Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1815,2,Mod(364,1815)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1815, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1815.364");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1815 = 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1815.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.4928479669\) |
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: | \( x^{12} + 21x^{10} + 164x^{8} + 589x^{6} + 965x^{4} + 576x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 364.8 | ||
Root | \(1.19557i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1815.364 |
Dual form | 1815.2.c.h.364.5 |
$q$-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 \(\left(\mathbb{Z}/1815\mathbb{Z}\right)^\times\).
\(n\) | \(727\) | \(1211\) | \(1696\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.19557i | 0.845395i | 0.906271 | + | 0.422698i | \(0.138917\pi\) | ||||
−0.906271 | + | 0.422698i | \(0.861083\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0.570614 | 0.285307 | ||||||||
\(5\) | 0.849151 | − | 2.06856i | 0.379752 | − | 0.925088i | ||||
\(6\) | −1.19557 | −0.488089 | ||||||||
\(7\) | − | 3.76208i | − | 1.42193i | −0.703227 | − | 0.710965i | \(-0.748258\pi\) | ||
0.703227 | − | 0.710965i | \(-0.251742\pi\) | |||||||
\(8\) | 3.07335i | 1.08659i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.47311 | + | 1.01522i | 0.782065 | + | 0.321040i | ||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.570614i | 0.164722i | ||||||||
\(13\) | − | 1.11079i | − | 0.308078i | −0.988065 | − | 0.154039i | \(-0.950772\pi\) | ||
0.988065 | − | 0.154039i | \(-0.0492282\pi\) | |||||||
\(14\) | 4.49782 | 1.20209 | ||||||||
\(15\) | 2.06856 | + | 0.849151i | 0.534100 | + | 0.219250i | ||||
\(16\) | −2.53317 | −0.633293 | ||||||||
\(17\) | − | 5.57117i | − | 1.35121i | −0.737265 | − | 0.675603i | \(-0.763883\pi\) | ||
0.737265 | − | 0.675603i | \(-0.236117\pi\) | |||||||
\(18\) | − | 1.19557i | − | 0.281798i | ||||||
\(19\) | −1.37094 | −0.314515 | −0.157257 | − | 0.987558i | \(-0.550265\pi\) | ||||
−0.157257 | + | 0.987558i | \(0.550265\pi\) | |||||||
\(20\) | 0.484538 | − | 1.18035i | 0.108346 | − | 0.263934i | ||||
\(21\) | 3.76208 | 0.820952 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.35369i | − | 0.490779i | −0.969425 | − | 0.245390i | \(-0.921084\pi\) | ||
0.969425 | − | 0.245390i | \(-0.0789159\pi\) | |||||||
\(24\) | −3.07335 | −0.627344 | ||||||||
\(25\) | −3.55789 | − | 3.51304i | −0.711577 | − | 0.702608i | ||||
\(26\) | 1.32803 | 0.260448 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | − | 2.14669i | − | 0.405687i | ||||||
\(29\) | −10.3637 | −1.92449 | −0.962244 | − | 0.272189i | \(-0.912252\pi\) | ||||
−0.962244 | + | 0.272189i | \(0.912252\pi\) | |||||||
\(30\) | −1.01522 | + | 2.47311i | −0.185353 | + | 0.451526i | ||||
\(31\) | 9.94621 | 1.78639 | 0.893196 | − | 0.449667i | \(-0.148457\pi\) | ||||
0.893196 | + | 0.449667i | \(0.148457\pi\) | |||||||
\(32\) | 3.11811i | 0.551210i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.66072 | 1.14230 | ||||||||
\(35\) | −7.78208 | − | 3.19457i | −1.31541 | − | 0.539981i | ||||
\(36\) | −0.570614 | −0.0951024 | ||||||||
\(37\) | 4.01410i | 0.659913i | 0.943996 | + | 0.329957i | \(0.107034\pi\) | ||||
−0.943996 | + | 0.329957i | \(0.892966\pi\) | |||||||
\(38\) | − | 1.63905i | − | 0.265889i | ||||||
\(39\) | 1.11079 | 0.177869 | ||||||||
\(40\) | 6.35740 | + | 2.60974i | 1.00519 | + | 0.412635i | ||||
\(41\) | −3.94075 | −0.615442 | −0.307721 | − | 0.951477i | \(-0.599566\pi\) | ||||
−0.307721 | + | 0.951477i | \(0.599566\pi\) | |||||||
\(42\) | 4.49782i | 0.694029i | ||||||||
\(43\) | − | 7.78774i | − | 1.18762i | −0.804605 | − | 0.593810i | \(-0.797623\pi\) | ||
0.804605 | − | 0.593810i | \(-0.202377\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.849151 | + | 2.06856i | −0.126584 | + | 0.308363i | ||||
\(46\) | 2.81400 | 0.414902 | ||||||||
\(47\) | − | 6.46038i | − | 0.942343i | −0.882042 | − | 0.471171i | \(-0.843831\pi\) | ||
0.882042 | − | 0.471171i | \(-0.156169\pi\) | |||||||
\(48\) | − | 2.53317i | − | 0.365632i | ||||||
\(49\) | −7.15321 | −1.02189 | ||||||||
\(50\) | 4.20008 | − | 4.25370i | 0.593981 | − | 0.601564i | ||||
\(51\) | 5.57117 | 0.780120 | ||||||||
\(52\) | − | 0.633833i | − | 0.0878969i | ||||||
\(53\) | 4.06788i | 0.558766i | 0.960180 | + | 0.279383i | \(0.0901300\pi\) | ||||
−0.960180 | + | 0.279383i | \(0.909870\pi\) | |||||||
\(54\) | 1.19557 | 0.162696 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 11.5622 | 1.54506 | ||||||||
\(57\) | − | 1.37094i | − | 0.181585i | ||||||
\(58\) | − | 12.3905i | − | 1.62695i | ||||||
\(59\) | 4.28445 | 0.557789 | 0.278894 | − | 0.960322i | \(-0.410032\pi\) | ||||
0.278894 | + | 0.960322i | \(0.410032\pi\) | |||||||
\(60\) | 1.18035 | + | 0.484538i | 0.152383 | + | 0.0625536i | ||||
\(61\) | 8.32914 | 1.06644 | 0.533218 | − | 0.845978i | \(-0.320982\pi\) | ||||
0.533218 | + | 0.845978i | \(0.320982\pi\) | |||||||
\(62\) | 11.8914i | 1.51021i | ||||||||
\(63\) | 3.76208i | 0.473977i | ||||||||
\(64\) | −8.79426 | −1.09928 | ||||||||
\(65\) | −2.29774 | − | 0.943230i | −0.284999 | − | 0.116993i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 9.15868i | − | 1.11891i | −0.828860 | − | 0.559455i | \(-0.811010\pi\) | ||
0.828860 | − | 0.559455i | \(-0.188990\pi\) | |||||||
\(68\) | − | 3.17899i | − | 0.385509i | ||||||
\(69\) | 2.35369 | 0.283352 | ||||||||
\(70\) | 3.81933 | − | 9.30402i | 0.456497 | − | 1.11204i | ||||
\(71\) | −2.85677 | −0.339037 | −0.169518 | − | 0.985527i | \(-0.554221\pi\) | ||||
−0.169518 | + | 0.985527i | \(0.554221\pi\) | |||||||
\(72\) | − | 3.07335i | − | 0.362197i | ||||||
\(73\) | − | 11.6534i | − | 1.36393i | −0.731386 | − | 0.681963i | \(-0.761126\pi\) | ||
0.731386 | − | 0.681963i | \(-0.238874\pi\) | |||||||
\(74\) | −4.79913 | −0.557887 | ||||||||
\(75\) | 3.51304 | − | 3.55789i | 0.405651 | − | 0.410829i | ||||
\(76\) | −0.782277 | −0.0897333 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.32803i | 0.150370i | ||||||||
\(79\) | −3.07812 | −0.346315 | −0.173158 | − | 0.984894i | \(-0.555397\pi\) | ||||
−0.173158 | + | 0.984894i | \(0.555397\pi\) | |||||||
\(80\) | −2.15104 | + | 5.24002i | −0.240494 | + | 0.585852i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 4.71144i | − | 0.520291i | ||||||
\(83\) | 4.64341i | 0.509680i | 0.966983 | + | 0.254840i | \(0.0820228\pi\) | ||||
−0.966983 | + | 0.254840i | \(0.917977\pi\) | |||||||
\(84\) | 2.14669 | 0.234224 | ||||||||
\(85\) | −11.5243 | − | 4.73076i | −1.24999 | − | 0.513123i | ||||
\(86\) | 9.31078 | 1.00401 | ||||||||
\(87\) | − | 10.3637i | − | 1.11110i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.5770 | 1.75716 | 0.878582 | − | 0.477592i | \(-0.158490\pi\) | ||||
0.878582 | + | 0.477592i | \(0.158490\pi\) | |||||||
\(90\) | −2.47311 | − | 1.01522i | −0.260688 | − | 0.107013i | ||||
\(91\) | −4.17888 | −0.438066 | ||||||||
\(92\) | − | 1.34305i | − | 0.140023i | ||||||
\(93\) | 9.94621i | 1.03137i | ||||||||
\(94\) | 7.72383 | 0.796652 | ||||||||
\(95\) | −1.16413 | + | 2.83587i | −0.119438 | + | 0.290954i | ||||
\(96\) | −3.11811 | −0.318241 | ||||||||
\(97\) | − | 18.1930i | − | 1.84722i | −0.383337 | − | 0.923608i | \(-0.625225\pi\) | ||
0.383337 | − | 0.923608i | \(-0.374775\pi\) | |||||||
\(98\) | − | 8.55216i | − | 0.863899i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.03018 | − | 2.00459i | −0.203018 | − | 0.200459i | ||||
\(101\) | −2.16756 | −0.215680 | −0.107840 | − | 0.994168i | \(-0.534393\pi\) | ||||
−0.107840 | + | 0.994168i | \(0.534393\pi\) | |||||||
\(102\) | 6.66072i | 0.659509i | ||||||||
\(103\) | 11.5176i | 1.13487i | 0.823420 | + | 0.567433i | \(0.192063\pi\) | ||||
−0.823420 | + | 0.567433i | \(0.807937\pi\) | |||||||
\(104\) | 3.41385 | 0.334755 | ||||||||
\(105\) | 3.19457 | − | 7.78208i | 0.311758 | − | 0.759453i | ||||
\(106\) | −4.86343 | −0.472378 | ||||||||
