Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(196,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("585.196");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.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: | \(4.67124851824\) |
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: | \( x^{16} - 5 x^{15} + 20 x^{14} - 44 x^{13} + 96 x^{12} - 107 x^{11} + 178 x^{10} - 19 x^{9} + 231 x^{8} + 326 x^{7} + 551 x^{6} + 859 x^{5} + 1118 x^{4} + 1215 x^{3} + 1103 x^{2} + \cdots + 268 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 391.7 | ||
Root | \(1.48460 + 1.66288i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 585.391 |
Dual form | 585.2.i.e.196.7 |
$q$-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 \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.984603 | + | 1.70538i | 0.696220 | + | 1.20589i | 0.969768 | + | 0.244030i | \(0.0784694\pi\) |
−0.273548 | + | 0.961858i | \(0.588197\pi\) | |||||||
\(3\) | −1.60495 | + | 0.651266i | −0.926616 | + | 0.376009i | ||||
\(4\) | −0.938888 | + | 1.62620i | −0.469444 | + | 0.813101i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | −2.69089 | − | 2.09581i | −1.09855 | − | 0.855611i | ||||
\(7\) | 1.51414 | + | 2.62256i | 0.572290 | + | 0.991236i | 0.996330 | + | 0.0855926i | \(0.0272783\pi\) |
−0.424040 | + | 0.905644i | \(0.639388\pi\) | |||||||
\(8\) | 0.240686 | 0.0850953 | ||||||||
\(9\) | 2.15171 | − | 2.09049i | 0.717235 | − | 0.696831i | ||||
\(10\) | 1.96921 | 0.622718 | ||||||||
\(11\) | 2.15197 | + | 3.72733i | 0.648844 | + | 1.12383i | 0.983399 | + | 0.181455i | \(0.0580807\pi\) |
−0.334555 | + | 0.942376i | \(0.608586\pi\) | |||||||
\(12\) | 0.447775 | − | 3.22143i | 0.129261 | − | 0.929947i | ||||
\(13\) | 0.500000 | − | 0.866025i | 0.138675 | − | 0.240192i | ||||
\(14\) | −2.98165 | + | 5.16437i | −0.796880 | + | 1.38024i | ||||
\(15\) | −0.238460 | + | 1.71556i | −0.0615702 | + | 0.442955i | ||||
\(16\) | 2.11476 | + | 3.66286i | 0.528689 | + | 0.915716i | ||||
\(17\) | −0.303306 | −0.0735625 | −0.0367812 | − | 0.999323i | \(-0.511710\pi\) | ||||
−0.0367812 | + | 0.999323i | \(0.511710\pi\) | |||||||
\(18\) | 5.68367 | + | 1.61117i | 1.33965 | + | 0.379757i | ||||
\(19\) | −6.04909 | −1.38776 | −0.693878 | − | 0.720092i | \(-0.744099\pi\) | ||||
−0.693878 | + | 0.720092i | \(0.744099\pi\) | |||||||
\(20\) | 0.938888 | + | 1.62620i | 0.209942 | + | 0.363630i | ||||
\(21\) | −4.13810 | − | 3.22297i | −0.903007 | − | 0.703309i | ||||
\(22\) | −4.23768 | + | 7.33988i | −0.903476 | + | 1.56487i | ||||
\(23\) | −1.47524 | + | 2.55520i | −0.307610 | + | 0.532796i | −0.977839 | − | 0.209358i | \(-0.932862\pi\) |
0.670229 | + | 0.742154i | \(0.266196\pi\) | |||||||
\(24\) | −0.386288 | + | 0.156751i | −0.0788507 | + | 0.0319966i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 1.96921 | 0.386193 | ||||||||
\(27\) | −2.09190 | + | 4.75646i | −0.402587 | + | 0.915382i | ||||
\(28\) | −5.68642 | −1.07463 | ||||||||
\(29\) | −4.44268 | − | 7.69494i | −0.824984 | − | 1.42891i | −0.901931 | − | 0.431880i | \(-0.857851\pi\) |
0.0769469 | − | 0.997035i | \(-0.475483\pi\) | |||||||
\(30\) | −3.16047 | + | 1.28248i | −0.577020 | + | 0.234147i | ||||
\(31\) | −0.0319947 | + | 0.0554165i | −0.00574643 | + | 0.00995310i | −0.868884 | − | 0.495015i | \(-0.835162\pi\) |
0.863138 | + | 0.504968i | \(0.168496\pi\) | |||||||
\(32\) | −3.92370 | + | 6.79606i | −0.693620 | + | 1.20138i | ||||
\(33\) | −5.88128 | − | 4.58065i | −1.02380 | − | 0.797389i | ||||
\(34\) | −0.298636 | − | 0.517253i | −0.0512156 | − | 0.0887081i | ||||
\(35\) | 3.02828 | 0.511872 | ||||||||
\(36\) | 1.37935 | + | 5.46184i | 0.229892 | + | 0.910307i | ||||
\(37\) | 11.1045 | 1.82556 | 0.912781 | − | 0.408450i | \(-0.133930\pi\) | ||||
0.912781 | + | 0.408450i | \(0.133930\pi\) | |||||||
\(38\) | −5.95595 | − | 10.3160i | −0.966183 | − | 1.67348i | ||||
\(39\) | −0.238460 | + | 1.71556i | −0.0381842 | + | 0.274709i | ||||
\(40\) | 0.120343 | − | 0.208440i | 0.0190279 | − | 0.0329573i | ||||
\(41\) | −4.09849 | + | 7.09879i | −0.640076 | + | 1.10865i | 0.345339 | + | 0.938478i | \(0.387764\pi\) |
−0.985415 | + | 0.170167i | \(0.945569\pi\) | |||||||
\(42\) | 1.42201 | − | 10.2304i | 0.219421 | − | 1.57858i | ||||
\(43\) | −1.45536 | − | 2.52075i | −0.221940 | − | 0.384411i | 0.733457 | − | 0.679736i | \(-0.237906\pi\) |
−0.955397 | + | 0.295324i | \(0.904572\pi\) | |||||||
\(44\) | −8.08184 | −1.21838 | ||||||||
\(45\) | −0.734568 | − | 2.90868i | −0.109503 | − | 0.433600i | ||||
\(46\) | −5.81012 | −0.856656 | ||||||||
\(47\) | 3.44432 | + | 5.96573i | 0.502405 | + | 0.870192i | 0.999996 | + | 0.00277976i | \(0.000884826\pi\) |
−0.497591 | + | 0.867412i | \(0.665782\pi\) | |||||||
\(48\) | −5.77957 | − | 4.50143i | −0.834209 | − | 0.649726i | ||||
\(49\) | −1.08523 | + | 1.87967i | −0.155033 | + | 0.268525i | ||||
\(50\) | 0.984603 | − | 1.70538i | 0.139244 | − | 0.241178i | ||||
\(51\) | 0.486789 | − | 0.197533i | 0.0681642 | − | 0.0276601i | ||||
\(52\) | 0.938888 | + | 1.62620i | 0.130200 | + | 0.225514i | ||||
\(53\) | 11.8296 | 1.62493 | 0.812463 | − | 0.583012i | \(-0.198126\pi\) | ||||
0.812463 | + | 0.583012i | \(0.198126\pi\) | |||||||
\(54\) | −10.1713 | + | 1.11573i | −1.38414 | + | 0.151832i | ||||
\(55\) | 4.30395 | 0.580344 | ||||||||
\(56\) | 0.364432 | + | 0.631214i | 0.0486992 | + | 0.0843495i | ||||
\(57\) | 9.70846 | − | 3.93957i | 1.28592 | − | 0.521808i | ||||
\(58\) | 8.74855 | − | 15.1529i | 1.14874 | − | 1.98968i | ||||
\(59\) | −4.57534 | + | 7.92472i | −0.595658 | + | 1.03171i | 0.397795 | + | 0.917474i | \(0.369775\pi\) |
−0.993454 | + | 0.114236i | \(0.963558\pi\) | |||||||
\(60\) | −2.56595 | − | 1.99850i | −0.331263 | − | 0.258005i | ||||
\(61\) | −0.657031 | − | 1.13801i | −0.0841241 | − | 0.145707i | 0.820894 | − | 0.571081i | \(-0.193476\pi\) |
−0.905018 | + | 0.425374i | \(0.860143\pi\) | |||||||
\(62\) | −0.126009 | −0.0160031 | ||||||||
\(63\) | 8.74043 | + | 2.47769i | 1.10119 | + | 0.312159i | ||||
\(64\) | −6.99415 | −0.874269 | ||||||||
\(65\) | −0.500000 | − | 0.866025i | −0.0620174 | − | 0.107417i | ||||
\(66\) | 2.02104 | − | 14.5400i | 0.248772 | − | 1.78975i | ||||
\(67\) | 7.91564 | − | 13.7103i | 0.967049 | − | 1.67498i | 0.263043 | − | 0.964784i | \(-0.415274\pi\) |
0.704006 | − | 0.710194i | \(-0.251393\pi\) | |||||||
\(68\) | 0.284770 | − | 0.493236i | 0.0345334 | − | 0.0598137i | ||||
\(69\) | 0.703575 | − | 5.06173i | 0.0847004 | − | 0.609361i | ||||
\(70\) | 2.98165 | + | 5.16437i | 0.356375 | + | 0.617260i | ||||
\(71\) | −2.85405 | −0.338714 | −0.169357 | − | 0.985555i | \(-0.554169\pi\) | ||||
−0.169357 | + | 0.985555i | \(0.554169\pi\) | |||||||
\(72\) | 0.517885 | − | 0.503152i | 0.0610333 | − | 0.0592971i | ||||
\(73\) | −11.2819 | −1.32045 | −0.660223 | − | 0.751070i | \(-0.729538\pi\) | ||||
−0.660223 | + | 0.751070i | \(0.729538\pi\) | |||||||
\(74\) | 10.9335 | + | 18.9374i | 1.27099 | + | 2.20142i | ||||
\(75\) | 1.36649 | + | 1.06429i | 0.157788 | + | 0.122894i | ||||
\(76\) | 5.67942 | − | 9.83704i | 0.651474 | − | 1.12839i | ||||
\(77\) | −6.51677 | + | 11.2874i | −0.742655 | + | 1.28632i | ||||
\(78\) | −3.16047 | + | 1.28248i | −0.357853 | + | 0.145212i | ||||
\(79\) | −5.17979 | − | 8.97167i | −0.582772 | − | 1.00939i | −0.995149 | − | 0.0983781i | \(-0.968635\pi\) |
0.412377 | − | 0.911013i | \(-0.364699\pi\) | |||||||
\(80\) | 4.22951 | 0.472874 | ||||||||
\(81\) | 0.259671 | − | 8.99625i | 0.0288524 | − | 0.999584i | ||||
\(82\) | −16.1415 | −1.78254 | ||||||||
\(83\) | 3.53463 | + | 6.12217i | 0.387977 | + | 0.671995i | 0.992177 | − | 0.124837i | \(-0.0398408\pi\) |
−0.604201 | + | 0.796832i | \(0.706507\pi\) | |||||||
\(84\) | 9.12640 | − | 3.70337i | 0.995772 | − | 0.404071i | ||||
\(85\) | −0.151653 | + | 0.262670i | −0.0164491 | + | 0.0284906i | ||||
\(86\) | 2.86590 | − | 4.96389i | 0.309038 | − | 0.535270i | ||||
\(87\) | 12.1417 | + | 9.45660i | 1.30173 | + | 1.01385i | ||||
\(88\) | 0.517949 | + | 0.897115i | 0.0552136 | + | 0.0956328i | ||||
\(89\) | 4.26865 | 0.452476 | 0.226238 | − | 0.974072i | \(-0.427357\pi\) | ||||
0.226238 | + | 0.974072i | \(0.427357\pi\) | |||||||
\(90\) | 4.23715 | − | 4.11661i | 0.446635 | − | 0.433929i | ||||
\(91\) | 3.02828 | 0.317450 | ||||||||
\(92\) | −2.77018 | − | 4.79809i | −0.288811 | − | 0.500235i | ||||
\(93\) | 0.0152590 | − | 0.109778i | 0.00158228 | − | 0.0113834i | ||||
\(94\) | −6.78257 | + | 11.7478i | −0.699569 | + | 1.21169i | ||||
\(95\) | −3.02455 | + | 5.23867i | −0.310312 | + | 0.537476i | ||||
\(96\) | 1.87130 | − | 13.4627i | 0.190988 | − | 1.37403i | ||||
\(97\) | −2.91854 | − | 5.05505i | −0.296333 | − | 0.513263i | 0.678961 | − | 0.734174i | \(-0.262430\pi\) |
−0.975294 | + | 0.220911i | \(0.929097\pi\) | |||||||
\(98\) | −4.27408 | −0.431747 | ||||||||
\(99\) | 12.4224 | + | 3.52142i | 1.24849 | + | 0.353916i | ||||
\(100\) | 1.87778 | 0.187778 | ||||||||
\(101\) | −5.32443 | − | 9.22219i | −0.529801 | − | 0.917642i | −0.999396 | − | 0.0347599i | \(-0.988933\pi\) |
0.469595 | − | 0.882882i | \(-0.344400\pi\) | |||||||
\(102\) | 0.816164 | + | 0.635671i | 0.0808122 | + | 0.0629408i | ||||
\(103\) | 8.95821 | − | 15.5161i | 0.882679 | − | 1.52885i | 0.0343282 | − | 0.999411i | \(-0.489071\pi\) |
0.848351 | − | 0.529434i | \(-0.177596\pi\) | |||||||
\(104\) | 0.120343 | − | 0.208440i | 0.0118006 | − | 0.0204392i | ||||
\(105\) | −4.86022 | + | 1.97221i | −0.474309 | + | 0.192468i | ||||
\(106\) | 11.6475 | + | 20.1741i | 1.13131 | + | 1.95948i | ||||
\(107\) | −1.12190 | −0.108458 | −0.0542288 | − | 0.998529i | \(-0.517270\pi\) | ||||
−0.0542288 | + | 0.998529i | \(0.517270\pi\) | |||||||
\(108\) | −5.77090 | − | 7.86764i | −0.555305 | − | 0.757064i | ||||
\(109\) | 14.1268 | 1.35310 | 0.676552 | − | 0.736394i | \(-0.263473\pi\) | ||||
0.676552 | + | 0.736394i | \(0.263473\pi\) | |||||||
\(110\) | 4.23768 | + | 7.33988i | 0.404047 | + | 0.699830i | ||||
