Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [57,3,Mod(11,57)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(57, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("57.11");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 57 = 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 57.h (of order \(6\), 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: | \(1.55313750685\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 44x^{14} + 686x^{12} + 4668x^{10} + 13913x^{8} + 18672x^{6} + 10976x^{4} + 2816x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 26.3 | ||
Root | \(2.98614i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 57.26 |
Dual form | 57.3.h.b.11.3 |
$q$-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 \(\left(\mathbb{Z}/57\mathbb{Z}\right)^\times\).
\(n\) | \(20\) | \(40\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00605 | + | 1.15819i | −1.00302 | + | 0.579096i | −0.909141 | − | 0.416487i | \(-0.863261\pi\) |
−0.0938821 | + | 0.995583i | \(0.529928\pi\) | |||||||
\(3\) | −1.67757 | + | 2.48712i | −0.559190 | + | 0.829040i | ||||
\(4\) | 0.682817 | − | 1.18267i | 0.170704 | − | 0.295668i | ||||
\(5\) | 2.24545 | − | 1.29641i | 0.449089 | − | 0.259282i | −0.258356 | − | 0.966050i | \(-0.583181\pi\) |
0.707446 | + | 0.706768i | \(0.249847\pi\) | |||||||
\(6\) | 0.484722 | − | 6.93222i | 0.0807869 | − | 1.15537i | ||||
\(7\) | −12.9625 | −1.85178 | −0.925890 | − | 0.377793i | \(-0.876683\pi\) | ||||
−0.925890 | + | 0.377793i | \(0.876683\pi\) | |||||||
\(8\) | − | 6.10220i | − | 0.762776i | ||||||
\(9\) | −3.37152 | − | 8.34463i | −0.374614 | − | 0.927181i | ||||
\(10\) | −3.00298 | + | 5.20132i | −0.300298 | + | 0.520132i | ||||
\(11\) | 14.5113i | 1.31920i | 0.751615 | + | 0.659602i | \(0.229275\pi\) | ||||
−0.751615 | + | 0.659602i | \(0.770725\pi\) | |||||||
\(12\) | 1.79598 | + | 3.68226i | 0.149665 | + | 0.306855i | ||||
\(13\) | 2.52007 | − | 4.36489i | 0.193851 | − | 0.335761i | −0.752672 | − | 0.658396i | \(-0.771235\pi\) |
0.946523 | + | 0.322635i | \(0.104569\pi\) | |||||||
\(14\) | 26.0033 | − | 15.0130i | 1.85738 | − | 1.07236i | ||||
\(15\) | −0.542568 | + | 7.75951i | −0.0361712 | + | 0.517301i | ||||
\(16\) | 9.79879 | + | 16.9720i | 0.612424 | + | 1.06075i | ||||
\(17\) | −15.9210 | + | 9.19202i | −0.936532 | + | 0.540707i | −0.888871 | − | 0.458157i | \(-0.848510\pi\) |
−0.0476602 | + | 0.998864i | \(0.515176\pi\) | |||||||
\(18\) | 16.4281 | + | 12.8348i | 0.912673 | + | 0.713047i | ||||
\(19\) | 2.86357 | + | 18.7830i | 0.150714 | + | 0.988577i | ||||
\(20\) | − | 3.54084i | − | 0.177042i | ||||||
\(21\) | 21.7454 | − | 32.2392i | 1.03550 | − | 1.53520i | ||||
\(22\) | −16.8068 | − | 29.1103i | −0.763946 | − | 1.32319i | ||||
\(23\) | −8.57128 | − | 4.94863i | −0.372664 | − | 0.215158i | 0.301957 | − | 0.953321i | \(-0.402360\pi\) |
−0.674622 | + | 0.738164i | \(0.735693\pi\) | |||||||
\(24\) | 15.1769 | + | 10.2369i | 0.632371 | + | 0.426536i | ||||
\(25\) | −9.13865 | + | 15.8286i | −0.365546 | + | 0.633144i | ||||
\(26\) | 11.6749i | 0.449034i | ||||||||
\(27\) | 26.4100 | + | 5.61331i | 0.978150 | + | 0.207900i | ||||
\(28\) | −8.85098 | + | 15.3304i | −0.316106 | + | 0.547513i | ||||
\(29\) | 7.48634 | + | 4.32224i | 0.258150 | + | 0.149043i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
−0.365340 | + | 0.930874i | \(0.619047\pi\) | |||||||
\(30\) | −7.89858 | − | 16.1943i | −0.263286 | − | 0.539811i | ||||
\(31\) | −13.3199 | −0.429673 | −0.214836 | − | 0.976650i | \(-0.568922\pi\) | ||||
−0.214836 | + | 0.976650i | \(0.568922\pi\) | |||||||
\(32\) | −18.1750 | − | 10.4933i | −0.567969 | − | 0.327917i | ||||
\(33\) | −36.0912 | − | 24.3436i | −1.09367 | − | 0.737686i | ||||
\(34\) | 21.2922 | − | 36.8792i | 0.626242 | − | 1.08468i | ||||
\(35\) | −29.1065 | + | 16.8047i | −0.831615 | + | 0.480133i | ||||
\(36\) | −12.1711 | − | 1.71044i | −0.338086 | − | 0.0475123i | ||||
\(37\) | 7.28478 | 0.196886 | 0.0984429 | − | 0.995143i | \(-0.468614\pi\) | ||||
0.0984429 | + | 0.995143i | \(0.468614\pi\) | |||||||
\(38\) | −27.4987 | − | 34.3630i | −0.723651 | − | 0.904288i | ||||
\(39\) | 6.62840 | + | 13.5901i | 0.169959 | + | 0.348464i | ||||
\(40\) | −7.91095 | − | 13.7022i | −0.197774 | − | 0.342554i | ||||
\(41\) | −11.5014 | + | 6.64034i | −0.280522 | + | 0.161960i | −0.633660 | − | 0.773612i | \(-0.718448\pi\) |
0.353138 | + | 0.935571i | \(0.385115\pi\) | |||||||
\(42\) | −6.28318 | + | 89.8587i | −0.149600 | + | 2.13949i | ||||
\(43\) | −19.6988 | − | 34.1193i | −0.458111 | − | 0.793471i | 0.540750 | − | 0.841183i | \(-0.318140\pi\) |
−0.998861 | + | 0.0477119i | \(0.984807\pi\) | |||||||
\(44\) | 17.1621 | + | 9.90852i | 0.390047 | + | 0.225194i | ||||
\(45\) | −18.3886 | − | 14.3665i | −0.408636 | − | 0.319257i | ||||
\(46\) | 22.9259 | 0.498388 | ||||||||
\(47\) | 13.5960 | + | 7.84964i | 0.289276 | + | 0.167014i | 0.637615 | − | 0.770355i | \(-0.279921\pi\) |
−0.348339 | + | 0.937369i | \(0.613254\pi\) | |||||||
\(48\) | −58.6495 | − | 4.10095i | −1.22187 | − | 0.0854364i | ||||
\(49\) | 119.025 | 2.42909 | ||||||||
\(50\) | − | 42.3372i | − | 0.846744i | ||||||
\(51\) | 3.84700 | − | 55.0178i | 0.0754315 | − | 1.07878i | ||||
\(52\) | −3.44149 | − | 5.96083i | −0.0661825 | − | 0.114631i | ||||
\(53\) | 41.6779 | + | 24.0628i | 0.786376 | + | 0.454014i | 0.838685 | − | 0.544617i | \(-0.183325\pi\) |
−0.0523092 | + | 0.998631i | \(0.516658\pi\) | |||||||
\(54\) | −59.4811 | + | 19.3273i | −1.10150 | + | 0.357914i | ||||
\(55\) | 18.8125 | + | 32.5842i | 0.342046 | + | 0.592441i | ||||
\(56\) | 79.0996i | 1.41249i | ||||||||
\(57\) | −51.5193 | − | 24.3877i | −0.903848 | − | 0.427854i | ||||
\(58\) | −20.0239 | −0.345240 | ||||||||
\(59\) | 64.8363 | − | 37.4333i | 1.09892 | − | 0.634462i | 0.162983 | − | 0.986629i | \(-0.447888\pi\) |
0.935937 | + | 0.352167i | \(0.114555\pi\) | |||||||
\(60\) | 8.80649 | + | 5.94000i | 0.146775 | + | 0.0990000i | ||||
\(61\) | −5.14506 | + | 8.91150i | −0.0843452 | + | 0.146090i | −0.905112 | − | 0.425173i | \(-0.860213\pi\) |
0.820767 | + | 0.571263i | \(0.193547\pi\) | |||||||
\(62\) | 26.7203 | − | 15.4269i | 0.430972 | − | 0.248822i | ||||
\(63\) | 43.7032 | + | 108.167i | 0.693702 | + | 1.71694i | ||||
\(64\) | −29.7771 | −0.465267 | ||||||||
\(65\) | − | 13.0682i | − | 0.201049i | ||||||
\(66\) | 100.595 | + | 7.03392i | 1.52417 | + | 0.106575i | ||||
\(67\) | −39.7483 | + | 68.8462i | −0.593259 | + | 1.02755i | 0.400531 | + | 0.916283i | \(0.368826\pi\) |
−0.993790 | + | 0.111271i | \(0.964508\pi\) | |||||||
\(68\) | 25.1058i | 0.369204i | ||||||||
\(69\) | 26.6868 | − | 13.0161i | 0.386765 | − | 0.188640i | ||||
\(70\) | 38.9260 | − | 67.4218i | 0.556086 | − | 0.963169i | ||||
\(71\) | 9.59520 | − | 5.53979i | 0.135144 | − | 0.0780252i | −0.430904 | − | 0.902398i | \(-0.641805\pi\) |
0.566048 | + | 0.824373i | \(0.308472\pi\) | |||||||
\(72\) | −50.9206 | + | 20.5737i | −0.707231 | + | 0.285746i | ||||
\(73\) | −4.59001 | − | 7.95013i | −0.0628768 | − | 0.108906i | 0.832873 | − | 0.553464i | \(-0.186694\pi\) |
−0.895750 | + | 0.444558i | \(0.853361\pi\) | |||||||
\(74\) | −14.6136 | + | 8.43717i | −0.197481 | + | 0.114016i | ||||
\(75\) | −24.0369 | − | 49.2825i | −0.320492 | − | 0.657100i | ||||
\(76\) | 24.1694 | + | 9.43865i | 0.318019 | + | 0.124193i | ||||
\(77\) | − | 188.101i | − | 2.44288i | ||||||
\(78\) | −29.0368 | − | 19.5854i | −0.372267 | − | 0.251095i | ||||
\(79\) | −54.2297 | − | 93.9286i | −0.686452 | − | 1.18897i | −0.972978 | − | 0.230897i | \(-0.925834\pi\) |
0.286526 | − | 0.958072i | \(-0.407499\pi\) | |||||||
\(80\) | 44.0053 | + | 25.4065i | 0.550066 | + | 0.317581i | ||||
\(81\) | −58.2657 | + | 56.2682i | −0.719329 | + | 0.694669i | ||||
\(82\) | 15.3816 | − | 26.6417i | 0.187580 | − | 0.324899i | ||||
\(83\) | 102.691i | 1.23724i | 0.785692 | + | 0.618618i | \(0.212307\pi\) | ||||
−0.785692 | + | 0.618618i | \(0.787693\pi\) | |||||||
\(84\) | −23.2803 | − | 47.7312i | −0.277146 | − | 0.568228i | ||||
\(85\) | −23.8332 | + | 41.2804i | −0.280391 | + | 0.485651i | ||||
\(86\) | 79.0333 | + | 45.6299i | 0.918992 | + | 0.530580i | ||||
\(87\) | −23.3088 | + | 11.3686i | −0.267917 | + | 0.130673i | ||||
\(88\) | 88.5506 | 1.00626 | ||||||||
\(89\) | −81.8385 | − | 47.2495i | −0.919534 | − | 0.530893i | −0.0360475 | − | 0.999350i | \(-0.511477\pi\) |
−0.883486 | + | 0.468457i | \(0.844810\pi\) | |||||||
\(90\) | 53.5277 | + | 7.52241i | 0.594752 | + | 0.0835823i | ||||
\(91\) | −32.6663 | + | 56.5797i | −0.358970 | + | 0.621755i | ||||
\(92\) | −11.7052 | + | 6.75802i | −0.127231 | + | 0.0734567i | ||||
\(93\) | 22.3450 | − | 33.1281i | 0.240269 | − | 0.356216i | ||||
\(94\) | −36.3656 | −0.386868 | ||||||||
\(95\) | 30.7804 | + | 38.4638i | 0.324004 | + | 0.404882i | ||||
\(96\) | 56.5880 | − | 27.6001i | 0.589459 | − | 0.287501i | ||||
\(97\) | 21.4597 | + | 37.1693i | 0.221234 | + | 0.383188i | 0.955183 | − | 0.296016i | \(-0.0956582\pi\) |
−0.733949 | + | 0.679205i | \(0.762325\pi\) | |||||||
\(98\) | −238.770 | + | 137.854i | −2.43643 | + | 1.40668i | ||||
\(99\) | 121.091 | − | 48.9250i | 1.22314 | − | 0.494192i | ||||
\(100\) | 12.4800 | + | 21.6161i | 0.124800 | + | 0.216161i | ||||
\(101\) | −168.914 | − | 97.5224i | −1.67241 | − | 0.965568i | −0.966282 | − | 0.257486i | \(-0.917106\pi\) |
−0.706131 | − | 0.708081i | \(-0.749561\pi\) | |||||||
\(102\) | 56.0038 | + | 114.824i | 0.549057 | + | 1.12572i | ||||
\(103\) | 79.0368 | 0.767348 | 0.383674 | − | 0.923469i | \(-0.374659\pi\) | ||||
0.383674 | + | 0.923469i | \(0.374659\pi\) | |||||||
\(104\) | −26.6354 | − | 15.3780i | −0.256110 | − | 0.147865i | ||||
\(105\) | 7.03301 | − | 100.582i | 0.0669811 | − | 0.957927i | ||||
\(106\) | −111.477 | −1.05167 | ||||||||
\(107\) | 66.8587i | 0.624848i | 0.949943 | + | 0.312424i | \(0.101141\pi\) | ||||
−0.949943 | + | 0.312424i | \(0.898859\pi\) | |||||||
\(108\) | 24.6719 | − | 27.4016i | 0.228444 | − | 0.253718i | ||||
