Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,6,Mod(67,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.67");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.5764215125\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 63 x^{10} - 126 x^{9} + 2784 x^{8} - 5290 x^{7} + 62015 x^{6} - 99530 x^{5} + \cdots + 5466244 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8}\cdot 7^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.5 | ||
Root | \(-0.455061 + 0.788188i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.67 |
Dual form | 147.6.e.p.79.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.65908 | + | 4.60566i | 0.470063 | + | 0.814173i | 0.999414 | − | 0.0342301i | \(-0.0108979\pi\) |
−0.529351 | + | 0.848403i | \(0.677565\pi\) | |||||||
\(3\) | −4.50000 | + | 7.79423i | −0.288675 | + | 0.500000i | ||||
\(4\) | 1.85862 | − | 3.21922i | 0.0580818 | − | 0.100601i | ||||
\(5\) | −51.7353 | − | 89.6081i | −0.925468 | − | 1.60296i | −0.790806 | − | 0.612067i | \(-0.790338\pi\) |
−0.134662 | − | 0.990892i | \(-0.542995\pi\) | |||||||
\(6\) | −47.8634 | −0.542782 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 189.950 | 1.04933 | ||||||||
\(9\) | −40.5000 | − | 70.1481i | −0.166667 | − | 0.288675i | ||||
\(10\) | 275.136 | − | 476.550i | 0.870057 | − | 1.50698i | ||||
\(11\) | −326.654 | + | 565.781i | −0.813966 | + | 1.40983i | 0.0961016 | + | 0.995372i | \(0.469363\pi\) |
−0.910068 | + | 0.414459i | \(0.863971\pi\) | |||||||
\(12\) | 16.7276 | + | 28.9730i | 0.0335336 | + | 0.0580818i | ||||
\(13\) | −138.055 | −0.226565 | −0.113282 | − | 0.993563i | \(-0.536137\pi\) | ||||
−0.113282 | + | 0.993563i | \(0.536137\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 931.235 | 1.06864 | ||||||||
\(16\) | 445.615 | + | 771.828i | 0.435171 | + | 0.753739i | ||||
\(17\) | −587.188 | + | 1017.04i | −0.492782 | + | 0.853523i | −0.999965 | − | 0.00831489i | \(-0.997353\pi\) |
0.507184 | + | 0.861838i | \(0.330687\pi\) | |||||||
\(18\) | 215.385 | − | 373.058i | 0.156688 | − | 0.271391i | ||||
\(19\) | 855.386 | + | 1481.57i | 0.543599 | + | 0.941541i | 0.998694 | + | 0.0510976i | \(0.0162720\pi\) |
−0.455095 | + | 0.890443i | \(0.650395\pi\) | |||||||
\(20\) | −384.625 | −0.215012 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3474.39 | −1.53046 | ||||||||
\(23\) | 2010.14 | + | 3481.67i | 0.792332 | + | 1.37236i | 0.924520 | + | 0.381134i | \(0.124466\pi\) |
−0.132188 | + | 0.991225i | \(0.542200\pi\) | |||||||
\(24\) | −854.774 | + | 1480.51i | −0.302917 | + | 0.524667i | ||||
\(25\) | −3790.57 | + | 6565.47i | −1.21298 | + | 2.10095i | ||||
\(26\) | −367.098 | − | 635.832i | −0.106500 | − | 0.184463i | ||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2649.46 | 0.585009 | 0.292505 | − | 0.956264i | \(-0.405511\pi\) | ||||
0.292505 | + | 0.956264i | \(0.405511\pi\) | |||||||
\(30\) | 2476.22 | + | 4288.95i | 0.502327 | + | 0.870057i | ||||
\(31\) | 1437.32 | − | 2489.52i | 0.268628 | − | 0.465277i | −0.699880 | − | 0.714260i | \(-0.746763\pi\) |
0.968508 | + | 0.248984i | \(0.0800966\pi\) | |||||||
\(32\) | 669.346 | − | 1159.34i | 0.115551 | − | 0.200141i | ||||
\(33\) | −2939.89 | − | 5092.03i | −0.469944 | − | 0.813966i | ||||
\(34\) | −6245.51 | −0.926554 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −301.096 | −0.0387212 | ||||||||
\(37\) | −1428.43 | − | 2474.12i | −0.171536 | − | 0.297110i | 0.767421 | − | 0.641144i | \(-0.221540\pi\) |
−0.938957 | + | 0.344034i | \(0.888206\pi\) | |||||||
\(38\) | −4549.08 | + | 7879.23i | −0.511051 | + | 0.885166i | ||||
\(39\) | 621.246 | − | 1076.03i | 0.0654037 | − | 0.113282i | ||||
\(40\) | −9827.10 | − | 17021.0i | −0.971126 | − | 1.68204i | ||||
\(41\) | 216.487 | 0.0201128 | 0.0100564 | − | 0.999949i | \(-0.496799\pi\) | ||||
0.0100564 | + | 0.999949i | \(0.496799\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2928.29 | 0.241514 | 0.120757 | − | 0.992682i | \(-0.461468\pi\) | ||||
0.120757 | + | 0.992682i | \(0.461468\pi\) | |||||||
\(44\) | 1214.25 | + | 2103.14i | 0.0945533 | + | 0.163771i | ||||
\(45\) | −4190.56 | + | 7258.26i | −0.308489 | + | 0.534319i | ||||
\(46\) | −10690.2 | + | 18516.0i | −0.744891 | + | 1.29019i | ||||
\(47\) | −7408.41 | − | 12831.7i | −0.489193 | − | 0.847307i | 0.510730 | − | 0.859741i | \(-0.329375\pi\) |
−0.999923 | + | 0.0124342i | \(0.996042\pi\) | |||||||
\(48\) | −8021.07 | −0.502492 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −40317.7 | −2.28071 | ||||||||
\(51\) | −5284.69 | − | 9153.35i | −0.284508 | − | 0.492782i | ||||
\(52\) | −256.591 | + | 444.429i | −0.0131593 | + | 0.0227926i | ||||
\(53\) | −10583.9 | + | 18331.8i | −0.517552 | + | 0.896427i | 0.482240 | + | 0.876039i | \(0.339823\pi\) |
−0.999792 | + | 0.0203878i | \(0.993510\pi\) | |||||||
\(54\) | 1938.47 | + | 3357.52i | 0.0904636 | + | 0.156688i | ||||
\(55\) | 67598.1 | 3.01320 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −15397.0 | −0.627694 | ||||||||
\(58\) | 7045.13 | + | 12202.5i | 0.274991 | + | 0.476299i | ||||
\(59\) | −17344.6 | + | 30041.7i | −0.648684 | + | 1.12355i | 0.334753 | + | 0.942306i | \(0.391347\pi\) |
−0.983437 | + | 0.181248i | \(0.941986\pi\) | |||||||
\(60\) | 1730.81 | − | 2997.85i | 0.0620685 | − | 0.107506i | ||||
\(61\) | 4376.56 | + | 7580.43i | 0.150594 | + | 0.260837i | 0.931446 | − | 0.363879i | \(-0.118548\pi\) |
−0.780852 | + | 0.624716i | \(0.785215\pi\) | |||||||
\(62\) | 15287.8 | 0.505087 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 35638.7 | 1.08761 | ||||||||
\(65\) | 7142.29 | + | 12370.8i | 0.209679 | + | 0.363174i | ||||
\(66\) | 15634.8 | − | 27080.2i | 0.441806 | − | 0.765231i | ||||
\(67\) | 6034.26 | − | 10451.6i | 0.164224 | − | 0.284444i | −0.772155 | − | 0.635434i | \(-0.780821\pi\) |
0.936379 | + | 0.350989i | \(0.114155\pi\) | |||||||
\(68\) | 2182.72 | + | 3780.58i | 0.0572433 | + | 0.0991484i | ||||
\(69\) | −36182.5 | −0.914906 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −35541.5 | −0.836738 | −0.418369 | − | 0.908277i | \(-0.637398\pi\) | ||||
−0.418369 | + | 0.908277i | \(0.637398\pi\) | |||||||
\(72\) | −7692.97 | − | 13324.6i | −0.174889 | − | 0.302917i | ||||
\(73\) | −16742.9 | + | 28999.5i | −0.367725 | + | 0.636918i | −0.989209 | − | 0.146508i | \(-0.953197\pi\) |
0.621484 | + | 0.783426i | \(0.286530\pi\) | |||||||
\(74\) | 7596.63 | − | 13157.8i | 0.161266 | − | 0.279320i | ||||
\(75\) | −34115.2 | − | 59089.2i | −0.700316 | − | 1.21298i | ||||
\(76\) | 6359.35 | 0.126293 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6607.76 | 0.122975 | ||||||||
\(79\) | −21567.4 | − | 37355.9i | −0.388804 | − | 0.673428i | 0.603485 | − | 0.797374i | \(-0.293778\pi\) |
−0.992289 | + | 0.123946i | \(0.960445\pi\) | |||||||
\(80\) | 46108.0 | − | 79861.5i | 0.805474 | − | 1.39512i | ||||
\(81\) | −3280.50 | + | 5681.99i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 575.656 | + | 997.066i | 0.00945428 | + | 0.0163753i | ||||
\(83\) | −43338.8 | −0.690529 | −0.345265 | − | 0.938505i | \(-0.612211\pi\) | ||||
−0.345265 | + | 0.938505i | \(0.612211\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 121513. | 1.82422 | ||||||||
\(86\) | 7786.54 | + | 13486.7i | 0.113527 | + | 0.196634i | ||||
\(87\) | −11922.6 | + | 20650.5i | −0.168878 | + | 0.292505i | ||||
\(88\) | −62047.9 | + | 107470.i | −0.854123 | + | 1.47938i | ||||
\(89\) | 51766.7 | + | 89662.5i | 0.692748 | + | 1.19987i | 0.970934 | + | 0.239347i | \(0.0769334\pi\) |
−0.278186 | + | 0.960527i | \(0.589733\pi\) | |||||||
\(90\) | −44572.0 | −0.580038 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 14944.3 | 0.184080 | ||||||||
\(93\) | 12935.9 | + | 22405.7i | 0.155092 | + | 0.268628i | ||||
\(94\) | 39399.1 | − | 68241.2i | 0.459903 | − | 0.796575i | ||||
\(95\) | 88507.3 | − | 153299.i | 1.00617 | − | 1.74273i | ||||
\(96\) | 6024.11 | + | 10434.1i | 0.0667137 | + | 0.115551i | ||||
\(97\) | −86294.4 | −0.931223 | −0.465611 | − | 0.884989i | \(-0.654165\pi\) | ||||
−0.465611 | + | 0.884989i | \(0.654165\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 52918.0 | 0.542644 | ||||||||
\(100\) | 14090.5 | + | 24405.4i | 0.140905 | + | 0.244054i | ||||
\(101\) | −91338.5 | + | 158203.i | −0.890944 | + | 1.54316i | −0.0521977 | + | 0.998637i | \(0.516623\pi\) |
−0.838746 | + | 0.544523i | \(0.816711\pi\) | |||||||
\(102\) | 28104.8 | − | 48678.9i | 0.267473 | − | 0.463277i | ||||
\(103\) | 20044.1 | + | 34717.4i | 0.186163 | + | 0.322444i | 0.943968 | − | 0.330038i | \(-0.107061\pi\) |
−0.757805 | + | 0.652481i | \(0.773728\pi\) | |||||||
\(104\) | −26223.5 | −0.237742 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −112573. | −0.973129 | ||||||||
\(107\) | 55103.7 | + | 95442.4i | 0.465287 | + | 0.805901i | 0.999214 | − | 0.0396292i | \(-0.0126177\pi\) |
−0.533927 | + | 0.845531i | \(0.679284\pi\) | |||||||
\(108\) | 1354.93 | − | 2346.81i | 0.0111779 | − | 0.0193606i | ||||
\(109\) | 111177. | − | 192564.i | 0.896289 | − | 1.55242i | 0.0640869 | − | 0.997944i | \(-0.479587\pi\) |
0.832202 | − | 0.554473i | \(-0.187080\pi\) | |||||||
\(110\) | 179749. | + | 311334.i | 1.41639 | + | 2.45327i | ||||
