Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [385,2,Mod(221,385)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(385, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("385.221");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 385 = 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 385.i (of order \(3\), degree \(2\), 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: | \(3.07424047782\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 17 x^{14} - 28 x^{13} + 127 x^{12} - 178 x^{11} + 612 x^{10} - 527 x^{9} + 1556 x^{8} + \cdots + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 331.7 | ||
Root | \(-0.735245 + 1.27348i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 385.331 |
Dual form | 385.2.i.c.221.7 |
$q$-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 \(\left(\mathbb{Z}/385\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(276\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.735245 | − | 1.27348i | 0.519897 | − | 0.900488i | −0.479836 | − | 0.877358i | \(-0.659304\pi\) |
0.999732 | − | 0.0231292i | \(-0.00736292\pi\) | |||||||
\(3\) | −0.359468 | − | 0.622616i | −0.207539 | − | 0.359468i | 0.743400 | − | 0.668847i | \(-0.233212\pi\) |
−0.950939 | + | 0.309380i | \(0.899879\pi\) | |||||||
\(4\) | −0.0811705 | − | 0.140591i | −0.0405853 | − | 0.0702957i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | −1.05719 | −0.431595 | ||||||||
\(7\) | 2.24301 | + | 1.40318i | 0.847777 | + | 0.530352i | ||||
\(8\) | 2.70226 | 0.955393 | ||||||||
\(9\) | 1.24157 | − | 2.15046i | 0.413855 | − | 0.716818i | ||||
\(10\) | 0.735245 | + | 1.27348i | 0.232505 | + | 0.402710i | ||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | ||||
\(12\) | −0.0583564 | + | 0.101076i | −0.0168460 | + | 0.0291782i | ||||
\(13\) | −1.35223 | −0.375041 | −0.187521 | − | 0.982261i | \(-0.560045\pi\) | ||||
−0.187521 | + | 0.982261i | \(0.560045\pi\) | |||||||
\(14\) | 3.43609 | − | 1.82475i | 0.918332 | − | 0.487684i | ||||
\(15\) | 0.718935 | 0.185628 | ||||||||
\(16\) | 2.14916 | − | 3.72246i | 0.537291 | − | 0.930615i | ||||
\(17\) | 0.271076 | + | 0.469517i | 0.0657456 | + | 0.113875i | 0.897024 | − | 0.441981i | \(-0.145724\pi\) |
−0.831279 | + | 0.555856i | \(0.812391\pi\) | |||||||
\(18\) | −1.82571 | − | 3.16222i | −0.430324 | − | 0.745343i | ||||
\(19\) | −0.0996235 | + | 0.172553i | −0.0228552 | + | 0.0395863i | −0.877227 | − | 0.480076i | \(-0.840609\pi\) |
0.854372 | + | 0.519663i | \(0.173942\pi\) | |||||||
\(20\) | 0.162341 | 0.0363006 | ||||||||
\(21\) | 0.0673544 | − | 1.90093i | 0.0146979 | − | 0.414817i | ||||
\(22\) | 1.47049 | 0.313510 | ||||||||
\(23\) | 1.98556 | − | 3.43910i | 0.414019 | − | 0.717102i | −0.581306 | − | 0.813685i | \(-0.697458\pi\) |
0.995325 | + | 0.0965834i | \(0.0307914\pi\) | |||||||
\(24\) | −0.971375 | − | 1.68247i | −0.198281 | − | 0.343433i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −0.994221 | + | 1.72204i | −0.194983 | + | 0.337720i | ||||
\(27\) | −3.94202 | −0.758642 | ||||||||
\(28\) | 0.0152091 | − | 0.429245i | 0.00287426 | − | 0.0811196i | ||||
\(29\) | 2.25572 | 0.418876 | 0.209438 | − | 0.977822i | \(-0.432837\pi\) | ||||
0.209438 | + | 0.977822i | \(0.432837\pi\) | |||||||
\(30\) | 0.528594 | − | 0.915551i | 0.0965076 | − | 0.167156i | ||||
\(31\) | −3.01637 | − | 5.22451i | −0.541756 | − | 0.938349i | −0.998803 | − | 0.0489069i | \(-0.984426\pi\) |
0.457047 | − | 0.889443i | \(-0.348907\pi\) | |||||||
\(32\) | −0.458065 | − | 0.793391i | −0.0809752 | − | 0.140253i | ||||
\(33\) | 0.359468 | − | 0.622616i | 0.0625753 | − | 0.108384i | ||||
\(34\) | 0.797229 | 0.136724 | ||||||||
\(35\) | −2.33669 | + | 1.24091i | −0.394973 | + | 0.209752i | ||||
\(36\) | −0.403114 | −0.0671857 | ||||||||
\(37\) | −3.88315 | + | 6.72581i | −0.638386 | + | 1.10572i | 0.347401 | + | 0.937717i | \(0.387064\pi\) |
−0.985787 | + | 0.168000i | \(0.946269\pi\) | |||||||
\(38\) | 0.146495 | + | 0.253737i | 0.0237647 | + | 0.0411616i | ||||
\(39\) | 0.486083 | + | 0.841921i | 0.0778356 | + | 0.134815i | ||||
\(40\) | −1.35113 | + | 2.34023i | −0.213632 | + | 0.370022i | ||||
\(41\) | 4.07178 | 0.635906 | 0.317953 | − | 0.948106i | \(-0.397005\pi\) | ||||
0.317953 | + | 0.948106i | \(0.397005\pi\) | |||||||
\(42\) | −2.37128 | − | 1.48342i | −0.365896 | − | 0.228897i | ||||
\(43\) | −9.85011 | −1.50213 | −0.751064 | − | 0.660230i | \(-0.770459\pi\) | ||||
−0.751064 | + | 0.660230i | \(0.770459\pi\) | |||||||
\(44\) | 0.0811705 | − | 0.140591i | 0.0122369 | − | 0.0211950i | ||||
\(45\) | 1.24157 | + | 2.15046i | 0.185082 | + | 0.320571i | ||||
\(46\) | −2.91975 | − | 5.05716i | −0.430494 | − | 0.745638i | ||||
\(47\) | −3.93074 | + | 6.80824i | −0.573357 | + | 0.993084i | 0.422861 | + | 0.906195i | \(0.361026\pi\) |
−0.996218 | + | 0.0868891i | \(0.972307\pi\) | |||||||
\(48\) | −3.09022 | −0.446035 | ||||||||
\(49\) | 3.06217 | + | 6.29469i | 0.437452 | + | 0.899242i | ||||
\(50\) | −1.47049 | −0.207959 | ||||||||
\(51\) | 0.194886 | − | 0.337553i | 0.0272895 | − | 0.0472668i | ||||
\(52\) | 0.109761 | + | 0.190112i | 0.0152211 | + | 0.0263638i | ||||
\(53\) | −4.51408 | − | 7.81862i | −0.620057 | − | 1.07397i | −0.989475 | − | 0.144707i | \(-0.953776\pi\) |
0.369417 | − | 0.929264i | \(-0.379557\pi\) | |||||||
\(54\) | −2.89835 | + | 5.02009i | −0.394415 | + | 0.683147i | ||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 6.06119 | + | 3.79176i | 0.809960 | + | 0.506695i | ||||
\(57\) | 0.143246 | 0.0189733 | ||||||||
\(58\) | 1.65851 | − | 2.87262i | 0.217772 | − | 0.377193i | ||||
\(59\) | 3.78709 | + | 6.55943i | 0.493037 | + | 0.853965i | 0.999968 | − | 0.00802163i | \(-0.00255339\pi\) |
−0.506931 | + | 0.861987i | \(0.669220\pi\) | |||||||
\(60\) | −0.0583564 | − | 0.101076i | −0.00753377 | − | 0.0130489i | ||||
\(61\) | −3.75537 | + | 6.50448i | −0.480825 | + | 0.832814i | −0.999758 | − | 0.0220013i | \(-0.992996\pi\) |
0.518933 | + | 0.854815i | \(0.326330\pi\) | |||||||
\(62\) | −8.87109 | −1.12663 | ||||||||
\(63\) | 5.80232 | − | 3.08135i | 0.731024 | − | 0.388213i | ||||
\(64\) | 7.24950 | 0.906187 | ||||||||
\(65\) | 0.676115 | − | 1.17107i | 0.0838618 | − | 0.145253i | ||||
\(66\) | −0.528594 | − | 0.915551i | −0.0650654 | − | 0.112697i | ||||
\(67\) | 4.00602 | + | 6.93864i | 0.489414 | + | 0.847689i | 0.999926 | − | 0.0121811i | \(-0.00387746\pi\) |
−0.510512 | + | 0.859871i | \(0.670544\pi\) | |||||||
\(68\) | 0.0440068 | − | 0.0762219i | 0.00533660 | − | 0.00924327i | ||||
\(69\) | −2.85498 | −0.343700 | ||||||||
\(70\) | −0.137765 | + | 3.88811i | −0.0164660 | + | 0.464718i | ||||
\(71\) | 6.96472 | 0.826560 | 0.413280 | − | 0.910604i | \(-0.364383\pi\) | ||||
0.413280 | + | 0.910604i | \(0.364383\pi\) | |||||||
\(72\) | 3.35503 | − | 5.81109i | 0.395394 | − | 0.684843i | ||||
\(73\) | −7.43549 | − | 12.8787i | −0.870259 | − | 1.50733i | −0.861729 | − | 0.507369i | \(-0.830618\pi\) |
−0.00852971 | − | 0.999964i | \(-0.502715\pi\) | |||||||
\(74\) | 5.71013 | + | 9.89024i | 0.663790 | + | 1.14972i | ||||
\(75\) | −0.359468 | + | 0.622616i | −0.0415078 | + | 0.0718935i | ||||
\(76\) | 0.0323460 | 0.00371034 | ||||||||
\(77\) | −0.0936863 | + | 2.64409i | −0.0106765 | + | 0.301322i | ||||
\(78\) | 1.42956 | 0.161866 | ||||||||
\(79\) | 0.181768 | − | 0.314832i | 0.0204505 | − | 0.0354214i | −0.855619 | − | 0.517606i | \(-0.826823\pi\) |
0.876070 | + | 0.482185i | \(0.160157\pi\) | |||||||
\(80\) | 2.14916 | + | 3.72246i | 0.240284 | + | 0.416184i | ||||
\(81\) | −2.30767 | − | 3.99700i | −0.256408 | − | 0.444111i | ||||
\(82\) | 2.99376 | − | 5.18534i | 0.330605 | − | 0.572625i | ||||
\(83\) | 3.87173 | 0.424978 | 0.212489 | − | 0.977163i | \(-0.431843\pi\) | ||||
0.212489 | + | 0.977163i | \(0.431843\pi\) | |||||||
\(84\) | −0.272722 | + | 0.144830i | −0.0297564 | + | 0.0158023i | ||||
\(85\) | −0.542152 | −0.0588046 | ||||||||
\(86\) | −7.24224 | + | 12.5439i | −0.780951 | + | 1.35265i | ||||
\(87\) | −0.810858 | − | 1.40445i | −0.0869331 | − | 0.150572i | ||||
\(88\) | 1.35113 | + | 2.34023i | 0.144031 | + | 0.249469i | ||||
\(89\) | 1.99114 | − | 3.44875i | 0.211060 | − | 0.365567i | −0.740986 | − | 0.671520i | \(-0.765642\pi\) |
0.952047 | + | 0.305953i | \(0.0989751\pi\) | |||||||
\(90\) | 3.65142 | 0.384894 | ||||||||
\(91\) | −3.03306 | − | 1.89742i | −0.317951 | − | 0.198904i | ||||
\(92\) | −0.644677 | −0.0672123 | ||||||||
\(93\) | −2.16858 | + | 3.75608i | −0.224871 | + | 0.389488i | ||||
\(94\) | 5.78011 | + | 10.0114i | 0.596173 | + | 1.03260i | ||||
\(95\) | −0.0996235 | − | 0.172553i | −0.0102212 | − | 0.0177036i | ||||
\(96\) | −0.329319 | + | 0.570397i | −0.0336110 | + | 0.0582159i | ||||
\(97\) | −16.6867 | −1.69427 | −0.847137 | − | 0.531375i | \(-0.821676\pi\) | ||||
−0.847137 | + | 0.531375i | \(0.821676\pi\) | |||||||
\(98\) | 10.2676 | + | 0.728526i | 1.03719 | + | 0.0735922i | ||||
\(99\) | 2.48313 | 0.249564 | ||||||||
\(100\) | −0.0811705 | + | 0.140591i | −0.00811705 | + | 0.0140591i | ||||
\(101\) | −2.41345 | − | 4.18022i | −0.240147 | − | 0.415947i | 0.720609 | − | 0.693342i | \(-0.243862\pi\) |
−0.960756 | + | 0.277395i | \(0.910529\pi\) | |||||||
\(102\) | −0.286578 | − | 0.496368i | −0.0283755 | − | 0.0491477i | ||||
\(103\) | −8.28537 | + | 14.3507i | −0.816382 | + | 1.41401i | 0.0919498 | + | 0.995764i | \(0.470690\pi\) |
−0.908331 | + | 0.418251i | \(0.862643\pi\) | |||||||
\(104\) | −3.65408 | −0.358312 | ||||||||
\(105\) | 1.61258 | + | 1.00880i | 0.157371 | + | 0.0984484i | ||||
\(106\) | −13.2758 | −1.28946 | ||||||||
\(107\) | −1.22575 | + | 2.12306i | −0.118498 | + | 0.205244i | −0.919173 | − | 0.393855i | \(-0.871141\pi\) |
0.800675 | + | 0.599099i | \(0.204475\pi\) | |||||||
\(108\) | 0.319976 | + | 0.554214i | 0.0307897 | + | 0.0533293i | ||||