\(109\) | 63.5369 | + | 110.049i | 0.582907 | + | 1.00962i | 0.995133 | + | 0.0985431i | \(0.0314182\pi\) |
−0.412226 | + | 0.911082i | \(0.635248\pi\) | |||||||
\(110\) | −75.4776 | − | 43.5770i | −0.686160 | − | 0.396155i | ||||
\(111\) | −12.2207 | + | 18.1181i | −0.110097 | + | 0.163226i | ||||
\(112\) | −127.016 | − | 219.999i | −1.13408 | − | 1.96428i | ||||
\(113\) | − | 2.22172i | − | 0.0196612i | −0.999952 | − | 0.00983062i | \(-0.996871\pi\) | ||
0.999952 | − | 0.00983062i | \(-0.00312924\pi\) | |||||||
\(114\) | 131.596 | − | 10.7464i | 1.15435 | − | 0.0942669i | ||||
\(115\) | −25.6618 | −0.223146 | ||||||||
\(116\) | 10.2236 | − | 5.90260i | 0.0881345 | − | 0.0508845i | ||||
\(117\) | −44.9198 | − | 6.31272i | −0.383930 | − | 0.0539549i | ||||
\(118\) | −86.7098 | + | 150.186i | −0.734829 | + | 1.27276i | ||||
\(119\) | 206.376 | − | 119.151i | 1.73425 | − | 1.00127i | ||||
\(120\) | 47.3501 | + | 3.31086i | 0.394584 | + | 0.0275905i | ||||
\(121\) | −89.5764 | −0.740301 | ||||||||
\(122\) | − | 23.8359i | − | 0.195376i | ||||||
\(123\) | 2.77909 | − | 39.7450i | 0.0225942 | − | 0.323130i | ||||
\(124\) | −9.09502 | + | 15.7530i | −0.0733469 | + | 0.127041i | ||||
\(125\) | 112.210i | 0.897681i | ||||||||
\(126\) | −212.949 | − | 166.371i | −1.69007 | − | 1.32041i | ||||
\(127\) | −38.2095 | + | 66.1809i | −0.300863 | + | 0.521109i | −0.976332 | − | 0.216279i | \(-0.930608\pi\) |
0.675469 | + | 0.737388i | \(0.263941\pi\) | |||||||
\(128\) | 132.434 | − | 76.4610i | 1.03464 | − | 0.597351i | ||||
\(129\) | 117.905 | + | 8.24425i | 0.913990 | + | 0.0639089i | ||||
\(130\) | 15.1354 | + | 26.2153i | 0.116426 | + | 0.201657i | ||||
\(131\) | −113.246 | + | 65.3825i | −0.864472 | + | 0.499103i | −0.865507 | − | 0.500896i | \(-0.833004\pi\) |
0.00103497 | + | 0.999999i | \(0.499671\pi\) | |||||||
\(132\) | −53.4342 | + | 26.0619i | −0.404805 | + | 0.197438i | ||||
\(133\) | −37.1190 | − | 243.473i | −0.279090 | − | 1.83063i | ||||
\(134\) | − | 184.145i | − | 1.37422i | ||||||
\(135\) | 66.5795 | − | 21.6338i | 0.493182 | − | 0.160251i | ||||
\(136\) | 56.0916 | + | 97.1534i | 0.412438 | + | 0.714363i | ||||
\(137\) | 155.716 | + | 89.9026i | 1.13661 | + | 0.656223i | 0.945589 | − | 0.325363i | \(-0.105486\pi\) |
0.191022 | + | 0.981586i | \(0.438820\pi\) | |||||||
\(138\) | −38.4597 | + | 57.0193i | −0.278694 | + | 0.413184i | ||||
\(139\) | 19.7717 | − | 34.2456i | 0.142242 | − | 0.246371i | −0.786098 | − | 0.618102i | \(-0.787902\pi\) |
0.928341 | + | 0.371730i | \(0.121235\pi\) | |||||||
\(140\) | 45.8980i | 0.327843i | ||||||||
\(141\) | −42.3312 | + | 20.6465i | −0.300221 | + | 0.146429i | ||||
\(142\) | −12.8323 | + | 22.2262i | −0.0903682 | + | 0.156522i | ||||
\(143\) | 63.3400 | + | 36.5693i | 0.442937 | + | 0.255730i | ||||
\(144\) | 108.588 | − | 138.989i | 0.754085 | − | 0.965200i | ||||
\(145\) | 22.4136 | 0.154576 | ||||||||
\(146\) | 18.4155 | + | 10.6322i | 0.126134 | + | 0.0728234i | ||||
\(147\) | −199.673 | + | 296.030i | −1.35832 | + | 2.01381i | ||||
\(148\) | 4.97417 | − | 8.61551i | 0.0336092 | − | 0.0582129i | ||||
\(149\) | 73.6580 | − | 42.5264i | 0.494349 | − | 0.285412i | −0.232028 | − | 0.972709i | \(-0.574536\pi\) |
0.726377 | + | 0.687297i | \(0.241203\pi\) | |||||||
\(150\) | 105.298 | + | 71.0236i | 0.701985 | + | 0.473491i | ||||
\(151\) | 109.565 | 0.725597 | 0.362799 | − | 0.931868i | \(-0.381821\pi\) | ||||
0.362799 | + | 0.931868i | \(0.381821\pi\) | |||||||
\(152\) | 114.618 | − | 17.4741i | 0.754063 | − | 0.114961i | ||||
\(153\) | 130.382 | + | 101.864i | 0.852171 | + | 0.665778i | ||||
\(154\) | 217.858 | + | 377.340i | 1.41466 | + | 2.45026i | ||||
\(155\) | −29.9090 | + | 17.2680i | −0.192961 | + | 0.111406i | ||||
\(156\) | 20.5986 | + | 1.44032i | 0.132043 | + | 0.00923281i | ||||
\(157\) | 17.5747 | + | 30.4402i | 0.111941 | + | 0.193887i | 0.916553 | − | 0.399914i | \(-0.130960\pi\) |
−0.804612 | + | 0.593801i | \(0.797627\pi\) | |||||||
\(158\) | 217.575 | + | 125.617i | 1.37705 | + | 0.795043i | ||||
\(159\) | −129.765 | + | 63.2910i | −0.816129 | + | 0.398057i | ||||
\(160\) | −54.4147 | −0.340092 | ||||||||
\(161\) | 111.105 | + | 64.1464i | 0.690092 | + | 0.398425i | ||||
\(162\) | 51.7143 | − | 180.360i | 0.319224 | − | 1.11333i | ||||
\(163\) | −245.638 | −1.50698 | −0.753491 | − | 0.657458i | \(-0.771632\pi\) | ||||
−0.753491 | + | 0.657458i | \(0.771632\pi\) | |||||||
\(164\) | 18.1365i | 0.110589i | ||||||||
\(165\) | −112.600 | − | 7.87334i | −0.682425 | − | 0.0477172i | ||||
\(166\) | −118.935 | − | 206.002i | −0.716479 | − | 1.24098i | ||||
\(167\) | −149.554 | − | 86.3451i | −0.895533 | − | 0.517036i | −0.0197849 | − | 0.999804i | \(-0.506298\pi\) |
−0.875748 | + | 0.482768i | \(0.839631\pi\) | |||||||
\(168\) | −196.730 | − | 132.695i | −1.17101 | − | 0.789851i | ||||
\(169\) | 71.7985 | + | 124.359i | 0.424843 | + | 0.735850i | ||||
\(170\) | − | 110.414i | − | 0.649493i | ||||||
\(171\) | 147.082 | − | 87.2227i | 0.860130 | − | 0.510074i | ||||
\(172\) | −53.8026 | −0.312806 | ||||||||
\(173\) | −181.949 | + | 105.048i | −1.05173 | + | 0.607216i | −0.923133 | − | 0.384481i | \(-0.874380\pi\) |
−0.128596 | + | 0.991697i | \(0.541047\pi\) | |||||||
\(174\) | 33.5916 | − | 49.8019i | 0.193055 | − | 0.286218i | ||||
\(175\) | 118.459 | − | 205.178i | 0.676910 | − | 1.17244i | ||||
\(176\) | −246.285 | + | 142.193i | −1.39935 | + | 0.807913i | ||||
\(177\) | −15.6664 | + | 224.053i | −0.0885108 | + | 1.26583i | ||||
\(178\) | 218.896 | 1.22975 | ||||||||
\(179\) | − | 284.096i | − | 1.58713i | −0.608485 | − | 0.793565i | \(-0.708223\pi\) | ||
0.608485 | − | 0.793565i | \(-0.291777\pi\) | |||||||
\(180\) | −29.5470 | + | 11.9380i | −0.164150 | + | 0.0663223i | ||||
\(181\) | 98.2666 | − | 170.203i | 0.542909 | − | 0.940346i | −0.455826 | − | 0.890069i | \(-0.650656\pi\) |
0.998735 | − | 0.0502775i | \(-0.0160106\pi\) | |||||||
\(182\) | − | 151.335i | − | 0.831513i | ||||||
\(183\) | −13.5328 | − | 27.7460i | −0.0739496 | − | 0.151618i | ||||
\(184\) | −30.1976 | + | 52.3037i | −0.164117 | + | 0.284259i | ||||
\(185\) | 16.3576 | − | 9.44405i | 0.0884194 | − | 0.0510489i | ||||
\(186\) | −6.45642 | + | 92.3362i | −0.0347119 | + | 0.496431i | ||||
\(187\) | −133.388 | − | 231.034i | −0.713303 | − | 1.23548i | ||||
\(188\) | 18.5671 | − | 10.7197i | 0.0987613 | − | 0.0570198i | ||||
\(189\) | −342.339 | − | 72.7623i | −1.81132 | − | 0.384986i | ||||
\(190\) | −106.295 | − | 41.5106i | −0.559450 | − | 0.218477i | ||||
\(191\) | 220.669i | 1.15534i | 0.816271 | + | 0.577669i | \(0.196037\pi\) | ||||
−0.816271 | + | 0.577669i | \(0.803963\pi\) | |||||||
\(192\) | 49.9531 | − | 74.0591i | 0.260172 | − | 0.385725i | ||||
\(193\) | −22.0264 | − | 38.1508i | −0.114126 | − | 0.197673i | 0.803304 | − | 0.595569i | \(-0.203074\pi\) |
−0.917430 | + | 0.397897i | \(0.869740\pi\) | |||||||
\(194\) | −86.0983 | − | 49.7089i | −0.443806 | − | 0.256231i | ||||
\(195\) | 32.5021 | + | 21.9227i | 0.166677 | + | 0.112424i | ||||
\(196\) | 81.2725 | − | 140.768i | 0.414655 | − | 0.718204i | ||||
\(197\) | − | 18.3774i | − | 0.0932864i | −0.998912 | − | 0.0466432i | \(-0.985148\pi\) | ||
0.998912 | − | 0.0466432i | \(-0.0148524\pi\) | |||||||
\(198\) | −186.250 | + | 238.392i | −0.940655 | + | 1.20400i | ||||
\(199\) | −122.441 | + | 212.074i | −0.615282 | + | 1.06570i | 0.375053 | + | 0.927003i | \(0.377625\pi\) |
−0.990335 | + | 0.138697i | \(0.955709\pi\) | |||||||
\(200\) | 96.5893 | + | 55.7659i | 0.482947 | + | 0.278829i | ||||
\(201\) | −104.548 | − | 214.353i | −0.520139 | − | 1.06643i | ||||
\(202\) | 451.798 | 2.23663 | ||||||||
\(203\) | −97.0414 | − | 56.0269i | −0.478037 | − | 0.275995i | ||||
\(204\) | −62.4412 | − | 42.1168i | −0.306084 | − | 0.206455i | ||||
\(205\) | −17.2172 | + | 29.8211i | −0.0839864 | + | 0.145469i | ||||
\(206\) | −158.552 | + | 91.5398i | −0.769668 | + | 0.444368i | ||||
\(207\) | −12.3962 | + | 88.2086i | −0.0598851 | + | 0.426128i | ||||
\(208\) | 98.7745 | 0.474877 | ||||||||
\(209\) | −272.564 | + | 41.5540i | −1.30414 | + | 0.198823i | ||||
\(210\) | 102.385 | + | 209.918i | 0.487548 | + | 0.999612i | ||||
\(211\) | −77.6926 | − | 134.568i | −0.368211 | − | 0.637761i | 0.621075 | − | 0.783751i | \(-0.286696\pi\) |
−0.989286 | + | 0.145991i | \(0.953363\pi\) | |||||||
\(212\) | 56.9168 | − | 32.8609i | 0.268475 | − | 0.155004i | ||||
\(213\) | −2.31849 | + | 33.1578i | −0.0108849 | + | 0.155670i | ||||
\(214\) | −77.4352 | − | 134.122i | −0.361847 | − | 0.626737i | ||||
\(215\) | −88.4651 | − | 51.0753i | −0.411465 | − | 0.237560i | ||||
\(216\) | 34.2536 | − | 161.160i | 0.158581 | − | 0.746109i | ||||
\(217\) | 172.658 | 0.795659 | ||||||||
\(218\) | −254.916 | − | 147.176i | −1.16934 | − | 0.675118i | ||||
\(219\) | 27.4730 | + | 1.92099i | 0.125447 | + | 0.00877165i | ||||
\(220\) | 51.3820 | 0.233555 | ||||||||
\(221\) | 92.6580i | 0.419267i | ||||||||
\(222\) | 3.53109 | − | 50.4997i | 0.0159058 | − | 0.227476i | ||||
\(223\) | 33.4142 | + | 57.8751i | 0.149839 | + | 0.259529i | 0.931168 | − | 0.364590i | \(-0.118791\pi\) |
−0.781329 | + | 0.624120i | \(0.785458\pi\) | |||||||
\(224\) | 235.593 | + | 136.020i | 1.05175 | + | 0.607230i | ||||
\(225\) | 162.895 | + | 22.8921i | 0.723978 | + | 0.101743i | ||||
\(226\) | 2.57318 | + | 4.45688i | 0.0113857 | + | 0.0197207i | ||||
\(227\) | 279.790i | 1.23255i | 0.787530 | + | 0.616277i | \(0.211360\pi\) | ||||
−0.787530 | + | 0.616277i | \(0.788640\pi\) | |||||||
\(228\) | −64.0209 | + | 44.2782i | −0.280793 | + | 0.194203i | ||||
\(229\) | 59.6619 | 0.260533 | 0.130266 | − | 0.991479i | \(-0.458417\pi\) | ||||
0.130266 | + | 0.991479i | \(0.458417\pi\) | |||||||
\(230\) | 51.4788 | − | 29.7213i | 0.223821 | − | 0.129223i | ||||
\(231\) | 467.831 | + | 315.553i | 2.02524 | + | 1.36603i | ||||
\(232\) | 26.3752 | − | 45.6832i | 0.113686 | − | 0.196910i | ||||
\(233\) | 190.157 | − | 109.787i | 0.816124 | − | 0.471189i | −0.0329541 | − | 0.999457i | \(-0.510492\pi\) |