\(111\) | 25711.8 | 0.198073 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −153473. | −1.13067 | −0.565335 | − | 0.824861i | \(-0.691253\pi\) | ||||
−0.565335 | + | 0.824861i | \(0.691253\pi\) | |||||||
\(114\) | −40941.7 | − | 70913.1i | −0.295055 | − | 0.511051i | ||||
\(115\) | 207990. | − | 360250.i | 1.46656 | − | 2.54015i | ||||
\(116\) | 4924.34 | − | 8529.21i | 0.0339784 | − | 0.0588524i | ||||
\(117\) | 5591.21 | + | 9684.27i | 0.0377608 | + | 0.0654037i | ||||
\(118\) | −184482. | −1.21969 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 176888. | 1.12136 | ||||||||
\(121\) | −132880. | − | 230155.i | −0.825082 | − | 1.42908i | ||||
\(122\) | −23275.2 | + | 40313.9i | −0.141578 | + | 0.245219i | ||||
\(123\) | −974.193 | + | 1687.35i | −0.00580607 | + | 0.0100564i | ||||
\(124\) | −5342.88 | − | 9254.14i | −0.0312048 | − | 0.0540483i | ||||
\(125\) | 461080. | 2.63938 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 142247. | 0.782591 | 0.391296 | − | 0.920265i | \(-0.372027\pi\) | ||||
0.391296 | + | 0.920265i | \(0.372027\pi\) | |||||||
\(128\) | 73347.1 | + | 127041.i | 0.395693 | + | 0.685360i | ||||
\(129\) | −13177.3 | + | 22823.7i | −0.0697191 | + | 0.120757i | ||||
\(130\) | −37983.8 | + | 65789.9i | −0.197124 | + | 0.341429i | ||||
\(131\) | −63500.2 | − | 109986.i | −0.323293 | − | 0.559961i | 0.657872 | − | 0.753130i | \(-0.271457\pi\) |
−0.981165 | + | 0.193169i | \(0.938123\pi\) | |||||||
\(132\) | −21856.5 | −0.109181 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 64182.2 | 0.308782 | ||||||||
\(135\) | −37715.0 | − | 65324.3i | −0.178106 | − | 0.308489i | ||||
\(136\) | −111536. | + | 193186.i | −0.517093 | + | 0.895631i | ||||
\(137\) | −49827.4 | + | 86303.6i | −0.226812 | + | 0.392851i | −0.956862 | − | 0.290544i | \(-0.906164\pi\) |
0.730049 | + | 0.683395i | \(0.239497\pi\) | |||||||
\(138\) | −96212.2 | − | 166644.i | −0.430063 | − | 0.744891i | ||||
\(139\) | 23441.9 | 0.102909 | 0.0514547 | − | 0.998675i | \(-0.483614\pi\) | ||||
0.0514547 | + | 0.998675i | \(0.483614\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 133351. | 0.564871 | ||||||||
\(142\) | −94507.5 | − | 163692.i | −0.393319 | − | 0.681249i | ||||
\(143\) | 45096.1 | − | 78108.8i | 0.184416 | − | 0.319418i | ||||
\(144\) | 36094.8 | − | 62518.1i | 0.145057 | − | 0.251246i | ||||
\(145\) | −137071. | − | 237413.i | −0.541408 | − | 0.937746i | ||||
\(146\) | −178082. | −0.691415 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10619.7 | −0.0398526 | ||||||||
\(149\) | −249352. | − | 431891.i | −0.920127 | − | 1.59371i | −0.799216 | − | 0.601043i | \(-0.794752\pi\) |
−0.120911 | − | 0.992663i | \(-0.538581\pi\) | |||||||
\(150\) | 181430. | − | 314245.i | 0.658386 | − | 1.14036i | ||||
\(151\) | 108169. | − | 187354.i | 0.386065 | − | 0.668684i | −0.605851 | − | 0.795578i | \(-0.707167\pi\) |
0.991916 | + | 0.126894i | \(0.0405007\pi\) | |||||||
\(152\) | 162480. | + | 281424.i | 0.570417 | + | 0.987991i | ||||
\(153\) | 95124.4 | 0.328521 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −297441. | −0.994426 | ||||||||
\(156\) | −2309.32 | − | 3999.86i | −0.00759753 | − | 0.0131593i | ||||
\(157\) | −213418. | + | 369651.i | −0.691007 | + | 1.19686i | 0.280501 | + | 0.959854i | \(0.409499\pi\) |
−0.971508 | + | 0.237006i | \(0.923834\pi\) | |||||||
\(158\) | 114699. | − | 198664.i | 0.365524 | − | 0.633107i | ||||
\(159\) | −95254.7 | − | 164986.i | −0.298809 | − | 0.517552i | ||||
\(160\) | −138515. | −0.427757 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −34892.4 | −0.104458 | ||||||||
\(163\) | 136598. | + | 236594.i | 0.402694 | + | 0.697486i | 0.994050 | − | 0.108925i | \(-0.0347407\pi\) |
−0.591356 | + | 0.806410i | \(0.701407\pi\) | |||||||
\(164\) | 402.367 | − | 696.921i | 0.00116819 | − | 0.00202336i | ||||
\(165\) | −304192. | + | 526875.i | −0.869836 | + | 1.50660i | ||||
\(166\) | −115241. | − | 199604.i | −0.324592 | − | 0.562210i | ||||
\(167\) | 600365. | 1.66581 | 0.832903 | − | 0.553420i | \(-0.186677\pi\) | ||||
0.832903 | + | 0.553420i | \(0.186677\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −352234. | −0.948668 | ||||||||
\(170\) | 323113. | + | 559648.i | 0.857496 | + | 1.48523i | ||||
\(171\) | 69286.3 | − | 120007.i | 0.181200 | − | 0.313847i | ||||
\(172\) | 5442.57 | − | 9426.81i | 0.0140276 | − | 0.0242965i | ||||
\(173\) | 250094. | + | 433176.i | 0.635313 | + | 1.10040i | 0.986449 | + | 0.164070i | \(0.0524624\pi\) |
−0.351135 | + | 0.936325i | \(0.614204\pi\) | |||||||
\(174\) | −126812. | −0.317532 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −582248. | −1.41686 | ||||||||
\(177\) | −156101. | − | 270375.i | −0.374518 | − | 0.648684i | ||||
\(178\) | −275303. | + | 476839.i | −0.651270 | + | 1.12803i | ||||
\(179\) | −144782. | + | 250769.i | −0.337739 | + | 0.584981i | −0.984007 | − | 0.178130i | \(-0.942995\pi\) |
0.646268 | + | 0.763110i | \(0.276329\pi\) | |||||||
\(180\) | 15577.3 | + | 26980.7i | 0.0358353 | + | 0.0620685i | ||||
\(181\) | 168243. | 0.381715 | 0.190858 | − | 0.981618i | \(-0.438873\pi\) | ||||
0.190858 | + | 0.981618i | \(0.438873\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −78778.1 | −0.173891 | ||||||||
\(184\) | 381826. | + | 661342.i | 0.831421 | + | 1.44006i | ||||
\(185\) | −147801. | + | 255999.i | −0.317503 | + | 0.549931i | ||||
\(186\) | −68795.2 | + | 119157.i | −0.145806 | + | 0.252544i | ||||
\(187\) | −383615. | − | 664440.i | −0.802216 | − | 1.38948i | ||||
\(188\) | −55077.6 | −0.113653 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 941391. | 1.89185 | ||||||||
\(191\) | 193055. | + | 334381.i | 0.382911 | + | 0.663222i | 0.991477 | − | 0.130282i | \(-0.0415882\pi\) |
−0.608566 | + | 0.793503i | \(0.708255\pi\) | |||||||
\(192\) | −160374. | + | 277777.i | −0.313965 | + | 0.543804i | ||||
\(193\) | 169841. | − | 294173.i | 0.328208 | − | 0.568473i | −0.653948 | − | 0.756539i | \(-0.726889\pi\) |
0.982156 | + | 0.188066i | \(0.0602220\pi\) | |||||||
\(194\) | −229464. | − | 397443.i | −0.437733 | − | 0.758176i | ||||
\(195\) | −128561. | −0.242116 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −460915. | −0.846166 | −0.423083 | − | 0.906091i | \(-0.639052\pi\) | ||||
−0.423083 | + | 0.906091i | \(0.639052\pi\) | |||||||
\(198\) | 140713. | + | 243722.i | 0.255077 | + | 0.441806i | ||||
\(199\) | 196444. | − | 340251.i | 0.351646 | − | 0.609069i | −0.634892 | − | 0.772601i | \(-0.718955\pi\) |
0.986538 | + | 0.163532i | \(0.0522887\pi\) | |||||||
\(200\) | −720019. | + | 1.24711e6i | −1.27283 | + | 2.20460i | ||||
\(201\) | 54308.3 | + | 94064.7i | 0.0948148 | + | 0.164224i | ||||
\(202\) | −971504. | −1.67520 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −39288.9 | −0.0660989 | ||||||||
\(205\) | −11200.0 | − | 19399.0i | −0.0186138 | − | 0.0322400i | ||||
\(206\) | −106598. | + | 184632.i | −0.175017 | + | 0.303138i | ||||
\(207\) | 162821. | − | 282015.i | 0.264111 | − | 0.457453i | ||||
\(208\) | −61519.3 | − | 106554.i | −0.0985945 | − | 0.170771i | ||||
\(209\) | −1.11766e6 | −1.76988 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −469348. | −0.725752 | −0.362876 | − | 0.931837i | \(-0.618205\pi\) | ||||
−0.362876 | + | 0.931837i | \(0.618205\pi\) | |||||||
\(212\) | 39342.7 | + | 68143.6i | 0.0601208 | + | 0.104132i | ||||
\(213\) | 159937. | − | 277018.i | 0.241545 | − | 0.418369i | ||||
\(214\) | −293050. | + | 507577.i | −0.437429 | + | 0.757649i | ||||
\(215\) | −151496. | − | 262398.i | −0.223514 | − | 0.387137i | ||||
\(216\) | 138473. | 0.201944 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.18251e6 | 1.68525 | ||||||||
\(219\) | −150686. | − | 260996.i | −0.212306 | − | 0.367725i | ||||
\(220\) | 125639. | − | 217613.i | 0.175012 | − | 0.303130i | ||||
\(221\) | 81064.0 | − | 140407.i | 0.111647 | − | 0.193378i | ||||
\(222\) | 68369.7 | + | 118420.i | 0.0931068 | + | 0.161266i | ||||
\(223\) | 83059.4 | 0.111848 | 0.0559238 | − | 0.998435i | \(-0.482190\pi\) | ||||
0.0559238 | + | 0.998435i | \(0.482190\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 614073. | 0.808656 | ||||||||
\(226\) | −408097. | − | 706844.i | −0.531486 | − | 0.920561i | ||||
\(227\) | −69884.4 | + | 121043.i | −0.0900152 | + | 0.155911i | −0.907517 | − | 0.420015i | \(-0.862025\pi\) |
0.817502 | + | 0.575926i | \(0.195358\pi\) | |||||||
\(228\) | −28617.1 | + | 49566.2i | −0.0364576 | + | 0.0631464i | ||||
\(229\) | −71923.5 | − | 124575.i | −0.0906321 | − | 0.156979i | 0.817145 | − | 0.576432i | \(-0.195555\pi\) |
−0.907777 | + | 0.419453i | \(0.862222\pi\) | |||||||
\(230\) | 2.21225e6 | 2.75749 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 503265. | 0.613870 | ||||||||
\(233\) | 186246. | + | 322588.i | 0.224749 | + | 0.389276i | 0.956244 | − | 0.292570i | \(-0.0945105\pi\) |
−0.731495 | + | 0.681847i | \(0.761177\pi\) | |||||||
\(234\) | −29734.9 | + | 51502.4i | −0.0354999 | + | 0.0614877i | ||||
\(235\) | −766552. | + | 1.32771e6i | −0.905465 | + | 1.56831i | ||||
\(236\) | 64473.9 | + | 111672.i | 0.0753535 | + | 0.130516i | ||||
\(237\) | 388213. | 0.448952 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −201182. | −0.227822 | −0.113911 | − | 0.993491i | \(-0.536338\pi\) | ||||
−0.113911 | + | 0.993491i | \(0.536338\pi\) | |||||||
