Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(257,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 9, 17]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.cc (of order \(18\), degree \(6\), not 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: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{18})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + \cdots + 19683 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 114) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 737.2 | ||
Root | \(-0.396613 + 1.68603i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.737 |
Dual form | 912.2.cc.c.641.2 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{11}{18}\right)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.779936 | + | 1.54651i | −0.450296 | + | 0.892879i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.86241 | + | 2.21954i | 0.832897 | + | 0.992608i | 0.999978 | + | 0.00666440i | \(0.00212136\pi\) |
−0.167081 | + | 0.985943i | \(0.553434\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.562083 | + | 0.973556i | −0.212447 | + | 0.367969i | −0.952480 | − | 0.304602i | \(-0.901477\pi\) |
0.740033 | + | 0.672571i | \(0.234810\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.78340 | − | 2.41236i | −0.594467 | − | 0.804120i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.70920 | + | 1.56416i | −0.816855 | + | 0.471611i | −0.849331 | − | 0.527861i | \(-0.822994\pi\) |
0.0324759 | + | 0.999473i | \(0.489661\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.18404 | − | 0.914087i | −1.43780 | − | 0.253522i | −0.600216 | − | 0.799838i | \(-0.704919\pi\) |
−0.837579 | + | 0.546316i | \(0.816030\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.88511 | + | 1.14915i | −1.26133 | + | 0.296709i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.880484 | + | 2.41911i | −0.213549 | + | 0.586720i | −0.999502 | − | 0.0315662i | \(-0.989951\pi\) |
0.785953 | + | 0.618286i | \(0.212173\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.13617 | − | 1.37554i | −0.948902 | − | 0.315571i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.06723 | − | 1.62858i | −0.232888 | − | 0.355385i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.31710 | − | 5.14492i | 0.900178 | − | 1.07279i | −0.0968152 | − | 0.995302i | \(-0.530866\pi\) |
0.996993 | − | 0.0774881i | \(-0.0246900\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.589524 | + | 3.34336i | −0.117905 | + | 0.668671i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.12168 | − | 0.876562i | 0.985668 | − | 0.168694i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.09635 | + | 0.399039i | −0.203587 | + | 0.0740998i | −0.441801 | − | 0.897113i | \(-0.645660\pi\) |
0.238214 | + | 0.971213i | \(0.423438\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.90801 | + | 2.25629i | 0.701899 | + | 0.405241i | 0.808054 | − | 0.589108i | \(-0.200521\pi\) |
−0.106155 | + | 0.994350i | \(0.533854\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.305986 | − | 5.40975i | −0.0532653 | − | 0.941717i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.20767 | + | 0.565599i | −0.542196 | + | 0.0956038i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 12.0703i | 1.98435i | 0.124859 | + | 0.992174i | \(0.460152\pi\) | ||||
−0.124859 | + | 0.992174i | \(0.539848\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.45687 | − | 7.30426i | 0.873799 | − | 1.16962i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.06170 | − | 6.02118i | −0.165809 | − | 0.940350i | −0.948226 | − | 0.317595i | \(-0.897125\pi\) |
0.782417 | − | 0.622755i | \(-0.213986\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.21295 | + | 1.85688i | −0.337471 | + | 0.283172i | −0.795736 | − | 0.605644i | \(-0.792916\pi\) |
0.458265 | + | 0.888816i | \(0.348471\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.03290 | − | 8.45114i | 0.303047 | − | 1.25982i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.377793 | − | 1.03798i | −0.0551068 | − | 0.151405i | 0.909085 | − | 0.416611i | \(-0.136782\pi\) |
−0.964192 | + | 0.265206i | \(0.914560\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.86813 | + | 4.96774i | 0.409732 | + | 0.709677i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.05446 | − | 3.24843i | −0.427710 | − | 0.454871i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.66806 | − | 4.75606i | −0.778568 | − | 0.653296i | 0.164320 | − | 0.986407i | \(-0.447457\pi\) |
−0.942887 | + | 0.333111i | \(0.891901\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.51736 | − | 3.10007i | −1.14848 | − | 0.418013i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.35324 | − | 5.32380i | 0.709054 | − | 0.705154i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.41833 | − | 2.33608i | −0.835596 | − | 0.304132i | −0.111442 | − | 0.993771i | \(-0.535547\pi\) |
−0.724153 | + | 0.689639i | \(0.757769\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.58223 | − | 4.68405i | −0.714732 | − | 0.599731i | 0.211191 | − | 0.977445i | \(-0.432266\pi\) |
−0.925922 | + | 0.377714i | \(0.876710\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.35099 | − | 0.380292i | 0.422184 | − | 0.0479123i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.62598 | − | 13.2086i | −0.945887 | − | 1.63832i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.42040 | + | 6.64999i | 0.295699 | + | 0.812425i | 0.995206 | + | 0.0977999i | \(0.0311805\pi\) |
−0.699508 | + | 0.714625i | \(0.746597\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.58962 | + | 10.6892i | 0.552525 | + | 1.28682i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.31294 | + | 2.77989i | −0.393174 | + | 0.329912i | −0.817848 | − | 0.575434i | \(-0.804833\pi\) |
0.424674 | + | 0.905346i | \(0.360389\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.30735 | − | 7.41438i | −0.153014 | − | 0.867787i | −0.960579 | − | 0.278008i | \(-0.910326\pi\) |
0.807565 | − | 0.589779i | \(-0.200785\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.71075 | − | 3.51931i | −0.543950 | − | 0.406375i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.51674i | − | 0.400770i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.30920 | + | 0.759829i | −0.484823 | + | 0.0854874i | −0.410717 | − | 0.911763i | \(-0.634722\pi\) |
−0.0741064 | + | 0.997250i | \(0.523610\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.63897 | + | 8.60441i | −0.293219 | + | 0.956045i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.5112 | + | 7.22333i | 1.37328 | + | 0.792863i | 0.991340 | − | 0.131324i | \(-0.0419227\pi\) |
0.381940 | + | 0.924187i | \(0.375256\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.00913 | + | 2.55111i | −0.760247 | + | 0.276707i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.237965 | − | 2.00675i | 0.0255125 | − | 0.215146i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.38095 | + | 13.5030i | −0.252380 | + | 1.43132i | 0.550331 | + | 0.834947i | \(0.314502\pi\) |
−0.802710 | + | 0.596369i | \(0.796609\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.80378 | − | 4.53316i | 0.398744 | − | 0.475205i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.53737 | + | 4.28402i | −0.677894 | + | 0.444232i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.65018 | − | 11.7422i | −0.477098 | − | 1.20473i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.47287 | + | 4.04669i | −0.149548 | + | 0.410879i | −0.991735 | − | 0.128307i | \(-0.959046\pi\) |
0.842187 | + | 0.539186i | \(0.181268\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.60490 | + | 3.74605i | 0.864825 | + | 0.376492i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.82418 | + | 1.02696i | 0.579528 | + | 0.102186i | 0.455725 | − | 0.890121i | \(-0.349380\pi\) |
0.123802 | + | 0.992307i | \(0.460491\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.2614 | + | 9.96588i | −1.70082 | + | 0.981967i | −0.755884 | + | 0.654706i | \(0.772792\pi\) |
−0.944934 | + | 0.327261i | \(0.893874\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.62707 | − | 5.40184i | 0.158786 | − | 0.527165i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.39183 | + | 4.14277i | −0.231227 | + | 0.400496i | −0.958169 | − | 0.286202i | \(-0.907607\pi\) |