0.849078 | + | 0.528268i | \(0.177158\pi\) | |||||||
\(234\) | 97.4226 | − | 39.3622i | 0.416336 | − | 0.168214i | ||||
\(235\) | 40.7054 | 0.173214 | ||||||||
\(236\) | − | 102.240i | − | 0.433221i | ||||||
\(237\) | 324.586 | + | 22.6960i | 1.36956 | + | 0.0957637i | ||||
\(238\) | −276.000 | + | 478.046i | −1.15966 | + | 2.00859i | ||||
\(239\) | 236.467i | 0.989403i | 0.869063 | + | 0.494701i | \(0.164723\pi\) | ||||
−0.869063 | + | 0.494701i | \(0.835277\pi\) | |||||||
\(240\) | −137.011 | + | 66.8253i | −0.570879 | + | 0.278439i | ||||
\(241\) | −131.676 | + | 228.069i | −0.546373 | + | 0.946346i | 0.452146 | + | 0.891944i | \(0.350659\pi\) |
−0.998519 | + | 0.0544020i | \(0.982675\pi\) | |||||||
\(242\) | 179.694 | − | 103.747i | 0.742539 | − | 0.428705i | ||||
\(243\) | −42.2011 | − | 239.307i | −0.173667 | − | 0.984804i | ||||
\(244\) | 7.02626 | + | 12.1698i | 0.0287962 | + | 0.0498764i | ||||
\(245\) | 267.265 | − | 154.306i | 1.09088 | − | 0.629819i | ||||
\(246\) | 40.4574 | + | 82.9491i | 0.164461 | + | 0.337191i | ||||
\(247\) | 89.2019 | + | 34.8352i | 0.361141 | + | 0.141033i | ||||
\(248\) | 81.2805i | 0.327744i | ||||||||
\(249\) | −255.404 | − | 172.271i | −1.02572 | − | 0.691850i | ||||
\(250\) | −129.961 | − | 225.099i | −0.519844 | − | 0.900395i | ||||
\(251\) | −264.789 | − | 152.876i | −1.05493 | − | 0.609067i | −0.130908 | − | 0.991395i | \(-0.541789\pi\) |
−0.924027 | + | 0.382328i | \(0.875123\pi\) | |||||||
\(252\) | 157.767 | + | 22.1715i | 0.626061 | + | 0.0879822i | ||||
\(253\) | 71.8108 | − | 124.380i | 0.283837 | − | 0.491621i | ||||
\(254\) | − | 177.016i | − | 0.696913i | ||||||
\(255\) | −62.6873 | − | 128.527i | −0.245833 | − | 0.504026i | ||||
\(256\) | −117.559 | + | 203.618i | −0.459214 | + | 0.795382i | ||||
\(257\) | −4.93952 | − | 2.85183i | −0.0192199 | − | 0.0110966i | 0.490359 | − | 0.871520i | \(-0.336866\pi\) |
−0.509579 | + | 0.860424i | \(0.670199\pi\) | |||||||
\(258\) | −246.071 | + | 120.018i | −0.953763 | + | 0.465186i | ||||
\(259\) | −94.4286 | −0.364589 | ||||||||
\(260\) | −15.4554 | − | 8.92316i | −0.0594437 | − | 0.0343198i | ||||
\(261\) | 10.8271 | − | 77.0433i | 0.0414833 | − | 0.295185i | ||||
\(262\) | 151.451 | − | 262.321i | 0.578058 | − | 1.00122i | ||||
\(263\) | 446.059 | − | 257.532i | 1.69604 | − | 0.979210i | 0.746595 | − | 0.665278i | \(-0.231687\pi\) |
0.949446 | − | 0.313931i | \(-0.101646\pi\) | |||||||
\(264\) | −148.550 | + | 220.236i | −0.562689 | + | 0.834227i | ||||
\(265\) | 124.781 | 0.470871 | ||||||||
\(266\) | 356.451 | + | 445.428i | 1.34004 | + | 1.67454i | ||||
\(267\) | 254.805 | − | 124.278i | 0.954325 | − | 0.465460i | ||||
\(268\) | 54.2817 | + | 94.0186i | 0.202544 | + | 0.350816i | ||||
\(269\) | −10.6070 | + | 6.12396i | −0.0394313 | + | 0.0227657i | −0.519586 | − | 0.854418i | \(-0.673914\pi\) |
0.480155 | + | 0.877184i | \(0.340580\pi\) | |||||||
\(270\) | −108.505 | + | 120.510i | −0.401872 | + | 0.446335i | ||||
\(271\) | −68.2273 | − | 118.173i | −0.251761 | − | 0.436063i | 0.712249 | − | 0.701926i | \(-0.247676\pi\) |
−0.964011 | + | 0.265863i | \(0.914343\pi\) | |||||||
\(272\) | −312.014 | − | 180.141i | −1.14711 | − | 0.662284i | ||||
\(273\) | −85.9204 | − | 176.161i | −0.314727 | − | 0.645279i | ||||
\(274\) | −416.498 | −1.52006 | ||||||||
\(275\) | −229.693 | − | 132.613i | −0.835246 | − | 0.482230i | ||||
\(276\) | 2.82834 | − | 40.4493i | 0.0102476 | − | 0.146556i | ||||
\(277\) | 161.723 | 0.583838 | 0.291919 | − | 0.956443i | \(-0.405706\pi\) | ||||
0.291919 | + | 0.956443i | \(0.405706\pi\) | |||||||
\(278\) | 91.5977i | 0.329488i | ||||||||
\(279\) | 44.9082 | + | 111.149i | 0.160961 | + | 0.398384i | ||||
\(280\) | 102.545 | + | 177.614i | 0.366234 | + | 0.634335i | ||||
\(281\) | 228.910 | + | 132.161i | 0.814626 | + | 0.470324i | 0.848560 | − | 0.529100i | \(-0.177470\pi\) |
−0.0339340 | + | 0.999424i | \(0.510804\pi\) | |||||||
\(282\) | 61.0057 | − | 90.4455i | 0.216332 | − | 0.320729i | ||||
\(283\) | −66.7580 | − | 115.628i | −0.235894 | − | 0.408581i | 0.723638 | − | 0.690180i | \(-0.242469\pi\) |
−0.959532 | + | 0.281599i | \(0.909135\pi\) | |||||||
\(284\) | − | 15.1306i | − | 0.0532769i | ||||||
\(285\) | −147.300 | + | 12.0289i | −0.516843 | + | 0.0422066i | ||||
\(286\) | −169.417 | −0.592368 | ||||||||
\(287\) | 149.087 | − | 86.0752i | 0.519465 | − | 0.299914i | ||||
\(288\) | −26.2856 | + | 187.042i | −0.0912695 | + | 0.649452i | ||||
\(289\) | 24.4863 | − | 42.4115i | 0.0847277 | − | 0.146753i | ||||
\(290\) | −44.9627 | + | 25.9592i | −0.155044 | + | 0.0895146i | ||||
\(291\) | −128.445 | − | 8.98122i | −0.441390 | − | 0.0308633i | ||||
\(292\) | −12.5365 | −0.0429333 | ||||||||
\(293\) | 407.093i | 1.38939i | 0.719302 | + | 0.694697i | \(0.244462\pi\) | ||||
−0.719302 | + | 0.694697i | \(0.755538\pi\) | |||||||
\(294\) | 57.6942 | − | 825.110i | 0.196239 | − | 2.80650i | ||||
\(295\) | 97.0577 | − | 168.109i | 0.329009 | − | 0.569860i | ||||
\(296\) | − | 44.4532i | − | 0.150180i | ||||||
\(297\) | −81.4562 | + | 383.243i | −0.274263 | + | 1.29038i | ||||
\(298\) | −98.5076 | + | 170.620i | −0.330562 | + | 0.572551i | ||||
\(299\) | −43.2004 | + | 24.9418i | −0.144483 | + | 0.0834173i | ||||
\(300\) | −74.6978 | − | 5.22309i | −0.248993 | − | 0.0174103i | ||||
\(301\) | 255.344 | + | 442.270i | 0.848320 | + | 1.46933i | ||||
\(302\) | −219.793 | + | 126.898i | −0.727791 | + | 0.420190i | ||||
\(303\) | 525.914 | − | 256.508i | 1.73569 | − | 0.846561i | ||||
\(304\) | −290.725 | + | 232.651i | −0.956332 | + | 0.765299i | ||||
\(305\) | 26.6804i | 0.0874767i | ||||||||
\(306\) | −379.531 | − | 53.3366i | −1.24030 | − | 0.174303i | ||||
\(307\) | −241.506 | − | 418.301i | −0.786666 | − | 1.36254i | −0.927999 | − | 0.372583i | \(-0.878472\pi\) |
0.141333 | − | 0.989962i | \(-0.454861\pi\) | |||||||
\(308\) | −222.463 | − | 128.439i | −0.722281 | − | 0.417009i | ||||
\(309\) | −132.590 | + | 196.574i | −0.429093 | + | 0.636162i | ||||
\(310\) | 39.9993 | − | 69.2808i | 0.129030 | − | 0.223486i | ||||
\(311\) | − | 125.771i | − | 0.404407i | −0.979344 | − | 0.202204i | \(-0.935190\pi\) | ||
0.979344 | − | 0.202204i | \(-0.0648103\pi\) | |||||||
\(312\) | 82.9296 | − | 40.4479i | 0.265800 | − | 0.129641i | ||||
\(313\) | −88.6402 | + | 153.529i | −0.283196 | + | 0.490509i | −0.972170 | − | 0.234277i | \(-0.924728\pi\) |
0.688974 | + | 0.724786i | \(0.258061\pi\) | |||||||
\(314\) | −70.5113 | − | 40.7097i | −0.224558 | − | 0.129649i | ||||
\(315\) | 238.362 | + | 186.226i | 0.756704 | + | 0.591193i | ||||
\(316\) | −148.116 | −0.468721 | ||||||||
\(317\) | 143.415 | + | 82.8007i | 0.452413 | + | 0.261201i | 0.708849 | − | 0.705360i | \(-0.249215\pi\) |
−0.256435 | + | 0.966561i | \(0.582548\pi\) | |||||||
\(318\) | 187.011 | − | 277.257i | 0.588084 | − | 0.871877i | ||||
\(319\) | −62.7211 | + | 108.636i | −0.196618 | + | 0.340552i | ||||
\(320\) | −66.8628 | + | 38.6033i | −0.208946 | + | 0.120635i | ||||
\(321\) | −166.286 | − | 112.160i | −0.518024 | − | 0.349409i | ||||
\(322\) | −297.176 | −0.922905 | ||||||||
\(323\) | −218.244 | − | 272.722i | −0.675679 | − | 0.844342i | ||||
\(324\) | 26.7621 | + | 107.330i | 0.0825992 | + | 0.331266i | ||||
\(325\) | 46.0600 | + | 79.7783i | 0.141723 | + | 0.245472i | ||||
\(326\) | 492.762 | − | 284.496i | 1.51154 | − | 0.872687i | ||||
\(327\) | −380.293 | − | 26.5912i | −1.16297 | − | 0.0813186i | ||||
\(328\) | 40.5207 | + | 70.1840i | 0.123539 | + | 0.213976i | ||||
\(329\) | −176.237 | − | 101.751i | −0.535676 | − | 0.309273i | ||||
\(330\) | 235.000 | − | 114.618i | 0.712122 | − | 0.347328i | ||||
\(331\) | 557.691 | 1.68487 | 0.842433 | − | 0.538801i | \(-0.181123\pi\) | ||||
0.842433 | + | 0.538801i | \(0.181123\pi\) | |||||||
\(332\) | 121.449 | + | 70.1189i | 0.365812 | + | 0.211201i | ||||
\(333\) | −24.5608 | − | 60.7888i | −0.0737561 | − | 0.182549i | ||||
\(334\) | 400.017 | 1.19765 | ||||||||
\(335\) | 206.120i | 0.615285i | ||||||||
\(336\) | 760.242 | + | 53.1584i | 2.26263 | + | 0.158209i | ||||
\(337\) | −114.909 | − | 199.028i | −0.340975 | − | 0.590587i | 0.643639 | − | 0.765329i | \(-0.277424\pi\) |
−0.984614 | + | 0.174743i | \(0.944091\pi\) | |||||||
\(338\) | −288.062 | − | 166.313i | −0.852256 | − | 0.492050i | ||||
\(339\) | 5.52569 | + | 3.72709i | 0.0163000 | + | 0.0109944i | ||||
\(340\) | 32.5474 | + | 56.3738i | 0.0957278 | + | 0.165805i | ||||
\(341\) | − | 193.288i | − | 0.566826i | ||||||
\(342\) | −194.033 | + | 345.322i | −0.567349 | + | 1.00971i | ||||
\(343\) | −907.701 | −2.64636 | ||||||||
\(344\) | −208.203 | + | 120.206i | −0.605240 | + | 0.349436i | ||||
\(345\) | 43.0495 | − | 63.8240i | 0.124781 | − | 0.184997i | ||||
\(346\) | 243.332 | − | 421.464i | 0.703273 | − | 1.21810i | ||||
\(347\) | −143.209 | + | 82.6818i | −0.412706 | + | 0.238276i | −0.691952 | − | 0.721944i | \(-0.743249\pi\) |
0.279246 | + | 0.960220i | \(0.409916\pi\) | |||||||
\(348\) | −2.47033 | + | 35.3293i | −0.00709865 | + | 0.101521i | ||||
\(349\) | −133.905 | −0.383682 | −0.191841 | − | 0.981426i | \(-0.561446\pi\) | ||||
−0.191841 | + | 0.981426i | \(0.561446\pi\) | |||||||
\(350\) | 548.794i | 1.56798i | ||||||||
\(351\) | 91.0566 | − | 101.131i | 0.259421 | − | 0.288122i | ||||
\(352\) | 152.272 | − | 263.742i | 0.432590 | − | 0.749267i | ||||
\(353\) | 24.6352i | 0.0697881i | 0.999391 | + | 0.0348941i | \(0.0111094\pi\) | ||||
−0.999391 | + | 0.0348941i | \(0.988891\pi\) | |||||||
\(354\) | −228.068 | − | 467.605i | −0.644261 | − | 1.32092i | ||||
\(355\) | 14.3637 | − | 24.8786i | 0.0404611 | − | 0.0700806i | ||||
\(356\) | −111.761 | + | 64.5255i | −0.313936 | + | 0.181251i | ||||
\(357\) | −49.8666 | + | 713.165i | −0.139682 | + | 1.99766i | ||||
\(358\) | 329.038 | + | 569.911i | 0.919101 | + | 1.59193i | ||||
\(359\) | 249.662 | − | 144.142i | 0.695436 | − | 0.401510i | −0.110209 | − | 0.993908i | \(-0.535152\pi\) |
0.805645 | + | 0.592398i | \(0.201819\pi\) | |||||||