\(111\) | −17.8221 | + | 7.23196i | −1.69159 | + | 0.686427i | ||||
\(112\) | −6.40406 | + | 11.0922i | −0.605127 | + | 1.04811i | ||||
\(113\) | 0.144808 | − | 0.250816i | 0.0136224 | − | 0.0235947i | −0.859134 | − | 0.511751i | \(-0.828997\pi\) |
0.872756 | + | 0.488156i | \(0.162330\pi\) | |||||||
\(114\) | 16.2775 | + | 12.6777i | 1.52452 | + | 1.18738i | ||||
\(115\) | 1.47524 | + | 2.55520i | 0.137567 | + | 0.238274i | ||||
\(116\) | 16.6847 | 1.54914 | ||||||||
\(117\) | −0.734568 | − | 2.90868i | −0.0679108 | − | 0.268907i | ||||
\(118\) | −18.0196 | −1.65884 | ||||||||
\(119\) | −0.459247 | − | 0.795439i | −0.0420991 | − | 0.0729178i | ||||
\(120\) | −0.0573940 | + | 0.412910i | −0.00523933 | + | 0.0376934i | ||||
\(121\) | −3.76198 | + | 6.51593i | −0.341998 | + | 0.592357i | ||||
\(122\) | 1.29383 | − | 2.24098i | 0.117138 | − | 0.202889i | ||||
\(123\) | 1.95465 | − | 14.0624i | 0.176245 | − | 1.26796i | ||||
\(124\) | −0.0600789 | − | 0.104060i | −0.00539525 | − | 0.00934484i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 4.38045 | + | 17.3453i | 0.390242 | + | 1.54524i | ||||
\(127\) | 4.70408 | 0.417419 | 0.208710 | − | 0.977978i | \(-0.433074\pi\) | ||||
0.208710 | + | 0.977978i | \(0.433074\pi\) | |||||||
\(128\) | 0.960946 | + | 1.66441i | 0.0849364 | + | 0.147114i | ||||
\(129\) | 3.97745 | + | 3.09785i | 0.350195 | + | 0.272750i | ||||
\(130\) | 0.984603 | − | 1.70538i | 0.0863554 | − | 0.149572i | ||||
\(131\) | 11.0430 | − | 19.1271i | 0.964835 | − | 1.67114i | 0.254779 | − | 0.966999i | \(-0.417997\pi\) |
0.710057 | − | 0.704145i | \(-0.248669\pi\) | |||||||
\(132\) | 12.9709 | − | 5.26343i | 1.12897 | − | 0.458123i | ||||
\(133\) | −9.15916 | − | 15.8641i | −0.794200 | − | 1.37559i | ||||
\(134\) | 31.1751 | 2.69311 | ||||||||
\(135\) | 3.07327 | + | 4.18987i | 0.264505 | + | 0.360607i | ||||
\(136\) | −0.0730014 | −0.00625982 | ||||||||
\(137\) | 1.08441 | + | 1.87825i | 0.0926473 | + | 0.160470i | 0.908624 | − | 0.417615i | \(-0.137134\pi\) |
−0.815977 | + | 0.578084i | \(0.803800\pi\) | |||||||
\(138\) | 9.32494 | − | 3.78394i | 0.793791 | − | 0.322110i | ||||
\(139\) | 0.606433 | − | 1.05037i | 0.0514370 | − | 0.0890914i | −0.839161 | − | 0.543884i | \(-0.816953\pi\) |
0.890597 | + | 0.454792i | \(0.150287\pi\) | |||||||
\(140\) | −2.84321 | + | 4.92459i | −0.240295 | + | 0.416203i | ||||
\(141\) | −9.41322 | − | 7.33152i | −0.792737 | − | 0.617425i | ||||
\(142\) | −2.81011 | − | 4.86726i | −0.235819 | − | 0.408451i | ||||
\(143\) | 4.30395 | 0.359914 | ||||||||
\(144\) | 12.2075 | + | 3.46052i | 1.01729 | + | 0.288377i | ||||
\(145\) | −8.88535 | −0.737888 | ||||||||
\(146\) | −11.1082 | − | 19.2399i | −0.919320 | − | 1.59231i | ||||
\(147\) | 0.517568 | − | 3.72354i | 0.0426883 | − | 0.307113i | ||||
\(148\) | −10.4258 | + | 18.0581i | −0.856999 | + | 1.48437i | ||||
\(149\) | −2.93510 | + | 5.08374i | −0.240453 | + | 0.416476i | −0.960843 | − | 0.277092i | \(-0.910629\pi\) |
0.720391 | + | 0.693569i | \(0.243963\pi\) | |||||||
\(150\) | −0.469578 | + | 3.37829i | −0.0383409 | + | 0.275836i | ||||
\(151\) | 4.65223 | + | 8.05789i | 0.378593 | + | 0.655742i | 0.990858 | − | 0.134911i | \(-0.0430747\pi\) |
−0.612265 | + | 0.790653i | \(0.709741\pi\) | |||||||
\(152\) | −1.45593 | −0.118092 | ||||||||
\(153\) | −0.652625 | + | 0.634059i | −0.0527616 | + | 0.0512606i | ||||
\(154\) | −25.6657 | −2.06820 | ||||||||
\(155\) | 0.0319947 | + | 0.0554165i | 0.00256988 | + | 0.00445116i | ||||
\(156\) | −2.56595 | − | 1.99850i | −0.205441 | − | 0.160008i | ||||
\(157\) | 9.14727 | − | 15.8435i | 0.730031 | − | 1.26445i | −0.226838 | − | 0.973933i | \(-0.572839\pi\) |
0.956869 | − | 0.290519i | \(-0.0938280\pi\) | |||||||
\(158\) | 10.2001 | − | 17.6671i | 0.811475 | − | 1.40552i | ||||
\(159\) | −18.9859 | + | 7.70425i | −1.50568 | + | 0.610986i | ||||
\(160\) | 3.92370 | + | 6.79606i | 0.310196 | + | 0.537275i | ||||
\(161\) | −8.93490 | −0.704169 | ||||||||
\(162\) | 15.5977 | − | 8.41490i | 1.22547 | − | 0.661137i | ||||
\(163\) | −11.9524 | −0.936186 | −0.468093 | − | 0.883679i | \(-0.655059\pi\) | ||||
−0.468093 | + | 0.883679i | \(0.655059\pi\) | |||||||
\(164\) | −7.69604 | − | 13.3299i | −0.600960 | − | 1.04089i | ||||
\(165\) | −6.90760 | + | 2.80301i | −0.537756 | + | 0.218214i | ||||
\(166\) | −6.96043 | + | 12.0558i | −0.540234 | + | 0.935712i | ||||
\(167\) | −6.66491 | + | 11.5440i | −0.515746 | + | 0.893298i | 0.484087 | + | 0.875020i | \(0.339152\pi\) |
−0.999833 | + | 0.0182782i | \(0.994182\pi\) | |||||||
\(168\) | −0.995982 | − | 0.775723i | −0.0768416 | − | 0.0598483i | ||||
\(169\) | −0.500000 | − | 0.866025i | −0.0384615 | − | 0.0666173i | ||||
\(170\) | −0.597272 | −0.0458087 | ||||||||
\(171\) | −13.0159 | + | 12.6456i | −0.995348 | + | 0.967032i | ||||
\(172\) | 5.46567 | 0.416753 | ||||||||
\(173\) | 8.28672 | + | 14.3530i | 0.630028 | + | 1.09124i | 0.987545 | + | 0.157334i | \(0.0502899\pi\) |
−0.357517 | + | 0.933906i | \(0.616377\pi\) | |||||||
\(174\) | −4.17236 | + | 30.0173i | −0.316306 | + | 2.27560i | ||||
\(175\) | 1.51414 | − | 2.62256i | 0.114458 | − | 0.198247i | ||||
\(176\) | −9.10179 | + | 15.7648i | −0.686073 | + | 1.18831i | ||||
\(177\) | 2.18207 | − | 15.6985i | 0.164015 | − | 1.17997i | ||||
\(178\) | 4.20293 | + | 7.27968i | 0.315023 | + | 0.545635i | ||||
\(179\) | 13.5386 | 1.01192 | 0.505961 | − | 0.862556i | \(-0.331138\pi\) | ||||
0.505961 | + | 0.862556i | \(0.331138\pi\) | |||||||
\(180\) | 5.41977 | + | 1.53637i | 0.403966 | + | 0.114514i | ||||
\(181\) | −3.59303 | −0.267068 | −0.133534 | − | 0.991044i | \(-0.542632\pi\) | ||||
−0.133534 | + | 0.991044i | \(0.542632\pi\) | |||||||
\(182\) | 2.98165 | + | 5.16437i | 0.221015 | + | 0.382809i | ||||
\(183\) | 1.79565 | + | 1.39854i | 0.132738 | + | 0.103383i | ||||
\(184\) | −0.355071 | + | 0.615000i | −0.0261762 | + | 0.0453384i | ||||
\(185\) | 5.55223 | − | 9.61674i | 0.408208 | − | 0.707037i | ||||
\(186\) | 0.202237 | − | 0.0820651i | 0.0148287 | − | 0.00601730i | ||||
\(187\) | −0.652706 | − | 1.13052i | −0.0477306 | − | 0.0826718i | ||||
\(188\) | −12.9353 | −0.943404 | ||||||||
\(189\) | −15.6416 | + | 1.71579i | −1.13776 | + | 0.124805i | ||||
\(190\) | −11.9119 | −0.864181 | ||||||||
\(191\) | −10.2707 | − | 17.7894i | −0.743161 | − | 1.28719i | −0.951049 | − | 0.309040i | \(-0.899992\pi\) |
0.207888 | − | 0.978153i | \(-0.433341\pi\) | |||||||
\(192\) | 11.2252 | − | 4.55505i | 0.810112 | − | 0.328733i | ||||
\(193\) | 0.763135 | − | 1.32179i | 0.0549316 | − | 0.0951444i | −0.837252 | − | 0.546817i | \(-0.815839\pi\) |
0.892184 | + | 0.451673i | \(0.149173\pi\) | |||||||
\(194\) | 5.74720 | − | 9.95445i | 0.412625 | − | 0.714688i | ||||
\(195\) | 1.36649 | + | 1.06429i | 0.0978561 | + | 0.0762155i | ||||
\(196\) | −2.03782 | − | 3.52960i | −0.145558 | − | 0.252114i | ||||
\(197\) | −1.07799 | −0.0768033 | −0.0384016 | − | 0.999262i | \(-0.512227\pi\) | ||||
−0.0384016 | + | 0.999262i | \(0.512227\pi\) | |||||||
\(198\) | 6.22573 | + | 24.6521i | 0.442443 | + | 1.75195i | ||||
\(199\) | 2.00263 | 0.141963 | 0.0709813 | − | 0.997478i | \(-0.477387\pi\) | ||||
0.0709813 | + | 0.997478i | \(0.477387\pi\) | |||||||
\(200\) | −0.120343 | − | 0.208440i | −0.00850953 | − | 0.0147389i | ||||
\(201\) | −3.77513 | + | 27.1595i | −0.266277 | + | 1.91568i | ||||
\(202\) | 10.4849 | − | 18.1604i | 0.737716 | − | 1.27776i | ||||
\(203\) | 13.4537 | − | 23.3024i | 0.944261 | − | 1.63551i | ||||
\(204\) | −0.135813 | + | 0.977079i | −0.00950879 | + | 0.0684092i | ||||
\(205\) | 4.09849 | + | 7.09879i | 0.286251 | + | 0.495801i | ||||
\(206\) | 35.2812 | 2.45815 | ||||||||
\(207\) | 2.16734 | + | 8.58203i | 0.150640 | + | 0.596492i | ||||
\(208\) | 4.22951 | 0.293264 | ||||||||
\(209\) | −13.0175 | − | 22.5469i | −0.900438 | − | 1.55960i | ||||
\(210\) | −8.14877 | − | 6.34669i | −0.562318 | − | 0.437963i | ||||
\(211\) | 0.117610 | − | 0.203707i | 0.00809663 | − | 0.0140238i | −0.861949 | − | 0.506996i | \(-0.830756\pi\) |
0.870045 | + | 0.492972i | \(0.164089\pi\) | |||||||
\(212\) | −11.1067 | + | 19.2374i | −0.762812 | + | 1.32123i | ||||
\(213\) | 4.58060 | − | 1.85875i | 0.313858 | − | 0.127359i | ||||
\(214\) | −1.10462 | − | 1.91326i | −0.0755104 | − | 0.130788i | ||||
\(215\) | −2.91072 | −0.198509 | ||||||||
\(216\) | −0.503492 | + | 1.14481i | −0.0342583 | + | 0.0778947i | ||||
\(217\) | −0.193778 | −0.0131545 | ||||||||
\(218\) | 13.9093 | + | 24.0917i | 0.942058 | + | 1.63169i | ||||
\(219\) | 18.1068 | − | 7.34751i | 1.22355 | − | 0.496499i | ||||
\(220\) | −4.04092 | + | 6.99908i | −0.272439 | + | 0.471878i | ||||
\(221\) | −0.151653 | + | 0.262670i | −0.0102013 | + | 0.0176691i | ||||
\(222\) | −29.8809 | − | 23.2728i | −2.00548 | − | 1.56197i | ||||
\(223\) | −0.224073 | − | 0.388107i | −0.0150051 | − | 0.0259895i | 0.858425 | − | 0.512938i | \(-0.171443\pi\) |
−0.873430 | + | 0.486949i | \(0.838110\pi\) | |||||||
\(224\) | −23.7641 | −1.58781 | ||||||||
\(225\) | −2.88627 | − | 0.818185i | −0.192418 | − | 0.0545456i | ||||
\(226\) | 0.570315 | 0.0379368 | ||||||||
\(227\) | 4.89779 | + | 8.48323i | 0.325078 | + | 0.563052i | 0.981528 | − | 0.191318i | \(-0.0612761\pi\) |
−0.656450 | + | 0.754369i | \(0.727943\pi\) | |||||||
\(228\) | −2.70863 | + | 19.4867i | −0.179383 | + | 1.29054i | ||||
\(229\) | −1.43116 | + | 2.47884i | −0.0945735 | + | 0.163806i | −0.909431 | − | 0.415856i | \(-0.863482\pi\) |
0.814857 | + | 0.579662i | \(0.196815\pi\) | |||||||
\(230\) | −2.90506 | + | 5.03172i | −0.191554 | + | 0.331782i | ||||
\(231\) | 3.10798 | − | 22.3598i | 0.204490 | − | 1.47117i | ||||
\(232\) | −1.06929 | − | 1.85206i | −0.0702023 | − | 0.121594i | ||||
\(233\) | −15.5072 | −1.01591 | −0.507955 | − | 0.861384i | \(-0.669598\pi\) | ||||
−0.507955 | + | 0.861384i | \(0.669598\pi\) | |||||||
\(234\) | 4.23715 | − | 4.11661i | 0.276991 | − | 0.269112i | ||||
\(235\) | 6.88864 | 0.449365 | ||||||||