0.726943 | + | 0.686698i | \(0.240941\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.52889 | − | 6.58908i | −0.529572 | − | 0.631119i | 0.433244 | − | 0.901276i | \(-0.357369\pi\) |
−0.962816 | + | 0.270157i | \(0.912924\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −18.6669 | − | 9.41408i | −1.77178 | − | 0.893545i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.1668 | 1.52085 | 0.760424 | − | 0.649427i | \(-0.224991\pi\) | ||||
0.760424 | + | 0.649427i | \(0.224991\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 19.4596 | 1.81462 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.04012 | + | 14.1360i | 0.650859 | + | 1.30687i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.86023 | − | 2.21694i | −0.170527 | − | 0.203226i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.606822 | + | 1.05105i | −0.0551656 | + | 0.0955496i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.1399 | + | 3.05421i | 0.914282 | + | 0.275389i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.02747 | − | 2.32526i | 0.360228 | − | 0.207978i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.59392 | − | 1.33901i | −0.673852 | − | 0.118818i | −0.173756 | − | 0.984789i | \(-0.555591\pi\) |
−0.500095 | + | 0.865970i | \(0.666702\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.14573 | − | 4.87060i | −0.100876 | − | 0.428832i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.757267 | − | 2.08057i | 0.0661627 | − | 0.181781i | −0.902205 | − | 0.431307i | \(-0.858053\pi\) |
0.968368 | + | 0.249526i | \(0.0802749\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.66404 | − | 3.25362i | 0.317712 | − | 0.282125i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.4843 | + | 9.73525i | 0.988407 | + | 0.837877i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.138747 | − | 0.165352i | 0.0118540 | − | 0.0141270i | −0.760085 | − | 0.649824i | \(-0.774843\pi\) |
0.771939 | + | 0.635697i | \(0.219287\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.25695 | + | 18.4711i | −0.276251 | + | 1.56670i | 0.458710 | + | 0.888586i | \(0.348312\pi\) |
−0.734961 | + | 0.678110i | \(0.762799\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.89990 | + | 0.225295i | 0.160000 | + | 0.0189732i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.4744 | − | 5.63222i | 1.29403 | − | 0.470990i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.92754 | − | 1.69022i | −0.243119 | − | 0.140365i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.91963 | + | 0.561072i | −0.818157 | + | 0.0462765i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.18590 | − | 0.738088i | 0.342923 | − | 0.0604665i | 0.000465272 | − | 1.00000i | \(-0.499852\pi\) |
0.342457 | + | 0.939533i | \(0.388741\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.94139i | − | 0.727640i | −0.931469 | − | 0.363820i | \(-0.881472\pi\) | ||
0.931469 | − | 0.363820i | \(-0.118528\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.40602 | − | 2.19019i | 0.598741 | − | 0.177067i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.27041 | + | 12.8761i | 0.182363 | + | 1.03423i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.55311 | − | 1.30322i | 0.123952 | − | 0.104008i | −0.578705 | − | 0.815537i | \(-0.696442\pi\) |
0.702656 | + | 0.711529i | \(0.251997\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.7760 | − | 5.05629i | 0.933900 | − | 0.400990i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.58230 | + | 7.09481i | 0.203514 | + | 0.559149i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.66573 | + | 8.08128i | 0.365448 | + | 0.632975i | 0.988848 | − | 0.148929i | \(-0.0475825\pi\) |
−0.623400 | + | 0.781903i | \(0.714249\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.4373 | − | 10.7543i | 0.890391 | − | 0.837225i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.70512 | − | 8.14356i | −0.751005 | − | 0.630168i | 0.184764 | − | 0.982783i | \(-0.440848\pi\) |
−0.935768 | + | 0.352615i | \(0.885292\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.8228 | + | 5.03107i | 1.06329 | + | 0.387006i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.05813 | + | 12.4311i | 0.310333 | + | 0.950628i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.86150 | − | 3.22532i | −0.673727 | − | 0.245217i | −0.0175755 | − | 0.999846i | \(-0.505595\pi\) |
−0.656152 | + | 0.754629i | \(0.727817\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.92358 | − | 2.45318i | −0.221002 | − | 0.185443i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.61867 | − | 8.10403i | 0.647819 | − | 0.609137i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.74454 | + | 6.48573i | 0.279880 | + | 0.484766i | 0.971355 | − | 0.237634i | \(-0.0763720\pi\) |
−0.691475 | + | 0.722401i | \(0.743039\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.46326 | + | 15.0102i | 0.406081 | + | 1.11570i | 0.959232 | + | 0.282618i | \(0.0912030\pi\) |
−0.553151 | + | 0.833081i | \(0.686575\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.5977 | − | 4.97973i | 0.857329 | − | 0.368112i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −26.7905 | + | 22.4799i | −1.96968 | + | 1.65276i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.39846 | − | 7.93107i | −0.102266 | − | 0.579977i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.02543 | + | 5.47894i | −0.147328 | + | 0.398534i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.61751i | 0.551184i | 0.961275 | + | 0.275592i | \(0.0888738\pi\) | ||||
−0.961275 | + | 0.275592i | \(0.911126\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.8171 | − | 2.08368i | 0.850616 | − | 0.149987i | 0.268688 | − | 0.963227i | \(-0.413410\pi\) |
0.581928 | + | 0.813241i | \(0.302299\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 26.3750 | − | 1.49182i | 1.88875 | − | 0.106831i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.2618 | + | 8.81139i | 1.08736 | + | 0.627786i | 0.932871 | − | 0.360210i | \(-0.117295\pi\) |
0.154485 | + | 0.987995i | \(0.450628\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.12679 | − | 0.774087i | 0.150764 | − | 0.0548736i | −0.265536 | − | 0.964101i | \(-0.585549\pi\) |
0.416300 | + | 0.909227i | \(0.363327\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.1720 | − | 1.44339i | −0.858549 | − | 0.101809i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.227753 | − | 1.29165i | 0.0159851 | − | 0.0906562i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.3869 | − | 13.5704i | 0.795297 | − | 0.947798i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −20.1105 | − | 1.23896i | −1.39778 | − | 0.0861135i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.3573 | − | 2.74299i | 0.923942 | − | 0.189737i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.31716 | − | 3.61886i | 0.0906769 | − | 0.249133i | −0.886061 | − | 0.463568i | \(-0.846569\pi\) |
0.976738 | + | 0.214435i | \(0.0687911\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.71525 | − | 7.29164i | −0.117527 | − | 0.499615i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.24284 | − | 1.45344i | −0.562157 | − | 0.0991235i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.39325 | + | 2.53644i | −0.298233 | + | 0.172185i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.4861 | + | 3.76090i | 0.843731 | + | 0.254138i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.77574 | − | 11.7359i | 0.455786 | − | 0.789444i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.57822 | + | 4.26435i | 0.239615 | + | 0.285562i | 0.872428 | − | 0.488743i | \(-0.162544\pi\) |
−0.632813 | + | 0.774305i | \(0.718100\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.11674 | − | 4.54039i | 0.607783 | − | 0.302693i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.7738 | 1.64430 | 0.822148 | − | 0.569274i | \(-0.192776\pi\) | ||||
0.822148 | + | 0.569274i | \(0.192776\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.7947 | −1.63848 | −0.819241 | − | 0.573449i | \(-0.805605\pi\) | ||||
−0.819241 | + | 0.573449i | \(0.805605\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.43869 | + | 2.74283i | 0.357839 | + | 0.180465i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.8205 | + | 16.4706i | 0.905410 | + | 1.07903i | 0.996534 | + | 0.0831862i | \(0.0265096\pi\) |