\(360\) | −87.6676 | + | 112.211i | −0.243521 | + | 0.311698i | ||||
\(361\) | −344.600 | + | 107.573i | −0.954570 | + | 0.297986i | ||||
\(362\) | 455.246i | 1.25759i | ||||||||
\(363\) | 150.271 | − | 222.787i | 0.413969 | − | 0.613739i | ||||
\(364\) | 44.6102 | + | 77.2671i | 0.122555 | + | 0.212272i | ||||
\(365\) | −20.6132 | − | 11.9011i | −0.0564746 | − | 0.0326056i | ||||
\(366\) | 59.2826 | + | 39.9863i | 0.161974 | + | 0.109252i | ||||
\(367\) | −100.002 | + | 173.208i | −0.272484 | + | 0.471956i | −0.969497 | − | 0.245102i | \(-0.921179\pi\) |
0.697013 | + | 0.717058i | \(0.254512\pi\) | |||||||
\(368\) | − | 193.962i | − | 0.527072i | ||||||
\(369\) | 94.1885 | + | 73.5869i | 0.255253 | + | 0.199423i | ||||
\(370\) | −21.8761 | + | 37.8904i | −0.0591245 | + | 0.102407i | ||||
\(371\) | −540.248 | − | 311.913i | −1.45620 | − | 0.840735i | ||||
\(372\) | −23.9221 | − | 49.0472i | −0.0643068 | − | 0.131847i | ||||
\(373\) | 256.433 | 0.687488 | 0.343744 | − | 0.939063i | \(-0.388305\pi\) | ||||
0.343744 | + | 0.939063i | \(0.388305\pi\) | |||||||
\(374\) | 535.164 | + | 308.977i | 1.43092 | + | 0.826142i | ||||
\(375\) | −279.080 | − | 188.240i | −0.744213 | − | 0.501974i | ||||
\(376\) | 47.9001 | − | 82.9654i | 0.127394 | − | 0.220653i | ||||
\(377\) | 37.7322 | − | 21.7847i | 0.100085 | − | 0.0577843i | ||||
\(378\) | 771.021 | − | 250.530i | 2.03974 | − | 0.662777i | ||||
\(379\) | 342.519 | 0.903743 | 0.451872 | − | 0.892083i | \(-0.350757\pi\) | ||||
0.451872 | + | 0.892083i | \(0.350757\pi\) | |||||||
\(380\) | 66.5075 | − | 10.1395i | 0.175020 | − | 0.0266828i | ||||
\(381\) | −100.501 | − | 206.055i | −0.263781 | − | 0.540826i | ||||
\(382\) | −255.577 | − | 442.673i | −0.669051 | − | 1.15883i | ||||
\(383\) | 400.758 | − | 231.378i | 1.04637 | − | 0.604120i | 0.124736 | − | 0.992190i | \(-0.460191\pi\) |
0.921630 | + | 0.388070i | \(0.126858\pi\) | |||||||
\(384\) | −32.0001 | + | 457.648i | −0.0833337 | + | 1.19179i | ||||
\(385\) | −243.857 | − | 422.372i | −0.633394 | − | 1.09707i | ||||
\(386\) | 88.3719 | + | 51.0215i | 0.228943 | + | 0.132180i | ||||
\(387\) | −218.298 | + | 279.413i | −0.564077 | + | 0.721997i | ||||
\(388\) | 58.6121 | 0.151062 | ||||||||
\(389\) | 509.472 | + | 294.144i | 1.30970 | + | 0.756154i | 0.982045 | − | 0.188645i | \(-0.0604095\pi\) |
0.327652 | + | 0.944799i | \(0.393743\pi\) | |||||||
\(390\) | −90.5914 | − | 6.33442i | −0.232286 | − | 0.0162421i | ||||
\(391\) | 181.952 | 0.465349 | ||||||||
\(392\) | − | 726.317i | − | 1.85285i | ||||||
\(393\) | 27.3636 | − | 391.340i | 0.0696276 | − | 0.995776i | ||||
\(394\) | 21.2846 | + | 36.8660i | 0.0540217 | + | 0.0935684i | ||||
\(395\) | −243.540 | − | 140.608i | −0.616556 | − | 0.355969i | ||||
\(396\) | 24.8206 | − | 176.618i | 0.0626784 | − | 0.446005i | ||||
\(397\) | 139.028 | + | 240.803i | 0.350196 | + | 0.606558i | 0.986284 | − | 0.165059i | \(-0.0527815\pi\) |
−0.636087 | + | 0.771617i | \(0.719448\pi\) | |||||||
\(398\) | − | 567.241i | − | 1.42523i | ||||||
\(399\) | 667.817 | + | 316.124i | 1.67373 | + | 0.792292i | ||||
\(400\) | −358.191 | −0.895477 | ||||||||
\(401\) | −196.863 | + | 113.659i | −0.490930 | + | 0.283438i | −0.724960 | − | 0.688791i | \(-0.758142\pi\) |
0.234030 | + | 0.972229i | \(0.424808\pi\) | |||||||
\(402\) | 457.990 | + | 308.916i | 1.13928 | + | 0.768447i | ||||
\(403\) | −33.5669 | + | 58.1397i | −0.0832927 | + | 0.144267i | ||||
\(404\) | −230.674 | + | 133.180i | −0.570976 | + | 0.329653i | ||||
\(405\) | −57.8858 | + | 201.883i | −0.142928 | + | 0.498478i | ||||
\(406\) | 259.560 | 0.639309 | ||||||||
\(407\) | 105.711i | 0.259733i | ||||||||
\(408\) | −335.730 | − | 23.4752i | −0.822867 | − | 0.0575373i | ||||
\(409\) | −366.906 | + | 635.501i | −0.897082 | + | 1.55379i | −0.0658749 | + | 0.997828i | \(0.520984\pi\) |
−0.831207 | + | 0.555963i | \(0.812349\pi\) | |||||||
\(410\) | − | 79.7633i | − | 0.194545i | ||||||
\(411\) | −484.822 | + | 236.466i | −1.17962 | + | 0.575343i | ||||
\(412\) | 53.9676 | − | 93.4747i | 0.130989 | − | 0.226880i | ||||
\(413\) | −840.438 | + | 485.227i | −2.03496 | + | 1.17488i | ||||
\(414\) | −77.2951 | − | 191.308i | −0.186703 | − | 0.462096i | ||||
\(415\) | 133.129 | + | 230.586i | 0.320793 | + | 0.555630i | ||||
\(416\) | −91.6045 | + | 52.8879i | −0.220203 | + | 0.127134i | ||||
\(417\) | 52.0045 | + | 106.624i | 0.124711 | + | 0.255693i | ||||
\(418\) | 498.649 | − | 399.041i | 1.19294 | − | 0.954644i | ||||
\(419\) | 82.9364i | 0.197939i | 0.995090 | + | 0.0989694i | \(0.0315546\pi\) | ||||
−0.995090 | + | 0.0989694i | \(0.968445\pi\) | |||||||
\(420\) | −114.154 | − | 76.9970i | −0.271795 | − | 0.183326i | ||||
\(421\) | 286.253 | + | 495.805i | 0.679936 | + | 1.17768i | 0.975000 | + | 0.222206i | \(0.0713257\pi\) |
−0.295064 | + | 0.955478i | \(0.595341\pi\) | |||||||
\(422\) | 311.710 | + | 179.966i | 0.738649 | + | 0.426459i | ||||
\(423\) | 19.6632 | − | 139.919i | 0.0464851 | − | 0.330777i | ||||
\(424\) | 146.836 | − | 254.327i | 0.346311 | − | 0.599828i | ||||
\(425\) | − | 336.010i | − | 0.790612i | ||||||
\(426\) | −33.7521 | − | 69.2014i | −0.0792303 | − | 0.162445i | ||||
\(427\) | 66.6926 | − | 115.515i | 0.156189 | − | 0.270527i | ||||
\(428\) | 79.0720 | + | 45.6523i | 0.184748 | + | 0.106664i | ||||
\(429\) | −197.210 | + | 96.1864i | −0.459696 | + | 0.224211i | ||||
\(430\) | 236.620 | 0.550279 | ||||||||
\(431\) | 356.453 | + | 205.799i | 0.827038 | + | 0.477491i | 0.852838 | − | 0.522176i | \(-0.174880\pi\) |
−0.0257993 | + | 0.999667i | \(0.508213\pi\) | |||||||
\(432\) | 163.517 | + | 503.235i | 0.378512 | + | 1.16490i | ||||
\(433\) | 216.998 | − | 375.852i | 0.501151 | − | 0.868018i | −0.498848 | − | 0.866689i | \(-0.666244\pi\) |
0.999999 | − | 0.00132924i | \(-0.000423110\pi\) | |||||||
\(434\) | −346.360 | + | 199.971i | −0.798065 | + | 0.460763i | ||||
\(435\) | −37.6003 | + | 55.7453i | −0.0864376 | + | 0.128150i | ||||
\(436\) | 173.536 | 0.398019 | ||||||||
\(437\) | 68.4055 | − | 175.165i | 0.156534 | − | 0.400835i | ||||
\(438\) | −57.3369 | + | 27.9654i | −0.130906 | + | 0.0638479i | ||||
\(439\) | 88.3728 | + | 153.066i | 0.201305 | + | 0.348670i | 0.948949 | − | 0.315429i | \(-0.102149\pi\) |
−0.747644 | + | 0.664099i | \(0.768815\pi\) | |||||||
\(440\) | 198.836 | − | 114.798i | 0.451899 | − | 0.260904i | ||||
\(441\) | −401.297 | − | 993.222i | −0.909970 | − | 2.25220i | ||||
\(442\) | −107.316 | − | 185.876i | −0.242796 | − | 0.420535i | ||||
\(443\) | 527.653 | + | 304.641i | 1.19109 | + | 0.687677i | 0.958554 | − | 0.284911i | \(-0.0919639\pi\) |
0.232537 | + | 0.972587i | \(0.425297\pi\) | |||||||
\(444\) | 13.0833 | + | 26.8245i | 0.0294669 | + | 0.0604155i | ||||
\(445\) | −245.019 | −0.550604 | ||||||||
\(446\) | −134.061 | − | 77.4001i | −0.300585 | − | 0.173543i | ||||
\(447\) | −17.7980 | + | 254.537i | −0.0398165 | + | 0.569434i | ||||
\(448\) | 385.984 | 0.861572 | ||||||||
\(449\) | 309.870i | 0.690134i | 0.938578 | + | 0.345067i | \(0.112144\pi\) | ||||
−0.938578 | + | 0.345067i | \(0.887856\pi\) | |||||||
\(450\) | −353.288 | + | 142.741i | −0.785085 | + | 0.317202i | ||||
\(451\) | −96.3597 | − | 166.900i | −0.213658 | − | 0.370066i | ||||
\(452\) | −2.62757 | − | 1.51703i | −0.00581321 | − | 0.00335626i | ||||
\(453\) | −183.803 | + | 272.502i | −0.405747 | + | 0.601549i | ||||
\(454\) | −324.050 | − | 561.271i | −0.713767 | − | 1.23628i | ||||
\(455\) | 169.396i | 0.372298i | ||||||||
\(456\) | −148.819 | + | 314.381i | −0.326357 | + | 0.689433i | ||||
\(457\) | 80.0797 | 0.175229 | 0.0876145 | − | 0.996154i | \(-0.472076\pi\) | ||||
0.0876145 | + | 0.996154i | \(0.472076\pi\) | |||||||
\(458\) | −119.685 | + | 69.1000i | −0.261320 | + | 0.150873i | ||||
\(459\) | −472.073 | + | 153.392i | −1.02848 | + | 0.334187i | ||||
\(460\) | −17.5223 | + | 30.3495i | −0.0380920 | + | 0.0659772i | ||||
\(461\) | −104.373 | + | 60.2600i | −0.226407 | + | 0.130716i | −0.608913 | − | 0.793237i | \(-0.708394\pi\) |
0.382507 | + | 0.923953i | \(0.375061\pi\) | |||||||
\(462\) | −1303.96 | − | 91.1769i | −2.82243 | − | 0.197353i | ||||
\(463\) | 381.609 | 0.824209 | 0.412105 | − | 0.911137i | \(-0.364794\pi\) | ||||
0.412105 | + | 0.911137i | \(0.364794\pi\) | |||||||
\(464\) | 169.411i | 0.365110i | ||||||||
\(465\) | 7.22692 | − | 103.356i | 0.0155418 | − | 0.222270i | ||||
\(466\) | −254.309 | + | 440.476i | −0.545728 | + | 0.945228i | ||||
\(467\) | − | 175.085i | − | 0.374915i | −0.982273 | − | 0.187457i | \(-0.939975\pi\) | ||
0.982273 | − | 0.187457i | \(-0.0600246\pi\) | |||||||
\(468\) | −38.1379 | + | 48.8150i | −0.0814912 | + | 0.104306i | ||||
\(469\) | 515.236 | − | 892.415i | 1.09858 | − | 1.90280i | ||||
\(470\) | −81.6569 | + | 47.1447i | −0.173738 | + | 0.100308i | ||||
\(471\) | −105.191 | − | 7.35529i | −0.223336 | − | 0.0156163i | ||||
\(472\) | −228.425 | − | 395.644i | −0.483952 | − | 0.838230i | ||||
\(473\) | 495.113 | − | 285.854i | 1.04675 | − | 0.604342i | ||||
\(474\) | −677.420 | + | 330.403i | −1.42916 | + | 0.697053i | ||||
\(475\) | −323.477 | − | 126.325i | −0.681005 | − | 0.265946i | ||||
\(476\) | − | 325.433i | − | 0.683684i | ||||||
\(477\) | 60.2767 | − | 428.915i | 0.126366 | − | 0.899193i | ||||
\(478\) | −273.874 | − | 474.364i | −0.572959 | − | 0.992394i | ||||
\(479\) | −643.175 | − | 371.337i | −1.34275 | − | 0.775234i | −0.355536 | − | 0.934663i | \(-0.615702\pi\) |
−0.987210 | + | 0.159428i | \(0.949035\pi\) | |||||||
\(480\) | 91.2844 | − | 135.336i | 0.190176 | − | 0.281950i | ||||
\(481\) | 18.3581 | − | 31.7972i | 0.0381666 | − | 0.0661065i | ||||
\(482\) | − | 610.024i | − | 1.26561i | ||||||
\(483\) | −345.926 | + | 168.721i | −0.716203 | + | 0.349319i | ||||
\(484\) | −61.1642 | + | 105.940i | −0.126372 | + | 0.218883i | ||||
\(485\) | 96.3732 | + | 55.6411i | 0.198708 | + | 0.114724i | ||||
\(486\) | 361.821 | + | 431.185i | 0.744488 | + | 0.887212i | ||||
\(487\) | −326.388 | −0.670201 | −0.335101 | − | 0.942182i | \(-0.608770\pi\) | ||||