\(240\) | 414972. | + | 718753.i | 0.465041 | + | 0.805474i | ||||
\(241\) | 21010.3 | − | 36390.9i | 0.0233018 | − | 0.0403599i | −0.854139 | − | 0.520044i | \(-0.825915\pi\) |
0.877441 | + | 0.479684i | \(0.159249\pi\) | |||||||
\(242\) | 706678. | − | 1.22400e6i | 0.775681 | − | 1.34352i | ||||
\(243\) | −29524.5 | − | 51137.9i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 32537.4 | 0.0349872 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −10361.8 | −0.0109169 | ||||||||
\(247\) | −118090. | − | 204538.i | −0.123160 | − | 0.213320i | ||||
\(248\) | 273019. | − | 472884.i | 0.281880 | − | 0.488231i | ||||
\(249\) | 195025. | − | 337793.i | 0.199339 | − | 0.345265i | ||||
\(250\) | 1.22605e6 | + | 2.12358e6i | 1.24067 | + | 2.14891i | ||||
\(251\) | −1.23330e6 | −1.23562 | −0.617809 | − | 0.786329i | \(-0.711979\pi\) | ||||
−0.617809 | + | 0.786329i | \(0.711979\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.62648e6 | −2.57972 | ||||||||
\(254\) | 378247. | + | 655143.i | 0.367867 | + | 0.637164i | ||||
\(255\) | −546810. | + | 947102.i | −0.526606 | + | 0.912108i | ||||
\(256\) | 180149. | − | 312027.i | 0.171803 | − | 0.297572i | ||||
\(257\) | −280344. | − | 485570.i | −0.264764 | − | 0.458584i | 0.702738 | − | 0.711449i | \(-0.251961\pi\) |
−0.967502 | + | 0.252865i | \(0.918627\pi\) | |||||||
\(258\) | −140158. | −0.131089 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 53099.2 | 0.0487141 | ||||||||
\(261\) | −107303. | − | 185855.i | −0.0975016 | − | 0.168878i | ||||
\(262\) | 337704. | − | 584920.i | 0.303936 | − | 0.526433i | ||||
\(263\) | 722618. | − | 1.25161e6i | 0.644198 | − | 1.11578i | −0.340288 | − | 0.940321i | \(-0.610525\pi\) |
0.984486 | − | 0.175462i | \(-0.0561420\pi\) | |||||||
\(264\) | −558431. | − | 967231.i | −0.493128 | − | 0.854123i | ||||
\(265\) | 2.19023e6 | 1.91591 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −931800. | −0.799916 | ||||||||
\(268\) | −22430.8 | − | 38851.2i | −0.0190769 | − | 0.0330421i | ||||
\(269\) | −208771. | + | 361602.i | −0.175910 | + | 0.304685i | −0.940476 | − | 0.339861i | \(-0.889620\pi\) |
0.764566 | + | 0.644545i | \(0.222953\pi\) | |||||||
\(270\) | 200574. | − | 347405.i | 0.167442 | − | 0.290019i | ||||
\(271\) | 214256. | + | 371102.i | 0.177219 | + | 0.306952i | 0.940927 | − | 0.338610i | \(-0.109957\pi\) |
−0.763708 | + | 0.645562i | \(0.776623\pi\) | |||||||
\(272\) | −1.04664e6 | −0.857778 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −529980. | −0.426465 | ||||||||
\(275\) | −2.47641e6 | − | 4.28927e6i | −1.97466 | − | 3.42020i | ||||
\(276\) | −67249.6 | + | 116480.i | −0.0531394 | + | 0.0920402i | ||||
\(277\) | 345444. | − | 598326.i | 0.270506 | − | 0.468531i | −0.698485 | − | 0.715625i | \(-0.746142\pi\) |
0.968992 | + | 0.247094i | \(0.0794755\pi\) | |||||||
\(278\) | 62333.7 | + | 107965.i | 0.0483739 | + | 0.0837860i | ||||
\(279\) | −232847. | −0.179085 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.91606e6 | 1.44758 | 0.723792 | − | 0.690018i | \(-0.242397\pi\) | ||||
0.723792 | + | 0.690018i | \(0.242397\pi\) | |||||||
\(282\) | 354592. | + | 614171.i | 0.265525 | + | 0.459903i | ||||
\(283\) | 812086. | − | 1.40657e6i | 0.602748 | − | 1.04399i | −0.389655 | − | 0.920961i | \(-0.627406\pi\) |
0.992403 | − | 0.123030i | \(-0.0392610\pi\) | |||||||
\(284\) | −66058.0 | + | 114416.i | −0.0485993 | + | 0.0841764i | ||||
\(285\) | 796566. | + | 1.37969e6i | 0.580911 | + | 1.00617i | ||||
\(286\) | 479656. | 0.346749 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −108434. | −0.0770343 | ||||||||
\(289\) | 20349.6 | + | 35246.6i | 0.0143322 | + | 0.0248241i | ||||
\(290\) | 728963. | − | 1.26260e6i | 0.508991 | − | 0.881599i | ||||
\(291\) | 388325. | − | 672599.i | 0.268821 | − | 0.465611i | ||||
\(292\) | 62237.3 | + | 107798.i | 0.0427163 | + | 0.0739868i | ||||
\(293\) | −531272. | −0.361533 | −0.180767 | − | 0.983526i | \(-0.557858\pi\) | ||||
−0.180767 | + | 0.983526i | \(0.557858\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.58930e6 | 2.40135 | ||||||||
\(296\) | −271331. | − | 469959.i | −0.179999 | − | 0.311767i | ||||
\(297\) | −238131. | + | 412455.i | −0.156648 | + | 0.271322i | ||||
\(298\) | 1.32609e6 | − | 2.29686e6i | 0.865035 | − | 1.49828i | ||||
\(299\) | −277509. | − | 480660.i | −0.179515 | − | 0.310928i | ||||
\(300\) | −253628. | −0.162703 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.15052e6 | 0.725899 | ||||||||
\(303\) | −822046. | − | 1.42383e6i | −0.514387 | − | 0.890944i | ||||
\(304\) | −762347. | + | 1.32042e6i | −0.473117 | + | 0.819463i | ||||
\(305\) | 452845. | − | 784351.i | 0.278740 | − | 0.482793i | ||||
\(306\) | 252943. | + | 438110.i | 0.154426 | + | 0.267473i | ||||
\(307\) | 409059. | 0.247708 | 0.123854 | − | 0.992300i | \(-0.460475\pi\) | ||||
0.123854 | + | 0.992300i | \(0.460475\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −360794. | −0.214963 | ||||||||
\(310\) | −790920. | − | 1.36991e6i | −0.467442 | − | 0.809634i | ||||
\(311\) | 154352. | − | 267345.i | 0.0904922 | − | 0.156737i | −0.817226 | − | 0.576317i | \(-0.804489\pi\) |
0.907718 | + | 0.419580i | \(0.137823\pi\) | |||||||
\(312\) | 118006. | − | 204392.i | 0.0686303 | − | 0.118871i | ||||
\(313\) | −318866. | − | 552293.i | −0.183970 | − | 0.318646i | 0.759259 | − | 0.650789i | \(-0.225562\pi\) |
−0.943229 | + | 0.332143i | \(0.892228\pi\) | |||||||
\(314\) | −2.26998e6 | −1.29927 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −160342. | −0.0903297 | ||||||||
\(317\) | 1.47162e6 | + | 2.54893e6i | 0.822525 | + | 1.42465i | 0.903796 | + | 0.427963i | \(0.140768\pi\) |
−0.0812718 | + | 0.996692i | \(0.525898\pi\) | |||||||
\(318\) | 506579. | − | 877421.i | 0.280918 | − | 0.486564i | ||||
\(319\) | −865458. | + | 1.49902e6i | −0.476178 | + | 0.824764i | ||||
\(320\) | −1.84378e6 | − | 3.19352e6i | −1.00655 | − | 1.74339i | ||||
\(321\) | −991866. | −0.537268 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.00909e6 | −1.07150 | ||||||||
\(324\) | 12194.4 | + | 21121.3i | 0.00645354 | + | 0.0111779i | ||||
\(325\) | 523306. | − | 906393.i | 0.274820 | − | 0.476002i | ||||
\(326\) | −726448. | + | 1.25824e6i | −0.378583 | + | 0.655724i | ||||
\(327\) | 1.00059e6 | + | 1.73307e6i | 0.517472 | + | 0.896289i | ||||
\(328\) | 41121.7 | 0.0211051 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.23548e6 | −1.63551 | ||||||||
\(331\) | 1.42496e6 | + | 2.46810e6i | 0.714878 | + | 1.23820i | 0.963007 | + | 0.269478i | \(0.0868510\pi\) |
−0.248129 | + | 0.968727i | \(0.579816\pi\) | |||||||
\(332\) | −80550.4 | + | 139517.i | −0.0401072 | + | 0.0694677i | ||||
\(333\) | −115703. | + | 200404.i | −0.0571788 | + | 0.0990365i | ||||
\(334\) | 1.59642e6 | + | 2.76507e6i | 0.783033 | + | 1.35625i | ||||
\(335\) | −1.24874e6 | −0.607937 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.46617e6 | 1.66255 | 0.831277 | − | 0.555859i | \(-0.187611\pi\) | ||||
0.831277 | + | 0.555859i | \(0.187611\pi\) | |||||||
\(338\) | −936617. | − | 1.62227e6i | −0.445934 | − | 0.772380i | ||||
\(339\) | 690629. | − | 1.19620e6i | 0.326397 | − | 0.565335i | ||||
\(340\) | 225847. | − | 391178.i | 0.105954 | − | 0.183517i | ||||
\(341\) | 939016. | + | 1.62642e6i | 0.437308 | + | 0.757439i | ||||
\(342\) | 736950. | 0.340701 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 556228. | 0.253429 | ||||||||
\(345\) | 1.87191e6 | + | 3.24225e6i | 0.846716 | + | 1.46656i | ||||
\(346\) | −1.33004e6 | + | 2.30369e6i | −0.597274 | + | 1.03451i | ||||
\(347\) | −7557.66 | + | 13090.3i | −0.00336949 | + | 0.00583612i | −0.867705 | − | 0.497079i | \(-0.834406\pi\) |
0.864336 | + | 0.502915i | \(0.167739\pi\) | |||||||
\(348\) | 44319.1 | + | 76762.9i | 0.0196175 | + | 0.0339784i | ||||
\(349\) | 3.24698e6 | 1.42698 | 0.713488 | − | 0.700667i | \(-0.247114\pi\) | ||||
0.713488 | + | 0.700667i | \(0.247114\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −100642. | −0.0436024 | ||||||||
\(352\) | 437289. | + | 757407.i | 0.188110 | + | 0.325816i | ||||
\(353\) | 883929. | − | 1.53101e6i | 0.377555 | − | 0.653945i | −0.613151 | − | 0.789966i | \(-0.710098\pi\) |
0.990706 | + | 0.136021i | \(0.0434315\pi\) | |||||||
\(354\) | 830169. | − | 1.43790e6i | 0.352094 | − | 0.609845i | ||||
\(355\) | 1.83875e6 | + | 3.18480e6i | 0.774374 | + | 1.34126i | ||||
\(356\) | 384858. | 0.160944 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.53994e6 | −0.635034 | ||||||||
\(359\) | 60790.4 | + | 105292.i | 0.0248942 | + | 0.0431181i | 0.878204 | − | 0.478286i | \(-0.158742\pi\) |
−0.853310 | + | 0.521404i | \(0.825408\pi\) | |||||||
\(360\) | −795995. | + | 1.37870e6i | −0.323709 | + | 0.560680i | ||||
\(361\) | −225323. | + | 390270.i | −0.0909990 | + | 0.157615i | ||||
\(362\) | 447370. | + | 774868.i | 0.179430 | + | 0.310782i | ||||
\(363\) | 2.39185e6 | 0.952723 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.46479e6 | 1.36127 | ||||||||
\(366\) | −209477. | − | 362825.i | −0.0817398 | − | 0.141578i | ||||
\(367\) | −1.04421e6 | + | 1.80862e6i | −0.404689 | + | 0.700942i | −0.994285 | − | 0.106756i | \(-0.965954\pi\) |
0.589596 | + | 0.807698i | \(0.299287\pi\) | |||||||