−0.0911239 | + | 0.995840i | \(0.529046\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.60022 | − | 2.77167i | 0.104387 | − | 0.180804i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.18582 | − | 7.25685i | 0.141984 | − | 0.471383i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.5128 | + | 6.06955i | −0.680015 | + | 0.392607i | −0.799861 | − | 0.600186i | \(-0.795093\pi\) |
0.119846 | + | 0.992793i | \(0.461760\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.4162 | − | 3.77626i | −1.37954 | − | 0.243250i | −0.565830 | − | 0.824522i | \(-0.691444\pi\) |
−0.813709 | + | 0.581272i | \(0.802555\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.2486 | − | 10.7921i | −0.721597 | − | 0.692313i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.68445 | + | 15.6179i | −0.363166 | + | 0.997791i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 20.1847 | + | 10.9117i | 1.28432 | + | 0.694295i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −20.9289 | + | 13.7149i | −1.32631 | + | 0.869149i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.5021 | + | 14.8994i | −0.789127 | + | 0.940445i | −0.999307 | − | 0.0372181i | \(-0.988150\pi\) |
0.210181 | + | 0.977663i | \(0.432595\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.64843 | + | 20.6913i | −0.229375 | + | 1.30085i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.52134 | − | 12.8294i | 0.0952702 | − | 0.803409i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.1861 | + | 3.70746i | −0.635395 | + | 0.231265i | −0.639578 | − | 0.768727i | \(-0.720891\pi\) |
0.00418306 | + | 0.999991i | \(0.498668\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.7511 | − | 6.78452i | −0.730180 | − | 0.421569i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.91786 | + | 1.93315i | 0.180611 | + | 0.119659i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 30.4663 | − | 5.37204i | 1.87863 | − | 0.331254i | 0.887150 | − | 0.461481i | \(-0.152682\pi\) |
0.991484 | + | 0.130227i | \(0.0415706\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 21.4382i | − | 1.31694i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −19.0256 | − | 14.2136i | −1.16435 | − | 0.869861i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.880210 | + | 4.99192i | 0.0536673 | + | 0.304363i | 0.999812 | − | 0.0193811i | \(-0.00616958\pi\) |
−0.946145 | + | 0.323744i | \(0.895058\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.01481 | + | 3.36882i | −0.243882 | + | 0.204641i | −0.756533 | − | 0.653956i | \(-0.773108\pi\) |
0.512650 | + | 0.858597i | \(0.328664\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.04389 | + | 9.41816i | 0.244747 | + | 0.570013i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.63240 | − | 9.97993i | −0.219042 | − | 0.601812i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.15677 | + | 3.73563i | 0.129588 | + | 0.224453i | 0.923517 | − | 0.383558i | \(-0.125301\pi\) |
−0.793929 | + | 0.608010i | \(0.791968\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.52655 | − | 13.4514i | −0.0913924 | − | 0.805314i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.43804 | − | 7.08036i | −0.503371 | − | 0.422379i | 0.355418 | − | 0.934707i | \(-0.384339\pi\) |
−0.858789 | + | 0.512329i | \(0.828783\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.71261 | + | 1.35128i | 0.220691 | + | 0.0803251i | 0.450000 | − | 0.893029i | \(-0.351424\pi\) |
−0.229308 | + | 0.973354i | \(0.573646\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 21.7863 | + | 1.96661i | 1.29051 | + | 0.116492i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.45871 | + | 2.35078i | 0.381246 | + | 0.138762i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.94592 | + | 6.66742i | 0.467407 | + | 0.392201i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.10951 | − | 5.43398i | −0.299525 | − | 0.318545i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.0719 | − | 17.4450i | −0.588406 | − | 1.01915i | −0.994441 | − | 0.105291i | \(-0.966422\pi\) |
0.406036 | − | 0.913857i | \(-0.366911\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.76857 | − | 18.5965i | −0.394081 | − | 1.08273i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.5046 | + | 10.3859i | −0.725590 | + | 0.602651i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −27.0830 | + | 22.7253i | −1.56625 | + | 1.31424i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.563920 | − | 3.19815i | −0.0325038 | − | 0.184338i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.13070 | + | 8.20620i | −0.352199 | + | 0.471434i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 21.1136i | − | 1.20896i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.45677 | − | 1.13850i | 0.368508 | − | 0.0649778i | 0.0136720 | − | 0.999907i | \(-0.495648\pi\) |
0.354836 | + | 0.934929i | \(0.384537\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.94956 | − | 34.4677i | −0.110906 | − | 1.96080i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.86672 | − | 1.07775i | −0.105852 | − | 0.0611137i | 0.446139 | − | 0.894963i | \(-0.352799\pi\) |
−0.551991 | + | 0.833850i | \(0.686132\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.9106 | − | 5.79098i | 0.899320 | − | 0.327326i | 0.149340 | − | 0.988786i | \(-0.452285\pi\) |
0.749980 | + | 0.661460i | \(0.230063\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.08499 | + | 6.72938i | 0.399194 | + | 0.379157i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.961500 | − | 5.45293i | 0.0540032 | − | 0.306267i | −0.945827 | − | 0.324670i | \(-0.894747\pi\) |
0.999831 | + | 0.0184023i | \(0.00585798\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.34608 | − | 2.79595i | 0.131355 | − | 0.156543i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.54137 | − | 6.93009i | −0.253474 | − | 0.386800i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.96942 | − | 8.79469i | 0.387789 | − | 0.489350i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.11224 | − | 16.7932i | 0.339046 | − | 0.931521i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 14.5023 | − | 3.41144i | 0.801977 | − | 0.188653i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.22288 | + | 0.215627i | 0.0674195 | + | 0.0118879i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.67525 | − | 3.85396i | 0.366905 | − | 0.211833i | −0.305200 | − | 0.952288i | \(-0.598723\pi\) |
0.672106 | + | 0.740455i | \(0.265390\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 29.1180 | − | 21.5262i | 1.59566 | − | 1.17963i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.2521 | + | 17.7572i | −0.560133 | + | 0.970179i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.14195 | + | 9.70320i | 0.443520 | + | 0.528567i | 0.940772 | − | 0.339039i | \(-0.110102\pi\) |
−0.497252 | + | 0.867606i | \(0.665657\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.6091 | + | 25.0022i | −0.684832 | + | 1.35793i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.1168 | −0.764466 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.3177 | −0.773081 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −15.1772 | + | 30.0945i | −0.817115 | + | 1.62023i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.93143 | + | 3.49354i | 0.157367 | + | 0.187543i | 0.838967 | − | 0.544182i | \(-0.183160\pi\) |
−0.681600 | + | 0.731725i | \(0.738716\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.809906 | − | 1.40280i | 0.0433533 | − | 0.0750901i | −0.843535 | − | 0.537075i | \(-0.819529\pi\) |
0.886888 | + | 0.461985i | \(0.152863\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −27.3523 | − | 0.137530i | −1.45996 | − | 0.00734079i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.92549 | − | 3.42108i | 0.315382 | − | 0.182086i | −0.333950 | − | 0.942591i | \(-0.608382\pi\) |
0.649332 | + | 0.760505i | \(0.275048\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.3401 | − | 2.17590i | −0.654947 | − | 0.115485i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.87938 | − | 1.14780i | 0.258244 | − | 0.0607481i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.39824 | + | 3.84165i | −0.0737965 | + | 0.202754i | −0.971106 | − | 0.238647i | \(-0.923296\pi\) |