−0.335101 | + | 0.942182i | \(0.608770\pi\) | |||||||
\(488\) | 54.3798 | + | 31.3962i | 0.111434 | + | 0.0643365i | ||||
\(489\) | 412.075 | − | 610.931i | 0.842689 | − | 1.24935i | ||||
\(490\) | −357.431 | + | 619.088i | −0.729451 | + | 1.26345i | ||||
\(491\) | 101.286 | − | 58.4774i | 0.206285 | − | 0.119099i | −0.393299 | − | 0.919411i | \(-0.628666\pi\) |
0.599584 | + | 0.800312i | \(0.295333\pi\) | |||||||
\(492\) | −45.1078 | − | 30.4253i | −0.0916824 | − | 0.0618401i | ||||
\(493\) | −158.920 | −0.322354 | ||||||||
\(494\) | −219.289 | + | 33.4319i | −0.443905 | + | 0.0676759i | ||||
\(495\) | 208.477 | − | 266.842i | 0.421165 | − | 0.539075i | ||||
\(496\) | −130.518 | − | 226.065i | −0.263142 | − | 0.455775i | ||||
\(497\) | −124.377 | + | 71.8093i | −0.250256 | + | 0.144486i | ||||
\(498\) | 711.874 | + | 49.7764i | 1.42947 | + | 0.0999525i | ||||
\(499\) | 454.624 | + | 787.431i | 0.911069 | + | 1.57802i | 0.812557 | + | 0.582882i | \(0.198075\pi\) |
0.0985126 | + | 0.995136i | \(0.468592\pi\) | |||||||
\(500\) | 132.708 | + | 76.6190i | 0.265416 | + | 0.153238i | ||||
\(501\) | 465.638 | − | 227.109i | 0.929417 | − | 0.453311i | ||||
\(502\) | 708.238 | 1.41083 | ||||||||
\(503\) | 125.027 | + | 72.1841i | 0.248562 | + | 0.143507i | 0.619105 | − | 0.785308i | \(-0.287495\pi\) |
−0.370544 | + | 0.928815i | \(0.620829\pi\) | |||||||
\(504\) | 660.057 | − | 266.686i | 1.30964 | − | 0.529139i | ||||
\(505\) | −505.716 | −1.00142 | ||||||||
\(506\) | 332.683i | 0.657476i | ||||||||
\(507\) | −429.742 | − | 30.0488i | −0.847617 | − | 0.0592679i | ||||
\(508\) | 52.1802 | + | 90.3788i | 0.102717 | + | 0.177911i | ||||
\(509\) | −150.436 | − | 86.8543i | −0.295552 | − | 0.170637i | 0.344891 | − | 0.938643i | \(-0.387916\pi\) |
−0.640443 | + | 0.768006i | \(0.721249\pi\) | |||||||
\(510\) | 274.612 | + | 185.227i | 0.538455 | + | 0.363190i | ||||
\(511\) | 59.4978 | + | 103.053i | 0.116434 | + | 0.201670i | ||||
\(512\) | 67.0653i | 0.130987i | ||||||||
\(513\) | −29.8075 | + | 512.133i | −0.0581044 | + | 0.998311i | ||||
\(514\) | 13.2119 | 0.0257040 | ||||||||
\(515\) | 177.473 | − | 102.464i | 0.344608 | − | 0.198959i | ||||
\(516\) | 90.2575 | − | 133.813i | 0.174918 | − | 0.259328i | ||||
\(517\) | −113.908 | + | 197.295i | −0.220325 | + | 0.381614i | ||||
\(518\) | 189.428 | − | 109.366i | 0.365692 | − | 0.211132i | ||||
\(519\) | 43.9644 | − | 628.755i | 0.0847099 | − | 1.21147i | ||||
\(520\) | −79.7446 | −0.153355 | ||||||||
\(521\) | − | 832.753i | − | 1.59837i | −0.601082 | − | 0.799187i | \(-0.705264\pi\) | ||
0.601082 | − | 0.799187i | \(-0.294736\pi\) | |||||||
\(522\) | 67.5112 | + | 167.092i | 0.129332 | + | 0.320100i | ||||
\(523\) | 109.560 | − | 189.763i | 0.209483 | − | 0.362836i | −0.742068 | − | 0.670324i | \(-0.766155\pi\) |
0.951552 | + | 0.307488i | \(0.0994884\pi\) | |||||||
\(524\) | 178.577i | 0.340796i | ||||||||
\(525\) | 311.577 | + | 638.822i | 0.593481 | + | 1.21680i | ||||
\(526\) | −596.543 | + | 1033.24i | −1.13411 | + | 1.96434i | ||||
\(527\) | 212.066 | − | 122.436i | 0.402402 | − | 0.232327i | ||||
\(528\) | 59.5099 | − | 851.078i | 0.112708 | − | 1.61189i | ||||
\(529\) | −215.522 | − | 373.295i | −0.407414 | − | 0.705662i | ||||
\(530\) | −250.316 | + | 144.520i | −0.472294 | + | 0.272679i | ||||
\(531\) | −530.964 | − | 414.828i | −0.999932 | − | 0.781220i | ||||
\(532\) | −313.295 | − | 122.348i | −0.588900 | − | 0.229978i | ||||
\(533\) | 66.9365i | 0.125584i | ||||||||
\(534\) | −367.213 | + | 544.420i | −0.687665 | + | 1.01951i | ||||
\(535\) | 86.6763 | + | 150.128i | 0.162012 | + | 0.280613i | ||||
\(536\) | 420.113 | + | 242.553i | 0.783793 | + | 0.452523i | ||||
\(537\) | 706.581 | + | 476.591i | 1.31579 | + | 0.887507i | ||||
\(538\) | 14.1854 | − | 24.5699i | 0.0263670 | − | 0.0456690i | ||||
\(539\) | 1727.21i | 3.20446i | ||||||||
\(540\) | 19.8758 | − | 93.5137i | 0.0368071 | − | 0.173174i | ||||
\(541\) | 167.676 | − | 290.423i | 0.309936 | − | 0.536826i | −0.668412 | − | 0.743791i | \(-0.733026\pi\) |
0.978348 | + | 0.206966i | \(0.0663589\pi\) | |||||||
\(542\) | 273.734 | + | 158.041i | 0.505045 | + | 0.291588i | ||||
\(543\) | 258.465 | + | 529.927i | 0.475995 | + | 0.975925i | ||||
\(544\) | 385.820 | 0.709228 | ||||||||
\(545\) | 285.337 | + | 164.740i | 0.523555 | + | 0.302275i | ||||
\(546\) | 376.389 | + | 253.875i | 0.689357 | + | 0.464973i | ||||
\(547\) | −128.897 | + | 223.256i | −0.235643 | + | 0.408146i | −0.959459 | − | 0.281847i | \(-0.909053\pi\) |
0.723816 | + | 0.689993i | \(0.242386\pi\) | |||||||
\(548\) | 212.651 | − | 122.774i | 0.388049 | − | 0.224040i | ||||
\(549\) | 91.7099 | + | 12.8883i | 0.167049 | + | 0.0234759i | ||||
\(550\) | 614.366 | 1.11703 | ||||||||
\(551\) | −59.7469 | + | 152.993i | −0.108434 | + | 0.277664i | ||||
\(552\) | −79.4271 | − | 162.848i | −0.143890 | − | 0.295015i | ||||
\(553\) | 702.950 | + | 1217.55i | 1.27116 | + | 2.20171i | ||||
\(554\) | −324.424 | + | 187.306i | −0.585603 | + | 0.338098i | ||||
\(555\) | −3.95249 | + | 56.5263i | −0.00712160 | + | 0.101849i | ||||
\(556\) | −27.0009 | − | 46.7669i | −0.0485628 | − | 0.0841132i | ||||
\(557\) | −97.9737 | − | 56.5652i | −0.175895 | − | 0.101553i | 0.409467 | − | 0.912325i | \(-0.365715\pi\) |
−0.585363 | + | 0.810772i | \(0.699048\pi\) | |||||||
\(558\) | −218.820 | − | 170.958i | −0.392151 | − | 0.306377i | ||||
\(559\) | −198.569 | −0.355222 | ||||||||
\(560\) | −570.417 | − | 329.330i | −1.01860 | − | 0.588090i | ||||
\(561\) | 798.376 | + | 55.8248i | 1.42313 | + | 0.0995095i | ||||
\(562\) | −612.272 | −1.08945 | ||||||||
\(563\) | − | 833.973i | − | 1.48130i | −0.671890 | − | 0.740651i | \(-0.734517\pi\) | ||
0.671890 | − | 0.740651i | \(-0.265483\pi\) | |||||||
\(564\) | −4.48638 | + | 64.1617i | −0.00795457 | + | 0.113762i | ||||
\(565\) | −2.88026 | − | 4.98876i | −0.00509780 | − | 0.00882966i | ||||
\(566\) | 267.840 | + | 154.637i | 0.473215 | + | 0.273211i | ||||
\(567\) | 755.266 | − | 729.375i | 1.33204 | − | 1.28637i | ||||
\(568\) | −33.8049 | − | 58.5519i | −0.0595158 | − | 0.103084i | ||||
\(569\) | 94.3305i | 0.165783i | 0.996559 | + | 0.0828915i | \(0.0264155\pi\) | ||||
−0.996559 | + | 0.0828915i | \(0.973585\pi\) | |||||||
\(570\) | 281.560 | − | 194.733i | 0.493964 | − | 0.341636i | ||||
\(571\) | 870.251 | 1.52408 | 0.762042 | − | 0.647528i | \(-0.224197\pi\) | ||||
0.762042 | + | 0.647528i | \(0.224197\pi\) | |||||||
\(572\) | 86.4992 | − | 49.9403i | 0.151222 | − | 0.0873082i | ||||
\(573\) | −548.831 | − | 370.188i | −0.957820 | − | 0.646053i | ||||
\(574\) | −199.383 | + | 345.342i | −0.347357 | + | 0.601641i | ||||
\(575\) | 156.660 | − | 90.4476i | 0.272452 | − | 0.157300i | ||||
\(576\) | 100.394 | + | 248.479i | 0.174295 | + | 0.431387i | ||||
\(577\) | −506.403 | −0.877648 | −0.438824 | − | 0.898573i | \(-0.644605\pi\) | ||||
−0.438824 | + | 0.898573i | \(0.644605\pi\) | |||||||
\(578\) | 113.439i | 0.196262i | ||||||||
\(579\) | 131.836 | + | 9.21839i | 0.227697 | + | 0.0159212i | ||||
\(580\) | 15.3044 | − | 26.5079i | 0.0263868 | − | 0.0457033i | ||||
\(581\) | − | 1331.12i | − | 2.29109i | ||||||
\(582\) | 268.068 | − | 130.747i | 0.460598 | − | 0.224651i | ||||
\(583\) | −349.181 | + | 604.799i | −0.598938 | + | 1.03739i | ||||
\(584\) | −48.5133 | + | 28.0092i | −0.0830707 | + | 0.0479609i | ||||
\(585\) | −109.049 | + | 44.0596i | −0.186408 | + | 0.0753156i | ||||
\(586\) | −471.491 | − | 816.647i | −0.804593 | − | 1.39360i | ||||
\(587\) | −566.798 | + | 327.241i | −0.965584 | + | 0.557480i | −0.897887 | − | 0.440226i | \(-0.854898\pi\) |
−0.0676970 | + | 0.997706i | \(0.521565\pi\) | |||||||
\(588\) | 213.767 | + | 438.282i | 0.363549 | + | 0.745378i | ||||
\(589\) | −38.1424 | − | 250.186i | −0.0647579 | − | 0.424765i | ||||
\(590\) | 449.646i | 0.762111i | ||||||||
\(591\) | 45.7068 | + | 30.8294i | 0.0773381 | + | 0.0521648i | ||||
\(592\) | 71.3820 | + | 123.637i | 0.120578 | + | 0.208847i | ||||
\(593\) | 99.8164 | + | 57.6290i | 0.168324 | + | 0.0971822i | 0.581796 | − | 0.813335i | \(-0.302350\pi\) |
−0.413471 | + | 0.910517i | \(0.635684\pi\) | |||||||
\(594\) | −280.464 | − | 863.145i | −0.472161 | − | 1.45311i | ||||
\(595\) | 308.937 | − | 535.095i | 0.519222 | − | 0.899319i | ||||
\(596\) | − | 116.151i | − | 0.194884i | ||||||
\(597\) | −322.051 | − | 660.295i | −0.539448 | − | 1.10602i | ||||
\(598\) | 57.7747 | − | 100.069i | 0.0966133 | − | 0.167339i | ||||
\(599\) | −860.681 | − | 496.914i | −1.43686 | − | 0.829573i | −0.439232 | − | 0.898373i | \(-0.644750\pi\) |
−0.997630 | + | 0.0688004i | \(0.978083\pi\) | |||||||
\(600\) | −300.732 | + | 146.678i | −0.501220 | + | 0.244463i | ||||
\(601\) | −315.591 | −0.525109 | −0.262555 | − | 0.964917i | \(-0.584565\pi\) | ||||
−0.262555 | + | 0.964917i | \(0.584565\pi\) | |||||||
\(602\) | −1024.47 | − | 591.476i | −1.70177 | − | 0.982518i | ||||
\(603\) | 708.508 | + | 99.5688i | 1.17497 | + | 0.165122i | ||||
\(604\) | 74.8129 | − | 129.580i | 0.123862 | − | 0.214536i | ||||
\(605\) | −201.139 | + | 116.128i | −0.332461 | + | 0.191947i | ||||
\(606\) | −757.923 | + | 1123.68i | −1.25070 | + | 1.85425i | ||||
\(607\) | −248.211 | −0.408915 | −0.204457 | − | 0.978875i | \(-0.565543\pi\) | ||||
−0.204457 | + | 0.978875i | \(0.565543\pi\) | |||||||
\(608\) | 145.051 | − | 371.429i | 0.238570 | − | 0.610903i | ||||
\(609\) | 302.139 | − | 147.365i | 0.496124 | − | 0.241978i | ||||
\(610\) | −30.9010 | − | 53.5222i | −0.0506574 | − | 0.0877412i | ||||
\(611\) | 68.5256 | − | 39.5633i | 0.112153 | − | 0.0647517i | ||||
\(612\) | 209.499 | − | 84.6449i | 0.342319 | − | 0.138309i | ||||
\(613\) | −310.127 | − | 537.155i | −0.505916 | − | 0.876272i | −0.999977 | − | 0.00684487i | \(-0.997821\pi\) |
0.494060 | − | 0.869428i | \(-0.335512\pi\) | |||||||
\(614\) | 968.946 | + | 559.421i | 1.57809 | + | 0.911110i | ||||
\(615\) | −45.2855 | − | 92.8482i | −0.0736350 | − | 0.150973i | ||||