\(109\) | −2.00770 | − | 3.47744i | −0.192303 | − | 0.333078i | 0.753710 | − | 0.657207i | \(-0.228262\pi\) |
−0.946013 | + | 0.324129i | \(0.894929\pi\) | |||||||
\(110\) | −0.735245 | + | 1.27348i | −0.0701029 | + | 0.121422i | ||||
\(111\) | 5.58347 | 0.529959 | ||||||||
\(112\) | 10.0439 | − | 5.33384i | 0.949057 | − | 0.504001i | ||||
\(113\) | −13.6765 | −1.28658 | −0.643290 | − | 0.765622i | \(-0.722431\pi\) | ||||
−0.643290 | + | 0.765622i | \(0.722431\pi\) | |||||||
\(114\) | 0.105321 | − | 0.182421i | 0.00986418 | − | 0.0170853i | ||||
\(115\) | 1.98556 | + | 3.43910i | 0.185155 | + | 0.320698i | ||||
\(116\) | −0.183098 | − | 0.317135i | −0.0170002 | − | 0.0294452i | ||||
\(117\) | −1.67888 | + | 2.90791i | −0.155213 | + | 0.268836i | ||||
\(118\) | 11.1378 | 1.02531 | ||||||||
\(119\) | −0.0507922 | + | 1.43350i | −0.00465611 | + | 0.131409i | ||||
\(120\) | 1.94275 | 0.177348 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | 5.52223 | + | 9.56478i | 0.499959 | + | 0.865954i | ||||
\(123\) | −1.46367 | − | 2.53516i | −0.131975 | − | 0.228588i | ||||
\(124\) | −0.489681 | + | 0.848152i | −0.0439746 | + | 0.0761663i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.342088 | − | 9.65469i | 0.0304756 | − | 0.860108i | ||||
\(127\) | 15.7491 | 1.39750 | 0.698752 | − | 0.715364i | \(-0.253739\pi\) | ||||
0.698752 | + | 0.715364i | \(0.253739\pi\) | |||||||
\(128\) | 6.24629 | − | 10.8189i | 0.552099 | − | 0.956263i | ||||
\(129\) | 3.54080 | + | 6.13284i | 0.311750 | + | 0.539966i | ||||
\(130\) | −0.994221 | − | 1.72204i | −0.0871989 | − | 0.151033i | ||||
\(131\) | 3.66206 | − | 6.34288i | 0.319956 | − | 0.554180i | −0.660523 | − | 0.750806i | \(-0.729665\pi\) |
0.980479 | + | 0.196626i | \(0.0629985\pi\) | |||||||
\(132\) | −0.116713 | −0.0101585 | ||||||||
\(133\) | −0.465579 | + | 0.247248i | −0.0403708 | + | 0.0214391i | ||||
\(134\) | 11.7816 | 1.01778 | ||||||||
\(135\) | 1.97101 | − | 3.41389i | 0.169637 | − | 0.293821i | ||||
\(136\) | 0.732517 | + | 1.26876i | 0.0628128 | + | 0.108795i | ||||
\(137\) | −3.85358 | − | 6.67459i | −0.329233 | − | 0.570249i | 0.653126 | − | 0.757249i | \(-0.273457\pi\) |
−0.982360 | + | 0.187000i | \(0.940124\pi\) | |||||||
\(138\) | −2.09911 | + | 3.63577i | −0.178688 | + | 0.309497i | ||||
\(139\) | −16.6345 | −1.41092 | −0.705461 | − | 0.708749i | \(-0.749260\pi\) | ||||
−0.705461 | + | 0.708749i | \(0.749260\pi\) | |||||||
\(140\) | 0.364132 | + | 0.227794i | 0.0307748 | + | 0.0192521i | ||||
\(141\) | 5.65189 | 0.475975 | ||||||||
\(142\) | 5.12078 | − | 8.86945i | 0.429726 | − | 0.744307i | ||||
\(143\) | −0.676115 | − | 1.17107i | −0.0565396 | − | 0.0979294i | ||||
\(144\) | −5.33666 | − | 9.24336i | −0.444721 | − | 0.770280i | ||||
\(145\) | −1.12786 | + | 1.95351i | −0.0936636 | + | 0.162230i | ||||
\(146\) | −21.8676 | −1.80978 | ||||||||
\(147\) | 2.81843 | − | 4.16929i | 0.232460 | − | 0.343877i | ||||
\(148\) | 1.26079 | 0.103636 | ||||||||
\(149\) | −4.15586 | + | 7.19816i | −0.340461 | + | 0.589696i | −0.984518 | − | 0.175281i | \(-0.943917\pi\) |
0.644057 | + | 0.764977i | \(0.277250\pi\) | |||||||
\(150\) | 0.528594 | + | 0.915551i | 0.0431595 | + | 0.0747544i | ||||
\(151\) | −3.79937 | − | 6.58071i | −0.309189 | − | 0.535530i | 0.668997 | − | 0.743266i | \(-0.266724\pi\) |
−0.978185 | + | 0.207735i | \(0.933391\pi\) | |||||||
\(152\) | −0.269208 | + | 0.466283i | −0.0218357 | + | 0.0378205i | ||||
\(153\) | 1.34623 | 0.108837 | ||||||||
\(154\) | 3.29832 | + | 2.06336i | 0.265786 | + | 0.166271i | ||||
\(155\) | 6.03274 | 0.484562 | ||||||||
\(156\) | 0.0789112 | − | 0.136678i | 0.00631796 | − | 0.0109430i | ||||
\(157\) | −3.83556 | − | 6.64339i | −0.306111 | − | 0.530200i | 0.671397 | − | 0.741098i | \(-0.265695\pi\) |
−0.977508 | + | 0.210898i | \(0.932361\pi\) | |||||||
\(158\) | −0.267289 | − | 0.462958i | −0.0212643 | − | 0.0368309i | ||||
\(159\) | −3.24533 | + | 5.62108i | −0.257372 | + | 0.445781i | ||||
\(160\) | 0.916129 | 0.0724264 | ||||||||
\(161\) | 9.27931 | − | 4.92782i | 0.731312 | − | 0.388367i | ||||
\(162\) | −6.78681 | −0.533222 | ||||||||
\(163\) | −8.47009 | + | 14.6706i | −0.663428 | + | 1.14909i | 0.316281 | + | 0.948666i | \(0.397566\pi\) |
−0.979709 | + | 0.200426i | \(0.935767\pi\) | |||||||
\(164\) | −0.330509 | − | 0.572458i | −0.0258084 | − | 0.0447015i | ||||
\(165\) | 0.359468 | + | 0.622616i | 0.0279845 | + | 0.0484706i | ||||
\(166\) | 2.84667 | − | 4.93058i | 0.220945 | − | 0.382687i | ||||
\(167\) | 12.0563 | 0.932945 | 0.466472 | − | 0.884536i | \(-0.345525\pi\) | ||||
0.466472 | + | 0.884536i | \(0.345525\pi\) | |||||||
\(168\) | 0.182009 | − | 5.13681i | 0.0140423 | − | 0.396313i | ||||
\(169\) | −11.1715 | −0.859344 | ||||||||
\(170\) | −0.398614 | + | 0.690420i | −0.0305723 | + | 0.0529528i | ||||
\(171\) | 0.247378 | + | 0.428472i | 0.0189175 | + | 0.0327660i | ||||
\(172\) | 0.799539 | + | 1.38484i | 0.0609642 | + | 0.105593i | ||||
\(173\) | 4.60695 | − | 7.97947i | 0.350260 | − | 0.606668i | −0.636035 | − | 0.771660i | \(-0.719427\pi\) |
0.986295 | + | 0.164993i | \(0.0527600\pi\) | |||||||
\(174\) | −2.38472 | −0.180785 | ||||||||
\(175\) | 0.0936863 | − | 2.64409i | 0.00708202 | − | 0.199875i | ||||
\(176\) | 4.29833 | 0.323999 | ||||||||
\(177\) | 2.72267 | − | 4.71581i | 0.204649 | − | 0.354462i | ||||
\(178\) | −2.92795 | − | 5.07135i | −0.219459 | − | 0.380114i | ||||
\(179\) | −2.16076 | − | 3.74255i | −0.161503 | − | 0.279731i | 0.773905 | − | 0.633302i | \(-0.218301\pi\) |
−0.935408 | + | 0.353570i | \(0.884967\pi\) | |||||||
\(180\) | 0.201557 | − | 0.349107i | 0.0150232 | − | 0.0260209i | ||||
\(181\) | −2.54375 | −0.189075 | −0.0945377 | − | 0.995521i | \(-0.530137\pi\) | ||||
−0.0945377 | + | 0.995521i | \(0.530137\pi\) | |||||||
\(182\) | −4.64638 | + | 2.46748i | −0.344412 | + | 0.182902i | ||||
\(183\) | 5.39973 | 0.399160 | ||||||||
\(184\) | 5.36551 | − | 9.29334i | 0.395551 | − | 0.685114i | ||||
\(185\) | −3.88315 | − | 6.72581i | −0.285495 | − | 0.494492i | ||||
\(186\) | 3.18887 | + | 5.52328i | 0.233819 | + | 0.404987i | ||||
\(187\) | −0.271076 | + | 0.469517i | −0.0198230 | + | 0.0343345i | ||||
\(188\) | 1.27624 | 0.0930794 | ||||||||
\(189\) | −8.84198 | − | 5.53136i | −0.643159 | − | 0.402347i | ||||
\(190\) | −0.292991 | −0.0212558 | ||||||||
\(191\) | −1.46281 | + | 2.53367i | −0.105845 | + | 0.183330i | −0.914083 | − | 0.405526i | \(-0.867088\pi\) |
0.808238 | + | 0.588856i | \(0.200422\pi\) | |||||||
\(192\) | −2.60596 | − | 4.51365i | −0.188069 | − | 0.325745i | ||||
\(193\) | −6.67993 | − | 11.5700i | −0.480832 | − | 0.832825i | 0.518926 | − | 0.854819i | \(-0.326332\pi\) |
−0.999758 | + | 0.0219936i | \(0.992999\pi\) | |||||||
\(194\) | −12.2688 | + | 21.2502i | −0.880847 | + | 1.52567i | ||||
\(195\) | −0.972166 | −0.0696183 | ||||||||
\(196\) | 0.636422 | − | 0.941458i | 0.0454587 | − | 0.0672470i | ||||
\(197\) | 11.2489 | 0.801454 | 0.400727 | − | 0.916198i | \(-0.368758\pi\) | ||||
0.400727 | + | 0.916198i | \(0.368758\pi\) | |||||||
\(198\) | 1.82571 | − | 3.16222i | 0.129748 | − | 0.224729i | ||||
\(199\) | 5.24565 | + | 9.08574i | 0.371855 | + | 0.644071i | 0.989851 | − | 0.142110i | \(-0.0453887\pi\) |
−0.617996 | + | 0.786181i | \(0.712055\pi\) | |||||||
\(200\) | −1.35113 | − | 2.34023i | −0.0955393 | − | 0.165479i | ||||
\(201\) | 2.88007 | − | 4.98843i | 0.203145 | − | 0.351857i | ||||
\(202\) | −7.09791 | −0.499407 | ||||||||
\(203\) | 5.05959 | + | 3.16518i | 0.355114 | + | 0.222152i | ||||
\(204\) | −0.0632760 | −0.00443021 | ||||||||
\(205\) | −2.03589 | + | 3.52627i | −0.142193 | + | 0.246285i | ||||
\(206\) | 12.1836 | + | 21.1025i | 0.848868 | + | 1.47028i | ||||
\(207\) | −4.93042 | − | 8.53974i | −0.342688 | − | 0.593553i | ||||
\(208\) | −2.90616 | + | 5.03362i | −0.201506 | + | 0.349019i | ||||
\(209\) | −0.199247 | −0.0137822 | ||||||||
\(210\) | 2.47032 | − | 1.31188i | 0.170468 | − | 0.0905280i | ||||
\(211\) | 8.48714 | 0.584279 | 0.292139 | − | 0.956376i | \(-0.405633\pi\) | ||||
0.292139 | + | 0.956376i | \(0.405633\pi\) | |||||||
\(212\) | −0.732821 | + | 1.26928i | −0.0503304 | + | 0.0871747i | ||||
\(213\) | −2.50359 | − | 4.33635i | −0.171543 | − | 0.297122i | ||||
\(214\) | 1.80246 | + | 3.12195i | 0.123213 | + | 0.213412i | ||||
\(215\) | 4.92505 | − | 8.53044i | 0.335886 | − | 0.581771i | ||||
\(216\) | −10.6524 | −0.724801 | ||||||||
\(217\) | 0.565185 | − | 15.9511i | 0.0383673 | − | 1.08283i | ||||
\(218\) | −5.90461 | −0.399911 | ||||||||
\(219\) | −5.34564 | + | 9.25892i | −0.361225 | + | 0.625660i | ||||
\(220\) | 0.0811705 | + | 0.140591i | 0.00547252 | + | 0.00947868i | ||||
\(221\) | −0.366557 | − | 0.634895i | −0.0246573 | − | 0.0427077i | ||||
\(222\) | 4.10522 | − | 7.11044i | 0.275524 | − | 0.477222i | ||||
\(223\) | 19.7906 | 1.32528 | 0.662640 | − | 0.748938i | \(-0.269436\pi\) | ||||
0.662640 | + | 0.748938i | \(0.269436\pi\) | |||||||
\(224\) | 0.0858288 | − | 2.42233i | 0.00573468 | − | 0.161849i | ||||
\(225\) | −2.48313 | −0.165542 | ||||||||
\(226\) | −10.0556 | + | 17.4168i | −0.668889 | + | 1.15855i | ||||
\(227\) | 1.14223 | + | 1.97839i | 0.0758122 | + | 0.131311i | 0.901439 | − | 0.432906i | \(-0.142512\pi\) |
−0.825627 | + | 0.564216i | \(0.809178\pi\) | |||||||
\(228\) | −0.0116273 | − | 0.0201391i | −0.000770038 | − | 0.00133375i | ||||
\(229\) | 13.1008 | − | 22.6912i | 0.865723 | − | 1.49948i | −0.000605448 | − | 1.00000i | \(-0.500193\pi\) |
0.866328 | − | 0.499476i | \(-0.166474\pi\) | |||||||
\(230\) | 5.83951 | 0.385046 | ||||||||
\(231\) | 1.67993 | − | 0.892135i | 0.110531 | − | 0.0586982i | ||||
\(232\) | 6.09553 | 0.400191 | ||||||||
\(233\) | −9.01622 | + | 15.6166i | −0.590672 | + | 1.02307i | 0.403470 | + | 0.914993i | \(0.367804\pi\) |