\(107\) | 4.23880i | 0.409780i | 0.978785 | + | 0.204890i | \(0.0656836\pi\) | ||||
−0.978785 | + | 0.204890i | \(0.934316\pi\) | |||||||
\(108\) | − | 0.570614i | − | 0.0549074i | ||||||
\(109\) | 16.2407 | 1.55557 | 0.777786 | − | 0.628529i | \(-0.216343\pi\) | ||||
0.777786 | + | 0.628529i | \(0.216343\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.01410 | −0.381001 | ||||||||
\(112\) | 9.52998i | 0.900498i | ||||||||
\(113\) | 13.0953i | 1.23190i | 0.787784 | + | 0.615952i | \(0.211229\pi\) | ||||
−0.787784 | + | 0.615952i | \(0.788771\pi\) | |||||||
\(114\) | 1.63905 | 0.153511 | ||||||||
\(115\) | −4.86876 | − | 1.99864i | −0.454014 | − | 0.186374i | ||||
\(116\) | −5.91367 | −0.549070 | ||||||||
\(117\) | 1.11079i | 0.102693i | ||||||||
\(118\) | 5.12236i | 0.471552i | ||||||||
\(119\) | −20.9592 | −1.92132 | ||||||||
\(120\) | −2.60974 | + | 6.35740i | −0.238235 | + | 0.580349i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 9.95806i | 0.901560i | ||||||||
\(123\) | − | 3.94075i | − | 0.355325i | ||||||
\(124\) | 5.67545 | 0.509671 | ||||||||
\(125\) | −10.2881 | + | 4.37660i | −0.920197 | + | 0.391455i | ||||
\(126\) | −4.49782 | −0.400698 | ||||||||
\(127\) | 8.72553i | 0.774266i | 0.922024 | + | 0.387133i | \(0.126535\pi\) | ||||
−0.922024 | + | 0.387133i | \(0.873465\pi\) | |||||||
\(128\) | − | 4.27792i | − | 0.378118i | ||||||
\(129\) | 7.78774 | 0.685672 | ||||||||
\(130\) | 1.12770 | − | 2.74711i | 0.0989055 | − | 0.240937i | ||||
\(131\) | 14.4100 | 1.25901 | 0.629504 | − | 0.776997i | \(-0.283258\pi\) | ||||
0.629504 | + | 0.776997i | \(0.283258\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.15757i | 0.447218i | ||||||||
\(134\) | 10.9498 | 0.945922 | ||||||||
\(135\) | −2.06856 | − | 0.849151i | −0.178033 | − | 0.0730833i | ||||
\(136\) | 17.1221 | 1.46821 | ||||||||
\(137\) | 9.98253i | 0.852865i | 0.904519 | + | 0.426433i | \(0.140230\pi\) | ||||
−0.904519 | + | 0.426433i | \(0.859770\pi\) | |||||||
\(138\) | 2.81400i | 0.239544i | ||||||||
\(139\) | −7.60360 | −0.644929 | −0.322465 | − | 0.946582i | \(-0.604511\pi\) | ||||
−0.322465 | + | 0.946582i | \(0.604511\pi\) | |||||||
\(140\) | −4.44057 | − | 1.82287i | −0.375296 | − | 0.154060i | ||||
\(141\) | 6.46038 | 0.544062 | ||||||||
\(142\) | − | 3.41547i | − | 0.286620i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.53317 | 0.211098 | ||||||||
\(145\) | −8.80033 | + | 21.4379i | −0.730828 | + | 1.78032i | ||||
\(146\) | 13.9324 | 1.15306 | ||||||||
\(147\) | − | 7.15321i | − | 0.589987i | ||||||
\(148\) | 2.29050i | 0.188278i | ||||||||
\(149\) | 6.47125 | 0.530146 | 0.265073 | − | 0.964228i | \(-0.414604\pi\) | ||||
0.265073 | + | 0.964228i | \(0.414604\pi\) | |||||||
\(150\) | 4.25370 | + | 4.20008i | 0.347313 | + | 0.342935i | ||||
\(151\) | −9.52872 | −0.775436 | −0.387718 | − | 0.921778i | \(-0.626737\pi\) | ||||
−0.387718 | + | 0.921778i | \(0.626737\pi\) | |||||||
\(152\) | − | 4.21337i | − | 0.341749i | ||||||
\(153\) | 5.57117i | 0.450402i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.44584 | − | 20.5743i | 0.678386 | − | 1.65257i | ||||
\(156\) | 0.633833 | 0.0507473 | ||||||||
\(157\) | 3.16690i | 0.252746i | 0.991983 | + | 0.126373i | \(0.0403336\pi\) | ||||
−0.991983 | + | 0.126373i | \(0.959666\pi\) | |||||||
\(158\) | − | 3.68010i | − | 0.292773i | ||||||
\(159\) | −4.06788 | −0.322604 | ||||||||
\(160\) | 6.45001 | + | 2.64775i | 0.509918 | + | 0.209323i | ||||
\(161\) | −8.85478 | −0.697854 | ||||||||
\(162\) | 1.19557i | 0.0939328i | ||||||||
\(163\) | 9.02020i | 0.706517i | 0.935526 | + | 0.353258i | \(0.114926\pi\) | ||||
−0.935526 | + | 0.353258i | \(0.885074\pi\) | |||||||
\(164\) | −2.24865 | −0.175590 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.55151 | −0.430881 | ||||||||
\(167\) | 3.13597i | 0.242669i | 0.992612 | + | 0.121334i | \(0.0387173\pi\) | ||||
−0.992612 | + | 0.121334i | \(0.961283\pi\) | |||||||
\(168\) | 11.5622i | 0.892040i | ||||||||
\(169\) | 11.7661 | 0.905088 | ||||||||
\(170\) | 5.65596 | − | 13.7781i | 0.433792 | − | 1.05673i | ||||
\(171\) | 1.37094 | 0.104838 | ||||||||
\(172\) | − | 4.44380i | − | 0.338836i | ||||||
\(173\) | 12.2424i | 0.930776i | 0.885107 | + | 0.465388i | \(0.154085\pi\) | ||||
−0.885107 | + | 0.465388i | \(0.845915\pi\) | |||||||
\(174\) | 12.3905 | 0.939321 | ||||||||
\(175\) | −13.2163 | + | 13.3850i | −0.999060 | + | 1.01181i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.28445i | 0.322039i | ||||||||
\(178\) | 19.8190i | 1.48550i | ||||||||
\(179\) | 8.46334 | 0.632579 | 0.316290 | − | 0.948663i | \(-0.397563\pi\) | ||||
0.316290 | + | 0.948663i | \(0.397563\pi\) | |||||||
\(180\) | −0.484538 | + | 1.18035i | −0.0361153 | + | 0.0879781i | ||||
\(181\) | 23.5514 | 1.75056 | 0.875282 | − | 0.483612i | \(-0.160675\pi\) | ||||
0.875282 | + | 0.483612i | \(0.160675\pi\) | |||||||
\(182\) | − | 4.99614i | − | 0.370339i | ||||||
\(183\) | 8.32914i | 0.615708i | ||||||||
\(184\) | 7.23372 | 0.533277 | ||||||||
\(185\) | 8.30340 | + | 3.40857i | 0.610478 | + | 0.250603i | ||||
\(186\) | −11.8914 | −0.871919 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 3.68638i | − | 0.268857i | ||||||
\(189\) | −3.76208 | −0.273651 | ||||||||
\(190\) | −3.39048 | − | 1.39180i | −0.245971 | − | 0.100972i | ||||
\(191\) | −19.2179 | −1.39056 | −0.695278 | − | 0.718741i | \(-0.744719\pi\) | ||||
−0.695278 | + | 0.718741i | \(0.744719\pi\) | |||||||
\(192\) | − | 8.79426i | − | 0.634671i | ||||||
\(193\) | 14.1416i | 1.01794i | 0.860785 | + | 0.508969i | \(0.169973\pi\) | ||||
−0.860785 | + | 0.508969i | \(0.830027\pi\) | |||||||
\(194\) | 21.7510 | 1.56163 | ||||||||
\(195\) | 0.943230 | − | 2.29774i | 0.0675461 | − | 0.164544i | ||||
\(196\) | −4.08173 | −0.291552 | ||||||||
\(197\) | 10.2965i | 0.733593i | 0.930301 | + | 0.366796i | \(0.119545\pi\) | ||||
−0.930301 | + | 0.366796i | \(0.880455\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −26.3053 | −1.86473 | −0.932367 | − | 0.361514i | \(-0.882260\pi\) | ||||
−0.932367 | + | 0.361514i | \(0.882260\pi\) | |||||||
\(200\) | 10.7968 | − | 10.9346i | 0.763449 | − | 0.773194i | ||||
\(201\) | 9.15868 | 0.646003 | ||||||||
\(202\) | − | 2.59147i | − | 0.182335i | ||||||
\(203\) | 38.9890i | 2.73649i | ||||||||
\(204\) | 3.17899 | 0.222574 | ||||||||
\(205\) | −3.34629 | + | 8.15168i | −0.233715 | + | 0.569338i | ||||
\(206\) | −13.7701 | −0.959410 | ||||||||
\(207\) | 2.35369i | 0.163593i | ||||||||
\(208\) | 2.81382i | 0.195104i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 9.30402 | + | 3.81933i | 0.642038 | + | 0.263559i | ||||
\(211\) | 0.360214 | 0.0247981 | 0.0123991 | − | 0.999923i | \(-0.496053\pi\) | ||||
0.0123991 | + | 0.999923i | \(0.496053\pi\) | |||||||
\(212\) | 2.32119i | 0.159420i | ||||||||
\(213\) | − | 2.85677i | − | 0.195743i | ||||||
\(214\) | −5.06777 | −0.346426 | ||||||||
\(215\) | −16.1094 | − | 6.61297i | −1.09865 | − | 0.451001i | ||||
\(216\) | 3.07335 | 0.209115 | ||||||||
\(217\) | − | 37.4184i | − | 2.54013i | ||||||
\(218\) | 19.4168i | 1.31507i | ||||||||
\(219\) | 11.6534 | 0.787463 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.18841 | −0.416277 | ||||||||
\(222\) | − | 4.79913i | − | 0.322096i | ||||||
\(223\) | − | 26.4883i | − | 1.77379i | −0.461971 | − | 0.886895i | \(-0.652858\pi\) | ||
0.461971 | − | 0.886895i | \(-0.347142\pi\) | |||||||
\(224\) | 11.7306 | 0.783782 | ||||||||
\(225\) | 3.55789 | + | 3.51304i | 0.237192 | + | 0.234203i | ||||
\(226\) | −15.6564 | −1.04145 | ||||||||
\(227\) | 23.3780i | 1.55165i | 0.630946 | + | 0.775827i | \(0.282667\pi\) | ||||
−0.630946 | + | 0.775827i | \(0.717333\pi\) | |||||||
\(228\) | − | 0.782277i | − | 0.0518075i | ||||||
\(229\) | 10.1085 | 0.667986 | 0.333993 | − | 0.942576i | \(-0.391604\pi\) | ||||
0.333993 | + | 0.942576i | \(0.391604\pi\) | |||||||
\(230\) | 2.38951 | − | 5.82094i | 0.157560 | − | 0.383821i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 31.8512i | − | 2.09113i | ||||||
