) | − | 0.988879i | − | 0.373761i | −0.982383 | − | 0.186881i | \(-0.940162\pi\) | ||
0.982383 | − | 0.186881i | \(-0.0598377\pi\) | |||||||
\(8\) | 7.30289i | 2.58196i | ||||||||
\(9\) | −1.57876 | −0.526255 | ||||||||
\(10\) | −1.92403 | + | 5.50457i | −0.608431 | + | 1.74070i | ||||
\(11\) | 0 | 0 | ||||||||
\(12\) | − | 10.2720i | − | 2.96527i | ||||||
\(13\) | 3.07624i | 0.853196i | 0.904441 | + | 0.426598i | \(0.140288\pi\) | ||||
−0.904441 | + | 0.426598i | \(0.859712\pi\) | |||||||
\(14\) | −2.57876 | −0.689204 | ||||||||
\(15\) | 1.57876 | − | 4.51678i | 0.407635 | − | 1.16623i | ||||
\(16\) | 9.44335 | 2.36084 | ||||||||
\(17\) | 1.61889i | 0.392638i | 0.980540 | + | 0.196319i | \(0.0628988\pi\) | ||||
−0.980540 | + | 0.196319i | \(0.937101\pi\) | |||||||
\(18\) | 4.11705i | 0.970397i | ||||||||
\(19\) | 6.58256 | 1.51014 | 0.755071 | − | 0.655643i | \(-0.227602\pi\) | ||||
0.755071 | + | 0.655643i | \(0.227602\pi\) | |||||||
\(20\) | 10.1330 | + | 3.54180i | 2.26580 | + | 0.791971i | ||||
\(21\) | 2.11601 | 0.461751 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.18097i | 1.08031i | 0.841566 | + | 0.540154i | \(0.181634\pi\) | ||||
−0.841566 | + | 0.540154i | \(0.818366\pi\) | |||||||
\(24\) | −15.6268 | −3.18980 | ||||||||
\(25\) | 3.91128 | + | 3.11479i | 0.782256 | + | 0.622957i | ||||
\(26\) | 8.02212 | 1.57327 | ||||||||
\(27\) | 3.04117i | 0.585273i | ||||||||
\(28\) | 4.74705i | 0.897109i | ||||||||
\(29\) | 7.31216 | 1.35783 | 0.678917 | − | 0.734215i | \(-0.262450\pi\) | ||||
0.678917 | + | 0.734215i | \(0.262450\pi\) | |||||||
\(30\) | −11.7787 | − | 4.11705i | −2.15049 | − | 0.751666i | ||||
\(31\) | −2.64291 | −0.474681 | −0.237341 | − | 0.971426i | \(-0.576276\pi\) | ||||
−0.237341 | + | 0.971426i | \(0.576276\pi\) | |||||||
\(32\) | − | 10.0203i | − | 1.77135i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.22168 | 0.724012 | ||||||||
\(35\) | −0.729602 | + | 2.08736i | −0.123325 | + | 0.352829i | ||||
\(36\) | 7.57876 | 1.26313 | ||||||||
\(37\) | − | 2.80399i | − | 0.460974i | −0.973075 | − | 0.230487i | \(-0.925968\pi\) | ||
0.973075 | − | 0.230487i | \(-0.0740319\pi\) | |||||||
\(38\) | − | 17.1658i | − | 2.78466i | ||||||
\(39\) | −6.58256 | −1.05405 | ||||||||
\(40\) | 5.38813 | − | 15.4152i | 0.851938 | − | 2.43736i | ||||
\(41\) | −1.38641 | −0.216520 | −0.108260 | − | 0.994123i | \(-0.534528\pi\) | ||||
−0.108260 | + | 0.994123i | \(0.534528\pi\) | |||||||
\(42\) | − | 5.51805i | − | 0.851454i | ||||||
\(43\) | 3.18585i | 0.485837i | 0.970047 | + | 0.242919i | \(0.0781048\pi\) | ||||
−0.970047 | + | 0.242919i | \(0.921895\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.33252 | + | 1.16482i | 0.496782 | + | 0.173642i | ||||
\(46\) | 13.5108 | 1.99205 | ||||||||
\(47\) | 2.13980i | 0.312123i | 0.987747 | + | 0.156061i | \(0.0498797\pi\) | ||||
−0.987747 | + | 0.156061i | \(0.950120\pi\) | |||||||
\(48\) | 20.2069i | 2.91662i | ||||||||
\(49\) | 6.02212 | 0.860303 | ||||||||
\(50\) | 8.12263 | − | 10.1997i | 1.14871 | − | 1.44246i | ||||
\(51\) | −3.46410 | −0.485071 | ||||||||
\(52\) | − | 14.7673i | − | 2.04786i | ||||||
\(53\) | − | 2.37698i | − | 0.326503i | −0.986584 | − | 0.163252i | \(-0.947802\pi\) | ||
0.986584 | − | 0.163252i | \(-0.0521982\pi\) | |||||||
\(54\) | 7.93065 | 1.07923 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.22168 | 0.965037 | ||||||||
\(57\) | 14.0854i | 1.86566i | ||||||||
\(58\) | − | 19.0684i | − | 2.50380i | ||||||
\(59\) | −12.2438 | −1.59401 | −0.797003 | − | 0.603975i | \(-0.793583\pi\) | ||||
−0.797003 | + | 0.603975i | \(0.793583\pi\) | |||||||
\(60\) | −7.57876 | + | 21.6825i | −0.978414 | + | 2.79921i | ||||
\(61\) | 1.00245 | 0.128350 | 0.0641752 | − | 0.997939i | \(-0.479558\pi\) | ||||
0.0641752 | + | 0.997939i | \(0.479558\pi\) | |||||||
\(62\) | 6.89210i | 0.875297i | ||||||||
\(63\) | 1.56121i | 0.196693i | ||||||||
\(64\) | −7.24380 | −0.905475 | ||||||||
\(65\) | 2.26967 | − | 6.49345i | 0.281519 | − | 0.805414i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.84499i | 1.20276i | 0.798964 | + | 0.601379i | \(0.205382\pi\) | ||||
−0.798964 | + | 0.601379i | \(0.794618\pi\) | |||||||
\(68\) | − | 7.77137i | − | 0.942417i | ||||||
\(69\) | −11.0863 | −1.33463 | ||||||||
\(70\) | 5.44335 | + | 1.90263i | 0.650605 | + | 0.227408i | ||||
\(71\) | −0.243796 | −0.0289333 | −0.0144666 | − | 0.999895i | \(-0.504605\pi\) | ||||
−0.0144666 | + | 0.999895i | \(0.504605\pi\) | |||||||
\(72\) | − | 11.5295i | − | 1.35877i | ||||||
\(73\) | 13.6688i | 1.59982i | 0.600122 | + | 0.799908i | \(0.295119\pi\) | ||||
−0.600122 | + | 0.799908i | \(0.704881\pi\) | |||||||
\(74\) | −7.31216 | −0.850021 | ||||||||
\(75\) | −6.66503 | + | 8.36938i | −0.769612 | + | 0.966412i | ||||
\(76\) | −31.5992 | −3.62467 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 17.1658i | 1.94364i | ||||||||
\(79\) | 7.69612 | 0.865881 | 0.432940 | − | 0.901423i | \(-0.357476\pi\) | ||||
0.432940 | + | 0.901423i | \(0.357476\pi\) | |||||||
\(80\) | −19.9334 | − | 6.96738i | −2.22862 | − | 0.778977i | ||||
\(81\) | −11.2438 | −1.24931 | ||||||||
\(82\) | 3.61542i | 0.399256i | ||||||||
\(83\) | − | 5.95515i | − | 0.653662i | −0.945083 | − | 0.326831i | \(-0.894019\pi\) | ||
0.945083 | − | 0.326831i | \(-0.105981\pi\) | |||||||
\(84\) | −10.1578 | −1.10830 | ||||||||
\(85\) | 1.19443 | − | 3.41721i | 0.129554 | − | 0.370648i | ||||
\(86\) | 8.30795 | 0.895869 | ||||||||
\(87\) | 15.6466i | 1.67749i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.00000 | −0.953998 | −0.476999 | − | 0.878904i | \(-0.658275\pi\) | ||||
−0.476999 | + | 0.878904i | \(0.658275\pi\) | |||||||
\(90\) | 3.03759 | − | 8.69042i | 0.320190 | − | 0.916051i | ||||
\(91\) | 3.04203 | 0.318891 | ||||||||
\(92\) | − | 24.8710i | − | 2.59298i | ||||||
\(93\) | − | 5.65532i | − | 0.586429i | ||||||
\(94\) | 5.58011 | 0.575544 | ||||||||
\(95\) | −13.8947 | − | 4.85666i | −1.42557 | − | 0.498283i | ||||
\(96\) | 21.4414 | 2.18836 | ||||||||
\(97\) | − | 12.7389i | − | 1.29344i | −0.762727 | − | 0.646721i | \(-0.776140\pi\) | ||
0.762727 | − | 0.646721i | \(-0.223860\pi\) | |||||||
\(98\) | − | 15.7043i | − | 1.58637i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −18.7759 | − | 14.9523i | −1.87759 | − | 1.49523i | ||||
\(101\) | −15.2811 | −1.52053 | −0.760264 | − | 0.649614i | \(-0.774931\pi\) | ||||
−0.760264 | + | 0.649614i | \(0.774931\pi\) | |||||||
\(102\) | 9.03357i | 0.894456i | ||||||||
\(103\) | 8.13220i | 0.801290i | 0.916233 | + | 0.400645i | \(0.131214\pi\) | ||||
−0.916233 | + | 0.400645i | \(0.868786\pi\) | |||||||
\(104\) | −22.4655 | −2.20292 | ||||||||
\(105\) | −4.46655 | − | 1.56121i | −0.435891 | − | 0.152358i | ||||
\(106\) | −6.19860 | −0.602061 | ||||||||
\(107\) | − | 6.62096i | − | 0.640072i | −0.947405 | − | 0.320036i | \(-0.896305\pi\) | ||
0.947405 | − | 0.320036i | \(-0.103695\pi\) | |||||||
\(108\) | − | 14.5989i | − | 1.40478i | ||||||
\(109\) | 2.84561 | 0.272560 | 0.136280 | − | 0.990670i | \(-0.456485\pi\) | ||||
0.136280 | + | 0.990670i | \(0.456485\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.00000 | 0.569495 | ||||||||
\(112\) | − | 9.33833i | − | 0.882390i | ||||||
\(113\) | 17.7400i | 1.66884i | 0.551129 | + | 0.834420i | \(0.314197\pi\) | ||||
−0.551129 | + | 0.834420i | \(0.685803\pi\) | |||||||
\(114\) | 36.7314 | 3.44021 | ||||||||
\(115\) | 3.82256 | − | 10.9362i | 0.356456 | − | 1.01981i | ||||
\(116\) | −35.1016 | −3.25910 | ||||||||
\(117\) | − | 4.85666i | − | 0.448998i | ||||||
\(118\) | 31.9290i | 2.93930i | ||||||||
\(119\) | 1.60088 | 0.146753 | ||||||||
\(120\) | 32.9856 | + | 11.5295i | 3.01116 | + | 1.05250i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 2.61415i | − | 0.236674i | ||||||
\(123\) | − | 2.96664i | − | 0.267493i | ||||||
\(124\) | 12.6872 | 1.13934 | ||||||||
\(125\) | −5.95797 | − | 9.46058i | −0.532897 | − | 0.846180i | ||||
\(126\) | 4.07126 | 0.362697 | ||||||||
\(127\) | 17.2712i | 1.53257i | 0.642498 | + | 0.766287i | \(0.277898\pi\) | ||||