\(616\) | −1147.83 | −1.86337 | ||||||||
\(617\) | 103.478 | + | 59.7430i | 0.167711 | + | 0.0968282i | 0.581506 | − | 0.813542i | \(-0.302464\pi\) |
−0.413795 | + | 0.910370i | \(0.635797\pi\) | |||||||
\(618\) | 38.3108 | − | 547.901i | 0.0619917 | − | 0.886571i | ||||
\(619\) | −1082.13 | −1.74819 | −0.874093 | − | 0.485758i | \(-0.838543\pi\) | ||||
−0.874093 | + | 0.485758i | \(0.838543\pi\) | |||||||
\(620\) | 47.1635i | 0.0760701i | ||||||||
\(621\) | −198.590 | − | 178.807i | −0.319790 | − | 0.287934i | ||||
\(622\) | 145.667 | + | 252.302i | 0.234191 | + | 0.405630i | ||||
\(623\) | 1060.83 | + | 612.470i | 1.70277 | + | 0.983097i | ||||
\(624\) | −165.701 | + | 245.664i | −0.265547 | + | 0.393692i | ||||
\(625\) | −82.9959 | − | 143.753i | −0.132793 | − | 0.230005i | ||||
\(626\) | − | 410.649i | − | 0.655989i | ||||||
\(627\) | 353.896 | − | 747.610i | 0.564427 | − | 1.19236i | ||||
\(628\) | 48.0011 | 0.0764349 | ||||||||
\(629\) | −115.981 | + | 66.9618i | −0.184390 | + | 0.106458i | ||||
\(630\) | −693.850 | − | 97.5089i | −1.10135 | − | 0.154776i | ||||
\(631\) | −343.394 | + | 594.777i | −0.544207 | + | 0.942594i | 0.454450 | + | 0.890772i | \(0.349836\pi\) |
−0.998656 | + | 0.0518212i | \(0.983497\pi\) | |||||||
\(632\) | −573.171 | + | 330.921i | −0.906917 | + | 0.523609i | ||||
\(633\) | 465.020 | + | 32.5156i | 0.734629 | + | 0.0513674i | ||||
\(634\) | −383.596 | −0.605042 | ||||||||
\(635\) | 198.141i | 0.312033i | ||||||||
\(636\) | −13.7528 | + | 196.685i | −0.0216239 | + | 0.309253i | ||||
\(637\) | 299.952 | − | 519.532i | 0.470882 | − | 0.815592i | ||||
\(638\) | − | 290.572i | − | 0.455443i | ||||||
\(639\) | −78.5780 | − | 61.3909i | −0.122970 | − | 0.0960733i | ||||
\(640\) | 198.249 | − | 343.378i | 0.309765 | − | 0.536528i | ||||
\(641\) | −424.021 | + | 244.809i | −0.661499 | + | 0.381917i | −0.792848 | − | 0.609419i | \(-0.791403\pi\) |
0.131349 | + | 0.991336i | \(0.458069\pi\) | |||||||
\(642\) | 463.480 | + | 32.4079i | 0.721931 | + | 0.0504796i | ||||
\(643\) | 267.440 | + | 463.220i | 0.415926 | + | 0.720405i | 0.995525 | − | 0.0944967i | \(-0.0301242\pi\) |
−0.579599 | + | 0.814902i | \(0.696791\pi\) | |||||||
\(644\) | 151.729 | − | 87.6005i | 0.235603 | − | 0.136026i | ||||
\(645\) | 275.437 | − | 134.341i | 0.427034 | − | 0.208280i | ||||
\(646\) | 753.673 | + | 294.325i | 1.16668 | + | 0.455611i | ||||
\(647\) | 919.847i | 1.42171i | 0.703338 | + | 0.710855i | \(0.251692\pi\) | ||||
−0.703338 | + | 0.710855i | \(0.748308\pi\) | |||||||
\(648\) | 343.360 | + | 355.549i | 0.529877 | + | 0.548687i | ||||
\(649\) | 543.203 | + | 940.856i | 0.836985 | + | 1.44970i | ||||
\(650\) | −184.797 | − | 106.693i | −0.284303 | − | 0.164143i | ||||
\(651\) | −289.646 | + | 429.421i | −0.444924 | + | 0.659633i | ||||
\(652\) | −167.726 | + | 290.510i | −0.257248 | + | 0.445567i | ||||
\(653\) | 190.014i | 0.290986i | 0.989359 | + | 0.145493i | \(0.0464768\pi\) | ||||
−0.989359 | + | 0.145493i | \(0.953523\pi\) | |||||||
\(654\) | 793.683 | − | 387.109i | 1.21358 | − | 0.591909i | ||||
\(655\) | −169.525 | + | 293.626i | −0.258817 | + | 0.448284i | ||||
\(656\) | −225.400 | − | 130.135i | −0.343597 | − | 0.198376i | ||||
\(657\) | −50.8655 | + | 65.1059i | −0.0774209 | + | 0.0990958i | ||||
\(658\) | 471.387 | 0.716394 | ||||||||
\(659\) | −985.973 | − | 569.252i | −1.49617 | − | 0.863812i | −0.496175 | − | 0.868222i | \(-0.665263\pi\) |
−0.999990 | + | 0.00441088i | \(0.998596\pi\) | |||||||
\(660\) | −86.1969 | + | 127.793i | −0.130601 | + | 0.193626i | ||||
\(661\) | 448.304 | − | 776.486i | 0.678221 | − | 1.17471i | −0.297295 | − | 0.954786i | \(-0.596084\pi\) |
0.975516 | − | 0.219928i | \(-0.0705823\pi\) | |||||||
\(662\) | −1118.75 | + | 645.913i | −1.68996 | + | 0.975699i | ||||
\(663\) | −230.452 | − | 155.440i | −0.347589 | − | 0.234450i | ||||
\(664\) | 626.639 | 0.943734 | ||||||||
\(665\) | −398.990 | − | 498.585i | −0.599985 | − | 0.749752i | ||||
\(666\) | 119.675 | + | 93.4990i | 0.179692 | + | 0.140389i | ||||
\(667\) | −42.7784 | − | 74.0943i | −0.0641355 | − | 0.111086i | ||||
\(668\) | −204.236 | + | 117.916i | −0.305742 | + | 0.176521i | ||||
\(669\) | −199.997 | − | 13.9844i | −0.298949 | − | 0.0209034i | ||||
\(670\) | −238.727 | − | 413.487i | −0.356309 | − | 0.617145i | ||||
\(671\) | −129.317 | − | 74.6612i | −0.192723 | − | 0.111269i | ||||
\(672\) | −733.520 | + | 357.765i | −1.09155 | + | 0.532389i | ||||
\(673\) | 246.938 | 0.366921 | 0.183461 | − | 0.983027i | \(-0.441270\pi\) | ||||
0.183461 | + | 0.983027i | \(0.441270\pi\) | |||||||
\(674\) | 461.025 | + | 266.173i | 0.684013 | + | 0.394915i | ||||
\(675\) | −330.203 | + | 366.736i | −0.489190 | + | 0.543313i | ||||
\(676\) | 196.101 | 0.290090 | ||||||||
\(677\) | 14.7839i | 0.0218374i | 0.999940 | + | 0.0109187i | \(0.00347561\pi\) | ||||
−0.999940 | + | 0.0109187i | \(0.996524\pi\) | |||||||
\(678\) | −15.4015 | − | 1.07692i | −0.0227160 | − | 0.00158837i | ||||
\(679\) | −278.170 | − | 481.805i | −0.409677 | − | 0.709581i | ||||
\(680\) | 251.901 | + | 145.435i | 0.370443 | + | 0.213875i | ||||
\(681\) | −695.870 | − | 469.366i | −1.02184 | − | 0.689231i | ||||
\(682\) | 223.864 | + | 387.744i | 0.328247 | + | 0.568540i | ||||
\(683\) | 267.556i | 0.391737i | 0.980630 | + | 0.195868i | \(0.0627525\pi\) | ||||
−0.980630 | + | 0.195868i | \(0.937248\pi\) | |||||||
\(684\) | −2.72567 | − | 233.507i | −0.00398490 | − | 0.341385i | ||||
\(685\) | 466.202 | 0.680587 | ||||||||
\(686\) | 1820.89 | − | 1051.29i | 2.65436 | − | 1.53249i | ||||
\(687\) | −100.087 | + | 148.386i | −0.145687 | + | 0.215992i | ||||
\(688\) | 386.048 | − | 668.655i | 0.561116 | − | 0.971882i | ||||
\(689\) | 210.062 | − | 121.280i | 0.304880 | − | 0.176023i | ||||
\(690\) | −12.4388 | + | 177.893i | −0.0180273 | + | 0.257817i | ||||
\(691\) | 217.415 | 0.314638 | 0.157319 | − | 0.987548i | \(-0.449715\pi\) | ||||
0.157319 | + | 0.987548i | \(0.449715\pi\) | |||||||
\(692\) | 286.915i | 0.414617i | ||||||||
\(693\) | −1569.64 | + | 634.189i | −2.26499 | + | 0.915135i | ||||
\(694\) | 191.523 | − | 331.727i | 0.275970 | − | 0.477993i | ||||
\(695\) | − | 102.529i | − | 0.147524i | ||||||
\(696\) | 69.3733 | + | 142.235i | 0.0996743 | + | 0.204361i | ||||
\(697\) | 122.076 | − | 211.442i | 0.175145 | − | 0.303361i | ||||
\(698\) | 268.619 | − | 155.088i | 0.384842 | − | 0.222188i | ||||
\(699\) | −45.9477 | + | 657.118i | −0.0657334 | + | 0.940083i | ||||
\(700\) | −161.772 | − | 280.197i | −0.231103 | − | 0.400282i | ||||
\(701\) | 450.584 | − | 260.145i | 0.642773 | − | 0.371105i | −0.142909 | − | 0.989736i | \(-0.545646\pi\) |
0.785682 | + | 0.618631i | \(0.212312\pi\) | |||||||
\(702\) | −65.5348 | + | 308.334i | −0.0933544 | + | 0.439223i | ||||
\(703\) | 20.8605 | + | 136.830i | 0.0296735 | + | 0.194637i | ||||
\(704\) | − | 432.103i | − | 0.613782i | ||||||
\(705\) | −68.2861 | + | 101.239i | −0.0968597 | + | 0.143602i | ||||
\(706\) | −28.5323 | − | 49.4194i | −0.0404140 | − | 0.0699991i | ||||
\(707\) | 2189.54 | + | 1264.13i | 3.09694 | + | 1.78802i | ||||
\(708\) | 254.284 | + | 171.515i | 0.359158 | + | 0.242253i | ||||
\(709\) | −87.0247 | + | 150.731i | −0.122743 | + | 0.212597i | −0.920848 | − | 0.389921i | \(-0.872502\pi\) |
0.798106 | + | 0.602518i | \(0.205836\pi\) | |||||||
\(710\) | 66.5436i | 0.0937233i | ||||||||
\(711\) | −600.962 | + | 769.209i | −0.845236 | + | 1.08187i | ||||
\(712\) | −288.326 | + | 499.395i | −0.404952 | + | 0.701398i | ||||
\(713\) | 114.168 | + | 65.9151i | 0.160124 | + | 0.0924475i | ||||
\(714\) | −725.948 | − | 1488.40i | −1.01673 | − | 2.08459i | ||||
\(715\) | 189.635 | 0.265224 | ||||||||
\(716\) | −335.993 | − | 193.986i | −0.469264 | − | 0.270930i | ||||
\(717\) | −588.122 | − | 396.690i | −0.820254 | − | 0.553264i | ||||
\(718\) | −333.889 | + | 578.312i | −0.465026 | + | 0.805449i | ||||
\(719\) | 1030.80 | − | 595.135i | 1.43366 | − | 0.827726i | 0.436266 | − | 0.899818i | \(-0.356301\pi\) |
0.997398 | + | 0.0720914i | \(0.0229673\pi\) | |||||||
\(720\) | 63.6427 | − | 452.867i | 0.0883927 | − | 0.628981i | ||||
\(721\) | −1024.51 | −1.42096 | ||||||||
\(722\) | 566.694 | − | 614.909i | 0.784894 | − | 0.851674i | ||||
\(723\) | −346.340 | − | 710.096i | −0.479032 | − | 0.982152i | ||||
\(724\) | −134.196 | − | 232.434i | −0.185354 | − | 0.321042i | ||||
\(725\) | −136.830 | + | 78.9989i | −0.188731 | + | 0.108964i | ||||
\(726\) | −43.4196 | + | 620.964i | −0.0598066 | + | 0.855322i | ||||
\(727\) | 126.262 | + | 218.692i | 0.173675 | + | 0.300814i | 0.939702 | − | 0.341995i | \(-0.111102\pi\) |
−0.766027 | + | 0.642808i | \(0.777769\pi\) | |||||||
\(728\) | 345.261 | + | 199.336i | 0.474259 | + | 0.273814i | ||||
\(729\) | 665.981 | + | 296.496i | 0.913555 | + | 0.406716i | ||||
\(730\) | 55.1348 | 0.0755272 | ||||||||
\(731\) | 627.250 | + | 362.143i | 0.858071 | + | 0.495407i | ||||
\(732\) | −42.0549 | − | 2.94060i | −0.0574520 | − | 0.00401722i | ||||
\(733\) | 292.708 | 0.399329 | 0.199664 | − | 0.979864i | \(-0.436015\pi\) | ||||
0.199664 | + | 0.979864i | \(0.436015\pi\) | |||||||
\(734\) | − | 463.285i | − | 0.631178i | ||||||
\(735\) | −64.5793 | + | 923.578i | −0.0878630 | + | 1.25657i | ||||
\(736\) | 103.855 | + | 179.883i | 0.141108 | + | 0.244406i | ||||
\(737\) | −999.044 | − | 576.798i | −1.35555 | − | 0.782630i | ||||
\(738\) | −274.174 | − | 38.5305i | −0.371510 | − | 0.0522094i | ||||
\(739\) | −0.332267 | − | 0.575503i | −0.000449617 | − | 0.000778759i | 0.865801 | − | 0.500389i | \(-0.166810\pi\) |
−0.866250 | + | 0.499611i | \(0.833476\pi\) | |||||||
\(740\) | − | 25.7942i | − | 0.0348571i | ||||||
\(741\) | −236.282 | + | 163.417i | −0.318869 | + | 0.220536i | ||||
\(742\) | 1445.02 | 1.94746 | ||||||||
\(743\) | −1247.93 | + | 720.493i | −1.67958 | + | 0.969708i | −0.717657 | + | 0.696396i | \(0.754786\pi\) |
−0.961926 | + | 0.273311i | \(0.911881\pi\) | |||||||
\(744\) | −202.154 | − | 136.354i | −0.271713 | − | 0.183271i | ||||