\(368\) | −1.79150e6 | + | 3.10297e6i | −0.689600 | + | 1.19442i | ||||
\(369\) | −8767.73 | − | 15186.2i | −0.00335213 | − | 0.00580607i | ||||
\(370\) | −1.57206e6 | −0.596985 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 96171.8 | 0.0360322 | ||||||||
\(373\) | 1.14677e6 | + | 1.98627e6i | 0.426782 | + | 0.739208i | 0.996585 | − | 0.0825735i | \(-0.0263139\pi\) |
−0.569803 | + | 0.821781i | \(0.692981\pi\) | |||||||
\(374\) | 2.04012e6 | − | 3.53359e6i | 0.754183 | − | 1.30628i | ||||
\(375\) | −2.07486e6 | + | 3.59376e6i | −0.761922 | + | 1.31969i | ||||
\(376\) | −1.40723e6 | − | 2.43739e6i | −0.513327 | − | 0.889108i | ||||
\(377\) | −365771. | −0.132543 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.93812e6 | −1.05068 | −0.525341 | − | 0.850892i | \(-0.676062\pi\) | ||||
−0.525341 | + | 0.850892i | \(0.676062\pi\) | |||||||
\(380\) | −329003. | − | 569849.i | −0.116880 | − | 0.202442i | ||||
\(381\) | −640113. | + | 1.10871e6i | −0.225915 | + | 0.391296i | ||||
\(382\) | −1.02670e6 | + | 1.77829e6i | −0.359985 | + | 0.623512i | ||||
\(383\) | −2.52303e6 | − | 4.37001e6i | −0.878871 | − | 1.52225i | −0.852581 | − | 0.522594i | \(-0.824964\pi\) |
−0.0262892 | − | 0.999654i | \(-0.508369\pi\) | |||||||
\(384\) | −1.32025e6 | −0.456907 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.80648e6 | 0.617113 | ||||||||
\(387\) | −118596. | − | 205414.i | −0.0402524 | − | 0.0697191i | ||||
\(388\) | −160388. | + | 277801.i | −0.0540871 | + | 0.0936816i | ||||
\(389\) | 538107. | − | 932029.i | 0.180300 | − | 0.312288i | −0.761683 | − | 0.647950i | \(-0.775627\pi\) |
0.941983 | + | 0.335662i | \(0.108960\pi\) | |||||||
\(390\) | −341854. | − | 592109.i | −0.113810 | − | 0.197124i | ||||
\(391\) | −4.72132e6 | −1.56179 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.14300e6 | 0.373307 | ||||||||
\(394\) | −1.22561e6 | − | 2.12282e6i | −0.397751 | − | 0.688925i | ||||
\(395\) | −2.23159e6 | + | 3.86523e6i | −0.719651 | + | 1.24647i | ||||
\(396\) | 98354.3 | − | 170355.i | 0.0315178 | − | 0.0545904i | ||||
\(397\) | −2.17173e6 | − | 3.76154e6i | −0.691559 | − | 1.19781i | −0.971327 | − | 0.237747i | \(-0.923591\pi\) |
0.279769 | − | 0.960067i | \(-0.409742\pi\) | |||||||
\(398\) | 2.08944e6 | 0.661183 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.75655e6 | −2.11142 | ||||||||
\(401\) | 352042. | + | 609754.i | 0.109328 | + | 0.189362i | 0.915498 | − | 0.402322i | \(-0.131797\pi\) |
−0.806170 | + | 0.591684i | \(0.798463\pi\) | |||||||
\(402\) | −288820. | + | 500251.i | −0.0891378 | + | 0.154391i | ||||
\(403\) | −198429. | + | 343690.i | −0.0608616 | + | 0.105415i | ||||
\(404\) | 339527. | + | 588078.i | 0.103495 | + | 0.179259i | ||||
\(405\) | 678870. | 0.205660 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.86642e6 | 0.558499 | ||||||||
\(408\) | −1.00383e6 | − | 1.73868e6i | −0.298544 | − | 0.517093i | ||||
\(409\) | 817500. | − | 1.41595e6i | 0.241646 | − | 0.418543i | −0.719537 | − | 0.694454i | \(-0.755646\pi\) |
0.961183 | + | 0.275911i | \(0.0889794\pi\) | |||||||
\(410\) | 59563.4 | − | 103167.i | 0.0174993 | − | 0.0303096i | ||||
\(411\) | −448447. | − | 776733.i | −0.130950 | − | 0.226812i | ||||
\(412\) | 149017. | 0.0432508 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.73182e6 | 0.496594 | ||||||||
\(415\) | 2.24215e6 | + | 3.88351e6i | 0.639063 | + | 1.10689i | ||||
\(416\) | −92406.3 | + | 160052.i | −0.0261799 | + | 0.0453449i | ||||
\(417\) | −105488. | + | 182711.i | −0.0297074 | + | 0.0514547i | ||||
\(418\) | −2.97195e6 | − | 5.14757e6i | −0.831957 | − | 1.44099i | ||||
\(419\) | −5.92839e6 | −1.64969 | −0.824844 | − | 0.565360i | \(-0.808737\pi\) | ||||
−0.824844 | + | 0.565360i | \(0.808737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.46170e6 | −1.50184 | −0.750918 | − | 0.660395i | \(-0.770389\pi\) | ||||
−0.750918 | + | 0.660395i | \(0.770389\pi\) | |||||||
\(422\) | −1.24803e6 | − | 2.16165e6i | −0.341149 | − | 0.590888i | ||||
\(423\) | −600081. | + | 1.03937e6i | −0.163064 | + | 0.282436i | ||||
\(424\) | −2.01040e6 | + | 3.48212e6i | −0.543085 | + | 0.940651i | ||||
\(425\) | −4.45156e6 | − | 7.71032e6i | −1.19547 | − | 2.07062i | ||||
\(426\) | 1.70113e6 | 0.454166 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 409667. | 0.108099 | ||||||||
\(429\) | 405865. | + | 702979.i | 0.106473 | + | 0.184416i | ||||
\(430\) | 805678. | − | 1.39547e6i | 0.210131 | − | 0.363958i | ||||
\(431\) | −1.72263e6 | + | 2.98369e6i | −0.446683 | + | 0.773677i | −0.998168 | − | 0.0605075i | \(-0.980728\pi\) |
0.551485 | + | 0.834185i | \(0.314061\pi\) | |||||||
\(432\) | 324854. | + | 562663.i | 0.0837487 | + | 0.145057i | ||||
\(433\) | 2.46833e6 | 0.632680 | 0.316340 | − | 0.948646i | \(-0.397546\pi\) | ||||
0.316340 | + | 0.948646i | \(0.397546\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.46727e6 | 0.625164 | ||||||||
\(436\) | −413271. | − | 715806.i | −0.104116 | − | 0.180335i | ||||
\(437\) | −3.43890e6 | + | 5.95634e6i | −0.861421 | + | 1.49202i | ||||
\(438\) | 801371. | − | 1.38802e6i | 0.199594 | − | 0.345708i | ||||
\(439\) | 3.06890e6 | + | 5.31549e6i | 0.760014 | + | 1.31638i | 0.942843 | + | 0.333238i | \(0.108141\pi\) |
−0.182829 | + | 0.983145i | \(0.558526\pi\) | |||||||
\(440\) | 1.28403e7 | 3.16185 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 862222. | 0.209925 | ||||||||
\(443\) | 896094. | + | 1.55208e6i | 0.216942 | + | 0.375755i | 0.953872 | − | 0.300215i | \(-0.0970583\pi\) |
−0.736929 | + | 0.675970i | \(0.763725\pi\) | |||||||
\(444\) | 47788.5 | − | 82772.0i | 0.0115044 | − | 0.0199263i | ||||
\(445\) | 5.35632e6 | − | 9.27742e6i | 1.28223 | − | 2.22089i | ||||
\(446\) | 220861. | + | 382543.i | 0.0525754 | + | 0.0910633i | ||||
\(447\) | 4.48834e6 | 1.06247 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.76014e6 | −0.880213 | −0.440107 | − | 0.897945i | \(-0.645059\pi\) | ||||
−0.440107 | + | 0.897945i | \(0.645059\pi\) | |||||||
\(450\) | 1.63287e6 | + | 2.82821e6i | 0.380119 | + | 0.658386i | ||||
\(451\) | −70716.4 | + | 122484.i | −0.0163711 | + | 0.0283557i | ||||
\(452\) | −285248. | + | 494064.i | −0.0656714 | + | 0.113746i | ||||
\(453\) | 973521. | + | 1.68619e6i | 0.222895 | + | 0.386065i | ||||
\(454\) | −743312. | −0.169251 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.92465e6 | −0.658660 | ||||||||
\(457\) | −3.77251e6 | − | 6.53418e6i | −0.844968 | − | 1.46353i | −0.885649 | − | 0.464355i | \(-0.846286\pi\) |
0.0406817 | − | 0.999172i | \(-0.487047\pi\) | |||||||
\(458\) | 382500. | − | 662510.i | 0.0852056 | − | 0.147580i | ||||
\(459\) | −428060. | + | 741421.i | −0.0948359 | + | 0.164261i | ||||
\(460\) | −773150. | − | 1.33913e6i | −0.170361 | − | 0.295073i | ||||
\(461\) | 359098. | 0.0786975 | 0.0393487 | − | 0.999226i | \(-0.487472\pi\) | ||||
0.0393487 | + | 0.999226i | \(0.487472\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −890950. | −0.193153 | −0.0965764 | − | 0.995326i | \(-0.530789\pi\) | ||||
−0.0965764 | + | 0.995326i | \(0.530789\pi\) | |||||||
\(464\) | 1.18064e6 | + | 2.04493e6i | 0.254579 | + | 0.440944i | ||||
\(465\) | 1.33849e6 | − | 2.31833e6i | 0.287066 | − | 0.497213i | ||||
\(466\) | −990486. | + | 1.71557e6i | −0.211292 | + | 0.365969i | ||||
\(467\) | 3.80660e6 | + | 6.59322e6i | 0.807690 | + | 1.39896i | 0.914460 | + | 0.404676i | \(0.132616\pi\) |
−0.106770 | + | 0.994284i | \(0.534051\pi\) | |||||||
\(468\) | 41567.7 | 0.00877287 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −8.15328e6 | −1.70250 | ||||||||
\(471\) | −1.92076e6 | − | 3.32686e6i | −0.398953 | − | 0.691007i | ||||
\(472\) | −3.29459e6 | + | 5.70641e6i | −0.680686 | + | 1.17898i | ||||
\(473\) | −956537. | + | 1.65677e6i | −0.196584 | + | 0.340494i | ||||
\(474\) | 1.03229e6 | + | 1.78798e6i | 0.211036 | + | 0.365524i | ||||
\(475\) | −1.29696e7 | −2.63751 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.71458e6 | 0.345035 | ||||||||
\(478\) | −534960. | − | 926577.i | −0.107091 | − | 0.185486i | ||||
\(479\) | 2.98004e6 | − | 5.16158e6i | 0.593448 | − | 1.02788i | −0.400316 | − | 0.916377i | \(-0.631100\pi\) |
0.993764 | − | 0.111505i | \(-0.0355672\pi\) | |||||||
\(480\) | 623318. | − | 1.07962e6i | 0.123483 | − | 0.213879i | ||||
\(481\) | 197202. | + | 341564.i | 0.0388641 | + | 0.0673146i | ||||
\(482\) | 223472. | 0.0438132 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −987895. | −0.191689 | ||||||||
\(485\) | 4.46447e6 | + | 7.73268e6i | 0.861817 | + | 1.49271i | ||||
\(486\) | 157016. | − | 271959.i | 0.0301545 | − | 0.0522292i | ||||
\(487\) | 128913. | − | 223284.i | 0.0246306 | − | 0.0426615i | −0.853447 | − | 0.521179i | \(-0.825492\pi\) |
0.878078 | + | 0.478518i | \(0.158826\pi\) | |||||||
\(488\) | 831327. | + | 1.43990e6i | 0.158024 | + | 0.273705i | ||||
\(489\) | −2.45876e6 | −0.464990 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 592660. | 0.110944 | 0.0554718 | − | 0.998460i | \(-0.482334\pi\) | ||||
0.0554718 | + | 0.998460i | \(0.482334\pi\) | |||||||
\(492\) | 3621.31 | + | 6272.28i | 0.000674454 | + | 0.00116819i | ||||
\(493\) | −1.55573e6 | + | 2.69461e6i | −0.288282 | + | 0.499319i | ||||
\(494\) | 628021. | − | 1.08776e6i | 0.115786 | − | 0.200548i | ||||