−0.642498 | + | 0.766287i | \(0.722102\pi\) | |||||||
\(128\) | − | 1.15041i | − | 0.101683i | ||||||
\(129\) | −6.81709 | −0.600212 | ||||||||
\(130\) | −16.9334 | − | 5.91878i | −1.48516 | − | 0.519111i | ||||
\(131\) | 5.12335 | 0.447629 | 0.223815 | − | 0.974632i | \(-0.428149\pi\) | ||||
0.223815 | + | 0.974632i | \(0.428149\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 6.50935i | − | 0.564432i | ||||||
\(134\) | 25.6734 | 2.21785 | ||||||||
\(135\) | 2.24380 | − | 6.41941i | 0.193115 | − | 0.552495i | ||||
\(136\) | −11.8226 | −1.01378 | ||||||||
\(137\) | 7.27817i | 0.621816i | 0.950440 | + | 0.310908i | \(0.100633\pi\) | ||||
−0.950440 | + | 0.310908i | \(0.899367\pi\) | |||||||
\(138\) | 28.9104i | 2.46102i | ||||||||
\(139\) | 11.5059 | 0.975915 | 0.487957 | − | 0.872867i | \(-0.337742\pi\) | ||||
0.487957 | + | 0.872867i | \(0.337742\pi\) | |||||||
\(140\) | 3.50241 | − | 10.0203i | 0.296008 | − | 0.846867i | ||||
\(141\) | −4.57876 | −0.385601 | ||||||||
\(142\) | 0.635763i | 0.0533521i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −14.9088 | −1.24240 | ||||||||
\(145\) | −15.4348 | − | 5.39497i | −1.28179 | − | 0.448028i | ||||
\(146\) | 35.6451 | 2.95001 | ||||||||
\(147\) | 12.8862i | 1.06283i | ||||||||
\(148\) | 13.4604i | 1.10644i | ||||||||
\(149\) | 10.3195 | 0.845407 | 0.422703 | − | 0.906268i | \(-0.361081\pi\) | ||||
0.422703 | + | 0.906268i | \(0.361081\pi\) | |||||||
\(150\) | 21.8254 | + | 17.3808i | 1.78203 | + | 1.41914i | ||||
\(151\) | 14.9700 | 1.21824 | 0.609119 | − | 0.793079i | \(-0.291523\pi\) | ||||
0.609119 | + | 0.793079i | \(0.291523\pi\) | |||||||
\(152\) | 48.0717i | 3.89913i | ||||||||
\(153\) | − | 2.55584i | − | 0.206627i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.57876 | + | 1.94996i | 0.448097 | + | 0.156625i | ||||
\(156\) | 31.5992 | 2.52996 | ||||||||
\(157\) | − | 18.0671i | − | 1.44191i | −0.692980 | − | 0.720957i | \(-0.743703\pi\) | ||
0.692980 | − | 0.720957i | \(-0.256297\pi\) | |||||||
\(158\) | − | 20.0697i | − | 1.59666i | ||||||
\(159\) | 5.08627 | 0.403367 | ||||||||
\(160\) | −7.39303 | + | 21.1512i | −0.584470 | + | 1.67215i | ||||
\(161\) | 5.12335 | 0.403777 | ||||||||
\(162\) | 29.3212i | 2.30369i | ||||||||
\(163\) | 21.4028i | 1.67639i | 0.545367 | + | 0.838197i | \(0.316390\pi\) | ||||
−0.545367 | + | 0.838197i | \(0.683610\pi\) | |||||||
\(164\) | 6.65536 | 0.519696 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.5296 | −1.20533 | ||||||||
\(167\) | − | 12.5761i | − | 0.973168i | −0.873634 | − | 0.486584i | \(-0.838243\pi\) | ||
0.873634 | − | 0.486584i | \(-0.161757\pi\) | |||||||
\(168\) | 15.4530i | 1.19222i | ||||||||
\(169\) | 3.53673 | 0.272056 | ||||||||
\(170\) | −8.91128 | − | 3.11479i | −0.683464 | − | 0.238893i | ||||
\(171\) | −10.3923 | −0.794719 | ||||||||
\(172\) | − | 15.2935i | − | 1.16612i | ||||||
\(173\) | − | 9.91066i | − | 0.753494i | −0.926316 | − | 0.376747i | \(-0.877043\pi\) | ||
0.926316 | − | 0.376747i | \(-0.122957\pi\) | |||||||
\(174\) | 40.8026 | 3.09324 | ||||||||
\(175\) | 3.08015 | − | 3.86778i | 0.232837 | − | 0.292377i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 26.1993i | − | 1.96926i | ||||||
\(178\) | 23.4699i | 1.75914i | ||||||||
\(179\) | 2.44335 | 0.182625 | 0.0913125 | − | 0.995822i | \(-0.470894\pi\) | ||||
0.0913125 | + | 0.995822i | \(0.470894\pi\) | |||||||
\(180\) | −15.9975 | − | 5.59167i | −1.19239 | − | 0.416778i | ||||
\(181\) | −14.2018 | −1.05561 | −0.527804 | − | 0.849366i | \(-0.676985\pi\) | ||||
−0.527804 | + | 0.849366i | \(0.676985\pi\) | |||||||
\(182\) | − | 7.93290i | − | 0.588026i | ||||||
\(183\) | 2.14504i | 0.158566i | ||||||||
\(184\) | −37.8361 | −2.78931 | ||||||||
\(185\) | −2.06881 | + | 5.91878i | −0.152102 | + | 0.435157i | ||||
\(186\) | −14.7477 | −1.08136 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 10.2720i | − | 0.749163i | ||||||
\(189\) | 3.00735 | 0.218752 | ||||||||
\(190\) | −12.6650 | + | 36.2342i | −0.918818 | + | 2.62870i | ||||
\(191\) | 17.4013 | 1.25912 | 0.629558 | − | 0.776954i | \(-0.283236\pi\) | ||||
0.629558 | + | 0.776954i | \(0.283236\pi\) | |||||||
\(192\) | − | 15.5003i | − | 1.11864i | ||||||
\(193\) | − | 11.0091i | − | 0.792456i | −0.918152 | − | 0.396228i | \(-0.870319\pi\) | ||
0.918152 | − | 0.396228i | \(-0.129681\pi\) | |||||||
\(194\) | −33.2201 | −2.38507 | ||||||||
\(195\) | 13.8947 | + | 4.85666i | 0.995021 | + | 0.347793i | ||||
\(196\) | −28.9088 | −2.06492 | ||||||||
\(197\) | − | 3.49279i | − | 0.248851i | −0.992229 | − | 0.124426i | \(-0.960291\pi\) | ||
0.992229 | − | 0.124426i | \(-0.0397088\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.84247 | −0.201498 | −0.100749 | − | 0.994912i | \(-0.532124\pi\) | ||||
−0.100749 | + | 0.994912i | \(0.532124\pi\) | |||||||
\(200\) | −22.7469 | + | 28.5637i | −1.60845 | + | 2.01976i | ||||
\(201\) | −21.0664 | −1.48591 | ||||||||
\(202\) | 39.8496i | 2.80381i | ||||||||
\(203\) | − | 7.23084i | − | 0.507505i | ||||||
\(204\) | 16.6292 | 1.16428 | ||||||||
\(205\) | 2.92648 | + | 1.02290i | 0.204394 | + | 0.0714424i | ||||
\(206\) | 21.2069 | 1.47755 | ||||||||
\(207\) | − | 8.17953i | − | 0.568517i | ||||||
\(208\) | 29.0500i | 2.01426i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −4.07126 | + | 11.6477i | −0.280944 | + | 0.803769i | ||||
\(211\) | −3.11846 | −0.214683 | −0.107342 | − | 0.994222i | \(-0.534234\pi\) | ||||
−0.107342 | + | 0.994222i | \(0.534234\pi\) | |||||||
\(212\) | 11.4105i | 0.783679i | ||||||||
\(213\) | − | 0.521676i | − | 0.0357447i | ||||||
\(214\) | −17.2659 | −1.18027 | ||||||||
\(215\) | 2.35054 | − | 6.72481i | 0.160306 | − | 0.458628i | ||||
\(216\) | −22.2093 | −1.51115 | ||||||||
\(217\) | 2.61352i | 0.177417i | ||||||||
\(218\) | − | 7.42068i | − | 0.502592i | ||||||
\(219\) | −29.2486 | −1.97644 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.98009 | −0.334997 | ||||||||
\(222\) | − | 15.6466i | − | 1.05013i | ||||||
\(223\) | − | 12.3692i | − | 0.828303i | −0.910208 | − | 0.414152i | \(-0.864078\pi\) | ||
0.910208 | − | 0.414152i | \(-0.135922\pi\) | |||||||
\(224\) | −9.90883 | −0.662061 | ||||||||
\(225\) | −6.17499 | − | 4.91751i | −0.411666 | − | 0.327834i | ||||
\(226\) | 46.2618 | 3.07729 | ||||||||
\(227\) | − | 13.6169i | − | 0.903786i | −0.892072 | − | 0.451893i | \(-0.850749\pi\) | ||
0.892072 | − | 0.451893i | \(-0.149251\pi\) | |||||||
\(228\) | − | 67.6161i | − | 4.47798i | ||||||
\(229\) | −5.84247 | −0.386081 | −0.193041 | − | 0.981191i | \(-0.561835\pi\) | ||||
−0.193041 | + | 0.981191i | \(0.561835\pi\) | |||||||
\(230\) | −28.5190 | − | 9.96834i | −1.88049 | − | 0.657293i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 53.3999i | 3.50588i | ||||||||
\(233\) | − | 23.4398i | − | 1.53559i | −0.640693 | − | 0.767797i | \(-0.721353\pi\) | ||
0.640693 | − | 0.767797i | \(-0.278647\pi\) | |||||||
\(234\) | −12.6650 | −0.827939 | ||||||||
\(235\) | 1.57876 | − | 4.51678i | 0.102987 | − | 0.294642i | ||||
\(236\) | 58.7756 | 3.82597 | ||||||||
\(237\) | 16.4682i | 1.06972i | ||||||||
\(238\) | − | 4.17473i | − | 0.270607i | ||||||
\(239\) | 6.58256 | 0.425790 | 0.212895 | − | 0.977075i | \(-0.431711\pi\) | ||||
0.212895 | + | 0.977075i | \(0.431711\pi\) | |||||||
\(240\) | 14.9088 | − | 42.6536i | 0.962361 | − | 2.75328i | ||||
\(241\) | 12.1627 | 0.783466 | 0.391733 | − | 0.920079i | \(-0.371876\pi\) | ||||
0.391733 | + | 0.920079i | \(0.371876\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 14.9360i | − | 0.958146i | ||||||
\(244\) | −4.81220 | −0.308069 | ||||||||
\(245\) | −12.7117 | − | 4.44316i | −0.812122 | − | 0.283863i | ||||
\(246\) | −7.73629 | −0.493248 | ||||||||
\(247\) | 20.2495i | 1.28845i | ||||||||
\(248\) | − | 19.3009i | − | 1.22561i | ||||||
\(249\) | 12.7428 | 0.807545 | ||||||||
\(250\) | −24.6710 | + | 15.5370i | −1.56033 | + | 0.982645i | ||||
\(251\) | −1.08627 | −0.0685646 | −0.0342823 | − | 0.999412i | \(-0.510915\pi\) | ||||