−0.994142 | + | 0.108081i | \(0.965529\pi\) | |||||||
\(234\) | 2.46878 | + | 4.27605i | 0.161389 | + | 0.279534i | ||||
\(235\) | −3.93074 | − | 6.80824i | −0.256413 | − | 0.444121i | ||||
\(236\) | 0.614800 | − | 1.06486i | 0.0400201 | − | 0.0693168i | ||||
\(237\) | −0.261359 | −0.0169771 | ||||||||
\(238\) | 1.78819 | + | 1.11866i | 0.115911 | + | 0.0725117i | ||||
\(239\) | 26.4144 | 1.70861 | 0.854304 | − | 0.519774i | \(-0.173984\pi\) | ||||
0.854304 | + | 0.519774i | \(0.173984\pi\) | |||||||
\(240\) | 1.54511 | − | 2.67621i | 0.0997364 | − | 0.172749i | ||||
\(241\) | −7.17106 | − | 12.4206i | −0.461928 | − | 0.800083i | 0.537129 | − | 0.843500i | \(-0.319509\pi\) |
−0.999057 | + | 0.0434170i | \(0.986176\pi\) | |||||||
\(242\) | 0.735245 | + | 1.27348i | 0.0472633 | + | 0.0818625i | ||||
\(243\) | −7.57209 | + | 13.1152i | −0.485750 | + | 0.841344i | ||||
\(244\) | 1.21930 | 0.0780577 | ||||||||
\(245\) | −6.98245 | − | 0.495430i | −0.446092 | − | 0.0316519i | ||||
\(246\) | −4.30464 | −0.274454 | ||||||||
\(247\) | 0.134714 | − | 0.233331i | 0.00857164 | − | 0.0148465i | ||||
\(248\) | −8.15102 | − | 14.1180i | −0.517590 | − | 0.896492i | ||||
\(249\) | −1.39176 | − | 2.41060i | −0.0881994 | − | 0.152766i | ||||
\(250\) | 0.735245 | − | 1.27348i | 0.0465010 | − | 0.0805421i | ||||
\(251\) | 7.73165 | 0.488018 | 0.244009 | − | 0.969773i | \(-0.421537\pi\) | ||||
0.244009 | + | 0.969773i | \(0.421537\pi\) | |||||||
\(252\) | −0.904188 | − | 0.565642i | −0.0569585 | − | 0.0356321i | ||||
\(253\) | 3.97113 | 0.249663 | ||||||||
\(254\) | 11.5794 | − | 20.0561i | 0.726558 | − | 1.25843i | ||||
\(255\) | 0.194886 | + | 0.337553i | 0.0122042 | + | 0.0211384i | ||||
\(256\) | −1.93560 | − | 3.35257i | −0.120975 | − | 0.209535i | ||||
\(257\) | 3.86407 | − | 6.69276i | 0.241034 | − | 0.417483i | −0.719975 | − | 0.694000i | \(-0.755847\pi\) |
0.961009 | + | 0.276517i | \(0.0891802\pi\) | |||||||
\(258\) | 10.4134 | 0.648311 | ||||||||
\(259\) | −18.1475 | + | 9.63729i | −1.12763 | + | 0.598832i | ||||
\(260\) | −0.219522 | −0.0136142 | ||||||||
\(261\) | 2.80062 | − | 4.85082i | 0.173354 | − | 0.300258i | ||||
\(262\) | −5.38503 | − | 9.32714i | −0.332688 | − | 0.576233i | ||||
\(263\) | −11.4831 | − | 19.8892i | −0.708076 | − | 1.22642i | −0.965570 | − | 0.260144i | \(-0.916230\pi\) |
0.257494 | − | 0.966280i | \(-0.417103\pi\) | |||||||
\(264\) | 0.971375 | − | 1.68247i | 0.0597840 | − | 0.103549i | ||||
\(265\) | 9.02817 | 0.554596 | ||||||||
\(266\) | −0.0274492 | + | 0.774694i | −0.00168302 | + | 0.0474995i | ||||
\(267\) | −2.86300 | −0.175213 | ||||||||
\(268\) | 0.650342 | − | 1.12643i | 0.0397260 | − | 0.0688074i | ||||
\(269\) | 10.7424 | + | 18.6064i | 0.654975 | + | 1.13445i | 0.981900 | + | 0.189400i | \(0.0606543\pi\) |
−0.326925 | + | 0.945050i | \(0.606012\pi\) | |||||||
\(270\) | −2.89835 | − | 5.02009i | −0.176388 | − | 0.305513i | ||||
\(271\) | 10.5662 | − | 18.3012i | 0.641851 | − | 1.11172i | −0.343168 | − | 0.939274i | \(-0.611500\pi\) |
0.985019 | − | 0.172445i | \(-0.0551667\pi\) | |||||||
\(272\) | 2.33035 | 0.141298 | ||||||||
\(273\) | −0.0910787 | + | 2.57050i | −0.00551233 | + | 0.155574i | ||||
\(274\) | −11.3333 | −0.684670 | ||||||||
\(275\) | 0.500000 | − | 0.866025i | 0.0301511 | − | 0.0522233i | ||||
\(276\) | 0.231741 | + | 0.401387i | 0.0139491 | + | 0.0241606i | ||||
\(277\) | 5.91140 | + | 10.2388i | 0.355181 | + | 0.615192i | 0.987149 | − | 0.159803i | \(-0.0510857\pi\) |
−0.631968 | + | 0.774995i | \(0.717752\pi\) | |||||||
\(278\) | −12.2305 | + | 21.1838i | −0.733534 | + | 1.27052i | ||||
\(279\) | −14.9801 | −0.896835 | ||||||||
\(280\) | −6.31435 | + | 3.35326i | −0.377355 | + | 0.200396i | ||||
\(281\) | 26.7399 | 1.59517 | 0.797584 | − | 0.603209i | \(-0.206111\pi\) | ||||
0.797584 | + | 0.603209i | \(0.206111\pi\) | |||||||
\(282\) | 4.15553 | − | 7.19758i | 0.247458 | − | 0.428610i | ||||
\(283\) | 5.86786 | + | 10.1634i | 0.348808 | + | 0.604153i | 0.986038 | − | 0.166520i | \(-0.0532532\pi\) |
−0.637230 | + | 0.770674i | \(0.719920\pi\) | |||||||
\(284\) | −0.565330 | − | 0.979180i | −0.0335462 | − | 0.0581037i | ||||
\(285\) | −0.0716228 | + | 0.124054i | −0.00424257 | + | 0.00734835i | ||||
\(286\) | −1.98844 | −0.117579 | ||||||||
\(287\) | 9.13304 | + | 5.71345i | 0.539107 | + | 0.337254i | ||||
\(288\) | −2.27487 | −0.134048 | ||||||||
\(289\) | 8.35304 | − | 14.4679i | 0.491355 | − | 0.851052i | ||||
\(290\) | 1.65851 | + | 2.87262i | 0.0973908 | + | 0.168686i | ||||
\(291\) | 5.99832 | + | 10.3894i | 0.351627 | + | 0.609037i | ||||
\(292\) | −1.20709 | + | 2.09073i | −0.0706394 | + | 0.122351i | ||||
\(293\) | 14.9197 | 0.871621 | 0.435810 | − | 0.900039i | \(-0.356462\pi\) | ||||
0.435810 | + | 0.900039i | \(0.356462\pi\) | |||||||
\(294\) | −3.23728 | − | 6.65467i | −0.188802 | − | 0.388108i | ||||
\(295\) | −7.57418 | −0.440986 | ||||||||
\(296\) | −10.4933 | + | 18.1749i | −0.609909 | + | 1.05639i | ||||
\(297\) | −1.97101 | − | 3.41389i | −0.114370 | − | 0.198094i | ||||
\(298\) | 6.11115 | + | 10.5848i | 0.354009 | + | 0.613162i | ||||
\(299\) | −2.68494 | + | 4.65045i | −0.155274 | + | 0.268943i | ||||
\(300\) | 0.116713 | 0.00673841 | ||||||||
\(301\) | −22.0939 | − | 13.8215i | −1.27347 | − | 0.796657i | ||||
\(302\) | −11.1739 | −0.642985 | ||||||||
\(303\) | −1.73512 | + | 3.00531i | −0.0996798 | + | 0.172650i | ||||
\(304\) | 0.428214 | + | 0.741689i | 0.0245598 | + | 0.0425388i | ||||
\(305\) | −3.75537 | − | 6.50448i | −0.215032 | − | 0.372446i | ||||
\(306\) | 0.989812 | − | 1.71441i | 0.0565838 | − | 0.0980060i | ||||
\(307\) | 31.0065 | 1.76964 | 0.884818 | − | 0.465937i | \(-0.154283\pi\) | ||||
0.884818 | + | 0.465937i | \(0.154283\pi\) | |||||||
\(308\) | 0.379341 | − | 0.201451i | 0.0216150 | − | 0.0114787i | ||||
\(309\) | 11.9133 | 0.677723 | ||||||||
\(310\) | 4.43554 | − | 7.68259i | 0.251922 | − | 0.436342i | ||||
\(311\) | 11.3287 | + | 19.6220i | 0.642394 | + | 1.11266i | 0.984897 | + | 0.173142i | \(0.0553921\pi\) |
−0.342503 | + | 0.939517i | \(0.611275\pi\) | |||||||
\(312\) | 1.31352 | + | 2.27509i | 0.0743636 | + | 0.128801i | ||||
\(313\) | 5.24515 | − | 9.08486i | 0.296473 | − | 0.513507i | −0.678853 | − | 0.734274i | \(-0.737523\pi\) |
0.975327 | + | 0.220767i | \(0.0708561\pi\) | |||||||
\(314\) | −11.2803 | −0.636585 | ||||||||
\(315\) | −0.232635 | + | 6.56563i | −0.0131075 | + | 0.369931i | ||||
\(316\) | −0.0590170 | −0.00331996 | ||||||||
\(317\) | −16.9666 | + | 29.3870i | −0.952938 | + | 1.65054i | −0.213919 | + | 0.976851i | \(0.568623\pi\) |
−0.739018 | + | 0.673685i | \(0.764710\pi\) | |||||||
\(318\) | 4.77223 | + | 8.26575i | 0.267613 | + | 0.463520i | ||||
\(319\) | 1.12786 | + | 1.95351i | 0.0631480 | + | 0.109375i | ||||
\(320\) | −3.62475 | + | 6.27825i | −0.202630 | + | 0.350965i | ||||
\(321\) | 1.76247 | 0.0983716 | ||||||||
\(322\) | 0.547082 | − | 15.4402i | 0.0304877 | − | 0.860448i | ||||
\(323\) | −0.108022 | −0.00601051 | ||||||||
\(324\) | −0.374630 | + | 0.648878i | −0.0208128 | + | 0.0360488i | ||||
\(325\) | 0.676115 | + | 1.17107i | 0.0375041 | + | 0.0649590i | ||||
\(326\) | 12.4552 | + | 21.5730i | 0.689828 | + | 1.19482i | ||||
\(327\) | −1.44341 | + | 2.50005i | −0.0798206 | + | 0.138253i | ||||
\(328\) | 11.0030 | 0.607540 | ||||||||
\(329\) | −18.3699 | + | 9.75540i | −1.01276 | + | 0.537832i | ||||
\(330\) | 1.05719 | 0.0581962 | ||||||||
\(331\) | −7.70042 | + | 13.3375i | −0.423253 | + | 0.733096i | −0.996256 | − | 0.0864575i | \(-0.972445\pi\) |
0.573002 | + | 0.819554i | \(0.305779\pi\) | |||||||
\(332\) | −0.314271 | − | 0.544333i | −0.0172478 | − | 0.0298741i | ||||
\(333\) | 9.64237 | + | 16.7011i | 0.528399 | + | 0.915214i | ||||
\(334\) | 8.86434 | − | 15.3535i | 0.485035 | − | 0.840105i | ||||
\(335\) | −8.01205 | −0.437745 | ||||||||
\(336\) | −6.93139 | − | 4.33614i | −0.378138 | − | 0.236556i | ||||
\(337\) | −14.6257 | −0.796710 | −0.398355 | − | 0.917231i | \(-0.630419\pi\) | ||||
−0.398355 | + | 0.917231i | \(0.630419\pi\) | |||||||
\(338\) | −8.21377 | + | 14.2267i | −0.446770 | + | 0.773829i | ||||
\(339\) | 4.91627 | + | 8.51523i | 0.267015 | + | 0.462484i | ||||
\(340\) | 0.0440068 | + | 0.0762219i | 0.00238660 | + | 0.00413371i | ||||
\(341\) | 3.01637 | − | 5.22451i | 0.163346 | − | 0.282923i | ||||
\(342\) | 0.727534 | 0.0393406 | ||||||||
\(343\) | −1.96412 | + | 18.4158i | −0.106053 | + | 0.994361i | ||||
\(344\) | −26.6175 | −1.43512 | ||||||||
\(345\) | 1.42749 | − | 2.47249i | 0.0768536 | − | 0.133114i | ||||
\(346\) | −6.77447 | − | 11.7337i | −0.364198 | − | 0.630809i | ||||
\(347\) | −0.557832 | − | 0.966193i | −0.0299460 | − | 0.0518680i | 0.850664 | − | 0.525710i | \(-0.176200\pi\) |
−0.880610 | + | 0.473842i | \(0.842867\pi\) | |||||||
\(348\) | −0.131635 | + | 0.227999i | −0.00705640 | + | 0.0122220i | ||||
\(349\) | 25.7539 | 1.37858 | 0.689289 | − | 0.724487i | \(-0.257923\pi\) | ||||
0.689289 | + | 0.724487i | \(0.257923\pi\) | |||||||
\(350\) | −3.29832 | − | 2.06336i | −0.176303 | − | 0.110291i | ||||
\(351\) | 5.33051 | 0.284522 | ||||||||
\(352\) | 0.458065 | − | 0.793391i | 0.0244149 | − | 0.0422879i | ||||
\(353\) | −7.64132 | − | 13.2352i | −0.406707 | − | 0.704436i | 0.587812 | − | 0.808998i | \(-0.299990\pi\) |
−0.994518 | + | 0.104561i | \(0.966656\pi\) | |||||||
\(354\) | −4.00366 | − | 6.93455i | −0.212792 | − | 0.368567i | ||||
\(355\) | −3.48236 | + | 6.03163i | −0.184825 | + | 0.320125i | ||||
\(356\) | −0.646487 | −0.0342637 | ||||||||
\(357\) | 0.910778 | − | 0.483673i | 0.0482035 | − | 0.0255987i | ||||
\(358\) | −6.35476 | −0.335859 | ||||||||
\(359\) | −3.41465 | + | 5.91435i | −0.180218 | + | 0.312147i | −0.941955 | − | 0.335740i | \(-0.891014\pi\) |
0.761736 | + | 0.647887i | \(0.224347\pi\) | |||||||