\(745\) | 110.263 | − | 190.982i | 0.148005 | − | 0.256351i | ||||
\(746\) | −514.417 | + | 296.999i | −0.689567 | + | 0.398122i | ||||
\(747\) | 856.915 | − | 346.224i | 1.14714 | − | 0.463486i | ||||
\(748\) | −364.317 | −0.487055 | ||||||||
\(749\) | − | 866.654i | − | 1.15708i | ||||||
\(750\) | 777.866 | + | 54.3907i | 1.03715 | + | 0.0725209i | ||||
\(751\) | 636.728 | − | 1102.84i | 0.847840 | − | 1.46850i | −0.0352923 | − | 0.999377i | \(-0.511236\pi\) |
0.883132 | − | 0.469124i | \(-0.155430\pi\) | |||||||
\(752\) | 307.668i | 0.409133i | ||||||||
\(753\) | 824.422 | − | 402.101i | 1.09485 | − | 0.533999i | ||||
\(754\) | −50.4617 | + | 87.4023i | −0.0669254 | + | 0.115918i | ||||
\(755\) | 246.023 | − | 142.041i | 0.325858 | − | 0.188134i | ||||
\(756\) | −319.809 | + | 355.192i | −0.423028 | + | 0.469831i | ||||
\(757\) | −78.7293 | − | 136.363i | −0.104002 | − | 0.180136i | 0.809328 | − | 0.587357i | \(-0.199831\pi\) |
−0.913330 | + | 0.407220i | \(0.866498\pi\) | |||||||
\(758\) | −687.109 | + | 396.702i | −0.906476 | + | 0.523354i | ||||
\(759\) | 188.880 | + | 387.258i | 0.248854 | + | 0.510222i | ||||
\(760\) | 234.714 | − | 187.828i | 0.308834 | − | 0.247143i | ||||
\(761\) | 191.065i | 0.251071i | 0.992089 | + | 0.125535i | \(0.0400649\pi\) | ||||
−0.992089 | + | 0.125535i | \(0.959935\pi\) | |||||||
\(762\) | 440.260 | + | 296.956i | 0.577769 | + | 0.389707i | ||||
\(763\) | −823.594 | − | 1426.51i | −1.07942 | − | 1.86960i | ||||
\(764\) | 260.980 | + | 150.677i | 0.341596 | + | 0.197221i | ||||
\(765\) | 424.824 | + | 59.7017i | 0.555325 | + | 0.0780415i | ||||
\(766\) | −535.960 | + | 928.310i | −0.699687 | + | 1.21189i | ||||
\(767\) | − | 377.338i | − | 0.491966i | ||||||
\(768\) | −309.209 | − | 633.965i | −0.402615 | − | 0.825476i | ||||
\(769\) | −288.447 | + | 499.605i | −0.375094 | + | 0.649682i | −0.990341 | − | 0.138652i | \(-0.955723\pi\) |
0.615247 | + | 0.788334i | \(0.289056\pi\) | |||||||
\(770\) | 978.375 | + | 564.865i | 1.27062 | + | 0.733591i | ||||
\(771\) | 15.3792 | − | 7.50102i | 0.0199471 | − | 0.00972895i | ||||
\(772\) | −60.1599 | −0.0779273 | ||||||||
\(773\) | −521.999 | − | 301.376i | −0.675290 | − | 0.389879i | 0.122788 | − | 0.992433i | \(-0.460816\pi\) |
−0.798078 | + | 0.602554i | \(0.794150\pi\) | |||||||
\(774\) | 114.302 | − | 813.346i | 0.147677 | − | 1.05083i | ||||
\(775\) | 121.725 | − | 210.835i | 0.157065 | − | 0.272045i | ||||
\(776\) | 226.815 | − | 130.951i | 0.292287 | − | 0.168752i | ||||
\(777\) | 158.411 | − | 234.855i | 0.203875 | − | 0.302259i | ||||
\(778\) | −1362.70 | −1.75154 | ||||||||
\(779\) | −157.661 | − | 197.016i | −0.202388 | − | 0.252908i | ||||
\(780\) | 48.1204 | − | 23.4701i | 0.0616928 | − | 0.0300899i | ||||
\(781\) | 80.3893 | + | 139.238i | 0.102931 | + | 0.178282i | ||||
\(782\) | −365.003 | + | 210.735i | −0.466756 | + | 0.269482i | ||||
\(783\) | 173.453 | + | 156.174i | 0.221523 | + | 0.199456i | ||||
\(784\) | 1166.30 | + | 2020.10i | 1.48763 | + | 2.57666i | ||||
\(785\) | 78.9260 | + | 45.5680i | 0.100543 | + | 0.0580484i | ||||
\(786\) | 398.354 | + | 816.738i | 0.506811 | + | 1.03911i | ||||
\(787\) | 428.637 | 0.544647 | 0.272324 | − | 0.962206i | \(-0.412208\pi\) | ||||
0.272324 | + | 0.962206i | \(0.412208\pi\) | |||||||
\(788\) | −21.7345 | − | 12.5484i | −0.0275818 | − | 0.0159244i | ||||
\(789\) | −107.781 | + | 1541.43i | −0.136605 | + | 1.95365i | ||||
\(790\) | 651.403 | 0.824561 | ||||||||
\(791\) | 28.7990i | 0.0364083i | ||||||||
\(792\) | −298.550 | − | 738.922i | −0.376958 | − | 0.932982i | ||||
\(793\) | 25.9318 | + | 44.9152i | 0.0327009 | + | 0.0566396i | ||||
\(794\) | −557.793 | − | 322.042i | −0.702510 | − | 0.405595i | ||||
\(795\) | −209.328 | + | 310.345i | −0.263306 | + | 0.390371i | ||||
\(796\) | 167.210 | + | 289.616i | 0.210062 | + | 0.363839i | ||||
\(797\) | 1161.58i | 1.45744i | 0.684814 | + | 0.728718i | \(0.259883\pi\) | ||||
−0.684814 | + | 0.728718i | \(0.740117\pi\) | |||||||
\(798\) | −1705.81 | + | 139.300i | −2.13760 | + | 0.174561i | ||||
\(799\) | −288.616 | −0.361222 | ||||||||
\(800\) | 332.190 | − | 191.790i | 0.415237 | − | 0.239737i | ||||
\(801\) | −118.359 | + | 842.215i | −0.147764 | + | 1.05145i | ||||
\(802\) | 263.277 | − | 456.010i | 0.328276 | − | 0.568591i | ||||
\(803\) | 115.366 | − | 66.6067i | 0.143669 | − | 0.0829474i | ||||
\(804\) | −324.897 | − | 22.7177i | −0.404100 | − | 0.0282559i | ||||
\(805\) | 332.640 | 0.413218 | ||||||||
\(806\) | − | 155.508i | − | 0.192938i | ||||||
\(807\) | 2.56298 | − | 36.6543i | 0.00317593 | − | 0.0454204i | ||||
\(808\) | −595.101 | + | 1030.75i | −0.736512 | + | 1.27568i | ||||
\(809\) | 1202.40i | 1.48628i | 0.669135 | + | 0.743141i | \(0.266665\pi\) | ||||
−0.669135 | + | 0.743141i | \(0.733335\pi\) | |||||||
\(810\) | −117.698 | − | 472.031i | −0.145306 | − | 0.582754i | ||||
\(811\) | 770.245 | − | 1334.10i | 0.949747 | − | 1.64501i | 0.203791 | − | 0.979014i | \(-0.434674\pi\) |
0.745956 | − | 0.665995i | \(-0.231993\pi\) | |||||||
\(812\) | −132.523 | + | 76.5122i | −0.163206 | + | 0.0942268i | ||||
\(813\) | 408.367 | + | 28.5542i | 0.502296 | + | 0.0351220i | ||||
\(814\) | −122.434 | − | 212.062i | −0.150410 | − | 0.260518i | ||||
\(815\) | −551.567 | + | 318.447i | −0.676770 | + | 0.390733i | ||||
\(816\) | 971.457 | − | 473.816i | 1.19051 | − | 0.580657i | ||||
\(817\) | 584.452 | − | 467.704i | 0.715364 | − | 0.572466i | ||||
\(818\) | − | 1699.79i | − | 2.07799i | ||||||
\(819\) | 582.271 | + | 81.8284i | 0.710954 | + | 0.0999125i | ||||
\(820\) | 23.5124 | + | 40.7246i | 0.0286736 | + | 0.0496642i | ||||
\(821\) | −353.637 | − | 204.172i | −0.430739 | − | 0.248687i | 0.268923 | − | 0.963162i | \(-0.413332\pi\) |
−0.699661 | + | 0.714475i | \(0.746666\pi\) | |||||||
\(822\) | 698.704 | − | 1035.88i | 0.850004 | − | 1.26019i | ||||
\(823\) | 251.418 | − | 435.469i | 0.305490 | − | 0.529124i | −0.671880 | − | 0.740660i | \(-0.734513\pi\) |
0.977370 | + | 0.211536i | \(0.0678464\pi\) | |||||||
\(824\) | − | 482.299i | − | 0.585314i | ||||||
\(825\) | 715.150 | − | 348.805i | 0.866849 | − | 0.422795i | ||||
\(826\) | 1123.97 | − | 1946.78i | 1.36074 | − | 2.35687i | ||||
\(827\) | −388.107 | − | 224.073i | −0.469295 | − | 0.270947i | 0.246650 | − | 0.969105i | \(-0.420670\pi\) |
−0.715944 | + | 0.698157i | \(0.754004\pi\) | |||||||
\(828\) | 95.8576 | + | 74.8910i | 0.115770 | + | 0.0904480i | ||||
\(829\) | −1218.01 | −1.46925 | −0.734624 | − | 0.678474i | \(-0.762642\pi\) | ||||
−0.734624 | + | 0.678474i | \(0.762642\pi\) | |||||||
\(830\) | −534.126 | − | 308.378i | −0.643526 | − | 0.371540i | ||||
\(831\) | −271.302 | + | 402.225i | −0.326476 | + | 0.484025i | ||||
\(832\) | −75.0403 | + | 129.974i | −0.0901927 | + | 0.156218i | ||||
\(833\) | −1895.01 | + | 1094.08i | −2.27492 | + | 1.31342i | ||||
\(834\) | −227.814 | − | 153.661i | −0.273159 | − | 0.184246i | ||||
\(835\) | −447.754 | −0.536233 | ||||||||
\(836\) | −136.967 | + | 350.728i | −0.163836 | + | 0.419531i | ||||
\(837\) | −351.778 | − | 74.7685i | −0.420284 | − | 0.0893291i | ||||
\(838\) | −96.0562 | − | 166.374i | −0.114626 | − | 0.198537i | ||||
\(839\) | −571.236 | + | 329.803i | −0.680853 | + | 0.393091i | −0.800176 | − | 0.599765i | \(-0.795261\pi\) |
0.119323 | + | 0.992855i | \(0.461928\pi\) | |||||||
\(840\) | −613.774 | − | 42.9169i | −0.730683 | − | 0.0510915i | ||||
\(841\) | −383.136 | − | 663.612i | −0.455572 | − | 0.789075i | ||||
\(842\) | −1148.47 | − | 663.072i | −1.36398 | − | 0.787496i | ||||
\(843\) | −712.713 | + | 347.617i | −0.845448 | + | 0.412357i | ||||
\(844\) | −212.199 | −0.251421 | ||||||||
\(845\) | 322.439 | + | 186.160i | 0.381585 | + | 0.220308i | ||||
\(846\) | 122.607 | + | 303.457i | 0.144926 | + | 0.358696i | ||||
\(847\) | 1161.13 | 1.37087 | ||||||||
\(848\) | 943.144i | 1.11220i | ||||||||
\(849\) | 399.573 | + | 27.9393i | 0.470639 | + | 0.0329085i | ||||
\(850\) | 389.164 | + | 674.052i | 0.457840 | + | 0.793003i | ||||
\(851\) | −62.4399 | − | 36.0497i | −0.0733724 | − | 0.0423616i | ||||
\(852\) | 37.6317 | + | 25.3827i | 0.0441687 | + | 0.0297919i | ||||
\(853\) | 124.756 | + | 216.084i | 0.146255 | + | 0.253322i | 0.929841 | − | 0.367963i | \(-0.119945\pi\) |
−0.783585 | + | 0.621284i | \(0.786611\pi\) | |||||||
\(854\) | 308.971i | 0.361793i | ||||||||
\(855\) | 217.189 | − | 386.533i | 0.254022 | − | 0.452085i | ||||
\(856\) | 407.986 | 0.476619 | ||||||||
\(857\) | −201.349 | + | 116.249i | −0.234947 | + | 0.135646i | −0.612852 | − | 0.790198i | \(-0.709978\pi\) |
0.377905 | + | 0.925844i | \(0.376644\pi\) | |||||||
\(858\) | 284.209 | − | 421.361i | 0.331246 | − | 0.491097i | ||||
\(859\) | −579.526 | + | 1003.77i | −0.674652 | + | 1.16853i | 0.301918 | + | 0.953334i | \(0.402373\pi\) |
−0.976570 | + | 0.215198i | \(0.930960\pi\) | |||||||
\(860\) | −120.811 | + | 69.7502i | −0.140478 | + | 0.0811048i | ||||
\(861\) | −36.0238 | + | 515.193i | −0.0418395 | + | 0.598366i | ||||
\(862\) | −953.417 | −1.10605 | ||||||||
\(863\) | − | 1022.32i | − | 1.18461i | −0.805714 | − | 0.592304i | \(-0.798218\pi\) | ||
0.805714 | − | 0.592304i | \(-0.201782\pi\) | |||||||
\(864\) | −421.100 | − | 379.152i | −0.487385 | − | 0.438833i | ||||
\(865\) | −272.371 | + | 471.761i | −0.314880 | + | 0.545389i | ||||
\(866\) | 1005.30i | 1.16086i | ||||||||
\(867\) | 64.4050 | + | 132.049i | 0.0742849 | + | 0.152305i | ||||
\(868\) | 117.894 | − | 204.198i | 0.135822 | − | 0.235251i | ||||
\(869\) | 1363.02 | − | 786.941i | 1.56849 | − | 0.905570i | ||||
\(870\) | 10.8643 | − | 155.376i | 0.0124878 | − | 0.178593i | ||||
\(871\) | 200.337 | + | 346.994i | 0.230008 | + | 0.398386i | ||||
\(872\) | 671.542 | − | 387.715i | 0.770117 | − | 0.444627i | ||||
\(873\) | 237.812 | − | 304.390i | 0.272408 | − | 0.348672i | ||||
\(874\) | 65.6499 | + | 430.616i | 0.0751143 | + | 0.492695i | ||||
\(875\) | − | 1454.52i | − | 1.66231i | ||||||