−0.0342823 | + | 0.999412i | \(0.510915\pi\) | |||||||
\(252\) | − | 7.49448i | − | 0.472108i | ||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 45.0393 | 2.82602 | ||||||||
\(255\) | 7.31216 | + | 2.55584i | 0.457905 | + | 0.160053i | ||||
\(256\) | −17.4876 | −1.09297 | ||||||||
\(257\) | 24.2494i | 1.51263i | 0.654205 | + | 0.756317i | \(0.273003\pi\) | ||||
−0.654205 | + | 0.756317i | \(0.726997\pi\) | |||||||
\(258\) | 17.7774i | 1.10677i | ||||||||
\(259\) | −2.77281 | −0.172294 | ||||||||
\(260\) | −10.8954 | + | 31.1714i | −0.675707 | + | 1.93317i | ||||
\(261\) | −11.5442 | −0.714566 | ||||||||
\(262\) | − | 13.3605i | − | 0.825415i | ||||||
\(263\) | − | 2.49816i | − | 0.154043i | −0.997029 | − | 0.0770216i | \(-0.975459\pi\) | ||
0.997029 | − | 0.0770216i | \(-0.0245410\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.75375 | + | 5.01742i | −0.107732 | + | 0.308217i | ||||
\(266\) | −16.9749 | −1.04080 | ||||||||
\(267\) | − | 19.2582i | − | 1.17859i | ||||||
\(268\) | − | 47.2603i | − | 2.88688i | ||||||
\(269\) | −16.0863 | −0.980797 | −0.490399 | − | 0.871498i | \(-0.663149\pi\) | ||||
−0.490399 | + | 0.871498i | \(0.663149\pi\) | |||||||
\(270\) | −16.7403 | − | 5.85129i | −1.01878 | − | 0.356098i | ||||
\(271\) | −2.00490 | −0.121789 | −0.0608944 | − | 0.998144i | \(-0.519395\pi\) | ||||
−0.0608944 | + | 0.998144i | \(0.519395\pi\) | |||||||
\(272\) | 15.2877i | 0.926954i | ||||||||
\(273\) | 6.50935i | 0.393964i | ||||||||
\(274\) | 18.9798 | 1.14661 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 53.2190 | 3.20341 | ||||||||
\(277\) | 19.3586i | 1.16315i | 0.813494 | + | 0.581573i | \(0.197562\pi\) | ||||
−0.813494 | + | 0.581573i | \(0.802438\pi\) | |||||||
\(278\) | − | 30.0046i | − | 1.79956i | ||||||
\(279\) | 4.17254 | 0.249803 | ||||||||
\(280\) | −15.2438 | − | 5.32821i | −0.910991 | − | 0.318421i | ||||
\(281\) | 2.91841 | 0.174098 | 0.0870488 | − | 0.996204i | \(-0.472256\pi\) | ||||
0.0870488 | + | 0.996204i | \(0.472256\pi\) | |||||||
\(282\) | 11.9403i | 0.711037i | ||||||||
\(283\) | − | 0.572327i | − | 0.0340213i | −0.999855 | − | 0.0170107i | \(-0.994585\pi\) | ||
0.999855 | − | 0.0170107i | \(-0.00541492\pi\) | |||||||
\(284\) | 1.17033 | 0.0694463 | ||||||||
\(285\) | 10.3923 | − | 29.7320i | 0.615587 | − | 1.76117i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.37099i | 0.0809268i | ||||||||
\(288\) | 15.8196i | 0.932181i | ||||||||
\(289\) | 14.3792 | 0.845836 | ||||||||
\(290\) | −14.0688 | + | 40.2503i | −0.826149 | + | 2.36358i | ||||
\(291\) | 27.2588 | 1.59794 | ||||||||
\(292\) | − | 65.6164i | − | 3.83991i | ||||||
\(293\) | − | 9.33258i | − | 0.545215i | −0.962125 | − | 0.272608i | \(-0.912114\pi\) | ||
0.962125 | − | 0.272608i | \(-0.0878860\pi\) | |||||||
\(294\) | 33.6041 | 1.95983 | ||||||||
\(295\) | 25.8447 | + | 9.03357i | 1.50474 | + | 0.525954i | ||||
\(296\) | 20.4773 | 1.19022 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 26.9109i | − | 1.55890i | ||||||
\(299\) | −15.9379 | −0.921714 | ||||||||
\(300\) | 31.9951 | − | 40.1767i | 1.84724 | − | 2.31960i | ||||
\(301\) | 3.15042 | 0.181587 | ||||||||
\(302\) | − | 39.0382i | − | 2.24639i | ||||||
\(303\) | − | 32.6986i | − | 1.87849i | ||||||
\(304\) | 62.1614 | 3.56520 | ||||||||
\(305\) | −2.11601 | − | 0.739614i | −0.121162 | − | 0.0423502i | ||||
\(306\) | −6.66503 | −0.381015 | ||||||||
\(307\) | 6.34982i | 0.362404i | 0.983446 | + | 0.181202i | \(0.0579987\pi\) | ||||
−0.983446 | + | 0.181202i | \(0.942001\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.4013 | −0.989927 | ||||||||
\(310\) | 5.08504 | − | 14.5481i | 0.288811 | − | 0.826277i | ||||
\(311\) | 22.5589 | 1.27920 | 0.639598 | − | 0.768710i | \(-0.279101\pi\) | ||||
0.639598 | + | 0.768710i | \(0.279101\pi\) | |||||||
\(312\) | − | 48.0717i | − | 2.72153i | ||||||
\(313\) | 25.5778i | 1.44574i | 0.690984 | + | 0.722870i | \(0.257177\pi\) | ||||
−0.690984 | + | 0.722870i | \(0.742823\pi\) | |||||||
\(314\) | −47.1148 | −2.65884 | ||||||||
\(315\) | 1.15187 | − | 3.29545i | 0.0649005 | − | 0.185678i | ||||
\(316\) | −36.9448 | −2.07830 | ||||||||
\(317\) | − | 24.8236i | − | 1.39423i | −0.716958 | − | 0.697117i | \(-0.754466\pi\) | ||
0.716958 | − | 0.697117i | \(-0.245534\pi\) | |||||||
\(318\) | − | 13.2638i | − | 0.743797i | ||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 15.2905 | + | 5.34453i | 0.854764 | + | 0.298768i | ||||
\(321\) | 14.1676 | 0.790756 | ||||||||
\(322\) | − | 13.3605i | − | 0.744552i | ||||||
\(323\) | 10.6564i | 0.592939i | ||||||||
\(324\) | 53.9752 | 2.99862 | ||||||||
\(325\) | −9.58183 | + | 12.0320i | −0.531505 | + | 0.667418i | ||||
\(326\) | 55.8134 | 3.09122 | ||||||||
\(327\) | 6.08905i | 0.336725i | ||||||||
\(328\) | − | 10.1248i | − | 0.559047i | ||||||
\(329\) | 2.11601 | 0.116659 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.80044 | −0.318821 | −0.159411 | − | 0.987212i | \(-0.550959\pi\) | ||||
−0.159411 | + | 0.987212i | \(0.550959\pi\) | |||||||
\(332\) | 28.5873i | 1.56893i | ||||||||
\(333\) | 4.42685i | 0.242590i | ||||||||
\(334\) | −32.7955 | −1.79449 | ||||||||
\(335\) | 7.26371 | − | 20.7812i | 0.396859 | − | 1.13540i | ||||
\(336\) | 19.9822 | 1.09012 | ||||||||
\(337\) | 0.0461700i | 0.00251504i | 0.999999 | + | 0.00125752i | \(0.000400281\pi\) | ||||
−0.999999 | + | 0.00125752i | \(0.999600\pi\) | |||||||
\(338\) | − | 9.22297i | − | 0.501664i | ||||||
\(339\) | −37.9602 | −2.06171 | ||||||||
\(340\) | −5.73378 | + | 16.4041i | −0.310958 | + | 0.889638i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 27.1007i | 1.46544i | ||||||||
\(343\) | − | 12.8773i | − | 0.695309i | ||||||
\(344\) | −23.2659 | −1.25441 | ||||||||
\(345\) | 23.4013 | + | 8.17953i | 1.25988 | + | 0.440371i | ||||
\(346\) | −25.8447 | −1.38942 | ||||||||
\(347\) | 31.5643i | 1.69446i | 0.531225 | + | 0.847231i | \(0.321732\pi\) | ||||
−0.531225 | + | 0.847231i | \(0.678268\pi\) | |||||||
\(348\) | − | 75.1106i | − | 4.02635i | ||||||
\(349\) | −30.3239 | −1.62320 | −0.811600 | − | 0.584213i | \(-0.801403\pi\) | ||||
−0.811600 | + | 0.584213i | \(0.801403\pi\) | |||||||
\(350\) | −10.0863 | − | 8.03230i | −0.539134 | − | 0.429344i | ||||
\(351\) | −9.35537 | −0.499353 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.1157i | 1.01743i | 0.860936 | + | 0.508714i | \(0.169879\pi\) | ||||
−0.860936 | + | 0.508714i | \(0.830121\pi\) | |||||||
\(354\) | −68.3217 | −3.63126 | ||||||||
\(355\) | 0.514615 | + | 0.179875i | 0.0273129 | + | 0.00954676i | ||||
\(356\) | 43.2040 | 2.28981 | ||||||||
\(357\) | 3.42558i | 0.181301i | ||||||||
\(358\) | − | 6.37170i | − | 0.336755i | ||||||
\(359\) | −26.8981 | −1.41963 | −0.709814 | − | 0.704390i | \(-0.751221\pi\) | ||||
−0.709814 | + | 0.704390i | \(0.751221\pi\) | |||||||
\(360\) | −8.50659 | + | 24.3370i | −0.448336 | + | 1.28267i | ||||
\(361\) | 24.3301 | 1.28053 | ||||||||
\(362\) | 37.0349i | 1.94651i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −14.6031 | −0.765410 | ||||||||
\(365\) | 10.0850 | − | 28.8527i | 0.527871 | − | 1.51022i | ||||
\(366\) | 5.59377 | 0.292391 | ||||||||
\(367\) | − | 8.04226i | − | 0.419803i | −0.977723 | − | 0.209901i | \(-0.932686\pi\) | ||
0.977723 | − | 0.209901i | \(-0.0673143\pi\) | |||||||
\(368\) | 48.9258i | 2.55043i | ||||||||
\(369\) | 2.18881 | 0.113945 | ||||||||
\(370\) | 15.4348 | + | 5.39497i | 0.802417 | + | 0.280471i | ||||
\(371\) | −2.35054 | −0.122034 | ||||||||
\(372\) | 27.1480i | 1.40756i | ||||||||
\(373\) | − | 27.7542i | − | 1.43706i | −0.695496 | − | 0.718530i | \(-0.744815\pi\) | ||
0.695496 | − | 0.718530i | \(-0.255185\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 20.2438 | − | 12.7489i | 1.04539 | − | 0.658350i | ||||
\(376\) | −15.6268 | −0.805889 | ||||||||
\(377\) | 22.4940i | 1.15850i | ||||||||
\(378\) | − | 7.84245i | − | 0.403372i | ||||||
\(379\) | 18.3151 | 0.940781 | 0.470391 | − | 0.882458i | \(-0.344113\pi\) | ||||
0.470391 | + | 0.882458i | \(0.344113\pi\) | |||||||