0.897310 | + | 0.441401i | \(0.145518\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.2158 | + | 11.3790i | 0.800829 | + | 0.598893i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.15217 | − | 1.75821i | −0.0604734 | − | 0.0922819i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.0217 | − | 16.7104i | 0.733927 | − | 0.874660i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.71891 | − | 9.74845i | 0.0897266 | − | 0.508865i | −0.906510 | − | 0.422185i | \(-0.861263\pi\) |
0.996236 | − | 0.0866798i | \(-0.0276257\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.6318 | + | 13.2994i | −0.657587 | + | 0.692337i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.81621 | − | 2.84487i | 0.405797 | − | 0.147698i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.90673 | + | 3.98760i | 0.357617 | + | 0.206470i | 0.668035 | − | 0.744130i | \(-0.267136\pi\) |
−0.310418 | + | 0.950600i | \(0.600469\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.454875 | + | 8.04209i | 0.0234897 | + | 0.415292i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.04829 | − | 1.06648i | 0.311503 | − | 0.0549264i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 10.7490i | − | 0.552141i | −0.961137 | − | 0.276071i | \(-0.910968\pi\) | ||
0.961137 | − | 0.276071i | \(-0.0890323\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.99358 | − | 10.6997i | 0.409523 | − | 0.548165i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.913805 | − | 5.18245i | −0.0466933 | − | 0.264811i | 0.952520 | − | 0.304477i | \(-0.0984816\pi\) |
−0.999213 | + | 0.0396663i | \(0.987371\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.80554 | − | 6.54963i | 0.397807 | − | 0.333800i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.42604 | + | 2.02686i | 0.428320 | + | 0.103031i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.43196 | + | 14.9242i | 0.275411 | + | 0.756686i | 0.997868 | + | 0.0652695i | \(0.0207907\pi\) |
−0.722457 | + | 0.691416i | \(0.756987\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.64499 | + | 14.9736i | 0.437196 | + | 0.757245i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.62701 | + | 2.79384i | 0.132515 | + | 0.140930i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.71199 | − | 8.14933i | −0.488663 | − | 0.410037i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −33.6599 | − | 12.2512i | −1.68934 | − | 0.614870i | −0.694799 | − | 0.719204i | \(-0.744507\pi\) |
−0.994542 | + | 0.104334i | \(0.966729\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.17405 | + | 8.20409i | 0.108839 | + | 0.410718i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.57564 | + | 2.02937i | 0.278434 | + | 0.101342i | 0.477463 | − | 0.878652i | \(-0.341557\pi\) |
−0.199029 | + | 0.979994i | \(0.563779\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.1968 | − | 15.2690i | −0.906449 | − | 0.760601i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −24.0127 | + | 10.1677i | −1.19320 | + | 0.505235i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.8799 | − | 32.7009i | −0.935841 | − | 1.62092i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.06715 | + | 24.9118i | 0.448342 | + | 1.23181i | 0.933878 | + | 0.357592i | \(0.116402\pi\) |
−0.485536 | + | 0.874217i | \(0.661375\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.147506 | + | 0.343539i | 0.00727592 | + | 0.0169455i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.88194 | − | 4.93553i | 0.289431 | − | 0.242862i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.26852 | + | 41.2218i | 0.356798 | + | 2.02350i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.0255 | − | 19.4432i | −1.27448 | − | 0.952136i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.21543i | 0.401350i | 0.979658 | + | 0.200675i | \(0.0643135\pi\) | ||||
−0.979658 | + | 0.200675i | \(0.935686\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.5911 | + | 2.92547i | −0.808603 | + | 0.142578i | −0.562641 | − | 0.826701i | \(-0.690215\pi\) |
−0.245961 | + | 0.969280i | \(0.579104\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.83022 | + | 2.76250i | −0.0889884 | + | 0.134317i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.56888 | − | 4.36989i | −0.367144 | − | 0.211971i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.69786 | − | 2.80179i | 0.372526 | − | 0.135588i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.35874 | + | 28.3241i | −0.162162 | + | 1.36750i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.03223 | − | 28.5392i | 0.242394 | − | 1.37469i | −0.584073 | − | 0.811701i | \(-0.698542\pi\) |
0.826467 | − | 0.562985i | \(-0.190347\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.6845 | + | 21.0756i | −0.849863 | + | 1.01283i | 0.149846 | + | 0.988709i | \(0.452122\pi\) |
−0.999709 | + | 0.0241176i | \(0.992322\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.89724 | − | 3.20922i | 0.234805 | − | 0.153870i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −24.9333 | + | 15.3419i | −1.19272 | + | 0.733902i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.19707 | − | 14.2788i | 0.248042 | − | 0.681491i | −0.751715 | − | 0.659488i | \(-0.770773\pi\) |
0.999758 | − | 0.0220034i | \(-0.00700448\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.86897 | − | 15.7784i | 0.327094 | − | 0.751353i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.75117 | − | 0.837760i | −0.225735 | − | 0.0398032i | 0.0596365 | − | 0.998220i | \(-0.481006\pi\) |
−0.285371 | + | 0.958417i | \(0.592117\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −34.4047 | + | 19.8636i | −1.63094 | + | 0.941624i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.12328 | + | 7.04921i | −0.100427 | + | 0.333416i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.78666 | − | 3.09458i | 0.0843176 | − | 0.146042i | −0.820783 | − | 0.571241i | \(-0.806462\pi\) |
0.905100 | + | 0.425198i | \(0.139796\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.2944 | + | 14.6519i | 0.578921 | + | 0.689932i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.8280 | + | 6.97372i | 0.649695 | + | 0.327654i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.1457 | 0.803804 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.0709 | 1.21955 | 0.609774 | − | 0.792576i | \(-0.291260\pi\) | ||||
0.609774 | + | 0.792576i | \(0.291260\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.38906 | + | 13.1617i | −0.111512 | + | 0.614336i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.46456 | + | 10.0877i | 0.394234 | + | 0.469830i | 0.926253 | − | 0.376903i | \(-0.123011\pi\) |
−0.532019 | + | 0.846732i | \(0.678567\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.6868 | − | 18.5101i | 0.496659 | − | 0.860238i | −0.503334 | − | 0.864092i | \(-0.667893\pi\) |
0.999993 | + | 0.00385369i | \(0.00122667\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −21.6838 | − | 6.53133i | −1.00556 | − | 0.302883i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.01942 | − | 4.63001i | 0.371094 | − | 0.214251i | −0.302842 | − | 0.953041i | \(-0.597935\pi\) |
0.673936 | + | 0.738789i | \(0.264602\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.83459 | − | 1.38145i | −0.361768 | − | 0.0637894i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.804111 | + | 3.41833i | 0.0370515 | + | 0.157508i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.09086 | − | 8.49206i | 0.142118 | − | 0.390465i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.03730 | − | 13.0178i | 0.322894 | − | 0.597296i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.36494 | + | 22.1554i | −0.0624961 | + | 1.01442i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.61743 | − | 4.31108i | 0.165284 | − | 0.196978i | −0.677045 | − | 0.735942i | \(-0.736740\pi\) |
0.842329 | + | 0.538964i | \(0.181184\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.0333 | − | 62.5731i | 0.503076 | − | 2.85309i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.9862 | − | 1.53994i | −0.590894 | − | 0.0700697i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.7249 | + | 4.26751i | −0.532400 | + | 0.193778i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.7438 | − | 10.2444i | −0.804048 | − | 0.464217i | 0.0408365 | − | 0.999166i | \(-0.486998\pi\) |