\(236\) | −8.59146 | − | 14.8808i | −0.559256 | − | 0.968660i | ||||
\(237\) | 14.1562 | + | 11.0256i | 0.919546 | + | 0.716191i | ||||
\(238\) | 0.904352 | − | 1.56638i | 0.0586204 | − | 0.101534i | ||||
\(239\) | 3.64054 | − | 6.30561i | 0.235487 | − | 0.407876i | −0.723927 | − | 0.689877i | \(-0.757665\pi\) |
0.959414 | + | 0.282001i | \(0.0909981\pi\) | |||||||
\(240\) | −6.78814 | + | 2.75454i | −0.438172 | + | 0.177805i | ||||
\(241\) | −5.49432 | − | 9.51644i | −0.353920 | − | 0.613008i | 0.633012 | − | 0.774142i | \(-0.281818\pi\) |
−0.986933 | + | 0.161134i | \(0.948485\pi\) | |||||||
\(242\) | −14.8162 | −0.952422 | ||||||||
\(243\) | 5.44219 | + | 14.6076i | 0.349117 | + | 0.937079i | ||||
\(244\) | 2.46751 | 0.157966 | ||||||||
\(245\) | 1.08523 | + | 1.87967i | 0.0693327 | + | 0.120088i | ||||
\(246\) | 25.9063 | − | 10.5124i | 1.65173 | − | 0.670249i | ||||
\(247\) | −3.02455 | + | 5.23867i | −0.192447 | + | 0.333328i | ||||
\(248\) | −0.00770068 | + | 0.0133380i | −0.000488994 | + | 0.000846962i | ||||
\(249\) | −9.66006 | − | 7.52376i | −0.612181 | − | 0.476799i | ||||
\(250\) | −0.984603 | − | 1.70538i | −0.0622718 | − | 0.107858i | ||||
\(251\) | 9.53838 | 0.602057 | 0.301029 | − | 0.953615i | \(-0.402670\pi\) | ||||
0.301029 | + | 0.953615i | \(0.402670\pi\) | |||||||
\(252\) | −12.2355 | + | 11.8874i | −0.770764 | + | 0.748838i | ||||
\(253\) | −12.6987 | −0.798364 | ||||||||
\(254\) | 4.63165 | + | 8.02225i | 0.290616 | + | 0.503361i | ||||
\(255\) | 0.0723264 | − | 0.520338i | 0.00452925 | − | 0.0325849i | ||||
\(256\) | −8.88645 | + | 15.3918i | −0.555403 | + | 0.961986i | ||||
\(257\) | −0.375550 | + | 0.650471i | −0.0234261 | + | 0.0405753i | −0.877501 | − | 0.479575i | \(-0.840791\pi\) |
0.854075 | + | 0.520150i | \(0.174124\pi\) | |||||||
\(258\) | −1.36681 | + | 9.83323i | −0.0850937 | + | 0.612190i | ||||
\(259\) | 16.8137 | + | 29.1222i | 1.04475 | + | 1.80956i | ||||
\(260\) | 1.87778 | 0.116455 | ||||||||
\(261\) | −25.6456 | − | 7.26986i | −1.58742 | − | 0.449993i | ||||
\(262\) | 43.4921 | 2.68695 | ||||||||
\(263\) | −10.4188 | − | 18.0458i | −0.642449 | − | 1.11275i | −0.984884 | − | 0.173212i | \(-0.944585\pi\) |
0.342436 | − | 0.939541i | \(-0.388748\pi\) | |||||||
\(264\) | −1.41554 | − | 1.10250i | −0.0871206 | − | 0.0678541i | ||||
\(265\) | 5.91482 | − | 10.2448i | 0.363345 | − | 0.629331i | ||||
\(266\) | 18.0363 | − | 31.2397i | 1.10588 | − | 1.91543i | ||||
\(267\) | −6.85095 | + | 2.78003i | −0.419272 | + | 0.170135i | ||||
\(268\) | 14.8638 | + | 25.7448i | 0.907950 | + | 1.57262i | ||||
\(269\) | −15.5184 | −0.946176 | −0.473088 | − | 0.881015i | \(-0.656861\pi\) | ||||
−0.473088 | + | 0.881015i | \(0.656861\pi\) | |||||||
\(270\) | −4.11939 | + | 9.36646i | −0.250698 | + | 0.570025i | ||||
\(271\) | 0.983023 | 0.0597144 | 0.0298572 | − | 0.999554i | \(-0.490495\pi\) | ||||
0.0298572 | + | 0.999554i | \(0.490495\pi\) | |||||||
\(272\) | −0.641417 | − | 1.11097i | −0.0388916 | − | 0.0673623i | ||||
\(273\) | −4.86022 | + | 1.97221i | −0.294154 | + | 0.119364i | ||||
\(274\) | −2.13543 | + | 3.69867i | −0.129006 | + | 0.223445i | ||||
\(275\) | 2.15197 | − | 3.72733i | 0.129769 | − | 0.224766i | ||||
\(276\) | 7.57082 | + | 5.89655i | 0.455710 | + | 0.354931i | ||||
\(277\) | −12.1412 | − | 21.0291i | −0.729492 | − | 1.26352i | −0.957098 | − | 0.289764i | \(-0.906423\pi\) |
0.227606 | − | 0.973753i | \(-0.426910\pi\) | |||||||
\(278\) | 2.38838 | 0.143246 | ||||||||
\(279\) | 0.0470046 | + | 0.186125i | 0.00281409 | + | 0.0111430i | ||||
\(280\) | 0.728863 | 0.0435579 | ||||||||
\(281\) | 1.52022 | + | 2.63310i | 0.0906888 | + | 0.157078i | 0.907801 | − | 0.419401i | \(-0.137760\pi\) |
−0.817112 | + | 0.576478i | \(0.804426\pi\) | |||||||
\(282\) | 3.23475 | − | 23.2718i | 0.192627 | − | 1.38581i | ||||
\(283\) | 12.6309 | − | 21.8774i | 0.750829 | − | 1.30047i | −0.196593 | − | 0.980485i | \(-0.562988\pi\) |
0.947421 | − | 0.319988i | \(-0.103679\pi\) | |||||||
\(284\) | 2.67964 | − | 4.64127i | 0.159007 | − | 0.275409i | ||||
\(285\) | 1.44247 | − | 10.3776i | 0.0854444 | − | 0.614714i | ||||
\(286\) | 4.23768 | + | 7.33988i | 0.250579 | + | 0.434016i | ||||
\(287\) | −24.8227 | −1.46524 | ||||||||
\(288\) | 5.76446 | + | 22.8256i | 0.339674 | + | 1.34501i | ||||
\(289\) | −16.9080 | −0.994589 | ||||||||
\(290\) | −8.74855 | − | 15.1529i | −0.513732 | − | 0.889811i | ||||
\(291\) | 7.97628 | + | 6.21235i | 0.467578 | + | 0.364174i | ||||
\(292\) | 10.5924 | − | 18.3466i | 0.619875 | − | 1.07366i | ||||
\(293\) | 13.2059 | − | 22.8732i | 0.771495 | − | 1.33627i | −0.165249 | − | 0.986252i | \(-0.552843\pi\) |
0.936744 | − | 0.350016i | \(-0.113824\pi\) | |||||||
\(294\) | 6.85967 | − | 2.78356i | 0.400064 | − | 0.162341i | ||||
\(295\) | 4.57534 | + | 7.92472i | 0.266387 | + | 0.461395i | ||||
\(296\) | 2.67269 | 0.155347 | ||||||||
\(297\) | −22.2306 | + | 2.43857i | −1.28995 | + | 0.141500i | ||||
\(298\) | −11.5596 | −0.669632 | ||||||||
\(299\) | 1.47524 | + | 2.55520i | 0.0853156 | + | 0.147771i | ||||
\(300\) | −3.01373 | + | 1.22293i | −0.173998 | + | 0.0706060i | ||||
\(301\) | 4.40723 | − | 7.63354i | 0.254028 | − | 0.439990i | ||||
\(302\) | −9.16120 | + | 15.8677i | −0.527168 | + | 0.913081i | ||||
\(303\) | 14.5515 | + | 11.3335i | 0.835963 | + | 0.651092i | ||||
\(304\) | −12.7923 | − | 22.1570i | −0.733691 | − | 1.27079i | ||||
\(305\) | −1.31406 | −0.0752429 | ||||||||
\(306\) | −1.72389 | − | 0.488679i | −0.0985482 | − | 0.0279359i | ||||
\(307\) | −15.3240 | −0.874586 | −0.437293 | − | 0.899319i | \(-0.644063\pi\) | ||||
−0.437293 | + | 0.899319i | \(0.644063\pi\) | |||||||
\(308\) | −12.2370 | − | 21.1952i | −0.697269 | − | 1.20771i | ||||
\(309\) | −4.27236 | + | 30.7367i | −0.243046 | + | 1.74855i | ||||
\(310\) | −0.0630043 | + | 0.109127i | −0.00357840 | + | 0.00619797i | ||||
\(311\) | −1.45646 | + | 2.52267i | −0.0825884 | + | 0.143047i | −0.904361 | − | 0.426768i | \(-0.859652\pi\) |
0.821773 | + | 0.569816i | \(0.192985\pi\) | |||||||
\(312\) | −0.0573940 | + | 0.412910i | −0.00324930 | + | 0.0233764i | ||||
\(313\) | 5.44556 | + | 9.43198i | 0.307801 | + | 0.533127i | 0.977881 | − | 0.209162i | \(-0.0670735\pi\) |
−0.670080 | + | 0.742289i | \(0.733740\pi\) | |||||||
\(314\) | 36.0257 | 2.03305 | ||||||||
\(315\) | 6.51596 | − | 6.33059i | 0.367133 | − | 0.356689i | ||||
\(316\) | 19.4530 | 1.09432 | ||||||||
\(317\) | 4.11235 | + | 7.12280i | 0.230973 | + | 0.400057i | 0.958095 | − | 0.286452i | \(-0.0924758\pi\) |
−0.727122 | + | 0.686508i | \(0.759143\pi\) | |||||||
\(318\) | −31.8323 | − | 24.7927i | −1.78507 | − | 1.39030i | ||||
\(319\) | 19.1210 | − | 33.1186i | 1.07057 | − | 1.85429i | ||||
\(320\) | −3.49707 | + | 6.05711i | −0.195492 | + | 0.338603i | ||||
\(321\) | 1.80058 | − | 0.730652i | 0.100499 | − | 0.0407810i | ||||
\(322\) | −8.79733 | − | 15.2374i | −0.490256 | − | 0.849149i | ||||
\(323\) | 1.83472 | 0.102087 | ||||||||
\(324\) | 14.3859 | + | 8.86875i | 0.799217 | + | 0.492708i | ||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | −11.7684 | − | 20.3835i | −0.651791 | − | 1.12894i | ||||
\(327\) | −22.6728 | + | 9.20032i | −1.25381 | + | 0.508779i | ||||
\(328\) | −0.986448 | + | 1.70858i | −0.0544675 | + | 0.0943405i | ||||
\(329\) | −10.4303 | + | 18.0659i | −0.575044 | + | 0.996005i | ||||
\(330\) | −11.5815 | − | 9.02025i | −0.637538 | − | 0.496548i | ||||
\(331\) | −9.02510 | − | 15.6319i | −0.496064 | − | 0.859209i | 0.503925 | − | 0.863747i | \(-0.331889\pi\) |
−0.999990 | + | 0.00453859i | \(0.998555\pi\) | |||||||
\(332\) | −13.2745 | −0.728533 | ||||||||
\(333\) | 23.8935 | − | 23.2138i | 1.30936 | − | 1.27211i | ||||
\(334\) | −26.2492 | −1.43629 | ||||||||
\(335\) | −7.91564 | − | 13.7103i | −0.432478 | − | 0.749073i | ||||
\(336\) | 3.05423 | − | 21.9731i | 0.166622 | − | 1.19873i | ||||
\(337\) | −18.3022 | + | 31.7004i | −0.996985 | + | 1.72683i | −0.431295 | + | 0.902211i | \(0.641943\pi\) |
−0.565690 | + | 0.824618i | \(0.691390\pi\) | |||||||
\(338\) | 0.984603 | − | 1.70538i | 0.0535554 | − | 0.0927606i | ||||
\(339\) | −0.0690621 | + | 0.496854i | −0.00375094 | + | 0.0269854i | ||||
\(340\) | −0.284770 | − | 0.493236i | −0.0154438 | − | 0.0267495i | ||||
\(341\) | −0.275407 | −0.0149141 | ||||||||
\(342\) | −34.3810 | − | 9.74614i | −1.85911 | − | 0.527011i | ||||
\(343\) | 14.6252 | 0.789686 | ||||||||
\(344\) | −0.350284 | − | 0.606710i | −0.0188861 | − | 0.0327116i | ||||
\(345\) | −4.03180 | − | 3.14018i | −0.217065 | − | 0.169062i | ||||
\(346\) | −16.3183 | + | 28.2641i | −0.877276 | + | 1.51949i | ||||
\(347\) | −2.91466 | + | 5.04835i | −0.156467 | + | 0.271009i | −0.933592 | − | 0.358337i | \(-0.883344\pi\) |
0.777125 | + | 0.629346i | \(0.216677\pi\) | |||||||
\(348\) | −26.7780 | + | 10.8662i | −1.43545 | + | 0.582488i | ||||
\(349\) | −1.50856 | − | 2.61290i | −0.0807513 | − | 0.139865i | 0.822822 | − | 0.568300i | \(-0.192399\pi\) |
−0.903573 | + | 0.428434i | \(0.859065\pi\) | |||||||
\(350\) | 5.96330 | 0.318752 | ||||||||
\(351\) | 3.07327 | + | 4.18987i | 0.164039 | + | 0.223639i | ||||
\(352\) | −33.7748 | −1.80020 | ||||||||
\(353\) | 4.68092 | + | 8.10759i | 0.249140 | + | 0.431524i | 0.963288 | − | 0.268472i | \(-0.0865187\pi\) |
−0.714147 | + | 0.699995i | \(0.753185\pi\) | |||||||
\(354\) | 28.9205 | − | 11.7355i | 1.53710 | − | 0.623737i | ||||
\(355\) | −1.42703 | + | 2.47168i | −0.0757388 | + | 0.131183i | ||||
\(356\) | −4.00778 | + | 6.94168i | −0.212412 | + | 0.367908i | ||||
\(357\) | 1.25511 | + | 0.977545i | 0.0664274 | + | 0.0517372i | ||||
\(358\) | 13.3302 | + | 23.0885i | 0.704521 | + | 1.22027i | ||||
\(359\) | 5.22577 | 0.275806 | 0.137903 | − | 0.990446i | \(-0.455964\pi\) | ||||
0.137903 | + | 0.990446i | \(0.455964\pi\) | |||||||
\(360\) | −0.176800 | − | 0.700078i | −0.00931819 | − | 0.0368973i | ||||
\(361\) | 17.5915 | 0.925868 | ||||||||
\(362\) | −3.53771 | − | 6.12749i | −0.185938 | − | 0.322054i | ||||