\(360\) | 3.35503 | + | 5.81109i | 0.176826 | + | 0.306271i | ||||
\(361\) | 9.48015 | + | 16.4201i | 0.498955 | + | 0.864216i | ||||
\(362\) | −1.87028 | + | 3.23942i | −0.0982997 | + | 0.170260i | ||||
\(363\) | 0.718935 | 0.0377343 | ||||||||
\(364\) | −0.0205663 | + | 0.580438i | −0.00107796 | + | 0.0304232i | ||||
\(365\) | 14.8710 | 0.778383 | ||||||||
\(366\) | 3.97012 | − | 6.87646i | 0.207522 | − | 0.359438i | ||||
\(367\) | 2.25814 | + | 3.91122i | 0.117874 | + | 0.204164i | 0.918925 | − | 0.394432i | \(-0.129059\pi\) |
−0.801051 | + | 0.598596i | \(0.795725\pi\) | |||||||
\(368\) | −8.53461 | − | 14.7824i | −0.444897 | − | 0.770584i | ||||
\(369\) | 5.05539 | − | 8.75619i | 0.263173 | − | 0.455829i | ||||
\(370\) | −11.4203 | −0.593711 | ||||||||
\(371\) | 0.845816 | − | 23.8713i | 0.0439126 | − | 1.23934i | ||||
\(372\) | 0.704098 | 0.0365058 | ||||||||
\(373\) | −2.12824 | + | 3.68622i | −0.110196 | + | 0.190865i | −0.915849 | − | 0.401522i | \(-0.868481\pi\) |
0.805653 | + | 0.592388i | \(0.201815\pi\) | |||||||
\(374\) | 0.398614 | + | 0.690420i | 0.0206119 | + | 0.0357008i | ||||
\(375\) | −0.359468 | − | 0.622616i | −0.0185628 | − | 0.0321518i | ||||
\(376\) | −10.6219 | + | 18.3976i | −0.547781 | + | 0.948785i | ||||
\(377\) | −3.05025 | −0.157096 | ||||||||
\(378\) | −13.5451 | + | 7.19319i | −0.696685 | + | 0.369978i | ||||
\(379\) | −12.2039 | −0.626871 | −0.313436 | − | 0.949609i | \(-0.601480\pi\) | ||||
−0.313436 | + | 0.949609i | \(0.601480\pi\) | |||||||
\(380\) | −0.0161730 | + | 0.0280124i | −0.000829656 | + | 0.00143701i | ||||
\(381\) | −5.66128 | − | 9.80562i | −0.290036 | − | 0.502357i | ||||
\(382\) | 2.15105 | + | 3.72573i | 0.110057 | + | 0.190625i | ||||
\(383\) | −5.51232 | + | 9.54761i | −0.281666 | + | 0.487860i | −0.971795 | − | 0.235826i | \(-0.924220\pi\) |
0.690129 | + | 0.723686i | \(0.257554\pi\) | |||||||
\(384\) | −8.98135 | −0.458328 | ||||||||
\(385\) | −2.24301 | − | 1.40318i | −0.114314 | − | 0.0715127i | ||||
\(386\) | −19.6455 | −0.999932 | ||||||||
\(387\) | −12.2296 | + | 21.1822i | −0.621663 | + | 1.07675i | ||||
\(388\) | 1.35447 | + | 2.34600i | 0.0687626 | + | 0.119100i | ||||
\(389\) | −15.2836 | − | 26.4720i | −0.774911 | − | 1.34219i | −0.934844 | − | 0.355058i | \(-0.884461\pi\) |
0.159933 | − | 0.987128i | \(-0.448872\pi\) | |||||||
\(390\) | −0.714780 | + | 1.23804i | −0.0361943 | + | 0.0626904i | ||||
\(391\) | 2.15295 | 0.108880 | ||||||||
\(392\) | 8.27477 | + | 17.0099i | 0.417939 | + | 0.859129i | ||||
\(393\) | −5.26557 | −0.265613 | ||||||||
\(394\) | 8.27073 | − | 14.3253i | 0.416673 | − | 0.721699i | ||||
\(395\) | 0.181768 | + | 0.314832i | 0.00914576 | + | 0.0158409i | ||||
\(396\) | −0.201557 | − | 0.349107i | −0.0101286 | − | 0.0175433i | ||||
\(397\) | 8.88315 | − | 15.3861i | 0.445832 | − | 0.772204i | −0.552277 | − | 0.833660i | \(-0.686241\pi\) |
0.998110 | + | 0.0614560i | \(0.0195744\pi\) | |||||||
\(398\) | 15.4274 | 0.773304 | ||||||||
\(399\) | 0.321301 | + | 0.201000i | 0.0160852 | + | 0.0100626i | ||||
\(400\) | −4.29833 | −0.214916 | ||||||||
\(401\) | −12.5534 | + | 21.7432i | −0.626889 | + | 1.08580i | 0.361283 | + | 0.932456i | \(0.382339\pi\) |
−0.988172 | + | 0.153348i | \(0.950995\pi\) | |||||||
\(402\) | −4.23512 | − | 7.33544i | −0.211228 | − | 0.365858i | ||||
\(403\) | 4.07883 | + | 7.06474i | 0.203181 | + | 0.351920i | ||||
\(404\) | −0.391802 | + | 0.678621i | −0.0194929 | + | 0.0337627i | ||||
\(405\) | 4.61534 | 0.229338 | ||||||||
\(406\) | 7.75084 | − | 4.11612i | 0.384668 | − | 0.204279i | ||||
\(407\) | −7.76630 | −0.384961 | ||||||||
\(408\) | 0.526633 | − | 0.912154i | 0.0260722 | − | 0.0451584i | ||||
\(409\) | −9.56236 | − | 16.5625i | −0.472828 | − | 0.818962i | 0.526688 | − | 0.850058i | \(-0.323434\pi\) |
−0.999516 | + | 0.0310962i | \(0.990100\pi\) | |||||||
\(410\) | 2.99376 | + | 5.18534i | 0.147851 | + | 0.256086i | ||||
\(411\) | −2.77047 | + | 4.79860i | −0.136657 | + | 0.236698i | ||||
\(412\) | 2.69011 | 0.132532 | ||||||||
\(413\) | −0.709597 | + | 20.0268i | −0.0349170 | + | 0.985456i | ||||
\(414\) | −14.5003 | −0.712649 | ||||||||
\(415\) | −1.93587 | + | 3.35302i | −0.0950279 | + | 0.164593i | ||||
\(416\) | 0.619409 | + | 1.07285i | 0.0303690 | + | 0.0526007i | ||||
\(417\) | 5.97957 | + | 10.3569i | 0.292821 | + | 0.507181i | ||||
\(418\) | −0.146495 | + | 0.253737i | −0.00716532 | + | 0.0124107i | ||||
\(419\) | −34.2881 | −1.67508 | −0.837542 | − | 0.546372i | \(-0.816008\pi\) | ||||
−0.837542 | + | 0.546372i | \(0.816008\pi\) | |||||||
\(420\) | 0.0109344 | − | 0.308599i | 0.000533543 | − | 0.0150581i | ||||
\(421\) | −13.2601 | −0.646258 | −0.323129 | − | 0.946355i | \(-0.604735\pi\) | ||||
−0.323129 | + | 0.946355i | \(0.604735\pi\) | |||||||
\(422\) | 6.24013 | − | 10.8082i | 0.303765 | − | 0.526136i | ||||
\(423\) | 9.76054 | + | 16.9058i | 0.474574 | + | 0.821986i | ||||
\(424\) | −12.1982 | − | 21.1279i | −0.592398 | − | 1.02606i | ||||
\(425\) | 0.271076 | − | 0.469517i | 0.0131491 | − | 0.0227749i | ||||
\(426\) | −7.36301 | −0.356739 | ||||||||
\(427\) | −17.5503 | + | 9.32015i | −0.849318 | + | 0.451034i | ||||
\(428\) | 0.397980 | 0.0192371 | ||||||||
\(429\) | −0.486083 | + | 0.841921i | −0.0234683 | + | 0.0406483i | ||||
\(430\) | −7.24224 | − | 12.5439i | −0.349252 | − | 0.604922i | ||||
\(431\) | 9.67826 | + | 16.7632i | 0.466185 | + | 0.807457i | 0.999254 | − | 0.0386152i | \(-0.0122947\pi\) |
−0.533069 | + | 0.846072i | \(0.678961\pi\) | |||||||
\(432\) | −8.47204 | + | 14.6740i | −0.407611 | + | 0.706003i | ||||
\(433\) | 14.8600 | 0.714127 | 0.357064 | − | 0.934080i | \(-0.383778\pi\) | ||||
0.357064 | + | 0.934080i | \(0.383778\pi\) | |||||||
\(434\) | −19.8979 | − | 12.4477i | −0.955131 | − | 0.597511i | ||||
\(435\) | 1.62172 | 0.0777553 | ||||||||
\(436\) | −0.325932 | + | 0.564531i | −0.0156093 | + | 0.0270361i | ||||
\(437\) | 0.395618 | + | 0.685230i | 0.0189250 | + | 0.0327790i | ||||
\(438\) | 7.86071 | + | 13.6151i | 0.375599 | + | 0.650557i | ||||
\(439\) | 10.5297 | − | 18.2379i | 0.502554 | − | 0.870448i | −0.497442 | − | 0.867497i | \(-0.665727\pi\) |
0.999996 | − | 0.00295114i | \(-0.000939379\pi\) | |||||||
\(440\) | −2.70226 | −0.128825 | ||||||||
\(441\) | 17.3383 | + | 1.23022i | 0.825635 | + | 0.0585819i | ||||
\(442\) | −1.07804 | −0.0512770 | ||||||||
\(443\) | 4.05594 | − | 7.02509i | 0.192704 | − | 0.333772i | −0.753442 | − | 0.657515i | \(-0.771608\pi\) |
0.946145 | + | 0.323742i | \(0.104941\pi\) | |||||||
\(444\) | −0.453213 | − | 0.784988i | −0.0215085 | − | 0.0372539i | ||||
\(445\) | 1.99114 | + | 3.44875i | 0.0943890 | + | 0.163487i | ||||
\(446\) | 14.5510 | − | 25.2030i | 0.689008 | − | 1.19340i | ||||
\(447\) | 5.97559 | 0.282636 | ||||||||
\(448\) | 16.2607 | + | 10.1724i | 0.768245 | + | 0.480599i | ||||
\(449\) | 35.4379 | 1.67242 | 0.836209 | − | 0.548411i | \(-0.184767\pi\) | ||||
0.836209 | + | 0.548411i | \(0.184767\pi\) | |||||||
\(450\) | −1.82571 | + | 3.16222i | −0.0860648 | + | 0.149069i | ||||
\(451\) | 2.03589 | + | 3.52627i | 0.0958664 | + | 0.166046i | ||||
\(452\) | 1.11013 | + | 1.92280i | 0.0522162 | + | 0.0904411i | ||||
\(453\) | −2.73150 | + | 4.73110i | −0.128337 | + | 0.222287i | ||||
\(454\) | 3.35926 | 0.157658 | ||||||||
\(455\) | 3.15975 | − | 1.67800i | 0.148131 | − | 0.0786657i | ||||
\(456\) | 0.387087 | 0.0181270 | ||||||||
\(457\) | −16.3267 | + | 28.2786i | −0.763730 | + | 1.32282i | 0.177186 | + | 0.984177i | \(0.443301\pi\) |
−0.940915 | + | 0.338641i | \(0.890033\pi\) | |||||||
\(458\) | −19.2645 | − | 33.3672i | −0.900173 | − | 1.55914i | ||||
\(459\) | −1.06859 | − | 1.85085i | −0.0498773 | − | 0.0863901i | ||||
\(460\) | 0.322339 | − | 0.558307i | 0.0150291 | − | 0.0260312i | ||||
\(461\) | −1.18996 | −0.0554219 | −0.0277109 | − | 0.999616i | \(-0.508822\pi\) | ||||
−0.0277109 | + | 0.999616i | \(0.508822\pi\) | |||||||
\(462\) | 0.0990440 | − | 2.79530i | 0.00460794 | − | 0.130049i | ||||
\(463\) | −17.3660 | −0.807068 | −0.403534 | − | 0.914965i | \(-0.632218\pi\) | ||||
−0.403534 | + | 0.914965i | \(0.632218\pi\) | |||||||
\(464\) | 4.84791 | − | 8.39682i | 0.225058 | − | 0.389813i | ||||
\(465\) | −2.16858 | − | 3.75608i | −0.100565 | − | 0.174184i | ||||
\(466\) | 13.2583 | + | 22.9640i | 0.614177 | + | 1.06379i | ||||
\(467\) | −6.54091 | + | 11.3292i | −0.302677 | + | 0.524252i | −0.976741 | − | 0.214421i | \(-0.931214\pi\) |
0.674064 | + | 0.738673i | \(0.264547\pi\) | |||||||
\(468\) | 0.545103 | 0.0251974 | ||||||||
\(469\) | −0.750619 | + | 21.1846i | −0.0346604 | + | 0.978214i | ||||
\(470\) | −11.5602 | −0.533233 | ||||||||
\(471\) | −2.75752 | + | 4.77617i | −0.127060 | + | 0.220074i | ||||
\(472\) | 10.2337 | + | 17.7253i | 0.471044 | + | 0.815872i | ||||
\(473\) | −4.92505 | − | 8.53044i | −0.226454 | − | 0.392230i | ||||
\(474\) | −0.192163 | + | 0.332837i | −0.00882635 | + | 0.0152877i | ||||
\(475\) | 0.199247 | 0.00914208 | ||||||||
\(476\) | 0.205661 | − | 0.109217i | 0.00942644 | − | 0.00500595i | ||||
\(477\) | −22.4181 | −1.02646 | ||||||||
\(478\) | 19.4211 | − | 33.6383i | 0.888299 | − | 1.53858i | ||||
\(479\) | −17.2054 | − | 29.8007i | −0.786136 | − | 1.36163i | −0.928318 | − | 0.371788i | \(-0.878745\pi\) |
0.142181 | − | 0.989841i | \(-0.454588\pi\) | |||||||
\(480\) | −0.329319 | − | 0.570397i | −0.0150313 | − | 0.0260349i | ||||
\(481\) | 5.25091 | − | 9.09485i | 0.239421 | − | 0.414689i | ||||
\(482\) | −21.0899 | −0.960620 | ||||||||
\(483\) | −6.40375 | − | 4.00606i | −0.291381 | − | 0.182282i | ||||
\(484\) | 0.162341 | 0.00737914 | ||||||||
\(485\) | 8.34333 | − | 14.4511i | 0.378851 | − | 0.656189i | ||||
\(486\) | 11.1347 | + | 19.2858i | 0.505080 | + | 0.874824i | ||||