\(380\) | 66.7008 | + | 23.3141i | 3.42168 | + | 1.19599i | ||||
\(381\) | −36.9571 | −1.89337 | ||||||||
\(382\) | − | 45.3786i | − | 2.32177i | ||||||
\(383\) | − | 17.4602i | − | 0.892177i | −0.894989 | − | 0.446088i | \(-0.852817\pi\) | ||
0.894989 | − | 0.446088i | \(-0.147183\pi\) | |||||||
\(384\) | 2.46165 | 0.125621 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −28.7093 | −1.46126 | ||||||||
\(387\) | − | 5.02970i | − | 0.255674i | ||||||
\(388\) | 61.1524i | 3.10455i | ||||||||
\(389\) | −13.5589 | −0.687461 | −0.343731 | − | 0.939068i | \(-0.611691\pi\) | ||||
−0.343731 | + | 0.939068i | \(0.611691\pi\) | |||||||
\(390\) | 12.6650 | − | 36.2342i | 0.641319 | − | 1.83479i | ||||
\(391\) | −8.38741 | −0.424169 | ||||||||
\(392\) | 43.9789i | 2.22127i | ||||||||
\(393\) | 10.9630i | 0.553009i | ||||||||
\(394\) | −9.10839 | −0.458874 | ||||||||
\(395\) | −16.2453 | − | 5.67825i | −0.817388 | − | 0.285704i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.42431i | 0.121673i | 0.998148 | + | 0.0608363i | \(0.0193767\pi\) | ||||
−0.998148 | + | 0.0608363i | \(0.980623\pi\) | |||||||
\(398\) | 7.41250i | 0.371555i | ||||||||
\(399\) | 13.9287 | 0.697309 | ||||||||
\(400\) | 36.9356 | + | 29.4140i | 1.84678 | + | 1.47070i | ||||
\(401\) | −16.4141 | −0.819682 | −0.409841 | − | 0.912157i | \(-0.634416\pi\) | ||||
−0.409841 | + | 0.912157i | \(0.634416\pi\) | |||||||
\(402\) | 54.9361i | 2.73996i | ||||||||
\(403\) | − | 8.13024i | − | 0.404996i | ||||||
\(404\) | 73.3561 | 3.64960 | ||||||||
\(405\) | 23.7338 | + | 8.29576i | 1.17934 | + | 0.412220i | ||||
\(406\) | −18.8563 | −0.935824 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | − | 25.2980i | − | 1.25244i | ||||||
\(409\) | −19.4748 | −0.962968 | −0.481484 | − | 0.876455i | \(-0.659902\pi\) | ||||
−0.481484 | + | 0.876455i | \(0.659902\pi\) | |||||||
\(410\) | 2.66748 | − | 7.63157i | 0.131738 | − | 0.376896i | ||||
\(411\) | −15.5739 | −0.768202 | ||||||||
\(412\) | − | 39.0382i | − | 1.92327i | ||||||
\(413\) | 12.1076i | 0.595778i | ||||||||
\(414\) | −21.3303 | −1.04833 | ||||||||
\(415\) | −4.39375 | + | 12.5704i | −0.215681 | + | 0.617054i | ||||
\(416\) | 30.8248 | 1.51131 | ||||||||
\(417\) | 24.6203i | 1.20566i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.84468 | 0.0901185 | 0.0450592 | − | 0.998984i | \(-0.485652\pi\) | ||||
0.0450592 | + | 0.998984i | \(0.485652\pi\) | |||||||
\(420\) | 21.4414 | + | 7.49448i | 1.04623 | + | 0.365693i | ||||
\(421\) | −21.1996 | −1.03320 | −0.516602 | − | 0.856226i | \(-0.672803\pi\) | ||||
−0.516602 | + | 0.856226i | \(0.672803\pi\) | |||||||
\(422\) | 8.13220i | 0.395869i | ||||||||
\(423\) | − | 3.37825i | − | 0.164256i | ||||||
\(424\) | 17.3588 | 0.843019 | ||||||||
\(425\) | −5.04249 | + | 6.33192i | −0.244596 | + | 0.307143i | ||||
\(426\) | −1.36041 | −0.0659121 | ||||||||
\(427\) | − | 0.991300i | − | 0.0479724i | ||||||
\(428\) | 31.7835i | 1.53632i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −17.5367 | − | 6.12966i | −0.845696 | − | 0.295599i | ||||
\(431\) | 26.3302 | 1.26828 | 0.634141 | − | 0.773217i | \(-0.281354\pi\) | ||||
0.634141 | + | 0.773217i | \(0.281354\pi\) | |||||||
\(432\) | 28.7188i | 1.38174i | ||||||||
\(433\) | − | 9.13347i | − | 0.438927i | −0.975621 | − | 0.219463i | \(-0.929569\pi\) | ||
0.975621 | − | 0.219463i | \(-0.0704306\pi\) | |||||||
\(434\) | 6.81545 | 0.327152 | ||||||||
\(435\) | 11.5442 | − | 33.0274i | 0.553501 | − | 1.58354i | ||||
\(436\) | −13.6602 | −0.654204 | ||||||||
\(437\) | 34.1040i | 1.63142i | ||||||||
\(438\) | 76.2736i | 3.64449i | ||||||||
\(439\) | −11.0836 | −0.528991 | −0.264496 | − | 0.964387i | \(-0.585205\pi\) | ||||
−0.264496 | + | 0.964387i | \(0.585205\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.50750 | −0.452738 | ||||||||
\(442\) | 12.9869i | 0.617724i | ||||||||
\(443\) | 17.6827i | 0.840131i | 0.907494 | + | 0.420066i | \(0.137993\pi\) | ||||
−0.907494 | + | 0.420066i | \(0.862007\pi\) | |||||||
\(444\) | −28.8026 | −1.36691 | ||||||||
\(445\) | 18.9975 | + | 6.64027i | 0.900570 | + | 0.314779i | ||||
\(446\) | −32.2560 | −1.52737 | ||||||||
\(447\) | 22.0817i | 1.04443i | ||||||||
\(448\) | 7.16324i | 0.338431i | ||||||||
\(449\) | −16.9287 | −0.798917 | −0.399458 | − | 0.916751i | \(-0.630802\pi\) | ||||
−0.399458 | + | 0.916751i | \(0.630802\pi\) | |||||||
\(450\) | −12.8237 | + | 16.1029i | −0.604516 | + | 0.759099i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 85.1599i | − | 4.00559i | ||||||
\(453\) | 32.0328i | 1.50503i | ||||||||
\(454\) | −35.5097 | −1.66655 | ||||||||
\(455\) | −6.42124 | − | 2.24443i | −0.301032 | − | 0.105221i | ||||
\(456\) | −102.864 | −4.81705 | ||||||||
\(457\) | − | 32.6109i | − | 1.52547i | −0.646709 | − | 0.762736i | \(-0.723855\pi\) | ||
0.646709 | − | 0.762736i | \(-0.276145\pi\) | |||||||
\(458\) | 15.2358i | 0.711922i | ||||||||
\(459\) | −4.92331 | −0.229800 | ||||||||
\(460\) | −18.3500 | + | 52.4986i | −0.855572 | + | 2.44776i | ||||
\(461\) | −7.96896 | −0.371152 | −0.185576 | − | 0.982630i | \(-0.559415\pi\) | ||||
−0.185576 | + | 0.982630i | \(0.559415\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 25.3879i | − | 1.17988i | −0.807449 | − | 0.589938i | \(-0.799152\pi\) | ||
0.807449 | − | 0.589938i | \(-0.200848\pi\) | |||||||
\(464\) | 69.0513 | 3.20563 | ||||||||
\(465\) | −4.17254 | + | 11.9375i | −0.193497 | + | 0.553587i | ||||
\(466\) | −61.1256 | −2.83159 | ||||||||
\(467\) | 16.3070i | 0.754599i | 0.926091 | + | 0.377299i | \(0.123147\pi\) | ||||
−0.926091 | + | 0.377299i | \(0.876853\pi\) | |||||||
\(468\) | 23.3141i | 1.07770i | ||||||||
\(469\) | 9.73550 | 0.449544 | ||||||||
\(470\) | −11.7787 | − | 4.11705i | −0.543311 | − | 0.189905i | ||||
\(471\) | 38.6601 | 1.78136 | ||||||||
\(472\) | − | 89.4152i | − | 4.11567i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 42.9452 | 1.97254 | ||||||||
\(475\) | 25.7462 | + | 20.5033i | 1.18132 | + | 0.940754i | ||||
\(476\) | −7.68494 | −0.352239 | ||||||||
\(477\) | 3.75269i | 0.171824i | ||||||||
\(478\) | − | 17.1658i | − | 0.785144i | ||||||
\(479\) | 34.7943 | 1.58979 | 0.794895 | − | 0.606747i | \(-0.207526\pi\) | ||||
0.794895 | + | 0.606747i | \(0.207526\pi\) | |||||||
\(480\) | −45.2594 | − | 15.8196i | −2.06580 | − | 0.722064i | ||||
\(481\) | 8.62577 | 0.393301 | ||||||||
\(482\) | − | 31.7174i | − | 1.44469i | ||||||
\(483\) | 10.9630i | 0.498833i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.39887 | + | 26.8898i | −0.426781 | + | 1.22100i | ||||
\(486\) | −38.9497 | −1.76679 | ||||||||
\(487\) | − | 2.52421i | − | 0.114383i | −0.998363 | − | 0.0571915i | \(-0.981785\pi\) | ||
0.998363 | − | 0.0571915i | \(-0.0182146\pi\) | |||||||
\(488\) | 7.32078i | 0.331396i | ||||||||
\(489\) | −45.7977 | −2.07105 | ||||||||
\(490\) | −11.5867 | + | 33.1492i | −0.523435 | + | 1.49753i | ||||
\(491\) | 19.3254 | 0.872143 | 0.436072 | − | 0.899912i | \(-0.356369\pi\) | ||||
0.436072 | + | 0.899912i | \(0.356369\pi\) | |||||||
\(492\) | 14.2412i | 0.642041i | ||||||||
\(493\) | 11.8376i | 0.533137i | ||||||||
\(494\) | 52.8061 | 2.37586 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −24.9580 | −1.12065 | ||||||||
\(497\) | 0.241085i | 0.0108141i | ||||||||
\(498\) | − | 33.2304i | − | 1.48909i | ||||||
\(499\) | −1.15753 | −0.0518181 | −0.0259090 | − | 0.999664i | \(-0.508248\pi\) | ||||
−0.0259090 | + | 0.999664i | \(0.508248\pi\) | |||||||
\(500\) | 28.6009 | + | 45.4150i | 1.27907 | + | 2.03102i | ||||
\(501\) | 26.9104 | 1.20227 | ||||||||
\(502\) | 2.83273i | 0.126431i | ||||||||
\(503\) | − | 17.9890i | − | 0.802089i | −0.916059 | − | 0.401044i | \(-0.868647\pi\) | ||
0.916059 | − | 0.401044i | \(-0.131353\pi\) | |||||||
\(504\) | −11.4013 | −0.507855 | ||||||||
\(505\) | 32.2560 | + | 11.2745i | 1.43537 | + | 0.501710i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.56792i | 0.336103i | ||||||||
\(508\) | − | 82.9096i | − | 3.67852i | ||||||