\(363\) | 1.79416 | − | 12.9078i | 0.0941692 | − | 0.677482i | ||||
\(364\) | −2.84321 | + | 4.92459i | −0.149025 | + | 0.258118i | ||||
\(365\) | −5.64095 | + | 9.77041i | −0.295261 | + | 0.511406i | ||||
\(366\) | −0.617054 | + | 4.43928i | −0.0322539 | + | 0.232045i | ||||
\(367\) | 2.15082 | + | 3.72532i | 0.112272 | + | 0.194460i | 0.916686 | − | 0.399609i | \(-0.130854\pi\) |
−0.804414 | + | 0.594069i | \(0.797521\pi\) | |||||||
\(368\) | −12.4791 | −0.650520 | ||||||||
\(369\) | 6.02124 | + | 23.8424i | 0.313453 | + | 1.24118i | ||||
\(370\) | 21.8670 | 1.13681 | ||||||||
\(371\) | 17.9117 | + | 31.0240i | 0.929930 | + | 1.61069i | ||||
\(372\) | 0.164194 | + | 0.127883i | 0.00851307 | + | 0.00663042i | ||||
\(373\) | −13.2650 | + | 22.9757i | −0.686836 | + | 1.18964i | 0.286019 | + | 0.958224i | \(0.407668\pi\) |
−0.972856 | + | 0.231412i | \(0.925666\pi\) | |||||||
\(374\) | 1.28531 | − | 2.22623i | 0.0664619 | − | 0.115115i | ||||
\(375\) | 1.60495 | − | 0.651266i | 0.0828791 | − | 0.0336312i | ||||
\(376\) | 0.828999 | + | 1.43587i | 0.0427523 | + | 0.0740492i | ||||
\(377\) | −8.88535 | −0.457619 | ||||||||
\(378\) | −18.3268 | − | 24.9855i | −0.942629 | − | 1.28511i | ||||
\(379\) | −3.48090 | −0.178802 | −0.0894008 | − | 0.995996i | \(-0.528495\pi\) | ||||
−0.0894008 | + | 0.995996i | \(0.528495\pi\) | |||||||
\(380\) | −5.67942 | − | 9.83704i | −0.291348 | − | 0.504629i | ||||
\(381\) | −7.54979 | + | 3.06360i | −0.386787 | + | 0.156953i | ||||
\(382\) | 20.2251 | − | 35.0309i | 1.03481 | − | 1.79234i | ||||
\(383\) | −12.3188 | + | 21.3368i | −0.629461 | + | 1.09026i | 0.358199 | + | 0.933645i | \(0.383391\pi\) |
−0.987660 | + | 0.156614i | \(0.949942\pi\) | |||||||
\(384\) | −2.62624 | − | 2.04545i | −0.134020 | − | 0.104382i | ||||
\(385\) | 6.51677 | + | 11.2874i | 0.332125 | + | 0.575258i | ||||
\(386\) | 3.00554 | 0.152978 | ||||||||
\(387\) | −8.40112 | − | 2.38150i | −0.427053 | − | 0.121059i | ||||
\(388\) | 10.9607 | 0.556446 | ||||||||
\(389\) | 9.20953 | + | 15.9514i | 0.466942 | + | 0.808767i | 0.999287 | − | 0.0377606i | \(-0.0120224\pi\) |
−0.532345 | + | 0.846527i | \(0.678689\pi\) | |||||||
\(390\) | −0.469578 | + | 3.37829i | −0.0237780 | + | 0.171066i | ||||
\(391\) | 0.447450 | − | 0.775007i | 0.0226285 | − | 0.0391938i | ||||
\(392\) | −0.261199 | + | 0.452410i | −0.0131926 | + | 0.0228502i | ||||
\(393\) | −5.26666 | + | 37.8900i | −0.265668 | + | 1.91130i | ||||
\(394\) | −1.06139 | − | 1.83838i | −0.0534720 | − | 0.0926162i | ||||
\(395\) | −10.3596 | −0.521248 | ||||||||
\(396\) | −17.3897 | + | 16.8950i | −0.873868 | + | 0.849008i | ||||
\(397\) | 15.1217 | 0.758934 | 0.379467 | − | 0.925205i | \(-0.376107\pi\) | ||||
0.379467 | + | 0.925205i | \(0.376107\pi\) | |||||||
\(398\) | 1.97180 | + | 3.41525i | 0.0988372 | + | 0.171191i | ||||
\(399\) | 25.0317 | + | 19.4960i | 1.25315 | + | 0.976022i | ||||
\(400\) | 2.11476 | − | 3.66286i | 0.105738 | − | 0.183143i | ||||
\(401\) | −0.137657 | + | 0.238429i | −0.00687426 | + | 0.0119066i | −0.869442 | − | 0.494035i | \(-0.835521\pi\) |
0.862568 | + | 0.505941i | \(0.168855\pi\) | |||||||
\(402\) | −50.0343 | + | 20.3033i | −2.49548 | + | 1.01263i | ||||
\(403\) | 0.0319947 | + | 0.0554165i | 0.00159377 | + | 0.00276049i | ||||
\(404\) | 19.9962 | 0.994847 | ||||||||
\(405\) | −7.66115 | − | 4.72301i | −0.380686 | − | 0.234688i | ||||
\(406\) | 52.9860 | 2.62965 | ||||||||
\(407\) | 23.8965 | + | 41.3899i | 1.18451 | + | 2.05162i | ||||
\(408\) | 0.117163 | − | 0.0475433i | 0.00580045 | − | 0.00235375i | ||||
\(409\) | 6.27626 | − | 10.8708i | 0.310341 | − | 0.537527i | −0.668095 | − | 0.744076i | \(-0.732890\pi\) |
0.978436 | + | 0.206549i | \(0.0662234\pi\) | |||||||
\(410\) | −8.07077 | + | 13.9790i | −0.398587 | + | 0.690373i | ||||
\(411\) | −2.96366 | − | 2.30825i | −0.146187 | − | 0.113858i | ||||
\(412\) | 16.8215 | + | 29.1357i | 0.828736 | + | 1.43541i | ||||
\(413\) | −27.7108 | −1.36356 | ||||||||
\(414\) | −12.5017 | + | 12.1460i | −0.614424 | + | 0.596945i | ||||
\(415\) | 7.06927 | 0.347017 | ||||||||
\(416\) | 3.92370 | + | 6.79606i | 0.192375 | + | 0.333204i | ||||
\(417\) | −0.289220 | + | 2.08074i | −0.0141632 | + | 0.101894i | ||||
\(418\) | 25.6341 | − | 44.3996i | 1.25381 | − | 2.17165i | ||||
\(419\) | −11.4351 | + | 19.8062i | −0.558641 | + | 0.967595i | 0.438969 | + | 0.898502i | \(0.355344\pi\) |
−0.997610 | + | 0.0690927i | \(0.977990\pi\) | |||||||
\(420\) | 1.35599 | − | 9.75538i | 0.0661653 | − | 0.476014i | ||||
\(421\) | 12.4879 | + | 21.6296i | 0.608622 | + | 1.05416i | 0.991468 | + | 0.130352i | \(0.0416106\pi\) |
−0.382846 | + | 0.923812i | \(0.625056\pi\) | |||||||
\(422\) | 0.463198 | 0.0225481 | ||||||||
\(423\) | 19.8825 | + | 5.63618i | 0.966720 | + | 0.274040i | ||||
\(424\) | 2.84723 | 0.138274 | ||||||||
\(425\) | 0.151653 | + | 0.262670i | 0.00735625 | + | 0.0127414i | ||||
\(426\) | 7.67996 | + | 5.98156i | 0.372095 | + | 0.289807i | ||||
\(427\) | 1.98967 | − | 3.44621i | 0.0962869 | − | 0.166774i | ||||
\(428\) | 1.05333 | − | 1.82443i | 0.0509148 | − | 0.0881870i | ||||
\(429\) | −6.90760 | + | 2.80301i | −0.333502 | + | 0.135331i | ||||
\(430\) | −2.86590 | − | 4.96389i | −0.138206 | − | 0.239380i | ||||
\(431\) | −34.4612 | −1.65994 | −0.829969 | − | 0.557809i | \(-0.811642\pi\) | ||||
−0.829969 | + | 0.557809i | \(0.811642\pi\) | |||||||
\(432\) | −21.8461 | + | 2.39640i | −1.05107 | + | 0.115297i | ||||
\(433\) | 15.6584 | 0.752495 | 0.376247 | − | 0.926519i | \(-0.377214\pi\) | ||||
0.376247 | + | 0.926519i | \(0.377214\pi\) | |||||||
\(434\) | −0.190794 | − | 0.330466i | −0.00915842 | − | 0.0158629i | ||||
\(435\) | 14.2605 | − | 5.78673i | 0.683739 | − | 0.277452i | ||||
\(436\) | −13.2635 | + | 22.9731i | −0.635207 | + | 1.10021i | ||||
\(437\) | 8.92389 | − | 15.4566i | 0.426888 | − | 0.739391i | ||||
\(438\) | 30.3584 | + | 23.6447i | 1.45058 | + | 1.12979i | ||||
\(439\) | 14.4634 | + | 25.0513i | 0.690299 | + | 1.19563i | 0.971740 | + | 0.236054i | \(0.0758542\pi\) |
−0.281441 | + | 0.959578i | \(0.590812\pi\) | |||||||
\(440\) | 1.03590 | 0.0493845 | ||||||||
\(441\) | 1.59435 | + | 6.31316i | 0.0759214 | + | 0.300627i | ||||
\(442\) | −0.597272 | −0.0284093 | ||||||||
\(443\) | 12.6006 | + | 21.8249i | 0.598673 | + | 1.03693i | 0.993017 | + | 0.117969i | \(0.0376385\pi\) |
−0.394344 | + | 0.918963i | \(0.629028\pi\) | |||||||
\(444\) | 4.97230 | − | 35.7722i | 0.235975 | − | 1.69768i | ||||
\(445\) | 2.13433 | − | 3.69676i | 0.101177 | − | 0.175243i | ||||
\(446\) | 0.441247 | − | 0.764262i | 0.0208936 | − | 0.0361889i | ||||
\(447\) | 1.39981 | − | 10.0707i | 0.0662087 | − | 0.476326i | ||||
\(448\) | −10.5901 | − | 18.3426i | −0.500336 | − | 0.866607i | ||||
\(449\) | −21.5777 | −1.01832 | −0.509158 | − | 0.860673i | \(-0.670043\pi\) | ||||
−0.509158 | + | 0.860673i | \(0.670043\pi\) | |||||||
\(450\) | −1.44652 | − | 5.72779i | −0.0681894 | − | 0.270011i | ||||
\(451\) | −35.2794 | −1.66124 | ||||||||
\(452\) | 0.271918 | + | 0.470975i | 0.0127899 | + | 0.0221528i | ||||
\(453\) | −12.7144 | − | 9.90265i | −0.597375 | − | 0.465267i | ||||
\(454\) | −9.64477 | + | 16.7052i | −0.452651 | + | 0.784015i | ||||
\(455\) | 1.51414 | − | 2.62256i | 0.0709839 | − | 0.122948i | ||||
\(456\) | 2.33669 | − | 0.948198i | 0.109426 | − | 0.0444034i | ||||
\(457\) | −0.247288 | − | 0.428315i | −0.0115676 | − | 0.0200357i | 0.860184 | − | 0.509984i | \(-0.170349\pi\) |
−0.871751 | + | 0.489949i | \(0.837016\pi\) | |||||||
\(458\) | −5.63649 | −0.263376 | ||||||||
\(459\) | 0.634487 | − | 1.44266i | 0.0296153 | − | 0.0673377i | ||||
\(460\) | −5.54036 | −0.258320 | ||||||||
\(461\) | −6.81679 | − | 11.8070i | −0.317490 | − | 0.549908i | 0.662474 | − | 0.749085i | \(-0.269507\pi\) |
−0.979964 | + | 0.199177i | \(0.936173\pi\) | |||||||
\(462\) | 41.1921 | − | 16.7152i | 1.91643 | − | 0.777662i | ||||
\(463\) | −10.3778 | + | 17.9749i | −0.482297 | + | 0.835363i | −0.999793 | − | 0.0203221i | \(-0.993531\pi\) |
0.517496 | + | 0.855686i | \(0.326864\pi\) | |||||||
\(464\) | 18.7903 | − | 32.5458i | 0.872320 | − | 1.51090i | ||||
\(465\) | −0.0874408 | − | 0.0681035i | −0.00405497 | − | 0.00315822i | ||||
\(466\) | −15.2684 | − | 26.4457i | −0.707296 | − | 1.22507i | ||||
\(467\) | −34.9625 | −1.61787 | −0.808935 | − | 0.587898i | \(-0.799956\pi\) | ||||
−0.808935 | + | 0.587898i | \(0.799956\pi\) | |||||||
\(468\) | 5.41977 | + | 1.53637i | 0.250529 | + | 0.0710186i | ||||
\(469\) | 47.9415 | 2.21373 | ||||||||
\(470\) | 6.78257 | + | 11.7478i | 0.312857 | + | 0.541884i | ||||
\(471\) | −4.36252 | + | 31.3853i | −0.201014 | + | 1.44616i | ||||
\(472\) | −1.10122 | + | 1.90737i | −0.0506877 | + | 0.0877937i | ||||
\(473\) | 6.26378 | − | 10.8492i | 0.288009 | − | 0.498846i | ||||
\(474\) | −4.86463 | + | 34.9977i | −0.223440 | + | 1.60750i | ||||
\(475\) | 3.02455 | + | 5.23867i | 0.138776 | + | 0.240366i | ||||
\(476\) | 1.72472 | 0.0790526 | ||||||||
\(477\) | 25.4539 | − | 24.7298i | 1.16545 | − | 1.13230i | ||||
\(478\) | 14.3380 | 0.655803 | ||||||||
\(479\) | −15.2877 | − | 26.4791i | −0.698512 | − | 1.20986i | −0.968982 | − | 0.247131i | \(-0.920512\pi\) |
0.270470 | − | 0.962728i | \(-0.412821\pi\) | |||||||
\(480\) | −10.7234 | − | 8.35193i | −0.489453 | − | 0.381212i | ||||
\(481\) | 5.55223 | − | 9.61674i | 0.253160 | − | 0.438486i | ||||
\(482\) | 10.8195 | − | 18.7398i | 0.492812 | − | 0.853576i | ||||
\(483\) | 14.3400 | − | 5.81900i | 0.652494 | − | 0.264773i | ||||
\(484\) | −7.06414 | − | 12.2355i | −0.321097 | − | 0.556157i | ||||
\(485\) | −5.83707 | −0.265048 | ||||||||
\(486\) | −19.5532 | + | 23.6637i | −0.886950 | + | 1.07341i | ||||
\(487\) | 38.2764 | 1.73447 | 0.867235 | − | 0.497899i | \(-0.165895\pi\) | ||||
0.867235 | + | 0.497899i | \(0.165895\pi\) | |||||||
\(488\) | −0.158138 | − | 0.273903i | −0.00715857 | − | 0.0123990i | ||||