\(487\) | 13.4835 | + | 23.3541i | 0.610994 | + | 1.05827i | 0.991073 | + | 0.133319i | \(0.0425636\pi\) |
−0.380079 | + | 0.924954i | \(0.624103\pi\) | |||||||
\(488\) | −10.1480 | + | 17.5768i | −0.459377 | + | 0.795664i | ||||
\(489\) | 12.1789 | 0.550748 | ||||||||
\(490\) | −5.76473 | + | 8.52775i | −0.260424 | + | 0.385245i | ||||
\(491\) | 34.2270 | 1.54464 | 0.772322 | − | 0.635232i | \(-0.219095\pi\) | ||||
0.772322 | + | 0.635232i | \(0.219095\pi\) | |||||||
\(492\) | −0.237615 | + | 0.411560i | −0.0107125 | + | 0.0185546i | ||||
\(493\) | 0.611471 | + | 1.05910i | 0.0275393 | + | 0.0476994i | ||||
\(494\) | −0.198095 | − | 0.343111i | −0.00891273 | − | 0.0154373i | ||||
\(495\) | −1.24157 | + | 2.15046i | −0.0558042 | + | 0.0966558i | ||||
\(496\) | −25.9307 | −1.16432 | ||||||||
\(497\) | 15.6219 | + | 9.77276i | 0.700739 | + | 0.438368i | ||||
\(498\) | −4.09315 | −0.183418 | ||||||||
\(499\) | 17.6946 | − | 30.6480i | 0.792120 | − | 1.37199i | −0.132533 | − | 0.991179i | \(-0.542311\pi\) |
0.924652 | − | 0.380813i | \(-0.124356\pi\) | |||||||
\(500\) | −0.0811705 | − | 0.140591i | −0.00363006 | − | 0.00628744i | ||||
\(501\) | −4.33385 | − | 7.50645i | −0.193622 | − | 0.335363i | ||||
\(502\) | 5.68466 | − | 9.84612i | 0.253719 | − | 0.439454i | ||||
\(503\) | 15.5682 | 0.694154 | 0.347077 | − | 0.937837i | \(-0.387174\pi\) | ||||
0.347077 | + | 0.937837i | \(0.387174\pi\) | |||||||
\(504\) | 15.6794 | − | 8.32660i | 0.698415 | − | 0.370896i | ||||
\(505\) | 4.82690 | 0.214794 | ||||||||
\(506\) | 2.91975 | − | 5.05716i | 0.129799 | − | 0.224818i | ||||
\(507\) | 4.01578 | + | 6.95554i | 0.178347 | + | 0.308906i | ||||
\(508\) | −1.27836 | − | 2.21418i | −0.0567181 | − | 0.0982386i | ||||
\(509\) | 6.04740 | − | 10.4744i | 0.268046 | − | 0.464270i | −0.700311 | − | 0.713838i | \(-0.746955\pi\) |
0.968357 | + | 0.249568i | \(0.0802887\pi\) | |||||||
\(510\) | 0.573156 | 0.0253798 | ||||||||
\(511\) | 1.39321 | − | 39.3203i | 0.0616319 | − | 1.73943i | ||||
\(512\) | 19.2926 | 0.852619 | ||||||||
\(513\) | 0.392717 | − | 0.680206i | 0.0173389 | − | 0.0300318i | ||||
\(514\) | −5.68207 | − | 9.84163i | −0.250625 | − | 0.434096i | ||||
\(515\) | −8.28537 | − | 14.3507i | −0.365097 | − | 0.632367i | ||||
\(516\) | 0.574817 | − | 0.995611i | 0.0253049 | − | 0.0438293i | ||||
\(517\) | −7.86148 | −0.345747 | ||||||||
\(518\) | −1.06992 | + | 30.1962i | −0.0470097 | + | 1.32675i | ||||
\(519\) | −6.62419 | −0.290770 | ||||||||
\(520\) | 1.82704 | − | 3.16452i | 0.0801209 | − | 0.138774i | ||||
\(521\) | −4.77090 | − | 8.26345i | −0.209017 | − | 0.362028i | 0.742388 | − | 0.669970i | \(-0.233693\pi\) |
−0.951405 | + | 0.307942i | \(0.900360\pi\) | |||||||
\(522\) | −4.11829 | − | 7.13308i | −0.180253 | − | 0.312207i | ||||
\(523\) | 17.3082 | − | 29.9787i | 0.756835 | − | 1.31088i | −0.187621 | − | 0.982241i | \(-0.560078\pi\) |
0.944457 | − | 0.328636i | \(-0.106589\pi\) | |||||||
\(524\) | −1.18901 | −0.0519420 | ||||||||
\(525\) | −1.67993 | + | 0.892135i | −0.0733182 | + | 0.0389360i | ||||
\(526\) | −33.7715 | −1.47251 | ||||||||
\(527\) | 1.63533 | − | 2.83248i | 0.0712361 | − | 0.123385i | ||||
\(528\) | −1.54511 | − | 2.67621i | −0.0672423 | − | 0.116467i | ||||
\(529\) | 3.61507 | + | 6.26148i | 0.157177 | + | 0.272238i | ||||
\(530\) | 6.63792 | − | 11.4972i | 0.288333 | − | 0.499407i | ||||
\(531\) | 18.8077 | 0.816184 | ||||||||
\(532\) | 0.0725522 | + | 0.0453872i | 0.00314554 | + | 0.00196779i | ||||
\(533\) | −5.50599 | −0.238491 | ||||||||
\(534\) | −2.10501 | + | 3.64598i | −0.0910925 | + | 0.157777i | ||||
\(535\) | −1.22575 | − | 2.12306i | −0.0529939 | − | 0.0917881i | ||||
\(536\) | 10.8253 | + | 18.7500i | 0.467582 | + | 0.809877i | ||||
\(537\) | −1.55345 | + | 2.69065i | −0.0670362 | + | 0.116110i | ||||
\(538\) | 31.5932 | 1.36208 | ||||||||
\(539\) | −3.92028 | + | 5.79926i | −0.168858 | + | 0.249792i | ||||
\(540\) | −0.639951 | −0.0275391 | ||||||||
\(541\) | −1.24370 | + | 2.15415i | −0.0534708 | + | 0.0926141i | −0.891522 | − | 0.452978i | \(-0.850362\pi\) |
0.838051 | + | 0.545592i | \(0.183695\pi\) | |||||||
\(542\) | −15.5375 | − | 26.9117i | −0.667393 | − | 1.15596i | ||||
\(543\) | 0.914396 | + | 1.58378i | 0.0392405 | + | 0.0679665i | ||||
\(544\) | 0.248341 | − | 0.430139i | 0.0106475 | − | 0.0184420i | ||||
\(545\) | 4.01540 | 0.172001 | ||||||||
\(546\) | 3.20652 | + | 2.00593i | 0.137226 | + | 0.0858460i | ||||
\(547\) | −27.1185 | −1.15950 | −0.579751 | − | 0.814794i | \(-0.696850\pi\) | ||||
−0.579751 | + | 0.814794i | \(0.696850\pi\) | |||||||
\(548\) | −0.625594 | + | 1.08356i | −0.0267241 | + | 0.0462874i | ||||
\(549\) | 9.32507 | + | 16.1515i | 0.397984 | + | 0.689329i | ||||
\(550\) | −0.735245 | − | 1.27348i | −0.0313510 | − | 0.0543014i | ||||
\(551\) | −0.224722 | + | 0.389231i | −0.00957350 | + | 0.0165818i | ||||
\(552\) | −7.71491 | −0.328368 | ||||||||
\(553\) | 0.849474 | − | 0.451117i | 0.0361233 | − | 0.0191834i | ||||
\(554\) | 17.3853 | 0.738631 | ||||||||
\(555\) | −2.79173 | + | 4.83543i | −0.118503 | + | 0.205252i | ||||
\(556\) | 1.35023 | + | 2.33867i | 0.0572626 | + | 0.0991818i | ||||
\(557\) | −11.1540 | − | 19.3194i | −0.472612 | − | 0.818587i | 0.526897 | − | 0.849929i | \(-0.323355\pi\) |
−0.999509 | + | 0.0313416i | \(0.990022\pi\) | |||||||
\(558\) | −11.0140 | + | 19.0769i | −0.466262 | + | 0.807589i | ||||
\(559\) | 13.3196 | 0.563360 | ||||||||
\(560\) | −0.402694 | + | 11.3652i | −0.0170169 | + | 0.480266i | ||||
\(561\) | 0.389772 | 0.0164562 | ||||||||
\(562\) | 19.6604 | − | 34.0527i | 0.829322 | − | 1.43643i | ||||
\(563\) | 4.40534 | + | 7.63027i | 0.185663 | + | 0.321577i | 0.943800 | − | 0.330518i | \(-0.107223\pi\) |
−0.758137 | + | 0.652095i | \(0.773890\pi\) | |||||||
\(564\) | −0.458767 | − | 0.794608i | −0.0193176 | − | 0.0334590i | ||||
\(565\) | 6.83827 | − | 11.8442i | 0.287688 | − | 0.498290i | ||||
\(566\) | 17.2573 | 0.725377 | ||||||||
\(567\) | 0.432394 | − | 12.2034i | 0.0181589 | − | 0.512494i | ||||
\(568\) | 18.8205 | 0.789690 | ||||||||
\(569\) | 8.94245 | − | 15.4888i | 0.374887 | − | 0.649323i | −0.615423 | − | 0.788197i | \(-0.711015\pi\) |
0.990310 | + | 0.138874i | \(0.0443482\pi\) | |||||||
\(570\) | 0.105321 | + | 0.182421i | 0.00441140 | + | 0.00764076i | ||||
\(571\) | 2.72561 | + | 4.72090i | 0.114063 | + | 0.197563i | 0.917405 | − | 0.397955i | \(-0.130280\pi\) |
−0.803342 | + | 0.595518i | \(0.796947\pi\) | |||||||
\(572\) | −0.109761 | + | 0.190112i | −0.00458935 | + | 0.00794898i | ||||
\(573\) | 2.10334 | 0.0878682 | ||||||||
\(574\) | 13.9910 | − | 7.42998i | 0.583973 | − | 0.310121i | ||||
\(575\) | −3.97113 | −0.165608 | ||||||||
\(576\) | 9.00073 | − | 15.5897i | 0.375030 | − | 0.649572i | ||||
\(577\) | 18.7699 | + | 32.5105i | 0.781403 | + | 1.35343i | 0.931124 | + | 0.364702i | \(0.118829\pi\) |
−0.149721 | + | 0.988728i | \(0.547838\pi\) | |||||||
\(578\) | −12.2831 | − | 21.2749i | −0.510908 | − | 0.884918i | ||||
\(579\) | −4.80244 | + | 8.31807i | −0.199583 | + | 0.345687i | ||||
\(580\) | 0.366196 | 0.0152054 | ||||||||
\(581\) | 8.68433 | + | 5.43274i | 0.360287 | + | 0.225388i | ||||
\(582\) | 17.6409 | 0.731240 | ||||||||
\(583\) | 4.51408 | − | 7.81862i | 0.186954 | − | 0.323814i | ||||
\(584\) | −20.0926 | − | 34.8015i | −0.831439 | − | 1.44009i | ||||
\(585\) | −1.67888 | − | 2.90791i | −0.0694133 | − | 0.120227i | ||||
\(586\) | 10.9697 | − | 19.0000i | 0.453153 | − | 0.784884i | ||||
\(587\) | −8.73112 | −0.360372 | −0.180186 | − | 0.983633i | \(-0.557670\pi\) | ||||
−0.180186 | + | 0.983633i | \(0.557670\pi\) | |||||||
\(588\) | −0.814940 | − | 0.0578230i | −0.0336076 | − | 0.00238458i | ||||
\(589\) | 1.20201 | 0.0495278 | ||||||||
\(590\) | −5.56888 | + | 9.64558i | −0.229267 | + | 0.397102i | ||||
\(591\) | −4.04363 | − | 7.00377i | −0.166333 | − | 0.288097i | ||||
\(592\) | 16.6911 | + | 28.9097i | 0.685998 | + | 1.18818i | ||||
\(593\) | 9.50761 | − | 16.4677i | 0.390431 | − | 0.676246i | −0.602076 | − | 0.798439i | \(-0.705659\pi\) |
0.992506 | + | 0.122193i | \(0.0389927\pi\) | |||||||
\(594\) | −5.79670 | −0.237841 | ||||||||
\(595\) | −1.21605 | − | 0.760737i | −0.0498532 | − | 0.0311872i | ||||
\(596\) | 1.34933 | 0.0552708 | ||||||||
\(597\) | 3.77129 | − | 6.53206i | 0.154348 | − | 0.267339i | ||||
\(598\) | 3.94818 | + | 6.83844i | 0.161453 | + | 0.279645i | ||||
\(599\) | 6.18177 | + | 10.7071i | 0.252580 | + | 0.437482i | 0.964235 | − | 0.265047i | \(-0.0853875\pi\) |
−0.711655 | + | 0.702529i | \(0.752054\pi\) | |||||||
\(600\) | −0.971375 | + | 1.68247i | −0.0396562 | + | 0.0686866i | ||||
\(601\) | −25.2886 | −1.03154 | −0.515772 | − | 0.856726i | \(-0.672495\pi\) | ||||
−0.515772 | + | 0.856726i | \(0.672495\pi\) | |||||||
\(602\) | −33.8458 | + | 17.9740i | −1.37945 | + | 0.732564i | ||||
\(603\) | 19.8950 | 0.810186 | ||||||||
\(604\) | −0.616794 | + | 1.06832i | −0.0250970 | + | 0.0434693i | ||||
\(605\) | −0.500000 | − | 0.866025i | −0.0203279 | − | 0.0352089i | ||||
\(606\) | 2.55147 | + | 4.41928i | 0.103646 | + | 0.179521i | ||||
\(607\) | 4.78467 | − | 8.28730i | 0.194204 | − | 0.336371i | −0.752435 | − | 0.658666i | \(-0.771121\pi\) |
0.946639 | + | 0.322295i | \(0.104454\pi\) | |||||||
\(608\) | 0.182536 | 0.00740281 | ||||||||
\(609\) | 0.151933 | − | 4.28796i | 0.00615662 | − | 0.173757i | ||||
\(610\) | −11.0445 | −0.447177 | ||||||||
\(611\) | 5.31526 | − | 9.20631i | 0.215033 | − | 0.372447i | ||||
\(612\) | −0.109275 | − | 0.189269i | −0.00441716 | − | 0.00765075i | ||||
\(613\) | −0.826926 | − | 1.43228i | −0.0333992 | − | 0.0578492i | 0.848843 | − | 0.528646i | \(-0.177300\pi\) |
−0.882242 | + | 0.470796i | \(0.843967\pi\) | |||||||
\(614\) | 22.7974 | − | 39.4863i | 0.920028 | − | 1.59354i | ||||
\(615\) | 2.92735 | 0.118042 | ||||||||