\(509\) | 11.3500 | 0.503079 | 0.251539 | − | 0.967847i | \(-0.419063\pi\) | ||||
0.251539 | + | 0.967847i | \(0.419063\pi\) | |||||||
\(510\) | 6.66503 | − | 19.0684i | 0.295133 | − | 0.844363i | ||||
\(511\) | 13.5168 | 0.597949 | ||||||||
\(512\) | 43.3027i | 1.91373i | ||||||||
\(513\) | 20.0187i | 0.883845i | ||||||||
\(514\) | 63.2367 | 2.78925 | ||||||||
\(515\) | 6.00000 | − | 17.1658i | 0.264392 | − | 0.756414i | ||||
\(516\) | 32.7251 | 1.44064 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 7.23084i | 0.317705i | ||||||||
\(519\) | 21.2069 | 0.930879 | ||||||||
\(520\) | 47.4210 | + | 16.5752i | 2.07955 | + | 0.726870i | ||||
\(521\) | 18.0243 | 0.789660 | 0.394830 | − | 0.918754i | \(-0.370803\pi\) | ||||
0.394830 | + | 0.918754i | \(0.370803\pi\) | |||||||
\(522\) | 30.1045i | 1.31764i | ||||||||
\(523\) | 18.0409i | 0.788874i | 0.918923 | + | 0.394437i | \(0.129060\pi\) | ||||
−0.918923 | + | 0.394437i | \(0.870940\pi\) | |||||||
\(524\) | −24.5944 | −1.07441 | ||||||||
\(525\) | 8.27630 | + | 6.59091i | 0.361207 | + | 0.287651i | ||||
\(526\) | −6.51461 | −0.284051 | ||||||||
\(527\) | − | 4.27858i | − | 0.186378i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.84247 | −0.167064 | ||||||||
\(530\) | 13.0842 | + | 4.57337i | 0.568343 | + | 0.198655i | ||||
\(531\) | 19.3301 | 0.838853 | ||||||||
\(532\) | 31.2478i | 1.35476i | ||||||||
\(533\) | − | 4.26492i | − | 0.184734i | ||||||
\(534\) | −50.2210 | −2.17327 | ||||||||
\(535\) | −4.88500 | + | 13.9758i | −0.211197 | + | 0.604226i | ||||
\(536\) | −71.8969 | −3.10547 | ||||||||
\(537\) | 5.22830i | 0.225618i | ||||||||
\(538\) | 41.9492i | 1.80856i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −10.7712 | + | 30.8160i | −0.463519 | + | 1.32611i | ||||
\(541\) | 6.34802 | 0.272923 | 0.136461 | − | 0.990645i | \(-0.456427\pi\) | ||||
0.136461 | + | 0.990645i | \(0.456427\pi\) | |||||||
\(542\) | 5.22830i | 0.224575i | ||||||||
\(543\) | − | 30.3890i | − | 1.30412i | ||||||
\(544\) | 16.2217 | 0.695499 | ||||||||
\(545\) | −6.00662 | − | 2.09951i | −0.257295 | − | 0.0899332i | ||||
\(546\) | 16.9749 | 0.726457 | ||||||||
\(547\) | − | 15.2300i | − | 0.651190i | −0.945509 | − | 0.325595i | \(-0.894435\pi\) | ||
0.945509 | − | 0.325595i | \(-0.105565\pi\) | |||||||
\(548\) | − | 34.9384i | − | 1.49250i | ||||||
\(549\) | −1.58263 | −0.0675450 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 48.1327 | 2.05052 | ||||||||
\(552\) | − | 80.9619i | − | 3.44597i | ||||||
\(553\) | − | 7.61053i | − | 0.323632i | ||||||
\(554\) | 50.4827 | 2.14480 | ||||||||
\(555\) | −12.6650 | − | 4.42685i | −0.537601 | − | 0.187909i | ||||
\(556\) | −55.2332 | −2.34241 | ||||||||
\(557\) | − | 40.9027i | − | 1.73310i | −0.499089 | − | 0.866551i | \(-0.666332\pi\) | ||
0.499089 | − | 0.866551i | \(-0.333668\pi\) | |||||||
\(558\) | − | 10.8810i | − | 0.460629i | ||||||
\(559\) | −9.80044 | −0.414515 | ||||||||
\(560\) | −6.88989 | + | 19.7117i | −0.291151 | + | 0.832972i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 7.61053i | − | 0.321031i | ||||||
\(563\) | 17.9993i | 0.758582i | 0.925277 | + | 0.379291i | \(0.123832\pi\) | ||||
−0.925277 | + | 0.379291i | \(0.876168\pi\) | |||||||
\(564\) | 21.9801 | 0.925529 | ||||||||
\(565\) | 13.0887 | − | 37.4463i | 0.550647 | − | 1.57538i | ||||
\(566\) | −1.49250 | −0.0627343 | ||||||||
\(567\) | 11.1188i | 0.466944i | ||||||||
\(568\) | − | 1.78042i | − | 0.0747047i | ||||||
\(569\) | −40.7200 | −1.70707 | −0.853536 | − | 0.521034i | \(-0.825546\pi\) | ||||
−0.853536 | + | 0.521034i | \(0.825546\pi\) | |||||||
\(570\) | −77.5340 | − | 27.1007i | −3.24754 | − | 1.13512i | ||||
\(571\) | −13.2417 | −0.554149 | −0.277075 | − | 0.960848i | \(-0.589365\pi\) | ||||
−0.277075 | + | 0.960848i | \(0.589365\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 37.2354i | 1.55553i | ||||||||
\(574\) | 3.57521 | 0.149226 | ||||||||
\(575\) | −16.1376 | + | 20.2642i | −0.672985 | + | 0.845077i | ||||
\(576\) | 11.4362 | 0.476510 | ||||||||
\(577\) | − | 0.659467i | − | 0.0274540i | −0.999906 | − | 0.0137270i | \(-0.995630\pi\) | ||
0.999906 | − | 0.0137270i | \(-0.00436957\pi\) | |||||||
\(578\) | − | 37.4976i | − | 1.55969i | ||||||
\(579\) | 23.5574 | 0.979013 | ||||||||
\(580\) | 74.0938 | + | 25.8982i | 3.07658 | + | 1.07537i | ||||
\(581\) | −5.88892 | −0.244313 | ||||||||
\(582\) | − | 71.0846i | − | 2.94655i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −99.8221 | −4.13067 | ||||||||
\(585\) | −3.58328 | + | 10.2516i | −0.148150 | + | 0.423853i | ||||
\(586\) | −24.3372 | −1.00536 | ||||||||
\(587\) | − | 12.0747i | − | 0.498378i | −0.968455 | − | 0.249189i | \(-0.919836\pi\) | ||
0.968455 | − | 0.249189i | \(-0.0801640\pi\) | |||||||
\(588\) | − | 61.8592i | − | 2.55103i | ||||||
\(589\) | −17.3971 | −0.716836 | ||||||||
\(590\) | 23.5574 | − | 67.3969i | 0.969844 | − | 2.77469i | ||||
\(591\) | 7.47390 | 0.307435 | ||||||||
\(592\) | − | 26.4791i | − | 1.08828i | ||||||
\(593\) | 38.3249i | 1.57382i | 0.617070 | + | 0.786908i | \(0.288320\pi\) | ||||
−0.617070 | + | 0.786908i | \(0.711680\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.37921 | − | 1.18114i | −0.138534 | − | 0.0484222i | ||||
\(596\) | −49.5382 | −2.02916 | ||||||||
\(597\) | − | 6.08233i | − | 0.248933i | ||||||
\(598\) | 41.5624i | 1.69961i | ||||||||
\(599\) | 4.28803 | 0.175204 | 0.0876022 | − | 0.996156i | \(-0.472080\pi\) | ||||
0.0876022 | + | 0.996156i | \(0.472080\pi\) | |||||||
\(600\) | −61.1207 | − | 48.6740i | −2.49524 | − | 1.98711i | ||||
\(601\) | 28.9413 | 1.18054 | 0.590270 | − | 0.807206i | \(-0.299021\pi\) | ||||
0.590270 | + | 0.807206i | \(0.299021\pi\) | |||||||
\(602\) | − | 8.21555i | − | 0.334841i | ||||||
\(603\) | − | 15.5429i | − | 0.632956i | ||||||
\(604\) | −71.8624 | −2.92404 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −85.2703 | −3.46387 | ||||||||
\(607\) | 11.0553i | 0.448721i | 0.974506 | + | 0.224361i | \(0.0720294\pi\) | ||||
−0.974506 | + | 0.224361i | \(0.927971\pi\) | |||||||
\(608\) | − | 65.9590i | − | 2.67499i | ||||||
\(609\) | 15.4726 | 0.626981 | ||||||||
\(610\) | −1.92874 | + | 5.51805i | −0.0780924 | + | 0.223419i | ||||
\(611\) | −6.58256 | −0.266302 | ||||||||
\(612\) | 12.2692i | 0.495951i | ||||||||
\(613\) | 10.5707i | 0.426947i | 0.976949 | + | 0.213474i | \(0.0684778\pi\) | ||||
−0.976949 | + | 0.213474i | \(0.931522\pi\) | |||||||
\(614\) | 16.5589 | 0.668261 | ||||||||
\(615\) | −2.18881 | + | 6.26209i | −0.0882612 | + | 0.252512i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.60816i | − | 0.0647421i | −0.999476 | − | 0.0323710i | \(-0.989694\pi\) | ||
0.999476 | − | 0.0323710i | \(-0.0103058\pi\) | |||||||
\(618\) | 45.3786i | 1.82539i | ||||||||
\(619\) | 36.9309 | 1.48438 | 0.742190 | − | 0.670189i | \(-0.233787\pi\) | ||||
0.742190 | + | 0.670189i | \(0.233787\pi\) | |||||||
\(620\) | −26.7805 | − | 9.36068i | −1.07553 | − | 0.375934i | ||||
\(621\) | −15.7562 | −0.632275 | ||||||||
\(622\) | − | 58.8282i | − | 2.35880i | ||||||
\(623\) | 8.89991i | 0.356567i | ||||||||
\(624\) | −62.1614 | −2.48845 | ||||||||
\(625\) | 5.59622 | + | 24.3656i | 0.223849 | + | 0.974624i | ||||
\(626\) | 66.7008 | 2.66590 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 86.7302i | 3.46091i | ||||||||
\(629\) | 4.53935 | 0.180996 | ||||||||
\(630\) | −8.59377 | − | 3.00381i | −0.342384 | − | 0.119674i | ||||
\(631\) | 43.0150 | 1.71240 | 0.856200 | − | 0.516644i | \(-0.172819\pi\) | ||||
0.856200 | + | 0.516644i | \(0.172819\pi\) | |||||||
\(632\) | 56.2039i | 2.23567i | ||||||||
\(633\) | − | 6.67289i | − | 0.265223i | ||||||
\(634\) | −64.7342 | −2.57092 | ||||||||
\(635\) | 12.7428 | − | 36.4568i | 0.505684 | − | 1.44674i | ||||
\(636\) | −24.4163 | −0.968171 | ||||||||
\(637\) | 18.5255i | 0.734007i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.384897 | 0.0152263 | ||||||||
\(640\) | −0.848781 | + | 2.42833i | −0.0335510 | + | 0.0959882i | ||||