\(495\) | −2.73772e6 | − | 4.74188e6i | −0.502200 | − | 0.869836i | ||||
\(496\) | 2.56198e6 | 0.467596 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.07434e6 | 0.374807 | ||||||||
\(499\) | 1.21121e6 | + | 2.09788e6i | 0.217755 | + | 0.377163i | 0.954121 | − | 0.299420i | \(-0.0967932\pi\) |
−0.736366 | + | 0.676583i | \(0.763460\pi\) | |||||||
\(500\) | 856972. | − | 1.48432e6i | 0.153300 | − | 0.265523i | ||||
\(501\) | −2.70164e6 | + | 4.67938e6i | −0.480876 | + | 0.832903i | ||||
\(502\) | −3.27944e6 | − | 5.68015e6i | −0.580818 | − | 1.00601i | ||||
\(503\) | 2.31849e6 | 0.408588 | 0.204294 | − | 0.978910i | \(-0.434510\pi\) | ||||
0.204294 | + | 0.978910i | \(0.434510\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.89017e7 | 3.29816 | ||||||||
\(506\) | −6.98402e6 | − | 1.20967e7i | −1.21263 | − | 2.10034i | ||||
\(507\) | 1.58505e6 | − | 2.74539e6i | 0.273857 | − | 0.474334i | ||||
\(508\) | 264384. | − | 457926.i | 0.0454543 | − | 0.0787292i | ||||
\(509\) | 4.24943e6 | + | 7.36023e6i | 0.727003 | + | 1.25921i | 0.958144 | + | 0.286286i | \(0.0924208\pi\) |
−0.231141 | + | 0.972920i | \(0.574246\pi\) | |||||||
\(510\) | −5.81604e6 | −0.990151 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 6.61033e6 | 1.11442 | ||||||||
\(513\) | 623577. | + | 1.08007e6i | 0.104616 | + | 0.181200i | ||||
\(514\) | 1.49091e6 | − | 2.58234e6i | 0.248911 | − | 0.431127i | ||||
\(515\) | 2.07397e6 | − | 3.59223e6i | 0.344576 | − | 0.596823i | ||||
\(516\) | 48983.1 | + | 84841.3i | 0.00809883 | + | 0.0140276i | ||||
\(517\) | 9.67995e6 | 1.59275 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.50169e6 | −0.733597 | ||||||||
\(520\) | 1.35668e6 | + | 2.34983e6i | 0.220023 | + | 0.381091i | ||||
\(521\) | 580461. | − | 1.00539e6i | 0.0936868 | − | 0.162270i | −0.815373 | − | 0.578936i | \(-0.803468\pi\) |
0.909060 | + | 0.416666i | \(0.136801\pi\) | |||||||
\(522\) | 570655. | − | 988404.i | 0.0916637 | − | 0.158766i | ||||
\(523\) | −614536. | − | 1.06441e6i | −0.0982411 | − | 0.170159i | 0.812716 | − | 0.582661i | \(-0.197988\pi\) |
−0.910957 | + | 0.412502i | \(0.864655\pi\) | |||||||
\(524\) | −472091. | −0.0751099 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.68598e6 | 1.21125 | ||||||||
\(527\) | 1.68796e6 | + | 2.92363e6i | 0.264750 | + | 0.458560i | ||||
\(528\) | 2.62012e6 | − | 4.53818e6i | 0.409012 | − | 0.708429i | ||||
\(529\) | −4.86316e6 | + | 8.42325e6i | −0.755579 | + | 1.30870i | ||||
\(530\) | 5.82400e6 | + | 1.00875e7i | 0.900600 | + | 1.55988i | ||||
\(531\) | 2.80982e6 | 0.432456 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −29887.1 | −0.00455686 | ||||||||
\(534\) | −2.47773e6 | − | 4.29155e6i | −0.376011 | − | 0.651270i | ||||
\(535\) | 5.70161e6 | − | 9.87547e6i | 0.861218 | − | 1.49167i | ||||
\(536\) | 1.14621e6 | − | 1.98529e6i | 0.172326 | − | 0.298477i | ||||
\(537\) | −1.30303e6 | − | 2.25692e6i | −0.194994 | − | 0.337739i | ||||
\(538\) | −2.22055e6 | −0.330754 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −280391. | −0.0413790 | ||||||||
\(541\) | 395140. | + | 684402.i | 0.0580440 | + | 0.100535i | 0.893587 | − | 0.448889i | \(-0.148180\pi\) |
−0.835543 | + | 0.549425i | \(0.814847\pi\) | |||||||
\(542\) | −1.13945e6 | + | 1.97358e6i | −0.166608 | + | 0.288573i | ||||
\(543\) | −757092. | + | 1.31132e6i | −0.110192 | + | 0.190858i | ||||
\(544\) | 786063. | + | 1.36150e6i | 0.113883 | + | 0.197252i | ||||
\(545\) | −2.30070e7 | −3.31795 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.74335e6 | 0.249124 | 0.124562 | − | 0.992212i | \(-0.460247\pi\) | ||||
0.124562 | + | 0.992212i | \(0.460247\pi\) | |||||||
\(548\) | 185220. | + | 320811.i | 0.0263474 | + | 0.0456350i | ||||
\(549\) | 354501. | − | 614015.i | 0.0501981 | − | 0.0869456i | ||||
\(550\) | 1.31699e7 | − | 2.28110e7i | 1.85642 | − | 3.21542i | ||||
\(551\) | 2.26631e6 | + | 3.92537e6i | 0.318010 | + | 0.550810i | ||||
\(552\) | −6.87287e6 | −0.960042 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.67424e6 | 0.508620 | ||||||||
\(555\) | −1.33021e6 | − | 2.30399e6i | −0.183310 | − | 0.317503i | ||||
\(556\) | 43569.5 | − | 75464.5i | 0.00597717 | − | 0.0103528i | ||||
\(557\) | 5.09171e6 | − | 8.81910e6i | 0.695385 | − | 1.20444i | −0.274665 | − | 0.961540i | \(-0.588567\pi\) |
0.970051 | − | 0.242903i | \(-0.0780996\pi\) | |||||||
\(558\) | −619157. | − | 1.07241e6i | −0.0841812 | − | 0.145806i | ||||
\(559\) | −404264. | −0.0547186 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.90506e6 | 0.926319 | ||||||||
\(562\) | 5.09496e6 | + | 8.82473e6i | 0.680456 | + | 1.17858i | ||||
\(563\) | 4.28710e6 | − | 7.42547e6i | 0.570023 | − | 0.987309i | −0.426540 | − | 0.904469i | \(-0.640268\pi\) |
0.996563 | − | 0.0828400i | \(-0.0263991\pi\) | |||||||
\(564\) | 247849. | − | 429288.i | 0.0328088 | − | 0.0568265i | ||||
\(565\) | 7.93997e6 | + | 1.37524e7i | 1.04640 | + | 1.81242i | ||||
\(566\) | 8.63760e6 | 1.13332 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.75109e6 | −0.878018 | ||||||||
\(569\) | −1.33980e6 | − | 2.32060e6i | −0.173484 | − | 0.300483i | 0.766152 | − | 0.642660i | \(-0.222169\pi\) |
−0.939636 | + | 0.342177i | \(0.888836\pi\) | |||||||
\(570\) | −4.23626e6 | + | 7.33741e6i | −0.546129 | + | 0.945923i | ||||
\(571\) | −3.72509e6 | + | 6.45204e6i | −0.478130 | + | 0.828145i | −0.999686 | − | 0.0250718i | \(-0.992019\pi\) |
0.521556 | + | 0.853217i | \(0.325352\pi\) | |||||||
\(572\) | −167633. | − | 290349.i | −0.0214225 | − | 0.0371048i | ||||
\(573\) | −3.47499e6 | −0.442148 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.04784e7 | −3.84434 | ||||||||
\(576\) | −1.44337e6 | − | 2.49999e6i | −0.181268 | − | 0.313965i | ||||
\(577\) | −2.86445e6 | + | 4.96138e6i | −0.358181 | + | 0.620387i | −0.987657 | − | 0.156632i | \(-0.949936\pi\) |
0.629476 | + | 0.777020i | \(0.283270\pi\) | |||||||
\(578\) | −108223. | + | 187447.i | −0.0134741 | + | 0.0233377i | ||||
\(579\) | 1.52857e6 | + | 2.64756e6i | 0.189491 | + | 0.328208i | ||||
\(580\) | −1.01905e6 | −0.125784 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 4.13034e6 | 0.505451 | ||||||||
\(583\) | −6.91452e6 | − | 1.19763e7i | −0.842540 | − | 1.45932i | ||||
\(584\) | −3.18031e6 | + | 5.50845e6i | −0.385866 | + | 0.668340i | ||||
\(585\) | 578526. | − | 1.00204e6i | 0.0698929 | − | 0.121058i | ||||
\(586\) | −1.41269e6 | − | 2.44686e6i | −0.169943 | − | 0.294350i | ||||
\(587\) | 1.41744e7 | 1.69788 | 0.848942 | − | 0.528486i | \(-0.177240\pi\) | ||||
0.848942 | + | 0.528486i | \(0.177240\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.91787e6 | 0.584102 | ||||||||
\(590\) | 9.54423e6 | + | 1.65311e7i | 1.12878 | + | 1.95511i | ||||
\(591\) | 2.07412e6 | − | 3.59248e6i | 0.244267 | − | 0.423083i | ||||
\(592\) | 1.27306e6 | − | 2.20501e6i | 0.149295 | − | 0.258587i | ||||
\(593\) | 3.04747e6 | + | 5.27837e6i | 0.355879 | + | 0.616401i | 0.987268 | − | 0.159066i | \(-0.0508482\pi\) |
−0.631389 | + | 0.775466i | \(0.717515\pi\) | |||||||
\(594\) | −2.53283e6 | −0.294537 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.85380e6 | −0.213771 | ||||||||
\(597\) | 1.76799e6 | + | 3.06226e6i | 0.203023 | + | 0.351646i | ||||
\(598\) | 1.47584e6 | − | 2.55623e6i | 0.168766 | − | 0.292312i | ||||
\(599\) | −987321. | + | 1.71009e6i | −0.112432 | + | 0.194738i | −0.916750 | − | 0.399460i | \(-0.869197\pi\) |
0.804318 | + | 0.594199i | \(0.202531\pi\) | |||||||
\(600\) | −6.48017e6 | − | 1.12240e7i | −0.734866 | − | 1.27283i | ||||
\(601\) | 5.14078e6 | 0.580554 | 0.290277 | − | 0.956943i | \(-0.406253\pi\) | ||||
0.290277 | + | 0.956943i | \(0.406253\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −977549. | −0.109483 | ||||||||
\(604\) | −402090. | − | 696440.i | −0.0448467 | − | 0.0776768i | ||||
\(605\) | −1.37492e7 | + | 2.38143e7i | −1.52717 | + | 2.64514i | ||||
\(606\) | 4.37177e6 | − | 7.57212e6i | 0.483588 | − | 0.837599i | ||||
\(607\) | 657412. | + | 1.13867e6i | 0.0724213 | + | 0.125437i | 0.899962 | − | 0.435968i | \(-0.143594\pi\) |
−0.827541 | + | 0.561406i | \(0.810261\pi\) | |||||||
\(608\) | 2.29020e6 | 0.251255 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.81660e6 | 0.524102 | ||||||||
\(611\) | 1.02277e6 | + | 1.77148e6i | 0.110834 | + | 0.191970i | ||||
\(612\) | 176800. | − | 306227.i | 0.0190811 | − | 0.0330495i | ||||
\(613\) | −6.70903e6 | + | 1.16204e7i | −0.721122 | + | 1.24902i | 0.239429 | + | 0.970914i | \(0.423040\pi\) |
−0.960551 | + | 0.278106i | \(0.910293\pi\) | |||||||
\(614\) | 1.08772e6 | + | 1.88399e6i | 0.116438 | + | 0.201677i | ||||
\(615\) | 201600. | 0.0214933 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.48394e7 | 1.56929 | 0.784646 | − | 0.619944i | \(-0.212845\pi\) | ||||
0.784646 | + | 0.619944i | \(0.212845\pi\) | |||||||
\(618\) | −959378. | − | 1.66169e6i | −0.101046 | − | 0.175017i | ||||
\(619\) | 5.72341e6 | − | 9.91324e6i | 0.600383 | − | 1.03989i | −0.392380 | − | 0.919803i | \(-0.628348\pi\) |
0.992763 | − | 0.120091i | \(-0.0383186\pi\) | |||||||
\(620\) | −552830. | + | 957530.i | −0.0577581 | + | 0.100040i | ||||
\(621\) | 1.46539e6 | + | 2.53814e6i | 0.152484 | + | 0.264111i | ||||