\(489\) | 19.1830 | − | 7.78421i | 0.867485 | − | 0.352014i | ||||
\(490\) | −2.13704 | + | 3.70146i | −0.0965416 | + | 0.167215i | ||||
\(491\) | −3.30374 | + | 5.72225i | −0.149096 | + | 0.258241i | −0.930894 | − | 0.365291i | \(-0.880970\pi\) |
0.781798 | + | 0.623532i | \(0.214303\pi\) | |||||||
\(492\) | 21.0331 | + | 16.3817i | 0.948244 | + | 0.738542i | ||||
\(493\) | 1.34749 | + | 2.33392i | 0.0606879 | + | 0.105114i | ||||
\(494\) | −11.9119 | −0.535942 | ||||||||
\(495\) | 9.26082 | − | 8.99737i | 0.416243 | − | 0.404402i | ||||
\(496\) | −0.270644 | −0.0121523 | ||||||||
\(497\) | −4.32143 | − | 7.48494i | −0.193843 | − | 0.335746i | ||||
\(498\) | 3.31957 | − | 23.8820i | 0.148754 | − | 1.07018i | ||||
\(499\) | 11.0238 | − | 19.0937i | 0.493491 | − | 0.854752i | −0.506480 | − | 0.862251i | \(-0.669054\pi\) |
0.999972 | + | 0.00749916i | \(0.00238708\pi\) | |||||||
\(500\) | 0.938888 | − | 1.62620i | 0.0419883 | − | 0.0727259i | ||||
\(501\) | 3.17863 | − | 22.8681i | 0.142011 | − | 1.02167i | ||||
\(502\) | 9.39153 | + | 16.2666i | 0.419164 | + | 0.726014i | ||||
\(503\) | −16.8779 | −0.752550 | −0.376275 | − | 0.926508i | \(-0.622795\pi\) | ||||
−0.376275 | + | 0.926508i | \(0.622795\pi\) | |||||||
\(504\) | 2.10370 | + | 0.596345i | 0.0937062 | + | 0.0265633i | ||||
\(505\) | −10.6489 | −0.473868 | ||||||||
\(506\) | −12.5032 | − | 21.6562i | −0.555836 | − | 0.962737i | ||||
\(507\) | 1.36649 | + | 1.06429i | 0.0606878 | + | 0.0472668i | ||||
\(508\) | −4.41660 | + | 7.64977i | −0.195955 | + | 0.339404i | ||||
\(509\) | 11.4775 | − | 19.8797i | 0.508732 | − | 0.881150i | −0.491216 | − | 0.871038i | \(-0.663448\pi\) |
0.999949 | − | 0.0101129i | \(-0.00321910\pi\) | |||||||
\(510\) | 0.958589 | − | 0.388983i | 0.0424470 | − | 0.0172244i | ||||
\(511\) | −17.0823 | − | 29.5875i | −0.755678 | − | 1.30887i | ||||
\(512\) | −31.1547 | −1.37686 | ||||||||
\(513\) | 12.6541 | − | 28.7723i | 0.558693 | − | 1.27033i | ||||
\(514\) | −1.47907 | −0.0652390 | ||||||||
\(515\) | −8.95821 | − | 15.5161i | −0.394746 | − | 0.683720i | ||||
\(516\) | −8.77211 | + | 3.55961i | −0.386171 | + | 0.156703i | ||||
\(517\) | −14.8242 | + | 25.6762i | −0.651966 | + | 1.12924i | ||||
\(518\) | −33.1096 | + | 57.3475i | −1.45475 | + | 2.51971i | ||||
\(519\) | −22.6474 | − | 17.6390i | −0.994110 | − | 0.774265i | ||||
\(520\) | −0.120343 | − | 0.208440i | −0.00527739 | − | 0.00914070i | ||||
\(521\) | 10.6723 | 0.467562 | 0.233781 | − | 0.972289i | \(-0.424890\pi\) | ||||
0.233781 | + | 0.972289i | \(0.424890\pi\) | |||||||
\(522\) | −12.8528 | − | 50.8934i | −0.562552 | − | 2.22754i | ||||
\(523\) | −2.51360 | −0.109912 | −0.0549559 | − | 0.998489i | \(-0.517502\pi\) | ||||
−0.0549559 | + | 0.998489i | \(0.517502\pi\) | |||||||
\(524\) | 20.7364 | + | 35.9164i | 0.905872 | + | 1.56902i | ||||
\(525\) | −0.722124 | + | 5.19518i | −0.0315161 | + | 0.226736i | ||||
\(526\) | 20.5167 | − | 35.5360i | 0.894571 | − | 1.54944i | ||||
\(527\) | 0.00970419 | − | 0.0168082i | 0.000422721 | − | 0.000732175i | ||||
\(528\) | 4.34083 | − | 31.2293i | 0.188910 | − | 1.35908i | ||||
\(529\) | 7.14730 | + | 12.3795i | 0.310752 | + | 0.538239i | ||||
\(530\) | 23.2950 | 1.01187 | ||||||||
\(531\) | 6.72180 | + | 26.6164i | 0.291701 | + | 1.15505i | ||||
\(532\) | 34.3977 | 1.49133 | ||||||||
\(533\) | 4.09849 | + | 7.09879i | 0.177525 | + | 0.307483i | ||||
\(534\) | −11.4865 | − | 8.94628i | −0.497069 | − | 0.387143i | ||||
\(535\) | −0.560948 | + | 0.971590i | −0.0242519 | + | 0.0420055i | ||||
\(536\) | 1.90518 | − | 3.29987i | 0.0822913 | − | 0.142533i | ||||
\(537\) | −21.7287 | + | 8.81723i | −0.937664 | + | 0.380492i | ||||
\(538\) | −15.2795 | − | 26.4649i | −0.658747 | − | 1.14098i | ||||
\(539\) | −9.34153 | −0.402368 | ||||||||
\(540\) | −9.69903 | + | 1.06393i | −0.417380 | + | 0.0457841i | ||||
\(541\) | −10.6855 | −0.459404 | −0.229702 | − | 0.973261i | \(-0.573775\pi\) | ||||
−0.229702 | + | 0.973261i | \(0.573775\pi\) | |||||||
\(542\) | 0.967888 | + | 1.67643i | 0.0415744 | + | 0.0720089i | ||||
\(543\) | 5.76662 | − | 2.34002i | 0.247469 | − | 0.100420i | ||||
\(544\) | 1.19008 | − | 2.06128i | 0.0510244 | − | 0.0883768i | ||||
\(545\) | 7.06341 | − | 12.2342i | 0.302563 | − | 0.524055i | ||||
\(546\) | −8.14877 | − | 6.34669i | −0.348735 | − | 0.271613i | ||||
\(547\) | 6.06138 | + | 10.4986i | 0.259166 | + | 0.448889i | 0.966019 | − | 0.258472i | \(-0.0832190\pi\) |
−0.706853 | + | 0.707361i | \(0.749886\pi\) | |||||||
\(548\) | −4.07255 | −0.173971 | ||||||||
\(549\) | −3.79274 | − | 1.07514i | −0.161870 | − | 0.0458860i | ||||
\(550\) | 8.47536 | 0.361391 | ||||||||
\(551\) | 26.8742 | + | 46.5474i | 1.14488 | + | 1.98299i | ||||
\(552\) | 0.169340 | − | 1.21829i | 0.00720761 | − | 0.0518538i | ||||
\(553\) | 15.6859 | − | 27.1687i | 0.667030 | − | 1.15533i | ||||
\(554\) | 23.9085 | − | 41.4107i | 1.01577 | − | 1.75937i | ||||
\(555\) | −2.64797 | + | 19.0503i | −0.112400 | + | 0.808642i | ||||
\(556\) | 1.13874 | + | 1.97236i | 0.0482935 | + | 0.0836468i | ||||
\(557\) | 13.7918 | 0.584377 | 0.292189 | − | 0.956361i | \(-0.405617\pi\) | ||||
0.292189 | + | 0.956361i | \(0.405617\pi\) | |||||||
\(558\) | −0.271133 | + | 0.263420i | −0.0114780 | + | 0.0111515i | ||||
\(559\) | −2.91072 | −0.123110 | ||||||||
\(560\) | 6.40406 | + | 11.0922i | 0.270621 | + | 0.468729i | ||||
\(561\) | 1.78383 | + | 1.38934i | 0.0753132 | + | 0.0586579i | ||||
\(562\) | −2.99363 | + | 5.18512i | −0.126279 | + | 0.218721i | ||||
\(563\) | 5.37453 | − | 9.30896i | 0.226509 | − | 0.392326i | −0.730262 | − | 0.683167i | \(-0.760602\pi\) |
0.956771 | + | 0.290842i | \(0.0939352\pi\) | |||||||
\(564\) | 20.7605 | − | 8.42433i | 0.874174 | − | 0.354728i | ||||
\(565\) | −0.144808 | − | 0.250816i | −0.00609214 | − | 0.0105519i | ||||
\(566\) | 49.7457 | 2.09097 | ||||||||
\(567\) | 23.9864 | − | 12.9406i | 1.00734 | − | 0.543453i | ||||
\(568\) | −0.686931 | −0.0288230 | ||||||||
\(569\) | −5.63062 | − | 9.75252i | −0.236048 | − | 0.408847i | 0.723529 | − | 0.690294i | \(-0.242519\pi\) |
−0.959577 | + | 0.281447i | \(0.909186\pi\) | |||||||
\(570\) | 19.1180 | − | 7.75782i | 0.800764 | − | 0.324939i | ||||
\(571\) | −12.9908 | + | 22.5007i | −0.543648 | + | 0.941627i | 0.455042 | + | 0.890470i | \(0.349624\pi\) |
−0.998691 | + | 0.0511568i | \(0.983709\pi\) | |||||||
\(572\) | −4.04092 | + | 6.99908i | −0.168959 | + | 0.292646i | ||||
\(573\) | 28.0695 | + | 21.8620i | 1.17262 | + | 0.913299i | ||||
\(574\) | −24.4405 | − | 42.3322i | −1.02013 | − | 1.76691i | ||||
\(575\) | 2.95049 | 0.123044 | ||||||||
\(576\) | −15.0493 | + | 14.6212i | −0.627056 | + | 0.609218i | ||||
\(577\) | 5.83579 | 0.242947 | 0.121474 | − | 0.992595i | \(-0.461238\pi\) | ||||
0.121474 | + | 0.992595i | \(0.461238\pi\) | |||||||
\(578\) | −16.6477 | − | 28.8346i | −0.692452 | − | 1.19936i | ||||
\(579\) | −0.363955 | + | 2.61840i | −0.0151254 | + | 0.108817i | ||||
\(580\) | 8.34235 | − | 14.4494i | 0.346397 | − | 0.599977i | ||||
\(581\) | −10.7039 | + | 18.5396i | −0.444071 | + | 0.769153i | ||||
\(582\) | −2.74096 | + | 19.7193i | −0.113616 | + | 0.817392i | ||||
\(583\) | 25.4571 | + | 44.0929i | 1.05432 | + | 1.82614i | ||||
\(584\) | −2.71539 | −0.112364 | ||||||||
\(585\) | −2.88627 | − | 0.818185i | −0.119333 | − | 0.0338278i | ||||
\(586\) | 52.0101 | 2.14852 | ||||||||
\(587\) | 5.70440 | + | 9.88032i | 0.235446 | + | 0.407804i | 0.959402 | − | 0.282042i | \(-0.0910116\pi\) |
−0.723956 | + | 0.689846i | \(0.757678\pi\) | |||||||
\(588\) | 5.56929 | + | 4.33766i | 0.229674 | + | 0.178882i | ||||
\(589\) | 0.193539 | − | 0.335220i | 0.00797464 | − | 0.0138125i | ||||
\(590\) | −9.00979 | + | 15.6054i | −0.370927 | + | 0.642465i | ||||
\(591\) | 1.73011 | − | 0.702055i | 0.0711672 | − | 0.0288787i | ||||
\(592\) | 23.4832 | + | 40.6741i | 0.965154 | + | 1.67170i | ||||
\(593\) | −21.1795 | −0.869737 | −0.434869 | − | 0.900494i | \(-0.643205\pi\) | ||||
−0.434869 | + | 0.900494i | \(0.643205\pi\) | |||||||
\(594\) | −26.0470 | − | 35.5107i | −1.06872 | − | 1.45702i | ||||
\(595\) | −0.918494 | −0.0376546 | ||||||||
\(596\) | −5.51146 | − | 9.54613i | −0.225758 | − | 0.391025i | ||||
\(597\) | −3.21411 | + | 1.30424i | −0.131545 | + | 0.0533792i | ||||
\(598\) | −2.90506 | + | 5.03172i | −0.118797 | + | 0.205762i | ||||
\(599\) | 7.41622 | − | 12.8453i | 0.303019 | − | 0.524844i | −0.673800 | − | 0.738914i | \(-0.735339\pi\) |
0.976818 | + | 0.214071i | \(0.0686722\pi\) | |||||||
\(600\) | 0.328894 | + | 0.256160i | 0.0134270 | + | 0.0104577i | ||||
\(601\) | −6.60333 | − | 11.4373i | −0.269355 | − | 0.466537i | 0.699340 | − | 0.714789i | \(-0.253477\pi\) |
−0.968695 | + | 0.248252i | \(0.920144\pi\) | |||||||
\(602\) | 17.3575 | 0.707438 | ||||||||
\(603\) | −11.6291 | − | 46.0481i | −0.473576 | − | 1.87522i | ||||
\(604\) | −17.4717 | −0.710912 | ||||||||
\(605\) | 3.76198 | + | 6.51593i | 0.152946 | + | 0.264910i | ||||
\(606\) | −5.00047 | + | 35.9749i | −0.203130 | + | 1.46138i | ||||
\(607\) | 16.7152 | − | 28.9516i | 0.678451 | − | 1.17511i | −0.296997 | − | 0.954879i | \(-0.595985\pi\) |
0.975447 | − | 0.220233i | \(-0.0706816\pi\) | |||||||
\(608\) | 23.7348 | − | 41.1100i | 0.962575 | − | 1.66723i | ||||
\(609\) | −6.41632 | + | 46.1610i | −0.260003 | + | 1.87054i | ||||
\(610\) | −1.29383 | − | 2.24098i | −0.0523856 | − | 0.0907345i | ||||
\(611\) | 6.88864 | 0.278684 | ||||||||
\(612\) | −0.418366 | − | 1.65661i | −0.0169114 | − | 0.0669644i | ||||
\(613\) | −33.4817 | −1.35231 | −0.676157 | − | 0.736758i | \(-0.736356\pi\) | ||||
−0.676157 | + | 0.736758i | \(0.736356\pi\) | |||||||
\(614\) | −15.0881 | − | 26.1333i | −0.608904 | − | 1.05465i | ||||
\(615\) | −11.2011 | − | 8.72397i | −0.451670 | − | 0.351785i | ||||
\(616\) | −1.56849 | + | 2.71671i | −0.0631964 | + | 0.109459i | ||||
\(617\) | 19.0566 | − | 33.0071i | 0.767191 | − | 1.32881i | −0.171889 | − | 0.985116i | \(-0.554987\pi\) |