\(616\) | −0.253165 | + | 7.14502i | −0.0102003 | + | 0.287881i | ||||
\(617\) | 4.35949 | 0.175506 | 0.0877531 | − | 0.996142i | \(-0.472031\pi\) | ||||
0.0877531 | + | 0.996142i | \(0.472031\pi\) | |||||||
\(618\) | 8.75919 | − | 15.1714i | 0.352346 | − | 0.610282i | ||||
\(619\) | 18.5995 | + | 32.2154i | 0.747579 | + | 1.29484i | 0.948980 | + | 0.315336i | \(0.102117\pi\) |
−0.201401 | + | 0.979509i | \(0.564550\pi\) | |||||||
\(620\) | −0.489681 | − | 0.848152i | −0.0196661 | − | 0.0340626i | ||||
\(621\) | −7.82713 | + | 13.5570i | −0.314092 | + | 0.544023i | ||||
\(622\) | 33.3176 | 1.33591 | ||||||||
\(623\) | 9.30536 | − | 4.94165i | 0.372811 | − | 0.197983i | ||||
\(624\) | 4.17869 | 0.167281 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −7.71294 | − | 13.3592i | −0.308271 | − | 0.533941i | ||||
\(627\) | 0.0716228 | + | 0.124054i | 0.00286034 | + | 0.00495425i | ||||
\(628\) | −0.622669 | + | 1.07849i | −0.0248472 | + | 0.0430366i | ||||
\(629\) | −4.21051 | −0.167884 | ||||||||
\(630\) | 8.19017 | + | 5.12360i | 0.326304 | + | 0.204129i | ||||
\(631\) | −35.1684 | −1.40003 | −0.700017 | − | 0.714126i | \(-0.746824\pi\) | ||||
−0.700017 | + | 0.714126i | \(0.746824\pi\) | |||||||
\(632\) | 0.491185 | − | 0.850758i | 0.0195383 | − | 0.0338413i | ||||
\(633\) | −3.05085 | − | 5.28423i | −0.121260 | − | 0.210029i | ||||
\(634\) | 24.9492 | + | 43.2132i | 0.990859 | + | 1.71622i | ||||
\(635\) | −7.87453 | + | 13.6391i | −0.312491 | + | 0.541251i | ||||
\(636\) | 1.05370 | 0.0417820 | ||||||||
\(637\) | −4.14076 | − | 8.51187i | −0.164063 | − | 0.337253i | ||||
\(638\) | 3.31701 | 0.131322 | ||||||||
\(639\) | 8.64716 | − | 14.9773i | 0.342076 | − | 0.592494i | ||||
\(640\) | 6.24629 | + | 10.8189i | 0.246906 | + | 0.427654i | ||||
\(641\) | 7.95259 | + | 13.7743i | 0.314108 | + | 0.544052i | 0.979248 | − | 0.202668i | \(-0.0649612\pi\) |
−0.665139 | + | 0.746719i | \(0.731628\pi\) | |||||||
\(642\) | 1.29585 | − | 2.24448i | 0.0511431 | − | 0.0885824i | ||||
\(643\) | 42.0439 | 1.65805 | 0.829024 | − | 0.559213i | \(-0.188897\pi\) | ||||
0.829024 | + | 0.559213i | \(0.188897\pi\) | |||||||
\(644\) | −1.44602 | − | 0.904599i | −0.0569810 | − | 0.0356462i | ||||
\(645\) | −7.08159 | −0.278837 | ||||||||
\(646\) | −0.0794227 | + | 0.137564i | −0.00312484 | + | 0.00541239i | ||||
\(647\) | −15.4828 | − | 26.8170i | −0.608692 | − | 1.05429i | −0.991456 | − | 0.130439i | \(-0.958361\pi\) |
0.382764 | − | 0.923846i | \(-0.374972\pi\) | |||||||
\(648\) | −6.23592 | − | 10.8009i | −0.244970 | − | 0.424301i | ||||
\(649\) | −3.78709 | + | 6.55943i | −0.148656 | + | 0.257480i | ||||
\(650\) | 1.98844 | 0.0779931 | ||||||||
\(651\) | −10.1346 | + | 5.38202i | −0.397206 | + | 0.210938i | ||||
\(652\) | 2.75009 | 0.107702 | ||||||||
\(653\) | 8.41697 | − | 14.5786i | 0.329381 | − | 0.570505i | −0.653008 | − | 0.757351i | \(-0.726493\pi\) |
0.982389 | + | 0.186846i | \(0.0598265\pi\) | |||||||
\(654\) | 2.12252 | + | 3.67631i | 0.0829969 | + | 0.143755i | ||||
\(655\) | 3.66206 | + | 6.34288i | 0.143089 | + | 0.247837i | ||||
\(656\) | 8.75093 | − | 15.1571i | 0.341667 | − | 0.591784i | ||||
\(657\) | −36.9266 | −1.44064 | ||||||||
\(658\) | −1.08303 | + | 30.5663i | −0.0422211 | + | 1.19160i | ||||
\(659\) | −37.5268 | −1.46184 | −0.730918 | − | 0.682465i | \(-0.760908\pi\) | ||||
−0.730918 | + | 0.682465i | \(0.760908\pi\) | |||||||
\(660\) | 0.0583564 | − | 0.101076i | 0.00227152 | − | 0.00393439i | ||||
\(661\) | −3.99088 | − | 6.91240i | −0.155227 | − | 0.268861i | 0.777915 | − | 0.628370i | \(-0.216278\pi\) |
−0.933142 | + | 0.359509i | \(0.882944\pi\) | |||||||
\(662\) | 11.3234 | + | 19.6127i | 0.440096 | + | 0.762269i | ||||
\(663\) | −0.263531 | + | 0.456449i | −0.0102347 | + | 0.0177270i | ||||
\(664\) | 10.4624 | 0.406021 | ||||||||
\(665\) | 0.0186667 | − | 0.526827i | 0.000723864 | − | 0.0204295i | ||||
\(666\) | 28.3580 | 1.09885 | ||||||||
\(667\) | 4.47887 | − | 7.75764i | 0.173423 | − | 0.300377i | ||||
\(668\) | −0.978617 | − | 1.69501i | −0.0378638 | − | 0.0655820i | ||||
\(669\) | −7.11409 | − | 12.3220i | −0.275047 | − | 0.476395i | ||||
\(670\) | −5.89082 | + | 10.2032i | −0.227582 | + | 0.394184i | ||||
\(671\) | −7.51073 | −0.289949 | ||||||||
\(672\) | −1.53904 | + | 0.817311i | −0.0593696 | + | 0.0315285i | ||||
\(673\) | −30.3125 | −1.16846 | −0.584230 | − | 0.811588i | \(-0.698603\pi\) | ||||
−0.584230 | + | 0.811588i | \(0.698603\pi\) | |||||||
\(674\) | −10.7534 | + | 18.6255i | −0.414207 | + | 0.717428i | ||||
\(675\) | 1.97101 | + | 3.41389i | 0.0758642 | + | 0.131401i | ||||
\(676\) | 0.906794 | + | 1.57061i | 0.0348767 | + | 0.0604082i | ||||
\(677\) | 8.70847 | − | 15.0835i | 0.334694 | − | 0.579706i | −0.648732 | − | 0.761017i | \(-0.724701\pi\) |
0.983426 | + | 0.181310i | \(0.0580339\pi\) | |||||||
\(678\) | 14.4587 | 0.555282 | ||||||||
\(679\) | −37.4283 | − | 23.4144i | −1.43637 | − | 0.898562i | ||||
\(680\) | −1.46503 | −0.0561815 | ||||||||
\(681\) | 0.821187 | − | 1.42234i | 0.0314679 | − | 0.0545041i | ||||
\(682\) | −4.43554 | − | 7.68259i | −0.169846 | − | 0.294181i | ||||
\(683\) | 5.00212 | + | 8.66393i | 0.191401 | + | 0.331516i | 0.945715 | − | 0.324998i | \(-0.105364\pi\) |
−0.754314 | + | 0.656514i | \(0.772030\pi\) | |||||||
\(684\) | 0.0401596 | − | 0.0695585i | 0.00153554 | − | 0.00265964i | ||||
\(685\) | 7.70716 | 0.294475 | ||||||||
\(686\) | 22.0081 | + | 16.0414i | 0.840273 | + | 0.612464i | ||||
\(687\) | −18.8372 | −0.718684 | ||||||||
\(688\) | −21.1695 | + | 36.6666i | −0.807079 | + | 1.39790i | ||||
\(689\) | 6.10408 | + | 10.5726i | 0.232547 | + | 0.402783i | ||||
\(690\) | −2.09911 | − | 3.63577i | −0.0799119 | − | 0.138411i | ||||
\(691\) | −15.6377 | + | 27.0852i | −0.594884 | + | 1.03037i | 0.398679 | + | 0.917091i | \(0.369469\pi\) |
−0.993563 | + | 0.113279i | \(0.963864\pi\) | |||||||
\(692\) | −1.49579 | −0.0568615 | ||||||||
\(693\) | 5.56968 | + | 3.48428i | 0.211575 | + | 0.132357i | ||||
\(694\) | −1.64057 | −0.0622753 | ||||||||
\(695\) | 8.31726 | − | 14.4059i | 0.315492 | − | 0.546448i | ||||
\(696\) | −2.19115 | − | 3.79518i | −0.0830552 | − | 0.143856i | ||||
\(697\) | 1.10376 | + | 1.91177i | 0.0418080 | + | 0.0724136i | ||||
\(698\) | 18.9355 | − | 32.7972i | 0.716718 | − | 1.24139i | ||||
\(699\) | 12.9642 | 0.490350 | ||||||||
\(700\) | −0.379341 | + | 0.201451i | −0.0143378 | + | 0.00761413i | ||||
\(701\) | −14.8672 | −0.561528 | −0.280764 | − | 0.959777i | \(-0.590588\pi\) | ||||
−0.280764 | + | 0.959777i | \(0.590588\pi\) | |||||||
\(702\) | 3.91923 | − | 6.78831i | 0.147922 | − | 0.256208i | ||||
\(703\) | −0.773706 | − | 1.34010i | −0.0291809 | − | 0.0505427i | ||||
\(704\) | 3.62475 | + | 6.27825i | 0.136613 | + | 0.236620i | ||||
\(705\) | −2.82595 | + | 4.89468i | −0.106431 | + | 0.184344i | ||||
\(706\) | −22.4730 | −0.845782 | ||||||||
\(707\) | 0.452215 | − | 12.7628i | 0.0170073 | − | 0.479994i | ||||
\(708\) | −0.884003 | −0.0332229 | ||||||||
\(709\) | −12.9287 | + | 22.3932i | −0.485549 | + | 0.840995i | −0.999862 | − | 0.0166075i | \(-0.994713\pi\) |
0.514314 | + | 0.857602i | \(0.328047\pi\) | |||||||
\(710\) | 5.12078 | + | 8.86945i | 0.192179 | + | 0.332864i | ||||
\(711\) | −0.451355 | − | 0.781770i | −0.0169271 | − | 0.0293187i | ||||
\(712\) | 5.38057 | − | 9.31942i | 0.201645 | − | 0.349260i | ||||
\(713\) | −23.9568 | −0.897189 | ||||||||
\(714\) | 0.0536969 | − | 1.51548i | 0.00200956 | − | 0.0567153i | ||||
\(715\) | 1.35223 | 0.0505705 | ||||||||
\(716\) | −0.350780 | + | 0.607569i | −0.0131093 | + | 0.0227059i | ||||
\(717\) | −9.49513 | − | 16.4461i | −0.354602 | − | 0.614189i | ||||
\(718\) | 5.02121 | + | 8.69699i | 0.187390 | + | 0.324569i | ||||
\(719\) | 5.45539 | − | 9.44901i | 0.203452 | − | 0.352388i | −0.746187 | − | 0.665737i | \(-0.768117\pi\) |
0.949638 | + | 0.313348i | \(0.101451\pi\) | |||||||
\(720\) | 10.6733 | 0.397771 | ||||||||
\(721\) | −38.7207 | + | 20.5628i | −1.44204 | + | 0.765799i | ||||
\(722\) | 27.8809 | 1.03762 | ||||||||
\(723\) | −5.15553 | + | 8.92963i | −0.191736 | + | 0.332097i | ||||
\(724\) | 0.206478 | + | 0.357630i | 0.00767368 | + | 0.0132912i | ||||
\(725\) | −1.12786 | − | 1.95351i | −0.0418876 | − | 0.0725515i | ||||
\(726\) | 0.528594 | − | 0.915551i | 0.0196179 | − | 0.0339793i | ||||
\(727\) | −30.6727 | −1.13759 | −0.568794 | − | 0.822480i | \(-0.692590\pi\) | ||||
−0.568794 | + | 0.822480i | \(0.692590\pi\) | |||||||
\(728\) | −8.19612 | − | 5.12733i | −0.303768 | − | 0.190031i | ||||
\(729\) | −2.95833 | −0.109568 | ||||||||
\(730\) | 10.9338 | − | 18.9379i | 0.404679 | − | 0.700924i | ||||
\(731\) | −2.67013 | − | 4.62480i | −0.0987582 | − | 0.171054i | ||||
\(732\) | −0.438299 | − | 0.759156i | −0.0162000 | − | 0.0280592i | ||||
\(733\) | −19.4276 | + | 33.6497i | −0.717576 | + | 1.24288i | 0.244381 | + | 0.969679i | \(0.421415\pi\) |
−0.961957 | + | 0.273199i | \(0.911918\pi\) | |||||||
\(734\) | 6.64116 | 0.245130 | ||||||||
\(735\) | 2.20150 | + | 4.52548i | 0.0812036 | + | 0.166925i | ||||
\(736\) | −3.63807 | −0.134101 | ||||||||
\(737\) | −4.00602 | + | 6.93864i | −0.147564 | + | 0.255588i | ||||
\(738\) | −7.43390 | − | 12.8759i | −0.273646 | − | 0.473968i | ||||
\(739\) | 12.0520 | + | 20.8747i | 0.443341 | + | 0.767888i | 0.997935 | − | 0.0642324i | \(-0.0204599\pi\) |
−0.554594 | + | 0.832121i | \(0.687127\pi\) | |||||||
\(740\) | −0.630395 | + | 1.09188i | −0.0231738 | + | 0.0401382i | ||||
\(741\) | −0.193701 | −0.00711579 | ||||||||
\(742\) | −29.7778 | − | 18.6284i | −1.09318 | − | 0.683870i | ||||
\(743\) | 1.57531 | 0.0577925 | 0.0288962 | − | 0.999582i | \(-0.490801\pi\) | ||||
0.0288962 | + | 0.999582i | \(0.490801\pi\) | |||||||
\(744\) | −5.86005 | + | 10.1499i | −0.214840 | + | 0.372114i | ||||