\(233\) | − | 4.17456i | − | 0.273485i | −0.990607 | − | 0.136742i | \(-0.956337\pi\) | ||
0.990607 | − | 0.136742i | \(-0.0436633\pi\) | |||||||
\(234\) | −1.32803 | −0.0868159 | ||||||||
\(235\) | −13.3637 | − | 5.48584i | −0.871751 | − | 0.357857i | ||||
\(236\) | 2.44477 | 0.159141 | ||||||||
\(237\) | − | 3.07812i | − | 0.199945i | ||||||
\(238\) | − | 25.0581i | − | 1.62428i | ||||||
\(239\) | 23.8799 | 1.54466 | 0.772332 | − | 0.635219i | \(-0.219090\pi\) | ||||
0.772332 | + | 0.635219i | \(0.219090\pi\) | |||||||
\(240\) | −5.24002 | − | 2.15104i | −0.338242 | − | 0.138849i | ||||
\(241\) | 15.6656 | 1.00911 | 0.504555 | − | 0.863380i | \(-0.331657\pi\) | ||||
0.504555 | + | 0.863380i | \(0.331657\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 4.75273 | 0.304262 | ||||||||
\(245\) | −6.07416 | + | 14.7969i | −0.388064 | + | 0.945336i | ||||
\(246\) | 4.71144 | 0.300390 | ||||||||
\(247\) | 1.52283i | 0.0968951i | ||||||||
\(248\) | 30.5682i | 1.94108i | ||||||||
\(249\) | −4.64341 | −0.294264 | ||||||||
\(250\) | −5.23253 | − | 12.3002i | −0.330934 | − | 0.777930i | ||||
\(251\) | −6.30803 | −0.398160 | −0.199080 | − | 0.979983i | \(-0.563795\pi\) | ||||
−0.199080 | + | 0.979983i | \(0.563795\pi\) | |||||||
\(252\) | 2.14669i | 0.135229i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −10.4320 | −0.654561 | ||||||||
\(255\) | 4.73076 | − | 11.5243i | 0.296252 | − | 0.721680i | ||||
\(256\) | −12.4740 | −0.779623 | ||||||||
\(257\) | − | 8.20364i | − | 0.511729i | −0.966713 | − | 0.255865i | \(-0.917640\pi\) | ||
0.966713 | − | 0.255865i | \(-0.0823601\pi\) | |||||||
\(258\) | 9.31078i | 0.579664i | ||||||||
\(259\) | 15.1013 | 0.938351 | ||||||||
\(260\) | −1.31112 | − | 0.538220i | −0.0813124 | − | 0.0333790i | ||||
\(261\) | 10.3637 | 0.641496 | ||||||||
\(262\) | 17.2282i | 1.06436i | ||||||||
\(263\) | − | 9.84566i | − | 0.607109i | −0.952814 | − | 0.303555i | \(-0.901826\pi\) | ||
0.952814 | − | 0.303555i | \(-0.0981735\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.41466 | + | 3.45425i | 0.516908 | + | 0.212193i | ||||
\(266\) | −6.16623 | −0.378076 | ||||||||
\(267\) | 16.5770i | 1.01450i | ||||||||
\(268\) | − | 5.22607i | − | 0.319233i | ||||||
\(269\) | −17.6147 | −1.07399 | −0.536994 | − | 0.843586i | \(-0.680440\pi\) | ||||
−0.536994 | + | 0.843586i | \(0.680440\pi\) | |||||||
\(270\) | 1.01522 | − | 2.47311i | 0.0617842 | − | 0.150509i | ||||
\(271\) | 1.25356 | 0.0761484 | 0.0380742 | − | 0.999275i | \(-0.487878\pi\) | ||||
0.0380742 | + | 0.999275i | \(0.487878\pi\) | |||||||
\(272\) | 14.1127i | 0.855709i | ||||||||
\(273\) | − | 4.17888i | − | 0.252917i | ||||||
\(274\) | −11.9348 | −0.721008 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.34305 | 0.0808422 | ||||||||
\(277\) | − | 16.3707i | − | 0.983623i | −0.870702 | − | 0.491811i | \(-0.836335\pi\) | ||
0.870702 | − | 0.491811i | \(-0.163665\pi\) | |||||||
\(278\) | − | 9.09063i | − | 0.545220i | ||||||
\(279\) | −9.94621 | −0.595464 | ||||||||
\(280\) | 9.81802 | − | 23.9170i | 0.586739 | − | 1.42932i | ||||
\(281\) | −11.7669 | −0.701953 | −0.350977 | − | 0.936384i | \(-0.614150\pi\) | ||||
−0.350977 | + | 0.936384i | \(0.614150\pi\) | |||||||
\(282\) | 7.72383i | 0.459947i | ||||||||
\(283\) | 3.16579i | 0.188186i | 0.995563 | + | 0.0940932i | \(0.0299952\pi\) | ||||
−0.995563 | + | 0.0940932i | \(0.970005\pi\) | |||||||
\(284\) | −1.63012 | −0.0967296 | ||||||||
\(285\) | −2.83587 | − | 1.16413i | −0.167982 | − | 0.0689573i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.8254i | 0.875115i | ||||||||
\(288\) | − | 3.11811i | − | 0.183737i | ||||||
\(289\) | −14.0379 | −0.825760 | ||||||||
\(290\) | −25.6305 | − | 10.5214i | −1.50507 | − | 0.617838i | ||||
\(291\) | 18.1930 | 1.06649 | ||||||||
\(292\) | − | 6.64959i | − | 0.389138i | ||||||
\(293\) | − | 19.0522i | − | 1.11304i | −0.830834 | − | 0.556521i | \(-0.812136\pi\) | ||
0.830834 | − | 0.556521i | \(-0.187864\pi\) | |||||||
\(294\) | 8.55216 | 0.498772 | ||||||||
\(295\) | 3.63815 | − | 8.86265i | 0.211821 | − | 0.516004i | ||||
\(296\) | −12.3367 | −0.717057 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7.73683i | 0.448183i | ||||||||
\(299\) | −2.61446 | −0.151198 | ||||||||
\(300\) | 2.00459 | − | 2.03018i | 0.115735 | − | 0.117213i | ||||
\(301\) | −29.2981 | −1.68871 | ||||||||
\(302\) | − | 11.3922i | − | 0.655550i | ||||||
\(303\) | − | 2.16756i | − | 0.124523i | ||||||
\(304\) | 3.47282 | 0.199180 | ||||||||
\(305\) | 7.07270 | − | 17.2293i | 0.404981 | − | 0.986548i | ||||
\(306\) | −6.66072 | −0.380768 | ||||||||
\(307\) | 10.6573i | 0.608242i | 0.952633 | + | 0.304121i | \(0.0983627\pi\) | ||||
−0.952633 | + | 0.304121i | \(0.901637\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.5176 | −0.655215 | ||||||||
\(310\) | 24.5981 | + | 10.0976i | 1.39708 | + | 0.573504i | ||||
\(311\) | −11.4350 | −0.648420 | −0.324210 | − | 0.945985i | \(-0.605098\pi\) | ||||
−0.324210 | + | 0.945985i | \(0.605098\pi\) | |||||||
\(312\) | 3.41385i | 0.193271i | ||||||||
\(313\) | − | 0.0233313i | − | 0.00131876i | −1.00000 | 0.000659382i | \(-0.999790\pi\) | |||
1.00000 | 0.000659382i | \(-0.000209888\pi\) | ||||||||
\(314\) | −3.78624 | −0.213670 | ||||||||
\(315\) | 7.78208 | + | 3.19457i | 0.438471 | + | 0.179994i | ||||
\(316\) | −1.75642 | −0.0988063 | ||||||||
\(317\) | − | 1.54123i | − | 0.0865640i | −0.999063 | − | 0.0432820i | \(-0.986219\pi\) | ||
0.999063 | − | 0.0432820i | \(-0.0137814\pi\) | |||||||
\(318\) | − | 4.86343i | − | 0.272728i | ||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −7.46766 | + | 18.1915i | −0.417455 | + | 1.01693i | ||||
\(321\) | −4.23880 | −0.236586 | ||||||||
\(322\) | − | 10.5865i | − | 0.589962i | ||||||
\(323\) | 7.63772i | 0.424974i | ||||||||
\(324\) | 0.570614 | 0.0317008 | ||||||||
\(325\) | −3.90225 | + | 3.95207i | −0.216458 | + | 0.219221i | ||||
\(326\) | −10.7843 | −0.597286 | ||||||||
\(327\) | 16.2407i | 0.898110i | ||||||||
\(328\) | − | 12.1113i | − | 0.668734i | ||||||
\(329\) | −24.3044 | −1.33995 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.57394 | −0.306372 | −0.153186 | − | 0.988197i | \(-0.548953\pi\) | ||||
−0.153186 | + | 0.988197i | \(0.548953\pi\) | |||||||
\(332\) | 2.64959i | 0.145415i | ||||||||
\(333\) | − | 4.01410i | − | 0.219971i | ||||||
\(334\) | −3.74927 | −0.205151 | ||||||||
\(335\) | −18.9453 | − | 7.77710i | −1.03509 | − | 0.424908i | ||||
\(336\) | −9.52998 | −0.519903 | ||||||||
\(337\) | − | 15.5366i | − | 0.846335i | −0.906052 | − | 0.423167i | \(-0.860918\pi\) | ||
0.906052 | − | 0.423167i | \(-0.139082\pi\) | |||||||
\(338\) | 14.0672i | 0.765157i | ||||||||
\(339\) | −13.0953 | −0.711240 | ||||||||
\(340\) | −6.57593 | − | 2.69944i | −0.356630 | − | 0.146398i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.63905i | 0.0886297i | ||||||||
\(343\) | 0.576403i | 0.0311228i | ||||||||
\(344\) | 23.9344 | 1.29046 | ||||||||
\(345\) | 1.99864 | − | 4.86876i | 0.107603 | − | 0.262125i | ||||
\(346\) | −14.6367 | −0.786873 | ||||||||
\(347\) | 2.00456i | 0.107611i | 0.998551 | + | 0.0538053i | \(0.0171350\pi\) | ||||
−0.998551 | + | 0.0538053i | \(0.982865\pi\) | |||||||
\(348\) | − | 5.91367i | − | 0.317006i | ||||||
\(349\) | 29.4300 | 1.57535 | 0.787675 | − | 0.616090i | \(-0.211284\pi\) | ||||
0.787675 | + | 0.616090i | \(0.211284\pi\) | |||||||
\(350\) | −16.0027 | − | 15.8010i | −0.855382 | − | 0.844601i | ||||
\(351\) | −1.11079 | −0.0592896 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.0526i | 1.33342i | 0.745319 | + | 0.666708i | \(0.232297\pi\) | ||||
−0.745319 | + | 0.666708i | \(0.767703\pi\) | |||||||
\(354\) | −5.12236 | −0.272250 | ||||||||
\(355\) | −2.42583 | + | 5.90941i | −0.128750 | + | 0.313639i | ||||
\(356\) | 9.45910 | 0.501331 | ||||||||
\(357\) | − | 20.9592i | − | 1.10928i | ||||||
\(358\) | 10.1185i | 0.534780i | ||||||||
\(359\) | 20.4849 | 1.08115 | 0.540576 | − | 0.841295i | \(-0.318206\pi\) | ||||