−0.844885 | + | 0.534948i | \(0.820331\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.1368 | + | 0.912725i | −0.729730 | + | 0.0412748i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.2309 | − | 5.68317i | 1.45456 | − | 0.256478i | 0.610196 | − | 0.792250i | \(-0.291091\pi\) |
0.844363 | + | 0.535772i | \(0.179979\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 3.00354i | − | 0.135273i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.71138 | + | 26.0756i | 0.346601 | + | 1.17201i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.844229 | − | 4.78786i | −0.0378689 | − | 0.214765i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.7157 | + | 13.1871i | −0.703533 | + | 0.590334i | −0.922776 | − | 0.385336i | \(-0.874086\pi\) |
0.219243 | + | 0.975670i | \(0.429641\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.1635 | − | 8.65763i | 0.900838 | − | 0.386794i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.95923 | + | 21.8678i | 0.354885 | + | 0.975037i | 0.980778 | + | 0.195128i | \(0.0625124\pi\) |
−0.625893 | + | 0.779909i | \(0.715265\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.56766 | + | 14.8396i | 0.381256 | + | 0.660354i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.5615 | + | 17.4532i | −0.824345 | + | 0.775122i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.6553 | − | 13.9754i | −0.738232 | − | 0.619450i | 0.194130 | − | 0.980976i | \(-0.437812\pi\) |
−0.932362 | + | 0.361525i | \(0.882256\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.95315 | + | 2.89471i | 0.351827 | + | 0.128054i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −22.3899 | − | 3.41950i | −0.988538 | − | 0.150974i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −54.2675 | − | 19.7518i | −2.39131 | − | 0.870367i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.64708 | + | 2.22116i | 0.116418 | + | 0.0976866i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.8994 | − | 11.1889i | 0.522326 | − | 0.491137i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.53777 | − | 13.0558i | −0.330236 | − | 0.571985i | 0.652322 | − | 0.757942i | \(-0.273795\pi\) |
−0.982558 | + | 0.185957i | \(0.940462\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.38040 | − | 6.54010i | −0.104088 | − | 0.285979i | 0.876706 | − | 0.481027i | \(-0.159736\pi\) |
−0.980794 | + | 0.195048i | \(0.937514\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.07407 | − | 2.60803i | 0.265094 | − | 0.113824i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.89914 | + | 7.46727i | −0.387653 | + | 0.325279i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.83894 | − | 21.7717i | −0.166911 | − | 0.946597i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.81098 | + | 19.6495i | 0.252175 | + | 0.852716i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 32.1845i | 1.39407i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.6496 | + | 2.40679i | −0.590124 | + | 0.104055i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.9508 | + | 0.732519i | −0.558867 | + | 0.0316105i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.5407 | − | 8.97240i | −0.669384 | − | 0.386469i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.63626 | + | 1.68746i | −0.199328 | + | 0.0725495i | −0.439755 | − | 0.898118i | \(-0.644935\pi\) |
0.240427 | + | 0.970667i | \(0.422713\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −27.4744 | − | 3.25799i | −1.17904 | − | 0.139814i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.32762 | − | 24.5432i | 0.185375 | − | 1.05131i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.08478 | + | 10.8268i | −0.388437 | + | 0.462922i | −0.924458 | − | 0.381283i | \(-0.875482\pi\) |
0.536021 | + | 0.844205i | \(0.319927\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.34427 | + | 21.8199i | −0.0573720 | + | 0.931250i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.08359 | − | 0.142413i | 0.216568 | − | 0.00606701i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.68239 | − | 4.62234i | 0.0715426 | − | 0.196562i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.8706 | − | 58.9648i | −0.588773 | − | 2.50292i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.424076 | + | 0.0747760i | 0.0179687 | + | 0.00316836i | 0.182625 | − | 0.983183i | \(-0.441540\pi\) |
−0.164657 | + | 0.986351i | \(0.552652\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.1694 | − | 7.60334i | 0.557005 | − | 0.321587i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13.3562 | + | 4.02299i | 0.563899 | + | 0.169851i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.44919 | − | 4.24212i | 0.103221 | − | 0.178784i | −0.809789 | − | 0.586721i | \(-0.800418\pi\) |
0.913010 | + | 0.407937i | \(0.133752\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.1093 | + | 35.8829i | 1.26671 | + | 1.50961i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.89355 | − | 7.40557i | −0.289502 | − | 0.311005i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.33523 | 0.391353 | 0.195677 | − | 0.980668i | \(-0.437310\pi\) | ||||
0.195677 | + | 0.980668i | \(0.437310\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.4478 | −0.981260 | −0.490630 | − | 0.871368i | \(-0.663233\pi\) | ||||
−0.490630 | + | 0.871368i | \(0.663233\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.7806 | − | 5.94117i | −0.492141 | − | 0.248196i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.6563 | + | 17.4667i | 0.611209 | + | 0.728410i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.23938 | + | 2.14667i | −0.0515960 | + | 0.0893669i | −0.890670 | − | 0.454651i | \(-0.849764\pi\) |
0.839074 | + | 0.544017i | \(0.183097\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.99417 | + | 19.9005i | −0.249109 | + | 0.827036i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.0646 | + | 8.12021i | −0.583499 | + | 0.336883i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.7951 | + | 4.01940i | 0.944078 | + | 0.166466i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −18.2637 | + | 41.9528i | −0.755112 | + | 1.73454i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.2139 | − | 36.3050i | 0.545398 | − | 1.49847i | −0.294462 | − | 0.955663i | \(-0.595140\pi\) |
0.839859 | − | 0.542804i | \(-0.182637\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.0605 | − | 14.7080i | −0.538150 | − | 0.606034i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −25.5301 | + | 16.7302i | −1.05017 | + | 0.688188i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.81505 | − | 3.35484i | 0.115600 | − | 0.137767i | −0.705141 | − | 0.709067i | \(-0.749116\pi\) |
0.820741 | + | 0.571300i | \(0.193561\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.45606 | − | 8.25771i | 0.0596925 | − | 0.338533i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.461622 | + | 3.89284i | −0.0188929 | + | 0.159323i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −40.2689 | + | 14.6567i | −1.64534 | + | 0.598855i | −0.987961 | − | 0.154704i | \(-0.950558\pi\) |
−0.657380 | + | 0.753559i | \(0.728335\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.0390 | − | 13.8789i | −0.980571 | − | 0.566133i | −0.0781288 | − | 0.996943i | \(-0.524895\pi\) |
−0.902443 | + | 0.430810i | \(0.858228\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.7256 | − | 17.6985i | 0.477505 | − | 0.720737i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.46299 | + | 0.610618i | −0.140791 | + | 0.0248252i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.1090i | 0.653844i | 0.945051 | + | 0.326922i | \(0.106011\pi\) | ||||
−0.945051 | + | 0.326922i | \(0.893989\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.81992 | + | 1.35963i | 0.0737470 | + | 0.0550950i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.00969 | + | 5.72626i | 0.0408478 | + | 0.231660i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.2068 | − | 14.4382i | 0.694975 | − | 0.583154i | −0.225364 | − | 0.974275i | \(-0.572357\pi\) |
0.920339 | + | 0.391121i | \(0.127913\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.1057 | + | 28.1940i | 0.488150 | + | 1.13689i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.8059 | − | 43.4264i | −0.636322 | − | 1.74828i | −0.662982 | − | 0.748636i | \(-0.730709\pi\) |