\(876\) | 21.0309 | − | 31.1798i | 0.0240079 | − | 0.0355934i | ||||
\(877\) | −275.511 | − | 477.199i | −0.314152 | − | 0.544127i | 0.665105 | − | 0.746750i | \(-0.268387\pi\) |
−0.979257 | + | 0.202623i | \(0.935053\pi\) | |||||||
\(878\) | −354.560 | − | 204.705i | −0.403827 | − | 0.233150i | ||||
\(879\) | −1012.49 | − | 682.926i | −1.15186 | − | 0.776935i | ||||
\(880\) | −368.680 | + | 638.572i | −0.418954 | + | 0.725650i | ||||
\(881\) | 206.484i | 0.234374i | 0.993110 | + | 0.117187i | \(0.0373877\pi\) | ||||
−0.993110 | + | 0.117187i | \(0.962612\pi\) | |||||||
\(882\) | 1955.36 | + | 1527.67i | 2.21696 | + | 1.73205i | ||||
\(883\) | −286.705 | + | 496.587i | −0.324694 | + | 0.562387i | −0.981450 | − | 0.191716i | \(-0.938595\pi\) |
0.656756 | + | 0.754103i | \(0.271928\pi\) | |||||||
\(884\) | 109.584 | + | 63.2684i | 0.123964 | + | 0.0715706i | ||||
\(885\) | 255.286 | + | 523.408i | 0.288458 | + | 0.591422i | ||||
\(886\) | −1411.33 | −1.59292 | ||||||||
\(887\) | 1402.91 | + | 809.970i | 1.58163 | + | 0.913157i | 0.994621 | + | 0.103579i | \(0.0330294\pi\) |
0.587013 | + | 0.809578i | \(0.300304\pi\) | |||||||
\(888\) | 110.560 | + | 74.5733i | 0.124505 | + | 0.0839790i | ||||
\(889\) | 495.290 | − | 857.867i | 0.557131 | − | 0.964980i | ||||
\(890\) | 491.519 | − | 283.779i | 0.552269 | − | 0.318852i | ||||
\(891\) | −816.522 | − | 845.508i | −0.916411 | − | 0.948942i | ||||
\(892\) | 91.2630 | 0.102313 | ||||||||
\(893\) | −108.506 | + | 277.851i | −0.121508 | + | 0.311143i | ||||
\(894\) | −259.099 | − | 531.227i | −0.289820 | − | 0.594214i | ||||
\(895\) | −368.305 | − | 637.923i | −0.411514 | − | 0.712763i | ||||
\(896\) | −1716.67 | + | 991.122i | −1.91593 | + | 1.10616i | ||||
\(897\) | 10.4385 | − | 149.286i | 0.0116372 | − | 0.166428i | ||||
\(898\) | −358.889 | − | 621.614i | −0.399654 | − | 0.692220i | ||||
\(899\) | −99.7170 | − | 57.5716i | −0.110920 | − | 0.0640396i | ||||
\(900\) | 138.301 | − | 177.020i | 0.153668 | − | 0.196689i | ||||
\(901\) | −884.741 | −0.981955 | ||||||||
\(902\) | 386.604 | + | 223.206i | 0.428608 | + | 0.247457i | ||||
\(903\) | −1528.34 | − | 106.866i | −1.69251 | − | 0.118345i | ||||
\(904\) | −13.5574 | −0.0149971 | ||||||||
\(905\) | − | 509.575i | − | 0.563066i | ||||||
\(906\) | 53.1086 | − | 759.531i | 0.0586188 | − | 0.838334i | ||||
\(907\) | 485.098 | + | 840.215i | 0.534838 | + | 0.926367i | 0.999171 | + | 0.0407060i | \(0.0129607\pi\) |
−0.464333 | + | 0.885661i | \(0.653706\pi\) | |||||||
\(908\) | 330.900 | + | 191.045i | 0.364427 | + | 0.210402i | ||||
\(909\) | −244.291 | + | 1738.32i | −0.268747 | + | 1.91234i | ||||
\(910\) | −196.192 | − | 339.815i | −0.215596 | − | 0.373423i | ||||
\(911\) | − | 1381.63i | − | 1.51660i | −0.651903 | − | 0.758302i | \(-0.726029\pi\) | ||
0.651903 | − | 0.758302i | \(-0.273971\pi\) | |||||||
\(912\) | −90.9193 | − | 1113.36i | −0.0996922 | − | 1.22078i | ||||
\(913\) | −1490.17 | −1.63217 | ||||||||
\(914\) | −160.644 | + | 92.7476i | −0.175759 | + | 0.101474i | ||||
\(915\) | −66.3574 | − | 44.7582i | −0.0725217 | − | 0.0489161i | ||||
\(916\) | 40.7382 | − | 70.5606i | 0.0444740 | − | 0.0770312i | ||||
\(917\) | 1467.95 | − | 847.519i | 1.60081 | − | 0.924230i | ||||
\(918\) | 769.344 | − | 854.462i | 0.838065 | − | 0.930787i | ||||
\(919\) | 821.947 | 0.894393 | 0.447197 | − | 0.894436i | \(-0.352422\pi\) | ||||
0.447197 | + | 0.894436i | \(0.352422\pi\) | |||||||
\(920\) | 156.594i | 0.170210i | ||||||||
\(921\) | 1445.51 | + | 101.074i | 1.56950 | + | 0.109744i | ||||
\(922\) | 139.585 | − | 241.769i | 0.151394 | − | 0.262222i | ||||
\(923\) | − | 55.8426i | − | 0.0605012i | ||||||
\(924\) | 692.639 | − | 337.826i | 0.749609 | − | 0.365612i | ||||
\(925\) | −66.5730 | + | 115.308i | −0.0719708 | + | 0.124657i | ||||
\(926\) | −765.525 | + | 441.976i | −0.826701 | + | 0.477296i | ||||
\(927\) | −266.474 | − | 659.533i | −0.287459 | − | 0.711470i | ||||
\(928\) | −90.7096 | − | 157.114i | −0.0977474 | − | 0.169303i | ||||
\(929\) | 692.122 | − | 399.597i | 0.745019 | − | 0.430137i | −0.0788725 | − | 0.996885i | \(-0.525132\pi\) |
0.823891 | + | 0.566748i | \(0.191799\pi\) | |||||||
\(930\) | 105.208 | + | 215.706i | 0.113127 | + | 0.231942i | ||||
\(931\) | 340.838 | + | 2235.65i | 0.366099 | + | 2.40134i | ||||
\(932\) | − | 299.858i | − | 0.321736i | ||||||
\(933\) | 312.807 | + | 210.989i | 0.335270 | + | 0.226140i | ||||
\(934\) | 202.782 | + | 351.229i | 0.217112 | + | 0.376048i | ||||
\(935\) | −599.030 | − | 345.850i | −0.640673 | − | 0.369893i | ||||
\(936\) | −38.5215 | + | 274.110i | −0.0411555 | + | 0.292853i | ||||
\(937\) | −490.300 | + | 849.224i | −0.523265 | + | 0.906322i | 0.476368 | + | 0.879246i | \(0.341953\pi\) |
−0.999633 | + | 0.0270763i | \(0.991380\pi\) | |||||||
\(938\) | 2386.97i | 2.54474i | ||||||||
\(939\) | −233.146 | − | 478.015i | −0.248291 | − | 0.509068i | ||||
\(940\) | 27.7943 | − | 48.1412i | 0.0295684 | − | 0.0512140i | ||||
\(941\) | 1436.55 | + | 829.394i | 1.52662 | + | 0.881396i | 0.999500 | + | 0.0316070i | \(0.0100625\pi\) |
0.527123 | + | 0.849789i | \(0.323271\pi\) | |||||||
\(942\) | 219.537 | − | 107.077i | 0.233055 | − | 0.113669i | ||||
\(943\) | 131.442 | 0.139388 | ||||||||
\(944\) | 1270.63 | + | 733.601i | 1.34601 | + | 0.777120i | ||||
\(945\) | −863.034 | + | 280.428i | −0.913264 | + | 0.296749i | ||||
\(946\) | −662.147 | + | 1146.87i | −0.699944 | + | 1.21234i | ||||
\(947\) | 688.131 | − | 397.293i | 0.726643 | − | 0.419528i | −0.0905498 | − | 0.995892i | \(-0.528862\pi\) |
0.817193 | + | 0.576364i | \(0.195529\pi\) | |||||||
\(948\) | 248.474 | − | 368.381i | 0.262104 | − | 0.388588i | ||||
\(949\) | −46.2685 | −0.0487550 | ||||||||
\(950\) | 795.219 | − | 121.236i | 0.837072 | − | 0.127617i | ||||
\(951\) | −446.524 | + | 217.786i | −0.469531 | + | 0.229008i | ||||
\(952\) | −727.084 | − | 1259.35i | −0.763744 | − | 1.32284i | ||||
\(953\) | 1144.81 | − | 660.959i | 1.20127 | − | 0.693556i | 0.240436 | − | 0.970665i | \(-0.422710\pi\) |
0.960838 | + | 0.277109i | \(0.0893763\pi\) | |||||||
\(954\) | 375.848 | + | 930.236i | 0.393971 | + | 0.975090i | ||||
\(955\) | 286.078 | + | 495.501i | 0.299558 | + | 0.518850i | ||||
\(956\) | 279.663 | + | 161.464i | 0.292535 | + | 0.168895i | ||||
\(957\) | −164.972 | − | 338.240i | −0.172385 | − | 0.353438i | ||||
\(958\) | 1720.32 | 1.79574 | ||||||||
\(959\) | −2018.46 | − | 1165.36i | −2.10475 | − | 1.21518i | ||||
\(960\) | 16.1561 | − | 231.056i | 0.0168293 | − | 0.240683i | ||||
\(961\) | −783.582 | −0.815381 | ||||||||
\(962\) | 85.0490i | 0.0884085i | ||||||||
\(963\) | 557.911 | − | 225.416i | 0.579347 | − | 0.234077i | ||||
\(964\) | 179.821 | + | 311.459i | 0.186536 | + | 0.323090i | ||||
\(965\) | −98.9181 | − | 57.1104i | −0.102506 | − | 0.0591818i | ||||
\(966\) | 498.532 | − | 739.111i | 0.516079 | − | 0.765125i | ||||
\(967\) | 466.235 | + | 807.543i | 0.482146 | + | 0.835101i | 0.999790 | − | 0.0204947i | \(-0.00652413\pi\) |
−0.517644 | + | 0.855596i | \(0.673191\pi\) | |||||||
\(968\) | 546.613i | 0.564683i | ||||||||
\(969\) | 1044.41 | − | 85.2892i | 1.07783 | − | 0.0880178i | ||||
\(970\) | −257.772 | −0.265745 | ||||||||
\(971\) | 1103.48 | − | 637.093i | 1.13643 | − | 0.656120i | 0.190889 | − | 0.981612i | \(-0.438863\pi\) |
0.945545 | + | 0.325491i | \(0.105530\pi\) | |||||||
\(972\) | −311.838 | − | 113.493i | −0.320821 | − | 0.116762i | ||||
\(973\) | −256.290 | + | 443.907i | −0.263402 | + | 0.456225i | ||||
\(974\) | 654.750 | − | 378.020i | 0.672227 | − | 0.388111i | ||||
\(975\) | −275.687 | − | 19.2769i | −0.282756 | − | 0.0197711i | ||||
\(976\) | −201.661 | −0.206620 | ||||||||
\(977\) | 1316.43i | 1.34742i | 0.738995 | + | 0.673711i | \(0.235301\pi\) | ||||
−0.738995 | + | 0.673711i | \(0.764699\pi\) | |||||||
\(978\) | −119.066 | + | 1702.82i | −0.121744 | + | 1.74112i | ||||
\(979\) | 685.649 | − | 1187.58i | 0.700357 | − | 1.21305i | ||||
\(980\) | − | 421.450i | − | 0.430051i | ||||||
\(981\) | 704.103 | − | 901.225i | 0.717740 | − | 0.918680i | ||||
\(982\) | −135.456 | + | 234.617i | −0.137939 | + | 0.238917i | ||||
\(983\) | 224.514 | − | 129.623i | 0.228397 | − | 0.131865i | −0.381435 | − | 0.924395i | \(-0.624570\pi\) |
0.609832 | + | 0.792531i | \(0.291237\pi\) | |||||||
\(984\) | −242.532 | − | 16.9586i | −0.246476 | − | 0.0172343i | ||||
\(985\) | −23.8246 | − | 41.2655i | −0.0241875 | − | 0.0418939i | ||||
\(986\) | 318.802 | − | 184.060i | 0.323329 | − | 0.186674i | ||||
\(987\) | 548.716 | − | 267.629i | 0.555944 | − | 0.271154i | ||||
\(988\) | 102.107 | − | 81.7107i | 0.103347 | − | 0.0827031i | ||||
\(989\) | 389.928i | 0.394265i | ||||||||
\(990\) | −109.160 | + | 776.753i | −0.110262 | + | 0.784599i | ||||
\(991\) | 263.205 | + | 455.885i | 0.265596 | + | 0.460025i | 0.967720 | − | 0.252030i | \(-0.0810980\pi\) |
−0.702124 | + | 0.712055i | \(0.747765\pi\) | |||||||
\(992\) | 242.088 | + | 139.770i | 0.244041 | + | 0.140897i | ||||
\(993\) | −935.564 | + | 1387.04i | −0.942160 | + | 1.39682i | ||||
\(994\) | 166.338 | − | 288.106i | 0.167342 | − | 0.289845i | ||||
\(995\) | 634.935i | 0.638126i | ||||||||
\(996\) | −378.134 | + | 184.430i | −0.379652 | + | 0.185171i | ||||
\(997\) | 946.796 | − | 1639.90i | 0.949645 | − | 1.64483i | 0.203474 | − | 0.979080i | \(-0.434777\pi\) |
0.746172 | − | 0.665753i | \(-0.231890\pi\) | |||||||
\(998\) | −1823.99 | − | 1053.08i | −1.82765 | − | 1.05519i | ||||
\(999\) | 192.391 | + | 40.8917i | 0.192584 | + | 0.0409327i |
(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 | 57.3.h.b.26.3 | yes | 16 | |
3.2 | odd | 2 | inner | 57.3.h.b.26.6 | yes | 16 | |
19.11 | even | 3 | inner | 57.3.h.b.11.6 | yes | 16 | |
57.11 | odd | 6 | inner | 57.3.h.b.11.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
57.3.h.b.11.3 | ✓ | 16 | 57.11 | odd | 6 | inner | |
57.3.h.b.11.6 | yes | 16 | 19.11 | even | 3 | inner | |
57.3.h.b.26.3 | yes | 16 | 1.1 | even | 1 | trivial | |
57.3.h.b.26.6 | yes | 16 | 3.2 | odd | 2 | inner |