0.540576 | + | 0.841295i | \(0.318206\pi\) | |||||||
\(360\) | −6.35740 | − | 2.60974i | −0.335065 | − | 0.137545i | ||||
\(361\) | −17.1205 | −0.901081 | ||||||||
\(362\) | 28.1574i | 1.47992i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.38453 | −0.124983 | ||||||||
\(365\) | −24.1058 | − | 9.89549i | −1.26175 | − | 0.517954i | ||||
\(366\) | −9.95806 | −0.520516 | ||||||||
\(367\) | 14.5810i | 0.761119i | 0.924756 | + | 0.380560i | \(0.124269\pi\) | ||||
−0.924756 | + | 0.380560i | \(0.875731\pi\) | |||||||
\(368\) | 5.96231i | 0.310807i | ||||||||
\(369\) | 3.94075 | 0.205147 | ||||||||
\(370\) | −4.07519 | + | 9.92729i | −0.211859 | + | 0.516095i | ||||
\(371\) | 15.3037 | 0.794527 | ||||||||
\(372\) | 5.67545i | 0.294259i | ||||||||
\(373\) | − | 1.60074i | − | 0.0828829i | −0.999141 | − | 0.0414415i | \(-0.986805\pi\) | ||
0.999141 | − | 0.0414415i | \(-0.0131950\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4.37660 | − | 10.2881i | −0.226007 | − | 0.531276i | ||||
\(376\) | 19.8550 | 1.02394 | ||||||||
\(377\) | 11.5119i | 0.592892i | ||||||||
\(378\) | − | 4.49782i | − | 0.231343i | ||||||
\(379\) | −14.2870 | −0.733875 | −0.366938 | − | 0.930246i | \(-0.619594\pi\) | ||||
−0.366938 | + | 0.930246i | \(0.619594\pi\) | |||||||
\(380\) | −0.664271 | + | 1.61819i | −0.0340764 | + | 0.0830112i | ||||
\(381\) | −8.72553 | −0.447023 | ||||||||
\(382\) | − | 22.9763i | − | 1.17557i | ||||||
\(383\) | − | 6.52801i | − | 0.333566i | −0.985994 | − | 0.166783i | \(-0.946662\pi\) | ||
0.985994 | − | 0.166783i | \(-0.0533379\pi\) | |||||||
\(384\) | 4.27792 | 0.218307 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.9073 | −0.860560 | ||||||||
\(387\) | 7.78774i | 0.395873i | ||||||||
\(388\) | − | 10.3812i | − | 0.527024i | ||||||
\(389\) | 27.3227 | 1.38532 | 0.692658 | − | 0.721266i | \(-0.256439\pi\) | ||||
0.692658 | + | 0.721266i | \(0.256439\pi\) | |||||||
\(390\) | 2.74711 | + | 1.12770i | 0.139105 | + | 0.0571031i | ||||
\(391\) | −13.1128 | −0.663144 | ||||||||
\(392\) | − | 21.9843i | − | 1.11038i | ||||||
\(393\) | 14.4100i | 0.726889i | ||||||||
\(394\) | −12.3101 | −0.620176 | ||||||||
\(395\) | −2.61379 | + | 6.36727i | −0.131514 | + | 0.320372i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.24918i | 0.163072i | 0.996670 | + | 0.0815359i | \(0.0259825\pi\) | ||||
−0.996670 | + | 0.0815359i | \(0.974017\pi\) | |||||||
\(398\) | − | 31.4498i | − | 1.57644i | ||||||
\(399\) | −5.15757 | −0.258201 | ||||||||
\(400\) | 9.01273 | + | 8.89913i | 0.450636 | + | 0.444957i | ||||
\(401\) | 11.2464 | 0.561620 | 0.280810 | − | 0.959763i | \(-0.409397\pi\) | ||||
0.280810 | + | 0.959763i | \(0.409397\pi\) | |||||||
\(402\) | 10.9498i | 0.546128i | ||||||||
\(403\) | − | 11.0482i | − | 0.550348i | ||||||
\(404\) | −1.23684 | −0.0615351 | ||||||||
\(405\) | 0.849151 | − | 2.06856i | 0.0421947 | − | 0.102788i | ||||
\(406\) | −46.6140 | −2.31341 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 17.1221i | 0.847672i | ||||||||
\(409\) | 14.4206 | 0.713052 | 0.356526 | − | 0.934285i | \(-0.383961\pi\) | ||||
0.356526 | + | 0.934285i | \(0.383961\pi\) | |||||||
\(410\) | −9.74589 | − | 4.00072i | −0.481315 | − | 0.197582i | ||||
\(411\) | −9.98253 | −0.492402 | ||||||||
\(412\) | 6.57213i | 0.323785i | ||||||||
\(413\) | − | 16.1184i | − | 0.793137i | ||||||
\(414\) | −2.81400 | −0.138301 | ||||||||
\(415\) | 9.60517 | + | 3.94295i | 0.471499 | + | 0.193552i | ||||
\(416\) | 3.46357 | 0.169816 | ||||||||
\(417\) | − | 7.60360i | − | 0.372350i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.6547 | −1.69299 | −0.846496 | − | 0.532396i | \(-0.821292\pi\) | ||||
−0.846496 | + | 0.532396i | \(0.821292\pi\) | |||||||
\(420\) | 1.82287 | − | 4.44057i | 0.0889468 | − | 0.216678i | ||||
\(421\) | 4.87769 | 0.237724 | 0.118862 | − | 0.992911i | \(-0.462075\pi\) | ||||
0.118862 | + | 0.992911i | \(0.462075\pi\) | |||||||
\(422\) | 0.430661i | 0.0209642i | ||||||||
\(423\) | 6.46038i | 0.314114i | ||||||||
\(424\) | −12.5020 | −0.607151 | ||||||||
\(425\) | −19.5717 | + | 19.8216i | −0.949369 | + | 0.961488i | ||||
\(426\) | 3.41547 | 0.165480 | ||||||||
\(427\) | − | 31.3348i | − | 1.51640i | ||||||
\(428\) | 2.41872i | 0.116913i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.90626 | − | 19.2599i | 0.381274 | − | 0.928796i | ||||
\(431\) | −12.1129 | −0.583458 | −0.291729 | − | 0.956501i | \(-0.594231\pi\) | ||||
−0.291729 | + | 0.956501i | \(0.594231\pi\) | |||||||
\(432\) | 2.53317i | 0.121877i | ||||||||
\(433\) | 31.2618i | 1.50234i | 0.660107 | + | 0.751172i | \(0.270511\pi\) | ||||
−0.660107 | + | 0.751172i | \(0.729489\pi\) | |||||||
\(434\) | 44.7363 | 2.14741 | ||||||||
\(435\) | −21.4379 | − | 8.80033i | −1.02787 | − | 0.421944i | ||||
\(436\) | 9.26715 | 0.443816 | ||||||||
\(437\) | 3.22677i | 0.154357i | ||||||||
\(438\) | 13.9324i | 0.665718i | ||||||||
\(439\) | 25.6088 | 1.22224 | 0.611122 | − | 0.791537i | \(-0.290719\pi\) | ||||
0.611122 | + | 0.791537i | \(0.290719\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.15321 | 0.340629 | ||||||||
\(442\) | − | 7.39867i | − | 0.351919i | ||||||
\(443\) | − | 2.26739i | − | 0.107727i | −0.998548 | − | 0.0538635i | \(-0.982846\pi\) | ||
0.998548 | − | 0.0538635i | \(-0.0171536\pi\) | |||||||
\(444\) | −2.29050 | −0.108702 | ||||||||
\(445\) | 14.0764 | − | 34.2906i | 0.667286 | − | 1.62553i | ||||
\(446\) | 31.6686 | 1.49955 | ||||||||
\(447\) | 6.47125i | 0.306080i | ||||||||
\(448\) | 33.0847i | 1.56310i | ||||||||
\(449\) | 13.7183 | 0.647406 | 0.323703 | − | 0.946159i | \(-0.395072\pi\) | ||||
0.323703 | + | 0.946159i | \(0.395072\pi\) | |||||||
\(450\) | −4.20008 | + | 4.25370i | −0.197994 | + | 0.200521i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 7.47238i | 0.351471i | ||||||||
\(453\) | − | 9.52872i | − | 0.447698i | ||||||
\(454\) | −27.9500 | −1.31176 | ||||||||
\(455\) | −3.54850 | + | 8.64427i | −0.166356 | + | 0.405250i | ||||
\(456\) | 4.21337 | 0.197309 | ||||||||
\(457\) | − | 16.1017i | − | 0.753208i | −0.926374 | − | 0.376604i | \(-0.877092\pi\) | ||
0.926374 | − | 0.376604i | \(-0.122908\pi\) | |||||||
\(458\) | 12.0854i | 0.564712i | ||||||||
\(459\) | −5.57117 | −0.260040 | ||||||||
\(460\) | −2.77818 | − | 1.14045i | −0.129533 | − | 0.0531739i | ||||
\(461\) | 0.225594 | 0.0105070 | 0.00525348 | − | 0.999986i | \(-0.498328\pi\) | ||||
0.00525348 | + | 0.999986i | \(0.498328\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.6080i | 0.678893i | 0.940625 | + | 0.339446i | \(0.110240\pi\) | ||||
−0.940625 | + | 0.339446i | \(0.889760\pi\) | |||||||
\(464\) | 26.2530 | 1.21876 | ||||||||
\(465\) | 20.5743 | + | 8.44584i | 0.954112 | + | 0.391666i | ||||
\(466\) | 4.99098 | 0.231203 | ||||||||
\(467\) | − | 39.8942i | − | 1.84608i | −0.384699 | − | 0.923042i | \(-0.625695\pi\) | ||
0.384699 | − | 0.923042i | \(-0.374305\pi\) | |||||||
\(468\) | 0.633833i | 0.0292990i | ||||||||
\(469\) | −34.4556 | −1.59101 | ||||||||
\(470\) | 6.55870 | − | 15.9772i | 0.302530 | − | 0.736974i | ||||
\(471\) | −3.16690 | −0.145923 | ||||||||
\(472\) | 13.1676i | 0.606089i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 3.68010 | 0.169033 | ||||||||
\(475\) | 4.87764 | + | 4.81616i | 0.223801 | + | 0.220981i | ||||
\(476\) | −11.9596 | −0.548167 | ||||||||
\(477\) | − | 4.06788i | − | 0.186255i | ||||||
\(478\) | 28.5501i | 1.30585i | ||||||||
\(479\) | −31.2539 | −1.42803 | −0.714013 | − | 0.700132i | \(-0.753124\pi\) | ||||
−0.714013 | + | 0.700132i | \(0.753124\pi\) | |||||||
\(480\) | −2.64775 | + | 6.45001i | −0.120853 | + | 0.294401i | ||||
\(481\) | 4.45882 | 0.203305 | ||||||||
\(482\) | 18.7293i | 0.853096i | ||||||||
\(483\) | − | 8.85478i | − | 0.402906i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −37.6333 | − | 15.4486i | −1.70884 | − | 0.701484i | ||||
\(486\) | −1.19557 | −0.0542321 | ||||||||
\(487\) | − | 19.7837i | − | 0.896487i | −0.893911 | − | 0.448244i | \(-0.852050\pi\) | ||