\(745\) | −4.15586 | − | 7.19816i | −0.152259 | − | 0.263720i | ||||
\(746\) | 3.12956 | + | 5.42056i | 0.114581 | + | 0.198461i | ||||
\(747\) | 4.80701 | − | 8.32599i | 0.175879 | − | 0.304632i | ||||
\(748\) | 0.0880135 | 0.00321809 | ||||||||
\(749\) | −5.72841 | + | 3.04210i | −0.209312 | + | 0.111156i | ||||
\(750\) | −1.05719 | −0.0386030 | ||||||||
\(751\) | 23.3817 | − | 40.4984i | 0.853212 | − | 1.47781i | −0.0250821 | − | 0.999685i | \(-0.507985\pi\) |
0.878294 | − | 0.478121i | \(-0.158682\pi\) | |||||||
\(752\) | 16.8956 | + | 29.2640i | 0.616119 | + | 1.06715i | ||||
\(753\) | −2.77928 | − | 4.81385i | −0.101283 | − | 0.175427i | ||||
\(754\) | −2.24268 | + | 3.88444i | −0.0816736 | + | 0.141463i | ||||
\(755\) | 7.59875 | 0.276547 | ||||||||
\(756\) | −0.0599547 | + | 1.69209i | −0.00218053 | + | 0.0615407i | ||||
\(757\) | 28.7476 | 1.04485 | 0.522425 | − | 0.852686i | \(-0.325028\pi\) | ||||
0.522425 | + | 0.852686i | \(0.325028\pi\) | |||||||
\(758\) | −8.97285 | + | 15.5414i | −0.325908 | + | 0.564490i | ||||
\(759\) | −1.42749 | − | 2.47249i | −0.0518147 | − | 0.0897457i | ||||
\(760\) | −0.269208 | − | 0.466283i | −0.00976522 | − | 0.0169138i | ||||
\(761\) | 14.3758 | − | 24.8996i | 0.521121 | − | 0.902608i | −0.478577 | − | 0.878045i | \(-0.658847\pi\) |
0.999698 | − | 0.0245626i | \(-0.00781931\pi\) | |||||||
\(762\) | −16.6497 | −0.603155 | ||||||||
\(763\) | 0.376188 | − | 10.6171i | 0.0136189 | − | 0.384365i | ||||
\(764\) | 0.474949 | 0.0171831 | ||||||||
\(765\) | −0.673117 | + | 1.16587i | −0.0243366 | + | 0.0421522i | ||||
\(766\) | 8.10581 | + | 14.0397i | 0.292875 | + | 0.507274i | ||||
\(767\) | −5.12102 | − | 8.86986i | −0.184909 | − | 0.320272i | ||||
\(768\) | −1.39157 | + | 2.41028i | −0.0502141 | + | 0.0869734i | ||||
\(769\) | −40.5398 | −1.46190 | −0.730951 | − | 0.682430i | \(-0.760923\pi\) | ||||
−0.730951 | + | 0.682430i | \(0.760923\pi\) | |||||||
\(770\) | −3.43609 | + | 1.82475i | −0.123828 | + | 0.0657593i | ||||
\(771\) | −5.55603 | −0.200095 | ||||||||
\(772\) | −1.08443 | + | 1.87828i | −0.0390294 | + | 0.0676009i | ||||
\(773\) | −17.6643 | − | 30.5954i | −0.635339 | − | 1.10044i | −0.986443 | − | 0.164103i | \(-0.947527\pi\) |
0.351104 | − | 0.936336i | \(-0.385806\pi\) | |||||||
\(774\) | 17.9834 | + | 31.1482i | 0.646402 | + | 1.11960i | ||||
\(775\) | −3.01637 | + | 5.22451i | −0.108351 | + | 0.187670i | ||||
\(776\) | −45.0917 | −1.61870 | ||||||||
\(777\) | 12.5238 | + | 7.83461i | 0.449287 | + | 0.281065i | ||||
\(778\) | −44.9489 | −1.61150 | ||||||||
\(779\) | −0.405645 | + | 0.702598i | −0.0145338 | + | 0.0251732i | ||||
\(780\) | 0.0789112 | + | 0.136678i | 0.00282548 | + | 0.00489387i | ||||
\(781\) | 3.48236 | + | 6.03163i | 0.124609 | + | 0.215829i | ||||
\(782\) | 1.58295 | − | 2.74175i | 0.0566062 | − | 0.0980447i | ||||
\(783\) | −8.89208 | −0.317777 | ||||||||
\(784\) | 30.0128 | + | 2.12952i | 1.07189 | + | 0.0760544i | ||||
\(785\) | 7.67112 | 0.273794 | ||||||||
\(786\) | −3.87149 | + | 6.70561i | −0.138091 | + | 0.239181i | ||||
\(787\) | 8.93406 | + | 15.4742i | 0.318465 | + | 0.551597i | 0.980168 | − | 0.198169i | \(-0.0634994\pi\) |
−0.661703 | + | 0.749766i | \(0.730166\pi\) | |||||||
\(788\) | −0.913082 | − | 1.58150i | −0.0325272 | − | 0.0563388i | ||||
\(789\) | −8.25558 | + | 14.2991i | −0.293906 | + | 0.509061i | ||||
\(790\) | 0.534577 | 0.0190194 | ||||||||
\(791\) | −30.6766 | − | 19.1907i | −1.09073 | − | 0.682341i | ||||
\(792\) | 6.71007 | 0.238432 | ||||||||
\(793\) | 5.07812 | − | 8.79556i | 0.180329 | − | 0.312340i | ||||
\(794\) | −13.0626 | − | 22.6251i | −0.463574 | − | 0.802933i | ||||
\(795\) | −3.24533 | − | 5.62108i | −0.115100 | − | 0.199359i | ||||
\(796\) | 0.851585 | − | 1.47499i | 0.0301836 | − | 0.0522796i | ||||
\(797\) | 10.2292 | 0.362336 | 0.181168 | − | 0.983452i | \(-0.442012\pi\) | ||||
0.181168 | + | 0.983452i | \(0.442012\pi\) | |||||||
\(798\) | 0.492204 | − | 0.261387i | 0.0174238 | − | 0.00925301i | ||||
\(799\) | −4.26211 | −0.150783 | ||||||||
\(800\) | −0.458065 | + | 0.793391i | −0.0161950 | + | 0.0280506i | ||||
\(801\) | −4.94426 | − | 8.56371i | −0.174697 | − | 0.302584i | ||||
\(802\) | 18.4597 | + | 31.9732i | 0.651835 | + | 1.12901i | ||||
\(803\) | 7.43549 | − | 12.8787i | 0.262393 | − | 0.454478i | ||||
\(804\) | −0.935108 | −0.0329787 | ||||||||
\(805\) | −0.372040 | + | 10.5000i | −0.0131127 | + | 0.370077i | ||||
\(806\) | 11.9958 | 0.422532 | ||||||||
\(807\) | 7.72309 | − | 13.3768i | 0.271866 | − | 0.470885i | ||||
\(808\) | −6.52177 | − | 11.2960i | −0.229435 | − | 0.397393i | ||||
\(809\) | 4.65584 | + | 8.06415i | 0.163691 | + | 0.283521i | 0.936190 | − | 0.351496i | \(-0.114327\pi\) |
−0.772499 | + | 0.635016i | \(0.780993\pi\) | |||||||
\(810\) | 3.39341 | − | 5.87755i | 0.119232 | − | 0.206516i | ||||
\(811\) | −19.7720 | −0.694291 | −0.347145 | − | 0.937811i | \(-0.612849\pi\) | ||||
−0.347145 | + | 0.937811i | \(0.612849\pi\) | |||||||
\(812\) | 0.0343075 | − | 0.968255i | 0.00120396 | − | 0.0339791i | ||||
\(813\) | −15.1928 | −0.532836 | ||||||||
\(814\) | −5.71013 | + | 9.89024i | −0.200140 | + | 0.346653i | ||||
\(815\) | −8.47009 | − | 14.6706i | −0.296694 | − | 0.513889i | ||||
\(816\) | −0.837684 | − | 1.45091i | −0.0293248 | − | 0.0507921i | ||||
\(817\) | 0.981302 | − | 1.69966i | 0.0343314 | − | 0.0594637i | ||||
\(818\) | −28.1227 | −0.983287 | ||||||||
\(819\) | −7.84607 | + | 4.16669i | −0.274164 | + | 0.145596i | ||||
\(820\) | 0.661018 | 0.0230837 | ||||||||
\(821\) | 11.2507 | − | 19.4867i | 0.392651 | − | 0.680091i | −0.600148 | − | 0.799889i | \(-0.704891\pi\) |
0.992798 | + | 0.119798i | \(0.0382248\pi\) | |||||||
\(822\) | 4.07395 | + | 7.05630i | 0.142095 | + | 0.246117i | ||||
\(823\) | 9.92317 | + | 17.1874i | 0.345900 | + | 0.599116i | 0.985517 | − | 0.169578i | \(-0.0542404\pi\) |
−0.639617 | + | 0.768694i | \(0.720907\pi\) | |||||||
\(824\) | −22.3892 | + | 38.7793i | −0.779965 | + | 1.35094i | ||||
\(825\) | −0.718935 | −0.0250301 | ||||||||
\(826\) | 24.9821 | + | 15.6283i | 0.869237 | + | 0.543777i | ||||
\(827\) | −39.2944 | −1.36640 | −0.683200 | − | 0.730231i | \(-0.739412\pi\) | ||||
−0.683200 | + | 0.730231i | \(0.739412\pi\) | |||||||
\(828\) | −0.800409 | + | 1.38635i | −0.0278161 | + | 0.0481790i | ||||
\(829\) | 5.13644 | + | 8.89657i | 0.178396 | + | 0.308991i | 0.941331 | − | 0.337484i | \(-0.109576\pi\) |
−0.762935 | + | 0.646475i | \(0.776243\pi\) | |||||||
\(830\) | 2.84667 | + | 4.93058i | 0.0988094 | + | 0.171143i | ||||
\(831\) | 4.24991 | − | 7.36106i | 0.147428 | − | 0.255353i | ||||
\(832\) | −9.80299 | −0.339857 | ||||||||
\(833\) | −2.12539 | + | 3.14408i | −0.0736403 | + | 0.108936i | ||||
\(834\) | 17.5858 | 0.608947 | ||||||||
\(835\) | −6.02815 | + | 10.4411i | −0.208613 | + | 0.361328i | ||||
\(836\) | 0.0161730 | + | 0.0280124i | 0.000559354 | + | 0.000968830i | ||||
\(837\) | 11.8906 | + | 20.5951i | 0.410999 | + | 0.711871i | ||||
\(838\) | −25.2102 | + | 43.6653i | −0.870871 | + | 1.50839i | ||||
\(839\) | −15.4080 | −0.531942 | −0.265971 | − | 0.963981i | \(-0.585693\pi\) | ||||
−0.265971 | + | 0.963981i | \(0.585693\pi\) | |||||||
\(840\) | 4.35760 | + | 2.72603i | 0.150352 | + | 0.0940569i | ||||
\(841\) | −23.9117 | −0.824543 | ||||||||
\(842\) | −9.74943 | + | 16.8865i | −0.335988 | + | 0.581947i | ||||
\(843\) | −9.61212 | − | 16.6487i | −0.331059 | − | 0.573411i | ||||
\(844\) | −0.688906 | − | 1.19322i | −0.0237131 | − | 0.0410723i | ||||
\(845\) | 5.58574 | − | 9.67478i | 0.192155 | − | 0.332823i | ||||
\(846\) | 28.7056 | 0.986918 | ||||||||
\(847\) | −2.33669 | + | 1.24091i | −0.0802898 | + | 0.0426382i | ||||
\(848\) | −38.8060 | −1.33260 | ||||||||
\(849\) | 4.21861 | − | 7.30685i | 0.144782 | − | 0.250770i | ||||
\(850\) | −0.398614 | − | 0.690420i | −0.0136724 | − | 0.0236812i | ||||
\(851\) | 15.4205 | + | 26.7091i | 0.528608 | + | 0.915575i | ||||
\(852\) | −0.406436 | + | 0.703967i | −0.0139243 | + | 0.0241175i | ||||
\(853\) | 26.8003 | 0.917624 | 0.458812 | − | 0.888533i | \(-0.348275\pi\) | ||||
0.458812 | + | 0.888533i | \(0.348275\pi\) | |||||||
\(854\) | −1.03471 | + | 29.2026i | −0.0354072 | + | 0.999291i | ||||
\(855\) | −0.494756 | −0.0169203 | ||||||||
\(856\) | −3.31230 | + | 5.73707i | −0.113212 | + | 0.196089i | ||||
\(857\) | 1.42206 | + | 2.46309i | 0.0485768 | + | 0.0841374i | 0.889291 | − | 0.457341i | \(-0.151198\pi\) |
−0.840715 | + | 0.541478i | \(0.817865\pi\) | |||||||
\(858\) | 0.714780 | + | 1.23804i | 0.0244022 | + | 0.0422658i | ||||
\(859\) | −20.4657 | + | 35.4476i | −0.698279 | + | 1.20946i | 0.270783 | + | 0.962640i | \(0.412717\pi\) |
−0.969063 | + | 0.246815i | \(0.920616\pi\) | |||||||
\(860\) | −1.59908 | −0.0545281 | ||||||||
\(861\) | 0.274253 | − | 7.74018i | 0.00934650 | − | 0.263785i | ||||
\(862\) | 28.4636 | 0.969473 | ||||||||
\(863\) | 11.8307 | − | 20.4914i | 0.402721 | − | 0.697534i | −0.591332 | − | 0.806428i | \(-0.701398\pi\) |
0.994053 | + | 0.108894i | \(0.0347310\pi\) | |||||||
\(864\) | 1.80570 | + | 3.12756i | 0.0614311 | + | 0.106402i | ||||
\(865\) | 4.60695 | + | 7.97947i | 0.156641 | + | 0.271310i | ||||
\(866\) | 10.9258 | − | 18.9240i | 0.371272 | − | 0.643063i | ||||
\(867\) | −12.0106 | −0.407901 | ||||||||
\(868\) | −2.28847 | + | 1.21530i | −0.0776757 | + | 0.0412500i | ||||
\(869\) | 0.363537 | 0.0123321 | ||||||||
\(870\) | 1.19236 | − | 2.06522i | 0.0404247 | − | 0.0700177i | ||||
\(871\) | −5.41707 | − | 9.38264i | −0.183550 | − | 0.317918i | ||||
\(872\) | −5.42533 | − | 9.39695i | −0.183725 | − | 0.318221i | ||||
\(873\) | −20.7176 | + | 35.8839i | −0.701184 | + | 1.21449i | ||||
\(874\) | 1.16350 | 0.0393561 | ||||||||
\(875\) | 2.24301 | + | 1.40318i | 0.0758275 | + | 0.0474362i | ||||