\(641\) | −22.3057 | −0.881024 | −0.440512 | − | 0.897747i | \(-0.645203\pi\) | ||||
−0.440512 | + | 0.897747i | \(0.645203\pi\) | |||||||
\(642\) | − | 36.9457i | − | 1.45813i | ||||||
\(643\) | − | 32.6187i | − | 1.28636i | −0.765716 | − | 0.643179i | \(-0.777615\pi\) | ||
0.765716 | − | 0.643179i | \(-0.222385\pi\) | |||||||
\(644\) | −24.5944 | −0.969153 | ||||||||
\(645\) | 14.3898 | + | 5.02970i | 0.566597 | + | 0.198044i | ||||
\(646\) | 27.7894 | 1.09336 | ||||||||
\(647\) | − | 9.79766i | − | 0.385186i | −0.981279 | − | 0.192593i | \(-0.938310\pi\) | ||
0.981279 | − | 0.192593i | \(-0.0616897\pi\) | |||||||
\(648\) | − | 82.1123i | − | 3.22567i | ||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 31.3768 | + | 24.9872i | 1.23070 | + | 0.980078i | ||||
\(651\) | −5.59242 | −0.219184 | ||||||||
\(652\) | − | 102.743i | − | 4.02372i | ||||||
\(653\) | − | 28.2492i | − | 1.10548i | −0.833355 | − | 0.552738i | \(-0.813583\pi\) | ||
0.833355 | − | 0.552738i | \(-0.186417\pi\) | |||||||
\(654\) | 15.8788 | 0.620911 | ||||||||
\(655\) | −10.8146 | − | 3.78005i | −0.422560 | − | 0.147699i | ||||
\(656\) | −13.0923 | −0.511169 | ||||||||
\(657\) | − | 21.5799i | − | 0.841911i | ||||||
\(658\) | − | 5.51805i | − | 0.215116i | ||||||
\(659\) | −35.4089 | −1.37934 | −0.689668 | − | 0.724126i | \(-0.742244\pi\) | ||||
−0.689668 | + | 0.724126i | \(0.742244\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.3615 | 1.33651 | 0.668254 | − | 0.743933i | \(-0.267042\pi\) | ||||
0.668254 | + | 0.743933i | \(0.267042\pi\) | |||||||
\(662\) | 15.1262i | 0.587896i | ||||||||
\(663\) | − | 10.6564i | − | 0.413861i | ||||||
\(664\) | 43.4898 | 1.68773 | ||||||||
\(665\) | −4.80265 | + | 13.7402i | −0.186239 | + | 0.532822i | ||||
\(666\) | 11.5442 | 0.447328 | ||||||||
\(667\) | 37.8841i | 1.46688i | ||||||||
\(668\) | 60.3709i | 2.33582i | ||||||||
\(669\) | 26.4677 | 1.02330 | ||||||||
\(670\) | −54.1925 | − | 18.9420i | −2.09364 | − | 0.731795i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | − | 21.2030i | − | 0.817922i | ||||||
\(673\) | − | 28.8989i | − | 1.11397i | −0.830523 | − | 0.556985i | \(-0.811958\pi\) | ||
0.830523 | − | 0.556985i | \(-0.188042\pi\) | |||||||
\(674\) | 0.120401 | 0.00463766 | ||||||||
\(675\) | −9.47258 | + | 11.8949i | −0.364600 | + | 0.457833i | ||||
\(676\) | −16.9779 | −0.652995 | ||||||||
\(677\) | − | 19.5778i | − | 0.752436i | −0.926531 | − | 0.376218i | \(-0.877224\pi\) | ||
0.926531 | − | 0.376218i | \(-0.122776\pi\) | |||||||
\(678\) | 98.9912i | 3.80174i | ||||||||
\(679\) | −12.5972 | −0.483438 | ||||||||
\(680\) | 24.9555 | + | 8.72277i | 0.957000 | + | 0.334503i | ||||
\(681\) | 29.1375 | 1.11655 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.84643i | 0.261971i | 0.991384 | + | 0.130986i | \(0.0418142\pi\) | ||||
−0.991384 | + | 0.130986i | \(0.958186\pi\) | |||||||
\(684\) | 49.8877 | 1.90750 | ||||||||
\(685\) | 5.36989 | − | 15.3630i | 0.205173 | − | 0.586992i | ||||
\(686\) | −33.5810 | −1.28213 | ||||||||
\(687\) | − | 12.5017i | − | 0.476971i | ||||||
\(688\) | 30.0851i | 1.14698i | ||||||||
\(689\) | 7.31216 | 0.278571 | ||||||||
\(690\) | 21.3303 | − | 61.0252i | 0.812031 | − | 2.32319i | ||||
\(691\) | −35.5739 | −1.35329 | −0.676647 | − | 0.736308i | \(-0.736568\pi\) | ||||
−0.676647 | + | 0.736308i | \(0.736568\pi\) | |||||||
\(692\) | 47.5755i | 1.80855i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 82.3124 | 3.12453 | ||||||||
\(695\) | −24.2870 | − | 8.48911i | −0.921259 | − | 0.322010i | ||||
\(696\) | −114.265 | −4.33122 | ||||||||
\(697\) | − | 2.24443i | − | 0.0850140i | ||||||
\(698\) | 79.0776i | 2.99313i | ||||||||
\(699\) | 50.1567 | 1.89710 | ||||||||
\(700\) | −14.7861 | + | 18.5671i | −0.558860 | + | 0.701769i | ||||
\(701\) | −0.307335 | −0.0116079 | −0.00580394 | − | 0.999983i | \(-0.501847\pi\) | ||||
−0.00580394 | + | 0.999983i | \(0.501847\pi\) | |||||||
\(702\) | 24.3966i | 0.920791i | ||||||||
\(703\) | − | 18.4575i | − | 0.696136i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.66503 | + | 3.37825i | 0.364006 | + | 0.127232i | ||||
\(706\) | 49.8493 | 1.87610 | ||||||||
\(707\) | 15.1112i | 0.568314i | ||||||||
\(708\) | 125.768i | 4.72666i | ||||||||
\(709\) | 4.14821 | 0.155789 | 0.0778947 | − | 0.996962i | \(-0.475180\pi\) | ||||
0.0778947 | + | 0.996962i | \(0.475180\pi\) | |||||||
\(710\) | 0.469071 | − | 1.34199i | 0.0176039 | − | 0.0503641i | ||||
\(711\) | −12.1504 | −0.455674 | ||||||||
\(712\) | − | 65.7261i | − | 2.46319i | ||||||
\(713\) | − | 13.6929i | − | 0.512802i | ||||||
\(714\) | 8.93310 | 0.334313 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.7292 | −0.438340 | ||||||||
\(717\) | 14.0854i | 0.526028i | ||||||||
\(718\) | 70.1439i | 2.61775i | ||||||||
\(719\) | 2.87391 | 0.107179 | 0.0535893 | − | 0.998563i | \(-0.482934\pi\) | ||||
0.0535893 | + | 0.998563i | \(0.482934\pi\) | |||||||
\(720\) | 31.4701 | + | 10.9998i | 1.17282 | + | 0.409940i | ||||
\(721\) | 8.04176 | 0.299491 | ||||||||
\(722\) | − | 63.4471i | − | 2.36126i | ||||||
\(723\) | 26.0257i | 0.967907i | ||||||||
\(724\) | 68.1747 | 2.53369 | ||||||||
\(725\) | 28.5999 | + | 22.7758i | 1.06217 | + | 0.845872i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.5703i | 1.02253i | 0.859424 | + | 0.511263i | \(0.170822\pi\) | ||||
−0.859424 | + | 0.511263i | \(0.829178\pi\) | |||||||
\(728\) | 22.2156i | 0.823366i | ||||||||
\(729\) | −1.77121 | −0.0656005 | ||||||||
\(730\) | −75.2411 | − | 26.2992i | −2.78480 | − | 0.973378i | ||||
\(731\) | −5.15753 | −0.190758 | ||||||||
\(732\) | − | 10.2972i | − | 0.380594i | ||||||
\(733\) | − | 36.9830i | − | 1.36600i | −0.730420 | − | 0.682998i | \(-0.760676\pi\) | ||
0.730420 | − | 0.682998i | \(-0.239324\pi\) | |||||||
\(734\) | −20.9723 | −0.774103 | ||||||||
\(735\) | 9.50750 | − | 27.2006i | 0.350690 | − | 1.00331i | ||||
\(736\) | 51.9147 | 1.91360 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | − | 5.70789i | − | 0.210110i | ||||||
\(739\) | 44.9643 | 1.65404 | 0.827020 | − | 0.562172i | \(-0.190034\pi\) | ||||
0.827020 | + | 0.562172i | \(0.190034\pi\) | |||||||
\(740\) | 9.93119 | − | 28.4128i | 0.365078 | − | 1.04447i | ||||
\(741\) | −43.3301 | −1.59177 | ||||||||
\(742\) | 6.12966i | 0.225027i | ||||||||
\(743\) | 26.6500i | 0.977693i | 0.872370 | + | 0.488847i | \(0.162582\pi\) | ||||
−0.872370 | + | 0.488847i | \(0.837418\pi\) | |||||||
\(744\) | 41.3002 | 1.51414 | ||||||||
\(745\) | −21.7828 | − | 7.61381i | −0.798060 | − | 0.278948i | ||||
\(746\) | −72.3765 | −2.64989 | ||||||||
\(747\) | 9.40177i | 0.343993i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.54733 | −0.239234 | ||||||||
\(750\) | −33.2461 | − | 52.7911i | −1.21398 | − | 1.92766i | ||||
\(751\) | 33.6451 | 1.22773 | 0.613864 | − | 0.789412i | \(-0.289614\pi\) | ||||
0.613864 | + | 0.789412i | \(0.289614\pi\) | |||||||
\(752\) | 20.2069i | 0.736871i | ||||||||
\(753\) | − | 2.32440i | − | 0.0847059i | ||||||
\(754\) | 58.6590 | 2.13624 | ||||||||
\(755\) | −31.5992 | − | 11.0450i | −1.15001 | − | 0.401967i | ||||
\(756\) | −14.4366 | −0.525054 | ||||||||
\(757\) | − | 1.34307i | − | 0.0488147i | −0.999702 | − | 0.0244074i | \(-0.992230\pi\) | ||
0.999702 | − | 0.0244074i | \(-0.00776988\pi\) | |||||||
\(758\) | − | 47.7614i | − | 1.73477i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 35.4677 | − | 101.472i | 1.28655 | − | 3.68076i | ||||
\(761\) | −1.62094 | −0.0587591 | −0.0293795 | − | 0.999568i | \(-0.509353\pi\) | ||||
−0.0293795 | + | 0.999568i | \(0.509353\pi\) | |||||||
\(762\) | 96.3754i | 3.49131i | ||||||||
\(763\) | − | 2.81396i | − | 0.101872i | ||||||
\(764\) | −83.5340 | −3.02216 | ||||||||
\(765\) | −1.88572 | + | 5.39497i | −0.0681783 | + | 0.195055i | ||||
\(766\) | −45.5322 | −1.64515 | ||||||||
\(767\) | − | 37.6649i | − | 1.36000i | ||||||
\(768\) | − | 37.4200i | − | 1.35028i | ||||||
\(769\) | 3.62584 | 0.130751 | 0.0653755 | − | 0.997861i | \(-0.479175\pi\) | ||||