0.0266596 | − | 0.999645i | \(-0.491513\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.8534 | + | 36.1192i | 0.838170 | + | 1.45175i | 0.891423 | + | 0.453172i | \(0.149708\pi\) |
−0.0532532 | + | 0.998581i | \(0.516959\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.6010 | − | 30.1349i | 0.706303 | − | 1.20927i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.8076 | − | 9.90779i | −0.473063 | − | 0.396947i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 28.6128 | + | 10.4142i | 1.14451 | + | 0.416568i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.17575 | + | 22.7965i | −0.246636 | + | 0.910406i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −29.1994 | − | 10.6277i | −1.16426 | − | 0.423755i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.34686 | + | 2.80835i | 0.133236 | + | 0.111799i | 0.706971 | − | 0.707243i | \(-0.250061\pi\) |
−0.573734 | + | 0.819042i | \(0.694506\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.56932 | + | 4.85948i | 0.181614 | + | 0.193147i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.1710 | − | 19.3488i | −0.443309 | − | 0.767834i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.3275 | − | 28.3747i | −0.409192 | − | 1.12425i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.6144 | + | 3.03436i | 0.499018 | + | 0.120038i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.18494 | − | 1.83339i | 0.0863001 | − | 0.0724144i | −0.598617 | − | 0.801035i | \(-0.704283\pi\) |
0.684917 | + | 0.728621i | \(0.259838\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.65253 | − | 43.3997i | −0.301786 | − | 1.71152i | −0.638258 | − | 0.769823i | \(-0.720345\pi\) |
0.336471 | − | 0.941694i | \(-0.390766\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.67664 | − | 11.6141i | 0.341643 | − | 0.457303i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.3269i | 0.799131i | 0.916705 | + | 0.399566i | \(0.130839\pi\) | ||||
−0.916705 | + | 0.399566i | \(0.869161\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21.0426 | − | 3.71037i | 0.825992 | − | 0.145645i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.496187 | − | 8.77247i | −0.0194471 | − | 0.343820i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 35.1702 | + | 20.3055i | 1.37632 | + | 0.794617i | 0.991714 | − | 0.128465i | \(-0.0410051\pi\) |
0.384603 | + | 0.923082i | \(0.374338\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.02826 | − | 2.19411i | 0.235543 | − | 0.0857308i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −15.5546 | + | 16.3766i | −0.606843 | + | 0.638912i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.33474 | − | 35.9261i | 0.246766 | − | 1.39948i | −0.569588 | − | 0.821930i | \(-0.692897\pi\) |
0.816354 | − | 0.577552i | \(-0.195992\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.71797 | + | 3.23916i | −0.105717 | + | 0.125989i | −0.816308 | − | 0.577616i | \(-0.803983\pi\) |
0.710591 | + | 0.703605i | \(0.248427\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.8651 | + | 19.6320i | 0.499640 | + | 0.762445i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.0455 | + | 2.07288i | 0.544660 | + | 0.0803830i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.68004 | + | 7.36334i | −0.103771 | + | 0.285110i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.38565 | + | 2.20783i | −0.362870 | + | 0.0853598i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.4500 | + | 3.95854i | 0.866672 | + | 0.152818i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.4627 | − | 12.9688i | 0.865874 | − | 0.499912i | −0.000101249 | − | 1.00000i | \(-0.500032\pi\) |
0.865975 | + | 0.500088i | \(0.166699\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.0886972 | + | 17.6404i | −0.00341396 | + | 0.678978i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.1874 | + | 28.0374i | −0.622132 | + | 1.07756i | 0.366956 | + | 0.930238i | \(0.380400\pi\) |
−0.989088 | + | 0.147326i | \(0.952934\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.11180 | − | 3.70850i | −0.119420 | − | 0.142319i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.3220 | + | 38.3130i | −0.740420 | + | 1.46816i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.5635 | 0.480728 | 0.240364 | − | 0.970683i | \(-0.422733\pi\) | ||||
0.240364 | + | 0.970683i | \(0.422733\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.625411 | 0.0238957 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19.3383 | − | 38.3454i | 0.737802 | − | 1.46297i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.0360 | + | 29.8367i | 0.953796 | + | 1.13669i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.86815 | − | 13.6280i | 0.299319 | − | 0.518435i | −0.676662 | − | 0.736294i | \(-0.736574\pi\) |
0.975980 | + | 0.217859i | \(0.0699073\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.48365 | + | 6.27176i | −0.322267 | + | 0.238244i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −47.0630 | + | 27.1719i | −1.78520 | + | 1.03069i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.5007 | + | 2.73319i | 0.587130 | + | 0.103527i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −36.2511 | + | 8.52752i | −1.37114 | + | 0.322541i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.8602 | − | 29.8381i | 0.410183 | − | 1.12697i | −0.546911 | − | 0.837191i | \(-0.684197\pi\) |
0.957094 | − | 0.289777i | \(-0.0935812\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.6033 | − | 49.9249i | 0.626204 | − | 1.88295i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.03835 | + | 4.63649i | 0.114431 | + | 0.174620i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.27347 | + | 5.09293i | −0.160721 | + | 0.191539i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.11366 | − | 34.6723i | 0.229603 | − | 1.30214i | −0.624084 | − | 0.781358i | \(-0.714528\pi\) |
0.853687 | − | 0.520787i | \(-0.174361\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.51801 | + | 9.04028i | 0.356953 | + | 0.339037i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 28.4797 | − | 10.3658i | 1.06657 | − | 0.388201i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 41.3206 | + | 23.8565i | 1.54530 | + | 0.892182i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.18735 | − | 20.9920i | −0.0443422 | − | 0.783961i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 14.7056 | − | 2.59299i | 0.548426 | − | 0.0967023i | 0.107432 | − | 0.994212i | \(-0.465737\pi\) |
0.440994 | + | 0.897510i | \(0.354626\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 22.4066i | − | 0.834465i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 22.5433 | − | 30.1752i | 0.838394 | − | 1.12223i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.687805 | − | 3.90074i | −0.0255444 | − | 0.144870i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.7799 | − | 19.1146i | 0.844860 | − | 0.708922i | −0.113791 | − | 0.993505i | \(-0.536300\pi\) |
0.958651 | + | 0.284583i | \(0.0918551\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.4633 | − | 8.97894i | 0.943084 | − | 0.332553i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.54354 | − | 6.98831i | −0.0940761 | − | 0.258472i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.63062 | + | 2.82432i | 0.0602284 | + | 0.104319i | 0.894567 | − | 0.446933i | \(-0.147484\pi\) |
−0.834339 | + | 0.551252i | \(0.814150\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −19.7198 | − | 20.9720i | −0.727375 | − | 0.773565i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −16.9590 | − | 14.2303i | −0.624692 | − | 0.524178i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.54154 | + | 2.01696i | 0.203849 | + | 0.0741950i | 0.441927 | − | 0.897051i | \(-0.354295\pi\) |
−0.238078 | + | 0.971246i | \(0.576517\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −32.6179 | + | 22.7055i | −1.19825 | + | 0.834106i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.7676 | + | 10.1066i | 1.01870 | + | 0.370775i | 0.796766 | − | 0.604288i | \(-0.206542\pi\) |
0.221930 | + | 0.975063i | \(0.428764\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.43410 | + | 7.91615i | 0.345639 | + | 0.290025i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.88714 | − | 43.0635i | −0.178811 | − | 1.57561i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.68881 | − | 4.65716i | −0.0982470 | − | 0.170169i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.20481 | + | 17.0476i | 0.226417 | + | 0.622074i | 0.999932 | − | 0.0117037i | \(-0.00372548\pi\) |