0.893911 | − | 0.448244i | \(-0.147950\pi\) | |||||||
\(488\) | 25.5983i | 1.15878i | ||||||||
\(489\) | −9.02020 | −0.407908 | ||||||||
\(490\) | −17.6907 | − | 7.26208i | −0.799183 | − | 0.328067i | ||||
\(491\) | 24.6747 | 1.11355 | 0.556777 | − | 0.830662i | \(-0.312038\pi\) | ||||
0.556777 | + | 0.830662i | \(0.312038\pi\) | |||||||
\(492\) | − | 2.24865i | − | 0.101377i | ||||||
\(493\) | 57.7378i | 2.60038i | ||||||||
\(494\) | −1.82064 | −0.0819146 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −25.1955 | −1.13131 | ||||||||
\(497\) | 10.7474i | 0.482087i | ||||||||
\(498\) | − | 5.55151i | − | 0.248769i | ||||||
\(499\) | −32.8239 | −1.46940 | −0.734700 | − | 0.678392i | \(-0.762677\pi\) | ||||
−0.734700 | + | 0.678392i | \(0.762677\pi\) | |||||||
\(500\) | −5.87055 | + | 2.49735i | −0.262539 | + | 0.111685i | ||||
\(501\) | −3.13597 | −0.140105 | ||||||||
\(502\) | − | 7.54169i | − | 0.336602i | ||||||
\(503\) | − | 5.72294i | − | 0.255173i | −0.991827 | − | 0.127587i | \(-0.959277\pi\) | ||
0.991827 | − | 0.127587i | \(-0.0407231\pi\) | |||||||
\(504\) | −11.5622 | −0.515020 | ||||||||
\(505\) | −1.84058 | + | 4.48373i | −0.0819049 | + | 0.199523i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.7661i | 0.522553i | ||||||||
\(508\) | 4.97891i | 0.220904i | ||||||||
\(509\) | −19.9144 | −0.882690 | −0.441345 | − | 0.897337i | \(-0.645499\pi\) | ||||
−0.441345 | + | 0.897337i | \(0.645499\pi\) | |||||||
\(510\) | 13.7781 | + | 5.65596i | 0.610104 | + | 0.250450i | ||||
\(511\) | −43.8410 | −1.93941 | ||||||||
\(512\) | − | 23.4693i | − | 1.03721i | ||||||
\(513\) | 1.37094i | 0.0605284i | ||||||||
\(514\) | 9.80802 | 0.432613 | ||||||||
\(515\) | 23.8249 | + | 9.78021i | 1.04985 | + | 0.430968i | ||||
\(516\) | 4.44380 | 0.195627 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 18.0547i | 0.793277i | ||||||||
\(519\) | −12.2424 | −0.537384 | ||||||||
\(520\) | 2.89887 | − | 7.06175i | 0.127124 | − | 0.309678i | ||||
\(521\) | −12.5924 | −0.551681 | −0.275841 | − | 0.961203i | \(-0.588956\pi\) | ||||
−0.275841 | + | 0.961203i | \(0.588956\pi\) | |||||||
\(522\) | 12.3905i | 0.542317i | ||||||||
\(523\) | 38.5086i | 1.68386i | 0.539584 | + | 0.841931i | \(0.318581\pi\) | ||||
−0.539584 | + | 0.841931i | \(0.681419\pi\) | |||||||
\(524\) | 8.22256 | 0.359204 | ||||||||
\(525\) | −13.3850 | − | 13.2163i | −0.584171 | − | 0.576808i | ||||
\(526\) | 11.7712 | 0.513247 | ||||||||
\(527\) | − | 55.4120i | − | 2.41379i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.4601 | 0.759136 | ||||||||
\(530\) | −4.12979 | + | 10.0603i | −0.179387 | + | 0.436992i | ||||
\(531\) | −4.28445 | −0.185930 | ||||||||
\(532\) | 2.94298i | 0.127595i | ||||||||
\(533\) | 4.37735i | 0.189604i | ||||||||
\(534\) | −19.8190 | −0.857652 | ||||||||
\(535\) | 8.76820 | + | 3.59938i | 0.379083 | + | 0.155615i | ||||
\(536\) | 28.1478 | 1.21580 | ||||||||
\(537\) | 8.46334i | 0.365220i | ||||||||
\(538\) | − | 21.0596i | − | 0.907944i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.18035 | − | 0.484538i | −0.0507942 | − | 0.0208512i | ||||
\(541\) | 11.7649 | 0.505812 | 0.252906 | − | 0.967491i | \(-0.418614\pi\) | ||||
0.252906 | + | 0.967491i | \(0.418614\pi\) | |||||||
\(542\) | 1.49872i | 0.0643755i | ||||||||
\(543\) | 23.5514i | 1.01069i | ||||||||
\(544\) | 17.3715 | 0.744799 | ||||||||
\(545\) | 13.7908 | − | 33.5948i | 0.590732 | − | 1.43904i | ||||
\(546\) | 4.99614 | 0.213815 | ||||||||
\(547\) | − | 14.6981i | − | 0.628444i | −0.949350 | − | 0.314222i | \(-0.898256\pi\) | ||
0.949350 | − | 0.314222i | \(-0.101744\pi\) | |||||||
\(548\) | 5.69618i | 0.243329i | ||||||||
\(549\) | −8.32914 | −0.355479 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.2080 | 0.605279 | ||||||||
\(552\) | 7.23372i | 0.307888i | ||||||||
\(553\) | 11.5801i | 0.492437i | ||||||||
\(554\) | 19.5724 | 0.831550 | ||||||||
\(555\) | −3.40857 | + | 8.30340i | −0.144686 | + | 0.352460i | ||||
\(556\) | −4.33873 | −0.184003 | ||||||||
\(557\) | 33.6038i | 1.42384i | 0.702261 | + | 0.711920i | \(0.252174\pi\) | ||||
−0.702261 | + | 0.711920i | \(0.747826\pi\) | |||||||
\(558\) | − | 11.8914i | − | 0.503403i | ||||||
\(559\) | −8.65056 | −0.365880 | ||||||||
\(560\) | 19.7133 | + | 8.09239i | 0.833041 | + | 0.341966i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 14.0681i | − | 0.593428i | ||||||
\(563\) | 23.3225i | 0.982928i | 0.870898 | + | 0.491464i | \(0.163538\pi\) | ||||
−0.870898 | + | 0.491464i | \(0.836462\pi\) | |||||||
\(564\) | 3.68638 | 0.155225 | ||||||||
\(565\) | 27.0885 | + | 11.1199i | 1.13962 | + | 0.467818i | ||||
\(566\) | −3.78492 | −0.159092 | ||||||||
\(567\) | − | 3.76208i | − | 0.157992i | ||||||
\(568\) | − | 8.77986i | − | 0.368395i | ||||||
\(569\) | −15.6575 | −0.656396 | −0.328198 | − | 0.944609i | \(-0.606441\pi\) | ||||
−0.328198 | + | 0.944609i | \(0.606441\pi\) | |||||||
\(570\) | 1.39180 | − | 3.39048i | 0.0582961 | − | 0.142011i | ||||
\(571\) | −0.295842 | −0.0123806 | −0.00619029 | − | 0.999981i | \(-0.501970\pi\) | ||||
−0.00619029 | + | 0.999981i | \(0.501970\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 19.2179i | − | 0.802838i | ||||||
\(574\) | −17.7248 | −0.739818 | ||||||||
\(575\) | −8.26862 | + | 8.37417i | −0.344825 | + | 0.349227i | ||||
\(576\) | 8.79426 | 0.366428 | ||||||||
\(577\) | − | 5.59077i | − | 0.232747i | −0.993206 | − | 0.116373i | \(-0.962873\pi\) | ||
0.993206 | − | 0.116373i | \(-0.0371269\pi\) | |||||||
\(578\) | − | 16.7833i | − | 0.698094i | ||||||
\(579\) | −14.1416 | −0.587707 | ||||||||
\(580\) | −5.02160 | + | 12.2328i | −0.208510 | + | 0.507938i | ||||
\(581\) | 17.4688 | 0.724730 | ||||||||
\(582\) | 21.7510i | 0.901606i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 35.8149 | 1.48203 | ||||||||
\(585\) | 2.29774 | + | 0.943230i | 0.0949998 | + | 0.0389977i | ||||
\(586\) | 22.7782 | 0.940960 | ||||||||
\(587\) | − | 22.3983i | − | 0.924477i | −0.886756 | − | 0.462239i | \(-0.847046\pi\) | ||
0.886756 | − | 0.462239i | \(-0.152954\pi\) | |||||||
\(588\) | − | 4.08173i | − | 0.168328i | ||||||
\(589\) | −13.6356 | −0.561847 | ||||||||
\(590\) | 10.5959 | + | 4.34966i | 0.436227 | + | 0.179073i | ||||
\(591\) | −10.2965 | −0.423540 | ||||||||
\(592\) | − | 10.1684i | − | 0.417918i | ||||||
\(593\) | − | 0.445411i | − | 0.0182908i | −0.999958 | − | 0.00914542i | \(-0.997089\pi\) | ||
0.999958 | − | 0.00914542i | \(-0.00291112\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.7975 | + | 43.3553i | −0.729626 | + | 1.77739i | ||||
\(596\) | 3.69259 | 0.151254 | ||||||||
\(597\) | − | 26.3053i | − | 1.07660i | ||||||
\(598\) | − | 3.12577i | − | 0.127822i | ||||||
\(599\) | 23.5775 | 0.963350 | 0.481675 | − | 0.876350i | \(-0.340029\pi\) | ||||
0.481675 | + | 0.876350i | \(0.340029\pi\) | |||||||
\(600\) | 10.9346 | + | 10.7968i | 0.446404 | + | 0.440777i | ||||
\(601\) | 5.95640 | 0.242967 | 0.121483 | − | 0.992593i | \(-0.461235\pi\) | ||||
0.121483 | + | 0.992593i | \(0.461235\pi\) | |||||||
\(602\) | − | 35.0279i | − | 1.42763i | ||||||
\(603\) | 9.15868i | 0.372970i | ||||||||
\(604\) | −5.43722 | −0.221237 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.59147 | 0.105271 | ||||||||
\(607\) | − | 43.9090i | − | 1.78221i | −0.453796 | − | 0.891106i | \(-0.649931\pi\) | ||
0.453796 | − | 0.891106i | \(-0.350069\pi\) | |||||||
\(608\) | − | 4.27474i | − | 0.173364i | ||||||
\(609\) | −38.9890 | −1.57991 | ||||||||
\(610\) | 20.5988 | + | 8.45590i | 0.834023 | + | 0.342369i | ||||
\(611\) | −7.17613 | −0.290315 | ||||||||
\(612\) | 3.17899i | 0.128503i | ||||||||
\(613\) | − | 29.3033i | − | 1.18355i | −0.806104 | − | 0.591774i | \(-0.798428\pi\) | ||
0.806104 | − | 0.591774i | \(-0.201572\pi\) | |||||||
\(614\) | −12.7415 | −0.514204 | ||||||||
\(615\) | −8.15168 | − | 3.34629i | −0.328707 | − | 0.134935i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 18.1925i | − | 0.732402i | −0.930536 | − | 0.366201i | \(-0.880658\pi\) | ||