0.0653755 | + | 0.997861i | \(0.479175\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −51.8889 | −1.86873 | ||||||||
\(772\) | 52.8488i | 1.90207i | ||||||||
\(773\) | − | 22.0996i | − | 0.794867i | −0.917631 | − | 0.397434i | \(-0.869901\pi\) | ||
0.917631 | − | 0.397434i | \(-0.130099\pi\) | |||||||
\(774\) | −13.1163 | −0.471455 | ||||||||
\(775\) | −10.3372 | − | 8.23211i | −0.371322 | − | 0.295706i | ||||
\(776\) | 93.0310 | 3.33962 | ||||||||
\(777\) | − | 5.93327i | − | 0.212855i | ||||||
\(778\) | 35.3583i | 1.26766i | ||||||||
\(779\) | −9.12609 | −0.326976 | ||||||||
\(780\) | −66.7008 | − | 23.3141i | −2.38827 | − | 0.834779i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 21.8724i | 0.782155i | ||||||||
\(783\) | 22.2375i | 0.794703i | ||||||||
\(784\) | 56.8690 | 2.03104 | ||||||||
\(785\) | −13.3301 | + | 38.1368i | −0.475770 | + | 1.36116i | ||||
\(786\) | 28.5889 | 1.01973 | ||||||||
\(787\) | 1.84385i | 0.0657263i | 0.999460 | + | 0.0328632i | \(0.0104626\pi\) | ||||
−0.999460 | + | 0.0328632i | \(0.989537\pi\) | |||||||
\(788\) | 16.7670i | 0.597298i | ||||||||
\(789\) | 5.34557 | 0.190307 | ||||||||
\(790\) | −14.8076 | + | 42.3638i | −0.526829 | + | 1.50724i | ||||
\(791\) | 17.5427 | 0.623748 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.08377i | 0.109508i | ||||||||
\(794\) | 6.32203 | 0.224360 | ||||||||
\(795\) | −10.7363 | − | 3.75269i | −0.380777 | − | 0.133094i | ||||
\(796\) | 13.6451 | 0.483638 | ||||||||
\(797\) | − | 48.4609i | − | 1.71657i | −0.513172 | − | 0.858286i | \(-0.671530\pi\) | ||
0.513172 | − | 0.858286i | \(-0.328470\pi\) | |||||||
\(798\) | − | 36.3229i | − | 1.28582i | ||||||
\(799\) | −3.46410 | −0.122551 | ||||||||
\(800\) | 31.2110 | − | 39.1921i | 1.10347 | − | 1.38565i | ||||
\(801\) | 14.2089 | 0.502046 | ||||||||
\(802\) | 42.8042i | 1.51147i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 101.128 | 3.56650 | ||||||||
\(805\) | −10.8146 | − | 3.78005i | −0.381164 | − | 0.133229i | ||||
\(806\) | −21.2018 | −0.746800 | ||||||||
\(807\) | − | 34.4215i | − | 1.21169i | ||||||
\(808\) | − | 111.596i | − | 3.92595i | ||||||
\(809\) | −16.5526 | −0.581958 | −0.290979 | − | 0.956729i | \(-0.593981\pi\) | ||||
−0.290979 | + | 0.956729i | \(0.593981\pi\) | |||||||
\(810\) | 21.6334 | − | 61.8923i | 0.760120 | − | 2.17467i | ||||
\(811\) | −14.7477 | −0.517863 | −0.258932 | − | 0.965896i | \(-0.583370\pi\) | ||||
−0.258932 | + | 0.965896i | \(0.583370\pi\) | |||||||
\(812\) | 34.7112i | 1.21813i | ||||||||
\(813\) | − | 4.29009i | − | 0.150460i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.7911 | − | 45.1778i | 0.553139 | − | 1.58251i | ||||
\(816\) | −32.7127 | −1.14517 | ||||||||
\(817\) | 20.9710i | 0.733683i | ||||||||
\(818\) | 50.7858i | 1.77568i | ||||||||
\(819\) | −4.80265 | −0.167818 | ||||||||
\(820\) | −14.0484 | − | 4.91037i | −0.490591 | − | 0.171478i | ||||
\(821\) | −41.1891 | −1.43751 | −0.718754 | − | 0.695264i | \(-0.755287\pi\) | ||||
−0.718754 | + | 0.695264i | \(0.755287\pi\) | |||||||
\(822\) | 40.6130i | 1.41654i | ||||||||
\(823\) | − | 2.43428i | − | 0.0848535i | −0.999100 | − | 0.0424268i | \(-0.986491\pi\) | ||
0.999100 | − | 0.0424268i | \(-0.0135089\pi\) | |||||||
\(824\) | −59.3886 | −2.06890 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 31.5739 | 1.09860 | ||||||||
\(827\) | − | 42.0173i | − | 1.46108i | −0.682868 | − | 0.730542i | \(-0.739268\pi\) | ||
0.682868 | − | 0.730542i | \(-0.260732\pi\) | |||||||
\(828\) | 39.2654i | 1.36457i | ||||||||
\(829\) | 12.9730 | 0.450570 | 0.225285 | − | 0.974293i | \(-0.427669\pi\) | ||||
0.225285 | + | 0.974293i | \(0.427669\pi\) | |||||||
\(830\) | 32.7805 | + | 11.4579i | 1.13783 | + | 0.397709i | ||||
\(831\) | −41.4236 | −1.43697 | ||||||||
\(832\) | − | 22.2837i | − | 0.772547i | ||||||
\(833\) | 9.74913i | 0.337787i | ||||||||
\(834\) | 64.2040 | 2.22320 | ||||||||
\(835\) | −9.27875 | + | 26.5461i | −0.321104 | + | 0.918667i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 8.03754i | − | 0.277818i | ||||||
\(838\) | − | 4.81049i | − | 0.166176i | ||||||
\(839\) | −30.4876 | −1.05255 | −0.526274 | − | 0.850315i | \(-0.676411\pi\) | ||||
−0.526274 | + | 0.850315i | \(0.676411\pi\) | |||||||
\(840\) | 11.4013 | − | 32.6187i | 0.393383 | − | 1.12545i | ||||
\(841\) | 24.4677 | 0.843713 | ||||||||
\(842\) | 55.2835i | 1.90519i | ||||||||
\(843\) | 6.24482i | 0.215083i | ||||||||
\(844\) | 14.9700 | 0.515287 | ||||||||
\(845\) | −7.46547 | − | 2.60943i | −0.256820 | − | 0.0897671i | ||||
\(846\) | −8.80968 | −0.302883 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 22.4466i | − | 0.770821i | ||||||
\(849\) | 1.22467 | 0.0420305 | ||||||||
\(850\) | 16.5122 | + | 13.1496i | 0.566363 | + | 0.451028i | ||||
\(851\) | 14.5274 | 0.497993 | ||||||||
\(852\) | 2.50428i | 0.0857951i | ||||||||
\(853\) | 40.7630i | 1.39570i | 0.716245 | + | 0.697849i | \(0.245859\pi\) | ||||
−0.716245 | + | 0.697849i | \(0.754141\pi\) | |||||||
\(854\) | −2.58508 | −0.0884596 | ||||||||
\(855\) | 21.9365 | + | 7.66752i | 0.750212 | + | 0.262224i | ||||
\(856\) | 48.3522 | 1.65264 | ||||||||
\(857\) | 5.21553i | 0.178159i | 0.996025 | + | 0.0890796i | \(0.0283925\pi\) | ||||
−0.996025 | + | 0.0890796i | \(0.971607\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.2632 | −1.47612 | −0.738061 | − | 0.674734i | \(-0.764258\pi\) | ||||
−0.738061 | + | 0.674734i | \(0.764258\pi\) | |||||||
\(860\) | −11.2836 | + | 32.2821i | −0.384769 | + | 1.10081i | ||||
\(861\) | −2.93364 | −0.0999783 | ||||||||
\(862\) | − | 68.6631i | − | 2.33867i | ||||||
\(863\) | − | 28.5863i | − | 0.973088i | −0.873656 | − | 0.486544i | \(-0.838257\pi\) | ||
0.873656 | − | 0.486544i | \(-0.161743\pi\) | |||||||
\(864\) | 30.4733 | 1.03672 | ||||||||
\(865\) | −7.31216 | + | 20.9198i | −0.248621 | + | 0.711295i | ||||
\(866\) | −23.8180 | −0.809367 | ||||||||
\(867\) | 30.7687i | 1.04496i | ||||||||
\(868\) | − | 12.5461i | − | 0.425841i | ||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −86.1278 | − | 30.1045i | −2.92001 | − | 1.02064i | ||||
\(871\) | −30.2856 | −1.02619 | ||||||||
\(872\) | 20.7812i | 0.703740i | ||||||||
\(873\) | 20.1118i | 0.680680i | ||||||||
\(874\) | 88.9354 | 3.00828 | ||||||||
\(875\) | −9.35537 | + | 5.89171i | −0.316269 | + | 0.199176i | ||||
\(876\) | 140.406 | 4.74389 | ||||||||
\(877\) | 25.3137i | 0.854784i | 0.904066 | + | 0.427392i | \(0.140568\pi\) | ||||
−0.904066 | + | 0.427392i | \(0.859432\pi\) | |||||||
\(878\) | 28.9034i | 0.975443i | ||||||||
\(879\) | 19.9699 | 0.673568 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.716380 | −0.0241355 | −0.0120677 | − | 0.999927i | \(-0.503841\pi\) | ||||
−0.0120677 | + | 0.999927i | \(0.503841\pi\) | |||||||
\(882\) | 24.7933i | 0.834835i | ||||||||
\(883\) | − | 28.7614i | − | 0.967899i | −0.875096 | − | 0.483950i | \(-0.839202\pi\) | ||
0.875096 | − | 0.483950i | \(-0.160798\pi\) | |||||||
\(884\) | 23.9066 | 0.804067 | ||||||||
\(885\) | −19.3301 | + | 55.3026i | −0.649773 | + | 1.85898i | ||||
\(886\) | 46.1124 | 1.54918 | ||||||||
\(887\) | 48.5426i | 1.62990i | 0.579532 | + | 0.814950i | \(0.303235\pi\) | ||||
−0.579532 | + | 0.814950i | \(0.696765\pi\) | |||||||
\(888\) | 43.8174i | 1.47041i | ||||||||
\(889\) | 17.0792 | 0.572817 | ||||||||
\(890\) | 17.3163 | − | 49.5412i | 0.580442 | − | 1.66062i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 59.3776i | 1.98811i | ||||||||
\(893\) | 14.0854i | 0.471350i | ||||||||
\(894\) | 57.5840 | 1.92590 | ||||||||
\(895\) | −5.15753 | − | 1.80273i | −0.172397 | − | 0.0602585i | ||||
\(896\) | −1.13762 | −0.0380051 | ||||||||
\(897\) | − | 34.1040i | − | 1.13870i | ||||||
\(898\) | 44.1462i | 1.47318i | ||||||||
\(899\) | −19.3254 | −0.644538 | ||||||||
\(900\) | 29.6427 | + | 23.6062i | 0.988089 | + | 0.786874i | ||||
\(901\) | 3.84806 | 0.128197 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.74128i | 0.224336i | ||||||||
\(904\) | −129.553 | −4.30889 | ||||||||
\(905\) | 29.9776 | + | 10.4782i | 0.996490 | + | 0.348306i | ||||