\(622\) | 1.64173e6 | 0.170148 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.10735e6 | 0.113847 | ||||||||
\(625\) | −1.20085e7 | − | 2.07994e7i | −1.22968 | − | 2.12986i | ||||
\(626\) | 1.69578e6 | − | 2.93718e6i | 0.172955 | − | 0.299567i | ||||
\(627\) | 5.02948e6 | − | 8.71131e6i | 0.510921 | − | 0.884942i | ||||
\(628\) | 793327. | + | 1.37408e6i | 0.0802699 | + | 0.139032i | ||||
\(629\) | 3.35504e6 | 0.338120 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.11608e7 | −1.11589 | −0.557944 | − | 0.829878i | \(-0.688410\pi\) | ||||
−0.557944 | + | 0.829878i | \(0.688410\pi\) | |||||||
\(632\) | −4.09673e6 | − | 7.09574e6i | −0.407985 | − | 0.706651i | ||||
\(633\) | 2.11206e6 | − | 3.65820e6i | 0.209507 | − | 0.362876i | ||||
\(634\) | −7.82633e6 | + | 1.35556e7i | −0.773277 | + | 1.33935i | ||||
\(635\) | −7.35921e6 | − | 1.27465e7i | −0.724263 | − | 1.25446i | ||||
\(636\) | −708169. | −0.0694215 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −9.20528e6 | −0.895334 | ||||||||
\(639\) | 1.43943e6 | + | 2.49316e6i | 0.139456 | + | 0.241545i | ||||
\(640\) | 7.58926e6 | − | 1.31450e7i | 0.732402 | − | 1.26856i | ||||
\(641\) | 8.60750e6 | − | 1.49086e7i | 0.827431 | − | 1.43315i | −0.0726153 | − | 0.997360i | \(-0.523135\pi\) |
0.900047 | − | 0.435793i | \(-0.143532\pi\) | |||||||
\(642\) | −2.63745e6 | − | 4.56820e6i | −0.252550 | − | 0.437429i | ||||
\(643\) | −2.73062e6 | −0.260456 | −0.130228 | − | 0.991484i | \(-0.541571\pi\) | ||||
−0.130228 | + | 0.991484i | \(0.541571\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.72692e6 | 0.258091 | ||||||||
\(646\) | −5.34232e6 | − | 9.25318e6i | −0.503673 | − | 0.872388i | ||||
\(647\) | 2.19984e6 | − | 3.81024e6i | 0.206600 | − | 0.357843i | −0.744041 | − | 0.668134i | \(-0.767093\pi\) |
0.950641 | + | 0.310291i | \(0.100427\pi\) | |||||||
\(648\) | −623130. | + | 1.07929e6i | −0.0582963 | + | 0.100972i | ||||
\(649\) | −1.13313e7 | − | 1.96265e7i | −1.05601 | − | 1.82907i | ||||
\(650\) | 5.56605e6 | 0.516730 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.01553e6 | 0.0935567 | ||||||||
\(653\) | −2.80250e6 | − | 4.85407e6i | −0.257195 | − | 0.445475i | 0.708294 | − | 0.705917i | \(-0.249465\pi\) |
−0.965489 | + | 0.260442i | \(0.916132\pi\) | |||||||
\(654\) | −5.32130e6 | + | 9.21676e6i | −0.486489 | + | 0.842624i | ||||
\(655\) | −6.57040e6 | + | 1.13803e7i | −0.598396 | + | 1.03645i | ||||
\(656\) | 96470.0 | + | 167091.i | 0.00875251 | + | 0.0151598i | ||||
\(657\) | 2.71235e6 | 0.245150 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.33959e7 | −1.20159 | −0.600796 | − | 0.799402i | \(-0.705150\pi\) | ||||
−0.600796 | + | 0.799402i | \(0.705150\pi\) | |||||||
\(660\) | 1.13075e6 | + | 1.95852e6i | 0.101043 | + | 0.175012i | ||||
\(661\) | −938286. | + | 1.62516e6i | −0.0835279 | + | 0.144675i | −0.904763 | − | 0.425915i | \(-0.859952\pi\) |
0.821235 | + | 0.570590i | \(0.193285\pi\) | |||||||
\(662\) | −7.57814e6 | + | 1.31257e7i | −0.672075 | + | 1.16407i | ||||
\(663\) | 729576. | + | 1.26366e6i | 0.0644595 | + | 0.111647i | ||||
\(664\) | −8.23220e6 | −0.724596 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.23065e6 | −0.107510 | ||||||||
\(667\) | 5.32579e6 | + | 9.22455e6i | 0.463521 | + | 0.802843i | ||||
\(668\) | 1.11585e6 | − | 1.93271e6i | 0.0967530 | − | 0.167581i | ||||
\(669\) | −373767. | + | 647384.i | −0.0322876 | + | 0.0559238i | ||||
\(670\) | −3.32048e6 | − | 5.75124e6i | −0.285768 | − | 0.494965i | ||||
\(671\) | −5.71849e6 | −0.490315 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.82367e6 | 0.240313 | 0.120156 | − | 0.992755i | \(-0.461660\pi\) | ||||
0.120156 | + | 0.992755i | \(0.461660\pi\) | |||||||
\(674\) | 9.21682e6 | + | 1.59640e7i | 0.781505 | + | 1.35361i | ||||
\(675\) | −2.76333e6 | + | 4.78623e6i | −0.233439 | + | 0.404328i | ||||
\(676\) | −654669. | + | 1.13392e6i | −0.0551004 | + | 0.0954367i | ||||
\(677\) | −4.65924e6 | − | 8.07005e6i | −0.390700 | − | 0.676713i | 0.601842 | − | 0.798615i | \(-0.294434\pi\) |
−0.992542 | + | 0.121902i | \(0.961100\pi\) | |||||||
\(678\) | 7.34574e6 | 0.613708 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.30814e7 | 1.91421 | ||||||||
\(681\) | −628960. | − | 1.08939e6i | −0.0519703 | − | 0.0900152i | ||||
\(682\) | −4.99383e6 | + | 8.64957e6i | −0.411124 | + | 0.712088i | ||||
\(683\) | 1.06809e7 | − | 1.84999e7i | 0.876108 | − | 1.51746i | 0.0205308 | − | 0.999789i | \(-0.493464\pi\) |
0.855577 | − | 0.517675i | \(-0.173202\pi\) | |||||||
\(684\) | −257554. | − | 446096.i | −0.0210488 | − | 0.0364576i | ||||
\(685\) | 1.03113e7 | 0.839631 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.29462e6 | 0.104653 | ||||||||
\(688\) | 1.30489e6 | + | 2.26014e6i | 0.105100 | + | 0.182039i | ||||
\(689\) | 1.46115e6 | − | 2.53079e6i | 0.117259 | − | 0.203099i | ||||
\(690\) | −9.95512e6 | + | 1.72428e7i | −0.796020 | + | 1.37875i | ||||
\(691\) | −5.54424e6 | − | 9.60290e6i | −0.441720 | − | 0.765081i | 0.556098 | − | 0.831117i | \(-0.312298\pi\) |
−0.997817 | + | 0.0660361i | \(0.978965\pi\) | |||||||
\(692\) | 1.85932e6 | 0.147601 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −80385.6 | −0.00633548 | ||||||||
\(695\) | −1.21277e6 | − | 2.10058e6i | −0.0952394 | − | 0.164959i | ||||
\(696\) | −2.26469e6 | + | 3.92256e6i | −0.177209 | + | 0.306935i | ||||
\(697\) | −127119. | + | 220176.i | −0.00991122 | + | 0.0171667i | ||||
\(698\) | 8.63398e6 | + | 1.49545e7i | 0.670768 | + | 1.16180i | ||||
\(699\) | −3.35243e6 | −0.259518 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.02256e7 | −1.55456 | −0.777279 | − | 0.629156i | \(-0.783401\pi\) | ||||
−0.777279 | + | 0.629156i | \(0.783401\pi\) | |||||||
\(702\) | −267614. | − | 463522.i | −0.0204959 | − | 0.0354999i | ||||
\(703\) | 2.44373e6 | − | 4.23266e6i | 0.186494 | − | 0.323017i | ||||
\(704\) | −1.16415e7 | + | 2.01637e7i | −0.885276 | + | 1.53334i | ||||
\(705\) | −6.89897e6 | − | 1.19494e7i | −0.522771 | − | 0.905465i | ||||
\(706\) | 9.40174e6 | 0.709899 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.16053e6 | −0.0870108 | ||||||||
\(709\) | 1.05417e7 | + | 1.82587e7i | 0.787580 | + | 1.36413i | 0.927446 | + | 0.373957i | \(0.121999\pi\) |
−0.139866 | + | 0.990170i | \(0.544667\pi\) | |||||||
\(710\) | −9.77874e6 | + | 1.69373e7i | −0.728009 | + | 1.26095i | ||||
\(711\) | −1.74696e6 | + | 3.02582e6i | −0.129601 | + | 0.224476i | ||||
\(712\) | 9.83306e6 | + | 1.70314e7i | 0.726924 | + | 1.25907i | ||||
\(713\) | 1.15569e7 | 0.851369 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.33224e6 | −0.682686 | ||||||||
\(716\) | 538188. | + | 932168.i | 0.0392330 | + | 0.0679535i | ||||
\(717\) | 905321. | − | 1.56806e6i | 0.0657665 | − | 0.113911i | ||||
\(718\) | −323293. | + | 559959.i | −0.0234037 | + | 0.0405364i | ||||
\(719\) | 2.94030e6 | + | 5.09275e6i | 0.212114 | + | 0.367392i | 0.952376 | − | 0.304926i | \(-0.0986319\pi\) |
−0.740262 | + | 0.672319i | \(0.765299\pi\) | |||||||
\(720\) | −7.46950e6 | −0.536983 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.39660e6 | −0.171101 | ||||||||
\(723\) | 189093. | + | 327518.i | 0.0134533 | + | 0.0233018i | ||||
\(724\) | 312699. | − | 541610.i | 0.0221707 | − | 0.0384008i | ||||
\(725\) | −1.00430e7 | + | 1.73950e7i | −0.709607 | + | 1.22908i | ||||
\(726\) | 6.36010e6 | + | 1.10160e7i | 0.447840 | + | 0.775681i | ||||
\(727\) | 9.23778e6 | 0.648233 | 0.324117 | − | 0.946017i | \(-0.394933\pi\) | ||||
0.324117 | + | 0.946017i | \(0.394933\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 9.21314e6 | + | 1.59576e7i | 0.639883 | + | 1.10831i | ||||
\(731\) | −1.71945e6 | + | 2.97818e6i | −0.119014 | + | 0.206138i | ||||
\(732\) | −146418. | + | 253604.i | −0.0100999 | + | 0.0174936i | ||||
\(733\) | −3.87556e6 | − | 6.71267e6i | −0.266425 | − | 0.461462i | 0.701511 | − | 0.712659i | \(-0.252509\pi\) |
−0.967936 | + | 0.251197i | \(0.919176\pi\) | |||||||
\(734\) | −1.11065e7 | −0.760917 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.38192e6 | 0.366220 | ||||||||
\(737\) | 3.94223e6 | + | 6.82814e6i | 0.267346 | + | 0.463056i | ||||
\(738\) | 46628.2 | − | 80762.3i | 0.00315143 | − | 0.00545843i | ||||
\(739\) | −5.14509e6 | + | 8.91155e6i | −0.346563 | + | 0.600264i | −0.985636 | − | 0.168881i | \(-0.945985\pi\) |
0.639074 | + | 0.769145i | \(0.279318\pi\) | |||||||
\(740\) | 549411. | + | 951607.i | 0.0368823 | + | 0.0638820i | ||||
\(741\) | 2.12562e6 | 0.142213 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.04494e6 | −0.135897 | −0.0679483 | − | 0.997689i | \(-0.521645\pi\) | ||||
−0.0679483 | + | 0.997689i | \(0.521645\pi\) | |||||||
\(744\) | 2.45718e6 | + | 4.25595e6i | 0.162744 | + | 0.281880i | ||||
\(745\) | −2.58006e7 | + | 4.46880e7i | −1.70310 | + | 2.94985i | ||||
\(746\) | −6.09872e6 | + | 1.05633e7i | −0.401228 | + | 0.694948i | ||||
\(747\) | 1.75522e6 | + | 3.04014e6i | 0.115088 | + | 0.199339i | ||||
\(748\) | −2.85197e6 | −0.186377 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.20688e7 | −1.43261 | ||||||||
\(751\) | 5.93708e6 | + | 1.02833e7i | 0.384125 | + | 0.665325i | 0.991647 | − | 0.128978i | \(-0.0411697\pi\) |
−0.607522 | + | 0.794303i | \(0.707836\pi\) | |||||||