0.930536 | − | 0.366201i | \(-0.119342\pi\) | |||||||
\(618\) | − | 13.7701i | − | 0.553916i | ||||||
\(619\) | 30.7056 | 1.23416 | 0.617081 | − | 0.786899i | \(-0.288315\pi\) | ||||
0.617081 | + | 0.786899i | \(0.288315\pi\) | |||||||
\(620\) | 4.81932 | − | 11.7400i | 0.193548 | − | 0.471490i | ||||
\(621\) | −2.35369 | −0.0944505 | ||||||||
\(622\) | − | 13.6713i | − | 0.548171i | ||||||
\(623\) | − | 62.3641i | − | 2.49857i | ||||||
\(624\) | −2.81382 | −0.112643 | ||||||||
\(625\) | 0.317092 | + | 24.9980i | 0.0126837 | + | 0.999920i | ||||
\(626\) | 0.0278942 | 0.00111488 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.80708i | 0.0721102i | ||||||||
\(629\) | 22.3632 | 0.891679 | ||||||||
\(630\) | −3.81933 | + | 9.30402i | −0.152166 | + | 0.370681i | ||||
\(631\) | 11.8334 | 0.471080 | 0.235540 | − | 0.971865i | \(-0.424314\pi\) | ||||
0.235540 | + | 0.971865i | \(0.424314\pi\) | |||||||
\(632\) | − | 9.46013i | − | 0.376304i | ||||||
\(633\) | 0.360214i | 0.0143172i | ||||||||
\(634\) | 1.84265 | 0.0731808 | ||||||||
\(635\) | 18.0493 | + | 7.40930i | 0.716264 | + | 0.294029i | ||||
\(636\) | −2.32119 | −0.0920412 | ||||||||
\(637\) | 7.94573i | 0.314821i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.85677 | 0.113012 | ||||||||
\(640\) | −8.84914 | − | 3.63260i | −0.349793 | − | 0.143591i | ||||
\(641\) | −38.6152 | −1.52521 | −0.762604 | − | 0.646865i | \(-0.776080\pi\) | ||||
−0.762604 | + | 0.646865i | \(0.776080\pi\) | |||||||
\(642\) | − | 5.06777i | − | 0.200009i | ||||||
\(643\) | 12.6400i | 0.498473i | 0.968443 | + | 0.249236i | \(0.0801796\pi\) | ||||
−0.968443 | + | 0.249236i | \(0.919820\pi\) | |||||||
\(644\) | −5.05266 | −0.199103 | ||||||||
\(645\) | 6.61297 | − | 16.1094i | 0.260385 | − | 0.634308i | ||||
\(646\) | −9.13143 | −0.359271 | ||||||||
\(647\) | − | 18.3632i | − | 0.721933i | −0.932579 | − | 0.360967i | \(-0.882447\pi\) | ||
0.932579 | − | 0.360967i | \(-0.117553\pi\) | |||||||
\(648\) | 3.07335i | 0.120732i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −4.72497 | − | 4.66542i | −0.185329 | − | 0.182993i | ||||
\(651\) | 37.4184 | 1.46654 | ||||||||
\(652\) | 5.14706i | 0.201574i | ||||||||
\(653\) | − | 16.7800i | − | 0.656653i | −0.944564 | − | 0.328327i | \(-0.893515\pi\) | ||
0.944564 | − | 0.328327i | \(-0.106485\pi\) | |||||||
\(654\) | −19.4168 | −0.759258 | ||||||||
\(655\) | 12.2363 | − | 29.8080i | 0.478111 | − | 1.16469i | ||||
\(656\) | 9.98259 | 0.389755 | ||||||||
\(657\) | 11.6534i | 0.454642i | ||||||||
\(658\) | − | 29.0576i | − | 1.13278i | ||||||
\(659\) | −28.8939 | −1.12554 | −0.562772 | − | 0.826612i | \(-0.690265\pi\) | ||||
−0.562772 | + | 0.826612i | \(0.690265\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.6886 | 1.23254 | 0.616272 | − | 0.787534i | \(-0.288642\pi\) | ||||
0.616272 | + | 0.787534i | \(0.288642\pi\) | |||||||
\(662\) | − | 6.66403i | − | 0.259005i | ||||||
\(663\) | − | 6.18841i | − | 0.240338i | ||||||
\(664\) | −14.2708 | −0.553815 | ||||||||
\(665\) | 10.6687 | + | 4.37956i | 0.413716 | + | 0.169832i | ||||
\(666\) | 4.79913 | 0.185962 | ||||||||
\(667\) | 24.3929i | 0.944498i | ||||||||
\(668\) | 1.78943i | 0.0692351i | ||||||||
\(669\) | 26.4883 | 1.02410 | ||||||||
\(670\) | 9.29806 | − | 22.6504i | 0.359216 | − | 0.875061i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 11.7306i | 0.452517i | ||||||||
\(673\) | 40.4250i | 1.55827i | 0.626857 | + | 0.779134i | \(0.284341\pi\) | ||||
−0.626857 | + | 0.779134i | \(0.715659\pi\) | |||||||
\(674\) | 18.5751 | 0.715487 | ||||||||
\(675\) | −3.51304 | + | 3.55789i | −0.135217 | + | 0.136943i | ||||
\(676\) | 6.71393 | 0.258228 | ||||||||
\(677\) | 38.3568i | 1.47417i | 0.675798 | + | 0.737087i | \(0.263799\pi\) | ||||
−0.675798 | + | 0.737087i | \(0.736201\pi\) | |||||||
\(678\) | − | 15.6564i | − | 0.601279i | ||||||
\(679\) | −68.4434 | −2.62661 | ||||||||
\(680\) | 14.5393 | − | 35.4182i | 0.557556 | − | 1.35823i | ||||
\(681\) | −23.3780 | −0.895848 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 15.0969i | − | 0.577668i | −0.957379 | − | 0.288834i | \(-0.906732\pi\) | ||
0.957379 | − | 0.288834i | \(-0.0932675\pi\) | |||||||
\(684\) | 0.782277 | 0.0299111 | ||||||||
\(685\) | 20.6495 | + | 8.47668i | 0.788976 | + | 0.323877i | ||||
\(686\) | −0.689130 | −0.0263111 | ||||||||
\(687\) | 10.1085i | 0.385662i | ||||||||
\(688\) | 19.7277i | 0.752111i | ||||||||
\(689\) | 4.51857 | 0.172144 | ||||||||
\(690\) | 5.82094 | + | 2.38951i | 0.221599 | + | 0.0909673i | ||||
\(691\) | −36.0997 | −1.37330 | −0.686648 | − | 0.726990i | \(-0.740919\pi\) | ||||
−0.686648 | + | 0.726990i | \(0.740919\pi\) | |||||||
\(692\) | 6.98572i | 0.265557i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.39660 | −0.0909735 | ||||||||
\(695\) | −6.45661 | + | 15.7285i | −0.244913 | + | 0.596617i | ||||
\(696\) | 31.8512 | 1.20732 | ||||||||
\(697\) | 21.9546i | 0.831589i | ||||||||
\(698\) | 35.1856i | 1.33179i | ||||||||
\(699\) | 4.17456 | 0.157897 | ||||||||
\(700\) | −7.54143 | + | 7.63769i | −0.285039 | + | 0.288678i | ||||
\(701\) | 34.0391 | 1.28564 | 0.642820 | − | 0.766017i | \(-0.277764\pi\) | ||||
0.642820 | + | 0.766017i | \(0.277764\pi\) | |||||||
\(702\) | − | 1.32803i | − | 0.0501232i | ||||||
\(703\) | − | 5.50307i | − | 0.207552i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.48584 | − | 13.3637i | 0.206609 | − | 0.503305i | ||||
\(706\) | −29.9521 | −1.12726 | ||||||||
\(707\) | 8.15452i | 0.306682i | ||||||||
\(708\) | 2.44477i | 0.0918801i | ||||||||
\(709\) | 1.10539 | 0.0415139 | 0.0207569 | − | 0.999785i | \(-0.493392\pi\) | ||||
0.0207569 | + | 0.999785i | \(0.493392\pi\) | |||||||
\(710\) | −7.06511 | − | 2.90025i | −0.265149 | − | 0.108844i | ||||
\(711\) | 3.07812 | 0.115438 | ||||||||
\(712\) | 50.9470i | 1.90932i | ||||||||
\(713\) | − | 23.4103i | − | 0.876724i | ||||||
\(714\) | 25.0581 | 0.937777 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.82930 | 0.180479 | ||||||||
\(717\) | 23.8799i | 0.891812i | ||||||||
\(718\) | 24.4911i | 0.914001i | ||||||||
\(719\) | 24.7383 | 0.922582 | 0.461291 | − | 0.887249i | \(-0.347386\pi\) | ||||
0.461291 | + | 0.887249i | \(0.347386\pi\) | |||||||
\(720\) | 2.15104 | − | 5.24002i | 0.0801647 | − | 0.195284i | ||||
\(721\) | 43.3302 | 1.61370 | ||||||||
\(722\) | − | 20.4688i | − | 0.761769i | ||||||
\(723\) | 15.6656i | 0.582609i | ||||||||
\(724\) | 13.4388 | 0.499449 | ||||||||
\(725\) | 36.8728 | + | 36.4080i | 1.36942 | + | 1.35216i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.81327i | 0.252690i | 0.991986 | + | 0.126345i | \(0.0403246\pi\) | ||||
−0.991986 | + | 0.126345i | \(0.959675\pi\) | |||||||
\(728\) | − | 12.8432i | − | 0.475999i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 11.8307 | − | 28.8201i | 0.437876 | − | 1.06668i | ||||
\(731\) | −43.3868 | −1.60472 | ||||||||
\(732\) | 4.75273i | 0.175666i | ||||||||
\(733\) | 32.9294i | 1.21628i | 0.793831 | + | 0.608138i | \(0.208083\pi\) | ||||
−0.793831 | + | 0.608138i | \(0.791917\pi\) | |||||||
\(734\) | −17.4325 | −0.643447 | ||||||||
\(735\) | −14.7969 | − | 6.07416i | −0.545790 | − | 0.224049i | ||||
\(736\) | 7.33909 | 0.270522 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 4.71144i | 0.173430i | ||||||||
\(739\) | −25.6642 | −0.944072 | −0.472036 | − | 0.881579i | \(-0.656481\pi\) | ||||
−0.472036 | + | 0.881579i | \(0.656481\pi\) | |||||||
\(740\) | 4.73804 | + | 1.94498i | 0.174174 | + | 0.0714989i | ||||
\(741\) | −1.52283 | −0.0559424 | ||||||||
\(742\) | 18.2966i | 0.671690i | ||||||||
\(743\) | 19.7267i | 0.723701i | 0.932236 | + | 0.361850i | \(0.117855\pi\) | ||||
−0.932236 | + | 0.361850i | \(0.882145\pi\) | |||||||
\(744\) | −30.5682 | −1.12068 | ||||||||
\(745\) | 5.49507 | − | 13.3862i | 0.201324 | − | 0.490432i | ||||
\(746\) | 1.91379 | 0.0700688 | ||||||||
\(747\) | − | 4.64341i | − | 0.169893i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.9467 | 0.582679 | ||||||||