−0.773515 | + | 0.633778i | \(0.781503\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.2913 | − | 30.9553i | −0.484363 | − | 1.12807i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.8458 | − | 16.6526i | 0.722261 | − | 0.606049i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.70068 | − | 20.9876i | −0.134504 | − | 0.762807i | −0.975204 | − | 0.221307i | \(-0.928968\pi\) |
0.840701 | − | 0.541500i | \(-0.182143\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −29.1537 | − | 21.7802i | −1.05821 | − | 0.790571i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.1728i | 1.05751i | 0.848774 | + | 0.528757i | \(0.177342\pi\) | ||||
−0.848774 | + | 0.528757i | \(0.822658\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.52252 | − | 1.67908i | 0.344739 | − | 0.0607867i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 18.6543 | + | 12.3589i | 0.674447 | + | 0.446837i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 31.1375 | + | 17.9773i | 1.12431 | + | 0.649122i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.9596 | + | 9.44854i | −0.936129 | + | 0.340723i | −0.764636 | − | 0.644462i | \(-0.777081\pi\) |
−0.171493 | + | 0.985185i | \(0.554859\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.21092 | − | 18.6446i | 0.0796244 | − | 0.671468i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.60654 | − | 43.1388i | 0.273588 | − | 1.55160i | −0.469823 | − | 0.882761i | \(-0.655682\pi\) |
0.743411 | − | 0.668835i | \(-0.233207\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.84744 | + | 11.7357i | −0.353731 | + | 0.421560i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 19.6575 | − | 12.8818i | 0.705208 | − | 0.462131i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.89104 | + | 26.3650i | −0.139411 | + | 0.944624i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.62724 | − | 12.7132i | 0.165576 | − | 0.454916i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.26538 | + | 3.00477i | −0.188169 | + | 0.107382i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.78507 | + | 1.02006i | 0.206478 | + | 0.0364077i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.9379 | + | 18.4393i | −1.13846 | + | 0.657291i | −0.946049 | − | 0.324023i | \(-0.894964\pi\) |
−0.192412 | + | 0.981314i | \(0.561631\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.4539 | + | 51.3064i | −0.550172 | + | 1.82656i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.08710 | + | 15.7393i | −0.323100 | + | 0.559626i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.6569 | + | 29.3850i | 0.875593 | + | 1.04349i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 33.1545 | + | 16.7204i | 1.17587 | + | 0.593013i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 47.4368 | 1.68030 | 0.840148 | − | 0.542357i | \(-0.182468\pi\) | ||||
0.840148 | + | 0.542357i | \(0.182468\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.84362 | 0.100600 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 36.8203 | − | 18.3376i | 1.30098 | − | 0.647926i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.1391 | + | 18.0421i | 0.534249 | + | 0.636693i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.9379 | + | 18.9450i | −0.385510 | + | 0.667723i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.40657 | − | 2.53212i | −0.295925 | − | 0.0891349i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −46.6699 | + | 26.9449i | −1.64083 | + | 0.947331i | −0.660286 | + | 0.751015i | \(0.729565\pi\) |
−0.980540 | + | 0.196317i | \(0.937102\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.26849 | − | 0.928977i | −0.185002 | − | 0.0326208i | 0.0803796 | − | 0.996764i | \(-0.474387\pi\) |
−0.265381 | + | 0.964144i | \(0.585498\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.07863 | − | 8.83641i | −0.0729008 | − | 0.309906i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.24719 | + | 25.4064i | −0.323915 | + | 0.889949i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.7073 | − | 4.63637i | 0.409588 | − | 0.162206i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −17.7193 | − | 1.09164i | −0.619162 | − | 0.0381450i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.7984 | + | 17.6360i | −0.516468 | + | 0.615502i | −0.959742 | − | 0.280884i | \(-0.909372\pi\) |
0.443274 | + | 0.896386i | \(0.353817\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.89577 | + | 10.7514i | −0.0660824 | + | 0.374772i | 0.933775 | + | 0.357862i | \(0.116494\pi\) |
−0.999857 | + | 0.0169103i | \(0.994617\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18.2671 | + | 2.16616i | 0.635979 | + | 0.0754160i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.866657 | + | 0.315437i | −0.0301366 | + | 0.0109688i | −0.357044 | − | 0.934087i | \(-0.616216\pi\) |
0.326908 | + | 0.945056i | \(0.393993\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.7431 | + | 21.2136i | 1.27614 | + | 0.736780i | 0.976137 | − | 0.217158i | \(-0.0696786\pi\) |
0.300004 | + | 0.953938i | \(0.403012\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.45935 | + | 0.421914i | −0.258762 | + | 0.0146360i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.5428 | + | 2.56430i | −0.503880 | + | 0.0888476i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 36.7076i | − | 1.27032i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21.9934 | + | 8.13039i | 0.760201 | + | 0.281027i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.73490 | + | 15.5104i | 0.0944194 | + | 0.535479i | 0.994924 | + | 0.100632i | \(0.0320864\pi\) |
−0.900504 | + | 0.434847i | \(0.856802\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.1725 | + | 17.7659i | −0.730087 | + | 0.612616i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.5310 | − | 7.52731i | 0.603799 | − | 0.259254i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.5770 | + | 40.0501i | 0.501465 | + | 1.37776i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.682168 | − | 1.18155i | −0.0234396 | − | 0.0405985i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.98536 | + | 4.68768i | −0.171097 | + | 0.160881i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 62.1009 | + | 52.1088i | 2.12879 | + | 1.78627i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.2008 | − | 10.9922i | −1.03405 | − | 0.376365i | −0.231431 | − | 0.972851i | \(-0.574341\pi\) |
−0.802623 | + | 0.596486i | \(0.796563\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −20.0333 | + | 32.1590i | −0.685125 | + | 1.09981i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.1422 | + | 8.42308i | 0.790524 | + | 0.287727i | 0.705554 | − | 0.708656i | \(-0.250698\pi\) |
0.0849699 | + | 0.996384i | \(0.472921\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.9557 | + | 10.0320i | 0.407923 | + | 0.342288i | 0.823547 | − | 0.567248i | \(-0.191992\pi\) |
−0.415623 | + | 0.909537i | \(0.636437\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.67289 | + | 8.15502i | −0.295571 | + | 0.277922i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.05542 | − | 12.2203i | −0.240169 | − | 0.415985i | 0.720593 | − | 0.693358i | \(-0.243870\pi\) |
−0.960762 | + | 0.277373i | \(0.910536\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.34505 | − | 25.6753i | −0.317741 | − | 0.872987i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.5086 | + | 7.08830i | −0.560660 | + | 0.240731i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.4860 | − | 8.79880i | 0.355713 | − | 0.298479i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.46878 | − | 36.6863i | −0.219186 | − | 1.24307i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.3888 | − | 3.66376i | 0.419297 | − | 0.123999i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.22796i | 0.176737i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.9817 | − | 3.17067i | 0.607200 | − | 0.107066i | 0.138410 | − | 0.990375i | \(-0.455801\pi\) |
0.468791 | + | 0.883309i | \(0.344690\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 34.8344 | − | 1.97029i | 1.17493 | − | 0.0664564i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.32331 | − | 3.07342i | −0.179347 | − | 0.103546i | 0.407639 | − | 0.913143i | \(-0.366352\pi\) |