0.939080 | − | 0.343698i | \(-0.111680\pi\) | |||||||
\(618\) | −56.6244 | + | 22.9774i | −2.27777 | + | 0.924287i | ||||
\(619\) | −21.3997 | − | 37.0653i | −0.860126 | − | 1.48978i | −0.871807 | − | 0.489849i | \(-0.837052\pi\) |
0.0116814 | − | 0.999932i | \(-0.496282\pi\) | |||||||
\(620\) | −0.120158 | −0.00482566 | ||||||||
\(621\) | −9.06764 | − | 12.3622i | −0.363872 | − | 0.496077i | ||||
\(622\) | −5.73615 | −0.229999 | ||||||||
\(623\) | 6.46333 | + | 11.1948i | 0.258948 | + | 0.448511i | ||||
\(624\) | −6.78814 | + | 2.75454i | −0.271743 | + | 0.110270i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −10.7234 | + | 18.5735i | −0.428594 | + | 0.742347i | ||||
\(627\) | 35.5764 | + | 27.7088i | 1.42078 | + | 1.10658i | ||||
\(628\) | 17.1765 | + | 29.7506i | 0.685418 | + | 1.18718i | ||||
\(629\) | −3.36805 | −0.134293 | ||||||||
\(630\) | 17.2117 | + | 4.87908i | 0.685731 | + | 0.194387i | ||||
\(631\) | −34.5751 | −1.37641 | −0.688206 | − | 0.725516i | \(-0.741601\pi\) | ||||
−0.688206 | + | 0.725516i | \(0.741601\pi\) | |||||||
\(632\) | −1.24670 | − | 2.15935i | −0.0495912 | − | 0.0858945i | ||||
\(633\) | −0.0560908 | + | 0.403535i | −0.00222941 | + | 0.0160391i | ||||
\(634\) | −8.09807 | + | 14.0263i | −0.321616 | + | 0.557054i | ||||
\(635\) | 2.35204 | − | 4.07385i | 0.0933378 | − | 0.161666i | ||||
\(636\) | 5.29702 | − | 38.1084i | 0.210040 | − | 1.51110i | ||||
\(637\) | 1.08523 | + | 1.87967i | 0.0429983 | + | 0.0744753i | ||||
\(638\) | 75.3066 | 2.98142 | ||||||||
\(639\) | −6.14108 | + | 5.96638i | −0.242938 | + | 0.236026i | ||||
\(640\) | 1.92189 | 0.0759694 | ||||||||
\(641\) | 10.5943 | + | 18.3499i | 0.418452 | + | 0.724779i | 0.995784 | − | 0.0917298i | \(-0.0292396\pi\) |
−0.577332 | + | 0.816509i | \(0.695906\pi\) | |||||||
\(642\) | 3.01890 | + | 2.35128i | 0.119146 | + | 0.0927976i | ||||
\(643\) | −12.9509 | + | 22.4316i | −0.510732 | + | 0.884614i | 0.489190 | + | 0.872177i | \(0.337292\pi\) |
−0.999923 | + | 0.0124372i | \(0.996041\pi\) | |||||||
\(644\) | 8.38887 | − | 14.5299i | 0.330568 | − | 0.572560i | ||||
\(645\) | 4.67154 | − | 1.89565i | 0.183942 | − | 0.0746412i | ||||
\(646\) | 1.80648 | + | 3.12891i | 0.0710748 | + | 0.123105i | ||||
\(647\) | −31.6341 | −1.24366 | −0.621832 | − | 0.783151i | \(-0.713611\pi\) | ||||
−0.621832 | + | 0.783151i | \(0.713611\pi\) | |||||||
\(648\) | 0.0624993 | − | 2.16527i | 0.00245520 | − | 0.0850599i | ||||
\(649\) | −39.3840 | −1.54596 | ||||||||
\(650\) | −0.984603 | − | 1.70538i | −0.0386193 | − | 0.0668906i | ||||
\(651\) | 0.311003 | − | 0.126201i | 0.0121892 | − | 0.00494620i | ||||
\(652\) | 11.2220 | − | 19.4370i | 0.439487 | − | 0.761213i | ||||
\(653\) | 8.56340 | − | 14.8322i | 0.335112 | − | 0.580430i | −0.648395 | − | 0.761304i | \(-0.724559\pi\) |
0.983506 | + | 0.180874i | \(0.0578926\pi\) | |||||||
\(654\) | −38.0138 | − | 29.6071i | −1.48646 | − | 1.15773i | ||||
\(655\) | −11.0430 | − | 19.1271i | −0.431488 | − | 0.747358i | ||||
\(656\) | −34.6692 | −1.35361 | ||||||||
\(657\) | −24.2753 | + | 23.5847i | −0.947070 | + | 0.920128i | ||||
\(658\) | −41.0790 | −1.60143 | ||||||||
\(659\) | −19.3254 | − | 33.4726i | −0.752812 | − | 1.30391i | −0.946455 | − | 0.322836i | \(-0.895364\pi\) |
0.193643 | − | 0.981072i | \(-0.437970\pi\) | |||||||
\(660\) | 1.92720 | − | 13.8649i | 0.0750161 | − | 0.539689i | ||||
\(661\) | 22.1320 | − | 38.3338i | 0.860836 | − | 1.49101i | −0.0102873 | − | 0.999947i | \(-0.503275\pi\) |
0.871123 | − | 0.491064i | \(-0.163392\pi\) | |||||||
\(662\) | 17.7723 | − | 30.7825i | 0.690740 | − | 1.19640i | ||||
\(663\) | 0.0723264 | − | 0.520338i | 0.00280892 | − | 0.0202083i | ||||
\(664\) | 0.850737 | + | 1.47352i | 0.0330150 | + | 0.0571836i | ||||
\(665\) | −18.3183 | −0.710354 | ||||||||
\(666\) | 63.1141 | + | 17.8912i | 2.44562 | + | 0.693271i | ||||
\(667\) | 26.2161 | 1.01509 | ||||||||
\(668\) | −12.5152 | − | 21.6770i | −0.484227 | − | 0.838707i | ||||
\(669\) | 0.612386 | + | 0.476959i | 0.0236762 | + | 0.0184403i | ||||
\(670\) | 15.5875 | − | 26.9984i | 0.602199 | − | 1.04304i | ||||
\(671\) | 2.82782 | − | 4.89793i | 0.109167 | − | 0.189083i | ||||
\(672\) | 38.1401 | − | 15.4768i | 1.47129 | − | 0.597029i | ||||
\(673\) | 14.2308 | + | 24.6485i | 0.548557 | + | 0.950129i | 0.998374 | + | 0.0570078i | \(0.0181560\pi\) |
−0.449817 | + | 0.893121i | \(0.648511\pi\) | |||||||
\(674\) | −72.0817 | −2.77648 | ||||||||
\(675\) | 5.16517 | − | 0.566589i | 0.198807 | − | 0.0218080i | ||||
\(676\) | 1.87778 | 0.0722221 | ||||||||
\(677\) | 6.81855 | + | 11.8101i | 0.262058 | + | 0.453898i | 0.966789 | − | 0.255577i | \(-0.0822654\pi\) |
−0.704730 | + | 0.709475i | \(0.748932\pi\) | |||||||
\(678\) | −0.915326 | + | 0.371427i | −0.0351529 | + | 0.0142646i | ||||
\(679\) | 8.83814 | − | 15.3081i | 0.339177 | − | 0.587471i | ||||
\(680\) | −0.0365007 | + | 0.0632211i | −0.00139974 | + | 0.00242442i | ||||
\(681\) | −13.3855 | − | 10.4254i | −0.512935 | − | 0.399501i | ||||
\(682\) | −0.271167 | − | 0.469675i | −0.0103835 | − | 0.0179848i | ||||
\(683\) | 47.3362 | 1.81127 | 0.905636 | − | 0.424057i | \(-0.139394\pi\) | ||||
0.905636 | + | 0.424057i | \(0.139394\pi\) | |||||||
\(684\) | −8.34383 | − | 33.0392i | −0.319035 | − | 1.26328i | ||||
\(685\) | 2.16882 | 0.0828663 | ||||||||
\(686\) | 14.4000 | + | 24.9415i | 0.549795 | + | 0.952273i | ||||
\(687\) | 0.682548 | − | 4.91046i | 0.0260408 | − | 0.187346i | ||||
\(688\) | 6.15545 | − | 10.6616i | 0.234674 | − | 0.406468i | ||||
\(689\) | 5.91482 | − | 10.2448i | 0.225337 | − | 0.390295i | ||||
\(690\) | 1.38548 | − | 9.96760i | 0.0527445 | − | 0.379460i | ||||
\(691\) | −8.31169 | − | 14.3963i | −0.316191 | − | 0.547660i | 0.663499 | − | 0.748178i | \(-0.269071\pi\) |
−0.979690 | + | 0.200518i | \(0.935738\pi\) | |||||||
\(692\) | −31.1212 | −1.18305 | ||||||||
\(693\) | 9.57402 | + | 37.9104i | 0.363687 | + | 1.44010i | ||||
\(694\) | −11.4791 | −0.435743 | ||||||||
\(695\) | −0.606433 | − | 1.05037i | −0.0230033 | − | 0.0398429i | ||||
\(696\) | 2.92234 | + | 2.27607i | 0.110771 | + | 0.0862742i | ||||
\(697\) | 1.24310 | − | 2.15310i | 0.0470856 | − | 0.0815546i | ||||
\(698\) | 2.97067 | − | 5.14534i | 0.112441 | − | 0.194754i | ||||
\(699\) | 24.8882 | − | 10.0993i | 0.941358 | − | 0.381991i | ||||
\(700\) | 2.84321 | + | 4.92459i | 0.107463 | + | 0.186132i | ||||
\(701\) | 21.7166 | 0.820223 | 0.410111 | − | 0.912035i | \(-0.365490\pi\) | ||||
0.410111 | + | 0.912035i | \(0.365490\pi\) | |||||||
\(702\) | −4.11939 | + | 9.36646i | −0.155476 | + | 0.353514i | ||||
\(703\) | −67.1719 | −2.53343 | ||||||||
\(704\) | −15.0512 | − | 26.0695i | −0.567264 | − | 0.982530i | ||||
\(705\) | −11.0559 | + | 4.48633i | −0.416389 | + | 0.168965i | ||||
\(706\) | −9.21770 | + | 15.9655i | −0.346913 | + | 0.600870i | ||||
\(707\) | 16.1239 | − | 27.9273i | 0.606400 | − | 1.05032i | ||||
\(708\) | 23.4802 | + | 18.2876i | 0.882441 | + | 0.687291i | ||||
\(709\) | 20.1493 | + | 34.8996i | 0.756723 | + | 1.31068i | 0.944513 | + | 0.328474i | \(0.106534\pi\) |
−0.187790 | + | 0.982209i | \(0.560132\pi\) | |||||||
\(710\) | −5.62022 | −0.210923 | ||||||||
\(711\) | −29.9006 | − | 8.47606i | −1.12136 | − | 0.317877i | ||||
\(712\) | 1.02740 | 0.0385036 | ||||||||
\(713\) | −0.0944002 | − | 0.163506i | −0.00353531 | − | 0.00612334i | ||||
\(714\) | −0.431304 | + | 3.10294i | −0.0161411 | + | 0.116124i | ||||
\(715\) | 2.15197 | − | 3.72733i | 0.0804792 | − | 0.139394i | ||||
\(716\) | −12.7112 | + | 22.0165i | −0.475041 | + | 0.822795i | ||||
\(717\) | −1.73625 | + | 12.4911i | −0.0648415 | + | 0.466490i | ||||
\(718\) | 5.14531 | + | 8.91194i | 0.192021 | + | 0.332591i | ||||
\(719\) | 42.5521 | 1.58693 | 0.793463 | − | 0.608619i | \(-0.208276\pi\) | ||||
0.793463 | + | 0.608619i | \(0.208276\pi\) | |||||||
\(720\) | 9.10066 | − | 8.84177i | 0.339162 | − | 0.329513i | ||||
\(721\) | 54.2559 | 2.02060 | ||||||||
\(722\) | 17.3206 | + | 30.0002i | 0.644608 | + | 1.11649i | ||||
\(723\) | 15.0158 | + | 11.6951i | 0.558444 | + | 0.434946i | ||||
\(724\) | 3.37345 | − | 5.84299i | 0.125373 | − | 0.217153i | ||||
\(725\) | −4.44268 | + | 7.69494i | −0.164997 | + | 0.285783i | ||||
\(726\) | 23.7792 | − | 9.64930i | 0.882530 | − | 0.358119i | ||||
\(727\) | 11.3584 | + | 19.6733i | 0.421259 | + | 0.729641i | 0.996063 | − | 0.0886497i | \(-0.0282552\pi\) |
−0.574804 | + | 0.818291i | \(0.694922\pi\) | |||||||
\(728\) | 0.728863 | 0.0270135 | ||||||||
\(729\) | −18.2479 | − | 19.9001i | −0.675847 | − | 0.737042i | ||||
\(730\) | −22.2164 | −0.822265 | ||||||||
\(731\) | 0.441419 | + | 0.764559i | 0.0163265 | + | 0.0282782i | ||||
\(732\) | −3.96022 | + | 1.60701i | −0.146374 | + | 0.0593967i | ||||
\(733\) | 14.2542 | − | 24.6889i | 0.526490 | − | 0.911907i | −0.473034 | − | 0.881044i | \(-0.656841\pi\) |
0.999524 | − | 0.0308627i | \(-0.00982547\pi\) | |||||||
\(734\) | −4.23540 | + | 7.33593i | −0.156332 | + | 0.270774i | ||||
\(735\) | −2.96590 | − | 2.31000i | −0.109399 | − | 0.0852056i | ||||
\(736\) | −11.5769 | − | 20.0517i | −0.426728 | − | 0.739115i | ||||
\(737\) | 68.1370 | 2.50986 | ||||||||
\(738\) | −34.7318 | + | 33.7438i | −1.27850 | + | 1.24213i | ||||
\(739\) | −10.2174 | −0.375852 | −0.187926 | − | 0.982183i | \(-0.560177\pi\) | ||||
−0.187926 | + | 0.982183i | \(0.560177\pi\) | |||||||
\(740\) | 10.4258 | + | 18.0581i | 0.383261 | + | 0.663828i | ||||
\(741\) | 1.44247 | − | 10.3776i | 0.0529904 | − | 0.381229i | ||||
\(742\) | −35.2719 | + | 61.0927i | −1.29487 | + | 2.24278i | ||||
\(743\) | −26.3337 | + | 45.6113i | −0.966090 | + | 1.67332i | −0.259433 | + | 0.965761i | \(0.583536\pi\) |
−0.706657 | + | 0.707556i | \(0.749798\pi\) | |||||||
\(744\) | 0.00367261 | − | 0.0264219i | 0.000134645 | − | 0.000968675i | ||||
\(745\) | 2.93510 | + | 5.08374i | 0.107534 | + | 0.186254i | ||||
\(746\) | −52.2431 | −1.91276 | ||||||||
\(747\) | 20.4038 | + | 5.78397i | 0.746538 | + | 0.211624i | ||||