\(752\) | 6.60260e6 | − | 1.14360e7i | 0.425765 | − | 0.737447i | ||||
\(753\) | 5.54984e6 | − | 9.61261e6i | 0.356692 | − | 0.617809i | ||||
\(754\) | −972613. | − | 1.68461e6i | −0.0623034 | − | 0.107913i | ||||
\(755\) | −2.23846e7 | −1.42916 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.48702e6 | −0.538289 | −0.269145 | − | 0.963100i | \(-0.586741\pi\) | ||||
−0.269145 | + | 0.963100i | \(0.586741\pi\) | |||||||
\(758\) | −7.81268e6 | − | 1.35320e7i | −0.493886 | − | 0.855436i | ||||
\(759\) | 1.18192e7 | − | 2.04714e7i | 0.744702 | − | 1.28986i | ||||
\(760\) | 1.68119e7 | − | 2.91191e7i | 1.05581 | − | 1.82871i | ||||
\(761\) | −1.19966e7 | − | 2.07787e7i | −0.750925 | − | 1.30064i | −0.947375 | − | 0.320126i | \(-0.896275\pi\) |
0.196450 | − | 0.980514i | \(-0.437059\pi\) | |||||||
\(762\) | −6.80844e6 | −0.424776 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.43526e6 | 0.0889607 | ||||||||
\(765\) | −4.92129e6 | − | 8.52392e6i | −0.304036 | − | 0.526606i | ||||
\(766\) | 1.34178e7 | − | 2.32404e7i | 0.826249 | − | 1.43111i | ||||
\(767\) | 2.39450e6 | − | 4.14739e6i | 0.146969 | − | 0.254558i | ||||
\(768\) | 1.62134e6 | + | 2.80824e6i | 0.0991906 | + | 0.171803i | ||||
\(769\) | −2.43194e7 | −1.48299 | −0.741494 | − | 0.670959i | \(-0.765883\pi\) | ||||
−0.741494 | + | 0.670959i | \(0.765883\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.04619e6 | 0.305723 | ||||||||
\(772\) | −631339. | − | 1.09351e6i | −0.0381258 | − | 0.0660359i | ||||
\(773\) | 2.69075e6 | − | 4.66051e6i | 0.161966 | − | 0.280534i | −0.773608 | − | 0.633665i | \(-0.781550\pi\) |
0.935574 | + | 0.353131i | \(0.114883\pi\) | |||||||
\(774\) | 630710. | − | 1.09242e6i | 0.0378423 | − | 0.0655447i | ||||
\(775\) | 1.08966e7 | + | 1.88734e7i | 0.651682 | + | 1.12875i | ||||
\(776\) | −1.63916e7 | −0.977164 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.72347e6 | 0.339009 | ||||||||
\(779\) | 185180. | + | 320742.i | 0.0109333 | + | 0.0189370i | ||||
\(780\) | −238946. | + | 413867.i | −0.0140626 | + | 0.0243571i | ||||
\(781\) | 1.16098e7 | − | 2.01087e7i | 0.681076 | − | 1.17966i | ||||
\(782\) | −1.25544e7 | − | 2.17448e7i | −0.734138 | − | 1.27156i | ||||
\(783\) | 1.93146e6 | 0.112585 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.41650e7 | 2.55802 | ||||||||
\(786\) | 3.03933e6 | + | 5.26428e6i | 0.175478 | + | 0.303936i | ||||
\(787\) | −1.40359e7 | + | 2.43109e7i | −0.807800 | + | 1.39915i | 0.106584 | + | 0.994304i | \(0.466009\pi\) |
−0.914384 | + | 0.404848i | \(0.867325\pi\) | |||||||
\(788\) | −856666. | + | 1.48379e6i | −0.0491469 | + | 0.0851249i | ||||
\(789\) | 6.50356e6 | + | 1.12645e7i | 0.371928 | + | 0.644198i | ||||
\(790\) | −2.37359e7 | −1.35312 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.00518e7 | 0.569415 | ||||||||
\(793\) | −604205. | − | 1.04651e6i | −0.0341194 | − | 0.0590965i | ||||
\(794\) | 1.15496e7 | − | 2.00045e7i | 0.650152 | − | 1.12610i | ||||
\(795\) | −9.85606e6 | + | 1.70712e7i | −0.553077 | + | 0.957957i | ||||
\(796\) | −730228. | − | 1.26479e6i | −0.0408485 | − | 0.0707517i | ||||
\(797\) | 1.97055e7 | 1.09886 | 0.549428 | − | 0.835541i | \(-0.314846\pi\) | ||||
0.549428 | + | 0.835541i | \(0.314846\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.74005e7 | 0.964262 | ||||||||
\(800\) | 5.07441e6 | + | 8.78913e6i | 0.280324 | + | 0.485536i | ||||
\(801\) | 4.19310e6 | − | 7.26266e6i | 0.230916 | − | 0.399958i | ||||
\(802\) | −1.87221e6 | + | 3.24276e6i | −0.102782 | + | 0.178024i | ||||
\(803\) | −1.09383e7 | − | 1.89456e7i | −0.598631 | − | 1.03686i | ||||
\(804\) | 403754. | 0.0220281 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.11056e6 | −0.114435 | ||||||||
\(807\) | −1.87894e6 | − | 3.25442e6i | −0.101562 | − | 0.175910i | ||||
\(808\) | −1.73497e7 | + | 3.00506e7i | −0.934898 | + | 1.61929i | ||||
\(809\) | 1.69704e6 | − | 2.93936e6i | 0.0911633 | − | 0.157900i | −0.816838 | − | 0.576868i | \(-0.804275\pi\) |
0.908001 | + | 0.418968i | \(0.137608\pi\) | |||||||
\(810\) | 1.80517e6 | + | 3.12664e6i | 0.0966730 | + | 0.167442i | ||||
\(811\) | 1.78837e7 | 0.954786 | 0.477393 | − | 0.878690i | \(-0.341582\pi\) | ||||
0.477393 | + | 0.878690i | \(0.341582\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.85661e6 | −0.204634 | ||||||||
\(814\) | 4.96294e6 | + | 8.59607e6i | 0.262530 | + | 0.454715i | ||||
\(815\) | 1.41338e7 | − | 2.44805e7i | 0.745360 | − | 1.29100i | ||||
\(816\) | 4.70988e6 | − | 8.15775e6i | 0.247619 | − | 0.428889i | ||||
\(817\) | 2.50482e6 | + | 4.33847e6i | 0.131287 | + | 0.227395i | ||||
\(818\) | 8.69518e6 | 0.454355 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −83266.3 | −0.00432449 | ||||||||
\(821\) | −4.63474e6 | − | 8.02761e6i | −0.239976 | − | 0.415651i | 0.720731 | − | 0.693215i | \(-0.243806\pi\) |
−0.960707 | + | 0.277564i | \(0.910473\pi\) | |||||||
\(822\) | 2.38491e6 | − | 4.13078e6i | 0.123110 | − | 0.213232i | ||||
\(823\) | 762896. | − | 1.32137e6i | 0.0392614 | − | 0.0680027i | −0.845727 | − | 0.533616i | \(-0.820833\pi\) |
0.884988 | + | 0.465613i | \(0.154166\pi\) | |||||||
\(824\) | 3.80737e6 | + | 6.59456e6i | 0.195347 | + | 0.338351i | ||||
\(825\) | 4.45754e7 | 2.28014 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 806595. | 0.0410102 | 0.0205051 | − | 0.999790i | \(-0.493473\pi\) | ||||
0.0205051 | + | 0.999790i | \(0.493473\pi\) | |||||||
\(828\) | −605246. | − | 1.04832e6i | −0.0306801 | − | 0.0531394i | ||||
\(829\) | 1.09637e7 | − | 1.89898e7i | 0.554080 | − | 0.959695i | −0.443894 | − | 0.896079i | \(-0.646403\pi\) |
0.997974 | − | 0.0636160i | \(-0.0202633\pi\) | |||||||
\(830\) | −1.19241e7 | + | 2.06531e7i | −0.600800 | + | 1.04062i | ||||
\(831\) | 3.10899e6 | + | 5.38493e6i | 0.156177 | + | 0.270506i | ||||
\(832\) | −4.92010e6 | −0.246414 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.12201e6 | −0.0558573 | ||||||||
\(835\) | −3.10600e7 | − | 5.37976e7i | −1.54165 | − | 2.67022i | ||||
\(836\) | −2.07731e6 | + | 3.59800e6i | −0.102798 | + | 0.178052i | ||||
\(837\) | 1.04781e6 | − | 1.81486e6i | 0.0516974 | − | 0.0895425i | ||||
\(838\) | −1.57641e7 | − | 2.73041e7i | −0.775457 | − | 1.34313i | ||||
\(839\) | −2.40115e7 | −1.17765 | −0.588823 | − | 0.808262i | \(-0.700409\pi\) | ||||
−0.588823 | + | 0.808262i | \(0.700409\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.34915e7 | −0.657764 | ||||||||
\(842\) | −1.45231e7 | − | 2.51547e7i | −0.705958 | − | 1.22275i | ||||
\(843\) | −8.62228e6 | + | 1.49342e7i | −0.417882 | + | 0.723792i | ||||
\(844\) | −872338. | + | 1.51093e6i | −0.0421530 | + | 0.0730112i | ||||
\(845\) | 1.82229e7 | + | 3.15630e7i | 0.877963 | + | 1.52068i | ||||
\(846\) | −6.38265e6 | −0.306602 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.88653e7 | −0.900895 | ||||||||
\(849\) | 7.30877e6 | + | 1.26592e7i | 0.347997 | + | 0.602748i | ||||
\(850\) | 2.36741e7 | − | 4.10047e7i | 1.12389 | − | 1.94664i | ||||
\(851\) | 5.74271e6 | − | 9.94666e6i | 0.271827 | − | 0.470819i | ||||
\(852\) | −594522. | − | 1.02974e6i | −0.0280588 | − | 0.0485993i | ||||
\(853\) | 2.26785e7 | 1.06719 | 0.533594 | − | 0.845741i | \(-0.320841\pi\) | ||||
0.533594 | + | 0.845741i | \(0.320841\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.43382e7 | −0.670778 | ||||||||
\(856\) | 1.04669e7 | + | 1.81293e7i | 0.488242 | + | 0.845660i | ||||
\(857\) | −2.53759e6 | + | 4.39524e6i | −0.118024 | + | 0.204423i | −0.918984 | − | 0.394294i | \(-0.870989\pi\) |
0.800961 | + | 0.598717i | \(0.204323\pi\) | |||||||
\(858\) | −2.15845e6 | + | 3.73855e6i | −0.100098 | + | 0.173374i | ||||
\(859\) | 8.57027e6 | + | 1.48441e7i | 0.396289 | + | 0.686392i | 0.993265 | − | 0.115867i | \(-0.0369646\pi\) |
−0.596976 | + | 0.802259i | \(0.703631\pi\) | |||||||
\(860\) | −1.12629e6 | −0.0519284 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.83224e7 | −0.839876 | ||||||||
\(863\) | −1.92343e7 | − | 3.33148e7i | −0.879122 | − | 1.52268i | −0.852306 | − | 0.523044i | \(-0.824796\pi\) |
−0.0268162 | − | 0.999640i | \(-0.508537\pi\) | |||||||
\(864\) | 487953. | − | 845159.i | 0.0222379 | − | 0.0385172i | ||||
\(865\) | 2.58774e7 | − | 4.48209e7i | 1.17593 | − | 2.03676i | ||||
\(866\) | 6.56349e6 | + | 1.13683e7i | 0.297399 | + | 0.515111i | ||||
\(867\) | −366294. | −0.0165494 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.81803e7 | 1.26589 | ||||||||
\(870\) | 6.56067e6 | + | 1.13634e7i | 0.293866 | + | 0.508991i | ||||
\(871\) | −833057. | + | 1.44290e6i | −0.0372074 | + | 0.0644451i | ||||
\(872\) | 2.11180e7 | − | 3.65775e7i | 0.940506 | − | 1.62900i | ||||
\(873\) | 3.49492e6 | + | 6.05339e6i | 0.155204 | + | 0.268821i | ||||
\(874\) | −3.65772e7 | −1.61969 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.12027e6 | −0.0493245 | ||||||||
\(877\) | 9.58353e6 | + | 1.65992e7i | 0.420752 | + | 0.728764i | 0.996013 | − | 0.0892057i | \(-0.0284329\pi\) |
−0.575261 | + | 0.817970i | \(0.695100\pi\) | |||||||
\(878\) | −1.63209e7 | + | 2.82686e7i | −0.714508 | + | 1.23756i | ||||
\(879\) | 2.39073e6 | − | 4.14086e6i | 0.104366 | − | 0.180767i | ||||
\(880\) | 3.01228e7 | + | 5.21742e7i | 1.31126 | + | 2.27117i | ||||
\(881\) | 4.15340e7 | 1.80287 | 0.901434 | − | 0.432916i | \(-0.142515\pi\) | ||||