\(906\) | 83.5340 | 2.77523 | ||||||||
\(907\) | 32.9984i | 1.09569i | 0.836578 | + | 0.547847i | \(0.184553\pi\) | ||||
−0.836578 | + | 0.547847i | \(0.815447\pi\) | |||||||
\(908\) | 65.3672i | 2.16929i | ||||||||
\(909\) | 24.1253 | 0.800185 | ||||||||
\(910\) | −5.85296 | + | 16.7451i | −0.194024 | + | 0.555094i | ||||
\(911\) | 22.9708 | 0.761056 | 0.380528 | − | 0.924769i | \(-0.375742\pi\) | ||||
0.380528 | + | 0.924769i | \(0.375742\pi\) | |||||||
\(912\) | 133.013i | 4.40451i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −85.0415 | −2.81292 | ||||||||
\(915\) | 1.58263 | − | 4.52784i | 0.0523201 | − | 0.149686i | ||||
\(916\) | 28.0464 | 0.926681 | ||||||||
\(917\) | − | 5.06638i | − | 0.167306i | ||||||
\(918\) | 12.8388i | 0.423744i | ||||||||
\(919\) | −54.6875 | −1.80398 | −0.901988 | − | 0.431762i | \(-0.857892\pi\) | ||||
−0.901988 | + | 0.431762i | \(0.857892\pi\) | |||||||
\(920\) | 79.8659 | + | 27.9158i | 2.63310 | + | 0.920355i | ||||
\(921\) | −13.5874 | −0.447719 | ||||||||
\(922\) | 20.7812i | 0.684392i | ||||||||
\(923\) | − | 0.749976i | − | 0.0246858i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.73384 | − | 10.9672i | 0.287167 | − | 0.360600i | ||||
\(926\) | −66.2057 | −2.17565 | ||||||||
\(927\) | − | 12.8388i | − | 0.421682i | ||||||
\(928\) | − | 73.2698i | − | 2.40520i | ||||||
\(929\) | 47.1128 | 1.54572 | 0.772860 | − | 0.634576i | \(-0.218825\pi\) | ||||
0.772860 | + | 0.634576i | \(0.218825\pi\) | |||||||
\(930\) | 31.1301 | + | 10.8810i | 1.02080 | + | 0.356802i | ||||
\(931\) | 39.6409 | 1.29918 | ||||||||
\(932\) | 112.522i | 3.68577i | ||||||||
\(933\) | 48.2715i | 1.58034i | ||||||||
\(934\) | 42.5249 | 1.39146 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 35.4677 | 1.15930 | ||||||||
\(937\) | 29.4666i | 0.962632i | 0.876547 | + | 0.481316i | \(0.159841\pi\) | ||||
−0.876547 | + | 0.481316i | \(0.840159\pi\) | |||||||
\(938\) | − | 25.3879i | − | 0.828945i | ||||||
\(939\) | −54.7314 | −1.78609 | ||||||||
\(940\) | −7.57876 | + | 21.6825i | −0.247192 | + | 0.707207i | ||||
\(941\) | 40.6051 | 1.32369 | 0.661844 | − | 0.749642i | \(-0.269774\pi\) | ||||
0.661844 | + | 0.749642i | \(0.269774\pi\) | |||||||
\(942\) | − | 100.817i | − | 3.28478i | ||||||
\(943\) | − | 7.18293i | − | 0.233908i | ||||||
\(944\) | −115.623 | −3.76319 | ||||||||
\(945\) | −6.34802 | − | 2.21884i | −0.206501 | − | 0.0721789i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 12.2120i | − | 0.396837i | −0.980117 | − | 0.198418i | \(-0.936420\pi\) | ||
0.980117 | − | 0.198418i | \(-0.0635805\pi\) | |||||||
\(948\) | − | 79.0546i | − | 2.56757i | ||||||
\(949\) | −42.0487 | −1.36496 | ||||||||
\(950\) | 53.4677 | − | 67.1401i | 1.73472 | − | 2.17831i | ||||
\(951\) | 53.1177 | 1.72246 | ||||||||
\(952\) | 11.6911i | 0.378910i | ||||||||
\(953\) | 6.22053i | 0.201503i | 0.994912 | + | 0.100751i | \(0.0321246\pi\) | ||||
−0.994912 | + | 0.100751i | \(0.967875\pi\) | |||||||
\(954\) | 9.78613 | 0.316838 | ||||||||
\(955\) | −36.7314 | − | 12.8388i | −1.18860 | − | 0.415455i | ||||
\(956\) | −31.5992 | −1.02199 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 90.7353i | − | 2.93152i | ||||||
\(959\) | 7.19723 | 0.232411 | ||||||||
\(960\) | −11.4362 | + | 32.7187i | −0.369103 | + | 1.05599i | ||||
\(961\) | −24.0150 | −0.774678 | ||||||||
\(962\) | − | 22.4940i | − | 0.725235i | ||||||
\(963\) | 10.4529i | 0.336841i | ||||||||
\(964\) | −58.3862 | −1.88049 | ||||||||
\(965\) | −8.12263 | + | 23.2385i | −0.261477 | + | 0.748075i | ||||
\(966\) | 28.5889 | 0.919832 | ||||||||
\(967\) | − | 51.2195i | − | 1.64711i | −0.567238 | − | 0.823554i | \(-0.691988\pi\) | ||
0.567238 | − | 0.823554i | \(-0.308012\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22.8026 | −0.732527 | ||||||||
\(970\) | 70.1223 | + | 24.5101i | 2.25149 | + | 0.786970i | ||||
\(971\) | 16.9708 | 0.544618 | 0.272309 | − | 0.962210i | \(-0.412213\pi\) | ||||
0.272309 | + | 0.962210i | \(0.412213\pi\) | |||||||
\(972\) | 71.6995i | 2.29976i | ||||||||
\(973\) | − | 11.3779i | − | 0.364759i | ||||||
\(974\) | −6.58256 | −0.210919 | ||||||||
\(975\) | −25.7462 | − | 20.5033i | −0.824539 | − | 0.656630i | ||||
\(976\) | 9.46648 | 0.303015 | ||||||||
\(977\) | 13.1659i | 0.421216i | 0.977571 | + | 0.210608i | \(0.0675443\pi\) | ||||
−0.977571 | + | 0.210608i | \(0.932456\pi\) | |||||||
\(978\) | 119.430i | 3.81894i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 61.0219 | + | 21.3292i | 1.94927 | + | 0.681335i | ||||
\(981\) | −4.49255 | −0.143436 | ||||||||
\(982\) | − | 50.3961i | − | 1.60821i | ||||||
\(983\) | 12.7962i | 0.408136i | 0.978957 | + | 0.204068i | \(0.0654164\pi\) | ||||
−0.978957 | + | 0.204068i | \(0.934584\pi\) | |||||||
\(984\) | 21.6650 | 0.690656 | ||||||||
\(985\) | −2.57701 | + | 7.37272i | −0.0821103 | + | 0.234915i | ||||
\(986\) | 30.8696 | 0.983088 | ||||||||
\(987\) | 4.52784i | 0.144123i | ||||||||
\(988\) | − | 97.2067i | − | 3.09256i | ||||||
\(989\) | −16.5058 | −0.524854 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.32786 | 0.0739468 | 0.0369734 | − | 0.999316i | \(-0.488228\pi\) | ||||
0.0369734 | + | 0.999316i | \(0.488228\pi\) | |||||||
\(992\) | 26.4827i | 0.840826i | ||||||||
\(993\) | − | 12.4118i | − | 0.393877i | ||||||
\(994\) | 0.628693 | 0.0199409 | ||||||||
\(995\) | 6.00000 | + | 2.09720i | 0.190213 | + | 0.0664856i | ||||
\(996\) | −61.1713 | −1.93829 | ||||||||
\(997\) | − | 19.1613i | − | 0.606843i | −0.952856 | − | 0.303422i | \(-0.901871\pi\) | ||
0.952856 | − | 0.303422i | \(-0.0981290\pi\) | |||||||
\(998\) | 3.01856i | 0.0955509i | ||||||||
\(999\) | 8.52742 | 0.269796 |
(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 | 605.2.b.h.364.2 | yes | 12 | |
5.2 | odd | 4 | 3025.2.a.bo.1.12 | 12 | |||
5.3 | odd | 4 | 3025.2.a.bo.1.1 | 12 | |||
5.4 | even | 2 | inner | 605.2.b.h.364.11 | yes | 12 | |
11.2 | odd | 10 | 605.2.j.k.444.12 | 48 | |||
11.3 | even | 5 | 605.2.j.k.9.1 | 48 | |||
11.4 | even | 5 | 605.2.j.k.269.12 | 48 | |||
11.5 | even | 5 | 605.2.j.k.124.11 | 48 | |||
11.6 | odd | 10 | 605.2.j.k.124.1 | 48 | |||
11.7 | odd | 10 | 605.2.j.k.269.2 | 48 | |||
11.8 | odd | 10 | 605.2.j.k.9.11 | 48 | |||
11.9 | even | 5 | 605.2.j.k.444.2 | 48 | |||
11.10 | odd | 2 | inner | 605.2.b.h.364.12 | yes | 12 | |
55.4 | even | 10 | 605.2.j.k.269.1 | 48 | |||
55.9 | even | 10 | 605.2.j.k.444.11 | 48 | |||
55.14 | even | 10 | 605.2.j.k.9.12 | 48 | |||
55.19 | odd | 10 | 605.2.j.k.9.2 | 48 | |||
55.24 | odd | 10 | 605.2.j.k.444.1 | 48 | |||
55.29 | odd | 10 | 605.2.j.k.269.11 | 48 | |||
55.32 | even | 4 | 3025.2.a.bo.1.2 | 12 | |||
55.39 | odd | 10 | 605.2.j.k.124.12 | 48 | |||
55.43 | even | 4 | 3025.2.a.bo.1.11 | 12 | |||
55.49 | even | 10 | 605.2.j.k.124.2 | 48 | |||
55.54 | odd | 2 | inner | 605.2.b.h.364.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.b.h.364.1 | ✓ | 12 | 55.54 | odd | 2 | inner | |
605.2.b.h.364.2 | yes | 12 | 1.1 | even | 1 | trivial | |
605.2.b.h.364.11 | yes | 12 | 5.4 | even | 2 | inner | |
605.2.b.h.364.12 | yes | 12 | 11.10 | odd | 2 | inner | |
605.2.j.k.9.1 | 48 | 11.3 | even | 5 | |||
605.2.j.k.9.2 | 48 | 55.19 | odd | 10 | |||
605.2.j.k.9.11 | 48 | 11.8 | odd | 10 | |||
605.2.j.k.9.12 | 48 | 55.14 | even | 10 | |||
605.2.j.k.124.1 | 48 | 11.6 | odd | 10 | |||
605.2.j.k.124.2 | 48 | 55.49 | even | 10 | |||
605.2.j.k.124.11 | 48 | 11.5 | even | 5 | |||
605.2.j.k.124.12 | 48 | 55.39 | odd | 10 | |||
605.2.j.k.269.1 | 48 | 55.4 | even | 10 | |||
605.2.j.k.269.2 | 48 | 11.7 | odd | 10 | |||
605.2.j.k.269.11 | 48 | 55.29 | odd | 10 | |||
605.2.j.k.269.12 | 48 | 11.4 | even | 5 | |||
605.2.j.k.444.1 | 48 | 55.24 | odd | 10 | |||
605.2.j.k.444.2 | 48 | 11.9 | even | 5 | |||
605.2.j.k.444.11 | 48 | 55.9 | even | 10 | |||
605.2.j.k.444.12 | 48 | 11.2 | odd | 10 | |||
3025.2.a.bo.1.1 | 12 | 5.3 | odd | 4 | |||
3025.2.a.bo.1.2 | 12 | 55.32 | even | 4 | |||
3025.2.a.bo.1.11 | 12 | 55.43 | even | 4 | |||
3025.2.a.bo.1.12 | 12 | 5.2 | odd | 4 |