\(748\) | 2.45127 | 0.0896273 | ||||||||
\(749\) | −1.69870 | − | 2.94224i | −0.0620693 | − | 0.107507i | ||||
\(750\) | 2.69089 | + | 2.09581i | 0.0982575 | + | 0.0765281i | ||||
\(751\) | −0.0215941 | + | 0.0374020i | −0.000787978 | + | 0.00136482i | −0.866419 | − | 0.499317i | \(-0.833584\pi\) |
0.865631 | + | 0.500682i | \(0.166917\pi\) | |||||||
\(752\) | −14.5678 | + | 25.2321i | −0.531232 | + | 0.920121i | ||||
\(753\) | −15.3086 | + | 6.21203i | −0.557876 | + | 0.226379i | ||||
\(754\) | −8.74855 | − | 15.1529i | −0.318603 | − | 0.551837i | ||||
\(755\) | 9.30445 | 0.338624 | ||||||||
\(756\) | 11.8955 | − | 27.0473i | 0.432633 | − | 0.983699i | ||||
\(757\) | −20.9410 | −0.761113 | −0.380557 | − | 0.924758i | \(-0.624268\pi\) | ||||
−0.380557 | + | 0.924758i | \(0.624268\pi\) | |||||||
\(758\) | −3.42730 | − | 5.93626i | −0.124485 | − | 0.215615i | ||||
\(759\) | 20.3808 | − | 8.27026i | 0.739777 | − | 0.300192i | ||||
\(760\) | −0.727965 | + | 1.26087i | −0.0264061 | + | 0.0457367i | ||||
\(761\) | −7.61100 | + | 13.1826i | −0.275899 | + | 0.477870i | −0.970361 | − | 0.241658i | \(-0.922309\pi\) |
0.694463 | + | 0.719529i | \(0.255642\pi\) | |||||||
\(762\) | −12.6582 | − | 9.85885i | −0.458557 | − | 0.357148i | ||||
\(763\) | 21.3900 | + | 37.0485i | 0.774369 | + | 1.34125i | ||||
\(764\) | 38.5721 | 1.39549 | ||||||||
\(765\) | 0.222799 | + | 0.882219i | 0.00805531 | + | 0.0318967i | ||||
\(766\) | −48.5165 | −1.75297 | ||||||||
\(767\) | 4.57534 | + | 7.92472i | 0.165206 | + | 0.286145i | ||||
\(768\) | 4.23813 | − | 30.4904i | 0.152930 | − | 1.10023i | ||||
\(769\) | 8.12917 | − | 14.0801i | 0.293145 | − | 0.507743i | −0.681406 | − | 0.731905i | \(-0.738631\pi\) |
0.974552 | + | 0.224163i | \(0.0719647\pi\) | |||||||
\(770\) | −12.8329 | + | 22.2272i | −0.462464 | + | 0.801012i | ||||
\(771\) | 0.179107 | − | 1.28855i | 0.00645039 | − | 0.0464061i | ||||
\(772\) | 1.43300 | + | 2.48202i | 0.0515746 | + | 0.0893299i | ||||
\(773\) | 14.6825 | 0.528093 | 0.264047 | − | 0.964510i | \(-0.414943\pi\) | ||||
0.264047 | + | 0.964510i | \(0.414943\pi\) | |||||||
\(774\) | −4.21040 | − | 16.6720i | −0.151340 | − | 0.599262i | ||||
\(775\) | 0.0639895 | 0.00229857 | ||||||||
\(776\) | −0.702451 | − | 1.21668i | −0.0252165 | − | 0.0436763i | ||||
\(777\) | −45.9513 | − | 35.7893i | −1.64849 | − | 1.28393i | ||||
\(778\) | −18.1355 | + | 31.4116i | −0.650188 | + | 1.12616i | ||||
\(779\) | 24.7921 | − | 42.9412i | 0.888270 | − | 1.53853i | ||||
\(780\) | −3.01373 | + | 1.22293i | −0.107909 | + | 0.0437880i | ||||
\(781\) | −6.14185 | − | 10.6380i | −0.219773 | − | 0.380657i | ||||
\(782\) | 1.76224 | 0.0630177 | ||||||||
\(783\) | 45.8944 | − | 5.03435i | 1.64013 | − | 0.179913i | ||||
\(784\) | −9.17997 | −0.327856 | ||||||||
\(785\) | −9.14727 | − | 15.8435i | −0.326480 | − | 0.565480i | ||||
\(786\) | −69.8025 | + | 28.3249i | −2.48977 | + | 1.01032i | ||||
\(787\) | 9.34140 | − | 16.1798i | 0.332985 | − | 0.576747i | −0.650111 | − | 0.759840i | \(-0.725277\pi\) |
0.983096 | + | 0.183093i | \(0.0586108\pi\) | |||||||
\(788\) | 1.01211 | − | 1.75302i | 0.0360548 | − | 0.0624488i | ||||
\(789\) | 28.4742 | + | 22.1772i | 1.01371 | + | 0.789529i | ||||
\(790\) | −10.2001 | − | 17.6671i | −0.362903 | − | 0.628566i | ||||
\(791\) | 0.877040 | 0.0311839 | ||||||||
\(792\) | 2.98989 | + | 0.847557i | 0.106241 | + | 0.0301166i | ||||
\(793\) | −1.31406 | −0.0466637 | ||||||||
\(794\) | 14.8888 | + | 25.7882i | 0.528385 | + | 0.915190i | ||||
\(795\) | −2.82090 | + | 20.2944i | −0.100047 | + | 0.719769i | ||||
\(796\) | −1.88024 | + | 3.25668i | −0.0666435 | + | 0.115430i | ||||
\(797\) | 11.1340 | − | 19.2846i | 0.394385 | − | 0.683095i | −0.598637 | − | 0.801020i | \(-0.704291\pi\) |
0.993022 | + | 0.117925i | \(0.0376243\pi\) | |||||||
\(798\) | −8.60187 | + | 61.8845i | −0.304503 | + | 2.19069i | ||||
\(799\) | −1.04468 | − | 1.80944i | −0.0369582 | − | 0.0640134i | ||||
\(800\) | 7.84741 | 0.277448 | ||||||||
\(801\) | 9.18488 | − | 8.92359i | 0.324532 | − | 0.315299i | ||||
\(802\) | −0.542150 | −0.0191440 | ||||||||
\(803\) | −24.2783 | − | 42.0513i | −0.856764 | − | 1.48396i | ||||
\(804\) | −40.6223 | − | 31.6388i | −1.43264 | − | 1.11581i | ||||
\(805\) | −4.46745 | + | 7.73785i | −0.157457 | + | 0.272723i | ||||
\(806\) | −0.0630043 | + | 0.109127i | −0.00221923 | + | 0.00384382i | ||||
\(807\) | 24.9063 | − | 10.1066i | 0.876742 | − | 0.355770i | ||||
\(808\) | −1.28152 | − | 2.21965i | −0.0450836 | − | 0.0780870i | ||||
\(809\) | −10.6028 | −0.372776 | −0.186388 | − | 0.982476i | \(-0.559678\pi\) | ||||
−0.186388 | + | 0.982476i | \(0.559678\pi\) | |||||||
\(810\) | 0.511347 | − | 17.7155i | 0.0179669 | − | 0.622459i | ||||
\(811\) | −29.8215 | −1.04718 | −0.523588 | − | 0.851972i | \(-0.675407\pi\) | ||||
−0.523588 | + | 0.851972i | \(0.675407\pi\) | |||||||
\(812\) | 25.2629 | + | 43.7567i | 0.886555 | + | 1.53556i | ||||
\(813\) | −1.57770 | + | 0.640210i | −0.0553323 | + | 0.0224531i | ||||
\(814\) | −47.0571 | + | 81.5053i | −1.64935 | + | 2.85676i | ||||
\(815\) | −5.97621 | + | 10.3511i | −0.209338 | + | 0.362583i | ||||
\(816\) | 1.75298 | + | 1.36531i | 0.0613664 | + | 0.0477954i | ||||
\(817\) | 8.80359 | + | 15.2483i | 0.307999 | + | 0.533469i | ||||
\(818\) | 24.7185 | 0.864262 | ||||||||
\(819\) | 6.51596 | − | 6.33059i | 0.227686 | − | 0.221209i | ||||
\(820\) | −15.3921 | −0.537515 | ||||||||
\(821\) | −9.61358 | − | 16.6512i | −0.335516 | − | 0.581131i | 0.648067 | − | 0.761583i | \(-0.275577\pi\) |
−0.983584 | + | 0.180451i | \(0.942244\pi\) | |||||||
\(822\) | 1.01843 | − | 7.32689i | 0.0355218 | − | 0.255555i | ||||
\(823\) | −6.02944 | + | 10.4433i | −0.210173 | + | 0.364030i | −0.951769 | − | 0.306817i | \(-0.900736\pi\) |
0.741595 | + | 0.670847i | \(0.234069\pi\) | |||||||
\(824\) | 2.15612 | − | 3.73450i | 0.0751118 | − | 0.130098i | ||||
\(825\) | −1.02632 | + | 7.38367i | −0.0357319 | + | 0.257066i | ||||
\(826\) | −27.2841 | − | 47.2575i | −0.949336 | − | 1.64430i | ||||
\(827\) | 12.5315 | 0.435765 | 0.217882 | − | 0.975975i | \(-0.430085\pi\) | ||||
0.217882 | + | 0.975975i | \(0.430085\pi\) | |||||||
\(828\) | −15.9910 | − | 4.53303i | −0.555725 | − | 0.157534i | ||||
\(829\) | −44.7564 | −1.55445 | −0.777227 | − | 0.629220i | \(-0.783374\pi\) | ||||
−0.777227 | + | 0.629220i | \(0.783374\pi\) | |||||||
\(830\) | 6.96043 | + | 12.0558i | 0.241600 | + | 0.418463i | ||||
\(831\) | 33.1815 | + | 25.8435i | 1.15105 | + | 0.896501i | ||||
\(832\) | −3.49707 | + | 6.05711i | −0.121239 | + | 0.209993i | ||||
\(833\) | 0.329156 | − | 0.570115i | 0.0114046 | − | 0.0197533i | ||||
\(834\) | −3.83323 | + | 1.55547i | −0.132734 | + | 0.0538616i | ||||
\(835\) | 6.66491 | + | 11.5440i | 0.230649 | + | 0.399495i | ||||
\(836\) | 48.8878 | 1.69082 | ||||||||
\(837\) | −0.196657 | − | 0.268108i | −0.00679745 | − | 0.00926716i | ||||
\(838\) | −45.0361 | −1.55575 | ||||||||
\(839\) | 9.95639 | + | 17.2450i | 0.343733 | + | 0.595363i | 0.985123 | − | 0.171852i | \(-0.0549752\pi\) |
−0.641390 | + | 0.767215i | \(0.721642\pi\) | |||||||
\(840\) | −1.16979 | + | 0.474684i | −0.0403615 | + | 0.0163781i | ||||
\(841\) | −24.9748 | + | 43.2575i | −0.861198 | + | 1.49164i | ||||
\(842\) | −24.5912 | + | 42.5932i | −0.847469 | + | 1.46786i | ||||
\(843\) | −4.15472 | − | 3.23592i | −0.143096 | − | 0.111451i | ||||
\(844\) | 0.220846 | + | 0.382516i | 0.00760183 | + | 0.0131668i | ||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 9.96452 | + | 39.4567i | 0.342587 | + | 1.35655i | ||||
\(847\) | −22.7846 | −0.782888 | ||||||||
\(848\) | 25.0168 | + | 43.3304i | 0.859081 | + | 1.48797i | ||||
\(849\) | −6.02393 | + | 43.3380i | −0.206741 | + | 1.48736i | ||||
\(850\) | −0.298636 | + | 0.517253i | −0.0102431 | + | 0.0177416i | ||||
\(851\) | −16.3818 | + | 28.3741i | −0.561561 | + | 0.972652i | ||||
\(852\) | −1.27797 | + | 9.19414i | −0.0437827 | + | 0.314986i | ||||
\(853\) | 1.60989 | + | 2.78841i | 0.0551215 | + | 0.0954732i | 0.892269 | − | 0.451503i | \(-0.149112\pi\) |
−0.837148 | + | 0.546976i | \(0.815779\pi\) | |||||||
\(854\) | 7.83614 | 0.268147 | ||||||||
\(855\) | 4.44347 | + | 17.5949i | 0.151963 | + | 0.601731i | ||||
\(856\) | −0.270024 | −0.00922924 | ||||||||
\(857\) | 1.58737 | + | 2.74941i | 0.0542236 | + | 0.0939180i | 0.891863 | − | 0.452305i | \(-0.149398\pi\) |
−0.837640 | + | 0.546223i | \(0.816065\pi\) | |||||||
\(858\) | −11.5815 | − | 9.02025i | −0.395385 | − | 0.307946i | ||||
\(859\) | −12.8326 | + | 22.2268i | −0.437844 | + | 0.758368i | −0.997523 | − | 0.0703416i | \(-0.977591\pi\) |
0.559679 | + | 0.828709i | \(0.310924\pi\) | |||||||
\(860\) | 2.73284 | − | 4.73341i | 0.0931889 | − | 0.161408i | ||||
\(861\) | 39.8391 | − | 16.1662i | 1.35771 | − | 0.550942i | ||||
\(862\) | −33.9306 | − | 58.7696i | −1.15568 | − | 2.00170i | ||||
\(863\) | −40.8808 | −1.39160 | −0.695799 | − | 0.718236i | \(-0.744950\pi\) | ||||
−0.695799 | + | 0.718236i | \(0.744950\pi\) | |||||||
\(864\) | −24.1172 | − | 32.8797i | −0.820483 | − | 1.11859i | ||||
\(865\) | 16.5734 | 0.563514 | ||||||||
\(866\) | 15.4173 | + | 26.7036i | 0.523902 | + | 0.907424i | ||||
\(867\) | 27.1364 | − | 11.0116i | 0.921602 | − | 0.373974i | ||||
\(868\) | 0.181936 | − | 0.315122i | 0.00617530 | − | 0.0106959i | ||||
\(869\) | 22.2936 | − | 38.6136i | 0.756257 | − | 1.30988i | ||||
\(870\) | 23.9095 | + | 18.6220i | 0.810609 | + | 0.631345i | ||||
\(871\) | −7.91564 | − | 13.7103i | −0.268211 | − | 0.464555i | ||||
\(872\) | 3.40013 | 0.115143 | ||||||||
\(873\) | −16.8474 | − | 4.77580i | −0.570198 | − | 0.161636i | ||||
\(874\) | 35.1460 | 1.18883 | ||||||||
\(875\) | −1.51414 | − | 2.62256i | −0.0511872 | − | 0.0886589i | ||||
\(876\) | −5.05175 | + | 36.3438i | −0.170683 | + | 1.22794i | ||||
\(877\) | −24.7475 | + | 42.8639i | −0.835663 | + | 1.44741i | 0.0578261 | + | 0.998327i | \(0.481583\pi\) |