\(750\) | 12.3002 | − | 5.23253i | 0.449138 | − | 0.191065i | ||||
\(751\) | −15.3758 | −0.561072 | −0.280536 | − | 0.959843i | \(-0.590512\pi\) | ||||
−0.280536 | + | 0.959843i | \(0.590512\pi\) | |||||||
\(752\) | 16.3652i | 0.596779i | ||||||||
\(753\) | − | 6.30803i | − | 0.229878i | ||||||
\(754\) | −13.7633 | −0.501228 | ||||||||
\(755\) | −8.09132 | + | 19.7107i | −0.294473 | + | 0.717347i | ||||
\(756\) | −2.14669 | −0.0780745 | ||||||||
\(757\) | − | 34.9995i | − | 1.27208i | −0.771657 | − | 0.636039i | \(-0.780572\pi\) | ||
0.771657 | − | 0.636039i | \(-0.219428\pi\) | |||||||
\(758\) | − | 17.0811i | − | 0.620414i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.71560 | − | 3.57778i | −0.316148 | − | 0.129780i | ||||
\(761\) | −20.7260 | −0.751319 | −0.375659 | − | 0.926758i | \(-0.622584\pi\) | ||||
−0.375659 | + | 0.926758i | \(0.622584\pi\) | |||||||
\(762\) | − | 10.4320i | − | 0.377911i | ||||||
\(763\) | − | 61.0986i | − | 2.21192i | ||||||
\(764\) | −10.9660 | −0.396735 | ||||||||
\(765\) | 11.5243 | + | 4.73076i | 0.416662 | + | 0.171041i | ||||
\(766\) | 7.80469 | 0.281995 | ||||||||
\(767\) | − | 4.75913i | − | 0.171842i | ||||||
\(768\) | − | 12.4740i | − | 0.450116i | ||||||
\(769\) | −13.6328 | −0.491613 | −0.245806 | − | 0.969319i | \(-0.579053\pi\) | ||||
−0.245806 | + | 0.969319i | \(0.579053\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.20364 | 0.295447 | ||||||||
\(772\) | 8.06943i | 0.290425i | ||||||||
\(773\) | 1.37046i | 0.0492919i | 0.999696 | + | 0.0246460i | \(0.00784585\pi\) | ||||
−0.999696 | + | 0.0246460i | \(0.992154\pi\) | |||||||
\(774\) | −9.31078 | −0.334669 | ||||||||
\(775\) | −35.3875 | − | 34.9415i | −1.27116 | − | 1.25513i | ||||
\(776\) | 55.9133 | 2.00717 | ||||||||
\(777\) | 15.1013i | 0.541757i | ||||||||
\(778\) | 32.6662i | 1.17114i | ||||||||
\(779\) | 5.40252 | 0.193565 | ||||||||
\(780\) | 0.538220 | − | 1.31112i | 0.0192714 | − | 0.0469457i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 15.6773i | − | 0.560619i | ||||||
\(783\) | 10.3637i | 0.370368i | ||||||||
\(784\) | 18.1203 | 0.647154 | ||||||||
\(785\) | 6.55091 | + | 2.68917i | 0.233812 | + | 0.0959807i | ||||
\(786\) | −17.2282 | −0.614508 | ||||||||
\(787\) | 23.6626i | 0.843482i | 0.906716 | + | 0.421741i | \(0.138581\pi\) | ||||
−0.906716 | + | 0.421741i | \(0.861419\pi\) | |||||||
\(788\) | 5.87531i | 0.209299i | ||||||||
\(789\) | 9.84566 | 0.350515 | ||||||||
\(790\) | −7.61252 | − | 3.12496i | −0.270841 | − | 0.111181i | ||||
\(791\) | 49.2656 | 1.75168 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 9.25193i | − | 0.328546i | ||||||
\(794\) | −3.88462 | −0.137860 | ||||||||
\(795\) | −3.45425 | + | 8.41466i | −0.122509 | + | 0.298437i | ||||
\(796\) | −15.0102 | −0.532022 | ||||||||
\(797\) | − | 17.9874i | − | 0.637146i | −0.947898 | − | 0.318573i | \(-0.896796\pi\) | ||
0.947898 | − | 0.318573i | \(-0.103204\pi\) | |||||||
\(798\) | − | 6.16623i | − | 0.218282i | ||||||
\(799\) | −35.9919 | −1.27330 | ||||||||
\(800\) | 10.9541 | − | 11.0939i | 0.387285 | − | 0.392228i | ||||
\(801\) | −16.5770 | −0.585721 | ||||||||
\(802\) | 13.4459i | 0.474790i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 5.22607 | 0.184309 | ||||||||
\(805\) | −7.51904 | + | 18.3166i | −0.265011 | + | 0.645577i | ||||
\(806\) | 13.2088 | 0.465262 | ||||||||
\(807\) | − | 17.6147i | − | 0.620067i | ||||||
\(808\) | − | 6.66166i | − | 0.234356i | ||||||
\(809\) | 48.0286 | 1.68860 | 0.844298 | − | 0.535873i | \(-0.180018\pi\) | ||||
0.844298 | + | 0.535873i | \(0.180018\pi\) | |||||||
\(810\) | 2.47311 | + | 1.01522i | 0.0868961 | + | 0.0356712i | ||||
\(811\) | 17.3727 | 0.610038 | 0.305019 | − | 0.952346i | \(-0.401337\pi\) | ||||
0.305019 | + | 0.952346i | \(0.401337\pi\) | |||||||
\(812\) | 22.2477i | 0.780740i | ||||||||
\(813\) | 1.25356i | 0.0439643i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.6588 | + | 7.65951i | 0.653590 | + | 0.268301i | ||||
\(816\) | −14.1127 | −0.494044 | ||||||||
\(817\) | 10.6765i | 0.373524i | ||||||||
\(818\) | 17.2408i | 0.602810i | ||||||||
\(819\) | 4.17888 | 0.146022 | ||||||||
\(820\) | −1.90944 | + | 4.65146i | −0.0666806 | + | 0.162436i | ||||
\(821\) | −4.97342 | −0.173573 | −0.0867867 | − | 0.996227i | \(-0.527660\pi\) | ||||
−0.0867867 | + | 0.996227i | \(0.527660\pi\) | |||||||
\(822\) | − | 11.9348i | − | 0.416274i | ||||||
\(823\) | 32.6485i | 1.13806i | 0.822318 | + | 0.569028i | \(0.192681\pi\) | ||||
−0.822318 | + | 0.569028i | \(0.807319\pi\) | |||||||
\(824\) | −35.3977 | −1.23314 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19.2707 | 0.670514 | ||||||||
\(827\) | 12.9363i | 0.449839i | 0.974377 | + | 0.224920i | \(0.0722119\pi\) | ||||
−0.974377 | + | 0.224920i | \(0.927788\pi\) | |||||||
\(828\) | 1.34305i | 0.0466743i | ||||||||
\(829\) | −32.7103 | −1.13607 | −0.568037 | − | 0.823003i | \(-0.692297\pi\) | ||||
−0.568037 | + | 0.823003i | \(0.692297\pi\) | |||||||
\(830\) | −4.71407 | + | 11.4836i | −0.163628 | + | 0.398603i | ||||
\(831\) | 16.3707 | 0.567895 | ||||||||
\(832\) | 9.76859i | 0.338665i | ||||||||
\(833\) | 39.8518i | 1.38078i | ||||||||
\(834\) | 9.09063 | 0.314783 | ||||||||
\(835\) | 6.48695 | + | 2.66291i | 0.224490 | + | 0.0921539i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 9.94621i | − | 0.343791i | ||||||
\(838\) | − | 41.4321i | − | 1.43125i | ||||||
\(839\) | −16.2411 | −0.560707 | −0.280353 | − | 0.959897i | \(-0.590452\pi\) | ||||
−0.280353 | + | 0.959897i | \(0.590452\pi\) | |||||||
\(840\) | 23.9170 | + | 9.81802i | 0.825216 | + | 0.338754i | ||||
\(841\) | 78.4059 | 2.70365 | ||||||||
\(842\) | 5.83162i | 0.200971i | ||||||||
\(843\) | − | 11.7669i | − | 0.405273i | ||||||
\(844\) | 0.205543 | 0.00707509 | ||||||||
\(845\) | 9.99123 | − | 24.3390i | 0.343709 | − | 0.837286i | ||||
\(846\) | −7.72383 | −0.265551 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 10.3046i | − | 0.353863i | ||||||
\(849\) | −3.16579 | −0.108649 | ||||||||
\(850\) | −23.6981 | − | 23.3994i | −0.812837 | − | 0.802592i | ||||
\(851\) | 9.44795 | 0.323872 | ||||||||
\(852\) | − | 1.63012i | − | 0.0558469i | ||||||
\(853\) | 6.01751i | 0.206035i | 0.994680 | + | 0.103018i | \(0.0328498\pi\) | ||||
−0.994680 | + | 0.103018i | \(0.967150\pi\) | |||||||
\(854\) | 37.4630 | 1.28196 | ||||||||
\(855\) | 1.16413 | − | 2.83587i | 0.0398125 | − | 0.0969846i | ||||
\(856\) | −13.0273 | −0.445264 | ||||||||
\(857\) | − | 1.48842i | − | 0.0508436i | −0.999677 | − | 0.0254218i | \(-0.991907\pi\) | ||
0.999677 | − | 0.0254218i | \(-0.00809288\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.62548 | 0.226059 | 0.113029 | − | 0.993592i | \(-0.463945\pi\) | ||||
0.113029 | + | 0.993592i | \(0.463945\pi\) | |||||||
\(860\) | −9.19226 | − | 3.77346i | −0.313454 | − | 0.128674i | ||||
\(861\) | −14.8254 | −0.505248 | ||||||||
\(862\) | − | 14.4818i | − | 0.493252i | ||||||
\(863\) | − | 25.6159i | − | 0.871976i | −0.899953 | − | 0.435988i | \(-0.856399\pi\) | ||
0.899953 | − | 0.435988i | \(-0.143601\pi\) | |||||||
\(864\) | 3.11811 | 0.106080 | ||||||||
\(865\) | 25.3242 | + | 10.3957i | 0.861050 | + | 0.353464i | ||||
\(866\) | −37.3756 | −1.27007 | ||||||||
\(867\) | − | 14.0379i | − | 0.476753i | ||||||
\(868\) | − | 21.3515i | − | 0.724717i | ||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 10.5214 | − | 25.6305i | 0.356709 | − | 0.868955i | ||||
\(871\) | −10.1734 | −0.344712 | ||||||||
\(872\) | 49.9132i | 1.69027i | ||||||||
\(873\) | 18.1930i | 0.615739i | ||||||||
\(874\) | −3.85782 | −0.130493 | ||||||||
\(875\) | 16.4651 | + | 38.7047i | 0.556622 | + | 1.30846i | ||||
\(876\) | 6.64959 | 0.224669 | ||||||||
\(877\) | 24.6934i | 0.833838i | 0.908944 | + | 0.416919i | \(0.136890\pi\) | ||||
−0.908944 | + | 0.416919i | \(0.863110\pi\) | |||||||
\(878\) | 30.6171i | 1.03328i | ||||||||
\(879\) | 19.0522 | 0.642615 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.6177 | −0.559866 | −0.279933 | − | 0.960020i | \(-0.590312\pi\) | ||||