−0.586986 | + | 0.809597i | \(0.699686\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51.4745 | + | 18.7352i | −1.73225 | + | 0.630489i | −0.998787 | − | 0.0492352i | \(-0.984322\pi\) |
−0.733468 | + | 0.679724i | \(0.762099\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 34.0387 | + | 4.03640i | 1.14420 | + | 0.135682i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.62578 | + | 43.2479i | −0.256049 | + | 1.45212i | 0.537318 | + | 0.843379i | \(0.319437\pi\) |
−0.793367 | + | 0.608744i | \(0.791674\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.57202 | − | 6.64047i | 0.186879 | − | 0.222714i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.30914 | − | 27.4388i | −0.211364 | − | 0.919236i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.134831 | + | 4.81292i | 0.00451194 | + | 0.161058i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.42145 | + | 20.3903i | −0.248072 | + | 0.681571i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.0220 | − | 59.6084i | −0.468180 | − | 1.99027i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.18490 | − | 0.914238i | −0.172926 | − | 0.0304915i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.4961 | − | 9.52401i | 0.549564 | − | 0.317291i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.38579 | + | 1.62224i | 0.179228 | + | 0.0539848i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23.1408 | + | 40.0811i | −0.769228 | + | 1.33234i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.7940 | + | 25.9730i | 0.723656 | + | 0.862420i | 0.994981 | − | 0.100068i | \(-0.0319060\pi\) |
−0.271324 | + | 0.962488i | \(0.587462\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.90944 | − | 15.8815i | −0.262340 | − | 0.526756i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.3654 | −0.509077 | −0.254539 | − | 0.967063i | \(-0.581924\pi\) | ||||
−0.254539 | + | 0.967063i | \(0.581924\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −45.1937 | −1.49569 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 32.6525 | + | 16.4673i | 1.07946 | + | 0.544391i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.59991 | + | 1.90670i | 0.0528336 | + | 0.0629646i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.10344 | − | 10.5715i | 0.201334 | − | 0.348720i | −0.747625 | − | 0.664121i | \(-0.768806\pi\) |
0.948958 | + | 0.315401i | \(0.102139\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.27516 | + | 10.8734i | −0.107920 | + | 0.358292i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.7155 | − | 11.3828i | 0.648944 | − | 0.374668i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40.3554 | − | 7.11574i | −1.32688 | − | 0.233964i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 54.8253 | + | 23.8676i | 1.80070 | + | 0.783915i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.30750 | − | 17.3297i | 0.206942 | − | 0.568569i | −0.792188 | − | 0.610278i | \(-0.791058\pi\) |
0.999130 | + | 0.0417085i | \(0.0132801\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.02970 | − | 24.4926i | −0.164842 | − | 0.802714i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.12268 | − | 2.04633i | 0.102232 | − | 0.0669938i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.9988 | − | 17.8749i | 0.490513 | − | 0.584570i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.35606 | + | 24.7045i | −0.142306 | + | 0.807060i | 0.827184 | + | 0.561931i | \(0.189941\pi\) |
−0.969491 | + | 0.245129i | \(0.921170\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.45342 | + | 29.1225i | −0.112698 | + | 0.950378i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −43.7853 | + | 15.9365i | −1.42736 | + | 0.519517i | −0.936174 | − | 0.351538i | \(-0.885659\pi\) |
−0.491187 | + | 0.871054i | \(0.663437\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −35.5619 | − | 20.5317i | −1.15806 | − | 0.668604i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −15.9329 | + | 5.70854i | −0.518297 | + | 0.185699i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −54.8110 | + | 9.66466i | −1.78112 | + | 0.314059i | −0.964690 | − | 0.263387i | \(-0.915160\pi\) |
−0.816429 | + | 0.577446i | \(0.804049\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39.6315i | 1.28649i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.68312 | + | 5.73991i | 0.249142 | + | 0.186129i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.28854 | + | 18.6502i | 0.106526 | + | 0.604140i | 0.990600 | + | 0.136792i | \(0.0436792\pi\) |
−0.884074 | + | 0.467348i | \(0.845210\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.9074 | + | 14.1870i | −0.547109 | + | 0.459079i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.49417 | + | 5.80889i | 0.0806252 | + | 0.187775i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.0829924 | + | 0.228020i | 0.00267997 | + | 0.00736314i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.31832 | − | 9.21160i | −0.171559 | − | 0.297148i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.2594 | − | 1.61826i | 0.459504 | − | 0.0521476i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.6332 | + | 22.3479i | 0.857353 | + | 0.719405i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.9285 | + | 8.70925i | 0.769488 | + | 0.280071i | 0.696782 | − | 0.717283i | \(-0.254614\pi\) |
0.0727056 | + | 0.997353i | \(0.476837\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.16540 | + | 17.6376i | 0.262310 | + | 0.566601i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.6975 | − | 5.34944i | −0.471664 | − | 0.171672i | 0.0952419 | − | 0.995454i | \(-0.469638\pi\) |
−0.566906 | + | 0.823782i | \(0.691860\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.1519 | − | 13.5531i | −0.517807 | − | 0.434492i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 21.2038 | + | 22.5503i | 0.679064 | + | 0.722187i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.2781 | + | 17.8022i | 0.328827 | + | 0.569544i | 0.982279 | − | 0.187423i | \(-0.0600135\pi\) |
−0.653453 | + | 0.756967i | \(0.726680\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.6704 | − | 40.3065i | −0.468867 | − | 1.28820i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.03501 | + | 25.0886i | −0.192683 | + | 0.801018i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.5443 | − | 12.2041i | 0.463890 | − | 0.389250i | −0.380670 | − | 0.924711i | \(-0.624307\pi\) |
0.844560 | + | 0.535461i | \(0.179862\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.86652 | + | 50.2845i | 0.282511 | + | 1.60220i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.28724 | + | 1.72302i | −0.0409732 | + | 0.0548444i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.4018i | 0.616941i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.2131 | − | 7.26698i | 1.30918 | − | 0.230843i | 0.524852 | − | 0.851193i | \(-0.324121\pi\) |
0.784325 | + | 0.620350i | \(0.213009\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.753924 | + | 13.3292i | 0.0239251 | + | 0.422989i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.67907 | + | 3.27881i | 0.180039 | + | 0.103945i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.4637 | − | 5.26435i | 0.458069 | − | 0.166724i | −0.102671 | − | 0.994715i | \(-0.532739\pi\) |
0.560740 | + | 0.827992i | \(0.310517\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.5804 | + | 61.8204i | 0.334748 | + | 1.95591i |
(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 | 912.2.cc.c.737.2 | 18 | ||
3.2 | odd | 2 | 912.2.cc.d.737.1 | 18 | |||
4.3 | odd | 2 | 114.2.l.b.53.2 | yes | 18 | ||
12.11 | even | 2 | 114.2.l.a.53.3 | ✓ | 18 | ||
19.14 | odd | 18 | 912.2.cc.d.641.1 | 18 | |||
57.14 | even | 18 | inner | 912.2.cc.c.641.2 | 18 | ||
76.71 | even | 18 | 114.2.l.a.71.3 | yes | 18 | ||
228.71 | odd | 18 | 114.2.l.b.71.2 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.2.l.a.53.3 | ✓ | 18 | 12.11 | even | 2 | ||
114.2.l.a.71.3 | yes | 18 | 76.71 | even | 18 | ||
114.2.l.b.53.2 | yes | 18 | 4.3 | odd | 2 | ||
114.2.l.b.71.2 | yes | 18 | 228.71 | odd | 18 | ||
912.2.cc.c.641.2 | 18 | 57.14 | even | 18 | inner | ||
912.2.cc.c.737.2 | 18 | 1.1 | even | 1 | trivial | ||
912.2.cc.d.641.1 | 18 | 19.14 | odd | 18 | |||
912.2.cc.d.737.1 | 18 | 3.2 | odd | 2 |