−0.893489 | + | 0.449084i | \(0.851750\pi\) | |||||||
\(878\) | −28.4814 | + | 49.3311i | −0.961199 | + | 1.66485i | ||||
\(879\) | −6.29815 | + | 45.3108i | −0.212431 | + | 1.52830i | ||||
\(880\) | 9.10179 | + | 15.7648i | 0.306821 | + | 0.531430i | ||||
\(881\) | −46.0194 | −1.55043 | −0.775216 | − | 0.631696i | \(-0.782359\pi\) | ||||
−0.775216 | + | 0.631696i | \(0.782359\pi\) | |||||||
\(882\) | −9.19656 | + | 8.93494i | −0.309664 | + | 0.300855i | ||||
\(883\) | −23.7208 | −0.798267 | −0.399134 | − | 0.916893i | \(-0.630689\pi\) | ||||
−0.399134 | + | 0.916893i | \(0.630689\pi\) | |||||||
\(884\) | −0.284770 | − | 0.493236i | −0.00957785 | − | 0.0165893i | ||||
\(885\) | −12.5043 | − | 9.73899i | −0.420327 | − | 0.327372i | ||||
\(886\) | −24.8132 | + | 42.9777i | −0.833616 | + | 1.44387i | ||||
\(887\) | −27.1668 | + | 47.0542i | −0.912170 | + | 1.57993i | −0.101178 | + | 0.994868i | \(0.532261\pi\) |
−0.810992 | + | 0.585057i | \(0.801072\pi\) | |||||||
\(888\) | −4.28952 | + | 1.74063i | −0.143947 | + | 0.0584117i | ||||
\(889\) | 7.12262 | + | 12.3367i | 0.238885 | + | 0.413761i | ||||
\(890\) | 8.40586 | 0.281765 | ||||||||
\(891\) | 34.0908 | − | 18.3918i | 1.14208 | − | 0.616149i | ||||
\(892\) | 0.841519 | 0.0281761 | ||||||||
\(893\) | −20.8350 | − | 36.0873i | −0.697216 | − | 1.20761i | ||||
\(894\) | 18.5526 | − | 7.52840i | 0.620492 | − | 0.251787i | ||||
\(895\) | 6.76930 | − | 11.7248i | 0.226273 | − | 0.391916i | ||||
\(896\) | −2.91001 | + | 5.04028i | −0.0972166 | + | 0.168384i | ||||
\(897\) | −4.03180 | − | 3.14018i | −0.134618 | − | 0.104848i | ||||
\(898\) | −21.2455 | − | 36.7983i | −0.708972 | − | 1.22798i | ||||
\(899\) | 0.568569 | 0.0189628 | ||||||||
\(900\) | 4.04042 | − | 3.92548i | 0.134681 | − | 0.130849i | ||||
\(901\) | −3.58800 | −0.119534 | ||||||||
\(902\) | −34.7362 | − | 60.1648i | −1.15659 | − | 2.00327i | ||||
\(903\) | −2.10190 | + | 15.1217i | −0.0699468 | + | 0.503219i | ||||
\(904\) | 0.0348533 | − | 0.0603678i | 0.00115920 | − | 0.00200780i | ||||
\(905\) | −1.79651 | + | 3.11165i | −0.0597182 | + | 0.103435i | ||||
\(906\) | 4.36916 | − | 31.4331i | 0.145156 | − | 1.04430i | ||||
\(907\) | −21.4464 | − | 37.1462i | −0.712116 | − | 1.23342i | −0.964061 | − | 0.265679i | \(-0.914404\pi\) |
0.251946 | − | 0.967741i | \(-0.418930\pi\) | |||||||
\(908\) | −18.3939 | −0.610423 | ||||||||
\(909\) | −30.7355 | − | 8.71274i | −1.01943 | − | 0.288983i | ||||
\(910\) | 5.96330 | 0.197682 | ||||||||
\(911\) | −13.5606 | − | 23.4877i | −0.449284 | − | 0.778183i | 0.549056 | − | 0.835786i | \(-0.314988\pi\) |
−0.998340 | + | 0.0576032i | \(0.981654\pi\) | |||||||
\(912\) | 34.9611 | + | 27.2296i | 1.15768 | + | 0.901661i | ||||
\(913\) | −15.2129 | + | 26.3495i | −0.503473 | + | 0.872040i | ||||
\(914\) | 0.486961 | − | 0.843441i | 0.0161072 | − | 0.0278986i | ||||
\(915\) | 2.10900 | − | 0.855803i | 0.0697213 | − | 0.0282920i | ||||
\(916\) | −2.68739 | − | 4.65470i | −0.0887939 | − | 0.153796i | ||||
\(917\) | 66.8828 | 2.20866 | ||||||||
\(918\) | 3.08501 | − | 0.338408i | 0.101820 | − | 0.0111691i | ||||
\(919\) | 2.27072 | 0.0749043 | 0.0374522 | − | 0.999298i | \(-0.488076\pi\) | ||||
0.0374522 | + | 0.999298i | \(0.488076\pi\) | |||||||
\(920\) | 0.355071 | + | 0.615000i | 0.0117063 | + | 0.0202760i | ||||
\(921\) | 24.5942 | − | 9.97999i | 0.810406 | − | 0.328852i | ||||
\(922\) | 13.4237 | − | 23.2505i | 0.442085 | − | 0.765714i | ||||
\(923\) | −1.42703 | + | 2.47168i | −0.0469712 | + | 0.0813565i | ||||
\(924\) | 33.4435 | + | 26.0475i | 1.10021 | + | 0.856901i | ||||
\(925\) | −5.55223 | − | 9.61674i | −0.182556 | − | 0.316197i | ||||
\(926\) | −40.8721 | −1.34314 | ||||||||
\(927\) | −13.1608 | − | 52.1131i | −0.432259 | − | 1.71162i | ||||
\(928\) | 69.7270 | 2.28890 | ||||||||
\(929\) | −0.235938 | − | 0.408657i | −0.00774088 | − | 0.0134076i | 0.862129 | − | 0.506689i | \(-0.169131\pi\) |
−0.869870 | + | 0.493281i | \(0.835797\pi\) | |||||||
\(930\) | 0.0300480 | − | 0.216175i | 0.000985314 | − | 0.00708865i | ||||
\(931\) | 6.56465 | − | 11.3703i | 0.215148 | − | 0.372647i | ||||
\(932\) | 14.5595 | − | 25.2178i | 0.476912 | − | 0.826036i | ||||
\(933\) | 0.694617 | − | 4.99729i | 0.0227407 | − | 0.163604i | ||||
\(934\) | −34.4242 | − | 59.6244i | −1.12639 | − | 1.95097i | ||||
\(935\) | −1.30541 | −0.0426915 | ||||||||
\(936\) | −0.176800 | − | 0.700078i | −0.00577889 | − | 0.0228828i | ||||
\(937\) | 44.6044 | 1.45716 | 0.728581 | − | 0.684960i | \(-0.240180\pi\) | ||||
0.728581 | + | 0.684960i | \(0.240180\pi\) | |||||||
\(938\) | 47.2033 | + | 81.7586i | 1.54124 | + | 2.66951i | ||||
\(939\) | −14.8826 | − | 11.5913i | −0.485674 | − | 0.378268i | ||||
\(940\) | −6.46765 | + | 11.2023i | −0.210952 | + | 0.365379i | ||||
\(941\) | −11.2513 | + | 19.4878i | −0.366781 | + | 0.635283i | −0.989060 | − | 0.147512i | \(-0.952873\pi\) |
0.622279 | + | 0.782795i | \(0.286207\pi\) | |||||||
\(942\) | −57.8194 | + | 23.4623i | −1.88386 | + | 0.764444i | ||||
\(943\) | −12.0926 | − | 20.9449i | −0.393788 | − | 0.682060i | ||||
\(944\) | −38.7029 | −1.25967 | ||||||||
\(945\) | −6.33486 | + | 14.4039i | −0.206073 | + | 0.468558i | ||||
\(946\) | 24.6694 | 0.802070 | ||||||||
\(947\) | 7.13395 | + | 12.3564i | 0.231822 | + | 0.401528i | 0.958344 | − | 0.285615i | \(-0.0921979\pi\) |
−0.726522 | + | 0.687143i | \(0.758865\pi\) | |||||||
\(948\) | −31.2210 | + | 12.6691i | −1.01401 | + | 0.411472i | ||||
\(949\) | −5.64095 | + | 9.77041i | −0.183113 | + | 0.317161i | ||||
\(950\) | −5.95595 | + | 10.3160i | −0.193237 | + | 0.334696i | ||||
\(951\) | −11.2389 | − | 8.75348i | −0.364448 | − | 0.283851i | ||||
\(952\) | −0.110534 | − | 0.191451i | −0.00358243 | − | 0.00620496i | ||||
\(953\) | −49.4934 | −1.60325 | −0.801624 | − | 0.597829i | \(-0.796030\pi\) | ||||
−0.801624 | + | 0.597829i | \(0.796030\pi\) | |||||||
\(954\) | 67.2358 | + | 19.0596i | 2.17684 | + | 0.617078i | ||||
\(955\) | −20.5414 | −0.664704 | ||||||||
\(956\) | 6.83612 | + | 11.8405i | 0.221096 | + | 0.382950i | ||||
\(957\) | −9.11922 | + | 65.6065i | −0.294782 | + | 2.12076i | ||||
\(958\) | 30.1046 | − | 52.1427i | 0.972636 | − | 1.68466i | ||||
\(959\) | −3.28389 | + | 5.68786i | −0.106042 | + | 0.183671i | ||||
\(960\) | 1.66783 | − | 11.9989i | 0.0538289 | − | 0.387262i | ||||
\(961\) | 15.4980 | + | 26.8432i | 0.499934 | + | 0.865911i | ||||
\(962\) | 21.8670 | 0.705020 | ||||||||
\(963\) | −2.41399 | + | 2.34531i | −0.0777897 | + | 0.0755767i | ||||
\(964\) | 20.6342 | 0.664583 | ||||||||
\(965\) | −0.763135 | − | 1.32179i | −0.0245662 | − | 0.0425499i | ||||
\(966\) | 24.0429 | + | 18.7258i | 0.773566 | + | 0.602494i | ||||
\(967\) | −14.6823 | + | 25.4305i | −0.472151 | + | 0.817789i | −0.999492 | − | 0.0318645i | \(-0.989855\pi\) |
0.527342 | + | 0.849653i | \(0.323189\pi\) | |||||||
\(968\) | −0.905454 | + | 1.56829i | −0.0291024 | + | 0.0504068i | ||||
\(969\) | −2.94463 | + | 1.19489i | −0.0945953 | + | 0.0383855i | ||||
\(970\) | −5.74720 | − | 9.95445i | −0.184532 | − | 0.319618i | ||||
\(971\) | −7.22467 | −0.231851 | −0.115925 | − | 0.993258i | \(-0.536983\pi\) | ||||
−0.115925 | + | 0.993258i | \(0.536983\pi\) | |||||||
\(972\) | −28.8645 | − | 4.86481i | −0.925830 | − | 0.156039i | ||||
\(973\) | 3.67289 | 0.117748 | ||||||||
\(974\) | 37.6871 | + | 65.2760i | 1.20757 | + | 2.09158i | ||||
\(975\) | 1.60495 | − | 0.651266i | 0.0513994 | − | 0.0208572i | ||||
\(976\) | 2.77892 | − | 4.81323i | 0.0889510 | − | 0.154068i | ||||
\(977\) | 20.3574 | − | 35.2601i | 0.651292 | − | 1.12807i | −0.331518 | − | 0.943449i | \(-0.607561\pi\) |
0.982810 | − | 0.184622i | \(-0.0591060\pi\) | |||||||
\(978\) | 32.1627 | + | 25.0500i | 1.02845 | + | 0.801011i | ||||
\(979\) | 9.18602 | + | 15.9107i | 0.293586 | + | 0.508507i | ||||
\(980\) | −4.07563 | −0.130191 | ||||||||
\(981\) | 30.3968 | − | 29.5320i | 0.970494 | − | 0.942886i | ||||
\(982\) | −13.0115 | −0.415214 | ||||||||
\(983\) | 17.2643 | + | 29.9027i | 0.550646 | + | 0.953747i | 0.998228 | + | 0.0595044i | \(0.0189520\pi\) |
−0.447582 | + | 0.894243i | \(0.647715\pi\) | |||||||
\(984\) | 0.470458 | − | 3.38462i | 0.0149976 | − | 0.107898i | ||||
\(985\) | −0.538993 | + | 0.933563i | −0.0171737 | + | 0.0297458i | ||||
\(986\) | −2.65349 | + | 4.59597i | −0.0845042 | + | 0.146366i | ||||
\(987\) | 4.97445 | − | 35.7877i | 0.158338 | − | 1.13914i | ||||
\(988\) | −5.67942 | − | 9.83704i | −0.180686 | − | 0.312958i | ||||
\(989\) | 8.58804 | 0.273084 | ||||||||
\(990\) | 24.4622 | + | 6.93441i | 0.777460 | + | 0.220390i | ||||
\(991\) | −14.9325 | −0.474346 | −0.237173 | − | 0.971467i | \(-0.576221\pi\) | ||||
−0.237173 | + | 0.971467i | \(0.576221\pi\) | |||||||
\(992\) | −0.251076 | − | 0.434876i | −0.00797167 | − | 0.0138073i | ||||
\(993\) | 24.6653 | + | 19.2107i | 0.782731 | + | 0.609632i | ||||
\(994\) | 8.50980 | − | 14.7394i | 0.269914 | − | 0.467505i | ||||
\(995\) | 1.00131 | − | 1.73433i | 0.0317438 | − | 0.0549819i | ||||
\(996\) | 21.3049 | − | 8.64523i | 0.675070 | − | 0.273935i | ||||
\(997\) | −9.74539 | − | 16.8795i | −0.308640 | − | 0.534580i | 0.669425 | − | 0.742879i | \(-0.266540\pi\) |
−0.978065 | + | 0.208300i | \(0.933207\pi\) | |||||||
\(998\) | 43.4161 | 1.37431 | ||||||||
\(999\) | −23.2295 | + | 52.8179i | −0.734948 | + | 1.67109i |
(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 | 585.2.i.e.391.7 | yes | 16 | |
3.2 | odd | 2 | 1755.2.i.f.1171.2 | 16 | |||
9.2 | odd | 6 | 1755.2.i.f.586.2 | 16 | |||
9.4 | even | 3 | 5265.2.a.bf.1.2 | 8 | |||
9.5 | odd | 6 | 5265.2.a.ba.1.7 | 8 | |||
9.7 | even | 3 | inner | 585.2.i.e.196.7 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.i.e.196.7 | ✓ | 16 | 9.7 | even | 3 | inner | |
585.2.i.e.391.7 | yes | 16 | 1.1 | even | 1 | trivial | |
1755.2.i.f.586.2 | 16 | 9.2 | odd | 6 | |||
1755.2.i.f.1171.2 | 16 | 3.2 | odd | 2 | |||
5265.2.a.ba.1.7 | 8 | 9.5 | odd | 6 | |||
5265.2.a.bf.1.2 | 8 | 9.4 | even | 3 |