0.901434 | + | 0.432916i | \(0.142515\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.31950e7 | −1.86437 | −0.932183 | − | 0.361987i | \(-0.882099\pi\) | ||||
−0.932183 | + | 0.361987i | \(0.882099\pi\) | |||||||
\(884\) | −301334. | − | 521926.i | −0.0129693 | − | 0.0224635i | ||||
\(885\) | −1.61519e7 | + | 2.79758e7i | −0.693209 | + | 1.20067i | ||||
\(886\) | −4.76557e6 | + | 8.25420e6i | −0.203953 | + | 0.353257i | ||||
\(887\) | −3.43754e6 | − | 5.95399e6i | −0.146703 | − | 0.254097i | 0.783304 | − | 0.621639i | \(-0.213533\pi\) |
−0.930007 | + | 0.367542i | \(0.880199\pi\) | |||||||
\(888\) | 4.88395e6 | 0.207845 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5.69715e7 | 2.41092 | ||||||||
\(891\) | −2.14318e6 | − | 3.71209e6i | −0.0904407 | − | 0.156648i | ||||
\(892\) | 154376. | − | 267387.i | 0.00649631 | − | 0.0112519i | ||||
\(893\) | 1.26741e7 | − | 2.19522e7i | 0.531849 | − | 0.921190i | ||||
\(894\) | 1.19348e7 | + | 2.06718e7i | 0.499428 | + | 0.865035i | ||||
\(895\) | 2.99613e7 | 1.25027 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.99517e6 | 0.207286 | ||||||||
\(898\) | −9.99850e6 | − | 1.73179e7i | −0.413756 | − | 0.716646i | ||||
\(899\) | 3.80814e6 | − | 6.59589e6i | 0.157150 | − | 0.272191i | ||||
\(900\) | 1.14133e6 | − | 1.97684e6i | 0.0469682 | − | 0.0813513i | ||||
\(901\) | −1.24294e7 | − | 2.15284e7i | −0.510081 | − | 0.883486i | ||||
\(902\) | −752162. | −0.0307819 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.91522e7 | −1.18645 | ||||||||
\(905\) | −8.70407e6 | − | 1.50759e7i | −0.353265 | − | 0.611874i | ||||
\(906\) | −5.17733e6 | + | 8.96741e6i | −0.209549 | + | 0.362950i | ||||
\(907\) | −7.48737e6 | + | 1.29685e7i | −0.302212 | + | 0.523446i | −0.976637 | − | 0.214897i | \(-0.931058\pi\) |
0.674425 | + | 0.738343i | \(0.264392\pi\) | |||||||
\(908\) | 259777. | + | 449947.i | 0.0104565 | + | 0.0181112i | ||||
\(909\) | 1.47968e7 | 0.593962 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.13061e7 | 1.24978 | 0.624889 | − | 0.780714i | \(-0.285144\pi\) | ||||
0.624889 | + | 0.780714i | \(0.285144\pi\) | |||||||
\(912\) | −6.86112e6 | − | 1.18838e7i | −0.273154 | − | 0.473117i | ||||
\(913\) | 1.41568e7 | − | 2.45203e7i | 0.562068 | − | 0.973530i | ||||
\(914\) | 2.00628e7 | − | 3.47498e7i | 0.794376 | − | 1.37590i | ||||
\(915\) | 4.07561e6 | + | 7.05916e6i | 0.160931 | + | 0.278740i | ||||
\(916\) | −534713. | −0.0210563 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.55298e6 | −0.178315 | ||||||||
\(919\) | −7.34952e6 | − | 1.27297e7i | −0.287058 | − | 0.497200i | 0.686048 | − | 0.727556i | \(-0.259344\pi\) |
−0.973106 | + | 0.230357i | \(0.926011\pi\) | |||||||
\(920\) | 3.95077e7 | − | 6.84294e7i | 1.53891 | − | 2.66547i | ||||
\(921\) | −1.84077e6 | + | 3.18830e6i | −0.0715072 | + | 0.123854i | ||||
\(922\) | 954870. | + | 1.65388e6i | 0.0369928 | + | 0.0640733i | ||||
\(923\) | 4.90666e6 | 0.189575 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.16583e7 | 0.832283 | ||||||||
\(926\) | −2.36910e6 | − | 4.10341e6i | −0.0907939 | − | 0.157260i | ||||
\(927\) | 1.62357e6 | − | 2.81211e6i | 0.0620543 | − | 0.107481i | ||||
\(928\) | 1.77341e6 | − | 3.07163e6i | 0.0675987 | − | 0.117084i | ||||
\(929\) | −8.42099e6 | − | 1.45856e7i | −0.320128 | − | 0.554478i | 0.660386 | − | 0.750926i | \(-0.270393\pi\) |
−0.980514 | + | 0.196448i | \(0.937059\pi\) | |||||||
\(930\) | 1.42366e7 | 0.539756 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.38464e6 | 0.0522153 | ||||||||
\(933\) | 1.38917e6 | + | 2.40611e6i | 0.0522457 | + | 0.0904922i | ||||
\(934\) | −2.02441e7 | + | 3.50637e7i | −0.759330 | + | 1.31520i | ||||
\(935\) | −3.96928e7 | + | 6.87499e7i | −1.48485 | + | 2.57184i | ||||
\(936\) | 1.06205e6 | + | 1.83952e6i | 0.0396237 | + | 0.0686303i | ||||
\(937\) | −3.22026e7 | −1.19824 | −0.599118 | − | 0.800661i | \(-0.704482\pi\) | ||||
−0.599118 | + | 0.800661i | \(0.704482\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.73959e6 | 0.212431 | ||||||||
\(940\) | 2.84946e6 | + | 4.93540e6i | 0.105182 | + | 0.182181i | ||||
\(941\) | −1.32532e7 | + | 2.29553e7i | −0.487919 | + | 0.845100i | −0.999903 | − | 0.0138946i | \(-0.995577\pi\) |
0.511985 | + | 0.858994i | \(0.328910\pi\) | |||||||
\(942\) | 1.02149e7 | − | 1.76928e7i | 0.375066 | − | 0.649634i | ||||
\(943\) | 435170. | + | 753736.i | 0.0159360 | + | 0.0276020i | ||||
\(944\) | −3.09160e7 | −1.12915 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.01740e7 | −0.369628 | ||||||||
\(947\) | 2.49341e7 | + | 4.31871e7i | 0.903481 | + | 1.56487i | 0.822944 | + | 0.568123i | \(0.192330\pi\) |
0.0805371 | + | 0.996752i | \(0.474336\pi\) | |||||||
\(948\) | 721541. | − | 1.24975e6i | 0.0260759 | − | 0.0451649i | ||||
\(949\) | 2.31143e6 | − | 4.00352e6i | 0.0833136 | − | 0.144303i | ||||
\(950\) | −3.44872e7 | − | 5.97336e7i | −1.23979 | − | 2.14738i | ||||
\(951\) | −2.64892e7 | −0.949770 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.46027e7 | −0.877508 | −0.438754 | − | 0.898607i | \(-0.644580\pi\) | ||||
−0.438754 | + | 0.898607i | \(0.644580\pi\) | |||||||
\(954\) | 4.55921e6 | + | 7.89679e6i | 0.162188 | + | 0.280918i | ||||
\(955\) | 1.99755e7 | − | 3.45986e7i | 0.708744 | − | 1.22758i | ||||
\(956\) | −373922. | + | 647651.i | −0.0132323 | + | 0.0229190i | ||||
\(957\) | −7.78912e6 | − | 1.34912e7i | −0.274921 | − | 0.476178i | ||||
\(958\) | 3.16966e7 | 1.11583 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.31880e7 | 1.16226 | ||||||||
\(961\) | 1.01828e7 | + | 1.76371e7i | 0.355678 | + | 0.616053i | ||||
\(962\) | −1.04875e6 | + | 1.81649e6i | −0.0365371 | + | 0.0632842i | ||||
\(963\) | 4.46340e6 | − | 7.73083e6i | 0.155096 | − | 0.268634i | ||||
\(964\) | −78100.2 | − | 135274.i | −0.00270682 | − | 0.00468835i | ||||
\(965\) | −3.51471e7 | −1.21498 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.59962e7 | 0.550111 | 0.275056 | − | 0.961428i | \(-0.411304\pi\) | ||||
0.275056 | + | 0.961428i | \(0.411304\pi\) | |||||||
\(968\) | −2.52406e7 | − | 4.37180e7i | −0.865787 | − | 1.49959i | ||||
\(969\) | 9.04090e6 | − | 1.56593e7i | 0.309316 | − | 0.535751i | ||||
\(970\) | −2.37427e7 | + | 4.11236e7i | −0.810216 | + | 1.40334i | ||||
\(971\) | −4.97212e6 | − | 8.61197e6i | −0.169236 | − | 0.293126i | 0.768915 | − | 0.639351i | \(-0.220797\pi\) |
−0.938152 | + | 0.346225i | \(0.887463\pi\) | |||||||
\(972\) | −219499. | −0.00745190 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.37116e6 | 0.0463118 | ||||||||
\(975\) | 4.70976e6 | + | 8.15754e6i | 0.158667 | + | 0.274820i | ||||
\(976\) | −3.90053e6 | + | 6.75591e6i | −0.131069 | + | 0.227017i | ||||
\(977\) | 6.04354e6 | − | 1.04677e7i | 0.202561 | − | 0.350845i | −0.746792 | − | 0.665058i | \(-0.768407\pi\) |
0.949353 | + | 0.314212i | \(0.101740\pi\) | |||||||
\(978\) | −6.53803e6 | − | 1.13242e7i | −0.218575 | − | 0.378583i | ||||
\(979\) | −6.76392e7 | −2.25549 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.80106e7 | −0.597526 | ||||||||
\(982\) | 1.57593e6 | + | 2.72959e6i | 0.0521505 | + | 0.0903273i | ||||
\(983\) | −1.71388e7 | + | 2.96853e7i | −0.565714 | + | 0.979846i | 0.431269 | + | 0.902224i | \(0.358066\pi\) |
−0.996983 | + | 0.0776222i | \(0.975267\pi\) | |||||||
\(984\) | −185048. | + | 320512.i | −0.00609250 | + | 0.0105525i | ||||
\(985\) | 2.38456e7 | + | 4.13017e7i | 0.783100 | + | 1.35637i | ||||
\(986\) | −1.65472e7 | −0.542043 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −877938. | −0.0286135 | ||||||||
\(989\) | 5.88627e6 | + | 1.01953e7i | 0.191359 | + | 0.331444i | ||||
\(990\) | 1.45596e7 | − | 2.52180e7i | 0.472131 | − | 0.817755i | ||||
\(991\) | 1.75049e7 | − | 3.03195e7i | 0.566209 | − | 0.980703i | −0.430727 | − | 0.902482i | \(-0.641743\pi\) |
0.996936 | − | 0.0782204i | \(-0.0249238\pi\) | |||||||
\(992\) | −1.92413e6 | − | 3.33270e6i | −0.0620806 | − | 0.107527i | ||||
\(993\) | −2.56492e7 | −0.825470 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.06523e7 | −1.30175 | ||||||||
\(996\) | −724954. | − | 1.25566e6i | −0.0231559 | − | 0.0401072i | ||||
\(997\) | −4.99615e6 | + | 8.65359e6i | −0.159183 | + | 0.275714i | −0.934574 | − | 0.355768i | \(-0.884219\pi\) |
0.775391 | + | 0.631481i | \(0.217553\pi\) | |||||||
\(998\) | −6.44141e6 | + | 1.11569e7i | −0.204717 | + | 0.354581i | ||||
\(999\) | −1.04133e6 | − | 1.80363e6i | −0.0330122 | − | 0.0571788i |
(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 | 147.6.e.p.67.5 | 12 | ||
7.2 | even | 3 | inner | 147.6.e.p.79.5 | 12 | ||
7.3 | odd | 6 | 147.6.a.n.1.2 | ✓ | 6 | ||
7.4 | even | 3 | 147.6.a.o.1.2 | yes | 6 | ||
7.5 | odd | 6 | 147.6.e.q.79.5 | 12 | |||
7.6 | odd | 2 | 147.6.e.q.67.5 | 12 | |||
21.11 | odd | 6 | 441.6.a.ba.1.5 | 6 | |||
21.17 | even | 6 | 441.6.a.bb.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.6.a.n.1.2 | ✓ | 6 | 7.3 | odd | 6 | ||
147.6.a.o.1.2 | yes | 6 | 7.4 | even | 3 | ||
147.6.e.p.67.5 | 12 | 1.1 | even | 1 | trivial | ||
147.6.e.p.79.5 | 12 | 7.2 | even | 3 | inner | ||
147.6.e.q.67.5 | 12 | 7.6 | odd | 2 | |||
147.6.e.q.79.5 | 12 | 7.5 | odd | 6 | |||
441.6.a.ba.1.5 | 6 | 21.11 | odd | 6 | |||
441.6.a.bb.1.5 | 6 | 21.17 | even | 6 |