−0.279933 | + | 0.960020i | \(0.590312\pi\) | |||||||
\(882\) | 8.55216i | 0.287966i | ||||||||
\(883\) | 17.9632i | 0.604511i | 0.953227 | + | 0.302255i | \(0.0977396\pi\) | ||||
−0.953227 | + | 0.302255i | \(0.902260\pi\) | |||||||
\(884\) | −3.53119 | −0.118767 | ||||||||
\(885\) | 8.86265 | + | 3.63815i | 0.297915 | + | 0.122295i | ||||
\(886\) | 2.71082 | 0.0910719 | ||||||||
\(887\) | − | 41.3644i | − | 1.38888i | −0.719551 | − | 0.694440i | \(-0.755652\pi\) | ||
0.719551 | − | 0.694440i | \(-0.244348\pi\) | |||||||
\(888\) | − | 12.3367i | − | 0.413993i | ||||||
\(889\) | 32.8261 | 1.10095 | ||||||||
\(890\) | 40.9968 | + | 16.8293i | 1.37422 | + | 0.564120i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 15.1146i | − | 0.506075i | ||||||
\(893\) | 8.85677i | 0.296381i | ||||||||
\(894\) | −7.73683 | −0.258758 | ||||||||
\(895\) | 7.18665 | − | 17.5069i | 0.240223 | − | 0.585192i | ||||
\(896\) | −16.0939 | −0.537658 | ||||||||
\(897\) | − | 2.61446i | − | 0.0872944i | ||||||
\(898\) | 16.4012i | 0.547313i | ||||||||
\(899\) | −103.079 | −3.43789 | ||||||||
\(900\) | 2.03018 | + | 2.00459i | 0.0676727 | + | 0.0668197i | ||||
\(901\) | 22.6629 | 0.755009 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 29.2981i | − | 0.974979i | ||||||
\(904\) | −40.2465 | −1.33858 | ||||||||
\(905\) | 19.9987 | − | 48.7176i | 0.664780 | − | 1.61943i | ||||
\(906\) | 11.3922 | 0.378482 | ||||||||
\(907\) | 43.8277i | 1.45528i | 0.685962 | + | 0.727638i | \(0.259382\pi\) | ||||
−0.685962 | + | 0.727638i | \(0.740618\pi\) | |||||||
\(908\) | 13.3398i | 0.442698i | ||||||||
\(909\) | 2.16756 | 0.0718934 | ||||||||
\(910\) | −10.3348 | − | 4.24248i | −0.342596 | − | 0.140637i | ||||
\(911\) | −3.01368 | −0.0998477 | −0.0499239 | − | 0.998753i | \(-0.515898\pi\) | ||||
−0.0499239 | + | 0.998753i | \(0.515898\pi\) | |||||||
\(912\) | 3.47282i | 0.114997i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 19.2508 | 0.636758 | ||||||||
\(915\) | 17.2293 | + | 7.07270i | 0.569584 | + | 0.233816i | ||||
\(916\) | 5.76803 | 0.190581 | ||||||||
\(917\) | − | 54.2115i | − | 1.79022i | ||||||
\(918\) | − | 6.66072i | − | 0.219836i | ||||||
\(919\) | −0.579650 | −0.0191209 | −0.00956045 | − | 0.999954i | \(-0.503043\pi\) | ||||
−0.00956045 | + | 0.999954i | \(0.503043\pi\) | |||||||
\(920\) | 6.14252 | − | 14.9634i | 0.202513 | − | 0.493328i | ||||
\(921\) | −10.6573 | −0.351168 | ||||||||
\(922\) | 0.269713i | 0.00888253i | ||||||||
\(923\) | 3.17328i | 0.104450i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.1017 | − | 14.2817i | 0.463660 | − | 0.469579i | ||||
\(926\) | −17.4649 | −0.573933 | ||||||||
\(927\) | − | 11.5176i | − | 0.378289i | ||||||
\(928\) | − | 32.3151i | − | 1.06080i | ||||||
\(929\) | 7.38827 | 0.242401 | 0.121201 | − | 0.992628i | \(-0.461326\pi\) | ||||
0.121201 | + | 0.992628i | \(0.461326\pi\) | |||||||
\(930\) | −10.0976 | + | 24.5981i | −0.331113 | + | 0.806602i | ||||
\(931\) | 9.80661 | 0.321399 | ||||||||
\(932\) | − | 2.38207i | − | 0.0780272i | ||||||
\(933\) | − | 11.4350i | − | 0.374365i | ||||||
\(934\) | 47.6963 | 1.56067 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.41385 | −0.111585 | ||||||||
\(937\) | − | 22.3759i | − | 0.730990i | −0.930813 | − | 0.365495i | \(-0.880900\pi\) | ||
0.930813 | − | 0.365495i | \(-0.119100\pi\) | |||||||
\(938\) | − | 41.1941i | − | 1.34504i | ||||||
\(939\) | 0.0233313 | 0.000761388 | ||||||||
\(940\) | −7.62551 | − | 3.13030i | −0.248717 | − | 0.102099i | ||||
\(941\) | −30.8195 | −1.00469 | −0.502343 | − | 0.864668i | \(-0.667529\pi\) | ||||
−0.502343 | + | 0.864668i | \(0.667529\pi\) | |||||||
\(942\) | − | 3.78624i | − | 0.123362i | ||||||
\(943\) | 9.27532i | 0.302046i | ||||||||
\(944\) | −10.8533 | −0.353243 | ||||||||
\(945\) | −3.19457 | + | 7.78208i | −0.103919 | + | 0.253151i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 6.42672i | − | 0.208840i | −0.994533 | − | 0.104420i | \(-0.966701\pi\) | ||
0.994533 | − | 0.104420i | \(-0.0332987\pi\) | |||||||
\(948\) | − | 1.75642i | − | 0.0570458i | ||||||
\(949\) | −12.9445 | −0.420196 | ||||||||
\(950\) | −5.75805 | + | 5.83155i | −0.186816 | + | 0.189201i | ||||
\(951\) | 1.54123 | 0.0499778 | ||||||||
\(952\) | − | 64.4148i | − | 2.08769i | ||||||
\(953\) | 33.1383i | 1.07345i | 0.843756 | + | 0.536727i | \(0.180340\pi\) | ||||
−0.843756 | + | 0.536727i | \(0.819660\pi\) | |||||||
\(954\) | 4.86343 | 0.157459 | ||||||||
\(955\) | −16.3189 | + | 39.7533i | −0.528066 | + | 1.28639i | ||||
\(956\) | 13.6262 | 0.440704 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 37.3662i | − | 1.20725i | ||||||
\(959\) | 37.5550 | 1.21272 | ||||||||
\(960\) | −18.1915 | − | 7.46766i | −0.587127 | − | 0.241018i | ||||
\(961\) | 67.9272 | 2.19120 | ||||||||
\(962\) | 5.33083i | 0.171873i | ||||||||
\(963\) | − | 4.23880i | − | 0.136593i | ||||||
\(964\) | 8.93901 | 0.287906 | ||||||||
\(965\) | 29.2528 | + | 12.0084i | 0.941682 | + | 0.386564i | ||||
\(966\) | 10.5865 | 0.340615 | ||||||||
\(967\) | 34.8065i | 1.11930i | 0.828728 | + | 0.559651i | \(0.189065\pi\) | ||||
−0.828728 | + | 0.559651i | \(0.810935\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.63772 | −0.245359 | ||||||||
\(970\) | 18.4699 | − | 44.9932i | 0.593031 | − | 1.44464i | ||||
\(971\) | 45.2026 | 1.45062 | 0.725310 | − | 0.688423i | \(-0.241697\pi\) | ||||
0.725310 | + | 0.688423i | \(0.241697\pi\) | |||||||
\(972\) | 0.570614i | 0.0183025i | ||||||||
\(973\) | 28.6053i | 0.917045i | ||||||||
\(974\) | 23.6528 | 0.757886 | ||||||||
\(975\) | −3.95207 | − | 3.90225i | −0.126567 | − | 0.124972i | ||||
\(976\) | −21.0991 | −0.675366 | ||||||||
\(977\) | 36.8788i | 1.17986i | 0.807455 | + | 0.589929i | \(0.200844\pi\) | ||||
−0.807455 | + | 0.589929i | \(0.799156\pi\) | |||||||
\(978\) | − | 10.7843i | − | 0.344843i | ||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −3.46600 | + | 8.44330i | −0.110717 | + | 0.269711i | ||||
\(981\) | −16.2407 | −0.518524 | ||||||||
\(982\) | 29.5003i | 0.941393i | ||||||||
\(983\) | − | 9.80072i | − | 0.312594i | −0.987710 | − | 0.156297i | \(-0.950044\pi\) | ||
0.987710 | − | 0.156297i | \(-0.0499558\pi\) | |||||||
\(984\) | 12.1113 | 0.386094 | ||||||||
\(985\) | 21.2989 | + | 8.74325i | 0.678638 | + | 0.278583i | ||||
\(986\) | −69.0296 | −2.19835 | ||||||||
\(987\) | − | 24.3044i | − | 0.773619i | ||||||
\(988\) | 0.868946i | 0.0276449i | ||||||||
\(989\) | −18.3300 | −0.582859 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.5716 | 1.66999 | 0.834995 | − | 0.550257i | \(-0.185470\pi\) | ||||
0.834995 | + | 0.550257i | \(0.185470\pi\) | |||||||
\(992\) | 31.0134i | 0.984677i | ||||||||
\(993\) | − | 5.57394i | − | 0.176884i | ||||||
\(994\) | −12.8493 | −0.407554 | ||||||||
\(995\) | −22.3372 | + | 54.4141i | −0.708136 | + | 1.72504i | ||||
\(996\) | −2.64959 | −0.0839556 | ||||||||
\(997\) | 9.95697i | 0.315340i | 0.987492 | + | 0.157670i | \(0.0503983\pi\) | ||||
−0.987492 | + | 0.157670i | \(0.949602\pi\) | |||||||
\(998\) | − | 39.2433i | − | 1.24222i | ||||||
\(999\) | 4.01410 | 0.127000 |
(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 | 1815.2.c.h.364.8 | yes | 12 | |
5.2 | odd | 4 | 9075.2.a.dp.1.3 | 6 | |||
5.3 | odd | 4 | 9075.2.a.dr.1.4 | 6 | |||
5.4 | even | 2 | inner | 1815.2.c.h.364.5 | ✓ | 12 | |
11.10 | odd | 2 | 1815.2.c.i.364.5 | yes | 12 | ||
55.32 | even | 4 | 9075.2.a.ds.1.4 | 6 | |||
55.43 | even | 4 | 9075.2.a.do.1.3 | 6 | |||
55.54 | odd | 2 | 1815.2.c.i.364.8 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1815.2.c.h.364.5 | ✓ | 12 | 5.4 | even | 2 | inner | |
1815.2.c.h.364.8 | yes | 12 | 1.1 | even | 1 | trivial | |
1815.2.c.i.364.5 | yes | 12 | 11.10 | odd | 2 | ||
1815.2.c.i.364.8 | yes | 12 | 55.54 | odd | 2 | ||
9075.2.a.do.1.3 | 6 | 55.43 | even | 4 | |||
9075.2.a.dp.1.3 | 6 | 5.2 | odd | 4 | |||
9075.2.a.dr.1.4 | 6 | 5.3 | odd | 4 | |||
9075.2.a.ds.1.4 | 6 | 55.32 | even | 4 |