\(876\) | 1.73563 | 0.0586416 | ||||||||
\(877\) | −11.1901 | + | 19.3818i | −0.377862 | + | 0.654476i | −0.990751 | − | 0.135693i | \(-0.956674\pi\) |
0.612889 | + | 0.790169i | \(0.290007\pi\) | |||||||
\(878\) | −15.4838 | − | 26.8187i | −0.522552 | − | 0.905087i | ||||
\(879\) | −5.36316 | − | 9.28927i | −0.180895 | − | 0.313319i | ||||
\(880\) | −2.14916 | + | 3.72246i | −0.0724483 | + | 0.125484i | ||||
\(881\) | −37.3337 | −1.25780 | −0.628902 | − | 0.777485i | \(-0.716495\pi\) | ||||
−0.628902 | + | 0.777485i | \(0.716495\pi\) | |||||||
\(882\) | 14.3146 | − | 21.1755i | 0.481997 | − | 0.713018i | ||||
\(883\) | 1.75761 | 0.0591482 | 0.0295741 | − | 0.999563i | \(-0.490585\pi\) | ||||
0.0295741 | + | 0.999563i | \(0.490585\pi\) | |||||||
\(884\) | −0.0595073 | + | 0.103070i | −0.00200145 | + | 0.00346661i | ||||
\(885\) | 2.72267 | + | 4.71581i | 0.0915216 | + | 0.158520i | ||||
\(886\) | −5.96422 | − | 10.3303i | −0.200372 | − | 0.347054i | ||||
\(887\) | 21.5115 | − | 37.2590i | 0.722286 | − | 1.25104i | −0.237795 | − | 0.971315i | \(-0.576425\pi\) |
0.960081 | − | 0.279721i | \(-0.0902419\pi\) | |||||||
\(888\) | 15.0880 | 0.506319 | ||||||||
\(889\) | 35.3253 | + | 22.0988i | 1.18477 | + | 0.741169i | ||||
\(890\) | 5.85590 | 0.196290 | ||||||||
\(891\) | 2.30767 | − | 3.99700i | 0.0773099 | − | 0.133905i | ||||
\(892\) | −1.60642 | − | 2.78240i | −0.0537868 | − | 0.0931615i | ||||
\(893\) | −0.783188 | − | 1.35652i | −0.0262084 | − | 0.0453942i | ||||
\(894\) | 4.39352 | − | 7.60980i | 0.146941 | − | 0.254510i | ||||
\(895\) | 4.32152 | 0.144453 | ||||||||
\(896\) | 29.1913 | − | 15.5022i | 0.975213 | − | 0.517891i | ||||
\(897\) | 3.86060 | 0.128902 | ||||||||
\(898\) | 26.0555 | − | 45.1295i | 0.869485 | − | 1.50599i | ||||
\(899\) | −6.80408 | − | 11.7850i | −0.226929 | − | 0.393052i | ||||
\(900\) | 0.201557 | + | 0.349107i | 0.00671857 | + | 0.0116369i | ||||
\(901\) | 2.44732 | − | 4.23888i | 0.0815320 | − | 0.141218i | ||||
\(902\) | 5.98752 | 0.199363 | ||||||||
\(903\) | −0.663448 | + | 18.7244i | −0.0220782 | + | 0.623108i | ||||
\(904\) | −36.9576 | −1.22919 | ||||||||
\(905\) | 1.27188 | − | 2.20295i | 0.0422786 | − | 0.0732286i | ||||
\(906\) | 4.01665 | + | 6.95704i | 0.133444 | + | 0.231132i | ||||
\(907\) | −3.67556 | − | 6.36626i | −0.122045 | − | 0.211388i | 0.798529 | − | 0.601956i | \(-0.205612\pi\) |
−0.920574 | + | 0.390568i | \(0.872279\pi\) | |||||||
\(908\) | 0.185430 | − | 0.321174i | 0.00615372 | − | 0.0106585i | ||||
\(909\) | −11.9858 | −0.397545 | ||||||||
\(910\) | 0.186290 | − | 5.25762i | 0.00617544 | − | 0.174288i | ||||
\(911\) | 55.4043 | 1.83563 | 0.917813 | − | 0.397014i | \(-0.129953\pi\) | ||||
0.917813 | + | 0.397014i | \(0.129953\pi\) | |||||||
\(912\) | 0.307858 | − | 0.533226i | 0.0101942 | − | 0.0176569i | ||||
\(913\) | 1.93587 | + | 3.35302i | 0.0640678 | + | 0.110969i | ||||
\(914\) | 24.0082 | + | 41.5835i | 0.794121 | + | 1.37546i | ||||
\(915\) | −2.69987 | + | 4.67630i | −0.0892548 | + | 0.154594i | ||||
\(916\) | −4.25358 | −0.140542 | ||||||||
\(917\) | 17.1142 | − | 9.08859i | 0.565162 | − | 0.300132i | ||||
\(918\) | −3.14269 | −0.103724 | ||||||||
\(919\) | −20.9476 | + | 36.2823i | −0.690997 | + | 1.19684i | 0.280514 | + | 0.959850i | \(0.409495\pi\) |
−0.971512 | + | 0.236992i | \(0.923838\pi\) | |||||||
\(920\) | 5.36551 | + | 9.29334i | 0.176896 | + | 0.306392i | ||||
\(921\) | −11.1458 | − | 19.3052i | −0.367268 | − | 0.636127i | ||||
\(922\) | −0.874910 | + | 1.51539i | −0.0288136 | + | 0.0499067i | ||||
\(923\) | −9.41791 | −0.309994 | ||||||||
\(924\) | −0.261788 | − | 0.163769i | −0.00861218 | − | 0.00538761i | ||||
\(925\) | 7.76630 | 0.255354 | ||||||||
\(926\) | −12.7683 | + | 22.1153i | −0.419592 | + | 0.726755i | ||||
\(927\) | 20.5737 | + | 35.6346i | 0.675728 | + | 1.17039i | ||||
\(928\) | −1.03326 | − | 1.78967i | −0.0339186 | − | 0.0587487i | ||||
\(929\) | −16.5737 | + | 28.7065i | −0.543767 | + | 0.941831i | 0.454917 | + | 0.890534i | \(0.349669\pi\) |
−0.998683 | + | 0.0512974i | \(0.983664\pi\) | |||||||
\(930\) | −6.37774 | −0.209134 | ||||||||
\(931\) | −1.39123 | − | 0.0987130i | −0.0455957 | − | 0.00323519i | ||||
\(932\) | 2.92741 | 0.0958904 | ||||||||
\(933\) | 8.14463 | − | 14.1069i | 0.266643 | − | 0.461840i | ||||
\(934\) | 9.61834 | + | 16.6594i | 0.314722 | + | 0.545114i | ||||
\(935\) | −0.271076 | − | 0.469517i | −0.00886513 | − | 0.0153549i | ||||
\(936\) | −4.53678 | + | 7.85793i | −0.148289 | + | 0.256844i | ||||
\(937\) | 41.2006 | 1.34597 | 0.672983 | − | 0.739658i | \(-0.265013\pi\) | ||||
0.672983 | + | 0.739658i | \(0.265013\pi\) | |||||||
\(938\) | 26.4263 | + | 16.5318i | 0.862849 | + | 0.539781i | ||||
\(939\) | −7.54184 | −0.246119 | ||||||||
\(940\) | −0.638120 | + | 1.10526i | −0.0208132 | + | 0.0360495i | ||||
\(941\) | 11.7212 | + | 20.3018i | 0.382101 | + | 0.661818i | 0.991362 | − | 0.131151i | \(-0.0418673\pi\) |
−0.609261 | + | 0.792969i | \(0.708534\pi\) | |||||||
\(942\) | 4.05491 | + | 7.02331i | 0.132116 | + | 0.228832i | ||||
\(943\) | 8.08479 | − | 14.0033i | 0.263277 | − | 0.456009i | ||||
\(944\) | 32.5563 | 1.05962 | ||||||||
\(945\) | 9.21129 | − | 4.89169i | 0.299643 | − | 0.159127i | ||||
\(946\) | −14.4845 | −0.470931 | ||||||||
\(947\) | 7.15527 | − | 12.3933i | 0.232515 | − | 0.402728i | −0.726033 | − | 0.687660i | \(-0.758638\pi\) |
0.958548 | + | 0.284932i | \(0.0919712\pi\) | |||||||
\(948\) | 0.0212147 | + | 0.0367449i | 0.000689021 | + | 0.00119342i | ||||
\(949\) | 10.0545 | + | 17.4149i | 0.326383 | + | 0.565312i | ||||
\(950\) | 0.146495 | − | 0.253737i | 0.00475294 | − | 0.00823233i | ||||
\(951\) | 24.3957 | 0.791086 | ||||||||
\(952\) | −0.137254 | + | 3.87369i | −0.00444842 | + | 0.125547i | ||||
\(953\) | 46.5779 | 1.50881 | 0.754403 | − | 0.656412i | \(-0.227927\pi\) | ||||
0.754403 | + | 0.656412i | \(0.227927\pi\) | |||||||
\(954\) | −16.4828 | + | 28.5491i | −0.533651 | + | 0.924311i | ||||
\(955\) | −1.46281 | − | 2.53367i | −0.0473355 | − | 0.0819876i | ||||
\(956\) | −2.14407 | − | 3.71364i | −0.0693443 | − | 0.120108i | ||||
\(957\) | 0.810858 | − | 1.40445i | 0.0262113 | − | 0.0453993i | ||||
\(958\) | −50.6008 | −1.63484 | ||||||||
\(959\) | 0.722055 | − | 20.3784i | 0.0233164 | − | 0.658054i | ||||
\(960\) | 5.21192 | 0.168214 | ||||||||
\(961\) | −2.69699 | + | 4.67132i | −0.0869997 | + | 0.150688i | ||||
\(962\) | −7.72142 | − | 13.3739i | −0.248948 | − | 0.431191i | ||||
\(963\) | 3.04370 | + | 5.27185i | 0.0980820 | + | 0.169883i | ||||
\(964\) | −1.16416 | + | 2.01638i | −0.0374950 | + | 0.0649432i | ||||
\(965\) | 13.3599 | 0.430069 | ||||||||
\(966\) | −9.80997 | + | 5.20963i | −0.315631 | + | 0.167617i | ||||
\(967\) | 14.4707 | 0.465347 | 0.232674 | − | 0.972555i | \(-0.425253\pi\) | ||||
0.232674 | + | 0.972555i | \(0.425253\pi\) | |||||||
\(968\) | −1.35113 | + | 2.34023i | −0.0434270 | + | 0.0752177i | ||||
\(969\) | 0.0388304 | + | 0.0672563i | 0.00124741 | + | 0.00216058i | ||||
\(970\) | −12.2688 | − | 21.2502i | −0.393927 | − | 0.682302i | ||||
\(971\) | −24.5176 | + | 42.4658i | −0.786809 | + | 1.36279i | 0.141104 | + | 0.989995i | \(0.454935\pi\) |
−0.927913 | + | 0.372798i | \(0.878398\pi\) | |||||||
\(972\) | 2.45852 | 0.0788572 | ||||||||
\(973\) | −37.3114 | − | 23.3412i | −1.19615 | − | 0.748286i | ||||
\(974\) | 39.6546 | 1.27062 | ||||||||
\(975\) | 0.486083 | − | 0.841921i | 0.0155671 | − | 0.0269630i | ||||
\(976\) | 16.1418 | + | 27.9584i | 0.516686 | + | 0.894927i | ||||
\(977\) | −25.6596 | − | 44.4438i | −0.820924 | − | 1.42188i | −0.904995 | − | 0.425422i | \(-0.860126\pi\) |
0.0840712 | − | 0.996460i | \(-0.473208\pi\) | |||||||
\(978\) | 8.95447 | − | 15.5096i | 0.286332 | − | 0.495942i | ||||
\(979\) | 3.98228 | 0.127274 | ||||||||
\(980\) | 0.497116 | + | 1.02189i | 0.0158798 | + | 0.0326430i | ||||
\(981\) | −9.97077 | −0.318342 | ||||||||
\(982\) | 25.1652 | − | 43.5875i | 0.803055 | − | 1.39093i | ||||
\(983\) | 25.8656 | + | 44.8004i | 0.824983 | + | 1.42891i | 0.901932 | + | 0.431877i | \(0.142149\pi\) |
−0.0769494 | + | 0.997035i | \(0.524518\pi\) | |||||||
\(984\) | −3.95523 | − | 6.85066i | −0.126088 | − | 0.218391i | ||||
\(985\) | −5.62447 | + | 9.74187i | −0.179210 | + | 0.310402i | ||||
\(986\) | 1.79832 | 0.0572703 | ||||||||
\(987\) | 12.6772 | + | 7.93063i | 0.403521 | + | 0.252435i | ||||
\(988\) | −0.0437392 | −0.00139153 | ||||||||
\(989\) | −19.5580 | + | 33.8755i | −0.621909 | + | 1.07718i | ||||
\(990\) | 1.82571 | + | 3.16222i | 0.0580249 | + | 0.100502i | ||||
\(991\) | 8.20598 | + | 14.2132i | 0.260672 | + | 0.451497i | 0.966421 | − | 0.256965i | \(-0.0827227\pi\) |
−0.705749 | + | 0.708462i | \(0.749389\pi\) | |||||||
\(992\) | −2.76339 | + | 4.78633i | −0.0877376 | + | 0.151966i | ||||
\(993\) | 11.0722 | 0.351366 | ||||||||
\(994\) | 23.9314 | − | 12.7089i | 0.759057 | − | 0.403101i | ||||
\(995\) | −10.4913 | −0.332597 | ||||||||
\(996\) | −0.225940 | + | 0.391340i | −0.00715919 | + | 0.0124001i | ||||
\(997\) | −19.3502 | − | 33.5155i | −0.612827 | − | 1.06145i | −0.990762 | − | 0.135615i | \(-0.956699\pi\) |
0.377935 | − | 0.925832i | \(-0.376634\pi\) | |||||||
\(998\) | −26.0197 | − | 45.0675i | −0.823641 | − | 1.42659i | ||||
\(999\) | 15.3074 | − | 26.5133i | 0.484306 | − | 0.838843i |
(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 | 385.2.i.c.331.7 | yes | 16 | |
7.2 | even | 3 | 2695.2.a.t.1.2 | 8 | |||
7.4 | even | 3 | inner | 385.2.i.c.221.7 | ✓ | 16 | |
7.5 | odd | 6 | 2695.2.a.s.1.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
385.2.i.c.221.7 | ✓ | 16 | 7.4 | even | 3 | inner | |
385.2.i.c.331.7 | yes | 16 | 1.1 | even | 1 | trivial | |
2695.2.a.s.1.2 | 8 | 7.5 | odd | 6 | |||
2695.2.a.t.1.2 | 8 | 7.2 | even | 3 |